diff --git a/-XKsFKIGjZ0.txt b/-XKsFKIGjZ0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a03441dffae2df67ea984249f880505434a856c0
--- /dev/null
+++ b/-XKsFKIGjZ0.txt
@@ -0,0 +1,2251 @@
+align:start position:0%
+ 
+so this is the car in the
+
+ align:start position:0%
+so this is the car in the
+ 
+
+ align:start position:0%
+so this is the car in the
+Department about seven cases now I'm
+
+ align:start position:0%
+Department about seven cases now I'm
+ 
+
+ align:start position:0%
+Department about seven cases now I'm
+we're going to walk to the next
+
+ align:start position:0%
+we're going to walk to the next
+ 
+
+ align:start position:0%
+we're going to walk to the next
+department is called the prefit
+
+ align:start position:0%
+department is called the prefit
+ 
+
+ align:start position:0%
+department is called the prefit
+department part of the value this like
+
+ align:start position:0%
+department part of the value this like
+ 
+
+ align:start position:0%
+department part of the value this like
+the second part of the value stre the
+
+ align:start position:0%
+the second part of the value stre the
+ 
+
+ align:start position:0%
+the second part of the value stre the
+second the value we got the cutting now
+
+ align:start position:0%
+second the value we got the cutting now
+ 
+
+ align:start position:0%
+second the value we got the cutting now
+we're going to do stitching exactly the
+
+ align:start position:0%
+we're going to do stitching exactly the
+ 
+
+ align:start position:0%
+we're going to do stitching exactly the
+pref is a shoe making technique many
+
+ align:start position:0%
+pref is a shoe making technique many
+ 
+
+ align:start position:0%
+pref is a shoe making technique many
+years ago when we didn't have computers
+
+ align:start position:0%
+years ago when we didn't have computers
+ 
+
+ align:start position:0%
+years ago when we didn't have computers
+the way a shoe was stitched is it used
+
+ align:start position:0%
+the way a shoe was stitched is it used
+ 
+
+ align:start position:0%
+the way a shoe was stitched is it used
+to be fitted two parts coming together
+
+ align:start position:0%
+to be fitted two parts coming together
+ 
+
+ align:start position:0%
+to be fitted two parts coming together
+and a very uh skillful stitchers to put
+
+ align:start position:0%
+and a very uh skillful stitchers to put
+ 
+
+ align:start position:0%
+and a very uh skillful stitchers to put
+it together but before be able to brief
+
+ align:start position:0%
+it together but before be able to brief
+ 
+
+ align:start position:0%
+it together but before be able to brief
+it and Stitch in need um be fitted used
+
+ align:start position:0%
+it and Stitch in need um be fitted used
+ 
+
+ align:start position:0%
+it and Stitch in need um be fitted used
+to be pre fitted which is you do marking
+
+ align:start position:0%
+to be pre fitted which is you do marking
+ 
+
+ align:start position:0%
+to be pre fitted which is you do marking
+you do embroidery you do other things
+
+ align:start position:0%
+you do embroidery you do other things
+ 
+
+ align:start position:0%
+you do embroidery you do other things
+before you go the Sho together that's
+
+ align:start position:0%
+before you go the Sho together that's
+ 
+
+ align:start position:0%
+before you go the Sho together that's
+where the name coming from pre so we do
+
+ align:start position:0%
+where the name coming from pre so we do
+ 
+
+ align:start position:0%
+where the name coming from pre so we do
+embroidery we put the
+
+ align:start position:0%
+embroidery we put the
+ 
+
+ align:start position:0%
+embroidery we put the
+logos or main USA logo is there and then
+
+ align:start position:0%
+logos or main USA logo is there and then
+ 
+
+ align:start position:0%
+logos or main USA logo is there and then
+you will see a series of operations
+
+ align:start position:0%
+you will see a series of operations
+ 
+
+ align:start position:0%
+you will see a series of operations
+miscellanous operations that are
+
+ align:start position:0%
+miscellanous operations that are
+ 
+
+ align:start position:0%
+miscellanous operations that are
+required to make a shoe for example
+
+ align:start position:0%
+required to make a shoe for example
+ 
+
+ align:start position:0%
+required to make a shoe for example
+reinforcement of the chip uh I talk
+
+ align:start position:0%
+reinforcement of the chip uh I talk
+ 
+
+ align:start position:0%
+reinforcement of the chip uh I talk
+about embroidery some shells take
+
+ align:start position:0%
+about embroidery some shells take
+ 
+
+ align:start position:0%
+about embroidery some shells take
+embroidery others do
+
+ align:start position:0%
+embroidery others do
+ 
+
+ align:start position:0%
+embroidery others do
+not here we have a machine called AR
+
+ align:start position:0%
+not here we have a machine called AR
+ 
+
+ align:start position:0%
+not here we have a machine called AR
+well radio frequency machine it's not
+
+ align:start position:0%
+well radio frequency machine it's not
+ 
+
+ align:start position:0%
+well radio frequency machine it's not
+being operated right now but as an
+
+ align:start position:0%
+being operated right now but as an
+ 
+
+ align:start position:0%
+being operated right now but as an
+example this is a part it will make this
+
+ align:start position:0%
+example this is a part it will make this
+ 
+
+ align:start position:0%
+example this is a part it will make this
+DEC you know it's a nice
+
+ align:start position:0%
+DEC you know it's a nice
+ 
+
+ align:start position:0%
+DEC you know it's a nice
+feature this what this machine is going
+
+ align:start position:0%
+feature this what this machine is going
+ 
+
+ align:start position:0%
+feature this what this machine is going
+to do again some cells have it some CS
+
+ align:start position:0%
+to do again some cells have it some CS
+ 
+
+ align:start position:0%
+to do again some cells have it some CS
+do not and if we go through the the the
+
+ align:start position:0%
+do not and if we go through the the the
+ 
+
+ align:start position:0%
+do not and if we go through the the the
+the team you'll see Associates making
+
+ align:start position:0%
+the team you'll see Associates making
+ 
+
+ align:start position:0%
+the team you'll see Associates making
+other miscellaneous operations to the
+
+ align:start position:0%
+other miscellaneous operations to the
+ 
+
+ align:start position:0%
+other miscellaneous operations to the
+part to the shoe so the flow of material
+
+ align:start position:0%
+part to the shoe so the flow of material
+ 
+
+ align:start position:0%
+part to the shoe so the flow of material
+starts over there goes to the so we'll
+
+ align:start position:0%
+starts over there goes to the so we'll
+ 
+
+ align:start position:0%
+starts over there goes to the so we'll
+go cutting prit we'll go to the computer
+
+ align:start position:0%
+go cutting prit we'll go to the computer
+ 
+
+ align:start position:0%
+go cutting prit we'll go to the computer
+stitching and we'll finish up stitching
+
+ align:start position:0%
+stitching and we'll finish up stitching
+ 
+
+ align:start position:0%
+stitching and we'll finish up stitching
+and then eventually uh the assembly
+
+ align:start position:0%
+and then eventually uh the assembly
+ 
+
+ align:start position:0%
+and then eventually uh the assembly
+where they put the so on so if if things
+
+ align:start position:0%
+where they put the so on so if if things
+ 
+
+ align:start position:0%
+where they put the so on so if if things
+are getting a little out of uh sequence
+
+ align:start position:0%
+are getting a little out of uh sequence
+ 
+
+ align:start position:0%
+are getting a little out of uh sequence
+timing wise could someone from here go
+
+ align:start position:0%
+timing wise could someone from here go
+ 
+
+ align:start position:0%
+timing wise could someone from here go
+over and help the brief it people this
+
+ align:start position:0%
+over and help the brief it people this
+ 
+
+ align:start position:0%
+over and help the brief it people this
+is this is a very good it's a very good
+
+ align:start position:0%
+is this is a very good it's a very good
+ 
+
+ align:start position:0%
+is this is a very good it's a very good
+point when we change from the bat and Q
+
+ align:start position:0%
+point when we change from the bat and Q
+ 
+
+ align:start position:0%
+point when we change from the bat and Q
+world to the lean world we change the
+
+ align:start position:0%
+world to the lean world we change the
+ 
+
+ align:start position:0%
+world to the lean world we change the
+man agement system in the past you have
+
+ align:start position:0%
+man agement system in the past you have
+ 
+
+ align:start position:0%
+man agement system in the past you have
+uh Associates and supervisors nobody in
+
+ align:start position:0%
+uh Associates and supervisors nobody in
+ 
+
+ align:start position:0%
+uh Associates and supervisors nobody in
+the middle in order to support thex time
+
+ align:start position:0%
+the middle in order to support thex time
+ 
+
+ align:start position:0%
+the middle in order to support thex time
+22 half seconds um and maintain that
+
+ align:start position:0%
+22 half seconds um and maintain that
+ 
+
+ align:start position:0%
+22 half seconds um and maintain that
+flow now we changed the system where we
+
+ align:start position:0%
+flow now we changed the system where we
+ 
+
+ align:start position:0%
+flow now we changed the system where we
+have a supervisor we have team leaders
+
+ align:start position:0%
+have a supervisor we have team leaders
+ 
+
+ align:start position:0%
+have a supervisor we have team leaders
+and then the associate so team leaders
+
+ align:start position:0%
+and then the associate so team leaders
+ 
+
+ align:start position:0%
+and then the associate so team leaders
+feeling if there is a disruption any
+
+ align:start position:0%
+feeling if there is a disruption any
+ 
+
+ align:start position:0%
+feeling if there is a disruption any
+kind bathroom break to a phone call to
+
+ align:start position:0%
+kind bathroom break to a phone call to
+ 
+
+ align:start position:0%
+kind bathroom break to a phone call to
+equality issue they will Champaign to
+
+ align:start position:0%
+equality issue they will Champaign to
+ 
+
+ align:start position:0%
+equality issue they will Champaign to
+maintain their the team leader will
+
+ align:start position:0%
+maintain their the team leader will
+ 
+
+ align:start position:0%
+maintain their the team leader will
+absolutely team later can do everything
+
+ align:start position:0%
+absolutely team later can do everything
+ 
+
+ align:start position:0%
+absolutely team later can do everything
+absolutely so we still in this team in
+
+ align:start position:0%
+absolutely so we still in this team in
+ 
+
+ align:start position:0%
+absolutely so we still in this team in
+the prefit we have bad the parts are pre
+
+ align:start position:0%
+the prefit we have bad the parts are pre
+ 
+
+ align:start position:0%
+the prefit we have bad the parts are pre
+fitted put a a reinforcement to the toe
+
+ align:start position:0%
+fitted put a a reinforcement to the toe
+ 
+
+ align:start position:0%
+fitted put a a reinforcement to the toe
+you make a little de uh you know uh you
+
+ align:start position:0%
+you make a little de uh you know uh you
+ 
+
+ align:start position:0%
+you make a little de uh you know uh you
+put those asso there are making a little
+
+ align:start position:0%
+put those asso there are making a little
+ 
+
+ align:start position:0%
+put those asso there are making a little
+hold on the part they're putting back on
+
+ align:start position:0%
+hold on the part they're putting back on
+ 
+
+ align:start position:0%
+hold on the part they're putting back on
+those bins that we talked before and
+
+ align:start position:0%
+those bins that we talked before and
+ 
+
+ align:start position:0%
+those bins that we talked before and
+brought filling badge to this department
+
+ align:start position:0%
+brought filling badge to this department
+ 
+
+ align:start position:0%
+brought filling badge to this department
+is called computer stitching computer
+
+ align:start position:0%
+is called computer stitching computer
+ 
+
+ align:start position:0%
+is called computer stitching computer
+stitching so what I'm going to show you
+
+ align:start position:0%
+stitching so what I'm going to show you
+ 
+
+ align:start position:0%
+stitching so what I'm going to show you
+right now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are uh stitching
+
+ align:start position:0%
+are uh stitching
+ 
+
+ align:start position:0%
+are uh stitching
+machines but they have a computer and
+
+ align:start position:0%
+machines but they have a computer and
+ 
+
+ align:start position:0%
+machines but they have a computer and
+cameras and the way it works you see an
+
+ align:start position:0%
+cameras and the way it works you see an
+ 
+
+ align:start position:0%
+cameras and the way it works you see an
+associate picking these kind of parts
+
+ align:start position:0%
+associate picking these kind of parts
+ 
+
+ align:start position:0%
+associate picking these kind of parts
+put was called a
+
+ align:start position:0%
+put was called a
+ 
+
+ align:start position:0%
+put was called a
+pallet these little holes that to put on
+
+ align:start position:0%
+pallet these little holes that to put on
+ 
+
+ align:start position:0%
+pallet these little holes that to put on
+pins and the pallet will be fed into
+
+ align:start position:0%
+pins and the pallet will be fed into
+ 
+
+ align:start position:0%
+pins and the pallet will be fed into
+this machine and you have lights taking
+
+ align:start position:0%
+this machine and you have lights taking
+ 
+
+ align:start position:0%
+this machine and you have lights taking
+pictures okay and a computer and taking
+
+ align:start position:0%
+pictures okay and a computer and taking
+ 
+
+ align:start position:0%
+pictures okay and a computer and taking
+a pictures three frames per second so
+
+ align:start position:0%
+a pictures three frames per second so
+ 
+
+ align:start position:0%
+a pictures three frames per second so
+the camera thr the computer this is The
+
+ align:start position:0%
+the camera thr the computer this is The
+ 
+
+ align:start position:0%
+the camera thr the computer this is The
+Edge and the computer tell the sewing
+
+ align:start position:0%
+Edge and the computer tell the sewing
+ 
+
+ align:start position:0%
+Edge and the computer tell the sewing
+machine where to put the Stitch okay
+
+ align:start position:0%
+machine where to put the Stitch okay
+ 
+
+ align:start position:0%
+machine where to put the Stitch okay
+okay okay at this computer stitching
+
+ align:start position:0%
+okay okay at this computer stitching
+ 
+
+ align:start position:0%
+okay okay at this computer stitching
+department is when we transition from
+
+ align:start position:0%
+department is when we transition from
+ 
+
+ align:start position:0%
+department is when we transition from
+the badge to the FL and that's what I'm
+
+ align:start position:0%
+the badge to the FL and that's what I'm
+ 
+
+ align:start position:0%
+the badge to the FL and that's what I'm
+going to show you okay
+
+ align:start position:0%
+going to show you okay
+ 
+
+ align:start position:0%
+going to show you okay
+great this associate here I I forgot to
+
+ align:start position:0%
+great this associate here I I forgot to
+ 
+
+ align:start position:0%
+great this associate here I I forgot to
+mention we talk about the different
+
+ align:start position:0%
+mention we talk about the different
+ 
+
+ align:start position:0%
+mention we talk about the different
+management system remember tag time flow
+
+ align:start position:0%
+management system remember tag time flow
+ 
+
+ align:start position:0%
+management system remember tag time flow
+supervisor team leader to help but also
+
+ align:start position:0%
+supervisor team leader to help but also
+ 
+
+ align:start position:0%
+supervisor team leader to help but also
+we want associ to be on the line
+
+ align:start position:0%
+we want associ to be on the line
+ 
+
+ align:start position:0%
+we want associ to be on the line
+producing the shoes at that tag time so
+
+ align:start position:0%
+producing the shoes at that tag time so
+ 
+
+ align:start position:0%
+producing the shoes at that tag time so
+another level is called the point of
+
+ align:start position:0%
+another level is called the point of
+ 
+
+ align:start position:0%
+another level is called the point of
+views okay asso the the goal point of
+
+ align:start position:0%
+views okay asso the the goal point of
+ 
+
+ align:start position:0%
+views okay asso the the goal point of
+view is to bring the parts to okay The
+
+ align:start position:0%
+view is to bring the parts to okay The
+ 
+
+ align:start position:0%
+view is to bring the parts to okay The
+Operators actually adding value to the
+
+ align:start position:0%
+Operators actually adding value to the
+ 
+
+ align:start position:0%
+Operators actually adding value to the
+shoe so this lady's a point of use
+
+ align:start position:0%
+shoe so this lady's a point of use
+ 
+
+ align:start position:0%
+shoe so this lady's a point of use
+associ called a point of use associ look
+
+ align:start position:0%
+associ called a point of use associ look
+ 
+
+ align:start position:0%
+associ called a point of use associ look
+pretty busy too very busy they have to
+
+ align:start position:0%
+pretty busy too very busy they have to
+ 
+
+ align:start position:0%
+pretty busy too very busy they have to
+distribute you know in case a case every
+
+ align:start position:0%
+distribute you know in case a case every
+ 
+
+ align:start position:0%
+distribute you know in case a case every
+9 minutes and they have uh a flow
+
+ align:start position:0%
+9 minutes and they have uh a flow
+ 
+
+ align:start position:0%
+9 minutes and they have uh a flow
+from this computer stitching into the
+
+ align:start position:0%
+from this computer stitching into the
+ 
+
+ align:start position:0%
+from this computer stitching into the
+next department and come back and flow
+
+ align:start position:0%
+next department and come back and flow
+ 
+
+ align:start position:0%
+next department and come back and flow
+everything is about flow so you want to
+
+ align:start position:0%
+everything is about flow so you want to
+ 
+
+ align:start position:0%
+everything is about flow so you want to
+keep this person want to have everything
+
+ align:start position:0%
+keep this person want to have everything
+ 
+
+ align:start position:0%
+keep this person want to have everything
+she needs to do what she needs to do
+
+ align:start position:0%
+she needs to do what she needs to do
+ 
+
+ align:start position:0%
+she needs to do what she needs to do
+exactly exactly this person in the past
+
+ align:start position:0%
+exactly exactly this person in the past
+ 
+
+ align:start position:0%
+exactly exactly this person in the past
+in the past world this person will leave
+
+ align:start position:0%
+in the past world this person will leave
+ 
+
+ align:start position:0%
+in the past world this person will leave
+the machine we go pick up the parts come
+
+ align:start position:0%
+the machine we go pick up the parts come
+ 
+
+ align:start position:0%
+the machine we go pick up the parts come
+back um lot of variability in the system
+
+ align:start position:0%
+back um lot of variability in the system
+ 
+
+ align:start position:0%
+back um lot of variability in the system
+and reduction of waste is to reduce
+
+ align:start position:0%
+and reduction of waste is to reduce
+ 
+
+ align:start position:0%
+and reduction of waste is to reduce
+variability at the same time they must
+
+ align:start position:0%
+variability at the same time they must
+ 
+
+ align:start position:0%
+variability at the same time they must
+have to work very closely together yes
+
+ align:start position:0%
+have to work very closely together yes
+ 
+
+ align:start position:0%
+have to work very closely together yes
+absolutely so here you have the computer
+
+ align:start position:0%
+absolutely so here you have the computer
+ 
+
+ align:start position:0%
+absolutely so here you have the computer
+stitching machine um these are the parts
+
+ align:start position:0%
+stitching machine um these are the parts
+ 
+
+ align:start position:0%
+stitching machine um these are the parts
+that came from The
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Cutting and the associate puts the parts
+
+ align:start position:0%
+Cutting and the associate puts the parts
+ 
+
+ align:start position:0%
+Cutting and the associate puts the parts
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+pallet is feding to the machine goes
+
+ align:start position:0%
+pallet is feding to the machine goes
+ 
+
+ align:start position:0%
+pallet is feding to the machine goes
+back in the machine you got the
+
+ align:start position:0%
+back in the machine you got the
+ 
+
+ align:start position:0%
+back in the machine you got the
+cameras taking pictur now it's stitching
+
+ align:start position:0%
+cameras taking pictur now it's stitching
+ 
+
+ align:start position:0%
+cameras taking pictur now it's stitching
+and then the sewing machines stitching
+
+ align:start position:0%
+and then the sewing machines stitching
+ 
+
+ align:start position:0%
+and then the sewing machines stitching
+where the computer s to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stitch they probably come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up here we got the part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now why only three parts is because
+
+ align:start position:0%
+okay now why only three parts is because
+ 
+
+ align:start position:0%
+okay now why only three parts is because
+under the T time of 2 2 and2 seconds
+
+ align:start position:0%
+under the T time of 2 2 and2 seconds
+ 
+
+ align:start position:0%
+under the T time of 2 2 and2 seconds
+that solid fits in this machine okay so
+
+ align:start position:0%
+that solid fits in this machine okay so
+ 
+
+ align:start position:0%
+that solid fits in this machine okay so
+we look at we take all the time that is
+
+ align:start position:0%
+we look at we take all the time that is
+ 
+
+ align:start position:0%
+we look at we take all the time that is
+required to stit a shoe we divide it by
+
+ align:start position:0%
+required to stit a shoe we divide it by
+ 
+
+ align:start position:0%
+required to stit a shoe we divide it by
+2 and 2 and a half seconds and that
+
+ align:start position:0%
+2 and 2 and a half seconds and that
+ 
+
+ align:start position:0%
+2 and 2 and a half seconds and that
+tells us how many asso we need to put to
+
+ align:start position:0%
+tells us how many asso we need to put to
+ 
+
+ align:start position:0%
+tells us how many asso we need to put to
+flow now when you switch to the tack
+
+ align:start position:0%
+flow now when you switch to the tack
+ 
+
+ align:start position:0%
+flow now when you switch to the tack
+time uh approach did you have to
+
+ align:start position:0%
+time uh approach did you have to
+ 
+
+ align:start position:0%
+time uh approach did you have to
+redesign some of these machines to
+
+ align:start position:0%
+redesign some of these machines to
+ 
+
+ align:start position:0%
+redesign some of these machines to
+completely okay in the the old machines
+
+ align:start position:0%
+completely okay in the the old machines
+ 
+
+ align:start position:0%
+completely okay in the the old machines
+didn't fit the tax I'm sorry the
+
+ align:start position:0%
+didn't fit the tax I'm sorry the
+ 
+
+ align:start position:0%
+didn't fit the tax I'm sorry the
+machines are okay we have to change the
+
+ align:start position:0%
+machines are okay we have to change the
+ 
+
+ align:start position:0%
+machines are okay we have to change the
+thinking of the designing of the pallets
+
+ align:start position:0%
+thinking of the designing of the pallets
+ 
+
+ align:start position:0%
+thinking of the designing of the pallets
+okay in the past in the B and and and Q
+
+ align:start position:0%
+okay in the past in the B and and and Q
+ 
+
+ align:start position:0%
+okay in the past in the B and and and Q
+world we were very proud when we could
+
+ align:start position:0%
+world we were very proud when we could
+ 
+
+ align:start position:0%
+world we were very proud when we could
+put as many layers as possible to save
+
+ align:start position:0%
+put as many layers as possible to save
+ 
+
+ align:start position:0%
+put as many layers as possible to save
+Machinery okay uh the Goos and machine
+
+ align:start position:0%
+Machinery okay uh the Goos and machine
+ 
+
+ align:start position:0%
+Machinery okay uh the Goos and machine
+efficiency right because you get reward
+
+ align:start position:0%
+efficiency right because you get reward
+ 
+
+ align:start position:0%
+efficiency right because you get reward
+in the in the Bat World for machine
+
+ align:start position:0%
+in the in the Bat World for machine
+ 
+
+ align:start position:0%
+in the in the Bat World for machine
+efficiency right now now the goal is
+
+ align:start position:0%
+efficiency right now now the goal is
+ 
+
+ align:start position:0%
+efficiency right now now the goal is
+into efficiency and
+
+ align:start position:0%
+into efficiency and
+ 
+
+ align:start position:0%
+into efficiency and
+Association okay so what we did is now
+
+ align:start position:0%
+Association okay so what we did is now
+ 
+
+ align:start position:0%
+Association okay so what we did is now
+we don't pack as many players as we can
+
+ align:start position:0%
+we don't pack as many players as we can
+ 
+
+ align:start position:0%
+we don't pack as many players as we can
+we only put enough layers to maintain
+
+ align:start position:0%
+we only put enough layers to maintain
+ 
+
+ align:start position:0%
+we only put enough layers to maintain
+flow the machine the same but the design
+
+ align:start position:0%
+flow the machine the same but the design
+ 
+
+ align:start position:0%
+flow the machine the same but the design
+of the pallet and the number of parts
+
+ align:start position:0%
+of the pallet and the number of parts
+ 
+
+ align:start position:0%
+of the pallet and the number of parts
+has changed radically very good and did
+
+ align:start position:0%
+has changed radically very good and did
+ 
+
+ align:start position:0%
+has changed radically very good and did
+and did the associates participate in
+
+ align:start position:0%
+and did the associates participate in
+ 
+
+ align:start position:0%
+and did the associates participate in
+that redesign oh absolutely I that's a
+
+ align:start position:0%
+that redesign oh absolutely I that's a
+ 
+
+ align:start position:0%
+that redesign oh absolutely I that's a
+great question I we talk about the team
+
+ align:start position:0%
+great question I we talk about the team
+ 
+
+ align:start position:0%
+great question I we talk about the team
+leaders that's one of the major major
+
+ align:start position:0%
+leaders that's one of the major major
+ 
+
+ align:start position:0%
+leaders that's one of the major major
+changes that you know we reading the
+
+ align:start position:0%
+changes that you know we reading the
+ 
+
+ align:start position:0%
+changes that you know we reading the
+books about ass Bas assets and I know we
+
+ align:start position:0%
+books about ass Bas assets and I know we
+ 
+
+ align:start position:0%
+books about ass Bas assets and I know we
+I think we're working you know uh
+
+ align:start position:0%
+I think we're working you know uh
+ 
+
+ align:start position:0%
+I think we're working you know uh
+talking about we also you know we doing
+
+ align:start position:0%
+talking about we also you know we doing
+ 
+
+ align:start position:0%
+talking about we also you know we doing
+great things here where Associates have
+
+ align:start position:0%
+great things here where Associates have
+ 
+
+ align:start position:0%
+great things here where Associates have
+in great part you know in the uh in the
+
+ align:start position:0%
+in great part you know in the uh in the
+ 
+
+ align:start position:0%
+in great part you know in the uh in the
+problem solving activity the design
+
+ align:start position:0%
+problem solving activity the design
+ 
+
+ align:start position:0%
+problem solving activity the design
+supervisors and team leaders consult
+
+ align:start position:0%
+supervisors and team leaders consult
+ 
+
+ align:start position:0%
+supervisors and team leaders consult
+them all the time uh that's going to
+
+ align:start position:0%
+them all the time uh that's going to
+ 
+
+ align:start position:0%
+them all the time uh that's going to
+makes a big big difference before we
+
+ align:start position:0%
+makes a big big difference before we
+ 
+
+ align:start position:0%
+makes a big big difference before we
+talk about that now you see single ke
+
+ align:start position:0%
+talk about that now you see single ke
+ 
+
+ align:start position:0%
+talk about that now you see single ke
+flow you have flow yep so we got a sell
+
+ align:start position:0%
+flow you have flow yep so we got a sell
+ 
+
+ align:start position:0%
+flow you have flow yep so we got a sell
+here have you have a cell exactly I mean
+
+ align:start position:0%
+here have you have a cell exactly I mean
+ 
+
+ align:start position:0%
+here have you have a cell exactly I mean
+this is a very good
+
+ align:start position:0%
+this is a very good
+ 
+
+ align:start position:0%
+this is a very good
+graphical realization of a cell you can
+
+ align:start position:0%
+graphical realization of a cell you can
+ 
+
+ align:start position:0%
+graphical realization of a cell you can
+see it all connected together it's a
+
+ align:start position:0%
+see it all connected together it's a
+ 
+
+ align:start position:0%
+see it all connected together it's a
+good point this is a good example of
+
+ align:start position:0%
+good point this is a good example of
+ 
+
+ align:start position:0%
+good point this is a good example of
+flowing of flowing and we ask them to
+
+ align:start position:0%
+flowing of flowing and we ask them to
+ 
+
+ align:start position:0%
+flowing of flowing and we ask them to
+not to have more than two pairs it says
+
+ align:start position:0%
+not to have more than two pairs it says
+ 
+
+ align:start position:0%
+not to have more than two pairs it says
+right there two pairs only two pairs
+
+ align:start position:0%
+right there two pairs only two pairs
+ 
+
+ align:start position:0%
+right there two pairs only two pairs
+only
+
+ align:start position:0%
+only
+ 
+
+ align:start position:0%
+only
+um Y and you got you got you got some
+
+ align:start position:0%
+um Y and you got you got you got some
+ 
+
+ align:start position:0%
+um Y and you got you got you got some
+visual work instructions here absolutely
+
+ align:start position:0%
+visual work instructions here absolutely
+ 
+
+ align:start position:0%
+visual work instructions here absolutely
+is that's part of the standarized work
+
+ align:start position:0%
+is that's part of the standarized work
+ 
+
+ align:start position:0%
+is that's part of the standarized work
+where we def find the stand ized web and
+
+ align:start position:0%
+where we def find the stand ized web and
+ 
+
+ align:start position:0%
+where we def find the stand ized web and
+visual management is big part of it and
+
+ align:start position:0%
+visual management is big part of it and
+ 
+
+ align:start position:0%
+visual management is big part of it and
+if if you have more if I see three pairs
+
+ align:start position:0%
+if if you have more if I see three pairs
+ 
+
+ align:start position:0%
+if if you have more if I see three pairs
+you know there a problem this asso
+
+ align:start position:0%
+you know there a problem this asso
+ 
+
+ align:start position:0%
+you know there a problem this asso
+problem is having problem the flow
+
+ align:start position:0%
+problem is having problem the flow
+ 
+
+ align:start position:0%
+problem is having problem the flow
+coordinator we call the flow coordinator
+
+ align:start position:0%
+coordinator we call the flow coordinator
+ 
+
+ align:start position:0%
+coordinator we call the flow coordinator
+the team leaders we call them flow
+
+ align:start position:0%
+the team leaders we call them flow
+ 
+
+ align:start position:0%
+the team leaders we call them flow
+coordinator coordinat yeah then we come
+
+ align:start position:0%
+coordinator coordinat yeah then we come
+ 
+
+ align:start position:0%
+coordinator coordinat yeah then we come
+up with that's much better than team
+
+ align:start position:0%
+up with that's much better than team
+ 
+
+ align:start position:0%
+up with that's much better than team
+leader yes um because the goal is to
+
+ align:start position:0%
+leader yes um because the goal is to
+ 
+
+ align:start position:0%
+leader yes um because the goal is to
+maintain the flow in a way well the
+
+ align:start position:0%
+maintain the flow in a way well the
+ 
+
+ align:start position:0%
+maintain the flow in a way well the
+title flow coordinator means team leader
+
+ align:start position:0%
+title flow coordinator means team leader
+ 
+
+ align:start position:0%
+title flow coordinator means team leader
+focuses on them FL coordinator focuses
+
+ align:start position:0%
+focuses on them FL coordinator focuses
+ 
+
+ align:start position:0%
+focuses on them FL coordinator focuses
+on what they're doing exactly exactly so
+
+ align:start position:0%
+on what they're doing exactly exactly so
+ 
+
+ align:start position:0%
+on what they're doing exactly exactly so
+so visually if you see three pair the
+
+ align:start position:0%
+so visually if you see three pair the
+ 
+
+ align:start position:0%
+so visually if you see three pair the
+floor for will come you know something
+
+ align:start position:0%
+floor for will come you know something
+ 
+
+ align:start position:0%
+floor for will come you know something
+is not right so uh visually it's very
+
+ align:start position:0%
+is not right so uh visually it's very
+ 
+
+ align:start position:0%
+is not right so uh visually it's very
+powerful so AIO I see some little red
+
+ align:start position:0%
+powerful so AIO I see some little red
+ 
+
+ align:start position:0%
+powerful so AIO I see some little red
+dots over say red color labels what are
+
+ align:start position:0%
+dots over say red color labels what are
+ 
+
+ align:start position:0%
+dots over say red color labels what are
+those for it could be that um this
+
+ align:start position:0%
+those for it could be that um this
+ 
+
+ align:start position:0%
+those for it could be that um this
+machine sometime are very sensitive to
+
+ align:start position:0%
+machine sometime are very sensitive to
+ 
+
+ align:start position:0%
+machine sometime are very sensitive to
+um to the shape of the part because you
+
+ align:start position:0%
+um to the shape of the part because you
+ 
+
+ align:start position:0%
+um to the shape of the part because you
+take a picture and the part is sort of
+
+ align:start position:0%
+take a picture and the part is sort of
+ 
+
+ align:start position:0%
+take a picture and the part is sort of
+warp it pulls the machine so in sh
+
+ align:start position:0%
+warp it pulls the machine so in sh
+ 
+
+ align:start position:0%
+warp it pulls the machine so in sh
+making technology we can have a stage
+
+ align:start position:0%
+making technology we can have a stage
+ 
+
+ align:start position:0%
+making technology we can have a stage
+run up so the associ put a little red
+
+ align:start position:0%
+run up so the associ put a little red
+ 
+
+ align:start position:0%
+run up so the associ put a little red
+dot and it goes by the flowable noce fix
+
+ align:start position:0%
+dot and it goes by the flowable noce fix
+ 
+
+ align:start position:0%
+dot and it goes by the flowable noce fix
+it quickly and put it back into the line
+
+ align:start position:0%
+it quickly and put it back into the line
+ 
+
+ align:start position:0%
+it quickly and put it back into the line
+now is that something that came out of
+
+ align:start position:0%
+now is that something that came out of
+ 
+
+ align:start position:0%
+now is that something that came out of
+an employee suggestion probably yeah and
+
+ align:start position:0%
+an employee suggestion probably yeah and
+ 
+
+ align:start position:0%
+an employee suggestion probably yeah and
+they they' like to have that and they
+
+ align:start position:0%
+they they' like to have that and they
+ 
+
+ align:start position:0%
+they they' like to have that and they
+identify themselves you know at least
+
+ align:start position:0%
+identify themselves you know at least
+ 
+
+ align:start position:0%
+identify themselves you know at least
+the defect is there but they take
+
+ align:start position:0%
+the defect is there but they take
+ 
+
+ align:start position:0%
+the defect is there but they take
+ownership that's a big thing that
+
+ align:start position:0%
+ownership that's a big thing that
+ 
+
+ align:start position:0%
+ownership that's a big thing that
+changed in the past they were trying to
+
+ align:start position:0%
+changed in the past they were trying to
+ 
+
+ align:start position:0%
+changed in the past they were trying to
+you know we had inspectors at the line
+
+ align:start position:0%
+you know we had inspectors at the line
+ 
+
+ align:start position:0%
+you know we had inspectors at the line
+putting the do now defs happen but now
+
+ align:start position:0%
+putting the do now defs happen but now
+ 
+
+ align:start position:0%
+putting the do now defs happen but now
+they have hhip and and we I'm very proud
+
+ align:start position:0%
+they have hhip and and we I'm very proud
+ 
+
+ align:start position:0%
+they have hhip and and we I'm very proud
+We we created really uh an environment
+
+ align:start position:0%
+We we created really uh an environment
+ 
+
+ align:start position:0%
+We we created really uh an environment
+that it's okay
+
+ align:start position:0%
+that it's okay
+ 
+
+ align:start position:0%
+that it's okay
+uh to show the mistakes and it's not
+
+ align:start position:0%
+uh to show the mistakes and it's not
+ 
+
+ align:start position:0%
+uh to show the mistakes and it's not
+it's not problem they're happy oh not a
+
+ align:start position:0%
+it's not problem they're happy oh not a
+ 
+
+ align:start position:0%
+it's not problem they're happy oh not a
+problem and very interestingly when we
+
+ align:start position:0%
+problem and very interestingly when we
+ 
+
+ align:start position:0%
+problem and very interestingly when we
+change from the bats to the lean uh
+
+ align:start position:0%
+change from the bats to the lean uh
+ 
+
+ align:start position:0%
+change from the bats to the lean uh
+standards are very important
+
+ align:start position:0%
+standards are very important
+ 
+
+ align:start position:0%
+standards are very important
+standardized work which is the
+
+ align:start position:0%
+standardized work which is the
+ 
+
+ align:start position:0%
+standardized work which is the
+definition sort of the best uh flow of
+
+ align:start position:0%
+definition sort of the best uh flow of
+ 
+
+ align:start position:0%
+definition sort of the best uh flow of
+product considering cost policy and
+
+ align:start position:0%
+product considering cost policy and
+ 
+
+ align:start position:0%
+product considering cost policy and
+economics and some people thought well
+
+ align:start position:0%
+economics and some people thought well
+ 
+
+ align:start position:0%
+economics and some people thought well
+if I have to do always the same uh
+
+ align:start position:0%
+if I have to do always the same uh
+ 
+
+ align:start position:0%
+if I have to do always the same uh
+management was concerned that associate
+
+ align:start position:0%
+management was concerned that associate
+ 
+
+ align:start position:0%
+management was concerned that associate
+with feel like robot and feedback that
+
+ align:start position:0%
+with feel like robot and feedback that
+ 
+
+ align:start position:0%
+with feel like robot and feedback that
+we got after few months of lean
+
+ align:start position:0%
+we got after few months of lean
+ 
+
+ align:start position:0%
+we got after few months of lean
+implementation is that they love to know
+
+ align:start position:0%
+implementation is that they love to know
+ 
+
+ align:start position:0%
+implementation is that they love to know
+what they have to do so management and
+
+ align:start position:0%
+what they have to do so management and
+ 
+
+ align:start position:0%
+what they have to do so management and
+even human
+
+ align:start position:0%
+even human
+ 
+
+ align:start position:0%
+even human
+resources concept that they would feel
+
+ align:start position:0%
+resources concept that they would feel
+ 
+
+ align:start position:0%
+resources concept that they would feel
+like robot was not correct and um what
+
+ align:start position:0%
+like robot was not correct and um what
+ 
+
+ align:start position:0%
+like robot was not correct and um what
+we trying to teach them is that sort of
+
+ align:start position:0%
+we trying to teach them is that sort of
+ 
+
+ align:start position:0%
+we trying to teach them is that sort of
+a paradox because standardized work
+
+ align:start position:0%
+a paradox because standardized work
+ 
+
+ align:start position:0%
+a paradox because standardized work
+always have to do the same thing
+
+ align:start position:0%
+always have to do the same thing
+ 
+
+ align:start position:0%
+always have to do the same thing
+but as you do always the same thing you
+
+ align:start position:0%
+but as you do always the same thing you
+ 
+
+ align:start position:0%
+but as you do always the same thing you
+have a foundation for problem solving
+
+ align:start position:0%
+have a foundation for problem solving
+ 
+
+ align:start position:0%
+have a foundation for problem solving
+for continuous Improvement so
+
+ align:start position:0%
+for continuous Improvement so
+ 
+
+ align:start position:0%
+for continuous Improvement so
+standardized work is a continuous
+
+ align:start position:0%
+standardized work is a continuous
+ 
+
+ align:start position:0%
+standardized work is a continuous
+improvement tool impr very it depends
+
+ align:start position:0%
+improvement tool impr very it depends
+ 
+
+ align:start position:0%
+improvement tool impr very it depends
+how you look at them so through that
+
+ align:start position:0%
+how you look at them so through that
+ 
+
+ align:start position:0%
+how you look at them so through that
+repetition they will recommend uh
+
+ align:start position:0%
+repetition they will recommend uh
+ 
+
+ align:start position:0%
+repetition they will recommend uh
+changes that's a really interesting
+
+ align:start position:0%
+changes that's a really interesting
+ 
+
+ align:start position:0%
+changes that's a really interesting
+approach because that makes standardized
+
+ align:start position:0%
+approach because that makes standardized
+ 
+
+ align:start position:0%
+approach because that makes standardized
+work be something where you're always
+
+ align:start position:0%
+work be something where you're always
+ 
+
+ align:start position:0%
+work be something where you're always
+trying to improve it compared to now we
+
+ align:start position:0%
+trying to improve it compared to now we
+ 
+
+ align:start position:0%
+trying to improve it compared to now we
+can forget about it right AB well that's
+
+ align:start position:0%
+can forget about it right AB well that's
+ 
+
+ align:start position:0%
+can forget about it right AB well that's
+the thing sometime we go crazy never
+
+ align:start position:0%
+the thing sometime we go crazy never
+ 
+
+ align:start position:0%
+the thing sometime we go crazy never
+stops once you get those spr rewi for
+
+ align:start position:0%
+stops once you get those spr rewi for
+ 
+
+ align:start position:0%
+stops once you get those spr rewi for
+continuous Improvement never stop then
+
+ align:start position:0%
+continuous Improvement never stop then
+ 
+
+ align:start position:0%
+continuous Improvement never stop then
+the goal of management is really change
+
+ align:start position:0%
+the goal of management is really change
+ 
+
+ align:start position:0%
+the goal of management is really change
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+radically um manage managers become more
+
+ align:start position:0%
+radically um manage managers become more
+ 
+
+ align:start position:0%
+radically um manage managers become more
+of teachers and coaches coaches always
+
+ align:start position:0%
+of teachers and coaches coaches always
+ 
+
+ align:start position:0%
+of teachers and coaches coaches always
+um challenging the thinking always uh
+
+ align:start position:0%
+um challenging the thinking always uh
+ 
+
+ align:start position:0%
+um challenging the thinking always uh
+production manag called they always have
+
+ align:start position:0%
+production manag called they always have
+ 
+
+ align:start position:0%
+production manag called they always have
+to uh put have like gentle tension you
+
+ align:start position:0%
+to uh put have like gentle tension you
+ 
+
+ align:start position:0%
+to uh put have like gentle tension you
+you will not in my experience or what I
+
+ align:start position:0%
+you will not in my experience or what I
+ 
+
+ align:start position:0%
+you will not in my experience or what I
+read you will not introduce link without
+
+ align:start position:0%
+read you will not introduce link without
+ 
+
+ align:start position:0%
+read you will not introduce link without
+that tension you know it's it's it's a
+
+ align:start position:0%
+that tension you know it's it's it's a
+ 
+
+ align:start position:0%
+that tension you know it's it's it's a
+you know it's like I read somewhere else
+
+ align:start position:0%
+you know it's like I read somewhere else
+ 
+
+ align:start position:0%
+you know it's like I read somewhere else
+you know this is like a pressure cooker
+
+ align:start position:0%
+you know this is like a pressure cooker
+ 
+
+ align:start position:0%
+you know this is like a pressure cooker
+it's always pressure to just has
+
+ align:start position:0%
+it's always pressure to just has
+ 
+
+ align:start position:0%
+it's always pressure to just has
+released the very good analys great
+
+ align:start position:0%
+released the very good analys great
+ 
+
+ align:start position:0%
+released the very good analys great
+right we should move on yes so here you
+
+ align:start position:0%
+right we should move on yes so here you
+ 
+
+ align:start position:0%
+right we should move on yes so here you
+got the uh the case ready for the next
+
+ align:start position:0%
+got the uh the case ready for the next
+ 
+
+ align:start position:0%
+got the uh the case ready for the next
+Department
+
+ align:start position:0%
+Department
+ 
+
+ align:start position:0%
+Department
+okay and the case will be sent to the
+
+ align:start position:0%
+okay and the case will be sent to the
+ 
+
+ align:start position:0%
+okay and the case will be sent to the
+stitching department so I think we
+
+ align:start position:0%
+stitching department so I think we
+ 
+
+ align:start position:0%
+stitching department so I think we
+should go around and I'll show you from
+
+ align:start position:0%
+should go around and I'll show you from
+ 
+
+ align:start position:0%
+should go around and I'll show you from
+the beginning okay very
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
\ No newline at end of file
diff --git a/-yo3YxfY47g.txt b/-yo3YxfY47g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7a0e71800f14201aee4b3e22ff05eac3edd3ea28
--- /dev/null
+++ b/-yo3YxfY47g.txt
@@ -0,0 +1,2331 @@
+align:start position:0%
+ 
+the law of large numbers gives a precise
+
+ align:start position:0%
+the law of large numbers gives a precise
+ 
+
+ align:start position:0%
+the law of large numbers gives a precise
+formal statement of the basic intuitive
+
+ align:start position:0%
+formal statement of the basic intuitive
+ 
+
+ align:start position:0%
+formal statement of the basic intuitive
+idea that underlies probability theory
+
+ align:start position:0%
+idea that underlies probability theory
+ 
+
+ align:start position:0%
+idea that underlies probability theory
+and in particular our interest in random
+
+ align:start position:0%
+and in particular our interest in random
+ 
+
+ align:start position:0%
+and in particular our interest in random
+variables and their expectations their
+
+ align:start position:0%
+variables and their expectations their
+ 
+
+ align:start position:0%
+variables and their expectations their
+means so let's begin by asking what the
+
+ align:start position:0%
+means so let's begin by asking what the
+ 
+
+ align:start position:0%
+means so let's begin by asking what the
+mean means why are we so interested in
+
+ align:start position:0%
+mean means why are we so interested in
+ 
+
+ align:start position:0%
+mean means why are we so interested in
+it for example if you roll a fair die
+
+ align:start position:0%
+it for example if you roll a fair die
+ 
+
+ align:start position:0%
+it for example if you roll a fair die
+with heads with faces one through six
+
+ align:start position:0%
+with heads with faces one through six
+ 
+
+ align:start position:0%
+with heads with faces one through six
+the mean value it's expected value is
+
+ align:start position:0%
+the mean value it's expected value is
+ 
+
+ align:start position:0%
+the mean value it's expected value is
+three and a half and you'll never roll
+
+ align:start position:0%
+three and a half and you'll never roll
+ 
+
+ align:start position:0%
+three and a half and you'll never roll
+three and a half because there is no
+
+ align:start position:0%
+three and a half because there is no
+ 
+
+ align:start position:0%
+three and a half because there is no
+three and a half face so why do we care
+
+ align:start position:0%
+three and a half face so why do we care
+ 
+
+ align:start position:0%
+three and a half face so why do we care
+about what this mean is if we're never
+
+ align:start position:0%
+about what this mean is if we're never
+ 
+
+ align:start position:0%
+about what this mean is if we're never
+going to roll it and the answer is that
+
+ align:start position:0%
+going to roll it and the answer is that
+ 
+
+ align:start position:0%
+going to roll it and the answer is that
+we believe that after many rolls if we
+
+ align:start position:0%
+we believe that after many rolls if we
+ 
+
+ align:start position:0%
+we believe that after many rolls if we
+take the average of the numbers that
+
+ align:start position:0%
+take the average of the numbers that
+ 
+
+ align:start position:0%
+take the average of the numbers that
+show on the dice that average is going
+
+ align:start position:0%
+show on the dice that average is going
+ 
+
+ align:start position:0%
+show on the dice that average is going
+to be near the mean it's gonna be near
+
+ align:start position:0%
+to be near the mean it's gonna be near
+ 
+
+ align:start position:0%
+to be near the mean it's gonna be near
+three and a half let's look at an even
+
+ align:start position:0%
+three and a half let's look at an even
+ 
+
+ align:start position:0%
+three and a half let's look at an even
+more basic example we if it's a fair die
+
+ align:start position:0%
+more basic example we if it's a fair die
+ 
+
+ align:start position:0%
+more basic example we if it's a fair die
+the probability of rolling a six as with
+
+ align:start position:0%
+the probability of rolling a six as with
+ 
+
+ align:start position:0%
+the probability of rolling a six as with
+any other number is 1/6 and the very
+
+ align:start position:0%
+any other number is 1/6 and the very
+ 
+
+ align:start position:0%
+any other number is 1/6 and the very
+meaning of the fact that the probability
+
+ align:start position:0%
+meaning of the fact that the probability
+ 
+
+ align:start position:0%
+meaning of the fact that the probability
+of rolling a six is 1/6 is that we
+
+ align:start position:0%
+of rolling a six is 1/6 is that we
+ 
+
+ align:start position:0%
+of rolling a six is 1/6 is that we
+expect that if you roll a lot of times
+
+ align:start position:0%
+expect that if you roll a lot of times
+ 
+
+ align:start position:0%
+expect that if you roll a lot of times
+if you roll about n times the fraction
+
+ align:start position:0%
+if you roll about n times the fraction
+ 
+
+ align:start position:0%
+if you roll about n times the fraction
+of sixes is going to be around and over
+
+ align:start position:0%
+of sixes is going to be around and over
+ 
+
+ align:start position:0%
+of sixes is going to be around and over
+six the fraction of six is going to be
+
+ align:start position:0%
+six the fraction of six is going to be
+ 
+
+ align:start position:0%
+six the fraction of six is going to be
+about one-sixth that of n rolls you'll
+
+ align:start position:0%
+about one-sixth that of n rolls you'll
+ 
+
+ align:start position:0%
+about one-sixth that of n rolls you'll
+get about n over six sixes that's that's
+
+ align:start position:0%
+get about n over six sixes that's that's
+ 
+
+ align:start position:0%
+get about n over six sixes that's that's
+almost the definition or the intuitive
+
+ align:start position:0%
+almost the definition or the intuitive
+ 
+
+ align:start position:0%
+almost the definition or the intuitive
+idea behind what we mean when we assign
+
+ align:start position:0%
+idea behind what we mean when we assign
+ 
+
+ align:start position:0%
+idea behind what we mean when we assign
+probability to some outcome it's that if
+
+ align:start position:0%
+probability to some outcome it's that if
+ 
+
+ align:start position:0%
+probability to some outcome it's that if
+we did it repeatedly the fraction of
+
+ align:start position:0%
+we did it repeatedly the fraction of
+ 
+
+ align:start position:0%
+we did it repeatedly the fraction of
+times that it came up would be equal to
+
+ align:start position:0%
+times that it came up would be equal to
+ 
+
+ align:start position:0%
+times that it came up would be equal to
+its probability or at least closely
+
+ align:start position:0%
+its probability or at least closely
+ 
+
+ align:start position:0%
+its probability or at least closely
+equal to it in the long run
+
+ align:start position:0%
+equal to it in the long run
+ 
+
+ align:start position:0%
+equal to it in the long run
+so let's look at what Jacob Bernoulli
+
+ align:start position:0%
+so let's look at what Jacob Bernoulli
+ 
+
+ align:start position:0%
+so let's look at what Jacob Bernoulli
+who is the discoverer of the law of
+
+ align:start position:0%
+who is the discoverer of the law of
+ 
+
+ align:start position:0%
+who is the discoverer of the law of
+large numbers had to say on the subject
+
+ align:start position:0%
+large numbers had to say on the subject
+ 
+
+ align:start position:0%
+large numbers had to say on the subject
+he was born in 1659 died in 1705 and his
+
+ align:start position:0%
+he was born in 1659 died in 1705 and his
+ 
+
+ align:start position:0%
+he was born in 1659 died in 1705 and his
+famous book the art of guessing are as
+
+ align:start position:0%
+famous book the art of guessing are as
+ 
+
+ align:start position:0%
+famous book the art of guessing are as
+konjac Tandy was actually published
+
+ align:start position:0%
+konjac Tandy was actually published
+ 
+
+ align:start position:0%
+konjac Tandy was actually published
+posthumously by his cousin and he said
+
+ align:start position:0%
+posthumously by his cousin and he said
+ 
+
+ align:start position:0%
+posthumously by his cousin and he said
+Bernoulli says even the stupidest man by
+
+ align:start position:0%
+Bernoulli says even the stupidest man by
+ 
+
+ align:start position:0%
+Bernoulli says even the stupidest man by
+some instinct of nature per se and by no
+
+ align:start position:0%
+some instinct of nature per se and by no
+ 
+
+ align:start position:0%
+some instinct of nature per se and by no
+previous instruction this is truly a
+
+ align:start position:0%
+previous instruction this is truly a
+ 
+
+ align:start position:0%
+previous instruction this is truly a
+knows for sure that the more
+
+ align:start position:0%
+knows for sure that the more
+ 
+
+ align:start position:0%
+knows for sure that the more
+observations that are taken the less the
+
+ align:start position:0%
+observations that are taken the less the
+ 
+
+ align:start position:0%
+observations that are taken the less the
+danger will be of straying from the mark
+
+ align:start position:0%
+danger will be of straying from the mark
+ 
+
+ align:start position:0%
+danger will be of straying from the mark
+all right what does he mean well like
+
+ align:start position:0%
+all right what does he mean well like
+ 
+
+ align:start position:0%
+all right what does he mean well like
+it's what we said a moment ago if you
+
+ align:start position:0%
+it's what we said a moment ago if you
+ 
+
+ align:start position:0%
+it's what we said a moment ago if you
+roll the fair die n times and the
+
+ align:start position:0%
+roll the fair die n times and the
+ 
+
+ align:start position:0%
+roll the fair die n times and the
+probability of a roll of is 1/6 then the
+
+ align:start position:0%
+probability of a roll of is 1/6 then the
+ 
+
+ align:start position:0%
+probability of a roll of is 1/6 then the
+average number of sixes which is the
+
+ align:start position:0%
+average number of sixes which is the
+ 
+
+ align:start position:0%
+average number of sixes which is the
+number of sixes rolled divided by n we
+
+ align:start position:0%
+number of sixes rolled divided by n we
+ 
+
+ align:start position:0%
+number of sixes rolled divided by n we
+believe intuitively that that number is
+
+ align:start position:0%
+believe intuitively that that number is
+ 
+
+ align:start position:0%
+believe intuitively that that number is
+gonna approach 1/6 as n approaches
+
+ align:start position:0%
+gonna approach 1/6 as n approaches
+ 
+
+ align:start position:0%
+gonna approach 1/6 as n approaches
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+that's what Bernoulli is saying that
+
+ align:start position:0%
+that's what Bernoulli is saying that
+ 
+
+ align:start position:0%
+that's what Bernoulli is saying that
+everybody understands that they
+
+ align:start position:0%
+everybody understands that they
+ 
+
+ align:start position:0%
+everybody understands that they
+intuitively are sure of it and who knows
+
+ align:start position:0%
+intuitively are sure of it and who knows
+ 
+
+ align:start position:0%
+intuitively are sure of it and who knows
+how they figure that out but that's what
+
+ align:start position:0%
+how they figure that out but that's what
+ 
+
+ align:start position:0%
+how they figure that out but that's what
+everyone thinks and he might be right
+
+ align:start position:0%
+everyone thinks and he might be right
+ 
+
+ align:start position:0%
+everyone thinks and he might be right
+now of course when you're doing this
+
+ align:start position:0%
+now of course when you're doing this
+ 
+
+ align:start position:0%
+now of course when you're doing this
+experiment of rolling n times and
+
+ align:start position:0%
+experiment of rolling n times and
+ 
+
+ align:start position:0%
+experiment of rolling n times and
+Counting the number of six and seeing if
+
+ align:start position:0%
+Counting the number of six and seeing if
+ 
+
+ align:start position:0%
+Counting the number of six and seeing if
+the fraction is close to 1/6 you might
+
+ align:start position:0%
+the fraction is close to 1/6 you might
+ 
+
+ align:start position:0%
+the fraction is close to 1/6 you might
+be unlucky and it's possible that you'd
+
+ align:start position:0%
+be unlucky and it's possible that you'd
+ 
+
+ align:start position:0%
+be unlucky and it's possible that you'd
+get an average that actually was way off
+
+ align:start position:0%
+get an average that actually was way off
+ 
+
+ align:start position:0%
+get an average that actually was way off
+1/6 but that would be unlucky and the
+
+ align:start position:0%
+1/6 but that would be unlucky and the
+ 
+
+ align:start position:0%
+1/6 but that would be unlucky and the
+question is how unlikely is it B is it
+
+ align:start position:0%
+question is how unlikely is it B is it
+ 
+
+ align:start position:0%
+question is how unlikely is it B is it
+to be that you'd get a number of a
+
+ align:start position:0%
+to be that you'd get a number of a
+ 
+
+ align:start position:0%
+to be that you'd get a number of a
+fraction of sixes that wasn't really
+
+ align:start position:0%
+fraction of sixes that wasn't really
+ 
+
+ align:start position:0%
+fraction of sixes that wasn't really
+close to 1/6 and with the law of large
+
+ align:start position:0%
+close to 1/6 and with the law of large
+ 
+
+ align:start position:0%
+close to 1/6 and with the law of large
+numbers is getting a grip on that and in
+
+ align:start position:0%
+numbers is getting a grip on that and in
+ 
+
+ align:start position:0%
+numbers is getting a grip on that and in
+fact subsequently we'll get a more even
+
+ align:start position:0%
+fact subsequently we'll get a more even
+ 
+
+ align:start position:0%
+fact subsequently we'll get a more even
+quantitative grip on it which will be
+
+ align:start position:0%
+quantitative grip on it which will be
+ 
+
+ align:start position:0%
+quantitative grip on it which will be
+crucial for applications in sampling and
+
+ align:start position:0%
+crucial for applications in sampling and
+ 
+
+ align:start position:0%
+crucial for applications in sampling and
+hypothesis testing but let's go on so
+
+ align:start position:0%
+hypothesis testing but let's go on so
+ 
+
+ align:start position:0%
+hypothesis testing but let's go on so
+let's look at some actual numbers which
+
+ align:start position:0%
+let's look at some actual numbers which
+ 
+
+ align:start position:0%
+let's look at some actual numbers which
+I calculated if you roll a die n times
+
+ align:start position:0%
+I calculated if you roll a die n times
+ 
+
+ align:start position:0%
+I calculated if you roll a die n times
+where n is 6 6600 1,200 3,000 or 6,000
+
+ align:start position:0%
+where n is 6 6600 1,200 3,000 or 6,000
+ 
+
+ align:start position:0%
+where n is 6 6600 1,200 3,000 or 6,000
+the probability that you're going to be
+
+ align:start position:0%
+the probability that you're going to be
+ 
+
+ align:start position:0%
+the probability that you're going to be
+within 10% of the expected number of
+
+ align:start position:0%
+within 10% of the expected number of
+ 
+
+ align:start position:0%
+within 10% of the expected number of
+sixes is given here so it turns out of
+
+ align:start position:0%
+sixes is given here so it turns out of
+ 
+
+ align:start position:0%
+sixes is given here so it turns out of
+course that in order to be within 10 if
+
+ align:start position:0%
+course that in order to be within 10 if
+ 
+
+ align:start position:0%
+course that in order to be within 10 if
+you're gonna roll six times the only way
+
+ align:start position:0%
+you're gonna roll six times the only way
+ 
+
+ align:start position:0%
+you're gonna roll six times the only way
+to be within 10% of the one expected six
+
+ align:start position:0%
+to be within 10% of the one expected six
+ 
+
+ align:start position:0%
+to be within 10% of the one expected six
+that you should roll is to roll exactly
+
+ align:start position:0%
+that you should roll is to roll exactly
+ 
+
+ align:start position:0%
+that you should roll is to roll exactly
+one six in six tries and the probability
+
+ align:start position:0%
+one six in six tries and the probability
+ 
+
+ align:start position:0%
+one six in six tries and the probability
+of that is about 40% point four as you
+
+ align:start position:0%
+of that is about 40% point four as you
+ 
+
+ align:start position:0%
+of that is about 40% point four as you
+can check yourself easily then it turns
+
+ align:start position:0%
+can check yourself easily then it turns
+ 
+
+ align:start position:0%
+can check yourself easily then it turns
+out that if you flip a roll
+
+ align:start position:0%
+out that if you flip a roll
+ 
+
+ align:start position:0%
+out that if you flip a roll
+60 times
+
+ align:start position:0%
+60 times
+ 
+
+ align:start position:0%
+60 times
+probability of being between 66 sorry
+
+ align:start position:0%
+probability of being between 66 sorry
+ 
+
+ align:start position:0%
+probability of being between 66 sorry
+the expected number in 60 rolls is going
+
+ align:start position:0%
+the expected number in 60 rolls is going
+ 
+
+ align:start position:0%
+the expected number in 60 rolls is going
+to be 10 so the probability of there
+
+ align:start position:0%
+to be 10 so the probability of there
+ 
+
+ align:start position:0%
+to be 10 so the probability of there
+being within 10 percent of 10 or 9 to 11
+
+ align:start position:0%
+being within 10 percent of 10 or 9 to 11
+ 
+
+ align:start position:0%
+being within 10 percent of 10 or 9 to 11
+sixes is 0.26 and likewise the
+
+ align:start position:0%
+sixes is 0.26 and likewise the
+ 
+
+ align:start position:0%
+sixes is 0.26 and likewise the
+probability of there being within 10
+
+ align:start position:0%
+probability of there being within 10
+ 
+
+ align:start position:0%
+probability of there being within 10
+percent of 100 which is the expected
+
+ align:start position:0%
+percent of 100 which is the expected
+ 
+
+ align:start position:0%
+percent of 100 which is the expected
+number of sixes when you roll 600 times
+
+ align:start position:0%
+number of sixes when you roll 600 times
+ 
+
+ align:start position:0%
+number of sixes when you roll 600 times
+is 0.72 and so on until finally the
+
+ align:start position:0%
+is 0.72 and so on until finally the
+ 
+
+ align:start position:0%
+is 0.72 and so on until finally the
+probability of being within 10 percent
+
+ align:start position:0%
+probability of being within 10 percent
+ 
+
+ align:start position:0%
+probability of being within 10 percent
+of a thousand which is the expected
+
+ align:start position:0%
+of a thousand which is the expected
+ 
+
+ align:start position:0%
+of a thousand which is the expected
+number when you roll 6,000 times that is
+
+ align:start position:0%
+number when you roll 6,000 times that is
+ 
+
+ align:start position:0%
+number when you roll 6,000 times that is
+between 900 and 1106 is in 6,000 rolls
+
+ align:start position:0%
+between 900 and 1106 is in 6,000 rolls
+ 
+
+ align:start position:0%
+between 900 and 1106 is in 6,000 rolls
+is point nine nine nine triple nines in
+
+ align:start position:0%
+is point nine nine nine triple nines in
+ 
+
+ align:start position:0%
+is point nine nine nine triple nines in
+fact it's a little bit bigger so it's
+
+ align:start position:0%
+fact it's a little bit bigger so it's
+ 
+
+ align:start position:0%
+fact it's a little bit bigger so it's
+really only about one chance in a
+
+ align:start position:0%
+really only about one chance in a
+ 
+
+ align:start position:0%
+really only about one chance in a
+thousand that your number of sixes won't
+
+ align:start position:0%
+thousand that your number of sixes won't
+ 
+
+ align:start position:0%
+thousand that your number of sixes won't
+fall in that interval within ten percent
+
+ align:start position:0%
+fall in that interval within ten percent
+ 
+
+ align:start position:0%
+fall in that interval within ten percent
+of the expected number well suppose I
+
+ align:start position:0%
+of the expected number well suppose I
+ 
+
+ align:start position:0%
+of the expected number well suppose I
+asked for a tighter tolerance and I'd
+
+ align:start position:0%
+asked for a tighter tolerance and I'd
+ 
+
+ align:start position:0%
+asked for a tighter tolerance and I'd
+like to know what's the probability of
+
+ align:start position:0%
+like to know what's the probability of
+ 
+
+ align:start position:0%
+like to know what's the probability of
+being within five percent well first of
+
+ align:start position:0%
+being within five percent well first of
+ 
+
+ align:start position:0%
+being within five percent well first of
+all notice of course that as the number
+
+ align:start position:0%
+all notice of course that as the number
+ 
+
+ align:start position:0%
+all notice of course that as the number
+of rolls get larger the probability of
+
+ align:start position:0%
+of rolls get larger the probability of
+ 
+
+ align:start position:0%
+of rolls get larger the probability of
+being in this given interval is of
+
+ align:start position:0%
+being in this given interval is of
+ 
+
+ align:start position:0%
+being in this given interval is of
+getting getting higher and higher which
+
+ align:start position:0%
+getting getting higher and higher which
+ 
+
+ align:start position:0%
+getting getting higher and higher which
+is what Bernoulli said and what we
+
+ align:start position:0%
+is what Bernoulli said and what we
+ 
+
+ align:start position:0%
+is what Bernoulli said and what we
+intuitively believe the more rolls the
+
+ align:start position:0%
+intuitively believe the more rolls the
+ 
+
+ align:start position:0%
+intuitively believe the more rolls the
+more likely you are to be close to what
+
+ align:start position:0%
+more likely you are to be close to what
+ 
+
+ align:start position:0%
+more likely you are to be close to what
+you expect if you tighten the tolerance
+
+ align:start position:0%
+you expect if you tighten the tolerance
+ 
+
+ align:start position:0%
+you expect if you tighten the tolerance
+of course then the probabilities wind up
+
+ align:start position:0%
+of course then the probabilities wind up
+ 
+
+ align:start position:0%
+of course then the probabilities wind up
+getting smaller that you'll do so well
+
+ align:start position:0%
+getting smaller that you'll do so well
+ 
+
+ align:start position:0%
+getting smaller that you'll do so well
+so if you want to be within 5% of the
+
+ align:start position:0%
+so if you want to be within 5% of the
+ 
+
+ align:start position:0%
+so if you want to be within 5% of the
+average in six rolls it means you still
+
+ align:start position:0%
+average in six rolls it means you still
+ 
+
+ align:start position:0%
+average in six rolls it means you still
+have to roll exactly 1/6 which means the
+
+ align:start position:0%
+have to roll exactly 1/6 which means the
+ 
+
+ align:start position:0%
+have to roll exactly 1/6 which means the
+probability is still 0.4 but if you're
+
+ align:start position:0%
+probability is still 0.4 but if you're
+ 
+
+ align:start position:0%
+probability is still 0.4 but if you're
+trying to be within 5% of the expected
+
+ align:start position:0%
+trying to be within 5% of the expected
+ 
+
+ align:start position:0%
+trying to be within 5% of the expected
+number 10 and 60 rolls meaning between 5
+
+ align:start position:0%
+number 10 and 60 rolls meaning between 5
+ 
+
+ align:start position:0%
+number 10 and 60 rolls meaning between 5
+and 15 that probability is only 0.14
+
+ align:start position:0%
+and 15 that probability is only 0.14
+ 
+
+ align:start position:0%
+and 15 that probability is only 0.14
+compared to the probability of 0.26 of
+
+ align:start position:0%
+compared to the probability of 0.26 of
+ 
+
+ align:start position:0%
+compared to the probability of 0.26 of
+being within 10% and if we jump down
+
+ align:start position:0%
+being within 10% and if we jump down
+ 
+
+ align:start position:0%
+being within 10% and if we jump down
+here say to 3,000 rolls
+
+ align:start position:0%
+here say to 3,000 rolls
+ 
+
+ align:start position:0%
+here say to 3,000 rolls
+the probability of being within 10% of
+
+ align:start position:0%
+the probability of being within 10% of
+ 
+
+ align:start position:0%
+the probability of being within 10% of
+500 which is the expected number in
+
+ align:start position:0%
+500 which is the expected number in
+ 
+
+ align:start position:0%
+500 which is the expected number in
+3,000 roles within 10% is 98% 9 8 but
+
+ align:start position:0%
+3,000 roles within 10% is 98% 9 8 but
+ 
+
+ align:start position:0%
+3,000 roles within 10% is 98% 9 8 but
+within being within 5% of 500 it's 0.78
+
+ align:start position:0%
+within being within 5% of 500 it's 0.78
+ 
+
+ align:start position:0%
+within being within 5% of 500 it's 0.78
+or about 3 little over 3/4 so what does
+
+ align:start position:0%
+or about 3 little over 3/4 so what does
+ 
+
+ align:start position:0%
+or about 3 little over 3/4 so what does
+that tell us well it means that if you
+
+ align:start position:0%
+that tell us well it means that if you
+ 
+
+ align:start position:0%
+that tell us well it means that if you
+enrolled three thousand times and you
+
+ align:start position:0%
+enrolled three thousand times and you
+ 
+
+ align:start position:0%
+enrolled three thousand times and you
+did not get within ten percent of the
+
+ align:start position:0%
+did not get within ten percent of the
+ 
+
+ align:start position:0%
+did not get within ten percent of the
+expected number of 500 that is you did
+
+ align:start position:0%
+expected number of 500 that is you did
+ 
+
+ align:start position:0%
+expected number of 500 that is you did
+not get in the interval between 450 and
+
+ align:start position:0%
+not get in the interval between 450 and
+ 
+
+ align:start position:0%
+not get in the interval between 450 and
+550 sixes you could be 98% confident
+
+ align:start position:0%
+550 sixes you could be 98% confident
+ 
+
+ align:start position:0%
+550 sixes you could be 98% confident
+that your die is loaded it's not
+
+ align:start position:0%
+that your die is loaded it's not
+ 
+
+ align:start position:0%
+that your die is loaded it's not
+weighted 1/6 to show a 6 and similarly
+
+ align:start position:0%
+weighted 1/6 to show a 6 and similarly
+ 
+
+ align:start position:0%
+weighted 1/6 to show a 6 and similarly
+if you did not get within 425 and for
+
+ align:start position:0%
+if you did not get within 425 and for
+ 
+
+ align:start position:0%
+if you did not get within 425 and for
+525 a 6 is in 3,000 rolls you can be 78%
+
+ align:start position:0%
+525 a 6 is in 3,000 rolls you can be 78%
+ 
+
+ align:start position:0%
+525 a 6 is in 3,000 rolls you can be 78%
+sure that your die is loaded and this is
+
+ align:start position:0%
+sure that your die is loaded and this is
+ 
+
+ align:start position:0%
+sure that your die is loaded and this is
+exactly why the law of large numbers is
+
+ align:start position:0%
+exactly why the law of large numbers is
+ 
+
+ align:start position:0%
+exactly why the law of large numbers is
+so important to us because it allows us
+
+ align:start position:0%
+so important to us because it allows us
+ 
+
+ align:start position:0%
+so important to us because it allows us
+to do an experiment and then assess
+
+ align:start position:0%
+to do an experiment and then assess
+ 
+
+ align:start position:0%
+to do an experiment and then assess
+whether what we think is true is
+
+ align:start position:0%
+whether what we think is true is
+ 
+
+ align:start position:0%
+whether what we think is true is
+verified by the outcome that we got in
+
+ align:start position:0%
+verified by the outcome that we got in
+ 
+
+ align:start position:0%
+verified by the outcome that we got in
+this experiment all right let's go on to
+
+ align:start position:0%
+this experiment all right let's go on to
+ 
+
+ align:start position:0%
+this experiment all right let's go on to
+see what else Bernoulli was concerned
+
+ align:start position:0%
+see what else Bernoulli was concerned
+ 
+
+ align:start position:0%
+see what else Bernoulli was concerned
+with in his time it certainly remains to
+
+ align:start position:0%
+with in his time it certainly remains to
+ 
+
+ align:start position:0%
+with in his time it certainly remains to
+be inquired whether after the number of
+
+ align:start position:0%
+be inquired whether after the number of
+ 
+
+ align:start position:0%
+be inquired whether after the number of
+observations has been increased the
+
+ align:start position:0%
+observations has been increased the
+ 
+
+ align:start position:0%
+observations has been increased the
+probability of obtaining the true ratio
+
+ align:start position:0%
+probability of obtaining the true ratio
+ 
+
+ align:start position:0%
+probability of obtaining the true ratio
+finally exceeds any given degree of
+
+ align:start position:0%
+finally exceeds any given degree of
+ 
+
+ align:start position:0%
+finally exceeds any given degree of
+certainty or whether the problem has so
+
+ align:start position:0%
+certainty or whether the problem has so
+ 
+
+ align:start position:0%
+certainty or whether the problem has so
+to speak its own asymptotes that is
+
+ align:start position:0%
+to speak its own asymptotes that is
+ 
+
+ align:start position:0%
+to speak its own asymptotes that is
+whether some degree of certainty is
+
+ align:start position:0%
+whether some degree of certainty is
+ 
+
+ align:start position:0%
+whether some degree of certainty is
+given which one can never exceed now
+
+ align:start position:0%
+given which one can never exceed now
+ 
+
+ align:start position:0%
+given which one can never exceed now
+that's a 17th century English that maybe
+
+ align:start position:0%
+that's a 17th century English that maybe
+ 
+
+ align:start position:0%
+that's a 17th century English that maybe
+a little bit hard to parse so let's
+
+ align:start position:0%
+a little bit hard to parse so let's
+ 
+
+ align:start position:0%
+a little bit hard to parse so let's
+translate it into math language what is
+
+ align:start position:0%
+translate it into math language what is
+ 
+
+ align:start position:0%
+translate it into math language what is
+it that Bernoulli is asking so what
+
+ align:start position:0%
+it that Bernoulli is asking so what
+ 
+
+ align:start position:0%
+it that Bernoulli is asking so what
+Bernoulli means is that he wants to
+
+ align:start position:0%
+Bernoulli means is that he wants to
+ 
+
+ align:start position:0%
+Bernoulli means is that he wants to
+think about taking a random variable R
+
+ align:start position:0%
+think about taking a random variable R
+ 
+
+ align:start position:0%
+think about taking a random variable R
+with an an expectation or mean of mu and
+
+ align:start position:0%
+with an an expectation or mean of mu and
+ 
+
+ align:start position:0%
+with an an expectation or mean of mu and
+he wants to make n trial observations of
+
+ align:start position:0%
+he wants to make n trial observations of
+ 
+
+ align:start position:0%
+he wants to make n trial observations of
+R and take the average of those
+
+ align:start position:0%
+R and take the average of those
+ 
+
+ align:start position:0%
+R and take the average of those
+observations
+
+ align:start position:0%
+observations
+ 
+
+ align:start position:0%
+observations
+and see how close they are to you all
+
+ align:start position:0%
+and see how close they are to you all
+ 
+
+ align:start position:0%
+and see how close they are to you all
+right what is it what is making any
+
+ align:start position:0%
+right what is it what is making any
+ 
+
+ align:start position:0%
+right what is it what is making any
+trial observations mean well formally
+
+ align:start position:0%
+trial observations mean well formally
+ 
+
+ align:start position:0%
+trial observations mean well formally
+the way we're gonna capture it is we're
+
+ align:start position:0%
+the way we're gonna capture it is we're
+ 
+
+ align:start position:0%
+the way we're gonna capture it is we're
+gonna think of having um a bunch of
+
+ align:start position:0%
+gonna think of having um a bunch of
+ 
+
+ align:start position:0%
+gonna think of having um a bunch of
+mutually independent identically
+
+ align:start position:0%
+mutually independent identically
+ 
+
+ align:start position:0%
+mutually independent identically
+distributed random variables r1 through
+
+ align:start position:0%
+distributed random variables r1 through
+ 
+
+ align:start position:0%
+distributed random variables r1 through
+RN this phrase identically independent
+
+ align:start position:0%
+RN this phrase identically independent
+ 
+
+ align:start position:0%
+RN this phrase identically independent
+identically distributed comes up so
+
+ align:start position:0%
+identically distributed comes up so
+ 
+
+ align:start position:0%
+identically distributed comes up so
+often that there's a standard
+
+ align:start position:0%
+often that there's a standard
+ 
+
+ align:start position:0%
+often that there's a standard
+abbreviation iid random variables so
+
+ align:start position:0%
+abbreviation iid random variables so
+ 
+
+ align:start position:0%
+abbreviation iid random variables so
+we're going to have n of them and think
+
+ align:start position:0%
+we're going to have n of them and think
+ 
+
+ align:start position:0%
+we're going to have n of them and think
+of those as being the n observations
+
+ align:start position:0%
+of those as being the n observations
+ 
+
+ align:start position:0%
+of those as being the n observations
+that we make of a given random variable
+
+ align:start position:0%
+that we make of a given random variable
+ 
+
+ align:start position:0%
+that we make of a given random variable
+on so r1 through RN each have exactly
+
+ align:start position:0%
+on so r1 through RN each have exactly
+ 
+
+ align:start position:0%
+on so r1 through RN each have exactly
+the same distribution is our and they're
+
+ align:start position:0%
+the same distribution is our and they're
+ 
+
+ align:start position:0%
+the same distribution is our and they're
+mutually independent and again since
+
+ align:start position:0%
+mutually independent and again since
+ 
+
+ align:start position:0%
+mutually independent and again since
+they're they have identical
+
+ align:start position:0%
+they're they have identical
+ 
+
+ align:start position:0%
+they're they have identical
+distributions they all have the same
+
+ align:start position:0%
+distributions they all have the same
+ 
+
+ align:start position:0%
+distributions they all have the same
+mean mu as the random variable R that we
+
+ align:start position:0%
+mean mu as the random variable R that we
+ 
+
+ align:start position:0%
+mean mu as the random variable R that we
+were trying to investigate so we model n
+
+ align:start position:0%
+were trying to investigate so we model n
+ 
+
+ align:start position:0%
+were trying to investigate so we model n
+independent trials repeated trials by
+
+ align:start position:0%
+independent trials repeated trials by
+ 
+
+ align:start position:0%
+independent trials repeated trials by
+saying that we have n random variables
+
+ align:start position:0%
+saying that we have n random variables
+ 
+
+ align:start position:0%
+saying that we have n random variables
+that are iid okay now what Bernoulli is
+
+ align:start position:0%
+that are iid okay now what Bernoulli is
+ 
+
+ align:start position:0%
+that are iid okay now what Bernoulli is
+proposing is that you take the average
+
+ align:start position:0%
+proposing is that you take the average
+ 
+
+ align:start position:0%
+proposing is that you take the average
+of those n random variables so you take
+
+ align:start position:0%
+of those n random variables so you take
+ 
+
+ align:start position:0%
+of those n random variables so you take
+R 1 through some of our 1 or 2 up
+
+ align:start position:0%
+R 1 through some of our 1 or 2 up
+ 
+
+ align:start position:0%
+R 1 through some of our 1 or 2 up
+through R and then divide by n that's
+
+ align:start position:0%
+through R and then divide by n that's
+ 
+
+ align:start position:0%
+through R and then divide by n that's
+the average value call that a sub n the
+
+ align:start position:0%
+the average value call that a sub n the
+ 
+
+ align:start position:0%
+the average value call that a sub n the
+average of the n observations of the n
+
+ align:start position:0%
+average of the n observations of the n
+ 
+
+ align:start position:0%
+average of the n observations of the n
+roll's
+
+ align:start position:0%
+roll's
+ 
+
+ align:start position:0%
+roll's
+and Bernoulli's question is is this
+
+ align:start position:0%
+and Bernoulli's question is is this
+ 
+
+ align:start position:0%
+and Bernoulli's question is is this
+average probably close to the mean mu if
+
+ align:start position:0%
+average probably close to the mean mu if
+ 
+
+ align:start position:0%
+average probably close to the mean mu if
+n is big what exactly does that mean
+
+ align:start position:0%
+n is big what exactly does that mean
+ 
+
+ align:start position:0%
+n is big what exactly does that mean
+probably close to MU means that the
+
+ align:start position:0%
+probably close to MU means that the
+ 
+
+ align:start position:0%
+probably close to MU means that the
+probability that the distance between
+
+ align:start position:0%
+probability that the distance between
+ 
+
+ align:start position:0%
+probability that the distance between
+the average and mu is less than or equal
+
+ align:start position:0%
+the average and mu is less than or equal
+ 
+
+ align:start position:0%
+the average and mu is less than or equal
+to Delta is what so Delta is talking
+
+ align:start position:0%
+to Delta is what so Delta is talking
+ 
+
+ align:start position:0%
+to Delta is what so Delta is talking
+about how close you are
+
+ align:start position:0%
+about how close you are
+ 
+
+ align:start position:0%
+about how close you are
+don't they as a parameter we expect it's
+
+ align:start position:0%
+don't they as a parameter we expect it's
+ 
+
+ align:start position:0%
+don't they as a parameter we expect it's
+got to be positive we're asking think of
+
+ align:start position:0%
+got to be positive we're asking think of
+ 
+
+ align:start position:0%
+got to be positive we're asking think of
+whatever close means to you does it mean
+
+ align:start position:0%
+whatever close means to you does it mean
+ 
+
+ align:start position:0%
+whatever close means to you does it mean
+0.1 does it mean point o 1 what amount
+
+ align:start position:0%
+0.1 does it mean point o 1 what amount
+ 
+
+ align:start position:0%
+0.1 does it mean point o 1 what amount
+would persuade you that um that the
+
+ align:start position:0%
+would persuade you that um that the
+ 
+
+ align:start position:0%
+would persuade you that um that the
+average was close to what it ought to be
+
+ align:start position:0%
+average was close to what it ought to be
+ 
+
+ align:start position:0%
+average was close to what it ought to be
+and we ask then whether the distance
+
+ align:start position:0%
+and we ask then whether the distance
+ 
+
+ align:start position:0%
+and we ask then whether the distance
+between the average and the mean is
+
+ align:start position:0%
+between the average and the mean is
+ 
+
+ align:start position:0%
+between the average and the mean is
+close less than or equal to Delta and
+
+ align:start position:0%
+close less than or equal to Delta and
+ 
+
+ align:start position:0%
+close less than or equal to Delta and
+Bernoulli wants to know what is the
+
+ align:start position:0%
+Bernoulli wants to know what is the
+ 
+
+ align:start position:0%
+Bernoulli wants to know what is the
+probability of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and what he goes on to say is therefore
+
+ align:start position:0%
+and what he goes on to say is therefore
+ 
+
+ align:start position:0%
+and what he goes on to say is therefore
+this is the problem which I now set
+
+ align:start position:0%
+this is the problem which I now set
+ 
+
+ align:start position:0%
+this is the problem which I now set
+forth and make known after I have
+
+ align:start position:0%
+forth and make known after I have
+ 
+
+ align:start position:0%
+forth and make known after I have
+pondered it pondered over it for 20
+
+ align:start position:0%
+pondered it pondered over it for 20
+ 
+
+ align:start position:0%
+pondered it pondered over it for 20
+years both its novelty and its very
+
+ align:start position:0%
+years both its novelty and its very
+ 
+
+ align:start position:0%
+years both its novelty and its very
+great usefulness coupled with its great
+
+ align:start position:0%
+great usefulness coupled with its great
+ 
+
+ align:start position:0%
+great usefulness coupled with its great
+difficulty can exceed in weight and
+
+ align:start position:0%
+difficulty can exceed in weight and
+ 
+
+ align:start position:0%
+difficulty can exceed in weight and
+value all the remaining chapters of this
+
+ align:start position:0%
+value all the remaining chapters of this
+ 
+
+ align:start position:0%
+value all the remaining chapters of this
+thesis now Bernoulli was right on about
+
+ align:start position:0%
+thesis now Bernoulli was right on about
+ 
+
+ align:start position:0%
+thesis now Bernoulli was right on about
+the usefulness of this result at least
+
+ align:start position:0%
+the usefulness of this result at least
+ 
+
+ align:start position:0%
+the usefulness of this result at least
+in its quantitative form and at the time
+
+ align:start position:0%
+in its quantitative form and at the time
+ 
+
+ align:start position:0%
+in its quantitative form and at the time
+it was really pretty difficult for him
+
+ align:start position:0%
+it was really pretty difficult for him
+ 
+
+ align:start position:0%
+it was really pretty difficult for him
+it took him like 200 pages to complete
+
+ align:start position:0%
+it took him like 200 pages to complete
+ 
+
+ align:start position:0%
+it took him like 200 pages to complete
+his proof in ARS konjac tandy nowadays
+
+ align:start position:0%
+his proof in ARS konjac tandy nowadays
+ 
+
+ align:start position:0%
+his proof in ARS konjac tandy nowadays
+we are going to do it in about a lecture
+
+ align:start position:0%
+we are going to do it in about a lecture
+ 
+
+ align:start position:0%
+we are going to do it in about a lecture
+worth of material and you'll be seeing
+
+ align:start position:0%
+worth of material and you'll be seeing
+ 
+
+ align:start position:0%
+worth of material and you'll be seeing
+that in some subsequent video segments
+
+ align:start position:0%
+that in some subsequent video segments
+ 
+
+ align:start position:0%
+that in some subsequent video segments
+so that's what happens with 300 years
+
+ align:start position:0%
+so that's what happens with 300 years
+ 
+
+ align:start position:0%
+so that's what happens with 300 years
+two or three hundred and fifty years to
+
+ align:start position:0%
+two or three hundred and fifty years to
+ 
+
+ align:start position:0%
+two or three hundred and fifty years to
+tune up a result what took 200 pages
+
+ align:start position:0%
+tune up a result what took 200 pages
+ 
+
+ align:start position:0%
+tune up a result what took 200 pages
+then now takes 10 or less pages in fact
+
+ align:start position:0%
+then now takes 10 or less pages in fact
+ 
+
+ align:start position:0%
+then now takes 10 or less pages in fact
+if it was really concise it could be
+
+ align:start position:0%
+if it was really concise it could be
+ 
+
+ align:start position:0%
+if it was really concise it could be
+done in a few in three pages alright so
+
+ align:start position:0%
+done in a few in three pages alright so
+ 
+
+ align:start position:0%
+done in a few in three pages alright so
+again coming back to Bernoulli's
+
+ align:start position:0%
+again coming back to Bernoulli's
+ 
+
+ align:start position:0%
+again coming back to Bernoulli's
+question Bernoulli's question is what is
+
+ align:start position:0%
+question Bernoulli's question is what is
+ 
+
+ align:start position:0%
+question Bernoulli's question is what is
+the probability that the average that
+
+ align:start position:0%
+the probability that the average that
+ 
+
+ align:start position:0%
+the probability that the average that
+the distance between the average and the
+
+ align:start position:0%
+the distance between the average and the
+ 
+
+ align:start position:0%
+the distance between the average and the
+mean is less than or equal to Delta as
+
+ align:start position:0%
+mean is less than or equal to Delta as
+ 
+
+ align:start position:0%
+mean is less than or equal to Delta as
+you take more and more tries as n goes
+
+ align:start position:0%
+you take more and more tries as n goes
+ 
+
+ align:start position:0%
+you take more and more tries as n goes
+to infinity and Bernoulli's answer to
+
+ align:start position:0%
+to infinity and Bernoulli's answer to
+ 
+
+ align:start position:0%
+to infinity and Bernoulli's answer to
+the question is that the probability is
+
+ align:start position:0%
+the question is that the probability is
+ 
+
+ align:start position:0%
+the question is that the probability is
+1 that is if you want to be have a
+
+ align:start position:0%
+1 that is if you want to be have a
+ 
+
+ align:start position:0%
+1 that is if you want to be have a
+certain degree of certainty of being
+
+ align:start position:0%
+certain degree of certainty of being
+ 
+
+ align:start position:0%
+certain degree of certainty of being
+close to the mean within though if you
+
+ align:start position:0%
+close to the mean within though if you
+ 
+
+ align:start position:0%
+close to the mean within though if you
+take enough trials you can be as certain
+
+ align:start position:0%
+take enough trials you can be as certain
+ 
+
+ align:start position:0%
+take enough trials you can be as certain
+as you want that you'll be as close as
+
+ align:start position:0%
+as you want that you'll be as close as
+ 
+
+ align:start position:0%
+as you want that you'll be as close as
+you want and that is called the weak law
+
+ align:start position:0%
+you want and that is called the weak law
+ 
+
+ align:start position:0%
+you want and that is called the weak law
+of large numbers and it's one of the
+
+ align:start position:0%
+of large numbers and it's one of the
+ 
+
+ align:start position:0%
+of large numbers and it's one of the
+basic transcendent rules and theorems of
+
+ align:start position:0%
+basic transcendent rules and theorems of
+ 
+
+ align:start position:0%
+basic transcendent rules and theorems of
+probability theory it's usually stated
+
+ align:start position:0%
+probability theory it's usually stated
+ 
+
+ align:start position:0%
+probability theory it's usually stated
+in the other way as that the limit of
+
+ align:start position:0%
+in the other way as that the limit of
+ 
+
+ align:start position:0%
+in the other way as that the limit of
+the probability that the average is a
+
+ align:start position:0%
+the probability that the average is a
+ 
+
+ align:start position:0%
+the probability that the average is a
+distance away from the mean Delta is 0
+
+ align:start position:0%
+distance away from the mean Delta is 0
+ 
+
+ align:start position:0%
+distance away from the mean Delta is 0
+it's the probability that it's it's
+
+ align:start position:0%
+it's the probability that it's it's
+ 
+
+ align:start position:0%
+it's the probability that it's it's
+extremely unlikely it can be as unlikely
+
+ align:start position:0%
+extremely unlikely it can be as unlikely
+ 
+
+ align:start position:0%
+extremely unlikely it can be as unlikely
+as you want to make it that it's more
+
+ align:start position:0%
+as you want to make it that it's more
+ 
+
+ align:start position:0%
+as you want to make it that it's more
+than any given tolerance from the mean
+
+ align:start position:0%
+than any given tolerance from the mean
+ 
+
+ align:start position:0%
+than any given tolerance from the mean
+as if you take a large enough number of
+
+ align:start position:0%
+as if you take a large enough number of
+ 
+
+ align:start position:0%
+as if you take a large enough number of
+trials now in this form it's not yet
+
+ align:start position:0%
+trials now in this form it's not yet
+ 
+
+ align:start position:0%
+trials now in this form it's not yet
+really use
+
+ align:start position:0%
+really use
+ 
+
+ align:start position:0%
+really use
+this is a romantic qualitative limit
+
+ align:start position:0%
+this is a romantic qualitative limit
+ 
+
+ align:start position:0%
+this is a romantic qualitative limit
+limiting result and to really use it you
+
+ align:start position:0%
+limiting result and to really use it you
+ 
+
+ align:start position:0%
+limiting result and to really use it you
+need to know something rather about the
+
+ align:start position:0%
+need to know something rather about the
+ 
+
+ align:start position:0%
+need to know something rather about the
+rate at which it approaches the limit
+
+ align:start position:0%
+rate at which it approaches the limit
+ 
+
+ align:start position:0%
+rate at which it approaches the limit
+which is what we're going to be seeing
+
+ align:start position:0%
+which is what we're going to be seeing
+ 
+
+ align:start position:0%
+which is what we're going to be seeing
+in a subsequent video and in fact the
+
+ align:start position:0%
+in a subsequent video and in fact the
+ 
+
+ align:start position:0%
+in a subsequent video and in fact the
+proof of this is going to follow easily
+
+ align:start position:0%
+proof of this is going to follow easily
+ 
+
+ align:start position:0%
+proof of this is going to follow easily
+from the chebyshev inequality bound and
+
+ align:start position:0%
+from the chebyshev inequality bound and
+ 
+
+ align:start position:0%
+from the chebyshev inequality bound and
+variance properties when we go about
+
+ align:start position:0%
+variance properties when we go about
+ 
+
+ align:start position:0%
+variance properties when we go about
+trying to get the quantitative version
+
+ align:start position:0%
+trying to get the quantitative version
+ 
+
+ align:start position:0%
+trying to get the quantitative version
+that explains the rate at which the
+
+ align:start position:0%
+that explains the rate at which the
+ 
+
+ align:start position:0%
+that explains the rate at which the
+limit is approached
\ No newline at end of file
diff --git a/0LqS5QtpSVE.txt b/0LqS5QtpSVE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5b755a08ccd82c8e25ce70b8c66724c8af86ff26
--- /dev/null
+++ b/0LqS5QtpSVE.txt
@@ -0,0 +1,2155 @@
+align:start position:0%
+ 
+now let's turn our attention to control
+
+ align:start position:0%
+now let's turn our attention to control
+ 
+
+ align:start position:0%
+now let's turn our attention to control
+hazards illustrated by the code fragment
+
+ align:start position:0%
+hazards illustrated by the code fragment
+ 
+
+ align:start position:0%
+hazards illustrated by the code fragment
+shown here which instruction should be
+
+ align:start position:0%
+shown here which instruction should be
+ 
+
+ align:start position:0%
+shown here which instruction should be
+executed after the B&E if the value in
+
+ align:start position:0%
+executed after the B&E if the value in
+ 
+
+ align:start position:0%
+executed after the B&E if the value in
+r3 is nonzero and it C should be
+
+ align:start position:0%
+r3 is nonzero and it C should be
+ 
+
+ align:start position:0%
+r3 is nonzero and it C should be
+executed if the value in r3 is 0 the
+
+ align:start position:0%
+executed if the value in r3 is 0 the
+ 
+
+ align:start position:0%
+executed if the value in r3 is 0 the
+next instruction should be sub if the
+
+ align:start position:0%
+next instruction should be sub if the
+ 
+
+ align:start position:0%
+next instruction should be sub if the
+current instruction is an explicit
+
+ align:start position:0%
+current instruction is an explicit
+ 
+
+ align:start position:0%
+current instruction is an explicit
+transfer of control in other words jumps
+
+ align:start position:0%
+transfer of control in other words jumps
+ 
+
+ align:start position:0%
+transfer of control in other words jumps
+or branches the choice of the next
+
+ align:start position:0%
+or branches the choice of the next
+ 
+
+ align:start position:0%
+or branches the choice of the next
+instruction depends on the execution of
+
+ align:start position:0%
+instruction depends on the execution of
+ 
+
+ align:start position:0%
+instruction depends on the execution of
+the current instruction what are the
+
+ align:start position:0%
+the current instruction what are the
+ 
+
+ align:start position:0%
+the current instruction what are the
+implications of this dependency on our
+
+ align:start position:0%
+implications of this dependency on our
+ 
+
+ align:start position:0%
+implications of this dependency on our
+execution pipeline how does the
+
+ align:start position:0%
+execution pipeline how does the
+ 
+
+ align:start position:0%
+execution pipeline how does the
+unpiloted determine the next instruction
+
+ align:start position:0%
+unpiloted determine the next instruction
+ 
+
+ align:start position:0%
+unpiloted determine the next instruction
+for branches BEQ or B&E the value to be
+
+ align:start position:0%
+for branches BEQ or B&E the value to be
+ 
+
+ align:start position:0%
+for branches BEQ or B&E the value to be
+loaded into the program counter depends
+
+ align:start position:0%
+loaded into the program counter depends
+ 
+
+ align:start position:0%
+loaded into the program counter depends
+on 1 the opcode in other words whether
+
+ align:start position:0%
+on 1 the opcode in other words whether
+ 
+
+ align:start position:0%
+on 1 the opcode in other words whether
+the instruction is a BEQ or be any to
+
+ align:start position:0%
+the instruction is a BEQ or be any to
+ 
+
+ align:start position:0%
+the instruction is a BEQ or be any to
+the current value of the program counter
+
+ align:start position:0%
+the current value of the program counter
+ 
+
+ align:start position:0%
+the current value of the program counter
+since that's used in the offset
+
+ align:start position:0%
+since that's used in the offset
+ 
+
+ align:start position:0%
+since that's used in the offset
+calculation and 3 the values stored in
+
+ align:start position:0%
+calculation and 3 the values stored in
+ 
+
+ align:start position:0%
+calculation and 3 the values stored in
+the register specified by the RA field
+
+ align:start position:0%
+the register specified by the RA field
+ 
+
+ align:start position:0%
+the register specified by the RA field
+of the instruction since that's the
+
+ align:start position:0%
+of the instruction since that's the
+ 
+
+ align:start position:0%
+of the instruction since that's the
+value tested by the branch for jump
+
+ align:start position:0%
+value tested by the branch for jump
+ 
+
+ align:start position:0%
+value tested by the branch for jump
+instructions the next value of the
+
+ align:start position:0%
+instructions the next value of the
+ 
+
+ align:start position:0%
+instructions the next value of the
+program counter depends once again on
+
+ align:start position:0%
+program counter depends once again on
+ 
+
+ align:start position:0%
+program counter depends once again on
+the opcode field and the value of the RA
+
+ align:start position:0%
+the opcode field and the value of the RA
+ 
+
+ align:start position:0%
+the opcode field and the value of the RA
+register for all other instructions the
+
+ align:start position:0%
+register for all other instructions the
+ 
+
+ align:start position:0%
+register for all other instructions the
+next PC value depends only on the opcode
+
+ align:start position:0%
+next PC value depends only on the opcode
+ 
+
+ align:start position:0%
+next PC value depends only on the opcode
+of the instruction and the value PC plus
+
+ align:start position:0%
+of the instruction and the value PC plus
+ 
+
+ align:start position:0%
+of the instruction and the value PC plus
+4 exceptions also change the program
+
+ align:start position:0%
+4 exceptions also change the program
+ 
+
+ align:start position:0%
+4 exceptions also change the program
+counter we'll deal with them later in
+
+ align:start position:0%
+counter we'll deal with them later in
+ 
+
+ align:start position:0%
+counter we'll deal with them later in
+the lecture the control hazard is
+
+ align:start position:0%
+the lecture the control hazard is
+ 
+
+ align:start position:0%
+the lecture the control hazard is
+triggered by jump and branches since
+
+ align:start position:0%
+triggered by jump and branches since
+ 
+
+ align:start position:0%
+triggered by jump and branches since
+their execution depends on the value in
+
+ align:start position:0%
+their execution depends on the value in
+ 
+
+ align:start position:0%
+their execution depends on the value in
+the RA register in other words they need
+
+ align:start position:0%
+the RA register in other words they need
+ 
+
+ align:start position:0%
+the RA register in other words they need
+to read from the register file which
+
+ align:start position:0%
+to read from the register file which
+ 
+
+ align:start position:0%
+to read from the register file which
+happens in the RF stage our bypass
+
+ align:start position:0%
+happens in the RF stage our bypass
+ 
+
+ align:start position:0%
+happens in the RF stage our bypass
+mechanisms ensure that we'll use the
+
+ align:start position:0%
+mechanisms ensure that we'll use the
+ 
+
+ align:start position:0%
+mechanisms ensure that we'll use the
+correct value for the RA register even
+
+ align:start position:0%
+correct value for the RA register even
+ 
+
+ align:start position:0%
+correct value for the RA register even
+if it's not yet written into the
+
+ align:start position:0%
+if it's not yet written into the
+ 
+
+ align:start position:0%
+if it's not yet written into the
+register file what we're concerned about
+
+ align:start position:0%
+register file what we're concerned about
+ 
+
+ align:start position:0%
+register file what we're concerned about
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is that the address of the instruction
+
+ align:start position:0%
+is that the address of the instruction
+ 
+
+ align:start position:0%
+is that the address of the instruction
+following the jumper branch will be
+
+ align:start position:0%
+following the jumper branch will be
+ 
+
+ align:start position:0%
+following the jumper branch will be
+loaded into the program counter at the
+
+ align:start position:0%
+loaded into the program counter at the
+ 
+
+ align:start position:0%
+loaded into the program counter at the
+end of the cycle when the jump or branch
+
+ align:start position:0%
+end of the cycle when the jump or branch
+ 
+
+ align:start position:0%
+end of the cycle when the jump or branch
+is in the RF stage but what should the I
+
+ align:start position:0%
+is in the RF stage but what should the I
+ 
+
+ align:start position:0%
+is in the RF stage but what should the I
+have stage be doing while all this is
+
+ align:start position:0%
+have stage be doing while all this is
+ 
+
+ align:start position:0%
+have stage be doing while all this is
+going on in the RF stage the answer is
+
+ align:start position:0%
+going on in the RF stage the answer is
+ 
+
+ align:start position:0%
+going on in the RF stage the answer is
+that in the case of jumps
+
+ align:start position:0%
+that in the case of jumps
+ 
+
+ align:start position:0%
+that in the case of jumps
+taken branches we don't know what the
+
+ align:start position:0%
+taken branches we don't know what the
+ 
+
+ align:start position:0%
+taken branches we don't know what the
+i/o state should be doing until those
+
+ align:start position:0%
+i/o state should be doing until those
+ 
+
+ align:start position:0%
+i/o state should be doing until those
+instructions are able to access the
+
+ align:start position:0%
+instructions are able to access the
+ 
+
+ align:start position:0%
+instructions are able to access the
+value of the RA register in the RF stage
+
+ align:start position:0%
+value of the RA register in the RF stage
+ 
+
+ align:start position:0%
+value of the RA register in the RF stage
+one solution is to stall the if' stage
+
+ align:start position:0%
+one solution is to stall the if' stage
+ 
+
+ align:start position:0%
+one solution is to stall the if' stage
+until the RF stage can compute the
+
+ align:start position:0%
+until the RF stage can compute the
+ 
+
+ align:start position:0%
+until the RF stage can compute the
+necessary result this was the first of
+
+ align:start position:0%
+necessary result this was the first of
+ 
+
+ align:start position:0%
+necessary result this was the first of
+our general strategies for dealing with
+
+ align:start position:0%
+our general strategies for dealing with
+ 
+
+ align:start position:0%
+our general strategies for dealing with
+hazards how would this work
+
+ align:start position:0%
+hazards how would this work
+ 
+
+ align:start position:0%
+hazards how would this work
+if the opcode and the RF stage is jump
+
+ align:start position:0%
+if the opcode and the RF stage is jump
+ 
+
+ align:start position:0%
+if the opcode and the RF stage is jump
+the EQ or be any stall the if' stage for
+
+ align:start position:0%
+the EQ or be any stall the if' stage for
+ 
+
+ align:start position:0%
+the EQ or be any stall the if' stage for
+one cycle in the example code shown here
+
+ align:start position:0%
+one cycle in the example code shown here
+ 
+
+ align:start position:0%
+one cycle in the example code shown here
+assume that the value in r3 is non zero
+
+ align:start position:0%
+assume that the value in r3 is non zero
+ 
+
+ align:start position:0%
+assume that the value in r3 is non zero
+when the BNE is executed in other words
+
+ align:start position:0%
+when the BNE is executed in other words
+ 
+
+ align:start position:0%
+when the BNE is executed in other words
+that the instruction following the B&E
+
+ align:start position:0%
+that the instruction following the B&E
+ 
+
+ align:start position:0%
+that the instruction following the B&E
+should be the ad c-- at the top of the
+
+ align:start position:0%
+should be the ad c-- at the top of the
+ 
+
+ align:start position:0%
+should be the ad c-- at the top of the
+loop the pipeline diagram shows the
+
+ align:start position:0%
+loop the pipeline diagram shows the
+ 
+
+ align:start position:0%
+loop the pipeline diagram shows the
+effect we're trying to achieve a no op
+
+ align:start position:0%
+effect we're trying to achieve a no op
+ 
+
+ align:start position:0%
+effect we're trying to achieve a no op
+is inserted into the pipeline and cycles
+
+ align:start position:0%
+is inserted into the pipeline and cycles
+ 
+
+ align:start position:0%
+is inserted into the pipeline and cycles
+four and eight then an execution resumes
+
+ align:start position:0%
+four and eight then an execution resumes
+ 
+
+ align:start position:0%
+four and eight then an execution resumes
+in the next cycle after the RF stage
+
+ align:start position:0%
+in the next cycle after the RF stage
+ 
+
+ align:start position:0%
+in the next cycle after the RF stage
+determines what instruction comes next
+
+ align:start position:0%
+determines what instruction comes next
+ 
+
+ align:start position:0%
+determines what instruction comes next
+note by the way that we're relying on
+
+ align:start position:0%
+note by the way that we're relying on
+ 
+
+ align:start position:0%
+note by the way that we're relying on
+our bypass logic to deliver the correct
+
+ align:start position:0%
+our bypass logic to deliver the correct
+ 
+
+ align:start position:0%
+our bypass logic to deliver the correct
+value for r3 from the mem stage since
+
+ align:start position:0%
+value for r3 from the mem stage since
+ 
+
+ align:start position:0%
+value for r3 from the mem stage since
+the adds the instruction that wrote into
+
+ align:start position:0%
+the adds the instruction that wrote into
+ 
+
+ align:start position:0%
+the adds the instruction that wrote into
+r3 is still in the pipeline in other
+
+ align:start position:0%
+r3 is still in the pipeline in other
+ 
+
+ align:start position:0%
+r3 is still in the pipeline in other
+words we have a data hazard to deal with
+
+ align:start position:0%
+words we have a data hazard to deal with
+ 
+
+ align:start position:0%
+words we have a data hazard to deal with
+- looking at say the right back stage in
+
+ align:start position:0%
+- looking at say the right back stage in
+ 
+
+ align:start position:0%
+- looking at say the right back stage in
+the pipeline diagram we see that it
+
+ align:start position:0%
+the pipeline diagram we see that it
+ 
+
+ align:start position:0%
+the pipeline diagram we see that it
+takes four cycles to execute one
+
+ align:start position:0%
+takes four cycles to execute one
+ 
+
+ align:start position:0%
+takes four cycles to execute one
+iteration of our three instruction loop
+
+ align:start position:0%
+iteration of our three instruction loop
+ 
+
+ align:start position:0%
+iteration of our three instruction loop
+so the effective CPI is 4/3 an increase
+
+ align:start position:0%
+so the effective CPI is 4/3 an increase
+ 
+
+ align:start position:0%
+so the effective CPI is 4/3 an increase
+of 33 percent using stall to deal with
+
+ align:start position:0%
+of 33 percent using stall to deal with
+ 
+
+ align:start position:0%
+of 33 percent using stall to deal with
+control hazards has had an impact on the
+
+ align:start position:0%
+control hazards has had an impact on the
+ 
+
+ align:start position:0%
+control hazards has had an impact on the
+instruction throughput of our execution
+
+ align:start position:0%
+instruction throughput of our execution
+ 
+
+ align:start position:0%
+instruction throughput of our execution
+pipeline we've already seen the logic
+
+ align:start position:0%
+pipeline we've already seen the logic
+ 
+
+ align:start position:0%
+pipeline we've already seen the logic
+needed to introduce no ops into the
+
+ align:start position:0%
+needed to introduce no ops into the
+ 
+
+ align:start position:0%
+needed to introduce no ops into the
+pipeline in this case we add a MUX to
+
+ align:start position:0%
+pipeline in this case we add a MUX to
+ 
+
+ align:start position:0%
+pipeline in this case we add a MUX to
+the instruction path in the if' stage
+
+ align:start position:0%
+the instruction path in the if' stage
+ 
+
+ align:start position:0%
+the instruction path in the if' stage
+controlled by the IR source if' signal
+
+ align:start position:0%
+controlled by the IR source if' signal
+ 
+
+ align:start position:0%
+controlled by the IR source if' signal
+we use the superscript on the control
+
+ align:start position:0%
+we use the superscript on the control
+ 
+
+ align:start position:0%
+we use the superscript on the control
+signals to indicate which pipeline state
+
+ align:start position:0%
+signals to indicate which pipeline state
+ 
+
+ align:start position:0%
+signals to indicate which pipeline state
+holds the logic if they control if the
+
+ align:start position:0%
+holds the logic if they control if the
+ 
+
+ align:start position:0%
+holds the logic if they control if the
+opcode in the RF stage has jumped BEQ or
+
+ align:start position:0%
+opcode in the RF stage has jumped BEQ or
+ 
+
+ align:start position:0%
+opcode in the RF stage has jumped BEQ or
+B&E we set IR source if' to one which
+
+ align:start position:0%
+B&E we set IR source if' to one which
+ 
+
+ align:start position:0%
+B&E we set IR source if' to one which
+causes a no op to replace the
+
+ align:start position:0%
+causes a no op to replace the
+ 
+
+ align:start position:0%
+causes a no op to replace the
+instruction that was being read from
+
+ align:start position:0%
+instruction that was being read from
+ 
+
+ align:start position:0%
+instruction that was being read from
+main memory and of course we'll be
+
+ align:start position:0%
+main memory and of course we'll be
+ 
+
+ align:start position:0%
+main memory and of course we'll be
+setting the PC
+
+ align:start position:0%
+setting the PC
+ 
+
+ align:start position:0%
+setting the PC
+roll signals to select the correct next
+
+ align:start position:0%
+roll signals to select the correct next
+ 
+
+ align:start position:0%
+roll signals to select the correct next
+PC value so the i/o stage will fetch the
+
+ align:start position:0%
+PC value so the i/o stage will fetch the
+ 
+
+ align:start position:0%
+PC value so the i/o stage will fetch the
+desired follow-on instruction in the
+
+ align:start position:0%
+desired follow-on instruction in the
+ 
+
+ align:start position:0%
+desired follow-on instruction in the
+next cycle if we replace an instruction
+
+ align:start position:0%
+next cycle if we replace an instruction
+ 
+
+ align:start position:0%
+next cycle if we replace an instruction
+with a no op we say we annulled the
+
+ align:start position:0%
+with a no op we say we annulled the
+ 
+
+ align:start position:0%
+with a no op we say we annulled the
+instruction the branch instructions in
+
+ align:start position:0%
+instruction the branch instructions in
+ 
+
+ align:start position:0%
+instruction the branch instructions in
+the beta is a make their branch decision
+
+ align:start position:0%
+the beta is a make their branch decision
+ 
+
+ align:start position:0%
+the beta is a make their branch decision
+in the RF stage since they only need the
+
+ align:start position:0%
+in the RF stage since they only need the
+ 
+
+ align:start position:0%
+in the RF stage since they only need the
+value in register RA but suppose the ISA
+
+ align:start position:0%
+value in register RA but suppose the ISA
+ 
+
+ align:start position:0%
+value in register RA but suppose the ISA
+had a branch where the branch decision
+
+ align:start position:0%
+had a branch where the branch decision
+ 
+
+ align:start position:0%
+had a branch where the branch decision
+was made in the ALU stage when the
+
+ align:start position:0%
+was made in the ALU stage when the
+ 
+
+ align:start position:0%
+was made in the ALU stage when the
+branch decision is made in the ALU stage
+
+ align:start position:0%
+branch decision is made in the ALU stage
+ 
+
+ align:start position:0%
+branch decision is made in the ALU stage
+we need to introduce to no ops into the
+
+ align:start position:0%
+we need to introduce to no ops into the
+ 
+
+ align:start position:0%
+we need to introduce to no ops into the
+pipeline replacing the now unwanted
+
+ align:start position:0%
+pipeline replacing the now unwanted
+ 
+
+ align:start position:0%
+pipeline replacing the now unwanted
+instructions in the RF and I of stages
+
+ align:start position:0%
+instructions in the RF and I of stages
+ 
+
+ align:start position:0%
+instructions in the RF and I of stages
+this would increase the effective CPI
+
+ align:start position:0%
+this would increase the effective CPI
+ 
+
+ align:start position:0%
+this would increase the effective CPI
+even further but the trade-off is that
+
+ align:start position:0%
+even further but the trade-off is that
+ 
+
+ align:start position:0%
+even further but the trade-off is that
+the more complex branches may reduce the
+
+ align:start position:0%
+the more complex branches may reduce the
+ 
+
+ align:start position:0%
+the more complex branches may reduce the
+number of instructions in the program if
+
+ align:start position:0%
+number of instructions in the program if
+ 
+
+ align:start position:0%
+number of instructions in the program if
+we annul instructions in all the earlier
+
+ align:start position:0%
+we annul instructions in all the earlier
+ 
+
+ align:start position:0%
+we annul instructions in all the earlier
+pipeline stages this is called flushing
+
+ align:start position:0%
+pipeline stages this is called flushing
+ 
+
+ align:start position:0%
+pipeline stages this is called flushing
+the pipeline since flushing the pipeline
+
+ align:start position:0%
+the pipeline since flushing the pipeline
+ 
+
+ align:start position:0%
+the pipeline since flushing the pipeline
+has a big impact on the effective CPI we
+
+ align:start position:0%
+has a big impact on the effective CPI we
+ 
+
+ align:start position:0%
+has a big impact on the effective CPI we
+do it when it's the only way to ensure
+
+ align:start position:0%
+do it when it's the only way to ensure
+ 
+
+ align:start position:0%
+do it when it's the only way to ensure
+the correct behavior of the execution
+
+ align:start position:0%
+the correct behavior of the execution
+ 
+
+ align:start position:0%
+the correct behavior of the execution
+pipeline we can be smarter about when we
+
+ align:start position:0%
+pipeline we can be smarter about when we
+ 
+
+ align:start position:0%
+pipeline we can be smarter about when we
+choose to flush the pipeline when
+
+ align:start position:0%
+choose to flush the pipeline when
+ 
+
+ align:start position:0%
+choose to flush the pipeline when
+executing branches the branch is
+
+ align:start position:0%
+executing branches the branch is
+ 
+
+ align:start position:0%
+executing branches the branch is
+not-taken it turns out that the pipeline
+
+ align:start position:0%
+not-taken it turns out that the pipeline
+ 
+
+ align:start position:0%
+not-taken it turns out that the pipeline
+has been doing the right thing by
+
+ align:start position:0%
+has been doing the right thing by
+ 
+
+ align:start position:0%
+has been doing the right thing by
+fetching the instruction following the
+
+ align:start position:0%
+fetching the instruction following the
+ 
+
+ align:start position:0%
+fetching the instruction following the
+branch starting execution of an
+
+ align:start position:0%
+branch starting execution of an
+ 
+
+ align:start position:0%
+branch starting execution of an
+instruction even when we're unsure
+
+ align:start position:0%
+instruction even when we're unsure
+ 
+
+ align:start position:0%
+instruction even when we're unsure
+whether we really want it executed is
+
+ align:start position:0%
+whether we really want it executed is
+ 
+
+ align:start position:0%
+whether we really want it executed is
+called speculation speculation is okay
+
+ align:start position:0%
+called speculation speculation is okay
+ 
+
+ align:start position:0%
+called speculation speculation is okay
+if we're able to annul the instruction
+
+ align:start position:0%
+if we're able to annul the instruction
+ 
+
+ align:start position:0%
+if we're able to annul the instruction
+before it has an effect on the CPU State
+
+ align:start position:0%
+before it has an effect on the CPU State
+ 
+
+ align:start position:0%
+before it has an effect on the CPU State
+for example by writing into the register
+
+ align:start position:0%
+for example by writing into the register
+ 
+
+ align:start position:0%
+for example by writing into the register
+file or main memory since these state
+
+ align:start position:0%
+file or main memory since these state
+ 
+
+ align:start position:0%
+file or main memory since these state
+changes called side-effects happen in
+
+ align:start position:0%
+changes called side-effects happen in
+ 
+
+ align:start position:0%
+changes called side-effects happen in
+the later pipeline stages an instruction
+
+ align:start position:0%
+the later pipeline stages an instruction
+ 
+
+ align:start position:0%
+the later pipeline stages an instruction
+can progress through the if' RF and ALU
+
+ align:start position:0%
+can progress through the if' RF and ALU
+ 
+
+ align:start position:0%
+can progress through the if' RF and ALU
+stages before we have to make a final
+
+ align:start position:0%
+stages before we have to make a final
+ 
+
+ align:start position:0%
+stages before we have to make a final
+decision about whether it should be
+
+ align:start position:0%
+decision about whether it should be
+ 
+
+ align:start position:0%
+decision about whether it should be
+annulled
+
+ align:start position:0%
+annulled
+ 
+
+ align:start position:0%
+annulled
+how does speculation help with control
+
+ align:start position:0%
+how does speculation help with control
+ 
+
+ align:start position:0%
+how does speculation help with control
+hazards guessing that the next value of
+
+ align:start position:0%
+hazards guessing that the next value of
+ 
+
+ align:start position:0%
+hazards guessing that the next value of
+the program counter is PC plus 4 is
+
+ align:start position:0%
+the program counter is PC plus 4 is
+ 
+
+ align:start position:0%
+the program counter is PC plus 4 is
+correct for all but jumps and taken
+
+ align:start position:0%
+correct for all but jumps and taken
+ 
+
+ align:start position:0%
+correct for all but jumps and taken
+branches here's our example again but
+
+ align:start position:0%
+branches here's our example again but
+ 
+
+ align:start position:0%
+branches here's our example again but
+this time let's assume that the BND is
+
+ align:start position:0%
+this time let's assume that the BND is
+ 
+
+ align:start position:0%
+this time let's assume that the BND is
+not taken in other words that the value
+
+ align:start position:0%
+not taken in other words that the value
+ 
+
+ align:start position:0%
+not taken in other words that the value
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+three is zero the sub instruction enters
+
+ align:start position:0%
+three is zero the sub instruction enters
+ 
+
+ align:start position:0%
+three is zero the sub instruction enters
+the pipeline at the start of cycle four
+
+ align:start position:0%
+the pipeline at the start of cycle four
+ 
+
+ align:start position:0%
+the pipeline at the start of cycle four
+at the end of cycle four we know whether
+
+ align:start position:0%
+at the end of cycle four we know whether
+ 
+
+ align:start position:0%
+at the end of cycle four we know whether
+or not doin all the sub if the branch is
+
+ align:start position:0%
+or not doin all the sub if the branch is
+ 
+
+ align:start position:0%
+or not doin all the sub if the branch is
+not-taken
+
+ align:start position:0%
+not-taken
+ 
+
+ align:start position:0%
+not-taken
+we want to execute the sub instruction
+
+ align:start position:0%
+we want to execute the sub instruction
+ 
+
+ align:start position:0%
+we want to execute the sub instruction
+so we just let it continue down the
+
+ align:start position:0%
+so we just let it continue down the
+ 
+
+ align:start position:0%
+so we just let it continue down the
+pipeline in other words instead of
+
+ align:start position:0%
+pipeline in other words instead of
+ 
+
+ align:start position:0%
+pipeline in other words instead of
+always annulling the instruction
+
+ align:start position:0%
+always annulling the instruction
+ 
+
+ align:start position:0%
+always annulling the instruction
+following the branch we only annul it if
+
+ align:start position:0%
+following the branch we only annul it if
+ 
+
+ align:start position:0%
+following the branch we only annul it if
+the branch was taken if the branch is
+
+ align:start position:0%
+the branch was taken if the branch is
+ 
+
+ align:start position:0%
+the branch was taken if the branch is
+not-taken
+
+ align:start position:0%
+not-taken
+ 
+
+ align:start position:0%
+not-taken
+the pipeline is speculated correctly and
+
+ align:start position:0%
+the pipeline is speculated correctly and
+ 
+
+ align:start position:0%
+the pipeline is speculated correctly and
+no instructions need to be annulled
+
+ align:start position:0%
+no instructions need to be annulled
+ 
+
+ align:start position:0%
+no instructions need to be annulled
+however if the BND is taken the sub is
+
+ align:start position:0%
+however if the BND is taken the sub is
+ 
+
+ align:start position:0%
+however if the BND is taken the sub is
+annulled at the end of cycle four and a
+
+ align:start position:0%
+annulled at the end of cycle four and a
+ 
+
+ align:start position:0%
+annulled at the end of cycle four and a
+no op is executed in cycle five so we
+
+ align:start position:0%
+no op is executed in cycle five so we
+ 
+
+ align:start position:0%
+no op is executed in cycle five so we
+only introduce a bubble in the pipeline
+
+ align:start position:0%
+only introduce a bubble in the pipeline
+ 
+
+ align:start position:0%
+only introduce a bubble in the pipeline
+when there's a taken branch fewer
+
+ align:start position:0%
+when there's a taken branch fewer
+ 
+
+ align:start position:0%
+when there's a taken branch fewer
+bubbles will decrease the impact of
+
+ align:start position:0%
+bubbles will decrease the impact of
+ 
+
+ align:start position:0%
+bubbles will decrease the impact of
+annulment on the effective CPI we'll be
+
+ align:start position:0%
+annulment on the effective CPI we'll be
+ 
+
+ align:start position:0%
+annulment on the effective CPI we'll be
+using the same data path circuitry as
+
+ align:start position:0%
+using the same data path circuitry as
+ 
+
+ align:start position:0%
+using the same data path circuitry as
+before we'll just be a bit more clever
+
+ align:start position:0%
+before we'll just be a bit more clever
+ 
+
+ align:start position:0%
+before we'll just be a bit more clever
+about when the value of the IRS or SIF
+
+ align:start position:0%
+about when the value of the IRS or SIF
+ 
+
+ align:start position:0%
+about when the value of the IRS or SIF
+control signal is set to one instead of
+
+ align:start position:0%
+control signal is set to one instead of
+ 
+
+ align:start position:0%
+control signal is set to one instead of
+setting it to one for all branches we
+
+ align:start position:0%
+setting it to one for all branches we
+ 
+
+ align:start position:0%
+setting it to one for all branches we
+only set it to one when the branch is
+
+ align:start position:0%
+only set it to one when the branch is
+ 
+
+ align:start position:0%
+only set it to one when the branch is
+taken our naive strategy of always
+
+ align:start position:0%
+taken our naive strategy of always
+ 
+
+ align:start position:0%
+taken our naive strategy of always
+speculating that the next instruction
+
+ align:start position:0%
+speculating that the next instruction
+ 
+
+ align:start position:0%
+speculating that the next instruction
+comes from PC plus four is wrong for
+
+ align:start position:0%
+comes from PC plus four is wrong for
+ 
+
+ align:start position:0%
+comes from PC plus four is wrong for
+jumps and taken branches looking at
+
+ align:start position:0%
+jumps and taken branches looking at
+ 
+
+ align:start position:0%
+jumps and taken branches looking at
+simulated execution traces will see that
+
+ align:start position:0%
+simulated execution traces will see that
+ 
+
+ align:start position:0%
+simulated execution traces will see that
+this error in speculation leads to about
+
+ align:start position:0%
+this error in speculation leads to about
+ 
+
+ align:start position:0%
+this error in speculation leads to about
+ten percent higher effective CPI can we
+
+ align:start position:0%
+ten percent higher effective CPI can we
+ 
+
+ align:start position:0%
+ten percent higher effective CPI can we
+do better this is an important question
+
+ align:start position:0%
+do better this is an important question
+ 
+
+ align:start position:0%
+do better this is an important question
+for CPUs with deep pipelines for example
+
+ align:start position:0%
+for CPUs with deep pipelines for example
+ 
+
+ align:start position:0%
+for CPUs with deep pipelines for example
+Intel's Nehalem processors from 2009
+
+ align:start position:0%
+Intel's Nehalem processors from 2009
+ 
+
+ align:start position:0%
+Intel's Nehalem processors from 2009
+resolves the more complex x86 branch
+
+ align:start position:0%
+resolves the more complex x86 branch
+ 
+
+ align:start position:0%
+resolves the more complex x86 branch
+instructions quite late in the pipeline
+
+ align:start position:0%
+instructions quite late in the pipeline
+ 
+
+ align:start position:0%
+instructions quite late in the pipeline
+since Nehalem is capable of executing
+
+ align:start position:0%
+since Nehalem is capable of executing
+ 
+
+ align:start position:0%
+since Nehalem is capable of executing
+multiple instruction C cycle flushing
+
+ align:start position:0%
+multiple instruction C cycle flushing
+ 
+
+ align:start position:0%
+multiple instruction C cycle flushing
+the pipeline and Nehalem actually
+
+ align:start position:0%
+the pipeline and Nehalem actually
+ 
+
+ align:start position:0%
+the pipeline and Nehalem actually
+involves the execution of many
+
+ align:start position:0%
+involves the execution of many
+ 
+
+ align:start position:0%
+involves the execution of many
+instructions resulting in a considerable
+
+ align:start position:0%
+instructions resulting in a considerable
+ 
+
+ align:start position:0%
+instructions resulting in a considerable
+hit on the CPI like many modern
+
+ align:start position:0%
+hit on the CPI like many modern
+ 
+
+ align:start position:0%
+hit on the CPI like many modern
+processor implementations Nehalem has a
+
+ align:start position:0%
+processor implementations Nehalem has a
+ 
+
+ align:start position:0%
+processor implementations Nehalem has a
+much more sophisticated speculation
+
+ align:start position:0%
+much more sophisticated speculation
+ 
+
+ align:start position:0%
+much more sophisticated speculation
+mechanism rather than always guessing
+
+ align:start position:0%
+mechanism rather than always guessing
+ 
+
+ align:start position:0%
+mechanism rather than always guessing
+the next instruction is at PC plus 4 it
+
+ align:start position:0%
+the next instruction is at PC plus 4 it
+ 
+
+ align:start position:0%
+the next instruction is at PC plus 4 it
+only does that for non branch
+
+ align:start position:0%
+only does that for non branch
+ 
+
+ align:start position:0%
+only does that for non branch
+instructions for branches it predicts
+
+ align:start position:0%
+instructions for branches it predicts
+ 
+
+ align:start position:0%
+instructions for branches it predicts
+the behavior of each individual branch
+
+ align:start position:0%
+the behavior of each individual branch
+ 
+
+ align:start position:0%
+the behavior of each individual branch
+based on what the branch
+
+ align:start position:0%
+based on what the branch
+ 
+
+ align:start position:0%
+based on what the branch
+did last time it was executed and some
+
+ align:start position:0%
+did last time it was executed and some
+ 
+
+ align:start position:0%
+did last time it was executed and some
+knowledge of how the branch is being
+
+ align:start position:0%
+knowledge of how the branch is being
+ 
+
+ align:start position:0%
+knowledge of how the branch is being
+used for example backwards branches at
+
+ align:start position:0%
+used for example backwards branches at
+ 
+
+ align:start position:0%
+used for example backwards branches at
+the end of loops which are taken for all
+
+ align:start position:0%
+the end of loops which are taken for all
+ 
+
+ align:start position:0%
+the end of loops which are taken for all
+but the final iteration of the loop can
+
+ align:start position:0%
+but the final iteration of the loop can
+ 
+
+ align:start position:0%
+but the final iteration of the loop can
+be identified by their negative branch
+
+ align:start position:0%
+be identified by their negative branch
+ 
+
+ align:start position:0%
+be identified by their negative branch
+offset values Nehalem can even determine
+
+ align:start position:0%
+offset values Nehalem can even determine
+ 
+
+ align:start position:0%
+offset values Nehalem can even determine
+if there's a correlation between branch
+
+ align:start position:0%
+if there's a correlation between branch
+ 
+
+ align:start position:0%
+if there's a correlation between branch
+instructions using the results of an
+
+ align:start position:0%
+instructions using the results of an
+ 
+
+ align:start position:0%
+instructions using the results of an
+another earlier branch to speculate on
+
+ align:start position:0%
+another earlier branch to speculate on
+ 
+
+ align:start position:0%
+another earlier branch to speculate on
+the branch decision of the current
+
+ align:start position:0%
+the branch decision of the current
+ 
+
+ align:start position:0%
+the branch decision of the current
+branch with these sophisticated
+
+ align:start position:0%
+branch with these sophisticated
+ 
+
+ align:start position:0%
+branch with these sophisticated
+strategies Nehalem speculation is
+
+ align:start position:0%
+strategies Nehalem speculation is
+ 
+
+ align:start position:0%
+strategies Nehalem speculation is
+correct 95 to 99 percent of the time
+
+ align:start position:0%
+correct 95 to 99 percent of the time
+ 
+
+ align:start position:0%
+correct 95 to 99 percent of the time
+greatly reducing the impact of branches
+
+ align:start position:0%
+greatly reducing the impact of branches
+ 
+
+ align:start position:0%
+greatly reducing the impact of branches
+on the effective CPI there's also the
+
+ align:start position:0%
+on the effective CPI there's also the
+ 
+
+ align:start position:0%
+on the effective CPI there's also the
+lazy option of changing the is a to deal
+
+ align:start position:0%
+lazy option of changing the is a to deal
+ 
+
+ align:start position:0%
+lazy option of changing the is a to deal
+with control hazards for example we
+
+ align:start position:0%
+with control hazards for example we
+ 
+
+ align:start position:0%
+with control hazards for example we
+could change the is a to specify that
+
+ align:start position:0%
+could change the is a to specify that
+ 
+
+ align:start position:0%
+could change the is a to specify that
+the instruction following a jumper
+
+ align:start position:0%
+the instruction following a jumper
+ 
+
+ align:start position:0%
+the instruction following a jumper
+branch is always executed in other words
+
+ align:start position:0%
+branch is always executed in other words
+ 
+
+ align:start position:0%
+branch is always executed in other words
+the transfer of control happens after
+
+ align:start position:0%
+the transfer of control happens after
+ 
+
+ align:start position:0%
+the transfer of control happens after
+the next instruction this change ensures
+
+ align:start position:0%
+the next instruction this change ensures
+ 
+
+ align:start position:0%
+the next instruction this change ensures
+that the guess of PC plus 4 as the
+
+ align:start position:0%
+that the guess of PC plus 4 as the
+ 
+
+ align:start position:0%
+that the guess of PC plus 4 as the
+address of the next instruction is
+
+ align:start position:0%
+address of the next instruction is
+ 
+
+ align:start position:0%
+address of the next instruction is
+always correct in the example shown here
+
+ align:start position:0%
+always correct in the example shown here
+ 
+
+ align:start position:0%
+always correct in the example shown here
+assuming we change the is a we can
+
+ align:start position:0%
+assuming we change the is a we can
+ 
+
+ align:start position:0%
+assuming we change the is a we can
+reorganize the execution order of the
+
+ align:start position:0%
+reorganize the execution order of the
+ 
+
+ align:start position:0%
+reorganize the execution order of the
+loop to place the mall instruction after
+
+ align:start position:0%
+loop to place the mall instruction after
+ 
+
+ align:start position:0%
+loop to place the mall instruction after
+the be any instruction in the so called
+
+ align:start position:0%
+the be any instruction in the so called
+ 
+
+ align:start position:0%
+the be any instruction in the so called
+branch delay slot since the instruction
+
+ align:start position:0%
+branch delay slot since the instruction
+ 
+
+ align:start position:0%
+branch delay slot since the instruction
+in the branch delay slot is always
+
+ align:start position:0%
+in the branch delay slot is always
+ 
+
+ align:start position:0%
+in the branch delay slot is always
+executed the mall instruction will be
+
+ align:start position:0%
+executed the mall instruction will be
+ 
+
+ align:start position:0%
+executed the mall instruction will be
+executed during each iteration of the
+
+ align:start position:0%
+executed during each iteration of the
+ 
+
+ align:start position:0%
+executed during each iteration of the
+loop the resulting execution is shown in
+
+ align:start position:0%
+loop the resulting execution is shown in
+ 
+
+ align:start position:0%
+loop the resulting execution is shown in
+this pipeline diagram assuming we can
+
+ align:start position:0%
+this pipeline diagram assuming we can
+ 
+
+ align:start position:0%
+this pipeline diagram assuming we can
+find an appropriate instruction to place
+
+ align:start position:0%
+find an appropriate instruction to place
+ 
+
+ align:start position:0%
+find an appropriate instruction to place
+in the delay slot the branch will have
+
+ align:start position:0%
+in the delay slot the branch will have
+ 
+
+ align:start position:0%
+in the delay slot the branch will have
+zero impact on the effect of CPI our
+
+ align:start position:0%
+zero impact on the effect of CPI our
+ 
+
+ align:start position:0%
+zero impact on the effect of CPI our
+branch delay slots a good idea seems
+
+ align:start position:0%
+branch delay slots a good idea seems
+ 
+
+ align:start position:0%
+branch delay slots a good idea seems
+like they reduce the negative impact
+
+ align:start position:0%
+like they reduce the negative impact
+ 
+
+ align:start position:0%
+like they reduce the negative impact
+that branches might have on instruction
+
+ align:start position:0%
+that branches might have on instruction
+ 
+
+ align:start position:0%
+that branches might have on instruction
+throughput the downside is that only
+
+ align:start position:0%
+throughput the downside is that only
+ 
+
+ align:start position:0%
+throughput the downside is that only
+half of the time can we find
+
+ align:start position:0%
+half of the time can we find
+ 
+
+ align:start position:0%
+half of the time can we find
+instructions to move to the branch delay
+
+ align:start position:0%
+instructions to move to the branch delay
+ 
+
+ align:start position:0%
+instructions to move to the branch delay
+slot the other half of the time we have
+
+ align:start position:0%
+slot the other half of the time we have
+ 
+
+ align:start position:0%
+slot the other half of the time we have
+to fill it with an explicit no op
+
+ align:start position:0%
+to fill it with an explicit no op
+ 
+
+ align:start position:0%
+to fill it with an explicit no op
+instruction increasing the size of the
+
+ align:start position:0%
+instruction increasing the size of the
+ 
+
+ align:start position:0%
+instruction increasing the size of the
+code and if we make the branch decision
+
+ align:start position:0%
+code and if we make the branch decision
+ 
+
+ align:start position:0%
+code and if we make the branch decision
+later in the pipeline there are more two
+
+ align:start position:0%
+later in the pipeline there are more two
+ 
+
+ align:start position:0%
+later in the pipeline there are more two
+branch delay slots which would be even
+
+ align:start position:0%
+branch delay slots which would be even
+ 
+
+ align:start position:0%
+branch delay slots which would be even
+harder to fill in practice it turns out
+
+ align:start position:0%
+harder to fill in practice it turns out
+ 
+
+ align:start position:0%
+harder to fill in practice it turns out
+that branch prediction works better than
+
+ align:start position:0%
+that branch prediction works better than
+ 
+
+ align:start position:0%
+that branch prediction works better than
+delay slots in reducing the impact of
+
+ align:start position:0%
+delay slots in reducing the impact of
+ 
+
+ align:start position:0%
+delay slots in reducing the impact of
+branches so
+
+ align:start position:0%
+branches so
+ 
+
+ align:start position:0%
+branches so
+once again we see it's problematic to
+
+ align:start position:0%
+once again we see it's problematic to
+ 
+
+ align:start position:0%
+once again we see it's problematic to
+alter the is a to improve the throughput
+
+ align:start position:0%
+alter the is a to improve the throughput
+ 
+
+ align:start position:0%
+alter the is a to improve the throughput
+of pipeline execution ISAs outlive
+
+ align:start position:0%
+of pipeline execution ISAs outlive
+ 
+
+ align:start position:0%
+of pipeline execution ISAs outlive
+implementations so it's best not to
+
+ align:start position:0%
+implementations so it's best not to
+ 
+
+ align:start position:0%
+implementations so it's best not to
+change the execution semantics to deal
+
+ align:start position:0%
+change the execution semantics to deal
+ 
+
+ align:start position:0%
+change the execution semantics to deal
+with performance issues created by a
+
+ align:start position:0%
+with performance issues created by a
+ 
+
+ align:start position:0%
+with performance issues created by a
+particular implementation
\ No newline at end of file
diff --git a/0aMDzMhf528.txt b/0aMDzMhf528.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e3776474fad1a075b69ef0b7c8205cbee8693854
--- /dev/null
+++ b/0aMDzMhf528.txt
@@ -0,0 +1,212 @@
+For this problem, assume that we have a computer
+system that has three devices D1, D2, and
+
+D3.
+
+Each of these devices can cause interrupts
+in our system.
+
+This table summarizes the interrupt characteristics
+of our three devices.
+
+For each device, we are given its service
+time which is the amount of time it takes
+
+to service an interrupt for that particular
+device.
+
+We are given an interrupt frequency which
+tells us how frequently the interrupts for
+
+that device arrive.
+
+You can assume that the first interrupt of
+each device can arrive at any time.
+
+The deadline is the longest amount of time
+that is allowed between the interrupt request
+
+and the completion of the interrupt handler.
+
+Assume we have a program P that takes 100
+seconds to execute when interrupts are disabled.
+
+We would like to figure out how long it would
+take to execute this program when interrupts
+
+are enabled.
+
+To answer this question, we need to determine
+the amount of cpu time that is dedicated to
+
+the handling of each of the three devices.
+
+D1 has a service time of 400us and it runs
+every 800us so it is using 400/800 or 50%
+
+of the cpu time.
+
+D2 has a service time of 250us and it runs
+every 1000us so it is using 250/1000 or 25%
+
+of the cpu time.
+
+D3 uses 100/800 or 12.5% of the cpu time.
+
+This means that the user programs have the
+remaining cpu time available to them.
+
+The remaining cpu time is 12.5% or 1/8 of
+the cpu time.
+
+If the user program can only run for one eighth
+of the time, that means that a program that
+
+takes 100 seconds without interrupts will
+take 800 seconds to run with interrupts enabled.
+
+We want to consider whether there is a weak
+priority ordering that could satisfy all of
+
+the constraints for this system?
+Recall that with a weak priority ordering,
+
+there is no preemption, so if an interrupt
+handler has begun running it runs to completion
+
+even if another interrupt of higher priority
+arrives before its completion.
+
+Upon completion, all interrupts that have
+arrived, regardless of their order of arrival,
+
+are processed in priority order.
+
+If there is a weak priority ordering that
+satisfies our system, then we should determine
+
+the priority ordering.
+
+If there is no such ordering, then we should
+identify the devices for which a weak priority
+
+ordering cannot guarantee meeting all the
+constraints.
+
+Returning to our device characteristics table
+and comparing our deadlines to the device
+
+service times, we see that in a weak priority
+system if the D1 handler which has a service
+
+time of 400us happens to be running when a
+D2 or D3 interrupt arrives, then the D2 or
+
+D3 devices could miss their deadlines because
+the service time of D1 plus their own service
+
+time is greater than their deadline.
+
+In other words, if D2 or D3 have to wait up
+to 400us before beginning to be serviced then
+
+their completion time won't be until 650us
+for D2 which is greater than its deadline
+
+of 300us, and 500us for D3 which is greater
+than its deadline of 400us.
+
+Thus, there is no weak priority system ordering
+which is guaranteed to satisfy all of our
+
+system constraints.
+
+Now, lets reconsider the same question assuming
+a strong priority ordering.
+
+Recall that with a strong priority ordering,
+the handler for a device with a higher priority
+
+will pre-empt a running handler of a lower
+priority device.
+
+In other words if the priority of A is greater
+than B and an A interrupt arrives midway through
+
+the handling of a B interrupt, then the B
+interrupt handler will get interrupted, the
+
+A handler will be run, and upon completion
+of the A handler, the B handler will be resumed.
+
+If there is a strong priority ordering that
+satisfies our system, then we should specify
+
+what it is.
+
+If there is no such ordering, then we should
+identify the devices for which even a strong
+
+priority ordering cannot guarantee meeting
+all the constraints.
+
+Since we now allow preemption of lower priority
+device handlers in order to satisfy the requirements
+
+of a higher priority handler, we are no longer
+faced with the issue that devices D2 and D3
+
+can't meet their deadlines if D1 happens to
+be running first.
+
+In addition, since at the beginning of our
+problem we determined that there is enough
+
+time to service all of our interrupts given
+their service times and interrupt frequencies,
+
+that means that there must exist a strong
+priority ordering that can satisfy all the
+
+constraints of our system.
+
+You can use the scheme that a device with
+a shorter deadline should have a higher priority
+
+than one with a longer deadline to arrive
+at a valid strong priority ordering.
+
+A valid strong priority ordering is D2 has
+the highest priority, then D3 and then D1.
+
+Another way of expressing this is D2 > D3
+> D1.
+
+Note that for this example, this priority
+ordering is the only valid ordering that will
+
+satisfy all the constraints of our strong
+priority system.
+
+To convince ourselves of this, let's take
+a closer look at other priority possibilities
+
+and determine what would happen in those situations.
+
+If D1 had a higher priority than either D2
+or D3, then the deadlines for D2 and D3 would
+
+not be guaranteed to be satisfied.
+
+This means that D1 must have the lowest priority.
+
+Now between D2 and D3, if D3 had a higher
+priority than D2, then if D3 was being serviced
+
+when a D2 interrupt arrived, the D2 interrupt
+may not complete until 350us which is beyond
+
+its deadline.
+
+So this shows us that D2 must have the highest
+priority, then D3 and finally D1.
\ No newline at end of file
diff --git a/0aa6fUHTTeU.txt b/0aa6fUHTTeU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..10270a76c863b2270fc08cc0bef4fe6bce706df8
--- /dev/null
+++ b/0aa6fUHTTeU.txt
@@ -0,0 +1,7931 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay ready to go
+
+ align:start position:0%
+ocw.mit.edu okay ready to go
+ 
+
+ align:start position:0%
+ocw.mit.edu okay ready to go
+on lecture five I guess this is um so
+
+ align:start position:0%
+on lecture five I guess this is um so
+ 
+
+ align:start position:0%
+on lecture five I guess this is um so
+this we've done the uh one-way wave
+
+ align:start position:0%
+this we've done the uh one-way wave
+ 
+
+ align:start position:0%
+this we've done the uh one-way wave
+equation uh first order equation and now
+
+ align:start position:0%
+equation uh first order equation and now
+ 
+
+ align:start position:0%
+equation uh first order equation and now
+it's just natural to see what about the
+
+ align:start position:0%
+it's just natural to see what about the
+ 
+
+ align:start position:0%
+it's just natural to see what about the
+Ordinary second order wave
+
+ align:start position:0%
+Ordinary second order wave
+ 
+
+ align:start position:0%
+Ordinary second order wave
+equation and uh on this board I've
+
+ align:start position:0%
+equation and uh on this board I've
+ 
+
+ align:start position:0%
+equation and uh on this board I've
+written it two ways I've written it as a
+
+ align:start position:0%
+written it two ways I've written it as a
+ 
+
+ align:start position:0%
+written it two ways I've written it as a
+second order equation so second time
+
+ align:start position:0%
+second order equation so second time
+ 
+
+ align:start position:0%
+second order equation so second time
+derivative appears that's going to make
+
+ align:start position:0%
+derivative appears that's going to make
+ 
+
+ align:start position:0%
+derivative appears that's going to make
+a change we're going to have uh if we'll
+
+ align:start position:0%
+a change we're going to have uh if we'll
+ 
+
+ align:start position:0%
+a change we're going to have uh if we'll
+have second differences in time so we're
+
+ align:start position:0%
+have second differences in time so we're
+ 
+
+ align:start position:0%
+have second differences in time so we're
+we're going to have more
+
+ align:start position:0%
+we're going to have more
+ 
+
+ align:start position:0%
+we're going to have more
+steps and uh of the same second
+
+ align:start position:0%
+steps and uh of the same second
+ 
+
+ align:start position:0%
+steps and uh of the same second
+difference a matching second difference
+
+ align:start position:0%
+difference a matching second difference
+ 
+
+ align:start position:0%
+difference a matching second difference
+in space and so that's one way then this
+
+ align:start position:0%
+in space and so that's one way then this
+ 
+
+ align:start position:0%
+in space and so that's one way then this
+is another important way to write the
+
+ align:start position:0%
+is another important way to write the
+ 
+
+ align:start position:0%
+is another important way to write the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+equation as a first order system so I
+
+ align:start position:0%
+equation as a first order system so I
+ 
+
+ align:start position:0%
+equation as a first order system so I
+can get back to first order systems and
+
+ align:start position:0%
+can get back to first order systems and
+ 
+
+ align:start position:0%
+can get back to first order systems and
+I can use all those
+
+ align:start position:0%
+I can use all those
+ 
+
+ align:start position:0%
+I can use all those
+methods uh fried LAX friedrick for
+
+ align:start position:0%
+methods uh fried LAX friedrick for
+ 
+
+ align:start position:0%
+methods uh fried LAX friedrick for
+example LAX wend whatever improvements
+
+ align:start position:0%
+example LAX wend whatever improvements
+ 
+
+ align:start position:0%
+example LAX wend whatever improvements
+we think of
+
+ align:start position:0%
+we think of
+ 
+
+ align:start position:0%
+we think of
+uh on this first order system d by DT of
+
+ align:start position:0%
+uh on this first order system d by DT of
+ 
+
+ align:start position:0%
+uh on this first order system d by DT of
+a vector is a matrix times d by the x of
+
+ align:start position:0%
+a vector is a matrix times d by the x of
+ 
+
+ align:start position:0%
+a vector is a matrix times d by the x of
+the vector so that's a you really have a
+
+ align:start position:0%
+the vector so that's a you really have a
+ 
+
+ align:start position:0%
+the vector so that's a you really have a
+choice here and written this way well
+
+ align:start position:0%
+choice here and written this way well
+ 
+
+ align:start position:0%
+choice here and written this way well
+notice a little bit
+
+ align:start position:0%
+notice a little bit
+ 
+
+ align:start position:0%
+notice a little bit
+of uh good thing good one good thing
+
+ align:start position:0%
+of uh good thing good one good thing
+ 
+
+ align:start position:0%
+of uh good thing good one good thing
+here The Matrix that shows up is
+
+ align:start position:0%
+here The Matrix that shows up is
+ 
+
+ align:start position:0%
+here The Matrix that shows up is
+symmetric that was by the careful choice
+
+ align:start position:0%
+symmetric that was by the careful choice
+ 
+
+ align:start position:0%
+symmetric that was by the careful choice
+of putting a c in there then you see
+
+ align:start position:0%
+of putting a c in there then you see
+ 
+
+ align:start position:0%
+of putting a c in there then you see
+that the first equation in this system
+
+ align:start position:0%
+that the first equation in this system
+ 
+
+ align:start position:0%
+that the first equation in this system
+is utt is C time C
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uxx so the first equation is the wave
+
+ align:start position:0%
+uxx so the first equation is the wave
+ 
+
+ align:start position:0%
+uxx so the first equation is the wave
+equation and what about the second
+
+ align:start position:0%
+equation and what about the second
+ 
+
+ align:start position:0%
+equation and what about the second
+equation this is typical when you reduce
+
+ align:start position:0%
+equation this is typical when you reduce
+ 
+
+ align:start position:0%
+equation this is typical when you reduce
+things to a to a lower order system that
+
+ align:start position:0%
+things to a to a lower order system that
+ 
+
+ align:start position:0%
+things to a to a lower order system that
+you get an equation here which is just
+
+ align:start position:0%
+you get an equation here which is just
+ 
+
+ align:start position:0%
+you get an equation here which is just
+an identity the derivative of C the time
+
+ align:start position:0%
+an identity the derivative of C the time
+ 
+
+ align:start position:0%
+an identity the derivative of C the time
+this is C uxt it's the the derivative
+
+ align:start position:0%
+this is C uxt it's the the derivative
+ 
+
+ align:start position:0%
+this is C uxt it's the the derivative
+and x and t from there and we have c
+
+ align:start position:0%
+and x and t from there and we have c
+ 
+
+ align:start position:0%
+and x and t from there and we have c
+times the X derivative of UT the cross
+
+ align:start position:0%
+times the X derivative of UT the cross
+ 
+
+ align:start position:0%
+times the X derivative of UT the cross
+derivative so that is an identity
+
+ align:start position:0%
+derivative so that is an identity
+ 
+
+ align:start position:0%
+derivative so that is an identity
+because U TX is the same as uxt we can
+
+ align:start position:0%
+because U TX is the same as uxt we can
+ 
+
+ align:start position:0%
+because U TX is the same as uxt we can
+take time and x and t derivatives in
+
+ align:start position:0%
+take time and x and t derivatives in
+ 
+
+ align:start position:0%
+take time and x and t derivatives in
+either order for for a function of x and
+
+ align:start position:0%
+either order for for a function of x and
+ 
+
+ align:start position:0%
+either order for for a function of x and
+t so we'll see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that I guess what I want to do in the
+
+ align:start position:0%
+that I guess what I want to do in the
+ 
+
+ align:start position:0%
+that I guess what I want to do in the
+lecture is not to
+
+ align:start position:0%
+lecture is not to
+ 
+
+ align:start position:0%
+lecture is not to
+repeat LAX freed Dres or LAX wend for
+
+ align:start position:0%
+repeat LAX freed Dres or LAX wend for
+ 
+
+ align:start position:0%
+repeat LAX freed Dres or LAX wend for
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+system that would
+
+ align:start position:0%
+system that would
+ 
+
+ align:start position:0%
+system that would
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+unexciting let me just mention what are
+
+ align:start position:0%
+unexciting let me just mention what are
+ 
+
+ align:start position:0%
+unexciting let me just mention what are
+the igen values of that Matrix so the
+
+ align:start position:0%
+the igen values of that Matrix so the
+ 
+
+ align:start position:0%
+the igen values of that Matrix so the
+igen value in the in a for a system it's
+
+ align:start position:0%
+igen value in the in a for a system it's
+ 
+
+ align:start position:0%
+igen value in the in a for a system it's
+the igen values of the Matrix that
+
+ align:start position:0%
+the igen values of the Matrix that
+ 
+
+ align:start position:0%
+the igen values of the Matrix that
+tell us what waves we've got what speeds
+
+ align:start position:0%
+tell us what waves we've got what speeds
+ 
+
+ align:start position:0%
+tell us what waves we've got what speeds
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+go where when it was one by1 of course
+
+ align:start position:0%
+go where when it was one by1 of course
+ 
+
+ align:start position:0%
+go where when it was one by1 of course
+it was just that single number c but
+
+ align:start position:0%
+it was just that single number c but
+ 
+
+ align:start position:0%
+it was just that single number c but
+what are the igen values of that Matrix
+
+ align:start position:0%
+what are the igen values of that Matrix
+ 
+
+ align:start position:0%
+what are the igen values of that Matrix
+now having made it a symmetric
+
+ align:start position:0%
+now having made it a symmetric
+ 
+
+ align:start position:0%
+now having made it a symmetric
+Matrix uh we know right away it has real
+
+ align:start position:0%
+Matrix uh we know right away it has real
+ 
+
+ align:start position:0%
+Matrix uh we know right away it has real
+igen values and so it's a wave
+
+ align:start position:0%
+igen values and so it's a wave
+ 
+
+ align:start position:0%
+igen values and so it's a wave
+problem for a heat equation we would we
+
+ align:start position:0%
+problem for a heat equation we would we
+ 
+
+ align:start position:0%
+problem for a heat equation we would we
+would see something
+
+ align:start position:0%
+would see something
+ 
+
+ align:start position:0%
+would see something
+different but this will be a wave
+
+ align:start position:0%
+different but this will be a wave
+ 
+
+ align:start position:0%
+different but this will be a wave
+equation and that this has two igen
+
+ align:start position:0%
+equation and that this has two igen
+ 
+
+ align:start position:0%
+equation and that this has two igen
+values and they are C and minus
+
+ align:start position:0%
+values and they are C and minus
+ 
+
+ align:start position:0%
+values and they are C and minus
+C just you could quickly check that that
+
+ align:start position:0%
+C just you could quickly check that that
+ 
+
+ align:start position:0%
+C just you could quickly check that that
+2x two Matrix has I values C and minus C
+
+ align:start position:0%
+2x two Matrix has I values C and minus C
+ 
+
+ align:start position:0%
+2x two Matrix has I values C and minus C
+they add up to zero which is the trace
+
+ align:start position:0%
+they add up to zero which is the trace
+ 
+
+ align:start position:0%
+they add up to zero which is the trace
+they multiply C * minus C is minus c^ 2
+
+ align:start position:0%
+they multiply C * minus C is minus c^ 2
+ 
+
+ align:start position:0%
+they multiply C * minus C is minus c^ 2
+which is the determinant so that's
+
+ align:start position:0%
+which is the determinant so that's
+ 
+
+ align:start position:0%
+which is the determinant so that's
+they're the right igen values so that's
+
+ align:start position:0%
+they're the right igen values so that's
+ 
+
+ align:start position:0%
+they're the right igen values so that's
+going to tell us what we'll find every
+
+ align:start position:0%
+going to tell us what we'll find every
+ 
+
+ align:start position:0%
+going to tell us what we'll find every
+way that the speeds of the waves are C
+
+ align:start position:0%
+way that the speeds of the waves are C
+ 
+
+ align:start position:0%
+way that the speeds of the waves are C
+and minus C which means a wave going one
+
+ align:start position:0%
+and minus C which means a wave going one
+ 
+
+ align:start position:0%
+and minus C which means a wave going one
+way with speed c and a wave going the
+
+ align:start position:0%
+way with speed c and a wave going the
+ 
+
+ align:start position:0%
+way with speed c and a wave going the
+other way with speed
+
+ align:start position:0%
+other way with speed
+ 
+
+ align:start position:0%
+other way with speed
+C that's so so it's a two-way wave
+
+ align:start position:0%
+C that's so so it's a two-way wave
+ 
+
+ align:start position:0%
+C that's so so it's a two-way wave
+equation and this is the equation of
+
+ align:start position:0%
+equation and this is the equation of
+ 
+
+ align:start position:0%
+equation and this is the equation of
+real uh that really happens and I wanted
+
+ align:start position:0%
+real uh that really happens and I wanted
+ 
+
+ align:start position:0%
+real uh that really happens and I wanted
+to say just a little bit about just two
+
+ align:start position:0%
+to say just a little bit about just two
+ 
+
+ align:start position:0%
+to say just a little bit about just two
+words about real problems because we
+
+ align:start position:0%
+words about real problems because we
+ 
+
+ align:start position:0%
+words about real problems because we
+can't in in these first days tackle the
+
+ align:start position:0%
+can't in in these first days tackle the
+ 
+
+ align:start position:0%
+can't in in these first days tackle the
+difficult problems of
+
+ align:start position:0%
+difficult problems of
+ 
+
+ align:start position:0%
+difficult problems of
+electromagnetism antenna Decay design uh
+
+ align:start position:0%
+electromagnetism antenna Decay design uh
+ 
+
+ align:start position:0%
+electromagnetism antenna Decay design uh
+um all kinds of uh wave problems I I
+
+ align:start position:0%
+um all kinds of uh wave problems I I
+ 
+
+ align:start position:0%
+um all kinds of uh wave problems I I
+guess I'm hoping some of you may be
+
+ align:start position:0%
+guess I'm hoping some of you may be
+ 
+
+ align:start position:0%
+guess I'm hoping some of you may be
+meeting real wave problems in other
+
+ align:start position:0%
+meeting real wave problems in other
+ 
+
+ align:start position:0%
+meeting real wave problems in other
+courses and
+
+ align:start position:0%
+courses and
+ 
+
+ align:start position:0%
+courses and
+would uh make a project that that uh
+
+ align:start position:0%
+would uh make a project that that uh
+ 
+
+ align:start position:0%
+would uh make a project that that uh
+tries our methods on real problems I I I
+
+ align:start position:0%
+tries our methods on real problems I I I
+ 
+
+ align:start position:0%
+tries our methods on real problems I I I
+just wanted to write down here one sort
+
+ align:start position:0%
+just wanted to write down here one sort
+ 
+
+ align:start position:0%
+just wanted to write down here one sort
+of typical real problem so in a real
+
+ align:start position:0%
+of typical real problem so in a real
+ 
+
+ align:start position:0%
+of typical real problem so in a real
+problem we we have a a variable
+
+ align:start position:0%
+problem we we have a a variable
+ 
+
+ align:start position:0%
+problem we we have a a variable
+coefficient X because maybe our material
+
+ align:start position:0%
+coefficient X because maybe our material
+ 
+
+ align:start position:0%
+coefficient X because maybe our material
+is not homogeneous it's not
+
+ align:start position:0%
+is not homogeneous it's not
+ 
+
+ align:start position:0%
+is not homogeneous it's not
+uniform and we have a forcing
+
+ align:start position:0%
+uniform and we have a forcing
+ 
+
+ align:start position:0%
+uniform and we have a forcing
+term I is put f for the amplitude to
+
+ align:start position:0%
+term I is put f for the amplitude to
+ 
+
+ align:start position:0%
+term I is put f for the amplitude to
+emphasize that's forcing term so F
+
+ align:start position:0%
+emphasize that's forcing term so F
+ 
+
+ align:start position:0%
+emphasize that's forcing term so F
+standing for forcing but it's an
+
+ align:start position:0%
+standing for forcing but it's an
+ 
+
+ align:start position:0%
+standing for forcing but it's an
+oscillating forcing term it's a this is
+
+ align:start position:0%
+oscillating forcing term it's a this is
+ 
+
+ align:start position:0%
+oscillating forcing term it's a this is
+what you're going to have and in
+
+ align:start position:0%
+what you're going to have and in
+ 
+
+ align:start position:0%
+what you're going to have and in
+electromagnetism the frequency is going
+
+ align:start position:0%
+electromagnetism the frequency is going
+ 
+
+ align:start position:0%
+electromagnetism the frequency is going
+to be very very
+
+ align:start position:0%
+to be very very
+ 
+
+ align:start position:0%
+to be very very
+high and then uh so this is a problem
+
+ align:start position:0%
+high and then uh so this is a problem
+ 
+
+ align:start position:0%
+high and then uh so this is a problem
+that you that's not easy numerically
+
+ align:start position:0%
+that you that's not easy numerically
+ 
+
+ align:start position:0%
+that you that's not easy numerically
+very very high
+
+ align:start position:0%
+very very high
+ 
+
+ align:start position:0%
+very very high
+frequencies would normally require very
+
+ align:start position:0%
+frequencies would normally require very
+ 
+
+ align:start position:0%
+frequencies would normally require very
+very small wavelengths very very small
+
+ align:start position:0%
+very small wavelengths very very small
+ 
+
+ align:start position:0%
+very small wavelengths very very small
+Delta X because you you remember there
+
+ align:start position:0%
+Delta X because you you remember there
+ 
+
+ align:start position:0%
+Delta X because you you remember there
+would be a k Delta X in the eror
+
+ align:start position:0%
+would be a k Delta X in the eror
+ 
+
+ align:start position:0%
+would be a k Delta X in the eror
+so if we took a big Delta X and or even
+
+ align:start position:0%
+so if we took a big Delta X and or even
+ 
+
+ align:start position:0%
+so if we took a big Delta X and or even
+an ordinary size Delta X and let the
+
+ align:start position:0%
+an ordinary size Delta X and let the
+ 
+
+ align:start position:0%
+an ordinary size Delta X and let the
+frequency go way way up high high
+
+ align:start position:0%
+frequency go way way up high high
+ 
+
+ align:start position:0%
+frequency go way way up high high
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+oscillation our K Delta X would be big
+
+ align:start position:0%
+oscillation our K Delta X would be big
+ 
+
+ align:start position:0%
+oscillation our K Delta X would be big
+and the accuracy would be poor and and
+
+ align:start position:0%
+and the accuracy would be poor and and
+ 
+
+ align:start position:0%
+and the accuracy would be poor and and
+the results useless so a lot of I'm
+
+ align:start position:0%
+the results useless so a lot of I'm
+ 
+
+ align:start position:0%
+the results useless so a lot of I'm
+really guess I'm thinking here about a
+
+ align:start position:0%
+really guess I'm thinking here about a
+ 
+
+ align:start position:0%
+really guess I'm thinking here about a
+course on wave
+
+ align:start position:0%
+course on wave
+ 
+
+ align:start position:0%
+course on wave
+propagation would study this as a first
+
+ align:start position:0%
+propagation would study this as a first
+ 
+
+ align:start position:0%
+propagation would study this as a first
+model problem
+
+ align:start position:0%
+model problem
+ 
+
+ align:start position:0%
+model problem
+get some do some analysis and then uh go
+
+ align:start position:0%
+get some do some analysis and then uh go
+ 
+
+ align:start position:0%
+get some do some analysis and then uh go
+into 2D and 3D that's uh that's the
+
+ align:start position:0%
+into 2D and 3D that's uh that's the
+ 
+
+ align:start position:0%
+into 2D and 3D that's uh that's the
+reality of of of wave theory is you get
+
+ align:start position:0%
+reality of of of wave theory is you get
+ 
+
+ align:start position:0%
+reality of of of wave theory is you get
+as you can get asymptotic results for K
+
+ align:start position:0%
+as you can get asymptotic results for K
+ 
+
+ align:start position:0%
+as you can get asymptotic results for K
+going to Infinity you get things things
+
+ align:start position:0%
+going to Infinity you get things things
+ 
+
+ align:start position:0%
+going to Infinity you get things things
+uh you're looking in in matching powers
+
+ align:start position:0%
+uh you're looking in in matching powers
+ 
+
+ align:start position:0%
+uh you're looking in in matching powers
+of K so to speak and you're getting
+
+ align:start position:0%
+of K so to speak and you're getting
+ 
+
+ align:start position:0%
+of K so to speak and you're getting
+plain waves and and interesting stuff
+
+ align:start position:0%
+plain waves and and interesting stuff
+ 
+
+ align:start position:0%
+plain waves and and interesting stuff
+that that's we can't do already right
+
+ align:start position:0%
+that that's we can't do already right
+ 
+
+ align:start position:0%
+that that's we can't do already right
+away here so I I'm going back to the
+
+ align:start position:0%
+away here so I I'm going back to the
+ 
+
+ align:start position:0%
+away here so I I'm going back to the
+ordinary wave equation either second
+
+ align:start position:0%
+ordinary wave equation either second
+ 
+
+ align:start position:0%
+ordinary wave equation either second
+start with second order UT is c^2 uxx
+
+ align:start position:0%
+start with second order UT is c^2 uxx
+ 
+
+ align:start position:0%
+start with second order UT is c^2 uxx
+okay that's our
+
+ align:start position:0%
+okay that's our
+ 
+
+ align:start position:0%
+okay that's our
+goal and as I said we don't want to see
+
+ align:start position:0%
+goal and as I said we don't want to see
+ 
+
+ align:start position:0%
+goal and as I said we don't want to see
+LAX friedricks and LAX wend again we
+
+ align:start position:0%
+LAX friedricks and LAX wend again we
+ 
+
+ align:start position:0%
+LAX friedricks and LAX wend again we
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+those it's uh rather one so one new
+
+ align:start position:0%
+those it's uh rather one so one new
+ 
+
+ align:start position:0%
+those it's uh rather one so one new
+method is going to show
+
+ align:start position:0%
+method is going to show
+ 
+
+ align:start position:0%
+method is going to show
+up one and it's Leap Frog is the right
+
+ align:start position:0%
+up one and it's Leap Frog is the right
+ 
+
+ align:start position:0%
+up one and it's Leap Frog is the right
+name natural name to give it Leap Frog
+
+ align:start position:0%
+name natural name to give it Leap Frog
+ 
+
+ align:start position:0%
+name natural name to give it Leap Frog
+because well in the time direction we
+
+ align:start position:0%
+because well in the time direction we
+ 
+
+ align:start position:0%
+because well in the time direction we
+have time n minus one n and n plus one
+
+ align:start position:0%
+have time n minus one n and n plus one
+ 
+
+ align:start position:0%
+have time n minus one n and n plus one
+there's a leap there but let me start
+
+ align:start position:0%
+there's a leap there but let me start
+ 
+
+ align:start position:0%
+there's a leap there but let me start
+with semi discreete we haven't done
+
+ align:start position:0%
+with semi discreete we haven't done
+ 
+
+ align:start position:0%
+with semi discreete we haven't done
+this until
+
+ align:start position:0%
+this until
+ 
+
+ align:start position:0%
+this until
+today semidiscrete
+
+ align:start position:0%
+today semidiscrete
+ 
+
+ align:start position:0%
+today semidiscrete
+means as you see that the time variable
+
+ align:start position:0%
+means as you see that the time variable
+ 
+
+ align:start position:0%
+means as you see that the time variable
+stays
+
+ align:start position:0%
+stays
+ 
+
+ align:start position:0%
+stays
+continuous we have ordinary differential
+
+ align:start position:0%
+continuous we have ordinary differential
+ 
+
+ align:start position:0%
+continuous we have ordinary differential
+equations in
+
+ align:start position:0%
+equations in
+ 
+
+ align:start position:0%
+equations in
+t but the space variable is what's
+
+ align:start position:0%
+t but the space variable is what's
+ 
+
+ align:start position:0%
+t but the space variable is what's
+getting discrete so the problem is like
+
+ align:start position:0%
+getting discrete so the problem is like
+ 
+
+ align:start position:0%
+getting discrete so the problem is like
+half discreete discrete in X but not
+
+ align:start position:0%
+half discreete discrete in X but not
+ 
+
+ align:start position:0%
+half discreete discrete in X but not
+there's a Delta X but there's no delta T
+
+ align:start position:0%
+there's a Delta X but there's no delta T
+ 
+
+ align:start position:0%
+there's a Delta X but there's no delta T
+yet so so it's natural to like analyze
+
+ align:start position:0%
+yet so so it's natural to like analyze
+ 
+
+ align:start position:0%
+yet so so it's natural to like analyze
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+problem and what so what do we have
+
+ align:start position:0%
+problem and what so what do we have
+ 
+
+ align:start position:0%
+problem and what so what do we have
+really we have in the X direction we
+
+ align:start position:0%
+really we have in the X direction we
+ 
+
+ align:start position:0%
+really we have in the X direction we
+have a mesh of width Delta X so we have
+
+ align:start position:0%
+have a mesh of width Delta X so we have
+ 
+
+ align:start position:0%
+have a mesh of width Delta X so we have
+unknowns that if that's
+
+ align:start position:0%
+unknowns that if that's
+ 
+
+ align:start position:0%
+unknowns that if that's
+zero J is measuring so J Delta J Delta X
+
+ align:start position:0%
+zero J is measuring so J Delta J Delta X
+ 
+
+ align:start position:0%
+zero J is measuring so J Delta J Delta X
+is the is the typical
+
+ align:start position:0%
+is the is the typical
+ 
+
+ align:start position:0%
+is the is the typical
+point point number J along there and
+
+ align:start position:0%
+point point number J along there and
+ 
+
+ align:start position:0%
+point point number J along there and
+then in the time direction we're going
+
+ align:start position:0%
+then in the time direction we're going
+ 
+
+ align:start position:0%
+then in the time direction we're going
+continuously so I don't have discrete
+
+ align:start position:0%
+continuously so I don't have discrete
+ 
+
+ align:start position:0%
+continuously so I don't have discrete
+steps
+
+ align:start position:0%
+steps
+ 
+
+ align:start position:0%
+steps
+so it's called because those are lines
+
+ align:start position:0%
+so it's called because those are lines
+ 
+
+ align:start position:0%
+so it's called because those are lines
+in the time Direction This is
+
+ align:start position:0%
+in the time Direction This is
+ 
+
+ align:start position:0%
+in the time Direction This is
+semidiscrete is also referred to as the
+
+ align:start position:0%
+semidiscrete is also referred to as the
+ 
+
+ align:start position:0%
+semidiscrete is also referred to as the
+method of
+
+ align:start position:0%
+method of
+ 
+
+ align:start position:0%
+method of
+lines so the method of lines is this is
+
+ align:start position:0%
+lines so the method of lines is this is
+ 
+
+ align:start position:0%
+lines so the method of lines is this is
+what we're doing here and it's all I
+
+ align:start position:0%
+what we're doing here and it's all I
+ 
+
+ align:start position:0%
+what we're doing here and it's all I
+want to do
+
+ align:start position:0%
+want to do
+ 
+
+ align:start position:0%
+want to do
+is what I always
+
+ align:start position:0%
+is what I always
+ 
+
+ align:start position:0%
+is what I always
+do take
+
+ align:start position:0%
+do take
+ 
+
+ align:start position:0%
+do take
+exponentials look at their growth
+
+ align:start position:0%
+exponentials look at their growth
+ 
+
+ align:start position:0%
+exponentials look at their growth
+factors understand the equation well
+
+ align:start position:0%
+factors understand the equation well
+ 
+
+ align:start position:0%
+factors understand the equation well
+actually I better do it first with the
+
+ align:start position:0%
+actually I better do it first with the
+ 
+
+ align:start position:0%
+actually I better do it first with the
+wave equation itself so so I guess my my
+
+ align:start position:0%
+wave equation itself so so I guess my my
+ 
+
+ align:start position:0%
+wave equation itself so so I guess my my
+Organization for today
+
+ align:start position:0%
+Organization for today
+ 
+
+ align:start position:0%
+Organization for today
+is first step is follow e to the
+
+ align:start position:0%
+is first step is follow e to the
+ 
+
+ align:start position:0%
+is first step is follow e to the
+ikx for the wave equation so I'll do
+
+ align:start position:0%
+ikx for the wave equation so I'll do
+ 
+
+ align:start position:0%
+ikx for the wave equation so I'll do
+that here
+
+ align:start position:0%
+that here
+ 
+
+ align:start position:0%
+that here
+utt equals c^2
+
+ align:start position:0%
+utt equals c^2
+ 
+
+ align:start position:0%
+utt equals c^2
+uxx and I'm going to look at U
+
+ align:start position:0%
+uxx and I'm going to look at U
+ 
+
+ align:start position:0%
+uxx and I'm going to look at U
+proportional to and I'll call this
+
+ align:start position:0%
+proportional to and I'll call this
+ 
+
+ align:start position:0%
+proportional to and I'll call this
+Factor G again G of t
+
+ align:start position:0%
+Factor G again G of t
+ 
+
+ align:start position:0%
+Factor G again G of t
+and times the frequency I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KX so I'm going to look for Pure
+
+ align:start position:0%
+KX so I'm going to look for Pure
+ 
+
+ align:start position:0%
+KX so I'm going to look for Pure
+exponentials okay and we'll quickly find
+
+ align:start position:0%
+exponentials okay and we'll quickly find
+ 
+
+ align:start position:0%
+exponentials okay and we'll quickly find
+them and then I'm going to do the same
+
+ align:start position:0%
+them and then I'm going to do the same
+ 
+
+ align:start position:0%
+them and then I'm going to do the same
+for semidiscrete where that X becomes J
+
+ align:start position:0%
+for semidiscrete where that X becomes J
+ 
+
+ align:start position:0%
+for semidiscrete where that X becomes J
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X and I'm at Point J and then I'm going
+
+ align:start position:0%
+X and I'm at Point J and then I'm going
+ 
+
+ align:start position:0%
+X and I'm at Point J and then I'm going
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+eventually look at the Le discrete now
+
+ align:start position:0%
+eventually look at the Le discrete now
+ 
+
+ align:start position:0%
+eventually look at the Le discrete now
+fully
+
+ align:start position:0%
+fully
+ 
+
+ align:start position:0%
+fully
+discrete discrete in time and discrete
+
+ align:start position:0%
+discrete discrete in time and discrete
+ 
+
+ align:start position:0%
+discrete discrete in time and discrete
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+space and
+
+ align:start position:0%
+space and
+ 
+
+ align:start position:0%
+space and
+uh the question of stability arises
+
+ align:start position:0%
+uh the question of stability arises
+ 
+
+ align:start position:0%
+uh the question of stability arises
+accuracy we can you pretty much we
+
+ align:start position:0%
+accuracy we can you pretty much we
+ 
+
+ align:start position:0%
+accuracy we can you pretty much we
+pretty much know the accuracy for second
+
+ align:start position:0%
+pretty much know the accuracy for second
+ 
+
+ align:start position:0%
+pretty much know the accuracy for second
+differences the that's a second order
+
+ align:start position:0%
+differences the that's a second order
+ 
+
+ align:start position:0%
+differences the that's a second order
+accurate thing because it's centered but
+
+ align:start position:0%
+accurate thing because it's centered but
+ 
+
+ align:start position:0%
+accurate thing because it's centered but
+stability is going to come
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's this is our first
+
+ align:start position:0%
+okay so that's this is our first
+ 
+
+ align:start position:0%
+okay so that's this is our first
+step and and and then I'll just mention
+
+ align:start position:0%
+step and and and then I'll just mention
+ 
+
+ align:start position:0%
+step and and and then I'll just mention
+what other point remains in this in this
+
+ align:start position:0%
+what other point remains in this in this
+ 
+
+ align:start position:0%
+what other point remains in this in this
+uh wave equation is to look at the uh
+
+ align:start position:0%
+uh wave equation is to look at the uh
+ 
+
+ align:start position:0%
+uh wave equation is to look at the uh
+first order
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system how does that look in
+
+ align:start position:0%
+system how does that look in
+ 
+
+ align:start position:0%
+system how does that look in
+uh space and
+
+ align:start position:0%
+uh space and
+ 
+
+ align:start position:0%
+uh space and
+time well as I
+
+ align:start position:0%
+time well as I
+ 
+
+ align:start position:0%
+time well as I
+said
+
+ align:start position:0%
+said
+ 
+
+ align:start position:0%
+said
+the obvious thing to do would be LAX
+
+ align:start position:0%
+the obvious thing to do would be LAX
+ 
+
+ align:start position:0%
+the obvious thing to do would be LAX
+friedricks or LAX wend but there's
+
+ align:start position:0%
+friedricks or LAX wend but there's
+ 
+
+ align:start position:0%
+friedricks or LAX wend but there's
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+idea and it brings in uh a staggered
+
+ align:start position:0%
+idea and it brings in uh a staggered
+ 
+
+ align:start position:0%
+idea and it brings in uh a staggered
+grid the well you'll see
+
+ align:start position:0%
+grid the well you'll see
+ 
+
+ align:start position:0%
+grid the well you'll see
+it somehow that staggered grid is really
+
+ align:start position:0%
+it somehow that staggered grid is really
+ 
+
+ align:start position:0%
+it somehow that staggered grid is really
+an important idea that we haven't met
+
+ align:start position:0%
+an important idea that we haven't met
+ 
+
+ align:start position:0%
+an important idea that we haven't met
+yet that some unknowns are on the
+
+ align:start position:0%
+yet that some unknowns are on the
+ 
+
+ align:start position:0%
+yet that some unknowns are on the
+standard
+
+ align:start position:0%
+standard
+ 
+
+ align:start position:0%
+standard
+grid
+
+ align:start position:0%
+grid
+ 
+
+ align:start position:0%
+grid
+ujn the other unknowns are on uh a a
+
+ align:start position:0%
+ujn the other unknowns are on uh a a
+ 
+
+ align:start position:0%
+ujn the other unknowns are on uh a a
+grid that's that's half a Delta X and
+
+ align:start position:0%
+grid that's that's half a Delta X and
+ 
+
+ align:start position:0%
+grid that's that's half a Delta X and
+half a delta T
+
+ align:start position:0%
+half a delta T
+ 
+
+ align:start position:0%
+half a delta T
+different and it's just right actually
+
+ align:start position:0%
+different and it's just right actually
+ 
+
+ align:start position:0%
+different and it's just right actually
+so that's the that's a premier method in
+
+ align:start position:0%
+so that's the that's a premier method in
+ 
+
+ align:start position:0%
+so that's the that's a premier method in
+electromagnetism so that's that's what's
+
+ align:start position:0%
+electromagnetism so that's that's what's
+ 
+
+ align:start position:0%
+electromagnetism so that's that's what's
+coming but let's start with the second
+
+ align:start position:0%
+coming but let's start with the second
+ 
+
+ align:start position:0%
+coming but let's start with the second
+order method because we haven't seen
+
+ align:start position:0%
+order method because we haven't seen
+ 
+
+ align:start position:0%
+order method because we haven't seen
+second order methods before okay second
+
+ align:start position:0%
+second order methods before okay second
+ 
+
+ align:start position:0%
+second order methods before okay second
+order equation plug in G
+
+ align:start position:0%
+order equation plug in G
+ 
+
+ align:start position:0%
+order equation plug in G
+okay so I have the second time
+
+ align:start position:0%
+okay so I have the second time
+ 
+
+ align:start position:0%
+okay so I have the second time
+derivative gives me G
+
+ align:start position:0%
+derivative gives me G
+ 
+
+ align:start position:0%
+derivative gives me G
+Prime Time e to the ik KX see I'm
+
+ align:start position:0%
+Prime Time e to the ik KX see I'm
+ 
+
+ align:start position:0%
+Prime Time e to the ik KX see I'm
+separating variables of course T here
+
+ align:start position:0%
+separating variables of course T here
+ 
+
+ align:start position:0%
+separating variables of course T here
+and X there and on the other side I have
+
+ align:start position:0%
+and X there and on the other side I have
+ 
+
+ align:start position:0%
+and X there and on the other side I have
+c^2 now I have the X variable so that's
+
+ align:start position:0%
+c^2 now I have the X variable so that's
+ 
+
+ align:start position:0%
+c^2 now I have the X variable so that's
+brings down an i k so that's I k^
+
+ align:start position:0%
+brings down an i k so that's I k^
+ 
+
+ align:start position:0%
+brings down an i k so that's I k^
+SAR time g e to the I
+
+ align:start position:0%
+SAR time g e to the I
+ 
+
+ align:start position:0%
+SAR time g e to the I
+KX good
+
+ align:start position:0%
+KX good
+ 
+
+ align:start position:0%
+KX good
+so simple but but uh substituting
+
+ align:start position:0%
+so simple but but uh substituting
+ 
+
+ align:start position:0%
+so simple but but uh substituting
+this is just a natural first step to see
+
+ align:start position:0%
+this is just a natural first step to see
+ 
+
+ align:start position:0%
+this is just a natural first step to see
+what's happening and then of course
+
+ align:start position:0%
+what's happening and then of course
+ 
+
+ align:start position:0%
+what's happening and then of course
+canceling e to the I KX leaves us with
+
+ align:start position:0%
+canceling e to the I KX leaves us with
+ 
+
+ align:start position:0%
+canceling e to the I KX leaves us with
+the equation for the G gble
+
+ align:start position:0%
+the equation for the G gble
+ 
+
+ align:start position:0%
+the equation for the G gble
+Prime is I'll make that i^2 minus minus
+
+ align:start position:0%
+Prime is I'll make that i^2 minus minus
+ 
+
+ align:start position:0%
+Prime is I'll make that i^2 minus minus
+c^ 2 k^ 2
+
+ align:start position:0%
+c^ 2 k^ 2
+ 
+
+ align:start position:0%
+c^ 2 k^ 2
+G and of course the new aspect is it's
+
+ align:start position:0%
+G and of course the new aspect is it's
+ 
+
+ align:start position:0%
+G and of course the new aspect is it's
+second order so it's got two solutions
+
+ align:start position:0%
+second order so it's got two solutions
+ 
+
+ align:start position:0%
+second order so it's got two solutions
+instead of just one it's constant
+
+ align:start position:0%
+instead of just one it's constant
+ 
+
+ align:start position:0%
+instead of just one it's constant
+coefficients of
+
+ align:start position:0%
+coefficients of
+ 
+
+ align:start position:0%
+coefficients of
+course and so we look for
+
+ align:start position:0%
+course and so we look for
+ 
+
+ align:start position:0%
+course and so we look for
+exponentials and the solution then would
+
+ align:start position:0%
+exponentials and the solution then would
+ 
+
+ align:start position:0%
+exponentials and the solution then would
+be two solutions are uh
+
+ align:start position:0%
+be two solutions are uh
+ 
+
+ align:start position:0%
+be two solutions are uh
+some there's a e to the I I guess I'm
+
+ align:start position:0%
+some there's a e to the I I guess I'm
+ 
+
+ align:start position:0%
+some there's a e to the I I guess I'm
+bringing back the i e e to the i c k t e
+
+ align:start position:0%
+bringing back the i e e to the i c k t e
+ 
+
+ align:start position:0%
+bringing back the i e e to the i c k t e
+to the I
+
+ align:start position:0%
+to the I
+ 
+
+ align:start position:0%
+to the I
+KX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and e to the minus i c k t e to the I
+
+ align:start position:0%
+and e to the minus i c k t e to the I
+ 
+
+ align:start position:0%
+and e to the minus i c k t e to the I
+KX so those are the two possible
+
+ align:start position:0%
+KX so those are the two possible
+ 
+
+ align:start position:0%
+KX so those are the two possible
+G's those are
+
+ align:start position:0%
+G's those are
+ 
+
+ align:start position:0%
+G's those are
+the those are if we take their second
+
+ align:start position:0%
+the those are if we take their second
+ 
+
+ align:start position:0%
+the those are if we take their second
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+derivative we get uh uh the same as
+
+ align:start position:0%
+derivative we get uh uh the same as
+ 
+
+ align:start position:0%
+derivative we get uh uh the same as
+taking the second X derivative there
+
+ align:start position:0%
+taking the second X derivative there
+ 
+
+ align:start position:0%
+taking the second X derivative there
+well we get the factor C is in the right
+
+ align:start position:0%
+well we get the factor C is in the right
+ 
+
+ align:start position:0%
+well we get the factor C is in the right
+place you you see it the second time
+
+ align:start position:0%
+place you you see it the second time
+ 
+
+ align:start position:0%
+place you you see it the second time
+derivative brings this Factor down just
+
+ align:start position:0%
+derivative brings this Factor down just
+ 
+
+ align:start position:0%
+derivative brings this Factor down just
+as we wanted but the point is that there
+
+ align:start position:0%
+as we wanted but the point is that there
+ 
+
+ align:start position:0%
+as we wanted but the point is that there
+are two of them there's a so this this I
+
+ align:start position:0%
+are two of them there's a so this this I
+ 
+
+ align:start position:0%
+are two of them there's a so this this I
+can write as e to the i k x minus C X
+
+ align:start position:0%
+can write as e to the i k x minus C X
+ 
+
+ align:start position:0%
+can write as e to the i k x minus C X
+Plus CT that's our old
+
+ align:start position:0%
+Plus CT that's our old
+ 
+
+ align:start position:0%
+Plus CT that's our old
+friend and this one I can write right as
+
+ align:start position:0%
+friend and this one I can write right as
+ 
+
+ align:start position:0%
+friend and this one I can write right as
+e to the i k xus
+
+ align:start position:0%
+e to the i k xus
+ 
+
+ align:start position:0%
+e to the i k xus
+CT which is our new friend the new wave
+
+ align:start position:0%
+CT which is our new friend the new wave
+ 
+
+ align:start position:0%
+CT which is our new friend the new wave
+the wave that's going to the right so
+
+ align:start position:0%
+the wave that's going to the right so
+ 
+
+ align:start position:0%
+the wave that's going to the right so
+this is a this X Plus CT is follows the
+
+ align:start position:0%
+this is a this X Plus CT is follows the
+ 
+
+ align:start position:0%
+this is a this X Plus CT is follows the
+characteristic lines to the left just
+
+ align:start position:0%
+characteristic lines to the left just
+ 
+
+ align:start position:0%
+characteristic lines to the left just
+the just the way we had in the oneway
+
+ align:start position:0%
+the just the way we had in the oneway
+ 
+
+ align:start position:0%
+the just the way we had in the oneway
+wave
+
+ align:start position:0%
+wave
+ 
+
+ align:start position:0%
+wave
+equation this x minus
+
+ align:start position:0%
+equation this x minus
+ 
+
+ align:start position:0%
+equation this x minus
+CT a con says constant on characteris
+
+ align:start position:0%
+CT a con says constant on characteris
+ 
+
+ align:start position:0%
+CT a con says constant on characteris
+itic lines going up to the
+
+ align:start position:0%
+itic lines going up to the
+ 
+
+ align:start position:0%
+itic lines going up to the
+right that it travels with speed
+
+ align:start position:0%
+right that it travels with speed
+ 
+
+ align:start position:0%
+right that it travels with speed
+C and uh the signal travels along those
+
+ align:start position:0%
+C and uh the signal travels along those
+ 
+
+ align:start position:0%
+C and uh the signal travels along those
+characteristics with speed C so that a
+
+ align:start position:0%
+characteristics with speed C so that a
+ 
+
+ align:start position:0%
+characteristics with speed C so that a
+an initial an initial value now maybe I
+
+ align:start position:0%
+an initial an initial value now maybe I
+ 
+
+ align:start position:0%
+an initial an initial value now maybe I
+draw draw a picture over
+
+ align:start position:0%
+draw draw a picture over
+ 
+
+ align:start position:0%
+draw draw a picture over
+here so here's T equals this is X as
+
+ align:start position:0%
+here so here's T equals this is X as
+ 
+
+ align:start position:0%
+here so here's T equals this is X as
+always this is Tal Z I have some initial
+
+ align:start position:0%
+always this is Tal Z I have some initial
+ 
+
+ align:start position:0%
+always this is Tal Z I have some initial
+value U at 0 0 and I also have an
+
+ align:start position:0%
+value U at 0 0 and I also have an
+ 
+
+ align:start position:0%
+value U at 0 0 and I also have an
+initial velocity because I'm
+
+ align:start position:0%
+initial velocity because I'm
+ 
+
+ align:start position:0%
+initial velocity because I'm
+in got a second order equation but
+
+ align:start position:0%
+in got a second order equation but
+ 
+
+ align:start position:0%
+in got a second order equation but
+information somehow pure exponential
+
+ align:start position:0%
+information somehow pure exponential
+ 
+
+ align:start position:0%
+information somehow pure exponential
+information travels along
+
+ align:start position:0%
+information travels along
+ 
+
+ align:start position:0%
+information travels along
+characteristics this way that's the new
+
+ align:start position:0%
+characteristics this way that's the new
+ 
+
+ align:start position:0%
+characteristics this way that's the new
+one and characteristics this way that's
+
+ align:start position:0%
+one and characteristics this way that's
+ 
+
+ align:start position:0%
+one and characteristics this way that's
+the old one this is this is time space
+
+ align:start position:0%
+the old one this is this is time space
+ 
+
+ align:start position:0%
+the old one this is this is time space
+I'm not graph I'm graphing the two
+
+ align:start position:0%
+I'm not graph I'm graphing the two
+ 
+
+ align:start position:0%
+I'm not graph I'm graphing the two
+characteristic lines now
+
+ align:start position:0%
+characteristic lines now
+ 
+
+ align:start position:0%
+characteristic lines now
+x minus CT equals well if it starts from
+
+ align:start position:0%
+x minus CT equals well if it starts from
+ 
+
+ align:start position:0%
+x minus CT equals well if it starts from
+zero then it would be zero and this is
+
+ align:start position:0%
+zero then it would be zero and this is
+ 
+
+ align:start position:0%
+zero then it would be zero and this is
+the X Plus
+
+ align:start position:0%
+the X Plus
+ 
+
+ align:start position:0%
+the X Plus
+CT equals z the one we had before the
+
+ align:start position:0%
+CT equals z the one we had before the
+ 
+
+ align:start position:0%
+CT equals z the one we had before the
+two characteristic lines
+
+ align:start position:0%
+two characteristic lines
+ 
+
+ align:start position:0%
+two characteristic lines
+okay waves are going both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways right and now what we were able to
+
+ align:start position:0%
+ways right and now what we were able to
+ 
+
+ align:start position:0%
+ways right and now what we were able to
+do with the first order
+
+ align:start position:0%
+do with the first order
+ 
+
+ align:start position:0%
+do with the first order
+equation we even got
+
+ align:start position:0%
+equation we even got
+ 
+
+ align:start position:0%
+equation we even got
+uh a completely explicit solution to the
+
+ align:start position:0%
+uh a completely explicit solution to the
+ 
+
+ align:start position:0%
+uh a completely explicit solution to the
+to the one-way wave equation and we can
+
+ align:start position:0%
+to the one-way wave equation and we can
+ 
+
+ align:start position:0%
+to the one-way wave equation and we can
+do the same for the two-way wave
+
+ align:start position:0%
+do the same for the two-way wave
+ 
+
+ align:start position:0%
+do the same for the two-way wave
+equation so I better write it down I
+
+ align:start position:0%
+equation so I better write it down I
+ 
+
+ align:start position:0%
+equation so I better write it down I
+better write down the solution so so let
+
+ align:start position:0%
+better write down the solution so so let
+ 
+
+ align:start position:0%
+better write down the solution so so let
+me just continue this same idea the
+
+ align:start position:0%
+me just continue this same idea the
+ 
+
+ align:start position:0%
+me just continue this same idea the
+general the complete
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution will be
+
+ align:start position:0%
+solution will be
+ 
+
+ align:start position:0%
+solution will be
+U of x and t is some function of x minus
+
+ align:start position:0%
+U of x and t is some function of x minus
+ 
+
+ align:start position:0%
+U of x and t is some function of x minus
+CT and some function of call it FS2 of x
+
+ align:start position:0%
+CT and some function of call it FS2 of x
+ 
+
+ align:start position:0%
+CT and some function of call it FS2 of x
++
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+CT oh not I've taken the
+
+ align:start position:0%
+CT oh not I've taken the
+ 
+
+ align:start position:0%
+CT oh not I've taken the
+jump the jump from one exponential a
+
+ align:start position:0%
+jump the jump from one exponential a
+ 
+
+ align:start position:0%
+jump the jump from one exponential a
+particular K that gave me these
+
+ align:start position:0%
+particular K that gave me these
+ 
+
+ align:start position:0%
+particular K that gave me these
+particular guys
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to all
+
+ align:start position:0%
+to all
+ 
+
+ align:start position:0%
+to all
+exponentials and assembling all
+
+ align:start position:0%
+exponentials and assembling all
+ 
+
+ align:start position:0%
+exponentials and assembling all
+exponentials into functions well so why
+
+ align:start position:0%
+exponentials into functions well so why
+ 
+
+ align:start position:0%
+exponentials into functions well so why
+is that okay it's only okay in this
+
+ align:start position:0%
+is that okay it's only okay in this
+ 
+
+ align:start position:0%
+is that okay it's only okay in this
+because of this very special situation
+
+ align:start position:0%
+because of this very special situation
+ 
+
+ align:start position:0%
+because of this very special situation
+that all frequencies are behaving the
+
+ align:start position:0%
+that all frequencies are behaving the
+ 
+
+ align:start position:0%
+that all frequencies are behaving the
+same here all
+
+ align:start position:0%
+same here all
+ 
+
+ align:start position:0%
+same here all
+frequencies I have no
+
+ align:start position:0%
+frequencies I have no
+ 
+
+ align:start position:0%
+frequencies I have no
+dispersion dispersion is is going to be
+
+ align:start position:0%
+dispersion dispersion is is going to be
+ 
+
+ align:start position:0%
+dispersion dispersion is is going to be
+different behavior of different
+
+ align:start position:0%
+different behavior of different
+ 
+
+ align:start position:0%
+different behavior of different
+frequencies so that's an important fact
+
+ align:start position:0%
+frequencies so that's an important fact
+ 
+
+ align:start position:0%
+frequencies so that's an important fact
+which we don't face
+
+ align:start position:0%
+which we don't face
+ 
+
+ align:start position:0%
+which we don't face
+here there will be dispersion in the
+
+ align:start position:0%
+here there will be dispersion in the
+ 
+
+ align:start position:0%
+here there will be dispersion in the
+discrete methods the semidiscrete and
+
+ align:start position:0%
+discrete methods the semidiscrete and
+ 
+
+ align:start position:0%
+discrete methods the semidiscrete and
+the discret methods different
+
+ align:start position:0%
+the discret methods different
+ 
+
+ align:start position:0%
+the discret methods different
+frequencies will travel at different
+
+ align:start position:0%
+frequencies will travel at different
+ 
+
+ align:start position:0%
+frequencies will travel at different
+speeds and that's what produces the
+
+ align:start position:0%
+speeds and that's what produces the
+ 
+
+ align:start position:0%
+speeds and that's what produces the
+oscillating error whatever shape the
+
+ align:start position:0%
+oscillating error whatever shape the
+ 
+
+ align:start position:0%
+oscillating error whatever shape the
+error has is because different Ks are
+
+ align:start position:0%
+error has is because different Ks are
+ 
+
+ align:start position:0%
+error has is because different Ks are
+doing slightly different things as we'll
+
+ align:start position:0%
+doing slightly different things as we'll
+ 
+
+ align:start position:0%
+doing slightly different things as we'll
+see when we do the discrete ones
+
+ align:start position:0%
+see when we do the discrete ones
+ 
+
+ align:start position:0%
+see when we do the discrete ones
+but in the continuous case every K we
+
+ align:start position:0%
+but in the continuous case every K we
+ 
+
+ align:start position:0%
+but in the continuous case every K we
+have the same traveling either with
+
+ align:start position:0%
+have the same traveling either with
+ 
+
+ align:start position:0%
+have the same traveling either with
+speed C or minus C and therefore we put
+
+ align:start position:0%
+speed C or minus C and therefore we put
+ 
+
+ align:start position:0%
+speed C or minus C and therefore we put
+them all together and we have a whole
+
+ align:start position:0%
+them all together and we have a whole
+ 
+
+ align:start position:0%
+them all together and we have a whole
+function traveling with speed C or minus
+
+ align:start position:0%
+function traveling with speed C or minus
+ 
+
+ align:start position:0%
+function traveling with speed C or minus
+C and now we got two
+
+ align:start position:0%
+C and now we got two
+ 
+
+ align:start position:0%
+C and now we got two
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+functions and we have we have to match
+
+ align:start position:0%
+functions and we have we have to match
+ 
+
+ align:start position:0%
+functions and we have we have to match
+two initial conditions we have to match
+
+ align:start position:0%
+two initial conditions we have to match
+ 
+
+ align:start position:0%
+two initial conditions we have to match
+we have to we have to match a u of X and
+
+ align:start position:0%
+we have to we have to match a u of X and
+ 
+
+ align:start position:0%
+we have to we have to match a u of X and
+zero and and the time derivative has to
+
+ align:start position:0%
+zero and and the time derivative has to
+ 
+
+ align:start position:0%
+zero and and the time derivative has to
+match a UT of X and zero so these are
+
+ align:start position:0%
+match a UT of X and zero so these are
+ 
+
+ align:start position:0%
+match a UT of X and zero so these are
+the initial
+
+ align:start position:0%
+the initial
+ 
+
+ align:start position:0%
+the initial
+conditions and uh you just match them up
+
+ align:start position:0%
+conditions and uh you just match them up
+ 
+
+ align:start position:0%
+conditions and uh you just match them up
+and you find the answer so you discover
+
+ align:start position:0%
+and you find the answer so you discover
+ 
+
+ align:start position:0%
+and you find the answer so you discover
+what these functions really are and it
+
+ align:start position:0%
+what these functions really are and it
+ 
+
+ align:start position:0%
+what these functions really are and it
+turns out that I think we had you
+
+ align:start position:0%
+turns out that I think we had you
+ 
+
+ align:start position:0%
+turns out that I think we had you
+remember before we had a u of x + C T
+
+ align:start position:0%
+remember before we had a u of x + C T
+ 
+
+ align:start position:0%
+remember before we had a u of x + C T
+and zero that was our that was
+
+ align:start position:0%
+and zero that was our that was
+ 
+
+ align:start position:0%
+and zero that was our that was
+everything in the
+
+ align:start position:0%
+everything in the
+ 
+
+ align:start position:0%
+everything in the
+solution to the oneway wave equation now
+
+ align:start position:0%
+solution to the oneway wave equation now
+ 
+
+ align:start position:0%
+solution to the oneway wave equation now
+we will have U of x minus
+
+ align:start position:0%
+we will have U of x minus
+ 
+
+ align:start position:0%
+we will have U of x minus
+ct0 and this divided by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two so there you see a waves going each
+
+ align:start position:0%
+two so there you see a waves going each
+ 
+
+ align:start position:0%
+two so there you see a waves going each
+way and the division by two makes us ma
+
+ align:start position:0%
+way and the division by two makes us ma
+ 
+
+ align:start position:0%
+way and the division by two makes us ma
+now we're matching the initial
+
+ align:start position:0%
+now we're matching the initial
+ 
+
+ align:start position:0%
+now we're matching the initial
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+so that would be the total answer if
+
+ align:start position:0%
+so that would be the total answer if
+ 
+
+ align:start position:0%
+so that would be the total answer if
+the equation if this if the body starts
+
+ align:start position:0%
+the equation if this if the body starts
+ 
+
+ align:start position:0%
+the equation if this if the body starts
+from rest with zero velocity but I
+
+ align:start position:0%
+from rest with zero velocity but I
+ 
+
+ align:start position:0%
+from rest with zero velocity but I
+haven't
+
+ align:start position:0%
+haven't
+ 
+
+ align:start position:0%
+haven't
+matched so I've only matched dudt equals
+
+ align:start position:0%
+matched so I've only matched dudt equals
+ 
+
+ align:start position:0%
+matched so I've only matched dudt equals
+z I think the time derivative of that
+
+ align:start position:0%
+z I think the time derivative of that
+ 
+
+ align:start position:0%
+z I think the time derivative of that
+would be zero yeah because the time
+
+ align:start position:0%
+would be zero yeah because the time
+ 
+
+ align:start position:0%
+would be zero yeah because the time
+derivative this would bring out a c this
+
+ align:start position:0%
+derivative this would bring out a c this
+ 
+
+ align:start position:0%
+derivative this would bring out a c this
+would bring out a minus C and at T
+
+ align:start position:0%
+would bring out a minus C and at T
+ 
+
+ align:start position:0%
+would bring out a minus C and at T
+equals z they'd cancel so I need
+
+ align:start position:0%
+equals z they'd cancel so I need
+ 
+
+ align:start position:0%
+equals z they'd cancel so I need
+uh another term and it turns out to be
+
+ align:start position:0%
+uh another term and it turns out to be
+ 
+
+ align:start position:0%
+uh another term and it turns out to be
+I'll just write it down it's got to
+
+ align:start position:0%
+I'll just write it down it's got to
+ 
+
+ align:start position:0%
+I'll just write it down it's got to
+depend on x minus CT and X+ CT and it's
+
+ align:start position:0%
+depend on x minus CT and X+ CT and it's
+ 
+
+ align:start position:0%
+depend on x minus CT and X+ CT and it's
+this it's the integral of this
+
+ align:start position:0%
+this it's the integral of this
+ 
+
+ align:start position:0%
+this it's the integral of this
+velocity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX all right well there's no reason to
+
+ align:start position:0%
+DX all right well there's no reason to
+ 
+
+ align:start position:0%
+DX all right well there's no reason to
+take time to derive that I think it's
+
+ align:start position:0%
+take time to derive that I think it's
+ 
+
+ align:start position:0%
+take time to derive that I think it's
+right and good check it
+
+ align:start position:0%
+right and good check it
+ 
+
+ align:start position:0%
+right and good check it
+right so what this means is that the
+
+ align:start position:0%
+right so what this means is that the
+ 
+
+ align:start position:0%
+right so what this means is that the
+initial velocity is
+
+ align:start position:0%
+initial velocity is
+ 
+
+ align:start position:0%
+initial velocity is
+uh uh yeah it it's entering somehow all
+
+ align:start position:0%
+uh uh yeah it it's entering somehow all
+ 
+
+ align:start position:0%
+uh uh yeah it it's entering somehow all
+along somehow the initial velocity is is
+
+ align:start position:0%
+along somehow the initial velocity is is
+ 
+
+ align:start position:0%
+along somehow the initial velocity is is
+affecting
+
+ align:start position:0%
+affecting
+ 
+
+ align:start position:0%
+affecting
+uh things within within
+
+ align:start position:0%
+uh things within within
+ 
+
+ align:start position:0%
+uh things within within
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+cone this characteristic cone of uh
+
+ align:start position:0%
+cone this characteristic cone of uh
+ 
+
+ align:start position:0%
+cone this characteristic cone of uh
+that's that's uh defined by the
+
+ align:start position:0%
+that's that's uh defined by the
+ 
+
+ align:start position:0%
+that's that's uh defined by the
+characteristic
+
+ align:start position:0%
+characteristic
+ 
+
+ align:start position:0%
+characteristic
+lines and in two Dimensions that cone
+
+ align:start position:0%
+lines and in two Dimensions that cone
+ 
+
+ align:start position:0%
+lines and in two Dimensions that cone
+will really look like a cone it'll look
+
+ align:start position:0%
+will really look like a cone it'll look
+ 
+
+ align:start position:0%
+will really look like a cone it'll look
+like an ice cream cone or maybe that's
+
+ align:start position:0%
+like an ice cream cone or maybe that's
+ 
+
+ align:start position:0%
+like an ice cream cone or maybe that's
+in three
+
+ align:start position:0%
+in three
+ 
+
+ align:start position:0%
+in three
+dimensions yeah
+
+ align:start position:0%
+dimensions yeah
+ 
+
+ align:start position:0%
+dimensions yeah
+whatever the in other words uh if the
+
+ align:start position:0%
+whatever the in other words uh if the
+ 
+
+ align:start position:0%
+whatever the in other words uh if the
+initial condition was a Delta function
+
+ align:start position:0%
+initial condition was a Delta function
+ 
+
+ align:start position:0%
+initial condition was a Delta function
+at the
+
+ align:start position:0%
+at the
+ 
+
+ align:start position:0%
+at the
+origin you could quickly see what the
+
+ align:start position:0%
+origin you could quickly see what the
+ 
+
+ align:start position:0%
+origin you could quickly see what the
+solution would
+
+ align:start position:0%
+solution would
+ 
+
+ align:start position:0%
+solution would
+be and if the Delta if the initial
+
+ align:start position:0%
+be and if the Delta if the initial
+ 
+
+ align:start position:0%
+be and if the Delta if the initial
+condition was a step function at the
+
+ align:start position:0%
+condition was a step function at the
+ 
+
+ align:start position:0%
+condition was a step function at the
+origin what would happen then suppose I
+
+ align:start position:0%
+origin what would happen then suppose I
+ 
+
+ align:start position:0%
+origin what would happen then suppose I
+start with a step function at the
+
+ align:start position:0%
+start with a step function at the
+ 
+
+ align:start position:0%
+start with a step function at the
+origin so like a wall of
+
+ align:start position:0%
+origin so like a wall of
+ 
+
+ align:start position:0%
+origin so like a wall of
+water and suppose it's at rest so it
+
+ align:start position:0%
+water and suppose it's at rest so it
+ 
+
+ align:start position:0%
+water and suppose it's at rest so it
+nothing it it's at at moment T equals
+
+ align:start position:0%
+nothing it it's at at moment T equals
+ 
+
+ align:start position:0%
+nothing it it's at at moment T equals
+zero I remove the
+
+ align:start position:0%
+zero I remove the
+ 
+
+ align:start position:0%
+zero I remove the
+dam and the water
+
+ align:start position:0%
+dam and the water
+ 
+
+ align:start position:0%
+dam and the water
+starts water flows then this term is
+
+ align:start position:0%
+starts water flows then this term is
+ 
+
+ align:start position:0%
+starts water flows then this term is
+zero because there was no initial
+
+ align:start position:0%
+zero because there was no initial
+ 
+
+ align:start position:0%
+zero because there was no initial
+velocity and this term is just half of
+
+ align:start position:0%
+velocity and this term is just half of
+ 
+
+ align:start position:0%
+velocity and this term is just half of
+that wall goes one way and half goes the
+
+ align:start position:0%
+that wall goes one way and half goes the
+ 
+
+ align:start position:0%
+that wall goes one way and half goes the
+other way and the the notes draw a
+
+ align:start position:0%
+other way and the the notes draw a
+ 
+
+ align:start position:0%
+other way and the the notes draw a
+picture of that solution yeah so
+
+ align:start position:0%
+picture of that solution yeah so
+ 
+
+ align:start position:0%
+picture of that solution yeah so
+that's okay I've kind of quickly
+
+ align:start position:0%
+that's okay I've kind of quickly
+ 
+
+ align:start position:0%
+that's okay I've kind of quickly
+disposed of
+
+ align:start position:0%
+disposed of
+ 
+
+ align:start position:0%
+disposed of
+the the solution of the wave
+
+ align:start position:0%
+the the solution of the wave
+ 
+
+ align:start position:0%
+the the solution of the wave
+equation and of course you know that
+
+ align:start position:0%
+equation and of course you know that
+ 
+
+ align:start position:0%
+equation and of course you know that
+that's too too easy this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh I mean that's good to know and good
+
+ align:start position:0%
+uh I mean that's good to know and good
+ 
+
+ align:start position:0%
+uh I mean that's good to know and good
+to compare when we meet real problems
+
+ align:start position:0%
+to compare when we meet real problems
+ 
+
+ align:start position:0%
+to compare when we meet real problems
+where C depends on X where there's a
+
+ align:start position:0%
+where C depends on X where there's a
+ 
+
+ align:start position:0%
+where C depends on X where there's a
+forcing term where there where there's
+
+ align:start position:0%
+forcing term where there where there's
+ 
+
+ align:start position:0%
+forcing term where there where there's
+real complications okay and but it's
+
+ align:start position:0%
+real complications okay and but it's
+ 
+
+ align:start position:0%
+real complications okay and but it's
+it's just pce to stay with the model
+
+ align:start position:0%
+it's just pce to stay with the model
+ 
+
+ align:start position:0%
+it's just pce to stay with the model
+problems for the at the beginning so I'm
+
+ align:start position:0%
+problems for the at the beginning so I'm
+ 
+
+ align:start position:0%
+problems for the at the beginning so I'm
+I'm going to stay with the model problem
+
+ align:start position:0%
+I'm going to stay with the model problem
+ 
+
+ align:start position:0%
+I'm going to stay with the model problem
+and move on
+
+ align:start position:0%
+and move on
+ 
+
+ align:start position:0%
+and move on
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+um discreet so so try to understand let
+
+ align:start position:0%
+um discreet so so try to understand let
+ 
+
+ align:start position:0%
+um discreet so so try to understand let
+me try to understand what happens if I
+
+ align:start position:0%
+me try to understand what happens if I
+ 
+
+ align:start position:0%
+me try to understand what happens if I
+make the space variable
+
+ align:start position:0%
+make the space variable
+ 
+
+ align:start position:0%
+make the space variable
+discret right yeah this is
+
+ align:start position:0%
+discret right yeah this is
+ 
+
+ align:start position:0%
+discret right yeah this is
+a oh I guess I should
+
+ align:start position:0%
+a oh I guess I should
+ 
+
+ align:start position:0%
+a oh I guess I should
+say another step toward reality would be
+
+ align:start position:0%
+say another step toward reality would be
+ 
+
+ align:start position:0%
+say another step toward reality would be
+have some
+
+ align:start position:0%
+have some
+ 
+
+ align:start position:0%
+have some
+boundaries I uh here this is on the
+
+ align:start position:0%
+boundaries I uh here this is on the
+ 
+
+ align:start position:0%
+boundaries I uh here this is on the
+whole line X from minus infinity to
+
+ align:start position:0%
+whole line X from minus infinity to
+ 
+
+ align:start position:0%
+whole line X from minus infinity to
+Infinity so reality would be that there
+
+ align:start position:0%
+Infinity so reality would be that there
+ 
+
+ align:start position:0%
+Infinity so reality would be that there
+would be this picture would have some
+
+ align:start position:0%
+would be this picture would have some
+ 
+
+ align:start position:0%
+would be this picture would have some
+boundary maybe
+
+ align:start position:0%
+boundary maybe
+ 
+
+ align:start position:0%
+boundary maybe
+there at say minus L and
+
+ align:start position:0%
+there at say minus L and
+ 
+
+ align:start position:0%
+there at say minus L and
+L and some boundary conditions there and
+
+ align:start position:0%
+L and some boundary conditions there and
+ 
+
+ align:start position:0%
+L and some boundary conditions there and
+on that
+
+ align:start position:0%
+on that
+ 
+
+ align:start position:0%
+on that
+boundary and that
+
+ align:start position:0%
+boundary and that
+ 
+
+ align:start position:0%
+boundary and that
+so now we have a finite problem that
+
+ align:start position:0%
+so now we have a finite problem that
+ 
+
+ align:start position:0%
+so now we have a finite problem that
+means the calculations are fine but it
+
+ align:start position:0%
+means the calculations are fine but it
+ 
+
+ align:start position:0%
+means the calculations are fine but it
+means some new effects are coming in
+
+ align:start position:0%
+means some new effects are coming in
+ 
+
+ align:start position:0%
+means some new effects are coming in
+waves can bounce back off the boundary
+
+ align:start position:0%
+waves can bounce back off the boundary
+ 
+
+ align:start position:0%
+waves can bounce back off the boundary
+partly they
+
+ align:start position:0%
+partly they
+ 
+
+ align:start position:0%
+partly they
+can go out be be lost go beyond go
+
+ align:start position:0%
+can go out be be lost go beyond go
+ 
+
+ align:start position:0%
+can go out be be lost go beyond go
+beyond or or or disappear depending what
+
+ align:start position:0%
+beyond or or or disappear depending what
+ 
+
+ align:start position:0%
+beyond or or or disappear depending what
+the boundary conditions are so that's
+
+ align:start position:0%
+the boundary conditions are so that's
+ 
+
+ align:start position:0%
+the boundary conditions are so that's
+another part of reality is boundary
+
+ align:start position:0%
+another part of reality is boundary
+ 
+
+ align:start position:0%
+another part of reality is boundary
+conditions I I I'm probably suggesting
+
+ align:start position:0%
+conditions I I I'm probably suggesting
+ 
+
+ align:start position:0%
+conditions I I I'm probably suggesting
+then some
+
+ align:start position:0%
+then some
+ 
+
+ align:start position:0%
+then some
+uh uh more realistic numerical
+
+ align:start position:0%
+uh uh more realistic numerical
+ 
+
+ align:start position:0%
+uh uh more realistic numerical
+experiments so a realistic numerical
+
+ align:start position:0%
+experiments so a realistic numerical
+ 
+
+ align:start position:0%
+experiments so a realistic numerical
+experiment would be put in some
+
+ align:start position:0%
+experiment would be put in some
+ 
+
+ align:start position:0%
+experiment would be put in some
+boundaries make this a finite
+
+ align:start position:0%
+boundaries make this a finite
+ 
+
+ align:start position:0%
+boundaries make this a finite
+system so so if that's zero let's let's
+
+ align:start position:0%
+system so so if that's zero let's let's
+ 
+
+ align:start position:0%
+system so so if that's zero let's let's
+just have a finite number and stop there
+
+ align:start position:0%
+just have a finite number and stop there
+ 
+
+ align:start position:0%
+just have a finite number and stop there
+this is this would be one boundary this
+
+ align:start position:0%
+this is this would be one boundary this
+ 
+
+ align:start position:0%
+this is this would be one boundary this
+would be the other then have just like
+
+ align:start position:0%
+would be the other then have just like
+ 
+
+ align:start position:0%
+would be the other then have just like
+seven unknowns in that problem there' be
+
+ align:start position:0%
+seven unknowns in that problem there' be
+ 
+
+ align:start position:0%
+seven unknowns in that problem there' be
+a 7 by seven Matrix over there and it
+
+ align:start position:0%
+a 7 by seven Matrix over there and it
+ 
+
+ align:start position:0%
+a 7 by seven Matrix over there and it
+would be the second difference Matrix
+
+ align:start position:0%
+would be the second difference Matrix
+ 
+
+ align:start position:0%
+would be the second difference Matrix
+that uh was so fundamental in uh is so
+
+ align:start position:0%
+that uh was so fundamental in uh is so
+ 
+
+ align:start position:0%
+that uh was so fundamental in uh is so
+fundamental in uh all of uh scientific
+
+ align:start position:0%
+fundamental in uh all of uh scientific
+ 
+
+ align:start position:0%
+fundamental in uh all of uh scientific
+Computing so we have here a second
+
+ align:start position:0%
+Computing so we have here a second
+ 
+
+ align:start position:0%
+Computing so we have here a second
+difference Matrix but it's infinite
+
+ align:start position:0%
+difference Matrix but it's infinite
+ 
+
+ align:start position:0%
+difference Matrix but it's infinite
+because because I haven't got a boundary
+
+ align:start position:0%
+because because I haven't got a boundary
+ 
+
+ align:start position:0%
+because because I haven't got a boundary
+right now so that that the fact of not
+
+ align:start position:0%
+right now so that that the fact of not
+ 
+
+ align:start position:0%
+right now so that that the fact of not
+having a boundary means forier is ready
+
+ align:start position:0%
+having a boundary means forier is ready
+ 
+
+ align:start position:0%
+having a boundary means forier is ready
+to go so I'm going to plug in I'm going
+
+ align:start position:0%
+to go so I'm going to plug in I'm going
+ 
+
+ align:start position:0%
+to go so I'm going to plug in I'm going
+to again I'm going to try
+
+ align:start position:0%
+to again I'm going to try
+ 
+
+ align:start position:0%
+to again I'm going to try
+U this is capital u now because I've
+
+ align:start position:0%
+U this is capital u now because I've
+ 
+
+ align:start position:0%
+U this is capital u now because I've
+discretized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something and uh oh I better write this
+
+ align:start position:0%
+something and uh oh I better write this
+ 
+
+ align:start position:0%
+something and uh oh I better write this
+in a in a form where we see the J so can
+
+ align:start position:0%
+in a in a form where we see the J so can
+ 
+
+ align:start position:0%
+in a in a form where we see the J so can
+I write this equation just again for U
+
+ align:start position:0%
+I write this equation just again for U
+ 
+
+ align:start position:0%
+I write this equation just again for U
+number J so tracking up this line for
+
+ align:start position:0%
+number J so tracking up this line for
+ 
+
+ align:start position:0%
+number J so tracking up this line for
+example or this one so I'm tracking up
+
+ align:start position:0%
+example or this one so I'm tracking up
+ 
+
+ align:start position:0%
+example or this one so I'm tracking up
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+line you see that U is now a system in
+
+ align:start position:0%
+line you see that U is now a system in
+ 
+
+ align:start position:0%
+line you see that U is now a system in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+case uh let's see I shouldn't have put
+
+ align:start position:0%
+case uh let's see I shouldn't have put
+ 
+
+ align:start position:0%
+case uh let's see I shouldn't have put
+this one in so that I'd have 1 two 3
+
+ align:start position:0%
+this one in so that I'd have 1 two 3
+ 
+
+ align:start position:0%
+this one in so that I'd have 1 two 3
+four five six seven that's good yep
+
+ align:start position:0%
+four five six seven that's good yep
+ 
+
+ align:start position:0%
+four five six seven that's good yep
+so so my unknowns are UJ tracking up
+
+ align:start position:0%
+so so my unknowns are UJ tracking up
+ 
+
+ align:start position:0%
+so so my unknowns are UJ tracking up
+that line
+
+ align:start position:0%
+that line
+ 
+
+ align:start position:0%
+that line
+each UJ is is is going in in the time
+
+ align:start position:0%
+each UJ is is is going in in the time
+ 
+
+ align:start position:0%
+each UJ is is is going in in the time
+Direction so my my so this equation is
+
+ align:start position:0%
+Direction so my my so this equation is
+ 
+
+ align:start position:0%
+Direction so my my so this equation is
+really uh the time
+
+ align:start position:0%
+really uh the time
+ 
+
+ align:start position:0%
+really uh the time
+derivative it's an ordinary
+
+ align:start position:0%
+derivative it's an ordinary
+ 
+
+ align:start position:0%
+derivative it's an ordinary
+derivative I can write D and not partial
+
+ align:start position:0%
+derivative I can write D and not partial
+ 
+
+ align:start position:0%
+derivative I can write D and not partial
+derivative because the only derivatives
+
+ align:start position:0%
+derivative because the only derivatives
+ 
+
+ align:start position:0%
+derivative because the only derivatives
+here are in time of
+
+ align:start position:0%
+here are in time of
+ 
+
+ align:start position:0%
+here are in time of
+UJ is c^2 over Delta
+
+ align:start position:0%
+UJ is c^2 over Delta
+ 
+
+ align:start position:0%
+UJ is c^2 over Delta
+x^2 time u j + 1 - 2 u
+
+ align:start position:0%
+x^2 time u j + 1 - 2 u
+ 
+
+ align:start position:0%
+x^2 time u j + 1 - 2 u
+j plus u j minus one that's my
+
+ align:start position:0%
+j plus u j minus one that's my
+ 
+
+ align:start position:0%
+j plus u j minus one that's my
+equation my system of equations sorry my
+
+ align:start position:0%
+equation my system of equations sorry my
+ 
+
+ align:start position:0%
+equation my system of equations sorry my
+system of
+
+ align:start position:0%
+system of
+ 
+
+ align:start position:0%
+system of
+equations and for the moment I'm
+
+ align:start position:0%
+equations and for the moment I'm
+ 
+
+ align:start position:0%
+equations and for the moment I'm
+thinking J goes from minus infinity to
+
+ align:start position:0%
+thinking J goes from minus infinity to
+ 
+
+ align:start position:0%
+thinking J goes from minus infinity to
+Infinity I'm not going to put in a
+
+ align:start position:0%
+Infinity I'm not going to put in a
+ 
+
+ align:start position:0%
+Infinity I'm not going to put in a
+boundary okay but what I will do of
+
+ align:start position:0%
+boundary okay but what I will do of
+ 
+
+ align:start position:0%
+boundary okay but what I will do of
+course is try you
+
+ align:start position:0%
+course is try you
+ 
+
+ align:start position:0%
+course is try you
+UJ is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+some is some growth factor that J is a
+
+ align:start position:0%
+some is some growth factor that J is a
+ 
+
+ align:start position:0%
+some is some growth factor that J is a
+space is counting space steps so the
+
+ align:start position:0%
+space is counting space steps so the
+ 
+
+ align:start position:0%
+space is counting space steps so the
+growth factor is in time and it's
+
+ align:start position:0%
+growth factor is in time and it's
+ 
+
+ align:start position:0%
+growth factor is in time and it's
+continuous in time because time is
+
+ align:start position:0%
+continuous in time because time is
+ 
+
+ align:start position:0%
+continuous in time because time is
+continuous but
+
+ align:start position:0%
+continuous but
+ 
+
+ align:start position:0%
+continuous but
+it's it's always e to the i k j Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+right that's the right thing to plug in
+
+ align:start position:0%
+right that's the right thing to plug in
+ 
+
+ align:start position:0%
+right that's the right thing to plug in
+I mean I guess what we're what I'm
+
+ align:start position:0%
+I mean I guess what we're what I'm
+ 
+
+ align:start position:0%
+I mean I guess what we're what I'm
+really uh the reason for really doing
+
+ align:start position:0%
+really uh the reason for really doing
+ 
+
+ align:start position:0%
+really uh the reason for really doing
+this is just
+
+ align:start position:0%
+this is just
+ 
+
+ align:start position:0%
+this is just
+to reinforce the idea that trying a pure
+
+ align:start position:0%
+to reinforce the idea that trying a pure
+ 
+
+ align:start position:0%
+to reinforce the idea that trying a pure
+exponential is a good thing to do it's
+
+ align:start position:0%
+exponential is a good thing to do it's
+ 
+
+ align:start position:0%
+exponential is a good thing to do it's
+even a good thing to do with variable
+
+ align:start position:0%
+even a good thing to do with variable
+ 
+
+ align:start position:0%
+even a good thing to do with variable
+coefficients and and and real
+
+ align:start position:0%
+coefficients and and and real
+ 
+
+ align:start position:0%
+coefficients and and and real
+problems and it's absolutely a good
+
+ align:start position:0%
+problems and it's absolutely a good
+ 
+
+ align:start position:0%
+problems and it's absolutely a good
+thing to do with these model problems
+
+ align:start position:0%
+thing to do with these model problems
+ 
+
+ align:start position:0%
+thing to do with these model problems
+okay plug it in and what
+
+ align:start position:0%
+okay plug it in and what
+ 
+
+ align:start position:0%
+okay plug it in and what
+happens okay so the so I get G
+
+ align:start position:0%
+happens okay so the so I get G
+ 
+
+ align:start position:0%
+happens okay so the so I get G
+Prime Times the exponential but of
+
+ align:start position:0%
+Prime Times the exponential but of
+ 
+
+ align:start position:0%
+Prime Times the exponential but of
+course you know in advance I'm going to
+
+ align:start position:0%
+course you know in advance I'm going to
+ 
+
+ align:start position:0%
+course you know in advance I'm going to
+cancel that exponential is c^2 over
+
+ align:start position:0%
+cancel that exponential is c^2 over
+ 
+
+ align:start position:0%
+cancel that exponential is c^2 over
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+x^2 times what goes there what what will
+
+ align:start position:0%
+x^2 times what goes there what what will
+ 
+
+ align:start position:0%
+x^2 times what goes there what what will
+cancel the exponential so so I'm I'm
+
+ align:start position:0%
+cancel the exponential so so I'm I'm
+ 
+
+ align:start position:0%
+cancel the exponential so so I'm I'm
+imagining that exponential is far out
+
+ align:start position:0%
+imagining that exponential is far out
+ 
+
+ align:start position:0%
+imagining that exponential is far out
+but here it is a j + one so
+
+ align:start position:0%
+but here it is a j + one so
+ 
+
+ align:start position:0%
+but here it is a j + one so
+I I I've incremented J by one so that's
+
+ align:start position:0%
+I I I've incremented J by one so that's
+ 
+
+ align:start position:0%
+I I I've incremented J by one so that's
+is going to give me an e to the i k
+
+ align:start position:0%
+is going to give me an e to the i k
+ 
+
+ align:start position:0%
+is going to give me an e to the i k
+Delta X
+
+ align:start position:0%
+Delta X
+ 
+
+ align:start position:0%
+Delta X
+right here I haven't incremented it and
+
+ align:start position:0%
+right here I haven't incremented it and
+ 
+
+ align:start position:0%
+right here I haven't incremented it and
+here I've incremented it by minus one so
+
+ align:start position:0%
+here I've incremented it by minus one so
+ 
+
+ align:start position:0%
+here I've incremented it by minus one so
+that will give me an e to the minus i k
+
+ align:start position:0%
+that will give me an e to the minus i k
+ 
+
+ align:start position:0%
+that will give me an e to the minus i k
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X all times this same exponential which
+
+ align:start position:0%
+X all times this same exponential which
+ 
+
+ align:start position:0%
+X all times this same exponential which
+appeared there and appeared there and
+
+ align:start position:0%
+appeared there and appeared there and
+ 
+
+ align:start position:0%
+appeared there and appeared there and
+got cancelled so that that's it there
+
+ align:start position:0%
+got cancelled so that that's it there
+ 
+
+ align:start position:0%
+got cancelled so that that's it there
+gouble
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime oh there's got to be a G right
+
+ align:start position:0%
+Prime oh there's got to be a G right
+ 
+
+ align:start position:0%
+Prime oh there's got to be a G right
+there's a g
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here right right when I plugged in on
+
+ align:start position:0%
+here right right when I plugged in on
+ 
+
+ align:start position:0%
+here right right when I plugged in on
+the right hand side I got a g that was
+
+ align:start position:0%
+the right hand side I got a g that was
+ 
+
+ align:start position:0%
+the right hand side I got a g that was
+so uninteresting I lost it
+
+ align:start position:0%
+so uninteresting I lost it
+ 
+
+ align:start position:0%
+so uninteresting I lost it
+okay what
+
+ align:start position:0%
+okay what
+ 
+
+ align:start position:0%
+okay what
+does what's G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there I guess the main point to see is
+
+ align:start position:0%
+there I guess the main point to see is
+ 
+
+ align:start position:0%
+there I guess the main point to see is
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantity which is divided Delta x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+s which is coming because we have
+
+ align:start position:0%
+s which is coming because we have
+ 
+
+ align:start position:0%
+s which is coming because we have
+differences instead of derivatives when
+
+ align:start position:0%
+differences instead of derivatives when
+ 
+
+ align:start position:0%
+differences instead of derivatives when
+we had derivatives that quantity was c^2
+
+ align:start position:0%
+we had derivatives that quantity was c^2
+ 
+
+ align:start position:0%
+we had derivatives that quantity was c^2
+I K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or in other words minus c^2
+
+ align:start position:0%
+or in other words minus c^2
+ 
+
+ align:start position:0%
+or in other words minus c^2
+K2 that this was this was
+
+ align:start position:0%
+K2 that this was this was
+ 
+
+ align:start position:0%
+K2 that this was this was
+the the
+
+ align:start position:0%
+the the
+ 
+
+ align:start position:0%
+the the
+correct uh factor and this one is the
+
+ align:start position:0%
+correct uh factor and this one is the
+ 
+
+ align:start position:0%
+correct uh factor and this one is the
+discrete factor and and it's worth just
+
+ align:start position:0%
+discrete factor and and it's worth just
+ 
+
+ align:start position:0%
+discrete factor and and it's worth just
+paying a moment of attention to the to
+
+ align:start position:0%
+paying a moment of attention to the to
+ 
+
+ align:start position:0%
+paying a moment of attention to the to
+compare the
+
+ align:start position:0%
+compare the
+ 
+
+ align:start position:0%
+compare the
+two to compare the two okay okay where
+
+ align:start position:0%
+two to compare the two okay okay where
+ 
+
+ align:start position:0%
+two to compare the two okay okay where
+am I going to write that
+
+ align:start position:0%
+am I going to write that
+ 
+
+ align:start position:0%
+am I going to write that
+comparison I guess it's going to be on
+
+ align:start position:0%
+comparison I guess it's going to be on
+ 
+
+ align:start position:0%
+comparison I guess it's going to be on
+the board that's hidden so I'm going
+
+ align:start position:0%
+the board that's hidden so I'm going
+ 
+
+ align:start position:0%
+the board that's hidden so I'm going
+to can you try to remember that let me
+
+ align:start position:0%
+to can you try to remember that let me
+ 
+
+ align:start position:0%
+to can you try to remember that let me
+let me Focus just on this quantity for
+
+ align:start position:0%
+let me Focus just on this quantity for
+ 
+
+ align:start position:0%
+let me Focus just on this quantity for
+the minute or even just on this
+
+ align:start position:0%
+the minute or even just on this
+ 
+
+ align:start position:0%
+the minute or even just on this
+one just because we see it so many times
+
+ align:start position:0%
+one just because we see it so many times
+ 
+
+ align:start position:0%
+one just because we see it so many times
+because it's coming directly from second
+
+ align:start position:0%
+because it's coming directly from second
+ 
+
+ align:start position:0%
+because it's coming directly from second
+differences uh for the moment let me
+
+ align:start position:0%
+differences uh for the moment let me
+ 
+
+ align:start position:0%
+differences uh for the moment let me
+take K Delta X I'll just call it Theta
+
+ align:start position:0%
+take K Delta X I'll just call it Theta
+ 
+
+ align:start position:0%
+take K Delta X I'll just call it Theta
+it's some angle so can I just do a
+
+ align:start position:0%
+it's some angle so can I just do a
+ 
+
+ align:start position:0%
+it's some angle so can I just do a
+little bit of trig with this
+
+ align:start position:0%
+little bit of trig with this
+ 
+
+ align:start position:0%
+little bit of trig with this
+factor
+
+ align:start position:0%
+factor
+ 
+
+ align:start position:0%
+factor
+to minus 2 cos Theta let's see I'm gonna
+
+ align:start position:0%
+to minus 2 cos Theta let's see I'm gonna
+ 
+
+ align:start position:0%
+to minus 2 cos Theta let's see I'm gonna
+I'm going to bring out a minus sign so
+
+ align:start position:0%
+I'm going to bring out a minus sign so
+ 
+
+ align:start position:0%
+I'm going to bring out a minus sign so
+I'm going to I'm going to put plus signs
+
+ align:start position:0%
+I'm going to I'm going to put plus signs
+ 
+
+ align:start position:0%
+I'm going to I'm going to put plus signs
+on those and minus signs on those oh oh
+
+ align:start position:0%
+on those and minus signs on those oh oh
+ 
+
+ align:start position:0%
+on those and minus signs on those oh oh
+of course you see the main point of of
+
+ align:start position:0%
+of course you see the main point of of
+ 
+
+ align:start position:0%
+of course you see the main point of of
+course that e the plus something e to
+
+ align:start position:0%
+course that e the plus something e to
+ 
+
+ align:start position:0%
+course that e the plus something e to
+the I Theta and e to the minus I Theta
+
+ align:start position:0%
+the I Theta and e to the minus I Theta
+ 
+
+ align:start position:0%
+the I Theta and e to the minus I Theta
+combined to
+
+ align:start position:0%
+combined to
+ 
+
+ align:start position:0%
+combined to
+give 2 cos Theta right so that's the key
+
+ align:start position:0%
+give 2 cos Theta right so that's the key
+ 
+
+ align:start position:0%
+give 2 cos Theta right so that's the key
+simplification that's going to make this
+
+ align:start position:0%
+simplification that's going to make this
+ 
+
+ align:start position:0%
+simplification that's going to make this
+much neater so I have 2 cos Theta minus
+
+ align:start position:0%
+much neater so I have 2 cos Theta minus
+ 
+
+ align:start position:0%
+much neater so I have 2 cos Theta minus
+2 have 2 cos Theta minus 2 and if I
+
+ align:start position:0%
+2 have 2 cos Theta minus 2 and if I
+ 
+
+ align:start position:0%
+2 have 2 cos Theta minus 2 and if I
+bring out a minus sign I'll have 2 minus
+
+ align:start position:0%
+bring out a minus sign I'll have 2 minus
+ 
+
+ align:start position:0%
+bring out a minus sign I'll have 2 minus
+2 cos Theta and that's what I want to
+
+ align:start position:0%
+2 cos Theta and that's what I want to
+ 
+
+ align:start position:0%
+2 cos Theta and that's what I want to
+write I want to write 2us 2 cos Theta I
+
+ align:start position:0%
+write I want to write 2us 2 cos Theta I
+ 
+
+ align:start position:0%
+write I want to write 2us 2 cos Theta I
+just want to see what
+
+ align:start position:0%
+just want to see what
+ 
+
+ align:start position:0%
+just want to see what
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+what that's uh I want to see what that
+
+ align:start position:0%
+what that's uh I want to see what that
+ 
+
+ align:start position:0%
+what that's uh I want to see what that
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+is right so that brought out a minus
+
+ align:start position:0%
+is right so that brought out a minus
+ 
+
+ align:start position:0%
+is right so that brought out a minus
+sign just to match that minus
+
+ align:start position:0%
+sign just to match that minus
+ 
+
+ align:start position:0%
+sign just to match that minus
+sign and uh the C squs
+
+ align:start position:0%
+sign and uh the C squs
+ 
+
+ align:start position:0%
+sign and uh the C squs
+match but what's different is this K
+
+ align:start position:0%
+match but what's different is this K
+ 
+
+ align:start position:0%
+match but what's different is this K
+squar is now gone into this
+
+ align:start position:0%
+squar is now gone into this
+ 
+
+ align:start position:0%
+squar is now gone into this
+2- 2 cos K Delta X I'll write it divided
+
+ align:start position:0%
+2- 2 cos K Delta X I'll write it divided
+ 
+
+ align:start position:0%
+2- 2 cos K Delta X I'll write it divided
+by Delta
+
+ align:start position:0%
+by Delta
+ 
+
+ align:start position:0%
+by Delta
+X2 do you see that this
+
+ align:start position:0%
+X2 do you see that this
+ 
+
+ align:start position:0%
+X2 do you see that this
+is that's the change k^2 which is a
+
+ align:start position:0%
+is that's the change k^2 which is a
+ 
+
+ align:start position:0%
+is that's the change k^2 which is a
+positive quantity became this which is
+
+ align:start position:0%
+positive quantity became this which is
+ 
+
+ align:start position:0%
+positive quantity became this which is
+also a positive quantity 2 minus 2 cos
+
+ align:start position:0%
+also a positive quantity 2 minus 2 cos
+ 
+
+ align:start position:0%
+also a positive quantity 2 minus 2 cos
+Theta but it's not a pure K
+
+ align:start position:0%
+Theta but it's not a pure K
+ 
+
+ align:start position:0%
+Theta but it's not a pure K
+squ we are getting
+
+ align:start position:0%
+squ we are getting
+ 
+
+ align:start position:0%
+squ we are getting
+dispersion different
+
+ align:start position:0%
+dispersion different
+ 
+
+ align:start position:0%
+dispersion different
+frequencies are showing up inside the
+
+ align:start position:0%
+frequencies are showing up inside the
+ 
+
+ align:start position:0%
+frequencies are showing up inside the
+cosine and that's not a linear function
+
+ align:start position:0%
+cosine and that's not a linear function
+ 
+
+ align:start position:0%
+cosine and that's not a linear function
+so we're seeing uh we're seeing
+
+ align:start position:0%
+so we're seeing uh we're seeing
+ 
+
+ align:start position:0%
+so we're seeing uh we're seeing
+different frequencies going their own
+
+ align:start position:0%
+different frequencies going their own
+ 
+
+ align:start position:0%
+different frequencies going their own
+way in a more uh more interesting more
+
+ align:start position:0%
+way in a more uh more interesting more
+ 
+
+ align:start position:0%
+way in a more uh more interesting more
+way than just what we saw here with K
+
+ align:start position:0%
+way than just what we saw here with K
+ 
+
+ align:start position:0%
+way than just what we saw here with K
+squ and of course when we take the
+
+ align:start position:0%
+squ and of course when we take the
+ 
+
+ align:start position:0%
+squ and of course when we take the
+square root as we did here that produced
+
+ align:start position:0%
+square root as we did here that produced
+ 
+
+ align:start position:0%
+square root as we did here that produced
+linear in K and no dispersion and and
+
+ align:start position:0%
+linear in K and no dispersion and and
+ 
+
+ align:start position:0%
+linear in K and no dispersion and and
+uh something simple but here when we
+
+ align:start position:0%
+uh something simple but here when we
+ 
+
+ align:start position:0%
+uh something simple but here when we
+take the square root okay let's take
+
+ align:start position:0%
+take the square root okay let's take
+ 
+
+ align:start position:0%
+take the square root okay let's take
+let's get ready to take the square root
+
+ align:start position:0%
+let's get ready to take the square root
+ 
+
+ align:start position:0%
+let's get ready to take the square root
+how can we take the square root of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that by writing it as a
+
+ align:start position:0%
+that by writing it as a
+ 
+
+ align:start position:0%
+that by writing it as a
+square it's never it's it's never
+
+ align:start position:0%
+square it's never it's it's never
+ 
+
+ align:start position:0%
+square it's never it's it's never
+negative and if I use a little
+
+ align:start position:0%
+negative and if I use a little
+ 
+
+ align:start position:0%
+negative and if I use a little
+trigonometry so I'm just going to write
+
+ align:start position:0%
+trigonometry so I'm just going to write
+ 
+
+ align:start position:0%
+trigonometry so I'm just going to write
+it down this is
+
+ align:start position:0%
+it down this is
+ 
+
+ align:start position:0%
+it down this is
+four I think it's sin
+
+ align:start position:0%
+four I think it's sin
+ 
+
+ align:start position:0%
+four I think it's sin
+squared of theta over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 that's just handy
+
+ align:start position:0%
+2 that's just handy
+ 
+
+ align:start position:0%
+2 that's just handy
+fact it's handy because I can take its
+
+ align:start position:0%
+fact it's handy because I can take its
+ 
+
+ align:start position:0%
+fact it's handy because I can take its
+square root and really see what so Theta
+
+ align:start position:0%
+square root and really see what so Theta
+ 
+
+ align:start position:0%
+square root and really see what so Theta
+remember this Theta is standing for K
+
+ align:start position:0%
+remember this Theta is standing for K
+ 
+
+ align:start position:0%
+remember this Theta is standing for K
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X so then I should I want to divide it
+
+ align:start position:0%
+X so then I should I want to divide it
+ 
+
+ align:start position:0%
+X so then I should I want to divide it
+by Delta x^ s can I bring down that
+
+ align:start position:0%
+by Delta x^ s can I bring down that
+ 
+
+ align:start position:0%
+by Delta x^ s can I bring down that
+quantity just so you see it again so
+
+ align:start position:0%
+quantity just so you see it again so
+ 
+
+ align:start position:0%
+quantity just so you see it again so
+this was the 2 - 2 cos Theta with the
+
+ align:start position:0%
+this was the 2 - 2 cos Theta with the
+ 
+
+ align:start position:0%
+this was the 2 - 2 cos Theta with the
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+sign and dividing by Delta
+
+ align:start position:0%
+sign and dividing by Delta
+ 
+
+ align:start position:0%
+sign and dividing by Delta
+x^2 and that's so it was G Prime well
+
+ align:start position:0%
+x^2 and that's so it was G Prime well
+ 
+
+ align:start position:0%
+x^2 and that's so it was G Prime well
+let's just write it so I have G I'm now
+
+ align:start position:0%
+let's just write it so I have G I'm now
+ 
+
+ align:start position:0%
+let's just write it so I have G I'm now
+going to copy what i g Prime was the
+
+ align:start position:0%
+going to copy what i g Prime was the
+ 
+
+ align:start position:0%
+going to copy what i g Prime was the
+minus sign time the c^ 2 time this 4 sin
+
+ align:start position:0%
+minus sign time the c^ 2 time this 4 sin
+ 
+
+ align:start position:0%
+minus sign time the c^ 2 time this 4 sin
+SAR of K Delta X on 2 divided by Delta
+
+ align:start position:0%
+SAR of K Delta X on 2 divided by Delta
+ 
+
+ align:start position:0%
+SAR of K Delta X on 2 divided by Delta
+x^2 well maybe I'll put the Delta X2
+
+ align:start position:0%
+x^2 well maybe I'll put the Delta X2
+ 
+
+ align:start position:0%
+x^2 well maybe I'll put the Delta X2
+over over there where it kind of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+belongs
+
+ align:start position:0%
+belongs
+ 
+
+ align:start position:0%
+belongs
+okay times G always forgetting
+
+ align:start position:0%
+okay times G always forgetting
+ 
+
+ align:start position:0%
+okay times G always forgetting
+G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we we're just following the
+
+ align:start position:0%
+okay so we we're just following the
+ 
+
+ align:start position:0%
+okay so we we're just following the
+golden way here of plugging in an
+
+ align:start position:0%
+golden way here of plugging in an
+ 
+
+ align:start position:0%
+golden way here of plugging in an
+exponential and seeing what happens and
+
+ align:start position:0%
+exponential and seeing what happens and
+ 
+
+ align:start position:0%
+exponential and seeing what happens and
+what happens is pretty nice the solution
+
+ align:start position:0%
+what happens is pretty nice the solution
+ 
+
+ align:start position:0%
+what happens is pretty nice the solution
+we can we now know what the solutions
+
+ align:start position:0%
+we can we now know what the solutions
+ 
+
+ align:start position:0%
+we can we now know what the solutions
+are there'll be two solutions it's a
+
+ align:start position:0%
+are there'll be two solutions it's a
+ 
+
+ align:start position:0%
+are there'll be two solutions it's a
+linear problem so the solutions will be
+
+ align:start position:0%
+linear problem so the solutions will be
+ 
+
+ align:start position:0%
+linear problem so the solutions will be
+exponential in t so the solution the the
+
+ align:start position:0%
+exponential in t so the solution the the
+ 
+
+ align:start position:0%
+exponential in t so the solution the the
+the solutions will have a plus or minus
+
+ align:start position:0%
+the solutions will have a plus or minus
+ 
+
+ align:start position:0%
+the solutions will have a plus or minus
+I because it's a minus sign so G can I
+
+ align:start position:0%
+I because it's a minus sign so G can I
+ 
+
+ align:start position:0%
+I because it's a minus sign so G can I
+write it this way G of the solution to
+
+ align:start position:0%
+write it this way G of the solution to
+ 
+
+ align:start position:0%
+write it this way G of the solution to
+this or the two the two exponential
+
+ align:start position:0%
+this or the two the two exponential
+ 
+
+ align:start position:0%
+this or the two the two exponential
+Solutions will be
+
+ align:start position:0%
+Solutions will be
+ 
+
+ align:start position:0%
+Solutions will be
+e to the plus or minus and I'm going to
+
+ align:start position:0%
+e to the plus or minus and I'm going to
+ 
+
+ align:start position:0%
+e to the plus or minus and I'm going to
+take the square root I * C * the square
+
+ align:start position:0%
+take the square root I * C * the square
+ 
+
+ align:start position:0%
+take the square root I * C * the square
+root of this well actually not that's
+
+ align:start position:0%
+root of this well actually not that's
+ 
+
+ align:start position:0%
+root of this well actually not that's
+not so hard two that was our Point
+
+ align:start position:0%
+not so hard two that was our Point
+ 
+
+ align:start position:0%
+not so hard two that was our Point
+wasn't it sorry I forgot about that sin
+
+ align:start position:0%
+wasn't it sorry I forgot about that sin
+ 
+
+ align:start position:0%
+wasn't it sorry I forgot about that sin
+K Delta X over
+
+ align:start position:0%
+K Delta X over
+ 
+
+ align:start position:0%
+K Delta X over
+2 / deltax and look here here's
+
+ align:start position:0%
+2 / deltax and look here here's
+ 
+
+ align:start position:0%
+2 / deltax and look here here's
+something nice bring the two down there
+
+ align:start position:0%
+something nice bring the two down there
+ 
+
+ align:start position:0%
+something nice bring the two down there
+what it make it 1/2 in the denominator
+
+ align:start position:0%
+what it make it 1/2 in the denominator
+ 
+
+ align:start position:0%
+what it make it 1/2 in the denominator
+do you see what what this expression
+
+ align:start position:0%
+do you see what what this expression
+ 
+
+ align:start position:0%
+do you see what what this expression
+is actually do you know its
+
+ align:start position:0%
+is actually do you know its
+ 
+
+ align:start position:0%
+is actually do you know its
+name you know it's the sync function
+
+ align:start position:0%
+name you know it's the sync function
+ 
+
+ align:start position:0%
+name you know it's the sync function
+it's the sync function right and for
+
+ align:start position:0%
+it's the sync function right and for
+ 
+
+ align:start position:0%
+it's the sync function right and for
+very small Delta X oh times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T right it it's just we just have an
+
+ align:start position:0%
+T right it it's just we just have an
+ 
+
+ align:start position:0%
+T right it it's just we just have an
+exponential of course we do this was a
+
+ align:start position:0%
+exponential of course we do this was a
+ 
+
+ align:start position:0%
+exponential of course we do this was a
+constant coefficient problem in t so and
+
+ align:start position:0%
+constant coefficient problem in t so and
+ 
+
+ align:start position:0%
+constant coefficient problem in t so and
+of second order so I had two
+
+ align:start position:0%
+of second order so I had two
+ 
+
+ align:start position:0%
+of second order so I had two
+exponentials and I just took the square
+
+ align:start position:0%
+exponentials and I just took the square
+ 
+
+ align:start position:0%
+exponentials and I just took the square
+root of that coefficient put it there
+
+ align:start position:0%
+root of that coefficient put it there
+ 
+
+ align:start position:0%
+root of that coefficient put it there
+times T absolutely
+
+ align:start position:0%
+times T absolutely
+ 
+
+ align:start position:0%
+times T absolutely
+straightforward and now so everything is
+
+ align:start position:0%
+straightforward and now so everything is
+ 
+
+ align:start position:0%
+straightforward and now so everything is
+this this quantity is the is the key one
+
+ align:start position:0%
+this this quantity is the is the key one
+ 
+
+ align:start position:0%
+this this quantity is the is the key one
+and this is the quantity
+
+ align:start position:0%
+and this is the quantity
+ 
+
+ align:start position:0%
+and this is the quantity
+which for small
+
+ align:start position:0%
+which for small
+ 
+
+ align:start position:0%
+which for small
+K or small Delta
+
+ align:start position:0%
+K or small Delta
+ 
+
+ align:start position:0%
+K or small Delta
+X is approximately
+
+ align:start position:0%
+X is approximately
+ 
+
+ align:start position:0%
+X is approximately
+what so so if if if K and Delta X are
+
+ align:start position:0%
+what so so if if if K and Delta X are
+ 
+
+ align:start position:0%
+what so so if if if K and Delta X are
+small or if even just Delta X is small
+
+ align:start position:0%
+small or if even just Delta X is small
+ 
+
+ align:start position:0%
+small or if even just Delta X is small
+what does this sync function look like
+
+ align:start position:0%
+what does this sync function look like
+ 
+
+ align:start position:0%
+what does this sync function look like
+what is that ratio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximately when K is
+
+ align:start position:0%
+approximately when K is
+ 
+
+ align:start position:0%
+approximately when K is
+small well what does the s of theta look
+
+ align:start position:0%
+small well what does the s of theta look
+ 
+
+ align:start position:0%
+small well what does the s of theta look
+like when Theta is a small
+
+ align:start position:0%
+like when Theta is a small
+ 
+
+ align:start position:0%
+like when Theta is a small
+angle looks like Theta right
+
+ align:start position:0%
+angle looks like Theta right
+ 
+
+ align:start position:0%
+angle looks like Theta right
+sin Theta is about
+
+ align:start position:0%
+sin Theta is about
+ 
+
+ align:start position:0%
+sin Theta is about
+Theta so this thing is about K Delta x
+
+ align:start position:0%
+Theta so this thing is about K Delta x
+ 
+
+ align:start position:0%
+Theta so this thing is about K Delta x
+over2 / Delta it's K so it's
+
+ align:start position:0%
+over2 / Delta it's K so it's
+ 
+
+ align:start position:0%
+over2 / Delta it's K so it's
+approximately
+
+ align:start position:0%
+approximately
+ 
+
+ align:start position:0%
+approximately
+k for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+small Delta X let's say Delta X is small
+
+ align:start position:0%
+small Delta X let's say Delta X is small
+ 
+
+ align:start position:0%
+small Delta X let's say Delta X is small
+that's a right that's the key thing to
+
+ align:start position:0%
+that's a right that's the key thing to
+ 
+
+ align:start position:0%
+that's a right that's the key thing to
+know about the sync
+
+ align:start position:0%
+know about the sync
+ 
+
+ align:start position:0%
+know about the sync
+function that it it begins by
+
+ align:start position:0%
+function that it it begins by
+ 
+
+ align:start position:0%
+function that it it begins by
+approximating the sign function but then
+
+ align:start position:0%
+approximating the sign function but then
+ 
+
+ align:start position:0%
+approximating the sign function but then
+of course when K Delta X gets large it
+
+ align:start position:0%
+of course when K Delta X gets large it
+ 
+
+ align:start position:0%
+of course when K Delta X gets large it
+wanders away it's not linear in K see it
+
+ align:start position:0%
+wanders away it's not linear in K see it
+ 
+
+ align:start position:0%
+wanders away it's not linear in K see it
+starts out practically linear in K and
+
+ align:start position:0%
+starts out practically linear in K and
+ 
+
+ align:start position:0%
+starts out practically linear in K and
+that K is exactly the right K that's the
+
+ align:start position:0%
+that K is exactly the right K that's the
+ 
+
+ align:start position:0%
+that K is exactly the right K that's the
+right Factor that's the K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here but in the differential equation it
+
+ align:start position:0%
+here but in the differential equation it
+ 
+
+ align:start position:0%
+here but in the differential equation it
+stayed K and in the difference equation
+
+ align:start position:0%
+stayed K and in the difference equation
+ 
+
+ align:start position:0%
+stayed K and in the difference equation
+as k for K Delta X moving moving moving
+
+ align:start position:0%
+as k for K Delta X moving moving moving
+ 
+
+ align:start position:0%
+as k for K Delta X moving moving moving
+away it it changes and
+
+ align:start position:0%
+away it it changes and
+ 
+
+ align:start position:0%
+away it it changes and
+uh that's why well of course that's the
+
+ align:start position:0%
+uh that's why well of course that's the
+ 
+
+ align:start position:0%
+uh that's why well of course that's the
+source of the
+
+ align:start position:0%
+source of the
+ 
+
+ align:start position:0%
+source of the
+error and we're seeing now why the
+
+ align:start position:0%
+error and we're seeing now why the
+ 
+
+ align:start position:0%
+error and we're seeing now why the
+method is probably second order accuracy
+
+ align:start position:0%
+method is probably second order accuracy
+ 
+
+ align:start position:0%
+method is probably second order accuracy
+yeah we we know that these second
+
+ align:start position:0%
+yeah we we know that these second
+ 
+
+ align:start position:0%
+yeah we we know that these second
+differences are second give second order
+
+ align:start position:0%
+differences are second give second order
+ 
+
+ align:start position:0%
+differences are second give second order
+accuracy this would be if I looked at
+
+ align:start position:0%
+accuracy this would be if I looked at
+ 
+
+ align:start position:0%
+accuracy this would be if I looked at
+the next term what's the next term in
+
+ align:start position:0%
+the next term what's the next term in
+ 
+
+ align:start position:0%
+the next term what's the next term in
+sin Theta sin Theta starts out Theta and
+
+ align:start position:0%
+sin Theta sin Theta starts out Theta and
+ 
+
+ align:start position:0%
+sin Theta sin Theta starts out Theta and
+what's the what's the term after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that everybody's tailor series or
+
+ align:start position:0%
+that everybody's tailor series or
+ 
+
+ align:start position:0%
+that everybody's tailor series or
+huming Theta Cub it's a Theta Cub term
+
+ align:start position:0%
+huming Theta Cub it's a Theta Cub term
+ 
+
+ align:start position:0%
+huming Theta Cub it's a Theta Cub term
+ex exactly it's a minus Theta Cube over
+
+ align:start position:0%
+ex exactly it's a minus Theta Cube over
+ 
+
+ align:start position:0%
+ex exactly it's a minus Theta Cube over
+6 3 factorial but it's a Theta Cub term
+
+ align:start position:0%
+6 3 factorial but it's a Theta Cub term
+ 
+
+ align:start position:0%
+6 3 factorial but it's a Theta Cub term
+and and so the Theta gave us the right
+
+ align:start position:0%
+and and so the Theta gave us the right
+ 
+
+ align:start position:0%
+and and so the Theta gave us the right
+thing and then two more powers of theta
+
+ align:start position:0%
+thing and then two more powers of theta
+ 
+
+ align:start position:0%
+thing and then two more powers of theta
+will give us a second order error right
+
+ align:start position:0%
+will give us a second order error right
+ 
+
+ align:start position:0%
+will give us a second order error right
+okay okay I better move since so that's
+
+ align:start position:0%
+okay okay I better move since so that's
+ 
+
+ align:start position:0%
+okay okay I better move since so that's
+the story for semidiscrete
+
+ align:start position:0%
+the story for semidiscrete
+ 
+
+ align:start position:0%
+the story for semidiscrete
+semidiscrete produced a pure
+
+ align:start position:0%
+semidiscrete produced a pure
+ 
+
+ align:start position:0%
+semidiscrete produced a pure
+exponential but with
+
+ align:start position:0%
+exponential but with
+ 
+
+ align:start position:0%
+exponential but with
+u with a phase Factor you could
+
+ align:start position:0%
+u with a phase Factor you could
+ 
+
+ align:start position:0%
+u with a phase Factor you could
+say that that wasn't linear in K where
+
+ align:start position:0%
+say that that wasn't linear in K where
+ 
+
+ align:start position:0%
+say that that wasn't linear in K where
+the real one was okay
+
+ align:start position:0%
+the real one was okay
+ 
+
+ align:start position:0%
+the real one was okay
+now what about let me move up to that
+
+ align:start position:0%
+now what about let me move up to that
+ 
+
+ align:start position:0%
+now what about let me move up to that
+board
+
+ align:start position:0%
+board
+ 
+
+ align:start position:0%
+board
+above
+
+ align:start position:0%
+above
+ 
+
+ align:start position:0%
+above
+where now we're going to have we have it
+
+ align:start position:0%
+where now we're going to have we have it
+ 
+
+ align:start position:0%
+where now we're going to have we have it
+it's discrete in time as well so we're
+
+ align:start position:0%
+it's discrete in time as well so we're
+ 
+
+ align:start position:0%
+it's discrete in time as well so we're
+going to have single
+
+ align:start position:0%
+going to have single
+ 
+
+ align:start position:0%
+going to have single
+steps well what's going to be the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference again I'm going to try you
+
+ align:start position:0%
+difference again I'm going to try you
+ 
+
+ align:start position:0%
+difference again I'm going to try you
+know I only have one idea here
+
+ align:start position:0%
+know I only have one idea here
+ 
+
+ align:start position:0%
+know I only have one idea here
+ujn will be some G
+
+ align:start position:0%
+ujn will be some G
+ 
+
+ align:start position:0%
+ujn will be some G
+some growth factor times e to the
+
+ align:start position:0%
+some growth factor times e to the
+ 
+
+ align:start position:0%
+some growth factor times e to the
+i j k deltax just same I'm going to try
+
+ align:start position:0%
+i j k deltax just same I'm going to try
+ 
+
+ align:start position:0%
+i j k deltax just same I'm going to try
+an e to the I
+
+ align:start position:0%
+an e to the I
+ 
+
+ align:start position:0%
+an e to the I
+KX and in the space variable it will be
+
+ align:start position:0%
+KX and in the space variable it will be
+ 
+
+ align:start position:0%
+KX and in the space variable it will be
+G and oh and after n steps it'll be GN
+
+ align:start position:0%
+G and oh and after n steps it'll be GN
+ 
+
+ align:start position:0%
+G and oh and after n steps it'll be GN
+times so this is the discrete this is
+
+ align:start position:0%
+times so this is the discrete this is
+ 
+
+ align:start position:0%
+times so this is the discrete this is
+right this is the
+
+ align:start position:0%
+right this is the
+ 
+
+ align:start position:0%
+right this is the
+uh anzats to use a fancy word this is
+
+ align:start position:0%
+uh anzats to use a fancy word this is
+ 
+
+ align:start position:0%
+uh anzats to use a fancy word this is
+what you plug
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a little crazy to use the word anzats
+
+ align:start position:0%
+in a little crazy to use the word anzats
+ 
+
+ align:start position:0%
+in a little crazy to use the word anzats
+which sounds fancy and the word plug
+
+ align:start position:0%
+which sounds fancy and the word plug
+ 
+
+ align:start position:0%
+which sounds fancy and the word plug
+Which is far from fancy I should say
+
+ align:start position:0%
+Which is far from fancy I should say
+ 
+
+ align:start position:0%
+Which is far from fancy I should say
+substitute of course okay so substitute
+
+ align:start position:0%
+substitute of course okay so substitute
+ 
+
+ align:start position:0%
+substitute of course okay so substitute
+it in all right do we know what the
+
+ align:start position:0%
+it in all right do we know what the
+ 
+
+ align:start position:0%
+it in all right do we know what the
+process is going to do when I plug it in
+
+ align:start position:0%
+process is going to do when I plug it in
+ 
+
+ align:start position:0%
+process is going to do when I plug it in
+sorry substitute it in on the left we
+
+ align:start position:0%
+sorry substitute it in on the left we
+ 
+
+ align:start position:0%
+sorry substitute it in on the left we
+get and I'm going to cancel I'm going to
+
+ align:start position:0%
+get and I'm going to cancel I'm going to
+ 
+
+ align:start position:0%
+get and I'm going to cancel I'm going to
+cancel this
+
+ align:start position:0%
+cancel this
+ 
+
+ align:start position:0%
+cancel this
+from every
+
+ align:start position:0%
+from every
+ 
+
+ align:start position:0%
+from every
+term so all I'm interested in is the
+
+ align:start position:0%
+term so all I'm interested in is the
+ 
+
+ align:start position:0%
+term so all I'm interested in is the
+well maybe I'll cancel G to the N minus
+
+ align:start position:0%
+well maybe I'll cancel G to the N minus
+ 
+
+ align:start position:0%
+well maybe I'll cancel G to the N minus
+one so let me write down what I get this
+
+ align:start position:0%
+one so let me write down what I get this
+ 
+
+ align:start position:0%
+one so let me write down what I get this
+is going to give me in the time
+
+ align:start position:0%
+is going to give me in the time
+ 
+
+ align:start position:0%
+is going to give me in the time
+Direction I'll have a g s minus a 2 G +
+
+ align:start position:0%
+Direction I'll have a g s minus a 2 G +
+ 
+
+ align:start position:0%
+Direction I'll have a g s minus a 2 G +
+a 1 over Delta t^
+
+ align:start position:0%
+a 1 over Delta t^
+ 
+
+ align:start position:0%
+a 1 over Delta t^
+2 and in the space Direction which is at
+
+ align:start position:0%
+2 and in the space Direction which is at
+ 
+
+ align:start position:0%
+2 and in the space Direction which is at
+the centered time so it's going to
+
+ align:start position:0%
+the centered time so it's going to
+ 
+
+ align:start position:0%
+the centered time so it's going to
+multiply a g it's going to be my same my
+
+ align:start position:0%
+multiply a g it's going to be my same my
+ 
+
+ align:start position:0%
+multiply a g it's going to be my same my
+very same thing I could maybe give it a
+
+ align:start position:0%
+very same thing I could maybe give it a
+ 
+
+ align:start position:0%
+very same thing I could maybe give it a
+name here I I I don't know whether
+
+ align:start position:0%
+name here I I I don't know whether
+ 
+
+ align:start position:0%
+name here I I I don't know whether
+should I give it a name or I know what
+
+ align:start position:0%
+should I give it a name or I know what
+ 
+
+ align:start position:0%
+should I give it a name or I know what
+it is anyway because it's the same thing
+
+ align:start position:0%
+it is anyway because it's the same thing
+ 
+
+ align:start position:0%
+it is anyway because it's the same thing
+that I had in the in the semidiscrete
+
+ align:start position:0%
+that I had in the in the semidiscrete
+ 
+
+ align:start position:0%
+that I had in the in the semidiscrete
+method it's this uh uh yeah let let's
+
+ align:start position:0%
+method it's this uh uh yeah let let's
+ 
+
+ align:start position:0%
+method it's this uh uh yeah let let's
+see what it looked like at this point it
+
+ align:start position:0%
+see what it looked like at this point it
+ 
+
+ align:start position:0%
+see what it looked like at this point it
+was um yeah there so there's a c oh look
+
+ align:start position:0%
+was um yeah there so there's a c oh look
+ 
+
+ align:start position:0%
+was um yeah there so there's a c oh look
+look let's let's do one thing let's let
+
+ align:start position:0%
+look let's let's do one thing let's let
+ 
+
+ align:start position:0%
+look let's let's do one thing let's let
+me get this Delta t^2 up there times the
+
+ align:start position:0%
+me get this Delta t^2 up there times the
+ 
+
+ align:start position:0%
+me get this Delta t^2 up there times the
+c^2 / the Delta x^2 let me just clean up
+
+ align:start position:0%
+c^2 / the Delta x^2 let me just clean up
+ 
+
+ align:start position:0%
+c^2 / the Delta x^2 let me just clean up
+those constants
+
+ align:start position:0%
+those constants
+ 
+
+ align:start position:0%
+those constants
+so so that when I multiply up by the
+
+ align:start position:0%
+so so that when I multiply up by the
+ 
+
+ align:start position:0%
+so so that when I multiply up by the
+Delta t^ 2 times the c^ 2 / the Delta
+
+ align:start position:0%
+Delta t^ 2 times the c^ 2 / the Delta
+ 
+
+ align:start position:0%
+Delta t^ 2 times the c^ 2 / the Delta
+x^2 what's
+
+ align:start position:0%
+x^2 what's
+ 
+
+ align:start position:0%
+x^2 what's
+that c delta T over Delta x^2 is my old
+
+ align:start position:0%
+that c delta T over Delta x^2 is my old
+ 
+
+ align:start position:0%
+that c delta T over Delta x^2 is my old
+ratio the Quant number r squ
+
+ align:start position:0%
+ratio the Quant number r squ
+ 
+
+ align:start position:0%
+ratio the Quant number r squ
+and then it's
+
+ align:start position:0%
+and then it's
+ 
+
+ align:start position:0%
+and then it's
+this time G so this will all be just
+
+ align:start position:0%
+this time G so this will all be just
+ 
+
+ align:start position:0%
+this time G so this will all be just
+exactly the same and that's what I
+
+ align:start position:0%
+exactly the same and that's what I
+ 
+
+ align:start position:0%
+exactly the same and that's what I
+simplified here but well let me just
+
+ align:start position:0%
+simplified here but well let me just
+ 
+
+ align:start position:0%
+simplified here but well let me just
+leave it
+
+ align:start position:0%
+leave it
+ 
+
+ align:start position:0%
+leave it
+as uh with a minus let me remember that
+
+ align:start position:0%
+as uh with a minus let me remember that
+ 
+
+ align:start position:0%
+as uh with a minus let me remember that
+I did take a minus so that I could write
+
+ align:start position:0%
+I did take a minus so that I could write
+ 
+
+ align:start position:0%
+I did take a minus so that I could write
+it as 2 minus 2 cosine of K Delta X time
+
+ align:start position:0%
+it as 2 minus 2 cosine of K Delta X time
+ 
+
+ align:start position:0%
+it as 2 minus 2 cosine of K Delta X time
+G is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I really think I have kept track of
+
+ align:start position:0%
+I really think I have kept track of
+ 
+
+ align:start position:0%
+I really think I have kept track of
+everything here the r squar coming from
+
+ align:start position:0%
+everything here the r squar coming from
+ 
+
+ align:start position:0%
+everything here the r squar coming from
+all this stuff the
+
+ align:start position:0%
+all this stuff the
+ 
+
+ align:start position:0%
+all this stuff the
+minus two coming here and the plus two
+
+ align:start position:0%
+minus two coming here and the plus two
+ 
+
+ align:start position:0%
+minus two coming here and the plus two
+cosine coming from there you okay with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that but there's one new ingredient here
+
+ align:start position:0%
+that but there's one new ingredient here
+ 
+
+ align:start position:0%
+that but there's one new ingredient here
+and again G to the N I cancelled G to
+
+ align:start position:0%
+and again G to the N I cancelled G to
+ 
+
+ align:start position:0%
+and again G to the N I cancelled G to
+the n minus1 time this from every
+
+ align:start position:0%
+the n minus1 time this from every
+ 
+
+ align:start position:0%
+the n minus1 time this from every
+term okay so the new ingredient that we
+
+ align:start position:0%
+term okay so the new ingredient that we
+ 
+
+ align:start position:0%
+term okay so the new ingredient that we
+just have five minutes to deal
+
+ align:start position:0%
+just have five minutes to deal
+ 
+
+ align:start position:0%
+just have five minutes to deal
+with is the fact that we have second we
+
+ align:start position:0%
+with is the fact that we have second we
+ 
+
+ align:start position:0%
+with is the fact that we have second we
+have G squar is showed
+
+ align:start position:0%
+have G squar is showed
+ 
+
+ align:start position:0%
+have G squar is showed
+up so why did g squ show up because it's
+
+ align:start position:0%
+up so why did g squ show up because it's
+ 
+
+ align:start position:0%
+up so why did g squ show up because it's
+a two it's a multi-step
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method and therefore I've got two G's of
+
+ align:start position:0%
+method and therefore I've got two G's of
+ 
+
+ align:start position:0%
+method and therefore I've got two G's of
+course I had two G's in all these other
+
+ align:start position:0%
+course I had two G's in all these other
+ 
+
+ align:start position:0%
+course I had two G's in all these other
+cases because I had second derivatives
+
+ align:start position:0%
+cases because I had second derivatives
+ 
+
+ align:start position:0%
+cases because I had second derivatives
+and now I have second difference so I
+
+ align:start position:0%
+and now I have second difference so I
+ 
+
+ align:start position:0%
+and now I have second difference so I
+have two G's so I have to solve for G
+
+ align:start position:0%
+have two G's so I have to solve for G
+ 
+
+ align:start position:0%
+have two G's so I have to solve for G
+and and what is stability going to
+
+ align:start position:0%
+and and what is stability going to
+ 
+
+ align:start position:0%
+and and what is stability going to
+depend on stability is going to be
+
+ align:start position:0%
+depend on stability is going to be
+ 
+
+ align:start position:0%
+depend on stability is going to be
+whether
+
+ align:start position:0%
+whether
+ 
+
+ align:start position:0%
+whether
+G both G's because there two of them now
+
+ align:start position:0%
+G both G's because there two of them now
+ 
+
+ align:start position:0%
+G both G's because there two of them now
+are less or equal one that that's what I
+
+ align:start position:0%
+are less or equal one that that's what I
+ 
+
+ align:start position:0%
+are less or equal one that that's what I
+have to check and and that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation and what do we
+
+ align:start position:0%
+equation and what do we
+ 
+
+ align:start position:0%
+equation and what do we
+figure we figure that if R is pretty big
+
+ align:start position:0%
+figure we figure that if R is pretty big
+ 
+
+ align:start position:0%
+figure we figure that if R is pretty big
+if R is big no way if R is Big the Quant
+
+ align:start position:0%
+if R is big no way if R is Big the Quant
+ 
+
+ align:start position:0%
+if R is big no way if R is Big the Quant
+test will
+
+ align:start position:0%
+test will
+ 
+
+ align:start position:0%
+test will
+fail and stability will fail but if R is
+
+ align:start position:0%
+fail and stability will fail but if R is
+ 
+
+ align:start position:0%
+fail and stability will fail but if R is
+small then I expect I have a right to
+
+ align:start position:0%
+small then I expect I have a right to
+ 
+
+ align:start position:0%
+small then I expect I have a right to
+hope for stability so it's going to be
+
+ align:start position:0%
+hope for stability so it's going to be
+ 
+
+ align:start position:0%
+hope for stability so it's going to be
+the size of R okay so I just have to
+
+ align:start position:0%
+the size of R okay so I just have to
+ 
+
+ align:start position:0%
+the size of R okay so I just have to
+I've got this quadratic equation I'm
+
+ align:start position:0%
+I've got this quadratic equation I'm
+ 
+
+ align:start position:0%
+I've got this quadratic equation I'm
+going to bring this thing over here I'm
+
+ align:start position:0%
+going to bring this thing over here I'm
+ 
+
+ align:start position:0%
+going to bring this thing over here I'm
+going to write this as g^ 2 minus 2 a g
+
+ align:start position:0%
+going to write this as g^ 2 minus 2 a g
+ 
+
+ align:start position:0%
+going to write this as g^ 2 minus 2 a g
++ 1 = Z where a is this quantity so I
+
+ align:start position:0%
++ 1 = Z where a is this quantity so I
+ 
+
+ align:start position:0%
++ 1 = Z where a is this quantity so I
+minus 2 a so a is a one from there and
+
+ align:start position:0%
+minus 2 a so a is a one from there and
+ 
+
+ align:start position:0%
+minus 2 a so a is a one from there and
+when I bring this
+
+ align:start position:0%
+when I bring this
+ 
+
+ align:start position:0%
+when I bring this
+over to the other side it's going to be
+
+ align:start position:0%
+over to the other side it's going to be
+ 
+
+ align:start position:0%
+over to the other side it's going to be
+a plus r
+
+ align:start position:0%
+a plus r
+ 
+
+ align:start position:0%
+a plus r
+2 factoring out the notice the two is
+
+ align:start position:0%
+2 factoring out the notice the two is
+ 
+
+ align:start position:0%
+2 factoring out the notice the two is
+everywhere so I put the two here the a
+
+ align:start position:0%
+everywhere so I put the two here the a
+ 
+
+ align:start position:0%
+everywhere so I put the two here the a
+is going to the a comes from the one
+
+ align:start position:0%
+is going to the a comes from the one
+ 
+
+ align:start position:0%
+is going to the a comes from the one
+there and from this time the R 2 1 + r
+
+ align:start position:0%
+there and from this time the R 2 1 + r
+ 
+
+ align:start position:0%
+there and from this time the R 2 1 + r
+- R 2 cos K Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X I'm just doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+algebra and it's coming out nicely it's
+
+ align:start position:0%
+algebra and it's coming out nicely it's
+ 
+
+ align:start position:0%
+algebra and it's coming out nicely it's
+coming out to a nice equation here with
+
+ align:start position:0%
+coming out to a nice equation here with
+ 
+
+ align:start position:0%
+coming out to a nice equation here with
+a slightly messy expression for a but if
+
+ align:start position:0%
+a slightly messy expression for a but if
+ 
+
+ align:start position:0%
+a slightly messy expression for a but if
+I now that I've named this quantity a I
+
+ align:start position:0%
+I now that I've named this quantity a I
+ 
+
+ align:start position:0%
+I now that I've named this quantity a I
+can can solve
+
+ align:start position:0%
+can can solve
+ 
+
+ align:start position:0%
+can can solve
+this so what's the solution I remember
+
+ align:start position:0%
+this so what's the solution I remember
+ 
+
+ align:start position:0%
+this so what's the solution I remember
+the quadratic formula and I get G
+
+ align:start position:0%
+the quadratic formula and I get G
+ 
+
+ align:start position:0%
+the quadratic formula and I get G
+as one I think plus or minus the square
+
+ align:start position:0%
+as one I think plus or minus the square
+ 
+
+ align:start position:0%
+as one I think plus or minus the square
+root
+
+ align:start position:0%
+root
+ 
+
+ align:start position:0%
+root
+of 1 - A
+
+ align:start position:0%
+of 1 - A
+ 
+
+ align:start position:0%
+of 1 - A
+2 that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+G oh maybe this is an a probably is I
+
+ align:start position:0%
+G oh maybe this is an a probably is I
+ 
+
+ align:start position:0%
+G oh maybe this is an a probably is I
+guess the quadratic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation takes a little memorizing but I
+
+ align:start position:0%
+equation takes a little memorizing but I
+ 
+
+ align:start position:0%
+equation takes a little memorizing but I
+guess the first point is that that
+
+ align:start position:0%
+guess the first point is that that
+ 
+
+ align:start position:0%
+guess the first point is that that
+coefficient shows up there and then the
+
+ align:start position:0%
+coefficient shows up there and then the
+ 
+
+ align:start position:0%
+coefficient shows up there and then the
+square root that we know
+
+ align:start position:0%
+square root that we know
+ 
+
+ align:start position:0%
+square root that we know
+okay so what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up again none of this is deep I'm just
+
+ align:start position:0%
+up again none of this is deep I'm just
+ 
+
+ align:start position:0%
+up again none of this is deep I'm just
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+my one one way path
+
+ align:start position:0%
+my one one way path
+ 
+
+ align:start position:0%
+my one one way path
+check stability check the size of G get
+
+ align:start position:0%
+check stability check the size of G get
+ 
+
+ align:start position:0%
+check stability check the size of G get
+an equation for G get a formula for G
+
+ align:start position:0%
+an equation for G get a formula for G
+ 
+
+ align:start position:0%
+an equation for G get a formula for G
+and look at it okay so a is
+
+ align:start position:0%
+and look at it okay so a is
+ 
+
+ align:start position:0%
+and look at it okay so a is
+some positive number and and the key is
+
+ align:start position:0%
+some positive number and and the key is
+ 
+
+ align:start position:0%
+some positive number and and the key is
+going to be whether a is bigger than one
+
+ align:start position:0%
+going to be whether a is bigger than one
+ 
+
+ align:start position:0%
+going to be whether a is bigger than one
+or smaller than one if a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is is that right 1 - A 2 or should that
+
+ align:start position:0%
+is is that right 1 - A 2 or should that
+ 
+
+ align:start position:0%
+is is that right 1 - A 2 or should that
+be a^ 2 -
+
+ align:start position:0%
+be a^ 2 -
+ 
+
+ align:start position:0%
+be a^ 2 -
+1 is it a 2us
+
+ align:start position:0%
+1 is it a 2us
+ 
+
+ align:start position:0%
+1 is it a 2us
+one yeah professors are not responsible
+
+ align:start position:0%
+one yeah professors are not responsible
+ 
+
+ align:start position:0%
+one yeah professors are not responsible
+for the quadratic formula
+
+ align:start position:0%
+for the quadratic formula
+ 
+
+ align:start position:0%
+for the quadratic formula
+because we proved that we could do it in
+
+ align:start position:0%
+because we proved that we could do it in
+ 
+
+ align:start position:0%
+because we proved that we could do it in
+third grade and that lost it absence I
+
+ align:start position:0%
+third grade and that lost it absence I
+ 
+
+ align:start position:0%
+third grade and that lost it absence I
+guess it's that right is that
+
+ align:start position:0%
+guess it's that right is that
+ 
+
+ align:start position:0%
+guess it's that right is that
+right yeah because look here here's the
+
+ align:start position:0%
+right yeah because look here here's the
+ 
+
+ align:start position:0%
+right yeah because look here here's the
+story suppose a is bigger than
+
+ align:start position:0%
+story suppose a is bigger than
+ 
+
+ align:start position:0%
+story suppose a is bigger than
+one suppose I'm really looking at the
+
+ align:start position:0%
+one suppose I'm really looking at the
+ 
+
+ align:start position:0%
+one suppose I'm really looking at the
+roots of this equation and and notice by
+
+ align:start position:0%
+roots of this equation and and notice by
+ 
+
+ align:start position:0%
+roots of this equation and and notice by
+the way the roots of that equation
+
+ align:start position:0%
+the way the roots of that equation
+ 
+
+ align:start position:0%
+the way the roots of that equation
+multiply to give one so I'm I'm pretty
+
+ align:start position:0%
+multiply to give one so I'm I'm pretty
+ 
+
+ align:start position:0%
+multiply to give one so I'm I'm pretty
+I'm on the edge here either both Roots
+
+ align:start position:0%
+I'm on the edge here either both Roots
+ 
+
+ align:start position:0%
+I'm on the edge here either both Roots
+have size one or one of those roots is
+
+ align:start position:0%
+have size one or one of those roots is
+ 
+
+ align:start position:0%
+have size one or one of those roots is
+too big and the test is going to be is a
+
+ align:start position:0%
+too big and the test is going to be is a
+ 
+
+ align:start position:0%
+too big and the test is going to be is a
+greater than one a greater than one will
+
+ align:start position:0%
+greater than one a greater than one will
+ 
+
+ align:start position:0%
+greater than one a greater than one will
+be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unstable and a less than one
+
+ align:start position:0%
+unstable and a less than one
+ 
+
+ align:start position:0%
+unstable and a less than one
+will be stable
+
+ align:start position:0%
+will be stable
+ 
+
+ align:start position:0%
+will be stable
+and I'll I'll connect a less than one to
+
+ align:start position:0%
+and I'll I'll connect a less than one to
+ 
+
+ align:start position:0%
+and I'll I'll connect a less than one to
+R less than
+
+ align:start position:0%
+R less than
+ 
+
+ align:start position:0%
+R less than
+one that will give me R less than one
+
+ align:start position:0%
+one that will give me R less than one
+ 
+
+ align:start position:0%
+one that will give me R less than one
+all right now i' I've given away the
+
+ align:start position:0%
+all right now i' I've given away the
+ 
+
+ align:start position:0%
+all right now i' I've given away the
+result because we time is pressing let
+
+ align:start position:0%
+result because we time is pressing let
+ 
+
+ align:start position:0%
+result because we time is pressing let
+me just take the take the remaining time
+
+ align:start position:0%
+me just take the take the remaining time
+ 
+
+ align:start position:0%
+me just take the take the remaining time
+to see this suppose a is bigger than
+
+ align:start position:0%
+to see this suppose a is bigger than
+ 
+
+ align:start position:0%
+to see this suppose a is bigger than
+one I'm just looking at the roots of
+
+ align:start position:0%
+one I'm just looking at the roots of
+ 
+
+ align:start position:0%
+one I'm just looking at the roots of
+this equation equation and here they are
+
+ align:start position:0%
+this equation equation and here they are
+ 
+
+ align:start position:0%
+this equation equation and here they are
+if a is bigger than
+
+ align:start position:0%
+if a is bigger than
+ 
+
+ align:start position:0%
+if a is bigger than
+one like two I have 2+ > 3 I'm way out
+
+ align:start position:0%
+one like two I have 2+ > 3 I'm way out
+ 
+
+ align:start position:0%
+one like two I have 2+ > 3 I'm way out
+right I'm bigger than one no question
+
+ align:start position:0%
+right I'm bigger than one no question
+ 
+
+ align:start position:0%
+right I'm bigger than one no question
+suppose a is less than
+
+ align:start position:0%
+suppose a is less than
+ 
+
+ align:start position:0%
+suppose a is less than
+one suppose a is a
+
+ align:start position:0%
+one suppose a is a
+ 
+
+ align:start position:0%
+one suppose a is a
+half then I have a half plus or minus
+
+ align:start position:0%
+half then I have a half plus or minus
+ 
+
+ align:start position:0%
+half then I have a half plus or minus
+the square root of
+
+ align:start position:0%
+the square root of
+ 
+
+ align:start position:0%
+the square root of
+what what's up here if a is smaller than
+
+ align:start position:0%
+what what's up here if a is smaller than
+ 
+
+ align:start position:0%
+what what's up here if a is smaller than
+one this is negative
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if it's negative its square root is
+
+ align:start position:0%
+and if it's negative its square root is
+ 
+
+ align:start position:0%
+and if it's negative its square root is
+imaginary so this is good I
+
+ align:start position:0%
+imaginary so this is good I
+ 
+
+ align:start position:0%
+imaginary so this is good I
+have a real part and then an imaginary
+
+ align:start position:0%
+have a real part and then an imaginary
+ 
+
+ align:start position:0%
+have a real part and then an imaginary
+part and then on some magic little bit
+
+ align:start position:0%
+part and then on some magic little bit
+ 
+
+ align:start position:0%
+part and then on some magic little bit
+of board I'm going to add their squares
+
+ align:start position:0%
+of board I'm going to add their squares
+ 
+
+ align:start position:0%
+of board I'm going to add their squares
+so I just want to take the real part
+
+ align:start position:0%
+so I just want to take the real part
+ 
+
+ align:start position:0%
+so I just want to take the real part
+squared and the imaginary part
+
+ align:start position:0%
+squared and the imaginary part
+ 
+
+ align:start position:0%
+squared and the imaginary part
+squared now the imaginary part is going
+
+ align:start position:0%
+squared now the imaginary part is going
+ 
+
+ align:start position:0%
+squared now the imaginary part is going
+to be 1 - A squ
+
+ align:start position:0%
+to be 1 - A squ
+ 
+
+ align:start position:0%
+to be 1 - A squ
+because when I bring out an
+
+ align:start position:0%
+because when I bring out an
+ 
+
+ align:start position:0%
+because when I bring out an
+I then I have a 1 - A S there and when I
+
+ align:start position:0%
+I then I have a 1 - A S there and when I
+ 
+
+ align:start position:0%
+I then I have a 1 - A S there and when I
+add them I get
+
+ align:start position:0%
+add them I get
+ 
+
+ align:start position:0%
+add them I get
+one let me just say again what I did I
+
+ align:start position:0%
+one let me just say again what I did I
+ 
+
+ align:start position:0%
+one let me just say again what I did I
+just figured out what is absolute value
+
+ align:start position:0%
+just figured out what is absolute value
+ 
+
+ align:start position:0%
+just figured out what is absolute value
+of g^ s as real part squared and
+
+ align:start position:0%
+of g^ s as real part squared and
+ 
+
+ align:start position:0%
+of g^ s as real part squared and
+imaginary part squared and I get the
+
+ align:start position:0%
+imaginary part squared and I get the
+ 
+
+ align:start position:0%
+imaginary part squared and I get the
+answer one so the conclusion is the
+
+ align:start position:0%
+answer one so the conclusion is the
+ 
+
+ align:start position:0%
+answer one so the conclusion is the
+roots are stable when a is below one
+
+ align:start position:0%
+roots are stable when a is below one
+ 
+
+ align:start position:0%
+roots are stable when a is below one
+and I have instability when a is above
+
+ align:start position:0%
+and I have instability when a is above
+ 
+
+ align:start position:0%
+and I have instability when a is above
+one and then if I track that down that
+
+ align:start position:0%
+one and then if I track that down that
+ 
+
+ align:start position:0%
+one and then if I track that down that
+reduces to the tests it just happens to
+
+ align:start position:0%
+reduces to the tests it just happens to
+ 
+
+ align:start position:0%
+reduces to the tests it just happens to
+be the same test on R whether R is below
+
+ align:start position:0%
+be the same test on R whether R is below
+ 
+
+ align:start position:0%
+be the same test on R whether R is below
+one which is the kurant Frick's ly
+
+ align:start position:0%
+one which is the kurant Frick's ly
+ 
+
+ align:start position:0%
+one which is the kurant Frick's ly
+condition that I'm staying inside the
+
+ align:start position:0%
+condition that I'm staying inside the
+ 
+
+ align:start position:0%
+condition that I'm staying inside the
+characteristics or R is bigger than one
+
+ align:start position:0%
+characteristics or R is bigger than one
+ 
+
+ align:start position:0%
+characteristics or R is bigger than one
+and I'm taking a delta T that isn't
+
+ align:start position:0%
+and I'm taking a delta T that isn't
+ 
+
+ align:start position:0%
+and I'm taking a delta T that isn't
+isn't stable okay so that I'm sorry to
+
+ align:start position:0%
+isn't stable okay so that I'm sorry to
+ 
+
+ align:start position:0%
+isn't stable okay so that I'm sorry to
+go slightly over the time thanks for
+
+ align:start position:0%
+go slightly over the time thanks for
+ 
+
+ align:start position:0%
+go slightly over the time thanks for
+staying with me I'll begin next time
+
+ align:start position:0%
+staying with me I'll begin next time
+ 
+
+ align:start position:0%
+staying with me I'll begin next time
+with this staggered grid that won't take
+
+ align:start position:0%
+with this staggered grid that won't take
+ 
+
+ align:start position:0%
+with this staggered grid that won't take
+the whole lecture but it's worth knowing
+
+ align:start position:0%
+the whole lecture but it's worth knowing
+ 
+
+ align:start position:0%
+the whole lecture but it's worth knowing
+because we see staggered grids in many
+
+ align:start position:0%
+because we see staggered grids in many
+ 
+
+ align:start position:0%
+because we see staggered grids in many
+of the best
+
+ align:start position:0%
+of the best
+ 
+
+ align:start position:0%
+of the best
+methods okay thanks have a good weekend
+
+ align:start position:0%
+methods okay thanks have a good weekend
+ 
+
+ align:start position:0%
+methods okay thanks have a good weekend
+and I guess it's Tuesday rather than
+
+ align:start position:0%
+and I guess it's Tuesday rather than
+ 
+
+ align:start position:0%
+and I guess it's Tuesday rather than
+Monday that I see you next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it with the like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say that I'm happy
\ No newline at end of file
diff --git a/13r9QY6cmjc.txt b/13r9QY6cmjc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..02b9ddb5676a959f60212d09f862e4e7412c8052
--- /dev/null
+++ b/13r9QY6cmjc.txt
@@ -0,0 +1,6555 @@
+align:start position:0%
+ 
+okay so we start this is the second
+
+ align:start position:0%
+okay so we start this is the second
+ 
+
+ align:start position:0%
+okay so we start this is the second
+lecture on eigenvalues so the first
+
+ align:start position:0%
+lecture on eigenvalues so the first
+ 
+
+ align:start position:0%
+lecture on eigenvalues so the first
+lecture was that reached the key
+
+ align:start position:0%
+lecture was that reached the key
+ 
+
+ align:start position:0%
+lecture was that reached the key
+equation ax equal lambda X X is the
+
+ align:start position:0%
+equation ax equal lambda X X is the
+ 
+
+ align:start position:0%
+equation ax equal lambda X X is the
+eigenvector and lambdas the eigenvalue
+
+ align:start position:0%
+eigenvector and lambdas the eigenvalue
+ 
+
+ align:start position:0%
+eigenvector and lambdas the eigenvalue
+now to use that and the the good way to
+
+ align:start position:0%
+now to use that and the the good way to
+ 
+
+ align:start position:0%
+now to use that and the the good way to
+after we found so so job one is to find
+
+ align:start position:0%
+after we found so so job one is to find
+ 
+
+ align:start position:0%
+after we found so so job one is to find
+the eigenvalues and find the
+
+ align:start position:0%
+the eigenvalues and find the
+ 
+
+ align:start position:0%
+the eigenvalues and find the
+eigenvectors now after we found them
+
+ align:start position:0%
+eigenvectors now after we found them
+ 
+
+ align:start position:0%
+eigenvectors now after we found them
+what do we do with them well the good
+
+ align:start position:0%
+what do we do with them well the good
+ 
+
+ align:start position:0%
+what do we do with them well the good
+way to see that is diagonalize the
+
+ align:start position:0%
+way to see that is diagonalize the
+ 
+
+ align:start position:0%
+way to see that is diagonalize the
+matrix so the matrix is a and I want to
+
+ align:start position:0%
+matrix so the matrix is a and I want to
+ 
+
+ align:start position:0%
+matrix so the matrix is a and I want to
+show first of all this is like the basic
+
+ align:start position:0%
+show first of all this is like the basic
+ 
+
+ align:start position:0%
+show first of all this is like the basic
+fact this this formula that's that's the
+
+ align:start position:0%
+fact this this formula that's that's the
+ 
+
+ align:start position:0%
+fact this this formula that's that's the
+key to today's lecture this matrix a I
+
+ align:start position:0%
+key to today's lecture this matrix a I
+ 
+
+ align:start position:0%
+key to today's lecture this matrix a I
+put its eigenvectors in the columns of a
+
+ align:start position:0%
+put its eigenvectors in the columns of a
+ 
+
+ align:start position:0%
+put its eigenvectors in the columns of a
+matrix s so s will be the eigenvector
+
+ align:start position:0%
+matrix s so s will be the eigenvector
+ 
+
+ align:start position:0%
+matrix s so s will be the eigenvector
+matrix and i want to look at this magic
+
+ align:start position:0%
+matrix and i want to look at this magic
+ 
+
+ align:start position:0%
+matrix and i want to look at this magic
+combination s inverse a s so can i show
+
+ align:start position:0%
+combination s inverse a s so can i show
+ 
+
+ align:start position:0%
+combination s inverse a s so can i show
+you how that how that what happens there
+
+ align:start position:0%
+you how that how that what happens there
+ 
+
+ align:start position:0%
+you how that how that what happens there
+and notice notice there's an S inverse
+
+ align:start position:0%
+and notice notice there's an S inverse
+ 
+
+ align:start position:0%
+and notice notice there's an S inverse
+we have to be able to invert this
+
+ align:start position:0%
+we have to be able to invert this
+ 
+
+ align:start position:0%
+we have to be able to invert this
+eigenvector matrix s so for that we need
+
+ align:start position:0%
+eigenvector matrix s so for that we need
+ 
+
+ align:start position:0%
+eigenvector matrix s so for that we need
+n independent eigenvectors so that's the
+
+ align:start position:0%
+n independent eigenvectors so that's the
+ 
+
+ align:start position:0%
+n independent eigenvectors so that's the
+that's the case okay so suppose we have
+
+ align:start position:0%
+that's the case okay so suppose we have
+ 
+
+ align:start position:0%
+that's the case okay so suppose we have
+n linearly independent eigen vectors of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+put them in the columns of this matrix s
+
+ align:start position:0%
+put them in the columns of this matrix s
+ 
+
+ align:start position:0%
+put them in the columns of this matrix s
+so I'm naturally going to call that the
+
+ align:start position:0%
+so I'm naturally going to call that the
+ 
+
+ align:start position:0%
+so I'm naturally going to call that the
+eigenvector matrix because it's got the
+
+ align:start position:0%
+eigenvector matrix because it's got the
+ 
+
+ align:start position:0%
+eigenvector matrix because it's got the
+eigenvectors in its columns and all i
+
+ align:start position:0%
+eigenvectors in its columns and all i
+ 
+
+ align:start position:0%
+eigenvectors in its columns and all i
+want to do is show you what happens when
+
+ align:start position:0%
+want to do is show you what happens when
+ 
+
+ align:start position:0%
+want to do is show you what happens when
+you multiply a times s so a times s so
+
+ align:start position:0%
+you multiply a times s so a times s so
+ 
+
+ align:start position:0%
+you multiply a times s so a times s so
+this is a times the matrix with the
+
+ align:start position:0%
+this is a times the matrix with the
+ 
+
+ align:start position:0%
+this is a times the matrix with the
+first eigenvector in this first column
+
+ align:start position:0%
+first eigenvector in this first column
+ 
+
+ align:start position:0%
+first eigenvector in this first column
+the second eigenvector in its second
+
+ align:start position:0%
+the second eigenvector in its second
+ 
+
+ align:start position:0%
+the second eigenvector in its second
+column the nth eigen vector in its nth
+
+ align:start position:0%
+column the nth eigen vector in its nth
+ 
+
+ align:start position:0%
+column the nth eigen vector in its nth
+column and how am I going to do this
+
+ align:start position:0%
+column and how am I going to do this
+ 
+
+ align:start position:0%
+column and how am I going to do this
+matrix multiplication well certainly
+
+ align:start position:0%
+matrix multiplication well certainly
+ 
+
+ align:start position:0%
+matrix multiplication well certainly
+I'll do it a column at a time and what
+
+ align:start position:0%
+I'll do it a column at a time and what
+ 
+
+ align:start position:0%
+I'll do it a column at a time and what
+do I get a times the first column gives
+
+ align:start position:0%
+do I get a times the first column gives
+ 
+
+ align:start position:0%
+do I get a times the first column gives
+me the first column of the answer but
+
+ align:start position:0%
+me the first column of the answer but
+ 
+
+ align:start position:0%
+me the first column of the answer but
+what is it that's an eigenvector a times
+
+ align:start position:0%
+what is it that's an eigenvector a times
+ 
+
+ align:start position:0%
+what is it that's an eigenvector a times
+x1 is equal to the lambda times the x 1
+
+ align:start position:0%
+x1 is equal to the lambda times the x 1
+ 
+
+ align:start position:0%
+x1 is equal to the lambda times the x 1
+and that lambdas we'll call lambda 1 of
+
+ align:start position:0%
+and that lambdas we'll call lambda 1 of
+ 
+
+ align:start position:0%
+and that lambdas we'll call lambda 1 of
+course so that's the first column ax 1
+
+ align:start position:0%
+course so that's the first column ax 1
+ 
+
+ align:start position:0%
+course so that's the first column ax 1
+is the same as lambda 1 X 1 IX 2 is
+
+ align:start position:0%
+is the same as lambda 1 X 1 IX 2 is
+ 
+
+ align:start position:0%
+is the same as lambda 1 X 1 IX 2 is
+lambda 2 X 2 so on along to in the nth
+
+ align:start position:0%
+lambda 2 X 2 so on along to in the nth
+ 
+
+ align:start position:0%
+lambda 2 X 2 so on along to in the nth
+column we now have lambda n xn looking
+
+ align:start position:0%
+column we now have lambda n xn looking
+ 
+
+ align:start position:0%
+column we now have lambda n xn looking
+good but the next step is even better so
+
+ align:start position:0%
+good but the next step is even better so
+ 
+
+ align:start position:0%
+good but the next step is even better so
+for the next step I want to separate out
+
+ align:start position:0%
+for the next step I want to separate out
+ 
+
+ align:start position:0%
+for the next step I want to separate out
+those eigenvalues those those
+
+ align:start position:0%
+those eigenvalues those those
+ 
+
+ align:start position:0%
+those eigenvalues those those
+multiplying numbers from the X's so then
+
+ align:start position:0%
+multiplying numbers from the X's so then
+ 
+
+ align:start position:0%
+multiplying numbers from the X's so then
+I'll have just what I want okay so how
+
+ align:start position:0%
+I'll have just what I want okay so how
+ 
+
+ align:start position:0%
+I'll have just what I want okay so how
+am I going to separate out so that that
+
+ align:start position:0%
+am I going to separate out so that that
+ 
+
+ align:start position:0%
+am I going to separate out so that that
+number lambda 1 is multiplying the first
+
+ align:start position:0%
+number lambda 1 is multiplying the first
+ 
+
+ align:start position:0%
+number lambda 1 is multiplying the first
+column so if I want to factor it out of
+
+ align:start position:0%
+column so if I want to factor it out of
+ 
+
+ align:start position:0%
+column so if I want to factor it out of
+the first column I better put here is
+
+ align:start position:0%
+the first column I better put here is
+ 
+
+ align:start position:0%
+the first column I better put here is
+going to be X 1 and that's going to
+
+ align:start position:0%
+going to be X 1 and that's going to
+ 
+
+ align:start position:0%
+going to be X 1 and that's going to
+multiply this matrix lambda 1 in the
+
+ align:start position:0%
+multiply this matrix lambda 1 in the
+ 
+
+ align:start position:0%
+multiply this matrix lambda 1 in the
+first entry in all zeros you see that
+
+ align:start position:0%
+first entry in all zeros you see that
+ 
+
+ align:start position:0%
+first entry in all zeros you see that
+that that's going to come out right for
+
+ align:start position:0%
+that that's going to come out right for
+ 
+
+ align:start position:0%
+that that's going to come out right for
+the first column because we remember how
+
+ align:start position:0%
+the first column because we remember how
+ 
+
+ align:start position:0%
+the first column because we remember how
+we're going back to that original
+
+ align:start position:0%
+we're going back to that original
+ 
+
+ align:start position:0%
+we're going back to that original
+punchline that if I want a number to
+
+ align:start position:0%
+punchline that if I want a number to
+ 
+
+ align:start position:0%
+punchline that if I want a number to
+multiply X 1 then I can do it by putting
+
+ align:start position:0%
+multiply X 1 then I can do it by putting
+ 
+
+ align:start position:0%
+multiply X 1 then I can do it by putting
+X 1 in that column in the first column
+
+ align:start position:0%
+X 1 in that column in the first column
+ 
+
+ align:start position:0%
+X 1 in that column in the first column
+and putting that number there what am I
+
+ align:start position:0%
+and putting that number there what am I
+ 
+
+ align:start position:0%
+and putting that number there what am I
+going to have here I'm going to have
+
+ align:start position:0%
+going to have here I'm going to have
+ 
+
+ align:start position:0%
+going to have here I'm going to have
+lambda what I'm going to have X 1 X 2 xn
+
+ align:start position:0%
+lambda what I'm going to have X 1 X 2 xn
+ 
+
+ align:start position:0%
+lambda what I'm going to have X 1 X 2 xn
+these are going to be my columns again
+
+ align:start position:0%
+these are going to be my columns again
+ 
+
+ align:start position:0%
+these are going to be my columns again
+I'm getting s back again I'm getting s
+
+ align:start position:0%
+I'm getting s back again I'm getting s
+ 
+
+ align:start position:0%
+I'm getting s back again I'm getting s
+back again but now what's it x on the
+
+ align:start position:0%
+back again but now what's it x on the
+ 
+
+ align:start position:0%
+back again but now what's it x on the
+right its x if I want if I want lambda n
+
+ align:start position:0%
+right its x if I want if I want lambda n
+ 
+
+ align:start position:0%
+right its x if I want if I want lambda n
+xn in the last column how do I do it
+
+ align:start position:0%
+xn in the last column how do I do it
+ 
+
+ align:start position:0%
+xn in the last column how do I do it
+well the last column here will be I'll
+
+ align:start position:0%
+well the last column here will be I'll
+ 
+
+ align:start position:0%
+well the last column here will be I'll
+take the last column use these
+
+ align:start position:0%
+take the last column use these
+ 
+
+ align:start position:0%
+take the last column use these
+coefficients put the lambda end down
+
+ align:start position:0%
+coefficients put the lambda end down
+ 
+
+ align:start position:0%
+coefficients put the lambda end down
+there and it will multiply that nth
+
+ align:start position:0%
+there and it will multiply that nth
+ 
+
+ align:start position:0%
+there and it will multiply that nth
+column and give me lambda n xn there
+
+ align:start position:0%
+column and give me lambda n xn there
+ 
+
+ align:start position:0%
+column and give me lambda n xn there
+there you see matrix multiplication just
+
+ align:start position:0%
+there you see matrix multiplication just
+ 
+
+ align:start position:0%
+there you see matrix multiplication just
+working for us so I started with a s I
+
+ align:start position:0%
+working for us so I started with a s I
+ 
+
+ align:start position:0%
+working for us so I started with a s I
+wrote down what it meant a times each
+
+ align:start position:0%
+wrote down what it meant a times each
+ 
+
+ align:start position:0%
+wrote down what it meant a times each
+eigenvector that gave me lambda times
+
+ align:start position:0%
+eigenvector that gave me lambda times
+ 
+
+ align:start position:0%
+eigenvector that gave me lambda times
+the eigenvector and then when I peeled
+
+ align:start position:0%
+the eigenvector and then when I peeled
+ 
+
+ align:start position:0%
+the eigenvector and then when I peeled
+off the lambdas they were on the
+
+ align:start position:0%
+off the lambdas they were on the
+ 
+
+ align:start position:0%
+off the lambdas they were on the
+right-hand side so I've got s my matrix
+
+ align:start position:0%
+right-hand side so I've got s my matrix
+ 
+
+ align:start position:0%
+right-hand side so I've got s my matrix
+back again and this matrix this diagonal
+
+ align:start position:0%
+back again and this matrix this diagonal
+ 
+
+ align:start position:0%
+back again and this matrix this diagonal
+matrix the eigen value matrix and I call
+
+ align:start position:0%
+matrix the eigen value matrix and I call
+ 
+
+ align:start position:0%
+matrix the eigen value matrix and I call
+it capital lambda using capital letters
+
+ align:start position:0%
+it capital lambda using capital letters
+ 
+
+ align:start position:0%
+it capital lambda using capital letters
+for matrices and lambda to prompt me
+
+ align:start position:0%
+for matrices and lambda to prompt me
+ 
+
+ align:start position:0%
+for matrices and lambda to prompt me
+that it's that it's eigen values that
+
+ align:start position:0%
+that it's that it's eigen values that
+ 
+
+ align:start position:0%
+that it's that it's eigen values that
+are in there so you see that the
+
+ align:start position:0%
+are in there so you see that the
+ 
+
+ align:start position:0%
+are in there so you see that the
+eigenvalues are just sitting down that
+
+ align:start position:0%
+eigenvalues are just sitting down that
+ 
+
+ align:start position:0%
+eigenvalues are just sitting down that
+diagonal if I had a column x2 here I
+
+ align:start position:0%
+diagonal if I had a column x2 here I
+ 
+
+ align:start position:0%
+diagonal if I had a column x2 here I
+would want the lambda 2 in the two tube
+
+ align:start position:0%
+would want the lambda 2 in the two tube
+ 
+
+ align:start position:0%
+would want the lambda 2 in the two tube
+position in the diagonal position to
+
+ align:start position:0%
+position in the diagonal position to
+ 
+
+ align:start position:0%
+position in the diagonal position to
+multiply that X 2 and give me the lambda
+
+ align:start position:0%
+multiply that X 2 and give me the lambda
+ 
+
+ align:start position:0%
+multiply that X 2 and give me the lambda
+2 X 2 that's my formula a s is s lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay that's that's the you see it's just
+
+ align:start position:0%
+okay that's that's the you see it's just
+ 
+
+ align:start position:0%
+okay that's that's the you see it's just
+a calculation now I mentioned and I have
+
+ align:start position:0%
+a calculation now I mentioned and I have
+ 
+
+ align:start position:0%
+a calculation now I mentioned and I have
+to mention again this business about an
+
+ align:start position:0%
+to mention again this business about an
+ 
+
+ align:start position:0%
+to mention again this business about an
+independent eigenvectors as it stands
+
+ align:start position:0%
+independent eigenvectors as it stands
+ 
+
+ align:start position:0%
+independent eigenvectors as it stands
+this is all fine whether I mean I could
+
+ align:start position:0%
+this is all fine whether I mean I could
+ 
+
+ align:start position:0%
+this is all fine whether I mean I could
+be repeating the same eigenvector but I
+
+ align:start position:0%
+be repeating the same eigenvector but I
+ 
+
+ align:start position:0%
+be repeating the same eigenvector but I
+am no interest in that I want to be able
+
+ align:start position:0%
+am no interest in that I want to be able
+ 
+
+ align:start position:0%
+am no interest in that I want to be able
+to invert s and that's where this comes
+
+ align:start position:0%
+to invert s and that's where this comes
+ 
+
+ align:start position:0%
+to invert s and that's where this comes
+in this n independent eigenvectors
+
+ align:start position:0%
+in this n independent eigenvectors
+ 
+
+ align:start position:0%
+in this n independent eigenvectors
+business comes in to tell me that that
+
+ align:start position:0%
+business comes in to tell me that that
+ 
+
+ align:start position:0%
+business comes in to tell me that that
+matrix is invertible so let me on the
+
+ align:start position:0%
+matrix is invertible so let me on the
+ 
+
+ align:start position:0%
+matrix is invertible so let me on the
+next board write down what I've got a s
+
+ align:start position:0%
+next board write down what I've got a s
+ 
+
+ align:start position:0%
+next board write down what I've got a s
+equals s lambda and now I can multiply
+
+ align:start position:0%
+equals s lambda and now I can multiply
+ 
+
+ align:start position:0%
+equals s lambda and now I can multiply
+on the left by s inverse so this is
+
+ align:start position:0%
+on the left by s inverse so this is
+ 
+
+ align:start position:0%
+on the left by s inverse so this is
+really I can do that provided s is
+
+ align:start position:0%
+really I can do that provided s is
+ 
+
+ align:start position:0%
+really I can do that provided s is
+invertible provided my assumption of n
+
+ align:start position:0%
+invertible provided my assumption of n
+ 
+
+ align:start position:0%
+invertible provided my assumption of n
+independent eigenvectors is satisfied
+
+ align:start position:0%
+independent eigenvectors is satisfied
+ 
+
+ align:start position:0%
+independent eigenvectors is satisfied
+and i mentioned at the end of last time
+
+ align:start position:0%
+and i mentioned at the end of last time
+ 
+
+ align:start position:0%
+and i mentioned at the end of last time
+and i'll say again that there's a small
+
+ align:start position:0%
+and i'll say again that there's a small
+ 
+
+ align:start position:0%
+and i'll say again that there's a small
+number of matrices for that don't have n
+
+ align:start position:0%
+number of matrices for that don't have n
+ 
+
+ align:start position:0%
+number of matrices for that don't have n
+independent eigenvectors so i've got to
+
+ align:start position:0%
+independent eigenvectors so i've got to
+ 
+
+ align:start position:0%
+independent eigenvectors so i've got to
+discuss that that technical point but
+
+ align:start position:0%
+discuss that that technical point but
+ 
+
+ align:start position:0%
+discuss that that technical point but
+the great the most matrices that we see
+
+ align:start position:0%
+the great the most matrices that we see
+ 
+
+ align:start position:0%
+the great the most matrices that we see
+have end n independent eigenvectors and
+
+ align:start position:0%
+have end n independent eigenvectors and
+ 
+
+ align:start position:0%
+have end n independent eigenvectors and
+we can diagonalize this is
+
+ align:start position:0%
+we can diagonalize this is
+ 
+
+ align:start position:0%
+we can diagonalize this is
+diagonalization i could also write it
+
+ align:start position:0%
+diagonalization i could also write it
+ 
+
+ align:start position:0%
+diagonalization i could also write it
+and I often will the other way round if
+
+ align:start position:0%
+and I often will the other way round if
+ 
+
+ align:start position:0%
+and I often will the other way round if
+I multiply on the right by s inverse if
+
+ align:start position:0%
+I multiply on the right by s inverse if
+ 
+
+ align:start position:0%
+I multiply on the right by s inverse if
+I took this equation at the top and
+
+ align:start position:0%
+I took this equation at the top and
+ 
+
+ align:start position:0%
+I took this equation at the top and
+multiply on the right by s inverse I
+
+ align:start position:0%
+multiply on the right by s inverse I
+ 
+
+ align:start position:0%
+multiply on the right by s inverse I
+could I would have a left here now s
+
+ align:start position:0%
+could I would have a left here now s
+ 
+
+ align:start position:0%
+could I would have a left here now s
+inverse is coming from the right so can
+
+ align:start position:0%
+inverse is coming from the right so can
+ 
+
+ align:start position:0%
+inverse is coming from the right so can
+you keep those two straight a multiplies
+
+ align:start position:0%
+you keep those two straight a multiplies
+ 
+
+ align:start position:0%
+you keep those two straight a multiplies
+its eigenvectors that's how i keep them
+
+ align:start position:0%
+its eigenvectors that's how i keep them
+ 
+
+ align:start position:0%
+its eigenvectors that's how i keep them
+straight so a multiplies s a multiplies
+
+ align:start position:0%
+straight so a multiplies s a multiplies
+ 
+
+ align:start position:0%
+straight so a multiplies s a multiplies
+this and then this s inverse makes the
+
+ align:start position:0%
+this and then this s inverse makes the
+ 
+
+ align:start position:0%
+this and then this s inverse makes the
+whole thing diagonal and this is another
+
+ align:start position:0%
+whole thing diagonal and this is another
+ 
+
+ align:start position:0%
+whole thing diagonal and this is another
+way of saying the same thing putting the
+
+ align:start position:0%
+way of saying the same thing putting the
+ 
+
+ align:start position:0%
+way of saying the same thing putting the
+S is on the other side of the equation
+
+ align:start position:0%
+S is on the other side of the equation
+ 
+
+ align:start position:0%
+S is on the other side of the equation
+vision a is s lambda s inverse so that's
+
+ align:start position:0%
+vision a is s lambda s inverse so that's
+ 
+
+ align:start position:0%
+vision a is s lambda s inverse so that's
+the that's the new factorization that's
+
+ align:start position:0%
+the that's the new factorization that's
+ 
+
+ align:start position:0%
+the that's the new factorization that's
+the replacement for Lu from elimination
+
+ align:start position:0%
+the replacement for Lu from elimination
+ 
+
+ align:start position:0%
+the replacement for Lu from elimination
+or QR from gram-schmidt and notice that
+
+ align:start position:0%
+or QR from gram-schmidt and notice that
+ 
+
+ align:start position:0%
+or QR from gram-schmidt and notice that
+the matrix so it's it's a matrix times
+
+ align:start position:0%
+the matrix so it's it's a matrix times
+ 
+
+ align:start position:0%
+the matrix so it's it's a matrix times
+the diagonal matrix times the inverse of
+
+ align:start position:0%
+the diagonal matrix times the inverse of
+ 
+
+ align:start position:0%
+the diagonal matrix times the inverse of
+the first one it's is that's the
+
+ align:start position:0%
+the first one it's is that's the
+ 
+
+ align:start position:0%
+the first one it's is that's the
+combination that we'll see throughout
+
+ align:start position:0%
+combination that we'll see throughout
+ 
+
+ align:start position:0%
+combination that we'll see throughout
+this chapter this this combination with
+
+ align:start position:0%
+this chapter this this combination with
+ 
+
+ align:start position:0%
+this chapter this this combination with
+an S and an S inverse okay can I just
+
+ align:start position:0%
+an S and an S inverse okay can I just
+ 
+
+ align:start position:0%
+an S and an S inverse okay can I just
+begin to use that for example what about
+
+ align:start position:0%
+begin to use that for example what about
+ 
+
+ align:start position:0%
+begin to use that for example what about
+a squared what are the eigenvalues and
+
+ align:start position:0%
+a squared what are the eigenvalues and
+ 
+
+ align:start position:0%
+a squared what are the eigenvalues and
+eigenvectors of a squared that's a
+
+ align:start position:0%
+eigenvectors of a squared that's a
+ 
+
+ align:start position:0%
+eigenvectors of a squared that's a
+straightforward question with it with an
+
+ align:start position:0%
+straightforward question with it with an
+ 
+
+ align:start position:0%
+straightforward question with it with an
+absolutely clean answer so let me let me
+
+ align:start position:0%
+absolutely clean answer so let me let me
+ 
+
+ align:start position:0%
+absolutely clean answer so let me let me
+consider a squared so I start with ax
+
+ align:start position:0%
+consider a squared so I start with ax
+ 
+
+ align:start position:0%
+consider a squared so I start with ax
+equal lambda X and I'm headed for a
+
+ align:start position:0%
+equal lambda X and I'm headed for a
+ 
+
+ align:start position:0%
+equal lambda X and I'm headed for a
+squared so let me multiply both sides by
+
+ align:start position:0%
+squared so let me multiply both sides by
+ 
+
+ align:start position:0%
+squared so let me multiply both sides by
+a that's one way to get a squared on the
+
+ align:start position:0%
+a that's one way to get a squared on the
+ 
+
+ align:start position:0%
+a that's one way to get a squared on the
+left so if I should write these ifs in
+
+ align:start position:0%
+left so if I should write these ifs in
+ 
+
+ align:start position:0%
+left so if I should write these ifs in
+here if ax equals lambda X then I
+
+ align:start position:0%
+here if ax equals lambda X then I
+ 
+
+ align:start position:0%
+here if ax equals lambda X then I
+multiply by a so I get a squared x
+
+ align:start position:0%
+multiply by a so I get a squared x
+ 
+
+ align:start position:0%
+multiply by a so I get a squared x
+equals while I'm multiplying by a so
+
+ align:start position:0%
+equals while I'm multiplying by a so
+ 
+
+ align:start position:0%
+equals while I'm multiplying by a so
+that's lambda a X that lambda was a
+
+ align:start position:0%
+that's lambda a X that lambda was a
+ 
+
+ align:start position:0%
+that's lambda a X that lambda was a
+number so I just put it on the left and
+
+ align:start position:0%
+number so I just put it on the left and
+ 
+
+ align:start position:0%
+number so I just put it on the left and
+what do I did tell me how to make that
+
+ align:start position:0%
+what do I did tell me how to make that
+ 
+
+ align:start position:0%
+what do I did tell me how to make that
+look better what have I got here
+
+ align:start position:0%
+look better what have I got here
+ 
+
+ align:start position:0%
+look better what have I got here
+for if a has the eigenvalue lambda and
+
+ align:start position:0%
+for if a has the eigenvalue lambda and
+ 
+
+ align:start position:0%
+for if a has the eigenvalue lambda and
+eigenvector x what's up with a squared a
+
+ align:start position:0%
+eigenvector x what's up with a squared a
+ 
+
+ align:start position:0%
+eigenvector x what's up with a squared a
+squared X I just multiplied by a but now
+
+ align:start position:0%
+squared X I just multiplied by a but now
+ 
+
+ align:start position:0%
+squared X I just multiplied by a but now
+for a X I'm going to substitute lambda X
+
+ align:start position:0%
+for a X I'm going to substitute lambda X
+ 
+
+ align:start position:0%
+for a X I'm going to substitute lambda X
+so I've got lambda squared X so from
+
+ align:start position:0%
+so I've got lambda squared X so from
+ 
+
+ align:start position:0%
+so I've got lambda squared X so from
+that simple calculation I my conclusion
+
+ align:start position:0%
+that simple calculation I my conclusion
+ 
+
+ align:start position:0%
+that simple calculation I my conclusion
+is that the eigenvalues of a squared are
+
+ align:start position:0%
+is that the eigenvalues of a squared are
+ 
+
+ align:start position:0%
+is that the eigenvalues of a squared are
+lambda squared and the eigenvectors i
+
+ align:start position:0%
+lambda squared and the eigenvectors i
+ 
+
+ align:start position:0%
+lambda squared and the eigenvectors i
+always think about both of those what
+
+ align:start position:0%
+always think about both of those what
+ 
+
+ align:start position:0%
+always think about both of those what
+can i say about the eigenvalues they're
+
+ align:start position:0%
+can i say about the eigenvalues they're
+ 
+
+ align:start position:0%
+can i say about the eigenvalues they're
+squared what can I say about the
+
+ align:start position:0%
+squared what can I say about the
+ 
+
+ align:start position:0%
+squared what can I say about the
+eigenvectors they're the same
+
+ align:start position:0%
+eigenvectors they're the same
+ 
+
+ align:start position:0%
+eigenvectors they're the same
+the same X is in s for a now let me see
+
+ align:start position:0%
+the same X is in s for a now let me see
+ 
+
+ align:start position:0%
+the same X is in s for a now let me see
+that also from this formula how can I
+
+ align:start position:0%
+that also from this formula how can I
+ 
+
+ align:start position:0%
+that also from this formula how can I
+see what a squared is looking like from
+
+ align:start position:0%
+see what a squared is looking like from
+ 
+
+ align:start position:0%
+see what a squared is looking like from
+this formula so let me that was one way
+
+ align:start position:0%
+this formula so let me that was one way
+ 
+
+ align:start position:0%
+this formula so let me that was one way
+to do it let me do it by just taking a
+
+ align:start position:0%
+to do it let me do it by just taking a
+ 
+
+ align:start position:0%
+to do it let me do it by just taking a
+squared from that a squared is s lambda
+
+ align:start position:0%
+squared from that a squared is s lambda
+ 
+
+ align:start position:0%
+squared from that a squared is s lambda
+s inverse that's a times s lambda s
+
+ align:start position:0%
+s inverse that's a times s lambda s
+ 
+
+ align:start position:0%
+s inverse that's a times s lambda s
+inverse that's a which is this is the
+
+ align:start position:0%
+inverse that's a which is this is the
+ 
+
+ align:start position:0%
+inverse that's a which is this is the
+beauty of eigenvalues eigenvectors
+
+ align:start position:0%
+beauty of eigenvalues eigenvectors
+ 
+
+ align:start position:0%
+beauty of eigenvalues eigenvectors
+having that s inverse and s is the
+
+ align:start position:0%
+having that s inverse and s is the
+ 
+
+ align:start position:0%
+having that s inverse and s is the
+identity so i've got s lambda squared s
+
+ align:start position:0%
+identity so i've got s lambda squared s
+ 
+
+ align:start position:0%
+identity so i've got s lambda squared s
+inverse you see what that's telling me
+
+ align:start position:0%
+inverse you see what that's telling me
+ 
+
+ align:start position:0%
+inverse you see what that's telling me
+it's telling me the same thing that I
+
+ align:start position:0%
+it's telling me the same thing that I
+ 
+
+ align:start position:0%
+it's telling me the same thing that I
+just learned here but in the in a matrix
+
+ align:start position:0%
+just learned here but in the in a matrix
+ 
+
+ align:start position:0%
+just learned here but in the in a matrix
+form it's telling me that the S is the
+
+ align:start position:0%
+form it's telling me that the S is the
+ 
+
+ align:start position:0%
+form it's telling me that the S is the
+same the eigenvectors are the same but
+
+ align:start position:0%
+same the eigenvectors are the same but
+ 
+
+ align:start position:0%
+same the eigenvectors are the same but
+the eigenvalues are squared because this
+
+ align:start position:0%
+the eigenvalues are squared because this
+ 
+
+ align:start position:0%
+the eigenvalues are squared because this
+is what's lambda squared that's still
+
+ align:start position:0%
+is what's lambda squared that's still
+ 
+
+ align:start position:0%
+is what's lambda squared that's still
+diagonal it's got little lambda 1
+
+ align:start position:0%
+diagonal it's got little lambda 1
+ 
+
+ align:start position:0%
+diagonal it's got little lambda 1
+squared lambda 2 squared down to lambda
+
+ align:start position:0%
+squared lambda 2 squared down to lambda
+ 
+
+ align:start position:0%
+squared lambda 2 squared down to lambda
+n squared on that diagonal those are the
+
+ align:start position:0%
+n squared on that diagonal those are the
+ 
+
+ align:start position:0%
+n squared on that diagonal those are the
+eigenvalues as we just learned of a
+
+ align:start position:0%
+eigenvalues as we just learned of a
+ 
+
+ align:start position:0%
+eigenvalues as we just learned of a
+squared okay so somehow those
+
+ align:start position:0%
+squared okay so somehow those
+ 
+
+ align:start position:0%
+squared okay so somehow those
+eigenvalues and eigenvectors are really
+
+ align:start position:0%
+eigenvalues and eigenvectors are really
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors are really
+giving you a way to to to see what's
+
+ align:start position:0%
+giving you a way to to to see what's
+ 
+
+ align:start position:0%
+giving you a way to to to see what's
+going on inside a matrix now of course I
+
+ align:start position:0%
+going on inside a matrix now of course I
+ 
+
+ align:start position:0%
+going on inside a matrix now of course I
+can continue that for to the case power
+
+ align:start position:0%
+can continue that for to the case power
+ 
+
+ align:start position:0%
+can continue that for to the case power
+a to the case power if I multiply if I
+
+ align:start position:0%
+a to the case power if I multiply if I
+ 
+
+ align:start position:0%
+a to the case power if I multiply if I
+have K of these together you see how s
+
+ align:start position:0%
+have K of these together you see how s
+ 
+
+ align:start position:0%
+have K of these together you see how s
+inverse s will keep canceling in the in
+
+ align:start position:0%
+inverse s will keep canceling in the in
+ 
+
+ align:start position:0%
+inverse s will keep canceling in the in
+the inside I'll have the s outside at
+
+ align:start position:0%
+the inside I'll have the s outside at
+ 
+
+ align:start position:0%
+the inside I'll have the s outside at
+the far left and lambda will be in there
+
+ align:start position:0%
+the far left and lambda will be in there
+ 
+
+ align:start position:0%
+the far left and lambda will be in there
+K times and s inverse so what's that
+
+ align:start position:0%
+K times and s inverse so what's that
+ 
+
+ align:start position:0%
+K times and s inverse so what's that
+telling me that's telling me that the
+
+ align:start position:0%
+telling me that's telling me that the
+ 
+
+ align:start position:0%
+telling me that's telling me that the
+eigenvalues of a of a to the K power are
+
+ align:start position:0%
+eigenvalues of a of a to the K power are
+ 
+
+ align:start position:0%
+eigenvalues of a of a to the K power are
+the K power
+
+ align:start position:0%
+the K power
+ 
+
+ align:start position:0%
+the K power
+the eigenvalues of a cubed are the cubes
+
+ align:start position:0%
+the eigenvalues of a cubed are the cubes
+ 
+
+ align:start position:0%
+the eigenvalues of a cubed are the cubes
+of the eigenvalues of a and the
+
+ align:start position:0%
+of the eigenvalues of a and the
+ 
+
+ align:start position:0%
+of the eigenvalues of a and the
+eigenvectors are the same the same okay
+
+ align:start position:0%
+eigenvectors are the same the same okay
+ 
+
+ align:start position:0%
+eigenvectors are the same the same okay
+in other words eigenvalues and
+
+ align:start position:0%
+in other words eigenvalues and
+ 
+
+ align:start position:0%
+in other words eigenvalues and
+eigenvectors give a great way to
+
+ align:start position:0%
+eigenvectors give a great way to
+ 
+
+ align:start position:0%
+eigenvectors give a great way to
+understand the powers of a matrix if I
+
+ align:start position:0%
+understand the powers of a matrix if I
+ 
+
+ align:start position:0%
+understand the powers of a matrix if I
+take this square of a matrix or the
+
+ align:start position:0%
+take this square of a matrix or the
+ 
+
+ align:start position:0%
+take this square of a matrix or the
+hundredth power of a matrix the pivots
+
+ align:start position:0%
+hundredth power of a matrix the pivots
+ 
+
+ align:start position:0%
+hundredth power of a matrix the pivots
+are all over the place
+
+ align:start position:0%
+are all over the place
+ 
+
+ align:start position:0%
+are all over the place
+Lu if I multiply lu x lu x lu x lu a
+
+ align:start position:0%
+Lu if I multiply lu x lu x lu x lu a
+ 
+
+ align:start position:0%
+Lu if I multiply lu x lu x lu x lu a
+hundred times i've got a hundred l use i
+
+ align:start position:0%
+hundred times i've got a hundred l use i
+ 
+
+ align:start position:0%
+hundred times i've got a hundred l use i
+can't do anything with them but when i
+
+ align:start position:0%
+can't do anything with them but when i
+ 
+
+ align:start position:0%
+can't do anything with them but when i
+multiply s lambda s inverse by itself
+
+ align:start position:0%
+multiply s lambda s inverse by itself
+ 
+
+ align:start position:0%
+multiply s lambda s inverse by itself
+when I look at the eigenvector picture a
+
+ align:start position:0%
+when I look at the eigenvector picture a
+ 
+
+ align:start position:0%
+when I look at the eigenvector picture a
+hundred times I get a hundred or 99 of
+
+ align:start position:0%
+hundred times I get a hundred or 99 of
+ 
+
+ align:start position:0%
+hundred times I get a hundred or 99 of
+these guys cancelling out inside and I
+
+ align:start position:0%
+these guys cancelling out inside and I
+ 
+
+ align:start position:0%
+these guys cancelling out inside and I
+get a to the hundredth is s lambda to
+
+ align:start position:0%
+get a to the hundredth is s lambda to
+ 
+
+ align:start position:0%
+get a to the hundredth is s lambda to
+the hundredth s inverse I mean
+
+ align:start position:0%
+the hundredth s inverse I mean
+ 
+
+ align:start position:0%
+the hundredth s inverse I mean
+eigenvalues tell you about powers of a
+
+ align:start position:0%
+eigenvalues tell you about powers of a
+ 
+
+ align:start position:0%
+eigenvalues tell you about powers of a
+matrix in a way that we had no no way to
+
+ align:start position:0%
+matrix in a way that we had no no way to
+ 
+
+ align:start position:0%
+matrix in a way that we had no no way to
+approach previously for example when
+
+ align:start position:0%
+approach previously for example when
+ 
+
+ align:start position:0%
+approach previously for example when
+does when do the powers of a matrix go
+
+ align:start position:0%
+does when do the powers of a matrix go
+ 
+
+ align:start position:0%
+does when do the powers of a matrix go
+to zero I would call that matrix stable
+
+ align:start position:0%
+to zero I would call that matrix stable
+ 
+
+ align:start position:0%
+to zero I would call that matrix stable
+maybe so so so I could write down a
+
+ align:start position:0%
+maybe so so so I could write down a
+ 
+
+ align:start position:0%
+maybe so so so I could write down a
+theorem I'll write it as a theorem just
+
+ align:start position:0%
+theorem I'll write it as a theorem just
+ 
+
+ align:start position:0%
+theorem I'll write it as a theorem just
+use that word to emphasize that here I'm
+
+ align:start position:0%
+use that word to emphasize that here I'm
+ 
+
+ align:start position:0%
+use that word to emphasize that here I'm
+getting this great fact from this
+
+ align:start position:0%
+getting this great fact from this
+ 
+
+ align:start position:0%
+getting this great fact from this
+eigenvalue picture okay a to the K
+
+ align:start position:0%
+eigenvalue picture okay a to the K
+ 
+
+ align:start position:0%
+eigenvalue picture okay a to the K
+approaches zero as K goes as K gets
+
+ align:start position:0%
+approaches zero as K goes as K gets
+ 
+
+ align:start position:0%
+approaches zero as K goes as K gets
+bigger if what what's the how can I tell
+
+ align:start position:0%
+bigger if what what's the how can I tell
+ 
+
+ align:start position:0%
+bigger if what what's the how can I tell
+for a matrix a if its powers go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's somewhere inside that matrix is
+
+ align:start position:0%
+what's somewhere inside that matrix is
+ 
+
+ align:start position:0%
+what's somewhere inside that matrix is
+that information that information is not
+
+ align:start position:0%
+that information that information is not
+ 
+
+ align:start position:0%
+that information that information is not
+present in the pivots it's present in
+
+ align:start position:0%
+present in the pivots it's present in
+ 
+
+ align:start position:0%
+present in the pivots it's present in
+the eigenvalues what do I need for the
+
+ align:start position:0%
+the eigenvalues what do I need for the
+ 
+
+ align:start position:0%
+the eigenvalues what do I need for the
+to know that if I take
+
+ align:start position:0%
+to know that if I take
+ 
+
+ align:start position:0%
+to know that if I take
+I earn higher powers of a that this
+
+ align:start position:0%
+I earn higher powers of a that this
+ 
+
+ align:start position:0%
+I earn higher powers of a that this
+matrix gets smaller and smaller well s
+
+ align:start position:0%
+matrix gets smaller and smaller well s
+ 
+
+ align:start position:0%
+matrix gets smaller and smaller well s
+and s inverse are not moving
+
+ align:start position:0%
+and s inverse are not moving
+ 
+
+ align:start position:0%
+and s inverse are not moving
+so it's this guy that has to get small
+
+ align:start position:0%
+so it's this guy that has to get small
+ 
+
+ align:start position:0%
+so it's this guy that has to get small
+and that's easy too easy to understand
+
+ align:start position:0%
+and that's easy too easy to understand
+ 
+
+ align:start position:0%
+and that's easy too easy to understand
+the requirement is all eigenvalues so
+
+ align:start position:0%
+the requirement is all eigenvalues so
+ 
+
+ align:start position:0%
+the requirement is all eigenvalues so
+what is a requirement the eigenvalues
+
+ align:start position:0%
+what is a requirement the eigenvalues
+ 
+
+ align:start position:0%
+what is a requirement the eigenvalues
+have to be less than one now I have to
+
+ align:start position:0%
+have to be less than one now I have to
+ 
+
+ align:start position:0%
+have to be less than one now I have to
+write that absolute value because those
+
+ align:start position:0%
+write that absolute value because those
+ 
+
+ align:start position:0%
+write that absolute value because those
+eigenvalues could be negative they could
+
+ align:start position:0%
+eigenvalues could be negative they could
+ 
+
+ align:start position:0%
+eigenvalues could be negative they could
+be complex numbers so I'm taking the
+
+ align:start position:0%
+be complex numbers so I'm taking the
+ 
+
+ align:start position:0%
+be complex numbers so I'm taking the
+absolute value half if all of those are
+
+ align:start position:0%
+absolute value half if all of those are
+ 
+
+ align:start position:0%
+absolute value half if all of those are
+below one that's in fact we practically
+
+ align:start position:0%
+below one that's in fact we practically
+ 
+
+ align:start position:0%
+below one that's in fact we practically
+see why let me just say that I that I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operating on one assumption here and I
+
+ align:start position:0%
+operating on one assumption here and I
+ 
+
+ align:start position:0%
+operating on one assumption here and I
+gotta keep remembering that that
+
+ align:start position:0%
+gotta keep remembering that that
+ 
+
+ align:start position:0%
+gotta keep remembering that that
+assumption is still present that
+
+ align:start position:0%
+assumption is still present that
+ 
+
+ align:start position:0%
+assumption is still present that
+assumption was that I had a full set of
+
+ align:start position:0%
+assumption was that I had a full set of
+ 
+
+ align:start position:0%
+assumption was that I had a full set of
+of n independent eigenvectors if I don't
+
+ align:start position:0%
+of n independent eigenvectors if I don't
+ 
+
+ align:start position:0%
+of n independent eigenvectors if I don't
+have that then I then this approach is
+
+ align:start position:0%
+have that then I then this approach is
+ 
+
+ align:start position:0%
+have that then I then this approach is
+not working so so again a pure
+
+ align:start position:0%
+not working so so again a pure
+ 
+
+ align:start position:0%
+not working so so again a pure
+eigenvalue approach eigenvector approach
+
+ align:start position:0%
+eigenvalue approach eigenvector approach
+ 
+
+ align:start position:0%
+eigenvalue approach eigenvector approach
+needs and independent eigenvectors if we
+
+ align:start position:0%
+needs and independent eigenvectors if we
+ 
+
+ align:start position:0%
+needs and independent eigenvectors if we
+don't have n independent eigenvectors we
+
+ align:start position:0%
+don't have n independent eigenvectors we
+ 
+
+ align:start position:0%
+don't have n independent eigenvectors we
+can't diagonalize the matrix we can't
+
+ align:start position:0%
+can't diagonalize the matrix we can't
+ 
+
+ align:start position:0%
+can't diagonalize the matrix we can't
+get to a diagonal matrix this this this
+
+ align:start position:0%
+get to a diagonal matrix this this this
+ 
+
+ align:start position:0%
+get to a diagonal matrix this this this
+diagonalization is only possible if s
+
+ align:start position:0%
+diagonalization is only possible if s
+ 
+
+ align:start position:0%
+diagonalization is only possible if s
+inverse makes sense
+
+ align:start position:0%
+inverse makes sense
+ 
+
+ align:start position:0%
+inverse makes sense
+okay can I can I follow up on that point
+
+ align:start position:0%
+okay can I can I follow up on that point
+ 
+
+ align:start position:0%
+okay can I can I follow up on that point
+now so so you see why what we get and
+
+ align:start position:0%
+now so so you see why what we get and
+ 
+
+ align:start position:0%
+now so so you see why what we get and
+and why we want it because we get
+
+ align:start position:0%
+and why we want it because we get
+ 
+
+ align:start position:0%
+and why we want it because we get
+information about the powers of a matrix
+
+ align:start position:0%
+information about the powers of a matrix
+ 
+
+ align:start position:0%
+information about the powers of a matrix
+just immediately from the eigenvalues
+
+ align:start position:0%
+just immediately from the eigenvalues
+ 
+
+ align:start position:0%
+just immediately from the eigenvalues
+okay now let me follow up on this
+
+ align:start position:0%
+okay now let me follow up on this
+ 
+
+ align:start position:0%
+okay now let me follow up on this
+business of which matrices are
+
+ align:start position:0%
+business of which matrices are
+ 
+
+ align:start position:0%
+business of which matrices are
+diagonalizable sorry about that long
+
+ align:start position:0%
+diagonalizable sorry about that long
+ 
+
+ align:start position:0%
+diagonalizable sorry about that long
+word so a matrix is
+
+ align:start position:0%
+word so a matrix is
+ 
+
+ align:start position:0%
+word so a matrix is
+sure so here's here's the main point a
+
+ align:start position:0%
+sure so here's here's the main point a
+ 
+
+ align:start position:0%
+sure so here's here's the main point a
+is sure to be to have n independent
+
+ align:start position:0%
+is sure to be to have n independent
+ 
+
+ align:start position:0%
+is sure to be to have n independent
+eigenvectors and and B now here comes
+
+ align:start position:0%
+eigenvectors and and B now here comes
+ 
+
+ align:start position:0%
+eigenvectors and and B now here comes
+that word diagonalizable if if so we
+
+ align:start position:0%
+that word diagonalizable if if so we
+ 
+
+ align:start position:0%
+that word diagonalizable if if so we
+might as well get the nice case out in
+
+ align:start position:0%
+might as well get the nice case out in
+ 
+
+ align:start position:0%
+might as well get the nice case out in
+the open the nice case is when if all
+
+ align:start position:0%
+the open the nice case is when if all
+ 
+
+ align:start position:0%
+the open the nice case is when if all
+the lambdas are different that means
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that means no repeated eigenvalues okay
+
+ align:start position:0%
+that means no repeated eigenvalues okay
+ 
+
+ align:start position:0%
+that means no repeated eigenvalues okay
+that's the nice case if my matrix and
+
+ align:start position:0%
+that's the nice case if my matrix and
+ 
+
+ align:start position:0%
+that's the nice case if my matrix and
+most Maitre if I do a random matrix in
+
+ align:start position:0%
+most Maitre if I do a random matrix in
+ 
+
+ align:start position:0%
+most Maitre if I do a random matrix in
+MATLAB and compute its eigenvalues so if
+
+ align:start position:0%
+MATLAB and compute its eigenvalues so if
+ 
+
+ align:start position:0%
+MATLAB and compute its eigenvalues so if
+I computed if I took I of ran of ten ten
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gave that MATLAB command the we'd get a
+
+ align:start position:0%
+gave that MATLAB command the we'd get a
+ 
+
+ align:start position:0%
+gave that MATLAB command the we'd get a
+random 10 by 10 matrix we would get a
+
+ align:start position:0%
+random 10 by 10 matrix we would get a
+ 
+
+ align:start position:0%
+random 10 by 10 matrix we would get a
+list of its ten eigenvalues and they
+
+ align:start position:0%
+list of its ten eigenvalues and they
+ 
+
+ align:start position:0%
+list of its ten eigenvalues and they
+would be different they would be
+
+ align:start position:0%
+would be different they would be
+ 
+
+ align:start position:0%
+would be different they would be
+distinct is the best word I would have a
+
+ align:start position:0%
+distinct is the best word I would have a
+ 
+
+ align:start position:0%
+distinct is the best word I would have a
+random matrix will have ten distinct
+
+ align:start position:0%
+random matrix will have ten distinct
+ 
+
+ align:start position:0%
+random matrix will have ten distinct
+that 10 by 10 matrix will have ten
+
+ align:start position:0%
+that 10 by 10 matrix will have ten
+ 
+
+ align:start position:0%
+that 10 by 10 matrix will have ten
+distinct eigenvalues and if it does the
+
+ align:start position:0%
+distinct eigenvalues and if it does the
+ 
+
+ align:start position:0%
+distinct eigenvalues and if it does the
+eigenvectors are automatically
+
+ align:start position:0%
+eigenvectors are automatically
+ 
+
+ align:start position:0%
+eigenvectors are automatically
+independent so that's a nice fact I
+
+ align:start position:0%
+independent so that's a nice fact I
+ 
+
+ align:start position:0%
+independent so that's a nice fact I
+could I'll refer you to the text for the
+
+ align:start position:0%
+could I'll refer you to the text for the
+ 
+
+ align:start position:0%
+could I'll refer you to the text for the
+proof that that a is sure to have an
+
+ align:start position:0%
+proof that that a is sure to have an
+ 
+
+ align:start position:0%
+proof that that a is sure to have an
+independent eigenvectors if the
+
+ align:start position:0%
+independent eigenvectors if the
+ 
+
+ align:start position:0%
+independent eigenvectors if the
+eigenvalues are different if if all the
+
+ align:start position:0%
+eigenvalues are different if if all the
+ 
+
+ align:start position:0%
+eigenvalues are different if if all the
+if all eigenvalues are
+
+ align:start position:0%
+if all eigenvalues are
+ 
+
+ align:start position:0%
+if all eigenvalues are
+it's just if some lambdas are repeated
+
+ align:start position:0%
+it's just if some lambdas are repeated
+ 
+
+ align:start position:0%
+it's just if some lambdas are repeated
+then I have to look more closely if an
+
+ align:start position:0%
+then I have to look more closely if an
+ 
+
+ align:start position:0%
+then I have to look more closely if an
+eigenvalue is repeated I have to look I
+
+ align:start position:0%
+eigenvalue is repeated I have to look I
+ 
+
+ align:start position:0%
+eigenvalue is repeated I have to look I
+have to count at the chick has it got
+
+ align:start position:0%
+have to count at the chick has it got
+ 
+
+ align:start position:0%
+have to count at the chick has it got
+say it's repeated three times so what's
+
+ align:start position:0%
+say it's repeated three times so what's
+ 
+
+ align:start position:0%
+say it's repeated three times so what's
+a possibility for the so it's so here's
+
+ align:start position:0%
+a possibility for the so it's so here's
+ 
+
+ align:start position:0%
+a possibility for the so it's so here's
+here's the repeated possibility and let
+
+ align:start position:0%
+here's the repeated possibility and let
+ 
+
+ align:start position:0%
+here's the repeated possibility and let
+me emphasize the conclusion that if I
+
+ align:start position:0%
+me emphasize the conclusion that if I
+ 
+
+ align:start position:0%
+me emphasize the conclusion that if I
+have repeated eigenvalues I may or may
+
+ align:start position:0%
+have repeated eigenvalues I may or may
+ 
+
+ align:start position:0%
+have repeated eigenvalues I may or may
+not I may or may not have have n
+
+ align:start position:0%
+not I may or may not have have n
+ 
+
+ align:start position:0%
+not I may or may not have have n
+independent eigenvectors I might I you
+
+ align:start position:0%
+independent eigenvectors I might I you
+ 
+
+ align:start position:0%
+independent eigenvectors I might I you
+know this isn't a completely negative
+
+ align:start position:0%
+know this isn't a completely negative
+ 
+
+ align:start position:0%
+know this isn't a completely negative
+case the identity matrix well suppose I
+
+ align:start position:0%
+case the identity matrix well suppose I
+ 
+
+ align:start position:0%
+case the identity matrix well suppose I
+take the ten by ten identity matrix what
+
+ align:start position:0%
+take the ten by ten identity matrix what
+ 
+
+ align:start position:0%
+take the ten by ten identity matrix what
+are the eigenvalues of that matrix so
+
+ align:start position:0%
+are the eigenvalues of that matrix so
+ 
+
+ align:start position:0%
+are the eigenvalues of that matrix so
+just let's take the easiest matrix the
+
+ align:start position:0%
+just let's take the easiest matrix the
+ 
+
+ align:start position:0%
+just let's take the easiest matrix the
+identity if I look for its eigenvalues
+
+ align:start position:0%
+identity if I look for its eigenvalues
+ 
+
+ align:start position:0%
+identity if I look for its eigenvalues
+they're all ones so that eigenvalue one
+
+ align:start position:0%
+they're all ones so that eigenvalue one
+ 
+
+ align:start position:0%
+they're all ones so that eigenvalue one
+is repeated ten times but there's no
+
+ align:start position:0%
+is repeated ten times but there's no
+ 
+
+ align:start position:0%
+is repeated ten times but there's no
+shortage of eigenvectors for the
+
+ align:start position:0%
+shortage of eigenvectors for the
+ 
+
+ align:start position:0%
+shortage of eigenvectors for the
+identity matrix in fact every vector is
+
+ align:start position:0%
+identity matrix in fact every vector is
+ 
+
+ align:start position:0%
+identity matrix in fact every vector is
+an eigenvector so i can take ten
+
+ align:start position:0%
+an eigenvector so i can take ten
+ 
+
+ align:start position:0%
+an eigenvector so i can take ten
+independent vectors oh well what happens
+
+ align:start position:0%
+independent vectors oh well what happens
+ 
+
+ align:start position:0%
+independent vectors oh well what happens
+to everything if a is the identity
+
+ align:start position:0%
+to everything if a is the identity
+ 
+
+ align:start position:0%
+to everything if a is the identity
+matrix let's just think that one through
+
+ align:start position:0%
+matrix let's just think that one through
+ 
+
+ align:start position:0%
+matrix let's just think that one through
+in our head if a is the identity matrix
+
+ align:start position:0%
+in our head if a is the identity matrix
+ 
+
+ align:start position:0%
+in our head if a is the identity matrix
+then it's got plenty of eigenvectors i
+
+ align:start position:0%
+then it's got plenty of eigenvectors i
+ 
+
+ align:start position:0%
+then it's got plenty of eigenvectors i
+choose ten independent vectors they're
+
+ align:start position:0%
+choose ten independent vectors they're
+ 
+
+ align:start position:0%
+choose ten independent vectors they're
+the columns of s and and what do i get
+
+ align:start position:0%
+the columns of s and and what do i get
+ 
+
+ align:start position:0%
+the columns of s and and what do i get
+from s inverse a s i get i again right
+
+ align:start position:0%
+from s inverse a s i get i again right
+ 
+
+ align:start position:0%
+from s inverse a s i get i again right
+if a is the idea and of course that's
+
+ align:start position:0%
+if a is the idea and of course that's
+ 
+
+ align:start position:0%
+if a is the idea and of course that's
+the correct lambda the matrix was
+
+ align:start position:0%
+the correct lambda the matrix was
+ 
+
+ align:start position:0%
+the correct lambda the matrix was
+already diagonal so if the matrix is
+
+ align:start position:0%
+already diagonal so if the matrix is
+ 
+
+ align:start position:0%
+already diagonal so if the matrix is
+already diagonal then the the lambda is
+
+ align:start position:0%
+already diagonal then the the lambda is
+ 
+
+ align:start position:0%
+already diagonal then the the lambda is
+the same as the matrix a diagonal matrix
+
+ align:start position:0%
+the same as the matrix a diagonal matrix
+ 
+
+ align:start position:0%
+the same as the matrix a diagonal matrix
+has got its eigenvalues sitting right
+
+ align:start position:0%
+has got its eigenvalues sitting right
+ 
+
+ align:start position:0%
+has got its eigenvalues sitting right
+there in
+
+ align:start position:0%
+there in
+ 
+
+ align:start position:0%
+there in
+front of you now if it's triangular the
+
+ align:start position:0%
+front of you now if it's triangular the
+ 
+
+ align:start position:0%
+front of you now if it's triangular the
+eigenvalues are still sitting there but
+
+ align:start position:0%
+eigenvalues are still sitting there but
+ 
+
+ align:start position:0%
+eigenvalues are still sitting there but
+so let's let's take a case where it's
+
+ align:start position:0%
+so let's let's take a case where it's
+ 
+
+ align:start position:0%
+so let's let's take a case where it's
+triangular suppose a is like 2 1 2 0 so
+
+ align:start position:0%
+triangular suppose a is like 2 1 2 0 so
+ 
+
+ align:start position:0%
+triangular suppose a is like 2 1 2 0 so
+there's a case that's going to be
+
+ align:start position:0%
+there's a case that's going to be
+ 
+
+ align:start position:0%
+there's a case that's going to be
+trouble there's a case that's going to
+
+ align:start position:0%
+trouble there's a case that's going to
+ 
+
+ align:start position:0%
+trouble there's a case that's going to
+be trouble
+
+ align:start position:0%
+be trouble
+ 
+
+ align:start position:0%
+be trouble
+first of all what are the eigen value if
+
+ align:start position:0%
+first of all what are the eigen value if
+ 
+
+ align:start position:0%
+first of all what are the eigen value if
+we start with a matrix the first thing
+
+ align:start position:0%
+we start with a matrix the first thing
+ 
+
+ align:start position:0%
+we start with a matrix the first thing
+we do will practically without thinking
+
+ align:start position:0%
+we do will practically without thinking
+ 
+
+ align:start position:0%
+we do will practically without thinking
+is compute the eigenvalues and
+
+ align:start position:0%
+is compute the eigenvalues and
+ 
+
+ align:start position:0%
+is compute the eigenvalues and
+eigenvectors okay so what are the
+
+ align:start position:0%
+eigenvectors okay so what are the
+ 
+
+ align:start position:0%
+eigenvectors okay so what are the
+eigenvalues you can tell me right away
+
+ align:start position:0%
+eigenvalues you can tell me right away
+ 
+
+ align:start position:0%
+eigenvalues you can tell me right away
+what they are they're two and two right
+
+ align:start position:0%
+what they are they're two and two right
+ 
+
+ align:start position:0%
+what they are they're two and two right
+it's a triangular matrix so when I do
+
+ align:start position:0%
+it's a triangular matrix so when I do
+ 
+
+ align:start position:0%
+it's a triangular matrix so when I do
+this determinant shall I do this
+
+ align:start position:0%
+this determinant shall I do this
+ 
+
+ align:start position:0%
+this determinant shall I do this
+determinant of a minus lambda I I'll get
+
+ align:start position:0%
+determinant of a minus lambda I I'll get
+ 
+
+ align:start position:0%
+determinant of a minus lambda I I'll get
+this 2 minus lambda 1 0 2 minus lambda
+
+ align:start position:0%
+this 2 minus lambda 1 0 2 minus lambda
+ 
+
+ align:start position:0%
+this 2 minus lambda 1 0 2 minus lambda
+right I take that determinant so I make
+
+ align:start position:0%
+right I take that determinant so I make
+ 
+
+ align:start position:0%
+right I take that determinant so I make
+those into vertical bars to mean
+
+ align:start position:0%
+those into vertical bars to mean
+ 
+
+ align:start position:0%
+those into vertical bars to mean
+determinant and what's the determinant
+
+ align:start position:0%
+determinant and what's the determinant
+ 
+
+ align:start position:0%
+determinant and what's the determinant
+to minus lambda square what are the
+
+ align:start position:0%
+to minus lambda square what are the
+ 
+
+ align:start position:0%
+to minus lambda square what are the
+roots lambda equal to twice so the
+
+ align:start position:0%
+roots lambda equal to twice so the
+ 
+
+ align:start position:0%
+roots lambda equal to twice so the
+eigenvalues are lambda equals 2 and 2
+
+ align:start position:0%
+eigenvalues are lambda equals 2 and 2
+ 
+
+ align:start position:0%
+eigenvalues are lambda equals 2 and 2
+okay fine
+
+ align:start position:0%
+okay fine
+ 
+
+ align:start position:0%
+okay fine
+now the next step find the eigenvectors
+
+ align:start position:0%
+now the next step find the eigenvectors
+ 
+
+ align:start position:0%
+now the next step find the eigenvectors
+so i hope for eigenvectors and what do I
+
+ align:start position:0%
+so i hope for eigenvectors and what do I
+ 
+
+ align:start position:0%
+so i hope for eigenvectors and what do I
+find for this guy
+
+ align:start position:0%
+find for this guy
+ 
+
+ align:start position:0%
+find for this guy
+I can Victor's for this guy when I
+
+ align:start position:0%
+I can Victor's for this guy when I
+ 
+
+ align:start position:0%
+I can Victor's for this guy when I
+subtract 2 minus the identity so a minus
+
+ align:start position:0%
+subtract 2 minus the identity so a minus
+ 
+
+ align:start position:0%
+subtract 2 minus the identity so a minus
+2 I as zeros here and I'm looking for
+
+ align:start position:0%
+2 I as zeros here and I'm looking for
+ 
+
+ align:start position:0%
+2 I as zeros here and I'm looking for
+the null space what's what are the
+
+ align:start position:0%
+the null space what's what are the
+ 
+
+ align:start position:0%
+the null space what's what are the
+eigenvectors
+
+ align:start position:0%
+eigenvectors
+ 
+
+ align:start position:0%
+eigenvectors
+they're there they're the null space of
+
+ align:start position:0%
+they're there they're the null space of
+ 
+
+ align:start position:0%
+they're there they're the null space of
+a minus lambda up the null space is only
+
+ align:start position:0%
+a minus lambda up the null space is only
+ 
+
+ align:start position:0%
+a minus lambda up the null space is only
+one dimension this is a case where I
+
+ align:start position:0%
+one dimension this is a case where I
+ 
+
+ align:start position:0%
+one dimension this is a case where I
+don't have enough eigenvectors my
+
+ align:start position:0%
+don't have enough eigenvectors my
+ 
+
+ align:start position:0%
+don't have enough eigenvectors my
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+simplicity is - I would say when I see
+
+ align:start position:0%
+simplicity is - I would say when I see
+ 
+
+ align:start position:0%
+simplicity is - I would say when I see
+when I count how often the eigenvalue is
+
+ align:start position:0%
+when I count how often the eigenvalue is
+ 
+
+ align:start position:0%
+when I count how often the eigenvalue is
+repeated
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the algebraic multiplicity
+
+ align:start position:0%
+that's the algebraic multiplicity
+ 
+
+ align:start position:0%
+that's the algebraic multiplicity
+that's the multiplicity how many times
+
+ align:start position:0%
+that's the multiplicity how many times
+ 
+
+ align:start position:0%
+that's the multiplicity how many times
+is it the root of the polynomial my
+
+ align:start position:0%
+is it the root of the polynomial my
+ 
+
+ align:start position:0%
+is it the root of the polynomial my
+polynomial is 2 minus lambda square it's
+
+ align:start position:0%
+polynomial is 2 minus lambda square it's
+ 
+
+ align:start position:0%
+polynomial is 2 minus lambda square it's
+a double root
+
+ align:start position:0%
+a double root
+ 
+
+ align:start position:0%
+a double root
+so my algebraic multiplicity is 2 but
+
+ align:start position:0%
+so my algebraic multiplicity is 2 but
+ 
+
+ align:start position:0%
+so my algebraic multiplicity is 2 but
+the geometric multiplicity which looks
+
+ align:start position:0%
+the geometric multiplicity which looks
+ 
+
+ align:start position:0%
+the geometric multiplicity which looks
+for vectors looks for eigenvectors and
+
+ align:start position:0%
+for vectors looks for eigenvectors and
+ 
+
+ align:start position:0%
+for vectors looks for eigenvectors and
+which means the null space of this thing
+
+ align:start position:0%
+which means the null space of this thing
+ 
+
+ align:start position:0%
+which means the null space of this thing
+and the only eigenvector is 1 0 that's
+
+ align:start position:0%
+and the only eigenvector is 1 0 that's
+ 
+
+ align:start position:0%
+and the only eigenvector is 1 0 that's
+in the null space 0 1 is not in the null
+
+ align:start position:0%
+in the null space 0 1 is not in the null
+ 
+
+ align:start position:0%
+in the null space 0 1 is not in the null
+space the null space is only one
+
+ align:start position:0%
+space the null space is only one
+ 
+
+ align:start position:0%
+space the null space is only one
+dimensional so there is a matrix my this
+
+ align:start position:0%
+dimensional so there is a matrix my this
+ 
+
+ align:start position:0%
+dimensional so there is a matrix my this
+a or the original a that are not
+
+ align:start position:0%
+a or the original a that are not
+ 
+
+ align:start position:0%
+a or the original a that are not
+diagonalizable I can't I can't find two
+
+ align:start position:0%
+diagonalizable I can't I can't find two
+ 
+
+ align:start position:0%
+diagonalizable I can't I can't find two
+independent eigenvectors there's only
+
+ align:start position:0%
+independent eigenvectors there's only
+ 
+
+ align:start position:0%
+independent eigenvectors there's only
+one okay so that's the case that I'm
+
+ align:start position:0%
+one okay so that's the case that I'm
+ 
+
+ align:start position:0%
+one okay so that's the case that I'm
+that's a case that I I'm not really
+
+ align:start position:0%
+that's a case that I I'm not really
+ 
+
+ align:start position:0%
+that's a case that I I'm not really
+handling for example when I wrote down
+
+ align:start position:0%
+handling for example when I wrote down
+ 
+
+ align:start position:0%
+handling for example when I wrote down
+up here that the powers went to 0 if the
+
+ align:start position:0%
+up here that the powers went to 0 if the
+ 
+
+ align:start position:0%
+up here that the powers went to 0 if the
+eigen guys were below 1 I didn't really
+
+ align:start position:0%
+eigen guys were below 1 I didn't really
+ 
+
+ align:start position:0%
+eigen guys were below 1 I didn't really
+handle that case of repeated eigen
+
+ align:start position:0%
+handle that case of repeated eigen
+ 
+
+ align:start position:0%
+handle that case of repeated eigen
+values because my reasoning was based on
+
+ align:start position:0%
+values because my reasoning was based on
+ 
+
+ align:start position:0%
+values because my reasoning was based on
+this form and this formula is based on n
+
+ align:start position:0%
+this form and this formula is based on n
+ 
+
+ align:start position:0%
+this form and this formula is based on n
+independent eigenvectors ok so just this
+
+ align:start position:0%
+independent eigenvectors ok so just this
+ 
+
+ align:start position:0%
+independent eigenvectors ok so just this
+just to say there are some matrices that
+
+ align:start position:0%
+just to say there are some matrices that
+ 
+
+ align:start position:0%
+just to say there are some matrices that
+we that we don't cover through
+
+ align:start position:0%
+we that we don't cover through
+ 
+
+ align:start position:0%
+we that we don't cover through
+diagonalization but the great majority
+
+ align:start position:0%
+diagonalization but the great majority
+ 
+
+ align:start position:0%
+diagonalization but the great majority
+we do okay and we're always okay if we
+
+ align:start position:0%
+we do okay and we're always okay if we
+ 
+
+ align:start position:0%
+we do okay and we're always okay if we
+have different distinct eigen oh okay
+
+ align:start position:0%
+have different distinct eigen oh okay
+ 
+
+ align:start position:0%
+have different distinct eigen oh okay
+that's like the typical case because for
+
+ align:start position:0%
+that's like the typical case because for
+ 
+
+ align:start position:0%
+that's like the typical case because for
+each eigen value there's at least one
+
+ align:start position:0%
+each eigen value there's at least one
+ 
+
+ align:start position:0%
+each eigen value there's at least one
+eigenvector the algebraic multiplicity
+
+ align:start position:0%
+eigenvector the algebraic multiplicity
+ 
+
+ align:start position:0%
+eigenvector the algebraic multiplicity
+one for every eigenvalue and the
+
+ align:start position:0%
+one for every eigenvalue and the
+ 
+
+ align:start position:0%
+one for every eigenvalue and the
+geometric multiplicity is 1 there's one
+
+ align:start position:0%
+geometric multiplicity is 1 there's one
+ 
+
+ align:start position:0%
+geometric multiplicity is 1 there's one
+eigenvector and they are independent
+
+ align:start position:0%
+eigenvector and they are independent
+ 
+
+ align:start position:0%
+eigenvector and they are independent
+okay okay now let me come back to the
+
+ align:start position:0%
+okay okay now let me come back to the
+ 
+
+ align:start position:0%
+okay okay now let me come back to the
+important case when when we're okay the
+
+ align:start position:0%
+important case when when we're okay the
+ 
+
+ align:start position:0%
+important case when when we're okay the
+important case when we are dying light
+
+ align:start position:0%
+important case when we are dying light
+ 
+
+ align:start position:0%
+important case when we are dying light
+let me look at so so so a quick let me
+
+ align:start position:0%
+let me look at so so so a quick let me
+ 
+
+ align:start position:0%
+let me look at so so so a quick let me
+solve this equation the equation will be
+
+ align:start position:0%
+solve this equation the equation will be
+ 
+
+ align:start position:0%
+solve this equation the equation will be
+each I start with some start with a
+
+ align:start position:0%
+each I start with some start with a
+ 
+
+ align:start position:0%
+each I start with some start with a
+given vector u0 and then my equation is
+
+ align:start position:0%
+given vector u0 and then my equation is
+ 
+
+ align:start position:0%
+given vector u0 and then my equation is
+that every step I multiply what I have
+
+ align:start position:0%
+that every step I multiply what I have
+ 
+
+ align:start position:0%
+that every step I multiply what I have
+by a I then then equation ought to be
+
+ align:start position:0%
+by a I then then equation ought to be
+ 
+
+ align:start position:0%
+by a I then then equation ought to be
+simple to handle and I'd like to be able
+
+ align:start position:0%
+simple to handle and I'd like to be able
+ 
+
+ align:start position:0%
+simple to handle and I'd like to be able
+to solve how would I find if I start
+
+ align:start position:0%
+to solve how would I find if I start
+ 
+
+ align:start position:0%
+to solve how would I find if I start
+with a vector you know it and I multiply
+
+ align:start position:0%
+with a vector you know it and I multiply
+ 
+
+ align:start position:0%
+with a vector you know it and I multiply
+by a a hundred times what if I got what
+
+ align:start position:0%
+by a a hundred times what if I got what
+ 
+
+ align:start position:0%
+by a a hundred times what if I got what
+I certainly write down a formula for the
+
+ align:start position:0%
+I certainly write down a formula for the
+ 
+
+ align:start position:0%
+I certainly write down a formula for the
+answer so what what so u1 is a you know
+
+ align:start position:0%
+answer so what what so u1 is a you know
+ 
+
+ align:start position:0%
+answer so what what so u1 is a you know
+and u2 is what's you to then you to I
+
+ align:start position:0%
+and u2 is what's you to then you to I
+ 
+
+ align:start position:0%
+and u2 is what's you to then you to I
+multiply u2 I get from you one by
+
+ align:start position:0%
+multiply u2 I get from you one by
+ 
+
+ align:start position:0%
+multiply u2 I get from you one by
+another multiplying by a so I've been a
+
+ align:start position:0%
+another multiplying by a so I've been a
+ 
+
+ align:start position:0%
+another multiplying by a so I've been a
+twice and my formula is you K after K
+
+ align:start position:0%
+twice and my formula is you K after K
+ 
+
+ align:start position:0%
+twice and my formula is you K after K
+steps I multiplied by a K times the
+
+ align:start position:0%
+steps I multiplied by a K times the
+ 
+
+ align:start position:0%
+steps I multiplied by a K times the
+original you know you see what I'm doing
+
+ align:start position:0%
+original you know you see what I'm doing
+ 
+
+ align:start position:0%
+original you know you see what I'm doing
+the next section is going to solve
+
+ align:start position:0%
+the next section is going to solve
+ 
+
+ align:start position:0%
+the next section is going to solve
+systems of
+
+ align:start position:0%
+systems of
+ 
+
+ align:start position:0%
+systems of
+rental equation I'm going to have
+
+ align:start position:0%
+rental equation I'm going to have
+ 
+
+ align:start position:0%
+rental equation I'm going to have
+derivative this this section is the nice
+
+ align:start position:0%
+derivative this this section is the nice
+ 
+
+ align:start position:0%
+derivative this this section is the nice
+one it's all difference equations I
+
+ align:start position:0%
+one it's all difference equations I
+ 
+
+ align:start position:0%
+one it's all difference equations I
+would call that a difference equation
+
+ align:start position:0%
+would call that a difference equation
+ 
+
+ align:start position:0%
+would call that a difference equation
+it's kinetic first-order I would call
+
+ align:start position:0%
+it's kinetic first-order I would call
+ 
+
+ align:start position:0%
+it's kinetic first-order I would call
+that a first-order system because it
+
+ align:start position:0%
+that a first-order system because it
+ 
+
+ align:start position:0%
+that a first-order system because it
+connects only it only goes up one level
+
+ align:start position:0%
+connects only it only goes up one level
+ 
+
+ align:start position:0%
+connects only it only goes up one level
+and it's a system because these are
+
+ align:start position:0%
+and it's a system because these are
+ 
+
+ align:start position:0%
+and it's a system because these are
+vectors and that's amazing and the
+
+ align:start position:0%
+vectors and that's amazing and the
+ 
+
+ align:start position:0%
+vectors and that's amazing and the
+solution is just that okay but that's a
+
+ align:start position:0%
+solution is just that okay but that's a
+ 
+
+ align:start position:0%
+solution is just that okay but that's a
+nice formula that's like that most
+
+ align:start position:0%
+nice formula that's like that most
+ 
+
+ align:start position:0%
+nice formula that's like that most
+compact formula I could ever get you
+
+ align:start position:0%
+compact formula I could ever get you
+ 
+
+ align:start position:0%
+compact formula I could ever get you
+what hundreds would be eighty to one
+
+ align:start position:0%
+what hundreds would be eighty to one
+ 
+
+ align:start position:0%
+what hundreds would be eighty to one
+hundred you know but how would I
+
+ align:start position:0%
+hundred you know but how would I
+ 
+
+ align:start position:0%
+hundred you know but how would I
+actually find you one hundred how would
+
+ align:start position:0%
+actually find you one hundred how would
+ 
+
+ align:start position:0%
+actually find you one hundred how would
+I find how would I discover what you 100
+
+ align:start position:0%
+I find how would I discover what you 100
+ 
+
+ align:start position:0%
+I find how would I discover what you 100
+is let me let me show you how here's the
+
+ align:start position:0%
+is let me let me show you how here's the
+ 
+
+ align:start position:0%
+is let me let me show you how here's the
+idea
+
+ align:start position:0%
+idea
+ 
+
+ align:start position:0%
+idea
+if so to solve to really stop shall I
+
+ align:start position:0%
+if so to solve to really stop shall I
+ 
+
+ align:start position:0%
+if so to solve to really stop shall I
+say to really to really solve it I would
+
+ align:start position:0%
+say to really to really solve it I would
+ 
+
+ align:start position:0%
+say to really to really solve it I would
+take this initial vector U naught and I
+
+ align:start position:0%
+take this initial vector U naught and I
+ 
+
+ align:start position:0%
+take this initial vector U naught and I
+would write it as a combination of
+
+ align:start position:0%
+would write it as a combination of
+ 
+
+ align:start position:0%
+would write it as a combination of
+eigenvectors to really solve right right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you not as a combination say certain
+
+ align:start position:0%
+you not as a combination say certain
+ 
+
+ align:start position:0%
+you not as a combination say certain
+amount of the first eigen vector plus is
+
+ align:start position:0%
+amount of the first eigen vector plus is
+ 
+
+ align:start position:0%
+amount of the first eigen vector plus is
+certain
+
+ align:start position:0%
+certain
+ 
+
+ align:start position:0%
+certain
+the second eigenvector plus a certain
+
+ align:start position:0%
+the second eigenvector plus a certain
+ 
+
+ align:start position:0%
+the second eigenvector plus a certain
+amount of the last time now multiply by
+
+ align:start position:0%
+amount of the last time now multiply by
+ 
+
+ align:start position:0%
+amount of the last time now multiply by
+a you want you got to see the magic of
+
+ align:start position:0%
+a you want you got to see the magic of
+ 
+
+ align:start position:0%
+a you want you got to see the magic of
+eigenvectors working multiplied by a so
+
+ align:start position:0%
+eigenvectors working multiplied by a so
+ 
+
+ align:start position:0%
+eigenvectors working multiplied by a so
+a you know is what so a times that a
+
+ align:start position:0%
+a you know is what so a times that a
+ 
+
+ align:start position:0%
+a you know is what so a times that a
+times so what I can separate it out into
+
+ align:start position:0%
+times so what I can separate it out into
+ 
+
+ align:start position:0%
+times so what I can separate it out into
+n separate pieces and that's the whole
+
+ align:start position:0%
+n separate pieces and that's the whole
+ 
+
+ align:start position:0%
+n separate pieces and that's the whole
+point that each of those pieces is going
+
+ align:start position:0%
+point that each of those pieces is going
+ 
+
+ align:start position:0%
+point that each of those pieces is going
+in its own merry way each of those
+
+ align:start position:0%
+in its own merry way each of those
+ 
+
+ align:start position:0%
+in its own merry way each of those
+pieces is an eigenvector and when I
+
+ align:start position:0%
+pieces is an eigenvector and when I
+ 
+
+ align:start position:0%
+pieces is an eigenvector and when I
+multiply by a what is this piece become
+
+ align:start position:0%
+multiply by a what is this piece become
+ 
+
+ align:start position:0%
+multiply by a what is this piece become
+so that's some amount of the first let's
+
+ align:start position:0%
+so that's some amount of the first let's
+ 
+
+ align:start position:0%
+so that's some amount of the first let's
+suppose the eigenvectors are normalized
+
+ align:start position:0%
+suppose the eigenvectors are normalized
+ 
+
+ align:start position:0%
+suppose the eigenvectors are normalized
+to be unit vectors so that says what the
+
+ align:start position:0%
+to be unit vectors so that says what the
+ 
+
+ align:start position:0%
+to be unit vectors so that says what the
+eigenvector is and I need some multiple
+
+ align:start position:0%
+eigenvector is and I need some multiple
+ 
+
+ align:start position:0%
+eigenvector is and I need some multiple
+of it to produce you know okay now when
+
+ align:start position:0%
+of it to produce you know okay now when
+ 
+
+ align:start position:0%
+of it to produce you know okay now when
+I multiply by a what do I get I get c1
+
+ align:start position:0%
+I multiply by a what do I get I get c1
+ 
+
+ align:start position:0%
+I multiply by a what do I get I get c1
+which is just a factor times ax 1 but
+
+ align:start position:0%
+which is just a factor times ax 1 but
+ 
+
+ align:start position:0%
+which is just a factor times ax 1 but
+they X 1 is lambda 1 X 1 when I multiply
+
+ align:start position:0%
+they X 1 is lambda 1 X 1 when I multiply
+ 
+
+ align:start position:0%
+they X 1 is lambda 1 X 1 when I multiply
+this by a I get C 2 lambda 2 X 2 and
+
+ align:start position:0%
+this by a I get C 2 lambda 2 X 2 and
+ 
+
+ align:start position:0%
+this by a I get C 2 lambda 2 X 2 and
+here I get C n lambda n
+
+ align:start position:0%
+here I get C n lambda n
+ 
+
+ align:start position:0%
+here I get C n lambda n
+and suppose I multiply by a to the
+
+ align:start position:0%
+and suppose I multiply by a to the
+ 
+
+ align:start position:0%
+and suppose I multiply by a to the
+hundredth power now can we can we having
+
+ align:start position:0%
+hundredth power now can we can we having
+ 
+
+ align:start position:0%
+hundredth power now can we can we having
+done it multiplied by a let's multiply
+
+ align:start position:0%
+done it multiplied by a let's multiply
+ 
+
+ align:start position:0%
+done it multiplied by a let's multiply
+by a to the hundredth what happens to
+
+ align:start position:0%
+by a to the hundredth what happens to
+ 
+
+ align:start position:0%
+by a to the hundredth what happens to
+this first term when I multiply by a to
+
+ align:start position:0%
+this first term when I multiply by a to
+ 
+
+ align:start position:0%
+this first term when I multiply by a to
+the 100 it's got that factor lambda to
+
+ align:start position:0%
+the 100 it's got that factor lambda to
+ 
+
+ align:start position:0%
+the 100 it's got that factor lambda to
+the hundredth that's the key that that's
+
+ align:start position:0%
+the hundredth that's the key that that's
+ 
+
+ align:start position:0%
+the hundredth that's the key that that's
+what I mean by going its own merry way
+
+ align:start position:0%
+what I mean by going its own merry way
+ 
+
+ align:start position:0%
+what I mean by going its own merry way
+if it is pure eigenvector it's exactly
+
+ align:start position:0%
+if it is pure eigenvector it's exactly
+ 
+
+ align:start position:0%
+if it is pure eigenvector it's exactly
+in a direction where multiplication by a
+
+ align:start position:0%
+in a direction where multiplication by a
+ 
+
+ align:start position:0%
+in a direction where multiplication by a
+just brings in a scalar factor lambda
+
+ align:start position:0%
+just brings in a scalar factor lambda
+ 
+
+ align:start position:0%
+just brings in a scalar factor lambda
+one so a hundred times brings in this
+
+ align:start position:0%
+one so a hundred times brings in this
+ 
+
+ align:start position:0%
+one so a hundred times brings in this
+100 times a hundred times lambda 200
+
+ align:start position:0%
+100 times a hundred times lambda 200
+ 
+
+ align:start position:0%
+100 times a hundred times lambda 200
+times lambda n actually what are we
+
+ align:start position:0%
+times lambda n actually what are we
+ 
+
+ align:start position:0%
+times lambda n actually what are we
+seeing here we're seeing this same
+
+ align:start position:0%
+seeing here we're seeing this same
+ 
+
+ align:start position:0%
+seeing here we're seeing this same
+lambda capital lambda to the hundredth
+
+ align:start position:0%
+lambda capital lambda to the hundredth
+ 
+
+ align:start position:0%
+lambda capital lambda to the hundredth
+as in the as in the diagonalization and
+
+ align:start position:0%
+as in the as in the diagonalization and
+ 
+
+ align:start position:0%
+as in the as in the diagonalization and
+we're seeing the S matrix that matrix s
+
+ align:start position:0%
+we're seeing the S matrix that matrix s
+ 
+
+ align:start position:0%
+we're seeing the S matrix that matrix s
+of eigenvector that's what this has got
+
+ align:start position:0%
+of eigenvector that's what this has got
+ 
+
+ align:start position:0%
+of eigenvector that's what this has got
+this has got to amount to a lambda to
+
+ align:start position:0%
+this has got to amount to a lambda to
+ 
+
+ align:start position:0%
+this has got to amount to a lambda to
+the hundredth power times and s times
+
+ align:start position:0%
+the hundredth power times and s times
+ 
+
+ align:start position:0%
+the hundredth power times and s times
+this vector C that's telling us how much
+
+ align:start position:0%
+this vector C that's telling us how much
+ 
+
+ align:start position:0%
+this vector C that's telling us how much
+of each one is in the original thing so
+
+ align:start position:0%
+of each one is in the original thing so
+ 
+
+ align:start position:0%
+of each one is in the original thing so
+if I had to really find a hundredth
+
+ align:start position:0%
+if I had to really find a hundredth
+ 
+
+ align:start position:0%
+if I had to really find a hundredth
+power I would take you not I would
+
+ align:start position:0%
+power I would take you not I would
+ 
+
+ align:start position:0%
+power I would take you not I would
+expand it as a combination of
+
+ align:start position:0%
+expand it as a combination of
+ 
+
+ align:start position:0%
+expand it as a combination of
+eigenvectors this is really s the
+
+ align:start position:0%
+eigenvectors this is really s the
+ 
+
+ align:start position:0%
+eigenvectors this is really s the
+eigenvector matrix times C the
+
+ align:start position:0%
+eigenvector matrix times C the
+ 
+
+ align:start position:0%
+eigenvector matrix times C the
+coefficient vector and then I would
+
+ align:start position:0%
+coefficient vector and then I would
+ 
+
+ align:start position:0%
+coefficient vector and then I would
+immediately did by inserting these
+
+ align:start position:0%
+immediately did by inserting these
+ 
+
+ align:start position:0%
+immediately did by inserting these
+hundreds powers of eigenvalues I'd have
+
+ align:start position:0%
+hundreds powers of eigenvalues I'd have
+ 
+
+ align:start position:0%
+hundreds powers of eigenvalues I'd have
+the answer so the the up there must be
+
+ align:start position:0%
+the answer so the the up there must be
+ 
+
+ align:start position:0%
+the answer so the the up there must be
+let's see okay it's so yeah so if you
+
+ align:start position:0%
+let's see okay it's so yeah so if you
+ 
+
+ align:start position:0%
+let's see okay it's so yeah so if you
+100 is
+
+ align:start position:0%
+100 is
+ 
+
+ align:start position:0%
+100 is
+one hundred times you know and you know
+
+ align:start position:0%
+one hundred times you know and you know
+ 
+
+ align:start position:0%
+one hundred times you know and you know
+it is SC then you see this formula is
+
+ align:start position:0%
+it is SC then you see this formula is
+ 
+
+ align:start position:0%
+it is SC then you see this formula is
+just this formula which is the way I
+
+ align:start position:0%
+just this formula which is the way I
+ 
+
+ align:start position:0%
+just this formula which is the way I
+would actually get hold of this of this
+
+ align:start position:0%
+would actually get hold of this of this
+ 
+
+ align:start position:0%
+would actually get hold of this of this
+you 100 which is let me put it here you
+
+ align:start position:0%
+you 100 which is let me put it here you
+ 
+
+ align:start position:0%
+you 100 which is let me put it here you
+100 the way right the way I would
+
+ align:start position:0%
+100 the way right the way I would
+ 
+
+ align:start position:0%
+100 the way right the way I would
+actually get hold of that see what what
+
+ align:start position:0%
+actually get hold of that see what what
+ 
+
+ align:start position:0%
+actually get hold of that see what what
+the solution is after a hundred steps
+
+ align:start position:0%
+the solution is after a hundred steps
+ 
+
+ align:start position:0%
+the solution is after a hundred steps
+would be expand the initial vector into
+
+ align:start position:0%
+would be expand the initial vector into
+ 
+
+ align:start position:0%
+would be expand the initial vector into
+eigenvectors and up and let each
+
+ align:start position:0%
+eigenvectors and up and let each
+ 
+
+ align:start position:0%
+eigenvectors and up and let each
+eigenvector go its own way multiplying
+
+ align:start position:0%
+eigenvector go its own way multiplying
+ 
+
+ align:start position:0%
+eigenvector go its own way multiplying
+by a hundred by lambda at every step and
+
+ align:start position:0%
+by a hundred by lambda at every step and
+ 
+
+ align:start position:0%
+by a hundred by lambda at every step and
+therefore by lambda to the hundredth
+
+ align:start position:0%
+therefore by lambda to the hundredth
+ 
+
+ align:start position:0%
+therefore by lambda to the hundredth
+power after a hundred steps can I do
+
+ align:start position:0%
+power after a hundred steps can I do
+ 
+
+ align:start position:0%
+power after a hundred steps can I do
+anything
+
+ align:start position:0%
+anything
+ 
+
+ align:start position:0%
+anything
+so that's that's the the formulas now
+
+ align:start position:0%
+so that's that's the the formulas now
+ 
+
+ align:start position:0%
+so that's that's the the formulas now
+let me take an example I'll use the
+
+ align:start position:0%
+let me take an example I'll use the
+ 
+
+ align:start position:0%
+let me take an example I'll use the
+Fibonacci sequence as an example so so
+
+ align:start position:0%
+Fibonacci sequence as an example so so
+ 
+
+ align:start position:0%
+Fibonacci sequence as an example so so
+Fibonacci example you remember the
+
+ align:start position:0%
+Fibonacci example you remember the
+ 
+
+ align:start position:0%
+Fibonacci example you remember the
+Fibonacci numbers if we start with 1 and
+
+ align:start position:0%
+Fibonacci numbers if we start with 1 and
+ 
+
+ align:start position:0%
+Fibonacci numbers if we start with 1 and
+1 as f naught oh I think I start with 0
+
+ align:start position:0%
+1 as f naught oh I think I start with 0
+ 
+
+ align:start position:0%
+1 as f naught oh I think I start with 0
+that's 0 and 1 be the first
+
+ align:start position:0%
+that's 0 and 1 be the first
+ 
+
+ align:start position:0%
+that's 0 and 1 be the first
+so there's F 0 and F 1 first to 7rg
+
+ align:start position:0%
+so there's F 0 and F 1 first to 7rg
+ 
+
+ align:start position:0%
+so there's F 0 and F 1 first to 7rg
+numbers and what's the rule for
+
+ align:start position:0%
+numbers and what's the rule for
+ 
+
+ align:start position:0%
+numbers and what's the rule for
+Fibonacci numbers I'm there the Sun the
+
+ align:start position:0%
+Fibonacci numbers I'm there the Sun the
+ 
+
+ align:start position:0%
+Fibonacci numbers I'm there the Sun the
+next one is the sum of those so it's 1
+
+ align:start position:0%
+next one is the sum of those so it's 1
+ 
+
+ align:start position:0%
+next one is the sum of those so it's 1
+the next one is the sum of those so it's
+
+ align:start position:0%
+the next one is the sum of those so it's
+ 
+
+ align:start position:0%
+the next one is the sum of those so it's
+2 the next one is the sum of those so
+
+ align:start position:0%
+2 the next one is the sum of those so
+ 
+
+ align:start position:0%
+2 the next one is the sum of those so
+it's 3 well it looks like 1 2 3 4 5 but
+
+ align:start position:0%
+it's 3 well it looks like 1 2 3 4 5 but
+ 
+
+ align:start position:0%
+it's 3 well it looks like 1 2 3 4 5 but
+somehow it's not going to do that way
+
+ align:start position:0%
+somehow it's not going to do that way
+ 
+
+ align:start position:0%
+somehow it's not going to do that way
+the next one is 5 right 2 or 3 makes 5
+
+ align:start position:0%
+the next one is 5 right 2 or 3 makes 5
+ 
+
+ align:start position:0%
+the next one is 5 right 2 or 3 makes 5
+the next one is 8 the next one is 13 and
+
+ align:start position:0%
+the next one is 8 the next one is 13 and
+ 
+
+ align:start position:0%
+the next one is 8 the next one is 13 and
+the 107 odd
+
+ align:start position:0%
+the 107 odd
+ 
+
+ align:start position:0%
+the 107 odd
+number is one that's my question
+
+ align:start position:0%
+number is one that's my question
+ 
+
+ align:start position:0%
+number is one that's my question
+how could I get a formula for the
+
+ align:start position:0%
+how could I get a formula for the
+ 
+
+ align:start position:0%
+how could I get a formula for the
+hundredth number and and for example how
+
+ align:start position:0%
+hundredth number and and for example how
+ 
+
+ align:start position:0%
+hundredth number and and for example how
+could I answer the question how fast are
+
+ align:start position:0%
+could I answer the question how fast are
+ 
+
+ align:start position:0%
+could I answer the question how fast are
+they growing how fast are those
+
+ align:start position:0%
+they growing how fast are those
+ 
+
+ align:start position:0%
+they growing how fast are those
+Fibonacci numbers growing they're
+
+ align:start position:0%
+Fibonacci numbers growing they're
+ 
+
+ align:start position:0%
+Fibonacci numbers growing they're
+certainly growing it's not a stable case
+
+ align:start position:0%
+certainly growing it's not a stable case
+ 
+
+ align:start position:0%
+certainly growing it's not a stable case
+whatever the eigenvalues of whatever
+
+ align:start position:0%
+whatever the eigenvalues of whatever
+ 
+
+ align:start position:0%
+whatever the eigenvalues of whatever
+matrix it is they're not smaller than
+
+ align:start position:0%
+matrix it is they're not smaller than
+ 
+
+ align:start position:0%
+matrix it is they're not smaller than
+one these numbers are growing but how
+
+ align:start position:0%
+one these numbers are growing but how
+ 
+
+ align:start position:0%
+one these numbers are growing but how
+fast are they growing the answer is is
+
+ align:start position:0%
+fast are they growing the answer is is
+ 
+
+ align:start position:0%
+fast are they growing the answer is is
+lies in the eigenvalue
+
+ align:start position:0%
+lies in the eigenvalue
+ 
+
+ align:start position:0%
+lies in the eigenvalue
+so I've got to find the matrix let me
+
+ align:start position:0%
+so I've got to find the matrix let me
+ 
+
+ align:start position:0%
+so I've got to find the matrix let me
+write down the Fibonacci rule FK plus 2
+
+ align:start position:0%
+write down the Fibonacci rule FK plus 2
+ 
+
+ align:start position:0%
+write down the Fibonacci rule FK plus 2
+is f k plus 1 plus f k right now that's
+
+ align:start position:0%
+is f k plus 1 plus f k right now that's
+ 
+
+ align:start position:0%
+is f k plus 1 plus f k right now that's
+not in my I want to write that as u k
+
+ align:start position:0%
+not in my I want to write that as u k
+ 
+
+ align:start position:0%
+not in my I want to write that as u k
+plus 1 and a UK but right now what I've
+
+ align:start position:0%
+plus 1 and a UK but right now what I've
+ 
+
+ align:start position:0%
+plus 1 and a UK but right now what I've
+got is a single equation not a system
+
+ align:start position:0%
+got is a single equation not a system
+ 
+
+ align:start position:0%
+got is a single equation not a system
+and it's second order it's like having a
+
+ align:start position:0%
+and it's second order it's like having a
+ 
+
+ align:start position:0%
+and it's second order it's like having a
+second order differential equation with
+
+ align:start position:0%
+second order differential equation with
+ 
+
+ align:start position:0%
+second order differential equation with
+second derivative I want to get first
+
+ align:start position:0%
+second derivative I want to get first
+ 
+
+ align:start position:0%
+second derivative I want to get first
+derivatives here I want to get first
+
+ align:start position:0%
+derivatives here I want to get first
+ 
+
+ align:start position:0%
+derivatives here I want to get first
+difference so the way the way to do it
+
+ align:start position:0%
+difference so the way the way to do it
+ 
+
+ align:start position:0%
+difference so the way the way to do it
+is to effuse UK will be a vector see it
+
+ align:start position:0%
+is to effuse UK will be a vector see it
+ 
+
+ align:start position:0%
+is to effuse UK will be a vector see it
+a small trick let that UK be a vector F
+
+ align:start position:0%
+a small trick let that UK be a vector F
+ 
+
+ align:start position:0%
+a small trick let that UK be a vector F
+k plus 1 and F K so I'm going to get a 2
+
+ align:start position:0%
+k plus 1 and F K so I'm going to get a 2
+ 
+
+ align:start position:0%
+k plus 1 and F K so I'm going to get a 2
+by 2 system first order instead of a 1
+
+ align:start position:0%
+by 2 system first order instead of a 1
+ 
+
+ align:start position:0%
+by 2 system first order instead of a 1
+instead of a scalar system second-order
+
+ align:start position:0%
+instead of a scalar system second-order
+ 
+
+ align:start position:0%
+instead of a scalar system second-order
+by a simple trick I'm just going to have
+
+ align:start position:0%
+by a simple trick I'm just going to have
+ 
+
+ align:start position:0%
+by a simple trick I'm just going to have
+in an equation FK plus 1 equals FK plus
+
+ align:start position:0%
+in an equation FK plus 1 equals FK plus
+ 
+
+ align:start position:0%
+in an equation FK plus 1 equals FK plus
+1 that will be my second equation then
+
+ align:start position:0%
+1 that will be my second equation then
+ 
+
+ align:start position:0%
+1 that will be my second equation then
+this is my system this is my unknown and
+
+ align:start position:0%
+this is my system this is my unknown and
+ 
+
+ align:start position:0%
+this is my system this is my unknown and
+what's my one-step equation so so now UK
+
+ align:start position:0%
+what's my one-step equation so so now UK
+ 
+
+ align:start position:0%
+what's my one-step equation so so now UK
+plus 1 that's so UK plus 1 is the left
+
+ align:start position:0%
+plus 1 that's so UK plus 1 is the left
+ 
+
+ align:start position:0%
+plus 1 that's so UK plus 1 is the left
+side and what have I got here on the
+
+ align:start position:0%
+side and what have I got here on the
+ 
+
+ align:start position:0%
+side and what have I got here on the
+right side I've got some matrix
+
+ align:start position:0%
+right side I've got some matrix
+ 
+
+ align:start position:0%
+right side I've got some matrix
+multiplying UK can you see that alright
+
+ align:start position:0%
+multiplying UK can you see that alright
+ 
+
+ align:start position:0%
+multiplying UK can you see that alright
+if you can see it then you can tell me
+
+ align:start position:0%
+if you can see it then you can tell me
+ 
+
+ align:start position:0%
+if you can see it then you can tell me
+what the matrix is
+
+ align:start position:0%
+what the matrix is
+ 
+
+ align:start position:0%
+what the matrix is
+do you see that I'm taking my system
+
+ align:start position:0%
+do you see that I'm taking my system
+ 
+
+ align:start position:0%
+do you see that I'm taking my system
+here artificially made it into a system
+
+ align:start position:0%
+here artificially made it into a system
+ 
+
+ align:start position:0%
+here artificially made it into a system
+I artificially made the unknown into a
+
+ align:start position:0%
+I artificially made the unknown into a
+ 
+
+ align:start position:0%
+I artificially made the unknown into a
+vector and now I'm ready to look at and
+
+ align:start position:0%
+vector and now I'm ready to look at and
+ 
+
+ align:start position:0%
+vector and now I'm ready to look at and
+see what the matrix so do you see the
+
+ align:start position:0%
+see what the matrix so do you see the
+ 
+
+ align:start position:0%
+see what the matrix so do you see the
+left side UK plus 1 is FK + 2 FK plus 1
+
+ align:start position:0%
+left side UK plus 1 is FK + 2 FK plus 1
+ 
+
+ align:start position:0%
+left side UK plus 1 is FK + 2 FK plus 1
+that's just what I want on the right
+
+ align:start position:0%
+that's just what I want on the right
+ 
+
+ align:start position:0%
+that's just what I want on the right
+side this remember this UK here I mean
+
+ align:start position:0%
+side this remember this UK here I mean
+ 
+
+ align:start position:0%
+side this remember this UK here I mean
+for the moment put it as FK plus 1 FK so
+
+ align:start position:0%
+for the moment put it as FK plus 1 FK so
+ 
+
+ align:start position:0%
+for the moment put it as FK plus 1 FK so
+what's the matrix well that is a 1 and a
+
+ align:start position:0%
+what's the matrix well that is a 1 and a
+ 
+
+ align:start position:0%
+what's the matrix well that is a 1 and a
+1 and that has a 1 and a 0
+
+ align:start position:0%
+1 and that has a 1 and a 0
+ 
+
+ align:start position:0%
+1 and that has a 1 and a 0
+there's the matrix you see that that
+
+ align:start position:0%
+there's the matrix you see that that
+ 
+
+ align:start position:0%
+there's the matrix you see that that
+gives me the right hand set so there's
+
+ align:start position:0%
+gives me the right hand set so there's
+ 
+
+ align:start position:0%
+gives me the right hand set so there's
+the matrix a and this is our friend UK
+
+ align:start position:0%
+the matrix a and this is our friend UK
+ 
+
+ align:start position:0%
+the matrix a and this is our friend UK
+so we've got so that simple trick would
+
+ align:start position:0%
+so we've got so that simple trick would
+ 
+
+ align:start position:0%
+so we've got so that simple trick would
+change the second order scalar problem
+
+ align:start position:0%
+change the second order scalar problem
+ 
+
+ align:start position:0%
+change the second order scalar problem
+to a first order system - but with two
+
+ align:start position:0%
+to a first order system - but with two
+ 
+
+ align:start position:0%
+to a first order system - but with two
+unknowns with a matrix and now what do I
+
+ align:start position:0%
+unknowns with a matrix and now what do I
+ 
+
+ align:start position:0%
+unknowns with a matrix and now what do I
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+well before I even think I find its
+
+ align:start position:0%
+well before I even think I find its
+ 
+
+ align:start position:0%
+well before I even think I find its
+eigen values and eigen values so what
+
+ align:start position:0%
+eigen values and eigen values so what
+ 
+
+ align:start position:0%
+eigen values and eigen values so what
+are the eigen values and I
+
+ align:start position:0%
+are the eigen values and I
+ 
+
+ align:start position:0%
+are the eigen values and I
+that mate that's the Iowa's first let me
+
+ align:start position:0%
+that mate that's the Iowa's first let me
+ 
+
+ align:start position:0%
+that mate that's the Iowa's first let me
+just like think for a minute
+
+ align:start position:0%
+just like think for a minute
+ 
+
+ align:start position:0%
+just like think for a minute
+it's two by two so this shouldn't be
+
+ align:start position:0%
+it's two by two so this shouldn't be
+ 
+
+ align:start position:0%
+it's two by two so this shouldn't be
+impossible to do let's do it okay so my
+
+ align:start position:0%
+impossible to do let's do it okay so my
+ 
+
+ align:start position:0%
+impossible to do let's do it okay so my
+matrix again is one one one zero it's
+
+ align:start position:0%
+matrix again is one one one zero it's
+ 
+
+ align:start position:0%
+matrix again is one one one zero it's
+symmetric by the way so what I will
+
+ align:start position:0%
+symmetric by the way so what I will
+ 
+
+ align:start position:0%
+symmetric by the way so what I will
+eventually know about symmetric matrices
+
+ align:start position:0%
+eventually know about symmetric matrices
+ 
+
+ align:start position:0%
+eventually know about symmetric matrices
+is that the eigenvalues will come out
+
+ align:start position:0%
+is that the eigenvalues will come out
+ 
+
+ align:start position:0%
+is that the eigenvalues will come out
+real I won't get any complex numbers
+
+ align:start position:0%
+real I won't get any complex numbers
+ 
+
+ align:start position:0%
+real I won't get any complex numbers
+here and the eigenvectors once I get
+
+ align:start position:0%
+here and the eigenvectors once I get
+ 
+
+ align:start position:0%
+here and the eigenvectors once I get
+those actually will be orthogonal but
+
+ align:start position:0%
+those actually will be orthogonal but
+ 
+
+ align:start position:0%
+those actually will be orthogonal but
+2x2 I'm more interested in what the
+
+ align:start position:0%
+2x2 I'm more interested in what the
+ 
+
+ align:start position:0%
+2x2 I'm more interested in what the
+actual numbers are what do I know about
+
+ align:start position:0%
+actual numbers are what do I know about
+ 
+
+ align:start position:0%
+actual numbers are what do I know about
+those two numbers what should it do you
+
+ align:start position:0%
+those two numbers what should it do you
+ 
+
+ align:start position:0%
+those two numbers what should it do you
+want me to find this determinant of a
+
+ align:start position:0%
+want me to find this determinant of a
+ 
+
+ align:start position:0%
+want me to find this determinant of a
+minus lambda hi sure so it's the
+
+ align:start position:0%
+minus lambda hi sure so it's the
+ 
+
+ align:start position:0%
+minus lambda hi sure so it's the
+determinant of 1 minus lambda 1 1 0
+
+ align:start position:0%
+determinant of 1 minus lambda 1 1 0
+ 
+
+ align:start position:0%
+determinant of 1 minus lambda 1 1 0
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus lambda
+
+ align:start position:0%
+minus lambda
+ 
+
+ align:start position:0%
+minus lambda
+yes okay okay there'll be two
+
+ align:start position:0%
+yes okay okay there'll be two
+ 
+
+ align:start position:0%
+yes okay okay there'll be two
+eigenvectors well tell me again what i
+
+ align:start position:0%
+eigenvectors well tell me again what i
+ 
+
+ align:start position:0%
+eigenvectors well tell me again what i
+know about the two eigenvalues before I
+
+ align:start position:0%
+know about the two eigenvalues before I
+ 
+
+ align:start position:0%
+know about the two eigenvalues before I
+go any further tell me something about
+
+ align:start position:0%
+go any further tell me something about
+ 
+
+ align:start position:0%
+go any further tell me something about
+these two eigenvalues what are they add
+
+ align:start position:0%
+these two eigenvalues what are they add
+ 
+
+ align:start position:0%
+these two eigenvalues what are they add
+up to lambda 1 plus lambda 2
+
+ align:start position:0%
+up to lambda 1 plus lambda 2
+ 
+
+ align:start position:0%
+up to lambda 1 plus lambda 2
+is is the same as the trace down the
+
+ align:start position:0%
+is is the same as the trace down the
+ 
+
+ align:start position:0%
+is is the same as the trace down the
+diagonal of the matrix 1 and 0 is 1 so
+
+ align:start position:0%
+diagonal of the matrix 1 and 0 is 1 so
+ 
+
+ align:start position:0%
+diagonal of the matrix 1 and 0 is 1 so
+lambda 1 plus lambda 2 should come out
+
+ align:start position:0%
+lambda 1 plus lambda 2 should come out
+ 
+
+ align:start position:0%
+lambda 1 plus lambda 2 should come out
+to be 1 and lambda 1 times lambda 2
+
+ align:start position:0%
+to be 1 and lambda 1 times lambda 2
+ 
+
+ align:start position:0%
+to be 1 and lambda 1 times lambda 2
+should come out to be the determinant
+
+ align:start position:0%
+should come out to be the determinant
+ 
+
+ align:start position:0%
+should come out to be the determinant
+which is minus 1 so I'm expecting the
+
+ align:start position:0%
+which is minus 1 so I'm expecting the
+ 
+
+ align:start position:0%
+which is minus 1 so I'm expecting the
+eigenvalues to head to 1 and to multiply
+
+ align:start position:0%
+eigenvalues to head to 1 and to multiply
+ 
+
+ align:start position:0%
+eigenvalues to head to 1 and to multiply
+2 minus 1 but let's just see a happy if
+
+ align:start position:0%
+2 minus 1 but let's just see a happy if
+ 
+
+ align:start position:0%
+2 minus 1 but let's just see a happy if
+I multiply this out I get that times
+
+ align:start position:0%
+I multiply this out I get that times
+ 
+
+ align:start position:0%
+I multiply this out I get that times
+that will be a lambda squared minus
+
+ align:start position:0%
+that will be a lambda squared minus
+ 
+
+ align:start position:0%
+that will be a lambda squared minus
+lambda minus 1 good lambda squared minus
+
+ align:start position:0%
+lambda minus 1 good lambda squared minus
+ 
+
+ align:start position:0%
+lambda minus 1 good lambda squared minus
+lambda minus 1 actually you see the
+
+ align:start position:0%
+lambda minus 1 actually you see the
+ 
+
+ align:start position:0%
+lambda minus 1 actually you see the
+compare that with the original equation
+
+ align:start position:0%
+compare that with the original equation
+ 
+
+ align:start position:0%
+compare that with the original equation
+that I started FK plus 2 minus FK plus 1
+
+ align:start position:0%
+that I started FK plus 2 minus FK plus 1
+ 
+
+ align:start position:0%
+that I started FK plus 2 minus FK plus 1
+minus FK is 0 the the recurrent the
+
+ align:start position:0%
+minus FK is 0 the the recurrent the
+ 
+
+ align:start position:0%
+minus FK is 0 the the recurrent the
+recursion with that be that the
+
+ align:start position:0%
+recursion with that be that the
+ 
+
+ align:start position:0%
+recursion with that be that the
+Fibonacci number satisfied is somehow
+
+ align:start position:0%
+Fibonacci number satisfied is somehow
+ 
+
+ align:start position:0%
+Fibonacci number satisfied is somehow
+showing up directly here for the
+
+ align:start position:0%
+showing up directly here for the
+ 
+
+ align:start position:0%
+showing up directly here for the
+eigenvalues when we set that to 0 okay
+
+ align:start position:0%
+eigenvalues when we set that to 0 okay
+ 
+
+ align:start position:0%
+eigenvalues when we set that to 0 okay
+that's all well I would like to be able
+
+ align:start position:0%
+that's all well I would like to be able
+ 
+
+ align:start position:0%
+that's all well I would like to be able
+to factor that that quadratic but I'm
+
+ align:start position:0%
+to factor that that quadratic but I'm
+ 
+
+ align:start position:0%
+to factor that that quadratic but I'm
+better off to use the quadratic formula
+
+ align:start position:0%
+better off to use the quadratic formula
+ 
+
+ align:start position:0%
+better off to use the quadratic formula
+land that is let's see minus B is 1 plus
+
+ align:start position:0%
+land that is let's see minus B is 1 plus
+ 
+
+ align:start position:0%
+land that is let's see minus B is 1 plus
+or minus square root of B squared which
+
+ align:start position:0%
+or minus square root of B squared which
+ 
+
+ align:start position:0%
+or minus square root of B squared which
+is 1 minus 4 times that times that which
+
+ align:start position:0%
+is 1 minus 4 times that times that which
+ 
+
+ align:start position:0%
+is 1 minus 4 times that times that which
+is plus 4 over 2 so that's the square
+
+ align:start position:0%
+is plus 4 over 2 so that's the square
+ 
+
+ align:start position:0%
+is plus 4 over 2 so that's the square
+root of 5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the eigenvalues are lambda 1 is 1/2
+
+ align:start position:0%
+so the eigenvalues are lambda 1 is 1/2
+ 
+
+ align:start position:0%
+so the eigenvalues are lambda 1 is 1/2
+of 1 plus square root of 5 and lambda 2
+
+ align:start position:0%
+of 1 plus square root of 5 and lambda 2
+ 
+
+ align:start position:0%
+of 1 plus square root of 5 and lambda 2
+is 1/2 of 1 minus square root of and
+
+ align:start position:0%
+is 1/2 of 1 minus square root of and
+ 
+
+ align:start position:0%
+is 1/2 of 1 minus square root of and
+sure enough they those add up to 1 and
+
+ align:start position:0%
+sure enough they those add up to 1 and
+ 
+
+ align:start position:0%
+sure enough they those add up to 1 and
+they multiply to give minus 1 okay those
+
+ align:start position:0%
+they multiply to give minus 1 okay those
+ 
+
+ align:start position:0%
+they multiply to give minus 1 okay those
+are the two I can go how what are those
+
+ align:start position:0%
+are the two I can go how what are those
+ 
+
+ align:start position:0%
+are the two I can go how what are those
+numbers approximately square root of 5
+
+ align:start position:0%
+numbers approximately square root of 5
+ 
+
+ align:start position:0%
+numbers approximately square root of 5
+well it's more than 2 what less than 3
+
+ align:start position:0%
+well it's more than 2 what less than 3
+ 
+
+ align:start position:0%
+well it's more than 2 what less than 3
+it could be nice to know these numbers I
+
+ align:start position:0%
+it could be nice to know these numbers I
+ 
+
+ align:start position:0%
+it could be nice to know these numbers I
+think I think that that so that number
+
+ align:start position:0%
+think I think that that so that number
+ 
+
+ align:start position:0%
+think I think that that so that number
+comes out bigger than 1 right yeah
+
+ align:start position:0%
+comes out bigger than 1 right yeah
+ 
+
+ align:start position:0%
+comes out bigger than 1 right yeah
+that's right this number comes out
+
+ align:start position:0%
+that's right this number comes out
+ 
+
+ align:start position:0%
+that's right this number comes out
+bigger than 1 it's about 1.618
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not exactly it suppose it's one point
+
+ align:start position:0%
+not exactly it suppose it's one point
+ 
+
+ align:start position:0%
+not exactly it suppose it's one point
+just like a face so then what's lambda 2
+
+ align:start position:0%
+just like a face so then what's lambda 2
+ 
+
+ align:start position:0%
+just like a face so then what's lambda 2
+is lambda 2 positive or negative
+
+ align:start position:0%
+is lambda 2 positive or negative
+ 
+
+ align:start position:0%
+is lambda 2 positive or negative
+negative right obviously negative and I
+
+ align:start position:0%
+negative right obviously negative and I
+ 
+
+ align:start position:0%
+negative right obviously negative and I
+knew that so it's minus and they add up
+
+ align:start position:0%
+knew that so it's minus and they add up
+ 
+
+ align:start position:0%
+knew that so it's minus and they add up
+to 1 so minus point 6 1 8 I guess ok and
+
+ align:start position:0%
+to 1 so minus point 6 1 8 I guess ok and
+ 
+
+ align:start position:0%
+to 1 so minus point 6 1 8 I guess ok and
+some more those are the two eigenvalues
+
+ align:start position:0%
+some more those are the two eigenvalues
+ 
+
+ align:start position:0%
+some more those are the two eigenvalues
+one eigenvalue bigger than one one
+
+ align:start position:0%
+one eigenvalue bigger than one one
+ 
+
+ align:start position:0%
+one eigenvalue bigger than one one
+eigenvalue smaller than one
+
+ align:start position:0%
+eigenvalue smaller than one
+ 
+
+ align:start position:0%
+eigenvalue smaller than one
+that's a great situation to be in of
+
+ align:start position:0%
+that's a great situation to be in of
+ 
+
+ align:start position:0%
+that's a great situation to be in of
+course the eigenvalues are different so
+
+ align:start position:0%
+course the eigenvalues are different so
+ 
+
+ align:start position:0%
+course the eigenvalues are different so
+there's no doubt whatever is this matrix
+
+ align:start position:0%
+there's no doubt whatever is this matrix
+ 
+
+ align:start position:0%
+there's no doubt whatever is this matrix
+diagonalizable is this matrix
+
+ align:start position:0%
+diagonalizable is this matrix
+ 
+
+ align:start position:0%
+diagonalizable is this matrix
+diagonalizable that original matrix a
+
+ align:start position:0%
+diagonalizable that original matrix a
+ 
+
+ align:start position:0%
+diagonalizable that original matrix a
+short we've got two distinct eigenvalues
+
+ align:start position:0%
+short we've got two distinct eigenvalues
+ 
+
+ align:start position:0%
+short we've got two distinct eigenvalues
+and we can find the eigenvectors in a
+
+ align:start position:0%
+and we can find the eigenvectors in a
+ 
+
+ align:start position:0%
+and we can find the eigenvectors in a
+moment but they'll be independent will
+
+ align:start position:0%
+moment but they'll be independent will
+ 
+
+ align:start position:0%
+moment but they'll be independent will
+be diagonalizable and now you can
+
+ align:start position:0%
+be diagonalizable and now you can
+ 
+
+ align:start position:0%
+be diagonalizable and now you can
+already answer my very first question
+
+ align:start position:0%
+already answer my very first question
+ 
+
+ align:start position:0%
+already answer my very first question
+how faster those Fibonacci numbers
+
+ align:start position:0%
+how faster those Fibonacci numbers
+ 
+
+ align:start position:0%
+how faster those Fibonacci numbers
+increasing how close they're increasing
+
+ align:start position:0%
+increasing how close they're increasing
+ 
+
+ align:start position:0%
+increasing how close they're increasing
+right they're not doubling at every step
+
+ align:start position:0%
+right they're not doubling at every step
+ 
+
+ align:start position:0%
+right they're not doubling at every step
+let's look again these numbers 5 8 13
+
+ align:start position:0%
+let's look again these numbers 5 8 13
+ 
+
+ align:start position:0%
+let's look again these numbers 5 8 13
+it's not obvious the next would be 21 34
+
+ align:start position:0%
+it's not obvious the next would be 21 34
+ 
+
+ align:start position:0%
+it's not obvious the next would be 21 34
+so to get some idea of what F 100 is can
+
+ align:start position:0%
+so to get some idea of what F 100 is can
+ 
+
+ align:start position:0%
+so to get some idea of what F 100 is can
+you give me any the crucial number so it
+
+ align:start position:0%
+you give me any the crucial number so it
+ 
+
+ align:start position:0%
+you give me any the crucial number so it
+these it's approximately what's
+
+ align:start position:0%
+these it's approximately what's
+ 
+
+ align:start position:0%
+these it's approximately what's
+controlling the growth of these
+
+ align:start position:0%
+controlling the growth of these
+ 
+
+ align:start position:0%
+controlling the growth of these
+Fibonacci numbers it's the eigen value
+
+ align:start position:0%
+Fibonacci numbers it's the eigen value
+ 
+
+ align:start position:0%
+Fibonacci numbers it's the eigen value
+and which eigen value is controlling
+
+ align:start position:0%
+and which eigen value is controlling
+ 
+
+ align:start position:0%
+and which eigen value is controlling
+that growth the big ones so F 100 will
+
+ align:start position:0%
+that growth the big ones so F 100 will
+ 
+
+ align:start position:0%
+that growth the big ones so F 100 will
+it be approximately some constant C one
+
+ align:start position:0%
+it be approximately some constant C one
+ 
+
+ align:start position:0%
+it be approximately some constant C one
+I guess times this lambda 1 is 1 plus
+
+ align:start position:0%
+I guess times this lambda 1 is 1 plus
+ 
+
+ align:start position:0%
+I guess times this lambda 1 is 1 plus
+square root of 5 over 2 to the hundredth
+
+ align:start position:0%
+square root of 5 over 2 to the hundredth
+ 
+
+ align:start position:0%
+square root of 5 over 2 to the hundredth
+power and the 200 in other words the
+
+ align:start position:0%
+power and the 200 in other words the
+ 
+
+ align:start position:0%
+power and the 200 in other words the
+eigen value these that the Fibonacci
+
+ align:start position:0%
+eigen value these that the Fibonacci
+ 
+
+ align:start position:0%
+eigen value these that the Fibonacci
+numbers are growing by about that factor
+
+ align:start position:0%
+numbers are growing by about that factor
+ 
+
+ align:start position:0%
+numbers are growing by about that factor
+you see that we we've got precise
+
+ align:start position:0%
+you see that we we've got precise
+ 
+
+ align:start position:0%
+you see that we we've got precise
+information about the about the
+
+ align:start position:0%
+information about the about the
+ 
+
+ align:start position:0%
+information about the about the
+Fibonacci
+
+ align:start position:0%
+Fibonacci
+ 
+
+ align:start position:0%
+Fibonacci
+numbers out of the Idaho okay and again
+
+ align:start position:0%
+numbers out of the Idaho okay and again
+ 
+
+ align:start position:0%
+numbers out of the Idaho okay and again
+why is that true let me go over to this
+
+ align:start position:0%
+why is that true let me go over to this
+ 
+
+ align:start position:0%
+why is that true let me go over to this
+board so what I'm doing here yeah the
+
+ align:start position:0%
+board so what I'm doing here yeah the
+ 
+
+ align:start position:0%
+board so what I'm doing here yeah the
+original eigen the original initial
+
+ align:start position:0%
+original eigen the original initial
+ 
+
+ align:start position:0%
+original eigen the original initial
+value is some combination of
+
+ align:start position:0%
+value is some combination of
+ 
+
+ align:start position:0%
+value is some combination of
+eigenvectors and then when we start
+
+ align:start position:0%
+eigenvectors and then when we start
+ 
+
+ align:start position:0%
+eigenvectors and then when we start
+multiple when we start going out the
+
+ align:start position:0%
+multiple when we start going out the
+ 
+
+ align:start position:0%
+multiple when we start going out the
+theory of Fibonacci numbers when we
+
+ align:start position:0%
+theory of Fibonacci numbers when we
+ 
+
+ align:start position:0%
+theory of Fibonacci numbers when we
+start multiplying by a 100 times
+
+ align:start position:0%
+start multiplying by a 100 times
+ 
+
+ align:start position:0%
+start multiplying by a 100 times
+it's his lambda 1 to the hundredth this
+
+ align:start position:0%
+it's his lambda 1 to the hundredth this
+ 
+
+ align:start position:0%
+it's his lambda 1 to the hundredth this
+term is is the one that's taken over its
+
+ align:start position:0%
+term is is the one that's taken over its
+ 
+
+ align:start position:0%
+term is is the one that's taken over its
+I mean that's be like one point six to
+
+ align:start position:0%
+I mean that's be like one point six to
+ 
+
+ align:start position:0%
+I mean that's be like one point six to
+the hundredth power the second term is
+
+ align:start position:0%
+the hundredth power the second term is
+ 
+
+ align:start position:0%
+the hundredth power the second term is
+practically nothing right the point six
+
+ align:start position:0%
+practically nothing right the point six
+ 
+
+ align:start position:0%
+practically nothing right the point six
+or minus point 6 to the hundredth power
+
+ align:start position:0%
+or minus point 6 to the hundredth power
+ 
+
+ align:start position:0%
+or minus point 6 to the hundredth power
+is an extremely small extremely small
+
+ align:start position:0%
+is an extremely small extremely small
+ 
+
+ align:start position:0%
+is an extremely small extremely small
+number so this is is this there were
+
+ align:start position:0%
+number so this is is this there were
+ 
+
+ align:start position:0%
+number so this is is this there were
+only two terms because we're two by two
+
+ align:start position:0%
+only two terms because we're two by two
+ 
+
+ align:start position:0%
+only two terms because we're two by two
+this number is this piece of it
+
+ align:start position:0%
+this number is this piece of it
+ 
+
+ align:start position:0%
+this number is this piece of it
+is there but it's it's disappeared where
+
+ align:start position:0%
+is there but it's it's disappeared where
+ 
+
+ align:start position:0%
+is there but it's it's disappeared where
+this piece is there and it's growing and
+
+ align:start position:0%
+this piece is there and it's growing and
+ 
+
+ align:start position:0%
+this piece is there and it's growing and
+controlling everything so so really that
+
+ align:start position:0%
+controlling everything so so really that
+ 
+
+ align:start position:0%
+controlling everything so so really that
+we're doing like problems that are
+
+ align:start position:0%
+we're doing like problems that are
+ 
+
+ align:start position:0%
+we're doing like problems that are
+revolving we're doing dynamic instead of
+
+ align:start position:0%
+revolving we're doing dynamic instead of
+ 
+
+ align:start position:0%
+revolving we're doing dynamic instead of
+ax equal B that's a static problem we're
+
+ align:start position:0%
+ax equal B that's a static problem we're
+ 
+
+ align:start position:0%
+ax equal B that's a static problem we're
+now we're doing dynamics a squared a
+
+ align:start position:0%
+now we're doing dynamics a squared a
+ 
+
+ align:start position:0%
+now we're doing dynamics a squared a
+cubed things are evolving in time and
+
+ align:start position:0%
+cubed things are evolving in time and
+ 
+
+ align:start position:0%
+cubed things are evolving in time and
+the eigenvalues are the crucial numbers
+
+ align:start position:0%
+the eigenvalues are the crucial numbers
+ 
+
+ align:start position:0%
+the eigenvalues are the crucial numbers
+okay I guess to complete this I better
+
+ align:start position:0%
+okay I guess to complete this I better
+ 
+
+ align:start position:0%
+okay I guess to complete this I better
+write down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we should complete the whole process
+
+ align:start position:0%
+so we should complete the whole process
+ 
+
+ align:start position:0%
+so we should complete the whole process
+by finding the eigen vectors okay well I
+
+ align:start position:0%
+by finding the eigen vectors okay well I
+ 
+
+ align:start position:0%
+by finding the eigen vectors okay well I
+have two up in the corner then I have to
+
+ align:start position:0%
+have two up in the corner then I have to
+ 
+
+ align:start position:0%
+have two up in the corner then I have to
+look at a minus lambda I so a minus
+
+ align:start position:0%
+look at a minus lambda I so a minus
+ 
+
+ align:start position:0%
+look at a minus lambda I so a minus
+lambda I is this 1 minus lambda 1 1 and
+
+ align:start position:0%
+lambda I is this 1 minus lambda 1 1 and
+ 
+
+ align:start position:0%
+lambda I is this 1 minus lambda 1 1 and
+minus lambda and now can we spot and
+
+ align:start position:0%
+minus lambda and now can we spot and
+ 
+
+ align:start position:0%
+minus lambda and now can we spot and
+eigenvector out of that that's s for
+
+ align:start position:0%
+eigenvector out of that that's s for
+ 
+
+ align:start position:0%
+eigenvector out of that that's s for
+these two lambdas this matrix is
+
+ align:start position:0%
+these two lambdas this matrix is
+ 
+
+ align:start position:0%
+these two lambdas this matrix is
+singular
+
+ align:start position:0%
+singular
+ 
+
+ align:start position:0%
+singular
+I guess the eigenvector 2x2 ought to be
+
+ align:start position:0%
+I guess the eigenvector 2x2 ought to be
+ 
+
+ align:start position:0%
+I guess the eigenvector 2x2 ought to be
+or easy so if I know that this matrix is
+
+ align:start position:0%
+or easy so if I know that this matrix is
+ 
+
+ align:start position:0%
+or easy so if I know that this matrix is
+singular then seems to me the eigen
+
+ align:start position:0%
+singular then seems to me the eigen
+ 
+
+ align:start position:0%
+singular then seems to me the eigen
+vector has to be lambda and one because
+
+ align:start position:0%
+vector has to be lambda and one because
+ 
+
+ align:start position:0%
+vector has to be lambda and one because
+that multiplication will give me the 0
+
+ align:start position:0%
+that multiplication will give me the 0
+ 
+
+ align:start position:0%
+that multiplication will give me the 0
+and this multiplication gives me better
+
+ align:start position:0%
+and this multiplication gives me better
+ 
+
+ align:start position:0%
+and this multiplication gives me better
+give me also 0 do you see why it does
+
+ align:start position:0%
+give me also 0 do you see why it does
+ 
+
+ align:start position:0%
+give me also 0 do you see why it does
+this is the minus lambda squared plus
+
+ align:start position:0%
+this is the minus lambda squared plus
+ 
+
+ align:start position:0%
+this is the minus lambda squared plus
+lambda plus 1 it's the thing that's 0
+
+ align:start position:0%
+lambda plus 1 it's the thing that's 0
+ 
+
+ align:start position:0%
+lambda plus 1 it's the thing that's 0
+because these lambdas are special
+
+ align:start position:0%
+because these lambdas are special
+ 
+
+ align:start position:0%
+because these lambdas are special
+there's the eigenvector x 1 is lambda 1
+
+ align:start position:0%
+there's the eigenvector x 1 is lambda 1
+ 
+
+ align:start position:0%
+there's the eigenvector x 1 is lambda 1
+1 and X 2 is lambda 2 1 I did that as a
+
+ align:start position:0%
+1 and X 2 is lambda 2 1 I did that as a
+ 
+
+ align:start position:0%
+1 and X 2 is lambda 2 1 I did that as a
+little trick that was available in the 2
+
+ align:start position:0%
+little trick that was available in the 2
+ 
+
+ align:start position:0%
+little trick that was available in the 2
+by 2 case so now I finally have to oh I
+
+ align:start position:0%
+by 2 case so now I finally have to oh I
+ 
+
+ align:start position:0%
+by 2 case so now I finally have to oh I
+have to take the initial you know so to
+
+ align:start position:0%
+have to take the initial you know so to
+ 
+
+ align:start position:0%
+have to take the initial you know so to
+complete this example entirely I have to
+
+ align:start position:0%
+complete this example entirely I have to
+ 
+
+ align:start position:0%
+complete this example entirely I have to
+say ok what was you 0 u 0 was F 1 F 2 so
+
+ align:start position:0%
+say ok what was you 0 u 0 was F 1 F 2 so
+ 
+
+ align:start position:0%
+say ok what was you 0 u 0 was F 1 F 2 so
+u 0 a starting vector
+
+ align:start position:0%
+u 0 a starting vector
+ 
+
+ align:start position:0%
+u 0 a starting vector
+f1 f0 and those were 1 and 0 so I have
+
+ align:start position:0%
+f1 f0 and those were 1 and 0 so I have
+ 
+
+ align:start position:0%
+f1 f0 and those were 1 and 0 so I have
+to use that vector so I have to look for
+
+ align:start position:0%
+to use that vector so I have to look for
+ 
+
+ align:start position:0%
+to use that vector so I have to look for
+from multiple of the first eigenvector
+
+ align:start position:0%
+from multiple of the first eigenvector
+ 
+
+ align:start position:0%
+from multiple of the first eigenvector
+and the second to produce u0 the 1 0
+
+ align:start position:0%
+and the second to produce u0 the 1 0
+ 
+
+ align:start position:0%
+and the second to produce u0 the 1 0
+which this is what we'll find c1 and c2
+
+ align:start position:0%
+which this is what we'll find c1 and c2
+ 
+
+ align:start position:0%
+which this is what we'll find c1 and c2
+and then I'm done so let me in the last
+
+ align:start position:0%
+and then I'm done so let me in the last
+ 
+
+ align:start position:0%
+and then I'm done so let me in the last
+five seconds grinding out a formula let
+
+ align:start position:0%
+five seconds grinding out a formula let
+ 
+
+ align:start position:0%
+five seconds grinding out a formula let
+me repeat the idea that I really it's
+
+ align:start position:0%
+me repeat the idea that I really it's
+ 
+
+ align:start position:0%
+me repeat the idea that I really it's
+the idea that central when things are
+
+ align:start position:0%
+the idea that central when things are
+ 
+
+ align:start position:0%
+the idea that central when things are
+revolving in time let me come back to
+
+ align:start position:0%
+revolving in time let me come back to
+ 
+
+ align:start position:0%
+revolving in time let me come back to
+this board because the ideas are here
+
+ align:start position:0%
+this board because the ideas are here
+ 
+
+ align:start position:0%
+this board because the ideas are here
+when things are evolving in time by a
+
+ align:start position:0%
+when things are evolving in time by a
+ 
+
+ align:start position:0%
+when things are evolving in time by a
+first order system starting from an
+
+ align:start position:0%
+first order system starting from an
+ 
+
+ align:start position:0%
+first order system starting from an
+original unit the key is find the
+
+ align:start position:0%
+original unit the key is find the
+ 
+
+ align:start position:0%
+original unit the key is find the
+eigenvalues and eigenvectors of a that
+
+ align:start position:0%
+eigenvalues and eigenvectors of a that
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors of a that
+will tell those eigenvectors are the
+
+ align:start position:0%
+will tell those eigenvectors are the
+ 
+
+ align:start position:0%
+will tell those eigenvectors are the
+eigenvalues will already tell you what's
+
+ align:start position:0%
+eigenvalues will already tell you what's
+ 
+
+ align:start position:0%
+eigenvalues will already tell you what's
+happening is the solution blowing up is
+
+ align:start position:0%
+happening is the solution blowing up is
+ 
+
+ align:start position:0%
+happening is the solution blowing up is
+it going to 0 what's it doing and then
+
+ align:start position:0%
+it going to 0 what's it doing and then
+ 
+
+ align:start position:0%
+it going to 0 what's it doing and then
+to find out exactly a formula you have
+
+ align:start position:0%
+to find out exactly a formula you have
+ 
+
+ align:start position:0%
+to find out exactly a formula you have
+to take your u0 and write it as a con
+
+ align:start position:0%
+to take your u0 and write it as a con
+ 
+
+ align:start position:0%
+to take your u0 and write it as a con
+nation of eigenvectors and then follow
+
+ align:start position:0%
+nation of eigenvectors and then follow
+ 
+
+ align:start position:0%
+nation of eigenvectors and then follow
+each eigenvector separate and that's
+
+ align:start position:0%
+each eigenvector separate and that's
+ 
+
+ align:start position:0%
+each eigenvector separate and that's
+really what this formula the formula for
+
+ align:start position:0%
+really what this formula the formula for
+ 
+
+ align:start position:0%
+really what this formula the formula for
+that that's what the formula for a to
+
+ align:start position:0%
+that that's what the formula for a to
+ 
+
+ align:start position:0%
+that that's what the formula for a to
+the K is doing so remember that formula
+
+ align:start position:0%
+the K is doing so remember that formula
+ 
+
+ align:start position:0%
+the K is doing so remember that formula
+for a to the K is s lambda to the K s
+
+ align:start position:0%
+for a to the K is s lambda to the K s
+ 
+
+ align:start position:0%
+for a to the K is s lambda to the K s
+inverse okay that's that's difference
+
+ align:start position:0%
+inverse okay that's that's difference
+ 
+
+ align:start position:0%
+inverse okay that's that's difference
+equations and you just have to so that
+
+ align:start position:0%
+equations and you just have to so that
+ 
+
+ align:start position:0%
+equations and you just have to so that
+the homework will give some examples
+
+ align:start position:0%
+the homework will give some examples
+ 
+
+ align:start position:0%
+the homework will give some examples
+different from Fibonacci to next time
+
+ align:start position:0%
+different from Fibonacci to next time
+ 
+
+ align:start position:0%
+different from Fibonacci to next time
+will be differentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/2qxY859dzzQ.txt b/2qxY859dzzQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6ed3af65086f4502ca7ee2d78f9f01ce8a9b0af
--- /dev/null
+++ b/2qxY859dzzQ.txt
@@ -0,0 +1,1364 @@
+PROFESSOR: Hi.
+
+Well, if you're ready,
+this will be the
+
+other big side of calculus.
+
+We still have two functions,
+as before.
+
+Let me call them the height and
+the slope: y of x and the
+
+slope, s of x.
+
+Function one and function two.
+
+That's what calculus is about.
+
+And earlier, we figured out how
+to go from function one if
+
+we knew that, how to
+find the slope.
+
+Of course, it was easy when
+function one was just a
+
+straight line.
+
+Then the slope was just
+up divided by across.
+
+But when function
+one was curving,
+
+we had to do something.
+
+We had to take just a small
+distance across, a small
+
+distance up and divide,
+and then let small
+
+get smaller and smaller.
+
+The result of that was function
+two, the derivative.
+
+Today, we're going
+the other way.
+
+We know the slope.
+
+We know s of x, and we want
+to find the height, y
+
+of x, of the graph.
+
+We know how the graph is sloping
+at every point, and we
+
+have to put all that information
+together to find
+
+its height.
+
+OK.
+
+Let me say the easiest way to
+do it, when it works, is to
+
+recognize if we are given a
+formula for the slope, to
+
+recognize maybe we know a height
+that goes with it.
+
+Let me take an example.
+
+So the one, and most important
+case of a height
+
+is x to some power.
+
+x to n.
+
+That's one that everybody
+learns.
+
+When y is x to the nth, the
+result of this process that
+
+produces function two going in
+that direction is dy/dx is
+
+that n comes down and we
+have one lower power.
+
+So if we happen to have that
+as our slope, that would be
+
+our height.
+
+Nothing more to do.
+
+But many other slopes
+are possible.
+
+Let's just stay with this
+another minute.
+
+What if the slope was
+x to the nth itself?
+
+What if we started with function
+two as x to the nth.
+
+Suppose dy/dx is x to the nth
+power, like x squared.
+
+Where does x squared
+come from?
+
+Well, look at this rule.
+
+That rule said that for these
+power functions, the power
+
+drops by one.
+
+So if I want to end up with x
+to the nth, going backwards,
+
+function one had better be,
+involve an x to the n plus 1.
+
+But that's not perfect, of
+course, because when I take
+
+the slope of that one, this
+factor, this power, this
+
+exponent, n plus n
+will come down.
+
+Just as n came down to here, n
+plus 1 will come down, and
+
+therefore I'd better divide by
+n plus 1 so that when I do
+
+take the slope, when I do go to
+number two, the n plus 1's
+
+will cancel.
+
+The power will drop by one, and
+I'll have x to the nth.
+
+OK, there's an example--
+
+quite a useful one--
+
+of going from step two to
+step one just by kind of
+
+recognizing what
+you want there.
+
+So this is one set that
+everybody learns.
+
+Another is sines and cosines,
+if you can fit it into that.
+
+Another is either
+the x or logx.
+
+That's pretty much the list.
+And then you learn, in the
+
+future, ways to change things
+around to fit into one of
+
+those forms. But then,
+of course, there
+
+are many, many cases--
+
+many, many functions, too-- that
+you don't fit, can't fit
+
+into a form where you can
+recognize from some list which
+
+you either have learned or you
+find on the web or you find in
+
+the calculator.
+
+A lot of lists have been made
+to help you go from two to
+
+one, but today we have
+to understand what
+
+is the actual process.
+
+What is the, what is the the
+reverse process to this one?
+
+And of course, this one involved
+a limit as delta x
+
+went to 0, because always I have
+to remember that things
+
+can be curving, things can be
+changing, I can't assume that
+
+they're saying the same.
+
+And then, the reverse
+direction.
+
+Maybe I just tell you first
+what the symbol is.
+
+If I have this s of x and I want
+to get back to y of x--
+
+so this is from two to one--
+
+one will be y of x.
+
+The symbol for y
+of x will be--
+
+it's, I'm just really wanting to
+draw that integral symbol.
+
+The integral, I would say the
+integral of s of x dx.
+
+And you'll see why--
+
+this is, that's an s--
+
+you'll see why that's a
+reasonable way to write it.
+
+But of course, first, we need
+the idea behind it.
+
+OK, so how am I going
+to proceed?
+
+Step one, I'll take steps, I
+won't try to get immediately
+
+to the case of continuous
+change.
+
+I'll take single, individual
+steps.
+
+Let me do that.
+
+And then, I'm going to
+take smaller steps.
+
+And then in the limit, I'm
+taking continuous steps.
+
+OK, so first, big steps.
+
+So let me put down, for example,
+suppose I have y's.
+
+Suppose the y's stepped up like
+0, 1, 4, 9, 16, whatever.
+
+So those are heights, and, of a
+graph that's sort of pieces
+
+of straight lines, only
+changing a few times.
+
+What would be the slopes?
+
+Going now, this is
+one going to two.
+
+The slope is s.
+
+Well, the slope, if the step
+size is one and I go up by
+
+one, the slope will be 1.
+
+Here I go up by 3.
+
+Here I go up by 5.
+
+Here I go up by 7.
+
+So if I, to go from there to
+there, I'm taking differences.
+
+I'm taking delta y's.
+
+These s's are delta y's.
+
+How do I go backwards?
+
+Suppose I gave you 1, 3, 5, 7,
+and I started y off at 0.
+
+How could you recover
+the rest of the y's?
+
+Well, that I would, that 1 plus
+3 is the 4, 1 plus 3 plus
+
+5 is the 9, 1 plus
+3 adds 7 more.
+
+You're up to 16 and onwards.
+
+So if going this way is a
+subtraction at each step,
+
+going this way is a kind
+of running addition.
+
+I add up all the slopes to
+see how far I've climbed.
+
+Let me do a second example,
+just to make that point.
+
+Let me start you this time,
+let me start you with the
+
+slopes, because that's
+today's job.
+
+Suppose the slopes are
+4, 3, 2, 1, 0.
+
+So if these were speeds,
+I would say,
+
+OK, I'm slowing down.
+
+I'm slowing down, but I'm
+still moving forward.
+
+Positive speeds, but putting
+the brakes on.
+
+What would be the distances?
+
+If the trip meter starts, start
+the trip meter at 0.
+
+OK.
+
+Then in the first second or
+hour, the first delta x we
+
+would go 4.
+
+And what goes there?
+
+7, right?
+
+I'm doing, I'm accumulating,
+adding up the distances.
+
+Here I was at 4.
+
+I went another three
+to 7, to 9, 10.
+
+Here's, I didn't move.
+
+No speed, zero slope, stays
+flat, hit the top at 10.
+
+OK, I could do this with any
+bunch of numbers and I can do
+
+it with letters.
+
+So now I move from arithmetic
+to algebra.
+
+Algebra just means I'll do it
+with any letters, but I'm not
+
+yet doing it continuously,
+which is what
+
+calculus will do.
+
+So with letters, I have here y0,
+y1, y2, y3, y4, let's say.
+
+So those are the y's.
+
+Now what are the slopes between
+them if the step
+
+across is 1?
+
+So what are the steps upward,
+what are the delta y's?
+
+Well, y1 minus y0, y2 minus y1,
+y3 minus y2, y4 minus y3.
+
+And then my question is these
+are the s's, these are the
+
+delta y's, you could say.
+
+These are the y's.
+
+What happens if I add
+all those delta y's?
+
+Do you see what happens?
+
+What happens if I add those
+four changes to
+
+get the total change?
+
+Well, when I add those, do you
+see that y1 will cancel minus
+
+y1, y2 will cancel minus y2,
+y3 will cancel minus y3.
+
+So the sum--
+
+and I use just a sigma symbol,
+but I'll just say sum and you
+
+know what I mean--
+
+of these delta y's is what?
+
+What happened after all
+those cancellations?
+
+Did everything cancel?
+
+No way.
+
+y4 is still there, minus
+y0 is still there.
+
+So it was y4 minus y0.
+
+The last y minus the first y.
+
+I'll just write y last minus
+y 0, y first. y end minus y
+
+start is the sum of
+the delta y's.
+
+Simple algebra.
+
+Reminding us again and again and
+again that the opposite,
+
+the inverse to go the other way
+from two to one, we add
+
+pieces to get back to the y's.
+
+Now I'm coming closer to what I
+want, but I'm moving toward
+
+calculus now.
+
+So calculus, I got there by
+delta y's over delta x's.
+
+So in moving toward calculus,
+what am I doing?
+
+I'm thinking of the changes
+delta y over
+
+smaller steps delta x.
+
+So I just want to
+take this step.
+
+I want to divide by delta x
+and multiply by delta x.
+
+Why do I do that?
+
+That's because it's this delta
+y over delta x that is--
+
+it's those ratios, whatever
+the size of delta x is.
+
+And it's going to get
+smaller and smaller.
+
+I'm going to look at the change
+over very short steps.
+
+Then it's that ratio
+that make sense.
+
+Delta y over delta x is
+a reasonable number.
+
+It's close to the s.
+
+It's close to dy dx, but it
+hasn't got there yet.
+
+I'm multiplying by the delta x,
+the small step that's going
+
+to 0 but hasn't got there yet.
+
+And I'm adding and I get the
+last one minus the first one.
+
+Now here comes the
+limiting step.
+
+So the limiting step will be
+the limit of this left hand
+
+side, this sum.
+
+So in the limit, I'll have more
+and more and more things.
+
+As delta x gets smaller, if
+I'm thinking of some fixed
+
+total change in x, I'm chopping
+that up into smaller
+
+and smaller pieces, more
+and more pieces.
+
+So more and more pieces of the
+slopes at different points
+
+along times the size of the
+piece give this answer.
+
+So now can I jump to the
+way that I would
+
+write this in the limit?
+
+So now let delta x go to 0.
+
+And I ask the right hand
+side, y last minus y
+
+first is not changing.
+
+y at the end--
+
+I'll write something different,
+y end minus y
+
+start, just to make that
+same point again.
+
+But it's this that's changing.
+
+As delta x goes to 0,
+this becomes dy dx.
+
+The little delta x's
+are going to 0.
+
+Here's the way I write it.
+
+So in that limit, I can't
+legally write that sigma, so
+
+this integral symbol is kind
+of copied from that sigma.
+
+But it's telling you that
+a limit has happened.
+
+And in that limit, this
+is dy dx and this, the
+
+notation, is dx.
+
+I've got what I predicted
+here, with s of x there.
+
+So what I hope this discussion
+has, by starting with numbers,
+
+by going to algebra, by looking
+at the sum of those
+
+things, which was simple, and
+then by going to the limit,
+
+which was not simple.
+
+So a whole lot of limit has been
+not fully explained, and
+
+I think the right thing to do
+now is to do an example.
+
+So let me move to an example.
+
+So I'll take a particular
+function and follow this
+
+process, this limiting process
+and see what it gives.
+
+And it will give us function one
+and, as a bonus, it will
+
+give us a new meaning
+for function one.
+
+Let's do it.
+
+So now I'm going to take
+a particular s of x.
+
+So here's x.
+
+Let me take s of x
+to be 2 minus 2x.
+
+I didn't want to take one
+totally simple that I already
+
+had started the lecture with,
+but it's not difficult either.
+
+We'll be able to see what's
+happening here.
+
+OK, so let me graph it, because
+I want to do this now
+
+with the graph.
+
+So at x equal 1, s of x has
+dropped to 0, where when x was
+
+0, it started at 2.
+
+So it started somewhere here.
+
+Here was 1, halfway down.
+
+It's going to come down
+in a straight line.
+
+And let me stop there.
+
+It could continue, but let me
+call y end is going to be 0
+
+and y start is going to be--
+
+well, we'll see about
+that, sorry.
+
+s at the end is 0.
+
+S at the end is 0.
+
+I don't yet know what
+y at the end is.
+
+It's not 0.
+
+So what's my idea?
+
+Well, not mine.
+
+Newton and Leibniz and a lot
+of people had these ideas.
+
+It's kind of interesting.
+
+So Archimedes.
+
+He goes way, way back, before
+Newton or Leibniz or anybody
+
+conceived of them.
+
+Archimedes figured out
+how to deal with a
+
+curve with a parabola.
+
+Archimedes got from a parabola,
+he got from x
+
+squared, the parabola, back to
+a height by special ideas.
+
+He was one of the great
+mathematicians of all time.
+
+But even Archimedes didn't see
+what you now see, this
+
+connection between function
+one and function two.
+
+If he had seen that, he would
+have gone further.
+
+All right, now let's see it.
+
+Let me take a delta
+x equal to 1/4.
+
+So this is delta x here, and
+this one is two delta x's, and
+
+this one is three delta x's, and
+the one is four delta x's
+
+in my original delta x, which is
+1/4, which is small but not
+
+really small.
+
+So now what do I do?
+
+Look at this first period.
+
+The slope, the s function,
+function two--
+
+see, over here is going
+to be function one.
+
+This is going to be the y,
+the integral of that.
+
+But I don't know what
+it is yet, so it's
+
+pretty open to question.
+
+OK, so now let's get there.
+
+So the point is that
+over this interval,
+
+the slope is changing.
+
+It's changing a significant
+amount.
+
+Not too much, but
+it's changing.
+
+And I don't know, from the
+algebra, I don't know how to
+
+deal with that.
+
+I'm just going to take a value
+within this sum value and stay
+
+with it within that interval,
+and I'll take
+
+the starting value.
+
+So over this first delta x, I'm
+going to pretend that the
+
+slope stays at 2.
+
+So I'm pretending that this
+is my slope function.
+
+Then over my next delta x, I'm
+going to pretend that it stays
+
+at probably 1 1/2.
+
+And then I'm going to pretend
+that it stays at 1, and I'm
+
+going to pretend that
+it stays at 1/2.
+
+If you allow me to go back to
+distance and speed, I'm
+
+chopping up the full time, the
+day, let's say, into four
+
+pieces and in each piece, the
+speed is changing, which I'm
+
+not ready to deal with,
+which algebra isn't
+
+ready to deal with.
+
+So the best I could do was say
+OK, so suppose the speed is
+
+constant at what it was at the
+start of that short time.
+
+So those would be delta t's
+rather than delta x's.
+
+The s would be representing
+speed, but no difference in
+
+the picture.
+
+So now let me do these things.
+
+Now I'm going to do this
+addition, which won't give me
+
+exactly the right y because
+those rectangles are not
+
+exactly right.
+
+But I'll get them better by
+taking smaller delta x's.
+
+Let me see, what
+do I have here?
+
+Over this first time, I
+have my slope, which
+
+I'm taking to b 2.
+
+So that's the delta y over delta
+x, that's the s, and
+
+then times the delta x.
+
+And what is that?
+
+We might as well just face it,
+that that 2 times that delta
+
+x, we can think of that
+as the area in
+
+that tall, thin rectangle.
+
+Well, I've introduced the word
+area for the first time.
+
+It never showed up on
+the previous board.
+
+It's the extra insight
+that's coming today.
+
+Now over the second short
+period, I'm going to keep fix
+
+my speed at 1 1/2.
+
+1 1/2 times delta x, because my
+speed I'm setting at 1 1/2,
+
+and this is how long I go so
+this is a distance or a change
+
+in height, a change in y.
+
+And you see what's coming.
+
+The next one will be a 1 times
+the delta x, and the last will
+
+be 1/2 times the delta x.
+
+This is adding the way
+I did in the algebra.
+
+And what do I get?
+
+Well, this, again, is the
+area of that piece.
+
+This one is the area of that
+piece, this one is the area of
+
+that piece.
+
+I get an overestimate because
+the true slopes dropped a
+
+little within each piece.
+
+I get some quantity which I can
+figure out, but it's not
+
+the right answer.
+
+It's not the final answer.
+
+And what is now the main
+step to get there?
+
+Chop delta x into half,
+you could say.
+
+Why not cut it in half?
+
+Now I'll have a different
+picture.
+
+Can you see what this
+picture is doing?
+
+Now over the first little half
+of the old step I am up here,
+
+but then I drop to here.
+
+Can I do this with an eraser?
+
+A little bit got chopped away, a
+little bit got chopped away.
+
+Where has it gone?
+
+I'm going to have
+this zig zag.
+
+That wasn't too bad.
+
+I'm replacing that with a sum of
+eight pieces, because delta
+
+x is now down to 1/8.
+
+This is what we said
+about that sum.
+
+That sum has got more and more
+terms because it has a term
+
+for every little delta x, and
+the size of that term is about
+
+like delta x multiplied
+by an s.
+
+So what I getting in the limit
+is a kind of running sum, a
+
+running counter, a mileage
+meter, a trip mileage, that's
+
+adding up distance
+based on speed.
+
+Do you see what I'm getting
+in the graph picture?
+
+What happens to the shaded part
+as delta x gets smaller
+
+and smaller?
+
+This shaded part is going
+to be the curve.
+
+These little long pieces are
+going to get reduced, reduced,
+
+reduced, and in the end
+the total height at
+
+1 is going to be--
+
+ta-da, this is the moment--
+
+the area under the
+slope curve.
+
+This y turns out to be
+the area under the s
+
+of x curve, or y.
+
+So at x equal 1, what is it?
+
+What's the area out to 1?
+
+Well, we've got a
+triangle there.
+
+Its base is 1, its
+height is 2.
+
+The area of a triangle is 1/2
+the base times the height, so
+
+I have 1/2 times 1 times 2.
+
+I've got 1.
+
+The area at the end is 1.
+
+But--
+
+well, I shouldn't say but.
+
+I should let you applaud first.
+What if I only went
+
+that far, halfway?
+
+What if that was s end?
+
+What if I want to know what
+is y at x equal 1/2?
+
+Then it'll be of course, just
+the area up to that point.
+
+Can I remove this part of the
+picture for a moment?
+
+I'm always looking at area.
+
+And the area of that, do we know
+what that area would be?
+
+It's not a triangle anymore,
+it's some kind of a trapezoid.
+
+As delta x goes to 0, I'm going
+to get the correct area,
+
+which will be what?
+
+Let's see, I have 1/2 as the
+base and the average height is
+
+about 1 1/2.
+
+Can I do that little
+calculation?
+
+The base is 1/2 and the average
+height is 1 1/2.
+
+I think I get 3/4.
+
+So halfway along, it's
+got up to 3/4.
+
+Where is 3/4?
+
+So this is 1, this is 3/4,
+this is 1/2, this is 1/4.
+
+So at 1, it's at 3/4.
+
+Halfway along, its at 3/4.
+
+I would like to know
+that graph now.
+
+I'm ready to jump
+to the limit.
+
+Let me do it the way I said at
+the very start of the lecture.
+
+Let me take this and
+try to guess.
+
+So, I'm taking a shortcut.
+
+Because do we go through this
+horrible process every time we
+
+want to do an integral?
+
+Of course we don't.
+
+The best way is, can we find a
+y function, a function, one,
+
+that has that derivative?
+
+Let's just try it.
+
+I'm allowed to take it in
+two pieces, that's a
+
+very valuable fact.
+
+So what has the derivative 2?
+
+If the slope is 2, what's
+the function?
+
+If the speed is 2, what's
+the distance?
+
+It's constant speed, 2, times
+the total distance.
+
+The slope of the 2x line
+is 2, clearly.
+
+What about the 2x?
+
+Which function has
+the slope 2x?
+
+Well, we saw it over here.
+
+The function that has the slope
+2x is x squared, because
+
+when I take the slope of x
+squared, the 2 comes down.
+
+The 2 shows up, I have
+one smaller power, x
+
+to the first power.
+
+This is the correct y, and I
+hope that my graph gets those
+
+points right.
+
+At x equal to 1, this is
+2 minus 1, this is the
+
+correct height, 1.
+
+At x equal to 1/2, all right,
+here is the moment of truth.
+
+Now set x equal to 1/2, and what
+do you get for this y?
+
+You get 2 times 1/2--
+that's 1--
+
+minus 1/2 squared, 1/4.
+
+Hey, miracle.
+
+3/4.
+
+This area I figured
+to be 3/4 and this
+
+approach also gave 3/4.
+
+Either way, multiplying
+those is 3/4,
+
+subtracting those is 3/4.
+
+What does my graph look like?
+
+What does the graph
+of that look like?
+
+What's the slope at the start?
+
+The slope at the start
+is s at the start.
+
+And s at the start, when
+x is 0, the slope is 2.
+
+So it starts out with
+a slope of 2.
+
+But it's slowing down, it's a
+little bit like this one where
+
+the car was slowing down, we're
+not picking up distance
+
+so quickly, we're not picking
+up height so quickly.
+
+But we're still going
+forward, we're still
+
+picking up some height.
+
+So it starts with a slope of 2,
+bends around to there, and
+
+I guess maybe that is--
+
+yes.
+
+That picture is almost
+good, but not great.
+
+So the slope is 2 and there.
+
+And what is the slope
+at this point?
+
+You can't tell from my picture,
+which isn't perfect.
+
+The slope, I'm told
+what it is.
+
+When x is 1, the slope
+is 2 minus 2.
+
+Slope 0.
+
+The slope is 0.
+
+We're not picking up any more
+height, any more area.
+
+And of course, that's right.
+
+At this point, we're not
+picking up more area.
+
+If I continue beyond here,
+we're losing area because
+
+below the axis, I'll count as
+negative area just because if
+
+it was speed, I'd be
+going backwards.
+
+That's what will happen here.
+
+I'll start down.
+
+If that continued, this
+would still be the
+
+correct thing to graph.
+
+If I do graph it, that's
+actually the top at x equal 1,
+
+and then it starts down and
+probably by, I don't know
+
+where, x equal something,
+maybe by x equal 2.
+
+Oh yeah, you can see.
+
+By x equal to 2, it's
+got down to 0 again.
+
+When x is 2, this is now 0 and
+you can see that when x is 2,
+
+we'll have the bad area--
+
+the car going backwards--
+
+will be identical to
+the forward area.
+
+The total area is 0, and I'll be
+at this point when x is 2.
+
+Let me just recap a moment.
+
+Today was about going
+from function two
+
+back to function one.
+
+The quickest way to do it is
+to find a function one that
+
+gives that function two
+and then you're in.
+
+But if you can't do that or if
+you want to understand what
+
+the real, behind it, limiting
+process is, it's like the
+
+algebra but it's this expression
+here that's
+
+concealing so much
+mathematics.
+
+Delta x going to 0, these ratios
+going to the actual
+
+function, and the delta x I
+replaced by the symbol dx,
+
+indicating an infinitesimal.
+
+We'll see it more.
+
+Thank you.
+
+NARRATOR: This has been
+a production of MIT
+
+OpenCourseWare and
+Gilbert Strang.
+
+Funding for this video was
+provided by the Lord
+
+Foundation.
+
+To help OCW continue to provide
+free and open access
+
+to MIT courses, please
+make a donation at
+
+ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/4-ehnTIyV0A.txt b/4-ehnTIyV0A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a20c0636ff97d860efaf1ae3ac90c8b557c86b28
--- /dev/null
+++ b/4-ehnTIyV0A.txt
@@ -0,0 +1,2369 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Ladies and gentlemen,
+welcome to this
+
+lecture on nonlinear finite
+element analysis of solids and
+
+structures.
+
+In the previous lectures, we
+talked about the basic process
+
+of the incremental solution
+that is used in
+
+finite element analysis.
+
+And we talked about quite some
+important continuum mechanics
+
+variables that we are employing
+in nonlinear finite
+
+element analysis.
+
+This was really preparatory work
+for the discussion of a
+
+general formulation that is very
+widely used to analyze
+
+nonlinear systems using
+finite elements.
+
+And this formulation is called
+the total Lagrangian
+
+formulation.
+
+This is the formulation that I'd
+like to discuss with you
+
+now in this lecture.
+
+The total Lagrangian formulation
+is a formulation
+
+that refers the stress and the
+strain variables at time t
+
+plus delta t to the original
+configuration at time zero.
+
+Total, in fact, means reference
+to the original
+
+configuration here.
+
+And notice we, of course,
+encountered this equation
+
+already earlier in the
+early lectures.
+
+We have on the left hand side
+again the total internal
+
+virtual work.
+
+And on the right hand side,
+the total external virtual
+
+work all at time
+t plus delta t.
+
+We have here the second
+Piola-Kirchhoff stress tensor.
+
+Here we have the Green-Lagrange
+strain tensor.
+
+And on the right hand side, of
+course, all the body forces,
+
+surface forces et cetera
+would enter.
+
+We discussed in a previous
+lecture how the right hand
+
+side is calculated in general
+and what it all contains.
+
+We also discussed that this
+equation here is quite
+
+equivalent to this equation.
+
+And in this equation, we have
+the Cauchy stress tensor
+
+operating on the virtual
+strain tensor, an
+
+infinitesimally small
+strain tensor.
+
+And this product is integrated
+over the volume at time
+
+t plus delta t.
+
+On the right hand side,
+we have the same
+
+quantity as up there.
+
+Now notice that we really want
+to solve, of course, this
+
+equation here in finite
+element analysis.
+
+But we discussed earlier that in
+order to do so effectively,
+
+we need to introduce a new
+stress measure, a new strain
+
+measure, and that, of course,
+brings us then to this
+
+equation up here.
+
+Let us recall briefly some of
+the important points that we
+
+made earlier in the
+other lectures.
+
+We said that this equation here,
+applied at time t plus
+
+delta t, is an expression
+of the equilibrium,
+
+compatibility, and the
+stress-strain law at time t
+
+plus delta t.
+
+Let's just look at this equation
+once more, where
+
+these quantities enter.
+
+Well, if equilibrium is
+satisfied locally everywhere
+
+in the continuum, then this
+equation must be holding for
+
+any virtual displacements that
+satisfy the displacement
+
+boundary conditions, and
+corresponding virtual strains.
+
+Notice that the virtual
+displacements enter on the
+
+right hand side, and these here
+are the corresponding
+
+virtual strains.
+
+The compatibility enters in
+here because we would, of
+
+course, use compatible virtual
+displacement, and we would
+
+calculate also the stresses from
+compatible displacements.
+
+The stress-strain law enters
+in the calculation of the
+
+stress here from the
+strains given.
+
+And once again we apply this
+at time t plus delta t.
+
+We also noted earlier that
+we will be using
+
+an incremental solution.
+
+Namely, that the solution at
+time t plus delta t will be
+
+calculated from the solution at
+time t by incrementing the
+
+displacements by ui.
+
+Notice that we will assume,
+of course, that
+
+the tui's are known.
+
+That the displacementts at time
+t are known, and that
+
+these are the unknown
+quantities that
+
+we're looking for.
+
+Of course, that gives us then
+the unknown quantities that we
+
+actually want to solve for.
+
+Our goal is, for the finite
+element solution to linearize
+
+the equation of the principle
+of virtual work, so as to
+
+obtain a set of equations,
+finite element equations, that
+
+read as follows.
+
+Here we have a stiffness
+matrix, a
+
+tangent stiffness matrix.
+
+Here we have an incremental
+displacement vector.
+
+And on the right hand side, we
+have a load vector, a vector
+
+of nodal point forces
+corresponding to the
+
+externally applied loads
+at time t plus delta t.
+
+And here we have a nodal point
+force vector that is
+
+equivalent to the current
+element stresses, in this
+
+particular instance at time
+t, as indicated by the
+
+superscript t here.
+
+Now this incremental
+displacement vector, of
+
+course, will be added to the
+displacement that we know
+
+already, and that correspond
+to time t.
+
+And that will give us then
+a first estimate for the
+
+solution, displacement
+solution, at time
+
+t plus delta t.
+
+Notice this is also summarized
+down here.
+
+Notice, however, that this
+vector here is only an
+
+approximation to the actual
+vector that we're looking for,
+
+because of the linearization
+process that leads us to this
+
+system of equations.
+
+The equation tku equals r
+minus f is, of course,
+
+applicable for a single element
+as well as a total
+
+assemblage of elements.
+
+In other words, this equation
+here, tk delta u1 equals t
+
+plus delta r minus tf, would be
+applicable to an element in
+
+which n then would mean just
+the degrees of freedom, the
+
+number of degrees of freedom
+of that element.
+
+And also for a total structure
+in which n then, of course
+
+means the total number of
+structural degrees of freedom.
+
+The tk matrix, the r vector,
+and the f vector would be
+
+constructed using the direct
+stiffness method the way we
+
+are used to it in the linear
+elastic analysis.
+
+In other words, there is
+nothing new here to be
+
+discussed really, as far as a
+construction of these matrices
+
+go, when we talk about a total
+element assemblage from the
+
+individual element matrices.
+
+However, an important point
+is that we cannot simply
+
+linearize the principle of
+virtual work when it is
+
+written in this form here.
+
+And the reason was, of course,
+that we cannot integrate over
+
+an unknown volume.
+
+The volume t plus delta t is
+unknown, or the volume at time
+
+t plus delta t is unknown, and
+we cannot directly increment
+
+the Cauchy stresses the way we
+discussed it already earlier.
+
+To linearize then, we need to
+choose a known reference
+
+configuration.
+
+And one known reference
+configuration that is a very
+
+natural one to use really,
+is the one
+
+corresponding to time zero.
+
+In this case, if we use that
+reference configuration, we
+
+talk about the total Lagrangian
+formulation.
+
+If we use as a reference
+configuration the
+
+configuration corresponding to
+time t, then we talk about the
+
+updated Lagrangian
+formulation.
+
+I'd like to make
+one point here.
+
+Namely, that of course we have
+calculated already from all
+
+the configurations from
+time zero to time t.
+
+So you may ask yourself, why
+is he not choosing as a
+
+reference configuration, for
+example, the configuration t
+
+minus delta t?
+
+In other words, one
+configuration prior to time t
+
+as a possibility.
+
+Well, it would be a possibility,
+but if you choose
+
+to do so, you would lose the
+advantages that you have in
+
+the updated Lagrangian
+formulation, and the
+
+advantages that you would have
+in the total Lagrangian
+
+formulation.
+
+Of course, there are differences
+here and we will
+
+talk about the advantages and
+disadvantages of either of
+
+these formulations.
+
+And you would be left with that
+choice of t minus delta t
+
+reference configuration,
+with basically all the
+
+disadvantages only.
+
+And therefore, we generally want
+to choose either this one
+
+or that one as the reference
+configuration.
+
+Let us now discusses the total
+Lagrangian formulation.
+
+In the total Lagrangian
+formulation, we use the
+
+reference configuration zero,
+and therefore we talk about
+
+this stress.
+
+We use this stress and that
+strain, this was a second
+
+Piola-Kirchhoff stress referred
+to the configuration
+
+at time zero.
+
+This is the Green-Lagrange
+strain referred to the
+
+configuration at time zero.
+
+The principle of virtual work
+once again, originally in this
+
+form, is now written
+in this form.
+
+We have had that already before
+on viewgraphs, and I
+
+don't think I need to go through
+those details again.
+
+But the important point is
+that this is the starting
+
+point of the total Lagrangian
+formulation.
+
+The formulation proceeds
+as follows.
+
+We know the solution at time t,
+therefore this stress, this
+
+displacement derivative, all
+the static and kinematic
+
+variables in fact, are known
+corresponding to the
+
+configuration at time t.
+
+And we can now decompose the
+stress corresponding to time t
+
+plus delta t into one known
+value and one unknown value.
+
+Similarly we proceed with
+the strain measures.
+
+The strain measures, the
+Green-Lagrange strain at time
+
+t plus delta t is decomposed
+into one value that we know
+
+already, and an increment.
+
+And, of course, remember these
+two increments are unknown.
+
+They are unknown, whereas these
+are known because we
+
+have calculated already
+the configuration
+
+corresponding to time t.
+
+In terms of displacements, we
+can directly develop that the
+
+Green-Lagrange strain at time
+t is written as shown here.
+
+We went over these different
+components already earlier.
+
+Notice once again that we have
+a product of displacement
+
+derivatives here,
+that this is, of
+
+course, a nonlinear term.
+
+And once again, as I pointed out
+in an earlier lecture, we
+
+have nothing neglected here.
+
+You see only quadratic terms.
+
+There are no cubic terms
+or higher-order terms.
+
+We have nothing neglected.
+
+This is a strain measure that
+holds for any amount of
+
+deformation, any amount
+of strain.
+
+Then we can also write this same
+strain, Green-Lagrange
+
+strain, corresponding to time t
+plus delta t, and this would
+
+be the result.
+
+Notice whatever we had here as t
+superscript has now become a
+
+t plus delta t superscript.
+
+That's in fact the
+only difference.
+
+If you subtract from this
+strain, that strain, we get
+
+the increment, and
+that increment is
+
+written out right here.
+
+Now, there are some interesting
+points regarding
+
+this incremental strain.
+
+This here is an increment in the
+strain that is linear in
+
+the displacement components.
+
+Similarly this one.
+
+Notice this one here, is, of
+course a product, product and
+
+may look, at first sight,
+as a nonlinear term.
+
+When you see products of
+displacements, you think of a
+
+nonlinearity.
+
+However, if you look closer,
+you find that
+
+there is a t here.
+
+Therefore, this part is known.
+
+Since this part is known, and
+this part is unknown, this
+
+total term is really linear in
+the incremental displacement.
+
+In fact, the incremental
+displacements don't even go in
+
+here, because we're
+differentiating here the
+
+displacements at time t with
+respect to the original
+
+coordinates.
+
+Therefore, this total
+term here is really
+
+still linear in ui.
+
+Linear in the incremental
+displacements.
+
+We call this part here, as
+given here, the initial
+
+displacement effect.
+
+The initial displacement effect
+because the initial
+
+displacements go into these
+derivatives here.
+
+We are differentiating the
+displacement at time t with
+
+respect to the original
+coordinates.
+
+This term, on the other hand
+here, is nonlinear in ui.
+
+It is nonlinear because here
+we're taking one term that
+
+depends on ui, and we multiply
+it by another term that
+
+depends on ui.
+
+Notice this a differentiation
+of uk, the incremental
+
+displacement, into the k
+direction with respect to the
+
+original coordinates.
+
+Coordinate axis xj
+here particular.
+
+So this is here, clearly
+a nonlinear term in ui.
+
+A quadratic term, as
+a matter of fact.
+
+We will look at this strain,
+of course, a little
+
+bit more just now.
+
+But keep in mind that there is
+one linear term that contains
+
+an initial displacement effect
+and a nonlinear term.
+
+I might add here that, of
+course, this initial
+
+displacement effect is
+zero if the initial
+
+displacements are zero.
+
+In other words, in our
+incremental solution, for
+
+example, if we are just starting
+the solution process,
+
+then the initial displacements
+are still zero.
+
+This term drops out.
+
+We note now regarding the
+formulation that the variation
+
+on the total Green-Lagrange
+strain tensor corresponding to
+
+time t plus delta t, is really
+equal to the variation in the
+
+increment of the Green-Lagrange
+strain tensor,
+
+from time t to time
+t plus delta t.
+
+In this picture we show
+what we mean by that.
+
+Here on the left hand side in
+black, you have the body in
+
+its original configuration.
+
+It moves to a configuration
+at time t.
+
+And then to a configuration,
+here shown in green, that
+
+corresponds to time
+t plus delta t.
+
+Notice here we have the
+displacement corresponding to
+
+time t, and then the
+displacement corresponding
+
+from time t to time
+t plus delta t.
+
+The total displacement,
+of course, here is the
+
+displacement from time zero
+to time t plus delta t.
+
+What we are doing, of course
+in the principle of virtual
+
+work, is to impose a variation
+in displacements about the
+
+configuration at time
+t plus delta t.
+
+And that variation is here
+indicated by the blue line.
+
+And if we impose this variation
+here, since the
+
+displacements at time t are
+constant, surely whatever
+
+these displacements were
+should not matter.
+
+And that is, in fact,
+expressed by this
+
+relationship here.
+
+If we vary here, since the
+displacements to ui are
+
+constant, they do not affect the
+variation on the strains.
+
+And therefore, we can simply
+vary the incremental strain,
+
+and we find that variation is
+indeed equal to the variation
+
+of the total strain.
+
+Of course, you can also
+prove that to yourself
+
+mathematically by just going
+through the arithmetic.
+
+In other words, applying the
+variation to this quantity,
+
+and then applying the variation
+to that quantity,
+
+which I've given you on the
+previous viewgraph, and you
+
+would find that indeed you
+get identically the same
+
+expressions.
+
+We can define a linear strain
+term, linear strain increment,
+
+as 0 eij, and the nonlinear
+strain increment as 0 eta ij.
+
+Notice that once again, here we
+have the quadratic terms.
+
+And, of course, when we add
+these two terms together, we
+
+get back our total strain
+increment from time t to time
+
+t plus delta t.
+
+If we take a variation on that
+increment, that is equivalent
+
+to taking a variation on
+the linear term and
+
+the nonlinear term.
+
+Notice that so far we
+have only talked
+
+about continuum mechanics.
+
+Of course we want to use the
+continuum mechanics principles
+
+that we discussed so far
+in the finite element
+
+discretization.
+
+But notice that these strain
+terms here that we talked
+
+about, are really continuum
+mechanics variables.
+
+There is an interesting
+observation.
+
+Namely, if we talk about this
+strain measure and that strain
+
+measure, rather the linear
+incremental strains and the
+
+nonlinear incremental strains,
+linear and nonlinear in ui,
+
+then if we apply these in finite
+element analysis, we
+
+have to remember that the
+displacements are interpolated
+
+in terms of nodal
+point variables.
+
+And what we're really looking
+for in finite element analysis
+
+are the nodal points
+variables.
+
+In isoparametric finite element
+analysis, which is the
+
+final element procedure that we
+will be using extensively,
+
+we interpolate the internal
+element displacements, tui, in
+
+terms of the nodal point
+displacements.
+
+Let me define a little bit
+more what this is here.
+
+This is, of course, the
+displacement from time zero to
+
+time t into the i's direction.
+
+We are summing here over all
+the finite element nodal
+
+points, the N nodal points.
+
+We have interpolation functions,
+hk, that we will
+
+talk more about later on.
+
+And we have here the nodal point
+displacement at time t
+
+into the i direction of
+the nodal point k.
+
+This k goes with that k.
+
+And we're summing over
+all the nodal points.
+
+Now notice that this is the
+linear relationship in
+
+isoparametric finite
+element analysis of
+
+solids, I should say.
+
+This is a linear relationship.
+
+And therefore, our linear strain
+terms that we talked
+
+earlier about, being linear in
+the incremental continuum
+
+mechanics displacements, are
+also linear in the incremental
+
+nodal point displacements.
+
+Similarly, this term here, which
+was nonlinear in the
+
+increments of displacements
+within the domain, from a
+
+continuum mechanics point of
+view, will also be nonlinear
+
+in the nodal point displacement
+increments.
+
+However, in the formulation of
+structural elements, with the
+
+incremental displacements,
+in fact also the total
+
+displacements, I interpolated
+using nodal point
+
+displacements and nodal
+point rotations.
+
+In other words, we also deal
+with nodal point rotations in
+
+order to calculate the total
+displacements of the element.
+
+And in that case, we have to
+recognize that the exact
+
+linear strain increment, the way
+we have defined it earlier
+
+linear in the incremental
+displacements, is still
+
+properly given as a linear
+strain increment in the nodal
+
+point variables.
+
+However, the term that we
+defined earlier as a nonlinear
+
+strain increment, this one, is
+not the full story of all the
+
+nonlinear strain increments.
+
+Because the rotations will put
+additional nonlinear strain
+
+increments into this
+term here.
+
+The reason being, that for large
+rotations, of course, we
+
+have cosine sine terms in these
+rotations and when we
+
+evaluate the total nonlinear
+strain term, we find that
+
+there are additional terms
+coming up here.
+
+Well, what is the effect of
+these two statements?
+
+It means that the right hand
+side force vector, or rather
+
+the vector t 0 f, the vector
+of nodal point forces
+
+corresponding to the internal
+elements stresses, is always
+
+correctly calculated.
+
+However, the stiffness matrix,
+t 0 k, for the formulation is
+
+only approximated because some
+of the nonlinear terms here
+
+have been dropped in the case
+of structural elements.
+
+Of course, you can also include
+the nonlinear terms.
+
+Then you would have to add these
+terms to this expression
+
+here, and then you would get a
+true tangent stiffness matrix.
+
+This means, of course, for an
+actual analysis, that when you
+
+form the equations, we have on
+the left hand side-- let me
+
+just put all of it in here--
+
+for the first iteration, we
+talked about the fact that we
+
+have a stiffness matrix times an
+increment in displacements.
+
+I already put a 1 there because
+it will be only an
+
+approximation to the
+total incremental
+
+displacement vector.
+
+Well, we notice then that this
+matrix here is approximated if
+
+you were to drop these
+additional terms.
+
+But the right hand side vector f
+here is properly calculated.
+
+Therefore if you iterate, you
+always get the exact solution,
+
+the correct solution.
+
+But the convergence in the
+iteration might be a bit
+
+slower than what you could
+have obtained if you had
+
+included these additional terms
+here that I referred to.
+
+Let us now continue with
+the continuum mechanics
+
+formulation.
+
+The equation of the principle of
+virtual work becomes, if we
+
+substitute the quantities that
+I defined earlier, directly
+
+this equation.
+
+Notice here we have now the
+increment in stress times the
+
+variation of the incremental
+Green-Lagrange strain, from
+
+time t to t plus delta t.
+
+Of course, it's integrated over
+the original volume plus
+
+this integral here.
+
+Here we have the total stress,
+second Piola-Kirchhoff stress,
+
+corresponding to time t
+operating on the nonlinear
+
+strain increment of the total
+
+Green-Lagrange strain increment.
+
+And once again, we are
+integrating over the total
+
+volume corresponding
+to time zero.
+
+And on the right hand side, we
+have the external virtual work
+
+minus the stress at time t,
+operating on the linear strain
+
+increment corresponding
+to the total
+
+Green-Lagrange strain increment.
+
+We have so far made no
+approximations, and this is a
+
+relationship that has to hold
+for any arbitrary variation in
+
+displacements which go in here,
+or any arbitrary virtual
+
+displacement that go in here.
+
+And of course, corresponding
+strains that appear here.
+
+In essence, what we have been
+doing is that we have
+
+established a variation on
+the configuration at time
+
+t plus delta t.
+
+We have looked at the principle
+of virtual work
+
+corresponding to time t plus
+delta t, but we have
+
+introduced this increment
+in displacement.
+
+Notice that this increment in
+displacement is measured from
+
+the displacement at time t.
+
+All we have done therefore, is
+to rewrite the principle of
+
+virtual work in terms of tu and
+u instead of dealing with
+
+t plus delta tu.
+
+No approximation being
+done yet so far.
+
+Of course, we really haven't
+been talking about finite
+
+elements either yet, when we
+just look at this basic
+
+equation of principle
+of virtual work.
+
+It is this principle or the
+equation that we are dealing
+
+with, is in general, a very
+complicated function of the
+
+unknown displacement
+increment.
+
+We obtain an approximate
+relationship in finite element
+
+analysis, by linearizing the
+governing equation, and, of
+
+course, then in the finite
+element sense cast it into
+
+this set of linear equations.
+
+The process of linearizing is
+a very important process,
+
+interesting process for us
+to study, and that's what
+
+I want to do now.
+
+We begin to look, in this
+linearization at all the
+
+individual terms that appear
+in the integral.
+
+And let us look first
+at this term here.
+
+This term is actually already
+linear in ui.
+
+So there is nothing
+much to linearize.
+
+t 0 sij does not contain ui.
+
+It's a known quantity.
+
+It's a known stress value.
+
+And notice that when we take
+the variation on this
+
+nonlinear strain increment, we
+directly get this expression,
+
+where this part here is
+a variation on the
+
+displacement increment.
+
+Similarly here.
+
+And of course, these are
+going to be constants.
+
+Therefore, this term here is
+linear in the incremental
+
+displacements.
+
+Linear in ui.
+
+So nothing to linearize there.
+
+The term on this viewgraph here,
+contains an incremental
+
+stress and an incremental
+strain.
+
+Notice this incremental strain
+contains the linear and the
+
+nonlinear term.
+
+And this, of course, this
+product is a linear functional
+
+off ui, sorry it contains
+linear terms,
+
+nonlinear terms as well.
+
+This stress here is, in general,
+a nonlinear function
+
+of 0 epsilon ij.
+
+The variation that we are
+taking here means we are
+
+taking a variation on
+the linear part and
+
+the nonlinear part.
+
+We will see actually that this
+one here is constant.
+
+But this one carries also terms
+of ui, so this total
+
+expression is linear in ui.
+
+And if we multiply these terms
+here, we want to end up in
+
+just one expression that has
+neglected all higher-order
+
+terms in ui, but just
+contains ui.
+
+Well, let us do so.
+
+The objective is expressed
+once more here, and we
+
+recognize that, of course, the
+variation on 0 epsilon ij
+
+contains only constant and
+linear terms in ui, the way I
+
+just expressed it.
+
+0 sij can be written as a Taylor
+series expansion in 0
+
+epsilon ij.
+
+This is the general
+expression.
+
+Here we take the partial of
+the stress at time t, with
+
+respect to the Green-Lagrange
+strain at time t, here we are
+
+having this bar with the t
+that denotes that we are
+
+actually doing this evaluation
+at time t.
+
+And here we have an increment in
+this strain, and of course,
+
+there are higher-order terms.
+
+These higher-order terms we will
+neglect, and therefore we
+
+get directly for this stress
+here, this expression.
+
+Notice we already have
+substituted for 0 epsilon rs,
+
+these two quantities.
+
+This one here is quadratic in
+ui, this one is linear in ui.
+
+And if we linearize this term,
+we get directly this one here.
+
+Notice that this is the
+appropriate stress-strain law
+
+that has to be used
+corresponding
+
+to this stress measure.
+
+And we will later on talk more
+about how we evaluate this
+
+stress-strain law.
+
+As an example, we may look
+here at this schematic
+
+solution, computed solution,
+over a number of time steps.
+
+We're going time 1, 2, 3, 4,
+5, up to t minus delta
+
+t and then to t.
+
+The stress-strain law relates
+basically the stress increment
+
+here to the strain increment.
+
+And notice it represents a
+tangent to this this curve.
+
+This green line here is a
+tangent to the red or the blue
+
+curve, the blue one now
+overlapping the red curve
+
+right there.
+
+So we have here the tangent, or
+the slope of this tangent
+
+is giving us the material
+tensor 0c.
+
+Of course, here we're talking
+just about one element.
+
+In general we have many elements
+corresponding to the
+
+strain and stress measures
+that we are dealing with.
+
+If we now substitute the result
+that we just looked at
+
+into the general equation--
+
+sorry to take this one down--
+
+into the general equation here,
+we see directly that
+
+this part here, of course,
+is the stress.
+
+And this part here gives
+us that part.
+
+We simply multiply out and look
+at the individual terms.
+
+We notice that this one
+does not contain ui.
+
+We notice that this one
+is linear in ui.
+
+So since this one is already
+linear in ui, this term will
+
+be quadratic in ui.
+
+We will have to drop it.
+
+This term here is linear in ui,
+but this one is constant,
+
+so this total term
+is linear in ui.
+
+And this is the one we keep,
+and which is then the
+
+linearized result.
+
+In other words, in summary once
+more, this total term
+
+here linearized is obtained
+via this expression here.
+
+The final linearized equation
+that we are then dealing with,
+
+now that we're substituting
+all these results into the
+
+original equation that we have
+developed, is as follows.
+
+Here we have one term that comes
+from the incremental
+
+stress times the variation
+on the total incremental
+
+Green-Lagrange strain.
+
+That all has reduced
+to this term.
+
+Here we did not have to
+linearize at all.
+
+We kept what we already had.
+
+And on the right hand side,
+did not linearize either,
+
+because this was a term that we
+had already there, and of
+
+course this is the external
+virtual work.
+
+Now it's interesting to note
+that these two terms here
+
+result into this expression,
+where this is the tangent
+
+stiffness matrix.
+
+Notice that tangent stiffness
+matrix contains the material
+
+tensor, as well as the
+current stresses.
+
+This incremental displacement
+here, vector, comes from this
+
+strain part and that
+strain part.
+
+Notice that this virtual
+displacement vector here comes
+
+from that strain part and
+also from that one here.
+
+Below here we have, of course,
+that the external virtual work
+
+results into a vector of nodal
+point forces times these
+
+virtual displacements.
+
+And this one here results into
+the force vector corresponding
+
+to the internal element
+stresses.
+
+And this is, of course, a very
+important quantity that we
+
+have to calculate accurately,
+as I pointed out earlier.
+
+Because we want ultimately in
+the iteration that this vector
+
+is equilibriating that vector,
+and if we do make a mistake in
+
+calculating this vector, then
+we might have converged, but
+
+we have converged to
+the wrong solution.
+
+So it's very important to
+recognize that this vector
+
+must be accurately calculated,
+by all means.
+
+However, the k matrix here, if
+we go back once more to the
+
+discussion of this matrix, the
+k matrix here is a tangent
+
+stiffness matrix.
+
+And this tangent stiffness
+matrix is selected such as to
+
+obtain, of course, in the
+incremental solution, an
+
+appropriate incremental
+displacement.
+
+We will see later on
+that this matrix is
+
+updated in the iteration.
+
+It depends on what kind of
+intuitive scheme we are using,
+
+depending on that scheme we
+are updating this matrix
+
+differently.
+
+In any case, it's a matrix that
+we will in quotes, "play
+
+around with", in order to
+accelerate the convergence.
+
+Therefore there is no unique
+matrix that can be used here,
+
+that should be used here.
+
+There are different
+possibilities that we will
+
+discuss in later lectures.
+
+But on the right hand side once
+again, this F vector is
+
+the F vector obtained from the
+current stresses, and that one
+
+has to be calculated uniquely
+in the correct way.
+
+Well, an important point is that
+this relationship here on
+
+the left hand side, is equal to
+the relationship given here
+
+on the right hand side.
+
+And this holds because
+this term here is
+
+equal to that term.
+
+We interpret, in fact, this
+right hand side as an out of
+
+balance virtual work term.
+
+Let's look once why this holds,
+because this might be a
+
+bit of a surprise.
+
+The mathematical explanation
+is given on this viewgraph.
+
+We had earlier already that
+the variation on the total
+
+Green-Lagrange strain is
+nothing else than the
+
+variation on the incremental
+total Green-Lagrange strain.
+
+Now if we look down here, we
+recognize that this variation
+
+here at ui equal to 0, is
+nothing else than the
+
+variation on the Green-Lagrange
+
+strain at time t.
+
+If ui is zero, then this term
+here is nothing else than the
+
+Green-Lagrange strain
+at time t.
+
+So we're looking here at
+the variation of the
+
+Green-Lagrange at time, t
+if I put ui equal to 0.
+
+Now let's look at these
+expressions here.
+
+If I evaluate this term here, at
+ui equal to 0, we find that
+
+this term here, being a
+constant, is recovered.
+
+But notice that this term here,
+with ui equal to 0,
+
+simply turns out to be 0.
+
+Therefore, this term is
+equal to that term.
+
+And this means, therefore, that
+the variation on t zero
+
+epsilon ij is equal to the
+variation on 0 eij, which we
+
+wanted to prove, of course.
+
+So this is the reason why this
+term here is equal to that
+
+term, as we have used it on
+the previous viewgraph.
+
+This result also makes physical
+sense, because if we
+
+look at the governing equation,
+we find that this
+
+term here, replaced, is
+nothing else than tr.
+
+Should be tr.
+
+And of course, the script
+r the external virtual
+
+work at time t.
+
+And this, of course, is here the
+out of balance load term.
+
+Now if, for example, the
+material is elastic, and the
+
+external virtual work has not
+changed, then clearly the
+
+displacements would
+not change.
+
+In other words, t plus delta tui
+would be equal to tui, and
+
+the incremental displacements
+would be 0.
+
+Therefore, equilibrium
+would be satisfied.
+
+Hence, this term, which we have
+here, must actually be
+
+equal to t 0 sij times variation
+t 0 epsilon ij, the
+
+way we discussed it just now.
+
+We may rewrite the linearized
+governing equation as given on
+
+this viewgraph.
+
+And I am rewriting it in this
+form because we anticipate
+
+that we need an iteration.
+
+We simply introduce here, an
+iteration counter 1, with the
+
+delta in front of the
+incremental strain value.
+
+And similarly we introduce a
+delta here, and an iteration
+
+counter 1 there.
+
+And on the right hand side, we
+introduce also an iteration
+
+counter, but one lower.
+
+In other words, 0 here, whereas
+we have a 1 there.
+
+Notice 0 here, a 1 here.
+
+And notice furthermore, that
+this term is nothing else than
+
+that term, and this term here
+is nothing else than the
+
+variation on t 0 epsilon ij.
+
+This would be the equation
+that we have developed
+
+already, just having introduced
+now a different
+
+notation which leads us towards
+what we want to deal
+
+with in the iteration.
+
+The governing equations from a
+finite element point of view,
+
+then would be as shown here.
+
+Notice tangent stiffness matrix,
+del u1, iteration
+
+counter, the external loads,
+which we still assume to be
+
+constant, by the way.
+
+We still assume deformation
+independent loading if we have
+
+deformation dependent loading,
+these would also
+
+change in the iteration.
+
+And here we have the vector
+corresponding to the internal
+
+element stresses at time t.
+
+We write that vector as t
+plus delta t 0, 0 there.
+
+And that means that we are
+really talking, at this point,
+
+about this vector.
+
+We calculate this incremental
+displacement vector and add it
+
+to the previous displacements,
+which, of course, in this
+
+particular instance, in the
+first iteration, are nothing
+
+else than tu.
+
+We add those, and obtain
+our first estimates of
+
+displacements, namely the
+estimate at the end of
+
+iteration 1.
+
+Having obtained now this
+estimate on displacements, we
+
+can repeat the process.
+
+And that is shown here on
+the next viewgraph.
+
+Notice that now I am talking
+about the right hand side,
+
+about the Green-Lagrange strains
+corresponding to time
+
+t plus delta t, and the
+first iteration.
+
+In other words, these are the
+Green-Lagrange strains
+
+corresponding to the end
+of the first iteration.
+
+They include now the incremental
+displacements that
+
+we just calculated.
+
+Similarly, these are the
+stresses corresponding to the
+
+end of the first iteration.
+
+And this is an out of balance
+virtual work term.
+
+If that is non-zero, we will
+have further increment in
+
+displacements.
+
+And that increment results,
+of course, into an
+
+increment of strains.
+
+Namely, the second increment.
+
+Here is the 2 that denotes
+the increment.
+
+Here is the 2 that denotes
+the increment.
+
+The finite element equations
+then would look as shown here.
+
+Same equation as before,
+but now with a 1
+
+here and a 2 there.
+
+We calculate the incremental
+displacements, we add them to
+
+what we had already and get a
+better approximation to the
+
+displacements corresponding
+to time t plus delta t.
+
+This process, of course, can now
+be repeated, and on this
+
+viewgraph we show how
+it's being done for
+
+every iteration k.
+
+In a particular iteration, we
+have now on the right hand
+
+side the external virtual work
+corresponding to time t plus
+
+delta t, the stresses
+corresponding to time t plus
+
+delta t and iteration
+k minus 1.
+
+At the end of iteration
+k minus 1, the strains
+
+corresponding to time t plus
+delta t, and at the end of
+
+iteration k minus 1.
+
+This is the out of balance
+virtual work term, and on the
+
+left hand side we have the same
+quantities as before, but
+
+now with the iteration
+counter k.
+
+When discretized, we obtain
+these equations here.
+
+Delta uk, the increment in the
+iteration k of displacements,
+
+r minus f, computed, of course,
+from the current
+
+displacements.
+
+From the current displacements
+we calculate that vector here.
+
+Notice this vector is obtained
+from this integral here.
+
+We repeat this process for
+iteration k 1, 2, 3 et cetera
+
+until convergence.
+
+We will have to talk about
+how we measure
+
+convergence and so on.
+
+But in this iteration we're
+adding up the total
+
+incremental displacements to
+obtain always a better
+
+estimate for the displacements
+corresponding to time t plus
+
+delta t, and here, of
+course, iteration k.
+
+Notice that the counter here
+goes from j equals 1 to k,
+
+that is this j and this k, of
+course, is nothing else than
+
+the k that we have on the
+left hand side here.
+
+Notice once again that the first
+iteration, when k is
+
+equal to 1, it amounts to
+nothing else than what we
+
+discussed already at the very
+beginning a little earlier in
+
+the lecture.
+
+We simply generalized that
+discussion now to an equation
+
+in which we iterate and always
+try to calculate another
+
+increment in displacements
+until the right
+
+hand side is 0.
+
+Notice when the right hand
+side is 0, the external
+
+virtual work is equilibrated by
+the internal virtual work,
+
+and of course, that is what
+we want to reach.
+
+That is what our criterion
+is for the analysis.
+
+The external virtual work must
+be equilibrated by the
+
+internal virtual work.
+
+In the finite element
+discretization, the whole
+
+process is as summarized
+on this viewgraph.
+
+Initially, we are given
+tu, the displacements
+
+corresponding to time t, and the
+externally applied loads
+
+corresponding to time
+t plus delta t.
+
+We compute the stiffness matrix,
+the tangent stiffness
+
+matrix corresponding
+to time t.
+
+We calculate this vector,
+the nodal point forces
+
+corresponding to the
+stresses at time t.
+
+Notice this 0 here refers always
+to the total Lagrangian
+
+formulation.
+
+Notice that this vector here
+is really the initial
+
+condition for the iteration.
+
+Similar, the displacements
+at time t are the initial
+
+conditions for the iteration
+for the displacements.
+
+Zero here.
+
+Zero there, meaning the initial
+
+conditions for our iteration.
+
+We set the iteration counter,
+k equal to 1, and we now go
+
+into the following loop.
+
+Notice on the right hand side,
+an out of balance load vector
+
+is calculated.
+
+And that out of balance load
+vector gives us an incremental
+
+displacement vector.
+
+Of course, the tangent stiffness
+matrix is involved
+
+in that calculation.
+
+Notice that this incremental
+displacement vector is added
+
+to the displacements that we had
+previously calculated, to
+
+obtain a new estimate on
+the displacements.
+
+And like that, we have now
+obtained a displacement vector
+
+that, of course, hopefully is
+closer to satisfying certain
+
+convergence criteria.
+
+We will have to talk about
+these convergence
+
+criteria later on.
+
+Basically, we check whether
+equilibrium is satisfied
+
+within a certain tolerance.
+
+If the equilibrium is not
+satisfied, we go here.
+
+We use these displacements that
+we just have calculated
+
+to compute a new vector
+of nodal point forces
+
+corresponding to the
+element stresses.
+
+Notice this vector now contains
+the information that
+
+we have just calculated in
+solving this equation here.
+
+This was information
+that we obtained.
+
+And that information is
+contained in this vector, and
+
+that vector is used right here
+to calculate this nodal point
+
+force vector.
+
+Having calculated that, we
+increase our iteration
+
+counter, come back here and
+like that we continue the
+
+iteration, looping around
+through here
+
+as I have just described.
+
+Notice at convergence once
+again, we want, of course,
+
+that r is equal to f, meaning
+that the external loads are
+
+equilibrated by the nodal point
+forces corresponding to
+
+the internal element stresses.
+
+Well, this brings us to the
+end of this lecture.
+
+You might recognize that this
+last viewgraph really contains
+
+a lot of information that, of
+course, we discussed in this
+
+lecture, but that also I
+referred to already in the
+
+first lecture.
+
+At that time, I tried to
+introduce you to this
+
+iteration process using rather
+physical concepts, not going
+
+through a lengthy mathematical
+derivation.
+
+We did not talk about continuum
+mechanics variables.
+
+We did not talk about total
+Lagrangian formulation, second
+
+Piola-Kirchhoff stresses,
+Green-Lagrange
+
+strains and so on.
+
+I hoped at that time to give
+you just a physical feel of
+
+how we are iterating.
+
+The same kind of equations, the
+same equations we looked
+
+at at that time, now I hope
+with this lecture, I have
+
+given you the mathematical
+basis of these equations.
+
+I hope you have learned how to
+derive these equations, how to
+
+work with these equations
+a little bit.
+
+And in some of the next
+lectures, we will look at how
+
+actually we do construct
+this k matrix
+
+for different elements.
+
+That is, of course, a very
+important consideration.
+
+How do we calculate this
+k matrix for 1D, 2D, 3D
+
+elements, shell elements,
+beam elements?
+
+How do we calculate this
+force vector for
+
+these different elements?
+
+We will have to discuss
+that as well.
+
+Notice that in this k matrix
+goes the material law.
+
+Whether we are dealing with an
+elasto-plastic material,
+
+rubber type material, all that
+will affect the actual
+
+ingredients, the
+actual elements
+
+here in that k matrix.
+
+We we also have to discuss how
+we can possibly make this
+
+convergence that I'm
+talking about fast.
+
+In other words, how can we
+accelerate the convergence of
+
+these iterations?
+
+So in essence, I like to just
+convey to you that what you
+
+see here you will see a
+number of times again.
+
+We will talk about the different
+parts that you have
+
+been looking at here already
+briefly once again in the
+
+upcoming lectures.
+
+Thank you very much for
+your attention.
\ No newline at end of file
diff --git a/4U9B9YgEqe4.txt b/4U9B9YgEqe4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..dc97471cd94eca13ca90ac6829ca558dce0c86c1
--- /dev/null
+++ b/4U9B9YgEqe4.txt
@@ -0,0 +1,499 @@
+align:start position:0%
+ 
+welcome back to 820 special relativity
+
+ align:start position:0%
+welcome back to 820 special relativity
+ 
+
+ align:start position:0%
+welcome back to 820 special relativity
+so if there is a time dilation effect
+
+ align:start position:0%
+so if there is a time dilation effect
+ 
+
+ align:start position:0%
+so if there is a time dilation effect
+through gravitational fields
+
+ align:start position:0%
+through gravitational fields
+ 
+
+ align:start position:0%
+through gravitational fields
+then there is also a redshift to the
+
+ align:start position:0%
+then there is also a redshift to the
+ 
+
+ align:start position:0%
+then there is also a redshift to the
+gravitational fields
+
+ align:start position:0%
+gravitational fields
+ 
+
+ align:start position:0%
+gravitational fields
+so a consequence of time dilation is a
+
+ align:start position:0%
+so a consequence of time dilation is a
+ 
+
+ align:start position:0%
+so a consequence of time dilation is a
+change in the light frequency and i ask
+
+ align:start position:0%
+change in the light frequency and i ask
+ 
+
+ align:start position:0%
+change in the light frequency and i ask
+you to estimate the magnitude of this
+
+ align:start position:0%
+you to estimate the magnitude of this
+ 
+
+ align:start position:0%
+you to estimate the magnitude of this
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+and the example you want to use is the
+
+ align:start position:0%
+and the example you want to use is the
+ 
+
+ align:start position:0%
+and the example you want to use is the
+one shown here so you have a tower which
+
+ align:start position:0%
+one shown here so you have a tower which
+ 
+
+ align:start position:0%
+one shown here so you have a tower which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+not randomly but 22 and a half meters
+
+ align:start position:0%
+not randomly but 22 and a half meters
+ 
+
+ align:start position:0%
+not randomly but 22 and a half meters
+tall
+
+ align:start position:0%
+tall
+ 
+
+ align:start position:0%
+tall
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+a light beam is sent down
+
+ align:start position:0%
+a light beam is sent down
+ 
+
+ align:start position:0%
+a light beam is sent down
+obviously the tower is built on this
+
+ align:start position:0%
+obviously the tower is built on this
+ 
+
+ align:start position:0%
+obviously the tower is built on this
+planet and this there's gravity is
+
+ align:start position:0%
+planet and this there's gravity is
+ 
+
+ align:start position:0%
+planet and this there's gravity is
+acting
+
+ align:start position:0%
+acting
+ 
+
+ align:start position:0%
+acting
+um so this this is basically an
+
+ align:start position:0%
+um so this this is basically an
+ 
+
+ align:start position:0%
+um so this this is basically an
+accelerating
+
+ align:start position:0%
+accelerating
+ 
+
+ align:start position:0%
+accelerating
+um reference frame
+
+ align:start position:0%
+um reference frame
+ 
+
+ align:start position:0%
+um reference frame
+the length of the tower is again 22
+
+ align:start position:0%
+the length of the tower is again 22
+ 
+
+ align:start position:0%
+the length of the tower is again 22
+meters and i would like you to just get
+
+ align:start position:0%
+meters and i would like you to just get
+ 
+
+ align:start position:0%
+meters and i would like you to just get
+a feeling
+
+ align:start position:0%
+a feeling
+ 
+
+ align:start position:0%
+a feeling
+how big can this effect be the effect of
+
+ align:start position:0%
+how big can this effect be the effect of
+ 
+
+ align:start position:0%
+how big can this effect be the effect of
+redshift here
+
+ align:start position:0%
+redshift here
+ 
+
+ align:start position:0%
+redshift here
+so please try to work this out
+
+ align:start position:0%
+so please try to work this out
+ 
+
+ align:start position:0%
+so please try to work this out
+the way to to think about this is first
+
+ align:start position:0%
+the way to to think about this is first
+ 
+
+ align:start position:0%
+the way to to think about this is first
+to say okay now the light you know the
+
+ align:start position:0%
+to say okay now the light you know the
+ 
+
+ align:start position:0%
+to say okay now the light you know the
+delta t for the light to travel
+
+ align:start position:0%
+delta t for the light to travel
+ 
+
+ align:start position:0%
+delta t for the light to travel
+um is l divided by c the speed of light
+
+ align:start position:0%
+um is l divided by c the speed of light
+ 
+
+ align:start position:0%
+um is l divided by c the speed of light
+is c the length is l
+
+ align:start position:0%
+is c the length is l
+ 
+
+ align:start position:0%
+is c the length is l
+the change in velocity
+
+ align:start position:0%
+the change in velocity
+ 
+
+ align:start position:0%
+the change in velocity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+g
+
+ align:start position:0%
+g
+ 
+
+ align:start position:0%
+g
+acceleration times l divided by c
+
+ align:start position:0%
+acceleration times l divided by c
+ 
+
+ align:start position:0%
+acceleration times l divided by c
+so the doppler shift then is the
+
+ align:start position:0%
+so the doppler shift then is the
+ 
+
+ align:start position:0%
+so the doppler shift then is the
+frequency the new frequency divided by
+
+ align:start position:0%
+frequency the new frequency divided by
+ 
+
+ align:start position:0%
+frequency the new frequency divided by
+the initial frequency
+
+ align:start position:0%
+the initial frequency
+ 
+
+ align:start position:0%
+the initial frequency
+and that can be approximated by one plus
+
+ align:start position:0%
+and that can be approximated by one plus
+ 
+
+ align:start position:0%
+and that can be approximated by one plus
+delta v over c so we find that it's one
+
+ align:start position:0%
+delta v over c so we find that it's one
+ 
+
+ align:start position:0%
+delta v over c so we find that it's one
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+g times l over c square
+
+ align:start position:0%
+g times l over c square
+ 
+
+ align:start position:0%
+g times l over c square
+now the speed of light is pretty fast
+
+ align:start position:0%
+now the speed of light is pretty fast
+ 
+
+ align:start position:0%
+now the speed of light is pretty fast
+um three times ten to the um to the nine
+
+ align:start position:0%
+um three times ten to the um to the nine
+ 
+
+ align:start position:0%
+um three times ten to the um to the nine
+meter per second
+
+ align:start position:0%
+meter per second
+ 
+
+ align:start position:0%
+meter per second
+and this distance is only 22 and a half
+
+ align:start position:0%
+and this distance is only 22 and a half
+ 
+
+ align:start position:0%
+and this distance is only 22 and a half
+meters so we find that this is a tiny
+
+ align:start position:0%
+meters so we find that this is a tiny
+ 
+
+ align:start position:0%
+meters so we find that this is a tiny
+tiny tiny effect but nevertheless
+
+ align:start position:0%
+tiny tiny effect but nevertheless
+ 
+
+ align:start position:0%
+tiny tiny effect but nevertheless
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+experimentalists at harvard tested this
+
+ align:start position:0%
+experimentalists at harvard tested this
+ 
+
+ align:start position:0%
+experimentalists at harvard tested this
+effect the pound replica and snyder in
+
+ align:start position:0%
+effect the pound replica and snyder in
+ 
+
+ align:start position:0%
+effect the pound replica and snyder in
+the 1950s and 50s and 60s were able to
+
+ align:start position:0%
+the 1950s and 50s and 60s were able to
+ 
+
+ align:start position:0%
+the 1950s and 50s and 60s were able to
+show this this very tiny um effect
+
+ align:start position:0%
+show this this very tiny um effect
+ 
+
+ align:start position:0%
+show this this very tiny um effect
+you want to know more about this you can
+
+ align:start position:0%
+you want to know more about this you can
+ 
+
+ align:start position:0%
+you want to know more about this you can
+for example look up a small description
+
+ align:start position:0%
+for example look up a small description
+ 
+
+ align:start position:0%
+for example look up a small description
+in wikipedia here
+
+ align:start position:0%
+in wikipedia here
+ 
+
+ align:start position:0%
+in wikipedia here
+but there's
+
+ align:start position:0%
+but there's
+ 
+
+ align:start position:0%
+but there's
+some quite some literature on those
+
+ align:start position:0%
+some quite some literature on those
+ 
+
+ align:start position:0%
+some quite some literature on those
+experimental tests
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/57uqU8G_z0E.txt b/57uqU8G_z0E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..cc52302e535e7e8e6a175553bea0fc879fc18e41
--- /dev/null
+++ b/57uqU8G_z0E.txt
@@ -0,0 +1,4019 @@
+align:start position:0%
+ 
+a long 15 minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there you go all right hello everybody
+
+ align:start position:0%
+there you go all right hello everybody
+ 
+
+ align:start position:0%
+there you go all right hello everybody
+my name is henry and today i'll be
+
+ align:start position:0%
+my name is henry and today i'll be
+ 
+
+ align:start position:0%
+my name is henry and today i'll be
+presenting my findings on an experiment
+
+ align:start position:0%
+presenting my findings on an experiment
+ 
+
+ align:start position:0%
+presenting my findings on an experiment
+that i conducted with my
+
+ align:start position:0%
+that i conducted with my
+ 
+
+ align:start position:0%
+that i conducted with my
+lab partner adeen over there thank you
+
+ align:start position:0%
+lab partner adeen over there thank you
+ 
+
+ align:start position:0%
+lab partner adeen over there thank you
+edin during our experiment we determined
+
+ align:start position:0%
+edin during our experiment we determined
+ 
+
+ align:start position:0%
+edin during our experiment we determined
+the angular
+
+ align:start position:0%
+the angular
+ 
+
+ align:start position:0%
+the angular
+dependency of the scattering rate of
+
+ align:start position:0%
+dependency of the scattering rate of
+ 
+
+ align:start position:0%
+dependency of the scattering rate of
+alpha particles
+
+ align:start position:0%
+alpha particles
+ 
+
+ align:start position:0%
+alpha particles
+through gold foil using this relation we
+
+ align:start position:0%
+through gold foil using this relation we
+ 
+
+ align:start position:0%
+through gold foil using this relation we
+are able to determine that rutherford
+
+ align:start position:0%
+are able to determine that rutherford
+ 
+
+ align:start position:0%
+are able to determine that rutherford
+scattering
+
+ align:start position:0%
+scattering
+ 
+
+ align:start position:0%
+scattering
+presents an accurate model for this
+
+ align:start position:0%
+presents an accurate model for this
+ 
+
+ align:start position:0%
+presents an accurate model for this
+these scattering
+
+ align:start position:0%
+these scattering
+ 
+
+ align:start position:0%
+these scattering
+effects in doing so we are able to
+
+ align:start position:0%
+effects in doing so we are able to
+ 
+
+ align:start position:0%
+effects in doing so we are able to
+extract some information
+
+ align:start position:0%
+extract some information
+ 
+
+ align:start position:0%
+extract some information
+about the actual nature of atoms and
+
+ align:start position:0%
+about the actual nature of atoms and
+ 
+
+ align:start position:0%
+about the actual nature of atoms and
+their atomic makeup
+
+ align:start position:0%
+their atomic makeup
+ 
+
+ align:start position:0%
+their atomic makeup
+so to give a bit of background i'm going
+
+ align:start position:0%
+so to give a bit of background i'm going
+ 
+
+ align:start position:0%
+so to give a bit of background i'm going
+to go through two different historical
+
+ align:start position:0%
+to go through two different historical
+ 
+
+ align:start position:0%
+to go through two different historical
+models of the atom
+
+ align:start position:0%
+models of the atom
+ 
+
+ align:start position:0%
+models of the atom
+and talk about the different
+
+ align:start position:0%
+and talk about the different
+ 
+
+ align:start position:0%
+and talk about the different
+experimental predictions that they
+
+ align:start position:0%
+experimental predictions that they
+ 
+
+ align:start position:0%
+experimental predictions that they
+uh predict so back in the early 19th
+
+ align:start position:0%
+uh predict so back in the early 19th
+ 
+
+ align:start position:0%
+uh predict so back in the early 19th
+century people weren't too sure what
+
+ align:start position:0%
+century people weren't too sure what
+ 
+
+ align:start position:0%
+century people weren't too sure what
+made up an atom
+
+ align:start position:0%
+made up an atom
+ 
+
+ align:start position:0%
+made up an atom
+they knew there are some electrons and
+
+ align:start position:0%
+they knew there are some electrons and
+ 
+
+ align:start position:0%
+they knew there are some electrons and
+some positive stuff going around
+
+ align:start position:0%
+some positive stuff going around
+ 
+
+ align:start position:0%
+some positive stuff going around
+somewhere but other than that
+
+ align:start position:0%
+somewhere but other than that
+ 
+
+ align:start position:0%
+somewhere but other than that
+they weren't too sure now the
+
+ align:start position:0%
+they weren't too sure now the
+ 
+
+ align:start position:0%
+they weren't too sure now the
+predominant theory at the time was jj
+
+ align:start position:0%
+predominant theory at the time was jj
+ 
+
+ align:start position:0%
+predominant theory at the time was jj
+thompson's plum pudding model
+
+ align:start position:0%
+thompson's plum pudding model
+ 
+
+ align:start position:0%
+thompson's plum pudding model
+shown here in this model you have these
+
+ align:start position:0%
+shown here in this model you have these
+ 
+
+ align:start position:0%
+shown here in this model you have these
+negatively charged electrons that sort
+
+ align:start position:0%
+negatively charged electrons that sort
+ 
+
+ align:start position:0%
+negatively charged electrons that sort
+of float around in this soup
+
+ align:start position:0%
+of float around in this soup
+ 
+
+ align:start position:0%
+of float around in this soup
+of positive charge i apologize for the
+
+ align:start position:0%
+of positive charge i apologize for the
+ 
+
+ align:start position:0%
+of positive charge i apologize for the
+plum pudding in the soup
+
+ align:start position:0%
+plum pudding in the soup
+ 
+
+ align:start position:0%
+plum pudding in the soup
+if you're getting hungry from all these
+
+ align:start position:0%
+if you're getting hungry from all these
+ 
+
+ align:start position:0%
+if you're getting hungry from all these
+metaphors there is food back there
+
+ align:start position:0%
+metaphors there is food back there
+ 
+
+ align:start position:0%
+metaphors there is food back there
+now the the the experimental predictions
+
+ align:start position:0%
+now the the the experimental predictions
+ 
+
+ align:start position:0%
+now the the the experimental predictions
+that we want to get out of this model
+
+ align:start position:0%
+that we want to get out of this model
+ 
+
+ align:start position:0%
+that we want to get out of this model
+is what it says about scattering so if
+
+ align:start position:0%
+is what it says about scattering so if
+ 
+
+ align:start position:0%
+is what it says about scattering so if
+we take one of these atoms and we shoot
+
+ align:start position:0%
+we take one of these atoms and we shoot
+ 
+
+ align:start position:0%
+we take one of these atoms and we shoot
+it through a material made up of other
+
+ align:start position:0%
+it through a material made up of other
+ 
+
+ align:start position:0%
+it through a material made up of other
+atoms
+
+ align:start position:0%
+atoms
+ 
+
+ align:start position:0%
+atoms
+what kind of scattering do we expect to
+
+ align:start position:0%
+what kind of scattering do we expect to
+ 
+
+ align:start position:0%
+what kind of scattering do we expect to
+see and you can see in this model here
+
+ align:start position:0%
+see and you can see in this model here
+ 
+
+ align:start position:0%
+see and you can see in this model here
+we don't really expect that much
+
+ align:start position:0%
+we don't really expect that much
+ 
+
+ align:start position:0%
+we don't really expect that much
+scattering so the atom will go through
+
+ align:start position:0%
+scattering so the atom will go through
+ 
+
+ align:start position:0%
+scattering so the atom will go through
+it might pass through a you know a
+
+ align:start position:0%
+it might pass through a you know a
+ 
+
+ align:start position:0%
+it might pass through a you know a
+slightly more negatively charged region
+
+ align:start position:0%
+slightly more negatively charged region
+ 
+
+ align:start position:0%
+slightly more negatively charged region
+here and move a bit that way
+
+ align:start position:0%
+here and move a bit that way
+ 
+
+ align:start position:0%
+here and move a bit that way
+deflect a little bit that way but you
+
+ align:start position:0%
+deflect a little bit that way but you
+ 
+
+ align:start position:0%
+deflect a little bit that way but you
+don't expect that much scattering
+
+ align:start position:0%
+don't expect that much scattering
+ 
+
+ align:start position:0%
+don't expect that much scattering
+overall
+
+ align:start position:0%
+overall
+ 
+
+ align:start position:0%
+overall
+doing out all the math we see that this
+
+ align:start position:0%
+doing out all the math we see that this
+ 
+
+ align:start position:0%
+doing out all the math we see that this
+predicts
+
+ align:start position:0%
+predicts
+ 
+
+ align:start position:0%
+predicts
+small angle scattering that dies off
+
+ align:start position:0%
+small angle scattering that dies off
+ 
+
+ align:start position:0%
+small angle scattering that dies off
+exponentially
+
+ align:start position:0%
+exponentially
+ 
+
+ align:start position:0%
+exponentially
+as a function of angle this dying off is
+
+ align:start position:0%
+as a function of angle this dying off is
+ 
+
+ align:start position:0%
+as a function of angle this dying off is
+controlled by this
+
+ align:start position:0%
+controlled by this
+ 
+
+ align:start position:0%
+controlled by this
+theta sub m called the mean multiple
+
+ align:start position:0%
+theta sub m called the mean multiple
+ 
+
+ align:start position:0%
+theta sub m called the mean multiple
+scattering rate
+
+ align:start position:0%
+scattering rate
+ 
+
+ align:start position:0%
+scattering rate
+for gold we predict this is about one
+
+ align:start position:0%
+for gold we predict this is about one
+ 
+
+ align:start position:0%
+for gold we predict this is about one
+so rutherford comes along and he looks
+
+ align:start position:0%
+so rutherford comes along and he looks
+ 
+
+ align:start position:0%
+so rutherford comes along and he looks
+at this and says ah
+
+ align:start position:0%
+at this and says ah
+ 
+
+ align:start position:0%
+at this and says ah
+i don't know about this let me try
+
+ align:start position:0%
+i don't know about this let me try
+ 
+
+ align:start position:0%
+i don't know about this let me try
+something else
+
+ align:start position:0%
+something else
+ 
+
+ align:start position:0%
+something else
+this right here is the rutherford model
+
+ align:start position:0%
+this right here is the rutherford model
+ 
+
+ align:start position:0%
+this right here is the rutherford model
+that he proposes in this model we have
+
+ align:start position:0%
+that he proposes in this model we have
+ 
+
+ align:start position:0%
+that he proposes in this model we have
+our negatively charged electrons
+
+ align:start position:0%
+our negatively charged electrons
+ 
+
+ align:start position:0%
+our negatively charged electrons
+but instead of this soup of positive
+
+ align:start position:0%
+but instead of this soup of positive
+ 
+
+ align:start position:0%
+but instead of this soup of positive
+charge we have a densely
+
+ align:start position:0%
+charge we have a densely
+ 
+
+ align:start position:0%
+charge we have a densely
+packed nucleus in the middle now because
+
+ align:start position:0%
+packed nucleus in the middle now because
+ 
+
+ align:start position:0%
+packed nucleus in the middle now because
+this nucleus is so
+
+ align:start position:0%
+this nucleus is so
+ 
+
+ align:start position:0%
+this nucleus is so
+dense and so tightly packed it allows
+
+ align:start position:0%
+dense and so tightly packed it allows
+ 
+
+ align:start position:0%
+dense and so tightly packed it allows
+for much stronger interactions between
+
+ align:start position:0%
+for much stronger interactions between
+ 
+
+ align:start position:0%
+for much stronger interactions between
+atoms when it comes to scattering
+
+ align:start position:0%
+atoms when it comes to scattering
+ 
+
+ align:start position:0%
+atoms when it comes to scattering
+for example you can imagine if two atoms
+
+ align:start position:0%
+for example you can imagine if two atoms
+ 
+
+ align:start position:0%
+for example you can imagine if two atoms
+collided
+
+ align:start position:0%
+collided
+ 
+
+ align:start position:0%
+collided
+the the the nuclei would interact and
+
+ align:start position:0%
+the the the nuclei would interact and
+ 
+
+ align:start position:0%
+the the the nuclei would interact and
+they just bounce
+
+ align:start position:0%
+they just bounce
+ 
+
+ align:start position:0%
+they just bounce
+straight off so doing now all the math
+
+ align:start position:0%
+straight off so doing now all the math
+ 
+
+ align:start position:0%
+straight off so doing now all the math
+again we see
+
+ align:start position:0%
+again we see
+ 
+
+ align:start position:0%
+again we see
+that this large this larger scattering
+
+ align:start position:0%
+that this large this larger scattering
+ 
+
+ align:start position:0%
+that this large this larger scattering
+angle
+
+ align:start position:0%
+angle
+ 
+
+ align:start position:0%
+angle
+dies off as one over sine to the fourth
+
+ align:start position:0%
+dies off as one over sine to the fourth
+ 
+
+ align:start position:0%
+dies off as one over sine to the fourth
+of theta over two now this predicts much
+
+ align:start position:0%
+of theta over two now this predicts much
+ 
+
+ align:start position:0%
+of theta over two now this predicts much
+higher rate
+
+ align:start position:0%
+higher rate
+ 
+
+ align:start position:0%
+higher rate
+at larger angles than this exponential
+
+ align:start position:0%
+at larger angles than this exponential
+ 
+
+ align:start position:0%
+at larger angles than this exponential
+falloff right here
+
+ align:start position:0%
+falloff right here
+ 
+
+ align:start position:0%
+falloff right here
+a small point to clarify about this
+
+ align:start position:0%
+a small point to clarify about this
+ 
+
+ align:start position:0%
+a small point to clarify about this
+equation here is that this equation is
+
+ align:start position:0%
+equation here is that this equation is
+ 
+
+ align:start position:0%
+equation here is that this equation is
+derived assuming large angles so for
+
+ align:start position:0%
+derived assuming large angles so for
+ 
+
+ align:start position:0%
+derived assuming large angles so for
+theta roughly larger than or equal to
+
+ align:start position:0%
+theta roughly larger than or equal to
+ 
+
+ align:start position:0%
+theta roughly larger than or equal to
+10. this is not a limit of the
+
+ align:start position:0%
+10. this is not a limit of the
+ 
+
+ align:start position:0%
+10. this is not a limit of the
+rutherford theory in and of itself
+
+ align:start position:0%
+rutherford theory in and of itself
+ 
+
+ align:start position:0%
+rutherford theory in and of itself
+you can derive a rutherford model for
+
+ align:start position:0%
+you can derive a rutherford model for
+ 
+
+ align:start position:0%
+you can derive a rutherford model for
+scattering for any angle
+
+ align:start position:0%
+scattering for any angle
+ 
+
+ align:start position:0%
+scattering for any angle
+but it starts to get really gross at
+
+ align:start position:0%
+but it starts to get really gross at
+ 
+
+ align:start position:0%
+but it starts to get really gross at
+small angles
+
+ align:start position:0%
+small angles
+ 
+
+ align:start position:0%
+small angles
+you can actually see this this diverges
+
+ align:start position:0%
+you can actually see this this diverges
+ 
+
+ align:start position:0%
+you can actually see this this diverges
+for theta equals to zero which is not
+
+ align:start position:0%
+for theta equals to zero which is not
+ 
+
+ align:start position:0%
+for theta equals to zero which is not
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so this equation right here is only
+
+ align:start position:0%
+so this equation right here is only
+ 
+
+ align:start position:0%
+so this equation right here is only
+valid for theta roughly greater than or
+
+ align:start position:0%
+valid for theta roughly greater than or
+ 
+
+ align:start position:0%
+valid for theta roughly greater than or
+equal to ten
+
+ align:start position:0%
+equal to ten
+ 
+
+ align:start position:0%
+equal to ten
+so for the purposes of this experiment
+
+ align:start position:0%
+so for the purposes of this experiment
+ 
+
+ align:start position:0%
+so for the purposes of this experiment
+we will restrict our viewing
+
+ align:start position:0%
+we will restrict our viewing
+ 
+
+ align:start position:0%
+we will restrict our viewing
+to theta greater than or equal to ten
+
+ align:start position:0%
+to theta greater than or equal to ten
+ 
+
+ align:start position:0%
+to theta greater than or equal to ten
+and these two models give us two
+
+ align:start position:0%
+and these two models give us two
+ 
+
+ align:start position:0%
+and these two models give us two
+different predictions that we can
+
+ align:start position:0%
+different predictions that we can
+ 
+
+ align:start position:0%
+different predictions that we can
+compare
+
+ align:start position:0%
+compare
+ 
+
+ align:start position:0%
+compare
+against actual data so we experi we
+
+ align:start position:0%
+against actual data so we experi we
+ 
+
+ align:start position:0%
+against actual data so we experi we
+experimentally measure scattering rates
+
+ align:start position:0%
+experimentally measure scattering rates
+ 
+
+ align:start position:0%
+experimentally measure scattering rates
+at various angles and by taking this
+
+ align:start position:0%
+at various angles and by taking this
+ 
+
+ align:start position:0%
+at various angles and by taking this
+data we can fit it
+
+ align:start position:0%
+data we can fit it
+ 
+
+ align:start position:0%
+data we can fit it
+to both the predicted rutherford and
+
+ align:start position:0%
+to both the predicted rutherford and
+ 
+
+ align:start position:0%
+to both the predicted rutherford and
+thomson model and come to a conclusion
+
+ align:start position:0%
+thomson model and come to a conclusion
+ 
+
+ align:start position:0%
+thomson model and come to a conclusion
+about which one more accurately predicts
+
+ align:start position:0%
+about which one more accurately predicts
+ 
+
+ align:start position:0%
+about which one more accurately predicts
+our model
+
+ align:start position:0%
+our model
+ 
+
+ align:start position:0%
+our model
+now let's talk a bit about the apparatus
+
+ align:start position:0%
+now let's talk a bit about the apparatus
+ 
+
+ align:start position:0%
+now let's talk a bit about the apparatus
+that lets us do this the first part of
+
+ align:start position:0%
+that lets us do this the first part of
+ 
+
+ align:start position:0%
+that lets us do this the first part of
+our apparatus is an alpha particle
+
+ align:start position:0%
+our apparatus is an alpha particle
+ 
+
+ align:start position:0%
+our apparatus is an alpha particle
+howitzer
+
+ align:start position:0%
+howitzer
+ 
+
+ align:start position:0%
+howitzer
+this howitzer contains an americium-241
+
+ align:start position:0%
+this howitzer contains an americium-241
+ 
+
+ align:start position:0%
+this howitzer contains an americium-241
+source
+
+ align:start position:0%
+source
+ 
+
+ align:start position:0%
+source
+which emits alpha particles which are
+
+ align:start position:0%
+which emits alpha particles which are
+ 
+
+ align:start position:0%
+which emits alpha particles which are
+two protons and two neutrons
+
+ align:start position:0%
+two protons and two neutrons
+ 
+
+ align:start position:0%
+two protons and two neutrons
+at approximately a constant energy these
+
+ align:start position:0%
+at approximately a constant energy these
+ 
+
+ align:start position:0%
+at approximately a constant energy these
+alpha particles shoot out of the
+
+ align:start position:0%
+alpha particles shoot out of the
+ 
+
+ align:start position:0%
+alpha particles shoot out of the
+howitzer right here in a sort of
+
+ align:start position:0%
+howitzer right here in a sort of
+ 
+
+ align:start position:0%
+howitzer right here in a sort of
+concentrated beam
+
+ align:start position:0%
+concentrated beam
+ 
+
+ align:start position:0%
+concentrated beam
+directed out of the howitzer
+
+ align:start position:0%
+directed out of the howitzer
+ 
+
+ align:start position:0%
+directed out of the howitzer
+these alpha particles hit a gold foil
+
+ align:start position:0%
+these alpha particles hit a gold foil
+ 
+
+ align:start position:0%
+these alpha particles hit a gold foil
+where something happens
+
+ align:start position:0%
+where something happens
+ 
+
+ align:start position:0%
+where something happens
+we don't know yet and it scatters off at
+
+ align:start position:0%
+we don't know yet and it scatters off at
+ 
+
+ align:start position:0%
+we don't know yet and it scatters off at
+an angle theta
+
+ align:start position:0%
+an angle theta
+ 
+
+ align:start position:0%
+an angle theta
+which is then detected by our solid
+
+ align:start position:0%
+which is then detected by our solid
+ 
+
+ align:start position:0%
+which is then detected by our solid
+state detector this detector registers
+
+ align:start position:0%
+state detector this detector registers
+ 
+
+ align:start position:0%
+state detector this detector registers
+the count as well as the energy of the
+
+ align:start position:0%
+the count as well as the energy of the
+ 
+
+ align:start position:0%
+the count as well as the energy of the
+incoming particle
+
+ align:start position:0%
+incoming particle
+ 
+
+ align:start position:0%
+incoming particle
+and sends it to an mca to be analyzed
+
+ align:start position:0%
+and sends it to an mca to be analyzed
+ 
+
+ align:start position:0%
+and sends it to an mca to be analyzed
+now there's a bit of a complication in
+
+ align:start position:0%
+now there's a bit of a complication in
+ 
+
+ align:start position:0%
+now there's a bit of a complication in
+the geometry of our setup
+
+ align:start position:0%
+the geometry of our setup
+ 
+
+ align:start position:0%
+the geometry of our setup
+you see what we want to measure is this
+
+ align:start position:0%
+you see what we want to measure is this
+ 
+
+ align:start position:0%
+you see what we want to measure is this
+angle theta here our scattering rate
+
+ align:start position:0%
+angle theta here our scattering rate
+ 
+
+ align:start position:0%
+angle theta here our scattering rate
+what we actually control in what we
+
+ align:start position:0%
+what we actually control in what we
+ 
+
+ align:start position:0%
+what we actually control in what we
+measure in our experiments
+
+ align:start position:0%
+measure in our experiments
+ 
+
+ align:start position:0%
+measure in our experiments
+is this angle phi which is the angle of
+
+ align:start position:0%
+is this angle phi which is the angle of
+ 
+
+ align:start position:0%
+is this angle phi which is the angle of
+our howitzer relative to our detector
+
+ align:start position:0%
+our howitzer relative to our detector
+ 
+
+ align:start position:0%
+our howitzer relative to our detector
+so at ph equals to zero the howitzer
+
+ align:start position:0%
+so at ph equals to zero the howitzer
+ 
+
+ align:start position:0%
+so at ph equals to zero the howitzer
+points dead on at our detector
+
+ align:start position:0%
+points dead on at our detector
+ 
+
+ align:start position:0%
+points dead on at our detector
+now in a sort of theoretical world
+
+ align:start position:0%
+now in a sort of theoretical world
+ 
+
+ align:start position:0%
+now in a sort of theoretical world
+where this solid state detector is
+
+ align:start position:0%
+where this solid state detector is
+ 
+
+ align:start position:0%
+where this solid state detector is
+infinitesimally small
+
+ align:start position:0%
+infinitesimally small
+ 
+
+ align:start position:0%
+infinitesimally small
+and our beam is also this
+
+ align:start position:0%
+and our beam is also this
+ 
+
+ align:start position:0%
+and our beam is also this
+infinitesimally point source
+
+ align:start position:0%
+infinitesimally point source
+ 
+
+ align:start position:0%
+infinitesimally point source
+we would expect fee to correspond
+
+ align:start position:0%
+we would expect fee to correspond
+ 
+
+ align:start position:0%
+we would expect fee to correspond
+exactly to theta so if equals to zero
+
+ align:start position:0%
+exactly to theta so if equals to zero
+ 
+
+ align:start position:0%
+exactly to theta so if equals to zero
+the howitzer pointed dead on
+
+ align:start position:0%
+the howitzer pointed dead on
+ 
+
+ align:start position:0%
+the howitzer pointed dead on
+we would expect any non-zero scattering
+
+ align:start position:0%
+we would expect any non-zero scattering
+ 
+
+ align:start position:0%
+we would expect any non-zero scattering
+to cause the particles to shoot off in a
+
+ align:start position:0%
+to cause the particles to shoot off in a
+ 
+
+ align:start position:0%
+to cause the particles to shoot off in a
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+and not be detected by our detector
+
+ align:start position:0%
+and not be detected by our detector
+ 
+
+ align:start position:0%
+and not be detected by our detector
+however in practice this is not actually
+
+ align:start position:0%
+however in practice this is not actually
+ 
+
+ align:start position:0%
+however in practice this is not actually
+the case
+
+ align:start position:0%
+the case
+ 
+
+ align:start position:0%
+the case
+our solid state detector is a few
+
+ align:start position:0%
+our solid state detector is a few
+ 
+
+ align:start position:0%
+our solid state detector is a few
+centimeters wide
+
+ align:start position:0%
+centimeters wide
+ 
+
+ align:start position:0%
+centimeters wide
+and because of this it allows for a
+
+ align:start position:0%
+and because of this it allows for a
+ 
+
+ align:start position:0%
+and because of this it allows for a
+range of angles theta
+
+ align:start position:0%
+range of angles theta
+ 
+
+ align:start position:0%
+range of angles theta
+that are detected given a certain
+
+ align:start position:0%
+that are detected given a certain
+ 
+
+ align:start position:0%
+that are detected given a certain
+howitzer angle in addition
+
+ align:start position:0%
+howitzer angle in addition
+ 
+
+ align:start position:0%
+howitzer angle in addition
+our beam has some width which allows for
+
+ align:start position:0%
+our beam has some width which allows for
+ 
+
+ align:start position:0%
+our beam has some width which allows for
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+angles that can be detected given a
+
+ align:start position:0%
+angles that can be detected given a
+ 
+
+ align:start position:0%
+angles that can be detected given a
+certain howitzer angle fee
+
+ align:start position:0%
+certain howitzer angle fee
+ 
+
+ align:start position:0%
+certain howitzer angle fee
+so this is a bunch of stuff going on we
+
+ align:start position:0%
+so this is a bunch of stuff going on we
+ 
+
+ align:start position:0%
+so this is a bunch of stuff going on we
+got a lot of different things
+
+ align:start position:0%
+got a lot of different things
+ 
+
+ align:start position:0%
+got a lot of different things
+contributing to uncertainty
+
+ align:start position:0%
+contributing to uncertainty
+ 
+
+ align:start position:0%
+contributing to uncertainty
+but we can account for this by
+
+ align:start position:0%
+but we can account for this by
+ 
+
+ align:start position:0%
+but we can account for this by
+essentially asking the simple question
+
+ align:start position:0%
+essentially asking the simple question
+ 
+
+ align:start position:0%
+essentially asking the simple question
+all right we have our howitzer at an
+
+ align:start position:0%
+all right we have our howitzer at an
+ 
+
+ align:start position:0%
+all right we have our howitzer at an
+angle fee what is the probability of a
+
+ align:start position:0%
+angle fee what is the probability of a
+ 
+
+ align:start position:0%
+angle fee what is the probability of a
+detection that we see
+
+ align:start position:0%
+detection that we see
+ 
+
+ align:start position:0%
+detection that we see
+having been having come from a particle
+
+ align:start position:0%
+having been having come from a particle
+ 
+
+ align:start position:0%
+having been having come from a particle
+being scattered at an angle theta
+
+ align:start position:0%
+being scattered at an angle theta
+ 
+
+ align:start position:0%
+being scattered at an angle theta
+again in this theoretical case where we
+
+ align:start position:0%
+again in this theoretical case where we
+ 
+
+ align:start position:0%
+again in this theoretical case where we
+have point sources and point detectors
+
+ align:start position:0%
+have point sources and point detectors
+ 
+
+ align:start position:0%
+have point sources and point detectors
+this probability would just correspond
+
+ align:start position:0%
+this probability would just correspond
+ 
+
+ align:start position:0%
+this probability would just correspond
+to a delta function centered at v
+
+ align:start position:0%
+to a delta function centered at v
+ 
+
+ align:start position:0%
+to a delta function centered at v
+however this is not practically the case
+
+ align:start position:0%
+however this is not practically the case
+ 
+
+ align:start position:0%
+however this is not practically the case
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+from simple geometric considerations
+
+ align:start position:0%
+from simple geometric considerations
+ 
+
+ align:start position:0%
+from simple geometric considerations
+which i can go into more detail later
+
+ align:start position:0%
+which i can go into more detail later
+ 
+
+ align:start position:0%
+which i can go into more detail later
+we expect as a first approximation a
+
+ align:start position:0%
+we expect as a first approximation a
+ 
+
+ align:start position:0%
+we expect as a first approximation a
+sort of triangle-shaped
+
+ align:start position:0%
+sort of triangle-shaped
+ 
+
+ align:start position:0%
+sort of triangle-shaped
+distribution around phi this is called
+
+ align:start position:0%
+distribution around phi this is called
+ 
+
+ align:start position:0%
+distribution around phi this is called
+the angular response function
+
+ align:start position:0%
+the angular response function
+ 
+
+ align:start position:0%
+the angular response function
+and we determine it by removing the gold
+
+ align:start position:0%
+and we determine it by removing the gold
+ 
+
+ align:start position:0%
+and we determine it by removing the gold
+foil from our detector so we just have
+
+ align:start position:0%
+foil from our detector so we just have
+ 
+
+ align:start position:0%
+foil from our detector so we just have
+our howitzer
+
+ align:start position:0%
+our howitzer
+ 
+
+ align:start position:0%
+our howitzer
+and our detector and we see how
+
+ align:start position:0%
+and our detector and we see how
+ 
+
+ align:start position:0%
+and our detector and we see how
+deviations in our
+
+ align:start position:0%
+deviations in our
+ 
+
+ align:start position:0%
+deviations in our
+fee affect our counting rates now again
+
+ align:start position:0%
+fee affect our counting rates now again
+ 
+
+ align:start position:0%
+fee affect our counting rates now again
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+to reference back in this theoretical
+
+ align:start position:0%
+to reference back in this theoretical
+ 
+
+ align:start position:0%
+to reference back in this theoretical
+scenario with point charges
+
+ align:start position:0%
+scenario with point charges
+ 
+
+ align:start position:0%
+scenario with point charges
+or point sources and point detectors we
+
+ align:start position:0%
+or point sources and point detectors we
+ 
+
+ align:start position:0%
+or point sources and point detectors we
+would expect to only see counts at
+
+ align:start position:0%
+would expect to only see counts at
+ 
+
+ align:start position:0%
+would expect to only see counts at
+fee equals to zero with our howitzer
+
+ align:start position:0%
+fee equals to zero with our howitzer
+ 
+
+ align:start position:0%
+fee equals to zero with our howitzer
+pointed dead on the detector
+
+ align:start position:0%
+pointed dead on the detector
+ 
+
+ align:start position:0%
+pointed dead on the detector
+and as soon as we move it a little bit
+
+ align:start position:0%
+and as soon as we move it a little bit
+ 
+
+ align:start position:0%
+and as soon as we move it a little bit
+the counts go away however this is not
+
+ align:start position:0%
+the counts go away however this is not
+ 
+
+ align:start position:0%
+the counts go away however this is not
+actually the case and by measuring these
+
+ align:start position:0%
+actually the case and by measuring these
+ 
+
+ align:start position:0%
+actually the case and by measuring these
+deviations we can determine our angular
+
+ align:start position:0%
+deviations we can determine our angular
+ 
+
+ align:start position:0%
+deviations we can determine our angular
+response function
+
+ align:start position:0%
+response function
+ 
+
+ align:start position:0%
+response function
+so we move our howitzer around we
+
+ align:start position:0%
+so we move our howitzer around we
+ 
+
+ align:start position:0%
+so we move our howitzer around we
+determine how our angle fee
+
+ align:start position:0%
+determine how our angle fee
+ 
+
+ align:start position:0%
+determine how our angle fee
+affects our counts and we get something
+
+ align:start position:0%
+affects our counts and we get something
+ 
+
+ align:start position:0%
+affects our counts and we get something
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+this is fitted to a triangle
+
+ align:start position:0%
+this is fitted to a triangle
+ 
+
+ align:start position:0%
+this is fitted to a triangle
+distribution now we can take a few
+
+ align:start position:0%
+distribution now we can take a few
+ 
+
+ align:start position:0%
+distribution now we can take a few
+things out of this
+
+ align:start position:0%
+things out of this
+ 
+
+ align:start position:0%
+things out of this
+i see a fellow in the crowd laughing at
+
+ align:start position:0%
+i see a fellow in the crowd laughing at
+ 
+
+ align:start position:0%
+i see a fellow in the crowd laughing at
+my chi-squared
+
+ align:start position:0%
+my chi-squared
+ 
+
+ align:start position:0%
+my chi-squared
+the chi-squared is not that good this is
+
+ align:start position:0%
+the chi-squared is not that good this is
+ 
+
+ align:start position:0%
+the chi-squared is not that good this is
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+we we acknowledge that a triangle is
+
+ align:start position:0%
+we we acknowledge that a triangle is
+ 
+
+ align:start position:0%
+we we acknowledge that a triangle is
+only a first approximation we don't
+
+ align:start position:0%
+only a first approximation we don't
+ 
+
+ align:start position:0%
+only a first approximation we don't
+expect
+
+ align:start position:0%
+expect
+ 
+
+ align:start position:0%
+expect
+our data to actually perfectly model
+
+ align:start position:0%
+our data to actually perfectly model
+ 
+
+ align:start position:0%
+our data to actually perfectly model
+this triangle
+
+ align:start position:0%
+this triangle
+ 
+
+ align:start position:0%
+this triangle
+distribution however it simplifies our
+
+ align:start position:0%
+distribution however it simplifies our
+ 
+
+ align:start position:0%
+distribution however it simplifies our
+math greatly
+
+ align:start position:0%
+math greatly
+ 
+
+ align:start position:0%
+math greatly
+so we use this triangle distribution and
+
+ align:start position:0%
+so we use this triangle distribution and
+ 
+
+ align:start position:0%
+so we use this triangle distribution and
+try to extract some data from this
+
+ align:start position:0%
+try to extract some data from this
+ 
+
+ align:start position:0%
+try to extract some data from this
+the second thing that we can see from
+
+ align:start position:0%
+the second thing that we can see from
+ 
+
+ align:start position:0%
+the second thing that we can see from
+this is that this distribution is
+
+ align:start position:0%
+this is that this distribution is
+ 
+
+ align:start position:0%
+this is that this distribution is
+actually a bit off-center
+
+ align:start position:0%
+actually a bit off-center
+ 
+
+ align:start position:0%
+actually a bit off-center
+at theta equals to negative two now
+
+ align:start position:0%
+at theta equals to negative two now
+ 
+
+ align:start position:0%
+at theta equals to negative two now
+normally we would expect
+
+ align:start position:0%
+normally we would expect
+ 
+
+ align:start position:0%
+normally we would expect
+the highest count rate when our howitzer
+
+ align:start position:0%
+the highest count rate when our howitzer
+ 
+
+ align:start position:0%
+the highest count rate when our howitzer
+is pointed dead on
+
+ align:start position:0%
+is pointed dead on
+ 
+
+ align:start position:0%
+is pointed dead on
+at our detector at theta equals to zero
+
+ align:start position:0%
+at our detector at theta equals to zero
+ 
+
+ align:start position:0%
+at our detector at theta equals to zero
+this offset indicates that the
+
+ align:start position:0%
+this offset indicates that the
+ 
+
+ align:start position:0%
+this offset indicates that the
+protractor that we use to measure angles
+
+ align:start position:0%
+protractor that we use to measure angles
+ 
+
+ align:start position:0%
+protractor that we use to measure angles
+is actually a little bit off
+
+ align:start position:0%
+is actually a little bit off
+ 
+
+ align:start position:0%
+is actually a little bit off
+and pointing that on actually
+
+ align:start position:0%
+and pointing that on actually
+ 
+
+ align:start position:0%
+and pointing that on actually
+corresponds to theta equals to 2.
+
+ align:start position:0%
+corresponds to theta equals to 2.
+ 
+
+ align:start position:0%
+corresponds to theta equals to 2.
+finally this gives us our angular
+
+ align:start position:0%
+finally this gives us our angular
+ 
+
+ align:start position:0%
+finally this gives us our angular
+response function if we replace
+
+ align:start position:0%
+response function if we replace
+ 
+
+ align:start position:0%
+response function if we replace
+zero with our howitzer angle phi this
+
+ align:start position:0%
+zero with our howitzer angle phi this
+ 
+
+ align:start position:0%
+zero with our howitzer angle phi this
+gives us the spread around phi
+
+ align:start position:0%
+gives us the spread around phi
+ 
+
+ align:start position:0%
+gives us the spread around phi
+of scattering angles theta that we
+
+ align:start position:0%
+of scattering angles theta that we
+ 
+
+ align:start position:0%
+of scattering angles theta that we
+detect
+
+ align:start position:0%
+detect
+ 
+
+ align:start position:0%
+detect
+we accommodate this in our equations via
+
+ align:start position:0%
+we accommodate this in our equations via
+ 
+
+ align:start position:0%
+we accommodate this in our equations via
+a convolution
+
+ align:start position:0%
+a convolution
+ 
+
+ align:start position:0%
+a convolution
+now this can intuitively be thought as
+
+ align:start position:0%
+now this can intuitively be thought as
+ 
+
+ align:start position:0%
+now this can intuitively be thought as
+taking these two rates which are given
+
+ align:start position:0%
+taking these two rates which are given
+ 
+
+ align:start position:0%
+taking these two rates which are given
+thompson and rutherford the probability
+
+ align:start position:0%
+thompson and rutherford the probability
+ 
+
+ align:start position:0%
+thompson and rutherford the probability
+of having a scattering at angle theta
+
+ align:start position:0%
+of having a scattering at angle theta
+ 
+
+ align:start position:0%
+of having a scattering at angle theta
+we then multiply it by the probability
+
+ align:start position:0%
+we then multiply it by the probability
+ 
+
+ align:start position:0%
+we then multiply it by the probability
+of an scattering angle theta being
+
+ align:start position:0%
+of an scattering angle theta being
+ 
+
+ align:start position:0%
+of an scattering angle theta being
+detected
+
+ align:start position:0%
+detected
+ 
+
+ align:start position:0%
+detected
+by our how its are positioned at an
+
+ align:start position:0%
+by our how its are positioned at an
+ 
+
+ align:start position:0%
+by our how its are positioned at an
+angle phi and then we integrate over all
+
+ align:start position:0%
+angle phi and then we integrate over all
+ 
+
+ align:start position:0%
+angle phi and then we integrate over all
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+this gives us two different counting
+
+ align:start position:0%
+this gives us two different counting
+ 
+
+ align:start position:0%
+this gives us two different counting
+rates as a function of our howitzer
+
+ align:start position:0%
+rates as a function of our howitzer
+ 
+
+ align:start position:0%
+rates as a function of our howitzer
+angle fee
+
+ align:start position:0%
+angle fee
+ 
+
+ align:start position:0%
+angle fee
+one for our rutherford theory and one
+
+ align:start position:0%
+one for our rutherford theory and one
+ 
+
+ align:start position:0%
+one for our rutherford theory and one
+for our thomson theory
+
+ align:start position:0%
+for our thomson theory
+ 
+
+ align:start position:0%
+for our thomson theory
+this gives us two equations that we can
+
+ align:start position:0%
+this gives us two equations that we can
+ 
+
+ align:start position:0%
+this gives us two equations that we can
+use to compare our data
+
+ align:start position:0%
+use to compare our data
+ 
+
+ align:start position:0%
+use to compare our data
+given geometric considerations about our
+
+ align:start position:0%
+given geometric considerations about our
+ 
+
+ align:start position:0%
+given geometric considerations about our
+apparatus
+
+ align:start position:0%
+apparatus
+ 
+
+ align:start position:0%
+apparatus
+so after that we are finally ready to go
+
+ align:start position:0%
+so after that we are finally ready to go
+ 
+
+ align:start position:0%
+so after that we are finally ready to go
+so we take our gold foil we put it back
+
+ align:start position:0%
+so we take our gold foil we put it back
+ 
+
+ align:start position:0%
+so we take our gold foil we put it back
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+we measure at different angles between
+
+ align:start position:0%
+we measure at different angles between
+ 
+
+ align:start position:0%
+we measure at different angles between
+fee equals to
+
+ align:start position:0%
+fee equals to
+ 
+
+ align:start position:0%
+fee equals to
+10 degrees and 60 degrees we let a
+
+ align:start position:0%
+10 degrees and 60 degrees we let a
+ 
+
+ align:start position:0%
+10 degrees and 60 degrees we let a
+detector
+
+ align:start position:0%
+detector
+ 
+
+ align:start position:0%
+detector
+detect for a while and over the period
+
+ align:start position:0%
+detect for a while and over the period
+ 
+
+ align:start position:0%
+detect for a while and over the period
+of time
+
+ align:start position:0%
+of time
+ 
+
+ align:start position:0%
+of time
+at any one of our measuring rates we get
+
+ align:start position:0%
+at any one of our measuring rates we get
+ 
+
+ align:start position:0%
+at any one of our measuring rates we get
+something that looks a bit like
+
+ align:start position:0%
+something that looks a bit like
+ 
+
+ align:start position:0%
+something that looks a bit like
+this now this mca bin number down here
+
+ align:start position:0%
+this now this mca bin number down here
+ 
+
+ align:start position:0%
+this now this mca bin number down here
+corresponds to the energy
+
+ align:start position:0%
+corresponds to the energy
+ 
+
+ align:start position:0%
+corresponds to the energy
+of the particles that we're detecting
+
+ align:start position:0%
+of the particles that we're detecting
+ 
+
+ align:start position:0%
+of the particles that we're detecting
+and on the y-axis here is our count rate
+
+ align:start position:0%
+and on the y-axis here is our count rate
+ 
+
+ align:start position:0%
+and on the y-axis here is our count rate
+now the first thing that you might think
+
+ align:start position:0%
+now the first thing that you might think
+ 
+
+ align:start position:0%
+now the first thing that you might think
+and the first thing that we thought as
+
+ align:start position:0%
+and the first thing that we thought as
+ 
+
+ align:start position:0%
+and the first thing that we thought as
+well is well
+
+ align:start position:0%
+well is well
+ 
+
+ align:start position:0%
+well is well
+this is about a gaussian right here
+
+ align:start position:0%
+this is about a gaussian right here
+ 
+
+ align:start position:0%
+this is about a gaussian right here
+that's our particle and everything below
+
+ align:start position:0%
+that's our particle and everything below
+ 
+
+ align:start position:0%
+that's our particle and everything below
+that is just noise
+
+ align:start position:0%
+that is just noise
+ 
+
+ align:start position:0%
+that is just noise
+however as we found out the energy loss
+
+ align:start position:0%
+however as we found out the energy loss
+ 
+
+ align:start position:0%
+however as we found out the energy loss
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+a material is actually described by a
+
+ align:start position:0%
+a material is actually described by a
+ 
+
+ align:start position:0%
+a material is actually described by a
+landau distribution
+
+ align:start position:0%
+landau distribution
+ 
+
+ align:start position:0%
+landau distribution
+which is a gaussian but with a slightly
+
+ align:start position:0%
+which is a gaussian but with a slightly
+ 
+
+ align:start position:0%
+which is a gaussian but with a slightly
+longer tail on one side
+
+ align:start position:0%
+longer tail on one side
+ 
+
+ align:start position:0%
+longer tail on one side
+what you see here is a gaussian with a
+
+ align:start position:0%
+what you see here is a gaussian with a
+ 
+
+ align:start position:0%
+what you see here is a gaussian with a
+slightly longer tail on one side
+
+ align:start position:0%
+slightly longer tail on one side
+ 
+
+ align:start position:0%
+slightly longer tail on one side
+so by fitting this to a landau distrib
+
+ align:start position:0%
+so by fitting this to a landau distrib
+ 
+
+ align:start position:0%
+so by fitting this to a landau distrib
+we fit this to a land out distribution
+
+ align:start position:0%
+we fit this to a land out distribution
+ 
+
+ align:start position:0%
+we fit this to a land out distribution
+and get chi
+
+ align:start position:0%
+and get chi
+ 
+
+ align:start position:0%
+and get chi
+squareds between 0.5 and 2 which
+
+ align:start position:0%
+squareds between 0.5 and 2 which
+ 
+
+ align:start position:0%
+squareds between 0.5 and 2 which
+indicates
+
+ align:start position:0%
+indicates
+ 
+
+ align:start position:0%
+indicates
+which suggests that all this did
+
+ align:start position:0%
+which suggests that all this did
+ 
+
+ align:start position:0%
+which suggests that all this did
+actually come from a land our
+
+ align:start position:0%
+actually come from a land our
+ 
+
+ align:start position:0%
+actually come from a land our
+distribution
+
+ align:start position:0%
+distribution
+ 
+
+ align:start position:0%
+distribution
+and all of these are valid scattering
+
+ align:start position:0%
+and all of these are valid scattering
+ 
+
+ align:start position:0%
+and all of these are valid scattering
+data points and not just
+
+ align:start position:0%
+data points and not just
+ 
+
+ align:start position:0%
+data points and not just
+noise we further confirmed this by
+
+ align:start position:0%
+noise we further confirmed this by
+ 
+
+ align:start position:0%
+noise we further confirmed this by
+measuring our noise by taking our
+
+ align:start position:0%
+measuring our noise by taking our
+ 
+
+ align:start position:0%
+measuring our noise by taking our
+howitzer pointed
+
+ align:start position:0%
+howitzer pointed
+ 
+
+ align:start position:0%
+howitzer pointed
+away from our detector and just letting
+
+ align:start position:0%
+away from our detector and just letting
+ 
+
+ align:start position:0%
+away from our detector and just letting
+our detector collect
+
+ align:start position:0%
+our detector collect
+ 
+
+ align:start position:0%
+our detector collect
+we ultimately determined that the noise
+
+ align:start position:0%
+we ultimately determined that the noise
+ 
+
+ align:start position:0%
+we ultimately determined that the noise
+within our energy range of interest
+
+ align:start position:0%
+within our energy range of interest
+ 
+
+ align:start position:0%
+within our energy range of interest
+is very small much smaller than any
+
+ align:start position:0%
+is very small much smaller than any
+ 
+
+ align:start position:0%
+is very small much smaller than any
+count rate that we
+
+ align:start position:0%
+count rate that we
+ 
+
+ align:start position:0%
+count rate that we
+care about in our experiment therefore
+
+ align:start position:0%
+care about in our experiment therefore
+ 
+
+ align:start position:0%
+care about in our experiment therefore
+because of this
+
+ align:start position:0%
+because of this
+ 
+
+ align:start position:0%
+because of this
+and the fact that our energy our
+
+ align:start position:0%
+and the fact that our energy our
+ 
+
+ align:start position:0%
+and the fact that our energy our
+distribution models land our
+
+ align:start position:0%
+distribution models land our
+ 
+
+ align:start position:0%
+distribution models land our
+distribution which is what we expect
+
+ align:start position:0%
+distribution which is what we expect
+ 
+
+ align:start position:0%
+distribution which is what we expect
+we conclude that we can use all the
+
+ align:start position:0%
+we conclude that we can use all the
+ 
+
+ align:start position:0%
+we conclude that we can use all the
+points that we detect
+
+ align:start position:0%
+points that we detect
+ 
+
+ align:start position:0%
+points that we detect
+as valid scattering data points but of
+
+ align:start position:0%
+as valid scattering data points but of
+ 
+
+ align:start position:0%
+as valid scattering data points but of
+course it comes with some good old
+
+ align:start position:0%
+course it comes with some good old
+ 
+
+ align:start position:0%
+course it comes with some good old
+counting uncertainty in addition we have
+
+ align:start position:0%
+counting uncertainty in addition we have
+ 
+
+ align:start position:0%
+counting uncertainty in addition we have
+some uncertainty
+
+ align:start position:0%
+some uncertainty
+ 
+
+ align:start position:0%
+some uncertainty
+in our angles we read the angles of our
+
+ align:start position:0%
+in our angles we read the angles of our
+ 
+
+ align:start position:0%
+in our angles we read the angles of our
+howitzer
+
+ align:start position:0%
+howitzer
+ 
+
+ align:start position:0%
+howitzer
+by eye from a little protractor that we
+
+ align:start position:0%
+by eye from a little protractor that we
+ 
+
+ align:start position:0%
+by eye from a little protractor that we
+have in our apparatus
+
+ align:start position:0%
+have in our apparatus
+ 
+
+ align:start position:0%
+have in our apparatus
+but our eyes aren't so good so we tack a
+
+ align:start position:0%
+but our eyes aren't so good so we tack a
+ 
+
+ align:start position:0%
+but our eyes aren't so good so we tack a
+plus or minus wonder uncertainty to
+
+ align:start position:0%
+plus or minus wonder uncertainty to
+ 
+
+ align:start position:0%
+plus or minus wonder uncertainty to
+angular measurements
+
+ align:start position:0%
+angular measurements
+ 
+
+ align:start position:0%
+angular measurements
+my lab partner thinks .5 i think one
+
+ align:start position:0%
+my lab partner thinks .5 i think one
+ 
+
+ align:start position:0%
+my lab partner thinks .5 i think one
+because i'm not a certain
+
+ align:start position:0%
+because i'm not a certain
+ 
+
+ align:start position:0%
+because i'm not a certain
+so we take all these measurements we
+
+ align:start position:0%
+so we take all these measurements we
+ 
+
+ align:start position:0%
+so we take all these measurements we
+divide by the amount of time that we
+
+ align:start position:0%
+divide by the amount of time that we
+ 
+
+ align:start position:0%
+divide by the amount of time that we
+collected to get a count rate
+
+ align:start position:0%
+collected to get a count rate
+ 
+
+ align:start position:0%
+collected to get a count rate
+we graph this as a function of our angle
+
+ align:start position:0%
+we graph this as a function of our angle
+ 
+
+ align:start position:0%
+we graph this as a function of our angle
+that we measured it at
+
+ align:start position:0%
+that we measured it at
+ 
+
+ align:start position:0%
+that we measured it at
+and fit this to a rutherford and
+
+ align:start position:0%
+and fit this to a rutherford and
+ 
+
+ align:start position:0%
+and fit this to a rutherford and
+thompson convolved fit
+
+ align:start position:0%
+thompson convolved fit
+ 
+
+ align:start position:0%
+thompson convolved fit
+and we see something like this
+
+ align:start position:0%
+and we see something like this
+ 
+
+ align:start position:0%
+and we see something like this
+and i i think this really speaks for
+
+ align:start position:0%
+and i i think this really speaks for
+ 
+
+ align:start position:0%
+and i i think this really speaks for
+itself this is
+
+ align:start position:0%
+itself this is
+ 
+
+ align:start position:0%
+itself this is
+this is not an error in my code this
+
+ align:start position:0%
+this is not an error in my code this
+ 
+
+ align:start position:0%
+this is not an error in my code this
+thompson is really just
+
+ align:start position:0%
+thompson is really just
+ 
+
+ align:start position:0%
+thompson is really just
+that bad in accounting for our data but
+
+ align:start position:0%
+that bad in accounting for our data but
+ 
+
+ align:start position:0%
+that bad in accounting for our data but
+we see here that the rutherford
+
+ align:start position:0%
+we see here that the rutherford
+ 
+
+ align:start position:0%
+we see here that the rutherford
+scattering
+
+ align:start position:0%
+scattering
+ 
+
+ align:start position:0%
+scattering
+prediction more accurately describes the
+
+ align:start position:0%
+prediction more accurately describes the
+ 
+
+ align:start position:0%
+prediction more accurately describes the
+gradual fall off
+
+ align:start position:0%
+gradual fall off
+ 
+
+ align:start position:0%
+gradual fall off
+of our scattering rates as the howitzer
+
+ align:start position:0%
+of our scattering rates as the howitzer
+ 
+
+ align:start position:0%
+of our scattering rates as the howitzer
+angle gets bigger as opposed to the
+
+ align:start position:0%
+angle gets bigger as opposed to the
+ 
+
+ align:start position:0%
+angle gets bigger as opposed to the
+thompson fit
+
+ align:start position:0%
+thompson fit
+ 
+
+ align:start position:0%
+thompson fit
+with a chi squared of two thousand
+
+ align:start position:0%
+with a chi squared of two thousand
+ 
+
+ align:start position:0%
+with a chi squared of two thousand
+uh now there are different ways of
+
+ align:start position:0%
+uh now there are different ways of
+ 
+
+ align:start position:0%
+uh now there are different ways of
+potentially giving thompson a better
+
+ align:start position:0%
+potentially giving thompson a better
+ 
+
+ align:start position:0%
+potentially giving thompson a better
+shot
+
+ align:start position:0%
+shot
+ 
+
+ align:start position:0%
+shot
+accommodating for it maybe giving it a
+
+ align:start position:0%
+accommodating for it maybe giving it a
+ 
+
+ align:start position:0%
+accommodating for it maybe giving it a
+better chance of describing our data
+
+ align:start position:0%
+better chance of describing our data
+ 
+
+ align:start position:0%
+better chance of describing our data
+and i can go into this in more detail
+
+ align:start position:0%
+and i can go into this in more detail
+ 
+
+ align:start position:0%
+and i can go into this in more detail
+later if people are interested
+
+ align:start position:0%
+later if people are interested
+ 
+
+ align:start position:0%
+later if people are interested
+but ultimately we see that thompson is
+
+ align:start position:0%
+but ultimately we see that thompson is
+ 
+
+ align:start position:0%
+but ultimately we see that thompson is
+fundamentally
+
+ align:start position:0%
+fundamentally
+ 
+
+ align:start position:0%
+fundamentally
+unable to account for this data whereas
+
+ align:start position:0%
+unable to account for this data whereas
+ 
+
+ align:start position:0%
+unable to account for this data whereas
+rutherford describes it quite well
+
+ align:start position:0%
+rutherford describes it quite well
+ 
+
+ align:start position:0%
+rutherford describes it quite well
+now there's an additional caveat to this
+
+ align:start position:0%
+now there's an additional caveat to this
+ 
+
+ align:start position:0%
+now there's an additional caveat to this
+chi squared that we have here
+
+ align:start position:0%
+chi squared that we have here
+ 
+
+ align:start position:0%
+chi squared that we have here
+so this chi squared comes from fitting
+
+ align:start position:0%
+so this chi squared comes from fitting
+ 
+
+ align:start position:0%
+so this chi squared comes from fitting
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+our our rutherford and thompson data
+
+ align:start position:0%
+our our rutherford and thompson data
+ 
+
+ align:start position:0%
+our our rutherford and thompson data
+convolved with our beam profile however
+
+ align:start position:0%
+convolved with our beam profile however
+ 
+
+ align:start position:0%
+convolved with our beam profile however
+our beam profile
+
+ align:start position:0%
+our beam profile
+ 
+
+ align:start position:0%
+our beam profile
+does have some uncertainty associated in
+
+ align:start position:0%
+does have some uncertainty associated in
+ 
+
+ align:start position:0%
+does have some uncertainty associated in
+that fit that we had
+
+ align:start position:0%
+that fit that we had
+ 
+
+ align:start position:0%
+that fit that we had
+there is some uncertainty in the
+
+ align:start position:0%
+there is some uncertainty in the
+ 
+
+ align:start position:0%
+there is some uncertainty in the
+triangle so to sort of estimate how this
+
+ align:start position:0%
+triangle so to sort of estimate how this
+ 
+
+ align:start position:0%
+triangle so to sort of estimate how this
+uncertainty affects our data
+
+ align:start position:0%
+uncertainty affects our data
+ 
+
+ align:start position:0%
+uncertainty affects our data
+we vary our beam profile within one
+
+ align:start position:0%
+we vary our beam profile within one
+ 
+
+ align:start position:0%
+we vary our beam profile within one
+standard deviation
+
+ align:start position:0%
+standard deviation
+ 
+
+ align:start position:0%
+standard deviation
+of its fit parameters and see how our
+
+ align:start position:0%
+of its fit parameters and see how our
+ 
+
+ align:start position:0%
+of its fit parameters and see how our
+goodness of fit changes
+
+ align:start position:0%
+goodness of fit changes
+ 
+
+ align:start position:0%
+goodness of fit changes
+and we see here that the goodness of fit
+
+ align:start position:0%
+and we see here that the goodness of fit
+ 
+
+ align:start position:0%
+and we see here that the goodness of fit
+for our rutherford model
+
+ align:start position:0%
+for our rutherford model
+ 
+
+ align:start position:0%
+for our rutherford model
+well it varies somewhat depending on the
+
+ align:start position:0%
+well it varies somewhat depending on the
+ 
+
+ align:start position:0%
+well it varies somewhat depending on the
+convolution that we
+
+ align:start position:0%
+convolution that we
+ 
+
+ align:start position:0%
+convolution that we
+use it doesn't it doesn't change a
+
+ align:start position:0%
+use it doesn't it doesn't change a
+ 
+
+ align:start position:0%
+use it doesn't it doesn't change a
+significant amount
+
+ align:start position:0%
+significant amount
+ 
+
+ align:start position:0%
+significant amount
+and it certainly doesn't change enough
+
+ align:start position:0%
+and it certainly doesn't change enough
+ 
+
+ align:start position:0%
+and it certainly doesn't change enough
+to warrant considering the thompson
+
+ align:start position:0%
+to warrant considering the thompson
+ 
+
+ align:start position:0%
+to warrant considering the thompson
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+the discrepancy between the chi squareds
+
+ align:start position:0%
+the discrepancy between the chi squareds
+ 
+
+ align:start position:0%
+the discrepancy between the chi squareds
+and sort of the visual discrepancy you
+
+ align:start position:0%
+and sort of the visual discrepancy you
+ 
+
+ align:start position:0%
+and sort of the visual discrepancy you
+see here
+
+ align:start position:0%
+see here
+ 
+
+ align:start position:0%
+see here
+very clearly suggests that rutherford
+
+ align:start position:0%
+very clearly suggests that rutherford
+ 
+
+ align:start position:0%
+very clearly suggests that rutherford
+does a much better job
+
+ align:start position:0%
+does a much better job
+ 
+
+ align:start position:0%
+does a much better job
+of predicting our data than thomson
+
+ align:start position:0%
+of predicting our data than thomson
+ 
+
+ align:start position:0%
+of predicting our data than thomson
+which again suggests a more rutherford
+
+ align:start position:0%
+which again suggests a more rutherford
+ 
+
+ align:start position:0%
+which again suggests a more rutherford
+makeup of the atom as opposed to the
+
+ align:start position:0%
+makeup of the atom as opposed to the
+ 
+
+ align:start position:0%
+makeup of the atom as opposed to the
+thomson plum pudding model
+
+ align:start position:0%
+thomson plum pudding model
+ 
+
+ align:start position:0%
+thomson plum pudding model
+so in conclusion thompson's plum pudding
+
+ align:start position:0%
+so in conclusion thompson's plum pudding
+ 
+
+ align:start position:0%
+so in conclusion thompson's plum pudding
+model is found to fundamentally be
+
+ align:start position:0%
+model is found to fundamentally be
+ 
+
+ align:start position:0%
+model is found to fundamentally be
+unable to describe the scattering rates
+
+ align:start position:0%
+unable to describe the scattering rates
+ 
+
+ align:start position:0%
+unable to describe the scattering rates
+that we observe at large angles
+
+ align:start position:0%
+that we observe at large angles
+ 
+
+ align:start position:0%
+that we observe at large angles
+the rutherford model more accurately
+
+ align:start position:0%
+the rutherford model more accurately
+ 
+
+ align:start position:0%
+the rutherford model more accurately
+predicts this gradual falloff
+
+ align:start position:0%
+predicts this gradual falloff
+ 
+
+ align:start position:0%
+predicts this gradual falloff
+which suggests a more rough more
+
+ align:start position:0%
+which suggests a more rough more
+ 
+
+ align:start position:0%
+which suggests a more rough more
+rutherford rutherford-like
+
+ align:start position:0%
+rutherford rutherford-like
+ 
+
+ align:start position:0%
+rutherford rutherford-like
+view of our atom and that's it thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+all for right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah um did you try the fit without
+
+ align:start position:0%
+yeah um did you try the fit without
+ 
+
+ align:start position:0%
+yeah um did you try the fit without
+using the
+
+ align:start position:0%
+using the
+ 
+
+ align:start position:0%
+using the
+triangular correction yes i did and
+
+ align:start position:0%
+triangular correction yes i did and
+ 
+
+ align:start position:0%
+triangular correction yes i did and
+this is another interesting point which
+
+ align:start position:0%
+this is another interesting point which
+ 
+
+ align:start position:0%
+this is another interesting point which
+shows
+
+ align:start position:0%
+shows
+ 
+
+ align:start position:0%
+shows
+that our convolution does benefit our
+
+ align:start position:0%
+that our convolution does benefit our
+ 
+
+ align:start position:0%
+that our convolution does benefit our
+data it does a much better
+
+ align:start position:0%
+data it does a much better
+ 
+
+ align:start position:0%
+data it does a much better
+not not much better not as bad as
+
+ align:start position:0%
+not not much better not as bad as
+ 
+
+ align:start position:0%
+not not much better not as bad as
+thompson relatively speaking but it does
+
+ align:start position:0%
+thompson relatively speaking but it does
+ 
+
+ align:start position:0%
+thompson relatively speaking but it does
+a noticeably better job at describing
+
+ align:start position:0%
+a noticeably better job at describing
+ 
+
+ align:start position:0%
+a noticeably better job at describing
+our data than
+
+ align:start position:0%
+our data than
+ 
+
+ align:start position:0%
+our data than
+the pure rutherford scattering one over
+
+ align:start position:0%
+the pure rutherford scattering one over
+ 
+
+ align:start position:0%
+the pure rutherford scattering one over
+signed to the fourth
+
+ align:start position:0%
+signed to the fourth
+ 
+
+ align:start position:0%
+signed to the fourth
+fit so the difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and sorry 8.18 is is yeah
+
+ align:start position:0%
+and sorry 8.18 is is yeah
+ 
+
+ align:start position:0%
+and sorry 8.18 is is yeah
+the that's a chi-squared of eight for
+
+ align:start position:0%
+the that's a chi-squared of eight for
+ 
+
+ align:start position:0%
+the that's a chi-squared of eight for
+just fitting with the raw rutherford
+
+ align:start position:0%
+just fitting with the raw rutherford
+ 
+
+ align:start position:0%
+just fitting with the raw rutherford
+scattering without the convolution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes um do you have any spots that show
+
+ align:start position:0%
+yes um do you have any spots that show
+ 
+
+ align:start position:0%
+yes um do you have any spots that show
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+distribution i i thought i did you saw
+
+ align:start position:0%
+distribution i i thought i did you saw
+ 
+
+ align:start position:0%
+distribution i i thought i did you saw
+me switch forward and then realize that
+
+ align:start position:0%
+me switch forward and then realize that
+ 
+
+ align:start position:0%
+me switch forward and then realize that
+it wasn't there so i switched back no uh
+
+ align:start position:0%
+it wasn't there so i switched back no uh
+ 
+
+ align:start position:0%
+it wasn't there so i switched back no uh
+so i don't have a picture of the land
+
+ align:start position:0%
+so i don't have a picture of the land
+ 
+
+ align:start position:0%
+so i don't have a picture of the land
+outfit
+
+ align:start position:0%
+outfit
+ 
+
+ align:start position:0%
+outfit
+one thing that i can describe which is
+
+ align:start position:0%
+one thing that i can describe which is
+ 
+
+ align:start position:0%
+one thing that i can describe which is
+um a small caveat to this
+
+ align:start position:0%
+um a small caveat to this
+ 
+
+ align:start position:0%
+um a small caveat to this
+is that the landau distribution
+
+ align:start position:0%
+is that the landau distribution
+ 
+
+ align:start position:0%
+is that the landau distribution
+describes energy loss
+
+ align:start position:0%
+describes energy loss
+ 
+
+ align:start position:0%
+describes energy loss
+this is usually a gaussian with one tail
+
+ align:start position:0%
+this is usually a gaussian with one tail
+ 
+
+ align:start position:0%
+this is usually a gaussian with one tail
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+this isn't too well it's a gaussian with
+
+ align:start position:0%
+this isn't too well it's a gaussian with
+ 
+
+ align:start position:0%
+this isn't too well it's a gaussian with
+a slightly longer tail on the right hand
+
+ align:start position:0%
+a slightly longer tail on the right hand
+ 
+
+ align:start position:0%
+a slightly longer tail on the right hand
+side
+
+ align:start position:0%
+side
+ 
+
+ align:start position:0%
+side
+now this is a gaussian with a slightly
+
+ align:start position:0%
+now this is a gaussian with a slightly
+ 
+
+ align:start position:0%
+now this is a gaussian with a slightly
+longer tail on the left hand side
+
+ align:start position:0%
+longer tail on the left hand side
+ 
+
+ align:start position:0%
+longer tail on the left hand side
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+what we see here is energy and energy
+
+ align:start position:0%
+what we see here is energy and energy
+ 
+
+ align:start position:0%
+what we see here is energy and energy
+loss is sort of the inverse of this
+
+ align:start position:0%
+loss is sort of the inverse of this
+ 
+
+ align:start position:0%
+loss is sort of the inverse of this
+so we actually fit this to a reverse
+
+ align:start position:0%
+so we actually fit this to a reverse
+ 
+
+ align:start position:0%
+so we actually fit this to a reverse
+landau distribution and
+
+ align:start position:0%
+landau distribution and
+ 
+
+ align:start position:0%
+landau distribution and
+throughout all our data we get chi
+
+ align:start position:0%
+throughout all our data we get chi
+ 
+
+ align:start position:0%
+throughout all our data we get chi
+squareds between or reduce type reduce
+
+ align:start position:0%
+squareds between or reduce type reduce
+ 
+
+ align:start position:0%
+squareds between or reduce type reduce
+chi squareds between 0.5
+
+ align:start position:0%
+chi squareds between 0.5
+ 
+
+ align:start position:0%
+chi squareds between 0.5
+and 2 which indicates good fit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh 60 degrees 60 degrees we collected
+
+ align:start position:0%
+uh 60 degrees 60 degrees we collected
+ 
+
+ align:start position:0%
+uh 60 degrees 60 degrees we collected
+over the course of five days
+
+ align:start position:0%
+over the course of five days
+ 
+
+ align:start position:0%
+over the course of five days
+and i don't think we could have actually
+
+ align:start position:0%
+and i don't think we could have actually
+ 
+
+ align:start position:0%
+and i don't think we could have actually
+collected data at much higher
+
+ align:start position:0%
+collected data at much higher
+ 
+
+ align:start position:0%
+collected data at much higher
+angles than that because our noise data
+
+ align:start position:0%
+angles than that because our noise data
+ 
+
+ align:start position:0%
+angles than that because our noise data
+our noise rate right here
+
+ align:start position:0%
+our noise rate right here
+ 
+
+ align:start position:0%
+our noise rate right here
+is 0.002 now this is still a bit
+
+ align:start position:0%
+is 0.002 now this is still a bit
+ 
+
+ align:start position:0%
+is 0.002 now this is still a bit
+smaller than our counting rate for 60
+
+ align:start position:0%
+smaller than our counting rate for 60
+ 
+
+ align:start position:0%
+smaller than our counting rate for 60
+degrees
+
+ align:start position:0%
+degrees
+ 
+
+ align:start position:0%
+degrees
+but if we started to go further we would
+
+ align:start position:0%
+but if we started to go further we would
+ 
+
+ align:start position:0%
+but if we started to go further we would
+start to enter the regime where noise
+
+ align:start position:0%
+start to enter the regime where noise
+ 
+
+ align:start position:0%
+start to enter the regime where noise
+becomes
+
+ align:start position:0%
+becomes
+ 
+
+ align:start position:0%
+becomes
+much more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that dominant five days or five days off
+
+ align:start position:0%
+that dominant five days or five days off
+ 
+
+ align:start position:0%
+that dominant five days or five days off
+the top of my head i believe
+
+ align:start position:0%
+the top of my head i believe
+ 
+
+ align:start position:0%
+the top of my head i believe
+400. you can actually see i know the
+
+ align:start position:0%
+400. you can actually see i know the
+ 
+
+ align:start position:0%
+400. you can actually see i know the
+rate here which you can very easily go
+
+ align:start position:0%
+rate here which you can very easily go
+ 
+
+ align:start position:0%
+rate here which you can very easily go
+backwards
+
+ align:start position:0%
+backwards
+ 
+
+ align:start position:0%
+backwards
+in the math oh i guess this is somewhere
+
+ align:start position:0%
+in the math oh i guess this is somewhere
+ 
+
+ align:start position:0%
+in the math oh i guess this is somewhere
+down here
+
+ align:start position:0%
+down here
+ 
+
+ align:start position:0%
+down here
+100 per day yeah something like that
+
+ align:start position:0%
+100 per day yeah something like that
+ 
+
+ align:start position:0%
+100 per day yeah something like that
+yes something like that yep
+
+ align:start position:0%
+yes something like that yep
+ 
+
+ align:start position:0%
+yes something like that yep
+and our the noise that we mentioned here
+
+ align:start position:0%
+and our the noise that we mentioned here
+ 
+
+ align:start position:0%
+and our the noise that we mentioned here
+is actually restricted to our energy of
+
+ align:start position:0%
+is actually restricted to our energy of
+ 
+
+ align:start position:0%
+is actually restricted to our energy of
+interest so
+
+ align:start position:0%
+interest so
+ 
+
+ align:start position:0%
+interest so
+there's a fair bit of noise at much
+
+ align:start position:0%
+there's a fair bit of noise at much
+ 
+
+ align:start position:0%
+there's a fair bit of noise at much
+lower energy levels specifically between
+
+ align:start position:0%
+lower energy levels specifically between
+ 
+
+ align:start position:0%
+lower energy levels specifically between
+this mca bin number of 0 and 50 down
+
+ align:start position:0%
+this mca bin number of 0 and 50 down
+ 
+
+ align:start position:0%
+this mca bin number of 0 and 50 down
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+there's a fair bit of noise there but
+
+ align:start position:0%
+there's a fair bit of noise there but
+ 
+
+ align:start position:0%
+there's a fair bit of noise there but
+once you start getting up to this larger
+
+ align:start position:0%
+once you start getting up to this larger
+ 
+
+ align:start position:0%
+once you start getting up to this larger
+area right here between
+
+ align:start position:0%
+area right here between
+ 
+
+ align:start position:0%
+area right here between
+50 and 1500 we start to see much less
+
+ align:start position:0%
+50 and 1500 we start to see much less
+ 
+
+ align:start position:0%
+50 and 1500 we start to see much less
+noise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's thank henry again
\ No newline at end of file
diff --git a/5QKJG0FZTio.txt b/5QKJG0FZTio.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8a7dabd4af5cf61580f33c4bb8f291df1a26115a
--- /dev/null
+++ b/5QKJG0FZTio.txt
@@ -0,0 +1,115 @@
+align:start position:0%
+ 
+we want to relate the small length area
+
+ align:start position:0%
+we want to relate the small length area
+ 
+
+ align:start position:0%
+we want to relate the small length area
+or volume element to Delta M the amount
+
+ align:start position:0%
+or volume element to Delta M the amount
+ 
+
+ align:start position:0%
+or volume element to Delta M the amount
+of mass contained
+
+ align:start position:0%
+of mass contained
+ 
+
+ align:start position:0%
+of mass contained
+within in one dimension this relation is
+
+ align:start position:0%
+within in one dimension this relation is
+ 
+
+ align:start position:0%
+within in one dimension this relation is
+called the linear density Lambda which
+
+ align:start position:0%
+called the linear density Lambda which
+ 
+
+ align:start position:0%
+called the linear density Lambda which
+is Delta M over Delta
+
+ align:start position:0%
+is Delta M over Delta
+ 
+
+ align:start position:0%
+is Delta M over Delta
+L for a uniform Rod of length L and
+
+ align:start position:0%
+L for a uniform Rod of length L and
+ 
+
+ align:start position:0%
+L for a uniform Rod of length L and
+total mass m Lambda is equal to m
+
+ align:start position:0%
+total mass m Lambda is equal to m
+ 
+
+ align:start position:0%
+total mass m Lambda is equal to m
+l in two Dimensions the area element
+
+ align:start position:0%
+l in two Dimensions the area element
+ 
+
+ align:start position:0%
+l in two Dimensions the area element
+contains an amount of mass Sigma * Delta
+
+ align:start position:0%
+contains an amount of mass Sigma * Delta
+ 
+
+ align:start position:0%
+contains an amount of mass Sigma * Delta
+a where Sigma has units of mass over
+
+ align:start position:0%
+a where Sigma has units of mass over
+ 
+
+ align:start position:0%
+a where Sigma has units of mass over
+area finally in three dimensions the
+
+ align:start position:0%
+area finally in three dimensions the
+ 
+
+ align:start position:0%
+area finally in three dimensions the
+volume density row connects the small
+
+ align:start position:0%
+volume density row connects the small
+ 
+
+ align:start position:0%
+volume density row connects the small
+Mass Delta m to the volume Delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+V
\ No newline at end of file
diff --git a/69H3kTwques.txt b/69H3kTwques.txt
new file mode 100644
index 0000000000000000000000000000000000000000..745f99bf3425708ec69261f7b0415c8355e63419
--- /dev/null
+++ b/69H3kTwques.txt
@@ -0,0 +1,411 @@
+[MUSIC PLAYING]
+
+PROFESSOR: Hello, everyone.
+
+Today we'll be taking a
+look at how light interacts
+
+with the surface
+of a solar cell.
+
+Right now I'm standing next
+to a solar module made up
+
+of individual
+silicon solar cells.
+
+If you look closely, these
+cells actually appear black.
+
+And they appear black for
+a very important reason.
+
+Solar engineers work very hard
+to make their solar cells as
+
+efficient as possible.
+
+Reflected light is lost
+energy, so good engineers
+
+will want to minimize the total
+amount of reflected light.
+
+To make solar cells absorb
+as much light as possible,
+
+and appear black, solar
+engineers do two things.
+
+First, they grow
+this very thin film
+
+of a dielectric
+layer on the surface.
+
+This layer is aptly called
+an anti-reflection coating.
+
+Second, they texture the wafer.
+
+And today we'll demonstrate
+how texturing is performed,
+
+and quantify its enhancement
+for reducing light reflection.
+
+Silicon wafers don't
+start out black.
+
+In fact, they appear gray.
+
+Polished wafers even
+look mirror-like,
+
+and reflect quite
+a bit of light.
+
+Here we see a polished wafer,
+which reflects around 1/3
+
+of the light off its surface.
+
+And to create the rough surface
+that reflects less light,
+
+solar engineers immerse
+their silicon wafers
+
+into a hot, wet
+chemical bath, which
+
+helps create tiny
+surface features.
+
+In this example,
+we use a solution
+
+of potassium hydroxide,
+or KOH, which
+
+is heated to around
+80 degrees Celsius.
+
+This violent
+reaction is actually
+
+etching into the
+silicon, and carving out
+
+little tiny pyramids
+on the surface.
+
+And the result is a wafer that
+loses its shiny appearance,
+
+and appears to
+have a dull finish.
+
+The textured wafer is
+left with a surface that
+
+is covered with microscopic
+pyramids, whose base
+
+is around a micron,
+or about 1/50
+
+of the width of a human hair.
+
+It turns out that this wafer
+only reflects about 1/3
+
+as much light as
+it previously did.
+
+The reason this KOH which
+bath work so well at texturing
+
+the silicon surface
+is due to the fact
+
+that these silicon wafers
+are large crystals, which
+
+in this case means that the
+atoms are formed in an ordered,
+
+repeating pattern.
+
+I have a model of the silicon
+crystal structure right here.
+
+On our model, I've highlighted
+the surface in red.
+
+Note that each silicon
+atom below the surface
+
+is actually bonded to
+four other silicon atoms,
+
+with four covalent bonds.
+
+Note that the surface
+atoms are only
+
+bonded to two other
+silicon atoms,
+
+and it has two bonds
+that are unbonded.
+
+The alkaline etch is able
+to remove silicon atoms more
+
+rapidly, when they have fewer
+bonds holding to the lattice.
+
+Hence, a solution quickly
+removes atoms on the surface.
+
+Now if I were acting
+as the KOH solution,
+
+I would remove
+all the atoms that
+
+only have two covalent bonds.
+
+Let's remove a few atoms.
+
+So this one only has
+two covalent bonds.
+
+It gets removed.
+
+These three atoms
+on the surface only
+
+have two covalent
+bonds holding them,
+
+so I'll remove them as well.
+
+Let's go ahead.
+
+Now we can see that after
+we have removed a few atoms,
+
+we have created some atoms below
+our original surface that only
+
+have two covalent bonds
+holding to the lattice.
+
+These atoms will also
+get removed by the KOH.
+
+Now if we continue
+this process, it
+
+would look something like this.
+
+So what we're going to do
+is measure the reflectivity
+
+of both a flat and
+a textured wafer.
+
+First, we'll measure
+the flat wafer,
+
+and use a laser pointer
+as a light source
+
+to simulate sunlight coming
+from very far away point.
+
+We'll shine light
+down on the surface,
+
+and measure the
+amount of light that
+
+gets reflected or
+bounced back away
+
+from the surface,
+which we'll label as R.
+
+So I'm standing next to our
+first experiment, which I just
+
+outlined in the previous sketch.
+
+We'll be using
+this laser pointer,
+
+shining it onto this silicon
+wafer, and into our photodiode.
+
+For those of you who don't
+know what a photodiode is,
+
+it is a tool that can
+measure the amount of light
+
+hitting its surface.
+
+The current that's read
+off of this ammeter
+
+will be proportional
+to the amount of light
+
+hitting our photodiode.
+
+To help visualize the beam path,
+we're going to use some steam.
+
+Now if we turn on our laser
+pointer, hits our photodiode,
+
+and we can get a good reading.
+
+And right now we see that it's
+reading around 0.9 milliamps.
+
+But how does this compare
+to a textured wafer?
+
+Let's find out.
+
+Now it's hard to
+measure the reflectivity
+
+of a textured wafer
+with a laser pointer,
+
+because it bounces the light
+off at several different angles,
+
+and we can't measure the entire
+beam with a photodiode alone.
+
+However, we can simulate
+what this would be like.
+
+Let's go to our
+sketch board to show
+
+how we can approximate
+this measurement.
+
+To measure the reflectivity
+of a textured surface,
+
+we'll create a 10,000
+to one scale model.
+
+We'll approximate
+our textured surface
+
+using two pieces of silicon.
+
+Again, we use a laser
+pointer as our light source,
+
+and shine it on one
+side of the pyramid.
+
+It'll bounce off that
+next surface, and off
+
+the adjacent side,
+and then we'll
+
+measure the amount
+of light reflected.
+
+Let's go to our
+experimental setup.
+
+So let's clarify our set up.
+
+The two angled lines in our
+drawing, the adjacent sides,
+
+on our atomic models, and the
+two angled, non-textured wafers
+
+in our set up, are all
+representing the pyramid
+
+structure of a
+textured wafer, just
+
+like the one visible in our
+scanning electron microscope
+
+image.
+
+Let's use some steam to
+visualize the beam path.
+
+Now that the steam
+has settled, we
+
+can get an accurate
+reading of the reflectivity
+
+of our modeled silicon surface.
+
+And I turn on our laser pointer.
+
+So now we can see
+that our photodiode
+
+is reading around
+0.33 milliamps.
+
+This corresponds to
+around a 9% reflectivity,
+
+which is quite a huge
+reduction from what
+
+we had before, by
+about a factor of 3.
+
+So in summary,
+today we learned how
+
+silicon is etched
+using a KOH solution,
+
+and how the resultant
+pyramids increase
+
+the efficiency of
+our solar cells,
+
+by reducing the amount
+of reflective losses
+
+by a factor of 3.
+
+If you found this
+interesting, please
+
+watch our other solar
+demos to learn more about
+
+how these exciting devices work.
+
+I'm Joe Sullivan from MIT,
+and thanks for watching.
+
+I'm out of here.
+
+[MUSIC PLAYING]
\ No newline at end of file
diff --git a/8IeL2koaHMk.txt b/8IeL2koaHMk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be4ce17e2936f68614bc649bf49e11519045d0a9
--- /dev/null
+++ b/8IeL2koaHMk.txt
@@ -0,0 +1,6842 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu did anybody have any
+
+ align:start position:0%
+ocw.mit.edu did anybody have any
+ 
+
+ align:start position:0%
+ocw.mit.edu did anybody have any
+questions about this PA path analysis
+
+ align:start position:0%
+questions about this PA path analysis
+ 
+
+ align:start position:0%
+questions about this PA path analysis
+which is where we ended the class last
+
+ align:start position:0%
+which is where we ended the class last
+ 
+
+ align:start position:0%
+which is where we ended the class last
+time it's a way to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+find the probability that for two
+
+ align:start position:0%
+find the probability that for two
+ 
+
+ align:start position:0%
+find the probability that for two
+individuals when you know they're too
+
+ align:start position:0%
+individuals when you know they're too
+ 
+
+ align:start position:0%
+individuals when you know they're too
+related in related in some way but if
+
+ align:start position:0%
+related in related in some way but if
+ 
+
+ align:start position:0%
+related in related in some way but if
+you have
+
+ align:start position:0%
+you have
+ 
+
+ align:start position:0%
+you have
+their uh you
+
+ align:start position:0%
+their uh you
+ 
+
+ align:start position:0%
+their uh you
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+can draw the family tree you're able to
+
+ align:start position:0%
+can draw the family tree you're able to
+ 
+
+ align:start position:0%
+can draw the family tree you're able to
+then using path
+
+ align:start position:0%
+then using path
+ 
+
+ align:start position:0%
+then using path
+analysis you
+
+ align:start position:0%
+analysis you
+ 
+
+ align:start position:0%
+analysis you
+can find the probability that the two El
+
+ align:start position:0%
+can find the probability that the two El
+ 
+
+ align:start position:0%
+can find the probability that the two El
+deals at one Locus are identical or how
+
+ align:start position:0%
+deals at one Locus are identical or how
+ 
+
+ align:start position:0%
+deals at one Locus are identical or how
+many of them are going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identical it's called the inbreeding
+
+ align:start position:0%
+identical it's called the inbreeding
+ 
+
+ align:start position:0%
+identical it's called the inbreeding
+coefficient or the coefficient of
+
+ align:start position:0%
+coefficient or the coefficient of
+ 
+
+ align:start position:0%
+coefficient or the coefficient of
+kinship uh both terms are
+
+ align:start position:0%
+kinship uh both terms are
+ 
+
+ align:start position:0%
+kinship uh both terms are
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+used but you can use the same thing to
+
+ align:start position:0%
+used but you can use the same thing to
+ 
+
+ align:start position:0%
+used but you can use the same thing to
+compute
+
+ align:start position:0%
+compute
+ 
+
+ align:start position:0%
+compute
+this how many genes do you get from your
+
+ align:start position:0%
+this how many genes do you get from your
+ 
+
+ align:start position:0%
+this how many genes do you get from your
+great-grandparent for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is the only slide from the
+
+ align:start position:0%
+right so this is the only slide from the
+ 
+
+ align:start position:0%
+right so this is the only slide from the
+previous uh the first class I didn't get
+
+ align:start position:0%
+previous uh the first class I didn't get
+ 
+
+ align:start position:0%
+previous uh the first class I didn't get
+to we were talking about Wilson's notes
+
+ align:start position:0%
+to we were talking about Wilson's notes
+ 
+
+ align:start position:0%
+to we were talking about Wilson's notes
+from EO Wilson's
+
+ align:start position:0%
+from EO Wilson's
+ 
+
+ align:start position:0%
+from EO Wilson's
+book we got these I read The Abridged
+
+ align:start position:0%
+book we got these I read The Abridged
+ 
+
+ align:start position:0%
+book we got these I read The Abridged
+Edition uh for making those notes
+
+ align:start position:0%
+Edition uh for making those notes
+ 
+
+ align:start position:0%
+Edition uh for making those notes
+but he talks about about the possibility
+
+ align:start position:0%
+but he talks about about the possibility
+ 
+
+ align:start position:0%
+but he talks about about the possibility
+of inbreeding taboos but when he
+
+ align:start position:0%
+of inbreeding taboos but when he
+ 
+
+ align:start position:0%
+of inbreeding taboos but when he
+introduces it he uses some more terms
+
+ align:start position:0%
+introduces it he uses some more terms
+ 
+
+ align:start position:0%
+introduces it he uses some more terms
+that are interesting he he talks
+
+ align:start position:0%
+that are interesting he he talks
+ 
+
+ align:start position:0%
+that are interesting he he talks
+introduces by defining the effective
+
+ align:start position:0%
+introduces by defining the effective
+ 
+
+ align:start position:0%
+introduces by defining the effective
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+number and that I've defined it at the
+
+ align:start position:0%
+number and that I've defined it at the
+ 
+
+ align:start position:0%
+number and that I've defined it at the
+bottom
+
+ align:start position:0%
+bottom
+ 
+
+ align:start position:0%
+bottom
+there the number of individuals in an
+
+ align:start position:0%
+there the number of individuals in an
+ 
+
+ align:start position:0%
+there the number of individuals in an
+ideal randomly breeding population with
+
+ align:start position:0%
+ideal randomly breeding population with
+ 
+
+ align:start position:0%
+ideal randomly breeding population with
+one:1 sex
+
+ align:start position:0%
+one:1 sex
+ 
+
+ align:start position:0%
+one:1 sex
+ratio that would have the same rate of
+
+ align:start position:0%
+ratio that would have the same rate of
+ 
+
+ align:start position:0%
+ratio that would have the same rate of
+heterozygosity decrease as the total
+
+ align:start position:0%
+heterozygosity decrease as the total
+ 
+
+ align:start position:0%
+heterozygosity decrease as the total
+population under
+
+ align:start position:0%
+population under
+ 
+
+ align:start position:0%
+population under
+consideration
+
+ align:start position:0%
+consideration
+ 
+
+ align:start position:0%
+consideration
+so it that's what makes it the effective
+
+ align:start position:0%
+so it that's what makes it the effective
+ 
+
+ align:start position:0%
+so it that's what makes it the effective
+population
+
+ align:start position:0%
+population
+ 
+
+ align:start position:0%
+population
+uh it's usually the smallest number you
+
+ align:start position:0%
+uh it's usually the smallest number you
+ 
+
+ align:start position:0%
+uh it's usually the smallest number you
+can have and and not have much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inbreeding at least you would not have
+
+ align:start position:0%
+inbreeding at least you would not have
+ 
+
+ align:start position:0%
+inbreeding at least you would not have
+any more inbreeding than you would if
+
+ align:start position:0%
+any more inbreeding than you would if
+ 
+
+ align:start position:0%
+any more inbreeding than you would if
+they were breed randomly in the whole
+
+ align:start position:0%
+they were breed randomly in the whole
+ 
+
+ align:start position:0%
+they were breed randomly in the whole
+the larger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+population and numbers aren't really big
+
+ align:start position:0%
+population and numbers aren't really big
+ 
+
+ align:start position:0%
+population and numbers aren't really big
+U they get as low as 10 in some animal
+
+ align:start position:0%
+U they get as low as 10 in some animal
+ 
+
+ align:start position:0%
+U they get as low as 10 in some animal
+some species but they often are more
+
+ align:start position:0%
+some species but they often are more
+ 
+
+ align:start position:0%
+some species but they often are more
+closer to
+
+ align:start position:0%
+closer to
+ 
+
+ align:start position:0%
+closer to
+100 um and then he talks about wri's
+
+ align:start position:0%
+100 um and then he talks about wri's
+ 
+
+ align:start position:0%
+100 um and then he talks about wri's
+Island model now what that
+
+ align:start position:0%
+Island model now what that
+ 
+
+ align:start position:0%
+Island model now what that
+is he he has a model of a population
+
+ align:start position:0%
+is he he has a model of a population
+ 
+
+ align:start position:0%
+is he he has a model of a population
+that's divided up into smaller
+
+ align:start position:0%
+that's divided up into smaller
+ 
+
+ align:start position:0%
+that's divided up into smaller
+groups and we know that it's probably at
+
+ align:start position:0%
+groups and we know that it's probably at
+ 
+
+ align:start position:0%
+groups and we know that it's probably at
+least very roughly many populations are
+
+ align:start position:0%
+least very roughly many populations are
+ 
+
+ align:start position:0%
+least very roughly many populations are
+divided that way certainly humans were
+
+ align:start position:0%
+divided that way certainly humans were
+ 
+
+ align:start position:0%
+divided that way certainly humans were
+throughout much of our
+
+ align:start position:0%
+throughout much of our
+ 
+
+ align:start position:0%
+throughout much of our
+Evolutions uh that's why he calls it an
+
+ align:start position:0%
+Evolutions uh that's why he calls it an
+ 
+
+ align:start position:0%
+Evolutions uh that's why he calls it an
+is the island model because he's got the
+
+ align:start position:0%
+is the island model because he's got the
+ 
+
+ align:start position:0%
+is the island model because he's got the
+population divided into these different
+
+ align:start position:0%
+population divided into these different
+ 
+
+ align:start position:0%
+population divided into these different
+groups that are
+
+ align:start position:0%
+groups that are
+ 
+
+ align:start position:0%
+groups that are
+form he computed what well how big would
+
+ align:start position:0%
+form he computed what well how big would
+ 
+
+ align:start position:0%
+form he computed what well how big would
+those groups have to be you know in
+
+ align:start position:0%
+those groups have to be you know in
+ 
+
+ align:start position:0%
+those groups have to be you know in
+order to meet this effective population
+
+ align:start position:0%
+order to meet this effective population
+ 
+
+ align:start position:0%
+order to meet this effective population
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+definition uh and then what are the
+
+ align:start position:0%
+definition uh and then what are the
+ 
+
+ align:start position:0%
+definition uh and then what are the
+advantages of a population being divided
+
+ align:start position:0%
+advantages of a population being divided
+ 
+
+ align:start position:0%
+advantages of a population being divided
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+way and there are very clear advantages
+
+ align:start position:0%
+way and there are very clear advantages
+ 
+
+ align:start position:0%
+way and there are very clear advantages
+because when you have smaller groups
+
+ align:start position:0%
+because when you have smaller groups
+ 
+
+ align:start position:0%
+because when you have smaller groups
+you're going
+
+ align:start position:0%
+you're going
+ 
+
+ align:start position:0%
+you're going
+to the genetic differences that appear
+
+ align:start position:0%
+to the genetic differences that appear
+ 
+
+ align:start position:0%
+to the genetic differences that appear
+in the different groups will
+
+ align:start position:0%
+in the different groups will
+ 
+
+ align:start position:0%
+in the different groups will
+differ and so you will have small
+
+ align:start position:0%
+differ and so you will have small
+ 
+
+ align:start position:0%
+differ and so you will have small
+genetic differences appearing in these
+
+ align:start position:0%
+genetic differences appearing in these
+ 
+
+ align:start position:0%
+genetic differences appearing in these
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+groups and they'll be maintained if
+
+ align:start position:0%
+groups and they'll be maintained if
+ 
+
+ align:start position:0%
+groups and they'll be maintained if
+they're not interbreeding of course they
+
+ align:start position:0%
+they're not interbreeding of course they
+ 
+
+ align:start position:0%
+they're not interbreeding of course they
+would share the gene as soon as they
+
+ align:start position:0%
+would share the gene as soon as they
+ 
+
+ align:start position:0%
+would share the gene as soon as they
+exchanged if mates uh mating involved
+
+ align:start position:0%
+exchanged if mates uh mating involved
+ 
+
+ align:start position:0%
+exchanged if mates uh mating involved
+movement from one group to the other but
+
+ align:start position:0%
+movement from one group to the other but
+ 
+
+ align:start position:0%
+movement from one group to the other but
+if they're truly isolated that wouldn't
+
+ align:start position:0%
+if they're truly isolated that wouldn't
+ 
+
+ align:start position:0%
+if they're truly isolated that wouldn't
+be happening what would be the advantage
+
+ align:start position:0%
+be happening what would be the advantage
+ 
+
+ align:start position:0%
+be happening what would be the advantage
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+that what would be the advantage if a
+
+ align:start position:0%
+that what would be the advantage if a
+ 
+
+ align:start position:0%
+that what would be the advantage if a
+population were divided that way well
+
+ align:start position:0%
+population were divided that way well
+ 
+
+ align:start position:0%
+population were divided that way well
+think if there were some big change in
+
+ align:start position:0%
+think if there were some big change in
+ 
+
+ align:start position:0%
+think if there were some big change in
+the environment or new Predators
+
+ align:start position:0%
+the environment or new Predators
+ 
+
+ align:start position:0%
+the environment or new Predators
+appeared affecting all the
+
+ align:start position:0%
+appeared affecting all the
+ 
+
+ align:start position:0%
+appeared affecting all the
+groups well well if there's genetic
+
+ align:start position:0%
+groups well well if there's genetic
+ 
+
+ align:start position:0%
+groups well well if there's genetic
+differences in the groups then you're
+
+ align:start position:0%
+differences in the groups then you're
+ 
+
+ align:start position:0%
+differences in the groups then you're
+going to get better survival in some
+
+ align:start position:0%
+going to get better survival in some
+ 
+
+ align:start position:0%
+going to get better survival in some
+groups than in
+
+ align:start position:0%
+groups than in
+ 
+
+ align:start position:0%
+groups than in
+others and that's what Wright uh was uh
+
+ align:start position:0%
+others and that's what Wright uh was uh
+ 
+
+ align:start position:0%
+others and that's what Wright uh was uh
+what his model was able to
+
+ align:start position:0%
+what his model was able to
+ 
+
+ align:start position:0%
+what his model was able to
+show and that's one of the and one of
+
+ align:start position:0%
+show and that's one of the and one of
+ 
+
+ align:start position:0%
+show and that's one of the and one of
+the consequences of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model many points points out these what
+
+ align:start position:0%
+model many points points out these what
+ 
+
+ align:start position:0%
+model many points points out these what
+we he calls opposed selection tendencies
+
+ align:start position:0%
+we he calls opposed selection tendencies
+ 
+
+ align:start position:0%
+we he calls opposed selection tendencies
+that affect soci soci ity two very
+
+ align:start position:0%
+that affect soci soci ity two very
+ 
+
+ align:start position:0%
+that affect soci soci ity two very
+different effects uh in small groups
+
+ align:start position:0%
+different effects uh in small groups
+ 
+
+ align:start position:0%
+different effects uh in small groups
+that you have a greater chance of
+
+ align:start position:0%
+that you have a greater chance of
+ 
+
+ align:start position:0%
+that you have a greater chance of
+inbreeding and
+
+ align:start position:0%
+inbreeding and
+ 
+
+ align:start position:0%
+inbreeding and
+inbreeding uh you generally lowers
+
+ align:start position:0%
+inbreeding uh you generally lowers
+ 
+
+ align:start position:0%
+inbreeding uh you generally lowers
+individual Fitness depresses performance
+
+ align:start position:0%
+individual Fitness depresses performance
+ 
+
+ align:start position:0%
+individual Fitness depresses performance
+lowers genetic adaptibility so that is
+
+ align:start position:0%
+lowers genetic adaptibility so that is
+ 
+
+ align:start position:0%
+lowers genetic adaptibility so that is
+more likely to
+
+ align:start position:0%
+more likely to
+ 
+
+ align:start position:0%
+more likely to
+happen uh especially if you're well
+
+ align:start position:0%
+happen uh especially if you're well
+ 
+
+ align:start position:0%
+happen uh especially if you're well
+below that effective population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number but in the small groups of
+
+ align:start position:0%
+number but in the small groups of
+ 
+
+ align:start position:0%
+number but in the small groups of
+related individuals there would be very
+
+ align:start position:0%
+related individuals there would be very
+ 
+
+ align:start position:0%
+related individuals there would be very
+clear advantages because of Greater
+
+ align:start position:0%
+clear advantages because of Greater
+ 
+
+ align:start position:0%
+clear advantages because of Greater
+amounts of altruistic behavior and close
+
+ align:start position:0%
+amounts of altruistic behavior and close
+ 
+
+ align:start position:0%
+amounts of altruistic behavior and close
+cooperation in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+groups and then he talks about a slight
+
+ align:start position:0%
+groups and then he talks about a slight
+ 
+
+ align:start position:0%
+groups and then he talks about a slight
+a somewhat different concept assortative
+
+ align:start position:0%
+a somewhat different concept assortative
+ 
+
+ align:start position:0%
+a somewhat different concept assortative
+mating also known as homogamy and this
+
+ align:start position:0%
+mating also known as homogamy and this
+ 
+
+ align:start position:0%
+mating also known as homogamy and this
+is a tendency you find in all uh animal
+
+ align:start position:0%
+is a tendency you find in all uh animal
+ 
+
+ align:start position:0%
+is a tendency you find in all uh animal
+groups and certainly in humans a
+
+ align:start position:0%
+groups and certainly in humans a
+ 
+
+ align:start position:0%
+groups and certainly in humans a
+tendency to choose a mate that looks
+
+ align:start position:0%
+tendency to choose a mate that looks
+ 
+
+ align:start position:0%
+tendency to choose a mate that looks
+similar to oneself or one's close
+
+ align:start position:0%
+similar to oneself or one's close
+ 
+
+ align:start position:0%
+similar to oneself or one's close
+relatives
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh and that what does that mean well it
+
+ align:start position:0%
+uh and that what does that mean well it
+ 
+
+ align:start position:0%
+uh and that what does that mean well it
+probably means that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+group I was talking to the TA about my
+
+ align:start position:0%
+group I was talking to the TA about my
+ 
+
+ align:start position:0%
+group I was talking to the TA about my
+worries that the second projector will
+
+ align:start position:0%
+worries that the second projector will
+ 
+
+ align:start position:0%
+worries that the second projector will
+go out too it's a small small chance
+
+ align:start position:0%
+go out too it's a small small chance
+ 
+
+ align:start position:0%
+go out too it's a small small chance
+it's in the connection but I
+
+ align:start position:0%
+it's in the connection but I
+ 
+
+ align:start position:0%
+it's in the connection but I
+don't so
+
+ align:start position:0%
+don't so
+ 
+
+ align:start position:0%
+don't so
+far so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what would be if you're going to always
+
+ align:start position:0%
+what would be if you're going to always
+ 
+
+ align:start position:0%
+what would be if you're going to always
+choose a mate someone that looks similar
+
+ align:start position:0%
+choose a mate someone that looks similar
+ 
+
+ align:start position:0%
+choose a mate someone that looks similar
+to yourself then the chances that you
+
+ align:start position:0%
+to yourself then the chances that you
+ 
+
+ align:start position:0%
+to yourself then the chances that you
+share genes of course are might be
+
+ align:start position:0%
+share genes of course are might be
+ 
+
+ align:start position:0%
+share genes of course are might be
+greater but that's only in a relatively
+
+ align:start position:0%
+greater but that's only in a relatively
+ 
+
+ align:start position:0%
+greater but that's only in a relatively
+small number of genes that affect the
+
+ align:start position:0%
+small number of genes that affect the
+ 
+
+ align:start position:0%
+small number of genes that affect the
+superficial
+
+ align:start position:0%
+superficial
+ 
+
+ align:start position:0%
+superficial
+appearance all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that was the end of that class
+
+ align:start position:0%
+right that was the end of that class
+ 
+
+ align:start position:0%
+right that was the end of that class
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I ask you to read the chapter on
+
+ align:start position:0%
+then I ask you to read the chapter on
+ 
+
+ align:start position:0%
+then I ask you to read the chapter on
+genes genetic influences on social
+
+ align:start position:0%
+genes genetic influences on social
+ 
+
+ align:start position:0%
+genes genetic influences on social
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+uh we want to know the difference
+
+ align:start position:0%
+uh we want to know the difference
+ 
+
+ align:start position:0%
+uh we want to know the difference
+between genetic
+
+ align:start position:0%
+between genetic
+ 
+
+ align:start position:0%
+between genetic
+determinants of Behavioral
+
+ align:start position:0%
+determinants of Behavioral
+ 
+
+ align:start position:0%
+determinants of Behavioral
+traits genetic determination and what
+
+ align:start position:0%
+traits genetic determination and what
+ 
+
+ align:start position:0%
+traits genetic determination and what
+sociobiologists uh what their view of
+
+ align:start position:0%
+sociobiologists uh what their view of
+ 
+
+ align:start position:0%
+sociobiologists uh what their view of
+concerning genes and behavior is because
+
+ align:start position:0%
+concerning genes and behavior is because
+ 
+
+ align:start position:0%
+concerning genes and behavior is because
+you know that they've been accused a lot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of basically saying genes are us you
+
+ align:start position:0%
+of basically saying genes are us you
+ 
+
+ align:start position:0%
+of basically saying genes are us you
+know major Trends are
+
+ align:start position:0%
+know major Trends are
+ 
+
+ align:start position:0%
+know major Trends are
+genetic uh do the genes determine the
+
+ align:start position:0%
+genetic uh do the genes determine the
+ 
+
+ align:start position:0%
+genetic uh do the genes determine the
+development of specific social behaviors
+
+ align:start position:0%
+development of specific social behaviors
+ 
+
+ align:start position:0%
+development of specific social behaviors
+and first of all I want you to think
+
+ align:start position:0%
+and first of all I want you to think
+ 
+
+ align:start position:0%
+and first of all I want you to think
+back to our discussion of ethology we
+
+ align:start position:0%
+back to our discussion of ethology we
+ 
+
+ align:start position:0%
+back to our discussion of ethology we
+talked about Conor Lawrence and fixed
+
+ align:start position:0%
+talked about Conor Lawrence and fixed
+ 
+
+ align:start position:0%
+talked about Conor Lawrence and fixed
+action
+
+ align:start position:0%
+action
+ 
+
+ align:start position:0%
+action
+patterns because ethology was founded on
+
+ align:start position:0%
+patterns because ethology was founded on
+ 
+
+ align:start position:0%
+patterns because ethology was founded on
+the basis of the hereditability
+
+ align:start position:0%
+the basis of the hereditability
+ 
+
+ align:start position:0%
+the basis of the hereditability
+fixed action patterns and many of them
+
+ align:start position:0%
+fixed action patterns and many of them
+ 
+
+ align:start position:0%
+fixed action patterns and many of them
+are of course social
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior but we also knew that a fixed
+
+ align:start position:0%
+behavior but we also knew that a fixed
+ 
+
+ align:start position:0%
+behavior but we also knew that a fixed
+action pattern is not you know totally
+
+ align:start position:0%
+action pattern is not you know totally
+ 
+
+ align:start position:0%
+action pattern is not you know totally
+determined by the genes it it depends on
+
+ align:start position:0%
+determined by the genes it it depends on
+ 
+
+ align:start position:0%
+determined by the genes it it depends on
+motivational
+
+ align:start position:0%
+motivational
+ 
+
+ align:start position:0%
+motivational
+levels uh and the motivational intensity
+
+ align:start position:0%
+levels uh and the motivational intensity
+ 
+
+ align:start position:0%
+levels uh and the motivational intensity
+is influenced by many environmental
+
+ align:start position:0%
+is influenced by many environmental
+ 
+
+ align:start position:0%
+is influenced by many environmental
+variables but the underlying action
+
+ align:start position:0%
+variables but the underlying action
+ 
+
+ align:start position:0%
+variables but the underlying action
+pattern especially on the motorcyle side
+
+ align:start position:0%
+pattern especially on the motorcyle side
+ 
+
+ align:start position:0%
+pattern especially on the motorcyle side
+the fixed motor pattern is considered
+
+ align:start position:0%
+the fixed motor pattern is considered
+ 
+
+ align:start position:0%
+the fixed motor pattern is considered
+genetic and there's plenty of evidence
+
+ align:start position:0%
+genetic and there's plenty of evidence
+ 
+
+ align:start position:0%
+genetic and there's plenty of evidence
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+that you can even get mouse
+
+ align:start position:0%
+that you can even get mouse
+ 
+
+ align:start position:0%
+that you can even get mouse
+populations uh that are genetically
+
+ align:start position:0%
+populations uh that are genetically
+ 
+
+ align:start position:0%
+populations uh that are genetically
+different that
+
+ align:start position:0%
+different that
+ 
+
+ align:start position:0%
+different that
+show differences in details of grooming
+
+ align:start position:0%
+show differences in details of grooming
+ 
+
+ align:start position:0%
+show differences in details of grooming
+behavior um and all the members that are
+
+ align:start position:0%
+behavior um and all the members that are
+ 
+
+ align:start position:0%
+behavior um and all the members that are
+have one gene will one genetic variant
+
+ align:start position:0%
+have one gene will one genetic variant
+ 
+
+ align:start position:0%
+have one gene will one genetic variant
+will show one type and all the
+
+ align:start position:0%
+will show one type and all the
+ 
+
+ align:start position:0%
+will show one type and all the
+individuals are almost identical and the
+
+ align:start position:0%
+individuals are almost identical and the
+ 
+
+ align:start position:0%
+individuals are almost identical and the
+other groups are a little bit different
+
+ align:start position:0%
+other groups are a little bit different
+ 
+
+ align:start position:0%
+other groups are a little bit different
+certainly pretty strong evidence for
+
+ align:start position:0%
+certainly pretty strong evidence for
+ 
+
+ align:start position:0%
+certainly pretty strong evidence for
+genetic influences on that behavior that
+
+ align:start position:0%
+genetic influences on that behavior that
+ 
+
+ align:start position:0%
+genetic influences on that behavior that
+is only social behavior of course if
+
+ align:start position:0%
+is only social behavior of course if
+ 
+
+ align:start position:0%
+is only social behavior of course if
+there's grooming of individuals grooming
+
+ align:start position:0%
+there's grooming of individuals grooming
+ 
+
+ align:start position:0%
+there's grooming of individuals grooming
+of each other by in in a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+group but I want you next to remember
+
+ align:start position:0%
+group but I want you next to remember
+ 
+
+ align:start position:0%
+group but I want you next to remember
+that the nature nurture
+
+ align:start position:0%
+that the nature nurture
+ 
+
+ align:start position:0%
+that the nature nurture
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+uh the way that controversy is normally
+
+ align:start position:0%
+uh the way that controversy is normally
+ 
+
+ align:start position:0%
+uh the way that controversy is normally
+dealt with now especially in so soci
+
+ align:start position:0%
+dealt with now especially in so soci
+ 
+
+ align:start position:0%
+dealt with now especially in so soci
+biology is to remember that where are we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here that both nature and nurture are
+
+ align:start position:0%
+here that both nature and nurture are
+ 
+
+ align:start position:0%
+here that both nature and nurture are
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+involved you never have a purely genetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinations and the other thing that
+
+ align:start position:0%
+determinations and the other thing that
+ 
+
+ align:start position:0%
+determinations and the other thing that
+elcock points out here is that the
+
+ align:start position:0%
+elcock points out here is that the
+ 
+
+ align:start position:0%
+elcock points out here is that the
+genetic studies most relevant to
+
+ align:start position:0%
+genetic studies most relevant to
+ 
+
+ align:start position:0%
+genetic studies most relevant to
+sociobiology are not developmental
+
+ align:start position:0%
+sociobiology are not developmental
+ 
+
+ align:start position:0%
+sociobiology are not developmental
+genetics at all but population
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genetics they deal most directly with
+
+ align:start position:0%
+genetics they deal most directly with
+ 
+
+ align:start position:0%
+genetics they deal most directly with
+the consequences of population changes
+
+ align:start position:0%
+the consequences of population changes
+ 
+
+ align:start position:0%
+the consequences of population changes
+and the frequency of different variants
+
+ align:start position:0%
+and the frequency of different variants
+ 
+
+ align:start position:0%
+and the frequency of different variants
+or alals of given genes not with the
+
+ align:start position:0%
+or alals of given genes not with the
+ 
+
+ align:start position:0%
+or alals of given genes not with the
+means by which these Al shaper influence
+
+ align:start position:0%
+means by which these Al shaper influence
+ 
+
+ align:start position:0%
+means by which these Al shaper influence
+the pathways the biochemical Pathways of
+
+ align:start position:0%
+the pathways the biochemical Pathways of
+ 
+
+ align:start position:0%
+the pathways the biochemical Pathways of
+developing
+
+ align:start position:0%
+developing
+ 
+
+ align:start position:0%
+developing
+individuals and so a lot of times the
+
+ align:start position:0%
+individuals and so a lot of times the
+ 
+
+ align:start position:0%
+individuals and so a lot of times the
+criticisms that sociobiologists are
+
+ align:start position:0%
+criticisms that sociobiologists are
+ 
+
+ align:start position:0%
+criticisms that sociobiologists are
+genetic determinists about social
+
+ align:start position:0%
+genetic determinists about social
+ 
+
+ align:start position:0%
+genetic determinists about social
+behavior is because they don't
+
+ align:start position:0%
+behavior is because they don't
+ 
+
+ align:start position:0%
+behavior is because they don't
+distinguish between ultimate approximate
+
+ align:start position:0%
+distinguish between ultimate approximate
+ 
+
+ align:start position:0%
+distinguish between ultimate approximate
+research and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+biology and uh he considers
+
+ align:start position:0%
+biology and uh he considers
+ 
+
+ align:start position:0%
+biology and uh he considers
+that the main problem with these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+criticisms
+
+ align:start position:0%
+criticisms
+ 
+
+ align:start position:0%
+criticisms
+uh especially the critics that argue in
+
+ align:start position:0%
+uh especially the critics that argue in
+ 
+
+ align:start position:0%
+uh especially the critics that argue in
+this extreme passion they talk about
+
+ align:start position:0%
+this extreme passion they talk about
+ 
+
+ align:start position:0%
+this extreme passion they talk about
+they say sociobiologists are talking
+
+ align:start position:0%
+they say sociobiologists are talking
+ 
+
+ align:start position:0%
+they say sociobiologists are talking
+about traits that are hereditary fixed
+
+ align:start position:0%
+about traits that are hereditary fixed
+ 
+
+ align:start position:0%
+about traits that are hereditary fixed
+inevitable unchangeable except by Fus
+
+ align:start position:0%
+inevitable unchangeable except by Fus
+ 
+
+ align:start position:0%
+inevitable unchangeable except by Fus
+selection for hereditary Alternatives
+
+ align:start position:0%
+selection for hereditary Alternatives
+ 
+
+ align:start position:0%
+selection for hereditary Alternatives
+well we know that that's can't be true
+
+ align:start position:0%
+well we know that that's can't be true
+ 
+
+ align:start position:0%
+well we know that that's can't be true
+because of
+
+ align:start position:0%
+because of
+ 
+
+ align:start position:0%
+because of
+the of the nature of what we know about
+
+ align:start position:0%
+the of the nature of what we know about
+ 
+
+ align:start position:0%
+the of the nature of what we know about
+how genes influence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior but let me ask you about just
+
+ align:start position:0%
+behavior but let me ask you about just
+ 
+
+ align:start position:0%
+behavior but let me ask you about just
+leaving these slides for a minute what
+
+ align:start position:0%
+leaving these slides for a minute what
+ 
+
+ align:start position:0%
+leaving these slides for a minute what
+about these studies of ethology where
+
+ align:start position:0%
+about these studies of ethology where
+ 
+
+ align:start position:0%
+about these studies of ethology where
+they're dealing with like the cat um
+
+ align:start position:0%
+they're dealing with like the cat um
+ 
+
+ align:start position:0%
+they're dealing with like the cat um
+mating behavior for
+
+ align:start position:0%
+mating behavior for
+ 
+
+ align:start position:0%
+mating behavior for
+example and you can find relationships
+
+ align:start position:0%
+example and you can find relationships
+ 
+
+ align:start position:0%
+example and you can find relationships
+across species and the behavior is
+
+ align:start position:0%
+across species and the behavior is
+ 
+
+ align:start position:0%
+across species and the behavior is
+almost identical in different groups is
+
+ align:start position:0%
+almost identical in different groups is
+ 
+
+ align:start position:0%
+almost identical in different groups is
+that not social behavior and isn't it
+
+ align:start position:0%
+that not social behavior and isn't it
+ 
+
+ align:start position:0%
+that not social behavior and isn't it
+genetically
+
+ align:start position:0%
+genetically
+ 
+
+ align:start position:0%
+genetically
+determined and I would argue that it
+
+ align:start position:0%
+determined and I would argue that it
+ 
+
+ align:start position:0%
+determined and I would argue that it
+certainly is you know but there are many
+
+ align:start position:0%
+certainly is you know but there are many
+ 
+
+ align:start position:0%
+certainly is you know but there are many
+learned aspects as well okay so you will
+
+ align:start position:0%
+learned aspects as well okay so you will
+ 
+
+ align:start position:0%
+learned aspects as well okay so you will
+find individual differences in group
+
+ align:start position:0%
+find individual differences in group
+ 
+
+ align:start position:0%
+find individual differences in group
+especially on the stimulus
+
+ align:start position:0%
+especially on the stimulus
+ 
+
+ align:start position:0%
+especially on the stimulus
+side uh they develop different
+
+ align:start position:0%
+side uh they develop different
+ 
+
+ align:start position:0%
+side uh they develop different
+preferences and so forth even when the
+
+ align:start position:0%
+preferences and so forth even when the
+ 
+
+ align:start position:0%
+preferences and so forth even when the
+motor motor side is fairly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed then Alcock talks about this
+
+ align:start position:0%
+fixed then Alcock talks about this
+ 
+
+ align:start position:0%
+fixed then Alcock talks about this
+review done in 1998 so that was a long
+
+ align:start position:0%
+review done in 1998 so that was a long
+ 
+
+ align:start position:0%
+review done in 1998 so that was a long
+time after the books appeared in
+
+ align:start position:0%
+time after the books appeared in
+ 
+
+ align:start position:0%
+time after the books appeared in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh about uh the study he called it the
+
+ align:start position:0%
+uh about uh the study he called it the
+ 
+
+ align:start position:0%
+uh about uh the study he called it the
+study of genetically determined social
+
+ align:start position:0%
+study of genetically determined social
+ 
+
+ align:start position:0%
+study of genetically determined social
+behavior that was the main theme of the
+
+ align:start position:0%
+behavior that was the main theme of the
+ 
+
+ align:start position:0%
+behavior that was the main theme of the
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+review but Wilson actually devotes an
+
+ align:start position:0%
+review but Wilson actually devotes an
+ 
+
+ align:start position:0%
+review but Wilson actually devotes an
+entire chapter in his book to explain
+
+ align:start position:0%
+entire chapter in his book to explain
+ 
+
+ align:start position:0%
+entire chapter in his book to explain
+that although genes are essential for
+
+ align:start position:0%
+that although genes are essential for
+ 
+
+ align:start position:0%
+that although genes are essential for
+the development of behavior they don't
+
+ align:start position:0%
+the development of behavior they don't
+ 
+
+ align:start position:0%
+the development of behavior they don't
+determine it by
+
+ align:start position:0%
+determine it by
+ 
+
+ align:start position:0%
+determine it by
+themselves of course I think most people
+
+ align:start position:0%
+themselves of course I think most people
+ 
+
+ align:start position:0%
+themselves of course I think most people
+who look at genes and Behavior now would
+
+ align:start position:0%
+who look at genes and Behavior now would
+ 
+
+ align:start position:0%
+who look at genes and Behavior now would
+say that that would have to be
+
+ align:start position:0%
+say that that would have to be
+ 
+
+ align:start position:0%
+say that that would have to be
+true you can go to an extreme Like
+
+ align:start position:0%
+true you can go to an extreme Like
+ 
+
+ align:start position:0%
+true you can go to an extreme Like
+Richard Alexander did here he just
+
+ align:start position:0%
+Richard Alexander did here he just
+ 
+
+ align:start position:0%
+Richard Alexander did here he just
+points out
+
+ align:start position:0%
+points out
+ 
+
+ align:start position:0%
+points out
+that genetic
+
+ align:start position:0%
+that genetic
+ 
+
+ align:start position:0%
+that genetic
+determinism is a ridiculous argument if
+
+ align:start position:0%
+determinism is a ridiculous argument if
+ 
+
+ align:start position:0%
+determinism is a ridiculous argument if
+you exclude environment completely
+
+ align:start position:0%
+you exclude environment completely
+ 
+
+ align:start position:0%
+you exclude environment completely
+environment outside the DNA because it's
+
+ align:start position:0%
+environment outside the DNA because it's
+ 
+
+ align:start position:0%
+environment outside the DNA because it's
+always there and there's always
+
+ align:start position:0%
+always there and there's always
+ 
+
+ align:start position:0%
+always there and there's always
+variables which of course makes us
+
+ align:start position:0%
+variables which of course makes us
+ 
+
+ align:start position:0%
+variables which of course makes us
+wonder why the claim has been so
+
+ align:start position:0%
+wonder why the claim has been so
+ 
+
+ align:start position:0%
+wonder why the claim has been so
+persistent so I'll deal with that
+
+ align:start position:0%
+persistent so I'll deal with that
+ 
+
+ align:start position:0%
+persistent so I'll deal with that
+next but this is the way Al Al
+
+ align:start position:0%
+next but this is the way Al Al
+ 
+
+ align:start position:0%
+next but this is the way Al Al
+summarizes it in basically about at
+
+ align:start position:0%
+summarizes it in basically about at
+ 
+
+ align:start position:0%
+summarizes it in basically about at
+least the chemical environment of the
+
+ align:start position:0%
+least the chemical environment of the
+ 
+
+ align:start position:0%
+least the chemical environment of the
+DNA is always involved and that is
+
+ align:start position:0%
+DNA is always involved and that is
+ 
+
+ align:start position:0%
+DNA is always involved and that is
+very but I want to point out that a lot
+
+ align:start position:0%
+very but I want to point out that a lot
+ 
+
+ align:start position:0%
+very but I want to point out that a lot
+of people who argue against the
+
+ align:start position:0%
+of people who argue against the
+ 
+
+ align:start position:0%
+of people who argue against the
+influence of genes they're much more
+
+ align:start position:0%
+influence of genes they're much more
+ 
+
+ align:start position:0%
+influence of genes they're much more
+concerned they're much more they just
+
+ align:start position:0%
+concerned they're much more they just
+ 
+
+ align:start position:0%
+concerned they're much more they just
+feel that environment and learning are a
+
+ align:start position:0%
+feel that environment and learning are a
+ 
+
+ align:start position:0%
+feel that environment and learning are a
+lot more important okay that you can
+
+ align:start position:0%
+lot more important okay that you can
+ 
+
+ align:start position:0%
+lot more important okay that you can
+discount a lot of the genetic factors
+
+ align:start position:0%
+discount a lot of the genetic factors
+ 
+
+ align:start position:0%
+discount a lot of the genetic factors
+they also get upset by thinking about
+
+ align:start position:0%
+they also get upset by thinking about
+ 
+
+ align:start position:0%
+they also get upset by thinking about
+behavior in a totally deterministic way
+
+ align:start position:0%
+behavior in a totally deterministic way
+ 
+
+ align:start position:0%
+behavior in a totally deterministic way
+they basically object to the basic
+
+ align:start position:0%
+they basically object to the basic
+ 
+
+ align:start position:0%
+they basically object to the basic
+Assumption of the scientist who's trying
+
+ align:start position:0%
+Assumption of the scientist who's trying
+ 
+
+ align:start position:0%
+Assumption of the scientist who's trying
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+explain you know physical causes of the
+
+ align:start position:0%
+explain you know physical causes of the
+ 
+
+ align:start position:0%
+explain you know physical causes of the
+effects of whatever they're
+
+ align:start position:0%
+effects of whatever they're
+ 
+
+ align:start position:0%
+effects of whatever they're
+investigating whether it's Behavior or
+
+ align:start position:0%
+investigating whether it's Behavior or
+ 
+
+ align:start position:0%
+investigating whether it's Behavior or
+anything else I mean psychologists can't
+
+ align:start position:0%
+anything else I mean psychologists can't
+ 
+
+ align:start position:0%
+anything else I mean psychologists can't
+do their work without assuming that
+
+ align:start position:0%
+do their work without assuming that
+ 
+
+ align:start position:0%
+do their work without assuming that
+there are specific effects on
+
+ align:start position:0%
+there are specific effects on
+ 
+
+ align:start position:0%
+there are specific effects on
+Behavior Uh including genetic
+
+ align:start position:0%
+Behavior Uh including genetic
+ 
+
+ align:start position:0%
+Behavior Uh including genetic
+effects and so there are people like it
+
+ align:start position:0%
+effects and so there are people like it
+ 
+
+ align:start position:0%
+effects and so there are people like it
+they don't like in general the
+
+ align:start position:0%
+they don't like in general the
+ 
+
+ align:start position:0%
+they don't like in general the
+deterministic approach that scientists
+
+ align:start position:0%
+deterministic approach that scientists
+ 
+
+ align:start position:0%
+deterministic approach that scientists
+take so it's a lot of times the
+
+ align:start position:0%
+take so it's a lot of times the
+ 
+
+ align:start position:0%
+take so it's a lot of times the
+criticisms of those people is much
+
+ align:start position:0%
+criticisms of those people is much
+ 
+
+ align:start position:0%
+criticisms of those people is much
+broader than just talking about
+
+ align:start position:0%
+broader than just talking about
+ 
+
+ align:start position:0%
+broader than just talking about
+sociobiology but sociobiology is what
+
+ align:start position:0%
+sociobiology but sociobiology is what
+ 
+
+ align:start position:0%
+sociobiology but sociobiology is what
+figures their ey more than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anything so this is an enduring myth
+
+ align:start position:0%
+anything so this is an enduring myth
+ 
+
+ align:start position:0%
+anything so this is an enduring myth
+according to
+
+ align:start position:0%
+according to
+ 
+
+ align:start position:0%
+according to
+elcock despite the fact that all
+
+ align:start position:0%
+elcock despite the fact that all
+ 
+
+ align:start position:0%
+elcock despite the fact that all
+biologists know that every trait of
+
+ align:start position:0%
+biologists know that every trait of
+ 
+
+ align:start position:0%
+biologists know that every trait of
+every organism develops through through
+
+ align:start position:0%
+every organism develops through through
+ 
+
+ align:start position:0%
+every organism develops through through
+this interaction of genes and
+
+ align:start position:0%
+this interaction of genes and
+ 
+
+ align:start position:0%
+this interaction of genes and
+environment but I think the myth
+
+ align:start position:0%
+environment but I think the myth
+ 
+
+ align:start position:0%
+environment but I think the myth
+persists they don't like this approach
+
+ align:start position:0%
+persists they don't like this approach
+ 
+
+ align:start position:0%
+persists they don't like this approach
+as I just pointed out for much more
+
+ align:start position:0%
+as I just pointed out for much more
+ 
+
+ align:start position:0%
+as I just pointed out for much more
+General reasons that have to do just
+
+ align:start position:0%
+General reasons that have to do just
+ 
+
+ align:start position:0%
+General reasons that have to do just
+with social biology so this is a
+
+ align:start position:0%
+with social biology so this is a
+ 
+
+ align:start position:0%
+with social biology so this is a
+convenience Truman to set it up like
+
+ align:start position:0%
+convenience Truman to set it up like
+ 
+
+ align:start position:0%
+convenience Truman to set it up like
+that I think it's the nature of human
+
+ align:start position:0%
+that I think it's the nature of human
+ 
+
+ align:start position:0%
+that I think it's the nature of human
+psychology we believe in our ability to
+
+ align:start position:0%
+psychology we believe in our ability to
+ 
+
+ align:start position:0%
+psychology we believe in our ability to
+change our behavior and other people's
+
+ align:start position:0%
+change our behavior and other people's
+ 
+
+ align:start position:0%
+change our behavior and other people's
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+and for many people the flexibility of
+
+ align:start position:0%
+and for many people the flexibility of
+ 
+
+ align:start position:0%
+and for many people the flexibility of
+human behavior is taken as mistakenly
+
+ align:start position:0%
+human behavior is taken as mistakenly
+ 
+
+ align:start position:0%
+human behavior is taken as mistakenly
+taken as evidence that cultural factors
+
+ align:start position:0%
+taken as evidence that cultural factors
+ 
+
+ align:start position:0%
+taken as evidence that cultural factors
+are the only real determinant of our
+
+ align:start position:0%
+are the only real determinant of our
+ 
+
+ align:start position:0%
+are the only real determinant of our
+actions in fact in some of the meetings
+
+ align:start position:0%
+actions in fact in some of the meetings
+ 
+
+ align:start position:0%
+actions in fact in some of the meetings
+where these arguments have come up uh
+
+ align:start position:0%
+where these arguments have come up uh
+ 
+
+ align:start position:0%
+where these arguments have come up uh
+people usually outside of sociobiology
+
+ align:start position:0%
+people usually outside of sociobiology
+ 
+
+ align:start position:0%
+people usually outside of sociobiology
+of course or behavioral
+
+ align:start position:0%
+of course or behavioral
+ 
+
+ align:start position:0%
+of course or behavioral
+biology we argue that culture is the
+
+ align:start position:0%
+biology we argue that culture is the
+ 
+
+ align:start position:0%
+biology we argue that culture is the
+only real determinant of human
+
+ align:start position:0%
+only real determinant of human
+ 
+
+ align:start position:0%
+only real determinant of human
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+and then I also feel that championing
+
+ align:start position:0%
+and then I also feel that championing
+ 
+
+ align:start position:0%
+and then I also feel that championing
+Free Will and freedom of action is
+
+ align:start position:0%
+Free Will and freedom of action is
+ 
+
+ align:start position:0%
+Free Will and freedom of action is
+pretty understandably very popular in
+
+ align:start position:0%
+pretty understandably very popular in
+ 
+
+ align:start position:0%
+pretty understandably very popular in
+fact I think humans haven't evolved an
+
+ align:start position:0%
+fact I think humans haven't evolved an
+ 
+
+ align:start position:0%
+fact I think humans haven't evolved an
+enthusiasm for freedom of action and a
+
+ align:start position:0%
+enthusiasm for freedom of action and a
+ 
+
+ align:start position:0%
+enthusiasm for freedom of action and a
+belief in Free Will so I think we should
+
+ align:start position:0%
+belief in Free Will so I think we should
+ 
+
+ align:start position:0%
+belief in Free Will so I think we should
+be thinking like sociobiologists about
+
+ align:start position:0%
+be thinking like sociobiologists about
+ 
+
+ align:start position:0%
+be thinking like sociobiologists about
+that why do does everybody feel that I
+
+ align:start position:0%
+that why do does everybody feel that I
+ 
+
+ align:start position:0%
+that why do does everybody feel that I
+mean yes there are some intellectuals
+
+ align:start position:0%
+mean yes there are some intellectuals
+ 
+
+ align:start position:0%
+mean yes there are some intellectuals
+that take a very deterministic approach
+
+ align:start position:0%
+that take a very deterministic approach
+ 
+
+ align:start position:0%
+that take a very deterministic approach
+say we think we have free will but we
+
+ align:start position:0%
+say we think we have free will but we
+ 
+
+ align:start position:0%
+say we think we have free will but we
+don't and they're being philosophical
+
+ align:start position:0%
+don't and they're being philosophical
+ 
+
+ align:start position:0%
+don't and they're being philosophical
+but in their own behavior do they
+
+ align:start position:0%
+but in their own behavior do they
+ 
+
+ align:start position:0%
+but in their own behavior do they
+believe in Free Will you bet you know we
+
+ align:start position:0%
+believe in Free Will you bet you know we
+ 
+
+ align:start position:0%
+believe in Free Will you bet you know we
+all do I think it's inherited and I
+
+ align:start position:0%
+all do I think it's inherited and I
+ 
+
+ align:start position:0%
+all do I think it's inherited and I
+think it's adaptive to be that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way all
+
+ align:start position:0%
+way all
+ 
+
+ align:start position:0%
+way all
+right can a difference in one ilal
+
+ align:start position:0%
+right can a difference in one ilal
+ 
+
+ align:start position:0%
+right can a difference in one ilal
+change of
+
+ align:start position:0%
+change of
+ 
+
+ align:start position:0%
+change of
+behavior and he has this interesting
+
+ align:start position:0%
+behavior and he has this interesting
+ 
+
+ align:start position:0%
+behavior and he has this interesting
+figure
+
+ align:start position:0%
+figure
+ 
+
+ align:start position:0%
+figure
+31 to expl expl how a difference in one
+
+ align:start position:0%
+31 to expl expl how a difference in one
+ 
+
+ align:start position:0%
+31 to expl expl how a difference in one
+ilil and he has them represented by the
+
+ align:start position:0%
+ilil and he has them represented by the
+ 
+
+ align:start position:0%
+ilil and he has them represented by the
+capital and small B could result in a
+
+ align:start position:0%
+capital and small B could result in a
+ 
+
+ align:start position:0%
+capital and small B could result in a
+behavioral difference between two adults
+
+ align:start position:0%
+behavioral difference between two adults
+ 
+
+ align:start position:0%
+behavioral difference between two adults
+and it's a kind of multiplier effect
+
+ align:start position:0%
+and it's a kind of multiplier effect
+ 
+
+ align:start position:0%
+and it's a kind of multiplier effect
+this is the way I've reproduced it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so you start with the fertilized egg
+
+ align:start position:0%
+um so you start with the fertilized egg
+ 
+
+ align:start position:0%
+um so you start with the fertilized egg
+okay and here's one individual notice
+
+ align:start position:0%
+okay and here's one individual notice
+ 
+
+ align:start position:0%
+okay and here's one individual notice
+he's got these most of the genes are the
+
+ align:start position:0%
+he's got these most of the genes are the
+ 
+
+ align:start position:0%
+he's got these most of the genes are the
+same except that this Gene here and this
+
+ align:start position:0%
+same except that this Gene here and this
+ 
+
+ align:start position:0%
+same except that this Gene here and this
+could be you know Big B little
+
+ align:start position:0%
+could be you know Big B little
+ 
+
+ align:start position:0%
+could be you know Big B little
+B but it's different from this
+
+ align:start position:0%
+B but it's different from this
+ 
+
+ align:start position:0%
+B but it's different from this
+individual who has the two recessive
+
+ align:start position:0%
+individual who has the two recessive
+ 
+
+ align:start position:0%
+individual who has the two recessive
+genes the same Locus so his behavior if
+
+ align:start position:0%
+genes the same Locus so his behavior if
+ 
+
+ align:start position:0%
+genes the same Locus so his behavior if
+it's going to be affected will be any
+
+ align:start position:0%
+it's going to be affected will be any
+ 
+
+ align:start position:0%
+it's going to be affected will be any
+effect of that one
+
+ align:start position:0%
+effect of that one
+ 
+
+ align:start position:0%
+effect of that one
+alil and this person doesn't even have
+
+ align:start position:0%
+alil and this person doesn't even have
+ 
+
+ align:start position:0%
+alil and this person doesn't even have
+that alil so he's got to be affected by
+
+ align:start position:0%
+that alil so he's got to be affected by
+ 
+
+ align:start position:0%
+that alil so he's got to be affected by
+the other one okay it's just one gene so
+
+ align:start position:0%
+the other one okay it's just one gene so
+ 
+
+ align:start position:0%
+the other one okay it's just one gene so
+one protein
+
+ align:start position:0%
+one protein
+ 
+
+ align:start position:0%
+one protein
+and that genetic difference of course U
+
+ align:start position:0%
+and that genetic difference of course U
+ 
+
+ align:start position:0%
+and that genetic difference of course U
+will interact with the environment and
+
+ align:start position:0%
+will interact with the environment and
+ 
+
+ align:start position:0%
+will interact with the environment and
+the environment can be
+
+ align:start position:0%
+the environment can be
+ 
+
+ align:start position:0%
+the environment can be
+different so the effects if the
+
+ align:start position:0%
+different so the effects if the
+ 
+
+ align:start position:0%
+different so the effects if the
+environment's different to these two
+
+ align:start position:0%
+environment's different to these two
+ 
+
+ align:start position:0%
+environment's different to these two
+individuals you're going to get
+
+ align:start position:0%
+individuals you're going to get
+ 
+
+ align:start position:0%
+individuals you're going to get
+differences that affects the adult but
+
+ align:start position:0%
+differences that affects the adult but
+ 
+
+ align:start position:0%
+differences that affects the adult but
+then as they develop of course and
+
+ align:start position:0%
+then as they develop of course and
+ 
+
+ align:start position:0%
+then as they develop of course and
+neurons develop we know that there are
+
+ align:start position:0%
+neurons develop we know that there are
+ 
+
+ align:start position:0%
+neurons develop we know that there are
+many effects of environment on that that
+
+ align:start position:0%
+many effects of environment on that that
+ 
+
+ align:start position:0%
+many effects of environment on that that
+are independent of these but that in
+
+ align:start position:0%
+are independent of these but that in
+ 
+
+ align:start position:0%
+are independent of these but that in
+fact is Sol
+
+ align:start position:0%
+fact is Sol
+ 
+
+ align:start position:0%
+fact is Sol
+could make a difference in the way these
+
+ align:start position:0%
+could make a difference in the way these
+ 
+
+ align:start position:0%
+could make a difference in the way these
+things happen during development so the
+
+ align:start position:0%
+things happen during development so the
+ 
+
+ align:start position:0%
+things happen during development so the
+the effect
+
+ align:start position:0%
+the effect
+ 
+
+ align:start position:0%
+the effect
+here could be present throughout
+
+ align:start position:0%
+here could be present throughout
+ 
+
+ align:start position:0%
+here could be present throughout
+development with environments as long as
+
+ align:start position:0%
+development with environments as long as
+ 
+
+ align:start position:0%
+development with environments as long as
+they're slightly
+
+ align:start position:0%
+they're slightly
+ 
+
+ align:start position:0%
+they're slightly
+different you know could lead to pretty
+
+ align:start position:0%
+different you know could lead to pretty
+ 
+
+ align:start position:0%
+different you know could lead to pretty
+big differences in two adults in spite
+
+ align:start position:0%
+big differences in two adults in spite
+ 
+
+ align:start position:0%
+big differences in two adults in spite
+of that it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ill and yet the differences developed
+
+ align:start position:0%
+ill and yet the differences developed
+ 
+
+ align:start position:0%
+ill and yet the differences developed
+specifically because of that one genetic
+
+ align:start position:0%
+specifically because of that one genetic
+ 
+
+ align:start position:0%
+specifically because of that one genetic
+difference so that's all that we we're
+
+ align:start position:0%
+difference so that's all that we we're
+ 
+
+ align:start position:0%
+difference so that's all that we we're
+talking about here so let's talk exactly
+
+ align:start position:0%
+talking about here so let's talk exactly
+ 
+
+ align:start position:0%
+talking about here so let's talk exactly
+how and why the relative frequency of
+
+ align:start position:0%
+how and why the relative frequency of
+ 
+
+ align:start position:0%
+how and why the relative frequency of
+the two Al could change over multiple
+
+ align:start position:0%
+the two Al could change over multiple
+ 
+
+ align:start position:0%
+the two Al could change over multiple
+Generations let's raise the
+
+ align:start position:0%
+Generations let's raise the
+ 
+
+ align:start position:0%
+Generations let's raise the
+possibilities from what we know okay and
+
+ align:start position:0%
+possibilities from what we know okay and
+ 
+
+ align:start position:0%
+possibilities from what we know okay and
+these are the things I could think
+
+ align:start position:0%
+these are the things I could think
+ 
+
+ align:start position:0%
+these are the things I could think
+of why B could increase and the
+
+ align:start position:0%
+of why B could increase and the
+ 
+
+ align:start position:0%
+of why B could increase and the
+recessive trait could
+
+ align:start position:0%
+recessive trait could
+ 
+
+ align:start position:0%
+recessive trait could
+decrease first of all if B the small the
+
+ align:start position:0%
+decrease first of all if B the small the
+ 
+
+ align:start position:0%
+decrease first of all if B the small the
+recessive trait resulted in death before
+
+ align:start position:0%
+recessive trait resulted in death before
+ 
+
+ align:start position:0%
+recessive trait resulted in death before
+the age of reproduction more often than
+
+ align:start position:0%
+the age of reproduction more often than
+ 
+
+ align:start position:0%
+the age of reproduction more often than
+the dominant
+
+ align:start position:0%
+the dominant
+ 
+
+ align:start position:0%
+the dominant
+trait I'm just going to refer to them
+
+ align:start position:0%
+trait I'm just going to refer to them
+ 
+
+ align:start position:0%
+trait I'm just going to refer to them
+that way because of this that's a common
+
+ align:start position:0%
+that way because of this that's a common
+ 
+
+ align:start position:0%
+that way because of this that's a common
+way of
+
+ align:start position:0%
+way of
+ 
+
+ align:start position:0%
+way of
+expressing for one ilal the recessive
+
+ align:start position:0%
+expressing for one ilal the recessive
+ 
+
+ align:start position:0%
+expressing for one ilal the recessive
+and dominant Al infecting that
+
+ align:start position:0%
+and dominant Al infecting that
+ 
+
+ align:start position:0%
+and dominant Al infecting that
+Gene a second thing could be be could
+
+ align:start position:0%
+Gene a second thing could be be could
+ 
+
+ align:start position:0%
+Gene a second thing could be be could
+result in behavioral a behavioral
+
+ align:start position:0%
+result in behavioral a behavioral
+ 
+
+ align:start position:0%
+result in behavioral a behavioral
+difference that reduce the probability
+
+ align:start position:0%
+difference that reduce the probability
+ 
+
+ align:start position:0%
+difference that reduce the probability
+of successful reproduction in a
+
+ align:start position:0%
+of successful reproduction in a
+ 
+
+ align:start position:0%
+of successful reproduction in a
+particular environment but not in all
+
+ align:start position:0%
+particular environment but not in all
+ 
+
+ align:start position:0%
+particular environment but not in all
+environments so at least in that
+
+ align:start position:0%
+environments so at least in that
+ 
+
+ align:start position:0%
+environments so at least in that
+particular environment the genes would
+
+ align:start position:0%
+particular environment the genes would
+ 
+
+ align:start position:0%
+particular environment the genes would
+change in their
+
+ align:start position:0%
+change in their
+ 
+
+ align:start position:0%
+change in their
+frequency all we need is probability
+
+ align:start position:0%
+frequency all we need is probability
+ 
+
+ align:start position:0%
+frequency all we need is probability
+differences and if the recessive trait
+
+ align:start position:0%
+differences and if the recessive trait
+ 
+
+ align:start position:0%
+differences and if the recessive trait
+resulted in no change in probability of
+
+ align:start position:0%
+resulted in no change in probability of
+ 
+
+ align:start position:0%
+resulted in no change in probability of
+reproduction but it did reduce parental
+
+ align:start position:0%
+reproduction but it did reduce parental
+ 
+
+ align:start position:0%
+reproduction but it did reduce parental
+care that alone you see would reduce in
+
+ align:start position:0%
+care that alone you see would reduce in
+ 
+
+ align:start position:0%
+care that alone you see would reduce in
+would result because you would have
+
+ align:start position:0%
+would result because you would have
+ 
+
+ align:start position:0%
+would result because you would have
+statistically anyway less
+
+ align:start position:0%
+statistically anyway less
+ 
+
+ align:start position:0%
+statistically anyway less
+Survival Of The Offspring and that would
+
+ align:start position:0%
+Survival Of The Offspring and that would
+ 
+
+ align:start position:0%
+Survival Of The Offspring and that would
+be enough then to lead to changes over
+
+ align:start position:0%
+be enough then to lead to changes over
+ 
+
+ align:start position:0%
+be enough then to lead to changes over
+multiple Generations in the frequency of
+
+ align:start position:0%
+multiple Generations in the frequency of
+ 
+
+ align:start position:0%
+multiple Generations in the frequency of
+those two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+genes all right
+
+ align:start position:0%
+genes all right
+ 
+
+ align:start position:0%
+genes all right
+so so let's talk about breeding or
+
+ align:start position:0%
+so so let's talk about breeding or
+ 
+
+ align:start position:0%
+so so let's talk about breeding or
+behavioral traits we know that animals
+
+ align:start position:0%
+behavioral traits we know that animals
+ 
+
+ align:start position:0%
+behavioral traits we know that animals
+are bred for physical traits you know
+
+ align:start position:0%
+are bred for physical traits you know
+ 
+
+ align:start position:0%
+are bred for physical traits you know
+how dogs have been bred to Loop
+
+ align:start position:0%
+how dogs have been bred to Loop
+ 
+
+ align:start position:0%
+how dogs have been bred to Loop
+different okay and
+
+ align:start position:0%
+different okay and
+ 
+
+ align:start position:0%
+different okay and
+uh it's we see it especially in farm
+
+ align:start position:0%
+uh it's we see it especially in farm
+ 
+
+ align:start position:0%
+uh it's we see it especially in farm
+animals we've read beef cattle so
+
+ align:start position:0%
+animals we've read beef cattle so
+ 
+
+ align:start position:0%
+animals we've read beef cattle so
+they're meteor
+
+ align:start position:0%
+they're meteor
+ 
+
+ align:start position:0%
+they're meteor
+uh what about Behavior it's been done in
+
+ align:start position:0%
+uh what about Behavior it's been done in
+ 
+
+ align:start position:0%
+uh what about Behavior it's been done in
+the laboratory for a number of
+
+ align:start position:0%
+the laboratory for a number of
+ 
+
+ align:start position:0%
+the laboratory for a number of
+particular behavioral traits where you
+
+ align:start position:0%
+particular behavioral traits where you
+ 
+
+ align:start position:0%
+particular behavioral traits where you
+ignore the phys any physical differences
+
+ align:start position:0%
+ignore the phys any physical differences
+ 
+
+ align:start position:0%
+ignore the phys any physical differences
+and you only you have a measure of
+
+ align:start position:0%
+and you only you have a measure of
+ 
+
+ align:start position:0%
+and you only you have a measure of
+behavior for example how louds crickets
+
+ align:start position:0%
+behavior for example how louds crickets
+ 
+
+ align:start position:0%
+behavior for example how louds crickets
+sing and the ones that sing louder you
+
+ align:start position:0%
+sing and the ones that sing louder you
+ 
+
+ align:start position:0%
+sing and the ones that sing louder you
+can breed those with each other the ones
+
+ align:start position:0%
+can breed those with each other the ones
+ 
+
+ align:start position:0%
+can breed those with each other the ones
+that see uh sing less and at the
+
+ align:start position:0%
+that see uh sing less and at the
+ 
+
+ align:start position:0%
+that see uh sing less and at the
+beginning they're probably all singing
+
+ align:start position:0%
+beginning they're probably all singing
+ 
+
+ align:start position:0%
+beginning they're probably all singing
+but some of them don't sing as loud as
+
+ align:start position:0%
+but some of them don't sing as loud as
+ 
+
+ align:start position:0%
+but some of them don't sing as loud as
+as others and if you keep reading you
+
+ align:start position:0%
+as others and if you keep reading you
+ 
+
+ align:start position:0%
+as others and if you keep reading you
+will eventually end up with a loud
+
+ align:start position:0%
+will eventually end up with a loud
+ 
+
+ align:start position:0%
+will eventually end up with a loud
+singing group and a pretty silent group
+
+ align:start position:0%
+singing group and a pretty silent group
+ 
+
+ align:start position:0%
+singing group and a pretty silent group
+okay it's also been done with fruit
+
+ align:start position:0%
+okay it's also been done with fruit
+ 
+
+ align:start position:0%
+okay it's also been done with fruit
+flies this has been the most common and
+
+ align:start position:0%
+flies this has been the most common and
+ 
+
+ align:start position:0%
+flies this has been the most common and
+probably the most famous experiments
+
+ align:start position:0%
+probably the most famous experiments
+ 
+
+ align:start position:0%
+probably the most famous experiments
+with fruit flies are the production of
+
+ align:start position:0%
+with fruit flies are the production of
+ 
+
+ align:start position:0%
+with fruit flies are the production of
+learning mutants first produced by chip
+
+ align:start position:0%
+learning mutants first produced by chip
+ 
+
+ align:start position:0%
+learning mutants first produced by chip
+Quinn of this department he most of that
+
+ align:start position:0%
+Quinn of this department he most of that
+ 
+
+ align:start position:0%
+Quinn of this department he most of that
+work he did when he was at
+
+ align:start position:0%
+work he did when he was at
+ 
+
+ align:start position:0%
+work he did when he was at
+Princeton and he produced strains of
+
+ align:start position:0%
+Princeton and he produced strains of
+ 
+
+ align:start position:0%
+Princeton and he produced strains of
+fruit
+
+ align:start position:0%
+fruit
+ 
+
+ align:start position:0%
+fruit
+flies that in a particular learning task
+
+ align:start position:0%
+flies that in a particular learning task
+ 
+
+ align:start position:0%
+flies that in a particular learning task
+that he had set up to screen the fruit
+
+ align:start position:0%
+that he had set up to screen the fruit
+ 
+
+ align:start position:0%
+that he had set up to screen the fruit
+flies um that were particularly stupid
+
+ align:start position:0%
+flies um that were particularly stupid
+ 
+
+ align:start position:0%
+flies um that were particularly stupid
+and he named them after vegetables so he
+
+ align:start position:0%
+and he named them after vegetables so he
+ 
+
+ align:start position:0%
+and he named them after vegetables so he
+has rudaba he has turnup and such
+
+ align:start position:0%
+has rudaba he has turnup and such
+ 
+
+ align:start position:0%
+has rudaba he has turnup and such
+individuals and he became well known for
+
+ align:start position:0%
+individuals and he became well known for
+ 
+
+ align:start position:0%
+individuals and he became well known for
+that work the learning mutants and crw
+
+ align:start position:0%
+that work the learning mutants and crw
+ 
+
+ align:start position:0%
+that work the learning mutants and crw
+cl it's also been done
+
+ align:start position:0%
+cl it's also been done
+ 
+
+ align:start position:0%
+cl it's also been done
+uh in mice and in rats in mice they've
+
+ align:start position:0%
+uh in mice and in rats in mice they've
+ 
+
+ align:start position:0%
+uh in mice and in rats in mice they've
+had produce facial learning differences
+
+ align:start position:0%
+had produce facial learning differences
+ 
+
+ align:start position:0%
+had produce facial learning differences
+in different groups and groups that
+
+ align:start position:0%
+in different groups and groups that
+ 
+
+ align:start position:0%
+in different groups and groups that
+different in nest building activity you
+
+ align:start position:0%
+different in nest building activity you
+ 
+
+ align:start position:0%
+different in nest building activity you
+just select the ones that are most
+
+ align:start position:0%
+just select the ones that are most
+ 
+
+ align:start position:0%
+just select the ones that are most
+vigorous about building big nests and
+
+ align:start position:0%
+vigorous about building big nests and
+ 
+
+ align:start position:0%
+vigorous about building big nests and
+the ones that don't build such big nests
+
+ align:start position:0%
+the ones that don't build such big nests
+ 
+
+ align:start position:0%
+the ones that don't build such big nests
+and don't nest in such a vigorous way
+
+ align:start position:0%
+and don't nest in such a vigorous way
+ 
+
+ align:start position:0%
+and don't nest in such a vigorous way
+and you you event if you breed them
+
+ align:start position:0%
+and you you event if you breed them
+ 
+
+ align:start position:0%
+and you you event if you breed them
+selectively for those behavioral traits
+
+ align:start position:0%
+selectively for those behavioral traits
+ 
+
+ align:start position:0%
+selectively for those behavioral traits
+you'll eventually get groups that uh are
+
+ align:start position:0%
+you'll eventually get groups that uh are
+ 
+
+ align:start position:0%
+you'll eventually get groups that uh are
+very very different in the way they
+
+ align:start position:0%
+very very different in the way they
+ 
+
+ align:start position:0%
+very very different in the way they
+build nests and you can do the same
+
+ align:start position:0%
+build nests and you can do the same
+ 
+
+ align:start position:0%
+build nests and you can do the same
+thing for spatial learning problems and
+
+ align:start position:0%
+thing for spatial learning problems and
+ 
+
+ align:start position:0%
+thing for spatial learning problems and
+there the best known is the rad
+
+ align:start position:0%
+there the best known is the rad
+ 
+
+ align:start position:0%
+there the best known is the rad
+experiments where they had what was
+
+ align:start position:0%
+experiments where they had what was
+ 
+
+ align:start position:0%
+experiments where they had what was
+called the HEB Williams
+
+ align:start position:0%
+called the HEB Williams
+ 
+
+ align:start position:0%
+called the HEB Williams
+maze a maze a fairly complex maze that
+
+ align:start position:0%
+maze a maze a fairly complex maze that
+ 
+
+ align:start position:0%
+maze a maze a fairly complex maze that
+they could change easily easily they
+
+ align:start position:0%
+they could change easily easily they
+ 
+
+ align:start position:0%
+they could change easily easily they
+could change the problem so the rat
+
+ align:start position:0%
+could change the problem so the rat
+ 
+
+ align:start position:0%
+could change the problem so the rat
+would be trained on one then they change
+
+ align:start position:0%
+would be trained on one then they change
+ 
+
+ align:start position:0%
+would be trained on one then they change
+the barriers around uh test them again
+
+ align:start position:0%
+the barriers around uh test them again
+ 
+
+ align:start position:0%
+the barriers around uh test them again
+and do that repeatedly and they'd come
+
+ align:start position:0%
+and do that repeatedly and they'd come
+ 
+
+ align:start position:0%
+and do that repeatedly and they'd come
+up with a measure of how intelligent it
+
+ align:start position:0%
+up with a measure of how intelligent it
+ 
+
+ align:start position:0%
+up with a measure of how intelligent it
+was called a rat intelligence test how
+
+ align:start position:0%
+was called a rat intelligence test how
+ 
+
+ align:start position:0%
+was called a rat intelligence test how
+learn how smart are they in learning
+
+ align:start position:0%
+learn how smart are they in learning
+ 
+
+ align:start position:0%
+learn how smart are they in learning
+mazes and of course some of them learn
+
+ align:start position:0%
+mazes and of course some of them learn
+ 
+
+ align:start position:0%
+mazes and of course some of them learn
+much better than others and so again we
+
+ align:start position:0%
+much better than others and so again we
+ 
+
+ align:start position:0%
+much better than others and so again we
+can selectively breathe them for how
+
+ align:start position:0%
+can selectively breathe them for how
+ 
+
+ align:start position:0%
+can selectively breathe them for how
+well they learn the maze we can have the
+
+ align:start position:0%
+well they learn the maze we can have the
+ 
+
+ align:start position:0%
+well they learn the maze we can have the
+ones that learn better we'll interbreed
+
+ align:start position:0%
+ones that learn better we'll interbreed
+ 
+
+ align:start position:0%
+ones that learn better we'll interbreed
+with those the ones that learn more
+
+ align:start position:0%
+with those the ones that learn more
+ 
+
+ align:start position:0%
+with those the ones that learn more
+poorly and you end up with a maze bright
+
+ align:start position:0%
+poorly and you end up with a maze bright
+ 
+
+ align:start position:0%
+poorly and you end up with a maze bright
+maze dull strain and then you cont test
+
+ align:start position:0%
+maze dull strain and then you cont test
+ 
+
+ align:start position:0%
+maze dull strain and then you cont test
+for other differences in you know what
+
+ align:start position:0%
+for other differences in you know what
+ 
+
+ align:start position:0%
+for other differences in you know what
+else happens to us animal what happens
+
+ align:start position:0%
+else happens to us animal what happens
+ 
+
+ align:start position:0%
+else happens to us animal what happens
+in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+brain it was the fruit fly work that led
+
+ align:start position:0%
+brain it was the fruit fly work that led
+ 
+
+ align:start position:0%
+brain it was the fruit fly work that led
+most directly to study to Neuroscience
+
+ align:start position:0%
+most directly to study to Neuroscience
+ 
+
+ align:start position:0%
+most directly to study to Neuroscience
+studies in fact chip after he came here
+
+ align:start position:0%
+studies in fact chip after he came here
+ 
+
+ align:start position:0%
+studies in fact chip after he came here
+eventually did zero in on particular
+
+ align:start position:0%
+eventually did zero in on particular
+ 
+
+ align:start position:0%
+eventually did zero in on particular
+gene or particular uh factor in the
+
+ align:start position:0%
+gene or particular uh factor in the
+ 
+
+ align:start position:0%
+gene or particular uh factor in the
+brain that was found by other groups
+
+ align:start position:0%
+brain that was found by other groups
+ 
+
+ align:start position:0%
+brain that was found by other groups
+also to be involved in
+
+ align:start position:0%
+also to be involved in
+ 
+
+ align:start position:0%
+also to be involved in
+learning okay
+
+ align:start position:0%
+learning okay
+ 
+
+ align:start position:0%
+learning okay
+so and when we deal with humans you the
+
+ align:start position:0%
+so and when we deal with humans you the
+ 
+
+ align:start position:0%
+so and when we deal with humans you the
+best studies probably that
+
+ align:start position:0%
+best studies probably that
+ 
+
+ align:start position:0%
+best studies probably that
+support genetic influences on Behavior
+
+ align:start position:0%
+support genetic influences on Behavior
+ 
+
+ align:start position:0%
+support genetic influences on Behavior
+are the twin
+
+ align:start position:0%
+are the twin
+ 
+
+ align:start position:0%
+are the twin
+studies do you all know know the
+
+ align:start position:0%
+studies do you all know know the
+ 
+
+ align:start position:0%
+studies do you all know know the
+experiments using studying concordance
+
+ align:start position:0%
+experiments using studying concordance
+ 
+
+ align:start position:0%
+experiments using studying concordance
+rates first of all you have to collect
+
+ align:start position:0%
+rates first of all you have to collect
+ 
+
+ align:start position:0%
+rates first of all you have to collect
+large numbers of identical
+
+ align:start position:0%
+large numbers of identical
+ 
+
+ align:start position:0%
+large numbers of identical
+twins uh so that you that you can either
+
+ align:start position:0%
+twins uh so that you that you can either
+ 
+
+ align:start position:0%
+twins uh so that you that you can either
+test them or find out a lot about
+
+ align:start position:0%
+test them or find out a lot about
+ 
+
+ align:start position:0%
+test them or find out a lot about
+them for example do they get become
+
+ align:start position:0%
+them for example do they get become
+ 
+
+ align:start position:0%
+them for example do they get become
+schizophrenic and so that's certainly a
+
+ align:start position:0%
+schizophrenic and so that's certainly a
+ 
+
+ align:start position:0%
+schizophrenic and so that's certainly a
+big behavioral difference the ones that
+
+ align:start position:0%
+big behavioral difference the ones that
+ 
+
+ align:start position:0%
+big behavioral difference the ones that
+become schizophrenic and the that don't
+
+ align:start position:0%
+become schizophrenic and the that don't
+ 
+
+ align:start position:0%
+become schizophrenic and the that don't
+so you find out well if a a a one of the
+
+ align:start position:0%
+so you find out well if a a a one of the
+ 
+
+ align:start position:0%
+so you find out well if a a a one of the
+twins you find out is schizophrenic what
+
+ align:start position:0%
+twins you find out is schizophrenic what
+ 
+
+ align:start position:0%
+twins you find out is schizophrenic what
+is the probability that his twin will
+
+ align:start position:0%
+is the probability that his twin will
+ 
+
+ align:start position:0%
+is the probability that his twin will
+have schizophrenia do you know what the
+
+ align:start position:0%
+have schizophrenia do you know what the
+ 
+
+ align:start position:0%
+have schizophrenia do you know what the
+difference what the probability is it's
+
+ align:start position:0%
+difference what the probability is it's
+ 
+
+ align:start position:0%
+difference what the probability is it's
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+2/3 okay so it's not totally
+
+ align:start position:0%
+2/3 okay so it's not totally
+ 
+
+ align:start position:0%
+2/3 okay so it's not totally
+genetic and it's interesting that that
+
+ align:start position:0%
+genetic and it's interesting that that
+ 
+
+ align:start position:0%
+genetic and it's interesting that that
+2/3 for schizophrenia also applies to
+
+ align:start position:0%
+2/3 for schizophrenia also applies to
+ 
+
+ align:start position:0%
+2/3 for schizophrenia also applies to
+the kind of diabetes I
+
+ align:start position:0%
+the kind of diabetes I
+ 
+
+ align:start position:0%
+the kind of diabetes I
+have if I had a twin brother okay would
+
+ align:start position:0%
+have if I had a twin brother okay would
+ 
+
+ align:start position:0%
+have if I had a twin brother okay would
+have to be a brother because I'd have to
+
+ align:start position:0%
+have to be a brother because I'd have to
+ 
+
+ align:start position:0%
+have to be a brother because I'd have to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+monozygotic okay the brother would have
+
+ align:start position:0%
+monozygotic okay the brother would have
+ 
+
+ align:start position:0%
+monozygotic okay the brother would have
+a 2third chance of having the same thing
+
+ align:start position:0%
+a 2third chance of having the same thing
+ 
+
+ align:start position:0%
+a 2third chance of having the same thing
+the concordance rate is not
+
+ align:start position:0%
+the concordance rate is not
+ 
+
+ align:start position:0%
+the concordance rate is not
+100% so that that just means there has
+
+ align:start position:0%
+100% so that that just means there has
+ 
+
+ align:start position:0%
+100% so that that just means there has
+to be environmental factors that also
+
+ align:start position:0%
+to be environmental factors that also
+ 
+
+ align:start position:0%
+to be environmental factors that also
+have a strong influence and the degree
+
+ align:start position:0%
+have a strong influence and the degree
+ 
+
+ align:start position:0%
+have a strong influence and the degree
+to which the genetics and environment uh
+
+ align:start position:0%
+to which the genetics and environment uh
+ 
+
+ align:start position:0%
+to which the genetics and environment uh
+play roles can be estimated from this
+
+ align:start position:0%
+play roles can be estimated from this
+ 
+
+ align:start position:0%
+play roles can be estimated from this
+studying concordance
+
+ align:start position:0%
+studying concordance
+ 
+
+ align:start position:0%
+studying concordance
+streats okay and that has been done for
+
+ align:start position:0%
+streats okay and that has been done for
+ 
+
+ align:start position:0%
+streats okay and that has been done for
+a number of different
+
+ align:start position:0%
+a number of different
+ 
+
+ align:start position:0%
+a number of different
+things
+
+ align:start position:0%
+things
+ 
+
+ align:start position:0%
+things
+uh about the selective reading for
+
+ align:start position:0%
+uh about the selective reading for
+ 
+
+ align:start position:0%
+uh about the selective reading for
+Behavioral
+
+ align:start position:0%
+Behavioral
+ 
+
+ align:start position:0%
+Behavioral
+traits um I like many of the examples in
+
+ align:start position:0%
+traits um I like many of the examples in
+ 
+
+ align:start position:0%
+traits um I like many of the examples in
+this book by Temple grandon a very
+
+ align:start position:0%
+this book by Temple grandon a very
+ 
+
+ align:start position:0%
+this book by Temple grandon a very
+interesting lady she's actually I
+
+ align:start position:0%
+interesting lady she's actually I
+ 
+
+ align:start position:0%
+interesting lady she's actually I
+believe to come here to give a talk once
+
+ align:start position:0%
+believe to come here to give a talk once
+ 
+
+ align:start position:0%
+believe to come here to give a talk once
+at least I've heard her I think when I I
+
+ align:start position:0%
+at least I've heard her I think when I I
+ 
+
+ align:start position:0%
+at least I've heard her I think when I I
+heard her she was
+
+ align:start position:0%
+heard her she was
+ 
+
+ align:start position:0%
+heard her she was
+uh promoting one of her books probably
+
+ align:start position:0%
+uh promoting one of her books probably
+ 
+
+ align:start position:0%
+uh promoting one of her books probably
+this one at at the bookstore in Porter
+
+ align:start position:0%
+this one at at the bookstore in Porter
+ 
+
+ align:start position:0%
+this one at at the bookstore in Porter
+Square where they get authors to come
+
+ align:start position:0%
+Square where they get authors to come
+ 
+
+ align:start position:0%
+Square where they get authors to come
+every week and sometimes twice a week to
+
+ align:start position:0%
+every week and sometimes twice a week to
+ 
+
+ align:start position:0%
+every week and sometimes twice a week to
+give talks on their new
+
+ align:start position:0%
+give talks on their new
+ 
+
+ align:start position:0%
+give talks on their new
+books and
+
+ align:start position:0%
+books and
+ 
+
+ align:start position:0%
+books and
+uh I met her she actually signed I had a
+
+ align:start position:0%
+uh I met her she actually signed I had a
+ 
+
+ align:start position:0%
+uh I met her she actually signed I had a
+copy of her book she signed it and uh
+
+ align:start position:0%
+copy of her book she signed it and uh
+ 
+
+ align:start position:0%
+copy of her book she signed it and uh
+talked to me about the teaching I was
+
+ align:start position:0%
+talked to me about the teaching I was
+ 
+
+ align:start position:0%
+talked to me about the teaching I was
+doing at MIT and so forth gave me
+
+ align:start position:0%
+doing at MIT and so forth gave me
+ 
+
+ align:start position:0%
+doing at MIT and so forth gave me
+permission cartlon to use anything in
+
+ align:start position:0%
+permission cartlon to use anything in
+ 
+
+ align:start position:0%
+permission cartlon to use anything in
+her book in class yes okay
+
+ align:start position:0%
+her book in class yes okay
+ 
+
+ align:start position:0%
+her book in class yes okay
+so she points out various things that
+
+ align:start position:0%
+so she points out various things that
+ 
+
+ align:start position:0%
+so she points out various things that
+behavioral traits that dogs have been
+
+ align:start position:0%
+behavioral traits that dogs have been
+ 
+
+ align:start position:0%
+behavioral traits that dogs have been
+bred
+
+ align:start position:0%
+bred
+ 
+
+ align:start position:0%
+bred
+for they've been bred as you know for
+
+ align:start position:0%
+for they've been bred as you know for
+ 
+
+ align:start position:0%
+for they've been bred as you know for
+herting Ability for example the sheep
+
+ align:start position:0%
+herting Ability for example the sheep
+ 
+
+ align:start position:0%
+herting Ability for example the sheep
+dog you know if you want a herge sheet
+
+ align:start position:0%
+dog you know if you want a herge sheet
+ 
+
+ align:start position:0%
+dog you know if you want a herge sheet
+and you you really do need dogs to do it
+
+ align:start position:0%
+and you you really do need dogs to do it
+ 
+
+ align:start position:0%
+and you you really do need dogs to do it
+efficiently you don't want to choose
+
+ align:start position:0%
+efficiently you don't want to choose
+ 
+
+ align:start position:0%
+efficiently you don't want to choose
+just any dog no matter how smarter he is
+
+ align:start position:0%
+just any dog no matter how smarter he is
+ 
+
+ align:start position:0%
+just any dog no matter how smarter he is
+how loyal they are genetically different
+
+ align:start position:0%
+how loyal they are genetically different
+ 
+
+ align:start position:0%
+how loyal they are genetically different
+and they have been bred specifically for
+
+ align:start position:0%
+and they have been bred specifically for
+ 
+
+ align:start position:0%
+and they have been bred specifically for
+hurting so the sheep dog is very very
+
+ align:start position:0%
+hurting so the sheep dog is very very
+ 
+
+ align:start position:0%
+hurting so the sheep dog is very very
+good you're enhancing certain fixed
+
+ align:start position:0%
+good you're enhancing certain fixed
+ 
+
+ align:start position:0%
+good you're enhancing certain fixed
+action patterns and decreasing the
+
+ align:start position:0%
+action patterns and decreasing the
+ 
+
+ align:start position:0%
+action patterns and decreasing the
+influence of other fixed action patterns
+
+ align:start position:0%
+influence of other fixed action patterns
+ 
+
+ align:start position:0%
+influence of other fixed action patterns
+in a way
+
+ align:start position:0%
+in a way
+ 
+
+ align:start position:0%
+in a way
+you're you're enhancing
+
+ align:start position:0%
+you're you're enhancing
+ 
+
+ align:start position:0%
+you're you're enhancing
+stalking uh detecting and stalking
+
+ align:start position:0%
+stalking uh detecting and stalking
+ 
+
+ align:start position:0%
+stalking uh detecting and stalking
+behavior but you're inhibiting the later
+
+ align:start position:0%
+behavior but you're inhibiting the later
+ 
+
+ align:start position:0%
+behavior but you're inhibiting the later
+parts of the predatory behavior they
+
+ align:start position:0%
+parts of the predatory behavior they
+ 
+
+ align:start position:0%
+parts of the predatory behavior they
+never attack the Sheep you've reduced I
+
+ align:start position:0%
+never attack the Sheep you've reduced I
+ 
+
+ align:start position:0%
+never attack the Sheep you've reduced I
+mean this is predatory attack is also
+
+ align:start position:0%
+mean this is predatory attack is also
+ 
+
+ align:start position:0%
+mean this is predatory attack is also
+deter by multiple genes they're M
+
+ align:start position:0%
+deter by multiple genes they're M
+ 
+
+ align:start position:0%
+deter by multiple genes they're M
+multiple
+
+ align:start position:0%
+multiple
+ 
+
+ align:start position:0%
+multiple
+components it's not a single fixed
+
+ align:start position:0%
+components it's not a single fixed
+ 
+
+ align:start position:0%
+components it's not a single fixed
+action pattern really at least on the
+
+ align:start position:0%
+action pattern really at least on the
+ 
+
+ align:start position:0%
+action pattern really at least on the
+motor side then retrievers same kind of
+
+ align:start position:0%
+motor side then retrievers same kind of
+ 
+
+ align:start position:0%
+motor side then retrievers same kind of
+thing some dogs are terrible at
+
+ align:start position:0%
+thing some dogs are terrible at
+ 
+
+ align:start position:0%
+thing some dogs are terrible at
+retrievers but if you get a golden
+
+ align:start position:0%
+retrievers but if you get a golden
+ 
+
+ align:start position:0%
+retrievers but if you get a golden
+retriever or laboratory retriever very
+
+ align:start position:0%
+retriever or laboratory retriever very
+ 
+
+ align:start position:0%
+retriever or laboratory retriever very
+easy because it's part of their genetics
+
+ align:start position:0%
+easy because it's part of their genetics
+ 
+
+ align:start position:0%
+easy because it's part of their genetics
+and of course they're trained for
+
+ align:start position:0%
+and of course they're trained for
+ 
+
+ align:start position:0%
+and of course they're trained for
+hunting uh pointing I remember my father
+
+ align:start position:0%
+hunting uh pointing I remember my father
+ 
+
+ align:start position:0%
+hunting uh pointing I remember my father
+who hunted peasants he had a a pointer
+
+ align:start position:0%
+who hunted peasants he had a a pointer
+ 
+
+ align:start position:0%
+who hunted peasants he had a a pointer
+when I was a little kid you know and
+
+ align:start position:0%
+when I was a little kid you know and
+ 
+
+ align:start position:0%
+when I was a little kid you know and
+I I I still remember that dog you know
+
+ align:start position:0%
+I I I still remember that dog you know
+ 
+
+ align:start position:0%
+I I I still remember that dog you know
+because he was so incredibly not just so
+
+ align:start position:0%
+because he was so incredibly not just so
+ 
+
+ align:start position:0%
+because he was so incredibly not just so
+incredibly loyal to my father and not to
+
+ align:start position:0%
+incredibly loyal to my father and not to
+ 
+
+ align:start position:0%
+incredibly loyal to my father and not to
+his kids uh he was so good at what he
+
+ align:start position:0%
+his kids uh he was so good at what he
+ 
+
+ align:start position:0%
+his kids uh he was so good at what he
+did you know he would stay right at my
+
+ align:start position:0%
+did you know he would stay right at my
+ 
+
+ align:start position:0%
+did you know he would stay right at my
+father's side and he would I mean they
+
+ align:start position:0%
+father's side and he would I mean they
+ 
+
+ align:start position:0%
+father's side and he would I mean they
+used for their incredibly good senses
+
+ align:start position:0%
+used for their incredibly good senses
+ 
+
+ align:start position:0%
+used for their incredibly good senses
+but also for their
+
+ align:start position:0%
+but also for their
+ 
+
+ align:start position:0%
+but also for their
+ability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to detect the Pheasant and then stop and
+
+ align:start position:0%
+to detect the Pheasant and then stop and
+ 
+
+ align:start position:0%
+to detect the Pheasant and then stop and
+withhold their their their tendency to
+
+ align:start position:0%
+withhold their their their tendency to
+ 
+
+ align:start position:0%
+withhold their their their tendency to
+what try to grab it and attack it
+
+ align:start position:0%
+what try to grab it and attack it
+ 
+
+ align:start position:0%
+what try to grab it and attack it
+themselves you know peasants are mostly
+
+ align:start position:0%
+themselves you know peasants are mostly
+ 
+
+ align:start position:0%
+themselves you know peasants are mostly
+on the ground they they can fly to get
+
+ align:start position:0%
+on the ground they they can fly to get
+ 
+
+ align:start position:0%
+on the ground they they can fly to get
+away uh so he would become rigid and go
+
+ align:start position:0%
+away uh so he would become rigid and go
+ 
+
+ align:start position:0%
+away uh so he would become rigid and go
+into this posture it was very obvious
+
+ align:start position:0%
+into this posture it was very obvious
+ 
+
+ align:start position:0%
+into this posture it was very obvious
+and then little signal from my father
+
+ align:start position:0%
+and then little signal from my father
+ 
+
+ align:start position:0%
+and then little signal from my father
+then the dog would rush
+
+ align:start position:0%
+then the dog would rush
+ 
+
+ align:start position:0%
+then the dog would rush
+forward not to try to kill the Pheasant
+
+ align:start position:0%
+forward not to try to kill the Pheasant
+ 
+
+ align:start position:0%
+forward not to try to kill the Pheasant
+but to flush it so he would fly up
+
+ align:start position:0%
+but to flush it so he would fly up
+ 
+
+ align:start position:0%
+but to flush it so he would fly up
+because people that hunt like this
+
+ align:start position:0%
+because people that hunt like this
+ 
+
+ align:start position:0%
+because people that hunt like this
+usually wait if they can't shoot them in
+
+ align:start position:0%
+usually wait if they can't shoot them in
+ 
+
+ align:start position:0%
+usually wait if they can't shoot them in
+the air if they're not good enough shots
+
+ align:start position:0%
+the air if they're not good enough shots
+ 
+
+ align:start position:0%
+the air if they're not good enough shots
+for that then they
+
+ align:start position:0%
+for that then they
+ 
+
+ align:start position:0%
+for that then they
+don't succeed in getting the
+
+ align:start position:0%
+don't succeed in getting the
+ 
+
+ align:start position:0%
+don't succeed in getting the
+Pheasant and I remember the situation
+
+ align:start position:0%
+Pheasant and I remember the situation
+ 
+
+ align:start position:0%
+Pheasant and I remember the situation
+where there were two pheasants full
+
+ align:start position:0%
+where there were two pheasants full
+ 
+
+ align:start position:0%
+where there were two pheasants full
+pulled up and my father had a double
+
+ align:start position:0%
+pulled up and my father had a double
+ 
+
+ align:start position:0%
+pulled up and my father had a double
+barrel shotgun and he got both pheasants
+
+ align:start position:0%
+barrel shotgun and he got both pheasants
+ 
+
+ align:start position:0%
+barrel shotgun and he got both pheasants
+and then another little signal up the
+
+ align:start position:0%
+and then another little signal up the
+ 
+
+ align:start position:0%
+and then another little signal up the
+dog went to retrieve them so he could do
+
+ align:start position:0%
+dog went to retrieve them so he could do
+ 
+
+ align:start position:0%
+dog went to retrieve them so he could do
+both of these things retrieving pointing
+
+ align:start position:0%
+both of these things retrieving pointing
+ 
+
+ align:start position:0%
+both of these things retrieving pointing
+hunting uh and yet many many breeds of
+
+ align:start position:0%
+hunting uh and yet many many breeds of
+ 
+
+ align:start position:0%
+hunting uh and yet many many breeds of
+animals you know you cannot train them
+
+ align:start position:0%
+animals you know you cannot train them
+ 
+
+ align:start position:0%
+animals you know you cannot train them
+in fact they weren't very good with
+
+ align:start position:0%
+in fact they weren't very good with
+ 
+
+ align:start position:0%
+in fact they weren't very good with
+children so as his kids started growing
+
+ align:start position:0%
+children so as his kids started growing
+ 
+
+ align:start position:0%
+children so as his kids started growing
+older uh he got he gave the pointer to a
+
+ align:start position:0%
+older uh he got he gave the pointer to a
+ 
+
+ align:start position:0%
+older uh he got he gave the pointer to a
+farmer who had a lot of
+
+ align:start position:0%
+farmer who had a lot of
+ 
+
+ align:start position:0%
+farmer who had a lot of
+space we were now living in in a
+
+ align:start position:0%
+space we were now living in in a
+ 
+
+ align:start position:0%
+space we were now living in in a
+town when he did that hunting we were
+
+ align:start position:0%
+town when he did that hunting we were
+ 
+
+ align:start position:0%
+town when he did that hunting we were
+still outside of the town but then he
+
+ align:start position:0%
+still outside of the town but then he
+ 
+
+ align:start position:0%
+still outside of the town but then he
+moved into the town so his kids could go
+
+ align:start position:0%
+moved into the town so his kids could go
+ 
+
+ align:start position:0%
+moved into the town so his kids could go
+to school and
+
+ align:start position:0%
+to school and
+ 
+
+ align:start position:0%
+to school and
+uh got a doxent much better family
+
+ align:start position:0%
+uh got a doxent much better family
+ 
+
+ align:start position:0%
+uh got a doxent much better family
+dog okay so that's the dog I became most
+
+ align:start position:0%
+dog okay so that's the dog I became most
+ 
+
+ align:start position:0%
+dog okay so that's the dog I became most
+familiar with as I was growing up farm
+
+ align:start position:0%
+familiar with as I was growing up farm
+ 
+
+ align:start position:0%
+familiar with as I was growing up farm
+animals we know have been bred very
+
+ align:start position:0%
+animals we know have been bred very
+ 
+
+ align:start position:0%
+animals we know have been bred very
+specifically uh not just for their
+
+ align:start position:0%
+specifically uh not just for their
+ 
+
+ align:start position:0%
+specifically uh not just for their
+physical nature but you can't help but
+
+ align:start position:0%
+physical nature but you can't help but
+ 
+
+ align:start position:0%
+physical nature but you can't help but
+when you're breeding quarm animals you
+
+ align:start position:0%
+when you're breeding quarm animals you
+ 
+
+ align:start position:0%
+when you're breeding quarm animals you
+don't you'll tend to choose the the ones
+
+ align:start position:0%
+don't you'll tend to choose the the ones
+ 
+
+ align:start position:0%
+don't you'll tend to choose the the ones
+that aren't as aggressive so aggression
+
+ align:start position:0%
+that aren't as aggressive so aggression
+ 
+
+ align:start position:0%
+that aren't as aggressive so aggression
+has been
+
+ align:start position:0%
+has been
+ 
+
+ align:start position:0%
+has been
+reduced in the cattle for
+
+ align:start position:0%
+reduced in the cattle for
+ 
+
+ align:start position:0%
+reduced in the cattle for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+uh and the the amount of meat they
+
+ align:start position:0%
+uh and the the amount of meat they
+ 
+
+ align:start position:0%
+uh and the the amount of meat they
+produce has been increased for chickens
+
+ align:start position:0%
+produce has been increased for chickens
+ 
+
+ align:start position:0%
+produce has been increased for chickens
+of course it's egg Ling
+
+ align:start position:0%
+of course it's egg Ling
+ 
+
+ align:start position:0%
+of course it's egg Ling
+ability and that's been
+
+ align:start position:0%
+ability and that's been
+ 
+
+ align:start position:0%
+ability and that's been
+enhanced
+
+ align:start position:0%
+enhanced
+ 
+
+ align:start position:0%
+enhanced
+uh they also breed chickens of course
+
+ align:start position:0%
+uh they also breed chickens of course
+ 
+
+ align:start position:0%
+uh they also breed chickens of course
+for meat um Bulls it's a little
+
+ align:start position:0%
+for meat um Bulls it's a little
+ 
+
+ align:start position:0%
+for meat um Bulls it's a little
+different and you find bulls that are
+
+ align:start position:0%
+different and you find bulls that are
+ 
+
+ align:start position:0%
+different and you find bulls that are
+breeders uh at cattle farms in the US
+
+ align:start position:0%
+breeders uh at cattle farms in the US
+ 
+
+ align:start position:0%
+breeders uh at cattle farms in the US
+where they breed cattle again they
+
+ align:start position:0%
+where they breed cattle again they
+ 
+
+ align:start position:0%
+where they breed cattle again they
+choose bulls that AR they have to limit
+
+ align:start position:0%
+choose bulls that AR they have to limit
+ 
+
+ align:start position:0%
+choose bulls that AR they have to limit
+their aggression but you want big mey
+
+ align:start position:0%
+their aggression but you want big mey
+ 
+
+ align:start position:0%
+their aggression but you want big mey
+bulls because that's what you're trying
+
+ align:start position:0%
+bulls because that's what you're trying
+ 
+
+ align:start position:0%
+bulls because that's what you're trying
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+breed
+
+ align:start position:0%
+breed
+ 
+
+ align:start position:0%
+breed
+uh my grandfather knew all about this
+
+ align:start position:0%
+uh my grandfather knew all about this
+ 
+
+ align:start position:0%
+uh my grandfather knew all about this
+kind of breeding of the Bulls because I
+
+ align:start position:0%
+kind of breeding of the Bulls because I
+ 
+
+ align:start position:0%
+kind of breeding of the Bulls because I
+remember he wanted to let us see how he
+
+ align:start position:0%
+remember he wanted to let us see how he
+ 
+
+ align:start position:0%
+remember he wanted to let us see how he
+did it and he went in on Horseback and
+
+ align:start position:0%
+did it and he went in on Horseback and
+ 
+
+ align:start position:0%
+did it and he went in on Horseback and
+got a bull and here comes the bull and
+
+ align:start position:0%
+got a bull and here comes the bull and
+ 
+
+ align:start position:0%
+got a bull and here comes the bull and
+we were all right there in the yard Here
+
+ align:start position:0%
+we were all right there in the yard Here
+ 
+
+ align:start position:0%
+we were all right there in the yard Here
+Comes This Charging
+
+ align:start position:0%
+Comes This Charging
+ 
+
+ align:start position:0%
+Comes This Charging
+Bull you can imagine what we felt you
+
+ align:start position:0%
+Bull you can imagine what we felt you
+ 
+
+ align:start position:0%
+Bull you can imagine what we felt you
+know here's his Charging Bull but the
+
+ align:start position:0%
+know here's his Charging Bull but the
+ 
+
+ align:start position:0%
+know here's his Charging Bull but the
+bull well known to my grandfather was
+
+ align:start position:0%
+bull well known to my grandfather was
+ 
+
+ align:start position:0%
+bull well known to my grandfather was
+not interested in kids at all he was
+
+ align:start position:0%
+not interested in kids at all he was
+ 
+
+ align:start position:0%
+not interested in kids at all he was
+only interested in one thing those
+
+ align:start position:0%
+only interested in one thing those
+ 
+
+ align:start position:0%
+only interested in one thing those
+females in the yard so my cousin opened
+
+ align:start position:0%
+females in the yard so my cousin opened
+ 
+
+ align:start position:0%
+females in the yard so my cousin opened
+the gate the bll ran through and
+
+ align:start position:0%
+the gate the bll ran through and
+ 
+
+ align:start position:0%
+the gate the bll ran through and
+immediately began soliciting the
+
+ align:start position:0%
+immediately began soliciting the
+ 
+
+ align:start position:0%
+immediately began soliciting the
+attentions of the
+
+ align:start position:0%
+attentions of the
+ 
+
+ align:start position:0%
+attentions of the
+females okay but of course if you're
+
+ align:start position:0%
+females okay but of course if you're
+ 
+
+ align:start position:0%
+females okay but of course if you're
+using the Bulls for other things like
+
+ align:start position:0%
+using the Bulls for other things like
+ 
+
+ align:start position:0%
+using the Bulls for other things like
+bull fighting then you breed them
+
+ align:start position:0%
+bull fighting then you breed them
+ 
+
+ align:start position:0%
+bull fighting then you breed them
+differently and there are Bull breeders
+
+ align:start position:0%
+differently and there are Bull breeders
+ 
+
+ align:start position:0%
+differently and there are Bull breeders
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+Spain uh that specifically breed bulls
+
+ align:start position:0%
+Spain uh that specifically breed bulls
+ 
+
+ align:start position:0%
+Spain uh that specifically breed bulls
+for their
+
+ align:start position:0%
+for their
+ 
+
+ align:start position:0%
+for their
+ferocity in in bull
+
+ align:start position:0%
+ferocity in in bull
+ 
+
+ align:start position:0%
+ferocity in in bull
+fighting and we know of course we're
+
+ align:start position:0%
+fighting and we know of course we're
+ 
+
+ align:start position:0%
+fighting and we know of course we're
+more familiar with breeding of horses
+
+ align:start position:0%
+more familiar with breeding of horses
+ 
+
+ align:start position:0%
+more familiar with breeding of horses
+and they've bread for various things you
+
+ align:start position:0%
+and they've bread for various things you
+ 
+
+ align:start position:0%
+and they've bread for various things you
+know for speed for thorough
+
+ align:start position:0%
+know for speed for thorough
+ 
+
+ align:start position:0%
+know for speed for thorough
+bread uh for hurting
+
+ align:start position:0%
+bread uh for hurting
+ 
+
+ align:start position:0%
+bread uh for hurting
+cattle the quarter horse they're
+
+ align:start position:0%
+cattle the quarter horse they're
+ 
+
+ align:start position:0%
+cattle the quarter horse they're
+actually faster than thorough bread and
+
+ align:start position:0%
+actually faster than thorough bread and
+ 
+
+ align:start position:0%
+actually faster than thorough bread and
+for a quarter of a mile but they can't
+
+ align:start position:0%
+for a quarter of a mile but they can't
+ 
+
+ align:start position:0%
+for a quarter of a mile but they can't
+keep up with the thorough bread in a
+
+ align:start position:0%
+keep up with the thorough bread in a
+ 
+
+ align:start position:0%
+keep up with the thorough bread in a
+longer
+
+ align:start position:0%
+longer
+ 
+
+ align:start position:0%
+longer
+race
+
+ align:start position:0%
+race
+ 
+
+ align:start position:0%
+race
+uh and uh so there's SE several breeds
+
+ align:start position:0%
+uh and uh so there's SE several breeds
+ 
+
+ align:start position:0%
+uh and uh so there's SE several breeds
+of horses we know that work horses that
+
+ align:start position:0%
+of horses we know that work horses that
+ 
+
+ align:start position:0%
+of horses we know that work horses that
+tend to be bigger meteor stronger but
+
+ align:start position:0%
+tend to be bigger meteor stronger but
+ 
+
+ align:start position:0%
+tend to be bigger meteor stronger but
+slow lower but they're used to pull
+
+ align:start position:0%
+slow lower but they're used to pull
+ 
+
+ align:start position:0%
+slow lower but they're used to pull
+things pull wagons pull plows and so
+
+ align:start position:0%
+things pull wagons pull plows and so
+ 
+
+ align:start position:0%
+things pull wagons pull plows and so
+forth a few of them now but some some of
+
+ align:start position:0%
+forth a few of them now but some some of
+ 
+
+ align:start position:0%
+forth a few of them now but some some of
+them are still maintained so very
+
+ align:start position:0%
+them are still maintained so very
+ 
+
+ align:start position:0%
+them are still maintained so very
+specific breeding for Behavioral
+
+ align:start position:0%
+specific breeding for Behavioral
+ 
+
+ align:start position:0%
+specific breeding for Behavioral
+trays so this question concerns the
+
+ align:start position:0%
+trays so this question concerns the
+ 
+
+ align:start position:0%
+trays so this question concerns the
+problems that often happen when animals
+
+ align:start position:0%
+problems that often happen when animals
+ 
+
+ align:start position:0%
+problems that often happen when animals
+are bred for a single physical trait
+
+ align:start position:0%
+are bred for a single physical trait
+ 
+
+ align:start position:0%
+are bred for a single physical trait
+what happens to
+
+ align:start position:0%
+what happens to
+ 
+
+ align:start position:0%
+what happens to
+them it's common for behavioral problems
+
+ align:start position:0%
+them it's common for behavioral problems
+ 
+
+ align:start position:0%
+them it's common for behavioral problems
+to appear and this is discussed quite a
+
+ align:start position:0%
+to appear and this is discussed quite a
+ 
+
+ align:start position:0%
+to appear and this is discussed quite a
+bit in the Temple grandin's book or the
+
+ align:start position:0%
+bit in the Temple grandin's book or the
+ 
+
+ align:start position:0%
+bit in the Temple grandin's book or the
+example I lik was colli dogs because
+
+ align:start position:0%
+example I lik was colli dogs because
+ 
+
+ align:start position:0%
+example I lik was colli dogs because
+when I was growing up I remember it was
+
+ align:start position:0%
+when I was growing up I remember it was
+ 
+
+ align:start position:0%
+when I was growing up I remember it was
+po the the remember Lassie who I don't
+
+ align:start position:0%
+po the the remember Lassie who I don't
+ 
+
+ align:start position:0%
+po the the remember Lassie who I don't
+know if you even know who Lassie is but
+
+ align:start position:0%
+know if you even know who Lassie is but
+ 
+
+ align:start position:0%
+know if you even know who Lassie is but
+that was a popular dog and Hollywood
+
+ align:start position:0%
+that was a popular dog and Hollywood
+ 
+
+ align:start position:0%
+that was a popular dog and Hollywood
+movies and it was
+
+ align:start position:0%
+movies and it was
+ 
+
+ align:start position:0%
+movies and it was
+Lassie grew up before this intense
+
+ align:start position:0%
+Lassie grew up before this intense
+ 
+
+ align:start position:0%
+Lassie grew up before this intense
+breeding in this period started to
+
+ align:start position:0%
+breeding in this period started to
+ 
+
+ align:start position:0%
+breeding in this period started to
+change the appearance of Coles to make
+
+ align:start position:0%
+change the appearance of Coles to make
+ 
+
+ align:start position:0%
+change the appearance of Coles to make
+them have narrower and narrower skulls
+
+ align:start position:0%
+them have narrower and narrower skulls
+ 
+
+ align:start position:0%
+them have narrower and narrower skulls
+emphasize the needle nose so she said
+
+ align:start position:0%
+emphasize the needle nose so she said
+ 
+
+ align:start position:0%
+emphasize the needle nose so she said
+the result was brainless ice
+
+ align:start position:0%
+the result was brainless ice
+ 
+
+ align:start position:0%
+the result was brainless ice
+picks not like lassia at
+
+ align:start position:0%
+picks not like lassia at
+ 
+
+ align:start position:0%
+picks not like lassia at
+all and that's the danger if you just
+
+ align:start position:0%
+all and that's the danger if you just
+ 
+
+ align:start position:0%
+all and that's the danger if you just
+ignore behavior when you're breeding for
+
+ align:start position:0%
+ignore behavior when you're breeding for
+ 
+
+ align:start position:0%
+ignore behavior when you're breeding for
+a particular physical trait and this is
+
+ align:start position:0%
+a particular physical trait and this is
+ 
+
+ align:start position:0%
+a particular physical trait and this is
+not the only example uh breeds of dogs
+
+ align:start position:0%
+not the only example uh breeds of dogs
+ 
+
+ align:start position:0%
+not the only example uh breeds of dogs
+you know have particular problems
+
+ align:start position:0%
+you know have particular problems
+ 
+
+ align:start position:0%
+you know have particular problems
+usually it's that they get certain
+
+ align:start position:0%
+usually it's that they get certain
+ 
+
+ align:start position:0%
+usually it's that they get certain
+diseases or or coer spaniels for example
+
+ align:start position:0%
+diseases or or coer spaniels for example
+ 
+
+ align:start position:0%
+diseases or or coer spaniels for example
+many of them get type of epilepsy you
+
+ align:start position:0%
+many of them get type of epilepsy you
+ 
+
+ align:start position:0%
+many of them get type of epilepsy you
+know that's certainly a major behavioral
+
+ align:start position:0%
+know that's certainly a major behavioral
+ 
+
+ align:start position:0%
+know that's certainly a major behavioral
+problem U behavioral disease that they
+
+ align:start position:0%
+problem U behavioral disease that they
+ 
+
+ align:start position:0%
+problem U behavioral disease that they
+get because of this breeding for their
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+appearance so is it true that no genes
+
+ align:start position:0%
+appearance so is it true that no genes
+ 
+
+ align:start position:0%
+appearance so is it true that no genes
+for human behavior have been
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+found the argument was that we can
+
+ align:start position:0%
+found the argument was that we can
+ 
+
+ align:start position:0%
+found the argument was that we can
+dispense with the direct evidence for a
+
+ align:start position:0%
+dispense with the direct evidence for a
+ 
+
+ align:start position:0%
+dispense with the direct evidence for a
+genetic basis of human social forms in a
+
+ align:start position:0%
+genetic basis of human social forms in a
+ 
+
+ align:start position:0%
+genetic basis of human social forms in a
+single word no
+
+ align:start position:0%
+single word no
+ 
+
+ align:start position:0%
+single word no
+evidence and here's another quote from
+
+ align:start position:0%
+evidence and here's another quote from
+ 
+
+ align:start position:0%
+evidence and here's another quote from
+this book called not in our Jeans by the
+
+ align:start position:0%
+this book called not in our Jeans by the
+ 
+
+ align:start position:0%
+this book called not in our Jeans by the
+Harvard Professor
+
+ align:start position:0%
+Harvard Professor
+ 
+
+ align:start position:0%
+Harvard Professor
+lanon Rose a British professor in cing I
+
+ align:start position:0%
+lanon Rose a British professor in cing I
+ 
+
+ align:start position:0%
+lanon Rose a British professor in cing I
+don't remember where he's
+
+ align:start position:0%
+don't remember where he's
+ 
+
+ align:start position:0%
+don't remember where he's
+from he said no one has ever been able
+
+ align:start position:0%
+from he said no one has ever been able
+ 
+
+ align:start position:0%
+from he said no one has ever been able
+to relate any aspect of human social
+
+ align:start position:0%
+to relate any aspect of human social
+ 
+
+ align:start position:0%
+to relate any aspect of human social
+behavior to any particular gene or set
+
+ align:start position:0%
+behavior to any particular gene or set
+ 
+
+ align:start position:0%
+behavior to any particular gene or set
+of Dreams is that true still I don't
+
+ align:start position:0%
+of Dreams is that true still I don't
+ 
+
+ align:start position:0%
+of Dreams is that true still I don't
+think so uh first of all in your book
+
+ align:start position:0%
+think so uh first of all in your book
+ 
+
+ align:start position:0%
+think so uh first of all in your book
+there Alcock just points out the absence
+
+ align:start position:0%
+there Alcock just points out the absence
+ 
+
+ align:start position:0%
+there Alcock just points out the absence
+of evidence isn't really evidence of
+
+ align:start position:0%
+of evidence isn't really evidence of
+ 
+
+ align:start position:0%
+of evidence isn't really evidence of
+absent of non-involvement of genes and
+
+ align:start position:0%
+absent of non-involvement of genes and
+ 
+
+ align:start position:0%
+absent of non-involvement of genes and
+soical
+
+ align:start position:0%
+soical
+ 
+
+ align:start position:0%
+soical
+development uh I guess it seemed to him
+
+ align:start position:0%
+development uh I guess it seemed to him
+ 
+
+ align:start position:0%
+development uh I guess it seemed to him
+that way and that was the argument he
+
+ align:start position:0%
+that way and that was the argument he
+ 
+
+ align:start position:0%
+that way and that was the argument he
+made but I would point out more recent
+
+ align:start position:0%
+made but I would point out more recent
+ 
+
+ align:start position:0%
+made but I would point out more recent
+evidence for specific
+
+ align:start position:0%
+evidence for specific
+ 
+
+ align:start position:0%
+evidence for specific
+genes
+
+ align:start position:0%
+genes
+ 
+
+ align:start position:0%
+genes
+uh we say for a social
+
+ align:start position:0%
+uh we say for a social
+ 
+
+ align:start position:0%
+uh we say for a social
+behavior but I want you to keep in mind
+
+ align:start position:0%
+behavior but I want you to keep in mind
+ 
+
+ align:start position:0%
+behavior but I want you to keep in mind
+that even though specific genes are
+
+ align:start position:0%
+that even though specific genes are
+ 
+
+ align:start position:0%
+that even though specific genes are
+being found are correlated with with
+
+ align:start position:0%
+being found are correlated with with
+ 
+
+ align:start position:0%
+being found are correlated with with
+various social behaviors and especially
+
+ align:start position:0%
+various social behaviors and especially
+ 
+
+ align:start position:0%
+various social behaviors and especially
+behavioral problems they're
+
+ align:start position:0%
+behavioral problems they're
+ 
+
+ align:start position:0%
+behavioral problems they're
+not genes code for
+
+ align:start position:0%
+not genes code for
+ 
+
+ align:start position:0%
+not genes code for
+proteins okay and if we look at these
+
+ align:start position:0%
+proteins okay and if we look at these
+ 
+
+ align:start position:0%
+proteins okay and if we look at these
+behaviors these abnormalities in humans
+
+ align:start position:0%
+behaviors these abnormalities in humans
+ 
+
+ align:start position:0%
+behaviors these abnormalities in humans
+autism schizophrenia and other mental
+
+ align:start position:0%
+autism schizophrenia and other mental
+ 
+
+ align:start position:0%
+autism schizophrenia and other mental
+diseases attention deficit hyperactivity
+
+ align:start position:0%
+diseases attention deficit hyperactivity
+ 
+
+ align:start position:0%
+diseases attention deficit hyperactivity
+disorder yes there's genetic
+
+ align:start position:0%
+disorder yes there's genetic
+ 
+
+ align:start position:0%
+disorder yes there's genetic
+contribution to all of these there's
+
+ align:start position:0%
+contribution to all of these there's
+ 
+
+ align:start position:0%
+contribution to all of these there's
+always multiple genes involved
+
+ align:start position:0%
+always multiple genes involved
+ 
+
+ align:start position:0%
+always multiple genes involved
+environmental effects are still
+
+ align:start position:0%
+environmental effects are still
+ 
+
+ align:start position:0%
+environmental effects are still
+strong
+
+ align:start position:0%
+strong
+ 
+
+ align:start position:0%
+strong
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so how could a gene that has what
+
+ align:start position:0%
+so how could a gene that has what
+ 
+
+ align:start position:0%
+so how could a gene that has what
+appears to be maladaptive consequences
+
+ align:start position:0%
+appears to be maladaptive consequences
+ 
+
+ align:start position:0%
+appears to be maladaptive consequences
+be present in some animals or people
+
+ align:start position:0%
+be present in some animals or people
+ 
+
+ align:start position:0%
+be present in some animals or people
+today why wasn't it
+
+ align:start position:0%
+today why wasn't it
+ 
+
+ align:start position:0%
+today why wasn't it
+lost but the first thing I asked when I
+
+ align:start position:0%
+lost but the first thing I asked when I
+ 
+
+ align:start position:0%
+lost but the first thing I asked when I
+got diabetes at age 24 know what's this
+
+ align:start position:0%
+got diabetes at age 24 know what's this
+ 
+
+ align:start position:0%
+got diabetes at age 24 know what's this
+Dean doing around could have
+
+ align:start position:0%
+Dean doing around could have
+ 
+
+ align:start position:0%
+Dean doing around could have
+disappeared a thousand years
+
+ align:start position:0%
+disappeared a thousand years
+ 
+
+ align:start position:0%
+disappeared a thousand years
+ago first of all it could be a recent
+
+ align:start position:0%
+ago first of all it could be a recent
+ 
+
+ align:start position:0%
+ago first of all it could be a recent
+mutation and well be
+
+ align:start position:0%
+mutation and well be
+ 
+
+ align:start position:0%
+mutation and well be
+lost or maybe it has its bad effects
+
+ align:start position:0%
+lost or maybe it has its bad effects
+ 
+
+ align:start position:0%
+lost or maybe it has its bad effects
+after
+
+ align:start position:0%
+after
+ 
+
+ align:start position:0%
+after
+reproduction I said I got it at age
+
+ align:start position:0%
+reproduction I said I got it at age
+ 
+
+ align:start position:0%
+reproduction I said I got it at age
+24 you
+
+ align:start position:0%
+24 you
+ 
+
+ align:start position:0%
+24 you
+know during the age of
+
+ align:start position:0%
+know during the age of
+ 
+
+ align:start position:0%
+know during the age of
+reproduction many effects do occur later
+
+ align:start position:0%
+reproduction many effects do occur later
+ 
+
+ align:start position:0%
+reproduction many effects do occur later
+uh it may have effects only in certain
+
+ align:start position:0%
+uh it may have effects only in certain
+ 
+
+ align:start position:0%
+uh it may have effects only in certain
+environments if I were in an environment
+
+ align:start position:0%
+environments if I were in an environment
+ 
+
+ align:start position:0%
+environments if I were in an environment
+I wasn't exposed to same viruses I may
+
+ align:start position:0%
+I wasn't exposed to same viruses I may
+ 
+
+ align:start position:0%
+I wasn't exposed to same viruses I may
+never have gotten it it's an autoimmune
+
+ align:start position:0%
+never have gotten it it's an autoimmune
+ 
+
+ align:start position:0%
+never have gotten it it's an autoimmune
+disease triggered by
+
+ align:start position:0%
+disease triggered by
+ 
+
+ align:start position:0%
+disease triggered by
+viruses it's also of course because of
+
+ align:start position:0%
+viruses it's also of course because of
+ 
+
+ align:start position:0%
+viruses it's also of course because of
+modern Medical Treatments but it's also
+
+ align:start position:0%
+modern Medical Treatments but it's also
+ 
+
+ align:start position:0%
+modern Medical Treatments but it's also
+remember genetic swamping if you've
+
+ align:start position:0%
+remember genetic swamping if you've
+ 
+
+ align:start position:0%
+remember genetic swamping if you've
+forgotten what that is go back and read
+
+ align:start position:0%
+forgotten what that is go back and read
+ 
+
+ align:start position:0%
+forgotten what that is go back and read
+it it was in my notes and you can find
+
+ align:start position:0%
+it it was in my notes and you can find
+ 
+
+ align:start position:0%
+it it was in my notes and you can find
+it also on the web and then I'm posting
+
+ align:start position:0%
+it also on the web and then I'm posting
+ 
+
+ align:start position:0%
+it also on the web and then I'm posting
+these homework questions it's already at
+
+ align:start position:0%
+these homework questions it's already at
+ 
+
+ align:start position:0%
+these homework questions it's already at
+the end of the class here but I am
+
+ align:start position:0%
+the end of the class here but I am
+ 
+
+ align:start position:0%
+the end of the class here but I am
+willing to give you I want you to spend
+
+ align:start position:0%
+willing to give you I want you to spend
+ 
+
+ align:start position:0%
+willing to give you I want you to spend
+most of the time on this one the other
+
+ align:start position:0%
+most of the time on this one the other
+ 
+
+ align:start position:0%
+most of the time on this one the other
+should be easier for you if you have
+
+ align:start position:0%
+should be easier for you if you have
+ 
+
+ align:start position:0%
+should be easier for you if you have
+trouble with those I'm happy to give you
+
+ align:start position:0%
+trouble with those I'm happy to give you
+ 
+
+ align:start position:0%
+trouble with those I'm happy to give you
+hints I'm asking you to do these or
+
+ align:start position:0%
+hints I'm asking you to do these or
+ 
+
+ align:start position:0%
+hints I'm asking you to do these or
+similar to homework I gave last year
+
+ align:start position:0%
+similar to homework I gave last year
+ 
+
+ align:start position:0%
+similar to homework I gave last year
+because I want you to think think about
+
+ align:start position:0%
+because I want you to think think about
+ 
+
+ align:start position:0%
+because I want you to think think about
+these things and be clear about the type
+
+ align:start position:0%
+these things and be clear about the type
+ 
+
+ align:start position:0%
+these things and be clear about the type
+of thinking you need to do and this is
+
+ align:start position:0%
+of thinking you need to do and this is
+ 
+
+ align:start position:0%
+of thinking you need to do and this is
+the one that causes the most controversy
+
+ align:start position:0%
+the one that causes the most controversy
+ 
+
+ align:start position:0%
+the one that causes the most controversy
+so think about that and you can ask me
+
+ align:start position:0%
+so think about that and you can ask me
+ 
+
+ align:start position:0%
+so think about that and you can ask me
+about it on Friday if you wish and I'm
+
+ align:start position:0%
+about it on Friday if you wish and I'm
+ 
+
+ align:start position:0%
+about it on Friday if you wish and I'm
+happy to give you some suggestions
\ No newline at end of file
diff --git a/9lc7mxULRF0.txt b/9lc7mxULRF0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..26585631d101b50f11ddc589d309773088be2bff
--- /dev/null
+++ b/9lc7mxULRF0.txt
@@ -0,0 +1,1995 @@
+align:start position:0%
+ 
+the molecules and born-oppenheimer hilar
+
+ align:start position:0%
+the molecules and born-oppenheimer hilar
+ 
+
+ align:start position:0%
+the molecules and born-oppenheimer hilar
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh we all know that molecules are a
+
+ align:start position:0%
+okay oh we all know that molecules are a
+ 
+
+ align:start position:0%
+okay oh we all know that molecules are a
+lot harder to solve than atoms and even
+
+ align:start position:0%
+lot harder to solve than atoms and even
+ 
+
+ align:start position:0%
+lot harder to solve than atoms and even
+atoms are not that easy once you have
+
+ align:start position:0%
+atoms are not that easy once you have
+ 
+
+ align:start position:0%
+atoms are not that easy once you have
+more than one electron because of the
+
+ align:start position:0%
+more than one electron because of the
+ 
+
+ align:start position:0%
+more than one electron because of the
+electrostatic repulsion but the
+
+ align:start position:0%
+electrostatic repulsion but the
+ 
+
+ align:start position:0%
+electrostatic repulsion but the
+molecules are significantly different in
+
+ align:start position:0%
+molecules are significantly different in
+ 
+
+ align:start position:0%
+molecules are significantly different in
+that one of the greatest simplicity's
+
+ align:start position:0%
+that one of the greatest simplicity's
+ 
+
+ align:start position:0%
+that one of the greatest simplicity's
+that we had with atoms is that the atom
+
+ align:start position:0%
+that we had with atoms is that the atom
+ 
+
+ align:start position:0%
+that we had with atoms is that the atom
+is such at the potential created by the
+
+ align:start position:0%
+is such at the potential created by the
+ 
+
+ align:start position:0%
+is such at the potential created by the
+nucleus is fairly symmetric when you
+
+ align:start position:0%
+nucleus is fairly symmetric when you
+ 
+
+ align:start position:0%
+nucleus is fairly symmetric when you
+have a molecule you have separate nuclei
+
+ align:start position:0%
+have a molecule you have separate nuclei
+ 
+
+ align:start position:0%
+have a molecule you have separate nuclei
+and therefore your spherical symmetry is
+
+ align:start position:0%
+and therefore your spherical symmetry is
+ 
+
+ align:start position:0%
+and therefore your spherical symmetry is
+gone and whether you have one electron
+
+ align:start position:0%
+gone and whether you have one electron
+ 
+
+ align:start position:0%
+gone and whether you have one electron
+or more than one electron there's no
+
+ align:start position:0%
+or more than one electron there's no
+ 
+
+ align:start position:0%
+or more than one electron there's no
+spherical symmetry all our tools of
+
+ align:start position:0%
+spherical symmetry all our tools of
+ 
+
+ align:start position:0%
+spherical symmetry all our tools of
+angular momentum don't help us much we
+
+ align:start position:0%
+angular momentum don't help us much we
+ 
+
+ align:start position:0%
+angular momentum don't help us much we
+have to start the problem and new so the
+
+ align:start position:0%
+have to start the problem and new so the
+ 
+
+ align:start position:0%
+have to start the problem and new so the
+difficulty with molecules is basically
+
+ align:start position:0%
+difficulty with molecules is basically
+ 
+
+ align:start position:0%
+difficulty with molecules is basically
+that the potential for the electrons
+
+ align:start position:0%
+that the potential for the electrons
+ 
+
+ align:start position:0%
+that the potential for the electrons
+where they move is not spherically
+
+ align:start position:0%
+where they move is not spherically
+ 
+
+ align:start position:0%
+where they move is not spherically
+symmetric there's another thing that
+
+ align:start position:0%
+symmetric there's another thing that
+ 
+
+ align:start position:0%
+symmetric there's another thing that
+helps us however is that there's a nice
+
+ align:start position:0%
+helps us however is that there's a nice
+ 
+
+ align:start position:0%
+helps us however is that there's a nice
+separation of mass scales you have the
+
+ align:start position:0%
+separation of mass scales you have the
+ 
+
+ align:start position:0%
+separation of mass scales you have the
+mass little m of the electron and the
+
+ align:start position:0%
+mass little m of the electron and the
+ 
+
+ align:start position:0%
+mass little m of the electron and the
+nuclear mass this could be the mass of
+
+ align:start position:0%
+nuclear mass this could be the mass of
+ 
+
+ align:start position:0%
+nuclear mass this could be the mass of
+one nucleus or a mass of a few nuclei or
+
+ align:start position:0%
+one nucleus or a mass of a few nuclei or
+ 
+
+ align:start position:0%
+one nucleus or a mass of a few nuclei or
+doesn't matter but this is small and
+
+ align:start position:0%
+doesn't matter but this is small and
+ 
+
+ align:start position:0%
+doesn't matter but this is small and
+typically 10 to the minus 4 you know an
+
+ align:start position:0%
+typically 10 to the minus 4 you know an
+ 
+
+ align:start position:0%
+typically 10 to the minus 4 you know an
+electron is about 2,000 times lighter
+
+ align:start position:0%
+electron is about 2,000 times lighter
+ 
+
+ align:start position:0%
+electron is about 2,000 times lighter
+than a single proton if you already have
+
+ align:start position:0%
+than a single proton if you already have
+ 
+
+ align:start position:0%
+than a single proton if you already have
+a nice nucleus with a couple of them
+
+ align:start position:0%
+a nice nucleus with a couple of them
+ 
+
+ align:start position:0%
+a nice nucleus with a couple of them
+you're several thousands already there
+
+ align:start position:0%
+you're several thousands already there
+ 
+
+ align:start position:0%
+you're several thousands already there
+so this is a nice number so we want to
+
+ align:start position:0%
+so this is a nice number so we want to
+ 
+
+ align:start position:0%
+so this is a nice number so we want to
+understand the scales of the physics of
+
+ align:start position:0%
+understand the scales of the physics of
+ 
+
+ align:start position:0%
+understand the scales of the physics of
+this so let's assume we have a molecule
+
+ align:start position:0%
+this so let's assume we have a molecule
+ 
+
+ align:start position:0%
+this so let's assume we have a molecule
+maybe has a few centers and then there's
+
+ align:start position:0%
+maybe has a few centers and then there's
+ 
+
+ align:start position:0%
+maybe has a few centers and then there's
+electronic cloud and it has a size of
+
+ align:start position:0%
+electronic cloud and it has a size of
+ 
+
+ align:start position:0%
+electronic cloud and it has a size of
+the order of a so we can estimate at
+
+ align:start position:0%
+the order of a so we can estimate at
+ 
+
+ align:start position:0%
+the order of a so we can estimate at
+first sight what are the energies
+
+ align:start position:0%
+first sight what are the energies
+ 
+
+ align:start position:0%
+first sight what are the energies
+involved here what is the energy of the
+
+ align:start position:0%
+involved here what is the energy of the
+ 
+
+ align:start position:0%
+involved here what is the energy of the
+electron for example and you could say
+
+ align:start position:0%
+electron for example and you could say
+ 
+
+ align:start position:0%
+electron for example and you could say
+the momentum of the electron is of the
+
+ align:start position:0%
+the momentum of the electron is of the
+ 
+
+ align:start position:0%
+the momentum of the electron is of the
+order of H bar times the size of the
+
+ align:start position:0%
+order of H bar times the size of the
+ 
+
+ align:start position:0%
+order of H bar times the size of the
+cloud it's an estimate and the energies
+
+ align:start position:0%
+cloud it's an estimate and the energies
+ 
+
+ align:start position:0%
+cloud it's an estimate and the energies
+electron energies are basically
+
+ align:start position:0%
+electron energies are basically
+ 
+
+ align:start position:0%
+electron energies are basically
+determined by the size in which they are
+
+ align:start position:0%
+determined by the size in which they are
+ 
+
+ align:start position:0%
+determined by the size in which they are
+confined which is a H bar and the mass
+
+ align:start position:0%
+confined which is a H bar and the mass
+ 
+
+ align:start position:0%
+confined which is a H bar and the mass
+of the electron those are the electronic
+
+ align:start position:0%
+of the electron those are the electronic
+ 
+
+ align:start position:0%
+of the electron those are the electronic
+energy so H squared over m a squared
+
+ align:start position:0%
+energy so H squared over m a squared
+ 
+
+ align:start position:0%
+energy so H squared over m a squared
+those are the right units is P squared
+
+ align:start position:0%
+those are the right units is P squared
+ 
+
+ align:start position:0%
+those are the right units is P squared
+over m the unit so it's natural like
+
+ align:start position:0%
+over m the unit so it's natural like
+ 
+
+ align:start position:0%
+over m the unit so it's natural like
+this so this is the electronic
+
+ align:start position:0%
+this so this is the electronic
+ 
+
+ align:start position:0%
+this so this is the electronic
+configuration and typical electronic
+
+ align:start position:0%
+configuration and typical electronic
+ 
+
+ align:start position:0%
+configuration and typical electronic
+energy so what is the approximate
+
+ align:start position:0%
+energy so what is the approximate
+ 
+
+ align:start position:0%
+energy so what is the approximate
+picture of the physics of a molecule
+
+ align:start position:0%
+picture of the physics of a molecule
+ 
+
+ align:start position:0%
+picture of the physics of a molecule
+basically you have nuclei and the nuclei
+
+ align:start position:0%
+basically you have nuclei and the nuclei
+ 
+
+ align:start position:0%
+basically you have nuclei and the nuclei
+repel each other they want to be away
+
+ align:start position:0%
+repel each other they want to be away
+ 
+
+ align:start position:0%
+repel each other they want to be away
+now the electrons come in and then they
+
+ align:start position:0%
+now the electrons come in and then they
+ 
+
+ align:start position:0%
+now the electrons come in and then they
+fly around the nuclei and the electrons
+
+ align:start position:0%
+fly around the nuclei and the electrons
+ 
+
+ align:start position:0%
+fly around the nuclei and the electrons
+attract the nuclei and attract the
+
+ align:start position:0%
+attract the nuclei and attract the
+ 
+
+ align:start position:0%
+attract the nuclei and attract the
+nuclei so the electrons reasonably place
+
+ align:start position:0%
+nuclei so the electrons reasonably place
+ 
+
+ align:start position:0%
+nuclei so the electrons reasonably place
+compensate the repulsion of the nuclei
+
+ align:start position:0%
+compensate the repulsion of the nuclei
+ 
+
+ align:start position:0%
+compensate the repulsion of the nuclei
+by creating some new attraction at the
+
+ align:start position:0%
+by creating some new attraction at the
+ 
+
+ align:start position:0%
+by creating some new attraction at the
+end you get some kind of equilibrium is
+
+ align:start position:0%
+end you get some kind of equilibrium is
+ 
+
+ align:start position:0%
+end you get some kind of equilibrium is
+not classical because you cannot
+
+ align:start position:0%
+not classical because you cannot
+ 
+
+ align:start position:0%
+not classical because you cannot
+it's stable equilibrium between
+
+ align:start position:0%
+it's stable equilibrium between
+ 
+
+ align:start position:0%
+it's stable equilibrium between
+classical particles this is one of the
+
+ align:start position:0%
+classical particles this is one of the
+ 
+
+ align:start position:0%
+classical particles this is one of the
+amazing things about quantum mechanics
+
+ align:start position:0%
+amazing things about quantum mechanics
+ 
+
+ align:start position:0%
+amazing things about quantum mechanics
+you know very well an atom would not
+
+ align:start position:0%
+you know very well an atom would not
+ 
+
+ align:start position:0%
+you know very well an atom would not
+exist without quantum mechanics you
+
+ align:start position:0%
+exist without quantum mechanics you
+ 
+
+ align:start position:0%
+exist without quantum mechanics you
+would have stable classical orbit
+
+ align:start position:0%
+would have stable classical orbit
+ 
+
+ align:start position:0%
+would have stable classical orbit
+circular orbits but they radiate energy
+
+ align:start position:0%
+circular orbits but they radiate energy
+ 
+
+ align:start position:0%
+circular orbits but they radiate energy
+so they indicate if you have a molecule
+
+ align:start position:0%
+so they indicate if you have a molecule
+ 
+
+ align:start position:0%
+so they indicate if you have a molecule
+you have two repelling charge positive
+
+ align:start position:0%
+you have two repelling charge positive
+ 
+
+ align:start position:0%
+you have two repelling charge positive
+charged particles in E&M you saw the
+
+ align:start position:0%
+charged particles in E&M you saw the
+ 
+
+ align:start position:0%
+charged particles in E&M you saw the
+case when you put a negative charge in
+
+ align:start position:0%
+case when you put a negative charge in
+ 
+
+ align:start position:0%
+case when you put a negative charge in
+the middle and you create a Calibri 'm
+
+ align:start position:0%
+the middle and you create a Calibri 'm
+ 
+
+ align:start position:0%
+the middle and you create a Calibri 'm
+but that's absolutely unstable you move
+
+ align:start position:0%
+but that's absolutely unstable you move
+ 
+
+ align:start position:0%
+but that's absolutely unstable you move
+that electric charge a middle a micron
+
+ align:start position:0%
+that electric charge a middle a micron
+ 
+
+ align:start position:0%
+that electric charge a middle a micron
+and then off it goes the whole thing is
+
+ align:start position:0%
+and then off it goes the whole thing is
+ 
+
+ align:start position:0%
+and then off it goes the whole thing is
+unstable but quantum mechanics of those
+
+ align:start position:0%
+unstable but quantum mechanics of those
+ 
+
+ align:start position:0%
+unstable but quantum mechanics of those
+problems and and our physical picture is
+
+ align:start position:0%
+problems and and our physical picture is
+ 
+
+ align:start position:0%
+problems and and our physical picture is
+that of repelling nuclei an attracting
+
+ align:start position:0%
+that of repelling nuclei an attracting
+ 
+
+ align:start position:0%
+that of repelling nuclei an attracting
+cloud of electric rate in an equilibrium
+
+ align:start position:0%
+cloud of electric rate in an equilibrium
+ 
+
+ align:start position:0%
+cloud of electric rate in an equilibrium
+in which the nuclei reasonably well
+
+ align:start position:0%
+in which the nuclei reasonably well
+ 
+
+ align:start position:0%
+in which the nuclei reasonably well
+localized they are quantum particles but
+
+ align:start position:0%
+localized they are quantum particles but
+ 
+
+ align:start position:0%
+localized they are quantum particles but
+they're reasonably well localized where
+
+ align:start position:0%
+they're reasonably well localized where
+ 
+
+ align:start position:0%
+they're reasonably well localized where
+the electrons are completely delocalized
+
+ align:start position:0%
+the electrons are completely delocalized
+ 
+
+ align:start position:0%
+the electrons are completely delocalized
+that is our picture they are moving in
+
+ align:start position:0%
+that is our picture they are moving in
+ 
+
+ align:start position:0%
+that is our picture they are moving in
+that way so our picture will be we have
+
+ align:start position:0%
+that way so our picture will be we have
+ 
+
+ align:start position:0%
+that way so our picture will be we have
+that and we'll have slow vibrations of
+
+ align:start position:0%
+that and we'll have slow vibrations of
+ 
+
+ align:start position:0%
+that and we'll have slow vibrations of
+the nuclei that are mostly localized and
+
+ align:start position:0%
+the nuclei that are mostly localized and
+ 
+
+ align:start position:0%
+the nuclei that are mostly localized and
+you can imagine calculating the
+
+ align:start position:0%
+you can imagine calculating the
+ 
+
+ align:start position:0%
+you can imagine calculating the
+electronic configuration for any
+
+ align:start position:0%
+electronic configuration for any
+ 
+
+ align:start position:0%
+electronic configuration for any
+particular separation of the nuclei and
+
+ align:start position:0%
+particular separation of the nuclei and
+ 
+
+ align:start position:0%
+particular separation of the nuclei and
+that's the cloud for this separation as
+
+ align:start position:0%
+that's the cloud for this separation as
+ 
+
+ align:start position:0%
+that's the cloud for this separation as
+the nuclei vibrate the electronic
+
+ align:start position:0%
+the nuclei vibrate the electronic
+ 
+
+ align:start position:0%
+the nuclei vibrate the electronic
+configuration probably adjusts
+
+ align:start position:0%
+configuration probably adjusts
+ 
+
+ align:start position:0%
+configuration probably adjusts
+adiabatically to this thing in the
+
+ align:start position:0%
+adiabatically to this thing in the
+ 
+
+ align:start position:0%
+adiabatically to this thing in the
+instantaneous eigenstates and they work
+
+ align:start position:0%
+instantaneous eigenstates and they work
+ 
+
+ align:start position:0%
+instantaneous eigenstates and they work
+that way we're going to do that
+
+ align:start position:0%
+that way we're going to do that
+ 
+
+ align:start position:0%
+that way we're going to do that
+in trying to understand things they also
+
+ align:start position:0%
+in trying to understand things they also
+ 
+
+ align:start position:0%
+in trying to understand things they also
+want to emphasize this kind of
+
+ align:start position:0%
+want to emphasize this kind of
+ 
+
+ align:start position:0%
+want to emphasize this kind of
+remarkable property of an elect
+
+ align:start position:0%
+remarkable property of an elect
+ 
+
+ align:start position:0%
+remarkable property of an elect
+turn to create the bound state so we are
+
+ align:start position:0%
+turn to create the bound state so we are
+ 
+
+ align:start position:0%
+turn to create the bound state so we are
+not amazed on the fact that if you have
+
+ align:start position:0%
+not amazed on the fact that if you have
+ 
+
+ align:start position:0%
+not amazed on the fact that if you have
+a proton and we can have an electron
+
+ align:start position:0%
+a proton and we can have an electron
+ 
+
+ align:start position:0%
+a proton and we can have an electron
+here we create a bound state and that's
+
+ align:start position:0%
+here we create a bound state and that's
+ 
+
+ align:start position:0%
+here we create a bound state and that's
+a hydrogen atom but suppose I bring in
+
+ align:start position:0%
+a hydrogen atom but suppose I bring in
+ 
+
+ align:start position:0%
+a hydrogen atom but suppose I bring in
+another proton from infinity
+
+ align:start position:0%
+another proton from infinity
+ 
+
+ align:start position:0%
+another proton from infinity
+well I if I bring it I'm gonna start
+
+ align:start position:0%
+well I if I bring it I'm gonna start
+ 
+
+ align:start position:0%
+well I if I bring it I'm gonna start
+bringing it here this kind of it's
+
+ align:start position:0%
+bringing it here this kind of it's
+ 
+
+ align:start position:0%
+bringing it here this kind of it's
+neutral but eventually this proton is
+
+ align:start position:0%
+neutral but eventually this proton is
+ 
+
+ align:start position:0%
+neutral but eventually this proton is
+going to polarize this thing okay I'm
+
+ align:start position:0%
+going to polarize this thing okay I'm
+ 
+
+ align:start position:0%
+going to polarize this thing okay I'm
+going to bring it and then if I come too
+
+ align:start position:0%
+going to bring it and then if I come too
+ 
+
+ align:start position:0%
+going to bring it and then if I come too
+close it repels it so there will be a
+
+ align:start position:0%
+close it repels it so there will be a
+ 
+
+ align:start position:0%
+close it repels it so there will be a
+force repelling it and we have to figure
+
+ align:start position:0%
+force repelling it and we have to figure
+ 
+
+ align:start position:0%
+force repelling it and we have to figure
+out what it does suppose I try to bring
+
+ align:start position:0%
+out what it does suppose I try to bring
+ 
+
+ align:start position:0%
+out what it does suppose I try to bring
+it in do you think that an electron is
+
+ align:start position:0%
+it in do you think that an electron is
+ 
+
+ align:start position:0%
+it in do you think that an electron is
+capable of stabilizing two protons can
+
+ align:start position:0%
+capable of stabilizing two protons can
+ 
+
+ align:start position:0%
+capable of stabilizing two protons can
+they create a cloud in which an electron
+
+ align:start position:0%
+they create a cloud in which an electron
+ 
+
+ align:start position:0%
+they create a cloud in which an electron
+stabilizes the two protons is that
+
+ align:start position:0%
+stabilizes the two protons is that
+ 
+
+ align:start position:0%
+stabilizes the two protons is that
+possible or not possible this a lot of
+
+ align:start position:0%
+possible or not possible this a lot of
+ 
+
+ align:start position:0%
+possible or not possible this a lot of
+protons for one single electron is that
+
+ align:start position:0%
+protons for one single electron is that
+ 
+
+ align:start position:0%
+protons for one single electron is that
+possible or not variety say yes yes any
+
+ align:start position:0%
+possible or not variety say yes yes any
+ 
+
+ align:start position:0%
+possible or not variety say yes yes any
+other opinions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can that happen can the electron produce
+
+ align:start position:0%
+can that happen can the electron produce
+ 
+
+ align:start position:0%
+can that happen can the electron produce
+a bound state of two protons exactly
+
+ align:start position:0%
+a bound state of two protons exactly
+ 
+
+ align:start position:0%
+a bound state of two protons exactly
+sorry it is were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay yes it can produce it and this
+
+ align:start position:0%
+okay yes it can produce it and this
+ 
+
+ align:start position:0%
+okay yes it can produce it and this
+would be called with an electron here
+
+ align:start position:0%
+would be called with an electron here
+ 
+
+ align:start position:0%
+would be called with an electron here
+the hydrogen molecule ion so h2 plus is
+
+ align:start position:0%
+the hydrogen molecule ion so h2 plus is
+ 
+
+ align:start position:0%
+the hydrogen molecule ion so h2 plus is
+a hydrogen molecule that had these two
+
+ align:start position:0%
+a hydrogen molecule that had these two
+ 
+
+ align:start position:0%
+a hydrogen molecule that had these two
+things and it lost one electron and yes
+
+ align:start position:0%
+things and it lost one electron and yes
+ 
+
+ align:start position:0%
+things and it lost one electron and yes
+this can be done and we'll analyze it
+
+ align:start position:0%
+this can be done and we'll analyze it
+ 
+
+ align:start position:0%
+this can be done and we'll analyze it
+and now you can get greedy and say can
+
+ align:start position:0%
+and now you can get greedy and say can
+ 
+
+ align:start position:0%
+and now you can get greedy and say can
+you get an electron to stabilize three
+
+ align:start position:0%
+you get an electron to stabilize three
+ 
+
+ align:start position:0%
+you get an electron to stabilize three
+protons yes or no no cannot get it it's
+
+ align:start position:0%
+protons yes or no no cannot get it it's
+ 
+
+ align:start position:0%
+protons yes or no no cannot get it it's
+just too much work for an electron it
+
+ align:start position:0%
+just too much work for an electron it
+ 
+
+ align:start position:0%
+just too much work for an electron it
+cannot do it there theorems like that
+
+ align:start position:0%
+cannot do it there theorems like that
+ 
+
+ align:start position:0%
+cannot do it there theorems like that
+Eliot liebe mathematical physicist has
+
+ align:start position:0%
+Eliot liebe mathematical physicist has
+ 
+
+ align:start position:0%
+Eliot liebe mathematical physicist has
+proven all kinds of this things and we
+
+ align:start position:0%
+proven all kinds of this things and we
+ 
+
+ align:start position:0%
+proven all kinds of this things and we
+might discuss some of that in the Homer
+
+ align:start position:0%
+might discuss some of that in the Homer
+ 
+
+ align:start position:0%
+might discuss some of that in the Homer
+is kind of nice stuff so we will be
+
+ align:start position:0%
+is kind of nice stuff so we will be
+ 
+
+ align:start position:0%
+is kind of nice stuff so we will be
+looking at the physics of those things
+
+ align:start position:0%
+looking at the physics of those things
+ 
+
+ align:start position:0%
+looking at the physics of those things
+with a little detail so now of let's go
+
+ align:start position:0%
+with a little detail so now of let's go
+ 
+
+ align:start position:0%
+with a little detail so now of let's go
+back to our molecule here and estimate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the vibrational nuclear energy so we
+
+ align:start position:0%
+the vibrational nuclear energy so we
+ 
+
+ align:start position:0%
+the vibrational nuclear energy so we
+have this picture the electrons are
+
+ align:start position:0%
+have this picture the electrons are
+ 
+
+ align:start position:0%
+have this picture the electrons are
+there the nuclei are kind of
+
+ align:start position:0%
+there the nuclei are kind of
+ 
+
+ align:start position:0%
+there the nuclei are kind of
+semi-classical they are roughly
+
+ align:start position:0%
+semi-classical they are roughly
+ 
+
+ align:start position:0%
+semi-classical they are roughly
+localized and they're varying and how
+
+ align:start position:0%
+localized and they're varying and how
+ 
+
+ align:start position:0%
+localized and they're varying and how
+would we estimate the nuclear vibration
+
+ align:start position:0%
+would we estimate the nuclear vibration
+ 
+
+ align:start position:0%
+would we estimate the nuclear vibration
+frequency so estimate nuclear vibration
+
+ align:start position:0%
+frequency so estimate nuclear vibration
+ 
+
+ align:start position:0%
+frequency so estimate nuclear vibration
+so we think of a harmonic oscillator P
+
+ align:start position:0%
+so we think of a harmonic oscillator P
+ 
+
+ align:start position:0%
+so we think of a harmonic oscillator P
+squared over two mass of the nucleons
+
+ align:start position:0%
+squared over two mass of the nucleons
+ 
+
+ align:start position:0%
+squared over two mass of the nucleons
+plus a restoring force age some nuclear
+
+ align:start position:0%
+plus a restoring force age some nuclear
+ 
+
+ align:start position:0%
+plus a restoring force age some nuclear
+oscillation so this is an estimate so
+
+ align:start position:0%
+oscillation so this is an estimate so
+ 
+
+ align:start position:0%
+oscillation so this is an estimate so
+it's not very rigorous but I think it
+
+ align:start position:0%
+it's not very rigorous but I think it
+ 
+
+ align:start position:0%
+it's not very rigorous but I think it
+will be clear enough now this restoring
+
+ align:start position:0%
+will be clear enough now this restoring
+ 
+
+ align:start position:0%
+will be clear enough now this restoring
+force has to do with the cloud of the
+
+ align:start position:0%
+force has to do with the cloud of the
+ 
+
+ align:start position:0%
+force has to do with the cloud of the
+electrons that are just and those things
+
+ align:start position:0%
+electrons that are just and those things
+ 
+
+ align:start position:0%
+electrons that are just and those things
+as you separate the nuclei you have to
+
+ align:start position:0%
+as you separate the nuclei you have to
+ 
+
+ align:start position:0%
+as you separate the nuclei you have to
+restore this the restoring energies due
+
+ align:start position:0%
+restore this the restoring energies due
+ 
+
+ align:start position:0%
+restore this the restoring energies due
+to the electrons and the Coulomb forces
+
+ align:start position:0%
+to the electrons and the Coulomb forces
+ 
+
+ align:start position:0%
+to the electrons and the Coulomb forces
+but it's not does not depend on the mass
+
+ align:start position:0%
+but it's not does not depend on the mass
+ 
+
+ align:start position:0%
+but it's not does not depend on the mass
+m the restoring force so this K depends
+
+ align:start position:0%
+m the restoring force so this K depends
+ 
+
+ align:start position:0%
+m the restoring force so this K depends
+on the electrons and Coulomb forces but
+
+ align:start position:0%
+on the electrons and Coulomb forces but
+ 
+
+ align:start position:0%
+on the electrons and Coulomb forces but
+definitely not on the mass of this
+
+ align:start position:0%
+definitely not on the mass of this
+ 
+
+ align:start position:0%
+definitely not on the mass of this
+quantity so k has units of e over l
+
+ align:start position:0%
+quantity so k has units of e over l
+ 
+
+ align:start position:0%
+quantity so k has units of e over l
+squared and for energy we have this
+
+ align:start position:0%
+squared and for energy we have this
+ 
+
+ align:start position:0%
+squared and for energy we have this
+energy of the electron and length the
+
+ align:start position:0%
+energy of the electron and length the
+ 
+
+ align:start position:0%
+energy of the electron and length the
+length the scale of the molecule so K is
+
+ align:start position:0%
+length the scale of the molecule so K is
+ 
+
+ align:start position:0%
+length the scale of the molecule so K is
+proportional to H squared over m a to
+
+ align:start position:0%
+proportional to H squared over m a to
+ 
+
+ align:start position:0%
+proportional to H squared over m a to
+the fourth
+
+ align:start position:0%
+the fourth
+ 
+
+ align:start position:0%
+the fourth
+it just cannot depend on the mass of the
+
+ align:start position:0%
+it just cannot depend on the mass of the
+ 
+
+ align:start position:0%
+it just cannot depend on the mass of the
+nuclei thats definitely not the origin
+
+ align:start position:0%
+nuclei thats definitely not the origin
+ 
+
+ align:start position:0%
+nuclei thats definitely not the origin
+of the restoring force so if the only
+
+ align:start position:0%
+of the restoring force so if the only
+ 
+
+ align:start position:0%
+of the restoring force so if the only
+mass you can use is the mass of the
+
+ align:start position:0%
+mass you can use is the mass of the
+ 
+
+ align:start position:0%
+mass you can use is the mass of the
+electron it can only be that but then
+
+ align:start position:0%
+electron it can only be that but then
+ 
+
+ align:start position:0%
+electron it can only be that but then
+the frequency Omega is square root of K
+
+ align:start position:0%
+the frequency Omega is square root of K
+ 
+
+ align:start position:0%
+the frequency Omega is square root of K
+over m that is the mass of the nuclei so
+
+ align:start position:0%
+over m that is the mass of the nuclei so
+ 
+
+ align:start position:0%
+over m that is the mass of the nuclei so
+the nuclear frequency is this and it's
+
+ align:start position:0%
+the nuclear frequency is this and it's
+ 
+
+ align:start position:0%
+the nuclear frequency is this and it's
+therefore equal to H squared over m a
+
+ align:start position:0%
+therefore equal to H squared over m a
+ 
+
+ align:start position:0%
+therefore equal to H squared over m a
+fourth one over m that was k
+
+ align:start position:0%
+fourth one over m that was k
+ 
+
+ align:start position:0%
+fourth one over m that was k
+and this is square root of little m over
+
+ align:start position:0%
+and this is square root of little m over
+ 
+
+ align:start position:0%
+and this is square root of little m over
+capital M times square root of H squared
+
+ align:start position:0%
+capital M times square root of H squared
+ 
+
+ align:start position:0%
+capital M times square root of H squared
+over m squared a to the fourth
+
+ align:start position:0%
+over m squared a to the fourth
+ 
+
+ align:start position:0%
+over m squared a to the fourth
+I borrowed a little m up and a little em
+
+ align:start position:0%
+I borrowed a little m up and a little em
+ 
+
+ align:start position:0%
+I borrowed a little m up and a little em
+down so from here we get that H bar
+
+ align:start position:0%
+down so from here we get that H bar
+ 
+
+ align:start position:0%
+down so from here we get that H bar
+Omega nuclear is square root of little m
+
+ align:start position:0%
+Omega nuclear is square root of little m
+ 
+
+ align:start position:0%
+Omega nuclear is square root of little m
+over capital M H squared over m a
+
+ align:start position:0%
+over capital M H squared over m a
+ 
+
+ align:start position:0%
+over capital M H squared over m a
+squared if you take the square root here
+
+ align:start position:0%
+squared if you take the square root here
+ 
+
+ align:start position:0%
+squared if you take the square root here
+you get h bar over m a squared but there
+
+ align:start position:0%
+you get h bar over m a squared but there
+ 
+
+ align:start position:0%
+you get h bar over m a squared but there
+was another H bar I put in and now we
+
+ align:start position:0%
+was another H bar I put in and now we
+ 
+
+ align:start position:0%
+was another H bar I put in and now we
+get a sensible equation in which we see
+
+ align:start position:0%
+get a sensible equation in which we see
+ 
+
+ align:start position:0%
+get a sensible equation in which we see
+that the nuclear energies for
+
+ align:start position:0%
+that the nuclear energies for
+ 
+
+ align:start position:0%
+that the nuclear energies for
+oscillation are much smaller
+
+ align:start position:0%
+oscillation are much smaller
+ 
+
+ align:start position:0%
+oscillation are much smaller
+significantly smaller so II nuclear
+
+ align:start position:0%
+significantly smaller so II nuclear
+ 
+
+ align:start position:0%
+significantly smaller so II nuclear
+oscillations go like square root of M
+
+ align:start position:0%
+oscillations go like square root of M
+ 
+
+ align:start position:0%
+oscillations go like square root of M
+over m is 10 to the minus 4 with a
+
+ align:start position:0%
+over m is 10 to the minus 4 with a
+ 
+
+ align:start position:0%
+over m is 10 to the minus 4 with a
+square root is 10 to the minus 2 times e
+
+ align:start position:0%
+square root is 10 to the minus 2 times e
+ 
+
+ align:start position:0%
+square root is 10 to the minus 2 times e
+electronic so it's considerably less
+
+ align:start position:0%
+electronic so it's considerably less
+ 
+
+ align:start position:0%
+electronic so it's considerably less
+which is this so of if you think I I
+
+ align:start position:0%
+which is this so of if you think I I
+ 
+
+ align:start position:0%
+which is this so of if you think I I
+want to make another observation here on
+
+ align:start position:0%
+want to make another observation here on
+ 
+
+ align:start position:0%
+want to make another observation here on
+time scales so Omega n we have it here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega N or we have it here as well is
+
+ align:start position:0%
+Omega N or we have it here as well is
+ 
+
+ align:start position:0%
+Omega N or we have it here as well is
+equal to this times this quantity so let
+
+ align:start position:0%
+equal to this times this quantity so let
+ 
+
+ align:start position:0%
+equal to this times this quantity so let
+me say this way the Omega electronic for
+
+ align:start position:0%
+me say this way the Omega electronic for
+ 
+
+ align:start position:0%
+me say this way the Omega electronic for
+vibrations
+
+ align:start position:0%
+vibrations
+ 
+
+ align:start position:0%
+vibrations
+is the electronic energy divided by
+
+ align:start position:0%
+is the electronic energy divided by
+ 
+
+ align:start position:0%
+is the electronic energy divided by
+h-bar and its h-bar over ma squared but
+
+ align:start position:0%
+h-bar and its h-bar over ma squared but
+ 
+
+ align:start position:0%
+h-bar and its h-bar over ma squared but
+here we see that that's precisely that
+
+ align:start position:0%
+here we see that that's precisely that
+ 
+
+ align:start position:0%
+here we see that that's precisely that
+square root so the Omega nuclear is
+
+ align:start position:0%
+square root so the Omega nuclear is
+ 
+
+ align:start position:0%
+square root so the Omega nuclear is
+equal to little M over m Omega
+
+ align:start position:0%
+equal to little M over m Omega
+ 
+
+ align:start position:0%
+equal to little M over m Omega
+electronic now that is nice because it
+
+ align:start position:0%
+electronic now that is nice because it
+ 
+
+ align:start position:0%
+electronic now that is nice because it
+says that the frequency associated to
+
+ align:start position:0%
+says that the frequency associated to
+ 
+
+ align:start position:0%
+says that the frequency associated to
+the nuclear thing is much smaller than
+
+ align:start position:0%
+the nuclear thing is much smaller than
+ 
+
+ align:start position:0%
+the nuclear thing is much smaller than
+the timescales associated with the
+
+ align:start position:0%
+the timescales associated with the
+ 
+
+ align:start position:0%
+the timescales associated with the
+electronic changes so this is a good
+
+ align:start position:0%
+electronic changes so this is a good
+ 
+
+ align:start position:0%
+electronic changes so this is a good
+reason for our adiabatic thinking that
+
+ align:start position:0%
+reason for our adiabatic thinking that
+ 
+
+ align:start position:0%
+reason for our adiabatic thinking that
+as the nuclei so lowly oscillate the
+
+ align:start position:0%
+as the nuclei so lowly oscillate the
+ 
+
+ align:start position:0%
+as the nuclei so lowly oscillate the
+electronic cloud remains in that
+
+ align:start position:0%
+electronic cloud remains in that
+ 
+
+ align:start position:0%
+electronic cloud remains in that
+particular eigenstate and doesn't jump
+
+ align:start position:0%
+particular eigenstate and doesn't jump
+ 
+
+ align:start position:0%
+particular eigenstate and doesn't jump
+it's our use of the adiabatic
+
+ align:start position:0%
+it's our use of the adiabatic
+ 
+
+ align:start position:0%
+it's our use of the adiabatic
+approximation our last comment is that
+
+ align:start position:0%
+approximation our last comment is that
+ 
+
+ align:start position:0%
+approximation our last comment is that
+the rotational energy of the molecule
+
+ align:start position:0%
+the rotational energy of the molecule
+ 
+
+ align:start position:0%
+the rotational energy of the molecule
+goes like the angular momentum squared
+
+ align:start position:0%
+goes like the angular momentum squared
+ 
+
+ align:start position:0%
+goes like the angular momentum squared
+over twice the moment of inertia l
+
+ align:start position:0%
+over twice the moment of inertia l
+ 
+
+ align:start position:0%
+over twice the moment of inertia l
+squared is H squared times some numbers
+
+ align:start position:0%
+squared is H squared times some numbers
+ 
+
+ align:start position:0%
+squared is H squared times some numbers
+as usual L times L plus one and here you
+
+ align:start position:0%
+as usual L times L plus one and here you
+ 
+
+ align:start position:0%
+as usual L times L plus one and here you
+get the mass of the molecule times the
+
+ align:start position:0%
+get the mass of the molecule times the
+ 
+
+ align:start position:0%
+get the mass of the molecule times the
+size squared of the molecules this
+
+ align:start position:0%
+size squared of the molecules this
+ 
+
+ align:start position:0%
+size squared of the molecules this
+energies are like little M over capital
+
+ align:start position:0%
+energies are like little M over capital
+ 
+
+ align:start position:0%
+energies are like little M over capital
+M times this is roughly H squared over
+
+ align:start position:0%
+M times this is roughly H squared over
+ 
+
+ align:start position:0%
+M times this is roughly H squared over
+little M a squared and therefore the
+
+ align:start position:0%
+little M a squared and therefore the
+ 
+
+ align:start position:0%
+little M a squared and therefore the
+rotational energies are even smaller
+
+ align:start position:0%
+rotational energies are even smaller
+ 
+
+ align:start position:0%
+rotational energies are even smaller
+than the electronic energies the
+
+ align:start position:0%
+than the electronic energies the
+ 
+
+ align:start position:0%
+than the electronic energies the
+rotational energies go like little M
+
+ align:start position:0%
+rotational energies go like little M
+ 
+
+ align:start position:0%
+rotational energies go like little M
+over capital n time
+
+ align:start position:0%
+over capital n time
+ 
+
+ align:start position:0%
+over capital n time
+electronic energies so you have the
+
+ align:start position:0%
+electronic energies so you have the
+ 
+
+ align:start position:0%
+electronic energies so you have the
+electronic energies the nuclear energies
+
+ align:start position:0%
+electronic energies the nuclear energies
+ 
+
+ align:start position:0%
+electronic energies the nuclear energies
+of oscillation which glow like square
+
+ align:start position:0%
+of oscillation which glow like square
+ 
+
+ align:start position:0%
+of oscillation which glow like square
+root and then finally the smallest of
+
+ align:start position:0%
+root and then finally the smallest of
+ 
+
+ align:start position:0%
+root and then finally the smallest of
+them are the rotation which the molecule
+
+ align:start position:0%
+them are the rotation which the molecule
+ 
+
+ align:start position:0%
+them are the rotation which the molecule
+rotates like a solid object we'll
+
+ align:start position:0%
+rotates like a solid object we'll
+ 
+
+ align:start position:0%
+rotates like a solid object we'll
+continue this next time and calculate
+
+ align:start position:0%
+continue this next time and calculate
+ 
+
+ align:start position:0%
+continue this next time and calculate
+the few more things and more
\ No newline at end of file
diff --git a/ArfHGPHL8kU.txt b/ArfHGPHL8kU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..be88e4b595cb8eb203dcf4983c4566ab8ad1eaa0
--- /dev/null
+++ b/ArfHGPHL8kU.txt
@@ -0,0 +1,283 @@
+align:start position:0%
+ 
+in this lecture we introduced the notion
+
+ align:start position:0%
+in this lecture we introduced the notion
+ 
+
+ align:start position:0%
+in this lecture we introduced the notion
+of a random variable a random variable
+
+ align:start position:0%
+of a random variable a random variable
+ 
+
+ align:start position:0%
+of a random variable a random variable
+is loosely speaking a numerical quantity
+
+ align:start position:0%
+is loosely speaking a numerical quantity
+ 
+
+ align:start position:0%
+is loosely speaking a numerical quantity
+whose value is determined by the outcome
+
+ align:start position:0%
+whose value is determined by the outcome
+ 
+
+ align:start position:0%
+whose value is determined by the outcome
+of a probabilistic experiment the weight
+
+ align:start position:0%
+of a probabilistic experiment the weight
+ 
+
+ align:start position:0%
+of a probabilistic experiment the weight
+of a randomly selected student is one
+
+ align:start position:0%
+of a randomly selected student is one
+ 
+
+ align:start position:0%
+of a randomly selected student is one
+example after giving a general
+
+ align:start position:0%
+example after giving a general
+ 
+
+ align:start position:0%
+example after giving a general
+definition we will focus exclusively on
+
+ align:start position:0%
+definition we will focus exclusively on
+ 
+
+ align:start position:0%
+definition we will focus exclusively on
+discrete random variables these are
+
+ align:start position:0%
+discrete random variables these are
+ 
+
+ align:start position:0%
+discrete random variables these are
+random variables that take values in
+
+ align:start position:0%
+random variables that take values in
+ 
+
+ align:start position:0%
+random variables that take values in
+finite or countably infinite sets for
+
+ align:start position:0%
+finite or countably infinite sets for
+ 
+
+ align:start position:0%
+finite or countably infinite sets for
+example random variables that take
+
+ align:start position:0%
+example random variables that take
+ 
+
+ align:start position:0%
+example random variables that take
+integer values are discrete twenty
+
+ align:start position:0%
+integer values are discrete twenty
+ 
+
+ align:start position:0%
+integer values are discrete twenty
+discrete random variable we will
+
+ align:start position:0%
+discrete random variable we will
+ 
+
+ align:start position:0%
+discrete random variable we will
+associate a probability mass function
+
+ align:start position:0%
+associate a probability mass function
+ 
+
+ align:start position:0%
+associate a probability mass function
+which tells us the likelihood of each
+
+ align:start position:0%
+which tells us the likelihood of each
+ 
+
+ align:start position:0%
+which tells us the likelihood of each
+possible value of the random variable
+
+ align:start position:0%
+possible value of the random variable
+ 
+
+ align:start position:0%
+possible value of the random variable
+then we will go over a few examples and
+
+ align:start position:0%
+then we will go over a few examples and
+ 
+
+ align:start position:0%
+then we will go over a few examples and
+introduce some common types of random
+
+ align:start position:0%
+introduce some common types of random
+ 
+
+ align:start position:0%
+introduce some common types of random
+variables and finally we will introduce
+
+ align:start position:0%
+variables and finally we will introduce
+ 
+
+ align:start position:0%
+variables and finally we will introduce
+a new concept the expected value of a
+
+ align:start position:0%
+a new concept the expected value of a
+ 
+
+ align:start position:0%
+a new concept the expected value of a
+random variable also called
+
+ align:start position:0%
+random variable also called
+ 
+
+ align:start position:0%
+random variable also called
+the expectation or mean it is a weighted
+
+ align:start position:0%
+the expectation or mean it is a weighted
+ 
+
+ align:start position:0%
+the expectation or mean it is a weighted
+average of the values of the random
+
+ align:start position:0%
+average of the values of the random
+ 
+
+ align:start position:0%
+average of the values of the random
+variable weighted according to their
+
+ align:start position:0%
+variable weighted according to their
+ 
+
+ align:start position:0%
+variable weighted according to their
+respective probabilities and has an
+
+ align:start position:0%
+respective probabilities and has an
+ 
+
+ align:start position:0%
+respective probabilities and has an
+intuitive interpretation as the average
+
+ align:start position:0%
+intuitive interpretation as the average
+ 
+
+ align:start position:0%
+intuitive interpretation as the average
+value we expect to see if we repeat the
+
+ align:start position:0%
+value we expect to see if we repeat the
+ 
+
+ align:start position:0%
+value we expect to see if we repeat the
+same probabilistic experiment
+
+ align:start position:0%
+same probabilistic experiment
+ 
+
+ align:start position:0%
+same probabilistic experiment
+independently a large number of times
+
+ align:start position:0%
+independently a large number of times
+ 
+
+ align:start position:0%
+independently a large number of times
+expected values play a central role in
+
+ align:start position:0%
+expected values play a central role in
+ 
+
+ align:start position:0%
+expected values play a central role in
+probability theory we will look into
+
+ align:start position:0%
+probability theory we will look into
+ 
+
+ align:start position:0%
+probability theory we will look into
+some of their properties and we will
+
+ align:start position:0%
+some of their properties and we will
+ 
+
+ align:start position:0%
+some of their properties and we will
+also calculate the expected values of
+
+ align:start position:0%
+also calculate the expected values of
+ 
+
+ align:start position:0%
+also calculate the expected values of
+the example random variables that we
+
+ align:start position:0%
+the example random variables that we
+ 
+
+ align:start position:0%
+the example random variables that we
+will have introduced
\ No newline at end of file
diff --git a/Bzqpuuoq4bI.txt b/Bzqpuuoq4bI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e1ad6404f9ed2cc4cfabfb0b00b7a2b5857f7242
--- /dev/null
+++ b/Bzqpuuoq4bI.txt
@@ -0,0 +1,162 @@
+In order to satisfy the static discipline,
+a circuit must produce outputs that are better
+
+than the acceptable inputs.
+
+This ensures that if you concatenate multiple
+gates together, for example one buffer followed
+
+by another buffer, then the input to each
+gate will be valid even if a small amount
+
+of noise was introduced by the previous gate.
+
+So taking a closer look at that, what that
+means is that if I have a valid input at my
+
+first buffer, and I am guaranteeing that the
+output that I produce is slightly better than
+
+my original input, then even if a little bit
+of noise was introduced, the input to the
+
+second buffer is still going to be considered
+a valid input.
+
+More concretely, to satisfy the static discipline,
+a valid low output must be less than a valid
+
+low input.
+
+The way that we specify this is that is that
+V<sub>ol</sub> < V<sub>il</sub>.
+
+Also, a valid high output must be greater
+than a valid high input.
+
+So V<sub>oh</sub> must be greater than V<sub>ih</sub>.
+
+If we put this all together, we have V<sub>ol</sub>
+< V<sub>il</sub> and V<sub>ih</sub> < V<sub>oh</sub>
+
+and of course we want our low inputs to be
+less than or equal to our high inputs, so
+
+V<sub>il</sub> <= V<sub>ih</sub>.
+
+Another way to think about this is to look
+at the orange and green arrows which show
+
+the ranges of valid inputs which are wider
+than the ranges of valid outputs.
+
+The other thing that is shown here are the
+noise margins which correspond to the area
+
+of valid inputs but invalid outputs.
+
+As we said earlier, a valid input must always
+produce a valid output.
+
+A valid input has V<sub>in</sub> < V<sub>il</sub>
+if its low or V<sub>in</sub> > V<sub>ih</sub>
+
+if its high.
+
+A valid output has V<sub>out</sub> < V<sub>ol</sub>
+if its low and V<sub>out</sub> > V<sub>oh</sub>
+
+if its high.
+
+In this problem, we want to determine whether
+specifications 1, 2, and 3 (which provide
+
+0.3 volt noise margins) satisfy the static
+discipline given the voltage transfer curve
+
+shown here.
+
+For each specification, we need to check the
+following two constraints:
+
+1) Is V<sub>ol</sub> < V<sub>il</sub> <= V<sub>ih</sub>
+< V<sub>oh</sub> - satisfying this constraint
+
+guarantees that the outputs produced are better
+in quality than the inputs.
+
+The second constraint is: Does a valid input
+produce a valid output?
+
+Since this curve shows an inverting function,
+this translates to:
+
+a) Does a valid input (where V<sub>in</sub>
+< V<sub>il</sub>) always produce a valid high
+
+output (where V<sub>out</sub> > V<sub>oh</sub>)?
+
+And b) Does a valid high input (where V<sub>in</sub>
+> V<sub>ih</sub>) always produce a valid low
+
+output (where V<sub>out</sub> < V<sub>ol</sub>)?
+
+If all of these constraints are satisfied,
+then that specification obeys the static discipline.
+
+If not, it doesn't.
+
+For all three specifications, we see that
+indeed V<sub>ol</sub> < V<sub>il</sub> < V<sub>ih</sub>
+
+< V<sub>oh</sub>, so the first constraint
+is satisfied for all three specifications.
+
+Now let's check the second constraint.
+
+For specification #1: If V<sub>in</sub> < V<sub>il</sub>
+which is equal to 0.4, then V<sub>out</sub>
+
+= 5 which is greater than V<sub>oh</sub> which
+is 4.9, so a valid low input produces a valid
+
+high output.
+
+If V<sub>in</sub> > V<sub>ih</sub> which equals
+4.6 then V<sub>out</sub> equals 0 which is
+
+less than V<sub>ol</sub> which is 0.1, so
+a valid high input produces a valid low output.
+
+Since all of the constraints are satisfied,
+specification #1 satisfies the static discipline.
+
+For specification #2: If V<sub>in</sub> < 0.9
+then V<sub>out</sub> >= 4 which is not greater
+
+than> V<sub>oh</sub> which is 4.4.
+
+So this specification does not satisfy the
+static discipline.
+
+For specification #3: If V<sub>in</sub> < 1.4
+then V<sub>out</sub> >= 4 which in this case
+
+is greater than V<sub>oh</sub> which is 3.9.
+
+So the first part of the constraint checks
+out.
+
+Now we need to check what happens when we
+have a valid high input.
+
+In this case, if V<sub>in</sub> > 3.6 then
+V<sub>out</sub> <= 1 which is less than V<sub>ol</sub>
+
+or 1.1, so this part of the constraint checks
+out as well.
+
+Since all the constraints are satisfied, that
+means that specification #3 also satisfies
+
+the static discipline.
\ No newline at end of file
diff --git a/CadZXGNauY0.txt b/CadZXGNauY0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d9f0ab71947a807c9750eb88e1509c7c4ccf649e
--- /dev/null
+++ b/CadZXGNauY0.txt
@@ -0,0 +1,2542 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+JOHN TSITSIKLIS:
+OK let's start.
+
+So we've had the quiz.
+
+And I guess there's both good
+and bad news in it.
+
+Yesterday, as you know,
+the bad news.
+
+The average was a little
+lower than what
+
+we would have wanted.
+
+On the other hand, the good news
+is that the distribution
+
+was nicely spread.
+
+And that's the main purpose of
+this quiz is basically for you
+
+to calibrate and see roughly
+where you are standing.
+
+The other piece of the good
+news is that, as you know,
+
+this quiz doesn't count for very
+much in your final grade.
+
+So it's really a matter of
+calibration and to get your
+
+mind set appropriately to
+prepare for the second quiz,
+
+which counts a lot more.
+
+And it's more substantial.
+
+And we'll make sure that
+the second quiz will
+
+have a higher average.
+
+All right.
+
+So let's go to our material.
+
+We're talking now
+these days about
+
+continuous random variables.
+
+And I'll remind you what
+we discussed last time.
+
+I'll remind you of the concept
+of the probability density
+
+function of a single
+random variable.
+
+And then we're going to rush
+through all the concepts that
+
+we covered for the case of
+discrete random variables and
+
+discuss their analogs for
+the continuous case.
+
+And talk about notions
+such as conditioning
+
+independence and so on.
+
+So the big picture is here.
+
+We have all those concepts that
+we developed for the case
+
+of discrete random variables.
+
+And now we will just talk about
+their analogs in the
+
+continuous case.
+
+We already discussed this analog
+last week, the density
+
+of a single random variable.
+
+Then there are certain concepts
+that show up both in
+
+the discrete and the
+continuous case.
+
+So we have the cumulative
+distribution function, which
+
+is a description of the
+probability distribution of a
+
+random variable and which
+applies whether you have a
+
+discrete or continuous
+random variable.
+
+Then there's the notion
+of the expected value.
+
+And in the two cases, the
+expected value is calculated
+
+in a slightly different way,
+but not very different.
+
+We have sums in one case,
+integrals in the other.
+
+And this is the general
+pattern that
+
+we're going to have.
+
+Formulas for the discrete case
+translate to corresponding
+
+formulas or expressions in
+the continuous case.
+
+We generically replace sums by
+integrals, and we replace must
+
+functions with density
+functions.
+
+Then the new pieces for today
+are going to be mostly the
+
+notion of a joint density
+function, which is how we
+
+describe the probability
+distribution of two random
+
+variables that are somehow
+related, in general, and then
+
+the notion of a conditional
+density function that tells us
+
+the distribution of one random
+variable X when you're told
+
+the value of another random
+variable Y. There's another
+
+concept, which is the
+conditional PDF given that the
+
+certain event has happened.
+
+This is a concept that's
+in some ways simpler.
+
+You've already seen a little
+bit of that in last week's
+
+recitation and tutorial.
+
+The idea is that we have a
+single random variable.
+
+It's described by a density.
+
+Then you're told that the
+certain event has occurred.
+
+Your model changes
+the universe that
+
+you are dealing with.
+
+In the new universe, you are
+dealing with a new density
+
+function, the one that applies
+given the knowledge that we
+
+have that the certain
+event has occurred.
+
+All right.
+
+So what exactly did
+we say about
+
+continuous random variables?
+
+The first thing is the
+definition, that a random
+
+variable is said to be
+continuous if we are given a
+
+certain object that we call
+the probability density
+
+function and we can calculate
+interval probabilities given
+
+this density function.
+
+So the definition is that the
+random variable is continuous
+
+if you can calculate
+probabilities associated with
+
+that random variable
+given that formula.
+
+So this formula tells you that
+the probability that your
+
+random variable falls inside
+this interval is the area
+
+under the density curve.
+
+OK.
+
+There's a few properties
+that a density
+
+function must satisfy.
+
+Since we're talking about
+probabilities, and
+
+probabilities are non-negative,
+we have that the
+
+density function is always
+a non-negative function.
+
+The total probability over
+the entire real line
+
+must be equal to 1.
+
+So the integral when you
+integrate over the entire real
+
+line has to be equal to 1.
+
+That's the second property.
+
+Another property that you get is
+that if you let a equal to
+
+b, this integral becomes 0.
+
+And that tells you that the
+probability of a single point
+
+in the continuous case
+is always equal to 0.
+
+So these are formal
+properties.
+
+When you want to think
+intuitively, the best way to
+
+think about what the density
+function is to think in terms
+
+of little intervals, the
+probability that my random
+
+variable falls inside
+the little interval.
+
+Well, inside that little
+interval, the density function
+
+here is roughly constant.
+
+So that integral becomes the
+value of the density times the
+
+length of the interval over
+which you are integrating,
+
+which is delta.
+
+And so the density function
+basically gives us
+
+probabilities of little events,
+of small events.
+
+And the density is to be
+interpreted as probability per
+
+unit length at a certain
+place in the diagram.
+
+So in that place in the diagram,
+the probability per
+
+unit length around this
+neighborhood would be the
+
+height of the density function
+at that point.
+
+What else?
+
+We have a formula for
+calculating expected values of
+
+functions of random variables.
+
+In the discrete case, we had the
+formula where here we had
+
+the sum, and instead of the
+density, we had the PMF.
+
+The same formula is also valid
+in the continuous case.
+
+And it's not too hard to derive,
+but we will not do it.
+
+But let's think of the
+intuition of what
+
+this formula says.
+
+You're trying to figure out on
+the average how much g(X) is
+
+going to be.
+
+And then you reason, and you
+say, well, X may turn out to
+
+take a particular value or a
+small interval of values.
+
+This is the probability
+that X falls
+
+inside the small interval.
+
+And when that happens, g(X)
+takes that value.
+
+So this fraction of the time,
+you fall in the little
+
+neighborhood of x, and
+you get so much.
+
+Then you average over all the
+possible x's that can happen.
+
+And that gives you the average
+value of the function g(X).
+
+OK.
+
+So this is the easy stuff.
+
+Now let's get to the
+new material.
+
+We want to talk about multiple
+random variables
+
+simultaneously.
+
+So we want to talk now about two
+random variables that are
+
+continuous, and in some sense
+that they are jointly
+
+continuous.
+
+And let's see what this means.
+
+The definition is similar to
+the definition we had for a
+
+single random variable, where
+I take this formula here as
+
+the definition of continuous
+random variables.
+
+Two random variables are said to
+be jointly continuous if we
+
+can calculate probabilities by
+integrating a certain function
+
+that we call the joint
+density function
+
+over the set of interest.
+
+So we have our two-dimensional
+plane.
+
+This is the x-y plane.
+
+There's a certain event S that
+we're interested in.
+
+We want to calculate
+the probability.
+
+How do we do that?
+
+We are given this function
+f_(X,Y), the joint density.
+
+It's a function of the two
+arguments x and y.
+
+So think of that function as
+being some kind of surface
+
+that sits on top of the
+two-dimensional plane.
+
+The probability of falling
+inside the set S, we calculate
+
+it by looking at the volume
+under the surface, that volume
+
+that sits on top of S. So the
+surface underneath it has a
+
+certain total volume.
+
+What should that total
+volume be?
+
+Well, we think of these volumes
+as probabilities.
+
+So the total probability
+should be equal to 1.
+
+The total volume under this
+surface, should be equal to 1.
+
+So that's one property
+that we want our
+
+density function to have.
+
+So when you integrate over the
+entire space, this is of the
+
+volume under your surface.
+
+That should be equal to 1.
+
+Of course, since we're talking
+about probabilities, the joint
+
+density should be a non-negative
+function.
+
+So think of the situation
+as having one pound of
+
+probability that's spread
+all over your space.
+
+And the height of this joint
+density function basically
+
+tells you how much probability
+tends to be accumulated in
+
+certain regions of space
+as opposed to other
+
+parts of the space.
+
+So wherever the density is big,
+that means that this is
+
+an area of the two-dimensional
+plane that's
+
+more likely to occur.
+
+Where the density is small, that
+means that those x-y's
+
+are less likely to occur.
+
+You have already seen
+one example
+
+of continuous densities.
+
+That was the example we had in
+the very beginning of the
+
+class with a uniform
+
+distribution on the unit square.
+
+That was a special
+case of a density
+
+function that was constant.
+
+So all places in the unit square
+were roughly equally
+
+likely as any other places.
+
+But in other models, some parts
+of the space may be more
+
+likely than others.
+
+And we describe those relative
+likelihoods using
+
+this density function.
+
+So if somebody gives us the
+density function, this
+
+determines for us probabilities
+of all the
+
+subsets of the two-dimensional
+plane.
+
+Now for an intuitive
+interpretation, it's good to
+
+think about small events.
+
+So let's take a particular x
+here and then x plus delta.
+
+So this is a small interval.
+
+Take another small interval
+here that goes from y to y
+
+plus delta.
+
+And let's look at the event that
+x falls here and y falls
+
+right there.
+
+What is this event?
+
+Well, this is the event
+that will fall
+
+inside this little rectangle.
+
+Using this rule for calculating
+probabilities,
+
+what is the probability of that
+rectangle going to be?
+
+Well, it should be the integral
+of the density over
+
+this rectangle.
+
+Or it's the volume under the
+surface that sits on top of
+
+that rectangle.
+
+Now, if the rectangle is very
+small, the joint density is
+
+not going to change very much
+in that neighborhood.
+
+So we can treat it
+as a constant.
+
+So the volume is going to
+be the height times
+
+the area of the base.
+
+The height at that point is
+whatever the function happens
+
+to be around that point.
+
+And the area of the base
+is delta squared.
+
+So this is the intuitive way
+to understand what a joint
+
+density function really
+tells you.
+
+It specifies for you
+probabilities of little
+
+squares, of little rectangles.
+
+And it allows you to think of
+the joint density function as
+
+probability per unit area.
+
+So these are the units of the
+density, its probability per
+
+unit area in the neighborhood
+of a certain point.
+
+So what do we do with this
+density function once we have
+
+it in our hands?
+
+Well, we can use it to calculate
+expected values.
+
+Suppose that you have a
+function of two random
+
+variables described by
+a joint density.
+
+You can find, perhaps, the
+distribution of this random
+
+variable and then use the
+basic definition of the
+
+expectation.
+
+Or you can calculate
+expectations directly, using
+
+the distribution of the original
+random variables.
+
+This is a formula that's again
+identical to the formula that
+
+we had for the discrete case.
+
+In the discrete case,
+we had a double sum
+
+here, and we had PMFs.
+
+So the intuition behind this
+formula is the same that one
+
+had for the discrete case.
+
+It's just that the mechanics
+are different.
+
+Then something that we did in
+the discrete case was to find
+
+a way to go from the joint
+density of the two random
+
+variables taken together to the
+density of just one of the
+
+random variables.
+
+So we had a formula for
+the discrete case.
+
+Let's see how things are
+going to work out in
+
+the continuous case.
+
+So in the continuous
+case, we have here
+
+our two random variables.
+
+And we have a density
+for them.
+
+And let's say that we want to
+calculate the probability that
+
+x falls inside this interval.
+
+So we're looking at the
+probability that our random
+
+variable X falls in the interval
+from little x to x
+
+plus delta.
+
+Now, by the properties that we
+already have for interpreting
+
+the density function of a single
+random variable, the
+
+probability of a little interval
+is approximately the
+
+density of that single random
+variable times delta.
+
+And now we want to find a
+formula for this marginal
+
+density in terms of
+the joint density.
+
+OK.
+
+So this is the probability
+that x
+
+falls inside this interval.
+
+In terms of the two-dimensional
+plane, this is
+
+the probability that (x,y)
+falls inside this strip.
+
+So to find that probability,
+we need to calculate the
+
+probability that (x,y) falls in
+here, which is going to be
+
+the double integral over the
+interval over this strip, of
+
+the joint density.
+
+And what are we integrating
+over?
+
+y goes from minus infinity
+to plus infinity.
+
+And the dummy variable x goes
+from little x to x plus delta.
+
+So to integrate over this strip,
+what we do is for any
+
+given y, we integrate
+in this dimension.
+
+This is the x integral.
+
+And then we integrate over
+the y dimension.
+
+Now what is this
+inner integral?
+
+Because x only varies very
+little, this is approximately
+
+constant in that range.
+
+So the integral with
+respect to x just
+
+becomes delta times f(x,y).
+
+And then we've got our dy.
+
+So this is what the inner
+integral will evaluate to.
+
+We are integrating over
+the little interval.
+
+So we're keeping y fixed.
+
+Integrating over here, we take
+the value of the density times
+
+how much we're integrating
+over.
+
+And we get this formula.
+
+OK.
+
+Now, this expression must be
+equal to that expression.
+
+So if we cancel the deltas, we
+see that the marginal density
+
+must be equal to the integral of
+the joint density, where we
+
+have integrated out
+the value of y.
+
+So this formula should come as
+no surprise at this point.
+
+It's exactly the same as the
+formula that we had for
+
+discrete random variables.
+
+But now we are replacing the
+sum with an integral.
+
+And instead of using the
+joint PMF, we are
+
+using the joint PDF.
+
+Then, continuing going down the
+list of things we did for
+
+discrete random variables, we
+can now introduce a definition
+
+of the notion of independence
+of two random variables.
+
+And by analogy with the discrete
+case, we define
+
+independence to be the
+following condition.
+
+Two random variables are
+independent if and only if
+
+their joint density function
+factors out as a product of
+
+their marginal densities.
+
+And this property needs to
+be true for all x and y.
+
+So this is the formal
+definition.
+
+Operationally and intuitively,
+what does it mean?
+
+Well, intuitively it means
+the same thing as in
+
+the discrete case.
+
+Knowing anything about X
+shouldn't tell you anything
+
+about Y. That is, information
+about X is not going to change
+
+your beliefs about Y. We are
+going to come back to this
+
+statement in a second.
+
+The other thing that it
+allows you to do--
+
+I'm not going to derive this--
+is it allows you to calculate
+
+probabilities by multiplying
+individual probabilities.
+
+So if you ask for the
+probability that x falls in a
+
+certain set A and y falls in a
+certain set B, then you can
+
+calculate that probability
+by multiplying individual
+
+probabilities.
+
+This takes just two lines of
+derivation, which I'm not
+
+going to do.
+
+But it comes back to
+the usual notion of
+
+independence of events.
+
+Basically, operationally
+independence means that you
+
+can multiply probabilities.
+
+So now let's look
+at an example.
+
+There's a sort of pretty famous
+and classical one.
+
+It goes back a lot more
+than a 100 years.
+
+And it's the famous
+Needle of Buffon.
+
+Buffon was a French naturalist
+who, for some reason, also
+
+decided to play with
+probability.
+
+And look at the following
+problem.
+
+So you have the two-dimensional
+plane.
+
+And on the plane we draw a
+bunch of parallel lines.
+
+And those parallel lines are
+separated by a length.
+
+And the lines are apart
+at distance d.
+
+And we throw a needle at random,
+completely at random.
+
+And we'll have to give a meaning
+to what "completely at
+
+random" means.
+
+And when we throw a needle,
+there's two possibilities.
+
+Either the needle is going to
+fall in a way that does not
+
+intersect any of the lines, or
+it's going to fall in a way
+
+that it intersects
+one of the lines.
+
+We're taking the needle to be
+shorter than this distance, so
+
+the needle cannot intersect
+two lines simultaneously.
+
+It either intersects 0, or it
+intersects one of the lines.
+
+The question is to find the
+probability that the needle is
+
+going to intersect a line.
+
+What's the probability
+of this?
+
+OK.
+
+We are going to approach this
+problem by using our standard
+
+four-step procedure.
+
+Set up your sample space,
+describe a probability law on
+
+that sample space, identify
+the event of interest, and
+
+then calculate.
+
+These four steps basically
+correspond to these three
+
+bullets and then the last
+equation down here.
+
+So first thing is to set
+up a sample space.
+
+We need some variables to
+describe what happened in the
+
+experiment.
+
+So what happens in the
+experiment is that the needle
+
+lands somewhere.
+
+And where it lands, we can
+describe this by specifying
+
+the location of the center
+of the needle.
+
+And what do we mean by the
+location of the center?
+
+Well, we can take as our
+variable to be the distance
+
+from the center of the needle
+to the nearest line.
+
+So it tells us the vertical
+distance of the center of the
+
+needle from the nearest line.
+
+The other thing that
+matters is the
+
+orientation of the needle.
+
+So we need one more variable,
+which we take to be the angle
+
+that the needle is forming
+with the lines.
+
+We can put the angle here,
+or you can put in there.
+
+Yes, it's still the
+same angle.
+
+So we have these two variables
+that described what happened
+
+in the experiment.
+
+And we can take our sample space
+to be the set of all
+
+possible x's and theta's.
+
+What are the possible x's?
+
+The lines are d apart, so the
+nearest line is going to be
+
+anywhere between
+0 and d/2 away.
+
+So that tells us what the
+possible x's will be.
+
+As for theta, it really
+depends how
+
+you define your angle.
+
+We are going to define our theta
+to be the acute angle
+
+that's formed between the needle
+and a line, if you were
+
+to extend it.
+
+So theta is going to be
+something between 0 and pi/2.
+
+So I guess these red pieces
+really correspond to the part
+
+of setting up the
+sample space.
+
+OK.
+
+So that's part one.
+
+Second part is we
+need a model.
+
+OK.
+
+Let's take our model to be that
+we basically know nothing
+
+about how the needle falls.
+
+It can fall in any possible way,
+and all possible ways are
+
+equally likely.
+
+Now, if you have those parallel
+lines, and you close
+
+your eyes completely and throw a
+needle completely at random,
+
+any x should be equally
+likely.
+
+So we describe that situation by
+saying that X should have a
+
+uniform distribution.
+
+That is, it should have a
+constant density over the
+
+range of interest.
+
+Similarly, if you kind of spin
+your needle completely at
+
+random, any angle should be as
+likely as any other angle.
+
+And we decide to model this
+situation by saying that theta
+
+also has a uniform
+distribution over
+
+the range of interest.
+
+And finally, where we put it
+should have nothing to do with
+
+how much we rotate it.
+
+And we capture this
+mathematically by saying that
+
+X is going to be independent
+of theta.
+
+Now, this is going
+to be our model.
+
+I'm not deriving the model
+from anything.
+
+I'm only saying that this sounds
+like a model that does
+
+not assume any knowledge or
+preference for certain values
+
+of x rather than other
+values of theta.
+
+In the absence of any other
+particular information you
+
+might have in your hands, that's
+the most reasonable
+
+model to come up with.
+
+So you model the problem
+that way.
+
+So what's the formula for
+the joint density?
+
+It's going to be the
+product of the
+
+densities of X and Theta.
+
+Why is it the product?
+
+This is because we assumed
+independence.
+
+And the density of X, since
+it's uniform, and since it
+
+needs to integrate to 1, that
+density needs to be 2/d.
+
+That's the density of X.
+And the density of
+
+Theta needs to be 2/pi.
+
+That's the value for the density
+of Theta so that the
+
+overall probability over this
+interval ends up being 1.
+
+So now we do have our joint
+density in our hands.
+
+The next thing to do
+is to identify
+
+the event of interest.
+
+And this is best done
+in a picture.
+
+And there's two possible
+situations
+
+that one could have.
+
+Either the needle falls this
+way, or it falls this way.
+
+So how can we tell if one or the
+other is going to happen?
+
+It has to do with whether this
+interval here is smaller than
+
+that or bigger than that.
+
+So we are comparing
+the height of this
+
+interval to that interval.
+
+This interval here
+is capital X.
+
+This interval here,
+what is it?
+
+This is half of the length of
+the needle, which is l/2.
+
+To find this height, we take l/2
+and multiply it with the
+
+sine of the angle
+that we have.
+
+So the length of this
+interval up here is
+
+l/2 times sine theta.
+
+If this is smaller than
+x, the needle does not
+
+intersect the line.
+
+If this is bigger than
+x, then the needle
+
+intersects the line.
+
+So the event of interest, that
+the needle intersects the
+
+line, is described this way
+in terms of x and theta.
+
+And now that we have the event
+of interest described
+
+mathematically, all that we
+need to do is to find the
+
+probability of this event, we
+integrate the joint density
+
+over the part of (x, theta)
+space in which this
+
+inequality is true.
+
+So it's a double integral over
+the set of all x's and theta's
+
+where this is true.
+
+The way to do this integral is
+we fix theta, and we integrate
+
+for x's that go from 0
+up to that number.
+
+And theta can be anything
+between 0 and pi/2.
+
+So the integral over this set
+is basically this double
+
+integral here.
+
+We already have a formula
+for the joint density.
+
+It's 4 over pi d, so
+we put it here.
+
+And now, fortunately,
+this is a pretty
+
+easy integral to evaluate.
+
+The integral with respect to x
+-- there's nothing in here.
+
+So the integral is just the
+length of the interval over
+
+which we're integrating.
+
+It's l/2 sine theta.
+
+And then we need to integrate
+this with respect to theta.
+
+We know that the integral of a
+sine is a negative cosine.
+
+You plug in the values for
+the negative cosine
+
+at the two end points.
+
+I'm sure you can do
+this integral .
+
+And we finally obtain the
+answer, which is amazingly
+
+simple for such a pretty
+complicated-looking problem.
+
+It's 2l over pi d.
+
+So some people a long, long time
+ago, after they looked at
+
+this answer, they said that
+maybe that gives us an
+
+interesting way where one could
+estimate the value by
+
+pi, for example,
+experimentally.
+
+How do you do that?
+
+Fix l and d, the dimensions
+of the problem.
+
+Throw a million needles on
+your piece of paper.
+
+See how often your needless
+do intersect the line.
+
+That gives you a number
+for this quantity.
+
+You know l and d, so you can
+use that to infer pi.
+
+And there's an apocryphal story
+about a wounded soldier
+
+in a hospital after the
+American Civil War who
+
+actually had heard about this
+and was spending his time in
+
+the hospital throwing needles
+on pieces of paper.
+
+I don't know if it's
+true or not.
+
+But let's do something
+similar here.
+
+So let's look at this diagram.
+
+We fix the dimensions.
+
+This is supposed to
+be our little d.
+
+That's supposed to
+be our little l.
+
+We have the formula from the
+previous slide that p
+
+is 2l over pi d.
+
+In this instance, we choose
+d to be twice l.
+
+So this number is 1/pi.
+
+So the probability that the
+needle hits the line is 1/pi.
+
+So I need needles that are
+3.1 centimeters long.
+
+I couldn't find such needles.
+
+But I could find paper clips
+that are 3.1 centimeters long.
+
+So let's start throwing paper
+clips at random and see how
+
+many of them will end up
+intersecting the lines.
+
+Good.
+
+OK.
+
+So out of eight paper clips,
+we have exactly four that
+
+intersected the line.
+
+So our estimate for the
+probability of intersecting
+
+the line is 1/2, which gives us
+an estimate for the value
+
+of pi, which is two.
+
+Well, I mean, within an
+engineering approximation,
+
+we're in the right
+ballpark, right?
+
+So this might look like a
+silly way of trying to
+
+estimate pi.
+
+And it probably is.
+
+On the other hand, this kind of
+methodology is being used
+
+especially by physicists and
+also by statisticians.
+
+It's used a lot.
+
+When is it used?
+
+If you have an integral to
+calculate, such as this
+
+integral, but you're not lucky,
+and your functions are
+
+not so simple where you can do
+your calculations by hand, and
+
+maybe the dimensions are
+larger-- instead of two random
+
+variables you have 100
+random variables, so
+
+it's a 100-fold integral--
+
+then there's no way to do
+that in the computer.
+
+But the way that you can
+actually do it is by
+
+generating random samples of
+your random variables, doing
+
+that simulation over and
+over many times.
+
+That is, by interpreting an
+integral as a probability, you
+
+can use simulation to estimate
+that probability.
+
+And that gives you a way of
+calculating integrals.
+
+And physicists do actually use
+that a lot, as well as
+
+statisticians, computer
+scientists, and so on.
+
+It's a so-called Monte
+Carlo method
+
+for evaluating integrals.
+
+And it's a basic piece of the
+toolbox in science these days.
+
+Finally, the harder concept
+of the day is the idea of
+
+conditioning.
+
+And here things become a little
+subtle when you deal
+
+with continuous random
+variables.
+
+OK.
+
+First, remember again our basic
+interpretation of what a
+
+density is.
+
+A density gives us
+
+probabilities of little intervals.
+
+So how should we define
+conditional densities?
+
+Conditional densities should
+again give us probabilities of
+
+little intervals, but inside a
+conditional world where we
+
+have been told something about
+the other random variable.
+
+So what we would like to be
+true is the following.
+
+We would like to define a
+concept of a conditional
+
+density of a random variable X
+given the value of another
+
+random variable Y. And it should
+behave the following
+
+way, that the conditional
+density gives us the
+
+probability of little
+intervals--
+
+same as here--
+
+given that we are told
+the value of y.
+
+And here's where the
+subtleties come.
+
+The main thing to notice is
+that here I didn't write
+
+"equal," I wrote "approximately
+equal." Why do
+
+we need that?
+
+Well, the thing is that
+conditional probabilities are
+
+not defined when you condition
+on an event that has 0
+
+probability.
+
+So we need the conditioning
+event here to have posed this
+
+probability.
+
+So instead of saying that Y is
+exactly equal to little y, we
+
+want to instead say we're in a
+new universe where capital Y
+
+is very close to little y.
+
+And then this notion of "very
+close" kind of takes the limit
+
+and takes it to be
+infinitesimally close.
+
+So this is the way to interpret
+conditional
+
+probabilities.
+
+That's what they should mean.
+
+Now, in practice, when you
+actually use probability, you
+
+forget about that subtlety.
+
+And you say, well, I've been
+told that Y is equal to 1.3.
+
+Give me the conditional
+distribution of X. But
+
+formally or rigorously, you
+should say I'm being told that
+
+Y is infinitesimally
+close to 1.3.
+
+Tell me the distribution of X.
+
+Now, if this is what we want,
+what should this quantity be?
+
+It's a conditional probability,
+so it should be
+
+the probability of two
+things happening--
+
+X being close to little x, Y
+being close to little y.
+
+And that's basically given to
+us by the joint density
+
+divided by the probability of
+the conditioning event, which
+
+has something to do with the
+density of Y itself.
+
+And if you do things carefully,
+you see that the
+
+only way to satisfy this
+relation is to define the
+
+conditional density by this
+particular formula.
+
+OK.
+
+Big discussion to come down in
+the end to what you should
+
+have probably guessed by now.
+
+We just take any formulas and
+expressions from the discrete
+
+case and replace PMFs by PDFs.
+
+So the conditional PDF is
+defined by this formula where
+
+here we have joint PDF and
+marginal PDF, as opposed to
+
+the discrete case where we
+had the joint PMF and
+
+the marginal PMF.
+
+So in some sense, it's just
+a syntactic change.
+
+In another sense, it's a little
+subtler on how you
+
+actually interpret it.
+
+Speaking about interpretation,
+what are some ways of thinking
+
+about the joint density?
+
+Well, the best way to think
+about it is that somebody has
+
+fixed little y for you.
+
+So little y is being
+fixed here.
+
+And we look at this density
+as a function of X.
+
+I've told you what Y is.
+
+Tell me what you know about X.
+And you tell me that X has a
+
+certain distribution.
+
+What does that distribution
+look like?
+
+It has exactly the same shape
+as the joint density.
+
+Remember, we fixed Y. So
+this is a constant.
+
+So the only thing that varies
+is X. So we get the function
+
+that behaves like the joint
+density when you fix y, which
+
+is really you take the joint
+density, and you
+
+take a slice of it.
+
+You fix a y, and you see
+how it varies with x.
+
+So in that sense, the
+conditional PDF is just a
+
+slice of the joint PDF.
+
+But we need to divide by a
+certain number, which just
+
+scales it and changes
+its shape.
+
+We're coming back to a
+picture in a second.
+
+But before going to the picture,
+lets go back to the
+
+interpretation of
+independence.
+
+If the two random the variables
+are independent,
+
+according to our definition in
+the previous slide, the joint
+
+density is going to factor
+as the product of
+
+the marginal densities.
+
+The density of Y in the
+numerator cancels the density
+
+in the denominator.
+
+And we're just left with
+the density of X.
+
+So in the case of independence,
+what we get is
+
+that the conditional is the
+same as the marginal.
+
+And that solidifies our
+intuition that in the case of
+
+independence, being told
+something about the value of Y
+
+does not change our beliefs
+about how X is distributed.
+
+So whatever we expected about X
+is going to remain true even
+
+after we are told something
+about Y.
+
+So let's look at
+some pictures.
+
+Here is what the joint
+PDF might look like.
+
+Here we've got our
+x and y-axis.
+
+And if you want to calculate the
+probability of a certain
+
+event, what you do is you look
+at that event and you see how
+
+much of that mass is sitting
+on top of that event.
+
+Now let's start slicing.
+
+Let's fix a value of x and look
+along that slice where we
+
+obtain this function.
+
+Now what does that slice do?
+
+That slice tells us for that
+particular x what the possible
+
+values of y are going to be
+and how likely they are.
+
+If we integrate over all
+y's, what do we get?
+
+Integrating over all y's just
+gives us the marginal density
+
+of X. It's the calculation
+that we did here.
+
+By integrating over all y's, we
+find the marginal density
+
+of X. So the total area under
+that slice gives us the
+
+marginal density of X. And by
+looking at the different
+
+slices, we find how likely the
+different values of x are
+
+going to be.
+
+How about the conditional?
+
+If we're interested in the
+conditional of Y given X, how
+
+would you think about it?
+
+This refers to a universe where
+we are told that capital
+
+X takes on a specific value.
+
+So we put ourselves in
+the universe where
+
+this line has happened.
+
+There's still possible values
+of y that can happen.
+
+And this shape kind of tells us
+the relative likelihoods of
+
+the different y's.
+
+And this is indeed going to be
+the shape of the conditional
+
+distribution of Y given
+that X has occurred.
+
+On the other hand, the
+conditional distribution must
+
+add up to 1.
+
+So the total probability over
+all of the different y's in
+
+this universe, that
+total probability
+
+should be equal to 1.
+
+Here it's not equal to 1.
+
+The total area is the
+marginal density.
+
+To make it equal to 1, we need
+to divide by the marginal
+
+density, which is basically to
+renormalize this shape so that
+
+the total area under that slice,
+under that shape, is
+
+equal to 1.
+
+So we start with the joint.
+
+We take the slices.
+
+And then we adjust the slices
+so that every slice has an
+
+area underneath equal to 1.
+
+And this gives us
+the conditional.
+
+So for example, down here--
+
+you can not even see it
+in this diagram--
+
+but after you renormalize it
+so that its total area is
+
+equal to 1, you get this sort of
+narrow spike that goes up.
+
+And so this is a plot of the
+conditional distributions that
+
+you get for the different
+values of x.
+
+Given a particular value of x,
+you're going to get this
+
+certain conditional
+distribution.
+
+So this picture is worth about
+as much as anything else in
+
+this particular chapter.
+
+Make sure you kind of understand
+exactly all these
+
+pieces of the picture.
+
+And finally, let's go, in the
+remaining time, through an
+
+example where we're going to
+throw in the bucket all the
+
+concepts and notations that
+we have introduced so far.
+
+So the example is as follows.
+
+We start with a stick that
+has a certain length.
+
+And we break it a completely
+random location.
+
+And--
+
+yes, this 1 should be l.
+
+OK.
+
+So it has length l.
+
+And we're going to break
+it at the random place.
+
+And we call that random place
+where we break it, we call it
+
+X.
+
+X can be anywhere, uniform
+distribution.
+
+So this means that X has a
+density that goes from 0 to l.
+
+I guess this capital L is
+supposed to be the same as the
+
+lower-case l.
+
+So that's the density of X. And
+since the density needs to
+
+integrate to 1, the height of
+that density has to be 1/l.
+
+Now, having broken the stick
+and given that we are left
+
+with this piece of the stick,
+I'm now going to break it
+
+again at a completely random
+place, meaning I'm going to
+
+choose a point where I break it
+uniformly over the length
+
+of the stick.
+
+What does this mean?
+
+And let's call Y the location
+where I break it.
+
+So Y is going to range
+between 0 and x.
+
+x is the stick that
+I'm left with.
+
+So I'm going to break it
+somewhere in between.
+
+So I pick a y between 0 and x.
+
+And of course, x
+is less than l.
+
+And I'm going to
+break it there.
+
+So y is uniform between
+0 and x.
+
+What does that mean, that the
+density of y, given that you
+
+have already told me x, ranges
+from 0 to little x?
+
+If I told you that the first
+break happened at a particular
+
+x, then y can only range
+over this interval.
+
+And I'm assuming a uniform
+
+distribution over that interval.
+
+So we have this kind of shape.
+
+And that fixes for
+us the height of
+
+the conditional density.
+
+So what's the joint density of
+those two random variables?
+
+By the definition of conditional
+densities, the
+
+conditional was defined as the
+ratio of this divided by that.
+
+So we can find the joint density
+by taking the marginal
+
+and then multiplying
+by the conditional.
+
+This is the same formula as
+in the discrete case.
+
+This is our very familiar
+multiplication rule, but
+
+adjusted to the case of
+continuous random variables.
+
+So Ps become Fs.
+
+OK.
+
+So we do have a formula
+for this.
+
+What is it?
+
+It's 1/l--
+
+that's the density of X --
+
+times 1/x, which is the
+conditional density of Y. This
+
+is the formula for the
+joint density.
+
+But we must be careful.
+
+This is a formula that's
+not valid anywhere.
+
+It's only valid for the x's
+and y's that are possible.
+
+And the x's and y's that are
+possible are given by these
+
+inequalities.
+
+So x can range from 0 to
+l, and y can only be
+
+smaller than x.
+
+So this is the formula
+for the density on
+
+this part of our space.
+
+The density is 0
+anywhere else.
+
+So what does it look like?
+
+It's basically a 1/x function.
+
+So it's sort of constant
+along that dimension.
+
+But as x goes to 0, your
+density goes up and
+
+can even blow up.
+
+It sort of looks like a sail
+that's raised and somewhat
+
+curved and has a point up
+there going to infinity.
+
+So this is the joint density.
+
+Now once you have in your hands
+a joint density, then
+
+you can answer in principle
+any problem.
+
+It's just a matter of plugging
+in and doing computations.
+
+How about calculating something
+like a conditional
+
+expectation of Y given
+a value of x?
+
+OK.
+
+That's a concept we have
+not defined so far.
+
+But how should we define it?
+
+Means the reasonable thing.
+
+We'll define it the same way
+as ordinary expectations
+
+except that since we're given
+some conditioning information,
+
+we should use the probability
+distribution that applies to
+
+that particular situation.
+
+So in a situation where we are
+told the value of x, the
+
+distribution that applies is the
+conditional distribution
+
+of Y. So it's going to be the
+conditional density of Y given
+
+the value of x.
+
+Now, we know what this is.
+
+It's given by 1/x.
+
+So we need to integrate
+y times 1/x dy.
+
+And what should we
+integrate over?
+
+Well, given the value of x, y
+can only range from 0 to x.
+
+So this is what we get.
+
+And you do your integral, and
+you get that this is x/2.
+
+Is it a surprise?
+
+It shouldn't be.
+
+This is just the expected value
+of Y in a universe where
+
+X has been realized and Y is
+given by this distribution.
+
+Y is uniform between 0 and x.
+
+The expected value of Y should
+be the midpoint of this
+
+interval, which is x/2.
+
+Now let's do fancier stuff.
+
+Since we have the joint
+distribution, we should be
+
+able to calculate
+the marginal.
+
+What is the distribution of Y?
+
+After breaking the stick twice,
+how big is the little
+
+piece that I'm left with?
+
+How do we find this?
+
+To find the marginal, we just
+take the joint and integrate
+
+out the variable that
+we don't want.
+
+A particular y can happen
+in many ways.
+
+It can happen together
+with any x.
+
+So we consider all the possible
+x's that can go
+
+together with this y and average
+over all those x's.
+
+So we plug in the formula for
+the joint density from the
+
+previous slide.
+
+We know that it's 1/lx.
+
+And what's the range
+of the x's?
+
+So to find the density of Y for
+a particular y up here,
+
+I'm going to integrate
+over x's.
+
+The density is 0
+here and there.
+
+The density is nonzero
+only in this part.
+
+So I need to integrate over x's
+going from here to there.
+
+So what's the "here"?
+
+This line goes up at
+the slope of 1.
+
+So this is the line
+x equals y.
+
+So if I fix y, it means that
+my integral starts from a
+
+value of x that is
+also equal to y.
+
+So where the integral starts
+from is at x equals y.
+
+And it goes all the way until
+the end of the length of our
+
+stick, which is l.
+
+So we need to integrate
+from little y up to l.
+
+So that's something that
+almost always comes up.
+
+It's not enough to have just
+this formula for integrating
+
+the joint density.
+
+You need to keep track
+of different regions.
+
+And if the joint density is 0
+in some regions, then you
+
+exclude those regions from
+the range of integration.
+
+So the range of integration is
+only over those values where
+
+the particular formula is valid,
+the places where the
+
+joint density is nonzero.
+
+All right.
+
+The integral of 1/x dx, that
+gives you a logarithm.
+
+So we evaluate this integral,
+and we get an
+
+expression of this kind.
+
+So the density of Y has a
+somewhat unexpected shape.
+
+So it's a logarithmic
+function.
+
+And it goes this way.
+
+It's for y going all
+the way to l.
+
+When y is equal to l, the
+logarithm of 1 is equal to 0.
+
+But when y approaches 0,
+logarithm of something big
+
+blows up, and we get a
+shape of this form.
+
+OK.
+
+Finally, we can calculate the
+expected value of Y. And we
+
+can do this by using the
+definition of the expectation.
+
+So integral of y times
+the density of y.
+
+We already found what that
+density is, so we
+
+can plug it in here.
+
+And we're integrating over
+the range of possible
+
+y's, from 0 to l.
+
+Now this involves the integral
+for y log y, which I'm sure
+
+you have encountered in your
+calculus classes but maybe do
+
+not remember how to do it.
+
+In any case, you look it
+up in some integral
+
+tables or do it by parts.
+
+And you get the final
+answer of l/4.
+
+And at this point, you say,
+that's a really simple answer.
+
+Shouldn't I have expected
+it to be l/4?
+
+I guess, yes.
+
+I mean, when you break it once,
+the expected value of
+
+what you are left with is going
+to be 1/2 of what you
+
+started with.
+
+When you break it the next time,
+the expected length of
+
+what you're left with should be
+1/2 of the piece that you
+
+are now breaking.
+
+So each time that you break it
+at random, you expected it to
+
+become smaller by
+a factor of 1/2.
+
+So if you break it twice, you
+are left something that's
+
+expected to be 1/4.
+
+This is reasoning on the
+average, which happens to give
+
+you the right answer
+in this case.
+
+But again, there's the warning
+that reasoning on the average
+
+doesn't always give you
+the right answer.
+
+So be careful about doing
+arguments of this type.
+
+Very good.
+
+See you on Wednesday.
\ No newline at end of file
diff --git a/D7nf7pKddwM.txt b/D7nf7pKddwM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ae63927427b8c247d2c1cf705e3b5c3322dec446
--- /dev/null
+++ b/D7nf7pKddwM.txt
@@ -0,0 +1,763 @@
+align:start position:0%
+ 
+welcome back to recitation uh in this
+
+ align:start position:0%
+welcome back to recitation uh in this
+ 
+
+ align:start position:0%
+welcome back to recitation uh in this
+segment I'm going to actually show uh
+
+ align:start position:0%
+segment I'm going to actually show uh
+ 
+
+ align:start position:0%
+segment I'm going to actually show uh
+well you're actually going to show the
+
+ align:start position:0%
+well you're actually going to show the
+ 
+
+ align:start position:0%
+well you're actually going to show the
+derivative of tangent X using the
+
+ align:start position:0%
+derivative of tangent X using the
+ 
+
+ align:start position:0%
+derivative of tangent X using the
+quotient rule so what what I'd like you
+
+ align:start position:0%
+quotient rule so what what I'd like you
+ 
+
+ align:start position:0%
+quotient rule so what what I'd like you
+to do I I wanted to remind you of what
+
+ align:start position:0%
+to do I I wanted to remind you of what
+ 
+
+ align:start position:0%
+to do I I wanted to remind you of what
+the quotient rule is so u and v are
+
+ align:start position:0%
+the quotient rule is so u and v are
+ 
+
+ align:start position:0%
+the quotient rule is so u and v are
+functions of X we want to take the
+
+ align:start position:0%
+functions of X we want to take the
+ 
+
+ align:start position:0%
+functions of X we want to take the
+derivative of U / V I've written the
+
+ align:start position:0%
+derivative of U / V I've written the
+ 
+
+ align:start position:0%
+derivative of U / V I've written the
+formula that you were given in class
+
+ align:start position:0%
+formula that you were given in class
+ 
+
+ align:start position:0%
+formula that you were given in class
+uh for this and I'm I'm asking for you
+
+ align:start position:0%
+uh for this and I'm I'm asking for you
+ 
+
+ align:start position:0%
+uh for this and I'm I'm asking for you
+to take DDX of tangent X using the
+
+ align:start position:0%
+to take DDX of tangent X using the
+ 
+
+ align:start position:0%
+to take DDX of tangent X using the
+quotient Rule and the hint I will give
+
+ align:start position:0%
+quotient Rule and the hint I will give
+ 
+
+ align:start position:0%
+quotient Rule and the hint I will give
+you is the reason we can obviously use
+
+ align:start position:0%
+you is the reason we can obviously use
+ 
+
+ align:start position:0%
+you is the reason we can obviously use
+the quotient rule is because tangent X
+
+ align:start position:0%
+the quotient rule is because tangent X
+ 
+
+ align:start position:0%
+the quotient rule is because tangent X
+is equal to a quotient of two functions
+
+ align:start position:0%
+is equal to a quotient of two functions
+ 
+
+ align:start position:0%
+is equal to a quotient of two functions
+of X it's sin x / cosine of x so I'm
+
+ align:start position:0%
+of X it's sin x / cosine of x so I'm
+ 
+
+ align:start position:0%
+of X it's sin x / cosine of x so I'm
+going to give you a minute to work this
+
+ align:start position:0%
+going to give you a minute to work this
+ 
+
+ align:start position:0%
+going to give you a minute to work this
+out for yourself and then when we come
+
+ align:start position:0%
+out for yourself and then when we come
+ 
+
+ align:start position:0%
+out for yourself and then when we come
+back I will do it uh for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you okay so we want to find the
+
+ align:start position:0%
+you okay so we want to find the
+ 
+
+ align:start position:0%
+you okay so we want to find the
+derivative of tangent X so let me let me
+
+ align:start position:0%
+derivative of tangent X so let me let me
+ 
+
+ align:start position:0%
+derivative of tangent X so let me let me
+work on this side of the board so I'm
+
+ align:start position:0%
+work on this side of the board so I'm
+ 
+
+ align:start position:0%
+work on this side of the board so I'm
+actually going to take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DDX of
+
+ align:start position:0%
+DDX of
+ 
+
+ align:start position:0%
+DDX of
+sinx divid cosine of
+
+ align:start position:0%
+sinx divid cosine of
+ 
+
+ align:start position:0%
+sinx divid cosine of
+x okay so I in this case sin x is U
+
+ align:start position:0%
+x okay so I in this case sin x is U
+ 
+
+ align:start position:0%
+x okay so I in this case sin x is U
+cosine X is V so using my quotient rule
+
+ align:start position:0%
+cosine X is V so using my quotient rule
+ 
+
+ align:start position:0%
+cosine X is V so using my quotient rule
+I know that first I have to take the
+
+ align:start position:0%
+I know that first I have to take the
+ 
+
+ align:start position:0%
+I know that first I have to take the
+derivative of sin x that's cosine X and
+
+ align:start position:0%
+derivative of sin x that's cosine X and
+ 
+
+ align:start position:0%
+derivative of sin x that's cosine X and
+then I multiply it by the denominator
+
+ align:start position:0%
+then I multiply it by the denominator
+ 
+
+ align:start position:0%
+then I multiply it by the denominator
+the V which is cosine X so my first term
+
+ align:start position:0%
+the V which is cosine X so my first term
+ 
+
+ align:start position:0%
+the V which is cosine X so my first term
+in the numerator
+
+ align:start position:0%
+in the numerator
+ 
+
+ align:start position:0%
+in the numerator
+is cosine 2 x again one cosine X comes
+
+ align:start position:0%
+is cosine 2 x again one cosine X comes
+ 
+
+ align:start position:0%
+is cosine 2 x again one cosine X comes
+from the derivative of sin x one cosine
+
+ align:start position:0%
+from the derivative of sin x one cosine
+ 
+
+ align:start position:0%
+from the derivative of sin x one cosine
+X is the V it's the cosine X in the
+
+ align:start position:0%
+X is the V it's the cosine X in the
+ 
+
+ align:start position:0%
+X is the V it's the cosine X in the
+denominator then I have to subtract V
+
+ align:start position:0%
+denominator then I have to subtract V
+ 
+
+ align:start position:0%
+denominator then I have to subtract V
+Prime U the derivative of cosine X is
+
+ align:start position:0%
+Prime U the derivative of cosine X is
+ 
+
+ align:start position:0%
+Prime U the derivative of cosine X is
+negative sinx I'll actually just write
+
+ align:start position:0%
+negative sinx I'll actually just write
+ 
+
+ align:start position:0%
+negative sinx I'll actually just write
+that one
+
+ align:start position:0%
+that one
+ 
+
+ align:start position:0%
+that one
+down and then I bring the U along for
+
+ align:start position:0%
+down and then I bring the U along for
+ 
+
+ align:start position:0%
+down and then I bring the U along for
+the ride so I multiply by sin x here
+
+ align:start position:0%
+the ride so I multiply by sin x here
+ 
+
+ align:start position:0%
+the ride so I multiply by sin x here
+and then I take v^2 in the denominator
+
+ align:start position:0%
+and then I take v^2 in the denominator
+ 
+
+ align:start position:0%
+and then I take v^2 in the denominator
+from the formula V again is cosine X so
+
+ align:start position:0%
+from the formula V again is cosine X so
+ 
+
+ align:start position:0%
+from the formula V again is cosine X so
+I take cosine 2 x in the denominator now
+
+ align:start position:0%
+I take cosine 2 x in the denominator now
+ 
+
+ align:start position:0%
+I take cosine 2 x in the denominator now
+this at this point is a little bit messy
+
+ align:start position:0%
+this at this point is a little bit messy
+ 
+
+ align:start position:0%
+this at this point is a little bit messy
+but the nice thing is that we can use
+
+ align:start position:0%
+but the nice thing is that we can use
+ 
+
+ align:start position:0%
+but the nice thing is that we can use
+some trigonometric identities to
+
+ align:start position:0%
+some trigonometric identities to
+ 
+
+ align:start position:0%
+some trigonometric identities to
+simplify this so let me first write out
+
+ align:start position:0%
+simplify this so let me first write out
+ 
+
+ align:start position:0%
+simplify this so let me first write out
+what it is a little more clearly minus a
+
+ align:start position:0%
+what it is a little more clearly minus a
+ 
+
+ align:start position:0%
+what it is a little more clearly minus a
+negative gives you a positive and then
+
+ align:start position:0%
+negative gives you a positive and then
+ 
+
+ align:start position:0%
+negative gives you a positive and then
+here I get sin x * sin x so I get sin^2
+
+ align:start position:0%
+here I get sin x * sin x so I get sin^2
+ 
+
+ align:start position:0%
+here I get sin x * sin x so I get sin^2
+X and then I keep div divid by cosine 2
+
+ align:start position:0%
+X and then I keep div divid by cosine 2
+ 
+
+ align:start position:0%
+X and then I keep div divid by cosine 2
+x now at this point some of you might
+
+ align:start position:0%
+x now at this point some of you might
+ 
+
+ align:start position:0%
+x now at this point some of you might
+have divided by cosine squ X here and
+
+ align:start position:0%
+have divided by cosine squ X here and
+ 
+
+ align:start position:0%
+have divided by cosine squ X here and
+gotten one and divided by cosine squ X
+
+ align:start position:0%
+gotten one and divided by cosine squ X
+ 
+
+ align:start position:0%
+gotten one and divided by cosine squ X
+here and gotten tangent squ X and then
+
+ align:start position:0%
+here and gotten tangent squ X and then
+ 
+
+ align:start position:0%
+here and gotten tangent squ X and then
+from there you uh you could simplify to
+
+ align:start position:0%
+from there you uh you could simplify to
+ 
+
+ align:start position:0%
+from there you uh you could simplify to
+another trigonometric function I'm going
+
+ align:start position:0%
+another trigonometric function I'm going
+ 
+
+ align:start position:0%
+another trigonometric function I'm going
+to go straight a different way to show
+
+ align:start position:0%
+to go straight a different way to show
+ 
+
+ align:start position:0%
+to go straight a different way to show
+you what that actually also equals so
+
+ align:start position:0%
+you what that actually also equals so
+ 
+
+ align:start position:0%
+you what that actually also equals so
+there at this point I want to stress
+
+ align:start position:0%
+there at this point I want to stress
+ 
+
+ align:start position:0%
+there at this point I want to stress
+there sort of two ways you can you can
+
+ align:start position:0%
+there sort of two ways you can you can
+ 
+
+ align:start position:0%
+there sort of two ways you can you can
+get to the same place but I'm going to
+
+ align:start position:0%
+get to the same place but I'm going to
+ 
+
+ align:start position:0%
+get to the same place but I'm going to
+use the fact that the numerator is is a
+
+ align:start position:0%
+use the fact that the numerator is is a
+ 
+
+ align:start position:0%
+use the fact that the numerator is is a
+very nice trigonometric identity that we
+
+ align:start position:0%
+very nice trigonometric identity that we
+ 
+
+ align:start position:0%
+very nice trigonometric identity that we
+know we know cosine s x plus sin s x
+
+ align:start position:0%
+know we know cosine s x plus sin s x
+ 
+
+ align:start position:0%
+know we know cosine s x plus sin s x
+always equals 1 so this is quite lovely
+
+ align:start position:0%
+always equals 1 so this is quite lovely
+ 
+
+ align:start position:0%
+always equals 1 so this is quite lovely
+the numerator simplifies to
+
+ align:start position:0%
+the numerator simplifies to
+ 
+
+ align:start position:0%
+the numerator simplifies to
+one the
+
+ align:start position:0%
+one the
+ 
+
+ align:start position:0%
+one the
+denominator stays cosine squ X what is
+
+ align:start position:0%
+denominator stays cosine squ X what is
+ 
+
+ align:start position:0%
+denominator stays cosine squ X what is
+this function one over cosine X is
+
+ align:start position:0%
+this function one over cosine X is
+ 
+
+ align:start position:0%
+this function one over cosine X is
+actually secant x so if you need at this
+
+ align:start position:0%
+actually secant x so if you need at this
+ 
+
+ align:start position:0%
+actually secant x so if you need at this
+point to
+
+ align:start position:0%
+point to
+ 
+
+ align:start position:0%
+point to
+rewrite the whole thing like this right
+
+ align:start position:0%
+rewrite the whole thing like this right
+ 
+
+ align:start position:0%
+rewrite the whole thing like this right
+1 squ is one and in the denominator we
+
+ align:start position:0%
+1 squ is one and in the denominator we
+ 
+
+ align:start position:0%
+1 squ is one and in the denominator we
+still get cosine X this tells you that
+
+ align:start position:0%
+still get cosine X this tells you that
+ 
+
+ align:start position:0%
+still get cosine X this tells you that
+uh that 1 cosine X is actually just
+
+ align:start position:0%
+uh that 1 cosine X is actually just
+ 
+
+ align:start position:0%
+uh that 1 cosine X is actually just
+equal to SEC
+
+ align:start position:0%
+equal to SEC
+ 
+
+ align:start position:0%
+equal to SEC
+X so again what I want to point out is
+
+ align:start position:0%
+X so again what I want to point out is
+ 
+
+ align:start position:0%
+X so again what I want to point out is
+we've now taken the derivative of
+
+ align:start position:0%
+we've now taken the derivative of
+ 
+
+ align:start position:0%
+we've now taken the derivative of
+tangent X and we got that that's secant
+
+ align:start position:0%
+tangent X and we got that that's secant
+ 
+
+ align:start position:0%
+tangent X and we got that that's secant
+s x Now using this quotient rule you can
+
+ align:start position:0%
+s x Now using this quotient rule you can
+ 
+
+ align:start position:0%
+s x Now using this quotient rule you can
+do the same kind of thing with cotangent
+
+ align:start position:0%
+do the same kind of thing with cotangent
+ 
+
+ align:start position:0%
+do the same kind of thing with cotangent
+x with cosecant x with secant x you can
+
+ align:start position:0%
+x with cosecant x with secant x you can
+ 
+
+ align:start position:0%
+x with cosecant x with secant x you can
+find all these derivatives of these
+
+ align:start position:0%
+find all these derivatives of these
+ 
+
+ align:start position:0%
+find all these derivatives of these
+trigonometric functions using the
+
+ align:start position:0%
+trigonometric functions using the
+ 
+
+ align:start position:0%
+trigonometric functions using the
+quotient rule um so if you want to know
+
+ align:start position:0%
+quotient rule um so if you want to know
+ 
+
+ align:start position:0%
+quotient rule um so if you want to know
+what the derivative of SEC X is you
+
+ align:start position:0%
+what the derivative of SEC X is you
+ 
+
+ align:start position:0%
+what the derivative of SEC X is you
+should take DDX of 1 / cosine X and use
+
+ align:start position:0%
+should take DDX of 1 / cosine X and use
+ 
+
+ align:start position:0%
+should take DDX of 1 / cosine X and use
+the quotient rule or in fact the chain
+
+ align:start position:0%
+the quotient rule or in fact the chain
+ 
+
+ align:start position:0%
+the quotient rule or in fact the chain
+rule would work well there also um to
+
+ align:start position:0%
+rule would work well there also um to
+ 
+
+ align:start position:0%
+rule would work well there also um to
+find that derivative so we are building
+
+ align:start position:0%
+find that derivative so we are building
+ 
+
+ align:start position:0%
+find that derivative so we are building
+up uh the number of derivatives we can
+
+ align:start position:0%
+up uh the number of derivatives we can
+ 
+
+ align:start position:0%
+up uh the number of derivatives we can
+find using these different rules so
+
+ align:start position:0%
+find using these different rules so
+ 
+
+ align:start position:0%
+find using these different rules so
+we'll stop there
\ No newline at end of file
diff --git a/DGoILxx9KsE.txt b/DGoILxx9KsE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8de4af7a93e76802206aafd06cf50edaec63f915
--- /dev/null
+++ b/DGoILxx9KsE.txt
@@ -0,0 +1,12592 @@
+align:start position:0%
+ 
+let me remind you from the reading list
+
+ align:start position:0%
+let me remind you from the reading list
+ 
+
+ align:start position:0%
+let me remind you from the reading list
+where we are
+
+ align:start position:0%
+where we are
+ 
+
+ align:start position:0%
+where we are
+we did the introductory lecture of
+
+ align:start position:0%
+we did the introductory lecture of
+ 
+
+ align:start position:0%
+we did the introductory lecture of
+course about economic science
+
+ align:start position:0%
+course about economic science
+ 
+
+ align:start position:0%
+course about economic science
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+last time we did our first nuts and
+
+ align:start position:0%
+last time we did our first nuts and
+ 
+
+ align:start position:0%
+last time we did our first nuts and
+bolts lecture on preferences consumer
+
+ align:start position:0%
+bolts lecture on preferences consumer
+ 
+
+ align:start position:0%
+bolts lecture on preferences consumer
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+with the associated uh
+
+ align:start position:0%
+with the associated uh
+ 
+
+ align:start position:0%
+with the associated uh
+starred readings
+
+ align:start position:0%
+starred readings
+ 
+
+ align:start position:0%
+starred readings
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+today we're going to do
+
+ align:start position:0%
+today we're going to do
+ 
+
+ align:start position:0%
+today we're going to do
+more the way we ended the last class on
+
+ align:start position:0%
+more the way we ended the last class on
+ 
+
+ align:start position:0%
+more the way we ended the last class on
+consumer behavior
+
+ align:start position:0%
+consumer behavior
+ 
+
+ align:start position:0%
+consumer behavior
+i'm showing this
+
+ align:start position:0%
+i'm showing this
+ 
+
+ align:start position:0%
+i'm showing this
+reading list because i just want to
+
+ align:start position:0%
+reading list because i just want to
+ 
+
+ align:start position:0%
+reading list because i just want to
+remind you that these starred articles
+
+ align:start position:0%
+remind you that these starred articles
+ 
+
+ align:start position:0%
+remind you that these starred articles
+do exist the nicholson and schneider
+
+ align:start position:0%
+do exist the nicholson and schneider
+ 
+
+ align:start position:0%
+do exist the nicholson and schneider
+chapter 5 from which this is drawn
+
+ align:start position:0%
+chapter 5 from which this is drawn
+ 
+
+ align:start position:0%
+chapter 5 from which this is drawn
+although not entirely and
+
+ align:start position:0%
+although not entirely and
+ 
+
+ align:start position:0%
+although not entirely and
+also this jensen and miller paper which
+
+ align:start position:0%
+also this jensen and miller paper which
+ 
+
+ align:start position:0%
+also this jensen and miller paper which
+i will say a few words about today
+
+ align:start position:0%
+i will say a few words about today
+ 
+
+ align:start position:0%
+i will say a few words about today
+because it fits into this lecture but
+
+ align:start position:0%
+because it fits into this lecture but
+ 
+
+ align:start position:0%
+because it fits into this lecture but
+also as i probably mentioned too many
+
+ align:start position:0%
+also as i probably mentioned too many
+ 
+
+ align:start position:0%
+also as i probably mentioned too many
+times that's also
+
+ align:start position:0%
+times that's also
+ 
+
+ align:start position:0%
+times that's also
+a big part of your first
+
+ align:start position:0%
+a big part of your first
+ 
+
+ align:start position:0%
+a big part of your first
+problem set and
+
+ align:start position:0%
+problem set and
+ 
+
+ align:start position:0%
+problem set and
+involves getting that paper reading the
+
+ align:start position:0%
+involves getting that paper reading the
+ 
+
+ align:start position:0%
+involves getting that paper reading the
+yellow markings as highlights accessing
+
+ align:start position:0%
+yellow markings as highlights accessing
+ 
+
+ align:start position:0%
+yellow markings as highlights accessing
+the data that these guys used
+
+ align:start position:0%
+the data that these guys used
+ 
+
+ align:start position:0%
+the data that these guys used
+and running through some of their
+
+ align:start position:0%
+and running through some of their
+ 
+
+ align:start position:0%
+and running through some of their
+calculations
+
+ align:start position:0%
+calculations
+ 
+
+ align:start position:0%
+calculations
+okay so that's the
+
+ align:start position:0%
+okay so that's the
+ 
+
+ align:start position:0%
+okay so that's the
+part of the starred readings for this
+
+ align:start position:0%
+part of the starred readings for this
+ 
+
+ align:start position:0%
+part of the starred readings for this
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+so in terms of the study guide consumer
+
+ align:start position:0%
+so in terms of the study guide consumer
+ 
+
+ align:start position:0%
+so in terms of the study guide consumer
+theory
+
+ align:start position:0%
+theory
+ 
+
+ align:start position:0%
+theory
+as i was alerting you last time
+
+ align:start position:0%
+as i was alerting you last time
+ 
+
+ align:start position:0%
+as i was alerting you last time
+there's a pretty good thorough review of
+
+ align:start position:0%
+there's a pretty good thorough review of
+ 
+
+ align:start position:0%
+there's a pretty good thorough review of
+what you should have learned or are
+
+ align:start position:0%
+what you should have learned or are
+ 
+
+ align:start position:0%
+what you should have learned or are
+learning from the topic of last time and
+
+ align:start position:0%
+learning from the topic of last time and
+ 
+
+ align:start position:0%
+learning from the topic of last time and
+i i will not go through all of this but
+
+ align:start position:0%
+i i will not go through all of this but
+ 
+
+ align:start position:0%
+i i will not go through all of this but
+i will ask a few questions get a few
+
+ align:start position:0%
+i will ask a few questions get a few
+ 
+
+ align:start position:0%
+i will ask a few questions get a few
+volunteers uh maybe even call on a
+
+ align:start position:0%
+volunteers uh maybe even call on a
+ 
+
+ align:start position:0%
+volunteers uh maybe even call on a
+couple of you so
+
+ align:start position:0%
+couple of you so
+ 
+
+ align:start position:0%
+couple of you so
+this one give a plausible example of a
+
+ align:start position:0%
+this one give a plausible example of a
+ 
+
+ align:start position:0%
+this one give a plausible example of a
+commodity point that could not be in
+
+ align:start position:0%
+commodity point that could not be in
+ 
+
+ align:start position:0%
+commodity point that could not be in
+typical consumption set
+
+ align:start position:0%
+typical consumption set
+ 
+
+ align:start position:0%
+typical consumption set
+and i'll take volunteers on that it's
+
+ align:start position:0%
+and i'll take volunteers on that it's
+ 
+
+ align:start position:0%
+and i'll take volunteers on that it's
+partly
+
+ align:start position:0%
+partly
+ 
+
+ align:start position:0%
+partly
+remembering the slide where i showed
+
+ align:start position:0%
+remembering the slide where i showed
+ 
+
+ align:start position:0%
+remembering the slide where i showed
+examples of consumption says does anyone
+
+ align:start position:0%
+examples of consumption says does anyone
+ 
+
+ align:start position:0%
+examples of consumption says does anyone
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+this question
+
+ align:start position:0%
+this question
+ 
+
+ align:start position:0%
+this question
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+uh one in feasible consumption set is
+
+ align:start position:0%
+uh one in feasible consumption set is
+ 
+
+ align:start position:0%
+uh one in feasible consumption set is
+like consuming 25 hours in a day or
+
+ align:start position:0%
+like consuming 25 hours in a day or
+ 
+
+ align:start position:0%
+like consuming 25 hours in a day or
+something like that
+
+ align:start position:0%
+something like that
+ 
+
+ align:start position:0%
+something like that
+that's good
+
+ align:start position:0%
+that's good
+ 
+
+ align:start position:0%
+that's good
+yup the that was one of the diagrams
+
+ align:start position:0%
+yup the that was one of the diagrams
+ 
+
+ align:start position:0%
+yup the that was one of the diagrams
+where the
+
+ align:start position:0%
+where the
+ 
+
+ align:start position:0%
+where the
+amount of leisure available for work or
+
+ align:start position:0%
+amount of leisure available for work or
+ 
+
+ align:start position:0%
+amount of leisure available for work or
+what or leisure the sum could not exceed
+
+ align:start position:0%
+what or leisure the sum could not exceed
+ 
+
+ align:start position:0%
+what or leisure the sum could not exceed
+25.
+
+ align:start position:0%
+25.
+ 
+
+ align:start position:0%
+25.
+there was another one which you might
+
+ align:start position:0%
+there was another one which you might
+ 
+
+ align:start position:0%
+there was another one which you might
+not have thought of given the way this
+
+ align:start position:0%
+not have thought of given the way this
+ 
+
+ align:start position:0%
+not have thought of given the way this
+is worded
+
+ align:start position:0%
+is worded
+ 
+
+ align:start position:0%
+is worded
+which is consumption of bread in new
+
+ align:start position:0%
+which is consumption of bread in new
+ 
+
+ align:start position:0%
+which is consumption of bread in new
+york at noon and consumption in boston
+
+ align:start position:0%
+york at noon and consumption in boston
+ 
+
+ align:start position:0%
+york at noon and consumption in boston
+at noon of bread
+
+ align:start position:0%
+at noon of bread
+ 
+
+ align:start position:0%
+at noon of bread
+and uh there was you're not allowed to
+
+ align:start position:0%
+and uh there was you're not allowed to
+ 
+
+ align:start position:0%
+and uh there was you're not allowed to
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+bread in the interior because you can't
+
+ align:start position:0%
+bread in the interior because you can't
+ 
+
+ align:start position:0%
+bread in the interior because you can't
+consume simultaneously in both new york
+
+ align:start position:0%
+consume simultaneously in both new york
+ 
+
+ align:start position:0%
+consume simultaneously in both new york
+and boston so that was another example
+
+ align:start position:0%
+and boston so that was another example
+ 
+
+ align:start position:0%
+and boston so that was another example
+but your your answer was great
+
+ align:start position:0%
+but your your answer was great
+ 
+
+ align:start position:0%
+but your your answer was great
+so can someone volunteer to give me
+
+ align:start position:0%
+so can someone volunteer to give me
+ 
+
+ align:start position:0%
+so can someone volunteer to give me
+the definition of local non-satiation
+
+ align:start position:0%
+the definition of local non-satiation
+ 
+
+ align:start position:0%
+the definition of local non-satiation
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that means that there is
+
+ align:start position:0%
+that means that there is
+ 
+
+ align:start position:0%
+that means that there is
+in that so if you
+
+ align:start position:0%
+in that so if you
+ 
+
+ align:start position:0%
+in that so if you
+have a bundle
+
+ align:start position:0%
+have a bundle
+ 
+
+ align:start position:0%
+have a bundle
+in um in any neighborhood of that bundle
+
+ align:start position:0%
+in um in any neighborhood of that bundle
+ 
+
+ align:start position:0%
+in um in any neighborhood of that bundle
+there is
+
+ align:start position:0%
+there is
+ 
+
+ align:start position:0%
+there is
+some other bundle that's referred to the
+
+ align:start position:0%
+some other bundle that's referred to the
+ 
+
+ align:start position:0%
+some other bundle that's referred to the
+bundle you originally had yeah there are
+
+ align:start position:0%
+bundle you originally had yeah there are
+ 
+
+ align:start position:0%
+bundle you originally had yeah there are
+no bliss points
+
+ align:start position:0%
+no bliss points
+ 
+
+ align:start position:0%
+no bliss points
+that's right
+
+ align:start position:0%
+that's right
+ 
+
+ align:start position:0%
+that's right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+that's an excellent answer
+
+ align:start position:0%
+that's an excellent answer
+ 
+
+ align:start position:0%
+that's an excellent answer
+yeah for i can't remember whether we did
+
+ align:start position:0%
+yeah for i can't remember whether we did
+ 
+
+ align:start position:0%
+yeah for i can't remember whether we did
+x or y but for
+
+ align:start position:0%
+x or y but for
+ 
+
+ align:start position:0%
+x or y but for
+for any x
+
+ align:start position:0%
+for any x
+ 
+
+ align:start position:0%
+for any x
+in the consumption set
+
+ align:start position:0%
+in the consumption set
+ 
+
+ align:start position:0%
+in the consumption set
+there's some other y
+
+ align:start position:0%
+there's some other y
+ 
+
+ align:start position:0%
+there's some other y
+uh no matter how close we are to x
+
+ align:start position:0%
+uh no matter how close we are to x
+ 
+
+ align:start position:0%
+uh no matter how close we are to x
+which is preferred
+
+ align:start position:0%
+which is preferred
+ 
+
+ align:start position:0%
+which is preferred
+to x and well and y has to be in the
+
+ align:start position:0%
+to x and well and y has to be in the
+ 
+
+ align:start position:0%
+to x and well and y has to be in the
+consumption set so both things have to
+
+ align:start position:0%
+consumption set so both things have to
+ 
+
+ align:start position:0%
+consumption set so both things have to
+be true it has to be available in this
+
+ align:start position:0%
+be true it has to be available in this
+ 
+
+ align:start position:0%
+be true it has to be available in this
+little
+
+ align:start position:0%
+little
+ 
+
+ align:start position:0%
+little
+ball or circle around x and it has to be
+
+ align:start position:0%
+ball or circle around x and it has to be
+ 
+
+ align:start position:0%
+ball or circle around x and it has to be
+preferred
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you gave a good
+
+ align:start position:0%
+and you gave a good
+ 
+
+ align:start position:0%
+and you gave a good
+counter example if there were a bliss
+
+ align:start position:0%
+counter example if there were a bliss
+ 
+
+ align:start position:0%
+counter example if there were a bliss
+point that means
+
+ align:start position:0%
+point that means
+ 
+
+ align:start position:0%
+point that means
+there's something that is
+
+ align:start position:0%
+there's something that is
+ 
+
+ align:start position:0%
+there's something that is
+maximal utility
+
+ align:start position:0%
+maximal utility
+ 
+
+ align:start position:0%
+maximal utility
+among all possible points so if we do
+
+ align:start position:0%
+among all possible points so if we do
+ 
+
+ align:start position:0%
+among all possible points so if we do
+a circle around that everything else
+
+ align:start position:0%
+a circle around that everything else
+ 
+
+ align:start position:0%
+a circle around that everything else
+would be inferior
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if if you went beyond the bliss point
+
+ align:start position:0%
+if if you went beyond the bliss point
+ 
+
+ align:start position:0%
+if if you went beyond the bliss point
+northeast of it
+
+ align:start position:0%
+northeast of it
+ 
+
+ align:start position:0%
+northeast of it
+you have too much of all the goods
+
+ align:start position:0%
+you have too much of all the goods
+ 
+
+ align:start position:0%
+you have too much of all the goods
+but then ironically
+
+ align:start position:0%
+but then ironically
+ 
+
+ align:start position:0%
+but then ironically
+you also have local non-satiation
+
+ align:start position:0%
+you also have local non-satiation
+ 
+
+ align:start position:0%
+you also have local non-satiation
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+given any point x
+
+ align:start position:0%
+given any point x
+ 
+
+ align:start position:0%
+given any point x
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+there's another point y which involves
+
+ align:start position:0%
+there's another point y which involves
+ 
+
+ align:start position:0%
+there's another point y which involves
+less than both goods
+
+ align:start position:0%
+less than both goods
+ 
+
+ align:start position:0%
+less than both goods
+that would be strictly preferred because
+
+ align:start position:0%
+that would be strictly preferred because
+ 
+
+ align:start position:0%
+that would be strictly preferred because
+you're moving to the bliss point
+
+ align:start position:0%
+you're moving to the bliss point
+ 
+
+ align:start position:0%
+you're moving to the bliss point
+so anyway the the point of this little
+
+ align:start position:0%
+so anyway the the point of this little
+ 
+
+ align:start position:0%
+so anyway the the point of this little
+discussion is that local
+
+ align:start position:0%
+discussion is that local
+ 
+
+ align:start position:0%
+discussion is that local
+non-satiation and global non-satiation
+
+ align:start position:0%
+non-satiation and global non-satiation
+ 
+
+ align:start position:0%
+non-satiation and global non-satiation
+are
+
+ align:start position:0%
+are
+ 
+
+ align:start position:0%
+are
+two different things
+
+ align:start position:0%
+two different things
+ 
+
+ align:start position:0%
+two different things
+thank you okay let's
+
+ align:start position:0%
+thank you okay let's
+ 
+
+ align:start position:0%
+thank you okay let's
+what does it mean for preference
+
+ align:start position:0%
+what does it mean for preference
+ 
+
+ align:start position:0%
+what does it mean for preference
+relation to be represented by a utility
+
+ align:start position:0%
+relation to be represented by a utility
+ 
+
+ align:start position:0%
+relation to be represented by a utility
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+give a preference relation given a
+
+ align:start position:0%
+give a preference relation given a
+ 
+
+ align:start position:0%
+give a preference relation given a
+preference relation is the utility
+
+ align:start position:0%
+preference relation is the utility
+ 
+
+ align:start position:0%
+preference relation is the utility
+function that represents it unique
+
+ align:start position:0%
+function that represents it unique
+ 
+
+ align:start position:0%
+function that represents it unique
+yes or no
+
+ align:start position:0%
+yes or no
+ 
+
+ align:start position:0%
+yes or no
+and explain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so um
+
+ align:start position:0%
+yeah so um
+ 
+
+ align:start position:0%
+yeah so um
+so so we say that a utility function
+
+ align:start position:0%
+so so we say that a utility function
+ 
+
+ align:start position:0%
+so so we say that a utility function
+sort of represents a preference if
+
+ align:start position:0%
+sort of represents a preference if
+ 
+
+ align:start position:0%
+sort of represents a preference if
+for example for any consumption bundle
+
+ align:start position:0%
+for example for any consumption bundle
+ 
+
+ align:start position:0%
+for example for any consumption bundle
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+x any two consumption bundles x and y if
+
+ align:start position:0%
+x any two consumption bundles x and y if
+ 
+
+ align:start position:0%
+x any two consumption bundles x and y if
+if um x is preferred to y then u of x is
+
+ align:start position:0%
+if um x is preferred to y then u of x is
+ 
+
+ align:start position:0%
+if um x is preferred to y then u of x is
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+greater than u of y
+
+ align:start position:0%
+greater than u of y
+ 
+
+ align:start position:0%
+greater than u of y
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and the utility function is not unique
+
+ align:start position:0%
+and the utility function is not unique
+ 
+
+ align:start position:0%
+and the utility function is not unique
+um it just has to respect the given
+
+ align:start position:0%
+um it just has to respect the given
+ 
+
+ align:start position:0%
+um it just has to respect the given
+ordering of the preferences so we could
+
+ align:start position:0%
+ordering of the preferences so we could
+ 
+
+ align:start position:0%
+ordering of the preferences so we could
+have like u and if we could have u or u
+
+ align:start position:0%
+have like u and if we could have u or u
+ 
+
+ align:start position:0%
+have like u and if we could have u or u
+squared or n cubed and all those would
+
+ align:start position:0%
+squared or n cubed and all those would
+ 
+
+ align:start position:0%
+squared or n cubed and all those would
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+excellent perfect answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any other comments or questions about
+
+ align:start position:0%
+any other comments or questions about
+ 
+
+ align:start position:0%
+any other comments or questions about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i had a question um on this slide it had
+
+ align:start position:0%
+i had a question um on this slide it had
+ 
+
+ align:start position:0%
+i had a question um on this slide it had
+said that um it was unique only up to an
+
+ align:start position:0%
+said that um it was unique only up to an
+ 
+
+ align:start position:0%
+said that um it was unique only up to an
+order preserving transformation what
+
+ align:start position:0%
+order preserving transformation what
+ 
+
+ align:start position:0%
+order preserving transformation what
+exactly is that i guess mean
+
+ align:start position:0%
+exactly is that i guess mean
+ 
+
+ align:start position:0%
+exactly is that i guess mean
+well if you had three points
+
+ align:start position:0%
+well if you had three points
+ 
+
+ align:start position:0%
+well if you had three points
+ordering them from low to high in terms
+
+ align:start position:0%
+ordering them from low to high in terms
+ 
+
+ align:start position:0%
+ordering them from low to high in terms
+of preference relation
+
+ align:start position:0%
+of preference relation
+ 
+
+ align:start position:0%
+of preference relation
+a x1 x2 x3
+
+ align:start position:0%
+a x1 x2 x3
+ 
+
+ align:start position:0%
+a x1 x2 x3
+where x3 is preferred to x2 is preferred
+
+ align:start position:0%
+where x3 is preferred to x2 is preferred
+ 
+
+ align:start position:0%
+where x3 is preferred to x2 is preferred
+to x1
+
+ align:start position:0%
+to x1
+ 
+
+ align:start position:0%
+to x1
+all we need to do is assign a higher
+
+ align:start position:0%
+all we need to do is assign a higher
+ 
+
+ align:start position:0%
+all we need to do is assign a higher
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+to the best one a lower number to the
+
+ align:start position:0%
+to the best one a lower number to the
+ 
+
+ align:start position:0%
+to the best one a lower number to the
+intermediate one so something like
+
+ align:start position:0%
+intermediate one so something like
+ 
+
+ align:start position:0%
+intermediate one so something like
+you know 15 5 1
+
+ align:start position:0%
+you know 15 5 1
+ 
+
+ align:start position:0%
+you know 15 5 1
+preserves the rank ordering those are
+
+ align:start position:0%
+preserves the rank ordering those are
+ 
+
+ align:start position:0%
+preserves the rank ordering those are
+utility number assignments
+
+ align:start position:0%
+utility number assignments
+ 
+
+ align:start position:0%
+utility number assignments
+but we could multiply
+
+ align:start position:0%
+but we could multiply
+ 
+
+ align:start position:0%
+but we could multiply
+by 2 and then we have
+
+ align:start position:0%
+by 2 and then we have
+ 
+
+ align:start position:0%
+by 2 and then we have
+30 10
+
+ align:start position:0%
+30 10
+ 
+
+ align:start position:0%
+30 10
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+but we're still assigning
+
+ align:start position:0%
+but we're still assigning
+ 
+
+ align:start position:0%
+but we're still assigning
+numbers from high to low uh to preserve
+
+ align:start position:0%
+numbers from high to low uh to preserve
+ 
+
+ align:start position:0%
+numbers from high to low uh to preserve
+the same rank ordering does that help
+
+ align:start position:0%
+the same rank ordering does that help
+ 
+
+ align:start position:0%
+the same rank ordering does that help
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+thank you okay
+
+ align:start position:0%
+thank you okay
+ 
+
+ align:start position:0%
+thank you okay
+so uh
+
+ align:start position:0%
+so uh
+ 
+
+ align:start position:0%
+so uh
+yes go on do you eventually need to i
+
+ align:start position:0%
+yes go on do you eventually need to i
+ 
+
+ align:start position:0%
+yes go on do you eventually need to i
+guess reintroduce some concept of
+
+ align:start position:0%
+guess reintroduce some concept of
+ 
+
+ align:start position:0%
+guess reintroduce some concept of
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+or not magnitude but have something
+
+ align:start position:0%
+or not magnitude but have something
+ 
+
+ align:start position:0%
+or not magnitude but have something
+beyond disordering if you want to like
+
+ align:start position:0%
+beyond disordering if you want to like
+ 
+
+ align:start position:0%
+beyond disordering if you want to like
+start talking about gambling or expected
+
+ align:start position:0%
+start talking about gambling or expected
+ 
+
+ align:start position:0%
+start talking about gambling or expected
+value yes absolutely and we're going to
+
+ align:start position:0%
+value yes absolutely and we're going to
+ 
+
+ align:start position:0%
+value yes absolutely and we're going to
+do that in two lectures
+
+ align:start position:0%
+do that in two lectures
+ 
+
+ align:start position:0%
+do that in two lectures
+so there the
+
+ align:start position:0%
+so there the
+ 
+
+ align:start position:0%
+so there the
+utility function
+
+ align:start position:0%
+utility function
+ 
+
+ align:start position:0%
+utility function
+will
+
+ align:start position:0%
+will
+ 
+
+ align:start position:0%
+will
+the ordinal representation matters
+
+ align:start position:0%
+the ordinal representation matters
+ 
+
+ align:start position:0%
+the ordinal representation matters
+uh and and the question will be how much
+
+ align:start position:0%
+uh and and the question will be how much
+ 
+
+ align:start position:0%
+uh and and the question will be how much
+more utility do you get
+
+ align:start position:0%
+more utility do you get
+ 
+
+ align:start position:0%
+more utility do you get
+or how much less
+
+ align:start position:0%
+or how much less
+ 
+
+ align:start position:0%
+or how much less
+depending on an adverse event
+
+ align:start position:0%
+depending on an adverse event
+ 
+
+ align:start position:0%
+depending on an adverse event
+so that the curvature literally
+
+ align:start position:0%
+so that the curvature literally
+ 
+
+ align:start position:0%
+so that the curvature literally
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you know represents your willingness to
+
+ align:start position:0%
+you know represents your willingness to
+ 
+
+ align:start position:0%
+you know represents your willingness to
+take gambles
+
+ align:start position:0%
+take gambles
+ 
+
+ align:start position:0%
+take gambles
+whereas with an ordinal function a
+
+ align:start position:0%
+whereas with an ordinal function a
+ 
+
+ align:start position:0%
+whereas with an ordinal function a
+linear function is fine linear
+
+ align:start position:0%
+linear function is fine linear
+ 
+
+ align:start position:0%
+linear function is fine linear
+function when you're facing gammas means
+
+ align:start position:0%
+function when you're facing gammas means
+ 
+
+ align:start position:0%
+function when you're facing gammas means
+you're risk neutral
+
+ align:start position:0%
+you're risk neutral
+ 
+
+ align:start position:0%
+you're risk neutral
+and you just you just rank based on
+
+ align:start position:0%
+and you just you just rank based on
+ 
+
+ align:start position:0%
+and you just you just rank based on
+expected values
+
+ align:start position:0%
+expected values
+ 
+
+ align:start position:0%
+expected values
+that's all a little bit early it's a
+
+ align:start position:0%
+that's all a little bit early it's a
+ 
+
+ align:start position:0%
+that's all a little bit early it's a
+great question and we're going to get
+
+ align:start position:0%
+great question and we're going to get
+ 
+
+ align:start position:0%
+great question and we're going to get
+there in two lectures
+
+ align:start position:0%
+there in two lectures
+ 
+
+ align:start position:0%
+there in two lectures
+we have time for one more here
+
+ align:start position:0%
+we have time for one more here
+ 
+
+ align:start position:0%
+we have time for one more here
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean for preferences to be
+
+ align:start position:0%
+what does it mean for preferences to be
+ 
+
+ align:start position:0%
+what does it mean for preferences to be
+homothetic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mrs is just depending on the ratio
+
+ align:start position:0%
+the mrs is just depending on the ratio
+ 
+
+ align:start position:0%
+the mrs is just depending on the ratio
+of two goods right
+
+ align:start position:0%
+of two goods right
+ 
+
+ align:start position:0%
+of two goods right
+not depending on the absolute quantity
+
+ align:start position:0%
+not depending on the absolute quantity
+ 
+
+ align:start position:0%
+not depending on the absolute quantity
+of each good
+
+ align:start position:0%
+of each good
+ 
+
+ align:start position:0%
+of each good
+yep perfect
+
+ align:start position:0%
+yep perfect
+ 
+
+ align:start position:0%
+yep perfect
+wow
+
+ align:start position:0%
+wow
+ 
+
+ align:start position:0%
+wow
+i'm very happy very impressed thank you
+
+ align:start position:0%
+i'm very happy very impressed thank you
+ 
+
+ align:start position:0%
+i'm very happy very impressed thank you
+all that that's tremendous okay so again
+
+ align:start position:0%
+all that that's tremendous okay so again
+ 
+
+ align:start position:0%
+all that that's tremendous okay so again
+these are just sort of ran somewhat
+
+ align:start position:0%
+these are just sort of ran somewhat
+ 
+
+ align:start position:0%
+these are just sort of ran somewhat
+randomly selected i
+
+ align:start position:0%
+randomly selected i
+ 
+
+ align:start position:0%
+randomly selected i
+do go over these before class to
+
+ align:start position:0%
+do go over these before class to
+ 
+
+ align:start position:0%
+do go over these before class to
+help me decide you know since i can't
+
+ align:start position:0%
+help me decide you know since i can't
+ 
+
+ align:start position:0%
+help me decide you know since i can't
+ask them all which one
+
+ align:start position:0%
+ask them all which one
+ 
+
+ align:start position:0%
+ask them all which one
+i would ask in class there's some of
+
+ align:start position:0%
+i would ask in class there's some of
+ 
+
+ align:start position:0%
+i would ask in class there's some of
+these that say draw a graph or
+
+ align:start position:0%
+these that say draw a graph or
+ 
+
+ align:start position:0%
+these that say draw a graph or
+so on and so forth so i know i didn't
+
+ align:start position:0%
+so on and so forth so i know i didn't
+ 
+
+ align:start position:0%
+so on and so forth so i know i didn't
+ask about those but none of them are
+
+ align:start position:0%
+ask about those but none of them are
+ 
+
+ align:start position:0%
+ask about those but none of them are
+supposed to be terribly hard
+
+ align:start position:0%
+supposed to be terribly hard
+ 
+
+ align:start position:0%
+supposed to be terribly hard
+um but it it is always a good review at
+
+ align:start position:0%
+um but it it is always a good review at
+ 
+
+ align:start position:0%
+um but it it is always a good review at
+a minimum
+
+ align:start position:0%
+a minimum
+ 
+
+ align:start position:0%
+a minimum
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+today is a lecture
+
+ align:start position:0%
+today is a lecture
+ 
+
+ align:start position:0%
+today is a lecture
+on income and substitution effects
+
+ align:start position:0%
+on income and substitution effects
+ 
+
+ align:start position:0%
+on income and substitution effects
+or really it's about
+
+ align:start position:0%
+or really it's about
+ 
+
+ align:start position:0%
+or really it's about
+consumer maximizing behavior
+
+ align:start position:0%
+consumer maximizing behavior
+ 
+
+ align:start position:0%
+consumer maximizing behavior
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when we solve the consumer's
+
+ align:start position:0%
+so when we solve the consumer's
+ 
+
+ align:start position:0%
+so when we solve the consumer's
+utility maximization problem we get
+
+ align:start position:0%
+utility maximization problem we get
+ 
+
+ align:start position:0%
+utility maximization problem we get
+individual demand functions it should
+
+ align:start position:0%
+individual demand functions it should
+ 
+
+ align:start position:0%
+individual demand functions it should
+say function
+
+ align:start position:0%
+say function
+ 
+
+ align:start position:0%
+say function
+with an s because if there are n goods
+
+ align:start position:0%
+with an s because if there are n goods
+ 
+
+ align:start position:0%
+with an s because if there are n goods
+little n
+
+ align:start position:0%
+little n
+ 
+
+ align:start position:0%
+little n
+then there's a demand for good 1 good 2
+
+ align:start position:0%
+then there's a demand for good 1 good 2
+ 
+
+ align:start position:0%
+then there's a demand for good 1 good 2
+good n and so on
+
+ align:start position:0%
+good n and so on
+ 
+
+ align:start position:0%
+good n and so on
+and what are the arguments in these
+
+ align:start position:0%
+and what are the arguments in these
+ 
+
+ align:start position:0%
+and what are the arguments in these
+demand functions
+
+ align:start position:0%
+demand functions
+ 
+
+ align:start position:0%
+demand functions
+the entire vector of prices denoted p 1
+
+ align:start position:0%
+the entire vector of prices denoted p 1
+ 
+
+ align:start position:0%
+the entire vector of prices denoted p 1
+through p n
+
+ align:start position:0%
+through p n
+ 
+
+ align:start position:0%
+through p n
+and income
+
+ align:start position:0%
+and income
+ 
+
+ align:start position:0%
+and income
+denoted as i and you can think about
+
+ align:start position:0%
+denoted as i and you can think about
+ 
+
+ align:start position:0%
+denoted as i and you can think about
+prices and income denominated in dollars
+
+ align:start position:0%
+prices and income denominated in dollars
+ 
+
+ align:start position:0%
+prices and income denominated in dollars
+or some unit of account
+
+ align:start position:0%
+or some unit of account
+ 
+
+ align:start position:0%
+or some unit of account
+we're going to be spending
+
+ align:start position:0%
+we're going to be spending
+ 
+
+ align:start position:0%
+we're going to be spending
+time looking at how the price of good k
+
+ align:start position:0%
+time looking at how the price of good k
+ 
+
+ align:start position:0%
+time looking at how the price of good k
+changes when we change the price of good
+
+ align:start position:0%
+changes when we change the price of good
+ 
+
+ align:start position:0%
+changes when we change the price of good
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+but you know of necessity other goods
+
+ align:start position:0%
+but you know of necessity other goods
+ 
+
+ align:start position:0%
+but you know of necessity other goods
+will be changing as well
+
+ align:start position:0%
+will be changing as well
+ 
+
+ align:start position:0%
+will be changing as well
+it's at best the implicit happenings in
+
+ align:start position:0%
+it's at best the implicit happenings in
+ 
+
+ align:start position:0%
+it's at best the implicit happenings in
+the diagrams
+
+ align:start position:0%
+the diagrams
+ 
+
+ align:start position:0%
+the diagrams
+okay so here is a little bit of a repeat
+
+ align:start position:0%
+okay so here is a little bit of a repeat
+ 
+
+ align:start position:0%
+okay so here is a little bit of a repeat
+but expanded from last time we've got
+
+ align:start position:0%
+but expanded from last time we've got
+ 
+
+ align:start position:0%
+but expanded from last time we've got
+two goods denoted x and y
+
+ align:start position:0%
+two goods denoted x and y
+ 
+
+ align:start position:0%
+two goods denoted x and y
+and this household has a certain amount
+
+ align:start position:0%
+and this household has a certain amount
+ 
+
+ align:start position:0%
+and this household has a certain amount
+of income i
+
+ align:start position:0%
+of income i
+ 
+
+ align:start position:0%
+of income i
+uh say i2 if income were i2 this would
+
+ align:start position:0%
+uh say i2 if income were i2 this would
+ 
+
+ align:start position:0%
+uh say i2 if income were i2 this would
+be the budget line which has a slope of
+
+ align:start position:0%
+be the budget line which has a slope of
+ 
+
+ align:start position:0%
+be the budget line which has a slope of
+px over py
+
+ align:start position:0%
+px over py
+ 
+
+ align:start position:0%
+px over py
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+and this is the tangency which is the
+
+ align:start position:0%
+and this is the tangency which is the
+ 
+
+ align:start position:0%
+and this is the tangency which is the
+maximum utility point denoted x2 y2
+
+ align:start position:0%
+maximum utility point denoted x2 y2
+ 
+
+ align:start position:0%
+maximum utility point denoted x2 y2
+associated with income i2
+
+ align:start position:0%
+associated with income i2
+ 
+
+ align:start position:0%
+associated with income i2
+what this diagram is featuring though is
+
+ align:start position:0%
+what this diagram is featuring though is
+ 
+
+ align:start position:0%
+what this diagram is featuring though is
+not a single maximization
+
+ align:start position:0%
+not a single maximization
+ 
+
+ align:start position:0%
+not a single maximization
+it's how the maximization point changes
+
+ align:start position:0%
+it's how the maximization point changes
+ 
+
+ align:start position:0%
+it's how the maximization point changes
+if you increase income so you would move
+
+ align:start position:0%
+if you increase income so you would move
+ 
+
+ align:start position:0%
+if you increase income so you would move
+from x to y 2 to x 3 y 3 for example
+
+ align:start position:0%
+from x to y 2 to x 3 y 3 for example
+ 
+
+ align:start position:0%
+from x to y 2 to x 3 y 3 for example
+and likewise if your income were less
+
+ align:start position:0%
+and likewise if your income were less
+ 
+
+ align:start position:0%
+and likewise if your income were less
+if this household's income were less
+
+ align:start position:0%
+if this household's income were less
+ 
+
+ align:start position:0%
+if this household's income were less
+they would move to
+
+ align:start position:0%
+they would move to
+ 
+
+ align:start position:0%
+they would move to
+y1 x1 so this
+
+ align:start position:0%
+y1 x1 so this
+ 
+
+ align:start position:0%
+y1 x1 so this
+you could connect these dots
+
+ align:start position:0%
+you could connect these dots
+ 
+
+ align:start position:0%
+you could connect these dots
+and as only income is varying and prices
+
+ align:start position:0%
+and as only income is varying and prices
+ 
+
+ align:start position:0%
+and as only income is varying and prices
+and the price ratios held fixed
+
+ align:start position:0%
+and the price ratios held fixed
+ 
+
+ align:start position:0%
+and the price ratios held fixed
+we could call the connected dots an
+
+ align:start position:0%
+we could call the connected dots an
+ 
+
+ align:start position:0%
+we could call the connected dots an
+income expansion path and i'll show you
+
+ align:start position:0%
+income expansion path and i'll show you
+ 
+
+ align:start position:0%
+income expansion path and i'll show you
+some examples of that momentarily
+
+ align:start position:0%
+some examples of that momentarily
+ 
+
+ align:start position:0%
+some examples of that momentarily
+here is
+
+ align:start position:0%
+here is
+ 
+
+ align:start position:0%
+here is
+a different experiment can we miss
+
+ align:start position:0%
+a different experiment can we miss
+ 
+
+ align:start position:0%
+a different experiment can we miss
+something well in this one
+
+ align:start position:0%
+something well in this one
+ 
+
+ align:start position:0%
+something well in this one
+you'll get lulled into thinking that as
+
+ align:start position:0%
+you'll get lulled into thinking that as
+ 
+
+ align:start position:0%
+you'll get lulled into thinking that as
+income changes the amount spent on both
+
+ align:start position:0%
+income changes the amount spent on both
+ 
+
+ align:start position:0%
+income changes the amount spent on both
+goods has to change increase but that's
+
+ align:start position:0%
+goods has to change increase but that's
+ 
+
+ align:start position:0%
+goods has to change increase but that's
+not necessarily the case
+
+ align:start position:0%
+not necessarily the case
+ 
+
+ align:start position:0%
+not necessarily the case
+so here again
+
+ align:start position:0%
+so here again
+ 
+
+ align:start position:0%
+so here again
+we're going from i1 to i2 to i3
+
+ align:start position:0%
+we're going from i1 to i2 to i3
+ 
+
+ align:start position:0%
+we're going from i1 to i2 to i3
+and tracing out the quantities from
+
+ align:start position:0%
+and tracing out the quantities from
+ 
+
+ align:start position:0%
+and tracing out the quantities from
+zy1 zy2 to zy3
+
+ align:start position:0%
+zy1 zy2 to zy3
+ 
+
+ align:start position:0%
+zy1 zy2 to zy3
+and here the
+
+ align:start position:0%
+and here the
+ 
+
+ align:start position:0%
+and here the
+quantity demanded of good
+
+ align:start position:0%
+quantity demanded of good
+ 
+
+ align:start position:0%
+quantity demanded of good
+y is increasing
+
+ align:start position:0%
+y is increasing
+ 
+
+ align:start position:0%
+y is increasing
+but the quantity demanded of good z is
+
+ align:start position:0%
+but the quantity demanded of good z is
+ 
+
+ align:start position:0%
+but the quantity demanded of good z is
+actually decreasing
+
+ align:start position:0%
+actually decreasing
+ 
+
+ align:start position:0%
+actually decreasing
+so there's nothing terribly peculiar
+
+ align:start position:0%
+so there's nothing terribly peculiar
+ 
+
+ align:start position:0%
+so there's nothing terribly peculiar
+about the shape of these indifference
+
+ align:start position:0%
+about the shape of these indifference
+ 
+
+ align:start position:0%
+about the shape of these indifference
+curves we didn't have to struggle too
+
+ align:start position:0%
+curves we didn't have to struggle too
+ 
+
+ align:start position:0%
+curves we didn't have to struggle too
+hard to get this phenomenon to happen
+
+ align:start position:0%
+hard to get this phenomenon to happen
+ 
+
+ align:start position:0%
+hard to get this phenomenon to happen
+but but anyway this phenomenon has a
+
+ align:start position:0%
+but but anyway this phenomenon has a
+ 
+
+ align:start position:0%
+but but anyway this phenomenon has a
+name namely
+
+ align:start position:0%
+name namely
+ 
+
+ align:start position:0%
+name namely
+the good
+
+ align:start position:0%
+the good
+ 
+
+ align:start position:0%
+the good
+y over here would be called a normal
+
+ align:start position:0%
+y over here would be called a normal
+ 
+
+ align:start position:0%
+y over here would be called a normal
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+and good z
+
+ align:start position:0%
+and good z
+ 
+
+ align:start position:0%
+and good z
+would be called an inferior good
+
+ align:start position:0%
+would be called an inferior good
+ 
+
+ align:start position:0%
+would be called an inferior good
+or a necessity
+
+ align:start position:0%
+or a necessity
+ 
+
+ align:start position:0%
+or a necessity
+because the amount that you consume of
+
+ align:start position:0%
+because the amount that you consume of
+ 
+
+ align:start position:0%
+because the amount that you consume of
+it diminishes as income goes up
+
+ align:start position:0%
+it diminishes as income goes up
+ 
+
+ align:start position:0%
+it diminishes as income goes up
+so here are those definitions
+
+ align:start position:0%
+so here are those definitions
+ 
+
+ align:start position:0%
+so here are those definitions
+a good for which the demand demand of
+
+ align:start position:0%
+a good for which the demand demand of
+ 
+
+ align:start position:0%
+a good for which the demand demand of
+good i goes down as income capital i
+
+ align:start position:0%
+good i goes down as income capital i
+ 
+
+ align:start position:0%
+good i goes down as income capital i
+goes up
+
+ align:start position:0%
+goes up
+ 
+
+ align:start position:0%
+goes up
+is said to be an inferior good it
+
+ align:start position:0%
+is said to be an inferior good it
+ 
+
+ align:start position:0%
+is said to be an inferior good it
+doesn't have to happen over the entire
+
+ align:start position:0%
+doesn't have to happen over the entire
+ 
+
+ align:start position:0%
+doesn't have to happen over the entire
+range of income and prices but it if it
+
+ align:start position:0%
+range of income and prices but it if it
+ 
+
+ align:start position:0%
+range of income and prices but it if it
+happens locally it's called an inferior
+
+ align:start position:0%
+happens locally it's called an inferior
+ 
+
+ align:start position:0%
+happens locally it's called an inferior
+good locally and likewise if the
+
+ align:start position:0%
+good locally and likewise if the
+ 
+
+ align:start position:0%
+good locally and likewise if the
+derivative with respect to income is
+
+ align:start position:0%
+derivative with respect to income is
+ 
+
+ align:start position:0%
+derivative with respect to income is
+positive then we call
+
+ align:start position:0%
+positive then we call
+ 
+
+ align:start position:0%
+positive then we call
+in some range the good to be a normal
+
+ align:start position:0%
+in some range the good to be a normal
+ 
+
+ align:start position:0%
+in some range the good to be a normal
+good or non-inferior good
+
+ align:start position:0%
+good or non-inferior good
+ 
+
+ align:start position:0%
+good or non-inferior good
+so there's something called engel's law
+
+ align:start position:0%
+so there's something called engel's law
+ 
+
+ align:start position:0%
+so there's something called engel's law
+and with the caveat that this is not one
+
+ align:start position:0%
+and with the caveat that this is not one
+ 
+
+ align:start position:0%
+and with the caveat that this is not one
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+it's actually comparing across
+
+ align:start position:0%
+it's actually comparing across
+ 
+
+ align:start position:0%
+it's actually comparing across
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+that differ in their annual income so
+
+ align:start position:0%
+that differ in their annual income so
+ 
+
+ align:start position:0%
+that differ in their annual income so
+here we're going
+
+ align:start position:0%
+here we're going
+ 
+
+ align:start position:0%
+here we're going
+from an annual income of 225
+
+ align:start position:0%
+from an annual income of 225
+ 
+
+ align:start position:0%
+from an annual income of 225
+to this is written in 1920 by the way
+
+ align:start position:0%
+to this is written in 1920 by the way
+ 
+
+ align:start position:0%
+to this is written in 1920 by the way
+don't be too alarmed it's been a lot of
+
+ align:start position:0%
+don't be too alarmed it's been a lot of
+ 
+
+ align:start position:0%
+don't be too alarmed it's been a lot of
+inflation
+
+ align:start position:0%
+inflation
+ 
+
+ align:start position:0%
+inflation
+so this in real purchasing power was
+
+ align:start position:0%
+so this in real purchasing power was
+ 
+
+ align:start position:0%
+so this in real purchasing power was
+more than you thought 300
+
+ align:start position:0%
+more than you thought 300
+ 
+
+ align:start position:0%
+more than you thought 300
+or this range 450 to 600 or
+
+ align:start position:0%
+or this range 450 to 600 or
+ 
+
+ align:start position:0%
+or this range 450 to 600 or
+750 to 1000
+
+ align:start position:0%
+750 to 1000
+ 
+
+ align:start position:0%
+750 to 1000
+okay and what you can see is the percent
+
+ align:start position:0%
+okay and what you can see is the percent
+ 
+
+ align:start position:0%
+okay and what you can see is the percent
+spent
+
+ align:start position:0%
+spent
+ 
+
+ align:start position:0%
+spent
+of the budget
+
+ align:start position:0%
+of the budget
+ 
+
+ align:start position:0%
+of the budget
+on food declines
+
+ align:start position:0%
+on food declines
+ 
+
+ align:start position:0%
+on food declines
+as we move to these
+
+ align:start position:0%
+as we move to these
+ 
+
+ align:start position:0%
+as we move to these
+income groups with higher and higher
+
+ align:start position:0%
+income groups with higher and higher
+ 
+
+ align:start position:0%
+income groups with higher and higher
+income
+
+ align:start position:0%
+income
+ 
+
+ align:start position:0%
+income
+so in some sense if all consumers were
+
+ align:start position:0%
+so in some sense if all consumers were
+ 
+
+ align:start position:0%
+so in some sense if all consumers were
+like and some had more income than
+
+ align:start position:0%
+like and some had more income than
+ 
+
+ align:start position:0%
+like and some had more income than
+others we'd be looking at what an
+
+ align:start position:0%
+others we'd be looking at what an
+ 
+
+ align:start position:0%
+others we'd be looking at what an
+individual household would do as its
+
+ align:start position:0%
+individual household would do as its
+ 
+
+ align:start position:0%
+individual household would do as its
+income changed
+
+ align:start position:0%
+income changed
+ 
+
+ align:start position:0%
+income changed
+and in this case food would be an
+
+ align:start position:0%
+and in this case food would be an
+ 
+
+ align:start position:0%
+and in this case food would be an
+inferior good you're saying what's going
+
+ align:start position:0%
+inferior good you're saying what's going
+ 
+
+ align:start position:0%
+inferior good you're saying what's going
+up clothing not by much
+
+ align:start position:0%
+up clothing not by much
+ 
+
+ align:start position:0%
+up clothing not by much
+lodging not at all
+
+ align:start position:0%
+lodging not at all
+ 
+
+ align:start position:0%
+lodging not at all
+what really expands as income goes up is
+
+ align:start position:0%
+what really expands as income goes up is
+ 
+
+ align:start position:0%
+what really expands as income goes up is
+services education health legal and
+
+ align:start position:0%
+services education health legal and
+ 
+
+ align:start position:0%
+services education health legal and
+other services in fact in the u.s
+
+ align:start position:0%
+other services in fact in the u.s
+ 
+
+ align:start position:0%
+other services in fact in the u.s
+economy looking over you know decades
+
+ align:start position:0%
+economy looking over you know decades
+ 
+
+ align:start position:0%
+economy looking over you know decades
+the fraction of services produced in gdp
+
+ align:start position:0%
+the fraction of services produced in gdp
+ 
+
+ align:start position:0%
+the fraction of services produced in gdp
+is just keeps going up and up which is
+
+ align:start position:0%
+is just keeps going up and up which is
+ 
+
+ align:start position:0%
+is just keeps going up and up which is
+reflective of the fact that as
+
+ align:start position:0%
+reflective of the fact that as
+ 
+
+ align:start position:0%
+reflective of the fact that as
+households have more income they demand
+
+ align:start position:0%
+households have more income they demand
+ 
+
+ align:start position:0%
+households have more income they demand
+more services and less food
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's pretty dated 1920 so i went on
+
+ align:start position:0%
+so that's pretty dated 1920 so i went on
+ 
+
+ align:start position:0%
+so that's pretty dated 1920 so i went on
+the web and looked this thing up
+
+ align:start position:0%
+the web and looked this thing up
+ 
+
+ align:start position:0%
+the web and looked this thing up
+engel's law today
+
+ align:start position:0%
+engel's law today
+ 
+
+ align:start position:0%
+engel's law today
+here we're dividing households into
+
+ align:start position:0%
+here we're dividing households into
+ 
+
+ align:start position:0%
+here we're dividing households into
+quintiles five groups
+
+ align:start position:0%
+quintiles five groups
+ 
+
+ align:start position:0%
+quintiles five groups
+an equal number of household in each
+
+ align:start position:0%
+an equal number of household in each
+ 
+
+ align:start position:0%
+an equal number of household in each
+group
+
+ align:start position:0%
+group
+ 
+
+ align:start position:0%
+group
+and we plot the fraction of so-called
+
+ align:start position:0%
+and we plot the fraction of so-called
+ 
+
+ align:start position:0%
+and we plot the fraction of so-called
+luxuries and necessities for each group
+
+ align:start position:0%
+luxuries and necessities for each group
+ 
+
+ align:start position:0%
+luxuries and necessities for each group
+now this is a bit problematic in the
+
+ align:start position:0%
+now this is a bit problematic in the
+ 
+
+ align:start position:0%
+now this is a bit problematic in the
+sense that necessities are defined as
+
+ align:start position:0%
+sense that necessities are defined as
+ 
+
+ align:start position:0%
+sense that necessities are defined as
+goods or services where consumption is
+
+ align:start position:0%
+goods or services where consumption is
+ 
+
+ align:start position:0%
+goods or services where consumption is
+proportionately lower as a person's
+
+ align:start position:0%
+proportionately lower as a person's
+ 
+
+ align:start position:0%
+proportionately lower as a person's
+income increases so again necessity or
+
+ align:start position:0%
+income increases so again necessity or
+ 
+
+ align:start position:0%
+income increases so again necessity or
+non-normal goods are as we defined it in
+
+ align:start position:0%
+non-normal goods are as we defined it in
+ 
+
+ align:start position:0%
+non-normal goods are as we defined it in
+the last three slides not too
+
+ align:start position:0%
+the last three slides not too
+ 
+
+ align:start position:0%
+the last three slides not too
+surprisingly the highest income groups
+
+ align:start position:0%
+surprisingly the highest income groups
+ 
+
+ align:start position:0%
+surprisingly the highest income groups
+the top 20 percent of the population the
+
+ align:start position:0%
+the top 20 percent of the population the
+ 
+
+ align:start position:0%
+the top 20 percent of the population the
+proportion of expenditure on luxuries is
+
+ align:start position:0%
+proportion of expenditure on luxuries is
+ 
+
+ align:start position:0%
+proportion of expenditure on luxuries is
+a lot higher than on necessities and
+
+ align:start position:0%
+a lot higher than on necessities and
+ 
+
+ align:start position:0%
+a lot higher than on necessities and
+that gap lowers until you get to the
+
+ align:start position:0%
+that gap lowers until you get to the
+ 
+
+ align:start position:0%
+that gap lowers until you get to the
+lowest group
+
+ align:start position:0%
+lowest group
+ 
+
+ align:start position:0%
+lowest group
+in which case the the fraction spent on
+
+ align:start position:0%
+in which case the the fraction spent on
+ 
+
+ align:start position:0%
+in which case the the fraction spent on
+necessities is a lot higher than
+
+ align:start position:0%
+necessities is a lot higher than
+ 
+
+ align:start position:0%
+necessities is a lot higher than
+luxuries
+
+ align:start position:0%
+luxuries
+ 
+
+ align:start position:0%
+luxuries
+now when i grabbed this there was a
+
+ align:start position:0%
+now when i grabbed this there was a
+ 
+
+ align:start position:0%
+now when i grabbed this there was a
+whole article about how poor people are
+
+ align:start position:0%
+whole article about how poor people are
+ 
+
+ align:start position:0%
+whole article about how poor people are
+extravagant because they're still
+
+ align:start position:0%
+extravagant because they're still
+ 
+
+ align:start position:0%
+extravagant because they're still
+spending money on luxury goods well i
+
+ align:start position:0%
+spending money on luxury goods well i
+ 
+
+ align:start position:0%
+spending money on luxury goods well i
+mean narrowly speaking yes that's true
+
+ align:start position:0%
+mean narrowly speaking yes that's true
+ 
+
+ align:start position:0%
+mean narrowly speaking yes that's true
+but again it's a little bit harsh
+
+ align:start position:0%
+but again it's a little bit harsh
+ 
+
+ align:start position:0%
+but again it's a little bit harsh
+because it doesn't mean they're driving
+
+ align:start position:0%
+because it doesn't mean they're driving
+ 
+
+ align:start position:0%
+because it doesn't mean they're driving
+around in a mercedes-benz it just means
+
+ align:start position:0%
+around in a mercedes-benz it just means
+ 
+
+ align:start position:0%
+around in a mercedes-benz it just means
+they're eating some fraction of what
+
+ align:start position:0%
+they're eating some fraction of what
+ 
+
+ align:start position:0%
+they're eating some fraction of what
+they spend on are normal goods
+
+ align:start position:0%
+they spend on are normal goods
+ 
+
+ align:start position:0%
+they spend on are normal goods
+is it wait um
+
+ align:start position:0%
+is it wait um
+ 
+
+ align:start position:0%
+is it wait um
+can you
+
+ align:start position:0%
+can you
+ 
+
+ align:start position:0%
+can you
+is there a wait is there a little bit of
+
+ align:start position:0%
+is there a wait is there a little bit of
+ 
+
+ align:start position:0%
+is there a wait is there a little bit of
+issue with how
+
+ align:start position:0%
+issue with how
+ 
+
+ align:start position:0%
+issue with how
+those two um
+
+ align:start position:0%
+those two um
+ 
+
+ align:start position:0%
+those two um
+i guess how the two lines are defined
+
+ align:start position:0%
+i guess how the two lines are defined
+ 
+
+ align:start position:0%
+i guess how the two lines are defined
+because the way you defined them it
+
+ align:start position:0%
+because the way you defined them it
+ 
+
+ align:start position:0%
+because the way you defined them it
+seems like you said luxuries are just
+
+ align:start position:0%
+seems like you said luxuries are just
+ 
+
+ align:start position:0%
+seems like you said luxuries are just
+what rich people buy and this is
+
+ align:start position:0%
+what rich people buy and this is
+ 
+
+ align:start position:0%
+what rich people buy and this is
+necessities are what poor people buy so
+
+ align:start position:0%
+necessities are what poor people buy so
+ 
+
+ align:start position:0%
+necessities are what poor people buy so
+doesn't this kind of get confirmed just
+
+ align:start position:0%
+doesn't this kind of get confirmed just
+ 
+
+ align:start position:0%
+doesn't this kind of get confirmed just
+by how you define it yes i think that's
+
+ align:start position:0%
+by how you define it yes i think that's
+ 
+
+ align:start position:0%
+by how you define it yes i think that's
+exactly right it's almost
+
+ align:start position:0%
+exactly right it's almost
+ 
+
+ align:start position:0%
+exactly right it's almost
+tautological i mean the way they defined
+
+ align:start position:0%
+tautological i mean the way they defined
+ 
+
+ align:start position:0%
+tautological i mean the way they defined
+it it has to be true that this blue line
+
+ align:start position:0%
+it it has to be true that this blue line
+ 
+
+ align:start position:0%
+it it has to be true that this blue line
+is going up and up uh as you go across
+
+ align:start position:0%
+is going up and up uh as you go across
+ 
+
+ align:start position:0%
+is going up and up uh as you go across
+the quintiles
+
+ align:start position:0%
+the quintiles
+ 
+
+ align:start position:0%
+the quintiles
+so i agree with that comment but i still
+
+ align:start position:0%
+so i agree with that comment but i still
+ 
+
+ align:start position:0%
+so i agree with that comment but i still
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+the graphs kind of how much is it going
+
+ align:start position:0%
+the graphs kind of how much is it going
+ 
+
+ align:start position:0%
+the graphs kind of how much is it going
+up what's the difference and so on could
+
+ align:start position:0%
+up what's the difference and so on could
+ 
+
+ align:start position:0%
+up what's the difference and so on could
+go up just a teeny little bit in which
+
+ align:start position:0%
+go up just a teeny little bit in which
+ 
+
+ align:start position:0%
+go up just a teeny little bit in which
+case that blue line would not move much
+
+ align:start position:0%
+case that blue line would not move much
+ 
+
+ align:start position:0%
+case that blue line would not move much
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well one takeaway from this is
+
+ align:start position:0%
+well one takeaway from this is
+ 
+
+ align:start position:0%
+well one takeaway from this is
+you know different households
+
+ align:start position:0%
+you know different households
+ 
+
+ align:start position:0%
+you know different households
+that differ in income do not spend the
+
+ align:start position:0%
+that differ in income do not spend the
+ 
+
+ align:start position:0%
+that differ in income do not spend the
+same fraction of their money on
+
+ align:start position:0%
+same fraction of their money on
+ 
+
+ align:start position:0%
+same fraction of their money on
+on goods so let me take a chance at the
+
+ align:start position:0%
+on goods so let me take a chance at the
+ 
+
+ align:start position:0%
+on goods so let me take a chance at the
+risk of so you know preview of coming
+
+ align:start position:0%
+risk of so you know preview of coming
+ 
+
+ align:start position:0%
+risk of so you know preview of coming
+attractions
+
+ align:start position:0%
+attractions
+ 
+
+ align:start position:0%
+attractions
+this is way back in lecture 18
+
+ align:start position:0%
+this is way back in lecture 18
+ 
+
+ align:start position:0%
+this is way back in lecture 18
+where we're going to talk about
+
+ align:start position:0%
+where we're going to talk about
+ 
+
+ align:start position:0%
+where we're going to talk about
+aggregation
+
+ align:start position:0%
+aggregation
+ 
+
+ align:start position:0%
+aggregation
+which has to do with whether we can
+
+ align:start position:0%
+which has to do with whether we can
+ 
+
+ align:start position:0%
+which has to do with whether we can
+represent demand functions as if they
+
+ align:start position:0%
+represent demand functions as if they
+ 
+
+ align:start position:0%
+represent demand functions as if they
+came from a single maximizing
+
+ align:start position:0%
+came from a single maximizing
+ 
+
+ align:start position:0%
+came from a single maximizing
+representative household or weaker that
+
+ align:start position:0%
+representative household or weaker that
+ 
+
+ align:start position:0%
+representative household or weaker that
+there is a group of households like the
+
+ align:start position:0%
+there is a group of households like the
+ 
+
+ align:start position:0%
+there is a group of households like the
+lower quintile
+
+ align:start position:0%
+lower quintile
+ 
+
+ align:start position:0%
+lower quintile
+and they're all alike and we could take
+
+ align:start position:0%
+and they're all alike and we could take
+ 
+
+ align:start position:0%
+and they're all alike and we could take
+a representative quintile low quintile
+
+ align:start position:0%
+a representative quintile low quintile
+ 
+
+ align:start position:0%
+a representative quintile low quintile
+household and talk about the demand as
+
+ align:start position:0%
+household and talk about the demand as
+ 
+
+ align:start position:0%
+household and talk about the demand as
+if it were coming from that one person
+
+ align:start position:0%
+if it were coming from that one person
+ 
+
+ align:start position:0%
+if it were coming from that one person
+what is a necessary and sufficient
+
+ align:start position:0%
+what is a necessary and sufficient
+ 
+
+ align:start position:0%
+what is a necessary and sufficient
+assumption for us to be able to do that
+
+ align:start position:0%
+assumption for us to be able to do that
+ 
+
+ align:start position:0%
+assumption for us to be able to do that
+kind of aggregation
+
+ align:start position:0%
+kind of aggregation
+ 
+
+ align:start position:0%
+kind of aggregation
+it is that these income in this case
+
+ align:start position:0%
+it is that these income in this case
+ 
+
+ align:start position:0%
+it is that these income in this case
+denoted wealth expansion paths are
+
+ align:start position:0%
+denoted wealth expansion paths are
+ 
+
+ align:start position:0%
+denoted wealth expansion paths are
+linear and have exactly the same slope
+
+ align:start position:0%
+linear and have exactly the same slope
+ 
+
+ align:start position:0%
+linear and have exactly the same slope
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+these guys will spend and i'm not trying
+
+ align:start position:0%
+these guys will spend and i'm not trying
+ 
+
+ align:start position:0%
+these guys will spend and i'm not trying
+to go through the entire lecture i'm
+
+ align:start position:0%
+to go through the entire lecture i'm
+ 
+
+ align:start position:0%
+to go through the entire lecture i'm
+just really trying to motivate you that
+
+ align:start position:0%
+just really trying to motivate you that
+ 
+
+ align:start position:0%
+just really trying to motivate you that
+we looked at some micro data and later
+
+ align:start position:0%
+we looked at some micro data and later
+ 
+
+ align:start position:0%
+we looked at some micro data and later
+we'll make some assumptions it's good to
+
+ align:start position:0%
+we'll make some assumptions it's good to
+ 
+
+ align:start position:0%
+we'll make some assumptions it's good to
+put the micro data about the assumptions
+
+ align:start position:0%
+put the micro data about the assumptions
+ 
+
+ align:start position:0%
+put the micro data about the assumptions
+on the table at the same time
+
+ align:start position:0%
+on the table at the same time
+ 
+
+ align:start position:0%
+on the table at the same time
+and compare them
+
+ align:start position:0%
+and compare them
+ 
+
+ align:start position:0%
+and compare them
+what's going on here is that if these
+
+ align:start position:0%
+what's going on here is that if these
+ 
+
+ align:start position:0%
+what's going on here is that if these
+income expansion paths are parallel
+
+ align:start position:0%
+income expansion paths are parallel
+ 
+
+ align:start position:0%
+income expansion paths are parallel
+then when we increase income for one
+
+ align:start position:0%
+then when we increase income for one
+ 
+
+ align:start position:0%
+then when we increase income for one
+household its expenditure would go up
+
+ align:start position:0%
+household its expenditure would go up
+ 
+
+ align:start position:0%
+household its expenditure would go up
+but because this line is parallel when
+
+ align:start position:0%
+but because this line is parallel when
+ 
+
+ align:start position:0%
+but because this line is parallel when
+we decrease expenditure for another one
+
+ align:start position:0%
+we decrease expenditure for another one
+ 
+
+ align:start position:0%
+we decrease expenditure for another one
+its expenditures will go down in exactly
+
+ align:start position:0%
+its expenditures will go down in exactly
+ 
+
+ align:start position:0%
+its expenditures will go down in exactly
+the same amount that this disguise went
+
+ align:start position:0%
+the same amount that this disguise went
+ 
+
+ align:start position:0%
+the same amount that this disguise went
+up so those income effects are
+
+ align:start position:0%
+up so those income effects are
+ 
+
+ align:start position:0%
+up so those income effects are
+completely offsetting and that turns out
+
+ align:start position:0%
+completely offsetting and that turns out
+ 
+
+ align:start position:0%
+completely offsetting and that turns out
+to be necessary and sufficient to add up
+
+ align:start position:0%
+to be necessary and sufficient to add up
+ 
+
+ align:start position:0%
+to be necessary and sufficient to add up
+all of income and drive demand as if
+
+ align:start position:0%
+all of income and drive demand as if
+ 
+
+ align:start position:0%
+all of income and drive demand as if
+we'd given all of income to one
+
+ align:start position:0%
+we'd given all of income to one
+ 
+
+ align:start position:0%
+we'd given all of income to one
+household
+
+ align:start position:0%
+household
+ 
+
+ align:start position:0%
+household
+all right well it was with some
+
+ align:start position:0%
+all right well it was with some
+ 
+
+ align:start position:0%
+all right well it was with some
+trepidation that i showed you this
+
+ align:start position:0%
+trepidation that i showed you this
+ 
+
+ align:start position:0%
+trepidation that i showed you this
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+that i thought you might like to know
+
+ align:start position:0%
+that i thought you might like to know
+ 
+
+ align:start position:0%
+that i thought you might like to know
+what's coming
+
+ align:start position:0%
+what's coming
+ 
+
+ align:start position:0%
+what's coming
+and we'll review all of that when we get
+
+ align:start position:0%
+and we'll review all of that when we get
+ 
+
+ align:start position:0%
+and we'll review all of that when we get
+to 18. okay so let's talk about income
+
+ align:start position:0%
+to 18. okay so let's talk about income
+ 
+
+ align:start position:0%
+to 18. okay so let's talk about income
+and substitution effects now instead of
+
+ align:start position:0%
+and substitution effects now instead of
+ 
+
+ align:start position:0%
+and substitution effects now instead of
+changing income
+
+ align:start position:0%
+changing income
+ 
+
+ align:start position:0%
+changing income
+we want to change a price
+
+ align:start position:0%
+we want to change a price
+ 
+
+ align:start position:0%
+we want to change a price
+we're going to focus on good x
+
+ align:start position:0%
+we're going to focus on good x
+ 
+
+ align:start position:0%
+we're going to focus on good x
+we're going to look at an initial point
+
+ align:start position:0%
+we're going to look at an initial point
+ 
+
+ align:start position:0%
+we're going to look at an initial point
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+y star x star
+
+ align:start position:0%
+y star x star
+ 
+
+ align:start position:0%
+y star x star
+and then we're going to lower the price
+
+ align:start position:0%
+and then we're going to lower the price
+ 
+
+ align:start position:0%
+and then we're going to lower the price
+of good x
+
+ align:start position:0%
+of good x
+ 
+
+ align:start position:0%
+of good x
+and not touch good y
+
+ align:start position:0%
+and not touch good y
+ 
+
+ align:start position:0%
+and not touch good y
+one way to kind of
+
+ align:start position:0%
+one way to kind of
+ 
+
+ align:start position:0%
+one way to kind of
+quickly convince yourself that the
+
+ align:start position:0%
+quickly convince yourself that the
+ 
+
+ align:start position:0%
+quickly convince yourself that the
+diagram is correct is that this point
+
+ align:start position:0%
+diagram is correct is that this point
+ 
+
+ align:start position:0%
+diagram is correct is that this point
+over here on the y-axis is taking all
+
+ align:start position:0%
+over here on the y-axis is taking all
+ 
+
+ align:start position:0%
+over here on the y-axis is taking all
+your income and devoting it to the
+
+ align:start position:0%
+your income and devoting it to the
+ 
+
+ align:start position:0%
+your income and devoting it to the
+purchase of good y the price of y hasn't
+
+ align:start position:0%
+purchase of good y the price of y hasn't
+ 
+
+ align:start position:0%
+purchase of good y the price of y hasn't
+changed so this point hasn't changed but
+
+ align:start position:0%
+changed so this point hasn't changed but
+ 
+
+ align:start position:0%
+changed so this point hasn't changed but
+the price of x is going down
+
+ align:start position:0%
+the price of x is going down
+ 
+
+ align:start position:0%
+the price of x is going down
+and logically
+
+ align:start position:0%
+and logically
+ 
+
+ align:start position:0%
+and logically
+the set of things you can buy is
+
+ align:start position:0%
+the set of things you can buy is
+ 
+
+ align:start position:0%
+the set of things you can buy is
+expanding
+
+ align:start position:0%
+expanding
+ 
+
+ align:start position:0%
+expanding
+so this budget line shifts to the right
+
+ align:start position:0%
+so this budget line shifts to the right
+ 
+
+ align:start position:0%
+so this budget line shifts to the right
+but not in a parallel fashion so what is
+
+ align:start position:0%
+but not in a parallel fashion so what is
+ 
+
+ align:start position:0%
+but not in a parallel fashion so what is
+the new purchase
+
+ align:start position:0%
+the new purchase
+ 
+
+ align:start position:0%
+the new purchase
+the new purchase is the tangency y
+
+ align:start position:0%
+the new purchase is the tangency y
+ 
+
+ align:start position:0%
+the new purchase is the tangency y
+double star and x double star and we're
+
+ align:start position:0%
+double star and x double star and we're
+ 
+
+ align:start position:0%
+double star and x double star and we're
+going to break that movement from the
+
+ align:start position:0%
+going to break that movement from the
+ 
+
+ align:start position:0%
+going to break that movement from the
+initial point to the subsequent point
+
+ align:start position:0%
+initial point to the subsequent point
+ 
+
+ align:start position:0%
+initial point to the subsequent point
+into two pieces
+
+ align:start position:0%
+into two pieces
+ 
+
+ align:start position:0%
+into two pieces
+one a price effect and two an income
+
+ align:start position:0%
+one a price effect and two an income
+ 
+
+ align:start position:0%
+one a price effect and two an income
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+so since the price of good x goes down
+
+ align:start position:0%
+so since the price of good x goes down
+ 
+
+ align:start position:0%
+so since the price of good x goes down
+px over py
+
+ align:start position:0%
+px over py
+ 
+
+ align:start position:0%
+px over py
+in absolute value is going down so
+
+ align:start position:0%
+in absolute value is going down so
+ 
+
+ align:start position:0%
+in absolute value is going down so
+there's a new
+
+ align:start position:0%
+there's a new
+ 
+
+ align:start position:0%
+there's a new
+budget line with a lower slope
+
+ align:start position:0%
+budget line with a lower slope
+ 
+
+ align:start position:0%
+budget line with a lower slope
+that is pivoting on the initial
+
+ align:start position:0%
+that is pivoting on the initial
+ 
+
+ align:start position:0%
+that is pivoting on the initial
+indifference curve u1
+
+ align:start position:0%
+indifference curve u1
+ 
+
+ align:start position:0%
+indifference curve u1
+so setting aside income effects which
+
+ align:start position:0%
+so setting aside income effects which
+ 
+
+ align:start position:0%
+so setting aside income effects which
+we'll get to momentarily
+
+ align:start position:0%
+we'll get to momentarily
+ 
+
+ align:start position:0%
+we'll get to momentarily
+the natural
+
+ align:start position:0%
+the natural
+ 
+
+ align:start position:0%
+the natural
+impact of lowering the price of good x
+
+ align:start position:0%
+impact of lowering the price of good x
+ 
+
+ align:start position:0%
+impact of lowering the price of good x
+is to increase the expenditure of good x
+
+ align:start position:0%
+is to increase the expenditure of good x
+ 
+
+ align:start position:0%
+is to increase the expenditure of good x
+and decrease the expenditure of good y
+
+ align:start position:0%
+and decrease the expenditure of good y
+ 
+
+ align:start position:0%
+and decrease the expenditure of good y
+so that's called the substitution effect
+
+ align:start position:0%
+so that's called the substitution effect
+ 
+
+ align:start position:0%
+so that's called the substitution effect
+and it's a movement from x star y star
+
+ align:start position:0%
+and it's a movement from x star y star
+ 
+
+ align:start position:0%
+and it's a movement from x star y star
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+but in fact of course income effectively
+
+ align:start position:0%
+but in fact of course income effectively
+ 
+
+ align:start position:0%
+but in fact of course income effectively
+purchasing power has gone up even though
+
+ align:start position:0%
+purchasing power has gone up even though
+ 
+
+ align:start position:0%
+purchasing power has gone up even though
+nominal income has not moved one good at
+
+ align:start position:0%
+nominal income has not moved one good at
+ 
+
+ align:start position:0%
+nominal income has not moved one good at
+least is cheaper so their effective
+
+ align:start position:0%
+least is cheaper so their effective
+ 
+
+ align:start position:0%
+least is cheaper so their effective
+income has gone up and that's
+
+ align:start position:0%
+income has gone up and that's
+ 
+
+ align:start position:0%
+income has gone up and that's
+represented by this parallel shift from
+
+ align:start position:0%
+represented by this parallel shift from
+ 
+
+ align:start position:0%
+represented by this parallel shift from
+b to
+
+ align:start position:0%
+b to
+ 
+
+ align:start position:0%
+b to
+x double star y double star and that
+
+ align:start position:0%
+x double star y double star and that
+ 
+
+ align:start position:0%
+x double star y double star and that
+last bit from b to there is called the
+
+ align:start position:0%
+last bit from b to there is called the
+ 
+
+ align:start position:0%
+last bit from b to there is called the
+income effect
+
+ align:start position:0%
+income effect
+ 
+
+ align:start position:0%
+income effect
+so the global movement is from x star
+
+ align:start position:0%
+so the global movement is from x star
+ 
+
+ align:start position:0%
+so the global movement is from x star
+to x double star
+
+ align:start position:0%
+to x double star
+ 
+
+ align:start position:0%
+to x double star
+with a corresponding movement from y
+
+ align:start position:0%
+with a corresponding movement from y
+ 
+
+ align:start position:0%
+with a corresponding movement from y
+star to y double star and it's broken
+
+ align:start position:0%
+star to y double star and it's broken
+ 
+
+ align:start position:0%
+star to y double star and it's broken
+into two pieces
+
+ align:start position:0%
+into two pieces
+ 
+
+ align:start position:0%
+into two pieces
+this substitution effect which
+
+ align:start position:0%
+this substitution effect which
+ 
+
+ align:start position:0%
+this substitution effect which
+corresponds with movement along the
+
+ align:start position:0%
+corresponds with movement along the
+ 
+
+ align:start position:0%
+corresponds with movement along the
+original indifference curve and the
+
+ align:start position:0%
+original indifference curve and the
+ 
+
+ align:start position:0%
+original indifference curve and the
+income effect of having higher effective
+
+ align:start position:0%
+income effect of having higher effective
+ 
+
+ align:start position:0%
+income effect of having higher effective
+purchasing power
+
+ align:start position:0%
+purchasing power
+ 
+
+ align:start position:0%
+purchasing power
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+a lot of today's lecture is just like
+
+ align:start position:0%
+a lot of today's lecture is just like
+ 
+
+ align:start position:0%
+a lot of today's lecture is just like
+going over this in various ways
+
+ align:start position:0%
+going over this in various ways
+ 
+
+ align:start position:0%
+going over this in various ways
+you can get mesmerized with the price
+
+ align:start position:0%
+you can get mesmerized with the price
+ 
+
+ align:start position:0%
+you can get mesmerized with the price
+decrease
+
+ align:start position:0%
+decrease
+ 
+
+ align:start position:0%
+decrease
+here is a price increase
+
+ align:start position:0%
+here is a price increase
+ 
+
+ align:start position:0%
+here is a price increase
+uh they're starting out
+
+ align:start position:0%
+uh they're starting out
+ 
+
+ align:start position:0%
+uh they're starting out
+with a tangency
+
+ align:start position:0%
+with a tangency
+ 
+
+ align:start position:0%
+with a tangency
+the uh price of good x still goes in
+
+ align:start position:0%
+the uh price of good x still goes in
+ 
+
+ align:start position:0%
+the uh price of good x still goes in
+this case up
+
+ align:start position:0%
+this case up
+ 
+
+ align:start position:0%
+this case up
+their purchasing power goes down the
+
+ align:start position:0%
+their purchasing power goes down the
+ 
+
+ align:start position:0%
+their purchasing power goes down the
+budget line rotates from this initial
+
+ align:start position:0%
+budget line rotates from this initial
+ 
+
+ align:start position:0%
+budget line rotates from this initial
+point inward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the total demand of the price
+
+ align:start position:0%
+so the total demand of the price
+ 
+
+ align:start position:0%
+so the total demand of the price
+increase is going
+
+ align:start position:0%
+increase is going
+ 
+
+ align:start position:0%
+increase is going
+down a reduction in x
+
+ align:start position:0%
+down a reduction in x
+ 
+
+ align:start position:0%
+down a reduction in x
+but again we can break that into two
+
+ align:start position:0%
+but again we can break that into two
+ 
+
+ align:start position:0%
+but again we can break that into two
+pieces
+
+ align:start position:0%
+pieces
+ 
+
+ align:start position:0%
+pieces
+one is the substitution effect the
+
+ align:start position:0%
+one is the substitution effect the
+ 
+
+ align:start position:0%
+one is the substitution effect the
+movement away from good x because it has
+
+ align:start position:0%
+movement away from good x because it has
+ 
+
+ align:start position:0%
+movement away from good x because it has
+a higher price relative to good y
+
+ align:start position:0%
+a higher price relative to good y
+ 
+
+ align:start position:0%
+a higher price relative to good y
+to point b
+
+ align:start position:0%
+to point b
+ 
+
+ align:start position:0%
+to point b
+and now we take into account the loss of
+
+ align:start position:0%
+and now we take into account the loss of
+ 
+
+ align:start position:0%
+and now we take into account the loss of
+effective purchasing power
+
+ align:start position:0%
+effective purchasing power
+ 
+
+ align:start position:0%
+effective purchasing power
+which is a shift in this budget line the
+
+ align:start position:0%
+which is a shift in this budget line the
+ 
+
+ align:start position:0%
+which is a shift in this budget line the
+dotted tangency line
+
+ align:start position:0%
+dotted tangency line
+ 
+
+ align:start position:0%
+dotted tangency line
+which is tangent at b to the actual new
+
+ align:start position:0%
+which is tangent at b to the actual new
+ 
+
+ align:start position:0%
+which is tangent at b to the actual new
+lower budget line
+
+ align:start position:0%
+lower budget line
+ 
+
+ align:start position:0%
+lower budget line
+so here we denote the
+
+ align:start position:0%
+so here we denote the
+ 
+
+ align:start position:0%
+so here we denote the
+the combination of the substitution and
+
+ align:start position:0%
+the combination of the substitution and
+ 
+
+ align:start position:0%
+the combination of the substitution and
+income effects
+
+ align:start position:0%
+income effects
+ 
+
+ align:start position:0%
+income effects
+this is really the previous diagram in
+
+ align:start position:0%
+this is really the previous diagram in
+ 
+
+ align:start position:0%
+this is really the previous diagram in
+reverse
+
+ align:start position:0%
+reverse
+ 
+
+ align:start position:0%
+reverse
+but i think it's useful
+
+ align:start position:0%
+but i think it's useful
+ 
+
+ align:start position:0%
+but i think it's useful
+to show both
+
+ align:start position:0%
+to show both
+ 
+
+ align:start position:0%
+to show both
+of course we can also start changing the
+
+ align:start position:0%
+of course we can also start changing the
+ 
+
+ align:start position:0%
+of course we can also start changing the
+price of y let's not do that right away
+
+ align:start position:0%
+price of y let's not do that right away
+ 
+
+ align:start position:0%
+price of y let's not do that right away
+i'll come back to that later but the
+
+ align:start position:0%
+i'll come back to that later but the
+ 
+
+ align:start position:0%
+i'll come back to that later but the
+principles remain the same
+
+ align:start position:0%
+principles remain the same
+ 
+
+ align:start position:0%
+principles remain the same
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's construct some demand curves
+
+ align:start position:0%
+let's construct some demand curves
+ 
+
+ align:start position:0%
+let's construct some demand curves
+as in the equation system we had
+
+ align:start position:0%
+as in the equation system we had
+ 
+
+ align:start position:0%
+as in the equation system we had
+initially
+
+ align:start position:0%
+initially
+ 
+
+ align:start position:0%
+initially
+if we keep lowering the price moving in
+
+ align:start position:0%
+if we keep lowering the price moving in
+ 
+
+ align:start position:0%
+if we keep lowering the price moving in
+this direction
+
+ align:start position:0%
+this direction
+ 
+
+ align:start position:0%
+this direction
+we trace out this tangency
+
+ align:start position:0%
+we trace out this tangency
+ 
+
+ align:start position:0%
+we trace out this tangency
+and those will be the demand at the
+
+ align:start position:0%
+and those will be the demand at the
+ 
+
+ align:start position:0%
+and those will be the demand at the
+associated prices so here
+
+ align:start position:0%
+associated prices so here
+ 
+
+ align:start position:0%
+associated prices so here
+we have say x
+
+ align:start position:0%
+we have say x
+ 
+
+ align:start position:0%
+we have say x
+prime at price p prime
+
+ align:start position:0%
+prime at price p prime
+ 
+
+ align:start position:0%
+prime at price p prime
+x double prime at price p double prime
+
+ align:start position:0%
+x double prime at price p double prime
+ 
+
+ align:start position:0%
+x double prime at price p double prime
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+this would would have been even better
+
+ align:start position:0%
+this would would have been even better
+ 
+
+ align:start position:0%
+this would would have been even better
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+these things were lined up but they were
+
+ align:start position:0%
+these things were lined up but they were
+ 
+
+ align:start position:0%
+these things were lined up but they were
+intended to be
+
+ align:start position:0%
+intended to be
+ 
+
+ align:start position:0%
+intended to be
+x triple prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at price p triple prime
+
+ align:start position:0%
+at price p triple prime
+ 
+
+ align:start position:0%
+at price p triple prime
+now again
+
+ align:start position:0%
+now again
+ 
+
+ align:start position:0%
+now again
+price is going down
+
+ align:start position:0%
+price is going down
+ 
+
+ align:start position:0%
+price is going down
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+demand is going up
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now just to alert you
+
+ align:start position:0%
+now just to alert you
+ 
+
+ align:start position:0%
+now just to alert you
+i don't know where this got started with
+
+ align:start position:0%
+i don't know where this got started with
+ 
+
+ align:start position:0%
+i don't know where this got started with
+marshall or whatever
+
+ align:start position:0%
+marshall or whatever
+ 
+
+ align:start position:0%
+marshall or whatever
+but usually we plot you know y as a
+
+ align:start position:0%
+but usually we plot you know y as a
+ 
+
+ align:start position:0%
+but usually we plot you know y as a
+function of x
+
+ align:start position:0%
+function of x
+ 
+
+ align:start position:0%
+function of x
+where x is on the y axis and y the
+
+ align:start position:0%
+where x is on the y axis and y the
+ 
+
+ align:start position:0%
+where x is on the y axis and y the
+dependent variable is on the y axis
+
+ align:start position:0%
+dependent variable is on the y axis
+ 
+
+ align:start position:0%
+dependent variable is on the y axis
+this is actually plotted in reverse
+
+ align:start position:0%
+this is actually plotted in reverse
+ 
+
+ align:start position:0%
+this is actually plotted in reverse
+because we're varying price as an
+
+ align:start position:0%
+because we're varying price as an
+ 
+
+ align:start position:0%
+because we're varying price as an
+exogenous variable
+
+ align:start position:0%
+exogenous variable
+ 
+
+ align:start position:0%
+exogenous variable
+and plotting the demand
+
+ align:start position:0%
+and plotting the demand
+ 
+
+ align:start position:0%
+and plotting the demand
+no big deal i don't think i can plot it
+
+ align:start position:0%
+no big deal i don't think i can plot it
+ 
+
+ align:start position:0%
+no big deal i don't think i can plot it
+the other way
+
+ align:start position:0%
+the other way
+ 
+
+ align:start position:0%
+the other way
+actually i could but
+
+ align:start position:0%
+actually i could but
+ 
+
+ align:start position:0%
+actually i could but
+you'll see why this
+
+ align:start position:0%
+you'll see why this
+ 
+
+ align:start position:0%
+you'll see why this
+can get confusing right i just thought
+
+ align:start position:0%
+can get confusing right i just thought
+ 
+
+ align:start position:0%
+can get confusing right i just thought
+i'd point it out along the way
+
+ align:start position:0%
+i'd point it out along the way
+ 
+
+ align:start position:0%
+i'd point it out along the way
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+now we come to giffen's paradox
+
+ align:start position:0%
+now we come to giffen's paradox
+ 
+
+ align:start position:0%
+now we come to giffen's paradox
+if the income effect of a price change
+
+ align:start position:0%
+if the income effect of a price change
+ 
+
+ align:start position:0%
+if the income effect of a price change
+is strong enough the change in the price
+
+ align:start position:0%
+is strong enough the change in the price
+ 
+
+ align:start position:0%
+is strong enough the change in the price
+and the resulting change in the quantity
+
+ align:start position:0%
+and the resulting change in the quantity
+ 
+
+ align:start position:0%
+and the resulting change in the quantity
+demanded could actually move in the same
+
+ align:start position:0%
+demanded could actually move in the same
+ 
+
+ align:start position:0%
+demanded could actually move in the same
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+so let me give you an example that's
+
+ align:start position:0%
+so let me give you an example that's
+ 
+
+ align:start position:0%
+so let me give you an example that's
+attributed to robert giffin
+
+ align:start position:0%
+attributed to robert giffin
+ 
+
+ align:start position:0%
+attributed to robert giffin
+who claimed to observe this in ireland
+
+ align:start position:0%
+who claimed to observe this in ireland
+ 
+
+ align:start position:0%
+who claimed to observe this in ireland
+where they had a famine so the potato
+
+ align:start position:0%
+where they had a famine so the potato
+ 
+
+ align:start position:0%
+where they had a famine so the potato
+crop was failing and the price of
+
+ align:start position:0%
+crop was failing and the price of
+ 
+
+ align:start position:0%
+crop was failing and the price of
+potatoes was rising and despite the rise
+
+ align:start position:0%
+potatoes was rising and despite the rise
+ 
+
+ align:start position:0%
+potatoes was rising and despite the rise
+in price people consumed more so the
+
+ align:start position:0%
+in price people consumed more so the
+ 
+
+ align:start position:0%
+in price people consumed more so the
+demand curve was upward sloping not
+
+ align:start position:0%
+demand curve was upward sloping not
+ 
+
+ align:start position:0%
+demand curve was upward sloping not
+downward sloping
+
+ align:start position:0%
+downward sloping
+ 
+
+ align:start position:0%
+downward sloping
+his explanation was potatoes are a big
+
+ align:start position:0%
+his explanation was potatoes are a big
+ 
+
+ align:start position:0%
+his explanation was potatoes are a big
+part of the budget when their price goes
+
+ align:start position:0%
+part of the budget when their price goes
+ 
+
+ align:start position:0%
+part of the budget when their price goes
+up the effective income goes down and
+
+ align:start position:0%
+up the effective income goes down and
+ 
+
+ align:start position:0%
+up the effective income goes down and
+that income effect dominates the lower
+
+ align:start position:0%
+that income effect dominates the lower
+ 
+
+ align:start position:0%
+that income effect dominates the lower
+income effect is what lowers the demand
+
+ align:start position:0%
+income effect is what lowers the demand
+ 
+
+ align:start position:0%
+income effect is what lowers the demand
+for the good but in effect prices go up
+
+ align:start position:0%
+for the good but in effect prices go up
+ 
+
+ align:start position:0%
+for the good but in effect prices go up
+and demand goes
+
+ align:start position:0%
+and demand goes
+ 
+
+ align:start position:0%
+and demand goes
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+income's going down but these this good
+
+ align:start position:0%
+income's going down but these this good
+ 
+
+ align:start position:0%
+income's going down but these this good
+is a necessity so you get sort of a
+
+ align:start position:0%
+is a necessity so you get sort of a
+ 
+
+ align:start position:0%
+is a necessity so you get sort of a
+negative sign on the income effect so
+
+ align:start position:0%
+negative sign on the income effect so
+ 
+
+ align:start position:0%
+negative sign on the income effect so
+the demand is going up so price and
+
+ align:start position:0%
+the demand is going up so price and
+ 
+
+ align:start position:0%
+the demand is going up so price and
+income are going up at the same time
+
+ align:start position:0%
+income are going up at the same time
+ 
+
+ align:start position:0%
+income are going up at the same time
+it's a bit of a mouthful no pun intended
+
+ align:start position:0%
+it's a bit of a mouthful no pun intended
+ 
+
+ align:start position:0%
+it's a bit of a mouthful no pun intended
+actually this could not have happened it
+
+ align:start position:0%
+actually this could not have happened it
+ 
+
+ align:start position:0%
+actually this could not have happened it
+would require that potatoes be an
+
+ align:start position:0%
+would require that potatoes be an
+ 
+
+ align:start position:0%
+would require that potatoes be an
+important part of the budget that
+
+ align:start position:0%
+important part of the budget that
+ 
+
+ align:start position:0%
+important part of the budget that
+potatoes be a necessity but what doesn't
+
+ align:start position:0%
+potatoes be a necessity but what doesn't
+ 
+
+ align:start position:0%
+potatoes be a necessity but what doesn't
+fit the facts is how are they consuming
+
+ align:start position:0%
+fit the facts is how are they consuming
+ 
+
+ align:start position:0%
+fit the facts is how are they consuming
+more potatoes
+
+ align:start position:0%
+more potatoes
+ 
+
+ align:start position:0%
+more potatoes
+when in fact there was a blight and
+
+ align:start position:0%
+when in fact there was a blight and
+ 
+
+ align:start position:0%
+when in fact there was a blight and
+there were no more potatoes to be had
+
+ align:start position:0%
+there were no more potatoes to be had
+ 
+
+ align:start position:0%
+there were no more potatoes to be had
+so something doesn't add up literally
+
+ align:start position:0%
+so something doesn't add up literally
+ 
+
+ align:start position:0%
+so something doesn't add up literally
+anyway all intermediate micro classes
+
+ align:start position:0%
+anyway all intermediate micro classes
+ 
+
+ align:start position:0%
+anyway all intermediate micro classes
+technically fix your feature gif and
+
+ align:start position:0%
+technically fix your feature gif and
+ 
+
+ align:start position:0%
+technically fix your feature gif and
+goods and then move on
+
+ align:start position:0%
+goods and then move on
+ 
+
+ align:start position:0%
+goods and then move on
+and you may be left wondering if it ever
+
+ align:start position:0%
+and you may be left wondering if it ever
+ 
+
+ align:start position:0%
+and you may be left wondering if it ever
+really happens in practice those
+
+ align:start position:0%
+really happens in practice those
+ 
+
+ align:start position:0%
+really happens in practice those
+searching
+
+ align:start position:0%
+searching
+ 
+
+ align:start position:0%
+searching
+around i discovered jensen and miller
+
+ align:start position:0%
+around i discovered jensen and miller
+ 
+
+ align:start position:0%
+around i discovered jensen and miller
+who actually
+
+ align:start position:0%
+who actually
+ 
+
+ align:start position:0%
+who actually
+ran an experiment
+
+ align:start position:0%
+ran an experiment
+ 
+
+ align:start position:0%
+ran an experiment
+so this is literally a randomized
+
+ align:start position:0%
+so this is literally a randomized
+ 
+
+ align:start position:0%
+so this is literally a randomized
+control trial
+
+ align:start position:0%
+control trial
+ 
+
+ align:start position:0%
+control trial
+they went to china two different
+
+ align:start position:0%
+they went to china two different
+ 
+
+ align:start position:0%
+they went to china two different
+provinces looked at relatively poor
+
+ align:start position:0%
+provinces looked at relatively poor
+ 
+
+ align:start position:0%
+provinces looked at relatively poor
+households and changed the price of
+
+ align:start position:0%
+households and changed the price of
+ 
+
+ align:start position:0%
+households and changed the price of
+these staple food item that was a big
+
+ align:start position:0%
+these staple food item that was a big
+ 
+
+ align:start position:0%
+these staple food item that was a big
+part of their budget
+
+ align:start position:0%
+part of their budget
+ 
+
+ align:start position:0%
+part of their budget
+now in order to make the comparison
+
+ align:start position:0%
+now in order to make the comparison
+ 
+
+ align:start position:0%
+now in order to make the comparison
+you've got to change the price so it was
+
+ align:start position:0%
+you've got to change the price so it was
+ 
+
+ align:start position:0%
+you've got to change the price so it was
+a randomized control trial meaning
+
+ align:start position:0%
+a randomized control trial meaning
+ 
+
+ align:start position:0%
+a randomized control trial meaning
+randomly some households were
+
+ align:start position:0%
+randomly some households were
+ 
+
+ align:start position:0%
+randomly some households were
+exposed to a lower price because they
+
+ align:start position:0%
+exposed to a lower price because they
+ 
+
+ align:start position:0%
+exposed to a lower price because they
+were given vouchers so that when they
+
+ align:start position:0%
+were given vouchers so that when they
+ 
+
+ align:start position:0%
+were given vouchers so that when they
+went to the store the sum of you unpaid
+
+ align:start position:0%
+went to the store the sum of you unpaid
+ 
+
+ align:start position:0%
+went to the store the sum of you unpaid
+plus vouchers equaled the stated price
+
+ align:start position:0%
+plus vouchers equaled the stated price
+ 
+
+ align:start position:0%
+plus vouchers equaled the stated price
+but they didn't have to pay for the
+
+ align:start position:0%
+but they didn't have to pay for the
+ 
+
+ align:start position:0%
+but they didn't have to pay for the
+vouchers so effectively from their point
+
+ align:start position:0%
+vouchers so effectively from their point
+ 
+
+ align:start position:0%
+vouchers so effectively from their point
+of view the price was lowered given the
+
+ align:start position:0%
+of view the price was lowered given the
+ 
+
+ align:start position:0%
+of view the price was lowered given the
+vouchers
+
+ align:start position:0%
+vouchers
+ 
+
+ align:start position:0%
+vouchers
+and the control group did not receive
+
+ align:start position:0%
+and the control group did not receive
+ 
+
+ align:start position:0%
+and the control group did not receive
+vouchers so the control group faced the
+
+ align:start position:0%
+vouchers so the control group faced the
+ 
+
+ align:start position:0%
+vouchers so the control group faced the
+normal market price and what jensen and
+
+ align:start position:0%
+normal market price and what jensen and
+ 
+
+ align:start position:0%
+normal market price and what jensen and
+miller are doing is comparing the
+
+ align:start position:0%
+miller are doing is comparing the
+ 
+
+ align:start position:0%
+miller are doing is comparing the
+control group with the treatment group
+
+ align:start position:0%
+control group with the treatment group
+ 
+
+ align:start position:0%
+control group with the treatment group
+and what they discovered was
+
+ align:start position:0%
+and what they discovered was
+ 
+
+ align:start position:0%
+and what they discovered was
+in hunan in the south rice was the
+
+ align:start position:0%
+in hunan in the south rice was the
+ 
+
+ align:start position:0%
+in hunan in the south rice was the
+staple good
+
+ align:start position:0%
+staple good
+ 
+
+ align:start position:0%
+staple good
+in gonzoo it's wheat they did surveys
+
+ align:start position:0%
+in gonzoo it's wheat they did surveys
+ 
+
+ align:start position:0%
+in gonzoo it's wheat they did surveys
+like engel
+
+ align:start position:0%
+like engel
+ 
+
+ align:start position:0%
+like engel
+before during and after the subsidy on
+
+ align:start position:0%
+before during and after the subsidy on
+ 
+
+ align:start position:0%
+before during and after the subsidy on
+both treatment and control groups and
+
+ align:start position:0%
+both treatment and control groups and
+ 
+
+ align:start position:0%
+both treatment and control groups and
+they found strong evidence that poor
+
+ align:start position:0%
+they found strong evidence that poor
+ 
+
+ align:start position:0%
+they found strong evidence that poor
+households in hunan experience this
+
+ align:start position:0%
+households in hunan experience this
+ 
+
+ align:start position:0%
+households in hunan experience this
+giffen behavior with respect to rice
+
+ align:start position:0%
+giffen behavior with respect to rice
+ 
+
+ align:start position:0%
+giffen behavior with respect to rice
+that is to say when the price of rice
+
+ align:start position:0%
+that is to say when the price of rice
+ 
+
+ align:start position:0%
+that is to say when the price of rice
+went down households reduced their
+
+ align:start position:0%
+went down households reduced their
+ 
+
+ align:start position:0%
+went down households reduced their
+demand for rice
+
+ align:start position:0%
+demand for rice
+ 
+
+ align:start position:0%
+demand for rice
+the evidence was
+
+ align:start position:0%
+the evidence was
+ 
+
+ align:start position:0%
+the evidence was
+mixed in the other province and i think
+
+ align:start position:0%
+mixed in the other province and i think
+ 
+
+ align:start position:0%
+mixed in the other province and i think
+i
+
+ align:start position:0%
+i
+ 
+
+ align:start position:0%
+i
+will choose not to say very much about
+
+ align:start position:0%
+will choose not to say very much about
+ 
+
+ align:start position:0%
+will choose not to say very much about
+this there were groups the very poorest
+
+ align:start position:0%
+this there were groups the very poorest
+ 
+
+ align:start position:0%
+this there were groups the very poorest
+and the least poor that responded in
+
+ align:start position:0%
+and the least poor that responded in
+ 
+
+ align:start position:0%
+and the least poor that responded in
+what you might think to be the ordinary
+
+ align:start position:0%
+what you might think to be the ordinary
+ 
+
+ align:start position:0%
+what you might think to be the ordinary
+way with price with demand down sloping
+
+ align:start position:0%
+way with price with demand down sloping
+ 
+
+ align:start position:0%
+way with price with demand down sloping
+but there was a good a group in the
+
+ align:start position:0%
+but there was a good a group in the
+ 
+
+ align:start position:0%
+but there was a good a group in the
+middle between the very poorest and the
+
+ align:start position:0%
+middle between the very poorest and the
+ 
+
+ align:start position:0%
+middle between the very poorest and the
+least poor which exhibited giffen
+
+ align:start position:0%
+least poor which exhibited giffen
+ 
+
+ align:start position:0%
+least poor which exhibited giffen
+behavior
+
+ align:start position:0%
+behavior
+ 
+
+ align:start position:0%
+behavior
+now as it's written on the slide this is
+
+ align:start position:0%
+now as it's written on the slide this is
+ 
+
+ align:start position:0%
+now as it's written on the slide this is
+a bit of a mystery
+
+ align:start position:0%
+a bit of a mystery
+ 
+
+ align:start position:0%
+a bit of a mystery
+why is it that we're getting this
+
+ align:start position:0%
+why is it that we're getting this
+ 
+
+ align:start position:0%
+why is it that we're getting this
+difference across the three groups
+
+ align:start position:0%
+difference across the three groups
+ 
+
+ align:start position:0%
+difference across the three groups
+or two groups plus one
+
+ align:start position:0%
+or two groups plus one
+ 
+
+ align:start position:0%
+or two groups plus one
+and i leave that for you because again
+
+ align:start position:0%
+and i leave that for you because again
+ 
+
+ align:start position:0%
+and i leave that for you because again
+the problem set features the entire
+
+ align:start position:0%
+the problem set features the entire
+ 
+
+ align:start position:0%
+the problem set features the entire
+article we try to make it easy by
+
+ align:start position:0%
+article we try to make it easy by
+ 
+
+ align:start position:0%
+article we try to make it easy by
+highlighting the text but somewhere in
+
+ align:start position:0%
+highlighting the text but somewhere in
+ 
+
+ align:start position:0%
+highlighting the text but somewhere in
+that paper is a discussion of why this
+
+ align:start position:0%
+that paper is a discussion of why this
+ 
+
+ align:start position:0%
+that paper is a discussion of why this
+result which is a bit hard to interpret
+
+ align:start position:0%
+result which is a bit hard to interpret
+ 
+
+ align:start position:0%
+result which is a bit hard to interpret
+here does have and
+
+ align:start position:0%
+here does have and
+ 
+
+ align:start position:0%
+here does have and
+the authors did give it an
+
+ align:start position:0%
+the authors did give it an
+ 
+
+ align:start position:0%
+the authors did give it an
+interpretation so that's advertising to
+
+ align:start position:0%
+interpretation so that's advertising to
+ 
+
+ align:start position:0%
+interpretation so that's advertising to
+go and grab that paper
+
+ align:start position:0%
+go and grab that paper
+ 
+
+ align:start position:0%
+go and grab that paper
+which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so is the demand like the amount of
+
+ align:start position:0%
+yeah so is the demand like the amount of
+ 
+
+ align:start position:0%
+yeah so is the demand like the amount of
+potatoes or rice you're consuming or
+
+ align:start position:0%
+potatoes or rice you're consuming or
+ 
+
+ align:start position:0%
+potatoes or rice you're consuming or
+like the proportion that is of your
+
+ align:start position:0%
+like the proportion that is of your
+ 
+
+ align:start position:0%
+like the proportion that is of your
+income that's increasing
+
+ align:start position:0%
+income that's increasing
+ 
+
+ align:start position:0%
+income that's increasing
+it's the quantity but obviously they
+
+ align:start position:0%
+it's the quantity but obviously they
+ 
+
+ align:start position:0%
+it's the quantity but obviously they
+have the prices
+
+ align:start position:0%
+have the prices
+ 
+
+ align:start position:0%
+have the prices
+so you can look both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the the definition
+
+ align:start position:0%
+but the the definition
+ 
+
+ align:start position:0%
+but the the definition
+we've been using of a given good
+
+ align:start position:0%
+we've been using of a given good
+ 
+
+ align:start position:0%
+we've been using of a given good
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+oops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well actually it never showed
+
+ align:start position:0%
+well actually it never showed
+ 
+
+ align:start position:0%
+well actually it never showed
+uh but it is the quantity in this case
+
+ align:start position:0%
+uh but it is the quantity in this case
+ 
+
+ align:start position:0%
+uh but it is the quantity in this case
+the quantity of potatoes
+
+ align:start position:0%
+the quantity of potatoes
+ 
+
+ align:start position:0%
+the quantity of potatoes
+not expenditure on potatoes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now i want to get to something
+
+ align:start position:0%
+so now i want to get to something
+ 
+
+ align:start position:0%
+so now i want to get to something
+effectively we've already been doing
+
+ align:start position:0%
+effectively we've already been doing
+ 
+
+ align:start position:0%
+effectively we've already been doing
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+compensated versus uncompensated demands
+
+ align:start position:0%
+compensated versus uncompensated demands
+ 
+
+ align:start position:0%
+compensated versus uncompensated demands
+so the uncompensated demand is the total
+
+ align:start position:0%
+so the uncompensated demand is the total
+ 
+
+ align:start position:0%
+so the uncompensated demand is the total
+demand sometimes called the marshallian
+
+ align:start position:0%
+demand sometimes called the marshallian
+ 
+
+ align:start position:0%
+demand sometimes called the marshallian
+demand
+
+ align:start position:0%
+demand
+ 
+
+ align:start position:0%
+demand
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+marshall who was an early english
+
+ align:start position:0%
+marshall who was an early english
+ 
+
+ align:start position:0%
+marshall who was an early english
+economist it shows the relationship
+
+ align:start position:0%
+economist it shows the relationship
+ 
+
+ align:start position:0%
+economist it shows the relationship
+between price of the good and the
+
+ align:start position:0%
+between price of the good and the
+ 
+
+ align:start position:0%
+between price of the good and the
+quantity purchased assuming that all
+
+ align:start position:0%
+quantity purchased assuming that all
+ 
+
+ align:start position:0%
+quantity purchased assuming that all
+other prices and income are held
+
+ align:start position:0%
+other prices and income are held
+ 
+
+ align:start position:0%
+other prices and income are held
+constant the compensated demand
+
+ align:start position:0%
+constant the compensated demand
+ 
+
+ align:start position:0%
+constant the compensated demand
+sometimes called the hixian demand shows
+
+ align:start position:0%
+sometimes called the hixian demand shows
+ 
+
+ align:start position:0%
+sometimes called the hixian demand shows
+the relationship between price and
+
+ align:start position:0%
+the relationship between price and
+ 
+
+ align:start position:0%
+the relationship between price and
+quantity it continues to assume that all
+
+ align:start position:0%
+quantity it continues to assume that all
+ 
+
+ align:start position:0%
+quantity it continues to assume that all
+the other prices are held fixed but
+
+ align:start position:0%
+the other prices are held fixed but
+ 
+
+ align:start position:0%
+the other prices are held fixed but
+instead of holding income fixed utility
+
+ align:start position:0%
+instead of holding income fixed utility
+ 
+
+ align:start position:0%
+instead of holding income fixed utility
+is held fixed so to go back to the
+
+ align:start position:0%
+is held fixed so to go back to the
+ 
+
+ align:start position:0%
+is held fixed so to go back to the
+earlier slides we were featuring the
+
+ align:start position:0%
+earlier slides we were featuring the
+ 
+
+ align:start position:0%
+earlier slides we were featuring the
+substitution effect as the movement
+
+ align:start position:0%
+substitution effect as the movement
+ 
+
+ align:start position:0%
+substitution effect as the movement
+along an indifference curve i.e holding
+
+ align:start position:0%
+along an indifference curve i.e holding
+ 
+
+ align:start position:0%
+along an indifference curve i.e holding
+utility fixed so when we looked at how
+
+ align:start position:0%
+utility fixed so when we looked at how
+ 
+
+ align:start position:0%
+utility fixed so when we looked at how
+much demand would change
+
+ align:start position:0%
+much demand would change
+ 
+
+ align:start position:0%
+much demand would change
+one way or the other as a function of
+
+ align:start position:0%
+one way or the other as a function of
+ 
+
+ align:start position:0%
+one way or the other as a function of
+the price change
+
+ align:start position:0%
+the price change
+ 
+
+ align:start position:0%
+the price change
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+went along the initial baseline
+
+ align:start position:0%
+went along the initial baseline
+ 
+
+ align:start position:0%
+went along the initial baseline
+indifference curve that was the
+
+ align:start position:0%
+indifference curve that was the
+ 
+
+ align:start position:0%
+indifference curve that was the
+compensated demand
+
+ align:start position:0%
+compensated demand
+ 
+
+ align:start position:0%
+compensated demand
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+more dramatically
+
+ align:start position:0%
+more dramatically
+ 
+
+ align:start position:0%
+more dramatically
+if we fix the initial
+
+ align:start position:0%
+if we fix the initial
+ 
+
+ align:start position:0%
+if we fix the initial
+point and change the price we would be
+
+ align:start position:0%
+point and change the price we would be
+ 
+
+ align:start position:0%
+point and change the price we would be
+for lower price pivoting along this
+
+ align:start position:0%
+for lower price pivoting along this
+ 
+
+ align:start position:0%
+for lower price pivoting along this
+indifference curve u2
+
+ align:start position:0%
+indifference curve u2
+ 
+
+ align:start position:0%
+indifference curve u2
+by construction
+
+ align:start position:0%
+by construction
+ 
+
+ align:start position:0%
+by construction
+we keep utility constant at u2
+
+ align:start position:0%
+we keep utility constant at u2
+ 
+
+ align:start position:0%
+we keep utility constant at u2
+and then plot the demands
+
+ align:start position:0%
+and then plot the demands
+ 
+
+ align:start position:0%
+and then plot the demands
+which are going up and we put that on
+
+ align:start position:0%
+which are going up and we put that on
+ 
+
+ align:start position:0%
+which are going up and we put that on
+the price quantity diagram and the
+
+ align:start position:0%
+the price quantity diagram and the
+ 
+
+ align:start position:0%
+the price quantity diagram and the
+demand curve is sloping down but this is
+
+ align:start position:0%
+demand curve is sloping down but this is
+ 
+
+ align:start position:0%
+demand curve is sloping down but this is
+the hixian demand that little h to
+
+ align:start position:0%
+the hixian demand that little h to
+ 
+
+ align:start position:0%
+the hixian demand that little h to
+remind us that it's hixed
+
+ align:start position:0%
+remind us that it's hixed
+ 
+
+ align:start position:0%
+remind us that it's hixed
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+putting both
+
+ align:start position:0%
+putting both
+ 
+
+ align:start position:0%
+putting both
+types of demand on the same diagram
+
+ align:start position:0%
+types of demand on the same diagram
+ 
+
+ align:start position:0%
+types of demand on the same diagram
+we have the normal demand of the
+
+ align:start position:0%
+we have the normal demand of the
+ 
+
+ align:start position:0%
+we have the normal demand of the
+marshalling demand
+
+ align:start position:0%
+marshalling demand
+ 
+
+ align:start position:0%
+marshalling demand
+and h for the hixian demand
+
+ align:start position:0%
+and h for the hixian demand
+ 
+
+ align:start position:0%
+and h for the hixian demand
+so as price goes down demand goes up but
+
+ align:start position:0%
+so as price goes down demand goes up but
+ 
+
+ align:start position:0%
+so as price goes down demand goes up but
+the demand goes up from two different
+
+ align:start position:0%
+the demand goes up from two different
+ 
+
+ align:start position:0%
+the demand goes up from two different
+effects one is the substitution effect
+
+ align:start position:0%
+effects one is the substitution effect
+ 
+
+ align:start position:0%
+effects one is the substitution effect
+holding utility constant and that's a
+
+ align:start position:0%
+holding utility constant and that's a
+ 
+
+ align:start position:0%
+holding utility constant and that's a
+point on the hixian demand
+
+ align:start position:0%
+point on the hixian demand
+ 
+
+ align:start position:0%
+point on the hixian demand
+and then the rest of it is this movement
+
+ align:start position:0%
+and then the rest of it is this movement
+ 
+
+ align:start position:0%
+and then the rest of it is this movement
+to the marshallian demand or ordinary
+
+ align:start position:0%
+to the marshallian demand or ordinary
+ 
+
+ align:start position:0%
+to the marshallian demand or ordinary
+demand which is the income effect that
+
+ align:start position:0%
+demand which is the income effect that
+ 
+
+ align:start position:0%
+demand which is the income effect that
+comes from the lower price
+
+ align:start position:0%
+comes from the lower price
+ 
+
+ align:start position:0%
+comes from the lower price
+and obviously we can go in the other
+
+ align:start position:0%
+and obviously we can go in the other
+ 
+
+ align:start position:0%
+and obviously we can go in the other
+direction starting here as sort of a
+
+ align:start position:0%
+direction starting here as sort of a
+ 
+
+ align:start position:0%
+direction starting here as sort of a
+baseline
+
+ align:start position:0%
+baseline
+ 
+
+ align:start position:0%
+baseline
+if we
+
+ align:start position:0%
+if we
+ 
+
+ align:start position:0%
+if we
+increase the price we would pivot along
+
+ align:start position:0%
+increase the price we would pivot along
+ 
+
+ align:start position:0%
+increase the price we would pivot along
+the indifference curve
+
+ align:start position:0%
+the indifference curve
+ 
+
+ align:start position:0%
+the indifference curve
+and get a lower demand due to the
+
+ align:start position:0%
+and get a lower demand due to the
+ 
+
+ align:start position:0%
+and get a lower demand due to the
+substitution effect but effective income
+
+ align:start position:0%
+substitution effect but effective income
+ 
+
+ align:start position:0%
+substitution effect but effective income
+has gone down so this sort of negative
+
+ align:start position:0%
+has gone down so this sort of negative
+ 
+
+ align:start position:0%
+has gone down so this sort of negative
+income effect kicks in and demand is
+
+ align:start position:0%
+income effect kicks in and demand is
+ 
+
+ align:start position:0%
+income effect kicks in and demand is
+even less
+
+ align:start position:0%
+even less
+ 
+
+ align:start position:0%
+even less
+so kind of intuitively the hixian demand
+
+ align:start position:0%
+so kind of intuitively the hixian demand
+ 
+
+ align:start position:0%
+so kind of intuitively the hixian demand
+is steeper than
+
+ align:start position:0%
+is steeper than
+ 
+
+ align:start position:0%
+is steeper than
+the ordinary demand curve because it has
+
+ align:start position:0%
+the ordinary demand curve because it has
+ 
+
+ align:start position:0%
+the ordinary demand curve because it has
+included those income effects
+
+ align:start position:0%
+included those income effects
+ 
+
+ align:start position:0%
+included those income effects
+or putting in another way the ordinary
+
+ align:start position:0%
+or putting in another way the ordinary
+ 
+
+ align:start position:0%
+or putting in another way the ordinary
+demand curve is quote flatter with a
+
+ align:start position:0%
+demand curve is quote flatter with a
+ 
+
+ align:start position:0%
+demand curve is quote flatter with a
+lower slope
+
+ align:start position:0%
+lower slope
+ 
+
+ align:start position:0%
+lower slope
+because there's a more dramatic larger
+
+ align:start position:0%
+because there's a more dramatic larger
+ 
+
+ align:start position:0%
+because there's a more dramatic larger
+change in the quantity as we change the
+
+ align:start position:0%
+change in the quantity as we change the
+ 
+
+ align:start position:0%
+change in the quantity as we change the
+price either the income effect is
+
+ align:start position:0%
+price either the income effect is
+ 
+
+ align:start position:0%
+price either the income effect is
+positive and demand goes up all the more
+
+ align:start position:0%
+positive and demand goes up all the more
+ 
+
+ align:start position:0%
+positive and demand goes up all the more
+or the income effect is negative and the
+
+ align:start position:0%
+or the income effect is negative and the
+ 
+
+ align:start position:0%
+or the income effect is negative and the
+demand decreases all the more
+
+ align:start position:0%
+demand decreases all the more
+ 
+
+ align:start position:0%
+demand decreases all the more
+so we could say be careful about this
+
+ align:start position:0%
+so we could say be careful about this
+ 
+
+ align:start position:0%
+so we could say be careful about this
+that in some sense the ordinary demand
+
+ align:start position:0%
+that in some sense the ordinary demand
+ 
+
+ align:start position:0%
+that in some sense the ordinary demand
+curve is more elastic at least here it
+
+ align:start position:0%
+curve is more elastic at least here it
+ 
+
+ align:start position:0%
+curve is more elastic at least here it
+has a higher derivative
+
+ align:start position:0%
+has a higher derivative
+ 
+
+ align:start position:0%
+has a higher derivative
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+there's a mathematical expression
+
+ align:start position:0%
+there's a mathematical expression
+ 
+
+ align:start position:0%
+there's a mathematical expression
+for the difference between the hixian
+
+ align:start position:0%
+for the difference between the hixian
+ 
+
+ align:start position:0%
+for the difference between the hixian
+demand and the ordinary demand
+
+ align:start position:0%
+demand and the ordinary demand
+ 
+
+ align:start position:0%
+demand and the ordinary demand
+namely the derivative of demand of good
+
+ align:start position:0%
+namely the derivative of demand of good
+ 
+
+ align:start position:0%
+namely the derivative of demand of good
+x as we change the price of x the slope
+
+ align:start position:0%
+x as we change the price of x the slope
+ 
+
+ align:start position:0%
+x as we change the price of x the slope
+of the ordinary demand curve is first
+
+ align:start position:0%
+of the ordinary demand curve is first
+ 
+
+ align:start position:0%
+of the ordinary demand curve is first
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+the substitution effect of the price
+
+ align:start position:0%
+the substitution effect of the price
+ 
+
+ align:start position:0%
+the substitution effect of the price
+change px but then this income effect
+
+ align:start position:0%
+change px but then this income effect
+ 
+
+ align:start position:0%
+change px but then this income effect
+kicks in
+
+ align:start position:0%
+kicks in
+ 
+
+ align:start position:0%
+kicks in
+and there's two pieces to the income
+
+ align:start position:0%
+and there's two pieces to the income
+ 
+
+ align:start position:0%
+and there's two pieces to the income
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+one has to do with how high is the
+
+ align:start position:0%
+one has to do with how high is the
+ 
+
+ align:start position:0%
+one has to do with how high is the
+marginal change in x as you change
+
+ align:start position:0%
+marginal change in x as you change
+ 
+
+ align:start position:0%
+marginal change in x as you change
+income the other is how much x you were
+
+ align:start position:0%
+income the other is how much x you were
+ 
+
+ align:start position:0%
+income the other is how much x you were
+eating to begin with you know think of
+
+ align:start position:0%
+eating to begin with you know think of
+ 
+
+ align:start position:0%
+eating to begin with you know think of
+potatoes and so on
+
+ align:start position:0%
+potatoes and so on
+ 
+
+ align:start position:0%
+potatoes and so on
+or those budget shares either angle or
+
+ align:start position:0%
+or those budget shares either angle or
+ 
+
+ align:start position:0%
+or those budget shares either angle or
+but this is x this is the quantity so it
+
+ align:start position:0%
+but this is x this is the quantity so it
+ 
+
+ align:start position:0%
+but this is x this is the quantity so it
+looks from this since we're subtracting
+
+ align:start position:0%
+looks from this since we're subtracting
+ 
+
+ align:start position:0%
+looks from this since we're subtracting
+say the income is factor is positive and
+
+ align:start position:0%
+say the income is factor is positive and
+ 
+
+ align:start position:0%
+say the income is factor is positive and
+x is positive then we're subtracting a
+
+ align:start position:0%
+x is positive then we're subtracting a
+ 
+
+ align:start position:0%
+x is positive then we're subtracting a
+positive number so it looks like this
+
+ align:start position:0%
+positive number so it looks like this
+ 
+
+ align:start position:0%
+positive number so it looks like this
+minus this must be lower than this so it
+
+ align:start position:0%
+minus this must be lower than this so it
+ 
+
+ align:start position:0%
+minus this must be lower than this so it
+looks like the ordinary demand should
+
+ align:start position:0%
+looks like the ordinary demand should
+ 
+
+ align:start position:0%
+looks like the ordinary demand should
+have a lower slope if this equation is
+
+ align:start position:0%
+have a lower slope if this equation is
+ 
+
+ align:start position:0%
+have a lower slope if this equation is
+accurate but in fact as i just said it's
+
+ align:start position:0%
+accurate but in fact as i just said it's
+ 
+
+ align:start position:0%
+accurate but in fact as i just said it's
+the other way around puzzle puzzle
+
+ align:start position:0%
+the other way around puzzle puzzle
+ 
+
+ align:start position:0%
+the other way around puzzle puzzle
+puzzle what's going on well it's this
+
+ align:start position:0%
+puzzle what's going on well it's this
+ 
+
+ align:start position:0%
+puzzle what's going on well it's this
+stupid way that we traditionally plot
+
+ align:start position:0%
+stupid way that we traditionally plot
+ 
+
+ align:start position:0%
+stupid way that we traditionally plot
+the dependent variable on the x axis
+
+ align:start position:0%
+the dependent variable on the x axis
+ 
+
+ align:start position:0%
+the dependent variable on the x axis
+so you know this is dx dp
+
+ align:start position:0%
+so you know this is dx dp
+ 
+
+ align:start position:0%
+so you know this is dx dp
+the response of the dependent variable
+
+ align:start position:0%
+the response of the dependent variable
+ 
+
+ align:start position:0%
+the response of the dependent variable
+to the independent variable which is you
+
+ align:start position:0%
+to the independent variable which is you
+ 
+
+ align:start position:0%
+to the independent variable which is you
+know one over the slope of this so this
+
+ align:start position:0%
+know one over the slope of this so this
+ 
+
+ align:start position:0%
+know one over the slope of this so this
+diagram is consistent with this equation
+
+ align:start position:0%
+diagram is consistent with this equation
+ 
+
+ align:start position:0%
+diagram is consistent with this equation
+it just takes a little bit of juggling
+
+ align:start position:0%
+it just takes a little bit of juggling
+ 
+
+ align:start position:0%
+it just takes a little bit of juggling
+to realize why
+
+ align:start position:0%
+to realize why
+ 
+
+ align:start position:0%
+to realize why
+anyway this is called slutsky's equation
+
+ align:start position:0%
+anyway this is called slutsky's equation
+ 
+
+ align:start position:0%
+anyway this is called slutsky's equation
+and again at the risk of trying to do
+
+ align:start position:0%
+and again at the risk of trying to do
+ 
+
+ align:start position:0%
+and again at the risk of trying to do
+too much too fast but on the other hand
+
+ align:start position:0%
+too much too fast but on the other hand
+ 
+
+ align:start position:0%
+too much too fast but on the other hand
+providing some motivation for where
+
+ align:start position:0%
+providing some motivation for where
+ 
+
+ align:start position:0%
+providing some motivation for where
+we're going eventually we'll get to
+
+ align:start position:0%
+we're going eventually we'll get to
+ 
+
+ align:start position:0%
+we're going eventually we'll get to
+lecture 19 and talk about whether there
+
+ align:start position:0%
+lecture 19 and talk about whether there
+ 
+
+ align:start position:0%
+lecture 19 and talk about whether there
+are rejectable restrictions on data as
+
+ align:start position:0%
+are rejectable restrictions on data as
+ 
+
+ align:start position:0%
+are rejectable restrictions on data as
+in the science lecture we have a model
+
+ align:start position:0%
+in the science lecture we have a model
+ 
+
+ align:start position:0%
+in the science lecture we have a model
+does the model fit the data or not can
+
+ align:start position:0%
+does the model fit the data or not can
+ 
+
+ align:start position:0%
+does the model fit the data or not can
+you even reject the model
+
+ align:start position:0%
+you even reject the model
+ 
+
+ align:start position:0%
+you even reject the model
+is it providing some guidance or you can
+
+ align:start position:0%
+is it providing some guidance or you can
+ 
+
+ align:start position:0%
+is it providing some guidance or you can
+always tweak things so the model is
+
+ align:start position:0%
+always tweak things so the model is
+ 
+
+ align:start position:0%
+always tweak things so the model is
+always true so this lecture 19 is about
+
+ align:start position:0%
+always true so this lecture 19 is about
+ 
+
+ align:start position:0%
+always true so this lecture 19 is about
+restrictions that can be tested
+
+ align:start position:0%
+restrictions that can be tested
+ 
+
+ align:start position:0%
+restrictions that can be tested
+and there's something called slutsky
+
+ align:start position:0%
+and there's something called slutsky
+ 
+
+ align:start position:0%
+and there's something called slutsky
+same guy
+
+ align:start position:0%
+same guy
+ 
+
+ align:start position:0%
+same guy
+slutsky's decomposition this equation is
+
+ align:start position:0%
+slutsky's decomposition this equation is
+ 
+
+ align:start position:0%
+slutsky's decomposition this equation is
+a generalization of the one i was just
+
+ align:start position:0%
+a generalization of the one i was just
+ 
+
+ align:start position:0%
+a generalization of the one i was just
+showing you with the exception that we
+
+ align:start position:0%
+showing you with the exception that we
+ 
+
+ align:start position:0%
+showing you with the exception that we
+put this substitution effect on the left
+
+ align:start position:0%
+put this substitution effect on the left
+ 
+
+ align:start position:0%
+put this substitution effect on the left
+and the regular derivative on the right
+
+ align:start position:0%
+and the regular derivative on the right
+ 
+
+ align:start position:0%
+and the regular derivative on the right
+so it looks like the signs are changing
+
+ align:start position:0%
+so it looks like the signs are changing
+ 
+
+ align:start position:0%
+so it looks like the signs are changing
+this becomes a plus
+
+ align:start position:0%
+this becomes a plus
+ 
+
+ align:start position:0%
+this becomes a plus
+this is a generalization in a number of
+
+ align:start position:0%
+this is a generalization in a number of
+ 
+
+ align:start position:0%
+this is a generalization in a number of
+respects
+
+ align:start position:0%
+respects
+ 
+
+ align:start position:0%
+respects
+we're looking at the demand for good l
+
+ align:start position:0%
+we're looking at the demand for good l
+ 
+
+ align:start position:0%
+we're looking at the demand for good l
+as we change the price of another good
+
+ align:start position:0%
+as we change the price of another good
+ 
+
+ align:start position:0%
+as we change the price of another good
+good k
+
+ align:start position:0%
+good k
+ 
+
+ align:start position:0%
+good k
+not the own effect
+
+ align:start position:0%
+not the own effect
+ 
+
+ align:start position:0%
+not the own effect
+of one good with respect to its own
+
+ align:start position:0%
+of one good with respect to its own
+ 
+
+ align:start position:0%
+of one good with respect to its own
+price but sort of a cross partial
+
+ align:start position:0%
+price but sort of a cross partial
+ 
+
+ align:start position:0%
+price but sort of a cross partial
+derivative although we still have this
+
+ align:start position:0%
+derivative although we still have this
+ 
+
+ align:start position:0%
+derivative although we still have this
+income effect over here and we're still
+
+ align:start position:0%
+income effect over here and we're still
+ 
+
+ align:start position:0%
+income effect over here and we're still
+weighting it by the initial quantity
+
+ align:start position:0%
+weighting it by the initial quantity
+ 
+
+ align:start position:0%
+weighting it by the initial quantity
+purchased so it turns out that
+
+ align:start position:0%
+purchased so it turns out that
+ 
+
+ align:start position:0%
+purchased so it turns out that
+what we want to do is ask whether
+
+ align:start position:0%
+what we want to do is ask whether
+ 
+
+ align:start position:0%
+what we want to do is ask whether
+observe demands
+
+ align:start position:0%
+observe demands
+ 
+
+ align:start position:0%
+observe demands
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+these guys really how demand is changing
+
+ align:start position:0%
+these guys really how demand is changing
+ 
+
+ align:start position:0%
+these guys really how demand is changing
+with prices and income whether there are
+
+ align:start position:0%
+with prices and income whether there are
+ 
+
+ align:start position:0%
+with prices and income whether there are
+patterns which could be rejected as
+
+ align:start position:0%
+patterns which could be rejected as
+ 
+
+ align:start position:0%
+patterns which could be rejected as
+being inconsistent with a model and the
+
+ align:start position:0%
+being inconsistent with a model and the
+ 
+
+ align:start position:0%
+being inconsistent with a model and the
+problem is that the restrictions are on
+
+ align:start position:0%
+problem is that the restrictions are on
+ 
+
+ align:start position:0%
+problem is that the restrictions are on
+these pixian demands and we don't see
+
+ align:start position:0%
+these pixian demands and we don't see
+ 
+
+ align:start position:0%
+these pixian demands and we don't see
+those we see the regular demands we
+
+ align:start position:0%
+those we see the regular demands we
+ 
+
+ align:start position:0%
+those we see the regular demands we
+don't see the hixing demands but it and
+
+ align:start position:0%
+don't see the hixing demands but it and
+ 
+
+ align:start position:0%
+don't see the hixing demands but it and
+i'll say more about this in a minute
+
+ align:start position:0%
+i'll say more about this in a minute
+ 
+
+ align:start position:0%
+i'll say more about this in a minute
+it turns out that with some math you can
+
+ align:start position:0%
+it turns out that with some math you can
+ 
+
+ align:start position:0%
+it turns out that with some math you can
+actually go back and forth between the
+
+ align:start position:0%
+actually go back and forth between the
+ 
+
+ align:start position:0%
+actually go back and forth between the
+regular demand and the hixian demand and
+
+ align:start position:0%
+regular demand and the hixian demand and
+ 
+
+ align:start position:0%
+regular demand and the hixian demand and
+there are restrictions so anyway i'm
+
+ align:start position:0%
+there are restrictions so anyway i'm
+ 
+
+ align:start position:0%
+there are restrictions so anyway i'm
+running an experiment now
+
+ align:start position:0%
+running an experiment now
+ 
+
+ align:start position:0%
+running an experiment now
+because i'm showing you things that are
+
+ align:start position:0%
+because i'm showing you things that are
+ 
+
+ align:start position:0%
+because i'm showing you things that are
+more toward the end of the class lecture
+
+ align:start position:0%
+more toward the end of the class lecture
+ 
+
+ align:start position:0%
+more toward the end of the class lecture
+set of lectures than at the beginning
+
+ align:start position:0%
+set of lectures than at the beginning
+ 
+
+ align:start position:0%
+set of lectures than at the beginning
+but but since we're introducing
+
+ align:start position:0%
+but but since we're introducing
+ 
+
+ align:start position:0%
+but but since we're introducing
+slutsky's equation today i thought i'd
+
+ align:start position:0%
+slutsky's equation today i thought i'd
+ 
+
+ align:start position:0%
+slutsky's equation today i thought i'd
+show you that we will come back to it
+
+ align:start position:0%
+show you that we will come back to it
+ 
+
+ align:start position:0%
+show you that we will come back to it
+and and use it in a subsequent lecture
+
+ align:start position:0%
+and and use it in a subsequent lecture
+ 
+
+ align:start position:0%
+and and use it in a subsequent lecture
+this is a lot simpler notation
+
+ align:start position:0%
+this is a lot simpler notation
+ 
+
+ align:start position:0%
+this is a lot simpler notation
+and don't worry about either the income
+
+ align:start position:0%
+and don't worry about either the income
+ 
+
+ align:start position:0%
+and don't worry about either the income
+expansion paths or this generalization
+
+ align:start position:0%
+expansion paths or this generalization
+ 
+
+ align:start position:0%
+expansion paths or this generalization
+of slutsky that was meant to be a
+
+ align:start position:0%
+of slutsky that was meant to be a
+ 
+
+ align:start position:0%
+of slutsky that was meant to be a
+preview of coming attractions and
+
+ align:start position:0%
+preview of coming attractions and
+ 
+
+ align:start position:0%
+preview of coming attractions and
+motivation not something you should be
+
+ align:start position:0%
+motivation not something you should be
+ 
+
+ align:start position:0%
+motivation not something you should be
+worried about learning right away
+
+ align:start position:0%
+worried about learning right away
+ 
+
+ align:start position:0%
+worried about learning right away
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+now i want to introduce something called
+
+ align:start position:0%
+now i want to introduce something called
+ 
+
+ align:start position:0%
+now i want to introduce something called
+duality
+
+ align:start position:0%
+duality
+ 
+
+ align:start position:0%
+duality
+this looks like an income expansion path
+
+ align:start position:0%
+this looks like an income expansion path
+ 
+
+ align:start position:0%
+this looks like an income expansion path
+as we increase income we get more and
+
+ align:start position:0%
+as we increase income we get more and
+ 
+
+ align:start position:0%
+as we increase income we get more and
+more points
+
+ align:start position:0%
+more points
+ 
+
+ align:start position:0%
+more points
+i think this is identical with the
+
+ align:start position:0%
+i think this is identical with the
+ 
+
+ align:start position:0%
+i think this is identical with the
+figure i showed you earlier
+
+ align:start position:0%
+figure i showed you earlier
+ 
+
+ align:start position:0%
+figure i showed you earlier
+but i want to use it for a different
+
+ align:start position:0%
+but i want to use it for a different
+ 
+
+ align:start position:0%
+but i want to use it for a different
+purpose
+
+ align:start position:0%
+purpose
+ 
+
+ align:start position:0%
+purpose
+i want to say
+
+ align:start position:0%
+i want to say
+ 
+
+ align:start position:0%
+i want to say
+suppose we're at this point with this
+
+ align:start position:0%
+suppose we're at this point with this
+ 
+
+ align:start position:0%
+suppose we're at this point with this
+intermediate income i2
+
+ align:start position:0%
+intermediate income i2
+ 
+
+ align:start position:0%
+intermediate income i2
+then we could be maximizing utility
+
+ align:start position:0%
+then we could be maximizing utility
+ 
+
+ align:start position:0%
+then we could be maximizing utility
+subject to that income level holding
+
+ align:start position:0%
+subject to that income level holding
+ 
+
+ align:start position:0%
+subject to that income level holding
+price is fixed and that would be x2 y2
+
+ align:start position:0%
+price is fixed and that would be x2 y2
+ 
+
+ align:start position:0%
+price is fixed and that would be x2 y2
+would be the maximal point of utility
+
+ align:start position:0%
+would be the maximal point of utility
+ 
+
+ align:start position:0%
+would be the maximal point of utility
+but suppose we did a different
+
+ align:start position:0%
+but suppose we did a different
+ 
+
+ align:start position:0%
+but suppose we did a different
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+suppose we wanted to achieve
+
+ align:start position:0%
+suppose we wanted to achieve
+ 
+
+ align:start position:0%
+suppose we wanted to achieve
+this utility level u2 by spending as
+
+ align:start position:0%
+this utility level u2 by spending as
+ 
+
+ align:start position:0%
+this utility level u2 by spending as
+little as possible the amount spent
+
+ align:start position:0%
+little as possible the amount spent
+ 
+
+ align:start position:0%
+little as possible the amount spent
+would be captured by these various
+
+ align:start position:0%
+would be captured by these various
+ 
+
+ align:start position:0%
+would be captured by these various
+possible budget lines so something
+
+ align:start position:0%
+possible budget lines so something
+ 
+
+ align:start position:0%
+possible budget lines so something
+called a minimizing expenditure problem
+
+ align:start position:0%
+called a minimizing expenditure problem
+ 
+
+ align:start position:0%
+called a minimizing expenditure problem
+minimal expenditure problem
+
+ align:start position:0%
+minimal expenditure problem
+ 
+
+ align:start position:0%
+minimal expenditure problem
+would be to find the budget line which
+
+ align:start position:0%
+would be to find the budget line which
+ 
+
+ align:start position:0%
+would be to find the budget line which
+is lowest closest to zero zero and still
+
+ align:start position:0%
+is lowest closest to zero zero and still
+ 
+
+ align:start position:0%
+is lowest closest to zero zero and still
+allows the household to get the utility
+
+ align:start position:0%
+allows the household to get the utility
+ 
+
+ align:start position:0%
+allows the household to get the utility
+level u2
+
+ align:start position:0%
+level u2
+ 
+
+ align:start position:0%
+level u2
+so at this point it's clear you could
+
+ align:start position:0%
+so at this point it's clear you could
+ 
+
+ align:start position:0%
+so at this point it's clear you could
+think of this as maximizing utility
+
+ align:start position:0%
+think of this as maximizing utility
+ 
+
+ align:start position:0%
+think of this as maximizing utility
+subject to a fixed budget or minimizing
+
+ align:start position:0%
+subject to a fixed budget or minimizing
+ 
+
+ align:start position:0%
+subject to a fixed budget or minimizing
+the expenses to get to a fixed level of
+
+ align:start position:0%
+the expenses to get to a fixed level of
+ 
+
+ align:start position:0%
+the expenses to get to a fixed level of
+utility
+
+ align:start position:0%
+utility
+ 
+
+ align:start position:0%
+utility
+both things are true and you can go back
+
+ align:start position:0%
+both things are true and you can go back
+ 
+
+ align:start position:0%
+both things are true and you can go back
+and forth and that is the essential idea
+
+ align:start position:0%
+and forth and that is the essential idea
+ 
+
+ align:start position:0%
+and forth and that is the essential idea
+of duality
+
+ align:start position:0%
+of duality
+ 
+
+ align:start position:0%
+of duality
+okay let's do it little bit more with
+
+ align:start position:0%
+okay let's do it little bit more with
+ 
+
+ align:start position:0%
+okay let's do it little bit more with
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+let's take a consumer with a consumption
+
+ align:start position:0%
+let's take a consumer with a consumption
+ 
+
+ align:start position:0%
+let's take a consumer with a consumption
+set
+
+ align:start position:0%
+set
+ 
+
+ align:start position:0%
+set
+an l dimensional commodity space with
+
+ align:start position:0%
+an l dimensional commodity space with
+ 
+
+ align:start position:0%
+an l dimensional commodity space with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+preferences represented by a continuous
+
+ align:start position:0%
+preferences represented by a continuous
+ 
+
+ align:start position:0%
+preferences represented by a continuous
+utility function
+
+ align:start position:0%
+utility function
+ 
+
+ align:start position:0%
+utility function
+and let's look at the utility
+
+ align:start position:0%
+and let's look at the utility
+ 
+
+ align:start position:0%
+and let's look at the utility
+maximization problem
+
+ align:start position:0%
+maximization problem
+ 
+
+ align:start position:0%
+maximization problem
+ump for short
+
+ align:start position:0%
+ump for short
+ 
+
+ align:start position:0%
+ump for short
+which is to maximize utility
+
+ align:start position:0%
+which is to maximize utility
+ 
+
+ align:start position:0%
+which is to maximize utility
+subject to being within the budget so
+
+ align:start position:0%
+subject to being within the budget so
+ 
+
+ align:start position:0%
+subject to being within the budget so
+this says choose a point in the
+
+ align:start position:0%
+this says choose a point in the
+ 
+
+ align:start position:0%
+this says choose a point in the
+consumption set
+
+ align:start position:0%
+consumption set
+ 
+
+ align:start position:0%
+consumption set
+all of the positive ortho
+
+ align:start position:0%
+all of the positive ortho
+ 
+
+ align:start position:0%
+all of the positive ortho
+which maximizes that utility function
+
+ align:start position:0%
+which maximizes that utility function
+ 
+
+ align:start position:0%
+which maximizes that utility function
+subject to the points under
+
+ align:start position:0%
+subject to the points under
+ 
+
+ align:start position:0%
+subject to the points under
+consideration have to be such that when
+
+ align:start position:0%
+consideration have to be such that when
+ 
+
+ align:start position:0%
+consideration have to be such that when
+you take the dot product of p and x p 1
+
+ align:start position:0%
+you take the dot product of p and x p 1
+ 
+
+ align:start position:0%
+you take the dot product of p and x p 1
+x 1 plus p 2 x 2 dot dot it cannot
+
+ align:start position:0%
+x 1 plus p 2 x 2 dot dot it cannot
+ 
+
+ align:start position:0%
+x 1 plus p 2 x 2 dot dot it cannot
+exceed wealth or income so that's the
+
+ align:start position:0%
+exceed wealth or income so that's the
+ 
+
+ align:start position:0%
+exceed wealth or income so that's the
+utility maximization problem
+
+ align:start position:0%
+utility maximization problem
+ 
+
+ align:start position:0%
+utility maximization problem
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+result of solving the maximization
+
+ align:start position:0%
+result of solving the maximization
+ 
+
+ align:start position:0%
+result of solving the maximization
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+can be substituted into utility in other
+
+ align:start position:0%
+can be substituted into utility in other
+ 
+
+ align:start position:0%
+can be substituted into utility in other
+words utility at the maximal solution
+
+ align:start position:0%
+words utility at the maximal solution
+ 
+
+ align:start position:0%
+words utility at the maximal solution
+and we're going to call that the value
+
+ align:start position:0%
+and we're going to call that the value
+ 
+
+ align:start position:0%
+and we're going to call that the value
+function or indirect utility function
+
+ align:start position:0%
+function or indirect utility function
+ 
+
+ align:start position:0%
+function or indirect utility function
+note that the maximized utility is a
+
+ align:start position:0%
+note that the maximized utility is a
+ 
+
+ align:start position:0%
+note that the maximized utility is a
+function of the parameters or the
+
+ align:start position:0%
+function of the parameters or the
+ 
+
+ align:start position:0%
+function of the parameters or the
+exogenous variables of the problem
+
+ align:start position:0%
+exogenous variables of the problem
+ 
+
+ align:start position:0%
+exogenous variables of the problem
+namely the price vector p
+
+ align:start position:0%
+namely the price vector p
+ 
+
+ align:start position:0%
+namely the price vector p
+and wealth w
+
+ align:start position:0%
+and wealth w
+ 
+
+ align:start position:0%
+and wealth w
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+in contrast the expenditure minimization
+
+ align:start position:0%
+in contrast the expenditure minimization
+ 
+
+ align:start position:0%
+in contrast the expenditure minimization
+problem emp
+
+ align:start position:0%
+problem emp
+ 
+
+ align:start position:0%
+problem emp
+is to
+
+ align:start position:0%
+is to
+ 
+
+ align:start position:0%
+is to
+given a certain level of utility
+
+ align:start position:0%
+given a certain level of utility
+ 
+
+ align:start position:0%
+given a certain level of utility
+minimize
+
+ align:start position:0%
+minimize
+ 
+
+ align:start position:0%
+minimize
+expenditures the dot product p dot x
+
+ align:start position:0%
+expenditures the dot product p dot x
+ 
+
+ align:start position:0%
+expenditures the dot product p dot x
+uh that allows you to achieve at least
+
+ align:start position:0%
+uh that allows you to achieve at least
+ 
+
+ align:start position:0%
+uh that allows you to achieve at least
+that utility
+
+ align:start position:0%
+that utility
+ 
+
+ align:start position:0%
+that utility
+getting more is fine but you know
+
+ align:start position:0%
+getting more is fine but you know
+ 
+
+ align:start position:0%
+getting more is fine but you know
+in most of the figures we show they'll
+
+ align:start position:0%
+in most of the figures we show they'll
+ 
+
+ align:start position:0%
+in most of the figures we show they'll
+this will be at inequality but just like
+
+ align:start position:0%
+this will be at inequality but just like
+ 
+
+ align:start position:0%
+this will be at inequality but just like
+you could spend less than your
+
+ align:start position:0%
+you could spend less than your
+ 
+
+ align:start position:0%
+you could spend less than your
+income in principle here you could
+
+ align:start position:0%
+income in principle here you could
+ 
+
+ align:start position:0%
+income in principle here you could
+achieve a higher level of utility but
+
+ align:start position:0%
+achieve a higher level of utility but
+ 
+
+ align:start position:0%
+achieve a higher level of utility but
+whatever you're doing here in the
+
+ align:start position:0%
+whatever you're doing here in the
+ 
+
+ align:start position:0%
+whatever you're doing here in the
+expenditure minimization problem you're
+
+ align:start position:0%
+expenditure minimization problem you're
+ 
+
+ align:start position:0%
+expenditure minimization problem you're
+trying to minimize total expenditures
+
+ align:start position:0%
+trying to minimize total expenditures
+ 
+
+ align:start position:0%
+trying to minimize total expenditures
+and we call the solution to that the e
+
+ align:start position:0%
+and we call the solution to that the e
+ 
+
+ align:start position:0%
+and we call the solution to that the e
+for expenditure
+
+ align:start position:0%
+for expenditure
+ 
+
+ align:start position:0%
+for expenditure
+minimum is a minimized expenditure at
+
+ align:start position:0%
+minimum is a minimized expenditure at
+ 
+
+ align:start position:0%
+minimum is a minimized expenditure at
+the optimum is a function of the
+
+ align:start position:0%
+the optimum is a function of the
+ 
+
+ align:start position:0%
+the optimum is a function of the
+parameters of the problem the same price
+
+ align:start position:0%
+parameters of the problem the same price
+ 
+
+ align:start position:0%
+parameters of the problem the same price
+vector p
+
+ align:start position:0%
+vector p
+ 
+
+ align:start position:0%
+vector p
+but now what's taken as a given is u
+
+ align:start position:0%
+but now what's taken as a given is u
+ 
+
+ align:start position:0%
+but now what's taken as a given is u
+not w but u
+
+ align:start position:0%
+not w but u
+ 
+
+ align:start position:0%
+not w but u
+so we'll have this
+
+ align:start position:0%
+so we'll have this
+ 
+
+ align:start position:0%
+so we'll have this
+notation for value function and
+
+ align:start position:0%
+notation for value function and
+ 
+
+ align:start position:0%
+notation for value function and
+expenditure functions
+
+ align:start position:0%
+expenditure functions
+ 
+
+ align:start position:0%
+expenditure functions
+expenditure functions and demands for
+
+ align:start position:0%
+expenditure functions and demands for
+ 
+
+ align:start position:0%
+expenditure functions and demands for
+that matter have certain properties
+
+ align:start position:0%
+that matter have certain properties
+ 
+
+ align:start position:0%
+that matter have certain properties
+it turns out the expenditure function is
+
+ align:start position:0%
+it turns out the expenditure function is
+ 
+
+ align:start position:0%
+it turns out the expenditure function is
+concave
+
+ align:start position:0%
+concave
+ 
+
+ align:start position:0%
+concave
+and the derivative of the expenditure
+
+ align:start position:0%
+and the derivative of the expenditure
+ 
+
+ align:start position:0%
+and the derivative of the expenditure
+function is demand
+
+ align:start position:0%
+function is demand
+ 
+
+ align:start position:0%
+function is demand
+so when you take the second derivative
+
+ align:start position:0%
+so when you take the second derivative
+ 
+
+ align:start position:0%
+so when you take the second derivative
+of demand
+
+ align:start position:0%
+of demand
+ 
+
+ align:start position:0%
+of demand
+it picks up the concavity of the level
+
+ align:start position:0%
+it picks up the concavity of the level
+ 
+
+ align:start position:0%
+it picks up the concavity of the level
+expenditure function
+
+ align:start position:0%
+expenditure function
+ 
+
+ align:start position:0%
+expenditure function
+and that's why
+
+ align:start position:0%
+and that's why
+ 
+
+ align:start position:0%
+and that's why
+that slutsky equation holds because
+
+ align:start position:0%
+that slutsky equation holds because
+ 
+
+ align:start position:0%
+that slutsky equation holds because
+we're looking at the matrix of second
+
+ align:start position:0%
+we're looking at the matrix of second
+ 
+
+ align:start position:0%
+we're looking at the matrix of second
+order conditions effectively
+
+ align:start position:0%
+order conditions effectively
+ 
+
+ align:start position:0%
+order conditions effectively
+but again just ignore me if that's
+
+ align:start position:0%
+but again just ignore me if that's
+ 
+
+ align:start position:0%
+but again just ignore me if that's
+confusing we'll get there in that
+
+ align:start position:0%
+confusing we'll get there in that
+ 
+
+ align:start position:0%
+confusing we'll get there in that
+lecture 19. for now i just want to focus
+
+ align:start position:0%
+lecture 19. for now i just want to focus
+ 
+
+ align:start position:0%
+lecture 19. for now i just want to focus
+on this
+
+ align:start position:0%
+on this
+ 
+
+ align:start position:0%
+on this
+relationship this duality and there's a
+
+ align:start position:0%
+relationship this duality and there's a
+ 
+
+ align:start position:0%
+relationship this duality and there's a
+number of ways to put it the notation is
+
+ align:start position:0%
+number of ways to put it the notation is
+ 
+
+ align:start position:0%
+number of ways to put it the notation is
+surprisingly subtle but if you work
+
+ align:start position:0%
+surprisingly subtle but if you work
+ 
+
+ align:start position:0%
+surprisingly subtle but if you work
+through it it's fine so suppose we're
+
+ align:start position:0%
+through it it's fine so suppose we're
+ 
+
+ align:start position:0%
+through it it's fine so suppose we're
+given a continuous utility function
+
+ align:start position:0%
+given a continuous utility function
+ 
+
+ align:start position:0%
+given a continuous utility function
+representing locally non-satiated
+
+ align:start position:0%
+representing locally non-satiated
+ 
+
+ align:start position:0%
+representing locally non-satiated
+preferences with a consumption set
+
+ align:start position:0%
+preferences with a consumption set
+ 
+
+ align:start position:0%
+preferences with a consumption set
+strictly positive price vector if x star
+
+ align:start position:0%
+strictly positive price vector if x star
+ 
+
+ align:start position:0%
+strictly positive price vector if x star
+is optimal under the utility max problem
+
+ align:start position:0%
+is optimal under the utility max problem
+ 
+
+ align:start position:0%
+is optimal under the utility max problem
+for a given wealth at those prices then
+
+ align:start position:0%
+for a given wealth at those prices then
+ 
+
+ align:start position:0%
+for a given wealth at those prices then
+x-star is optimal in the expenditure
+
+ align:start position:0%
+x-star is optimal in the expenditure
+ 
+
+ align:start position:0%
+x-star is optimal in the expenditure
+minimization problem when the required
+
+ align:start position:0%
+minimization problem when the required
+ 
+
+ align:start position:0%
+minimization problem when the required
+utility level is the utility you
+
+ align:start position:0%
+utility level is the utility you
+ 
+
+ align:start position:0%
+utility level is the utility you
+achieved under the utility maximization
+
+ align:start position:0%
+achieved under the utility maximization
+ 
+
+ align:start position:0%
+achieved under the utility maximization
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+i showed you a picture of that just a
+
+ align:start position:0%
+i showed you a picture of that just a
+ 
+
+ align:start position:0%
+i showed you a picture of that just a
+minute ago
+
+ align:start position:0%
+minute ago
+ 
+
+ align:start position:0%
+minute ago
+and the minimize expenditure when you
+
+ align:start position:0%
+and the minimize expenditure when you
+ 
+
+ align:start position:0%
+and the minimize expenditure when you
+solve the emp
+
+ align:start position:0%
+solve the emp
+ 
+
+ align:start position:0%
+solve the emp
+is exactly the wealth that you had in
+
+ align:start position:0%
+is exactly the wealth that you had in
+ 
+
+ align:start position:0%
+is exactly the wealth that you had in
+the utility maximization problem
+
+ align:start position:0%
+the utility maximization problem
+ 
+
+ align:start position:0%
+the utility maximization problem
+well let me go back
+
+ align:start position:0%
+well let me go back
+ 
+
+ align:start position:0%
+well let me go back
+so i started here
+
+ align:start position:0%
+so i started here
+ 
+
+ align:start position:0%
+so i started here
+we had income i
+
+ align:start position:0%
+we had income i
+ 
+
+ align:start position:0%
+we had income i
+prices were given
+
+ align:start position:0%
+prices were given
+ 
+
+ align:start position:0%
+prices were given
+we maximized utility ended up at u2
+
+ align:start position:0%
+we maximized utility ended up at u2
+ 
+
+ align:start position:0%
+we maximized utility ended up at u2
+given i and p
+
+ align:start position:0%
+given i and p
+ 
+
+ align:start position:0%
+given i and p
+we had a certain
+
+ align:start position:0%
+we had a certain
+ 
+
+ align:start position:0%
+we had a certain
+optimizing solution
+
+ align:start position:0%
+optimizing solution
+ 
+
+ align:start position:0%
+optimizing solution
+here called
+
+ align:start position:0%
+here called
+ 
+
+ align:start position:0%
+here called
+x2 y2 that solves the utility
+
+ align:start position:0%
+x2 y2 that solves the utility
+ 
+
+ align:start position:0%
+x2 y2 that solves the utility
+maximization problem
+
+ align:start position:0%
+maximization problem
+ 
+
+ align:start position:0%
+maximization problem
+and then i said what if
+
+ align:start position:0%
+and then i said what if
+ 
+
+ align:start position:0%
+and then i said what if
+we fix the utility level instead
+
+ align:start position:0%
+we fix the utility level instead
+ 
+
+ align:start position:0%
+we fix the utility level instead
+and solve the expenditure minimization
+
+ align:start position:0%
+and solve the expenditure minimization
+ 
+
+ align:start position:0%
+and solve the expenditure minimization
+problem which is finding the expenditure
+
+ align:start position:0%
+problem which is finding the expenditure
+ 
+
+ align:start position:0%
+problem which is finding the expenditure
+level earmarked by these budget lines
+
+ align:start position:0%
+level earmarked by these budget lines
+ 
+
+ align:start position:0%
+level earmarked by these budget lines
+which is minimal
+
+ align:start position:0%
+which is minimal
+ 
+
+ align:start position:0%
+which is minimal
+and yet allows us to achieve the utility
+
+ align:start position:0%
+and yet allows us to achieve the utility
+ 
+
+ align:start position:0%
+and yet allows us to achieve the utility
+level u2
+
+ align:start position:0%
+level u2
+ 
+
+ align:start position:0%
+level u2
+so this budget line which was a budget
+
+ align:start position:0%
+so this budget line which was a budget
+ 
+
+ align:start position:0%
+so this budget line which was a budget
+line for the utility maximization
+
+ align:start position:0%
+line for the utility maximization
+ 
+
+ align:start position:0%
+line for the utility maximization
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+is kind of the minute minimized
+
+ align:start position:0%
+is kind of the minute minimized
+ 
+
+ align:start position:0%
+is kind of the minute minimized
+expenditure line
+
+ align:start position:0%
+expenditure line
+ 
+
+ align:start position:0%
+expenditure line
+for the expenditure minimization problem
+
+ align:start position:0%
+for the expenditure minimization problem
+ 
+
+ align:start position:0%
+for the expenditure minimization problem
+i don't maybe the picture is just easier
+
+ align:start position:0%
+i don't maybe the picture is just easier
+ 
+
+ align:start position:0%
+i don't maybe the picture is just easier
+but the notation says that
+
+ align:start position:0%
+but the notation says that
+ 
+
+ align:start position:0%
+but the notation says that
+and actually goes the other way
+
+ align:start position:0%
+and actually goes the other way
+ 
+
+ align:start position:0%
+and actually goes the other way
+if x star were solving the expenditure
+
+ align:start position:0%
+if x star were solving the expenditure
+ 
+
+ align:start position:0%
+if x star were solving the expenditure
+minimization problem
+
+ align:start position:0%
+minimization problem
+ 
+
+ align:start position:0%
+minimization problem
+when the acquired utility level is
+
+ align:start position:0%
+when the acquired utility level is
+ 
+
+ align:start position:0%
+when the acquired utility level is
+parameter u
+
+ align:start position:0%
+parameter u
+ 
+
+ align:start position:0%
+parameter u
+then x star is also optimal the same x
+
+ align:start position:0%
+then x star is also optimal the same x
+ 
+
+ align:start position:0%
+then x star is also optimal the same x
+in the utility maximization problem
+
+ align:start position:0%
+in the utility maximization problem
+ 
+
+ align:start position:0%
+in the utility maximization problem
+where we give the guys wealth equal to
+
+ align:start position:0%
+where we give the guys wealth equal to
+ 
+
+ align:start position:0%
+where we give the guys wealth equal to
+the minimized expenditure
+
+ align:start position:0%
+the minimized expenditure
+ 
+
+ align:start position:0%
+the minimized expenditure
+and when they
+
+ align:start position:0%
+and when they
+ 
+
+ align:start position:0%
+and when they
+solve the utility maximization problem
+
+ align:start position:0%
+solve the utility maximization problem
+ 
+
+ align:start position:0%
+solve the utility maximization problem
+at that level of wealth
+
+ align:start position:0%
+at that level of wealth
+ 
+
+ align:start position:0%
+at that level of wealth
+they end up exactly with the u that we
+
+ align:start position:0%
+they end up exactly with the u that we
+ 
+
+ align:start position:0%
+they end up exactly with the u that we
+started with in the expenditure
+
+ align:start position:0%
+started with in the expenditure
+ 
+
+ align:start position:0%
+started with in the expenditure
+minimization problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relatedly
+
+ align:start position:0%
+relatedly
+ 
+
+ align:start position:0%
+relatedly
+and this is the most compact notation of
+
+ align:start position:0%
+and this is the most compact notation of
+ 
+
+ align:start position:0%
+and this is the most compact notation of
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+that's kind of cool
+
+ align:start position:0%
+that's kind of cool
+ 
+
+ align:start position:0%
+that's kind of cool
+another way to state the proposition is
+
+ align:start position:0%
+another way to state the proposition is
+ 
+
+ align:start position:0%
+another way to state the proposition is
+to say that
+
+ align:start position:0%
+to say that
+ 
+
+ align:start position:0%
+to say that
+given equation 3 when we start given a
+
+ align:start position:0%
+given equation 3 when we start given a
+ 
+
+ align:start position:0%
+given equation 3 when we start given a
+price vector p
+
+ align:start position:0%
+price vector p
+ 
+
+ align:start position:0%
+price vector p
+we are fixing prices p
+
+ align:start position:0%
+we are fixing prices p
+ 
+
+ align:start position:0%
+we are fixing prices p
+we give the guy income or wealth w
+
+ align:start position:0%
+we give the guy income or wealth w
+ 
+
+ align:start position:0%
+we give the guy income or wealth w
+we solve the utility maximization
+
+ align:start position:0%
+we solve the utility maximization
+ 
+
+ align:start position:0%
+we solve the utility maximization
+problem we substitute the maximizing
+
+ align:start position:0%
+problem we substitute the maximizing
+ 
+
+ align:start position:0%
+problem we substitute the maximizing
+demands into utility
+
+ align:start position:0%
+demands into utility
+ 
+
+ align:start position:0%
+demands into utility
+we get the indirect utility function now
+
+ align:start position:0%
+we get the indirect utility function now
+ 
+
+ align:start position:0%
+we get the indirect utility function now
+starting with that level of utility we
+
+ align:start position:0%
+starting with that level of utility we
+ 
+
+ align:start position:0%
+starting with that level of utility we
+do the expenditure minimization problem
+
+ align:start position:0%
+do the expenditure minimization problem
+ 
+
+ align:start position:0%
+do the expenditure minimization problem
+and the minimized expenditures at that p
+
+ align:start position:0%
+and the minimized expenditures at that p
+ 
+
+ align:start position:0%
+and the minimized expenditures at that p
+and particular utility level is w all
+
+ align:start position:0%
+and particular utility level is w all
+ 
+
+ align:start position:0%
+and particular utility level is w all
+over again so it's like feeding back to
+
+ align:start position:0%
+over again so it's like feeding back to
+ 
+
+ align:start position:0%
+over again so it's like feeding back to
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+likewise here
+
+ align:start position:0%
+likewise here
+ 
+
+ align:start position:0%
+likewise here
+we start with the parametrized level of
+
+ align:start position:0%
+we start with the parametrized level of
+ 
+
+ align:start position:0%
+we start with the parametrized level of
+u in the expenditure minimization
+
+ align:start position:0%
+u in the expenditure minimization
+ 
+
+ align:start position:0%
+u in the expenditure minimization
+problem taking in p vector p is given
+
+ align:start position:0%
+problem taking in p vector p is given
+ 
+
+ align:start position:0%
+problem taking in p vector p is given
+at that level u
+
+ align:start position:0%
+at that level u
+ 
+
+ align:start position:0%
+at that level u
+we solve for the minimized expenditure
+
+ align:start position:0%
+we solve for the minimized expenditure
+ 
+
+ align:start position:0%
+we solve for the minimized expenditure
+which we called e of p and u
+
+ align:start position:0%
+which we called e of p and u
+ 
+
+ align:start position:0%
+which we called e of p and u
+and if we take that minimized
+
+ align:start position:0%
+and if we take that minimized
+ 
+
+ align:start position:0%
+and if we take that minimized
+expenditure and substituted it as a
+
+ align:start position:0%
+expenditure and substituted it as a
+ 
+
+ align:start position:0%
+expenditure and substituted it as a
+wealth term and solve the utility
+
+ align:start position:0%
+wealth term and solve the utility
+ 
+
+ align:start position:0%
+wealth term and solve the utility
+maximization problem at that wealth we
+
+ align:start position:0%
+maximization problem at that wealth we
+ 
+
+ align:start position:0%
+maximization problem at that wealth we
+would get that the indirect utility
+
+ align:start position:0%
+would get that the indirect utility
+ 
+
+ align:start position:0%
+would get that the indirect utility
+is exactly the u that we started with
+
+ align:start position:0%
+is exactly the u that we started with
+ 
+
+ align:start position:0%
+is exactly the u that we started with
+so it it it is a bit of a mouthful the
+
+ align:start position:0%
+so it it it is a bit of a mouthful the
+ 
+
+ align:start position:0%
+so it it it is a bit of a mouthful the
+notation is quite compact and you may
+
+ align:start position:0%
+notation is quite compact and you may
+ 
+
+ align:start position:0%
+notation is quite compact and you may
+just sort of like have a whiteout moment
+
+ align:start position:0%
+just sort of like have a whiteout moment
+ 
+
+ align:start position:0%
+just sort of like have a whiteout moment
+when you see it but it is repeating in
+
+ align:start position:0%
+when you see it but it is repeating in
+ 
+
+ align:start position:0%
+when you see it but it is repeating in
+different ways in related notation
+
+ align:start position:0%
+different ways in related notation
+ 
+
+ align:start position:0%
+different ways in related notation
+oh this also means that e and v are
+
+ align:start position:0%
+oh this also means that e and v are
+ 
+
+ align:start position:0%
+oh this also means that e and v are
+inverses of one another in the sense
+
+ align:start position:0%
+inverses of one another in the sense
+ 
+
+ align:start position:0%
+inverses of one another in the sense
+that take e and multiply by some
+
+ align:start position:0%
+that take e and multiply by some
+ 
+
+ align:start position:0%
+that take e and multiply by some
+imagined e inverse and you'd get rid of
+
+ align:start position:0%
+imagined e inverse and you'd get rid of
+ 
+
+ align:start position:0%
+imagined e inverse and you'd get rid of
+e on the left hand side and have an e
+
+ align:start position:0%
+e on the left hand side and have an e
+ 
+
+ align:start position:0%
+e on the left hand side and have an e
+inverse on the right hand side so you'd
+
+ align:start position:0%
+inverse on the right hand side so you'd
+ 
+
+ align:start position:0%
+inverse on the right hand side so you'd
+have the value function is an inverse of
+
+ align:start position:0%
+have the value function is an inverse of
+ 
+
+ align:start position:0%
+have the value function is an inverse of
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+i said that wrong actually
+
+ align:start position:0%
+i said that wrong actually
+ 
+
+ align:start position:0%
+i said that wrong actually
+if if you take e
+
+ align:start position:0%
+if if you take e
+ 
+
+ align:start position:0%
+if if you take e
+and get rid of it by taking e inverse
+
+ align:start position:0%
+and get rid of it by taking e inverse
+ 
+
+ align:start position:0%
+and get rid of it by taking e inverse
+when you take the inverse of the
+
+ align:start position:0%
+when you take the inverse of the
+ 
+
+ align:start position:0%
+when you take the inverse of the
+expenditure function you end up with a
+
+ align:start position:0%
+expenditure function you end up with a
+ 
+
+ align:start position:0%
+expenditure function you end up with a
+value function
+
+ align:start position:0%
+value function
+ 
+
+ align:start position:0%
+value function
+and likewise when you take the inverse
+
+ align:start position:0%
+and likewise when you take the inverse
+ 
+
+ align:start position:0%
+and likewise when you take the inverse
+of the value function
+
+ align:start position:0%
+of the value function
+ 
+
+ align:start position:0%
+of the value function
+you'll end up with the expenditure
+
+ align:start position:0%
+you'll end up with the expenditure
+ 
+
+ align:start position:0%
+you'll end up with the expenditure
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+okay i said it right that time
+
+ align:start position:0%
+okay i said it right that time
+ 
+
+ align:start position:0%
+okay i said it right that time
+there's a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+you keep saying indirect use your
+
+ align:start position:0%
+you keep saying indirect use your
+ 
+
+ align:start position:0%
+you keep saying indirect use your
+functioning function or i guess what do
+
+ align:start position:0%
+functioning function or i guess what do
+ 
+
+ align:start position:0%
+functioning function or i guess what do
+you mean when you say indirect
+
+ align:start position:0%
+you mean when you say indirect
+ 
+
+ align:start position:0%
+you mean when you say indirect
+uh it has a label i mean these looks
+
+ align:start position:0%
+uh it has a label i mean these looks
+ 
+
+ align:start position:0%
+uh it has a label i mean these looks
+like value
+
+ align:start position:0%
+like value
+ 
+
+ align:start position:0%
+like value
+we say value function but it's called
+
+ align:start position:0%
+we say value function but it's called
+ 
+
+ align:start position:0%
+we say value function but it's called
+the indirect utility function in the
+
+ align:start position:0%
+the indirect utility function in the
+ 
+
+ align:start position:0%
+the indirect utility function in the
+literature okay that's the name that we
+
+ align:start position:0%
+literature okay that's the name that we
+ 
+
+ align:start position:0%
+literature okay that's the name that we
+give it
+
+ align:start position:0%
+give it
+ 
+
+ align:start position:0%
+give it
+okay so hicksian demand
+
+ align:start position:0%
+okay so hicksian demand
+ 
+
+ align:start position:0%
+okay so hicksian demand
+is solving the expenditure minimization
+
+ align:start position:0%
+is solving the expenditure minimization
+ 
+
+ align:start position:0%
+is solving the expenditure minimization
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+and we have the hixian demand or demand
+
+ align:start position:0%
+and we have the hixian demand or demand
+ 
+
+ align:start position:0%
+and we have the hixian demand or demand
+correspondence if there's more than one
+
+ align:start position:0%
+correspondence if there's more than one
+ 
+
+ align:start position:0%
+correspondence if there's more than one
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and then the diagrams there's been a
+
+ align:start position:0%
+and then the diagrams there's been a
+ 
+
+ align:start position:0%
+and then the diagrams there's been a
+unique solution this looks like it's a
+
+ align:start position:0%
+unique solution this looks like it's a
+ 
+
+ align:start position:0%
+unique solution this looks like it's a
+new slide but actually right from the
+
+ align:start position:0%
+new slide but actually right from the
+ 
+
+ align:start position:0%
+new slide but actually right from the
+very beginning where we were talking
+
+ align:start position:0%
+very beginning where we were talking
+ 
+
+ align:start position:0%
+very beginning where we were talking
+about price effects and income effects
+
+ align:start position:0%
+about price effects and income effects
+ 
+
+ align:start position:0%
+about price effects and income effects
+and we defined the price effect as a
+
+ align:start position:0%
+and we defined the price effect as a
+ 
+
+ align:start position:0%
+and we defined the price effect as a
+substitution effect we were moving along
+
+ align:start position:0%
+substitution effect we were moving along
+ 
+
+ align:start position:0%
+substitution effect we were moving along
+a given indifference curve so we're
+
+ align:start position:0%
+a given indifference curve so we're
+ 
+
+ align:start position:0%
+a given indifference curve so we're
+really talking about hixing demands all
+
+ align:start position:0%
+really talking about hixing demands all
+ 
+
+ align:start position:0%
+really talking about hixing demands all
+along and again for the third time we
+
+ align:start position:0%
+along and again for the third time we
+ 
+
+ align:start position:0%
+along and again for the third time we
+have a different way of stating the
+
+ align:start position:0%
+have a different way of stating the
+ 
+
+ align:start position:0%
+have a different way of stating the
+problem that the ordinary demand is
+
+ align:start position:0%
+problem that the ordinary demand is
+ 
+
+ align:start position:0%
+problem that the ordinary demand is
+equal to the hixian demand evaluated at
+
+ align:start position:0%
+equal to the hixian demand evaluated at
+ 
+
+ align:start position:0%
+equal to the hixian demand evaluated at
+a utility level which is the indirect
+
+ align:start position:0%
+a utility level which is the indirect
+ 
+
+ align:start position:0%
+a utility level which is the indirect
+utility of the utility maximization
+
+ align:start position:0%
+utility of the utility maximization
+ 
+
+ align:start position:0%
+utility of the utility maximization
+problem and likewise for the expenditure
+
+ align:start position:0%
+problem and likewise for the expenditure
+ 
+
+ align:start position:0%
+problem and likewise for the expenditure
+minimization problem this is as i've
+
+ align:start position:0%
+minimization problem this is as i've
+ 
+
+ align:start position:0%
+minimization problem this is as i've
+been saying true you know starting at
+
+ align:start position:0%
+been saying true you know starting at
+ 
+
+ align:start position:0%
+been saying true you know starting at
+this point you start looking at it one
+
+ align:start position:0%
+this point you start looking at it one
+ 
+
+ align:start position:0%
+this point you start looking at it one
+way or the other you send end up with
+
+ align:start position:0%
+way or the other you send end up with
+ 
+
+ align:start position:0%
+way or the other you send end up with
+exactly the same point
+
+ align:start position:0%
+exactly the same point
+ 
+
+ align:start position:0%
+exactly the same point
+but if we start actually taking discrete
+
+ align:start position:0%
+but if we start actually taking discrete
+ 
+
+ align:start position:0%
+but if we start actually taking discrete
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+things are a bit different and in fact
+
+ align:start position:0%
+things are a bit different and in fact
+ 
+
+ align:start position:0%
+things are a bit different and in fact
+we were actually doing that at the
+
+ align:start position:0%
+we were actually doing that at the
+ 
+
+ align:start position:0%
+we were actually doing that at the
+beginning right we were talking about
+
+ align:start position:0%
+beginning right we were talking about
+ 
+
+ align:start position:0%
+beginning right we were talking about
+a non-trivial decrease in the price of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's talk about discrete changes and
+
+ align:start position:0%
+so let's talk about discrete changes and
+ 
+
+ align:start position:0%
+so let's talk about discrete changes and
+compensated demand
+
+ align:start position:0%
+compensated demand
+ 
+
+ align:start position:0%
+compensated demand
+we start with p and w we have the
+
+ align:start position:0%
+we start with p and w we have the
+ 
+
+ align:start position:0%
+we start with p and w we have the
+maximized demand x
+
+ align:start position:0%
+maximized demand x
+ 
+
+ align:start position:0%
+maximized demand x
+for that given
+
+ align:start position:0%
+for that given
+ 
+
+ align:start position:0%
+for that given
+w but we change p
+
+ align:start position:0%
+w but we change p
+ 
+
+ align:start position:0%
+w but we change p
+from p to p prime
+
+ align:start position:0%
+from p to p prime
+ 
+
+ align:start position:0%
+from p to p prime
+then w prime
+
+ align:start position:0%
+then w prime
+ 
+
+ align:start position:0%
+then w prime
+would say be the minimized expenditure
+
+ align:start position:0%
+would say be the minimized expenditure
+ 
+
+ align:start position:0%
+would say be the minimized expenditure
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+the level of utility u the initial level
+
+ align:start position:0%
+the level of utility u the initial level
+ 
+
+ align:start position:0%
+the level of utility u the initial level
+of utility
+
+ align:start position:0%
+of utility
+ 
+
+ align:start position:0%
+of utility
+at the baseline
+
+ align:start position:0%
+at the baseline
+ 
+
+ align:start position:0%
+at the baseline
+but with the new different price vector
+
+ align:start position:0%
+but with the new different price vector
+ 
+
+ align:start position:0%
+but with the new different price vector
+p prime
+
+ align:start position:0%
+p prime
+ 
+
+ align:start position:0%
+p prime
+and we call that
+
+ align:start position:0%
+and we call that
+ 
+
+ align:start position:0%
+and we call that
+new wealth as opposed to old wealth call
+
+ align:start position:0%
+new wealth as opposed to old wealth call
+ 
+
+ align:start position:0%
+new wealth as opposed to old wealth call
+it w prime so in words
+
+ align:start position:0%
+it w prime so in words
+ 
+
+ align:start position:0%
+it w prime so in words
+that level of income or wealth w prime
+
+ align:start position:0%
+that level of income or wealth w prime
+ 
+
+ align:start position:0%
+that level of income or wealth w prime
+is the one that under the new price
+
+ align:start position:0%
+is the one that under the new price
+ 
+
+ align:start position:0%
+is the one that under the new price
+vector p prime would minimize the
+
+ align:start position:0%
+vector p prime would minimize the
+ 
+
+ align:start position:0%
+vector p prime would minimize the
+expenses
+
+ align:start position:0%
+expenses
+ 
+
+ align:start position:0%
+expenses
+at p prime of achieving the old utility
+
+ align:start position:0%
+at p prime of achieving the old utility
+ 
+
+ align:start position:0%
+at p prime of achieving the old utility
+level remember when we changed the price
+
+ align:start position:0%
+level remember when we changed the price
+ 
+
+ align:start position:0%
+level remember when we changed the price
+we just rotated along the indifference
+
+ align:start position:0%
+we just rotated along the indifference
+ 
+
+ align:start position:0%
+we just rotated along the indifference
+curve going one way or the other
+
+ align:start position:0%
+curve going one way or the other
+ 
+
+ align:start position:0%
+curve going one way or the other
+that's all this english and all this
+
+ align:start position:0%
+that's all this english and all this
+ 
+
+ align:start position:0%
+that's all this english and all this
+notation means
+
+ align:start position:0%
+notation means
+ 
+
+ align:start position:0%
+notation means
+we're just compensating
+
+ align:start position:0%
+we're just compensating
+ 
+
+ align:start position:0%
+we're just compensating
+the agent for the change in
+
+ align:start position:0%
+the agent for the change in
+ 
+
+ align:start position:0%
+the agent for the change in
+purchasing power
+
+ align:start position:0%
+purchasing power
+ 
+
+ align:start position:0%
+purchasing power
+but of course demand doesn't stay
+
+ align:start position:0%
+but of course demand doesn't stay
+ 
+
+ align:start position:0%
+but of course demand doesn't stay
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+because the new demand x star will be
+
+ align:start position:0%
+because the new demand x star will be
+ 
+
+ align:start position:0%
+because the new demand x star will be
+different as the prices are different
+
+ align:start position:0%
+different as the prices are different
+ 
+
+ align:start position:0%
+different as the prices are different
+and the hixian demand includes the price
+
+ align:start position:0%
+and the hixian demand includes the price
+ 
+
+ align:start position:0%
+and the hixian demand includes the price
+substitution effect is defined by it
+
+ align:start position:0%
+substitution effect is defined by it
+ 
+
+ align:start position:0%
+substitution effect is defined by it
+so the hixian demand at the old utility
+
+ align:start position:0%
+so the hixian demand at the old utility
+ 
+
+ align:start position:0%
+so the hixian demand at the old utility
+level and prices p prime
+
+ align:start position:0%
+level and prices p prime
+ 
+
+ align:start position:0%
+level and prices p prime
+is different from the original baseline
+
+ align:start position:0%
+is different from the original baseline
+ 
+
+ align:start position:0%
+is different from the original baseline
+purchase
+
+ align:start position:0%
+purchase
+ 
+
+ align:start position:0%
+purchase
+anyway if you understood the income and
+
+ align:start position:0%
+anyway if you understood the income and
+ 
+
+ align:start position:0%
+anyway if you understood the income and
+substitution effects at the beginning
+
+ align:start position:0%
+substitution effects at the beginning
+ 
+
+ align:start position:0%
+substitution effects at the beginning
+that's all this slide is saying where we
+
+ align:start position:0%
+that's all this slide is saying where we
+ 
+
+ align:start position:0%
+that's all this slide is saying where we
+have you know non-trivial discrete
+
+ align:start position:0%
+have you know non-trivial discrete
+ 
+
+ align:start position:0%
+have you know non-trivial discrete
+changes in the price here's
+
+ align:start position:0%
+changes in the price here's
+ 
+
+ align:start position:0%
+changes in the price here's
+the picture again
+
+ align:start position:0%
+the picture again
+ 
+
+ align:start position:0%
+the picture again
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+be forewarned
+
+ align:start position:0%
+be forewarned
+ 
+
+ align:start position:0%
+be forewarned
+that that somehow to make it more
+
+ align:start position:0%
+that that somehow to make it more
+ 
+
+ align:start position:0%
+that that somehow to make it more
+interesting we're gonna change the price
+
+ align:start position:0%
+interesting we're gonna change the price
+ 
+
+ align:start position:0%
+interesting we're gonna change the price
+of good two instead of good one
+
+ align:start position:0%
+of good two instead of good one
+ 
+
+ align:start position:0%
+of good two instead of good one
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we are going to
+
+ align:start position:0%
+we are going to
+ 
+
+ align:start position:0%
+we are going to
+increase the price so the original
+
+ align:start position:0%
+increase the price so the original
+ 
+
+ align:start position:0%
+increase the price so the original
+baseline
+
+ align:start position:0%
+baseline
+ 
+
+ align:start position:0%
+baseline
+budget is from w
+
+ align:start position:0%
+budget is from w
+ 
+
+ align:start position:0%
+budget is from w
+to w over p2
+
+ align:start position:0%
+to w over p2
+ 
+
+ align:start position:0%
+to w over p2
+why just w
+
+ align:start position:0%
+why just w
+ 
+
+ align:start position:0%
+why just w
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+there's an assumption down here
+
+ align:start position:0%
+there's an assumption down here
+ 
+
+ align:start position:0%
+there's an assumption down here
+that we only care about the price ratio
+
+ align:start position:0%
+that we only care about the price ratio
+ 
+
+ align:start position:0%
+that we only care about the price ratio
+so let's denominate everything in units
+
+ align:start position:0%
+so let's denominate everything in units
+ 
+
+ align:start position:0%
+so let's denominate everything in units
+of good
+
+ align:start position:0%
+of good
+ 
+
+ align:start position:0%
+of good
+on the x-axis
+
+ align:start position:0%
+on the x-axis
+ 
+
+ align:start position:0%
+on the x-axis
+p1 the first good equals one
+
+ align:start position:0%
+p1 the first good equals one
+ 
+
+ align:start position:0%
+p1 the first good equals one
+so we don't need to worry anymore about
+
+ align:start position:0%
+so we don't need to worry anymore about
+ 
+
+ align:start position:0%
+so we don't need to worry anymore about
+the price of the first good because
+
+ align:start position:0%
+the price of the first good because
+ 
+
+ align:start position:0%
+the price of the first good because
+it's one and the question is what's the
+
+ align:start position:0%
+it's one and the question is what's the
+ 
+
+ align:start position:0%
+it's one and the question is what's the
+price of the second good relative to
+
+ align:start position:0%
+price of the second good relative to
+ 
+
+ align:start position:0%
+price of the second good relative to
+one this case the price of the second
+
+ align:start position:0%
+one this case the price of the second
+ 
+
+ align:start position:0%
+one this case the price of the second
+good p2
+
+ align:start position:0%
+good p2
+ 
+
+ align:start position:0%
+good p2
+is going up
+
+ align:start position:0%
+is going up
+ 
+
+ align:start position:0%
+is going up
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+you would go from w over p2 attainable
+
+ align:start position:0%
+you would go from w over p2 attainable
+ 
+
+ align:start position:0%
+you would go from w over p2 attainable
+to w over p2 prime attainable
+
+ align:start position:0%
+to w over p2 prime attainable
+ 
+
+ align:start position:0%
+to w over p2 prime attainable
+when you go from a price p2 to p2 prime
+
+ align:start position:0%
+when you go from a price p2 to p2 prime
+ 
+
+ align:start position:0%
+when you go from a price p2 to p2 prime
+this is like the earlier diagram where
+
+ align:start position:0%
+this is like the earlier diagram where
+ 
+
+ align:start position:0%
+this is like the earlier diagram where
+we fixed a point on the y-axis and
+
+ align:start position:0%
+we fixed a point on the y-axis and
+ 
+
+ align:start position:0%
+we fixed a point on the y-axis and
+pivoted
+
+ align:start position:0%
+pivoted
+ 
+
+ align:start position:0%
+pivoted
+on the x-axis but this is the other way
+
+ align:start position:0%
+on the x-axis but this is the other way
+ 
+
+ align:start position:0%
+on the x-axis but this is the other way
+around because we're changing the price
+
+ align:start position:0%
+around because we're changing the price
+ 
+
+ align:start position:0%
+around because we're changing the price
+of good two and not the price of good
+
+ align:start position:0%
+of good two and not the price of good
+ 
+
+ align:start position:0%
+of good two and not the price of good
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we start here and we have an
+
+ align:start position:0%
+okay so we start here and we have an
+ 
+
+ align:start position:0%
+okay so we start here and we have an
+income a lower budget line
+
+ align:start position:0%
+income a lower budget line
+ 
+
+ align:start position:0%
+income a lower budget line
+now we want to break that into two
+
+ align:start position:0%
+now we want to break that into two
+ 
+
+ align:start position:0%
+now we want to break that into two
+pieces namely the substitution effect
+
+ align:start position:0%
+pieces namely the substitution effect
+ 
+
+ align:start position:0%
+pieces namely the substitution effect
+and the income effect
+
+ align:start position:0%
+and the income effect
+ 
+
+ align:start position:0%
+and the income effect
+what is the substitution effect
+
+ align:start position:0%
+what is the substitution effect
+ 
+
+ align:start position:0%
+what is the substitution effect
+at this higher price of p2
+
+ align:start position:0%
+at this higher price of p2
+ 
+
+ align:start position:0%
+at this higher price of p2
+it's p1 over p2 if you remember the
+
+ align:start position:0%
+it's p1 over p2 if you remember the
+ 
+
+ align:start position:0%
+it's p1 over p2 if you remember the
+slope
+
+ align:start position:0%
+slope
+ 
+
+ align:start position:0%
+slope
+so as p2 goes up that slope goes down
+
+ align:start position:0%
+so as p2 goes up that slope goes down
+ 
+
+ align:start position:0%
+so as p2 goes up that slope goes down
+so we're going to rotate along this
+
+ align:start position:0%
+so we're going to rotate along this
+ 
+
+ align:start position:0%
+so we're going to rotate along this
+indifference curve
+
+ align:start position:0%
+indifference curve
+ 
+
+ align:start position:0%
+indifference curve
+and effectively maximize utility
+
+ align:start position:0%
+and effectively maximize utility
+ 
+
+ align:start position:0%
+and effectively maximize utility
+which is giving you this point what's
+
+ align:start position:0%
+which is giving you this point what's
+ 
+
+ align:start position:0%
+which is giving you this point what's
+the maximal utility you can get
+
+ align:start position:0%
+the maximal utility you can get
+ 
+
+ align:start position:0%
+the maximal utility you can get
+or the minimize expenditure rotating
+
+ align:start position:0%
+or the minimize expenditure rotating
+ 
+
+ align:start position:0%
+or the minimize expenditure rotating
+along this indifference curve and then
+
+ align:start position:0%
+along this indifference curve and then
+ 
+
+ align:start position:0%
+along this indifference curve and then
+the income effect is moving from here a
+
+ align:start position:0%
+the income effect is moving from here a
+ 
+
+ align:start position:0%
+the income effect is moving from here a
+parallel shift back to here
+
+ align:start position:0%
+parallel shift back to here
+ 
+
+ align:start position:0%
+parallel shift back to here
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+our initial level of wealth w was on
+
+ align:start position:0%
+our initial level of wealth w was on
+ 
+
+ align:start position:0%
+our initial level of wealth w was on
+this good one axis and our new level of
+
+ align:start position:0%
+this good one axis and our new level of
+ 
+
+ align:start position:0%
+this good one axis and our new level of
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+is this minimized expenditure at the new
+
+ align:start position:0%
+is this minimized expenditure at the new
+ 
+
+ align:start position:0%
+is this minimized expenditure at the new
+prices p prime given utility level u so
+
+ align:start position:0%
+prices p prime given utility level u so
+ 
+
+ align:start position:0%
+prices p prime given utility level u so
+we've gone from w to w prime
+
+ align:start position:0%
+we've gone from w to w prime
+ 
+
+ align:start position:0%
+we've gone from w to w prime
+that's the change in wealth
+
+ align:start position:0%
+that's the change in wealth
+ 
+
+ align:start position:0%
+that's the change in wealth
+in terms of good one
+
+ align:start position:0%
+in terms of good one
+ 
+
+ align:start position:0%
+in terms of good one
+initial wealth new wealth in terms of
+
+ align:start position:0%
+initial wealth new wealth in terms of
+ 
+
+ align:start position:0%
+initial wealth new wealth in terms of
+good one this must therefore be
+
+ align:start position:0%
+good one this must therefore be
+ 
+
+ align:start position:0%
+good one this must therefore be
+the change in wealth and that's the
+
+ align:start position:0%
+the change in wealth and that's the
+ 
+
+ align:start position:0%
+the change in wealth and that's the
+change in wealth which is positive
+
+ align:start position:0%
+change in wealth which is positive
+ 
+
+ align:start position:0%
+change in wealth which is positive
+which you may have been wondering about
+
+ align:start position:0%
+which you may have been wondering about
+ 
+
+ align:start position:0%
+which you may have been wondering about
+which is necessary to compensate the
+
+ align:start position:0%
+which is necessary to compensate the
+ 
+
+ align:start position:0%
+which is necessary to compensate the
+agent for the fact that the price of
+
+ align:start position:0%
+agent for the fact that the price of
+ 
+
+ align:start position:0%
+agent for the fact that the price of
+good two has gone up
+
+ align:start position:0%
+good two has gone up
+ 
+
+ align:start position:0%
+good two has gone up
+we have to compensate the agent for the
+
+ align:start position:0%
+we have to compensate the agent for the
+ 
+
+ align:start position:0%
+we have to compensate the agent for the
+adverse price change by giving him or
+
+ align:start position:0%
+adverse price change by giving him or
+ 
+
+ align:start position:0%
+adverse price change by giving him or
+her more income
+
+ align:start position:0%
+her more income
+ 
+
+ align:start position:0%
+her more income
+and this is that level of income
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+as i keep saying but it's probably been
+
+ align:start position:0%
+as i keep saying but it's probably been
+ 
+
+ align:start position:0%
+as i keep saying but it's probably been
+more or less an abstract statement i'm
+
+ align:start position:0%
+more or less an abstract statement i'm
+ 
+
+ align:start position:0%
+more or less an abstract statement i'm
+really interested in economies
+
+ align:start position:0%
+really interested in economies
+ 
+
+ align:start position:0%
+really interested in economies
+real economies where we have something
+
+ align:start position:0%
+real economies where we have something
+ 
+
+ align:start position:0%
+real economies where we have something
+going on over time
+
+ align:start position:0%
+going on over time
+ 
+
+ align:start position:0%
+going on over time
+or something with a geography or
+
+ align:start position:0%
+or something with a geography or
+ 
+
+ align:start position:0%
+or something with a geography or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+having to do with uncertainty and
+
+ align:start position:0%
+having to do with uncertainty and
+ 
+
+ align:start position:0%
+having to do with uncertainty and
+gambles and states of the world
+
+ align:start position:0%
+gambles and states of the world
+ 
+
+ align:start position:0%
+gambles and states of the world
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+having memorized or shown you all those
+
+ align:start position:0%
+having memorized or shown you all those
+ 
+
+ align:start position:0%
+having memorized or shown you all those
+figures with some very interesting
+
+ align:start position:0%
+figures with some very interesting
+ 
+
+ align:start position:0%
+figures with some very interesting
+concepts and a little bit of data along
+
+ align:start position:0%
+concepts and a little bit of data along
+ 
+
+ align:start position:0%
+concepts and a little bit of data along
+the way
+
+ align:start position:0%
+the way
+ 
+
+ align:start position:0%
+the way
+one may nevertheless walk away with the
+
+ align:start position:0%
+one may nevertheless walk away with the
+ 
+
+ align:start position:0%
+one may nevertheless walk away with the
+impression that we're talking about a
+
+ align:start position:0%
+impression that we're talking about a
+ 
+
+ align:start position:0%
+impression that we're talking about a
+static world where we have rice and
+
+ align:start position:0%
+static world where we have rice and
+ 
+
+ align:start position:0%
+static world where we have rice and
+other goods or potatoes and other goods
+
+ align:start position:0%
+other goods or potatoes and other goods
+ 
+
+ align:start position:0%
+other goods or potatoes and other goods
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we're just comparing wheat to apples as
+
+ align:start position:0%
+we're just comparing wheat to apples as
+ 
+
+ align:start position:0%
+we're just comparing wheat to apples as
+we change prices but no the framework
+
+ align:start position:0%
+we change prices but no the framework
+ 
+
+ align:start position:0%
+we change prices but no the framework
+applies to any goods
+
+ align:start position:0%
+applies to any goods
+ 
+
+ align:start position:0%
+applies to any goods
+in including goods that are earmarked by
+
+ align:start position:0%
+in including goods that are earmarked by
+ 
+
+ align:start position:0%
+in including goods that are earmarked by
+time so
+
+ align:start position:0%
+time so
+ 
+
+ align:start position:0%
+time so
+suppose we have
+
+ align:start position:0%
+suppose we have
+ 
+
+ align:start position:0%
+suppose we have
+two time periods only
+
+ align:start position:0%
+two time periods only
+ 
+
+ align:start position:0%
+two time periods only
+and we'll call consumption c1
+
+ align:start position:0%
+and we'll call consumption c1
+ 
+
+ align:start position:0%
+and we'll call consumption c1
+consumption in date one and c2
+
+ align:start position:0%
+consumption in date one and c2
+ 
+
+ align:start position:0%
+consumption in date one and c2
+consumption in day two and we're gonna
+
+ align:start position:0%
+consumption in day two and we're gonna
+ 
+
+ align:start position:0%
+consumption in day two and we're gonna
+give
+
+ align:start position:0%
+give
+ 
+
+ align:start position:0%
+give
+income as an endowment
+
+ align:start position:0%
+income as an endowment
+ 
+
+ align:start position:0%
+income as an endowment
+meaning
+
+ align:start position:0%
+meaning
+ 
+
+ align:start position:0%
+meaning
+how much income they have
+
+ align:start position:0%
+how much income they have
+ 
+
+ align:start position:0%
+how much income they have
+in the first date one and how much
+
+ align:start position:0%
+in the first date one and how much
+ 
+
+ align:start position:0%
+in the first date one and how much
+income they have in the second date too
+
+ align:start position:0%
+income they have in the second date too
+ 
+
+ align:start position:0%
+income they have in the second date too
+yeah using income is a bit tricky here
+
+ align:start position:0%
+yeah using income is a bit tricky here
+ 
+
+ align:start position:0%
+yeah using income is a bit tricky here
+because we used that before in in the
+
+ align:start position:0%
+because we used that before in in the
+ 
+
+ align:start position:0%
+because we used that before in in the
+static optimization problem so think of
+
+ align:start position:0%
+static optimization problem so think of
+ 
+
+ align:start position:0%
+static optimization problem so think of
+it as money then
+
+ align:start position:0%
+it as money then
+ 
+
+ align:start position:0%
+it as money then
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+in date one money at day two now what is
+
+ align:start position:0%
+in date one money at day two now what is
+ 
+
+ align:start position:0%
+in date one money at day two now what is
+the budget line well
+
+ align:start position:0%
+the budget line well
+ 
+
+ align:start position:0%
+the budget line well
+if they just
+
+ align:start position:0%
+if they just
+ 
+
+ align:start position:0%
+if they just
+eat their money
+
+ align:start position:0%
+eat their money
+ 
+
+ align:start position:0%
+eat their money
+they would have consumption equal to m1
+
+ align:start position:0%
+they would have consumption equal to m1
+ 
+
+ align:start position:0%
+they would have consumption equal to m1
+and m2
+
+ align:start position:0%
+and m2
+ 
+
+ align:start position:0%
+and m2
+but the way this is drawn they don't
+
+ align:start position:0%
+but the way this is drawn they don't
+ 
+
+ align:start position:0%
+but the way this is drawn they don't
+want to do that they want to move in one
+
+ align:start position:0%
+want to do that they want to move in one
+ 
+
+ align:start position:0%
+want to do that they want to move in one
+direction or another
+
+ align:start position:0%
+direction or another
+ 
+
+ align:start position:0%
+direction or another
+so what is this budget line this budget
+
+ align:start position:0%
+so what is this budget line this budget
+ 
+
+ align:start position:0%
+so what is this budget line this budget
+line reflects the possibility of giving
+
+ align:start position:0%
+line reflects the possibility of giving
+ 
+
+ align:start position:0%
+line reflects the possibility of giving
+up money tomorrow and getting more
+
+ align:start position:0%
+up money tomorrow and getting more
+ 
+
+ align:start position:0%
+up money tomorrow and getting more
+consumption today
+
+ align:start position:0%
+consumption today
+ 
+
+ align:start position:0%
+consumption today
+that's borrowing or giving up money
+
+ align:start position:0%
+that's borrowing or giving up money
+ 
+
+ align:start position:0%
+that's borrowing or giving up money
+today and getting more consumption
+
+ align:start position:0%
+today and getting more consumption
+ 
+
+ align:start position:0%
+today and getting more consumption
+tomorrow that's lending so the slope of
+
+ align:start position:0%
+tomorrow that's lending so the slope of
+ 
+
+ align:start position:0%
+tomorrow that's lending so the slope of
+this heavy blue line represents the
+
+ align:start position:0%
+this heavy blue line represents the
+ 
+
+ align:start position:0%
+this heavy blue line represents the
+trade-off of the price of goods today
+
+ align:start position:0%
+trade-off of the price of goods today
+ 
+
+ align:start position:0%
+trade-off of the price of goods today
+for the price of goods tomorrow which
+
+ align:start position:0%
+for the price of goods tomorrow which
+ 
+
+ align:start position:0%
+for the price of goods tomorrow which
+you kind of knew all along but probably
+
+ align:start position:0%
+you kind of knew all along but probably
+ 
+
+ align:start position:0%
+you kind of knew all along but probably
+forgot
+
+ align:start position:0%
+forgot
+ 
+
+ align:start position:0%
+forgot
+why because the slope of the budget line
+
+ align:start position:0%
+why because the slope of the budget line
+ 
+
+ align:start position:0%
+why because the slope of the budget line
+is p1 over p2 p1 being consumption at
+
+ align:start position:0%
+is p1 over p2 p1 being consumption at
+ 
+
+ align:start position:0%
+is p1 over p2 p1 being consumption at
+day one
+
+ align:start position:0%
+day one
+ 
+
+ align:start position:0%
+day one
+p2 being sorry the price of consumption
+
+ align:start position:0%
+p2 being sorry the price of consumption
+ 
+
+ align:start position:0%
+p2 being sorry the price of consumption
+at day two but the economics of the
+
+ align:start position:0%
+at day two but the economics of the
+ 
+
+ align:start position:0%
+at day two but the economics of the
+problem you know doesn't write p1 over
+
+ align:start position:0%
+problem you know doesn't write p1 over
+ 
+
+ align:start position:0%
+problem you know doesn't write p1 over
+p2 it writes r as an interest rate
+
+ align:start position:0%
+p2 it writes r as an interest rate
+ 
+
+ align:start position:0%
+p2 it writes r as an interest rate
+why is it the interest rate because if
+
+ align:start position:0%
+why is it the interest rate because if
+ 
+
+ align:start position:0%
+why is it the interest rate because if
+you gave up some of your money today and
+
+ align:start position:0%
+you gave up some of your money today and
+ 
+
+ align:start position:0%
+you gave up some of your money today and
+put it in the bank
+
+ align:start position:0%
+put it in the bank
+ 
+
+ align:start position:0%
+put it in the bank
+you would get the principal and interest
+
+ align:start position:0%
+you would get the principal and interest
+ 
+
+ align:start position:0%
+you would get the principal and interest
+back tomorrow
+
+ align:start position:0%
+back tomorrow
+ 
+
+ align:start position:0%
+back tomorrow
+so one plus r which is also the slope of
+
+ align:start position:0%
+so one plus r which is also the slope of
+ 
+
+ align:start position:0%
+so one plus r which is also the slope of
+this line
+
+ align:start position:0%
+this line
+ 
+
+ align:start position:0%
+this line
+reflects the trade-off between
+
+ align:start position:0%
+reflects the trade-off between
+ 
+
+ align:start position:0%
+reflects the trade-off between
+consumption today
+
+ align:start position:0%
+consumption today
+ 
+
+ align:start position:0%
+consumption today
+and consumption tomorrow as made
+
+ align:start position:0%
+and consumption tomorrow as made
+ 
+
+ align:start position:0%
+and consumption tomorrow as made
+possible by this interest rate
+
+ align:start position:0%
+possible by this interest rate
+ 
+
+ align:start position:0%
+possible by this interest rate
+okay so then as per the entire lecture
+
+ align:start position:0%
+okay so then as per the entire lecture
+ 
+
+ align:start position:0%
+okay so then as per the entire lecture
+we try to change a price or here let's
+
+ align:start position:0%
+we try to change a price or here let's
+ 
+
+ align:start position:0%
+we try to change a price or here let's
+increase the interest rate so it's still
+
+ align:start position:0%
+increase the interest rate so it's still
+ 
+
+ align:start position:0%
+increase the interest rate so it's still
+possible to eat your money in both
+
+ align:start position:0%
+possible to eat your money in both
+ 
+
+ align:start position:0%
+possible to eat your money in both
+periods but now that the interest rate
+
+ align:start position:0%
+periods but now that the interest rate
+ 
+
+ align:start position:0%
+periods but now that the interest rate
+has gone up the budget line is steeper
+
+ align:start position:0%
+has gone up the budget line is steeper
+ 
+
+ align:start position:0%
+has gone up the budget line is steeper
+for a given surrendering of one unit of
+
+ align:start position:0%
+for a given surrendering of one unit of
+ 
+
+ align:start position:0%
+for a given surrendering of one unit of
+consumption today
+
+ align:start position:0%
+consumption today
+ 
+
+ align:start position:0%
+consumption today
+you get a higher one plus r tomorrow
+
+ align:start position:0%
+you get a higher one plus r tomorrow
+ 
+
+ align:start position:0%
+you get a higher one plus r tomorrow
+so this paler blue line crosses through
+
+ align:start position:0%
+so this paler blue line crosses through
+ 
+
+ align:start position:0%
+so this paler blue line crosses through
+the endowment point but it's steeper and
+
+ align:start position:0%
+the endowment point but it's steeper and
+ 
+
+ align:start position:0%
+the endowment point but it's steeper and
+as drawn with these indifference curves
+
+ align:start position:0%
+as drawn with these indifference curves
+ 
+
+ align:start position:0%
+as drawn with these indifference curves
+the household would move from this point
+
+ align:start position:0%
+the household would move from this point
+ 
+
+ align:start position:0%
+the household would move from this point
+to this point
+
+ align:start position:0%
+to this point
+ 
+
+ align:start position:0%
+to this point
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+let's talk about income and substitution
+
+ align:start position:0%
+let's talk about income and substitution
+ 
+
+ align:start position:0%
+let's talk about income and substitution
+effects
+
+ align:start position:0%
+effects
+ 
+
+ align:start position:0%
+effects
+consumption tomorrow at day two goes up
+
+ align:start position:0%
+consumption tomorrow at day two goes up
+ 
+
+ align:start position:0%
+consumption tomorrow at day two goes up
+and up why
+
+ align:start position:0%
+and up why
+ 
+
+ align:start position:0%
+and up why
+to effects and they're both moving in
+
+ align:start position:0%
+to effects and they're both moving in
+ 
+
+ align:start position:0%
+to effects and they're both moving in
+the same direction the increase in the
+
+ align:start position:0%
+the same direction the increase in the
+ 
+
+ align:start position:0%
+the same direction the increase in the
+interest rate effectively means they
+
+ align:start position:0%
+interest rate effectively means they
+ 
+
+ align:start position:0%
+interest rate effectively means they
+have more income they can take their
+
+ align:start position:0%
+have more income they can take their
+ 
+
+ align:start position:0%
+have more income they can take their
+endowment of money tomorrow and it will
+
+ align:start position:0%
+endowment of money tomorrow and it will
+ 
+
+ align:start position:0%
+endowment of money tomorrow and it will
+be worth more so there's an income
+
+ align:start position:0%
+be worth more so there's an income
+ 
+
+ align:start position:0%
+be worth more so there's an income
+effect associated with the price change
+
+ align:start position:0%
+effect associated with the price change
+ 
+
+ align:start position:0%
+effect associated with the price change
+not only that there's a substitution
+
+ align:start position:0%
+not only that there's a substitution
+ 
+
+ align:start position:0%
+not only that there's a substitution
+effect why because as the interest rate
+
+ align:start position:0%
+effect why because as the interest rate
+ 
+
+ align:start position:0%
+effect why because as the interest rate
+goes up the opportunity cost of eating
+
+ align:start position:0%
+goes up the opportunity cost of eating
+ 
+
+ align:start position:0%
+goes up the opportunity cost of eating
+today goes up it's more painful to eat
+
+ align:start position:0%
+today goes up it's more painful to eat
+ 
+
+ align:start position:0%
+today goes up it's more painful to eat
+today because you could get even more
+
+ align:start position:0%
+today because you could get even more
+ 
+
+ align:start position:0%
+today because you could get even more
+tomorrow by putting the money in the
+
+ align:start position:0%
+tomorrow by putting the money in the
+ 
+
+ align:start position:0%
+tomorrow by putting the money in the
+bank at a higher interest rate so the
+
+ align:start position:0%
+bank at a higher interest rate so the
+ 
+
+ align:start position:0%
+bank at a higher interest rate so the
+substitution effect
+
+ align:start position:0%
+substitution effect
+ 
+
+ align:start position:0%
+substitution effect
+moves them with these nice smooth
+
+ align:start position:0%
+moves them with these nice smooth
+ 
+
+ align:start position:0%
+moves them with these nice smooth
+indifference curves away from
+
+ align:start position:0%
+indifference curves away from
+ 
+
+ align:start position:0%
+indifference curves away from
+consumption today toward higher
+
+ align:start position:0%
+consumption today toward higher
+ 
+
+ align:start position:0%
+consumption today toward higher
+consumption tomorrow
+
+ align:start position:0%
+consumption tomorrow
+ 
+
+ align:start position:0%
+consumption tomorrow
+so the income and substitution effects
+
+ align:start position:0%
+so the income and substitution effects
+ 
+
+ align:start position:0%
+so the income and substitution effects
+in this diagram work in the same
+
+ align:start position:0%
+in this diagram work in the same
+ 
+
+ align:start position:0%
+in this diagram work in the same
+direction for good two but it it's not
+
+ align:start position:0%
+direction for good two but it it's not
+ 
+
+ align:start position:0%
+direction for good two but it it's not
+true for good one at date one
+
+ align:start position:0%
+true for good one at date one
+ 
+
+ align:start position:0%
+true for good one at date one
+or at least it could be ambiguous
+
+ align:start position:0%
+or at least it could be ambiguous
+ 
+
+ align:start position:0%
+or at least it could be ambiguous
+why there's an income effect which
+
+ align:start position:0%
+why there's an income effect which
+ 
+
+ align:start position:0%
+why there's an income effect which
+should increase consumption at date one
+
+ align:start position:0%
+should increase consumption at date one
+ 
+
+ align:start position:0%
+should increase consumption at date one
+but there's a price effect which should
+
+ align:start position:0%
+but there's a price effect which should
+ 
+
+ align:start position:0%
+but there's a price effect which should
+decrease consumption at day one
+
+ align:start position:0%
+decrease consumption at day one
+ 
+
+ align:start position:0%
+decrease consumption at day one
+and those can in principle move in
+
+ align:start position:0%
+and those can in principle move in
+ 
+
+ align:start position:0%
+and those can in principle move in
+opposite directions
+
+ align:start position:0%
+opposite directions
+ 
+
+ align:start position:0%
+opposite directions
+in this case date one consumption is
+
+ align:start position:0%
+in this case date one consumption is
+ 
+
+ align:start position:0%
+in this case date one consumption is
+going down
+
+ align:start position:0%
+going down
+ 
+
+ align:start position:0%
+going down
+so the substitution effect is dominating
+
+ align:start position:0%
+so the substitution effect is dominating
+ 
+
+ align:start position:0%
+so the substitution effect is dominating
+the income effect
+
+ align:start position:0%
+the income effect
+ 
+
+ align:start position:0%
+the income effect
+but it didn't have to go that way you
+
+ align:start position:0%
+but it didn't have to go that way you
+ 
+
+ align:start position:0%
+but it didn't have to go that way you
+could have drawn the indifference curves
+
+ align:start position:0%
+could have drawn the indifference curves
+ 
+
+ align:start position:0%
+could have drawn the indifference curves
+and gotten an increase in the
+
+ align:start position:0%
+and gotten an increase in the
+ 
+
+ align:start position:0%
+and gotten an increase in the
+consumption of date of that good okay
+
+ align:start position:0%
+consumption of date of that good okay
+ 
+
+ align:start position:0%
+consumption of date of that good okay
+let's start out with a different but
+
+ align:start position:0%
+let's start out with a different but
+ 
+
+ align:start position:0%
+let's start out with a different but
+related diagram suppose they have money
+
+ align:start position:0%
+related diagram suppose they have money
+ 
+
+ align:start position:0%
+related diagram suppose they have money
+today and tomorrow as endowments and
+
+ align:start position:0%
+today and tomorrow as endowments and
+ 
+
+ align:start position:0%
+today and tomorrow as endowments and
+this guy is actually doing what
+
+ align:start position:0%
+this guy is actually doing what
+ 
+
+ align:start position:0%
+this guy is actually doing what
+originally borrowing getting more
+
+ align:start position:0%
+originally borrowing getting more
+ 
+
+ align:start position:0%
+originally borrowing getting more
+consumption today than the money he or
+
+ align:start position:0%
+consumption today than the money he or
+ 
+
+ align:start position:0%
+consumption today than the money he or
+she has at the expense of paying it back
+
+ align:start position:0%
+she has at the expense of paying it back
+ 
+
+ align:start position:0%
+she has at the expense of paying it back
+with interest tomorrow therefore having
+
+ align:start position:0%
+with interest tomorrow therefore having
+ 
+
+ align:start position:0%
+with interest tomorrow therefore having
+less consumption than the money that he
+
+ align:start position:0%
+less consumption than the money that he
+ 
+
+ align:start position:0%
+less consumption than the money that he
+or she originally had so
+
+ align:start position:0%
+or she originally had so
+ 
+
+ align:start position:0%
+or she originally had so
+we'd end up with this tangency and now
+
+ align:start position:0%
+we'd end up with this tangency and now
+ 
+
+ align:start position:0%
+we'd end up with this tangency and now
+we still increase the interest rate that
+
+ align:start position:0%
+we still increase the interest rate that
+ 
+
+ align:start position:0%
+we still increase the interest rate that
+makes this pale
+
+ align:start position:0%
+makes this pale
+ 
+
+ align:start position:0%
+makes this pale
+blue line steeper
+
+ align:start position:0%
+blue line steeper
+ 
+
+ align:start position:0%
+blue line steeper
+and you can see consumption is moving
+
+ align:start position:0%
+and you can see consumption is moving
+ 
+
+ align:start position:0%
+and you can see consumption is moving
+inwards so actually
+
+ align:start position:0%
+inwards so actually
+ 
+
+ align:start position:0%
+inwards so actually
+consumption of both goods in the diagram
+
+ align:start position:0%
+consumption of both goods in the diagram
+ 
+
+ align:start position:0%
+consumption of both goods in the diagram
+is going down but let's think about
+
+ align:start position:0%
+is going down but let's think about
+ 
+
+ align:start position:0%
+is going down but let's think about
+income and substitution effects because
+
+ align:start position:0%
+income and substitution effects because
+ 
+
+ align:start position:0%
+income and substitution effects because
+they were borrowing originally as
+
+ align:start position:0%
+they were borrowing originally as
+ 
+
+ align:start position:0%
+they were borrowing originally as
+opposed to lending intuitively an
+
+ align:start position:0%
+opposed to lending intuitively an
+ 
+
+ align:start position:0%
+opposed to lending intuitively an
+increase in the interest rate is a bad
+
+ align:start position:0%
+increase in the interest rate is a bad
+ 
+
+ align:start position:0%
+increase in the interest rate is a bad
+situation for them
+
+ align:start position:0%
+situation for them
+ 
+
+ align:start position:0%
+situation for them
+they were borrowing and now the interest
+
+ align:start position:0%
+they were borrowing and now the interest
+ 
+
+ align:start position:0%
+they were borrowing and now the interest
+rate is higher so the income effect is
+
+ align:start position:0%
+rate is higher so the income effect is
+ 
+
+ align:start position:0%
+rate is higher so the income effect is
+negative and that could show up with
+
+ align:start position:0%
+negative and that could show up with
+ 
+
+ align:start position:0%
+negative and that could show up with
+both goods on the other hand the
+
+ align:start position:0%
+both goods on the other hand the
+ 
+
+ align:start position:0%
+both goods on the other hand the
+substitution effect should still push
+
+ align:start position:0%
+substitution effect should still push
+ 
+
+ align:start position:0%
+substitution effect should still push
+them in the direction of higher
+
+ align:start position:0%
+them in the direction of higher
+ 
+
+ align:start position:0%
+them in the direction of higher
+consumption tomorrow that's the
+
+ align:start position:0%
+consumption tomorrow that's the
+ 
+
+ align:start position:0%
+consumption tomorrow that's the
+substitution effect so for one of these
+
+ align:start position:0%
+substitution effect so for one of these
+ 
+
+ align:start position:0%
+substitution effect so for one of these
+goods
+
+ align:start position:0%
+goods
+ 
+
+ align:start position:0%
+goods
+consumption today is unambiguous but
+
+ align:start position:0%
+consumption today is unambiguous but
+ 
+
+ align:start position:0%
+consumption today is unambiguous but
+consumption tomorrow is ambiguous
+
+ align:start position:0%
+consumption tomorrow is ambiguous
+ 
+
+ align:start position:0%
+consumption tomorrow is ambiguous
+despite the way it's drawn because the
+
+ align:start position:0%
+despite the way it's drawn because the
+ 
+
+ align:start position:0%
+despite the way it's drawn because the
+income and substitution effects work in
+
+ align:start position:0%
+income and substitution effects work in
+ 
+
+ align:start position:0%
+income and substitution effects work in
+the opposite direction
+
+ align:start position:0%
+the opposite direction
+ 
+
+ align:start position:0%
+the opposite direction
+so take a look at those there's a lot
+
+ align:start position:0%
+so take a look at those there's a lot
+ 
+
+ align:start position:0%
+so take a look at those there's a lot
+going on in fact that's kind of the
+
+ align:start position:0%
+going on in fact that's kind of the
+ 
+
+ align:start position:0%
+going on in fact that's kind of the
+point that when we move from apple's
+
+ align:start position:0%
+point that when we move from apple's
+ 
+
+ align:start position:0%
+point that when we move from apple's
+wheats and so on with prices and income
+
+ align:start position:0%
+wheats and so on with prices and income
+ 
+
+ align:start position:0%
+wheats and so on with prices and income
+to an applied problem like you know
+
+ align:start position:0%
+to an applied problem like you know
+ 
+
+ align:start position:0%
+to an applied problem like you know
+what's happening in the us with these
+
+ align:start position:0%
+what's happening in the us with these
+ 
+
+ align:start position:0%
+what's happening in the us with these
+lower and lower interest rates well
+
+ align:start position:0%
+lower and lower interest rates well
+ 
+
+ align:start position:0%
+lower and lower interest rates well
+if we looked at consumer behavior
+
+ align:start position:0%
+if we looked at consumer behavior
+ 
+
+ align:start position:0%
+if we looked at consumer behavior
+there's income effects
+
+ align:start position:0%
+there's income effects
+ 
+
+ align:start position:0%
+there's income effects
+there's uh substitution effects it can
+
+ align:start position:0%
+there's uh substitution effects it can
+ 
+
+ align:start position:0%
+there's uh substitution effects it can
+go in different directions and be in
+
+ align:start position:0%
+go in different directions and be in
+ 
+
+ align:start position:0%
+go in different directions and be in
+conflict and that's an important part of
+
+ align:start position:0%
+conflict and that's an important part of
+ 
+
+ align:start position:0%
+conflict and that's an important part of
+understanding the impact on the
+
+ align:start position:0%
+understanding the impact on the
+ 
+
+ align:start position:0%
+understanding the impact on the
+households and the impact on the economy
+
+ align:start position:0%
+households and the impact on the economy
+ 
+
+ align:start position:0%
+households and the impact on the economy
+and and it's actually a lot more work to
+
+ align:start position:0%
+and and it's actually a lot more work to
+ 
+
+ align:start position:0%
+and and it's actually a lot more work to
+go through this slide in the previous
+
+ align:start position:0%
+go through this slide in the previous
+ 
+
+ align:start position:0%
+go through this slide in the previous
+one than you might have imagined even
+
+ align:start position:0%
+one than you might have imagined even
+ 
+
+ align:start position:0%
+one than you might have imagined even
+though
+
+ align:start position:0%
+though
+ 
+
+ align:start position:0%
+though
+say you were totally sure you could
+
+ align:start position:0%
+say you were totally sure you could
+ 
+
+ align:start position:0%
+say you were totally sure you could
+shift these curves around
+
+ align:start position:0%
+shift these curves around
+ 
+
+ align:start position:0%
+shift these curves around
+in whatever way you wanted when you get
+
+ align:start position:0%
+in whatever way you wanted when you get
+ 
+
+ align:start position:0%
+in whatever way you wanted when you get
+to the economic application we kind of
+
+ align:start position:0%
+to the economic application we kind of
+ 
+
+ align:start position:0%
+to the economic application we kind of
+do it all over again with the new
+
+ align:start position:0%
+do it all over again with the new
+ 
+
+ align:start position:0%
+do it all over again with the new
+realistic labels and it and it and
+
+ align:start position:0%
+realistic labels and it and it and
+ 
+
+ align:start position:0%
+realistic labels and it and it and
+brings that tool to life
+
+ align:start position:0%
+brings that tool to life
+ 
+
+ align:start position:0%
+brings that tool to life
+okay well that's the last slide for
+
+ align:start position:0%
+okay well that's the last slide for
+ 
+
+ align:start position:0%
+okay well that's the last slide for
+today that's the uh the end of this
+
+ align:start position:0%
+today that's the uh the end of this
+ 
+
+ align:start position:0%
+today that's the uh the end of this
+lecture all right thank you very much
\ No newline at end of file
diff --git a/DYfP7BDhvHI.txt b/DYfP7BDhvHI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d4024844d59aa57959a2d2e3817c59febab019f6
--- /dev/null
+++ b/DYfP7BDhvHI.txt
@@ -0,0 +1,16440 @@
+align:start position:0%
+ 
+um so anyway uh today's lecture you know
+
+ align:start position:0%
+um so anyway uh today's lecture you know
+ 
+
+ align:start position:0%
+um so anyway uh today's lecture you know
+I I was doing uh I did Static
+
+ align:start position:0%
+I I was doing uh I did Static
+ 
+
+ align:start position:0%
+I I was doing uh I did Static
+competition last week today sort of my
+
+ align:start position:0%
+competition last week today sort of my
+ 
+
+ align:start position:0%
+competition last week today sort of my
+plan is I'm going to start with empirics
+
+ align:start position:0%
+plan is I'm going to start with empirics
+ 
+
+ align:start position:0%
+plan is I'm going to start with empirics
+of static competition I'm going to fill
+
+ align:start position:0%
+of static competition I'm going to fill
+ 
+
+ align:start position:0%
+of static competition I'm going to fill
+in in the middle some extra theory that
+
+ align:start position:0%
+in in the middle some extra theory that
+ 
+
+ align:start position:0%
+in in the middle some extra theory that
+I didn't have time to do last uh doe
+
+ align:start position:0%
+I didn't have time to do last uh doe
+ 
+
+ align:start position:0%
+I didn't have time to do last uh doe
+last Wednesday and then like the paper
+
+ align:start position:0%
+last Wednesday and then like the paper
+ 
+
+ align:start position:0%
+last Wednesday and then like the paper
+at the end I'm going to do very very
+
+ align:start position:0%
+at the end I'm going to do very very
+ 
+
+ align:start position:0%
+at the end I'm going to do very very
+quickly because I just was reading it
+
+ align:start position:0%
+quickly because I just was reading it
+ 
+
+ align:start position:0%
+quickly because I just was reading it
+over making the notes and I realized
+
+ align:start position:0%
+over making the notes and I realized
+ 
+
+ align:start position:0%
+over making the notes and I realized
+that you know Tobias is going to be
+
+ align:start position:0%
+that you know Tobias is going to be
+ 
+
+ align:start position:0%
+that you know Tobias is going to be
+spending an awful long awful lot of time
+
+ align:start position:0%
+spending an awful long awful lot of time
+ 
+
+ align:start position:0%
+spending an awful long awful lot of time
+next Monday explaining sort of what the
+
+ align:start position:0%
+next Monday explaining sort of what the
+ 
+
+ align:start position:0%
+next Monday explaining sort of what the
+model is about and the estimation of it
+
+ align:start position:0%
+model is about and the estimation of it
+ 
+
+ align:start position:0%
+model is about and the estimation of it
+and I figured that it'd be much better
+
+ align:start position:0%
+and I figured that it'd be much better
+ 
+
+ align:start position:0%
+and I figured that it'd be much better
+to wait until after he's done that and
+
+ align:start position:0%
+to wait until after he's done that and
+ 
+
+ align:start position:0%
+to wait until after he's done that and
+you can just look at my slides on it um
+
+ align:start position:0%
+you can just look at my slides on it um
+ 
+
+ align:start position:0%
+you can just look at my slides on it um
+and I'll just sort of stick with basic
+
+ align:start position:0%
+and I'll just sort of stick with basic
+ 
+
+ align:start position:0%
+and I'll just sort of stick with basic
+comments so anyway I'm going to first
+
+ align:start position:0%
+comments so anyway I'm going to first
+ 
+
+ align:start position:0%
+comments so anyway I'm going to first
+sort of cover you know one of my
+
+ align:start position:0%
+sort of cover you know one of my
+ 
+
+ align:start position:0%
+sort of cover you know one of my
+favorite papers in the course so this is
+
+ align:start position:0%
+favorite papers in the course so this is
+ 
+
+ align:start position:0%
+favorite papers in the course so this is
+uh breast hands paper competition and
+
+ align:start position:0%
+uh breast hands paper competition and
+ 
+
+ align:start position:0%
+uh breast hands paper competition and
+collusion in the American automobile
+
+ align:start position:0%
+collusion in the American automobile
+ 
+
+ align:start position:0%
+collusion in the American automobile
+industry the 1955 price War um you I
+
+ align:start position:0%
+industry the 1955 price War um you I
+ 
+
+ align:start position:0%
+industry the 1955 price War um you I
+should say in some sense it I I it's one
+
+ align:start position:0%
+should say in some sense it I I it's one
+ 
+
+ align:start position:0%
+should say in some sense it I I it's one
+of my favorite papers I took the star
+
+ align:start position:0%
+of my favorite papers I took the star
+ 
+
+ align:start position:0%
+of my favorite papers I took the star
+off it this year because in some ways I
+
+ align:start position:0%
+off it this year because in some ways I
+ 
+
+ align:start position:0%
+off it this year because in some ways I
+think it's as the paper gets more and
+
+ align:start position:0%
+think it's as the paper gets more and
+ 
+
+ align:start position:0%
+think it's as the paper gets more and
+more dated you can appreciate it more by
+
+ align:start position:0%
+more dated you can appreciate it more by
+ 
+
+ align:start position:0%
+more dated you can appreciate it more by
+hearing about what it does than by
+
+ align:start position:0%
+hearing about what it does than by
+ 
+
+ align:start position:0%
+hearing about what it does than by
+actually reading it you know there's
+
+ align:start position:0%
+actually reading it you know there's
+ 
+
+ align:start position:0%
+actually reading it you know there's
+just sort of many things that you read
+
+ align:start position:0%
+just sort of many things that you read
+ 
+
+ align:start position:0%
+just sort of many things that you read
+and you're like wow that sounds like a
+
+ align:start position:0%
+and you're like wow that sounds like a
+ 
+
+ align:start position:0%
+and you're like wow that sounds like a
+40y old way to do something and so I'll
+
+ align:start position:0%
+40y old way to do something and so I'll
+ 
+
+ align:start position:0%
+40y old way to do something and so I'll
+just leave out the 40-year-old parts
+
+ align:start position:0%
+just leave out the 40-year-old parts
+ 
+
+ align:start position:0%
+just leave out the 40-year-old parts
+that were a bit awkward and probably had
+
+ align:start position:0%
+that were a bit awkward and probably had
+ 
+
+ align:start position:0%
+that were a bit awkward and probably had
+hadap some trouble publishing it to
+
+ align:start position:0%
+hadap some trouble publishing it to
+ 
+
+ align:start position:0%
+hadap some trouble publishing it to
+begin with and I'll sort of give you the
+
+ align:start position:0%
+begin with and I'll sort of give you the
+ 
+
+ align:start position:0%
+begin with and I'll sort of give you the
+main ideas so you know this is a paper
+
+ align:start position:0%
+main ideas so you know this is a paper
+ 
+
+ align:start position:0%
+main ideas so you know this is a paper
+on the io economic history boundary um
+
+ align:start position:0%
+on the io economic history boundary um
+ 
+
+ align:start position:0%
+on the io economic history boundary um
+the to applied topic is what caused the
+
+ align:start position:0%
+the to applied topic is what caused the
+ 
+
+ align:start position:0%
+the to applied topic is what caused the
+1955 surge in US Auto Sales uh and it
+
+ align:start position:0%
+1955 surge in US Auto Sales uh and it
+ 
+
+ align:start position:0%
+1955 surge in US Auto Sales uh and it
+has this interesting hypothesis which is
+
+ align:start position:0%
+has this interesting hypothesis which is
+ 
+
+ align:start position:0%
+has this interesting hypothesis which is
+you know that the 1955 surgeon Auto
+
+ align:start position:0%
+you know that the 1955 surgeon Auto
+ 
+
+ align:start position:0%
+you know that the 1955 surgeon Auto
+Sales was due to a breakdown in
+
+ align:start position:0%
+Sales was due to a breakdown in
+ 
+
+ align:start position:0%
+Sales was due to a breakdown in
+collusion that at the time uh there were
+
+ align:start position:0%
+collusion that at the time uh there were
+ 
+
+ align:start position:0%
+collusion that at the time uh there were
+very few foreign cars sold in the United
+
+ align:start position:0%
+very few foreign cars sold in the United
+ 
+
+ align:start position:0%
+very few foreign cars sold in the United
+States there were largely three American
+
+ align:start position:0%
+States there were largely three American
+ 
+
+ align:start position:0%
+States there were largely three American
+autom makers and his hypothesis that the
+
+ align:start position:0%
+autom makers and his hypothesis that the
+ 
+
+ align:start position:0%
+autom makers and his hypothesis that the
+us automakers were colluding to set set
+
+ align:start position:0%
+us automakers were colluding to set set
+ 
+
+ align:start position:0%
+us automakers were colluding to set set
+Monopoly prices and then in 1955 the
+
+ align:start position:0%
+Monopoly prices and then in 1955 the
+ 
+
+ align:start position:0%
+Monopoly prices and then in 1955 the
+collusion broke down prices Dro many
+
+ align:start position:0%
+collusion broke down prices Dro many
+ 
+
+ align:start position:0%
+collusion broke down prices Dro many
+more cars were sold anyway that's and
+
+ align:start position:0%
+more cars were sold anyway that's and
+ 
+
+ align:start position:0%
+more cars were sold anyway that's and
+then the firms got it figured out again
+
+ align:start position:0%
+then the firms got it figured out again
+ 
+
+ align:start position:0%
+then the firms got it figured out again
+in 1956 prices went back up um you know
+
+ align:start position:0%
+in 1956 prices went back up um you know
+ 
+
+ align:start position:0%
+in 1956 prices went back up um you know
+paper besides having this sort of
+
+ align:start position:0%
+paper besides having this sort of
+ 
+
+ align:start position:0%
+paper besides having this sort of
+interesting historical fact it it has
+
+ align:start position:0%
+interesting historical fact it it has
+ 
+
+ align:start position:0%
+interesting historical fact it it has
+been a really influential as a model for
+
+ align:start position:0%
+been a really influential as a model for
+ 
+
+ align:start position:0%
+been a really influential as a model for
+future work in some sense I I see this
+
+ align:start position:0%
+future work in some sense I I see this
+ 
+
+ align:start position:0%
+future work in some sense I I see this
+as the first structural empirical paper
+
+ align:start position:0%
+as the first structural empirical paper
+ 
+
+ align:start position:0%
+as the first structural empirical paper
+in IO and I think that you know what you
+
+ align:start position:0%
+in IO and I think that you know what you
+ 
+
+ align:start position:0%
+in IO and I think that you know what you
+can think of is that the um really sort
+
+ align:start position:0%
+can think of is that the um really sort
+ 
+
+ align:start position:0%
+can think of is that the um really sort
+of you know many future papers have sort
+
+ align:start position:0%
+of you know many future papers have sort
+ 
+
+ align:start position:0%
+of you know many future papers have sort
+of picked up on breast and hand's
+
+ align:start position:0%
+of picked up on breast and hand's
+ 
+
+ align:start position:0%
+of picked up on breast and hand's
+methodology and sort of adopted this as
+
+ align:start position:0%
+methodology and sort of adopted this as
+ 
+
+ align:start position:0%
+methodology and sort of adopted this as
+a different way of doing things so I
+
+ align:start position:0%
+a different way of doing things so I
+ 
+
+ align:start position:0%
+a different way of doing things so I
+will explain what it was that Brean was
+
+ align:start position:0%
+will explain what it was that Brean was
+ 
+
+ align:start position:0%
+will explain what it was that Brean was
+trying to do in this paper um but for
+
+ align:start position:0%
+trying to do in this paper um but for
+ 
+
+ align:start position:0%
+trying to do in this paper um but for
+the first on the applied topic you know
+
+ align:start position:0%
+the first on the applied topic you know
+ 
+
+ align:start position:0%
+the first on the applied topic you know
+here's a you know he starts with this
+
+ align:start position:0%
+here's a you know he starts with this
+ 
+
+ align:start position:0%
+here's a you know he starts with this
+sort of simple table of of car sales by
+
+ align:start position:0%
+sort of simple table of of car sales by
+ 
+
+ align:start position:0%
+sort of simple table of of car sales by
+year in the United States and you get
+
+ align:start position:0%
+year in the United States and you get
+ 
+
+ align:start position:0%
+year in the United States and you get
+this sort of striking finding which you
+
+ align:start position:0%
+this sort of striking finding which you
+ 
+
+ align:start position:0%
+this sort of striking finding which you
+know is in 1954 us automakers produced 5
+
+ align:start position:0%
+know is in 1954 us automakers produced 5
+ 
+
+ align:start position:0%
+know is in 1954 us automakers produced 5
+a half million cars in 1955 they
+
+ align:start position:0%
+a half million cars in 1955 they
+ 
+
+ align:start position:0%
+a half million cars in 1955 they
+produced 7.9 million cars in 1956 they
+
+ align:start position:0%
+produced 7.9 million cars in 1956 they
+ 
+
+ align:start position:0%
+produced 7.9 million cars in 1956 they
+produced 5.8 million cars so those was
+
+ align:start position:0%
+produced 5.8 million cars so those was
+ 
+
+ align:start position:0%
+produced 5.8 million cars so those was
+you know like cars are a big part of the
+
+ align:start position:0%
+you know like cars are a big part of the
+ 
+
+ align:start position:0%
+you know like cars are a big part of the
+economy and this cars being produced
+
+ align:start position:0%
+economy and this cars being produced
+ 
+
+ align:start position:0%
+economy and this cars being produced
+going up by 40% in one year is a really
+
+ align:start position:0%
+going up by 40% in one year is a really
+ 
+
+ align:start position:0%
+going up by 40% in one year is a really
+striking fact um if you look at it sales
+
+ align:start position:0%
+striking fact um if you look at it sales
+ 
+
+ align:start position:0%
+striking fact um if you look at it sales
+in dollars it's still a big jump the
+
+ align:start position:0%
+in dollars it's still a big jump the
+ 
+
+ align:start position:0%
+in dollars it's still a big jump the
+jump in dollars of car sales is not as
+
+ align:start position:0%
+jump in dollars of car sales is not as
+ 
+
+ align:start position:0%
+jump in dollars of car sales is not as
+big as the jump in unit Car Sales uh and
+
+ align:start position:0%
+big as the jump in unit Car Sales uh and
+ 
+
+ align:start position:0%
+big as the jump in unit Car Sales uh and
+part that's because prices were lower
+
+ align:start position:0%
+part that's because prices were lower
+ 
+
+ align:start position:0%
+part that's because prices were lower
+and in part that's because people did
+
+ align:start position:0%
+and in part that's because people did
+ 
+
+ align:start position:0%
+and in part that's because people did
+buy smaller cars um
+
+ align:start position:0%
+buy smaller cars um
+ 
+
+ align:start position:0%
+buy smaller cars um
+and then if you look at what was going
+
+ align:start position:0%
+and then if you look at what was going
+ 
+
+ align:start position:0%
+and then if you look at what was going
+on in the US economy it was sort of a
+
+ align:start position:0%
+on in the US economy it was sort of a
+ 
+
+ align:start position:0%
+on in the US economy it was sort of a
+boom time in the US economy you can see
+
+ align:start position:0%
+boom time in the US economy you can see
+ 
+
+ align:start position:0%
+boom time in the US economy you can see
+non-auto durable goods spending went
+
+ align:start position:0%
+non-auto durable goods spending went
+ 
+
+ align:start position:0%
+non-auto durable goods spending went
+from 14.5 to 16 billion and then
+
+ align:start position:0%
+from 14.5 to 16 billion and then
+ 
+
+ align:start position:0%
+from 14.5 to 16 billion and then
+continued increasing to 17 billion the
+
+ align:start position:0%
+continued increasing to 17 billion the
+ 
+
+ align:start position:0%
+continued increasing to 17 billion the
+next year so it was a good year for the
+
+ align:start position:0%
+next year so it was a good year for the
+ 
+
+ align:start position:0%
+next year so it was a good year for the
+US economy but not a 40% larger increase
+
+ align:start position:0%
+US economy but not a 40% larger increase
+ 
+
+ align:start position:0%
+US economy but not a 40% larger increase
+in car sales boom in the US econom I
+
+ align:start position:0%
+in car sales boom in the US econom I
+ 
+
+ align:start position:0%
+in car sales boom in the US econom I
+mean there really are not 40% boom in
+
+ align:start position:0%
+mean there really are not 40% boom in
+ 
+
+ align:start position:0%
+mean there really are not 40% boom in
+car sales uh General macro uh shocks um
+
+ align:start position:0%
+car sales uh General macro uh shocks um
+ 
+
+ align:start position:0%
+car sales uh General macro uh shocks um
+you can find explanations in the popular
+
+ align:start position:0%
+you can find explanations in the popular
+ 
+
+ align:start position:0%
+you can find explanations in the popular
+press of what caused the 1955 thing as a
+
+ align:start position:0%
+press of what caused the 1955 thing as a
+ 
+
+ align:start position:0%
+press of what caused the 1955 thing as a
+cultural phenomenon you know here's a
+
+ align:start position:0%
+cultural phenomenon you know here's a
+ 
+
+ align:start position:0%
+cultural phenomenon you know here's a
+quote from c talk describing this where
+
+ align:start position:0%
+quote from c talk describing this where
+ 
+
+ align:start position:0%
+quote from c talk describing this where
+they sort of talk about how rock music
+
+ align:start position:0%
+they sort of talk about how rock music
+ 
+
+ align:start position:0%
+they sort of talk about how rock music
+and Drive-In restaurants were becoming a
+
+ align:start position:0%
+and Drive-In restaurants were becoming a
+ 
+
+ align:start position:0%
+and Drive-In restaurants were becoming a
+thing and there were Sleek new designs
+
+ align:start position:0%
+thing and there were Sleek new designs
+ 
+
+ align:start position:0%
+thing and there were Sleek new designs
+for cars and whatever um you apparently
+
+ align:start position:0%
+for cars and whatever um you apparently
+ 
+
+ align:start position:0%
+for cars and whatever um you apparently
+back in the 1950s Paul Samuelson taught
+
+ align:start position:0%
+back in the 1950s Paul Samuelson taught
+ 
+
+ align:start position:0%
+back in the 1950s Paul Samuelson taught
+both uh 121 through you know taught both
+
+ align:start position:0%
+both uh 121 through you know taught both
+ 
+
+ align:start position:0%
+both uh 121 through you know taught both
+in the in the micro sequence 121 through
+
+ align:start position:0%
+in the in the micro sequence 121 through
+ 
+
+ align:start position:0%
+in the in the micro sequence 121 through
+124 and in the chometric sequence uh 381
+
+ align:start position:0%
+124 and in the chometric sequence uh 381
+ 
+
+ align:start position:0%
+124 and in the chometric sequence uh 381
+382 I think the numbers were still the
+
+ align:start position:0%
+382 I think the numbers were still the
+ 
+
+ align:start position:0%
+382 I think the numbers were still the
+same 50 years or 70 years ago that is
+
+ align:start position:0%
+same 50 years or 70 years ago that is
+ 
+
+ align:start position:0%
+same 50 years or 70 years ago that is
+now um uh but you know Paul apparently
+
+ align:start position:0%
+now um uh but you know Paul apparently
+ 
+
+ align:start position:0%
+now um uh but you know Paul apparently
+you know this was pre
+
+ align:start position:0%
+you know this was pre
+ 
+
+ align:start position:0%
+you know this was pre
+14192 but there was a required seconde
+
+ align:start position:0%
+14192 but there was a required seconde
+ 
+
+ align:start position:0%
+14192 but there was a required seconde
+econometrics paper uh and you know Paul
+
+ align:start position:0%
+econometrics paper uh and you know Paul
+ 
+
+ align:start position:0%
+econometrics paper uh and you know Paul
+samelson apparently when teaching the
+
+ align:start position:0%
+samelson apparently when teaching the
+ 
+
+ align:start position:0%
+samelson apparently when teaching the
+second year conom metrics course would
+
+ align:start position:0%
+second year conom metrics course would
+ 
+
+ align:start position:0%
+second year conom metrics course would
+say that he would flunk any paper that
+
+ align:start position:0%
+say that he would flunk any paper that
+ 
+
+ align:start position:0%
+say that he would flunk any paper that
+claimed it was providing an explanation
+
+ align:start position:0%
+claimed it was providing an explanation
+ 
+
+ align:start position:0%
+claimed it was providing an explanation
+for 1955 Auto Sales where by explanation
+
+ align:start position:0%
+for 1955 Auto Sales where by explanation
+ 
+
+ align:start position:0%
+for 1955 Auto Sales where by explanation
+he sort of meant you know you're
+
+ align:start position:0%
+he sort of meant you know you're
+ 
+
+ align:start position:0%
+he sort of meant you know you're
+regressing Auto Sales on a bunch of
+
+ align:start position:0%
+regressing Auto Sales on a bunch of
+ 
+
+ align:start position:0%
+regressing Auto Sales on a bunch of
+right- hand side variabl like the price
+
+ align:start position:0%
+right- hand side variabl like the price
+ 
+
+ align:start position:0%
+right- hand side variabl like the price
+of steel and whatever um okay so what
+
+ align:start position:0%
+of steel and whatever um okay so what
+ 
+
+ align:start position:0%
+of steel and whatever um okay so what
+were cars in 1955 so I got some
+
+ align:start position:0%
+were cars in 1955 so I got some
+ 
+
+ align:start position:0%
+were cars in 1955 so I got some
+illustrations here so um 1955 Mercury
+
+ align:start position:0%
+illustrations here so um 1955 Mercury
+ 
+
+ align:start position:0%
+illustrations here so um 1955 Mercury
+Montclair 1955 Chevy Bair 1955 Ford
+
+ align:start position:0%
+Montclair 1955 Chevy Bair 1955 Ford
+ 
+
+ align:start position:0%
+Montclair 1955 Chevy Bair 1955 Ford
+Thunderbird you know you can see right
+
+ align:start position:0%
+Thunderbird you know you can see right
+ 
+
+ align:start position:0%
+Thunderbird you know you can see right
+the 55 Thunderbird is a very cute car um
+
+ align:start position:0%
+the 55 Thunderbird is a very cute car um
+ 
+
+ align:start position:0%
+the 55 Thunderbird is a very cute car um
+the other cars just look pretty generic
+
+ align:start position:0%
+the other cars just look pretty generic
+ 
+
+ align:start position:0%
+the other cars just look pretty generic
+to me you know here's the for contrast
+
+ align:start position:0%
+to me you know here's the for contrast
+ 
+
+ align:start position:0%
+to me you know here's the for contrast
+here's the 1955 Chevy ba Air versus the
+
+ align:start position:0%
+here's the 1955 Chevy ba Air versus the
+ 
+
+ align:start position:0%
+here's the 1955 Chevy ba Air versus the
+1954 Chevy ba air and you can see that
+
+ align:start position:0%
+1954 Chevy ba air and you can see that
+ 
+
+ align:start position:0%
+1954 Chevy ba air and you can see that
+you know they sort of seem to have taken
+
+ align:start position:0%
+you know they sort of seem to have taken
+ 
+
+ align:start position:0%
+you know they sort of seem to have taken
+away a little bit of this wheel thing
+
+ align:start position:0%
+away a little bit of this wheel thing
+ 
+
+ align:start position:0%
+away a little bit of this wheel thing
+that stuck out here and they smoothed
+
+ align:start position:0%
+that stuck out here and they smoothed
+ 
+
+ align:start position:0%
+that stuck out here and they smoothed
+out the grill instead of these big
+
+ align:start position:0%
+out the grill instead of these big
+ 
+
+ align:start position:0%
+out the grill instead of these big
+things they went to small things you
+
+ align:start position:0%
+things they went to small things you
+ 
+
+ align:start position:0%
+things they went to small things you
+know it it fits with the sleeker car
+
+ align:start position:0%
+know it it fits with the sleeker car
+ 
+
+ align:start position:0%
+know it it fits with the sleeker car
+Theory but it's it doesn't look all that
+
+ align:start position:0%
+Theory but it's it doesn't look all that
+ 
+
+ align:start position:0%
+Theory but it's it doesn't look all that
+different to me um you know perhaps
+
+ align:start position:0%
+different to me um you know perhaps
+ 
+
+ align:start position:0%
+different to me um you know perhaps
+Sunday perhaps today someone could write
+
+ align:start position:0%
+Sunday perhaps today someone could write
+ 
+
+ align:start position:0%
+Sunday perhaps today someone could write
+a machine learning thing judging the
+
+ align:start position:0%
+a machine learning thing judging the
+ 
+
+ align:start position:0%
+a machine learning thing judging the
+sleekness of cars and seeing how much
+
+ align:start position:0%
+sleekness of cars and seeing how much
+ 
+
+ align:start position:0%
+sleekness of cars and seeing how much
+the sleekness of cars increase affects
+
+ align:start position:0%
+the sleekness of cars increase affects
+ 
+
+ align:start position:0%
+the sleekness of cars increase affects
+increase sales or something like that I
+
+ align:start position:0%
+increase sales or something like that I
+ 
+
+ align:start position:0%
+increase sales or something like that I
+don't know
+
+ align:start position:0%
+don't know
+ 
+
+ align:start position:0%
+don't know
+um okay anyway so his hypothesis is that
+
+ align:start position:0%
+um okay anyway so his hypothesis is that
+ 
+
+ align:start position:0%
+um okay anyway so his hypothesis is that
+this was called caused by a breakdown
+
+ align:start position:0%
+this was called caused by a breakdown
+ 
+
+ align:start position:0%
+this was called caused by a breakdown
+and collusion among the big three
+
+ align:start position:0%
+and collusion among the big three
+ 
+
+ align:start position:0%
+and collusion among the big three
+um you know in general if you're writing
+
+ align:start position:0%
+um you know in general if you're writing
+ 
+
+ align:start position:0%
+um you know in general if you're writing
+an you know like there are several types
+
+ align:start position:0%
+an you know like there are several types
+ 
+
+ align:start position:0%
+an you know like there are several types
+of paper empirical papers one can write
+
+ align:start position:0%
+of paper empirical papers one can write
+ 
+
+ align:start position:0%
+of paper empirical papers one can write
+if you're writing a here's a fact I have
+
+ align:start position:0%
+if you're writing a here's a fact I have
+ 
+
+ align:start position:0%
+if you're writing a here's a fact I have
+an explanation for that fact um
+
+ align:start position:0%
+an explanation for that fact um
+ 
+
+ align:start position:0%
+an explanation for that fact um
+generally you know if you or if the fact
+
+ align:start position:0%
+generally you know if you or if the fact
+ 
+
+ align:start position:0%
+generally you know if you or if the fact
+is well known and you're proposing an
+
+ align:start position:0%
+is well known and you're proposing an
+ 
+
+ align:start position:0%
+is well known and you're proposing an
+explanation for it there are a thousand
+
+ align:start position:0%
+explanation for it there are a thousand
+ 
+
+ align:start position:0%
+explanation for it there are a thousand
+explanations for any fact you can come
+
+ align:start position:0%
+explanations for any fact you can come
+ 
+
+ align:start position:0%
+explanations for any fact you can come
+up with so generally the way you try to
+
+ align:start position:0%
+up with so generally the way you try to
+ 
+
+ align:start position:0%
+up with so generally the way you try to
+make the case that your explanation is
+
+ align:start position:0%
+make the case that your explanation is
+ 
+
+ align:start position:0%
+make the case that your explanation is
+correct and convincing is to think of a
+
+ align:start position:0%
+correct and convincing is to think of a
+ 
+
+ align:start position:0%
+correct and convincing is to think of a
+lot of other predictions that go along
+
+ align:start position:0%
+lot of other predictions that go along
+ 
+
+ align:start position:0%
+lot of other predictions that go along
+with your explanation that people
+
+ align:start position:0%
+with your explanation that people
+ 
+
+ align:start position:0%
+with your explanation that people
+haven't talked about yet and then show
+
+ align:start position:0%
+haven't talked about yet and then show
+ 
+
+ align:start position:0%
+haven't talked about yet and then show
+that here's a bunch of other
+
+ align:start position:0%
+that here's a bunch of other
+ 
+
+ align:start position:0%
+that here's a bunch of other
+implications of my theory now I'm going
+
+ align:start position:0%
+implications of my theory now I'm going
+ 
+
+ align:start position:0%
+implications of my theory now I'm going
+to look at the data in more detail and
+
+ align:start position:0%
+to look at the data in more detail and
+ 
+
+ align:start position:0%
+to look at the data in more detail and
+to these other implications in my theory
+
+ align:start position:0%
+to these other implications in my theory
+ 
+
+ align:start position:0%
+to these other implications in my theory
+are true as well okay um and that's what
+
+ align:start position:0%
+are true as well okay um and that's what
+ 
+
+ align:start position:0%
+are true as well okay um and that's what
+breaston Han is trying to do and his
+
+ align:start position:0%
+breaston Han is trying to do and his
+ 
+
+ align:start position:0%
+breaston Han is trying to do and his
+idea is that you know motivated by the
+
+ align:start position:0%
+idea is that you know motivated by the
+ 
+
+ align:start position:0%
+idea is that you know motivated by the
+then recent literature on differentiated
+
+ align:start position:0%
+then recent literature on differentiated
+ 
+
+ align:start position:0%
+then recent literature on differentiated
+product competition was that if there
+
+ align:start position:0%
+product competition was that if there
+ 
+
+ align:start position:0%
+product competition was that if there
+was a shift from from collusion to
+
+ align:start position:0%
+was a shift from from collusion to
+ 
+
+ align:start position:0%
+was a shift from from collusion to
+competition it ought to have a different
+
+ align:start position:0%
+competition it ought to have a different
+ 
+
+ align:start position:0%
+competition it ought to have a different
+effect on different car models in
+
+ align:start position:0%
+effect on different car models in
+ 
+
+ align:start position:0%
+effect on different car models in
+particular car models that were close in
+
+ align:start position:0%
+particular car models that were close in
+ 
+
+ align:start position:0%
+particular car models that were close in
+product space to other car models uh
+
+ align:start position:0%
+product space to other car models uh
+ 
+
+ align:start position:0%
+product space to other car models uh
+would see a much bigger drop in price
+
+ align:start position:0%
+would see a much bigger drop in price
+ 
+
+ align:start position:0%
+would see a much bigger drop in price
+than car models that were very
+
+ align:start position:0%
+than car models that were very
+ 
+
+ align:start position:0%
+than car models that were very
+distinctive so like on my previous slide
+
+ align:start position:0%
+distinctive so like on my previous slide
+ 
+
+ align:start position:0%
+distinctive so like on my previous slide
+um you know you can see the Ford
+
+ align:start position:0%
+um you know you can see the Ford
+ 
+
+ align:start position:0%
+um you know you can see the Ford
+Thunderbird it was an original car it it
+
+ align:start position:0%
+Thunderbird it was an original car it it
+ 
+
+ align:start position:0%
+Thunderbird it was an original car it it
+looks very different from those other
+
+ align:start position:0%
+looks very different from those other
+ 
+
+ align:start position:0%
+looks very different from those other
+cars maybe if you're colluding or in
+
+ align:start position:0%
+cars maybe if you're colluding or in
+ 
+
+ align:start position:0%
+cars maybe if you're colluding or in
+competition it doesn't matter so much
+
+ align:start position:0%
+competition it doesn't matter so much
+ 
+
+ align:start position:0%
+competition it doesn't matter so much
+for the price of the Ford Thunderbird
+
+ align:start position:0%
+for the price of the Ford Thunderbird
+ 
+
+ align:start position:0%
+for the price of the Ford Thunderbird
+you can sort of you still have a lot of
+
+ align:start position:0%
+you can sort of you still have a lot of
+ 
+
+ align:start position:0%
+you can sort of you still have a lot of
+Market power but at least to my mind if
+
+ align:start position:0%
+Market power but at least to my mind if
+ 
+
+ align:start position:0%
+Market power but at least to my mind if
+if you're looking at the Mercury
+
+ align:start position:0%
+if you're looking at the Mercury
+ 
+
+ align:start position:0%
+if you're looking at the Mercury
+Monclair versus the Chevy
+
+ align:start position:0%
+Monclair versus the Chevy
+ 
+
+ align:start position:0%
+Monclair versus the Chevy
+belir you know I would have to spend
+
+ align:start position:0%
+belir you know I would have to spend
+ 
+
+ align:start position:0%
+belir you know I would have to spend
+some time learning to recognize the
+
+ align:start position:0%
+some time learning to recognize the
+ 
+
+ align:start position:0%
+some time learning to recognize the
+difference between those two if you were
+
+ align:start position:0%
+difference between those two if you were
+ 
+
+ align:start position:0%
+difference between those two if you were
+sort of showing the pictures of them and
+
+ align:start position:0%
+sort of showing the pictures of them and
+ 
+
+ align:start position:0%
+sort of showing the pictures of them and
+so you might think if there was berran
+
+ align:start position:0%
+so you might think if there was berran
+ 
+
+ align:start position:0%
+so you might think if there was berran
+competition between Mercury and Chevy
+
+ align:start position:0%
+competition between Mercury and Chevy
+ 
+
+ align:start position:0%
+competition between Mercury and Chevy
+the price of the B and the Montclair uh
+
+ align:start position:0%
+the price of the B and the Montclair uh
+ 
+
+ align:start position:0%
+the price of the B and the Montclair uh
+they could get in very tough competition
+
+ align:start position:0%
+they could get in very tough competition
+ 
+
+ align:start position:0%
+they could get in very tough competition
+and drive uh prices down towards cost
+
+ align:start position:0%
+and drive uh prices down towards cost
+ 
+
+ align:start position:0%
+and drive uh prices down towards cost
+okay um so just you know breast and hand
+
+ align:start position:0%
+okay um so just you know breast and hand
+ 
+
+ align:start position:0%
+okay um so just you know breast and hand
+has these sort of pictures illustrating
+
+ align:start position:0%
+has these sort of pictures illustrating
+ 
+
+ align:start position:0%
+has these sort of pictures illustrating
+this he sort of supposes that you know
+
+ align:start position:0%
+this he sort of supposes that you know
+ 
+
+ align:start position:0%
+this he sort of supposes that you know
+suppose that this was just a pure
+
+ align:start position:0%
+suppose that this was just a pure
+ 
+
+ align:start position:0%
+suppose that this was just a pure
+one-dimensional vertical competition
+
+ align:start position:0%
+one-dimensional vertical competition
+ 
+
+ align:start position:0%
+one-dimensional vertical competition
+model like I described last time so we
+
+ align:start position:0%
+model like I described last time so we
+ 
+
+ align:start position:0%
+model like I described last time so we
+put quality on the x axis uh the solid
+
+ align:start position:0%
+put quality on the x axis uh the solid
+ 
+
+ align:start position:0%
+put quality on the x axis uh the solid
+line is supposed to represent cost and
+
+ align:start position:0%
+line is supposed to represent cost and
+ 
+
+ align:start position:0%
+line is supposed to represent cost and
+then these are the prices of the
+
+ align:start position:0%
+then these are the prices of the
+ 
+
+ align:start position:0%
+then these are the prices of the
+different car models where General
+
+ align:start position:0%
+different car models where General
+ 
+
+ align:start position:0%
+different car models where General
+Motors and Ford are the two firms
+
+ align:start position:0%
+Motors and Ford are the two firms
+ 
+
+ align:start position:0%
+Motors and Ford are the two firms
+producing them and it it is true that
+
+ align:start position:0%
+producing them and it it is true that
+ 
+
+ align:start position:0%
+producing them and it it is true that
+generally General Motors tend to produce
+
+ align:start position:0%
+generally General Motors tend to produce
+ 
+
+ align:start position:0%
+generally General Motors tend to produce
+the bigger cars and Ford tended to
+
+ align:start position:0%
+the bigger cars and Ford tended to
+ 
+
+ align:start position:0%
+the bigger cars and Ford tended to
+produce the smaller cars so GM sort of
+
+ align:start position:0%
+produce the smaller cars so GM sort of
+ 
+
+ align:start position:0%
+produce the smaller cars so GM sort of
+with its Cadillac division had a lot of
+
+ align:start position:0%
+with its Cadillac division had a lot of
+ 
+
+ align:start position:0%
+with its Cadillac division had a lot of
+the upper end of the quality Spectrum
+
+ align:start position:0%
+the upper end of the quality Spectrum
+ 
+
+ align:start position:0%
+the upper end of the quality Spectrum
+more to itself
+
+ align:start position:0%
+more to itself
+ 
+
+ align:start position:0%
+more to itself
+okay and what he says is that you know
+
+ align:start position:0%
+okay and what he says is that you know
+ 
+
+ align:start position:0%
+okay and what he says is that you know
+in this vertical differentiation model
+
+ align:start position:0%
+in this vertical differentiation model
+ 
+
+ align:start position:0%
+in this vertical differentiation model
+if you have models that are relatively
+
+ align:start position:0%
+if you have models that are relatively
+ 
+
+ align:start position:0%
+if you have models that are relatively
+far apart like models 4 and five if you
+
+ align:start position:0%
+far apart like models 4 and five if you
+ 
+
+ align:start position:0%
+far apart like models 4 and five if you
+view these as very different in quality
+
+ align:start position:0%
+view these as very different in quality
+ 
+
+ align:start position:0%
+view these as very different in quality
+space then if you're if these are the
+
+ align:start position:0%
+space then if you're if these are the
+ 
+
+ align:start position:0%
+space then if you're if these are the
+collusive prices and they start
+
+ align:start position:0%
+collusive prices and they start
+ 
+
+ align:start position:0%
+collusive prices and they start
+competing with each other it may be that
+
+ align:start position:0%
+competing with each other it may be that
+ 
+
+ align:start position:0%
+competing with each other it may be that
+prices for four and five don't drop very
+
+ align:start position:0%
+prices for four and five don't drop very
+ 
+
+ align:start position:0%
+prices for four and five don't drop very
+very much because they're still far
+
+ align:start position:0%
+very much because they're still far
+ 
+
+ align:start position:0%
+very much because they're still far
+enough apart that the they you know the
+
+ align:start position:0%
+enough apart that the they you know the
+ 
+
+ align:start position:0%
+enough apart that the they you know the
+marginal consumers are small relative to
+
+ align:start position:0%
+marginal consumers are small relative to
+ 
+
+ align:start position:0%
+marginal consumers are small relative to
+Total demand so you don't do much to try
+
+ align:start position:0%
+Total demand so you don't do much to try
+ 
+
+ align:start position:0%
+Total demand so you don't do much to try
+to attract more marginal
+
+ align:start position:0%
+to attract more marginal
+ 
+
+ align:start position:0%
+to attract more marginal
+consumers um but on the other hand if
+
+ align:start position:0%
+consumers um but on the other hand if
+ 
+
+ align:start position:0%
+consumers um but on the other hand if
+you look at models two and three that
+
+ align:start position:0%
+you look at models two and three that
+ 
+
+ align:start position:0%
+you look at models two and three that
+are very similar um so this could be my
+
+ align:start position:0%
+are very similar um so this could be my
+ 
+
+ align:start position:0%
+are very similar um so this could be my
+Belair and
+
+ align:start position:0%
+Belair and
+ 
+
+ align:start position:0%
+Belair and
+Montclair if they're colluding they may
+
+ align:start position:0%
+Montclair if they're colluding they may
+ 
+
+ align:start position:0%
+Montclair if they're colluding they may
+charge fairly high
+
+ align:start position:0%
+charge fairly high
+ 
+
+ align:start position:0%
+charge fairly high
+prices and then if they start competing
+
+ align:start position:0%
+prices and then if they start competing
+ 
+
+ align:start position:0%
+prices and then if they start competing
+with each other prices may get driven
+
+ align:start position:0%
+with each other prices may get driven
+ 
+
+ align:start position:0%
+with each other prices may get driven
+very low because they're very close in
+
+ align:start position:0%
+very low because they're very close in
+ 
+
+ align:start position:0%
+very low because they're very close in
+product space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know so if you had that as an
+
+ align:start position:0%
+and you know so if you had that as an
+ 
+
+ align:start position:0%
+and you know so if you had that as an
+idea and you thought about how you could
+
+ align:start position:0%
+idea and you thought about how you could
+ 
+
+ align:start position:0%
+idea and you thought about how you could
+test that you know breaston hand could
+
+ align:start position:0%
+test that you know breaston hand could
+ 
+
+ align:start position:0%
+test that you know breaston hand could
+have taken this sort of what I'd call
+
+ align:start position:0%
+have taken this sort of what I'd call
+ 
+
+ align:start position:0%
+have taken this sort of what I'd call
+the classic reduced form approach in IO
+
+ align:start position:0%
+the classic reduced form approach in IO
+ 
+
+ align:start position:0%
+the classic reduced form approach in IO
+which is you make predictions you test
+
+ align:start position:0%
+which is you make predictions you test
+ 
+
+ align:start position:0%
+which is you make predictions you test
+the predictions and so what you could
+
+ align:start position:0%
+the predictions and so what you could
+ 
+
+ align:start position:0%
+the predictions and so what you could
+have looked for is you know our price
+
+ align:start position:0%
+have looked for is you know our price
+ 
+
+ align:start position:0%
+have looked for is you know our price
+drops from 1954 to
+
+ align:start position:0%
+drops from 1954 to
+ 
+
+ align:start position:0%
+drops from 1954 to
+1955 larger for car models that are
+
+ align:start position:0%
+1955 larger for car models that are
+ 
+
+ align:start position:0%
+1955 larger for car models that are
+closer in product space and that would
+
+ align:start position:0%
+closer in product space and that would
+ 
+
+ align:start position:0%
+closer in product space and that would
+be sort of an auxil prediction of a
+
+ align:start position:0%
+be sort of an auxil prediction of a
+ 
+
+ align:start position:0%
+be sort of an auxil prediction of a
+breakdown in
+
+ align:start position:0%
+breakdown in
+ 
+
+ align:start position:0%
+breakdown in
+collusion um but you know breast andan
+
+ align:start position:0%
+collusion um but you know breast andan
+ 
+
+ align:start position:0%
+collusion um but you know breast andan
+thought that you know this is really not
+
+ align:start position:0%
+thought that you know this is really not
+ 
+
+ align:start position:0%
+thought that you know this is really not
+all you could do with that theory you
+
+ align:start position:0%
+all you could do with that theory you
+ 
+
+ align:start position:0%
+all you could do with that theory you
+know the one thing is that the theory is
+
+ align:start position:0%
+know the one thing is that the theory is
+ 
+
+ align:start position:0%
+know the one thing is that the theory is
+more complicated than that you know like
+
+ align:start position:0%
+more complicated than that you know like
+ 
+
+ align:start position:0%
+more complicated than that you know like
+if if you remember the sort of vertical
+
+ align:start position:0%
+if if you remember the sort of vertical
+ 
+
+ align:start position:0%
+if if you remember the sort of vertical
+competition model every firm does have a
+
+ align:start position:0%
+competition model every firm does have a
+ 
+
+ align:start position:0%
+competition model every firm does have a
+first order condition that's pinned out
+
+ align:start position:0%
+first order condition that's pinned out
+ 
+
+ align:start position:0%
+first order condition that's pinned out
+to the firm above and to the firm below
+
+ align:start position:0%
+to the firm above and to the firm below
+ 
+
+ align:start position:0%
+to the firm above and to the firm below
+and those two first order conditions are
+
+ align:start position:0%
+and those two first order conditions are
+ 
+
+ align:start position:0%
+and those two first order conditions are
+going to pin down the prices but those
+
+ align:start position:0%
+going to pin down the prices but those
+ 
+
+ align:start position:0%
+going to pin down the prices but those
+things are going to involve the prices
+
+ align:start position:0%
+things are going to involve the prices
+ 
+
+ align:start position:0%
+things are going to involve the prices
+of the low next low lower quality model
+
+ align:start position:0%
+of the low next low lower quality model
+ 
+
+ align:start position:0%
+of the low next low lower quality model
+and the lower model below that and the
+
+ align:start position:0%
+and the lower model below that and the
+ 
+
+ align:start position:0%
+and the lower model below that and the
+model below that and so it is a system
+
+ align:start position:0%
+model below that and so it is a system
+ 
+
+ align:start position:0%
+model below that and so it is a system
+of n equations and N unknowns and any
+
+ align:start position:0%
+of n equations and N unknowns and any
+ 
+
+ align:start position:0%
+of n equations and N unknowns and any
+change in the competition you know like
+
+ align:start position:0%
+change in the competition you know like
+ 
+
+ align:start position:0%
+change in the competition you know like
+the change any in any one place is going
+
+ align:start position:0%
+the change any in any one place is going
+ 
+
+ align:start position:0%
+the change any in any one place is going
+to have Ripple effects throughout the
+
+ align:start position:0%
+to have Ripple effects throughout the
+ 
+
+ align:start position:0%
+to have Ripple effects throughout the
+distribution and will change the prices
+
+ align:start position:0%
+distribution and will change the prices
+ 
+
+ align:start position:0%
+distribution and will change the prices
+of the higher price models even if
+
+ align:start position:0%
+of the higher price models even if
+ 
+
+ align:start position:0%
+of the higher price models even if
+they're not in very close competition um
+
+ align:start position:0%
+they're not in very close competition um
+ 
+
+ align:start position:0%
+they're not in very close competition um
+and then the other thing that Brean said
+
+ align:start position:0%
+and then the other thing that Brean said
+ 
+
+ align:start position:0%
+and then the other thing that Brean said
+is that you know our theories are
+
+ align:start position:0%
+is that you know our theories are
+ 
+
+ align:start position:0%
+is that you know our theories are
+quantitative theories not just
+
+ align:start position:0%
+quantitative theories not just
+ 
+
+ align:start position:0%
+quantitative theories not just
+qualitative theories they don't just
+
+ align:start position:0%
+qualitative theories they don't just
+ 
+
+ align:start position:0%
+qualitative theories they don't just
+predict that prices will go down they
+
+ align:start position:0%
+predict that prices will go down they
+ 
+
+ align:start position:0%
+predict that prices will go down they
+really are predicting how much the
+
+ align:start position:0%
+really are predicting how much the
+ 
+
+ align:start position:0%
+really are predicting how much the
+prices would go down and how much the
+
+ align:start position:0%
+prices would go down and how much the
+ 
+
+ align:start position:0%
+prices would go down and how much the
+prices would go down depend on things
+
+ align:start position:0%
+prices would go down depend on things
+ 
+
+ align:start position:0%
+prices would go down depend on things
+that we in theory could measure uh and
+
+ align:start position:0%
+that we in theory could measure uh and
+ 
+
+ align:start position:0%
+that we in theory could measure uh and
+so really to give a more complete test
+
+ align:start position:0%
+so really to give a more complete test
+ 
+
+ align:start position:0%
+so really to give a more complete test
+of the theory we should really see
+
+ align:start position:0%
+of the theory we should really see
+ 
+
+ align:start position:0%
+of the theory we should really see
+whether the theory can qual can
+
+ align:start position:0%
+whether the theory can qual can
+ 
+
+ align:start position:0%
+whether the theory can qual can
+quantitatively amount account for
+
+ align:start position:0%
+quantitatively amount account for
+ 
+
+ align:start position:0%
+quantitatively amount account for
+everything instead of just qualitatively
+
+ align:start position:0%
+everything instead of just qualitatively
+ 
+
+ align:start position:0%
+everything instead of just qualitatively
+account for everything um so what did
+
+ align:start position:0%
+account for everything um so what did
+ 
+
+ align:start position:0%
+account for everything um so what did
+breast andan do and this is where the
+
+ align:start position:0%
+breast andan do and this is where the
+ 
+
+ align:start position:0%
+breast andan do and this is where the
+paper starts to look awfully primitive
+
+ align:start position:0%
+paper starts to look awfully primitive
+ 
+
+ align:start position:0%
+paper starts to look awfully primitive
+these days um you know he he basically
+
+ align:start position:0%
+these days um you know he he basically
+ 
+
+ align:start position:0%
+these days um you know he he basically
+wrote down the standard vertical
+
+ align:start position:0%
+wrote down the standard vertical
+ 
+
+ align:start position:0%
+wrote down the standard vertical
+differentiation model that I Des cried
+
+ align:start position:0%
+differentiation model that I Des cried
+ 
+
+ align:start position:0%
+differentiation model that I Des cried
+in lecture um so Suppose there are n
+
+ align:start position:0%
+in lecture um so Suppose there are n
+ 
+
+ align:start position:0%
+in lecture um so Suppose there are n
+models with qualities V1 through
+
+ align:start position:0%
+models with qualities V1 through
+ 
+
+ align:start position:0%
+models with qualities V1 through
+VN and suppose that the quality of a car
+
+ align:start position:0%
+VN and suppose that the quality of a car
+ 
+
+ align:start position:0%
+VN and suppose that the quality of a car
+is simply a function of observable
+
+ align:start position:0%
+is simply a function of observable
+ 
+
+ align:start position:0%
+is simply a function of observable
+characteristics uh what function of
+
+ align:start position:0%
+characteristics uh what function of
+ 
+
+ align:start position:0%
+characteristics uh what function of
+observable characteristics you know
+
+ align:start position:0%
+observable characteristics you know
+ 
+
+ align:start position:0%
+observable characteristics you know
+basically it's just x * square root of x
+
+ align:start position:0%
+basically it's just x * square root of x
+ 
+
+ align:start position:0%
+basically it's just x * square root of x
+x beta uh where X would contain things
+
+ align:start position:0%
+x beta uh where X would contain things
+ 
+
+ align:start position:0%
+x beta uh where X would contain things
+like uh the horsepower of the car
+
+ align:start position:0%
+like uh the horsepower of the car
+ 
+
+ align:start position:0%
+like uh the horsepower of the car
+whether it had a V8 engine the size in
+
+ align:start position:0%
+whether it had a V8 engine the size in
+ 
+
+ align:start position:0%
+whether it had a V8 engine the size in
+cubic inches the weight of the car
+
+ align:start position:0%
+cubic inches the weight of the car
+ 
+
+ align:start position:0%
+cubic inches the weight of the car
+whether head air conditioning things
+
+ align:start position:0%
+whether head air conditioning things
+ 
+
+ align:start position:0%
+whether head air conditioning things
+like that um he then assumes that
+
+ align:start position:0%
+like that um he then assumes that
+ 
+
+ align:start position:0%
+like that um he then assumes that
+there's again just like in the vertical
+
+ align:start position:0%
+there's again just like in the vertical
+ 
+
+ align:start position:0%
+there's again just like in the vertical
+differentiation model uh there's a mass
+
+ align:start position:0%
+differentiation model uh there's a mass
+ 
+
+ align:start position:0%
+differentiation model uh there's a mass
+of consumers with types Theta
+
+ align:start position:0%
+of consumers with types Theta
+ 
+
+ align:start position:0%
+of consumers with types Theta
+distributed uniform on some interval 0
+
+ align:start position:0%
+distributed uniform on some interval 0
+ 
+
+ align:start position:0%
+distributed uniform on some interval 0
+to Vmax and there's a density Delta on
+
+ align:start position:0%
+to Vmax and there's a density Delta on
+ 
+
+ align:start position:0%
+to Vmax and there's a density Delta on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+interval and then he says that the
+
+ align:start position:0%
+interval and then he says that the
+ 
+
+ align:start position:0%
+interval and then he says that the
+utility of a type Theta consumer from
+
+ align:start position:0%
+utility of a type Theta consumer from
+ 
+
+ align:start position:0%
+utility of a type Theta consumer from
+buying model I is going to be Theta VI
+
+ align:start position:0%
+buying model I is going to be Theta VI
+ 
+
+ align:start position:0%
+buying model I is going to be Theta VI
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+Pi so pure vertical model uh and then he
+
+ align:start position:0%
+Pi so pure vertical model uh and then he
+ 
+
+ align:start position:0%
+Pi so pure vertical model uh and then he
+has the cost of producing Q units at
+
+ align:start position:0%
+has the cost of producing Q units at
+ 
+
+ align:start position:0%
+has the cost of producing Q units at
+quality V is uh some constant that's or
+
+ align:start position:0%
+quality V is uh some constant that's or
+ 
+
+ align:start position:0%
+quality V is uh some constant that's or
+some function of v that's going to end
+
+ align:start position:0%
+some function of v that's going to end
+ 
+
+ align:start position:0%
+some function of v that's going to end
+up being irrelevant and then Q mu e to
+
+ align:start position:0%
+up being irrelevant and then Q mu e to
+ 
+
+ align:start position:0%
+up being irrelevant and then Q mu e to
+the V power so you know costs you again
+
+ align:start position:0%
+the V power so you know costs you again
+ 
+
+ align:start position:0%
+the V power so you know costs you again
+you know V somehow is like the square
+
+ align:start position:0%
+you know V somehow is like the square
+ 
+
+ align:start position:0%
+you know V somehow is like the square
+root of the observable variables and
+
+ align:start position:0%
+root of the observable variables and
+ 
+
+ align:start position:0%
+root of the observable variables and
+then costs are exponentially increasing
+
+ align:start position:0%
+then costs are exponentially increasing
+ 
+
+ align:start position:0%
+then costs are exponentially increasing
+in v as you try to raise quality uh and
+
+ align:start position:0%
+in v as you try to raise quality uh and
+ 
+
+ align:start position:0%
+in v as you try to raise quality uh and
+then there there is just it's a constant
+
+ align:start position:0%
+then there there is just it's a constant
+ 
+
+ align:start position:0%
+then there there is just it's a constant
+marginal cost so mu time e to the V is
+
+ align:start position:0%
+marginal cost so mu time e to the V is
+ 
+
+ align:start position:0%
+marginal cost so mu time e to the V is
+the is the marginal cost of producing a
+
+ align:start position:0%
+the is the marginal cost of producing a
+ 
+
+ align:start position:0%
+the is the marginal cost of producing a
+single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+car okay but then sort of what you know
+
+ align:start position:0%
+car okay but then sort of what you know
+ 
+
+ align:start position:0%
+car okay but then sort of what you know
+breast hand's thought was is that you
+
+ align:start position:0%
+breast hand's thought was is that you
+ 
+
+ align:start position:0%
+breast hand's thought was is that you
+know this is a model that I can fully
+
+ align:start position:0%
+know this is a model that I can fully
+ 
+
+ align:start position:0%
+know this is a model that I can fully
+specify and if you fully specify the
+
+ align:start position:0%
+specify and if you fully specify the
+ 
+
+ align:start position:0%
+specify and if you fully specify the
+prim you if you fully specify The
+
+ align:start position:0%
+prim you if you fully specify The
+ 
+
+ align:start position:0%
+prim you if you fully specify The
+Primitives which is um you know the
+
+ align:start position:0%
+Primitives which is um you know the
+ 
+
+ align:start position:0%
+Primitives which is um you know the
+production functions of the firms the uh
+
+ align:start position:0%
+production functions of the firms the uh
+ 
+
+ align:start position:0%
+production functions of the firms the uh
+preferences of the consumers and the
+
+ align:start position:0%
+preferences of the consumers and the
+ 
+
+ align:start position:0%
+preferences of the consumers and the
+model of firm
+
+ align:start position:0%
+model of firm
+ 
+
+ align:start position:0%
+model of firm
+Behavior then you can fully predict
+
+ align:start position:0%
+Behavior then you can fully predict
+ 
+
+ align:start position:0%
+Behavior then you can fully predict
+what's going to happen so you sort of
+
+ align:start position:0%
+what's going to happen so you sort of
+ 
+
+ align:start position:0%
+what's going to happen so you sort of
+basically once once you fix the
+
+ align:start position:0%
+basically once once you fix the
+ 
+
+ align:start position:0%
+basically once once you fix the
+parameters beta mu in the production
+
+ align:start position:0%
+parameters beta mu in the production
+ 
+
+ align:start position:0%
+parameters beta mu in the production
+function and Delta in Vmax in the um
+
+ align:start position:0%
+function and Delta in Vmax in the um
+ 
+
+ align:start position:0%
+function and Delta in Vmax in the um
+consumer preferences you can fully
+
+ align:start position:0%
+consumer preferences you can fully
+ 
+
+ align:start position:0%
+consumer preferences you can fully
+predict what's going to happen under any
+
+ align:start position:0%
+predict what's going to happen under any
+ 
+
+ align:start position:0%
+predict what's going to happen under any
+model of behavior and so in particular
+
+ align:start position:0%
+model of behavior and so in particular
+ 
+
+ align:start position:0%
+model of behavior and so in particular
+like you know collusive pricing just
+
+ align:start position:0%
+like you know collusive pricing just
+ 
+
+ align:start position:0%
+like you know collusive pricing just
+becomes the multi-product Monopoly model
+
+ align:start position:0%
+becomes the multi-product Monopoly model
+ 
+
+ align:start position:0%
+becomes the multi-product Monopoly model
+that we covered um static competition
+
+ align:start position:0%
+that we covered um static competition
+ 
+
+ align:start position:0%
+that we covered um static competition
+would be another natural model know
+
+ align:start position:0%
+would be another natural model know
+ 
+
+ align:start position:0%
+would be another natural model know
+would people often apply to a situation
+
+ align:start position:0%
+would people often apply to a situation
+ 
+
+ align:start position:0%
+would people often apply to a situation
+like this um and then breast Nan also
+
+ align:start position:0%
+like this um and then breast Nan also
+ 
+
+ align:start position:0%
+like this um and then breast Nan also
+considers two other models um one of
+
+ align:start position:0%
+considers two other models um one of
+ 
+
+ align:start position:0%
+considers two other models um one of
+these is like
+
+ align:start position:0%
+these is like
+ 
+
+ align:start position:0%
+these is like
+you know non-cooperative static
+
+ align:start position:0%
+you know non-cooperative static
+ 
+
+ align:start position:0%
+you know non-cooperative static
+competition between all products so this
+
+ align:start position:0%
+competition between all products so this
+ 
+
+ align:start position:0%
+competition between all products so this
+is as if every Ford Model is run by a
+
+ align:start position:0%
+is as if every Ford Model is run by a
+ 
+
+ align:start position:0%
+is as if every Ford Model is run by a
+different manager who's competing
+
+ align:start position:0%
+different manager who's competing
+ 
+
+ align:start position:0%
+different manager who's competing
+aggressively against every other Ford
+
+ align:start position:0%
+aggressively against every other Ford
+ 
+
+ align:start position:0%
+aggressively against every other Ford
+product so every product in the model in
+
+ align:start position:0%
+product so every product in the model in
+ 
+
+ align:start position:0%
+product so every product in the model in
+the in the market is run by a different
+
+ align:start position:0%
+the in the market is run by a different
+ 
+
+ align:start position:0%
+the in the market is run by a different
+manager who's not who's profit
+
+ align:start position:0%
+manager who's not who's profit
+ 
+
+ align:start position:0%
+manager who's not who's profit
+maximizing solely based on that car and
+
+ align:start position:0%
+maximizing solely based on that car and
+ 
+
+ align:start position:0%
+maximizing solely based on that car and
+then he's got a fourth one you know this
+
+ align:start position:0%
+then he's got a fourth one you know this
+ 
+
+ align:start position:0%
+then he's got a fourth one you know this
+is one of those ones where it's based on
+
+ align:start position:0%
+is one of those ones where it's based on
+ 
+
+ align:start position:0%
+is one of those ones where it's based on
+somebody's paper from the 1970s and I
+
+ align:start position:0%
+somebody's paper from the 1970s and I
+ 
+
+ align:start position:0%
+somebody's paper from the 1970s and I
+have a hard time it's sort of perfect
+
+ align:start position:0%
+have a hard time it's sort of perfect
+ 
+
+ align:start position:0%
+have a hard time it's sort of perfect
+competition you have a hard time making
+
+ align:start position:0%
+competition you have a hard time making
+ 
+
+ align:start position:0%
+competition you have a hard time making
+out today what is that model and what
+
+ align:start position:0%
+out today what is that model and what
+ 
+
+ align:start position:0%
+out today what is that model and what
+would be the justification for it but
+
+ align:start position:0%
+would be the justification for it but
+ 
+
+ align:start position:0%
+would be the justification for it but
+he's got four different models he notes
+
+ align:start position:0%
+he's got four different models he notes
+ 
+
+ align:start position:0%
+he's got four different models he notes
+that under any of those four models you
+
+ align:start position:0%
+that under any of those four models you
+ 
+
+ align:start position:0%
+that under any of those four models you
+can work out what should happen given
+
+ align:start position:0%
+can work out what should happen given
+ 
+
+ align:start position:0%
+can work out what should happen given
+any set of parameters so then you can
+
+ align:start position:0%
+any set of parameters so then you can
+ 
+
+ align:start position:0%
+any set of parameters so then you can
+invert that relationship and say you
+
+ align:start position:0%
+invert that relationship and say you
+ 
+
+ align:start position:0%
+invert that relationship and say you
+know given any one of these models and
+
+ align:start position:0%
+know given any one of these models and
+ 
+
+ align:start position:0%
+know given any one of these models and
+one of these models applied to any in
+
+ align:start position:0%
+one of these models applied to any in
+ 
+
+ align:start position:0%
+one of these models applied to any in
+for any of any behavioral model in any
+
+ align:start position:0%
+for any of any behavioral model in any
+ 
+
+ align:start position:0%
+for any of any behavioral model in any
+year 1954 55 or 56 I can figure out what
+
+ align:start position:0%
+year 1954 55 or 56 I can figure out what
+ 
+
+ align:start position:0%
+year 1954 55 or 56 I can figure out what
+would be the parameters that best
+
+ align:start position:0%
+would be the parameters that best
+ 
+
+ align:start position:0%
+would be the parameters that best
+explain the data and then breast Nan's
+
+ align:start position:0%
+explain the data and then breast Nan's
+ 
+
+ align:start position:0%
+explain the data and then breast Nan's
+idea was for each model of firm behavior
+
+ align:start position:0%
+idea was for each model of firm behavior
+ 
+
+ align:start position:0%
+idea was for each model of firm behavior
+in each year I figure out what
+
+ align:start position:0%
+in each year I figure out what
+ 
+
+ align:start position:0%
+in each year I figure out what
+parameters best explain the data and
+
+ align:start position:0%
+parameters best explain the data and
+ 
+
+ align:start position:0%
+parameters best explain the data and
+then ask how well does that model
+
+ align:start position:0%
+then ask how well does that model
+ 
+
+ align:start position:0%
+then ask how well does that model
+explain the data with those parameters
+
+ align:start position:0%
+explain the data with those parameters
+ 
+
+ align:start position:0%
+explain the data with those parameters
+and then I pick out whichever model fits
+
+ align:start position:0%
+and then I pick out whichever model fits
+ 
+
+ align:start position:0%
+and then I pick out whichever model fits
+best in every year um to sort of say
+
+ align:start position:0%
+best in every year um to sort of say
+ 
+
+ align:start position:0%
+best in every year um to sort of say
+this is how the firms behaved in that
+
+ align:start position:0%
+this is how the firms behaved in that
+ 
+
+ align:start position:0%
+this is how the firms behaved in that
+year okay um and the way he does this is
+
+ align:start position:0%
+year okay um and the way he does this is
+ 
+
+ align:start position:0%
+year okay um and the way he does this is
+again this seems archaic but it's a set
+
+ align:start position:0%
+again this seems archaic but it's a set
+ 
+
+ align:start position:0%
+again this seems archaic but it's a set
+of non- nested hypotheses hypothesis
+
+ align:start position:0%
+of non- nested hypotheses hypothesis
+ 
+
+ align:start position:0%
+of non- nested hypotheses hypothesis
+tests where he looks at how well the you
+
+ align:start position:0%
+tests where he looks at how well the you
+ 
+
+ align:start position:0%
+tests where he looks at how well the you
+know looks at the model fits the model
+
+ align:start position:0%
+know looks at the model fits the model
+ 
+
+ align:start position:0%
+know looks at the model fits the model
+to the data and then like in a
+
+ align:start position:0%
+to the data and then like in a
+ 
+
+ align:start position:0%
+to the data and then like in a
+likelihood ratio sense says do the
+
+ align:start position:0%
+likelihood ratio sense says do the
+ 
+
+ align:start position:0%
+likelihood ratio sense says do the
+predictions of the other model help
+
+ align:start position:0%
+predictions of the other model help
+ 
+
+ align:start position:0%
+predictions of the other model help
+explain the errors like do the
+
+ align:start position:0%
+explain the errors like do the
+ 
+
+ align:start position:0%
+explain the errors like do the
+predictions of model two help explain
+
+ align:start position:0%
+predictions of model two help explain
+ 
+
+ align:start position:0%
+predictions of model two help explain
+the errors in model one and if
+
+ align:start position:0%
+the errors in model one and if
+ 
+
+ align:start position:0%
+the errors in model one and if
+predictions of model two help explain
+
+ align:start position:0%
+predictions of model two help explain
+ 
+
+ align:start position:0%
+predictions of model two help explain
+the errors of model one then model one
+
+ align:start position:0%
+the errors of model one then model one
+ 
+
+ align:start position:0%
+the errors of model one then model one
+is rejected by model two and model one
+
+ align:start position:0%
+is rejected by model two and model one
+ 
+
+ align:start position:0%
+is rejected by model two and model one
+is not the correct model and so what he
+
+ align:start position:0%
+is not the correct model and so what he
+ 
+
+ align:start position:0%
+is not the correct model and so what he
+looks for is is there one of these four
+
+ align:start position:0%
+looks for is is there one of these four
+ 
+
+ align:start position:0%
+looks for is is there one of these four
+Mo in each year year by year is there
+
+ align:start position:0%
+Mo in each year year by year is there
+ 
+
+ align:start position:0%
+Mo in each year year by year is there
+one of these four models that's not
+
+ align:start position:0%
+one of these four models that's not
+ 
+
+ align:start position:0%
+one of these four models that's not
+rejected by the other
+
+ align:start position:0%
+rejected by the other
+ 
+
+ align:start position:0%
+rejected by the other
+model and then the other thing that
+
+ align:start position:0%
+model and then the other thing that
+ 
+
+ align:start position:0%
+model and then the other thing that
+brehan really also pioneered uh and this
+
+ align:start position:0%
+brehan really also pioneered uh and this
+ 
+
+ align:start position:0%
+brehan really also pioneered uh and this
+was you know paper IND thesis was the
+
+ align:start position:0%
+was you know paper IND thesis was the
+ 
+
+ align:start position:0%
+was you know paper IND thesis was the
+idea of a
+
+ align:start position:0%
+idea of a
+ 
+
+ align:start position:0%
+idea of a
+counterfactual his thought was that you
+
+ align:start position:0%
+counterfactual his thought was that you
+ 
+
+ align:start position:0%
+counterfactual his thought was that you
+know if we do this and we figure out
+
+ align:start position:0%
+know if we do this and we figure out
+ 
+
+ align:start position:0%
+know if we do this and we figure out
+what is the correct model on each year
+
+ align:start position:0%
+what is the correct model on each year
+ 
+
+ align:start position:0%
+what is the correct model on each year
+then I can do a counterfactual and
+
+ align:start position:0%
+then I can do a counterfactual and
+ 
+
+ align:start position:0%
+then I can do a counterfactual and
+predict what would have happened under
+
+ align:start position:0%
+predict what would have happened under
+ 
+
+ align:start position:0%
+predict what would have happened under
+any other model or any other government
+
+ align:start position:0%
+any other model or any other government
+ 
+
+ align:start position:0%
+any other model or any other government
+policy I could tell you what if the
+
+ align:start position:0%
+policy I could tell you what if the
+ 
+
+ align:start position:0%
+policy I could tell you what if the
+government had had a 5% sales tax on
+
+ align:start position:0%
+government had had a 5% sales tax on
+ 
+
+ align:start position:0%
+government had had a 5% sales tax on
+cars what would happen if the firms had
+
+ align:start position:0%
+cars what would happen if the firms had
+ 
+
+ align:start position:0%
+cars what would happen if the firms had
+colluded instead of comp with each other
+
+ align:start position:0%
+colluded instead of comp with each other
+ 
+
+ align:start position:0%
+colluded instead of comp with each other
+what would have happened in you know any
+
+ align:start position:0%
+what would have happened in you know any
+ 
+
+ align:start position:0%
+what would have happened in you know any
+any other thing change you can think of
+
+ align:start position:0%
+any other thing change you can think of
+ 
+
+ align:start position:0%
+any other thing change you can think of
+to the industry you can sort of predict
+
+ align:start position:0%
+to the industry you can sort of predict
+ 
+
+ align:start position:0%
+to the industry you can sort of predict
+what would have happened under his model
+
+ align:start position:0%
+what would have happened under his model
+ 
+
+ align:start position:0%
+what would have happened under his model
+and gives you the sort of counterfactual
+
+ align:start position:0%
+and gives you the sort of counterfactual
+ 
+
+ align:start position:0%
+and gives you the sort of counterfactual
+prediction
+
+ align:start position:0%
+prediction
+ 
+
+ align:start position:0%
+prediction
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+okay okay so what are the main applied
+
+ align:start position:0%
+okay okay so what are the main applied
+ 
+
+ align:start position:0%
+okay okay so what are the main applied
+results of the paper um and you know I I
+
+ align:start position:0%
+results of the paper um and you know I I
+ 
+
+ align:start position:0%
+results of the paper um and you know I I
+sort of always think that like you know
+
+ align:start position:0%
+sort of always think that like you know
+ 
+
+ align:start position:0%
+sort of always think that like you know
+some maybe someday someone will rewrite
+
+ align:start position:0%
+some maybe someday someone will rewrite
+ 
+
+ align:start position:0%
+some maybe someday someone will rewrite
+this paper you know obviously this is
+
+ align:start position:0%
+this paper you know obviously this is
+ 
+
+ align:start position:0%
+this paper you know obviously this is
+primitive data like minimal data from
+
+ align:start position:0%
+primitive data like minimal data from
+ 
+
+ align:start position:0%
+primitive data like minimal data from
+the 1950s maybe someone will rewrite
+
+ align:start position:0%
+the 1950s maybe someone will rewrite
+ 
+
+ align:start position:0%
+the 1950s maybe someone will rewrite
+this paper and sort of say from more
+
+ align:start position:0%
+this paper and sort of say from more
+ 
+
+ align:start position:0%
+this paper and sort of say from more
+modern perspective what do we think
+
+ align:start position:0%
+modern perspective what do we think
+ 
+
+ align:start position:0%
+modern perspective what do we think
+actually happened but you know what does
+
+ align:start position:0%
+actually happened but you know what does
+ 
+
+ align:start position:0%
+actually happened but you know what does
+this analysis say first one says that
+
+ align:start position:0%
+this analysis say first one says that
+ 
+
+ align:start position:0%
+this analysis say first one says that
+the you know collusive model fits the
+
+ align:start position:0%
+the you know collusive model fits the
+ 
+
+ align:start position:0%
+the you know collusive model fits the
+data best in 1954 and
+
+ align:start position:0%
+data best in 1954 and
+ 
+
+ align:start position:0%
+data best in 1954 and
+1956 and the static competition model
+
+ align:start position:0%
+1956 and the static competition model
+ 
+
+ align:start position:0%
+1956 and the static competition model
+fits the data best in
+
+ align:start position:0%
+fits the data best in
+ 
+
+ align:start position:0%
+fits the data best in
+1955 so that's his evidence for his main
+
+ align:start position:0%
+1955 so that's his evidence for his main
+ 
+
+ align:start position:0%
+1955 so that's his evidence for his main
+hypothesis that there was this breakdown
+
+ align:start position:0%
+hypothesis that there was this breakdown
+ 
+
+ align:start position:0%
+hypothesis that there was this breakdown
+inclusion and the clusive model fits the
+
+ align:start position:0%
+inclusion and the clusive model fits the
+ 
+
+ align:start position:0%
+inclusion and the clusive model fits the
+patterns best in
+
+ align:start position:0%
+patterns best in
+ 
+
+ align:start position:0%
+patterns best in
+5456 the competitive model in 55
+
+ align:start position:0%
+5456 the competitive model in 55
+ 
+
+ align:start position:0%
+5456 the competitive model in 55
+um further supporting that is you know
+
+ align:start position:0%
+um further supporting that is you know
+ 
+
+ align:start position:0%
+um further supporting that is you know
+his model has a bunch of parameters the
+
+ align:start position:0%
+his model has a bunch of parameters the
+ 
+
+ align:start position:0%
+his model has a bunch of parameters the
+MU and the Delta and the V-Max and
+
+ align:start position:0%
+MU and the Delta and the V-Max and
+ 
+
+ align:start position:0%
+MU and the Delta and the V-Max and
+especially the betas that sort of talk
+
+ align:start position:0%
+especially the betas that sort of talk
+ 
+
+ align:start position:0%
+especially the betas that sort of talk
+about the which relate to the how
+
+ align:start position:0%
+about the which relate to the how
+ 
+
+ align:start position:0%
+about the which relate to the how
+valuable is horsepower how valuable is
+
+ align:start position:0%
+valuable is horsepower how valuable is
+ 
+
+ align:start position:0%
+valuable is horsepower how valuable is
+air conditioning things like that um
+
+ align:start position:0%
+air conditioning things like that um
+ 
+
+ align:start position:0%
+air conditioning things like that um
+what he notes is that if you estimate
+
+ align:start position:0%
+what he notes is that if you estimate
+ 
+
+ align:start position:0%
+what he notes is that if you estimate
+the collusive model in 54 and 56 and
+
+ align:start position:0%
+the collusive model in 54 and 56 and
+ 
+
+ align:start position:0%
+the collusive model in 54 and 56 and
+then estimate the static competition
+
+ align:start position:0%
+then estimate the static competition
+ 
+
+ align:start position:0%
+then estimate the static competition
+model in
+
+ align:start position:0%
+model in
+ 
+
+ align:start position:0%
+model in
+55 the parameters like the betas turn
+
+ align:start position:0%
+55 the parameters like the betas turn
+ 
+
+ align:start position:0%
+55 the parameters like the betas turn
+out to be fairly similar between 54 56
+
+ align:start position:0%
+out to be fairly similar between 54 56
+ 
+
+ align:start position:0%
+out to be fairly similar between 54 56
+and 55 and that's sort of further
+
+ align:start position:0%
+and 55 and that's sort of further
+ 
+
+ align:start position:0%
+and 55 and that's sort of further
+supporting evidence that you know like
+
+ align:start position:0%
+supporting evidence that you know like
+ 
+
+ align:start position:0%
+supporting evidence that you know like
+consumer preferences towards horsepower
+
+ align:start position:0%
+consumer preferences towards horsepower
+ 
+
+ align:start position:0%
+consumer preferences towards horsepower
+should probably be fairly stable over
+
+ align:start position:0%
+should probably be fairly stable over
+ 
+
+ align:start position:0%
+should probably be fairly stable over
+time and so what he notes is that if you
+
+ align:start position:0%
+time and so what he notes is that if you
+ 
+
+ align:start position:0%
+time and so what he notes is that if you
+do this model in these two years the
+
+ align:start position:0%
+do this model in these two years the
+ 
+
+ align:start position:0%
+do this model in these two years the
+other model in 55 then the preference
+
+ align:start position:0%
+other model in 55 then the preference
+ 
+
+ align:start position:0%
+other model in 55 then the preference
+parameters are fairly similar across the
+
+ align:start position:0%
+parameters are fairly similar across the
+ 
+
+ align:start position:0%
+parameters are fairly similar across the
+years um whereas if you try to fix any
+
+ align:start position:0%
+years um whereas if you try to fix any
+ 
+
+ align:start position:0%
+years um whereas if you try to fix any
+one model and use any one model to
+
+ align:start position:0%
+one model and use any one model to
+ 
+
+ align:start position:0%
+one model and use any one model to
+explain what happens the parameters need
+
+ align:start position:0%
+explain what happens the parameters need
+ 
+
+ align:start position:0%
+explain what happens the parameters need
+to change a lot from 54 to 55 from 55 to
+
+ align:start position:0%
+to change a lot from 54 to 55 from 55 to
+ 
+
+ align:start position:0%
+to change a lot from 54 to 55 from 55 to
+56 you know in some sense you need you
+
+ align:start position:0%
+56 you know in some sense you need you
+ 
+
+ align:start position:0%
+56 you know in some sense you need you
+know prices did go down despite the fact
+
+ align:start position:0%
+know prices did go down despite the fact
+ 
+
+ align:start position:0%
+know prices did go down despite the fact
+that demand is going way up and so you
+
+ align:start position:0%
+that demand is going way up and so you
+ 
+
+ align:start position:0%
+that demand is going way up and so you
+need something to say that suddenly cars
+
+ align:start position:0%
+need something to say that suddenly cars
+ 
+
+ align:start position:0%
+need something to say that suddenly cars
+got a lot cheaper and you know cars got
+
+ align:start position:0%
+got a lot cheaper and you know cars got
+ 
+
+ align:start position:0%
+got a lot cheaper and you know cars got
+a lot cheaper to produce and people
+
+ align:start position:0%
+a lot cheaper to produce and people
+ 
+
+ align:start position:0%
+a lot cheaper to produce and people
+valued cars more than they used to Value
+
+ align:start position:0%
+valued cars more than they used to Value
+ 
+
+ align:start position:0%
+valued cars more than they used to Value
+cars during that one year whereas if you
+
+ align:start position:0%
+cars during that one year whereas if you
+ 
+
+ align:start position:0%
+cars during that one year whereas if you
+sort of uh use this change in Behavior
+
+ align:start position:0%
+sort of uh use this change in Behavior
+ 
+
+ align:start position:0%
+sort of uh use this change in Behavior
+then the parameter estimates are fairly
+
+ align:start position:0%
+then the parameter estimates are fairly
+ 
+
+ align:start position:0%
+then the parameter estimates are fairly
+stable across time and so that's
+
+ align:start position:0%
+stable across time and so that's
+ 
+
+ align:start position:0%
+stable across time and so that's
+supporting evidence
+
+ align:start position:0%
+supporting evidence
+ 
+
+ align:start position:0%
+supporting evidence
+um then what's in his counterfactual um
+
+ align:start position:0%
+um then what's in his counterfactual um
+ 
+
+ align:start position:0%
+um then what's in his counterfactual um
+the counterfactual he does is suppose
+
+ align:start position:0%
+the counterfactual he does is suppose
+ 
+
+ align:start position:0%
+the counterfactual he does is suppose
+firms had colluded in 1955 instead of
+
+ align:start position:0%
+firms had colluded in 1955 instead of
+ 
+
+ align:start position:0%
+firms had colluded in 1955 instead of
+engaging in differentiated product
+
+ align:start position:0%
+engaging in differentiated product
+ 
+
+ align:start position:0%
+engaging in differentiated product
+competition uh and what he finds is that
+
+ align:start position:0%
+competition uh and what he finds is that
+ 
+
+ align:start position:0%
+competition uh and what he finds is that
+prices would have been 6% higher uh and
+
+ align:start position:0%
+prices would have been 6% higher uh and
+ 
+
+ align:start position:0%
+prices would have been 6% higher uh and
+demand would have been six 11% lower so
+
+ align:start position:0%
+demand would have been six 11% lower so
+ 
+
+ align:start position:0%
+demand would have been six 11% lower so
+this was you know a 40% jump in Auto
+
+ align:start position:0%
+this was you know a 40% jump in Auto
+ 
+
+ align:start position:0%
+this was you know a 40% jump in Auto
+Sales his model is not fully explaining
+
+ align:start position:0%
+Sales his model is not fully explaining
+ 
+
+ align:start position:0%
+Sales his model is not fully explaining
+it his model is saying I'm explaining uh
+
+ align:start position:0%
+it his model is saying I'm explaining uh
+ 
+
+ align:start position:0%
+it his model is saying I'm explaining uh
+you know a little more than 25% of the
+
+ align:start position:0%
+you know a little more than 25% of the
+ 
+
+ align:start position:0%
+you know a little more than 25% of the
+Boom in auto sales as as coming from uh
+
+ align:start position:0%
+Boom in auto sales as as coming from uh
+ 
+
+ align:start position:0%
+Boom in auto sales as as coming from uh
+as coming from the change in collusion
+
+ align:start position:0%
+as coming from the change in collusion
+ 
+
+ align:start position:0%
+as coming from the change in collusion
+so in some sense you know he's already
+
+ align:start position:0%
+so in some sense you know he's already
+ 
+
+ align:start position:0%
+so in some sense you know he's already
+sort of letting you know that his model
+
+ align:start position:0%
+sort of letting you know that his model
+ 
+
+ align:start position:0%
+sort of letting you know that his model
+at least the model as he's estimated
+
+ align:start position:0%
+at least the model as he's estimated
+ 
+
+ align:start position:0%
+at least the model as he's estimated
+isn't fully correct because it's not
+
+ align:start position:0%
+isn't fully correct because it's not
+ 
+
+ align:start position:0%
+isn't fully correct because it's not
+fully accounting for the jump in sales
+
+ align:start position:0%
+fully accounting for the jump in sales
+ 
+
+ align:start position:0%
+fully accounting for the jump in sales
+now there was a you know 10% jump in
+
+ align:start position:0%
+now there was a you know 10% jump in
+ 
+
+ align:start position:0%
+now there was a you know 10% jump in
+non-auto durable good sales he would
+
+ align:start position:0%
+non-auto durable good sales he would
+ 
+
+ align:start position:0%
+non-auto durable good sales he would
+have said just the sort of background
+
+ align:start position:0%
+have said just the sort of background
+ 
+
+ align:start position:0%
+have said just the sort of background
+change in US economy income or change in
+
+ align:start position:0%
+change in US economy income or change in
+ 
+
+ align:start position:0%
+change in US economy income or change in
+income maybe could have explained 10%
+
+ align:start position:0%
+income maybe could have explained 10%
+ 
+
+ align:start position:0%
+income maybe could have explained 10%
+also but so you thing his model is
+
+ align:start position:0%
+also but so you thing his model is
+ 
+
+ align:start position:0%
+also but so you thing his model is
+explaining part of what's going
+
+ align:start position:0%
+explaining part of what's going
+ 
+
+ align:start position:0%
+explaining part of what's going
+on um but it is you know it is a very
+
+ align:start position:0%
+on um but it is you know it is a very
+ 
+
+ align:start position:0%
+on um but it is you know it is a very
+nice use of the you know use of the
+
+ align:start position:0%
+nice use of the you know use of the
+ 
+
+ align:start position:0%
+nice use of the you know use of the
+counterfactual to give us a sense of
+
+ align:start position:0%
+counterfactual to give us a sense of
+ 
+
+ align:start position:0%
+counterfactual to give us a sense of
+what would have happened in another
+
+ align:start position:0%
+what would have happened in another
+ 
+
+ align:start position:0%
+what would have happened in another
+world and that you know now you know you
+
+ align:start position:0%
+world and that you know now you know you
+ 
+
+ align:start position:0%
+world and that you know now you know you
+just see every IO paper now has
+
+ align:start position:0%
+just see every IO paper now has
+ 
+
+ align:start position:0%
+just see every IO paper now has
+counterfactuals which I think started
+
+ align:start position:0%
+counterfactuals which I think started
+ 
+
+ align:start position:0%
+counterfactuals which I think started
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um as I said you know if you read the
+
+ align:start position:0%
+um as I said you know if you read the
+ 
+
+ align:start position:0%
+um as I said you know if you read the
+paper there are all kinds of things that
+
+ align:start position:0%
+paper there are all kinds of things that
+ 
+
+ align:start position:0%
+paper there are all kinds of things that
+are going to seem odd to you like you
+
+ align:start position:0%
+are going to seem odd to you like you
+ 
+
+ align:start position:0%
+are going to seem odd to you like you
+know this sort of adoption of the pure
+
+ align:start position:0%
+know this sort of adoption of the pure
+ 
+
+ align:start position:0%
+know this sort of adoption of the pure
+vertical model you know
+
+ align:start position:0%
+vertical model you know
+ 
+
+ align:start position:0%
+vertical model you know
+clearly you know I I don't think the the
+
+ align:start position:0%
+clearly you know I I don't think the the
+ 
+
+ align:start position:0%
+clearly you know I I don't think the the
+the Mercury Montclair and the Chevy ba
+
+ align:start position:0%
+the Mercury Montclair and the Chevy ba
+ 
+
+ align:start position:0%
+the Mercury Montclair and the Chevy ba
+air are so similar that there would be
+
+ align:start position:0%
+air are so similar that there would be
+ 
+
+ align:start position:0%
+air are so similar that there would be
+purely Bertrand competition between them
+
+ align:start position:0%
+purely Bertrand competition between them
+ 
+
+ align:start position:0%
+purely Bertrand competition between them
+you know if you thought about doing that
+
+ align:start position:0%
+you know if you thought about doing that
+ 
+
+ align:start position:0%
+you know if you thought about doing that
+in today's car market you know there are
+
+ align:start position:0%
+in today's car market you know there are
+ 
+
+ align:start position:0%
+in today's car market you know there are
+pickup trucks um there are convertibles
+
+ align:start position:0%
+pickup trucks um there are convertibles
+ 
+
+ align:start position:0%
+pickup trucks um there are convertibles
+there are sport sedans there are you
+
+ align:start position:0%
+there are sport sedans there are you
+ 
+
+ align:start position:0%
+there are sport sedans there are you
+know electric vehicles if you try to put
+
+ align:start position:0%
+know electric vehicles if you try to put
+ 
+
+ align:start position:0%
+know electric vehicles if you try to put
+them on a one-dimensional quality space
+
+ align:start position:0%
+them on a one-dimensional quality space
+ 
+
+ align:start position:0%
+them on a one-dimensional quality space
+you know some of them like some pickup
+
+ align:start position:0%
+you know some of them like some pickup
+ 
+
+ align:start position:0%
+you know some of them like some pickup
+truck is going to nearly coincide with a
+
+ align:start position:0%
+truck is going to nearly coincide with a
+ 
+
+ align:start position:0%
+truck is going to nearly coincide with a
+Honda Accord and you know
+
+ align:start position:0%
+Honda Accord and you know
+ 
+
+ align:start position:0%
+Honda Accord and you know
+clearly you need to have some kind of
+
+ align:start position:0%
+clearly you need to have some kind of
+ 
+
+ align:start position:0%
+clearly you need to have some kind of
+horizontal differentiation as well as as
+
+ align:start position:0%
+horizontal differentiation as well as as
+ 
+
+ align:start position:0%
+horizontal differentiation as well as as
+vertical
+
+ align:start position:0%
+vertical
+ 
+
+ align:start position:0%
+vertical
+differentiation um you know the anyway a
+
+ align:start position:0%
+differentiation um you know the anyway a
+ 
+
+ align:start position:0%
+differentiation um you know the anyway a
+number of aspects when you when you sort
+
+ align:start position:0%
+number of aspects when you when you sort
+ 
+
+ align:start position:0%
+number of aspects when you when you sort
+of see how people do modern empirical
+
+ align:start position:0%
+of see how people do modern empirical
+ 
+
+ align:start position:0%
+of see how people do modern empirical
+work that look very different but I
+
+ align:start position:0%
+work that look very different but I
+ 
+
+ align:start position:0%
+work that look very different but I
+think the in some ways
+
+ align:start position:0%
+think the in some ways
+ 
+
+ align:start position:0%
+think the in some ways
+the basic ideas still seem very spoton
+
+ align:start position:0%
+the basic ideas still seem very spoton
+ 
+
+ align:start position:0%
+the basic ideas still seem very spoton
+in particular one thing I think he does
+
+ align:start position:0%
+in particular one thing I think he does
+ 
+
+ align:start position:0%
+in particular one thing I think he does
+better than many current models is he
+
+ align:start position:0%
+better than many current models is he
+ 
+
+ align:start position:0%
+better than many current models is he
+does take very seriously this idea of I
+
+ align:start position:0%
+does take very seriously this idea of I
+ 
+
+ align:start position:0%
+does take very seriously this idea of I
+want this empir this structure work only
+
+ align:start position:0%
+want this empir this structure work only
+ 
+
+ align:start position:0%
+want this empir this structure work only
+works if I choose the right framework
+
+ align:start position:0%
+works if I choose the right framework
+ 
+
+ align:start position:0%
+works if I choose the right framework
+and he's going to sort of come up with
+
+ align:start position:0%
+and he's going to sort of come up with
+ 
+
+ align:start position:0%
+and he's going to sort of come up with
+four different models and put a lot of
+
+ align:start position:0%
+four different models and put a lot of
+ 
+
+ align:start position:0%
+four different models and put a lot of
+effort into testing the four different
+
+ align:start position:0%
+effort into testing the four different
+ 
+
+ align:start position:0%
+effort into testing the four different
+structural models against each other
+
+ align:start position:0%
+structural models against each other
+ 
+
+ align:start position:0%
+structural models against each other
+whereas now very often it's like it's
+
+ align:start position:0%
+whereas now very often it's like it's
+ 
+
+ align:start position:0%
+whereas now very often it's like it's
+hard to estimate even any one model so
+
+ align:start position:0%
+hard to estimate even any one model so
+ 
+
+ align:start position:0%
+hard to estimate even any one model so
+you see a lot of papers that have here's
+
+ align:start position:0%
+you see a lot of papers that have here's
+ 
+
+ align:start position:0%
+you see a lot of papers that have here's
+my one model and I can estimate that and
+
+ align:start position:0%
+my one model and I can estimate that and
+ 
+
+ align:start position:0%
+my one model and I can estimate that and
+I can talk about how well it fits by
+
+ align:start position:0%
+I can talk about how well it fits by
+ 
+
+ align:start position:0%
+I can talk about how well it fits by
+sort of putting up a graph and showing
+
+ align:start position:0%
+sort of putting up a graph and showing
+ 
+
+ align:start position:0%
+sort of putting up a graph and showing
+some x's and y's and show the Y's are
+
+ align:start position:0%
+some x's and y's and show the Y's are
+ 
+
+ align:start position:0%
+some x's and y's and show the Y's are
+close to the Y hats but um you know I
+
+ align:start position:0%
+close to the Y hats but um you know I
+ 
+
+ align:start position:0%
+close to the Y hats but um you know I
+think it is doing a very nice job on
+
+ align:start position:0%
+think it is doing a very nice job on
+ 
+
+ align:start position:0%
+think it is doing a very nice job on
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+Dimension so uh any questions on breast
+
+ align:start position:0%
+Dimension so uh any questions on breast
+ 
+
+ align:start position:0%
+Dimension so uh any questions on breast
+andan yeah why would like collusion
+
+ align:start position:0%
+andan yeah why would like collusion
+ 
+
+ align:start position:0%
+andan yeah why would like collusion
+break down for just one year and then
+
+ align:start position:0%
+break down for just one year and then
+ 
+
+ align:start position:0%
+break down for just one year and then
+all of a sudden the next year it's back
+
+ align:start position:0%
+all of a sudden the next year it's back
+ 
+
+ align:start position:0%
+all of a sudden the next year it's back
+at it again yeah so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you a little hard to say you know the
+
+ align:start position:0%
+um you a little hard to say you know the
+ 
+
+ align:start position:0%
+um you a little hard to say you know the
+the um I I will in a couple weeks be
+
+ align:start position:0%
+the um I I will in a couple weeks be
+ 
+
+ align:start position:0%
+the um I I will in a couple weeks be
+discussing sort of models of repeated
+
+ align:start position:0%
+discussing sort of models of repeated
+ 
+
+ align:start position:0%
+discussing sort of models of repeated
+game collusion and in you know models of
+
+ align:start position:0%
+game collusion and in you know models of
+ 
+
+ align:start position:0%
+game collusion and in you know models of
+repeated game collusion you do get this
+
+ align:start position:0%
+repeated game collusion you do get this
+ 
+
+ align:start position:0%
+repeated game collusion you do get this
+phenomenon of the way you support
+
+ align:start position:0%
+phenomenon of the way you support
+ 
+
+ align:start position:0%
+phenomenon of the way you support
+collusion is via price Wars to punish
+
+ align:start position:0%
+collusion is via price Wars to punish
+ 
+
+ align:start position:0%
+collusion is via price Wars to punish
+somebody who cheats so that is if you
+
+ align:start position:0%
+somebody who cheats so that is if you
+ 
+
+ align:start position:0%
+somebody who cheats so that is if you
+you're trying to collude you think that
+
+ align:start position:0%
+you're trying to collude you think that
+ 
+
+ align:start position:0%
+you're trying to collude you think that
+someone is cheating on the collusive
+
+ align:start position:0%
+someone is cheating on the collusive
+ 
+
+ align:start position:0%
+someone is cheating on the collusive
+agreements and their dealers are
+
+ align:start position:0%
+agreements and their dealers are
+ 
+
+ align:start position:0%
+agreements and their dealers are
+charging you know like you've all agreed
+
+ align:start position:0%
+charging you know like you've all agreed
+ 
+
+ align:start position:0%
+charging you know like you've all agreed
+that we're going to charge $7,000 for
+
+ align:start position:0%
+that we're going to charge $7,000 for
+ 
+
+ align:start position:0%
+that we're going to charge $7,000 for
+our Bel a and Montclair and you think
+
+ align:start position:0%
+our Bel a and Montclair and you think
+ 
+
+ align:start position:0%
+our Bel a and Montclair and you think
+the other guys dealers are actually
+
+ align:start position:0%
+the other guys dealers are actually
+ 
+
+ align:start position:0%
+the other guys dealers are actually
+giving consumers cuts and offering it
+
+ align:start position:0%
+giving consumers cuts and offering it
+ 
+
+ align:start position:0%
+giving consumers cuts and offering it
+for 6,500 instead of 7,000 even though
+
+ align:start position:0%
+for 6,500 instead of 7,000 even though
+ 
+
+ align:start position:0%
+for 6,500 instead of 7,000 even though
+the list price is 7,000 you might decide
+
+ align:start position:0%
+the list price is 7,000 you might decide
+ 
+
+ align:start position:0%
+the list price is 7,000 you might decide
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+we're GNA have to punish you for doing
+
+ align:start position:0%
+we're GNA have to punish you for doing
+ 
+
+ align:start position:0%
+we're GNA have to punish you for doing
+that and we're g to have we're going to
+
+ align:start position:0%
+that and we're g to have we're going to
+ 
+
+ align:start position:0%
+that and we're g to have we're going to
+sort of abandon colluding this year and
+
+ align:start position:0%
+sort of abandon colluding this year and
+ 
+
+ align:start position:0%
+sort of abandon colluding this year and
+we're going to all learn how bad it is
+
+ align:start position:0%
+we're going to all learn how bad it is
+ 
+
+ align:start position:0%
+we're going to all learn how bad it is
+and then go back to cooperating the next
+
+ align:start position:0%
+and then go back to cooperating the next
+ 
+
+ align:start position:0%
+and then go back to cooperating the next
+year um you know so you could tell some
+
+ align:start position:0%
+year um you know so you could tell some
+ 
+
+ align:start position:0%
+year um you know so you could tell some
+story like that I I I don't you know he
+
+ align:start position:0%
+story like that I I I don't you know he
+ 
+
+ align:start position:0%
+story like that I I I don't you know he
+doesn't have
+
+ align:start position:0%
+doesn't have
+ 
+
+ align:start position:0%
+doesn't have
+any there there's no discussion in the
+
+ align:start position:0%
+any there there's no discussion in the
+ 
+
+ align:start position:0%
+any there there's no discussion in the
+paper of like why collusion would have
+
+ align:start position:0%
+paper of like why collusion would have
+ 
+
+ align:start position:0%
+paper of like why collusion would have
+brought down and there's no narrative
+
+ align:start position:0%
+brought down and there's no narrative
+ 
+
+ align:start position:0%
+brought down and there's no narrative
+evidence at all of the executives
+
+ align:start position:0%
+evidence at all of the executives
+ 
+
+ align:start position:0%
+evidence at all of the executives
+talking to each other and having
+
+ align:start position:0%
+talking to each other and having
+ 
+
+ align:start position:0%
+talking to each other and having
+anything going wrong um but it is true
+
+ align:start position:0%
+anything going wrong um but it is true
+ 
+
+ align:start position:0%
+anything going wrong um but it is true
+that actually you know like I
+
+ align:start position:0%
+that actually you know like I
+ 
+
+ align:start position:0%
+that actually you know like I
+think when we look at we're going to
+
+ align:start position:0%
+think when we look at we're going to
+ 
+
+ align:start position:0%
+think when we look at we're going to
+start study several other papers on
+
+ align:start position:0%
+start study several other papers on
+ 
+
+ align:start position:0%
+start study several other papers on
+cartels like almost all the cartels we
+
+ align:start position:0%
+cartels like almost all the cartels we
+ 
+
+ align:start position:0%
+cartels like almost all the cartels we
+study are finite lived like they go on
+
+ align:start position:0%
+study are finite lived like they go on
+ 
+
+ align:start position:0%
+study are finite lived like they go on
+they're colluding with each other for
+
+ align:start position:0%
+they're colluding with each other for
+ 
+
+ align:start position:0%
+they're colluding with each other for
+some number of years and then it breaks
+
+ align:start position:0%
+some number of years and then it breaks
+ 
+
+ align:start position:0%
+some number of years and then it breaks
+down at some point um you know in part
+
+ align:start position:0%
+down at some point um you know in part
+ 
+
+ align:start position:0%
+down at some point um you know in part
+because also it's illegal um but it's
+
+ align:start position:0%
+because also it's illegal um but it's
+ 
+
+ align:start position:0%
+because also it's illegal um but it's
+you know so people are afraid of getting
+
+ align:start position:0%
+you know so people are afraid of getting
+ 
+
+ align:start position:0%
+you know so people are afraid of getting
+caught or something goes wrong and they
+
+ align:start position:0%
+caught or something goes wrong and they
+ 
+
+ align:start position:0%
+caught or something goes wrong and they
+can't discuss it with each other and get
+
+ align:start position:0%
+can't discuss it with each other and get
+ 
+
+ align:start position:0%
+can't discuss it with each other and get
+things back
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else okay um so second thing I I was
+
+ align:start position:0%
+else okay um so second thing I I was
+ 
+
+ align:start position:0%
+else okay um so second thing I I was
+going to do then I was going to jump
+
+ align:start position:0%
+going to do then I was going to jump
+ 
+
+ align:start position:0%
+going to do then I was going to jump
+ahead before I get to Miller and
+
+ align:start position:0%
+ahead before I get to Miller and
+ 
+
+ align:start position:0%
+ahead before I get to Miller and
+Weinberg and just do do uh you know half
+
+ align:start position:0%
+Weinberg and just do do uh you know half
+ 
+
+ align:start position:0%
+Weinberg and just do do uh you know half
+hour 40 minutes on oligopoly price
+
+ align:start position:0%
+hour 40 minutes on oligopoly price
+ 
+
+ align:start position:0%
+hour 40 minutes on oligopoly price
+discrimination and you know I think in
+
+ align:start position:0%
+discrimination and you know I think in
+ 
+
+ align:start position:0%
+discrimination and you know I think in
+terr's textbook and in many other places
+
+ align:start position:0%
+terr's textbook and in many other places
+ 
+
+ align:start position:0%
+terr's textbook and in many other places
+price discrimination is typically taught
+
+ align:start position:0%
+price discrimination is typically taught
+ 
+
+ align:start position:0%
+price discrimination is typically taught
+as a monopoly topic um and you know I
+
+ align:start position:0%
+as a monopoly topic um and you know I
+ 
+
+ align:start position:0%
+as a monopoly topic um and you know I
+think that was because historically you
+
+ align:start position:0%
+think that was because historically you
+ 
+
+ align:start position:0%
+think that was because historically you
+had Monopoly and perfect competition as
+
+ align:start position:0%
+had Monopoly and perfect competition as
+ 
+
+ align:start position:0%
+had Monopoly and perfect competition as
+the two models with perfect competition
+
+ align:start position:0%
+the two models with perfect competition
+ 
+
+ align:start position:0%
+the two models with perfect competition
+price equals marginal cost you can't
+
+ align:start position:0%
+price equals marginal cost you can't
+ 
+
+ align:start position:0%
+price equals marginal cost you can't
+price discriminate but you know with
+
+ align:start position:0%
+price discriminate but you know with
+ 
+
+ align:start position:0%
+price discriminate but you know with
+imperfect competition price isn't equal
+
+ align:start position:0%
+imperfect competition price isn't equal
+ 
+
+ align:start position:0%
+imperfect competition price isn't equal
+to marginal cost there's no reason why
+
+ align:start position:0%
+to marginal cost there's no reason why
+ 
+
+ align:start position:0%
+to marginal cost there's no reason why
+oligopolies can't price discriminate
+
+ align:start position:0%
+oligopolies can't price discriminate
+ 
+
+ align:start position:0%
+oligopolies can't price discriminate
+just like monopolies price discriminate
+
+ align:start position:0%
+just like monopolies price discriminate
+ 
+
+ align:start position:0%
+just like monopolies price discriminate
+uh in particular there was an early
+
+ align:start position:0%
+uh in particular there was an early
+ 
+
+ align:start position:0%
+uh in particular there was an early
+paper in this um Bornstein and Rose uh
+
+ align:start position:0%
+paper in this um Bornstein and Rose uh
+ 
+
+ align:start position:0%
+paper in this um Bornstein and Rose uh
+1994 jpe look at Price dispersion in
+
+ align:start position:0%
+1994 jpe look at Price dispersion in
+ 
+
+ align:start position:0%
+1994 jpe look at Price dispersion in
+Airline markets and what they find is
+
+ align:start position:0%
+Airline markets and what they find is
+ 
+
+ align:start position:0%
+Airline markets and what they find is
+that if you look at uh Airline City pair
+
+ align:start position:0%
+that if you look at uh Airline City pair
+ 
+
+ align:start position:0%
+that if you look at uh Airline City pair
+markets like you know Boston to New York
+
+ align:start position:0%
+markets like you know Boston to New York
+ 
+
+ align:start position:0%
+markets like you know Boston to New York
+New York to Phoenix
+
+ align:start position:0%
+New York to Phoenix
+ 
+
+ align:start position:0%
+New York to Phoenix
+whatever the markets that have more
+
+ align:start position:0%
+whatever the markets that have more
+ 
+
+ align:start position:0%
+whatever the markets that have more
+competition tend to have more price
+
+ align:start position:0%
+competition tend to have more price
+ 
+
+ align:start position:0%
+competition tend to have more price
+dispers
+
+ align:start position:0%
+dispers
+ 
+
+ align:start position:0%
+dispers
+on the same plane so like you know if
+
+ align:start position:0%
+on the same plane so like you know if
+ 
+
+ align:start position:0%
+on the same plane so like you know if
+you look at a flight you know from
+
+ align:start position:0%
+you look at a flight you know from
+ 
+
+ align:start position:0%
+you look at a flight you know from
+Boston to New York there are a lot of
+
+ align:start position:0%
+Boston to New York there are a lot of
+ 
+
+ align:start position:0%
+Boston to New York there are a lot of
+people on that flight they all PID
+
+ align:start position:0%
+people on that flight they all PID
+ 
+
+ align:start position:0%
+people on that flight they all PID
+different prices and the Bornstein Row's
+
+ align:start position:0%
+different prices and the Bornstein Row's
+ 
+
+ align:start position:0%
+different prices and the Bornstein Row's
+finding is that the heterogeneity in
+
+ align:start position:0%
+finding is that the heterogeneity in
+ 
+
+ align:start position:0%
+finding is that the heterogeneity in
+prices on a flight is actually larger in
+
+ align:start position:0%
+prices on a flight is actually larger in
+ 
+
+ align:start position:0%
+prices on a flight is actually larger in
+the more competitive markets not smaller
+
+ align:start position:0%
+the more competitive markets not smaller
+ 
+
+ align:start position:0%
+the more competitive markets not smaller
+and the more competitive markets um so
+
+ align:start position:0%
+and the more competitive markets um so
+ 
+
+ align:start position:0%
+and the more competitive markets um so
+it's an indication that it's not the
+
+ align:start position:0%
+it's an indication that it's not the
+ 
+
+ align:start position:0%
+it's an indication that it's not the
+case that competition that we often see
+
+ align:start position:0%
+case that competition that we often see
+ 
+
+ align:start position:0%
+case that competition that we often see
+makes it impossible to price
+
+ align:start position:0%
+makes it impossible to price
+ 
+
+ align:start position:0%
+makes it impossible to price
+discriminate okay so how would we model
+
+ align:start position:0%
+discriminate okay so how would we model
+ 
+
+ align:start position:0%
+discriminate okay so how would we model
+price discrimination well let me first
+
+ align:start position:0%
+price discrimination well let me first
+ 
+
+ align:start position:0%
+price discrimination well let me first
+start start with um third degree price
+
+ align:start position:0%
+start start with um third degree price
+ 
+
+ align:start position:0%
+start start with um third degree price
+discrimination so you have you know two
+
+ align:start position:0%
+discrimination so you have you know two
+ 
+
+ align:start position:0%
+discrimination so you have you know two
+firms competing in two separate markets
+
+ align:start position:0%
+firms competing in two separate markets
+ 
+
+ align:start position:0%
+firms competing in two separate markets
+and suppos there's no cross Market
+
+ align:start position:0%
+and suppos there's no cross Market
+ 
+
+ align:start position:0%
+and suppos there's no cross Market
+Arbitrage so you know this is two firms
+
+ align:start position:0%
+Arbitrage so you know this is two firms
+ 
+
+ align:start position:0%
+Arbitrage so you know this is two firms
+selling uh cell phone service in Boston
+
+ align:start position:0%
+selling uh cell phone service in Boston
+ 
+
+ align:start position:0%
+selling uh cell phone service in Boston
+the same two firm selling or two firm
+
+ align:start position:0%
+the same two firm selling or two firm
+ 
+
+ align:start position:0%
+the same two firm selling or two firm
+selling cable TV service in Boston and
+
+ align:start position:0%
+selling cable TV service in Boston and
+ 
+
+ align:start position:0%
+selling cable TV service in Boston and
+selling cable TV service in Philadelphia
+
+ align:start position:0%
+selling cable TV service in Philadelphia
+ 
+
+ align:start position:0%
+selling cable TV service in Philadelphia
+you know you can't arbit you can't like
+
+ align:start position:0%
+you know you can't arbit you can't like
+ 
+
+ align:start position:0%
+you know you can't arbit you can't like
+get a buy cable TV in Boston and then
+
+ align:start position:0%
+get a buy cable TV in Boston and then
+ 
+
+ align:start position:0%
+get a buy cable TV in Boston and then
+use it in Philadelphia or vice versa you
+
+ align:start position:0%
+use it in Philadelphia or vice versa you
+ 
+
+ align:start position:0%
+use it in Philadelphia or vice versa you
+have to buy the service at your service
+
+ align:start position:0%
+have to buy the service at your service
+ 
+
+ align:start position:0%
+have to buy the service at your service
+address um and you know so you could
+
+ align:start position:0%
+address um and you know so you could
+ 
+
+ align:start position:0%
+address um and you know so you could
+have these same two firms competing and
+
+ align:start position:0%
+have these same two firms competing and
+ 
+
+ align:start position:0%
+have these same two firms competing and
+they're competing in these two different
+
+ align:start position:0%
+they're competing in these two different
+ 
+
+ align:start position:0%
+they're competing in these two different
+markets okay um so suppose that you know
+
+ align:start position:0%
+markets okay um so suppose that you know
+ 
+
+ align:start position:0%
+markets okay um so suppose that you know
+every each of the markets has hotelling
+
+ align:start position:0%
+every each of the markets has hotelling
+ 
+
+ align:start position:0%
+every each of the markets has hotelling
+preferences and the type Theta consumers
+
+ align:start position:0%
+preferences and the type Theta consumers
+ 
+
+ align:start position:0%
+preferences and the type Theta consumers
+in Market M get
+
+ align:start position:0%
+in Market M get
+ 
+
+ align:start position:0%
+in Market M get
+utility V minus P price of firm one and
+
+ align:start position:0%
+utility V minus P price of firm one and
+ 
+
+ align:start position:0%
+utility V minus P price of firm one and
+M minus TM Theta if they buy from firm
+
+ align:start position:0%
+M minus TM Theta if they buy from firm
+ 
+
+ align:start position:0%
+M minus TM Theta if they buy from firm
+one and V minus p2m minus tm1 minus
+
+ align:start position:0%
+one and V minus p2m minus tm1 minus
+ 
+
+ align:start position:0%
+one and V minus p2m minus tm1 minus
+Theta if they buy it from firm two so
+
+ align:start position:0%
+Theta if they buy it from firm two so
+ 
+
+ align:start position:0%
+Theta if they buy it from firm two so
+this is just competition on two
+
+ align:start position:0%
+this is just competition on two
+ 
+
+ align:start position:0%
+this is just competition on two
+lines you know this
+
+ align:start position:0%
+lines you know this
+ 
+
+ align:start position:0%
+lines you know this
+is this is Market one and it has some
+
+ align:start position:0%
+is this is Market one and it has some
+ 
+
+ align:start position:0%
+is this is Market one and it has some
+parameter
+
+ align:start position:0%
+parameter
+ 
+
+ align:start position:0%
+parameter
+T1 and this is Market
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 uh and it has some parameter
+
+ align:start position:0%
+2 uh and it has some parameter
+ 
+
+ align:start position:0%
+2 uh and it has some parameter
+T2 I think I made T2 the high
+
+ align:start position:0%
+T2 I think I made T2 the high
+ 
+
+ align:start position:0%
+T2 I think I made T2 the high
+guys okay so you just have you're
+
+ align:start position:0%
+guys okay so you just have you're
+ 
+
+ align:start position:0%
+guys okay so you just have you're
+competing on this line you're competing
+
+ align:start position:0%
+competing on this line you're competing
+ 
+
+ align:start position:0%
+competing on this line you're competing
+on this line these markets are
+
+ align:start position:0%
+on this line these markets are
+ 
+
+ align:start position:0%
+on this line these markets are
+completely separate well you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know price discrimination is just just
+
+ align:start position:0%
+know price discrimination is just just
+ 
+
+ align:start position:0%
+know price discrimination is just just
+like third degree in Monopoly it's just
+
+ align:start position:0%
+like third degree in Monopoly it's just
+ 
+
+ align:start position:0%
+like third degree in Monopoly it's just
+two totally separate markets so if we
+
+ align:start position:0%
+two totally separate markets so if we
+ 
+
+ align:start position:0%
+two totally separate markets so if we
+have competition here what's going to
+
+ align:start position:0%
+have competition here what's going to
+ 
+
+ align:start position:0%
+have competition here what's going to
+happen is you're going to get you know P
+
+ align:start position:0%
+happen is you're going to get you know P
+ 
+
+ align:start position:0%
+happen is you're going to get you know P
+star equals c plus T1 you have
+
+ align:start position:0%
+star equals c plus T1 you have
+ 
+
+ align:start position:0%
+star equals c plus T1 you have
+competition here you're going to get P2
+
+ align:start position:0%
+competition here you're going to get P2
+ 
+
+ align:start position:0%
+competition here you're going to get P2
+star is C plus
+
+ align:start position:0%
+star is C plus
+ 
+
+ align:start position:0%
+star is C plus
+T2 right we just compete on a line here
+
+ align:start position:0%
+T2 right we just compete on a line here
+ 
+
+ align:start position:0%
+T2 right we just compete on a line here
+we get hoteling here we compete on this
+
+ align:start position:0%
+we get hoteling here we compete on this
+ 
+
+ align:start position:0%
+we get hoteling here we compete on this
+line we get hoteling here
+
+ align:start position:0%
+line we get hoteling here
+ 
+
+ align:start position:0%
+line we get hoteling here
+the prices are different across markets
+
+ align:start position:0%
+the prices are different across markets
+ 
+
+ align:start position:0%
+the prices are different across markets
+we're discriminating against consumers
+
+ align:start position:0%
+we're discriminating against consumers
+ 
+
+ align:start position:0%
+we're discriminating against consumers
+in this market you the high types end up
+
+ align:start position:0%
+in this market you the high types end up
+ 
+
+ align:start position:0%
+in this market you the high types end up
+paying more what are high types a high
+
+ align:start position:0%
+paying more what are high types a high
+ 
+
+ align:start position:0%
+paying more what are high types a high
+type is somebody who lives in a market
+
+ align:start position:0%
+type is somebody who lives in a market
+ 
+
+ align:start position:0%
+type is somebody who lives in a market
+where there's more heterogen Adan taste
+
+ align:start position:0%
+where there's more heterogen Adan taste
+ 
+
+ align:start position:0%
+where there's more heterogen Adan taste
+so if there's more heterogen Adan taste
+
+ align:start position:0%
+so if there's more heterogen Adan taste
+ 
+
+ align:start position:0%
+so if there's more heterogen Adan taste
+in Market 2 than in Market one then
+
+ align:start position:0%
+in Market 2 than in Market one then
+ 
+
+ align:start position:0%
+in Market 2 than in Market one then
+people in Market 2 end up paying more
+
+ align:start position:0%
+people in Market 2 end up paying more
+ 
+
+ align:start position:0%
+people in Market 2 end up paying more
+than people in Market
+
+ align:start position:0%
+than people in Market
+ 
+
+ align:start position:0%
+than people in Market
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+okay um the one policy question you get
+
+ align:start position:0%
+okay um the one policy question you get
+ 
+
+ align:start position:0%
+okay um the one policy question you get
+is well what would happen in a market
+
+ align:start position:0%
+is well what would happen in a market
+ 
+
+ align:start position:0%
+is well what would happen in a market
+like this if we banned um people
+
+ align:start position:0%
+like this if we banned um people
+ 
+
+ align:start position:0%
+like this if we banned um people
+from uh what would happen if we Bann
+
+ align:start position:0%
+from uh what would happen if we Bann
+ 
+
+ align:start position:0%
+from uh what would happen if we Bann
+people from uh price discriminating and
+
+ align:start position:0%
+people from uh price discriminating and
+ 
+
+ align:start position:0%
+people from uh price discriminating and
+say you have to charge the same Mar
+
+ align:start position:0%
+say you have to charge the same Mar
+ 
+
+ align:start position:0%
+say you have to charge the same Mar
+price in both markets uh it turns out
+
+ align:start position:0%
+price in both markets uh it turns out
+ 
+
+ align:start position:0%
+price in both markets uh it turns out
+like in this model you just sort of get
+
+ align:start position:0%
+like in this model you just sort of get
+ 
+
+ align:start position:0%
+like in this model you just sort of get
+an average markup so if instead
+
+ align:start position:0%
+an average markup so if instead
+ 
+
+ align:start position:0%
+an average markup so if instead
+of being allowed to price separately you
+
+ align:start position:0%
+of being allowed to price separately you
+ 
+
+ align:start position:0%
+of being allowed to price separately you
+force them to charge the same price what
+
+ align:start position:0%
+force them to charge the same price what
+ 
+
+ align:start position:0%
+force them to charge the same price what
+you get is price equals C + 2 T1 T2 over
+
+ align:start position:0%
+you get is price equals C + 2 T1 T2 over
+ 
+
+ align:start position:0%
+you get is price equals C + 2 T1 T2 over
+T1 + T2
+
+ align:start position:0%
+T1 + T2
+ 
+
+ align:start position:0%
+T1 + T2
+okay um this is uh what mathematicians
+
+ align:start position:0%
+okay um this is uh what mathematicians
+ 
+
+ align:start position:0%
+okay um this is uh what mathematicians
+refer to as the harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mean of um T1 and T2 and you know basic
+
+ align:start position:0%
+mean of um T1 and T2 and you know basic
+ 
+
+ align:start position:0%
+mean of um T1 and T2 and you know basic
+math fact is that if T1 is less than T2
+
+ align:start position:0%
+math fact is that if T1 is less than T2
+ 
+
+ align:start position:0%
+math fact is that if T1 is less than T2
+then T1 is less than 2 T1 T2 over T1 +
+
+ align:start position:0%
+then T1 is less than 2 T1 T2 over T1 +
+ 
+
+ align:start position:0%
+then T1 is less than 2 T1 T2 over T1 +
+T2 Which is less than or equal to T1 1 +
+
+ align:start position:0%
+T2 Which is less than or equal to T1 1 +
+ 
+
+ align:start position:0%
+T2 Which is less than or equal to T1 1 +
+T2 over 2 less than or equal to T2 okay
+
+ align:start position:0%
+T2 over 2 less than or equal to T2 okay
+ 
+
+ align:start position:0%
+T2 over 2 less than or equal to T2 okay
+this is the called the arithmetic
+
+ align:start position:0%
+this is the called the arithmetic
+ 
+
+ align:start position:0%
+this is the called the arithmetic
+harmonic mean inequality so it it's the
+
+ align:start position:0%
+harmonic mean inequality so it it's the
+ 
+
+ align:start position:0%
+harmonic mean inequality so it it's the
+you can think of this as this is the
+
+ align:start position:0%
+you can think of this as this is the
+ 
+
+ align:start position:0%
+you can think of this as this is the
+reciprocal of the average of the
+
+ align:start position:0%
+reciprocal of the average of the
+ 
+
+ align:start position:0%
+reciprocal of the average of the
+reciprocals of T1 and T2 so it always
+
+ align:start position:0%
+reciprocals of T1 and T2 so it always
+ 
+
+ align:start position:0%
+reciprocals of T1 and T2 so it always
+lies between T1 and T2 and it is less
+
+ align:start position:0%
+lies between T1 and T2 and it is less
+ 
+
+ align:start position:0%
+lies between T1 and T2 and it is less
+than the arithmetic mean of T1 and T2
+
+ align:start position:0%
+than the arithmetic mean of T1 and T2
+ 
+
+ align:start position:0%
+than the arithmetic mean of T1 and T2
+but justes the way the math works this
+
+ align:start position:0%
+but justes the way the math works this
+ 
+
+ align:start position:0%
+but justes the way the math works this
+is the price that you end up charging if
+
+ align:start position:0%
+is the price that you end up charging if
+ 
+
+ align:start position:0%
+is the price that you end up charging if
+you ban price discrimination um so what
+
+ align:start position:0%
+you ban price discrimination um so what
+ 
+
+ align:start position:0%
+you ban price discrimination um so what
+is Banning price discrimination do you
+
+ align:start position:0%
+is Banning price discrimination do you
+ 
+
+ align:start position:0%
+is Banning price discrimination do you
+know typically it makes the high types
+
+ align:start position:0%
+know typically it makes the high types
+ 
+
+ align:start position:0%
+know typically it makes the high types
+better off typically it makes the low
+
+ align:start position:0%
+better off typically it makes the low
+ 
+
+ align:start position:0%
+better off typically it makes the low
+types worse off um it does eliminate a
+
+ align:start position:0%
+types worse off um it does eliminate a
+ 
+
+ align:start position:0%
+types worse off um it does eliminate a
+misallocation of markets you know in
+
+ align:start position:0%
+misallocation of markets you know in
+ 
+
+ align:start position:0%
+misallocation of markets you know in
+many models if you have a high price in
+
+ align:start position:0%
+many models if you have a high price in
+ 
+
+ align:start position:0%
+many models if you have a high price in
+one market and a low price in another
+
+ align:start position:0%
+one market and a low price in another
+ 
+
+ align:start position:0%
+one market and a low price in another
+Market there are people in the high
+
+ align:start position:0%
+Market there are people in the high
+ 
+
+ align:start position:0%
+Market there are people in the high
+Market who would like the good who
+
+ align:start position:0%
+Market who would like the good who
+ 
+
+ align:start position:0%
+Market who would like the good who
+aren't getting it and there are people
+
+ align:start position:0%
+aren't getting it and there are people
+ 
+
+ align:start position:0%
+aren't getting it and there are people
+in the low Market who don't like the
+
+ align:start position:0%
+in the low Market who don't like the
+ 
+
+ align:start position:0%
+in the low Market who don't like the
+good as much who are getting it that's a
+
+ align:start position:0%
+good as much who are getting it that's a
+ 
+
+ align:start position:0%
+good as much who are getting it that's a
+misallocation like there is in price
+
+ align:start position:0%
+misallocation like there is in price
+ 
+
+ align:start position:0%
+misallocation like there is in price
+discrimination models um so Banning
+
+ align:start position:0%
+discrimination models um so Banning
+ 
+
+ align:start position:0%
+discrimination models um so Banning
+price eliminates that
+
+ align:start position:0%
+price eliminates that
+ 
+
+ align:start position:0%
+price eliminates that
+inefficiency that inefficiency isn't
+
+ align:start position:0%
+inefficiency that inefficiency isn't
+ 
+
+ align:start position:0%
+inefficiency that inefficiency isn't
+present in hoteling because in hoteling
+
+ align:start position:0%
+present in hoteling because in hoteling
+ 
+
+ align:start position:0%
+present in hoteling because in hoteling
+everybody buys at least if he is big
+
+ align:start position:0%
+everybody buys at least if he is big
+ 
+
+ align:start position:0%
+everybody buys at least if he is big
+enough um and then you know
+
+ align:start position:0%
+enough um and then you know
+ 
+
+ align:start position:0%
+enough um and then you know
+welfare can go either way um so there
+
+ align:start position:0%
+welfare can go either way um so there
+ 
+
+ align:start position:0%
+welfare can go either way um so there
+are you know you know here again there
+
+ align:start position:0%
+are you know you know here again there
+ 
+
+ align:start position:0%
+are you know you know here again there
+are no welfare changes it's just a
+
+ align:start position:0%
+are no welfare changes it's just a
+ 
+
+ align:start position:0%
+are no welfare changes it's just a
+transfer because everybody buy you know
+
+ align:start position:0%
+transfer because everybody buy you know
+ 
+
+ align:start position:0%
+transfer because everybody buy you know
+all all efficient transactions take
+
+ align:start position:0%
+all all efficient transactions take
+ 
+
+ align:start position:0%
+all all efficient transactions take
+place the first best is achieved in both
+
+ align:start position:0%
+place the first best is achieved in both
+ 
+
+ align:start position:0%
+place the first best is achieved in both
+both models um so it's just a pure
+
+ align:start position:0%
+both models um so it's just a pure
+ 
+
+ align:start position:0%
+both models um so it's just a pure
+transfer but in general you know Banning
+
+ align:start position:0%
+transfer but in general you know Banning
+ 
+
+ align:start position:0%
+transfer but in general you know Banning
+price discrimination can increase so
+
+ align:start position:0%
+price discrimination can increase so
+ 
+
+ align:start position:0%
+price discrimination can increase so
+total social welfare or it can decrease
+
+ align:start position:0%
+total social welfare or it can decrease
+ 
+
+ align:start position:0%
+total social welfare or it can decrease
+total social
+
+ align:start position:0%
+total social
+ 
+
+ align:start position:0%
+total social
+welfare
+
+ align:start position:0%
+welfare
+ 
+
+ align:start position:0%
+welfare
+um okay um there's a set of papers in
+
+ align:start position:0%
+um okay um there's a set of papers in
+ 
+
+ align:start position:0%
+um okay um there's a set of papers in
+the 1980s noting that this is the
+
+ align:start position:0%
+the 1980s noting that this is the
+ 
+
+ align:start position:0%
+the 1980s noting that this is the
+typical effect of banning price
+
+ align:start position:0%
+typical effect of banning price
+ 
+
+ align:start position:0%
+typical effect of banning price
+discrimination in oligopoly markets but
+
+ align:start position:0%
+discrimination in oligopoly markets but
+ 
+
+ align:start position:0%
+discrimination in oligopoly markets but
+the typical effects don't have to hold
+
+ align:start position:0%
+the typical effects don't have to hold
+ 
+
+ align:start position:0%
+the typical effects don't have to hold
+um so there's a paper by T and Vias a88
+
+ align:start position:0%
+um so there's a paper by T and Vias a88
+ 
+
+ align:start position:0%
+um so there's a paper by T and Vias a88
+that makes the point that allowing price
+
+ align:start position:0%
+that makes the point that allowing price
+ 
+
+ align:start position:0%
+that makes the point that allowing price
+discrimination can make all consumers
+
+ align:start position:0%
+discrimination can make all consumers
+ 
+
+ align:start position:0%
+discrimination can make all consumers
+better off so price discrimination can
+
+ align:start position:0%
+better off so price discrimination can
+ 
+
+ align:start position:0%
+better off so price discrimination can
+make everybody better off um because of
+
+ align:start position:0%
+make everybody better off um because of
+ 
+
+ align:start position:0%
+make everybody better off um because of
+this effect that t and Vias highlight
+
+ align:start position:0%
+this effect that t and Vias highlight
+ 
+
+ align:start position:0%
+this effect that t and Vias highlight
+when you let firms price discriminate it
+
+ align:start position:0%
+when you let firms price discriminate it
+ 
+
+ align:start position:0%
+when you let firms price discriminate it
+lets firms aggressively Target rals
+
+ align:start position:0%
+lets firms aggressively Target rals
+ 
+
+ align:start position:0%
+lets firms aggressively Target rals
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+consumers uh and that can sort of
+
+ align:start position:0%
+consumers uh and that can sort of
+ 
+
+ align:start position:0%
+consumers uh and that can sort of
+intensify price competition so the exam
+
+ align:start position:0%
+intensify price competition so the exam
+ 
+
+ align:start position:0%
+intensify price competition so the exam
+simplest example that t and Vias gave
+
+ align:start position:0%
+simplest example that t and Vias gave
+ 
+
+ align:start position:0%
+simplest example that t and Vias gave
+was you know consider again the
+
+ align:start position:0%
+was you know consider again the
+ 
+
+ align:start position:0%
+was you know consider again the
+hotelling model and I'm going to give
+
+ align:start position:0%
+hotelling model and I'm going to give
+ 
+
+ align:start position:0%
+hotelling model and I'm going to give
+the hotelling model a different
+
+ align:start position:0%
+the hotelling model a different
+ 
+
+ align:start position:0%
+the hotelling model a different
+interpretation so we have these two
+
+ align:start position:0%
+interpretation so we have these two
+ 
+
+ align:start position:0%
+interpretation so we have these two
+firms and they're
+
+ align:start position:0%
+firms and they're
+ 
+
+ align:start position:0%
+firms and they're
+competing and the consumers have some
+
+ align:start position:0%
+competing and the consumers have some
+ 
+
+ align:start position:0%
+competing and the consumers have some
+types
+
+ align:start position:0%
+types
+ 
+
+ align:start position:0%
+types
+data and I'm going to assume that um the
+
+ align:start position:0%
+data and I'm going to assume that um the
+ 
+
+ align:start position:0%
+data and I'm going to assume that um the
+firms can observe Theta you know so
+
+ align:start position:0%
+firms can observe Theta you know so
+ 
+
+ align:start position:0%
+firms can observe Theta you know so
+maybe these are two firms uh selling
+
+ align:start position:0%
+maybe these are two firms uh selling
+ 
+
+ align:start position:0%
+maybe these are two firms uh selling
+Lumber to home builders and they know
+
+ align:start position:0%
+Lumber to home builders and they know
+ 
+
+ align:start position:0%
+Lumber to home builders and they know
+where the home builder job site is and
+
+ align:start position:0%
+where the home builder job site is and
+ 
+
+ align:start position:0%
+where the home builder job site is and
+so they know how long it's going to take
+
+ align:start position:0%
+so they know how long it's going to take
+ 
+
+ align:start position:0%
+so they know how long it's going to take
+the home builder to truck the lumber
+
+ align:start position:0%
+the home builder to truck the lumber
+ 
+
+ align:start position:0%
+the home builder to truck the lumber
+from their warehouse to his Factory site
+
+ align:start position:0%
+from their warehouse to his Factory site
+ 
+
+ align:start position:0%
+from their warehouse to his Factory site
+so they know his Theta and that's the
+
+ align:start position:0%
+so they know his Theta and that's the
+ 
+
+ align:start position:0%
+so they know his Theta and that's the
+Theta is determining willingness to pay
+
+ align:start position:0%
+Theta is determining willingness to pay
+ 
+
+ align:start position:0%
+Theta is determining willingness to pay
+you know through some means that's known
+
+ align:start position:0%
+you know through some means that's known
+ 
+
+ align:start position:0%
+you know through some means that's known
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+sellers and so here you know
+
+ align:start position:0%
+sellers and so here you know
+ 
+
+ align:start position:0%
+sellers and so here you know
+discrimination would be firm set Theta
+
+ align:start position:0%
+discrimination would be firm set Theta
+ 
+
+ align:start position:0%
+discrimination would be firm set Theta
+dependent prices instead of theta
+
+ align:start position:0%
+dependent prices instead of theta
+ 
+
+ align:start position:0%
+dependent prices instead of theta
+independent prices because they observe
+
+ align:start position:0%
+independent prices because they observe
+ 
+
+ align:start position:0%
+independent prices because they observe
+Theta okay well first you know what
+
+ align:start position:0%
+Theta okay well first you know what
+ 
+
+ align:start position:0%
+Theta okay well first you know what
+happens in this model if firms are if
+
+ align:start position:0%
+happens in this model if firms are if
+ 
+
+ align:start position:0%
+happens in this model if firms are if
+they're not allowed to to um price
+
+ align:start position:0%
+they're not allowed to to um price
+ 
+
+ align:start position:0%
+they're not allowed to to um price
+discriminate then you just get P star
+
+ align:start position:0%
+discriminate then you just get P star
+ 
+
+ align:start position:0%
+discriminate then you just get P star
+equals c plus
+
+ align:start position:0%
+equals c plus
+ 
+
+ align:start position:0%
+equals c plus
+T right because if if I know the
+
+ align:start position:0%
+T right because if if I know the
+ 
+
+ align:start position:0%
+T right because if if I know the
+locations but I don't know I'm not
+
+ align:start position:0%
+locations but I don't know I'm not
+ 
+
+ align:start position:0%
+locations but I don't know I'm not
+allowed to charge different prices and I
+
+ align:start position:0%
+allowed to charge different prices and I
+ 
+
+ align:start position:0%
+allowed to charge different prices and I
+just charge C plus T to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everybody what's going to happen if I
+
+ align:start position:0%
+everybody what's going to happen if I
+ 
+
+ align:start position:0%
+everybody what's going to happen if I
+now start discriminating well if I'm
+
+ align:start position:0%
+now start discriminating well if I'm
+ 
+
+ align:start position:0%
+now start discriminating well if I'm
+firm one or let say I'm firm
+
+ align:start position:0%
+firm one or let say I'm firm
+ 
+
+ align:start position:0%
+firm one or let say I'm firm
+two and I'm trying to sell to a consumer
+
+ align:start position:0%
+two and I'm trying to sell to a consumer
+ 
+
+ align:start position:0%
+two and I'm trying to sell to a consumer
+over here I know that that consumer
+
+ align:start position:0%
+over here I know that that consumer
+ 
+
+ align:start position:0%
+over here I know that that consumer
+prefers firm one per firm one's product
+
+ align:start position:0%
+prefers firm one per firm one's product
+ 
+
+ align:start position:0%
+prefers firm one per firm one's product
+to my product and so to get that firm to
+
+ align:start position:0%
+to my product and so to get that firm to
+ 
+
+ align:start position:0%
+to my product and so to get that firm to
+get that consumer I'm going to have to
+
+ align:start position:0%
+get that consumer I'm going to have to
+ 
+
+ align:start position:0%
+get that consumer I'm going to have to
+undercut firm one
+
+ align:start position:0%
+undercut firm one
+ 
+
+ align:start position:0%
+undercut firm one
+um in pricing to this consumer there's
+
+ align:start position:0%
+um in pricing to this consumer there's
+ 
+
+ align:start position:0%
+um in pricing to this consumer there's
+no product differentiation left right we
+
+ align:start position:0%
+no product differentiation left right we
+ 
+
+ align:start position:0%
+no product differentiation left right we
+know this consumer has some value V1 for
+
+ align:start position:0%
+know this consumer has some value V1 for
+ 
+
+ align:start position:0%
+know this consumer has some value V1 for
+firm one's product and some value V2 for
+
+ align:start position:0%
+firm one's product and some value V2 for
+ 
+
+ align:start position:0%
+firm one's product and some value V2 for
+firm 2's product and we're just pricing
+
+ align:start position:0%
+firm 2's product and we're just pricing
+ 
+
+ align:start position:0%
+firm 2's product and we're just pricing
+to that consumer like in a beran
+
+ align:start position:0%
+to that consumer like in a beran
+ 
+
+ align:start position:0%
+to that consumer like in a beran
+competition model so what's going to
+
+ align:start position:0%
+competition model so what's going to
+ 
+
+ align:start position:0%
+competition model so what's going to
+happen is Bertrand competition is just
+
+ align:start position:0%
+happen is Bertrand competition is just
+ 
+
+ align:start position:0%
+happen is Bertrand competition is just
+going to force prices down until you
+
+ align:start position:0%
+going to force prices down until you
+ 
+
+ align:start position:0%
+going to force prices down until you
+know P2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+star equals
+
+ align:start position:0%
+star equals
+ 
+
+ align:start position:0%
+star equals
+c and P1 star is going to be so P2 star
+
+ align:start position:0%
+c and P1 star is going to be so P2 star
+ 
+
+ align:start position:0%
+c and P1 star is going to be so P2 star
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+theta is C and P1 star of theta is going
+
+ align:start position:0%
+theta is C and P1 star of theta is going
+ 
+
+ align:start position:0%
+theta is C and P1 star of theta is going
+to be firm one's Advantage which
+
+ align:start position:0%
+to be firm one's Advantage which
+ 
+
+ align:start position:0%
+to be firm one's Advantage which
+isga Theta minus 1us
+
+ align:start position:0%
+isga Theta minus 1us
+ 
+
+ align:start position:0%
+isga Theta minus 1us
+Theta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um m - 1us Theta so that's uh
+
+ align:start position:0%
+um m - 1us Theta so that's uh
+ 
+
+ align:start position:0%
+um m - 1us Theta so that's uh
+1us C+ so C plus 1 - 2 Theta so what
+
+ align:start position:0%
+1us C+ so C plus 1 - 2 Theta so what
+ 
+
+ align:start position:0%
+1us C+ so C plus 1 - 2 Theta so what
+firm one is going to do is firm one is
+
+ align:start position:0%
+firm one is going to do is firm one is
+ 
+
+ align:start position:0%
+firm one is going to do is firm one is
+going to price at its Advantage relative
+
+ align:start position:0%
+going to price at its Advantage relative
+ 
+
+ align:start position:0%
+going to price at its Advantage relative
+to firm two and the consumer is going to
+
+ align:start position:0%
+to firm two and the consumer is going to
+ 
+
+ align:start position:0%
+to firm two and the consumer is going to
+buy from firm
+
+ align:start position:0%
+buy from firm
+ 
+
+ align:start position:0%
+buy from firm
+one and so what you get if you over here
+
+ align:start position:0%
+one and so what you get if you over here
+ 
+
+ align:start position:0%
+one and so what you get if you over here
+I've tried to graph what is price
+
+ align:start position:0%
+I've tried to graph what is price
+ 
+
+ align:start position:0%
+I've tried to graph what is price
+equilibrium price paid as a function of
+
+ align:start position:0%
+equilibrium price paid as a function of
+ 
+
+ align:start position:0%
+equilibrium price paid as a function of
+theta and all these consumers over here
+
+ align:start position:0%
+theta and all these consumers over here
+ 
+
+ align:start position:0%
+theta and all these consumers over here
+hereby from firm one uh as you come to
+
+ align:start position:0%
+hereby from firm one uh as you come to
+ 
+
+ align:start position:0%
+hereby from firm one uh as you come to
+the middle of the line at the middle of
+
+ align:start position:0%
+the middle of the line at the middle of
+ 
+
+ align:start position:0%
+the middle of the line at the middle of
+the line they're in pure berr
+
+ align:start position:0%
+the line they're in pure berr
+ 
+
+ align:start position:0%
+the line they're in pure berr
+competition the consumer has the same
+
+ align:start position:0%
+competition the consumer has the same
+ 
+
+ align:start position:0%
+competition the consumer has the same
+preferences for both so they both price
+
+ align:start position:0%
+preferences for both so they both price
+ 
+
+ align:start position:0%
+preferences for both so they both price
+at C and then you go back up here to C
+
+ align:start position:0%
+at C and then you go back up here to C
+ 
+
+ align:start position:0%
+at C and then you go back up here to C
+plus T at the end so no discrimination
+
+ align:start position:0%
+plus T at the end so no discrimination
+ 
+
+ align:start position:0%
+plus T at the end so no discrimination
+everyone pays C plus
+
+ align:start position:0%
+everyone pays C plus
+ 
+
+ align:start position:0%
+everyone pays C plus
+t uh in with discrimination the worst
+
+ align:start position:0%
+t uh in with discrimination the worst
+ 
+
+ align:start position:0%
+t uh in with discrimination the worst
+case is you pay C plus T if if someone
+
+ align:start position:0%
+case is you pay C plus T if if someone
+ 
+
+ align:start position:0%
+case is you pay C plus T if if someone
+knows you're fully captive and like
+
+ align:start position:0%
+knows you're fully captive and like
+ 
+
+ align:start position:0%
+knows you're fully captive and like
+their product by T better and then
+
+ align:start position:0%
+their product by T better and then
+ 
+
+ align:start position:0%
+their product by T better and then
+otherwise you pay C in the
+
+ align:start position:0%
+otherwise you pay C in the
+ 
+
+ align:start position:0%
+otherwise you pay C in the
+middle okay so all the consumers are
+
+ align:start position:0%
+middle okay so all the consumers are
+ 
+
+ align:start position:0%
+middle okay so all the consumers are
+better off and they're better off
+
+ align:start position:0%
+better off and they're better off
+ 
+
+ align:start position:0%
+better off and they're better off
+because the rivals are cutting prices to
+
+ align:start position:0%
+because the rivals are cutting prices to
+ 
+
+ align:start position:0%
+because the rivals are cutting prices to
+Target consumers who don't want to buy
+
+ align:start position:0%
+Target consumers who don't want to buy
+ 
+
+ align:start position:0%
+Target consumers who don't want to buy
+from them and that targeting the rivals
+
+ align:start position:0%
+from them and that targeting the rivals
+ 
+
+ align:start position:0%
+from them and that targeting the rivals
+consumers is an intens allowing them to
+
+ align:start position:0%
+consumers is an intens allowing them to
+ 
+
+ align:start position:0%
+consumers is an intens allowing them to
+do that intensifies the competition and
+
+ align:start position:0%
+do that intensifies the competition and
+ 
+
+ align:start position:0%
+do that intensifies the competition and
+that intensifies competition Cuts prices
+
+ align:start position:0%
+that intensifies competition Cuts prices
+ 
+
+ align:start position:0%
+that intensifies competition Cuts prices
+for everybody so that's the sort of
+
+ align:start position:0%
+for everybody so that's the sort of
+ 
+
+ align:start position:0%
+for everybody so that's the sort of
+thought that price discrimination can be
+
+ align:start position:0%
+thought that price discrimination can be
+ 
+
+ align:start position:0%
+thought that price discrimination can be
+a universal good for
+
+ align:start position:0%
+a universal good for
+ 
+
+ align:start position:0%
+a universal good for
+consumers
+
+ align:start position:0%
+consumers
+ 
+
+ align:start position:0%
+consumers
+okay uh
+
+ align:start position:0%
+okay uh
+ 
+
+ align:start position:0%
+okay uh
+second insight though uh came uh you
+
+ align:start position:0%
+second insight though uh came uh you
+ 
+
+ align:start position:0%
+second insight though uh came uh you
+know uh Ken courts a decade later was
+
+ align:start position:0%
+know uh Ken courts a decade later was
+ 
+
+ align:start position:0%
+know uh Ken courts a decade later was
+that that's true but there's a second
+
+ align:start position:0%
+that that's true but there's a second
+ 
+
+ align:start position:0%
+that that's true but there's a second
+effect and price discrimination can
+
+ align:start position:0%
+effect and price discrimination can
+ 
+
+ align:start position:0%
+effect and price discrimination can
+actually make prices higher for all
+
+ align:start position:0%
+actually make prices higher for all
+ 
+
+ align:start position:0%
+actually make prices higher for all
+consumers and it's it's the thought that
+
+ align:start position:0%
+consumers and it's it's the thought that
+ 
+
+ align:start position:0%
+consumers and it's it's the thought that
+you know price discrimination makes your
+
+ align:start position:0%
+you know price discrimination makes your
+ 
+
+ align:start position:0%
+you know price discrimination makes your
+pricing more
+
+ align:start position:0%
+pricing more
+ 
+
+ align:start position:0%
+pricing more
+flexible one thing that lets you do is
+
+ align:start position:0%
+flexible one thing that lets you do is
+ 
+
+ align:start position:0%
+flexible one thing that lets you do is
+Target your Rivals consumers and that's
+
+ align:start position:0%
+Target your Rivals consumers and that's
+ 
+
+ align:start position:0%
+Target your Rivals consumers and that's
+good for competition the other thing it
+
+ align:start position:0%
+good for competition the other thing it
+ 
+
+ align:start position:0%
+good for competition the other thing it
+does is let you exploit people who are
+
+ align:start position:0%
+does is let you exploit people who are
+ 
+
+ align:start position:0%
+does is let you exploit people who are
+captive to you and so courts looked at
+
+ align:start position:0%
+captive to you and so courts looked at
+ 
+
+ align:start position:0%
+captive to you and so courts looked at
+this specification where if you think
+
+ align:start position:0%
+this specification where if you think
+ 
+
+ align:start position:0%
+this specification where if you think
+about it so over here what I've tried to
+
+ align:start position:0%
+about it so over here what I've tried to
+ 
+
+ align:start position:0%
+about it so over here what I've tried to
+graph is
+
+ align:start position:0%
+graph is
+ 
+
+ align:start position:0%
+graph is
+um uh you know what that's a graph of is
+
+ align:start position:0%
+um uh you know what that's a graph of is
+ 
+
+ align:start position:0%
+um uh you know what that's a graph of is
+what is uh
+
+ align:start position:0%
+what is uh
+ 
+
+ align:start position:0%
+what is uh
+V the value that you get for buying from
+
+ align:start position:0%
+V the value that you get for buying from
+ 
+
+ align:start position:0%
+V the value that you get for buying from
+firm Theta and what he assumes is that
+
+ align:start position:0%
+firm Theta and what he assumes is that
+ 
+
+ align:start position:0%
+firm Theta and what he assumes is that
+you get value two from buying from a
+
+ align:start position:0%
+you get value two from buying from a
+ 
+
+ align:start position:0%
+you get value two from buying from a
+consumer you know so these are uh value
+
+ align:start position:0%
+consumer you know so these are uh value
+ 
+
+ align:start position:0%
+consumer you know so these are uh value
+they get buying from firm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one your value goes like this the
+
+ align:start position:0%
+one your value goes like this the
+ 
+
+ align:start position:0%
+one your value goes like this the
+farther your preferred type Theta is
+
+ align:start position:0%
+farther your preferred type Theta is
+ 
+
+ align:start position:0%
+farther your preferred type Theta is
+from firm one's product um the lower is
+
+ align:start position:0%
+from firm one's product um the lower is
+ 
+
+ align:start position:0%
+from firm one's product um the lower is
+the utility you get from
+
+ align:start position:0%
+the utility you get from
+ 
+
+ align:start position:0%
+the utility you get from
+it and then once the product is too far
+
+ align:start position:0%
+it and then once the product is too far
+ 
+
+ align:start position:0%
+it and then once the product is too far
+from what you want your utility just
+
+ align:start position:0%
+from what you want your utility just
+ 
+
+ align:start position:0%
+from what you want your utility just
+drops to zero like so I have this
+
+ align:start position:0%
+drops to zero like so I have this
+ 
+
+ align:start position:0%
+drops to zero like so I have this
+decreasing you know distance from firm
+
+ align:start position:0%
+decreasing you know distance from firm
+ 
+
+ align:start position:0%
+decreasing you know distance from firm
+one I like it less and less and then
+
+ align:start position:0%
+one I like it less and less and then
+ 
+
+ align:start position:0%
+one I like it less and less and then
+once it gets to some point I'm like I
+
+ align:start position:0%
+once it gets to some point I'm like I
+ 
+
+ align:start position:0%
+once it gets to some point I'm like I
+can't use that and then your utility
+
+ align:start position:0%
+can't use that and then your utility
+ 
+
+ align:start position:0%
+can't use that and then your utility
+drops to zero so that's my utility
+
+ align:start position:0%
+drops to zero so that's my utility
+ 
+
+ align:start position:0%
+drops to zero so that's my utility
+buying from firm one
+
+ align:start position:0%
+buying from firm one
+ 
+
+ align:start position:0%
+buying from firm one
+and my utility buying from firm two does
+
+ align:start position:0%
+and my utility buying from firm two does
+ 
+
+ align:start position:0%
+and my utility buying from firm two does
+the opposite it's zero here and then it
+
+ align:start position:0%
+the opposite it's zero here and then it
+ 
+
+ align:start position:0%
+the opposite it's zero here and then it
+goes up like that so these high Theta
+
+ align:start position:0%
+goes up like that so these high Theta
+ 
+
+ align:start position:0%
+goes up like that so these high Theta
+consumers really like and get utility
+
+ align:start position:0%
+consumers really like and get utility
+ 
+
+ align:start position:0%
+consumers really like and get utility
+two from buying from one's product the
+
+ align:start position:0%
+two from buying from one's product the
+ 
+
+ align:start position:0%
+two from buying from one's product the
+guy in the middle gets utility one from
+
+ align:start position:0%
+guy in the middle gets utility one from
+ 
+
+ align:start position:0%
+guy in the middle gets utility one from
+both and vice versa so in some sense
+
+ align:start position:0%
+both and vice versa so in some sense
+ 
+
+ align:start position:0%
+both and vice versa so in some sense
+I've eliminated that targeting your
+
+ align:start position:0%
+I've eliminated that targeting your
+ 
+
+ align:start position:0%
+I've eliminated that targeting your
+Rivals uh competitors effect by saying
+
+ align:start position:0%
+Rivals uh competitors effect by saying
+ 
+
+ align:start position:0%
+Rivals uh competitors effect by saying
+that anyone who gets utility from one
+
+ align:start position:0%
+that anyone who gets utility from one
+ 
+
+ align:start position:0%
+that anyone who gets utility from one
+firm gets zero utility from the other
+
+ align:start position:0%
+firm gets zero utility from the other
+ 
+
+ align:start position:0%
+firm gets zero utility from the other
+firm so letting them Target your rivals
+
+ align:start position:0%
+firm so letting them Target your rivals
+ 
+
+ align:start position:0%
+firm so letting them Target your rivals
+consumers doesn't actually create any
+
+ align:start position:0%
+consumers doesn't actually create any
+ 
+
+ align:start position:0%
+consumers doesn't actually create any
+competition um so you know what would
+
+ align:start position:0%
+competition um so you know what would
+ 
+
+ align:start position:0%
+competition um so you know what would
+happen in this
+
+ align:start position:0%
+happen in this
+ 
+
+ align:start position:0%
+happen in this
+model um in this model if I ban
+
+ align:start position:0%
+model um in this model if I ban
+ 
+
+ align:start position:0%
+model um in this model if I ban
+competition if I ban price
+
+ align:start position:0%
+competition if I ban price
+ 
+
+ align:start position:0%
+competition if I ban price
+discrimination sorry if I ban price
+
+ align:start position:0%
+discrimination sorry if I ban price
+ 
+
+ align:start position:0%
+discrimination sorry if I ban price
+discrimination firm one is essentially
+
+ align:start position:0%
+discrimination firm one is essentially
+ 
+
+ align:start position:0%
+discrimination firm one is essentially
+pricing as if it had a linear demand
+
+ align:start position:0%
+pricing as if it had a linear demand
+ 
+
+ align:start position:0%
+pricing as if it had a linear demand
+curve you know it's a linear demand
+
+ align:start position:0%
+curve you know it's a linear demand
+ 
+
+ align:start position:0%
+curve you know it's a linear demand
+curve that cuts off but if you remember
+
+ align:start position:0%
+curve that cuts off but if you remember
+ 
+
+ align:start position:0%
+curve that cuts off but if you remember
+if you have a linear demand curve that
+
+ align:start position:0%
+if you have a linear demand curve that
+ 
+
+ align:start position:0%
+if you have a linear demand curve that
+looks like this even if it continues you
+
+ align:start position:0%
+looks like this even if it continues you
+ 
+
+ align:start position:0%
+looks like this even if it continues you
+still would price at
+
+ align:start position:0%
+still would price at
+ 
+
+ align:start position:0%
+still would price at
+one so with
+
+ align:start position:0%
+one so with
+ 
+
+ align:start position:0%
+one so with
+if you ban price discrimination firm one
+
+ align:start position:0%
+if you ban price discrimination firm one
+ 
+
+ align:start position:0%
+if you ban price discrimination firm one
+is going to set P star equals one firm
+
+ align:start position:0%
+is going to set P star equals one firm
+ 
+
+ align:start position:0%
+is going to set P star equals one firm
+two is going to set P star equals one
+
+ align:start position:0%
+two is going to set P star equals one
+ 
+
+ align:start position:0%
+two is going to set P star equals one
+because they're both just pricing to the
+
+ align:start position:0%
+because they're both just pricing to the
+ 
+
+ align:start position:0%
+because they're both just pricing to the
+linear demand curve 2 minus
+
+ align:start position:0%
+linear demand curve 2 minus
+ 
+
+ align:start position:0%
+linear demand curve 2 minus
+P whereas if you allow them to
+
+ align:start position:0%
+P whereas if you allow them to
+ 
+
+ align:start position:0%
+P whereas if you allow them to
+discriminate I do first-degree price
+
+ align:start position:0%
+discriminate I do first-degree price
+ 
+
+ align:start position:0%
+discriminate I do first-degree price
+discrimination this guy pays two this
+
+ align:start position:0%
+discrimination this guy pays two this
+ 
+
+ align:start position:0%
+discrimination this guy pays two this
+guy pays 1.9 this guy pays 1.8 and so on
+
+ align:start position:0%
+guy pays 1.9 this guy pays 1.8 and so on
+ 
+
+ align:start position:0%
+guy pays 1.9 this guy pays 1.8 and so on
+till this guy pays one so basically I
+
+ align:start position:0%
+till this guy pays one so basically I
+ 
+
+ align:start position:0%
+till this guy pays one so basically I
+just raise prices to everyone because
+
+ align:start position:0%
+just raise prices to everyone because
+ 
+
+ align:start position:0%
+just raise prices to everyone because
+letting me price discriminate lets me
+
+ align:start position:0%
+letting me price discriminate lets me
+ 
+
+ align:start position:0%
+letting me price discriminate lets me
+exploit all of lets me extract all of
+
+ align:start position:0%
+exploit all of lets me extract all of
+ 
+
+ align:start position:0%
+exploit all of lets me extract all of
+their Surplus when I don't have
+
+ align:start position:0%
+their Surplus when I don't have
+ 
+
+ align:start position:0%
+their Surplus when I don't have
+competition and here I've designed the
+
+ align:start position:0%
+competition and here I've designed the
+ 
+
+ align:start position:0%
+competition and here I've designed the
+oligopoly so there really isn't any
+
+ align:start position:0%
+oligopoly so there really isn't any
+ 
+
+ align:start position:0%
+oligopoly so there really isn't any
+competition so you know I think courts'
+
+ align:start position:0%
+competition so you know I think courts'
+ 
+
+ align:start position:0%
+competition so you know I think courts'
+basic Insight was that there are these
+
+ align:start position:0%
+basic Insight was that there are these
+ 
+
+ align:start position:0%
+basic Insight was that there are these
+two effects and we shouldn't necessarily
+
+ align:start position:0%
+two effects and we shouldn't necessarily
+ 
+
+ align:start position:0%
+two effects and we shouldn't necessarily
+expect either of those two effects to
+
+ align:start position:0%
+expect either of those two effects to
+ 
+
+ align:start position:0%
+expect either of those two effects to
+dominate you know price discrimination
+
+ align:start position:0%
+dominate you know price discrimination
+ 
+
+ align:start position:0%
+dominate you know price discrimination
+can be good because it intensifies
+
+ align:start position:0%
+can be good because it intensifies
+ 
+
+ align:start position:0%
+can be good because it intensifies
+competition it can be bad because it has
+
+ align:start position:0%
+competition it can be bad because it has
+ 
+
+ align:start position:0%
+competition it can be bad because it has
+more exploitation and it's just going to
+
+ align:start position:0%
+more exploitation and it's just going to
+ 
+
+ align:start position:0%
+more exploitation and it's just going to
+matter on the distribution of relative
+
+ align:start position:0%
+matter on the distribution of relative
+ 
+
+ align:start position:0%
+matter on the distribution of relative
+preferences for firm one versus firm 2's
+
+ align:start position:0%
+preferences for firm one versus firm 2's
+ 
+
+ align:start position:0%
+preferences for firm one versus firm 2's
+products whether the exploitation effect
+
+ align:start position:0%
+products whether the exploitation effect
+ 
+
+ align:start position:0%
+products whether the exploitation effect
+dominates and makes prices go up or the
+
+ align:start position:0%
+dominates and makes prices go up or the
+ 
+
+ align:start position:0%
+dominates and makes prices go up or the
+the competition effect dominates and
+
+ align:start position:0%
+the competition effect dominates and
+ 
+
+ align:start position:0%
+the competition effect dominates and
+makes prices go down um as I said you
+
+ align:start position:0%
+makes prices go down um as I said you
+ 
+
+ align:start position:0%
+makes prices go down um as I said you
+know like right the this hoteling model
+
+ align:start position:0%
+know like right the this hoteling model
+ 
+
+ align:start position:0%
+know like right the this hoteling model
+it's like it's an intermediate effect
+
+ align:start position:0%
+it's like it's an intermediate effect
+ 
+
+ align:start position:0%
+it's like it's an intermediate effect
+it's like you charge intermediate prices
+
+ align:start position:0%
+it's like you charge intermediate prices
+ 
+
+ align:start position:0%
+it's like you charge intermediate prices
+and you know you're lose the ability to
+
+ align:start position:0%
+and you know you're lose the ability to
+ 
+
+ align:start position:0%
+and you know you're lose the ability to
+compete and discriminate in a way that
+
+ align:start position:0%
+compete and discriminate in a way that
+ 
+
+ align:start position:0%
+compete and discriminate in a way that
+makes you just sort of charge something
+
+ align:start position:0%
+makes you just sort of charge something
+ 
+
+ align:start position:0%
+makes you just sort of charge something
+in between what you would have charged
+
+ align:start position:0%
+in between what you would have charged
+ 
+
+ align:start position:0%
+in between what you would have charged
+the high and low types
+
+ align:start position:0%
+the high and low types
+ 
+
+ align:start position:0%
+the high and low types
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay any questions on that argument yeah
+
+ align:start position:0%
+okay any questions on that argument yeah
+ 
+
+ align:start position:0%
+okay any questions on that argument yeah
+is it this just kind of arguing that if
+
+ align:start position:0%
+is it this just kind of arguing that if
+ 
+
+ align:start position:0%
+is it this just kind of arguing that if
+it's not action oligopoly monopoly yeah
+
+ align:start position:0%
+it's not action oligopoly monopoly yeah
+ 
+
+ align:start position:0%
+it's not action oligopoly monopoly yeah
+that's right it so he he made it a
+
+ align:start position:0%
+that's right it so he he made it a
+ 
+
+ align:start position:0%
+that's right it so he he made it a
+monopoly so it's but then obviously like
+
+ align:start position:0%
+monopoly so it's but then obviously like
+ 
+
+ align:start position:0%
+monopoly so it's but then obviously like
+you could have it be an oligopoly like
+
+ align:start position:0%
+you could have it be an oligopoly like
+ 
+
+ align:start position:0%
+you could have it be an oligopoly like
+this and you would get the same results
+
+ align:start position:0%
+this and you would get the same results
+ 
+
+ align:start position:0%
+this and you would get the same results
+right like if it was an oligopoly where
+
+ align:start position:0%
+right like if it was an oligopoly where
+ 
+
+ align:start position:0%
+right like if it was an oligopoly where
+it really was an oligopoly but most of
+
+ align:start position:0%
+it really was an oligopoly but most of
+ 
+
+ align:start position:0%
+it really was an oligopoly but most of
+them got low utility from one and high
+
+ align:start position:0%
+them got low utility from one and high
+ 
+
+ align:start position:0%
+them got low utility from one and high
+from the other then you would still get
+
+ align:start position:0%
+from the other then you would still get
+ 
+
+ align:start position:0%
+from the other then you would still get
+the same effect there but it it's yeah
+
+ align:start position:0%
+the same effect there but it it's yeah
+ 
+
+ align:start position:0%
+the same effect there but it it's yeah
+he's arguing that it's basically it's
+
+ align:start position:0%
+he's arguing that it's basically it's
+ 
+
+ align:start position:0%
+he's arguing that it's basically it's
+adjacent to the Monopoly model and in
+
+ align:start position:0%
+adjacent to the Monopoly model and in
+ 
+
+ align:start position:0%
+adjacent to the Monopoly model and in
+the Monopoly model it goes this way so
+
+ align:start position:0%
+the Monopoly model it goes this way so
+ 
+
+ align:start position:0%
+the Monopoly model it goes this way so
+oligopoly models near that one it's
+
+ align:start position:0%
+oligopoly models near that one it's
+ 
+
+ align:start position:0%
+oligopoly models near that one it's
+going to go the same way
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah okay um so that that was sort of
+
+ align:start position:0%
+yeah okay um so that that was sort of
+ 
+
+ align:start position:0%
+yeah okay um so that that was sort of
+oligopoly third degree price
+
+ align:start position:0%
+oligopoly third degree price
+ 
+
+ align:start position:0%
+oligopoly third degree price
+discrimination what about second degree
+
+ align:start position:0%
+discrimination what about second degree
+ 
+
+ align:start position:0%
+discrimination what about second degree
+price discrimination and I do think that
+
+ align:start position:0%
+price discrimination and I do think that
+ 
+
+ align:start position:0%
+price discrimination and I do think that
+you know oligopoly second degree price
+
+ align:start position:0%
+you know oligopoly second degree price
+ 
+
+ align:start position:0%
+you know oligopoly second degree price
+discrimination is a really important
+
+ align:start position:0%
+discrimination is a really important
+ 
+
+ align:start position:0%
+discrimination is a really important
+topic because you know I think many many
+
+ align:start position:0%
+topic because you know I think many many
+ 
+
+ align:start position:0%
+topic because you know I think many many
+products people
+
+ align:start position:0%
+products people
+ 
+
+ align:start position:0%
+products people
+buy there is second degree
+
+ align:start position:0%
+buy there is second degree
+ 
+
+ align:start position:0%
+buy there is second degree
+discrimination there like you know
+
+ align:start position:0%
+discrimination there like you know
+ 
+
+ align:start position:0%
+discrimination there like you know
+you're buying phones there is the iPhone
+
+ align:start position:0%
+you're buying phones there is the iPhone
+ 
+
+ align:start position:0%
+you're buying phones there is the iPhone
+13 and the iPhone 14 and the 128
+
+ align:start position:0%
+13 and the iPhone 14 and the 128
+ 
+
+ align:start position:0%
+13 and the iPhone 14 and the 128
+megabyte and the 512 megabyte version
+
+ align:start position:0%
+megabyte and the 512 megabyte version
+ 
+
+ align:start position:0%
+megabyte and the 512 megabyte version
+you know you're buying cable TV and it's
+
+ align:start position:0%
+you know you're buying cable TV and it's
+ 
+
+ align:start position:0%
+you know you're buying cable TV and it's
+cable TV package one package two package
+
+ align:start position:0%
+cable TV package one package two package
+ 
+
+ align:start position:0%
+cable TV package one package two package
+three package four all with increasing
+
+ align:start position:0%
+three package four all with increasing
+ 
+
+ align:start position:0%
+three package four all with increasing
+features you know you have competing
+
+ align:start position:0%
+features you know you have competing
+ 
+
+ align:start position:0%
+features you know you have competing
+firm selling TVs everyone's got the you
+
+ align:start position:0%
+firm selling TVs everyone's got the you
+ 
+
+ align:start position:0%
+firm selling TVs everyone's got the you
+know 42in TV and the 49 in TV and the 55
+
+ align:start position:0%
+know 42in TV and the 49 in TV and the 55
+ 
+
+ align:start position:0%
+know 42in TV and the 49 in TV and the 55
+in TV and the 62in TV and each of those
+
+ align:start position:0%
+in TV and the 62in TV and each of those
+ 
+
+ align:start position:0%
+in TV and the 62in TV and each of those
+TVs has the 4K or doesn't have the 4K
+
+ align:start position:0%
+TVs has the 4K or doesn't have the 4K
+ 
+
+ align:start position:0%
+TVs has the 4K or doesn't have the 4K
+but it's you know you generally see
+
+ align:start position:0%
+but it's you know you generally see
+ 
+
+ align:start position:0%
+but it's you know you generally see
+firms in olop Industries are selling
+
+ align:start position:0%
+firms in olop Industries are selling
+ 
+
+ align:start position:0%
+firms in olop Industries are selling
+multiple products competing with
+
+ align:start position:0%
+multiple products competing with
+ 
+
+ align:start position:0%
+multiple products competing with
+multiple products of each other
+
+ align:start position:0%
+multiple products of each other
+ 
+
+ align:start position:0%
+multiple products of each other
+um you know so if you're talking about
+
+ align:start position:0%
+um you know so if you're talking about
+ 
+
+ align:start position:0%
+um you know so if you're talking about
+oligopoly second degree discrimination
+
+ align:start position:0%
+oligopoly second degree discrimination
+ 
+
+ align:start position:0%
+oligopoly second degree discrimination
+or the the cars in breaston hand's
+
+ align:start position:0%
+or the the cars in breaston hand's
+ 
+
+ align:start position:0%
+or the the cars in breaston hand's
+example right like it's Ford is
+
+ align:start position:0%
+example right like it's Ford is
+ 
+
+ align:start position:0%
+example right like it's Ford is
+producing a line of cards GM is
+
+ align:start position:0%
+producing a line of cards GM is
+ 
+
+ align:start position:0%
+producing a line of cards GM is
+producing a line of cars those cars are
+
+ align:start position:0%
+producing a line of cars those cars are
+ 
+
+ align:start position:0%
+producing a line of cars those cars are
+competing against other models and
+
+ align:start position:0%
+competing against other models and
+ 
+
+ align:start position:0%
+competing against other models and
+there's sort of vertical constraints
+
+ align:start position:0%
+there's sort of vertical constraints
+ 
+
+ align:start position:0%
+there's sort of vertical constraints
+within the firm and there's also
+
+ align:start position:0%
+within the firm and there's also
+ 
+
+ align:start position:0%
+within the firm and there's also
+competition across the firms um so you
+
+ align:start position:0%
+competition across the firms um so you
+ 
+
+ align:start position:0%
+competition across the firms um so you
+know clearly you want to have vertical
+
+ align:start position:0%
+know clearly you want to have vertical
+ 
+
+ align:start position:0%
+know clearly you want to have vertical
+differentiation and you want to have
+
+ align:start position:0%
+differentiation and you want to have
+ 
+
+ align:start position:0%
+differentiation and you want to have
+horizontal different
+
+ align:start position:0%
+horizontal different
+ 
+
+ align:start position:0%
+horizontal different
+iation and then the substitution
+
+ align:start position:0%
+iation and then the substitution
+ 
+
+ align:start position:0%
+iation and then the substitution
+patterns there's going to be cross firm
+
+ align:start position:0%
+patterns there's going to be cross firm
+ 
+
+ align:start position:0%
+patterns there's going to be cross firm
+substitution going on and there's going
+
+ align:start position:0%
+substitution going on and there's going
+ 
+
+ align:start position:0%
+substitution going on and there's going
+to be within firm substitution going on
+
+ align:start position:0%
+to be within firm substitution going on
+ 
+
+ align:start position:0%
+to be within firm substitution going on
+and it just turns out it's hard to write
+
+ align:start position:0%
+and it just turns out it's hard to write
+ 
+
+ align:start position:0%
+and it just turns out it's hard to write
+down a nice tractable model that has you
+
+ align:start position:0%
+down a nice tractable model that has you
+ 
+
+ align:start position:0%
+down a nice tractable model that has you
+know the two dimensions of consumer
+
+ align:start position:0%
+know the two dimensions of consumer
+ 
+
+ align:start position:0%
+know the two dimensions of consumer
+tastes and has both substitution
+
+ align:start position:0%
+tastes and has both substitution
+ 
+
+ align:start position:0%
+tastes and has both substitution
+patterns mattering in the sort of
+
+ align:start position:0%
+patterns mattering in the sort of
+ 
+
+ align:start position:0%
+patterns mattering in the sort of
+binding IC constraints and The Binding
+
+ align:start position:0%
+binding IC constraints and The Binding
+ 
+
+ align:start position:0%
+binding IC constraints and The Binding
+cross firm constraints um so what the
+
+ align:start position:0%
+cross firm constraints um so what the
+ 
+
+ align:start position:0%
+cross firm constraints um so what the
+literatures tend to do is is do a few
+
+ align:start position:0%
+literatures tend to do is is do a few
+ 
+
+ align:start position:0%
+literatures tend to do is is do a few
+different special cases one thing it's
+
+ align:start position:0%
+different special cases one thing it's
+ 
+
+ align:start position:0%
+different special cases one thing it's
+done is to assume independent horizontal
+
+ align:start position:0%
+done is to assume independent horizontal
+ 
+
+ align:start position:0%
+done is to assume independent horizontal
+and vertical preferences and there's
+
+ align:start position:0%
+and vertical preferences and there's
+ 
+
+ align:start position:0%
+and vertical preferences and there's
+this observation that if you make
+
+ align:start position:0%
+this observation that if you make
+ 
+
+ align:start position:0%
+this observation that if you make
+horizontal and vertical preferences
+
+ align:start position:0%
+horizontal and vertical preferences
+ 
+
+ align:start position:0%
+horizontal and vertical preferences
+independent you get a surprisingly
+
+ align:start position:0%
+independent you get a surprisingly
+ 
+
+ align:start position:0%
+independent you get a surprisingly
+tractable model that you can do even
+
+ align:start position:0%
+tractable model that you can do even
+ 
+
+ align:start position:0%
+tractable model that you can do even
+with a Continuum of types um the other
+
+ align:start position:0%
+with a Continuum of types um the other
+ 
+
+ align:start position:0%
+with a Continuum of types um the other
+thing that people do is have discrete
+
+ align:start position:0%
+thing that people do is have discrete
+ 
+
+ align:start position:0%
+thing that people do is have discrete
+vertical types and when you have
+
+ align:start position:0%
+vertical types and when you have
+ 
+
+ align:start position:0%
+vertical types and when you have
+discrete vertical types um you can
+
+ align:start position:0%
+discrete vertical types um you can
+ 
+
+ align:start position:0%
+discrete vertical types um you can
+sometimes make the IC constraints the
+
+ align:start position:0%
+sometimes make the IC constraints the
+ 
+
+ align:start position:0%
+sometimes make the IC constraints the
+within firm IC constraints non-binding
+
+ align:start position:0%
+within firm IC constraints non-binding
+ 
+
+ align:start position:0%
+within firm IC constraints non-binding
+and eliminate the number of constraints
+
+ align:start position:0%
+and eliminate the number of constraints
+ 
+
+ align:start position:0%
+and eliminate the number of constraints
+you have to solve for um and then a
+
+ align:start position:0%
+you have to solve for um and then a
+ 
+
+ align:start position:0%
+you have to solve for um and then a
+third approach you sometimes see people
+
+ align:start position:0%
+third approach you sometimes see people
+ 
+
+ align:start position:0%
+third approach you sometimes see people
+do is actually just eliminate the
+
+ align:start position:0%
+do is actually just eliminate the
+ 
+
+ align:start position:0%
+do is actually just eliminate the
+vertical differentiation entirely and
+
+ align:start position:0%
+vertical differentiation entirely and
+ 
+
+ align:start position:0%
+vertical differentiation entirely and
+talk about uh second degree
+
+ align:start position:0%
+talk about uh second degree
+ 
+
+ align:start position:0%
+talk about uh second degree
+discrimination in a model that doesn't
+
+ align:start position:0%
+discrimination in a model that doesn't
+ 
+
+ align:start position:0%
+discrimination in a model that doesn't
+have vertical uh
+
+ align:start position:0%
+have vertical uh
+ 
+
+ align:start position:0%
+have vertical uh
+differentiation
+
+ align:start position:0%
+differentiation
+ 
+
+ align:start position:0%
+differentiation
+um okay so let me go I'll start with
+
+ align:start position:0%
+um okay so let me go I'll start with
+ 
+
+ align:start position:0%
+um okay so let me go I'll start with
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+a you know overview of what happens in
+
+ align:start position:0%
+a you know overview of what happens in
+ 
+
+ align:start position:0%
+a you know overview of what happens in
+this independent model so um you know
+
+ align:start position:0%
+this independent model so um you know
+ 
+
+ align:start position:0%
+this independent model so um you know
+stole has a chapter of the handbook in
+
+ align:start position:0%
+stole has a chapter of the handbook in
+ 
+
+ align:start position:0%
+stole has a chapter of the handbook in
+IO that surveys this literature that's
+
+ align:start position:0%
+IO that surveys this literature that's
+ 
+
+ align:start position:0%
+IO that surveys this literature that's
+pretty big
+
+ align:start position:0%
+pretty big
+ 
+
+ align:start position:0%
+pretty big
+um and seemingly General you have these
+
+ align:start position:0%
+um and seemingly General you have these
+ 
+
+ align:start position:0%
+um and seemingly General you have these
+firms J they can produce a range of
+
+ align:start position:0%
+firms J they can produce a range of
+ 
+
+ align:start position:0%
+firms J they can produce a range of
+qualities s at some constant marginal
+
+ align:start position:0%
+qualities s at some constant marginal
+ 
+
+ align:start position:0%
+qualities s at some constant marginal
+cost C of s so typically they actually
+
+ align:start position:0%
+cost C of s so typically they actually
+ 
+
+ align:start position:0%
+cost C of s so typically they actually
+have a Continuum of s's they could
+
+ align:start position:0%
+have a Continuum of s's they could
+ 
+
+ align:start position:0%
+have a Continuum of s's they could
+produce if they wanted to uh consumer
+
+ align:start position:0%
+produce if they wanted to uh consumer
+ 
+
+ align:start position:0%
+produce if they wanted to uh consumer
+eyes utility from buying a good of
+
+ align:start position:0%
+eyes utility from buying a good of
+ 
+
+ align:start position:0%
+eyes utility from buying a good of
+quality s from firm J is Theta I of s so
+
+ align:start position:0%
+quality s from firm J is Theta I of s so
+ 
+
+ align:start position:0%
+quality s from firm J is Theta I of s so
+this is the vertical preference High
+
+ align:start position:0%
+this is the vertical preference High
+ 
+
+ align:start position:0%
+this is the vertical preference High
+types like are willing to pay more for
+
+ align:start position:0%
+types like are willing to pay more for
+ 
+
+ align:start position:0%
+types like are willing to pay more for
+Quality minus the price plus the epon i
+
+ align:start position:0%
+Quality minus the price plus the epon i
+ 
+
+ align:start position:0%
+Quality minus the price plus the epon i
+j so this is the logit like error um
+
+ align:start position:0%
+j so this is the logit like error um
+ 
+
+ align:start position:0%
+j so this is the logit like error um
+that we've had in our
+
+ align:start position:0%
+that we've had in our
+ 
+
+ align:start position:0%
+that we've had in our
+models and then models assume that the
+
+ align:start position:0%
+models and then models assume that the
+ 
+
+ align:start position:0%
+models and then models assume that the
+Theta I and the Epsilon I JS are all
+
+ align:start position:0%
+Theta I and the Epsilon I JS are all
+ 
+
+ align:start position:0%
+Theta I and the Epsilon I JS are all
+independent and Theta I is distributed F
+
+ align:start position:0%
+independent and Theta I is distributed F
+ 
+
+ align:start position:0%
+independent and Theta I is distributed F
+Theta Epsilon i j is dist distributed F
+
+ align:start position:0%
+Theta Epsilon i j is dist distributed F
+ 
+
+ align:start position:0%
+Theta Epsilon i j is dist distributed F
+Epsilon and they're pretty General in
+
+ align:start position:0%
+Epsilon and they're pretty General in
+ 
+
+ align:start position:0%
+Epsilon and they're pretty General in
+terms of what distribution of theta is
+
+ align:start position:0%
+terms of what distribution of theta is
+ 
+
+ align:start position:0%
+terms of what distribution of theta is
+in what distribution of epsilons you
+
+ align:start position:0%
+in what distribution of epsilons you
+ 
+
+ align:start position:0%
+in what distribution of epsilons you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+okay so let me Define SAR of theta to be
+
+ align:start position:0%
+okay so let me Define SAR of theta to be
+ 
+
+ align:start position:0%
+okay so let me Define SAR of theta to be
+the efficient quality for a consumer uh
+
+ align:start position:0%
+the efficient quality for a consumer uh
+ 
+
+ align:start position:0%
+the efficient quality for a consumer uh
+of type uh that should say type Theta to
+
+ align:start position:0%
+of type uh that should say type Theta to
+ 
+
+ align:start position:0%
+of type uh that should say type Theta to
+buy so you have a consumer this should
+
+ align:start position:0%
+buy so you have a consumer this should
+ 
+
+ align:start position:0%
+buy so you have a consumer this should
+be a Theta instead of a v so you know if
+
+ align:start position:0%
+be a Theta instead of a v so you know if
+ 
+
+ align:start position:0%
+be a Theta instead of a v so you know if
+you have a type Theta consumer they
+
+ align:start position:0%
+you have a type Theta consumer they
+ 
+
+ align:start position:0%
+you have a type Theta consumer they
+ought to be buying quality the maximize
+
+ align:start position:0%
+ought to be buying quality the maximize
+ 
+
+ align:start position:0%
+ought to be buying quality the maximize
+is Theta Time s minus C of s so this is
+
+ align:start position:0%
+is Theta Time s minus C of s so this is
+ 
+
+ align:start position:0%
+is Theta Time s minus C of s so this is
+if the goods were sold at Cost what
+
+ align:start position:0%
+if the goods were sold at Cost what
+ 
+
+ align:start position:0%
+if the goods were sold at Cost what
+would they buy that's the efficient
+
+ align:start position:0%
+would they buy that's the efficient
+ 
+
+ align:start position:0%
+would they buy that's the efficient
+thing to sell to them
+
+ align:start position:0%
+thing to sell to them
+ 
+
+ align:start position:0%
+thing to sell to them
+okay um so just an example of a for of a
+
+ align:start position:0%
+okay um so just an example of a for of a
+ 
+
+ align:start position:0%
+okay um so just an example of a for of a
+model fitting this consider a hoteling
+
+ align:start position:0%
+model fitting this consider a hoteling
+ 
+
+ align:start position:0%
+model fitting this consider a hoteling
+like model and suppose that Epsilon i1
+
+ align:start position:0%
+like model and suppose that Epsilon i1
+ 
+
+ align:start position:0%
+like model and suppose that Epsilon i1
+is distributed uniform on 0 to T and
+
+ align:start position:0%
+is distributed uniform on 0 to T and
+ 
+
+ align:start position:0%
+is distributed uniform on 0 to T and
+Epsilon I2 is is just the negative of
+
+ align:start position:0%
+Epsilon I2 is is just the negative of
+ 
+
+ align:start position:0%
+Epsilon I2 is is just the negative of
+Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one then a nashy equ that model is just
+
+ align:start position:0%
+one then a nashy equ that model is just
+ 
+
+ align:start position:0%
+one then a nashy equ that model is just
+PJs is C of S Plus t for all J and S so
+
+ align:start position:0%
+PJs is C of S Plus t for all J and S so
+ 
+
+ align:start position:0%
+PJs is C of S Plus t for all J and S so
+if you imagine it it's as if we've got
+
+ align:start position:0%
+if you imagine it it's as if we've got
+ 
+
+ align:start position:0%
+if you imagine it it's as if we've got
+this uh you know
+
+ align:start position:0%
+this uh you know
+ 
+
+ align:start position:0%
+this uh you know
+I've got this Continuum of hotelling
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lines so you have these different
+
+ align:start position:0%
+lines so you have these different
+ 
+
+ align:start position:0%
+lines so you have these different
+quality levels S1 S2 S3 S4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+S5 on each line let's imagine I charge
+
+ align:start position:0%
+S5 on each line let's imagine I charge
+ 
+
+ align:start position:0%
+S5 on each line let's imagine I charge
+uh P star equals c of
+
+ align:start position:0%
+uh P star equals c of
+ 
+
+ align:start position:0%
+uh P star equals c of
+s so quality of you know
+
+ align:start position:0%
+s so quality of you know
+ 
+
+ align:start position:0%
+s so quality of you know
+yeah price for Quality s is C of S Plus
+
+ align:start position:0%
+yeah price for Quality s is C of S Plus
+ 
+
+ align:start position:0%
+yeah price for Quality s is C of S Plus
+t Okay so imagine you had that
+
+ align:start position:0%
+t Okay so imagine you had that
+ 
+
+ align:start position:0%
+t Okay so imagine you had that
+pricing that every every quality I sell
+
+ align:start position:0%
+pricing that every every quality I sell
+ 
+
+ align:start position:0%
+pricing that every every quality I sell
+at the Cost Plus T then what are
+
+ align:start position:0%
+at the Cost Plus T then what are
+ 
+
+ align:start position:0%
+at the Cost Plus T then what are
+consumers going to do you know the
+
+ align:start position:0%
+consumers going to do you know the
+ 
+
+ align:start position:0%
+consumers going to do you know the
+markups are the same for every quality
+
+ align:start position:0%
+markups are the same for every quality
+ 
+
+ align:start position:0%
+markups are the same for every quality
+level so when I'm deciding which quality
+
+ align:start position:0%
+level so when I'm deciding which quality
+ 
+
+ align:start position:0%
+level so when I'm deciding which quality
+level to buy I buy the efficient quality
+
+ align:start position:0%
+level to buy I buy the efficient quality
+ 
+
+ align:start position:0%
+level to buy I buy the efficient quality
+level I buy s if I'm a type Theta
+
+ align:start position:0%
+level I buy s if I'm a type Theta
+ 
+
+ align:start position:0%
+level I buy s if I'm a type Theta
+consumer I buy SAR of theta
+
+ align:start position:0%
+consumer I buy SAR of theta
+ 
+
+ align:start position:0%
+consumer I buy SAR of theta
+so all the consumers for whom S3 is the
+
+ align:start position:0%
+so all the consumers for whom S3 is the
+ 
+
+ align:start position:0%
+so all the consumers for whom S3 is the
+optimal quality are like okay I'm either
+
+ align:start position:0%
+optimal quality are like okay I'm either
+ 
+
+ align:start position:0%
+optimal quality are like okay I'm either
+going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buy quality S3 from firm one or I'm
+
+ align:start position:0%
+buy quality S3 from firm one or I'm
+ 
+
+ align:start position:0%
+buy quality S3 from firm one or I'm
+going to buy quality 3 from S2 who do I
+
+ align:start position:0%
+going to buy quality 3 from S2 who do I
+ 
+
+ align:start position:0%
+going to buy quality 3 from S2 who do I
+buy from well again it depends on my it
+
+ align:start position:0%
+buy from well again it depends on my it
+ 
+
+ align:start position:0%
+buy from well again it depends on my it
+depends on my now I'm calling this an
+
+ align:start position:0%
+depends on my now I'm calling this an
+ 
+
+ align:start position:0%
+depends on my now I'm calling this an
+Epsilon i1 and an Epsilon
+
+ align:start position:0%
+Epsilon i1 and an Epsilon
+ 
+
+ align:start position:0%
+Epsilon i1 and an Epsilon
+I2
+
+ align:start position:0%
+I2
+ 
+
+ align:start position:0%
+I2
+but if I if my taste is I really like
+
+ align:start position:0%
+but if I if my taste is I really like
+ 
+
+ align:start position:0%
+but if I if my taste is I really like
+firm one's product I buy from firm one
+
+ align:start position:0%
+firm one's product I buy from firm one
+ 
+
+ align:start position:0%
+firm one's product I buy from firm one
+if my Epsilon is I really buy firm two's
+
+ align:start position:0%
+if my Epsilon is I really buy firm two's
+ 
+
+ align:start position:0%
+if my Epsilon is I really buy firm two's
+product I buy from firm two and so it's
+
+ align:start position:0%
+product I buy from firm two and so it's
+ 
+
+ align:start position:0%
+product I buy from firm two and so it's
+just the you know like as far as if the
+
+ align:start position:0%
+just the you know like as far as if the
+ 
+
+ align:start position:0%
+just the you know like as far as if the
+firm Cuts its price it's just like the
+
+ align:start position:0%
+firm Cuts its price it's just like the
+ 
+
+ align:start position:0%
+firm Cuts its price it's just like the
+competition on a line model and if it
+
+ align:start position:0%
+competition on a line model and if it
+ 
+
+ align:start position:0%
+competition on a line model and if it
+cuts its price it will attract you know
+
+ align:start position:0%
+cuts its price it will attract you know
+ 
+
+ align:start position:0%
+cuts its price it will attract you know
+more consumers from the other side it
+
+ align:start position:0%
+more consumers from the other side it
+ 
+
+ align:start position:0%
+more consumers from the other side it
+would have you know this increase in
+
+ align:start position:0%
+would have you know this increase in
+ 
+
+ align:start position:0%
+would have you know this increase in
+demand one half plus P2 minus P1 over
+
+ align:start position:0%
+demand one half plus P2 minus P1 over
+ 
+
+ align:start position:0%
+demand one half plus P2 minus P1 over
+2T but they're just basically competing
+
+ align:start position:0%
+2T but they're just basically competing
+ 
+
+ align:start position:0%
+2T but they're just basically competing
+on a line against the other firm for
+
+ align:start position:0%
+on a line against the other firm for
+ 
+
+ align:start position:0%
+on a line against the other firm for
+this quality level and so the same
+
+ align:start position:0%
+this quality level and so the same
+ 
+
+ align:start position:0%
+this quality level and so the same
+hoteling First St condition applies and
+
+ align:start position:0%
+hoteling First St condition applies and
+ 
+
+ align:start position:0%
+hoteling First St condition applies and
+they chart price C plus t on each line
+
+ align:start position:0%
+they chart price C plus t on each line
+ 
+
+ align:start position:0%
+they chart price C plus t on each line
+and so if the firms are doing this
+
+ align:start position:0%
+and so if the firms are doing this
+ 
+
+ align:start position:0%
+and so if the firms are doing this
+they're playing hotelling on each line
+
+ align:start position:0%
+they're playing hotelling on each line
+ 
+
+ align:start position:0%
+they're playing hotelling on each line
+they're pricing at C plus t on each line
+
+ align:start position:0%
+they're pricing at C plus t on each line
+ 
+
+ align:start position:0%
+they're pricing at C plus t on each line
+all consumers do buy the best quality
+
+ align:start position:0%
+all consumers do buy the best quality
+ 
+
+ align:start position:0%
+all consumers do buy the best quality
+for them and so the result here is that
+
+ align:start position:0%
+for them and so the result here is that
+ 
+
+ align:start position:0%
+for them and so the result here is that
+when you have competitive secondary
+
+ align:start position:0%
+when you have competitive secondary
+ 
+
+ align:start position:0%
+when you have competitive secondary
+discrimination secondary discrimination
+
+ align:start position:0%
+discrimination secondary discrimination
+ 
+
+ align:start position:0%
+discrimination secondary discrimination
+goes away the firms are not using
+
+ align:start position:0%
+goes away the firms are not using
+ 
+
+ align:start position:0%
+goes away the firms are not using
+different quality levels to discriminate
+
+ align:start position:0%
+different quality levels to discriminate
+ 
+
+ align:start position:0%
+different quality levels to discriminate
+among consumers they just are charging
+
+ align:start position:0%
+among consumers they just are charging
+ 
+
+ align:start position:0%
+among consumers they just are charging
+you know it's not like the iPhone with
+
+ align:start position:0%
+you know it's not like the iPhone with
+ 
+
+ align:start position:0%
+you know it's not like the iPhone with
+512 megabytes cost $300 more than the
+
+ align:start position:0%
+512 megabytes cost $300 more than the
+ 
+
+ align:start position:0%
+512 megabytes cost $300 more than the
+iPhone with 128 megabytes
+
+ align:start position:0%
+iPhone with 128 megabytes
+ 
+
+ align:start position:0%
+iPhone with 128 megabytes
+they give them all at the same markup
+
+ align:start position:0%
+they give them all at the same markup
+ 
+
+ align:start position:0%
+they give them all at the same markup
+and all consumers buy the efficient
+
+ align:start position:0%
+and all consumers buy the efficient
+ 
+
+ align:start position:0%
+and all consumers buy the efficient
+quality so all of that quality
+
+ align:start position:0%
+quality so all of that quality
+ 
+
+ align:start position:0%
+quality so all of that quality
+distortions second in secondary
+
+ align:start position:0%
+distortions second in secondary
+ 
+
+ align:start position:0%
+distortions second in secondary
+discrimination goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+away okay um and you know I I sort of
+
+ align:start position:0%
+away okay um and you know I I sort of
+ 
+
+ align:start position:0%
+away okay um and you know I I sort of
+gave this example in the hoteling model
+
+ align:start position:0%
+gave this example in the hoteling model
+ 
+
+ align:start position:0%
+gave this example in the hoteling model
+but you know stall shows that this is
+
+ align:start position:0%
+but you know stall shows that this is
+ 
+
+ align:start position:0%
+but you know stall shows that this is
+really very general so there's this very
+
+ align:start position:0%
+really very general so there's this very
+ 
+
+ align:start position:0%
+really very general so there's this very
+general thing of for F's distribut of
+
+ align:start position:0%
+general thing of for F's distribut of
+ 
+
+ align:start position:0%
+general thing of for F's distribut of
+Epsilon satisfying some conditions
+
+ align:start position:0%
+Epsilon satisfying some conditions
+ 
+
+ align:start position:0%
+Epsilon satisfying some conditions
+industries of Epsilon satisfying some
+
+ align:start position:0%
+industries of Epsilon satisfying some
+ 
+
+ align:start position:0%
+industries of Epsilon satisfying some
+conditions as long as the Theta and
+
+ align:start position:0%
+conditions as long as the Theta and
+ 
+
+ align:start position:0%
+conditions as long as the Theta and
+Epsilon are are independent this always
+
+ align:start position:0%
+Epsilon are are independent this always
+ 
+
+ align:start position:0%
+Epsilon are are independent this always
+happens you just get competition on many
+
+ align:start position:0%
+happens you just get competition on many
+ 
+
+ align:start position:0%
+happens you just get competition on many
+lines and constant markups across
+
+ align:start position:0%
+lines and constant markups across
+ 
+
+ align:start position:0%
+lines and constant markups across
+Goods um and I I think the thing that I
+
+ align:start position:0%
+Goods um and I I think the thing that I
+ 
+
+ align:start position:0%
+Goods um and I I think the thing that I
+want to most point out most about this
+
+ align:start position:0%
+want to most point out most about this
+ 
+
+ align:start position:0%
+want to most point out most about this
+model is that it seems very general but
+
+ align:start position:0%
+model is that it seems very general but
+ 
+
+ align:start position:0%
+model is that it seems very general but
+it's got this hidden special and
+
+ align:start position:0%
+it's got this hidden special and
+ 
+
+ align:start position:0%
+it's got this hidden special and
+incorrect assumption in it which is that
+
+ align:start position:0%
+incorrect assumption in it which is that
+ 
+
+ align:start position:0%
+incorrect assumption in it which is that
+the thetas and the epsilons are going to
+
+ align:start position:0%
+the thetas and the epsilons are going to
+ 
+
+ align:start position:0%
+the thetas and the epsilons are going to
+be uh
+
+ align:start position:0%
+be uh
+ 
+
+ align:start position:0%
+be uh
+independent okay and I you know a good
+
+ align:start position:0%
+independent okay and I you know a good
+ 
+
+ align:start position:0%
+independent okay and I you know a good
+example to think about this is you know
+
+ align:start position:0%
+example to think about this is you know
+ 
+
+ align:start position:0%
+example to think about this is you know
+think about um uh think about you and uh
+
+ align:start position:0%
+think about um uh think about you and uh
+ 
+
+ align:start position:0%
+think about um uh think about you and uh
+a CEO of some company flying to Europe
+
+ align:start position:0%
+a CEO of some company flying to Europe
+ 
+
+ align:start position:0%
+a CEO of some company flying to Europe
+and you're told that there are two
+
+ align:start position:0%
+and you're told that there are two
+ 
+
+ align:start position:0%
+and you're told that there are two
+flights available to go to Paris there's
+
+ align:start position:0%
+flights available to go to Paris there's
+ 
+
+ align:start position:0%
+flights available to go to Paris there's
+a Delta flight or an Air France flight
+
+ align:start position:0%
+a Delta flight or an Air France flight
+ 
+
+ align:start position:0%
+a Delta flight or an Air France flight
+okay um you know you might say that sort
+
+ align:start position:0%
+okay um you know you might say that sort
+ 
+
+ align:start position:0%
+okay um you know you might say that sort
+of you know some people like Air France
+
+ align:start position:0%
+of you know some people like Air France
+ 
+
+ align:start position:0%
+of you know some people like Air France
+better than Delta some people like de
+
+ align:start position:0%
+better than Delta some people like de
+ 
+
+ align:start position:0%
+better than Delta some people like de
+Delta better than Air France um you know
+
+ align:start position:0%
+Delta better than Air France um you know
+ 
+
+ align:start position:0%
+Delta better than Air France um you know
+it may be that the preferences that
+
+ align:start position:0%
+it may be that the preferences that
+ 
+
+ align:start position:0%
+it may be that the preferences that
+students have on Delta versus Air France
+
+ align:start position:0%
+students have on Delta versus Air France
+ 
+
+ align:start position:0%
+students have on Delta versus Air France
+and the preferences that the CEOs have
+
+ align:start position:0%
+and the preferences that the CEOs have
+ 
+
+ align:start position:0%
+and the preferences that the CEOs have
+on Delta versus Air France are
+
+ align:start position:0%
+on Delta versus Air France are
+ 
+
+ align:start position:0%
+on Delta versus Air France are
+uncorrelated that yeah they're both like
+
+ align:start position:0%
+uncorrelated that yeah they're both like
+ 
+
+ align:start position:0%
+uncorrelated that yeah they're both like
+you can model them as uniform on zero to
+
+ align:start position:0%
+you can model them as uniform on zero to
+ 
+
+ align:start position:0%
+you can model them as uniform on zero to
+T for their dis utility for Air France
+
+ align:start position:0%
+T for their dis utility for Air France
+ 
+
+ align:start position:0%
+T for their dis utility for Air France
+relative their ideal Airline disly for
+
+ align:start position:0%
+relative their ideal Airline disly for
+ 
+
+ align:start position:0%
+relative their ideal Airline disly for
+Delta but what's uncorrelated as
+
+ align:start position:0%
+Delta but what's uncorrelated as
+ 
+
+ align:start position:0%
+Delta but what's uncorrelated as
+reasonable independent is not reasonable
+
+ align:start position:0%
+reasonable independent is not reasonable
+ 
+
+ align:start position:0%
+reasonable independent is not reasonable
+because how much are you willing to pay
+
+ align:start position:0%
+because how much are you willing to pay
+ 
+
+ align:start position:0%
+because how much are you willing to pay
+those of you who really like Air France
+
+ align:start position:0%
+those of you who really like Air France
+ 
+
+ align:start position:0%
+those of you who really like Air France
+how much extra are you willing to pay
+
+ align:start position:0%
+how much extra are you willing to pay
+ 
+
+ align:start position:0%
+how much extra are you willing to pay
+for to go to on Air France maybe it's 20
+
+ align:start position:0%
+for to go to on Air France maybe it's 20
+ 
+
+ align:start position:0%
+for to go to on Air France maybe it's 20
+bucks maybe it's 10 bucks I don't know
+
+ align:start position:0%
+bucks maybe it's 10 bucks I don't know
+ 
+
+ align:start position:0%
+bucks maybe it's 10 bucks I don't know
+um the CEOs they may pay $5,000 more to
+
+ align:start position:0%
+um the CEOs they may pay $5,000 more to
+ 
+
+ align:start position:0%
+um the CEOs they may pay $5,000 more to
+go on Air France relative to Delta if
+
+ align:start position:0%
+go on Air France relative to Delta if
+ 
+
+ align:start position:0%
+go on Air France relative to Delta if
+they like it because for them the 5,000
+
+ align:start position:0%
+they like it because for them the 5,000
+ 
+
+ align:start position:0%
+they like it because for them the 5,000
+is sort of rounding error and so you
+
+ align:start position:0%
+is sort of rounding error and so you
+ 
+
+ align:start position:0%
+is sort of rounding error and so you
+know I think what's reasonable there is
+
+ align:start position:0%
+know I think what's reasonable there is
+ 
+
+ align:start position:0%
+know I think what's reasonable there is
+the uncorrelated preferences for you
+
+ align:start position:0%
+the uncorrelated preferences for you
+ 
+
+ align:start position:0%
+the uncorrelated preferences for you
+know that the businessmen and the
+
+ align:start position:0%
+know that the businessmen and the
+ 
+
+ align:start position:0%
+know that the businessmen and the
+students may have the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well same you know uncorrelated
+
+ align:start position:0%
+well same you know uncorrelated
+ 
+
+ align:start position:0%
+well same you know uncorrelated
+preferences for Del you know this for
+
+ align:start position:0%
+preferences for Del you know this for
+ 
+
+ align:start position:0%
+preferences for Del you know this for
+Delta versus Air France but they
+
+ align:start position:0%
+Delta versus Air France but they
+ 
+
+ align:start position:0%
+Delta versus Air France but they
+wouldn't have independent preferences
+
+ align:start position:0%
+wouldn't have independent preferences
+ 
+
+ align:start position:0%
+wouldn't have independent preferences
+what it really might look like is you
+
+ align:start position:0%
+what it really might look like is you
+ 
+
+ align:start position:0%
+what it really might look like is you
+know you'd have the student
+
+ align:start position:0%
+know you'd have the student
+ 
+
+ align:start position:0%
+know you'd have the student
+line uh you have the student line
+
+ align:start position:0%
+line uh you have the student line
+ 
+
+ align:start position:0%
+line uh you have the student line
+where T is very small and then you have
+
+ align:start position:0%
+where T is very small and then you have
+ 
+
+ align:start position:0%
+where T is very small and then you have
+the uh businessman line where T is very
+
+ align:start position:0%
+the uh businessman line where T is very
+ 
+
+ align:start position:0%
+the uh businessman line where T is very
+very big
+
+ align:start position:0%
+very big
+ 
+
+ align:start position:0%
+very big
+you know they have a higher vertical
+
+ align:start position:0%
+you know they have a higher vertical
+ 
+
+ align:start position:0%
+you know they have a higher vertical
+willingness to pay for the good but then
+
+ align:start position:0%
+willingness to pay for the good but then
+ 
+
+ align:start position:0%
+willingness to pay for the good but then
+having in addition to higher vertical
+
+ align:start position:0%
+having in addition to higher vertical
+ 
+
+ align:start position:0%
+having in addition to higher vertical
+willingness to pay they just have much
+
+ align:start position:0%
+willingness to pay they just have much
+ 
+
+ align:start position:0%
+willingness to pay they just have much
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+intense horizontal preferences as
+
+ align:start position:0%
+intense horizontal preferences as
+ 
+
+ align:start position:0%
+intense horizontal preferences as
+measured in dollars that's not covered
+
+ align:start position:0%
+measured in dollars that's not covered
+ 
+
+ align:start position:0%
+measured in dollars that's not covered
+by the independence
+
+ align:start position:0%
+by the independence
+ 
+
+ align:start position:0%
+by the independence
+case Independence would say there should
+
+ align:start position:0%
+case Independence would say there should
+ 
+
+ align:start position:0%
+case Independence would say there should
+be one line up here like this where
+
+ align:start position:0%
+be one line up here like this where
+ 
+
+ align:start position:0%
+be one line up here like this where
+again they'll all shift from Air France
+
+ align:start position:0%
+again they'll all shift from Air France
+ 
+
+ align:start position:0%
+again they'll all shift from Air France
+to Delta for 20 bucks which is just not
+
+ align:start position:0%
+to Delta for 20 bucks which is just not
+ 
+
+ align:start position:0%
+to Delta for 20 bucks which is just not
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+true
+
+ align:start position:0%
+true
+ 
+
+ align:start position:0%
+true
+okay and it's the
+
+ align:start position:0%
+okay and it's the
+ 
+
+ align:start position:0%
+okay and it's the
+independence in some sense that results
+
+ align:start position:0%
+independence in some sense that results
+ 
+
+ align:start position:0%
+independence in some sense that results
+in the constant
+
+ align:start position:0%
+in the constant
+ 
+
+ align:start position:0%
+in the constant
+markups so you know second op so a
+
+ align:start position:0%
+markups so you know second op so a
+ 
+
+ align:start position:0%
+markups so you know second op so a
+second way people model this is just
+
+ align:start position:0%
+second way people model this is just
+ 
+
+ align:start position:0%
+second way people model this is just
+let's go with this discrete type space
+
+ align:start position:0%
+let's go with this discrete type space
+ 
+
+ align:start position:0%
+let's go with this discrete type space
+so there's just you know two
+
+ align:start position:0%
+so there's just you know two
+ 
+
+ align:start position:0%
+so there's just you know two
+qualities um SL and Sh SL is the coach
+
+ align:start position:0%
+qualities um SL and Sh SL is the coach
+ 
+
+ align:start position:0%
+qualities um SL and Sh SL is the coach
+class seat where your knees are pressed
+
+ align:start position:0%
+class seat where your knees are pressed
+ 
+
+ align:start position:0%
+class seat where your knees are pressed
+into the seat in front of you and then
+
+ align:start position:0%
+into the seat in front of you and then
+ 
+
+ align:start position:0%
+into the seat in front of you and then
+sh is the LI flat bed with the nice TV
+
+ align:start position:0%
+sh is the LI flat bed with the nice TV
+ 
+
+ align:start position:0%
+sh is the LI flat bed with the nice TV
+and the champagne and glasses when you
+
+ align:start position:0%
+and the champagne and glasses when you
+ 
+
+ align:start position:0%
+and the champagne and glasses when you
+walk on the plane and everything else
+
+ align:start position:0%
+walk on the plane and everything else
+ 
+
+ align:start position:0%
+walk on the plane and everything else
+okay and so what you can think of here
+
+ align:start position:0%
+okay and so what you can think of here
+ 
+
+ align:start position:0%
+okay and so what you can think of here
+is you know model this is I can model
+
+ align:start position:0%
+is you know model this is I can model
+ 
+
+ align:start position:0%
+is you know model this is I can model
+that as the uh vertical differentiation
+
+ align:start position:0%
+that as the uh vertical differentiation
+ 
+
+ align:start position:0%
+that as the uh vertical differentiation
+model where consumers have a discrete
+
+ align:start position:0%
+model where consumers have a discrete
+ 
+
+ align:start position:0%
+model where consumers have a discrete
+vertical type TL or
+
+ align:start position:0%
+vertical type TL or
+ 
+
+ align:start position:0%
+vertical type TL or
+th and then they have horizontal types
+
+ align:start position:0%
+th and then they have horizontal types
+ 
+
+ align:start position:0%
+th and then they have horizontal types
+Epsilon i1 and Epsilon I2 just like in
+
+ align:start position:0%
+Epsilon i1 and Epsilon I2 just like in
+ 
+
+ align:start position:0%
+Epsilon i1 and Epsilon I2 just like in
+the hoteling model and let's instead
+
+ align:start position:0%
+the hoteling model and let's instead
+ 
+
+ align:start position:0%
+the hoteling model and let's instead
+then specify the utility instead of
+
+ align:start position:0%
+then specify the utility instead of
+ 
+
+ align:start position:0%
+then specify the utility instead of
+being Theta S Plus EP minus P plus
+
+ align:start position:0%
+being Theta S Plus EP minus P plus
+ 
+
+ align:start position:0%
+being Theta S Plus EP minus P plus
+Epsilon we'll M have the Theta multiply
+
+ align:start position:0%
+Epsilon we'll M have the Theta multiply
+ 
+
+ align:start position:0%
+Epsilon we'll M have the Theta multiply
+s minus
+
+ align:start position:0%
+s minus
+ 
+
+ align:start position:0%
+s minus
+Epsilon so that if you have you know
+
+ align:start position:0%
+Epsilon so that if you have you know
+ 
+
+ align:start position:0%
+Epsilon so that if you have you know
+everybody has in has
+
+ align:start position:0%
+everybody has in has
+ 
+
+ align:start position:0%
+everybody has in has
+um uh everyone has horizontal
+
+ align:start position:0%
+um uh everyone has horizontal
+ 
+
+ align:start position:0%
+um uh everyone has horizontal
+preferences of the same intensity in
+
+ align:start position:0%
+preferences of the same intensity in
+ 
+
+ align:start position:0%
+preferences of the same intensity in
+utils but when you convert the utils to
+
+ align:start position:0%
+utils but when you convert the utils to
+ 
+
+ align:start position:0%
+utils but when you convert the utils to
+Dollars by multiplying by this Theta the
+
+ align:start position:0%
+Dollars by multiplying by this Theta the
+ 
+
+ align:start position:0%
+Dollars by multiplying by this Theta the
+preferences in dollar terms are much
+
+ align:start position:0%
+preferences in dollar terms are much
+ 
+
+ align:start position:0%
+preferences in dollar terms are much
+more intense for the businessmen than
+
+ align:start position:0%
+more intense for the businessmen than
+ 
+
+ align:start position:0%
+more intense for the businessmen than
+they are for the students so the Theta
+
+ align:start position:0%
+they are for the students so the Theta
+ 
+
+ align:start position:0%
+they are for the students so the Theta
+the vertical
+
+ align:start position:0%
+the vertical
+ 
+
+ align:start position:0%
+the vertical
+type multiplies both the quality and the
+
+ align:start position:0%
+type multiplies both the quality and the
+ 
+
+ align:start position:0%
+type multiplies both the quality and the
+relative preference of Delta Air
+
+ align:start position:0%
+relative preference of Delta Air
+ 
+
+ align:start position:0%
+relative preference of Delta Air
+France okay so in this model it's
+
+ align:start position:0%
+France okay so in this model it's
+ 
+
+ align:start position:0%
+France okay so in this model it's
+reasonable to assume that the thetas and
+
+ align:start position:0%
+reasonable to assume that the thetas and
+ 
+
+ align:start position:0%
+reasonable to assume that the thetas and
+the epsilons are now independent so you
+
+ align:start position:0%
+the epsilons are now independent so you
+ 
+
+ align:start position:0%
+the epsilons are now independent so you
+have this willingness to pay for Quality
+
+ align:start position:0%
+have this willingness to pay for Quality
+ 
+
+ align:start position:0%
+have this willingness to pay for Quality
+um whether it be quality of the the nice
+
+ align:start position:0%
+um whether it be quality of the the nice
+ 
+
+ align:start position:0%
+um whether it be quality of the the nice
+seed or quality of the Air France food
+
+ align:start position:0%
+seed or quality of the Air France food
+ 
+
+ align:start position:0%
+seed or quality of the Air France food
+and then you have a idiosyncratic taste
+
+ align:start position:0%
+and then you have a idiosyncratic taste
+ 
+
+ align:start position:0%
+and then you have a idiosyncratic taste
+for the Air France food versus the Delta
+
+ align:start position:0%
+for the Air France food versus the Delta
+ 
+
+ align:start position:0%
+for the Air France food versus the Delta
+food okay uh anyway so I'm going to
+
+ align:start position:0%
+food okay uh anyway so I'm going to
+ 
+
+ align:start position:0%
+food okay uh anyway so I'm going to
+assume for this numerical example that
+
+ align:start position:0%
+assume for this numerical example that
+ 
+
+ align:start position:0%
+assume for this numerical example that
+the thetas and the epsilons are
+
+ align:start position:0%
+the thetas and the epsilons are
+ 
+
+ align:start position:0%
+the thetas and the epsilons are
+independent and half the people are high
+
+ align:start position:0%
+independent and half the people are high
+ 
+
+ align:start position:0%
+independent and half the people are high
+types um so what happens here well you
+
+ align:start position:0%
+types um so what happens here well you
+ 
+
+ align:start position:0%
+types um so what happens here well you
+know simple fact I got conditions under
+
+ align:start position:0%
+know simple fact I got conditions under
+ 
+
+ align:start position:0%
+know simple fact I got conditions under
+which this is true but under some set of
+
+ align:start position:0%
+which this is true but under some set of
+ 
+
+ align:start position:0%
+which this is true but under some set of
+conditions what you get is you know if
+
+ align:start position:0%
+conditions what you get is you know if
+ 
+
+ align:start position:0%
+conditions what you get is you know if
+this is a line that has length TL and
+
+ align:start position:0%
+this is a line that has length TL and
+ 
+
+ align:start position:0%
+this is a line that has length TL and
+this is a line that has length uh
+
+ align:start position:0%
+this is a line that has length uh
+ 
+
+ align:start position:0%
+this is a line that has length uh
+th you get P star equals c plus TL
+
+ align:start position:0%
+th you get P star equals c plus TL
+ 
+
+ align:start position:0%
+th you get P star equals c plus TL
+here and you get P star equals c plus th
+
+ align:start position:0%
+here and you get P star equals c plus th
+ 
+
+ align:start position:0%
+here and you get P star equals c plus th
+here all right so on the big line you
+
+ align:start position:0%
+here all right so on the big line you
+ 
+
+ align:start position:0%
+here all right so on the big line you
+price with with the big amount of
+
+ align:start position:0%
+price with with the big amount of
+ 
+
+ align:start position:0%
+price with with the big amount of
+differentiation on the little line you
+
+ align:start position:0%
+differentiation on the little line you
+ 
+
+ align:start position:0%
+differentiation on the little line you
+price in the little amount of
+
+ align:start position:0%
+price in the little amount of
+ 
+
+ align:start position:0%
+price in the little amount of
+differentiation and all the low types by
+
+ align:start position:0%
+differentiation and all the low types by
+ 
+
+ align:start position:0%
+differentiation and all the low types by
+the low quality product all the high
+
+ align:start position:0%
+the low quality product all the high
+ 
+
+ align:start position:0%
+the low quality product all the high
+types by the high quality product what
+
+ align:start position:0%
+types by the high quality product what
+ 
+
+ align:start position:0%
+types by the high quality product what
+has to be true for that you know it has
+
+ align:start position:0%
+has to be true for that you know it has
+ 
+
+ align:start position:0%
+has to be true for that you know it has
+to be that the th times uh Delta s is
+
+ align:start position:0%
+to be that the th times uh Delta s is
+ 
+
+ align:start position:0%
+to be that the th times uh Delta s is
+the willingness to pay of high types to
+
+ align:start position:0%
+the willingness to pay of high types to
+ 
+
+ align:start position:0%
+the willingness to pay of high types to
+get the high quality product TL Delta s
+
+ align:start position:0%
+get the high quality product TL Delta s
+ 
+
+ align:start position:0%
+get the high quality product TL Delta s
+is the willingness to pay of the low
+
+ align:start position:0%
+is the willingness to pay of the low
+ 
+
+ align:start position:0%
+is the willingness to pay of the low
+types to get the high quality product
+
+ align:start position:0%
+types to get the high quality product
+ 
+
+ align:start position:0%
+types to get the high quality product
+and it just has to be
+
+ align:start position:0%
+and it just has to be
+ 
+
+ align:start position:0%
+and it just has to be
+that the markups that result from
+
+ align:start position:0%
+that the markups that result from
+ 
+
+ align:start position:0%
+that the markups that result from
+different uh differenti different
+
+ align:start position:0%
+different uh differenti different
+ 
+
+ align:start position:0%
+different uh differenti different
+degrees of differentiation
+
+ align:start position:0%
+degrees of differentiation
+ 
+
+ align:start position:0%
+degrees of differentiation
+are exactly between the willingness to
+
+ align:start position:0%
+are exactly between the willingness to
+ 
+
+ align:start position:0%
+are exactly between the willingness to
+pay the high types and the low types so
+
+ align:start position:0%
+pay the high types and the low types so
+ 
+
+ align:start position:0%
+pay the high types and the low types so
+here you know just in this under those
+
+ align:start position:0%
+here you know just in this under those
+ 
+
+ align:start position:0%
+here you know just in this under those
+assumptions the IC constraints are all
+
+ align:start position:0%
+assumptions the IC constraints are all
+ 
+
+ align:start position:0%
+assumptions the IC constraints are all
+non-binding you know there are no
+
+ align:start position:0%
+non-binding you know there are no
+ 
+
+ align:start position:0%
+non-binding you know there are no
+consumers who are indifferent between
+
+ align:start position:0%
+consumers who are indifferent between
+ 
+
+ align:start position:0%
+consumers who are indifferent between
+buying a first class ticket or a coach
+
+ align:start position:0%
+buying a first class ticket or a coach
+ 
+
+ align:start position:0%
+buying a first class ticket or a coach
+class ticket in this model I've written
+
+ align:start position:0%
+class ticket in this model I've written
+ 
+
+ align:start position:0%
+class ticket in this model I've written
+down there are the sort of students are
+
+ align:start position:0%
+down there are the sort of students are
+ 
+
+ align:start position:0%
+down there are the sort of students are
+are just in competition on align to buy
+
+ align:start position:0%
+are just in competition on align to buy
+ 
+
+ align:start position:0%
+are just in competition on align to buy
+the low class tickets these are kind of
+
+ align:start position:0%
+the low class tickets these are kind of
+ 
+
+ align:start position:0%
+the low class tickets these are kind of
+by the high cost tickets it requires a
+
+ align:start position:0%
+by the high cost tickets it requires a
+ 
+
+ align:start position:0%
+by the high cost tickets it requires a
+coincidence right The Coincidence is
+
+ align:start position:0%
+coincidence right The Coincidence is
+ 
+
+ align:start position:0%
+coincidence right The Coincidence is
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+th minus TL is in this range that makes
+
+ align:start position:0%
+th minus TL is in this range that makes
+ 
+
+ align:start position:0%
+th minus TL is in this range that makes
+both of the IC constraints non-binding
+
+ align:start position:0%
+both of the IC constraints non-binding
+ 
+
+ align:start position:0%
+both of the IC constraints non-binding
+and makes the businessman buy the
+
+ align:start position:0%
+and makes the businessman buy the
+ 
+
+ align:start position:0%
+and makes the businessman buy the
+business class tickets the students buy
+
+ align:start position:0%
+business class tickets the students buy
+ 
+
+ align:start position:0%
+business class tickets the students buy
+this the the coach class
+
+ align:start position:0%
+this the the coach class
+ 
+
+ align:start position:0%
+this the the coach class
+tickets um but you know this is a I
+
+ align:start position:0%
+tickets um but you know this is a I
+ 
+
+ align:start position:0%
+tickets um but you know this is a I
+don't know this is a perfectly
+
+ align:start position:0%
+don't know this is a perfectly
+ 
+
+ align:start position:0%
+don't know this is a perfectly
+reasonable model of secondary oligopoly
+
+ align:start position:0%
+reasonable model of secondary oligopoly
+ 
+
+ align:start position:0%
+reasonable model of secondary oligopoly
+price discrimination you know again it
+
+ align:start position:0%
+price discrimination you know again it
+ 
+
+ align:start position:0%
+price discrimination you know again it
+does say that competition determines
+
+ align:start position:0%
+does say that competition determines
+ 
+
+ align:start position:0%
+does say that competition determines
+markups so it is a very different
+
+ align:start position:0%
+markups so it is a very different
+ 
+
+ align:start position:0%
+markups so it is a very different
+mathematical structure from what you get
+
+ align:start position:0%
+mathematical structure from what you get
+ 
+
+ align:start position:0%
+mathematical structure from what you get
+in the um uh it's a different
+
+ align:start position:0%
+in the um uh it's a different
+ 
+
+ align:start position:0%
+in the um uh it's a different
+mathematical structure from what you get
+
+ align:start position:0%
+mathematical structure from what you get
+ 
+
+ align:start position:0%
+mathematical structure from what you get
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+um uh second degree Monopoly price
+
+ align:start position:0%
+um uh second degree Monopoly price
+ 
+
+ align:start position:0%
+um uh second degree Monopoly price
+discrimination model where it's the IC
+
+ align:start position:0%
+discrimination model where it's the IC
+ 
+
+ align:start position:0%
+discrimination model where it's the IC
+constraints and the manipulating quality
+
+ align:start position:0%
+constraints and the manipulating quality
+ 
+
+ align:start position:0%
+constraints and the manipulating quality
+to do things um you know it it is the
+
+ align:start position:0%
+to do things um you know it it is the
+ 
+
+ align:start position:0%
+to do things um you know it it is the
+case that you can still get you can
+
+ align:start position:0%
+case that you can still get you can
+ 
+
+ align:start position:0%
+case that you can still get you can
+think of you can get
+
+ align:start position:0%
+think of you can get
+ 
+
+ align:start position:0%
+think of you can get
+um you know I set these sh and SL
+
+ align:start position:0%
+um you know I set these sh and SL
+ 
+
+ align:start position:0%
+um you know I set these sh and SL
+exogenous it could be that you can get
+
+ align:start position:0%
+exogenous it could be that you can get
+ 
+
+ align:start position:0%
+exogenous it could be that you can get
+sort of manipulation of the qualities
+
+ align:start position:0%
+sort of manipulation of the qualities
+ 
+
+ align:start position:0%
+sort of manipulation of the qualities
+here where firms charge an choose a
+
+ align:start position:0%
+here where firms charge an choose a
+ 
+
+ align:start position:0%
+here where firms charge an choose a
+quality level SL that prevents the
+
+ align:start position:0%
+quality level SL that prevents the
+ 
+
+ align:start position:0%
+quality level SL that prevents the
+businessmen from take you know some
+
+ align:start position:0%
+businessmen from take you know some
+ 
+
+ align:start position:0%
+businessmen from take you know some
+sense they choose how far apart to make
+
+ align:start position:0%
+sense they choose how far apart to make
+ 
+
+ align:start position:0%
+sense they choose how far apart to make
+these lines so that this price
+
+ align:start position:0%
+these lines so that this price
+ 
+
+ align:start position:0%
+these lines so that this price
+discrimination scheme holds up um you
+
+ align:start position:0%
+discrimination scheme holds up um you
+ 
+
+ align:start position:0%
+discrimination scheme holds up um you
+know if if SL were too high I increase
+
+ align:start position:0%
+know if if SL were too high I increase
+ 
+
+ align:start position:0%
+know if if SL were too high I increase
+SL at some point the IR constraint would
+
+ align:start position:0%
+SL at some point the IR constraint would
+ 
+
+ align:start position:0%
+SL at some point the IR constraint would
+start binding and the high types would
+
+ align:start position:0%
+start binding and the high types would
+ 
+
+ align:start position:0%
+start binding and the high types would
+jump down and start buying the low
+
+ align:start position:0%
+jump down and start buying the low
+ 
+
+ align:start position:0%
+jump down and start buying the low
+quality B uh good
+
+ align:start position:0%
+quality B uh good
+ 
+
+ align:start position:0%
+quality B uh good
+instead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay okay and we say you know
+
+ align:start position:0%
+okay okay and we say you know
+ 
+
+ align:start position:0%
+okay okay and we say you know
+interesting about this model is this
+
+ align:start position:0%
+interesting about this model is this
+ 
+
+ align:start position:0%
+interesting about this model is this
+model is also a model of multiple
+
+ align:start position:0%
+model is also a model of multiple
+ 
+
+ align:start position:0%
+model is also a model of multiple
+equilib
+
+ align:start position:0%
+equilib
+ 
+
+ align:start position:0%
+equilib
+sometimes this model has two equilibria
+
+ align:start position:0%
+sometimes this model has two equilibria
+ 
+
+ align:start position:0%
+sometimes this model has two equilibria
+one where the firms discriminate and one
+
+ align:start position:0%
+one where the firms discriminate and one
+ 
+
+ align:start position:0%
+one where the firms discriminate and one
+where the firms just sell the high
+
+ align:start position:0%
+where the firms just sell the high
+ 
+
+ align:start position:0%
+where the firms just sell the high
+quality good to everybody and in some
+
+ align:start position:0%
+quality good to everybody and in some
+ 
+
+ align:start position:0%
+quality good to everybody and in some
+sense there's this just this
+
+ align:start position:0%
+sense there's this just this
+ 
+
+ align:start position:0%
+sense there's this just this
+complimentarity if you're you know right
+
+ align:start position:0%
+complimentarity if you're you know right
+ 
+
+ align:start position:0%
+complimentarity if you're you know right
+we we know these things have upward
+
+ align:start position:0%
+we we know these things have upward
+ 
+
+ align:start position:0%
+we we know these things have upward
+sloping reaction functions where you try
+
+ align:start position:0%
+sloping reaction functions where you try
+ 
+
+ align:start position:0%
+sloping reaction functions where you try
+tend to sort of you know you only go one
+
+ align:start position:0%
+tend to sort of you know you only go one
+ 
+
+ align:start position:0%
+tend to sort of you know you only go one
+half to one but like you know as your
+
+ align:start position:0%
+half to one but like you know as your
+ 
+
+ align:start position:0%
+half to one but like you know as your
+rival raises their price you raise your
+
+ align:start position:0%
+rival raises their price you raise your
+ 
+
+ align:start position:0%
+rival raises their price you raise your
+price that same thing means if your
+
+ align:start position:0%
+price that same thing means if your
+ 
+
+ align:start position:0%
+price that same thing means if your
+rival is spreading its prices for the
+
+ align:start position:0%
+rival is spreading its prices for the
+ 
+
+ align:start position:0%
+rival is spreading its prices for the
+high and low quality good apart you want
+
+ align:start position:0%
+high and low quality good apart you want
+ 
+
+ align:start position:0%
+high and low quality good apart you want
+to spread your prices apart
+
+ align:start position:0%
+to spread your prices apart
+ 
+
+ align:start position:0%
+to spread your prices apart
+but you can actually have two equilibria
+
+ align:start position:0%
+but you can actually have two equilibria
+ 
+
+ align:start position:0%
+but you can actually have two equilibria
+one where the lowquality good doesn't
+
+ align:start position:0%
+one where the lowquality good doesn't
+ 
+
+ align:start position:0%
+one where the lowquality good doesn't
+exist in the F they just compete for
+
+ align:start position:0%
+exist in the F they just compete for
+ 
+
+ align:start position:0%
+exist in the F they just compete for
+everybody with selling the high quality
+
+ align:start position:0%
+everybody with selling the high quality
+ 
+
+ align:start position:0%
+everybody with selling the high quality
+good and then the other where this
+
+ align:start position:0%
+good and then the other where this
+ 
+
+ align:start position:0%
+good and then the other where this
+discrimination
+
+ align:start position:0%
+discrimination
+ 
+
+ align:start position:0%
+discrimination
+occurs okay but the discriminatory
+
+ align:start position:0%
+occurs okay but the discriminatory
+ 
+
+ align:start position:0%
+occurs okay but the discriminatory
+equilibrium is better for the firms than
+
+ align:start position:0%
+equilibrium is better for the firms than
+ 
+
+ align:start position:0%
+equilibrium is better for the firms than
+the one where they don't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+discriminate okay any questions on that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+model okay so then the final Theory
+
+ align:start position:0%
+model okay so then the final Theory
+ 
+
+ align:start position:0%
+model okay so then the final Theory
+topic I wanted to get to us a little bit
+
+ align:start position:0%
+topic I wanted to get to us a little bit
+ 
+
+ align:start position:0%
+topic I wanted to get to us a little bit
+on um add-on pricing um so but first let
+
+ align:start position:0%
+on um add-on pricing um so but first let
+ 
+
+ align:start position:0%
+on um add-on pricing um so but first let
+me go back to uh laen matuda uh Journal
+
+ align:start position:0%
+me go back to uh laen matuda uh Journal
+ 
+
+ align:start position:0%
+me go back to uh laen matuda uh Journal
+business
+
+ align:start position:0%
+business
+ 
+
+ align:start position:0%
+business
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+um you know LA and mudas were thinking
+
+ align:start position:0%
+um you know LA and mudas were thinking
+ 
+
+ align:start position:0%
+um you know LA and mudas were thinking
+of this question of you
+
+ align:start position:0%
+of this question of you
+ 
+
+ align:start position:0%
+of this question of you
+know why is it that turkeys are on sale
+
+ align:start position:0%
+know why is it that turkeys are on sale
+ 
+
+ align:start position:0%
+know why is it that turkeys are on sale
+on Thanksgiving wouldn't you think that
+
+ align:start position:0%
+on Thanksgiving wouldn't you think that
+ 
+
+ align:start position:0%
+on Thanksgiving wouldn't you think that
+the one day of the year when turkey
+
+ align:start position:0%
+the one day of the year when turkey
+ 
+
+ align:start position:0%
+the one day of the year when turkey
+demand is a hundred times higher than it
+
+ align:start position:0%
+demand is a hundred times higher than it
+ 
+
+ align:start position:0%
+demand is a hundred times higher than it
+is any other day of the year turkey
+
+ align:start position:0%
+is any other day of the year turkey
+ 
+
+ align:start position:0%
+is any other day of the year turkey
+prices would be high instead of low um
+
+ align:start position:0%
+prices would be high instead of low um
+ 
+
+ align:start position:0%
+prices would be high instead of low um
+and let's think about the following
+
+ align:start position:0%
+and let's think about the following
+ 
+
+ align:start position:0%
+and let's think about the following
+model so suppose and you know think of
+
+ align:start position:0%
+model so suppose and you know think of
+ 
+
+ align:start position:0%
+model so suppose and you know think of
+this as a model of people competing you
+
+ align:start position:0%
+this as a model of people competing you
+ 
+
+ align:start position:0%
+this as a model of people competing you
+know uh this is competing
+
+ align:start position:0%
+know uh this is competing
+ 
+
+ align:start position:0%
+know uh this is competing
+supermarkets um and the supermarkets are
+
+ align:start position:0%
+supermarkets um and the supermarkets are
+ 
+
+ align:start position:0%
+supermarkets um and the supermarkets are
+selling two different products um V1 and
+
+ align:start position:0%
+selling two different products um V1 and
+ 
+
+ align:start position:0%
+selling two different products um V1 and
+V2 and consumers actually all want to
+
+ align:start position:0%
+V2 and consumers actually all want to
+ 
+
+ align:start position:0%
+V2 and consumers actually all want to
+buy both products they want to buy the
+
+ align:start position:0%
+buy both products they want to buy the
+ 
+
+ align:start position:0%
+buy both products they want to buy the
+the turkey and they want to buy the
+
+ align:start position:0%
+the turkey and they want to buy the
+ 
+
+ align:start position:0%
+the turkey and they want to buy the
+stuffing or the cranberry sauce sauce or
+
+ align:start position:0%
+stuffing or the cranberry sauce sauce or
+ 
+
+ align:start position:0%
+stuffing or the cranberry sauce sauce or
+whatever um and so what my utility is I
+
+ align:start position:0%
+whatever um and so what my utility is I
+ 
+
+ align:start position:0%
+whatever um and so what my utility is I
+get V1 + V2 minus P11 - p12 minus t
+
+ align:start position:0%
+get V1 + V2 minus P11 - p12 minus t
+ 
+
+ align:start position:0%
+get V1 + V2 minus P11 - p12 minus t
+Theta if I am type Theta and I drive to
+
+ align:start position:0%
+Theta if I am type Theta and I drive to
+ 
+
+ align:start position:0%
+Theta if I am type Theta and I drive to
+store one and I buy both products there
+
+ align:start position:0%
+store one and I buy both products there
+ 
+
+ align:start position:0%
+store one and I buy both products there
+are at these
+
+ align:start position:0%
+are at these
+ 
+
+ align:start position:0%
+are at these
+prices or I can go to firm drive to firm
+
+ align:start position:0%
+prices or I can go to firm drive to firm
+ 
+
+ align:start position:0%
+prices or I can go to firm drive to firm
+two and again get V1 minus p21 plus V2
+
+ align:start position:0%
+two and again get V1 minus p21 plus V2
+ 
+
+ align:start position:0%
+two and again get V1 minus p21 plus V2
+minus P22 minus t * 1 minus Theta if I
+
+ align:start position:0%
+minus P22 minus t * 1 minus Theta if I
+ 
+
+ align:start position:0%
+minus P22 minus t * 1 minus Theta if I
+drive and buy the products from firm two
+
+ align:start position:0%
+drive and buy the products from firm two
+ 
+
+ align:start position:0%
+drive and buy the products from firm two
+and then I can if I want um split my
+
+ align:start position:0%
+and then I can if I want um split my
+ 
+
+ align:start position:0%
+and then I can if I want um split my
+shopping and get V1 minus P11 by buying
+
+ align:start position:0%
+shopping and get V1 minus P11 by buying
+ 
+
+ align:start position:0%
+shopping and get V1 minus P11 by buying
+the turkey at store one and then get V2
+
+ align:start position:0%
+the turkey at store one and then get V2
+ 
+
+ align:start position:0%
+the turkey at store one and then get V2
+minus P22 from buying the cranberry
+
+ align:start position:0%
+minus P22 from buying the cranberry
+ 
+
+ align:start position:0%
+minus P22 from buying the cranberry
+sauce at firm two but then I have
+
+ align:start position:0%
+sauce at firm two but then I have
+ 
+
+ align:start position:0%
+sauce at firm two but then I have
+incurred both driving
+
+ align:start position:0%
+incurred both driving
+ 
+
+ align:start position:0%
+incurred both driving
+costs uh and so while in matuda consider
+
+ align:start position:0%
+costs uh and so while in matuda consider
+ 
+
+ align:start position:0%
+costs uh and so while in matuda consider
+this multi-stage game where what firms
+
+ align:start position:0%
+this multi-stage game where what firms
+ 
+
+ align:start position:0%
+this multi-stage game where what firms
+do is you know imagine there were per
+
+ align:start position:0%
+do is you know imagine there were per
+ 
+
+ align:start position:0%
+do is you know imagine there were per
+product advertising costs so you don't
+
+ align:start position:0%
+product advertising costs so you don't
+ 
+
+ align:start position:0%
+product advertising costs so you don't
+want to advertise the price of every
+
+ align:start position:0%
+want to advertise the price of every
+ 
+
+ align:start position:0%
+want to advertise the price of every
+product in your store that's clearly
+
+ align:start position:0%
+product in your store that's clearly
+ 
+
+ align:start position:0%
+product in your store that's clearly
+true with supermarkets you you've got
+
+ align:start position:0%
+true with supermarkets you you've got
+ 
+
+ align:start position:0%
+true with supermarkets you you've got
+10,000 products there you can't
+
+ align:start position:0%
+10,000 products there you can't
+ 
+
+ align:start position:0%
+10,000 products there you can't
+advertise all of them so in the extreme
+
+ align:start position:0%
+advertise all of them so in the extreme
+ 
+
+ align:start position:0%
+advertise all of them so in the extreme
+case suppose you choose an advertise the
+
+ align:start position:0%
+case suppose you choose an advertise the
+ 
+
+ align:start position:0%
+case suppose you choose an advertise the
+price of one
+
+ align:start position:0%
+price of one
+ 
+
+ align:start position:0%
+price of one
+good and then after choosing the price
+
+ align:start position:0%
+good and then after choosing the price
+ 
+
+ align:start position:0%
+good and then after choosing the price
+of your one good you choose an
+
+ align:start position:0%
+of your one good you choose an
+ 
+
+ align:start position:0%
+of your one good you choose an
+unadvertised price for the other good
+
+ align:start position:0%
+unadvertised price for the other good
+ 
+
+ align:start position:0%
+unadvertised price for the other good
+which is kept secret until consumers
+
+ align:start position:0%
+which is kept secret until consumers
+ 
+
+ align:start position:0%
+which is kept secret until consumers
+arrive at the
+
+ align:start position:0%
+arrive at the
+ 
+
+ align:start position:0%
+arrive at the
+store consumers drive to one firm and
+
+ align:start position:0%
+store consumers drive to one firm and
+ 
+
+ align:start position:0%
+store consumers drive to one firm and
+current cost either T Theta or T1 minus
+
+ align:start position:0%
+current cost either T Theta or T1 minus
+ 
+
+ align:start position:0%
+current cost either T Theta or T1 minus
+Theta when they get there they learn the
+
+ align:start position:0%
+Theta when they get there they learn the
+ 
+
+ align:start position:0%
+Theta when they get there they learn the
+price for the unver IED good and then
+
+ align:start position:0%
+price for the unver IED good and then
+ 
+
+ align:start position:0%
+price for the unver IED good and then
+consumers after learning the price of
+
+ align:start position:0%
+consumers after learning the price of
+ 
+
+ align:start position:0%
+consumers after learning the price of
+the unadvertised good they either buy
+
+ align:start position:0%
+the unadvertised good they either buy
+ 
+
+ align:start position:0%
+the unadvertised good they either buy
+one or both products there or they
+
+ align:start position:0%
+one or both products there or they
+ 
+
+ align:start position:0%
+one or both products there or they
+decide to drive to the other firm and
+
+ align:start position:0%
+decide to drive to the other firm and
+ 
+
+ align:start position:0%
+decide to drive to the other firm and
+buy at the at firm two
+
+ align:start position:0%
+buy at the at firm two
+ 
+
+ align:start position:0%
+buy at the at firm two
+instead
+
+ align:start position:0%
+instead
+ 
+
+ align:start position:0%
+instead
+okay you know proposition first um in
+
+ align:start position:0%
+okay you know proposition first um in
+ 
+
+ align:start position:0%
+okay you know proposition first um in
+the above model equilibrium prices
+
+ align:start position:0%
+the above model equilibrium prices
+ 
+
+ align:start position:0%
+the above model equilibrium prices
+satisfy P1 Star Plus P2 star is C1 plus
+
+ align:start position:0%
+satisfy P1 Star Plus P2 star is C1 plus
+ 
+
+ align:start position:0%
+satisfy P1 Star Plus P2 star is C1 plus
+C2 plus T again this is just the
+
+ align:start position:0%
+C2 plus T again this is just the
+ 
+
+ align:start position:0%
+C2 plus T again this is just the
+hoteling competition on a line model uh
+
+ align:start position:0%
+hoteling competition on a line model uh
+ 
+
+ align:start position:0%
+hoteling competition on a line model uh
+in equilibrium the price of the bundle
+
+ align:start position:0%
+in equilibrium the price of the bundle
+ 
+
+ align:start position:0%
+in equilibrium the price of the bundle
+is going to be C plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T um but the individual prices are not
+
+ align:start position:0%
+T um but the individual prices are not
+ 
+
+ align:start position:0%
+T um but the individual prices are not
+like C plus t over2 for each the
+
+ align:start position:0%
+like C plus t over2 for each the
+ 
+
+ align:start position:0%
+like C plus t over2 for each the
+individual prices are P two star equals
+
+ align:start position:0%
+individual prices are P two star equals
+ 
+
+ align:start position:0%
+individual prices are P two star equals
+V2 and pj1 star is C1 plus C2 plus T
+
+ align:start position:0%
+V2 and pj1 star is C1 plus C2 plus T
+ 
+
+ align:start position:0%
+V2 and pj1 star is C1 plus C2 plus T
+minus V2 so
+
+ align:start position:0%
+minus V2 so
+ 
+
+ align:start position:0%
+minus V2 so
+basically uh cranberry sauce is always
+
+ align:start position:0%
+basically uh cranberry sauce is always
+ 
+
+ align:start position:0%
+basically uh cranberry sauce is always
+incredibly expensive on Thanksgiving you
+
+ align:start position:0%
+incredibly expensive on Thanksgiving you
+ 
+
+ align:start position:0%
+incredibly expensive on Thanksgiving you
+know you sort of have this advertised
+
+ align:start position:0%
+know you sort of have this advertised
+ 
+
+ align:start position:0%
+know you sort of have this advertised
+product the advertised product you show
+
+ align:start position:0%
+product the advertised product you show
+ 
+
+ align:start position:0%
+product the advertised product you show
+up at the store to buy the unadvertised
+
+ align:start position:0%
+up at the store to buy the unadvertised
+ 
+
+ align:start position:0%
+up at the store to buy the unadvertised
+product and you find that wow that is
+
+ align:start position:0%
+product and you find that wow that is
+ 
+
+ align:start position:0%
+product and you find that wow that is
+exactly my full willingness to pay I'm
+
+ align:start position:0%
+exactly my full willingness to pay I'm
+ 
+
+ align:start position:0%
+exactly my full willingness to pay I'm
+basically indifferent to walking out
+
+ align:start position:0%
+basically indifferent to walking out
+ 
+
+ align:start position:0%
+basically indifferent to walking out
+versus spending $11 buying
+
+ align:start position:0%
+versus spending $11 buying
+ 
+
+ align:start position:0%
+versus spending $11 buying
+cranberries but you know in
+
+ align:start position:0%
+cranberries but you know in
+ 
+
+ align:start position:0%
+cranberries but you know in
+equilibrium both firms are charging $11
+
+ align:start position:0%
+equilibrium both firms are charging $11
+ 
+
+ align:start position:0%
+equilibrium both firms are charging $11
+for The Cranberries so there's the
+
+ align:start position:0%
+for The Cranberries so there's the
+ 
+
+ align:start position:0%
+for The Cranberries so there's the
+advertised price for the turkey the
+
+ align:start position:0%
+advertised price for the turkey the
+ 
+
+ align:start position:0%
+advertised price for the turkey the
+advertised price of the turkey is a
+
+ align:start position:0%
+advertised price of the turkey is a
+ 
+
+ align:start position:0%
+advertised price of the turkey is a
+great deal and it just is a great deal
+
+ align:start position:0%
+great deal and it just is a great deal
+ 
+
+ align:start position:0%
+great deal and it just is a great deal
+reflecting how much they're going to rip
+
+ align:start position:0%
+reflecting how much they're going to rip
+ 
+
+ align:start position:0%
+reflecting how much they're going to rip
+you off for everything else you buy when
+
+ align:start position:0%
+you off for everything else you buy when
+ 
+
+ align:start position:0%
+you off for everything else you buy when
+you get into the store to buy the turkey
+
+ align:start position:0%
+you get into the store to buy the turkey
+ 
+
+ align:start position:0%
+you get into the store to buy the turkey
+that's a good deal and in equilibrium
+
+ align:start position:0%
+that's a good deal and in equilibrium
+ 
+
+ align:start position:0%
+that's a good deal and in equilibrium
+it's all
+
+ align:start position:0%
+it's all
+ 
+
+ align:start position:0%
+it's all
+neutral okay in equili it's as if you
+
+ align:start position:0%
+neutral okay in equili it's as if you
+ 
+
+ align:start position:0%
+neutral okay in equili it's as if you
+advertise the prices for everything we
+
+ align:start position:0%
+advertise the prices for everything we
+ 
+
+ align:start position:0%
+advertise the prices for everything we
+would get exactly the same outcome it's
+
+ align:start position:0%
+would get exactly the same outcome it's
+ 
+
+ align:start position:0%
+would get exactly the same outcome it's
+it's C+ T pricing it's just in a
+
+ align:start position:0%
+it's C+ T pricing it's just in a
+ 
+
+ align:start position:0%
+it's C+ T pricing it's just in a
+distorted way where one good is really
+
+ align:start position:0%
+distorted way where one good is really
+ 
+
+ align:start position:0%
+distorted way where one good is really
+cheap and then the other goods are
+
+ align:start position:0%
+cheap and then the other goods are
+ 
+
+ align:start position:0%
+cheap and then the other goods are
+expensive okay um and actually you know
+
+ align:start position:0%
+expensive okay um and actually you know
+ 
+
+ align:start position:0%
+expensive okay um and actually you know
+there's actually a paper on on
+
+ align:start position:0%
+there's actually a paper on on
+ 
+
+ align:start position:0%
+there's actually a paper on on
+Thanksgiving noting that in fact it is
+
+ align:start position:0%
+Thanksgiving noting that in fact it is
+ 
+
+ align:start position:0%
+Thanksgiving noting that in fact it is
+true that turkeys are cheapest on
+
+ align:start position:0%
+true that turkeys are cheapest on
+ 
+
+ align:start position:0%
+true that turkeys are cheapest on
+Thanksgiving on any other day of the
+
+ align:start position:0%
+Thanksgiving on any other day of the
+ 
+
+ align:start position:0%
+Thanksgiving on any other day of the
+year and everything else in the grocery
+
+ align:start position:0%
+year and everything else in the grocery
+ 
+
+ align:start position:0%
+year and everything else in the grocery
+store is on average more expensive than
+
+ align:start position:0%
+store is on average more expensive than
+ 
+
+ align:start position:0%
+store is on average more expensive than
+any other day of the year that is a sort
+
+ align:start position:0%
+any other day of the year that is a sort
+ 
+
+ align:start position:0%
+any other day of the year that is a sort
+of this is sort of what firms seem to do
+
+ align:start position:0%
+of this is sort of what firms seem to do
+ 
+
+ align:start position:0%
+of this is sort of what firms seem to do
+is you know turkeys are a loss leader
+
+ align:start position:0%
+is you know turkeys are a loss leader
+ 
+
+ align:start position:0%
+is you know turkeys are a loss leader
+why actually why are turkeys a good loss
+
+ align:start position:0%
+why actually why are turkeys a good loss
+ 
+
+ align:start position:0%
+why actually why are turkeys a good loss
+leader milk is often also a loss leader
+
+ align:start position:0%
+leader milk is often also a loss leader
+ 
+
+ align:start position:0%
+leader milk is often also a loss leader
+at like convenience stores like you know
+
+ align:start position:0%
+at like convenience stores like you know
+ 
+
+ align:start position:0%
+at like convenience stores like you know
+a gallon of milk seems relatively cheap
+
+ align:start position:0%
+a gallon of milk seems relatively cheap
+ 
+
+ align:start position:0%
+a gallon of milk seems relatively cheap
+compared to a bag of potato chips turkey
+
+ align:start position:0%
+compared to a bag of potato chips turkey
+ 
+
+ align:start position:0%
+compared to a bag of potato chips turkey
+and milk are Lo good loss leaders
+
+ align:start position:0%
+and milk are Lo good loss leaders
+ 
+
+ align:start position:0%
+and milk are Lo good loss leaders
+because you don't want to have a lost
+
+ align:start position:0%
+because you don't want to have a lost
+ 
+
+ align:start position:0%
+because you don't want to have a lost
+leader where people come in and stock up
+
+ align:start position:0%
+leader where people come in and stock up
+ 
+
+ align:start position:0%
+leader where people come in and stock up
+and buy 23 of the thing that's
+
+ align:start position:0%
+and buy 23 of the thing that's
+ 
+
+ align:start position:0%
+and buy 23 of the thing that's
+advertised as a great deal and then not
+
+ align:start position:0%
+advertised as a great deal and then not
+ 
+
+ align:start position:0%
+advertised as a great deal and then not
+buy anything else at your store and
+
+ align:start position:0%
+buy anything else at your store and
+ 
+
+ align:start position:0%
+buy anything else at your store and
+exploit you and sort of save it up and
+
+ align:start position:0%
+exploit you and sort of save it up and
+ 
+
+ align:start position:0%
+exploit you and sort of save it up and
+live off that for the next six months
+
+ align:start position:0%
+live off that for the next six months
+ 
+
+ align:start position:0%
+live off that for the next six months
+like Ramen noodles would be a terrible
+
+ align:start position:0%
+like Ramen noodles would be a terrible
+ 
+
+ align:start position:0%
+like Ramen noodles would be a terrible
+loss leader because you'd get the
+
+ align:start position:0%
+loss leader because you'd get the
+ 
+
+ align:start position:0%
+loss leader because you'd get the
+student comes in buys like you know the
+
+ align:start position:0%
+student comes in buys like you know the
+ 
+
+ align:start position:0%
+student comes in buys like you know the
+case of ramen noodles and just leaves
+
+ align:start position:0%
+case of ramen noodles and just leaves
+ 
+
+ align:start position:0%
+case of ramen noodles and just leaves
+with just that but turkeys you really
+
+ align:start position:0%
+with just that but turkeys you really
+ 
+
+ align:start position:0%
+with just that but turkeys you really
+don't want more than one you know
+
+ align:start position:0%
+don't want more than one you know
+ 
+
+ align:start position:0%
+don't want more than one you know
+gallons of milk you really don't want
+
+ align:start position:0%
+gallons of milk you really don't want
+ 
+
+ align:start position:0%
+gallons of milk you really don't want
+more than one so something that you can
+
+ align:start position:0%
+more than one so something that you can
+ 
+
+ align:start position:0%
+more than one so something that you can
+sort of give people a very good deal on
+
+ align:start position:0%
+sort of give people a very good deal on
+ 
+
+ align:start position:0%
+sort of give people a very good deal on
+they buy exactly one and then you rip
+
+ align:start position:0%
+they buy exactly one and then you rip
+ 
+
+ align:start position:0%
+they buy exactly one and then you rip
+them off for everything else that's sort
+
+ align:start position:0%
+them off for everything else that's sort
+ 
+
+ align:start position:0%
+them off for everything else that's sort
+of how you choose your lost
+
+ align:start position:0%
+of how you choose your lost
+ 
+
+ align:start position:0%
+of how you choose your lost
+leaders okay uh but you know the LA and
+
+ align:start position:0%
+leaders okay uh but you know the LA and
+ 
+
+ align:start position:0%
+leaders okay uh but you know the LA and
+matus model says that this is how loss
+
+ align:start position:0%
+matus model says that this is how loss
+ 
+
+ align:start position:0%
+matus model says that this is how loss
+leaders work um uh but they are neutral
+
+ align:start position:0%
+leaders work um uh but they are neutral
+ 
+
+ align:start position:0%
+leaders work um uh but they are neutral
+e economically it's not like Banning
+
+ align:start position:0%
+e economically it's not like Banning
+ 
+
+ align:start position:0%
+e economically it's not like Banning
+them would do any anyone any good or
+
+ align:start position:0%
+them would do any anyone any good or
+ 
+
+ align:start position:0%
+them would do any anyone any good or
+something you know right it's they're
+
+ align:start position:0%
+something you know right it's they're
+ 
+
+ align:start position:0%
+something you know right it's they're
+they're completely neutral for the
+
+ align:start position:0%
+they're completely neutral for the
+ 
+
+ align:start position:0%
+they're completely neutral for the
+firm's profits and neutral for consumers
+
+ align:start position:0%
+firm's profits and neutral for consumers
+ 
+
+ align:start position:0%
+firm's profits and neutral for consumers
+and they do economize an advertising
+
+ align:start position:0%
+and they do economize an advertising
+ 
+
+ align:start position:0%
+and they do economize an advertising
+cost so in that sense they're
+
+ align:start position:0%
+cost so in that sense they're
+ 
+
+ align:start position:0%
+cost so in that sense they're
+good I put carman's picture up there I I
+
+ align:start position:0%
+good I put carman's picture up there I I
+ 
+
+ align:start position:0%
+good I put carman's picture up there I I
+sort of respect you know Carmen at one
+
+ align:start position:0%
+sort of respect you know Carmen at one
+ 
+
+ align:start position:0%
+sort of respect you know Carmen at one
+point was a very successful Economist
+
+ align:start position:0%
+point was a very successful Economist
+ 
+
+ align:start position:0%
+point was a very successful Economist
+and then um uh had been a professor at
+
+ align:start position:0%
+and then um uh had been a professor at
+ 
+
+ align:start position:0%
+and then um uh had been a professor at
+Berkeley and dropped out and became a
+
+ align:start position:0%
+Berkeley and dropped out and became a
+ 
+
+ align:start position:0%
+Berkeley and dropped out and became a
+novelist and actually is a successful
+
+ align:start position:0%
+novelist and actually is a successful
+ 
+
+ align:start position:0%
+novelist and actually is a successful
+novelist although she writes in Spanish
+
+ align:start position:0%
+novelist although she writes in Spanish
+ 
+
+ align:start position:0%
+novelist although she writes in Spanish
+so I've never read any of her books but
+
+ align:start position:0%
+so I've never read any of her books but
+ 
+
+ align:start position:0%
+so I've never read any of her books but
+uh anyway won several prizes for her
+
+ align:start position:0%
+uh anyway won several prizes for her
+ 
+
+ align:start position:0%
+uh anyway won several prizes for her
+fiction writing after she decided to
+
+ align:start position:0%
+fiction writing after she decided to
+ 
+
+ align:start position:0%
+fiction writing after she decided to
+have a second career um okay
+
+ align:start position:0%
+have a second career um okay
+ 
+
+ align:start position:0%
+have a second career um okay
+um uh add-on pricing so
+
+ align:start position:0%
+um uh add-on pricing so
+ 
+
+ align:start position:0%
+um uh add-on pricing so
+um so add-on pricing sort of thinks
+
+ align:start position:0%
+um so add-on pricing sort of thinks
+ 
+
+ align:start position:0%
+um so add-on pricing sort of thinks
+about basically this loss leader idea in
+
+ align:start position:0%
+about basically this loss leader idea in
+ 
+
+ align:start position:0%
+about basically this loss leader idea in
+a vertical um competitive price
+
+ align:start position:0%
+a vertical um competitive price
+ 
+
+ align:start position:0%
+a vertical um competitive price
+discrimination model so there are many
+
+ align:start position:0%
+discrimination model so there are many
+ 
+
+ align:start position:0%
+discrimination model so there are many
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+where firms that are sort of practicing
+
+ align:start position:0%
+where firms that are sort of practicing
+ 
+
+ align:start position:0%
+where firms that are sort of practicing
+second degree price discrimination do
+
+ align:start position:0%
+second degree price discrimination do
+ 
+
+ align:start position:0%
+second degree price discrimination do
+have non-visible prices for add-ons so
+
+ align:start position:0%
+have non-visible prices for add-ons so
+ 
+
+ align:start position:0%
+have non-visible prices for add-ons so
+for instance you go to a hotel and it
+
+ align:start position:0%
+for instance you go to a hotel and it
+ 
+
+ align:start position:0%
+for instance you go to a hotel and it
+like it's very easy to find the price of
+
+ align:start position:0%
+like it's very easy to find the price of
+ 
+
+ align:start position:0%
+like it's very easy to find the price of
+a hotel online and compare price of
+
+ align:start position:0%
+a hotel online and compare price of
+ 
+
+ align:start position:0%
+a hotel online and compare price of
+hotels it's very hard to compare what's
+
+ align:start position:0%
+hotels it's very hard to compare what's
+ 
+
+ align:start position:0%
+hotels it's very hard to compare what's
+the price of the beer in the mini bar or
+
+ align:start position:0%
+the price of the beer in the mini bar or
+ 
+
+ align:start position:0%
+the price of the beer in the mini bar or
+what's the price of the sparkling water
+
+ align:start position:0%
+what's the price of the sparkling water
+ 
+
+ align:start position:0%
+what's the price of the sparkling water
+in the mini bar what's the price of a
+
+ align:start position:0%
+in the mini bar what's the price of a
+ 
+
+ align:start position:0%
+in the mini bar what's the price of a
+Quant in the hotel lobby if I'm in a
+
+ align:start position:0%
+Quant in the hotel lobby if I'm in a
+ 
+
+ align:start position:0%
+Quant in the hotel lobby if I'm in a
+hurry to get somewhere
+
+ align:start position:0%
+hurry to get somewhere
+ 
+
+ align:start position:0%
+hurry to get somewhere
+um you know rental cars it's very easy
+
+ align:start position:0%
+um you know rental cars it's very easy
+ 
+
+ align:start position:0%
+um you know rental cars it's very easy
+to compare the price of the rental car
+
+ align:start position:0%
+to compare the price of the rental car
+ 
+
+ align:start position:0%
+to compare the price of the rental car
+it's very hard to figure out what will I
+
+ align:start position:0%
+it's very hard to figure out what will I
+ 
+
+ align:start position:0%
+it's very hard to figure out what will I
+pay for the car seat if I need a car
+
+ align:start position:0%
+pay for the car seat if I need a car
+ 
+
+ align:start position:0%
+pay for the car seat if I need a car
+seat for my infant when I get there you
+
+ align:start position:0%
+seat for my infant when I get there you
+ 
+
+ align:start position:0%
+seat for my infant when I get there you
+know I don't know I guess you guys are
+
+ align:start position:0%
+know I don't know I guess you guys are
+ 
+
+ align:start position:0%
+know I don't know I guess you guys are
+too young to have infants but you know
+
+ align:start position:0%
+too young to have infants but you know
+ 
+
+ align:start position:0%
+too young to have infants but you know
+it's it's sort of striking to you that
+
+ align:start position:0%
+it's it's sort of striking to you that
+ 
+
+ align:start position:0%
+it's it's sort of striking to you that
+you sort of like you go to rent a car
+
+ align:start position:0%
+you sort of like you go to rent a car
+ 
+
+ align:start position:0%
+you sort of like you go to rent a car
+and you can rent a $20,000 car for1
+
+ align:start position:0%
+and you can rent a $20,000 car for1
+ 
+
+ align:start position:0%
+and you can rent a $20,000 car for1
+19.95 a day and then you want to rent a
+
+ align:start position:0%
+19.95 a day and then you want to rent a
+ 
+
+ align:start position:0%
+19.95 a day and then you want to rent a
+$37 car seat because you don't want to C
+
+ align:start position:0%
+$37 car seat because you don't want to C
+ 
+
+ align:start position:0%
+$37 car seat because you don't want to C
+lug it on the plane and it's like 13.95
+
+ align:start position:0%
+lug it on the plane and it's like 13.95
+ 
+
+ align:start position:0%
+lug it on the plane and it's like 13.95
+a day and you're like you know how can
+
+ align:start position:0%
+a day and you're like you know how can
+ 
+
+ align:start position:0%
+a day and you're like you know how can
+this be that like they can rent me a
+
+ align:start position:0%
+this be that like they can rent me a
+ 
+
+ align:start position:0%
+this be that like they can rent me a
+$20,000 car for $20 and then the $37 car
+
+ align:start position:0%
+$20,000 car for $20 and then the $37 car
+ 
+
+ align:start position:0%
+$20,000 car for $20 and then the $37 car
+SE either charging me $13 a day or
+
+ align:start position:0%
+SE either charging me $13 a day or
+ 
+
+ align:start position:0%
+SE either charging me $13 a day or
+making me carry this enormous think
+
+ align:start position:0%
+making me carry this enormous think
+ 
+
+ align:start position:0%
+making me carry this enormous think
+piece of plastic on the airplane and
+
+ align:start position:0%
+piece of plastic on the airplane and
+ 
+
+ align:start position:0%
+piece of plastic on the airplane and
+it's you know obviously it's it's this
+
+ align:start position:0%
+it's you know obviously it's it's this
+ 
+
+ align:start position:0%
+it's you know obviously it's it's this
+sort of same add-on pricing thing where
+
+ align:start position:0%
+sort of same add-on pricing thing where
+ 
+
+ align:start position:0%
+sort of same add-on pricing thing where
+it's very easy to compare the prices of
+
+ align:start position:0%
+it's very easy to compare the prices of
+ 
+
+ align:start position:0%
+it's very easy to compare the prices of
+the cars and not of the and not of the
+
+ align:start position:0%
+the cars and not of the and not of the
+ 
+
+ align:start position:0%
+the cars and not of the and not of the
+car seats therefore the car seat is
+
+ align:start position:0%
+car seats therefore the car seat is
+ 
+
+ align:start position:0%
+car seats therefore the car seat is
+priced at V2 what is your disutility
+
+ align:start position:0%
+priced at V2 what is your disutility
+ 
+
+ align:start position:0%
+priced at V2 what is your disutility
+from carrying a car seat on a plane
+
+ align:start position:0%
+from carrying a car seat on a plane
+ 
+
+ align:start position:0%
+from carrying a car seat on a plane
+that's what they'll charge you uh and
+
+ align:start position:0%
+that's what they'll charge you uh and
+ 
+
+ align:start position:0%
+that's what they'll charge you uh and
+then the you know cars are sort of some
+
+ align:start position:0%
+then the you know cars are sort of some
+ 
+
+ align:start position:0%
+then the you know cars are sort of some
+sense the loss leader to make money
+
+ align:start position:0%
+sense the loss leader to make money
+ 
+
+ align:start position:0%
+sense the loss leader to make money
+selling the car seats in the rental car
+
+ align:start position:0%
+selling the car seats in the rental car
+ 
+
+ align:start position:0%
+selling the car seats in the rental car
+insurance um you know uh inkjet printers
+
+ align:start position:0%
+insurance um you know uh inkjet printers
+ 
+
+ align:start position:0%
+insurance um you know uh inkjet printers
+I mentioned earlier that right again
+
+ align:start position:0%
+I mentioned earlier that right again
+ 
+
+ align:start position:0%
+I mentioned earlier that right again
+like the inkjet printer is very cheap
+
+ align:start position:0%
+like the inkjet printer is very cheap
+ 
+
+ align:start position:0%
+like the inkjet printer is very cheap
+but they've sort of invented this inkjet
+
+ align:start position:0%
+but they've sort of invented this inkjet
+ 
+
+ align:start position:0%
+but they've sort of invented this inkjet
+printer that has almost no ink in it
+
+ align:start position:0%
+printer that has almost no ink in it
+ 
+
+ align:start position:0%
+printer that has almost no ink in it
+when you buy it and then it's got the
+
+ align:start position:0%
+when you buy it and then it's got the
+ 
+
+ align:start position:0%
+when you buy it and then it's got the
+starter cartridge and then the sort of
+
+ align:start position:0%
+starter cartridge and then the sort of
+ 
+
+ align:start position:0%
+starter cartridge and then the sort of
+regular cartridge for the internet
+
+ align:start position:0%
+regular cartridge for the internet
+ 
+
+ align:start position:0%
+regular cartridge for the internet
+printer is much more expensive and
+
+ align:start position:0%
+printer is much more expensive and
+ 
+
+ align:start position:0%
+printer is much more expensive and
+that's sort of the Hidden feature when
+
+ align:start position:0%
+that's sort of the Hidden feature when
+ 
+
+ align:start position:0%
+that's sort of the Hidden feature when
+you buy the
+
+ align:start position:0%
+you buy the
+ 
+
+ align:start position:0%
+you buy the
+cartridge so you know to think about how
+
+ align:start position:0%
+cartridge so you know to think about how
+ 
+
+ align:start position:0%
+cartridge so you know to think about how
+this works in vertical competition
+
+ align:start position:0%
+this works in vertical competition
+ 
+
+ align:start position:0%
+this works in vertical competition
+um you know L mudas was purely additive
+
+ align:start position:0%
+um you know L mudas was purely additive
+ 
+
+ align:start position:0%
+um you know L mudas was purely additive
+competition it wasn't a vertical model
+
+ align:start position:0%
+competition it wasn't a vertical model
+ 
+
+ align:start position:0%
+competition it wasn't a vertical model
+so imagine you have firms advertised
+
+ align:start position:0%
+so imagine you have firms advertised
+ 
+
+ align:start position:0%
+so imagine you have firms advertised
+prices for their lowquality goods like
+
+ align:start position:0%
+prices for their lowquality goods like
+ 
+
+ align:start position:0%
+prices for their lowquality goods like
+the rental car without a car
+
+ align:start position:0%
+the rental car without a car
+ 
+
+ align:start position:0%
+the rental car without a car
+seat
+
+ align:start position:0%
+seat
+ 
+
+ align:start position:0%
+seat
+um cost SL and both sh both have cost c
+
+ align:start position:0%
+um cost SL and both sh both have cost c
+ 
+
+ align:start position:0%
+um cost SL and both sh both have cost c
+as if the car seat is essentially free
+
+ align:start position:0%
+as if the car seat is essentially free
+ 
+
+ align:start position:0%
+as if the car seat is essentially free
+for them to
+
+ align:start position:0%
+for them to
+ 
+
+ align:start position:0%
+for them to
+provide um consumers incur some cost um
+
+ align:start position:0%
+provide um consumers incur some cost um
+ 
+
+ align:start position:0%
+provide um consumers incur some cost um
+to visit Jay and learn the price uh so
+
+ align:start position:0%
+to visit Jay and learn the price uh so
+ 
+
+ align:start position:0%
+to visit Jay and learn the price uh so
+consumers have to visit the firm to
+
+ align:start position:0%
+consumers have to visit the firm to
+ 
+
+ align:start position:0%
+consumers have to visit the firm to
+learn the price of the um uh upgrades
+
+ align:start position:0%
+learn the price of the um uh upgrades
+ 
+
+ align:start position:0%
+learn the price of the um uh upgrades
+you have to spend some time on the
+
+ align:start position:0%
+you have to spend some time on the
+ 
+
+ align:start position:0%
+you have to spend some time on the
+website learning what it costs to get a
+
+ align:start position:0%
+website learning what it costs to get a
+ 
+
+ align:start position:0%
+website learning what it costs to get a
+car seat added to your rental car and
+
+ align:start position:0%
+car seat added to your rental car and
+ 
+
+ align:start position:0%
+car seat added to your rental car and
+then that would let you upgrade in
+
+ align:start position:0%
+then that would let you upgrade in
+ 
+
+ align:start position:0%
+then that would let you upgrade in
+quality and then again let's do the
+
+ align:start position:0%
+quality and then again let's do the
+ 
+
+ align:start position:0%
+quality and then again let's do the
+competition on two lines so Epsilon i1
+
+ align:start position:0%
+competition on two lines so Epsilon i1
+ 
+
+ align:start position:0%
+competition on two lines so Epsilon i1
+Epsilon I2 independent again you know
+
+ align:start position:0%
+Epsilon I2 independent again you know
+ 
+
+ align:start position:0%
+Epsilon I2 independent again you know
+same thing this
+
+ align:start position:0%
+same thing this
+ 
+
+ align:start position:0%
+same thing this
+setup so this setup where what you do is
+
+ align:start position:0%
+setup so this setup where what you do is
+ 
+
+ align:start position:0%
+setup so this setup where what you do is
+Imagine This setup where you're only
+
+ align:start position:0%
+Imagine This setup where you're only
+ 
+
+ align:start position:0%
+Imagine This setup where you're only
+advertising the price of the lowquality
+
+ align:start position:0%
+advertising the price of the lowquality
+ 
+
+ align:start position:0%
+advertising the price of the lowquality
+good and then consumers have to pay
+
+ align:start position:0%
+good and then consumers have to pay
+ 
+
+ align:start position:0%
+good and then consumers have to pay
+something after they arrive or after
+
+ align:start position:0%
+something after they arrive or after
+ 
+
+ align:start position:0%
+something after they arrive or after
+they've spent some time in investigating
+
+ align:start position:0%
+they've spent some time in investigating
+ 
+
+ align:start position:0%
+they've spent some time in investigating
+your firm to learn what it cost to
+
+ align:start position:0%
+your firm to learn what it cost to
+ 
+
+ align:start position:0%
+your firm to learn what it cost to
+upgrade to the high quality
+
+ align:start position:0%
+upgrade to the high quality
+ 
+
+ align:start position:0%
+upgrade to the high quality
+good um what happens um well you know
+
+ align:start position:0%
+good um what happens um well you know
+ 
+
+ align:start position:0%
+good um what happens um well you know
+there's an equilibrium where like and
+
+ align:start position:0%
+there's an equilibrium where like and
+ 
+
+ align:start position:0%
+there's an equilibrium where like and
+law and
+
+ align:start position:0%
+law and
+ 
+
+ align:start position:0%
+law and
+matus um the price of the upgrade is the
+
+ align:start position:0%
+matus um the price of the upgrade is the
+ 
+
+ align:start position:0%
+matus um the price of the upgrade is the
+full value for the
+
+ align:start position:0%
+full value for the
+ 
+
+ align:start position:0%
+full value for the
+upgrade uh for the high types so the
+
+ align:start position:0%
+upgrade uh for the high types so the
+ 
+
+ align:start position:0%
+upgrade uh for the high types so the
+price of the upgrade is what are the
+
+ align:start position:0%
+price of the upgrade is what are the
+ 
+
+ align:start position:0%
+price of the upgrade is what are the
+businessmen willing to pay for the
+
+ align:start position:0%
+businessmen willing to pay for the
+ 
+
+ align:start position:0%
+businessmen willing to pay for the
+rental car
+
+ align:start position:0%
+rental car
+ 
+
+ align:start position:0%
+rental car
+seat um and then price of the low
+
+ align:start position:0%
+seat um and then price of the low
+ 
+
+ align:start position:0%
+seat um and then price of the low
+quality good ends up being this um which
+
+ align:start position:0%
+quality good ends up being this um which
+ 
+
+ align:start position:0%
+quality good ends up being this um which
+I won't get into um but main applied
+
+ align:start position:0%
+I won't get into um but main applied
+ 
+
+ align:start position:0%
+I won't get into um but main applied
+conclusions are that profits in this
+
+ align:start position:0%
+conclusions are that profits in this
+ 
+
+ align:start position:0%
+conclusions are that profits in this
+game are higher than the profits in the
+
+ align:start position:0%
+game are higher than the profits in the
+ 
+
+ align:start position:0%
+game are higher than the profits in the
+game where PL and pH are both visible so
+
+ align:start position:0%
+game where PL and pH are both visible so
+ 
+
+ align:start position:0%
+game where PL and pH are both visible so
+in this competitive price discrimination
+
+ align:start position:0%
+in this competitive price discrimination
+ 
+
+ align:start position:0%
+in this competitive price discrimination
+model add-on pricing or these these the
+
+ align:start position:0%
+model add-on pricing or these these the
+ 
+
+ align:start position:0%
+model add-on pricing or these these the
+sort of loss leaders are not uh neutral
+
+ align:start position:0%
+sort of loss leaders are not uh neutral
+ 
+
+ align:start position:0%
+sort of loss leaders are not uh neutral
+they raise prices and not only do they
+
+ align:start position:0%
+they raise prices and not only do they
+ 
+
+ align:start position:0%
+they raise prices and not only do they
+raise prices but they make all consumers
+
+ align:start position:0%
+raise prices but they make all consumers
+ 
+
+ align:start position:0%
+raise prices but they make all consumers
+worse off um than in the game where the
+
+ align:start position:0%
+worse off um than in the game where the
+ 
+
+ align:start position:0%
+worse off um than in the game where the
+the lowquality good didn't exist so if I
+
+ align:start position:0%
+the lowquality good didn't exist so if I
+ 
+
+ align:start position:0%
+the lowquality good didn't exist so if I
+ban the production of of rental cars
+
+ align:start position:0%
+ban the production of of rental cars
+ 
+
+ align:start position:0%
+ban the production of of rental cars
+that don't come with a car seat if you
+
+ align:start position:0%
+that don't come with a car seat if you
+ 
+
+ align:start position:0%
+that don't come with a car seat if you
+ask for it for free all consumers would
+
+ align:start position:0%
+ask for it for free all consumers would
+ 
+
+ align:start position:0%
+ask for it for free all consumers would
+be better off the low types would be
+
+ align:start position:0%
+be better off the low types would be
+ 
+
+ align:start position:0%
+be better off the low types would be
+better off and the high types would be
+
+ align:start position:0%
+better off and the high types would be
+ 
+
+ align:start position:0%
+better off and the high types would be
+better off um the high types are better
+
+ align:start position:0%
+better off um the high types are better
+ 
+
+ align:start position:0%
+better off um the high types are better
+off because they would pay a low price
+
+ align:start position:0%
+off because they would pay a low price
+ 
+
+ align:start position:0%
+off because they would pay a low price
+without this add-on pricing scheme the
+
+ align:start position:0%
+without this add-on pricing scheme the
+ 
+
+ align:start position:0%
+without this add-on pricing scheme the
+low types are better off because they're
+
+ align:start position:0%
+low types are better off because they're
+ 
+
+ align:start position:0%
+low types are better off because they're
+getting a better quality good instead of
+
+ align:start position:0%
+getting a better quality good instead of
+ 
+
+ align:start position:0%
+getting a better quality good instead of
+having to carry their car seats on the
+
+ align:start position:0%
+having to carry their car seats on the
+ 
+
+ align:start position:0%
+having to carry their car seats on the
+plane okay
+
+ align:start position:0%
+plane okay
+ 
+
+ align:start position:0%
+plane okay
+I'm short on time so when I I skip that
+
+ align:start position:0%
+I'm short on time so when I I skip that
+ 
+
+ align:start position:0%
+I'm short on time so when I I skip that
+but let just sort of give you the
+
+ align:start position:0%
+but let just sort of give you the
+ 
+
+ align:start position:0%
+but let just sort of give you the
+intuition for these why that add-on
+
+ align:start position:0%
+intuition for these why that add-on
+ 
+
+ align:start position:0%
+intuition for these why that add-on
+pricing becomes
+
+ align:start position:0%
+pricing becomes
+ 
+
+ align:start position:0%
+pricing becomes
+non-neutral you know imagine think about
+
+ align:start position:0%
+non-neutral you know imagine think about
+ 
+
+ align:start position:0%
+non-neutral you know imagine think about
+reducing your price to P star minus DP
+
+ align:start position:0%
+reducing your price to P star minus DP
+ 
+
+ align:start position:0%
+reducing your price to P star minus DP
+in the add-on model and doing the same
+
+ align:start position:0%
+in the add-on model and doing the same
+ 
+
+ align:start position:0%
+in the add-on model and doing the same
+in the model with no low quality
+
+ align:start position:0%
+in the model with no low quality
+ 
+
+ align:start position:0%
+in the model with no low quality
+good in both models what you lose from a
+
+ align:start position:0%
+good in both models what you lose from a
+ 
+
+ align:start position:0%
+good in both models what you lose from a
+price cut is 1 half DP from charging the
+
+ align:start position:0%
+price cut is 1 half DP from charging the
+ 
+
+ align:start position:0%
+price cut is 1 half DP from charging the
+lower prices to the half the consumers
+
+ align:start position:0%
+lower prices to the half the consumers
+ 
+
+ align:start position:0%
+lower prices to the half the consumers
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+serving in both models what you're
+
+ align:start position:0%
+serving in both models what you're
+ 
+
+ align:start position:0%
+serving in both models what you're
+gaining is
+
+ align:start position:0%
+gaining is
+ 
+
+ align:start position:0%
+gaining is
+from the price cut is the number of
+
+ align:start position:0%
+from the price cut is the number of
+ 
+
+ align:start position:0%
+from the price cut is the number of
+customers gained times the per customer
+
+ align:start position:0%
+customers gained times the per customer
+ 
+
+ align:start position:0%
+customers gained times the per customer
+profit on the marginal consumer that you
+
+ align:start position:0%
+profit on the marginal consumer that you
+ 
+
+ align:start position:0%
+profit on the marginal consumer that you
+gain and so because you know in both
+
+ align:start position:0%
+gain and so because you know in both
+ 
+
+ align:start position:0%
+gain and so because you know in both
+models if you try to make you know in
+
+ align:start position:0%
+models if you try to make you know in
+ 
+
+ align:start position:0%
+models if you try to make you know in
+both models the first order condition
+
+ align:start position:0%
+both models the first order condition
+ 
+
+ align:start position:0%
+both models the first order condition
+this has to equal
+
+ align:start position:0%
+this has to equal
+ 
+
+ align:start position:0%
+this has to equal
+this the 1 half DP is the same in both
+
+ align:start position:0%
+this the 1 half DP is the same in both
+ 
+
+ align:start position:0%
+this the 1 half DP is the same in both
+the number of customers gained in both
+
+ align:start position:0%
+the number of customers gained in both
+ 
+
+ align:start position:0%
+the number of customers gained in both
+therefore the per customer profit on the
+
+ align:start position:0%
+therefore the per customer profit on the
+ 
+
+ align:start position:0%
+therefore the per customer profit on the
+marginal consumer is the same in both
+
+ align:start position:0%
+marginal consumer is the same in both
+ 
+
+ align:start position:0%
+marginal consumer is the same in both
+models so in both models the per
+
+ align:start position:0%
+models so in both models the per
+ 
+
+ align:start position:0%
+models so in both models the per
+customer profit you make on the marginal
+
+ align:start position:0%
+customer profit you make on the marginal
+ 
+
+ align:start position:0%
+customer profit you make on the marginal
+consumer is the
+
+ align:start position:0%
+consumer is the
+ 
+
+ align:start position:0%
+consumer is the
+same um
+
+ align:start position:0%
+same um
+ 
+
+ align:start position:0%
+same um
+but profits are based on profits on the
+
+ align:start position:0%
+but profits are based on profits on the
+ 
+
+ align:start position:0%
+but profits are based on profits on the
+average consumer not the marginal
+
+ align:start position:0%
+average consumer not the marginal
+ 
+
+ align:start position:0%
+average consumer not the marginal
+consumer and if you think about what
+
+ align:start position:0%
+consumer and if you think about what
+ 
+
+ align:start position:0%
+consumer and if you think about what
+goes on in a model like this when I cut
+
+ align:start position:0%
+goes on in a model like this when I cut
+ 
+
+ align:start position:0%
+goes on in a model like this when I cut
+my price who do I get by like I offer my
+
+ align:start position:0%
+my price who do I get by like I offer my
+ 
+
+ align:start position:0%
+my price who do I get by like I offer my
+rental car for $1 less than than every
+
+ align:start position:0%
+rental car for $1 less than than every
+ 
+
+ align:start position:0%
+rental car for $1 less than than every
+than everybody else's rental car my
+
+ align:start position:0%
+than everybody else's rental car my
+ 
+
+ align:start position:0%
+than everybody else's rental car my
+rental car is $38.95 a day instead of $
+
+ align:start position:0%
+rental car is $38.95 a day instead of $
+ 
+
+ align:start position:0%
+rental car is $38.95 a day instead of $
+39.95 a day I get all the cheap skates
+
+ align:start position:0%
+39.95 a day I get all the cheap skates
+ 
+
+ align:start position:0%
+39.95 a day I get all the cheap skates
+and I get all the cheap skates where the
+
+ align:start position:0%
+and I get all the cheap skates where the
+ 
+
+ align:start position:0%
+and I get all the cheap skates where the
+low types were willing to carry their
+
+ align:start position:0%
+low types were willing to carry their
+ 
+
+ align:start position:0%
+low types were willing to carry their
+car seat on a plane and spend extra time
+
+ align:start position:0%
+car seat on a plane and spend extra time
+ 
+
+ align:start position:0%
+car seat on a plane and spend extra time
+waiting at the gate to get their car
+
+ align:start position:0%
+waiting at the gate to get their car
+ 
+
+ align:start position:0%
+waiting at the gate to get their car
+seat and and carrying it through the
+
+ align:start position:0%
+seat and and carrying it through the
+ 
+
+ align:start position:0%
+seat and and carrying it through the
+airport to save the 13.95 a day and so
+
+ align:start position:0%
+airport to save the 13.95 a day and so
+ 
+
+ align:start position:0%
+airport to save the 13.95 a day and so
+because the cheap skates are an
+
+ align:start position:0%
+because the cheap skates are an
+ 
+
+ align:start position:0%
+because the cheap skates are an
+adversely selected population relative
+
+ align:start position:0%
+adversely selected population relative
+ 
+
+ align:start position:0%
+adversely selected population relative
+to the full population so I when I cut
+
+ align:start position:0%
+to the full population so I when I cut
+ 
+
+ align:start position:0%
+to the full population so I when I cut
+my price in this add-on model I get a
+
+ align:start position:0%
+my price in this add-on model I get a
+ 
+
+ align:start position:0%
+my price in this add-on model I get a
+bunch of cheap
+
+ align:start position:0%
+bunch of cheap
+ 
+
+ align:start position:0%
+bunch of cheap
+skates if the marginal profit so there's
+
+ align:start position:0%
+skates if the marginal profit so there's
+ 
+
+ align:start position:0%
+skates if the marginal profit so there's
+in the add-on model there's this big gap
+
+ align:start position:0%
+in the add-on model there's this big gap
+ 
+
+ align:start position:0%
+in the add-on model there's this big gap
+between the profits on the marginal
+
+ align:start position:0%
+between the profits on the marginal
+ 
+
+ align:start position:0%
+between the profits on the marginal
+consumers and the profits on the average
+
+ align:start position:0%
+consumers and the profits on the average
+ 
+
+ align:start position:0%
+consumers and the profits on the average
+consumers whereas in the single good
+
+ align:start position:0%
+consumers whereas in the single good
+ 
+
+ align:start position:0%
+consumers whereas in the single good
+product the marginal and average
+
+ align:start position:0%
+product the marginal and average
+ 
+
+ align:start position:0%
+product the marginal and average
+consumers are exactly the
+
+ align:start position:0%
+consumers are exactly the
+ 
+
+ align:start position:0%
+consumers are exactly the
+same so what we've done is we've just
+
+ align:start position:0%
+same so what we've done is we've just
+ 
+
+ align:start position:0%
+same so what we've done is we've just
+created this gap between marginal
+
+ align:start position:0%
+created this gap between marginal
+ 
+
+ align:start position:0%
+created this gap between marginal
+consumers and average consumers and that
+
+ align:start position:0%
+consumers and average consumers and that
+ 
+
+ align:start position:0%
+consumers and average consumers and that
+ends up raising equilibrium prices some
+
+ align:start position:0%
+ends up raising equilibrium prices some
+ 
+
+ align:start position:0%
+ends up raising equilibrium prices some
+you've some you've created an adverse
+
+ align:start position:0%
+you've some you've created an adverse
+ 
+
+ align:start position:0%
+you've some you've created an adverse
+selection problem and that adverse
+
+ align:start position:0%
+selection problem and that adverse
+ 
+
+ align:start position:0%
+selection problem and that adverse
+selection
+
+ align:start position:0%
+selection
+ 
+
+ align:start position:0%
+selection
+problem uh makes it hard for firms to
+
+ align:start position:0%
+problem uh makes it hard for firms to
+ 
+
+ align:start position:0%
+problem uh makes it hard for firms to
+price compete against other firms
+
+ align:start position:0%
+price compete against other firms
+ 
+
+ align:start position:0%
+price compete against other firms
+because if you cut prices you just get
+
+ align:start position:0%
+because if you cut prices you just get
+ 
+
+ align:start position:0%
+because if you cut prices you just get
+cheap skates on whom you lose money
+
+ align:start position:0%
+cheap skates on whom you lose money
+ 
+
+ align:start position:0%
+cheap skates on whom you lose money
+money renting the cars so
+
+ align:start position:0%
+money renting the cars so
+ 
+
+ align:start position:0%
+money renting the cars so
+cheap okay any questions no so okay
+
+ align:start position:0%
+cheap okay any questions no so okay
+ 
+
+ align:start position:0%
+cheap okay any questions no so okay
+that leave me with uh 10 minutes and I I
+
+ align:start position:0%
+that leave me with uh 10 minutes and I I
+ 
+
+ align:start position:0%
+that leave me with uh 10 minutes and I I
+said I would do this paper very quickly
+
+ align:start position:0%
+said I would do this paper very quickly
+ 
+
+ align:start position:0%
+said I would do this paper very quickly
+because this really follows very much
+
+ align:start position:0%
+because this really follows very much
+ 
+
+ align:start position:0%
+because this really follows very much
+methodology Tobias is talking about on
+
+ align:start position:0%
+methodology Tobias is talking about on
+ 
+
+ align:start position:0%
+methodology Tobias is talking about on
+Monday um of next week so you know
+
+ align:start position:0%
+Monday um of next week so you know
+ 
+
+ align:start position:0%
+Monday um of next week so you know
+Miller and Weinberg is is a very similar
+
+ align:start position:0%
+Miller and Weinberg is is a very similar
+ 
+
+ align:start position:0%
+Miller and Weinberg is is a very similar
+paper to breast and hand and it's a much
+
+ align:start position:0%
+paper to breast and hand and it's a much
+ 
+
+ align:start position:0%
+paper to breast and hand and it's a much
+more modern well done um you know
+
+ align:start position:0%
+more modern well done um you know
+ 
+
+ align:start position:0%
+more modern well done um you know
+Frontier quality um uh piece of Applied
+
+ align:start position:0%
+Frontier quality um uh piece of Applied
+ 
+
+ align:start position:0%
+Frontier quality um uh piece of Applied
+work um the applied question is whether
+
+ align:start position:0%
+work um the applied question is whether
+ 
+
+ align:start position:0%
+work um the applied question is whether
+us beer price the rise in US beer prices
+
+ align:start position:0%
+us beer price the rise in US beer prices
+ 
+
+ align:start position:0%
+us beer price the rise in US beer prices
+following the 2008 uh joint venture of
+
+ align:start position:0%
+following the 2008 uh joint venture of
+ 
+
+ align:start position:0%
+following the 2008 uh joint venture of
+Miller and Kors can be explained as a
+
+ align:start position:0%
+Miller and Kors can be explained as a
+ 
+
+ align:start position:0%
+Miller and Kors can be explained as a
+consequence of just static price
+
+ align:start position:0%
+consequence of just static price
+ 
+
+ align:start position:0%
+consequence of just static price
+competition or if we need some degree of
+
+ align:start position:0%
+competition or if we need some degree of
+ 
+
+ align:start position:0%
+competition or if we need some degree of
+cooperation or collusion among the firms
+
+ align:start position:0%
+cooperation or collusion among the firms
+ 
+
+ align:start position:0%
+cooperation or collusion among the firms
+to understand what happens and so what
+
+ align:start position:0%
+to understand what happens and so what
+ 
+
+ align:start position:0%
+to understand what happens and so what
+it does is it estimates a model that
+
+ align:start position:0%
+it does is it estimates a model that
+ 
+
+ align:start position:0%
+it does is it estimates a model that
+assumes that the firms were paying
+
+ align:start position:0%
+assumes that the firms were paying
+ 
+
+ align:start position:0%
+assumes that the firms were paying
+static uh you know natur equ static
+
+ align:start position:0%
+static uh you know natur equ static
+ 
+
+ align:start position:0%
+static uh you know natur equ static
+differentiated product competition
+
+ align:start position:0%
+differentiated product competition
+ 
+
+ align:start position:0%
+differentiated product competition
+before the merger and then after the
+
+ align:start position:0%
+before the merger and then after the
+ 
+
+ align:start position:0%
+before the merger and then after the
+merger um Miller Kors and anheiser Bush
+
+ align:start position:0%
+merger um Miller Kors and anheiser Bush
+ 
+
+ align:start position:0%
+merger um Miller Kors and anheiser Bush
+are partially
+
+ align:start position:0%
+are partially
+ 
+
+ align:start position:0%
+are partially
+Cooperative uh and then the partial
+
+ align:start position:0%
+Cooperative uh and then the partial
+ 
+
+ align:start position:0%
+Cooperative uh and then the partial
+Cooperative model what it does is it
+
+ align:start position:0%
+Cooperative model what it does is it
+ 
+
+ align:start position:0%
+Cooperative model what it does is it
+like Brean had three or four models they
+
+ align:start position:0%
+like Brean had three or four models they
+ 
+
+ align:start position:0%
+like Brean had three or four models they
+have a Continuum of models the Continuum
+
+ align:start position:0%
+have a Continuum of models the Continuum
+ 
+
+ align:start position:0%
+have a Continuum of models the Continuum
+of models is assume it's as if each firm
+
+ align:start position:0%
+of models is assume it's as if each firm
+ 
+
+ align:start position:0%
+of models is assume it's as if each firm
+is maximizing their own profit plus
+
+ align:start position:0%
+is maximizing their own profit plus
+ 
+
+ align:start position:0%
+is maximizing their own profit plus
+Kappa times the profit of the other
+
+ align:start position:0%
+Kappa times the profit of the other
+ 
+
+ align:start position:0%
+Kappa times the profit of the other
+firms so Kappa equals one would be full
+
+ align:start position:0%
+firms so Kappa equals one would be full
+ 
+
+ align:start position:0%
+firms so Kappa equals one would be full
+collusion usion Kappa equals z would be
+
+ align:start position:0%
+collusion usion Kappa equals z would be
+ 
+
+ align:start position:0%
+collusion usion Kappa equals z would be
+static competition and Kappa in between
+
+ align:start position:0%
+static competition and Kappa in between
+ 
+
+ align:start position:0%
+static competition and Kappa in between
+is some degree of partial collusion
+
+ align:start position:0%
+is some degree of partial collusion
+ 
+
+ align:start position:0%
+is some degree of partial collusion
+between the firms okay and then what
+
+ align:start position:0%
+between the firms okay and then what
+ 
+
+ align:start position:0%
+between the firms okay and then what
+they note is that in this model with
+
+ align:start position:0%
+they note is that in this model with
+ 
+
+ align:start position:0%
+they note is that in this model with
+this sort of Contin of models you can
+
+ align:start position:0%
+this sort of Contin of models you can
+ 
+
+ align:start position:0%
+this sort of Contin of models you can
+test whether Kappa equals zero to say
+
+ align:start position:0%
+test whether Kappa equals zero to say
+ 
+
+ align:start position:0%
+test whether Kappa equals zero to say
+does the static competition model
+
+ align:start position:0%
+does the static competition model
+ 
+
+ align:start position:0%
+does the static competition model
+explain what's going on or you know do I
+
+ align:start position:0%
+explain what's going on or you know do I
+ 
+
+ align:start position:0%
+explain what's going on or you know do I
+need to have some degree of collusion
+
+ align:start position:0%
+need to have some degree of collusion
+ 
+
+ align:start position:0%
+need to have some degree of collusion
+starting after the the Miller cores merg
+
+ align:start position:0%
+starting after the the Miller cores merg
+ 
+
+ align:start position:0%
+starting after the the Miller cores merg
+to understand why prices are what they
+
+ align:start position:0%
+to understand why prices are what they
+ 
+
+ align:start position:0%
+to understand why prices are what they
+are so anyway I I won't go into the
+
+ align:start position:0%
+are so anyway I I won't go into the
+ 
+
+ align:start position:0%
+are so anyway I I won't go into the
+details here but um background you know
+
+ align:start position:0%
+details here but um background you know
+ 
+
+ align:start position:0%
+details here but um background you know
+I think even graduate students drink
+
+ align:start position:0%
+I think even graduate students drink
+ 
+
+ align:start position:0%
+I think even graduate students drink
+craft beer these days but you know
+
+ align:start position:0%
+craft beer these days but you know
+ 
+
+ align:start position:0%
+craft beer these days but you know
+despite the incredible rise in craft
+
+ align:start position:0%
+despite the incredible rise in craft
+ 
+
+ align:start position:0%
+despite the incredible rise in craft
+beer most Americans still drink really
+
+ align:start position:0%
+beer most Americans still drink really
+ 
+
+ align:start position:0%
+beer most Americans still drink really
+cheap beer um so you know most Americans
+
+ align:start position:0%
+cheap beer um so you know most Americans
+ 
+
+ align:start position:0%
+cheap beer um so you know most Americans
+drink Bud Light Coors Light uh Miller
+
+ align:start position:0%
+drink Bud Light Coors Light uh Miller
+ 
+
+ align:start position:0%
+drink Bud Light Coors Light uh Miller
+Light you know maybe May that's least
+
+ align:start position:0%
+Light you know maybe May that's least
+ 
+
+ align:start position:0%
+Light you know maybe May that's least
+most sales because people buy budlight
+
+ align:start position:0%
+most sales because people buy budlight
+ 
+
+ align:start position:0%
+most sales because people buy budlight
+in 30 packs um but um there's been
+
+ align:start position:0%
+in 30 packs um but um there's been
+ 
+
+ align:start position:0%
+in 30 packs um but um there's been
+tremendous consolidation of beer
+
+ align:start position:0%
+tremendous consolidation of beer
+ 
+
+ align:start position:0%
+tremendous consolidation of beer
+ownership in the past 20 years globally
+
+ align:start position:0%
+ownership in the past 20 years globally
+ 
+
+ align:start position:0%
+ownership in the past 20 years globally
+so basically in every country around the
+
+ align:start position:0%
+so basically in every country around the
+ 
+
+ align:start position:0%
+so basically in every country around the
+world the same three companies sell all
+
+ align:start position:0%
+world the same three companies sell all
+ 
+
+ align:start position:0%
+world the same three companies sell all
+the beer uh and so you know the same
+
+ align:start position:0%
+the beer uh and so you know the same
+ 
+
+ align:start position:0%
+the beer uh and so you know the same
+companies that sell anheiser bush in the
+
+ align:start position:0%
+companies that sell anheiser bush in the
+ 
+
+ align:start position:0%
+companies that sell anheiser bush in the
+United States are also ones that sell
+
+ align:start position:0%
+United States are also ones that sell
+ 
+
+ align:start position:0%
+United States are also ones that sell
+Becks and Germany and celella Arta and
+
+ align:start position:0%
+Becks and Germany and celella Arta and
+ 
+
+ align:start position:0%
+Becks and Germany and celella Arta and
+England and whatever but these companies
+
+ align:start position:0%
+England and whatever but these companies
+ 
+
+ align:start position:0%
+England and whatever but these companies
+have put together portfolios of beers
+
+ align:start position:0%
+have put together portfolios of beers
+ 
+
+ align:start position:0%
+have put together portfolios of beers
+um you know prior to the N 2008 Miller
+
+ align:start position:0%
+um you know prior to the N 2008 Miller
+ 
+
+ align:start position:0%
+um you know prior to the N 2008 Miller
+Kors joint venture um anheiser bush
+
+ align:start position:0%
+Kors joint venture um anheiser bush
+ 
+
+ align:start position:0%
+Kors joint venture um anheiser bush
+inbev had a market share of about
+
+ align:start position:0%
+inbev had a market share of about
+ 
+
+ align:start position:0%
+inbev had a market share of about
+35% Miller had a a market share of 18% K
+
+ align:start position:0%
+35% Miller had a a market share of 18% K
+ 
+
+ align:start position:0%
+35% Miller had a a market share of 18% K
+had an market share of 11% and again you
+
+ align:start position:0%
+had an market share of 11% and again you
+ 
+
+ align:start position:0%
+had an market share of 11% and again you
+know those are market shares in the
+
+ align:start position:0%
+know those are market shares in the
+ 
+
+ align:start position:0%
+know those are market shares in the
+whole Beer Market if you take away the
+
+ align:start position:0%
+whole Beer Market if you take away the
+ 
+
+ align:start position:0%
+whole Beer Market if you take away the
+premium beers there are many submarkets
+
+ align:start position:0%
+premium beers there are many submarkets
+ 
+
+ align:start position:0%
+premium beers there are many submarkets
+in which those firms have much higher
+
+ align:start position:0%
+in which those firms have much higher
+ 
+
+ align:start position:0%
+in which those firms have much higher
+shares okay and despite the fact that
+
+ align:start position:0%
+shares okay and despite the fact that
+ 
+
+ align:start position:0%
+shares okay and despite the fact that
+sort of these were the overall market
+
+ align:start position:0%
+sort of these were the overall market
+ 
+
+ align:start position:0%
+sort of these were the overall market
+shares um Miller and KS were in 2008
+
+ align:start position:0%
+shares um Miller and KS were in 2008
+ 
+
+ align:start position:0%
+shares um Miller and KS were in 2008
+allowed to form a joint venture and sell
+
+ align:start position:0%
+allowed to form a joint venture and sell
+ 
+
+ align:start position:0%
+allowed to form a joint venture and sell
+their beer together
+
+ align:start position:0%
+their beer together
+ 
+
+ align:start position:0%
+their beer together
+um so and Miller cores argued that yes
+
+ align:start position:0%
+um so and Miller cores argued that yes
+ 
+
+ align:start position:0%
+um so and Miller cores argued that yes
+it looks like the second and third
+
+ align:start position:0%
+it looks like the second and third
+ 
+
+ align:start position:0%
+it looks like the second and third
+biggest firms in the market are merging
+
+ align:start position:0%
+biggest firms in the market are merging
+ 
+
+ align:start position:0%
+biggest firms in the market are merging
+together to be create a three- firm
+
+ align:start position:0%
+together to be create a three- firm
+ 
+
+ align:start position:0%
+together to be create a three- firm
+competition to two- firm competition but
+
+ align:start position:0%
+competition to two- firm competition but
+ 
+
+ align:start position:0%
+competition to two- firm competition but
+this is going to be good for consumers
+
+ align:start position:0%
+this is going to be good for consumers
+ 
+
+ align:start position:0%
+this is going to be good for consumers
+because there's going to be enough cost
+
+ align:start position:0%
+because there's going to be enough cost
+ 
+
+ align:start position:0%
+because there's going to be enough cost
+savings that we're going to have an
+
+ align:start position:0%
+savings that we're going to have an
+ 
+
+ align:start position:0%
+savings that we're going to have an
+incentive to lower our prices particular
+
+ align:start position:0%
+incentive to lower our prices particular
+ 
+
+ align:start position:0%
+incentive to lower our prices particular
+you know Kors was mostly brewed in
+
+ align:start position:0%
+you know Kors was mostly brewed in
+ 
+
+ align:start position:0%
+you know Kors was mostly brewed in
+Colorado and then had to be shipped all
+
+ align:start position:0%
+Colorado and then had to be shipped all
+ 
+
+ align:start position:0%
+Colorado and then had to be shipped all
+across the United States which is
+
+ align:start position:0%
+across the United States which is
+ 
+
+ align:start position:0%
+across the United States which is
+expensive they're like if only we could
+
+ align:start position:0%
+expensive they're like if only we could
+ 
+
+ align:start position:0%
+expensive they're like if only we could
+produce all the Kors beer and all those
+
+ align:start position:0%
+produce all the Kors beer and all those
+ 
+
+ align:start position:0%
+produce all the Kors beer and all those
+Miller plants that are distributed
+
+ align:start position:0%
+Miller plants that are distributed
+ 
+
+ align:start position:0%
+Miller plants that are distributed
+around the country and then share trucks
+
+ align:start position:0%
+around the country and then share trucks
+ 
+
+ align:start position:0%
+around the country and then share trucks
+shipping the Miller and Coors to all the
+
+ align:start position:0%
+shipping the Miller and Coors to all the
+ 
+
+ align:start position:0%
+shipping the Miller and Coors to all the
+beer distributors then we'd save on the
+
+ align:start position:0%
+beer distributors then we'd save on the
+ 
+
+ align:start position:0%
+beer distributors then we'd save on the
+trucking costs we'd save on the shipping
+
+ align:start position:0%
+trucking costs we'd save on the shipping
+ 
+
+ align:start position:0%
+trucking costs we'd save on the shipping
+costs cost will go down so much that
+
+ align:start position:0%
+costs cost will go down so much that
+ 
+
+ align:start position:0%
+costs cost will go down so much that
+consumers will be better off uh and the
+
+ align:start position:0%
+consumers will be better off uh and the
+ 
+
+ align:start position:0%
+consumers will be better off uh and the
+justice department approved the merger
+
+ align:start position:0%
+justice department approved the merger
+ 
+
+ align:start position:0%
+justice department approved the merger
+um uh anyway um you know very beautiful
+
+ align:start position:0%
+um uh anyway um you know very beautiful
+ 
+
+ align:start position:0%
+um uh anyway um you know very beautiful
+graph to sort of giving the basic thing
+
+ align:start position:0%
+graph to sort of giving the basic thing
+ 
+
+ align:start position:0%
+graph to sort of giving the basic thing
+of did what the firms tell the justice
+
+ align:start position:0%
+of did what the firms tell the justice
+ 
+
+ align:start position:0%
+of did what the firms tell the justice
+department come true here are the graphs
+
+ align:start position:0%
+department come true here are the graphs
+ 
+
+ align:start position:0%
+department come true here are the graphs
+of the prices for Miller Light Bud Light
+
+ align:start position:0%
+of the prices for Miller Light Bud Light
+ 
+
+ align:start position:0%
+of the prices for Miller Light Bud Light
+Kors light leading up to the time of the
+
+ align:start position:0%
+Kors light leading up to the time of the
+ 
+
+ align:start position:0%
+Kors light leading up to the time of the
+merg merer and you can see beer prices
+
+ align:start position:0%
+merg merer and you can see beer prices
+ 
+
+ align:start position:0%
+merg merer and you can see beer prices
+were trending down um after the merger
+
+ align:start position:0%
+were trending down um after the merger
+ 
+
+ align:start position:0%
+were trending down um after the merger
+there was this temporary sale on Miller
+
+ align:start position:0%
+there was this temporary sale on Miller
+ 
+
+ align:start position:0%
+there was this temporary sale on Miller
+Light but then by a couple months after
+
+ align:start position:0%
+Light but then by a couple months after
+ 
+
+ align:start position:0%
+Light but then by a couple months after
+the merger prices went up
+
+ align:start position:0%
+the merger prices went up
+ 
+
+ align:start position:0%
+the merger prices went up
+there so there's just a very
+
+ align:start position:0%
+there so there's just a very
+ 
+
+ align:start position:0%
+there so there's just a very
+clear departure from Trend and the
+
+ align:start position:0%
+clear departure from Trend and the
+ 
+
+ align:start position:0%
+clear departure from Trend and the
+prices of budlight Miller Light Coors
+
+ align:start position:0%
+prices of budlight Miller Light Coors
+ 
+
+ align:start position:0%
+prices of budlight Miller Light Coors
+Light jump after the Miller Kors
+
+ align:start position:0%
+Light jump after the Miller Kors
+ 
+
+ align:start position:0%
+Light jump after the Miller Kors
+merger okay um their competitor prices
+
+ align:start position:0%
+merger okay um their competitor prices
+ 
+
+ align:start position:0%
+merger okay um their competitor prices
+didn't do so much so that two largest
+
+ align:start position:0%
+didn't do so much so that two largest
+ 
+
+ align:start position:0%
+didn't do so much so that two largest
+Brands not sold by uh anheiser Bush
+
+ align:start position:0%
+Brands not sold by uh anheiser Bush
+ 
+
+ align:start position:0%
+Brands not sold by uh anheiser Bush
+inbev or Miller Kors are Heineken and
+
+ align:start position:0%
+inbev or Miller Kors are Heineken and
+ 
+
+ align:start position:0%
+inbev or Miller Kors are Heineken and
+Corona um Heineken and Corona
+
+ align:start position:0%
+Corona um Heineken and Corona
+ 
+
+ align:start position:0%
+Corona um Heineken and Corona
+prices you know you don't notice maybe
+
+ align:start position:0%
+prices you know you don't notice maybe
+ 
+
+ align:start position:0%
+prices you know you don't notice maybe
+you look and see there's a little jump
+
+ align:start position:0%
+you look and see there's a little jump
+ 
+
+ align:start position:0%
+you look and see there's a little jump
+up here but it seems like they're mostly
+
+ align:start position:0%
+up here but it seems like they're mostly
+ 
+
+ align:start position:0%
+up here but it seems like they're mostly
+on Trend so if we take that as a
+
+ align:start position:0%
+on Trend so if we take that as a
+ 
+
+ align:start position:0%
+on Trend so if we take that as a
+differences and differences thing to say
+
+ align:start position:0%
+differences and differences thing to say
+ 
+
+ align:start position:0%
+differences and differences thing to say
+there doesn't seem to be a difference in
+
+ align:start position:0%
+there doesn't seem to be a difference in
+ 
+
+ align:start position:0%
+there doesn't seem to be a difference in
+the cost of producing beer if there's no
+
+ align:start position:0%
+the cost of producing beer if there's no
+ 
+
+ align:start position:0%
+the cost of producing beer if there's no
+difference in the cost of producing beer
+
+ align:start position:0%
+difference in the cost of producing beer
+ 
+
+ align:start position:0%
+difference in the cost of producing beer
+what you get is that the 12 packs of the
+
+ align:start position:0%
+what you get is that the 12 packs of the
+ 
+
+ align:start position:0%
+what you get is that the 12 packs of the
+flagship Brands went up by about uh 10%
+
+ align:start position:0%
+flagship Brands went up by about uh 10%
+ 
+
+ align:start position:0%
+flagship Brands went up by about uh 10%
+overall prices went up by about 5% you
+
+ align:start position:0%
+overall prices went up by about 5% you
+ 
+
+ align:start position:0%
+overall prices went up by about 5% you
+know it's basically it's as if they you
+
+ align:start position:0%
+know it's basically it's as if they you
+ 
+
+ align:start position:0%
+know it's basically it's as if they you
+know like a 12 if a 12pack of Bud Light
+
+ align:start position:0%
+know like a 12 if a 12pack of Bud Light
+ 
+
+ align:start position:0%
+know like a 12 if a 12pack of Bud Light
+cost 10 bucks it's like they went from
+
+ align:start position:0%
+cost 10 bucks it's like they went from
+ 
+
+ align:start position:0%
+cost 10 bucks it's like they went from
+10 to 11 the 20 packs it seems like the
+
+ align:start position:0%
+10 to 11 the 20 packs it seems like the
+ 
+
+ align:start position:0%
+10 to 11 the 20 packs it seems like the
+the 30 packs it seem like they went from
+
+ align:start position:0%
+the 30 packs it seem like they went from
+ 
+
+ align:start position:0%
+the 30 packs it seem like they went from
+from 18 to 19 but it's basically like
+
+ align:start position:0%
+from 18 to 19 but it's basically like
+ 
+
+ align:start position:0%
+from 18 to 19 but it's basically like
+prices go up by 5% on average but 10% on
+
+ align:start position:0%
+prices go up by 5% on average but 10% on
+ 
+
+ align:start position:0%
+prices go up by 5% on average but 10% on
+this sort of 12pack of the standard
+
+ align:start position:0%
+this sort of 12pack of the standard
+ 
+
+ align:start position:0%
+this sort of 12pack of the standard
+Flagship beers okay um so um why does
+
+ align:start position:0%
+Flagship beers okay um so um why does
+ 
+
+ align:start position:0%
+Flagship beers okay um so um why does
+this happen again you know there is sort
+
+ align:start position:0%
+this happen again you know there is sort
+ 
+
+ align:start position:0%
+this happen again you know there is sort
+of a there are three things going on
+
+ align:start position:0%
+of a there are three things going on
+ 
+
+ align:start position:0%
+of a there are three things going on
+here there are costs are presumably
+
+ align:start position:0%
+here there are costs are presumably
+ 
+
+ align:start position:0%
+here there are costs are presumably
+going down because they're now Brewing
+
+ align:start position:0%
+going down because they're now Brewing
+ 
+
+ align:start position:0%
+going down because they're now Brewing
+Kors all over the country um but Miller
+
+ align:start position:0%
+Kors all over the country um but Miller
+ 
+
+ align:start position:0%
+Kors all over the country um but Miller
+Kors has this unilateral incentive to
+
+ align:start position:0%
+Kors has this unilateral incentive to
+ 
+
+ align:start position:0%
+Kors has this unilateral incentive to
+raise its prices because it knows if
+
+ align:start position:0%
+raise its prices because it knows if
+ 
+
+ align:start position:0%
+raise its prices because it knows if
+someone goes in to buy Kors light and
+
+ align:start position:0%
+someone goes in to buy Kors light and
+ 
+
+ align:start position:0%
+someone goes in to buy Kors light and
+the price is now higher than they expect
+
+ align:start position:0%
+the price is now higher than they expect
+ 
+
+ align:start position:0%
+the price is now higher than they expect
+they may switch to Miller Light and
+
+ align:start position:0%
+they may switch to Miller Light and
+ 
+
+ align:start position:0%
+they may switch to Miller Light and
+that's not a bad thing anymore um and
+
+ align:start position:0%
+that's not a bad thing anymore um and
+ 
+
+ align:start position:0%
+that's not a bad thing anymore um and
+then there's this possible collusion
+
+ align:start position:0%
+then there's this possible collusion
+ 
+
+ align:start position:0%
+then there's this possible collusion
+third effect so anyway what do they do
+
+ align:start position:0%
+third effect so anyway what do they do
+ 
+
+ align:start position:0%
+third effect so anyway what do they do
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+random coefficients low at demand uh
+
+ align:start position:0%
+random coefficients low at demand uh
+ 
+
+ align:start position:0%
+random coefficients low at demand uh
+Tobias will tell you more about what
+
+ align:start position:0%
+Tobias will tell you more about what
+ 
+
+ align:start position:0%
+Tobias will tell you more about what
+that means but basically you know your
+
+ align:start position:0%
+that means but basically you know your
+ 
+
+ align:start position:0%
+that means but basically you know your
+utility from buying a brand J of beer if
+
+ align:start position:0%
+utility from buying a brand J of beer if
+ 
+
+ align:start position:0%
+utility from buying a brand J of beer if
+you live in region r at time T is
+
+ align:start position:0%
+you live in region r at time T is
+ 
+
+ align:start position:0%
+you live in region r at time T is
+characteristics of the beers times beta
+
+ align:start position:0%
+characteristics of the beers times beta
+ 
+
+ align:start position:0%
+characteristics of the beers times beta
+minus a disutility from paying for the
+
+ align:start position:0%
+minus a disutility from paying for the
+ 
+
+ align:start position:0%
+minus a disutility from paying for the
+beers plus a bunch of fixed effect the
+
+ align:start position:0%
+beers plus a bunch of fixed effect the
+ 
+
+ align:start position:0%
+beers plus a bunch of fixed effect the
+beer uh brand fixed effect the time
+
+ align:start position:0%
+beer uh brand fixed effect the time
+ 
+
+ align:start position:0%
+beer uh brand fixed effect the time
+fixed effect an unobserved quality of
+
+ align:start position:0%
+fixed effect an unobserved quality of
+ 
+
+ align:start position:0%
+fixed effect an unobserved quality of
+the beer and this sort of idiosyncratic
+
+ align:start position:0%
+the beer and this sort of idiosyncratic
+ 
+
+ align:start position:0%
+the beer and this sort of idiosyncratic
+Epsilon like like in the hotelling model
+
+ align:start position:0%
+Epsilon like like in the hotelling model
+ 
+
+ align:start position:0%
+Epsilon like like in the hotelling model
+some people like Kors relative to Bud
+
+ align:start position:0%
+some people like Kors relative to Bud
+ 
+
+ align:start position:0%
+some people like Kors relative to Bud
+wise or just taste wise um what's
+
+ align:start position:0%
+wise or just taste wise um what's
+ 
+
+ align:start position:0%
+wise or just taste wise um what's
+different from the standard loit model
+
+ align:start position:0%
+different from the standard loit model
+ 
+
+ align:start position:0%
+different from the standard loit model
+is it's a random coefficients where the
+
+ align:start position:0%
+is it's a random coefficients where the
+ 
+
+ align:start position:0%
+is it's a random coefficients where the
+different people have different
+
+ align:start position:0%
+different people have different
+ 
+
+ align:start position:0%
+different people have different
+preferences over the
+
+ align:start position:0%
+preferences over the
+ 
+
+ align:start position:0%
+preferences over the
+characteristics and some people are more
+
+ align:start position:0%
+characteristics and some people are more
+ 
+
+ align:start position:0%
+characteristics and some people are more
+price sensitive and some people are less
+
+ align:start position:0%
+price sensitive and some people are less
+ 
+
+ align:start position:0%
+price sensitive and some people are less
+price sensitive so the random
+
+ align:start position:0%
+price sensitive so the random
+ 
+
+ align:start position:0%
+price sensitive so the random
+coefficients mean that not everyone has
+
+ align:start position:0%
+coefficients mean that not everyone has
+ 
+
+ align:start position:0%
+coefficients mean that not everyone has
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+coefficients you know some people like
+
+ align:start position:0%
+coefficients you know some people like
+ 
+
+ align:start position:0%
+coefficients you know some people like
+hoppiness and some people don't like
+
+ align:start position:0%
+hoppiness and some people don't like
+ 
+
+ align:start position:0%
+hoppiness and some people don't like
+hoppiness some people dislike paying
+
+ align:start position:0%
+hoppiness some people dislike paying
+ 
+
+ align:start position:0%
+hoppiness some people dislike paying
+money other people don't care care so
+
+ align:start position:0%
+money other people don't care care so
+ 
+
+ align:start position:0%
+money other people don't care care so
+much about how much they're paying okay
+
+ align:start position:0%
+much about how much they're paying okay
+ 
+
+ align:start position:0%
+much about how much they're paying okay
+they estimate this model they have some
+
+ align:start position:0%
+they estimate this model they have some
+ 
+
+ align:start position:0%
+they estimate this model they have some
+instruments for price I will skip over
+
+ align:start position:0%
+instruments for price I will skip over
+ 
+
+ align:start position:0%
+instruments for price I will skip over
+but they find a bunch of charts like
+
+ align:start position:0%
+but they find a bunch of charts like
+ 
+
+ align:start position:0%
+but they find a bunch of charts like
+this so this chart says um these are
+
+ align:start position:0%
+this so this chart says um these are
+ 
+
+ align:start position:0%
+this so this chart says um these are
+price eloc it says if you raise the
+
+ align:start position:0%
+price eloc it says if you raise the
+ 
+
+ align:start position:0%
+price eloc it says if you raise the
+price of Budweiser by 1% sales of
+
+ align:start position:0%
+price of Budweiser by 1% sales of
+ 
+
+ align:start position:0%
+price of Budweiser by 1% sales of
+Budweiser go down by
+
+ align:start position:0%
+Budweiser go down by
+ 
+
+ align:start position:0%
+Budweiser go down by
+4.4% or sales of Bud Light but then
+
+ align:start position:0%
+4.4% or sales of Bud Light but then
+ 
+
+ align:start position:0%
+4.4% or sales of Bud Light but then
+people will buy other things and so in
+
+ align:start position:0%
+people will buy other things and so in
+ 
+
+ align:start position:0%
+people will buy other things and so in
+particular Kors Budweiser sales will go
+
+ align:start position:0%
+particular Kors Budweiser sales will go
+ 
+
+ align:start position:0%
+particular Kors Budweiser sales will go
+up by 0.3% cor sales by over
+
+ align:start position:0%
+up by 0.3% cor sales by over
+ 
+
+ align:start position:0%
+up by 0.3% cor sales by over
+36% Coors Light sales will go up by 351
+
+ align:start position:0%
+36% Coors Light sales will go up by 351
+ 
+
+ align:start position:0%
+36% Coors Light sales will go up by 351
+per Corona sales will go up by
+
+ align:start position:0%
+per Corona sales will go up by
+ 
+
+ align:start position:0%
+per Corona sales will go up by
+2279 we have this sort of substitution
+
+ align:start position:0%
+2279 we have this sort of substitution
+ 
+
+ align:start position:0%
+2279 we have this sort of substitution
+Matrix they've
+
+ align:start position:0%
+Matrix they've
+ 
+
+ align:start position:0%
+Matrix they've
+estimated and then they say you know
+
+ align:start position:0%
+estimated and then they say you know
+ 
+
+ align:start position:0%
+estimated and then they say you know
+it's a two-step estimation first we
+
+ align:start position:0%
+it's a two-step estimation first we
+ 
+
+ align:start position:0%
+it's a two-step estimation first we
+estimate demand to find all the
+
+ align:start position:0%
+estimate demand to find all the
+ 
+
+ align:start position:0%
+estimate demand to find all the
+elasticities then we say what's going to
+
+ align:start position:0%
+elasticities then we say what's going to
+ 
+
+ align:start position:0%
+elasticities then we say what's going to
+happen What would happen under the
+
+ align:start position:0%
+happen What would happen under the
+ 
+
+ align:start position:0%
+happen What would happen under the
+different um models of
+
+ align:start position:0%
+different um models of
+ 
+
+ align:start position:0%
+different um models of
+behavior and let me see two things I
+
+ align:start position:0%
+behavior and let me see two things I
+ 
+
+ align:start position:0%
+behavior and let me see two things I
+want to say one thing they find is that
+
+ align:start position:0%
+want to say one thing they find is that
+ 
+
+ align:start position:0%
+want to say one thing they find is that
+you know they estimate which Kappa model
+
+ align:start position:0%
+you know they estimate which Kappa model
+ 
+
+ align:start position:0%
+you know they estimate which Kappa model
+best fits the data and they find that in
+
+ align:start position:0%
+best fits the data and they find that in
+ 
+
+ align:start position:0%
+best fits the data and they find that in
+the post period kappas of like 0.25 to
+
+ align:start position:0%
+the post period kappas of like 0.25 to
+ 
+
+ align:start position:0%
+the post period kappas of like 0.25 to
+37 best fit the data so it's as if the
+
+ align:start position:0%
+37 best fit the data so it's as if the
+ 
+
+ align:start position:0%
+37 best fit the data so it's as if the
+firms Budweiser and Miller are putting
+
+ align:start position:0%
+firms Budweiser and Miller are putting
+ 
+
+ align:start position:0%
+firms Budweiser and Miller are putting
+weight on each other's prices and
+
+ align:start position:0%
+weight on each other's prices and
+ 
+
+ align:start position:0%
+weight on each other's prices and
+starting to price higher than seems
+
+ align:start position:0%
+starting to price higher than seems
+ 
+
+ align:start position:0%
+starting to price higher than seems
+optimal after the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+merger and um here's the sort of
+
+ align:start position:0%
+merger and um here's the sort of
+ 
+
+ align:start position:0%
+merger and um here's the sort of
+counterfactual so this is what beer
+
+ align:start position:0%
+counterfactual so this is what beer
+ 
+
+ align:start position:0%
+counterfactual so this is what beer
+prices of 12 so 12 packs were like nine
+
+ align:start position:0%
+prices of 12 so 12 packs were like nine
+ 
+
+ align:start position:0%
+prices of 12 so 12 packs were like nine
+bucks or whatever before the merger so
+
+ align:start position:0%
+bucks or whatever before the merger so
+ 
+
+ align:start position:0%
+bucks or whatever before the merger so
+we have this long-term trend of
+
+ align:start position:0%
+we have this long-term trend of
+ 
+
+ align:start position:0%
+we have this long-term trend of
+declining prices of 12 packs of cheap
+
+ align:start position:0%
+declining prices of 12 packs of cheap
+ 
+
+ align:start position:0%
+declining prices of 12 packs of cheap
+beer they think absent the merger it
+
+ align:start position:0%
+beer they think absent the merger it
+ 
+
+ align:start position:0%
+beer they think absent the merger it
+would have continued along this path
+
+ align:start position:0%
+would have continued along this path
+ 
+
+ align:start position:0%
+would have continued along this path
+with some Rises and Falls um I don't
+
+ align:start position:0%
+with some Rises and Falls um I don't
+ 
+
+ align:start position:0%
+with some Rises and Falls um I don't
+know if that's due to costs but then we
+
+ align:start position:0%
+know if that's due to costs but then we
+ 
+
+ align:start position:0%
+know if that's due to costs but then we
+have three things happening the first is
+
+ align:start position:0%
+have three things happening the first is
+ 
+
+ align:start position:0%
+have three things happening the first is
+this unilateral incentive of Miller Kors
+
+ align:start position:0%
+this unilateral incentive of Miller Kors
+ 
+
+ align:start position:0%
+this unilateral incentive of Miller Kors
+to raise its prices because it knows
+
+ align:start position:0%
+to raise its prices because it knows
+ 
+
+ align:start position:0%
+to raise its prices because it knows
+that customers it loses when it raises
+
+ align:start position:0%
+that customers it loses when it raises
+ 
+
+ align:start position:0%
+that customers it loses when it raises
+the price of Coors go to Miller and
+
+ align:start position:0%
+the price of Coors go to Miller and
+ 
+
+ align:start position:0%
+the price of Coors go to Miller and
+that's no longer a bad thing um that
+
+ align:start position:0%
+that's no longer a bad thing um that
+ 
+
+ align:start position:0%
+that's no longer a bad thing um that
+would cause prices to go up for this
+
+ align:start position:0%
+would cause prices to go up for this
+ 
+
+ align:start position:0%
+would cause prices to go up for this
+much but then there were savings from
+
+ align:start position:0%
+much but then there were savings from
+ 
+
+ align:start position:0%
+much but then there were savings from
+CES being cheaper to produce and they
+
+ align:start position:0%
+CES being cheaper to produce and they
+ 
+
+ align:start position:0%
+CES being cheaper to produce and they
+say that the K savings would have been
+
+ align:start position:0%
+say that the K savings would have been
+ 
+
+ align:start position:0%
+say that the K savings would have been
+enough to offset that Kors was not lying
+
+ align:start position:0%
+enough to offset that Kors was not lying
+ 
+
+ align:start position:0%
+enough to offset that Kors was not lying
+before the merger when they said that
+
+ align:start position:0%
+before the merger when they said that
+ 
+
+ align:start position:0%
+before the merger when they said that
+our costs are going to go down by enough
+
+ align:start position:0%
+our costs are going to go down by enough
+ 
+
+ align:start position:0%
+our costs are going to go down by enough
+that it's going to offset our incentive
+
+ align:start position:0%
+that it's going to offset our incentive
+ 
+
+ align:start position:0%
+that it's going to offset our incentive
+to raise prices and they would sort of
+
+ align:start position:0%
+to raise prices and they would sort of
+ 
+
+ align:start position:0%
+to raise prices and they would sort of
+say the cost savings are this big so
+
+ align:start position:0%
+say the cost savings are this big so
+ 
+
+ align:start position:0%
+say the cost savings are this big so
+that would have caused this to
+
+ align:start position:0%
+that would have caused this to
+ 
+
+ align:start position:0%
+that would have caused this to
+happen however um the third effect is
+
+ align:start position:0%
+happen however um the third effect is
+ 
+
+ align:start position:0%
+happen however um the third effect is
+that it looks like they're now
+
+ align:start position:0%
+that it looks like they're now
+ 
+
+ align:start position:0%
+that it looks like they're now
+coordinating they pricing and that
+
+ align:start position:0%
+coordinating they pricing and that
+ 
+
+ align:start position:0%
+coordinating they pricing and that
+increase in collusion is enough to go
+
+ align:start position:0%
+increase in collusion is enough to go
+ 
+
+ align:start position:0%
+increase in collusion is enough to go
+from these triangles to this line up
+
+ align:start position:0%
+from these triangles to this line up
+ 
+
+ align:start position:0%
+from these triangles to this line up
+here so the arguing is that there are
+
+ align:start position:0%
+here so the arguing is that there are
+ 
+
+ align:start position:0%
+here so the arguing is that there are
+sort of three roughly equally sized
+
+ align:start position:0%
+sort of three roughly equally sized
+ 
+
+ align:start position:0%
+sort of three roughly equally sized
+effect the Miller cor is internalizing
+
+ align:start position:0%
+effect the Miller cor is internalizing
+ 
+
+ align:start position:0%
+effect the Miller cor is internalizing
+it's uh doing multiproduct Monopoly
+
+ align:start position:0%
+it's uh doing multiproduct Monopoly
+ 
+
+ align:start position:0%
+it's uh doing multiproduct Monopoly
+pricing the cost savings on producing Cs
+
+ align:start position:0%
+pricing the cost savings on producing Cs
+ 
+
+ align:start position:0%
+pricing the cost savings on producing Cs
+and the anheiser bush bush Miller
+
+ align:start position:0%
+and the anheiser bush bush Miller
+ 
+
+ align:start position:0%
+and the anheiser bush bush Miller
+Cooperative Behavior All roughly equal
+
+ align:start position:0%
+Cooperative Behavior All roughly equal
+ 
+
+ align:start position:0%
+Cooperative Behavior All roughly equal
+sizes but combining together to cause
+
+ align:start position:0%
+sizes but combining together to cause
+ 
+
+ align:start position:0%
+sizes but combining together to cause
+this increase in the 12 packs
+
+ align:start position:0%
+this increase in the 12 packs
+ 
+
+ align:start position:0%
+this increase in the 12 packs
+okay um anyway I think to sort of
+
+ align:start position:0%
+okay um anyway I think to sort of
+ 
+
+ align:start position:0%
+okay um anyway I think to sort of
+appreciate you know paper has some
+
+ align:start position:0%
+appreciate you know paper has some
+ 
+
+ align:start position:0%
+appreciate you know paper has some
+strengths and weaknesses or whatever to
+
+ align:start position:0%
+strengths and weaknesses or whatever to
+ 
+
+ align:start position:0%
+strengths and weaknesses or whatever to
+appreciate those it's easier after
+
+ align:start position:0%
+appreciate those it's easier after
+ 
+
+ align:start position:0%
+appreciate those it's easier after
+tobias's Monday lecture so I figured I
+
+ align:start position:0%
+tobias's Monday lecture so I figured I
+ 
+
+ align:start position:0%
+tobias's Monday lecture so I figured I
+would just skip those and maybe you can
+
+ align:start position:0%
+would just skip those and maybe you can
+ 
+
+ align:start position:0%
+would just skip those and maybe you can
+sort of go back and reread the paper
+
+ align:start position:0%
+sort of go back and reread the paper
+ 
+
+ align:start position:0%
+sort of go back and reread the paper
+after tobias's talk next Monday and
+
+ align:start position:0%
+after tobias's talk next Monday and
+ 
+
+ align:start position:0%
+after tobias's talk next Monday and
+think about you know what what do we
+
+ align:start position:0%
+think about you know what what do we
+ 
+
+ align:start position:0%
+think about you know what what do we
+think of the various aspects of the
+
+ align:start position:0%
+think of the various aspects of the
+ 
+
+ align:start position:0%
+think of the various aspects of the
+estimation
+
+ align:start position:0%
+estimation
+ 
+
+ align:start position:0%
+estimation
+strategy okay but it it is it is it is a
+
+ align:start position:0%
+strategy okay but it it is it is it is a
+ 
+
+ align:start position:0%
+strategy okay but it it is it is it is a
+breast and hand like idea of estimate
+
+ align:start position:0%
+breast and hand like idea of estimate
+ 
+
+ align:start position:0%
+breast and hand like idea of estimate
+multiple models see which ones fit best
+
+ align:start position:0%
+multiple models see which ones fit best
+ 
+
+ align:start position:0%
+multiple models see which ones fit best
+and sort of that's how I determine how
+
+ align:start position:0%
+and sort of that's how I determine how
+ 
+
+ align:start position:0%
+and sort of that's how I determine how
+how firms are
+
+ align:start position:0%
+how firms are
+ 
+
+ align:start position:0%
+how firms are
+behaving okay any
+
+ align:start position:0%
+behaving okay any
+ 
+
+ align:start position:0%
+behaving okay any
+questions okay then we are done uh I
+
+ align:start position:0%
+questions okay then we are done uh I
+ 
+
+ align:start position:0%
+questions okay then we are done uh I
+guess I get a I get a week off um Tobias
+
+ align:start position:0%
+guess I get a I get a week off um Tobias
+ 
+
+ align:start position:0%
+guess I get a I get a week off um Tobias
+is GNA be here um the G gandan Novo is
+
+ align:start position:0%
+is GNA be here um the G gandan Novo is
+ 
+
+ align:start position:0%
+is GNA be here um the G gandan Novo is
+published in like a whatever Handbook of
+
+ align:start position:0%
+published in like a whatever Handbook of
+ 
+
+ align:start position:0%
+published in like a whatever Handbook of
+IO that's expensive and hard to find but
+
+ align:start position:0%
+IO that's expensive and hard to find but
+ 
+
+ align:start position:0%
+IO that's expensive and hard to find but
+if you look at the same exact document
+
+ align:start position:0%
+if you look at the same exact document
+ 
+
+ align:start position:0%
+if you look at the same exact document
+as NBR working paper
+
+ align:start position:0%
+as NBR working paper
+ 
+
+ align:start position:0%
+as NBR working paper
+29257 so if you look at that version uh
+
+ align:start position:0%
+29257 so if you look at that version uh
+ 
+
+ align:start position:0%
+29257 so if you look at that version uh
+that's easy to find for
\ No newline at end of file
diff --git a/Dqko567cE9I.txt b/Dqko567cE9I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f6a054b80e9e471ec2e8ef99e956276e48c5b7b0
--- /dev/null
+++ b/Dqko567cE9I.txt
@@ -0,0 +1,13416 @@
+align:start position:0%
+ 
+all right so let's
+
+ align:start position:0%
+all right so let's
+ 
+
+ align:start position:0%
+all right so let's
+get started are there any questions from
+
+ align:start position:0%
+get started are there any questions from
+ 
+
+ align:start position:0%
+get started are there any questions from
+last time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as you are no doubt well aware
+
+ align:start position:0%
+as you are no doubt well aware
+ 
+
+ align:start position:0%
+as you are no doubt well aware
+this is the last lecture i'm going to
+
+ align:start position:0%
+this is the last lecture i'm going to
+ 
+
+ align:start position:0%
+this is the last lecture i'm going to
+give
+
+ align:start position:0%
+give
+ 
+
+ align:start position:0%
+give
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+the exam is a week from
+
+ align:start position:0%
+the exam is a week from
+ 
+
+ align:start position:0%
+the exam is a week from
+yesterday on monday
+
+ align:start position:0%
+yesterday on monday
+ 
+
+ align:start position:0%
+yesterday on monday
+so what i want to do today is is to
+
+ align:start position:0%
+so what i want to do today is is to
+ 
+
+ align:start position:0%
+so what i want to do today is is to
+review
+
+ align:start position:0%
+review
+ 
+
+ align:start position:0%
+review
+the material and see if there are
+
+ align:start position:0%
+the material and see if there are
+ 
+
+ align:start position:0%
+the material and see if there are
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+so today we're covering the material
+
+ align:start position:0%
+so today we're covering the material
+ 
+
+ align:start position:0%
+so today we're covering the material
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+lectures
+
+ align:start position:0%
+lectures
+ 
+
+ align:start position:0%
+lectures
+16 on 16 through 21
+
+ align:start position:0%
+16 on 16 through 21
+ 
+
+ align:start position:0%
+16 on 16 through 21
+and normally you know the exam would
+
+ align:start position:0%
+and normally you know the exam would
+ 
+
+ align:start position:0%
+and normally you know the exam would
+cover 16 through 21 and i could have
+
+ align:start position:0%
+cover 16 through 21 and i could have
+ 
+
+ align:start position:0%
+cover 16 through 21 and i could have
+written that in there i am just trying
+
+ align:start position:0%
+written that in there i am just trying
+ 
+
+ align:start position:0%
+written that in there i am just trying
+to avoid confusion though because the
+
+ align:start position:0%
+to avoid confusion though because the
+ 
+
+ align:start position:0%
+to avoid confusion though because the
+course is cumulative and one thing
+
+ align:start position:0%
+course is cumulative and one thing
+ 
+
+ align:start position:0%
+course is cumulative and one thing
+builds on another you know essentially
+
+ align:start position:0%
+builds on another you know essentially
+ 
+
+ align:start position:0%
+builds on another you know essentially
+it will focus
+
+ align:start position:0%
+it will focus
+ 
+
+ align:start position:0%
+it will focus
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+16 onwards but you should be
+
+ align:start position:0%
+16 onwards but you should be
+ 
+
+ align:start position:0%
+16 onwards but you should be
+by now very familiar with the earlier
+
+ align:start position:0%
+by now very familiar with the earlier
+ 
+
+ align:start position:0%
+by now very familiar with the earlier
+material and some of it may come up
+
+ align:start position:0%
+material and some of it may come up
+ 
+
+ align:start position:0%
+material and some of it may come up
+so this is just to prevent me from
+
+ align:start position:0%
+so this is just to prevent me from
+ 
+
+ align:start position:0%
+so this is just to prevent me from
+misleading you if i said it was only on
+
+ align:start position:0%
+misleading you if i said it was only on
+ 
+
+ align:start position:0%
+misleading you if i said it was only on
+the last one third of the class you know
+
+ align:start position:0%
+the last one third of the class you know
+ 
+
+ align:start position:0%
+the last one third of the class you know
+then you
+
+ align:start position:0%
+then you
+ 
+
+ align:start position:0%
+then you
+you may get lulled into uh thinking that
+
+ align:start position:0%
+you may get lulled into uh thinking that
+ 
+
+ align:start position:0%
+you may get lulled into uh thinking that
+it's quite narrowly about only those
+
+ align:start position:0%
+it's quite narrowly about only those
+ 
+
+ align:start position:0%
+it's quite narrowly about only those
+things as opposed to
+
+ align:start position:0%
+things as opposed to
+ 
+
+ align:start position:0%
+things as opposed to
+the things on which it is building
+
+ align:start position:0%
+the things on which it is building
+ 
+
+ align:start position:0%
+the things on which it is building
+anyway just one word of clarification
+
+ align:start position:0%
+anyway just one word of clarification
+ 
+
+ align:start position:0%
+anyway just one word of clarification
+and again it's only
+
+ align:start position:0%
+and again it's only
+ 
+
+ align:start position:0%
+and again it's only
+the third midterm it doesn't count
+
+ align:start position:0%
+the third midterm it doesn't count
+ 
+
+ align:start position:0%
+the third midterm it doesn't count
+anything special in terms of
+
+ align:start position:0%
+anything special in terms of
+ 
+
+ align:start position:0%
+anything special in terms of
+your grade let's see
+
+ align:start position:0%
+your grade let's see
+ 
+
+ align:start position:0%
+your grade let's see
+so last time we talked about money
+
+ align:start position:0%
+so last time we talked about money
+ 
+
+ align:start position:0%
+so last time we talked about money
+uh bitcoin in particular
+
+ align:start position:0%
+uh bitcoin in particular
+ 
+
+ align:start position:0%
+uh bitcoin in particular
+and i singled out two questions
+
+ align:start position:0%
+and i singled out two questions
+ 
+
+ align:start position:0%
+and i singled out two questions
+one of which i kind of mentioned in
+
+ align:start position:0%
+one of which i kind of mentioned in
+ 
+
+ align:start position:0%
+one of which i kind of mentioned in
+class but let's get you guys engaged in
+
+ align:start position:0%
+class but let's get you guys engaged in
+ 
+
+ align:start position:0%
+class but let's get you guys engaged in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+a central banker namely dudley at new
+
+ align:start position:0%
+a central banker namely dudley at new
+ 
+
+ align:start position:0%
+a central banker namely dudley at new
+york fed
+
+ align:start position:0%
+york fed
+ 
+
+ align:start position:0%
+york fed
+has heard to say that unlike fiat money
+
+ align:start position:0%
+has heard to say that unlike fiat money
+ 
+
+ align:start position:0%
+has heard to say that unlike fiat money
+bitcoin's positive value in markets is
+
+ align:start position:0%
+bitcoin's positive value in markets is
+ 
+
+ align:start position:0%
+bitcoin's positive value in markets is
+just a bubble
+
+ align:start position:0%
+just a bubble
+ 
+
+ align:start position:0%
+just a bubble
+and with wild fluctuations so bitcoin
+
+ align:start position:0%
+and with wild fluctuations so bitcoin
+ 
+
+ align:start position:0%
+and with wild fluctuations so bitcoin
+should be regulated if not banned
+
+ align:start position:0%
+should be regulated if not banned
+ 
+
+ align:start position:0%
+should be regulated if not banned
+altogether
+
+ align:start position:0%
+altogether
+ 
+
+ align:start position:0%
+altogether
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+it says discuss this statement using the
+
+ align:start position:0%
+it says discuss this statement using the
+ 
+
+ align:start position:0%
+it says discuss this statement using the
+tools you have learned in the class
+
+ align:start position:0%
+tools you have learned in the class
+ 
+
+ align:start position:0%
+tools you have learned in the class
+so could i get some volunteers to answer
+
+ align:start position:0%
+so could i get some volunteers to answer
+ 
+
+ align:start position:0%
+so could i get some volunteers to answer
+that question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to be honest and pretty unsure but i do
+
+ align:start position:0%
+to be honest and pretty unsure but i do
+ 
+
+ align:start position:0%
+to be honest and pretty unsure but i do
+remember we talked about how you can
+
+ align:start position:0%
+remember we talked about how you can
+ 
+
+ align:start position:0%
+remember we talked about how you can
+have equilibrium with bubbles
+
+ align:start position:0%
+have equilibrium with bubbles
+ 
+
+ align:start position:0%
+have equilibrium with bubbles
+um so they're not like inherently
+
+ align:start position:0%
+um so they're not like inherently
+ 
+
+ align:start position:0%
+um so they're not like inherently
+something that you have to regulate it's
+
+ align:start position:0%
+something that you have to regulate it's
+ 
+
+ align:start position:0%
+something that you have to regulate it's
+possible to still have an equilibrium
+
+ align:start position:0%
+possible to still have an equilibrium
+ 
+
+ align:start position:0%
+possible to still have an equilibrium
+despite bitcoin being overvalued
+
+ align:start position:0%
+despite bitcoin being overvalued
+ 
+
+ align:start position:0%
+despite bitcoin being overvalued
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's true
+
+ align:start position:0%
+that's true
+ 
+
+ align:start position:0%
+that's true
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the question actually asks about fiat
+
+ align:start position:0%
+the question actually asks about fiat
+ 
+
+ align:start position:0%
+the question actually asks about fiat
+money i kind of slipped that in there
+
+ align:start position:0%
+money i kind of slipped that in there
+ 
+
+ align:start position:0%
+money i kind of slipped that in there
+that unlike fiat money bitcoin
+
+ align:start position:0%
+that unlike fiat money bitcoin
+ 
+
+ align:start position:0%
+that unlike fiat money bitcoin
+is just a bubble
+
+ align:start position:0%
+is just a bubble
+ 
+
+ align:start position:0%
+is just a bubble
+can you maybe respond to that part
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+maria or anyone else for that matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i mean i guess that is somewhat true as
+
+ align:start position:0%
+i mean i guess that is somewhat true as
+ 
+
+ align:start position:0%
+i mean i guess that is somewhat true as
+in it's not tied to like a tangible
+
+ align:start position:0%
+in it's not tied to like a tangible
+ 
+
+ align:start position:0%
+in it's not tied to like a tangible
+um kind of asset
+
+ align:start position:0%
+um kind of asset
+ 
+
+ align:start position:0%
+um kind of asset
+underlying it
+
+ align:start position:0%
+underlying it
+ 
+
+ align:start position:0%
+underlying it
+i'm not sure what exactly you're looking
+
+ align:start position:0%
+i'm not sure what exactly you're looking
+ 
+
+ align:start position:0%
+i'm not sure what exactly you're looking
+for here though
+
+ align:start position:0%
+for here though
+ 
+
+ align:start position:0%
+for here though
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+fiat money is a bubble
+
+ align:start position:0%
+fiat money is a bubble
+ 
+
+ align:start position:0%
+fiat money is a bubble
+it's a bubble the way that
+
+ align:start position:0%
+it's a bubble the way that
+ 
+
+ align:start position:0%
+it's a bubble the way that
+bitcoin is potentially a bubble
+
+ align:start position:0%
+bitcoin is potentially a bubble
+ 
+
+ align:start position:0%
+bitcoin is potentially a bubble
+uh fiat money used to be backed by gold
+
+ align:start position:0%
+uh fiat money used to be backed by gold
+ 
+
+ align:start position:0%
+uh fiat money used to be backed by gold
+so there if you didn't want to hold the
+
+ align:start position:0%
+so there if you didn't want to hold the
+ 
+
+ align:start position:0%
+so there if you didn't want to hold the
+notes you could go to the federal
+
+ align:start position:0%
+notes you could go to the federal
+ 
+
+ align:start position:0%
+notes you could go to the federal
+reserve and
+
+ align:start position:0%
+reserve and
+ 
+
+ align:start position:0%
+reserve and
+and demand a real commodity
+
+ align:start position:0%
+and demand a real commodity
+ 
+
+ align:start position:0%
+and demand a real commodity
+so then it would not
+
+ align:start position:0%
+so then it would not
+ 
+
+ align:start position:0%
+so then it would not
+potentially be a bubble because
+
+ align:start position:0%
+potentially be a bubble because
+ 
+
+ align:start position:0%
+potentially be a bubble because
+it was just a certificate for a
+
+ align:start position:0%
+it was just a certificate for a
+ 
+
+ align:start position:0%
+it was just a certificate for a
+commodity that would have real value
+
+ align:start position:0%
+commodity that would have real value
+ 
+
+ align:start position:0%
+commodity that would have real value
+but when nixon broke the link to gold
+
+ align:start position:0%
+but when nixon broke the link to gold
+ 
+
+ align:start position:0%
+but when nixon broke the link to gold
+then fiat money is just
+
+ align:start position:0%
+then fiat money is just
+ 
+
+ align:start position:0%
+then fiat money is just
+pieces of paper
+
+ align:start position:0%
+pieces of paper
+ 
+
+ align:start position:0%
+pieces of paper
+and nevertheless it has value so it
+
+ align:start position:0%
+and nevertheless it has value so it
+ 
+
+ align:start position:0%
+and nevertheless it has value so it
+so the point of the lecture was that
+
+ align:start position:0%
+so the point of the lecture was that
+ 
+
+ align:start position:0%
+so the point of the lecture was that
+fiat money is a bubble
+
+ align:start position:0%
+fiat money is a bubble
+ 
+
+ align:start position:0%
+fiat money is a bubble
+now we used yeah the word bubble
+
+ align:start position:0%
+now we used yeah the word bubble
+ 
+
+ align:start position:0%
+now we used yeah the word bubble
+is almost deliberately provocative
+
+ align:start position:0%
+is almost deliberately provocative
+ 
+
+ align:start position:0%
+is almost deliberately provocative
+because it kind of sounds bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but dudley who made this statement
+
+ align:start position:0%
+but dudley who made this statement
+ 
+
+ align:start position:0%
+but dudley who made this statement
+seem to have not
+
+ align:start position:0%
+seem to have not
+ 
+
+ align:start position:0%
+seem to have not
+let's say forgotten seems to have
+
+ align:start position:0%
+let's say forgotten seems to have
+ 
+
+ align:start position:0%
+let's say forgotten seems to have
+forgotten
+
+ align:start position:0%
+forgotten
+ 
+
+ align:start position:0%
+forgotten
+that his domain fiat money is
+
+ align:start position:0%
+that his domain fiat money is
+ 
+
+ align:start position:0%
+that his domain fiat money is
+potentially fragile as well
+
+ align:start position:0%
+potentially fragile as well
+ 
+
+ align:start position:0%
+potentially fragile as well
+now the difference is you know the
+
+ align:start position:0%
+now the difference is you know the
+ 
+
+ align:start position:0%
+now the difference is you know the
+federal reserve behaves itself by and
+
+ align:start position:0%
+federal reserve behaves itself by and
+ 
+
+ align:start position:0%
+federal reserve behaves itself by and
+large
+
+ align:start position:0%
+large
+ 
+
+ align:start position:0%
+large
+hard not to jump in with some
+
+ align:start position:0%
+hard not to jump in with some
+ 
+
+ align:start position:0%
+hard not to jump in with some
+parenthetical comments on that but let's
+
+ align:start position:0%
+parenthetical comments on that but let's
+ 
+
+ align:start position:0%
+parenthetical comments on that but let's
+argue that that's the case so then with
+
+ align:start position:0%
+argue that that's the case so then with
+ 
+
+ align:start position:0%
+argue that that's the case so then with
+forward guidance and so on
+
+ align:start position:0%
+forward guidance and so on
+ 
+
+ align:start position:0%
+forward guidance and so on
+noah no one is expecting high inflation
+
+ align:start position:0%
+noah no one is expecting high inflation
+ 
+
+ align:start position:0%
+noah no one is expecting high inflation
+which
+
+ align:start position:0%
+which
+ 
+
+ align:start position:0%
+which
+you know would lead to speculations
+
+ align:start position:0%
+you know would lead to speculations
+ 
+
+ align:start position:0%
+you know would lead to speculations
+about how much
+
+ align:start position:0%
+about how much
+ 
+
+ align:start position:0%
+about how much
+the money is really worth and so on so
+
+ align:start position:0%
+the money is really worth and so on so
+ 
+
+ align:start position:0%
+the money is really worth and so on so
+that whereas with bitcoin you know we
+
+ align:start position:0%
+that whereas with bitcoin you know we
+ 
+
+ align:start position:0%
+that whereas with bitcoin you know we
+don't have a long history
+
+ align:start position:0%
+don't have a long history
+ 
+
+ align:start position:0%
+don't have a long history
+we haven't set expectations and so on so
+
+ align:start position:0%
+we haven't set expectations and so on so
+ 
+
+ align:start position:0%
+we haven't set expectations and so on so
+there are differences between the two
+
+ align:start position:0%
+there are differences between the two
+ 
+
+ align:start position:0%
+there are differences between the two
+but in a in a model
+
+ align:start position:0%
+but in a in a model
+ 
+
+ align:start position:0%
+but in a in a model
+it's pretty hard to make a distinction
+
+ align:start position:0%
+it's pretty hard to make a distinction
+ 
+
+ align:start position:0%
+it's pretty hard to make a distinction
+because they're both
+
+ align:start position:0%
+because they're both
+ 
+
+ align:start position:0%
+because they're both
+essentially worthless even though they
+
+ align:start position:0%
+essentially worthless even though they
+ 
+
+ align:start position:0%
+essentially worthless even though they
+have value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's what i was looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the second question
+
+ align:start position:0%
+the second question
+ 
+
+ align:start position:0%
+the second question
+should currency pay interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or more specifically
+
+ align:start position:0%
+or more specifically
+ 
+
+ align:start position:0%
+or more specifically
+what did we learn in the lecture about
+
+ align:start position:0%
+what did we learn in the lecture about
+ 
+
+ align:start position:0%
+what did we learn in the lecture about
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is it ready to see a non-zero price of
+
+ align:start position:0%
+is it ready to see a non-zero price of
+ 
+
+ align:start position:0%
+is it ready to see a non-zero price of
+of a currency
+
+ align:start position:0%
+of a currency
+ 
+
+ align:start position:0%
+of a currency
+because um and remember we
+
+ align:start position:0%
+because um and remember we
+ 
+
+ align:start position:0%
+because um and remember we
+we say that cash
+
+ align:start position:0%
+we say that cash
+ 
+
+ align:start position:0%
+we say that cash
+has positive value because um it can be
+
+ align:start position:0%
+has positive value because um it can be
+ 
+
+ align:start position:0%
+has positive value because um it can be
+used to pay taxes and
+
+ align:start position:0%
+used to pay taxes and
+ 
+
+ align:start position:0%
+used to pay taxes and
+there's a cash in advance so
+
+ align:start position:0%
+there's a cash in advance so
+ 
+
+ align:start position:0%
+there's a cash in advance so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um so so if the price is equal to zero
+
+ align:start position:0%
+um so so if the price is equal to zero
+ 
+
+ align:start position:0%
+um so so if the price is equal to zero
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+no nobody will demand the
+
+ align:start position:0%
+no nobody will demand the
+ 
+
+ align:start position:0%
+no nobody will demand the
+demand currency right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah you're
+
+ align:start position:0%
+uh yeah you're
+ 
+
+ align:start position:0%
+uh yeah you're
+speaking to the levels
+
+ align:start position:0%
+speaking to the levels
+ 
+
+ align:start position:0%
+speaking to the levels
+so the point of having cash in advance
+
+ align:start position:0%
+so the point of having cash in advance
+ 
+
+ align:start position:0%
+so the point of having cash in advance
+or taxes and so on is that money would
+
+ align:start position:0%
+or taxes and so on is that money would
+ 
+
+ align:start position:0%
+or taxes and so on is that money would
+always have value because
+
+ align:start position:0%
+always have value because
+ 
+
+ align:start position:0%
+always have value because
+there's something you need to do with it
+
+ align:start position:0%
+there's something you need to do with it
+ 
+
+ align:start position:0%
+there's something you need to do with it
+either buy stuff or pay taxes in it
+
+ align:start position:0%
+either buy stuff or pay taxes in it
+ 
+
+ align:start position:0%
+either buy stuff or pay taxes in it
+but this question
+
+ align:start position:0%
+but this question
+ 
+
+ align:start position:0%
+but this question
+interest implies something about how the
+
+ align:start position:0%
+interest implies something about how the
+ 
+
+ align:start position:0%
+interest implies something about how the
+price of money is changing over time
+
+ align:start position:0%
+price of money is changing over time
+ 
+
+ align:start position:0%
+price of money is changing over time
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+or that currency you know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how can i put this the mechanical way to
+
+ align:start position:0%
+how can i put this the mechanical way to
+ 
+
+ align:start position:0%
+how can i put this the mechanical way to
+get currency to bear interest even
+
+ align:start position:0%
+get currency to bear interest even
+ 
+
+ align:start position:0%
+get currency to bear interest even
+though you can't take it necessarily to
+
+ align:start position:0%
+though you can't take it necessarily to
+ 
+
+ align:start position:0%
+though you can't take it necessarily to
+a bank
+
+ align:start position:0%
+a bank
+ 
+
+ align:start position:0%
+a bank
+and exchange it for more money
+
+ align:start position:0%
+and exchange it for more money
+ 
+
+ align:start position:0%
+and exchange it for more money
+is is to have
+
+ align:start position:0%
+is is to have
+ 
+
+ align:start position:0%
+is is to have
+the thing that money exchanges against
+
+ align:start position:0%
+the thing that money exchanges against
+ 
+
+ align:start position:0%
+the thing that money exchanges against
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+be lowering in in price in other words
+
+ align:start position:0%
+be lowering in in price in other words
+ 
+
+ align:start position:0%
+be lowering in in price in other words
+a deflation
+
+ align:start position:0%
+a deflation
+ 
+
+ align:start position:0%
+a deflation
+where the nominal price level is going
+
+ align:start position:0%
+where the nominal price level is going
+ 
+
+ align:start position:0%
+where the nominal price level is going
+down
+
+ align:start position:0%
+down
+ 
+
+ align:start position:0%
+down
+means that you can buy more goods with
+
+ align:start position:0%
+means that you can buy more goods with
+ 
+
+ align:start position:0%
+means that you can buy more goods with
+money tomorrow than you can buy with it
+
+ align:start position:0%
+money tomorrow than you can buy with it
+ 
+
+ align:start position:0%
+money tomorrow than you can buy with it
+today and that's effectively like paying
+
+ align:start position:0%
+today and that's effectively like paying
+ 
+
+ align:start position:0%
+today and that's effectively like paying
+interest
+
+ align:start position:0%
+interest
+ 
+
+ align:start position:0%
+interest
+the way to remember that is inflation is
+
+ align:start position:0%
+the way to remember that is inflation is
+ 
+
+ align:start position:0%
+the way to remember that is inflation is
+bad obviously because the purchasing
+
+ align:start position:0%
+bad obviously because the purchasing
+ 
+
+ align:start position:0%
+bad obviously because the purchasing
+power of money is going down
+
+ align:start position:0%
+power of money is going down
+ 
+
+ align:start position:0%
+power of money is going down
+it takes more and more money to buy
+
+ align:start position:0%
+it takes more and more money to buy
+ 
+
+ align:start position:0%
+it takes more and more money to buy
+goods with deflation
+
+ align:start position:0%
+goods with deflation
+ 
+
+ align:start position:0%
+goods with deflation
+the purchasing power of money is going
+
+ align:start position:0%
+the purchasing power of money is going
+ 
+
+ align:start position:0%
+the purchasing power of money is going
+up
+
+ align:start position:0%
+up
+ 
+
+ align:start position:0%
+up
+so that's effectively a way to pay
+
+ align:start position:0%
+so that's effectively a way to pay
+ 
+
+ align:start position:0%
+so that's effectively a way to pay
+interest and
+
+ align:start position:0%
+interest and
+ 
+
+ align:start position:0%
+interest and
+what did we learn in class about whether
+
+ align:start position:0%
+what did we learn in class about whether
+ 
+
+ align:start position:0%
+what did we learn in class about whether
+or not
+
+ align:start position:0%
+or not
+ 
+
+ align:start position:0%
+or not
+it's optimal to engineer that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any volunteers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry i know it's the end of the
+
+ align:start position:0%
+yeah sorry i know it's the end of the
+ 
+
+ align:start position:0%
+yeah sorry i know it's the end of the
+term and you're all very very busy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the answer was
+
+ align:start position:0%
+so the answer was
+ 
+
+ align:start position:0%
+so the answer was
+in that model of money with spatially
+
+ align:start position:0%
+in that model of money with spatially
+ 
+
+ align:start position:0%
+in that model of money with spatially
+separated agents
+
+ align:start position:0%
+separated agents
+ 
+
+ align:start position:0%
+separated agents
+uh there was a monetary equilibrium
+
+ align:start position:0%
+uh there was a monetary equilibrium
+ 
+
+ align:start position:0%
+uh there was a monetary equilibrium
+with a constant price level but it was
+
+ align:start position:0%
+with a constant price level but it was
+ 
+
+ align:start position:0%
+with a constant price level but it was
+not pareto optimal
+
+ align:start position:0%
+not pareto optimal
+ 
+
+ align:start position:0%
+not pareto optimal
+and to get to one of the pareto optimal
+
+ align:start position:0%
+and to get to one of the pareto optimal
+ 
+
+ align:start position:0%
+and to get to one of the pareto optimal
+allocations
+
+ align:start position:0%
+allocations
+ 
+
+ align:start position:0%
+allocations
+it was necessary to engineer this kind
+
+ align:start position:0%
+it was necessary to engineer this kind
+ 
+
+ align:start position:0%
+it was necessary to engineer this kind
+of deflation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's an example of paying interest
+
+ align:start position:0%
+so that's an example of paying interest
+ 
+
+ align:start position:0%
+so that's an example of paying interest
+on money
+
+ align:start position:0%
+on money
+ 
+
+ align:start position:0%
+on money
+is actually
+
+ align:start position:0%
+is actually
+ 
+
+ align:start position:0%
+is actually
+something the federal reserve should be
+
+ align:start position:0%
+something the federal reserve should be
+ 
+
+ align:start position:0%
+something the federal reserve should be
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+because i hope it's coming back to you
+
+ align:start position:0%
+because i hope it's coming back to you
+ 
+
+ align:start position:0%
+because i hope it's coming back to you
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+anyway those were the two main
+
+ align:start position:0%
+anyway those were the two main
+ 
+
+ align:start position:0%
+anyway those were the two main
+ingredients of this
+
+ align:start position:0%
+ingredients of this
+ 
+
+ align:start position:0%
+ingredients of this
+last very last lecture on bubbles so i
+
+ align:start position:0%
+last very last lecture on bubbles so i
+ 
+
+ align:start position:0%
+last very last lecture on bubbles so i
+probably won't
+
+ align:start position:0%
+probably won't
+ 
+
+ align:start position:0%
+probably won't
+if history is any god i won't have time
+
+ align:start position:0%
+if history is any god i won't have time
+ 
+
+ align:start position:0%
+if history is any god i won't have time
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+open up lecture this last lecture 21 and
+
+ align:start position:0%
+open up lecture this last lecture 21 and
+ 
+
+ align:start position:0%
+open up lecture this last lecture 21 and
+review it but those were the
+
+ align:start position:0%
+review it but those were the
+ 
+
+ align:start position:0%
+review it but those were the
+the two principal components
+
+ align:start position:0%
+the two principal components
+ 
+
+ align:start position:0%
+the two principal components
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+money as a bubble and uh
+
+ align:start position:0%
+money as a bubble and uh
+ 
+
+ align:start position:0%
+money as a bubble and uh
+and this policy aspect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+again the study guide should help you
+
+ align:start position:0%
+again the study guide should help you
+ 
+
+ align:start position:0%
+again the study guide should help you
+prepare for the exam
+
+ align:start position:0%
+prepare for the exam
+ 
+
+ align:start position:0%
+prepare for the exam
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+and now we're ready to
+
+ align:start position:0%
+and now we're ready to
+ 
+
+ align:start position:0%
+and now we're ready to
+to review
+
+ align:start position:0%
+to review
+ 
+
+ align:start position:0%
+to review
+the lectures
+
+ align:start position:0%
+the lectures
+ 
+
+ align:start position:0%
+the lectures
+there's only six of them
+
+ align:start position:0%
+there's only six of them
+ 
+
+ align:start position:0%
+there's only six of them
+so this material is probably pretty
+
+ align:start position:0%
+so this material is probably pretty
+ 
+
+ align:start position:0%
+so this material is probably pretty
+fresh in your minds i think what i'll do
+
+ align:start position:0%
+fresh in your minds i think what i'll do
+ 
+
+ align:start position:0%
+fresh in your minds i think what i'll do
+rather than obviously i wouldn't have
+
+ align:start position:0%
+rather than obviously i wouldn't have
+ 
+
+ align:start position:0%
+rather than obviously i wouldn't have
+time anyway to go over all the
+
+ align:start position:0%
+time anyway to go over all the
+ 
+
+ align:start position:0%
+time anyway to go over all the
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+slides of each lecture i will try to
+
+ align:start position:0%
+slides of each lecture i will try to
+ 
+
+ align:start position:0%
+slides of each lecture i will try to
+remind you what we did and maybe maybe
+
+ align:start position:0%
+remind you what we did and maybe maybe
+ 
+
+ align:start position:0%
+remind you what we did and maybe maybe
+draw some connections to the other
+
+ align:start position:0%
+draw some connections to the other
+ 
+
+ align:start position:0%
+draw some connections to the other
+lectures and how things are kind of
+
+ align:start position:0%
+lectures and how things are kind of
+ 
+
+ align:start position:0%
+lectures and how things are kind of
+fitting together so this was the lecture
+
+ align:start position:0%
+fitting together so this was the lecture
+ 
+
+ align:start position:0%
+fitting together so this was the lecture
+on the fundamental welfare theorems
+
+ align:start position:0%
+on the fundamental welfare theorems
+ 
+
+ align:start position:0%
+on the fundamental welfare theorems
+namely that competitive equilibria
+
+ align:start position:0%
+namely that competitive equilibria
+ 
+
+ align:start position:0%
+namely that competitive equilibria
+under certain assumptions are pareto
+
+ align:start position:0%
+under certain assumptions are pareto
+ 
+
+ align:start position:0%
+under certain assumptions are pareto
+optimal and any optimum can be supported
+
+ align:start position:0%
+optimal and any optimum can be supported
+ 
+
+ align:start position:0%
+optimal and any optimum can be supported
+with transfers so this lecture was about
+
+ align:start position:0%
+with transfers so this lecture was about
+ 
+
+ align:start position:0%
+with transfers so this lecture was about
+sufficient assumptions and the
+
+ align:start position:0%
+sufficient assumptions and the
+ 
+
+ align:start position:0%
+sufficient assumptions and the
+corresponding proofs
+
+ align:start position:0%
+corresponding proofs
+ 
+
+ align:start position:0%
+corresponding proofs
+and it ended with extensions to
+
+ align:start position:0%
+and it ended with extensions to
+ 
+
+ align:start position:0%
+and it ended with extensions to
+more general commodity spaces so
+
+ align:start position:0%
+more general commodity spaces so
+ 
+
+ align:start position:0%
+more general commodity spaces so
+you may remember that i did this i
+
+ align:start position:0%
+you may remember that i did this i
+ 
+
+ align:start position:0%
+you may remember that i did this i
+showed this back to the earlier lectures
+
+ align:start position:0%
+showed this back to the earlier lectures
+ 
+
+ align:start position:0%
+showed this back to the earlier lectures
+the first part of the course on risk
+
+ align:start position:0%
+the first part of the course on risk
+ 
+
+ align:start position:0%
+the first part of the course on risk
+sharing i showed the income movements of
+
+ align:start position:0%
+sharing i showed the income movements of
+ 
+
+ align:start position:0%
+sharing i showed the income movements of
+households over time and compared to
+
+ align:start position:0%
+households over time and compared to
+ 
+
+ align:start position:0%
+households over time and compared to
+each other and including the consumption
+
+ align:start position:0%
+each other and including the consumption
+ 
+
+ align:start position:0%
+each other and including the consumption
+we noted this gradient here that the
+
+ align:start position:0%
+we noted this gradient here that the
+ 
+
+ align:start position:0%
+we noted this gradient here that the
+average level of consumption is
+
+ align:start position:0%
+average level of consumption is
+ 
+
+ align:start position:0%
+average level of consumption is
+increasing as one moves from landless
+
+ align:start position:0%
+increasing as one moves from landless
+ 
+
+ align:start position:0%
+increasing as one moves from landless
+households to larger
+
+ align:start position:0%
+households to larger
+ 
+
+ align:start position:0%
+households to larger
+landowners in the risk sharing framework
+
+ align:start position:0%
+landowners in the risk sharing framework
+ 
+
+ align:start position:0%
+landowners in the risk sharing framework
+that was related to lambda the pareto
+
+ align:start position:0%
+that was related to lambda the pareto
+ 
+
+ align:start position:0%
+that was related to lambda the pareto
+weight
+
+ align:start position:0%
+weight
+ 
+
+ align:start position:0%
+weight
+and very clearly for certain functional
+
+ align:start position:0%
+and very clearly for certain functional
+ 
+
+ align:start position:0%
+and very clearly for certain functional
+forms it was exactly that parade of
+
+ align:start position:0%
+forms it was exactly that parade of
+ 
+
+ align:start position:0%
+forms it was exactly that parade of
+weight of one household relative to the
+
+ align:start position:0%
+weight of one household relative to the
+ 
+
+ align:start position:0%
+weight of one household relative to the
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+but the
+
+ align:start position:0%
+but the
+ 
+
+ align:start position:0%
+but the
+motivation here was to introduce the
+
+ align:start position:0%
+motivation here was to introduce the
+ 
+
+ align:start position:0%
+motivation here was to introduce the
+welfare theorems so then the the issue
+
+ align:start position:0%
+welfare theorems so then the the issue
+ 
+
+ align:start position:0%
+welfare theorems so then the the issue
+was whether the lambdas that are
+
+ align:start position:0%
+was whether the lambdas that are
+ 
+
+ align:start position:0%
+was whether the lambdas that are
+implicit in that diagram are related to
+
+ align:start position:0%
+implicit in that diagram are related to
+ 
+
+ align:start position:0%
+implicit in that diagram are related to
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+like land holdings and the number of
+
+ align:start position:0%
+like land holdings and the number of
+ 
+
+ align:start position:0%
+like land holdings and the number of
+plow animals and so on
+
+ align:start position:0%
+plow animals and so on
+ 
+
+ align:start position:0%
+plow animals and so on
+so i was sort of anticipating a
+
+ align:start position:0%
+so i was sort of anticipating a
+ 
+
+ align:start position:0%
+so i was sort of anticipating a
+connection between
+
+ align:start position:0%
+connection between
+ 
+
+ align:start position:0%
+connection between
+lambdas as in
+
+ align:start position:0%
+lambdas as in
+ 
+
+ align:start position:0%
+lambdas as in
+the pareto problem of pareto optimal
+
+ align:start position:0%
+the pareto problem of pareto optimal
+ 
+
+ align:start position:0%
+the pareto problem of pareto optimal
+allocations versus the wealth
+
+ align:start position:0%
+allocations versus the wealth
+ 
+
+ align:start position:0%
+allocations versus the wealth
+that may be needed in a competitive
+
+ align:start position:0%
+that may be needed in a competitive
+ 
+
+ align:start position:0%
+that may be needed in a competitive
+equilibrium you'll see that again or be
+
+ align:start position:0%
+equilibrium you'll see that again or be
+ 
+
+ align:start position:0%
+equilibrium you'll see that again or be
+reminded of it momentarily
+
+ align:start position:0%
+reminded of it momentarily
+ 
+
+ align:start position:0%
+reminded of it momentarily
+so the first welfare theorem
+
+ align:start position:0%
+so the first welfare theorem
+ 
+
+ align:start position:0%
+so the first welfare theorem
+is that any price equilibrium
+
+ align:start position:0%
+is that any price equilibrium
+ 
+
+ align:start position:0%
+is that any price equilibrium
+competitive equilibrium including a
+
+ align:start position:0%
+competitive equilibrium including a
+ 
+
+ align:start position:0%
+competitive equilibrium including a
+price equilibrium with transfers is
+
+ align:start position:0%
+price equilibrium with transfers is
+ 
+
+ align:start position:0%
+price equilibrium with transfers is
+pareto optimal under minimal sufficient
+
+ align:start position:0%
+pareto optimal under minimal sufficient
+ 
+
+ align:start position:0%
+pareto optimal under minimal sufficient
+assumptions namely
+
+ align:start position:0%
+assumptions namely
+ 
+
+ align:start position:0%
+assumptions namely
+rational preferences which we haven't
+
+ align:start position:0%
+rational preferences which we haven't
+ 
+
+ align:start position:0%
+rational preferences which we haven't
+reviewed for a while but it was in
+
+ align:start position:0%
+reviewed for a while but it was in
+ 
+
+ align:start position:0%
+reviewed for a while but it was in
+lecture two
+
+ align:start position:0%
+lecture two
+ 
+
+ align:start position:0%
+lecture two
+complete
+
+ align:start position:0%
+complete
+ 
+
+ align:start position:0%
+complete
+transitive
+
+ align:start position:0%
+transitive
+ 
+
+ align:start position:0%
+transitive
+and continuous preferences
+
+ align:start position:0%
+and continuous preferences
+ 
+
+ align:start position:0%
+and continuous preferences
+and local non-satiation with those two
+
+ align:start position:0%
+and local non-satiation with those two
+ 
+
+ align:start position:0%
+and local non-satiation with those two
+assumptions we get this
+
+ align:start position:0%
+assumptions we get this
+ 
+
+ align:start position:0%
+assumptions we get this
+sufficient for this theorem
+
+ align:start position:0%
+sufficient for this theorem
+ 
+
+ align:start position:0%
+sufficient for this theorem
+so this was a picture
+
+ align:start position:0%
+so this was a picture
+ 
+
+ align:start position:0%
+so this was a picture
+in our familiar edgeworth box
+
+ align:start position:0%
+in our familiar edgeworth box
+ 
+
+ align:start position:0%
+in our familiar edgeworth box
+of a competitive equilibrium being
+
+ align:start position:0%
+of a competitive equilibrium being
+ 
+
+ align:start position:0%
+of a competitive equilibrium being
+pareto optimal
+
+ align:start position:0%
+pareto optimal
+ 
+
+ align:start position:0%
+pareto optimal
+uh the proof
+
+ align:start position:0%
+uh the proof
+ 
+
+ align:start position:0%
+uh the proof
+you may remember relied on
+
+ align:start position:0%
+you may remember relied on
+ 
+
+ align:start position:0%
+you may remember relied on
+starting with a given allocation
+
+ align:start position:0%
+starting with a given allocation
+ 
+
+ align:start position:0%
+starting with a given allocation
+the star allocation and then conjuring
+
+ align:start position:0%
+the star allocation and then conjuring
+ 
+
+ align:start position:0%
+the star allocation and then conjuring
+up by contradiction that there might be
+
+ align:start position:0%
+up by contradiction that there might be
+ 
+
+ align:start position:0%
+up by contradiction that there might be
+something pareto improving we prove this
+
+ align:start position:0%
+something pareto improving we prove this
+ 
+
+ align:start position:0%
+something pareto improving we prove this
+little lemma
+
+ align:start position:0%
+little lemma
+ 
+
+ align:start position:0%
+little lemma
+that anything which is weakly better has
+
+ align:start position:0%
+that anything which is weakly better has
+ 
+
+ align:start position:0%
+that anything which is weakly better has
+to cost us at least as much
+
+ align:start position:0%
+to cost us at least as much
+ 
+
+ align:start position:0%
+to cost us at least as much
+and then we just went through the math
+
+ align:start position:0%
+and then we just went through the math
+ 
+
+ align:start position:0%
+and then we just went through the math
+summing up over all the households
+
+ align:start position:0%
+summing up over all the households
+ 
+
+ align:start position:0%
+summing up over all the households
+obviously if it's strictly better for
+
+ align:start position:0%
+obviously if it's strictly better for
+ 
+
+ align:start position:0%
+obviously if it's strictly better for
+some households i prime then it must
+
+ align:start position:0%
+some households i prime then it must
+ 
+
+ align:start position:0%
+some households i prime then it must
+have costed more or otherwise they would
+
+ align:start position:0%
+have costed more or otherwise they would
+ 
+
+ align:start position:0%
+have costed more or otherwise they would
+have chosen so we get in equation one
+
+ align:start position:0%
+have chosen so we get in equation one
+ 
+
+ align:start position:0%
+have chosen so we get in equation one
+the statement about total expenditures
+
+ align:start position:0%
+the statement about total expenditures
+ 
+
+ align:start position:0%
+the statement about total expenditures
+the value of total expenditure summing
+
+ align:start position:0%
+the value of total expenditure summing
+ 
+
+ align:start position:0%
+the value of total expenditure summing
+up over
+
+ align:start position:0%
+up over
+ 
+
+ align:start position:0%
+up over
+all the households i'm going quickly now
+
+ align:start position:0%
+all the households i'm going quickly now
+ 
+
+ align:start position:0%
+all the households i'm going quickly now
+we used profit maximization we coupled
+
+ align:start position:0%
+we used profit maximization we coupled
+ 
+
+ align:start position:0%
+we used profit maximization we coupled
+equations one and two
+
+ align:start position:0%
+equations one and two
+ 
+
+ align:start position:0%
+equations one and two
+to get a statement about resource
+
+ align:start position:0%
+to get a statement about resource
+ 
+
+ align:start position:0%
+to get a statement about resource
+constraints and at the bottom line
+
+ align:start position:0%
+constraints and at the bottom line
+ 
+
+ align:start position:0%
+constraints and at the bottom line
+concluded that this alternative
+
+ align:start position:0%
+concluded that this alternative
+ 
+
+ align:start position:0%
+concluded that this alternative
+pareto-dominating allocation would not
+
+ align:start position:0%
+pareto-dominating allocation would not
+ 
+
+ align:start position:0%
+pareto-dominating allocation would not
+be feasible in contradiction to what we
+
+ align:start position:0%
+be feasible in contradiction to what we
+ 
+
+ align:start position:0%
+be feasible in contradiction to what we
+assumed
+
+ align:start position:0%
+assumed
+ 
+
+ align:start position:0%
+assumed
+so that was qed that was the end of the
+
+ align:start position:0%
+so that was qed that was the end of the
+ 
+
+ align:start position:0%
+so that was qed that was the end of the
+proof of the first welfare theorem
+
+ align:start position:0%
+proof of the first welfare theorem
+ 
+
+ align:start position:0%
+proof of the first welfare theorem
+now later even today we'll review it you
+
+ align:start position:0%
+now later even today we'll review it you
+ 
+
+ align:start position:0%
+now later even today we'll review it you
+know this thing fails with
+
+ align:start position:0%
+know this thing fails with
+ 
+
+ align:start position:0%
+know this thing fails with
+if these sums are infinite sums and
+
+ align:start position:0%
+if these sums are infinite sums and
+ 
+
+ align:start position:0%
+if these sums are infinite sums and
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+have finite value
+
+ align:start position:0%
+have finite value
+ 
+
+ align:start position:0%
+have finite value
+then the second welfare theorem was
+
+ align:start position:0%
+then the second welfare theorem was
+ 
+
+ align:start position:0%
+then the second welfare theorem was
+illustrated here
+
+ align:start position:0%
+illustrated here
+ 
+
+ align:start position:0%
+illustrated here
+that we have pareto optimum
+
+ align:start position:0%
+that we have pareto optimum
+ 
+
+ align:start position:0%
+that we have pareto optimum
+characterized by tangency of
+
+ align:start position:0%
+characterized by tangency of
+ 
+
+ align:start position:0%
+characterized by tangency of
+indifference curves
+
+ align:start position:0%
+indifference curves
+ 
+
+ align:start position:0%
+indifference curves
+but that nevertheless uh it's not
+
+ align:start position:0%
+but that nevertheless uh it's not
+ 
+
+ align:start position:0%
+but that nevertheless uh it's not
+reachable
+
+ align:start position:0%
+reachable
+ 
+
+ align:start position:0%
+reachable
+if we start from the endowment and start
+
+ align:start position:0%
+if we start from the endowment and start
+ 
+
+ align:start position:0%
+if we start from the endowment and start
+drawing potential budget lines
+
+ align:start position:0%
+drawing potential budget lines
+ 
+
+ align:start position:0%
+drawing potential budget lines
+through the endowment point as you would
+
+ align:start position:0%
+through the endowment point as you would
+ 
+
+ align:start position:0%
+through the endowment point as you would
+for candidate budget lines in a
+
+ align:start position:0%
+for candidate budget lines in a
+ 
+
+ align:start position:0%
+for candidate budget lines in a
+competitive equilibria so i mean this
+
+ align:start position:0%
+competitive equilibria so i mean this
+ 
+
+ align:start position:0%
+competitive equilibria so i mean this
+was meant to illustrate that
+
+ align:start position:0%
+was meant to illustrate that
+ 
+
+ align:start position:0%
+was meant to illustrate that
+to get to this particular pareto optimum
+
+ align:start position:0%
+to get to this particular pareto optimum
+ 
+
+ align:start position:0%
+to get to this particular pareto optimum
+as in the second welfare theorem
+
+ align:start position:0%
+as in the second welfare theorem
+ 
+
+ align:start position:0%
+as in the second welfare theorem
+we're going to have to take some value
+
+ align:start position:0%
+we're going to have to take some value
+ 
+
+ align:start position:0%
+we're going to have to take some value
+away from agent a over here
+
+ align:start position:0%
+away from agent a over here
+ 
+
+ align:start position:0%
+away from agent a over here
+and give it to agent b
+
+ align:start position:0%
+and give it to agent b
+ 
+
+ align:start position:0%
+and give it to agent b
+and and that's what this said the tax on
+
+ align:start position:0%
+and and that's what this said the tax on
+ 
+
+ align:start position:0%
+and and that's what this said the tax on
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+is equal to the subsidy on b
+
+ align:start position:0%
+is equal to the subsidy on b
+ 
+
+ align:start position:0%
+is equal to the subsidy on b
+t being transfer so negative is a tax
+
+ align:start position:0%
+t being transfer so negative is a tax
+ 
+
+ align:start position:0%
+t being transfer so negative is a tax
+so then we could get as in the second
+
+ align:start position:0%
+so then we could get as in the second
+ 
+
+ align:start position:0%
+so then we could get as in the second
+welfare theorem to any allocation
+
+ align:start position:0%
+welfare theorem to any allocation
+ 
+
+ align:start position:0%
+welfare theorem to any allocation
+along
+
+ align:start position:0%
+along
+ 
+
+ align:start position:0%
+along
+that contract curve where the inference
+
+ align:start position:0%
+that contract curve where the inference
+ 
+
+ align:start position:0%
+that contract curve where the inference
+curves are tangent by reallocating
+
+ align:start position:0%
+curves are tangent by reallocating
+ 
+
+ align:start position:0%
+curves are tangent by reallocating
+wealth now to prove it we went through
+
+ align:start position:0%
+wealth now to prove it we went through
+ 
+
+ align:start position:0%
+wealth now to prove it we went through
+this constructive argument we defined an
+
+ align:start position:0%
+this constructive argument we defined an
+ 
+
+ align:start position:0%
+this constructive argument we defined an
+economy and this slide or a version of
+
+ align:start position:0%
+economy and this slide or a version of
+ 
+
+ align:start position:0%
+economy and this slide or a version of
+it shows up at least three times
+
+ align:start position:0%
+it shows up at least three times
+ 
+
+ align:start position:0%
+it shows up at least three times
+in these six lectures so an economy
+
+ align:start position:0%
+in these six lectures so an economy
+ 
+
+ align:start position:0%
+in these six lectures so an economy
+consisting of preferences endowments
+
+ align:start position:0%
+consisting of preferences endowments
+ 
+
+ align:start position:0%
+consisting of preferences endowments
+production sets and profit shares
+
+ align:start position:0%
+production sets and profit shares
+ 
+
+ align:start position:0%
+production sets and profit shares
+here assuming a lot more concavity and
+
+ align:start position:0%
+here assuming a lot more concavity and
+ 
+
+ align:start position:0%
+here assuming a lot more concavity and
+convexity and preferences production
+
+ align:start position:0%
+convexity and preferences production
+ 
+
+ align:start position:0%
+convexity and preferences production
+sets etc and then we get the second
+
+ align:start position:0%
+sets etc and then we get the second
+ 
+
+ align:start position:0%
+sets etc and then we get the second
+welfare theorem that any pareto optimum
+
+ align:start position:0%
+welfare theorem that any pareto optimum
+ 
+
+ align:start position:0%
+welfare theorem that any pareto optimum
+can be supported for some wealth any
+
+ align:start position:0%
+can be supported for some wealth any
+ 
+
+ align:start position:0%
+can be supported for some wealth any
+pareto optimum associated with some
+
+ align:start position:0%
+pareto optimum associated with some
+ 
+
+ align:start position:0%
+pareto optimum associated with some
+lambda vector of maximized weighted
+
+ align:start position:0%
+lambda vector of maximized weighted
+ 
+
+ align:start position:0%
+lambda vector of maximized weighted
+utilities can be supported by a suitable
+
+ align:start position:0%
+utilities can be supported by a suitable
+ 
+
+ align:start position:0%
+utilities can be supported by a suitable
+redistribution of wealth the way we
+
+ align:start position:0%
+redistribution of wealth the way we
+ 
+
+ align:start position:0%
+redistribution of wealth the way we
+prove this was to go back to what you
+
+ align:start position:0%
+prove this was to go back to what you
+ 
+
+ align:start position:0%
+prove this was to go back to what you
+know about
+
+ align:start position:0%
+know about
+ 
+
+ align:start position:0%
+know about
+lagrangians so this was i think also in
+
+ align:start position:0%
+lagrangians so this was i think also in
+ 
+
+ align:start position:0%
+lagrangians so this was i think also in
+the second lecture of the class
+
+ align:start position:0%
+the second lecture of the class
+ 
+
+ align:start position:0%
+the second lecture of the class
+and you've used it over and over again
+
+ align:start position:0%
+and you've used it over and over again
+ 
+
+ align:start position:0%
+and you've used it over and over again
+maximizing concave functions on convex
+
+ align:start position:0%
+maximizing concave functions on convex
+ 
+
+ align:start position:0%
+maximizing concave functions on convex
+sets you know generating all these
+
+ align:start position:0%
+sets you know generating all these
+ 
+
+ align:start position:0%
+sets you know generating all these
+shadow prices
+
+ align:start position:0%
+shadow prices
+ 
+
+ align:start position:0%
+shadow prices
+so we used it here three times first we
+
+ align:start position:0%
+so we used it here three times first we
+ 
+
+ align:start position:0%
+so we used it here three times first we
+use it for the pareto problem so
+
+ align:start position:0%
+use it for the pareto problem so
+ 
+
+ align:start position:0%
+use it for the pareto problem so
+we're starting with a pareto optimal
+
+ align:start position:0%
+we're starting with a pareto optimal
+ 
+
+ align:start position:0%
+we're starting with a pareto optimal
+allocation so we know again from things
+
+ align:start position:0%
+allocation so we know again from things
+ 
+
+ align:start position:0%
+allocation so we know again from things
+you did earlier in the class
+
+ align:start position:0%
+you did earlier in the class
+ 
+
+ align:start position:0%
+you did earlier in the class
+when we introduced the notion of pareto
+
+ align:start position:0%
+when we introduced the notion of pareto
+ 
+
+ align:start position:0%
+when we introduced the notion of pareto
+optimality i don't remember the lecture
+
+ align:start position:0%
+optimality i don't remember the lecture
+ 
+
+ align:start position:0%
+optimality i don't remember the lecture
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+we maximize weighted sums of utilities
+
+ align:start position:0%
+we maximize weighted sums of utilities
+ 
+
+ align:start position:0%
+we maximize weighted sums of utilities
+lambdas being these weights subject to
+
+ align:start position:0%
+lambdas being these weights subject to
+ 
+
+ align:start position:0%
+lambdas being these weights subject to
+resource constraints and production
+
+ align:start position:0%
+resource constraints and production
+ 
+
+ align:start position:0%
+resource constraints and production
+constraints that's all written down here
+
+ align:start position:0%
+constraints that's all written down here
+ 
+
+ align:start position:0%
+constraints that's all written down here
+the solution to any one of these pareto
+
+ align:start position:0%
+the solution to any one of these pareto
+ 
+
+ align:start position:0%
+the solution to any one of these pareto
+problems is pareto optimal and all the
+
+ align:start position:0%
+problems is pareto optimal and all the
+ 
+
+ align:start position:0%
+problems is pareto optimal and all the
+optima can be described as solutions for
+
+ align:start position:0%
+optima can be described as solutions for
+ 
+
+ align:start position:0%
+optima can be described as solutions for
+some lambdas so we go start thinking
+
+ align:start position:0%
+some lambdas so we go start thinking
+ 
+
+ align:start position:0%
+some lambdas so we go start thinking
+about these so-called pareto problems as
+
+ align:start position:0%
+about these so-called pareto problems as
+ 
+
+ align:start position:0%
+about these so-called pareto problems as
+equivalent with pareto optimal
+
+ align:start position:0%
+equivalent with pareto optimal
+ 
+
+ align:start position:0%
+equivalent with pareto optimal
+allocations use the lagrangian set it up
+
+ align:start position:0%
+allocations use the lagrangian set it up
+ 
+
+ align:start position:0%
+allocations use the lagrangian set it up
+this way
+
+ align:start position:0%
+this way
+ 
+
+ align:start position:0%
+this way
+and get the first order conditions
+
+ align:start position:0%
+and get the first order conditions
+ 
+
+ align:start position:0%
+and get the first order conditions
+including the primal
+
+ align:start position:0%
+including the primal
+ 
+
+ align:start position:0%
+including the primal
+dual feasibility on the shadow prices
+
+ align:start position:0%
+dual feasibility on the shadow prices
+ 
+
+ align:start position:0%
+dual feasibility on the shadow prices
+complementary slackness and all of that
+
+ align:start position:0%
+complementary slackness and all of that
+ 
+
+ align:start position:0%
+complementary slackness and all of that
+the point is that with all that
+
+ align:start position:0%
+the point is that with all that
+ 
+
+ align:start position:0%
+the point is that with all that
+concavity and convexity as appropriate
+
+ align:start position:0%
+concavity and convexity as appropriate
+ 
+
+ align:start position:0%
+concavity and convexity as appropriate
+these first order conditions from
+
+ align:start position:0%
+these first order conditions from
+ 
+
+ align:start position:0%
+these first order conditions from
+differentiating the lagrangian are not
+
+ align:start position:0%
+differentiating the lagrangian are not
+ 
+
+ align:start position:0%
+differentiating the lagrangian are not
+only necessary they're sufficient so any
+
+ align:start position:0%
+only necessary they're sufficient so any
+ 
+
+ align:start position:0%
+only necessary they're sufficient so any
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+to these first order conditions
+
+ align:start position:0%
+to these first order conditions
+ 
+
+ align:start position:0%
+to these first order conditions
+allocations and shadow prices that
+
+ align:start position:0%
+allocations and shadow prices that
+ 
+
+ align:start position:0%
+allocations and shadow prices that
+satisfy the first order conditions
+
+ align:start position:0%
+satisfy the first order conditions
+ 
+
+ align:start position:0%
+satisfy the first order conditions
+will be
+
+ align:start position:0%
+will be
+ 
+
+ align:start position:0%
+will be
+pareto optimal will be a solution to the
+
+ align:start position:0%
+pareto optimal will be a solution to the
+ 
+
+ align:start position:0%
+pareto optimal will be a solution to the
+pareto problem
+
+ align:start position:0%
+pareto problem
+ 
+
+ align:start position:0%
+pareto problem
+so we did that
+
+ align:start position:0%
+so we did that
+ 
+
+ align:start position:0%
+so we did that
+then we went to the second part reminded
+
+ align:start position:0%
+then we went to the second part reminded
+ 
+
+ align:start position:0%
+then we went to the second part reminded
+ourselves of the definition of a
+
+ align:start position:0%
+ourselves of the definition of a
+ 
+
+ align:start position:0%
+ourselves of the definition of a
+competitive equilibrium with transfers
+
+ align:start position:0%
+competitive equilibrium with transfers
+ 
+
+ align:start position:0%
+competitive equilibrium with transfers
+namely consumer optimization firm
+
+ align:start position:0%
+namely consumer optimization firm
+ 
+
+ align:start position:0%
+namely consumer optimization firm
+maximization of profits and so on along
+
+ align:start position:0%
+maximization of profits and so on along
+ 
+
+ align:start position:0%
+maximization of profits and so on along
+with a feasible distribution of wealth
+
+ align:start position:0%
+with a feasible distribution of wealth
+ 
+
+ align:start position:0%
+with a feasible distribution of wealth
+as i was just saying so here's the
+
+ align:start position:0%
+as i was just saying so here's the
+ 
+
+ align:start position:0%
+as i was just saying so here's the
+second and third time we're going to use
+
+ align:start position:0%
+second and third time we're going to use
+ 
+
+ align:start position:0%
+second and third time we're going to use
+the lagrangian for the consumer
+
+ align:start position:0%
+the lagrangian for the consumer
+ 
+
+ align:start position:0%
+the lagrangian for the consumer
+optimization problem and use it for the
+
+ align:start position:0%
+optimization problem and use it for the
+ 
+
+ align:start position:0%
+optimization problem and use it for the
+firm profit maximization here's the
+
+ align:start position:0%
+firm profit maximization here's the
+ 
+
+ align:start position:0%
+firm profit maximization here's the
+consumer maximization problem maximizing
+
+ align:start position:0%
+consumer maximization problem maximizing
+ 
+
+ align:start position:0%
+consumer maximization problem maximizing
+utilities subject to a budget we get
+
+ align:start position:0%
+utilities subject to a budget we get
+ 
+
+ align:start position:0%
+utilities subject to a budget we get
+this first order condition and again
+
+ align:start position:0%
+this first order condition and again
+ 
+
+ align:start position:0%
+this first order condition and again
+with the concavity in the constraint
+
+ align:start position:0%
+with the concavity in the constraint
+ 
+
+ align:start position:0%
+with the concavity in the constraint
+setting in the objective function and
+
+ align:start position:0%
+setting in the objective function and
+ 
+
+ align:start position:0%
+setting in the objective function and
+convexity in the constraint set these
+
+ align:start position:0%
+convexity in the constraint set these
+ 
+
+ align:start position:0%
+convexity in the constraint set these
+are not only necessary but they're
+
+ align:start position:0%
+are not only necessary but they're
+ 
+
+ align:start position:0%
+are not only necessary but they're
+sufficient condition for an optimum all
+
+ align:start position:0%
+sufficient condition for an optimum all
+ 
+
+ align:start position:0%
+sufficient condition for an optimum all
+we need to do is find the mu i at given
+
+ align:start position:0%
+we need to do is find the mu i at given
+ 
+
+ align:start position:0%
+we need to do is find the mu i at given
+prices p and an x i star and it will be
+
+ align:start position:0%
+prices p and an x i star and it will be
+ 
+
+ align:start position:0%
+prices p and an x i star and it will be
+maximizing for the consumer
+
+ align:start position:0%
+maximizing for the consumer
+ 
+
+ align:start position:0%
+maximizing for the consumer
+each consumer
+
+ align:start position:0%
+each consumer
+ 
+
+ align:start position:0%
+each consumer
+likewise for the
+
+ align:start position:0%
+likewise for the
+ 
+
+ align:start position:0%
+likewise for the
+firm maximization we have
+
+ align:start position:0%
+firm maximization we have
+ 
+
+ align:start position:0%
+firm maximization we have
+unnecessary and sufficient conditions in
+
+ align:start position:0%
+unnecessary and sufficient conditions in
+ 
+
+ align:start position:0%
+unnecessary and sufficient conditions in
+the to find candidates for the
+
+ align:start position:0%
+the to find candidates for the
+ 
+
+ align:start position:0%
+the to find candidates for the
+decentralized competitive equilibria
+
+ align:start position:0%
+decentralized competitive equilibria
+ 
+
+ align:start position:0%
+decentralized competitive equilibria
+and then all we did was match them up
+
+ align:start position:0%
+and then all we did was match them up
+ 
+
+ align:start position:0%
+and then all we did was match them up
+now i think the tricky thing here is to
+
+ align:start position:0%
+now i think the tricky thing here is to
+ 
+
+ align:start position:0%
+now i think the tricky thing here is to
+remember what the given is and what the
+
+ align:start position:0%
+remember what the given is and what the
+ 
+
+ align:start position:0%
+remember what the given is and what the
+objective function the given was a
+
+ align:start position:0%
+objective function the given was a
+ 
+
+ align:start position:0%
+objective function the given was a
+pareto optimal allocation so for the
+
+ align:start position:0%
+pareto optimal allocation so for the
+ 
+
+ align:start position:0%
+pareto optimal allocation so for the
+consumer we started out with these
+
+ align:start position:0%
+consumer we started out with these
+ 
+
+ align:start position:0%
+consumer we started out with these
+conditions which are the necessary and
+
+ align:start position:0%
+conditions which are the necessary and
+ 
+
+ align:start position:0%
+conditions which are the necessary and
+sufficient conditions from the pareto
+
+ align:start position:0%
+sufficient conditions from the pareto
+ 
+
+ align:start position:0%
+sufficient conditions from the pareto
+problem being satisfied so we have the
+
+ align:start position:0%
+problem being satisfied so we have the
+ 
+
+ align:start position:0%
+problem being satisfied so we have the
+gamma
+
+ align:start position:0%
+gamma
+ 
+
+ align:start position:0%
+gamma
+sub l for commodity l as a given the
+
+ align:start position:0%
+sub l for commodity l as a given the
+ 
+
+ align:start position:0%
+sub l for commodity l as a given the
+lambdas were given because we had a
+
+ align:start position:0%
+lambdas were given because we had a
+ 
+
+ align:start position:0%
+lambdas were given because we had a
+given certain candidate pareto optimum
+
+ align:start position:0%
+given certain candidate pareto optimum
+ 
+
+ align:start position:0%
+given certain candidate pareto optimum
+these are all satisfied we're looking
+
+ align:start position:0%
+these are all satisfied we're looking
+ 
+
+ align:start position:0%
+these are all satisfied we're looking
+for this thing we're trying to see if
+
+ align:start position:0%
+for this thing we're trying to see if
+ 
+
+ align:start position:0%
+for this thing we're trying to see if
+consumers are going to be maximizing so
+
+ align:start position:0%
+consumers are going to be maximizing so
+ 
+
+ align:start position:0%
+consumers are going to be maximizing so
+the candidate for the price would be the
+
+ align:start position:0%
+the candidate for the price would be the
+ 
+
+ align:start position:0%
+the candidate for the price would be the
+lagrange multiplier and the candidate
+
+ align:start position:0%
+lagrange multiplier and the candidate
+ 
+
+ align:start position:0%
+lagrange multiplier and the candidate
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+marginality of income the shadow price
+
+ align:start position:0%
+marginality of income the shadow price
+ 
+
+ align:start position:0%
+marginality of income the shadow price
+and the budget constraint would be one
+
+ align:start position:0%
+and the budget constraint would be one
+ 
+
+ align:start position:0%
+and the budget constraint would be one
+over lambda okay so here i go back to
+
+ align:start position:0%
+over lambda okay so here i go back to
+ 
+
+ align:start position:0%
+over lambda okay so here i go back to
+the slides of the rocky mountain in
+
+ align:start position:0%
+the slides of the rocky mountain in
+ 
+
+ align:start position:0%
+the slides of the rocky mountain in
+kansas this establishes a direct
+
+ align:start position:0%
+kansas this establishes a direct
+ 
+
+ align:start position:0%
+kansas this establishes a direct
+relationship between the pareto weights
+
+ align:start position:0%
+relationship between the pareto weights
+ 
+
+ align:start position:0%
+relationship between the pareto weights
+and the pareto problem and the marginal
+
+ align:start position:0%
+and the pareto problem and the marginal
+ 
+
+ align:start position:0%
+and the pareto problem and the marginal
+utility of wealth and hence the level of
+
+ align:start position:0%
+utility of wealth and hence the level of
+ 
+
+ align:start position:0%
+utility of wealth and hence the level of
+wealth it's quite general it's super
+
+ align:start position:0%
+wealth it's quite general it's super
+ 
+
+ align:start position:0%
+wealth it's quite general it's super
+robust
+
+ align:start position:0%
+robust
+ 
+
+ align:start position:0%
+robust
+and so then the rest of this was just
+
+ align:start position:0%
+and so then the rest of this was just
+ 
+
+ align:start position:0%
+and so then the rest of this was just
+you know the tedious part of
+
+ align:start position:0%
+you know the tedious part of
+ 
+
+ align:start position:0%
+you know the tedious part of
+constructing the wealth as the valuation
+
+ align:start position:0%
+constructing the wealth as the valuation
+ 
+
+ align:start position:0%
+constructing the wealth as the valuation
+of expenditure and making sure that they
+
+ align:start position:0%
+of expenditure and making sure that they
+ 
+
+ align:start position:0%
+of expenditure and making sure that they
+all add up we refer to this way of
+
+ align:start position:0%
+all add up we refer to this way of
+ 
+
+ align:start position:0%
+all add up we refer to this way of
+finding the prices from the second
+
+ align:start position:0%
+finding the prices from the second
+ 
+
+ align:start position:0%
+finding the prices from the second
+welfare theorem as margin of utility
+
+ align:start position:0%
+welfare theorem as margin of utility
+ 
+
+ align:start position:0%
+welfare theorem as margin of utility
+pricing
+
+ align:start position:0%
+pricing
+ 
+
+ align:start position:0%
+pricing
+i mean more accurately
+
+ align:start position:0%
+i mean more accurately
+ 
+
+ align:start position:0%
+i mean more accurately
+it's the lambda weighted margin
+
+ align:start position:0%
+it's the lambda weighted margin
+ 
+
+ align:start position:0%
+it's the lambda weighted margin
+utilities which are equated all over the
+
+ align:start position:0%
+utilities which are equated all over the
+ 
+
+ align:start position:0%
+utilities which are equated all over the
+households not the levels
+
+ align:start position:0%
+households not the levels
+ 
+
+ align:start position:0%
+households not the levels
+but when you take ratios across
+
+ align:start position:0%
+but when you take ratios across
+ 
+
+ align:start position:0%
+but when you take ratios across
+different goods l and k the marginal
+
+ align:start position:0%
+different goods l and k the marginal
+ 
+
+ align:start position:0%
+different goods l and k the marginal
+rates of substa the lambdas cancel out
+
+ align:start position:0%
+rates of substa the lambdas cancel out
+ 
+
+ align:start position:0%
+rates of substa the lambdas cancel out
+so the marginal rates of substitution
+
+ align:start position:0%
+so the marginal rates of substitution
+ 
+
+ align:start position:0%
+so the marginal rates of substitution
+are equated over all the households as
+
+ align:start position:0%
+are equated over all the households as
+ 
+
+ align:start position:0%
+are equated over all the households as
+they are in this picture
+
+ align:start position:0%
+they are in this picture
+ 
+
+ align:start position:0%
+they are in this picture
+along this orange green orange green
+
+ align:start position:0%
+along this orange green orange green
+ 
+
+ align:start position:0%
+along this orange green orange green
+yellow orange line
+
+ align:start position:0%
+yellow orange line
+ 
+
+ align:start position:0%
+yellow orange line
+yeah and this made the wealth add up
+
+ align:start position:0%
+yeah and this made the wealth add up
+ 
+
+ align:start position:0%
+yeah and this made the wealth add up
+now we did a second proof of the welfare
+
+ align:start position:0%
+now we did a second proof of the welfare
+ 
+
+ align:start position:0%
+now we did a second proof of the welfare
+theorem
+
+ align:start position:0%
+theorem
+ 
+
+ align:start position:0%
+theorem
+which is namely
+
+ align:start position:0%
+which is namely
+ 
+
+ align:start position:0%
+which is namely
+one nuance thing which is instead of
+
+ align:start position:0%
+one nuance thing which is instead of
+ 
+
+ align:start position:0%
+one nuance thing which is instead of
+just maximizing utility subject to
+
+ align:start position:0%
+just maximizing utility subject to
+ 
+
+ align:start position:0%
+just maximizing utility subject to
+budget we minimize expenditures subject
+
+ align:start position:0%
+budget we minimize expenditures subject
+ 
+
+ align:start position:0%
+budget we minimize expenditures subject
+to achieving a certain level of utility
+
+ align:start position:0%
+to achieving a certain level of utility
+ 
+
+ align:start position:0%
+to achieving a certain level of utility
+that kind of conjured up
+
+ align:start position:0%
+that kind of conjured up
+ 
+
+ align:start position:0%
+that kind of conjured up
+you know this
+
+ align:start position:0%
+you know this
+ 
+
+ align:start position:0%
+you know this
+so this is
+
+ align:start position:0%
+so this is
+ 
+
+ align:start position:0%
+so this is
+sort of the in
+
+ align:start position:0%
+sort of the in
+ 
+
+ align:start position:0%
+sort of the in
+the target and different curve
+
+ align:start position:0%
+the target and different curve
+ 
+
+ align:start position:0%
+the target and different curve
+as it were
+
+ align:start position:0%
+as it were
+ 
+
+ align:start position:0%
+as it were
+as if it were coming from one consumer
+
+ align:start position:0%
+as if it were coming from one consumer
+ 
+
+ align:start position:0%
+as if it were coming from one consumer
+interesting comment
+
+ align:start position:0%
+interesting comment
+ 
+
+ align:start position:0%
+interesting comment
+but it's just the aggregated
+
+ align:start position:0%
+but it's just the aggregated
+ 
+
+ align:start position:0%
+but it's just the aggregated
+better than set
+
+ align:start position:0%
+better than set
+ 
+
+ align:start position:0%
+better than set
+associated with
+
+ align:start position:0%
+associated with
+ 
+
+ align:start position:0%
+associated with
+the pareto optimal allocation
+
+ align:start position:0%
+the pareto optimal allocation
+ 
+
+ align:start position:0%
+the pareto optimal allocation
+the other part of this diagram is two
+
+ align:start position:0%
+the other part of this diagram is two
+ 
+
+ align:start position:0%
+the other part of this diagram is two
+production functions
+
+ align:start position:0%
+production functions
+ 
+
+ align:start position:0%
+production functions
+different from each other but aggregated
+
+ align:start position:0%
+different from each other but aggregated
+ 
+
+ align:start position:0%
+different from each other but aggregated
+up to an aggregated production function
+
+ align:start position:0%
+up to an aggregated production function
+ 
+
+ align:start position:0%
+up to an aggregated production function
+and then you can see as if it were a
+
+ align:start position:0%
+and then you can see as if it were a
+ 
+
+ align:start position:0%
+and then you can see as if it were a
+robinson crusoe representative consumer
+
+ align:start position:0%
+robinson crusoe representative consumer
+ 
+
+ align:start position:0%
+robinson crusoe representative consumer
+you know the optimum is characterized by
+
+ align:start position:0%
+you know the optimum is characterized by
+ 
+
+ align:start position:0%
+you know the optimum is characterized by
+a maximal utility level subject to the
+
+ align:start position:0%
+a maximal utility level subject to the
+ 
+
+ align:start position:0%
+a maximal utility level subject to the
+single production set and then
+
+ align:start position:0%
+single production set and then
+ 
+
+ align:start position:0%
+single production set and then
+my point is that we get this
+
+ align:start position:0%
+my point is that we get this
+ 
+
+ align:start position:0%
+my point is that we get this
+separating hyperplane
+
+ align:start position:0%
+separating hyperplane
+ 
+
+ align:start position:0%
+separating hyperplane
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+all these definitions supporting
+
+ align:start position:0%
+all these definitions supporting
+ 
+
+ align:start position:0%
+all these definitions supporting
+hyperplane etc
+
+ align:start position:0%
+hyperplane etc
+ 
+
+ align:start position:0%
+hyperplane etc
+that's really where
+
+ align:start position:0%
+that's really where
+ 
+
+ align:start position:0%
+that's really where
+given all the convexity that's all you
+
+ align:start position:0%
+given all the convexity that's all you
+ 
+
+ align:start position:0%
+given all the convexity that's all you
+need to do these convex sets are
+
+ align:start position:0%
+need to do these convex sets are
+ 
+
+ align:start position:0%
+need to do these convex sets are
+separated from each other so this is a
+
+ align:start position:0%
+separated from each other so this is a
+ 
+
+ align:start position:0%
+separated from each other so this is a
+quite general proof and it works in many
+
+ align:start position:0%
+quite general proof and it works in many
+ 
+
+ align:start position:0%
+quite general proof and it works in many
+spaces not just finite dimensional
+
+ align:start position:0%
+spaces not just finite dimensional
+ 
+
+ align:start position:0%
+spaces not just finite dimensional
+euclidean spaces
+
+ align:start position:0%
+euclidean spaces
+ 
+
+ align:start position:0%
+euclidean spaces
+and you know we're about to review
+
+ align:start position:0%
+and you know we're about to review
+ 
+
+ align:start position:0%
+and you know we're about to review
+the representative consumer as i said
+
+ align:start position:0%
+the representative consumer as i said
+ 
+
+ align:start position:0%
+the representative consumer as i said
+this looks all the world like
+
+ align:start position:0%
+this looks all the world like
+ 
+
+ align:start position:0%
+this looks all the world like
+like a representative consumer because
+
+ align:start position:0%
+like a representative consumer because
+ 
+
+ align:start position:0%
+like a representative consumer because
+i've seemingly added up the indifference
+
+ align:start position:0%
+i've seemingly added up the indifference
+ 
+
+ align:start position:0%
+i've seemingly added up the indifference
+curves
+
+ align:start position:0%
+curves
+ 
+
+ align:start position:0%
+curves
+but one should be aware that it is not
+
+ align:start position:0%
+but one should be aware that it is not
+ 
+
+ align:start position:0%
+but one should be aware that it is not
+the gorman consumer that's going on here
+
+ align:start position:0%
+the gorman consumer that's going on here
+ 
+
+ align:start position:0%
+the gorman consumer that's going on here
+and this particular pareto optimum
+
+ align:start position:0%
+and this particular pareto optimum
+ 
+
+ align:start position:0%
+and this particular pareto optimum
+you know is is sensitive to the
+
+ align:start position:0%
+you know is is sensitive to the
+ 
+
+ align:start position:0%
+you know is is sensitive to the
+distribution of wealth you just can't
+
+ align:start position:0%
+distribution of wealth you just can't
+ 
+
+ align:start position:0%
+distribution of wealth you just can't
+see that i did not go through that when
+
+ align:start position:0%
+see that i did not go through that when
+ 
+
+ align:start position:0%
+see that i did not go through that when
+i lectured gave this lecture because we
+
+ align:start position:0%
+i lectured gave this lecture because we
+ 
+
+ align:start position:0%
+i lectured gave this lecture because we
+hadn't gotten to gorman and it wouldn't
+
+ align:start position:0%
+hadn't gotten to gorman and it wouldn't
+ 
+
+ align:start position:0%
+hadn't gotten to gorman and it wouldn't
+have made any sense
+
+ align:start position:0%
+have made any sense
+ 
+
+ align:start position:0%
+have made any sense
+but though i might as well say it now
+
+ align:start position:0%
+but though i might as well say it now
+ 
+
+ align:start position:0%
+but though i might as well say it now
+if you don't have a gorman
+
+ align:start position:0%
+if you don't have a gorman
+ 
+
+ align:start position:0%
+if you don't have a gorman
+representative consumer then you know as
+
+ align:start position:0%
+representative consumer then you know as
+ 
+
+ align:start position:0%
+representative consumer then you know as
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+increase this guy's budget line and
+
+ align:start position:0%
+increase this guy's budget line and
+ 
+
+ align:start position:0%
+increase this guy's budget line and
+decreases this one
+
+ align:start position:0%
+decreases this one
+ 
+
+ align:start position:0%
+decreases this one
+you may you may change the the shape of
+
+ align:start position:0%
+you may you may change the the shape of
+ 
+
+ align:start position:0%
+you may you may change the the shape of
+this seemingly aggregated up
+
+ align:start position:0%
+this seemingly aggregated up
+ 
+
+ align:start position:0%
+this seemingly aggregated up
+indifference curve and therefore change
+
+ align:start position:0%
+indifference curve and therefore change
+ 
+
+ align:start position:0%
+indifference curve and therefore change
+the whole optimal allocation so
+
+ align:start position:0%
+the whole optimal allocation so
+ 
+
+ align:start position:0%
+the whole optimal allocation so
+hopefully that helps you kind of think
+
+ align:start position:0%
+hopefully that helps you kind of think
+ 
+
+ align:start position:0%
+hopefully that helps you kind of think
+about the hidden way in which
+
+ align:start position:0%
+about the hidden way in which
+ 
+
+ align:start position:0%
+about the hidden way in which
+heterogeneity is entering into this
+
+ align:start position:0%
+heterogeneity is entering into this
+ 
+
+ align:start position:0%
+heterogeneity is entering into this
+picture
+
+ align:start position:0%
+picture
+ 
+
+ align:start position:0%
+picture
+and and this lecture i finished it off
+
+ align:start position:0%
+and and this lecture i finished it off
+ 
+
+ align:start position:0%
+and and this lecture i finished it off
+in an abstract way by saying
+
+ align:start position:0%
+in an abstract way by saying
+ 
+
+ align:start position:0%
+in an abstract way by saying
+the proofs of the welfare theorems are
+
+ align:start position:0%
+the proofs of the welfare theorems are
+ 
+
+ align:start position:0%
+the proofs of the welfare theorems are
+quite general that does not require
+
+ align:start position:0%
+quite general that does not require
+ 
+
+ align:start position:0%
+quite general that does not require
+finite dimensional
+
+ align:start position:0%
+finite dimensional
+ 
+
+ align:start position:0%
+finite dimensional
+commodity spaces
+
+ align:start position:0%
+commodity spaces
+ 
+
+ align:start position:0%
+commodity spaces
+i gave you the
+
+ align:start position:0%
+i gave you the
+ 
+
+ align:start position:0%
+i gave you the
+sufficient assumptions for the two
+
+ align:start position:0%
+sufficient assumptions for the two
+ 
+
+ align:start position:0%
+sufficient assumptions for the two
+welfare theorems
+
+ align:start position:0%
+welfare theorems
+ 
+
+ align:start position:0%
+welfare theorems
+and kind of quit there
+
+ align:start position:0%
+and kind of quit there
+ 
+
+ align:start position:0%
+and kind of quit there
+if we had more time i could have gone
+
+ align:start position:0%
+if we had more time i could have gone
+ 
+
+ align:start position:0%
+if we had more time i could have gone
+into greater detail
+
+ align:start position:0%
+into greater detail
+ 
+
+ align:start position:0%
+into greater detail
+i only asserted without proving it
+
+ align:start position:0%
+i only asserted without proving it
+ 
+
+ align:start position:0%
+i only asserted without proving it
+that if we took what we did earlier in
+
+ align:start position:0%
+that if we took what we did earlier in
+ 
+
+ align:start position:0%
+that if we took what we did earlier in
+the course about pareto optima with
+
+ align:start position:0%
+the course about pareto optima with
+ 
+
+ align:start position:0%
+the course about pareto optima with
+obstacles to trade
+
+ align:start position:0%
+obstacles to trade
+ 
+
+ align:start position:0%
+obstacles to trade
+with incentive constraints and
+
+ align:start position:0%
+with incentive constraints and
+ 
+
+ align:start position:0%
+with incentive constraints and
+potentially non-convex consumption sets
+
+ align:start position:0%
+potentially non-convex consumption sets
+ 
+
+ align:start position:0%
+potentially non-convex consumption sets
+because of discrete choices
+
+ align:start position:0%
+because of discrete choices
+ 
+
+ align:start position:0%
+because of discrete choices
+we could nevertheless introduce
+
+ align:start position:0%
+we could nevertheless introduce
+ 
+
+ align:start position:0%
+we could nevertheless introduce
+lotteries
+
+ align:start position:0%
+lotteries
+ 
+
+ align:start position:0%
+lotteries
+and that would have turned the space
+
+ align:start position:0%
+and that would have turned the space
+ 
+
+ align:start position:0%
+and that would have turned the space
+into a convex set and the theorems as in
+
+ align:start position:0%
+into a convex set and the theorems as in
+ 
+
+ align:start position:0%
+into a convex set and the theorems as in
+deru you know what it would apply to
+
+ align:start position:0%
+deru you know what it would apply to
+ 
+
+ align:start position:0%
+deru you know what it would apply to
+that so although this lecture just
+
+ align:start position:0%
+that so although this lecture just
+ 
+
+ align:start position:0%
+that so although this lecture just
+proves the welfare theorems carefully
+
+ align:start position:0%
+proves the welfare theorems carefully
+ 
+
+ align:start position:0%
+proves the welfare theorems carefully
+for finite dimensional commodity spaces
+
+ align:start position:0%
+for finite dimensional commodity spaces
+ 
+
+ align:start position:0%
+for finite dimensional commodity spaces
+and only asserted that the theorems
+
+ align:start position:0%
+and only asserted that the theorems
+ 
+
+ align:start position:0%
+and only asserted that the theorems
+extend
+
+ align:start position:0%
+extend
+ 
+
+ align:start position:0%
+extend
+it would cover
+
+ align:start position:0%
+it would cover
+ 
+
+ align:start position:0%
+it would cover
+competitive equilibria
+
+ align:start position:0%
+competitive equilibria
+ 
+
+ align:start position:0%
+competitive equilibria
+in contract space
+
+ align:start position:0%
+in contract space
+ 
+
+ align:start position:0%
+in contract space
+where households can buy whatever
+
+ align:start position:0%
+where households can buy whatever
+ 
+
+ align:start position:0%
+where households can buy whatever
+contracts they want
+
+ align:start position:0%
+contracts they want
+ 
+
+ align:start position:0%
+contracts they want
+granted at certain prices and firms as
+
+ align:start position:0%
+granted at certain prices and firms as
+ 
+
+ align:start position:0%
+granted at certain prices and firms as
+intermediaries will create contracts
+
+ align:start position:0%
+intermediaries will create contracts
+ 
+
+ align:start position:0%
+intermediaries will create contracts
+that maximize profits
+
+ align:start position:0%
+that maximize profits
+ 
+
+ align:start position:0%
+that maximize profits
+tying some of the loose ends together
+
+ align:start position:0%
+tying some of the loose ends together
+ 
+
+ align:start position:0%
+tying some of the loose ends together
+but without actually going through much
+
+ align:start position:0%
+but without actually going through much
+ 
+
+ align:start position:0%
+but without actually going through much
+of the details there so that was lecture
+
+ align:start position:0%
+of the details there so that was lecture
+ 
+
+ align:start position:0%
+of the details there so that was lecture
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+about 16.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well we'll come back to it again because
+
+ align:start position:0%
+well we'll come back to it again because
+ 
+
+ align:start position:0%
+well we'll come back to it again because
+we're going to go through the failures
+
+ align:start position:0%
+we're going to go through the failures
+ 
+
+ align:start position:0%
+we're going to go through the failures
+or review them quickly then this was the
+
+ align:start position:0%
+or review them quickly then this was the
+ 
+
+ align:start position:0%
+or review them quickly then this was the
+existence lecture the point being that
+
+ align:start position:0%
+existence lecture the point being that
+ 
+
+ align:start position:0%
+existence lecture the point being that
+that for example the first welfare
+
+ align:start position:0%
+that for example the first welfare
+ 
+
+ align:start position:0%
+that for example the first welfare
+theorem assumes existence of an
+
+ align:start position:0%
+theorem assumes existence of an
+ 
+
+ align:start position:0%
+theorem assumes existence of an
+equilibrium and then assures everybody
+
+ align:start position:0%
+equilibrium and then assures everybody
+ 
+
+ align:start position:0%
+equilibrium and then assures everybody
+that it would be optimal under
+
+ align:start position:0%
+that it would be optimal under
+ 
+
+ align:start position:0%
+that it would be optimal under
+sufficient conditions but if the model
+
+ align:start position:0%
+sufficient conditions but if the model
+ 
+
+ align:start position:0%
+sufficient conditions but if the model
+could be vacuous if there is no
+
+ align:start position:0%
+could be vacuous if there is no
+ 
+
+ align:start position:0%
+could be vacuous if there is no
+competitive equilibrium so we're we're
+
+ align:start position:0%
+competitive equilibrium so we're we're
+ 
+
+ align:start position:0%
+competitive equilibrium so we're we're
+dealing with things like that directly
+
+ align:start position:0%
+dealing with things like that directly
+ 
+
+ align:start position:0%
+dealing with things like that directly
+in this lecture and this was a listing
+
+ align:start position:0%
+in this lecture and this was a listing
+ 
+
+ align:start position:0%
+in this lecture and this was a listing
+of the things covered so the main
+
+ align:start position:0%
+of the things covered so the main
+ 
+
+ align:start position:0%
+of the things covered so the main
+mathematical object tool really was a
+
+ align:start position:0%
+mathematical object tool really was a
+ 
+
+ align:start position:0%
+mathematical object tool really was a
+fixed point theorem
+
+ align:start position:0%
+fixed point theorem
+ 
+
+ align:start position:0%
+fixed point theorem
+this was an example that some function
+
+ align:start position:0%
+this was an example that some function
+ 
+
+ align:start position:0%
+this was an example that some function
+has across the 45 degree line in which
+
+ align:start position:0%
+has across the 45 degree line in which
+ 
+
+ align:start position:0%
+has across the 45 degree line in which
+case whatever you put in you get back
+
+ align:start position:0%
+case whatever you put in you get back
+ 
+
+ align:start position:0%
+case whatever you put in you get back
+out the argument in the range is the
+
+ align:start position:0%
+out the argument in the range is the
+ 
+
+ align:start position:0%
+out the argument in the range is the
+argument in the domain under the under
+
+ align:start position:0%
+argument in the domain under the under
+ 
+
+ align:start position:0%
+argument in the domain under the under
+the function f and it was sufficient for
+
+ align:start position:0%
+the function f and it was sufficient for
+ 
+
+ align:start position:0%
+the function f and it was sufficient for
+this to have the set of faces of values
+
+ align:start position:0%
+this to have the set of faces of values
+ 
+
+ align:start position:0%
+this to have the set of faces of values
+in the domain and the range being
+
+ align:start position:0%
+in the domain and the range being
+ 
+
+ align:start position:0%
+in the domain and the range being
+non-empty convex and compact and for the
+
+ align:start position:0%
+non-empty convex and compact and for the
+ 
+
+ align:start position:0%
+non-empty convex and compact and for the
+function f to be continuous and that's
+
+ align:start position:0%
+function f to be continuous and that's
+ 
+
+ align:start position:0%
+function f to be continuous and that's
+brower's fixed point theorem
+
+ align:start position:0%
+brower's fixed point theorem
+ 
+
+ align:start position:0%
+brower's fixed point theorem
+i should say though well we're about to
+
+ align:start position:0%
+i should say though well we're about to
+ 
+
+ align:start position:0%
+i should say though well we're about to
+get there that this is all about
+
+ align:start position:0%
+get there that this is all about
+ 
+
+ align:start position:0%
+get there that this is all about
+existence it it's not about how to find
+
+ align:start position:0%
+existence it it's not about how to find
+ 
+
+ align:start position:0%
+existence it it's not about how to find
+it and at least one of you has asked me
+
+ align:start position:0%
+it and at least one of you has asked me
+ 
+
+ align:start position:0%
+it and at least one of you has asked me
+questions about that
+
+ align:start position:0%
+questions about that
+ 
+
+ align:start position:0%
+questions about that
+anyway this is brower's fixed point
+
+ align:start position:0%
+anyway this is brower's fixed point
+ 
+
+ align:start position:0%
+anyway this is brower's fixed point
+theorem it's paired with kakutani's
+
+ align:start position:0%
+theorem it's paired with kakutani's
+ 
+
+ align:start position:0%
+theorem it's paired with kakutani's
+fixed point theorem and the way in which
+
+ align:start position:0%
+fixed point theorem and the way in which
+ 
+
+ align:start position:0%
+fixed point theorem and the way in which
+they differed primarily was not the set
+
+ align:start position:0%
+they differed primarily was not the set
+ 
+
+ align:start position:0%
+they differed primarily was not the set
+a which is still compact and convex and
+
+ align:start position:0%
+a which is still compact and convex and
+ 
+
+ align:start position:0%
+a which is still compact and convex and
+non-empty but the function f which is no
+
+ align:start position:0%
+non-empty but the function f which is no
+ 
+
+ align:start position:0%
+non-empty but the function f which is no
+longer single necessarily single valued
+
+ align:start position:0%
+longer single necessarily single valued
+ 
+
+ align:start position:0%
+longer single necessarily single valued
+it could be multiple values or there are
+
+ align:start position:0%
+it could be multiple values or there are
+ 
+
+ align:start position:0%
+it could be multiple values or there are
+multiple values in the range for for any
+
+ align:start position:0%
+multiple values in the range for for any
+ 
+
+ align:start position:0%
+multiple values in the range for for any
+particular input x in the domain and of
+
+ align:start position:0%
+particular input x in the domain and of
+ 
+
+ align:start position:0%
+particular input x in the domain and of
+course not anything goes and had to be
+
+ align:start position:0%
+course not anything goes and had to be
+ 
+
+ align:start position:0%
+course not anything goes and had to be
+convex value and continuous in a certain
+
+ align:start position:0%
+convex value and continuous in a certain
+ 
+
+ align:start position:0%
+convex value and continuous in a certain
+sense and then with kakutani again we
+
+ align:start position:0%
+sense and then with kakutani again we
+ 
+
+ align:start position:0%
+sense and then with kakutani again we
+have a fixed point
+
+ align:start position:0%
+have a fixed point
+ 
+
+ align:start position:0%
+have a fixed point
+so these are very powerful tools and
+
+ align:start position:0%
+so these are very powerful tools and
+ 
+
+ align:start position:0%
+so these are very powerful tools and
+they're used for competitive equilibria
+
+ align:start position:0%
+they're used for competitive equilibria
+ 
+
+ align:start position:0%
+they're used for competitive equilibria
+in one way or another and used in
+
+ align:start position:0%
+in one way or another and used in
+ 
+
+ align:start position:0%
+in one way or another and used in
+games
+
+ align:start position:0%
+games
+ 
+
+ align:start position:0%
+games
+and we
+
+ align:start position:0%
+and we
+ 
+
+ align:start position:0%
+and we
+actually
+
+ align:start position:0%
+actually
+ 
+
+ align:start position:0%
+actually
+combined those at the end of this
+
+ align:start position:0%
+combined those at the end of this
+ 
+
+ align:start position:0%
+combined those at the end of this
+lecture to have a game that would be
+
+ align:start position:0%
+lecture to have a game that would be
+ 
+
+ align:start position:0%
+lecture to have a game that would be
+achieved under a nash equilibrium as a
+
+ align:start position:0%
+achieved under a nash equilibrium as a
+ 
+
+ align:start position:0%
+achieved under a nash equilibrium as a
+volreisian equilibrium okay
+
+ align:start position:0%
+volreisian equilibrium okay
+ 
+
+ align:start position:0%
+volreisian equilibrium okay
+so here are
+
+ align:start position:0%
+so here are
+ 
+
+ align:start position:0%
+so here are
+what happens if you don't assume
+
+ align:start position:0%
+what happens if you don't assume
+ 
+
+ align:start position:0%
+what happens if you don't assume
+continuity of the function you get these
+
+ align:start position:0%
+continuity of the function you get these
+ 
+
+ align:start position:0%
+continuity of the function you get these
+jumps so if the aggregate demand for an
+
+ align:start position:0%
+jumps so if the aggregate demand for an
+ 
+
+ align:start position:0%
+jumps so if the aggregate demand for an
+economy somehow had jumps like this then
+
+ align:start position:0%
+economy somehow had jumps like this then
+ 
+
+ align:start position:0%
+economy somehow had jumps like this then
+you could not be assured that there
+
+ align:start position:0%
+you could not be assured that there
+ 
+
+ align:start position:0%
+you could not be assured that there
+would exist a competitive equilibrium
+
+ align:start position:0%
+would exist a competitive equilibrium
+ 
+
+ align:start position:0%
+would exist a competitive equilibrium
+and we're we're looking for the
+
+ align:start position:0%
+and we're we're looking for the
+ 
+
+ align:start position:0%
+and we're we're looking for the
+existence
+
+ align:start position:0%
+existence
+ 
+
+ align:start position:0%
+existence
+of prices
+
+ align:start position:0%
+of prices
+ 
+
+ align:start position:0%
+of prices
+such that you put prices in to each of
+
+ align:start position:0%
+such that you put prices in to each of
+ 
+
+ align:start position:0%
+such that you put prices in to each of
+the agents
+
+ align:start position:0%
+the agents
+ 
+
+ align:start position:0%
+the agents
+maximization problems
+
+ align:start position:0%
+maximization problems
+ 
+
+ align:start position:0%
+maximization problems
+look at their demands
+
+ align:start position:0%
+look at their demands
+ 
+
+ align:start position:0%
+look at their demands
+see if demands add up to supply and if
+
+ align:start position:0%
+see if demands add up to supply and if
+ 
+
+ align:start position:0%
+see if demands add up to supply and if
+we find the price that makes that happen
+
+ align:start position:0%
+we find the price that makes that happen
+ 
+
+ align:start position:0%
+we find the price that makes that happen
+and this all of this can be formulated
+
+ align:start position:0%
+and this all of this can be formulated
+ 
+
+ align:start position:0%
+and this all of this can be formulated
+as a fixed point now i did not go
+
+ align:start position:0%
+as a fixed point now i did not go
+ 
+
+ align:start position:0%
+as a fixed point now i did not go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+the math of this because it's
+
+ align:start position:0%
+the math of this because it's
+ 
+
+ align:start position:0%
+the math of this because it's
+surprisingly tedious
+
+ align:start position:0%
+surprisingly tedious
+ 
+
+ align:start position:0%
+surprisingly tedious
+however let me say that the existence
+
+ align:start position:0%
+however let me say that the existence
+ 
+
+ align:start position:0%
+however let me say that the existence
+proof is the existence of a competitive
+
+ align:start position:0%
+proof is the existence of a competitive
+ 
+
+ align:start position:0%
+proof is the existence of a competitive
+equilibrium as in at least one fixed
+
+ align:start position:0%
+equilibrium as in at least one fixed
+ 
+
+ align:start position:0%
+equilibrium as in at least one fixed
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+herbert scarf did a lot of work on this
+
+ align:start position:0%
+herbert scarf did a lot of work on this
+ 
+
+ align:start position:0%
+herbert scarf did a lot of work on this
+subject and in his proof of the
+
+ align:start position:0%
+subject and in his proof of the
+ 
+
+ align:start position:0%
+subject and in his proof of the
+volrasian equilibrium he actually did
+
+ align:start position:0%
+volrasian equilibrium he actually did
+ 
+
+ align:start position:0%
+volrasian equilibrium he actually did
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+which was to go back to brower and
+
+ align:start position:0%
+which was to go back to brower and
+ 
+
+ align:start position:0%
+which was to go back to brower and
+actually show how to find the fixed
+
+ align:start position:0%
+actually show how to find the fixed
+ 
+
+ align:start position:0%
+actually show how to find the fixed
+point that is to say in an algorithm
+
+ align:start position:0%
+point that is to say in an algorithm
+ 
+
+ align:start position:0%
+point that is to say in an algorithm
+take a guess
+
+ align:start position:0%
+take a guess
+ 
+
+ align:start position:0%
+take a guess
+look at directional derivatives
+
+ align:start position:0%
+look at directional derivatives
+ 
+
+ align:start position:0%
+look at directional derivatives
+formulate a new guess
+
+ align:start position:0%
+formulate a new guess
+ 
+
+ align:start position:0%
+formulate a new guess
+and iterate until you get to
+
+ align:start position:0%
+and iterate until you get to
+ 
+
+ align:start position:0%
+and iterate until you get to
+the end or approximately the end however
+
+ align:start position:0%
+the end or approximately the end however
+ 
+
+ align:start position:0%
+the end or approximately the end however
+close the computer can make it and he
+
+ align:start position:0%
+close the computer can make it and he
+ 
+
+ align:start position:0%
+close the computer can make it and he
+would have constructively found the
+
+ align:start position:0%
+would have constructively found the
+ 
+
+ align:start position:0%
+would have constructively found the
+brower's fixed point which works much
+
+ align:start position:0%
+brower's fixed point which works much
+ 
+
+ align:start position:0%
+brower's fixed point which works much
+more generally than just finding the
+
+ align:start position:0%
+more generally than just finding the
+ 
+
+ align:start position:0%
+more generally than just finding the
+existence of a competitive equilibrium
+
+ align:start position:0%
+existence of a competitive equilibrium
+ 
+
+ align:start position:0%
+existence of a competitive equilibrium
+this comes up later when we talked about
+
+ align:start position:0%
+this comes up later when we talked about
+ 
+
+ align:start position:0%
+this comes up later when we talked about
+restrictions on data having to do with
+
+ align:start position:0%
+restrictions on data having to do with
+ 
+
+ align:start position:0%
+restrictions on data having to do with
+algorithms and what the algorithms
+
+ align:start position:0%
+algorithms and what the algorithms
+ 
+
+ align:start position:0%
+algorithms and what the algorithms
+actually look like when computing
+
+ align:start position:0%
+actually look like when computing
+ 
+
+ align:start position:0%
+actually look like when computing
+solutions to individual problems and
+
+ align:start position:0%
+solutions to individual problems and
+ 
+
+ align:start position:0%
+solutions to individual problems and
+defining a competitive equilibria anyway
+
+ align:start position:0%
+defining a competitive equilibria anyway
+ 
+
+ align:start position:0%
+defining a competitive equilibria anyway
+i just wanted to draw your attention to
+
+ align:start position:0%
+i just wanted to draw your attention to
+ 
+
+ align:start position:0%
+i just wanted to draw your attention to
+the distinction as an overview that's my
+
+ align:start position:0%
+the distinction as an overview that's my
+ 
+
+ align:start position:0%
+the distinction as an overview that's my
+job today between existence of a
+
+ align:start position:0%
+job today between existence of a
+ 
+
+ align:start position:0%
+job today between existence of a
+competitive equilibrium and how to find
+
+ align:start position:0%
+competitive equilibrium and how to find
+ 
+
+ align:start position:0%
+competitive equilibrium and how to find
+the competitive equilibrium
+
+ align:start position:0%
+the competitive equilibrium
+ 
+
+ align:start position:0%
+the competitive equilibrium
+algorithmically
+
+ align:start position:0%
+algorithmically
+ 
+
+ align:start position:0%
+algorithmically
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+what we did do in this lecture
+
+ align:start position:0%
+what we did do in this lecture
+ 
+
+ align:start position:0%
+what we did do in this lecture
+was to prove the existence of a
+
+ align:start position:0%
+was to prove the existence of a
+ 
+
+ align:start position:0%
+was to prove the existence of a
+competitive equilibrium using the second
+
+ align:start position:0%
+competitive equilibrium using the second
+ 
+
+ align:start position:0%
+competitive equilibrium using the second
+welfare theorem which we just reviewed
+
+ align:start position:0%
+welfare theorem which we just reviewed
+ 
+
+ align:start position:0%
+welfare theorem which we just reviewed
+in lecture 16. so the idea is instead of
+
+ align:start position:0%
+in lecture 16. so the idea is instead of
+ 
+
+ align:start position:0%
+in lecture 16. so the idea is instead of
+iterating on candidate prices
+
+ align:start position:0%
+iterating on candidate prices
+ 
+
+ align:start position:0%
+iterating on candidate prices
+to find where supply is equal to demand
+
+ align:start position:0%
+to find where supply is equal to demand
+ 
+
+ align:start position:0%
+to find where supply is equal to demand
+we iterate on these lambda weights
+
+ align:start position:0%
+we iterate on these lambda weights
+ 
+
+ align:start position:0%
+we iterate on these lambda weights
+and uh and the idea is very much here's
+
+ align:start position:0%
+and uh and the idea is very much here's
+ 
+
+ align:start position:0%
+and uh and the idea is very much here's
+that economy again i promised you it
+
+ align:start position:0%
+that economy again i promised you it
+ 
+
+ align:start position:0%
+that economy again i promised you it
+would keep coming back the statement of
+
+ align:start position:0%
+would keep coming back the statement of
+ 
+
+ align:start position:0%
+would keep coming back the statement of
+the economy with the convexity and
+
+ align:start position:0%
+the economy with the convexity and
+ 
+
+ align:start position:0%
+the economy with the convexity and
+concavity
+
+ align:start position:0%
+concavity
+ 
+
+ align:start position:0%
+concavity
+the idea is to
+
+ align:start position:0%
+the idea is to
+ 
+
+ align:start position:0%
+the idea is to
+go back to the pareto problem this is
+
+ align:start position:0%
+go back to the pareto problem this is
+ 
+
+ align:start position:0%
+go back to the pareto problem this is
+now the second time today that this is
+
+ align:start position:0%
+now the second time today that this is
+ 
+
+ align:start position:0%
+now the second time today that this is
+the pareto problem has come up we just
+
+ align:start position:0%
+the pareto problem has come up we just
+ 
+
+ align:start position:0%
+the pareto problem has come up we just
+used it in 16 for the second welfare
+
+ align:start position:0%
+used it in 16 for the second welfare
+ 
+
+ align:start position:0%
+used it in 16 for the second welfare
+theorem here it is again stated rather
+
+ align:start position:0%
+theorem here it is again stated rather
+ 
+
+ align:start position:0%
+theorem here it is again stated rather
+succinctly to remind us of these lambda
+
+ align:start position:0%
+succinctly to remind us of these lambda
+ 
+
+ align:start position:0%
+succinctly to remind us of these lambda
+i weights such that when we max we get
+
+ align:start position:0%
+i weights such that when we max we get
+ 
+
+ align:start position:0%
+i weights such that when we max we get
+pareto optima so we start with those
+
+ align:start position:0%
+pareto optima so we start with those
+ 
+
+ align:start position:0%
+pareto optima so we start with those
+lambdas
+
+ align:start position:0%
+lambdas
+ 
+
+ align:start position:0%
+lambdas
+and then we
+
+ align:start position:0%
+and then we
+ 
+
+ align:start position:0%
+and then we
+essentially
+
+ align:start position:0%
+essentially
+ 
+
+ align:start position:0%
+essentially
+look at the
+
+ align:start position:0%
+look at the
+ 
+
+ align:start position:0%
+look at the
+solution to the pareto problem these x
+
+ align:start position:0%
+solution to the pareto problem these x
+ 
+
+ align:start position:0%
+solution to the pareto problem these x
+hats
+
+ align:start position:0%
+hats
+ 
+
+ align:start position:0%
+hats
+for those particular lambdas look at the
+
+ align:start position:0%
+for those particular lambdas look at the
+ 
+
+ align:start position:0%
+for those particular lambdas look at the
+prices which you now know and remember
+
+ align:start position:0%
+prices which you now know and remember
+ 
+
+ align:start position:0%
+prices which you now know and remember
+are the shadow prices on the resource
+
+ align:start position:0%
+are the shadow prices on the resource
+ 
+
+ align:start position:0%
+are the shadow prices on the resource
+constraints and we generate the wealth
+
+ align:start position:0%
+constraints and we generate the wealth
+ 
+
+ align:start position:0%
+constraints and we generate the wealth
+associating with this purchasing power
+
+ align:start position:0%
+associating with this purchasing power
+ 
+
+ align:start position:0%
+associating with this purchasing power
+so what we're going to look for to get a
+
+ align:start position:0%
+so what we're going to look for to get a
+ 
+
+ align:start position:0%
+so what we're going to look for to get a
+standard volraisian equilibrium
+
+ align:start position:0%
+standard volraisian equilibrium
+ 
+
+ align:start position:0%
+standard volraisian equilibrium
+is particular lambdas such that
+
+ align:start position:0%
+is particular lambdas such that
+ 
+
+ align:start position:0%
+is particular lambdas such that
+the valuation
+
+ align:start position:0%
+the valuation
+ 
+
+ align:start position:0%
+the valuation
+of privately owned resources for a given
+
+ align:start position:0%
+of privately owned resources for a given
+ 
+
+ align:start position:0%
+of privately owned resources for a given
+household eye is equal to
+
+ align:start position:0%
+household eye is equal to
+ 
+
+ align:start position:0%
+household eye is equal to
+the wealth coming from the lambdas
+
+ align:start position:0%
+the wealth coming from the lambdas
+ 
+
+ align:start position:0%
+the wealth coming from the lambdas
+here this is a better statement of it a
+
+ align:start position:0%
+here this is a better statement of it a
+ 
+
+ align:start position:0%
+here this is a better statement of it a
+particular lambda star the fixed point
+
+ align:start position:0%
+particular lambda star the fixed point
+ 
+
+ align:start position:0%
+particular lambda star the fixed point
+find me please the fixed point would be
+
+ align:start position:0%
+find me please the fixed point would be
+ 
+
+ align:start position:0%
+find me please the fixed point would be
+such that
+
+ align:start position:0%
+such that
+ 
+
+ align:start position:0%
+such that
+when we substitute lambda in the pareto
+
+ align:start position:0%
+when we substitute lambda in the pareto
+ 
+
+ align:start position:0%
+when we substitute lambda in the pareto
+problem and generate the optimal
+
+ align:start position:0%
+problem and generate the optimal
+ 
+
+ align:start position:0%
+problem and generate the optimal
+allocations we'll have some valuation at
+
+ align:start position:0%
+allocations we'll have some valuation at
+ 
+
+ align:start position:0%
+allocations we'll have some valuation at
+those shadow prices
+
+ align:start position:0%
+those shadow prices
+ 
+
+ align:start position:0%
+those shadow prices
+of the expenditures which when we sum up
+
+ align:start position:0%
+of the expenditures which when we sum up
+ 
+
+ align:start position:0%
+of the expenditures which when we sum up
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+and summed up over all the commodities l
+
+ align:start position:0%
+and summed up over all the commodities l
+ 
+
+ align:start position:0%
+and summed up over all the commodities l
+would be exactly equal to the right-hand
+
+ align:start position:0%
+would be exactly equal to the right-hand
+ 
+
+ align:start position:0%
+would be exactly equal to the right-hand
+side of the budget the valuation of
+
+ align:start position:0%
+side of the budget the valuation of
+ 
+
+ align:start position:0%
+side of the budget the valuation of
+purchasing power that the consumer has
+
+ align:start position:0%
+purchasing power that the consumer has
+ 
+
+ align:start position:0%
+purchasing power that the consumer has
+as a result of owning the endowment and
+
+ align:start position:0%
+as a result of owning the endowment and
+ 
+
+ align:start position:0%
+as a result of owning the endowment and
+getting shares in the profits of the
+
+ align:start position:0%
+getting shares in the profits of the
+ 
+
+ align:start position:0%
+getting shares in the profits of the
+firms when the firms are maximizing at
+
+ align:start position:0%
+firms when the firms are maximizing at
+ 
+
+ align:start position:0%
+firms when the firms are maximizing at
+that same lambda star so this is the
+
+ align:start position:0%
+that same lambda star so this is the
+ 
+
+ align:start position:0%
+that same lambda star so this is the
+fixed point
+
+ align:start position:0%
+fixed point
+ 
+
+ align:start position:0%
+fixed point
+i think i mentioned in a sort of
+
+ align:start position:0%
+i think i mentioned in a sort of
+ 
+
+ align:start position:0%
+i think i mentioned in a sort of
+question and answer at the beginning of
+
+ align:start position:0%
+question and answer at the beginning of
+ 
+
+ align:start position:0%
+question and answer at the beginning of
+lecture 18 when we reviewed 17 that i
+
+ align:start position:0%
+lecture 18 when we reviewed 17 that i
+ 
+
+ align:start position:0%
+lecture 18 when we reviewed 17 that i
+felt i hadn't done a good enough job
+
+ align:start position:0%
+felt i hadn't done a good enough job
+ 
+
+ align:start position:0%
+felt i hadn't done a good enough job
+explaining the intuition for this
+
+ align:start position:0%
+explaining the intuition for this
+ 
+
+ align:start position:0%
+explaining the intuition for this
+mapping but it does come from the second
+
+ align:start position:0%
+mapping but it does come from the second
+ 
+
+ align:start position:0%
+mapping but it does come from the second
+welfare theorem start with a given guess
+
+ align:start position:0%
+welfare theorem start with a given guess
+ 
+
+ align:start position:0%
+welfare theorem start with a given guess
+about the lambda that pins down
+
+ align:start position:0%
+about the lambda that pins down
+ 
+
+ align:start position:0%
+about the lambda that pins down
+which particular pareto optimum we're
+
+ align:start position:0%
+which particular pareto optimum we're
+ 
+
+ align:start position:0%
+which particular pareto optimum we're
+targeting and suppose it were the case
+
+ align:start position:0%
+targeting and suppose it were the case
+ 
+
+ align:start position:0%
+targeting and suppose it were the case
+that the valuation of expenditure at
+
+ align:start position:0%
+that the valuation of expenditure at
+ 
+
+ align:start position:0%
+that the valuation of expenditure at
+that optimum for consumer i were
+
+ align:start position:0%
+that optimum for consumer i were
+ 
+
+ align:start position:0%
+that optimum for consumer i were
+strictly greater than the valuation of
+
+ align:start position:0%
+strictly greater than the valuation of
+ 
+
+ align:start position:0%
+strictly greater than the valuation of
+his or her
+
+ align:start position:0%
+his or her
+ 
+
+ align:start position:0%
+his or her
+privately owned resources
+
+ align:start position:0%
+privately owned resources
+ 
+
+ align:start position:0%
+privately owned resources
+well in this case we gave this consumer
+
+ align:start position:0%
+well in this case we gave this consumer
+ 
+
+ align:start position:0%
+well in this case we gave this consumer
+too much they can't afford it so the
+
+ align:start position:0%
+too much they can't afford it so the
+ 
+
+ align:start position:0%
+too much they can't afford it so the
+obvious way to iterate
+
+ align:start position:0%
+obvious way to iterate
+ 
+
+ align:start position:0%
+obvious way to iterate
+if indeed you were even searching
+
+ align:start position:0%
+if indeed you were even searching
+ 
+
+ align:start position:0%
+if indeed you were even searching
+is to reduce the lambda for this
+
+ align:start position:0%
+is to reduce the lambda for this
+ 
+
+ align:start position:0%
+is to reduce the lambda for this
+household and increase the lambdas for
+
+ align:start position:0%
+household and increase the lambdas for
+ 
+
+ align:start position:0%
+household and increase the lambdas for
+the other so this is very much like that
+
+ align:start position:0%
+the other so this is very much like that
+ 
+
+ align:start position:0%
+the other so this is very much like that
+edgeworth box diagram for the second
+
+ align:start position:0%
+edgeworth box diagram for the second
+ 
+
+ align:start position:0%
+edgeworth box diagram for the second
+welfare theorem where i said you know
+
+ align:start position:0%
+welfare theorem where i said you know
+ 
+
+ align:start position:0%
+welfare theorem where i said you know
+household a
+
+ align:start position:0%
+household a
+ 
+
+ align:start position:0%
+household a
+has to give up stuff this would be
+
+ align:start position:0%
+has to give up stuff this would be
+ 
+
+ align:start position:0%
+has to give up stuff this would be
+household a if the inequality is greater
+
+ align:start position:0%
+household a if the inequality is greater
+ 
+
+ align:start position:0%
+household a if the inequality is greater
+than or equal to and household b would
+
+ align:start position:0%
+than or equal to and household b would
+ 
+
+ align:start position:0%
+than or equal to and household b would
+be the recipient and be getting the
+
+ align:start position:0%
+be the recipient and be getting the
+ 
+
+ align:start position:0%
+be the recipient and be getting the
+transfers for household b you'd be under
+
+ align:start position:0%
+transfers for household b you'd be under
+ 
+
+ align:start position:0%
+transfers for household b you'd be under
+valuing evaluation of the resources that
+
+ align:start position:0%
+valuing evaluation of the resources that
+ 
+
+ align:start position:0%
+valuing evaluation of the resources that
+the assigned optimum could be less than
+
+ align:start position:0%
+the assigned optimum could be less than
+ 
+
+ align:start position:0%
+the assigned optimum could be less than
+the evaluation of their privately owned
+
+ align:start position:0%
+the evaluation of their privately owned
+ 
+
+ align:start position:0%
+the evaluation of their privately owned
+resources
+
+ align:start position:0%
+resources
+ 
+
+ align:start position:0%
+resources
+now again negishi didn't actually show
+
+ align:start position:0%
+now again negishi didn't actually show
+ 
+
+ align:start position:0%
+now again negishi didn't actually show
+that one could find the fixed point by
+
+ align:start position:0%
+that one could find the fixed point by
+ 
+
+ align:start position:0%
+that one could find the fixed point by
+iterating on the lambdas but but in
+
+ align:start position:0%
+iterating on the lambdas but but in
+ 
+
+ align:start position:0%
+iterating on the lambdas but but in
+practice
+
+ align:start position:0%
+practice
+ 
+
+ align:start position:0%
+practice
+it typically works so as a numerical
+
+ align:start position:0%
+it typically works so as a numerical
+ 
+
+ align:start position:0%
+it typically works so as a numerical
+algorithm you could just be trying out
+
+ align:start position:0%
+algorithm you could just be trying out
+ 
+
+ align:start position:0%
+algorithm you could just be trying out
+candidates lambda checking out these
+
+ align:start position:0%
+candidates lambda checking out these
+ 
+
+ align:start position:0%
+candidates lambda checking out these
+kinds of budget equations and and so on
+
+ align:start position:0%
+kinds of budget equations and and so on
+ 
+
+ align:start position:0%
+kinds of budget equations and and so on
+so here again this links up to lambda
+
+ align:start position:0%
+so here again this links up to lambda
+ 
+
+ align:start position:0%
+so here again this links up to lambda
+equal marginal utility of income that's
+
+ align:start position:0%
+equal marginal utility of income that's
+ 
+
+ align:start position:0%
+equal marginal utility of income that's
+the kansas rocky mountain pictures at
+
+ align:start position:0%
+the kansas rocky mountain pictures at
+ 
+
+ align:start position:0%
+the kansas rocky mountain pictures at
+the beginning and i reinforced that when
+
+ align:start position:0%
+the beginning and i reinforced that when
+ 
+
+ align:start position:0%
+the beginning and i reinforced that when
+we went through the second welfare
+
+ align:start position:0%
+we went through the second welfare
+ 
+
+ align:start position:0%
+we went through the second welfare
+theorem so this proof of the existence
+
+ align:start position:0%
+theorem so this proof of the existence
+ 
+
+ align:start position:0%
+theorem so this proof of the existence
+is working off the same sort of
+
+ align:start position:0%
+is working off the same sort of
+ 
+
+ align:start position:0%
+is working off the same sort of
+equivalence between the lambdas and the
+
+ align:start position:0%
+equivalence between the lambdas and the
+ 
+
+ align:start position:0%
+equivalence between the lambdas and the
+inverse marginal utility of wealth this
+
+ align:start position:0%
+inverse marginal utility of wealth this
+ 
+
+ align:start position:0%
+inverse marginal utility of wealth this
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+computer science part
+
+ align:start position:0%
+computer science part
+ 
+
+ align:start position:0%
+computer science part
+that it looks like it might be
+
+ align:start position:0%
+that it looks like it might be
+ 
+
+ align:start position:0%
+that it looks like it might be
+hard to find actually constructively so
+
+ align:start position:0%
+hard to find actually constructively so
+ 
+
+ align:start position:0%
+hard to find actually constructively so
+these guys algorithmically want to find
+
+ align:start position:0%
+these guys algorithmically want to find
+ 
+
+ align:start position:0%
+these guys algorithmically want to find
+the valerian equilibrium not just
+
+ align:start position:0%
+the valerian equilibrium not just
+ 
+
+ align:start position:0%
+the valerian equilibrium not just
+be happy with
+
+ align:start position:0%
+be happy with
+ 
+
+ align:start position:0%
+be happy with
+the notion that there's a fixed point so
+
+ align:start position:0%
+the notion that there's a fixed point so
+ 
+
+ align:start position:0%
+the notion that there's a fixed point so
+that it exists and this literature works
+
+ align:start position:0%
+that it exists and this literature works
+ 
+
+ align:start position:0%
+that it exists and this literature works
+on the same they kind of discovered
+
+ align:start position:0%
+on the same they kind of discovered
+ 
+
+ align:start position:0%
+on the same they kind of discovered
+again negishi so that's why i told you
+
+ align:start position:0%
+again negishi so that's why i told you
+ 
+
+ align:start position:0%
+again negishi so that's why i told you
+about it and you but you get a better
+
+ align:start position:0%
+about it and you but you get a better
+ 
+
+ align:start position:0%
+about it and you but you get a better
+sense here and i gave you a hint of that
+
+ align:start position:0%
+sense here and i gave you a hint of that
+ 
+
+ align:start position:0%
+sense here and i gave you a hint of that
+with respect to herb scarf that the way
+
+ align:start position:0%
+with respect to herb scarf that the way
+ 
+
+ align:start position:0%
+with respect to herb scarf that the way
+to find it is to sort of periodically
+
+ align:start position:0%
+to find it is to sort of periodically
+ 
+
+ align:start position:0%
+to find it is to sort of periodically
+look at the aggregate demand arctic or
+
+ align:start position:0%
+look at the aggregate demand arctic or
+ 
+
+ align:start position:0%
+look at the aggregate demand arctic or
+oracle as it were and take a local
+
+ align:start position:0%
+oracle as it were and take a local
+ 
+
+ align:start position:0%
+oracle as it were and take a local
+derivative of it to see kind of which
+
+ align:start position:0%
+derivative of it to see kind of which
+ 
+
+ align:start position:0%
+derivative of it to see kind of which
+way you ought to move
+
+ align:start position:0%
+way you ought to move
+ 
+
+ align:start position:0%
+way you ought to move
+so it's a little bit harder than what i
+
+ align:start position:0%
+so it's a little bit harder than what i
+ 
+
+ align:start position:0%
+so it's a little bit harder than what i
+said about just iterating on nigishi's
+
+ align:start position:0%
+said about just iterating on nigishi's
+ 
+
+ align:start position:0%
+said about just iterating on nigishi's
+algorithm
+
+ align:start position:0%
+algorithm
+ 
+
+ align:start position:0%
+algorithm
+but their point is that they designed an
+
+ align:start position:0%
+but their point is that they designed an
+ 
+
+ align:start position:0%
+but their point is that they designed an
+algorithm that finds the competitive
+
+ align:start position:0%
+algorithm that finds the competitive
+ 
+
+ align:start position:0%
+algorithm that finds the competitive
+equilibrium using negishi and it's not
+
+ align:start position:0%
+equilibrium using negishi and it's not
+ 
+
+ align:start position:0%
+equilibrium using negishi and it's not
+that hard in the sense that it's
+
+ align:start position:0%
+that hard in the sense that it's
+ 
+
+ align:start position:0%
+that hard in the sense that it's
+polynomial of degree 3 and the number of
+
+ align:start position:0%
+polynomial of degree 3 and the number of
+ 
+
+ align:start position:0%
+polynomial of degree 3 and the number of
+goods which is n
+
+ align:start position:0%
+goods which is n
+ 
+
+ align:start position:0%
+goods which is n
+so it's a polynomial rather than
+
+ align:start position:0%
+so it's a polynomial rather than
+ 
+
+ align:start position:0%
+so it's a polynomial rather than
+exponentially hard
+
+ align:start position:0%
+exponentially hard
+ 
+
+ align:start position:0%
+exponentially hard
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so then we went to the second part of
+
+ align:start position:0%
+so then we went to the second part of
+ 
+
+ align:start position:0%
+so then we went to the second part of
+the lecture which was strategic form
+
+ align:start position:0%
+the lecture which was strategic form
+ 
+
+ align:start position:0%
+the lecture which was strategic form
+games this looks quite different you
+
+ align:start position:0%
+games this looks quite different you
+ 
+
+ align:start position:0%
+games this looks quite different you
+have utility functions again but they
+
+ align:start position:0%
+have utility functions again but they
+ 
+
+ align:start position:0%
+have utility functions again but they
+can be a function of other people's
+
+ align:start position:0%
+can be a function of other people's
+ 
+
+ align:start position:0%
+can be a function of other people's
+strategies not just your own
+
+ align:start position:0%
+strategies not just your own
+ 
+
+ align:start position:0%
+strategies not just your own
+finite set of players that's kind of
+
+ align:start position:0%
+finite set of players that's kind of
+ 
+
+ align:start position:0%
+finite set of players that's kind of
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+and we talked about strategy profiles
+
+ align:start position:0%
+and we talked about strategy profiles
+ 
+
+ align:start position:0%
+and we talked about strategy profiles
+what household eye is doing or trader i
+
+ align:start position:0%
+what household eye is doing or trader i
+ 
+
+ align:start position:0%
+what household eye is doing or trader i
+versus what all the others are doing
+
+ align:start position:0%
+versus what all the others are doing
+ 
+
+ align:start position:0%
+versus what all the others are doing
+and we defined mixed strategies
+
+ align:start position:0%
+and we defined mixed strategies
+ 
+
+ align:start position:0%
+and we defined mixed strategies
+where the players are randomizing
+
+ align:start position:0%
+where the players are randomizing
+ 
+
+ align:start position:0%
+where the players are randomizing
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+a finite set of discrete actions
+
+ align:start position:0%
+a finite set of discrete actions
+ 
+
+ align:start position:0%
+a finite set of discrete actions
+so this is one place in the class in the
+
+ align:start position:0%
+so this is one place in the class in the
+ 
+
+ align:start position:0%
+so this is one place in the class in the
+course where again these lotteries come
+
+ align:start position:0%
+course where again these lotteries come
+ 
+
+ align:start position:0%
+course where again these lotteries come
+up to convexify things in this case and
+
+ align:start position:0%
+up to convexify things in this case and
+ 
+
+ align:start position:0%
+up to convexify things in this case and
+indeed the convexification
+
+ align:start position:0%
+indeed the convexification
+ 
+
+ align:start position:0%
+indeed the convexification
+is what allows
+
+ align:start position:0%
+is what allows
+ 
+
+ align:start position:0%
+is what allows
+us to prove the existence of this mixed
+
+ align:start position:0%
+us to prove the existence of this mixed
+ 
+
+ align:start position:0%
+us to prove the existence of this mixed
+strategy equilibrium
+
+ align:start position:0%
+strategy equilibrium
+ 
+
+ align:start position:0%
+strategy equilibrium
+a mixed strategy equilibrium is a set of
+
+ align:start position:0%
+a mixed strategy equilibrium is a set of
+ 
+
+ align:start position:0%
+a mixed strategy equilibrium is a set of
+randomization routines for each player
+
+ align:start position:0%
+randomization routines for each player
+ 
+
+ align:start position:0%
+randomization routines for each player
+stacked up in a vector
+
+ align:start position:0%
+stacked up in a vector
+ 
+
+ align:start position:0%
+stacked up in a vector
+such that given what all the other
+
+ align:start position:0%
+such that given what all the other
+ 
+
+ align:start position:0%
+such that given what all the other
+players i are doing minus i all the
+
+ align:start position:0%
+players i are doing minus i all the
+ 
+
+ align:start position:0%
+players i are doing minus i all the
+others but player i wants to do is the i
+
+ align:start position:0%
+others but player i wants to do is the i
+ 
+
+ align:start position:0%
+others but player i wants to do is the i
+star sigma star vector component of that
+
+ align:start position:0%
+star sigma star vector component of that
+ 
+
+ align:start position:0%
+star sigma star vector component of that
+vector better than any other component
+
+ align:start position:0%
+vector better than any other component
+ 
+
+ align:start position:0%
+vector better than any other component
+so this is the definition of a mixed
+
+ align:start position:0%
+so this is the definition of a mixed
+ 
+
+ align:start position:0%
+so this is the definition of a mixed
+strategy equilibrium
+
+ align:start position:0%
+strategy equilibrium
+ 
+
+ align:start position:0%
+strategy equilibrium
+and then we kind of have this
+
+ align:start position:0%
+and then we kind of have this
+ 
+
+ align:start position:0%
+and then we kind of have this
+interesting side note here
+
+ align:start position:0%
+interesting side note here
+ 
+
+ align:start position:0%
+interesting side note here
+and this is a third mean a third related
+
+ align:start position:0%
+and this is a third mean a third related
+ 
+
+ align:start position:0%
+and this is a third mean a third related
+but not identical statement which is you
+
+ align:start position:0%
+but not identical statement which is you
+ 
+
+ align:start position:0%
+but not identical statement which is you
+have a candidate for an equilibrium
+
+ align:start position:0%
+have a candidate for an equilibrium
+ 
+
+ align:start position:0%
+have a candidate for an equilibrium
+how do you know it really is an
+
+ align:start position:0%
+how do you know it really is an
+ 
+
+ align:start position:0%
+how do you know it really is an
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+this is well it's related to the idea of
+
+ align:start position:0%
+this is well it's related to the idea of
+ 
+
+ align:start position:0%
+this is well it's related to the idea of
+the fixed point momentarily i'll show
+
+ align:start position:0%
+the fixed point momentarily i'll show
+ 
+
+ align:start position:0%
+the fixed point momentarily i'll show
+you that but
+
+ align:start position:0%
+you that but
+ 
+
+ align:start position:0%
+you that but
+but here the question is
+
+ align:start position:0%
+but here the question is
+ 
+
+ align:start position:0%
+but here the question is
+how many things do you have to check at
+
+ align:start position:0%
+how many things do you have to check at
+ 
+
+ align:start position:0%
+how many things do you have to check at
+the candidate mixed equilibrium nash
+
+ align:start position:0%
+the candidate mixed equilibrium nash
+ 
+
+ align:start position:0%
+the candidate mixed equilibrium nash
+mixed strategy nash equilibrium and
+
+ align:start position:0%
+mixed strategy nash equilibrium and
+ 
+
+ align:start position:0%
+mixed strategy nash equilibrium and
+it turns out you only need to to check
+
+ align:start position:0%
+it turns out you only need to to check
+ 
+
+ align:start position:0%
+it turns out you only need to to check
+pure strategy deviations here
+
+ align:start position:0%
+pure strategy deviations here
+ 
+
+ align:start position:0%
+pure strategy deviations here
+and rather than
+
+ align:start position:0%
+and rather than
+ 
+
+ align:start position:0%
+and rather than
+all possible mixed strategies
+
+ align:start position:0%
+all possible mixed strategies
+ 
+
+ align:start position:0%
+all possible mixed strategies
+thank goodness because that would be
+
+ align:start position:0%
+thank goodness because that would be
+ 
+
+ align:start position:0%
+thank goodness because that would be
+hard and the reason for that is if you
+
+ align:start position:0%
+hard and the reason for that is if you
+ 
+
+ align:start position:0%
+hard and the reason for that is if you
+can find
+
+ align:start position:0%
+can find
+ 
+
+ align:start position:0%
+can find
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+degenerate action which dominates the
+
+ align:start position:0%
+degenerate action which dominates the
+ 
+
+ align:start position:0%
+degenerate action which dominates the
+supposed mixed strategy maximum that's
+
+ align:start position:0%
+supposed mixed strategy maximum that's
+ 
+
+ align:start position:0%
+supposed mixed strategy maximum that's
+enough that's a particular degenerate
+
+ align:start position:0%
+enough that's a particular degenerate
+ 
+
+ align:start position:0%
+enough that's a particular degenerate
+mixed strategy to show that you could do
+
+ align:start position:0%
+mixed strategy to show that you could do
+ 
+
+ align:start position:0%
+mixed strategy to show that you could do
+better and if there were
+
+ align:start position:0%
+better and if there were
+ 
+
+ align:start position:0%
+better and if there were
+multiple ones that were doing better you
+
+ align:start position:0%
+multiple ones that were doing better you
+ 
+
+ align:start position:0%
+multiple ones that were doing better you
+pick the best one that dominates to
+
+ align:start position:0%
+pick the best one that dominates to
+ 
+
+ align:start position:0%
+pick the best one that dominates to
+break up the solution and if there were
+
+ align:start position:0%
+break up the solution and if there were
+ 
+
+ align:start position:0%
+break up the solution and if there were
+two or more we
+
+ align:start position:0%
+two or more we
+ 
+
+ align:start position:0%
+two or more we
+that generated the same utility you
+
+ align:start position:0%
+that generated the same utility you
+ 
+
+ align:start position:0%
+that generated the same utility you
+could randomize over them but there's no
+
+ align:start position:0%
+could randomize over them but there's no
+ 
+
+ align:start position:0%
+could randomize over them but there's no
+need because they all generate the same
+
+ align:start position:0%
+need because they all generate the same
+ 
+
+ align:start position:0%
+need because they all generate the same
+utility so you might as well pick one so
+
+ align:start position:0%
+utility so you might as well pick one so
+ 
+
+ align:start position:0%
+utility so you might as well pick one so
+that's the intuition
+
+ align:start position:0%
+that's the intuition
+ 
+
+ align:start position:0%
+that's the intuition
+for why it's enough to look to check a
+
+ align:start position:0%
+for why it's enough to look to check a
+ 
+
+ align:start position:0%
+for why it's enough to look to check a
+given candidate profile against these
+
+ align:start position:0%
+given candidate profile against these
+ 
+
+ align:start position:0%
+given candidate profile against these
+degenerate
+
+ align:start position:0%
+degenerate
+ 
+
+ align:start position:0%
+degenerate
+actions
+
+ align:start position:0%
+actions
+ 
+
+ align:start position:0%
+actions
+not mixed strategies
+
+ align:start position:0%
+not mixed strategies
+ 
+
+ align:start position:0%
+not mixed strategies
+okay the the rest of it is
+
+ align:start position:0%
+okay the the rest of it is
+ 
+
+ align:start position:0%
+okay the the rest of it is
+you know remembering
+
+ align:start position:0%
+you know remembering
+ 
+
+ align:start position:0%
+you know remembering
+these exactly these kinds of responses
+
+ align:start position:0%
+these exactly these kinds of responses
+ 
+
+ align:start position:0%
+these exactly these kinds of responses
+these sort of
+
+ align:start position:0%
+these sort of
+ 
+
+ align:start position:0%
+these sort of
+better than sen sets or you know uh
+
+ align:start position:0%
+better than sen sets or you know uh
+ 
+
+ align:start position:0%
+better than sen sets or you know uh
+best response sets
+
+ align:start position:0%
+best response sets
+ 
+
+ align:start position:0%
+best response sets
+for each player so
+
+ align:start position:0%
+for each player so
+ 
+
+ align:start position:0%
+for each player so
+given the others are doing you want a
+
+ align:start position:0%
+given the others are doing you want a
+ 
+
+ align:start position:0%
+given the others are doing you want a
+best response for player i obviously is
+
+ align:start position:0%
+best response for player i obviously is
+ 
+
+ align:start position:0%
+best response for player i obviously is
+going to maximize hopefully generating
+
+ align:start position:0%
+going to maximize hopefully generating
+ 
+
+ align:start position:0%
+going to maximize hopefully generating
+the same mixed strategy as a candidate
+
+ align:start position:0%
+the same mixed strategy as a candidate
+ 
+
+ align:start position:0%
+the same mixed strategy as a candidate
+but maybe not if it's not a
+
+ align:start position:0%
+but maybe not if it's not a
+ 
+
+ align:start position:0%
+but maybe not if it's not a
+mixed strategy equilibrium
+
+ align:start position:0%
+mixed strategy equilibrium
+ 
+
+ align:start position:0%
+mixed strategy equilibrium
+but all the other guys are doing the
+
+ align:start position:0%
+but all the other guys are doing the
+ 
+
+ align:start position:0%
+but all the other guys are doing the
+same so we're going to look for a fixed
+
+ align:start position:0%
+same so we're going to look for a fixed
+ 
+
+ align:start position:0%
+same so we're going to look for a fixed
+point in the space of best response
+
+ align:start position:0%
+point in the space of best response
+ 
+
+ align:start position:0%
+point in the space of best response
+strategies
+
+ align:start position:0%
+strategies
+ 
+
+ align:start position:0%
+strategies
+and the proof of the existence of the
+
+ align:start position:0%
+and the proof of the existence of the
+ 
+
+ align:start position:0%
+and the proof of the existence of the
+mixed strategy nash equilibrium had to
+
+ align:start position:0%
+mixed strategy nash equilibrium had to
+ 
+
+ align:start position:0%
+mixed strategy nash equilibrium had to
+do with the convexity of these best
+
+ align:start position:0%
+do with the convexity of these best
+ 
+
+ align:start position:0%
+do with the convexity of these best
+responses
+
+ align:start position:0%
+responses
+ 
+
+ align:start position:0%
+responses
+as in kakutani for example
+
+ align:start position:0%
+as in kakutani for example
+ 
+
+ align:start position:0%
+as in kakutani for example
+in particular all this stuff okay i'm a
+
+ align:start position:0%
+in particular all this stuff okay i'm a
+ 
+
+ align:start position:0%
+in particular all this stuff okay i'm a
+little worried i'm going to get bogged
+
+ align:start position:0%
+little worried i'm going to get bogged
+ 
+
+ align:start position:0%
+little worried i'm going to get bogged
+down in the weeds but i did want you to
+
+ align:start position:0%
+down in the weeds but i did want you to
+ 
+
+ align:start position:0%
+down in the weeds but i did want you to
+on the other hand
+
+ align:start position:0%
+on the other hand
+ 
+
+ align:start position:0%
+on the other hand
+kind of see the big picture
+
+ align:start position:0%
+kind of see the big picture
+ 
+
+ align:start position:0%
+kind of see the big picture
+so so now we have
+
+ align:start position:0%
+so so now we have
+ 
+
+ align:start position:0%
+so so now we have
+two parts the nash equilibrium for
+
+ align:start position:0%
+two parts the nash equilibrium for
+ 
+
+ align:start position:0%
+two parts the nash equilibrium for
+strategic games and the valrazian
+
+ align:start position:0%
+strategic games and the valrazian
+ 
+
+ align:start position:0%
+strategic games and the valrazian
+equilibria they
+
+ align:start position:0%
+equilibria they
+ 
+
+ align:start position:0%
+equilibria they
+they're all using fixed points
+
+ align:start position:0%
+they're all using fixed points
+ 
+
+ align:start position:0%
+they're all using fixed points
+but the economic problem looks kind of
+
+ align:start position:0%
+but the economic problem looks kind of
+ 
+
+ align:start position:0%
+but the economic problem looks kind of
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+so i finished this lecture off by
+
+ align:start position:0%
+so i finished this lecture off by
+ 
+
+ align:start position:0%
+so i finished this lecture off by
+drawing the connection
+
+ align:start position:0%
+drawing the connection
+ 
+
+ align:start position:0%
+drawing the connection
+like how do you actually set up a market
+
+ align:start position:0%
+like how do you actually set up a market
+ 
+
+ align:start position:0%
+like how do you actually set up a market
+to find a valrayan equilibria
+
+ align:start position:0%
+to find a valrayan equilibria
+ 
+
+ align:start position:0%
+to find a valrayan equilibria
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+we did that with respect to these limit
+
+ align:start position:0%
+we did that with respect to these limit
+ 
+
+ align:start position:0%
+we did that with respect to these limit
+order strategies on the supply and
+
+ align:start position:0%
+order strategies on the supply and
+ 
+
+ align:start position:0%
+order strategies on the supply and
+demand side
+
+ align:start position:0%
+demand side
+ 
+
+ align:start position:0%
+demand side
+and then wrote it down as a game so once
+
+ align:start position:0%
+and then wrote it down as a game so once
+ 
+
+ align:start position:0%
+and then wrote it down as a game so once
+we wrote this down as a game where
+
+ align:start position:0%
+we wrote this down as a game where
+ 
+
+ align:start position:0%
+we wrote this down as a game where
+players decide
+
+ align:start position:0%
+players decide
+ 
+
+ align:start position:0%
+players decide
+what to bid given what others are
+
+ align:start position:0%
+what to bid given what others are
+ 
+
+ align:start position:0%
+what to bid given what others are
+bidding
+
+ align:start position:0%
+bidding
+ 
+
+ align:start position:0%
+bidding
+it is a strategic form game and we
+
+ align:start position:0%
+it is a strategic form game and we
+ 
+
+ align:start position:0%
+it is a strategic form game and we
+characterize the equilibrium turned out
+
+ align:start position:0%
+characterize the equilibrium turned out
+ 
+
+ align:start position:0%
+characterize the equilibrium turned out
+you needed some penalties
+
+ align:start position:0%
+you needed some penalties
+ 
+
+ align:start position:0%
+you needed some penalties
+otherwise
+
+ align:start position:0%
+otherwise
+ 
+
+ align:start position:0%
+otherwise
+they would spend more than they have and
+
+ align:start position:0%
+they would spend more than they have and
+ 
+
+ align:start position:0%
+they would spend more than they have and
+that can't be consistent with
+
+ align:start position:0%
+that can't be consistent with
+ 
+
+ align:start position:0%
+that can't be consistent with
+maximization well it would be
+
+ align:start position:0%
+maximization well it would be
+ 
+
+ align:start position:0%
+maximization well it would be
+maximization but there'd be no limit
+
+ align:start position:0%
+maximization but there'd be no limit
+ 
+
+ align:start position:0%
+maximization but there'd be no limit
+so it would not be consistent with
+
+ align:start position:0%
+so it would not be consistent with
+ 
+
+ align:start position:0%
+so it would not be consistent with
+finding the vol resin equilibria
+
+ align:start position:0%
+finding the vol resin equilibria
+ 
+
+ align:start position:0%
+finding the vol resin equilibria
+so we did have to sort of find the
+
+ align:start position:0%
+so we did have to sort of find the
+ 
+
+ align:start position:0%
+so we did have to sort of find the
+optimal penalty structure in order to
+
+ align:start position:0%
+optimal penalty structure in order to
+ 
+
+ align:start position:0%
+optimal penalty structure in order to
+prove the theorem that any volran
+
+ align:start position:0%
+prove the theorem that any volran
+ 
+
+ align:start position:0%
+prove the theorem that any volran
+equilibrium could be supported as a
+
+ align:start position:0%
+equilibrium could be supported as a
+ 
+
+ align:start position:0%
+equilibrium could be supported as a
+mixed strategy equilibrium in this
+
+ align:start position:0%
+mixed strategy equilibrium in this
+ 
+
+ align:start position:0%
+mixed strategy equilibrium in this
+market gain and the other
+
+ align:start position:0%
+market gain and the other
+ 
+
+ align:start position:0%
+market gain and the other
+direction is also true so that
+
+ align:start position:0%
+direction is also true so that
+ 
+
+ align:start position:0%
+direction is also true so that
+was lecture 17 are there any questions
+
+ align:start position:0%
+was lecture 17 are there any questions
+ 
+
+ align:start position:0%
+was lecture 17 are there any questions
+about what we are doing in lecture 17.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+18 was aggregation
+
+ align:start position:0%
+18 was aggregation
+ 
+
+ align:start position:0%
+18 was aggregation
+and again this is getting more recent so
+
+ align:start position:0%
+and again this is getting more recent so
+ 
+
+ align:start position:0%
+and again this is getting more recent so
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+a little more fresh in your minds
+
+ align:start position:0%
+a little more fresh in your minds
+ 
+
+ align:start position:0%
+a little more fresh in your minds
+we want to do this positive and
+
+ align:start position:0%
+we want to do this positive and
+ 
+
+ align:start position:0%
+we want to do this positive and
+normative
+
+ align:start position:0%
+normative
+ 
+
+ align:start position:0%
+normative
+and i would say the content of this
+
+ align:start position:0%
+and i would say the content of this
+ 
+
+ align:start position:0%
+and i would say the content of this
+lecture is what do we have to assume
+
+ align:start position:0%
+lecture is what do we have to assume
+ 
+
+ align:start position:0%
+lecture is what do we have to assume
+like it or not in order to be in the
+
+ align:start position:0%
+like it or not in order to be in the
+ 
+
+ align:start position:0%
+like it or not in order to be in the
+land of macro where you have a
+
+ align:start position:0%
+land of macro where you have a
+ 
+
+ align:start position:0%
+land of macro where you have a
+representative consumer
+
+ align:start position:0%
+representative consumer
+ 
+
+ align:start position:0%
+representative consumer
+and is usable in the sense that what the
+
+ align:start position:0%
+and is usable in the sense that what the
+ 
+
+ align:start position:0%
+and is usable in the sense that what the
+representative consumer would do which
+
+ align:start position:0%
+representative consumer would do which
+ 
+
+ align:start position:0%
+representative consumer would do which
+from a positive economic standpoint
+
+ align:start position:0%
+from a positive economic standpoint
+ 
+
+ align:start position:0%
+from a positive economic standpoint
+generate aggregate demand as if you had
+
+ align:start position:0%
+generate aggregate demand as if you had
+ 
+
+ align:start position:0%
+generate aggregate demand as if you had
+all the underlying households but you
+
+ align:start position:0%
+all the underlying households but you
+ 
+
+ align:start position:0%
+all the underlying households but you
+don't need to do it you just use the
+
+ align:start position:0%
+don't need to do it you just use the
+ 
+
+ align:start position:0%
+don't need to do it you just use the
+representative consumer so it's a very
+
+ align:start position:0%
+representative consumer so it's a very
+ 
+
+ align:start position:0%
+representative consumer so it's a very
+powerful tool but again for you to
+
+ align:start position:0%
+powerful tool but again for you to
+ 
+
+ align:start position:0%
+powerful tool but again for you to
+decide
+
+ align:start position:0%
+decide
+ 
+
+ align:start position:0%
+decide
+how strong or potentially unrealistic
+
+ align:start position:0%
+how strong or potentially unrealistic
+ 
+
+ align:start position:0%
+how strong or potentially unrealistic
+are the underlying assumption set that
+
+ align:start position:0%
+are the underlying assumption set that
+ 
+
+ align:start position:0%
+are the underlying assumption set that
+allows us to do this
+
+ align:start position:0%
+allows us to do this
+ 
+
+ align:start position:0%
+allows us to do this
+so we reviewed the notion of the
+
+ align:start position:0%
+so we reviewed the notion of the
+ 
+
+ align:start position:0%
+so we reviewed the notion of the
+indirect utility function which is the
+
+ align:start position:0%
+indirect utility function which is the
+ 
+
+ align:start position:0%
+indirect utility function which is the
+maximized utility after solving max
+
+ align:start position:0%
+maximized utility after solving max
+ 
+
+ align:start position:0%
+maximized utility after solving max
+utility subject to budget given the
+
+ align:start position:0%
+utility subject to budget given the
+ 
+
+ align:start position:0%
+utility subject to budget given the
+parameters the price and the wealth of a
+
+ align:start position:0%
+parameters the price and the wealth of a
+ 
+
+ align:start position:0%
+parameters the price and the wealth of a
+household and
+
+ align:start position:0%
+household and
+ 
+
+ align:start position:0%
+household and
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+quickly reviewed some properties of the
+
+ align:start position:0%
+quickly reviewed some properties of the
+ 
+
+ align:start position:0%
+quickly reviewed some properties of the
+indirect utility functions in particular
+
+ align:start position:0%
+indirect utility functions in particular
+ 
+
+ align:start position:0%
+indirect utility functions in particular
+roy's identity which miraculously says
+
+ align:start position:0%
+roy's identity which miraculously says
+ 
+
+ align:start position:0%
+roy's identity which miraculously says
+that if you start differentiating the
+
+ align:start position:0%
+that if you start differentiating the
+ 
+
+ align:start position:0%
+that if you start differentiating the
+indirect utility function with respect
+
+ align:start position:0%
+indirect utility function with respect
+ 
+
+ align:start position:0%
+indirect utility function with respect
+to prices and respect to wealth and
+
+ align:start position:0%
+to prices and respect to wealth and
+ 
+
+ align:start position:0%
+to prices and respect to wealth and
+start taking ratios you'll get the
+
+ align:start position:0%
+start taking ratios you'll get the
+ 
+
+ align:start position:0%
+start taking ratios you'll get the
+underlying demands
+
+ align:start position:0%
+underlying demands
+ 
+
+ align:start position:0%
+underlying demands
+and this was a tool and it's kind of
+
+ align:start position:0%
+and this was a tool and it's kind of
+ 
+
+ align:start position:0%
+and this was a tool and it's kind of
+heavily used again now for the third
+
+ align:start position:0%
+heavily used again now for the third
+ 
+
+ align:start position:0%
+heavily used again now for the third
+time it just came from the lagrangian
+
+ align:start position:0%
+time it just came from the lagrangian
+ 
+
+ align:start position:0%
+time it just came from the lagrangian
+problem for the individual household
+
+ align:start position:0%
+problem for the individual household
+ 
+
+ align:start position:0%
+problem for the individual household
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+roy's identity came from that
+
+ align:start position:0%
+roy's identity came from that
+ 
+
+ align:start position:0%
+roy's identity came from that
+and then we got to gorman which is a
+
+ align:start position:0%
+and then we got to gorman which is a
+ 
+
+ align:start position:0%
+and then we got to gorman which is a
+particular representation of these
+
+ align:start position:0%
+particular representation of these
+ 
+
+ align:start position:0%
+particular representation of these
+indirect utility functions as a function
+
+ align:start position:0%
+indirect utility functions as a function
+ 
+
+ align:start position:0%
+indirect utility functions as a function
+of prices and wealth namely this thing
+
+ align:start position:0%
+of prices and wealth namely this thing
+ 
+
+ align:start position:0%
+of prices and wealth namely this thing
+in six
+
+ align:start position:0%
+in six
+ 
+
+ align:start position:0%
+in six
+so it's separable it has kind of an
+
+ align:start position:0%
+so it's separable it has kind of an
+ 
+
+ align:start position:0%
+so it's separable it has kind of an
+intercept as a function of p
+
+ align:start position:0%
+intercept as a function of p
+ 
+
+ align:start position:0%
+intercept as a function of p
+slope term on wealth as a function of p
+
+ align:start position:0%
+slope term on wealth as a function of p
+ 
+
+ align:start position:0%
+slope term on wealth as a function of p
+i noted that the cobb douglas would
+
+ align:start position:0%
+i noted that the cobb douglas would
+ 
+
+ align:start position:0%
+i noted that the cobb douglas would
+satisfy this we actually did the math
+
+ align:start position:0%
+satisfy this we actually did the math
+ 
+
+ align:start position:0%
+satisfy this we actually did the math
+this math is never very hard to do as
+
+ align:start position:0%
+this math is never very hard to do as
+ 
+
+ align:start position:0%
+this math is never very hard to do as
+long as you remember that when you have
+
+ align:start position:0%
+long as you remember that when you have
+ 
+
+ align:start position:0%
+long as you remember that when you have
+these cobb douglas utility function
+
+ align:start position:0%
+these cobb douglas utility function
+ 
+
+ align:start position:0%
+these cobb douglas utility function
+these coefficients represent expenditure
+
+ align:start position:0%
+these coefficients represent expenditure
+ 
+
+ align:start position:0%
+these coefficients represent expenditure
+shares so p1 times x1
+
+ align:start position:0%
+shares so p1 times x1
+ 
+
+ align:start position:0%
+shares so p1 times x1
+is alpha share of wealth w
+
+ align:start position:0%
+is alpha share of wealth w
+ 
+
+ align:start position:0%
+is alpha share of wealth w
+likewise p2 x2 is one minus alpha share
+
+ align:start position:0%
+likewise p2 x2 is one minus alpha share
+ 
+
+ align:start position:0%
+likewise p2 x2 is one minus alpha share
+of wealth w for the second good
+
+ align:start position:0%
+of wealth w for the second good
+ 
+
+ align:start position:0%
+of wealth w for the second good
+so you can plot them down right away and
+
+ align:start position:0%
+so you can plot them down right away and
+ 
+
+ align:start position:0%
+so you can plot them down right away and
+just substitute into the given utility
+
+ align:start position:0%
+just substitute into the given utility
+ 
+
+ align:start position:0%
+just substitute into the given utility
+function and you end up with this
+
+ align:start position:0%
+function and you end up with this
+ 
+
+ align:start position:0%
+function and you end up with this
+functional form i also noted that
+
+ align:start position:0%
+functional form i also noted that
+ 
+
+ align:start position:0%
+functional form i also noted that
+although
+
+ align:start position:0%
+although
+ 
+
+ align:start position:0%
+although
+this is special
+
+ align:start position:0%
+this is special
+ 
+
+ align:start position:0%
+this is special
+in that the intercepts are zero it also
+
+ align:start position:0%
+in that the intercepts are zero it also
+ 
+
+ align:start position:0%
+in that the intercepts are zero it also
+seemingly assumed that the coefficients
+
+ align:start position:0%
+seemingly assumed that the coefficients
+ 
+
+ align:start position:0%
+seemingly assumed that the coefficients
+b are
+
+ align:start position:0%
+b are
+ 
+
+ align:start position:0%
+b are
+the same but no this was a particular
+
+ align:start position:0%
+the same but no this was a particular
+ 
+
+ align:start position:0%
+the same but no this was a particular
+indirect utility function for a
+
+ align:start position:0%
+indirect utility function for a
+ 
+
+ align:start position:0%
+indirect utility function for a
+household a given household we have to
+
+ align:start position:0%
+household a given household we have to
+ 
+
+ align:start position:0%
+household a given household we have to
+start putting i in the utility function
+
+ align:start position:0%
+start putting i in the utility function
+ 
+
+ align:start position:0%
+start putting i in the utility function
+to to decide and if
+
+ align:start position:0%
+to to decide and if
+ 
+
+ align:start position:0%
+to to decide and if
+if these alphas were different across
+
+ align:start position:0%
+if these alphas were different across
+ 
+
+ align:start position:0%
+if these alphas were different across
+different households we would need an
+
+ align:start position:0%
+different households we would need an
+ 
+
+ align:start position:0%
+different households we would need an
+alpha i on them and then this thing the
+
+ align:start position:0%
+alpha i on them and then this thing the
+ 
+
+ align:start position:0%
+alpha i on them and then this thing the
+gorman form would be violated
+
+ align:start position:0%
+gorman form would be violated
+ 
+
+ align:start position:0%
+gorman form would be violated
+so the first part of the positive
+
+ align:start position:0%
+so the first part of the positive
+ 
+
+ align:start position:0%
+so the first part of the positive
+representative consumer was just saying
+
+ align:start position:0%
+representative consumer was just saying
+ 
+
+ align:start position:0%
+representative consumer was just saying
+a definition of aggregate demand namely
+
+ align:start position:0%
+a definition of aggregate demand namely
+ 
+
+ align:start position:0%
+a definition of aggregate demand namely
+it's the sum of the demands over all the
+
+ align:start position:0%
+it's the sum of the demands over all the
+ 
+
+ align:start position:0%
+it's the sum of the demands over all the
+individual households at price vector p
+
+ align:start position:0%
+individual households at price vector p
+ 
+
+ align:start position:0%
+individual households at price vector p
+in wealth wi
+
+ align:start position:0%
+in wealth wi
+ 
+
+ align:start position:0%
+in wealth wi
+and the gorman part
+
+ align:start position:0%
+and the gorman part
+ 
+
+ align:start position:0%
+and the gorman part
+is to find
+
+ align:start position:0%
+is to find
+ 
+
+ align:start position:0%
+is to find
+that that demand
+
+ align:start position:0%
+that that demand
+ 
+
+ align:start position:0%
+that that demand
+this guy here
+
+ align:start position:0%
+this guy here
+ 
+
+ align:start position:0%
+this guy here
+depends on the vector of wealth in a
+
+ align:start position:0%
+depends on the vector of wealth in a
+ 
+
+ align:start position:0%
+depends on the vector of wealth in a
+particular way namely it's just the sum
+
+ align:start position:0%
+particular way namely it's just the sum
+ 
+
+ align:start position:0%
+particular way namely it's just the sum
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+or in other words it's enough
+
+ align:start position:0%
+or in other words it's enough
+ 
+
+ align:start position:0%
+or in other words it's enough
+we should be able to find
+
+ align:start position:0%
+we should be able to find
+ 
+
+ align:start position:0%
+we should be able to find
+a utility function
+
+ align:start position:0%
+a utility function
+ 
+
+ align:start position:0%
+a utility function
+and give this mythical representative
+
+ align:start position:0%
+and give this mythical representative
+ 
+
+ align:start position:0%
+and give this mythical representative
+household all the wealth in the economy
+
+ align:start position:0%
+household all the wealth in the economy
+ 
+
+ align:start position:0%
+household all the wealth in the economy
+and have that
+
+ align:start position:0%
+and have that
+ 
+
+ align:start position:0%
+and have that
+household maximize utility
+
+ align:start position:0%
+household maximize utility
+ 
+
+ align:start position:0%
+household maximize utility
+generating aggregate demand which would
+
+ align:start position:0%
+generating aggregate demand which would
+ 
+
+ align:start position:0%
+generating aggregate demand which would
+be the sum of the individual demands if
+
+ align:start position:0%
+be the sum of the individual demands if
+ 
+
+ align:start position:0%
+be the sum of the individual demands if
+we'd bothered to keep track of the micro
+
+ align:start position:0%
+we'd bothered to keep track of the micro
+ 
+
+ align:start position:0%
+we'd bothered to keep track of the micro
+economy and the individual wealth levels
+
+ align:start position:0%
+economy and the individual wealth levels
+ 
+
+ align:start position:0%
+economy and the individual wealth levels
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this statement was necessary but
+
+ align:start position:0%
+this statement was necessary but
+ 
+
+ align:start position:0%
+this statement was necessary but
+but it's about to be sufficient
+
+ align:start position:0%
+but it's about to be sufficient
+ 
+
+ align:start position:0%
+but it's about to be sufficient
+if the individual households have this
+
+ align:start position:0%
+if the individual households have this
+ 
+
+ align:start position:0%
+if the individual households have this
+particular indirect utility function of
+
+ align:start position:0%
+particular indirect utility function of
+ 
+
+ align:start position:0%
+particular indirect utility function of
+the gorman forum
+
+ align:start position:0%
+the gorman forum
+ 
+
+ align:start position:0%
+the gorman forum
+with the i only on the a
+
+ align:start position:0%
+with the i only on the a
+ 
+
+ align:start position:0%
+with the i only on the a
+intercept piece
+
+ align:start position:0%
+intercept piece
+ 
+
+ align:start position:0%
+intercept piece
+although w depends on i but that's
+
+ align:start position:0%
+although w depends on i but that's
+ 
+
+ align:start position:0%
+although w depends on i but that's
+because it's individual households
+
+ align:start position:0%
+because it's individual households
+ 
+
+ align:start position:0%
+because it's individual households
+wealth
+
+ align:start position:0%
+wealth
+ 
+
+ align:start position:0%
+wealth
+then the utility function we're looking
+
+ align:start position:0%
+then the utility function we're looking
+ 
+
+ align:start position:0%
+then the utility function we're looking
+for is just going to be an aggregated
+
+ align:start position:0%
+for is just going to be an aggregated
+ 
+
+ align:start position:0%
+for is just going to be an aggregated
+version
+
+ align:start position:0%
+version
+ 
+
+ align:start position:0%
+version
+sort of aggregating up the intercept
+
+ align:start position:0%
+sort of aggregating up the intercept
+ 
+
+ align:start position:0%
+sort of aggregating up the intercept
+terms
+
+ align:start position:0%
+terms
+ 
+
+ align:start position:0%
+terms
+and imposing the same coefficient
+
+ align:start position:0%
+and imposing the same coefficient
+ 
+
+ align:start position:0%
+and imposing the same coefficient
+on the wealth
+
+ align:start position:0%
+on the wealth
+ 
+
+ align:start position:0%
+on the wealth
+across all the households
+
+ align:start position:0%
+across all the households
+ 
+
+ align:start position:0%
+across all the households
+now do you like it or not
+
+ align:start position:0%
+now do you like it or not
+ 
+
+ align:start position:0%
+now do you like it or not
+you know it is going to require that we
+
+ align:start position:0%
+you know it is going to require that we
+ 
+
+ align:start position:0%
+you know it is going to require that we
+have these linear expansion paths if we
+
+ align:start position:0%
+have these linear expansion paths if we
+ 
+
+ align:start position:0%
+have these linear expansion paths if we
+go back to the micro economy and see how
+
+ align:start position:0%
+go back to the micro economy and see how
+ 
+
+ align:start position:0%
+go back to the micro economy and see how
+they're behaving that giving wealth to
+
+ align:start position:0%
+they're behaving that giving wealth to
+ 
+
+ align:start position:0%
+they're behaving that giving wealth to
+one guy would increase utility and
+
+ align:start position:0%
+one guy would increase utility and
+ 
+
+ align:start position:0%
+one guy would increase utility and
+consumption
+
+ align:start position:0%
+consumption
+ 
+
+ align:start position:0%
+consumption
+in exactly the same way that consumption
+
+ align:start position:0%
+in exactly the same way that consumption
+ 
+
+ align:start position:0%
+in exactly the same way that consumption
+would be decreased for the other one so
+
+ align:start position:0%
+would be decreased for the other one so
+ 
+
+ align:start position:0%
+would be decreased for the other one so
+moving wealth around because the slopes
+
+ align:start position:0%
+moving wealth around because the slopes
+ 
+
+ align:start position:0%
+moving wealth around because the slopes
+of these lines are the same they're
+
+ align:start position:0%
+of these lines are the same they're
+ 
+
+ align:start position:0%
+of these lines are the same they're
+parallel lines moving wealth around has
+
+ align:start position:0%
+parallel lines moving wealth around has
+ 
+
+ align:start position:0%
+parallel lines moving wealth around has
+no effect on aggregate demand it's just
+
+ align:start position:0%
+no effect on aggregate demand it's just
+ 
+
+ align:start position:0%
+no effect on aggregate demand it's just
+a restatement of the positive part of
+
+ align:start position:0%
+a restatement of the positive part of
+ 
+
+ align:start position:0%
+a restatement of the positive part of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+representative consumer
+
+ align:start position:0%
+representative consumer
+ 
+
+ align:start position:0%
+representative consumer
+if you're listening to macro economists
+
+ align:start position:0%
+if you're listening to macro economists
+ 
+
+ align:start position:0%
+if you're listening to macro economists
+worried a lot about marginal propensity
+
+ align:start position:0%
+worried a lot about marginal propensity
+ 
+
+ align:start position:0%
+worried a lot about marginal propensity
+to consume out of wealth and out of
+
+ align:start position:0%
+to consume out of wealth and out of
+ 
+
+ align:start position:0%
+to consume out of wealth and out of
+transfers you know they're trying to
+
+ align:start position:0%
+transfers you know they're trying to
+ 
+
+ align:start position:0%
+transfers you know they're trying to
+find transfers to particular constrained
+
+ align:start position:0%
+find transfers to particular constrained
+ 
+
+ align:start position:0%
+find transfers to particular constrained
+households in a way that they would eat
+
+ align:start position:0%
+households in a way that they would eat
+ 
+
+ align:start position:0%
+households in a way that they would eat
+a lot as if there was a special virtue
+
+ align:start position:0%
+a lot as if there was a special virtue
+ 
+
+ align:start position:0%
+a lot as if there was a special virtue
+of pumping up aggregate demand well they
+
+ align:start position:0%
+of pumping up aggregate demand well they
+ 
+
+ align:start position:0%
+of pumping up aggregate demand well they
+don't have gorman in mind because
+
+ align:start position:0%
+don't have gorman in mind because
+ 
+
+ align:start position:0%
+don't have gorman in mind because
+aggregate demand is not determined by
+
+ align:start position:0%
+aggregate demand is not determined by
+ 
+
+ align:start position:0%
+aggregate demand is not determined by
+the distribution of wealth under gorman
+
+ align:start position:0%
+the distribution of wealth under gorman
+ 
+
+ align:start position:0%
+the distribution of wealth under gorman
+it's determined by the aggregate wealth
+
+ align:start position:0%
+it's determined by the aggregate wealth
+ 
+
+ align:start position:0%
+it's determined by the aggregate wealth
+so it wouldn't matter who you gave the
+
+ align:start position:0%
+so it wouldn't matter who you gave the
+ 
+
+ align:start position:0%
+so it wouldn't matter who you gave the
+money to if it were gorman world
+
+ align:start position:0%
+money to if it were gorman world
+ 
+
+ align:start position:0%
+money to if it were gorman world
+positive representative consumer
+
+ align:start position:0%
+positive representative consumer
+ 
+
+ align:start position:0%
+positive representative consumer
+the proof of it i'm not going to go
+
+ align:start position:0%
+the proof of it i'm not going to go
+ 
+
+ align:start position:0%
+the proof of it i'm not going to go
+through
+
+ align:start position:0%
+through
+ 
+
+ align:start position:0%
+through
+it's basically using roy's identity over
+
+ align:start position:0%
+it's basically using roy's identity over
+ 
+
+ align:start position:0%
+it's basically using roy's identity over
+and over again
+
+ align:start position:0%
+and over again
+ 
+
+ align:start position:0%
+and over again
+and exploiting the linearity
+
+ align:start position:0%
+and exploiting the linearity
+ 
+
+ align:start position:0%
+and exploiting the linearity
+adding up and then taking you know
+
+ align:start position:0%
+adding up and then taking you know
+ 
+
+ align:start position:0%
+adding up and then taking you know
+taking it back down
+
+ align:start position:0%
+taking it back down
+ 
+
+ align:start position:0%
+taking it back down
+these are examples of gorman aggregate
+
+ align:start position:0%
+these are examples of gorman aggregate
+ 
+
+ align:start position:0%
+these are examples of gorman aggregate
+preferences
+
+ align:start position:0%
+preferences
+ 
+
+ align:start position:0%
+preferences
+allowing variation in the intercepts so
+
+ align:start position:0%
+allowing variation in the intercepts so
+ 
+
+ align:start position:0%
+allowing variation in the intercepts so
+households do not have to be all alike
+
+ align:start position:0%
+households do not have to be all alike
+ 
+
+ align:start position:0%
+households do not have to be all alike
+and the normative household
+
+ align:start position:0%
+and the normative household
+ 
+
+ align:start position:0%
+and the normative household
+normative in addition to being positive
+
+ align:start position:0%
+normative in addition to being positive
+ 
+
+ align:start position:0%
+normative in addition to being positive
+is another definition
+
+ align:start position:0%
+is another definition
+ 
+
+ align:start position:0%
+is another definition
+namely
+
+ align:start position:0%
+namely
+ 
+
+ align:start position:0%
+namely
+we're looking we have the underlying
+
+ align:start position:0%
+we're looking we have the underlying
+ 
+
+ align:start position:0%
+we're looking we have the underlying
+micro economy with a heterogeneity
+
+ align:start position:0%
+micro economy with a heterogeneity
+ 
+
+ align:start position:0%
+micro economy with a heterogeneity
+across all the households
+
+ align:start position:0%
+across all the households
+ 
+
+ align:start position:0%
+across all the households
+we're looking for this fictitious
+
+ align:start position:0%
+we're looking for this fictitious
+ 
+
+ align:start position:0%
+we're looking for this fictitious
+utility function u star
+
+ align:start position:0%
+utility function u star
+ 
+
+ align:start position:0%
+utility function u star
+which we
+
+ align:start position:0%
+which we
+ 
+
+ align:start position:0%
+which we
+label the utility function of the
+
+ align:start position:0%
+label the utility function of the
+ 
+
+ align:start position:0%
+label the utility function of the
+normative representative household
+
+ align:start position:0%
+normative representative household
+ 
+
+ align:start position:0%
+normative representative household
+to satisfy two properties namely
+
+ align:start position:0%
+to satisfy two properties namely
+ 
+
+ align:start position:0%
+to satisfy two properties namely
+if we want to see if something x and y
+
+ align:start position:0%
+if we want to see if something x and y
+ 
+
+ align:start position:0%
+if we want to see if something x and y
+is pareto optimal then
+
+ align:start position:0%
+is pareto optimal then
+ 
+
+ align:start position:0%
+is pareto optimal then
+we can search for alternative
+
+ align:start position:0%
+we can search for alternative
+ 
+
+ align:start position:0%
+we can search for alternative
+allocations in parade or dominate
+
+ align:start position:0%
+allocations in parade or dominate
+ 
+
+ align:start position:0%
+allocations in parade or dominate
+in the normal micro land of all these
+
+ align:start position:0%
+in the normal micro land of all these
+ 
+
+ align:start position:0%
+in the normal micro land of all these
+different households you have to check
+
+ align:start position:0%
+different households you have to check
+ 
+
+ align:start position:0%
+different households you have to check
+out each and every one to see if they're
+
+ align:start position:0%
+out each and every one to see if they're
+ 
+
+ align:start position:0%
+out each and every one to see if they're
+better off
+
+ align:start position:0%
+better off
+ 
+
+ align:start position:0%
+better off
+under the proposed alternative
+
+ align:start position:0%
+under the proposed alternative
+ 
+
+ align:start position:0%
+under the proposed alternative
+with gorman
+
+ align:start position:0%
+with gorman
+ 
+
+ align:start position:0%
+with gorman
+normative you don't have to do that you
+
+ align:start position:0%
+normative you don't have to do that you
+ 
+
+ align:start position:0%
+normative you don't have to do that you
+just sum up all the demands in the
+
+ align:start position:0%
+just sum up all the demands in the
+ 
+
+ align:start position:0%
+just sum up all the demands in the
+baseline
+
+ align:start position:0%
+baseline
+ 
+
+ align:start position:0%
+baseline
+and in the alternative
+
+ align:start position:0%
+and in the alternative
+ 
+
+ align:start position:0%
+and in the alternative
+and evaluate that sum under this
+
+ align:start position:0%
+and evaluate that sum under this
+ 
+
+ align:start position:0%
+and evaluate that sum under this
+mythical utility function u star
+
+ align:start position:0%
+mythical utility function u star
+ 
+
+ align:start position:0%
+mythical utility function u star
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+if something creator dominates then it
+
+ align:start position:0%
+if something creator dominates then it
+ 
+
+ align:start position:0%
+if something creator dominates then it
+has to have a higher return under ustar
+
+ align:start position:0%
+has to have a higher return under ustar
+ 
+
+ align:start position:0%
+has to have a higher return under ustar
+so that makes the search a whole lot
+
+ align:start position:0%
+so that makes the search a whole lot
+ 
+
+ align:start position:0%
+so that makes the search a whole lot
+easier
+
+ align:start position:0%
+easier
+ 
+
+ align:start position:0%
+easier
+and the flip side is the same
+
+ align:start position:0%
+and the flip side is the same
+ 
+
+ align:start position:0%
+and the flip side is the same
+with an important caveat
+
+ align:start position:0%
+with an important caveat
+ 
+
+ align:start position:0%
+with an important caveat
+you start with a baseline and you find a
+
+ align:start position:0%
+you start with a baseline and you find a
+ 
+
+ align:start position:0%
+you start with a baseline and you find a
+prime allocation
+
+ align:start position:0%
+prime allocation
+ 
+
+ align:start position:0%
+prime allocation
+which is dominant under u star after you
+
+ align:start position:0%
+which is dominant under u star after you
+ 
+
+ align:start position:0%
+which is dominant under u star after you
+sum up then we should be able to do
+
+ align:start position:0%
+sum up then we should be able to do
+ 
+
+ align:start position:0%
+sum up then we should be able to do
+better so there there is a way in the
+
+ align:start position:0%
+better so there there is a way in the
+ 
+
+ align:start position:0%
+better so there there is a way in the
+micro space
+
+ align:start position:0%
+micro space
+ 
+
+ align:start position:0%
+micro space
+to assign
+
+ align:start position:0%
+to assign
+ 
+
+ align:start position:0%
+to assign
+allocations
+
+ align:start position:0%
+allocations
+ 
+
+ align:start position:0%
+allocations
+that add up to the prime bundle but are
+
+ align:start position:0%
+that add up to the prime bundle but are
+ 
+
+ align:start position:0%
+that add up to the prime bundle but are
+not necessarily the actual prime
+
+ align:start position:0%
+not necessarily the actual prime
+ 
+
+ align:start position:0%
+not necessarily the actual prime
+allocation a way to do that in such a
+
+ align:start position:0%
+allocation a way to do that in such a
+ 
+
+ align:start position:0%
+allocation a way to do that in such a
+way that everyone is at least as well
+
+ align:start position:0%
+way that everyone is at least as well
+ 
+
+ align:start position:0%
+way that everyone is at least as well
+off and some people are better off
+
+ align:start position:0%
+off and some people are better off
+ 
+
+ align:start position:0%
+off and some people are better off
+so the point of this is
+
+ align:start position:0%
+so the point of this is
+ 
+
+ align:start position:0%
+so the point of this is
+it's very strong when it works it's a
+
+ align:start position:0%
+it's very strong when it works it's a
+ 
+
+ align:start position:0%
+it's very strong when it works it's a
+way of evaluating allocations but is it
+
+ align:start position:0%
+way of evaluating allocations but is it
+ 
+
+ align:start position:0%
+way of evaluating allocations but is it
+is not to say that you don't have to
+
+ align:start position:0%
+is not to say that you don't have to
+ 
+
+ align:start position:0%
+is not to say that you don't have to
+worry about the distribution
+
+ align:start position:0%
+worry about the distribution
+ 
+
+ align:start position:0%
+worry about the distribution
+you could make people better off as i've
+
+ align:start position:0%
+you could make people better off as i've
+ 
+
+ align:start position:0%
+you could make people better off as i've
+said before i think when i gave this
+
+ align:start position:0%
+said before i think when i gave this
+ 
+
+ align:start position:0%
+said before i think when i gave this
+lecture free trade could make everyone
+
+ align:start position:0%
+lecture free trade could make everyone
+ 
+
+ align:start position:0%
+lecture free trade could make everyone
+better off but you shouldn't stop there
+
+ align:start position:0%
+better off but you shouldn't stop there
+ 
+
+ align:start position:0%
+better off but you shouldn't stop there
+because even under gorman you have to
+
+ align:start position:0%
+because even under gorman you have to
+ 
+
+ align:start position:0%
+because even under gorman you have to
+redistribute
+
+ align:start position:0%
+redistribute
+ 
+
+ align:start position:0%
+redistribute
+wealth in such a way as to to let it
+
+ align:start position:0%
+wealth in such a way as to to let it
+ 
+
+ align:start position:0%
+wealth in such a way as to to let it
+pareto dominate the
+
+ align:start position:0%
+pareto dominate the
+ 
+
+ align:start position:0%
+pareto dominate the
+tariff equilibrium
+
+ align:start position:0%
+tariff equilibrium
+ 
+
+ align:start position:0%
+tariff equilibrium
+maybe that's a lesson that trait
+
+ align:start position:0%
+maybe that's a lesson that trait
+ 
+
+ align:start position:0%
+maybe that's a lesson that trait
+theorists kind of forgot to emphasize
+
+ align:start position:0%
+theorists kind of forgot to emphasize
+ 
+
+ align:start position:0%
+theorists kind of forgot to emphasize
+so we did this in
+
+ align:start position:0%
+so we did this in
+ 
+
+ align:start position:0%
+so we did this in
+we actually did the proof in the space
+
+ align:start position:0%
+we actually did the proof in the space
+ 
+
+ align:start position:0%
+we actually did the proof in the space
+of indirect utilities and again i don't
+
+ align:start position:0%
+of indirect utilities and again i don't
+ 
+
+ align:start position:0%
+of indirect utilities and again i don't
+want to
+
+ align:start position:0%
+want to
+ 
+
+ align:start position:0%
+want to
+go through that too much
+
+ align:start position:0%
+go through that too much
+ 
+
+ align:start position:0%
+go through that too much
+so at the end we have the application of
+
+ align:start position:0%
+so at the end we have the application of
+ 
+
+ align:start position:0%
+so at the end we have the application of
+those positive and normative
+
+ align:start position:0%
+those positive and normative
+ 
+
+ align:start position:0%
+those positive and normative
+representative consumers to this slide
+
+ align:start position:0%
+representative consumers to this slide
+ 
+
+ align:start position:0%
+representative consumers to this slide
+this is the third time that i've shown
+
+ align:start position:0%
+this is the third time that i've shown
+ 
+
+ align:start position:0%
+this is the third time that i've shown
+you this economy
+
+ align:start position:0%
+you this economy
+ 
+
+ align:start position:0%
+you this economy
+and at least maybe the third time we
+
+ align:start position:0%
+and at least maybe the third time we
+ 
+
+ align:start position:0%
+and at least maybe the third time we
+talked about the pareto problem in this
+
+ align:start position:0%
+talked about the pareto problem in this
+ 
+
+ align:start position:0%
+talked about the pareto problem in this
+economy this pareto problem of course
+
+ align:start position:0%
+economy this pareto problem of course
+ 
+
+ align:start position:0%
+economy this pareto problem of course
+has the lambda weights as well it should
+
+ align:start position:0%
+has the lambda weights as well it should
+ 
+
+ align:start position:0%
+has the lambda weights as well it should
+but if we have a positive and normative
+
+ align:start position:0%
+but if we have a positive and normative
+ 
+
+ align:start position:0%
+but if we have a positive and normative
+representative consumer
+
+ align:start position:0%
+representative consumer
+ 
+
+ align:start position:0%
+representative consumer
+then amazingly we can drop the pareto
+
+ align:start position:0%
+then amazingly we can drop the pareto
+ 
+
+ align:start position:0%
+then amazingly we can drop the pareto
+weights and just maximize u-star
+
+ align:start position:0%
+weights and just maximize u-star
+ 
+
+ align:start position:0%
+weights and just maximize u-star
+so it's as if there's a single
+
+ align:start position:0%
+so it's as if there's a single
+ 
+
+ align:start position:0%
+so it's as if there's a single
+representative consumer with an
+
+ align:start position:0%
+representative consumer with an
+ 
+
+ align:start position:0%
+representative consumer with an
+aggregated production technology like
+
+ align:start position:0%
+aggregated production technology like
+ 
+
+ align:start position:0%
+aggregated production technology like
+robinson crusoe and this is a much much
+
+ align:start position:0%
+robinson crusoe and this is a much much
+ 
+
+ align:start position:0%
+robinson crusoe and this is a much much
+easier problem to solve hence the power
+
+ align:start position:0%
+easier problem to solve hence the power
+ 
+
+ align:start position:0%
+easier problem to solve hence the power
+of it for macro
+
+ align:start position:0%
+of it for macro
+ 
+
+ align:start position:0%
+of it for macro
+because we're solving it in the space of
+
+ align:start position:0%
+because we're solving it in the space of
+ 
+
+ align:start position:0%
+because we're solving it in the space of
+macros and again typically people forget
+
+ align:start position:0%
+macros and again typically people forget
+ 
+
+ align:start position:0%
+macros and again typically people forget
+to think about the underlying
+
+ align:start position:0%
+to think about the underlying
+ 
+
+ align:start position:0%
+to think about the underlying
+distribution and the underlying wealth
+
+ align:start position:0%
+distribution and the underlying wealth
+ 
+
+ align:start position:0%
+distribution and the underlying wealth
+distribution of welfare gains
+
+ align:start position:0%
+distribution of welfare gains
+ 
+
+ align:start position:0%
+distribution of welfare gains
+that and maybe even losses to sort of
+
+ align:start position:0%
+that and maybe even losses to sort of
+ 
+
+ align:start position:0%
+that and maybe even losses to sort of
+stick with the aggregates
+
+ align:start position:0%
+stick with the aggregates
+ 
+
+ align:start position:0%
+stick with the aggregates
+so are there any questions about lecture
+
+ align:start position:0%
+so are there any questions about lecture
+ 
+
+ align:start position:0%
+so are there any questions about lecture
+18.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+19 went the other direction and i paired
+
+ align:start position:0%
+19 went the other direction and i paired
+ 
+
+ align:start position:0%
+19 went the other direction and i paired
+them deliberately
+
+ align:start position:0%
+them deliberately
+ 
+
+ align:start position:0%
+them deliberately
+instead of saying look at all the
+
+ align:start position:0%
+instead of saying look at all the
+ 
+
+ align:start position:0%
+instead of saying look at all the
+special things you can do if you assume
+
+ align:start position:0%
+special things you can do if you assume
+ 
+
+ align:start position:0%
+special things you can do if you assume
+special structure like linear income
+
+ align:start position:0%
+special structure like linear income
+ 
+
+ align:start position:0%
+special structure like linear income
+expansion pass
+
+ align:start position:0%
+expansion pass
+ 
+
+ align:start position:0%
+expansion pass
+let's try to avoid any restrictions
+
+ align:start position:0%
+let's try to avoid any restrictions
+ 
+
+ align:start position:0%
+let's try to avoid any restrictions
+whatsoever on utility and production
+
+ align:start position:0%
+whatsoever on utility and production
+ 
+
+ align:start position:0%
+whatsoever on utility and production
+sets and so on and still see whether
+
+ align:start position:0%
+sets and so on and still see whether
+ 
+
+ align:start position:0%
+sets and so on and still see whether
+we can say anything at all
+
+ align:start position:0%
+we can say anything at all
+ 
+
+ align:start position:0%
+we can say anything at all
+so the spirit of this is very different
+
+ align:start position:0%
+so the spirit of this is very different
+ 
+
+ align:start position:0%
+so the spirit of this is very different
+from the previous lecture this is about
+
+ align:start position:0%
+from the previous lecture this is about
+ 
+
+ align:start position:0%
+from the previous lecture this is about
+not assuming gorman aggregation we're
+
+ align:start position:0%
+not assuming gorman aggregation we're
+ 
+
+ align:start position:0%
+not assuming gorman aggregation we're
+not even assuming
+
+ align:start position:0%
+not even assuming
+ 
+
+ align:start position:0%
+not even assuming
+anything much at all about expansion
+
+ align:start position:0%
+anything much at all about expansion
+ 
+
+ align:start position:0%
+anything much at all about expansion
+paths
+
+ align:start position:0%
+paths
+ 
+
+ align:start position:0%
+paths
+could have gift and goods
+
+ align:start position:0%
+could have gift and goods
+ 
+
+ align:start position:0%
+could have gift and goods
+what can what if anything can we say or
+
+ align:start position:0%
+what can what if anything can we say or
+ 
+
+ align:start position:0%
+what can what if anything can we say or
+given data can we just always accept
+
+ align:start position:0%
+given data can we just always accept
+ 
+
+ align:start position:0%
+given data can we just always accept
+that there's an economy that would have
+
+ align:start position:0%
+that there's an economy that would have
+ 
+
+ align:start position:0%
+that there's an economy that would have
+generated the data
+
+ align:start position:0%
+generated the data
+ 
+
+ align:start position:0%
+generated the data
+and we've talked about this
+
+ align:start position:0%
+and we've talked about this
+ 
+
+ align:start position:0%
+and we've talked about this
+at the beginning of the following class
+
+ align:start position:0%
+at the beginning of the following class
+ 
+
+ align:start position:0%
+at the beginning of the following class
+so we want to put as little structure as
+
+ align:start position:0%
+so we want to put as little structure as
+ 
+
+ align:start position:0%
+so we want to put as little structure as
+possible and we did this
+
+ align:start position:0%
+possible and we did this
+ 
+
+ align:start position:0%
+possible and we did this
+a couple of ways with an infinite amount
+
+ align:start position:0%
+a couple of ways with an infinite amount
+ 
+
+ align:start position:0%
+a couple of ways with an infinite amount
+of data with a finite amount of data we
+
+ align:start position:0%
+of data with a finite amount of data we
+ 
+
+ align:start position:0%
+of data with a finite amount of data we
+did it in partial equilibrium under
+
+ align:start position:0%
+did it in partial equilibrium under
+ 
+
+ align:start position:0%
+did it in partial equilibrium under
+consumer choice and then we made some
+
+ align:start position:0%
+consumer choice and then we made some
+ 
+
+ align:start position:0%
+consumer choice and then we made some
+connections to
+
+ align:start position:0%
+connections to
+ 
+
+ align:start position:0%
+connections to
+to general equilibrium theory
+
+ align:start position:0%
+to general equilibrium theory
+ 
+
+ align:start position:0%
+to general equilibrium theory
+the slotsky thing
+
+ align:start position:0%
+the slotsky thing
+ 
+
+ align:start position:0%
+the slotsky thing
+came from a property namely that we
+
+ align:start position:0%
+came from a property namely that we
+ 
+
+ align:start position:0%
+came from a property namely that we
+minimized the expenditure necessary to
+
+ align:start position:0%
+minimized the expenditure necessary to
+ 
+
+ align:start position:0%
+minimized the expenditure necessary to
+achieve a certain level of utility
+
+ align:start position:0%
+achieve a certain level of utility
+ 
+
+ align:start position:0%
+achieve a certain level of utility
+that expenditure function is concave
+
+ align:start position:0%
+that expenditure function is concave
+ 
+
+ align:start position:0%
+that expenditure function is concave
+and then the derivative of the
+
+ align:start position:0%
+and then the derivative of the
+ 
+
+ align:start position:0%
+and then the derivative of the
+expenditure function
+
+ align:start position:0%
+expenditure function
+ 
+
+ align:start position:0%
+expenditure function
+a bit like roy's identity not quite is
+
+ align:start position:0%
+a bit like roy's identity not quite is
+ 
+
+ align:start position:0%
+a bit like roy's identity not quite is
+the hixing demands
+
+ align:start position:0%
+the hixing demands
+ 
+
+ align:start position:0%
+the hixing demands
+so the second derivative of the
+
+ align:start position:0%
+so the second derivative of the
+ 
+
+ align:start position:0%
+so the second derivative of the
+expenditure function a matrix really
+
+ align:start position:0%
+expenditure function a matrix really
+ 
+
+ align:start position:0%
+expenditure function a matrix really
+across partial derivatives has to be
+
+ align:start position:0%
+across partial derivatives has to be
+ 
+
+ align:start position:0%
+across partial derivatives has to be
+symmetric and negative semi-definite
+
+ align:start position:0%
+symmetric and negative semi-definite
+ 
+
+ align:start position:0%
+symmetric and negative semi-definite
+this statement is what led to the
+
+ align:start position:0%
+this statement is what led to the
+ 
+
+ align:start position:0%
+this statement is what led to the
+slutsky equation this is a version of
+
+ align:start position:0%
+slutsky equation this is a version of
+ 
+
+ align:start position:0%
+slutsky equation this is a version of
+that equation i guess for the purposes
+
+ align:start position:0%
+that equation i guess for the purposes
+ 
+
+ align:start position:0%
+that equation i guess for the purposes
+of the lecture in terms of
+
+ align:start position:0%
+of the lecture in terms of
+ 
+
+ align:start position:0%
+of the lecture in terms of
+what's the point of it all one is we get
+
+ align:start position:0%
+what's the point of it all one is we get
+ 
+
+ align:start position:0%
+what's the point of it all one is we get
+restrictions from the data
+
+ align:start position:0%
+restrictions from the data
+ 
+
+ align:start position:0%
+restrictions from the data
+assuming preferences are
+
+ align:start position:0%
+assuming preferences are
+ 
+
+ align:start position:0%
+assuming preferences are
+regular
+
+ align:start position:0%
+regular
+ 
+
+ align:start position:0%
+regular
+we get restrictions on
+
+ align:start position:0%
+we get restrictions on
+ 
+
+ align:start position:0%
+we get restrictions on
+something we never see
+
+ align:start position:0%
+something we never see
+ 
+
+ align:start position:0%
+something we never see
+namely these compensated hixi and demand
+
+ align:start position:0%
+namely these compensated hixi and demand
+ 
+
+ align:start position:0%
+namely these compensated hixi and demand
+functions as i think we went through in
+
+ align:start position:0%
+functions as i think we went through in
+ 
+
+ align:start position:0%
+functions as i think we went through in
+lecture three
+
+ align:start position:0%
+lecture three
+ 
+
+ align:start position:0%
+lecture three
+but fortunately we're able to write out
+
+ align:start position:0%
+but fortunately we're able to write out
+ 
+
+ align:start position:0%
+but fortunately we're able to write out
+the left-hand side
+
+ align:start position:0%
+the left-hand side
+ 
+
+ align:start position:0%
+the left-hand side
+the slutsky derivative cross-partial
+
+ align:start position:0%
+the slutsky derivative cross-partial
+ 
+
+ align:start position:0%
+the slutsky derivative cross-partial
+derivatives in terms of observables on
+
+ align:start position:0%
+derivatives in terms of observables on
+ 
+
+ align:start position:0%
+derivatives in terms of observables on
+the right-hand side which are directly
+
+ align:start position:0%
+the right-hand side which are directly
+ 
+
+ align:start position:0%
+the right-hand side which are directly
+from the consumer's optimization problem
+
+ align:start position:0%
+from the consumer's optimization problem
+ 
+
+ align:start position:0%
+from the consumer's optimization problem
+how demand changes with prices
+
+ align:start position:0%
+how demand changes with prices
+ 
+
+ align:start position:0%
+how demand changes with prices
+how demands change with wealth and of
+
+ align:start position:0%
+how demands change with wealth and of
+ 
+
+ align:start position:0%
+how demands change with wealth and of
+course we would be observing the actual
+
+ align:start position:0%
+course we would be observing the actual
+ 
+
+ align:start position:0%
+course we would be observing the actual
+allocations this is with infinite data
+
+ align:start position:0%
+allocations this is with infinite data
+ 
+
+ align:start position:0%
+allocations this is with infinite data
+so again we're allowed conceptually to
+
+ align:start position:0%
+so again we're allowed conceptually to
+ 
+
+ align:start position:0%
+so again we're allowed conceptually to
+think about
+
+ align:start position:0%
+think about
+ 
+
+ align:start position:0%
+think about
+having all these derivatives
+
+ align:start position:0%
+having all these derivatives
+ 
+
+ align:start position:0%
+having all these derivatives
+for infinite testimony small changes
+
+ align:start position:0%
+for infinite testimony small changes
+ 
+
+ align:start position:0%
+for infinite testimony small changes
+available to us
+
+ align:start position:0%
+available to us
+ 
+
+ align:start position:0%
+available to us
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+as i went through in class from lecture
+
+ align:start position:0%
+as i went through in class from lecture
+ 
+
+ align:start position:0%
+as i went through in class from lecture
+three
+
+ align:start position:0%
+three
+ 
+
+ align:start position:0%
+three
+when we did the income and substitution
+
+ align:start position:0%
+when we did the income and substitution
+ 
+
+ align:start position:0%
+when we did the income and substitution
+effects we kind of had written
+
+ align:start position:0%
+effects we kind of had written
+ 
+
+ align:start position:0%
+effects we kind of had written
+with the s on the right hand side and d
+
+ align:start position:0%
+with the s on the right hand side and d
+ 
+
+ align:start position:0%
+with the s on the right hand side and d
+x d p on the left hand side
+
+ align:start position:0%
+x d p on the left hand side
+ 
+
+ align:start position:0%
+x d p on the left hand side
+so there was a negative sign but it's
+
+ align:start position:0%
+so there was a negative sign but it's
+ 
+
+ align:start position:0%
+so there was a negative sign but it's
+all the same
+
+ align:start position:0%
+all the same
+ 
+
+ align:start position:0%
+all the same
+it's all equivalent
+
+ align:start position:0%
+it's all equivalent
+ 
+
+ align:start position:0%
+it's all equivalent
+okay so then
+
+ align:start position:0%
+okay so then
+ 
+
+ align:start position:0%
+okay so then
+we're saying like slutsky would be
+
+ align:start position:0%
+we're saying like slutsky would be
+ 
+
+ align:start position:0%
+we're saying like slutsky would be
+satisfied and a couple of other things
+
+ align:start position:0%
+satisfied and a couple of other things
+ 
+
+ align:start position:0%
+satisfied and a couple of other things
+are satisfied if we have
+
+ align:start position:0%
+are satisfied if we have
+ 
+
+ align:start position:0%
+are satisfied if we have
+the premise of an underlying
+
+ align:start position:0%
+the premise of an underlying
+ 
+
+ align:start position:0%
+the premise of an underlying
+rational consumer maximizing utility and
+
+ align:start position:0%
+rational consumer maximizing utility and
+ 
+
+ align:start position:0%
+rational consumer maximizing utility and
+we reviewed this in the discussion
+
+ align:start position:0%
+we reviewed this in the discussion
+ 
+
+ align:start position:0%
+we reviewed this in the discussion
+of the subsequent class we have
+
+ align:start position:0%
+of the subsequent class we have
+ 
+
+ align:start position:0%
+of the subsequent class we have
+homogeneity of degree zero
+
+ align:start position:0%
+homogeneity of degree zero
+ 
+
+ align:start position:0%
+homogeneity of degree zero
+and vol ross law spending your budget
+
+ align:start position:0%
+and vol ross law spending your budget
+ 
+
+ align:start position:0%
+and vol ross law spending your budget
+no price solution and spending and being
+
+ align:start position:0%
+no price solution and spending and being
+ 
+
+ align:start position:0%
+no price solution and spending and being
+on the budget line that plus slutsky are
+
+ align:start position:0%
+on the budget line that plus slutsky are
+ 
+
+ align:start position:0%
+on the budget line that plus slutsky are
+the restrictions
+
+ align:start position:0%
+the restrictions
+ 
+
+ align:start position:0%
+the restrictions
+implied by having a
+
+ align:start position:0%
+implied by having a
+ 
+
+ align:start position:0%
+implied by having a
+utility maximizing rational household
+
+ align:start position:0%
+utility maximizing rational household
+ 
+
+ align:start position:0%
+utility maximizing rational household
+and it turned out
+
+ align:start position:0%
+and it turned out
+ 
+
+ align:start position:0%
+and it turned out
+that it goes the other way as well
+
+ align:start position:0%
+that it goes the other way as well
+ 
+
+ align:start position:0%
+that it goes the other way as well
+that is to say if you had data that
+
+ align:start position:0%
+that is to say if you had data that
+ 
+
+ align:start position:0%
+that is to say if you had data that
+satisfied these three properties then
+
+ align:start position:0%
+satisfied these three properties then
+ 
+
+ align:start position:0%
+satisfied these three properties then
+there would be an underlying utility
+
+ align:start position:0%
+there would be an underlying utility
+ 
+
+ align:start position:0%
+there would be an underlying utility
+function that's
+
+ align:start position:0%
+function that's
+ 
+
+ align:start position:0%
+function that's
+quasi-concave increasing and so on that
+
+ align:start position:0%
+quasi-concave increasing and so on that
+ 
+
+ align:start position:0%
+quasi-concave increasing and so on that
+would have generated the data
+
+ align:start position:0%
+would have generated the data
+ 
+
+ align:start position:0%
+would have generated the data
+so this kind of seemingly bears some
+
+ align:start position:0%
+so this kind of seemingly bears some
+ 
+
+ align:start position:0%
+so this kind of seemingly bears some
+similarity to gorman in the sense of
+
+ align:start position:0%
+similarity to gorman in the sense of
+ 
+
+ align:start position:0%
+similarity to gorman in the sense of
+could we generate the aggregate demand
+
+ align:start position:0%
+could we generate the aggregate demand
+ 
+
+ align:start position:0%
+could we generate the aggregate demand
+by maximizing a utility function
+
+ align:start position:0%
+by maximizing a utility function
+ 
+
+ align:start position:0%
+by maximizing a utility function
+could we find a utility function u star
+
+ align:start position:0%
+could we find a utility function u star
+ 
+
+ align:start position:0%
+could we find a utility function u star
+such that given the household all the
+
+ align:start position:0%
+such that given the household all the
+ 
+
+ align:start position:0%
+such that given the household all the
+wealth the solution of that problem
+
+ align:start position:0%
+wealth the solution of that problem
+ 
+
+ align:start position:0%
+wealth the solution of that problem
+would be the underlying demands here
+
+ align:start position:0%
+would be the underlying demands here
+ 
+
+ align:start position:0%
+would be the underlying demands here
+though we're giving the the data
+
+ align:start position:0%
+though we're giving the the data
+ 
+
+ align:start position:0%
+though we're giving the the data
+including demands
+
+ align:start position:0%
+including demands
+ 
+
+ align:start position:0%
+including demands
+for a given household and trying to find
+
+ align:start position:0%
+for a given household and trying to find
+ 
+
+ align:start position:0%
+for a given household and trying to find
+whether or not there exists a utility
+
+ align:start position:0%
+whether or not there exists a utility
+ 
+
+ align:start position:0%
+whether or not there exists a utility
+function that would generate demands
+
+ align:start position:0%
+function that would generate demands
+ 
+
+ align:start position:0%
+function that would generate demands
+with all these properties and the answer
+
+ align:start position:0%
+with all these properties and the answer
+ 
+
+ align:start position:0%
+with all these properties and the answer
+is yes
+
+ align:start position:0%
+is yes
+ 
+
+ align:start position:0%
+is yes
+that it's sufficient and necessary to
+
+ align:start position:0%
+that it's sufficient and necessary to
+ 
+
+ align:start position:0%
+that it's sufficient and necessary to
+have these properties
+
+ align:start position:0%
+have these properties
+ 
+
+ align:start position:0%
+have these properties
+so the theory has content you just need
+
+ align:start position:0%
+so the theory has content you just need
+ 
+
+ align:start position:0%
+so the theory has content you just need
+to scroll through this list in the data
+
+ align:start position:0%
+to scroll through this list in the data
+ 
+
+ align:start position:0%
+to scroll through this list in the data
+and see if you can
+
+ align:start position:0%
+and see if you can
+ 
+
+ align:start position:0%
+and see if you can
+violate one of them
+
+ align:start position:0%
+violate one of them
+ 
+
+ align:start position:0%
+violate one of them
+and it would it could not have had come
+
+ align:start position:0%
+and it would it could not have had come
+ 
+
+ align:start position:0%
+and it would it could not have had come
+from a maximizing household
+
+ align:start position:0%
+from a maximizing household
+ 
+
+ align:start position:0%
+from a maximizing household
+convexity was not testable
+
+ align:start position:0%
+convexity was not testable
+ 
+
+ align:start position:0%
+convexity was not testable
+not with this demand theory
+
+ align:start position:0%
+not with this demand theory
+ 
+
+ align:start position:0%
+not with this demand theory
+because you generate the same data and
+
+ align:start position:0%
+because you generate the same data and
+ 
+
+ align:start position:0%
+because you generate the same data and
+we actually made a connection to
+
+ align:start position:0%
+we actually made a connection to
+ 
+
+ align:start position:0%
+we actually made a connection to
+computer science
+
+ align:start position:0%
+computer science
+ 
+
+ align:start position:0%
+computer science
+so this part this is testing with finite
+
+ align:start position:0%
+so this part this is testing with finite
+ 
+
+ align:start position:0%
+so this part this is testing with finite
+data not an infinite amount of data and
+
+ align:start position:0%
+data not an infinite amount of data and
+ 
+
+ align:start position:0%
+data not an infinite amount of data and
+the key here was the beginning at least
+
+ align:start position:0%
+the key here was the beginning at least
+ 
+
+ align:start position:0%
+the key here was the beginning at least
+this weak axiom of revealed preference
+
+ align:start position:0%
+this weak axiom of revealed preference
+ 
+
+ align:start position:0%
+this weak axiom of revealed preference
+which you should all know
+
+ align:start position:0%
+which you should all know
+ 
+
+ align:start position:0%
+which you should all know
+and again we reviewed it in the
+
+ align:start position:0%
+and again we reviewed it in the
+ 
+
+ align:start position:0%
+and again we reviewed it in the
+subsequent lecture at the beginning
+
+ align:start position:0%
+subsequent lecture at the beginning
+ 
+
+ align:start position:0%
+subsequent lecture at the beginning
+that that sort of pairwise if we have
+
+ align:start position:0%
+that that sort of pairwise if we have
+ 
+
+ align:start position:0%
+that that sort of pairwise if we have
+two observations
+
+ align:start position:0%
+two observations
+ 
+
+ align:start position:0%
+two observations
+prices and
+
+ align:start position:0%
+prices and
+ 
+
+ align:start position:0%
+prices and
+demands in situation one in situation
+
+ align:start position:0%
+demands in situation one in situation
+ 
+
+ align:start position:0%
+demands in situation one in situation
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+then a price p2 if they're observed
+
+ align:start position:0%
+then a price p2 if they're observed
+ 
+
+ align:start position:0%
+then a price p2 if they're observed
+choosing x2 it better be the case
+
+ align:start position:0%
+choosing x2 it better be the case
+ 
+
+ align:start position:0%
+choosing x2 it better be the case
+and x1 was available and not chosen it
+
+ align:start position:0%
+and x1 was available and not chosen it
+ 
+
+ align:start position:0%
+and x1 was available and not chosen it
+better be the case that price is p1
+
+ align:start position:0%
+better be the case that price is p1
+ 
+
+ align:start position:0%
+better be the case that price is p1
+where they're choosing x1 they don't
+
+ align:start position:0%
+where they're choosing x1 they don't
+ 
+
+ align:start position:0%
+where they're choosing x1 they don't
+have x2 available otherwise they they
+
+ align:start position:0%
+have x2 available otherwise they they
+ 
+
+ align:start position:0%
+have x2 available otherwise they they
+were supposed to have chosen it if it
+
+ align:start position:0%
+were supposed to have chosen it if it
+ 
+
+ align:start position:0%
+were supposed to have chosen it if it
+had been interior in the budget
+
+ align:start position:0%
+had been interior in the budget
+ 
+
+ align:start position:0%
+had been interior in the budget
+according to the first statement it
+
+ align:start position:0%
+according to the first statement it
+ 
+
+ align:start position:0%
+according to the first statement it
+would be utility maximizing
+
+ align:start position:0%
+would be utility maximizing
+ 
+
+ align:start position:0%
+would be utility maximizing
+so this is putting restrictions on data
+
+ align:start position:0%
+so this is putting restrictions on data
+ 
+
+ align:start position:0%
+so this is putting restrictions on data
+the the weak axiom of real preferences
+
+ align:start position:0%
+the the weak axiom of real preferences
+ 
+
+ align:start position:0%
+the the weak axiom of real preferences
+looking at pairwise observations as we
+
+ align:start position:0%
+looking at pairwise observations as we
+ 
+
+ align:start position:0%
+looking at pairwise observations as we
+move prices and demands around
+
+ align:start position:0%
+move prices and demands around
+ 
+
+ align:start position:0%
+move prices and demands around
+to see if it's quote rational
+
+ align:start position:0%
+to see if it's quote rational
+ 
+
+ align:start position:0%
+to see if it's quote rational
+weak axiom of revealed preference
+
+ align:start position:0%
+weak axiom of revealed preference
+ 
+
+ align:start position:0%
+weak axiom of revealed preference
+and then we generalize that that
+
+ align:start position:0%
+and then we generalize that that
+ 
+
+ align:start position:0%
+and then we generalize that that
+we called those directly revealed
+
+ align:start position:0%
+we called those directly revealed
+ 
+
+ align:start position:0%
+we called those directly revealed
+preferred pairwise comparisons
+
+ align:start position:0%
+preferred pairwise comparisons
+ 
+
+ align:start position:0%
+preferred pairwise comparisons
+and then we
+
+ align:start position:0%
+and then we
+ 
+
+ align:start position:0%
+and then we
+went on to talk about
+
+ align:start position:0%
+went on to talk about
+ 
+
+ align:start position:0%
+went on to talk about
+indirectly revealed preferred or just
+
+ align:start position:0%
+indirectly revealed preferred or just
+ 
+
+ align:start position:0%
+indirectly revealed preferred or just
+revealed preferred
+
+ align:start position:0%
+revealed preferred
+ 
+
+ align:start position:0%
+revealed preferred
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the content of this was we never see all
+
+ align:start position:0%
+the content of this was we never see all
+ 
+
+ align:start position:0%
+the content of this was we never see all
+the pairwise comparisons
+
+ align:start position:0%
+the pairwise comparisons
+ 
+
+ align:start position:0%
+the pairwise comparisons
+we never see
+
+ align:start position:0%
+we never see
+ 
+
+ align:start position:0%
+we never see
+you know
+
+ align:start position:0%
+you know
+ 
+
+ align:start position:0%
+you know
+xt directly
+
+ align:start position:0%
+xt directly
+ 
+
+ align:start position:0%
+xt directly
+compared to xs but we do see it
+
+ align:start position:0%
+compared to xs but we do see it
+ 
+
+ align:start position:0%
+compared to xs but we do see it
+indirectly
+
+ align:start position:0%
+indirectly
+ 
+
+ align:start position:0%
+indirectly
+because we have xt
+
+ align:start position:0%
+because we have xt
+ 
+
+ align:start position:0%
+because we have xt
+in this case revealed directly preferred
+
+ align:start position:0%
+in this case revealed directly preferred
+ 
+
+ align:start position:0%
+in this case revealed directly preferred
+to xr1 xr1 revealed preferred xr2
+
+ align:start position:0%
+to xr1 xr1 revealed preferred xr2
+ 
+
+ align:start position:0%
+to xr1 xr1 revealed preferred xr2
+and so on down the chain
+
+ align:start position:0%
+and so on down the chain
+ 
+
+ align:start position:0%
+and so on down the chain
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+under one of those
+
+ align:start position:0%
+under one of those
+ 
+
+ align:start position:0%
+under one of those
+properties of a rational consumer
+
+ align:start position:0%
+properties of a rational consumer
+ 
+
+ align:start position:0%
+properties of a rational consumer
+namely transitivity
+
+ align:start position:0%
+namely transitivity
+ 
+
+ align:start position:0%
+namely transitivity
+if we had a sequence of revealed
+
+ align:start position:0%
+if we had a sequence of revealed
+ 
+
+ align:start position:0%
+if we had a sequence of revealed
+directly preferred
+
+ align:start position:0%
+directly preferred
+ 
+
+ align:start position:0%
+directly preferred
+and under transitivity xt should be
+
+ align:start position:0%
+and under transitivity xt should be
+ 
+
+ align:start position:0%
+and under transitivity xt should be
+revealed preferred
+
+ align:start position:0%
+revealed preferred
+ 
+
+ align:start position:0%
+revealed preferred
+directly preferred xs too so when you
+
+ align:start position:0%
+directly preferred xs too so when you
+ 
+
+ align:start position:0%
+directly preferred xs too so when you
+can do the pairwise comparison at tns
+
+ align:start position:0%
+can do the pairwise comparison at tns
+ 
+
+ align:start position:0%
+can do the pairwise comparison at tns
+it better be the case they don't they
+
+ align:start position:0%
+it better be the case they don't they
+ 
+
+ align:start position:0%
+it better be the case they don't they
+don't violate that xt is preferred x
+
+ align:start position:0%
+don't violate that xt is preferred x
+ 
+
+ align:start position:0%
+don't violate that xt is preferred x
+weekly preferred xs
+
+ align:start position:0%
+weekly preferred xs
+ 
+
+ align:start position:0%
+weekly preferred xs
+so this second part
+
+ align:start position:0%
+so this second part
+ 
+
+ align:start position:0%
+so this second part
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+assuming underlying consumer rationality
+
+ align:start position:0%
+assuming underlying consumer rationality
+ 
+
+ align:start position:0%
+assuming underlying consumer rationality
+in order to set up a situation where we
+
+ align:start position:0%
+in order to set up a situation where we
+ 
+
+ align:start position:0%
+in order to set up a situation where we
+can actually impose the test
+
+ align:start position:0%
+can actually impose the test
+ 
+
+ align:start position:0%
+can actually impose the test
+then we did that in computational
+
+ align:start position:0%
+then we did that in computational
+ 
+
+ align:start position:0%
+then we did that in computational
+economics
+
+ align:start position:0%
+economics
+ 
+
+ align:start position:0%
+economics
+which i mentioned i elaborated on in the
+
+ align:start position:0%
+which i mentioned i elaborated on in the
+ 
+
+ align:start position:0%
+which i mentioned i elaborated on in the
+subsequent lecture
+
+ align:start position:0%
+subsequent lecture
+ 
+
+ align:start position:0%
+subsequent lecture
+and we took it to general equilibrium so
+
+ align:start position:0%
+and we took it to general equilibrium so
+ 
+
+ align:start position:0%
+and we took it to general equilibrium so
+are there any
+
+ align:start position:0%
+are there any
+ 
+
+ align:start position:0%
+are there any
+questions about and risk sharing any
+
+ align:start position:0%
+questions about and risk sharing any
+ 
+
+ align:start position:0%
+questions about and risk sharing any
+questions about
+
+ align:start position:0%
+questions about
+ 
+
+ align:start position:0%
+questions about
+lecture 19.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these reviews get faster and faster as
+
+ align:start position:0%
+these reviews get faster and faster as
+ 
+
+ align:start position:0%
+these reviews get faster and faster as
+we approach the end of the hour
+
+ align:start position:0%
+we approach the end of the hour
+ 
+
+ align:start position:0%
+we approach the end of the hour
+but on the other hand it's more and more
+
+ align:start position:0%
+but on the other hand it's more and more
+ 
+
+ align:start position:0%
+but on the other hand it's more and more
+recent so not so worried
+
+ align:start position:0%
+recent so not so worried
+ 
+
+ align:start position:0%
+recent so not so worried
+21 we already did so that just leaves us
+
+ align:start position:0%
+21 we already did so that just leaves us
+ 
+
+ align:start position:0%
+21 we already did so that just leaves us
+with 20
+
+ align:start position:0%
+with 20
+ 
+
+ align:start position:0%
+with 20
+and 20 is pretty familiar
+
+ align:start position:0%
+and 20 is pretty familiar
+ 
+
+ align:start position:0%
+and 20 is pretty familiar
+which was
+
+ align:start position:0%
+which was
+ 
+
+ align:start position:0%
+which was
+the failure of the welfare theorem so we
+
+ align:start position:0%
+the failure of the welfare theorem so we
+ 
+
+ align:start position:0%
+the failure of the welfare theorem so we
+kind of covered
+
+ align:start position:0%
+kind of covered
+ 
+
+ align:start position:0%
+kind of covered
+sufficient assumptions already
+
+ align:start position:0%
+sufficient assumptions already
+ 
+
+ align:start position:0%
+sufficient assumptions already
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+for the fourth third or fourth time i'm
+
+ align:start position:0%
+for the fourth third or fourth time i'm
+ 
+
+ align:start position:0%
+for the fourth third or fourth time i'm
+showing you this economy again
+
+ align:start position:0%
+showing you this economy again
+ 
+
+ align:start position:0%
+showing you this economy again
+in all of its glory with the convexity
+
+ align:start position:0%
+in all of its glory with the convexity
+ 
+
+ align:start position:0%
+in all of its glory with the convexity
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+concavity
+
+ align:start position:0%
+concavity
+ 
+
+ align:start position:0%
+concavity
+in the appropriate spots
+
+ align:start position:0%
+in the appropriate spots
+ 
+
+ align:start position:0%
+in the appropriate spots
+statement of the second welfare theorem
+
+ align:start position:0%
+statement of the second welfare theorem
+ 
+
+ align:start position:0%
+statement of the second welfare theorem
+you actually saw this slide before in
+
+ align:start position:0%
+you actually saw this slide before in
+ 
+
+ align:start position:0%
+you actually saw this slide before in
+the review today
+
+ align:start position:0%
+the review today
+ 
+
+ align:start position:0%
+the review today
+and the second welfare theorem
+
+ align:start position:0%
+and the second welfare theorem
+ 
+
+ align:start position:0%
+and the second welfare theorem
+says that
+
+ align:start position:0%
+says that
+ 
+
+ align:start position:0%
+says that
+any pareto optimum
+
+ align:start position:0%
+any pareto optimum
+ 
+
+ align:start position:0%
+any pareto optimum
+can be supported as a volrazian
+
+ align:start position:0%
+can be supported as a volrazian
+ 
+
+ align:start position:0%
+can be supported as a volrazian
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+so here's a case where everything's
+
+ align:start position:0%
+so here's a case where everything's
+ 
+
+ align:start position:0%
+so here's a case where everything's
+working out fine
+
+ align:start position:0%
+working out fine
+ 
+
+ align:start position:0%
+working out fine
+here's the pareto optimum obviously
+
+ align:start position:0%
+here's the pareto optimum obviously
+ 
+
+ align:start position:0%
+here's the pareto optimum obviously
+this is the supporting hyperplane again
+
+ align:start position:0%
+this is the supporting hyperplane again
+ 
+
+ align:start position:0%
+this is the supporting hyperplane again
+so it's going to be a competitive
+
+ align:start position:0%
+so it's going to be a competitive
+ 
+
+ align:start position:0%
+so it's going to be a competitive
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+the second welfare theorem
+
+ align:start position:0%
+the second welfare theorem
+ 
+
+ align:start position:0%
+the second welfare theorem
+has a sufficient assumption is the
+
+ align:start position:0%
+has a sufficient assumption is the
+ 
+
+ align:start position:0%
+has a sufficient assumption is the
+convexity
+
+ align:start position:0%
+convexity
+ 
+
+ align:start position:0%
+convexity
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+as i said i think last time or in answer
+
+ align:start position:0%
+as i said i think last time or in answer
+ 
+
+ align:start position:0%
+as i said i think last time or in answer
+to this
+
+ align:start position:0%
+to this
+ 
+
+ align:start position:0%
+to this
+that second to last time
+
+ align:start position:0%
+that second to last time
+ 
+
+ align:start position:0%
+that second to last time
+you know the starting point here is
+
+ align:start position:0%
+you know the starting point here is
+ 
+
+ align:start position:0%
+you know the starting point here is
+something that's pareto optimal and it's
+
+ align:start position:0%
+something that's pareto optimal and it's
+ 
+
+ align:start position:0%
+something that's pareto optimal and it's
+easy to lose track of the direction of
+
+ align:start position:0%
+easy to lose track of the direction of
+ 
+
+ align:start position:0%
+easy to lose track of the direction of
+the argument
+
+ align:start position:0%
+the argument
+ 
+
+ align:start position:0%
+the argument
+is this pareto optimal yes it certainly
+
+ align:start position:0%
+is this pareto optimal yes it certainly
+ 
+
+ align:start position:0%
+is this pareto optimal yes it certainly
+is or at least you can imagine so
+
+ align:start position:0%
+is or at least you can imagine so
+ 
+
+ align:start position:0%
+is or at least you can imagine so
+this is the indifference curve that's
+
+ align:start position:0%
+this is the indifference curve that's
+ 
+
+ align:start position:0%
+this is the indifference curve that's
+tangent locally and you could try to
+
+ align:start position:0%
+tangent locally and you could try to
+ 
+
+ align:start position:0%
+tangent locally and you could try to
+move away from there globally
+
+ align:start position:0%
+move away from there globally
+ 
+
+ align:start position:0%
+move away from there globally
+but whatever you do
+
+ align:start position:0%
+but whatever you do
+ 
+
+ align:start position:0%
+but whatever you do
+it has to be on this production set to
+
+ align:start position:0%
+it has to be on this production set to
+ 
+
+ align:start position:0%
+it has to be on this production set to
+be feasible
+
+ align:start position:0%
+be feasible
+ 
+
+ align:start position:0%
+be feasible
+and that's going to be
+
+ align:start position:0%
+and that's going to be
+ 
+
+ align:start position:0%
+and that's going to be
+associated with a lower level of an
+
+ align:start position:0%
+associated with a lower level of an
+ 
+
+ align:start position:0%
+associated with a lower level of an
+indifference curve so this is the best
+
+ align:start position:0%
+indifference curve so this is the best
+ 
+
+ align:start position:0%
+indifference curve so this is the best
+level of utility achievable within and
+
+ align:start position:0%
+level of utility achievable within and
+ 
+
+ align:start position:0%
+level of utility achievable within and
+on the production set and likewise over
+
+ align:start position:0%
+on the production set and likewise over
+ 
+
+ align:start position:0%
+on the production set and likewise over
+here oh
+
+ align:start position:0%
+here oh
+ 
+
+ align:start position:0%
+here oh
+but then the second forgetting the
+
+ align:start position:0%
+but then the second forgetting the
+ 
+
+ align:start position:0%
+but then the second forgetting the
+second part of the theorem is
+
+ align:start position:0%
+second part of the theorem is
+ 
+
+ align:start position:0%
+second part of the theorem is
+can it be supported as a competitive
+
+ align:start position:0%
+can it be supported as a competitive
+ 
+
+ align:start position:0%
+can it be supported as a competitive
+equilibrium the answer is no
+
+ align:start position:0%
+equilibrium the answer is no
+ 
+
+ align:start position:0%
+equilibrium the answer is no
+because given this imagine supporting
+
+ align:start position:0%
+because given this imagine supporting
+ 
+
+ align:start position:0%
+because given this imagine supporting
+hyper plane
+
+ align:start position:0%
+hyper plane
+ 
+
+ align:start position:0%
+hyper plane
+the household would be better off moving
+
+ align:start position:0%
+the household would be better off moving
+ 
+
+ align:start position:0%
+the household would be better off moving
+away to some extreme have a higher
+
+ align:start position:0%
+away to some extreme have a higher
+ 
+
+ align:start position:0%
+away to some extreme have a higher
+utility so it's not going to be
+
+ align:start position:0%
+utility so it's not going to be
+ 
+
+ align:start position:0%
+utility so it's not going to be
+consistent with utility maximization and
+
+ align:start position:0%
+consistent with utility maximization and
+ 
+
+ align:start position:0%
+consistent with utility maximization and
+this one is not consistent with profit
+
+ align:start position:0%
+this one is not consistent with profit
+ 
+
+ align:start position:0%
+this one is not consistent with profit
+maximization even though it is still a
+
+ align:start position:0%
+maximization even though it is still a
+ 
+
+ align:start position:0%
+maximization even though it is still a
+pareto optimal point as you could sort
+
+ align:start position:0%
+pareto optimal point as you could sort
+ 
+
+ align:start position:0%
+pareto optimal point as you could sort
+of construct graphically
+
+ align:start position:0%
+of construct graphically
+ 
+
+ align:start position:0%
+of construct graphically
+so i showed you this picture earlier
+
+ align:start position:0%
+so i showed you this picture earlier
+ 
+
+ align:start position:0%
+so i showed you this picture earlier
+this is kind of an aggregated version of
+
+ align:start position:0%
+this is kind of an aggregated version of
+ 
+
+ align:start position:0%
+this is kind of an aggregated version of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+just says those assumptions are
+
+ align:start position:0%
+just says those assumptions are
+ 
+
+ align:start position:0%
+just says those assumptions are
+sufficient they're not necessarily
+
+ align:start position:0%
+sufficient they're not necessarily
+ 
+
+ align:start position:0%
+sufficient they're not necessarily
+necessary
+
+ align:start position:0%
+necessary
+ 
+
+ align:start position:0%
+necessary
+the first welfare theorem is a
+
+ align:start position:0%
+the first welfare theorem is a
+ 
+
+ align:start position:0%
+the first welfare theorem is a
+competitive equilibrium is optimal this
+
+ align:start position:0%
+competitive equilibrium is optimal this
+ 
+
+ align:start position:0%
+competitive equilibrium is optimal this
+one assumes the existence of a
+
+ align:start position:0%
+one assumes the existence of a
+ 
+
+ align:start position:0%
+one assumes the existence of a
+competitive equilibrium
+
+ align:start position:0%
+competitive equilibrium
+ 
+
+ align:start position:0%
+competitive equilibrium
+all we need is rationality and
+
+ align:start position:0%
+all we need is rationality and
+ 
+
+ align:start position:0%
+all we need is rationality and
+non-satiation but this was a picture
+
+ align:start position:0%
+non-satiation but this was a picture
+ 
+
+ align:start position:0%
+non-satiation but this was a picture
+showing that if we don't have
+
+ align:start position:0%
+showing that if we don't have
+ 
+
+ align:start position:0%
+showing that if we don't have
+non-satiation locally we're not
+
+ align:start position:0%
+non-satiation locally we're not
+ 
+
+ align:start position:0%
+non-satiation locally we're not
+necessarily going to show that the
+
+ align:start position:0%
+necessarily going to show that the
+ 
+
+ align:start position:0%
+necessarily going to show that the
+competitive equilibrium is pareto
+
+ align:start position:0%
+competitive equilibrium is pareto
+ 
+
+ align:start position:0%
+competitive equilibrium is pareto
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+because we're given the competitive
+
+ align:start position:0%
+because we're given the competitive
+ 
+
+ align:start position:0%
+because we're given the competitive
+equilibrium we can find something pareto
+
+ align:start position:0%
+equilibrium we can find something pareto
+ 
+
+ align:start position:0%
+equilibrium we can find something pareto
+dominating
+
+ align:start position:0%
+dominating
+ 
+
+ align:start position:0%
+dominating
+then we went through this pollution
+
+ align:start position:0%
+then we went through this pollution
+ 
+
+ align:start position:0%
+then we went through this pollution
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+which is like not allowing
+
+ align:start position:0%
+which is like not allowing
+ 
+
+ align:start position:0%
+which is like not allowing
+trade in all the goods and again the
+
+ align:start position:0%
+trade in all the goods and again the
+ 
+
+ align:start position:0%
+trade in all the goods and again the
+intuition for this
+
+ align:start position:0%
+intuition for this
+ 
+
+ align:start position:0%
+intuition for this
+this miraculous price system when it
+
+ align:start position:0%
+this miraculous price system when it
+ 
+
+ align:start position:0%
+this miraculous price system when it
+works
+
+ align:start position:0%
+works
+ 
+
+ align:start position:0%
+works
+means that households only have to
+
+ align:start position:0%
+means that households only have to
+ 
+
+ align:start position:0%
+means that households only have to
+evaluate things on the margin at those
+
+ align:start position:0%
+evaluate things on the margin at those
+ 
+
+ align:start position:0%
+evaluate things on the margin at those
+prices they internalize
+
+ align:start position:0%
+prices they internalize
+ 
+
+ align:start position:0%
+prices they internalize
+through the prices
+
+ align:start position:0%
+through the prices
+ 
+
+ align:start position:0%
+through the prices
+and make the right decision the prices
+
+ align:start position:0%
+and make the right decision the prices
+ 
+
+ align:start position:0%
+and make the right decision the prices
+reflect the social trade-off
+
+ align:start position:0%
+reflect the social trade-off
+ 
+
+ align:start position:0%
+reflect the social trade-off
+of increasing or decreasing
+
+ align:start position:0%
+of increasing or decreasing
+ 
+
+ align:start position:0%
+of increasing or decreasing
+demands
+
+ align:start position:0%
+demands
+ 
+
+ align:start position:0%
+demands
+and of course they're much aware of
+
+ align:start position:0%
+and of course they're much aware of
+ 
+
+ align:start position:0%
+and of course they're much aware of
+their utility consequences their
+
+ align:start position:0%
+their utility consequences their
+ 
+
+ align:start position:0%
+their utility consequences their
+marginal rate of substitution
+
+ align:start position:0%
+marginal rate of substitution
+ 
+
+ align:start position:0%
+marginal rate of substitution
+so if we get it right in a competitive
+
+ align:start position:0%
+so if we get it right in a competitive
+ 
+
+ align:start position:0%
+so if we get it right in a competitive
+equilibrium in complete markets and the
+
+ align:start position:0%
+equilibrium in complete markets and the
+ 
+
+ align:start position:0%
+equilibrium in complete markets and the
+price system conveys all the right
+
+ align:start position:0%
+price system conveys all the right
+ 
+
+ align:start position:0%
+price system conveys all the right
+things on the margin and all the people
+
+ align:start position:0%
+things on the margin and all the people
+ 
+
+ align:start position:0%
+things on the margin and all the people
+have to do
+
+ align:start position:0%
+have to do
+ 
+
+ align:start position:0%
+have to do
+is take from god this price system from
+
+ align:start position:0%
+is take from god this price system from
+ 
+
+ align:start position:0%
+is take from god this price system from
+adam smith you might say
+
+ align:start position:0%
+adam smith you might say
+ 
+
+ align:start position:0%
+adam smith you might say
+as if by an invisible hand namely the
+
+ align:start position:0%
+as if by an invisible hand namely the
+ 
+
+ align:start position:0%
+as if by an invisible hand namely the
+price system
+
+ align:start position:0%
+price system
+ 
+
+ align:start position:0%
+price system
+be guided to
+
+ align:start position:0%
+be guided to
+ 
+
+ align:start position:0%
+be guided to
+pareto optimal allocations but likewise
+
+ align:start position:0%
+pareto optimal allocations but likewise
+ 
+
+ align:start position:0%
+pareto optimal allocations but likewise
+if we screw up the markets
+
+ align:start position:0%
+if we screw up the markets
+ 
+
+ align:start position:0%
+if we screw up the markets
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the whole thing falls apart and this
+
+ align:start position:0%
+the whole thing falls apart and this
+ 
+
+ align:start position:0%
+the whole thing falls apart and this
+pollution example was where we didn't
+
+ align:start position:0%
+pollution example was where we didn't
+ 
+
+ align:start position:0%
+pollution example was where we didn't
+have a price for all the goods so we
+
+ align:start position:0%
+have a price for all the goods so we
+ 
+
+ align:start position:0%
+have a price for all the goods so we
+don't have a rate of substitution of one
+
+ align:start position:0%
+don't have a rate of substitution of one
+ 
+
+ align:start position:0%
+don't have a rate of substitution of one
+good for the other
+
+ align:start position:0%
+good for the other
+ 
+
+ align:start position:0%
+good for the other
+in the market and
+
+ align:start position:0%
+in the market and
+ 
+
+ align:start position:0%
+in the market and
+and households and firms make
+
+ align:start position:0%
+and households and firms make
+ 
+
+ align:start position:0%
+and households and firms make
+inefficient choices so we did that with
+
+ align:start position:0%
+inefficient choices so we did that with
+ 
+
+ align:start position:0%
+inefficient choices so we did that with
+the pollution as a leading example we
+
+ align:start position:0%
+the pollution as a leading example we
+ 
+
+ align:start position:0%
+the pollution as a leading example we
+went to aero to generalize it where
+
+ align:start position:0%
+went to aero to generalize it where
+ 
+
+ align:start position:0%
+went to aero to generalize it where
+households care about others consumption
+
+ align:start position:0%
+households care about others consumption
+ 
+
+ align:start position:0%
+households care about others consumption
+either they're altruistic or envious and
+
+ align:start position:0%
+either they're altruistic or envious and
+ 
+
+ align:start position:0%
+either they're altruistic or envious and
+the same thing kind of works this is the
+
+ align:start position:0%
+the same thing kind of works this is the
+ 
+
+ align:start position:0%
+the same thing kind of works this is the
+fourth or fifth time today that we talk
+
+ align:start position:0%
+fourth or fifth time today that we talk
+ 
+
+ align:start position:0%
+fourth or fifth time today that we talk
+about a pareto problem
+
+ align:start position:0%
+about a pareto problem
+ 
+
+ align:start position:0%
+about a pareto problem
+an associated first order conditions
+
+ align:start position:0%
+an associated first order conditions
+ 
+
+ align:start position:0%
+an associated first order conditions
+generating shadow prices so we're
+
+ align:start position:0%
+generating shadow prices so we're
+ 
+
+ align:start position:0%
+generating shadow prices so we're
+following exactly the same steps as in
+
+ align:start position:0%
+following exactly the same steps as in
+ 
+
+ align:start position:0%
+following exactly the same steps as in
+the second welfare theorem
+
+ align:start position:0%
+the second welfare theorem
+ 
+
+ align:start position:0%
+the second welfare theorem
+and finding a way despite the
+
+ align:start position:0%
+and finding a way despite the
+ 
+
+ align:start position:0%
+and finding a way despite the
+externalities and utility functions to
+
+ align:start position:0%
+externalities and utility functions to
+ 
+
+ align:start position:0%
+externalities and utility functions to
+support the pareto optimal allocation as
+
+ align:start position:0%
+support the pareto optimal allocation as
+ 
+
+ align:start position:0%
+support the pareto optimal allocation as
+a competitive equilibrium
+
+ align:start position:0%
+a competitive equilibrium
+ 
+
+ align:start position:0%
+a competitive equilibrium
+we already talked about failure
+
+ align:start position:0%
+we already talked about failure
+ 
+
+ align:start position:0%
+we already talked about failure
+when we have an infinite number of goods
+
+ align:start position:0%
+when we have an infinite number of goods
+ 
+
+ align:start position:0%
+when we have an infinite number of goods
+this was
+
+ align:start position:0%
+this was
+ 
+
+ align:start position:0%
+this was
+an example of how to pareto dominate an
+
+ align:start position:0%
+an example of how to pareto dominate an
+ 
+
+ align:start position:0%
+an example of how to pareto dominate an
+allocation
+
+ align:start position:0%
+allocation
+ 
+
+ align:start position:0%
+allocation
+by essentially
+
+ align:start position:0%
+by essentially
+ 
+
+ align:start position:0%
+by essentially
+giving
+
+ align:start position:0%
+giving
+ 
+
+ align:start position:0%
+giving
+the first household some goods the
+
+ align:start position:0%
+the first household some goods the
+ 
+
+ align:start position:0%
+the first household some goods the
+second had
+
+ align:start position:0%
+second had
+ 
+
+ align:start position:0%
+second had
+and then the third giving to the second
+
+ align:start position:0%
+and then the third giving to the second
+ 
+
+ align:start position:0%
+and then the third giving to the second
+and so on
+
+ align:start position:0%
+and so on
+ 
+
+ align:start position:0%
+and so on
+this is exactly what's going on in the
+
+ align:start position:0%
+this is exactly what's going on in the
+ 
+
+ align:start position:0%
+this is exactly what's going on in the
+overlapping generations monetary economy
+
+ align:start position:0%
+overlapping generations monetary economy
+ 
+
+ align:start position:0%
+overlapping generations monetary economy
+of lecture 21. money is worthless
+
+ align:start position:0%
+of lecture 21. money is worthless
+ 
+
+ align:start position:0%
+of lecture 21. money is worthless
+it's just pieces of paper there's no
+
+ align:start position:0%
+it's just pieces of paper there's no
+ 
+
+ align:start position:0%
+it's just pieces of paper there's no
+intrinsic value
+
+ align:start position:0%
+intrinsic value
+ 
+
+ align:start position:0%
+intrinsic value
+but if household 2 here came up with
+
+ align:start position:0%
+but if household 2 here came up with
+ 
+
+ align:start position:0%
+but if household 2 here came up with
+money
+
+ align:start position:0%
+money
+ 
+
+ align:start position:0%
+money
+and gave it to household took money
+
+ align:start position:0%
+and gave it to household took money
+ 
+
+ align:start position:0%
+and gave it to household took money
+sorry from household one
+
+ align:start position:0%
+sorry from household one
+ 
+
+ align:start position:0%
+sorry from household one
+and exchange it for goods
+
+ align:start position:0%
+and exchange it for goods
+ 
+
+ align:start position:0%
+and exchange it for goods
+you know then one gets the goods and two
+
+ align:start position:0%
+you know then one gets the goods and two
+ 
+
+ align:start position:0%
+you know then one gets the goods and two
+gets the money
+
+ align:start position:0%
+gets the money
+ 
+
+ align:start position:0%
+gets the money
+and then two can pass the money along to
+
+ align:start position:0%
+and then two can pass the money along to
+ 
+
+ align:start position:0%
+and then two can pass the money along to
+household three
+
+ align:start position:0%
+household three
+ 
+
+ align:start position:0%
+household three
+so there is a connection between this
+
+ align:start position:0%
+so there is a connection between this
+ 
+
+ align:start position:0%
+so there is a connection between this
+artificial example
+
+ align:start position:0%
+artificial example
+ 
+
+ align:start position:0%
+artificial example
+and the fact
+
+ align:start position:0%
+and the fact
+ 
+
+ align:start position:0%
+and the fact
+that we get
+
+ align:start position:0%
+that we get
+ 
+
+ align:start position:0%
+that we get
+a non-optimal autarky equilibrium
+
+ align:start position:0%
+a non-optimal autarky equilibrium
+ 
+
+ align:start position:0%
+a non-optimal autarky equilibrium
+dominated by
+
+ align:start position:0%
+dominated by
+ 
+
+ align:start position:0%
+dominated by
+a monetary equilibrium in the
+
+ align:start position:0%
+a monetary equilibrium in the
+ 
+
+ align:start position:0%
+a monetary equilibrium in the
+overlapping
+
+ align:start position:0%
+overlapping
+ 
+
+ align:start position:0%
+overlapping
+generations model
+
+ align:start position:0%
+generations model
+ 
+
+ align:start position:0%
+generations model
+which we talked about at the beginning
+
+ align:start position:0%
+which we talked about at the beginning
+ 
+
+ align:start position:0%
+which we talked about at the beginning
+of class okay
+
+ align:start position:0%
+of class okay
+ 
+
+ align:start position:0%
+of class okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+essentially that was that was it for
+
+ align:start position:0%
+essentially that was that was it for
+ 
+
+ align:start position:0%
+essentially that was that was it for
+lecture 23
+
+ align:start position:0%
+lecture 23
+ 
+
+ align:start position:0%
+lecture 23
+and we already reviewed lecture 21 so
+
+ align:start position:0%
+and we already reviewed lecture 21 so
+ 
+
+ align:start position:0%
+and we already reviewed lecture 21 so
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i enjoy teaching the class i i really
+
+ align:start position:0%
+i enjoy teaching the class i i really
+ 
+
+ align:start position:0%
+i enjoy teaching the class i i really
+enjoy the interaction with you guys
+
+ align:start position:0%
+enjoy the interaction with you guys
+ 
+
+ align:start position:0%
+enjoy the interaction with you guys
+you're
+
+ align:start position:0%
+you're
+ 
+
+ align:start position:0%
+you're
+really doing well
+
+ align:start position:0%
+really doing well
+ 
+
+ align:start position:0%
+really doing well
+it's a great joy to me i hope you like
+
+ align:start position:0%
+it's a great joy to me i hope you like
+ 
+
+ align:start position:0%
+it's a great joy to me i hope you like
+this way of learning economics and
+
+ align:start position:0%
+this way of learning economics and
+ 
+
+ align:start position:0%
+this way of learning economics and
+you're really quite well trained now
+
+ align:start position:0%
+you're really quite well trained now
+ 
+
+ align:start position:0%
+you're really quite well trained now
+thank you very much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/DzqE7tj7eIM.txt b/DzqE7tj7eIM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..427837511d2b364ce47b6b21b33f7dcc69cab4c6
--- /dev/null
+++ b/DzqE7tj7eIM.txt
@@ -0,0 +1,2531 @@
+align:start position:0%
+ 
+okay um so today begins uh igen values
+
+ align:start position:0%
+okay um so today begins uh igen values
+ 
+
+ align:start position:0%
+okay um so today begins uh igen values
+and igen
+
+ align:start position:0%
+and igen
+ 
+
+ align:start position:0%
+and igen
+vectors and the reason we want those
+
+ align:start position:0%
+vectors and the reason we want those
+ 
+
+ align:start position:0%
+vectors and the reason we want those
+need those is to solve systems of linear
+
+ align:start position:0%
+need those is to solve systems of linear
+ 
+
+ align:start position:0%
+need those is to solve systems of linear
+equations systems meaning more than one
+
+ align:start position:0%
+equations systems meaning more than one
+ 
+
+ align:start position:0%
+equations systems meaning more than one
+equation n equations n equal 2 in the
+
+ align:start position:0%
+equation n equations n equal 2 in the
+ 
+
+ align:start position:0%
+equation n equations n equal 2 in the
+examples here so so Lan value is a
+
+ align:start position:0%
+examples here so so Lan value is a
+ 
+
+ align:start position:0%
+examples here so so Lan value is a
+number I Vector is a vector they're both
+
+ align:start position:0%
+number I Vector is a vector they're both
+ 
+
+ align:start position:0%
+number I Vector is a vector they're both
+hiding in the
+
+ align:start position:0%
+hiding in the
+ 
+
+ align:start position:0%
+hiding in the
+Matrix once we find them we can use them
+
+ align:start position:0%
+Matrix once we find them we can use them
+ 
+
+ align:start position:0%
+Matrix once we find them we can use them
+let me show you the reason igen values
+
+ align:start position:0%
+let me show you the reason igen values
+ 
+
+ align:start position:0%
+let me show you the reason igen values
+were created invented discovered uh was
+
+ align:start position:0%
+were created invented discovered uh was
+ 
+
+ align:start position:0%
+were created invented discovered uh was
+solving differential equations which is
+
+ align:start position:0%
+solving differential equations which is
+ 
+
+ align:start position:0%
+solving differential equations which is
+our purpose so Y is now a vector because
+
+ align:start position:0%
+our purpose so Y is now a vector because
+ 
+
+ align:start position:0%
+our purpose so Y is now a vector because
+so this is a system of
+
+ align:start position:0%
+so this is a system of
+ 
+
+ align:start position:0%
+so this is a system of
+equations I'll do an example in a minute
+
+ align:start position:0%
+equations I'll do an example in a minute
+ 
+
+ align:start position:0%
+equations I'll do an example in a minute
+a is a matrix so why so we have n
+
+ align:start position:0%
+a is a matrix so why so we have n
+ 
+
+ align:start position:0%
+a is a matrix so why so we have n
+equations n components of Y and a is an
+
+ align:start position:0%
+equations n components of Y and a is an
+ 
+
+ align:start position:0%
+equations n components of Y and a is an
+N byn Matrix n rows n columns good and
+
+ align:start position:0%
+N byn Matrix n rows n columns good and
+ 
+
+ align:start position:0%
+N byn Matrix n rows n columns good and
+now I can tell you right away where igen
+
+ align:start position:0%
+now I can tell you right away where igen
+ 
+
+ align:start position:0%
+now I can tell you right away where igen
+values and igen vectors pay off they
+
+ align:start position:0%
+values and igen vectors pay off they
+ 
+
+ align:start position:0%
+values and igen vectors pay off they
+they come into the solution we look for
+
+ align:start position:0%
+they come into the solution we look for
+ 
+
+ align:start position:0%
+they come into the solution we look for
+Solutions of that kind when we had one
+
+ align:start position:0%
+Solutions of that kind when we had one
+ 
+
+ align:start position:0%
+Solutions of that kind when we had one
+equation we looked for Solutions just e
+
+ align:start position:0%
+equation we looked for Solutions just e
+ 
+
+ align:start position:0%
+equation we looked for Solutions just e
+to the
+
+ align:start position:0%
+to the
+ 
+
+ align:start position:0%
+to the
+St and we found that number s now we
+
+ align:start position:0%
+St and we found that number s now we
+ 
+
+ align:start position:0%
+St and we found that number s now we
+have e to the Lambda T we changed s to
+
+ align:start position:0%
+have e to the Lambda T we changed s to
+ 
+
+ align:start position:0%
+have e to the Lambda T we changed s to
+Lambda no problem and but multiplied by
+
+ align:start position:0%
+Lambda no problem and but multiplied by
+ 
+
+ align:start position:0%
+Lambda no problem and but multiplied by
+a vector because our unknown is a vector
+
+ align:start position:0%
+a vector because our unknown is a vector
+ 
+
+ align:start position:0%
+a vector because our unknown is a vector
+this is a vector but that does not
+
+ align:start position:0%
+this is a vector but that does not
+ 
+
+ align:start position:0%
+this is a vector but that does not
+depend on time that's the beauty of it
+
+ align:start position:0%
+depend on time that's the beauty of it
+ 
+
+ align:start position:0%
+depend on time that's the beauty of it
+all the time dependence is in the
+
+ align:start position:0%
+all the time dependence is in the
+ 
+
+ align:start position:0%
+all the time dependence is in the
+exponential as always and X is just
+
+ align:start position:0%
+exponential as always and X is just
+ 
+
+ align:start position:0%
+exponential as always and X is just
+multiples of that exponential as you'll
+
+ align:start position:0%
+multiples of that exponential as you'll
+ 
+
+ align:start position:0%
+multiples of that exponential as you'll
+see okay so I look for Solutions like
+
+ align:start position:0%
+see okay so I look for Solutions like
+ 
+
+ align:start position:0%
+see okay so I look for Solutions like
+that I plug that into the differential
+
+ align:start position:0%
+that I plug that into the differential
+ 
+
+ align:start position:0%
+that I plug that into the differential
+equation and what happens so here's my
+
+ align:start position:0%
+equation and what happens so here's my
+ 
+
+ align:start position:0%
+equation and what happens so here's my
+equation I'm plugging in e to the Lambda
+
+ align:start position:0%
+equation I'm plugging in e to the Lambda
+ 
+
+ align:start position:0%
+equation I'm plugging in e to the Lambda
+TX that's y That's a * y there now the
+
+ align:start position:0%
+TX that's y That's a * y there now the
+ 
+
+ align:start position:0%
+TX that's y That's a * y there now the
+derivative of y the time derivative
+
+ align:start position:0%
+derivative of y the time derivative
+ 
+
+ align:start position:0%
+derivative of y the time derivative
+brings down a Lambda so
+
+ align:start position:0%
+brings down a Lambda so
+ 
+
+ align:start position:0%
+brings down a Lambda so
+to get the derivative I include the
+
+ align:start position:0%
+to get the derivative I include the
+ 
+
+ align:start position:0%
+to get the derivative I include the
+Lambda so do you see that substituting
+
+ align:start position:0%
+Lambda so do you see that substituting
+ 
+
+ align:start position:0%
+Lambda so do you see that substituting
+into the equation with this nice
+
+ align:start position:0%
+into the equation with this nice
+ 
+
+ align:start position:0%
+into the equation with this nice
+notation is just this has to be true my
+
+ align:start position:0%
+notation is just this has to be true my
+ 
+
+ align:start position:0%
+notation is just this has to be true my
+equation changed to that form okay now I
+
+ align:start position:0%
+equation changed to that form okay now I
+ 
+
+ align:start position:0%
+equation changed to that form okay now I
+cancel e to the Lambda T just the way I
+
+ align:start position:0%
+cancel e to the Lambda T just the way I
+ 
+
+ align:start position:0%
+cancel e to the Lambda T just the way I
+was always canceling e to the S so I
+
+ align:start position:0%
+was always canceling e to the S so I
+ 
+
+ align:start position:0%
+was always canceling e to the S so I
+cancel e to the Lambda T because it's
+
+ align:start position:0%
+cancel e to the Lambda T because it's
+ 
+
+ align:start position:0%
+cancel e to the Lambda T because it's
+never zero and I have the biggest
+
+ align:start position:0%
+never zero and I have the biggest
+ 
+
+ align:start position:0%
+never zero and I have the biggest
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+ax The Matrix times my I Vector is equal
+
+ align:start position:0%
+ax The Matrix times my I Vector is equal
+ 
+
+ align:start position:0%
+ax The Matrix times my I Vector is equal
+to Lambda X the number the I value times
+
+ align:start position:0%
+to Lambda X the number the I value times
+ 
+
+ align:start position:0%
+to Lambda X the number the I value times
+the igen vector not linear
+
+ align:start position:0%
+the igen vector not linear
+ 
+
+ align:start position:0%
+the igen vector not linear
+notice two unknowns here that are
+
+ align:start position:0%
+notice two unknowns here that are
+ 
+
+ align:start position:0%
+notice two unknowns here that are
+multiplied a number Lambda times a
+
+ align:start position:0%
+multiplied a number Lambda times a
+ 
+
+ align:start position:0%
+multiplied a number Lambda times a
+vector X so what what am I looking for
+
+ align:start position:0%
+vector X so what what am I looking for
+ 
+
+ align:start position:0%
+vector X so what what am I looking for
+I'm looking for vectors
+
+ align:start position:0%
+I'm looking for vectors
+ 
+
+ align:start position:0%
+I'm looking for vectors
+X the igen vectors so that mult
+
+ align:start position:0%
+X the igen vectors so that mult
+ 
+
+ align:start position:0%
+X the igen vectors so that mult
+multiplying by a multiplying a * X gives
+
+ align:start position:0%
+multiplying by a multiplying a * X gives
+ 
+
+ align:start position:0%
+multiplying by a multiplying a * X gives
+a number time x it's in the same
+
+ align:start position:0%
+a number time x it's in the same
+ 
+
+ align:start position:0%
+a number time x it's in the same
+direction as X just the length is
+
+ align:start position:0%
+direction as X just the length is
+ 
+
+ align:start position:0%
+direction as X just the length is
+changed well if Lambda was be was one I
+
+ align:start position:0%
+changed well if Lambda was be was one I
+ 
+
+ align:start position:0%
+changed well if Lambda was be was one I
+would have ax equal x that's allowed if
+
+ align:start position:0%
+would have ax equal x that's allowed if
+ 
+
+ align:start position:0%
+would have ax equal x that's allowed if
+Lambda is zero I would have ax equals z
+
+ align:start position:0%
+Lambda is zero I would have ax equals z
+ 
+
+ align:start position:0%
+Lambda is zero I would have ax equals z
+that's all right I don't want X to be
+
+ align:start position:0%
+that's all right I don't want X to be
+ 
+
+ align:start position:0%
+that's all right I don't want X to be
+zero that's useless that's no that's no
+
+ align:start position:0%
+zero that's useless that's no that's no
+ 
+
+ align:start position:0%
+zero that's useless that's no that's no
+help to know that zero is a solution
+
+ align:start position:0%
+help to know that zero is a solution
+ 
+
+ align:start position:0%
+help to know that zero is a solution
+it's the it's so X should be not zero
+
+ align:start position:0%
+it's the it's so X should be not zero
+ 
+
+ align:start position:0%
+it's the it's so X should be not zero
+Lambda can be any number and it can be
+
+ align:start position:0%
+Lambda can be any number and it can be
+ 
+
+ align:start position:0%
+Lambda can be any number and it can be
+real it could be complex number as you
+
+ align:start position:0%
+real it could be complex number as you
+ 
+
+ align:start position:0%
+real it could be complex number as you
+will see even if the Matrix is real
+
+ align:start position:0%
+will see even if the Matrix is real
+ 
+
+ align:start position:0%
+will see even if the Matrix is real
+Lambda could be complex anyway ax equal
+
+ align:start position:0%
+Lambda could be complex anyway ax equal
+ 
+
+ align:start position:0%
+Lambda could be complex anyway ax equal
+lamb X that's the big equation it got a
+
+ align:start position:0%
+lamb X that's the big equation it got a
+ 
+
+ align:start position:0%
+lamb X that's the big equation it got a
+box around it okay so now I'm ready to
+
+ align:start position:0%
+box around it okay so now I'm ready to
+ 
+
+ align:start position:0%
+box around it okay so now I'm ready to
+do an
+
+ align:start position:0%
+do an
+ 
+
+ align:start position:0%
+do an
+example and in this example first of all
+
+ align:start position:0%
+example and in this example first of all
+ 
+
+ align:start position:0%
+example and in this example first of all
+I'm going to to spot the igen values and
+
+ align:start position:0%
+I'm going to to spot the igen values and
+ 
+
+ align:start position:0%
+I'm going to to spot the igen values and
+IG vectors without a system just go for
+
+ align:start position:0%
+IG vectors without a system just go for
+ 
+
+ align:start position:0%
+IG vectors without a system just go for
+it in the 2x two case okay so I'll give
+
+ align:start position:0%
+it in the 2x two case okay so I'll give
+ 
+
+ align:start position:0%
+it in the 2x two case okay so I'll give
+a 2X two Matrix a we'll find the lambdas
+
+ align:start position:0%
+a 2X two Matrix a we'll find the lambdas
+ 
+
+ align:start position:0%
+a 2X two Matrix a we'll find the lambdas
+and the x's and then we'll have the
+
+ align:start position:0%
+and the x's and then we'll have the
+ 
+
+ align:start position:0%
+and the x's and then we'll have the
+solution to the system of differential
+
+ align:start position:0%
+solution to the system of differential
+ 
+
+ align:start position:0%
+solution to the system of differential
+equations
+
+ align:start position:0%
+equations
+ 
+
+ align:start position:0%
+equations
+good okay there's the
+
+ align:start position:0%
+good okay there's the
+ 
+
+ align:start position:0%
+good okay there's the
+system there's the first equation for y1
+
+ align:start position:0%
+system there's the first equation for y1
+ 
+
+ align:start position:0%
+system there's the first equation for y1
+prime meaning derivative
+
+ align:start position:0%
+prime meaning derivative
+ 
+
+ align:start position:0%
+prime meaning derivative
+time d by DT time derivative is a linear
+
+ align:start position:0%
+time d by DT time derivative is a linear
+ 
+
+ align:start position:0%
+time d by DT time derivative is a linear
+constant coefficients second one linear
+
+ align:start position:0%
+constant coefficients second one linear
+ 
+
+ align:start position:0%
+constant coefficients second one linear
+constant coefficients three and three
+
+ align:start position:0%
+constant coefficients three and three
+ 
+
+ align:start position:0%
+constant coefficients three and three
+those numbers 5 1 3 3 go into the Matrix
+
+ align:start position:0%
+those numbers 5 1 3 3 go into the Matrix
+ 
+
+ align:start position:0%
+those numbers 5 1 3 3 go into the Matrix
+then that problem is exactly y Prime the
+
+ align:start position:0%
+then that problem is exactly y Prime the
+ 
+
+ align:start position:0%
+then that problem is exactly y Prime the
+vector derivative of the vector equal a
+
+ align:start position:0%
+vector derivative of the vector equal a
+ 
+
+ align:start position:0%
+vector derivative of the vector equal a
+* y okay that's my problem now I values
+
+ align:start position:0%
+* y okay that's my problem now I values
+ 
+
+ align:start position:0%
+* y okay that's my problem now I values
+and I vectors will solve it okay so I
+
+ align:start position:0%
+and I vectors will solve it okay so I
+ 
+
+ align:start position:0%
+and I vectors will solve it okay so I
+just look at that matrix it's Matrix
+
+ align:start position:0%
+just look at that matrix it's Matrix
+ 
+
+ align:start position:0%
+just look at that matrix it's Matrix
+question what are the IG values what are
+
+ align:start position:0%
+question what are the IG values what are
+ 
+
+ align:start position:0%
+question what are the IG values what are
+the igen vectors of that Matrix okay and
+
+ align:start position:0%
+the igen vectors of that Matrix okay and
+ 
+
+ align:start position:0%
+the igen vectors of that Matrix okay and
+remember I want I
+
+ align:start position:0%
+remember I want I
+ 
+
+ align:start position:0%
+remember I want I
+want a x = Lambda
+
+ align:start position:0%
+want a x = Lambda
+ 
+
+ align:start position:0%
+want a x = Lambda
+X I've spotted the first igen Vector one
+
+ align:start position:0%
+X I've spotted the first igen Vector one
+ 
+
+ align:start position:0%
+X I've spotted the first igen Vector one
+one we can just check does it Work If I
+
+ align:start position:0%
+one we can just check does it Work If I
+ 
+
+ align:start position:0%
+one we can just check does it Work If I
+multiply a a by that IG Vector 1 one do
+
+ align:start position:0%
+multiply a a by that IG Vector 1 one do
+ 
+
+ align:start position:0%
+multiply a a by that IG Vector 1 one do
+you see what happens when I multiply by
+
+ align:start position:0%
+you see what happens when I multiply by
+ 
+
+ align:start position:0%
+you see what happens when I multiply by
+one that gives me a six that gives me a
+
+ align:start position:0%
+one that gives me a six that gives me a
+ 
+
+ align:start position:0%
+one that gives me a six that gives me a
+six so a * that Vector is
+
+ align:start position:0%
+six so a * that Vector is
+ 
+
+ align:start position:0%
+six so a * that Vector is
+66 and that is 6 * 1 one so there you go
+
+ align:start position:0%
+66 and that is 6 * 1 one so there you go
+ 
+
+ align:start position:0%
+66 and that is 6 * 1 one so there you go
+found the first igen value If I multiply
+
+ align:start position:0%
+found the first igen value If I multiply
+ 
+
+ align:start position:0%
+found the first igen value If I multiply
+a by X I get 6 by X I get the Vector
+
+ align:start position:0%
+a by X I get 6 by X I get the Vector
+ 
+
+ align:start position:0%
+a by X I get 6 by X I get the Vector
+66 now the second one again I've worked
+
+ align:start position:0%
+66 now the second one again I've worked
+ 
+
+ align:start position:0%
+66 now the second one again I've worked
+in advance produce this igen vector and
+
+ align:start position:0%
+in advance produce this igen vector and
+ 
+
+ align:start position:0%
+in advance produce this igen vector and
+I think is 1us 3 so let's multiply by a
+
+ align:start position:0%
+I think is 1us 3 so let's multiply by a
+ 
+
+ align:start position:0%
+I think is 1us 3 so let's multiply by a
+try the second I Vector I should call
+
+ align:start position:0%
+try the second I Vector I should call
+ 
+
+ align:start position:0%
+try the second I Vector I should call
+this first one maybe X1 and Lambda 1 and
+
+ align:start position:0%
+this first one maybe X1 and Lambda 1 and
+ 
+
+ align:start position:0%
+this first one maybe X1 and Lambda 1 and
+I should call this one X2 and Lambda 2
+
+ align:start position:0%
+I should call this one X2 and Lambda 2
+ 
+
+ align:start position:0%
+I should call this one X2 and Lambda 2
+and we can find out what Lambda 2 is if
+
+ align:start position:0%
+and we can find out what Lambda 2 is if
+ 
+
+ align:start position:0%
+and we can find out what Lambda 2 is if
+I know once I find the I vectors of
+
+ align:start position:0%
+I know once I find the I vectors of
+ 
+
+ align:start position:0%
+I know once I find the I vectors of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+I just do a * X to to recognize the
+
+ align:start position:0%
+I just do a * X to to recognize the
+ 
+
+ align:start position:0%
+I just do a * X to to recognize the
+Lambda the igen value so 51 * this is 5
+
+ align:start position:0%
+Lambda the igen value so 51 * this is 5
+ 
+
+ align:start position:0%
+Lambda the igen value so 51 * this is 5
+- 3 is a two it's a two so I've get so
+
+ align:start position:0%
+- 3 is a two it's a two so I've get so
+ 
+
+ align:start position:0%
+- 3 is a two it's a two so I've get so
+here I got a
+
+ align:start position:0%
+here I got a
+ 
+
+ align:start position:0%
+here I got a
+two and from 3 3 it's 3 - 9 is - 6
+
+ align:start position:0%
+two and from 3 3 it's 3 - 9 is - 6
+ 
+
+ align:start position:0%
+two and from 3 3 it's 3 - 9 is - 6
+that's what I got for
+
+ align:start position:0%
+that's what I got for
+ 
+
+ align:start position:0%
+that's what I got for
+ax there was the X
+
+ align:start position:0%
+ax there was the X
+ 
+
+ align:start position:0%
+ax there was the X
+when I did the multiplication ax came
+
+ align:start position:0%
+when I did the multiplication ax came
+ 
+
+ align:start position:0%
+when I did the multiplication ax came
+out to be 2 - 6 and
+
+ align:start position:0%
+out to be 2 - 6 and
+ 
+
+ align:start position:0%
+out to be 2 - 6 and
+good that output is two times the input
+
+ align:start position:0%
+good that output is two times the input
+ 
+
+ align:start position:0%
+good that output is two times the input
+the I value is
+
+ align:start position:0%
+the I value is
+ 
+
+ align:start position:0%
+the I value is
+two right I'm looking for
+
+ align:start position:0%
+two right I'm looking for
+ 
+
+ align:start position:0%
+two right I'm looking for
+inputs the IG Vector so that the output
+
+ align:start position:0%
+inputs the IG Vector so that the output
+ 
+
+ align:start position:0%
+inputs the IG Vector so that the output
+is a number times that IG vector and
+
+ align:start position:0%
+is a number times that IG vector and
+ 
+
+ align:start position:0%
+is a number times that IG vector and
+that number is Lambda the I value so I
+
+ align:start position:0%
+that number is Lambda the I value so I
+ 
+
+ align:start position:0%
+that number is Lambda the I value so I
+have now found the two and and I expect
+
+ align:start position:0%
+have now found the two and and I expect
+ 
+
+ align:start position:0%
+have now found the two and and I expect
+two for a 2X two Matrix you'll see soon
+
+ align:start position:0%
+two for a 2X two Matrix you'll see soon
+ 
+
+ align:start position:0%
+two for a 2X two Matrix you'll see soon
+see why I expect two igen values and
+
+ align:start position:0%
+see why I expect two igen values and
+ 
+
+ align:start position:0%
+see why I expect two igen values and
+each igen value should have an igen
+
+ align:start position:0%
+each igen value should have an igen
+ 
+
+ align:start position:0%
+each igen value should have an igen
+Vector so uh here they are for this
+
+ align:start position:0%
+Vector so uh here they are for this
+ 
+
+ align:start position:0%
+Vector so uh here they are for this
+Matrix so I've got the answers now y of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T which which stands for y1 and Y2 of t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+are okay it's e to the Lambda TX that's
+
+ align:start position:0%
+are okay it's e to the Lambda TX that's
+ 
+
+ align:start position:0%
+are okay it's e to the Lambda TX that's
+remember that's the picture that we're
+
+ align:start position:0%
+remember that's the picture that we're
+ 
+
+ align:start position:0%
+remember that's the picture that we're
+looking for so the first one is e to the
+
+ align:start position:0%
+looking for so the first one is e to the
+ 
+
+ align:start position:0%
+looking for so the first one is e to the
+6t * X which
+
+ align:start position:0%
+6t * X which
+ 
+
+ align:start position:0%
+6t * X which
+is1 if I put that into the equation it
+
+ align:start position:0%
+is1 if I put that into the equation it
+ 
+
+ align:start position:0%
+is1 if I put that into the equation it
+will solve the equation also have
+
+ align:start position:0%
+will solve the equation also have
+ 
+
+ align:start position:0%
+will solve the equation also have
+another one e to the Lambda 2 was 2 t
+
+ align:start position:0%
+another one e to the Lambda 2 was 2 t
+ 
+
+ align:start position:0%
+another one e to the Lambda 2 was 2 t
+e to the Lambda T * its I Vector 1 -
+
+ align:start position:0%
+e to the Lambda T * its I Vector 1 -
+ 
+
+ align:start position:0%
+e to the Lambda T * its I Vector 1 -
+3 that's a solution also one solution
+
+ align:start position:0%
+3 that's a solution also one solution
+ 
+
+ align:start position:0%
+3 that's a solution also one solution
+another solution and what do I do with
+
+ align:start position:0%
+another solution and what do I do with
+ 
+
+ align:start position:0%
+another solution and what do I do with
+linear equations I take
+
+ align:start position:0%
+linear equations I take
+ 
+
+ align:start position:0%
+linear equations I take
+combinations any number C1 of that plus
+
+ align:start position:0%
+combinations any number C1 of that plus
+ 
+
+ align:start position:0%
+combinations any number C1 of that plus
+any number C2 of that is still a
+
+ align:start position:0%
+any number C2 of that is still a
+ 
+
+ align:start position:0%
+any number C2 of that is still a
+solution that's superposition adding
+
+ align:start position:0%
+solution that's superposition adding
+ 
+
+ align:start position:0%
+solution that's superposition adding
+solutions to linear equations there
+
+ align:start position:0%
+solutions to linear equations there
+ 
+
+ align:start position:0%
+solutions to linear equations there
+these are n equations there's no there's
+
+ align:start position:0%
+these are n equations there's no there's
+ 
+
+ align:start position:0%
+these are n equations there's no there's
+no Force term in these equations I'm not
+
+ align:start position:0%
+no Force term in these equations I'm not
+ 
+
+ align:start position:0%
+no Force term in these equations I'm not
+dealing with a force term I'm looking
+
+ align:start position:0%
+dealing with a force term I'm looking
+ 
+
+ align:start position:0%
+dealing with a force term I'm looking
+for the null Solutions the solutions of
+
+ align:start position:0%
+for the null Solutions the solutions of
+ 
+
+ align:start position:0%
+for the null Solutions the solutions of
+the equations themselves and there I
+
+ align:start position:0%
+the equations themselves and there I
+ 
+
+ align:start position:0%
+the equations themselves and there I
+have two Co two solutions two
+
+ align:start position:0%
+have two Co two solutions two
+ 
+
+ align:start position:0%
+have two Co two solutions two
+coefficients to choose how do I choose
+
+ align:start position:0%
+coefficients to choose how do I choose
+ 
+
+ align:start position:0%
+coefficients to choose how do I choose
+them of course I match the initial
+
+ align:start position:0%
+them of course I match the initial
+ 
+
+ align:start position:0%
+them of course I match the initial
+condition so at T equals z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at tal 0 at t = 0 I would have y of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 that's my given initial condition my
+
+ align:start position:0%
+0 that's my given initial condition my
+ 
+
+ align:start position:0%
+0 that's my given initial condition my
+y1 and Y2 will be so I'm setting T
+
+ align:start position:0%
+y1 and Y2 will be so I'm setting T
+ 
+
+ align:start position:0%
+y1 and Y2 will be so I'm setting T
+equals z so that's one of course when T
+
+ align:start position:0%
+equals z so that's one of course when T
+ 
+
+ align:start position:0%
+equals z so that's one of course when T
+is zero that's one so I just have C1 * 1
+
+ align:start position:0%
+is zero that's one so I just have C1 * 1
+ 
+
+ align:start position:0%
+is zero that's one so I just have C1 * 1
+1 and C2 *
+
+ align:start position:0%
+1 and C2 *
+ 
+
+ align:start position:0%
+1 and C2 *
+that that's 1 again at t = 0 * 1 -
+
+ align:start position:0%
+that that's 1 again at t = 0 * 1 -
+ 
+
+ align:start position:0%
+that that's 1 again at t = 0 * 1 -
+3 that's what
+
+ align:start position:0%
+3 that's what
+ 
+
+ align:start position:0%
+3 that's what
+determines C1 and C2 C1 and C2 come from
+
+ align:start position:0%
+determines C1 and C2 C1 and C2 come from
+ 
+
+ align:start position:0%
+determines C1 and C2 C1 and C2 come from
+the initial conditions just the way they
+
+ align:start position:0%
+the initial conditions just the way they
+ 
+
+ align:start position:0%
+the initial conditions just the way they
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+did so I'm solving two first order
+
+ align:start position:0%
+did so I'm solving two first order
+ 
+
+ align:start position:0%
+did so I'm solving two first order
+linear constant coefficient equations
+
+ align:start position:0%
+linear constant coefficient equations
+ 
+
+ align:start position:0%
+linear constant coefficient equations
+homogeneous meaning no no Force term and
+
+ align:start position:0%
+homogeneous meaning no no Force term and
+ 
+
+ align:start position:0%
+homogeneous meaning no no Force term and
+uh I I'm looking for I so I get a null
+
+ align:start position:0%
+uh I I'm looking for I so I get a null
+ 
+
+ align:start position:0%
+uh I I'm looking for I so I get a null
+solution with constants to choose and
+
+ align:start position:0%
+solution with constants to choose and
+ 
+
+ align:start position:0%
+solution with constants to choose and
+all as as always those constants come
+
+ align:start position:0%
+all as as always those constants come
+ 
+
+ align:start position:0%
+all as as always those constants come
+from matching the initial conditions so
+
+ align:start position:0%
+from matching the initial conditions so
+ 
+
+ align:start position:0%
+from matching the initial conditions so
+the there the initial condition here is
+
+ align:start position:0%
+the there the initial condition here is
+ 
+
+ align:start position:0%
+the there the initial condition here is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+vector so if for example y of Z was 2
+
+ align:start position:0%
+vector so if for example y of Z was 2
+ 
+
+ align:start position:0%
+vector so if for example y of Z was 2
+minus 2 then I would want one of those
+
+ align:start position:0%
+minus 2 then I would want one of those
+ 
+
+ align:start position:0%
+minus 2 then I would want one of those
+and one of
+
+ align:start position:0%
+and one of
+ 
+
+ align:start position:0%
+and one of
+those okay that's that's I've used igen
+
+ align:start position:0%
+those okay that's that's I've used igen
+ 
+
+ align:start position:0%
+those okay that's that's I've used igen
+values and igen vectors to solve a
+
+ align:start position:0%
+values and igen vectors to solve a
+ 
+
+ align:start position:0%
+values and igen vectors to solve a
+linear system their first and primary
+
+ align:start position:0%
+linear system their first and primary
+ 
+
+ align:start position:0%
+linear system their first and primary
+purpose okay but how do I find those
+
+ align:start position:0%
+purpose okay but how do I find those
+ 
+
+ align:start position:0%
+purpose okay but how do I find those
+igen values and igen vectors what about
+
+ align:start position:0%
+igen values and igen vectors what about
+ 
+
+ align:start position:0%
+igen values and igen vectors what about
+other properties what what's going on
+
+ align:start position:0%
+other properties what what's going on
+ 
+
+ align:start position:0%
+other properties what what's going on
+with igen values and igen vectors may I
+
+ align:start position:0%
+with igen values and igen vectors may I
+ 
+
+ align:start position:0%
+with igen values and igen vectors may I
+begin on this just a couple more minutes
+
+ align:start position:0%
+begin on this just a couple more minutes
+ 
+
+ align:start position:0%
+begin on this just a couple more minutes
+about IG value Val and ion vectors basic
+
+ align:start position:0%
+about IG value Val and ion vectors basic
+ 
+
+ align:start position:0%
+about IG value Val and ion vectors basic
+facts and then I'll come next time next
+
+ align:start position:0%
+facts and then I'll come next time next
+ 
+
+ align:start position:0%
+facts and then I'll come next time next
+video of how to find them okay basic
+
+ align:start position:0%
+video of how to find them okay basic
+ 
+
+ align:start position:0%
+video of how to find them okay basic
+facts basic facts so
+
+ align:start position:0%
+facts basic facts so
+ 
+
+ align:start position:0%
+facts basic facts so
+start
+
+ align:start position:0%
+start
+ 
+
+ align:start position:0%
+start
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+Ax = Lambda
+
+ align:start position:0%
+Ax = Lambda
+ 
+
+ align:start position:0%
+Ax = Lambda
+X let's suppose we found
+
+ align:start position:0%
+X let's suppose we found
+ 
+
+ align:start position:0%
+X let's suppose we found
+those could you tell me the igen values
+
+ align:start position:0%
+those could you tell me the igen values
+ 
+
+ align:start position:0%
+those could you tell me the igen values
+and igen vectors of a
+
+ align:start position:0%
+and igen vectors of a
+ 
+
+ align:start position:0%
+and igen vectors of a
+squared this is
+
+ align:start position:0%
+squared this is
+ 
+
+ align:start position:0%
+squared this is
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+uh I would like to know what the igon
+
+ align:start position:0%
+uh I would like to know what the igon
+ 
+
+ align:start position:0%
+uh I would like to know what the igon
+values and I vectors of a^ squ are are
+
+ align:start position:0%
+values and I vectors of a^ squ are are
+ 
+
+ align:start position:0%
+values and I vectors of a^ squ are are
+they connected with these so I found the
+
+ align:start position:0%
+they connected with these so I found the
+ 
+
+ align:start position:0%
+they connected with these so I found the
+suppose I know the X and I know the
+
+ align:start position:0%
+suppose I know the X and I know the
+ 
+
+ align:start position:0%
+suppose I know the X and I know the
+Lambda what about for a what about for a
+
+ align:start position:0%
+Lambda what about for a what about for a
+ 
+
+ align:start position:0%
+Lambda what about for a what about for a
+squ well the good thing is that the ion
+
+ align:start position:0%
+squ well the good thing is that the ion
+ 
+
+ align:start position:0%
+squ well the good thing is that the ion
+vectors are the same for a s so let me
+
+ align:start position:0%
+vectors are the same for a s so let me
+ 
+
+ align:start position:0%
+vectors are the same for a s so let me
+show you I I say that same X so I'm this
+
+ align:start position:0%
+show you I I say that same X so I'm this
+ 
+
+ align:start position:0%
+show you I I say that same X so I'm this
+is the
+
+ align:start position:0%
+is the
+ 
+
+ align:start position:0%
+is the
+same X same Vector same ion Vector the
+
+ align:start position:0%
+same X same Vector same ion Vector the
+ 
+
+ align:start position:0%
+same X same Vector same ion Vector the
+igen value would be different of course
+
+ align:start position:0%
+igen value would be different of course
+ 
+
+ align:start position:0%
+igen value would be different of course
+for a^ S but the I Vector is the same
+
+ align:start position:0%
+for a^ S but the I Vector is the same
+ 
+
+ align:start position:0%
+for a^ S but the I Vector is the same
+okay and let's see what happens for a s
+
+ align:start position:0%
+okay and let's see what happens for a s
+ 
+
+ align:start position:0%
+okay and let's see what happens for a s
+so that's a * ax right 1 a and another
+
+ align:start position:0%
+so that's a * ax right 1 a and another
+ 
+
+ align:start position:0%
+so that's a * ax right 1 a and another
+ax but ax is Lambda X
+
+ align:start position:0%
+ax but ax is Lambda X
+ 
+
+ align:start position:0%
+ax but ax is Lambda X
+are you good with that that's just a *
+
+ align:start position:0%
+are you good with that that's just a *
+ 
+
+ align:start position:0%
+are you good with that that's just a *
+ax so that okay now Lambda is a number I
+
+ align:start position:0%
+ax so that okay now Lambda is a number I
+ 
+
+ align:start position:0%
+ax so that okay now Lambda is a number I
+like I like to bring it out front where
+
+ align:start position:0%
+like I like to bring it out front where
+ 
+
+ align:start position:0%
+like I like to bring it out front where
+I can see
+
+ align:start position:0%
+I can see
+ 
+
+ align:start position:0%
+I can see
+it so I I didn't do anything there this
+
+ align:start position:0%
+it so I I didn't do anything there this
+ 
+
+ align:start position:0%
+it so I I didn't do anything there this
+number Lambda was multiplying everything
+
+ align:start position:0%
+number Lambda was multiplying everything
+ 
+
+ align:start position:0%
+number Lambda was multiplying everything
+so put it in front now ax I have again
+
+ align:start position:0%
+so put it in front now ax I have again
+ 
+
+ align:start position:0%
+so put it in front now ax I have again
+the ax that's again the Lambda X because
+
+ align:start position:0%
+the ax that's again the Lambda X because
+ 
+
+ align:start position:0%
+the ax that's again the Lambda X because
+I'm looking at this same X same X so I
+
+ align:start position:0%
+I'm looking at this same X same X so I
+ 
+
+ align:start position:0%
+I'm looking at this same X same X so I
+get the same Lambda so that's a Lambda X
+
+ align:start position:0%
+get the same Lambda so that's a Lambda X
+ 
+
+ align:start position:0%
+get the same Lambda so that's a Lambda X
+another Lambda I have Lambda 2
+
+ align:start position:0%
+another Lambda I have Lambda 2
+ 
+
+ align:start position:0%
+another Lambda I have Lambda 2
+x that's what I wanted a^ 2 x is Lambda
+
+ align:start position:0%
+x that's what I wanted a^ 2 x is Lambda
+ 
+
+ align:start position:0%
+x that's what I wanted a^ 2 x is Lambda
+2 x conclusion the I vectors stay the
+
+ align:start position:0%
+2 x conclusion the I vectors stay the
+ 
+
+ align:start position:0%
+2 x conclusion the I vectors stay the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+Lambda goes to Lambda
+
+ align:start position:0%
+Lambda goes to Lambda
+ 
+
+ align:start position:0%
+Lambda goes to Lambda
+squared the the I values are squared so
+
+ align:start position:0%
+squared the the I values are squared so
+ 
+
+ align:start position:0%
+squared the the I values are squared so
+if I had my example again of oh let me
+
+ align:start position:0%
+if I had my example again of oh let me
+ 
+
+ align:start position:0%
+if I had my example again of oh let me
+find that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix suppose I wanted suppose I had
+
+ align:start position:0%
+Matrix suppose I wanted suppose I had
+ 
+
+ align:start position:0%
+Matrix suppose I wanted suppose I had
+that same
+
+ align:start position:0%
+that same
+ 
+
+ align:start position:0%
+that same
+Matrix and I was interested in a squar
+
+ align:start position:0%
+Matrix and I was interested in a squar
+ 
+
+ align:start position:0%
+Matrix and I was interested in a squar
+then the igen values would be
+
+ align:start position:0%
+then the igen values would be
+ 
+
+ align:start position:0%
+then the igen values would be
+36 and four the
+
+ align:start position:0%
+36 and four the
+ 
+
+ align:start position:0%
+36 and four the
+squares suppose I'm looking at the N
+
+ align:start position:0%
+squares suppose I'm looking at the N
+ 
+
+ align:start position:0%
+squares suppose I'm looking at the N
+power of a matrix you may say why look
+
+ align:start position:0%
+power of a matrix you may say why look
+ 
+
+ align:start position:0%
+power of a matrix you may say why look
+at the N power but there are many
+
+ align:start position:0%
+at the N power but there are many
+ 
+
+ align:start position:0%
+at the N power but there are many
+examples to look at the N power of a
+
+ align:start position:0%
+examples to look at the N power of a
+ 
+
+ align:start position:0%
+examples to look at the N power of a
+matrix mat the thousandth power so let's
+
+ align:start position:0%
+matrix mat the thousandth power so let's
+ 
+
+ align:start position:0%
+matrix mat the thousandth power so let's
+just write down the conclusion same
+
+ align:start position:0%
+just write down the conclusion same
+ 
+
+ align:start position:0%
+just write down the conclusion same
+same uh reasoning a to the n x
+
+ align:start position:0%
+same uh reasoning a to the n x
+ 
+
+ align:start position:0%
+same uh reasoning a to the n x
+is Lambda is the same X and every time I
+
+ align:start position:0%
+is Lambda is the same X and every time I
+ 
+
+ align:start position:0%
+is Lambda is the same X and every time I
+multiply by a I multiply by a Lambda so
+
+ align:start position:0%
+multiply by a I multiply by a Lambda so
+ 
+
+ align:start position:0%
+multiply by a I multiply by a Lambda so
+I get Lambda n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times so there's the handy rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that really tells us something about
+
+ align:start position:0%
+that really tells us something about
+ 
+
+ align:start position:0%
+that really tells us something about
+what what igen values are good for igen
+
+ align:start position:0%
+what what igen values are good for igen
+ 
+
+ align:start position:0%
+what what igen values are good for igen
+values are good for things that move in
+
+ align:start position:0%
+values are good for things that move in
+ 
+
+ align:start position:0%
+values are good for things that move in
+time e differential
+
+ align:start position:0%
+time e differential
+ 
+
+ align:start position:0%
+time e differential
+equations uh that that is really moving
+
+ align:start position:0%
+equations uh that that is really moving
+ 
+
+ align:start position:0%
+equations uh that that is really moving
+in time n equal 1 is the first first
+
+ align:start position:0%
+in time n equal 1 is the first first
+ 
+
+ align:start position:0%
+in time n equal 1 is the first first
+time or n equals z is the start take one
+
+ align:start position:0%
+time or n equals z is the start take one
+ 
+
+ align:start position:0%
+time or n equals z is the start take one
+step to n equal 1 take another step to n
+
+ align:start position:0%
+step to n equal 1 take another step to n
+ 
+
+ align:start position:0%
+step to n equal 1 take another step to n
+equal 2 keep going every time step
+
+ align:start position:0%
+equal 2 keep going every time step
+ 
+
+ align:start position:0%
+equal 2 keep going every time step
+brings a multiplication by Lambda so
+
+ align:start position:0%
+brings a multiplication by Lambda so
+ 
+
+ align:start position:0%
+brings a multiplication by Lambda so
+that is uh a very useful rule another
+
+ align:start position:0%
+that is uh a very useful rule another
+ 
+
+ align:start position:0%
+that is uh a very useful rule another
+handy rule is what about a plus the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identity suppose I add the identity
+
+ align:start position:0%
+identity suppose I add the identity
+ 
+
+ align:start position:0%
+identity suppose I add the identity
+Matrix to
+
+ align:start position:0%
+Matrix to
+ 
+
+ align:start position:0%
+Matrix to
+my uh to my original Matrix what happens
+
+ align:start position:0%
+my uh to my original Matrix what happens
+ 
+
+ align:start position:0%
+my uh to my original Matrix what happens
+to the igen values what happens to the
+
+ align:start position:0%
+to the igen values what happens to the
+ 
+
+ align:start position:0%
+to the igen values what happens to the
+igen vectors basic question or I could
+
+ align:start position:0%
+igen vectors basic question or I could
+ 
+
+ align:start position:0%
+igen vectors basic question or I could
+multiply a constant times the identity
+
+ align:start position:0%
+multiply a constant times the identity
+ 
+
+ align:start position:0%
+multiply a constant times the identity
+two times the identity seven times the
+
+ align:start position:0%
+two times the identity seven times the
+ 
+
+ align:start position:0%
+two times the identity seven times the
+identity and I want to know what about
+
+ align:start position:0%
+identity and I want to know what about
+ 
+
+ align:start position:0%
+identity and I want to know what about
+its ion vectors and the answer is same
+
+ align:start position:0%
+its ion vectors and the answer is same
+ 
+
+ align:start position:0%
+its ion vectors and the answer is same
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+X's same
+
+ align:start position:0%
+X's same
+ 
+
+ align:start position:0%
+X's same
+x i I show that by figuring out what I
+
+ align:start position:0%
+x i I show that by figuring out what I
+ 
+
+ align:start position:0%
+x i I show that by figuring out what I
+have here this is ax which is Lambda X
+
+ align:start position:0%
+have here this is ax which is Lambda X
+ 
+
+ align:start position:0%
+have here this is ax which is Lambda X
+and this is C * the identity time x the
+
+ align:start position:0%
+and this is C * the identity time x the
+ 
+
+ align:start position:0%
+and this is C * the identity time x the
+identity doesn't do anything so that's
+
+ align:start position:0%
+identity doesn't do anything so that's
+ 
+
+ align:start position:0%
+identity doesn't do anything so that's
+just
+
+ align:start position:0%
+just
+ 
+
+ align:start position:0%
+just
+CX so what do I have
+
+ align:start position:0%
+CX so what do I have
+ 
+
+ align:start position:0%
+CX so what do I have
+now I've seen that the IG value is
+
+ align:start position:0%
+now I've seen that the IG value is
+ 
+
+ align:start position:0%
+now I've seen that the IG value is
+Lambda +
+
+ align:start position:0%
+Lambda +
+ 
+
+ align:start position:0%
+Lambda +
+C so there is the I
+
+ align:start position:0%
+C so there is the I
+ 
+
+ align:start position:0%
+C so there is the I
+values
+
+ align:start position:0%
+values
+ 
+
+ align:start position:0%
+values
+for when I I think about this as
+
+ align:start position:0%
+for when I I think about this as
+ 
+
+ align:start position:0%
+for when I I think about this as
+shifting a by a multi of the identity
+
+ align:start position:0%
+shifting a by a multi of the identity
+ 
+
+ align:start position:0%
+shifting a by a multi of the identity
+shifting a adding adding five times the
+
+ align:start position:0%
+shifting a adding adding five times the
+ 
+
+ align:start position:0%
+shifting a adding adding five times the
+identity to it if I add five five times
+
+ align:start position:0%
+identity to it if I add five five times
+ 
+
+ align:start position:0%
+identity to it if I add five five times
+the identity to any Matrix the igen
+
+ align:start position:0%
+the identity to any Matrix the igen
+ 
+
+ align:start position:0%
+the identity to any Matrix the igen
+values of that Matrix go up by
+
+ align:start position:0%
+values of that Matrix go up by
+ 
+
+ align:start position:0%
+values of that Matrix go up by
+five and the igen vectors stay the same
+
+ align:start position:0%
+five and the igen vectors stay the same
+ 
+
+ align:start position:0%
+five and the igen vectors stay the same
+so for as long as I keep working with
+
+ align:start position:0%
+so for as long as I keep working with
+ 
+
+ align:start position:0%
+so for as long as I keep working with
+that one Matrix a taking Powers taking
+
+ align:start position:0%
+that one Matrix a taking Powers taking
+ 
+
+ align:start position:0%
+that one Matrix a taking Powers taking
+adding adding multiples of the identity
+
+ align:start position:0%
+adding adding multiples of the identity
+ 
+
+ align:start position:0%
+adding adding multiples of the identity
+in the later taking expon exponentials
+
+ align:start position:0%
+in the later taking expon exponentials
+ 
+
+ align:start position:0%
+in the later taking expon exponentials
+whatever I do I keep the same igen
+
+ align:start position:0%
+whatever I do I keep the same igen
+ 
+
+ align:start position:0%
+whatever I do I keep the same igen
+vectors and everything is easy the a
+
+ align:start position:0%
+vectors and everything is easy the a
+ 
+
+ align:start position:0%
+vectors and everything is easy the a
+diff but don't think if I had two two
+
+ align:start position:0%
+diff but don't think if I had two two
+ 
+
+ align:start position:0%
+diff but don't think if I had two two
+matrices A and B with different igen
+
+ align:start position:0%
+matrices A and B with different igen
+ 
+
+ align:start position:0%
+matrices A and B with different igen
+vectors then I don't know what the igen
+
+ align:start position:0%
+vectors then I don't know what the igen
+ 
+
+ align:start position:0%
+vectors then I don't know what the igen
+vectors of a plus b would be I don't
+
+ align:start position:0%
+vectors of a plus b would be I don't
+ 
+
+ align:start position:0%
+vectors of a plus b would be I don't
+know those I can't tell the I vectors of
+
+ align:start position:0%
+know those I can't tell the I vectors of
+ 
+
+ align:start position:0%
+know those I can't tell the I vectors of
+a * B because a has has its own little
+
+ align:start position:0%
+a * B because a has has its own little
+ 
+
+ align:start position:0%
+a * B because a has has its own little
+igen vectors and B has its igen vectors
+
+ align:start position:0%
+igen vectors and B has its igen vectors
+ 
+
+ align:start position:0%
+igen vectors and B has its igen vectors
+and unless they're the same I can't
+
+ align:start position:0%
+and unless they're the same I can't
+ 
+
+ align:start position:0%
+and unless they're the same I can't
+easily combine A and B but these are the
+
+ align:start position:0%
+easily combine A and B but these are the
+ 
+
+ align:start position:0%
+easily combine A and B but these are the
+this shows what I as long as I'm staying
+
+ align:start position:0%
+this shows what I as long as I'm staying
+ 
+
+ align:start position:0%
+this shows what I as long as I'm staying
+with one a and it's powers
+
+ align:start position:0%
+with one a and it's powers
+ 
+
+ align:start position:0%
+with one a and it's powers
+and steps like that no problem okay I'll
+
+ align:start position:0%
+and steps like that no problem okay I'll
+ 
+
+ align:start position:0%
+and steps like that no problem okay I'll
+stop there for a first look at igen
+
+ align:start position:0%
+stop there for a first look at igen
+ 
+
+ align:start position:0%
+stop there for a first look at igen
+values and igen vectors
\ No newline at end of file
diff --git a/FEK07tdpX3I.txt b/FEK07tdpX3I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bceaef16fb87435adb65d9b6a95719729c664718
--- /dev/null
+++ b/FEK07tdpX3I.txt
@@ -0,0 +1,475 @@
+align:start position:0%
+ 
+welcome back to 8701
+
+ align:start position:0%
+welcome back to 8701
+ 
+
+ align:start position:0%
+welcome back to 8701
+in this short section we want to look at
+
+ align:start position:0%
+in this short section we want to look at
+ 
+
+ align:start position:0%
+in this short section we want to look at
+the weak interaction a little bit more
+
+ align:start position:0%
+the weak interaction a little bit more
+ 
+
+ align:start position:0%
+the weak interaction a little bit more
+and specifically discuss neutral
+
+ align:start position:0%
+and specifically discuss neutral
+ 
+
+ align:start position:0%
+and specifically discuss neutral
+currents we looked
+
+ align:start position:0%
+currents we looked
+ 
+
+ align:start position:0%
+currents we looked
+in some detail charge currents
+
+ align:start position:0%
+in some detail charge currents
+ 
+
+ align:start position:0%
+in some detail charge currents
+specifically the interaction with quarks
+
+ align:start position:0%
+specifically the interaction with quarks
+ 
+
+ align:start position:0%
+specifically the interaction with quarks
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+we want to look at the z border
+
+ align:start position:0%
+we want to look at the z border
+ 
+
+ align:start position:0%
+we want to look at the z border
+specifically in the weak interaction
+
+ align:start position:0%
+specifically in the weak interaction
+ 
+
+ align:start position:0%
+specifically in the weak interaction
+via the neutral current
+
+ align:start position:0%
+via the neutral current
+ 
+
+ align:start position:0%
+via the neutral current
+so studying those two processes here
+
+ align:start position:0%
+so studying those two processes here
+ 
+
+ align:start position:0%
+so studying those two processes here
+where there's an electron in the
+
+ align:start position:0%
+where there's an electron in the
+ 
+
+ align:start position:0%
+where there's an electron in the
+positron
+
+ align:start position:0%
+positron
+ 
+
+ align:start position:0%
+positron
+through some process including a z-boson
+
+ align:start position:0%
+through some process including a z-boson
+ 
+
+ align:start position:0%
+through some process including a z-boson
+or a photon
+
+ align:start position:0%
+or a photon
+ 
+
+ align:start position:0%
+or a photon
+resulting in a muon and an antimurr
+
+ align:start position:0%
+resulting in a muon and an antimurr
+ 
+
+ align:start position:0%
+resulting in a muon and an antimurr
+those processes have been studied in
+
+ align:start position:0%
+those processes have been studied in
+ 
+
+ align:start position:0%
+those processes have been studied in
+great detail at slack
+
+ align:start position:0%
+great detail at slack
+ 
+
+ align:start position:0%
+great detail at slack
+and at cern with the slc and the large
+
+ align:start position:0%
+and at cern with the slc and the large
+ 
+
+ align:start position:0%
+and at cern with the slc and the large
+electron position collider
+
+ align:start position:0%
+electron position collider
+ 
+
+ align:start position:0%
+electron position collider
+so if we want to you know calculate the
+
+ align:start position:0%
+so if we want to you know calculate the
+ 
+
+ align:start position:0%
+so if we want to you know calculate the
+cross section and
+
+ align:start position:0%
+cross section and
+ 
+
+ align:start position:0%
+cross section and
+study the cross section of the center of
+
+ align:start position:0%
+study the cross section of the center of
+ 
+
+ align:start position:0%
+study the cross section of the center of
+mass energy
+
+ align:start position:0%
+mass energy
+ 
+
+ align:start position:0%
+mass energy
+we see a number of interesting effects
+
+ align:start position:0%
+we see a number of interesting effects
+ 
+
+ align:start position:0%
+we see a number of interesting effects
+at low energies and at very large
+
+ align:start position:0%
+at low energies and at very large
+ 
+
+ align:start position:0%
+at low energies and at very large
+energies
+
+ align:start position:0%
+energies
+ 
+
+ align:start position:0%
+energies
+the cross section runs with one over the
+
+ align:start position:0%
+the cross section runs with one over the
+ 
+
+ align:start position:0%
+the cross section runs with one over the
+energy squared
+
+ align:start position:0%
+energy squared
+ 
+
+ align:start position:0%
+energy squared
+but at the mass of the z-border we see
+
+ align:start position:0%
+but at the mass of the z-border we see
+ 
+
+ align:start position:0%
+but at the mass of the z-border we see
+this enormous resonance here so the
+
+ align:start position:0%
+this enormous resonance here so the
+ 
+
+ align:start position:0%
+this enormous resonance here so the
+resonance is about 200
+
+ align:start position:0%
+resonance is about 200
+ 
+
+ align:start position:0%
+resonance is about 200
+the cross-section at the resonance from
+
+ align:start position:0%
+the cross-section at the resonance from
+ 
+
+ align:start position:0%
+the cross-section at the resonance from
+the z-border is about 200 times that of
+
+ align:start position:0%
+the z-border is about 200 times that of
+ 
+
+ align:start position:0%
+the z-border is about 200 times that of
+just the photon exchange so this allows
+
+ align:start position:0%
+just the photon exchange so this allows
+ 
+
+ align:start position:0%
+just the photon exchange so this allows
+you to study the z-boson
+
+ align:start position:0%
+you to study the z-boson
+ 
+
+ align:start position:0%
+you to study the z-boson
+with great precision um at those
+
+ align:start position:0%
+with great precision um at those
+ 
+
+ align:start position:0%
+with great precision um at those
+colliders you have
+
+ align:start position:0%
+colliders you have
+ 
+
+ align:start position:0%
+colliders you have
+sizable cross-section when you're on
+
+ align:start position:0%
+sizable cross-section when you're on
+ 
+
+ align:start position:0%
+sizable cross-section when you're on
+electron position colliders
+
+ align:start position:0%
+electron position colliders
+ 
+
+ align:start position:0%
+electron position colliders
+and then you can with precision look at
+
+ align:start position:0%
+and then you can with precision look at
+ 
+
+ align:start position:0%
+and then you can with precision look at
+you know what is the rate into
+
+ align:start position:0%
+you know what is the rate into
+ 
+
+ align:start position:0%
+you know what is the rate into
+an antivirus what is the rate in the
+
+ align:start position:0%
+an antivirus what is the rate in the
+ 
+
+ align:start position:0%
+an antivirus what is the rate in the
+quark antiqua and so on and you can
+
+ align:start position:0%
+quark antiqua and so on and you can
+ 
+
+ align:start position:0%
+quark antiqua and so on and you can
+study the mass the width of the z
+
+ align:start position:0%
+study the mass the width of the z
+ 
+
+ align:start position:0%
+study the mass the width of the z
+both on um with with an enormous
+
+ align:start position:0%
+both on um with with an enormous
+ 
+
+ align:start position:0%
+both on um with with an enormous
+level of precision again so i will not
+
+ align:start position:0%
+level of precision again so i will not
+ 
+
+ align:start position:0%
+level of precision again so i will not
+go into too much detail here um please
+
+ align:start position:0%
+go into too much detail here um please
+ 
+
+ align:start position:0%
+go into too much detail here um please
+have a look at chapter
+
+ align:start position:0%
+have a look at chapter
+ 
+
+ align:start position:0%
+have a look at chapter
+9.6 in griffiths for example but there's
+
+ align:start position:0%
+9.6 in griffiths for example but there's
+ 
+
+ align:start position:0%
+9.6 in griffiths for example but there's
+many other resources where you can learn
+
+ align:start position:0%
+many other resources where you can learn
+ 
+
+ align:start position:0%
+many other resources where you can learn
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+more about neutral currents neutral
+
+ align:start position:0%
+more about neutral currents neutral
+ 
+
+ align:start position:0%
+more about neutral currents neutral
+currents
+
+ align:start position:0%
+currents
+ 
+
+ align:start position:0%
+currents
+electro weak neutral currents are
+
+ align:start position:0%
+electro weak neutral currents are
+ 
+
+ align:start position:0%
+electro weak neutral currents are
+specifically important in the study of
+
+ align:start position:0%
+specifically important in the study of
+ 
+
+ align:start position:0%
+specifically important in the study of
+neutrinos
+
+ align:start position:0%
+neutrinos
+ 
+
+ align:start position:0%
+neutrinos
+as we have as we will discuss more in
+
+ align:start position:0%
+as we have as we will discuss more in
+ 
+
+ align:start position:0%
+as we have as we will discuss more in
+the lectures as well
\ No newline at end of file
diff --git a/Fxy3tsWDcpY.txt b/Fxy3tsWDcpY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..40b9b9b25153d50a7a4a793902af9ee8886eabb6
--- /dev/null
+++ b/Fxy3tsWDcpY.txt
@@ -0,0 +1,15123 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu well let's get
+
+ align:start position:0%
+ocw.mit.edu well let's get
+ 
+
+ align:start position:0%
+ocw.mit.edu well let's get
+started I'd like to introduce Lewis
+
+ align:start position:0%
+started I'd like to introduce Lewis
+ 
+
+ align:start position:0%
+started I'd like to introduce Lewis
+Watts it's a great pleasure to have him
+
+ align:start position:0%
+Watts it's a great pleasure to have him
+ 
+
+ align:start position:0%
+Watts it's a great pleasure to have him
+here Lewis is a professor um at the
+
+ align:start position:0%
+here Lewis is a professor um at the
+ 
+
+ align:start position:0%
+here Lewis is a professor um at the
+University of California Santa Cruz
+
+ align:start position:0%
+University of California Santa Cruz
+ 
+
+ align:start position:0%
+University of California Santa Cruz
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+actually has an architectural degree we
+
+ align:start position:0%
+actually has an architectural degree we
+ 
+
+ align:start position:0%
+actually has an architectural degree we
+started studying architecture in
+
+ align:start position:0%
+started studying architecture in
+ 
+
+ align:start position:0%
+started studying architecture in
+graduate school and then drifted towards
+
+ align:start position:0%
+graduate school and then drifted towards
+ 
+
+ align:start position:0%
+graduate school and then drifted towards
+photography his undergraduate degree
+
+ align:start position:0%
+photography his undergraduate degree
+ 
+
+ align:start position:0%
+photography his undergraduate degree
+from Berkeley is in political science
+
+ align:start position:0%
+from Berkeley is in political science
+ 
+
+ align:start position:0%
+from Berkeley is in political science
+and so he came to photography uh after
+
+ align:start position:0%
+and so he came to photography uh after
+ 
+
+ align:start position:0%
+and so he came to photography uh after
+um an undergraduate career in the
+
+ align:start position:0%
+um an undergraduate career in the
+ 
+
+ align:start position:0%
+um an undergraduate career in the
+liberal arts and Lou taught for many
+
+ align:start position:0%
+liberal arts and Lou taught for many
+ 
+
+ align:start position:0%
+liberal arts and Lou taught for many
+years at Berkeley a photography course
+
+ align:start position:0%
+years at Berkeley a photography course
+ 
+
+ align:start position:0%
+years at Berkeley a photography course
+that before I met him I had heard about
+
+ align:start position:0%
+that before I met him I had heard about
+ 
+
+ align:start position:0%
+that before I met him I had heard about
+it from my Berkeley colleagues it was
+
+ align:start position:0%
+it from my Berkeley colleagues it was
+ 
+
+ align:start position:0%
+it from my Berkeley colleagues it was
+known for all the landscape architecture
+
+ align:start position:0%
+known for all the landscape architecture
+ 
+
+ align:start position:0%
+known for all the landscape architecture
+and architecture and planning students
+
+ align:start position:0%
+and architecture and planning students
+ 
+
+ align:start position:0%
+and architecture and planning students
+that that took it um and used
+
+ align:start position:0%
+that that took it um and used
+ 
+
+ align:start position:0%
+that that took it um and used
+photography as a way with L of
+
+ align:start position:0%
+photography as a way with L of
+ 
+
+ align:start position:0%
+photography as a way with L of
+investigating their own culture and and
+
+ align:start position:0%
+investigating their own culture and and
+ 
+
+ align:start position:0%
+investigating their own culture and and
+other cultures and the way they were
+
+ align:start position:0%
+other cultures and the way they were
+ 
+
+ align:start position:0%
+other cultures and the way they were
+expressed in urban
+
+ align:start position:0%
+expressed in urban
+ 
+
+ align:start position:0%
+expressed in urban
+form Lou is uh has had a a distinguished
+
+ align:start position:0%
+form Lou is uh has had a a distinguished
+ 
+
+ align:start position:0%
+form Lou is uh has had a a distinguished
+career he's had many solo exhibitions of
+
+ align:start position:0%
+career he's had many solo exhibitions of
+ 
+
+ align:start position:0%
+career he's had many solo exhibitions of
+his photographs uh been in many many
+
+ align:start position:0%
+his photographs uh been in many many
+ 
+
+ align:start position:0%
+his photographs uh been in many many
+group exhibition positions uh all over
+
+ align:start position:0%
+group exhibition positions uh all over
+ 
+
+ align:start position:0%
+group exhibition positions uh all over
+including the Smithsonian his uh his
+
+ align:start position:0%
+including the Smithsonian his uh his
+ 
+
+ align:start position:0%
+including the Smithsonian his uh his
+work is in the collection of the
+
+ align:start position:0%
+work is in the collection of the
+ 
+
+ align:start position:0%
+work is in the collection of the
+Smithsonian and uh San Francisco uh the
+
+ align:start position:0%
+Smithsonian and uh San Francisco uh the
+ 
+
+ align:start position:0%
+Smithsonian and uh San Francisco uh the
+Museum of Modern Art in San Francisco
+
+ align:start position:0%
+Museum of Modern Art in San Francisco
+ 
+
+ align:start position:0%
+Museum of Modern Art in San Francisco
+he's also as for a photographer done a
+
+ align:start position:0%
+he's also as for a photographer done a
+ 
+
+ align:start position:0%
+he's also as for a photographer done a
+number of in unusual things um including
+
+ align:start position:0%
+number of in unusual things um including
+ 
+
+ align:start position:0%
+number of in unusual things um including
+uh working with the National Park
+
+ align:start position:0%
+uh working with the National Park
+ 
+
+ align:start position:0%
+uh working with the National Park
+Service on and planners on a Heritage
+
+ align:start position:0%
+Service on and planners on a Heritage
+ 
+
+ align:start position:0%
+Service on and planners on a Heritage
+Trail in Richmond California documenting
+
+ align:start position:0%
+Trail in Richmond California documenting
+ 
+
+ align:start position:0%
+Trail in Richmond California documenting
+um the area where the shipyards were
+
+ align:start position:0%
+um the area where the shipyards were
+ 
+
+ align:start position:0%
+um the area where the shipyards were
+during the second world war and he's
+
+ align:start position:0%
+during the second world war and he's
+ 
+
+ align:start position:0%
+during the second world war and he's
+recently just published a book on um the
+
+ align:start position:0%
+recently just published a book on um the
+ 
+
+ align:start position:0%
+recently just published a book on um the
+San Francisco Filmore which I think
+
+ align:start position:0%
+San Francisco Filmore which I think
+ 
+
+ align:start position:0%
+San Francisco Filmore which I think
+he'll tell you a little bit about the
+
+ align:start position:0%
+he'll tell you a little bit about the
+ 
+
+ align:start position:0%
+he'll tell you a little bit about the
+culture of jazz uh in San Francisco it
+
+ align:start position:0%
+culture of jazz uh in San Francisco it
+ 
+
+ align:start position:0%
+culture of jazz uh in San Francisco it
+gives me a great pleasure to um to have
+
+ align:start position:0%
+gives me a great pleasure to um to have
+ 
+
+ align:start position:0%
+gives me a great pleasure to um to have
+Lewis here and I won't say anymore uh uh
+
+ align:start position:0%
+Lewis here and I won't say anymore uh uh
+ 
+
+ align:start position:0%
+Lewis here and I won't say anymore uh uh
+he really needs no more introduction at
+
+ align:start position:0%
+he really needs no more introduction at
+ 
+
+ align:start position:0%
+he really needs no more introduction at
+all thank welcome well thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well let's see I'm um I actually went to
+
+ align:start position:0%
+well let's see I'm um I actually went to
+ 
+
+ align:start position:0%
+well let's see I'm um I actually went to
+high school in Boston some 40 years ago
+
+ align:start position:0%
+high school in Boston some 40 years ago
+ 
+
+ align:start position:0%
+high school in Boston some 40 years ago
+and I for some reason I've only been
+
+ align:start position:0%
+and I for some reason I've only been
+ 
+
+ align:start position:0%
+and I for some reason I've only been
+back a few times so it's interesting to
+
+ align:start position:0%
+back a few times so it's interesting to
+ 
+
+ align:start position:0%
+back a few times so it's interesting to
+be here and it sort of brings up some
+
+ align:start position:0%
+be here and it sort of brings up some
+ 
+
+ align:start position:0%
+be here and it sort of brings up some
+things from my past um um a lot of my
+
+ align:start position:0%
+things from my past um um a lot of my
+ 
+
+ align:start position:0%
+things from my past um um a lot of my
+work is informed by um I think migration
+
+ align:start position:0%
+work is informed by um I think migration
+ 
+
+ align:start position:0%
+work is informed by um I think migration
+um my fa my father both of my parents
+
+ align:start position:0%
+um my fa my father both of my parents
+ 
+
+ align:start position:0%
+um my fa my father both of my parents
+are from the south uh my father's from
+
+ align:start position:0%
+are from the south uh my father's from
+ 
+
+ align:start position:0%
+are from the south uh my father's from
+Georg Georgia my mother's from uh
+
+ align:start position:0%
+Georg Georgia my mother's from uh
+ 
+
+ align:start position:0%
+Georg Georgia my mother's from uh
+Arkansas and I was actually born in
+
+ align:start position:0%
+Arkansas and I was actually born in
+ 
+
+ align:start position:0%
+Arkansas and I was actually born in
+Little Rock Arkansas but I was conceived
+
+ align:start position:0%
+Little Rock Arkansas but I was conceived
+ 
+
+ align:start position:0%
+Little Rock Arkansas but I was conceived
+in Seattle because my father was
+
+ align:start position:0%
+in Seattle because my father was
+ 
+
+ align:start position:0%
+in Seattle because my father was
+discharged from Fort Lewis in Tacoma and
+
+ align:start position:0%
+discharged from Fort Lewis in Tacoma and
+ 
+
+ align:start position:0%
+discharged from Fort Lewis in Tacoma and
+went into Seattle and um ended up
+
+ align:start position:0%
+went into Seattle and um ended up
+ 
+
+ align:start position:0%
+went into Seattle and um ended up
+getting a job with the Urban League and
+
+ align:start position:0%
+getting a job with the Urban League and
+ 
+
+ align:start position:0%
+getting a job with the Urban League and
+my mother came to join him and then went
+
+ align:start position:0%
+my mother came to join him and then went
+ 
+
+ align:start position:0%
+my mother came to join him and then went
+back to Little Rock because she knew the
+
+ align:start position:0%
+back to Little Rock because she knew the
+ 
+
+ align:start position:0%
+back to Little Rock because she knew the
+doctor so it's been helpful when I'm
+
+ align:start position:0%
+doctor so it's been helpful when I'm
+ 
+
+ align:start position:0%
+doctor so it's been helpful when I'm
+photographing in the South I can say I
+
+ align:start position:0%
+photographing in the South I can say I
+ 
+
+ align:start position:0%
+photographing in the South I can say I
+I'm I'm from here even though I just was
+
+ align:start position:0%
+I'm I'm from here even though I just was
+ 
+
+ align:start position:0%
+I'm I'm from here even though I just was
+there for four months um so a lot of my
+
+ align:start position:0%
+there for four months um so a lot of my
+ 
+
+ align:start position:0%
+there for four months um so a lot of my
+work um actually so photography caught
+
+ align:start position:0%
+work um actually so photography caught
+ 
+
+ align:start position:0%
+work um actually so photography caught
+me when I was a in the first year of a
+
+ align:start position:0%
+me when I was a in the first year of a
+ 
+
+ align:start position:0%
+me when I was a in the first year of a
+um graduate program for non- Majors uh
+
+ align:start position:0%
+um graduate program for non- Majors uh
+ 
+
+ align:start position:0%
+um graduate program for non- Majors uh
+in architecture at Berkeley and I um
+
+ align:start position:0%
+in architecture at Berkeley and I um
+ 
+
+ align:start position:0%
+in architecture at Berkeley and I um
+ended up actually getting degree in
+
+ align:start position:0%
+ended up actually getting degree in
+ 
+
+ align:start position:0%
+ended up actually getting degree in
+design rather than a master of
+
+ align:start position:0%
+design rather than a master of
+ 
+
+ align:start position:0%
+design rather than a master of
+architecture um and have had had the
+
+ align:start position:0%
+architecture um and have had had the
+ 
+
+ align:start position:0%
+architecture um and have had had the
+opportunity to to teach uh primarily um
+
+ align:start position:0%
+opportunity to to teach uh primarily um
+ 
+
+ align:start position:0%
+opportunity to to teach uh primarily um
+uh seniors and graduate students in the
+
+ align:start position:0%
+uh seniors and graduate students in the
+ 
+
+ align:start position:0%
+uh seniors and graduate students in the
+College of environmental design and a
+
+ align:start position:0%
+College of environmental design and a
+ 
+
+ align:start position:0%
+College of environmental design and a
+few others Berkeley does not really have
+
+ align:start position:0%
+few others Berkeley does not really have
+ 
+
+ align:start position:0%
+few others Berkeley does not really have
+a photo program um but it was
+
+ align:start position:0%
+a photo program um but it was
+ 
+
+ align:start position:0%
+a photo program um but it was
+interesting to me that um uh a most of
+
+ align:start position:0%
+interesting to me that um uh a most of
+ 
+
+ align:start position:0%
+interesting to me that um uh a most of
+the Architects did not want to do do
+
+ align:start position:0%
+the Architects did not want to do do
+ 
+
+ align:start position:0%
+the Architects did not want to do do
+architectural Photography they were
+
+ align:start position:0%
+architectural Photography they were
+ 
+
+ align:start position:0%
+architectural Photography they were
+interested in sort of uh expand uh
+
+ align:start position:0%
+interested in sort of uh expand uh
+ 
+
+ align:start position:0%
+interested in sort of uh expand uh
+exploring the medium kind of another
+
+ align:start position:0%
+exploring the medium kind of another
+ 
+
+ align:start position:0%
+exploring the medium kind of another
+ways and then they would use it in their
+
+ align:start position:0%
+ways and then they would use it in their
+ 
+
+ align:start position:0%
+ways and then they would use it in their
+research later but in the class they
+
+ align:start position:0%
+research later but in the class they
+ 
+
+ align:start position:0%
+research later but in the class they
+wanted I basically taught it as a fine
+
+ align:start position:0%
+wanted I basically taught it as a fine
+ 
+
+ align:start position:0%
+wanted I basically taught it as a fine
+arts class um and my own work um I was
+
+ align:start position:0%
+arts class um and my own work um I was
+ 
+
+ align:start position:0%
+arts class um and my own work um I was
+very interested in photographing in West
+
+ align:start position:0%
+very interested in photographing in West
+ 
+
+ align:start position:0%
+very interested in photographing in West
+Oakland which is um an area that was
+
+ align:start position:0%
+Oakland which is um an area that was
+ 
+
+ align:start position:0%
+Oakland which is um an area that was
+populated during World War II by a lot
+
+ align:start position:0%
+populated during World War II by a lot
+ 
+
+ align:start position:0%
+populated during World War II by a lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+African-Americans um who came to work in
+
+ align:start position:0%
+African-Americans um who came to work in
+ 
+
+ align:start position:0%
+African-Americans um who came to work in
+the shipyards uh during World War II
+
+ align:start position:0%
+the shipyards uh during World War II
+ 
+
+ align:start position:0%
+the shipyards uh during World War II
+basically World War II most of you know
+
+ align:start position:0%
+basically World War II most of you know
+ 
+
+ align:start position:0%
+basically World War II most of you know
+into the depression and all of a sudden
+
+ align:start position:0%
+into the depression and all of a sudden
+ 
+
+ align:start position:0%
+into the depression and all of a sudden
+there was work when the war effort began
+
+ align:start position:0%
+there was work when the war effort began
+ 
+
+ align:start position:0%
+there was work when the war effort began
+and what I noticed in West Oakland where
+
+ align:start position:0%
+and what I noticed in West Oakland where
+ 
+
+ align:start position:0%
+and what I noticed in West Oakland where
+there all these sort of evidences of the
+
+ align:start position:0%
+there all these sort of evidences of the
+ 
+
+ align:start position:0%
+there all these sort of evidences of the
+Southern background of either the
+
+ align:start position:0%
+Southern background of either the
+ 
+
+ align:start position:0%
+Southern background of either the
+inhabitants or the parents of the
+
+ align:start position:0%
+inhabitants or the parents of the
+ 
+
+ align:start position:0%
+inhabitants or the parents of the
+inhabitants and how those traces were
+
+ align:start position:0%
+inhabitants and how those traces were
+ 
+
+ align:start position:0%
+inhabitants and how those traces were
+left in the landscape and that's what I
+
+ align:start position:0%
+left in the landscape and that's what I
+ 
+
+ align:start position:0%
+left in the landscape and that's what I
+was interested in photographing I'm the
+
+ align:start position:0%
+was interested in photographing I'm the
+ 
+
+ align:start position:0%
+was interested in photographing I'm the
+son of um two social scientists and it's
+
+ align:start position:0%
+son of um two social scientists and it's
+ 
+
+ align:start position:0%
+son of um two social scientists and it's
+funny when I first started doing
+
+ align:start position:0%
+funny when I first started doing
+ 
+
+ align:start position:0%
+funny when I first started doing
+photography I said well all this
+
+ align:start position:0%
+photography I said well all this
+ 
+
+ align:start position:0%
+photography I said well all this
+sociology and history I've left behind
+
+ align:start position:0%
+sociology and history I've left behind
+ 
+
+ align:start position:0%
+sociology and history I've left behind
+but of course it informs all the work
+
+ align:start position:0%
+but of course it informs all the work
+ 
+
+ align:start position:0%
+but of course it informs all the work
+that I do so what I want to show you is
+
+ align:start position:0%
+that I do so what I want to show you is
+ 
+
+ align:start position:0%
+that I do so what I want to show you is
+a uh a a couple of projects one is a um
+
+ align:start position:0%
+a uh a a couple of projects one is a um
+ 
+
+ align:start position:0%
+a uh a a couple of projects one is a um
+a visual history project um I'll talk a
+
+ align:start position:0%
+a visual history project um I'll talk a
+ 
+
+ align:start position:0%
+a visual history project um I'll talk a
+little bit about I I decided not to show
+
+ align:start position:0%
+little bit about I I decided not to show
+ 
+
+ align:start position:0%
+little bit about I I decided not to show
+slides but this signage project project
+
+ align:start position:0%
+slides but this signage project project
+ 
+
+ align:start position:0%
+slides but this signage project project
+was um part of a team that was um uh
+
+ align:start position:0%
+was um part of a team that was um uh
+ 
+
+ align:start position:0%
+was um part of a team that was um uh
+commissioned by the the the de
+
+ align:start position:0%
+commissioned by the the the de
+ 
+
+ align:start position:0%
+commissioned by the the the de
+Redevelopment agency of the city of
+
+ align:start position:0%
+Redevelopment agency of the city of
+ 
+
+ align:start position:0%
+Redevelopment agency of the city of
+Richmond which is just nor north of uh
+
+ align:start position:0%
+Richmond which is just nor north of uh
+ 
+
+ align:start position:0%
+Richmond which is just nor north of uh
+Berkeley in um San Francisco and which
+
+ align:start position:0%
+Berkeley in um San Francisco and which
+ 
+
+ align:start position:0%
+Berkeley in um San Francisco and which
+was during World War II the um side of
+
+ align:start position:0%
+was during World War II the um side of
+ 
+
+ align:start position:0%
+was during World War II the um side of
+the Kaiser shipyards and uh that was
+
+ align:start position:0%
+the Kaiser shipyards and uh that was
+ 
+
+ align:start position:0%
+the Kaiser shipyards and uh that was
+also a place where a lot of people from
+
+ align:start position:0%
+also a place where a lot of people from
+ 
+
+ align:start position:0%
+also a place where a lot of people from
+all over the country came because there
+
+ align:start position:0%
+all over the country came because there
+ 
+
+ align:start position:0%
+all over the country came because there
+was work it was the first place where
+
+ align:start position:0%
+was work it was the first place where
+ 
+
+ align:start position:0%
+was work it was the first place where
+there was an integrated Workforce it was
+
+ align:start position:0%
+there was an integrated Workforce it was
+ 
+
+ align:start position:0%
+there was an integrated Workforce it was
+the birth of Rosie the Riveter um where
+
+ align:start position:0%
+the birth of Rosie the Riveter um where
+ 
+
+ align:start position:0%
+the birth of Rosie the Riveter um where
+women were actually welding as it's
+
+ align:start position:0%
+women were actually welding as it's
+ 
+
+ align:start position:0%
+women were actually welding as it's
+supposed to riveting but um but where
+
+ align:start position:0%
+supposed to riveting but um but where
+ 
+
+ align:start position:0%
+supposed to riveting but um but where
+women were uh integral part of the
+
+ align:start position:0%
+women were uh integral part of the
+ 
+
+ align:start position:0%
+women were uh integral part of the
+workforce um it was also a place that
+
+ align:start position:0%
+workforce um it was also a place that
+ 
+
+ align:start position:0%
+workforce um it was also a place that
+had segregated housing and um uh kind of
+
+ align:start position:0%
+had segregated housing and um uh kind of
+ 
+
+ align:start position:0%
+had segregated housing and um uh kind of
+sort of had patterns that were happening
+
+ align:start position:0%
+sort of had patterns that were happening
+ 
+
+ align:start position:0%
+sort of had patterns that were happening
+in other parts of the country but there
+
+ align:start position:0%
+in other parts of the country but there
+ 
+
+ align:start position:0%
+in other parts of the country but there
+was actually very little Trace so um a
+
+ align:start position:0%
+was actually very little Trace so um a
+ 
+
+ align:start position:0%
+was actually very little Trace so um a
+what uh people had been trying to do was
+
+ align:start position:0%
+what uh people had been trying to do was
+ 
+
+ align:start position:0%
+what uh people had been trying to do was
+to make the um sort of access to the Bay
+
+ align:start position:0%
+to make the um sort of access to the Bay
+ 
+
+ align:start position:0%
+to make the um sort of access to the Bay
+there was only something like a half
+
+ align:start position:0%
+there was only something like a half
+ 
+
+ align:start position:0%
+there was only something like a half
+mile access and uh there's now almost
+
+ align:start position:0%
+mile access and uh there's now almost
+ 
+
+ align:start position:0%
+mile access and uh there's now almost
+Total Access and eventually there's
+
+ align:start position:0%
+Total Access and eventually there's
+ 
+
+ align:start position:0%
+Total Access and eventually there's
+going to be a trail it'll um circum
+
+ align:start position:0%
+going to be a trail it'll um circum
+ 
+
+ align:start position:0%
+going to be a trail it'll um circum
+Amulet the bay and and like I can ride
+
+ align:start position:0%
+Amulet the bay and and like I can ride
+ 
+
+ align:start position:0%
+Amulet the bay and and like I can ride
+from my house in Port Richmond to
+
+ align:start position:0%
+from my house in Port Richmond to
+ 
+
+ align:start position:0%
+from my house in Port Richmond to
+Emeryville or to Oakland without bring
+
+ align:start position:0%
+Emeryville or to Oakland without bring
+ 
+
+ align:start position:0%
+Emeryville or to Oakland without bring
+in traffic going just along the bay and
+
+ align:start position:0%
+in traffic going just along the bay and
+ 
+
+ align:start position:0%
+in traffic going just along the bay and
+so in the area in Richmond there are
+
+ align:start position:0%
+so in the area in Richmond there are
+ 
+
+ align:start position:0%
+so in the area in Richmond there are
+these signs that have um dorothia Lang
+
+ align:start position:0%
+these signs that have um dorothia Lang
+ 
+
+ align:start position:0%
+these signs that have um dorothia Lang
+and other people's photographs and text
+
+ align:start position:0%
+and other people's photographs and text
+ 
+
+ align:start position:0%
+and other people's photographs and text
+of uh the social impact when the
+
+ align:start position:0%
+of uh the social impact when the
+ 
+
+ align:start position:0%
+of uh the social impact when the
+population of Richmond C trip in a
+
+ align:start position:0%
+population of Richmond C trip in a
+ 
+
+ align:start position:0%
+population of Richmond C trip in a
+course of 6 months so it was interesting
+
+ align:start position:0%
+course of 6 months so it was interesting
+ 
+
+ align:start position:0%
+course of 6 months so it was interesting
+to me to uh both collect that and also
+
+ align:start position:0%
+to me to uh both collect that and also
+ 
+
+ align:start position:0%
+to me to uh both collect that and also
+place that in a in an area where people
+
+ align:start position:0%
+place that in a in an area where people
+ 
+
+ align:start position:0%
+place that in a in an area where people
+who are using the the space for
+
+ align:start position:0%
+who are using the the space for
+ 
+
+ align:start position:0%
+who are using the the space for
+recreation the trail can actually see um
+
+ align:start position:0%
+recreation the trail can actually see um
+ 
+
+ align:start position:0%
+recreation the trail can actually see um
+this history which would been hidden so
+
+ align:start position:0%
+this history which would been hidden so
+ 
+
+ align:start position:0%
+this history which would been hidden so
+another um uh history project that I've
+
+ align:start position:0%
+another um uh history project that I've
+ 
+
+ align:start position:0%
+another um uh history project that I've
+been working on actually for about the
+
+ align:start position:0%
+been working on actually for about the
+ 
+
+ align:start position:0%
+been working on actually for about the
+last 10 or 15 years is um based on a set
+
+ align:start position:0%
+last 10 or 15 years is um based on a set
+ 
+
+ align:start position:0%
+last 10 or 15 years is um based on a set
+of photographs I found in a Sho shine
+
+ align:start position:0%
+of photographs I found in a Sho shine
+ 
+
+ align:start position:0%
+of photographs I found in a Sho shine
+parlor um uh
+
+ align:start position:0%
+parlor um uh
+ 
+
+ align:start position:0%
+parlor um uh
+and this is uh red pal or hopefully this
+
+ align:start position:0%
+and this is uh red pal or hopefully this
+ 
+
+ align:start position:0%
+and this is uh red pal or hopefully this
+will be hold on just a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sec
+
+ align:start position:0%
+sec
+ 
+
+ align:start position:0%
+sec
+okay this is uh red pal in front of his
+
+ align:start position:0%
+okay this is uh red pal in front of his
+ 
+
+ align:start position:0%
+okay this is uh red pal in front of his
+uh shine parlor and red uh like a lot of
+
+ align:start position:0%
+uh shine parlor and red uh like a lot of
+ 
+
+ align:start position:0%
+uh shine parlor and red uh like a lot of
+um uh Barbers and beauticians and in
+
+ align:start position:0%
+um uh Barbers and beauticians and in
+ 
+
+ align:start position:0%
+um uh Barbers and beauticians and in
+this case uh shine parlor was actually a
+
+ align:start position:0%
+this case uh shine parlor was actually a
+ 
+
+ align:start position:0%
+this case uh shine parlor was actually a
+a uh archivist and he had photographs of
+
+ align:start position:0%
+a uh archivist and he had photographs of
+ 
+
+ align:start position:0%
+a uh archivist and he had photographs of
+every one who had uh been in this area
+
+ align:start position:0%
+every one who had uh been in this area
+ 
+
+ align:start position:0%
+every one who had uh been in this area
+in San Francisco The Filmore District
+
+ align:start position:0%
+in San Francisco The Filmore District
+ 
+
+ align:start position:0%
+in San Francisco The Filmore District
+which um had uh sort of instantly became
+
+ align:start position:0%
+which um had uh sort of instantly became
+ 
+
+ align:start position:0%
+which um had uh sort of instantly became
+a little Harlem in the early 40s uh when
+
+ align:start position:0%
+a little Harlem in the early 40s uh when
+ 
+
+ align:start position:0%
+a little Harlem in the early 40s uh when
+um uh people came West and in San
+
+ align:start position:0%
+um uh people came West and in San
+ 
+
+ align:start position:0%
+um uh people came West and in San
+Francisco the only place where there was
+
+ align:start position:0%
+Francisco the only place where there was
+ 
+
+ align:start position:0%
+Francisco the only place where there was
+available housing was what had been
+
+ align:start position:0%
+available housing was what had been
+ 
+
+ align:start position:0%
+available housing was what had been
+Japan town because the Japanese had been
+
+ align:start position:0%
+Japan town because the Japanese had been
+ 
+
+ align:start position:0%
+Japan town because the Japanese had been
+recently intered and it was uh it it
+
+ align:start position:0%
+recently intered and it was uh it it
+ 
+
+ align:start position:0%
+recently intered and it was uh it it
+already sort of had a built-in um uh set
+
+ align:start position:0%
+already sort of had a built-in um uh set
+ 
+
+ align:start position:0%
+already sort of had a built-in um uh set
+of of uh institutions that were um sort
+
+ align:start position:0%
+of of uh institutions that were um sort
+ 
+
+ align:start position:0%
+of of uh institutions that were um sort
+of taken over by African-Americans there
+
+ align:start position:0%
+of taken over by African-Americans there
+ 
+
+ align:start position:0%
+of taken over by African-Americans there
+were already there were clubs at at its
+
+ align:start position:0%
+were already there were clubs at at its
+ 
+
+ align:start position:0%
+were already there were clubs at at its
+height there were probably eight or nine
+
+ align:start position:0%
+height there were probably eight or nine
+ 
+
+ align:start position:0%
+height there were probably eight or nine
+jazz clubs there were three
+
+ align:start position:0%
+jazz clubs there were three
+ 
+
+ align:start position:0%
+jazz clubs there were three
+african-american-owned
+
+ align:start position:0%
+african-american-owned
+ 
+
+ align:start position:0%
+african-american-owned
+hotels um and there was a critical mass
+
+ align:start position:0%
+hotels um and there was a critical mass
+ 
+
+ align:start position:0%
+hotels um and there was a critical mass
+um of of people who had come to work in
+
+ align:start position:0%
+um of of people who had come to work in
+ 
+
+ align:start position:0%
+um of of people who had come to work in
+both um Hunter point and in the East Bay
+
+ align:start position:0%
+both um Hunter point and in the East Bay
+ 
+
+ align:start position:0%
+both um Hunter point and in the East Bay
+in the the shipyards and so um when I
+
+ align:start position:0%
+in the the shipyards and so um when I
+ 
+
+ align:start position:0%
+in the the shipyards and so um when I
+walked in in
+
+ align:start position:0%
+walked in in
+ 
+
+ align:start position:0%
+walked in in
+1989 uh someone had sent me to a shine
+
+ align:start position:0%
+1989 uh someone had sent me to a shine
+ 
+
+ align:start position:0%
+1989 uh someone had sent me to a shine
+parlor I got really excited and I said
+
+ align:start position:0%
+parlor I got really excited and I said
+ 
+
+ align:start position:0%
+parlor I got really excited and I said
+wow can I photograph walls and he was
+
+ align:start position:0%
+wow can I photograph walls and he was
+ 
+
+ align:start position:0%
+wow can I photograph walls and he was
+having none of it he basically threw me
+
+ align:start position:0%
+having none of it he basically threw me
+ 
+
+ align:start position:0%
+having none of it he basically threw me
+out of his Club of his shop so I came
+
+ align:start position:0%
+out of his Club of his shop so I came
+ 
+
+ align:start position:0%
+out of his Club of his shop so I came
+back a month later armed with some
+
+ align:start position:0%
+back a month later armed with some
+ 
+
+ align:start position:0%
+back a month later armed with some
+people that knew him and he was gone and
+
+ align:start position:0%
+people that knew him and he was gone and
+ 
+
+ align:start position:0%
+people that knew him and he was gone and
+the walls were bare um here's a picture
+
+ align:start position:0%
+the walls were bare um here's a picture
+ 
+
+ align:start position:0%
+the walls were bare um here's a picture
+of the um you can see if you can see in
+
+ align:start position:0%
+of the um you can see if you can see in
+ 
+
+ align:start position:0%
+of the um you can see if you can see in
+the walls there's a picture of Bobby
+
+ align:start position:0%
+the walls there's a picture of Bobby
+ 
+
+ align:start position:0%
+the walls there's a picture of Bobby
+Kennedy and Sitting Bull and Joseph
+
+ align:start position:0%
+Kennedy and Sitting Bull and Joseph
+ 
+
+ align:start position:0%
+Kennedy and Sitting Bull and Joseph
+Stalin and Jackie Robinson I mean really
+
+ align:start position:0%
+Stalin and Jackie Robinson I mean really
+ 
+
+ align:start position:0%
+Stalin and Jackie Robinson I mean really
+had and on other walls there were a lot
+
+ align:start position:0%
+had and on other walls there were a lot
+ 
+
+ align:start position:0%
+had and on other walls there were a lot
+of uh Jazz musicians so um what he was
+
+ align:start position:0%
+of uh Jazz musicians so um what he was
+ 
+
+ align:start position:0%
+of uh Jazz musicians so um what he was
+gone when I came back and it turned out
+
+ align:start position:0%
+gone when I came back and it turned out
+ 
+
+ align:start position:0%
+gone when I came back and it turned out
+uh after 5 years of searching that he
+
+ align:start position:0%
+uh after 5 years of searching that he
+ 
+
+ align:start position:0%
+uh after 5 years of searching that he
+had had a stroke literally two weeks
+
+ align:start position:0%
+had had a stroke literally two weeks
+ 
+
+ align:start position:0%
+had had a stroke literally two weeks
+after I'd seen him and so in the mid 90s
+
+ align:start position:0%
+after I'd seen him and so in the mid 90s
+ 
+
+ align:start position:0%
+after I'd seen him and so in the mid 90s
+I was working for the Redevelopment
+
+ align:start position:0%
+I was working for the Redevelopment
+ 
+
+ align:start position:0%
+I was working for the Redevelopment
+agency who will um come up a little
+
+ align:start position:0%
+agency who will um come up a little
+ 
+
+ align:start position:0%
+agency who will um come up a little
+later in the story uh because they were
+
+ align:start position:0%
+later in the story uh because they were
+ 
+
+ align:start position:0%
+later in the story uh because they were
+uh attempting to make a jazz
+
+ align:start position:0%
+uh attempting to make a jazz
+ 
+
+ align:start position:0%
+uh attempting to make a jazz
+preservation District in an area where
+
+ align:start position:0%
+preservation District in an area where
+ 
+
+ align:start position:0%
+preservation District in an area where
+very most of the trace of
+
+ align:start position:0%
+very most of the trace of
+ 
+
+ align:start position:0%
+very most of the trace of
+African-Americans had disappeared in the
+
+ align:start position:0%
+African-Americans had disappeared in the
+ 
+
+ align:start position:0%
+African-Americans had disappeared in the
+late 60s due to
+
+ align:start position:0%
+late 60s due to
+ 
+
+ align:start position:0%
+late 60s due to
+Redevelopment and for the h 100th time I
+
+ align:start position:0%
+Redevelopment and for the h 100th time I
+ 
+
+ align:start position:0%
+Redevelopment and for the h 100th time I
+asked uh Reggie Pettis the barber in the
+
+ align:start position:0%
+asked uh Reggie Pettis the barber in the
+ 
+
+ align:start position:0%
+asked uh Reggie Pettis the barber in the
+barber shop across the street do you
+
+ align:start position:0%
+barber shop across the street do you
+ 
+
+ align:start position:0%
+barber shop across the street do you
+know what happened to the photographs
+
+ align:start position:0%
+know what happened to the photographs
+ 
+
+ align:start position:0%
+know what happened to the photographs
+and he he said oh they're in my back
+
+ align:start position:0%
+and he he said oh they're in my back
+ 
+
+ align:start position:0%
+and he he said oh they're in my back
+room so what had happened was when when
+
+ align:start position:0%
+room so what had happened was when when
+ 
+
+ align:start position:0%
+room so what had happened was when when
+red um who's on the uh left had a stroke
+
+ align:start position:0%
+red um who's on the uh left had a stroke
+ 
+
+ align:start position:0%
+red um who's on the uh left had a stroke
+uh the landlord took all the photographs
+
+ align:start position:0%
+uh the landlord took all the photographs
+ 
+
+ align:start position:0%
+uh the landlord took all the photographs
+down um and was about to throw them out
+
+ align:start position:0%
+down um and was about to throw them out
+ 
+
+ align:start position:0%
+down um and was about to throw them out
+and Reggie rescued them and they'd been
+
+ align:start position:0%
+and Reggie rescued them and they'd been
+ 
+
+ align:start position:0%
+and Reggie rescued them and they'd been
+sitting in his back
+
+ align:start position:0%
+sitting in his back
+ 
+
+ align:start position:0%
+sitting in his back
+room and a lot of them were in in uh
+
+ align:start position:0%
+room and a lot of them were in in uh
+ 
+
+ align:start position:0%
+room and a lot of them were in in uh
+pretty bad shape so this was the
+
+ align:start position:0%
+pretty bad shape so this was the
+ 
+
+ align:start position:0%
+pretty bad shape so this was the
+opportunity in this case 10 years ago or
+
+ align:start position:0%
+opportunity in this case 10 years ago or
+ 
+
+ align:start position:0%
+opportunity in this case 10 years ago or
+8 years ago to learn Photoshop and um
+
+ align:start position:0%
+8 years ago to learn Photoshop and um
+ 
+
+ align:start position:0%
+8 years ago to learn Photoshop and um
+actually I had learned and I had
+
+ align:start position:0%
+actually I had learned and I had
+ 
+
+ align:start position:0%
+actually I had learned and I had
+students show me Photoshop probably four
+
+ align:start position:0%
+students show me Photoshop probably four
+ 
+
+ align:start position:0%
+students show me Photoshop probably four
+or five times but I really had not I was
+
+ align:start position:0%
+or five times but I really had not I was
+ 
+
+ align:start position:0%
+or five times but I really had not I was
+shooting film and I didn't really have
+
+ align:start position:0%
+shooting film and I didn't really have
+ 
+
+ align:start position:0%
+shooting film and I didn't really have
+that much interest but this was a
+
+ align:start position:0%
+that much interest but this was a
+ 
+
+ align:start position:0%
+that much interest but this was a
+project that was really important and so
+
+ align:start position:0%
+project that was really important and so
+ 
+
+ align:start position:0%
+project that was really important and so
+with Photoshop I was able to learn to
+
+ align:start position:0%
+with Photoshop I was able to learn to
+ 
+
+ align:start position:0%
+with Photoshop I was able to learn to
+restore the images and uh events they
+
+ align:start position:0%
+restore the images and uh events they
+ 
+
+ align:start position:0%
+restore the images and uh events they
+were using a report and then uh my
+
+ align:start position:0%
+were using a report and then uh my
+ 
+
+ align:start position:0%
+were using a report and then uh my
+friends at the San Francisco art
+
+ align:start position:0%
+friends at the San Francisco art
+ 
+
+ align:start position:0%
+friends at the San Francisco art
+commission said well you need to show
+
+ align:start position:0%
+commission said well you need to show
+ 
+
+ align:start position:0%
+commission said well you need to show
+these people need to see them so they
+
+ align:start position:0%
+these people need to see them so they
+ 
+
+ align:start position:0%
+these people need to see them so they
+were uh exhibited a number of times um
+
+ align:start position:0%
+were uh exhibited a number of times um
+ 
+
+ align:start position:0%
+were uh exhibited a number of times um
+some people doing research on the um the
+
+ align:start position:0%
+some people doing research on the um the
+ 
+
+ align:start position:0%
+some people doing research on the um the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh area we're doing films used them and
+
+ align:start position:0%
+uh area we're doing films used them and
+ 
+
+ align:start position:0%
+uh area we're doing films used them and
+and they were used in a uh neighborhood
+
+ align:start position:0%
+and they were used in a uh neighborhood
+ 
+
+ align:start position:0%
+and they were used in a uh neighborhood
+documentary that kqbd the uh PBS station
+
+ align:start position:0%
+documentary that kqbd the uh PBS station
+ 
+
+ align:start position:0%
+documentary that kqbd the uh PBS station
+in San Francisco did on the Filmore and
+
+ align:start position:0%
+in San Francisco did on the Filmore and
+ 
+
+ align:start position:0%
+in San Francisco did on the Filmore and
+I was an adviser for that so in this
+
+ align:start position:0%
+I was an adviser for that so in this
+ 
+
+ align:start position:0%
+I was an adviser for that so in this
+group of photographs were photographs of
+
+ align:start position:0%
+group of photographs were photographs of
+ 
+
+ align:start position:0%
+group of photographs were photographs of
+life in this community um a lot of
+
+ align:start position:0%
+life in this community um a lot of
+ 
+
+ align:start position:0%
+life in this community um a lot of
+pictures of entertainers this is a VOD
+
+ align:start position:0%
+pictures of entertainers this is a VOD
+ 
+
+ align:start position:0%
+pictures of entertainers this is a VOD
+villian this picture is probably from
+
+ align:start position:0%
+villian this picture is probably from
+ 
+
+ align:start position:0%
+villian this picture is probably from
+the' 40s cuz the in front of the um
+
+ align:start position:0%
+the' 40s cuz the in front of the um
+ 
+
+ align:start position:0%
+the' 40s cuz the in front of the um
+California theater and you can see that
+
+ align:start position:0%
+California theater and you can see that
+ 
+
+ align:start position:0%
+California theater and you can see that
+the uh movie post ERS are World War II
+
+ align:start position:0%
+the uh movie post ERS are World War II
+ 
+
+ align:start position:0%
+the uh movie post ERS are World War II
+vintage here's a picture of Charlie
+
+ align:start position:0%
+vintage here's a picture of Charlie
+ 
+
+ align:start position:0%
+vintage here's a picture of Charlie
+Parker in front of uh in inside Jimbo's
+
+ align:start position:0%
+Parker in front of uh in inside Jimbo's
+ 
+
+ align:start position:0%
+Parker in front of uh in inside Jimbo's
+Bop city um an after hours place where a
+
+ align:start position:0%
+Bop city um an after hours place where a
+ 
+
+ align:start position:0%
+Bop city um an after hours place where a
+lot of musicians would come to jam after
+
+ align:start position:0%
+lot of musicians would come to jam after
+ 
+
+ align:start position:0%
+lot of musicians would come to jam after
+they came here's a publicity shot of Joe
+
+ align:start position:0%
+they came here's a publicity shot of Joe
+ 
+
+ align:start position:0%
+they came here's a publicity shot of Joe
+Lewis with Joe Lewis liquor and um the
+
+ align:start position:0%
+Lewis with Joe Lewis liquor and um the
+ 
+
+ align:start position:0%
+Lewis with Joe Lewis liquor and um the
+uh some some older gentlemen in front of
+
+ align:start position:0%
+uh some some older gentlemen in front of
+ 
+
+ align:start position:0%
+uh some some older gentlemen in front of
+the Burger King on Filmore said that
+
+ align:start position:0%
+the Burger King on Filmore said that
+ 
+
+ align:start position:0%
+the Burger King on Filmore said that
+that was the worst rot gut they ever
+
+ align:start position:0%
+that was the worst rot gut they ever
+ 
+
+ align:start position:0%
+that was the worst rot gut they ever
+tasted so it was interesting that I
+
+ align:start position:0%
+tasted so it was interesting that I
+ 
+
+ align:start position:0%
+tasted so it was interesting that I
+would eventually when I first got the
+
+ align:start position:0%
+would eventually when I first got the
+ 
+
+ align:start position:0%
+would eventually when I first got the
+photographs there was no labels I didn't
+
+ align:start position:0%
+photographs there was no labels I didn't
+ 
+
+ align:start position:0%
+photographs there was no labels I didn't
+know any of the people and as they
+
+ align:start position:0%
+know any of the people and as they
+ 
+
+ align:start position:0%
+know any of the people and as they
+started to have a public life I started
+
+ align:start position:0%
+started to have a public life I started
+ 
+
+ align:start position:0%
+started to have a public life I started
+meeting people um and I started meeting
+
+ align:start position:0%
+meeting people um and I started meeting
+ 
+
+ align:start position:0%
+meeting people um and I started meeting
+other photographers and other people who
+
+ align:start position:0%
+other photographers and other people who
+ 
+
+ align:start position:0%
+other photographers and other people who
+had had um collections this woman was
+
+ align:start position:0%
+had had um collections this woman was
+ 
+
+ align:start position:0%
+had had um collections this woman was
+named Vera the
+
+ align:start position:0%
+named Vera the
+ 
+
+ align:start position:0%
+named Vera the
+body here's a photograph taken probably
+
+ align:start position:0%
+body here's a photograph taken probably
+ 
+
+ align:start position:0%
+body here's a photograph taken probably
+after the Japanese came back a very U
+
+ align:start position:0%
+after the Japanese came back a very U
+ 
+
+ align:start position:0%
+after the Japanese came back a very U
+Multicultural wedding party and people
+
+ align:start position:0%
+Multicultural wedding party and people
+ 
+
+ align:start position:0%
+Multicultural wedding party and people
+said that that was one of the things
+
+ align:start position:0%
+said that that was one of the things
+ 
+
+ align:start position:0%
+said that that was one of the things
+that this community was um very
+
+ align:start position:0%
+that this community was um very
+ 
+
+ align:start position:0%
+that this community was um very
+Multicultural I did eventually did a
+
+ align:start position:0%
+Multicultural I did eventually did a
+ 
+
+ align:start position:0%
+Multicultural I did eventually did a
+public art uh piece on the street and
+
+ align:start position:0%
+public art uh piece on the street and
+ 
+
+ align:start position:0%
+public art uh piece on the street and
+and I remember seeing an old man in
+
+ align:start position:0%
+and I remember seeing an old man in
+ 
+
+ align:start position:0%
+and I remember seeing an old man in
+front of one of the posters and he said
+
+ align:start position:0%
+front of one of the posters and he said
+ 
+
+ align:start position:0%
+front of one of the posters and he said
+he came every day because it was the
+
+ align:start position:0%
+he came every day because it was the
+ 
+
+ align:start position:0%
+he came every day because it was the
+best time of his life here's a picture
+
+ align:start position:0%
+best time of his life here's a picture
+ 
+
+ align:start position:0%
+best time of his life here's a picture
+of Chad Baker uh inside
+
+ align:start position:0%
+of Chad Baker uh inside
+ 
+
+ align:start position:0%
+of Chad Baker uh inside
+jimbos there's if you see um uh just to
+
+ align:start position:0%
+jimbos there's if you see um uh just to
+ 
+
+ align:start position:0%
+jimbos there's if you see um uh just to
+the uh left is El Fitzgerald and next to
+
+ align:start position:0%
+the uh left is El Fitzgerald and next to
+ 
+
+ align:start position:0%
+the uh left is El Fitzgerald and next to
+her is is someone I had a lot of
+
+ align:start position:0%
+her is is someone I had a lot of
+ 
+
+ align:start position:0%
+her is is someone I had a lot of
+pictures of whose name was um uh Robert
+
+ align:start position:0%
+pictures of whose name was um uh Robert
+ 
+
+ align:start position:0%
+pictures of whose name was um uh Robert
+Lee and I called Robert Lee probably I
+
+ align:start position:0%
+Lee and I called Robert Lee probably I
+ 
+
+ align:start position:0%
+Lee and I called Robert Lee probably I
+tried to to meet with him probably over
+
+ align:start position:0%
+tried to to meet with him probably over
+ 
+
+ align:start position:0%
+tried to to meet with him probably over
+the course of two years and he always
+
+ align:start position:0%
+the course of two years and he always
+ 
+
+ align:start position:0%
+the course of two years and he always
+put me off he said oh my cat in the
+
+ align:start position:0%
+put me off he said oh my cat in the
+ 
+
+ align:start position:0%
+put me off he said oh my cat in the
+garage or I got to go to the hospital
+
+ align:start position:0%
+garage or I got to go to the hospital
+ 
+
+ align:start position:0%
+garage or I got to go to the hospital
+and then he died and so I was never able
+
+ align:start position:0%
+and then he died and so I was never able
+ 
+
+ align:start position:0%
+and then he died and so I was never able
+to talk to him and I know he would have
+
+ align:start position:0%
+to talk to him and I know he would have
+ 
+
+ align:start position:0%
+to talk to him and I know he would have
+had the some of these stories here's a
+
+ align:start position:0%
+had the some of these stories here's a
+ 
+
+ align:start position:0%
+had the some of these stories here's a
+picture of him at uh Jack which was a
+
+ align:start position:0%
+picture of him at uh Jack which was a
+ 
+
+ align:start position:0%
+picture of him at uh Jack which was a
+famous bar a lot of the clubs um had um
+
+ align:start position:0%
+famous bar a lot of the clubs um had um
+ 
+
+ align:start position:0%
+famous bar a lot of the clubs um had um
+pictures of of uh Jazz and other
+
+ align:start position:0%
+pictures of of uh Jazz and other
+ 
+
+ align:start position:0%
+pictures of of uh Jazz and other
+entertainers on the uh um painted on the
+
+ align:start position:0%
+entertainers on the uh um painted on the
+ 
+
+ align:start position:0%
+entertainers on the uh um painted on the
+back of the seats and I was told that
+
+ align:start position:0%
+back of the seats and I was told that
+ 
+
+ align:start position:0%
+back of the seats and I was told that
+this woman is actually now a prominent
+
+ align:start position:0%
+this woman is actually now a prominent
+ 
+
+ align:start position:0%
+this woman is actually now a prominent
+socialite in San Francisco who probably
+
+ align:start position:0%
+socialite in San Francisco who probably
+ 
+
+ align:start position:0%
+socialite in San Francisco who probably
+would not be happy to know this
+
+ align:start position:0%
+would not be happy to know this
+ 
+
+ align:start position:0%
+would not be happy to know this
+Photograph still
+
+ align:start position:0%
+Photograph still
+ 
+
+ align:start position:0%
+Photograph still
+existed um here's a a barber uh shop
+
+ align:start position:0%
+existed um here's a a barber uh shop
+ 
+
+ align:start position:0%
+existed um here's a a barber uh shop
+where um someone's getting his hair
+
+ align:start position:0%
+where um someone's getting his hair
+ 
+
+ align:start position:0%
+where um someone's getting his hair
+processed um this is uh one of the
+
+ align:start position:0%
+processed um this is uh one of the
+ 
+
+ align:start position:0%
+processed um this is uh one of the
+publicity pictures this was a group
+
+ align:start position:0%
+publicity pictures this was a group
+ 
+
+ align:start position:0%
+publicity pictures this was a group
+called The Four Naturals and I actually
+
+ align:start position:0%
+called The Four Naturals and I actually
+ 
+
+ align:start position:0%
+called The Four Naturals and I actually
+have three or four of these this kind of
+
+ align:start position:0%
+have three or four of these this kind of
+ 
+
+ align:start position:0%
+have three or four of these this kind of
+motif where The Pianist who was always
+
+ align:start position:0%
+motif where The Pianist who was always
+ 
+
+ align:start position:0%
+motif where The Pianist who was always
+different was at this kind of um rounded
+
+ align:start position:0%
+different was at this kind of um rounded
+ 
+
+ align:start position:0%
+different was at this kind of um rounded
+faux keyboard The Pianist is actually
+
+ align:start position:0%
+faux keyboard The Pianist is actually
+ 
+
+ align:start position:0%
+faux keyboard The Pianist is actually
+Frank Jackson Who Um I met and who
+
+ align:start position:0%
+Frank Jackson Who Um I met and who
+ 
+
+ align:start position:0%
+Frank Jackson Who Um I met and who
+actually gave uh contributed photographs
+
+ align:start position:0%
+actually gave uh contributed photographs
+ 
+
+ align:start position:0%
+actually gave uh contributed photographs
+and oral history here's another
+
+ align:start position:0%
+and oral history here's another
+ 
+
+ align:start position:0%
+and oral history here's another
+photograph of him um and when we there's
+
+ align:start position:0%
+photograph of him um and when we there's
+ 
+
+ align:start position:0%
+photograph of him um and when we there's
+an exhibit of this work and um a lot of
+
+ align:start position:0%
+an exhibit of this work and um a lot of
+ 
+
+ align:start position:0%
+an exhibit of this work and um a lot of
+the musicians from the period played um
+
+ align:start position:0%
+the musicians from the period played um
+ 
+
+ align:start position:0%
+the musicians from the period played um
+but here's a picture Frank um celebrated
+
+ align:start position:0%
+but here's a picture Frank um celebrated
+ 
+
+ align:start position:0%
+but here's a picture Frank um celebrated
+his 80th birthday uh couple of months
+
+ align:start position:0%
+his 80th birthday uh couple of months
+ 
+
+ align:start position:0%
+his 80th birthday uh couple of months
+ago at Yoshi's in Oakland so he's still
+
+ align:start position:0%
+ago at Yoshi's in Oakland so he's still
+ 
+
+ align:start position:0%
+ago at Yoshi's in Oakland so he's still
+playing and that's been thrilling to
+
+ align:start position:0%
+playing and that's been thrilling to
+ 
+
+ align:start position:0%
+playing and that's been thrilling to
+meet people who I've been looking
+
+ align:start position:0%
+meet people who I've been looking
+ 
+
+ align:start position:0%
+meet people who I've been looking
+photographs up and actually hear them
+
+ align:start position:0%
+photographs up and actually hear them
+ 
+
+ align:start position:0%
+photographs up and actually hear them
+playing um when I did a neighborhood
+
+ align:start position:0%
+playing um when I did a neighborhood
+ 
+
+ align:start position:0%
+playing um when I did a neighborhood
+walk in there was a a gentleman who kept
+
+ align:start position:0%
+walk in there was a a gentleman who kept
+ 
+
+ align:start position:0%
+walk in there was a a gentleman who kept
+correcting me as I was sort of saying
+
+ align:start position:0%
+correcting me as I was sort of saying
+ 
+
+ align:start position:0%
+correcting me as I was sort of saying
+things as I believed them and it turned
+
+ align:start position:0%
+things as I believed them and it turned
+ 
+
+ align:start position:0%
+things as I believed them and it turned
+out he was uh Wesley Johnson Jr and his
+
+ align:start position:0%
+out he was uh Wesley Johnson Jr and his
+ 
+
+ align:start position:0%
+out he was uh Wesley Johnson Jr and his
+father own the Texas Playhouse which was
+
+ align:start position:0%
+father own the Texas Playhouse which was
+ 
+
+ align:start position:0%
+father own the Texas Playhouse which was
+basically sort of a hangout for uh
+
+ align:start position:0%
+basically sort of a hangout for uh
+ 
+
+ align:start position:0%
+basically sort of a hangout for uh
+people from Texas and his signature was
+
+ align:start position:0%
+people from Texas and his signature was
+ 
+
+ align:start position:0%
+people from Texas and his signature was
+sort of wearing that white 10 gallon
+
+ align:start position:0%
+sort of wearing that white 10 gallon
+ 
+
+ align:start position:0%
+sort of wearing that white 10 gallon
+ston hat here's a p here he is posing
+
+ align:start position:0%
+ston hat here's a p here he is posing
+ 
+
+ align:start position:0%
+ston hat here's a p here he is posing
+with uh T-Bone Walker who was a star of
+
+ align:start position:0%
+with uh T-Bone Walker who was a star of
+ 
+
+ align:start position:0%
+with uh T-Bone Walker who was a star of
+the day um uh and if you if you've heard
+
+ align:start position:0%
+the day um uh and if you if you've heard
+ 
+
+ align:start position:0%
+the day um uh and if you if you've heard
+him play you know where Chuck Barry
+
+ align:start position:0%
+him play you know where Chuck Barry
+ 
+
+ align:start position:0%
+him play you know where Chuck Barry
+Chuck Barry got all his licks so he the
+
+ align:start position:0%
+Chuck Barry got all his licks so he the
+ 
+
+ align:start position:0%
+Chuck Barry got all his licks so he the
+the after meeting with Wesley he
+
+ align:start position:0%
+the after meeting with Wesley he
+ 
+
+ align:start position:0%
+the after meeting with Wesley he
+actually gave us his father's albums and
+
+ align:start position:0%
+actually gave us his father's albums and
+ 
+
+ align:start position:0%
+actually gave us his father's albums and
+it turned out his father had given Red a
+
+ align:start position:0%
+it turned out his father had given Red a
+ 
+
+ align:start position:0%
+it turned out his father had given Red a
+lot of the work that he had on his walls
+
+ align:start position:0%
+lot of the work that he had on his walls
+ 
+
+ align:start position:0%
+lot of the work that he had on his walls
+so the sort of all these connecting and
+
+ align:start position:0%
+so the sort of all these connecting and
+ 
+
+ align:start position:0%
+so the sort of all these connecting and
+the sort of collection of images and
+
+ align:start position:0%
+the sort of collection of images and
+ 
+
+ align:start position:0%
+the sort of collection of images and
+Arch kept growing and growing um here's
+
+ align:start position:0%
+Arch kept growing and growing um here's
+ 
+
+ align:start position:0%
+Arch kept growing and growing um here's
+a picture of some church lady so it was
+
+ align:start position:0%
+a picture of some church lady so it was
+ 
+
+ align:start position:0%
+a picture of some church lady so it was
+a nightclub but I think people would use
+
+ align:start position:0%
+a nightclub but I think people would use
+ 
+
+ align:start position:0%
+a nightclub but I think people would use
+it for other things um on the walls he
+
+ align:start position:0%
+it for other things um on the walls he
+ 
+
+ align:start position:0%
+it for other things um on the walls he
+had these murals um these were all Texas
+
+ align:start position:0%
+had these murals um these were all Texas
+ 
+
+ align:start position:0%
+had these murals um these were all Texas
+musicians Saunders King was a wellknown
+
+ align:start position:0%
+musicians Saunders King was a wellknown
+ 
+
+ align:start position:0%
+musicians Saunders King was a wellknown
+and had a hit in a star in San Francisco
+
+ align:start position:0%
+and had a hit in a star in San Francisco
+ 
+
+ align:start position:0%
+and had a hit in a star in San Francisco
+and V his daughter is married to Carlos
+
+ align:start position:0%
+and V his daughter is married to Carlos
+ 
+
+ align:start position:0%
+and V his daughter is married to Carlos
+Santana um I think who else is here uh
+
+ align:start position:0%
+Santana um I think who else is here uh
+ 
+
+ align:start position:0%
+Santana um I think who else is here uh
+John Hinton I'm not sure but Ivory Joe
+
+ align:start position:0%
+John Hinton I'm not sure but Ivory Joe
+ 
+
+ align:start position:0%
+John Hinton I'm not sure but Ivory Joe
+Hunter was a Pianist from Texas so in
+
+ align:start position:0%
+Hunter was a Pianist from Texas so in
+ 
+
+ align:start position:0%
+Hunter was a Pianist from Texas so in
+his album I noticed there were all these
+
+ align:start position:0%
+his album I noticed there were all these
+ 
+
+ align:start position:0%
+his album I noticed there were all these
+paintings and I saw them in other
+
+ align:start position:0%
+paintings and I saw them in other
+ 
+
+ align:start position:0%
+paintings and I saw them in other
+people's photographs that were on the
+
+ align:start position:0%
+people's photographs that were on the
+ 
+
+ align:start position:0%
+people's photographs that were on the
+walls they were done by um uh an artist
+
+ align:start position:0%
+walls they were done by um uh an artist
+ 
+
+ align:start position:0%
+walls they were done by um uh an artist
+named um I'm going to probably get his
+
+ align:start position:0%
+named um I'm going to probably get his
+ 
+
+ align:start position:0%
+named um I'm going to probably get his
+name wrong I think it's Hinton and he
+
+ align:start position:0%
+name wrong I think it's Hinton and he
+ 
+
+ align:start position:0%
+name wrong I think it's Hinton and he
+actually designed the logo for
+
+ align:start position:0%
+actually designed the logo for
+ 
+
+ align:start position:0%
+actually designed the logo for
+Fisherman's Warf and designed the
+
+ align:start position:0%
+Fisherman's Warf and designed the
+ 
+
+ align:start position:0%
+Fisherman's Warf and designed the
+Oakland Paramount which is a really
+
+ align:start position:0%
+Oakland Paramount which is a really
+ 
+
+ align:start position:0%
+Oakland Paramount which is a really
+strong Art Deco so I kept seeing these
+
+ align:start position:0%
+strong Art Deco so I kept seeing these
+ 
+
+ align:start position:0%
+strong Art Deco so I kept seeing these
+paintings and one day I got a letter um
+
+ align:start position:0%
+paintings and one day I got a letter um
+ 
+
+ align:start position:0%
+paintings and one day I got a letter um
+from someone said I have the paintings
+
+ align:start position:0%
+from someone said I have the paintings
+ 
+
+ align:start position:0%
+from someone said I have the paintings
+in my basement um here's a picture of of
+
+ align:start position:0%
+in my basement um here's a picture of of
+ 
+
+ align:start position:0%
+in my basement um here's a picture of of
+Wesley with his two bartender and his
+
+ align:start position:0%
+Wesley with his two bartender and his
+ 
+
+ align:start position:0%
+Wesley with his two bartender and his
+partner and so I went to see um this
+
+ align:start position:0%
+partner and so I went to see um this
+ 
+
+ align:start position:0%
+partner and so I went to see um this
+gentleman and there were these paintings
+
+ align:start position:0%
+gentleman and there were these paintings
+ 
+
+ align:start position:0%
+gentleman and there were these paintings
+I'd been looking at for 5 years they're
+
+ align:start position:0%
+I'd been looking at for 5 years they're
+ 
+
+ align:start position:0%
+I'd been looking at for 5 years they're
+absolutely beautiful and they're they're
+
+ align:start position:0%
+absolutely beautiful and they're they're
+ 
+
+ align:start position:0%
+absolutely beautiful and they're they're
+they're uh gold flaked and they're 50
+
+ align:start position:0%
+they're uh gold flaked and they're 50
+ 
+
+ align:start position:0%
+they're uh gold flaked and they're 50
+years old and in incredible shape so
+
+ align:start position:0%
+years old and in incredible shape so
+ 
+
+ align:start position:0%
+years old and in incredible shape so
+they're in the exhibit um which is
+
+ align:start position:0%
+they're in the exhibit um which is
+ 
+
+ align:start position:0%
+they're in the exhibit um which is
+thrilling and and it turned out when the
+
+ align:start position:0%
+thrilling and and it turned out when the
+ 
+
+ align:start position:0%
+thrilling and and it turned out when the
+Texas Playhouse was being um demolished
+
+ align:start position:0%
+Texas Playhouse was being um demolished
+ 
+
+ align:start position:0%
+Texas Playhouse was being um demolished
+as we're a lot of the clubs in the late
+
+ align:start position:0%
+as we're a lot of the clubs in the late
+ 
+
+ align:start position:0%
+as we're a lot of the clubs in the late
+60s the Ukrainian contractor said oh
+
+ align:start position:0%
+60s the Ukrainian contractor said oh
+ 
+
+ align:start position:0%
+60s the Ukrainian contractor said oh
+great I can uh bring these paintings
+
+ align:start position:0%
+great I can uh bring these paintings
+ 
+
+ align:start position:0%
+great I can uh bring these paintings
+home and and Salvage the plywood so when
+
+ align:start position:0%
+home and and Salvage the plywood so when
+ 
+
+ align:start position:0%
+home and and Salvage the plywood so when
+he brought him home his wife said you
+
+ align:start position:0%
+he brought him home his wife said you
+ 
+
+ align:start position:0%
+he brought him home his wife said you
+will do no such thing that's this is Art
+
+ align:start position:0%
+will do no such thing that's this is Art
+ 
+
+ align:start position:0%
+will do no such thing that's this is Art
+so they gave the paintings to their
+
+ align:start position:0%
+so they gave the paintings to their
+ 
+
+ align:start position:0%
+so they gave the paintings to their
+neighbors African American neighbors who
+
+ align:start position:0%
+neighbors African American neighbors who
+ 
+
+ align:start position:0%
+neighbors African American neighbors who
+had grown up in the Filmore and Willie
+
+ align:start position:0%
+had grown up in the Filmore and Willie
+ 
+
+ align:start position:0%
+had grown up in the Filmore and Willie
+had kept them I mean he' kept them in a
+
+ align:start position:0%
+had kept them I mean he' kept them in a
+ 
+
+ align:start position:0%
+had kept them I mean he' kept them in a
+dry uh dark room for the last 30 years
+
+ align:start position:0%
+dry uh dark room for the last 30 years
+ 
+
+ align:start position:0%
+dry uh dark room for the last 30 years
+so he was again an incredible conser
+
+ align:start position:0%
+so he was again an incredible conser
+ 
+
+ align:start position:0%
+so he was again an incredible conser
+conservator his um here's a photograph
+
+ align:start position:0%
+conservator his um here's a photograph
+ 
+
+ align:start position:0%
+conservator his um here's a photograph
+of Lionel Hampton and it turned out I'd
+
+ align:start position:0%
+of Lionel Hampton and it turned out I'd
+ 
+
+ align:start position:0%
+of Lionel Hampton and it turned out I'd
+been looking at this photograph for a
+
+ align:start position:0%
+been looking at this photograph for a
+ 
+
+ align:start position:0%
+been looking at this photograph for a
+long time and this is um Robert brassard
+
+ align:start position:0%
+long time and this is um Robert brassard
+ 
+
+ align:start position:0%
+long time and this is um Robert brassard
+who is the uncle of my friend Tony
+
+ align:start position:0%
+who is the uncle of my friend Tony
+ 
+
+ align:start position:0%
+who is the uncle of my friend Tony
+brassard who's a a writer who does a
+
+ align:start position:0%
+brassard who's a a writer who does a
+ 
+
+ align:start position:0%
+brassard who's a a writer who does a
+remembrance of him and they lived in the
+
+ align:start position:0%
+remembrance of him and they lived in the
+ 
+
+ align:start position:0%
+remembrance of him and they lived in the
+East Bay but they would get dressed up
+
+ align:start position:0%
+East Bay but they would get dressed up
+ 
+
+ align:start position:0%
+East Bay but they would get dressed up
+every weekend this was a sweetheart they
+
+ align:start position:0%
+every weekend this was a sweetheart they
+ 
+
+ align:start position:0%
+every weekend this was a sweetheart they
+never married but they were uh went
+
+ align:start position:0%
+never married but they were uh went
+ 
+
+ align:start position:0%
+never married but they were uh went
+together for a long time and they would
+
+ align:start position:0%
+together for a long time and they would
+ 
+
+ align:start position:0%
+together for a long time and they would
+dress and go to the film War every
+
+ align:start position:0%
+dress and go to the film War every
+ 
+
+ align:start position:0%
+dress and go to the film War every
+weekend and so here he is in front of
+
+ align:start position:0%
+weekend and so here he is in front of
+ 
+
+ align:start position:0%
+weekend and so here he is in front of
+this painting that I've actually now
+
+ align:start position:0%
+this painting that I've actually now
+ 
+
+ align:start position:0%
+this painting that I've actually now
+touched it's sort of it um one of the
+
+ align:start position:0%
+touched it's sort of it um one of the
+ 
+
+ align:start position:0%
+touched it's sort of it um one of the
+the clubs that was prominent in this
+
+ align:start position:0%
+the clubs that was prominent in this
+ 
+
+ align:start position:0%
+the clubs that was prominent in this
+neighborhood was the Filmore the same
+
+ align:start position:0%
+neighborhood was the Filmore the same
+ 
+
+ align:start position:0%
+neighborhood was the Filmore the same
+Filmore that some of you have probably
+
+ align:start position:0%
+Filmore that some of you have probably
+ 
+
+ align:start position:0%
+Filmore that some of you have probably
+heard of and that Bill Graham eventually
+
+ align:start position:0%
+heard of and that Bill Graham eventually
+ 
+
+ align:start position:0%
+heard of and that Bill Graham eventually
+ran but before that it was a rhythm and
+
+ align:start position:0%
+ran but before that it was a rhythm and
+ 
+
+ align:start position:0%
+ran but before that it was a rhythm and
+blues venue um run by Charles Sullivan
+
+ align:start position:0%
+blues venue um run by Charles Sullivan
+ 
+
+ align:start position:0%
+blues venue um run by Charles Sullivan
+who is the considered the mayor of of
+
+ align:start position:0%
+who is the considered the mayor of of
+ 
+
+ align:start position:0%
+who is the considered the mayor of of
+the Filmore and here's a poster of
+
+ align:start position:0%
+the Filmore and here's a poster of
+ 
+
+ align:start position:0%
+the Filmore and here's a poster of
+Little Richard uh playing at the fil
+
+ align:start position:0%
+Little Richard uh playing at the fil
+ 
+
+ align:start position:0%
+Little Richard uh playing at the fil
+more I love there was this sort of
+
+ align:start position:0%
+more I love there was this sort of
+ 
+
+ align:start position:0%
+more I love there was this sort of
+aesthetic I've seen all over the the
+
+ align:start position:0%
+aesthetic I've seen all over the the
+ 
+
+ align:start position:0%
+aesthetic I've seen all over the the
+country at the Howard Theater in
+
+ align:start position:0%
+country at the Howard Theater in
+ 
+
+ align:start position:0%
+country at the Howard Theater in
+Washington at the the Regal in Chicago
+
+ align:start position:0%
+Washington at the the Regal in Chicago
+ 
+
+ align:start position:0%
+Washington at the the Regal in Chicago
+there was a certain way of doing offset
+
+ align:start position:0%
+there was a certain way of doing offset
+ 
+
+ align:start position:0%
+there was a certain way of doing offset
+printing in Rhythm uh Blues venues so
+
+ align:start position:0%
+printing in Rhythm uh Blues venues so
+ 
+
+ align:start position:0%
+printing in Rhythm uh Blues venues so
+here's uh Little Richard who's returning
+
+ align:start position:0%
+here's uh Little Richard who's returning
+ 
+
+ align:start position:0%
+here's uh Little Richard who's returning
+from a Triumph in England and um uh John
+
+ align:start position:0%
+from a Triumph in England and um uh John
+ 
+
+ align:start position:0%
+from a Triumph in England and um uh John
+Godard who now has a incredible record
+
+ align:start position:0%
+Godard who now has a incredible record
+ 
+
+ align:start position:0%
+Godard who now has a incredible record
+store in mil valy California was a
+
+ align:start position:0%
+store in mil valy California was a
+ 
+
+ align:start position:0%
+store in mil valy California was a
+14-year-old kid who took the bus in to
+
+ align:start position:0%
+14-year-old kid who took the bus in to
+ 
+
+ align:start position:0%
+14-year-old kid who took the bus in to
+see Little Richard and and took a
+
+ align:start position:0%
+see Little Richard and and took a
+ 
+
+ align:start position:0%
+see Little Richard and and took a
+picture with the Brownie and Little
+
+ align:start position:0%
+picture with the Brownie and Little
+ 
+
+ align:start position:0%
+picture with the Brownie and Little
+Richard had this left-handed guitarist
+
+ align:start position:0%
+Richard had this left-handed guitarist
+ 
+
+ align:start position:0%
+Richard had this left-handed guitarist
+who was really frustrating John because
+
+ align:start position:0%
+who was really frustrating John because
+ 
+
+ align:start position:0%
+who was really frustrating John because
+he kept getting in the way of Little
+
+ align:start position:0%
+he kept getting in the way of Little
+ 
+
+ align:start position:0%
+he kept getting in the way of Little
+Richard and that guitarist was James
+
+ align:start position:0%
+Richard and that guitarist was James
+ 
+
+ align:start position:0%
+Richard and that guitarist was James
+Marshall Hendricks this is I think one
+
+ align:start position:0%
+Marshall Hendricks this is I think one
+ 
+
+ align:start position:0%
+Marshall Hendricks this is I think one
+of the few and Little Richard fired him
+
+ align:start position:0%
+of the few and Little Richard fired him
+ 
+
+ align:start position:0%
+of the few and Little Richard fired him
+after 6 months cuz he was too weird
+
+ align:start position:0%
+after 6 months cuz he was too weird
+ 
+
+ align:start position:0%
+after 6 months cuz he was too weird
+which I thought was quite interesting so
+
+ align:start position:0%
+which I thought was quite interesting so
+ 
+
+ align:start position:0%
+which I thought was quite interesting so
+anyway in this collection here's a a
+
+ align:start position:0%
+anyway in this collection here's a a
+ 
+
+ align:start position:0%
+anyway in this collection here's a a
+picture in front of um Melrose records
+
+ align:start position:0%
+picture in front of um Melrose records
+ 
+
+ align:start position:0%
+picture in front of um Melrose records
+and in the window is a a sign for a a
+
+ align:start position:0%
+and in the window is a a sign for a a
+ 
+
+ align:start position:0%
+and in the window is a a sign for a a
+hit of the day called bbo is dead bill
+
+ align:start position:0%
+hit of the day called bbo is dead bill
+ 
+
+ align:start position:0%
+hit of the day called bbo is dead bill
+was a governor of Mississippi who was a
+
+ align:start position:0%
+was a governor of Mississippi who was a
+ 
+
+ align:start position:0%
+was a governor of Mississippi who was a
+St segregationist and when he died
+
+ align:start position:0%
+St segregationist and when he died
+ 
+
+ align:start position:0%
+St segregationist and when he died
+someone made a hit in celebration of
+
+ align:start position:0%
+someone made a hit in celebration of
+ 
+
+ align:start position:0%
+someone made a hit in celebration of
+that fact so in the meantime um this
+
+ align:start position:0%
+that fact so in the meantime um this
+ 
+
+ align:start position:0%
+that fact so in the meantime um this
+sort of collection is growing and I met
+
+ align:start position:0%
+sort of collection is growing and I met
+ 
+
+ align:start position:0%
+sort of collection is growing and I met
+a friend a woman um Janet Alvarado whose
+
+ align:start position:0%
+a friend a woman um Janet Alvarado whose
+ 
+
+ align:start position:0%
+a friend a woman um Janet Alvarado whose
+father had come to San Francisco in the
+
+ align:start position:0%
+father had come to San Francisco in the
+ 
+
+ align:start position:0%
+father had come to San Francisco in the
+first wave of Filipino immigrants there
+
+ align:start position:0%
+first wave of Filipino immigrants there
+ 
+
+ align:start position:0%
+first wave of Filipino immigrants there
+was sort of a bachelor society and he
+
+ align:start position:0%
+was sort of a bachelor society and he
+ 
+
+ align:start position:0%
+was sort of a bachelor society and he
+had taught himself photography and he
+
+ align:start position:0%
+had taught himself photography and he
+ 
+
+ align:start position:0%
+had taught himself photography and he
+worked in the kitchen in the predio the
+
+ align:start position:0%
+worked in the kitchen in the predio the
+ 
+
+ align:start position:0%
+worked in the kitchen in the predio the
+army base in San Francisco and as is the
+
+ align:start position:0%
+army base in San Francisco and as is the
+ 
+
+ align:start position:0%
+army base in San Francisco and as is the
+case a lot of people of color worked in
+
+ align:start position:0%
+case a lot of people of color worked in
+ 
+
+ align:start position:0%
+case a lot of people of color worked in
+the predio and he lived in in the
+
+ align:start position:0%
+the predio and he lived in in the
+ 
+
+ align:start position:0%
+the predio and he lived in in the
+Filmore and went to to uh clubs he also
+
+ align:start position:0%
+Filmore and went to to uh clubs he also
+ 
+
+ align:start position:0%
+Filmore and went to to uh clubs he also
+did a lot of photography of Filipino and
+
+ align:start position:0%
+did a lot of photography of Filipino and
+ 
+
+ align:start position:0%
+did a lot of photography of Filipino and
+Hispanic communities and in fact the
+
+ align:start position:0%
+Hispanic communities and in fact the
+ 
+
+ align:start position:0%
+Hispanic communities and in fact the
+Smithsonian has an exhibit that his
+
+ align:start position:0%
+Smithsonian has an exhibit that his
+ 
+
+ align:start position:0%
+Smithsonian has an exhibit that his
+daughter um organized um but he has
+
+ align:start position:0%
+daughter um organized um but he has
+ 
+
+ align:start position:0%
+daughter um organized um but he has
+thousands of 4x5 negatives so he um this
+
+ align:start position:0%
+thousands of 4x5 negatives so he um this
+ 
+
+ align:start position:0%
+thousands of 4x5 negatives so he um this
+is a picture in a house party that he
+
+ align:start position:0%
+is a picture in a house party that he
+ 
+
+ align:start position:0%
+is a picture in a house party that he
+took um that he contributed to the book
+
+ align:start position:0%
+took um that he contributed to the book
+ 
+
+ align:start position:0%
+took um that he contributed to the book
+and then here's a photograph done by
+
+ align:start position:0%
+and then here's a photograph done by
+ 
+
+ align:start position:0%
+and then here's a photograph done by
+Steve Jackson who is the official
+
+ align:start position:0%
+Steve Jackson who is the official
+ 
+
+ align:start position:0%
+Steve Jackson who is the official
+photographer of the um Jimbo's Bob city
+
+ align:start position:0%
+photographer of the um Jimbo's Bob city
+ 
+
+ align:start position:0%
+photographer of the um Jimbo's Bob city
+which I said was a a well-known after
+
+ align:start position:0%
+which I said was a a well-known after
+ 
+
+ align:start position:0%
+which I said was a a well-known after
+hours place there was actually a Bop
+
+ align:start position:0%
+hours place there was actually a Bop
+ 
+
+ align:start position:0%
+hours place there was actually a Bop
+city in in New York and um someone uh
+
+ align:start position:0%
+city in in New York and um someone uh
+ 
+
+ align:start position:0%
+city in in New York and um someone uh
+slim gayer who was a musician and tried
+
+ align:start position:0%
+slim gayer who was a musician and tried
+ 
+
+ align:start position:0%
+slim gayer who was a musician and tried
+to be an entrepreneur opened up a club
+
+ align:start position:0%
+to be an entrepreneur opened up a club
+ 
+
+ align:start position:0%
+to be an entrepreneur opened up a club
+called vout City if you know about slim
+
+ align:start position:0%
+called vout City if you know about slim
+ 
+
+ align:start position:0%
+called vout City if you know about slim
+and slam vout and vout oon was a a
+
+ align:start position:0%
+and slam vout and vout oon was a a
+ 
+
+ align:start position:0%
+and slam vout and vout oon was a a
+saying of the day but it didn't last
+
+ align:start position:0%
+saying of the day but it didn't last
+ 
+
+ align:start position:0%
+saying of the day but it didn't last
+very long so um uh it was taken over by
+
+ align:start position:0%
+very long so um uh it was taken over by
+ 
+
+ align:start position:0%
+very long so um uh it was taken over by
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh someone else and it basically opened
+
+ align:start position:0%
+uh someone else and it basically opened
+ 
+
+ align:start position:0%
+uh someone else and it basically opened
+at 2 a.m. uh you had to bring your own
+
+ align:start position:0%
+at 2 a.m. uh you had to bring your own
+ 
+
+ align:start position:0%
+at 2 a.m. uh you had to bring your own
+liquor and a lot of the musicians who
+
+ align:start position:0%
+liquor and a lot of the musicians who
+ 
+
+ align:start position:0%
+liquor and a lot of the musicians who
+were playing would come there was a sort
+
+ align:start position:0%
+were playing would come there was a sort
+ 
+
+ align:start position:0%
+were playing would come there was a sort
+of house Rhythm Section and people would
+
+ align:start position:0%
+of house Rhythm Section and people would
+ 
+
+ align:start position:0%
+of house Rhythm Section and people would
+show up so on this is on the cover of
+
+ align:start position:0%
+show up so on this is on the cover of
+ 
+
+ align:start position:0%
+show up so on this is on the cover of
+the book and um on the left is John
+
+ align:start position:0%
+the book and um on the left is John
+ 
+
+ align:start position:0%
+the book and um on the left is John
+handy who lives in the Bay Area who's
+
+ align:start position:0%
+handy who lives in the Bay Area who's
+ 
+
+ align:start position:0%
+handy who lives in the Bay Area who's
+well known that's poy po Dexter next to
+
+ align:start position:0%
+well known that's poy po Dexter next to
+ 
+
+ align:start position:0%
+well known that's poy po Dexter next to
+him uh and then next to him was at the
+
+ align:start position:0%
+him uh and then next to him was at the
+ 
+
+ align:start position:0%
+him uh and then next to him was at the
+time a young saxophone player John col
+
+ align:start position:0%
+time a young saxophone player John col
+ 
+
+ align:start position:0%
+time a young saxophone player John col
+train and next to him was Frank fiser so
+
+ align:start position:0%
+train and next to him was Frank fiser so
+ 
+
+ align:start position:0%
+train and next to him was Frank fiser so
+so um a couple of months ago when the
+
+ align:start position:0%
+so um a couple of months ago when the
+ 
+
+ align:start position:0%
+so um a couple of months ago when the
+exhibit opened we had a a concert with
+
+ align:start position:0%
+exhibit opened we had a a concert with
+ 
+
+ align:start position:0%
+exhibit opened we had a a concert with
+the Filmore preservation big band and
+
+ align:start position:0%
+the Filmore preservation big band and
+ 
+
+ align:start position:0%
+the Filmore preservation big band and
+two of the re surviving members that's
+
+ align:start position:0%
+two of the re surviving members that's
+ 
+
+ align:start position:0%
+two of the re surviving members that's
+John handy second from the left and
+
+ align:start position:0%
+John handy second from the left and
+ 
+
+ align:start position:0%
+John handy second from the left and
+Frank fiser next to him so again it was
+
+ align:start position:0%
+Frank fiser next to him so again it was
+ 
+
+ align:start position:0%
+Frank fiser next to him so again it was
+just thrilling and they still could play
+
+ align:start position:0%
+just thrilling and they still could play
+ 
+
+ align:start position:0%
+just thrilling and they still could play
+um they they were able to play and I I
+
+ align:start position:0%
+um they they were able to play and I I
+ 
+
+ align:start position:0%
+um they they were able to play and I I
+love that whole thing coming together so
+
+ align:start position:0%
+love that whole thing coming together so
+ 
+
+ align:start position:0%
+love that whole thing coming together so
+what happened was there would sort of
+
+ align:start position:0%
+what happened was there would sort of
+ 
+
+ align:start position:0%
+what happened was there would sort of
+move a foot to uh redevelop this area it
+
+ align:start position:0%
+move a foot to uh redevelop this area it
+ 
+
+ align:start position:0%
+move a foot to uh redevelop this area it
+was it had a stock of uh Victorian house
+
+ align:start position:0%
+was it had a stock of uh Victorian house
+ 
+
+ align:start position:0%
+was it had a stock of uh Victorian house
+houses um and um I have we have uh
+
+ align:start position:0%
+houses um and um I have we have uh
+ 
+
+ align:start position:0%
+houses um and um I have we have uh
+photographs from the Redevelopment
+
+ align:start position:0%
+photographs from the Redevelopment
+ 
+
+ align:start position:0%
+photographs from the Redevelopment
+agency where buildings were numbered and
+
+ align:start position:0%
+agency where buildings were numbered and
+ 
+
+ align:start position:0%
+agency where buildings were numbered and
+a lot of them were torn down and a lot
+
+ align:start position:0%
+a lot of them were torn down and a lot
+ 
+
+ align:start position:0%
+a lot of them were torn down and a lot
+of people were displaced with the idea
+
+ align:start position:0%
+of people were displaced with the idea
+ 
+
+ align:start position:0%
+of people were displaced with the idea
+that they would be put on a list and be
+
+ align:start position:0%
+that they would be put on a list and be
+ 
+
+ align:start position:0%
+that they would be put on a list and be
+the first to be able to come back and so
+
+ align:start position:0%
+the first to be able to come back and so
+ 
+
+ align:start position:0%
+the first to be able to come back and so
+it turned out that much of the Filmore
+
+ align:start position:0%
+it turned out that much of the Filmore
+ 
+
+ align:start position:0%
+it turned out that much of the Filmore
+looked like this for years and years
+
+ align:start position:0%
+looked like this for years and years
+ 
+
+ align:start position:0%
+looked like this for years and years
+that that um the buildings seemed to be
+
+ align:start position:0%
+that that um the buildings seemed to be
+ 
+
+ align:start position:0%
+that that um the buildings seemed to be
+people were displaced and the buildings
+
+ align:start position:0%
+people were displaced and the buildings
+ 
+
+ align:start position:0%
+people were displaced and the buildings
+were torn down quickly but it turned out
+
+ align:start position:0%
+were torn down quickly but it turned out
+ 
+
+ align:start position:0%
+were torn down quickly but it turned out
+I think one family on that list was able
+
+ align:start position:0%
+I think one family on that list was able
+ 
+
+ align:start position:0%
+I think one family on that list was able
+to resettle so um that obviously was
+
+ align:start position:0%
+to resettle so um that obviously was
+ 
+
+ align:start position:0%
+to resettle so um that obviously was
+devastating to a lot of people and it's
+
+ align:start position:0%
+devastating to a lot of people and it's
+ 
+
+ align:start position:0%
+devastating to a lot of people and it's
+no accident that a large percentage of
+
+ align:start position:0%
+no accident that a large percentage of
+ 
+
+ align:start position:0%
+no accident that a large percentage of
+the people who died in Guana with Jim
+
+ align:start position:0%
+the people who died in Guana with Jim
+ 
+
+ align:start position:0%
+the people who died in Guana with Jim
+Jones who had a church right next to the
+
+ align:start position:0%
+Jones who had a church right next to the
+ 
+
+ align:start position:0%
+Jones who had a church right next to the
+Filmore Auditorium were people from the
+
+ align:start position:0%
+Filmore Auditorium were people from the
+ 
+
+ align:start position:0%
+Filmore Auditorium were people from the
+Filmore or The Offspring of people um
+
+ align:start position:0%
+Filmore or The Offspring of people um
+ 
+
+ align:start position:0%
+Filmore or The Offspring of people um
+and there was no Trace PE there was
+
+ align:start position:0%
+and there was no Trace PE there was
+ 
+
+ align:start position:0%
+and there was no Trace PE there was
+there people I think people have studied
+
+ align:start position:0%
+there people I think people have studied
+ 
+
+ align:start position:0%
+there people I think people have studied
+their planners here who that the Filmore
+
+ align:start position:0%
+their planners here who that the Filmore
+ 
+
+ align:start position:0%
+their planners here who that the Filmore
+has been studied a lot as a sort of
+
+ align:start position:0%
+has been studied a lot as a sort of
+ 
+
+ align:start position:0%
+has been studied a lot as a sort of
+attempt at um Redevelopment that didn't
+
+ align:start position:0%
+attempt at um Redevelopment that didn't
+ 
+
+ align:start position:0%
+attempt at um Redevelopment that didn't
+go very well and some people say that it
+
+ align:start position:0%
+go very well and some people say that it
+ 
+
+ align:start position:0%
+go very well and some people say that it
+was the intention of the developers that
+
+ align:start position:0%
+was the intention of the developers that
+ 
+
+ align:start position:0%
+was the intention of the developers that
+they didn't like the idea of they're in
+
+ align:start position:0%
+they didn't like the idea of they're in
+ 
+
+ align:start position:0%
+they didn't like the idea of they're in
+a prominent area in San Francisco was
+
+ align:start position:0%
+a prominent area in San Francisco was
+ 
+
+ align:start position:0%
+a prominent area in San Francisco was
+African-American Community it turned out
+
+ align:start position:0%
+African-American Community it turned out
+ 
+
+ align:start position:0%
+African-American Community it turned out
+a lot of them were displaced to other
+
+ align:start position:0%
+a lot of them were displaced to other
+ 
+
+ align:start position:0%
+a lot of them were displaced to other
+places but some of them ended up in the
+
+ align:start position:0%
+places but some of them ended up in the
+ 
+
+ align:start position:0%
+places but some of them ended up in the
+area um uh so it was important to me uh
+
+ align:start position:0%
+area um uh so it was important to me uh
+ 
+
+ align:start position:0%
+area um uh so it was important to me uh
+the first sort of pup that to exhibit
+
+ align:start position:0%
+the first sort of pup that to exhibit
+ 
+
+ align:start position:0%
+the first sort of pup that to exhibit
+that work and then this is actually um
+
+ align:start position:0%
+that work and then this is actually um
+ 
+
+ align:start position:0%
+that work and then this is actually um
+sort of storefront installation that's
+
+ align:start position:0%
+sort of storefront installation that's
+ 
+
+ align:start position:0%
+sort of storefront installation that's
+on the side of some of the clubs and um
+
+ align:start position:0%
+on the side of some of the clubs and um
+ 
+
+ align:start position:0%
+on the side of some of the clubs and um
+some of that the the the area is being
+
+ align:start position:0%
+some of that the the the area is being
+ 
+
+ align:start position:0%
+some of that the the the area is being
+redeveloped a jazz club Yoshi's which is
+
+ align:start position:0%
+redeveloped a jazz club Yoshi's which is
+ 
+
+ align:start position:0%
+redeveloped a jazz club Yoshi's which is
+in the East Bay is going to be moving
+
+ align:start position:0%
+in the East Bay is going to be moving
+ 
+
+ align:start position:0%
+in the East Bay is going to be moving
+across the street from where this is but
+
+ align:start position:0%
+across the street from where this is but
+ 
+
+ align:start position:0%
+across the street from where this is but
+it it's basically preservation District
+
+ align:start position:0%
+it it's basically preservation District
+ 
+
+ align:start position:0%
+it it's basically preservation District
+it's not really the it will not be the
+
+ align:start position:0%
+it's not really the it will not be the
+ 
+
+ align:start position:0%
+it's not really the it will not be the
+same and it won't be the same Community
+
+ align:start position:0%
+same and it won't be the same Community
+ 
+
+ align:start position:0%
+same and it won't be the same Community
+but I think the book and um is an
+
+ align:start position:0%
+but I think the book and um is an
+ 
+
+ align:start position:0%
+but I think the book and um is an
+attempt and the people who lived in the
+
+ align:start position:0%
+attempt and the people who lived in the
+ 
+
+ align:start position:0%
+attempt and the people who lived in the
+community say that the book is important
+
+ align:start position:0%
+community say that the book is important
+ 
+
+ align:start position:0%
+community say that the book is important
+to them because at least now that
+
+ align:start position:0%
+to them because at least now that
+ 
+
+ align:start position:0%
+to them because at least now that
+history has a public face
+
+ align:start position:0%
+history has a public face
+ 
+
+ align:start position:0%
+history has a public face
+so that was um that was me sort of
+
+ align:start position:0%
+so that was um that was me sort of
+ 
+
+ align:start position:0%
+so that was um that was me sort of
+manipulating and looking at and handling
+
+ align:start position:0%
+manipulating and looking at and handling
+ 
+
+ align:start position:0%
+manipulating and looking at and handling
+other people's photographs and
+
+ align:start position:0%
+other people's photographs and
+ 
+
+ align:start position:0%
+other people's photographs and
+manipulating with the idea of trying to
+
+ align:start position:0%
+manipulating with the idea of trying to
+ 
+
+ align:start position:0%
+manipulating with the idea of trying to
+bring them back to I think the the
+
+ align:start position:0%
+bring them back to I think the the
+ 
+
+ align:start position:0%
+bring them back to I think the the
+condition that I I think that the uh R
+
+ align:start position:0%
+condition that I I think that the uh R
+ 
+
+ align:start position:0%
+condition that I I think that the uh R
+photographers wanted so my own work um
+
+ align:start position:0%
+photographers wanted so my own work um
+ 
+
+ align:start position:0%
+photographers wanted so my own work um
+I'll show a little bit of the work uh
+
+ align:start position:0%
+I'll show a little bit of the work uh
+ 
+
+ align:start position:0%
+I'll show a little bit of the work uh
+the first kind of work I've done West
+
+ align:start position:0%
+the first kind of work I've done West
+ 
+
+ align:start position:0%
+the first kind of work I've done West
+Oakland was always a place that was
+
+ align:start position:0%
+Oakland was always a place that was
+ 
+
+ align:start position:0%
+Oakland was always a place that was
+interested in photographing and I'm very
+
+ align:start position:0%
+interested in photographing and I'm very
+ 
+
+ align:start position:0%
+interested in photographing and I'm very
+interested in markings some of you know
+
+ align:start position:0%
+interested in markings some of you know
+ 
+
+ align:start position:0%
+interested in markings some of you know
+Walker Evans um you'll see uh sort of
+
+ align:start position:0%
+Walker Evans um you'll see uh sort of
+ 
+
+ align:start position:0%
+Walker Evans um you'll see uh sort of
+evidence of my interest in kind of signs
+
+ align:start position:0%
+evidence of my interest in kind of signs
+ 
+
+ align:start position:0%
+evidence of my interest in kind of signs
+and what they mean and then I'm also
+
+ align:start position:0%
+and what they mean and then I'm also
+ 
+
+ align:start position:0%
+and what they mean and then I'm also
+interested in kind of symbolic so I
+
+ align:start position:0%
+interested in kind of symbolic so I
+ 
+
+ align:start position:0%
+interested in kind of symbolic so I
+thought that this I was told that this
+
+ align:start position:0%
+thought that this I was told that this
+ 
+
+ align:start position:0%
+thought that this I was told that this
+Ghost Town meant that this was a crack
+
+ align:start position:0%
+Ghost Town meant that this was a crack
+ 
+
+ align:start position:0%
+Ghost Town meant that this was a crack
+house but it turns out this community
+
+ align:start position:0%
+house but it turns out this community
+ 
+
+ align:start position:0%
+house but it turns out this community
+which is about a 20 block area in West
+
+ align:start position:0%
+which is about a 20 block area in West
+ 
+
+ align:start position:0%
+which is about a 20 block area in West
+Oakland calls itself ghost town and I've
+
+ align:start position:0%
+Oakland calls itself ghost town and I've
+ 
+
+ align:start position:0%
+Oakland calls itself ghost town and I've
+seen in um uh people sell t-shirts it's
+
+ align:start position:0%
+seen in um uh people sell t-shirts it's
+ 
+
+ align:start position:0%
+seen in um uh people sell t-shirts it's
+sort of like a sense of identity this is
+
+ align:start position:0%
+sort of like a sense of identity this is
+ 
+
+ align:start position:0%
+sort of like a sense of identity this is
+um uh can you read the text yeah um I
+
+ align:start position:0%
+um uh can you read the text yeah um I
+ 
+
+ align:start position:0%
+um uh can you read the text yeah um I
+sort of asked people there was a a
+
+ align:start position:0%
+sort of asked people there was a a
+ 
+
+ align:start position:0%
+sort of asked people there was a a
+Palestinian
+
+ align:start position:0%
+Palestinian
+ 
+
+ align:start position:0%
+Palestinian
+uh Market at the end of this block and I
+
+ align:start position:0%
+uh Market at the end of this block and I
+ 
+
+ align:start position:0%
+uh Market at the end of this block and I
+asked them about this signage and they
+
+ align:start position:0%
+asked them about this signage and they
+ 
+
+ align:start position:0%
+asked them about this signage and they
+either didn't want to talk about it and
+
+ align:start position:0%
+either didn't want to talk about it and
+ 
+
+ align:start position:0%
+either didn't want to talk about it and
+I asked people in the street but is
+
+ align:start position:0%
+I asked people in the street but is
+ 
+
+ align:start position:0%
+I asked people in the street but is
+obviously um interesting and sort of
+
+ align:start position:0%
+obviously um interesting and sort of
+ 
+
+ align:start position:0%
+obviously um interesting and sort of
+reflective of changing demographics in
+
+ align:start position:0%
+reflective of changing demographics in
+ 
+
+ align:start position:0%
+reflective of changing demographics in
+this particular neighborhood then here's
+
+ align:start position:0%
+this particular neighborhood then here's
+ 
+
+ align:start position:0%
+this particular neighborhood then here's
+basically uh a kind of more conscious
+
+ align:start position:0%
+basically uh a kind of more conscious
+ 
+
+ align:start position:0%
+basically uh a kind of more conscious
+marking of a nightclub facade in West
+
+ align:start position:0%
+marking of a nightclub facade in West
+ 
+
+ align:start position:0%
+marking of a nightclub facade in West
+Oakland and I love this is probably one
+
+ align:start position:0%
+Oakland and I love this is probably one
+ 
+
+ align:start position:0%
+Oakland and I love this is probably one
+of the first pictures I took when I
+
+ align:start position:0%
+of the first pictures I took when I
+ 
+
+ align:start position:0%
+of the first pictures I took when I
+decided to become a photographer and
+
+ align:start position:0%
+decided to become a photographer and
+ 
+
+ align:start position:0%
+decided to become a photographer and
+this is uh I I think really hand painted
+
+ align:start position:0%
+this is uh I I think really hand painted
+ 
+
+ align:start position:0%
+this is uh I I think really hand painted
+and very reminiscent of what I've seen
+
+ align:start position:0%
+and very reminiscent of what I've seen
+ 
+
+ align:start position:0%
+and very reminiscent of what I've seen
+in rural in Louisiana and actually right
+
+ align:start position:0%
+in rural in Louisiana and actually right
+ 
+
+ align:start position:0%
+in rural in Louisiana and actually right
+after I took the picture of the sign
+
+ align:start position:0%
+after I took the picture of the sign
+ 
+
+ align:start position:0%
+after I took the picture of the sign
+disappeared and I was told later when I
+
+ align:start position:0%
+disappeared and I was told later when I
+ 
+
+ align:start position:0%
+disappeared and I was told later when I
+had to show at the Oakland Museum that
+
+ align:start position:0%
+had to show at the Oakland Museum that
+ 
+
+ align:start position:0%
+had to show at the Oakland Museum that
+um the house was sold not long after I
+
+ align:start position:0%
+um the house was sold not long after I
+ 
+
+ align:start position:0%
+um the house was sold not long after I
+took it but it basically someone
+
+ align:start position:0%
+took it but it basically someone
+ 
+
+ align:start position:0%
+took it but it basically someone
+probably came in the 40s and 50s uh had
+
+ align:start position:0%
+probably came in the 40s and 50s uh had
+ 
+
+ align:start position:0%
+probably came in the 40s and 50s uh had
+chickens in the backyard and just like
+
+ align:start position:0%
+chickens in the backyard and just like
+ 
+
+ align:start position:0%
+chickens in the backyard and just like
+they had done in Texas Louisiana you
+
+ align:start position:0%
+they had done in Texas Louisiana you
+ 
+
+ align:start position:0%
+they had done in Texas Louisiana you
+could go get fresh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+poultry um this is uh some people have
+
+ align:start position:0%
+poultry um this is uh some people have
+ 
+
+ align:start position:0%
+poultry um this is uh some people have
+asked me about this picture U some
+
+ align:start position:0%
+asked me about this picture U some
+ 
+
+ align:start position:0%
+asked me about this picture U some
+people in interpret as someone
+
+ align:start position:0%
+people in interpret as someone
+ 
+
+ align:start position:0%
+people in interpret as someone
+incarcerated sort of behind um uh walls
+
+ align:start position:0%
+incarcerated sort of behind um uh walls
+ 
+
+ align:start position:0%
+incarcerated sort of behind um uh walls
+um and they I've been a number of other
+
+ align:start position:0%
+um and they I've been a number of other
+ 
+
+ align:start position:0%
+um and they I've been a number of other
+interpretations the other thing is this
+
+ align:start position:0%
+interpretations the other thing is this
+ 
+
+ align:start position:0%
+interpretations the other thing is this
+was at one time 512 which I thought is
+
+ align:start position:0%
+was at one time 512 which I thought is
+ 
+
+ align:start position:0%
+was at one time 512 which I thought is
+interesting I I don't know if you can
+
+ align:start position:0%
+interesting I I don't know if you can
+ 
+
+ align:start position:0%
+interesting I I don't know if you can
+read it um but it's basically uh
+
+ align:start position:0%
+read it um but it's basically uh
+ 
+
+ align:start position:0%
+read it um but it's basically uh
+probably retail space that someone's
+
+ align:start position:0%
+probably retail space that someone's
+ 
+
+ align:start position:0%
+probably retail space that someone's
+using now to live in and they put up
+
+ align:start position:0%
+using now to live in and they put up
+ 
+
+ align:start position:0%
+using now to live in and they put up
+this Photograph to for both privacy and
+
+ align:start position:0%
+this Photograph to for both privacy and
+ 
+
+ align:start position:0%
+this Photograph to for both privacy and
+as kind of reflection here's a converted
+
+ align:start position:0%
+as kind of reflection here's a converted
+ 
+
+ align:start position:0%
+as kind of reflection here's a converted
+storefront church and this again
+
+ align:start position:0%
+storefront church and this again
+ 
+
+ align:start position:0%
+storefront church and this again
+reminded me of the South um this this
+
+ align:start position:0%
+reminded me of the South um this this
+ 
+
+ align:start position:0%
+reminded me of the South um this this
+church has since and this building has
+
+ align:start position:0%
+church has since and this building has
+ 
+
+ align:start position:0%
+church has since and this building has
+since uh uh had other uses this picture
+
+ align:start position:0%
+since uh uh had other uses this picture
+ 
+
+ align:start position:0%
+since uh uh had other uses this picture
+was taken in '93 there's always a lot of
+
+ align:start position:0%
+was taken in '93 there's always a lot of
+ 
+
+ align:start position:0%
+was taken in '93 there's always a lot of
+that um kind of uh change in terms of
+
+ align:start position:0%
+that um kind of uh change in terms of
+ 
+
+ align:start position:0%
+that um kind of uh change in terms of
+how things are used but this whole idea
+
+ align:start position:0%
+how things are used but this whole idea
+ 
+
+ align:start position:0%
+how things are used but this whole idea
+of impro improvising and how that gets
+
+ align:start position:0%
+of impro improvising and how that gets
+ 
+
+ align:start position:0%
+of impro improvising and how that gets
+reflected in the environment is really
+
+ align:start position:0%
+reflected in the environment is really
+ 
+
+ align:start position:0%
+reflected in the environment is really
+important to me this is a photograph
+
+ align:start position:0%
+important to me this is a photograph
+ 
+
+ align:start position:0%
+important to me this is a photograph
+that um led me to meet an spurn I heard
+
+ align:start position:0%
+that um led me to meet an spurn I heard
+ 
+
+ align:start position:0%
+that um led me to meet an spurn I heard
+that my friend Walter Hood who uh I've
+
+ align:start position:0%
+that my friend Walter Hood who uh I've
+ 
+
+ align:start position:0%
+that my friend Walter Hood who uh I've
+done some work was showing slides of
+
+ align:start position:0%
+done some work was showing slides of
+ 
+
+ align:start position:0%
+done some work was showing slides of
+West Oakland and some things that he was
+
+ align:start position:0%
+West Oakland and some things that he was
+ 
+
+ align:start position:0%
+West Oakland and some things that he was
+doing and I guess either in the middle
+
+ align:start position:0%
+doing and I guess either in the middle
+ 
+
+ align:start position:0%
+doing and I guess either in the middle
+of his lecture or right afterwards she
+
+ align:start position:0%
+of his lecture or right afterwards she
+ 
+
+ align:start position:0%
+of his lecture or right afterwards she
+um yelled out for him to stop and say
+
+ align:start position:0%
+um yelled out for him to stop and say
+ 
+
+ align:start position:0%
+um yelled out for him to stop and say
+what's the story with that photograph
+
+ align:start position:0%
+what's the story with that photograph
+ 
+
+ align:start position:0%
+what's the story with that photograph
+and um which shows her incredibly good
+
+ align:start position:0%
+and um which shows her incredibly good
+ 
+
+ align:start position:0%
+and um which shows her incredibly good
+taste um but um what's interesting about
+
+ align:start position:0%
+taste um but um what's interesting about
+ 
+
+ align:start position:0%
+taste um but um what's interesting about
+it you know one of the rules is you
+
+ align:start position:0%
+it you know one of the rules is you
+ 
+
+ align:start position:0%
+it you know one of the rules is you
+shouldn't shoot in the middle of the day
+
+ align:start position:0%
+shouldn't shoot in the middle of the day
+ 
+
+ align:start position:0%
+shouldn't shoot in the middle of the day
+because um the angle of sun makes it
+
+ align:start position:0%
+because um the angle of sun makes it
+ 
+
+ align:start position:0%
+because um the angle of sun makes it
+harder to see people but of course uh I
+
+ align:start position:0%
+harder to see people but of course uh I
+ 
+
+ align:start position:0%
+harder to see people but of course uh I
+photograph when I can and I would not
+
+ align:start position:0%
+photograph when I can and I would not
+ 
+
+ align:start position:0%
+photograph when I can and I would not
+have been able to make this image
+
+ align:start position:0%
+have been able to make this image
+ 
+
+ align:start position:0%
+have been able to make this image
+without if it had not been in the middle
+
+ align:start position:0%
+without if it had not been in the middle
+ 
+
+ align:start position:0%
+without if it had not been in the middle
+of the day and the the couple things
+
+ align:start position:0%
+of the day and the the couple things
+ 
+
+ align:start position:0%
+of the day and the the couple things
+going on the Safeway cart is the basket
+
+ align:start position:0%
+going on the Safeway cart is the basket
+ 
+
+ align:start position:0%
+going on the Safeway cart is the basket
+the um you know what they're doing is
+
+ align:start position:0%
+the um you know what they're doing is
+ 
+
+ align:start position:0%
+the um you know what they're doing is
+played out on the
+
+ align:start position:0%
+played out on the
+ 
+
+ align:start position:0%
+played out on the
+street and um they didn't even they
+
+ align:start position:0%
+street and um they didn't even they
+ 
+
+ align:start position:0%
+street and um they didn't even they
+didn't even look up they were they were
+
+ align:start position:0%
+didn't even look up they were they were
+ 
+
+ align:start position:0%
+didn't even look up they were they were
+really into
+
+ align:start position:0%
+really into
+ 
+
+ align:start position:0%
+really into
+playing this was uh this uh domino game
+
+ align:start position:0%
+playing this was uh this uh domino game
+ 
+
+ align:start position:0%
+playing this was uh this uh domino game
+at the new Chicago new California Barber
+
+ align:start position:0%
+at the new Chicago new California Barber
+ 
+
+ align:start position:0%
+at the new Chicago new California Barber
+Shop had been going on almost
+
+ align:start position:0%
+Shop had been going on almost
+ 
+
+ align:start position:0%
+Shop had been going on almost
+continuously for about 20 years it's no
+
+ align:start position:0%
+continuously for about 20 years it's no
+ 
+
+ align:start position:0%
+continuously for about 20 years it's no
+longer in existence also and when when I
+
+ align:start position:0%
+longer in existence also and when when I
+ 
+
+ align:start position:0%
+longer in existence also and when when I
+photographed I photographed probably
+
+ align:start position:0%
+photographed I photographed probably
+ 
+
+ align:start position:0%
+photographed I photographed probably
+maybe over the course of a week and when
+
+ align:start position:0%
+maybe over the course of a week and when
+ 
+
+ align:start position:0%
+maybe over the course of a week and when
+I first saw this picture I really didn't
+
+ align:start position:0%
+I first saw this picture I really didn't
+ 
+
+ align:start position:0%
+I first saw this picture I really didn't
+like it compositionally but this is
+
+ align:start position:0%
+like it compositionally but this is
+ 
+
+ align:start position:0%
+like it compositionally but this is
+really the photograph the photograph is
+
+ align:start position:0%
+really the photograph the photograph is
+ 
+
+ align:start position:0%
+really the photograph the photograph is
+about their hands and how their hands
+
+ align:start position:0%
+about their hands and how their hands
+ 
+
+ align:start position:0%
+about their hands and how their hands
+kind of represent the kind of community
+
+ align:start position:0%
+kind of represent the kind of community
+ 
+
+ align:start position:0%
+kind of represent the kind of community
+and communion that they have plus I
+
+ align:start position:0%
+and communion that they have plus I
+ 
+
+ align:start position:0%
+and communion that they have plus I
+think he had a good hand so then right
+
+ align:start position:0%
+think he had a good hand so then right
+ 
+
+ align:start position:0%
+think he had a good hand so then right
+next door was this guy with a raccoon on
+
+ align:start position:0%
+next door was this guy with a raccoon on
+ 
+
+ align:start position:0%
+next door was this guy with a raccoon on
+a leash and in the barber shop they were
+
+ align:start position:0%
+a leash and in the barber shop they were
+ 
+
+ align:start position:0%
+a leash and in the barber shop they were
+taking bets as to who would win in a
+
+ align:start position:0%
+taking bets as to who would win in a
+ 
+
+ align:start position:0%
+taking bets as to who would win in a
+fight between a pitbull and the raccoon
+
+ align:start position:0%
+fight between a pitbull and the raccoon
+ 
+
+ align:start position:0%
+fight between a pitbull and the raccoon
+and I think I put my money on the
+
+ align:start position:0%
+and I think I put my money on the
+ 
+
+ align:start position:0%
+and I think I put my money on the
+Raccoon although this raccoon had
+
+ align:start position:0%
+Raccoon although this raccoon had
+ 
+
+ align:start position:0%
+Raccoon although this raccoon had
+actually been caught as a a what's a
+
+ align:start position:0%
+actually been caught as a a what's a
+ 
+
+ align:start position:0%
+actually been caught as a a what's a
+young raccoon a pup and um was was uh
+
+ align:start position:0%
+young raccoon a pup and um was was uh
+ 
+
+ align:start position:0%
+young raccoon a pup and um was was uh
+trained and I know when I used to live
+
+ align:start position:0%
+trained and I know when I used to live
+ 
+
+ align:start position:0%
+trained and I know when I used to live
+in Ren County raccoons would come in to
+
+ align:start position:0%
+in Ren County raccoons would come in to
+ 
+
+ align:start position:0%
+in Ren County raccoons would come in to
+my house through the window go into the
+
+ align:start position:0%
+my house through the window go into the
+ 
+
+ align:start position:0%
+my house through the window go into the
+kitchen open the the counter take the
+
+ align:start position:0%
+kitchen open the the counter take the
+ 
+
+ align:start position:0%
+kitchen open the the counter take the
+lid off the K cat kibble take their fill
+
+ align:start position:0%
+lid off the K cat kibble take their fill
+ 
+
+ align:start position:0%
+lid off the K cat kibble take their fill
+and put the lid back and then leave and
+
+ align:start position:0%
+and put the lid back and then leave and
+ 
+
+ align:start position:0%
+and put the lid back and then leave and
+did that regularly so I'm not sure I was
+
+ align:start position:0%
+did that regularly so I'm not sure I was
+ 
+
+ align:start position:0%
+did that regularly so I'm not sure I was
+talking earlier about the whole notion
+
+ align:start position:0%
+talking earlier about the whole notion
+ 
+
+ align:start position:0%
+talking earlier about the whole notion
+of um how do you photograph strangers
+
+ align:start position:0%
+of um how do you photograph strangers
+ 
+
+ align:start position:0%
+of um how do you photograph strangers
+and I think this Photograph sort of uh
+
+ align:start position:0%
+and I think this Photograph sort of uh
+ 
+
+ align:start position:0%
+and I think this Photograph sort of uh
+is interesting that I asked her if I
+
+ align:start position:0%
+is interesting that I asked her if I
+ 
+
+ align:start position:0%
+is interesting that I asked her if I
+could photograph this is actually in
+
+ align:start position:0%
+could photograph this is actually in
+ 
+
+ align:start position:0%
+could photograph this is actually in
+East Oakland and I think this Photograph
+
+ align:start position:0%
+East Oakland and I think this Photograph
+ 
+
+ align:start position:0%
+East Oakland and I think this Photograph
+I think she's looking at me much more
+
+ align:start position:0%
+I think she's looking at me much more
+ 
+
+ align:start position:0%
+I think she's looking at me much more
+intently than I'm looking at her which I
+
+ align:start position:0%
+intently than I'm looking at her which I
+ 
+
+ align:start position:0%
+intently than I'm looking at her which I
+think it's the
+
+ align:start position:0%
+think it's the
+ 
+
+ align:start position:0%
+think it's the
+photograph so I was very interested in
+
+ align:start position:0%
+photograph so I was very interested in
+ 
+
+ align:start position:0%
+photograph so I was very interested in
+people would tell stories of arriving in
+
+ align:start position:0%
+people would tell stories of arriving in
+ 
+
+ align:start position:0%
+people would tell stories of arriving in
+West Oakland in 1943 with $10 in their
+
+ align:start position:0%
+West Oakland in 1943 with $10 in their
+ 
+
+ align:start position:0%
+West Oakland in 1943 with $10 in their
+pocket and how they had raised a family
+
+ align:start position:0%
+pocket and how they had raised a family
+ 
+
+ align:start position:0%
+pocket and how they had raised a family
+you know two or three generation
+
+ align:start position:0%
+you know two or three generation
+ 
+
+ align:start position:0%
+you know two or three generation
+and there's a really beautiful um old uh
+
+ align:start position:0%
+and there's a really beautiful um old uh
+ 
+
+ align:start position:0%
+and there's a really beautiful um old uh
+uh railroad station which is closed
+
+ align:start position:0%
+uh railroad station which is closed
+ 
+
+ align:start position:0%
+uh railroad station which is closed
+because of seismic conditions and so
+
+ align:start position:0%
+because of seismic conditions and so
+ 
+
+ align:start position:0%
+because of seismic conditions and so
+there's a new one that uh is in Jack
+
+ align:start position:0%
+there's a new one that uh is in Jack
+ 
+
+ align:start position:0%
+there's a new one that uh is in Jack
+London Square and I was interested in
+
+ align:start position:0%
+London Square and I was interested in
+ 
+
+ align:start position:0%
+London Square and I was interested in
+photographing it and so I went one day
+
+ align:start position:0%
+photographing it and so I went one day
+ 
+
+ align:start position:0%
+photographing it and so I went one day
+and there was a guy waiting in a a
+
+ align:start position:0%
+and there was a guy waiting in a a
+ 
+
+ align:start position:0%
+and there was a guy waiting in a a
+Cadillac with these really beautiful
+
+ align:start position:0%
+Cadillac with these really beautiful
+ 
+
+ align:start position:0%
+Cadillac with these really beautiful
+cowboy boots and like a fool I said
+
+ align:start position:0%
+cowboy boots and like a fool I said
+ 
+
+ align:start position:0%
+cowboy boots and like a fool I said
+could you move cuz I want to photograph
+
+ align:start position:0%
+could you move cuz I want to photograph
+ 
+
+ align:start position:0%
+could you move cuz I want to photograph
+the building you know I immediately
+
+ align:start position:0%
+the building you know I immediately
+ 
+
+ align:start position:0%
+the building you know I immediately
+regretted it and so um I got another
+
+ align:start position:0%
+regretted it and so um I got another
+ 
+
+ align:start position:0%
+regretted it and so um I got another
+chance I went back and here's a woman
+
+ align:start position:0%
+chance I went back and here's a woman
+ 
+
+ align:start position:0%
+chance I went back and here's a woman
+who just come from Stockton dressed up
+
+ align:start position:0%
+who just come from Stockton dressed up
+ 
+
+ align:start position:0%
+who just come from Stockton dressed up
+for her daughter's wedding and so I sort
+
+ align:start position:0%
+for her daughter's wedding and so I sort
+ 
+
+ align:start position:0%
+for her daughter's wedding and so I sort
+of saw that this was taken in '97 but I
+
+ align:start position:0%
+of saw that this was taken in '97 but I
+ 
+
+ align:start position:0%
+of saw that this was taken in '97 but I
+saw that as kind of being indication of
+
+ align:start position:0%
+saw that as kind of being indication of
+ 
+
+ align:start position:0%
+saw that as kind of being indication of
+that idea of transference and the kind
+
+ align:start position:0%
+that idea of transference and the kind
+ 
+
+ align:start position:0%
+that idea of transference and the kind
+of indicating these stories I heard um
+
+ align:start position:0%
+of indicating these stories I heard um
+ 
+
+ align:start position:0%
+of indicating these stories I heard um
+and I love that the shopping cart in the
+
+ align:start position:0%
+and I love that the shopping cart in the
+ 
+
+ align:start position:0%
+and I love that the shopping cart in the
+ghetto is a is the SUV of the ghetto and
+
+ align:start position:0%
+ghetto is a is the SUV of the ghetto and
+ 
+
+ align:start position:0%
+ghetto is a is the SUV of the ghetto and
+absolutely is a convenience uh a means
+
+ align:start position:0%
+absolutely is a convenience uh a means
+ 
+
+ align:start position:0%
+absolutely is a convenience uh a means
+for transfering uh in some cases there's
+
+ align:start position:0%
+for transfering uh in some cases there's
+ 
+
+ align:start position:0%
+for transfering uh in some cases there's
+like lines of them it's also uh
+
+ align:start position:0%
+like lines of them it's also uh
+ 
+
+ align:start position:0%
+like lines of them it's also uh
+important in the economy terms of
+
+ align:start position:0%
+important in the economy terms of
+ 
+
+ align:start position:0%
+important in the economy terms of
+recycling so um uh so that's sort of
+
+ align:start position:0%
+recycling so um uh so that's sort of
+ 
+
+ align:start position:0%
+recycling so um uh so that's sort of
+West Oakland and here's a photograph
+
+ align:start position:0%
+West Oakland and here's a photograph
+ 
+
+ align:start position:0%
+West Oakland and here's a photograph
+taken in hiana Florida um I sort of read
+
+ align:start position:0%
+taken in hiana Florida um I sort of read
+ 
+
+ align:start position:0%
+taken in hiana Florida um I sort of read
+about the whole notion West African
+
+ align:start position:0%
+about the whole notion West African
+ 
+
+ align:start position:0%
+about the whole notion West African
+notion of the swep swept clean yard
+
+ align:start position:0%
+notion of the swep swept clean yard
+ 
+
+ align:start position:0%
+notion of the swep swept clean yard
+which is all over the South um so here
+
+ align:start position:0%
+which is all over the South um so here
+ 
+
+ align:start position:0%
+which is all over the South um so here
+was an example this is a swept clean
+
+ align:start position:0%
+was an example this is a swept clean
+ 
+
+ align:start position:0%
+was an example this is a swept clean
+yard with a satellite
+
+ align:start position:0%
+yard with a satellite
+ 
+
+ align:start position:0%
+yard with a satellite
+dish um I went to Beal Street and saw
+
+ align:start position:0%
+dish um I went to Beal Street and saw
+ 
+
+ align:start position:0%
+dish um I went to Beal Street and saw
+this peeling mural some people think
+
+ align:start position:0%
+this peeling mural some people think
+ 
+
+ align:start position:0%
+this peeling mural some people think
+that's Bessie Smith some think it's it's
+
+ align:start position:0%
+that's Bessie Smith some think it's it's
+ 
+
+ align:start position:0%
+that's Bessie Smith some think it's it's
+Billy Holiday um couldn't find it when I
+
+ align:start position:0%
+Billy Holiday um couldn't find it when I
+ 
+
+ align:start position:0%
+Billy Holiday um couldn't find it when I
+was there a couple of months ago so it
+
+ align:start position:0%
+was there a couple of months ago so it
+ 
+
+ align:start position:0%
+was there a couple of months ago so it
+was gone uh Bradford marcelus used it on
+
+ align:start position:0%
+was gone uh Bradford marcelus used it on
+ 
+
+ align:start position:0%
+was gone uh Bradford marcelus used it on
+the cover of one of his albums but I
+
+ align:start position:0%
+the cover of one of his albums but I
+ 
+
+ align:start position:0%
+the cover of one of his albums but I
+sort of saw it as symbolic sort of B
+
+ align:start position:0%
+sort of saw it as symbolic sort of B
+ 
+
+ align:start position:0%
+sort of saw it as symbolic sort of B
+Street the same thing happened it was
+
+ align:start position:0%
+Street the same thing happened it was
+ 
+
+ align:start position:0%
+Street the same thing happened it was
+about to be um it was a thriving
+
+ align:start position:0%
+about to be um it was a thriving
+ 
+
+ align:start position:0%
+about to be um it was a thriving
+African-American Community it was about
+
+ align:start position:0%
+African-American Community it was about
+ 
+
+ align:start position:0%
+African-American Community it was about
+to be um destroyed and it's basically
+
+ align:start position:0%
+to be um destroyed and it's basically
+ 
+
+ align:start position:0%
+to be um destroyed and it's basically
+now a tourist area so the culture was um
+
+ align:start position:0%
+now a tourist area so the culture was um
+ 
+
+ align:start position:0%
+now a tourist area so the culture was um
+the means for it to survive but it's not
+
+ align:start position:0%
+the means for it to survive but it's not
+ 
+
+ align:start position:0%
+the means for it to survive but it's not
+it it had to take another reiteration
+
+ align:start position:0%
+it it had to take another reiteration
+ 
+
+ align:start position:0%
+it it had to take another reiteration
+I'm really interested in what's going to
+
+ align:start position:0%
+I'm really interested in what's going to
+ 
+
+ align:start position:0%
+I'm really interested in what's going to
+happen in New Orleans and we'll talk
+
+ align:start position:0%
+happen in New Orleans and we'll talk
+ 
+
+ align:start position:0%
+happen in New Orleans and we'll talk
+more about that um this is Tula
+
+ align:start position:0%
+more about that um this is Tula
+ 
+
+ align:start position:0%
+more about that um this is Tula
+Louisiana um kind of a bayou uh light
+
+ align:start position:0%
+Louisiana um kind of a bayou uh light
+ 
+
+ align:start position:0%
+Louisiana um kind of a bayou uh light
+tree this is in the Third Ward in
+
+ align:start position:0%
+tree this is in the Third Ward in
+ 
+
+ align:start position:0%
+tree this is in the Third Ward in
+Houston I um was uh worked with a number
+
+ align:start position:0%
+Houston I um was uh worked with a number
+ 
+
+ align:start position:0%
+Houston I um was uh worked with a number
+of uh uh Architects um in at that that
+
+ align:start position:0%
+of uh uh Architects um in at that that
+ 
+
+ align:start position:0%
+of uh uh Architects um in at that that
+time in rice they had a conference on
+
+ align:start position:0%
+time in rice they had a conference on
+ 
+
+ align:start position:0%
+time in rice they had a conference on
+shotgun houses and the project Rous
+
+ align:start position:0%
+shotgun houses and the project Rous
+ 
+
+ align:start position:0%
+shotgun houses and the project Rous
+which is in the the Third Ward is um
+
+ align:start position:0%
+which is in the the Third Ward is um
+ 
+
+ align:start position:0%
+which is in the the Third Ward is um
+series of of shotgun houses that were
+
+ align:start position:0%
+series of of shotgun houses that were
+ 
+
+ align:start position:0%
+series of of shotgun houses that were
+sort of reconfigured some of you may
+
+ align:start position:0%
+sort of reconfigured some of you may
+ 
+
+ align:start position:0%
+sort of reconfigured some of you may
+know about it and artists come and do in
+
+ align:start position:0%
+know about it and artists come and do in
+ 
+
+ align:start position:0%
+know about it and artists come and do in
+do residencies and installation actually
+
+ align:start position:0%
+do residencies and installation actually
+ 
+
+ align:start position:0%
+do residencies and installation actually
+run by um uh unwed mothers who um sort
+
+ align:start position:0%
+run by um uh unwed mothers who um sort
+ 
+
+ align:start position:0%
+run by um uh unwed mothers who um sort
+of administer it but the neighborhood in
+
+ align:start position:0%
+of administer it but the neighborhood in
+ 
+
+ align:start position:0%
+of administer it but the neighborhood in
+Houston was very interesting to me and
+
+ align:start position:0%
+Houston was very interesting to me and
+ 
+
+ align:start position:0%
+Houston was very interesting to me and
+here's you know that sort of ongoing
+
+ align:start position:0%
+here's you know that sort of ongoing
+ 
+
+ align:start position:0%
+here's you know that sort of ongoing
+I've seen domino games in Kingston
+
+ align:start position:0%
+I've seen domino games in Kingston
+ 
+
+ align:start position:0%
+I've seen domino games in Kingston
+Jamaica all over the south in carem um
+
+ align:start position:0%
+Jamaica all over the south in carem um
+ 
+
+ align:start position:0%
+Jamaica all over the south in carem um
+again I'm always interested in the sort
+
+ align:start position:0%
+again I'm always interested in the sort
+ 
+
+ align:start position:0%
+again I'm always interested in the sort
+of stories that get told on the
+
+ align:start position:0%
+of stories that get told on the
+ 
+
+ align:start position:0%
+of stories that get told on the
+street um the Third Ward is the home of
+
+ align:start position:0%
+street um the Third Ward is the home of
+ 
+
+ align:start position:0%
+street um the Third Ward is the home of
+uh um Barbara Jordan and uh Mickey
+
+ align:start position:0%
+uh um Barbara Jordan and uh Mickey
+ 
+
+ align:start position:0%
+uh um Barbara Jordan and uh Mickey
+Leland and lightning Hopkins a lot of
+
+ align:start position:0%
+Leland and lightning Hopkins a lot of
+ 
+
+ align:start position:0%
+Leland and lightning Hopkins a lot of
+people the third W come from the third W
+
+ align:start position:0%
+people the third W come from the third W
+ 
+
+ align:start position:0%
+people the third W come from the third W
+this project Ro house in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+background and this sort of interesting
+
+ align:start position:0%
+background and this sort of interesting
+ 
+
+ align:start position:0%
+background and this sort of interesting
+story in the
+
+ align:start position:0%
+story in the
+ 
+
+ align:start position:0%
+story in the
+foreground so this is sort of the
+
+ align:start position:0%
+foreground so this is sort of the
+ 
+
+ align:start position:0%
+foreground so this is sort of the
+courtyard of of um project Rouse so
+
+ align:start position:0%
+courtyard of of um project Rouse so
+ 
+
+ align:start position:0%
+courtyard of of um project Rouse so
+project rowhouse in some ways was kind
+
+ align:start position:0%
+project rowhouse in some ways was kind
+ 
+
+ align:start position:0%
+project rowhouse in some ways was kind
+of um formalized but the shotgun house
+
+ align:start position:0%
+of um formalized but the shotgun house
+ 
+
+ align:start position:0%
+of um formalized but the shotgun house
+is very interesting uh it's like the
+
+ align:start position:0%
+is very interesting uh it's like the
+ 
+
+ align:start position:0%
+is very interesting uh it's like the
+perfect design pre uh air conditioner
+
+ align:start position:0%
+perfect design pre uh air conditioner
+ 
+
+ align:start position:0%
+perfect design pre uh air conditioner
+because of the Cross ventilation High
+
+ align:start position:0%
+because of the Cross ventilation High
+ 
+
+ align:start position:0%
+because of the Cross ventilation High
+ceilings and um I know uh I've got the
+
+ align:start position:0%
+ceilings and um I know uh I've got the
+ 
+
+ align:start position:0%
+ceilings and um I know uh I've got the
+chance to stay with friends of mine in
+
+ align:start position:0%
+chance to stay with friends of mine in
+ 
+
+ align:start position:0%
+chance to stay with friends of mine in
+Baton Rouge it's actually a really nice
+
+ align:start position:0%
+Baton Rouge it's actually a really nice
+ 
+
+ align:start position:0%
+Baton Rouge it's actually a really nice
+kind of uh house we can't use them in
+
+ align:start position:0%
+kind of uh house we can't use them in
+ 
+
+ align:start position:0%
+kind of uh house we can't use them in
+California because you can just put them
+
+ align:start position:0%
+California because you can just put them
+ 
+
+ align:start position:0%
+California because you can just put them
+on concrete blocks but that won't work
+
+ align:start position:0%
+on concrete blocks but that won't work
+ 
+
+ align:start position:0%
+on concrete blocks but that won't work
+for seismic so um I uh love going to New
+
+ align:start position:0%
+for seismic so um I uh love going to New
+ 
+
+ align:start position:0%
+for seismic so um I uh love going to New
+York I'm really regret not being able to
+
+ align:start position:0%
+York I'm really regret not being able to
+ 
+
+ align:start position:0%
+York I'm really regret not being able to
+go this trip um but here the you'll sort
+
+ align:start position:0%
+go this trip um but here the you'll sort
+ 
+
+ align:start position:0%
+go this trip um but here the you'll sort
+of see kind of similar kind of
+
+ align:start position:0%
+of see kind of similar kind of
+ 
+
+ align:start position:0%
+of see kind of similar kind of
+references I'm very interested Ed in
+
+ align:start position:0%
+references I'm very interested Ed in
+ 
+
+ align:start position:0%
+references I'm very interested Ed in
+especially how the sort of um the
+
+ align:start position:0%
+especially how the sort of um the
+ 
+
+ align:start position:0%
+especially how the sort of um the
+African-American church which I have
+
+ align:start position:0%
+African-American church which I have
+ 
+
+ align:start position:0%
+African-American church which I have
+some problems with but but also which I
+
+ align:start position:0%
+some problems with but but also which I
+ 
+
+ align:start position:0%
+some problems with but but also which I
+think is incredible thank God for it
+
+ align:start position:0%
+think is incredible thank God for it
+ 
+
+ align:start position:0%
+think is incredible thank God for it
+because it it's a source of a lot of my
+
+ align:start position:0%
+because it it's a source of a lot of my
+ 
+
+ align:start position:0%
+because it it's a source of a lot of my
+photography I have some things I really
+
+ align:start position:0%
+photography I have some things I really
+ 
+
+ align:start position:0%
+photography I have some things I really
+admire about it also um but you can kind
+
+ align:start position:0%
+admire about it also um but you can kind
+ 
+
+ align:start position:0%
+admire about it also um but you can kind
+of see this referencing the thing I this
+
+ align:start position:0%
+of see this referencing the thing I this
+ 
+
+ align:start position:0%
+of see this referencing the thing I this
+is in Harlem uh this is actually a
+
+ align:start position:0%
+is in Harlem uh this is actually a
+ 
+
+ align:start position:0%
+is in Harlem uh this is actually a
+Haitian uh Church
+
+ align:start position:0%
+Haitian uh Church
+ 
+
+ align:start position:0%
+Haitian uh Church
+um and I I just love that kind of
+
+ align:start position:0%
+um and I I just love that kind of
+ 
+
+ align:start position:0%
+um and I I just love that kind of
+evidence of hand and expression a
+
+ align:start position:0%
+evidence of hand and expression a
+ 
+
+ align:start position:0%
+evidence of hand and expression a
+collective expression of Faith as shown
+
+ align:start position:0%
+collective expression of Faith as shown
+ 
+
+ align:start position:0%
+collective expression of Faith as shown
+in a visual sense now I may have it
+
+ align:start position:0%
+in a visual sense now I may have it
+ 
+
+ align:start position:0%
+in a visual sense now I may have it
+wrong I think this is 127th Street in
+
+ align:start position:0%
+wrong I think this is 127th Street in
+ 
+
+ align:start position:0%
+wrong I think this is 127th Street in
+Harlem I believe it that was designed by
+
+ align:start position:0%
+Harlem I believe it that was designed by
+ 
+
+ align:start position:0%
+Harlem I believe it that was designed by
+the asers but looks like Southern
+
+ align:start position:0%
+the asers but looks like Southern
+ 
+
+ align:start position:0%
+the asers but looks like Southern
+architecture to me so I I actually love
+
+ align:start position:0%
+architecture to me so I I actually love
+ 
+
+ align:start position:0%
+architecture to me so I I actually love
+um kind of this little one block with uh
+
+ align:start position:0%
+um kind of this little one block with uh
+ 
+
+ align:start position:0%
+um kind of this little one block with uh
+kind of scale and um architecture which
+
+ align:start position:0%
+kind of scale and um architecture which
+ 
+
+ align:start position:0%
+kind of scale and um architecture which
+seems much different than New York um I
+
+ align:start position:0%
+seems much different than New York um I
+ 
+
+ align:start position:0%
+seems much different than New York um I
+was scheduled to do a residency in New
+
+ align:start position:0%
+was scheduled to do a residency in New
+ 
+
+ align:start position:0%
+was scheduled to do a residency in New
+Orleans um actually this during the
+
+ align:start position:0%
+Orleans um actually this during the
+ 
+
+ align:start position:0%
+Orleans um actually this during the
+summer and I was working on my book so
+
+ align:start position:0%
+summer and I was working on my book so
+ 
+
+ align:start position:0%
+summer and I was working on my book so
+it was delayed and then all of a sudden
+
+ align:start position:0%
+it was delayed and then all of a sudden
+ 
+
+ align:start position:0%
+it was delayed and then all of a sudden
+Katrina hit so I was not able to go so I
+
+ align:start position:0%
+Katrina hit so I was not able to go so I
+ 
+
+ align:start position:0%
+Katrina hit so I was not able to go so I
+went um I went to New York um and stay
+
+ align:start position:0%
+went um I went to New York um and stay
+ 
+
+ align:start position:0%
+went um I went to New York um and stay
+actually stayed in Brooklyn and
+
+ align:start position:0%
+actually stayed in Brooklyn and
+ 
+
+ align:start position:0%
+actually stayed in Brooklyn and
+photographed a sort of some examples of
+
+ align:start position:0%
+photographed a sort of some examples of
+ 
+
+ align:start position:0%
+photographed a sort of some examples of
+both gentrification and people fighting
+
+ align:start position:0%
+both gentrification and people fighting
+ 
+
+ align:start position:0%
+both gentrification and people fighting
+it um I would spent a little time in
+
+ align:start position:0%
+it um I would spent a little time in
+ 
+
+ align:start position:0%
+it um I would spent a little time in
+Washington and then I went to Chicago
+
+ align:start position:0%
+Washington and then I went to Chicago
+ 
+
+ align:start position:0%
+Washington and then I went to Chicago
+where um a friend of mine who I remember
+
+ align:start position:0%
+where um a friend of mine who I remember
+ 
+
+ align:start position:0%
+where um a friend of mine who I remember
+as being in the Black Panthers is now an
+
+ align:start position:0%
+as being in the Black Panthers is now an
+ 
+
+ align:start position:0%
+as being in the Black Panthers is now an
+Alderman and was organized ing um her
+
+ align:start position:0%
+Alderman and was organized ing um her
+ 
+
+ align:start position:0%
+Alderman and was organized ing um her
+district and uh just north of uh Wrigley
+
+ align:start position:0%
+district and uh just north of uh Wrigley
+ 
+
+ align:start position:0%
+district and uh just north of uh Wrigley
+Field on the North side and instead of
+
+ align:start position:0%
+Field on the North side and instead of
+ 
+
+ align:start position:0%
+Field on the North side and instead of
+the recurring pattern where a lot of
+
+ align:start position:0%
+the recurring pattern where a lot of
+ 
+
+ align:start position:0%
+the recurring pattern where a lot of
+people were being displaced she was um
+
+ align:start position:0%
+people were being displaced she was um
+ 
+
+ align:start position:0%
+people were being displaced she was um
+um sort of having community-based
+
+ align:start position:0%
+um sort of having community-based
+ 
+
+ align:start position:0%
+um sort of having community-based
+Redevelopment and she had seen the
+
+ align:start position:0%
+Redevelopment and she had seen the
+ 
+
+ align:start position:0%
+Redevelopment and she had seen the
+Filmore um project and was interested in
+
+ align:start position:0%
+Filmore um project and was interested in
+ 
+
+ align:start position:0%
+Filmore um project and was interested in
+in me talking to them about doing public
+
+ align:start position:0%
+in me talking to them about doing public
+ 
+
+ align:start position:0%
+in me talking to them about doing public
+art and kind of expressions of history
+
+ align:start position:0%
+art and kind of expressions of history
+ 
+
+ align:start position:0%
+art and kind of expressions of history
+in the the sort of area that they were
+
+ align:start position:0%
+in the the sort of area that they were
+ 
+
+ align:start position:0%
+in the the sort of area that they were
+communicating and I hadn't been to
+
+ align:start position:0%
+communicating and I hadn't been to
+ 
+
+ align:start position:0%
+communicating and I hadn't been to
+Chicago in 30 years and um got a chance
+
+ align:start position:0%
+Chicago in 30 years and um got a chance
+ 
+
+ align:start position:0%
+Chicago in 30 years and um got a chance
+to go to Cabrini Green um which is just
+
+ align:start position:0%
+to go to Cabrini Green um which is just
+ 
+
+ align:start position:0%
+to go to Cabrini Green um which is just
+barely left but um was kind of wandering
+
+ align:start position:0%
+barely left but um was kind of wandering
+ 
+
+ align:start position:0%
+barely left but um was kind of wandering
+around and saw some people with video
+
+ align:start position:0%
+around and saw some people with video
+ 
+
+ align:start position:0%
+around and saw some people with video
+and there was a group that was
+
+ align:start position:0%
+and there was a group that was
+ 
+
+ align:start position:0%
+and there was a group that was
+interviewing people who were to trying
+
+ align:start position:0%
+interviewing people who were to trying
+ 
+
+ align:start position:0%
+interviewing people who were to trying
+to prevent them from being displaced
+
+ align:start position:0%
+to prevent them from being displaced
+ 
+
+ align:start position:0%
+to prevent them from being displaced
+because a lot of people have been
+
+ align:start position:0%
+because a lot of people have been
+ 
+
+ align:start position:0%
+because a lot of people have been
+displaced and they were going to
+
+ align:start position:0%
+displaced and they were going to
+ 
+
+ align:start position:0%
+displaced and they were going to
+actually go to the UN with with
+
+ align:start position:0%
+actually go to the UN with with
+ 
+
+ align:start position:0%
+actually go to the UN with with
+interviews so I had seen photographs of
+
+ align:start position:0%
+interviews so I had seen photographs of
+ 
+
+ align:start position:0%
+interviews so I had seen photographs of
+it I think the good times was was based
+
+ align:start position:0%
+it I think the good times was was based
+ 
+
+ align:start position:0%
+it I think the good times was was based
+in Cabrini Green and I've been hearing
+
+ align:start position:0%
+in Cabrini Green and I've been hearing
+ 
+
+ align:start position:0%
+in Cabrini Green and I've been hearing
+about it for years um and there's this
+
+ align:start position:0%
+about it for years um and there's this
+ 
+
+ align:start position:0%
+about it for years um and there's this
+whole thing about these exterior um
+
+ align:start position:0%
+whole thing about these exterior um
+ 
+
+ align:start position:0%
+whole thing about these exterior um
+corridors and like 3T Square elevators
+
+ align:start position:0%
+corridors and like 3T Square elevators
+ 
+
+ align:start position:0%
+corridors and like 3T Square elevators
+and incredible mass and I'd seen
+
+ align:start position:0%
+and incredible mass and I'd seen
+ 
+
+ align:start position:0%
+and incredible mass and I'd seen
+photographs of and I had to photograph
+
+ align:start position:0%
+photographs of and I had to photograph
+ 
+
+ align:start position:0%
+photographs of and I had to photograph
+it um it was very interesting
+
+ align:start position:0%
+it um it was very interesting
+ 
+
+ align:start position:0%
+it um it was very interesting
+um uh and this was sort of my attempt to
+
+ align:start position:0%
+um uh and this was sort of my attempt to
+ 
+
+ align:start position:0%
+um uh and this was sort of my attempt to
+get back to photographing after having
+
+ align:start position:0%
+get back to photographing after having
+ 
+
+ align:start position:0%
+get back to photographing after having
+been working on other projects and we
+
+ align:start position:0%
+been working on other projects and we
+ 
+
+ align:start position:0%
+been working on other projects and we
+were talking about it earlier I wasn't
+
+ align:start position:0%
+were talking about it earlier I wasn't
+ 
+
+ align:start position:0%
+were talking about it earlier I wasn't
+sure if I was still a photographer I had
+
+ align:start position:0%
+sure if I was still a photographer I had
+ 
+
+ align:start position:0%
+sure if I was still a photographer I had
+to kind of work my way back through it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so uh from there I went to see my friend
+
+ align:start position:0%
+so uh from there I went to see my friend
+ 
+
+ align:start position:0%
+so uh from there I went to see my friend
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh Laura Lawson who's a teaches
+
+ align:start position:0%
+uh Laura Lawson who's a teaches
+ 
+
+ align:start position:0%
+uh Laura Lawson who's a teaches
+landscape and who I worked on a book of
+
+ align:start position:0%
+landscape and who I worked on a book of
+ 
+
+ align:start position:0%
+landscape and who I worked on a book of
+Community Gardens with and she had been
+
+ align:start position:0%
+Community Gardens with and she had been
+ 
+
+ align:start position:0%
+Community Gardens with and she had been
+talking about East St Louis so she took
+
+ align:start position:0%
+talking about East St Louis so she took
+ 
+
+ align:start position:0%
+talking about East St Louis so she took
+me to East St Louis um this is a bridge
+
+ align:start position:0%
+me to East St Louis um this is a bridge
+ 
+
+ align:start position:0%
+me to East St Louis um this is a bridge
+that um I didn't you know I heard about
+
+ align:start position:0%
+that um I didn't you know I heard about
+ 
+
+ align:start position:0%
+that um I didn't you know I heard about
+least St Louis it's the home of Miles
+
+ align:start position:0%
+least St Louis it's the home of Miles
+ 
+
+ align:start position:0%
+least St Louis it's the home of Miles
+Davis is probably the source of one of
+
+ align:start position:0%
+Davis is probably the source of one of
+ 
+
+ align:start position:0%
+Davis is probably the source of one of
+the large the the most um the biggest
+
+ align:start position:0%
+the large the the most um the biggest
+ 
+
+ align:start position:0%
+the large the the most um the biggest
+race riots um in the country in the
+
+ align:start position:0%
+race riots um in the country in the
+ 
+
+ align:start position:0%
+race riots um in the country in the
+history of the country and there was a
+
+ align:start position:0%
+history of the country and there was a
+ 
+
+ align:start position:0%
+history of the country and there was a
+bridge where you could walk to St Louis
+
+ align:start position:0%
+bridge where you could walk to St Louis
+ 
+
+ align:start position:0%
+bridge where you could walk to St Louis
+that has been closed that's this has
+
+ align:start position:0%
+that has been closed that's this has
+ 
+
+ align:start position:0%
+that has been closed that's this has
+been closed I think for the last 50
+
+ align:start position:0%
+been closed I think for the last 50
+ 
+
+ align:start position:0%
+been closed I think for the last 50
+years and this is sort of the yellow
+
+ align:start position:0%
+years and this is sort of the yellow
+ 
+
+ align:start position:0%
+years and this is sort of the yellow
+brick road where you can kind of see the
+
+ align:start position:0%
+brick road where you can kind of see the
+ 
+
+ align:start position:0%
+brick road where you can kind of see the
+archway from this bridge um that's sort
+
+ align:start position:0%
+archway from this bridge um that's sort
+ 
+
+ align:start position:0%
+archway from this bridge um that's sort
+of in uh
+
+ align:start position:0%
+of in uh
+ 
+
+ align:start position:0%
+of in uh
+disrepair um I was interested in this
+
+ align:start position:0%
+disrepair um I was interested in this
+ 
+
+ align:start position:0%
+disrepair um I was interested in this
+the the kind of results the Onyx Club
+
+ align:start position:0%
+the the kind of results the Onyx Club
+ 
+
+ align:start position:0%
+the the kind of results the Onyx Club
+there was a club Alabama which I know
+
+ align:start position:0%
+there was a club Alabama which I know
+ 
+
+ align:start position:0%
+there was a club Alabama which I know
+there was one in Central Avenue and it
+
+ align:start position:0%
+there was one in Central Avenue and it
+ 
+
+ align:start position:0%
+there was one in Central Avenue and it
+was also one in San Francisco that
+
+ align:start position:0%
+was also one in San Francisco that
+ 
+
+ align:start position:0%
+was also one in San Francisco that
+seemed to be recurring theme um so that
+
+ align:start position:0%
+seemed to be recurring theme um so that
+ 
+
+ align:start position:0%
+seemed to be recurring theme um so that
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+both interesting uh to me and both kind
+
+ align:start position:0%
+both interesting uh to me and both kind
+ 
+
+ align:start position:0%
+both interesting uh to me and both kind
+of places that I I'm going to go back
+
+ align:start position:0%
+of places that I I'm going to go back
+ 
+
+ align:start position:0%
+of places that I I'm going to go back
+and do some more work
+
+ align:start position:0%
+and do some more work
+ 
+
+ align:start position:0%
+and do some more work
+um um so I'm going to show you a little
+
+ align:start position:0%
+um um so I'm going to show you a little
+ 
+
+ align:start position:0%
+um um so I'm going to show you a little
+bit of a color work I've been kind of
+
+ align:start position:0%
+bit of a color work I've been kind of
+ 
+
+ align:start position:0%
+bit of a color work I've been kind of
+Shifting back and forth I got a dig well
+
+ align:start position:0%
+Shifting back and forth I got a dig well
+ 
+
+ align:start position:0%
+Shifting back and forth I got a dig well
+I got a um my I moved and gave up my
+
+ align:start position:0%
+I got a um my I moved and gave up my
+ 
+
+ align:start position:0%
+I got a um my I moved and gave up my
+dark room and then simultaneously got a
+
+ align:start position:0%
+dark room and then simultaneously got a
+ 
+
+ align:start position:0%
+dark room and then simultaneously got a
+job in Santa Cruz and wasn't sure if I
+
+ align:start position:0%
+job in Santa Cruz and wasn't sure if I
+ 
+
+ align:start position:0%
+job in Santa Cruz and wasn't sure if I
+was going to to be moving there I'm not
+
+ align:start position:0%
+was going to to be moving there I'm not
+ 
+
+ align:start position:0%
+was going to to be moving there I'm not
+um and uh sort of simultaneously to me
+
+ align:start position:0%
+um and uh sort of simultaneously to me
+ 
+
+ align:start position:0%
+um and uh sort of simultaneously to me
+working on the book I started doing
+
+ align:start position:0%
+working on the book I started doing
+ 
+
+ align:start position:0%
+working on the book I started doing
+output put digitally and started doing
+
+ align:start position:0%
+output put digitally and started doing
+ 
+
+ align:start position:0%
+output put digitally and started doing
+more color I didn't do I did some color
+
+ align:start position:0%
+more color I didn't do I did some color
+ 
+
+ align:start position:0%
+more color I didn't do I did some color
+and I printed color but because I didn't
+
+ align:start position:0%
+and I printed color but because I didn't
+ 
+
+ align:start position:0%
+and I printed color but because I didn't
+have access I um had and would really
+
+ align:start position:0%
+have access I um had and would really
+ 
+
+ align:start position:0%
+have access I um had and would really
+like black and white I started doing I I
+
+ align:start position:0%
+like black and white I started doing I I
+ 
+
+ align:start position:0%
+like black and white I started doing I I
+did color all along but I kind of
+
+ align:start position:0%
+did color all along but I kind of
+ 
+
+ align:start position:0%
+did color all along but I kind of
+started actualizing it this's another
+
+ align:start position:0%
+started actualizing it this's another
+ 
+
+ align:start position:0%
+started actualizing it this's another
+nightclub facade at East Oakland this is
+
+ align:start position:0%
+nightclub facade at East Oakland this is
+ 
+
+ align:start position:0%
+nightclub facade at East Oakland this is
+in Richmond a sort of a nicely um
+
+ align:start position:0%
+in Richmond a sort of a nicely um
+ 
+
+ align:start position:0%
+in Richmond a sort of a nicely um
+appointed
+
+ align:start position:0%
+appointed
+ 
+
+ align:start position:0%
+appointed
+Treehouse this is um also hian uh
+
+ align:start position:0%
+Treehouse this is um also hian uh
+ 
+
+ align:start position:0%
+Treehouse this is um also hian uh
+Florida Lower East Side in New York with
+
+ align:start position:0%
+Florida Lower East Side in New York with
+ 
+
+ align:start position:0%
+Florida Lower East Side in New York with
+basketballs Brooklyn very near where
+
+ align:start position:0%
+basketballs Brooklyn very near where
+ 
+
+ align:start position:0%
+basketballs Brooklyn very near where
+ebitz fille used to
+
+ align:start position:0%
+ebitz fille used to
+ 
+
+ align:start position:0%
+ebitz fille used to
+be uh Eatonville Florida home of zoril
+
+ align:start position:0%
+be uh Eatonville Florida home of zoril
+ 
+
+ align:start position:0%
+be uh Eatonville Florida home of zoril
+Hurston another uh Church in Richmond it
+
+ align:start position:0%
+Hurston another uh Church in Richmond it
+ 
+
+ align:start position:0%
+Hurston another uh Church in Richmond it
+looks very much like churches I see in
+
+ align:start position:0%
+looks very much like churches I see in
+ 
+
+ align:start position:0%
+looks very much like churches I see in
+the South so when I came back U I did
+
+ align:start position:0%
+the South so when I came back U I did
+ 
+
+ align:start position:0%
+the South so when I came back U I did
+get to New Orleans you'll see some of
+
+ align:start position:0%
+get to New Orleans you'll see some of
+ 
+
+ align:start position:0%
+get to New Orleans you'll see some of
+those later but when I came back I was
+
+ align:start position:0%
+those later but when I came back I was
+ 
+
+ align:start position:0%
+those later but when I came back I was
+commissioned to um uh work on uh a
+
+ align:start position:0%
+commissioned to um uh work on uh a
+ 
+
+ align:start position:0%
+commissioned to um uh work on uh a
+public art project in uh on Vermont
+
+ align:start position:0%
+public art project in uh on Vermont
+ 
+
+ align:start position:0%
+public art project in uh on Vermont
+Street in uh what is now called South
+
+ align:start position:0%
+Street in uh what is now called South
+ 
+
+ align:start position:0%
+Street in uh what is now called South
+Central Los Angeles but it but until uh
+
+ align:start position:0%
+Central Los Angeles but it but until uh
+ 
+
+ align:start position:0%
+Central Los Angeles but it but until uh
+prior to the Watts Riots was just
+
+ align:start position:0%
+prior to the Watts Riots was just
+ 
+
+ align:start position:0%
+prior to the Watts Riots was just
+Central Los Angeles and this is the
+
+ align:start position:0%
+Central Los Angeles and this is the
+ 
+
+ align:start position:0%
+Central Los Angeles and this is the
+first public um sort of county building
+
+ align:start position:0%
+first public um sort of county building
+ 
+
+ align:start position:0%
+first public um sort of county building
+in this neighborhood since the Rodney
+
+ align:start position:0%
+in this neighborhood since the Rodney
+ 
+
+ align:start position:0%
+in this neighborhood since the Rodney
+King riots basically sort of nothing's
+
+ align:start position:0%
+King riots basically sort of nothing's
+ 
+
+ align:start position:0%
+King riots basically sort of nothing's
+happened there were all these promises
+
+ align:start position:0%
+happened there were all these promises
+ 
+
+ align:start position:0%
+happened there were all these promises
+that were going to be made and the is
+
+ align:start position:0%
+that were going to be made and the is
+ 
+
+ align:start position:0%
+that were going to be made and the is
+privately developed and the developer
+
+ align:start position:0%
+privately developed and the developer
+ 
+
+ align:start position:0%
+privately developed and the developer
+who was a photo collector wanted to have
+
+ align:start position:0%
+who was a photo collector wanted to have
+ 
+
+ align:start position:0%
+who was a photo collector wanted to have
+photography and public art so he
+
+ align:start position:0%
+photography and public art so he
+ 
+
+ align:start position:0%
+photography and public art so he
+basically commiss missed six artists to
+
+ align:start position:0%
+basically commiss missed six artists to
+ 
+
+ align:start position:0%
+basically commiss missed six artists to
+um uh work for a month and then do a
+
+ align:start position:0%
+um uh work for a month and then do a
+ 
+
+ align:start position:0%
+um uh work for a month and then do a
+proposal and this was a neighborhood
+
+ align:start position:0%
+proposal and this was a neighborhood
+ 
+
+ align:start position:0%
+proposal and this was a neighborhood
+I've been looking for in La for like 30
+
+ align:start position:0%
+I've been looking for in La for like 30
+ 
+
+ align:start position:0%
+I've been looking for in La for like 30
+years it's not it's not it's farther
+
+ align:start position:0%
+years it's not it's not it's farther
+ 
+
+ align:start position:0%
+years it's not it's not it's farther
+more Central than Compton and Watts it
+
+ align:start position:0%
+more Central than Compton and Watts it
+ 
+
+ align:start position:0%
+more Central than Compton and Watts it
+has a lot of storefront churches um it's
+
+ align:start position:0%
+has a lot of storefront churches um it's
+ 
+
+ align:start position:0%
+has a lot of storefront churches um it's
+half perhaps slightly more Hispanic it
+
+ align:start position:0%
+half perhaps slightly more Hispanic it
+ 
+
+ align:start position:0%
+half perhaps slightly more Hispanic it
+had all these kind of things that you
+
+ align:start position:0%
+had all these kind of things that you
+ 
+
+ align:start position:0%
+had all these kind of things that you
+can kind of see from my work I'm
+
+ align:start position:0%
+can kind of see from my work I'm
+ 
+
+ align:start position:0%
+can kind of see from my work I'm
+interested in and I love these converted
+
+ align:start position:0%
+interested in and I love these converted
+ 
+
+ align:start position:0%
+interested in and I love these converted
+buildings you know the the whole idea of
+
+ align:start position:0%
+buildings you know the the whole idea of
+ 
+
+ align:start position:0%
+buildings you know the the whole idea of
+the theater being used having different
+
+ align:start position:0%
+the theater being used having different
+ 
+
+ align:start position:0%
+the theater being used having different
+reiterations has been real interesting
+
+ align:start position:0%
+reiterations has been real interesting
+ 
+
+ align:start position:0%
+reiterations has been real interesting
+to me and again the kind of markings how
+
+ align:start position:0%
+to me and again the kind of markings how
+ 
+
+ align:start position:0%
+to me and again the kind of markings how
+how is both Faith
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expressed and the other thing I like
+
+ align:start position:0%
+expressed and the other thing I like
+ 
+
+ align:start position:0%
+expressed and the other thing I like
+about La is um if if I need to go
+
+ align:start position:0%
+about La is um if if I need to go
+ 
+
+ align:start position:0%
+about La is um if if I need to go
+someplace really different from the Bay
+
+ align:start position:0%
+someplace really different from the Bay
+ 
+
+ align:start position:0%
+someplace really different from the Bay
+Area I can go to La and feel like I'm
+
+ align:start position:0%
+Area I can go to La and feel like I'm
+ 
+
+ align:start position:0%
+Area I can go to La and feel like I'm
+going to Nepal because the light is
+
+ align:start position:0%
+going to Nepal because the light is
+ 
+
+ align:start position:0%
+going to Nepal because the light is
+different the light is really different
+
+ align:start position:0%
+different the light is really different
+ 
+
+ align:start position:0%
+different the light is really different
+I think something happened I think it's
+
+ align:start position:0%
+I think something happened I think it's
+ 
+
+ align:start position:0%
+I think something happened I think it's
+really is a different Zone the things
+
+ align:start position:0%
+really is a different Zone the things
+ 
+
+ align:start position:0%
+really is a different Zone the things
+that people talk about are different the
+
+ align:start position:0%
+that people talk about are different the
+ 
+
+ align:start position:0%
+that people talk about are different the
+colors they wear are different the cars
+
+ align:start position:0%
+colors they wear are different the cars
+ 
+
+ align:start position:0%
+colors they wear are different the cars
+and their interest in cars are different
+
+ align:start position:0%
+and their interest in cars are different
+ 
+
+ align:start position:0%
+and their interest in cars are different
+and and I always find it really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+refreshing so again uh I love the fact
+
+ align:start position:0%
+refreshing so again uh I love the fact
+ 
+
+ align:start position:0%
+refreshing so again uh I love the fact
+that people's hearts were on their
+
+ align:start position:0%
+that people's hearts were on their
+ 
+
+ align:start position:0%
+that people's hearts were on their
+sleeves um this is the area where
+
+ align:start position:0%
+sleeves um this is the area where
+ 
+
+ align:start position:0%
+sleeves um this is the area where
+Pepperdine University used to be there's
+
+ align:start position:0%
+Pepperdine University used to be there's
+ 
+
+ align:start position:0%
+Pepperdine University used to be there's
+now the khaw Christian Center which is
+
+ align:start position:0%
+now the khaw Christian Center which is
+ 
+
+ align:start position:0%
+now the khaw Christian Center which is
+one of these mega churches with
+
+ align:start position:0%
+one of these mega churches with
+ 
+
+ align:start position:0%
+one of these mega churches with
+something like 10,000 members and inside
+
+ align:start position:0%
+something like 10,000 members and inside
+ 
+
+ align:start position:0%
+something like 10,000 members and inside
+this huge building called the the faith
+
+ align:start position:0%
+this huge building called the the faith
+ 
+
+ align:start position:0%
+this huge building called the the faith
+Dome they have services that are
+
+ align:start position:0%
+Dome they have services that are
+ 
+
+ align:start position:0%
+Dome they have services that are
+televised and in fact they encourage you
+
+ align:start position:0%
+televised and in fact they encourage you
+ 
+
+ align:start position:0%
+televised and in fact they encourage you
+to sit in the front because they don't
+
+ align:start position:0%
+to sit in the front because they don't
+ 
+
+ align:start position:0%
+to sit in the front because they don't
+like to have empty seats it's bad for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+business so they didn't actually like me
+
+ align:start position:0%
+business so they didn't actually like me
+ 
+
+ align:start position:0%
+business so they didn't actually like me
+taking this picture in fact they um but
+
+ align:start position:0%
+taking this picture in fact they um but
+ 
+
+ align:start position:0%
+taking this picture in fact they um but
+it's it was interesting so this was a
+
+ align:start position:0%
+it's it was interesting so this was a
+ 
+
+ align:start position:0%
+it's it was interesting so this was a
+kind of mega church is almost corporate
+
+ align:start position:0%
+kind of mega church is almost corporate
+ 
+
+ align:start position:0%
+kind of mega church is almost corporate
+in nature and then right next to it was
+
+ align:start position:0%
+in nature and then right next to it was
+ 
+
+ align:start position:0%
+in nature and then right next to it was
+a very small Multicultural uh
+
+ align:start position:0%
+a very small Multicultural uh
+ 
+
+ align:start position:0%
+a very small Multicultural uh
+bilingual um uh Pentecostal Church where
+
+ align:start position:0%
+bilingual um uh Pentecostal Church where
+ 
+
+ align:start position:0%
+bilingual um uh Pentecostal Church where
+everything was done in two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+languages and then in a farther up
+
+ align:start position:0%
+languages and then in a farther up
+ 
+
+ align:start position:0%
+languages and then in a farther up
+kinshaw this guy's been here for Years
+
+ align:start position:0%
+kinshaw this guy's been here for Years
+ 
+
+ align:start position:0%
+kinshaw this guy's been here for Years
+love that
+
+ align:start position:0%
+love that
+ 
+
+ align:start position:0%
+love that
+sign and it was interesting that that I
+
+ align:start position:0%
+sign and it was interesting that that I
+ 
+
+ align:start position:0%
+sign and it was interesting that that I
+kind of hit this when I had sort of
+
+ align:start position:0%
+kind of hit this when I had sort of
+ 
+
+ align:start position:0%
+kind of hit this when I had sort of
+gotten some momentum going I don't know
+
+ align:start position:0%
+gotten some momentum going I don't know
+ 
+
+ align:start position:0%
+gotten some momentum going I don't know
+if I could have taken these pictures
+
+ align:start position:0%
+if I could have taken these pictures
+ 
+
+ align:start position:0%
+if I could have taken these pictures
+Well Pro I'd like to think I would but
+
+ align:start position:0%
+Well Pro I'd like to think I would but
+ 
+
+ align:start position:0%
+Well Pro I'd like to think I would but
+um I don't know if I would have uh I I
+
+ align:start position:0%
+um I don't know if I would have uh I I
+ 
+
+ align:start position:0%
+um I don't know if I would have uh I I
+know I'm sort of uh on a role because no
+
+ align:start position:0%
+know I'm sort of uh on a role because no
+ 
+
+ align:start position:0%
+know I'm sort of uh on a role because no
+one questioned me and we were talking
+
+ align:start position:0%
+one questioned me and we were talking
+ 
+
+ align:start position:0%
+one questioned me and we were talking
+about it I you get to hear the story
+
+ align:start position:0%
+about it I you get to hear the story
+ 
+
+ align:start position:0%
+about it I you get to hear the story
+twice I had a paper out Ben you probably
+
+ align:start position:0%
+twice I had a paper out Ben you probably
+ 
+
+ align:start position:0%
+twice I had a paper out Ben you probably
+heard the story also I had a paper out
+
+ align:start position:0%
+heard the story also I had a paper out
+ 
+
+ align:start position:0%
+heard the story also I had a paper out
+when I was a kid and the only thing I
+
+ align:start position:0%
+when I was a kid and the only thing I
+ 
+
+ align:start position:0%
+when I was a kid and the only thing I
+learned from it was that dogs will chase
+
+ align:start position:0%
+learned from it was that dogs will chase
+ 
+
+ align:start position:0%
+learned from it was that dogs will chase
+you if you're frightened of them and
+
+ align:start position:0%
+you if you're frightened of them and
+ 
+
+ align:start position:0%
+you if you're frightened of them and
+that absolutely applies to photography
+
+ align:start position:0%
+that absolutely applies to photography
+ 
+
+ align:start position:0%
+that absolutely applies to photography
+if you're feeling uncomfortable with
+
+ align:start position:0%
+if you're feeling uncomfortable with
+ 
+
+ align:start position:0%
+if you're feeling uncomfortable with
+what you're doing people will pick up on
+
+ align:start position:0%
+what you're doing people will pick up on
+ 
+
+ align:start position:0%
+what you're doing people will pick up on
+it they actually will pick up on it more
+
+ align:start position:0%
+it they actually will pick up on it more
+ 
+
+ align:start position:0%
+it they actually will pick up on it more
+in California than in New York and maybe
+
+ align:start position:0%
+in California than in New York and maybe
+ 
+
+ align:start position:0%
+in California than in New York and maybe
+even especially in New York cuz in New
+
+ align:start position:0%
+even especially in New York cuz in New
+ 
+
+ align:start position:0%
+even especially in New York cuz in New
+York I photograph people doing illegal
+
+ align:start position:0%
+York I photograph people doing illegal
+ 
+
+ align:start position:0%
+York I photograph people doing illegal
+things in didn't even look up in
+
+ align:start position:0%
+things in didn't even look up in
+ 
+
+ align:start position:0%
+things in didn't even look up in
+California everybody's in cars so the
+
+ align:start position:0%
+California everybody's in cars so the
+ 
+
+ align:start position:0%
+California everybody's in cars so the
+idea of actually facing someone face to
+
+ align:start position:0%
+idea of actually facing someone face to
+ 
+
+ align:start position:0%
+idea of actually facing someone face to
+face is a little more foreign and people
+
+ align:start position:0%
+face is a little more foreign and people
+ 
+
+ align:start position:0%
+face is a little more foreign and people
+are more suspicious but if you are if
+
+ align:start position:0%
+are more suspicious but if you are if
+ 
+
+ align:start position:0%
+are more suspicious but if you are if
+you know this whole thing about stealing
+
+ align:start position:0%
+you know this whole thing about stealing
+ 
+
+ align:start position:0%
+you know this whole thing about stealing
+Souls you can only steal someone's Soul
+
+ align:start position:0%
+Souls you can only steal someone's Soul
+ 
+
+ align:start position:0%
+Souls you can only steal someone's Soul
+if that's your intent I really believe
+
+ align:start position:0%
+if that's your intent I really believe
+ 
+
+ align:start position:0%
+if that's your intent I really believe
+that and people can pick up on it and
+
+ align:start position:0%
+that and people can pick up on it and
+ 
+
+ align:start position:0%
+that and people can pick up on it and
+especially um uh people of color and
+
+ align:start position:0%
+especially um uh people of color and
+ 
+
+ align:start position:0%
+especially um uh people of color and
+people in um communities that have been
+
+ align:start position:0%
+people in um communities that have been
+ 
+
+ align:start position:0%
+people in um communities that have been
+under the gun and that have been
+
+ align:start position:0%
+under the gun and that have been
+ 
+
+ align:start position:0%
+under the gun and that have been
+exploited by media can absolutely their
+
+ align:start position:0%
+exploited by media can absolutely their
+ 
+
+ align:start position:0%
+exploited by media can absolutely their
+ detector is um pretty stri on
+
+ align:start position:0%
+ detector is um pretty stri on
+ 
+
+ align:start position:0%
+ detector is um pretty stri on
+so it was interesting to me I could kind
+
+ align:start position:0%
+so it was interesting to me I could kind
+ 
+
+ align:start position:0%
+so it was interesting to me I could kind
+of judge by the way people reacting to
+
+ align:start position:0%
+of judge by the way people reacting to
+ 
+
+ align:start position:0%
+of judge by the way people reacting to
+me that both I was really into doing
+
+ align:start position:0%
+me that both I was really into doing
+ 
+
+ align:start position:0%
+me that both I was really into doing
+this and that maybe my heart was pure as
+
+ align:start position:0%
+this and that maybe my heart was pure as
+ 
+
+ align:start position:0%
+this and that maybe my heart was pure as
+pure as it could
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get so there's sort of the everpresent
+
+ align:start position:0%
+get so there's sort of the everpresent
+ 
+
+ align:start position:0%
+get so there's sort of the everpresent
+palm and the representation of it I
+
+ align:start position:0%
+palm and the representation of it I
+ 
+
+ align:start position:0%
+palm and the representation of it I
+photographed there was a motel I didn't
+
+ align:start position:0%
+photographed there was a motel I didn't
+ 
+
+ align:start position:0%
+photographed there was a motel I didn't
+include it but it's the motel where Sam
+
+ align:start position:0%
+include it but it's the motel where Sam
+ 
+
+ align:start position:0%
+include it but it's the motel where Sam
+Cook was killed which is right up the
+
+ align:start position:0%
+Cook was killed which is right up the
+ 
+
+ align:start position:0%
+Cook was killed which is right up the
+street from from here here um there's
+
+ align:start position:0%
+street from from here here um there's
+ 
+
+ align:start position:0%
+street from from here here um there's
+like you know you sort of drive and
+
+ align:start position:0%
+like you know you sort of drive and
+ 
+
+ align:start position:0%
+like you know you sort of drive and
+someone will have four drum sets just
+
+ align:start position:0%
+someone will have four drum sets just
+ 
+
+ align:start position:0%
+someone will have four drum sets just
+set up in an empty lot selling it and
+
+ align:start position:0%
+set up in an empty lot selling it and
+ 
+
+ align:start position:0%
+set up in an empty lot selling it and
+then there's besides the kind of
+
+ align:start position:0%
+then there's besides the kind of
+ 
+
+ align:start position:0%
+then there's besides the kind of
+religious iconography there these
+
+ align:start position:0%
+religious iconography there these
+ 
+
+ align:start position:0%
+religious iconography there these
+incredible I think they're really
+
+ align:start position:0%
+incredible I think they're really
+ 
+
+ align:start position:0%
+incredible I think they're really
+beautiful um sort of you know uh
+
+ align:start position:0%
+beautiful um sort of you know uh
+ 
+
+ align:start position:0%
+beautiful um sort of you know uh
+vernacular expressions of
+
+ align:start position:0%
+vernacular expressions of
+ 
+
+ align:start position:0%
+vernacular expressions of
+Commerce so right next to the uh kinof
+
+ align:start position:0%
+Commerce so right next to the uh kinof
+ 
+
+ align:start position:0%
+Commerce so right next to the uh kinof
+um Christian Center was a neighborhood
+
+ align:start position:0%
+um Christian Center was a neighborhood
+ 
+
+ align:start position:0%
+um Christian Center was a neighborhood
+called Vermont nolles which has some of
+
+ align:start position:0%
+called Vermont nolles which has some of
+ 
+
+ align:start position:0%
+called Vermont nolles which has some of
+the nicest houses housing stock in Los
+
+ align:start position:0%
+the nicest houses housing stock in Los
+ 
+
+ align:start position:0%
+the nicest houses housing stock in Los
+Angeles 100% African-American in fact
+
+ align:start position:0%
+Angeles 100% African-American in fact
+ 
+
+ align:start position:0%
+Angeles 100% African-American in fact
+they're very suspicious of this new
+
+ align:start position:0%
+they're very suspicious of this new
+ 
+
+ align:start position:0%
+they're very suspicious of this new
+building but um again people there sort
+
+ align:start position:0%
+building but um again people there sort
+ 
+
+ align:start position:0%
+building but um again people there sort
+of stereotypes about where black people
+
+ align:start position:0%
+of stereotypes about where black people
+ 
+
+ align:start position:0%
+of stereotypes about where black people
+live and what their lives are like and
+
+ align:start position:0%
+live and what their lives are like and
+ 
+
+ align:start position:0%
+live and what their lives are like and
+here was this incredibly immaculately
+
+ align:start position:0%
+here was this incredibly immaculately
+ 
+
+ align:start position:0%
+here was this incredibly immaculately
+landscaped uh neighborhood um that uh
+
+ align:start position:0%
+landscaped uh neighborhood um that uh
+ 
+
+ align:start position:0%
+landscaped uh neighborhood um that uh
+people are fighting to try to live in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a lot of these are on Vermont Vermont is
+
+ align:start position:0%
+a lot of these are on Vermont Vermont is
+ 
+
+ align:start position:0%
+a lot of these are on Vermont Vermont is
+the second busiest bus travel people do
+
+ align:start position:0%
+the second busiest bus travel people do
+ 
+
+ align:start position:0%
+the second busiest bus travel people do
+take buses in La contrary to popular and
+
+ align:start position:0%
+take buses in La contrary to popular and
+ 
+
+ align:start position:0%
+take buses in La contrary to popular and
+and so that was part of the idea was my
+
+ align:start position:0%
+and so that was part of the idea was my
+ 
+
+ align:start position:0%
+and so that was part of the idea was my
+idea was I wanted to make these
+
+ align:start position:0%
+idea was I wanted to make these
+ 
+
+ align:start position:0%
+idea was I wanted to make these
+photographs large in kind of light boxes
+
+ align:start position:0%
+photographs large in kind of light boxes
+ 
+
+ align:start position:0%
+photographs large in kind of light boxes
+that you'd be able to see regardless of
+
+ align:start position:0%
+that you'd be able to see regardless of
+ 
+
+ align:start position:0%
+that you'd be able to see regardless of
+how you were passing by uh vehicle or
+
+ align:start position:0%
+how you were passing by uh vehicle or
+ 
+
+ align:start position:0%
+how you were passing by uh vehicle or
+foot traffic and also if you were using
+
+ align:start position:0%
+foot traffic and also if you were using
+ 
+
+ align:start position:0%
+foot traffic and also if you were using
+the building
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my proposal although I didn't get to
+
+ align:start position:0%
+so my proposal although I didn't get to
+ 
+
+ align:start position:0%
+so my proposal although I didn't get to
+reiterate it was um uh I had uh
+
+ align:start position:0%
+reiterate it was um uh I had uh
+ 
+
+ align:start position:0%
+reiterate it was um uh I had uh
+contracted with um a sign maker and
+
+ align:start position:0%
+contracted with um a sign maker and
+ 
+
+ align:start position:0%
+contracted with um a sign maker and
+someone who makes these huge boxes for
+
+ align:start position:0%
+someone who makes these huge boxes for
+ 
+
+ align:start position:0%
+someone who makes these huge boxes for
+advertising and I was going to place
+
+ align:start position:0%
+advertising and I was going to place
+ 
+
+ align:start position:0%
+advertising and I was going to place
+them on the building um I was actually
+
+ align:start position:0%
+them on the building um I was actually
+ 
+
+ align:start position:0%
+them on the building um I was actually
+in the middle of working on the book so
+
+ align:start position:0%
+in the middle of working on the book so
+ 
+
+ align:start position:0%
+in the middle of working on the book so
+my presentation was to show and be very
+
+ align:start position:0%
+my presentation was to show and be very
+ 
+
+ align:start position:0%
+my presentation was to show and be very
+enthusiastic about the images which I
+
+ align:start position:0%
+enthusiastic about the images which I
+ 
+
+ align:start position:0%
+enthusiastic about the images which I
+was actually more interested in even
+
+ align:start position:0%
+was actually more interested in even
+ 
+
+ align:start position:0%
+was actually more interested in even
+than doing the public art so what they
+
+ align:start position:0%
+than doing the public art so what they
+ 
+
+ align:start position:0%
+than doing the public art so what they
+they someone else is going to do um the
+
+ align:start position:0%
+they someone else is going to do um the
+ 
+
+ align:start position:0%
+they someone else is going to do um the
+sort of imagery on the outside of the
+
+ align:start position:0%
+sort of imagery on the outside of the
+ 
+
+ align:start position:0%
+sort of imagery on the outside of the
+building but they are are going to use
+
+ align:start position:0%
+building but they are are going to use
+ 
+
+ align:start position:0%
+building but they are are going to use
+my photographs of the community inside
+
+ align:start position:0%
+my photographs of the community inside
+ 
+
+ align:start position:0%
+my photographs of the community inside
+the building so that the clients will
+
+ align:start position:0%
+the building so that the clients will
+ 
+
+ align:start position:0%
+the building so that the clients will
+actually see them and they I thought I
+
+ align:start position:0%
+actually see them and they I thought I
+ 
+
+ align:start position:0%
+actually see them and they I thought I
+mean I was really interested that the
+
+ align:start position:0%
+mean I was really interested that the
+ 
+
+ align:start position:0%
+mean I was really interested that the
+the story was more complex and meets the
+
+ align:start position:0%
+the story was more complex and meets the
+ 
+
+ align:start position:0%
+the story was more complex and meets the
+eye and I thought it was interested and
+
+ align:start position:0%
+eye and I thought it was interested and
+ 
+
+ align:start position:0%
+eye and I thought it was interested and
+important that the clients and the
+
+ align:start position:0%
+important that the clients and the
+ 
+
+ align:start position:0%
+important that the clients and the
+people in Community saw a reflection of
+
+ align:start position:0%
+people in Community saw a reflection of
+ 
+
+ align:start position:0%
+people in Community saw a reflection of
+that because they know that but a lot of
+
+ align:start position:0%
+that because they know that but a lot of
+ 
+
+ align:start position:0%
+that because they know that but a lot of
+other people
+
+ align:start position:0%
+other people
+ 
+
+ align:start position:0%
+other people
+don't so naturally I was very
+
+ align:start position:0%
+don't so naturally I was very
+ 
+
+ align:start position:0%
+don't so naturally I was very
+disappointed and paying quite close
+
+ align:start position:0%
+disappointed and paying quite close
+ 
+
+ align:start position:0%
+disappointed and paying quite close
+attention to the course of Katrina as it
+
+ align:start position:0%
+attention to the course of Katrina as it
+ 
+
+ align:start position:0%
+attention to the course of Katrina as it
+was bearing on New Orleans uh the the
+
+ align:start position:0%
+was bearing on New Orleans uh the the
+ 
+
+ align:start position:0%
+was bearing on New Orleans uh the the
+year before I had been there right after
+
+ align:start position:0%
+year before I had been there right after
+ 
+
+ align:start position:0%
+year before I had been there right after
+I can't remember the name of the
+
+ align:start position:0%
+I can't remember the name of the
+ 
+
+ align:start position:0%
+I can't remember the name of the
+hurricane that AED at the last minute
+
+ align:start position:0%
+hurricane that AED at the last minute
+ 
+
+ align:start position:0%
+hurricane that AED at the last minute
+and I hadn't really thought about it but
+
+ align:start position:0%
+and I hadn't really thought about it but
+ 
+
+ align:start position:0%
+and I hadn't really thought about it but
+a lot of people left and it was
+
+ align:start position:0%
+a lot of people left and it was
+ 
+
+ align:start position:0%
+a lot of people left and it was
+interesting it was really on class lines
+
+ align:start position:0%
+interesting it was really on class lines
+ 
+
+ align:start position:0%
+interesting it was really on class lines
+who left and who didn't and on the one
+
+ align:start position:0%
+who left and who didn't and on the one
+ 
+
+ align:start position:0%
+who left and who didn't and on the one
+hand you know know it would be
+
+ align:start position:0%
+hand you know know it would be
+ 
+
+ align:start position:0%
+hand you know know it would be
+interesting as a what am I as a
+
+ align:start position:0%
+interesting as a what am I as a
+ 
+
+ align:start position:0%
+interesting as a what am I as a
+photographer social scientist or the son
+
+ align:start position:0%
+photographer social scientist or the son
+ 
+
+ align:start position:0%
+photographer social scientist or the son
+of social scientist to have been with
+
+ align:start position:0%
+of social scientist to have been with
+ 
+
+ align:start position:0%
+of social scientist to have been with
+there with a hurricane uh because i' you
+
+ align:start position:0%
+there with a hurricane uh because i' you
+ 
+
+ align:start position:0%
+there with a hurricane uh because i' you
+know like to experience it of course
+
+ align:start position:0%
+know like to experience it of course
+ 
+
+ align:start position:0%
+know like to experience it of course
+everybody who lives there said are you
+
+ align:start position:0%
+everybody who lives there said are you
+ 
+
+ align:start position:0%
+everybody who lives there said are you
+out of your mind uh and people I know
+
+ align:start position:0%
+out of your mind uh and people I know
+ 
+
+ align:start position:0%
+out of your mind uh and people I know
+that we're stuck there really you know
+
+ align:start position:0%
+that we're stuck there really you know
+ 
+
+ align:start position:0%
+that we're stuck there really you know
+especially after with all that we've
+
+ align:start position:0%
+especially after with all that we've
+ 
+
+ align:start position:0%
+especially after with all that we've
+heard so anyway um in East St Louis um
+
+ align:start position:0%
+heard so anyway um in East St Louis um
+ 
+
+ align:start position:0%
+heard so anyway um in East St Louis um
+before New Orleans was closed you had to
+
+ align:start position:0%
+before New Orleans was closed you had to
+ 
+
+ align:start position:0%
+before New Orleans was closed you had to
+show ID you know and it did it opened up
+
+ align:start position:0%
+show ID you know and it did it opened up
+ 
+
+ align:start position:0%
+show ID you know and it did it opened up
+although there's no way to get there so
+
+ align:start position:0%
+although there's no way to get there so
+ 
+
+ align:start position:0%
+although there's no way to get there so
+I had to rent a car in Memphis driveth
+
+ align:start position:0%
+I had to rent a car in Memphis driveth
+ 
+
+ align:start position:0%
+I had to rent a car in Memphis driveth
+through Mississippi actually took
+
+ align:start position:0%
+through Mississippi actually took
+ 
+
+ align:start position:0%
+through Mississippi actually took
+picture of cotton for the first time I
+
+ align:start position:0%
+picture of cotton for the first time I
+ 
+
+ align:start position:0%
+picture of cotton for the first time I
+once drove all the way across the
+
+ align:start position:0%
+once drove all the way across the
+ 
+
+ align:start position:0%
+once drove all the way across the
+country and the first place I saw cotton
+
+ align:start position:0%
+country and the first place I saw cotton
+ 
+
+ align:start position:0%
+country and the first place I saw cotton
+was in Bakersfield I don't know what
+
+ align:start position:0%
+was in Bakersfield I don't know what
+ 
+
+ align:start position:0%
+was in Bakersfield I don't know what
+that's about so anyway but New Orleans
+
+ align:start position:0%
+that's about so anyway but New Orleans
+ 
+
+ align:start position:0%
+that's about so anyway but New Orleans
+is a place I have gone to seven or eight
+
+ align:start position:0%
+is a place I have gone to seven or eight
+ 
+
+ align:start position:0%
+is a place I have gone to seven or eight
+times in the last 12 years and uh I you
+
+ align:start position:0%
+times in the last 12 years and uh I you
+ 
+
+ align:start position:0%
+times in the last 12 years and uh I you
+know was very anxious to go I went in
+
+ align:start position:0%
+know was very anxious to go I went in
+ 
+
+ align:start position:0%
+know was very anxious to go I went in
+October um but I had been there before
+
+ align:start position:0%
+October um but I had been there before
+ 
+
+ align:start position:0%
+October um but I had been there before
+and what I wanted to show you this is uh
+
+ align:start position:0%
+and what I wanted to show you this is uh
+ 
+
+ align:start position:0%
+and what I wanted to show you this is uh
+John Scott who's a a MacArthur fellow
+
+ align:start position:0%
+John Scott who's a a MacArthur fellow
+ 
+
+ align:start position:0%
+John Scott who's a a MacArthur fellow
+sculptor who teaches at Xavier
+
+ align:start position:0%
+sculptor who teaches at Xavier
+ 
+
+ align:start position:0%
+sculptor who teaches at Xavier
+University and this is a spirit house
+
+ align:start position:0%
+University and this is a spirit house
+ 
+
+ align:start position:0%
+University and this is a spirit house
+which is again based on the model of the
+
+ align:start position:0%
+which is again based on the model of the
+ 
+
+ align:start position:0%
+which is again based on the model of the
+shotgun house and on the walls are these
+
+ align:start position:0%
+shotgun house and on the walls are these
+ 
+
+ align:start position:0%
+shotgun house and on the walls are these
+cutouts that have narratives of the
+
+ align:start position:0%
+cutouts that have narratives of the
+ 
+
+ align:start position:0%
+cutouts that have narratives of the
+African-American story in Louisiana the
+
+ align:start position:0%
+African-American story in Louisiana the
+ 
+
+ align:start position:0%
+African-American story in Louisiana the
+relationship with the Indians and uh it
+
+ align:start position:0%
+relationship with the Indians and uh it
+ 
+
+ align:start position:0%
+relationship with the Indians and uh it
+was um built it's on St
+
+ align:start position:0%
+was um built it's on St
+ 
+
+ align:start position:0%
+was um built it's on St
+um I think it's on St Bernard's um and
+
+ align:start position:0%
+um I think it's on St Bernard's um and
+ 
+
+ align:start position:0%
+um I think it's on St Bernard's um and
+so I was very curious to see if it
+
+ align:start position:0%
+so I was very curious to see if it
+ 
+
+ align:start position:0%
+so I was very curious to see if it
+surviv the hurricane so that was one of
+
+ align:start position:0%
+surviv the hurricane so that was one of
+ 
+
+ align:start position:0%
+surviv the hurricane so that was one of
+the first places I went when I
+
+ align:start position:0%
+the first places I went when I
+ 
+
+ align:start position:0%
+the first places I went when I
+arrived um St Rock is in the Bywater and
+
+ align:start position:0%
+arrived um St Rock is in the Bywater and
+ 
+
+ align:start position:0%
+arrived um St Rock is in the Bywater and
+St Rox is the miracle is the patron
+
+ align:start position:0%
+St Rox is the miracle is the patron
+ 
+
+ align:start position:0%
+St Rox is the miracle is the patron
+saint of miracle cures and this is a
+
+ align:start position:0%
+saint of miracle cures and this is a
+ 
+
+ align:start position:0%
+saint of miracle cures and this is a
+picture I took
+
+ align:start position:0%
+picture I took
+ 
+
+ align:start position:0%
+picture I took
+in 2000 of this chapel and I'm assuming
+
+ align:start position:0%
+in 2000 of this chapel and I'm assuming
+ 
+
+ align:start position:0%
+in 2000 of this chapel and I'm assuming
+he must be the patron saint because
+
+ align:start position:0%
+he must be the patron saint because
+ 
+
+ align:start position:0%
+he must be the patron saint because
+there are all these braces and um alleys
+
+ align:start position:0%
+there are all these braces and um alleys
+ 
+
+ align:start position:0%
+there are all these braces and um alleys
+and I took this picture uh in 2004 this
+
+ align:start position:0%
+and I took this picture uh in 2004 this
+ 
+
+ align:start position:0%
+and I took this picture uh in 2004 this
+is in the chapel and there's this Crush
+
+ align:start position:0%
+is in the chapel and there's this Crush
+ 
+
+ align:start position:0%
+is in the chapel and there's this Crush
+which is pretty spooky one thing I have
+
+ align:start position:0%
+which is pretty spooky one thing I have
+ 
+
+ align:start position:0%
+which is pretty spooky one thing I have
+to say about New Orleans and the whole
+
+ align:start position:0%
+to say about New Orleans and the whole
+ 
+
+ align:start position:0%
+to say about New Orleans and the whole
+notion of faith faith seems much more
+
+ align:start position:0%
+notion of faith faith seems much more
+ 
+
+ align:start position:0%
+notion of faith faith seems much more
+viable when it's 100° and 100% humidity
+
+ align:start position:0%
+viable when it's 100° and 100% humidity
+ 
+
+ align:start position:0%
+viable when it's 100° and 100% humidity
+sort of a particular kind of Fai this is
+
+ align:start position:0%
+sort of a particular kind of Fai this is
+ 
+
+ align:start position:0%
+sort of a particular kind of Fai this is
+what that Chapel looked like in
+
+ align:start position:0%
+what that Chapel looked like in
+ 
+
+ align:start position:0%
+what that Chapel looked like in
+October and as is
+
+ align:start position:0%
+October and as is
+ 
+
+ align:start position:0%
+October and as is
+this so the Bywater did um flood this is
+
+ align:start position:0%
+this so the Bywater did um flood this is
+ 
+
+ align:start position:0%
+this so the Bywater did um flood this is
+the budoo spiritualist church on Rampart
+
+ align:start position:0%
+the budoo spiritualist church on Rampart
+ 
+
+ align:start position:0%
+the budoo spiritualist church on Rampart
+Street I love the fact that the streets
+
+ align:start position:0%
+Street I love the fact that the streets
+ 
+
+ align:start position:0%
+Street I love the fact that the streets
+in New Orleans are actually named after
+
+ align:start position:0%
+in New Orleans are actually named after
+ 
+
+ align:start position:0%
+in New Orleans are actually named after
+Jazz well it's the other way around
+
+ align:start position:0%
+Jazz well it's the other way around
+ 
+
+ align:start position:0%
+Jazz well it's the other way around
+there's a lot of jazz especially um well
+
+ align:start position:0%
+there's a lot of jazz especially um well
+ 
+
+ align:start position:0%
+there's a lot of jazz especially um well
+through the history of jazz but uh BAS
+
+ align:start position:0%
+through the history of jazz but uh BAS
+ 
+
+ align:start position:0%
+through the history of jazz but uh BAS
+Street Rampart Street I mean they were
+
+ align:start position:0%
+Street Rampart Street I mean they were
+ 
+
+ align:start position:0%
+Street Rampart Street I mean they were
+based on these streets and then the
+
+ align:start position:0%
+based on these streets and then the
+ 
+
+ align:start position:0%
+based on these streets and then the
+other streets are named after the muses
+
+ align:start position:0%
+other streets are named after the muses
+ 
+
+ align:start position:0%
+other streets are named after the muses
+so in 1994 when I first went I was uh
+
+ align:start position:0%
+so in 1994 when I first went I was uh
+ 
+
+ align:start position:0%
+so in 1994 when I first went I was uh
+walking in uh T this is a Calo uh
+
+ align:start position:0%
+walking in uh T this is a Calo uh
+ 
+
+ align:start position:0%
+walking in uh T this is a Calo uh
+housing project and I heard music you
+
+ align:start position:0%
+housing project and I heard music you
+ 
+
+ align:start position:0%
+housing project and I heard music you
+know I was looking for uh funerals I
+
+ align:start position:0%
+know I was looking for uh funerals I
+ 
+
+ align:start position:0%
+know I was looking for uh funerals I
+knew about the tradition and here were
+
+ align:start position:0%
+knew about the tradition and here were
+ 
+
+ align:start position:0%
+knew about the tradition and here were
+these um 15 and 16 year olds a brass
+
+ align:start position:0%
+these um 15 and 16 year olds a brass
+ 
+
+ align:start position:0%
+these um 15 and 16 year olds a brass
+band playing better than a lot of
+
+ align:start position:0%
+band playing better than a lot of
+ 
+
+ align:start position:0%
+band playing better than a lot of
+professional musicians I know um it
+
+ align:start position:0%
+professional musicians I know um it
+ 
+
+ align:start position:0%
+professional musicians I know um it
+turned out that this woman's son had
+
+ align:start position:0%
+turned out that this woman's son had
+ 
+
+ align:start position:0%
+turned out that this woman's son had
+died died at Sea and so they were having
+
+ align:start position:0%
+died died at Sea and so they were having
+ 
+
+ align:start position:0%
+died died at Sea and so they were having
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+wake and um the thing that was immediate
+
+ align:start position:0%
+wake and um the thing that was immediate
+ 
+
+ align:start position:0%
+wake and um the thing that was immediate
+to me was that sort of expressions of
+
+ align:start position:0%
+to me was that sort of expressions of
+ 
+
+ align:start position:0%
+to me was that sort of expressions of
+culture in New Orleans are certainly an
+
+ align:start position:0%
+culture in New Orleans are certainly an
+ 
+
+ align:start position:0%
+culture in New Orleans are certainly an
+amalgam of a lot of things um Africa uh
+
+ align:start position:0%
+amalgam of a lot of things um Africa uh
+ 
+
+ align:start position:0%
+amalgam of a lot of things um Africa uh
+um Native American Europe Caribbean um
+
+ align:start position:0%
+um Native American Europe Caribbean um
+ 
+
+ align:start position:0%
+um Native American Europe Caribbean um
+but then there's all these things that
+
+ align:start position:0%
+but then there's all these things that
+ 
+
+ align:start position:0%
+but then there's all these things that
+are very unique there are people that do
+
+ align:start position:0%
+are very unique there are people that do
+ 
+
+ align:start position:0%
+are very unique there are people that do
+things in New Orleans that they haven't
+
+ align:start position:0%
+things in New Orleans that they haven't
+ 
+
+ align:start position:0%
+things in New Orleans that they haven't
+done anywhere else there's the story of
+
+ align:start position:0%
+done anywhere else there's the story of
+ 
+
+ align:start position:0%
+done anywhere else there's the story of
+Congo Square the SLA the French let the
+
+ align:start position:0%
+Congo Square the SLA the French let the
+ 
+
+ align:start position:0%
+Congo Square the SLA the French let the
+slaves play instruments the Americans
+
+ align:start position:0%
+slaves play instruments the Americans
+ 
+
+ align:start position:0%
+slaves play instruments the Americans
+did not not so there's some argument
+
+ align:start position:0%
+did not not so there's some argument
+ 
+
+ align:start position:0%
+did not not so there's some argument
+about where Jazz invented but um the
+
+ align:start position:0%
+about where Jazz invented but um the
+ 
+
+ align:start position:0%
+about where Jazz invented but um the
+people the New Orleans apologists say
+
+ align:start position:0%
+people the New Orleans apologists say
+ 
+
+ align:start position:0%
+people the New Orleans apologists say
+that that's where it's from and so again
+
+ align:start position:0%
+that that's where it's from and so again
+ 
+
+ align:start position:0%
+that that's where it's from and so again
+um I was going to say without an agenda
+
+ align:start position:0%
+um I was going to say without an agenda
+ 
+
+ align:start position:0%
+um I was going to say without an agenda
+I have an agenda but I'm I'm sort of
+
+ align:start position:0%
+I have an agenda but I'm I'm sort of
+ 
+
+ align:start position:0%
+I have an agenda but I'm I'm sort of
+interested and and it was interested
+
+ align:start position:0%
+interested and and it was interested
+ 
+
+ align:start position:0%
+interested and and it was interested
+putting these slides together because
+
+ align:start position:0%
+putting these slides together because
+ 
+
+ align:start position:0%
+putting these slides together because
+I'm trying to sort of make some sense of
+
+ align:start position:0%
+I'm trying to sort of make some sense of
+ 
+
+ align:start position:0%
+I'm trying to sort of make some sense of
+what is the thread that runs and maybe
+
+ align:start position:0%
+what is the thread that runs and maybe
+ 
+
+ align:start position:0%
+what is the thread that runs and maybe
+you can tell me um this is someone
+
+ align:start position:0%
+you can tell me um this is someone
+ 
+
+ align:start position:0%
+you can tell me um this is someone
+playing air guitar outside of a blues
+
+ align:start position:0%
+playing air guitar outside of a blues
+ 
+
+ align:start position:0%
+playing air guitar outside of a blues
+Club in the French
+
+ align:start position:0%
+Club in the French
+ 
+
+ align:start position:0%
+Club in the French
+Quarter here's uh this is actually on
+
+ align:start position:0%
+Quarter here's uh this is actually on
+ 
+
+ align:start position:0%
+Quarter here's uh this is actually on
+Rampart Street this is in t this is pre
+
+ align:start position:0%
+Rampart Street this is in t this is pre
+ 
+
+ align:start position:0%
+Rampart Street this is in t this is pre
+Katrina and uh there's basically a
+
+ align:start position:0%
+Katrina and uh there's basically a
+ 
+
+ align:start position:0%
+Katrina and uh there's basically a
+demonstration to try to fight um
+
+ align:start position:0%
+demonstration to try to fight um
+ 
+
+ align:start position:0%
+demonstration to try to fight um
+gentrification T again has real
+
+ align:start position:0%
+gentrification T again has real
+ 
+
+ align:start position:0%
+gentrification T again has real
+interesting housing stock it's right off
+
+ align:start position:0%
+interesting housing stock it's right off
+ 
+
+ align:start position:0%
+interesting housing stock it's right off
+the French quarter and there sort of
+
+ align:start position:0%
+the French quarter and there sort of
+ 
+
+ align:start position:0%
+the French quarter and there sort of
+it's changing this is actually was at
+
+ align:start position:0%
+it's changing this is actually was at
+ 
+
+ align:start position:0%
+it's changing this is actually was at
+the dedication of the spirit house um so
+
+ align:start position:0%
+the dedication of the spirit house um so
+ 
+
+ align:start position:0%
+the dedication of the spirit house um so
+I finally got to see my uh marching band
+
+ align:start position:0%
+I finally got to see my uh marching band
+ 
+
+ align:start position:0%
+I finally got to see my uh marching band
+this a t Brass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Band I'm sort of uh
+
+ align:start position:0%
+Band I'm sort of uh
+ 
+
+ align:start position:0%
+Band I'm sort of uh
+uh I I think I think I see better in
+
+ align:start position:0%
+uh I I think I think I see better in
+ 
+
+ align:start position:0%
+uh I I think I think I see better in
+black and white I also see better with
+
+ align:start position:0%
+black and white I also see better with
+ 
+
+ align:start position:0%
+black and white I also see better with
+non autofocusing cameras but I do love
+
+ align:start position:0%
+non autofocusing cameras but I do love
+ 
+
+ align:start position:0%
+non autofocusing cameras but I do love
+my Nikon d70 it was actually a problem
+
+ align:start position:0%
+my Nikon d70 it was actually a problem
+ 
+
+ align:start position:0%
+my Nikon d70 it was actually a problem
+during the trip because I was switching
+
+ align:start position:0%
+during the trip because I was switching
+ 
+
+ align:start position:0%
+during the trip because I was switching
+back and forth and and I don't think I
+
+ align:start position:0%
+back and forth and and I don't think I
+ 
+
+ align:start position:0%
+back and forth and and I don't think I
+want to keep doing that so I either am
+
+ align:start position:0%
+want to keep doing that so I either am
+ 
+
+ align:start position:0%
+want to keep doing that so I either am
+going to either go high-end digital or
+
+ align:start position:0%
+going to either go high-end digital or
+ 
+
+ align:start position:0%
+going to either go high-end digital or
+shoot more film and just use digital for
+
+ align:start position:0%
+shoot more film and just use digital for
+ 
+
+ align:start position:0%
+shoot more film and just use digital for
+taking notes but don't hold me to
+
+ align:start position:0%
+taking notes but don't hold me to
+ 
+
+ align:start position:0%
+taking notes but don't hold me to
+that so you're going to see photographs
+
+ align:start position:0%
+that so you're going to see photographs
+ 
+
+ align:start position:0%
+that so you're going to see photographs
+uh you're going to see more in a couple
+
+ align:start position:0%
+uh you're going to see more in a couple
+ 
+
+ align:start position:0%
+uh you're going to see more in a couple
+of weeks but you'll see some post
+
+ align:start position:0%
+of weeks but you'll see some post
+ 
+
+ align:start position:0%
+of weeks but you'll see some post
+Katrina photographs but and I've been
+
+ align:start position:0%
+Katrina photographs but and I've been
+ 
+
+ align:start position:0%
+Katrina photographs but and I've been
+showing them and I after 4 days of being
+
+ align:start position:0%
+showing them and I after 4 days of being
+ 
+
+ align:start position:0%
+showing them and I after 4 days of being
+there I arrived at like 7:30 at night I
+
+ align:start position:0%
+there I arrived at like 7:30 at night I
+ 
+
+ align:start position:0%
+there I arrived at like 7:30 at night I
+stayed with some friends that had
+
+ align:start position:0%
+stayed with some friends that had
+ 
+
+ align:start position:0%
+stayed with some friends that had
+literally come back a couple hours
+
+ align:start position:0%
+literally come back a couple hours
+ 
+
+ align:start position:0%
+literally come back a couple hours
+before I had and they'd been there for
+
+ align:start position:0%
+before I had and they'd been there for
+ 
+
+ align:start position:0%
+before I had and they'd been there for
+they' been gone for a month and a half
+
+ align:start position:0%
+they' been gone for a month and a half
+ 
+
+ align:start position:0%
+they' been gone for a month and a half
+it was the lights were sort of twick
+
+ align:start position:0%
+it was the lights were sort of twick
+ 
+
+ align:start position:0%
+it was the lights were sort of twick
+flickering cuz the power wasn't full
+
+ align:start position:0%
+flickering cuz the power wasn't full
+ 
+
+ align:start position:0%
+flickering cuz the power wasn't full
+there was nobody on the streets it was
+
+ align:start position:0%
+there was nobody on the streets it was
+ 
+
+ align:start position:0%
+there was nobody on the streets it was
+scary it was very spooky and I sort of
+
+ align:start position:0%
+scary it was very spooky and I sort of
+ 
+
+ align:start position:0%
+scary it was very spooky and I sort of
+ran out of my car under their house but
+
+ align:start position:0%
+ran out of my car under their house but
+ 
+
+ align:start position:0%
+ran out of my car under their house but
+um then I photographed 12 hours a day
+
+ align:start position:0%
+um then I photographed 12 hours a day
+ 
+
+ align:start position:0%
+um then I photographed 12 hours a day
+for 5 days straight and then I Got U
+
+ align:start position:0%
+for 5 days straight and then I Got U
+ 
+
+ align:start position:0%
+for 5 days straight and then I Got U
+destruction
+
+ align:start position:0%
+destruction
+ 
+
+ align:start position:0%
+destruction
+fatigue um here's a sort of something in
+
+ align:start position:0%
+fatigue um here's a sort of something in
+ 
+
+ align:start position:0%
+fatigue um here's a sort of something in
+the Katrina um talking about sellouts
+
+ align:start position:0%
+the Katrina um talking about sellouts
+ 
+
+ align:start position:0%
+the Katrina um talking about sellouts
+this is taken uh on the River Road
+
+ align:start position:0%
+this is taken uh on the River Road
+ 
+
+ align:start position:0%
+this is taken uh on the River Road
+between um Baton Rouge and Louisiana and
+
+ align:start position:0%
+between um Baton Rouge and Louisiana and
+ 
+
+ align:start position:0%
+between um Baton Rouge and Louisiana and
+uh New Orleans called cancer alley it
+
+ align:start position:0%
+uh New Orleans called cancer alley it
+ 
+
+ align:start position:0%
+uh New Orleans called cancer alley it
+has one of the highest incidents of
+
+ align:start position:0%
+has one of the highest incidents of
+ 
+
+ align:start position:0%
+has one of the highest incidents of
+cancer in the country because all the
+
+ align:start position:0%
+cancer in the country because all the
+ 
+
+ align:start position:0%
+cancer in the country because all the
+petrochemical companies that dump into
+
+ align:start position:0%
+petrochemical companies that dump into
+ 
+
+ align:start position:0%
+petrochemical companies that dump into
+the water this is actually in Baton
+
+ align:start position:0%
+the water this is actually in Baton
+ 
+
+ align:start position:0%
+the water this is actually in Baton
+Rouge a place I've spent some time I've
+
+ align:start position:0%
+Rouge a place I've spent some time I've
+ 
+
+ align:start position:0%
+Rouge a place I've spent some time I've
+done um
+
+ align:start position:0%
+done um
+ 
+
+ align:start position:0%
+done um
+uh some things in I've had some shows
+
+ align:start position:0%
+uh some things in I've had some shows
+ 
+
+ align:start position:0%
+uh some things in I've had some shows
+there and done some things at LSU so
+
+ align:start position:0%
+there and done some things at LSU so
+ 
+
+ align:start position:0%
+there and done some things at LSU so
+I've actually been spending time in as
+
+ align:start position:0%
+I've actually been spending time in as
+ 
+
+ align:start position:0%
+I've actually been spending time in as
+much time in Baton Rouge although I
+
+ align:start position:0%
+much time in Baton Rouge although I
+ 
+
+ align:start position:0%
+much time in Baton Rouge although I
+always go back to New Orleans this is
+
+ align:start position:0%
+always go back to New Orleans this is
+ 
+
+ align:start position:0%
+always go back to New Orleans this is
+the Sweet Olive Cemetery an
+
+ align:start position:0%
+the Sweet Olive Cemetery an
+ 
+
+ align:start position:0%
+the Sweet Olive Cemetery an
+African-American Cemetery that had just
+
+ align:start position:0%
+African-American Cemetery that had just
+ 
+
+ align:start position:0%
+African-American Cemetery that had just
+had had been sort of been to ruins and
+
+ align:start position:0%
+had had been sort of been to ruins and
+ 
+
+ align:start position:0%
+had had been sort of been to ruins and
+was just starting to be um uh restored
+
+ align:start position:0%
+was just starting to be um uh restored
+ 
+
+ align:start position:0%
+was just starting to be um uh restored
+and I always thought this coffee pot was
+
+ align:start position:0%
+and I always thought this coffee pot was
+ 
+
+ align:start position:0%
+and I always thought this coffee pot was
+like this what you know incredible
+
+ align:start position:0%
+like this what you know incredible
+ 
+
+ align:start position:0%
+like this what you know incredible
+expression of culture and I think it is
+
+ align:start position:0%
+expression of culture and I think it is
+ 
+
+ align:start position:0%
+expression of culture and I think it is
+but it also is a receptacle for the
+
+ align:start position:0%
+but it also is a receptacle for the
+ 
+
+ align:start position:0%
+but it also is a receptacle for the
+flowers you know always has a practical
+
+ align:start position:0%
+flowers you know always has a practical
+ 
+
+ align:start position:0%
+flowers you know always has a practical
+use this is um a a doll house in the
+
+ align:start position:0%
+use this is um a a doll house in the
+ 
+
+ align:start position:0%
+use this is um a a doll house in the
+form the shape of a shotgun house um
+
+ align:start position:0%
+form the shape of a shotgun house um
+ 
+
+ align:start position:0%
+form the shape of a shotgun house um
+it's a crypt for a
+
+ align:start position:0%
+it's a crypt for a
+ 
+
+ align:start position:0%
+it's a crypt for a
+child I love that and then I love these
+
+ align:start position:0%
+child I love that and then I love these
+ 
+
+ align:start position:0%
+child I love that and then I love these
+kind of hand scratching on the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gravestones so after having kind of both
+
+ align:start position:0%
+gravestones so after having kind of both
+ 
+
+ align:start position:0%
+gravestones so after having kind of both
+shown and looked at all my post Catrina
+
+ align:start position:0%
+shown and looked at all my post Catrina
+ 
+
+ align:start position:0%
+shown and looked at all my post Catrina
+what I realized was I really missed and
+
+ align:start position:0%
+what I realized was I really missed and
+ 
+
+ align:start position:0%
+what I realized was I really missed and
+was more interested in Pre Catrina or in
+
+ align:start position:0%
+was more interested in Pre Catrina or in
+ 
+
+ align:start position:0%
+was more interested in Pre Catrina or in
+New Orleans as it was and maybe will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it seemed appropriate at the time this
+
+ align:start position:0%
+it seemed appropriate at the time this
+ 
+
+ align:start position:0%
+it seemed appropriate at the time this
+is like about 12 years ago to shoot
+
+ align:start position:0%
+is like about 12 years ago to shoot
+ 
+
+ align:start position:0%
+is like about 12 years ago to shoot
+infrared in New Orleans although it's
+
+ align:start position:0%
+infrared in New Orleans although it's
+ 
+
+ align:start position:0%
+infrared in New Orleans although it's
+not necessary because the spirits are
+
+ align:start position:0%
+not necessary because the spirits are
+ 
+
+ align:start position:0%
+not necessary because the spirits are
+already there this is one of the few
+
+ align:start position:0%
+already there this is one of the few
+ 
+
+ align:start position:0%
+already there this is one of the few
+cemeteries in Orleans that where with
+
+ align:start position:0%
+cemeteries in Orleans that where with
+ 
+
+ align:start position:0%
+cemeteries in Orleans that where with
+Graves in the grounds Hope Cemetery
+
+ align:start position:0%
+Graves in the grounds Hope Cemetery
+ 
+
+ align:start position:0%
+Graves in the grounds Hope Cemetery
+another African-American Cemetery um
+
+ align:start position:0%
+another African-American Cemetery um
+ 
+
+ align:start position:0%
+another African-American Cemetery um
+this is in St Louis cemeter and this is
+
+ align:start position:0%
+this is in St Louis cemeter and this is
+ 
+
+ align:start position:0%
+this is in St Louis cemeter and this is
+Marie lao's uh grave uh uh Crypt you
+
+ align:start position:0%
+Marie lao's uh grave uh uh Crypt you
+ 
+
+ align:start position:0%
+Marie lao's uh grave uh uh Crypt you
+know because the water table so high
+
+ align:start position:0%
+know because the water table so high
+ 
+
+ align:start position:0%
+know because the water table so high
+most of the graves are above uh ground
+
+ align:start position:0%
+most of the graves are above uh ground
+ 
+
+ align:start position:0%
+most of the graves are above uh ground
+and then there's all this
+
+ align:start position:0%
+and then there's all this
+ 
+
+ align:start position:0%
+and then there's all this
+technology um this is maybe a drawing
+
+ align:start position:0%
+technology um this is maybe a drawing
+ 
+
+ align:start position:0%
+technology um this is maybe a drawing
+but the there's all these both
+
+ align:start position:0%
+but the there's all these both
+ 
+
+ align:start position:0%
+but the there's all these both
+photographs and drawings on the graves
+
+ align:start position:0%
+photographs and drawings on the graves
+ 
+
+ align:start position:0%
+photographs and drawings on the graves
+that at least when I've visited over the
+
+ align:start position:0%
+that at least when I've visited over the
+ 
+
+ align:start position:0%
+that at least when I've visited over the
+course of 10 years have not faded at all
+
+ align:start position:0%
+course of 10 years have not faded at all
+ 
+
+ align:start position:0%
+course of 10 years have not faded at all
+and I'm not sure I know the signs we did
+
+ align:start position:0%
+and I'm not sure I know the signs we did
+ 
+
+ align:start position:0%
+and I'm not sure I know the signs we did
+uh in richm are done with sort of inkjet
+
+ align:start position:0%
+uh in richm are done with sort of inkjet
+ 
+
+ align:start position:0%
+uh in richm are done with sort of inkjet
+printers using porcelain inks and then
+
+ align:start position:0%
+printers using porcelain inks and then
+ 
+
+ align:start position:0%
+printers using porcelain inks and then
+they're fired so there is it is possible
+
+ align:start position:0%
+they're fired so there is it is possible
+ 
+
+ align:start position:0%
+they're fired so there is it is possible
+to now
+
+ align:start position:0%
+to now
+ 
+
+ align:start position:0%
+to now
+display continuous tone photographs in
+
+ align:start position:0%
+display continuous tone photographs in
+ 
+
+ align:start position:0%
+display continuous tone photographs in
+uh sort of outside environments but
+
+ align:start position:0%
+uh sort of outside environments but
+ 
+
+ align:start position:0%
+uh sort of outside environments but
+someone in New Orleans has been hip to
+
+ align:start position:0%
+someone in New Orleans has been hip to
+ 
+
+ align:start position:0%
+someone in New Orleans has been hip to
+this technology before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so uh maybe in in
+
+ align:start position:0%
+that so uh maybe in in
+ 
+
+ align:start position:0%
+that so uh maybe in in
+19 99 or something said well you got to
+
+ align:start position:0%
+19 99 or something said well you got to
+ 
+
+ align:start position:0%
+19 99 or something said well you got to
+go to Fatz Domino's house Fats Domino
+
+ align:start position:0%
+go to Fatz Domino's house Fats Domino
+ 
+
+ align:start position:0%
+go to Fatz Domino's house Fats Domino
+lives in the Lower Ninth Ward lived um
+
+ align:start position:0%
+lives in the Lower Ninth Ward lived um
+ 
+
+ align:start position:0%
+lives in the Lower Ninth Ward lived um
+has this incredible house with all this
+
+ align:start position:0%
+has this incredible house with all this
+ 
+
+ align:start position:0%
+has this incredible house with all this
+nomenclature and I finally found it I
+
+ align:start position:0%
+nomenclature and I finally found it I
+ 
+
+ align:start position:0%
+nomenclature and I finally found it I
+mean I didn't know it was a ninth W but
+
+ align:start position:0%
+mean I didn't know it was a ninth W but
+ 
+
+ align:start position:0%
+mean I didn't know it was a ninth W but
+someone um took me there so I took this
+
+ align:start position:0%
+someone um took me there so I took this
+ 
+
+ align:start position:0%
+someone um took me there so I took this
+picture which I thought was really
+
+ align:start position:0%
+picture which I thought was really
+ 
+
+ align:start position:0%
+picture which I thought was really
+interesting and then um uh I was able to
+
+ align:start position:0%
+interesting and then um uh I was able to
+ 
+
+ align:start position:0%
+interesting and then um uh I was able to
+get access to the Lower Ninth by being
+
+ align:start position:0%
+get access to the Lower Ninth by being
+ 
+
+ align:start position:0%
+get access to the Lower Ninth by being
+embedded with the National Guard you'll
+
+ align:start position:0%
+embedded with the National Guard you'll
+ 
+
+ align:start position:0%
+embedded with the National Guard you'll
+see a little of that later um and I
+
+ align:start position:0%
+see a little of that later um and I
+ 
+
+ align:start position:0%
+see a little of that later um and I
+found his house again he actually there
+
+ align:start position:0%
+found his house again he actually there
+ 
+
+ align:start position:0%
+found his house again he actually there
+was rumors that he had died but he was
+
+ align:start position:0%
+was rumors that he had died but he was
+ 
+
+ align:start position:0%
+was rumors that he had died but he was
+rescued from the second story of his
+
+ align:start position:0%
+rescued from the second story of his
+ 
+
+ align:start position:0%
+rescued from the second story of his
+house in the back um but this was the
+
+ align:start position:0%
+house in the back um but this was the
+ 
+
+ align:start position:0%
+house in the back um but this was the
+graffiti on on front of his house um
+
+ align:start position:0%
+graffiti on on front of his house um
+ 
+
+ align:start position:0%
+graffiti on on front of his house um
+because the the the rumor was that he
+
+ align:start position:0%
+because the the the rumor was that he
+ 
+
+ align:start position:0%
+because the the the rumor was that he
+was dead
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I it's interesting I think I need to
+
+ align:start position:0%
+so I it's interesting I think I need to
+ 
+
+ align:start position:0%
+so I it's interesting I think I need to
+print some of these it I've sort of lost
+
+ align:start position:0%
+print some of these it I've sort of lost
+ 
+
+ align:start position:0%
+print some of these it I've sort of lost
+a little interest in this I mean it's
+
+ align:start position:0%
+a little interest in this I mean it's
+ 
+
+ align:start position:0%
+a little interest in this I mean it's
+incredibly interesting and I think it
+
+ align:start position:0%
+incredibly interesting and I think it
+ 
+
+ align:start position:0%
+incredibly interesting and I think it
+fits within my interest um and what was
+
+ align:start position:0%
+fits within my interest um and what was
+ 
+
+ align:start position:0%
+fits within my interest um and what was
+left was a variety of ways that people
+
+ align:start position:0%
+left was a variety of ways that people
+ 
+
+ align:start position:0%
+left was a variety of ways that people
+were leaving their calling cards or the
+
+ align:start position:0%
+were leaving their calling cards or the
+ 
+
+ align:start position:0%
+were leaving their calling cards or the
+buildings became sort of the the wall
+
+ align:start position:0%
+buildings became sort of the the wall
+ 
+
+ align:start position:0%
+buildings became sort of the the wall
+where news um was
+
+ align:start position:0%
+where news um was
+ 
+
+ align:start position:0%
+where news um was
+left I saw this sign and I thought oh
+
+ align:start position:0%
+left I saw this sign and I thought oh
+ 
+
+ align:start position:0%
+left I saw this sign and I thought oh
+someone must be doing some kind of like
+
+ align:start position:0%
+someone must be doing some kind of like
+ 
+
+ align:start position:0%
+someone must be doing some kind of like
+19th century photo technique but of
+
+ align:start position:0%
+19th century photo technique but of
+ 
+
+ align:start position:0%
+19th century photo technique but of
+course this is really about restoring
+
+ align:start position:0%
+course this is really about restoring
+ 
+
+ align:start position:0%
+course this is really about restoring
+wet photographs was I was I was thinking
+
+ align:start position:0%
+wet photographs was I was I was thinking
+ 
+
+ align:start position:0%
+wet photographs was I was I was thinking
+wow maybe I'll you know check that
+
+ align:start position:0%
+wow maybe I'll you know check that
+ 
+
+ align:start position:0%
+wow maybe I'll you know check that
+out this is in the lower
+
+ align:start position:0%
+out this is in the lower
+ 
+
+ align:start position:0%
+out this is in the lower
+n99th in California I say if um the
+
+ align:start position:0%
+n99th in California I say if um the
+ 
+
+ align:start position:0%
+n99th in California I say if um the
+earthquake hits empty your refrigerator
+
+ align:start position:0%
+earthquake hits empty your refrigerator
+ 
+
+ align:start position:0%
+earthquake hits empty your refrigerator
+there's the there's sort of um uh the
+
+ align:start position:0%
+there's the there's sort of um uh the
+ 
+
+ align:start position:0%
+there's the there's sort of um uh the
+refrigerators basically were these toxic
+
+ align:start position:0%
+refrigerators basically were these toxic
+ 
+
+ align:start position:0%
+refrigerators basically were these toxic
+that had to be um uh duct tape clothes
+
+ align:start position:0%
+that had to be um uh duct tape clothes
+ 
+
+ align:start position:0%
+that had to be um uh duct tape clothes
+because literally they would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explode and the SP there was a lot of
+
+ align:start position:0%
+explode and the SP there was a lot of
+ 
+
+ align:start position:0%
+explode and the SP there was a lot of
+you know markings by FEMA and SP SPCA
+
+ align:start position:0%
+you know markings by FEMA and SP SPCA
+ 
+
+ align:start position:0%
+you know markings by FEMA and SP SPCA
+and I couldn't help but think of
+
+ align:start position:0%
+and I couldn't help but think of
+ 
+
+ align:start position:0%
+and I couldn't help but think of
+Moses and the the uh the
+
+ align:start position:0%
+Moses and the the uh the
+ 
+
+ align:start position:0%
+Moses and the the uh the
+Nazis and maybe some more benevolent
+
+ align:start position:0%
+Nazis and maybe some more benevolent
+ 
+
+ align:start position:0%
+Nazis and maybe some more benevolent
+things and some of the markings were
+
+ align:start position:0%
+things and some of the markings were
+ 
+
+ align:start position:0%
+things and some of the markings were
+actually really beautiful but they were
+
+ align:start position:0%
+actually really beautiful but they were
+ 
+
+ align:start position:0%
+actually really beautiful but they were
+also kind of spooky and then there was
+
+ align:start position:0%
+also kind of spooky and then there was
+ 
+
+ align:start position:0%
+also kind of spooky and then there was
+the everpresent because especially in a
+
+ align:start position:0%
+the everpresent because especially in a
+ 
+
+ align:start position:0%
+the everpresent because especially in a
+lot of areas it flooded multiple times
+
+ align:start position:0%
+lot of areas it flooded multiple times
+ 
+
+ align:start position:0%
+lot of areas it flooded multiple times
+there were these incredible lines all
+
+ align:start position:0%
+there were these incredible lines all
+ 
+
+ align:start position:0%
+there were these incredible lines all
+over everything that that sort of marked
+
+ align:start position:0%
+over everything that that sort of marked
+ 
+
+ align:start position:0%
+over everything that that sort of marked
+where the and because the water was so
+
+ align:start position:0%
+where the and because the water was so
+ 
+
+ align:start position:0%
+where the and because the water was so
+toxic it really did it sort of etched
+
+ align:start position:0%
+toxic it really did it sort of etched
+ 
+
+ align:start position:0%
+toxic it really did it sort of etched
+into a lot of
+
+ align:start position:0%
+into a lot of
+ 
+
+ align:start position:0%
+into a lot of
+surfaces and they were sort of the
+
+ align:start position:0%
+surfaces and they were sort of the
+ 
+
+ align:start position:0%
+surfaces and they were sort of the
+everpresent editorial
+
+ align:start position:0%
+everpresent editorial
+ 
+
+ align:start position:0%
+everpresent editorial
+comments I guess they're selling
+
+ align:start position:0%
+comments I guess they're selling
+ 
+
+ align:start position:0%
+comments I guess they're selling
+T-shirts in the French
+
+ align:start position:0%
+T-shirts in the French
+ 
+
+ align:start position:0%
+T-shirts in the French
+Quarter and a lot of uh you see a lot of
+
+ align:start position:0%
+Quarter and a lot of uh you see a lot of
+ 
+
+ align:start position:0%
+Quarter and a lot of uh you see a lot of
+abandoned bus buses uh they were
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+commandeered so what you're seeing I
+
+ align:start position:0%
+commandeered so what you're seeing I
+ 
+
+ align:start position:0%
+commandeered so what you're seeing I
+shot a lot of black black and white
+
+ align:start position:0%
+shot a lot of black black and white
+ 
+
+ align:start position:0%
+shot a lot of black black and white
+which I'm just sort of getting
+
+ align:start position:0%
+which I'm just sort of getting
+ 
+
+ align:start position:0%
+which I'm just sort of getting
+to this is in the Cooper housing project
+
+ align:start position:0%
+to this is in the Cooper housing project
+ 
+
+ align:start position:0%
+to this is in the Cooper housing project
+you'll see a little bit of that later
+
+ align:start position:0%
+you'll see a little bit of that later
+ 
+
+ align:start position:0%
+you'll see a little bit of that later
+which was completely abandoned and I
+
+ align:start position:0%
+which was completely abandoned and I
+ 
+
+ align:start position:0%
+which was completely abandoned and I
+understand now is actually in pretty
+
+ align:start position:0%
+understand now is actually in pretty
+ 
+
+ align:start position:0%
+understand now is actually in pretty
+good shape and they won't let the people
+
+ align:start position:0%
+good shape and they won't let the people
+ 
+
+ align:start position:0%
+good shape and they won't let the people
+back something like 300,000 abandoned
+
+ align:start position:0%
+back something like 300,000 abandoned
+ 
+
+ align:start position:0%
+back something like 300,000 abandoned
+cars in in New Orleans
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I would say Aesthetics are real
+
+ align:start position:0%
+so I would say Aesthetics are real
+ 
+
+ align:start position:0%
+so I would say Aesthetics are real
+important to me that you know kind of I
+
+ align:start position:0%
+important to me that you know kind of I
+ 
+
+ align:start position:0%
+important to me that you know kind of I
+think I do have there's certain things
+
+ align:start position:0%
+think I do have there's certain things
+ 
+
+ align:start position:0%
+think I do have there's certain things
+that I'm very interested in for a
+
+ align:start position:0%
+that I'm very interested in for a
+ 
+
+ align:start position:0%
+that I'm very interested in for a
+variety of reasons and I I tried this is
+
+ align:start position:0%
+variety of reasons and I I tried this is
+ 
+
+ align:start position:0%
+variety of reasons and I I tried this is
+the city park um at post this is the
+
+ align:start position:0%
+the city park um at post this is the
+ 
+
+ align:start position:0%
+the city park um at post this is the
+Martin Luther King library in the lower
+
+ align:start position:0%
+Martin Luther King library in the lower
+ 
+
+ align:start position:0%
+Martin Luther King library in the lower
+9th this is um the Cooper uh uh housing
+
+ align:start position:0%
+9th this is um the Cooper uh uh housing
+ 
+
+ align:start position:0%
+9th this is um the Cooper uh uh housing
+project um he was leaving the next week
+
+ align:start position:0%
+project um he was leaving the next week
+ 
+
+ align:start position:0%
+project um he was leaving the next week
+to go to California but he'd been he'd
+
+ align:start position:0%
+to go to California but he'd been he'd
+ 
+
+ align:start position:0%
+to go to California but he'd been he'd
+come back after the hurricane and been
+
+ align:start position:0%
+come back after the hurricane and been
+ 
+
+ align:start position:0%
+come back after the hurricane and been
+living there by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+himself if you're familiar with um
+
+ align:start position:0%
+himself if you're familiar with um
+ 
+
+ align:start position:0%
+himself if you're familiar with um
+Southern wrap gold teeth are quite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+big so I was on St claw's and actually I
+
+ align:start position:0%
+big so I was on St claw's and actually I
+ 
+
+ align:start position:0%
+big so I was on St claw's and actually I
+saw these guys with Scientology t-shirts
+
+ align:start position:0%
+saw these guys with Scientology t-shirts
+ 
+
+ align:start position:0%
+saw these guys with Scientology t-shirts
+in the courtyard of this and I was going
+
+ align:start position:0%
+in the courtyard of this and I was going
+ 
+
+ align:start position:0%
+in the courtyard of this and I was going
+what is that about so of course it was
+
+ align:start position:0%
+what is that about so of course it was
+ 
+
+ align:start position:0%
+what is that about so of course it was
+also a place where the National Guard
+
+ align:start position:0%
+also a place where the National Guard
+ 
+
+ align:start position:0%
+also a place where the National Guard
+was and to even get access I had to go
+
+ align:start position:0%
+was and to even get access I had to go
+ 
+
+ align:start position:0%
+was and to even get access I had to go
+through six layers of bureaucracy and i'
+
+ align:start position:0%
+through six layers of bureaucracy and i'
+ 
+
+ align:start position:0%
+through six layers of bureaucracy and i'
+had sort of given up um I had to call
+
+ align:start position:0%
+had sort of given up um I had to call
+ 
+
+ align:start position:0%
+had sort of given up um I had to call
+the chief of police this was right after
+
+ align:start position:0%
+the chief of police this was right after
+ 
+
+ align:start position:0%
+the chief of police this was right after
+there was the um African the 65-year-old
+
+ align:start position:0%
+there was the um African the 65-year-old
+ 
+
+ align:start position:0%
+there was the um African the 65-year-old
+African-American teacher was beaten up
+
+ align:start position:0%
+African-American teacher was beaten up
+ 
+
+ align:start position:0%
+African-American teacher was beaten up
+in the French Quarter so I was referred
+
+ align:start position:0%
+in the French Quarter so I was referred
+ 
+
+ align:start position:0%
+in the French Quarter so I was referred
+to the Public Public Relations person of
+
+ align:start position:0%
+to the Public Public Relations person of
+ 
+
+ align:start position:0%
+to the Public Public Relations person of
+the New Orleans police and he never did
+
+ align:start position:0%
+the New Orleans police and he never did
+ 
+
+ align:start position:0%
+the New Orleans police and he never did
+call me but he said just say I said it
+
+ align:start position:0%
+call me but he said just say I said it
+ 
+
+ align:start position:0%
+call me but he said just say I said it
+was fine because I was trying to get
+
+ align:start position:0%
+was fine because I was trying to get
+ 
+
+ align:start position:0%
+was fine because I was trying to get
+access to the National Guard because I
+
+ align:start position:0%
+access to the National Guard because I
+ 
+
+ align:start position:0%
+access to the National Guard because I
+couldn't get into the ninth ward so I
+
+ align:start position:0%
+couldn't get into the ninth ward so I
+ 
+
+ align:start position:0%
+couldn't get into the ninth ward so I
+got a call so at the end of the 5 days
+
+ align:start position:0%
+got a call so at the end of the 5 days
+ 
+
+ align:start position:0%
+got a call so at the end of the 5 days
+when I was really pretty burned out
+
+ align:start position:0%
+when I was really pretty burned out
+ 
+
+ align:start position:0%
+when I was really pretty burned out
+saying you want want to be embedded with
+
+ align:start position:0%
+saying you want want to be embedded with
+ 
+
+ align:start position:0%
+saying you want want to be embedded with
+the National Guard and I said hell yes
+
+ align:start position:0%
+the National Guard and I said hell yes
+ 
+
+ align:start position:0%
+the National Guard and I said hell yes
+uh I couldn't help but obviously
+
+ align:start position:0%
+uh I couldn't help but obviously
+ 
+
+ align:start position:0%
+uh I couldn't help but obviously
+thinking about other situations where
+
+ align:start position:0%
+thinking about other situations where
+ 
+
+ align:start position:0%
+thinking about other situations where
+embedding was going on there's a lot I
+
+ align:start position:0%
+embedding was going on there's a lot I
+ 
+
+ align:start position:0%
+embedding was going on there's a lot I
+thought about Iraq a lot while I was in
+
+ align:start position:0%
+thought about Iraq a lot while I was in
+ 
+
+ align:start position:0%
+thought about Iraq a lot while I was in
+New Orleans so I won't I'll spare you
+
+ align:start position:0%
+New Orleans so I won't I'll spare you
+ 
+
+ align:start position:0%
+New Orleans so I won't I'll spare you
+the picture of me posing with an M16 but
+
+ align:start position:0%
+the picture of me posing with an M16 but
+ 
+
+ align:start position:0%
+the picture of me posing with an M16 but
+these were the 18 and 19 year old kids
+
+ align:start position:0%
+these were the 18 and 19 year old kids
+ 
+
+ align:start position:0%
+these were the 18 and 19 year old kids
+some of whom would just come back from
+
+ align:start position:0%
+some of whom would just come back from
+ 
+
+ align:start position:0%
+some of whom would just come back from
+Iraq and who said New Orleans was much
+
+ align:start position:0%
+Iraq and who said New Orleans was much
+ 
+
+ align:start position:0%
+Iraq and who said New Orleans was much
+more upsetting to them than Iraq was but
+
+ align:start position:0%
+more upsetting to them than Iraq was but
+ 
+
+ align:start position:0%
+more upsetting to them than Iraq was but
+and who were not allowed to leave this
+
+ align:start position:0%
+and who were not allowed to leave this
+ 
+
+ align:start position:0%
+and who were not allowed to leave this
+uh Monastery where they were staying uh
+
+ align:start position:0%
+uh Monastery where they were staying uh
+ 
+
+ align:start position:0%
+uh Monastery where they were staying uh
+the a Convent where they were staying so
+
+ align:start position:0%
+the a Convent where they were staying so
+ 
+
+ align:start position:0%
+the a Convent where they were staying so
+many of them knew nothing about New
+
+ align:start position:0%
+many of them knew nothing about New
+ 
+
+ align:start position:0%
+many of them knew nothing about New
+Orleans they knew they were patrolling
+
+ align:start position:0%
+Orleans they knew they were patrolling
+ 
+
+ align:start position:0%
+Orleans they knew they were patrolling
+the ninth ward but they had not been to
+
+ align:start position:0%
+the ninth ward but they had not been to
+ 
+
+ align:start position:0%
+the ninth ward but they had not been to
+the French
+
+ align:start position:0%
+the French
+ 
+
+ align:start position:0%
+the French
+Quarter
+
+ align:start position:0%
+Quarter
+ 
+
+ align:start position:0%
+Quarter
+um it was interesting that a couple of
+
+ align:start position:0%
+um it was interesting that a couple of
+ 
+
+ align:start position:0%
+um it was interesting that a couple of
+the people when I asked if I could
+
+ align:start position:0%
+the people when I asked if I could
+ 
+
+ align:start position:0%
+the people when I asked if I could
+photograph a couple of these guys says
+
+ align:start position:0%
+photograph a couple of these guys says
+ 
+
+ align:start position:0%
+photograph a couple of these guys says
+no way and the other one said we're not
+
+ align:start position:0%
+no way and the other one said we're not
+ 
+
+ align:start position:0%
+no way and the other one said we're not
+going to pose for you but go
+
+ align:start position:0%
+going to pose for you but go
+ 
+
+ align:start position:0%
+going to pose for you but go
+ahead that's when I knew maybe I was
+
+ align:start position:0%
+ahead that's when I knew maybe I was
+ 
+
+ align:start position:0%
+ahead that's when I knew maybe I was
+onto something a lot of uh private
+
+ align:start position:0%
+onto something a lot of uh private
+ 
+
+ align:start position:0%
+onto something a lot of uh private
+Securities of blackwat um a lot of
+
+ align:start position:0%
+Securities of blackwat um a lot of
+ 
+
+ align:start position:0%
+Securities of blackwat um a lot of
+people walking around with guns on their
+
+ align:start position:0%
+people walking around with guns on their
+ 
+
+ align:start position:0%
+people walking around with guns on their
+hips this is on Canal Street
+
+ align:start position:0%
+hips this is on Canal Street
+ 
+
+ align:start position:0%
+hips this is on Canal Street
+so here's I did get into the the lower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+9th this was literally right by the
+
+ align:start position:0%
+9th this was literally right by the
+ 
+
+ align:start position:0%
+9th this was literally right by the
+barge I'm not going to show the barge
+
+ align:start position:0%
+barge I'm not going to show the barge
+ 
+
+ align:start position:0%
+barge I'm not going to show the barge
+but there there was a lot of evidence um
+
+ align:start position:0%
+but there there was a lot of evidence um
+ 
+
+ align:start position:0%
+but there there was a lot of evidence um
+you're going to see some work in a
+
+ align:start position:0%
+you're going to see some work in a
+ 
+
+ align:start position:0%
+you're going to see some work in a
+couple of weeks of someone who really
+
+ align:start position:0%
+couple of weeks of someone who really
+ 
+
+ align:start position:0%
+couple of weeks of someone who really
+concentrated on kind of
+
+ align:start position:0%
+concentrated on kind of
+ 
+
+ align:start position:0%
+concentrated on kind of
+ephemera uh in New Orleans someone who
+
+ align:start position:0%
+ephemera uh in New Orleans someone who
+ 
+
+ align:start position:0%
+ephemera uh in New Orleans someone who
+was sitting in this
+
+ align:start position:0%
+was sitting in this
+ 
+
+ align:start position:0%
+was sitting in this
+room that uh this the foundation of the
+
+ align:start position:0%
+room that uh this the foundation of the
+ 
+
+ align:start position:0%
+room that uh this the foundation of the
+house that's behind it the the flood
+
+ align:start position:0%
+house that's behind it the the flood
+ 
+
+ align:start position:0%
+house that's behind it the the flood
+complet it kept it intact but moved it
+
+ align:start position:0%
+complet it kept it intact but moved it
+ 
+
+ align:start position:0%
+complet it kept it intact but moved it
+um half a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+block so when I was there I actually
+
+ align:start position:0%
+block so when I was there I actually
+ 
+
+ align:start position:0%
+block so when I was there I actually
+they didn't open up the city till the
+
+ align:start position:0%
+they didn't open up the city till the
+ 
+
+ align:start position:0%
+they didn't open up the city till the
+standing water was gone so I didn't see
+
+ align:start position:0%
+standing water was gone so I didn't see
+ 
+
+ align:start position:0%
+standing water was gone so I didn't see
+standing water in New Orleans this is a
+
+ align:start position:0%
+standing water in New Orleans this is a
+ 
+
+ align:start position:0%
+standing water in New Orleans this is a
+picture I took in 1994 on the River Road
+
+ align:start position:0%
+picture I took in 1994 on the River Road
+ 
+
+ align:start position:0%
+picture I took in 1994 on the River Road
+during a tropical rainstorm and this is
+
+ align:start position:0%
+during a tropical rainstorm and this is
+ 
+
+ align:start position:0%
+during a tropical rainstorm and this is
+a picture I took leaving the 9th Ward
+
+ align:start position:0%
+a picture I took leaving the 9th Ward
+ 
+
+ align:start position:0%
+a picture I took leaving the 9th Ward
+the first day they allowed people to
+
+ align:start position:0%
+the first day they allowed people to
+ 
+
+ align:start position:0%
+the first day they allowed people to
+drive in they had a fir truck that was
+
+ align:start position:0%
+drive in they had a fir truck that was
+ 
+
+ align:start position:0%
+drive in they had a fir truck that was
+rinsing off the cars it literally when
+
+ align:start position:0%
+rinsing off the cars it literally when
+ 
+
+ align:start position:0%
+rinsing off the cars it literally when
+you walked out of the the um got out of
+
+ align:start position:0%
+you walked out of the the um got out of
+ 
+
+ align:start position:0%
+you walked out of the the um got out of
+the car in the ninth ward even with a
+
+ align:start position:0%
+the car in the ninth ward even with a
+ 
+
+ align:start position:0%
+the car in the ninth ward even with a
+mask on I would get nauseous the the
+
+ align:start position:0%
+mask on I would get nauseous the the
+ 
+
+ align:start position:0%
+mask on I would get nauseous the the
+dust was uh and I think I I understand
+
+ align:start position:0%
+dust was uh and I think I I understand
+ 
+
+ align:start position:0%
+dust was uh and I think I I understand
+it's um becoming an issue for people
+
+ align:start position:0%
+it's um becoming an issue for people
+ 
+
+ align:start position:0%
+it's um becoming an issue for people
+that are
+
+ align:start position:0%
+that are
+ 
+
+ align:start position:0%
+that are
+there here's a photograph I took um in
+
+ align:start position:0%
+there here's a photograph I took um in
+ 
+
+ align:start position:0%
+there here's a photograph I took um in
+the lunchroom in New Orleans about 5
+
+ align:start position:0%
+the lunchroom in New Orleans about 5
+ 
+
+ align:start position:0%
+the lunchroom in New Orleans about 5
+years ago and I thought it was interest
+
+ align:start position:0%
+years ago and I thought it was interest
+ 
+
+ align:start position:0%
+years ago and I thought it was interest
+well no it was after
+
+ align:start position:0%
+well no it was after
+ 
+
+ align:start position:0%
+well no it was after
+911 um and in fact some people think
+
+ align:start position:0%
+911 um and in fact some people think
+ 
+
+ align:start position:0%
+911 um and in fact some people think
+it's supposed to be a representation of
+
+ align:start position:0%
+it's supposed to be a representation of
+ 
+
+ align:start position:0%
+it's supposed to be a representation of
+New York it's actually someone trying to
+
+ align:start position:0%
+New York it's actually someone trying to
+ 
+
+ align:start position:0%
+New York it's actually someone trying to
+make the skyline of New Orleans look
+
+ align:start position:0%
+make the skyline of New Orleans look
+ 
+
+ align:start position:0%
+make the skyline of New Orleans look
+like um New York and I thought it was
+
+ align:start position:0%
+like um New York and I thought it was
+ 
+
+ align:start position:0%
+like um New York and I thought it was
+interesting that um uh the sort of
+
+ align:start position:0%
+interesting that um uh the sort of
+ 
+
+ align:start position:0%
+interesting that um uh the sort of
+notion of New Orleans and disaster this
+
+ align:start position:0%
+notion of New Orleans and disaster this
+ 
+
+ align:start position:0%
+notion of New Orleans and disaster this
+was kind of a reference to another
+
+ align:start position:0%
+was kind of a reference to another
+ 
+
+ align:start position:0%
+was kind of a reference to another
+disaster was kind of manifested in this
+
+ align:start position:0%
+disaster was kind of manifested in this
+ 
+
+ align:start position:0%
+disaster was kind of manifested in this
+kind of trump little um uh
+
+ align:start position:0%
+kind of trump little um uh
+ 
+
+ align:start position:0%
+kind of trump little um uh
+mural so I
+
+ align:start position:0%
+mural so I
+ 
+
+ align:start position:0%
+mural so I
+think that is
+
+ align:start position:0%
+think that is
+ 
+
+ align:start position:0%
+think that is
+it and I'd be very curious if anybody
+
+ align:start position:0%
+it and I'd be very curious if anybody
+ 
+
+ align:start position:0%
+it and I'd be very curious if anybody
+has questions or or comments um it was
+
+ align:start position:0%
+has questions or or comments um it was
+ 
+
+ align:start position:0%
+has questions or or comments um it was
+interesting to put this show together
+
+ align:start position:0%
+interesting to put this show together
+ 
+
+ align:start position:0%
+interesting to put this show together
+because uh a I'm sort of realizing how
+
+ align:start position:0%
+because uh a I'm sort of realizing how
+ 
+
+ align:start position:0%
+because uh a I'm sort of realizing how
+much of my work I haven't gotten to
+
+ align:start position:0%
+much of my work I haven't gotten to
+ 
+
+ align:start position:0%
+much of my work I haven't gotten to
+digitized yet and the there's a certain
+
+ align:start position:0%
+digitized yet and the there's a certain
+ 
+
+ align:start position:0%
+digitized yet and the there's a certain
+thread but but things have changed um
+
+ align:start position:0%
+thread but but things have changed um
+ 
+
+ align:start position:0%
+thread but but things have changed um
+and some things that I kind of felt I
+
+ align:start position:0%
+and some things that I kind of felt I
+ 
+
+ align:start position:0%
+and some things that I kind of felt I
+was pretty clear about became less clear
+
+ align:start position:0%
+was pretty clear about became less clear
+ 
+
+ align:start position:0%
+was pretty clear about became less clear
+as I was putting some work today there's
+
+ align:start position:0%
+as I was putting some work today there's
+ 
+
+ align:start position:0%
+as I was putting some work today there's
+other things I'm I'm pretty clear about
+
+ align:start position:0%
+other things I'm I'm pretty clear about
+ 
+
+ align:start position:0%
+other things I'm I'm pretty clear about
+in terms of way I'm working but I'm I'm
+
+ align:start position:0%
+in terms of way I'm working but I'm I'm
+ 
+
+ align:start position:0%
+in terms of way I'm working but I'm I'm
+interested in your reactions or if
+
+ align:start position:0%
+interested in your reactions or if
+ 
+
+ align:start position:0%
+interested in your reactions or if
+anybody has questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or if people are ready to eat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+whatever well maybe I'll just use the7
+
+ align:start position:0%
+whatever well maybe I'll just use the7
+ 
+
+ align:start position:0%
+whatever well maybe I'll just use the7
+foring I thought that folks might I'm
+
+ align:start position:0%
+foring I thought that folks might I'm
+ 
+
+ align:start position:0%
+foring I thought that folks might I'm
+interested soes you're using photography
+
+ align:start position:0%
+interested soes you're using photography
+ 
+
+ align:start position:0%
+interested soes you're using photography
+a certain way as investigation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+youan
+
+ align:start position:0%
+youan
+ 
+
+ align:start position:0%
+youan
+you I have to how you contr that
+
+ align:start position:0%
+you I have to how you contr that
+ 
+
+ align:start position:0%
+you I have to how you contr that
+whatever else you
+
+ align:start position:0%
+whatever else you
+ 
+
+ align:start position:0%
+whatever else you
+were well I think the probably the most
+
+ align:start position:0%
+were well I think the probably the most
+ 
+
+ align:start position:0%
+were well I think the probably the most
+boring thing I can imagine and there's a
+
+ align:start position:0%
+boring thing I can imagine and there's a
+ 
+
+ align:start position:0%
+boring thing I can imagine and there's a
+lot of people that do it and a lot of
+
+ align:start position:0%
+lot of people that do it and a lot of
+ 
+
+ align:start position:0%
+lot of people that do it and a lot of
+people get pleasure that they' like to
+
+ align:start position:0%
+people get pleasure that they' like to
+ 
+
+ align:start position:0%
+people get pleasure that they' like to
+talk about equipment in fact there
+
+ align:start position:0%
+talk about equipment in fact there
+ 
+
+ align:start position:0%
+talk about equipment in fact there
+there's a great it doesn't exist anymore
+
+ align:start position:0%
+there's a great it doesn't exist anymore
+ 
+
+ align:start position:0%
+there's a great it doesn't exist anymore
+there's this famous swap meat in um uh
+
+ align:start position:0%
+there's this famous swap meat in um uh
+ 
+
+ align:start position:0%
+there's this famous swap meat in um uh
+Oakland that was every Sunday it was
+
+ align:start position:0%
+Oakland that was every Sunday it was
+ 
+
+ align:start position:0%
+Oakland that was every Sunday it was
+always a great place to find used
+
+ align:start position:0%
+always a great place to find used
+ 
+
+ align:start position:0%
+always a great place to find used
+equipment but there were people that go
+
+ align:start position:0%
+equipment but there were people that go
+ 
+
+ align:start position:0%
+equipment but there were people that go
+every day and they never took a picture
+
+ align:start position:0%
+every day and they never took a picture
+ 
+
+ align:start position:0%
+every day and they never took a picture
+all they did was talk about equipment
+
+ align:start position:0%
+all they did was talk about equipment
+ 
+
+ align:start position:0%
+all they did was talk about equipment
+but I do think that the tool I really
+
+ align:start position:0%
+but I do think that the tool I really
+ 
+
+ align:start position:0%
+but I do think that the tool I really
+feel it's important the tools you use
+
+ align:start position:0%
+feel it's important the tools you use
+ 
+
+ align:start position:0%
+feel it's important the tools you use
+are very important I um I think I bought
+
+ align:start position:0%
+are very important I um I think I bought
+ 
+
+ align:start position:0%
+are very important I um I think I bought
+a couple times cameras with autofocus
+
+ align:start position:0%
+a couple times cameras with autofocus
+ 
+
+ align:start position:0%
+a couple times cameras with autofocus
+and zooms and and couldn't use them you
+
+ align:start position:0%
+and zooms and and couldn't use them you
+ 
+
+ align:start position:0%
+and zooms and and couldn't use them you
+know I I knew I could tell I mean I
+
+ align:start position:0%
+know I I knew I could tell I mean I
+ 
+
+ align:start position:0%
+know I I knew I could tell I mean I
+would borrow them or rent them um the
+
+ align:start position:0%
+would borrow them or rent them um the
+ 
+
+ align:start position:0%
+would borrow them or rent them um the
+sort of more help I have seeing the
+
+ align:start position:0%
+sort of more help I have seeing the
+ 
+
+ align:start position:0%
+sort of more help I have seeing the
+worse I see it's changed a little bit
+
+ align:start position:0%
+worse I see it's changed a little bit
+ 
+
+ align:start position:0%
+worse I see it's changed a little bit
+cuz my eyesight is left but so I had a I
+
+ align:start position:0%
+cuz my eyesight is left but so I had a I
+ 
+
+ align:start position:0%
+cuz my eyesight is left but so I had a I
+had three lias and they were all stolen
+
+ align:start position:0%
+had three lias and they were all stolen
+ 
+
+ align:start position:0%
+had three lias and they were all stolen
+so I had this decision I am going to
+
+ align:start position:0%
+so I had this decision I am going to
+ 
+
+ align:start position:0%
+so I had this decision I am going to
+change cuz I love the lia but it was
+
+ align:start position:0%
+change cuz I love the lia but it was
+ 
+
+ align:start position:0%
+change cuz I love the lia but it was
+small It's too convenient so I'm going
+
+ align:start position:0%
+small It's too convenient so I'm going
+ 
+
+ align:start position:0%
+small It's too convenient so I'm going
+to get something that's more of a paint
+
+ align:start position:0%
+to get something that's more of a paint
+ 
+
+ align:start position:0%
+to get something that's more of a paint
+I also use a lot of the black and white
+
+ align:start position:0%
+I also use a lot of the black and white
+ 
+
+ align:start position:0%
+I also use a lot of the black and white
+I use a Fuji 6x9 which is called a Texas
+
+ align:start position:0%
+I use a Fuji 6x9 which is called a Texas
+ 
+
+ align:start position:0%
+I use a Fuji 6x9 which is called a Texas
+like it looks like a Leica on steroids
+
+ align:start position:0%
+like it looks like a Leica on steroids
+ 
+
+ align:start position:0%
+like it looks like a Leica on steroids
+it's a rangefinder that shoots 6x9
+
+ align:start position:0%
+it's a rangefinder that shoots 6x9
+ 
+
+ align:start position:0%
+it's a rangefinder that shoots 6x9
+images uh so I like it because it's the
+
+ align:start position:0%
+images uh so I like it because it's the
+ 
+
+ align:start position:0%
+images uh so I like it because it's the
+biggest negative I can make hand holding
+
+ align:start position:0%
+biggest negative I can make hand holding
+ 
+
+ align:start position:0%
+biggest negative I can make hand holding
+without using a a view uh like a press
+
+ align:start position:0%
+without using a a view uh like a press
+ 
+
+ align:start position:0%
+without using a a view uh like a press
+camera um but I finally found the this
+
+ align:start position:0%
+camera um but I finally found the this
+ 
+
+ align:start position:0%
+camera um but I finally found the this
+Nikon and Canon and a couple other
+
+ align:start position:0%
+Nikon and Canon and a couple other
+ 
+
+ align:start position:0%
+Nikon and Canon and a couple other
+people made digital cameras for people
+
+ align:start position:0%
+people made digital cameras for people
+ 
+
+ align:start position:0%
+people made digital cameras for people
+like me because the one thing I did not
+
+ align:start position:0%
+like me because the one thing I did not
+ 
+
+ align:start position:0%
+like me because the one thing I did not
+could not tolerate was pushing the
+
+ align:start position:0%
+could not tolerate was pushing the
+ 
+
+ align:start position:0%
+could not tolerate was pushing the
+shutter and it not going so most of the
+
+ align:start position:0%
+shutter and it not going so most of the
+ 
+
+ align:start position:0%
+shutter and it not going so most of the
+the newer generation cameras don't take
+
+ align:start position:0%
+the newer generation cameras don't take
+ 
+
+ align:start position:0%
+the newer generation cameras don't take
+long to recycle because the idea is I I
+
+ align:start position:0%
+long to recycle because the idea is I I
+ 
+
+ align:start position:0%
+long to recycle because the idea is I I
+want to take the picture when it's
+
+ align:start position:0%
+want to take the picture when it's
+ 
+
+ align:start position:0%
+want to take the picture when it's
+happening I don't want anything else to
+
+ align:start position:0%
+happening I don't want anything else to
+ 
+
+ align:start position:0%
+happening I don't want anything else to
+get in the way of that including
+
+ align:start position:0%
+get in the way of that including
+ 
+
+ align:start position:0%
+get in the way of that including
+autofocus so I actually surprisingly
+
+ align:start position:0%
+autofocus so I actually surprisingly
+ 
+
+ align:start position:0%
+autofocus so I actually surprisingly
+really like this camera it's a a a
+
+ align:start position:0%
+really like this camera it's a a a
+ 
+
+ align:start position:0%
+really like this camera it's a a a
+single lens reflex it looks like a film
+
+ align:start position:0%
+single lens reflex it looks like a film
+ 
+
+ align:start position:0%
+single lens reflex it looks like a film
+camera it came with a zoom lens I said
+
+ align:start position:0%
+camera it came with a zoom lens I said
+ 
+
+ align:start position:0%
+camera it came with a zoom lens I said
+and ideally I was going to be able to
+
+ align:start position:0%
+and ideally I was going to be able to
+ 
+
+ align:start position:0%
+and ideally I was going to be able to
+use my lenses you can but it doesn't
+
+ align:start position:0%
+use my lenses you can but it doesn't
+ 
+
+ align:start position:0%
+use my lenses you can but it doesn't
+translate I had you know fixed Focus
+
+ align:start position:0%
+translate I had you know fixed Focus
+ 
+
+ align:start position:0%
+translate I had you know fixed Focus
+lenses so I've been using it a lot in
+
+ align:start position:0%
+lenses so I've been using it a lot in
+ 
+
+ align:start position:0%
+lenses so I've been using it a lot in
+fact I use it exclusively for a while
+
+ align:start position:0%
+fact I use it exclusively for a while
+ 
+
+ align:start position:0%
+fact I use it exclusively for a while
+but I knew and and I use it to make a
+
+ align:start position:0%
+but I knew and and I use it to make a
+ 
+
+ align:start position:0%
+but I knew and and I use it to make a
+living I do a lot of architectural
+
+ align:start position:0%
+living I do a lot of architectural
+ 
+
+ align:start position:0%
+living I do a lot of architectural
+photography it's great I can make give
+
+ align:start position:0%
+photography it's great I can make give
+ 
+
+ align:start position:0%
+photography it's great I can make give
+files that the Architects can use I use
+
+ align:start position:0%
+files that the Architects can use I use
+ 
+
+ align:start position:0%
+files that the Architects can use I use
+it for architectural Pres
+
+ align:start position:0%
+it for architectural Pres
+ 
+
+ align:start position:0%
+it for architectural Pres
+reservation um and so it's I know it's
+
+ align:start position:0%
+reservation um and so it's I know it's
+ 
+
+ align:start position:0%
+reservation um and so it's I know it's
+part of
+
+ align:start position:0%
+part of
+ 
+
+ align:start position:0%
+part of
+my no that's not not taking that's that
+
+ align:start position:0%
+my no that's not not taking that's that
+ 
+
+ align:start position:0%
+my no that's not not taking that's that
+is using it on this trip my
+
+ align:start position:0%
+is using it on this trip my
+ 
+
+ align:start position:0%
+is using it on this trip my
+rationalization was I would use the
+
+ align:start position:0%
+rationalization was I would use the
+ 
+
+ align:start position:0%
+rationalization was I would use the
+digital camera to get instant feedback
+
+ align:start position:0%
+digital camera to get instant feedback
+ 
+
+ align:start position:0%
+digital camera to get instant feedback
+to make pictures that were good but the
+
+ align:start position:0%
+to make pictures that were good but the
+ 
+
+ align:start position:0%
+to make pictures that were good but the
+real serious photographs would be in
+
+ align:start position:0%
+real serious photographs would be in
+ 
+
+ align:start position:0%
+real serious photographs would be in
+black and white but you know sometime it
+
+ align:start position:0%
+black and white but you know sometime it
+ 
+
+ align:start position:0%
+black and white but you know sometime it
+depend on which camera I had in my hands
+
+ align:start position:0%
+depend on which camera I had in my hands
+ 
+
+ align:start position:0%
+depend on which camera I had in my hands
+they got in each other's way in that way
+
+ align:start position:0%
+they got in each other's way in that way
+ 
+
+ align:start position:0%
+they got in each other's way in that way
+so in terms of that kind of work this
+
+ align:start position:0%
+so in terms of that kind of work this
+ 
+
+ align:start position:0%
+so in terms of that kind of work this
+kind of my own personal investigation I
+
+ align:start position:0%
+kind of my own personal investigation I
+ 
+
+ align:start position:0%
+kind of my own personal investigation I
+have some decisions to make um and so in
+
+ align:start position:0%
+have some decisions to make um and so in
+ 
+
+ align:start position:0%
+have some decisions to make um and so in
+that case either I'll leave the digital
+
+ align:start position:0%
+that case either I'll leave the digital
+ 
+
+ align:start position:0%
+that case either I'll leave the digital
+at home and just shoot film or keep it
+
+ align:start position:0%
+at home and just shoot film or keep it
+ 
+
+ align:start position:0%
+at home and just shoot film or keep it
+in the bag and and shoot more film
+
+ align:start position:0%
+in the bag and and shoot more film
+ 
+
+ align:start position:0%
+in the bag and and shoot more film
+because what happened was there's some
+
+ align:start position:0%
+because what happened was there's some
+ 
+
+ align:start position:0%
+because what happened was there's some
+pictures that I should have taken in
+
+ align:start position:0%
+pictures that I should have taken in
+ 
+
+ align:start position:0%
+pictures that I should have taken in
+black and white that didn't exist
+
+ align:start position:0%
+black and white that didn't exist
+ 
+
+ align:start position:0%
+black and white that didn't exist
+anymore so that's but I you know I I'm
+
+ align:start position:0%
+anymore so that's but I you know I I'm
+ 
+
+ align:start position:0%
+anymore so that's but I you know I I'm
+not the other alternative would be to
+
+ align:start position:0%
+not the other alternative would be to
+ 
+
+ align:start position:0%
+not the other alternative would be to
+get a
+
+ align:start position:0%
+get a
+ 
+
+ align:start position:0%
+get a
+$3,000 you know 20 megapixel digital
+
+ align:start position:0%
+$3,000 you know 20 megapixel digital
+ 
+
+ align:start position:0%
+$3,000 you know 20 megapixel digital
+camera and then cuz what I want to do be
+
+ align:start position:0%
+camera and then cuz what I want to do be
+ 
+
+ align:start position:0%
+camera and then cuz what I want to do be
+able to make big pictures my question
+
+ align:start position:0%
+able to make big pictures my question
+ 
+
+ align:start position:0%
+able to make big pictures my question
+wasn't really
+
+ align:start position:0%
+wasn't really
+ 
+
+ align:start position:0%
+wasn't really
+directed direct what of research right
+
+ align:start position:0%
+directed direct what of research right
+ 
+
+ align:start position:0%
+directed direct what of research right
+what is
+
+ align:start position:0%
+what is
+ 
+
+ align:start position:0%
+what is
+it how does photography take you I I
+
+ align:start position:0%
+it how does photography take you I I
+ 
+
+ align:start position:0%
+it how does photography take you I I
+want the materials and the medium to be
+
+ align:start position:0%
+want the materials and the medium to be
+ 
+
+ align:start position:0%
+want the materials and the medium to be
+as close to translating my ideas as
+
+ align:start position:0%
+as close to translating my ideas as
+ 
+
+ align:start position:0%
+as close to translating my ideas as
+possible there are sometimes when
+
+ align:start position:0%
+possible there are sometimes when
+ 
+
+ align:start position:0%
+possible there are sometimes when
+digital does do that and sometimes when
+
+ align:start position:0%
+digital does do that and sometimes when
+ 
+
+ align:start position:0%
+digital does do that and sometimes when
+it absolutely does not and I don't know
+
+ align:start position:0%
+it absolutely does not and I don't know
+ 
+
+ align:start position:0%
+it absolutely does not and I don't know
+if I can be any clearer than that I it
+
+ align:start position:0%
+if I can be any clearer than that I it
+ 
+
+ align:start position:0%
+if I can be any clearer than that I it
+is you know I kept saying oh I hate
+
+ align:start position:0%
+is you know I kept saying oh I hate
+ 
+
+ align:start position:0%
+is you know I kept saying oh I hate
+technology I'm a lead eyem of course
+
+ align:start position:0%
+technology I'm a lead eyem of course
+ 
+
+ align:start position:0%
+technology I'm a lead eyem of course
+this is as I'm trying to find my Palm
+
+ align:start position:0%
+this is as I'm trying to find my Palm
+ 
+
+ align:start position:0%
+this is as I'm trying to find my Palm
+Pilot and my you know so that that's
+
+ align:start position:0%
+Pilot and my you know so that that's
+ 
+
+ align:start position:0%
+Pilot and my you know so that that's
+obviously not the case and um we were
+
+ align:start position:0%
+obviously not the case and um we were
+ 
+
+ align:start position:0%
+obviously not the case and um we were
+talking about it whatever I have usually
+
+ align:start position:0%
+talking about it whatever I have usually
+ 
+
+ align:start position:0%
+talking about it whatever I have usually
+I learn whatever else I can do when I
+
+ align:start position:0%
+I learn whatever else I can do when I
+ 
+
+ align:start position:0%
+I learn whatever else I can do when I
+need to do it and I think that's that's
+
+ align:start position:0%
+need to do it and I think that's that's
+ 
+
+ align:start position:0%
+need to do it and I think that's that's
+the case in terms of Photography um
+
+ align:start position:0%
+the case in terms of Photography um
+ 
+
+ align:start position:0%
+the case in terms of Photography um
+so I think maybe ultimately every
+
+ align:start position:0%
+so I think maybe ultimately every
+ 
+
+ align:start position:0%
+so I think maybe ultimately every
+picture I take is note taking and I need
+
+ align:start position:0%
+picture I take is note taking and I need
+ 
+
+ align:start position:0%
+picture I take is note taking and I need
+to find a variety I want the sort of
+
+ align:start position:0%
+to find a variety I want the sort of
+ 
+
+ align:start position:0%
+to find a variety I want the sort of
+ways to
+
+ align:start position:0%
+ways to
+ 
+
+ align:start position:0%
+ways to
+translate my reaction into things I mean
+
+ align:start position:0%
+translate my reaction into things I mean
+ 
+
+ align:start position:0%
+translate my reaction into things I mean
+I use the camera we've talked about that
+
+ align:start position:0%
+I use the camera we've talked about that
+ 
+
+ align:start position:0%
+I use the camera we've talked about that
+the camera really is my excuse to go
+
+ align:start position:0%
+the camera really is my excuse to go
+ 
+
+ align:start position:0%
+the camera really is my excuse to go
+into places I have no business in being
+
+ align:start position:0%
+into places I have no business in being
+ 
+
+ align:start position:0%
+into places I have no business in being
+and so I want the tool I use that
+
+ align:start position:0%
+and so I want the tool I use that
+ 
+
+ align:start position:0%
+and so I want the tool I use that
+records that experience to be something
+
+ align:start position:0%
+records that experience to be something
+ 
+
+ align:start position:0%
+records that experience to be something
+I feel comfortable with and that does
+
+ align:start position:0%
+I feel comfortable with and that does
+ 
+
+ align:start position:0%
+I feel comfortable with and that does
+what I want to do it in the case of the
+
+ align:start position:0%
+what I want to do it in the case of the
+ 
+
+ align:start position:0%
+what I want to do it in the case of the
+medium format camera allows me if I scan
+
+ align:start position:0%
+medium format camera allows me if I scan
+ 
+
+ align:start position:0%
+medium format camera allows me if I scan
+them to be able to I can make 45 48 in
+
+ align:start position:0%
+them to be able to I can make 45 48 in
+ 
+
+ align:start position:0%
+them to be able to I can make 45 48 in
+prints if I want it's harder I can't do
+
+ align:start position:0%
+prints if I want it's harder I can't do
+ 
+
+ align:start position:0%
+prints if I want it's harder I can't do
+that with a d70 because it's too it
+
+ align:start position:0%
+that with a d70 because it's too it
+ 
+
+ align:start position:0%
+that with a d70 because it's too it
+makes too small a file
+
+ align:start position:0%
+makes too small a file
+ 
+
+ align:start position:0%
+makes too small a file
+so I don't you know I'm doing the very
+
+ align:start position:0%
+so I don't you know I'm doing the very
+ 
+
+ align:start position:0%
+so I don't you know I'm doing the very
+thing I said I don't like but it's I I'm
+
+ align:start position:0%
+thing I said I don't like but it's I I'm
+ 
+
+ align:start position:0%
+thing I said I don't like but it's I I'm
+kind of into talking about the tools
+
+ align:start position:0%
+kind of into talking about the tools
+ 
+
+ align:start position:0%
+kind of into talking about the tools
+enough that so I know if there's
+
+ align:start position:0%
+enough that so I know if there's
+ 
+
+ align:start position:0%
+enough that so I know if there's
+something else I can use that will allow
+
+ align:start position:0%
+something else I can use that will allow
+ 
+
+ align:start position:0%
+something else I can use that will allow
+me to do what I need to I will uh I'll
+
+ align:start position:0%
+me to do what I need to I will uh I'll
+ 
+
+ align:start position:0%
+me to do what I need to I will uh I'll
+I'll get that or I'll find out about it
+
+ align:start position:0%
+I'll get that or I'll find out about it
+ 
+
+ align:start position:0%
+I'll get that or I'll find out about it
+or in a lot of cases I'll ask one of my
+
+ align:start position:0%
+or in a lot of cases I'll ask one of my
+ 
+
+ align:start position:0%
+or in a lot of cases I'll ask one of my
+students about it because they may know
+
+ align:start position:0%
+students about it because they may know
+ 
+
+ align:start position:0%
+students about it because they may know
+more about it than I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do yes I'm curious about uh sort of this
+
+ align:start position:0%
+do yes I'm curious about uh sort of this
+ 
+
+ align:start position:0%
+do yes I'm curious about uh sort of this
+act of like recognition
+
+ align:start position:0%
+act of like recognition
+ 
+
+ align:start position:0%
+act of like recognition
+sort of like you know here's the
+
+ align:start position:0%
+sort of like you know here's the
+ 
+
+ align:start position:0%
+sort of like you know here's the
+hometown of Zer hen or here's the block
+
+ align:start position:0%
+hometown of Zer hen or here's the block
+ 
+
+ align:start position:0%
+hometown of Zer hen or here's the block
+next to where Sam Cooks was killed or
+
+ align:start position:0%
+next to where Sam Cooks was killed or
+ 
+
+ align:start position:0%
+next to where Sam Cooks was killed or
+this is where FS Domino's hous it's
+
+ align:start position:0%
+this is where FS Domino's hous it's
+ 
+
+ align:start position:0%
+this is where FS Domino's hous it's
+almost like there's a certain sort of
+
+ align:start position:0%
+almost like there's a certain sort of
+ 
+
+ align:start position:0%
+almost like there's a certain sort of
+cultural Consciousness that these places
+
+ align:start position:0%
+cultural Consciousness that these places
+ 
+
+ align:start position:0%
+cultural Consciousness that these places
+sort of Blossom from and kind of
+
+ align:start position:0%
+sort of Blossom from and kind of
+ 
+
+ align:start position:0%
+sort of Blossom from and kind of
+recording that with the camera I'm
+
+ align:start position:0%
+recording that with the camera I'm
+ 
+
+ align:start position:0%
+recording that with the camera I'm
+curious to talk about that because it's
+
+ align:start position:0%
+curious to talk about that because it's
+ 
+
+ align:start position:0%
+curious to talk about that because it's
+it's one way to kind of Define the
+
+ align:start position:0%
+it's one way to kind of Define the
+ 
+
+ align:start position:0%
+it's one way to kind of Define the
+really complete um sort of idea of
+
+ align:start position:0%
+really complete um sort of idea of
+ 
+
+ align:start position:0%
+really complete um sort of idea of
+culture uh by
+
+ align:start position:0%
+culture uh by
+ 
+
+ align:start position:0%
+culture uh by
+moving I how that differs from Oakland
+
+ align:start position:0%
+moving I how that differs from Oakland
+ 
+
+ align:start position:0%
+moving I how that differs from Oakland
+looking around Oakland well you know I I
+
+ align:start position:0%
+looking around Oakland well you know I I
+ 
+
+ align:start position:0%
+looking around Oakland well you know I I
+sort of like to say well I just go plac
+
+ align:start position:0%
+sort of like to say well I just go plac
+ 
+
+ align:start position:0%
+sort of like to say well I just go plac
+and react to place but I
+
+ align:start position:0%
+and react to place but I
+ 
+
+ align:start position:0%
+and react to place but I
+very directed and structured the places
+
+ align:start position:0%
+very directed and structured the places
+ 
+
+ align:start position:0%
+very directed and structured the places
+I go to then riff if I am riffing I mean
+
+ align:start position:0%
+I go to then riff if I am riffing I mean
+ 
+
+ align:start position:0%
+I go to then riff if I am riffing I mean
+in other words I place myself in a
+
+ align:start position:0%
+in other words I place myself in a
+ 
+
+ align:start position:0%
+in other words I place myself in a
+particular situation and then react to S
+
+ align:start position:0%
+particular situation and then react to S
+ 
+
+ align:start position:0%
+particular situation and then react to S
+circumstances uh I know in um a lot of
+
+ align:start position:0%
+circumstances uh I know in um a lot of
+ 
+
+ align:start position:0%
+circumstances uh I know in um a lot of
+communities of color I'm going to find
+
+ align:start position:0%
+communities of color I'm going to find
+ 
+
+ align:start position:0%
+communities of color I'm going to find
+examples of
+
+ align:start position:0%
+examples of
+ 
+
+ align:start position:0%
+examples of
+improvisation um I'm also going to find
+
+ align:start position:0%
+improvisation um I'm also going to find
+ 
+
+ align:start position:0%
+improvisation um I'm also going to find
+out sort of things like in the Third
+
+ align:start position:0%
+out sort of things like in the Third
+ 
+
+ align:start position:0%
+out sort of things like in the Third
+Ward um that lot is where lightning
+
+ align:start position:0%
+Ward um that lot is where lightning
+ 
+
+ align:start position:0%
+Ward um that lot is where lightning
+Hopkins was raised and that's
+
+ align:start position:0%
+Hopkins was raised and that's
+ 
+
+ align:start position:0%
+Hopkins was raised and that's
+interesting to me because it tells me a
+
+ align:start position:0%
+interesting to me because it tells me a
+ 
+
+ align:start position:0%
+interesting to me because it tells me a
+little bit about um I mean it's sort of
+
+ align:start position:0%
+little bit about um I mean it's sort of
+ 
+
+ align:start position:0%
+little bit about um I mean it's sort of
+thrilling to me I have some problems
+
+ align:start position:0%
+thrilling to me I have some problems
+ 
+
+ align:start position:0%
+thrilling to me I have some problems
+with the South and actually I can
+
+ align:start position:0%
+with the South and actually I can
+ 
+
+ align:start position:0%
+with the South and actually I can
+usually only be in the South for about
+
+ align:start position:0%
+usually only be in the South for about
+ 
+
+ align:start position:0%
+usually only be in the South for about
+two weeks at a time but I keep going
+
+ align:start position:0%
+two weeks at a time but I keep going
+ 
+
+ align:start position:0%
+two weeks at a time but I keep going
+back uh because the south is a very
+
+ align:start position:0%
+back uh because the south is a very
+ 
+
+ align:start position:0%
+back uh because the south is a very
+Dynamic area on a lot of different
+
+ align:start position:0%
+Dynamic area on a lot of different
+ 
+
+ align:start position:0%
+Dynamic area on a lot of different
+levels but kind of those those
+
+ align:start position:0%
+levels but kind of those those
+ 
+
+ align:start position:0%
+levels but kind of those those
+manifestations of culture are real
+
+ align:start position:0%
+manifestations of culture are real
+ 
+
+ align:start position:0%
+manifestations of culture are real
+important because they they sort of give
+
+ align:start position:0%
+important because they they sort of give
+ 
+
+ align:start position:0%
+important because they they sort of give
+me they sort of help inform me in terms
+
+ align:start position:0%
+me they sort of help inform me in terms
+ 
+
+ align:start position:0%
+me they sort of help inform me in terms
+of kind of the things I'm reacting to
+
+ align:start position:0%
+of kind of the things I'm reacting to
+ 
+
+ align:start position:0%
+of kind of the things I'm reacting to
+maybe not as instinctively I'd like to
+
+ align:start position:0%
+maybe not as instinctively I'd like to
+ 
+
+ align:start position:0%
+maybe not as instinctively I'd like to
+State a and so uh sometimes I find those
+
+ align:start position:0%
+State a and so uh sometimes I find those
+ 
+
+ align:start position:0%
+State a and so uh sometimes I find those
+things after the fact sometimes I find
+
+ align:start position:0%
+things after the fact sometimes I find
+ 
+
+ align:start position:0%
+things after the fact sometimes I find
+them in the course the the the act of
+
+ align:start position:0%
+them in the course the the the act of
+ 
+
+ align:start position:0%
+them in the course the the the act of
+photographing opens up the conversation
+
+ align:start position:0%
+photographing opens up the conversation
+ 
+
+ align:start position:0%
+photographing opens up the conversation
+you know people say so what are you
+
+ align:start position:0%
+you know people say so what are you
+ 
+
+ align:start position:0%
+you know people say so what are you
+doing and I'll say I'm you know real
+
+ align:start position:0%
+doing and I'll say I'm you know real
+ 
+
+ align:start position:0%
+doing and I'll say I'm you know real
+interested in kind of finding
+
+ align:start position:0%
+interested in kind of finding
+ 
+
+ align:start position:0%
+interested in kind of finding
+reflections of culture and history you
+
+ align:start position:0%
+reflections of culture and history you
+ 
+
+ align:start position:0%
+reflections of culture and history you
+know in this block and someone say well
+
+ align:start position:0%
+know in this block and someone say well
+ 
+
+ align:start position:0%
+know in this block and someone say well
+you know so and so used to be there or
+
+ align:start position:0%
+you know so and so used to be there or
+ 
+
+ align:start position:0%
+you know so and so used to be there or
+you should knock on that door
+
+ align:start position:0%
+you should knock on that door
+ 
+
+ align:start position:0%
+you should knock on that door
+it it opens up things and some of the
+
+ align:start position:0%
+it it opens up things and some of the
+ 
+
+ align:start position:0%
+it it opens up things and some of the
+stories are you know kind of uh kind of
+
+ align:start position:0%
+stories are you know kind of uh kind of
+ 
+
+ align:start position:0%
+stories are you know kind of uh kind of
+national significance and some of them
+
+ align:start position:0%
+national significance and some of them
+ 
+
+ align:start position:0%
+national significance and some of them
+and probably more interesting or are
+
+ align:start position:0%
+and probably more interesting or are
+ 
+
+ align:start position:0%
+and probably more interesting or are
+personal so it's kind of both an excuse
+
+ align:start position:0%
+personal so it's kind of both an excuse
+ 
+
+ align:start position:0%
+personal so it's kind of both an excuse
+and the the vehicle by which
+
+ align:start position:0%
+and the the vehicle by which
+ 
+
+ align:start position:0%
+and the the vehicle by which
+I um can both Drive the work and can
+
+ align:start position:0%
+I um can both Drive the work and can
+ 
+
+ align:start position:0%
+I um can both Drive the work and can
+inform the sort of aesthetic decisions
+
+ align:start position:0%
+inform the sort of aesthetic decisions
+ 
+
+ align:start position:0%
+inform the sort of aesthetic decisions
+I'm making I think that answers it yes
+
+ align:start position:0%
+I'm making I think that answers it yes
+ 
+
+ align:start position:0%
+I'm making I think that answers it yes
+began this series of with the
+
+ align:start position:0%
+began this series of with the
+ 
+
+ align:start position:0%
+began this series of with the
+photographer who shoots from the air
+
+ align:start position:0%
+photographer who shoots from the air
+ 
+
+ align:start position:0%
+photographer who shoots from the air
+gentleman and we had a photographer who
+
+ align:start position:0%
+gentleman and we had a photographer who
+ 
+
+ align:start position:0%
+gentleman and we had a photographer who
+always looks at the high point of a city
+
+ align:start position:0%
+always looks at the high point of a city
+ 
+
+ align:start position:0%
+always looks at the high point of a city
+and takes an image
+
+ align:start position:0%
+and takes an image
+ 
+
+ align:start position:0%
+and takes an image
+downar looking at
+
+ align:start position:0%
+downar looking at
+ 
+
+ align:start position:0%
+downar looking at
+the photographs in New Jersey and I'm
+
+ align:start position:0%
+the photographs in New Jersey and I'm
+ 
+
+ align:start position:0%
+the photographs in New Jersey and I'm
+wondering if if you ever have
+
+ align:start position:0%
+wondering if if you ever have
+ 
+
+ align:start position:0%
+wondering if if you ever have
+a a tendency or a wish to photograph
+
+ align:start position:0%
+a a tendency or a wish to photograph
+ 
+
+ align:start position:0%
+a a tendency or a wish to photograph
+from on high uh or whether the subject
+
+ align:start position:0%
+from on high uh or whether the subject
+ 
+
+ align:start position:0%
+from on high uh or whether the subject
+matter that you take is always uh with
+
+ align:start position:0%
+matter that you take is always uh with
+ 
+
+ align:start position:0%
+matter that you take is always uh with
+your feet on the ground I think my
+
+ align:start position:0%
+your feet on the ground I think my
+ 
+
+ align:start position:0%
+your feet on the ground I think my
+tendency is I want to get as close to it
+
+ align:start position:0%
+tendency is I want to get as close to it
+ 
+
+ align:start position:0%
+tendency is I want to get as close to it
+as possible I don't like telephoto
+
+ align:start position:0%
+as possible I don't like telephoto
+ 
+
+ align:start position:0%
+as possible I don't like telephoto
+lenses I don't photograph with them very
+
+ align:start position:0%
+lenses I don't photograph with them very
+ 
+
+ align:start position:0%
+lenses I don't photograph with them very
+well I know people that photograph
+
+ align:start position:0%
+well I know people that photograph
+ 
+
+ align:start position:0%
+well I know people that photograph
+really well I need to have be sort of in
+
+ align:start position:0%
+really well I need to have be sort of in
+ 
+
+ align:start position:0%
+really well I need to have be sort of in
+physical contact with what I photograph
+
+ align:start position:0%
+physical contact with what I photograph
+ 
+
+ align:start position:0%
+physical contact with what I photograph
+I mean I do and I do like if I can get
+
+ align:start position:0%
+I mean I do and I do like if I can get
+ 
+
+ align:start position:0%
+I mean I do and I do like if I can get
+to a place where I can kind of see more
+
+ align:start position:0%
+to a place where I can kind of see more
+ 
+
+ align:start position:0%
+to a place where I can kind of see more
+context I will do that but I think my
+
+ align:start position:0%
+context I will do that but I think my
+ 
+
+ align:start position:0%
+context I will do that but I think my
+first inclination is to get close to
+
+ align:start position:0%
+first inclination is to get close to
+ 
+
+ align:start position:0%
+first inclination is to get close to
+something I think that shows in the work
+
+ align:start position:0%
+something I think that shows in the work
+ 
+
+ align:start position:0%
+something I think that shows in the work
+um I I'm kind of interested in the
+
+ align:start position:0%
+um I I'm kind of interested in the
+ 
+
+ align:start position:0%
+um I I'm kind of interested in the
+detail I'm very interested in the kind
+
+ align:start position:0%
+detail I'm very interested in the kind
+ 
+
+ align:start position:0%
+detail I'm very interested in the kind
+of bones of things and the texture
+
+ align:start position:0%
+of bones of things and the texture
+ 
+
+ align:start position:0%
+of bones of things and the texture
+uh both the sort of physical texture I
+
+ align:start position:0%
+uh both the sort of physical texture I
+ 
+
+ align:start position:0%
+uh both the sort of physical texture I
+actually hate when students say that yes
+
+ align:start position:0%
+actually hate when students say that yes
+ 
+
+ align:start position:0%
+actually hate when students say that yes
+I was really interested in but I am
+
+ align:start position:0%
+I was really interested in but I am
+ 
+
+ align:start position:0%
+I was really interested in but I am
+interested in that so I you know um but
+
+ align:start position:0%
+interested in that so I you know um but
+ 
+
+ align:start position:0%
+interested in that so I you know um but
+I'm interested in it for what it
+
+ align:start position:0%
+I'm interested in it for what it
+ 
+
+ align:start position:0%
+I'm interested in it for what it
+reflects the kind of you know that
+
+ align:start position:0%
+reflects the kind of you know that
+ 
+
+ align:start position:0%
+reflects the kind of you know that
+what's what always I loved about New
+
+ align:start position:0%
+what's what always I loved about New
+ 
+
+ align:start position:0%
+what's what always I loved about New
+Orleans is uh you know before the
+
+ align:start position:0%
+Orleans is uh you know before the
+ 
+
+ align:start position:0%
+Orleans is uh you know before the
+hurricane it already looks because it
+
+ align:start position:0%
+hurricane it already looks because it
+ 
+
+ align:start position:0%
+hurricane it already looks because it
+the climate is so hard that the patina
+
+ align:start position:0%
+the climate is so hard that the patina
+ 
+
+ align:start position:0%
+the climate is so hard that the patina
+of everything is just absolutely
+
+ align:start position:0%
+of everything is just absolutely
+ 
+
+ align:start position:0%
+of everything is just absolutely
+spectacular because it's there and so I
+
+ align:start position:0%
+spectacular because it's there and so I
+ 
+
+ align:start position:0%
+spectacular because it's there and so I
+I want to get close enough that that'll
+
+ align:start position:0%
+I want to get close enough that that'll
+ 
+
+ align:start position:0%
+I want to get close enough that that'll
+show in the photographs is there is
+
+ align:start position:0%
+show in the photographs is there is
+ 
+
+ align:start position:0%
+show in the photographs is there is
+there any kind of a setup shot I don't
+
+ align:start position:0%
+there any kind of a setup shot I don't
+ 
+
+ align:start position:0%
+there any kind of a setup shot I don't
+know what I mean something that gives
+
+ align:start position:0%
+know what I mean something that gives
+ 
+
+ align:start position:0%
+know what I mean something that gives
+you an entry point that is a larger
+
+ align:start position:0%
+you an entry point that is a larger
+ 
+
+ align:start position:0%
+you an entry point that is a larger
+context than the details that you find
+
+ align:start position:0%
+context than the details that you find
+ 
+
+ align:start position:0%
+context than the details that you find
+yeah I I I don't I think I like to have
+
+ align:start position:0%
+yeah I I I don't I think I like to have
+ 
+
+ align:start position:0%
+yeah I I I don't I think I like to have
+some hint of where something is or I'll
+
+ align:start position:0%
+some hint of where something is or I'll
+ 
+
+ align:start position:0%
+some hint of where something is or I'll
+at least do that in the photographs and
+
+ align:start position:0%
+at least do that in the photographs and
+ 
+
+ align:start position:0%
+at least do that in the photographs and
+then I have a decision to make you know
+
+ align:start position:0%
+then I have a decision to make you know
+ 
+
+ align:start position:0%
+then I have a decision to make you know
+whether I'm going to include that or not
+
+ align:start position:0%
+whether I'm going to include that or not
+ 
+
+ align:start position:0%
+whether I'm going to include that or not
+um uh you know sometimes I'll take one
+
+ align:start position:0%
+um uh you know sometimes I'll take one
+ 
+
+ align:start position:0%
+um uh you know sometimes I'll take one
+picture sort of whatever it feels like
+
+ align:start position:0%
+picture sort of whatever it feels like
+ 
+
+ align:start position:0%
+picture sort of whatever it feels like
+and leave but I think my tend my way of
+
+ align:start position:0%
+and leave but I think my tend my way of
+ 
+
+ align:start position:0%
+and leave but I think my tend my way of
+working usually is to kind of linger at
+
+ align:start position:0%
+working usually is to kind of linger at
+ 
+
+ align:start position:0%
+working usually is to kind of linger at
+a place and um kind of look at it from
+
+ align:start position:0%
+a place and um kind of look at it from
+ 
+
+ align:start position:0%
+a place and um kind of look at it from
+different areas angles or look at that
+
+ align:start position:0%
+different areas angles or look at that
+ 
+
+ align:start position:0%
+different areas angles or look at that
+phenomenon as it exists say in a number
+
+ align:start position:0%
+phenomenon as it exists say in a number
+ 
+
+ align:start position:0%
+phenomenon as it exists say in a number
+of different
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+iterations yeah what's your personal
+
+ align:start position:0%
+iterations yeah what's your personal
+ 
+
+ align:start position:0%
+iterations yeah what's your personal
+position regarding government's action
+
+ align:start position:0%
+position regarding government's action
+ 
+
+ align:start position:0%
+position regarding government's action
+krina because you never mentioned
+
+ align:start position:0%
+krina because you never mentioned
+ 
+
+ align:start position:0%
+krina because you never mentioned
+anything while you were talking about it
+
+ align:start position:0%
+anything while you were talking about it
+ 
+
+ align:start position:0%
+anything while you were talking about it
+and I don't know the contrast between
+
+ align:start position:0%
+and I don't know the contrast between
+ 
+
+ align:start position:0%
+and I don't know the contrast between
+the photos
+
+ align:start position:0%
+the photos
+ 
+
+ align:start position:0%
+the photos
+well I I'd be interested I will answer
+
+ align:start position:0%
+well I I'd be interested I will answer
+ 
+
+ align:start position:0%
+well I I'd be interested I will answer
+that from the photographs what would you
+
+ align:start position:0%
+that from the photographs what would you
+ 
+
+ align:start position:0%
+that from the photographs what would you
+think my is there any hint in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+images and there may not be you know the
+
+ align:start position:0%
+images and there may not be you know the
+ 
+
+ align:start position:0%
+images and there may not be you know the
+thing is you said that you were going to
+
+ align:start position:0%
+thing is you said that you were going to
+ 
+
+ align:start position:0%
+thing is you said that you were going to
+go there initially before the H right
+
+ align:start position:0%
+go there initially before the H right
+ 
+
+ align:start position:0%
+go there initially before the H right
+and to me it seems like you sort of
+
+ align:start position:0%
+and to me it seems like you sort of
+ 
+
+ align:start position:0%
+and to me it seems like you sort of
+photographed as if the H wouldn't have
+
+ align:start position:0%
+photographed as if the H wouldn't have
+ 
+
+ align:start position:0%
+photographed as if the H wouldn't have
+happened well to respect but like it
+
+ align:start position:0%
+happened well to respect but like it
+ 
+
+ align:start position:0%
+happened well to respect but like it
+still has that sort of quest that you
+
+ align:start position:0%
+still has that sort of quest that you
+ 
+
+ align:start position:0%
+still has that sort of quest that you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+the way of looking that uh it continues
+
+ align:start position:0%
+the way of looking that uh it continues
+ 
+
+ align:start position:0%
+the way of looking that uh it continues
+regarding the geography as geography
+
+ align:start position:0%
+regarding the geography as geography
+ 
+
+ align:start position:0%
+regarding the geography as geography
+changes well it's interesting that I
+
+ align:start position:0%
+changes well it's interesting that I
+ 
+
+ align:start position:0%
+changes well it's interesting that I
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+shown a like
+
+ align:start position:0%
+shown a like
+ 
+
+ align:start position:0%
+shown a like
+150 image presentation of post Katrina
+
+ align:start position:0%
+150 image presentation of post Katrina
+ 
+
+ align:start position:0%
+150 image presentation of post Katrina
+work I think four or five times in the
+
+ align:start position:0%
+work I think four or five times in the
+ 
+
+ align:start position:0%
+work I think four or five times in the
+last couple of months and the last two
+
+ align:start position:0%
+last couple of months and the last two
+ 
+
+ align:start position:0%
+last couple of months and the last two
+times I showed it I was sick of it it
+
+ align:start position:0%
+times I showed it I was sick of it it
+ 
+
+ align:start position:0%
+times I showed it I was sick of it it
+was sort of like I it sort of like
+
+ align:start position:0%
+was sort of like I it sort of like
+ 
+
+ align:start position:0%
+was sort of like I it sort of like
+that's not I mean I obviously was drawn
+
+ align:start position:0%
+that's not I mean I obviously was drawn
+ 
+
+ align:start position:0%
+that's not I mean I obviously was drawn
+there I had to go there and I wanted to
+
+ align:start position:0%
+there I had to go there and I wanted to
+ 
+
+ align:start position:0%
+there I had to go there and I wanted to
+photograph it but I'm more interested in
+
+ align:start position:0%
+photograph it but I'm more interested in
+ 
+
+ align:start position:0%
+photograph it but I'm more interested in
+I mean one of the things that I missed I
+
+ align:start position:0%
+I mean one of the things that I missed I
+ 
+
+ align:start position:0%
+I mean one of the things that I missed I
+was there literally the first time after
+
+ align:start position:0%
+was there literally the first time after
+ 
+
+ align:start position:0%
+was there literally the first time after
+the hurricane when you could go there
+
+ align:start position:0%
+the hurricane when you could go there
+ 
+
+ align:start position:0%
+the hurricane when you could go there
+without having to show ID you know L
+
+ align:start position:0%
+without having to show ID you know L
+ 
+
+ align:start position:0%
+without having to show ID you know L
+that's I went made a beine and and the
+
+ align:start position:0%
+that's I went made a beine and and the
+ 
+
+ align:start position:0%
+that's I went made a beine and and the
+thing that happened almost everybody I
+
+ align:start position:0%
+thing that happened almost everybody I
+ 
+
+ align:start position:0%
+thing that happened almost everybody I
+knew was not there the streets were
+
+ align:start position:0%
+knew was not there the streets were
+ 
+
+ align:start position:0%
+knew was not there the streets were
+empty there's incredible Devastation
+
+ align:start position:0%
+empty there's incredible Devastation
+ 
+
+ align:start position:0%
+empty there's incredible Devastation
+which actually I haven't seen a
+
+ align:start position:0%
+which actually I haven't seen a
+ 
+
+ align:start position:0%
+which actually I haven't seen a
+photograph that really shows including
+
+ align:start position:0%
+photograph that really shows including
+ 
+
+ align:start position:0%
+photograph that really shows including
+my own I made a decision I've made a
+
+ align:start position:0%
+my own I made a decision I've made a
+ 
+
+ align:start position:0%
+my own I made a decision I've made a
+decision now and I think I'm going to
+
+ align:start position:0%
+decision now and I think I'm going to
+ 
+
+ align:start position:0%
+decision now and I think I'm going to
+revisit it cuz I haven't really printed
+
+ align:start position:0%
+revisit it cuz I haven't really printed
+ 
+
+ align:start position:0%
+revisit it cuz I haven't really printed
+it that that that's not the destruction
+
+ align:start position:0%
+it that that that's not the destruction
+ 
+
+ align:start position:0%
+it that that that's not the destruction
+pictures are of less interest to me and
+
+ align:start position:0%
+pictures are of less interest to me and
+ 
+
+ align:start position:0%
+pictures are of less interest to me and
+they don't even really speak to really
+
+ align:start position:0%
+they don't even really speak to really
+ 
+
+ align:start position:0%
+they don't even really speak to really
+what's going on they don't speak to the
+
+ align:start position:0%
+what's going on they don't speak to the
+ 
+
+ align:start position:0%
+what's going on they don't speak to the
+fact that people have been displaced
+
+ align:start position:0%
+fact that people have been displaced
+ 
+
+ align:start position:0%
+fact that people have been displaced
+they don't speak to the fact that the
+
+ align:start position:0%
+they don't speak to the fact that the
+ 
+
+ align:start position:0%
+they don't speak to the fact that the
+Lower Ninth Ward had something like 60
+
+ align:start position:0%
+Lower Ninth Ward had something like 60
+ 
+
+ align:start position:0%
+Lower Ninth Ward had something like 60
+or 70% homeowners they don't I didn't
+
+ align:start position:0%
+or 70% homeowners they don't I didn't
+ 
+
+ align:start position:0%
+or 70% homeowners they don't I didn't
+show it there's an area called Lake View
+
+ align:start position:0%
+show it there's an area called Lake View
+ 
+
+ align:start position:0%
+show it there's an area called Lake View
+which was a middle class primarily white
+
+ align:start position:0%
+which was a middle class primarily white
+ 
+
+ align:start position:0%
+which was a middle class primarily white
+area that was right by the 7th Avenue
+
+ align:start position:0%
+area that was right by the 7th Avenue
+ 
+
+ align:start position:0%
+area that was right by the 7th Avenue
+Canal which had much it's a landfill it
+
+ align:start position:0%
+Canal which had much it's a landfill it
+ 
+
+ align:start position:0%
+Canal which had much it's a landfill it
+had houses that are probably 30 or 40
+
+ align:start position:0%
+had houses that are probably 30 or 40
+ 
+
+ align:start position:0%
+had houses that are probably 30 or 40
+years old except for where the barge
+
+ align:start position:0%
+years old except for where the barge
+ 
+
+ align:start position:0%
+years old except for where the barge
+basically leveled house the housing
+
+ align:start position:0%
+basically leveled house the housing
+ 
+
+ align:start position:0%
+basically leveled house the housing
+damage was actually worse in Lake View
+
+ align:start position:0%
+damage was actually worse in Lake View
+ 
+
+ align:start position:0%
+damage was actually worse in Lake View
+because those houses weren't as well
+
+ align:start position:0%
+because those houses weren't as well
+ 
+
+ align:start position:0%
+because those houses weren't as well
+made as the earlier houses
+
+ align:start position:0%
+made as the earlier houses
+ 
+
+ align:start position:0%
+made as the earlier houses
+um uh but I'm more interested in like I
+
+ align:start position:0%
+um uh but I'm more interested in like I
+ 
+
+ align:start position:0%
+um uh but I'm more interested in like I
+live in Richmond and that was settled by
+
+ align:start position:0%
+live in Richmond and that was settled by
+ 
+
+ align:start position:0%
+live in Richmond and that was settled by
+a lot of people from Louisiana and
+
+ align:start position:0%
+a lot of people from Louisiana and
+ 
+
+ align:start position:0%
+a lot of people from Louisiana and
+there's not shotgun houses in Richmond
+
+ align:start position:0%
+there's not shotgun houses in Richmond
+ 
+
+ align:start position:0%
+there's not shotgun houses in Richmond
+but there the way people personalize
+
+ align:start position:0%
+but there the way people personalize
+ 
+
+ align:start position:0%
+but there the way people personalize
+their spaces with iron fences looks
+
+ align:start position:0%
+their spaces with iron fences looks
+ 
+
+ align:start position:0%
+their spaces with iron fences looks
+exactly like the ninth W it's really
+
+ align:start position:0%
+exactly like the ninth W it's really
+ 
+
+ align:start position:0%
+exactly like the ninth W it's really
+amazing so that you know I guess for
+
+ align:start position:0%
+amazing so that you know I guess for
+ 
+
+ align:start position:0%
+amazing so that you know I guess for
+this talk I was more interested in the
+
+ align:start position:0%
+this talk I was more interested in the
+ 
+
+ align:start position:0%
+this talk I was more interested in the
+whole idea of transference um and at
+
+ align:start position:0%
+whole idea of transference um and at
+ 
+
+ align:start position:0%
+whole idea of transference um and at
+least for here less I'm less interested
+
+ align:start position:0%
+least for here less I'm less interested
+ 
+
+ align:start position:0%
+least for here less I'm less interested
+in the effects of the hurricane the
+
+ align:start position:0%
+in the effects of the hurricane the
+ 
+
+ align:start position:0%
+in the effects of the hurricane the
+physical effects of the hurricane I am
+
+ align:start position:0%
+physical effects of the hurricane I am
+ 
+
+ align:start position:0%
+physical effects of the hurricane I am
+very interested in the social I'm also
+
+ align:start position:0%
+very interested in the social I'm also
+ 
+
+ align:start position:0%
+very interested in the social I'm also
+interested in terms of when I talk to
+
+ align:start position:0%
+interested in terms of when I talk to
+ 
+
+ align:start position:0%
+interested in terms of when I talk to
+people you know there were all these
+
+ align:start position:0%
+people you know there were all these
+ 
+
+ align:start position:0%
+people you know there were all these
+stories well there were stories that
+
+ align:start position:0%
+stories well there were stories that
+ 
+
+ align:start position:0%
+stories well there were stories that
+there were gangs of black people killing
+
+ align:start position:0%
+there were gangs of black people killing
+ 
+
+ align:start position:0%
+there were gangs of black people killing
+people in the Garden District which
+
+ align:start position:0%
+people in the Garden District which
+ 
+
+ align:start position:0%
+people in the Garden District which
+wasn't true there were stories that
+
+ align:start position:0%
+wasn't true there were stories that
+ 
+
+ align:start position:0%
+wasn't true there were stories that
+multiple people were raped in the
+
+ align:start position:0%
+multiple people were raped in the
+ 
+
+ align:start position:0%
+multiple people were raped in the
+Astrodome which which was also not true
+
+ align:start position:0%
+Astrodome which which was also not true
+ 
+
+ align:start position:0%
+Astrodome which which was also not true
+people were smoking Kraken it was
+
+ align:start position:0%
+people were smoking Kraken it was
+ 
+
+ align:start position:0%
+people were smoking Kraken it was
+horrendous but it was interesting that
+
+ align:start position:0%
+horrendous but it was interesting that
+ 
+
+ align:start position:0%
+horrendous but it was interesting that
+the hurricane well what it did reflect
+
+ align:start position:0%
+the hurricane well what it did reflect
+ 
+
+ align:start position:0%
+the hurricane well what it did reflect
+is the the I Love New Orleans but I also
+
+ align:start position:0%
+is the the I Love New Orleans but I also
+ 
+
+ align:start position:0%
+is the the I Love New Orleans but I also
+hate it because the racism the racism is
+
+ align:start position:0%
+hate it because the racism the racism is
+ 
+
+ align:start position:0%
+hate it because the racism the racism is
+almost breathtaking it's so palpable and
+
+ align:start position:0%
+almost breathtaking it's so palpable and
+ 
+
+ align:start position:0%
+almost breathtaking it's so palpable and
+that's one of the things I don't like
+
+ align:start position:0%
+that's one of the things I don't like
+ 
+
+ align:start position:0%
+that's one of the things I don't like
+about the south and I I don't want to
+
+ align:start position:0%
+about the south and I I don't want to
+ 
+
+ align:start position:0%
+about the south and I I don't want to
+you know um
+
+ align:start position:0%
+you know um
+ 
+
+ align:start position:0%
+you know um
+uh there's some things fauler said in
+
+ align:start position:0%
+uh there's some things fauler said in
+ 
+
+ align:start position:0%
+uh there's some things fauler said in
+the South the past isn't really the past
+
+ align:start position:0%
+the South the past isn't really the past
+ 
+
+ align:start position:0%
+the South the past isn't really the past
+in history is right just below the C and
+
+ align:start position:0%
+in history is right just below the C and
+ 
+
+ align:start position:0%
+in history is right just below the C and
+that's absolutely the truth and that's
+
+ align:start position:0%
+that's absolutely the truth and that's
+ 
+
+ align:start position:0%
+that's absolutely the truth and that's
+those are things I'm really interested
+
+ align:start position:0%
+those are things I'm really interested
+ 
+
+ align:start position:0%
+those are things I'm really interested
+in photographing but there's also
+
+ align:start position:0%
+in photographing but there's also
+ 
+
+ align:start position:0%
+in photographing but there's also
+elements about that I am disgusted by
+
+ align:start position:0%
+elements about that I am disgusted by
+ 
+
+ align:start position:0%
+elements about that I am disgusted by
+and can't be around for long periods of
+
+ align:start position:0%
+and can't be around for long periods of
+ 
+
+ align:start position:0%
+and can't be around for long periods of
+time so but I did really was very upset
+
+ align:start position:0%
+time so but I did really was very upset
+ 
+
+ align:start position:0%
+time so but I did really was very upset
+to not have a chance to be in New
+
+ align:start position:0%
+to not have a chance to be in New
+ 
+
+ align:start position:0%
+to not have a chance to be in New
+Orleans I was going to be at the AY
+
+ align:start position:0%
+Orleans I was going to be at the AY
+ 
+
+ align:start position:0%
+Orleans I was going to be at the AY
+Museum of Southern art because there New
+
+ align:start position:0%
+Museum of Southern art because there New
+ 
+
+ align:start position:0%
+Museum of Southern art because there New
+Orleans is an incredible Art Center
+
+ align:start position:0%
+Orleans is an incredible Art Center
+ 
+
+ align:start position:0%
+Orleans is an incredible Art Center
+there's I sort of said New Orleans is a
+
+ align:start position:0%
+there's I sort of said New Orleans is a
+ 
+
+ align:start position:0%
+there's I sort of said New Orleans is a
+place where there's not much mediocrity
+
+ align:start position:0%
+place where there's not much mediocrity
+ 
+
+ align:start position:0%
+place where there's not much mediocrity
+there's incredible genius and incredible
+
+ align:start position:0%
+there's incredible genius and incredible
+ 
+
+ align:start position:0%
+there's incredible genius and incredible
+Inc competence and there's there um
+
+ align:start position:0%
+Inc competence and there's there um
+ 
+
+ align:start position:0%
+Inc competence and there's there um
+artists incredible artists artists that
+
+ align:start position:0%
+artists incredible artists artists that
+ 
+
+ align:start position:0%
+artists incredible artists artists that
+we don't even know visual artists
+
+ align:start position:0%
+we don't even know visual artists
+ 
+
+ align:start position:0%
+we don't even know visual artists
+musicians uh acting and I I in the
+
+ align:start position:0%
+musicians uh acting and I I in the
+ 
+
+ align:start position:0%
+musicians uh acting and I I in the
+course of visiting have gotten a chance
+
+ align:start position:0%
+course of visiting have gotten a chance
+ 
+
+ align:start position:0%
+course of visiting have gotten a chance
+to meet some of them but and this would
+
+ align:start position:0%
+to meet some of them but and this would
+ 
+
+ align:start position:0%
+to meet some of them but and this would
+have been a chance to sort of get you
+
+ align:start position:0%
+have been a chance to sort of get you
+ 
+
+ align:start position:0%
+have been a chance to sort of get you
+know further below the beneath the
+
+ align:start position:0%
+know further below the beneath the
+ 
+
+ align:start position:0%
+know further below the beneath the
+surface and I guess at this point
+
+ align:start position:0%
+surface and I guess at this point
+ 
+
+ align:start position:0%
+surface and I guess at this point
+because I've been dealing with the
+
+ align:start position:0%
+because I've been dealing with the
+ 
+
+ align:start position:0%
+because I've been dealing with the
+destruction I'm much more interested in
+
+ align:start position:0%
+destruction I'm much more interested in
+ 
+
+ align:start position:0%
+destruction I'm much more interested in
+kind of what New Orleans was and what it
+
+ align:start position:0%
+kind of what New Orleans was and what it
+ 
+
+ align:start position:0%
+kind of what New Orleans was and what it
+will be I I'm going to go in May and
+
+ align:start position:0%
+will be I I'm going to go in May and
+ 
+
+ align:start position:0%
+will be I I'm going to go in May and
+kind of uh work with a colleague of mine
+
+ align:start position:0%
+kind of uh work with a colleague of mine
+ 
+
+ align:start position:0%
+kind of uh work with a colleague of mine
+um we're going to kind of examine how
+
+ align:start position:0%
+um we're going to kind of examine how
+ 
+
+ align:start position:0%
+um we're going to kind of examine how
+something like the Jazz Fest and the
+
+ align:start position:0%
+something like the Jazz Fest and the
+ 
+
+ align:start position:0%
+something like the Jazz Fest and the
+role of culture whether that will be
+
+ align:start position:0%
+role of culture whether that will be
+ 
+
+ align:start position:0%
+role of culture whether that will be
+used to make New Orleans into a boutique
+
+ align:start position:0%
+used to make New Orleans into a boutique
+ 
+
+ align:start position:0%
+used to make New Orleans into a boutique
+or a theme park or to sort of bring back
+
+ align:start position:0%
+or a theme park or to sort of bring back
+ 
+
+ align:start position:0%
+or a theme park or to sort of bring back
+what was before and as someone told me
+
+ align:start position:0%
+what was before and as someone told me
+ 
+
+ align:start position:0%
+what was before and as someone told me
+it's probably going to be a combination
+
+ align:start position:0%
+it's probably going to be a combination
+ 
+
+ align:start position:0%
+it's probably going to be a combination
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+both all right thank you
+
+ align:start position:0%
+both all right thank you
+ 
+
+ align:start position:0%
+both all right thank you
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
\ No newline at end of file
diff --git a/GZQ-8pg7bgk.txt b/GZQ-8pg7bgk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b071ad44719c7a41097b20189f1b3fb2f89099ce
--- /dev/null
+++ b/GZQ-8pg7bgk.txt
@@ -0,0 +1,12603 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we talked about
+
+ align:start position:0%
+we talked about
+ 
+
+ align:start position:0%
+we talked about
+path integral
+
+ align:start position:0%
+path integral
+ 
+
+ align:start position:0%
+path integral
+formulation of quantum mechanics
+
+ align:start position:0%
+formulation of quantum mechanics
+ 
+
+ align:start position:0%
+formulation of quantum mechanics
+so let me just quickly remind you the
+
+ align:start position:0%
+so let me just quickly remind you the
+ 
+
+ align:start position:0%
+so let me just quickly remind you the
+main idea
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay so classically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if we specify the initial location
+
+ align:start position:0%
+if we specify the initial location
+ 
+
+ align:start position:0%
+if we specify the initial location
+say if you add T Prime X Prime
+
+ align:start position:0%
+say if you add T Prime X Prime
+ 
+
+ align:start position:0%
+say if you add T Prime X Prime
+and then the final location
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and X
+
+ align:start position:0%
+T and X
+ 
+
+ align:start position:0%
+T and X
+said time T you add X and then there's a
+
+ align:start position:0%
+said time T you add X and then there's a
+ 
+
+ align:start position:0%
+said time T you add X and then there's a
+unique trajectory okay
+
+ align:start position:0%
+unique trajectory okay
+ 
+
+ align:start position:0%
+unique trajectory okay
+and it's a unique detection
+
+ align:start position:0%
+and it's a unique detection
+ 
+
+ align:start position:0%
+and it's a unique detection
+so Quantum mechanically
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you ask a different question
+
+ align:start position:0%
+you ask a different question
+ 
+
+ align:start position:0%
+you ask a different question
+you ask what is the transition amplitude
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you say at T Prime
+
+ align:start position:0%
+if you say at T Prime
+ 
+
+ align:start position:0%
+if you say at T Prime
+you add location X Prime and what's the
+
+ align:start position:0%
+you add location X Prime and what's the
+ 
+
+ align:start position:0%
+you add location X Prime and what's the
+transition amplitude at time T you add
+
+ align:start position:0%
+transition amplitude at time T you add
+ 
+
+ align:start position:0%
+transition amplitude at time T you add
+location X
+
+ align:start position:0%
+location X
+ 
+
+ align:start position:0%
+location X
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the answer for this question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now is equal to
+
+ align:start position:0%
+now is equal to
+ 
+
+ align:start position:0%
+now is equal to
+you just sum
+
+ align:start position:0%
+you just sum
+ 
+
+ align:start position:0%
+you just sum
+of all possible path
+
+ align:start position:0%
+of all possible path
+ 
+
+ align:start position:0%
+of all possible path
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+T Prime and X Prime and the TX okay
+
+ align:start position:0%
+T Prime and X Prime and the TX okay
+ 
+
+ align:start position:0%
+T Prime and X Prime and the TX okay
+so it's just sum of all possible paths
+
+ align:start position:0%
+so it's just sum of all possible paths
+ 
+
+ align:start position:0%
+so it's just sum of all possible paths
+and with some weight okay
+
+ align:start position:0%
+and with some weight okay
+ 
+
+ align:start position:0%
+and with some weight okay
+so more explicitly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and with the weight you sum of all paths
+
+ align:start position:0%
+and with the weight you sum of all paths
+ 
+
+ align:start position:0%
+and with the weight you sum of all paths
+and the weight is given by experiential
+
+ align:start position:0%
+and the weight is given by experiential
+ 
+
+ align:start position:0%
+and the weight is given by experiential
+i h
+
+ align:start position:0%
+i h
+ 
+
+ align:start position:0%
+i h
+s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so for each pass you have action
+
+ align:start position:0%
+so for each pass you have action
+ 
+
+ align:start position:0%
+so for each pass you have action
+and then just evaluate for each part the
+
+ align:start position:0%
+and then just evaluate for each part the
+ 
+
+ align:start position:0%
+and then just evaluate for each part the
+action and then yeah here also
+
+ align:start position:0%
+action and then yeah here also
+ 
+
+ align:start position:0%
+action and then yeah here also
+we explicit H bar here and because the
+
+ align:start position:0%
+we explicit H bar here and because the
+ 
+
+ align:start position:0%
+we explicit H bar here and because the
+action has the unit of H bar and yeah so
+
+ align:start position:0%
+action has the unit of H bar and yeah so
+ 
+
+ align:start position:0%
+action has the unit of H bar and yeah so
+this would be the
+
+ align:start position:0%
+this would be the
+ 
+
+ align:start position:0%
+this would be the
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the quantum mechanical answer okay so
+
+ align:start position:0%
+the quantum mechanical answer okay so
+ 
+
+ align:start position:0%
+the quantum mechanical answer okay so
+this is a formulation of quantum
+
+ align:start position:0%
+this is a formulation of quantum
+ 
+
+ align:start position:0%
+this is a formulation of quantum
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+even in path integral
+
+ align:start position:0%
+even in path integral
+ 
+
+ align:start position:0%
+even in path integral
+and so we can write this more explicitly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mathematically mathematical rotation
+
+ align:start position:0%
+mathematically mathematical rotation
+ 
+
+ align:start position:0%
+mathematically mathematical rotation
+for disarming over Parts is the
+
+ align:start position:0%
+for disarming over Parts is the
+ 
+
+ align:start position:0%
+for disarming over Parts is the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+say we
+
+ align:start position:0%
+say we
+ 
+
+ align:start position:0%
+say we
+introduce a rotation like this which you
+
+ align:start position:0%
+introduce a rotation like this which you
+ 
+
+ align:start position:0%
+introduce a rotation like this which you
+integrate over all possible trajectories
+
+ align:start position:0%
+integrate over all possible trajectories
+ 
+
+ align:start position:0%
+integrate over all possible trajectories
+between x t Prime equal to X
+
+ align:start position:0%
+between x t Prime equal to X
+ 
+
+ align:start position:0%
+between x t Prime equal to X
+and x t or X Prime and x t equal to X
+
+ align:start position:0%
+and x t or X Prime and x t equal to X
+ 
+
+ align:start position:0%
+and x t or X Prime and x t equal to X
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+you integrate under the U with weight
+
+ align:start position:0%
+you integrate under the U with weight
+ 
+
+ align:start position:0%
+you integrate under the U with weight
+as
+
+ align:start position:0%
+as
+ 
+
+ align:start position:0%
+as
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+and the x t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and x t is a function of x t
+
+ align:start position:0%
+and x t is a function of x t
+ 
+
+ align:start position:0%
+and x t is a function of x t
+which give you
+
+ align:start position:0%
+which give you
+ 
+
+ align:start position:0%
+which give you
+which you increase integrate from T
+
+ align:start position:0%
+which you increase integrate from T
+ 
+
+ align:start position:0%
+which you increase integrate from T
+Prime to T
+
+ align:start position:0%
+Prime to T
+ 
+
+ align:start position:0%
+Prime to T
+we have t
+
+ align:start position:0%
+we have t
+ 
+
+ align:start position:0%
+we have t
+double Prime
+
+ align:start position:0%
+double Prime
+ 
+
+ align:start position:0%
+double Prime
+so one half m x dot Square minus BX okay
+
+ align:start position:0%
+so one half m x dot Square minus BX okay
+ 
+
+ align:start position:0%
+so one half m x dot Square minus BX okay
+so this is for the one dimensional
+
+ align:start position:0%
+so this is for the one dimensional
+ 
+
+ align:start position:0%
+so this is for the one dimensional
+particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also this
+
+ align:start position:0%
+and also this
+ 
+
+ align:start position:0%
+and also this
+so all the trajectory with this fixed
+
+ align:start position:0%
+so all the trajectory with this fixed
+ 
+
+ align:start position:0%
+so all the trajectory with this fixed
+endpoint and T Prime should be equal to
+
+ align:start position:0%
+endpoint and T Prime should be equal to
+ 
+
+ align:start position:0%
+endpoint and T Prime should be equal to
+X Prime and the time T could be equal to
+
+ align:start position:0%
+X Prime and the time T could be equal to
+ 
+
+ align:start position:0%
+X Prime and the time T could be equal to
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+and also this integration is a shorthand
+
+ align:start position:0%
+and also this integration is a shorthand
+ 
+
+ align:start position:0%
+and also this integration is a shorthand
+notation
+
+ align:start position:0%
+notation
+ 
+
+ align:start position:0%
+notation
+for limit
+
+ align:start position:0%
+for limit
+ 
+
+ align:start position:0%
+for limit
+so this DX t
+
+ align:start position:0%
+so this DX t
+ 
+
+ align:start position:0%
+so this DX t
+should be understood as a limit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you take angles Infinity
+
+ align:start position:0%
+when you take angles Infinity
+ 
+
+ align:start position:0%
+when you take angles Infinity
+this factor of
+
+ align:start position:0%
+this factor of
+ 
+
+ align:start position:0%
+this factor of
+n divided by 2 pi I
+
+ align:start position:0%
+n divided by 2 pi I
+ 
+
+ align:start position:0%
+n divided by 2 pi I
+delta T So essentially you divide your
+
+ align:start position:0%
+delta T So essentially you divide your
+ 
+
+ align:start position:0%
+delta T So essentially you divide your
+path
+
+ align:start position:0%
+path
+ 
+
+ align:start position:0%
+path
+by by intervals of delta T
+
+ align:start position:0%
+by by intervals of delta T
+ 
+
+ align:start position:0%
+by by intervals of delta T
+and then you integrate over all possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah okay so so you separate the path
+
+ align:start position:0%
+yeah okay so so you separate the path
+ 
+
+ align:start position:0%
+yeah okay so so you separate the path
+from t t Prime to T
+
+ align:start position:0%
+from t t Prime to T
+ 
+
+ align:start position:0%
+from t t Prime to T
+by by n segment
+
+ align:start position:0%
+by by n segment
+ 
+
+ align:start position:0%
+by by n segment
+so this is the t i
+
+ align:start position:0%
+so this is the t i
+ 
+
+ align:start position:0%
+so this is the t i
+and then location will be x i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is TI and location and then you
+
+ align:start position:0%
+so this is TI and location and then you
+ 
+
+ align:start position:0%
+so this is TI and location and then you
+integrate the x i of that okay
+
+ align:start position:0%
+integrate the x i of that okay
+ 
+
+ align:start position:0%
+integrate the x i of that okay
+so so this is the
+
+ align:start position:0%
+so so this is the
+ 
+
+ align:start position:0%
+so so this is the
+um formulation of fast integral
+
+ align:start position:0%
+um formulation of fast integral
+ 
+
+ align:start position:0%
+um formulation of fast integral
+for quantum mechanics
+
+ align:start position:0%
+for quantum mechanics
+ 
+
+ align:start position:0%
+for quantum mechanics
+any questions on this
+
+ align:start position:0%
+any questions on this
+ 
+
+ align:start position:0%
+any questions on this
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh yeah yeah in principle you can also
+
+ align:start position:0%
+uh yeah yeah in principle you can also
+ 
+
+ align:start position:0%
+uh yeah yeah in principle you can also
+do this in momentum basis yeah momentum
+
+ align:start position:0%
+do this in momentum basis yeah momentum
+ 
+
+ align:start position:0%
+do this in momentum basis yeah momentum
+space and and also you can actually also
+
+ align:start position:0%
+space and and also you can actually also
+ 
+
+ align:start position:0%
+space and and also you can actually also
+generalize
+
+ align:start position:0%
+generalize
+ 
+
+ align:start position:0%
+generalize
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah but
+
+ align:start position:0%
+yeah but
+ 
+
+ align:start position:0%
+yeah but
+yeah we will talk about the how you
+
+ align:start position:0%
+yeah we will talk about the how you
+ 
+
+ align:start position:0%
+yeah we will talk about the how you
+generalize this uh to to other bases and
+
+ align:start position:0%
+generalize this uh to to other bases and
+ 
+
+ align:start position:0%
+generalize this uh to to other bases and
+uh but but this is the fundamental
+
+ align:start position:0%
+uh but but this is the fundamental
+ 
+
+ align:start position:0%
+uh but but this is the fundamental
+formulation and uh when you write it in
+
+ align:start position:0%
+formulation and uh when you write it in
+ 
+
+ align:start position:0%
+formulation and uh when you write it in
+other bases you essentially you reduce
+
+ align:start position:0%
+other bases you essentially you reduce
+ 
+
+ align:start position:0%
+other bases you essentially you reduce
+to this basis and because this is the
+
+ align:start position:0%
+to this basis and because this is the
+ 
+
+ align:start position:0%
+to this basis and because this is the
+most intuitive way yeah
+
+ align:start position:0%
+most intuitive way yeah
+ 
+
+ align:start position:0%
+most intuitive way yeah
+to to uh to formulate it
+
+ align:start position:0%
+to to uh to formulate it
+ 
+
+ align:start position:0%
+to to uh to formulate it
+any other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay create
+
+ align:start position:0%
+okay create
+ 
+
+ align:start position:0%
+okay create
+so a simple example
+
+ align:start position:0%
+so a simple example
+ 
+
+ align:start position:0%
+so a simple example
+is just a free particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you have a free particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just then then the S is
+
+ align:start position:0%
+let me just then then the S is
+ 
+
+ align:start position:0%
+let me just then then the S is
+particularly simple you just the
+
+ align:start position:0%
+particularly simple you just the
+ 
+
+ align:start position:0%
+particularly simple you just the
+integration
+
+ align:start position:0%
+integration
+ 
+
+ align:start position:0%
+integration
+of one half MX Square
+
+ align:start position:0%
+of one half MX Square
+ 
+
+ align:start position:0%
+of one half MX Square
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we described
+
+ align:start position:0%
+so we described
+ 
+
+ align:start position:0%
+so we described
+edible s is equal to this
+
+ align:start position:0%
+edible s is equal to this
+ 
+
+ align:start position:0%
+edible s is equal to this
+and then this is like a gaussian
+
+ align:start position:0%
+and then this is like a gaussian
+ 
+
+ align:start position:0%
+and then this is like a gaussian
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+okay because this is quadratic in x
+
+ align:start position:0%
+okay because this is quadratic in x
+ 
+
+ align:start position:0%
+okay because this is quadratic in x
+okay so this is like a gaussian integral
+
+ align:start position:0%
+okay so this is like a gaussian integral
+ 
+
+ align:start position:0%
+okay so this is like a gaussian integral
+and so you can reduce so so in this case
+
+ align:start position:0%
+and so you can reduce so so in this case
+ 
+
+ align:start position:0%
+and so you can reduce so so in this case
+you have a gaussian integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and schematically
+
+ align:start position:0%
+and schematically
+ 
+
+ align:start position:0%
+and schematically
+you have something like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can
+
+ align:start position:0%
+you can
+ 
+
+ align:start position:0%
+you can
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when axis of this form you can write it
+
+ align:start position:0%
+when axis of this form you can write it
+ 
+
+ align:start position:0%
+when axis of this form you can write it
+in this general form
+
+ align:start position:0%
+in this general form
+ 
+
+ align:start position:0%
+in this general form
+you can write the path integral in this
+
+ align:start position:0%
+you can write the path integral in this
+ 
+
+ align:start position:0%
+you can write the path integral in this
+general form and the K in this case will
+
+ align:start position:0%
+general form and the K in this case will
+ 
+
+ align:start position:0%
+general form and the K in this case will
+be some Delta function yeah I wrote down
+
+ align:start position:0%
+be some Delta function yeah I wrote down
+ 
+
+ align:start position:0%
+be some Delta function yeah I wrote down
+K last time explicitly
+
+ align:start position:0%
+K last time explicitly
+ 
+
+ align:start position:0%
+K last time explicitly
+and then this is like a golfing integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in the Gauss integral we can just
+
+ align:start position:0%
+and in the Gauss integral we can just
+ 
+
+ align:start position:0%
+and in the Gauss integral we can just
+directly
+
+ align:start position:0%
+directly
+ 
+
+ align:start position:0%
+directly
+write down its answer
+
+ align:start position:0%
+write down its answer
+ 
+
+ align:start position:0%
+write down its answer
+and some constant divided by Delta k
+
+ align:start position:0%
+and some constant divided by Delta k
+ 
+
+ align:start position:0%
+and some constant divided by Delta k
+so this determinant is defined in the
+
+ align:start position:0%
+so this determinant is defined in the
+ 
+
+ align:start position:0%
+so this determinant is defined in the
+space of functions okay so and C is some
+
+ align:start position:0%
+space of functions okay so and C is some
+ 
+
+ align:start position:0%
+space of functions okay so and C is some
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you may also view this just as
+
+ align:start position:0%
+so you may also view this just as
+ 
+
+ align:start position:0%
+so you may also view this just as
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+lateral yeah so this also just follows
+
+ align:start position:0%
+lateral yeah so this also just follows
+ 
+
+ align:start position:0%
+lateral yeah so this also just follows
+from this continuous okay follow from
+
+ align:start position:0%
+from this continuous okay follow from
+ 
+
+ align:start position:0%
+from this continuous okay follow from
+this discrete case which you take a
+
+ align:start position:0%
+this discrete case which you take a
+ 
+
+ align:start position:0%
+this discrete case which you take a
+Continuum limit
+
+ align:start position:0%
+Continuum limit
+ 
+
+ align:start position:0%
+Continuum limit
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah this is the same as you do the
+
+ align:start position:0%
+yeah yeah this is the same as you do the
+ 
+
+ align:start position:0%
+yeah yeah this is the same as you do the
+standard gaussian integral with the I
+
+ align:start position:0%
+standard gaussian integral with the I
+ 
+
+ align:start position:0%
+standard gaussian integral with the I
+yeah that integral you can also do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know it's a it's a
+
+ align:start position:0%
+you know it's a it's a
+ 
+
+ align:start position:0%
+you know it's a it's a
+yeah just with a single
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this integral
+
+ align:start position:0%
+so this integral
+ 
+
+ align:start position:0%
+so this integral
+we can Define right
+
+ align:start position:0%
+we can Define right
+ 
+
+ align:start position:0%
+we can Define right
+yeah this integral is we know how to do
+
+ align:start position:0%
+yeah this integral is we know how to do
+ 
+
+ align:start position:0%
+yeah this integral is we know how to do
+this integral it's the same as this one
+
+ align:start position:0%
+this integral it's the same as this one
+ 
+
+ align:start position:0%
+this integral it's the same as this one
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+so yeah
+
+ align:start position:0%
+so yeah
+ 
+
+ align:start position:0%
+so yeah
+so you have to
+
+ align:start position:0%
+so you have to
+ 
+
+ align:start position:0%
+so you have to
+do a really mathematical trick to do
+
+ align:start position:0%
+do a really mathematical trick to do
+ 
+
+ align:start position:0%
+do a really mathematical trick to do
+this integral and but but this integral
+
+ align:start position:0%
+this integral and but but this integral
+ 
+
+ align:start position:0%
+this integral and but but this integral
+is defined yeah we can give a value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good so so so this uh is the
+
+ align:start position:0%
+good so so so this uh is the
+ 
+
+ align:start position:0%
+good so so so this uh is the
+path integral
+
+ align:start position:0%
+path integral
+ 
+
+ align:start position:0%
+path integral
+for for quantum mechanics with one
+
+ align:start position:0%
+for for quantum mechanics with one
+ 
+
+ align:start position:0%
+for for quantum mechanics with one
+degree of freedom
+
+ align:start position:0%
+degree of freedom
+ 
+
+ align:start position:0%
+degree of freedom
+so now we can just immediately
+
+ align:start position:0%
+so now we can just immediately
+ 
+
+ align:start position:0%
+so now we can just immediately
+generalize these two more the good
+
+ align:start position:0%
+generalize these two more the good
+ 
+
+ align:start position:0%
+generalize these two more the good
+freedom
+
+ align:start position:0%
+freedom
+ 
+
+ align:start position:0%
+freedom
+okay and there's nothing really change
+
+ align:start position:0%
+okay and there's nothing really change
+ 
+
+ align:start position:0%
+okay and there's nothing really change
+when you have more than one degree
+
+ align:start position:0%
+when you have more than one degree
+ 
+
+ align:start position:0%
+when you have more than one degree
+Freedom just integrate over so if you
+
+ align:start position:0%
+Freedom just integrate over so if you
+ 
+
+ align:start position:0%
+Freedom just integrate over so if you
+have say
+
+ align:start position:0%
+have say
+ 
+
+ align:start position:0%
+have say
+three particles then you just integrate
+
+ align:start position:0%
+three particles then you just integrate
+ 
+
+ align:start position:0%
+three particles then you just integrate
+the dx1 dx2 dx3 and then use the same
+
+ align:start position:0%
+the dx1 dx2 dx3 and then use the same
+ 
+
+ align:start position:0%
+the dx1 dx2 dx3 and then use the same
+action okay
+
+ align:start position:0%
+action okay
+ 
+
+ align:start position:0%
+action okay
+so you just uh uh straightforward
+
+ align:start position:0%
+so you just uh uh straightforward
+ 
+
+ align:start position:0%
+so you just uh uh straightforward
+generalize
+
+ align:start position:0%
+generalize
+ 
+
+ align:start position:0%
+generalize
+and then we can generalize to field
+
+ align:start position:0%
+and then we can generalize to field
+ 
+
+ align:start position:0%
+and then we can generalize to field
+Theory because Fields here we just take
+
+ align:start position:0%
+Theory because Fields here we just take
+ 
+
+ align:start position:0%
+Theory because Fields here we just take
+an alarm with equals freedom to Infinity
+
+ align:start position:0%
+an alarm with equals freedom to Infinity
+ 
+
+ align:start position:0%
+an alarm with equals freedom to Infinity
+okay so so we can now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to field Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case from the uh
+
+ align:start position:0%
+so in this case from the uh
+ 
+
+ align:start position:0%
+so in this case from the uh
+we just need to replace
+
+ align:start position:0%
+we just need to replace
+ 
+
+ align:start position:0%
+we just need to replace
+in the different places by so remember
+
+ align:start position:0%
+in the different places by so remember
+ 
+
+ align:start position:0%
+in the different places by so remember
+so the dynamical variable for single
+
+ align:start position:0%
+so the dynamical variable for single
+ 
+
+ align:start position:0%
+so the dynamical variable for single
+particle
+
+ align:start position:0%
+particle
+ 
+
+ align:start position:0%
+particle
+you have this operator
+
+ align:start position:0%
+you have this operator
+ 
+
+ align:start position:0%
+you have this operator
+and then when you go to field Theory
+
+ align:start position:0%
+and then when you go to field Theory
+ 
+
+ align:start position:0%
+and then when you go to field Theory
+the counterpart of this
+
+ align:start position:0%
+the counterpart of this
+ 
+
+ align:start position:0%
+the counterpart of this
+is the Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay is the
+
+ align:start position:0%
+okay is the
+ 
+
+ align:start position:0%
+okay is the
+is the Phi is the field variable
+
+ align:start position:0%
+is the Phi is the field variable
+ 
+
+ align:start position:0%
+is the Phi is the field variable
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+so this quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you go to field Theory
+
+ align:start position:0%
+when you go to field Theory
+ 
+
+ align:start position:0%
+when you go to field Theory
+the corresponding quantity
+
+ align:start position:0%
+the corresponding quantity
+ 
+
+ align:start position:0%
+the corresponding quantity
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+5X
+
+ align:start position:0%
+5X
+ 
+
+ align:start position:0%
+5X
+smt
+
+ align:start position:0%
+smt
+ 
+
+ align:start position:0%
+smt
+and the Phi X say Phi Prime X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and time T Prime
+
+ align:start position:0%
+and time T Prime
+ 
+
+ align:start position:0%
+and time T Prime
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again the way to think about this is
+
+ align:start position:0%
+again the way to think about this is
+ 
+
+ align:start position:0%
+again the way to think about this is
+just you should view this X as label
+
+ align:start position:0%
+just you should view this X as label
+ 
+
+ align:start position:0%
+just you should view this X as label
+and then this is just like I see we have
+
+ align:start position:0%
+and then this is just like I see we have
+ 
+
+ align:start position:0%
+and then this is just like I see we have
+infinite number of of positions okay I
+
+ align:start position:0%
+infinite number of of positions okay I
+ 
+
+ align:start position:0%
+infinite number of of positions okay I
+just have infinite number five which are
+
+ align:start position:0%
+just have infinite number five which are
+ 
+
+ align:start position:0%
+just have infinite number five which are
+eigenvalues of this operator at time T
+
+ align:start position:0%
+eigenvalues of this operator at time T
+ 
+
+ align:start position:0%
+eigenvalues of this operator at time T
+at T Prime and similarly here okay
+
+ align:start position:0%
+at T Prime and similarly here okay
+ 
+
+ align:start position:0%
+at T Prime and similarly here okay
+and the um
+
+ align:start position:0%
+and the um
+ 
+
+ align:start position:0%
+and the um
+so so again he this one you can write it
+
+ align:start position:0%
+so so again he this one you can write it
+ 
+
+ align:start position:0%
+so so again he this one you can write it
+in the form
+
+ align:start position:0%
+in the form
+ 
+
+ align:start position:0%
+in the form
+in terms of the position eigen state so
+
+ align:start position:0%
+in terms of the position eigen state so
+ 
+
+ align:start position:0%
+in terms of the position eigen state so
+this is the position I can stay in field
+
+ align:start position:0%
+this is the position I can stay in field
+ 
+
+ align:start position:0%
+this is the position I can stay in field
+Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is the position I can say
+
+ align:start position:0%
+okay so this is the position I can say
+ 
+
+ align:start position:0%
+okay so this is the position I can say
+in field Theory and then we can use the
+
+ align:start position:0%
+in field Theory and then we can use the
+ 
+
+ align:start position:0%
+in field Theory and then we can use the
+same Technique we discussed last time
+
+ align:start position:0%
+same Technique we discussed last time
+ 
+
+ align:start position:0%
+same Technique we discussed last time
+you just split this into many many
+
+ align:start position:0%
+you just split this into many many
+ 
+
+ align:start position:0%
+you just split this into many many
+infinitesimal pieces by split in the
+
+ align:start position:0%
+infinitesimal pieces by split in the
+ 
+
+ align:start position:0%
+infinitesimal pieces by split in the
+time interval from T Prime to T
+
+ align:start position:0%
+time interval from T Prime to T
+ 
+
+ align:start position:0%
+time interval from T Prime to T
+and split into many pieces and then just
+
+ align:start position:0%
+and split into many pieces and then just
+ 
+
+ align:start position:0%
+and split into many pieces and then just
+do it over and over and insert the
+
+ align:start position:0%
+do it over and over and insert the
+ 
+
+ align:start position:0%
+do it over and over and insert the
+complete side of state of Phi
+
+ align:start position:0%
+complete side of state of Phi
+ 
+
+ align:start position:0%
+complete side of state of Phi
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then I just uh so h
+
+ align:start position:0%
+and then I just uh so h
+ 
+
+ align:start position:0%
+and then I just uh so h
+is now
+
+ align:start position:0%
+is now
+ 
+
+ align:start position:0%
+is now
+of course it's the field counterpart of
+
+ align:start position:0%
+of course it's the field counterpart of
+ 
+
+ align:start position:0%
+of course it's the field counterpart of
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+just H equal to but the details of this
+
+ align:start position:0%
+just H equal to but the details of this
+ 
+
+ align:start position:0%
+just H equal to but the details of this
+does not matter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+say say this is the hamiltonian you can
+
+ align:start position:0%
+say say this is the hamiltonian you can
+ 
+
+ align:start position:0%
+say say this is the hamiltonian you can
+just insert this into here and then you
+
+ align:start position:0%
+just insert this into here and then you
+ 
+
+ align:start position:0%
+just insert this into here and then you
+just repeat the same procedure okay just
+
+ align:start position:0%
+just repeat the same procedure okay just
+ 
+
+ align:start position:0%
+just repeat the same procedure okay just
+keep in mind
+
+ align:start position:0%
+keep in mind
+ 
+
+ align:start position:0%
+keep in mind
+now you just have infinite number of
+
+ align:start position:0%
+now you just have infinite number of
+ 
+
+ align:start position:0%
+now you just have infinite number of
+this freedom
+
+ align:start position:0%
+this freedom
+ 
+
+ align:start position:0%
+this freedom
+okay that's the only difference we just
+
+ align:start position:0%
+okay that's the only difference we just
+ 
+
+ align:start position:0%
+okay that's the only difference we just
+your rotation become a little bit more
+
+ align:start position:0%
+your rotation become a little bit more
+ 
+
+ align:start position:0%
+your rotation become a little bit more
+complicated
+
+ align:start position:0%
+complicated
+ 
+
+ align:start position:0%
+complicated
+but if you keep a very clear mind
+
+ align:start position:0%
+but if you keep a very clear mind
+ 
+
+ align:start position:0%
+but if you keep a very clear mind
+with the correspondence with a single
+
+ align:start position:0%
+with the correspondence with a single
+ 
+
+ align:start position:0%
+with the correspondence with a single
+particle case
+
+ align:start position:0%
+particle case
+ 
+
+ align:start position:0%
+particle case
+okay then everything is the same okay
+
+ align:start position:0%
+okay then everything is the same okay
+ 
+
+ align:start position:0%
+okay then everything is the same okay
+just if you understand how to translate
+
+ align:start position:0%
+just if you understand how to translate
+ 
+
+ align:start position:0%
+just if you understand how to translate
+the notation here to the rotation here
+
+ align:start position:0%
+the notation here to the rotation here
+ 
+
+ align:start position:0%
+the notation here to the rotation here
+then everything is just exactly the same
+
+ align:start position:0%
+then everything is just exactly the same
+ 
+
+ align:start position:0%
+then everything is just exactly the same
+okay just everything goes through so I
+
+ align:start position:0%
+okay just everything goes through so I
+ 
+
+ align:start position:0%
+okay just everything goes through so I
+will not repeat that procedure
+
+ align:start position:0%
+will not repeat that procedure
+ 
+
+ align:start position:0%
+will not repeat that procedure
+and now you just find this quantity okay
+
+ align:start position:0%
+and now you just find this quantity okay
+ 
+
+ align:start position:0%
+and now you just find this quantity okay
+then again we can write this in terms of
+
+ align:start position:0%
+then again we can write this in terms of
+ 
+
+ align:start position:0%
+then again we can write this in terms of
+path integral
+
+ align:start position:0%
+path integral
+ 
+
+ align:start position:0%
+path integral
+so now this can be written as
+
+ align:start position:0%
+so now this can be written as
+ 
+
+ align:start position:0%
+so now this can be written as
+you can pass integral Phi now you
+
+ align:start position:0%
+you can pass integral Phi now you
+ 
+
+ align:start position:0%
+you can pass integral Phi now you
+integrate over all possible
+
+ align:start position:0%
+integrate over all possible
+ 
+
+ align:start position:0%
+integrate over all possible
+configuration of Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is the boundary condition
+
+ align:start position:0%
+which is the boundary condition
+ 
+
+ align:start position:0%
+which is the boundary condition
+Phi T Prime x equal to 5 Prime X
+
+ align:start position:0%
+Phi T Prime x equal to 5 Prime X
+ 
+
+ align:start position:0%
+Phi T Prime x equal to 5 Prime X
+and Phi TX
+
+ align:start position:0%
+and Phi TX
+ 
+
+ align:start position:0%
+and Phi TX
+equal to 5X
+
+ align:start position:0%
+equal to 5X
+ 
+
+ align:start position:0%
+equal to 5X
+and again you just have exponential
+
+ align:start position:0%
+and again you just have exponential
+ 
+
+ align:start position:0%
+and again you just have exponential
+is 5.
+
+ align:start position:0%
+is 5.
+ 
+
+ align:start position:0%
+is 5.
+and S is its action for Phi
+
+ align:start position:0%
+and S is its action for Phi
+ 
+
+ align:start position:0%
+and S is its action for Phi
+so now the s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in this case yeah this is the
+
+ align:start position:0%
+so in this case yeah this is the
+ 
+
+ align:start position:0%
+so in this case yeah this is the
+integration of the language density and
+
+ align:start position:0%
+integration of the language density and
+ 
+
+ align:start position:0%
+integration of the language density and
+L is
+
+ align:start position:0%
+L is
+ 
+
+ align:start position:0%
+L is
+one half
+
+ align:start position:0%
+one half
+ 
+
+ align:start position:0%
+one half
+yeah it just what we wrote down before
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay some potential Phi okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so for any scalar field still these
+
+ align:start position:0%
+so so for any scalar field still these
+ 
+
+ align:start position:0%
+so so for any scalar field still these
+just work identically
+
+ align:start position:0%
+just work identically
+ 
+
+ align:start position:0%
+just work identically
+okay and again you just get the
+
+ align:start position:0%
+okay and again you just get the
+ 
+
+ align:start position:0%
+okay and again you just get the
+integration over the lagrangian and
+
+ align:start position:0%
+integration over the lagrangian and
+ 
+
+ align:start position:0%
+integration over the lagrangian and
+which is the become full integral of the
+
+ align:start position:0%
+which is the become full integral of the
+ 
+
+ align:start position:0%
+which is the become full integral of the
+logon intensity okay
+
+ align:start position:0%
+logon intensity okay
+ 
+
+ align:start position:0%
+logon intensity okay
+any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so whenever you get confused
+
+ align:start position:0%
+so whenever you get confused
+ 
+
+ align:start position:0%
+so whenever you get confused
+about the uh whenever you get confused
+
+ align:start position:0%
+about the uh whenever you get confused
+ 
+
+ align:start position:0%
+about the uh whenever you get confused
+about passing the going Fields Theory
+
+ align:start position:0%
+about passing the going Fields Theory
+ 
+
+ align:start position:0%
+about passing the going Fields Theory
+then try to translate
+
+ align:start position:0%
+then try to translate
+ 
+
+ align:start position:0%
+then try to translate
+into a a the language of a single
+
+ align:start position:0%
+into a a the language of a single
+ 
+
+ align:start position:0%
+into a a the language of a single
+particle okay but by doing this kind of
+
+ align:start position:0%
+particle okay but by doing this kind of
+ 
+
+ align:start position:0%
+particle okay but by doing this kind of
+replacement and then you will be able to
+
+ align:start position:0%
+replacement and then you will be able to
+ 
+
+ align:start position:0%
+replacement and then you will be able to
+settle your problem
+
+ align:start position:0%
+settle your problem
+ 
+
+ align:start position:0%
+settle your problem
+and then whenever you get confused about
+
+ align:start position:0%
+and then whenever you get confused about
+ 
+
+ align:start position:0%
+and then whenever you get confused about
+the passing the goal in this quantum
+
+ align:start position:0%
+the passing the goal in this quantum
+ 
+
+ align:start position:0%
+the passing the goal in this quantum
+mechanics
+
+ align:start position:0%
+mechanics
+ 
+
+ align:start position:0%
+mechanics
+then just retail reduce it about about
+
+ align:start position:0%
+then just retail reduce it about about
+ 
+
+ align:start position:0%
+then just retail reduce it about about
+uh reduce it by finally dimensional
+
+ align:start position:0%
+uh reduce it by finally dimensional
+ 
+
+ align:start position:0%
+uh reduce it by finally dimensional
+integral and then you should be able to
+
+ align:start position:0%
+integral and then you should be able to
+ 
+
+ align:start position:0%
+integral and then you should be able to
+understand okay just just always uh
+
+ align:start position:0%
+understand okay just just always uh
+ 
+
+ align:start position:0%
+understand okay just just always uh
+reduce it to the simple case and often
+
+ align:start position:0%
+reduce it to the simple case and often
+ 
+
+ align:start position:0%
+reduce it to the simple case and often
+your confusion can be understood in that
+
+ align:start position:0%
+your confusion can be understood in that
+ 
+
+ align:start position:0%
+your confusion can be understood in that
+simpler case okay
+
+ align:start position:0%
+simpler case okay
+ 
+
+ align:start position:0%
+simpler case okay
+and uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so now let me explain a little bit
+
+ align:start position:0%
+good so now let me explain a little bit
+ 
+
+ align:start position:0%
+good so now let me explain a little bit
+what what this rotation means
+
+ align:start position:0%
+what what this rotation means
+ 
+
+ align:start position:0%
+what what this rotation means
+okay so so so this says in words means
+
+ align:start position:0%
+okay so so so this says in words means
+ 
+
+ align:start position:0%
+okay so so so this says in words means
+you integrate over all possible
+
+ align:start position:0%
+you integrate over all possible
+ 
+
+ align:start position:0%
+you integrate over all possible
+configurations of Phi
+
+ align:start position:0%
+configurations of Phi
+ 
+
+ align:start position:0%
+configurations of Phi
+between T and T Prime
+
+ align:start position:0%
+between T and T Prime
+ 
+
+ align:start position:0%
+between T and T Prime
+and and with the uh the final uh the
+
+ align:start position:0%
+and and with the uh the final uh the
+ 
+
+ align:start position:0%
+and and with the uh the final uh the
+final configuration the the initial
+
+ align:start position:0%
+final configuration the the initial
+ 
+
+ align:start position:0%
+final configuration the the initial
+configuration to be Phi Prime and the
+
+ align:start position:0%
+configuration to be Phi Prime and the
+ 
+
+ align:start position:0%
+configuration to be Phi Prime and the
+final configuration to be five okay f i
+
+ align:start position:0%
+final configuration to be five okay f i
+ 
+
+ align:start position:0%
+final configuration to be five okay f i
+x and the initial TV 5 Prime X Okay so
+
+ align:start position:0%
+x and the initial TV 5 Prime X Okay so
+ 
+
+ align:start position:0%
+x and the initial TV 5 Prime X Okay so
+so so let me just say a previously txt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you think about it in terms of
+
+ align:start position:0%
+if you think about it in terms of
+ 
+
+ align:start position:0%
+if you think about it in terms of
+discrete case corresponding to you just
+
+ align:start position:0%
+discrete case corresponding to you just
+ 
+
+ align:start position:0%
+discrete case corresponding to you just
+sum take the product of all the I
+
+ align:start position:0%
+sum take the product of all the I
+ 
+
+ align:start position:0%
+sum take the product of all the I
+at different time with DX I okay so in
+
+ align:start position:0%
+at different time with DX I okay so in
+ 
+
+ align:start position:0%
+at different time with DX I okay so in
+the Continuum limit it's like you just
+
+ align:start position:0%
+the Continuum limit it's like you just
+ 
+
+ align:start position:0%
+the Continuum limit it's like you just
+take the product of all possible value
+
+ align:start position:0%
+take the product of all possible value
+ 
+
+ align:start position:0%
+take the product of all possible value
+of T and then the integrate over the
+
+ align:start position:0%
+of T and then the integrate over the
+ 
+
+ align:start position:0%
+of T and then the integrate over the
+value of x at that particular value of T
+
+ align:start position:0%
+value of x at that particular value of T
+ 
+
+ align:start position:0%
+value of x at that particular value of T
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the meaning of this txt which
+
+ align:start position:0%
+so that's the meaning of this txt which
+ 
+
+ align:start position:0%
+so that's the meaning of this txt which
+is yeah up to a pre-factor
+
+ align:start position:0%
+is yeah up to a pre-factor
+ 
+
+ align:start position:0%
+is yeah up to a pre-factor
+corresponding to that so similarly Phi
+
+ align:start position:0%
+corresponding to that so similarly Phi
+ 
+
+ align:start position:0%
+corresponding to that so similarly Phi
+is the same thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now remember 5x is the now become the
+
+ align:start position:0%
+so now remember 5x is the now become the
+ 
+
+ align:start position:0%
+so now remember 5x is the now become the
+dynamical variable so so this now become
+
+ align:start position:0%
+dynamical variable so so this now become
+ 
+
+ align:start position:0%
+dynamical variable so so this now become
+sum over
+
+ align:start position:0%
+sum over
+ 
+
+ align:start position:0%
+sum over
+take product over t
+
+ align:start position:0%
+take product over t
+ 
+
+ align:start position:0%
+take product over t
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+oh yeah no no first you think of take
+
+ align:start position:0%
+oh yeah no no first you think of take
+ 
+
+ align:start position:0%
+oh yeah no no first you think of take
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+over X so this is a label of X you have
+
+ align:start position:0%
+over X so this is a label of X you have
+ 
+
+ align:start position:0%
+over X so this is a label of X you have
+so so X are the labels of Phi and you
+
+ align:start position:0%
+so so X are the labels of Phi and you
+ 
+
+ align:start position:0%
+so so X are the labels of Phi and you
+take all possible value of x
+
+ align:start position:0%
+take all possible value of x
+ 
+
+ align:start position:0%
+take all possible value of x
+and then then each of them is just like
+
+ align:start position:0%
+and then then each of them is just like
+ 
+
+ align:start position:0%
+and then then each of them is just like
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so just like
+
+ align:start position:0%
+okay so so just like
+ 
+
+ align:start position:0%
+okay so so just like
+you have such so many different
+
+ align:start position:0%
+you have such so many different
+ 
+
+ align:start position:0%
+you have such so many different
+variables
+
+ align:start position:0%
+variables
+ 
+
+ align:start position:0%
+variables
+each X label one or a degrees Freedom
+
+ align:start position:0%
+each X label one or a degrees Freedom
+ 
+
+ align:start position:0%
+each X label one or a degrees Freedom
+okay and then you have Phi T and now and
+
+ align:start position:0%
+okay and then you have Phi T and now and
+ 
+
+ align:start position:0%
+okay and then you have Phi T and now and
+now and then you use this one then you
+
+ align:start position:0%
+now and then you use this one then you
+ 
+
+ align:start position:0%
+now and then you use this one then you
+have
+
+ align:start position:0%
+have
+ 
+
+ align:start position:0%
+have
+p x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so is it clear what this equation means
+
+ align:start position:0%
+so is it clear what this equation means
+ 
+
+ align:start position:0%
+so is it clear what this equation means
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tells you
+
+ align:start position:0%
+tells you
+ 
+
+ align:start position:0%
+tells you
+that you have many many different the
+
+ align:start position:0%
+that you have many many different the
+ 
+
+ align:start position:0%
+that you have many many different the
+good freedom so this step is just
+
+ align:start position:0%
+good freedom so this step is just
+ 
+
+ align:start position:0%
+good freedom so this step is just
+enumerate you all possible the good
+
+ align:start position:0%
+enumerate you all possible the good
+ 
+
+ align:start position:0%
+enumerate you all possible the good
+Freedom which are labeled by X
+
+ align:start position:0%
+Freedom which are labeled by X
+ 
+
+ align:start position:0%
+Freedom which are labeled by X
+just like your standard integral if you
+
+ align:start position:0%
+just like your standard integral if you
+ 
+
+ align:start position:0%
+just like your standard integral if you
+have five dimensional integral and each
+
+ align:start position:0%
+have five dimensional integral and each
+ 
+
+ align:start position:0%
+have five dimensional integral and each
+in and then you just have a product of
+
+ align:start position:0%
+in and then you just have a product of
+ 
+
+ align:start position:0%
+in and then you just have a product of
+five different variables okay here we
+
+ align:start position:0%
+five different variables okay here we
+ 
+
+ align:start position:0%
+five different variables okay here we
+have all different possible value of x
+
+ align:start position:0%
+have all different possible value of x
+ 
+
+ align:start position:0%
+have all different possible value of x
+variables and that variable is a
+
+ align:start position:0%
+variables and that variable is a
+ 
+
+ align:start position:0%
+variables and that variable is a
+function of t
+
+ align:start position:0%
+function of t
+ 
+
+ align:start position:0%
+function of t
+and then now we use this equation and
+
+ align:start position:0%
+and then now we use this equation and
+ 
+
+ align:start position:0%
+and then now we use this equation and
+not each of them
+
+ align:start position:0%
+not each of them
+ 
+
+ align:start position:0%
+not each of them
+is like here okay and then and then now
+
+ align:start position:0%
+is like here okay and then and then now
+ 
+
+ align:start position:0%
+is like here okay and then and then now
+you have the product the all possible
+
+ align:start position:0%
+you have the product the all possible
+ 
+
+ align:start position:0%
+you have the product the all possible
+value of T and then you integrate then
+
+ align:start position:0%
+value of T and then you integrate then
+ 
+
+ align:start position:0%
+value of T and then you integrate then
+all possible values of Phi say at point
+
+ align:start position:0%
+all possible values of Phi say at point
+ 
+
+ align:start position:0%
+all possible values of Phi say at point
+x and the T
+
+ align:start position:0%
+x and the T
+ 
+
+ align:start position:0%
+x and the T
+okay but remember T always is between t
+
+ align:start position:0%
+okay but remember T always is between t
+ 
+
+ align:start position:0%
+okay but remember T always is between t
+Prime and T okay
+
+ align:start position:0%
+Prime and T okay
+ 
+
+ align:start position:0%
+Prime and T okay
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you mean here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah here I just write it in the
+
+ align:start position:0%
+yeah here I just write it in the
+ 
+
+ align:start position:0%
+yeah here I just write it in the
+Continuum form
+
+ align:start position:0%
+Continuum form
+ 
+
+ align:start position:0%
+Continuum form
+so here label it by TI
+
+ align:start position:0%
+so here label it by TI
+ 
+
+ align:start position:0%
+so here label it by TI
+inside each location TI I have dxi in
+
+ align:start position:0%
+inside each location TI I have dxi in
+ 
+
+ align:start position:0%
+inside each location TI I have dxi in
+that form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but if I go to Continuum limit and go to
+
+ align:start position:0%
+but if I go to Continuum limit and go to
+ 
+
+ align:start position:0%
+but if I go to Continuum limit and go to
+infinite limit essentially at each point
+
+ align:start position:0%
+infinite limit essentially at each point
+ 
+
+ align:start position:0%
+infinite limit essentially at each point
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+I have integration over X
+
+ align:start position:0%
+I have integration over X
+ 
+
+ align:start position:0%
+I have integration over X
+and and so that's roughly the yeah uh uh
+
+ align:start position:0%
+and and so that's roughly the yeah uh uh
+ 
+
+ align:start position:0%
+and and so that's roughly the yeah uh uh
+uh the Continuum of a form of that and
+
+ align:start position:0%
+uh the Continuum of a form of that and
+ 
+
+ align:start position:0%
+uh the Continuum of a form of that and
+and here it's similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so so so once you have load this
+
+ align:start position:0%
+good so so so once you have load this
+ 
+
+ align:start position:0%
+good so so so once you have load this
+trick
+
+ align:start position:0%
+trick
+ 
+
+ align:start position:0%
+trick
+to the reduction and I think you will be
+
+ align:start position:0%
+to the reduction and I think you will be
+ 
+
+ align:start position:0%
+to the reduction and I think you will be
+able to settle all your confusions about
+
+ align:start position:0%
+able to settle all your confusions about
+ 
+
+ align:start position:0%
+able to settle all your confusions about
+these definitions okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so other than that
+
+ align:start position:0%
+so other than that
+ 
+
+ align:start position:0%
+so other than that
+other than this additional label X
+
+ align:start position:0%
+other than this additional label X
+ 
+
+ align:start position:0%
+other than this additional label X
+okay so other than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+additional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+label
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah because as you called here label X
+
+ align:start position:0%
+yeah because as you called here label X
+ 
+
+ align:start position:0%
+yeah because as you called here label X
+so the field series path integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm gonna fall off
+
+ align:start position:0%
+I'm gonna fall off
+ 
+
+ align:start position:0%
+I'm gonna fall off
+a scalar field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+identical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to that in-ground mechanics okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to emphasize this point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here actually you can Define this
+
+ align:start position:0%
+so here actually you can Define this
+ 
+
+ align:start position:0%
+so here actually you can Define this
+General it doesn't matter what your V is
+
+ align:start position:0%
+General it doesn't matter what your V is
+ 
+
+ align:start position:0%
+General it doesn't matter what your V is
+okay you can choose whatever V you want
+
+ align:start position:0%
+okay you can choose whatever V you want
+ 
+
+ align:start position:0%
+okay you can choose whatever V you want
+uh the story does not change
+
+ align:start position:0%
+uh the story does not change
+ 
+
+ align:start position:0%
+uh the story does not change
+uh just like when we do the uh when we
+
+ align:start position:0%
+uh just like when we do the uh when we
+ 
+
+ align:start position:0%
+uh just like when we do the uh when we
+do the single particle case it doesn't
+
+ align:start position:0%
+do the single particle case it doesn't
+ 
+
+ align:start position:0%
+do the single particle case it doesn't
+matter what this V is okay you can
+
+ align:start position:0%
+matter what this V is okay you can
+ 
+
+ align:start position:0%
+matter what this V is okay you can
+choose arbitrary three you want
+
+ align:start position:0%
+choose arbitrary three you want
+ 
+
+ align:start position:0%
+choose arbitrary three you want
+but if we choose V to be
+
+ align:start position:0%
+but if we choose V to be
+ 
+
+ align:start position:0%
+but if we choose V to be
+when V is the um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the free Theory
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then in this case of course a
+
+ align:start position:0%
+then in this case of course a
+ 
+
+ align:start position:0%
+then in this case of course a
+particularly simple and then in this
+
+ align:start position:0%
+particularly simple and then in this
+ 
+
+ align:start position:0%
+particularly simple and then in this
+case the the path integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+causing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so again gaussing are we allowed to
+
+ align:start position:0%
+so again gaussing are we allowed to
+ 
+
+ align:start position:0%
+so again gaussing are we allowed to
+write it again so so again that formula
+
+ align:start position:0%
+write it again so so again that formula
+ 
+
+ align:start position:0%
+write it again so so again that formula
+and the uh this formula applies
+
+ align:start position:0%
+and the uh this formula applies
+ 
+
+ align:start position:0%
+and the uh this formula applies
+just this case in a more complicated
+
+ align:start position:0%
+just this case in a more complicated
+ 
+
+ align:start position:0%
+just this case in a more complicated
+space a k is operating in a more
+
+ align:start position:0%
+space a k is operating in a more
+ 
+
+ align:start position:0%
+space a k is operating in a more
+complicated space okay so now you not
+
+ align:start position:0%
+complicated space okay so now you not
+ 
+
+ align:start position:0%
+complicated space okay so now you not
+only have the space of t but you also
+
+ align:start position:0%
+only have the space of t but you also
+ 
+
+ align:start position:0%
+only have the space of t but you also
+have the space of X okay
+
+ align:start position:0%
+have the space of X okay
+ 
+
+ align:start position:0%
+have the space of X okay
+but once you generalize to some space or
+
+ align:start position:0%
+but once you generalize to some space or
+ 
+
+ align:start position:0%
+but once you generalize to some space or
+functions doesn't matter this function
+
+ align:start position:0%
+functions doesn't matter this function
+ 
+
+ align:start position:0%
+functions doesn't matter this function
+become more complicated okay and uh so
+
+ align:start position:0%
+become more complicated okay and uh so
+ 
+
+ align:start position:0%
+become more complicated okay and uh so
+conceptually they're the same okay
+
+ align:start position:0%
+conceptually they're the same okay
+ 
+
+ align:start position:0%
+conceptually they're the same okay
+conceptually the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+so now for the for interacting Theory
+
+ align:start position:0%
+so now for the for interacting Theory
+ 
+
+ align:start position:0%
+so now for the for interacting Theory
+then essentially
+
+ align:start position:0%
+then essentially
+ 
+
+ align:start position:0%
+then essentially
+then the then the quantum filter will
+
+ align:start position:0%
+then the then the quantum filter will
+ 
+
+ align:start position:0%
+then the then the quantum filter will
+then reduce to two in this path integral
+
+ align:start position:0%
+then reduce to two in this path integral
+ 
+
+ align:start position:0%
+then reduce to two in this path integral
+okay if you don't know how to do this
+
+ align:start position:0%
+okay if you don't know how to do this
+ 
+
+ align:start position:0%
+okay if you don't know how to do this
+part integral and then then essentially
+
+ align:start position:0%
+part integral and then then essentially
+ 
+
+ align:start position:0%
+part integral and then then essentially
+you learn how to solve the theory okay
+
+ align:start position:0%
+you learn how to solve the theory okay
+ 
+
+ align:start position:0%
+you learn how to solve the theory okay
+you know how to solve the theory
+
+ align:start position:0%
+you know how to solve the theory
+ 
+
+ align:start position:0%
+you know how to solve the theory
+and uh so as I said in the free Siri
+
+ align:start position:0%
+and uh so as I said in the free Siri
+ 
+
+ align:start position:0%
+and uh so as I said in the free Siri
+case it's essentially reduced to
+
+ align:start position:0%
+case it's essentially reduced to
+ 
+
+ align:start position:0%
+case it's essentially reduced to
+gaussian integral then everything this
+
+ align:start position:0%
+gaussian integral then everything this
+ 
+
+ align:start position:0%
+gaussian integral then everything this
+is simple and which we will go back to
+
+ align:start position:0%
+is simple and which we will go back to
+ 
+
+ align:start position:0%
+is simple and which we will go back to
+discuss that they may you know live in
+
+ align:start position:0%
+discuss that they may you know live in
+ 
+
+ align:start position:0%
+discuss that they may you know live in
+more detail later
+
+ align:start position:0%
+more detail later
+ 
+
+ align:start position:0%
+more detail later
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+now let's just think a little bit uh uh
+
+ align:start position:0%
+now let's just think a little bit uh uh
+ 
+
+ align:start position:0%
+now let's just think a little bit uh uh
+how to treat the interacting case okay
+
+ align:start position:0%
+how to treat the interacting case okay
+ 
+
+ align:start position:0%
+how to treat the interacting case okay
+so so recall our goal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to compute this object
+
+ align:start position:0%
+is to compute this object
+ 
+
+ align:start position:0%
+is to compute this object
+the vacuum expectation value of time
+
+ align:start position:0%
+the vacuum expectation value of time
+ 
+
+ align:start position:0%
+the vacuum expectation value of time
+ordered correlation functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay we want to compute this object okay
+
+ align:start position:0%
+okay we want to compute this object okay
+ 
+
+ align:start position:0%
+okay we want to compute this object okay
+so so now we will discuss how we use
+
+ align:start position:0%
+so so now we will discuss how we use
+ 
+
+ align:start position:0%
+so so now we will discuss how we use
+passenger going to compute this object
+
+ align:start position:0%
+passenger going to compute this object
+ 
+
+ align:start position:0%
+passenger going to compute this object
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so before doing that
+
+ align:start position:0%
+okay so before doing that
+ 
+
+ align:start position:0%
+okay so before doing that
+let's first try to do this
+
+ align:start position:0%
+let's first try to do this
+ 
+
+ align:start position:0%
+let's first try to do this
+in uh um
+
+ align:start position:0%
+in uh um
+ 
+
+ align:start position:0%
+in uh um
+so so before doing that let's first
+
+ align:start position:0%
+so so before doing that let's first
+ 
+
+ align:start position:0%
+so so before doing that let's first
+discuss how to do this in quantum
+
+ align:start position:0%
+discuss how to do this in quantum
+ 
+
+ align:start position:0%
+discuss how to do this in quantum
+mechanics okay before doing this in
+
+ align:start position:0%
+mechanics okay before doing this in
+ 
+
+ align:start position:0%
+mechanics okay before doing this in
+field Theory and before we can just
+
+ align:start position:0%
+field Theory and before we can just
+ 
+
+ align:start position:0%
+field Theory and before we can just
+first understand how we compute the
+
+ align:start position:0%
+first understand how we compute the
+ 
+
+ align:start position:0%
+first understand how we compute the
+similar object in quantum mechanics and
+
+ align:start position:0%
+similar object in quantum mechanics and
+ 
+
+ align:start position:0%
+similar object in quantum mechanics and
+once we understand how to do that again
+
+ align:start position:0%
+once we understand how to do that again
+ 
+
+ align:start position:0%
+once we understand how to do that again
+the generation to field series will be
+
+ align:start position:0%
+the generation to field series will be
+ 
+
+ align:start position:0%
+the generation to field series will be
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good so so first we talk about
+
+ align:start position:0%
+good so so first we talk about
+ 
+
+ align:start position:0%
+good so so first we talk about
+time ordered
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in quantum mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we will be introducing a a number of
+
+ align:start position:0%
+so we will be introducing a a number of
+ 
+
+ align:start position:0%
+so we will be introducing a a number of
+tricks
+
+ align:start position:0%
+tricks
+ 
+
+ align:start position:0%
+tricks
+and those tricks will then take over
+
+ align:start position:0%
+and those tricks will then take over
+ 
+
+ align:start position:0%
+and those tricks will then take over
+to field CV okay
+
+ align:start position:0%
+to field CV okay
+ 
+
+ align:start position:0%
+to field CV okay
+then we'll be carried over to field
+
+ align:start position:0%
+then we'll be carried over to field
+ 
+
+ align:start position:0%
+then we'll be carried over to field
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+so again let's just consider this system
+
+ align:start position:0%
+so again let's just consider this system
+ 
+
+ align:start position:0%
+so again let's just consider this system
+okay let's consider system like this
+
+ align:start position:0%
+okay let's consider system like this
+ 
+
+ align:start position:0%
+okay let's consider system like this
+just visit the lagranging of this phone
+
+ align:start position:0%
+just visit the lagranging of this phone
+ 
+
+ align:start position:0%
+just visit the lagranging of this phone
+okay just one particle theory okay
+
+ align:start position:0%
+okay just one particle theory okay
+ 
+
+ align:start position:0%
+okay just one particle theory okay
+and then the analog
+
+ align:start position:0%
+and then the analog
+ 
+
+ align:start position:0%
+and then the analog
+the analog of this object
+
+ align:start position:0%
+the analog of this object
+ 
+
+ align:start position:0%
+the analog of this object
+is this object
+
+ align:start position:0%
+is this object
+ 
+
+ align:start position:0%
+is this object
+isn't it called GN
+
+ align:start position:0%
+isn't it called GN
+ 
+
+ align:start position:0%
+isn't it called GN
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so let's call the zero is the vacuum of
+
+ align:start position:0%
+so let's call the zero is the vacuum of
+ 
+
+ align:start position:0%
+so let's call the zero is the vacuum of
+the field Theory oh of this quantum
+
+ align:start position:0%
+the field Theory oh of this quantum
+ 
+
+ align:start position:0%
+the field Theory oh of this quantum
+mechanical system and then you have time
+
+ align:start position:0%
+mechanical system and then you have time
+ 
+
+ align:start position:0%
+mechanical system and then you have time
+ordered
+
+ align:start position:0%
+ordered
+ 
+
+ align:start position:0%
+ordered
+and then you have xt1
+
+ align:start position:0%
+and then you have xt1
+ 
+
+ align:start position:0%
+and then you have xt1
+because the dynamic variable here for
+
+ align:start position:0%
+because the dynamic variable here for
+ 
+
+ align:start position:0%
+because the dynamic variable here for
+for quantum mechanics just X
+
+ align:start position:0%
+for quantum mechanics just X
+ 
+
+ align:start position:0%
+for quantum mechanics just X
+and x t n a different time
+
+ align:start position:0%
+and x t n a different time
+ 
+
+ align:start position:0%
+and x t n a different time
+and then yeah okay so we we want to
+
+ align:start position:0%
+and then yeah okay so we we want to
+ 
+
+ align:start position:0%
+and then yeah okay so we we want to
+compute such object uh uh uh in quantum
+
+ align:start position:0%
+compute such object uh uh uh in quantum
+ 
+
+ align:start position:0%
+compute such object uh uh uh in quantum
+mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so our goal
+
+ align:start position:0%
+so so our goal
+ 
+
+ align:start position:0%
+so so our goal
+is to develop techniques yeah so you
+
+ align:start position:0%
+is to develop techniques yeah so you
+ 
+
+ align:start position:0%
+is to develop techniques yeah so you
+should imagine all these are operators
+
+ align:start position:0%
+should imagine all these are operators
+ 
+
+ align:start position:0%
+should imagine all these are operators
+okay all these operators
+
+ align:start position:0%
+okay all these operators
+ 
+
+ align:start position:0%
+okay all these operators
+so our goal is to develop type links to
+
+ align:start position:0%
+so our goal is to develop type links to
+ 
+
+ align:start position:0%
+so our goal is to develop type links to
+calculate this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+so before doing that
+
+ align:start position:0%
+so before doing that
+ 
+
+ align:start position:0%
+so before doing that
+let's first understand how to unders how
+
+ align:start position:0%
+let's first understand how to unders how
+ 
+
+ align:start position:0%
+let's first understand how to unders how
+to do this time ordering
+
+ align:start position:0%
+to do this time ordering
+ 
+
+ align:start position:0%
+to do this time ordering
+uh uh using using pass integral okay how
+
+ align:start position:0%
+uh uh using using pass integral okay how
+ 
+
+ align:start position:0%
+uh uh using using pass integral okay how
+do you do the time ordering partner
+
+ align:start position:0%
+do you do the time ordering partner
+ 
+
+ align:start position:0%
+do you do the time ordering partner
+so before I do that do you have any
+
+ align:start position:0%
+so before I do that do you have any
+ 
+
+ align:start position:0%
+so before I do that do you have any
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so it turns out actually past integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+some of the natural the most natural
+
+ align:start position:0%
+some of the natural the most natural
+ 
+
+ align:start position:0%
+some of the natural the most natural
+object to think about such kind of time
+
+ align:start position:0%
+object to think about such kind of time
+ 
+
+ align:start position:0%
+object to think about such kind of time
+all the correlation functions okay and
+
+ align:start position:0%
+all the correlation functions okay and
+ 
+
+ align:start position:0%
+all the correlation functions okay and
+we will see in a minute okay the the
+
+ align:start position:0%
+we will see in a minute okay the the
+ 
+
+ align:start position:0%
+we will see in a minute okay the the
+part in the exactly the most natural
+
+ align:start position:0%
+part in the exactly the most natural
+ 
+
+ align:start position:0%
+part in the exactly the most natural
+thing to uh the most natural framework
+
+ align:start position:0%
+thing to uh the most natural framework
+ 
+
+ align:start position:0%
+thing to uh the most natural framework
+to think about this kind of order
+
+ align:start position:0%
+to think about this kind of order
+ 
+
+ align:start position:0%
+to think about this kind of order
+correlation functions so before doing
+
+ align:start position:0%
+correlation functions so before doing
+ 
+
+ align:start position:0%
+correlation functions so before doing
+that let's consider one simple example
+
+ align:start position:0%
+that let's consider one simple example
+ 
+
+ align:start position:0%
+that let's consider one simple example
+okay so firstly you can see there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's consider some other time T1
+
+ align:start position:0%
+so let's consider some other time T1
+ 
+
+ align:start position:0%
+so let's consider some other time T1
+between t Prime and the T okay so so we
+
+ align:start position:0%
+between t Prime and the T okay so so we
+ 
+
+ align:start position:0%
+between t Prime and the T okay so so we
+can see that again we go back to this
+
+ align:start position:0%
+can see that again we go back to this
+ 
+
+ align:start position:0%
+can see that again we go back to this
+problem
+
+ align:start position:0%
+problem
+ 
+
+ align:start position:0%
+problem
+okay we go back to this problem but we
+
+ align:start position:0%
+okay we go back to this problem but we
+ 
+
+ align:start position:0%
+okay we go back to this problem but we
+can see the sometime in between t Prime
+
+ align:start position:0%
+can see the sometime in between t Prime
+ 
+
+ align:start position:0%
+can see the sometime in between t Prime
+and T okay so now let's consider this
+
+ align:start position:0%
+and T okay so now let's consider this
+ 
+
+ align:start position:0%
+and T okay so now let's consider this
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+so the simplest case of this one
+
+ align:start position:0%
+so the simplest case of this one
+ 
+
+ align:start position:0%
+so the simplest case of this one
+you just take n equal to one okay just
+
+ align:start position:0%
+you just take n equal to one okay just
+ 
+
+ align:start position:0%
+you just take n equal to one okay just
+have one of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's consider the simplest case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so as you can see that this object
+
+ align:start position:0%
+so as you can see that this object
+ 
+
+ align:start position:0%
+so as you can see that this object
+so this is easy to do
+
+ align:start position:0%
+so this is easy to do
+ 
+
+ align:start position:0%
+so this is easy to do
+we can just use the same Technique we
+
+ align:start position:0%
+we can just use the same Technique we
+ 
+
+ align:start position:0%
+we can just use the same Technique we
+used before
+
+ align:start position:0%
+used before
+ 
+
+ align:start position:0%
+used before
+so essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+most of tricks
+
+ align:start position:0%
+most of tricks
+ 
+
+ align:start position:0%
+most of tricks
+in quantum mechanics
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just reduce to one trick
+
+ align:start position:0%
+just reduce to one trick
+ 
+
+ align:start position:0%
+just reduce to one trick
+or yet yeah I say most of the case Okay
+
+ align:start position:0%
+or yet yeah I say most of the case Okay
+ 
+
+ align:start position:0%
+or yet yeah I say most of the case Okay
+most of the case tricks in quantum
+
+ align:start position:0%
+most of the case tricks in quantum
+ 
+
+ align:start position:0%
+most of the case tricks in quantum
+mechanics be excused to one trick uh
+
+ align:start position:0%
+mechanics be excused to one trick uh
+ 
+
+ align:start position:0%
+mechanics be excused to one trick uh
+what is that trick
+
+ align:start position:0%
+what is that trick
+ 
+
+ align:start position:0%
+what is that trick
+which we already used over and over
+
+ align:start position:0%
+which we already used over and over
+ 
+
+ align:start position:0%
+which we already used over and over
+saying driving the path integral
+
+ align:start position:0%
+saying driving the path integral
+ 
+
+ align:start position:0%
+saying driving the path integral
+yeah insert the identities
+
+ align:start position:0%
+yeah insert the identities
+ 
+
+ align:start position:0%
+yeah insert the identities
+so so if you know how to insert
+
+ align:start position:0%
+so so if you know how to insert
+ 
+
+ align:start position:0%
+so so if you know how to insert
+identities at the right location at the
+
+ align:start position:0%
+identities at the right location at the
+ 
+
+ align:start position:0%
+identities at the right location at the
+right time and essentially uh you can
+
+ align:start position:0%
+right time and essentially uh you can
+ 
+
+ align:start position:0%
+right time and essentially uh you can
+you can uh yeah you know all the tricks
+
+ align:start position:0%
+you can uh yeah you know all the tricks
+ 
+
+ align:start position:0%
+you can uh yeah you know all the tricks
+in quantum mechanics
+
+ align:start position:0%
+in quantum mechanics
+ 
+
+ align:start position:0%
+in quantum mechanics
+and so here we do the same thing
+
+ align:start position:0%
+and so here we do the same thing
+ 
+
+ align:start position:0%
+and so here we do the same thing
+so I've been since this is T1
+
+ align:start position:0%
+so I've been since this is T1
+ 
+
+ align:start position:0%
+so I've been since this is T1
+so we just insert the complete set of a
+
+ align:start position:0%
+so we just insert the complete set of a
+ 
+
+ align:start position:0%
+so we just insert the complete set of a
+position against State at T1
+
+ align:start position:0%
+position against State at T1
+ 
+
+ align:start position:0%
+position against State at T1
+so let's just do this
+
+ align:start position:0%
+so let's just do this
+ 
+
+ align:start position:0%
+so let's just do this
+so we integrate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x 1 T1
+
+ align:start position:0%
+x 1 T1
+ 
+
+ align:start position:0%
+x 1 T1
+okay X1 T1
+
+ align:start position:0%
+okay X1 T1
+ 
+
+ align:start position:0%
+okay X1 T1
+X hat
+
+ align:start position:0%
+X hat
+ 
+
+ align:start position:0%
+X hat
+T1
+
+ align:start position:0%
+T1
+ 
+
+ align:start position:0%
+T1
+keep run
+
+ align:start position:0%
+keep run
+ 
+
+ align:start position:0%
+keep run
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so these are the
+
+ align:start position:0%
+so so these are the
+ 
+
+ align:start position:0%
+so so these are the
+so this integrates to one okay
+
+ align:start position:0%
+so this integrates to one okay
+ 
+
+ align:start position:0%
+so this integrates to one okay
+so this integrate C1
+
+ align:start position:0%
+so this integrate C1
+ 
+
+ align:start position:0%
+so this integrate C1
+so since this is so since this is
+
+ align:start position:0%
+so since this is so since this is
+ 
+
+ align:start position:0%
+so since this is so since this is
+agnosticated T1 so this act on this we
+
+ align:start position:0%
+agnosticated T1 so this act on this we
+ 
+
+ align:start position:0%
+agnosticated T1 so this act on this we
+you just uh you you just get your
+
+ align:start position:0%
+you just uh you you just get your
+ 
+
+ align:start position:0%
+you just uh you you just get your
+eigenvalue
+
+ align:start position:0%
+eigenvalue
+ 
+
+ align:start position:0%
+eigenvalue
+so so we just get
+
+ align:start position:0%
+so so we just get
+ 
+
+ align:start position:0%
+so so we just get
+dx1
+
+ align:start position:0%
+dx1
+ 
+
+ align:start position:0%
+dx1
+X1 so you just get eigen value
+
+ align:start position:0%
+X1 so you just get eigen value
+ 
+
+ align:start position:0%
+X1 so you just get eigen value
+and then you cut x t
+
+ align:start position:0%
+and then you cut x t
+ 
+
+ align:start position:0%
+and then you cut x t
+X1 T1
+
+ align:start position:0%
+X1 T1
+ 
+
+ align:start position:0%
+X1 T1
+T1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now
+
+ align:start position:0%
+but now
+ 
+
+ align:start position:0%
+but now
+we know how to do both of them
+
+ align:start position:0%
+we know how to do both of them
+ 
+
+ align:start position:0%
+we know how to do both of them
+we just plug in our password a a formula
+
+ align:start position:0%
+we just plug in our password a a formula
+ 
+
+ align:start position:0%
+we just plug in our password a a formula
+to uh to both of them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so you can do this explicitly
+
+ align:start position:0%
+so so you can do this explicitly
+ 
+
+ align:start position:0%
+so so you can do this explicitly
+plug in
+
+ align:start position:0%
+plug in
+ 
+
+ align:start position:0%
+plug in
+plug in this expression there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay plug in this expression there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it's also very intuitive you know
+
+ align:start position:0%
+but it's also very intuitive you know
+ 
+
+ align:start position:0%
+but it's also very intuitive you know
+what this looks like
+
+ align:start position:0%
+what this looks like
+ 
+
+ align:start position:0%
+what this looks like
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this is like the following
+
+ align:start position:0%
+so this is like the following
+ 
+
+ align:start position:0%
+so this is like the following
+so previously we
+
+ align:start position:0%
+so previously we
+ 
+
+ align:start position:0%
+so previously we
+we just do all the paths
+
+ align:start position:0%
+we just do all the paths
+ 
+
+ align:start position:0%
+we just do all the paths
+between these two
+
+ align:start position:0%
+between these two
+ 
+
+ align:start position:0%
+between these two
+okay so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we uh uh so now you have this x t
+
+ align:start position:0%
+we uh uh so now you have this x t
+ 
+
+ align:start position:0%
+we uh uh so now you have this x t
+and now we have T1
+
+ align:start position:0%
+and now we have T1
+ 
+
+ align:start position:0%
+and now we have T1
+so suppose this is the time T1
+
+ align:start position:0%
+so suppose this is the time T1
+ 
+
+ align:start position:0%
+so suppose this is the time T1
+it's suppose T goes up and so this is T
+
+ align:start position:0%
+it's suppose T goes up and so this is T
+ 
+
+ align:start position:0%
+it's suppose T goes up and so this is T
+Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so suppose this is the time T1 and this
+
+ align:start position:0%
+so suppose this is the time T1 and this
+ 
+
+ align:start position:0%
+so suppose this is the time T1 and this
+is TI Prime X Prime okay
+
+ align:start position:0%
+is TI Prime X Prime okay
+ 
+
+ align:start position:0%
+is TI Prime X Prime okay
+so this corresponding to you you first
+
+ align:start position:0%
+so this corresponding to you you first
+ 
+
+ align:start position:0%
+so this corresponding to you you first
+do the path integral to to some location
+
+ align:start position:0%
+do the path integral to to some location
+ 
+
+ align:start position:0%
+do the path integral to to some location
+T1 integrate over all paths here
+
+ align:start position:0%
+T1 integrate over all paths here
+ 
+
+ align:start position:0%
+T1 integrate over all paths here
+and then you multiply X1
+
+ align:start position:0%
+and then you multiply X1
+ 
+
+ align:start position:0%
+and then you multiply X1
+and then you do all the path integral
+
+ align:start position:0%
+and then you do all the path integral
+ 
+
+ align:start position:0%
+and then you do all the path integral
+here okay and then you integrate over X1
+
+ align:start position:0%
+here okay and then you integrate over X1
+ 
+
+ align:start position:0%
+here okay and then you integrate over X1
+okay you integrate x y okay
+
+ align:start position:0%
+okay you integrate x y okay
+ 
+
+ align:start position:0%
+okay you integrate x y okay
+so now if you without this X1
+
+ align:start position:0%
+so now if you without this X1
+ 
+
+ align:start position:0%
+so now if you without this X1
+okay if we dot X1 then of course this is
+
+ align:start position:0%
+okay if we dot X1 then of course this is
+ 
+
+ align:start position:0%
+okay if we dot X1 then of course this is
+trivially equal to the previous web
+
+ align:start position:0%
+trivially equal to the previous web
+ 
+
+ align:start position:0%
+trivially equal to the previous web
+because the uh you do all possible parts
+
+ align:start position:0%
+because the uh you do all possible parts
+ 
+
+ align:start position:0%
+because the uh you do all possible parts
+to T1 and open the bar from T1 to T and
+
+ align:start position:0%
+to T1 and open the bar from T1 to T and
+ 
+
+ align:start position:0%
+to T1 and open the bar from T1 to T and
+then you integrate over all possible
+
+ align:start position:0%
+then you integrate over all possible
+ 
+
+ align:start position:0%
+then you integrate over all possible
+location here then it's the same as you
+
+ align:start position:0%
+location here then it's the same as you
+ 
+
+ align:start position:0%
+location here then it's the same as you
+integrate from here to there uh the
+
+ align:start position:0%
+integrate from here to there uh the
+ 
+
+ align:start position:0%
+integrate from here to there uh the
+arbitrary path okay so the div the only
+
+ align:start position:0%
+arbitrary path okay so the div the only
+ 
+
+ align:start position:0%
+arbitrary path okay so the div the only
+difference is now we multiply by x y
+
+ align:start position:0%
+difference is now we multiply by x y
+ 
+
+ align:start position:0%
+difference is now we multiply by x y
+okay and the value at T1
+
+ align:start position:0%
+okay and the value at T1
+ 
+
+ align:start position:0%
+okay and the value at T1
+and now we can immediately write down
+
+ align:start position:0%
+and now we can immediately write down
+ 
+
+ align:start position:0%
+and now we can immediately write down
+using pass integral what's this object
+
+ align:start position:0%
+using pass integral what's this object
+ 
+
+ align:start position:0%
+using pass integral what's this object
+so this object is essentially
+
+ align:start position:0%
+so this object is essentially
+ 
+
+ align:start position:0%
+so this object is essentially
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+it's just equal to
+
+ align:start position:0%
+it's just equal to
+ 
+
+ align:start position:0%
+it's just equal to
+so now I will
+
+ align:start position:0%
+so now I will
+ 
+
+ align:start position:0%
+so now I will
+use a simplified rotation say here right
+
+ align:start position:0%
+use a simplified rotation say here right
+ 
+
+ align:start position:0%
+use a simplified rotation say here right
+X Prime T Prime x t
+
+ align:start position:0%
+X Prime T Prime x t
+ 
+
+ align:start position:0%
+X Prime T Prime x t
+to be to be those limits okay
+
+ align:start position:0%
+to be to be those limits okay
+ 
+
+ align:start position:0%
+to be to be those limits okay
+without name it
+
+ align:start position:0%
+without name it
+ 
+
+ align:start position:0%
+without name it
+and then again we integrate all possible
+
+ align:start position:0%
+and then again we integrate all possible
+ 
+
+ align:start position:0%
+and then again we integrate all possible
+Parts between them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but then
+
+ align:start position:0%
+but then
+ 
+
+ align:start position:0%
+but then
+we just have X T1
+
+ align:start position:0%
+we just have X T1
+ 
+
+ align:start position:0%
+we just have X T1
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay it just you integrate over all
+
+ align:start position:0%
+okay it just you integrate over all
+ 
+
+ align:start position:0%
+okay it just you integrate over all
+positive between them just add this time
+
+ align:start position:0%
+positive between them just add this time
+ 
+
+ align:start position:0%
+positive between them just add this time
+T1 you multiply in the integrand the
+
+ align:start position:0%
+T1 you multiply in the integrand the
+ 
+
+ align:start position:0%
+T1 you multiply in the integrand the
+value of x at one yeah so this is
+
+ align:start position:0%
+value of x at one yeah so this is
+ 
+
+ align:start position:0%
+value of x at one yeah so this is
+essentially just a the X1 here okay
+
+ align:start position:0%
+essentially just a the X1 here okay
+ 
+
+ align:start position:0%
+essentially just a the X1 here okay
+is this clear
+
+ align:start position:0%
+is this clear
+ 
+
+ align:start position:0%
+is this clear
+you can do this explicitly by plugging
+
+ align:start position:0%
+you can do this explicitly by plugging
+ 
+
+ align:start position:0%
+you can do this explicitly by plugging
+the formulas and manipulating you'll get
+
+ align:start position:0%
+the formulas and manipulating you'll get
+ 
+
+ align:start position:0%
+the formulas and manipulating you'll get
+this but it's much easier to understand
+
+ align:start position:0%
+this but it's much easier to understand
+ 
+
+ align:start position:0%
+this but it's much easier to understand
+it heuristically
+
+ align:start position:0%
+it heuristically
+ 
+
+ align:start position:0%
+it heuristically
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+using a diagram
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so this is a very very
+
+ align:start position:0%
+so this is a very very
+ 
+
+ align:start position:0%
+so this is a very very
+suggestive
+
+ align:start position:0%
+suggestive
+ 
+
+ align:start position:0%
+suggestive
+it tells you
+
+ align:start position:0%
+it tells you
+ 
+
+ align:start position:0%
+it tells you
+when we insert or operate here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we do is just we translate the
+
+ align:start position:0%
+what we do is just we translate the
+ 
+
+ align:start position:0%
+what we do is just we translate the
+eigenvalue of this operator
+
+ align:start position:0%
+eigenvalue of this operator
+ 
+
+ align:start position:0%
+eigenvalue of this operator
+okay plugged it in the integrand
+
+ align:start position:0%
+okay plugged it in the integrand
+ 
+
+ align:start position:0%
+okay plugged it in the integrand
+okay plug in the integrand
+
+ align:start position:0%
+okay plug in the integrand
+ 
+
+ align:start position:0%
+okay plug in the integrand
+so so now you can do the same thing
+
+ align:start position:0%
+so so now you can do the same thing
+ 
+
+ align:start position:0%
+so so now you can do the same thing
+suppose you have
+
+ align:start position:0%
+suppose you have
+ 
+
+ align:start position:0%
+suppose you have
+two operators okay
+
+ align:start position:0%
+two operators okay
+ 
+
+ align:start position:0%
+two operators okay
+so now let's look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have two operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can immediately almost
+
+ align:start position:0%
+so you can immediately almost
+ 
+
+ align:start position:0%
+so you can immediately almost
+immediately write down
+
+ align:start position:0%
+immediately write down
+ 
+
+ align:start position:0%
+immediately write down
+if you try to generalize that what would
+
+ align:start position:0%
+if you try to generalize that what would
+ 
+
+ align:start position:0%
+if you try to generalize that what would
+you write down this the uh the answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good so so you just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but this is almost cracked
+
+ align:start position:0%
+but this is almost cracked
+ 
+
+ align:start position:0%
+but this is almost cracked
+not completely correct
+
+ align:start position:0%
+not completely correct
+ 
+
+ align:start position:0%
+not completely correct
+for one reason
+
+ align:start position:0%
+for one reason
+ 
+
+ align:start position:0%
+for one reason
+it's actually one of you asked before
+
+ align:start position:0%
+it's actually one of you asked before
+ 
+
+ align:start position:0%
+it's actually one of you asked before
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly this
+
+ align:start position:0%
+exactly this
+ 
+
+ align:start position:0%
+exactly this
+is only equal to that
+
+ align:start position:0%
+is only equal to that
+ 
+
+ align:start position:0%
+is only equal to that
+only when
+
+ align:start position:0%
+only when
+ 
+
+ align:start position:0%
+only when
+only for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+When Ty is greater than T Cube
+
+ align:start position:0%
+When Ty is greater than T Cube
+ 
+
+ align:start position:0%
+When Ty is greater than T Cube
+so remember
+
+ align:start position:0%
+so remember
+ 
+
+ align:start position:0%
+so remember
+all these paths they don't come back in
+
+ align:start position:0%
+all these paths they don't come back in
+ 
+
+ align:start position:0%
+all these paths they don't come back in
+time okay the at the past they go
+
+ align:start position:0%
+time okay the at the past they go
+ 
+
+ align:start position:0%
+time okay the at the past they go
+forward in time they don't come back
+
+ align:start position:0%
+forward in time they don't come back
+ 
+
+ align:start position:0%
+forward in time they don't come back
+say so so here it's like you have to uh
+
+ align:start position:0%
+say so so here it's like you have to uh
+ 
+
+ align:start position:0%
+say so so here it's like you have to uh
+insert the two uh here just insert the
+
+ align:start position:0%
+insert the two uh here just insert the
+ 
+
+ align:start position:0%
+insert the two uh here just insert the
+two sets of complete States one is here
+
+ align:start position:0%
+two sets of complete States one is here
+ 
+
+ align:start position:0%
+two sets of complete States one is here
+when it's here
+
+ align:start position:0%
+when it's here
+ 
+
+ align:start position:0%
+when it's here
+but the passing go cannot come back okay
+
+ align:start position:0%
+but the passing go cannot come back okay
+ 
+
+ align:start position:0%
+but the passing go cannot come back okay
+so the order here have to be the same as
+
+ align:start position:0%
+so the order here have to be the same as
+ 
+
+ align:start position:0%
+so the order here have to be the same as
+the ordering over the path integral
+
+ align:start position:0%
+the ordering over the path integral
+ 
+
+ align:start position:0%
+the ordering over the path integral
+okay I have to be the same ordinary
+
+ align:start position:0%
+okay I have to be the same ordinary
+ 
+
+ align:start position:0%
+okay I have to be the same ordinary
+Parts integral so that means this is
+
+ align:start position:0%
+Parts integral so that means this is
+ 
+
+ align:start position:0%
+Parts integral so that means this is
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+okay or only for T1 greater than T2
+
+ align:start position:0%
+okay or only for T1 greater than T2
+ 
+
+ align:start position:0%
+okay or only for T1 greater than T2
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but
+
+ align:start position:0%
+so but
+ 
+
+ align:start position:0%
+so but
+the same thing happens
+
+ align:start position:0%
+the same thing happens
+ 
+
+ align:start position:0%
+the same thing happens
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+for T2 greater than T1
+
+ align:start position:0%
+for T2 greater than T1
+ 
+
+ align:start position:0%
+for T2 greater than T1
+so suppose T2 is greater than T1
+
+ align:start position:0%
+so suppose T2 is greater than T1
+ 
+
+ align:start position:0%
+so suppose T2 is greater than T1
+if you start this expression then we can
+
+ align:start position:0%
+if you start this expression then we can
+ 
+
+ align:start position:0%
+if you start this expression then we can
+ask what could the the correspond in the
+
+ align:start position:0%
+ask what could the the correspond in the
+ 
+
+ align:start position:0%
+ask what could the the correspond in the
+operated form so what do you think will
+
+ align:start position:0%
+operated form so what do you think will
+ 
+
+ align:start position:0%
+operated form so what do you think will
+be the operator form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so for for T1 greater than T2 we
+
+ align:start position:0%
+yeah so for for T1 greater than T2 we
+ 
+
+ align:start position:0%
+yeah so for for T1 greater than T2 we
+have this equal to that okay
+
+ align:start position:0%
+have this equal to that okay
+ 
+
+ align:start position:0%
+have this equal to that okay
+but now let's ask the post
+
+ align:start position:0%
+but now let's ask the post
+ 
+
+ align:start position:0%
+but now let's ask the post
+it's off the t2 greater than T1 but on
+
+ align:start position:0%
+it's off the t2 greater than T1 but on
+ 
+
+ align:start position:0%
+it's off the t2 greater than T1 but on
+the right hand side we still have this
+
+ align:start position:0%
+the right hand side we still have this
+ 
+
+ align:start position:0%
+the right hand side we still have this
+one but what should be the left hand
+
+ align:start position:0%
+one but what should be the left hand
+ 
+
+ align:start position:0%
+one but what should be the left hand
+side
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly just exchange X2 and T1 because
+
+ align:start position:0%
+exactly just exchange X2 and T1 because
+ 
+
+ align:start position:0%
+exactly just exchange X2 and T1 because
+because always follows the time order so
+
+ align:start position:0%
+because always follows the time order so
+ 
+
+ align:start position:0%
+because always follows the time order so
+that means the order here has always to
+
+ align:start position:0%
+that means the order here has always to
+ 
+
+ align:start position:0%
+that means the order here has always to
+be time ordered so that means that the
+
+ align:start position:0%
+be time ordered so that means that the
+ 
+
+ align:start position:0%
+be time ordered so that means that the
+correct formula which applies to for all
+
+ align:start position:0%
+correct formula which applies to for all
+ 
+
+ align:start position:0%
+correct formula which applies to for all
+T1 T2
+
+ align:start position:0%
+T1 T2
+ 
+
+ align:start position:0%
+T1 T2
+it's just you time order them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's just your time order them
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so so no matter for uh for what the
+
+ align:start position:0%
+okay so so no matter for uh for what the
+ 
+
+ align:start position:0%
+okay so so no matter for uh for what the
+old value of q1 and T2 if you time order
+
+ align:start position:0%
+old value of q1 and T2 if you time order
+ 
+
+ align:start position:0%
+old value of q1 and T2 if you time order
+them so that the the X with the larger
+
+ align:start position:0%
+them so that the the X with the larger
+ 
+
+ align:start position:0%
+them so that the the X with the larger
+time always sit in the front then it's
+
+ align:start position:0%
+time always sit in the front then it's
+ 
+
+ align:start position:0%
+time always sit in the front then it's
+always equal to this one
+
+ align:start position:0%
+always equal to this one
+ 
+
+ align:start position:0%
+always equal to this one
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so this now just immediately generalized
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so so this tells you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because of the part in the growth in the
+
+ align:start position:0%
+because of the part in the growth in the
+ 
+
+ align:start position:0%
+because of the part in the growth in the
+past integral the time only goes forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the time only goes forward
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the
+
+ align:start position:0%
+then the
+ 
+
+ align:start position:0%
+then the
+time ordering
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+naturally rise
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is impossible books okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can immediately generalize this
+
+ align:start position:0%
+so you can immediately generalize this
+ 
+
+ align:start position:0%
+so you can immediately generalize this
+so for any t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for any
+
+ align:start position:0%
+for any
+ 
+
+ align:start position:0%
+for any
+P1
+
+ align:start position:0%
+P1
+ 
+
+ align:start position:0%
+P1
+TN
+
+ align:start position:0%
+TN
+ 
+
+ align:start position:0%
+TN
+between t Prime and T
+
+ align:start position:0%
+between t Prime and T
+ 
+
+ align:start position:0%
+between t Prime and T
+then you always have
+
+ align:start position:0%
+then you always have
+ 
+
+ align:start position:0%
+then you always have
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+time ordered
+
+ align:start position:0%
+time ordered
+ 
+
+ align:start position:0%
+time ordered
+X hide T1
+
+ align:start position:0%
+X hide T1
+ 
+
+ align:start position:0%
+X hide T1
+x t n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 and this is equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+and X T1
+
+ align:start position:0%
+and X T1
+ 
+
+ align:start position:0%
+and X T1
+x t n
+
+ align:start position:0%
+x t n
+ 
+
+ align:start position:0%
+x t n
+exponential is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's why
+
+ align:start position:0%
+so that's why
+ 
+
+ align:start position:0%
+so that's why
+why we say earlier
+
+ align:start position:0%
+why we say earlier
+ 
+
+ align:start position:0%
+why we say earlier
+that you didn't pass integral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our goal is to compute this object so
+
+ align:start position:0%
+so our goal is to compute this object so
+ 
+
+ align:start position:0%
+so our goal is to compute this object so
+that's why actually Union passes go to
+
+ align:start position:0%
+that's why actually Union passes go to
+ 
+
+ align:start position:0%
+that's why actually Union passes go to
+compute it is very natural
+
+ align:start position:0%
+compute it is very natural
+ 
+
+ align:start position:0%
+compute it is very natural
+because the time ordering is just very
+
+ align:start position:0%
+because the time ordering is just very
+ 
+
+ align:start position:0%
+because the time ordering is just very
+natural from the point of view of parts
+
+ align:start position:0%
+natural from the point of view of parts
+ 
+
+ align:start position:0%
+natural from the point of view of parts
+in the group okay yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hmm
+
+ align:start position:0%
+hmm
+ 
+
+ align:start position:0%
+hmm
+oh oh sorry sorry yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+good
+ 
+
+ align:start position:0%
+good
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+any question on this
+
+ align:start position:0%
+any question on this
+ 
+
+ align:start position:0%
+any question on this
+so this is a key formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is a key formula
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good any questions on this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have got the time ordering
+
+ align:start position:0%
+so now we have got the time ordering
+ 
+
+ align:start position:0%
+so now we have got the time ordering
+okay now we want to compute but here is
+
+ align:start position:0%
+okay now we want to compute but here is
+ 
+
+ align:start position:0%
+okay now we want to compute but here is
+the vacuum correlation function
+
+ align:start position:0%
+the vacuum correlation function
+ 
+
+ align:start position:0%
+the vacuum correlation function
+okay so we have to actually go to the
+
+ align:start position:0%
+okay so we have to actually go to the
+ 
+
+ align:start position:0%
+okay so we have to actually go to the
+vacuum okay uh uh uh here uh it's in in
+
+ align:start position:0%
+vacuum okay uh uh uh here uh it's in in
+ 
+
+ align:start position:0%
+vacuum okay uh uh uh here uh it's in in
+such kind of between the position
+
+ align:start position:0%
+such kind of between the position
+ 
+
+ align:start position:0%
+such kind of between the position
+against state
+
+ align:start position:0%
+against state
+ 
+
+ align:start position:0%
+against state
+okay so now we have to see how to do
+
+ align:start position:0%
+okay so now we have to see how to do
+ 
+
+ align:start position:0%
+okay so now we have to see how to do
+this for the vacuum
+
+ align:start position:0%
+this for the vacuum
+ 
+
+ align:start position:0%
+this for the vacuum
+so so now let me just introduce a
+
+ align:start position:0%
+so so now let me just introduce a
+ 
+
+ align:start position:0%
+so so now let me just introduce a
+simplified rotation so let me call this
+
+ align:start position:0%
+simplified rotation so let me call this
+ 
+
+ align:start position:0%
+simplified rotation so let me call this
+whole scene X
+
+ align:start position:0%
+whole scene X
+ 
+
+ align:start position:0%
+whole scene X
+capital x okay
+
+ align:start position:0%
+capital x okay
+ 
+
+ align:start position:0%
+capital x okay
+code is hosting capital X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+we want to consider the vacuum query
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the idea is very simple
+
+ align:start position:0%
+so the idea is very simple
+ 
+
+ align:start position:0%
+so the idea is very simple
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+so everyone who can see the a vacuum
+
+ align:start position:0%
+so everyone who can see the a vacuum
+ 
+
+ align:start position:0%
+so everyone who can see the a vacuum
+every function we want to increase it in
+
+ align:start position:0%
+every function we want to increase it in
+ 
+
+ align:start position:0%
+every function we want to increase it in
+the in the GN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T1
+
+ align:start position:0%
+T1
+ 
+
+ align:start position:0%
+T1
+PN
+
+ align:start position:0%
+PN
+ 
+
+ align:start position:0%
+PN
+belongs to minus infinity to plus
+
+ align:start position:0%
+belongs to minus infinity to plus
+ 
+
+ align:start position:0%
+belongs to minus infinity to plus
+infinity okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you want to compute this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the GN using our rotation
+
+ align:start position:0%
+okay and the GN using our rotation
+ 
+
+ align:start position:0%
+okay and the GN using our rotation
+be not equal to zero
+
+ align:start position:0%
+be not equal to zero
+ 
+
+ align:start position:0%
+be not equal to zero
+X zero okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so outside the load is zero for that
+
+ align:start position:0%
+so outside the load is zero for that
+ 
+
+ align:start position:0%
+so outside the load is zero for that
+so now again
+
+ align:start position:0%
+so now again
+ 
+
+ align:start position:0%
+so now again
+we insert the company side of State
+
+ align:start position:0%
+we insert the company side of State
+ 
+
+ align:start position:0%
+we insert the company side of State
+okay again we insert the complete set of
+
+ align:start position:0%
+okay again we insert the complete set of
+ 
+
+ align:start position:0%
+okay again we insert the complete set of
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+we insert one
+
+ align:start position:0%
+we insert one
+ 
+
+ align:start position:0%
+we insert one
+equal to DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is also equal to DX Prime
+
+ align:start position:0%
+which is also equal to DX Prime
+ 
+
+ align:start position:0%
+which is also equal to DX Prime
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+T equals to plus infinity
+
+ align:start position:0%
+T equals to plus infinity
+ 
+
+ align:start position:0%
+T equals to plus infinity
+and T Prime goes to minus infinity
+
+ align:start position:0%
+and T Prime goes to minus infinity
+ 
+
+ align:start position:0%
+and T Prime goes to minus infinity
+into the here
+
+ align:start position:0%
+into the here
+ 
+
+ align:start position:0%
+into the here
+okay so you insert that into here
+
+ align:start position:0%
+okay so you insert that into here
+ 
+
+ align:start position:0%
+okay so you insert that into here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah so let me I need a bigger space
+
+ align:start position:0%
+so yeah so let me I need a bigger space
+ 
+
+ align:start position:0%
+so yeah so let me I need a bigger space
+so let me just write it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if you do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this trick is General
+
+ align:start position:0%
+so this trick is General
+ 
+
+ align:start position:0%
+so this trick is General
+does not restrict to the vacuum
+
+ align:start position:0%
+does not restrict to the vacuum
+ 
+
+ align:start position:0%
+does not restrict to the vacuum
+okay so in any case evaluating any state
+
+ align:start position:0%
+okay so in any case evaluating any state
+ 
+
+ align:start position:0%
+okay so in any case evaluating any state
+you can reduce it
+
+ align:start position:0%
+you can reduce it
+ 
+
+ align:start position:0%
+you can reduce it
+to the path integral
+
+ align:start position:0%
+to the path integral
+ 
+
+ align:start position:0%
+to the path integral
+by by doing this trick
+
+ align:start position:0%
+by by doing this trick
+ 
+
+ align:start position:0%
+by by doing this trick
+of inserting this guys
+
+ align:start position:0%
+of inserting this guys
+ 
+
+ align:start position:0%
+of inserting this guys
+so then we have GN
+
+ align:start position:0%
+so then we have GN
+ 
+
+ align:start position:0%
+so then we have GN
+now just equal to
+
+ align:start position:0%
+now just equal to
+ 
+
+ align:start position:0%
+now just equal to
+now we have limit T equals to plus
+
+ align:start position:0%
+now we have limit T equals to plus
+ 
+
+ align:start position:0%
+now we have limit T equals to plus
+infinity
+
+ align:start position:0%
+infinity
+ 
+
+ align:start position:0%
+infinity
+T Prime goes to minus infinity
+
+ align:start position:0%
+T Prime goes to minus infinity
+ 
+
+ align:start position:0%
+T Prime goes to minus infinity
+then we have DX DX Prime
+
+ align:start position:0%
+then we have DX DX Prime
+ 
+
+ align:start position:0%
+then we have DX DX Prime
+so we insert one here
+
+ align:start position:0%
+so we insert one here
+ 
+
+ align:start position:0%
+so we insert one here
+and the one here okay in both places
+
+ align:start position:0%
+and the one here okay in both places
+ 
+
+ align:start position:0%
+and the one here okay in both places
+here we insert the upper line here we
+
+ align:start position:0%
+here we insert the upper line here we
+ 
+
+ align:start position:0%
+here we insert the upper line here we
+insert the lower line okay
+
+ align:start position:0%
+insert the lower line okay
+ 
+
+ align:start position:0%
+insert the lower line okay
+then we have
+
+ align:start position:0%
+then we have
+ 
+
+ align:start position:0%
+then we have
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+then x t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+and then X Prime T Prime
+
+ align:start position:0%
+and then X Prime T Prime
+ 
+
+ align:start position:0%
+and then X Prime T Prime
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+okay times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we just have
+
+ align:start position:0%
+we just have
+ 
+
+ align:start position:0%
+we just have
+yeah so so let me just save some
+
+ align:start position:0%
+yeah so so let me just save some
+ 
+
+ align:start position:0%
+yeah so so let me just save some
+so so this then become
+
+ align:start position:0%
+so so this then become
+ 
+
+ align:start position:0%
+so so this then become
+DX DX Prime
+
+ align:start position:0%
+DX DX Prime
+ 
+
+ align:start position:0%
+DX DX Prime
+so these two are simple
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so essentially they just become the
+
+ align:start position:0%
+so essentially they just become the
+ 
+
+ align:start position:0%
+so essentially they just become the
+vacuum
+
+ align:start position:0%
+vacuum
+ 
+
+ align:start position:0%
+vacuum
+a wave function
+
+ align:start position:0%
+a wave function
+ 
+
+ align:start position:0%
+a wave function
+okay so we have
+
+ align:start position:0%
+okay so we have
+ 
+
+ align:start position:0%
+okay so we have
+PSI zero
+
+ align:start position:0%
+PSI zero
+ 
+
+ align:start position:0%
+PSI zero
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+X and say 0 x Prime
+
+ align:start position:0%
+X and say 0 x Prime
+ 
+
+ align:start position:0%
+X and say 0 x Prime
+and then we have this path integral
+
+ align:start position:0%
+and then we have this path integral
+ 
+
+ align:start position:0%
+and then we have this path integral
+which we already know how to do
+
+ align:start position:0%
+which we already know how to do
+ 
+
+ align:start position:0%
+which we already know how to do
+okay we already and then we have this
+
+ align:start position:0%
+okay we already and then we have this
+ 
+
+ align:start position:0%
+okay we already and then we have this
+pass integral
+
+ align:start position:0%
+pass integral
+ 
+
+ align:start position:0%
+pass integral
+okay then we have that path in the group
+
+ align:start position:0%
+okay then we have that path in the group
+ 
+
+ align:start position:0%
+okay then we have that path in the group
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so so so so you just insert
+
+ align:start position:0%
+yeah so so so so you just insert
+ 
+
+ align:start position:0%
+yeah so so so so you just insert
+so let me call Star you just insert the
+
+ align:start position:0%
+so let me call Star you just insert the
+ 
+
+ align:start position:0%
+so let me call Star you just insert the
+star here
+
+ align:start position:0%
+star here
+ 
+
+ align:start position:0%
+star here
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now with t and t Prime uh to
+
+ align:start position:0%
+and now with t and t Prime uh to
+ 
+
+ align:start position:0%
+and now with t and t Prime uh to
+Infinity okay everything finds Infinity
+
+ align:start position:0%
+Infinity okay everything finds Infinity
+ 
+
+ align:start position:0%
+Infinity okay everything finds Infinity
+and this yeah the reason we take T Prime
+
+ align:start position:0%
+and this yeah the reason we take T Prime
+ 
+
+ align:start position:0%
+and this yeah the reason we take T Prime
+and T got Infinity is obvious because we
+
+ align:start position:0%
+and T got Infinity is obvious because we
+ 
+
+ align:start position:0%
+and T got Infinity is obvious because we
+want to include
+
+ align:start position:0%
+want to include
+ 
+
+ align:start position:0%
+want to include
+so here the T have to be go between the
+
+ align:start position:0%
+so here the T have to be go between the
+ 
+
+ align:start position:0%
+so here the T have to be go between the
+T Prime and the T so if you want to have
+
+ align:start position:0%
+T Prime and the T so if you want to have
+ 
+
+ align:start position:0%
+T Prime and the T so if you want to have
+arbitrary t
+
+ align:start position:0%
+arbitrary t
+ 
+
+ align:start position:0%
+arbitrary t
+and then we want to the uh T Prime to go
+
+ align:start position:0%
+and then we want to the uh T Prime to go
+ 
+
+ align:start position:0%
+and then we want to the uh T Prime to go
+to minus infinity and t equal to plus
+
+ align:start position:0%
+to minus infinity and t equal to plus
+ 
+
+ align:start position:0%
+to minus infinity and t equal to plus
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so we have used that the
+
+ align:start position:0%
+so we have used that the
+ 
+
+ align:start position:0%
+so we have used that the
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+P Prime 0 is just equal to size zero
+
+ align:start position:0%
+P Prime 0 is just equal to size zero
+ 
+
+ align:start position:0%
+P Prime 0 is just equal to size zero
+X Prime just the ground state wave
+
+ align:start position:0%
+X Prime just the ground state wave
+ 
+
+ align:start position:0%
+X Prime just the ground state wave
+function okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that means that so this trick
+
+ align:start position:0%
+so that means that so this trick
+ 
+
+ align:start position:0%
+so that means that so this trick
+actually works in in uh for other states
+
+ align:start position:0%
+actually works in in uh for other states
+ 
+
+ align:start position:0%
+actually works in in uh for other states
+too okay you can do the similar trick
+
+ align:start position:0%
+too okay you can do the similar trick
+ 
+
+ align:start position:0%
+too okay you can do the similar trick
+and uh and you just
+
+ align:start position:0%
+and uh and you just
+ 
+
+ align:start position:0%
+and uh and you just
+essentially get two more integrals to do
+
+ align:start position:0%
+essentially get two more integrals to do
+ 
+
+ align:start position:0%
+essentially get two more integrals to do
+and uh you take that path integral and
+
+ align:start position:0%
+and uh you take that path integral and
+ 
+
+ align:start position:0%
+and uh you take that path integral and
+then you just uh integrate it over the
+
+ align:start position:0%
+then you just uh integrate it over the
+ 
+
+ align:start position:0%
+then you just uh integrate it over the
+initial and the final wave functions
+
+ align:start position:0%
+initial and the final wave functions
+ 
+
+ align:start position:0%
+initial and the final wave functions
+okay an integrate of ignition the follow
+
+ align:start position:0%
+okay an integrate of ignition the follow
+ 
+
+ align:start position:0%
+okay an integrate of ignition the follow
+wave functions
+
+ align:start position:0%
+wave functions
+ 
+
+ align:start position:0%
+wave functions
+so so the trick applies to any state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you understand not just the vacuum
+
+ align:start position:0%
+you understand not just the vacuum
+ 
+
+ align:start position:0%
+you understand not just the vacuum
+correlation functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this the energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah sorry say it again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah yeah it's a wrong State it's
+
+ align:start position:0%
+yeah yeah yeah it's a wrong State it's
+ 
+
+ align:start position:0%
+yeah yeah yeah it's a wrong State it's
+the it's the lowest energizing State
+
+ align:start position:0%
+the it's the lowest energizing State
+ 
+
+ align:start position:0%
+the it's the lowest energizing State
+yeah yeah it doesn't matter you can also
+
+ align:start position:0%
+yeah yeah it doesn't matter you can also
+ 
+
+ align:start position:0%
+yeah yeah it doesn't matter you can also
+take a other
+
+ align:start position:0%
+take a other
+ 
+
+ align:start position:0%
+take a other
+you can take other states too it just
+
+ align:start position:0%
+you can take other states too it just
+ 
+
+ align:start position:0%
+you can take other states too it just
+will be some wave function too yeah will
+
+ align:start position:0%
+will be some wave function too yeah will
+ 
+
+ align:start position:0%
+will be some wave function too yeah will
+be some wave function there
+
+ align:start position:0%
+be some wave function there
+ 
+
+ align:start position:0%
+be some wave function there
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+oh yeah yeah if you're not take yeah
+
+ align:start position:0%
+oh yeah yeah if you're not take yeah
+ 
+
+ align:start position:0%
+oh yeah yeah if you're not take yeah
+that's a very good question so if you
+
+ align:start position:0%
+that's a very good question so if you
+ 
+
+ align:start position:0%
+that's a very good question so if you
+don't take
+
+ align:start position:0%
+don't take
+ 
+
+ align:start position:0%
+don't take
+uh so if you take other states
+
+ align:start position:0%
+uh so if you take other states
+ 
+
+ align:start position:0%
+uh so if you take other states
+and then in general there may be some
+
+ align:start position:0%
+and then in general there may be some
+ 
+
+ align:start position:0%
+and then in general there may be some
+dependence on T and T Prime and T in
+
+ align:start position:0%
+dependence on T and T Prime and T in
+ 
+
+ align:start position:0%
+dependence on T and T Prime and T in
+this wave function yeah indeed yeah
+
+ align:start position:0%
+this wave function yeah indeed yeah
+ 
+
+ align:start position:0%
+this wave function yeah indeed yeah
+so and so you have to take the limit
+
+ align:start position:0%
+so and so you have to take the limit
+ 
+
+ align:start position:0%
+so and so you have to take the limit
+also in the wave function
+
+ align:start position:0%
+also in the wave function
+ 
+
+ align:start position:0%
+also in the wave function
+yeah but here we are using the
+
+ align:start position:0%
+yeah but here we are using the
+ 
+
+ align:start position:0%
+yeah but here we are using the
+simplification that the the ground state
+
+ align:start position:0%
+simplification that the the ground state
+ 
+
+ align:start position:0%
+simplification that the the ground state
+is actually time independent good that's
+
+ align:start position:0%
+is actually time independent good that's
+ 
+
+ align:start position:0%
+is actually time independent good that's
+a good question
+
+ align:start position:0%
+a good question
+ 
+
+ align:start position:0%
+a good question
+other questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay good
+
+ align:start position:0%
+okay good
+ 
+
+ align:start position:0%
+okay good
+so this works essentially
+
+ align:start position:0%
+so this works essentially
+ 
+
+ align:start position:0%
+so this works essentially
+for any state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but for the ground state actually
+
+ align:start position:0%
+but for the ground state actually
+ 
+
+ align:start position:0%
+but for the ground state actually
+there's another trick
+
+ align:start position:0%
+there's another trick
+ 
+
+ align:start position:0%
+there's another trick
+which can simplify the problem
+
+ align:start position:0%
+which can simplify the problem
+ 
+
+ align:start position:0%
+which can simplify the problem
+which you don't even have to do this two
+
+ align:start position:0%
+which you don't even have to do this two
+ 
+
+ align:start position:0%
+which you don't even have to do this two
+additional integral
+
+ align:start position:0%
+additional integral
+ 
+
+ align:start position:0%
+additional integral
+okay you can actually directly
+
+ align:start position:0%
+okay you can actually directly
+ 
+
+ align:start position:0%
+okay you can actually directly
+so for the ground state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the vacuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this actually
+
+ align:start position:0%
+this actually
+ 
+
+ align:start position:0%
+this actually
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+trick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to get rid of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to get to make the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these two additional integrals are
+
+ align:start position:0%
+these two additional integrals are
+ 
+
+ align:start position:0%
+these two additional integrals are
+necessary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let me tell you how you do this
+
+ align:start position:0%
+so now let me tell you how you do this
+ 
+
+ align:start position:0%
+so now let me tell you how you do this
+trick and this trick is very important
+
+ align:start position:0%
+trick and this trick is very important
+ 
+
+ align:start position:0%
+trick and this trick is very important
+also in Quantum field series
+
+ align:start position:0%
+also in Quantum field series
+ 
+
+ align:start position:0%
+also in Quantum field series
+because if you do harmonic oscillator of
+
+ align:start position:0%
+because if you do harmonic oscillator of
+ 
+
+ align:start position:0%
+because if you do harmonic oscillator of
+course
+
+ align:start position:0%
+course
+ 
+
+ align:start position:0%
+course
+you know the wave function
+
+ align:start position:0%
+you know the wave function
+ 
+
+ align:start position:0%
+you know the wave function
+but if I give you a harmonic oscillator
+
+ align:start position:0%
+but if I give you a harmonic oscillator
+ 
+
+ align:start position:0%
+but if I give you a harmonic oscillator
+which we don't know how to solve the way
+
+ align:start position:0%
+which we don't know how to solve the way
+ 
+
+ align:start position:0%
+which we don't know how to solve the way
+the gun State wave function and then
+
+ align:start position:0%
+the gun State wave function and then
+ 
+
+ align:start position:0%
+the gun State wave function and then
+this then this will be a nightmare okay
+
+ align:start position:0%
+this then this will be a nightmare okay
+ 
+
+ align:start position:0%
+this then this will be a nightmare okay
+because then you don't know the wave
+
+ align:start position:0%
+because then you don't know the wave
+ 
+
+ align:start position:0%
+because then you don't know the wave
+function and for Quantum field theory in
+
+ align:start position:0%
+function and for Quantum field theory in
+ 
+
+ align:start position:0%
+function and for Quantum field theory in
+particular in the interacting case we
+
+ align:start position:0%
+particular in the interacting case we
+ 
+
+ align:start position:0%
+particular in the interacting case we
+don't know the wave function
+
+ align:start position:0%
+don't know the wave function
+ 
+
+ align:start position:0%
+don't know the wave function
+okay so so so so so so even though this
+
+ align:start position:0%
+okay so so so so so so even though this
+ 
+
+ align:start position:0%
+okay so so so so so so even though this
+formally give you the answer
+
+ align:start position:0%
+formally give you the answer
+ 
+
+ align:start position:0%
+formally give you the answer
+but in practice it's actually often not
+
+ align:start position:0%
+but in practice it's actually often not
+ 
+
+ align:start position:0%
+but in practice it's actually often not
+convenient to use
+
+ align:start position:0%
+convenient to use
+ 
+
+ align:start position:0%
+convenient to use
+but fortunately for the ground state
+
+ align:start position:0%
+but fortunately for the ground state
+ 
+
+ align:start position:0%
+but fortunately for the ground state
+there's additional trick which actually
+
+ align:start position:0%
+there's additional trick which actually
+ 
+
+ align:start position:0%
+there's additional trick which actually
+you don't need to use the ground state
+
+ align:start position:0%
+you don't need to use the ground state
+ 
+
+ align:start position:0%
+you don't need to use the ground state
+wave function tool okay so so now I'm uh
+
+ align:start position:0%
+wave function tool okay so so now I'm uh
+ 
+
+ align:start position:0%
+wave function tool okay so so now I'm uh
+so now I tell you this additional tube
+
+ align:start position:0%
+so now I tell you this additional tube
+ 
+
+ align:start position:0%
+so now I tell you this additional tube
+but this trick only specific to the
+
+ align:start position:0%
+but this trick only specific to the
+ 
+
+ align:start position:0%
+but this trick only specific to the
+vacuum okay you cannot apply to other
+
+ align:start position:0%
+vacuum okay you cannot apply to other
+ 
+
+ align:start position:0%
+vacuum okay you cannot apply to other
+states
+
+ align:start position:0%
+states
+ 
+
+ align:start position:0%
+states
+okay so this is specific to vacuum
+
+ align:start position:0%
+okay so this is specific to vacuum
+ 
+
+ align:start position:0%
+okay so this is specific to vacuum
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so now let's forget about this scene
+
+ align:start position:0%
+so now let's forget about this scene
+ 
+
+ align:start position:0%
+so now let's forget about this scene
+okay now let's forget about this scene
+
+ align:start position:0%
+okay now let's forget about this scene
+ 
+
+ align:start position:0%
+okay now let's forget about this scene
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+coming back from here okay
+
+ align:start position:0%
+coming back from here okay
+ 
+
+ align:start position:0%
+coming back from here okay
+so nowadays coming back from here now
+
+ align:start position:0%
+so nowadays coming back from here now
+ 
+
+ align:start position:0%
+so nowadays coming back from here now
+let's coming back from here just
+
+ align:start position:0%
+let's coming back from here just
+ 
+
+ align:start position:0%
+let's coming back from here just
+consider
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again I take
+
+ align:start position:0%
+again I take
+ 
+
+ align:start position:0%
+again I take
+limit he goes to plus infinity
+
+ align:start position:0%
+limit he goes to plus infinity
+ 
+
+ align:start position:0%
+limit he goes to plus infinity
+and T Prime goes to minus infinity
+
+ align:start position:0%
+and T Prime goes to minus infinity
+ 
+
+ align:start position:0%
+and T Prime goes to minus infinity
+let's look at this object
+
+ align:start position:0%
+let's look at this object
+ 
+
+ align:start position:0%
+let's look at this object
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+X Prime T Prime okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+again we are going to
+
+ align:start position:0%
+again we are going to
+ 
+
+ align:start position:0%
+again we are going to
+insert identity okay now we are again
+
+ align:start position:0%
+insert identity okay now we are again
+ 
+
+ align:start position:0%
+insert identity okay now we are again
+going to insert the identity and now we
+
+ align:start position:0%
+going to insert the identity and now we
+ 
+
+ align:start position:0%
+going to insert the identity and now we
+insert the identity in a different way
+
+ align:start position:0%
+insert the identity in a different way
+ 
+
+ align:start position:0%
+insert the identity in a different way
+again we insert the identity here
+
+ align:start position:0%
+again we insert the identity here
+ 
+
+ align:start position:0%
+again we insert the identity here
+I mean so the identity here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now we instead identity expressed
+
+ align:start position:0%
+but now we instead identity expressed
+ 
+
+ align:start position:0%
+but now we instead identity expressed
+in the company side of energizing States
+
+ align:start position:0%
+in the company side of energizing States
+ 
+
+ align:start position:0%
+in the company side of energizing States
+okay so now we saw inserted the complete
+
+ align:start position:0%
+okay so now we saw inserted the complete
+ 
+
+ align:start position:0%
+okay so now we saw inserted the complete
+set of energizing state
+
+ align:start position:0%
+set of energizing state
+ 
+
+ align:start position:0%
+set of energizing state
+so I just formally labeled it by m
+
+ align:start position:0%
+so I just formally labeled it by m
+ 
+
+ align:start position:0%
+so I just formally labeled it by m
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's just insert in the two
+
+ align:start position:0%
+so now let's just insert in the two
+ 
+
+ align:start position:0%
+so now let's just insert in the two
+places
+
+ align:start position:0%
+places
+ 
+
+ align:start position:0%
+places
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so so so we now we have two
+
+ align:start position:0%
+okay so so so we now we have two
+ 
+
+ align:start position:0%
+okay so so so we now we have two
+identities then we have n and M
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have n m
+
+ align:start position:0%
+we have n m
+ 
+
+ align:start position:0%
+we have n m
+so now I will uh so you keep this in
+
+ align:start position:0%
+so now I will uh so you keep this in
+ 
+
+ align:start position:0%
+so now I will uh so you keep this in
+mind I will not
+
+ align:start position:0%
+mind I will not
+ 
+
+ align:start position:0%
+mind I will not
+copy this over and over okay so keep
+
+ align:start position:0%
+copy this over and over okay so keep
+ 
+
+ align:start position:0%
+copy this over and over okay so keep
+this limit in mind oh it's t Prime
+
+ align:start position:0%
+this limit in mind oh it's t Prime
+ 
+
+ align:start position:0%
+this limit in mind oh it's t Prime
+equals to minus infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have and then we have x t
+
+ align:start position:0%
+so now we have and then we have x t
+ 
+
+ align:start position:0%
+so now we have and then we have x t
+with m
+
+ align:start position:0%
+with m
+ 
+
+ align:start position:0%
+with m
+and m x
+
+ align:start position:0%
+and m x
+ 
+
+ align:start position:0%
+and m x
+with n
+
+ align:start position:0%
+with n
+ 
+
+ align:start position:0%
+with n
+and N with X Prime T Prime
+
+ align:start position:0%
+and N with X Prime T Prime
+ 
+
+ align:start position:0%
+and N with X Prime T Prime
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if we look at this sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if we look at this sum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it well n and m equal to zero
+
+ align:start position:0%
+it well n and m equal to zero
+ 
+
+ align:start position:0%
+it well n and m equal to zero
+this is the object we want
+
+ align:start position:0%
+this is the object we want
+ 
+
+ align:start position:0%
+this is the object we want
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+this is the object we want but this also
+
+ align:start position:0%
+this is the object we want but this also
+ 
+
+ align:start position:0%
+this is the object we want but this also
+contains many many other
+
+ align:start position:0%
+contains many many other
+ 
+
+ align:start position:0%
+contains many many other
+stuff
+
+ align:start position:0%
+stuff
+ 
+
+ align:start position:0%
+stuff
+so now we will use a trick
+
+ align:start position:0%
+so now we will use a trick
+ 
+
+ align:start position:0%
+so now we will use a trick
+to isolate n equal to 0 and m equal to
+
+ align:start position:0%
+to isolate n equal to 0 and m equal to
+ 
+
+ align:start position:0%
+to isolate n equal to 0 and m equal to
+zero piece
+
+ align:start position:0%
+zero piece
+ 
+
+ align:start position:0%
+zero piece
+okay to isolate that piece okay
+
+ align:start position:0%
+okay to isolate that piece okay
+ 
+
+ align:start position:0%
+okay to isolate that piece okay
+that's what we are going to do now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is the commonly
+
+ align:start position:0%
+so this is the commonly
+ 
+
+ align:start position:0%
+so this is the commonly
+used
+
+ align:start position:0%
+used
+ 
+
+ align:start position:0%
+used
+technique
+
+ align:start position:0%
+technique
+ 
+
+ align:start position:0%
+technique
+in Quantum field Theory
+
+ align:start position:0%
+in Quantum field Theory
+ 
+
+ align:start position:0%
+in Quantum field Theory
+not only in Quantum velocity actually in
+
+ align:start position:0%
+not only in Quantum velocity actually in
+ 
+
+ align:start position:0%
+not only in Quantum velocity actually in
+in many areas of physics
+
+ align:start position:0%
+in many areas of physics
+ 
+
+ align:start position:0%
+in many areas of physics
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so um so now let's first to explain that
+
+ align:start position:0%
+so um so now let's first to explain that
+ 
+
+ align:start position:0%
+so um so now let's first to explain that
+you can just look at this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's look at this object okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this object is
+
+ align:start position:0%
+so this object is
+ 
+
+ align:start position:0%
+so this object is
+limit T Prime goes to minus infinity
+
+ align:start position:0%
+limit T Prime goes to minus infinity
+ 
+
+ align:start position:0%
+limit T Prime goes to minus infinity
+some energizing State n and X Prime T
+
+ align:start position:0%
+some energizing State n and X Prime T
+ 
+
+ align:start position:0%
+some energizing State n and X Prime T
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+so again this is written in the
+
+ align:start position:0%
+so again this is written in the
+ 
+
+ align:start position:0%
+so again this is written in the
+Heisenberg picture
+
+ align:start position:0%
+Heisenberg picture
+ 
+
+ align:start position:0%
+Heisenberg picture
+so we need to so translate to you more
+
+ align:start position:0%
+so we need to so translate to you more
+ 
+
+ align:start position:0%
+so we need to so translate to you more
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+language of the shorting a picture so we
+
+ align:start position:0%
+language of the shorting a picture so we
+ 
+
+ align:start position:0%
+language of the shorting a picture so we
+need to write it as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+and then you have expansion i h t Prime
+
+ align:start position:0%
+and then you have expansion i h t Prime
+ 
+
+ align:start position:0%
+and then you have expansion i h t Prime
+and then X Prime okay so now it's the
+
+ align:start position:0%
+and then X Prime okay so now it's the
+ 
+
+ align:start position:0%
+and then X Prime okay so now it's the
+standard shooting a picture
+
+ align:start position:0%
+standard shooting a picture
+ 
+
+ align:start position:0%
+standard shooting a picture
+state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now since n is in the jagging state
+
+ align:start position:0%
+so now since n is in the jagging state
+ 
+
+ align:start position:0%
+so now since n is in the jagging state
+we can just act the uh this one okay so
+
+ align:start position:0%
+we can just act the uh this one okay so
+ 
+
+ align:start position:0%
+we can just act the uh this one okay so
+this is just equal to
+
+ align:start position:0%
+this is just equal to
+ 
+
+ align:start position:0%
+this is just equal to
+limit T Prime equals to minus infinity
+
+ align:start position:0%
+limit T Prime equals to minus infinity
+ 
+
+ align:start position:0%
+limit T Prime equals to minus infinity
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and X Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+so now
+ 
+
+ align:start position:0%
+so now
+we will
+
+ align:start position:0%
+we will
+ 
+
+ align:start position:0%
+we will
+try to select the ground state
+
+ align:start position:0%
+try to select the ground state
+ 
+
+ align:start position:0%
+try to select the ground state
+and we do that by doing the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now imagine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+giving en a small imaginary part
+
+ align:start position:0%
+giving en a small imaginary part
+ 
+
+ align:start position:0%
+giving en a small imaginary part
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay imagine yeah take
+
+ align:start position:0%
+okay imagine yeah take
+ 
+
+ align:start position:0%
+okay imagine yeah take
+en
+
+ align:start position:0%
+en
+ 
+
+ align:start position:0%
+en
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+e n y minus i absolute
+
+ align:start position:0%
+e n y minus i absolute
+ 
+
+ align:start position:0%
+e n y minus i absolute
+hmm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so Epson is a small positive number
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so which is equivalent to taking
+
+ align:start position:0%
+okay so which is equivalent to taking
+ 
+
+ align:start position:0%
+okay so which is equivalent to taking
+so or you just take H your hamiltonian
+
+ align:start position:0%
+so or you just take H your hamiltonian
+ 
+
+ align:start position:0%
+so or you just take H your hamiltonian
+take it into one minus Epsilon
+
+ align:start position:0%
+take it into one minus Epsilon
+ 
+
+ align:start position:0%
+take it into one minus Epsilon
+you can make a give you the hamiltonian
+
+ align:start position:0%
+you can make a give you the hamiltonian
+ 
+
+ align:start position:0%
+you can make a give you the hamiltonian
+a slightly imaginary part okay it's
+
+ align:start position:0%
+a slightly imaginary part okay it's
+ 
+
+ align:start position:0%
+a slightly imaginary part okay it's
+equivalent okay
+
+ align:start position:0%
+equivalent okay
+ 
+
+ align:start position:0%
+equivalent okay
+so now with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with this
+
+ align:start position:0%
+with this
+ 
+
+ align:start position:0%
+with this
+and now we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so limit
+
+ align:start position:0%
+so limit
+ 
+
+ align:start position:0%
+so limit
+P Prime goes to minus infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have experiential
+
+ align:start position:0%
+so now we have experiential
+ 
+
+ align:start position:0%
+so now we have experiential
+i e n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one minus I Epsilon t
+
+ align:start position:0%
+one minus I Epsilon t
+ 
+
+ align:start position:0%
+one minus I Epsilon t
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+and N X Prime
+
+ align:start position:0%
+and N X Prime
+ 
+
+ align:start position:0%
+and N X Prime
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is just equal to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+supposed to be normalized our state
+
+ align:start position:0%
+supposed to be normalized our state
+ 
+
+ align:start position:0%
+supposed to be normalized our state
+so that easier yeah so so by definition
+
+ align:start position:0%
+so that easier yeah so so by definition
+ 
+
+ align:start position:0%
+so that easier yeah so so by definition
+en are greater than e0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+greater than e0 for n greater than zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the effect of this
+
+ align:start position:0%
+so the effect of this
+ 
+
+ align:start position:0%
+so the effect of this
+putting apps on here
+
+ align:start position:0%
+putting apps on here
+ 
+
+ align:start position:0%
+putting apps on here
+when you multiply it
+
+ align:start position:0%
+when you multiply it
+ 
+
+ align:start position:0%
+when you multiply it
+is to give you a factor like this
+
+ align:start position:0%
+is to give you a factor like this
+ 
+
+ align:start position:0%
+is to give you a factor like this
+explain
+
+ align:start position:0%
+explain
+ 
+
+ align:start position:0%
+explain
+Epsilon e n
+
+ align:start position:0%
+Epsilon e n
+ 
+
+ align:start position:0%
+Epsilon e n
+times T Prime okay so it'll give you a
+
+ align:start position:0%
+times T Prime okay so it'll give you a
+ 
+
+ align:start position:0%
+times T Prime okay so it'll give you a
+real Factor like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so now T go t Prime goes to minus
+
+ align:start position:0%
+so now T go t Prime goes to minus
+ 
+
+ align:start position:0%
+so now T go t Prime goes to minus
+infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and e n is greater than e0
+
+ align:start position:0%
+and e n is greater than e0
+ 
+
+ align:start position:0%
+and e n is greater than e0
+so for any state
+
+ align:start position:0%
+so for any state
+ 
+
+ align:start position:0%
+so for any state
+which is not ground state will this
+
+ align:start position:0%
+which is not ground state will this
+ 
+
+ align:start position:0%
+which is not ground state will this
+Factor will be experientially small it
+
+ align:start position:0%
+Factor will be experientially small it
+ 
+
+ align:start position:0%
+Factor will be experientially small it
+goes to zero so the ratio between this
+
+ align:start position:0%
+goes to zero so the ratio between this
+ 
+
+ align:start position:0%
+goes to zero so the ratio between this
+factor and the ground state goes to zero
+
+ align:start position:0%
+factor and the ground state goes to zero
+ 
+
+ align:start position:0%
+factor and the ground state goes to zero
+for any excited States
+
+ align:start position:0%
+for any excited States
+ 
+
+ align:start position:0%
+for any excited States
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+because of the e n minus e0 or greater
+
+ align:start position:0%
+because of the e n minus e0 or greater
+ 
+
+ align:start position:0%
+because of the e n minus e0 or greater
+than zero okay and this goes to minus
+
+ align:start position:0%
+than zero okay and this goes to minus
+ 
+
+ align:start position:0%
+than zero okay and this goes to minus
+infinity and Epsilon is positive okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this implies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this implies so so we continue
+
+ align:start position:0%
+so so this implies so so we continue
+ 
+
+ align:start position:0%
+so so this implies so so we continue
+sorry it's just uh so let's continue
+
+ align:start position:0%
+sorry it's just uh so let's continue
+ 
+
+ align:start position:0%
+sorry it's just uh so let's continue
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+so this means
+
+ align:start position:0%
+so this means
+ 
+
+ align:start position:0%
+so this means
+we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+essentially zero
+
+ align:start position:0%
+essentially zero
+ 
+
+ align:start position:0%
+essentially zero
+for m not equal to zero
+
+ align:start position:0%
+for m not equal to zero
+ 
+
+ align:start position:0%
+for m not equal to zero
+and therefore an expression i e zero
+
+ align:start position:0%
+and therefore an expression i e zero
+ 
+
+ align:start position:0%
+and therefore an expression i e zero
+y minus Epsilon T Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for n equal to zero
+
+ align:start position:0%
+for n equal to zero
+ 
+
+ align:start position:0%
+for n equal to zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you just take out the overall Factor
+
+ align:start position:0%
+you just take out the overall Factor
+ 
+
+ align:start position:0%
+you just take out the overall Factor
+corresponding to the ground state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah then all the other coefficient will
+
+ align:start position:0%
+yeah then all the other coefficient will
+ 
+
+ align:start position:0%
+yeah then all the other coefficient will
+go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a mathematical trick
+
+ align:start position:0%
+it's a mathematical trick
+ 
+
+ align:start position:0%
+it's a mathematical trick
+and at the end of the day we said
+
+ align:start position:0%
+and at the end of the day we said
+ 
+
+ align:start position:0%
+and at the end of the day we said
+Epsilon go to zero
+
+ align:start position:0%
+Epsilon go to zero
+ 
+
+ align:start position:0%
+Epsilon go to zero
+and you just go back to the original
+
+ align:start position:0%
+and you just go back to the original
+ 
+
+ align:start position:0%
+and you just go back to the original
+hamiltonian so this is just a trick if
+
+ align:start position:0%
+hamiltonian so this is just a trick if
+ 
+
+ align:start position:0%
+hamiltonian so this is just a trick if
+you're doing this order properly it just
+
+ align:start position:0%
+you're doing this order properly it just
+ 
+
+ align:start position:0%
+you're doing this order properly it just
+laterally selects the ground state for
+
+ align:start position:0%
+laterally selects the ground state for
+ 
+
+ align:start position:0%
+laterally selects the ground state for
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+yeah yeah just a pure mathematical trick
+
+ align:start position:0%
+yeah yeah just a pure mathematical trick
+ 
+
+ align:start position:0%
+yeah yeah just a pure mathematical trick
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I have some uh for me write this
+
+ align:start position:0%
+yeah I have some uh for me write this
+ 
+
+ align:start position:0%
+yeah I have some uh for me write this
+absent we always assume Epson is greater
+
+ align:start position:0%
+absent we always assume Epson is greater
+ 
+
+ align:start position:0%
+absent we always assume Epson is greater
+than zero
+
+ align:start position:0%
+than zero
+ 
+
+ align:start position:0%
+than zero
+so uh so yeah yeah
+
+ align:start position:0%
+so uh so yeah yeah
+ 
+
+ align:start position:0%
+so uh so yeah yeah
+you always assume uh yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh I can
+
+ align:start position:0%
+oh I can
+ 
+
+ align:start position:0%
+oh I can
+uh um
+
+ align:start position:0%
+uh um
+ 
+
+ align:start position:0%
+uh um
+I have a path integral
+
+ align:start position:0%
+I have a path integral
+ 
+
+ align:start position:0%
+I have a path integral
+and uh
+
+ align:start position:0%
+and uh
+ 
+
+ align:start position:0%
+and uh
+essentially that I can design the rule I
+
+ align:start position:0%
+essentially that I can design the rule I
+ 
+
+ align:start position:0%
+essentially that I can design the rule I
+want
+
+ align:start position:0%
+want
+ 
+
+ align:start position:0%
+want
+as far as at the end of the day I get
+
+ align:start position:0%
+as far as at the end of the day I get
+ 
+
+ align:start position:0%
+as far as at the end of the day I get
+the uh the desired desired quantity yeah
+
+ align:start position:0%
+the uh the desired desired quantity yeah
+ 
+
+ align:start position:0%
+the uh the desired desired quantity yeah
+yeah but but the order of limit is very
+
+ align:start position:0%
+yeah but but the order of limit is very
+ 
+
+ align:start position:0%
+yeah but but the order of limit is very
+important you have to be very careful
+
+ align:start position:0%
+important you have to be very careful
+ 
+
+ align:start position:0%
+important you have to be very careful
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now here is not the no here you cannot
+
+ align:start position:0%
+now here is not the no here you cannot
+ 
+
+ align:start position:0%
+now here is not the no here you cannot
+do extreme stationary phase because if
+
+ align:start position:0%
+do extreme stationary phase because if
+ 
+
+ align:start position:0%
+do extreme stationary phase because if
+you just yeah yeah yeah you really need
+
+ align:start position:0%
+you just yeah yeah yeah you really need
+ 
+
+ align:start position:0%
+you just yeah yeah yeah you really need
+to suppress the other contribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not only suppress them you just they
+
+ align:start position:0%
+not only suppress them you just they
+ 
+
+ align:start position:0%
+not only suppress them you just they
+have to go to zero yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generally go to zero okay so similarly
+
+ align:start position:0%
+generally go to zero okay so similarly
+ 
+
+ align:start position:0%
+generally go to zero okay so similarly
+with the same trick just the same scene
+
+ align:start position:0%
+with the same trick just the same scene
+ 
+
+ align:start position:0%
+with the same trick just the same scene
+in one shot
+
+ align:start position:0%
+in one shot
+ 
+
+ align:start position:0%
+in one shot
+okay selects n equal to zero
+
+ align:start position:0%
+okay selects n equal to zero
+ 
+
+ align:start position:0%
+okay selects n equal to zero
+but you see actually also selects m
+
+ align:start position:0%
+but you see actually also selects m
+ 
+
+ align:start position:0%
+but you see actually also selects m
+equal to zero
+
+ align:start position:0%
+equal to zero
+ 
+
+ align:start position:0%
+equal to zero
+because you see with the same sign
+
+ align:start position:0%
+because you see with the same sign
+ 
+
+ align:start position:0%
+because you see with the same sign
+okay with the same sign
+
+ align:start position:0%
+okay with the same sign
+ 
+
+ align:start position:0%
+okay with the same sign
+you can easily check yourself
+
+ align:start position:0%
+you can easily check yourself
+ 
+
+ align:start position:0%
+you can easily check yourself
+when T goes to plus infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these now become
+
+ align:start position:0%
+so these now become
+ 
+
+ align:start position:0%
+so these now become
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+to equal to plus infinity
+
+ align:start position:0%
+to equal to plus infinity
+ 
+
+ align:start position:0%
+to equal to plus infinity
+so exponential minus i e m
+
+ align:start position:0%
+so exponential minus i e m
+ 
+
+ align:start position:0%
+so exponential minus i e m
+one minus Epsilon t
+
+ align:start position:0%
+one minus Epsilon t
+ 
+
+ align:start position:0%
+one minus Epsilon t
+times x n
+
+ align:start position:0%
+times x n
+ 
+
+ align:start position:0%
+times x n
+and then again this become
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero for m not equal for m not equal to
+
+ align:start position:0%
+zero for m not equal for m not equal to
+ 
+
+ align:start position:0%
+zero for m not equal for m not equal to
+for n no m not equal to zero and then
+
+ align:start position:0%
+for n no m not equal to zero and then
+ 
+
+ align:start position:0%
+for n no m not equal to zero and then
+then the ground state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this simple trick
+
+ align:start position:0%
+so so this simple trick
+ 
+
+ align:start position:0%
+so so this simple trick
+beautifully
+
+ align:start position:0%
+beautifully
+ 
+
+ align:start position:0%
+beautifully
+select
+
+ align:start position:0%
+select
+ 
+
+ align:start position:0%
+select
+the uh the m equal to zero and N equal
+
+ align:start position:0%
+the uh the m equal to zero and N equal
+ 
+
+ align:start position:0%
+the uh the m equal to zero and N equal
+to zero piece okay so now we can write
+
+ align:start position:0%
+to zero piece okay so now we can write
+ 
+
+ align:start position:0%
+to zero piece okay so now we can write
+so now we can write
+
+ align:start position:0%
+so now we can write
+ 
+
+ align:start position:0%
+so now we can write
+so so this is just the ground state wave
+
+ align:start position:0%
+so so this is just the ground state wave
+ 
+
+ align:start position:0%
+so so this is just the ground state wave
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+and this is just a ground state wave
+
+ align:start position:0%
+and this is just a ground state wave
+ 
+
+ align:start position:0%
+and this is just a ground state wave
+function okay so now we have
+
+ align:start position:0%
+function okay so now we have
+ 
+
+ align:start position:0%
+function okay so now we have
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+T Prime go to minus infinity and T
+
+ align:start position:0%
+T Prime go to minus infinity and T
+ 
+
+ align:start position:0%
+T Prime go to minus infinity and T
+equals to plus infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x t x
+
+ align:start position:0%
+x t x
+ 
+
+ align:start position:0%
+x t x
+Prime T Prime
+
+ align:start position:0%
+Prime T Prime
+ 
+
+ align:start position:0%
+Prime T Prime
+so not equal to so you have the ground
+
+ align:start position:0%
+so not equal to so you have the ground
+ 
+
+ align:start position:0%
+so not equal to so you have the ground
+state wave function star X
+
+ align:start position:0%
+state wave function star X
+ 
+
+ align:start position:0%
+state wave function star X
+um Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+now 0 x
+
+ align:start position:0%
+now 0 x
+ 
+
+ align:start position:0%
+now 0 x
+0 and then you have this phase Factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and with everything else goes to zero
+
+ align:start position:0%
+and with everything else goes to zero
+ 
+
+ align:start position:0%
+and with everything else goes to zero
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so to look at that
+
+ align:start position:0%
+so to look at that
+ 
+
+ align:start position:0%
+so to look at that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so this is the so now up to those
+
+ align:start position:0%
+and so this is the so now up to those
+ 
+
+ align:start position:0%
+and so this is the so now up to those
+factors
+
+ align:start position:0%
+factors
+ 
+
+ align:start position:0%
+factors
+after those factors we get what we want
+
+ align:start position:0%
+after those factors we get what we want
+ 
+
+ align:start position:0%
+after those factors we get what we want
+okay we get what we want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so but still you have another low in
+
+ align:start position:0%
+so but still you have another low in
+ 
+
+ align:start position:0%
+so but still you have another low in
+factors
+
+ align:start position:0%
+factors
+ 
+
+ align:start position:0%
+factors
+but they can be easily got off
+
+ align:start position:0%
+but they can be easily got off
+ 
+
+ align:start position:0%
+but they can be easily got off
+they can be easy they get rid of us
+
+ align:start position:0%
+they can be easy they get rid of us
+ 
+
+ align:start position:0%
+they can be easy they get rid of us
+using the following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you also similarly
+
+ align:start position:0%
+so now you also similarly
+ 
+
+ align:start position:0%
+so now you also similarly
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+exactly the same reasoning whether you
+
+ align:start position:0%
+exactly the same reasoning whether you
+ 
+
+ align:start position:0%
+exactly the same reasoning whether you
+so in this discussion whether you have X
+
+ align:start position:0%
+so in this discussion whether you have X
+ 
+
+ align:start position:0%
+so in this discussion whether you have X
+there or what's the form of X doesn't
+
+ align:start position:0%
+there or what's the form of X doesn't
+ 
+
+ align:start position:0%
+there or what's the form of X doesn't
+matter okay X can be anything
+
+ align:start position:0%
+matter okay X can be anything
+ 
+
+ align:start position:0%
+matter okay X can be anything
+so X can be anything so so
+
+ align:start position:0%
+so X can be anything so so
+ 
+
+ align:start position:0%
+so X can be anything so so
+so you can just take x equal to 1 okay
+
+ align:start position:0%
+so you can just take x equal to 1 okay
+ 
+
+ align:start position:0%
+so you can just take x equal to 1 okay
+and then you also have
+
+ align:start position:0%
+and then you also have
+ 
+
+ align:start position:0%
+and then you also have
+limit T goes to plus infinity
+
+ align:start position:0%
+limit T goes to plus infinity
+ 
+
+ align:start position:0%
+limit T goes to plus infinity
+T Prime goes to minus infinity
+
+ align:start position:0%
+T Prime goes to minus infinity
+ 
+
+ align:start position:0%
+T Prime goes to minus infinity
+the x t
+
+ align:start position:0%
+the x t
+ 
+
+ align:start position:0%
+the x t
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+so this is also equal to psi 0 x sine
+
+ align:start position:0%
+so this is also equal to psi 0 x sine
+ 
+
+ align:start position:0%
+so this is also equal to psi 0 x sine
+zero star
+
+ align:start position:0%
+zero star
+ 
+
+ align:start position:0%
+zero star
+X Prime
+
+ align:start position:0%
+X Prime
+ 
+
+ align:start position:0%
+X Prime
+and now is the zero with zero okay
+
+ align:start position:0%
+and now is the zero with zero okay
+ 
+
+ align:start position:0%
+and now is the zero with zero okay
+because the uh if set x equal to 1 okay
+
+ align:start position:0%
+because the uh if set x equal to 1 okay
+ 
+
+ align:start position:0%
+because the uh if set x equal to 1 okay
+and then you just ground state and so so
+
+ align:start position:0%
+and then you just ground state and so so
+ 
+
+ align:start position:0%
+and then you just ground state and so so
+this is just equal to one
+
+ align:start position:0%
+this is just equal to one
+ 
+
+ align:start position:0%
+this is just equal to one
+and then you have the same factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we can just find the GN
+
+ align:start position:0%
+now we can just find the GN
+ 
+
+ align:start position:0%
+now we can just find the GN
+okay so this object is GN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so GN then can be found as the ratio
+
+ align:start position:0%
+so GN then can be found as the ratio
+ 
+
+ align:start position:0%
+so GN then can be found as the ratio
+between the two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+take the limit t plus infinity T Prime
+
+ align:start position:0%
+take the limit t plus infinity T Prime
+ 
+
+ align:start position:0%
+take the limit t plus infinity T Prime
+go to minus infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+have x t
+
+ align:start position:0%
+have x t
+ 
+
+ align:start position:0%
+have x t
+X Prime T Prime
+
+ align:start position:0%
+X Prime T Prime
+ 
+
+ align:start position:0%
+X Prime T Prime
+and x t
+
+ align:start position:0%
+and x t
+ 
+
+ align:start position:0%
+and x t
+and x x t
+
+ align:start position:0%
+and x x t
+ 
+
+ align:start position:0%
+and x x t
+okay you can just find that as a ratio
+
+ align:start position:0%
+okay you can just find that as a ratio
+ 
+
+ align:start position:0%
+okay you can just find that as a ratio
+between the two
+
+ align:start position:0%
+between the two
+ 
+
+ align:start position:0%
+between the two
+so this gives you the expression
+
+ align:start position:0%
+so this gives you the expression
+ 
+
+ align:start position:0%
+so this gives you the expression
+for calculating this cooling function
+
+ align:start position:0%
+for calculating this cooling function
+ 
+
+ align:start position:0%
+for calculating this cooling function
+okay uh this correlation function
+
+ align:start position:0%
+okay uh this correlation function
+ 
+
+ align:start position:0%
+okay uh this correlation function
+so in the axis any time order the
+
+ align:start position:0%
+so in the axis any time order the
+ 
+
+ align:start position:0%
+so in the axis any time order the
+product okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and therefore now for each of them below
+
+ align:start position:0%
+and therefore now for each of them below
+ 
+
+ align:start position:0%
+and therefore now for each of them below
+the path integral
+
+ align:start position:0%
+the path integral
+ 
+
+ align:start position:0%
+the path integral
+and then you can just write down the
+
+ align:start position:0%
+and then you can just write down the
+ 
+
+ align:start position:0%
+and then you can just write down the
+pattern and go for each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now you see
+
+ align:start position:0%
+so now you see
+ 
+
+ align:start position:0%
+so now you see
+this GN is in principle or a physical
+
+ align:start position:0%
+this GN is in principle or a physical
+ 
+
+ align:start position:0%
+this GN is in principle or a physical
+observable that actually involving the
+
+ align:start position:0%
+observable that actually involving the
+ 
+
+ align:start position:0%
+observable that actually involving the
+ratio of two passing goals
+
+ align:start position:0%
+ratio of two passing goals
+ 
+
+ align:start position:0%
+ratio of two passing goals
+when without any X and Y with some x a
+
+ align:start position:0%
+when without any X and Y with some x a
+ 
+
+ align:start position:0%
+when without any X and Y with some x a
+visual desired correlation functions so
+
+ align:start position:0%
+visual desired correlation functions so
+ 
+
+ align:start position:0%
+visual desired correlation functions so
+as I mentioned before
+
+ align:start position:0%
+as I mentioned before
+ 
+
+ align:start position:0%
+as I mentioned before
+that when you evaluate the path
+
+ align:start position:0%
+that when you evaluate the path
+ 
+
+ align:start position:0%
+that when you evaluate the path
+integrals you will get that kind of C
+
+ align:start position:0%
+integrals you will get that kind of C
+ 
+
+ align:start position:0%
+integrals you will get that kind of C
+between upstairs and downstairs NATO we
+
+ align:start position:0%
+between upstairs and downstairs NATO we
+ 
+
+ align:start position:0%
+between upstairs and downstairs NATO we
+will see explicitly
+
+ align:start position:0%
+will see explicitly
+ 
+
+ align:start position:0%
+will see explicitly
+okay so yeah so this is a beautiful
+
+ align:start position:0%
+okay so yeah so this is a beautiful
+ 
+
+ align:start position:0%
+okay so yeah so this is a beautiful
+formula okay and uh and the
+
+ align:start position:0%
+formula okay and uh and the
+ 
+
+ align:start position:0%
+formula okay and uh and the
+um yeah
+
+ align:start position:0%
+um yeah
+ 
+
+ align:start position:0%
+um yeah
+and and then you don't have to
+
+ align:start position:0%
+and and then you don't have to
+ 
+
+ align:start position:0%
+and and then you don't have to
+you don't have to uh uh uh
+
+ align:start position:0%
+you don't have to uh uh uh
+ 
+
+ align:start position:0%
+you don't have to uh uh uh
+um yeah yeah so all those factors
+
+ align:start position:0%
+um yeah yeah so all those factors
+ 
+
+ align:start position:0%
+um yeah yeah so all those factors
+canceled you don't need to know the
+
+ align:start position:0%
+canceled you don't need to know the
+ 
+
+ align:start position:0%
+canceled you don't need to know the
+ground state wave function you can just
+
+ align:start position:0%
+ground state wave function you can just
+ 
+
+ align:start position:0%
+ground state wave function you can just
+perform that path in the code
+
+ align:start position:0%
+perform that path in the code
+ 
+
+ align:start position:0%
+perform that path in the code
+okay uh perform that path in the ground
+
+ align:start position:0%
+okay uh perform that path in the ground
+ 
+
+ align:start position:0%
+okay uh perform that path in the ground
+and here in principle you can also take
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arbitrary
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and x Prime
+
+ align:start position:0%
+x and x Prime
+ 
+
+ align:start position:0%
+x and x Prime
+okay you can take aperture X and the
+
+ align:start position:0%
+okay you can take aperture X and the
+ 
+
+ align:start position:0%
+okay you can take aperture X and the
+exponent doesn't matter
+
+ align:start position:0%
+exponent doesn't matter
+ 
+
+ align:start position:0%
+exponent doesn't matter
+so conventionally we just take x equal
+
+ align:start position:0%
+so conventionally we just take x equal
+ 
+
+ align:start position:0%
+so conventionally we just take x equal
+to X Prime equal to zero
+
+ align:start position:0%
+to X Prime equal to zero
+ 
+
+ align:start position:0%
+to X Prime equal to zero
+that's for Simplicity okay
+
+ align:start position:0%
+that's for Simplicity okay
+ 
+
+ align:start position:0%
+that's for Simplicity okay
+we can just take them to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay any questions on this
+
+ align:start position:0%
+okay any questions on this
+ 
+
+ align:start position:0%
+okay any questions on this
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah I just the only thing matters is
+
+ align:start position:0%
+yeah I just the only thing matters is
+ 
+
+ align:start position:0%
+yeah I just the only thing matters is
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+so they only come into this
+
+ align:start position:0%
+so they only come into this
+ 
+
+ align:start position:0%
+so they only come into this
+pre-factor and then cancel the between
+
+ align:start position:0%
+pre-factor and then cancel the between
+ 
+
+ align:start position:0%
+pre-factor and then cancel the between
+the two it doesn't matter
+
+ align:start position:0%
+the two it doesn't matter
+ 
+
+ align:start position:0%
+the two it doesn't matter
+yeah so yeah all the uh the factors
+
+ align:start position:0%
+yeah so yeah all the uh the factors
+ 
+
+ align:start position:0%
+yeah so yeah all the uh the factors
+there and this Factor they just cancel
+
+ align:start position:0%
+there and this Factor they just cancel
+ 
+
+ align:start position:0%
+there and this Factor they just cancel
+and you just have to be this
+
+ align:start position:0%
+and you just have to be this
+ 
+
+ align:start position:0%
+and you just have to be this
+x0 left so so it doesn't matter they
+
+ align:start position:0%
+x0 left so so it doesn't matter they
+ 
+
+ align:start position:0%
+x0 left so so it doesn't matter they
+cancel anyway so it doesn't matter where
+
+ align:start position:0%
+cancel anyway so it doesn't matter where
+ 
+
+ align:start position:0%
+cancel anyway so it doesn't matter where
+you put x and x Prime
+
+ align:start position:0%
+you put x and x Prime
+ 
+
+ align:start position:0%
+you put x and x Prime
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so normally when you calculate that
+
+ align:start position:0%
+so so normally when you calculate that
+ 
+
+ align:start position:0%
+so so normally when you calculate that
+at the end and then you take Epsilon
+
+ align:start position:0%
+at the end and then you take Epsilon
+ 
+
+ align:start position:0%
+at the end and then you take Epsilon
+goes to zero yeah so we just normally
+
+ align:start position:0%
+goes to zero yeah so we just normally
+ 
+
+ align:start position:0%
+goes to zero yeah so we just normally
+believe that it implicit
+
+ align:start position:0%
+believe that it implicit
+ 
+
+ align:start position:0%
+believe that it implicit
+yeah when you do the path integral you
+
+ align:start position:0%
+yeah when you do the path integral you
+ 
+
+ align:start position:0%
+yeah when you do the path integral you
+keep a small Epsilon
+
+ align:start position:0%
+keep a small Epsilon
+ 
+
+ align:start position:0%
+keep a small Epsilon
+and so after you finish doing the
+
+ align:start position:0%
+and so after you finish doing the
+ 
+
+ align:start position:0%
+and so after you finish doing the
+passing after you finish in the end you
+
+ align:start position:0%
+passing after you finish in the end you
+ 
+
+ align:start position:0%
+passing after you finish in the end you
+take the absolute zero
+
+ align:start position:0%
+take the absolute zero
+ 
+
+ align:start position:0%
+take the absolute zero
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+I'm sorry also on why we can take x and
+
+ align:start position:0%
+I'm sorry also on why we can take x and
+ 
+
+ align:start position:0%
+I'm sorry also on why we can take x and
+x Prime equals
+
+ align:start position:0%
+x Prime equals
+ 
+
+ align:start position:0%
+x Prime equals
+like the balance depend on X and X Prime
+
+ align:start position:0%
+like the balance depend on X and X Prime
+ 
+
+ align:start position:0%
+like the balance depend on X and X Prime
+now the bounds does not depend on it's
+
+ align:start position:0%
+now the bounds does not depend on it's
+ 
+
+ align:start position:0%
+now the bounds does not depend on it's
+only the the particle is only limited by
+
+ align:start position:0%
+only the the particle is only limited by
+ 
+
+ align:start position:0%
+only the the particle is only limited by
+T and T T Prime t
+
+ align:start position:0%
+T and T T Prime t
+ 
+
+ align:start position:0%
+T and T T Prime t
+yeah initial value uh they're the same
+
+ align:start position:0%
+yeah initial value uh they're the same
+ 
+
+ align:start position:0%
+yeah initial value uh they're the same
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+of course specific value of this path
+
+ align:start position:0%
+of course specific value of this path
+ 
+
+ align:start position:0%
+of course specific value of this path
+integral will depend on X and X Prime
+
+ align:start position:0%
+integral will depend on X and X Prime
+ 
+
+ align:start position:0%
+integral will depend on X and X Prime
+but the console between offset and
+
+ align:start position:0%
+but the console between offset and
+ 
+
+ align:start position:0%
+but the console between offset and
+downstairs
+
+ align:start position:0%
+downstairs
+ 
+
+ align:start position:0%
+downstairs
+so so the canceled yeah and so in the
+
+ align:start position:0%
+so so the canceled yeah and so in the
+ 
+
+ align:start position:0%
+so so the canceled yeah and so in the
+end this right hand side does not depend
+
+ align:start position:0%
+end this right hand side does not depend
+ 
+
+ align:start position:0%
+end this right hand side does not depend
+on X and X Prime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah also you see here
+
+ align:start position:0%
+yeah also you see here
+ 
+
+ align:start position:0%
+yeah also you see here
+if this formula makes any sense
+
+ align:start position:0%
+if this formula makes any sense
+ 
+
+ align:start position:0%
+if this formula makes any sense
+the left hand side does not depend on X
+
+ align:start position:0%
+the left hand side does not depend on X
+ 
+
+ align:start position:0%
+the left hand side does not depend on X
+and X Prime so so the right hand side
+
+ align:start position:0%
+and X Prime so so the right hand side
+ 
+
+ align:start position:0%
+and X Prime so so the right hand side
+must not depend on X X prime otherwise
+
+ align:start position:0%
+must not depend on X X prime otherwise
+ 
+
+ align:start position:0%
+must not depend on X X prime otherwise
+this formula immediately wrong
+
+ align:start position:0%
+this formula immediately wrong
+ 
+
+ align:start position:0%
+this formula immediately wrong
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's right that's right yeah just when
+
+ align:start position:0%
+that's right that's right yeah just when
+ 
+
+ align:start position:0%
+that's right that's right yeah just when
+you do the calculation you keep a small
+
+ align:start position:0%
+you do the calculation you keep a small
+ 
+
+ align:start position:0%
+you do the calculation you keep a small
+Epsilon when you do the path integral it
+
+ align:start position:0%
+Epsilon when you do the path integral it
+ 
+
+ align:start position:0%
+Epsilon when you do the path integral it
+keeps more absolute but but when you
+
+ align:start position:0%
+keeps more absolute but but when you
+ 
+
+ align:start position:0%
+keeps more absolute but but when you
+finally calculate the value answer you
+
+ align:start position:0%
+finally calculate the value answer you
+ 
+
+ align:start position:0%
+finally calculate the value answer you
+can set Epsilon to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um no you have to keep Epsilon
+
+ align:start position:0%
+um no you have to keep Epsilon
+ 
+
+ align:start position:0%
+um no you have to keep Epsilon
+this you have to take first
+
+ align:start position:0%
+this you have to take first
+ 
+
+ align:start position:0%
+this you have to take first
+so this is part of your calculation
+
+ align:start position:0%
+so this is part of your calculation
+ 
+
+ align:start position:0%
+so this is part of your calculation
+you have to always take this first
+
+ align:start position:0%
+you have to always take this first
+ 
+
+ align:start position:0%
+you have to always take this first
+and the big because the final answer
+
+ align:start position:0%
+and the big because the final answer
+ 
+
+ align:start position:0%
+and the big because the final answer
+also does not depend on T and T Prime
+
+ align:start position:0%
+also does not depend on T and T Prime
+ 
+
+ align:start position:0%
+also does not depend on T and T Prime
+and because this is the vacuum uh this
+
+ align:start position:0%
+and because this is the vacuum uh this
+ 
+
+ align:start position:0%
+and because this is the vacuum uh this
+correlation function does not depend on
+
+ align:start position:0%
+correlation function does not depend on
+ 
+
+ align:start position:0%
+correlation function does not depend on
+your T and T Prime so so you uh you
+
+ align:start position:0%
+your T and T Prime so so you uh you
+ 
+
+ align:start position:0%
+your T and T Prime so so you uh you
+always
+
+ align:start position:0%
+always
+ 
+
+ align:start position:0%
+always
+set the uh yeah you keep a small Epsilon
+
+ align:start position:0%
+set the uh yeah you keep a small Epsilon
+ 
+
+ align:start position:0%
+set the uh yeah you keep a small Epsilon
+take this limit first and do the
+
+ align:start position:0%
+take this limit first and do the
+ 
+
+ align:start position:0%
+take this limit first and do the
+calculation
+
+ align:start position:0%
+calculation
+ 
+
+ align:start position:0%
+calculation
+do the calculation and then when you
+
+ align:start position:0%
+do the calculation and then when you
+ 
+
+ align:start position:0%
+do the calculation and then when you
+calculate everything at the end of the
+
+ align:start position:0%
+calculate everything at the end of the
+ 
+
+ align:start position:0%
+calculate everything at the end of the
+day then you set Epsilon to zero
+
+ align:start position:0%
+day then you set Epsilon to zero
+ 
+
+ align:start position:0%
+day then you set Epsilon to zero
+and then that guarantee you choose the
+
+ align:start position:0%
+and then that guarantee you choose the
+ 
+
+ align:start position:0%
+and then that guarantee you choose the
+vacuum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go to this
+
+ align:start position:0%
+go to this
+ 
+
+ align:start position:0%
+go to this
+this of
+
+ align:start position:0%
+this of
+ 
+
+ align:start position:0%
+this of
+one more
+
+ align:start position:0%
+one more
+ 
+
+ align:start position:0%
+one more
+uh a trick we have to do okay sorry it
+
+ align:start position:0%
+uh a trick we have to do okay sorry it
+ 
+
+ align:start position:0%
+uh a trick we have to do okay sorry it
+had too many tricks there's one more
+
+ align:start position:0%
+had too many tricks there's one more
+ 
+
+ align:start position:0%
+had too many tricks there's one more
+trick we have to do
+
+ align:start position:0%
+trick we have to do
+ 
+
+ align:start position:0%
+trick we have to do
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so so now we have told you how to
+
+ align:start position:0%
+so so now we have told you how to
+ 
+
+ align:start position:0%
+so so now we have told you how to
+calculate this guy for arbitrary X
+
+ align:start position:0%
+calculate this guy for arbitrary X
+ 
+
+ align:start position:0%
+calculate this guy for arbitrary X
+but often it's actually
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's actually uh not
+
+ align:start position:0%
+it's actually uh not
+ 
+
+ align:start position:0%
+it's actually uh not
+it's not the smartest way
+
+ align:start position:0%
+it's not the smartest way
+ 
+
+ align:start position:0%
+it's not the smartest way
+to directly calculate such a endpoint
+
+ align:start position:0%
+to directly calculate such a endpoint
+ 
+
+ align:start position:0%
+to directly calculate such a endpoint
+function okay
+
+ align:start position:0%
+function okay
+ 
+
+ align:start position:0%
+function okay
+it's also not the smartest way
+
+ align:start position:0%
+it's also not the smartest way
+ 
+
+ align:start position:0%
+it's also not the smartest way
+so so there's something a little bit
+
+ align:start position:0%
+so so there's something a little bit
+ 
+
+ align:start position:0%
+so so there's something a little bit
+uh more
+
+ align:start position:0%
+uh more
+ 
+
+ align:start position:0%
+uh more
+uh uh more clever it's called generating
+
+ align:start position:0%
+uh uh more clever it's called generating
+ 
+
+ align:start position:0%
+uh uh more clever it's called generating
+functional
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so some of you may have seen this
+
+ align:start position:0%
+so some of you may have seen this
+ 
+
+ align:start position:0%
+so some of you may have seen this
+say in your high school math competition
+
+ align:start position:0%
+say in your high school math competition
+ 
+
+ align:start position:0%
+say in your high school math competition
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+so suppose we wanted to integral like
+
+ align:start position:0%
+so suppose we wanted to integral like
+ 
+
+ align:start position:0%
+so suppose we wanted to integral like
+this okay
+
+ align:start position:0%
+this okay
+ 
+
+ align:start position:0%
+this okay
+so let's do again let's go back to
+
+ align:start position:0%
+so let's do again let's go back to
+ 
+
+ align:start position:0%
+so let's do again let's go back to
+ordinary integral
+
+ align:start position:0%
+ordinary integral
+ 
+
+ align:start position:0%
+ordinary integral
+so let's just I suppose we wanted to
+
+ align:start position:0%
+so let's just I suppose we wanted to
+ 
+
+ align:start position:0%
+so let's just I suppose we wanted to
+integral like this so so you have a
+
+ align:start position:0%
+integral like this so so you have a
+ 
+
+ align:start position:0%
+integral like this so so you have a
+parallel let's just say
+
+ align:start position:0%
+parallel let's just say
+ 
+
+ align:start position:0%
+parallel let's just say
+this we have some face like what you do
+
+ align:start position:0%
+this we have some face like what you do
+ 
+
+ align:start position:0%
+this we have some face like what you do
+in the past integral and we want to
+
+ align:start position:0%
+in the past integral and we want to
+ 
+
+ align:start position:0%
+in the past integral and we want to
+calculate x to the power n
+
+ align:start position:0%
+calculate x to the power n
+ 
+
+ align:start position:0%
+calculate x to the power n
+okay I need some integer
+
+ align:start position:0%
+okay I need some integer
+ 
+
+ align:start position:0%
+okay I need some integer
+uh here yeah here like you have endpoint
+
+ align:start position:0%
+uh here yeah here like you have endpoint
+ 
+
+ align:start position:0%
+uh here yeah here like you have endpoint
+function yeah yeah suppose we want to
+
+ align:start position:0%
+function yeah yeah suppose we want to
+ 
+
+ align:start position:0%
+function yeah yeah suppose we want to
+calculate this
+
+ align:start position:0%
+calculate this
+ 
+
+ align:start position:0%
+calculate this
+so you can just calculate this guy is
+
+ align:start position:0%
+so you can just calculate this guy is
+ 
+
+ align:start position:0%
+so you can just calculate this guy is
+fine okay but but there's a better way
+
+ align:start position:0%
+fine okay but but there's a better way
+ 
+
+ align:start position:0%
+fine okay but but there's a better way
+uh often there's a better way it is that
+
+ align:start position:0%
+uh often there's a better way it is that
+ 
+
+ align:start position:0%
+uh often there's a better way it is that
+instead of calculate this for individual
+
+ align:start position:0%
+instead of calculate this for individual
+ 
+
+ align:start position:0%
+instead of calculate this for individual
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+you can actually consider a following
+
+ align:start position:0%
+you can actually consider a following
+ 
+
+ align:start position:0%
+you can actually consider a following
+quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the d a
+
+ align:start position:0%
+the d a
+ 
+
+ align:start position:0%
+the d a
+uh and which is defined to be
+
+ align:start position:0%
+uh and which is defined to be
+ 
+
+ align:start position:0%
+uh and which is defined to be
+DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expansion I
+
+ align:start position:0%
+expansion I
+ 
+
+ align:start position:0%
+expansion I
+Lambda f x
+
+ align:start position:0%
+Lambda f x
+ 
+
+ align:start position:0%
+Lambda f x
+then plus I
+
+ align:start position:0%
+then plus I
+ 
+
+ align:start position:0%
+then plus I
+say ax
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so you can see that this object
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this object when you expand this
+
+ align:start position:0%
+so this object when you expand this
+ 
+
+ align:start position:0%
+so this object when you expand this
+exponential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I don't need this anymore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah let me just erase this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now if you so why we are interested
+
+ align:start position:0%
+so now if you so why we are interested
+ 
+
+ align:start position:0%
+so now if you so why we are interested
+in this object
+
+ align:start position:0%
+in this object
+ 
+
+ align:start position:0%
+in this object
+because imagine you you expanded this
+
+ align:start position:0%
+because imagine you you expanded this
+ 
+
+ align:start position:0%
+because imagine you you expanded this
+exponential Factor
+
+ align:start position:0%
+exponential Factor
+ 
+
+ align:start position:0%
+exponential Factor
+and then you
+
+ align:start position:0%
+and then you
+ 
+
+ align:start position:0%
+and then you
+essentially you get the a
+
+ align:start position:0%
+essentially you get the a
+ 
+
+ align:start position:0%
+essentially you get the a
+is exponential n equal to zero to
+
+ align:start position:0%
+is exponential n equal to zero to
+ 
+
+ align:start position:0%
+is exponential n equal to zero to
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and factorial
+
+ align:start position:0%
+and factorial
+ 
+
+ align:start position:0%
+and factorial
+i a n d n okay so if you expand this
+
+ align:start position:0%
+i a n d n okay so if you expand this
+ 
+
+ align:start position:0%
+i a n d n okay so if you expand this
+thing in power series of a or power
+
+ align:start position:0%
+thing in power series of a or power
+ 
+
+ align:start position:0%
+thing in power series of a or power
+Series yeah if you expand this and then
+
+ align:start position:0%
+Series yeah if you expand this and then
+ 
+
+ align:start position:0%
+Series yeah if you expand this and then
+just n's term will give you an X power n
+
+ align:start position:0%
+just n's term will give you an X power n
+ 
+
+ align:start position:0%
+just n's term will give you an X power n
+and then it's the same that we just
+
+ align:start position:0%
+and then it's the same that we just
+ 
+
+ align:start position:0%
+and then it's the same that we just
+expand
+
+ align:start position:0%
+expand
+ 
+
+ align:start position:0%
+expand
+this is the a in power series
+
+ align:start position:0%
+this is the a in power series
+ 
+
+ align:start position:0%
+this is the a in power series
+and then the M would be the end
+
+ align:start position:0%
+and then the M would be the end
+ 
+
+ align:start position:0%
+and then the M would be the end
+coefficient
+
+ align:start position:0%
+coefficient
+ 
+
+ align:start position:0%
+coefficient
+okay so so if you compute
+
+ align:start position:0%
+okay so so if you compute
+ 
+
+ align:start position:0%
+okay so so if you compute
+the a in one shot
+
+ align:start position:0%
+the a in one shot
+ 
+
+ align:start position:0%
+the a in one shot
+and then and then the the the the N you
+
+ align:start position:0%
+and then and then the the the the N you
+ 
+
+ align:start position:0%
+and then and then the the the the N you
+can just do about about Taylor series
+
+ align:start position:0%
+can just do about about Taylor series
+ 
+
+ align:start position:0%
+can just do about about Taylor series
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so sometimes we also write the n
+
+ align:start position:0%
+so sometimes we also write the n
+ 
+
+ align:start position:0%
+so sometimes we also write the n
+as say I to the power n
+
+ align:start position:0%
+as say I to the power n
+ 
+
+ align:start position:0%
+as say I to the power n
+then you take n derivative of the a
+
+ align:start position:0%
+then you take n derivative of the a
+ 
+
+ align:start position:0%
+then you take n derivative of the a
+over a
+
+ align:start position:0%
+over a
+ 
+
+ align:start position:0%
+over a
+and then you set a equal to zero okay
+
+ align:start position:0%
+and then you set a equal to zero okay
+ 
+
+ align:start position:0%
+and then you set a equal to zero okay
+so this is the same thing
+
+ align:start position:0%
+so this is the same thing
+ 
+
+ align:start position:0%
+so this is the same thing
+so when you set Take N derivatives
+
+ align:start position:0%
+so when you set Take N derivatives
+ 
+
+ align:start position:0%
+so when you set Take N derivatives
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+you get rid of the earlier the lower
+
+ align:start position:0%
+you get rid of the earlier the lower
+ 
+
+ align:start position:0%
+you get rid of the earlier the lower
+powers
+
+ align:start position:0%
+powers
+ 
+
+ align:start position:0%
+powers
+and then the higher Powers you get rid
+
+ align:start position:0%
+and then the higher Powers you get rid
+ 
+
+ align:start position:0%
+and then the higher Powers you get rid
+of by setting a equal to zero
+
+ align:start position:0%
+of by setting a equal to zero
+ 
+
+ align:start position:0%
+of by setting a equal to zero
+okay so then that's just pick this term
+
+ align:start position:0%
+okay so then that's just pick this term
+ 
+
+ align:start position:0%
+okay so then that's just pick this term
+okay pick the end
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so this is so d a is called the
+
+ align:start position:0%
+so so this is so d a is called the
+ 
+
+ align:start position:0%
+so so this is so d a is called the
+generating function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay a generating function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh okay so now when we want to so one
+
+ align:start position:0%
+oh okay so now when we want to so one
+ 
+
+ align:start position:0%
+oh okay so now when we want to so one
+final remark
+
+ align:start position:0%
+final remark
+ 
+
+ align:start position:0%
+final remark
+so now we want to compute this guy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this GN
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is equal to t x 1 say x n
+
+ align:start position:0%
+is equal to t x 1 say x n
+ 
+
+ align:start position:0%
+is equal to t x 1 say x n
+so xc1 x t n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again instead of computing each one of
+
+ align:start position:0%
+again instead of computing each one of
+ 
+
+ align:start position:0%
+again instead of computing each one of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+we can consider such a so-called
+
+ align:start position:0%
+we can consider such a so-called
+ 
+
+ align:start position:0%
+we can consider such a so-called
+generating function of generation of
+
+ align:start position:0%
+generating function of generation of
+ 
+
+ align:start position:0%
+generating function of generation of
+this idea we can consider Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+JT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can consider this object dxt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now add I
+
+ align:start position:0%
+and now add I
+ 
+
+ align:start position:0%
+and now add I
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+so minus infinity to plus infinity JT
+
+ align:start position:0%
+so minus infinity to plus infinity JT
+ 
+
+ align:start position:0%
+so minus infinity to plus infinity JT
+x t
+
+ align:start position:0%
+x t
+ 
+
+ align:start position:0%
+x t
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so remember this is just the path
+
+ align:start position:0%
+so remember this is just the path
+ 
+
+ align:start position:0%
+so remember this is just the path
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+so let's just look at the upstairs okay
+
+ align:start position:0%
+so let's just look at the upstairs okay
+ 
+
+ align:start position:0%
+so let's just look at the upstairs okay
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+expansion I X
+
+ align:start position:0%
+expansion I X
+ 
+
+ align:start position:0%
+expansion I X
+commission is
+
+ align:start position:0%
+commission is
+ 
+
+ align:start position:0%
+commission is
+x t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now this does the same thing so now
+
+ align:start position:0%
+so now this does the same thing so now
+ 
+
+ align:start position:0%
+so now this does the same thing so now
+if you take this imagine you expand this
+
+ align:start position:0%
+if you take this imagine you expand this
+ 
+
+ align:start position:0%
+if you take this imagine you expand this
+Factor
+
+ align:start position:0%
+Factor
+ 
+
+ align:start position:0%
+Factor
+okay and then
+
+ align:start position:0%
+okay and then
+ 
+
+ align:start position:0%
+okay and then
+to ends power then you will generate
+
+ align:start position:0%
+to ends power then you will generate
+ 
+
+ align:start position:0%
+to ends power then you will generate
+this term as a coefficient okay we will
+
+ align:start position:0%
+this term as a coefficient okay we will
+ 
+
+ align:start position:0%
+this term as a coefficient okay we will
+discuss that in more detail next time
+
+ align:start position:0%
+discuss that in more detail next time
+ 
+
+ align:start position:0%
+discuss that in more detail next time
+okay so so so so so often instead of
+
+ align:start position:0%
+okay so so so so so often instead of
+ 
+
+ align:start position:0%
+okay so so so so so often instead of
+computing
+
+ align:start position:0%
+computing
+ 
+
+ align:start position:0%
+computing
+this object directly
+
+ align:start position:0%
+this object directly
+ 
+
+ align:start position:0%
+this object directly
+we compute a generating functional
+
+ align:start position:0%
+we compute a generating functional
+ 
+
+ align:start position:0%
+we compute a generating functional
+so-called generating functional and then
+
+ align:start position:0%
+so-called generating functional and then
+ 
+
+ align:start position:0%
+so-called generating functional and then
+and then which often makes sense much
+
+ align:start position:0%
+and then which often makes sense much
+ 
+
+ align:start position:0%
+and then which often makes sense much
+easier
+
+ align:start position:0%
+easier
+ 
+
+ align:start position:0%
+easier
+okay I often makes things much easier
+
+ align:start position:0%
+okay I often makes things much easier
+ 
+
+ align:start position:0%
+okay I often makes things much easier
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah so this this preparation and then
+
+ align:start position:0%
+yeah so this this preparation and then
+ 
+
+ align:start position:0%
+yeah so this this preparation and then
+we are ready to
+
+ align:start position:0%
+we are ready to
+ 
+
+ align:start position:0%
+we are ready to
+tackle
+
+ align:start position:0%
+tackle
+ 
+
+ align:start position:0%
+tackle
+how to treat this thing
+
+ align:start position:0%
+how to treat this thing
+ 
+
+ align:start position:0%
+how to treat this thing
+in uh how to uh actually finding such
+
+ align:start position:0%
+in uh how to uh actually finding such
+ 
+
+ align:start position:0%
+in uh how to uh actually finding such
+object in quantum mechanics
+
+ align:start position:0%
+object in quantum mechanics
+ 
+
+ align:start position:0%
+object in quantum mechanics
+and once we have that doing field Theory
+
+ align:start position:0%
+and once we have that doing field Theory
+ 
+
+ align:start position:0%
+and once we have that doing field Theory
+will be automatic
+
+ align:start position:0%
+will be automatic
+ 
+
+ align:start position:0%
+will be automatic
+and then then you will
+
+ align:start position:0%
+and then then you will
+ 
+
+ align:start position:0%
+and then then you will
+then know how to actually calculate the
+
+ align:start position:0%
+then know how to actually calculate the
+ 
+
+ align:start position:0%
+then know how to actually calculate the
+scattering amplitude which is a good
+
+ align:start position:0%
+scattering amplitude which is a good
+ 
+
+ align:start position:0%
+scattering amplitude which is a good
+achievement yeah
+
+ align:start position:0%
+achievement yeah
+ 
+
+ align:start position:0%
+achievement yeah
+okay so so let's stop here
\ No newline at end of file
diff --git a/GyFVgJZ0hIs.txt b/GyFVgJZ0hIs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..34817f0036d3f9e8d66bd9ea3392b40b122e0d41
--- /dev/null
+++ b/GyFVgJZ0hIs.txt
@@ -0,0 +1,1811 @@
+align:start position:0%
+ 
+in 6042 we're going to be pretty
+
+ align:start position:0%
+in 6042 we're going to be pretty
+ 
+
+ align:start position:0%
+in 6042 we're going to be pretty
+concerned with proofs we're going to try
+
+ align:start position:0%
+concerned with proofs we're going to try
+ 
+
+ align:start position:0%
+concerned with proofs we're going to try
+to help you learn how to do rudimentary
+
+ align:start position:0%
+to help you learn how to do rudimentary
+ 
+
+ align:start position:0%
+to help you learn how to do rudimentary
+proofs uh and not be afraid of them the
+
+ align:start position:0%
+proofs uh and not be afraid of them the
+ 
+
+ align:start position:0%
+proofs uh and not be afraid of them the
+most important skill in some ways is the
+
+ align:start position:0%
+most important skill in some ways is the
+ 
+
+ align:start position:0%
+most important skill in some ways is the
+ability to distinguish a very plausible
+
+ align:start position:0%
+ability to distinguish a very plausible
+ 
+
+ align:start position:0%
+ability to distinguish a very plausible
+argument that might not be totally right
+
+ align:start position:0%
+argument that might not be totally right
+ 
+
+ align:start position:0%
+argument that might not be totally right
+from a proof which is totally right
+
+ align:start position:0%
+from a proof which is totally right
+ 
+
+ align:start position:0%
+from a proof which is totally right
+that's an important skill and it's a
+
+ align:start position:0%
+that's an important skill and it's a
+ 
+
+ align:start position:0%
+that's an important skill and it's a
+it's a basic understanding of what math
+
+ align:start position:0%
+it's a basic understanding of what math
+ 
+
+ align:start position:0%
+it's a basic understanding of what math
+is it's that distinction between knowing
+
+ align:start position:0%
+is it's that distinction between knowing
+ 
+
+ align:start position:0%
+is it's that distinction between knowing
+when a thing is mathematically
+
+ align:start position:0%
+when a thing is mathematically
+ 
+
+ align:start position:0%
+when a thing is mathematically
+absolutely uh unarguable and and uh
+
+ align:start position:0%
+absolutely uh unarguable and and uh
+ 
+
+ align:start position:0%
+absolutely uh unarguable and and uh
+inevitable as opposed to something
+
+ align:start position:0%
+inevitable as opposed to something
+ 
+
+ align:start position:0%
+inevitable as opposed to something
+that's just very likely it's interesting
+
+ align:start position:0%
+that's just very likely it's interesting
+ 
+
+ align:start position:0%
+that's just very likely it's interesting
+physicists by and large do a lot of math
+
+ align:start position:0%
+physicists by and large do a lot of math
+ 
+
+ align:start position:0%
+physicists by and large do a lot of math
+and they tend not to worry so much about
+
+ align:start position:0%
+and they tend not to worry so much about
+ 
+
+ align:start position:0%
+and they tend not to worry so much about
+proofs but all the theoreticians and the
+
+ align:start position:0%
+proofs but all the theoreticians and the
+ 
+
+ align:start position:0%
+proofs but all the theoreticians and the
+mathematicians are uh in agreement that
+
+ align:start position:0%
+mathematicians are uh in agreement that
+ 
+
+ align:start position:0%
+mathematicians are uh in agreement that
+that you don't really understand the
+
+ align:start position:0%
+that you don't really understand the
+ 
+
+ align:start position:0%
+that you don't really understand the
+subject until you know how to prove the
+
+ align:start position:0%
+subject until you know how to prove the
+ 
+
+ align:start position:0%
+subject until you know how to prove the
+basic facts pragmatically the value of
+
+ align:start position:0%
+basic facts pragmatically the value of
+ 
+
+ align:start position:0%
+basic facts pragmatically the value of
+proofs is that uh there's an awful lot
+
+ align:start position:0%
+proofs is that uh there's an awful lot
+ 
+
+ align:start position:0%
+proofs is that uh there's an awful lot
+of content in this subject and in in
+
+ align:start position:0%
+of content in this subject and in in
+ 
+
+ align:start position:0%
+of content in this subject and in in
+many other mathematical subjects and if
+
+ align:start position:0%
+many other mathematical subjects and if
+ 
+
+ align:start position:0%
+many other mathematical subjects and if
+your only way to figure out what the
+
+ align:start position:0%
+your only way to figure out what the
+ 
+
+ align:start position:0%
+your only way to figure out what the
+exact details are is memorization you're
+
+ align:start position:0%
+exact details are is memorization you're
+ 
+
+ align:start position:0%
+exact details are is memorization you're
+going to get lost most of these rules
+
+ align:start position:0%
+going to get lost most of these rules
+ 
+
+ align:start position:0%
+going to get lost most of these rules
+and and theorems that we prove I can
+
+ align:start position:0%
+and and theorems that we prove I can
+ 
+
+ align:start position:0%
+and and theorems that we prove I can
+never remember them exactly but I know
+
+ align:start position:0%
+never remember them exactly but I know
+ 
+
+ align:start position:0%
+never remember them exactly but I know
+how to prove them so I can debug them
+
+ align:start position:0%
+how to prove them so I can debug them
+ 
+
+ align:start position:0%
+how to prove them so I can debug them
+and get them exactly right so let's
+
+ align:start position:0%
+and get them exactly right so let's
+ 
+
+ align:start position:0%
+and get them exactly right so let's
+begin by looking at uh some just
+
+ align:start position:0%
+begin by looking at uh some just
+ 
+
+ align:start position:0%
+begin by looking at uh some just
+examples of proofs before we start to
+
+ align:start position:0%
+examples of proofs before we start to
+ 
+
+ align:start position:0%
+examples of proofs before we start to
+get try to get abstract about what they
+
+ align:start position:0%
+get try to get abstract about what they
+ 
+
+ align:start position:0%
+get try to get abstract about what they
+are and we'll look at um a famous
+
+ align:start position:0%
+are and we'll look at um a famous
+ 
+
+ align:start position:0%
+are and we'll look at um a famous
+theorem that you've all seen from early
+
+ align:start position:0%
+theorem that you've all seen from early
+ 
+
+ align:start position:0%
+theorem that you've all seen from early
+on in high school the Pythagorean
+
+ align:start position:0%
+on in high school the Pythagorean
+ 
+
+ align:start position:0%
+on in high school the Pythagorean
+theorem it says that if I have a right
+
+ align:start position:0%
+theorem it says that if I have a right
+ 
+
+ align:start position:0%
+theorem it says that if I have a right
+triangle with sides A and B and
+
+ align:start position:0%
+triangle with sides A and B and
+ 
+
+ align:start position:0%
+triangle with sides A and B and
+hypotenuse
+
+ align:start position:0%
+hypotenuse
+ 
+
+ align:start position:0%
+hypotenuse
+C uh then there's a relationship between
+
+ align:start position:0%
+C uh then there's a relationship between
+ 
+
+ align:start position:0%
+C uh then there's a relationship between
+the a b and c namely that A2 + B2 equal
+
+ align:start position:0%
+the a b and c namely that A2 + B2 equal
+ 
+
+ align:start position:0%
+the a b and c namely that A2 + B2 equal
+c^2 now this is as I said completely
+
+ align:start position:0%
+c^2 now this is as I said completely
+ 
+
+ align:start position:0%
+c^2 now this is as I said completely
+familiar but is it obvious well every
+
+ align:start position:0%
+familiar but is it obvious well every
+ 
+
+ align:start position:0%
+familiar but is it obvious well every
+once in a while students say it's
+
+ align:start position:0%
+once in a while students say it's
+ 
+
+ align:start position:0%
+once in a while students say it's
+obvious but what I think they really
+
+ align:start position:0%
+obvious but what I think they really
+ 
+
+ align:start position:0%
+obvious but what I think they really
+mean is that it's familiar it's not
+
+ align:start position:0%
+mean is that it's familiar it's not
+ 
+
+ align:start position:0%
+mean is that it's familiar it's not
+obvious part of the argument for the
+
+ align:start position:0%
+obvious part of the argument for the
+ 
+
+ align:start position:0%
+obvious part of the argument for the
+fact that it's not obvious is that for
+
+ align:start position:0%
+fact that it's not obvious is that for
+ 
+
+ align:start position:0%
+fact that it's not obvious is that for
+thousands of years people have kept
+
+ align:start position:0%
+thousands of years people have kept
+ 
+
+ align:start position:0%
+thousands of years people have kept
+feeling the need to prove it in order to
+
+ align:start position:0%
+feeling the need to prove it in order to
+ 
+
+ align:start position:0%
+feeling the need to prove it in order to
+be sure that it's true and explain why
+
+ align:start position:0%
+be sure that it's true and explain why
+ 
+
+ align:start position:0%
+be sure that it's true and explain why
+it's true there's a citation in the
+
+ align:start position:0%
+it's true there's a citation in the
+ 
+
+ align:start position:0%
+it's true there's a citation in the
+notes of a a website devoted to
+
+ align:start position:0%
+notes of a a website devoted to
+ 
+
+ align:start position:0%
+notes of a a website devoted to
+collecting Pythagorean theorem proofs
+
+ align:start position:0%
+collecting Pythagorean theorem proofs
+ 
+
+ align:start position:0%
+collecting Pythagorean theorem proofs
+there was over a hundred of them
+
+ align:start position:0%
+there was over a hundred of them
+ 
+
+ align:start position:0%
+there was over a hundred of them
+including one by a former president of
+
+ align:start position:0%
+including one by a former president of
+ 
+
+ align:start position:0%
+including one by a former president of
+the United States um so let's look at
+
+ align:start position:0%
+the United States um so let's look at
+ 
+
+ align:start position:0%
+the United States um so let's look at
+one of my favorite proofs of the
+
+ align:start position:0%
+one of my favorite proofs of the
+ 
+
+ align:start position:0%
+one of my favorite proofs of the
+Pythagorean theorem and it goes this way
+
+ align:start position:0%
+Pythagorean theorem and it goes this way
+ 
+
+ align:start position:0%
+Pythagorean theorem and it goes this way
+um there are four triangles that are all
+
+ align:start position:0%
+um there are four triangles that are all
+ 
+
+ align:start position:0%
+um there are four triangles that are all
+the same size four copies of this ABC
+
+ align:start position:0%
+the same size four copies of this ABC
+ 
+
+ align:start position:0%
+the same size four copies of this ABC
+triangle which we've put in different
+
+ align:start position:0%
+triangle which we've put in different
+ 
+
+ align:start position:0%
+triangle which we've put in different
+colors to distinguish them and a square
+
+ align:start position:0%
+colors to distinguish them and a square
+ 
+
+ align:start position:0%
+colors to distinguish them and a square
+uh which for the moment is of unknown
+
+ align:start position:0%
+uh which for the moment is of unknown
+ 
+
+ align:start position:0%
+uh which for the moment is of unknown
+size uh and the proof of the Pythagorean
+
+ align:start position:0%
+size uh and the proof of the Pythagorean
+ 
+
+ align:start position:0%
+size uh and the proof of the Pythagorean
+theorem is going to consist of taking
+
+ align:start position:0%
+theorem is going to consist of taking
+ 
+
+ align:start position:0%
+theorem is going to consist of taking
+these four shapes and reassembling them
+
+ align:start position:0%
+these four shapes and reassembling them
+ 
+
+ align:start position:0%
+these four shapes and reassembling them
+so that they form a c by C
+
+ align:start position:0%
+so that they form a c by C
+ 
+
+ align:start position:0%
+so that they form a c by C
+Square first and then finding a second
+
+ align:start position:0%
+Square first and then finding a second
+ 
+
+ align:start position:0%
+Square first and then finding a second
+Arrangement so that they form two
+
+ align:start position:0%
+Arrangement so that they form two
+ 
+
+ align:start position:0%
+Arrangement so that they form two
+squares and a a by a square and a b by b
+
+ align:start position:0%
+squares and a a by a square and a b by b
+ 
+
+ align:start position:0%
+squares and a a by a square and a b by b
+square then by the theorem of
+
+ align:start position:0%
+square then by the theorem of
+ 
+
+ align:start position:0%
+square then by the theorem of
+conservation of paper or conservation of
+
+ align:start position:0%
+conservation of paper or conservation of
+ 
+
+ align:start position:0%
+conservation of paper or conservation of
+area uh it has to be that the uh the C
+
+ align:start position:0%
+area uh it has to be that the uh the C
+ 
+
+ align:start position:0%
+area uh it has to be that the uh the C
+by C uh area is the same as the a by a
+
+ align:start position:0%
+by C uh area is the same as the a by a
+ 
+
+ align:start position:0%
+by C uh area is the same as the a by a
+plus b by B area and so a^2 + B2 is
+
+ align:start position:0%
+plus b by B area and so a^2 + B2 is
+ 
+
+ align:start position:0%
+plus b by B area and so a^2 + B2 is
+equal to c^2 well let's look at those
+
+ align:start position:0%
+equal to c^2 well let's look at those
+ 
+
+ align:start position:0%
+equal to c^2 well let's look at those
+rearrangements and probably you should
+
+ align:start position:0%
+rearrangements and probably you should
+ 
+
+ align:start position:0%
+rearrangements and probably you should
+take a moment to try it yourself before
+
+ align:start position:0%
+take a moment to try it yourself before
+ 
+
+ align:start position:0%
+take a moment to try it yourself before
+I pop the solution up but there's the
+
+ align:start position:0%
+I pop the solution up but there's the
+ 
+
+ align:start position:0%
+I pop the solution up but there's the
+solution to the first one it's the
+
+ align:start position:0%
+solution to the first one it's the
+ 
+
+ align:start position:0%
+solution to the first one it's the
+easier of the two this is the c C
+
+ align:start position:0%
+easier of the two this is the c C
+ 
+
+ align:start position:0%
+easier of the two this is the c C
+Arrangement the hint is that if it's
+
+ align:start position:0%
+Arrangement the hint is that if it's
+ 
+
+ align:start position:0%
+Arrangement the hint is that if it's
+going to be C by C you don't have a lot
+
+ align:start position:0%
+going to be C by C you don't have a lot
+ 
+
+ align:start position:0%
+going to be C by C you don't have a lot
+of choice except to put the c c long
+
+ align:start position:0%
+of choice except to put the c c long
+ 
+
+ align:start position:0%
+of choice except to put the c c long
+hypo hypotenuses on the outside and then
+
+ align:start position:0%
+hypo hypotenuses on the outside and then
+ 
+
+ align:start position:0%
+hypo hypotenuses on the outside and then
+it's a matter of just fiddling the the
+
+ align:start position:0%
+it's a matter of just fiddling the the
+ 
+
+ align:start position:0%
+it's a matter of just fiddling the the
+the Triangles around so they fit
+
+ align:start position:0%
+the Triangles around so they fit
+ 
+
+ align:start position:0%
+the Triangles around so they fit
+together and you discover there's a
+
+ align:start position:0%
+together and you discover there's a
+ 
+
+ align:start position:0%
+together and you discover there's a
+square in the middle and that's just
+
+ align:start position:0%
+square in the middle and that's just
+ 
+
+ align:start position:0%
+square in the middle and that's just
+where that extra square that is provided
+
+ align:start position:0%
+where that extra square that is provided
+ 
+
+ align:start position:0%
+where that extra square that is provided
+will fit also this enables you to figure
+
+ align:start position:0%
+will fit also this enables you to figure
+ 
+
+ align:start position:0%
+will fit also this enables you to figure
+out the dimensions of the square are
+
+ align:start position:0%
+out the dimensions of the square are
+ 
+
+ align:start position:0%
+out the dimensions of the square are
+because if you look at it this is a b
+
+ align:start position:0%
+because if you look at it this is a b
+ 
+
+ align:start position:0%
+because if you look at it this is a b
+side we're letting B be the longer of
+
+ align:start position:0%
+side we're letting B be the longer of
+ 
+
+ align:start position:0%
+side we're letting B be the longer of
+the two sides of the triangle
+
+ align:start position:0%
+the two sides of the triangle
+ 
+
+ align:start position:0%
+the two sides of the triangle
+and this is the a side the shorter side
+
+ align:start position:0%
+and this is the a side the shorter side
+ 
+
+ align:start position:0%
+and this is the a side the shorter side
+of another triangle so what's left here
+
+ align:start position:0%
+of another triangle so what's left here
+ 
+
+ align:start position:0%
+of another triangle so what's left here
+has to be B minus a so now we know that
+
+ align:start position:0%
+has to be B minus a so now we know that
+ 
+
+ align:start position:0%
+has to be B minus a so now we know that
+it's a B minus a by B minus a squ from
+
+ align:start position:0%
+it's a B minus a by B minus a squ from
+ 
+
+ align:start position:0%
+it's a B minus a by B minus a squ from
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+Arrangement um and that's what we've uh
+
+ align:start position:0%
+Arrangement um and that's what we've uh
+ 
+
+ align:start position:0%
+Arrangement um and that's what we've uh
+indicated here now the next Arrangement
+
+ align:start position:0%
+indicated here now the next Arrangement
+ 
+
+ align:start position:0%
+indicated here now the next Arrangement
+is the following uh we're going to take
+
+ align:start position:0%
+is the following uh we're going to take
+ 
+
+ align:start position:0%
+is the following uh we're going to take
+the two the two of the triangles and
+
+ align:start position:0%
+the two the two of the triangles and
+ 
+
+ align:start position:0%
+the two the two of the triangles and
+form a rectangle and another two
+
+ align:start position:0%
+form a rectangle and another two
+ 
+
+ align:start position:0%
+form a rectangle and another two
+triangles form a rectangle line them up
+
+ align:start position:0%
+triangles form a rectangle line them up
+ 
+
+ align:start position:0%
+triangles form a rectangle line them up
+in this way and fit the B minus a by B
+
+ align:start position:0%
+in this way and fit the B minus a by B
+ 
+
+ align:start position:0%
+in this way and fit the B minus a by B
+minus a squ Square there now where are
+
+ align:start position:0%
+minus a squ Square there now where are
+ 
+
+ align:start position:0%
+minus a squ Square there now where are
+the two squares well I didn't say that
+
+ align:start position:0%
+the two squares well I didn't say that
+ 
+
+ align:start position:0%
+the two squares well I didn't say that
+the A by A and B by B squ needed to be
+
+ align:start position:0%
+the A by A and B by B squ needed to be
+ 
+
+ align:start position:0%
+the A by A and B by B squ needed to be
+separate in fact they're not there're
+
+ align:start position:0%
+separate in fact they're not there're
+ 
+
+ align:start position:0%
+separate in fact they're not there're
+attached but where are they well let's
+
+ align:start position:0%
+attached but where are they well let's
+ 
+
+ align:start position:0%
+attached but where are they well let's
+look at this uh line how long is it well
+
+ align:start position:0%
+look at this uh line how long is it well
+ 
+
+ align:start position:0%
+look at this uh line how long is it well
+it's a plus B minus a long which means
+
+ align:start position:0%
+it's a plus B minus a long which means
+ 
+
+ align:start position:0%
+it's a plus B minus a long which means
+that it's B long and suddenly there's a
+
+ align:start position:0%
+that it's B long and suddenly there's a
+ 
+
+ align:start position:0%
+that it's B long and suddenly there's a
+b and there's a b and I've got a B by
+
+ align:start position:0%
+b and there's a b and I've got a B by
+ 
+
+ align:start position:0%
+b and there's a b and I've got a B by
+B rectangle right there but wait a
+
+ align:start position:0%
+B rectangle right there but wait a
+ 
+
+ align:start position:0%
+B rectangle right there but wait a
+second here's a B minus a and it's lined
+
+ align:start position:0%
+second here's a B minus a and it's lined
+ 
+
+ align:start position:0%
+second here's a B minus a and it's lined
+up up against a b side so if I look at
+
+ align:start position:0%
+up up against a b side so if I look at
+ 
+
+ align:start position:0%
+up up against a b side so if I look at
+what's left it's B minus B minus a it
+
+ align:start position:0%
+what's left it's B minus B minus a it
+ 
+
+ align:start position:0%
+what's left it's B minus B minus a it
+tells me that that little piece is a and
+
+ align:start position:0%
+tells me that that little piece is a and
+ 
+
+ align:start position:0%
+tells me that that little piece is a and
+so sure enough when I add this uh hidden
+
+ align:start position:0%
+so sure enough when I add this uh hidden
+ 
+
+ align:start position:0%
+so sure enough when I add this uh hidden
+Line This conceptual line to separate
+
+ align:start position:0%
+Line This conceptual line to separate
+ 
+
+ align:start position:0%
+Line This conceptual line to separate
+the two squares this part's a by a and
+
+ align:start position:0%
+the two squares this part's a by a and
+ 
+
+ align:start position:0%
+the two squares this part's a by a and
+that part's B by B and we've proved the
+
+ align:start position:0%
+that part's B by B and we've proved the
+ 
+
+ align:start position:0%
+that part's B by B and we've proved the
+Pythagorean
+
+ align:start position:0%
+Pythagorean
+ 
+
+ align:start position:0%
+Pythagorean
+theorem so what about this proof um it
+
+ align:start position:0%
+theorem so what about this proof um it
+ 
+
+ align:start position:0%
+theorem so what about this proof um it
+it's really very elegant and it's abs
+
+ align:start position:0%
+it's really very elegant and it's abs
+ 
+
+ align:start position:0%
+it's really very elegant and it's abs
+correct and I hope it's kind of
+
+ align:start position:0%
+correct and I hope it's kind of
+ 
+
+ align:start position:0%
+correct and I hope it's kind of
+convincing uh and so this is a wonderful
+
+ align:start position:0%
+convincing uh and so this is a wonderful
+ 
+
+ align:start position:0%
+convincing uh and so this is a wonderful
+case of a proof by picture that really
+
+ align:start position:0%
+case of a proof by picture that really
+ 
+
+ align:start position:0%
+case of a proof by picture that really
+works in this case but unfortunately
+
+ align:start position:0%
+works in this case but unfortunately
+ 
+
+ align:start position:0%
+works in this case but unfortunately
+proof by pictures worry mathematicians
+
+ align:start position:0%
+proof by pictures worry mathematicians
+ 
+
+ align:start position:0%
+proof by pictures worry mathematicians
+and they're legitimately worrisome uh
+
+ align:start position:0%
+and they're legitimately worrisome uh
+ 
+
+ align:start position:0%
+and they're legitimately worrisome uh
+because there's lots of hidden
+
+ align:start position:0%
+because there's lots of hidden
+ 
+
+ align:start position:0%
+because there's lots of hidden
+assumptions and and exercise that you
+
+ align:start position:0%
+assumptions and and exercise that you
+ 
+
+ align:start position:0%
+assumptions and and exercise that you
+can go through is to go back and think
+
+ align:start position:0%
+can go through is to go back and think
+ 
+
+ align:start position:0%
+can go through is to go back and think
+about all of the geometric information
+
+ align:start position:0%
+about all of the geometric information
+ 
+
+ align:start position:0%
+about all of the geometric information
+that's kind of being taken for granted
+
+ align:start position:0%
+that's kind of being taken for granted
+ 
+
+ align:start position:0%
+that's kind of being taken for granted
+in this picture like over here how did
+
+ align:start position:0%
+in this picture like over here how did
+ 
+
+ align:start position:0%
+in this picture like over here how did
+we know that that was a right angle that
+
+ align:start position:0%
+we know that that was a right angle that
+ 
+
+ align:start position:0%
+we know that that was a right angle that
+this thing was a rectangle we needed
+
+ align:start position:0%
+this thing was a rectangle we needed
+ 
+
+ align:start position:0%
+this thing was a rectangle we needed
+that to be a right angle because we were
+
+ align:start position:0%
+that to be a right angle because we were
+ 
+
+ align:start position:0%
+that to be a right angle because we were
+claiming that this was a square well how
+
+ align:start position:0%
+claiming that this was a square well how
+ 
+
+ align:start position:0%
+claiming that this was a square well how
+did we know that that was a rectangle
+
+ align:start position:0%
+did we know that that was a rectangle
+ 
+
+ align:start position:0%
+did we know that that was a rectangle
+well the answers are obvious we're using
+
+ align:start position:0%
+well the answers are obvious we're using
+ 
+
+ align:start position:0%
+well the answers are obvious we're using
+the fact that the uh that the
+
+ align:start position:0%
+the fact that the uh that the
+ 
+
+ align:start position:0%
+the fact that the uh that the
+complementary angles of a right triangle
+
+ align:start position:0%
+complementary angles of a right triangle
+ 
+
+ align:start position:0%
+complementary angles of a right triangle
+sum to 90 de because the angles of a
+
+ align:start position:0%
+sum to 90 de because the angles of a
+ 
+
+ align:start position:0%
+sum to 90 de because the angles of a
+triangle in general sum to 180 degrees
+
+ align:start position:0%
+triangle in general sum to 180 degrees
+ 
+
+ align:start position:0%
+triangle in general sum to 180 degrees
+we're using that in a bunch of other
+
+ align:start position:0%
+we're using that in a bunch of other
+ 
+
+ align:start position:0%
+we're using that in a bunch of other
+places we're Al also using the fact that
+
+ align:start position:0%
+places we're Al also using the fact that
+ 
+
+ align:start position:0%
+places we're Al also using the fact that
+this is a straight line which may or may
+
+ align:start position:0%
+this is a straight line which may or may
+ 
+
+ align:start position:0%
+this is a straight line which may or may
+not be obvious uh but it's true and
+
+ align:start position:0%
+not be obvious uh but it's true and
+ 
+
+ align:start position:0%
+not be obvious uh but it's true and
+that's why it's safe to add those
+
+ align:start position:0%
+that's why it's safe to add those
+ 
+
+ align:start position:0%
+that's why it's safe to add those
+distances to figure out what it was my
+
+ align:start position:0%
+distances to figure out what it was my
+ 
+
+ align:start position:0%
+distances to figure out what it was my
+point is that there were really a whole
+
+ align:start position:0%
+point is that there were really a whole
+ 
+
+ align:start position:0%
+point is that there were really a whole
+lot of hidden assumptions in the diagram
+
+ align:start position:0%
+lot of hidden assumptions in the diagram
+ 
+
+ align:start position:0%
+lot of hidden assumptions in the diagram
+that it's easy to overlook and be fooled
+
+ align:start position:0%
+that it's easy to overlook and be fooled
+ 
+
+ align:start position:0%
+that it's easy to overlook and be fooled
+by so let me show you an example of
+
+ align:start position:0%
+by so let me show you an example of
+ 
+
+ align:start position:0%
+by so let me show you an example of
+getting fooled by a proof by diagram and
+
+ align:start position:0%
+getting fooled by a proof by diagram and
+ 
+
+ align:start position:0%
+getting fooled by a proof by diagram and
+here's how to get infinitely rich Let's
+
+ align:start position:0%
+here's how to get infinitely rich Let's
+ 
+
+ align:start position:0%
+here's how to get infinitely rich Let's
+imagine that I have a 10 by 11 piece of
+
+ align:start position:0%
+imagine that I have a 10 by 11 piece of
+ 
+
+ align:start position:0%
+imagine that I have a 10 by 11 piece of
+gold foil nice actually they could be
+
+ align:start position:0%
+gold foil nice actually they could be
+ 
+
+ align:start position:0%
+gold foil nice actually they could be
+slabs of gold but but let's think of
+
+ align:start position:0%
+slabs of gold but but let's think of
+ 
+
+ align:start position:0%
+slabs of gold but but let's think of
+this as a a rectangular shape that's
+
+ align:start position:0%
+this as a a rectangular shape that's
+ 
+
+ align:start position:0%
+this as a a rectangular shape that's
+made out of gold and it's going to be
+
+ align:start position:0%
+made out of gold and it's going to be
+ 
+
+ align:start position:0%
+made out of gold and it's going to be
+rectangles those are right angles there
+
+ align:start position:0%
+rectangles those are right angles there
+ 
+
+ align:start position:0%
+rectangles those are right angles there
+and what I'm going to do is Mark off the
+
+ align:start position:0%
+and what I'm going to do is Mark off the
+ 
+
+ align:start position:0%
+and what I'm going to do is Mark off the
+corners I'm going to uh mark off a
+
+ align:start position:0%
+corners I'm going to uh mark off a
+ 
+
+ align:start position:0%
+corners I'm going to uh mark off a
+length down of one and then I'm going to
+
+ align:start position:0%
+length down of one and then I'm going to
+ 
+
+ align:start position:0%
+length down of one and then I'm going to
+mark off a length of one so that and and
+
+ align:start position:0%
+mark off a length of one so that and and
+ 
+
+ align:start position:0%
+mark off a length of one so that and and
+shift it so that it touches the diagonal
+
+ align:start position:0%
+shift it so that it touches the diagonal
+ 
+
+ align:start position:0%
+shift it so that it touches the diagonal
+and do the same thing in this lower
+
+ align:start position:0%
+and do the same thing in this lower
+ 
+
+ align:start position:0%
+and do the same thing in this lower
+corner and now let's just shift these
+
+ align:start position:0%
+corner and now let's just shift these
+ 
+
+ align:start position:0%
+corner and now let's just shift these
+shapes um the top one going uh Southwest
+
+ align:start position:0%
+shapes um the top one going uh Southwest
+ 
+
+ align:start position:0%
+shapes um the top one going uh Southwest
+and the and the second one going
+
+ align:start position:0%
+and the and the second one going
+ 
+
+ align:start position:0%
+and the and the second one going
+Northeast and what I wind up with is
+
+ align:start position:0%
+Northeast and what I wind up with is
+ 
+
+ align:start position:0%
+Northeast and what I wind up with is
+this picture so that I've now got those
+
+ align:start position:0%
+this picture so that I've now got those
+ 
+
+ align:start position:0%
+this picture so that I've now got those
+little red triangles protruding above
+
+ align:start position:0%
+little red triangles protruding above
+ 
+
+ align:start position:0%
+little red triangles protruding above
+the shape okay cool well what are we
+
+ align:start position:0%
+the shape okay cool well what are we
+ 
+
+ align:start position:0%
+the shape okay cool well what are we
+know um this is now side 10 because I've
+
+ align:start position:0%
+know um this is now side 10 because I've
+ 
+
+ align:start position:0%
+know um this is now side 10 because I've
+subtracted one from its length here um
+
+ align:start position:0%
+subtracted one from its length here um
+ 
+
+ align:start position:0%
+subtracted one from its length here um
+and this is side 11 because that used to
+
+ align:start position:0%
+and this is side 11 because that used to
+ 
+
+ align:start position:0%
+and this is side 11 because that used to
+be 10 and I've added one to its length
+
+ align:start position:0%
+be 10 and I've added one to its length
+ 
+
+ align:start position:0%
+be 10 and I've added one to its length
+there so that's cool because now what I
+
+ align:start position:0%
+there so that's cool because now what I
+ 
+
+ align:start position:0%
+there so that's cool because now what I
+can do is take those protruding
+
+ align:start position:0%
+can do is take those protruding
+ 
+
+ align:start position:0%
+can do is take those protruding
+triangles out and they'll form a little
+
+ align:start position:0%
+triangles out and they'll form a little
+ 
+
+ align:start position:0%
+triangles out and they'll form a little
+one by one rectangle Square uh and
+
+ align:start position:0%
+one by one rectangle Square uh and
+ 
+
+ align:start position:0%
+one by one rectangle Square uh and
+suddenly I have this little bit of gold
+
+ align:start position:0%
+suddenly I have this little bit of gold
+ 
+
+ align:start position:0%
+suddenly I have this little bit of gold
+that's extra but look what's here it's a
+
+ align:start position:0%
+that's extra but look what's here it's a
+ 
+
+ align:start position:0%
+that's extra but look what's here it's a
+10 by
+
+ align:start position:0%
+10 by
+ 
+
+ align:start position:0%
+10 by
+11 rectangular shape of gold foil again
+
+ align:start position:0%
+11 rectangular shape of gold foil again
+ 
+
+ align:start position:0%
+11 rectangular shape of gold foil again
+so I just rotate this by 90° and I start
+
+ align:start position:0%
+so I just rotate this by 90° and I start
+ 
+
+ align:start position:0%
+so I just rotate this by 90° and I start
+all over again I can keep generating
+
+ align:start position:0%
+all over again I can keep generating
+ 
+
+ align:start position:0%
+all over again I can keep generating
+these little one by one shapes of gold
+
+ align:start position:0%
+these little one by one shapes of gold
+ 
+
+ align:start position:0%
+these little one by one shapes of gold
+foil forever I can get infinitely Rich
+
+ align:start position:0%
+foil forever I can get infinitely Rich
+ 
+
+ align:start position:0%
+foil forever I can get infinitely Rich
+okay well there's something wrong with
+
+ align:start position:0%
+okay well there's something wrong with
+ 
+
+ align:start position:0%
+okay well there's something wrong with
+that it's violating all kinds of confer
+
+ align:start position:0%
+that it's violating all kinds of confer
+ 
+
+ align:start position:0%
+that it's violating all kinds of confer
+conservation principles not to mention
+
+ align:start position:0%
+conservation principles not to mention
+ 
+
+ align:start position:0%
+conservation principles not to mention
+that it would undermine the price of
+
+ align:start position:0%
+that it would undermine the price of
+ 
+
+ align:start position:0%
+that it would undermine the price of
+gold so what's the bug well um if you
+
+ align:start position:0%
+gold so what's the bug well um if you
+ 
+
+ align:start position:0%
+gold so what's the bug well um if you
+probably can spot this but maybe you've
+
+ align:start position:0%
+probably can spot this but maybe you've
+ 
+
+ align:start position:0%
+probably can spot this but maybe you've
+been fooled uh what's going on is
+
+ align:start position:0%
+been fooled uh what's going on is
+ 
+
+ align:start position:0%
+been fooled uh what's going on is
+there's an implicit assumption that
+
+ align:start position:0%
+there's an implicit assumption that
+ 
+
+ align:start position:0%
+there's an implicit assumption that
+those little triangles that I cut off
+
+ align:start position:0%
+those little triangles that I cut off
+ 
+
+ align:start position:0%
+those little triangles that I cut off
+were right triangles and that this line
+
+ align:start position:0%
+were right triangles and that this line
+ 
+
+ align:start position:0%
+were right triangles and that this line
+that I claimed was of length 11 um was a
+
+ align:start position:0%
+that I claimed was of length 11 um was a
+ 
+
+ align:start position:0%
+that I claimed was of length 11 um was a
+straight line and it's not those
+
+ align:start position:0%
+straight line and it's not those
+ 
+
+ align:start position:0%
+straight line and it's not those
+triangles are a are have two sides that
+
+ align:start position:0%
+triangles are a are have two sides that
+ 
+
+ align:start position:0%
+triangles are a are have two sides that
+are of length one they're isoceles
+
+ align:start position:0%
+are of length one they're isoceles
+ 
+
+ align:start position:0%
+are of length one they're isoceles
+triangles but they're lying up against a
+
+ align:start position:0%
+triangles but they're lying up against a
+ 
+
+ align:start position:0%
+triangles but they're lying up against a
+diag diagonal that's not
+
+ align:start position:0%
+diag diagonal that's not
+ 
+
+ align:start position:0%
+diag diagonal that's not
+45° um and so they're not right
+
+ align:start position:0%
+45° um and so they're not right
+ 
+
+ align:start position:0%
+45° um and so they're not right
+triangles and that line isn't straight
+
+ align:start position:0%
+triangles and that line isn't straight
+ 
+
+ align:start position:0%
+triangles and that line isn't straight
+and 10 and 11 were close enough that it
+
+ align:start position:0%
+and 10 and 11 were close enough that it
+ 
+
+ align:start position:0%
+and 10 and 11 were close enough that it
+wasn't visually obvious so this is a way
+
+ align:start position:0%
+wasn't visually obvious so this is a way
+ 
+
+ align:start position:0%
+wasn't visually obvious so this is a way
+to Simply put one over on you with a
+
+ align:start position:0%
+to Simply put one over on you with a
+ 
+
+ align:start position:0%
+to Simply put one over on you with a
+proof by picture and if I had been asked
+
+ align:start position:0%
+proof by picture and if I had been asked
+ 
+
+ align:start position:0%
+proof by picture and if I had been asked
+to justify how do I know it's a straight
+
+ align:start position:0%
+to justify how do I know it's a straight
+ 
+
+ align:start position:0%
+to justify how do I know it's a straight
+line that bug would have emerged but
+
+ align:start position:0%
+line that bug would have emerged but
+ 
+
+ align:start position:0%
+line that bug would have emerged but
+you're not likely to notice that if it
+
+ align:start position:0%
+you're not likely to notice that if it
+ 
+
+ align:start position:0%
+you're not likely to notice that if it
+isn't visually obvious which is why we
+
+ align:start position:0%
+isn't visually obvious which is why we
+ 
+
+ align:start position:0%
+isn't visually obvious which is why we
+worry about some of these proof SP
\ No newline at end of file
diff --git a/HNDawwNfu5w.txt b/HNDawwNfu5w.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f1f408f43ba92df50a60f278ddded084531f4beb
--- /dev/null
+++ b/HNDawwNfu5w.txt
@@ -0,0 +1,17683 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a creative common license. Your support
+
+ align:start position:0%
+a creative common license. Your support
+ 
+
+ align:start position:0%
+a creative common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Anyway, uh today uh we have a guest
+
+ align:start position:0%
+>> Anyway, uh today uh we have a guest
+ 
+
+ align:start position:0%
+>> Anyway, uh today uh we have a guest
+speaker who's the audio director for the
+
+ align:start position:0%
+speaker who's the audio director for the
+ 
+
+ align:start position:0%
+speaker who's the audio director for the
+Singapore Academy.
+
+ align:start position:0%
+Singapore Academy.
+ 
+
+ align:start position:0%
+Singapore Academy.
+That's where we are. And um and he's
+
+ align:start position:0%
+That's where we are. And um and he's
+ 
+
+ align:start position:0%
+That's where we are. And um and he's
+going to run through brainstorming uh as
+
+ align:start position:0%
+going to run through brainstorming uh as
+ 
+
+ align:start position:0%
+going to run through brainstorming uh as
+an exercise. Um but we're not actually
+
+ align:start position:0%
+an exercise. Um but we're not actually
+ 
+
+ align:start position:0%
+an exercise. Um but we're not actually
+planning out the game that you're going
+
+ align:start position:0%
+planning out the game that you're going
+ 
+
+ align:start position:0%
+planning out the game that you're going
+to be doing for your first assignment in
+
+ align:start position:0%
+to be doing for your first assignment in
+ 
+
+ align:start position:0%
+to be doing for your first assignment in
+this class. I think this is a you're
+
+ align:start position:0%
+this class. I think this is a you're
+ 
+
+ align:start position:0%
+this class. I think this is a you're
+doing other
+
+ align:start position:0%
+doing other
+ 
+
+ align:start position:0%
+doing other
+>> Yeah, these will just be just be
+
+ align:start position:0%
+>> Yeah, these will just be just be
+ 
+
+ align:start position:0%
+>> Yeah, these will just be just be
+practice. So basically the the groups
+
+ align:start position:0%
+practice. So basically the the groups
+ 
+
+ align:start position:0%
+practice. So basically the the groups
+there will be a group activity involved
+
+ align:start position:0%
+there will be a group activity involved
+ 
+
+ align:start position:0%
+there will be a group activity involved
+in this but the the things that that
+
+ align:start position:0%
+in this but the the things that that
+ 
+
+ align:start position:0%
+in this but the the things that that
+that you're working on don't have to be
+
+ align:start position:0%
+that you're working on don't have to be
+ 
+
+ align:start position:0%
+that you're working on don't have to be
+the same groups that you will eventually
+
+ align:start position:0%
+the same groups that you will eventually
+ 
+
+ align:start position:0%
+the same groups that you will eventually
+be using for your first assignment. The
+
+ align:start position:0%
+be using for your first assignment. The
+ 
+
+ align:start position:0%
+be using for your first assignment. The
+idea is just sort of to get used to the
+
+ align:start position:0%
+idea is just sort of to get used to the
+ 
+
+ align:start position:0%
+idea is just sort of to get used to the
+process of brainstorming and sort of a
+
+ align:start position:0%
+process of brainstorming and sort of a
+ 
+
+ align:start position:0%
+process of brainstorming and sort of a
+general rules of thumb uh and before I
+
+ align:start position:0%
+general rules of thumb uh and before I
+ 
+
+ align:start position:0%
+general rules of thumb uh and before I
+spoil the entire talk.
+
+ align:start position:0%
+spoil the entire talk.
+ 
+
+ align:start position:0%
+spoil the entire talk.
+>> Yeah that's okay. So uh yeah just my
+
+ align:start position:0%
+>> Yeah that's okay. So uh yeah just my
+ 
+
+ align:start position:0%
+>> Yeah that's okay. So uh yeah just my
+name is Apstein. A little bit of
+
+ align:start position:0%
+name is Apstein. A little bit of
+ 
+
+ align:start position:0%
+name is Apstein. A little bit of
+background on myself. Um I'm the audio
+
+ align:start position:0%
+background on myself. Um I'm the audio
+ 
+
+ align:start position:0%
+background on myself. Um I'm the audio
+director here. Uh I've been working in
+
+ align:start position:0%
+director here. Uh I've been working in
+ 
+
+ align:start position:0%
+director here. Uh I've been working in
+sound design uh officially for uh a
+
+ align:start position:0%
+sound design uh officially for uh a
+ 
+
+ align:start position:0%
+sound design uh officially for uh a
+number of years now, five some odd
+
+ align:start position:0%
+number of years now, five some odd
+ 
+
+ align:start position:0%
+number of years now, five some odd
+years. Uh unofficially uh way longer
+
+ align:start position:0%
+years. Uh unofficially uh way longer
+ 
+
+ align:start position:0%
+years. Uh unofficially uh way longer
+than that. Um uh doing TV TV and video
+
+ align:start position:0%
+than that. Um uh doing TV TV and video
+ 
+
+ align:start position:0%
+than that. Um uh doing TV TV and video
+game sound design. And then uh and then
+
+ align:start position:0%
+game sound design. And then uh and then
+ 
+
+ align:start position:0%
+game sound design. And then uh and then
+before that I I was a high school
+
+ align:start position:0%
+before that I I was a high school
+ 
+
+ align:start position:0%
+before that I I was a high school
+teacher. Um and so I think you know to
+
+ align:start position:0%
+teacher. Um and so I think you know to
+ 
+
+ align:start position:0%
+teacher. Um and so I think you know to
+the extent that um uh talking about kind
+
+ align:start position:0%
+the extent that um uh talking about kind
+ 
+
+ align:start position:0%
+the extent that um uh talking about kind
+of creative collaboration uh I have a
+
+ align:start position:0%
+of creative collaboration uh I have a
+ 
+
+ align:start position:0%
+of creative collaboration uh I have a
+fair amount of experience ranging even
+
+ align:start position:0%
+fair amount of experience ranging even
+ 
+
+ align:start position:0%
+fair amount of experience ranging even
+back to to when I was uh teaching high
+
+ align:start position:0%
+back to to when I was uh teaching high
+ 
+
+ align:start position:0%
+back to to when I was uh teaching high
+school for trying to uh encourage what
+
+ align:start position:0%
+school for trying to uh encourage what
+ 
+
+ align:start position:0%
+school for trying to uh encourage what
+what we might call organized uh
+
+ align:start position:0%
+what we might call organized uh
+ 
+
+ align:start position:0%
+what we might call organized uh
+ideiation. Um I guess first I'll I'll
+
+ align:start position:0%
+ideiation. Um I guess first I'll I'll
+ 
+
+ align:start position:0%
+ideiation. Um I guess first I'll I'll
+thank you guys for for reading uh
+
+ align:start position:0%
+thank you guys for for reading uh
+ 
+
+ align:start position:0%
+thank you guys for for reading uh
+reading the text. Um it is it is funny.
+
+ align:start position:0%
+reading the text. Um it is it is funny.
+ 
+
+ align:start position:0%
+reading the text. Um it is it is funny.
+it does have these kind of um I guess
+
+ align:start position:0%
+it does have these kind of um I guess
+ 
+
+ align:start position:0%
+it does have these kind of um I guess
+now a little antiquated 1950s sort of
+
+ align:start position:0%
+now a little antiquated 1950s sort of
+ 
+
+ align:start position:0%
+now a little antiquated 1950s sort of
+references and um you know some of his
+
+ align:start position:0%
+references and um you know some of his
+ 
+
+ align:start position:0%
+references and um you know some of his
+uh some of his uh scientific evidence
+
+ align:start position:0%
+uh some of his uh scientific evidence
+ 
+
+ align:start position:0%
+uh some of his uh scientific evidence
+for uh for for why brainstorming is good
+
+ align:start position:0%
+for uh for for why brainstorming is good
+ 
+
+ align:start position:0%
+for uh for for why brainstorming is good
+is is not particularly well supported.
+
+ align:start position:0%
+is is not particularly well supported.
+ 
+
+ align:start position:0%
+is is not particularly well supported.
+was like, "We got 95 ideas." And I was
+
+ align:start position:0%
+was like, "We got 95 ideas." And I was
+ 
+
+ align:start position:0%
+was like, "We got 95 ideas." And I was
+like, "Well, how many ideas did you
+
+ align:start position:0%
+like, "Well, how many ideas did you
+ 
+
+ align:start position:0%
+like, "Well, how many ideas did you
+get?" You know, doing it the other way
+
+ align:start position:0%
+get?" You know, doing it the other way
+ 
+
+ align:start position:0%
+get?" You know, doing it the other way
+doesn't, you know, he doesn't tell you,
+
+ align:start position:0%
+doesn't, you know, he doesn't tell you,
+ 
+
+ align:start position:0%
+doesn't, you know, he doesn't tell you,
+but hey, 95, that's a big number, you
+
+ align:start position:0%
+but hey, 95, that's a big number, you
+ 
+
+ align:start position:0%
+but hey, 95, that's a big number, you
+know. So, um, you know, a little a
+
+ align:start position:0%
+know. So, um, you know, a little a
+ 
+
+ align:start position:0%
+know. So, um, you know, a little a
+little bit of background about Alex
+
+ align:start position:0%
+little bit of background about Alex
+ 
+
+ align:start position:0%
+little bit of background about Alex
+Osborne. He was, um, he was an
+
+ align:start position:0%
+Osborne. He was, um, he was an
+ 
+
+ align:start position:0%
+Osborne. He was, um, he was an
+advertising, uh, executive. Um, and so
+
+ align:start position:0%
+advertising, uh, executive. Um, and so
+ 
+
+ align:start position:0%
+advertising, uh, executive. Um, and so
+you can kind of see where brainstorming
+
+ align:start position:0%
+you can kind of see where brainstorming
+ 
+
+ align:start position:0%
+you can kind of see where brainstorming
+and advertising is a is a creative
+
+ align:start position:0%
+and advertising is a is a creative
+ 
+
+ align:start position:0%
+and advertising is a is a creative
+industry, right? It's a design industry.
+
+ align:start position:0%
+industry, right? It's a design industry.
+ 
+
+ align:start position:0%
+industry, right? It's a design industry.
+And so getting multiple people in
+
+ align:start position:0%
+And so getting multiple people in
+ 
+
+ align:start position:0%
+And so getting multiple people in
+interdisciplinary kind of you know
+
+ align:start position:0%
+interdisciplinary kind of you know
+ 
+
+ align:start position:0%
+interdisciplinary kind of you know
+different skills working together um on
+
+ align:start position:0%
+different skills working together um on
+ 
+
+ align:start position:0%
+different skills working together um on
+a on a creative project it can be a
+
+ align:start position:0%
+a on a creative project it can be a
+ 
+
+ align:start position:0%
+a on a creative project it can be a
+challenge. Um and so you can see how
+
+ align:start position:0%
+challenge. Um and so you can see how
+ 
+
+ align:start position:0%
+challenge. Um and so you can see how
+brainstorming came out of the work he
+
+ align:start position:0%
+brainstorming came out of the work he
+ 
+
+ align:start position:0%
+brainstorming came out of the work he
+was doing in advertising. So um so just
+
+ align:start position:0%
+was doing in advertising. So um so just
+ 
+
+ align:start position:0%
+was doing in advertising. So um so just
+to get started I I would say you know
+
+ align:start position:0%
+to get started I I would say you know
+ 
+
+ align:start position:0%
+to get started I I would say you know
+you've read it so you have a sense but
+
+ align:start position:0%
+you've read it so you have a sense but
+ 
+
+ align:start position:0%
+you've read it so you have a sense but
+but kind of forget what you think you
+
+ align:start position:0%
+but kind of forget what you think you
+ 
+
+ align:start position:0%
+but kind of forget what you think you
+know brainstorming is. Um some of what
+
+ align:start position:0%
+know brainstorming is. Um some of what
+ 
+
+ align:start position:0%
+know brainstorming is. Um some of what
+you think it is will apply. um some of
+
+ align:start position:0%
+you think it is will apply. um some of
+ 
+
+ align:start position:0%
+you think it is will apply. um some of
+the most fundamental principles um to
+
+ align:start position:0%
+the most fundamental principles um to
+ 
+
+ align:start position:0%
+the most fundamental principles um to
+brainstorming maybe you don't you don't
+
+ align:start position:0%
+brainstorming maybe you don't you don't
+ 
+
+ align:start position:0%
+brainstorming maybe you don't you don't
+realize or you didn't realize until you
+
+ align:start position:0%
+realize or you didn't realize until you
+ 
+
+ align:start position:0%
+realize or you didn't realize until you
+did the reading and and that's a little
+
+ align:start position:0%
+did the reading and and that's a little
+ 
+
+ align:start position:0%
+did the reading and and that's a little
+bit of what I want to talk about. I
+
+ align:start position:0%
+bit of what I want to talk about. I
+ 
+
+ align:start position:0%
+bit of what I want to talk about. I
+think the the foundation for his
+
+ align:start position:0%
+think the the foundation for his
+ 
+
+ align:start position:0%
+think the the foundation for his
+brainstorming idea is actually really
+
+ align:start position:0%
+brainstorming idea is actually really
+ 
+
+ align:start position:0%
+brainstorming idea is actually really
+solid and it's something something that
+
+ align:start position:0%
+solid and it's something something that
+ 
+
+ align:start position:0%
+solid and it's something something that
+you know we should explore today. Um
+
+ align:start position:0%
+you know we should explore today. Um
+ 
+
+ align:start position:0%
+you know we should explore today. Um
+why why brainstorming for video game
+
+ align:start position:0%
+why why brainstorming for video game
+ 
+
+ align:start position:0%
+why why brainstorming for video game
+design um is an interesting question. Um
+
+ align:start position:0%
+design um is an interesting question. Um
+ 
+
+ align:start position:0%
+design um is an interesting question. Um
+but I sort of touched on that a little
+
+ align:start position:0%
+but I sort of touched on that a little
+ 
+
+ align:start position:0%
+but I sort of touched on that a little
+bit with relation to advertising, right?
+
+ align:start position:0%
+bit with relation to advertising, right?
+ 
+
+ align:start position:0%
+bit with relation to advertising, right?
+I mean, we're talking about a creative
+
+ align:start position:0%
+I mean, we're talking about a creative
+ 
+
+ align:start position:0%
+I mean, we're talking about a creative
+industry where you've got people with
+
+ align:start position:0%
+industry where you've got people with
+ 
+
+ align:start position:0%
+industry where you've got people with
+various skill sets, whether they're
+
+ align:start position:0%
+various skill sets, whether they're
+ 
+
+ align:start position:0%
+various skill sets, whether they're
+artists or sound designers or uh game
+
+ align:start position:0%
+artists or sound designers or uh game
+ 
+
+ align:start position:0%
+artists or sound designers or uh game
+designers explicitly or producers. Um,
+
+ align:start position:0%
+designers explicitly or producers. Um,
+ 
+
+ align:start position:0%
+designers explicitly or producers. Um,
+all of these people kind of existing in
+
+ align:start position:0%
+all of these people kind of existing in
+ 
+
+ align:start position:0%
+all of these people kind of existing in
+a collaborative environment together.
+
+ align:start position:0%
+a collaborative environment together.
+ 
+
+ align:start position:0%
+a collaborative environment together.
+They're bringing different things to the
+
+ align:start position:0%
+They're bringing different things to the
+ 
+
+ align:start position:0%
+They're bringing different things to the
+table. How do you get them to to kind of
+
+ align:start position:0%
+table. How do you get them to to kind of
+ 
+
+ align:start position:0%
+table. How do you get them to to kind of
+work together and and and be
+
+ align:start position:0%
+work together and and and be
+ 
+
+ align:start position:0%
+work together and and and be
+collaboratively creative? And so this
+
+ align:start position:0%
+collaboratively creative? And so this
+ 
+
+ align:start position:0%
+collaboratively creative? And so this
+is, you know, a first step in that
+
+ align:start position:0%
+is, you know, a first step in that
+ 
+
+ align:start position:0%
+is, you know, a first step in that
+process. And so this is this is why
+
+ align:start position:0%
+process. And so this is this is why
+ 
+
+ align:start position:0%
+process. And so this is this is why
+brainstorming is particularly useful um
+
+ align:start position:0%
+brainstorming is particularly useful um
+ 
+
+ align:start position:0%
+brainstorming is particularly useful um
+for game design. And then the other
+
+ align:start position:0%
+for game design. And then the other
+ 
+
+ align:start position:0%
+for game design. And then the other
+thing um the other thing that I I think
+
+ align:start position:0%
+thing um the other thing that I I think
+ 
+
+ align:start position:0%
+thing um the other thing that I I think
+is important to understand and we'll
+
+ align:start position:0%
+is important to understand and we'll
+ 
+
+ align:start position:0%
+is important to understand and we'll
+talk about it a bit more is is um the
+
+ align:start position:0%
+talk about it a bit more is is um the
+ 
+
+ align:start position:0%
+talk about it a bit more is is um the
+kind of social pressures um that are
+
+ align:start position:0%
+kind of social pressures um that are
+ 
+
+ align:start position:0%
+kind of social pressures um that are
+created in creative envir professional
+
+ align:start position:0%
+created in creative envir professional
+ 
+
+ align:start position:0%
+created in creative envir professional
+creative environments even
+
+ align:start position:0%
+creative environments even
+ 
+
+ align:start position:0%
+creative environments even
+non-professional actually I mean it it
+
+ align:start position:0%
+non-professional actually I mean it it
+ 
+
+ align:start position:0%
+non-professional actually I mean it it
+would exist in an educational
+
+ align:start position:0%
+would exist in an educational
+ 
+
+ align:start position:0%
+would exist in an educational
+environment too um you guys are all at
+
+ align:start position:0%
+environment too um you guys are all at
+ 
+
+ align:start position:0%
+environment too um you guys are all at
+MIT it's one of the most prestigious
+
+ align:start position:0%
+MIT it's one of the most prestigious
+ 
+
+ align:start position:0%
+MIT it's one of the most prestigious
+universities um you know in the world
+
+ align:start position:0%
+universities um you know in the world
+ 
+
+ align:start position:0%
+universities um you know in the world
+right and so you're probably no stranger
+
+ align:start position:0%
+right and so you're probably no stranger
+ 
+
+ align:start position:0%
+right and so you're probably no stranger
+to the idea of of kind of social
+
+ align:start position:0%
+to the idea of of kind of social
+ 
+
+ align:start position:0%
+to the idea of of kind of social
+pressure in uh in the process of
+
+ align:start position:0%
+pressure in uh in the process of
+ 
+
+ align:start position:0%
+pressure in uh in the process of
+ideiation, right? Um you sit there and
+
+ align:start position:0%
+ideiation, right? Um you sit there and
+ 
+
+ align:start position:0%
+ideiation, right? Um you sit there and
+you say if I say this idea, am I going
+
+ align:start position:0%
+you say if I say this idea, am I going
+ 
+
+ align:start position:0%
+you say if I say this idea, am I going
+to look like an idiot? Um and and
+
+ align:start position:0%
+to look like an idiot? Um and and
+ 
+
+ align:start position:0%
+to look like an idiot? Um and and
+usually the outcome from that is if I
+
+ align:start position:0%
+usually the outcome from that is if I
+ 
+
+ align:start position:0%
+usually the outcome from that is if I
+don't say anything, it's it's you know,
+
+ align:start position:0%
+don't say anything, it's it's you know,
+ 
+
+ align:start position:0%
+don't say anything, it's it's you know,
+maybe I don't get the gain of presenting
+
+ align:start position:0%
+maybe I don't get the gain of presenting
+ 
+
+ align:start position:0%
+maybe I don't get the gain of presenting
+a good idea, but I don't get the hit of
+
+ align:start position:0%
+a good idea, but I don't get the hit of
+ 
+
+ align:start position:0%
+a good idea, but I don't get the hit of
+making a bad idea. And so it's like, you
+
+ align:start position:0%
+making a bad idea. And so it's like, you
+ 
+
+ align:start position:0%
+making a bad idea. And so it's like, you
+know, self-preservation. It's like why
+
+ align:start position:0%
+know, self-preservation. It's like why
+ 
+
+ align:start position:0%
+know, self-preservation. It's like why
+take the risk uh if if it's not worth
+
+ align:start position:0%
+take the risk uh if if it's not worth
+ 
+
+ align:start position:0%
+take the risk uh if if it's not worth
+it. Um and so you know I think MIT is an
+
+ align:start position:0%
+it. Um and so you know I think MIT is an
+ 
+
+ align:start position:0%
+it. Um and so you know I think MIT is an
+interesting place to talk about
+
+ align:start position:0%
+interesting place to talk about
+ 
+
+ align:start position:0%
+interesting place to talk about
+brainstorming and and this kind of
+
+ align:start position:0%
+brainstorming and and this kind of
+ 
+
+ align:start position:0%
+brainstorming and and this kind of
+organized ideation because there is you
+
+ align:start position:0%
+organized ideation because there is you
+ 
+
+ align:start position:0%
+organized ideation because there is you
+know social and academic pressure here
+
+ align:start position:0%
+know social and academic pressure here
+ 
+
+ align:start position:0%
+know social and academic pressure here
+too. Uh pressure to be right, pressure
+
+ align:start position:0%
+too. Uh pressure to be right, pressure
+ 
+
+ align:start position:0%
+too. Uh pressure to be right, pressure
+to not say something that would seem
+
+ align:start position:0%
+to not say something that would seem
+ 
+
+ align:start position:0%
+to not say something that would seem
+wrong and that sort of pressure is is
+
+ align:start position:0%
+wrong and that sort of pressure is is
+ 
+
+ align:start position:0%
+wrong and that sort of pressure is is
+completely uh antithetical to the idea
+
+ align:start position:0%
+completely uh antithetical to the idea
+ 
+
+ align:start position:0%
+completely uh antithetical to the idea
+of a brainstorming session. Um and so
+
+ align:start position:0%
+of a brainstorming session. Um and so
+ 
+
+ align:start position:0%
+of a brainstorming session. Um and so
+that's that's kind of a a basis for why
+
+ align:start position:0%
+that's that's kind of a a basis for why
+ 
+
+ align:start position:0%
+that's that's kind of a a basis for why
+not only it's good for video games but
+
+ align:start position:0%
+not only it's good for video games but
+ 
+
+ align:start position:0%
+not only it's good for video games but
+why it's also good to talk about talk
+
+ align:start position:0%
+why it's also good to talk about talk
+ 
+
+ align:start position:0%
+why it's also good to talk about talk
+about here at MIT. So
+
+ align:start position:0%
+about here at MIT. So
+ 
+
+ align:start position:0%
+about here at MIT. So
+there are four uh basic principles of
+
+ align:start position:0%
+there are four uh basic principles of
+ 
+
+ align:start position:0%
+there are four uh basic principles of
+brainstorming. Um you know these were
+
+ align:start position:0%
+brainstorming. Um you know these were
+ 
+
+ align:start position:0%
+brainstorming. Um you know these were
+outlined by Alex Osborne. He he was an
+
+ align:start position:0%
+outlined by Alex Osborne. He he was an
+ 
+
+ align:start position:0%
+outlined by Alex Osborne. He he was an
+ad agent. Um and uh I guess it was you
+
+ align:start position:0%
+ad agent. Um and uh I guess it was you
+ 
+
+ align:start position:0%
+ad agent. Um and uh I guess it was you
+know early he says it was like 1938 when
+
+ align:start position:0%
+know early he says it was like 1938 when
+ 
+
+ align:start position:0%
+know early he says it was like 1938 when
+he first started using it. People
+
+ align:start position:0%
+he first started using it. People
+ 
+
+ align:start position:0%
+he first started using it. People
+started kind of talking about it since
+
+ align:start position:0%
+started kind of talking about it since
+ 
+
+ align:start position:0%
+started kind of talking about it since
+then. Um and and it kind of I like when
+
+ align:start position:0%
+then. Um and and it kind of I like when
+ 
+
+ align:start position:0%
+then. Um and and it kind of I like when
+he said it sort of spiraled out of
+
+ align:start position:0%
+he said it sort of spiraled out of
+ 
+
+ align:start position:0%
+he said it sort of spiraled out of
+control that people sort of ran away
+
+ align:start position:0%
+control that people sort of ran away
+ 
+
+ align:start position:0%
+control that people sort of ran away
+with it. They're like ah this is a great
+
+ align:start position:0%
+with it. They're like ah this is a great
+ 
+
+ align:start position:0%
+with it. They're like ah this is a great
+idea but then they were they were kind
+
+ align:start position:0%
+idea but then they were they were kind
+ 
+
+ align:start position:0%
+idea but then they were they were kind
+of practicing it wrong. Um and so uh you
+
+ align:start position:0%
+of practicing it wrong. Um and so uh you
+ 
+
+ align:start position:0%
+of practicing it wrong. Um and so uh you
+know in in applied imaginations which is
+
+ align:start position:0%
+know in in applied imaginations which is
+ 
+
+ align:start position:0%
+know in in applied imaginations which is
+where the text um you know you guys
+
+ align:start position:0%
+where the text um you know you guys
+ 
+
+ align:start position:0%
+where the text um you know you guys
+read. It's sort of him reflecting on
+
+ align:start position:0%
+read. It's sort of him reflecting on
+ 
+
+ align:start position:0%
+read. It's sort of him reflecting on
+this brainstorming idea and saying this
+
+ align:start position:0%
+this brainstorming idea and saying this
+ 
+
+ align:start position:0%
+this brainstorming idea and saying this
+is really how it how it should be uh how
+
+ align:start position:0%
+is really how it how it should be uh how
+ 
+
+ align:start position:0%
+is really how it how it should be uh how
+it should be exercised. Um the first
+
+ align:start position:0%
+it should be exercised. Um the first
+ 
+
+ align:start position:0%
+it should be exercised. Um the first
+principle is single-handedly the most
+
+ align:start position:0%
+principle is single-handedly the most
+ 
+
+ align:start position:0%
+principle is single-handedly the most
+important principle. Um and that's no
+
+ align:start position:0%
+important principle. Um and that's no
+ 
+
+ align:start position:0%
+important principle. Um and that's no
+criticism. Um, that's a that's kind of a
+
+ align:start position:0%
+criticism. Um, that's a that's kind of a
+ 
+
+ align:start position:0%
+criticism. Um, that's a that's kind of a
+blanket way of of saying it, but but
+
+ align:start position:0%
+blanket way of of saying it, but but
+ 
+
+ align:start position:0%
+blanket way of of saying it, but but
+really in a more uh in a more um broad
+
+ align:start position:0%
+really in a more uh in a more um broad
+ 
+
+ align:start position:0%
+really in a more uh in a more um broad
+sense, it's it's kind of saying uh you
+
+ align:start position:0%
+sense, it's it's kind of saying uh you
+ 
+
+ align:start position:0%
+sense, it's it's kind of saying uh you
+know, judgment needs to be excluded. Um,
+
+ align:start position:0%
+know, judgment needs to be excluded. Um,
+ 
+
+ align:start position:0%
+know, judgment needs to be excluded. Um,
+in some sense, it's kind of um kind of
+
+ align:start position:0%
+in some sense, it's kind of um kind of
+ 
+
+ align:start position:0%
+in some sense, it's kind of um kind of
+both positive and negative, but but
+
+ align:start position:0%
+both positive and negative, but but
+ 
+
+ align:start position:0%
+both positive and negative, but but
+especially you don't want to criticize
+
+ align:start position:0%
+especially you don't want to criticize
+ 
+
+ align:start position:0%
+especially you don't want to criticize
+each other's work. Um, you also don't
+
+ align:start position:0%
+each other's work. Um, you also don't
+ 
+
+ align:start position:0%
+each other's work. Um, you also don't
+want to spend time during a brainstorm
+
+ align:start position:0%
+want to spend time during a brainstorm
+ 
+
+ align:start position:0%
+want to spend time during a brainstorm
+session talking about how good an idea
+
+ align:start position:0%
+session talking about how good an idea
+ 
+
+ align:start position:0%
+session talking about how good an idea
+is, right? If if someone throws out an
+
+ align:start position:0%
+is, right? If if someone throws out an
+ 
+
+ align:start position:0%
+is, right? If if someone throws out an
+idea um and and someone's like, "Oh,
+
+ align:start position:0%
+idea um and and someone's like, "Oh,
+ 
+
+ align:start position:0%
+idea um and and someone's like, "Oh,
+this is the best idea. We don't even
+
+ align:start position:0%
+this is the best idea. We don't even
+ 
+
+ align:start position:0%
+this is the best idea. We don't even
+need to keep going anymore." Then it's
+
+ align:start position:0%
+need to keep going anymore." Then it's
+ 
+
+ align:start position:0%
+need to keep going anymore." Then it's
+like, "Oh, no. Wait, now we're not
+
+ align:start position:0%
+like, "Oh, no. Wait, now we're not
+ 
+
+ align:start position:0%
+like, "Oh, no. Wait, now we're not
+brainstorming anymore." Um and so
+
+ align:start position:0%
+brainstorming anymore." Um and so
+ 
+
+ align:start position:0%
+brainstorming anymore." Um and so
+really, you know, judgment is is is
+
+ align:start position:0%
+really, you know, judgment is is is
+ 
+
+ align:start position:0%
+really, you know, judgment is is is
+absolutely supposed to be excluded from
+
+ align:start position:0%
+absolutely supposed to be excluded from
+ 
+
+ align:start position:0%
+absolutely supposed to be excluded from
+the process. Um
+
+ align:start position:0%
+the process. Um
+ 
+
+ align:start position:0%
+the process. Um
+I think that uh this is the primary uh
+
+ align:start position:0%
+I think that uh this is the primary uh
+ 
+
+ align:start position:0%
+I think that uh this is the primary uh
+principle that goes against that social
+
+ align:start position:0%
+principle that goes against that social
+ 
+
+ align:start position:0%
+principle that goes against that social
+pressure, right? Because the social
+
+ align:start position:0%
+pressure, right? Because the social
+ 
+
+ align:start position:0%
+pressure, right? Because the social
+pressure of judgment, the people who are
+
+ align:start position:0%
+pressure of judgment, the people who are
+ 
+
+ align:start position:0%
+pressure of judgment, the people who are
+saying, whether you have an executive
+
+ align:start position:0%
+saying, whether you have an executive
+ 
+
+ align:start position:0%
+saying, whether you have an executive
+who's in charge of you, a boss who's
+
+ align:start position:0%
+who's in charge of you, a boss who's
+ 
+
+ align:start position:0%
+who's in charge of you, a boss who's
+saying whether or not the ideas are good
+
+ align:start position:0%
+saying whether or not the ideas are good
+ 
+
+ align:start position:0%
+saying whether or not the ideas are good
+or bad, or whether you have colleagues
+
+ align:start position:0%
+or bad, or whether you have colleagues
+ 
+
+ align:start position:0%
+or bad, or whether you have colleagues
+that are saying whether or not ideas are
+
+ align:start position:0%
+that are saying whether or not ideas are
+ 
+
+ align:start position:0%
+that are saying whether or not ideas are
+good or bad, that sort of social
+
+ align:start position:0%
+good or bad, that sort of social
+ 
+
+ align:start position:0%
+good or bad, that sort of social
+pressure that forces people to stay
+
+ align:start position:0%
+pressure that forces people to stay
+ 
+
+ align:start position:0%
+pressure that forces people to stay
+quiet and maybe hold on to good ideas or
+
+ align:start position:0%
+quiet and maybe hold on to good ideas or
+ 
+
+ align:start position:0%
+quiet and maybe hold on to good ideas or
+throw away good ideas. Um, you know, if
+
+ align:start position:0%
+throw away good ideas. Um, you know, if
+ 
+
+ align:start position:0%
+throw away good ideas. Um, you know, if
+everybody's on board with the lack of
+
+ align:start position:0%
+everybody's on board with the lack of
+ 
+
+ align:start position:0%
+everybody's on board with the lack of
+criticism, then you you kind of have
+
+ align:start position:0%
+criticism, then you you kind of have
+ 
+
+ align:start position:0%
+criticism, then you you kind of have
+more freedom to to kind of express
+
+ align:start position:0%
+more freedom to to kind of express
+ 
+
+ align:start position:0%
+more freedom to to kind of express
+yourself. Um, you know, just just kind
+
+ align:start position:0%
+yourself. Um, you know, just just kind
+ 
+
+ align:start position:0%
+yourself. Um, you know, just just kind
+of pulling back to the text a little
+
+ align:start position:0%
+of pulling back to the text a little
+ 
+
+ align:start position:0%
+of pulling back to the text a little
+bit, um, you know, there was this this
+
+ align:start position:0%
+bit, um, you know, there was this this
+ 
+
+ align:start position:0%
+bit, um, you know, there was this this
+great quote um from this vice president.
+
+ align:start position:0%
+great quote um from this vice president.
+ 
+
+ align:start position:0%
+great quote um from this vice president.
+I just I'll read to you guys again. Uh
+
+ align:start position:0%
+I just I'll read to you guys again. Uh
+ 
+
+ align:start position:0%
+I just I'll read to you guys again. Uh
+you know, he said, "It was hard to get
+
+ align:start position:0%
+you know, he said, "It was hard to get
+ 
+
+ align:start position:0%
+you know, he said, "It was hard to get
+through my head uh what you were trying
+
+ align:start position:0%
+through my head uh what you were trying
+ 
+
+ align:start position:0%
+through my head uh what you were trying
+to do with us. Uh my 15 years of
+
+ align:start position:0%
+to do with us. Uh my 15 years of
+ 
+
+ align:start position:0%
+to do with us. Uh my 15 years of
+conference after conference in my
+
+ align:start position:0%
+conference after conference in my
+ 
+
+ align:start position:0%
+conference after conference in my
+company have conditioned me against
+
+ align:start position:0%
+company have conditioned me against
+ 
+
+ align:start position:0%
+company have conditioned me against
+shooting while um almost all of us
+
+ align:start position:0%
+shooting while um almost all of us
+ 
+
+ align:start position:0%
+shooting while um almost all of us
+officers rate each other on the basis of
+
+ align:start position:0%
+officers rate each other on the basis of
+ 
+
+ align:start position:0%
+officers rate each other on the basis of
+judgment. Uh we are far more apt to look
+
+ align:start position:0%
+judgment. Uh we are far more apt to look
+ 
+
+ align:start position:0%
+judgment. Uh we are far more apt to look
+up to the other fellow if he makes no
+
+ align:start position:0%
+up to the other fellow if he makes no
+ 
+
+ align:start position:0%
+up to the other fellow if he makes no
+mistakes than if he suggests lots of
+
+ align:start position:0%
+mistakes than if he suggests lots of
+ 
+
+ align:start position:0%
+mistakes than if he suggests lots of
+ideas." That's something that may sound
+
+ align:start position:0%
+ideas." That's something that may sound
+ 
+
+ align:start position:0%
+ideas." That's something that may sound
+familiar to you. Um so I've always kept
+
+ align:start position:0%
+familiar to you. Um so I've always kept
+ 
+
+ align:start position:0%
+familiar to you. Um so I've always kept
+myself from spouting any suggestions
+
+ align:start position:0%
+myself from spouting any suggestions
+ 
+
+ align:start position:0%
+myself from spouting any suggestions
+which could be sneered at. uh I wish our
+
+ align:start position:0%
+which could be sneered at. uh I wish our
+ 
+
+ align:start position:0%
+which could be sneered at. uh I wish our
+people would feel free to shoot ideas
+
+ align:start position:0%
+people would feel free to shoot ideas
+ 
+
+ align:start position:0%
+people would feel free to shoot ideas
+the way we have been doing in these
+
+ align:start position:0%
+the way we have been doing in these
+ 
+
+ align:start position:0%
+the way we have been doing in these
+brainstorm sessions. And so really like
+
+ align:start position:0%
+brainstorm sessions. And so really like
+ 
+
+ align:start position:0%
+brainstorm sessions. And so really like
+um this this lack of criticism, this
+
+ align:start position:0%
+um this this lack of criticism, this
+ 
+
+ align:start position:0%
+um this this lack of criticism, this
+sort of creating a safe environment for
+
+ align:start position:0%
+sort of creating a safe environment for
+ 
+
+ align:start position:0%
+sort of creating a safe environment for
+ideiation um is is the most fundamental
+
+ align:start position:0%
+ideiation um is is the most fundamental
+ 
+
+ align:start position:0%
+ideiation um is is the most fundamental
+principle in this brainstorm. Um and it
+
+ align:start position:0%
+principle in this brainstorm. Um and it
+ 
+
+ align:start position:0%
+principle in this brainstorm. Um and it
+really goes right at those social
+
+ align:start position:0%
+really goes right at those social
+ 
+
+ align:start position:0%
+really goes right at those social
+pressures which which can stop you know
+
+ align:start position:0%
+pressures which which can stop you know
+ 
+
+ align:start position:0%
+pressures which which can stop you know
+creativity and really hamper creativity.
+
+ align:start position:0%
+creativity and really hamper creativity.
+ 
+
+ align:start position:0%
+creativity and really hamper creativity.
+Um any questions about that? That sort
+
+ align:start position:0%
+Um any questions about that? That sort
+ 
+
+ align:start position:0%
+Um any questions about that? That sort
+of makes sense, right? This principle of
+
+ align:start position:0%
+of makes sense, right? This principle of
+ 
+
+ align:start position:0%
+of makes sense, right? This principle of
+of no criticism. Cool. Um,
+
+ align:start position:0%
+of no criticism. Cool. Um,
+ 
+
+ align:start position:0%
+of no criticism. Cool. Um,
+principle number two, uh, freewheeling,
+
+ align:start position:0%
+principle number two, uh, freewheeling,
+ 
+
+ align:start position:0%
+principle number two, uh, freewheeling,
+as uh, Mr. Osborne likes to call it. The
+
+ align:start position:0%
+as uh, Mr. Osborne likes to call it. The
+ 
+
+ align:start position:0%
+as uh, Mr. Osborne likes to call it. The
+wilder idea the better. This is also
+
+ align:start position:0%
+wilder idea the better. This is also
+ 
+
+ align:start position:0%
+wilder idea the better. This is also
+hard, uh, to kind of get used to. Um,
+
+ align:start position:0%
+hard, uh, to kind of get used to. Um,
+ 
+
+ align:start position:0%
+hard, uh, to kind of get used to. Um,
+again, it was like the guy said in that
+
+ align:start position:0%
+again, it was like the guy said in that
+ 
+
+ align:start position:0%
+again, it was like the guy said in that
+quote, you know, you you resist the urge
+
+ align:start position:0%
+quote, you know, you you resist the urge
+ 
+
+ align:start position:0%
+quote, you know, you you resist the urge
+to throw out something that's absolutely
+
+ align:start position:0%
+to throw out something that's absolutely
+ 
+
+ align:start position:0%
+to throw out something that's absolutely
+crazy and absolutely wild for the fear
+
+ align:start position:0%
+crazy and absolutely wild for the fear
+ 
+
+ align:start position:0%
+crazy and absolutely wild for the fear
+of ridicule. Well, if we eliminate the
+
+ align:start position:0%
+of ridicule. Well, if we eliminate the
+ 
+
+ align:start position:0%
+of ridicule. Well, if we eliminate the
+fear of ridicule and we understand that
+
+ align:start position:0%
+fear of ridicule and we understand that
+ 
+
+ align:start position:0%
+fear of ridicule and we understand that
+we're just trying to get every idea that
+
+ align:start position:0%
+we're just trying to get every idea that
+ 
+
+ align:start position:0%
+we're just trying to get every idea that
+we can um then freewheeling is is
+
+ align:start position:0%
+we can um then freewheeling is is
+ 
+
+ align:start position:0%
+we can um then freewheeling is is
+absolutely encouraged and you need to
+
+ align:start position:0%
+absolutely encouraged and you need to
+ 
+
+ align:start position:0%
+absolutely encouraged and you need to
+kind of get past that um past that oh
+
+ align:start position:0%
+kind of get past that um past that oh
+ 
+
+ align:start position:0%
+kind of get past that um past that oh
+you know this is whatever we're known
+
+ align:start position:0%
+you know this is whatever we're known
+ 
+
+ align:start position:0%
+you know this is whatever we're known
+whatever like this um and I can you know
+
+ align:start position:0%
+whatever like this um and I can you know
+ 
+
+ align:start position:0%
+whatever like this um and I can you know
+I I put up Kadamari dysi up here because
+
+ align:start position:0%
+I I put up Kadamari dysi up here because
+ 
+
+ align:start position:0%
+I I put up Kadamari dysi up here because
+you know that that's the sort of idea
+
+ align:start position:0%
+you know that that's the sort of idea
+ 
+
+ align:start position:0%
+you know that that's the sort of idea
+that someone throws out at a at a at a
+
+ align:start position:0%
+that someone throws out at a at a at a
+ 
+
+ align:start position:0%
+that someone throws out at a at a at a
+meeting um and if there's criticism
+
+ align:start position:0%
+meeting um and if there's criticism
+ 
+
+ align:start position:0%
+meeting um and if there's criticism
+someone will be like that's the dumbest
+
+ align:start position:0%
+someone will be like that's the dumbest
+ 
+
+ align:start position:0%
+someone will be like that's the dumbest
+thing I've ever heard. you can't just
+
+ align:start position:0%
+thing I've ever heard. you can't just
+ 
+
+ align:start position:0%
+thing I've ever heard. you can't just
+roll around picking up stuff for the
+
+ align:start position:0%
+roll around picking up stuff for the
+ 
+
+ align:start position:0%
+roll around picking up stuff for the
+king of the cosmos. That's insane. Um
+
+ align:start position:0%
+king of the cosmos. That's insane. Um
+ 
+
+ align:start position:0%
+king of the cosmos. That's insane. Um
+and and it probably, you know, it
+
+ align:start position:0%
+and and it probably, you know, it
+ 
+
+ align:start position:0%
+and and it probably, you know, it
+probably was a synthesis of a lot of
+
+ align:start position:0%
+probably was a synthesis of a lot of
+ 
+
+ align:start position:0%
+probably was a synthesis of a lot of
+different ideas that that kind of
+
+ align:start position:0%
+different ideas that that kind of
+ 
+
+ align:start position:0%
+different ideas that that kind of
+created that game, which we'll talk
+
+ align:start position:0%
+created that game, which we'll talk
+ 
+
+ align:start position:0%
+created that game, which we'll talk
+about later, but um really, you know,
+
+ align:start position:0%
+about later, but um really, you know,
+ 
+
+ align:start position:0%
+about later, but um really, you know,
+having these like kind of wild, crazy
+
+ align:start position:0%
+having these like kind of wild, crazy
+ 
+
+ align:start position:0%
+having these like kind of wild, crazy
+ideas. You may think it's over the edge,
+
+ align:start position:0%
+ideas. You may think it's over the edge,
+ 
+
+ align:start position:0%
+ideas. You may think it's over the edge,
+and it might be over the edge. Um, but
+
+ align:start position:0%
+and it might be over the edge. Um, but
+ 
+
+ align:start position:0%
+and it might be over the edge. Um, but
+it is it is way easier to make something
+
+ align:start position:0%
+it is it is way easier to make something
+ 
+
+ align:start position:0%
+it is it is way easier to make something
+feasible than it is to take something
+
+ align:start position:0%
+feasible than it is to take something
+ 
+
+ align:start position:0%
+feasible than it is to take something
+that's pretty um pretty normal and make
+
+ align:start position:0%
+that's pretty um pretty normal and make
+ 
+
+ align:start position:0%
+that's pretty um pretty normal and make
+it make it innovative and interesting,
+
+ align:start position:0%
+it make it innovative and interesting,
+ 
+
+ align:start position:0%
+it make it innovative and interesting,
+right? It's it's much easier to kind of
+
+ align:start position:0%
+right? It's it's much easier to kind of
+ 
+
+ align:start position:0%
+right? It's it's much easier to kind of
+go go in that backward direction. Um,
+
+ align:start position:0%
+go go in that backward direction. Um,
+ 
+
+ align:start position:0%
+go go in that backward direction. Um,
+and so really the wilder idea the idea
+
+ align:start position:0%
+and so really the wilder idea the idea
+ 
+
+ align:start position:0%
+and so really the wilder idea the idea
+you can come up with the the the
+
+ align:start position:0%
+you can come up with the the the
+ 
+
+ align:start position:0%
+you can come up with the the the
+stronger. Um,
+
+ align:start position:0%
+stronger. Um,
+ 
+
+ align:start position:0%
+stronger. Um,
+any questions about principle number
+
+ align:start position:0%
+any questions about principle number
+ 
+
+ align:start position:0%
+any questions about principle number
+two? Making sense on board? Cool. Uh,
+
+ align:start position:0%
+two? Making sense on board? Cool. Uh,
+ 
+
+ align:start position:0%
+two? Making sense on board? Cool. Uh,
+quantity. Um, this is really the the
+
+ align:start position:0%
+quantity. Um, this is really the the
+ 
+
+ align:start position:0%
+quantity. Um, this is really the the
+goal of of a brainstorming session. Come
+
+ align:start position:0%
+goal of of a brainstorming session. Come
+ 
+
+ align:start position:0%
+goal of of a brainstorming session. Come
+up with as many ideas as you can, right?
+
+ align:start position:0%
+up with as many ideas as you can, right?
+ 
+
+ align:start position:0%
+up with as many ideas as you can, right?
+Um, it it stands to reason that if you
+
+ align:start position:0%
+Um, it it stands to reason that if you
+ 
+
+ align:start position:0%
+Um, it it stands to reason that if you
+have lots of ideas, there's a greater
+
+ align:start position:0%
+have lots of ideas, there's a greater
+ 
+
+ align:start position:0%
+have lots of ideas, there's a greater
+likelihood that you'll have a useful one
+
+ align:start position:0%
+likelihood that you'll have a useful one
+ 
+
+ align:start position:0%
+likelihood that you'll have a useful one
+um than if say you have two. Your
+
+ align:start position:0%
+um than if say you have two. Your
+ 
+
+ align:start position:0%
+um than if say you have two. Your
+choices are limited. You didn't pick the
+
+ align:start position:0%
+choices are limited. You didn't pick the
+ 
+
+ align:start position:0%
+choices are limited. You didn't pick the
+better of the two, I suppose, but it
+
+ align:start position:0%
+better of the two, I suppose, but it
+ 
+
+ align:start position:0%
+better of the two, I suppose, but it
+might not be the best idea you have. Um,
+
+ align:start position:0%
+might not be the best idea you have. Um,
+ 
+
+ align:start position:0%
+might not be the best idea you have. Um,
+and so really this is, you know, this
+
+ align:start position:0%
+and so really this is, you know, this
+ 
+
+ align:start position:0%
+and so really this is, you know, this
+adds on to that wild idea. Throw
+
+ align:start position:0%
+adds on to that wild idea. Throw
+ 
+
+ align:start position:0%
+adds on to that wild idea. Throw
+everything out you can. you need to just
+
+ align:start position:0%
+everything out you can. you need to just
+ 
+
+ align:start position:0%
+everything out you can. you need to just
+get everything um out and everything on
+
+ align:start position:0%
+get everything um out and everything on
+ 
+
+ align:start position:0%
+get everything um out and everything on
+on on the page um in order to even be
+
+ align:start position:0%
+on on the page um in order to even be
+ 
+
+ align:start position:0%
+on on the page um in order to even be
+able to start judging it. And that's the
+
+ align:start position:0%
+able to start judging it. And that's the
+ 
+
+ align:start position:0%
+able to start judging it. And that's the
+important thing too that that needs to
+
+ align:start position:0%
+important thing too that that needs to
+ 
+
+ align:start position:0%
+important thing too that that needs to
+be um that needs to be clarified is that
+
+ align:start position:0%
+be um that needs to be clarified is that
+ 
+
+ align:start position:0%
+be um that needs to be clarified is that
+brainstorming is a first step in a
+
+ align:start position:0%
+brainstorming is a first step in a
+ 
+
+ align:start position:0%
+brainstorming is a first step in a
+creative process. It's not the whole
+
+ align:start position:0%
+creative process. It's not the whole
+ 
+
+ align:start position:0%
+creative process. It's not the whole
+process. It's not like, oh, we've got
+
+ align:start position:0%
+process. It's not like, oh, we've got
+ 
+
+ align:start position:0%
+process. It's not like, oh, we've got
+this creative problem that we need to
+
+ align:start position:0%
+this creative problem that we need to
+ 
+
+ align:start position:0%
+this creative problem that we need to
+solve. We'll have a brainstorming
+
+ align:start position:0%
+solve. We'll have a brainstorming
+ 
+
+ align:start position:0%
+solve. We'll have a brainstorming
+session, then we'll have it. Um, and
+
+ align:start position:0%
+session, then we'll have it. Um, and
+ 
+
+ align:start position:0%
+session, then we'll have it. Um, and
+actually that's that's something that
+
+ align:start position:0%
+actually that's that's something that
+ 
+
+ align:start position:0%
+actually that's that's something that
+hampers brainstorming a lot is that you
+
+ align:start position:0%
+hampers brainstorming a lot is that you
+ 
+
+ align:start position:0%
+hampers brainstorming a lot is that you
+have the brainstorming session, you come
+
+ align:start position:0%
+have the brainstorming session, you come
+ 
+
+ align:start position:0%
+have the brainstorming session, you come
+up with these great ideas and then
+
+ align:start position:0%
+up with these great ideas and then
+ 
+
+ align:start position:0%
+up with these great ideas and then
+everybody leaves and you never return to
+
+ align:start position:0%
+everybody leaves and you never return to
+ 
+
+ align:start position:0%
+everybody leaves and you never return to
+it or you never kind of reflect on which
+
+ align:start position:0%
+it or you never kind of reflect on which
+ 
+
+ align:start position:0%
+it or you never kind of reflect on which
+of these ideas is going to be best or
+
+ align:start position:0%
+of these ideas is going to be best or
+ 
+
+ align:start position:0%
+of these ideas is going to be best or
+you kind of just end up picking one. And
+
+ align:start position:0%
+you kind of just end up picking one. And
+ 
+
+ align:start position:0%
+you kind of just end up picking one. And
+so the judgment needs to happen as well.
+
+ align:start position:0%
+so the judgment needs to happen as well.
+ 
+
+ align:start position:0%
+so the judgment needs to happen as well.
+Um, but not now, you know, during the
+
+ align:start position:0%
+Um, but not now, you know, during the
+ 
+
+ align:start position:0%
+Um, but not now, you know, during the
+brainstorm session. It's just get
+
+ align:start position:0%
+brainstorm session. It's just get
+ 
+
+ align:start position:0%
+brainstorm session. It's just get
+everything out that you can. Um,
+
+ align:start position:0%
+everything out that you can. Um,
+ 
+
+ align:start position:0%
+everything out that you can. Um,
+it it really just it kind of stands for
+
+ align:start position:0%
+it it really just it kind of stands for
+ 
+
+ align:start position:0%
+it it really just it kind of stands for
+reason. And I I kind of made fun of
+
+ align:start position:0%
+reason. And I I kind of made fun of
+ 
+
+ align:start position:0%
+reason. And I I kind of made fun of
+Storm when he was like, you know,
+
+ align:start position:0%
+Storm when he was like, you know,
+ 
+
+ align:start position:0%
+Storm when he was like, you know,
+saying, well, in this inst in the
+
+ align:start position:0%
+saying, well, in this inst in the
+ 
+
+ align:start position:0%
+saying, well, in this inst in the
+government they had 95 ideas and we you
+
+ align:start position:0%
+government they had 95 ideas and we you
+ 
+
+ align:start position:0%
+government they had 95 ideas and we you
+know came up with eight good desires
+
+ align:start position:0%
+know came up with eight good desires
+ 
+
+ align:start position:0%
+know came up with eight good desires
+which you know how many did you come up
+
+ align:start position:0%
+which you know how many did you come up
+ 
+
+ align:start position:0%
+which you know how many did you come up
+with before but but it's true just the
+
+ align:start position:0%
+with before but but it's true just the
+ 
+
+ align:start position:0%
+with before but but it's true just the
+more you have the better you're going to
+
+ align:start position:0%
+more you have the better you're going to
+ 
+
+ align:start position:0%
+more you have the better you're going to
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+and then this one is related to that
+
+ align:start position:0%
+and then this one is related to that
+ 
+
+ align:start position:0%
+and then this one is related to that
+which is the idea of synthesis or
+
+ align:start position:0%
+which is the idea of synthesis or
+ 
+
+ align:start position:0%
+which is the idea of synthesis or
+building on ideas um which is that often
+
+ align:start position:0%
+building on ideas um which is that often
+ 
+
+ align:start position:0%
+building on ideas um which is that often
+times the best idea the best creative
+
+ align:start position:0%
+times the best idea the best creative
+ 
+
+ align:start position:0%
+times the best idea the best creative
+idea is not going to be something that's
+
+ align:start position:0%
+idea is not going to be something that's
+ 
+
+ align:start position:0%
+idea is not going to be something that's
+just kind of a unique idea that stands
+
+ align:start position:0%
+just kind of a unique idea that stands
+ 
+
+ align:start position:0%
+just kind of a unique idea that stands
+alone in this corpus of ideas that
+
+ align:start position:0%
+alone in this corpus of ideas that
+ 
+
+ align:start position:0%
+alone in this corpus of ideas that
+you've collected over the brainstorm
+
+ align:start position:0%
+you've collected over the brainstorm
+ 
+
+ align:start position:0%
+you've collected over the brainstorm
+it's going to be an idea that is a
+
+ align:start position:0%
+it's going to be an idea that is a
+ 
+
+ align:start position:0%
+it's going to be an idea that is a
+synthesis of of of one idea and another
+
+ align:start position:0%
+synthesis of of of one idea and another
+ 
+
+ align:start position:0%
+synthesis of of of one idea and another
+or someone suggests an idea and then
+
+ align:start position:0%
+or someone suggests an idea and then
+ 
+
+ align:start position:0%
+or someone suggests an idea and then
+that makes you think of something else
+
+ align:start position:0%
+that makes you think of something else
+ 
+
+ align:start position:0%
+that makes you think of something else
+that's related to it and you kind of
+
+ align:start position:0%
+that's related to it and you kind of
+ 
+
+ align:start position:0%
+that's related to it and you kind of
+build on that and and you can see in
+
+ align:start position:0%
+build on that and and you can see in
+ 
+
+ align:start position:0%
+build on that and and you can see in
+really positive good brainstorming
+
+ align:start position:0%
+really positive good brainstorming
+ 
+
+ align:start position:0%
+really positive good brainstorming
+sessions um there's momentum and one of
+
+ align:start position:0%
+sessions um there's momentum and one of
+ 
+
+ align:start position:0%
+sessions um there's momentum and one of
+the things that can really hurt that
+
+ align:start position:0%
+the things that can really hurt that
+ 
+
+ align:start position:0%
+the things that can really hurt that
+momentum is when people are starting to
+
+ align:start position:0%
+momentum is when people are starting to
+ 
+
+ align:start position:0%
+momentum is when people are starting to
+riff on an idea then someone's like oh
+
+ align:start position:0%
+riff on an idea then someone's like oh
+ 
+
+ align:start position:0%
+riff on an idea then someone's like oh
+but you know in other news you know we
+
+ align:start position:0%
+but you know in other news you know we
+ 
+
+ align:start position:0%
+but you know in other news you know we
+could do this and so it's really
+
+ align:start position:0%
+could do this and so it's really
+ 
+
+ align:start position:0%
+could do this and so it's really
+encouraged that you synthesize ideas if
+
+ align:start position:0%
+encouraged that you synthesize ideas if
+ 
+
+ align:start position:0%
+encouraged that you synthesize ideas if
+you have that other left field idea
+
+ align:start position:0%
+you have that other left field idea
+ 
+
+ align:start position:0%
+you have that other left field idea
+don't throw it away right jot it down so
+
+ align:start position:0%
+don't throw it away right jot it down so
+ 
+
+ align:start position:0%
+don't throw it away right jot it down so
+that you can bring it up later but don't
+
+ align:start position:0%
+that you can bring it up later but don't
+ 
+
+ align:start position:0%
+that you can bring it up later but don't
+don't kind of kill the momentum of the
+
+ align:start position:0%
+don't kind of kill the momentum of the
+ 
+
+ align:start position:0%
+don't kind of kill the momentum of the
+synthesis if that's happening. Um it's
+
+ align:start position:0%
+synthesis if that's happening. Um it's
+ 
+
+ align:start position:0%
+synthesis if that's happening. Um it's
+it's you know kind of really important
+
+ align:start position:0%
+it's you know kind of really important
+ 
+
+ align:start position:0%
+it's you know kind of really important
+that you start um it's the collaborative
+
+ align:start position:0%
+that you start um it's the collaborative
+ 
+
+ align:start position:0%
+that you start um it's the collaborative
+part of this creative uh ideiation. Um
+
+ align:start position:0%
+part of this creative uh ideiation. Um
+ 
+
+ align:start position:0%
+part of this creative uh ideiation. Um
+it's this combining of ideas that's
+
+ align:start position:0%
+it's this combining of ideas that's
+ 
+
+ align:start position:0%
+it's this combining of ideas that's
+going to create um good ideas. And
+
+ align:start position:0%
+going to create um good ideas. And
+ 
+
+ align:start position:0%
+going to create um good ideas. And
+that's that's just um I I think we can
+
+ align:start position:0%
+that's that's just um I I think we can
+ 
+
+ align:start position:0%
+that's that's just um I I think we can
+kind of take that as a given that if you
+
+ align:start position:0%
+kind of take that as a given that if you
+ 
+
+ align:start position:0%
+kind of take that as a given that if you
+collect a bunch of skilled, thoughtful,
+
+ align:start position:0%
+collect a bunch of skilled, thoughtful,
+ 
+
+ align:start position:0%
+collect a bunch of skilled, thoughtful,
+creative people together um combining
+
+ align:start position:0%
+creative people together um combining
+ 
+
+ align:start position:0%
+creative people together um combining
+their ideas is going to create something
+
+ align:start position:0%
+their ideas is going to create something
+ 
+
+ align:start position:0%
+their ideas is going to create something
+that's better than just the any one idea
+
+ align:start position:0%
+that's better than just the any one idea
+ 
+
+ align:start position:0%
+that's better than just the any one idea
+that one creative uh professional is
+
+ align:start position:0%
+that one creative uh professional is
+ 
+
+ align:start position:0%
+that one creative uh professional is
+going to have or at least just a
+
+ align:start position:0%
+going to have or at least just a
+ 
+
+ align:start position:0%
+going to have or at least just a
+different solution that might be more
+
+ align:start position:0%
+different solution that might be more
+ 
+
+ align:start position:0%
+different solution that might be more
+ideal given the problem. And so, you
+
+ align:start position:0%
+ideal given the problem. And so, you
+ 
+
+ align:start position:0%
+ideal given the problem. And so, you
+know, you can think of things like, you
+
+ align:start position:0%
+know, you can think of things like, you
+ 
+
+ align:start position:0%
+know, you can think of things like, you
+know, Lego's pretty awesome. Um, Star
+
+ align:start position:0%
+know, Lego's pretty awesome. Um, Star
+ 
+
+ align:start position:0%
+know, Lego's pretty awesome. Um, Star
+Wars is also pretty awesome,
+
+ align:start position:0%
+Wars is also pretty awesome,
+ 
+
+ align:start position:0%
+Wars is also pretty awesome,
+but you know, Lego Star Wars move is is
+
+ align:start position:0%
+but you know, Lego Star Wars move is is
+ 
+
+ align:start position:0%
+but you know, Lego Star Wars move is is
+also awesome. You know, similarly, um,
+
+ align:start position:0%
+also awesome. You know, similarly, um,
+ 
+
+ align:start position:0%
+also awesome. You know, similarly, um,
+you know, Marvel's dope. Um, Capcom's
+
+ align:start position:0%
+you know, Marvel's dope. Um, Capcom's
+ 
+
+ align:start position:0%
+you know, Marvel's dope. Um, Capcom's
+also pretty dope. Marvel versus Capcom
+
+ align:start position:0%
+also pretty dope. Marvel versus Capcom
+ 
+
+ align:start position:0%
+also pretty dope. Marvel versus Capcom
+is tremendously dope. So, um, you know,
+
+ align:start position:0%
+is tremendously dope. So, um, you know,
+ 
+
+ align:start position:0%
+is tremendously dope. So, um, you know,
+building on ideas can create obviously
+
+ align:start position:0%
+building on ideas can create obviously
+ 
+
+ align:start position:0%
+building on ideas can create obviously
+really interesting things and that's,
+
+ align:start position:0%
+really interesting things and that's,
+ 
+
+ align:start position:0%
+really interesting things and that's,
+you know, it's a good idea to kind of
+
+ align:start position:0%
+you know, it's a good idea to kind of
+ 
+
+ align:start position:0%
+you know, it's a good idea to kind of
+keep working on that in your brainstorm
+
+ align:start position:0%
+keep working on that in your brainstorm
+ 
+
+ align:start position:0%
+keep working on that in your brainstorm
+sessions, like what can you what can you
+
+ align:start position:0%
+sessions, like what can you what can you
+ 
+
+ align:start position:0%
+sessions, like what can you what can you
+put together? Um,
+
+ align:start position:0%
+put together? Um,
+ 
+
+ align:start position:0%
+put together? Um,
+so how is it organized? Um, you know,
+
+ align:start position:0%
+so how is it organized? Um, you know,
+ 
+
+ align:start position:0%
+so how is it organized? Um, you know,
+we've kind of talked about basic
+
+ align:start position:0%
+we've kind of talked about basic
+ 
+
+ align:start position:0%
+we've kind of talked about basic
+principles. Any questions about those
+
+ align:start position:0%
+principles. Any questions about those
+ 
+
+ align:start position:0%
+principles. Any questions about those
+four principles? Do they all make sense?
+
+ align:start position:0%
+four principles? Do they all make sense?
+ 
+
+ align:start position:0%
+four principles? Do they all make sense?
+Do they all seem to be grounded in
+
+ align:start position:0%
+Do they all seem to be grounded in
+ 
+
+ align:start position:0%
+Do they all seem to be grounded in
+the greatest? All right. Um,
+
+ align:start position:0%
+the greatest? All right. Um,
+ 
+
+ align:start position:0%
+the greatest? All right. Um,
+so the question becomes then, how do you
+
+ align:start position:0%
+so the question becomes then, how do you
+ 
+
+ align:start position:0%
+so the question becomes then, how do you
+organize um how do you organize your
+
+ align:start position:0%
+organize um how do you organize your
+ 
+
+ align:start position:0%
+organize um how do you organize your
+brainstorm? One of the points that Alex
+
+ align:start position:0%
+brainstorm? One of the points that Alex
+ 
+
+ align:start position:0%
+brainstorm? One of the points that Alex
+Osborne makes is that um it needs to
+
+ align:start position:0%
+Osborne makes is that um it needs to
+ 
+
+ align:start position:0%
+Osborne makes is that um it needs to
+have a casual spirit or a casual
+
+ align:start position:0%
+have a casual spirit or a casual
+ 
+
+ align:start position:0%
+have a casual spirit or a casual
+atmosphere. He refers to it as a picnic,
+
+ align:start position:0%
+atmosphere. He refers to it as a picnic,
+ 
+
+ align:start position:0%
+atmosphere. He refers to it as a picnic,
+which is another one of those I haven't
+
+ align:start position:0%
+which is another one of those I haven't
+ 
+
+ align:start position:0%
+which is another one of those I haven't
+been on a picnic in a really long time,
+
+ align:start position:0%
+been on a picnic in a really long time,
+ 
+
+ align:start position:0%
+been on a picnic in a really long time,
+but um but you know, it's like yes, we
+
+ align:start position:0%
+but um but you know, it's like yes, we
+ 
+
+ align:start position:0%
+but um but you know, it's like yes, we
+brought our lunches in and then we
+
+ align:start position:0%
+brought our lunches in and then we
+ 
+
+ align:start position:0%
+brought our lunches in and then we
+talked afterwards. It's like what we
+
+ align:start position:0%
+talked afterwards. It's like what we
+ 
+
+ align:start position:0%
+talked afterwards. It's like what we
+call those lunch meetings now. But um
+
+ align:start position:0%
+call those lunch meetings now. But um
+ 
+
+ align:start position:0%
+call those lunch meetings now. But um
+but he has a good point that if um if a
+
+ align:start position:0%
+but he has a good point that if um if a
+ 
+
+ align:start position:0%
+but he has a good point that if um if a
+large part of the brainstorming session
+
+ align:start position:0%
+large part of the brainstorming session
+ 
+
+ align:start position:0%
+large part of the brainstorming session
+is intended to combat um social
+
+ align:start position:0%
+is intended to combat um social
+ 
+
+ align:start position:0%
+is intended to combat um social
+pressures that stop you from being
+
+ align:start position:0%
+pressures that stop you from being
+ 
+
+ align:start position:0%
+pressures that stop you from being
+creative, that inhibit your creativity,
+
+ align:start position:0%
+creative, that inhibit your creativity,
+ 
+
+ align:start position:0%
+creative, that inhibit your creativity,
+then it would stand to reason that
+
+ align:start position:0%
+then it would stand to reason that
+ 
+
+ align:start position:0%
+then it would stand to reason that
+creating a casual spirit, a casual
+
+ align:start position:0%
+creating a casual spirit, a casual
+ 
+
+ align:start position:0%
+creating a casual spirit, a casual
+environment um for this process is
+
+ align:start position:0%
+environment um for this process is
+ 
+
+ align:start position:0%
+environment um for this process is
+important. Um, and so I have, you know,
+
+ align:start position:0%
+important. Um, and so I have, you know,
+ 
+
+ align:start position:0%
+important. Um, and so I have, you know,
+it's hard to most video game processes
+
+ align:start position:0%
+it's hard to most video game processes
+ 
+
+ align:start position:0%
+it's hard to most video game processes
+and most video game companies have a
+
+ align:start position:0%
+and most video game companies have a
+ 
+
+ align:start position:0%
+and most video game companies have a
+pretty casual spirit and environment
+
+ align:start position:0%
+pretty casual spirit and environment
+ 
+
+ align:start position:0%
+pretty casual spirit and environment
+because of the nature of the work in
+
+ align:start position:0%
+because of the nature of the work in
+ 
+
+ align:start position:0%
+because of the nature of the work in
+general. Um, so sometimes this might not
+
+ align:start position:0%
+general. Um, so sometimes this might not
+ 
+
+ align:start position:0%
+general. Um, so sometimes this might not
+be that hard, but um, you know, things
+
+ align:start position:0%
+be that hard, but um, you know, things
+ 
+
+ align:start position:0%
+be that hard, but um, you know, things
+to consider are like what is the makeup
+
+ align:start position:0%
+to consider are like what is the makeup
+ 
+
+ align:start position:0%
+to consider are like what is the makeup
+of your team, right? If there's, you
+
+ align:start position:0%
+of your team, right? If there's, you
+ 
+
+ align:start position:0%
+of your team, right? If there's, you
+know, if your president of the company
+
+ align:start position:0%
+know, if your president of the company
+ 
+
+ align:start position:0%
+know, if your president of the company
+does a really bad job of putting himself
+
+ align:start position:0%
+does a really bad job of putting himself
+ 
+
+ align:start position:0%
+does a really bad job of putting himself
+or herself on the same level as all the
+
+ align:start position:0%
+or herself on the same level as all the
+ 
+
+ align:start position:0%
+or herself on the same level as all the
+people, you might want to exclude that
+
+ align:start position:0%
+people, you might want to exclude that
+ 
+
+ align:start position:0%
+people, you might want to exclude that
+person from the brainstorming session
+
+ align:start position:0%
+person from the brainstorming session
+ 
+
+ align:start position:0%
+person from the brainstorming session
+because then everybody's going to feel
+
+ align:start position:0%
+because then everybody's going to feel
+ 
+
+ align:start position:0%
+because then everybody's going to feel
+the pressure of the president, you know,
+
+ align:start position:0%
+the pressure of the president, you know,
+ 
+
+ align:start position:0%
+the pressure of the president, you know,
+and we, you know, do we need to make an
+
+ align:start position:0%
+and we, you know, do we need to make an
+ 
+
+ align:start position:0%
+and we, you know, do we need to make an
+idea that makes that person happy. It's,
+
+ align:start position:0%
+idea that makes that person happy. It's,
+ 
+
+ align:start position:0%
+idea that makes that person happy. It's,
+you know, you have to think these things
+
+ align:start position:0%
+you know, you have to think these things
+ 
+
+ align:start position:0%
+you know, you have to think these things
+through in terms of what the environment
+
+ align:start position:0%
+through in terms of what the environment
+ 
+
+ align:start position:0%
+through in terms of what the environment
+is going to be for your brainstorming
+
+ align:start position:0%
+is going to be for your brainstorming
+ 
+
+ align:start position:0%
+is going to be for your brainstorming
+session and and who's involved. Um, so
+
+ align:start position:0%
+session and and who's involved. Um, so
+ 
+
+ align:start position:0%
+session and and who's involved. Um, so
+it it is an important point is an
+
+ align:start position:0%
+it it is an important point is an
+ 
+
+ align:start position:0%
+it it is an important point is an
+important step. um you know starting
+
+ align:start position:0%
+important step. um you know starting
+ 
+
+ align:start position:0%
+important step. um you know starting
+with a a bad or or a worthless idea uh
+
+ align:start position:0%
+with a a bad or or a worthless idea uh
+ 
+
+ align:start position:0%
+with a a bad or or a worthless idea uh
+encourages that freewheeling sense. Um
+
+ align:start position:0%
+encourages that freewheeling sense. Um
+ 
+
+ align:start position:0%
+encourages that freewheeling sense. Um
+you know a lot of times people will
+
+ align:start position:0%
+you know a lot of times people will
+ 
+
+ align:start position:0%
+you know a lot of times people will
+contribute ideas that feel safe. Again
+
+ align:start position:0%
+contribute ideas that feel safe. Again
+ 
+
+ align:start position:0%
+contribute ideas that feel safe. Again
+you want to come up with the most ideas
+
+ align:start position:0%
+you want to come up with the most ideas
+ 
+
+ align:start position:0%
+you want to come up with the most ideas
+that you can. Um so you know having
+
+ align:start position:0%
+that you can. Um so you know having
+ 
+
+ align:start position:0%
+that you can. Um so you know having
+someone with the courage or even
+
+ align:start position:0%
+someone with the courage or even
+ 
+
+ align:start position:0%
+someone with the courage or even
+bringing to the beginning of it a a
+
+ align:start position:0%
+bringing to the beginning of it a a
+ 
+
+ align:start position:0%
+bringing to the beginning of it a a
+crazy worthless bad freewheeling idea
+
+ align:start position:0%
+crazy worthless bad freewheeling idea
+ 
+
+ align:start position:0%
+crazy worthless bad freewheeling idea
+can help kind of encourage people to
+
+ align:start position:0%
+can help kind of encourage people to
+ 
+
+ align:start position:0%
+can help kind of encourage people to
+keep doing that. So, um, you know,
+
+ align:start position:0%
+keep doing that. So, um, you know,
+ 
+
+ align:start position:0%
+keep doing that. So, um, you know,
+either starting with someone who has a
+
+ align:start position:0%
+either starting with someone who has a
+ 
+
+ align:start position:0%
+either starting with someone who has a
+crazy idea or even bringing it to the
+
+ align:start position:0%
+crazy idea or even bringing it to the
+ 
+
+ align:start position:0%
+crazy idea or even bringing it to the
+brainstorm at the very beginning can be
+
+ align:start position:0%
+brainstorm at the very beginning can be
+ 
+
+ align:start position:0%
+brainstorm at the very beginning can be
+a really good thing as well. Um, this is
+
+ align:start position:0%
+a really good thing as well. Um, this is
+ 
+
+ align:start position:0%
+a really good thing as well. Um, this is
+kind of a key one. Don't uh don't
+
+ align:start position:0%
+kind of a key one. Don't uh don't
+ 
+
+ align:start position:0%
+kind of a key one. Don't uh don't
+interrupt anyone. Um, it it's really
+
+ align:start position:0%
+interrupt anyone. Um, it it's really
+ 
+
+ align:start position:0%
+interrupt anyone. Um, it it's really
+important in a brainstorming session to
+
+ align:start position:0%
+important in a brainstorming session to
+ 
+
+ align:start position:0%
+important in a brainstorming session to
+encourage um that every voice is heard.
+
+ align:start position:0%
+encourage um that every voice is heard.
+ 
+
+ align:start position:0%
+encourage um that every voice is heard.
+Um, you know, there's there's these kind
+
+ align:start position:0%
+Um, you know, there's there's these kind
+ 
+
+ align:start position:0%
+Um, you know, there's there's these kind
+of uh let me see if I can find that
+
+ align:start position:0%
+of uh let me see if I can find that
+ 
+
+ align:start position:0%
+of uh let me see if I can find that
+quote from that one guy. Um, yeah, here
+
+ align:start position:0%
+quote from that one guy. Um, yeah, here
+ 
+
+ align:start position:0%
+quote from that one guy. Um, yeah, here
+we go. Um, it's great. I was think up or
+
+ align:start position:0%
+we go. Um, it's great. I was think up or
+ 
+
+ align:start position:0%
+we go. Um, it's great. I was think up or
+think up or shut up.
+
+ align:start position:0%
+think up or shut up.
+ 
+
+ align:start position:0%
+think up or shut up.
+>> Oh, well, yeah, there's that one, too,
+
+ align:start position:0%
+>> Oh, well, yeah, there's that one, too,
+ 
+
+ align:start position:0%
+>> Oh, well, yeah, there's that one, too,
+which is a good one. Yeah, but um uh let
+
+ align:start position:0%
+which is a good one. Yeah, but um uh let
+ 
+
+ align:start position:0%
+which is a good one. Yeah, but um uh let
+me just It's talking about the spirit of
+
+ align:start position:0%
+me just It's talking about the spirit of
+ 
+
+ align:start position:0%
+me just It's talking about the spirit of
+a brainstorm session is important. Uh
+
+ align:start position:0%
+a brainstorm session is important. Uh
+ 
+
+ align:start position:0%
+a brainstorm session is important. Uh
+self- encouragement is needed almost as
+
+ align:start position:0%
+self- encouragement is needed almost as
+ 
+
+ align:start position:0%
+self- encouragement is needed almost as
+much as mutual encouragement. Uh a
+
+ align:start position:0%
+much as mutual encouragement. Uh a
+ 
+
+ align:start position:0%
+much as mutual encouragement. Uh a
+perfectionism complex will throttle
+
+ align:start position:0%
+perfectionism complex will throttle
+ 
+
+ align:start position:0%
+perfectionism complex will throttle
+effort and abort ideas. Uh he says, "One
+
+ align:start position:0%
+effort and abort ideas. Uh he says, "One
+ 
+
+ align:start position:0%
+effort and abort ideas. Uh he says, "One
+of the ablest members kept mom
+
+ align:start position:0%
+of the ablest members kept mom
+ 
+
+ align:start position:0%
+of the ablest members kept mom
+throughout one of our sessions. I button
+
+ align:start position:0%
+throughout one of our sessions. I button
+ 
+
+ align:start position:0%
+throughout one of our sessions. I button
+hold him, never heard that expression,
+
+ align:start position:0%
+hold him, never heard that expression,
+ 
+
+ align:start position:0%
+hold him, never heard that expression,
+afterward and begged him to spout
+
+ align:start position:0%
+afterward and begged him to spout
+ 
+
+ align:start position:0%
+afterward and begged him to spout
+whatever ideas might come to his mind in
+
+ align:start position:0%
+whatever ideas might come to his mind in
+ 
+
+ align:start position:0%
+whatever ideas might come to his mind in
+our next meeting." And this is this is
+
+ align:start position:0%
+our next meeting." And this is this is
+ 
+
+ align:start position:0%
+our next meeting." And this is this is
+where it gets good. this is the, you
+
+ align:start position:0%
+where it gets good. this is the, you
+ 
+
+ align:start position:0%
+where it gets good. this is the, you
+know, really able uh member of this ad
+
+ align:start position:0%
+know, really able uh member of this ad
+ 
+
+ align:start position:0%
+know, really able uh member of this ad
+team. He says, "All right, I'll try."
+
+ align:start position:0%
+team. He says, "All right, I'll try."
+ 
+
+ align:start position:0%
+team. He says, "All right, I'll try."
+Uh, but here's what happened. After our
+
+ align:start position:0%
+Uh, but here's what happened. After our
+ 
+
+ align:start position:0%
+Uh, but here's what happened. After our
+first meeting, I jotted down about 15
+
+ align:start position:0%
+first meeting, I jotted down about 15
+ 
+
+ align:start position:0%
+first meeting, I jotted down about 15
+ideas with the thought that I would
+
+ align:start position:0%
+ideas with the thought that I would
+ 
+
+ align:start position:0%
+ideas with the thought that I would
+bring them to our next session. When I
+
+ align:start position:0%
+bring them to our next session. When I
+ 
+
+ align:start position:0%
+bring them to our next session. When I
+looked them over, I decided they were
+
+ align:start position:0%
+looked them over, I decided they were
+ 
+
+ align:start position:0%
+looked them over, I decided they were
+worthless, so I just tore up the list.
+
+ align:start position:0%
+worthless, so I just tore up the list.
+ 
+
+ align:start position:0%
+worthless, so I just tore up the list.
+Um, and you know, Alice kind of goes on
+
+ align:start position:0%
+Um, and you know, Alice kind of goes on
+ 
+
+ align:start position:0%
+Um, and you know, Alice kind of goes on
+to say, "It took a while to encourage
+
+ align:start position:0%
+to say, "It took a while to encourage
+ 
+
+ align:start position:0%
+to say, "It took a while to encourage
+this guy to understand that there's no
+
+ align:start position:0%
+this guy to understand that there's no
+ 
+
+ align:start position:0%
+this guy to understand that there's no
+such thing as a worthless idea. Um, that
+
+ align:start position:0%
+such thing as a worthless idea. Um, that
+ 
+
+ align:start position:0%
+such thing as a worthless idea. Um, that
+that it can either be expanded upon or
+
+ align:start position:0%
+that it can either be expanded upon or
+ 
+
+ align:start position:0%
+that it can either be expanded upon or
+revise." And that's kind of that
+
+ align:start position:0%
+revise." And that's kind of that
+ 
+
+ align:start position:0%
+revise." And that's kind of that
+synthesis thing, right? that that you
+
+ align:start position:0%
+synthesis thing, right? that that you
+ 
+
+ align:start position:0%
+synthesis thing, right? that that you
+know having a wild idea and and um you
+
+ align:start position:0%
+know having a wild idea and and um you
+ 
+
+ align:start position:0%
+know having a wild idea and and um you
+know getting back to this idea of the
+
+ align:start position:0%
+know getting back to this idea of the
+ 
+
+ align:start position:0%
+know getting back to this idea of the
+interruption. Nothing will stop a person
+
+ align:start position:0%
+interruption. Nothing will stop a person
+ 
+
+ align:start position:0%
+interruption. Nothing will stop a person
+from wanting to contribute if um more
+
+ align:start position:0%
+from wanting to contribute if um more
+ 
+
+ align:start position:0%
+from wanting to contribute if um more
+than than not being able to even have
+
+ align:start position:0%
+than than not being able to even have
+ 
+
+ align:start position:0%
+than than not being able to even have
+their voice be heard, right? Like
+
+ align:start position:0%
+their voice be heard, right? Like
+ 
+
+ align:start position:0%
+their voice be heard, right? Like
+they're trying to say something and then
+
+ align:start position:0%
+they're trying to say something and then
+ 
+
+ align:start position:0%
+they're trying to say something and then
+they just get cut out by somebody else
+
+ align:start position:0%
+they just get cut out by somebody else
+ 
+
+ align:start position:0%
+they just get cut out by somebody else
+who's like, "No, but this is better." Um
+
+ align:start position:0%
+who's like, "No, but this is better." Um
+ 
+
+ align:start position:0%
+who's like, "No, but this is better." Um
+you know, especially for a shy person or
+
+ align:start position:0%
+you know, especially for a shy person or
+ 
+
+ align:start position:0%
+you know, especially for a shy person or
+a person who's otherwise feeling like my
+
+ align:start position:0%
+a person who's otherwise feeling like my
+ 
+
+ align:start position:0%
+a person who's otherwise feeling like my
+ideas are worthless. Um they they won't
+
+ align:start position:0%
+ideas are worthless. Um they they won't
+ 
+
+ align:start position:0%
+ideas are worthless. Um they they won't
+be able to get it out because they've
+
+ align:start position:0%
+be able to get it out because they've
+ 
+
+ align:start position:0%
+be able to get it out because they've
+then been they've then been cut short.
+
+ align:start position:0%
+then been they've then been cut short.
+ 
+
+ align:start position:0%
+then been they've then been cut short.
+Um so this you know some of this
+
+ align:start position:0%
+Um so this you know some of this
+ 
+
+ align:start position:0%
+Um so this you know some of this
+responsibility falls on what we might
+
+ align:start position:0%
+responsibility falls on what we might
+ 
+
+ align:start position:0%
+responsibility falls on what we might
+call the leader which I'll talk about
+
+ align:start position:0%
+call the leader which I'll talk about
+ 
+
+ align:start position:0%
+call the leader which I'll talk about
+later of of the of the group. Um but
+
+ align:start position:0%
+later of of the of the group. Um but
+ 
+
+ align:start position:0%
+later of of the of the group. Um but
+really it it's kind of a collective
+
+ align:start position:0%
+really it it's kind of a collective
+ 
+
+ align:start position:0%
+really it it's kind of a collective
+responsibility that everybody kind of um
+
+ align:start position:0%
+responsibility that everybody kind of um
+ 
+
+ align:start position:0%
+responsibility that everybody kind of um
+make sure that as someone is expressing
+
+ align:start position:0%
+make sure that as someone is expressing
+ 
+
+ align:start position:0%
+make sure that as someone is expressing
+an idea that it's maintained. Adding to
+
+ align:start position:0%
+an idea that it's maintained. Adding to
+ 
+
+ align:start position:0%
+an idea that it's maintained. Adding to
+that you know
+
+ align:start position:0%
+that you know
+ 
+
+ align:start position:0%
+that you know
+keep the keep the description of your
+
+ align:start position:0%
+keep the keep the description of your
+ 
+
+ align:start position:0%
+keep the keep the description of your
+idea short. Um you know if people are
+
+ align:start position:0%
+idea short. Um you know if people are
+ 
+
+ align:start position:0%
+idea short. Um you know if people are
+sitting here and it's like you've now
+
+ align:start position:0%
+sitting here and it's like you've now
+ 
+
+ align:start position:0%
+sitting here and it's like you've now
+hijacked the 30 minute brainstorming
+
+ align:start position:0%
+hijacked the 30 minute brainstorming
+ 
+
+ align:start position:0%
+hijacked the 30 minute brainstorming
+session with your one idea that took
+
+ align:start position:0%
+session with your one idea that took
+ 
+
+ align:start position:0%
+session with your one idea that took
+five minutes to explain. um that that
+
+ align:start position:0%
+five minutes to explain. um that that
+ 
+
+ align:start position:0%
+five minutes to explain. um that that
+can also hamper it, right? Part of it is
+
+ align:start position:0%
+can also hamper it, right? Part of it is
+ 
+
+ align:start position:0%
+can also hamper it, right? Part of it is
+not only don't interrupt people, but
+
+ align:start position:0%
+not only don't interrupt people, but
+ 
+
+ align:start position:0%
+not only don't interrupt people, but
+also make sure that when you are
+
+ align:start position:0%
+also make sure that when you are
+ 
+
+ align:start position:0%
+also make sure that when you are
+contributing, you are allowing for other
+
+ align:start position:0%
+contributing, you are allowing for other
+ 
+
+ align:start position:0%
+contributing, you are allowing for other
+people to contribute as well. Um
+
+ align:start position:0%
+people to contribute as well. Um
+ 
+
+ align:start position:0%
+people to contribute as well. Um
+something that maybe is not considered
+
+ align:start position:0%
+something that maybe is not considered
+ 
+
+ align:start position:0%
+something that maybe is not considered
+as much. Um for the organization,
+
+ align:start position:0%
+as much. Um for the organization,
+ 
+
+ align:start position:0%
+as much. Um for the organization,
+designate a leader. I hate that term,
+
+ align:start position:0%
+designate a leader. I hate that term,
+ 
+
+ align:start position:0%
+designate a leader. I hate that term,
+but that's what he used in the book. Um
+
+ align:start position:0%
+but that's what he used in the book. Um
+ 
+
+ align:start position:0%
+but that's what he used in the book. Um
+I I tend to use the term clerk, which is
+
+ align:start position:0%
+I I tend to use the term clerk, which is
+ 
+
+ align:start position:0%
+I I tend to use the term clerk, which is
+kind of a quaker idea, which I I kind of
+
+ align:start position:0%
+kind of a quaker idea, which I I kind of
+ 
+
+ align:start position:0%
+kind of a quaker idea, which I I kind of
+grab on to. A clerk, you know, being
+
+ align:start position:0%
+grab on to. A clerk, you know, being
+ 
+
+ align:start position:0%
+grab on to. A clerk, you know, being
+more of a facilitator than an actual
+
+ align:start position:0%
+more of a facilitator than an actual
+ 
+
+ align:start position:0%
+more of a facilitator than an actual
+leader. Um you know, leader suggests,
+
+ align:start position:0%
+leader. Um you know, leader suggests,
+ 
+
+ align:start position:0%
+leader. Um you know, leader suggests,
+you know, boss. It's always not great
+
+ align:start position:0%
+you know, boss. It's always not great
+ 
+
+ align:start position:0%
+you know, boss. It's always not great
+for a for a, you know, everyone's even
+
+ align:start position:0%
+for a for a, you know, everyone's even
+ 
+
+ align:start position:0%
+for a for a, you know, everyone's even
+sort of brainstorming session. Um, and
+
+ align:start position:0%
+sort of brainstorming session. Um, and
+ 
+
+ align:start position:0%
+sort of brainstorming session. Um, and
+then of course the secretary or as he
+
+ align:start position:0%
+then of course the secretary or as he
+ 
+
+ align:start position:0%
+then of course the secretary or as he
+calls it an associate theater. Um, you
+
+ align:start position:0%
+calls it an associate theater. Um, you
+ 
+
+ align:start position:0%
+calls it an associate theater. Um, you
+know, this is someone who who writes
+
+ align:start position:0%
+know, this is someone who who writes
+ 
+
+ align:start position:0%
+know, this is someone who who writes
+stuff down. You know, there's some of
+
+ align:start position:0%
+stuff down. You know, there's some of
+ 
+
+ align:start position:0%
+stuff down. You know, there's some of
+that that good old fashioned hierarchy
+
+ align:start position:0%
+that that good old fashioned hierarchy
+ 
+
+ align:start position:0%
+that that good old fashioned hierarchy
+going on in this in this text, but um
+
+ align:start position:0%
+going on in this in this text, but um
+ 
+
+ align:start position:0%
+going on in this in this text, but um
+but you know, obviously we'll talk a
+
+ align:start position:0%
+but you know, obviously we'll talk a
+ 
+
+ align:start position:0%
+but you know, obviously we'll talk a
+little bit more about what the roles of
+
+ align:start position:0%
+little bit more about what the roles of
+ 
+
+ align:start position:0%
+little bit more about what the roles of
+these people are, but but having those
+
+ align:start position:0%
+these people are, but but having those
+ 
+
+ align:start position:0%
+these people are, but but having those
+those roles uh defined early is
+
+ align:start position:0%
+those roles uh defined early is
+ 
+
+ align:start position:0%
+those roles uh defined early is
+important. Um,
+
+ align:start position:0%
+important. Um,
+ 
+
+ align:start position:0%
+important. Um,
+and then this is this is something to
+
+ align:start position:0%
+and then this is this is something to
+ 
+
+ align:start position:0%
+and then this is this is something to
+talk about a bit explaining the process
+
+ align:start position:0%
+talk about a bit explaining the process
+ 
+
+ align:start position:0%
+talk about a bit explaining the process
+and the principal question at the start
+
+ align:start position:0%
+and the principal question at the start
+ 
+
+ align:start position:0%
+and the principal question at the start
+of the session. Um, you know, I don't
+
+ align:start position:0%
+of the session. Um, you know, I don't
+ 
+
+ align:start position:0%
+of the session. Um, you know, I don't
+know how how many of you had heard of
+
+ align:start position:0%
+know how how many of you had heard of
+ 
+
+ align:start position:0%
+know how how many of you had heard of
+these four principles of brainstorming
+
+ align:start position:0%
+these four principles of brainstorming
+ 
+
+ align:start position:0%
+these four principles of brainstorming
+explicitly prior to reading this text?
+
+ align:start position:0%
+explicitly prior to reading this text?
+ 
+
+ align:start position:0%
+explicitly prior to reading this text?
+Anybody? Oh, well,
+
+ align:start position:0%
+Anybody? Oh, well,
+ 
+
+ align:start position:0%
+Anybody? Oh, well,
+I know you heard from me. But, um, but
+
+ align:start position:0%
+I know you heard from me. But, um, but
+ 
+
+ align:start position:0%
+I know you heard from me. But, um, but
+yeah, the um, you know, the process is
+
+ align:start position:0%
+yeah, the um, you know, the process is
+ 
+
+ align:start position:0%
+yeah, the um, you know, the process is
+something that it needs to be clear
+
+ align:start position:0%
+something that it needs to be clear
+ 
+
+ align:start position:0%
+something that it needs to be clear
+otherwise people won't remember to do.
+
+ align:start position:0%
+otherwise people won't remember to do.
+ 
+
+ align:start position:0%
+otherwise people won't remember to do.
+And you'll see when we do the exercise,
+
+ align:start position:0%
+And you'll see when we do the exercise,
+ 
+
+ align:start position:0%
+And you'll see when we do the exercise,
+it's it's even hard sometimes to curb
+
+ align:start position:0%
+it's it's even hard sometimes to curb
+ 
+
+ align:start position:0%
+it's it's even hard sometimes to curb
+your criticism. You know, it's it's just
+
+ align:start position:0%
+your criticism. You know, it's it's just
+ 
+
+ align:start position:0%
+your criticism. You know, it's it's just
+when especially when you're comfortable
+
+ align:start position:0%
+when especially when you're comfortable
+ 
+
+ align:start position:0%
+when especially when you're comfortable
+with people and you may not mean it in a
+
+ align:start position:0%
+with people and you may not mean it in a
+ 
+
+ align:start position:0%
+with people and you may not mean it in a
+malicious way. You may not mean it in a
+
+ align:start position:0%
+malicious way. You may not mean it in a
+ 
+
+ align:start position:0%
+malicious way. You may not mean it in a
+way to kind of uh you know stop the
+
+ align:start position:0%
+way to kind of uh you know stop the
+ 
+
+ align:start position:0%
+way to kind of uh you know stop the
+brainstorming session, but you just be
+
+ align:start position:0%
+brainstorming session, but you just be
+ 
+
+ align:start position:0%
+brainstorming session, but you just be
+like, "Oh, that's nuts." You know, we're
+
+ align:start position:0%
+like, "Oh, that's nuts." You know, we're
+ 
+
+ align:start position:0%
+like, "Oh, that's nuts." You know, we're
+laughing and everybody's having a good
+
+ align:start position:0%
+laughing and everybody's having a good
+ 
+
+ align:start position:0%
+laughing and everybody's having a good
+time. And then you kind of like think
+
+ align:start position:0%
+time. And then you kind of like think
+ 
+
+ align:start position:0%
+time. And then you kind of like think
+back and like wait, you know, that was
+
+ align:start position:0%
+back and like wait, you know, that was
+ 
+
+ align:start position:0%
+back and like wait, you know, that was
+me passing judgment on an idea and
+
+ align:start position:0%
+me passing judgment on an idea and
+ 
+
+ align:start position:0%
+me passing judgment on an idea and
+possibly inhibiting the kind of the kind
+
+ align:start position:0%
+possibly inhibiting the kind of the kind
+ 
+
+ align:start position:0%
+possibly inhibiting the kind of the kind
+of ideation that we're trying to get
+
+ align:start position:0%
+of ideation that we're trying to get
+ 
+
+ align:start position:0%
+of ideation that we're trying to get
+across. So, um explaining the process at
+
+ align:start position:0%
+across. So, um explaining the process at
+ 
+
+ align:start position:0%
+across. So, um explaining the process at
+the beginning regardless of the group is
+
+ align:start position:0%
+the beginning regardless of the group is
+ 
+
+ align:start position:0%
+the beginning regardless of the group is
+really important and that is usually
+
+ align:start position:0%
+really important and that is usually
+ 
+
+ align:start position:0%
+really important and that is usually
+responsibility that falls on the leader
+
+ align:start position:0%
+responsibility that falls on the leader
+ 
+
+ align:start position:0%
+responsibility that falls on the leader
+or the secretary, whoever is organizing
+
+ align:start position:0%
+or the secretary, whoever is organizing
+ 
+
+ align:start position:0%
+or the secretary, whoever is organizing
+the session, right? They even suggest in
+
+ align:start position:0%
+the session, right? They even suggest in
+ 
+
+ align:start position:0%
+the session, right? They even suggest in
+the text have it posted have the four
+
+ align:start position:0%
+the text have it posted have the four
+ 
+
+ align:start position:0%
+the text have it posted have the four
+principles up so that everybody can kind
+
+ align:start position:0%
+principles up so that everybody can kind
+ 
+
+ align:start position:0%
+principles up so that everybody can kind
+of remind themselves through the process
+
+ align:start position:0%
+of remind themselves through the process
+ 
+
+ align:start position:0%
+of remind themselves through the process
+what these four principles are. Um but
+
+ align:start position:0%
+what these four principles are. Um but
+ 
+
+ align:start position:0%
+what these four principles are. Um but
+explaining the process is really
+
+ align:start position:0%
+explaining the process is really
+ 
+
+ align:start position:0%
+explaining the process is really
+important and this this is I can't even
+
+ align:start position:0%
+important and this this is I can't even
+ 
+
+ align:start position:0%
+important and this this is I can't even
+this is so important. Um having the
+
+ align:start position:0%
+this is so important. Um having the
+ 
+
+ align:start position:0%
+this is so important. Um having the
+principal question and the goal of the
+
+ align:start position:0%
+principal question and the goal of the
+ 
+
+ align:start position:0%
+principal question and the goal of the
+brainstorming session clear at the start
+
+ align:start position:0%
+brainstorming session clear at the start
+ 
+
+ align:start position:0%
+brainstorming session clear at the start
+um you know obviously it's it's this is
+
+ align:start position:0%
+um you know obviously it's it's this is
+ 
+
+ align:start position:0%
+um you know obviously it's it's this is
+encouraging freewheeling. It's
+
+ align:start position:0%
+encouraging freewheeling. It's
+ 
+
+ align:start position:0%
+encouraging freewheeling. It's
+encouraging free thought. that's
+
+ align:start position:0%
+encouraging free thought. that's
+ 
+
+ align:start position:0%
+encouraging free thought. that's
+encouraging this all kind of you know
+
+ align:start position:0%
+encouraging this all kind of you know
+ 
+
+ align:start position:0%
+encouraging this all kind of you know
+wide openen creativity and yet at the
+
+ align:start position:0%
+wide openen creativity and yet at the
+ 
+
+ align:start position:0%
+wide openen creativity and yet at the
+same time if you do that in an unbounded
+
+ align:start position:0%
+same time if you do that in an unbounded
+ 
+
+ align:start position:0%
+same time if you do that in an unbounded
+sort of way you might end up with things
+
+ align:start position:0%
+sort of way you might end up with things
+ 
+
+ align:start position:0%
+sort of way you might end up with things
+that that really in the end you don't
+
+ align:start position:0%
+that that really in the end you don't
+ 
+
+ align:start position:0%
+that that really in the end you don't
+have too many useful ideas you've got
+
+ align:start position:0%
+have too many useful ideas you've got
+ 
+
+ align:start position:0%
+have too many useful ideas you've got
+useful ideas for something else not for
+
+ align:start position:0%
+useful ideas for something else not for
+ 
+
+ align:start position:0%
+useful ideas for something else not for
+the actual creative problem that you
+
+ align:start position:0%
+the actual creative problem that you
+ 
+
+ align:start position:0%
+the actual creative problem that you
+have. So, I mean, you take it from an ad
+
+ align:start position:0%
+have. So, I mean, you take it from an ad
+ 
+
+ align:start position:0%
+have. So, I mean, you take it from an ad
+ad concept, you know, so you've got a
+
+ align:start position:0%
+ad concept, you know, so you've got a
+ 
+
+ align:start position:0%
+ad concept, you know, so you've got a
+vodka company that's like, "Oh, we need
+
+ align:start position:0%
+vodka company that's like, "Oh, we need
+ 
+
+ align:start position:0%
+vodka company that's like, "Oh, we need
+we need an advertisement for our, you
+
+ align:start position:0%
+we need an advertisement for our, you
+ 
+
+ align:start position:0%
+we need an advertisement for our, you
+know, awesome vodka or whatever." And
+
+ align:start position:0%
+know, awesome vodka or whatever." And
+ 
+
+ align:start position:0%
+know, awesome vodka or whatever." And
+so, you're like, "All right, well, we
+
+ align:start position:0%
+so, you're like, "All right, well, we
+ 
+
+ align:start position:0%
+so, you're like, "All right, well, we
+have a brainstorm session." Then a bunch
+
+ align:start position:0%
+have a brainstorm session." Then a bunch
+ 
+
+ align:start position:0%
+have a brainstorm session." Then a bunch
+of people come up with ideas. Now,
+
+ align:start position:0%
+of people come up with ideas. Now,
+ 
+
+ align:start position:0%
+of people come up with ideas. Now,
+you're selling dryers. Um, because it
+
+ align:start position:0%
+you're selling dryers. Um, because it
+ 
+
+ align:start position:0%
+you're selling dryers. Um, because it
+was wide open, right? And it's like,
+
+ align:start position:0%
+was wide open, right? And it's like,
+ 
+
+ align:start position:0%
+was wide open, right? And it's like,
+"Oh, we've got these great ad ideas for
+
+ align:start position:0%
+"Oh, we've got these great ad ideas for
+ 
+
+ align:start position:0%
+"Oh, we've got these great ad ideas for
+dryers, but they're just really, really
+
+ align:start position:0%
+dryers, but they're just really, really
+ 
+
+ align:start position:0%
+dryers, but they're just really, really
+not going to work." You know, bringing
+
+ align:start position:0%
+not going to work." You know, bringing
+ 
+
+ align:start position:0%
+not going to work." You know, bringing
+it back to a video game contest. um you
+
+ align:start position:0%
+it back to a video game contest. um you
+ 
+
+ align:start position:0%
+it back to a video game contest. um you
+know, you've got a contract with a
+
+ align:start position:0%
+know, you've got a contract with a
+ 
+
+ align:start position:0%
+know, you've got a contract with a
+producer to make a first-person shooter,
+
+ align:start position:0%
+producer to make a first-person shooter,
+ 
+
+ align:start position:0%
+producer to make a first-person shooter,
+and in your brainstorming session,
+
+ align:start position:0%
+and in your brainstorming session,
+ 
+
+ align:start position:0%
+and in your brainstorming session,
+you've designed um a cool cute
+
+ align:start position:0%
+you've designed um a cool cute
+ 
+
+ align:start position:0%
+you've designed um a cool cute
+platformer. Um neat, but that's not
+
+ align:start position:0%
+platformer. Um neat, but that's not
+ 
+
+ align:start position:0%
+platformer. Um neat, but that's not
+where the money's coming from, right?
+
+ align:start position:0%
+where the money's coming from, right?
+ 
+
+ align:start position:0%
+where the money's coming from, right?
+So, so bounding the brainstorm session
+
+ align:start position:0%
+So, so bounding the brainstorm session
+ 
+
+ align:start position:0%
+So, so bounding the brainstorm session
+is important, too. And and you'll kind
+
+ align:start position:0%
+is important, too. And and you'll kind
+ 
+
+ align:start position:0%
+is important, too. And and you'll kind
+of see that in the exercises that we do
+
+ align:start position:0%
+of see that in the exercises that we do
+ 
+
+ align:start position:0%
+of see that in the exercises that we do
+today, how it's important to to bound
+
+ align:start position:0%
+today, how it's important to to bound
+ 
+
+ align:start position:0%
+today, how it's important to to bound
+that. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes.
+
+ align:start position:0%
+yes.
+ 
+
+ align:start position:0%
+yes.
+Oh, and write down everything. Yeah,
+
+ align:start position:0%
+Oh, and write down everything. Yeah,
+ 
+
+ align:start position:0%
+Oh, and write down everything. Yeah,
+sorry, I forgot about that. This is an
+
+ align:start position:0%
+sorry, I forgot about that. This is an
+ 
+
+ align:start position:0%
+sorry, I forgot about that. This is an
+important uh important question. Uh
+
+ align:start position:0%
+important uh important question. Uh
+ 
+
+ align:start position:0%
+important uh important question. Uh
+important point um you know you this
+
+ align:start position:0%
+important point um you know you this
+ 
+
+ align:start position:0%
+important point um you know you this
+happens to all of us but you have this
+
+ align:start position:0%
+happens to all of us but you have this
+ 
+
+ align:start position:0%
+happens to all of us but you have this
+great idea and then you don't write it
+
+ align:start position:0%
+great idea and then you don't write it
+ 
+
+ align:start position:0%
+great idea and then you don't write it
+down and then you you go to bed and then
+
+ align:start position:0%
+down and then you you go to bed and then
+ 
+
+ align:start position:0%
+down and then you you go to bed and then
+the next day you're like oh I had this
+
+ align:start position:0%
+the next day you're like oh I had this
+ 
+
+ align:start position:0%
+the next day you're like oh I had this
+great idea great idea and you can't
+
+ align:start position:0%
+great idea great idea and you can't
+ 
+
+ align:start position:0%
+great idea great idea and you can't
+remember it right and so um writing down
+
+ align:start position:0%
+remember it right and so um writing down
+ 
+
+ align:start position:0%
+remember it right and so um writing down
+everything is absolutely essential.
+
+ align:start position:0%
+everything is absolutely essential.
+ 
+
+ align:start position:0%
+everything is absolutely essential.
+You'll never you know you'd be amazed
+
+ align:start position:0%
+You'll never you know you'd be amazed
+ 
+
+ align:start position:0%
+You'll never you know you'd be amazed
+the number of times that you know a week
+
+ align:start position:0%
+the number of times that you know a week
+ 
+
+ align:start position:0%
+the number of times that you know a week
+later you're like oh we could put these
+
+ align:start position:0%
+later you're like oh we could put these
+ 
+
+ align:start position:0%
+later you're like oh we could put these
+two ideas together um as long as you can
+
+ align:start position:0%
+two ideas together um as long as you can
+ 
+
+ align:start position:0%
+two ideas together um as long as you can
+remember what those ideas were. Um, and
+
+ align:start position:0%
+remember what those ideas were. Um, and
+ 
+
+ align:start position:0%
+remember what those ideas were. Um, and
+so what you think, you know, it's hard
+
+ align:start position:0%
+so what you think, you know, it's hard
+ 
+
+ align:start position:0%
+so what you think, you know, it's hard
+to not mentally pass judgment on things
+
+ align:start position:0%
+to not mentally pass judgment on things
+ 
+
+ align:start position:0%
+to not mentally pass judgment on things
+during the brainstorm session. And what
+
+ align:start position:0%
+during the brainstorm session. And what
+ 
+
+ align:start position:0%
+during the brainstorm session. And what
+you think might be great now may a week
+
+ align:start position:0%
+you think might be great now may a week
+ 
+
+ align:start position:0%
+you think might be great now may a week
+later not be as great and what you
+
+ align:start position:0%
+later not be as great and what you
+ 
+
+ align:start position:0%
+later not be as great and what you
+didn't think, you know, will be. And so
+
+ align:start position:0%
+didn't think, you know, will be. And so
+ 
+
+ align:start position:0%
+didn't think, you know, will be. And so
+making sure to have everything written
+
+ align:start position:0%
+making sure to have everything written
+ 
+
+ align:start position:0%
+making sure to have everything written
+down is really important. And and they
+
+ align:start position:0%
+down is really important. And and they
+ 
+
+ align:start position:0%
+down is really important. And and they
+even suggest, you know, having um two
+
+ align:start position:0%
+even suggest, you know, having um two
+ 
+
+ align:start position:0%
+even suggest, you know, having um two
+secretaries if you need if you've got a
+
+ align:start position:0%
+secretaries if you need if you've got a
+ 
+
+ align:start position:0%
+secretaries if you need if you've got a
+large group or lots of ideas and they're
+
+ align:start position:0%
+large group or lots of ideas and they're
+ 
+
+ align:start position:0%
+large group or lots of ideas and they're
+each writing every other one um can be
+
+ align:start position:0%
+each writing every other one um can be
+ 
+
+ align:start position:0%
+each writing every other one um can be
+helpful to make sure that you get
+
+ align:start position:0%
+helpful to make sure that you get
+ 
+
+ align:start position:0%
+helpful to make sure that you get
+everything right so that you get
+
+ align:start position:0%
+everything right so that you get
+ 
+
+ align:start position:0%
+everything right so that you get
+everything. So um
+
+ align:start position:0%
+everything. So um
+ 
+
+ align:start position:0%
+everything. So um
+next is the question of what sort of
+
+ align:start position:0%
+next is the question of what sort of
+ 
+
+ align:start position:0%
+next is the question of what sort of
+problems are suitable to a brainstorming
+
+ align:start position:0%
+problems are suitable to a brainstorming
+ 
+
+ align:start position:0%
+problems are suitable to a brainstorming
+session. Uh the great example that Alex
+
+ align:start position:0%
+session. Uh the great example that Alex
+ 
+
+ align:start position:0%
+session. Uh the great example that Alex
+Osborne gives is um setting up a
+
+ align:start position:0%
+Osborne gives is um setting up a
+ 
+
+ align:start position:0%
+Osborne gives is um setting up a
+brainstorm session on whether or not to
+
+ align:start position:0%
+brainstorm session on whether or not to
+ 
+
+ align:start position:0%
+brainstorm session on whether or not to
+get married um is not a particularly
+
+ align:start position:0%
+get married um is not a particularly
+ 
+
+ align:start position:0%
+get married um is not a particularly
+suitable question. I that was sort of an
+
+ align:start position:0%
+suitable question. I that was sort of an
+ 
+
+ align:start position:0%
+suitable question. I that was sort of an
+interesting uh interesting concept. He's
+
+ align:start position:0%
+interesting uh interesting concept. He's
+ 
+
+ align:start position:0%
+interesting uh interesting concept. He's
+like well to decide to get married you
+
+ align:start position:0%
+like well to decide to get married you
+ 
+
+ align:start position:0%
+like well to decide to get married you
+you apparently list the pros and cons.
+
+ align:start position:0%
+you apparently list the pros and cons.
+ 
+
+ align:start position:0%
+you apparently list the pros and cons.
+That's not exactly the process I went
+
+ align:start position:0%
+That's not exactly the process I went
+ 
+
+ align:start position:0%
+That's not exactly the process I went
+through before I got married. I was like
+
+ align:start position:0%
+through before I got married. I was like
+ 
+
+ align:start position:0%
+through before I got married. I was like
+well honey I'm going to have to write
+
+ align:start position:0%
+well honey I'm going to have to write
+ 
+
+ align:start position:0%
+well honey I'm going to have to write
+this down. Um
+
+ align:start position:0%
+this down. Um
+ 
+
+ align:start position:0%
+this down. Um
+but fair enough that that wasn't the
+
+ align:start position:0%
+but fair enough that that wasn't the
+ 
+
+ align:start position:0%
+but fair enough that that wasn't the
+suggestion that he came up with. And he
+
+ align:start position:0%
+suggestion that he came up with. And he
+ 
+
+ align:start position:0%
+suggestion that he came up with. And he
+has a good point, right? I mean it's the
+
+ align:start position:0%
+has a good point, right? I mean it's the
+ 
+
+ align:start position:0%
+has a good point, right? I mean it's the
+question of whether or not to get
+
+ align:start position:0%
+question of whether or not to get
+ 
+
+ align:start position:0%
+question of whether or not to get
+married is a judgment call. Um it is not
+
+ align:start position:0%
+married is a judgment call. Um it is not
+ 
+
+ align:start position:0%
+married is a judgment call. Um it is not
+a creative uh ideation process. And so
+
+ align:start position:0%
+a creative uh ideation process. And so
+ 
+
+ align:start position:0%
+a creative uh ideation process. And so
+that's not a particularly useful um kind
+
+ align:start position:0%
+that's not a particularly useful um kind
+ 
+
+ align:start position:0%
+that's not a particularly useful um kind
+of uh problem that's suitable to the
+
+ align:start position:0%
+of uh problem that's suitable to the
+ 
+
+ align:start position:0%
+of uh problem that's suitable to the
+brainstorming process. Um you know, you
+
+ align:start position:0%
+brainstorming process. Um you know, you
+ 
+
+ align:start position:0%
+brainstorming process. Um you know, you
+want you want a uh you want a problem
+
+ align:start position:0%
+want you want a uh you want a problem
+ 
+
+ align:start position:0%
+want you want a uh you want a problem
+that is going to be benefited by having
+
+ align:start position:0%
+that is going to be benefited by having
+ 
+
+ align:start position:0%
+that is going to be benefited by having
+a large uh a large selection, a large
+
+ align:start position:0%
+a large uh a large selection, a large
+ 
+
+ align:start position:0%
+a large uh a large selection, a large
+corpus of ideas. And so those are the
+
+ align:start position:0%
+corpus of ideas. And so those are the
+ 
+
+ align:start position:0%
+corpus of ideas. And so those are the
+kind of problems that are more more
+
+ align:start position:0%
+kind of problems that are more more
+ 
+
+ align:start position:0%
+kind of problems that are more more
+useful. And you know, you'll see when we
+
+ align:start position:0%
+useful. And you know, you'll see when we
+ 
+
+ align:start position:0%
+useful. And you know, you'll see when we
+do our example exercise what some of
+
+ align:start position:0%
+do our example exercise what some of
+ 
+
+ align:start position:0%
+do our example exercise what some of
+those might be. Um I also kind of put
+
+ align:start position:0%
+those might be. Um I also kind of put
+ 
+
+ align:start position:0%
+those might be. Um I also kind of put
+here that um you know having a clear
+
+ align:start position:0%
+here that um you know having a clear
+ 
+
+ align:start position:0%
+here that um you know having a clear
+definition of the aim is really
+
+ align:start position:0%
+definition of the aim is really
+ 
+
+ align:start position:0%
+definition of the aim is really
+essential. It's sort of what we talked
+
+ align:start position:0%
+essential. It's sort of what we talked
+ 
+
+ align:start position:0%
+essential. It's sort of what we talked
+about before. Um you need to make sure
+
+ align:start position:0%
+about before. Um you need to make sure
+ 
+
+ align:start position:0%
+about before. Um you need to make sure
+that everybody understands and
+
+ align:start position:0%
+that everybody understands and
+ 
+
+ align:start position:0%
+that everybody understands and
+everybody's on the same page. Otherwise
+
+ align:start position:0%
+everybody's on the same page. Otherwise
+ 
+
+ align:start position:0%
+everybody's on the same page. Otherwise
+you end up with stuff that um that might
+
+ align:start position:0%
+you end up with stuff that um that might
+ 
+
+ align:start position:0%
+you end up with stuff that um that might
+be useful for something else but not
+
+ align:start position:0%
+be useful for something else but not
+ 
+
+ align:start position:0%
+be useful for something else but not
+useful for what you're you're
+
+ align:start position:0%
+useful for what you're you're
+ 
+
+ align:start position:0%
+useful for what you're you're
+particularly trying to do. Um and so
+
+ align:start position:0%
+particularly trying to do. Um and so
+ 
+
+ align:start position:0%
+particularly trying to do. Um and so
+making that clear for everybody is
+
+ align:start position:0%
+making that clear for everybody is
+ 
+
+ align:start position:0%
+making that clear for everybody is
+really important. Um, keeping the
+
+ align:start position:0%
+really important. Um, keeping the
+ 
+
+ align:start position:0%
+really important. Um, keeping the
+problem as simple as possible, um, you
+
+ align:start position:0%
+problem as simple as possible, um, you
+ 
+
+ align:start position:0%
+problem as simple as possible, um, you
+know, is also really important. Trying
+
+ align:start position:0%
+know, is also really important. Trying
+ 
+
+ align:start position:0%
+know, is also really important. Trying
+to keep simple language, uh, for the
+
+ align:start position:0%
+to keep simple language, uh, for the
+ 
+
+ align:start position:0%
+to keep simple language, uh, for the
+problem. Uh, keep it, you know, keep it
+
+ align:start position:0%
+problem. Uh, keep it, you know, keep it
+ 
+
+ align:start position:0%
+problem. Uh, keep it, you know, keep it
+constrained in a way that that, um, is
+
+ align:start position:0%
+constrained in a way that that, um, is
+ 
+
+ align:start position:0%
+constrained in a way that that, um, is
+simple enough so that people can kind of
+
+ align:start position:0%
+simple enough so that people can kind of
+ 
+
+ align:start position:0%
+simple enough so that people can kind of
+work on it as opposed to just feeling
+
+ align:start position:0%
+work on it as opposed to just feeling
+ 
+
+ align:start position:0%
+work on it as opposed to just feeling
+limited by it. Um, if that makes any
+
+ align:start position:0%
+limited by it. Um, if that makes any
+ 
+
+ align:start position:0%
+limited by it. Um, if that makes any
+sense. You know, something is overly
+
+ align:start position:0%
+sense. You know, something is overly
+ 
+
+ align:start position:0%
+sense. You know, something is overly
+complicated and overly constrained. Um,
+
+ align:start position:0%
+complicated and overly constrained. Um,
+ 
+
+ align:start position:0%
+complicated and overly constrained. Um,
+then it becomes a well, how do I fit
+
+ align:start position:0%
+then it becomes a well, how do I fit
+ 
+
+ align:start position:0%
+then it becomes a well, how do I fit
+everything into this? You know, how do I
+
+ align:start position:0%
+everything into this? You know, how do I
+ 
+
+ align:start position:0%
+everything into this? You know, how do I
+match every single one of these things?
+
+ align:start position:0%
+match every single one of these things?
+ 
+
+ align:start position:0%
+match every single one of these things?
+If it's simpler, then it's a little bit
+
+ align:start position:0%
+If it's simpler, then it's a little bit
+ 
+
+ align:start position:0%
+If it's simpler, then it's a little bit
+easier to kind of work on and kind of be
+
+ align:start position:0%
+easier to kind of work on and kind of be
+ 
+
+ align:start position:0%
+easier to kind of work on and kind of be
+creative. So, keeping problems simple.
+
+ align:start position:0%
+creative. So, keeping problems simple.
+ 
+
+ align:start position:0%
+creative. So, keeping problems simple.
+Um, which isn't to say that complex
+
+ align:start position:0%
+Um, which isn't to say that complex
+ 
+
+ align:start position:0%
+Um, which isn't to say that complex
+problems couldn't be dealt with, but
+
+ align:start position:0%
+problems couldn't be dealt with, but
+ 
+
+ align:start position:0%
+problems couldn't be dealt with, but
+just divide this divide them into sub
+
+ align:start position:0%
+just divide this divide them into sub
+ 
+
+ align:start position:0%
+just divide this divide them into sub
+problems, right? Divide them into little
+
+ align:start position:0%
+problems, right? Divide them into little
+ 
+
+ align:start position:0%
+problems, right? Divide them into little
+little sections. So, there might be
+
+ align:start position:0%
+little sections. So, there might be
+ 
+
+ align:start position:0%
+little sections. So, there might be
+something like, you know, how could we
+
+ align:start position:0%
+something like, you know, how could we
+ 
+
+ align:start position:0%
+something like, you know, how could we
+deal with the UI? Um, you know, how
+
+ align:start position:0%
+deal with the UI? Um, you know, how
+ 
+
+ align:start position:0%
+deal with the UI? Um, you know, how
+could it look in this uh in this game,
+
+ align:start position:0%
+could it look in this uh in this game,
+ 
+
+ align:start position:0%
+could it look in this uh in this game,
+you know? So, rather than say, well, how
+
+ align:start position:0%
+you know? So, rather than say, well, how
+ 
+
+ align:start position:0%
+you know? So, rather than say, well, how
+are we going to design our first person
+
+ align:start position:0%
+are we going to design our first person
+ 
+
+ align:start position:0%
+are we going to design our first person
+shooter? You've got a brainstorming
+
+ align:start position:0%
+shooter? You've got a brainstorming
+ 
+
+ align:start position:0%
+shooter? You've got a brainstorming
+session about what the UI could look
+
+ align:start position:0%
+session about what the UI could look
+ 
+
+ align:start position:0%
+session about what the UI could look
+like for the first person shooter.
+
+ align:start position:0%
+like for the first person shooter.
+ 
+
+ align:start position:0%
+like for the first person shooter.
+you've got maybe a brainstorming session
+
+ align:start position:0%
+you've got maybe a brainstorming session
+ 
+
+ align:start position:0%
+you've got maybe a brainstorming session
+for um you know what the fiction for
+
+ align:start position:0%
+for um you know what the fiction for
+ 
+
+ align:start position:0%
+for um you know what the fiction for
+this first person shooter might be.
+
+ align:start position:0%
+this first person shooter might be.
+ 
+
+ align:start position:0%
+this first person shooter might be.
+You're dividing it into sub problems
+
+ align:start position:0%
+You're dividing it into sub problems
+ 
+
+ align:start position:0%
+You're dividing it into sub problems
+rather than having it be this gigantic
+
+ align:start position:0%
+rather than having it be this gigantic
+ 
+
+ align:start position:0%
+rather than having it be this gigantic
+you know model of of a thing. And you
+
+ align:start position:0%
+you know model of of a thing. And you
+ 
+
+ align:start position:0%
+you know model of of a thing. And you
+can see how that would be a problem,
+
+ align:start position:0%
+can see how that would be a problem,
+ 
+
+ align:start position:0%
+can see how that would be a problem,
+right? Because if you just brainstorm on
+
+ align:start position:0%
+right? Because if you just brainstorm on
+ 
+
+ align:start position:0%
+right? Because if you just brainstorm on
+what's our first person shooter going to
+
+ align:start position:0%
+what's our first person shooter going to
+ 
+
+ align:start position:0%
+what's our first person shooter going to
+be, you're going to get ideas about the
+
+ align:start position:0%
+be, you're going to get ideas about the
+ 
+
+ align:start position:0%
+be, you're going to get ideas about the
+UI. You're going to get ideas about the
+
+ align:start position:0%
+UI. You're going to get ideas about the
+ 
+
+ align:start position:0%
+UI. You're going to get ideas about the
+fiction. You're going to get ideas about
+
+ align:start position:0%
+fiction. You're going to get ideas about
+ 
+
+ align:start position:0%
+fiction. You're going to get ideas about
+what sort of guns you should use or what
+
+ align:start position:0%
+what sort of guns you should use or what
+ 
+
+ align:start position:0%
+what sort of guns you should use or what
+they should sound like. And it'll just
+
+ align:start position:0%
+they should sound like. And it'll just
+ 
+
+ align:start position:0%
+they should sound like. And it'll just
+be lots of interesting ideas but we get
+
+ align:start position:0%
+be lots of interesting ideas but we get
+ 
+
+ align:start position:0%
+be lots of interesting ideas but we get
+all over the place.
+
+ align:start position:0%
+all over the place.
+ 
+
+ align:start position:0%
+all over the place.
+uh and yeah uh problems should be
+
+ align:start position:0%
+uh and yeah uh problems should be
+ 
+
+ align:start position:0%
+uh and yeah uh problems should be
+clearly and simply articulated. I think
+
+ align:start position:0%
+clearly and simply articulated. I think
+ 
+
+ align:start position:0%
+clearly and simply articulated. I think
+that's what I sort of said by should be
+
+ align:start position:0%
+that's what I sort of said by should be
+ 
+
+ align:start position:0%
+that's what I sort of said by should be
+simple just you know make sure that
+
+ align:start position:0%
+simple just you know make sure that
+ 
+
+ align:start position:0%
+simple just you know make sure that
+they're articulated in the simple way.
+
+ align:start position:0%
+they're articulated in the simple way.
+ 
+
+ align:start position:0%
+they're articulated in the simple way.
+Sometimes you can have a simple problem
+
+ align:start position:0%
+Sometimes you can have a simple problem
+ 
+
+ align:start position:0%
+Sometimes you can have a simple problem
+that's not articulated particularly
+
+ align:start position:0%
+that's not articulated particularly
+ 
+
+ align:start position:0%
+that's not articulated particularly
+clearly. Um so it's just something um
+
+ align:start position:0%
+clearly. Um so it's just something um
+ 
+
+ align:start position:0%
+clearly. Um so it's just something um
+responsibilities of the leader clerk
+
+ align:start position:0%
+responsibilities of the leader clerk
+ 
+
+ align:start position:0%
+responsibilities of the leader clerk
+whatever um
+
+ align:start position:0%
+whatever um
+ 
+
+ align:start position:0%
+whatever um
+the first being uh to understand and
+
+ align:start position:0%
+the first being uh to understand and
+ 
+
+ align:start position:0%
+the first being uh to understand and
+explain the problem and the aim of the
+
+ align:start position:0%
+explain the problem and the aim of the
+ 
+
+ align:start position:0%
+explain the problem and the aim of the
+brainstorm session. I mean a lot of
+
+ align:start position:0%
+brainstorm session. I mean a lot of
+ 
+
+ align:start position:0%
+brainstorm session. I mean a lot of
+times people uh maybe will write a memo
+
+ align:start position:0%
+times people uh maybe will write a memo
+ 
+
+ align:start position:0%
+times people uh maybe will write a memo
+beforehand um you know as the
+
+ align:start position:0%
+beforehand um you know as the
+ 
+
+ align:start position:0%
+beforehand um you know as the
+facilitator of the of the thing as the
+
+ align:start position:0%
+facilitator of the of the thing as the
+ 
+
+ align:start position:0%
+facilitator of the of the thing as the
+person who perhaps wants to see the
+
+ align:start position:0%
+person who perhaps wants to see the
+ 
+
+ align:start position:0%
+person who perhaps wants to see the
+brainstorm be a success uh the most
+
+ align:start position:0%
+brainstorm be a success uh the most
+ 
+
+ align:start position:0%
+brainstorm be a success uh the most
+maybe um you know having a clear
+
+ align:start position:0%
+maybe um you know having a clear
+ 
+
+ align:start position:0%
+maybe um you know having a clear
+understanding of the problem and
+
+ align:start position:0%
+understanding of the problem and
+ 
+
+ align:start position:0%
+understanding of the problem and
+explaining that to the group is an
+
+ align:start position:0%
+explaining that to the group is an
+ 
+
+ align:start position:0%
+explaining that to the group is an
+important job for the leader um I use
+
+ align:start position:0%
+important job for the leader um I use
+ 
+
+ align:start position:0%
+important job for the leader um I use
+this term facilitating the session uh
+
+ align:start position:0%
+this term facilitating the session uh
+ 
+
+ align:start position:0%
+this term facilitating the session uh
+encouraging ideiation discouraging
+
+ align:start position:0%
+encouraging ideiation discouraging
+ 
+
+ align:start position:0%
+encouraging ideiation discouraging
+criticism you're kind of the watch guard
+
+ align:start position:0%
+criticism you're kind of the watch guard
+ 
+
+ align:start position:0%
+criticism you're kind of the watch guard
+for the process not necessarily um you
+
+ align:start position:0%
+for the process not necessarily um you
+ 
+
+ align:start position:0%
+for the process not necessarily um you
+can sometimes be a contributor and a
+
+ align:start position:0%
+can sometimes be a contributor and a
+ 
+
+ align:start position:0%
+can sometimes be a contributor and a
+watchdog for the process. But most
+
+ align:start position:0%
+watchdog for the process. But most
+ 
+
+ align:start position:0%
+watchdog for the process. But most
+importantly is that you are a watchdog
+
+ align:start position:0%
+importantly is that you are a watchdog
+ 
+
+ align:start position:0%
+importantly is that you are a watchdog
+for the process. Um it's you'll you'll
+
+ align:start position:0%
+for the process. Um it's you'll you'll
+ 
+
+ align:start position:0%
+for the process. Um it's you'll you'll
+see as we do it, it's just so easy to
+
+ align:start position:0%
+see as we do it, it's just so easy to
+ 
+
+ align:start position:0%
+see as we do it, it's just so easy to
+kind of slip into these conversational
+
+ align:start position:0%
+kind of slip into these conversational
+ 
+
+ align:start position:0%
+kind of slip into these conversational
+habits that are contrary to
+
+ align:start position:0%
+habits that are contrary to
+ 
+
+ align:start position:0%
+habits that are contrary to
+brainstorming uh brainstorming process
+
+ align:start position:0%
+brainstorming uh brainstorming process
+ 
+
+ align:start position:0%
+brainstorming uh brainstorming process
+and uh and so having someone who's
+
+ align:start position:0%
+and uh and so having someone who's
+ 
+
+ align:start position:0%
+and uh and so having someone who's
+constantly like making sure don't
+
+ align:start position:0%
+constantly like making sure don't
+ 
+
+ align:start position:0%
+constantly like making sure don't
+criticize encouraging people like oh I
+
+ align:start position:0%
+criticize encouraging people like oh I
+ 
+
+ align:start position:0%
+criticize encouraging people like oh I
+haven't heard from this person. Do you
+
+ align:start position:0%
+haven't heard from this person. Do you
+ 
+
+ align:start position:0%
+haven't heard from this person. Do you
+have any ideas? You know, even kind of
+
+ align:start position:0%
+have any ideas? You know, even kind of
+ 
+
+ align:start position:0%
+have any ideas? You know, even kind of
+pulling people out is important. Um and
+
+ align:start position:0%
+pulling people out is important. Um and
+ 
+
+ align:start position:0%
+pulling people out is important. Um and
+that comes to that ensuring that no
+
+ align:start position:0%
+that comes to that ensuring that no
+ 
+
+ align:start position:0%
+that comes to that ensuring that no
+voices are lost during the discussion,
+
+ align:start position:0%
+voices are lost during the discussion,
+ 
+
+ align:start position:0%
+voices are lost during the discussion,
+right? I mean we had that abbleist
+
+ align:start position:0%
+right? I mean we had that abbleist
+ 
+
+ align:start position:0%
+right? I mean we had that abbleist
+member who had 15 ideas that he wrote
+
+ align:start position:0%
+member who had 15 ideas that he wrote
+ 
+
+ align:start position:0%
+member who had 15 ideas that he wrote
+down and he's like they're worthless.
+
+ align:start position:0%
+down and he's like they're worthless.
+ 
+
+ align:start position:0%
+down and he's like they're worthless.
+Well, in some ways it's the part of the
+
+ align:start position:0%
+Well, in some ways it's the part of the
+ 
+
+ align:start position:0%
+Well, in some ways it's the part of the
+leader either during the session or
+
+ align:start position:0%
+leader either during the session or
+ 
+
+ align:start position:0%
+leader either during the session or
+after the session to try to encourage,
+
+ align:start position:0%
+after the session to try to encourage,
+ 
+
+ align:start position:0%
+after the session to try to encourage,
+you know, those able members to
+
+ align:start position:0%
+you know, those able members to
+ 
+
+ align:start position:0%
+you know, those able members to
+contribute. Um yeah, I mean it's some of
+
+ align:start position:0%
+contribute. Um yeah, I mean it's some of
+ 
+
+ align:start position:0%
+contribute. Um yeah, I mean it's some of
+the most crackpot ideas become the best
+
+ align:start position:0%
+the most crackpot ideas become the best
+ 
+
+ align:start position:0%
+the most crackpot ideas become the best
+ones. So you really want to make sure
+
+ align:start position:0%
+ones. So you really want to make sure
+ 
+
+ align:start position:0%
+ones. So you really want to make sure
+every voice is heard. Um and then
+
+ align:start position:0%
+every voice is heard. Um and then
+ 
+
+ align:start position:0%
+every voice is heard. Um and then
+encouraging the synthesis, encouraging
+
+ align:start position:0%
+encouraging the synthesis, encouraging
+ 
+
+ align:start position:0%
+encouraging the synthesis, encouraging
+people to kind of riff on other ideas.
+
+ align:start position:0%
+people to kind of riff on other ideas.
+ 
+
+ align:start position:0%
+people to kind of riff on other ideas.
+Um you know, trying to find ways for
+
+ align:start position:0%
+Um you know, trying to find ways for
+ 
+
+ align:start position:0%
+Um you know, trying to find ways for
+people to build on each other even
+
+ align:start position:0%
+people to build on each other even
+ 
+
+ align:start position:0%
+people to build on each other even
+offering synthesis towards a direction.
+
+ align:start position:0%
+offering synthesis towards a direction.
+ 
+
+ align:start position:0%
+offering synthesis towards a direction.
+So maybe you have a couple ideas you're
+
+ align:start position:0%
+So maybe you have a couple ideas you're
+ 
+
+ align:start position:0%
+So maybe you have a couple ideas you're
+like, "Oh, like you know, one and 10 are
+
+ align:start position:0%
+like, "Oh, like you know, one and 10 are
+ 
+
+ align:start position:0%
+like, "Oh, like you know, one and 10 are
+kind of similar, but like you know, are
+
+ align:start position:0%
+kind of similar, but like you know, are
+ 
+
+ align:start position:0%
+kind of similar, but like you know, are
+there any ways we can combine this?" And
+
+ align:start position:0%
+there any ways we can combine this?" And
+ 
+
+ align:start position:0%
+there any ways we can combine this?" And
+like, "Yeah, we could, you know, give
+
+ align:start position:0%
+like, "Yeah, we could, you know, give
+ 
+
+ align:start position:0%
+like, "Yeah, we could, you know, give
+him a helmet." Awesome.
+
+ align:start position:0%
+him a helmet." Awesome.
+ 
+
+ align:start position:0%
+him a helmet." Awesome.
+So on so forth. I don't know what what
+
+ align:start position:0%
+So on so forth. I don't know what what
+ 
+
+ align:start position:0%
+So on so forth. I don't know what what
+two things can combine to get a helmet,
+
+ align:start position:0%
+two things can combine to get a helmet,
+ 
+
+ align:start position:0%
+two things can combine to get a helmet,
+but can't get shot in the head. How
+
+ align:start position:0%
+but can't get shot in the head. How
+ 
+
+ align:start position:0%
+but can't get shot in the head. How
+about a helmet? All right. Um, so
+
+ align:start position:0%
+about a helmet? All right. Um, so
+ 
+
+ align:start position:0%
+about a helmet? All right. Um, so
+responsibilities for the secretary. most
+
+ align:start position:0%
+responsibilities for the secretary. most
+ 
+
+ align:start position:0%
+responsibilities for the secretary. most
+obviously record every and all ideas.
+
+ align:start position:0%
+obviously record every and all ideas.
+ 
+
+ align:start position:0%
+obviously record every and all ideas.
+It's like write it all down. You have to
+
+ align:start position:0%
+It's like write it all down. You have to
+ 
+
+ align:start position:0%
+It's like write it all down. You have to
+write it all down. This is so important.
+
+ align:start position:0%
+write it all down. This is so important.
+ 
+
+ align:start position:0%
+write it all down. This is so important.
+Um this one is often overlooked. Uh
+
+ align:start position:0%
+Um this one is often overlooked. Uh
+ 
+
+ align:start position:0%
+Um this one is often overlooked. Uh
+monitoring the schedule and the duration
+
+ align:start position:0%
+monitoring the schedule and the duration
+ 
+
+ align:start position:0%
+monitoring the schedule and the duration
+of the session. Um something I learned a
+
+ align:start position:0%
+of the session. Um something I learned a
+ 
+
+ align:start position:0%
+of the session. Um something I learned a
+long long long time ago is one of the
+
+ align:start position:0%
+long long long time ago is one of the
+ 
+
+ align:start position:0%
+long long long time ago is one of the
+worst things that can happen is meetings
+
+ align:start position:0%
+worst things that can happen is meetings
+ 
+
+ align:start position:0%
+worst things that can happen is meetings
+that run over or meetings that start
+
+ align:start position:0%
+that run over or meetings that start
+ 
+
+ align:start position:0%
+that run over or meetings that start
+late or meetings um you know that don't
+
+ align:start position:0%
+late or meetings um you know that don't
+ 
+
+ align:start position:0%
+late or meetings um you know that don't
+adhere to a schedule. no no better way
+
+ align:start position:0%
+adhere to a schedule. no no better way
+ 
+
+ align:start position:0%
+adhere to a schedule. no no better way
+to kind of uh you know lose your
+
+ align:start position:0%
+to kind of uh you know lose your
+ 
+
+ align:start position:0%
+to kind of uh you know lose your
+employees or lose your staff um than to
+
+ align:start position:0%
+employees or lose your staff um than to
+ 
+
+ align:start position:0%
+employees or lose your staff um than to
+to kind of bite into their time. Um and
+
+ align:start position:0%
+to kind of bite into their time. Um and
+ 
+
+ align:start position:0%
+to kind of bite into their time. Um and
+so you know making sure that it's
+
+ align:start position:0%
+so you know making sure that it's
+ 
+
+ align:start position:0%
+so you know making sure that it's
+constrained and that it meets the
+
+ align:start position:0%
+constrained and that it meets the
+ 
+
+ align:start position:0%
+constrained and that it meets the
+duration is really important. And so you
+
+ align:start position:0%
+duration is really important. And so you
+ 
+
+ align:start position:0%
+duration is really important. And so you
+know may seem simple but timing the
+
+ align:start position:0%
+know may seem simple but timing the
+ 
+
+ align:start position:0%
+know may seem simple but timing the
+thing. Um and then of course if
+
+ align:start position:0%
+thing. Um and then of course if
+ 
+
+ align:start position:0%
+thing. Um and then of course if
+applicable participating in the
+
+ align:start position:0%
+applicable participating in the
+ 
+
+ align:start position:0%
+applicable participating in the
+brainstorming you know like I said all
+
+ align:start position:0%
+brainstorming you know like I said all
+ 
+
+ align:start position:0%
+brainstorming you know like I said all
+voices um all voices should be heard and
+
+ align:start position:0%
+voices um all voices should be heard and
+ 
+
+ align:start position:0%
+voices um all voices should be heard and
+that you know oftentimes would mean that
+
+ align:start position:0%
+that you know oftentimes would mean that
+ 
+
+ align:start position:0%
+that you know oftentimes would mean that
+the secretary is a uh is a creative
+
+ align:start position:0%
+the secretary is a uh is a creative
+ 
+
+ align:start position:0%
+the secretary is a uh is a creative
+professional as well. Um And so make
+
+ align:start position:0%
+professional as well. Um And so make
+ 
+
+ align:start position:0%
+professional as well. Um And so make
+sure that you participate quickly.
+
+ align:start position:0%
+sure that you participate quickly.
+ 
+
+ align:start position:0%
+sure that you participate quickly.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+we've got a few exercises now to get you
+
+ align:start position:0%
+we've got a few exercises now to get you
+ 
+
+ align:start position:0%
+we've got a few exercises now to get you
+acclimated to the idea of brainstorming.
+
+ align:start position:0%
+acclimated to the idea of brainstorming.
+ 
+
+ align:start position:0%
+acclimated to the idea of brainstorming.
+Um the first one is an actual individual
+
+ align:start position:0%
+Um the first one is an actual individual
+ 
+
+ align:start position:0%
+Um the first one is an actual individual
+brainstorm. So uh if you have paper,
+
+ align:start position:0%
+brainstorm. So uh if you have paper,
+ 
+
+ align:start position:0%
+brainstorm. So uh if you have paper,
+grab some paper.
+
+ align:start position:0%
+grab some paper.
+ 
+
+ align:start position:0%
+grab some paper.
+If anyone's lacking either writing
+
+ align:start position:0%
+If anyone's lacking either writing
+ 
+
+ align:start position:0%
+If anyone's lacking either writing
+equipment or paper,
+
+ align:start position:0%
+equipment or paper,
+ 
+
+ align:start position:0%
+equipment or paper,
+>> you could use a note card, too. It's
+
+ align:start position:0%
+>> you could use a note card, too. It's
+ 
+
+ align:start position:0%
+>> you could use a note card, too. It's
+really just something to write on other
+
+ align:start position:0%
+really just something to write on other
+ 
+
+ align:start position:0%
+really just something to write on other
+than the table.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Not cards are totally fine.
+
+ align:start position:0%
+Not cards are totally fine.
+ 
+
+ align:start position:0%
+Not cards are totally fine.
+>> Um, I'll, as you guys are getting ready,
+
+ align:start position:0%
+>> Um, I'll, as you guys are getting ready,
+ 
+
+ align:start position:0%
+>> Um, I'll, as you guys are getting ready,
+I'll continue to talk. This is actually
+
+ align:start position:0%
+I'll continue to talk. This is actually
+ 
+
+ align:start position:0%
+I'll continue to talk. This is actually
+something that I didn't mention in the
+
+ align:start position:0%
+something that I didn't mention in the
+ 
+
+ align:start position:0%
+something that I didn't mention in the
+process, but what is actually very
+
+ align:start position:0%
+process, but what is actually very
+ 
+
+ align:start position:0%
+process, but what is actually very
+useful to the brainstorming process. I
+
+ align:start position:0%
+useful to the brainstorming process. I
+ 
+
+ align:start position:0%
+useful to the brainstorming process. I
+think doing warm-ups before your actual
+
+ align:start position:0%
+think doing warm-ups before your actual
+ 
+
+ align:start position:0%
+think doing warm-ups before your actual
+brainstorm is useful. Um, you know,
+
+ align:start position:0%
+brainstorm is useful. Um, you know,
+ 
+
+ align:start position:0%
+brainstorm is useful. Um, you know,
+people show up just for lunch,
+
+ align:start position:0%
+people show up just for lunch,
+ 
+
+ align:start position:0%
+people show up just for lunch,
+especially because one of those eating.
+
+ align:start position:0%
+especially because one of those eating.
+ 
+
+ align:start position:0%
+especially because one of those eating.
+Um, you know, people, you know,
+
+ align:start position:0%
+Um, you know, people, you know,
+ 
+
+ align:start position:0%
+Um, you know, people, you know,
+sometimes they're tired. People just
+
+ align:start position:0%
+sometimes they're tired. People just
+ 
+
+ align:start position:0%
+sometimes they're tired. People just
+might have other things on the brain.
+
+ align:start position:0%
+might have other things on the brain.
+ 
+
+ align:start position:0%
+might have other things on the brain.
+So, getting getting in the habit,
+
+ align:start position:0%
+So, getting getting in the habit,
+ 
+
+ align:start position:0%
+So, getting getting in the habit,
+getting warmed up to uh being creative,
+
+ align:start position:0%
+getting warmed up to uh being creative,
+ 
+
+ align:start position:0%
+getting warmed up to uh being creative,
+um, is important. I I tend to find it's
+
+ align:start position:0%
+um, is important. I I tend to find it's
+ 
+
+ align:start position:0%
+um, is important. I I tend to find it's
+a rare it's a rare kind of person who
+
+ align:start position:0%
+a rare it's a rare kind of person who
+ 
+
+ align:start position:0%
+a rare it's a rare kind of person who
+you just sort of give a blank piece of
+
+ align:start position:0%
+you just sort of give a blank piece of
+ 
+
+ align:start position:0%
+you just sort of give a blank piece of
+paper to and you're like, "Ah, make
+
+ align:start position:0%
+paper to and you're like, "Ah, make
+ 
+
+ align:start position:0%
+paper to and you're like, "Ah, make
+something. Go be creative." And they're
+
+ align:start position:0%
+something. Go be creative." And they're
+ 
+
+ align:start position:0%
+something. Go be creative." And they're
+like, they just like whip something out,
+
+ align:start position:0%
+like, they just like whip something out,
+ 
+
+ align:start position:0%
+like, they just like whip something out,
+right? You got you got to kind of get
+
+ align:start position:0%
+right? You got you got to kind of get
+ 
+
+ align:start position:0%
+right? You got you got to kind of get
+warmed up. Um, you know, visual artists
+
+ align:start position:0%
+warmed up. Um, you know, visual artists
+ 
+
+ align:start position:0%
+warmed up. Um, you know, visual artists
+sketch constantly and that that makes
+
+ align:start position:0%
+sketch constantly and that that makes
+ 
+
+ align:start position:0%
+sketch constantly and that that makes
+sense and I make film sketches. Um, I I
+
+ align:start position:0%
+sense and I make film sketches. Um, I I
+ 
+
+ align:start position:0%
+sense and I make film sketches. Um, I I
+just make dumb pieces of music that I'll
+
+ align:start position:0%
+just make dumb pieces of music that I'll
+ 
+
+ align:start position:0%
+just make dumb pieces of music that I'll
+maybe never use for anything, but maybe
+
+ align:start position:0%
+maybe never use for anything, but maybe
+ 
+
+ align:start position:0%
+maybe never use for anything, but maybe
+I will. Um, who knows? I make stupid
+
+ align:start position:0%
+I will. Um, who knows? I make stupid
+ 
+
+ align:start position:0%
+I will. Um, who knows? I make stupid
+sound effects in the shower. Um, I
+
+ align:start position:0%
+sound effects in the shower. Um, I
+ 
+
+ align:start position:0%
+sound effects in the shower. Um, I
+consider that warming up for work. Um,
+
+ align:start position:0%
+consider that warming up for work. Um,
+ 
+
+ align:start position:0%
+consider that warming up for work. Um,
+so, uh, you know, you have to kind of
+
+ align:start position:0%
+so, uh, you know, you have to kind of
+ 
+
+ align:start position:0%
+so, uh, you know, you have to kind of
+get warmed up. And so, this is just a
+
+ align:start position:0%
+get warmed up. And so, this is just a
+ 
+
+ align:start position:0%
+get warmed up. And so, this is just a
+really quick five minute, uh, five
+
+ align:start position:0%
+really quick five minute, uh, five
+ 
+
+ align:start position:0%
+really quick five minute, uh, five
+minute warm up. And the idea is, um,
+
+ align:start position:0%
+minute warm up. And the idea is, um,
+ 
+
+ align:start position:0%
+minute warm up. And the idea is, um,
+write anything that comes to your mind
+
+ align:start position:0%
+write anything that comes to your mind
+ 
+
+ align:start position:0%
+write anything that comes to your mind
+for this specific problem. And I'll show
+
+ align:start position:0%
+for this specific problem. And I'll show
+ 
+
+ align:start position:0%
+for this specific problem. And I'll show
+you a picture. brainstorm possible uses.
+
+ align:start position:0%
+you a picture. brainstorm possible uses.
+ 
+
+ align:start position:0%
+you a picture. brainstorm possible uses.
+It's not really brainstorm. It's more of
+
+ align:start position:0%
+It's not really brainstorm. It's more of
+ 
+
+ align:start position:0%
+It's not really brainstorm. It's more of
+just like a you individually come up
+
+ align:start position:0%
+just like a you individually come up
+ 
+
+ align:start position:0%
+just like a you individually come up
+with creative ideas uh creative uses uh
+
+ align:start position:0%
+with creative ideas uh creative uses uh
+ 
+
+ align:start position:0%
+with creative ideas uh creative uses uh
+for the following item and I'll give you
+
+ align:start position:0%
+for the following item and I'll give you
+ 
+
+ align:start position:0%
+for the following item and I'll give you
+five minutes starting now.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Hopefully was good for a warm up. Quick
+
+ align:start position:0%
+Hopefully was good for a warm up. Quick
+ 
+
+ align:start position:0%
+Hopefully was good for a warm up. Quick
+question and show
+
+ align:start position:0%
+question and show
+ 
+
+ align:start position:0%
+question and show
+and be honest.
+
+ align:start position:0%
+and be honest.
+ 
+
+ align:start position:0%
+and be honest.
+This is a safe mind.
+
+ align:start position:0%
+This is a safe mind.
+ 
+
+ align:start position:0%
+This is a safe mind.
+How many of you had an idea that you did
+
+ align:start position:0%
+How many of you had an idea that you did
+ 
+
+ align:start position:0%
+How many of you had an idea that you did
+not write down? How many of you self
+
+ align:start position:0%
+not write down? How many of you self
+ 
+
+ align:start position:0%
+not write down? How many of you self
+censored yourself with an idea?
+
+ align:start position:0%
+censored yourself with an idea?
+ 
+
+ align:start position:0%
+censored yourself with an idea?
+Yeah. You're like, "Oh, that's just
+
+ align:start position:0%
+Yeah. You're like, "Oh, that's just
+ 
+
+ align:start position:0%
+Yeah. You're like, "Oh, that's just
+dumb." See, it's really it's hard to get
+
+ align:start position:0%
+dumb." See, it's really it's hard to get
+ 
+
+ align:start position:0%
+dumb." See, it's really it's hard to get
+out of the habit of doing that. It's
+
+ align:start position:0%
+out of the habit of doing that. It's
+ 
+
+ align:start position:0%
+out of the habit of doing that. It's
+hard to get out of this kind of this
+
+ align:start position:0%
+hard to get out of this kind of this
+ 
+
+ align:start position:0%
+hard to get out of this kind of this
+habit of self- judgment. Um, and it's
+
+ align:start position:0%
+habit of self- judgment. Um, and it's
+ 
+
+ align:start position:0%
+habit of self- judgment. Um, and it's
+really important. Um, you know, that
+
+ align:start position:0%
+really important. Um, you know, that
+ 
+
+ align:start position:0%
+really important. Um, you know, that
+that dumb idea that you think was
+
+ align:start position:0%
+that dumb idea that you think was
+ 
+
+ align:start position:0%
+that dumb idea that you think was
+worthless might be a good one. Does
+
+ align:start position:0%
+worthless might be a good one. Does
+ 
+
+ align:start position:0%
+worthless might be a good one. Does
+anyone who raised their hand want to
+
+ align:start position:0%
+anyone who raised their hand want to
+ 
+
+ align:start position:0%
+anyone who raised their hand want to
+share what their censored idea was? just
+
+ align:start position:0%
+share what their censored idea was? just
+ 
+
+ align:start position:0%
+share what their censored idea was? just
+to exercise the demons, so to speak.
+
+ align:start position:0%
+to exercise the demons, so to speak.
+ 
+
+ align:start position:0%
+to exercise the demons, so to speak.
+>> No, nothing.
+
+ align:start position:0%
+>> No, nothing.
+ 
+
+ align:start position:0%
+>> No, nothing.
+>> All right. Who wants to share some ideas
+
+ align:start position:0%
+>> All right. Who wants to share some ideas
+ 
+
+ align:start position:0%
+>> All right. Who wants to share some ideas
+that they did write down? All right.
+
+ align:start position:0%
+that they did write down? All right.
+ 
+
+ align:start position:0%
+that they did write down? All right.
+Here we go.
+
+ align:start position:0%
+Here we go.
+ 
+
+ align:start position:0%
+Here we go.
+>> See, I have a lot.
+
+ align:start position:0%
+>> See, I have a lot.
+ 
+
+ align:start position:0%
+>> See, I have a lot.
+>> Yeah. Well, throw throw us a couple that
+
+ align:start position:0%
+>> Yeah. Well, throw throw us a couple that
+ 
+
+ align:start position:0%
+>> Yeah. Well, throw throw us a couple that
+are your favorite.
+
+ align:start position:0%
+are your favorite.
+ 
+
+ align:start position:0%
+are your favorite.
+>> See, lockpick, MacGyver, connecting
+
+ align:start position:0%
+>> See, lockpick, MacGyver, connecting
+ 
+
+ align:start position:0%
+>> See, lockpick, MacGyver, connecting
+circuits.
+
+ align:start position:0%
+circuits.
+ 
+
+ align:start position:0%
+circuits.
+>> There you go.
+
+ align:start position:0%
+>> There you go.
+ 
+
+ align:start position:0%
+>> There you go.
+>> Carrying cards, um, a knife, clothes
+
+ align:start position:0%
+>> Carrying cards, um, a knife, clothes
+ 
+
+ align:start position:0%
+>> Carrying cards, um, a knife, clothes
+hanger, chopsticks, a dowster, um, stir.
+
+ align:start position:0%
+hanger, chopsticks, a dowster, um, stir.
+ 
+
+ align:start position:0%
+hanger, chopsticks, a dowster, um, stir.
+See, connect batteries. Air of tires
+
+ align:start position:0%
+See, connect batteries. Air of tires
+ 
+
+ align:start position:0%
+See, connect batteries. Air of tires
+emote tool nose picker
+
+ align:start position:0%
+emote tool nose picker
+ 
+
+ align:start position:0%
+emote tool nose picker
+>> staple. A staple
+
+ align:start position:0%
+>> staple. A staple
+ 
+
+ align:start position:0%
+>> staple. A staple
+>> and a paper bra. I have a lot of things.
+
+ align:start position:0%
+>> and a paper bra. I have a lot of things.
+ 
+
+ align:start position:0%
+>> and a paper bra. I have a lot of things.
+>> Yeah. Good. No, that's awesome.
+
+ align:start position:0%
+>> Yeah. Good. No, that's awesome.
+ 
+
+ align:start position:0%
+>> Yeah. Good. No, that's awesome.
+>> All right. I got Let's see. Um
+
+ align:start position:0%
+>> All right. I got Let's see. Um
+ 
+
+ align:start position:0%
+>> All right. I got Let's see. Um
+fingernail cleaner, an eyelash
+
+ align:start position:0%
+fingernail cleaner, an eyelash
+ 
+
+ align:start position:0%
+fingernail cleaner, an eyelash
+straightener, basically a rail gun ammo,
+
+ align:start position:0%
+straightener, basically a rail gun ammo,
+ 
+
+ align:start position:0%
+straightener, basically a rail gun ammo,
+a balloon annihilator, and an official
+
+ align:start position:0%
+a balloon annihilator, and an official
+ 
+
+ align:start position:0%
+a balloon annihilator, and an official
+Tamagotchi TM resetter.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. resets a lot of things. How about
+
+ align:start position:0%
+>> Yeah. resets a lot of things. How about
+ 
+
+ align:start position:0%
+>> Yeah. resets a lot of things. How about
+over the side? Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Catch fish with it by turning into
+
+ align:start position:0%
+>> Catch fish with it by turning into
+ 
+
+ align:start position:0%
+>> Catch fish with it by turning into
+scratch messages with it. Use it as a
+
+ align:start position:0%
+scratch messages with it. Use it as a
+ 
+
+ align:start position:0%
+scratch messages with it. Use it as a
+key ring. Conduct electricity with it.
+
+ align:start position:0%
+key ring. Conduct electricity with it.
+ 
+
+ align:start position:0%
+key ring. Conduct electricity with it.
+Make it into jewelry. Um fix umbrellas
+
+ align:start position:0%
+Make it into jewelry. Um fix umbrellas
+ 
+
+ align:start position:0%
+Make it into jewelry. Um fix umbrellas
+and what have you with it, which I've
+
+ align:start position:0%
+and what have you with it, which I've
+ 
+
+ align:start position:0%
+and what have you with it, which I've
+done before.
+
+ align:start position:0%
+done before.
+ 
+
+ align:start position:0%
+done before.
+Money clip. Use it as a skewer for
+
+ align:start position:0%
+Money clip. Use it as a skewer for
+ 
+
+ align:start position:0%
+Money clip. Use it as a skewer for
+cooking.
+
+ align:start position:0%
+cooking.
+ 
+
+ align:start position:0%
+cooking.
+uh put it on top of a door and so when
+
+ align:start position:0%
+uh put it on top of a door and so when
+ 
+
+ align:start position:0%
+uh put it on top of a door and so when
+people open it falls on the ground you
+
+ align:start position:0%
+people open it falls on the ground you
+ 
+
+ align:start position:0%
+people open it falls on the ground you
+know somebody's been in your room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> oil
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+accessory
+
+ align:start position:0%
+accessory
+ 
+
+ align:start position:0%
+accessory
+that's a good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> uh I had a hair styling accessory
+
+ align:start position:0%
+>> uh I had a hair styling accessory
+ 
+
+ align:start position:0%
+>> uh I had a hair styling accessory
+projectile something you could mel down
+
+ align:start position:0%
+projectile something you could mel down
+ 
+
+ align:start position:0%
+projectile something you could mel down
+to for metal and porn out stuff.
+
+ align:start position:0%
+to for metal and porn out stuff.
+ 
+
+ align:start position:0%
+to for metal and porn out stuff.
+>> Uh that's something you could bend and
+
+ align:start position:0%
+>> Uh that's something you could bend and
+ 
+
+ align:start position:0%
+>> Uh that's something you could bend and
+put on chairs and people sit down and
+
+ align:start position:0%
+put on chairs and people sit down and
+ 
+
+ align:start position:0%
+put on chairs and people sit down and
+poke them. Um modern art. Um I thought
+
+ align:start position:0%
+poke them. Um modern art. Um I thought
+ 
+
+ align:start position:0%
+poke them. Um modern art. Um I thought
+of you could like try to get a bunch and
+
+ align:start position:0%
+of you could like try to get a bunch and
+ 
+
+ align:start position:0%
+of you could like try to get a bunch and
+fill a dorm room with it as a prank or
+
+ align:start position:0%
+fill a dorm room with it as a prank or
+ 
+
+ align:start position:0%
+fill a dorm room with it as a prank or
+something. Um toothpick
+
+ align:start position:0%
+something. Um toothpick
+ 
+
+ align:start position:0%
+something. Um toothpick
+hold stuff open for emergency surgery.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Cool.
+
+ align:start position:0%
+>> Cool.
+ 
+
+ align:start position:0%
+>> Cool.
+I thought you could uh bend it into an
+
+ align:start position:0%
+I thought you could uh bend it into an
+ 
+
+ align:start position:0%
+I thought you could uh bend it into an
+interesting flat shape and then put it
+
+ align:start position:0%
+interesting flat shape and then put it
+ 
+
+ align:start position:0%
+interesting flat shape and then put it
+in ink and use it as a stamp.
+
+ align:start position:0%
+in ink and use it as a stamp.
+ 
+
+ align:start position:0%
+in ink and use it as a stamp.
+>> Very nice. Very cool. Um cool. Yeah. Go
+
+ align:start position:0%
+>> Very nice. Very cool. Um cool. Yeah. Go
+ 
+
+ align:start position:0%
+>> Very nice. Very cool. Um cool. Yeah. Go
+ahead.
+
+ align:start position:0%
+ahead.
+ 
+
+ align:start position:0%
+ahead.
+>> Uh game bits and tokens holder for
+
+ align:start position:0%
+>> Uh game bits and tokens holder for
+ 
+
+ align:start position:0%
+>> Uh game bits and tokens holder for
+dipping something into liquids. Um pie
+
+ align:start position:0%
+dipping something into liquids. Um pie
+ 
+
+ align:start position:0%
+dipping something into liquids. Um pie
+clips and keeping small boards together.
+
+ align:start position:0%
+clips and keeping small boards together.
+ 
+
+ align:start position:0%
+clips and keeping small boards together.
+>> Sure.
+
+ align:start position:0%
+>> Sure.
+ 
+
+ align:start position:0%
+>> Sure.
+>> Mini rock garden.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Good
+
+ align:start position:0%
+Good
+ 
+
+ align:start position:0%
+Good
+>> heat generator. If you uh work hard in
+
+ align:start position:0%
+>> heat generator. If you uh work hard in
+ 
+
+ align:start position:0%
+>> heat generator. If you uh work hard in
+it by bending it and then bending it and
+
+ align:start position:0%
+it by bending it and then bending it and
+ 
+
+ align:start position:0%
+it by bending it and then bending it and
+then it gets hot.
+
+ align:start position:0%
+then it gets hot.
+ 
+
+ align:start position:0%
+then it gets hot.
+>> Very nice.
+
+ align:start position:0%
+>> Very nice.
+ 
+
+ align:start position:0%
+>> Very nice.
+>> As long as it doesn't break.
+
+ align:start position:0%
+>> As long as it doesn't break.
+ 
+
+ align:start position:0%
+>> As long as it doesn't break.
+>> I think of a souvenir as a totem for a
+
+ align:start position:0%
+>> I think of a souvenir as a totem for a
+ 
+
+ align:start position:0%
+>> I think of a souvenir as a totem for a
+lost robot.
+
+ align:start position:0%
+lost robot.
+ 
+
+ align:start position:0%
+lost robot.
+>> That's good.
+
+ align:start position:0%
+>> That's good.
+ 
+
+ align:start position:0%
+>> That's good.
+>> You say that again.
+
+ align:start position:0%
+>> You say that again.
+ 
+
+ align:start position:0%
+>> You say that again.
+>> Let's say like there's a robot made by
+
+ align:start position:0%
+>> Let's say like there's a robot made by
+ 
+
+ align:start position:0%
+>> Let's say like there's a robot made by
+human but it's lost in space. They have
+
+ align:start position:0%
+human but it's lost in space. They have
+ 
+
+ align:start position:0%
+human but it's lost in space. They have
+to remind it become like a secret thing.
+
+ align:start position:0%
+to remind it become like a secret thing.
+ 
+
+ align:start position:0%
+to remind it become like a secret thing.
+>> Yeah. My favorite use for a paperclip is
+
+ align:start position:0%
+>> Yeah. My favorite use for a paperclip is
+ 
+
+ align:start position:0%
+>> Yeah. My favorite use for a paperclip is
+cleaning the lint out of my uh iPhone
+
+ align:start position:0%
+cleaning the lint out of my uh iPhone
+ 
+
+ align:start position:0%
+cleaning the lint out of my uh iPhone
+ear jack, which drives me absolutely
+
+ align:start position:0%
+ear jack, which drives me absolutely
+ 
+
+ align:start position:0%
+ear jack, which drives me absolutely
+nuts. So, I'm running on reserve battery
+
+ align:start position:0%
+nuts. So, I'm running on reserve battery
+ 
+
+ align:start position:0%
+nuts. So, I'm running on reserve battery
+power and my slideshow has been
+
+ align:start position:0%
+power and my slideshow has been
+ 
+
+ align:start position:0%
+power and my slideshow has been
+suspended on in my office. There's a uh
+
+ align:start position:0%
+suspended on in my office. There's a uh
+ 
+
+ align:start position:0%
+suspended on in my office. There's a uh
+there's a air.
+
+ align:start position:0%
+there's a air.
+ 
+
+ align:start position:0%
+there's a air.
+So, um
+
+ align:start position:0%
+So, um
+ 
+
+ align:start position:0%
+So, um
+so yeah, how did we feel about that
+
+ align:start position:0%
+so yeah, how did we feel about that
+ 
+
+ align:start position:0%
+so yeah, how did we feel about that
+exercise? Got you loosened up a little
+
+ align:start position:0%
+exercise? Got you loosened up a little
+ 
+
+ align:start position:0%
+exercise? Got you loosened up a little
+bit. Got you thinking about some ideas.
+
+ align:start position:0%
+bit. Got you thinking about some ideas.
+ 
+
+ align:start position:0%
+bit. Got you thinking about some ideas.
+Got you feeling a little creative juices
+
+ align:start position:0%
+Got you feeling a little creative juices
+ 
+
+ align:start position:0%
+Got you feeling a little creative juices
+fine. We've got three more exercises
+
+ align:start position:0%
+fine. We've got three more exercises
+ 
+
+ align:start position:0%
+fine. We've got three more exercises
+that we're going to do. Um,
+
+ align:start position:0%
+that we're going to do. Um,
+ 
+
+ align:start position:0%
+that we're going to do. Um,
+so much brainstorming.
+
+ align:start position:0%
+so much brainstorming.
+ 
+
+ align:start position:0%
+so much brainstorming.
+This is the hardest work I've ever done
+
+ align:start position:0%
+This is the hardest work I've ever done
+ 
+
+ align:start position:0%
+This is the hardest work I've ever done
+to get my chicken. No. Um, yeah. So,
+
+ align:start position:0%
+to get my chicken. No. Um, yeah. So,
+ 
+
+ align:start position:0%
+to get my chicken. No. Um, yeah. So,
+we've got a few more exercise to get you
+
+ align:start position:0%
+we've got a few more exercise to get you
+ 
+
+ align:start position:0%
+we've got a few more exercise to get you
+guys kind of comfortable, get you guys,
+
+ align:start position:0%
+guys kind of comfortable, get you guys,
+ 
+
+ align:start position:0%
+guys kind of comfortable, get you guys,
+you know, relaxed with this kind of
+
+ align:start position:0%
+you know, relaxed with this kind of
+ 
+
+ align:start position:0%
+you know, relaxed with this kind of
+brainstorming process. The next one is
+
+ align:start position:0%
+brainstorming process. The next one is
+ 
+
+ align:start position:0%
+brainstorming process. The next one is
+going to be a group exercise. Um, I'm
+
+ align:start position:0%
+going to be a group exercise. Um, I'm
+ 
+
+ align:start position:0%
+going to be a group exercise. Um, I'm
+going to wait to describe it until I can
+
+ align:start position:0%
+going to wait to describe it until I can
+ 
+
+ align:start position:0%
+going to wait to describe it until I can
+get uh get my slideshow. Anybody else
+
+ align:start position:0%
+get uh get my slideshow. Anybody else
+ 
+
+ align:start position:0%
+get uh get my slideshow. Anybody else
+have any particularly choice paperclip
+
+ align:start position:0%
+have any particularly choice paperclip
+ 
+
+ align:start position:0%
+have any particularly choice paperclip
+ideas? Start one.
+
+ align:start position:0%
+ideas? Start one.
+ 
+
+ align:start position:0%
+ideas? Start one.
+>> A sign sine wave generator.
+
+ align:start position:0%
+>> A sign sine wave generator.
+ 
+
+ align:start position:0%
+>> A sign sine wave generator.
+>> Very good.
+
+ align:start position:0%
+>> Very good.
+ 
+
+ align:start position:0%
+>> Very good.
+wireframe doll.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Hold up. Stop looking at
+
+ align:start position:0%
+>> Hold up. Stop looking at
+ 
+
+ align:start position:0%
+>> Hold up. Stop looking at
+it like as a spear.
+
+ align:start position:0%
+it like as a spear.
+ 
+
+ align:start position:0%
+it like as a spear.
+>> Oh, yeah.
+
+ align:start position:0%
+>> Oh, yeah.
+ 
+
+ align:start position:0%
+>> Oh, yeah.
+Man versus Wild like catch fish with it
+
+ align:start position:0%
+Man versus Wild like catch fish with it
+ 
+
+ align:start position:0%
+Man versus Wild like catch fish with it
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+>> something to chew on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Launcher rubber band launcher
+
+ align:start position:0%
+>> Launcher rubber band launcher
+ 
+
+ align:start position:0%
+>> Launcher rubber band launcher
+>> letting air out tires.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You heard of the guy who had an
+
+ align:start position:0%
+You heard of the guy who had an
+ 
+
+ align:start position:0%
+You heard of the guy who had an
+oversized red tape equip and ended up
+
+ align:start position:0%
+oversized red tape equip and ended up
+ 
+
+ align:start position:0%
+oversized red tape equip and ended up
+trading it for a house
+
+ align:start position:0%
+trading it for a house
+ 
+
+ align:start position:0%
+trading it for a house
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+towards a house.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Pretty cool. So, so hopefully that got
+
+ align:start position:0%
+>> Pretty cool. So, so hopefully that got
+ 
+
+ align:start position:0%
+>> Pretty cool. So, so hopefully that got
+you loosened up. I do want to just
+
+ align:start position:0%
+you loosened up. I do want to just
+ 
+
+ align:start position:0%
+you loosened up. I do want to just
+emphasize again for those of you who
+
+ align:start position:0%
+emphasize again for those of you who
+ 
+
+ align:start position:0%
+emphasize again for those of you who
+raised your hand and even those of you
+
+ align:start position:0%
+raised your hand and even those of you
+ 
+
+ align:start position:0%
+raised your hand and even those of you
+who did not raise your hand because you
+
+ align:start position:0%
+who did not raise your hand because you
+ 
+
+ align:start position:0%
+who did not raise your hand because you
+were censoring the truth because you're
+
+ align:start position:0%
+were censoring the truth because you're
+ 
+
+ align:start position:0%
+were censoring the truth because you're
+afraid try not to self censor. Um really
+
+ align:start position:0%
+afraid try not to self censor. Um really
+ 
+
+ align:start position:0%
+afraid try not to self censor. Um really
+it's important to brainstorming. I bet
+
+ align:start position:0%
+it's important to brainstorming. I bet
+ 
+
+ align:start position:0%
+it's important to brainstorming. I bet
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+>> Yeah, I know. Stop self-centering. I bet
+
+ align:start position:0%
+>> Yeah, I know. Stop self-centering. I bet
+ 
+
+ align:start position:0%
+>> Yeah, I know. Stop self-centering. I bet
+I bet those crappy ideas that you write
+
+ align:start position:0%
+I bet those crappy ideas that you write
+ 
+
+ align:start position:0%
+I bet those crappy ideas that you write
+down are actually really awesome. So um
+
+ align:start position:0%
+down are actually really awesome. So um
+ 
+
+ align:start position:0%
+down are actually really awesome. So um
+activity number two uh we're going to
+
+ align:start position:0%
+activity number two uh we're going to
+ 
+
+ align:start position:0%
+activity number two uh we're going to
+work as one large group. Um this is our
+
+ align:start position:0%
+work as one large group. Um this is our
+ 
+
+ align:start position:0%
+work as one large group. Um this is our
+con shell. Doesn't look like one, I
+
+ align:start position:0%
+con shell. Doesn't look like one, I
+ 
+
+ align:start position:0%
+con shell. Doesn't look like one, I
+know, but um you know the principle
+
+ align:start position:0%
+know, but um you know the principle
+ 
+
+ align:start position:0%
+know, but um you know the principle
+still applies. Um this is just to kind
+
+ align:start position:0%
+still applies. Um this is just to kind
+ 
+
+ align:start position:0%
+still applies. Um this is just to kind
+of get us in the habit in the shape of
+
+ align:start position:0%
+of get us in the habit in the shape of
+ 
+
+ align:start position:0%
+of get us in the habit in the shape of
+uh kind of speaking one at a time uh not
+
+ align:start position:0%
+uh kind of speaking one at a time uh not
+ 
+
+ align:start position:0%
+uh kind of speaking one at a time uh not
+interrupting each other. Um and in some
+
+ align:start position:0%
+interrupting each other. Um and in some
+ 
+
+ align:start position:0%
+interrupting each other. Um and in some
+senses building on each other's ideas
+
+ align:start position:0%
+senses building on each other's ideas
+ 
+
+ align:start position:0%
+senses building on each other's ideas
+too, right? There's something in the
+
+ align:start position:0%
+too, right? There's something in the
+ 
+
+ align:start position:0%
+too, right? There's something in the
+physical kind of passing of the ball
+
+ align:start position:0%
+physical kind of passing of the ball
+ 
+
+ align:start position:0%
+physical kind of passing of the ball
+after you've heard someone's idea that
+
+ align:start position:0%
+after you've heard someone's idea that
+ 
+
+ align:start position:0%
+after you've heard someone's idea that
+might encourage that sort of synthesis
+
+ align:start position:0%
+might encourage that sort of synthesis
+ 
+
+ align:start position:0%
+might encourage that sort of synthesis
+of ideas as you're going. Um I will be
+
+ align:start position:0%
+of ideas as you're going. Um I will be
+ 
+
+ align:start position:0%
+of ideas as you're going. Um I will be
+your fearless leader. Um all that means
+
+ align:start position:0%
+your fearless leader. Um all that means
+ 
+
+ align:start position:0%
+your fearless leader. Um all that means
+is I just kind of make sure you're not
+
+ align:start position:0%
+is I just kind of make sure you're not
+ 
+
+ align:start position:0%
+is I just kind of make sure you're not
+interrupting each other. Um uh and we're
+
+ align:start position:0%
+interrupting each other. Um uh and we're
+ 
+
+ align:start position:0%
+interrupting each other. Um uh and we're
+going to brainstorm solutions to uh a a
+
+ align:start position:0%
+going to brainstorm solutions to uh a a
+ 
+
+ align:start position:0%
+going to brainstorm solutions to uh a a
+design problem. Uh this one I think is
+
+ align:start position:0%
+design problem. Uh this one I think is
+ 
+
+ align:start position:0%
+design problem. Uh this one I think is
+actually a lot of fun. Um so I will show
+
+ align:start position:0%
+actually a lot of fun. Um so I will show
+ 
+
+ align:start position:0%
+actually a lot of fun. Um so I will show
+you the design problem. I will maybe
+
+ align:start position:0%
+you the design problem. I will maybe
+ 
+
+ align:start position:0%
+you the design problem. I will maybe
+throw out an idea and then I will toss
+
+ align:start position:0%
+throw out an idea and then I will toss
+ 
+
+ align:start position:0%
+throw out an idea and then I will toss
+the con shell to first person who wants
+
+ align:start position:0%
+the con shell to first person who wants
+ 
+
+ align:start position:0%
+the con shell to first person who wants
+it and then it doesn't have to come back
+
+ align:start position:0%
+it and then it doesn't have to come back
+ 
+
+ align:start position:0%
+it and then it doesn't have to come back
+to me. Just anyone who wants it throw up
+
+ align:start position:0%
+to me. Just anyone who wants it throw up
+ 
+
+ align:start position:0%
+to me. Just anyone who wants it throw up
+your hand and we'll kind of keep moving
+
+ align:start position:0%
+your hand and we'll kind of keep moving
+ 
+
+ align:start position:0%
+your hand and we'll kind of keep moving
+around. Please close the lids on your
+
+ align:start position:0%
+around. Please close the lids on your
+ 
+
+ align:start position:0%
+around. Please close the lids on your
+drinks.
+
+ align:start position:0%
+drinks.
+ 
+
+ align:start position:0%
+drinks.
+put put away put away your crystal stuff
+
+ align:start position:0%
+put put away put away your crystal stuff
+ 
+
+ align:start position:0%
+put put away put away your crystal stuff
+that you don't want to shatter. Um, so
+
+ align:start position:0%
+that you don't want to shatter. Um, so
+ 
+
+ align:start position:0%
+that you don't want to shatter. Um, so
+we will take approximately 15 minutes on
+
+ align:start position:0%
+we will take approximately 15 minutes on
+ 
+
+ align:start position:0%
+we will take approximately 15 minutes on
+this. We'll see how our momentum goes.
+
+ align:start position:0%
+this. We'll see how our momentum goes.
+ 
+
+ align:start position:0%
+this. We'll see how our momentum goes.
+Um, so you just finished updating Tetris
+
+ align:start position:0%
+Um, so you just finished updating Tetris
+ 
+
+ align:start position:0%
+Um, so you just finished updating Tetris
+for Xbox Live Arcade. Awesome. I don't
+
+ align:start position:0%
+for Xbox Live Arcade. Awesome. I don't
+ 
+
+ align:start position:0%
+for Xbox Live Arcade. Awesome. I don't
+know how you got the rights, but that's
+
+ align:start position:0%
+know how you got the rights, but that's
+ 
+
+ align:start position:0%
+know how you got the rights, but that's
+great. Um, Microsoft is demanding a set
+
+ align:start position:0%
+great. Um, Microsoft is demanding a set
+ 
+
+ align:start position:0%
+great. Um, Microsoft is demanding a set
+of achievements uh for integrating the
+
+ align:start position:0%
+of achievements uh for integrating the
+ 
+
+ align:start position:0%
+of achievements uh for integrating the
+game into their online service because
+
+ align:start position:0%
+game into their online service because
+ 
+
+ align:start position:0%
+game into their online service because
+unless you have achievements, it's not a
+
+ align:start position:0%
+unless you have achievements, it's not a
+ 
+
+ align:start position:0%
+unless you have achievements, it's not a
+real game. Um,
+
+ align:start position:0%
+real game. Um,
+ 
+
+ align:start position:0%
+real game. Um,
+so we are going to brainstorm possible
+
+ align:start position:0%
+so we are going to brainstorm possible
+ 
+
+ align:start position:0%
+so we are going to brainstorm possible
+player achievements uh for your new
+
+ align:start position:0%
+player achievements uh for your new
+ 
+
+ align:start position:0%
+player achievements uh for your new
+version of Tetris. You know what
+
+ align:start position:0%
+version of Tetris. You know what
+ 
+
+ align:start position:0%
+version of Tetris. You know what
+achievements are, right? Those little
+
+ align:start position:0%
+achievements are, right? Those little
+ 
+
+ align:start position:0%
+achievements are, right? Those little
+things that pop up on your Xbox every
+
+ align:start position:0%
+things that pop up on your Xbox every
+ 
+
+ align:start position:0%
+things that pop up on your Xbox every
+time you do anything. Um, so that is our
+
+ align:start position:0%
+time you do anything. Um, so that is our
+ 
+
+ align:start position:0%
+time you do anything. Um, so that is our
+idea for Tetris achievements. And I'll
+
+ align:start position:0%
+idea for Tetris achievements. And I'll
+ 
+
+ align:start position:0%
+idea for Tetris achievements. And I'll
+start. Uh, how about for actually
+
+ align:start position:0%
+start. Uh, how about for actually
+ 
+
+ align:start position:0%
+start. Uh, how about for actually
+getting four lines? You get a Tetris
+
+ align:start position:0%
+getting four lines? You get a Tetris
+ 
+
+ align:start position:0%
+getting four lines? You get a Tetris
+achievement must be next.
+
+ align:start position:0%
+achievement must be next.
+ 
+
+ align:start position:0%
+achievement must be next.
+>> Uh, you get an achievement for losing as
+
+ align:start position:0%
+>> Uh, you get an achievement for losing as
+ 
+
+ align:start position:0%
+>> Uh, you get an achievement for losing as
+quickly as possible, which I think would
+
+ align:start position:0%
+quickly as possible, which I think would
+ 
+
+ align:start position:0%
+quickly as possible, which I think would
+just be like Very good.
+
+ align:start position:0%
+just be like Very good.
+ 
+
+ align:start position:0%
+just be like Very good.
+>> Getting three lines with S piece.
+
+ align:start position:0%
+>> Getting three lines with S piece.
+ 
+
+ align:start position:0%
+>> Getting three lines with S piece.
+>> Uh drawing some sort of unique little
+
+ align:start position:0%
+>> Uh drawing some sort of unique little
+ 
+
+ align:start position:0%
+>> Uh drawing some sort of unique little
+picture with the Tetris blocks like uh
+
+ align:start position:0%
+picture with the Tetris blocks like uh
+ 
+
+ align:start position:0%
+picture with the Tetris blocks like uh
+you know something perhaps
+
+ align:start position:0%
+you know something perhaps
+ 
+
+ align:start position:0%
+you know something perhaps
+>> putting one of each block down.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Uh lasting for a certain amount of time
+
+ align:start position:0%
+>> Uh lasting for a certain amount of time
+ 
+
+ align:start position:0%
+>> Uh lasting for a certain amount of time
+without them ever getting above a
+
+ align:start position:0%
+without them ever getting above a
+ 
+
+ align:start position:0%
+without them ever getting above a
+certain height.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a certain amount of time without ever
+
+ align:start position:0%
+a certain amount of time without ever
+ 
+
+ align:start position:0%
+a certain amount of time without ever
+rotating a piece.
+
+ align:start position:0%
+rotating a piece.
+ 
+
+ align:start position:0%
+rotating a piece.
+>> Modern Tetris games have a system where
+
+ align:start position:0%
+>> Modern Tetris games have a system where
+ 
+
+ align:start position:0%
+>> Modern Tetris games have a system where
+you can rotate indefinitely when your
+
+ align:start position:0%
+you can rotate indefinitely when your
+ 
+
+ align:start position:0%
+you can rotate indefinitely when your
+piece is down. So, you rotate
+
+ align:start position:0%
+piece is down. So, you rotate
+ 
+
+ align:start position:0%
+piece is down. So, you rotate
+indefinitely for a minute or two or
+
+ align:start position:0%
+indefinitely for a minute or two or
+ 
+
+ align:start position:0%
+indefinitely for a minute or two or
+three minutes.
+
+ align:start position:0%
+three minutes.
+ 
+
+ align:start position:0%
+three minutes.
+>> Lasting a certain amount of time without
+
+ align:start position:0%
+>> Lasting a certain amount of time without
+ 
+
+ align:start position:0%
+>> Lasting a certain amount of time without
+ever clearing a line with a straight
+
+ align:start position:0%
+ever clearing a line with a straight
+ 
+
+ align:start position:0%
+ever clearing a line with a straight
+piece.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Putting your piece down underneath
+
+ align:start position:0%
+Putting your piece down underneath
+ 
+
+ align:start position:0%
+Putting your piece down underneath
+another piece
+
+ align:start position:0%
+another piece
+ 
+
+ align:start position:0%
+another piece
+>> into a little hole.
+
+ align:start position:0%
+>> into a little hole.
+ 
+
+ align:start position:0%
+>> into a little hole.
+>> The teeth.
+
+ align:start position:0%
+>> The teeth.
+ 
+
+ align:start position:0%
+>> The teeth.
+>> There you go. Spelling USSR with your
+
+ align:start position:0%
+>> There you go. Spelling USSR with your
+ 
+
+ align:start position:0%
+>> There you go. Spelling USSR with your
+pieces.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> How's the bathroom?
+
+ align:start position:0%
+>> How's the bathroom?
+ 
+
+ align:start position:0%
+>> How's the bathroom?
+>> Um, making like a congeration of all the
+
+ align:start position:0%
+>> Um, making like a congeration of all the
+ 
+
+ align:start position:0%
+>> Um, making like a congeration of all the
+pieces into like the shape of a regular
+
+ align:start position:0%
+pieces into like the shape of a regular
+ 
+
+ align:start position:0%
+pieces into like the shape of a regular
+piece.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Very cool.
+
+ align:start position:0%
+>> Very cool.
+ 
+
+ align:start position:0%
+>> Very cool.
+Uh, basically only moving the pieces in
+
+ align:start position:0%
+Uh, basically only moving the pieces in
+ 
+
+ align:start position:0%
+Uh, basically only moving the pieces in
+B to the music that's playing
+
+ align:start position:0%
+B to the music that's playing
+ 
+
+ align:start position:0%
+B to the music that's playing
+>> spelling your say with your pieces. I
+
+ align:start position:0%
+>> spelling your say with your pieces. I
+ 
+
+ align:start position:0%
+>> spelling your say with your pieces. I
+don't know if it's possible, but doing
+
+ align:start position:0%
+don't know if it's possible, but doing
+ 
+
+ align:start position:0%
+don't know if it's possible, but doing
+it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Uh, high score and high score without
+
+ align:start position:0%
+>> Uh, high score and high score without
+ 
+
+ align:start position:0%
+>> Uh, high score and high score without
+clearing lines.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Uh, managing to clear the entire board
+
+ align:start position:0%
+>> Uh, managing to clear the entire board
+ 
+
+ align:start position:0%
+>> Uh, managing to clear the entire board
+in a game that has already reached the
+
+ align:start position:0%
+in a game that has already reached the
+ 
+
+ align:start position:0%
+in a game that has already reached the
+top line but not quite.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+putting a piece down without actually uh
+
+ align:start position:0%
+putting a piece down without actually uh
+ 
+
+ align:start position:0%
+putting a piece down without actually uh
+looking at the piece at all.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Most pieces per time.
+
+ align:start position:0%
+>> Most pieces per time.
+ 
+
+ align:start position:0%
+>> Most pieces per time.
+>> Sure.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> One day of continuous tetris
+
+ align:start position:0%
+>> One day of continuous tetris
+ 
+
+ align:start position:0%
+>> One day of continuous tetris
+marathon
+
+ align:start position:0%
+marathon
+ 
+
+ align:start position:0%
+marathon
+>> breaking the previous high.
+
+ align:start position:0%
+>> breaking the previous high.
+ 
+
+ align:start position:0%
+>> breaking the previous high.
+Only ever shifting pieces either right
+
+ align:start position:0%
+Only ever shifting pieces either right
+ 
+
+ align:start position:0%
+Only ever shifting pieces either right
+or the left the entire game.
+
+ align:start position:0%
+or the left the entire game.
+ 
+
+ align:start position:0%
+or the left the entire game.
+>> Ah,
+
+ align:start position:0%
+>> Ah,
+ 
+
+ align:start position:0%
+>> Ah,
+>> doing the marathon challenge but only
+
+ align:start position:0%
+>> doing the marathon challenge but only
+ 
+
+ align:start position:0%
+>> doing the marathon challenge but only
+listening to one piece of music the
+
+ align:start position:0%
+listening to one piece of music the
+ 
+
+ align:start position:0%
+listening to one piece of music the
+entire time.
+
+ align:start position:0%
+entire time.
+ 
+
+ align:start position:0%
+entire time.
+>> The same
+
+ align:start position:0%
+>> The same
+ 
+
+ align:start position:0%
+>> The same
+>> clearing a level by dropping pieces
+
+ align:start position:0%
+>> clearing a level by dropping pieces
+ 
+
+ align:start position:0%
+>> clearing a level by dropping pieces
+before they fall five spaces.
+
+ align:start position:0%
+before they fall five spaces.
+ 
+
+ align:start position:0%
+before they fall five spaces.
+>> All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Rotating every single piece that you
+
+ align:start position:0%
+>> Rotating every single piece that you
+ 
+
+ align:start position:0%
+>> Rotating every single piece that you
+play.
+
+ align:start position:0%
+play.
+ 
+
+ align:start position:0%
+play.
+>> Oh, very good.
+
+ align:start position:0%
+>> Oh, very good.
+ 
+
+ align:start position:0%
+>> Oh, very good.
+uh never going above a certain line for
+
+ align:start position:0%
+uh never going above a certain line for
+ 
+
+ align:start position:0%
+uh never going above a certain line for
+a certain amount of time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> All of the above but on different equity
+
+ align:start position:0%
+>> All of the above but on different equity
+ 
+
+ align:start position:0%
+>> All of the above but on different equity
+levels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> uh clearing three lines with a T.
+
+ align:start position:0%
+>> uh clearing three lines with a T.
+ 
+
+ align:start position:0%
+>> uh clearing three lines with a T.
+>> Sure.
+
+ align:start position:0%
+>> Sure.
+ 
+
+ align:start position:0%
+>> Sure.
+>> Starting up the game,
+
+ align:start position:0%
+>> Starting up the game,
+ 
+
+ align:start position:0%
+>> Starting up the game,
+>> clearing a kind of screen
+
+ align:start position:0%
+>> clearing a kind of screen
+ 
+
+ align:start position:0%
+>> clearing a kind of screen
+>> using the L block.
+
+ align:start position:0%
+>> using the L block.
+ 
+
+ align:start position:0%
+>> using the L block.
+Doesn't matter how.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+different color. So, you know, lines
+
+ align:start position:0%
+different color. So, you know, lines
+ 
+
+ align:start position:0%
+different color. So, you know, lines
+always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> rotating a piece 720°
+
+ align:start position:0%
+>> rotating a piece 720°
+ 
+
+ align:start position:0%
+>> rotating a piece 720°
+>> only matching pieces such that the new
+
+ align:start position:0%
+>> only matching pieces such that the new
+ 
+
+ align:start position:0%
+>> only matching pieces such that the new
+blocks that fall down are touching
+
+ align:start position:0%
+blocks that fall down are touching
+ 
+
+ align:start position:0%
+blocks that fall down are touching
+blocks of the same color.
+
+ align:start position:0%
+blocks of the same color.
+ 
+
+ align:start position:0%
+blocks of the same color.
+>> Clear two four block segments with two
+
+ align:start position:0%
+>> Clear two four block segments with two
+ 
+
+ align:start position:0%
+>> Clear two four block segments with two
+consecutive uh lines.
+
+ align:start position:0%
+consecutive uh lines.
+ 
+
+ align:start position:0%
+consecutive uh lines.
+Uh, clearing a level using only
+
+ align:start position:0%
+Uh, clearing a level using only
+ 
+
+ align:start position:0%
+Uh, clearing a level using only
+tetrises.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Sorry, you can't talk anymore.
+
+ align:start position:0%
+>> Sorry, you can't talk anymore.
+ 
+
+ align:start position:0%
+>> Sorry, you can't talk anymore.
+>> Challenging somebody on your friends
+
+ align:start position:0%
+>> Challenging somebody on your friends
+ 
+
+ align:start position:0%
+>> Challenging somebody on your friends
+list to beat the score.
+
+ align:start position:0%
+list to beat the score.
+ 
+
+ align:start position:0%
+list to beat the score.
+>> Um, fighting against someone on friends
+
+ align:start position:0%
+>> Um, fighting against someone on friends
+ 
+
+ align:start position:0%
+>> Um, fighting against someone on friends
+list to lose faster.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Having no holes in the block for
+
+ align:start position:0%
+>> Having no holes in the block for
+ 
+
+ align:start position:0%
+>> Having no holes in the block for
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Uh, inviting a friend on one of your
+
+ align:start position:0%
+Uh, inviting a friend on one of your
+ 
+
+ align:start position:0%
+Uh, inviting a friend on one of your
+Xbox Live friends to play with you.
+
+ align:start position:0%
+Xbox Live friends to play with you.
+ 
+
+ align:start position:0%
+Xbox Live friends to play with you.
+>> Five consecutive line clears.
+
+ align:start position:0%
+>> Five consecutive line clears.
+ 
+
+ align:start position:0%
+>> Five consecutive line clears.
+>> Beating one of your friends on Xbox Live
+
+ align:start position:0%
+>> Beating one of your friends on Xbox Live
+ 
+
+ align:start position:0%
+>> Beating one of your friends on Xbox Live
+when you play with them.
+
+ align:start position:0%
+when you play with them.
+ 
+
+ align:start position:0%
+when you play with them.
+>> Losing to a friend on Xbox Live.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Playing with a friend for one hour
+
+ align:start position:0%
+>> Playing with a friend for one hour
+ 
+
+ align:start position:0%
+>> Playing with a friend for one hour
+continuously one day.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beating a score set by the original
+
+ align:start position:0%
+Beating a score set by the original
+ 
+
+ align:start position:0%
+Beating a score set by the original
+creator of Tetris.
+
+ align:start position:0%
+creator of Tetris.
+ 
+
+ align:start position:0%
+creator of Tetris.
+>> Clearing a line somewhere above the
+
+ align:start position:0%
+>> Clearing a line somewhere above the
+ 
+
+ align:start position:0%
+>> Clearing a line somewhere above the
+first line. The first line only has one
+
+ align:start position:0%
+first line. The first line only has one
+ 
+
+ align:start position:0%
+first line. The first line only has one
+block filled in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I think it definitely is.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Someone's going to have ideas. There's
+
+ align:start position:0%
+>> Someone's going to have ideas. There's
+ 
+
+ align:start position:0%
+>> Someone's going to have ideas. There's
+an idea.
+
+ align:start position:0%
+an idea.
+ 
+
+ align:start position:0%
+an idea.
+lose all the telem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> losing 100 times.
+
+ align:start position:0%
+>> losing 100 times.
+ 
+
+ align:start position:0%
+>> losing 100 times.
+>> Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Playing on increasingly ridiculous
+
+ align:start position:0%
+>> Playing on increasingly ridiculous
+ 
+
+ align:start position:0%
+>> Playing on increasingly ridiculous
+difficulties with achievements for each
+
+ align:start position:0%
+difficulties with achievements for each
+ 
+
+ align:start position:0%
+difficulties with achievements for each
+four speeds.
+
+ align:start position:0%
+four speeds.
+ 
+
+ align:start position:0%
+four speeds.
+using the speed
+
+ align:start position:0%
+using the speed
+ 
+
+ align:start position:0%
+using the speed
+>> completing a Tetris challenge, which is
+
+ align:start position:0%
+>> completing a Tetris challenge, which is
+ 
+
+ align:start position:0%
+>> completing a Tetris challenge, which is
+presumably some kind of thing where you
+
+ align:start position:0%
+presumably some kind of thing where you
+ 
+
+ align:start position:0%
+presumably some kind of thing where you
+have to drop blocks in the right
+
+ align:start position:0%
+have to drop blocks in the right
+ 
+
+ align:start position:0%
+have to drop blocks in the right
+sequence in order to clear all the
+
+ align:start position:0%
+sequence in order to clear all the
+ 
+
+ align:start position:0%
+sequence in order to clear all the
+lines. Yeah.
+
+ align:start position:0%
+lines. Yeah.
+ 
+
+ align:start position:0%
+lines. Yeah.
+>> Clearing a thousand lines.
+
+ align:start position:0%
+>> Clearing a thousand lines.
+ 
+
+ align:start position:0%
+>> Clearing a thousand lines.
+>> Uh playing invisible mode.
+
+ align:start position:0%
+>> Uh playing invisible mode.
+ 
+
+ align:start position:0%
+>> Uh playing invisible mode.
+>> Uh playing for a certain amount of time
+
+ align:start position:0%
+>> Uh playing for a certain amount of time
+ 
+
+ align:start position:0%
+>> Uh playing for a certain amount of time
+while holding down the down key
+
+ align:start position:0%
+while holding down the down key
+ 
+
+ align:start position:0%
+while holding down the down key
+continuously.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I don't know if you only rotating in one
+
+ align:start position:0%
+>> I don't know if you only rotating in one
+ 
+
+ align:start position:0%
+>> I don't know if you only rotating in one
+direction always. I don't know if
+
+ align:start position:0%
+direction always. I don't know if
+ 
+
+ align:start position:0%
+direction always. I don't know if
+someone said that or not.
+
+ align:start position:0%
+someone said that or not.
+ 
+
+ align:start position:0%
+someone said that or not.
+>> Getting 10 achievements in Tetris.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Getting every achievement in
+
+ align:start position:0%
+>> Getting every achievement in
+ 
+
+ align:start position:0%
+>> Getting every achievement in
+>> the Tetris.
+
+ align:start position:0%
+>> the Tetris.
+ 
+
+ align:start position:0%
+>> the Tetris.
+>> Oh no. How can you get it?
+
+ align:start position:0%
+>> Oh no. How can you get it?
+ 
+
+ align:start position:0%
+>> Oh no. How can you get it?
+>> It's a paradox. It's impossible.
+
+ align:start position:0%
+>> It's a paradox. It's impossible.
+ 
+
+ align:start position:0%
+>> It's a paradox. It's impossible.
+>> Always having blocks on the far left and
+
+ align:start position:0%
+>> Always having blocks on the far left and
+ 
+
+ align:start position:0%
+>> Always having blocks on the far left and
+on the far right column.
+
+ align:start position:0%
+on the far right column.
+ 
+
+ align:start position:0%
+on the far right column.
+Cool.
+
+ align:start position:0%
+Cool.
+ 
+
+ align:start position:0%
+Cool.
+I think that that had some that had some
+
+ align:start position:0%
+I think that that had some that had some
+ 
+
+ align:start position:0%
+I think that that had some that had some
+decent momentum, but you know, I think
+
+ align:start position:0%
+decent momentum, but you know, I think
+ 
+
+ align:start position:0%
+decent momentum, but you know, I think
+like our mission was accomplished,
+
+ align:start position:0%
+like our mission was accomplished,
+ 
+
+ align:start position:0%
+like our mission was accomplished,
+right? Like we were really only giving
+
+ align:start position:0%
+right? Like we were really only giving
+ 
+
+ align:start position:0%
+right? Like we were really only giving
+one idea at a time because it was only
+
+ align:start position:0%
+one idea at a time because it was only
+ 
+
+ align:start position:0%
+one idea at a time because it was only
+the person who had the ball was talking.
+
+ align:start position:0%
+the person who had the ball was talking.
+ 
+
+ align:start position:0%
+the person who had the ball was talking.
+Um that, you know, probably with a
+
+ align:start position:0%
+Um that, you know, probably with a
+ 
+
+ align:start position:0%
+Um that, you know, probably with a
+little bit more speed and momentum, but
+
+ align:start position:0%
+little bit more speed and momentum, but
+ 
+
+ align:start position:0%
+little bit more speed and momentum, but
+it was nice. Like we did had a little
+
+ align:start position:0%
+it was nice. Like we did had a little
+ 
+
+ align:start position:0%
+it was nice. Like we did had a little
+building on ideas. You know, we're
+
+ align:start position:0%
+building on ideas. You know, we're
+ 
+
+ align:start position:0%
+building on ideas. You know, we're
+starting to get this kind of brainstorm.
+
+ align:start position:0%
+starting to get this kind of brainstorm.
+ 
+
+ align:start position:0%
+starting to get this kind of brainstorm.
+There was still some shyness, which is,
+
+ align:start position:0%
+There was still some shyness, which is,
+ 
+
+ align:start position:0%
+There was still some shyness, which is,
+you know, people have different
+
+ align:start position:0%
+you know, people have different
+ 
+
+ align:start position:0%
+you know, people have different
+personalities, but stop being shy.
+
+ align:start position:0%
+personalities, but stop being shy.
+ 
+
+ align:start position:0%
+personalities, but stop being shy.
+You're allowed to have your different
+
+ align:start position:0%
+You're allowed to have your different
+ 
+
+ align:start position:0%
+You're allowed to have your different
+personalities, but stop it. No. Um, so
+
+ align:start position:0%
+personalities, but stop it. No. Um, so
+ 
+
+ align:start position:0%
+personalities, but stop it. No. Um, so
+that's activity number two. Um,
+
+ align:start position:0%
+that's activity number two. Um,
+ 
+
+ align:start position:0%
+that's activity number two. Um,
+any questions about that process? How do
+
+ align:start position:0%
+any questions about that process? How do
+ 
+
+ align:start position:0%
+any questions about that process? How do
+you feel about it? Any thoughts on it
+
+ align:start position:0%
+you feel about it? Any thoughts on it
+ 
+
+ align:start position:0%
+you feel about it? Any thoughts on it
+before we go on to the next activity?
+
+ align:start position:0%
+before we go on to the next activity?
+ 
+
+ align:start position:0%
+before we go on to the next activity?
+>> All right, next activity. Actually, this
+
+ align:start position:0%
+>> All right, next activity. Actually, this
+ 
+
+ align:start position:0%
+>> All right, next activity. Actually, this
+might be this is our last activity.
+
+ align:start position:0%
+might be this is our last activity.
+ 
+
+ align:start position:0%
+might be this is our last activity.
+Sorry, I said, but there's only three.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Um, okay. So, this one is a more formal
+
+ align:start position:0%
+>> Um, okay. So, this one is a more formal
+ 
+
+ align:start position:0%
+>> Um, okay. So, this one is a more formal
+uh a more formal uh brainstorm. And
+
+ align:start position:0%
+uh a more formal uh brainstorm. And
+ 
+
+ align:start position:0%
+uh a more formal uh brainstorm. And
+actually, I screwed up that last one. We
+
+ align:start position:0%
+actually, I screwed up that last one. We
+ 
+
+ align:start position:0%
+actually, I screwed up that last one. We
+didn't have a secretary. So all of those
+
+ align:start position:0%
+didn't have a secretary. So all of those
+ 
+
+ align:start position:0%
+didn't have a secretary. So all of those
+great Tetris ideas are now lost. I can't
+
+ align:start position:0%
+great Tetris ideas are now lost. I can't
+ 
+
+ align:start position:0%
+great Tetris ideas are now lost. I can't
+remember any.
+
+ align:start position:0%
+remember any.
+ 
+
+ align:start position:0%
+remember any.
+>> Oh yes.
+
+ align:start position:0%
+>> Oh yes.
+ 
+
+ align:start position:0%
+>> Oh yes.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+>> Do we not have that 1950s or something?
+
+ align:start position:0%
+>> Do we not have that 1950s or something?
+ 
+
+ align:start position:0%
+>> Do we not have that 1950s or something?
+>> Let me just get these waxers.
+
+ align:start position:0%
+>> Let me just get these waxers.
+ 
+
+ align:start position:0%
+>> Let me just get these waxers.
+So uh what we're going to do is we're
+
+ align:start position:0%
+So uh what we're going to do is we're
+ 
+
+ align:start position:0%
+So uh what we're going to do is we're
+going to separate the two design teams.
+
+ align:start position:0%
+going to separate the two design teams.
+ 
+
+ align:start position:0%
+going to separate the two design teams.
+Um so it'll just totally be by by
+
+ align:start position:0%
+Um so it'll just totally be by by
+ 
+
+ align:start position:0%
+Um so it'll just totally be by by
+location. We'll just kind of get half of
+
+ align:start position:0%
+location. We'll just kind of get half of
+ 
+
+ align:start position:0%
+location. We'll just kind of get half of
+you over here and half of you over
+
+ align:start position:0%
+you over here and half of you over
+ 
+
+ align:start position:0%
+you over here and half of you over
+there. Um, I want the team to designate
+
+ align:start position:0%
+there. Um, I want the team to designate
+ 
+
+ align:start position:0%
+there. Um, I want the team to designate
+one leader. That's gonna be the person
+
+ align:start position:0%
+one leader. That's gonna be the person
+ 
+
+ align:start position:0%
+one leader. That's gonna be the person
+who's responsible. Clerk for
+
+ align:start position:0%
+who's responsible. Clerk for
+ 
+
+ align:start position:0%
+who's responsible. Clerk for
+facilitating it. Oh, did I say clerk
+
+ align:start position:0%
+facilitating it. Oh, did I say clerk
+ 
+
+ align:start position:0%
+facilitating it. Oh, did I say clerk
+there? A leader and a secretary. It's
+
+ align:start position:0%
+there? A leader and a secretary. It's
+ 
+
+ align:start position:0%
+there? A leader and a secretary. It's
+supposed to be a clerk, leader, and a
+
+ align:start position:0%
+supposed to be a clerk, leader, and a
+ 
+
+ align:start position:0%
+supposed to be a clerk, leader, and a
+secretary. Um, so one person to write
+
+ align:start position:0%
+secretary. Um, so one person to write
+ 
+
+ align:start position:0%
+secretary. Um, so one person to write
+everything down, one person to obviously
+
+ align:start position:0%
+everything down, one person to obviously
+ 
+
+ align:start position:0%
+everything down, one person to obviously
+facilitate and and we're going to do a
+
+ align:start position:0%
+facilitate and and we're going to do a
+ 
+
+ align:start position:0%
+facilitate and and we're going to do a
+we're going to do a kind of a 20 or so
+
+ align:start position:0%
+we're going to do a kind of a 20 or so
+ 
+
+ align:start position:0%
+we're going to do a kind of a 20 or so
+minute uh brainstorm uh for a game
+
+ align:start position:0%
+minute uh brainstorm uh for a game
+ 
+
+ align:start position:0%
+minute uh brainstorm uh for a game
+pitch. Um, what do I mean by game pitch?
+
+ align:start position:0%
+pitch. Um, what do I mean by game pitch?
+ 
+
+ align:start position:0%
+pitch. Um, what do I mean by game pitch?
+It's kind of think of the uh think of
+
+ align:start position:0%
+It's kind of think of the uh think of
+ 
+
+ align:start position:0%
+It's kind of think of the uh think of
+the you're in an elevator with Miiamoto
+
+ align:start position:0%
+the you're in an elevator with Miiamoto
+ 
+
+ align:start position:0%
+the you're in an elevator with Miiamoto
+or you're in an elevator with you know
+
+ align:start position:0%
+or you're in an elevator with you know
+ 
+
+ align:start position:0%
+or you're in an elevator with you know
+Philip Han and uh you have this game
+
+ align:start position:0%
+Philip Han and uh you have this game
+ 
+
+ align:start position:0%
+Philip Han and uh you have this game
+idea that you need to pitch but you're
+
+ align:start position:0%
+idea that you need to pitch but you're
+ 
+
+ align:start position:0%
+idea that you need to pitch but you're
+only going to the 10th floor or so and
+
+ align:start position:0%
+only going to the 10th floor or so and
+ 
+
+ align:start position:0%
+only going to the 10th floor or so and
+so really you've got like 30 seconds a
+
+ align:start position:0%
+so really you've got like 30 seconds a
+ 
+
+ align:start position:0%
+so really you've got like 30 seconds a
+minute 2 minutes maybe um to kind of get
+
+ align:start position:0%
+minute 2 minutes maybe um to kind of get
+ 
+
+ align:start position:0%
+minute 2 minutes maybe um to kind of get
+the core information about this game
+
+ align:start position:0%
+the core information about this game
+ 
+
+ align:start position:0%
+the core information about this game
+app. Um so that can be something like a
+
+ align:start position:0%
+app. Um so that can be something like a
+ 
+
+ align:start position:0%
+app. Um so that can be something like a
+title maybe a tagline for it um any main
+
+ align:start position:0%
+title maybe a tagline for it um any main
+ 
+
+ align:start position:0%
+title maybe a tagline for it um any main
+features uh you might have for it. Um,
+
+ align:start position:0%
+features uh you might have for it. Um,
+ 
+
+ align:start position:0%
+features uh you might have for it. Um,
+of course it would be way too easy or
+
+ align:start position:0%
+of course it would be way too easy or
+ 
+
+ align:start position:0%
+of course it would be way too easy or
+way actually crazy for me to be like any
+
+ align:start position:0%
+way actually crazy for me to be like any
+ 
+
+ align:start position:0%
+way actually crazy for me to be like any
+game at all because there's lots of
+
+ align:start position:0%
+game at all because there's lots of
+ 
+
+ align:start position:0%
+game at all because there's lots of
+different types of games obviously. So
+
+ align:start position:0%
+different types of games obviously. So
+ 
+
+ align:start position:0%
+different types of games obviously. So
+it's going to be a game based on the
+
+ align:start position:0%
+it's going to be a game based on the
+ 
+
+ align:start position:0%
+it's going to be a game based on the
+following constraint. So what I'd like
+
+ align:start position:0%
+following constraint. So what I'd like
+ 
+
+ align:start position:0%
+following constraint. So what I'd like
+to do first before I give you the
+
+ align:start position:0%
+to do first before I give you the
+ 
+
+ align:start position:0%
+to do first before I give you the
+constraint is let's divide ourselves in
+
+ align:start position:0%
+constraint is let's divide ourselves in
+ 
+
+ align:start position:0%
+constraint is let's divide ourselves in
+half. We can kind of draw this like
+
+ align:start position:0%
+half. We can kind of draw this like
+ 
+
+ align:start position:0%
+half. We can kind of draw this like
+imaginary line diagonally dividing the
+
+ align:start position:0%
+imaginary line diagonally dividing the
+ 
+
+ align:start position:0%
+imaginary line diagonally dividing the
+two of you back there and and we'll just
+
+ align:start position:0%
+two of you back there and and we'll just
+ 
+
+ align:start position:0%
+two of you back there and and we'll just
+get we just get one half here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And once I give you the constraint,
+
+ align:start position:0%
+And once I give you the constraint,
+ 
+
+ align:start position:0%
+And once I give you the constraint,
+we'll actually find a separate room for
+
+ align:start position:0%
+we'll actually find a separate room for
+ 
+
+ align:start position:0%
+we'll actually find a separate room for
+for the other team for one of the teams.
+
+ align:start position:0%
+for the other team for one of the teams.
+ 
+
+ align:start position:0%
+for the other team for one of the teams.
+>> You're stuck on the little wire.
+
+ align:start position:0%
+>> You're stuck on the little wire.
+ 
+
+ align:start position:0%
+>> You're stuck on the little wire.
+>> That's an achievement right there.
+
+ align:start position:0%
+>> That's an achievement right there.
+ 
+
+ align:start position:0%
+>> That's an achievement right there.
+>> I always think that when I'm watching my
+
+ align:start position:0%
+>> I always think that when I'm watching my
+ 
+
+ align:start position:0%
+>> I always think that when I'm watching my
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+think like something happens,
+
+ align:start position:0%
+think like something happens,
+ 
+
+ align:start position:0%
+think like something happens,
+>> especially when someone
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you watch this movie.
+
+ align:start position:0%
+you watch this movie.
+ 
+
+ align:start position:0%
+you watch this movie.
+If someone has a piece of paper, they
+
+ align:start position:0%
+If someone has a piece of paper, they
+ 
+
+ align:start position:0%
+If someone has a piece of paper, they
+can down there, right?
+
+ align:start position:0%
+can down there, right?
+ 
+
+ align:start position:0%
+can down there, right?
+>> Yeah, just write out a piece of paper.
+
+ align:start position:0%
+>> Yeah, just write out a piece of paper.
+ 
+
+ align:start position:0%
+>> Yeah, just write out a piece of paper.
+So, um, so these are your teams. You
+
+ align:start position:0%
+So, um, so these are your teams. You
+ 
+
+ align:start position:0%
+So, um, so these are your teams. You
+guys will go into that room. You guys
+
+ align:start position:0%
+guys will go into that room. You guys
+ 
+
+ align:start position:0%
+guys will go into that room. You guys
+stay out here. Um, as soon as I give you
+
+ align:start position:0%
+stay out here. Um, as soon as I give you
+ 
+
+ align:start position:0%
+stay out here. Um, as soon as I give you
+the constraint, designate a designate a
+
+ align:start position:0%
+the constraint, designate a designate a
+ 
+
+ align:start position:0%
+the constraint, designate a designate a
+clerk/ leader, um, leader and a
+
+ align:start position:0%
+clerk/ leader, um, leader and a
+ 
+
+ align:start position:0%
+clerk/ leader, um, leader and a
+secretary, someone to write everything
+
+ align:start position:0%
+secretary, someone to write everything
+ 
+
+ align:start position:0%
+secretary, someone to write everything
+down because our groups are relatively
+
+ align:start position:0%
+down because our groups are relatively
+ 
+
+ align:start position:0%
+down because our groups are relatively
+small, right? We can have the leader and
+
+ align:start position:0%
+small, right? We can have the leader and
+ 
+
+ align:start position:0%
+small, right? We can have the leader and
+the uh the secretary involved in the
+
+ align:start position:0%
+the uh the secretary involved in the
+ 
+
+ align:start position:0%
+the uh the secretary involved in the
+brainstorming process. Please don't be
+
+ align:start position:0%
+brainstorming process. Please don't be
+ 
+
+ align:start position:0%
+brainstorming process. Please don't be
+afraid of contributing. But if you are
+
+ align:start position:0%
+afraid of contributing. But if you are
+ 
+
+ align:start position:0%
+afraid of contributing. But if you are
+designated as this leader, keep in mind
+
+ align:start position:0%
+designated as this leader, keep in mind
+ 
+
+ align:start position:0%
+designated as this leader, keep in mind
+your primary responsibility is
+
+ align:start position:0%
+your primary responsibility is
+ 
+
+ align:start position:0%
+your primary responsibility is
+facilitating the brainstorm. You want to
+
+ align:start position:0%
+facilitating the brainstorm. You want to
+ 
+
+ align:start position:0%
+facilitating the brainstorm. You want to
+make sure it runs smoothly. You want to
+
+ align:start position:0%
+make sure it runs smoothly. You want to
+ 
+
+ align:start position:0%
+make sure it runs smoothly. You want to
+make sure people are not criticizing
+
+ align:start position:0%
+make sure people are not criticizing
+ 
+
+ align:start position:0%
+make sure people are not criticizing
+ideas. You want to make sure that it's
+
+ align:start position:0%
+ideas. You want to make sure that it's
+ 
+
+ align:start position:0%
+ideas. You want to make sure that it's
+going okay. Any questions on this before
+
+ align:start position:0%
+going okay. Any questions on this before
+ 
+
+ align:start position:0%
+going okay. Any questions on this before
+I give you your constraints?
+
+ align:start position:0%
+I give you your constraints?
+ 
+
+ align:start position:0%
+I give you your constraints?
+Everything make sense? All good. Okay.
+
+ align:start position:0%
+Everything make sense? All good. Okay.
+ 
+
+ align:start position:0%
+Everything make sense? All good. Okay.
+Here are the constraints for the game.
+
+ align:start position:0%
+Here are the constraints for the game.
+ 
+
+ align:start position:0%
+Here are the constraints for the game.
+Uh it must have zombies. It must have a
+
+ align:start position:0%
+Uh it must have zombies. It must have a
+ 
+
+ align:start position:0%
+Uh it must have zombies. It must have a
+love. It must be massively multiplayer.
+
+ align:start position:0%
+love. It must be massively multiplayer.
+ 
+
+ align:start position:0%
+love. It must be massively multiplayer.
+Um so that those are the constraints for
+
+ align:start position:0%
+Um so that those are the constraints for
+ 
+
+ align:start position:0%
+Um so that those are the constraints for
+your game. that's what the publisher is
+
+ align:start position:0%
+your game. that's what the publisher is
+ 
+
+ align:start position:0%
+your game. that's what the publisher is
+going to give you money for. Um uh so
+
+ align:start position:0%
+going to give you money for. Um uh so
+ 
+
+ align:start position:0%
+going to give you money for. Um uh so
+you need to develop a pitch a pitch for
+
+ align:start position:0%
+you need to develop a pitch a pitch for
+ 
+
+ align:start position:0%
+you need to develop a pitch a pitch for
+this game idea. Um a title tagline what
+
+ align:start position:0%
+this game idea. Um a title tagline what
+ 
+
+ align:start position:0%
+this game idea. Um a title tagline what
+what have you. All right. So you guys
+
+ align:start position:0%
+what have you. All right. So you guys
+ 
+
+ align:start position:0%
+what have you. All right. So you guys
+we'll we'll take you in this room over
+
+ align:start position:0%
+we'll we'll take you in this room over
+ 
+
+ align:start position:0%
+we'll we'll take you in this room over
+here. You guys stay here. Designate a
+
+ align:start position:0%
+here. You guys stay here. Designate a
+ 
+
+ align:start position:0%
+here. You guys stay here. Designate a
+leader and a secretary and then start
+
+ align:start position:0%
+leader and a secretary and then start
+ 
+
+ align:start position:0%
+leader and a secretary and then start
+brainstorming.
+
+ align:start position:0%
+brainstorming.
+ 
+
+ align:start position:0%
+brainstorming.
+Secretary
+
+ align:start position:0%
+Secretary
+ 
+
+ align:start position:0%
+Secretary
+>> Oh, I love this. It's like I don't want
+
+ align:start position:0%
+>> Oh, I love this. It's like I don't want
+ 
+
+ align:start position:0%
+>> Oh, I love this. It's like I don't want
+to be the leader. I don't want to be the
+
+ align:start position:0%
+to be the leader. I don't want to be the
+ 
+
+ align:start position:0%
+to be the leader. I don't want to be the
+secretary.
+
+ align:start position:0%
+secretary.
+ 
+
+ align:start position:0%
+secretary.
+>> I said I'll do it. Oh
+
+ align:start position:0%
+>> I said I'll do it. Oh
+ 
+
+ align:start position:0%
+>> I said I'll do it. Oh
+secretary. Wait, he wanted to be the
+
+ align:start position:0%
+secretary. Wait, he wanted to be the
+ 
+
+ align:start position:0%
+secretary. Wait, he wanted to be the
+secretary.
+
+ align:start position:0%
+secretary.
+ 
+
+ align:start position:0%
+secretary.
+>> Oh, you're secretary.
+
+ align:start position:0%
+>> Oh, you're secretary.
+ 
+
+ align:start position:0%
+>> Oh, you're secretary.
+>> One of your secretary wants to use
+
+ align:start position:0%
+>> One of your secretary wants to use
+ 
+
+ align:start position:0%
+>> One of your secretary wants to use
+leader. So you get a leader then.
+
+ align:start position:0%
+leader. So you get a leader then.
+ 
+
+ align:start position:0%
+leader. So you get a leader then.
+>> Because you're interested in those game
+
+ align:start position:0%
+>> Because you're interested in those game
+ 
+
+ align:start position:0%
+>> Because you're interested in those game
+and you lost.
+
+ align:start position:0%
+and you lost.
+ 
+
+ align:start position:0%
+and you lost.
+>> Brings up the age question.
+
+ align:start position:0%
+>> Brings up the age question.
+ 
+
+ align:start position:0%
+>> Brings up the age question.
+>> If they're both vampires or they're both
+
+ align:start position:0%
+>> If they're both vampires or they're both
+ 
+
+ align:start position:0%
+>> If they're both vampires or they're both
+zombies, does it count as necessities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+manages to have
+
+ align:start position:0%
+manages to have
+ 
+
+ align:start position:0%
+manages to have
+>> encompass all of those except the
+
+ align:start position:0%
+>> encompass all of those except the
+ 
+
+ align:start position:0%
+>> encompass all of those except the
+massively multiplayer parties licensed
+
+ align:start position:0%
+massively multiplayer parties licensed
+ 
+
+ align:start position:0%
+massively multiplayer parties licensed
+title right there. Make it Nazi zombies.
+
+ align:start position:0%
+title right there. Make it Nazi zombies.
+ 
+
+ align:start position:0%
+title right there. Make it Nazi zombies.
+Two Nazi zombie. No, a forbidden love. A
+
+ align:start position:0%
+Two Nazi zombie. No, a forbidden love. A
+ 
+
+ align:start position:0%
+Two Nazi zombie. No, a forbidden love. A
+Nazi zombies in love with like an allied
+
+ align:start position:0%
+Nazi zombies in love with like an allied
+ 
+
+ align:start position:0%
+Nazi zombies in love with like an allied
+zombie
+
+ align:start position:0%
+zombie
+ 
+
+ align:start position:0%
+zombie
+>> and Jewish.
+
+ align:start position:0%
+>> and Jewish.
+ 
+
+ align:start position:0%
+>> and Jewish.
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> And then it's So there's two factions.
+
+ align:start position:0%
+>> And then it's So there's two factions.
+ 
+
+ align:start position:0%
+>> And then it's So there's two factions.
+It could be Well, they're all people
+
+ align:start position:0%
+It could be Well, they're all people
+ 
+
+ align:start position:0%
+It could be Well, they're all people
+like online. One group there's like two
+
+ align:start position:0%
+like online. One group there's like two
+ 
+
+ align:start position:0%
+like online. One group there's like two
+factions. There's the ally group and the
+
+ align:start position:0%
+factions. There's the ally group and the
+ 
+
+ align:start position:0%
+factions. There's the ally group and the
+axis group.
+
+ align:start position:0%
+axis group.
+ 
+
+ align:start position:0%
+axis group.
+>> What if What if they're all Nazis?
+
+ align:start position:0%
+>> What if What if they're all Nazis?
+ 
+
+ align:start position:0%
+>> What if What if they're all Nazis?
+>> What What What if there's two factions?
+
+ align:start position:0%
+>> What What What if there's two factions?
+ 
+
+ align:start position:0%
+>> What What What if there's two factions?
+There's the zombies and the humans and
+
+ align:start position:0%
+There's the zombies and the humans and
+ 
+
+ align:start position:0%
+There's the zombies and the humans and
+they're drawn into war because there's a
+
+ align:start position:0%
+they're drawn into war because there's a
+ 
+
+ align:start position:0%
+they're drawn into war because there's a
+love there's a love story between a a
+
+ align:start position:0%
+love there's a love story between a a
+ 
+
+ align:start position:0%
+love there's a love story between a a
+zombie and a human and the leaders get
+
+ align:start position:0%
+zombie and a human and the leaders get
+ 
+
+ align:start position:0%
+zombie and a human and the leaders get
+pissed over this and so we're in war
+
+ align:start position:0%
+pissed over this and so we're in war
+ 
+
+ align:start position:0%
+pissed over this and so we're in war
+because of of like Rome and Julietesque
+
+ align:start position:0%
+because of of like Rome and Julietesque
+ 
+
+ align:start position:0%
+because of of like Rome and Julietesque
+zombie humans.
+
+ align:start position:0%
+zombie humans.
+ 
+
+ align:start position:0%
+zombie humans.
+>> What you're saying is we're having
+
+ align:start position:0%
+>> What you're saying is we're having
+ 
+
+ align:start position:0%
+>> What you're saying is we're having
+intelligent zombies.
+
+ align:start position:0%
+intelligent zombies.
+ 
+
+ align:start position:0%
+intelligent zombies.
+>> Yeah, intelligent zombies.
+
+ align:start position:0%
+>> Yeah, intelligent zombies.
+ 
+
+ align:start position:0%
+>> Yeah, intelligent zombies.
+>> Well, clearly they're semi-intm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hitler into this though just because
+
+ align:start position:0%
+Hitler into this though just because
+ 
+
+ align:start position:0%
+Hitler into this though just because
+it's Nazis. There must be a zombie
+
+ align:start position:0%
+it's Nazis. There must be a zombie
+ 
+
+ align:start position:0%
+it's Nazis. There must be a zombie
+Hitler. Who said this?
+
+ align:start position:0%
+Hitler. Who said this?
+ 
+
+ align:start position:0%
+Hitler. Who said this?
+>> Wait, what is your name?
+
+ align:start position:0%
+>> Wait, what is your name?
+ 
+
+ align:start position:0%
+>> Wait, what is your name?
+>> Bobby.
+
+ align:start position:0%
+>> Bobby.
+ 
+
+ align:start position:0%
+>> Bobby.
+>> What is your name?
+
+ align:start position:0%
+>> What is your name?
+ 
+
+ align:start position:0%
+>> What is your name?
+>> What is your name? Jason.
+
+ align:start position:0%
+>> What is your name? Jason.
+ 
+
+ align:start position:0%
+>> What is your name? Jason.
+>> Brian. On Jason's idea of is it
+
+ align:start position:0%
+>> Brian. On Jason's idea of is it
+ 
+
+ align:start position:0%
+>> Brian. On Jason's idea of is it
+necrophilia? I I think because there's a
+
+ align:start position:0%
+necrophilia? I I think because there's a
+ 
+
+ align:start position:0%
+necrophilia? I I think because there's a
+love story, the title could be necroilia
+
+ align:start position:0%
+love story, the title could be necroilia
+ 
+
+ align:start position:0%
+love story, the title could be necroilia
+question mark.
+
+ align:start position:0%
+question mark.
+ 
+
+ align:start position:0%
+question mark.
+>> Is it?
+
+ align:start position:0%
+>> Is it?
+ 
+
+ align:start position:0%
+>> Is it?
+>> Is it nec?
+
+ align:start position:0%
+>> Is it nec?
+ 
+
+ align:start position:0%
+>> Is it nec?
+>> Is it necroilia?
+
+ align:start position:0%
+>> Is it necroilia?
+ 
+
+ align:start position:0%
+>> Is it necroilia?
+>> Probably. Probably.
+
+ align:start position:0%
+>> Probably. Probably.
+ 
+
+ align:start position:0%
+>> Probably. Probably.
+>> Is it I like it as a love story, but is
+
+ align:start position:0%
+>> Is it I like it as a love story, but is
+ 
+
+ align:start position:0%
+>> Is it I like it as a love story, but is
+it a sex story?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So, wait. How about this?
+
+ align:start position:0%
+>> So, wait. How about this?
+ 
+
+ align:start position:0%
+>> So, wait. How about this?
+>> Or maybe even zombie strippers that fall
+
+ align:start position:0%
+>> Or maybe even zombie strippers that fall
+ 
+
+ align:start position:0%
+>> Or maybe even zombie strippers that fall
+in love with.
+
+ align:start position:0%
+in love with.
+ 
+
+ align:start position:0%
+in love with.
+>> Have you seen Zombie Strippers?
+
+ align:start position:0%
+>> Have you seen Zombie Strippers?
+ 
+
+ align:start position:0%
+>> Have you seen Zombie Strippers?
+>> No.
+
+ align:start position:0%
+>> No.
+ 
+
+ align:start position:0%
+>> No.
+>> It's a terrible, wonderful, terrible
+
+ align:start position:0%
+>> It's a terrible, wonderful, terrible
+ 
+
+ align:start position:0%
+>> It's a terrible, wonderful, terrible
+movie.
+
+ align:start position:0%
+movie.
+ 
+
+ align:start position:0%
+movie.
+>> I'll watch it.
+
+ align:start position:0%
+>> I'll watch it.
+ 
+
+ align:start position:0%
+>> I'll watch it.
+>> You should not. Should
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> um So the actually how about we have the
+
+ align:start position:0%
+>> um So the actually how about we have the
+ 
+
+ align:start position:0%
+>> um So the actually how about we have the
+zombies as the good guys? That way like
+
+ align:start position:0%
+zombies as the good guys? That way like
+ 
+
+ align:start position:0%
+zombies as the good guys? That way like
+the allies are trying to like make a
+
+ align:start position:0%
+the allies are trying to like make a
+ 
+
+ align:start position:0%
+the allies are trying to like make a
+weapon that will destroy like half the
+
+ align:start position:0%
+weapon that will destroy like half the
+ 
+
+ align:start position:0%
+weapon that will destroy like half the
+world and the zombies are like, "No,
+
+ align:start position:0%
+world and the zombies are like, "No,
+ 
+
+ align:start position:0%
+world and the zombies are like, "No,
+that will be bad. Let's make everyone
+
+ align:start position:0%
+that will be bad. Let's make everyone
+ 
+
+ align:start position:0%
+that will be bad. Let's make everyone
+else obvious so they agree with us."
+
+ align:start position:0%
+else obvious so they agree with us."
+ 
+
+ align:start position:0%
+else obvious so they agree with us."
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+>> what if what if
+
+ align:start position:0%
+>> what if what if
+ 
+
+ align:start position:0%
+>> what if what if
+>> what if you're just a zombie and
+
+ align:start position:0%
+>> what if you're just a zombie and
+ 
+
+ align:start position:0%
+>> what if you're just a zombie and
+everyone is trying to kill you, so you
+
+ align:start position:0%
+everyone is trying to kill you, so you
+ 
+
+ align:start position:0%
+everyone is trying to kill you, so you
+want to make everyone zombies so the
+
+ align:start position:0%
+want to make everyone zombies so the
+ 
+
+ align:start position:0%
+want to make everyone zombies so the
+world will be peaceful and happy.
+
+ align:start position:0%
+world will be peaceful and happy.
+ 
+
+ align:start position:0%
+world will be peaceful and happy.
+>> You want everyone to love you.
+
+ align:start position:0%
+>> You want everyone to love you.
+ 
+
+ align:start position:0%
+>> You want everyone to love you.
+>> Yeah,
+
+ align:start position:0%
+>> Yeah,
+ 
+
+ align:start position:0%
+>> Yeah,
+>> I like that a lot.
+
+ align:start position:0%
+>> I like that a lot.
+ 
+
+ align:start position:0%
+>> I like that a lot.
+>> And that's then
+
+ align:start position:0%
+>> And that's then
+ 
+
+ align:start position:0%
+>> And that's then
+even better. Love zombies. Like, who
+
+ align:start position:0%
+even better. Love zombies. Like, who
+ 
+
+ align:start position:0%
+even better. Love zombies. Like, who
+says they have to be undead? They can be
+
+ align:start position:0%
+says they have to be undead? They can be
+ 
+
+ align:start position:0%
+says they have to be undead? They can be
+infected by emotion.
+
+ align:start position:0%
+infected by emotion.
+ 
+
+ align:start position:0%
+infected by emotion.
+>> That's a tagline right there.
+
+ align:start position:0%
+>> That's a tagline right there.
+ 
+
+ align:start position:0%
+>> That's a tagline right there.
+>> Nudest zombies. What if what if like 95%
+
+ align:start position:0%
+>> Nudest zombies. What if what if like 95%
+ 
+
+ align:start position:0%
+>> Nudest zombies. What if what if like 95%
+of the world is zombie and so then the
+
+ align:start position:0%
+of the world is zombie and so then the
+ 
+
+ align:start position:0%
+of the world is zombie and so then the
+weird creatures that are like scary are
+
+ align:start position:0%
+weird creatures that are like scary are
+ 
+
+ align:start position:0%
+weird creatures that are like scary are
+the humans and they're like sentient
+
+ align:start position:0%
+the humans and they're like sentient
+ 
+
+ align:start position:0%
+the humans and they're like sentient
+they do weird things but the zombies all
+
+ align:start position:0%
+they do weird things but the zombies all
+ 
+
+ align:start position:0%
+they do weird things but the zombies all
+are happy and love each other.
+
+ align:start position:0%
+are happy and love each other.
+ 
+
+ align:start position:0%
+are happy and love each other.
+>> Maybe the humans have the love disease.
+
+ align:start position:0%
+>> Maybe the humans have the love disease.
+ 
+
+ align:start position:0%
+>> Maybe the humans have the love disease.
+>> They're trying to zombies
+
+ align:start position:0%
+>> They're trying to zombies
+ 
+
+ align:start position:0%
+>> They're trying to zombies
+like they're infecting zombies with
+
+ align:start position:0%
+like they're infecting zombies with
+ 
+
+ align:start position:0%
+like they're infecting zombies with
+love.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> So then each person would be I either
+
+ align:start position:0%
+>> So then each person would be I either
+ 
+
+ align:start position:0%
+>> So then each person would be I either
+start as a zombie or a human. They have
+
+ align:start position:0%
+start as a zombie or a human. They have
+ 
+
+ align:start position:0%
+start as a zombie or a human. They have
+to complete a bunch of little tasks
+
+ align:start position:0%
+to complete a bunch of little tasks
+ 
+
+ align:start position:0%
+to complete a bunch of little tasks
+before they can come, you know, and they
+
+ align:start position:0%
+before they can come, you know, and they
+ 
+
+ align:start position:0%
+before they can come, you know, and they
+like play challenges against each other.
+
+ align:start position:0%
+like play challenges against each other.
+ 
+
+ align:start position:0%
+like play challenges against each other.
+So be like zombie against zombie and one
+
+ align:start position:0%
+So be like zombie against zombie and one
+ 
+
+ align:start position:0%
+So be like zombie against zombie and one
+of them is infected, one of them isn't.
+
+ align:start position:0%
+of them is infected, one of them isn't.
+ 
+
+ align:start position:0%
+of them is infected, one of them isn't.
+>> So humans can infect zombies with blood
+
+ align:start position:0%
+>> So humans can infect zombies with blood
+ 
+
+ align:start position:0%
+>> So humans can infect zombies with blood
+that makes them not zombies.
+
+ align:start position:0%
+that makes them not zombies.
+ 
+
+ align:start position:0%
+that makes them not zombies.
+>> What if no zombies? What what if what if
+
+ align:start position:0%
+>> What if no zombies? What what if what if
+ 
+
+ align:start position:0%
+>> What if no zombies? What what if what if
+there's a dynamic what what if there's a
+
+ align:start position:0%
+there's a dynamic what what if there's a
+ 
+
+ align:start position:0%
+there's a dynamic what what if there's a
+dynamic between so there's there's two
+
+ align:start position:0%
+dynamic between so there's there's two
+ 
+
+ align:start position:0%
+dynamic between so there's there's two
+factions zombies and humans and every
+
+ align:start position:0%
+factions zombies and humans and every
+ 
+
+ align:start position:0%
+factions zombies and humans and every
+player is given a match and in this
+
+ align:start position:0%
+player is given a match and in this
+ 
+
+ align:start position:0%
+player is given a match and in this
+massive multiplayer world that one of
+
+ align:start position:0%
+massive multiplayer world that one of
+ 
+
+ align:start position:0%
+massive multiplayer world that one of
+their main objectives is to find their
+
+ align:start position:0%
+their main objectives is to find their
+ 
+
+ align:start position:0%
+their main objectives is to find their
+match who's in the opposing faction
+
+ align:start position:0%
+match who's in the opposing faction
+ 
+
+ align:start position:0%
+match who's in the opposing faction
+buried deep among hostile hordes of
+
+ align:start position:0%
+buried deep among hostile hordes of
+ 
+
+ align:start position:0%
+buried deep among hostile hordes of
+either humans or zombies find them and
+
+ align:start position:0%
+either humans or zombies find them and
+ 
+
+ align:start position:0%
+either humans or zombies find them and
+like live happily ever after together
+
+ align:start position:0%
+like live happily ever after together
+ 
+
+ align:start position:0%
+like live happily ever after together
+>> and become either zombies or humans
+
+ align:start position:0%
+>> and become either zombies or humans
+ 
+
+ align:start position:0%
+>> and become either zombies or humans
+together.
+
+ align:start position:0%
+together.
+ 
+
+ align:start position:0%
+together.
+>> Correct.
+
+ align:start position:0%
+>> Correct.
+ 
+
+ align:start position:0%
+>> Correct.
+>> But love zombies
+
+ align:start position:0%
+>> But love zombies
+ 
+
+ align:start position:0%
+>> But love zombies
+>> find a cure or just get bitten
+
+ align:start position:0%
+>> find a cure or just get bitten
+ 
+
+ align:start position:0%
+>> find a cure or just get bitten
+>> and become love zombies.
+
+ align:start position:0%
+>> and become love zombies.
+ 
+
+ align:start position:0%
+>> and become love zombies.
+>> Love zombies.
+
+ align:start position:0%
+>> Love zombies.
+ 
+
+ align:start position:0%
+>> Love zombies.
+>> Love zombies.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ask the question. Is there truly a
+
+ align:start position:0%
+Ask the question. Is there truly a
+ 
+
+ align:start position:0%
+Ask the question. Is there truly a
+difference between being in love and
+
+ align:start position:0%
+difference between being in love and
+ 
+
+ align:start position:0%
+difference between being in love and
+being undead?
+
+ align:start position:0%
+being undead?
+ 
+
+ align:start position:0%
+being undead?
+>> That's a great tagline.
+
+ align:start position:0%
+>> That's a great tagline.
+ 
+
+ align:start position:0%
+>> That's a great tagline.
+>> Maybe some task.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> What's even more blind? Having your eyes
+
+ align:start position:0%
+>> What's even more blind? Having your eyes
+ 
+
+ align:start position:0%
+>> What's even more blind? Having your eyes
+guided out by a zombie or being in love?
+
+ align:start position:0%
+guided out by a zombie or being in love?
+ 
+
+ align:start position:0%
+guided out by a zombie or being in love?
+>> So, so then we can draw it into not the
+
+ align:start position:0%
+>> So, so then we can draw it into not the
+ 
+
+ align:start position:0%
+>> So, so then we can draw it into not the
+actual Nazi zombie game.
+
+ align:start position:0%
+actual Nazi zombie game.
+ 
+
+ align:start position:0%
+actual Nazi zombie game.
+>> Maybe the Nazi zombies from the other
+
+ align:start position:0%
+>> Maybe the Nazi zombies from the other
+ 
+
+ align:start position:0%
+>> Maybe the Nazi zombies from the other
+point of view. So, they're just trying
+
+ align:start position:0%
+point of view. So, they're just trying
+ 
+
+ align:start position:0%
+point of view. So, they're just trying
+to have love and and the humans are
+
+ align:start position:0%
+to have love and and the humans are
+ 
+
+ align:start position:0%
+to have love and and the humans are
+trying to kill them.
+
+ align:start position:0%
+trying to kill them.
+ 
+
+ align:start position:0%
+trying to kill them.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+>> wait. Are we having Nazis?
+
+ align:start position:0%
+>> wait. Are we having Nazis?
+ 
+
+ align:start position:0%
+>> wait. Are we having Nazis?
+>> We can.
+
+ align:start position:0%
+>> We can.
+ 
+
+ align:start position:0%
+>> We can.
+>> Some of the ideas can include Nazis and
+
+ align:start position:0%
+>> Some of the ideas can include Nazis and
+ 
+
+ align:start position:0%
+>> Some of the ideas can include Nazis and
+some of them can't and we can decide.
+
+ align:start position:0%
+some of them can't and we can decide.
+ 
+
+ align:start position:0%
+some of them can't and we can decide.
+>> Should we be getting to the point of
+
+ align:start position:0%
+>> Should we be getting to the point of
+ 
+
+ align:start position:0%
+>> Should we be getting to the point of
+judgment towards the end of the thing so
+
+ align:start position:0%
+judgment towards the end of the thing so
+ 
+
+ align:start position:0%
+judgment towards the end of the thing so
+we can finalize a pitch in a thing or
+
+ align:start position:0%
+we can finalize a pitch in a thing or
+ 
+
+ align:start position:0%
+we can finalize a pitch in a thing or
+whatever? Just just come up
+
+ align:start position:0%
+whatever? Just just come up
+ 
+
+ align:start position:0%
+whatever? Just just come up
+>> with just brainstorming. That's awesome.
+
+ align:start position:0%
+>> with just brainstorming. That's awesome.
+ 
+
+ align:start position:0%
+>> with just brainstorming. That's awesome.
+>> Yeah, it's just fun.
+
+ align:start position:0%
+>> Yeah, it's just fun.
+ 
+
+ align:start position:0%
+>> Yeah, it's just fun.
+>> Yeah. Yeah.
+
+ align:start position:0%
+>> Yeah. Yeah.
+ 
+
+ align:start position:0%
+>> Yeah. Yeah.
+>> How about um the player is a human
+
+ align:start position:0%
+>> How about um the player is a human
+ 
+
+ align:start position:0%
+>> How about um the player is a human
+fighting against the zombies and you
+
+ align:start position:0%
+fighting against the zombies and you
+ 
+
+ align:start position:0%
+fighting against the zombies and you
+have some kind of companion may or may
+
+ align:start position:0%
+have some kind of companion may or may
+ 
+
+ align:start position:0%
+have some kind of companion may or may
+not be a cube but that accompanies you
+
+ align:start position:0%
+not be a cube but that accompanies you
+ 
+
+ align:start position:0%
+not be a cube but that accompanies you
+on your journey to defeat the zombies.
+
+ align:start position:0%
+on your journey to defeat the zombies.
+ 
+
+ align:start position:0%
+on your journey to defeat the zombies.
+>> So companion cube I like better.
+
+ align:start position:0%
+>> So companion cube I like better.
+ 
+
+ align:start position:0%
+>> So companion cube I like better.
+>> Do plants love each other?
+
+ align:start position:0%
+>> Do plants love each other?
+ 
+
+ align:start position:0%
+>> Do plants love each other?
+>> That way that is a heart like that's
+
+ align:start position:0%
+>> That way that is a heart like that's
+ 
+
+ align:start position:0%
+>> That way that is a heart like that's
+like a love story between you and your
+
+ align:start position:0%
+like a love story between you and your
+ 
+
+ align:start position:0%
+like a love story between you and your
+cube.
+
+ align:start position:0%
+cube.
+ 
+
+ align:start position:0%
+cube.
+>> But can the can the cube become a
+
+ align:start position:0%
+>> But can the can the cube become a
+ 
+
+ align:start position:0%
+>> But can the can the cube become a
+zombie?
+
+ align:start position:0%
+zombie?
+ 
+
+ align:start position:0%
+zombie?
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> I mean it could be a person like Left
+
+ align:start position:0%
+>> I mean it could be a person like Left
+ 
+
+ align:start position:0%
+>> I mean it could be a person like Left
+for Dead. like four people against all
+
+ align:start position:0%
+for Dead. like four people against all
+ 
+
+ align:start position:0%
+for Dead. like four people against all
+the zombies that they're always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> or witches. Maybe you're trying to get
+
+ align:start position:0%
+>> or witches. Maybe you're trying to get
+ 
+
+ align:start position:0%
+>> or witches. Maybe you're trying to get
+>> the love story is you and the witch
+
+ align:start position:0%
+>> the love story is you and the witch
+ 
+
+ align:start position:0%
+>> the love story is you and the witch
+consuming the thing and like
+
+ align:start position:0%
+consuming the thing and like
+ 
+
+ align:start position:0%
+consuming the thing and like
+>> what if so all players play zombies and
+
+ align:start position:0%
+>> what if so all players play zombies and
+ 
+
+ align:start position:0%
+>> what if so all players play zombies and
+most missions are stuff like you have to
+
+ align:start position:0%
+most missions are stuff like you have to
+ 
+
+ align:start position:0%
+most missions are stuff like you have to
+infect a city and just run around like
+
+ align:start position:0%
+infect a city and just run around like
+ 
+
+ align:start position:0%
+infect a city and just run around like
+binding people into the entire city that
+
+ align:start position:0%
+binding people into the entire city that
+ 
+
+ align:start position:0%
+binding people into the entire city that
+you've like conquered or turned into
+
+ align:start position:0%
+you've like conquered or turned into
+ 
+
+ align:start position:0%
+you've like conquered or turned into
+zombified. Your ultimate goal is that
+
+ align:start position:0%
+zombified. Your ultimate goal is that
+ 
+
+ align:start position:0%
+zombified. Your ultimate goal is that
+your girlfriend from back when you were
+
+ align:start position:0%
+your girlfriend from back when you were
+ 
+
+ align:start position:0%
+your girlfriend from back when you were
+human or your boyfriend from back when
+
+ align:start position:0%
+human or your boyfriend from back when
+ 
+
+ align:start position:0%
+human or your boyfriend from back when
+you were human is at some place and you
+
+ align:start position:0%
+you were human is at some place and you
+ 
+
+ align:start position:0%
+you were human is at some place and you
+want to infect all cities until you can
+
+ align:start position:0%
+want to infect all cities until you can
+ 
+
+ align:start position:0%
+want to infect all cities until you can
+get there and then infect her so that
+
+ align:start position:0%
+get there and then infect her so that
+ 
+
+ align:start position:0%
+get there and then infect her so that
+you guys can live happily ever after.
+
+ align:start position:0%
+you guys can live happily ever after.
+ 
+
+ align:start position:0%
+you guys can live happily ever after.
+>> A you could also
+
+ align:start position:0%
+>> A you could also
+ 
+
+ align:start position:0%
+>> A you could also
+>> also building on the idea of being
+
+ align:start position:0%
+>> also building on the idea of being
+ 
+
+ align:start position:0%
+>> also building on the idea of being
+zombies trying to infect cities.
+
+ align:start position:0%
+zombies trying to infect cities.
+ 
+
+ align:start position:0%
+zombies trying to infect cities.
+>> Oh god,
+
+ align:start position:0%
+>> Oh god,
+ 
+
+ align:start position:0%
+>> Oh god,
+>> you are zombies uh with Cupid's love
+
+ align:start position:0%
+>> you are zombies uh with Cupid's love
+ 
+
+ align:start position:0%
+>> you are zombies uh with Cupid's love
+arrows
+
+ align:start position:0%
+arrows
+ 
+
+ align:start position:0%
+arrows
+>> trying to infect the entire city with
+
+ align:start position:0%
+>> trying to infect the entire city with
+ 
+
+ align:start position:0%
+>> trying to infect the entire city with
+love at which point no no productivity
+
+ align:start position:0%
+love at which point no no productivity
+ 
+
+ align:start position:0%
+love at which point no no productivity
+is all gone in the city. zombie with
+
+ align:start position:0%
+is all gone in the city. zombie with
+ 
+
+ align:start position:0%
+is all gone in the city. zombie with
+love arrows infecting people.
+
+ align:start position:0%
+love arrows infecting people.
+ 
+
+ align:start position:0%
+love arrows infecting people.
+>> It could be set in the 1950s where
+
+ align:start position:0%
+>> It could be set in the 1950s where
+ 
+
+ align:start position:0%
+>> It could be set in the 1950s where
+everyone's like trying to be productive
+
+ align:start position:0%
+everyone's like trying to be productive
+ 
+
+ align:start position:0%
+everyone's like trying to be productive
+and not love each other.
+
+ align:start position:0%
+and not love each other.
+ 
+
+ align:start position:0%
+and not love each other.
+>> No, what if what if you build along the
+
+ align:start position:0%
+>> No, what if what if you build along the
+ 
+
+ align:start position:0%
+>> No, what if what if you build along the
+lines of, you know, having to infect the
+
+ align:start position:0%
+lines of, you know, having to infect the
+ 
+
+ align:start position:0%
+lines of, you know, having to infect the
+city, but you have to do that. One
+
+ align:start position:0%
+city, but you have to do that. One
+ 
+
+ align:start position:0%
+city, but you have to do that. One
+zombie can't infect an entire city,
+
+ align:start position:0%
+zombie can't infect an entire city,
+ 
+
+ align:start position:0%
+zombie can't infect an entire city,
+right? So, you have to like ally with
+
+ align:start position:0%
+right? So, you have to like ally with
+ 
+
+ align:start position:0%
+right? So, you have to like ally with
+other zombies, but they're like
+
+ align:start position:0%
+other zombies, but they're like
+ 
+
+ align:start position:0%
+other zombies, but they're like
+different factions of zombies. Kind of
+
+ align:start position:0%
+different factions of zombies. Kind of
+ 
+
+ align:start position:0%
+different factions of zombies. Kind of
+like two zombie mob families, right,
+
+ align:start position:0%
+like two zombie mob families, right,
+ 
+
+ align:start position:0%
+like two zombie mob families, right,
+that are trying to infect. They have two
+
+ align:start position:0%
+that are trying to infect. They have two
+ 
+
+ align:start position:0%
+that are trying to infect. They have two
+different, you know, varieties of this
+
+ align:start position:0%
+different, you know, varieties of this
+ 
+
+ align:start position:0%
+different, you know, varieties of this
+lovely in
+
+ align:start position:0%
+lovely in
+ 
+
+ align:start position:0%
+lovely in
+>> Oh, wait. Could there be like a drug
+
+ align:start position:0%
+>> Oh, wait. Could there be like a drug
+ 
+
+ align:start position:0%
+>> Oh, wait. Could there be like a drug
+trade? So like the like they have to
+
+ align:start position:0%
+trade? So like the like they have to
+ 
+
+ align:start position:0%
+trade? So like the like they have to
+infect people with like a certain drug.
+
+ align:start position:0%
+infect people with like a certain drug.
+ 
+
+ align:start position:0%
+infect people with like a certain drug.
+So it's like a drug war as well. And
+
+ align:start position:0%
+So it's like a drug war as well. And
+ 
+
+ align:start position:0%
+So it's like a drug war as well. And
+this the three swords good swords are
+
+ align:start position:0%
+this the three swords good swords are
+ 
+
+ align:start position:0%
+this the three swords good swords are
+cool.
+
+ align:start position:0%
+cool.
+ 
+
+ align:start position:0%
+cool.
+>> Zombie.
+
+ align:start position:0%
+>> Zombie.
+ 
+
+ align:start position:0%
+>> Zombie.
+>> What if
+
+ align:start position:0%
+>> What if
+ 
+
+ align:start position:0%
+>> What if
+>> what if when you have a zombie virus
+
+ align:start position:0%
+>> what if when you have a zombie virus
+ 
+
+ align:start position:0%
+>> what if when you have a zombie virus
+instead of wanting to eat people you are
+
+ align:start position:0%
+instead of wanting to eat people you are
+ 
+
+ align:start position:0%
+instead of wanting to eat people you are
+overcome with an urge to passionately
+
+ align:start position:0%
+overcome with an urge to passionately
+ 
+
+ align:start position:0%
+overcome with an urge to passionately
+make out with them. And if you make out
+
+ align:start position:0%
+make out with them. And if you make out
+ 
+
+ align:start position:0%
+make out with them. And if you make out
+with somebody then they turn into a love
+
+ align:start position:0%
+with somebody then they turn into a love
+ 
+
+ align:start position:0%
+with somebody then they turn into a love
+zombie too. And so there's no like
+
+ align:start position:0%
+zombie too. And so there's no like
+ 
+
+ align:start position:0%
+zombie too. And so there's no like
+decomposition going on so much as there
+
+ align:start position:0%
+decomposition going on so much as there
+ 
+
+ align:start position:0%
+decomposition going on so much as there
+is like hordes of people running through
+
+ align:start position:0%
+is like hordes of people running through
+ 
+
+ align:start position:0%
+is like hordes of people running through
+streets trying to passionately make out
+
+ align:start position:0%
+streets trying to passionately make out
+ 
+
+ align:start position:0%
+streets trying to passionately make out
+with each other. So wait
+
+ align:start position:0%
+with each other. So wait
+ 
+
+ align:start position:0%
+with each other. So wait
+>> being decaying and like decrepit. W
+
+ align:start position:0%
+>> being decaying and like decrepit. W
+ 
+
+ align:start position:0%
+>> being decaying and like decrepit. W
+zombies suddenly become very attractive.
+
+ align:start position:0%
+zombies suddenly become very attractive.
+ 
+
+ align:start position:0%
+zombies suddenly become very attractive.
+So you
+
+ align:start position:0%
+So you
+ 
+
+ align:start position:0%
+So you
+>> wait and they start like they start like
+
+ align:start position:0%
+>> wait and they start like they start like
+ 
+
+ align:start position:0%
+>> wait and they start like they start like
+taking care of their appearance and
+
+ align:start position:0%
+taking care of their appearance and
+ 
+
+ align:start position:0%
+taking care of their appearance and
+stuff.
+
+ align:start position:0%
+stuff.
+ 
+
+ align:start position:0%
+stuff.
+>> So when is limit is there I'm well after
+
+ align:start position:0%
+>> So when is limit is there I'm well after
+ 
+
+ align:start position:0%
+>> So when is limit is there I'm well after
+the zombies make out.
+
+ align:start position:0%
+the zombies make out.
+ 
+
+ align:start position:0%
+the zombies make out.
+>> What what's next?
+
+ align:start position:0%
+>> What what's next?
+ 
+
+ align:start position:0%
+>> What what's next?
+>> Well they get for
+
+ align:start position:0%
+>> Well they get for
+ 
+
+ align:start position:0%
+>> Well they get for
+Okay. So what if we just like make a
+
+ align:start position:0%
+Okay. So what if we just like make a
+ 
+
+ align:start position:0%
+Okay. So what if we just like make a
+like World of Warcraft type of MMO but
+
+ align:start position:0%
+like World of Warcraft type of MMO but
+ 
+
+ align:start position:0%
+like World of Warcraft type of MMO but
+every player player humans you have a
+
+ align:start position:0%
+every player player humans you have a
+ 
+
+ align:start position:0%
+every player player humans you have a
+zombie companion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> pet zombie?
+
+ align:start position:0%
+>> pet zombie?
+ 
+
+ align:start position:0%
+>> pet zombie?
+>> Yeah zombie
+
+ align:start position:0%
+>> Yeah zombie
+ 
+
+ align:start position:0%
+>> Yeah zombie
+peties
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> no but they had
+
+ align:start position:0%
+>> no but they had
+ 
+
+ align:start position:0%
+>> no but they had
+>> the dead Pokemon. No, they had a pet as
+
+ align:start position:0%
+>> the dead Pokemon. No, they had a pet as
+ 
+
+ align:start position:0%
+>> the dead Pokemon. No, they had a pet as
+a pet.
+
+ align:start position:0%
+a pet.
+ 
+
+ align:start position:0%
+a pet.
+>> I think it's called
+
+ align:start position:0%
+>> I think it's called
+ 
+
+ align:start position:0%
+>> I think it's called
+>> Ph. It's like I think
+
+ align:start position:0%
+>> Ph. It's like I think
+ 
+
+ align:start position:0%
+>> Ph. It's like I think
+>> it's a movie called Phto.
+
+ align:start position:0%
+>> it's a movie called Phto.
+ 
+
+ align:start position:0%
+>> it's a movie called Phto.
+>> I've not seen it, but
+
+ align:start position:0%
+>> I've not seen it, but
+ 
+
+ align:start position:0%
+>> I've not seen it, but
+>> I've seen the trailer.
+
+ align:start position:0%
+>> I've seen the trailer.
+ 
+
+ align:start position:0%
+>> I've seen the trailer.
+>> So, what if you have to fight like with
+
+ align:start position:0%
+>> So, what if you have to fight like with
+ 
+
+ align:start position:0%
+>> So, what if you have to fight like with
+Pokemon zombies
+
+ align:start position:0%
+Pokemon zombies
+ 
+
+ align:start position:0%
+Pokemon zombies
+different powerups?
+
+ align:start position:0%
+different powerups?
+ 
+
+ align:start position:0%
+different powerups?
+>> Different kinds of zombies like uh like
+
+ align:start position:0%
+>> Different kinds of zombies like uh like
+ 
+
+ align:start position:0%
+>> Different kinds of zombies like uh like
+Left 4 Dead. There's, you know, the big
+
+ align:start position:0%
+Left 4 Dead. There's, you know, the big
+ 
+
+ align:start position:0%
+Left 4 Dead. There's, you know, the big
+fat ones that like vomit and you know,
+
+ align:start position:0%
+fat ones that like vomit and you know,
+ 
+
+ align:start position:0%
+fat ones that like vomit and you know,
+>> spitters. I hate spitters. But smokers.
+
+ align:start position:0%
+>> spitters. I hate spitters. But smokers.
+ 
+
+ align:start position:0%
+>> spitters. I hate spitters. But smokers.
+Smokers are the worst.
+
+ align:start position:0%
+Smokers are the worst.
+ 
+
+ align:start position:0%
+Smokers are the worst.
+>> Well, instead of pyro, you have blood
+
+ align:start position:0%
+>> Well, instead of pyro, you have blood
+ 
+
+ align:start position:0%
+>> Well, instead of pyro, you have blood
+potions. Man, he said smokers are the
+
+ align:start position:0%
+potions. Man, he said smokers are the
+ 
+
+ align:start position:0%
+potions. Man, he said smokers are the
+worst. That sounds like a dating s.
+
+ align:start position:0%
+worst. That sounds like a dating s.
+ 
+
+ align:start position:0%
+worst. That sounds like a dating s.
+I do I like the Pokemon idea. So, you
+
+ align:start position:0%
+I do I like the Pokemon idea. So, you
+ 
+
+ align:start position:0%
+I do I like the Pokemon idea. So, you
+can have um instead of like you're
+
+ align:start position:0%
+can have um instead of like you're
+ 
+
+ align:start position:0%
+can have um instead of like you're
+humans, but you just have to capture all
+
+ align:start position:0%
+humans, but you just have to capture all
+ 
+
+ align:start position:0%
+humans, but you just have to capture all
+the poke like different types of zombies
+
+ align:start position:0%
+the poke like different types of zombies
+ 
+
+ align:start position:0%
+the poke like different types of zombies
+and then you fight other people with
+
+ align:start position:0%
+and then you fight other people with
+ 
+
+ align:start position:0%
+and then you fight other people with
+their zombies and it's like match for
+
+ align:start position:0%
+their zombies and it's like match for
+ 
+
+ align:start position:0%
+their zombies and it's like match for
+zombie versus zombie.
+
+ align:start position:0%
+zombie versus zombie.
+ 
+
+ align:start position:0%
+zombie versus zombie.
+What if the love story is not for the
+
+ align:start position:0%
+What if the love story is not for the
+ 
+
+ align:start position:0%
+What if the love story is not for the
+player, but is in is in the story of the
+
+ align:start position:0%
+player, but is in is in the story of the
+ 
+
+ align:start position:0%
+player, but is in is in the story of the
+game in that the reason that you're
+
+ align:start position:0%
+game in that the reason that you're
+ 
+
+ align:start position:0%
+game in that the reason that you're
+waging war at the moment is because
+
+ align:start position:0%
+waging war at the moment is because
+ 
+
+ align:start position:0%
+waging war at the moment is because
+you're trying to steal a cure to
+
+ align:start position:0%
+you're trying to steal a cure to
+ 
+
+ align:start position:0%
+you're trying to steal a cure to
+zombieism because your fearless leader
+
+ align:start position:0%
+zombieism because your fearless leader
+ 
+
+ align:start position:0%
+zombieism because your fearless leader
+20 ranks up, you're president of
+
+ align:start position:0%
+20 ranks up, you're president of
+ 
+
+ align:start position:0%
+20 ranks up, you're president of
+whatever's girlfriend has been zombified
+
+ align:start position:0%
+whatever's girlfriend has been zombified
+ 
+
+ align:start position:0%
+whatever's girlfriend has been zombified
+or his wife has been zombified. And so
+
+ align:start position:0%
+or his wife has been zombified. And so
+ 
+
+ align:start position:0%
+or his wife has been zombified. And so
+the whole game, you're all the means in
+
+ align:start position:0%
+the whole game, you're all the means in
+ 
+
+ align:start position:0%
+the whole game, you're all the means in
+a quest to to try to find this cure, but
+
+ align:start position:0%
+a quest to to try to find this cure, but
+ 
+
+ align:start position:0%
+a quest to to try to find this cure, but
+you don't realize you're trying to find
+
+ align:start position:0%
+you don't realize you're trying to find
+ 
+
+ align:start position:0%
+you don't realize you're trying to find
+a cure for it's not for like your use or
+
+ align:start position:0%
+a cure for it's not for like your use or
+ 
+
+ align:start position:0%
+a cure for it's not for like your use or
+your girlfriend's use or whatever of
+
+ align:start position:0%
+your girlfriend's use or whatever of
+ 
+
+ align:start position:0%
+your girlfriend's use or whatever of
+people you love. It's for your leaders.
+
+ align:start position:0%
+people you love. It's for your leaders.
+ 
+
+ align:start position:0%
+people you love. It's for your leaders.
+>> And what if she is actually the leader
+
+ align:start position:0%
+>> And what if she is actually the leader
+ 
+
+ align:start position:0%
+>> And what if she is actually the leader
+of the zombies and
+
+ align:start position:0%
+of the zombies and
+ 
+
+ align:start position:0%
+of the zombies and
+>> Oh crap.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> What if the zombies are aliens?
+
+ align:start position:0%
+>> What if the zombies are aliens?
+ 
+
+ align:start position:0%
+>> What if the zombies are aliens?
+>> Zombie aliens.
+
+ align:start position:0%
+>> Zombie aliens.
+ 
+
+ align:start position:0%
+>> Zombie aliens.
+>> The blood. What if the zombies are
+
+ align:start position:0%
+>> The blood. What if the zombies are
+ 
+
+ align:start position:0%
+>> The blood. What if the zombies are
+ninjas?
+
+ align:start position:0%
+ninjas?
+ 
+
+ align:start position:0%
+ninjas?
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> You can learn a lot.
+
+ align:start position:0%
+>> You can learn a lot.
+ 
+
+ align:start position:0%
+>> You can learn a lot.
+>> Combine the Pokemon of zombie ID with
+
+ align:start position:0%
+>> Combine the Pokemon of zombie ID with
+ 
+
+ align:start position:0%
+>> Combine the Pokemon of zombie ID with
+like the Sims where you like have a
+
+ align:start position:0%
+like the Sims where you like have a
+ 
+
+ align:start position:0%
+like the Sims where you like have a
+zombie that's under your control and
+
+ align:start position:0%
+zombie that's under your control and
+ 
+
+ align:start position:0%
+zombie that's under your control and
+you're trying to like teach your zombie
+
+ align:start position:0%
+you're trying to like teach your zombie
+ 
+
+ align:start position:0%
+you're trying to like teach your zombie
+to love and like maybe you're a
+
+ align:start position:0%
+to love and like maybe you're a
+ 
+
+ align:start position:0%
+to love and like maybe you're a
+different avatar. like a human avatar
+
+ align:start position:0%
+different avatar. like a human avatar
+ 
+
+ align:start position:0%
+different avatar. like a human avatar
+and you go through quests where you like
+
+ align:start position:0%
+and you go through quests where you like
+ 
+
+ align:start position:0%
+and you go through quests where you like
+take your zombie places and teach your
+
+ align:start position:0%
+take your zombie places and teach your
+ 
+
+ align:start position:0%
+take your zombie places and teach your
+zombie things
+
+ align:start position:0%
+zombie things
+ 
+
+ align:start position:0%
+zombie things
+>> and not to bite people and
+
+ align:start position:0%
+>> and not to bite people and
+ 
+
+ align:start position:0%
+>> and not to bite people and
+>> yeah exactly like I don't I don't know
+
+ align:start position:0%
+>> yeah exactly like I don't I don't know
+ 
+
+ align:start position:0%
+>> yeah exactly like I don't I don't know
+train your zombie
+
+ align:start position:0%
+train your zombie
+ 
+
+ align:start position:0%
+train your zombie
+>> maybe have so with the whole thing with
+
+ align:start position:0%
+>> maybe have so with the whole thing with
+ 
+
+ align:start position:0%
+>> maybe have so with the whole thing with
+the ninja pir ninja zombies might not
+
+ align:start position:0%
+the ninja pir ninja zombies might not
+ 
+
+ align:start position:0%
+the ninja pir ninja zombies might not
+have pirate pirates as well pirate
+
+ align:start position:0%
+have pirate pirates as well pirate
+ 
+
+ align:start position:0%
+have pirate pirates as well pirate
+zombies maybe
+
+ align:start position:0%
+zombies maybe
+ 
+
+ align:start position:0%
+zombies maybe
+>> pirate versus ninja
+
+ align:start position:0%
+>> pirate versus ninja
+ 
+
+ align:start position:0%
+>> pirate versus ninja
+>> zombies
+
+ align:start position:0%
+>> zombies
+ 
+
+ align:start position:0%
+>> zombies
+>> zombie edition special edition
+
+ align:start position:0%
+>> zombie edition special edition
+ 
+
+ align:start position:0%
+>> zombie edition special edition
+>> in space wrapped in bacon
+
+ align:start position:0%
+>> in space wrapped in bacon
+ 
+
+ align:start position:0%
+>> in space wrapped in bacon
+>> yes
+
+ align:start position:0%
+>> yes
+ 
+
+ align:start position:0%
+>> yes
+>> time traveling zombies
+
+ align:start position:0%
+>> time traveling zombies
+ 
+
+ align:start position:0%
+>> time traveling zombies
+I would be a great game to make just
+
+ align:start position:0%
+I would be a great game to make just
+ 
+
+ align:start position:0%
+I would be a great game to make just
+like pirate zombies versus ninja zombies
+
+ align:start position:0%
+like pirate zombies versus ninja zombies
+ 
+
+ align:start position:0%
+like pirate zombies versus ninja zombies
+in space wrapped in bacon and just make
+
+ align:start position:0%
+in space wrapped in bacon and just make
+ 
+
+ align:start position:0%
+in space wrapped in bacon and just make
+that game great.
+
+ align:start position:0%
+that game great.
+ 
+
+ align:start position:0%
+that game great.
+>> So is it necia probably
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> pirate edition the ninja.
+
+ align:start position:0%
+>> pirate edition the ninja.
+ 
+
+ align:start position:0%
+>> pirate edition the ninja.
+>> So maybe you should divide into little
+
+ align:start position:0%
+>> So maybe you should divide into little
+ 
+
+ align:start position:0%
+>> So maybe you should divide into little
+sub brainstorms for like a name tagline
+
+ align:start position:0%
+sub brainstorms for like a name tagline
+ 
+
+ align:start position:0%
+sub brainstorms for like a name tagline
+all that. Do we as a name do we have
+
+ align:start position:0%
+all that. Do we as a name do we have
+ 
+
+ align:start position:0%
+all that. Do we as a name do we have
+anyone more brainstorming?
+
+ align:start position:0%
+anyone more brainstorming?
+ 
+
+ align:start position:0%
+anyone more brainstorming?
+I think we should figure out like a
+
+ align:start position:0%
+I think we should figure out like a
+ 
+
+ align:start position:0%
+I think we should figure out like a
+mechanic that works. So far, we have a
+
+ align:start position:0%
+mechanic that works. So far, we have a
+ 
+
+ align:start position:0%
+mechanic that works. So far, we have a
+lot of ideas about like what the game
+
+ align:start position:0%
+lot of ideas about like what the game
+ 
+
+ align:start position:0%
+lot of ideas about like what the game
+world is. We have no idea like how you
+
+ align:start position:0%
+world is. We have no idea like how you
+ 
+
+ align:start position:0%
+world is. We have no idea like how you
+play the game. So, maybe more
+
+ align:start position:0%
+play the game. So, maybe more
+ 
+
+ align:start position:0%
+play the game. So, maybe more
+brainstorming on that then.
+
+ align:start position:0%
+brainstorming on that then.
+ 
+
+ align:start position:0%
+brainstorming on that then.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> It's massive multiplayer. ones working
+
+ align:start position:0%
+>> It's massive multiplayer. ones working
+ 
+
+ align:start position:0%
+>> It's massive multiplayer. ones working
+such as typical WoW style RPG, typical
+
+ align:start position:0%
+such as typical WoW style RPG, typical
+ 
+
+ align:start position:0%
+such as typical WoW style RPG, typical
+passive player FPS,
+
+ align:start position:0%
+passive player FPS,
+ 
+
+ align:start position:0%
+passive player FPS,
+Pokemon style RPG,
+
+ align:start position:0%
+Pokemon style RPG,
+ 
+
+ align:start position:0%
+Pokemon style RPG,
+>> Pokemon seem like Pokemon FPS
+
+ align:start position:0%
+>> Pokemon seem like Pokemon FPS
+ 
+
+ align:start position:0%
+>> Pokemon seem like Pokemon FPS
+>> or as we were saying before like The
+
+ align:start position:0%
+>> or as we were saying before like The
+ 
+
+ align:start position:0%
+>> or as we were saying before like The
+Sims Online.
+
+ align:start position:0%
+Sims Online.
+ 
+
+ align:start position:0%
+Sims Online.
+>> The Sims Online was so good.
+
+ align:start position:0%
+>> The Sims Online was so good.
+ 
+
+ align:start position:0%
+>> The Sims Online was so good.
+>> Did you play as a Pokemon?
+
+ align:start position:0%
+>> Did you play as a Pokemon?
+ 
+
+ align:start position:0%
+>> Did you play as a Pokemon?
+>> Yeah, maybe play as a Pokemon, but it's
+
+ align:start position:0%
+>> Yeah, maybe play as a Pokemon, but it's
+ 
+
+ align:start position:0%
+>> Yeah, maybe play as a Pokemon, but it's
+a first person shooter.
+
+ align:start position:0%
+a first person shooter.
+ 
+
+ align:start position:0%
+a first person shooter.
+>> But more like,
+
+ align:start position:0%
+>> But more like,
+ 
+
+ align:start position:0%
+>> But more like,
+>> but you still have like an RPG first
+
+ align:start position:0%
+>> but you still have like an RPG first
+ 
+
+ align:start position:0%
+>> but you still have like an RPG first
+person shooter as Pokemon. Wait
+
+ align:start position:0%
+person shooter as Pokemon. Wait
+ 
+
+ align:start position:0%
+person shooter as Pokemon. Wait
+a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> zombie.
+
+ align:start position:0%
+>> zombie.
+ 
+
+ align:start position:0%
+>> zombie.
+>> Wait, you have to you have to fight you
+
+ align:start position:0%
+>> Wait, you have to you have to fight you
+ 
+
+ align:start position:0%
+>> Wait, you have to you have to fight you
+have battles with uh words like uh
+
+ align:start position:0%
+have battles with uh words like uh
+ 
+
+ align:start position:0%
+have battles with uh words like uh
+Monkey Island.
+
+ align:start position:0%
+Monkey Island.
+ 
+
+ align:start position:0%
+Monkey Island.
+>> I like that text based zombie love.
+
+ align:start position:0%
+>> I like that text based zombie love.
+ 
+
+ align:start position:0%
+>> I like that text based zombie love.
+>> Text based zombie love.
+
+ align:start position:0%
+>> Text based zombie love.
+ 
+
+ align:start position:0%
+>> Text based zombie love.
+>> And then his really really long tongue
+
+ align:start position:0%
+>> And then his really really long tongue
+ 
+
+ align:start position:0%
+>> And then his really really long tongue
+down your throat.
+
+ align:start position:0%
+down your throat.
+ 
+
+ align:start position:0%
+down your throat.
+>> Zombie make out.
+
+ align:start position:0%
+>> Zombie make out.
+ 
+
+ align:start position:0%
+>> Zombie make out.
+>> Son of a title. So, if it's massively
+
+ align:start position:0%
+>> Son of a title. So, if it's massively
+ 
+
+ align:start position:0%
+>> Son of a title. So, if it's massively
+multiplayer, what if you, you know, you
+
+ align:start position:0%
+multiplayer, what if you, you know, you
+ 
+
+ align:start position:0%
+multiplayer, what if you, you know, you
+randomly get paired with five other
+
+ align:start position:0%
+randomly get paired with five other
+ 
+
+ align:start position:0%
+randomly get paired with five other
+players who are playing this game and
+
+ align:start position:0%
+players who are playing this game and
+ 
+
+ align:start position:0%
+players who are playing this game and
+you all have some kind of task you have
+
+ align:start position:0%
+you all have some kind of task you have
+ 
+
+ align:start position:0%
+you all have some kind of task you have
+to complete and you're given these
+
+ align:start position:0%
+to complete and you're given these
+ 
+
+ align:start position:0%
+to complete and you're given these
+particular zombie Pokemon that you can
+
+ align:start position:0%
+particular zombie Pokemon that you can
+ 
+
+ align:start position:0%
+particular zombie Pokemon that you can
+use to complete this particular task.
+
+ align:start position:0%
+use to complete this particular task.
+ 
+
+ align:start position:0%
+use to complete this particular task.
+>> So, you working those with those five.
+
+ align:start position:0%
+>> So, you working those with those five.
+ 
+
+ align:start position:0%
+>> So, you working those with those five.
+>> Wait, we have zombie pokeballs.
+
+ align:start position:0%
+>> Wait, we have zombie pokeballs.
+ 
+
+ align:start position:0%
+>> Wait, we have zombie pokeballs.
+>> What?
+
+ align:start position:0%
+>> What?
+ 
+
+ align:start position:0%
+>> What?
+>> We have a title.
+
+ align:start position:0%
+>> We have a title.
+ 
+
+ align:start position:0%
+>> We have a title.
+>> So, uh, Necroilia
+
+ align:start position:0%
+>> So, uh, Necroilia
+ 
+
+ align:start position:0%
+>> So, uh, Necroilia
+with F E L.
+
+ align:start position:0%
+with F E L.
+ 
+
+ align:start position:0%
+with F E L.
+>> The first zombie sex game.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Oh no.
+
+ align:start position:0%
+Oh no.
+ 
+
+ align:start position:0%
+Oh no.
+>> What if wait if it's going to be popular
+
+ align:start position:0%
+>> What if wait if it's going to be popular
+ 
+
+ align:start position:0%
+>> What if wait if it's going to be popular
+in Japan? You have to have tentful
+
+ align:start position:0%
+in Japan? You have to have tentful
+ 
+
+ align:start position:0%
+in Japan? You have to have tentful
+somewhere.
+
+ align:start position:0%
+somewhere.
+ 
+
+ align:start position:0%
+somewhere.
+>> What if you are a zombie and all the
+
+ align:start position:0%
+>> What if you are a zombie and all the
+ 
+
+ align:start position:0%
+>> What if you are a zombie and all the
+players are zombies and the NPCs are the
+
+ align:start position:0%
+players are zombies and the NPCs are the
+ 
+
+ align:start position:0%
+players are zombies and the NPCs are the
+humans and you like try to go on quests
+
+ align:start position:0%
+humans and you like try to go on quests
+ 
+
+ align:start position:0%
+humans and you like try to go on quests
+to make yourself more attractive and
+
+ align:start position:0%
+to make yourself more attractive and
+ 
+
+ align:start position:0%
+to make yourself more attractive and
+like learn human customs and you get
+
+ align:start position:0%
+like learn human customs and you get
+ 
+
+ align:start position:0%
+like learn human customs and you get
+points for like seducing humans.
+
+ align:start position:0%
+points for like seducing humans.
+ 
+
+ align:start position:0%
+points for like seducing humans.
+>> Yes.
+
+ align:start position:0%
+>> Yes.
+ 
+
+ align:start position:0%
+>> Yes.
+>> You have to make sure your your brain
+
+ align:start position:0%
+>> You have to make sure your your brain
+ 
+
+ align:start position:0%
+>> You have to make sure your your brain
+speed meter doesn't get too low though.
+
+ align:start position:0%
+speed meter doesn't get too low though.
+ 
+
+ align:start position:0%
+speed meter doesn't get too low though.
+>> So you have to eat them in seduce them
+
+ align:start position:0%
+>> So you have to eat them in seduce them
+ 
+
+ align:start position:0%
+>> So you have to eat them in seduce them
+in. And then if you like eat them with
+
+ align:start position:0%
+in. And then if you like eat them with
+ 
+
+ align:start position:0%
+in. And then if you like eat them with
+certain you
+
+ align:start position:0%
+certain you
+ 
+
+ align:start position:0%
+certain you
+>> eat the ones you don't want.
+
+ align:start position:0%
+>> eat the ones you don't want.
+ 
+
+ align:start position:0%
+>> eat the ones you don't want.
+>> You Yeah,
+
+ align:start position:0%
+>> You Yeah,
+ 
+
+ align:start position:0%
+>> You Yeah,
+>> that actually sounds like a fun vampire
+
+ align:start position:0%
+>> that actually sounds like a fun vampire
+ 
+
+ align:start position:0%
+>> that actually sounds like a fun vampire
+game. I'm going to put that out there.
+
+ align:start position:0%
+game. I'm going to put that out there.
+ 
+
+ align:start position:0%
+game. I'm going to put that out there.
+You're a vampire. You have to seduce a
+
+ align:start position:0%
+You're a vampire. You have to seduce a
+ 
+
+ align:start position:0%
+You're a vampire. You have to seduce a
+human female to bring back to drink.
+
+ align:start position:0%
+human female to bring back to drink.
+ 
+
+ align:start position:0%
+human female to bring back to drink.
+>> It's like prototype or or you have to
+
+ align:start position:0%
+>> It's like prototype or or you have to
+ 
+
+ align:start position:0%
+>> It's like prototype or or you have to
+seduce a human because you want to
+
+ align:start position:0%
+seduce a human because you want to
+ 
+
+ align:start position:0%
+seduce a human because you want to
+seduce a human, but at the same time you
+
+ align:start position:0%
+seduce a human, but at the same time you
+ 
+
+ align:start position:0%
+seduce a human, but at the same time you
+have to eat humans. So you have to hide
+
+ align:start position:0%
+have to eat humans. So you have to hide
+ 
+
+ align:start position:0%
+have to eat humans. So you have to hide
+the fact you're eating humans for the
+
+ align:start position:0%
+the fact you're eating humans for the
+ 
+
+ align:start position:0%
+the fact you're eating humans for the
+human decision.
+
+ align:start position:0%
+human decision.
+ 
+
+ align:start position:0%
+human decision.
+>> Oh, I see. So you have a human
+
+ align:start position:0%
+>> Oh, I see. So you have a human
+ 
+
+ align:start position:0%
+>> Oh, I see. So you have a human
+girlfriend and then like you eat other
+
+ align:start position:0%
+girlfriend and then like you eat other
+ 
+
+ align:start position:0%
+girlfriend and then like you eat other
+humans.
+
+ align:start position:0%
+humans.
+ 
+
+ align:start position:0%
+humans.
+>> Like while she's not looking like it's
+
+ align:start position:0%
+>> Like while she's not looking like it's
+ 
+
+ align:start position:0%
+>> Like while she's not looking like it's
+true.
+
+ align:start position:0%
+true.
+ 
+
+ align:start position:0%
+true.
+>> Have you been eating other girlfriends
+
+ align:start position:0%
+>> Have you been eating other girlfriends
+ 
+
+ align:start position:0%
+>> Have you been eating other girlfriends
+without me? Where's my stepdad? Uh,
+
+ align:start position:0%
+without me? Where's my stepdad? Uh,
+ 
+
+ align:start position:0%
+without me? Where's my stepdad? Uh,
+>> about that.
+
+ align:start position:0%
+>> about that.
+ 
+
+ align:start position:0%
+>> about that.
+>> Oh, that's who that guy was. I thought
+
+ align:start position:0%
+>> Oh, that's who that guy was. I thought
+ 
+
+ align:start position:0%
+>> Oh, that's who that guy was. I thought
+he was the delivery guy.
+
+ align:start position:0%
+he was the delivery guy.
+ 
+
+ align:start position:0%
+he was the delivery guy.
+>> Let's see. Zombies meets American
+
+ align:start position:0%
+>> Let's see. Zombies meets American
+ 
+
+ align:start position:0%
+>> Let's see. Zombies meets American
+Psycho.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> You've never seen American Psycho? Oh,
+
+ align:start position:0%
+>> You've never seen American Psycho? Oh,
+ 
+
+ align:start position:0%
+>> You've never seen American Psycho? Oh,
+>> Psycho.
+
+ align:start position:0%
+>> Psycho.
+ 
+
+ align:start position:0%
+>> Psycho.
+>> He goes around killing random people,
+
+ align:start position:0%
+>> He goes around killing random people,
+ 
+
+ align:start position:0%
+>> He goes around killing random people,
+but he has a girlfriend. I bet he's
+
+ align:start position:0%
+but he has a girlfriend. I bet he's
+ 
+
+ align:start position:0%
+but he has a girlfriend. I bet he's
+crazy. That's
+
+ align:start position:0%
+crazy. That's
+ 
+
+ align:start position:0%
+crazy. That's
+psycho,
+
+ align:start position:0%
+psycho,
+ 
+
+ align:start position:0%
+psycho,
+>> but better.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So necroilia
+
+ align:start position:0%
+So necroilia
+ 
+
+ align:start position:0%
+So necroilia
+>> get infected with emotion.
+
+ align:start position:0%
+>> get infected with emotion.
+ 
+
+ align:start position:0%
+>> get infected with emotion.
+>> Necroilia infected with love. Brains
+
+ align:start position:0%
+>> Necroilia infected with love. Brains
+ 
+
+ align:start position:0%
+>> Necroilia infected with love. Brains
+>> love after.
+
+ align:start position:0%
+>> love after.
+ 
+
+ align:start position:0%
+>> love after.
+>> It's a perfect movie. It's a perfect
+
+ align:start position:0%
+>> It's a perfect movie. It's a perfect
+ 
+
+ align:start position:0%
+>> It's a perfect movie. It's a perfect
+game.
+
+ align:start position:0%
+game.
+ 
+
+ align:start position:0%
+game.
+>> All right, guys. I'm going to have you
+
+ align:start position:0%
+>> All right, guys. I'm going to have you
+ 
+
+ align:start position:0%
+>> All right, guys. I'm going to have you
+uh have you stop. We're going to read
+
+ align:start position:0%
+uh have you stop. We're going to read
+ 
+
+ align:start position:0%
+uh have you stop. We're going to read
+the other.
+
+ align:start position:0%
+the other.
+ 
+
+ align:start position:0%
+the other.
+>> Love After Life.
+
+ align:start position:0%
+>> Love After Life.
+ 
+
+ align:start position:0%
+>> Love After Life.
+>> I like it. I like it.
+
+ align:start position:0%
+>> I like it. I like it.
+ 
+
+ align:start position:0%
+>> I like it. I like it.
+>> That's really good.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think that was
+
+ align:start position:0%
+I think that was
+ 
+
+ align:start position:0%
+I think that was
+>> that was good.
+
+ align:start position:0%
+>> that was good.
+ 
+
+ align:start position:0%
+>> that was good.
+>> All right, guys. So, our publisher is
+
+ align:start position:0%
+>> All right, guys. So, our publisher is
+ 
+
+ align:start position:0%
+>> All right, guys. So, our publisher is
+going to give us so much.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> It may it may seem kind of kind of odd
+
+ align:start position:0%
+>> It may it may seem kind of kind of odd
+ 
+
+ align:start position:0%
+>> It may it may seem kind of kind of odd
+to have you guys do this brainstorming,
+
+ align:start position:0%
+to have you guys do this brainstorming,
+ 
+
+ align:start position:0%
+to have you guys do this brainstorming,
+then what I actually want to talk about
+
+ align:start position:0%
+then what I actually want to talk about
+ 
+
+ align:start position:0%
+then what I actually want to talk about
+is rather than the ideas that you came
+
+ align:start position:0%
+is rather than the ideas that you came
+ 
+
+ align:start position:0%
+is rather than the ideas that you came
+up with because I'm sure they're all
+
+ align:start position:0%
+up with because I'm sure they're all
+ 
+
+ align:start position:0%
+up with because I'm sure they're all
+really good.
+
+ align:start position:0%
+really good.
+ 
+
+ align:start position:0%
+really good.
+>> I know. So, sad. But what what really
+
+ align:start position:0%
+>> I know. So, sad. But what what really
+ 
+
+ align:start position:0%
+>> I know. So, sad. But what what really
+matters is the process, right? Because
+
+ align:start position:0%
+matters is the process, right? Because
+ 
+
+ align:start position:0%
+matters is the process, right? Because
+um the point of brainstorming is to
+
+ align:start position:0%
+um the point of brainstorming is to
+ 
+
+ align:start position:0%
+um the point of brainstorming is to
+withhold judgment. judging judging which
+
+ align:start position:0%
+withhold judgment. judging judging which
+ 
+
+ align:start position:0%
+withhold judgment. judging judging which
+of your ideas is best um shouldn't have
+
+ align:start position:0%
+of your ideas is best um shouldn't have
+ 
+
+ align:start position:0%
+of your ideas is best um shouldn't have
+even been happening at this stage. And
+
+ align:start position:0%
+even been happening at this stage. And
+ 
+
+ align:start position:0%
+even been happening at this stage. And
+so, you know, one one kind of question,
+
+ align:start position:0%
+so, you know, one one kind of question,
+ 
+
+ align:start position:0%
+so, you know, one one kind of question,
+you know, we'll come back to what went
+
+ align:start position:0%
+you know, we'll come back to what went
+ 
+
+ align:start position:0%
+you know, we'll come back to what went
+well, but um what what sort of uh
+
+ align:start position:0%
+well, but um what what sort of uh
+ 
+
+ align:start position:0%
+well, but um what what sort of uh
+stumbling blocks did you guys run into
+
+ align:start position:0%
+stumbling blocks did you guys run into
+ 
+
+ align:start position:0%
+stumbling blocks did you guys run into
+in this process as you were doing it?
+
+ align:start position:0%
+in this process as you were doing it?
+ 
+
+ align:start position:0%
+in this process as you were doing it?
+Did it did it all go perfectly or I
+
+ align:start position:0%
+Did it did it all go perfectly or I
+ 
+
+ align:start position:0%
+Did it did it all go perfectly or I
+highly doubt, but what sort of things
+
+ align:start position:0%
+highly doubt, but what sort of things
+ 
+
+ align:start position:0%
+highly doubt, but what sort of things
+>> I was going to say like we were trying
+
+ align:start position:0%
+>> I was going to say like we were trying
+ 
+
+ align:start position:0%
+>> I was going to say like we were trying
+to design this whole game. So, sometimes
+
+ align:start position:0%
+to design this whole game. So, sometimes
+ 
+
+ align:start position:0%
+to design this whole game. So, sometimes
+we say features and they would push
+
+ align:start position:0%
+we say features and they would push
+ 
+
+ align:start position:0%
+we say features and they would push
+games.
+
+ align:start position:0%
+games.
+ 
+
+ align:start position:0%
+games.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> So it might have been
+
+ align:start position:0%
+>> So it might have been
+ 
+
+ align:start position:0%
+>> So it might have been
+like things you want.
+
+ align:start position:0%
+like things you want.
+ 
+
+ align:start position:0%
+like things you want.
+>> Yeah. Yeah. In some senses it may have
+
+ align:start position:0%
+>> Yeah. Yeah. In some senses it may have
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. In some senses it may have
+been constrained in one area, right?
+
+ align:start position:0%
+been constrained in one area, right?
+ 
+
+ align:start position:0%
+been constrained in one area, right?
+Yeah. Sure. Zombies and a love story but
+
+ align:start position:0%
+Yeah. Sure. Zombies and a love story but
+ 
+
+ align:start position:0%
+Yeah. Sure. Zombies and a love story but
+but then it was like asking for a whole
+
+ align:start position:0%
+but then it was like asking for a whole
+ 
+
+ align:start position:0%
+but then it was like asking for a whole
+lot and so it could have been can we
+
+ align:start position:0%
+lot and so it could have been can we
+ 
+
+ align:start position:0%
+lot and so it could have been can we
+just brainstorm the title or can we just
+
+ align:start position:0%
+just brainstorm the title or can we just
+ 
+
+ align:start position:0%
+just brainstorm the title or can we just
+brainstorm this? Can we just brainstorm
+
+ align:start position:0%
+brainstorm this? Can we just brainstorm
+ 
+
+ align:start position:0%
+brainstorm this? Can we just brainstorm
+that? What about
+
+ align:start position:0%
+that? What about
+ 
+
+ align:start position:0%
+that? What about
+>> we very briefly got sidetracked on
+
+ align:start position:0%
+>> we very briefly got sidetracked on
+ 
+
+ align:start position:0%
+>> we very briefly got sidetracked on
+Pokemon?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I think I think zombies for a second we
+
+ align:start position:0%
+I think I think zombies for a second we
+ 
+
+ align:start position:0%
+I think I think zombies for a second we
+got like it was like Pokemon only
+
+ align:start position:0%
+got like it was like Pokemon only
+ 
+
+ align:start position:0%
+got like it was like Pokemon only
+Pokemon first person shooter but that
+
+ align:start position:0%
+Pokemon first person shooter but that
+ 
+
+ align:start position:0%
+Pokemon first person shooter but that
+was like 25 seconds.
+
+ align:start position:0%
+was like 25 seconds.
+ 
+
+ align:start position:0%
+was like 25 seconds.
+>> Any other thoughts? I mean the whole
+
+ align:start position:0%
+>> Any other thoughts? I mean the whole
+ 
+
+ align:start position:0%
+>> Any other thoughts? I mean the whole
+recruit be like your help you had
+
+ align:start position:0%
+recruit be like your help you had
+ 
+
+ align:start position:0%
+recruit be like your help you had
+personally but if you had any challenges
+
+ align:start position:0%
+personally but if you had any challenges
+ 
+
+ align:start position:0%
+personally but if you had any challenges
+with like you know
+
+ align:start position:0%
+with like you know
+ 
+
+ align:start position:0%
+with like you know
+>> so I feel like if somebody says a really
+
+ align:start position:0%
+>> so I feel like if somebody says a really
+ 
+
+ align:start position:0%
+>> so I feel like if somebody says a really
+good idea and everyone's kind of stuck
+
+ align:start position:0%
+good idea and everyone's kind of stuck
+ 
+
+ align:start position:0%
+good idea and everyone's kind of stuck
+on that idea and you have to kind of get
+
+ align:start position:0%
+on that idea and you have to kind of get
+ 
+
+ align:start position:0%
+on that idea and you have to kind of get
+through that whole idea before any other
+
+ align:start position:0%
+through that whole idea before any other
+ 
+
+ align:start position:0%
+through that whole idea before any other
+ideas can come out.
+
+ align:start position:0%
+ideas can come out.
+ 
+
+ align:start position:0%
+ideas can come out.
+>> Yeah. Yeah. It's true.
+
+ align:start position:0%
+>> Yeah. Yeah. It's true.
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. It's true.
+like what other kind of noise are there?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah. So like a few other ones.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Sure.
+
+ align:start position:0%
+>> Sure.
+ 
+
+ align:start position:0%
+>> Sure.
+>> Kind of hard to like jump in my own
+
+ align:start position:0%
+>> Kind of hard to like jump in my own
+ 
+
+ align:start position:0%
+>> Kind of hard to like jump in my own
+ideas.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah, it's really hard to brainstorm. I
+
+ align:start position:0%
+>> Yeah, it's really hard to brainstorm. I
+ 
+
+ align:start position:0%
+>> Yeah, it's really hard to brainstorm. I
+mean you guys actually I mean both
+
+ align:start position:0%
+mean you guys actually I mean both
+ 
+
+ align:start position:0%
+mean you guys actually I mean both
+groups but I I stopped it with you guys
+
+ align:start position:0%
+groups but I I stopped it with you guys
+ 
+
+ align:start position:0%
+groups but I I stopped it with you guys
+and you guys had this interesting kind
+
+ align:start position:0%
+and you guys had this interesting kind
+ 
+
+ align:start position:0%
+and you guys had this interesting kind
+of momentum going and I was watching you
+
+ align:start position:0%
+of momentum going and I was watching you
+ 
+
+ align:start position:0%
+of momentum going and I was watching you
+trying to write it all down. It was it
+
+ align:start position:0%
+trying to write it all down. It was it
+ 
+
+ align:start position:0%
+trying to write it all down. It was it
+was way hard like because like ideas
+
+ align:start position:0%
+was way hard like because like ideas
+ 
+
+ align:start position:0%
+was way hard like because like ideas
+were coming in like as you were
+
+ align:start position:0%
+were coming in like as you were
+ 
+
+ align:start position:0%
+were coming in like as you were
+finishing the last idea. So it is you
+
+ align:start position:0%
+finishing the last idea. So it is you
+ 
+
+ align:start position:0%
+finishing the last idea. So it is you
+know if a group has really good momentum
+
+ align:start position:0%
+know if a group has really good momentum
+ 
+
+ align:start position:0%
+know if a group has really good momentum
+it's I I actually I really like the idea
+
+ align:start position:0%
+it's I I actually I really like the idea
+ 
+
+ align:start position:0%
+it's I I actually I really like the idea
+of having two people where each person's
+
+ align:start position:0%
+of having two people where each person's
+ 
+
+ align:start position:0%
+of having two people where each person's
+writing every other one. Of course the
+
+ align:start position:0%
+writing every other one. Of course the
+ 
+
+ align:start position:0%
+writing every other one. Of course the
+difficulty is then you kind of pull two
+
+ align:start position:0%
+difficulty is then you kind of pull two
+ 
+
+ align:start position:0%
+difficulty is then you kind of pull two
+people out of contributing right. So
+
+ align:start position:0%
+people out of contributing right. So
+ 
+
+ align:start position:0%
+people out of contributing right. So
+it's you know the organization of the
+
+ align:start position:0%
+it's you know the organization of the
+ 
+
+ align:start position:0%
+it's you know the organization of the
+actual group is is kind of important
+
+ align:start position:0%
+actual group is is kind of important
+ 
+
+ align:start position:0%
+actual group is is kind of important
+that works.
+
+ align:start position:0%
+that works.
+ 
+
+ align:start position:0%
+that works.
+>> Do you ever recommend using like a tape
+
+ align:start position:0%
+>> Do you ever recommend using like a tape
+ 
+
+ align:start position:0%
+>> Do you ever recommend using like a tape
+recorder like you're doing for this
+
+ align:start position:0%
+recorder like you're doing for this
+ 
+
+ align:start position:0%
+recorder like you're doing for this
+class?
+
+ align:start position:0%
+class?
+ 
+
+ align:start position:0%
+class?
+>> Yeah. Yeah. Absolutely. I mean that it's
+
+ align:start position:0%
+>> Yeah. Yeah. Absolutely. I mean that it's
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Absolutely. I mean that it's
+it certainly makes sense. One of the
+
+ align:start position:0%
+it certainly makes sense. One of the
+ 
+
+ align:start position:0%
+it certainly makes sense. One of the
+things that you know, one of the things
+
+ align:start position:0%
+things that you know, one of the things
+ 
+
+ align:start position:0%
+things that you know, one of the things
+that Osborne says, which I think is
+
+ align:start position:0%
+that Osborne says, which I think is
+ 
+
+ align:start position:0%
+that Osborne says, which I think is
+>> can't put a shape or cord down. Remember
+
+ align:start position:0%
+>> can't put a shape or cord down. Remember
+ 
+
+ align:start position:0%
+>> can't put a shape or cord down. Remember
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+>> Yeah. Yeah. But he also says like it's
+
+ align:start position:0%
+>> Yeah. Yeah. But he also says like it's
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. But he also says like it's
+the one of the most important things for
+
+ align:start position:0%
+the one of the most important things for
+ 
+
+ align:start position:0%
+the one of the most important things for
+the secretary scribe is to is to number
+
+ align:start position:0%
+the secretary scribe is to is to number
+ 
+
+ align:start position:0%
+the secretary scribe is to is to number
+things so that you know how many you
+
+ align:start position:0%
+things so that you know how many you
+ 
+
+ align:start position:0%
+things so that you know how many you
+have. I'm sort of like is that is that
+
+ align:start position:0%
+have. I'm sort of like is that is that
+ 
+
+ align:start position:0%
+have. I'm sort of like is that is that
+just to support your work? Like be like,
+
+ align:start position:0%
+just to support your work? Like be like,
+ 
+
+ align:start position:0%
+just to support your work? Like be like,
+look, you know, we came up with 110
+
+ align:start position:0%
+look, you know, we came up with 110
+ 
+
+ align:start position:0%
+look, you know, we came up with 110
+ideas. That's amazing. You know, it's
+
+ align:start position:0%
+ideas. That's amazing. You know, it's
+ 
+
+ align:start position:0%
+ideas. That's amazing. You know, it's
+like how many doesn't seem to matter as
+
+ align:start position:0%
+like how many doesn't seem to matter as
+ 
+
+ align:start position:0%
+like how many doesn't seem to matter as
+much as the quality of the ideas. So, um
+
+ align:start position:0%
+much as the quality of the ideas. So, um
+ 
+
+ align:start position:0%
+much as the quality of the ideas. So, um
+I thought it was weird that you said
+
+ align:start position:0%
+I thought it was weird that you said
+ 
+
+ align:start position:0%
+I thought it was weird that you said
+that. But um yeah, I mean tape
+
+ align:start position:0%
+that. But um yeah, I mean tape
+ 
+
+ align:start position:0%
+that. But um yeah, I mean tape
+recording, video recording, any way of
+
+ align:start position:0%
+recording, video recording, any way of
+ 
+
+ align:start position:0%
+recording, video recording, any way of
+documenting the process I think is the
+
+ align:start position:0%
+documenting the process I think is the
+ 
+
+ align:start position:0%
+documenting the process I think is the
+most important problem. Um and and
+
+ align:start position:0%
+most important problem. Um and and
+ 
+
+ align:start position:0%
+most important problem. Um and and
+actually you know he does make a good
+
+ align:start position:0%
+actually you know he does make a good
+ 
+
+ align:start position:0%
+actually you know he does make a good
+point of saying you know one of the
+
+ align:start position:0%
+point of saying you know one of the
+ 
+
+ align:start position:0%
+point of saying you know one of the
+problems with brainstorming as it kind
+
+ align:start position:0%
+problems with brainstorming as it kind
+ 
+
+ align:start position:0%
+problems with brainstorming as it kind
+of evolved from when he first introduced
+
+ align:start position:0%
+of evolved from when he first introduced
+ 
+
+ align:start position:0%
+of evolved from when he first introduced
+it at this one place and when people
+
+ align:start position:0%
+it at this one place and when people
+ 
+
+ align:start position:0%
+it at this one place and when people
+started kind of running with it without
+
+ align:start position:0%
+started kind of running with it without
+ 
+
+ align:start position:0%
+started kind of running with it without
+thinking about the principles is they
+
+ align:start position:0%
+thinking about the principles is they
+ 
+
+ align:start position:0%
+thinking about the principles is they
+would brainstorm and then that was sort
+
+ align:start position:0%
+would brainstorm and then that was sort
+ 
+
+ align:start position:0%
+would brainstorm and then that was sort
+of it and it was like you really have to
+
+ align:start position:0%
+of it and it was like you really have to
+ 
+
+ align:start position:0%
+of it and it was like you really have to
+kind of look back at what you've come up
+
+ align:start position:0%
+kind of look back at what you've come up
+ 
+
+ align:start position:0%
+kind of look back at what you've come up
+with. Um it's really important to kind
+
+ align:start position:0%
+with. Um it's really important to kind
+ 
+
+ align:start position:0%
+with. Um it's really important to kind
+of reflect on what you've done as a
+
+ align:start position:0%
+of reflect on what you've done as a
+ 
+
+ align:start position:0%
+of reflect on what you've done as a
+second step. Um, you know, and so, uh,
+
+ align:start position:0%
+second step. Um, you know, and so, uh,
+ 
+
+ align:start position:0%
+second step. Um, you know, and so, uh,
+that's kind of important, too. How about
+
+ align:start position:0%
+that's kind of important, too. How about
+ 
+
+ align:start position:0%
+that's kind of important, too. How about
+the judgment thing? Was there I mean,
+
+ align:start position:0%
+the judgment thing? Was there I mean,
+ 
+
+ align:start position:0%
+the judgment thing? Was there I mean,
+people I I didn't notice a whole lot of
+
+ align:start position:0%
+people I I didn't notice a whole lot of
+ 
+
+ align:start position:0%
+people I I didn't notice a whole lot of
+like criticism, but like I don't think
+
+ align:start position:0%
+like criticism, but like I don't think
+ 
+
+ align:start position:0%
+like criticism, but like I don't think
+anybody was really good. I was like, oh,
+
+ align:start position:0%
+anybody was really good. I was like, oh,
+ 
+
+ align:start position:0%
+anybody was really good. I was like, oh,
+that's a terrible idea. But did you find
+
+ align:start position:0%
+that's a terrible idea. But did you find
+ 
+
+ align:start position:0%
+that's a terrible idea. But did you find
+it hard to not pass judgment on ideas as
+
+ align:start position:0%
+it hard to not pass judgment on ideas as
+ 
+
+ align:start position:0%
+it hard to not pass judgment on ideas as
+they were coming out, even your own?
+
+ align:start position:0%
+they were coming out, even your own?
+ 
+
+ align:start position:0%
+they were coming out, even your own?
+>> Yeah. I mean, I definitely let more than
+
+ align:start position:0%
+>> Yeah. I mean, I definitely let more than
+ 
+
+ align:start position:0%
+>> Yeah. I mean, I definitely let more than
+one like, I like that slip, you know,
+
+ align:start position:0%
+one like, I like that slip, you know,
+ 
+
+ align:start position:0%
+one like, I like that slip, you know,
+like, oh, that's
+
+ align:start position:0%
+like, oh, that's
+ 
+
+ align:start position:0%
+like, oh, that's
+>> generally that's okay. I mean like you
+
+ align:start position:0%
+>> generally that's okay. I mean like you
+ 
+
+ align:start position:0%
+>> generally that's okay. I mean like you
+know it's it's you know what you want to
+
+ align:start position:0%
+know it's it's you know what you want to
+ 
+
+ align:start position:0%
+know it's it's you know what you want to
+avoid is like the oh my god we've got to
+
+ align:start position:0%
+avoid is like the oh my god we've got to
+ 
+
+ align:start position:0%
+avoid is like the oh my god we've got to
+do this one you know like that's that
+
+ align:start position:0%
+do this one you know like that's that
+ 
+
+ align:start position:0%
+do this one you know like that's that
+will that will derail everything because
+
+ align:start position:0%
+will that will derail everything because
+ 
+
+ align:start position:0%
+will that will derail everything because
+then it's like you know just a loud the
+
+ align:start position:0%
+then it's like you know just a loud the
+ 
+
+ align:start position:0%
+then it's like you know just a loud the
+loud voice that proclaims that we're
+
+ align:start position:0%
+loud voice that proclaims that we're
+ 
+
+ align:start position:0%
+loud voice that proclaims that we're
+done because we got the idea will derail
+
+ align:start position:0%
+done because we got the idea will derail
+ 
+
+ align:start position:0%
+done because we got the idea will derail
+things but you know nothing encourages a
+
+ align:start position:0%
+things but you know nothing encourages a
+ 
+
+ align:start position:0%
+things but you know nothing encourages a
+person who's shy more than feeling like
+
+ align:start position:0%
+person who's shy more than feeling like
+ 
+
+ align:start position:0%
+person who's shy more than feeling like
+their idea actually was good or
+
+ align:start position:0%
+their idea actually was good or
+ 
+
+ align:start position:0%
+their idea actually was good or
+meritorious and so yeah you know that
+
+ align:start position:0%
+meritorious and so yeah you know that
+ 
+
+ align:start position:0%
+meritorious and so yeah you know that
+sort of stuff is fine u you know you
+
+ align:start position:0%
+sort of stuff is fine u you know you
+ 
+
+ align:start position:0%
+sort of stuff is fine u you know you
+want to avoid the stop the process
+
+ align:start position:0%
+want to avoid the stop the process
+ 
+
+ align:start position:0%
+want to avoid the stop the process
+>> I I think I did say at some point like
+
+ align:start position:0%
+>> I I think I did say at some point like
+ 
+
+ align:start position:0%
+>> I I think I did say at some point like
+We've got our title which is probably
+
+ align:start position:0%
+We've got our title which is probably
+ 
+
+ align:start position:0%
+We've got our title which is probably
+not.
+
+ align:start position:0%
+not.
+ 
+
+ align:start position:0%
+not.
+>> Yeah. I mean it's it's really it's just
+
+ align:start position:0%
+>> Yeah. I mean it's it's really it's just
+ 
+
+ align:start position:0%
+>> Yeah. I mean it's it's really it's just
+a hard thing to kind of train yourself
+
+ align:start position:0%
+a hard thing to kind of train yourself
+ 
+
+ align:start position:0%
+a hard thing to kind of train yourself
+from doing.
+
+ align:start position:0%
+from doing.
+ 
+
+ align:start position:0%
+from doing.
+>> Come on. Is it necroilia title?
+
+ align:start position:0%
+>> Come on. Is it necroilia title?
+ 
+
+ align:start position:0%
+>> Come on. Is it necroilia title?
+>> How
+
+ align:start position:0%
+>> How
+ 
+
+ align:start position:0%
+>> How
+many self-censorers still out there
+
+ align:start position:0%
+many self-censorers still out there
+ 
+
+ align:start position:0%
+many self-censorers still out there
+where a lot of people thought of ideas
+
+ align:start position:0%
+where a lot of people thought of ideas
+ 
+
+ align:start position:0%
+where a lot of people thought of ideas
+but then just didn't contribute?
+
+ align:start position:0%
+but then just didn't contribute?
+ 
+
+ align:start position:0%
+but then just didn't contribute?
+It's good if you didn't. It's great. I
+
+ align:start position:0%
+It's good if you didn't. It's great. I
+ 
+
+ align:start position:0%
+It's good if you didn't. It's great. I
+mean it's great if you if everybody felt
+
+ align:start position:0%
+mean it's great if you if everybody felt
+ 
+
+ align:start position:0%
+mean it's great if you if everybody felt
+like a cool that's that's really good.
+
+ align:start position:0%
+like a cool that's that's really good.
+ 
+
+ align:start position:0%
+like a cool that's that's really good.
+That's really good. So um so I would say
+
+ align:start position:0%
+That's really good. So um so I would say
+ 
+
+ align:start position:0%
+That's really good. So um so I would say
+that's one thing what that went well.
+
+ align:start position:0%
+that's one thing what that went well.
+ 
+
+ align:start position:0%
+that's one thing what that went well.
+What other things went well you guys?
+
+ align:start position:0%
+What other things went well you guys?
+ 
+
+ align:start position:0%
+What other things went well you guys?
+>> The tagline Yeah, specifically just
+
+ align:start position:0%
+>> The tagline Yeah, specifically just
+ 
+
+ align:start position:0%
+>> The tagline Yeah, specifically just
+coming up with tagline.
+
+ align:start position:0%
+coming up with tagline.
+ 
+
+ align:start position:0%
+coming up with tagline.
+>> Well, just in love
+
+ align:start position:0%
+>> Well, just in love
+ 
+
+ align:start position:0%
+>> Well, just in love
+life. Is it love after life?
+
+ align:start position:0%
+life. Is it love after life?
+ 
+
+ align:start position:0%
+life. Is it love after life?
+>> Love after life.
+
+ align:start position:0%
+>> Love after life.
+ 
+
+ align:start position:0%
+>> Love after life.
+>> That's cool. I mean, did you guys feel
+
+ align:start position:0%
+>> That's cool. I mean, did you guys feel
+ 
+
+ align:start position:0%
+>> That's cool. I mean, did you guys feel
+like you had momentum? It seemed to me
+
+ align:start position:0%
+like you had momentum? It seemed to me
+ 
+
+ align:start position:0%
+like you had momentum? It seemed to me
+watching that there was momentum
+
+ align:start position:0%
+watching that there was momentum
+ 
+
+ align:start position:0%
+watching that there was momentum
+building that it was
+
+ align:start position:0%
+building that it was
+ 
+
+ align:start position:0%
+building that it was
+>> I think you did a really good job of
+
+ align:start position:0%
+>> I think you did a really good job of
+ 
+
+ align:start position:0%
+>> I think you did a really good job of
+taking a lot of different ideas that we
+
+ align:start position:0%
+taking a lot of different ideas that we
+ 
+
+ align:start position:0%
+taking a lot of different ideas that we
+had and started synthesizing them into
+
+ align:start position:0%
+had and started synthesizing them into
+ 
+
+ align:start position:0%
+had and started synthesizing them into
+different things. Oh, that idea would
+
+ align:start position:0%
+different things. Oh, that idea would
+ 
+
+ align:start position:0%
+different things. Oh, that idea would
+work well if we did this. Oh, and then
+
+ align:start position:0%
+work well if we did this. Oh, and then
+ 
+
+ align:start position:0%
+work well if we did this. Oh, and then
+we could use like that name and that
+
+ align:start position:0%
+we could use like that name and that
+ 
+
+ align:start position:0%
+we could use like that name and that
+would fit there.
+
+ align:start position:0%
+would fit there.
+ 
+
+ align:start position:0%
+would fit there.
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Who are the two leaders for the two
+
+ align:start position:0%
+>> Who are the two leaders for the two
+ 
+
+ align:start position:0%
+>> Who are the two leaders for the two
+groups? the clips.
+
+ align:start position:0%
+groups? the clips.
+ 
+
+ align:start position:0%
+groups? the clips.
+>> Did you did you guys feel like you had
+
+ align:start position:0%
+>> Did you did you guys feel like you had
+ 
+
+ align:start position:0%
+>> Did you did you guys feel like you had
+to do much facilitating
+
+ align:start position:0%
+to do much facilitating
+ 
+
+ align:start position:0%
+to do much facilitating
+>> really? So, the hard part is really just
+
+ align:start position:0%
+>> really? So, the hard part is really just
+ 
+
+ align:start position:0%
+>> really? So, the hard part is really just
+at the beginning where it's like how do
+
+ align:start position:0%
+at the beginning where it's like how do
+ 
+
+ align:start position:0%
+at the beginning where it's like how do
+we want to just approach this thing? And
+
+ align:start position:0%
+we want to just approach this thing? And
+ 
+
+ align:start position:0%
+we want to just approach this thing? And
+so, I guess we decided to start with the
+
+ align:start position:0%
+so, I guess we decided to start with the
+ 
+
+ align:start position:0%
+so, I guess we decided to start with the
+title or like it was either the titles
+
+ align:start position:0%
+title or like it was either the titles
+ 
+
+ align:start position:0%
+title or like it was either the titles
+or the main features and we were just
+
+ align:start position:0%
+or the main features and we were just
+ 
+
+ align:start position:0%
+or the main features and we were just
+like, all right, let's bunch of random
+
+ align:start position:0%
+like, all right, let's bunch of random
+ 
+
+ align:start position:0%
+like, all right, let's bunch of random
+titles, see
+
+ align:start position:0%
+titles, see
+ 
+
+ align:start position:0%
+titles, see
+>> forgot I was the lead.
+
+ align:start position:0%
+>> forgot I was the lead.
+ 
+
+ align:start position:0%
+>> forgot I was the lead.
+>> I didn't lead anything.
+
+ align:start position:0%
+>> I didn't lead anything.
+ 
+
+ align:start position:0%
+>> I didn't lead anything.
+you know, if if you don't have a whole
+
+ align:start position:0%
+you know, if if you don't have a whole
+ 
+
+ align:start position:0%
+you know, if if you don't have a whole
+lot of facilitating to do, it generally
+
+ align:start position:0%
+lot of facilitating to do, it generally
+ 
+
+ align:start position:0%
+lot of facilitating to do, it generally
+means that the group is running. Okay.
+
+ align:start position:0%
+means that the group is running. Okay.
+ 
+
+ align:start position:0%
+means that the group is running. Okay.
+Um, you know, I do think I do think you
+
+ align:start position:0%
+Um, you know, I do think I do think you
+ 
+
+ align:start position:0%
+Um, you know, I do think I do think you
+have a good point. A lot of the
+
+ align:start position:0%
+have a good point. A lot of the
+ 
+
+ align:start position:0%
+have a good point. A lot of the
+facilitators work comes at the beginning
+
+ align:start position:0%
+facilitators work comes at the beginning
+ 
+
+ align:start position:0%
+facilitators work comes at the beginning
+of the process or even before the
+
+ align:start position:0%
+of the process or even before the
+ 
+
+ align:start position:0%
+of the process or even before the
+process even began, making sure the
+
+ align:start position:0%
+process even began, making sure the
+ 
+
+ align:start position:0%
+process even began, making sure the
+constraints are clear and that you guys
+
+ align:start position:0%
+constraints are clear and that you guys
+ 
+
+ align:start position:0%
+constraints are clear and that you guys
+know what you're going to be working on.
+
+ align:start position:0%
+know what you're going to be working on.
+ 
+
+ align:start position:0%
+know what you're going to be working on.
+Um, okay. So, bringing this back, this
+
+ align:start position:0%
+Um, okay. So, bringing this back, this
+ 
+
+ align:start position:0%
+Um, okay. So, bringing this back, this
+is a game design class, right? I mean, I
+
+ align:start position:0%
+is a game design class, right? I mean, I
+ 
+
+ align:start position:0%
+is a game design class, right? I mean, I
+sort of touched on it early, but you
+
+ align:start position:0%
+sort of touched on it early, but you
+ 
+
+ align:start position:0%
+sort of touched on it early, but you
+know, how how do you guys see this um
+
+ align:start position:0%
+know, how how do you guys see this um
+ 
+
+ align:start position:0%
+know, how how do you guys see this um
+being a useful kind of mechanic or
+
+ align:start position:0%
+being a useful kind of mechanic or
+ 
+
+ align:start position:0%
+being a useful kind of mechanic or
+useful tool in you know what it's funny?
+
+ align:start position:0%
+useful tool in you know what it's funny?
+ 
+
+ align:start position:0%
+useful tool in you know what it's funny?
+I call it mechanic. Maybe you catch that
+
+ align:start position:0%
+I call it mechanic. Maybe you catch that
+ 
+
+ align:start position:0%
+I call it mechanic. Maybe you catch that
+paragraph in Alex where the guy was
+
+ align:start position:0%
+paragraph in Alex where the guy was
+ 
+
+ align:start position:0%
+paragraph in Alex where the guy was
+saying when my team feels like they're
+
+ align:start position:0%
+saying when my team feels like they're
+ 
+
+ align:start position:0%
+saying when my team feels like they're
+playing, it's a way more productive
+
+ align:start position:0%
+playing, it's a way more productive
+ 
+
+ align:start position:0%
+playing, it's a way more productive
+brainstorm than when not. And I thought
+
+ align:start position:0%
+brainstorm than when not. And I thought
+ 
+
+ align:start position:0%
+brainstorm than when not. And I thought
+that was really interesting, right?
+
+ align:start position:0%
+that was really interesting, right?
+ 
+
+ align:start position:0%
+that was really interesting, right?
+Because like there are elements of of
+
+ align:start position:0%
+Because like there are elements of of
+ 
+
+ align:start position:0%
+Because like there are elements of of
+giness to this. Um which I think is kind
+
+ align:start position:0%
+giness to this. Um which I think is kind
+ 
+
+ align:start position:0%
+giness to this. Um which I think is kind
+of interesting. Um, so you know, how do
+
+ align:start position:0%
+of interesting. Um, so you know, how do
+ 
+
+ align:start position:0%
+of interesting. Um, so you know, how do
+you guys think this could improve, you
+
+ align:start position:0%
+you guys think this could improve, you
+ 
+
+ align:start position:0%
+you guys think this could improve, you
+know, the general game design of the
+
+ align:start position:0%
+know, the general game design of the
+ 
+
+ align:start position:0%
+know, the general game design of the
+process?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> I feel like after you you have a game
+
+ align:start position:0%
+>> I feel like after you you have a game
+ 
+
+ align:start position:0%
+>> I feel like after you you have a game
+and you're testing it and there's like a
+
+ align:start position:0%
+and you're testing it and there's like a
+ 
+
+ align:start position:0%
+and you're testing it and there's like a
+major flaw that you know it's taking too
+
+ align:start position:0%
+major flaw that you know it's taking too
+ 
+
+ align:start position:0%
+major flaw that you know it's taking too
+long or or something like that and
+
+ align:start position:0%
+long or or something like that and
+ 
+
+ align:start position:0%
+long or or something like that and
+everyone sits down and brainstorm like
+
+ align:start position:0%
+everyone sits down and brainstorm like
+ 
+
+ align:start position:0%
+everyone sits down and brainstorm like
+okay this is exactly what our problem is
+
+ align:start position:0%
+okay this is exactly what our problem is
+ 
+
+ align:start position:0%
+okay this is exactly what our problem is
+fix it.
+
+ align:start position:0%
+fix it.
+ 
+
+ align:start position:0%
+fix it.
+>> Yeah. Yeah. Kind of overcoming
+
+ align:start position:0%
+>> Yeah. Yeah. Kind of overcoming
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Kind of overcoming
+roadblocks. Yeah. Sure. never to have
+
+ align:start position:0%
+roadblocks. Yeah. Sure. never to have
+ 
+
+ align:start position:0%
+roadblocks. Yeah. Sure. never to have
+come up with half the cool ideas that we
+
+ align:start position:0%
+come up with half the cool ideas that we
+ 
+
+ align:start position:0%
+come up with half the cool ideas that we
+came up with in the process and just me
+
+ align:start position:0%
+came up with in the process and just me
+ 
+
+ align:start position:0%
+came up with in the process and just me
+thinking alone never to come up with
+
+ align:start position:0%
+thinking alone never to come up with
+ 
+
+ align:start position:0%
+thinking alone never to come up with
+like Pokemon zombies.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Well, this is good just in general make
+
+ align:start position:0%
+>> Well, this is good just in general make
+ 
+
+ align:start position:0%
+>> Well, this is good just in general make
+to think up a game because maybe it's
+
+ align:start position:0%
+to think up a game because maybe it's
+ 
+
+ align:start position:0%
+to think up a game because maybe it's
+like oh every single game has been
+
+ align:start position:0%
+like oh every single game has been
+ 
+
+ align:start position:0%
+like oh every single game has been
+decide people made games of all types.
+
+ align:start position:0%
+decide people made games of all types.
+ 
+
+ align:start position:0%
+decide people made games of all types.
+How am I going to make an unique game?
+
+ align:start position:0%
+How am I going to make an unique game?
+ 
+
+ align:start position:0%
+How am I going to make an unique game?
+It's brainstorm like hm those two things
+
+ align:start position:0%
+It's brainstorm like hm those two things
+ 
+
+ align:start position:0%
+It's brainstorm like hm those two things
+I've I've never seen that before. That
+
+ align:start position:0%
+I've I've never seen that before. That
+ 
+
+ align:start position:0%
+I've I've never seen that before. That
+could be interesting. Yeah, and that's a
+
+ align:start position:0%
+could be interesting. Yeah, and that's a
+ 
+
+ align:start position:0%
+could be interesting. Yeah, and that's a
+really good point actually. The
+
+ align:start position:0%
+really good point actually. The
+ 
+
+ align:start position:0%
+really good point actually. The
+synthesis
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+thing is is actually I think something
+
+ align:start position:0%
+thing is is actually I think something
+ 
+
+ align:start position:0%
+thing is is actually I think something
+that's really important, right? Because
+
+ align:start position:0%
+that's really important, right? Because
+ 
+
+ align:start position:0%
+that's really important, right? Because
+um we do we tend to see a lot of recycle
+
+ align:start position:0%
+um we do we tend to see a lot of recycle
+ 
+
+ align:start position:0%
+um we do we tend to see a lot of recycle
+mechanics and what what becomes an
+
+ align:start position:0%
+mechanics and what what becomes an
+ 
+
+ align:start position:0%
+mechanics and what what becomes an
+interesting thing in a game often times
+
+ align:start position:0%
+interesting thing in a game often times
+ 
+
+ align:start position:0%
+interesting thing in a game often times
+is not that it's a completely new uh
+
+ align:start position:0%
+is not that it's a completely new uh
+ 
+
+ align:start position:0%
+is not that it's a completely new uh
+rule, right? It's the way that rule
+
+ align:start position:0%
+rule, right? It's the way that rule
+ 
+
+ align:start position:0%
+rule, right? It's the way that rule
+interacts with the other rules in the
+
+ align:start position:0%
+interacts with the other rules in the
+ 
+
+ align:start position:0%
+interacts with the other rules in the
+system. Um and and you know in some
+
+ align:start position:0%
+system. Um and and you know in some
+ 
+
+ align:start position:0%
+system. Um and and you know in some
+instances also how that rule is read and
+
+ align:start position:0%
+instances also how that rule is read and
+ 
+
+ align:start position:0%
+instances also how that rule is read and
+interpreted by the player or perhaps
+
+ align:start position:0%
+interpreted by the player or perhaps
+ 
+
+ align:start position:0%
+interpreted by the player or perhaps
+intended to be read and interpreted by
+
+ align:start position:0%
+intended to be read and interpreted by
+ 
+
+ align:start position:0%
+intended to be read and interpreted by
+the player. So um yeah, I think the
+
+ align:start position:0%
+the player. So um yeah, I think the
+ 
+
+ align:start position:0%
+the player. So um yeah, I think the
+synthesis is actually an interesting
+
+ align:start position:0%
+synthesis is actually an interesting
+ 
+
+ align:start position:0%
+synthesis is actually an interesting
+part of it where people can bring a lot
+
+ align:start position:0%
+part of it where people can bring a lot
+ 
+
+ align:start position:0%
+part of it where people can bring a lot
+of different ideas from a lot of
+
+ align:start position:0%
+of different ideas from a lot of
+ 
+
+ align:start position:0%
+of different ideas from a lot of
+different experiences with games um to
+
+ align:start position:0%
+different experiences with games um to
+ 
+
+ align:start position:0%
+different experiences with games um to
+kind of fuse these ideas together. Um
+
+ align:start position:0%
+kind of fuse these ideas together. Um
+ 
+
+ align:start position:0%
+kind of fuse these ideas together. Um
+just uh
+
+ align:start position:0%
+just uh
+ 
+
+ align:start position:0%
+just uh
+when it comes to coming up with ideas
+
+ align:start position:0%
+when it comes to coming up with ideas
+ 
+
+ align:start position:0%
+when it comes to coming up with ideas
+for games, nice thing about
+
+ align:start position:0%
+for games, nice thing about
+ 
+
+ align:start position:0%
+for games, nice thing about
+brainstorming is that it gets past the
+
+ align:start position:0%
+brainstorming is that it gets past the
+ 
+
+ align:start position:0%
+brainstorming is that it gets past the
+good idea that everyone happens to like.
+
+ align:start position:0%
+good idea that everyone happens to like.
+ 
+
+ align:start position:0%
+good idea that everyone happens to like.
+uh which is uh a problem that we
+
+ align:start position:0%
+uh which is uh a problem that we
+ 
+
+ align:start position:0%
+uh which is uh a problem that we
+sometimes have in the SP is people the
+
+ align:start position:0%
+sometimes have in the SP is people the
+ 
+
+ align:start position:0%
+sometimes have in the SP is people the
+people will find one idea they will
+
+ align:start position:0%
+people will find one idea they will
+ 
+
+ align:start position:0%
+people will find one idea they will
+never think past it that's because they
+
+ align:start position:0%
+never think past it that's because they
+ 
+
+ align:start position:0%
+never think past it that's because they
+were happy to find one that everybody
+
+ align:start position:0%
+were happy to find one that everybody
+ 
+
+ align:start position:0%
+were happy to find one that everybody
+>> yeah and so you guys are dividing into
+
+ align:start position:0%
+>> yeah and so you guys are dividing into
+ 
+
+ align:start position:0%
+>> yeah and so you guys are dividing into
+design teams and one of the things that
+
+ align:start position:0%
+design teams and one of the things that
+ 
+
+ align:start position:0%
+design teams and one of the things that
+I would encourage I don't know how it's
+
+ align:start position:0%
+I would encourage I don't know how it's
+ 
+
+ align:start position:0%
+I would encourage I don't know how it's
+set up schedule-wise but try to try to
+
+ align:start position:0%
+set up schedule-wise but try to try to
+ 
+
+ align:start position:0%
+set up schedule-wise but try to try to
+divide the brainstorming process from
+
+ align:start position:0%
+divide the brainstorming process from
+ 
+
+ align:start position:0%
+divide the brainstorming process from
+the judgment you know like I kind of
+
+ align:start position:0%
+the judgment you know like I kind of
+ 
+
+ align:start position:0%
+the judgment you know like I kind of
+said it's it's true like even even if
+
+ align:start position:0%
+said it's it's true like even even if
+ 
+
+ align:start position:0%
+said it's it's true like even even if
+you do the brainstorm it can help you
+
+ align:start position:0%
+you do the brainstorm it can help you
+ 
+
+ align:start position:0%
+you do the brainstorm it can help you
+get over. But a lot of times whatever
+
+ align:start position:0%
+get over. But a lot of times whatever
+ 
+
+ align:start position:0%
+get over. But a lot of times whatever
+had momentum during that brainstorm or
+
+ align:start position:0%
+had momentum during that brainstorm or
+ 
+
+ align:start position:0%
+had momentum during that brainstorm or
+whatever got the most yuck during that
+
+ align:start position:0%
+whatever got the most yuck during that
+ 
+
+ align:start position:0%
+whatever got the most yuck during that
+brainstorm, right, is going to be like
+
+ align:start position:0%
+brainstorm, right, is going to be like
+ 
+
+ align:start position:0%
+brainstorm, right, is going to be like
+the popular strong idea. And then when
+
+ align:start position:0%
+the popular strong idea. And then when
+ 
+
+ align:start position:0%
+the popular strong idea. And then when
+you come back to it with a little space,
+
+ align:start position:0%
+you come back to it with a little space,
+ 
+
+ align:start position:0%
+you come back to it with a little space,
+you might be like, "Oh, you know, like,
+
+ align:start position:0%
+you might be like, "Oh, you know, like,
+ 
+
+ align:start position:0%
+you might be like, "Oh, you know, like,
+yeah, that is a really good idea, but
+
+ align:start position:0%
+yeah, that is a really good idea, but
+ 
+
+ align:start position:0%
+yeah, that is a really good idea, but
+there was this other thing that got
+
+ align:start position:0%
+there was this other thing that got
+ 
+
+ align:start position:0%
+there was this other thing that got
+mentioned like a half an hour earlier
+
+ align:start position:0%
+mentioned like a half an hour earlier
+ 
+
+ align:start position:0%
+mentioned like a half an hour earlier
+that's really interesting. Maybe we
+
+ align:start position:0%
+that's really interesting. Maybe we
+ 
+
+ align:start position:0%
+that's really interesting. Maybe we
+could incorporate that somehow." And so
+
+ align:start position:0%
+could incorporate that somehow." And so
+ 
+
+ align:start position:0%
+could incorporate that somehow." And so
+kind of, you know, making the judgment
+
+ align:start position:0%
+kind of, you know, making the judgment
+ 
+
+ align:start position:0%
+kind of, you know, making the judgment
+happen in a in a separate phase can be
+
+ align:start position:0%
+happen in a in a separate phase can be
+ 
+
+ align:start position:0%
+happen in a in a separate phase can be
+really important. Um because it's true,
+
+ align:start position:0%
+really important. Um because it's true,
+ 
+
+ align:start position:0%
+really important. Um because it's true,
+creativity is like this, it's a little
+
+ align:start position:0%
+creativity is like this, it's a little
+ 
+
+ align:start position:0%
+creativity is like this, it's a little
+bit more organic. It's not necessarily a
+
+ align:start position:0%
+bit more organic. It's not necessarily a
+ 
+
+ align:start position:0%
+bit more organic. It's not necessarily a
+a strictly logical process, right? Um so
+
+ align:start position:0%
+a strictly logical process, right? Um so
+ 
+
+ align:start position:0%
+a strictly logical process, right? Um so
+applying logic later can be a good thing
+
+ align:start position:0%
+applying logic later can be a good thing
+ 
+
+ align:start position:0%
+applying logic later can be a good thing
+I think to the creative process.
+
+ align:start position:0%
+I think to the creative process.
+ 
+
+ align:start position:0%
+I think to the creative process.
+Cool. Any questions about brainstorming
+
+ align:start position:0%
+Cool. Any questions about brainstorming
+ 
+
+ align:start position:0%
+Cool. Any questions about brainstorming
+at all? You are incredibly enlightened
+
+ align:start position:0%
+at all? You are incredibly enlightened
+ 
+
+ align:start position:0%
+at all? You are incredibly enlightened
+by Alex Osbor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the forum actually people reading
+
+ align:start position:0%
+on the forum actually people reading
+ 
+
+ align:start position:0%
+on the forum actually people reading
+about using things like Google or Google
+
+ align:start position:0%
+about using things like Google or Google
+ 
+
+ align:start position:0%
+about using things like Google or Google
+Docs where things are automatically
+
+ align:start position:0%
+Docs where things are automatically
+ 
+
+ align:start position:0%
+Docs where things are automatically
+recorded because everyone's basically
+
+ align:start position:0%
+recorded because everyone's basically
+ 
+
+ align:start position:0%
+recorded because everyone's basically
+typing in their years.
+
+ align:start position:0%
+typing in their years.
+ 
+
+ align:start position:0%
+typing in their years.
+>> Yeah. I mean, I think it's interesting.
+
+ align:start position:0%
+>> Yeah. I mean, I think it's interesting.
+ 
+
+ align:start position:0%
+>> Yeah. I mean, I think it's interesting.
+I I don't have a whole lot of experience
+
+ align:start position:0%
+I I don't have a whole lot of experience
+ 
+
+ align:start position:0%
+I I don't have a whole lot of experience
+with Well, I should reframe. Um I I
+
+ align:start position:0%
+with Well, I should reframe. Um I I
+ 
+
+ align:start position:0%
+with Well, I should reframe. Um I I
+Well, I don't have a lot of experience
+
+ align:start position:0%
+Well, I don't have a lot of experience
+ 
+
+ align:start position:0%
+Well, I don't have a lot of experience
+with remote brainstorming, but I did
+
+ align:start position:0%
+with remote brainstorming, but I did
+ 
+
+ align:start position:0%
+with remote brainstorming, but I did
+have a um I did, you know, so one of the
+
+ align:start position:0%
+have a um I did, you know, so one of the
+ 
+
+ align:start position:0%
+have a um I did, you know, so one of the
+games I worked on this summer was this
+
+ align:start position:0%
+games I worked on this summer was this
+ 
+
+ align:start position:0%
+games I worked on this summer was this
+game called Yet One Word where um you
+
+ align:start position:0%
+game called Yet One Word where um you
+ 
+
+ align:start position:0%
+game called Yet One Word where um you
+were asked a lot of personal questions.
+
+ align:start position:0%
+were asked a lot of personal questions.
+ 
+
+ align:start position:0%
+were asked a lot of personal questions.
+And so, we had to think of personal
+
+ align:start position:0%
+And so, we had to think of personal
+ 
+
+ align:start position:0%
+And so, we had to think of personal
+questions. And at one, so we were like,
+
+ align:start position:0%
+questions. And at one, so we were like,
+ 
+
+ align:start position:0%
+questions. And at one, so we were like,
+well, if you have ideas, write it down
+
+ align:start position:0%
+well, if you have ideas, write it down
+ 
+
+ align:start position:0%
+well, if you have ideas, write it down
+in Google Doc. And at one point myself
+
+ align:start position:0%
+in Google Doc. And at one point myself
+ 
+
+ align:start position:0%
+in Google Doc. And at one point myself
+and two of the other designers were all
+
+ align:start position:0%
+and two of the other designers were all
+ 
+
+ align:start position:0%
+and two of the other designers were all
+in the Google doc at the same time. And
+
+ align:start position:0%
+in the Google doc at the same time. And
+ 
+
+ align:start position:0%
+in the Google doc at the same time. And
+you could actually see it that sort of
+
+ align:start position:0%
+you could actually see it that sort of
+ 
+
+ align:start position:0%
+you could actually see it that sort of
+brainstorming momentum happen. Someone
+
+ align:start position:0%
+brainstorming momentum happen. Someone
+ 
+
+ align:start position:0%
+brainstorming momentum happen. Someone
+would type something in and then like
+
+ align:start position:0%
+would type something in and then like
+ 
+
+ align:start position:0%
+would type something in and then like
+someone would type next like a that's so
+
+ align:start position:0%
+someone would type next like a that's so
+ 
+
+ align:start position:0%
+someone would type next like a that's so
+funny and then like write an idea that's
+
+ align:start position:0%
+funny and then like write an idea that's
+ 
+
+ align:start position:0%
+funny and then like write an idea that's
+related to that, right? And and you're
+
+ align:start position:0%
+related to that, right? And and you're
+ 
+
+ align:start position:0%
+related to that, right? And and you're
+kind of seeing it happen in this digital
+
+ align:start position:0%
+kind of seeing it happen in this digital
+ 
+
+ align:start position:0%
+kind of seeing it happen in this digital
+space. So I think it can we've gotten so
+
+ align:start position:0%
+space. So I think it can we've gotten so
+ 
+
+ align:start position:0%
+space. So I think it can we've gotten so
+accustomed to having these kind of um
+
+ align:start position:0%
+accustomed to having these kind of um
+ 
+
+ align:start position:0%
+accustomed to having these kind of um
+digital personalities, right? these
+
+ align:start position:0%
+digital personalities, right? these
+ 
+
+ align:start position:0%
+digital personalities, right? these
+digital personas in IMing and text
+
+ align:start position:0%
+digital personas in IMing and text
+ 
+
+ align:start position:0%
+digital personas in IMing and text
+messaging and all that other stuff that
+
+ align:start position:0%
+messaging and all that other stuff that
+ 
+
+ align:start position:0%
+messaging and all that other stuff that
+I I think we've gotten pretty adept at
+
+ align:start position:0%
+I I think we've gotten pretty adept at
+ 
+
+ align:start position:0%
+I I think we've gotten pretty adept at
+typing fast enough to get ideas out. But
+
+ align:start position:0%
+typing fast enough to get ideas out. But
+ 
+
+ align:start position:0%
+typing fast enough to get ideas out. But
+I think it could totally work. Um
+
+ align:start position:0%
+I think it could totally work. Um
+ 
+
+ align:start position:0%
+I think it could totally work. Um
+there's something to be said for like
+
+ align:start position:0%
+there's something to be said for like
+ 
+
+ align:start position:0%
+there's something to be said for like
+the momentum that gets generated in
+
+ align:start position:0%
+the momentum that gets generated in
+ 
+
+ align:start position:0%
+the momentum that gets generated in
+person. Um but yeah, I mean
+
+ align:start position:0%
+person. Um but yeah, I mean
+ 
+
+ align:start position:0%
+person. Um but yeah, I mean
+>> yeah I mean I was it's so funny. I was
+
+ align:start position:0%
+>> yeah I mean I was it's so funny. I was
+ 
+
+ align:start position:0%
+>> yeah I mean I was it's so funny. I was
+going to say like no that's a terrible
+
+ align:start position:0%
+going to say like no that's a terrible
+ 
+
+ align:start position:0%
+going to say like no that's a terrible
+idea you have to be around each other. I
+
+ align:start position:0%
+idea you have to be around each other. I
+ 
+
+ align:start position:0%
+idea you have to be around each other. I
+was like actually it worked. Um, I mean
+
+ align:start position:0%
+was like actually it worked. Um, I mean
+ 
+
+ align:start position:0%
+was like actually it worked. Um, I mean
+I think it all depends a little bit on
+
+ align:start position:0%
+I think it all depends a little bit on
+ 
+
+ align:start position:0%
+I think it all depends a little bit on
+personalities and people that are
+
+ align:start position:0%
+personalities and people that are
+ 
+
+ align:start position:0%
+personalities and people that are
+involved.
+
+ align:start position:0%
+involved.
+ 
+
+ align:start position:0%
+involved.
+Certainly for a prolonged brainstorm you
+
+ align:start position:0%
+Certainly for a prolonged brainstorm you
+ 
+
+ align:start position:0%
+Certainly for a prolonged brainstorm you
+one of the things Alex Osbourne says is
+
+ align:start position:0%
+one of the things Alex Osbourne says is
+ 
+
+ align:start position:0%
+one of the things Alex Osbourne says is
+like time box it if if you you know if
+
+ align:start position:0%
+like time box it if if you you know if
+ 
+
+ align:start position:0%
+like time box it if if you you know if
+you don't time box it's going to be a
+
+ align:start position:0%
+you don't time box it's going to be a
+ 
+
+ align:start position:0%
+you don't time box it's going to be a
+problem. I think for in person that's
+
+ align:start position:0%
+problem. I think for in person that's
+ 
+
+ align:start position:0%
+problem. I think for in person that's
+true. Um you know it's so easy to get
+
+ align:start position:0%
+true. Um you know it's so easy to get
+ 
+
+ align:start position:0%
+true. Um you know it's so easy to get
+onto a Google document now whenever you
+
+ align:start position:0%
+onto a Google document now whenever you
+ 
+
+ align:start position:0%
+onto a Google document now whenever you
+have an idea that actually having kind
+
+ align:start position:0%
+have an idea that actually having kind
+ 
+
+ align:start position:0%
+have an idea that actually having kind
+of a long phone brainstorm where anytime
+
+ align:start position:0%
+of a long phone brainstorm where anytime
+ 
+
+ align:start position:0%
+of a long phone brainstorm where anytime
+someone has an idea over a week or
+
+ align:start position:0%
+someone has an idea over a week or
+ 
+
+ align:start position:0%
+someone has an idea over a week or
+something like that write it down. um
+
+ align:start position:0%
+something like that write it down. um
+ 
+
+ align:start position:0%
+something like that write it down. um
+you know that's also useful too because
+
+ align:start position:0%
+you know that's also useful too because
+ 
+
+ align:start position:0%
+you know that's also useful too because
+then you know you separated the
+
+ align:start position:0%
+then you know you separated the
+ 
+
+ align:start position:0%
+then you know you separated the
+processes collecting and then but you
+
+ align:start position:0%
+processes collecting and then but you
+ 
+
+ align:start position:0%
+processes collecting and then but you
+still should do that sort of building on
+
+ align:start position:0%
+still should do that sort of building on
+ 
+
+ align:start position:0%
+still should do that sort of building on
+ideas.
+
+ align:start position:0%
+ideas.
+ 
+
+ align:start position:0%
+ideas.
+>> It's probably easier to do those
+
+ align:start position:0%
+>> It's probably easier to do those
+ 
+
+ align:start position:0%
+>> It's probably easier to do those
+synthesis when you're at least
+
+ align:start position:0%
+synthesis when you're at least
+ 
+
+ align:start position:0%
+synthesis when you're at least
+simultaneously on the line online or in
+
+ align:start position:0%
+simultaneously on the line online or in
+ 
+
+ align:start position:0%
+simultaneously on the line online or in
+the same room.
+
+ align:start position:0%
+the same room.
+ 
+
+ align:start position:0%
+the same room.
+>> Yep. Yeah. Yeah. And to see the ideas
+
+ align:start position:0%
+>> Yep. Yeah. Yeah. And to see the ideas
+ 
+
+ align:start position:0%
+>> Yep. Yeah. Yeah. And to see the ideas
+come out as they come out.
+
+ align:start position:0%
+come out as they come out.
+ 
+
+ align:start position:0%
+come out as they come out.
+>> Yeah. It's it's kind of it's a little
+
+ align:start position:0%
+>> Yeah. It's it's kind of it's a little
+ 
+
+ align:start position:0%
+>> Yeah. It's it's kind of it's a little
+uncommon to just read something and be
+
+ align:start position:0%
+uncommon to just read something and be
+ 
+
+ align:start position:0%
+uncommon to just read something and be
+like, "Oh, yeah. What about this when it
+
+ align:start position:0%
+like, "Oh, yeah. What about this when it
+ 
+
+ align:start position:0%
+like, "Oh, yeah. What about this when it
+first shows up?" When it first kind of
+
+ align:start position:0%
+first shows up?" When it first kind of
+ 
+
+ align:start position:0%
+first shows up?" When it first kind of
+comes into existence as you're trying to
+
+ align:start position:0%
+comes into existence as you're trying to
+ 
+
+ align:start position:0%
+comes into existence as you're trying to
+think of things that can spur ideas, you
+
+ align:start position:0%
+think of things that can spur ideas, you
+ 
+
+ align:start position:0%
+think of things that can spur ideas, you
+know, the other danger about doing it
+
+ align:start position:0%
+know, the other danger about doing it
+ 
+
+ align:start position:0%
+know, the other danger about doing it
+like, "Okay, this document is open for
+
+ align:start position:0%
+like, "Okay, this document is open for
+ 
+
+ align:start position:0%
+like, "Okay, this document is open for
+the next 24 hours. Everyone throw your
+
+ align:start position:0%
+the next 24 hours. Everyone throw your
+ 
+
+ align:start position:0%
+the next 24 hours. Everyone throw your
+ideas in." Is that then people start
+
+ align:start position:0%
+ideas in." Is that then people start
+ 
+
+ align:start position:0%
+ideas in." Is that then people start
+spending too long on any one idea
+
+ align:start position:0%
+spending too long on any one idea
+ 
+
+ align:start position:0%
+spending too long on any one idea
+thinking about what they're going to
+
+ align:start position:0%
+thinking about what they're going to
+ 
+
+ align:start position:0%
+thinking about what they're going to
+write down before they write it down and
+
+ align:start position:0%
+write down before they write it down and
+ 
+
+ align:start position:0%
+write down before they write it down and
+it's like, "No, that's not the point."
+
+ align:start position:0%
+it's like, "No, that's not the point."
+ 
+
+ align:start position:0%
+it's like, "No, that's not the point."
+>> Yeah. Yeah. Think of the paperclip
+
+ align:start position:0%
+>> Yeah. Yeah. Think of the paperclip
+ 
+
+ align:start position:0%
+>> Yeah. Yeah. Think of the paperclip
+experience and those of you that raised
+
+ align:start position:0%
+experience and those of you that raised
+ 
+
+ align:start position:0%
+experience and those of you that raised
+your hand for saying that you were
+
+ align:start position:0%
+your hand for saying that you were
+ 
+
+ align:start position:0%
+your hand for saying that you were
+self-censoring on your own. Like you
+
+ align:start position:0%
+self-censoring on your own. Like you
+ 
+
+ align:start position:0%
+self-censoring on your own. Like you
+didn't even have to I wasn't going to
+
+ align:start position:0%
+didn't even have to I wasn't going to
+ 
+
+ align:start position:0%
+didn't even have to I wasn't going to
+make you all hand in those paperclip
+
+ align:start position:0%
+make you all hand in those paperclip
+ 
+
+ align:start position:0%
+make you all hand in those paperclip
+ideas and you were self-censoring,
+
+ align:start position:0%
+ideas and you were self-censoring,
+ 
+
+ align:start position:0%
+ideas and you were self-censoring,
+right? So yeah, the same same sort of
+
+ align:start position:0%
+right? So yeah, the same same sort of
+ 
+
+ align:start position:0%
+right? So yeah, the same same sort of
+thing applies. Like you might you might
+
+ align:start position:0%
+thing applies. Like you might you might
+ 
+
+ align:start position:0%
+thing applies. Like you might you might
+censor yourself or spend a lot of time
+
+ align:start position:0%
+censor yourself or spend a lot of time
+ 
+
+ align:start position:0%
+censor yourself or spend a lot of time
+on ideas. So
+
+ align:start position:0%
+on ideas. So
+ 
+
+ align:start position:0%
+on ideas. So
+yeah, any other thoughts, questions?
+
+ align:start position:0%
+yeah, any other thoughts, questions?
+ 
+
+ align:start position:0%
+yeah, any other thoughts, questions?
+Cool. Well, I hope this was helpful. I
+
+ align:start position:0%
+Cool. Well, I hope this was helpful. I
+ 
+
+ align:start position:0%
+Cool. Well, I hope this was helpful. I
+hope it'll be helpful for your game
+
+ align:start position:0%
+hope it'll be helpful for your game
+ 
+
+ align:start position:0%
+hope it'll be helpful for your game
+design stuff. Um, email me if you do
+
+ align:start position:0%
+design stuff. Um, email me if you do
+ 
+
+ align:start position:0%
+design stuff. Um, email me if you do
+have any questions about this stuff. I
+
+ align:start position:0%
+have any questions about this stuff. I
+ 
+
+ align:start position:0%
+have any questions about this stuff. I
+mean, I can try to try to help out, but
+
+ align:start position:0%
+mean, I can try to try to help out, but
+ 
+
+ align:start position:0%
+mean, I can try to try to help out, but
+you know,
+
+ align:start position:0%
+you know,
+ 
+
+ align:start position:0%
+you know,
+other than that, good luck on your your
+
+ align:start position:0%
+other than that, good luck on your your
+ 
+
+ align:start position:0%
+other than that, good luck on your your
+game design for this class and for the
+
+ align:start position:0%
+game design for this class and for the
+ 
+
+ align:start position:0%
+game design for this class and for the
+rest of the cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I do like that on the the keynote
+
+ align:start position:0%
+I do like that on the the keynote
+ 
+
+ align:start position:0%
+I do like that on the the keynote
+things. It says end of show.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Uh let's see now. Uh we're going to play
+
+ align:start position:0%
+>> Uh let's see now. Uh we're going to play
+ 
+
+ align:start position:0%
+>> Uh let's see now. Uh we're going to play
+some card games, but before that, just a
+
+ align:start position:0%
+some card games, but before that, just a
+ 
+
+ align:start position:0%
+some card games, but before that, just a
+little bit of admin. Um on Monday you'll
+
+ align:start position:0%
+little bit of admin. Um on Monday you'll
+ 
+
+ align:start position:0%
+little bit of admin. Um on Monday you'll
+notice that uh we had two readings, one
+
+ align:start position:0%
+notice that uh we had two readings, one
+ 
+
+ align:start position:0%
+notice that uh we had two readings, one
+of which you've already done. So it
+
+ align:start position:0%
+of which you've already done. So it
+ 
+
+ align:start position:0%
+of which you've already done. So it
+doesn't matter. Um this is the other
+
+ align:start position:0%
+doesn't matter. Um this is the other
+ 
+
+ align:start position:0%
+doesn't matter. Um this is the other
+reading. It's a little bit dry. Tough it
+
+ align:start position:0%
+reading. It's a little bit dry. Tough it
+ 
+
+ align:start position:0%
+reading. It's a little bit dry. Tough it
+out. Caffeinate yourself reading it.
+
+ align:start position:0%
+out. Caffeinate yourself reading it.
+ 
+
+ align:start position:0%
+out. Caffeinate yourself reading it.
+Tough it out. It is worth it. It's
+
+ align:start position:0%
+Tough it out. It is worth it. It's
+ 
+
+ align:start position:0%
+Tough it out. It is worth it. It's
+translation. So
+
+ align:start position:0%
+translation. So
+ 
+
+ align:start position:0%
+translation. So
+uh let's see now. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there there's at least one person um
+
+ align:start position:0%
+there there's at least one person um
+ 
+
+ align:start position:0%
+there there's at least one person um
+who hasn't form that we need to fill
+
+ align:start position:0%
+who hasn't form that we need to fill
+ 
+
+ align:start position:0%
+who hasn't form that we need to fill
+out.
+
+ align:start position:0%
+out.
+ 
+
+ align:start position:0%
+out.
+So just just come up here
+
+ align:start position:0%
+So just just come up here
+ 
+
+ align:start position:0%
+So just just come up here
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+at least four
+
+ align:start position:0%
+at least four
+ 
+
+ align:start position:0%
+at least four
+more time.
+
+ align:start position:0%
+more time.
+ 
+
+ align:start position:0%
+more time.
+>> Yeah, I'm not sure if we have enough to
+
+ align:start position:0%
+>> Yeah, I'm not sure if we have enough to
+ 
+
+ align:start position:0%
+>> Yeah, I'm not sure if we have enough to
+get through all of them, but most of
+
+ align:start position:0%
+get through all of them, but most of
+ 
+
+ align:start position:0%
+get through all of them, but most of
+them are pretty short. Uh uh a lot of
+
+ align:start position:0%
+them are pretty short. Uh uh a lot of
+ 
+
+ align:start position:0%
+them are pretty short. Uh uh a lot of
+them the delay is going to be set up
+
+ align:start position:0%
+them the delay is going to be set up
+ 
+
+ align:start position:0%
+them the delay is going to be set up
+which is why they couldn't first because
+
+ align:start position:0%
+which is why they couldn't first because
+ 
+
+ align:start position:0%
+which is why they couldn't first because
+uh uh that takes a lot of set up. That
+
+ align:start position:0%
+uh uh that takes a lot of set up. That
+ 
+
+ align:start position:0%
+uh uh that takes a lot of set up. That
+being said, um if you do get a chance to
+
+ align:start position:0%
+being said, um if you do get a chance to
+ 
+
+ align:start position:0%
+being said, um if you do get a chance to
+look at a rule and study the cards, um
+
+ align:start position:0%
+look at a rule and study the cards, um
+ 
+
+ align:start position:0%
+look at a rule and study the cards, um
+what like even though they've done a
+
+ align:start position:0%
+what like even though they've done a
+ 
+
+ align:start position:0%
+what like even though they've done a
+bunch of really really smart things on
+
+ align:start position:0%
+bunch of really really smart things on
+ 
+
+ align:start position:0%
+bunch of really really smart things on
+the cards just to make it easier for you
+
+ align:start position:0%
+the cards just to make it easier for you
+ 
+
+ align:start position:0%
+the cards just to make it easier for you
+to set up uh and you want to kind of
+
+ align:start position:0%
+to set up uh and you want to kind of
+ 
+
+ align:start position:0%
+to set up uh and you want to kind of
+paying attention to that, but the the
+
+ align:start position:0%
+paying attention to that, but the the
+ 
+
+ align:start position:0%
+paying attention to that, but the the
+the aim of the today is pretty much just
+
+ align:start position:0%
+the aim of the today is pretty much just
+ 
+
+ align:start position:0%
+the aim of the today is pretty much just
+variety. We have four fairly different
+
+ align:start position:0%
+variety. We have four fairly different
+ 
+
+ align:start position:0%
+variety. We have four fairly different
+kinds of games that use cards in a very
+
+ align:start position:0%
+kinds of games that use cards in a very
+ 
+
+ align:start position:0%
+kinds of games that use cards in a very
+different way. Uh and if you don't get a
+
+ align:start position:0%
+different way. Uh and if you don't get a
+ 
+
+ align:start position:0%
+different way. Uh and if you don't get a
+chance necessarily to play all of them,
+
+ align:start position:0%
+chance necessarily to play all of them,
+ 
+
+ align:start position:0%
+chance necessarily to play all of them,
+at least get a chance to look at other
+
+ align:start position:0%
+at least get a chance to look at other
+ 
+
+ align:start position:0%
+at least get a chance to look at other
+people playing with them and if you
+
+ align:start position:0%
+people playing with them and if you
+ 
+
+ align:start position:0%
+people playing with them and if you
+wanted to like check them out in the
+
+ align:start position:0%
+wanted to like check them out in the
+ 
+
+ align:start position:0%
+wanted to like check them out in the
+middle of the week or something just
+
+ align:start position:0%
+middle of the week or something just
+ 
+
+ align:start position:0%
+middle of the week or something just
+kick around the office but you know your
+
+ align:start position:0%
+kick around the office but you know your
+ 
+
+ align:start position:0%
+kick around the office but you know your
+time to come back here next week or
+
+ align:start position:0%
+time to come back here next week or
+ 
+
+ align:start position:0%
+time to come back here next week or
+something
+
+ align:start position:0%
+something
+ 
+
+ align:start position:0%
+something
+but uh that's basically it if we can
+
+ align:start position:0%
+but uh that's basically it if we can
+ 
+
+ align:start position:0%
+but uh that's basically it if we can
+just keep um uh if we can clear the
+
+ align:start position:0%
+just keep um uh if we can clear the
+ 
+
+ align:start position:0%
+just keep um uh if we can clear the
+tables we need them for the cards uh
\ No newline at end of file
diff --git a/Hgi3PSZI6Jw.txt b/Hgi3PSZI6Jw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4410b980066736d9b6375a765cd881a162f5d7ad
--- /dev/null
+++ b/Hgi3PSZI6Jw.txt
@@ -0,0 +1,7131 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh
+
+ align:start position:0%
+oh
+ 
+
+ align:start position:0%
+oh
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+hi we've spent the last couple of
+
+ align:start position:0%
+hi we've spent the last couple of
+ 
+
+ align:start position:0%
+hi we've spent the last couple of
+sessions looking at compensating
+
+ align:start position:0%
+sessions looking at compensating
+ 
+
+ align:start position:0%
+sessions looking at compensating
+feedback systems we started this
+
+ align:start position:0%
+feedback systems we started this
+ 
+
+ align:start position:0%
+feedback systems we started this
+discussion rather generally without
+
+ align:start position:0%
+discussion rather generally without
+ 
+
+ align:start position:0%
+discussion rather generally without
+really considering the realities that
+
+ align:start position:0%
+really considering the realities that
+ 
+
+ align:start position:0%
+really considering the realities that
+the system physical configuration often
+
+ align:start position:0%
+the system physical configuration often
+ 
+
+ align:start position:0%
+the system physical configuration often
+times forces upon us last time we did an
+
+ align:start position:0%
+times forces upon us last time we did an
+ 
+
+ align:start position:0%
+times forces upon us last time we did an
+example where we considered some of the
+
+ align:start position:0%
+example where we considered some of the
+ 
+
+ align:start position:0%
+example where we considered some of the
+constraints that actually apply in a
+
+ align:start position:0%
+constraints that actually apply in a
+ 
+
+ align:start position:0%
+constraints that actually apply in a
+physical
+
+ align:start position:0%
+physical
+ 
+
+ align:start position:0%
+physical
+system the topology we were using for
+
+ align:start position:0%
+system the topology we were using for
+ 
+
+ align:start position:0%
+system the topology we were using for
+that demonstration and in fact generally
+
+ align:start position:0%
+that demonstration and in fact generally
+ 
+
+ align:start position:0%
+that demonstration and in fact generally
+for our discussion to this point has
+
+ align:start position:0%
+for our discussion to this point has
+ 
+
+ align:start position:0%
+for our discussion to this point has
+been what's known as series or Cascade
+
+ align:start position:0%
+been what's known as series or Cascade
+ 
+
+ align:start position:0%
+been what's known as series or Cascade
+compensation and for that we have our
+
+ align:start position:0%
+compensation and for that we have our
+ 
+
+ align:start position:0%
+compensation and for that we have our
+general feedback form the type we
+
+ align:start position:0%
+general feedback form the type we
+ 
+
+ align:start position:0%
+general feedback form the type we
+feedback system form the kind we've been
+
+ align:start position:0%
+feedback system form the kind we've been
+ 
+
+ align:start position:0%
+feedback system form the kind we've been
+considering to this point where we have
+
+ align:start position:0%
+considering to this point where we have
+ 
+
+ align:start position:0%
+considering to this point where we have
+a forward path a a feedback path F very
+
+ align:start position:0%
+a forward path a a feedback path F very
+ 
+
+ align:start position:0%
+a forward path a a feedback path F very
+frequently the physical situation
+
+ align:start position:0%
+frequently the physical situation
+ 
+
+ align:start position:0%
+frequently the physical situation
+constrains the transfer functions of
+
+ align:start position:0%
+constrains the transfer functions of
+ 
+
+ align:start position:0%
+constrains the transfer functions of
+these two elements we frequently
+
+ align:start position:0%
+these two elements we frequently
+ 
+
+ align:start position:0%
+these two elements we frequently
+consider the element shown a fixed
+
+ align:start position:0%
+consider the element shown a fixed
+ 
+
+ align:start position:0%
+consider the element shown a fixed
+element f is very very frequently
+
+ align:start position:0%
+element f is very very frequently
+ 
+
+ align:start position:0%
+element f is very very frequently
+constrained by the ideal closed loop
+
+ align:start position:0%
+constrained by the ideal closed loop
+ 
+
+ align:start position:0%
+constrained by the ideal closed loop
+gain for our configuration to implement
+
+ align:start position:0%
+gain for our configuration to implement
+ 
+
+ align:start position:0%
+gain for our configuration to implement
+the series compensation or Cascade
+
+ align:start position:0%
+the series compensation or Cascade
+ 
+
+ align:start position:0%
+the series compensation or Cascade
+compensation that we've been considering
+
+ align:start position:0%
+compensation that we've been considering
+ 
+
+ align:start position:0%
+compensation that we've been considering
+up till now we add one more or possibly
+
+ align:start position:0%
+up till now we add one more or possibly
+ 
+
+ align:start position:0%
+up till now we add one more or possibly
+more than one element somewhere in the
+
+ align:start position:0%
+more than one element somewhere in the
+ 
+
+ align:start position:0%
+more than one element somewhere in the
+Loop we add it in series or in Cascade
+
+ align:start position:0%
+Loop we add it in series or in Cascade
+ 
+
+ align:start position:0%
+Loop we add it in series or in Cascade
+with the fixed elements we could add it
+
+ align:start position:0%
+with the fixed elements we could add it
+ 
+
+ align:start position:0%
+with the fixed elements we could add it
+here here here here the effect of adding
+
+ align:start position:0%
+here here here here the effect of adding
+ 
+
+ align:start position:0%
+here here here here the effect of adding
+it in any of those places on the loop
+
+ align:start position:0%
+it in any of those places on the loop
+ 
+
+ align:start position:0%
+it in any of those places on the loop
+transmission is identical of course and
+
+ align:start position:0%
+transmission is identical of course and
+ 
+
+ align:start position:0%
+transmission is identical of course and
+so it has the same effect on stability
+
+ align:start position:0%
+so it has the same effect on stability
+ 
+
+ align:start position:0%
+so it has the same effect on stability
+regardless of where we locate it however
+
+ align:start position:0%
+regardless of where we locate it however
+ 
+
+ align:start position:0%
+regardless of where we locate it however
+the actual closed loop gain of the
+
+ align:start position:0%
+the actual closed loop gain of the
+ 
+
+ align:start position:0%
+the actual closed loop gain of the
+system varies as a function of where we
+
+ align:start position:0%
+system varies as a function of where we
+ 
+
+ align:start position:0%
+system varies as a function of where we
+locate the series compensating element
+
+ align:start position:0%
+locate the series compensating element
+ 
+
+ align:start position:0%
+locate the series compensating element
+today I'd like to consider another way
+
+ align:start position:0%
+today I'd like to consider another way
+ 
+
+ align:start position:0%
+today I'd like to consider another way
+of compensating a feedback system
+
+ align:start position:0%
+of compensating a feedback system
+ 
+
+ align:start position:0%
+of compensating a feedback system
+uh in particular feedback or minor Loop
+
+ align:start position:0%
+uh in particular feedback or minor Loop
+ 
+
+ align:start position:0%
+uh in particular feedback or minor Loop
+compensation the topology for feedback
+
+ align:start position:0%
+compensation the topology for feedback
+ 
+
+ align:start position:0%
+compensation the topology for feedback
+compensation is shown in this view graph
+
+ align:start position:0%
+compensation is shown in this view graph
+ 
+
+ align:start position:0%
+compensation is shown in this view graph
+and this is a fundamentally different
+
+ align:start position:0%
+and this is a fundamentally different
+ 
+
+ align:start position:0%
+and this is a fundamentally different
+kind of topology from what we have with
+
+ align:start position:0%
+kind of topology from what we have with
+ 
+
+ align:start position:0%
+kind of topology from what we have with
+series
+
+ align:start position:0%
+series
+ 
+
+ align:start position:0%
+series
+compensation here we have a a two-loop
+
+ align:start position:0%
+compensation here we have a a two-loop
+ 
+
+ align:start position:0%
+compensation here we have a a two-loop
+system we have of course the input and
+
+ align:start position:0%
+system we have of course the input and
+ 
+
+ align:start position:0%
+system we have of course the input and
+the output and as always we have a a
+
+ align:start position:0%
+the output and as always we have a a
+ 
+
+ align:start position:0%
+the output and as always we have a a
+feedback element here and this feedback
+
+ align:start position:0%
+feedback element here and this feedback
+ 
+
+ align:start position:0%
+feedback element here and this feedback
+element labeled F1 is of of course the
+
+ align:start position:0%
+element labeled F1 is of of course the
+ 
+
+ align:start position:0%
+element labeled F1 is of of course the
+element that links the output back to
+
+ align:start position:0%
+element that links the output back to
+ 
+
+ align:start position:0%
+element that links the output back to
+the summing point in the system and so
+
+ align:start position:0%
+the summing point in the system and so
+ 
+
+ align:start position:0%
+the summing point in the system and so
+we choose F1 as a function of the
+
+ align:start position:0%
+we choose F1 as a function of the
+ 
+
+ align:start position:0%
+we choose F1 as a function of the
+desired or ideal Clos Loop gain of our
+
+ align:start position:0%
+desired or ideal Clos Loop gain of our
+ 
+
+ align:start position:0%
+desired or ideal Clos Loop gain of our
+feedback system in particular the ideal
+
+ align:start position:0%
+feedback system in particular the ideal
+ 
+
+ align:start position:0%
+feedback system in particular the ideal
+Clos Loop gain of this system is simply
+
+ align:start position:0%
+Clos Loop gain of this system is simply
+ 
+
+ align:start position:0%
+Clos Loop gain of this system is simply
+one over
+
+ align:start position:0%
+one over
+ 
+
+ align:start position:0%
+one over
+F1 in addition to the overall Loop which
+
+ align:start position:0%
+F1 in addition to the overall Loop which
+ 
+
+ align:start position:0%
+F1 in addition to the overall Loop which
+involves F1 this is oftentimes called an
+
+ align:start position:0%
+involves F1 this is oftentimes called an
+ 
+
+ align:start position:0%
+involves F1 this is oftentimes called an
+outer or a major Loop we have an inner
+
+ align:start position:0%
+outer or a major Loop we have an inner
+ 
+
+ align:start position:0%
+outer or a major Loop we have an inner
+or a minor
+
+ align:start position:0%
+or a minor
+ 
+
+ align:start position:0%
+or a minor
+Loop here and we show elements A2 and F2
+
+ align:start position:0%
+Loop here and we show elements A2 and F2
+ 
+
+ align:start position:0%
+Loop here and we show elements A2 and F2
+associated with that minor
+
+ align:start position:0%
+associated with that minor
+ 
+
+ align:start position:0%
+associated with that minor
+Loop very frequently in this sort of
+
+ align:start position:0%
+Loop very frequently in this sort of
+ 
+
+ align:start position:0%
+Loop very frequently in this sort of
+feedback topology or system that's
+
+ align:start position:0%
+feedback topology or system that's
+ 
+
+ align:start position:0%
+feedback topology or system that's
+feedback compensated the elements A1 and
+
+ align:start position:0%
+feedback compensated the elements A1 and
+ 
+
+ align:start position:0%
+feedback compensated the elements A1 and
+A2 are fixed
+
+ align:start position:0%
+A2 are fixed
+ 
+
+ align:start position:0%
+A2 are fixed
+elements and the element F1 is of course
+
+ align:start position:0%
+elements and the element F1 is of course
+ 
+
+ align:start position:0%
+elements and the element F1 is of course
+chosen as a function of the ideal closed
+
+ align:start position:0%
+chosen as a function of the ideal closed
+ 
+
+ align:start position:0%
+chosen as a function of the ideal closed
+loop gain the way we then try to do
+
+ align:start position:0%
+loop gain the way we then try to do
+ 
+
+ align:start position:0%
+loop gain the way we then try to do
+compensation or try to affect
+
+ align:start position:0%
+compensation or try to affect
+ 
+
+ align:start position:0%
+compensation or try to affect
+compensation for this kind of a system
+
+ align:start position:0%
+compensation for this kind of a system
+ 
+
+ align:start position:0%
+compensation for this kind of a system
+very frequently boils down to the choice
+
+ align:start position:0%
+very frequently boils down to the choice
+ 
+
+ align:start position:0%
+very frequently boils down to the choice
+of the element used or the transfer
+
+ align:start position:0%
+of the element used or the transfer
+ 
+
+ align:start position:0%
+of the element used or the transfer
+function used for F2 so our hope is that
+
+ align:start position:0%
+function used for F2 so our hope is that
+ 
+
+ align:start position:0%
+function used for F2 so our hope is that
+we can select
+
+ align:start position:0%
+we can select
+ 
+
+ align:start position:0%
+we can select
+F2 in order to get acceptable
+
+ align:start position:0%
+F2 in order to get acceptable
+ 
+
+ align:start position:0%
+F2 in order to get acceptable
+performance from the overall
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system we can
+
+ align:start position:0%
+system we can
+ 
+
+ align:start position:0%
+system we can
+consider the transfer function V out
+
+ align:start position:0%
+consider the transfer function V out
+ 
+
+ align:start position:0%
+consider the transfer function V out
+over va va in the
+
+ align:start position:0%
+over va va in the
+ 
+
+ align:start position:0%
+over va va in the
+previous View graph was the voltage just
+
+ align:start position:0%
+previous View graph was the voltage just
+ 
+
+ align:start position:0%
+previous View graph was the voltage just
+out of the summing point in the major
+
+ align:start position:0%
+out of the summing point in the major
+ 
+
+ align:start position:0%
+out of the summing point in the major
+Loop and that transfer function is of
+
+ align:start position:0%
+Loop and that transfer function is of
+ 
+
+ align:start position:0%
+Loop and that transfer function is of
+course as
+
+ align:start position:0%
+course as
+ 
+
+ align:start position:0%
+course as
+always uh A1 that's a cascaded element
+
+ align:start position:0%
+always uh A1 that's a cascaded element
+ 
+
+ align:start position:0%
+always uh A1 that's a cascaded element
+and then we have a a reduction of the
+
+ align:start position:0%
+and then we have a a reduction of the
+ 
+
+ align:start position:0%
+and then we have a a reduction of the
+minor Loop the minor Loop has a forward
+
+ align:start position:0%
+minor Loop the minor Loop has a forward
+ 
+
+ align:start position:0%
+minor Loop the minor Loop has a forward
+path A2 and a feedback path F2 and so
+
+ align:start position:0%
+path A2 and a feedback path F2 and so
+ 
+
+ align:start position:0%
+path A2 and a feedback path F2 and so
+when we collapse the minor Loop we get a
+
+ align:start position:0%
+when we collapse the minor Loop we get a
+ 
+
+ align:start position:0%
+when we collapse the minor Loop we get a
+transfer function from the input to the
+
+ align:start position:0%
+transfer function from the input to the
+ 
+
+ align:start position:0%
+transfer function from the input to the
+output of the minor Loop that's simply
+
+ align:start position:0%
+output of the minor Loop that's simply
+ 
+
+ align:start position:0%
+output of the minor Loop that's simply
+A2 over 1 minus the transmission of the
+
+ align:start position:0%
+A2 over 1 minus the transmission of the
+ 
+
+ align:start position:0%
+A2 over 1 minus the transmission of the
+minor Loop uh in particular 1+ A2
+
+ align:start position:0%
+minor Loop uh in particular 1+ A2
+ 
+
+ align:start position:0%
+minor Loop uh in particular 1+ A2
+F2
+
+ align:start position:0%
+F2
+ 
+
+ align:start position:0%
+F2
+consequently the transfer function from
+
+ align:start position:0%
+consequently the transfer function from
+ 
+
+ align:start position:0%
+consequently the transfer function from
+here to here the effectively the forward
+
+ align:start position:0%
+here to here the effectively the forward
+ 
+
+ align:start position:0%
+here to here the effectively the forward
+path of the major Loop is simply A1 * A2
+
+ align:start position:0%
+path of the major Loop is simply A1 * A2
+ 
+
+ align:start position:0%
+path of the major Loop is simply A1 * A2
+over 1 + A2 F2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using that value for the forward path of
+
+ align:start position:0%
+using that value for the forward path of
+ 
+
+ align:start position:0%
+using that value for the forward path of
+our major loop system we can write the
+
+ align:start position:0%
+our major loop system we can write the
+ 
+
+ align:start position:0%
+our major loop system we can write the
+overall output to input transfer
+
+ align:start position:0%
+overall output to input transfer
+ 
+
+ align:start position:0%
+overall output to input transfer
+function for the system and in
+
+ align:start position:0%
+function for the system and in
+ 
+
+ align:start position:0%
+function for the system and in
+particular it's our forward path the
+
+ align:start position:0%
+particular it's our forward path the
+ 
+
+ align:start position:0%
+particular it's our forward path the
+expression here divided by 1 minus the
+
+ align:start position:0%
+expression here divided by 1 minus the
+ 
+
+ align:start position:0%
+expression here divided by 1 minus the
+loop transmission of the major Loop uh
+
+ align:start position:0%
+loop transmission of the major Loop uh
+ 
+
+ align:start position:0%
+loop transmission of the major Loop uh
+the loop transmission of the major Loop
+
+ align:start position:0%
+the loop transmission of the major Loop
+ 
+
+ align:start position:0%
+the loop transmission of the major Loop
+is simply minus
+
+ align:start position:0%
+is simply minus
+ 
+
+ align:start position:0%
+is simply minus
+or the negative of loop transmission for
+
+ align:start position:0%
+or the negative of loop transmission for
+ 
+
+ align:start position:0%
+or the negative of loop transmission for
+the major Loop is simply this expression
+
+ align:start position:0%
+the major Loop is simply this expression
+ 
+
+ align:start position:0%
+the major Loop is simply this expression
+times fub1 consequently we get the input
+
+ align:start position:0%
+times fub1 consequently we get the input
+ 
+
+ align:start position:0%
+times fub1 consequently we get the input
+to Output transfer function for the
+
+ align:start position:0%
+to Output transfer function for the
+ 
+
+ align:start position:0%
+to Output transfer function for the
+overall system as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+shown we could certainly adjust
+
+ align:start position:0%
+shown we could certainly adjust
+ 
+
+ align:start position:0%
+shown we could certainly adjust
+parameters in this system by choosing F2
+
+ align:start position:0%
+parameters in this system by choosing F2
+ 
+
+ align:start position:0%
+parameters in this system by choosing F2
+to get a desired closed loop transfer
+
+ align:start position:0%
+to get a desired closed loop transfer
+ 
+
+ align:start position:0%
+to get a desired closed loop transfer
+function hopefully to accomplish
+
+ align:start position:0%
+function hopefully to accomplish
+ 
+
+ align:start position:0%
+function hopefully to accomplish
+stability objectives and so forth and we
+
+ align:start position:0%
+stability objectives and so forth and we
+ 
+
+ align:start position:0%
+stability objectives and so forth and we
+could go through an exact mathematical
+
+ align:start position:0%
+could go through an exact mathematical
+ 
+
+ align:start position:0%
+could go through an exact mathematical
+development that would tell us the
+
+ align:start position:0%
+development that would tell us the
+ 
+
+ align:start position:0%
+development that would tell us the
+effect on overall performance of
+
+ align:start position:0%
+effect on overall performance of
+ 
+
+ align:start position:0%
+effect on overall performance of
+particular choices of the quantity F2
+
+ align:start position:0%
+particular choices of the quantity F2
+ 
+
+ align:start position:0%
+particular choices of the quantity F2
+however that's not usually what we do
+
+ align:start position:0%
+however that's not usually what we do
+ 
+
+ align:start position:0%
+however that's not usually what we do
+the Hope in minor Loop compensation is
+
+ align:start position:0%
+the Hope in minor Loop compensation is
+ 
+
+ align:start position:0%
+the Hope in minor Loop compensation is
+that we're able to make the minor
+
+ align:start position:0%
+that we're able to make the minor
+ 
+
+ align:start position:0%
+that we're able to make the minor
+Loop effectively honest if you will
+
+ align:start position:0%
+Loop effectively honest if you will
+ 
+
+ align:start position:0%
+Loop effectively honest if you will
+controlled by feedback at the major Loop
+
+ align:start position:0%
+controlled by feedback at the major Loop
+ 
+
+ align:start position:0%
+controlled by feedback at the major Loop
+crossover frequency in other words what
+
+ align:start position:0%
+crossover frequency in other words what
+ 
+
+ align:start position:0%
+crossover frequency in other words what
+we do is hope that the loop transmission
+
+ align:start position:0%
+we do is hope that the loop transmission
+ 
+
+ align:start position:0%
+we do is hope that the loop transmission
+of the minor Loop the A2 F2 product at
+
+ align:start position:0%
+of the minor Loop the A2 F2 product at
+ 
+
+ align:start position:0%
+of the minor Loop the A2 F2 product at
+the frequency particularly of crossover
+
+ align:start position:0%
+the frequency particularly of crossover
+ 
+
+ align:start position:0%
+the frequency particularly of crossover
+of the major Loop we hope that that A2
+
+ align:start position:0%
+of the major Loop we hope that that A2
+ 
+
+ align:start position:0%
+of the major Loop we hope that that A2
+F2 product is large if that's true then
+
+ align:start position:0%
+F2 product is large if that's true then
+ 
+
+ align:start position:0%
+F2 product is large if that's true then
+the transfer function from here to here
+
+ align:start position:0%
+the transfer function from here to here
+ 
+
+ align:start position:0%
+the transfer function from here to here
+is about equal to 1 over F2 if we didn't
+
+ align:start position:0%
+is about equal to 1 over F2 if we didn't
+ 
+
+ align:start position:0%
+is about equal to 1 over F2 if we didn't
+have everything else if this were just
+
+ align:start position:0%
+have everything else if this were just
+ 
+
+ align:start position:0%
+have everything else if this were just
+if this were the only part of our
+
+ align:start position:0%
+if this were the only part of our
+ 
+
+ align:start position:0%
+if this were the only part of our
+feedback system we'd of course argue
+
+ align:start position:0%
+feedback system we'd of course argue
+ 
+
+ align:start position:0%
+feedback system we'd of course argue
+that any frequency where the loop
+
+ align:start position:0%
+that any frequency where the loop
+ 
+
+ align:start position:0%
+that any frequency where the loop
+transmission magnitude was large
+
+ align:start position:0%
+transmission magnitude was large
+ 
+
+ align:start position:0%
+transmission magnitude was large
+compared to one the input to Output
+
+ align:start position:0%
+compared to one the input to Output
+ 
+
+ align:start position:0%
+compared to one the input to Output
+transfer function of that minor Loop
+
+ align:start position:0%
+transfer function of that minor Loop
+ 
+
+ align:start position:0%
+transfer function of that minor Loop
+would simply be equal to 1/ F2 and so
+
+ align:start position:0%
+would simply be equal to 1/ F2 and so
+ 
+
+ align:start position:0%
+would simply be equal to 1/ F2 and so
+our hope is as to say that at the
+
+ align:start position:0%
+our hope is as to say that at the
+ 
+
+ align:start position:0%
+our hope is as to say that at the
+crossover of the major Loop that
+
+ align:start position:0%
+crossover of the major Loop that
+ 
+
+ align:start position:0%
+crossover of the major Loop that
+condition is satisfied and the transfer
+
+ align:start position:0%
+condition is satisfied and the transfer
+ 
+
+ align:start position:0%
+condition is satisfied and the transfer
+function from here to here is about 1
+
+ align:start position:0%
+function from here to here is about 1
+ 
+
+ align:start position:0%
+function from here to here is about 1
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+F2 if that's
+
+ align:start position:0%
+F2 if that's
+ 
+
+ align:start position:0%
+F2 if that's
+true we're able to
+
+ align:start position:0%
+true we're able to
+ 
+
+ align:start position:0%
+true we're able to
+design using an approximation that says
+
+ align:start position:0%
+design using an approximation that says
+ 
+
+ align:start position:0%
+design using an approximation that says
+the negative the loop transmission for
+
+ align:start position:0%
+the negative the loop transmission for
+ 
+
+ align:start position:0%
+the negative the loop transmission for
+the overall Loop is simply equal to A2
+
+ align:start position:0%
+the overall Loop is simply equal to A2
+ 
+
+ align:start position:0%
+the overall Loop is simply equal to A2
+A1 F1 divided by F2 the elements A1 and
+
+ align:start position:0%
+A1 F1 divided by F2 the elements A1 and
+ 
+
+ align:start position:0%
+A1 F1 divided by F2 the elements A1 and
+F1 are elements associated with the
+
+ align:start position:0%
+F1 are elements associated with the
+ 
+
+ align:start position:0%
+F1 are elements associated with the
+major Loop one over F2 is the
+
+ align:start position:0%
+major Loop one over F2 is the
+ 
+
+ align:start position:0%
+major Loop one over F2 is the
+approximate input to Output transmission
+
+ align:start position:0%
+approximate input to Output transmission
+ 
+
+ align:start position:0%
+approximate input to Output transmission
+of the minor Loop and again our hope is
+
+ align:start position:0%
+of the minor Loop and again our hope is
+ 
+
+ align:start position:0%
+of the minor Loop and again our hope is
+as I indicated that the quantity A2 F2
+
+ align:start position:0%
+as I indicated that the quantity A2 F2
+ 
+
+ align:start position:0%
+as I indicated that the quantity A2 F2
+evaluated at Omega C where Omega C is
+
+ align:start position:0%
+evaluated at Omega C where Omega C is
+ 
+
+ align:start position:0%
+evaluated at Omega C where Omega C is
+the crossover frequency of the major
+
+ align:start position:0%
+the crossover frequency of the major
+ 
+
+ align:start position:0%
+the crossover frequency of the major
+Loop is considerably larger than one
+
+ align:start position:0%
+Loop is considerably larger than one
+ 
+
+ align:start position:0%
+Loop is considerably larger than one
+that's the condition necessary to use
+
+ align:start position:0%
+that's the condition necessary to use
+ 
+
+ align:start position:0%
+that's the condition necessary to use
+this approximation for the transmission
+
+ align:start position:0%
+this approximation for the transmission
+ 
+
+ align:start position:0%
+this approximation for the transmission
+of the major loop as our design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tool why do we feel we might be able to
+
+ align:start position:0%
+tool why do we feel we might be able to
+ 
+
+ align:start position:0%
+tool why do we feel we might be able to
+accomplish this sort of a thing well the
+
+ align:start position:0%
+accomplish this sort of a thing well the
+ 
+
+ align:start position:0%
+accomplish this sort of a thing well the
+thing that saves us generally or the
+
+ align:start position:0%
+thing that saves us generally or the
+ 
+
+ align:start position:0%
+thing that saves us generally or the
+thing that allows us to make the minor
+
+ align:start position:0%
+thing that allows us to make the minor
+ 
+
+ align:start position:0%
+thing that allows us to make the minor
+Loop have very high gain or very high
+
+ align:start position:0%
+Loop have very high gain or very high
+ 
+
+ align:start position:0%
+Loop have very high gain or very high
+Loop transmission magnitude at the
+
+ align:start position:0%
+Loop transmission magnitude at the
+ 
+
+ align:start position:0%
+Loop transmission magnitude at the
+crossover frequency of the major Loop
+
+ align:start position:0%
+crossover frequency of the major Loop
+ 
+
+ align:start position:0%
+crossover frequency of the major Loop
+really reflects the fact that there's
+
+ align:start position:0%
+really reflects the fact that there's
+ 
+
+ align:start position:0%
+really reflects the fact that there's
+relatively fewer elements in the minor
+
+ align:start position:0%
+relatively fewer elements in the minor
+ 
+
+ align:start position:0%
+relatively fewer elements in the minor
+Loop than there are in the overall
+
+ align:start position:0%
+Loop than there are in the overall
+ 
+
+ align:start position:0%
+Loop than there are in the overall
+Loop we recognize of course that as we
+
+ align:start position:0%
+Loop we recognize of course that as we
+ 
+
+ align:start position:0%
+Loop we recognize of course that as we
+increase the complexity of a feedback
+
+ align:start position:0%
+increase the complexity of a feedback
+ 
+
+ align:start position:0%
+increase the complexity of a feedback
+system increase the number of elements
+
+ align:start position:0%
+system increase the number of elements
+ 
+
+ align:start position:0%
+system increase the number of elements
+in a loop because of the low pass nature
+
+ align:start position:0%
+in a loop because of the low pass nature
+ 
+
+ align:start position:0%
+in a loop because of the low pass nature
+of those elements it becomes
+
+ align:start position:0%
+of those elements it becomes
+ 
+
+ align:start position:0%
+of those elements it becomes
+progressively more difficult to
+
+ align:start position:0%
+progressively more difficult to
+ 
+
+ align:start position:0%
+progressively more difficult to
+stabilize the loop we get more and more
+
+ align:start position:0%
+stabilize the loop we get more and more
+ 
+
+ align:start position:0%
+stabilize the loop we get more and more
+poles really associated with the energy
+
+ align:start position:0%
+poles really associated with the energy
+ 
+
+ align:start position:0%
+poles really associated with the energy
+storage becomes more difficult to
+
+ align:start position:0%
+storage becomes more difficult to
+ 
+
+ align:start position:0%
+storage becomes more difficult to
+stabilize the resultant Loop
+
+ align:start position:0%
+stabilize the resultant Loop
+ 
+
+ align:start position:0%
+stabilize the resultant Loop
+consequently Loops that contain fewer
+
+ align:start position:0%
+consequently Loops that contain fewer
+ 
+
+ align:start position:0%
+consequently Loops that contain fewer
+elements generally can be stabilized to
+
+ align:start position:0%
+elements generally can be stabilized to
+ 
+
+ align:start position:0%
+elements generally can be stabilized to
+have higher crossover frequencies than
+
+ align:start position:0%
+have higher crossover frequencies than
+ 
+
+ align:start position:0%
+have higher crossover frequencies than
+Loops which include more elements here
+
+ align:start position:0%
+Loops which include more elements here
+ 
+
+ align:start position:0%
+Loops which include more elements here
+as a say the minor Loop or the inner
+
+ align:start position:0%
+as a say the minor Loop or the inner
+ 
+
+ align:start position:0%
+as a say the minor Loop or the inner
+loop is a small fraction of the overall
+
+ align:start position:0%
+loop is a small fraction of the overall
+ 
+
+ align:start position:0%
+loop is a small fraction of the overall
+system and so there's at least some hope
+
+ align:start position:0%
+system and so there's at least some hope
+ 
+
+ align:start position:0%
+system and so there's at least some hope
+that we're able to make this Loop have a
+
+ align:start position:0%
+that we're able to make this Loop have a
+ 
+
+ align:start position:0%
+that we're able to make this Loop have a
+much higher crossover frequency than the
+
+ align:start position:0%
+much higher crossover frequency than the
+ 
+
+ align:start position:0%
+much higher crossover frequency than the
+overall Loop uh consequently we would
+
+ align:start position:0%
+overall Loop uh consequently we would
+ 
+
+ align:start position:0%
+overall Loop uh consequently we would
+find out that were true that the loop
+
+ align:start position:0%
+find out that were true that the loop
+ 
+
+ align:start position:0%
+find out that were true that the loop
+transmission magnitude of this Loop
+
+ align:start position:0%
+transmission magnitude of this Loop
+ 
+
+ align:start position:0%
+transmission magnitude of this Loop
+would be large at the crossover
+
+ align:start position:0%
+would be large at the crossover
+ 
+
+ align:start position:0%
+would be large at the crossover
+frequency of the major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+loop again assuming that uh that
+
+ align:start position:0%
+loop again assuming that uh that
+ 
+
+ align:start position:0%
+loop again assuming that uh that
+condition satisfied we go ahead and we
+
+ align:start position:0%
+condition satisfied we go ahead and we
+ 
+
+ align:start position:0%
+condition satisfied we go ahead and we
+can express the transfer function V out
+
+ align:start position:0%
+can express the transfer function V out
+ 
+
+ align:start position:0%
+can express the transfer function V out
+over VA again this is effectively the
+
+ align:start position:0%
+over VA again this is effectively the
+ 
+
+ align:start position:0%
+over VA again this is effectively the
+overall forward path transmission of our
+
+ align:start position:0%
+overall forward path transmission of our
+ 
+
+ align:start position:0%
+overall forward path transmission of our
+major Loop
+
+ align:start position:0%
+major Loop
+ 
+
+ align:start position:0%
+major Loop
+this is an exact expression for it at
+
+ align:start position:0%
+this is an exact expression for it at
+ 
+
+ align:start position:0%
+this is an exact expression for it at
+frequencies where the magnitude of the
+
+ align:start position:0%
+frequencies where the magnitude of the
+ 
+
+ align:start position:0%
+frequencies where the magnitude of the
+minor Loop transmission is much much
+
+ align:start position:0%
+minor Loop transmission is much much
+ 
+
+ align:start position:0%
+minor Loop transmission is much much
+larger than one and this is the case
+
+ align:start position:0%
+larger than one and this is the case
+ 
+
+ align:start position:0%
+larger than one and this is the case
+that we hope exists uh particularly at
+
+ align:start position:0%
+that we hope exists uh particularly at
+ 
+
+ align:start position:0%
+that we hope exists uh particularly at
+crossover of the major Loop so we can
+
+ align:start position:0%
+crossover of the major Loop so we can
+ 
+
+ align:start position:0%
+crossover of the major Loop so we can
+use this as our design tool the
+
+ align:start position:0%
+use this as our design tool the
+ 
+
+ align:start position:0%
+use this as our design tool the
+effective forward path of our overall
+
+ align:start position:0%
+effective forward path of our overall
+ 
+
+ align:start position:0%
+effective forward path of our overall
+system is A1 over F2 or is approximately
+
+ align:start position:0%
+system is A1 over F2 or is approximately
+ 
+
+ align:start position:0%
+system is A1 over F2 or is approximately
+A1 over F2 if we have the Other Extreme
+
+ align:start position:0%
+A1 over F2 if we have the Other Extreme
+ 
+
+ align:start position:0%
+A1 over F2 if we have the Other Extreme
+if the magnitude of the minor Loop
+
+ align:start position:0%
+if the magnitude of the minor Loop
+ 
+
+ align:start position:0%
+if the magnitude of the minor Loop
+transmission is small compared to one
+
+ align:start position:0%
+transmission is small compared to one
+ 
+
+ align:start position:0%
+transmission is small compared to one
+then the minor Loop is effectively
+
+ align:start position:0%
+then the minor Loop is effectively
+ 
+
+ align:start position:0%
+then the minor Loop is effectively
+working on an open loop basis the
+
+ align:start position:0%
+working on an open loop basis the
+ 
+
+ align:start position:0%
+working on an open loop basis the
+forward path for our major loop system
+
+ align:start position:0%
+forward path for our major loop system
+ 
+
+ align:start position:0%
+forward path for our major loop system
+simply becomes A1 A2 the transfer
+
+ align:start position:0%
+simply becomes A1 A2 the transfer
+ 
+
+ align:start position:0%
+simply becomes A1 A2 the transfer
+function F2 doesn't really influence the
+
+ align:start position:0%
+function F2 doesn't really influence the
+ 
+
+ align:start position:0%
+function F2 doesn't really influence the
+results very much in that
+
+ align:start position:0%
+results very much in that
+ 
+
+ align:start position:0%
+results very much in that
+case there's a nice graphical
+
+ align:start position:0%
+case there's a nice graphical
+ 
+
+ align:start position:0%
+case there's a nice graphical
+interpretation of this what we can do is
+
+ align:start position:0%
+interpretation of this what we can do is
+ 
+
+ align:start position:0%
+interpretation of this what we can do is
+plot the two limiting cases plot the two
+
+ align:start position:0%
+plot the two limiting cases plot the two
+ 
+
+ align:start position:0%
+plot the two limiting cases plot the two
+approximations in other words we plot A1
+
+ align:start position:0%
+approximations in other words we plot A1
+ 
+
+ align:start position:0%
+approximations in other words we plot A1
+A2 and we also plot A1 over F2 we do
+
+ align:start position:0%
+A2 and we also plot A1 over F2 we do
+ 
+
+ align:start position:0%
+A2 and we also plot A1 over F2 we do
+that in bod plot form uh here's an
+
+ align:start position:0%
+that in bod plot form uh here's an
+ 
+
+ align:start position:0%
+that in bod plot form uh here's an
+assumed form for the plot A1 A2 I've
+
+ align:start position:0%
+assumed form for the plot A1 A2 I've
+ 
+
+ align:start position:0%
+assumed form for the plot A1 A2 I've
+assumed a two- pole kind of of
+
+ align:start position:0%
+assumed a two- pole kind of of
+ 
+
+ align:start position:0%
+assumed a two- pole kind of of
+transmission for
+
+ align:start position:0%
+transmission for
+ 
+
+ align:start position:0%
+transmission for
+that and then we also plot the quantity
+
+ align:start position:0%
+that and then we also plot the quantity
+ 
+
+ align:start position:0%
+that and then we also plot the quantity
+A1 over F2 that's the other limiting
+
+ align:start position:0%
+A1 over F2 that's the other limiting
+ 
+
+ align:start position:0%
+A1 over F2 that's the other limiting
+case and I've shown that here I've
+
+ align:start position:0%
+case and I've shown that here I've
+ 
+
+ align:start position:0%
+case and I've shown that here I've
+assumed in this plot that the quantity
+
+ align:start position:0%
+assumed in this plot that the quantity
+ 
+
+ align:start position:0%
+assumed in this plot that the quantity
+A1 over fub1 is single pole in nature uh
+
+ align:start position:0%
+A1 over fub1 is single pole in nature uh
+ 
+
+ align:start position:0%
+A1 over fub1 is single pole in nature uh
+and in fact as I've drawn it it reflects
+
+ align:start position:0%
+and in fact as I've drawn it it reflects
+ 
+
+ align:start position:0%
+and in fact as I've drawn it it reflects
+a pole at the or origin this would tell
+
+ align:start position:0%
+a pole at the or origin this would tell
+ 
+
+ align:start position:0%
+a pole at the or origin this would tell
+us that F1 is proportional to S if f1's
+
+ align:start position:0%
+us that F1 is proportional to S if f1's
+ 
+
+ align:start position:0%
+us that F1 is proportional to S if f1's
+proportional to s or at least one
+
+ align:start position:0%
+proportional to s or at least one
+ 
+
+ align:start position:0%
+proportional to s or at least one
+possibility is to have F1 proportional
+
+ align:start position:0%
+possibility is to have F1 proportional
+ 
+
+ align:start position:0%
+possibility is to have F1 proportional
+to S and A1 be frequency
+
+ align:start position:0%
+to S and A1 be frequency
+ 
+
+ align:start position:0%
+to S and A1 be frequency
+independent we'll see that that sort of
+
+ align:start position:0%
+independent we'll see that that sort of
+ 
+
+ align:start position:0%
+independent we'll see that that sort of
+transfer function is very frequently
+
+ align:start position:0%
+transfer function is very frequently
+ 
+
+ align:start position:0%
+transfer function is very frequently
+used for the quantity uh F2 I'm sorry
+
+ align:start position:0%
+used for the quantity uh F2 I'm sorry
+ 
+
+ align:start position:0%
+used for the quantity uh F2 I'm sorry
+this this should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F2 the U we find that that the transfer
+
+ align:start position:0%
+F2 the U we find that that the transfer
+ 
+
+ align:start position:0%
+F2 the U we find that that the transfer
+function of the feedback element in the
+
+ align:start position:0%
+function of the feedback element in the
+ 
+
+ align:start position:0%
+function of the feedback element in the
+minor Loop very frequently is a zero at
+
+ align:start position:0%
+minor Loop very frequently is a zero at
+ 
+
+ align:start position:0%
+minor Loop very frequently is a zero at
+the origin we'll see an example of that
+
+ align:start position:0%
+the origin we'll see an example of that
+ 
+
+ align:start position:0%
+the origin we'll see an example of that
+uh in the next lecture when we we do an
+
+ align:start position:0%
+uh in the next lecture when we we do an
+ 
+
+ align:start position:0%
+uh in the next lecture when we we do an
+example of this kind of compensation
+
+ align:start position:0%
+example of this kind of compensation
+ 
+
+ align:start position:0%
+example of this kind of compensation
+using an operational amplifier another
+
+ align:start position:0%
+using an operational amplifier another
+ 
+
+ align:start position:0%
+using an operational amplifier another
+possibility that you may very may be
+
+ align:start position:0%
+possibility that you may very may be
+ 
+
+ align:start position:0%
+possibility that you may very may be
+familiar with is the use of a tachometer
+
+ align:start position:0%
+familiar with is the use of a tachometer
+ 
+
+ align:start position:0%
+familiar with is the use of a tachometer
+in a Servo mechanism and what one does
+
+ align:start position:0%
+in a Servo mechanism and what one does
+ 
+
+ align:start position:0%
+in a Servo mechanism and what one does
+with a tachometer is measure the output
+
+ align:start position:0%
+with a tachometer is measure the output
+ 
+
+ align:start position:0%
+with a tachometer is measure the output
+velocity of the system and feed that
+
+ align:start position:0%
+velocity of the system and feed that
+ 
+
+ align:start position:0%
+velocity of the system and feed that
+back in a way that forms a minor Loop
+
+ align:start position:0%
+back in a way that forms a minor Loop
+ 
+
+ align:start position:0%
+back in a way that forms a minor Loop
+well the tachometer of course introduces
+
+ align:start position:0%
+well the tachometer of course introduces
+ 
+
+ align:start position:0%
+well the tachometer of course introduces
+a differentiation between output
+
+ align:start position:0%
+a differentiation between output
+ 
+
+ align:start position:0%
+a differentiation between output
+position and its signal so if we use a
+
+ align:start position:0%
+position and its signal so if we use a
+ 
+
+ align:start position:0%
+position and its signal so if we use a
+tachometer for monor Loop feedback in a
+
+ align:start position:0%
+tachometer for monor Loop feedback in a
+ 
+
+ align:start position:0%
+tachometer for monor Loop feedback in a
+in a Servo mechanism when we model that
+
+ align:start position:0%
+in a Servo mechanism when we model that
+ 
+
+ align:start position:0%
+in a Servo mechanism when we model that
+sort of a system we find that we formed
+
+ align:start position:0%
+sort of a system we find that we formed
+ 
+
+ align:start position:0%
+sort of a system we find that we formed
+a minor Loop Loop where the value of the
+
+ align:start position:0%
+a minor Loop Loop where the value of the
+ 
+
+ align:start position:0%
+a minor Loop Loop where the value of the
+feedback transfer function in the minor
+
+ align:start position:0%
+feedback transfer function in the minor
+ 
+
+ align:start position:0%
+feedback transfer function in the minor
+Loop is in fact proportional to S and in
+
+ align:start position:0%
+Loop is in fact proportional to S and in
+ 
+
+ align:start position:0%
+Loop is in fact proportional to S and in
+those sorts of cases why the quantity A1
+
+ align:start position:0%
+those sorts of cases why the quantity A1
+ 
+
+ align:start position:0%
+those sorts of cases why the quantity A1
+over F2 can very easily have this sort
+
+ align:start position:0%
+over F2 can very easily have this sort
+ 
+
+ align:start position:0%
+over F2 can very easily have this sort
+of form well once we' plotted these two
+
+ align:start position:0%
+of form well once we' plotted these two
+ 
+
+ align:start position:0%
+of form well once we' plotted these two
+transfer functions uh in particular the
+
+ align:start position:0%
+transfer functions uh in particular the
+ 
+
+ align:start position:0%
+transfer functions uh in particular the
+two limiting approximations A1 over F2
+
+ align:start position:0%
+two limiting approximations A1 over F2
+ 
+
+ align:start position:0%
+two limiting approximations A1 over F2
+uh which is the approximation that holds
+
+ align:start position:0%
+uh which is the approximation that holds
+ 
+
+ align:start position:0%
+uh which is the approximation that holds
+when the loop transmission of the minor
+
+ align:start position:0%
+when the loop transmission of the minor
+ 
+
+ align:start position:0%
+when the loop transmission of the minor
+Loop is large compared to one
+
+ align:start position:0%
+Loop is large compared to one
+ 
+
+ align:start position:0%
+Loop is large compared to one
+and the A1 A2 product which is the
+
+ align:start position:0%
+and the A1 A2 product which is the
+ 
+
+ align:start position:0%
+and the A1 A2 product which is the
+approximation that holds when the
+
+ align:start position:0%
+approximation that holds when the
+ 
+
+ align:start position:0%
+approximation that holds when the
+transmission of the minor Loop is small
+
+ align:start position:0%
+transmission of the minor Loop is small
+ 
+
+ align:start position:0%
+transmission of the minor Loop is small
+compared to one we can very easily
+
+ align:start position:0%
+compared to one we can very easily
+ 
+
+ align:start position:0%
+compared to one we can very easily
+determine which of these approximations
+
+ align:start position:0%
+determine which of these approximations
+ 
+
+ align:start position:0%
+determine which of these approximations
+holds at any given
+
+ align:start position:0%
+holds at any given
+ 
+
+ align:start position:0%
+holds at any given
+frequency consider a frequency for
+
+ align:start position:0%
+frequency consider a frequency for
+ 
+
+ align:start position:0%
+frequency consider a frequency for
+example between here and here where the
+
+ align:start position:0%
+example between here and here where the
+ 
+
+ align:start position:0%
+example between here and here where the
+A1 A2 product exceeds the A1 over F2
+
+ align:start position:0%
+A1 A2 product exceeds the A1 over F2
+ 
+
+ align:start position:0%
+A1 A2 product exceeds the A1 over F2
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+in other words this condition if that's
+
+ align:start position:0%
+in other words this condition if that's
+ 
+
+ align:start position:0%
+in other words this condition if that's
+true and we simply divide both sides by
+
+ align:start position:0%
+true and we simply divide both sides by
+ 
+
+ align:start position:0%
+true and we simply divide both sides by
+A1 over F2 we find that over this entire
+
+ align:start position:0%
+A1 over F2 we find that over this entire
+ 
+
+ align:start position:0%
+A1 over F2 we find that over this entire
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+range the A2 F2 product is large
+
+ align:start position:0%
+range the A2 F2 product is large
+ 
+
+ align:start position:0%
+range the A2 F2 product is large
+compared to one or at least greater than
+
+ align:start position:0%
+compared to one or at least greater than
+ 
+
+ align:start position:0%
+compared to one or at least greater than
+one if we consider the entire frequency
+
+ align:start position:0%
+one if we consider the entire frequency
+ 
+
+ align:start position:0%
+one if we consider the entire frequency
+range it's certainly large much greater
+
+ align:start position:0%
+range it's certainly large much greater
+ 
+
+ align:start position:0%
+range it's certainly large much greater
+than one possibly over this frequency
+
+ align:start position:0%
+than one possibly over this frequency
+ 
+
+ align:start position:0%
+than one possibly over this frequency
+range
+
+ align:start position:0%
+range
+ 
+
+ align:start position:0%
+range
+and if we look above we find out that at
+
+ align:start position:0%
+and if we look above we find out that at
+ 
+
+ align:start position:0%
+and if we look above we find out that at
+frequencies where that condition is
+
+ align:start position:0%
+frequencies where that condition is
+ 
+
+ align:start position:0%
+frequencies where that condition is
+satisfied in particular where A2 F2 is
+
+ align:start position:0%
+satisfied in particular where A2 F2 is
+ 
+
+ align:start position:0%
+satisfied in particular where A2 F2 is
+much much larger than one why an
+
+ align:start position:0%
+much much larger than one why an
+ 
+
+ align:start position:0%
+much much larger than one why an
+approximation to the forward path of our
+
+ align:start position:0%
+approximation to the forward path of our
+ 
+
+ align:start position:0%
+approximation to the forward path of our
+system is simply A1 over F2 so that says
+
+ align:start position:0%
+system is simply A1 over F2 so that says
+ 
+
+ align:start position:0%
+system is simply A1 over F2 so that says
+that in this frequency range we should
+
+ align:start position:0%
+that in this frequency range we should
+ 
+
+ align:start position:0%
+that in this frequency range we should
+use
+
+ align:start position:0%
+use
+ 
+
+ align:start position:0%
+use
+this line as an approximation to the
+
+ align:start position:0%
+this line as an approximation to the
+ 
+
+ align:start position:0%
+this line as an approximation to the
+forward path transfer function of our
+
+ align:start position:0%
+forward path transfer function of our
+ 
+
+ align:start position:0%
+forward path transfer function of our
+overall system
+
+ align:start position:0%
+overall system
+ 
+
+ align:start position:0%
+overall system
+if we reverse the inequality in other
+
+ align:start position:0%
+if we reverse the inequality in other
+ 
+
+ align:start position:0%
+if we reverse the inequality in other
+words if we're working at frequencies
+
+ align:start position:0%
+words if we're working at frequencies
+ 
+
+ align:start position:0%
+words if we're working at frequencies
+either below this frequency or above
+
+ align:start position:0%
+either below this frequency or above
+ 
+
+ align:start position:0%
+either below this frequency or above
+this one where A1 A2 is less than A1
+
+ align:start position:0%
+this one where A1 A2 is less than A1
+ 
+
+ align:start position:0%
+this one where A1 A2 is less than A1
+over F2 the equal the inequality simply
+
+ align:start position:0%
+over F2 the equal the inequality simply
+ 
+
+ align:start position:0%
+over F2 the equal the inequality simply
+reverses and we find out that here and
+
+ align:start position:0%
+reverses and we find out that here and
+ 
+
+ align:start position:0%
+reverses and we find out that here and
+here in in those frequency ranges we
+
+ align:start position:0%
+here in in those frequency ranges we
+ 
+
+ align:start position:0%
+here in in those frequency ranges we
+should use A1 A2 as our approximation to
+
+ align:start position:0%
+should use A1 A2 as our approximation to
+ 
+
+ align:start position:0%
+should use A1 A2 as our approximation to
+the forward path transfer function of
+
+ align:start position:0%
+the forward path transfer function of
+ 
+
+ align:start position:0%
+the forward path transfer function of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+well a very simple way to do this is to
+
+ align:start position:0%
+well a very simple way to do this is to
+ 
+
+ align:start position:0%
+well a very simple way to do this is to
+Simply use the lower of these two curves
+
+ align:start position:0%
+Simply use the lower of these two curves
+ 
+
+ align:start position:0%
+Simply use the lower of these two curves
+at all frequencies that's a consequence
+
+ align:start position:0%
+at all frequencies that's a consequence
+ 
+
+ align:start position:0%
+at all frequencies that's a consequence
+of Simply checking the inequalities and
+
+ align:start position:0%
+of Simply checking the inequalities and
+ 
+
+ align:start position:0%
+of Simply checking the inequalities and
+so we conclude at least where the much
+
+ align:start position:0%
+so we conclude at least where the much
+ 
+
+ align:start position:0%
+so we conclude at least where the much
+greater than and much less than
+
+ align:start position:0%
+greater than and much less than
+ 
+
+ align:start position:0%
+greater than and much less than
+conditions were satisfied for example in
+
+ align:start position:0%
+conditions were satisfied for example in
+ 
+
+ align:start position:0%
+conditions were satisfied for example in
+this frequency
+
+ align:start position:0%
+this frequency
+ 
+
+ align:start position:0%
+this frequency
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+range in this frequency
+
+ align:start position:0%
+range in this frequency
+ 
+
+ align:start position:0%
+range in this frequency
+range and in this frequency range we
+
+ align:start position:0%
+range and in this frequency range we
+ 
+
+ align:start position:0%
+range and in this frequency range we
+could simply select the lower of the two
+
+ align:start position:0%
+could simply select the lower of the two
+ 
+
+ align:start position:0%
+could simply select the lower of the two
+curves as being a very good
+
+ align:start position:0%
+curves as being a very good
+ 
+
+ align:start position:0%
+curves as being a very good
+approximation to the forward path
+
+ align:start position:0%
+approximation to the forward path
+ 
+
+ align:start position:0%
+approximation to the forward path
+transfer function of our overall system
+
+ align:start position:0%
+transfer function of our overall system
+ 
+
+ align:start position:0%
+transfer function of our overall system
+we have to worry a little bit about what
+
+ align:start position:0%
+we have to worry a little bit about what
+ 
+
+ align:start position:0%
+we have to worry a little bit about what
+happens where the magnitude uh the
+
+ align:start position:0%
+happens where the magnitude uh the
+ 
+
+ align:start position:0%
+happens where the magnitude uh the
+magnitudes are about equal in other
+
+ align:start position:0%
+magnitudes are about equal in other
+ 
+
+ align:start position:0%
+magnitudes are about equal in other
+words in this frequency range and in
+
+ align:start position:0%
+words in this frequency range and in
+ 
+
+ align:start position:0%
+words in this frequency range and in
+this frequency range uh and if we did
+
+ align:start position:0%
+this frequency range uh and if we did
+ 
+
+ align:start position:0%
+this frequency range uh and if we did
+that carefully we'd find out that for
+
+ align:start position:0%
+that carefully we'd find out that for
+ 
+
+ align:start position:0%
+that carefully we'd find out that for
+this this sort of situation where the
+
+ align:start position:0%
+this this sort of situation where the
+ 
+
+ align:start position:0%
+this this sort of situation where the
+slope of the two curves differ by one
+
+ align:start position:0%
+slope of the two curves differ by one
+ 
+
+ align:start position:0%
+slope of the two curves differ by one
+unit on logarithmic coordinates at the
+
+ align:start position:0%
+unit on logarithmic coordinates at the
+ 
+
+ align:start position:0%
+unit on logarithmic coordinates at the
+intersections uh we get basically uh the
+
+ align:start position:0%
+intersections uh we get basically uh the
+ 
+
+ align:start position:0%
+intersections uh we get basically uh the
+usual sort of single pole
+
+ align:start position:0%
+usual sort of single pole
+ 
+
+ align:start position:0%
+usual sort of single pole
+matching between the the two
+
+ align:start position:0%
+matching between the the two
+ 
+
+ align:start position:0%
+matching between the the two
+curves so the only place we have to take
+
+ align:start position:0%
+curves so the only place we have to take
+ 
+
+ align:start position:0%
+curves so the only place we have to take
+any particular care is in the immediate
+
+ align:start position:0%
+any particular care is in the immediate
+ 
+
+ align:start position:0%
+any particular care is in the immediate
+vicinity where the magnit uh where the
+
+ align:start position:0%
+vicinity where the magnit uh where the
+ 
+
+ align:start position:0%
+vicinity where the magnit uh where the
+magnitudes are are equal other than that
+
+ align:start position:0%
+magnitudes are are equal other than that
+ 
+
+ align:start position:0%
+magnitudes are are equal other than that
+we can just go ahead and approximate the
+
+ align:start position:0%
+we can just go ahead and approximate the
+ 
+
+ align:start position:0%
+we can just go ahead and approximate the
+forward path transfer function of our
+
+ align:start position:0%
+forward path transfer function of our
+ 
+
+ align:start position:0%
+forward path transfer function of our
+system as simply the lower of the two
+
+ align:start position:0%
+system as simply the lower of the two
+ 
+
+ align:start position:0%
+system as simply the lower of the two
+curves we'll very rapidly sort of relax
+
+ align:start position:0%
+curves we'll very rapidly sort of relax
+ 
+
+ align:start position:0%
+curves we'll very rapidly sort of relax
+this and and make an even cruder
+
+ align:start position:0%
+this and and make an even cruder
+ 
+
+ align:start position:0%
+this and and make an even cruder
+approximation and and really not worry
+
+ align:start position:0%
+approximation and and really not worry
+ 
+
+ align:start position:0%
+approximation and and really not worry
+too much about uh exactly what goes on
+
+ align:start position:0%
+too much about uh exactly what goes on
+ 
+
+ align:start position:0%
+too much about uh exactly what goes on
+in this vicinity and this vicinity uh
+
+ align:start position:0%
+in this vicinity and this vicinity uh
+ 
+
+ align:start position:0%
+in this vicinity and this vicinity uh
+simply go blindly ahead and take the
+
+ align:start position:0%
+simply go blindly ahead and take the
+ 
+
+ align:start position:0%
+simply go blindly ahead and take the
+lower of the two curves at all
+
+ align:start position:0%
+lower of the two curves at all
+ 
+
+ align:start position:0%
+lower of the two curves at all
+frequencies we find out that very
+
+ align:start position:0%
+frequencies we find out that very
+ 
+
+ align:start position:0%
+frequencies we find out that very
+frequently gives us completely
+
+ align:start position:0%
+frequently gives us completely
+ 
+
+ align:start position:0%
+frequently gives us completely
+satisfactory information for use as a
+
+ align:start position:0%
+satisfactory information for use as a
+ 
+
+ align:start position:0%
+satisfactory information for use as a
+design
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tool I mentioned that one common kind
+
+ align:start position:0%
+tool I mentioned that one common kind
+ 
+
+ align:start position:0%
+tool I mentioned that one common kind
+kind of a system that uses this sort of
+
+ align:start position:0%
+kind of a system that uses this sort of
+ 
+
+ align:start position:0%
+kind of a system that uses this sort of
+minor Loop compensation is that of a
+
+ align:start position:0%
+minor Loop compensation is that of a
+ 
+
+ align:start position:0%
+minor Loop compensation is that of a
+Servo mechanism where tachometric
+
+ align:start position:0%
+Servo mechanism where tachometric
+ 
+
+ align:start position:0%
+Servo mechanism where tachometric
+feedback is used the tachometer provides
+
+ align:start position:0%
+feedback is used the tachometer provides
+ 
+
+ align:start position:0%
+feedback is used the tachometer provides
+a zero at the origin at least if our if
+
+ align:start position:0%
+a zero at the origin at least if our if
+ 
+
+ align:start position:0%
+a zero at the origin at least if our if
+we consider the input to the tachometer
+
+ align:start position:0%
+we consider the input to the tachometer
+ 
+
+ align:start position:0%
+we consider the input to the tachometer
+to be mechanical position uh then it
+
+ align:start position:0%
+to be mechanical position uh then it
+ 
+
+ align:start position:0%
+to be mechanical position uh then it
+provides a differentiation of zero at
+
+ align:start position:0%
+provides a differentiation of zero at
+ 
+
+ align:start position:0%
+provides a differentiation of zero at
+the origin in its transfer function
+
+ align:start position:0%
+the origin in its transfer function
+ 
+
+ align:start position:0%
+the origin in its transfer function
+there's another case where monor Loop
+
+ align:start position:0%
+there's another case where monor Loop
+ 
+
+ align:start position:0%
+there's another case where monor Loop
+feedback is frequently used and that's
+
+ align:start position:0%
+feedback is frequently used and that's
+ 
+
+ align:start position:0%
+feedback is frequently used and that's
+in the design of most modern operational
+
+ align:start position:0%
+in the design of most modern operational
+ 
+
+ align:start position:0%
+in the design of most modern operational
+amplifiers
+
+ align:start position:0%
+amplifiers
+ 
+
+ align:start position:0%
+amplifiers
+this can be done either internal to the
+
+ align:start position:0%
+this can be done either internal to the
+ 
+
+ align:start position:0%
+this can be done either internal to the
+amplifier there are a number of
+
+ align:start position:0%
+amplifier there are a number of
+ 
+
+ align:start position:0%
+amplifier there are a number of
+amplifiers available where there's an
+
+ align:start position:0%
+amplifiers available where there's an
+ 
+
+ align:start position:0%
+amplifiers available where there's an
+internal minor Loop compensating element
+
+ align:start position:0%
+internal minor Loop compensating element
+ 
+
+ align:start position:0%
+internal minor Loop compensating element
+the 741 which is familiar to most of you
+
+ align:start position:0%
+the 741 which is familiar to most of you
+ 
+
+ align:start position:0%
+the 741 which is familiar to most of you
+is probably the best example or the most
+
+ align:start position:0%
+is probably the best example or the most
+ 
+
+ align:start position:0%
+is probably the best example or the most
+widely used example of that kind of an
+
+ align:start position:0%
+widely used example of that kind of an
+ 
+
+ align:start position:0%
+widely used example of that kind of an
+amplifier there are also several
+
+ align:start position:0%
+amplifier there are also several
+ 
+
+ align:start position:0%
+amplifier there are also several
+operational amplifiers available where
+
+ align:start position:0%
+operational amplifiers available where
+ 
+
+ align:start position:0%
+operational amplifiers available where
+provision is included for the user to
+
+ align:start position:0%
+provision is included for the user to
+ 
+
+ align:start position:0%
+provision is included for the user to
+complete compensating the amplifier
+
+ align:start position:0%
+complete compensating the amplifier
+ 
+
+ align:start position:0%
+complete compensating the amplifier
+really by forming a minor
+
+ align:start position:0%
+really by forming a minor
+ 
+
+ align:start position:0%
+really by forming a minor
+Loop and an amplifier like that uh we
+
+ align:start position:0%
+Loop and an amplifier like that uh we
+ 
+
+ align:start position:0%
+Loop and an amplifier like that uh we
+might be able to
+
+ align:start position:0%
+might be able to
+ 
+
+ align:start position:0%
+might be able to
+represent this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way here we have the symbol for the
+
+ align:start position:0%
+way here we have the symbol for the
+ 
+
+ align:start position:0%
+way here we have the symbol for the
+operational amplifier anyway and a very
+
+ align:start position:0%
+operational amplifier anyway and a very
+ 
+
+ align:start position:0%
+operational amplifier anyway and a very
+common way of Designing these amplifiers
+
+ align:start position:0%
+common way of Designing these amplifiers
+ 
+
+ align:start position:0%
+common way of Designing these amplifiers
+is to basically use a two-stage design
+
+ align:start position:0%
+is to basically use a two-stage design
+ 
+
+ align:start position:0%
+is to basically use a two-stage design
+there's some sort of an input
+
+ align:start position:0%
+there's some sort of an input
+ 
+
+ align:start position:0%
+there's some sort of an input
+differential stage that takes the
+
+ align:start position:0%
+differential stage that takes the
+ 
+
+ align:start position:0%
+differential stage that takes the
+difference between the two voltages
+
+ align:start position:0%
+difference between the two voltages
+ 
+
+ align:start position:0%
+difference between the two voltages
+applied to the input terminals of the
+
+ align:start position:0%
+applied to the input terminals of the
+ 
+
+ align:start position:0%
+applied to the input terminals of the
+operational amplifier generally provides
+
+ align:start position:0%
+operational amplifier generally provides
+ 
+
+ align:start position:0%
+operational amplifier generally provides
+an output current proportional to that
+
+ align:start position:0%
+an output current proportional to that
+ 
+
+ align:start position:0%
+an output current proportional to that
+difference and then there's a second
+
+ align:start position:0%
+difference and then there's a second
+ 
+
+ align:start position:0%
+difference and then there's a second
+stage that provides very high voltage
+
+ align:start position:0%
+stage that provides very high voltage
+ 
+
+ align:start position:0%
+stage that provides very high voltage
+gain that that uses the output of the
+
+ align:start position:0%
+gain that that uses the output of the
+ 
+
+ align:start position:0%
+gain that that uses the output of the
+first stage and amplifies it by a large
+
+ align:start position:0%
+first stage and amplifies it by a large
+ 
+
+ align:start position:0%
+first stage and amplifies it by a large
+amount and by using appropriate design
+
+ align:start position:0%
+amount and by using appropriate design
+ 
+
+ align:start position:0%
+amount and by using appropriate design
+techniques in these two stage amplifiers
+
+ align:start position:0%
+techniques in these two stage amplifiers
+ 
+
+ align:start position:0%
+techniques in these two stage amplifiers
+or amplifiers that have really only two
+
+ align:start position:0%
+or amplifiers that have really only two
+ 
+
+ align:start position:0%
+or amplifiers that have really only two
+stages of voltage gain it's possible to
+
+ align:start position:0%
+stages of voltage gain it's possible to
+ 
+
+ align:start position:0%
+stages of voltage gain it's possible to
+get the kinds of of open loop gains at
+
+ align:start position:0%
+get the kinds of of open loop gains at
+ 
+
+ align:start position:0%
+get the kinds of of open loop gains at
+low frequencies the one normally
+
+ align:start position:0%
+low frequencies the one normally
+ 
+
+ align:start position:0%
+low frequencies the one normally
+Associates with operational amplifiers
+
+ align:start position:0%
+Associates with operational amplifiers
+ 
+
+ align:start position:0%
+Associates with operational amplifiers
+somewhere on the order of 100,000 to a
+
+ align:start position:0%
+somewhere on the order of 100,000 to a
+ 
+
+ align:start position:0%
+somewhere on the order of 100,000 to a
+million implying a voltage gain if it's
+
+ align:start position:0%
+million implying a voltage gain if it's
+ 
+
+ align:start position:0%
+million implying a voltage gain if it's
+equally distributed between the two
+
+ align:start position:0%
+equally distributed between the two
+ 
+
+ align:start position:0%
+equally distributed between the two
+stages of something like a thousand per
+
+ align:start position:0%
+stages of something like a thousand per
+ 
+
+ align:start position:0%
+stages of something like a thousand per
+stage well the way one then forms a
+
+ align:start position:0%
+stage well the way one then forms a
+ 
+
+ align:start position:0%
+stage well the way one then forms a
+minor Loop is to connect a compensating
+
+ align:start position:0%
+minor Loop is to connect a compensating
+ 
+
+ align:start position:0%
+minor Loop is to connect a compensating
+network from the output of the second
+
+ align:start position:0%
+network from the output of the second
+ 
+
+ align:start position:0%
+network from the output of the second
+stage back to the input of the second
+
+ align:start position:0%
+stage back to the input of the second
+ 
+
+ align:start position:0%
+stage back to the input of the second
+stage so a a minor Loops formed uh in
+
+ align:start position:0%
+stage so a a minor Loops formed uh in
+ 
+
+ align:start position:0%
+stage so a a minor Loops formed uh in
+general we could form that minor Loop
+
+ align:start position:0%
+general we could form that minor Loop
+ 
+
+ align:start position:0%
+general we could form that minor Loop
+using a two-port compensating Network
+
+ align:start position:0%
+using a two-port compensating Network
+ 
+
+ align:start position:0%
+using a two-port compensating Network
+and we'll see how that works but we form
+
+ align:start position:0%
+and we'll see how that works but we form
+ 
+
+ align:start position:0%
+and we'll see how that works but we form
+the monor loop around simply the second
+
+ align:start position:0%
+the monor loop around simply the second
+ 
+
+ align:start position:0%
+the monor loop around simply the second
+stage of the operational amplifier and
+
+ align:start position:0%
+stage of the operational amplifier and
+ 
+
+ align:start position:0%
+stage of the operational amplifier and
+consequently if we compare this topology
+
+ align:start position:0%
+consequently if we compare this topology
+ 
+
+ align:start position:0%
+consequently if we compare this topology
+with our earlier topology for a minor
+
+ align:start position:0%
+with our earlier topology for a minor
+ 
+
+ align:start position:0%
+with our earlier topology for a minor
+Loop compensated system uh this might
+
+ align:start position:0%
+Loop compensated system uh this might
+ 
+
+ align:start position:0%
+Loop compensated system uh this might
+represent the first stage of the
+
+ align:start position:0%
+represent the first stage of the
+ 
+
+ align:start position:0%
+represent the first stage of the
+operational amplifier this would
+
+ align:start position:0%
+operational amplifier this would
+ 
+
+ align:start position:0%
+operational amplifier this would
+represent the second stage with the
+
+ align:start position:0%
+represent the second stage with the
+ 
+
+ align:start position:0%
+represent the second stage with the
+two-port network providing the function
+
+ align:start position:0%
+two-port network providing the function
+ 
+
+ align:start position:0%
+two-port network providing the function
+F2 the feedback around the second stage
+
+ align:start position:0%
+F2 the feedback around the second stage
+ 
+
+ align:start position:0%
+F2 the feedback around the second stage
+which forms the minor Loop and then of
+
+ align:start position:0%
+which forms the minor Loop and then of
+ 
+
+ align:start position:0%
+which forms the minor Loop and then of
+course when we go to connect the
+
+ align:start position:0%
+course when we go to connect the
+ 
+
+ align:start position:0%
+course when we go to connect the
+operational amplifier in an overall
+
+ align:start position:0%
+operational amplifier in an overall
+ 
+
+ align:start position:0%
+operational amplifier in an overall
+feedback system in some overall feedback
+
+ align:start position:0%
+feedback system in some overall feedback
+ 
+
+ align:start position:0%
+feedback system in some overall feedback
+connection we add an external path F1 to
+
+ align:start position:0%
+connection we add an external path F1 to
+ 
+
+ align:start position:0%
+connection we add an external path F1 to
+complete the major
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Loop once again here's the the way we
+
+ align:start position:0%
+Loop once again here's the the way we
+ 
+
+ align:start position:0%
+Loop once again here's the the way we
+sort of implement the previous topology
+
+ align:start position:0%
+sort of implement the previous topology
+ 
+
+ align:start position:0%
+sort of implement the previous topology
+for an operational
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+amplifier I'd like to look at a a very
+
+ align:start position:0%
+amplifier I'd like to look at a a very
+ 
+
+ align:start position:0%
+amplifier I'd like to look at a a very
+simplified representation of how such an
+
+ align:start position:0%
+simplified representation of how such an
+ 
+
+ align:start position:0%
+simplified representation of how such an
+operational amplifier works or so that
+
+ align:start position:0%
+operational amplifier works or so that
+ 
+
+ align:start position:0%
+operational amplifier works or so that
+we can can begin to look at the
+
+ align:start position:0%
+we can can begin to look at the
+ 
+
+ align:start position:0%
+we can can begin to look at the
+performance of this kind of an
+
+ align:start position:0%
+performance of this kind of an
+ 
+
+ align:start position:0%
+performance of this kind of an
+amplifier uh I've taken a few Liberties
+
+ align:start position:0%
+amplifier uh I've taken a few Liberties
+ 
+
+ align:start position:0%
+amplifier uh I've taken a few Liberties
+here with the construction of actual
+
+ align:start position:0%
+here with the construction of actual
+ 
+
+ align:start position:0%
+here with the construction of actual
+amplifiers there are some minor
+
+ align:start position:0%
+amplifiers there are some minor
+ 
+
+ align:start position:0%
+amplifiers there are some minor
+differences between the topology I'll
+
+ align:start position:0%
+differences between the topology I'll
+ 
+
+ align:start position:0%
+differences between the topology I'll
+present which is is very schematic in
+
+ align:start position:0%
+present which is is very schematic in
+ 
+
+ align:start position:0%
+present which is is very schematic in
+nature and the actual topology is used
+
+ align:start position:0%
+nature and the actual topology is used
+ 
+
+ align:start position:0%
+nature and the actual topology is used
+but they don't change any significant
+
+ align:start position:0%
+but they don't change any significant
+ 
+
+ align:start position:0%
+but they don't change any significant
+answers and so we'll we'll go ahead and
+
+ align:start position:0%
+answers and so we'll we'll go ahead and
+ 
+
+ align:start position:0%
+answers and so we'll we'll go ahead and
+look at this some what simplified
+
+ align:start position:0%
+look at this some what simplified
+ 
+
+ align:start position:0%
+look at this some what simplified
+representation bearing in mind that it
+
+ align:start position:0%
+representation bearing in mind that it
+ 
+
+ align:start position:0%
+representation bearing in mind that it
+does give us the correct answer for the
+
+ align:start position:0%
+does give us the correct answer for the
+ 
+
+ align:start position:0%
+does give us the correct answer for the
+transfer function of the operational
+
+ align:start position:0%
+transfer function of the operational
+ 
+
+ align:start position:0%
+transfer function of the operational
+amplifier we might have a differential
+
+ align:start position:0%
+amplifier we might have a differential
+ 
+
+ align:start position:0%
+amplifier we might have a differential
+input stage uh I've shown it constructed
+
+ align:start position:0%
+input stage uh I've shown it constructed
+ 
+
+ align:start position:0%
+input stage uh I've shown it constructed
+out of PNP transistors and that's the
+
+ align:start position:0%
+out of PNP transistors and that's the
+ 
+
+ align:start position:0%
+out of PNP transistors and that's the
+way it's done uh in amplifiers like the
+
+ align:start position:0%
+way it's done uh in amplifiers like the
+ 
+
+ align:start position:0%
+way it's done uh in amplifiers like the
+741 or at least the topological function
+
+ align:start position:0%
+741 or at least the topological function
+ 
+
+ align:start position:0%
+741 or at least the topological function
+of the input stage is the same as if it
+
+ align:start position:0%
+of the input stage is the same as if it
+ 
+
+ align:start position:0%
+of the input stage is the same as if it
+were constructed simply of PNP
+
+ align:start position:0%
+were constructed simply of PNP
+ 
+
+ align:start position:0%
+were constructed simply of PNP
+transistors and that differential pair
+
+ align:start position:0%
+transistors and that differential pair
+ 
+
+ align:start position:0%
+transistors and that differential pair
+of trans ancestors is generally biased
+
+ align:start position:0%
+of trans ancestors is generally biased
+ 
+
+ align:start position:0%
+of trans ancestors is generally biased
+with a current
+
+ align:start position:0%
+with a current
+ 
+
+ align:start position:0%
+with a current
+Source I've assumed for purposes of
+
+ align:start position:0%
+Source I've assumed for purposes of
+ 
+
+ align:start position:0%
+Source I've assumed for purposes of
+calculating the transfer function of the
+
+ align:start position:0%
+calculating the transfer function of the
+ 
+
+ align:start position:0%
+calculating the transfer function of the
+amplifier that we apply an input to only
+
+ align:start position:0%
+amplifier that we apply an input to only
+ 
+
+ align:start position:0%
+amplifier that we apply an input to only
+one side of the differential pair uh
+
+ align:start position:0%
+one side of the differential pair uh
+ 
+
+ align:start position:0%
+one side of the differential pair uh
+ground the other side so here's our our
+
+ align:start position:0%
+ground the other side so here's our our
+ 
+
+ align:start position:0%
+ground the other side so here's our our
+input signal
+
+ align:start position:0%
+input signal
+ 
+
+ align:start position:0%
+input signal
+VI and again in a little Distortion of
+
+ align:start position:0%
+VI and again in a little Distortion of
+ 
+
+ align:start position:0%
+VI and again in a little Distortion of
+reality but one that that does lead us
+
+ align:start position:0%
+reality but one that that does lead us
+ 
+
+ align:start position:0%
+reality but one that that does lead us
+to the correct result uh I assume that
+
+ align:start position:0%
+to the correct result uh I assume that
+ 
+
+ align:start position:0%
+to the correct result uh I assume that
+the first stage is loaded with a current
+
+ align:start position:0%
+the first stage is loaded with a current
+ 
+
+ align:start position:0%
+the first stage is loaded with a current
+Source in fact a fixed magnitude current
+
+ align:start position:0%
+Source in fact a fixed magnitude current
+ 
+
+ align:start position:0%
+Source in fact a fixed magnitude current
+source and what we generally do would be
+
+ align:start position:0%
+source and what we generally do would be
+ 
+
+ align:start position:0%
+source and what we generally do would be
+to connect or select this current source
+
+ align:start position:0%
+to connect or select this current source
+ 
+
+ align:start position:0%
+to connect or select this current source
+to have a value 1/ half of the current
+
+ align:start position:0%
+to have a value 1/ half of the current
+ 
+
+ align:start position:0%
+to have a value 1/ half of the current
+used to bias the entire first stage uh
+
+ align:start position:0%
+used to bias the entire first stage uh
+ 
+
+ align:start position:0%
+used to bias the entire first stage uh
+the rationale for that of course being
+
+ align:start position:0%
+the rationale for that of course being
+ 
+
+ align:start position:0%
+the rationale for that of course being
+that if these transistors are well
+
+ align:start position:0%
+that if these transistors are well
+ 
+
+ align:start position:0%
+that if these transistors are well
+matched when we had VI equal to zero the
+
+ align:start position:0%
+matched when we had VI equal to zero the
+ 
+
+ align:start position:0%
+matched when we had VI equal to zero the
+current applied to the emitter of the
+
+ align:start position:0%
+current applied to the emitter of the
+ 
+
+ align:start position:0%
+current applied to the emitter of the
+differential p pair would divide equally
+
+ align:start position:0%
+differential p pair would divide equally
+ 
+
+ align:start position:0%
+differential p pair would divide equally
+between the two members of the pair uh
+
+ align:start position:0%
+between the two members of the pair uh
+ 
+
+ align:start position:0%
+between the two members of the pair uh
+consequently the quiescent current with
+
+ align:start position:0%
+consequently the quiescent current with
+ 
+
+ align:start position:0%
+consequently the quiescent current with
+Zer volts applied to the differential
+
+ align:start position:0%
+Zer volts applied to the differential
+ 
+
+ align:start position:0%
+Zer volts applied to the differential
+pair The quiescent Collector current of
+
+ align:start position:0%
+pair The quiescent Collector current of
+ 
+
+ align:start position:0%
+pair The quiescent Collector current of
+this transistor would be 1/2 of the bias
+
+ align:start position:0%
+this transistor would be 1/2 of the bias
+ 
+
+ align:start position:0%
+this transistor would be 1/2 of the bias
+current
+
+ align:start position:0%
+current
+ 
+
+ align:start position:0%
+current
+uh the second stage of the amplifier is
+
+ align:start position:0%
+uh the second stage of the amplifier is
+ 
+
+ align:start position:0%
+uh the second stage of the amplifier is
+modeled uh uh even more diagrammatically
+
+ align:start position:0%
+modeled uh uh even more diagrammatically
+ 
+
+ align:start position:0%
+modeled uh uh even more diagrammatically
+than the first stage here we at least
+
+ align:start position:0%
+than the first stage here we at least
+ 
+
+ align:start position:0%
+than the first stage here we at least
+show a couple of transistors the second
+
+ align:start position:0%
+show a couple of transistors the second
+ 
+
+ align:start position:0%
+show a couple of transistors the second
+stage we simply assume has some put
+
+ align:start position:0%
+stage we simply assume has some put
+ 
+
+ align:start position:0%
+stage we simply assume has some put
+admittance while I've shown it as a
+
+ align:start position:0%
+admittance while I've shown it as a
+ 
+
+ align:start position:0%
+admittance while I've shown it as a
+resistor or a conductance why in general
+
+ align:start position:0%
+resistor or a conductance why in general
+ 
+
+ align:start position:0%
+resistor or a conductance why in general
+it's a a frequency dependent element
+
+ align:start position:0%
+it's a a frequency dependent element
+ 
+
+ align:start position:0%
+it's a a frequency dependent element
+let's call that
+
+ align:start position:0%
+let's call that
+ 
+
+ align:start position:0%
+let's call that
+Yi and the voltage across the input of
+
+ align:start position:0%
+Yi and the voltage across the input of
+ 
+
+ align:start position:0%
+Yi and the voltage across the input of
+the second stage the incremental voltage
+
+ align:start position:0%
+the second stage the incremental voltage
+ 
+
+ align:start position:0%
+the second stage the incremental voltage
+is a little bit of a problem with
+
+ align:start position:0%
+is a little bit of a problem with
+ 
+
+ align:start position:0%
+is a little bit of a problem with
+grounds but at least the incremental
+
+ align:start position:0%
+grounds but at least the incremental
+ 
+
+ align:start position:0%
+grounds but at least the incremental
+component of the voltage across the
+
+ align:start position:0%
+component of the voltage across the
+ 
+
+ align:start position:0%
+component of the voltage across the
+input to the second stage we'll call VA
+
+ align:start position:0%
+input to the second stage we'll call VA
+ 
+
+ align:start position:0%
+input to the second stage we'll call VA
+and the output voltage of the second
+
+ align:start position:0%
+and the output voltage of the second
+ 
+
+ align:start position:0%
+and the output voltage of the second
+stage which we assume is identically the
+
+ align:start position:0%
+stage which we assume is identically the
+ 
+
+ align:start position:0%
+stage which we assume is identically the
+output voltage of the operational
+
+ align:start position:0%
+output voltage of the operational
+ 
+
+ align:start position:0%
+output voltage of the operational
+amplifier usually there's some kind of
+
+ align:start position:0%
+amplifier usually there's some kind of
+ 
+
+ align:start position:0%
+amplifier usually there's some kind of
+of buffering in a mitter follower or
+
+ align:start position:0%
+of buffering in a mitter follower or
+ 
+
+ align:start position:0%
+of buffering in a mitter follower or
+something like that between the second
+
+ align:start position:0%
+something like that between the second
+ 
+
+ align:start position:0%
+something like that between the second
+stage itself and the output to make the
+
+ align:start position:0%
+stage itself and the output to make the
+ 
+
+ align:start position:0%
+stage itself and the output to make the
+second stage less sensitive to loads
+
+ align:start position:0%
+second stage less sensitive to loads
+ 
+
+ align:start position:0%
+second stage less sensitive to loads
+applied to the amplifier anyway we
+
+ align:start position:0%
+applied to the amplifier anyway we
+ 
+
+ align:start position:0%
+applied to the amplifier anyway we
+assume that we can model the second
+
+ align:start position:0%
+assume that we can model the second
+ 
+
+ align:start position:0%
+assume that we can model the second
+stage as a dependent voltage source and
+
+ align:start position:0%
+stage as a dependent voltage source and
+ 
+
+ align:start position:0%
+stage as a dependent voltage source and
+we'll call the gain from the input to
+
+ align:start position:0%
+we'll call the gain from the input to
+ 
+
+ align:start position:0%
+we'll call the gain from the input to
+the second stage to the output of the
+
+ align:start position:0%
+the second stage to the output of the
+ 
+
+ align:start position:0%
+the second stage to the output of the
+second stage simply a subi so we model
+
+ align:start position:0%
+second stage simply a subi so we model
+ 
+
+ align:start position:0%
+second stage simply a subi so we model
+the second stage as an input admittance
+
+ align:start position:0%
+the second stage as an input admittance
+ 
+
+ align:start position:0%
+the second stage as an input admittance
+y subi and a dependent generator whose
+
+ align:start position:0%
+y subi and a dependent generator whose
+ 
+
+ align:start position:0%
+y subi and a dependent generator whose
+magnitude is AI times the voltage
+
+ align:start position:0%
+magnitude is AI times the voltage
+ 
+
+ align:start position:0%
+magnitude is AI times the voltage
+applied to the input of the second stage
+
+ align:start position:0%
+applied to the input of the second stage
+ 
+
+ align:start position:0%
+applied to the input of the second stage
+we then form a minor Loop by connecting
+
+ align:start position:0%
+we then form a minor Loop by connecting
+ 
+
+ align:start position:0%
+we then form a minor Loop by connecting
+a compensating network from the output
+
+ align:start position:0%
+a compensating network from the output
+ 
+
+ align:start position:0%
+a compensating network from the output
+to a two-port
+
+ align:start position:0%
+to a two-port
+ 
+
+ align:start position:0%
+to a two-port
+network and the second side of the
+
+ align:start position:0%
+network and the second side of the
+ 
+
+ align:start position:0%
+network and the second side of the
+two-port network or the second Port of
+
+ align:start position:0%
+two-port network or the second Port of
+ 
+
+ align:start position:0%
+two-port network or the second Port of
+the two-port network is connected back
+
+ align:start position:0%
+the two-port network is connected back
+ 
+
+ align:start position:0%
+the two-port network is connected back
+to the input of the second stage we'll
+
+ align:start position:0%
+to the input of the second stage we'll
+ 
+
+ align:start position:0%
+to the input of the second stage we'll
+find it convenient to represent present
+
+ align:start position:0%
+find it convenient to represent present
+ 
+
+ align:start position:0%
+find it convenient to represent present
+the two Port uh in terms of its
+
+ align:start position:0%
+the two Port uh in terms of its
+ 
+
+ align:start position:0%
+the two Port uh in terms of its
+shortcircuit transfer
+
+ align:start position:0%
+shortcircuit transfer
+ 
+
+ align:start position:0%
+shortcircuit transfer
+admittance at least as I've shown things
+
+ align:start position:0%
+admittance at least as I've shown things
+ 
+
+ align:start position:0%
+admittance at least as I've shown things
+where we apply the voltage from a
+
+ align:start position:0%
+where we apply the voltage from a
+ 
+
+ align:start position:0%
+where we apply the voltage from a
+voltage source to one side of the two
+
+ align:start position:0%
+voltage source to one side of the two
+ 
+
+ align:start position:0%
+voltage source to one side of the two
+Port we don't have to worry about
+
+ align:start position:0%
+Port we don't have to worry about
+ 
+
+ align:start position:0%
+Port we don't have to worry about
+parameters of the two port at this side
+
+ align:start position:0%
+parameters of the two port at this side
+ 
+
+ align:start position:0%
+parameters of the two port at this side
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+network uh they can't really affect
+
+ align:start position:0%
+network uh they can't really affect
+ 
+
+ align:start position:0%
+network uh they can't really affect
+operation if this model is valid since
+
+ align:start position:0%
+operation if this model is valid since
+ 
+
+ align:start position:0%
+operation if this model is valid since
+the input parameters on the two Port
+
+ align:start position:0%
+the input parameters on the two Port
+ 
+
+ align:start position:0%
+the input parameters on the two Port
+can't affect the voltage of of this
+
+ align:start position:0%
+can't affect the voltage of of this
+ 
+
+ align:start position:0%
+can't affect the voltage of of this
+Source uh however we do have to worry
+
+ align:start position:0%
+Source uh however we do have to worry
+ 
+
+ align:start position:0%
+Source uh however we do have to worry
+about modeling the two port at its
+
+ align:start position:0%
+about modeling the two port at its
+ 
+
+ align:start position:0%
+about modeling the two port at its
+output side and we'll do that in an
+
+ align:start position:0%
+output side and we'll do that in an
+ 
+
+ align:start position:0%
+output side and we'll do that in an
+admittance form where we show the two
+
+ align:start position:0%
+admittance form where we show the two
+ 
+
+ align:start position:0%
+admittance form where we show the two
+Port as a y sub a uh uh an output
+
+ align:start position:0%
+Port as a y sub a uh uh an output
+ 
+
+ align:start position:0%
+Port as a y sub a uh uh an output
+admittance at this port and a
+
+ align:start position:0%
+admittance at this port and a
+ 
+
+ align:start position:0%
+admittance at this port and a
+shortcircuit transfer admittance a
+
+ align:start position:0%
+shortcircuit transfer admittance a
+ 
+
+ align:start position:0%
+shortcircuit transfer admittance a
+dependent current Source uh which is
+
+ align:start position:0%
+dependent current Source uh which is
+ 
+
+ align:start position:0%
+dependent current Source uh which is
+dependent on the voltage applied to this
+
+ align:start position:0%
+dependent on the voltage applied to this
+ 
+
+ align:start position:0%
+dependent on the voltage applied to this
+side of the two Port so we can model our
+
+ align:start position:0%
+side of the two Port so we can model our
+ 
+
+ align:start position:0%
+side of the two Port so we can model our
+two port at this side as say is this
+
+ align:start position:0%
+two port at this side as say is this
+ 
+
+ align:start position:0%
+two port at this side as say is this
+admittance this dependent current source
+
+ align:start position:0%
+admittance this dependent current source
+ 
+
+ align:start position:0%
+admittance this dependent current source
+of course to evaluate the quantity y
+
+ align:start position:0%
+of course to evaluate the quantity y
+ 
+
+ align:start position:0%
+of course to evaluate the quantity y
+subc we'd perform an experiment where
+
+ align:start position:0%
+subc we'd perform an experiment where
+ 
+
+ align:start position:0%
+subc we'd perform an experiment where
+we'd incrementally short this port of
+
+ align:start position:0%
+we'd incrementally short this port of
+ 
+
+ align:start position:0%
+we'd incrementally short this port of
+the two port and would then measure the
+
+ align:start position:0%
+the two port and would then measure the
+ 
+
+ align:start position:0%
+the two port and would then measure the
+relationship between that shortcircuit
+
+ align:start position:0%
+relationship between that shortcircuit
+ 
+
+ align:start position:0%
+relationship between that shortcircuit
+current that we observed and the voltage
+
+ align:start position:0%
+current that we observed and the voltage
+ 
+
+ align:start position:0%
+current that we observed and the voltage
+V subn we' find that I Y subc was simply
+
+ align:start position:0%
+V subn we' find that I Y subc was simply
+ 
+
+ align:start position:0%
+V subn we' find that I Y subc was simply
+the ratio of the shortcircuit current to
+
+ align:start position:0%
+the ratio of the shortcircuit current to
+ 
+
+ align:start position:0%
+the ratio of the shortcircuit current to
+the voltage applied to this part of the
+
+ align:start position:0%
+the voltage applied to this part of the
+ 
+
+ align:start position:0%
+the voltage applied to this part of the
+network let me point out that my
+
+ align:start position:0%
+network let me point out that my
+ 
+
+ align:start position:0%
+network let me point out that my
+convention here is a little bit at
+
+ align:start position:0%
+convention here is a little bit at
+ 
+
+ align:start position:0%
+convention here is a little bit at
+variance with standard two-port
+
+ align:start position:0%
+variance with standard two-port
+ 
+
+ align:start position:0%
+variance with standard two-port
+convention and I've chosen to do that
+
+ align:start position:0%
+convention and I've chosen to do that
+ 
+
+ align:start position:0%
+convention and I've chosen to do that
+simply to save some minus signs in the
+
+ align:start position:0%
+simply to save some minus signs in the
+ 
+
+ align:start position:0%
+simply to save some minus signs in the
+development the usual convention defines
+
+ align:start position:0%
+development the usual convention defines
+ 
+
+ align:start position:0%
+development the usual convention defines
+currents in a two-port being into the
+
+ align:start position:0%
+currents in a two-port being into the
+ 
+
+ align:start position:0%
+currents in a two-port being into the
+network uh the way I've defined my
+
+ align:start position:0%
+network uh the way I've defined my
+ 
+
+ align:start position:0%
+network uh the way I've defined my
+shortcircuit transfer admittance is
+
+ align:start position:0%
+shortcircuit transfer admittance is
+ 
+
+ align:start position:0%
+shortcircuit transfer admittance is
+considering the current out of the the
+
+ align:start position:0%
+considering the current out of the the
+ 
+
+ align:start position:0%
+considering the current out of the the
+network and say my reason for doing that
+
+ align:start position:0%
+network and say my reason for doing that
+ 
+
+ align:start position:0%
+network and say my reason for doing that
+is is just that it saves some minus
+
+ align:start position:0%
+is is just that it saves some minus
+ 
+
+ align:start position:0%
+is is just that it saves some minus
+signs in the development and hopefully
+
+ align:start position:0%
+signs in the development and hopefully
+ 
+
+ align:start position:0%
+signs in the development and hopefully
+some confusion I've I've always found
+
+ align:start position:0%
+some confusion I've I've always found
+ 
+
+ align:start position:0%
+some confusion I've I've always found
+that that I work a little bit better
+
+ align:start position:0%
+that that I work a little bit better
+ 
+
+ align:start position:0%
+that that I work a little bit better
+with fewer minus sign so that's the
+
+ align:start position:0%
+with fewer minus sign so that's the
+ 
+
+ align:start position:0%
+with fewer minus sign so that's the
+reason for violating standard
+
+ align:start position:0%
+reason for violating standard
+ 
+
+ align:start position:0%
+reason for violating standard
+conventions in in this
+
+ align:start position:0%
+conventions in in this
+ 
+
+ align:start position:0%
+conventions in in this
+development the effect of the first
+
+ align:start position:0%
+development the effect of the first
+ 
+
+ align:start position:0%
+development the effect of the first
+stage on incremental signals is simply
+
+ align:start position:0%
+stage on incremental signals is simply
+ 
+
+ align:start position:0%
+stage on incremental signals is simply
+to inject or remove a current from this
+
+ align:start position:0%
+to inject or remove a current from this
+ 
+
+ align:start position:0%
+to inject or remove a current from this
+sde that's proportional to an applied
+
+ align:start position:0%
+sde that's proportional to an applied
+ 
+
+ align:start position:0%
+sde that's proportional to an applied
+input voltage if the input transistors
+
+ align:start position:0%
+input voltage if the input transistors
+ 
+
+ align:start position:0%
+input voltage if the input transistors
+are perfectly matched under quient
+
+ align:start position:0%
+are perfectly matched under quient
+ 
+
+ align:start position:0%
+are perfectly matched under quient
+conditions The Collector current of this
+
+ align:start position:0%
+conditions The Collector current of this
+ 
+
+ align:start position:0%
+conditions The Collector current of this
+transistor is identically equal to the
+
+ align:start position:0%
+transistor is identically equal to the
+ 
+
+ align:start position:0%
+transistor is identically equal to the
+current ass assciated with this current
+
+ align:start position:0%
+current ass assciated with this current
+ 
+
+ align:start position:0%
+current ass assciated with this current
+Source if we then apply an incremental
+
+ align:start position:0%
+Source if we then apply an incremental
+ 
+
+ align:start position:0%
+Source if we then apply an incremental
+input voltage about the quient operating
+
+ align:start position:0%
+input voltage about the quient operating
+ 
+
+ align:start position:0%
+input voltage about the quient operating
+point of Z Volts for the input voltage
+
+ align:start position:0%
+point of Z Volts for the input voltage
+ 
+
+ align:start position:0%
+point of Z Volts for the input voltage
+that voltage effectively divides equally
+
+ align:start position:0%
+that voltage effectively divides equally
+ 
+
+ align:start position:0%
+that voltage effectively divides equally
+between the two input transistors
+
+ align:start position:0%
+between the two input transistors
+ 
+
+ align:start position:0%
+between the two input transistors
+consequently we get an incremental
+
+ align:start position:0%
+consequently we get an incremental
+ 
+
+ align:start position:0%
+consequently we get an incremental
+change in The Collector current of this
+
+ align:start position:0%
+change in The Collector current of this
+ 
+
+ align:start position:0%
+change in The Collector current of this
+transistor that's one/ half of the input
+
+ align:start position:0%
+transistor that's one/ half of the input
+ 
+
+ align:start position:0%
+transistor that's one/ half of the input
+voltage the amount of voltage that's
+
+ align:start position:0%
+voltage the amount of voltage that's
+ 
+
+ align:start position:0%
+voltage the amount of voltage that's
+applied to the base toit Junction of
+
+ align:start position:0%
+applied to the base toit Junction of
+ 
+
+ align:start position:0%
+applied to the base toit Junction of
+this transistor being 1/2 of the input
+
+ align:start position:0%
+this transistor being 1/2 of the input
+ 
+
+ align:start position:0%
+this transistor being 1/2 of the input
+voltage because of the symmetry of the
+
+ align:start position:0%
+voltage because of the symmetry of the
+ 
+
+ align:start position:0%
+voltage because of the symmetry of the
+circuit times the trans conductance of
+
+ align:start position:0%
+circuit times the trans conductance of
+ 
+
+ align:start position:0%
+circuit times the trans conductance of
+this transistor we assume that the trans
+
+ align:start position:0%
+this transistor we assume that the trans
+ 
+
+ align:start position:0%
+this transistor we assume that the trans
+conductances of the two input
+
+ align:start position:0%
+conductances of the two input
+ 
+
+ align:start position:0%
+conductances of the two input
+transistors are equal so the effect of
+
+ align:start position:0%
+transistors are equal so the effect of
+ 
+
+ align:start position:0%
+transistors are equal so the effect of
+the first stage is to Simply cause an
+
+ align:start position:0%
+the first stage is to Simply cause an
+ 
+
+ align:start position:0%
+the first stage is to Simply cause an
+incremental current at this node and the
+
+ align:start position:0%
+incremental current at this node and the
+ 
+
+ align:start position:0%
+incremental current at this node and the
+constant proportionality between that
+
+ align:start position:0%
+constant proportionality between that
+ 
+
+ align:start position:0%
+constant proportionality between that
+incremental current and the input
+
+ align:start position:0%
+incremental current and the input
+ 
+
+ align:start position:0%
+incremental current and the input
+voltage is simply GM /
+
+ align:start position:0%
+voltage is simply GM /
+ 
+
+ align:start position:0%
+voltage is simply GM /
+two we're then able to model the overall
+
+ align:start position:0%
+two we're then able to model the overall
+ 
+
+ align:start position:0%
+two we're then able to model the overall
+system as follows we can replace the
+
+ align:start position:0%
+system as follows we can replace the
+ 
+
+ align:start position:0%
+system as follows we can replace the
+differential Pair by a dependent current
+
+ align:start position:0%
+differential Pair by a dependent current
+ 
+
+ align:start position:0%
+differential Pair by a dependent current
+Source whose magnitude is gmvi / 2 so
+
+ align:start position:0%
+Source whose magnitude is gmvi / 2 so
+ 
+
+ align:start position:0%
+Source whose magnitude is gmvi / 2 so
+that's dependent current Source reflects
+
+ align:start position:0%
+that's dependent current Source reflects
+ 
+
+ align:start position:0%
+that's dependent current Source reflects
+the transmission from the input voltage
+
+ align:start position:0%
+the transmission from the input voltage
+ 
+
+ align:start position:0%
+the transmission from the input voltage
+to this current we
+
+ align:start position:0%
+to this current we
+ 
+
+ align:start position:0%
+to this current we
+combine these two admittances to get an
+
+ align:start position:0%
+combine these two admittances to get an
+ 
+
+ align:start position:0%
+combine these two admittances to get an
+admittance that's Yi + ya a uh the
+
+ align:start position:0%
+admittance that's Yi + ya a uh the
+ 
+
+ align:start position:0%
+admittance that's Yi + ya a uh the
+voltage across that admittance is VA and
+
+ align:start position:0%
+voltage across that admittance is VA and
+ 
+
+ align:start position:0%
+voltage across that admittance is VA and
+the output voltage as it was above is
+
+ align:start position:0%
+the output voltage as it was above is
+ 
+
+ align:start position:0%
+the output voltage as it was above is
+simply AI times that voltage V Suba we
+
+ align:start position:0%
+simply AI times that voltage V Suba we
+ 
+
+ align:start position:0%
+simply AI times that voltage V Suba we
+complete the minor Loop or model the
+
+ align:start position:0%
+complete the minor Loop or model the
+ 
+
+ align:start position:0%
+complete the minor Loop or model the
+effect of
+
+ align:start position:0%
+effect of
+ 
+
+ align:start position:0%
+effect of
+the two-port network as far as its
+
+ align:start position:0%
+the two-port network as far as its
+ 
+
+ align:start position:0%
+the two-port network as far as its
+feedback effect simply as a dependent
+
+ align:start position:0%
+feedback effect simply as a dependent
+ 
+
+ align:start position:0%
+feedback effect simply as a dependent
+generator whose magnitude is y subc
+
+ align:start position:0%
+generator whose magnitude is y subc
+ 
+
+ align:start position:0%
+generator whose magnitude is y subc
+times now vo recognizing that v o and VM
+
+ align:start position:0%
+times now vo recognizing that v o and VM
+ 
+
+ align:start position:0%
+times now vo recognizing that v o and VM
+are identical and so we represent the
+
+ align:start position:0%
+are identical and so we represent the
+ 
+
+ align:start position:0%
+are identical and so we represent the
+dependent generator associated with the
+
+ align:start position:0%
+dependent generator associated with the
+ 
+
+ align:start position:0%
+dependent generator associated with the
+two port in this way we've already taken
+
+ align:start position:0%
+two port in this way we've already taken
+ 
+
+ align:start position:0%
+two port in this way we've already taken
+care of the output admittance of the two
+
+ align:start position:0%
+care of the output admittance of the two
+ 
+
+ align:start position:0%
+care of the output admittance of the two
+ports since we've lumped it into this
+
+ align:start position:0%
+ports since we've lumped it into this
+ 
+
+ align:start position:0%
+ports since we've lumped it into this
+admittance we can then use this
+
+ align:start position:0%
+admittance we can then use this
+ 
+
+ align:start position:0%
+admittance we can then use this
+representation to determine what becomes
+
+ align:start position:0%
+representation to determine what becomes
+ 
+
+ align:start position:0%
+representation to determine what becomes
+the open loop transfer function of the
+
+ align:start position:0%
+the open loop transfer function of the
+ 
+
+ align:start position:0%
+the open loop transfer function of the
+operational amplifier we of course have
+
+ align:start position:0%
+operational amplifier we of course have
+ 
+
+ align:start position:0%
+operational amplifier we of course have
+considered the operational amplifier
+
+ align:start position:0%
+considered the operational amplifier
+ 
+
+ align:start position:0%
+considered the operational amplifier
+from an input applied to the
+
+ align:start position:0%
+from an input applied to the
+ 
+
+ align:start position:0%
+from an input applied to the
+differential input stage to the output
+
+ align:start position:0%
+differential input stage to the output
+ 
+
+ align:start position:0%
+differential input stage to the output
+of the amplifier so this is what we
+
+ align:start position:0%
+of the amplifier so this is what we
+ 
+
+ align:start position:0%
+of the amplifier so this is what we
+commonly consider the open loop transfer
+
+ align:start position:0%
+commonly consider the open loop transfer
+ 
+
+ align:start position:0%
+commonly consider the open loop transfer
+function of the operational
+
+ align:start position:0%
+function of the operational
+ 
+
+ align:start position:0%
+function of the operational
+amplifier we can most easily uh
+
+ align:start position:0%
+amplifier we can most easily uh
+ 
+
+ align:start position:0%
+amplifier we can most easily uh
+determine that quantity
+
+ align:start position:0%
+determine that quantity
+ 
+
+ align:start position:0%
+determine that quantity
+uh by first writing a node equation at
+
+ align:start position:0%
+uh by first writing a node equation at
+ 
+
+ align:start position:0%
+uh by first writing a node equation at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+node and that's the equation shown here
+
+ align:start position:0%
+node and that's the equation shown here
+ 
+
+ align:start position:0%
+node and that's the equation shown here
+uh we have a current coming out of the
+
+ align:start position:0%
+uh we have a current coming out of the
+ 
+
+ align:start position:0%
+uh we have a current coming out of the
+node that's GM VI over two if we we can
+
+ align:start position:0%
+node that's GM VI over two if we we can
+ 
+
+ align:start position:0%
+node that's GM VI over two if we we can
+move that over to the left we get a
+
+ align:start position:0%
+move that over to the left we get a
+ 
+
+ align:start position:0%
+move that over to the left we get a
+minus gmvi over two on the left side of
+
+ align:start position:0%
+minus gmvi over two on the left side of
+ 
+
+ align:start position:0%
+minus gmvi over two on the left side of
+the equation uh there's a current going
+
+ align:start position:0%
+the equation uh there's a current going
+ 
+
+ align:start position:0%
+the equation uh there's a current going
+uh out of the node in question through
+
+ align:start position:0%
+uh out of the node in question through
+ 
+
+ align:start position:0%
+uh out of the node in question through
+the combined admittance Yi + ya a the
+
+ align:start position:0%
+the combined admittance Yi + ya a the
+ 
+
+ align:start position:0%
+the combined admittance Yi + ya a the
+voltage across that admittance is VA so
+
+ align:start position:0%
+voltage across that admittance is VA so
+ 
+
+ align:start position:0%
+voltage across that admittance is VA so
+we get a current through that combined
+
+ align:start position:0%
+we get a current through that combined
+ 
+
+ align:start position:0%
+we get a current through that combined
+admittance that's simply VA *
+
+ align:start position:0%
+admittance that's simply VA *
+ 
+
+ align:start position:0%
+admittance that's simply VA *
+yi+ ya a and we get a current into the
+
+ align:start position:0%
+yi+ ya a and we get a current into the
+ 
+
+ align:start position:0%
+yi+ ya a and we get a current into the
+node that's YC * V that represents the
+
+ align:start position:0%
+node that's YC * V that represents the
+ 
+
+ align:start position:0%
+node that's YC * V that represents the
+shortcircuit transfer admittance of our
+
+ align:start position:0%
+shortcircuit transfer admittance of our
+ 
+
+ align:start position:0%
+shortcircuit transfer admittance of our
+compensating two Port uh the second
+
+ align:start position:0%
+compensating two Port uh the second
+ 
+
+ align:start position:0%
+compensating two Port uh the second
+equation uh reflects the fact that V out
+
+ align:start position:0%
+equation uh reflects the fact that V out
+ 
+
+ align:start position:0%
+equation uh reflects the fact that V out
+is simply minus AI time VA the
+
+ align:start position:0%
+is simply minus AI time VA the
+ 
+
+ align:start position:0%
+is simply minus AI time VA the
+relationship for the dependent generator
+
+ align:start position:0%
+relationship for the dependent generator
+ 
+
+ align:start position:0%
+relationship for the dependent generator
+in the second stage rearranging terms we
+
+ align:start position:0%
+in the second stage rearranging terms we
+ 
+
+ align:start position:0%
+in the second stage rearranging terms we
+get 0 equal AI VA plus
+
+ align:start position:0%
+get 0 equal AI VA plus
+ 
+
+ align:start position:0%
+get 0 equal AI VA plus
+v and when we solve this set of
+
+ align:start position:0%
+v and when we solve this set of
+ 
+
+ align:start position:0%
+v and when we solve this set of
+equations for the output or input to
+
+ align:start position:0%
+equations for the output or input to
+ 
+
+ align:start position:0%
+equations for the output or input to
+Output transfer function we obtain GM
+
+ align:start position:0%
+Output transfer function we obtain GM
+ 
+
+ align:start position:0%
+Output transfer function we obtain GM
+over2 uh times AI over Yi + y a over 1 +
+
+ align:start position:0%
+over2 uh times AI over Yi + y a over 1 +
+ 
+
+ align:start position:0%
+over2 uh times AI over Yi + y a over 1 +
+AI y c over Yi + ya
+
+ align:start position:0%
+AI y c over Yi + ya
+ 
+
+ align:start position:0%
+AI y c over Yi + ya
+a there's a very nice physical
+
+ align:start position:0%
+a there's a very nice physical
+ 
+
+ align:start position:0%
+a there's a very nice physical
+significance associated with the terms
+
+ align:start position:0%
+significance associated with the terms
+ 
+
+ align:start position:0%
+significance associated with the terms
+in that final equation in particular
+
+ align:start position:0%
+in that final equation in particular
+ 
+
+ align:start position:0%
+in that final equation in particular
+let's consider the
+
+ align:start position:0%
+let's consider the
+ 
+
+ align:start position:0%
+let's consider the
+numerator here we have gm/ 2 * AI over
+
+ align:start position:0%
+numerator here we have gm/ 2 * AI over
+ 
+
+ align:start position:0%
+numerator here we have gm/ 2 * AI over
+Yi + ya
+
+ align:start position:0%
+Yi + ya
+ 
+
+ align:start position:0%
+Yi + ya
+a what's
+
+ align:start position:0%
+a what's
+ 
+
+ align:start position:0%
+a what's
+that well consider what would happen if
+
+ align:start position:0%
+that well consider what would happen if
+ 
+
+ align:start position:0%
+that well consider what would happen if
+we disabled the feedback network if we
+
+ align:start position:0%
+we disabled the feedback network if we
+ 
+
+ align:start position:0%
+we disabled the feedback network if we
+made YC equal to
+
+ align:start position:0%
+made YC equal to
+ 
+
+ align:start position:0%
+made YC equal to
+zero uh possibly by
+
+ align:start position:0%
+zero uh possibly by
+ 
+
+ align:start position:0%
+zero uh possibly by
+disconnecting
+
+ align:start position:0%
+disconnecting
+ 
+
+ align:start position:0%
+disconnecting
+uh the input Port of the compensating
+
+ align:start position:0%
+uh the input Port of the compensating
+ 
+
+ align:start position:0%
+uh the input Port of the compensating
+network from V out and simply shorting
+
+ align:start position:0%
+network from V out and simply shorting
+ 
+
+ align:start position:0%
+network from V out and simply shorting
+it that would of course disable this
+
+ align:start position:0%
+it that would of course disable this
+ 
+
+ align:start position:0%
+it that would of course disable this
+generator since VM would then be zero uh
+
+ align:start position:0%
+generator since VM would then be zero uh
+ 
+
+ align:start position:0%
+generator since VM would then be zero uh
+however we would keep the loading
+
+ align:start position:0%
+however we would keep the loading
+ 
+
+ align:start position:0%
+however we would keep the loading
+associated with the two-port network uh
+
+ align:start position:0%
+associated with the two-port network uh
+ 
+
+ align:start position:0%
+associated with the two-port network uh
+we lump that admittance y Suba with Y
+
+ align:start position:0%
+we lump that admittance y Suba with Y
+ 
+
+ align:start position:0%
+we lump that admittance y Suba with Y
+subi to say all we've done really is
+
+ align:start position:0%
+subi to say all we've done really is
+ 
+
+ align:start position:0%
+subi to say all we've done really is
+make YC uh or the magnitude of this
+
+ align:start position:0%
+make YC uh or the magnitude of this
+ 
+
+ align:start position:0%
+make YC uh or the magnitude of this
+generator equal to zero and then
+
+ align:start position:0%
+generator equal to zero and then
+ 
+
+ align:start position:0%
+generator equal to zero and then
+calculate the gain that results in the
+
+ align:start position:0%
+calculate the gain that results in the
+ 
+
+ align:start position:0%
+calculate the gain that results in the
+absence of minor Loop feedback disabling
+
+ align:start position:0%
+absence of minor Loop feedback disabling
+ 
+
+ align:start position:0%
+absence of minor Loop feedback disabling
+this generator effectively makes F in
+
+ align:start position:0%
+this generator effectively makes F in
+ 
+
+ align:start position:0%
+this generator effectively makes F in
+the minor Loop zero well the gain would
+
+ align:start position:0%
+the minor Loop zero well the gain would
+ 
+
+ align:start position:0%
+the minor Loop zero well the gain would
+simply be gm/ 2 that gets us to a
+
+ align:start position:0%
+simply be gm/ 2 that gets us to a
+ 
+
+ align:start position:0%
+simply be gm/ 2 that gets us to a
+current times Yi + ya a I'm sorry
+
+ align:start position:0%
+current times Yi + ya a I'm sorry
+ 
+
+ align:start position:0%
+current times Yi + ya a I'm sorry
+divided by Yi + ya a that gets us the
+
+ align:start position:0%
+divided by Yi + ya a that gets us the
+ 
+
+ align:start position:0%
+divided by Yi + ya a that gets us the
+voltage at this point we multiply that
+
+ align:start position:0%
+voltage at this point we multiply that
+ 
+
+ align:start position:0%
+voltage at this point we multiply that
+voltage by a sub I to get the overall
+
+ align:start position:0%
+voltage by a sub I to get the overall
+ 
+
+ align:start position:0%
+voltage by a sub I to get the overall
+output voltage so the physical
+
+ align:start position:0%
+output voltage so the physical
+ 
+
+ align:start position:0%
+output voltage so the physical
+significance of the quantity gm/ 2 * AI
+
+ align:start position:0%
+significance of the quantity gm/ 2 * AI
+ 
+
+ align:start position:0%
+significance of the quantity gm/ 2 * AI
+over Yi plus ya a is that it's the open
+
+ align:start position:0%
+over Yi plus ya a is that it's the open
+ 
+
+ align:start position:0%
+over Yi plus ya a is that it's the open
+loop voltage gain of the operational
+
+ align:start position:0%
+loop voltage gain of the operational
+ 
+
+ align:start position:0%
+loop voltage gain of the operational
+amplifier with the minor Loop disabled
+
+ align:start position:0%
+amplifier with the minor Loop disabled
+ 
+
+ align:start position:0%
+amplifier with the minor Loop disabled
+but considering the loading that the
+
+ align:start position:0%
+but considering the loading that the
+ 
+
+ align:start position:0%
+but considering the loading that the
+output side of the two-port compensating
+
+ align:start position:0%
+output side of the two-port compensating
+ 
+
+ align:start position:0%
+output side of the two-port compensating
+Network applies to the second stage we
+
+ align:start position:0%
+Network applies to the second stage we
+ 
+
+ align:start position:0%
+Network applies to the second stage we
+see that because the quantity y Suba
+
+ align:start position:0%
+see that because the quantity y Suba
+ 
+
+ align:start position:0%
+see that because the quantity y Suba
+appears in the expression the
+
+ align:start position:0%
+appears in the expression the
+ 
+
+ align:start position:0%
+appears in the expression the
+denominator has a very familiar looking
+
+ align:start position:0%
+denominator has a very familiar looking
+ 
+
+ align:start position:0%
+denominator has a very familiar looking
+feedback Form 1 plus something it'd be
+
+ align:start position:0%
+feedback Form 1 plus something it'd be
+ 
+
+ align:start position:0%
+feedback Form 1 plus something it'd be
+very reassuring if that's something were
+
+ align:start position:0%
+very reassuring if that's something were
+ 
+
+ align:start position:0%
+very reassuring if that's something were
+minus the loop transmission so let's
+
+ align:start position:0%
+minus the loop transmission so let's
+ 
+
+ align:start position:0%
+minus the loop transmission so let's
+consider the quantity a subi times y c
+
+ align:start position:0%
+consider the quantity a subi times y c
+ 
+
+ align:start position:0%
+consider the quantity a subi times y c
+over Yi + ya a well as we suspected
+
+ align:start position:0%
+over Yi + ya a well as we suspected
+ 
+
+ align:start position:0%
+over Yi + ya a well as we suspected
+that's precisely the negative of a loop
+
+ align:start position:0%
+that's precisely the negative of a loop
+ 
+
+ align:start position:0%
+that's precisely the negative of a loop
+transmission and in particular it's the
+
+ align:start position:0%
+transmission and in particular it's the
+ 
+
+ align:start position:0%
+transmission and in particular it's the
+transmission around the minor Loop uh
+
+ align:start position:0%
+transmission around the minor Loop uh
+ 
+
+ align:start position:0%
+transmission around the minor Loop uh
+let's consider the minor Loop Loop if we
+
+ align:start position:0%
+let's consider the minor Loop Loop if we
+ 
+
+ align:start position:0%
+let's consider the minor Loop Loop if we
+forget about a driving input to the
+
+ align:start position:0%
+forget about a driving input to the
+ 
+
+ align:start position:0%
+forget about a driving input to the
+overall system here uh around the minor
+
+ align:start position:0%
+overall system here uh around the minor
+ 
+
+ align:start position:0%
+overall system here uh around the minor
+Loop we get a product y Sub C divided by
+
+ align:start position:0%
+Loop we get a product y Sub C divided by
+ 
+
+ align:start position:0%
+Loop we get a product y Sub C divided by
+this admittance to get us a voltage here
+
+ align:start position:0%
+this admittance to get us a voltage here
+ 
+
+ align:start position:0%
+this admittance to get us a voltage here
+so we get a y c over Yi + y a we
+
+ align:start position:0%
+so we get a y c over Yi + y a we
+ 
+
+ align:start position:0%
+so we get a y c over Yi + y a we
+multiply that by a sub I and if we keep
+
+ align:start position:0%
+multiply that by a sub I and if we keep
+ 
+
+ align:start position:0%
+multiply that by a sub I and if we keep
+track of things there's a minus sign
+
+ align:start position:0%
+track of things there's a minus sign
+ 
+
+ align:start position:0%
+track of things there's a minus sign
+associated with that Loop
+
+ align:start position:0%
+associated with that Loop
+ 
+
+ align:start position:0%
+associated with that Loop
+transmission so the quantity y c over Yi
+
+ align:start position:0%
+transmission so the quantity y c over Yi
+ 
+
+ align:start position:0%
+transmission so the quantity y c over Yi
++ ya a all multiplied by AI is the
+
+ align:start position:0%
++ ya a all multiplied by AI is the
+ 
+
+ align:start position:0%
++ ya a all multiplied by AI is the
+negative of the transmission around the
+
+ align:start position:0%
+negative of the transmission around the
+ 
+
+ align:start position:0%
+negative of the transmission around the
+minor
+
+ align:start position:0%
+minor
+ 
+
+ align:start position:0%
+minor
+Loop so we have the numerator of this
+
+ align:start position:0%
+Loop so we have the numerator of this
+ 
+
+ align:start position:0%
+Loop so we have the numerator of this
+expression being the gain the amplifier
+
+ align:start position:0%
+expression being the gain the amplifier
+ 
+
+ align:start position:0%
+expression being the gain the amplifier
+would have if the monitor Loop were
+
+ align:start position:0%
+would have if the monitor Loop were
+ 
+
+ align:start position:0%
+would have if the monitor Loop were
+disabled but its loading were considered
+
+ align:start position:0%
+disabled but its loading were considered
+ 
+
+ align:start position:0%
+disabled but its loading were considered
+the denominator of of this expression is
+
+ align:start position:0%
+the denominator of of this expression is
+ 
+
+ align:start position:0%
+the denominator of of this expression is
+one minus the loop transmission of the
+
+ align:start position:0%
+one minus the loop transmission of the
+ 
+
+ align:start position:0%
+one minus the loop transmission of the
+minor
+
+ align:start position:0%
+minor
+ 
+
+ align:start position:0%
+minor
+Loop and again there's the familiar
+
+ align:start position:0%
+Loop and again there's the familiar
+ 
+
+ align:start position:0%
+Loop and again there's the familiar
+limiting cases this goes right back to
+
+ align:start position:0%
+limiting cases this goes right back to
+ 
+
+ align:start position:0%
+limiting cases this goes right back to
+what we did earlier in our general
+
+ align:start position:0%
+what we did earlier in our general
+ 
+
+ align:start position:0%
+what we did earlier in our general
+discussion of feedback compensation
+
+ align:start position:0%
+discussion of feedback compensation
+ 
+
+ align:start position:0%
+discussion of feedback compensation
+let's consider the quantity V out over
+
+ align:start position:0%
+let's consider the quantity V out over
+ 
+
+ align:start position:0%
+let's consider the quantity V out over
+VI the open loop transfer function of
+
+ align:start position:0%
+VI the open loop transfer function of
+ 
+
+ align:start position:0%
+VI the open loop transfer function of
+the amplifier for those two limiting
+
+ align:start position:0%
+the amplifier for those two limiting
+ 
+
+ align:start position:0%
+the amplifier for those two limiting
+cases well if the transmission around
+
+ align:start position:0%
+cases well if the transmission around
+ 
+
+ align:start position:0%
+cases well if the transmission around
+the minor Loop the magnitude of the
+
+ align:start position:0%
+the minor Loop the magnitude of the
+ 
+
+ align:start position:0%
+the minor Loop the magnitude of the
+transmission around the minor Loop the
+
+ align:start position:0%
+transmission around the minor Loop the
+ 
+
+ align:start position:0%
+transmission around the minor Loop the
+AI YC over Yi + ya a product is much
+
+ align:start position:0%
+AI YC over Yi + ya a product is much
+ 
+
+ align:start position:0%
+AI YC over Yi + ya a product is much
+larger than one in other words if this
+
+ align:start position:0%
+larger than one in other words if this
+ 
+
+ align:start position:0%
+larger than one in other words if this
+term is Big compared to one in the
+
+ align:start position:0%
+term is Big compared to one in the
+ 
+
+ align:start position:0%
+term is Big compared to one in the
+denominator we can ignore the one the
+
+ align:start position:0%
+denominator we can ignore the one the
+ 
+
+ align:start position:0%
+denominator we can ignore the one the
+AIS cancel out the Yi plus y a cancel
+
+ align:start position:0%
+AIS cancel out the Yi plus y a cancel
+ 
+
+ align:start position:0%
+AIS cancel out the Yi plus y a cancel
+out and under those conditions the open
+
+ align:start position:0%
+out and under those conditions the open
+ 
+
+ align:start position:0%
+out and under those conditions the open
+loop transfer function of the of the
+
+ align:start position:0%
+loop transfer function of the of the
+ 
+
+ align:start position:0%
+loop transfer function of the of the
+amplifier is simply GM / 2 * y Sub
+
+ align:start position:0%
+amplifier is simply GM / 2 * y Sub
+ 
+
+ align:start position:0%
+amplifier is simply GM / 2 * y Sub
+C uh in the other limiting case where
+
+ align:start position:0%
+C uh in the other limiting case where
+ 
+
+ align:start position:0%
+C uh in the other limiting case where
+the transmission around the minor Loop
+
+ align:start position:0%
+the transmission around the minor Loop
+ 
+
+ align:start position:0%
+the transmission around the minor Loop
+is small compared to one or the
+
+ align:start position:0%
+is small compared to one or the
+ 
+
+ align:start position:0%
+is small compared to one or the
+magnitude of the transmission around the
+
+ align:start position:0%
+magnitude of the transmission around the
+ 
+
+ align:start position:0%
+magnitude of the transmission around the
+minor Loop is small compared to one uh
+
+ align:start position:0%
+minor Loop is small compared to one uh
+ 
+
+ align:start position:0%
+minor Loop is small compared to one uh
+we find out that the input to Output
+
+ align:start position:0%
+we find out that the input to Output
+ 
+
+ align:start position:0%
+we find out that the input to Output
+transfer function for the amplifier it's
+
+ align:start position:0%
+transfer function for the amplifier it's
+ 
+
+ align:start position:0%
+transfer function for the amplifier it's
+open loop Loop transfer function uh is
+
+ align:start position:0%
+open loop Loop transfer function uh is
+ 
+
+ align:start position:0%
+open loop Loop transfer function uh is
+simply that that would result uh with
+
+ align:start position:0%
+simply that that would result uh with
+ 
+
+ align:start position:0%
+simply that that would result uh with
+the minor Loop disabled that's the
+
+ align:start position:0%
+the minor Loop disabled that's the
+ 
+
+ align:start position:0%
+the minor Loop disabled that's the
+effect of of having the transmission
+
+ align:start position:0%
+effect of of having the transmission
+ 
+
+ align:start position:0%
+effect of of having the transmission
+around the minor Loop small uh and in
+
+ align:start position:0%
+around the minor Loop small uh and in
+ 
+
+ align:start position:0%
+around the minor Loop small uh and in
+that case we get GM over2 times AI over
+
+ align:start position:0%
+that case we get GM over2 times AI over
+ 
+
+ align:start position:0%
+that case we get GM over2 times AI over
+Yi plus
+
+ align:start position:0%
+Yi plus
+ 
+
+ align:start position:0%
+Yi plus
+ya well exactly as we did in our general
+
+ align:start position:0%
+ya well exactly as we did in our general
+ 
+
+ align:start position:0%
+ya well exactly as we did in our general
+discussion of minor Loop compensation a
+
+ align:start position:0%
+discussion of minor Loop compensation a
+ 
+
+ align:start position:0%
+discussion of minor Loop compensation a
+very convenient way to to look at this
+
+ align:start position:0%
+very convenient way to to look at this
+ 
+
+ align:start position:0%
+very convenient way to to look at this
+and a very nice way to do design is to
+
+ align:start position:0%
+and a very nice way to do design is to
+ 
+
+ align:start position:0%
+and a very nice way to do design is to
+draw these two quantities
+
+ align:start position:0%
+draw these two quantities
+ 
+
+ align:start position:0%
+draw these two quantities
+we draw G subm over 2 y Sub C which is
+
+ align:start position:0%
+we draw G subm over 2 y Sub C which is
+ 
+
+ align:start position:0%
+we draw G subm over 2 y Sub C which is
+the approximation that we would use when
+
+ align:start position:0%
+the approximation that we would use when
+ 
+
+ align:start position:0%
+the approximation that we would use when
+the transmission around the minor Loop
+
+ align:start position:0%
+the transmission around the minor Loop
+ 
+
+ align:start position:0%
+the transmission around the minor Loop
+has a magnitude large compared to
+
+ align:start position:0%
+has a magnitude large compared to
+ 
+
+ align:start position:0%
+has a magnitude large compared to
+one and we similarly draw the open loop
+
+ align:start position:0%
+one and we similarly draw the open loop
+ 
+
+ align:start position:0%
+one and we similarly draw the open loop
+gain of the amplifier in the absence of
+
+ align:start position:0%
+gain of the amplifier in the absence of
+ 
+
+ align:start position:0%
+gain of the amplifier in the absence of
+minor Loop feedback but considering the
+
+ align:start position:0%
+minor Loop feedback but considering the
+ 
+
+ align:start position:0%
+minor Loop feedback but considering the
+loading associated with the two-port
+
+ align:start position:0%
+loading associated with the two-port
+ 
+
+ align:start position:0%
+loading associated with the two-port
+feedback Network that quantity is of
+
+ align:start position:0%
+feedback Network that quantity is of
+ 
+
+ align:start position:0%
+feedback Network that quantity is of
+course G sub M AI over 2 Yi + y a we
+
+ align:start position:0%
+course G sub M AI over 2 Yi + y a we
+ 
+
+ align:start position:0%
+course G sub M AI over 2 Yi + y a we
+draw those two quantities on our usual B
+
+ align:start position:0%
+draw those two quantities on our usual B
+ 
+
+ align:start position:0%
+draw those two quantities on our usual B
+plot
+
+ align:start position:0%
+plot
+ 
+
+ align:start position:0%
+plot
+coordinates and we look for the the two
+
+ align:start position:0%
+coordinates and we look for the the two
+ 
+
+ align:start position:0%
+coordinates and we look for the the two
+look to see which curve is is greater in
+
+ align:start position:0%
+look to see which curve is is greater in
+ 
+
+ align:start position:0%
+look to see which curve is is greater in
+magnitude uh if in fact for example this
+
+ align:start position:0%
+magnitude uh if in fact for example this
+ 
+
+ align:start position:0%
+magnitude uh if in fact for example this
+quantity the open loop transfer function
+
+ align:start position:0%
+quantity the open loop transfer function
+ 
+
+ align:start position:0%
+quantity the open loop transfer function
+of the amplifier and the absence of
+
+ align:start position:0%
+of the amplifier and the absence of
+ 
+
+ align:start position:0%
+of the amplifier and the absence of
+minor Loop feedback is greater than this
+
+ align:start position:0%
+minor Loop feedback is greater than this
+ 
+
+ align:start position:0%
+minor Loop feedback is greater than this
+quantity uh the Imp ation which we can
+
+ align:start position:0%
+quantity uh the Imp ation which we can
+ 
+
+ align:start position:0%
+quantity uh the Imp ation which we can
+get by by
+
+ align:start position:0%
+get by by
+ 
+
+ align:start position:0%
+get by by
+simply multiplying both sides of this
+
+ align:start position:0%
+simply multiplying both sides of this
+ 
+
+ align:start position:0%
+simply multiplying both sides of this
+equation by the reciprocal of this term
+
+ align:start position:0%
+equation by the reciprocal of this term
+ 
+
+ align:start position:0%
+equation by the reciprocal of this term
+is that the magnitude of the
+
+ align:start position:0%
+is that the magnitude of the
+ 
+
+ align:start position:0%
+is that the magnitude of the
+transmission around the minor Loop is
+
+ align:start position:0%
+transmission around the minor Loop is
+ 
+
+ align:start position:0%
+transmission around the minor Loop is
+large compared to one if that's true our
+
+ align:start position:0%
+large compared to one if that's true our
+ 
+
+ align:start position:0%
+large compared to one if that's true our
+earlier approximation tells us that we
+
+ align:start position:0%
+earlier approximation tells us that we
+ 
+
+ align:start position:0%
+earlier approximation tells us that we
+use this as our estimate of the open
+
+ align:start position:0%
+use this as our estimate of the open
+ 
+
+ align:start position:0%
+use this as our estimate of the open
+loop transfer function of the amplifier
+
+ align:start position:0%
+loop transfer function of the amplifier
+ 
+
+ align:start position:0%
+loop transfer function of the amplifier
+it's exactly the sort of thing that we
+
+ align:start position:0%
+it's exactly the sort of thing that we
+ 
+
+ align:start position:0%
+it's exactly the sort of thing that we
+did over
+
+ align:start position:0%
+did over
+ 
+
+ align:start position:0%
+did over
+here uh in this case this curve would be
+
+ align:start position:0%
+here uh in this case this curve would be
+ 
+
+ align:start position:0%
+here uh in this case this curve would be
+GM over 2 y Sub
+
+ align:start position:0%
+GM over 2 y Sub
+ 
+
+ align:start position:0%
+GM over 2 y Sub
+C uh so we can we can show what would
+
+ align:start position:0%
+C uh so we can we can show what would
+ 
+
+ align:start position:0%
+C uh so we can we can show what would
+happen for our operational amplifier
+
+ align:start position:0%
+happen for our operational amplifier
+ 
+
+ align:start position:0%
+happen for our operational amplifier
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+curve would
+
+ align:start position:0%
+curve would
+ 
+
+ align:start position:0%
+curve would
+be G
+
+ align:start position:0%
+be G
+ 
+
+ align:start position:0%
+be G
+subm over 2 y Sub
+
+ align:start position:0%
+subm over 2 y Sub
+ 
+
+ align:start position:0%
+subm over 2 y Sub
+C and this curve would be not not this
+
+ align:start position:0%
+C and this curve would be not not this
+ 
+
+ align:start position:0%
+C and this curve would be not not this
+quantity but rather
+
+ align:start position:0%
+quantity but rather
+ 
+
+ align:start position:0%
+quantity but rather
+G subm over 2
+
+ align:start position:0%
+G subm over 2
+ 
+
+ align:start position:0%
+G subm over 2
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+AI over Yi plus ya a so we plot those
+
+ align:start position:0%
+AI over Yi plus ya a so we plot those
+ 
+
+ align:start position:0%
+AI over Yi plus ya a so we plot those
+two quantities once again as in our
+
+ align:start position:0%
+two quantities once again as in our
+ 
+
+ align:start position:0%
+two quantities once again as in our
+general discussion of monor loop
+
+ align:start position:0%
+general discussion of monor loop
+ 
+
+ align:start position:0%
+general discussion of monor loop
+feedback we'd estimate the overall
+
+ align:start position:0%
+feedback we'd estimate the overall
+ 
+
+ align:start position:0%
+feedback we'd estimate the overall
+forward path transfer function of our
+
+ align:start position:0%
+forward path transfer function of our
+ 
+
+ align:start position:0%
+forward path transfer function of our
+system in this case uh the open loop
+
+ align:start position:0%
+system in this case uh the open loop
+ 
+
+ align:start position:0%
+system in this case uh the open loop
+transfer function of the operational
+
+ align:start position:0%
+transfer function of the operational
+ 
+
+ align:start position:0%
+transfer function of the operational
+amplifier as simply the lower of those
+
+ align:start position:0%
+amplifier as simply the lower of those
+ 
+
+ align:start position:0%
+amplifier as simply the lower of those
+two curves at all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequencies we'll find out that this
+
+ align:start position:0%
+frequencies we'll find out that this
+ 
+
+ align:start position:0%
+frequencies we'll find out that this
+sort of estimate works very well for at
+
+ align:start position:0%
+sort of estimate works very well for at
+ 
+
+ align:start position:0%
+sort of estimate works very well for at
+least one available operational
+
+ align:start position:0%
+least one available operational
+ 
+
+ align:start position:0%
+least one available operational
+amplifier in fact most modern
+
+ align:start position:0%
+amplifier in fact most modern
+ 
+
+ align:start position:0%
+amplifier in fact most modern
+operational amplifiers the ones that are
+
+ align:start position:0%
+operational amplifiers the ones that are
+ 
+
+ align:start position:0%
+operational amplifiers the ones that are
+currently being designed use this sort
+
+ align:start position:0%
+currently being designed use this sort
+ 
+
+ align:start position:0%
+currently being designed use this sort
+of two two-stage topology several of the
+
+ align:start position:0%
+of two two-stage topology several of the
+ 
+
+ align:start position:0%
+of two two-stage topology several of the
+available ones allow the user to select
+
+ align:start position:0%
+available ones allow the user to select
+ 
+
+ align:start position:0%
+available ones allow the user to select
+the compensating element we'll find out
+
+ align:start position:0%
+the compensating element we'll find out
+ 
+
+ align:start position:0%
+the compensating element we'll find out
+that that gives us a very very powerful
+
+ align:start position:0%
+that that gives us a very very powerful
+ 
+
+ align:start position:0%
+that that gives us a very very powerful
+handle on the performance of the
+
+ align:start position:0%
+handle on the performance of the
+ 
+
+ align:start position:0%
+handle on the performance of the
+operational
+
+ align:start position:0%
+operational
+ 
+
+ align:start position:0%
+operational
+amplifier there are a number of popular
+
+ align:start position:0%
+amplifier there are a number of popular
+ 
+
+ align:start position:0%
+amplifier there are a number of popular
+operational amplifiers which do use
+
+ align:start position:0%
+operational amplifiers which do use
+ 
+
+ align:start position:0%
+operational amplifiers which do use
+minor Loop compensation say a good
+
+ align:start position:0%
+minor Loop compensation say a good
+ 
+
+ align:start position:0%
+minor Loop compensation say a good
+example of that is the
+
+ align:start position:0%
+example of that is the
+ 
+
+ align:start position:0%
+example of that is the
+741 and it's a fine amplifier in certain
+
+ align:start position:0%
+741 and it's a fine amplifier in certain
+ 
+
+ align:start position:0%
+741 and it's a fine amplifier in certain
+applications but it really doesn't have
+
+ align:start position:0%
+applications but it really doesn't have
+ 
+
+ align:start position:0%
+applications but it really doesn't have
+anywhere near the flexibility of those
+
+ align:start position:0%
+anywhere near the flexibility of those
+ 
+
+ align:start position:0%
+anywhere near the flexibility of those
+amplifiers that we're able to compensate
+
+ align:start position:0%
+amplifiers that we're able to compensate
+ 
+
+ align:start position:0%
+amplifiers that we're able to compensate
+ourselves and in fact I feel that one of
+
+ align:start position:0%
+ourselves and in fact I feel that one of
+ 
+
+ align:start position:0%
+ourselves and in fact I feel that one of
+the reasons for the popularity of the
+
+ align:start position:0%
+the reasons for the popularity of the
+ 
+
+ align:start position:0%
+the reasons for the popularity of the
+741 is simply that an awful lot of
+
+ align:start position:0%
+741 is simply that an awful lot of
+ 
+
+ align:start position:0%
+741 is simply that an awful lot of
+people who are designing with
+
+ align:start position:0%
+people who are designing with
+ 
+
+ align:start position:0%
+people who are designing with
+operational amplifiers have haven't made
+
+ align:start position:0%
+operational amplifiers have haven't made
+ 
+
+ align:start position:0%
+operational amplifiers have haven't made
+the effort to learn how to compensate
+
+ align:start position:0%
+the effort to learn how to compensate
+ 
+
+ align:start position:0%
+the effort to learn how to compensate
+those amplifiers themselves hopefully
+
+ align:start position:0%
+those amplifiers themselves hopefully
+ 
+
+ align:start position:0%
+those amplifiers themselves hopefully
+this sort of a development will will
+
+ align:start position:0%
+this sort of a development will will
+ 
+
+ align:start position:0%
+this sort of a development will will
+help in fact because of the ease of
+
+ align:start position:0%
+help in fact because of the ease of
+ 
+
+ align:start position:0%
+help in fact because of the ease of
+applying this approximation and as we'll
+
+ align:start position:0%
+applying this approximation and as we'll
+ 
+
+ align:start position:0%
+applying this approximation and as we'll
+see next time because of the very good
+
+ align:start position:0%
+see next time because of the very good
+ 
+
+ align:start position:0%
+see next time because of the very good
+results that we get using the
+
+ align:start position:0%
+results that we get using the
+ 
+
+ align:start position:0%
+results that we get using the
+approximation why we're able to very
+
+ align:start position:0%
+approximation why we're able to very
+ 
+
+ align:start position:0%
+approximation why we're able to very
+readily determine sort of a a quote
+
+ align:start position:0%
+readily determine sort of a a quote
+ 
+
+ align:start position:0%
+readily determine sort of a a quote
+Optimum compensation for many many
+
+ align:start position:0%
+Optimum compensation for many many
+ 
+
+ align:start position:0%
+Optimum compensation for many many
+feedback configurations using these
+
+ align:start position:0%
+feedback configurations using these
+ 
+
+ align:start position:0%
+feedback configurations using these
+sorts of operational amplifiers so I'd
+
+ align:start position:0%
+sorts of operational amplifiers so I'd
+ 
+
+ align:start position:0%
+sorts of operational amplifiers so I'd
+like to look into that next time and do
+
+ align:start position:0%
+like to look into that next time and do
+ 
+
+ align:start position:0%
+like to look into that next time and do
+a an actual example using a commercially
+
+ align:start position:0%
+a an actual example using a commercially
+ 
+
+ align:start position:0%
+a an actual example using a commercially
+available operational amplifier
+
+ align:start position:0%
+available operational amplifier
+ 
+
+ align:start position:0%
+available operational amplifier
+determining the kinds of compensation we
+
+ align:start position:0%
+determining the kinds of compensation we
+ 
+
+ align:start position:0%
+determining the kinds of compensation we
+should use as a function of application
+
+ align:start position:0%
+should use as a function of application
+ 
+
+ align:start position:0%
+should use as a function of application
+thank you
\ No newline at end of file
diff --git a/IGk-7EKR35A.txt b/IGk-7EKR35A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bf74764f5749ccad4be956bbcca958746470fce7
--- /dev/null
+++ b/IGk-7EKR35A.txt
@@ -0,0 +1,1515 @@
+align:start position:0%
+ 
+hi everyone welcome back so in this
+
+ align:start position:0%
+hi everyone welcome back so in this
+ 
+
+ align:start position:0%
+hi everyone welcome back so in this
+problem I'd like to take a look at
+
+ align:start position:0%
+problem I'd like to take a look at
+ 
+
+ align:start position:0%
+problem I'd like to take a look at
+convolution in green formula and
+
+ align:start position:0%
+convolution in green formula and
+ 
+
+ align:start position:0%
+convolution in green formula and
+specifically for part one we're just
+
+ align:start position:0%
+specifically for part one we're just
+ 
+
+ align:start position:0%
+specifically for part one we're just
+asked to compute the convolution of t
+
+ align:start position:0%
+asked to compute the convolution of t
+ 
+
+ align:start position:0%
+asked to compute the convolution of t
+with itself T in the second part we're
+
+ align:start position:0%
+with itself T in the second part we're
+ 
+
+ align:start position:0%
+with itself T in the second part we're
+asked to conf compute the convolution of
+
+ align:start position:0%
+asked to conf compute the convolution of
+ 
+
+ align:start position:0%
+asked to conf compute the convolution of
+e to Theus KT with another exponential e
+
+ align:start position:0%
+e to Theus KT with another exponential e
+ 
+
+ align:start position:0%
+e to Theus KT with another exponential e
+to the A and then in Part B were to use
+
+ align:start position:0%
+to the A and then in Part B were to use
+ 
+
+ align:start position:0%
+to the A and then in Part B were to use
+the result from part A as well as
+
+ align:start position:0%
+the result from part A as well as
+ 
+
+ align:start position:0%
+the result from part A as well as
+Green's formula to solve x do plus KX =
+
+ align:start position:0%
+Green's formula to solve x do plus KX =
+ 
+
+ align:start position:0%
+Green's formula to solve x do plus KX =
+e to the A and specifically we're
+
+ align:start position:0%
+e to the A and specifically we're
+ 
+
+ align:start position:0%
+e to the A and specifically we're
+interested in the rest initial condition
+
+ align:start position:0%
+interested in the rest initial condition
+ 
+
+ align:start position:0%
+interested in the rest initial condition
+solution to this formula okay so I'll
+
+ align:start position:0%
+solution to this formula okay so I'll
+ 
+
+ align:start position:0%
+solution to this formula okay so I'll
+let you think about this problem and
+
+ align:start position:0%
+let you think about this problem and
+ 
+
+ align:start position:0%
+let you think about this problem and
+I'll be back in a minute
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi everyone welcome back okay so for
+
+ align:start position:0%
+hi everyone welcome back okay so for
+ 
+
+ align:start position:0%
+hi everyone welcome back okay so for
+part one we're asked to compute the
+
+ align:start position:0%
+part one we're asked to compute the
+ 
+
+ align:start position:0%
+part one we're asked to compute the
+convolution of two functions t with
+
+ align:start position:0%
+convolution of two functions t with
+ 
+
+ align:start position:0%
+convolution of two functions t with
+itself and I'll just quickly write down
+
+ align:start position:0%
+itself and I'll just quickly write down
+ 
+
+ align:start position:0%
+itself and I'll just quickly write down
+the formula for a convolution so if I
+
+ align:start position:0%
+the formula for a convolution so if I
+ 
+
+ align:start position:0%
+the formula for a convolution so if I
+have two
+
+ align:start position:0%
+have two
+ 
+
+ align:start position:0%
+have two
+functions f and
+
+ align:start position:0%
+functions f and
+ 
+
+ align:start position:0%
+functions f and
+g then the convolution is defined as in
+
+ align:start position:0%
+g then the convolution is defined as in
+ 
+
+ align:start position:0%
+g then the convolution is defined as in
+this case the integral from zero to T of
+
+ align:start position:0%
+this case the integral from zero to T of
+ 
+
+ align:start position:0%
+this case the integral from zero to T of
+f so the function f evaluated at we're
+
+ align:start position:0%
+f so the function f evaluated at we're
+ 
+
+ align:start position:0%
+f so the function f evaluated at we're
+going to use to as the integration
+
+ align:start position:0%
+going to use to as the integration
+ 
+
+ align:start position:0%
+going to use to as the integration
+variable multiplied by G T minus
+
+ align:start position:0%
+variable multiplied by G T minus
+ 
+
+ align:start position:0%
+variable multiplied by G T minus
+to D
+
+ align:start position:0%
+to D
+ 
+
+ align:start position:0%
+to D
+to so notice how the variable T appears
+
+ align:start position:0%
+to so notice how the variable T appears
+ 
+
+ align:start position:0%
+to so notice how the variable T appears
+in two places in this uh formula it
+
+ align:start position:0%
+in two places in this uh formula it
+ 
+
+ align:start position:0%
+in two places in this uh formula it
+appears in one place in the argument of
+
+ align:start position:0%
+appears in one place in the argument of
+ 
+
+ align:start position:0%
+appears in one place in the argument of
+G and it appears in the bound of
+
+ align:start position:0%
+G and it appears in the bound of
+ 
+
+ align:start position:0%
+G and it appears in the bound of
+integration meanwhile too is the Integra
+
+ align:start position:0%
+integration meanwhile too is the Integra
+ 
+
+ align:start position:0%
+integration meanwhile too is the Integra
+in uh it's the variable we're
+
+ align:start position:0%
+in uh it's the variable we're
+ 
+
+ align:start position:0%
+in uh it's the variable we're
+integrating over and T appears in two
+
+ align:start position:0%
+integrating over and T appears in two
+ 
+
+ align:start position:0%
+integrating over and T appears in two
+places as well one in F and one in G
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if we're interested in t
+
+ align:start position:0%
+okay so if we're interested in t
+ 
+
+ align:start position:0%
+okay so if we're interested in t
+convolved with
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t we have the integral from 0 to
+
+ align:start position:0%
+t we have the integral from 0 to
+ 
+
+ align:start position:0%
+t we have the integral from 0 to
+T
+
+ align:start position:0%
+T
+ 
+
+ align:start position:0%
+T
+of to
+
+ align:start position:0%
+of to
+ 
+
+ align:start position:0%
+of to
+times T minus
+
+ align:start position:0%
+times T minus
+ 
+
+ align:start position:0%
+times T minus
+to so notice how f is just T and G is T
+
+ align:start position:0%
+to so notice how f is just T and G is T
+ 
+
+ align:start position:0%
+to so notice how f is just T and G is T
+so when we insert to and T minus ta into
+
+ align:start position:0%
+so when we insert to and T minus ta into
+ 
+
+ align:start position:0%
+so when we insert to and T minus ta into
+the the function we end up just getting
+
+ align:start position:0%
+the the function we end up just getting
+ 
+
+ align:start position:0%
+the the function we end up just getting
+to time T minus ta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DT and just expanding this out we have t
+
+ align:start position:0%
+DT and just expanding this out we have t
+ 
+
+ align:start position:0%
+DT and just expanding this out we have t
+*
+
+ align:start position:0%
+*
+ 
+
+ align:start position:0%
+*
+to minus to^ 2 D
+
+ align:start position:0%
+to minus to^ 2 D
+ 
+
+ align:start position:0%
+to minus to^ 2 D
+to so in the integral the variable T
+
+ align:start position:0%
+to so in the integral the variable T
+ 
+
+ align:start position:0%
+to so in the integral the variable T
+always appears just as a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant so in this case we have t to
+
+ align:start position:0%
+constant so in this case we have t to
+ 
+
+ align:start position:0%
+constant so in this case we have t to
+integrated becomes t^2 over 2 when I
+
+ align:start position:0%
+integrated becomes t^2 over 2 when I
+ 
+
+ align:start position:0%
+integrated becomes t^2 over 2 when I
+integrate from0 to uh t
+
+ align:start position:0%
+integrate from0 to uh t
+ 
+
+ align:start position:0%
+integrate from0 to uh t
+t^ squar integrates to
+
+ align:start position:0%
+t^ squar integrates to
+ 
+
+ align:start position:0%
+t^ squar integrates to
+1/3 T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cubed and zero drops out from the other
+
+ align:start position:0%
+cubed and zero drops out from the other
+ 
+
+ align:start position:0%
+cubed and zero drops out from the other
+end of the integral so we end up with t
+
+ align:start position:0%
+end of the integral so we end up with t
+ 
+
+ align:start position:0%
+end of the integral so we end up with t
+cubed 12 -
+
+ align:start position:0%
+cubed 12 -
+ 
+
+ align:start position:0%
+cubed 12 -
+1/3 which is equal to 1 16 T
+
+ align:start position:0%
+1/3 which is equal to 1 16 T
+ 
+
+ align:start position:0%
+1/3 which is equal to 1 16 T
+cubed okay so there's the answer we're
+
+ align:start position:0%
+cubed okay so there's the answer we're
+ 
+
+ align:start position:0%
+cubed okay so there's the answer we're
+looking for for Part B or for question
+
+ align:start position:0%
+looking for for Part B or for question
+ 
+
+ align:start position:0%
+looking for for Part B or for question
+two again we have another computation to
+
+ align:start position:0%
+two again we have another computation to
+ 
+
+ align:start position:0%
+two again we have another computation to
+do so we have more integrals to work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+out and in this case it's two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exponentials so we have 0 to
+
+ align:start position:0%
+exponentials so we have 0 to
+ 
+
+ align:start position:0%
+exponentials so we have 0 to
+T the first one's going to be e to the
+
+ align:start position:0%
+T the first one's going to be e to the
+ 
+
+ align:start position:0%
+T the first one's going to be e to the
+KT
+
+ align:start position:0%
+KT
+ 
+
+ align:start position:0%
+KT
+sorry e to the K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to and the second one is e to the A T
+
+ align:start position:0%
+to and the second one is e to the A T
+ 
+
+ align:start position:0%
+to and the second one is e to the A T
+minus to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+D so I can just expand things out and I
+
+ align:start position:0%
+D so I can just expand things out and I
+ 
+
+ align:start position:0%
+D so I can just expand things out and I
+get e to the a
+
+ align:start position:0%
+get e to the a
+ 
+
+ align:start position:0%
+get e to the a
+t time e to the minus uh
+
+ align:start position:0%
+t time e to the minus uh
+ 
+
+ align:start position:0%
+t time e to the minus uh
+A+
+
+ align:start position:0%
+A+
+ 
+
+ align:start position:0%
+A+
+K to D
+
+ align:start position:0%
+K to D
+ 
+
+ align:start position:0%
+K to D
+to 0 to
+
+ align:start position:0%
+to 0 to
+ 
+
+ align:start position:0%
+to 0 to
+T and again because T is just a dummy
+
+ align:start position:0%
+T and again because T is just a dummy
+ 
+
+ align:start position:0%
+T and again because T is just a dummy
+variable in this integral we're not
+
+ align:start position:0%
+variable in this integral we're not
+ 
+
+ align:start position:0%
+variable in this integral we're not
+integrating over T I can just think of e
+
+ align:start position:0%
+integrating over T I can just think of e
+ 
+
+ align:start position:0%
+integrating over T I can just think of e
+to the a t as a constant so I'm really
+
+ align:start position:0%
+to the a t as a constant so I'm really
+ 
+
+ align:start position:0%
+to the a t as a constant so I'm really
+just integrating the function e to the
+
+ align:start position:0%
+just integrating the function e to the
+ 
+
+ align:start position:0%
+just integrating the function e to the
+minus a plus K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to and when I integrate this function I
+
+ align:start position:0%
+to and when I integrate this function I
+ 
+
+ align:start position:0%
+to and when I integrate this function I
+get one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over minus a + k eus a +
+
+ align:start position:0%
+over minus a + k eus a +
+ 
+
+ align:start position:0%
+over minus a + k eus a +
+k to evaluated at the
+
+ align:start position:0%
+k to evaluated at the
+ 
+
+ align:start position:0%
+k to evaluated at the
+bounds 0 and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+P so the negative sign here just flips
+
+ align:start position:0%
+P so the negative sign here just flips
+ 
+
+ align:start position:0%
+P so the negative sign here just flips
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+bounds so a plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K substituting in zero just gives us
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one and then substituting in t gives us
+
+ align:start position:0%
+one and then substituting in t gives us
+ 
+
+ align:start position:0%
+one and then substituting in t gives us
+e to the
+
+ align:start position:0%
+e to the
+ 
+
+ align:start position:0%
+e to the
+minus a + k t
+
+ align:start position:0%
+minus a + k t
+ 
+
+ align:start position:0%
+minus a + k t
+okay and I can expand out multiply out e
+
+ align:start position:0%
+okay and I can expand out multiply out e
+ 
+
+ align:start position:0%
+okay and I can expand out multiply out e
+to the a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t and when the dust
+
+ align:start position:0%
+t and when the dust
+ 
+
+ align:start position:0%
+t and when the dust
+settles we have e to the A T
+
+ align:start position:0%
+settles we have e to the A T
+ 
+
+ align:start position:0%
+settles we have e to the A T
+minus E to the minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT okay so this is just the uh the
+
+ align:start position:0%
+KT okay so this is just the uh the
+ 
+
+ align:start position:0%
+KT okay so this is just the uh the
+computation of the convolution e to the
+
+ align:start position:0%
+computation of the convolution e to the
+ 
+
+ align:start position:0%
+computation of the convolution e to the
+minus KT and e to the a t so note now if
+
+ align:start position:0%
+minus KT and e to the a t so note now if
+ 
+
+ align:start position:0%
+minus KT and e to the a t so note now if
+if for example K were to equal negative
+
+ align:start position:0%
+if for example K were to equal negative
+ 
+
+ align:start position:0%
+if for example K were to equal negative
+a we would have zero in the denominator
+
+ align:start position:0%
+a we would have zero in the denominator
+ 
+
+ align:start position:0%
+a we would have zero in the denominator
+and zero in the numerator so one way to
+
+ align:start position:0%
+and zero in the numerator so one way to
+ 
+
+ align:start position:0%
+and zero in the numerator so one way to
+compute the Special K when case when K
+
+ align:start position:0%
+compute the Special K when case when K
+ 
+
+ align:start position:0%
+compute the Special K when case when K
+is equal to negative a is to use lel's
+
+ align:start position:0%
+is equal to negative a is to use lel's
+ 
+
+ align:start position:0%
+is equal to negative a is to use lel's
+Rule and differentiate the top and the
+
+ align:start position:0%
+Rule and differentiate the top and the
+ 
+
+ align:start position:0%
+Rule and differentiate the top and the
+bottom uh for example with respect to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K another alternative way of computing
+
+ align:start position:0%
+K another alternative way of computing
+ 
+
+ align:start position:0%
+K another alternative way of computing
+uh the special case when uh a is equal
+
+ align:start position:0%
+uh the special case when uh a is equal
+ 
+
+ align:start position:0%
+uh the special case when uh a is equal
+to negative k is just to plug in e to
+
+ align:start position:0%
+to negative k is just to plug in e to
+ 
+
+ align:start position:0%
+to negative k is just to plug in e to
+the uh e to the K and then just work out
+
+ align:start position:0%
+the uh e to the K and then just work out
+ 
+
+ align:start position:0%
+the uh e to the K and then just work out
+this integral and you'll obtain a
+
+ align:start position:0%
+this integral and you'll obtain a
+ 
+
+ align:start position:0%
+this integral and you'll obtain a
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+answer okay and now lastly for Part B
+
+ align:start position:0%
+answer okay and now lastly for Part B
+ 
+
+ align:start position:0%
+answer okay and now lastly for Part B
+we're interested in the differential
+
+ align:start position:0%
+we're interested in the differential
+ 
+
+ align:start position:0%
+we're interested in the differential
+equation x dot plus
+
+ align:start position:0%
+equation x dot plus
+ 
+
+ align:start position:0%
+equation x dot plus
+KX equal e to a T and we're interested
+
+ align:start position:0%
+KX equal e to a T and we're interested
+ 
+
+ align:start position:0%
+KX equal e to a T and we're interested
+in finding uh the particular solution
+
+ align:start position:0%
+in finding uh the particular solution
+ 
+
+ align:start position:0%
+in finding uh the particular solution
+that has rest initial
+
+ align:start position:0%
+that has rest initial
+ 
+
+ align:start position:0%
+that has rest initial
+conditions so for example X of 0 is
+
+ align:start position:0%
+conditions so for example X of 0 is
+ 
+
+ align:start position:0%
+conditions so for example X of 0 is
+equal a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero and uh we want to use Green's
+
+ align:start position:0%
+zero and uh we want to use Green's
+ 
+
+ align:start position:0%
+zero and uh we want to use Green's
+formula so just recall that uh there's
+
+ align:start position:0%
+formula so just recall that uh there's
+ 
+
+ align:start position:0%
+formula so just recall that uh there's
+the impulse response
+
+ align:start position:0%
+the impulse response
+ 
+
+ align:start position:0%
+the impulse response
+formula or the weight function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+W which solves the same differential
+
+ align:start position:0%
+W which solves the same differential
+ 
+
+ align:start position:0%
+W which solves the same differential
+equation but with the Delta function on
+
+ align:start position:0%
+equation but with the Delta function on
+ 
+
+ align:start position:0%
+equation but with the Delta function on
+the right hand
+
+ align:start position:0%
+the right hand
+ 
+
+ align:start position:0%
+the right hand
+side and
+
+ align:start position:0%
+side and
+ 
+
+ align:start position:0%
+side and
+W in this case
+
+ align:start position:0%
+W in this case
+ 
+
+ align:start position:0%
+W in this case
+as we've seen in lecture is actually e
+
+ align:start position:0%
+as we've seen in lecture is actually e
+ 
+
+ align:start position:0%
+as we've seen in lecture is actually e
+uh to the negative
+
+ align:start position:0%
+uh to the negative
+ 
+
+ align:start position:0%
+uh to the negative
+KT when T is bigger than zero and it's
+
+ align:start position:0%
+KT when T is bigger than zero and it's
+ 
+
+ align:start position:0%
+KT when T is bigger than zero and it's
+zero when T is less than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero so notice how e minus KT is exactly
+
+ align:start position:0%
+zero so notice how e minus KT is exactly
+ 
+
+ align:start position:0%
+zero so notice how e minus KT is exactly
+the function that we convolved in part
+
+ align:start position:0%
+the function that we convolved in part
+ 
+
+ align:start position:0%
+the function that we convolved in part
+a uh specifically we convolved it with e
+
+ align:start position:0%
+a uh specifically we convolved it with e
+ 
+
+ align:start position:0%
+a uh specifically we convolved it with e
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+a so for example Green's formula says
+
+ align:start position:0%
+a so for example Green's formula says
+ 
+
+ align:start position:0%
+a so for example Green's formula says
+that the particular solution that has
+
+ align:start position:0%
+that the particular solution that has
+ 
+
+ align:start position:0%
+that the particular solution that has
+rest initial condition
+
+ align:start position:0%
+rest initial condition
+ 
+
+ align:start position:0%
+rest initial condition
+is going to be the weight
+
+ align:start position:0%
+is going to be the weight
+ 
+
+ align:start position:0%
+is going to be the weight
+function convolved with the right hand
+
+ align:start position:0%
+function convolved with the right hand
+ 
+
+ align:start position:0%
+function convolved with the right hand
+side of the differential
+
+ align:start position:0%
+side of the differential
+ 
+
+ align:start position:0%
+side of the differential
+equation e to the a
+
+ align:start position:0%
+equation e to the a
+ 
+
+ align:start position:0%
+equation e to the a
+t in this case on the domain of
+
+ align:start position:0%
+t in this case on the domain of
+ 
+
+ align:start position:0%
+t in this case on the domain of
+integration for the convolution W is
+
+ align:start position:0%
+integration for the convolution W is
+ 
+
+ align:start position:0%
+integration for the convolution W is
+just e the minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT so we have e minus KT involved with E
+
+ align:start position:0%
+KT so we have e minus KT involved with E
+ 
+
+ align:start position:0%
+KT so we have e minus KT involved with E
+the a t so Green's formula gives us uh
+
+ align:start position:0%
+the a t so Green's formula gives us uh
+ 
+
+ align:start position:0%
+the a t so Green's formula gives us uh
+the equation for the solution to this
+
+ align:start position:0%
+the equation for the solution to this
+ 
+
+ align:start position:0%
+the equation for the solution to this
+differential equation which has rest
+
+ align:start position:0%
+differential equation which has rest
+ 
+
+ align:start position:0%
+differential equation which has rest
+initial
+
+ align:start position:0%
+initial
+ 
+
+ align:start position:0%
+initial
+conditions and specifically we've
+
+ align:start position:0%
+conditions and specifically we've
+ 
+
+ align:start position:0%
+conditions and specifically we've
+already worked this out from part A so I
+
+ align:start position:0%
+already worked this out from part A so I
+ 
+
+ align:start position:0%
+already worked this out from part A so I
+can just write down what the answer
+
+ align:start position:0%
+can just write down what the answer
+ 
+
+ align:start position:0%
+can just write down what the answer
+is it's 1 over a plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+k e to the A T minus eus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KT and just as a quick check to make
+
+ align:start position:0%
+KT and just as a quick check to make
+ 
+
+ align:start position:0%
+KT and just as a quick check to make
+sure that we've done everything
+
+ align:start position:0%
+sure that we've done everything
+ 
+
+ align:start position:0%
+sure that we've done everything
+correctly we can plug in t equals 0 and
+
+ align:start position:0%
+correctly we can plug in t equals 0 and
+ 
+
+ align:start position:0%
+correctly we can plug in t equals 0 and
+when T equals 0 we have 1us 1 which
+
+ align:start position:0%
+when T equals 0 we have 1us 1 which
+ 
+
+ align:start position:0%
+when T equals 0 we have 1us 1 which
+gives us Z so indeed this x is the
+
+ align:start position:0%
+gives us Z so indeed this x is the
+ 
+
+ align:start position:0%
+gives us Z so indeed this x is the
+solution to this differential equation
+
+ align:start position:0%
+solution to this differential equation
+ 
+
+ align:start position:0%
+solution to this differential equation
+which has rest initial
+
+ align:start position:0%
+which has rest initial
+ 
+
+ align:start position:0%
+which has rest initial
+conditions okay so I'd uh just like to
+
+ align:start position:0%
+conditions okay so I'd uh just like to
+ 
+
+ align:start position:0%
+conditions okay so I'd uh just like to
+conclude this problem uh quick recap uh
+
+ align:start position:0%
+conclude this problem uh quick recap uh
+ 
+
+ align:start position:0%
+conclude this problem uh quick recap uh
+we worked out several convolutions and
+
+ align:start position:0%
+we worked out several convolutions and
+ 
+
+ align:start position:0%
+we worked out several convolutions and
+uh specifically we were able to use
+
+ align:start position:0%
+uh specifically we were able to use
+ 
+
+ align:start position:0%
+uh specifically we were able to use
+green
+
+ align:start position:0%
+green
+ 
+
+ align:start position:0%
+green
+formula uh in addition to the
+
+ align:start position:0%
+formula uh in addition to the
+ 
+
+ align:start position:0%
+formula uh in addition to the
+convolution that we worked out to
+
+ align:start position:0%
+convolution that we worked out to
+ 
+
+ align:start position:0%
+convolution that we worked out to
+compute the solution with rest initial
+
+ align:start position:0%
+compute the solution with rest initial
+ 
+
+ align:start position:0%
+compute the solution with rest initial
+conditions to an OD uh moreover Green's
+
+ align:start position:0%
+conditions to an OD uh moreover Green's
+ 
+
+ align:start position:0%
+conditions to an OD uh moreover Green's
+function is very useful because notice
+
+ align:start position:0%
+function is very useful because notice
+ 
+
+ align:start position:0%
+function is very useful because notice
+how we could have computed the
+
+ align:start position:0%
+how we could have computed the
+ 
+
+ align:start position:0%
+how we could have computed the
+convolution for any right- hand side
+
+ align:start position:0%
+convolution for any right- hand side
+ 
+
+ align:start position:0%
+convolution for any right- hand side
+function here so uh in some sense we're
+
+ align:start position:0%
+function here so uh in some sense we're
+ 
+
+ align:start position:0%
+function here so uh in some sense we're
+able to generalize and find solutions to
+
+ align:start position:0%
+able to generalize and find solutions to
+ 
+
+ align:start position:0%
+able to generalize and find solutions to
+differential equations which have
+
+ align:start position:0%
+differential equations which have
+ 
+
+ align:start position:0%
+differential equations which have
+arbitrary right- hand side forcings not
+
+ align:start position:0%
+arbitrary right- hand side forcings not
+ 
+
+ align:start position:0%
+arbitrary right- hand side forcings not
+just signs and cosiness periodic
+
+ align:start position:0%
+just signs and cosiness periodic
+ 
+
+ align:start position:0%
+just signs and cosiness periodic
+functions or other simple functions
+
+ align:start position:0%
+functions or other simple functions
+ 
+
+ align:start position:0%
+functions or other simple functions
+which we've been looking at in the
+
+ align:start position:0%
+which we've been looking at in the
+ 
+
+ align:start position:0%
+which we've been looking at in the
+past so I'd like to conclude here and
+
+ align:start position:0%
+past so I'd like to conclude here and
+ 
+
+ align:start position:0%
+past so I'd like to conclude here and
+I'll see you next time
\ No newline at end of file
diff --git a/ITE9w9wKVKU.txt b/ITE9w9wKVKU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a558b124cd6e008020943b53f4206be6f9f6ae75
--- /dev/null
+++ b/ITE9w9wKVKU.txt
@@ -0,0 +1,8531 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+professor of urban studies and planning
+
+ align:start position:0%
+professor of urban studies and planning
+ 
+
+ align:start position:0%
+professor of urban studies and planning
+at MIT and this is another installment
+
+ align:start position:0%
+at MIT and this is another installment
+ 
+
+ align:start position:0%
+at MIT and this is another installment
+of my lecture series on Urban Energy
+
+ align:start position:0%
+of my lecture series on Urban Energy
+ 
+
+ align:start position:0%
+of my lecture series on Urban Energy
+Systems and policies
+
+ align:start position:0%
+Systems and policies
+ 
+
+ align:start position:0%
+Systems and policies
+today we're going to talk about
+
+ align:start position:0%
+today we're going to talk about
+ 
+
+ align:start position:0%
+today we're going to talk about
+renewable energy and we've been talking
+
+ align:start position:0%
+renewable energy and we've been talking
+ 
+
+ align:start position:0%
+renewable energy and we've been talking
+in this plots about consumption how we
+
+ align:start position:0%
+in this plots about consumption how we
+ 
+
+ align:start position:0%
+in this plots about consumption how we
+consume energy in our personal
+
+ align:start position:0%
+consume energy in our personal
+ 
+
+ align:start position:0%
+consume energy in our personal
+transportation and our buildings and our
+
+ align:start position:0%
+transportation and our buildings and our
+ 
+
+ align:start position:0%
+transportation and our buildings and our
+consumption of material Goods quite
+
+ align:start position:0%
+consumption of material Goods quite
+ 
+
+ align:start position:0%
+consumption of material Goods quite
+often produced by industrial
+
+ align:start position:0%
+often produced by industrial
+ 
+
+ align:start position:0%
+often produced by industrial
+manufacturing processes and I've
+
+ align:start position:0%
+manufacturing processes and I've
+ 
+
+ align:start position:0%
+manufacturing processes and I've
+emphasized in the class that we need to
+
+ align:start position:0%
+emphasized in the class that we need to
+ 
+
+ align:start position:0%
+emphasized in the class that we need to
+make all those uses more efficient in
+
+ align:start position:0%
+make all those uses more efficient in
+ 
+
+ align:start position:0%
+make all those uses more efficient in
+order for us to help decarbonate cities
+
+ align:start position:0%
+order for us to help decarbonate cities
+ 
+
+ align:start position:0%
+order for us to help decarbonate cities
+but now it's time for us to turn to talk
+
+ align:start position:0%
+but now it's time for us to turn to talk
+ 
+
+ align:start position:0%
+but now it's time for us to turn to talk
+about renewable energy the fundamental
+
+ align:start position:0%
+about renewable energy the fundamental
+ 
+
+ align:start position:0%
+about renewable energy the fundamental
+building blocks now enabled cities to
+
+ align:start position:0%
+building blocks now enabled cities to
+ 
+
+ align:start position:0%
+building blocks now enabled cities to
+transition from their current energy
+
+ align:start position:0%
+transition from their current energy
+ 
+
+ align:start position:0%
+transition from their current energy
+sources which mostly depend on fossil
+
+ align:start position:0%
+sources which mostly depend on fossil
+ 
+
+ align:start position:0%
+sources which mostly depend on fossil
+fuels to renewable energy energy sources
+
+ align:start position:0%
+fuels to renewable energy energy sources
+ 
+
+ align:start position:0%
+fuels to renewable energy energy sources
+that will help cities decarbonize and
+
+ align:start position:0%
+that will help cities decarbonize and
+ 
+
+ align:start position:0%
+that will help cities decarbonize and
+avoid the worst consequences of climate
+
+ align:start position:0%
+avoid the worst consequences of climate
+ 
+
+ align:start position:0%
+avoid the worst consequences of climate
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+so today in the first part I'll talk
+
+ align:start position:0%
+so today in the first part I'll talk
+ 
+
+ align:start position:0%
+so today in the first part I'll talk
+about wind energy
+
+ align:start position:0%
+about wind energy
+ 
+
+ align:start position:0%
+about wind energy
+the materials for today if you have the
+
+ align:start position:0%
+the materials for today if you have the
+ 
+
+ align:start position:0%
+the materials for today if you have the
+PDF or hard copies you can click on
+
+ align:start position:0%
+PDF or hard copies you can click on
+ 
+
+ align:start position:0%
+PDF or hard copies you can click on
+these pink links and they'll take you to
+
+ align:start position:0%
+these pink links and they'll take you to
+ 
+
+ align:start position:0%
+these pink links and they'll take you to
+the various resources these are the
+
+ align:start position:0%
+the various resources these are the
+ 
+
+ align:start position:0%
+the various resources these are the
+materials will be this we'll be
+
+ align:start position:0%
+materials will be this we'll be
+ 
+
+ align:start position:0%
+materials will be this we'll be
+discussing today
+
+ align:start position:0%
+discussing today
+ 
+
+ align:start position:0%
+discussing today
+and just to refresh our memory where we
+
+ align:start position:0%
+and just to refresh our memory where we
+ 
+
+ align:start position:0%
+and just to refresh our memory where we
+are uh these are again the
+
+ align:start position:0%
+are uh these are again the
+ 
+
+ align:start position:0%
+are uh these are again the
+decarborization pathways from the
+
+ align:start position:0%
+decarborization pathways from the
+ 
+
+ align:start position:0%
+decarborization pathways from the
+Williams NL 2021 paper this is the 100
+
+ align:start position:0%
+Williams NL 2021 paper this is the 100
+ 
+
+ align:start position:0%
+Williams NL 2021 paper this is the 100
+renewable energy scenario so on the left
+
+ align:start position:0%
+renewable energy scenario so on the left
+ 
+
+ align:start position:0%
+renewable energy scenario so on the left
+hand side of the Sankey diagram you can
+
+ align:start position:0%
+hand side of the Sankey diagram you can
+ 
+
+ align:start position:0%
+hand side of the Sankey diagram you can
+see that all of our primary energy
+
+ align:start position:0%
+see that all of our primary energy
+ 
+
+ align:start position:0%
+see that all of our primary energy
+sources are essentially uh decarbonized
+
+ align:start position:0%
+sources are essentially uh decarbonized
+ 
+
+ align:start position:0%
+sources are essentially uh decarbonized
+renewable energy sources solar wind and
+
+ align:start position:0%
+renewable energy sources solar wind and
+ 
+
+ align:start position:0%
+renewable energy sources solar wind and
+biomass being the three largest sources
+
+ align:start position:0%
+biomass being the three largest sources
+ 
+
+ align:start position:0%
+biomass being the three largest sources
+of energy
+
+ align:start position:0%
+of energy
+ 
+
+ align:start position:0%
+of energy
+and what I want to emphasize in this
+
+ align:start position:0%
+and what I want to emphasize in this
+ 
+
+ align:start position:0%
+and what I want to emphasize in this
+class is that we're going to over the
+
+ align:start position:0%
+class is that we're going to over the
+ 
+
+ align:start position:0%
+class is that we're going to over the
+next few classes is we're going to talk
+
+ align:start position:0%
+next few classes is we're going to talk
+ 
+
+ align:start position:0%
+next few classes is we're going to talk
+about your renewable toolbox like high
+
+ align:start position:0%
+about your renewable toolbox like high
+ 
+
+ align:start position:0%
+about your renewable toolbox like high
+defines sustainable energy or a
+
+ align:start position:0%
+defines sustainable energy or a
+ 
+
+ align:start position:0%
+defines sustainable energy or a
+sustainable production of energy as
+
+ align:start position:0%
+sustainable production of energy as
+ 
+
+ align:start position:0%
+sustainable production of energy as
+categories of wind
+
+ align:start position:0%
+categories of wind
+ 
+
+ align:start position:0%
+categories of wind
+solar hydropower wave power high power
+
+ align:start position:0%
+solar hydropower wave power high power
+ 
+
+ align:start position:0%
+solar hydropower wave power high power
+geothermal power and Makai gives nuclear
+
+ align:start position:0%
+geothermal power and Makai gives nuclear
+ 
+
+ align:start position:0%
+geothermal power and Makai gives nuclear
+a question mark because it's not clear
+
+ align:start position:0%
+a question mark because it's not clear
+ 
+
+ align:start position:0%
+a question mark because it's not clear
+whether or not it's not clear to look
+
+ align:start position:0%
+whether or not it's not clear to look
+ 
+
+ align:start position:0%
+whether or not it's not clear to look
+high and still to me what their nuclear
+
+ align:start position:0%
+high and still to me what their nuclear
+ 
+
+ align:start position:0%
+high and still to me what their nuclear
+power counts as sustainable
+
+ align:start position:0%
+power counts as sustainable
+ 
+
+ align:start position:0%
+power counts as sustainable
+but what I wanted to set up a renewable
+
+ align:start position:0%
+but what I wanted to set up a renewable
+ 
+
+ align:start position:0%
+but what I wanted to set up a renewable
+toolbox and we're going to develop this
+
+ align:start position:0%
+toolbox and we're going to develop this
+ 
+
+ align:start position:0%
+toolbox and we're going to develop this
+theme in the next few lectures is that
+
+ align:start position:0%
+theme in the next few lectures is that
+ 
+
+ align:start position:0%
+theme in the next few lectures is that
+it has becoming decently cheap
+
+ align:start position:0%
+it has becoming decently cheap
+ 
+
+ align:start position:0%
+it has becoming decently cheap
+increasingly clean but these fundamental
+
+ align:start position:0%
+increasingly clean but these fundamental
+ 
+
+ align:start position:0%
+increasingly clean but these fundamental
+Technologies require transitioning our
+
+ align:start position:0%
+Technologies require transitioning our
+ 
+
+ align:start position:0%
+Technologies require transitioning our
+energy system and how it works because
+
+ align:start position:0%
+energy system and how it works because
+ 
+
+ align:start position:0%
+energy system and how it works because
+they work in different ways in our
+
+ align:start position:0%
+they work in different ways in our
+ 
+
+ align:start position:0%
+they work in different ways in our
+existing fossil fuel resources
+
+ align:start position:0%
+existing fossil fuel resources
+ 
+
+ align:start position:0%
+existing fossil fuel resources
+and so just to kind of give a definition
+
+ align:start position:0%
+and so just to kind of give a definition
+ 
+
+ align:start position:0%
+and so just to kind of give a definition
+of renewal resources why we are focused
+
+ align:start position:0%
+of renewal resources why we are focused
+ 
+
+ align:start position:0%
+of renewal resources why we are focused
+on particular Technologies there are
+
+ align:start position:0%
+on particular Technologies there are
+ 
+
+ align:start position:0%
+on particular Technologies there are
+technologies that drive Energy natural
+
+ align:start position:0%
+technologies that drive Energy natural
+ 
+
+ align:start position:0%
+technologies that drive Energy natural
+processes they can be regenerative over
+
+ align:start position:0%
+processes they can be regenerative over
+ 
+
+ align:start position:0%
+processes they can be regenerative over
+short periods of time and they will not
+
+ align:start position:0%
+short periods of time and they will not
+ 
+
+ align:start position:0%
+short periods of time and they will not
+be depleted
+
+ align:start position:0%
+be depleted
+ 
+
+ align:start position:0%
+be depleted
+we can talk about whether or not
+
+ align:start position:0%
+we can talk about whether or not
+ 
+
+ align:start position:0%
+we can talk about whether or not
+Renewables are defined as clean Net Zero
+
+ align:start position:0%
+Renewables are defined as clean Net Zero
+ 
+
+ align:start position:0%
+Renewables are defined as clean Net Zero
+or carbon free all these definitions or
+
+ align:start position:0%
+or carbon free all these definitions or
+ 
+
+ align:start position:0%
+or carbon free all these definitions or
+these uh various descriptors have
+
+ align:start position:0%
+these uh various descriptors have
+ 
+
+ align:start position:0%
+these uh various descriptors have
+different uh slightly different meanings
+
+ align:start position:0%
+different uh slightly different meanings
+ 
+
+ align:start position:0%
+different uh slightly different meanings
+and of course I want to emphasize Energy
+
+ align:start position:0%
+and of course I want to emphasize Energy
+ 
+
+ align:start position:0%
+and of course I want to emphasize Energy
+Efficiency is also necessary for us to
+
+ align:start position:0%
+Efficiency is also necessary for us to
+ 
+
+ align:start position:0%
+Efficiency is also necessary for us to
+achieve decarbonization the 100
+
+ align:start position:0%
+achieve decarbonization the 100
+ 
+
+ align:start position:0%
+achieve decarbonization the 100
+renewable scenario I showed you in the
+
+ align:start position:0%
+renewable scenario I showed you in the
+ 
+
+ align:start position:0%
+renewable scenario I showed you in the
+last slide and for the Williams NL
+
+ align:start position:0%
+last slide and for the Williams NL
+ 
+
+ align:start position:0%
+last slide and for the Williams NL
+papers and many most of the
+
+ align:start position:0%
+papers and many most of the
+ 
+
+ align:start position:0%
+papers and many most of the
+decomposition studies all emphasize the
+
+ align:start position:0%
+decomposition studies all emphasize the
+ 
+
+ align:start position:0%
+decomposition studies all emphasize the
+fact that we can't build renewable
+
+ align:start position:0%
+fact that we can't build renewable
+ 
+
+ align:start position:0%
+fact that we can't build renewable
+resources as fast as we need to to meet
+
+ align:start position:0%
+resources as fast as we need to to meet
+ 
+
+ align:start position:0%
+resources as fast as we need to to meet
+our mid-century goal so it's going to be
+
+ align:start position:0%
+our mid-century goal so it's going to be
+ 
+
+ align:start position:0%
+our mid-century goal so it's going to be
+necessary to use Energy Efficiency and
+
+ align:start position:0%
+necessary to use Energy Efficiency and
+ 
+
+ align:start position:0%
+necessary to use Energy Efficiency and
+that can be the Technologies products
+
+ align:start position:0%
+that can be the Technologies products
+ 
+
+ align:start position:0%
+that can be the Technologies products
+services or changes in behaviors or
+
+ align:start position:0%
+services or changes in behaviors or
+ 
+
+ align:start position:0%
+services or changes in behaviors or
+expectations and reduce the energy
+
+ align:start position:0%
+expectations and reduce the energy
+ 
+
+ align:start position:0%
+expectations and reduce the energy
+required for certain processes or tasks
+
+ align:start position:0%
+required for certain processes or tasks
+ 
+
+ align:start position:0%
+required for certain processes or tasks
+or services and we also talked about
+
+ align:start position:0%
+or services and we also talked about
+ 
+
+ align:start position:0%
+or services and we also talked about
+about that a few lectures ago
+
+ align:start position:0%
+about that a few lectures ago
+ 
+
+ align:start position:0%
+about that a few lectures ago
+and the other thing I want to emphasize
+
+ align:start position:0%
+and the other thing I want to emphasize
+ 
+
+ align:start position:0%
+and the other thing I want to emphasize
+about your renewal toolbox is that it
+
+ align:start position:0%
+about your renewal toolbox is that it
+ 
+
+ align:start position:0%
+about your renewal toolbox is that it
+has different limitations we have to
+
+ align:start position:0%
+has different limitations we have to
+ 
+
+ align:start position:0%
+has different limitations we have to
+think about some key factors or key
+
+ align:start position:0%
+think about some key factors or key
+ 
+
+ align:start position:0%
+think about some key factors or key
+categories of problems to solve
+
+ align:start position:0%
+categories of problems to solve
+ 
+
+ align:start position:0%
+categories of problems to solve
+first there's the total potential of
+
+ align:start position:0%
+first there's the total potential of
+ 
+
+ align:start position:0%
+first there's the total potential of
+renewable energy that we can achieve in
+
+ align:start position:0%
+renewable energy that we can achieve in
+ 
+
+ align:start position:0%
+renewable energy that we can achieve in
+a meaningful period of time
+
+ align:start position:0%
+a meaningful period of time
+ 
+
+ align:start position:0%
+a meaningful period of time
+second as you may have heard many
+
+ align:start position:0%
+second as you may have heard many
+ 
+
+ align:start position:0%
+second as you may have heard many
+renewable Technologies may be
+
+ align:start position:0%
+renewable Technologies may be
+ 
+
+ align:start position:0%
+renewable Technologies may be
+intermittent in terms of how they derive
+
+ align:start position:0%
+intermittent in terms of how they derive
+ 
+
+ align:start position:0%
+intermittent in terms of how they derive
+energy from natural processes and
+
+ align:start position:0%
+energy from natural processes and
+ 
+
+ align:start position:0%
+energy from natural processes and
+something I've emphasized in this class
+
+ align:start position:0%
+something I've emphasized in this class
+ 
+
+ align:start position:0%
+something I've emphasized in this class
+and I think is particularly relevant to
+
+ align:start position:0%
+and I think is particularly relevant to
+ 
+
+ align:start position:0%
+and I think is particularly relevant to
+cities and land use is how much land use
+
+ align:start position:0%
+cities and land use is how much land use
+ 
+
+ align:start position:0%
+cities and land use is how much land use
+or how much land TIG is required to
+
+ align:start position:0%
+or how much land TIG is required to
+ 
+
+ align:start position:0%
+or how much land TIG is required to
+build renewable resources renewable
+
+ align:start position:0%
+build renewable resources renewable
+ 
+
+ align:start position:0%
+build renewable resources renewable
+resources are quite often less energy
+
+ align:start position:0%
+resources are quite often less energy
+ 
+
+ align:start position:0%
+resources are quite often less energy
+dense than a fossil fuel energy systems
+
+ align:start position:0%
+dense than a fossil fuel energy systems
+ 
+
+ align:start position:0%
+dense than a fossil fuel energy systems
+but just to give you a sense of kind of
+
+ align:start position:0%
+but just to give you a sense of kind of
+ 
+
+ align:start position:0%
+but just to give you a sense of kind of
+the intermittency or what the kind of
+
+ align:start position:0%
+the intermittency or what the kind of
+ 
+
+ align:start position:0%
+the intermittency or what the kind of
+sources of energy for wind and solar
+
+ align:start position:0%
+sources of energy for wind and solar
+ 
+
+ align:start position:0%
+sources of energy for wind and solar
+look like there's a few kind of fun
+
+ align:start position:0%
+look like there's a few kind of fun
+ 
+
+ align:start position:0%
+look like there's a few kind of fun
+fun visualizations I'll click on here in
+
+ align:start position:0%
+fun visualizations I'll click on here in
+ 
+
+ align:start position:0%
+fun visualizations I'll click on here in
+a moment
+
+ align:start position:0%
+a moment
+ 
+
+ align:start position:0%
+a moment
+if we look at the wind right now across
+
+ align:start position:0%
+if we look at the wind right now across
+ 
+
+ align:start position:0%
+if we look at the wind right now across
+the United States that first link takes
+
+ align:start position:0%
+the United States that first link takes
+ 
+
+ align:start position:0%
+the United States that first link takes
+us to this wind map that you can see
+
+ align:start position:0%
+us to this wind map that you can see
+ 
+
+ align:start position:0%
+us to this wind map that you can see
+here you can see that the wind has a
+
+ align:start position:0%
+here you can see that the wind has a
+ 
+
+ align:start position:0%
+here you can see that the wind has a
+directionality it's concentrated in some
+
+ align:start position:0%
+directionality it's concentrated in some
+ 
+
+ align:start position:0%
+directionality it's concentrated in some
+places quite clearly blowing in the
+
+ align:start position:0%
+places quite clearly blowing in the
+ 
+
+ align:start position:0%
+places quite clearly blowing in the
+Mountain West and the Midwest and Texas
+
+ align:start position:0%
+Mountain West and the Midwest and Texas
+ 
+
+ align:start position:0%
+Mountain West and the Midwest and Texas
+much more than it is here on the East
+
+ align:start position:0%
+much more than it is here on the East
+ 
+
+ align:start position:0%
+much more than it is here on the East
+Coast where we I'm recording this video
+
+ align:start position:0%
+Coast where we I'm recording this video
+ 
+
+ align:start position:0%
+Coast where we I'm recording this video
+if we look at the global map of wind you
+
+ align:start position:0%
+if we look at the global map of wind you
+ 
+
+ align:start position:0%
+if we look at the global map of wind you
+can also see something something very
+
+ align:start position:0%
+can also see something something very
+ 
+
+ align:start position:0%
+can also see something something very
+different you can see that the wind is
+
+ align:start position:0%
+different you can see that the wind is
+ 
+
+ align:start position:0%
+different you can see that the wind is
+much stronger over the oceans than it is
+
+ align:start position:0%
+much stronger over the oceans than it is
+ 
+
+ align:start position:0%
+much stronger over the oceans than it is
+over the land
+
+ align:start position:0%
+over the land
+ 
+
+ align:start position:0%
+over the land
+uh this is a pretty neat little
+
+ align:start position:0%
+uh this is a pretty neat little
+ 
+
+ align:start position:0%
+uh this is a pretty neat little
+visualization you can actually see any
+
+ align:start position:0%
+visualization you can actually see any
+ 
+
+ align:start position:0%
+visualization you can actually see any
+part of the world and see where the wind
+
+ align:start position:0%
+part of the world and see where the wind
+ 
+
+ align:start position:0%
+part of the world and see where the wind
+is and of course these little vectors
+
+ align:start position:0%
+is and of course these little vectors
+ 
+
+ align:start position:0%
+is and of course these little vectors
+and these kind of fields of vectors show
+
+ align:start position:0%
+and these kind of fields of vectors show
+ 
+
+ align:start position:0%
+and these kind of fields of vectors show
+you that uh there may be a storm off of
+
+ align:start position:0%
+you that uh there may be a storm off of
+ 
+
+ align:start position:0%
+you that uh there may be a storm off of
+I think Mexico here there may be some
+
+ align:start position:0%
+I think Mexico here there may be some
+ 
+
+ align:start position:0%
+I think Mexico here there may be some
+very strong winds in the upper North
+
+ align:start position:0%
+very strong winds in the upper North
+ 
+
+ align:start position:0%
+very strong winds in the upper North
+Atlantic but you can see in almost all
+
+ align:start position:0%
+Atlantic but you can see in almost all
+ 
+
+ align:start position:0%
+Atlantic but you can see in almost all
+the cases that the wind is much stronger
+
+ align:start position:0%
+the cases that the wind is much stronger
+ 
+
+ align:start position:0%
+the cases that the wind is much stronger
+offshore than it is onshore and that'll
+
+ align:start position:0%
+offshore than it is onshore and that'll
+ 
+
+ align:start position:0%
+offshore than it is onshore and that'll
+be a key theme we'll talk about today
+
+ align:start position:0%
+be a key theme we'll talk about today
+ 
+
+ align:start position:0%
+be a key theme we'll talk about today
+so just going back to our slides on wind
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again to emphasize that your renewal
+
+ align:start position:0%
+again to emphasize that your renewal
+ 
+
+ align:start position:0%
+again to emphasize that your renewal
+toolbox is going to require deploying
+
+ align:start position:0%
+toolbox is going to require deploying
+ 
+
+ align:start position:0%
+toolbox is going to require deploying
+these at scale that's going to require
+
+ align:start position:0%
+these at scale that's going to require
+ 
+
+ align:start position:0%
+these at scale that's going to require
+us to essentially build a new Energy
+
+ align:start position:0%
+us to essentially build a new Energy
+ 
+
+ align:start position:0%
+us to essentially build a new Energy
+System to avoid climate change and so
+
+ align:start position:0%
+System to avoid climate change and so
+ 
+
+ align:start position:0%
+System to avoid climate change and so
+you just want to focus on the building
+
+ align:start position:0%
+you just want to focus on the building
+ 
+
+ align:start position:0%
+you just want to focus on the building
+block for a second and what the
+
+ align:start position:0%
+block for a second and what the
+ 
+
+ align:start position:0%
+block for a second and what the
+challenge is uh the first building block
+
+ align:start position:0%
+challenge is uh the first building block
+ 
+
+ align:start position:0%
+challenge is uh the first building block
+is going to be a solar
+
+ align:start position:0%
+is going to be a solar
+ 
+
+ align:start position:0%
+is going to be a solar
+I'll talk about how a Solar Technologies
+
+ align:start position:0%
+I'll talk about how a Solar Technologies
+ 
+
+ align:start position:0%
+I'll talk about how a Solar Technologies
+have drastically cheaper in the next
+
+ align:start position:0%
+have drastically cheaper in the next
+ 
+
+ align:start position:0%
+have drastically cheaper in the next
+lecture but we have to build
+
+ align:start position:0%
+lecture but we have to build
+ 
+
+ align:start position:0%
+lecture but we have to build
+approximately 47 times more solar in the
+
+ align:start position:0%
+approximately 47 times more solar in the
+ 
+
+ align:start position:0%
+approximately 47 times more solar in the
+United States to achieve our mid-century
+
+ align:start position:0%
+United States to achieve our mid-century
+ 
+
+ align:start position:0%
+United States to achieve our mid-century
+goals wind as another building block
+
+ align:start position:0%
+goals wind as another building block
+ 
+
+ align:start position:0%
+goals wind as another building block
+that has been very successful probably
+
+ align:start position:0%
+that has been very successful probably
+ 
+
+ align:start position:0%
+that has been very successful probably
+our highest amount of capacity of
+
+ align:start position:0%
+our highest amount of capacity of
+ 
+
+ align:start position:0%
+our highest amount of capacity of
+renewable energy coming from wind right
+
+ align:start position:0%
+renewable energy coming from wind right
+ 
+
+ align:start position:0%
+renewable energy coming from wind right
+now we still have to actually increase
+
+ align:start position:0%
+now we still have to actually increase
+ 
+
+ align:start position:0%
+now we still have to actually increase
+the amount we've built by 28 times over
+
+ align:start position:0%
+the amount we've built by 28 times over
+ 
+
+ align:start position:0%
+the amount we've built by 28 times over
+what we've built over the last 40 years
+
+ align:start position:0%
+what we've built over the last 40 years
+ 
+
+ align:start position:0%
+what we've built over the last 40 years
+and storage geothermal analog
+
+ align:start position:0%
+and storage geothermal analog
+ 
+
+ align:start position:0%
+and storage geothermal analog
+electrolysis that can be used to create
+
+ align:start position:0%
+electrolysis that can be used to create
+ 
+
+ align:start position:0%
+electrolysis that can be used to create
+hydrogen from renewable resources those
+
+ align:start position:0%
+hydrogen from renewable resources those
+ 
+
+ align:start position:0%
+hydrogen from renewable resources those
+are fundamentally building blocks that
+
+ align:start position:0%
+are fundamentally building blocks that
+ 
+
+ align:start position:0%
+are fundamentally building blocks that
+are going to be part of the annual
+
+ align:start position:0%
+are going to be part of the annual
+ 
+
+ align:start position:0%
+are going to be part of the annual
+toolbox but I want to emphasize this
+
+ align:start position:0%
+toolbox but I want to emphasize this
+ 
+
+ align:start position:0%
+toolbox but I want to emphasize this
+toolbox is probably the toolbox you'll
+
+ align:start position:0%
+toolbox is probably the toolbox you'll
+ 
+
+ align:start position:0%
+toolbox is probably the toolbox you'll
+be using for much of your careers and to
+
+ align:start position:0%
+be using for much of your careers and to
+ 
+
+ align:start position:0%
+be using for much of your careers and to
+your credit or to your advantage all
+
+ align:start position:0%
+your credit or to your advantage all
+ 
+
+ align:start position:0%
+your credit or to your advantage all
+these building blocks have gotten
+
+ align:start position:0%
+these building blocks have gotten
+ 
+
+ align:start position:0%
+these building blocks have gotten
+increasingly cheap over time will
+
+ align:start position:0%
+increasingly cheap over time will
+ 
+
+ align:start position:0%
+increasingly cheap over time will
+probably get cheaper over time
+
+ align:start position:0%
+probably get cheaper over time
+ 
+
+ align:start position:0%
+probably get cheaper over time
+all you have to figure out in your
+
+ align:start position:0%
+all you have to figure out in your
+ 
+
+ align:start position:0%
+all you have to figure out in your
+careers is
+
+ align:start position:0%
+careers is
+ 
+
+ align:start position:0%
+careers is
+um give you a to-do list for your
+
+ align:start position:0%
+um give you a to-do list for your
+ 
+
+ align:start position:0%
+um give you a to-do list for your
+careers all you have to do is figure out
+
+ align:start position:0%
+careers all you have to do is figure out
+ 
+
+ align:start position:0%
+careers all you have to do is figure out
+how to finance these new technologies
+
+ align:start position:0%
+how to finance these new technologies
+ 
+
+ align:start position:0%
+how to finance these new technologies
+which sometimes have our higher upfront
+
+ align:start position:0%
+which sometimes have our higher upfront
+ 
+
+ align:start position:0%
+which sometimes have our higher upfront
+costs
+
+ align:start position:0%
+costs
+ 
+
+ align:start position:0%
+costs
+all you should do is figure out how to
+
+ align:start position:0%
+all you should do is figure out how to
+ 
+
+ align:start position:0%
+all you should do is figure out how to
+install the capacity the 47 times more
+
+ align:start position:0%
+install the capacity the 47 times more
+ 
+
+ align:start position:0%
+install the capacity the 47 times more
+solar 28 times more win to generate
+
+ align:start position:0%
+solar 28 times more win to generate
+ 
+
+ align:start position:0%
+solar 28 times more win to generate
+electricity or energy
+
+ align:start position:0%
+electricity or energy
+ 
+
+ align:start position:0%
+electricity or energy
+you have to figure out how to transmit
+
+ align:start position:0%
+you have to figure out how to transmit
+ 
+
+ align:start position:0%
+you have to figure out how to transmit
+this power across by the places that is
+
+ align:start position:0%
+this power across by the places that is
+ 
+
+ align:start position:0%
+this power across by the places that is
+generated to the places that it's needed
+
+ align:start position:0%
+generated to the places that it's needed
+ 
+
+ align:start position:0%
+generated to the places that it's needed
+we'll have to figure out how to
+
+ align:start position:0%
+we'll have to figure out how to
+ 
+
+ align:start position:0%
+we'll have to figure out how to
+distribute this power within cities I'll
+
+ align:start position:0%
+distribute this power within cities I'll
+ 
+
+ align:start position:0%
+distribute this power within cities I'll
+have to figure out how to balance this
+
+ align:start position:0%
+have to figure out how to balance this
+ 
+
+ align:start position:0%
+have to figure out how to balance this
+power across the grid because
+
+ align:start position:0%
+power across the grid because
+ 
+
+ align:start position:0%
+power across the grid because
+electricity cannot very easily be stored
+
+ align:start position:0%
+electricity cannot very easily be stored
+ 
+
+ align:start position:0%
+electricity cannot very easily be stored
+though we'll talk about storage you have
+
+ align:start position:0%
+though we'll talk about storage you have
+ 
+
+ align:start position:0%
+though we'll talk about storage you have
+to figure out how to balance the system
+
+ align:start position:0%
+to figure out how to balance the system
+ 
+
+ align:start position:0%
+to figure out how to balance the system
+so that when you're generating power in
+
+ align:start position:0%
+so that when you're generating power in
+ 
+
+ align:start position:0%
+so that when you're generating power in
+one part of the continental US like you
+
+ align:start position:0%
+one part of the continental US like you
+ 
+
+ align:start position:0%
+one part of the continental US like you
+saw the wind blowing them out in the
+
+ align:start position:0%
+saw the wind blowing them out in the
+ 
+
+ align:start position:0%
+saw the wind blowing them out in the
+west it can be consumed elsewhere like
+
+ align:start position:0%
+west it can be consumed elsewhere like
+ 
+
+ align:start position:0%
+west it can be consumed elsewhere like
+on the West Coast
+
+ align:start position:0%
+on the West Coast
+ 
+
+ align:start position:0%
+on the West Coast
+you have to figure out how to make this
+
+ align:start position:0%
+you have to figure out how to make this
+ 
+
+ align:start position:0%
+you have to figure out how to make this
+grid reliable you have to figure out how
+
+ align:start position:0%
+grid reliable you have to figure out how
+ 
+
+ align:start position:0%
+grid reliable you have to figure out how
+to make this grid resilient in the face
+
+ align:start position:0%
+to make this grid resilient in the face
+ 
+
+ align:start position:0%
+to make this grid resilient in the face
+of increasing climate changes
+
+ align:start position:0%
+of increasing climate changes
+ 
+
+ align:start position:0%
+of increasing climate changes
+and of course you have to cite all these
+
+ align:start position:0%
+and of course you have to cite all these
+ 
+
+ align:start position:0%
+and of course you have to cite all these
+resources and all these transformation
+
+ align:start position:0%
+resources and all these transformation
+ 
+
+ align:start position:0%
+resources and all these transformation
+lines so again your renewable toolbox
+
+ align:start position:0%
+lines so again your renewable toolbox
+ 
+
+ align:start position:0%
+lines so again your renewable toolbox
+has fundamentally really interesting
+
+ align:start position:0%
+has fundamentally really interesting
+ 
+
+ align:start position:0%
+has fundamentally really interesting
+really increasingly cheap and cost
+
+ align:start position:0%
+really increasingly cheap and cost
+ 
+
+ align:start position:0%
+really increasingly cheap and cost
+effective building blocks on the
+
+ align:start position:0%
+effective building blocks on the
+ 
+
+ align:start position:0%
+effective building blocks on the
+left-hand side this is your to-do list
+
+ align:start position:0%
+left-hand side this is your to-do list
+ 
+
+ align:start position:0%
+left-hand side this is your to-do list
+to build a new Energy System on the
+
+ align:start position:0%
+to build a new Energy System on the
+ 
+
+ align:start position:0%
+to build a new Energy System on the
+right hand side
+
+ align:start position:0%
+right hand side
+ 
+
+ align:start position:0%
+right hand side
+so the agenda for our next few classes
+
+ align:start position:0%
+so the agenda for our next few classes
+ 
+
+ align:start position:0%
+so the agenda for our next few classes
+is going to emphasize a series of
+
+ align:start position:0%
+is going to emphasize a series of
+ 
+
+ align:start position:0%
+is going to emphasize a series of
+different Technologies and I'll try to
+
+ align:start position:0%
+different Technologies and I'll try to
+ 
+
+ align:start position:0%
+different Technologies and I'll try to
+teach you a series of different concepts
+
+ align:start position:0%
+teach you a series of different concepts
+ 
+
+ align:start position:0%
+teach you a series of different concepts
+that are useful to think about the
+
+ align:start position:0%
+that are useful to think about the
+ 
+
+ align:start position:0%
+that are useful to think about the
+nature of those Technologies so today
+
+ align:start position:0%
+nature of those Technologies so today
+ 
+
+ align:start position:0%
+nature of those Technologies so today
+we'll talk about win Basics and we'll
+
+ align:start position:0%
+we'll talk about win Basics and we'll
+ 
+
+ align:start position:0%
+we'll talk about win Basics and we'll
+use that to illustrate capacity factors
+
+ align:start position:0%
+use that to illustrate capacity factors
+ 
+
+ align:start position:0%
+use that to illustrate capacity factors
+and levelized costs of energy
+
+ align:start position:0%
+and levelized costs of energy
+ 
+
+ align:start position:0%
+and levelized costs of energy
+on the next lecture we'll talk about
+
+ align:start position:0%
+on the next lecture we'll talk about
+ 
+
+ align:start position:0%
+on the next lecture we'll talk about
+solar Basics including adoption costs
+
+ align:start position:0%
+solar Basics including adoption costs
+ 
+
+ align:start position:0%
+solar Basics including adoption costs
+learning curves and citing issues
+
+ align:start position:0%
+learning curves and citing issues
+ 
+
+ align:start position:0%
+learning curves and citing issues
+and then the third lecture from now
+
+ align:start position:0%
+and then the third lecture from now
+ 
+
+ align:start position:0%
+and then the third lecture from now
+we'll talk about storage and geothermal
+
+ align:start position:0%
+we'll talk about storage and geothermal
+ 
+
+ align:start position:0%
+we'll talk about storage and geothermal
+as examples of how we might develop new
+
+ align:start position:0%
+as examples of how we might develop new
+ 
+
+ align:start position:0%
+as examples of how we might develop new
+niches or new technologies in the
+
+ align:start position:0%
+niches or new technologies in the
+ 
+
+ align:start position:0%
+niches or new technologies in the
+existing Energy System
+
+ align:start position:0%
+existing Energy System
+ 
+
+ align:start position:0%
+existing Energy System
+uh renewable energy potential what is it
+
+ align:start position:0%
+uh renewable energy potential what is it
+ 
+
+ align:start position:0%
+uh renewable energy potential what is it
+uh there's a potential amount of
+
+ align:start position:0%
+uh there's a potential amount of
+ 
+
+ align:start position:0%
+uh there's a potential amount of
+renewable resource that can be generated
+
+ align:start position:0%
+renewable resource that can be generated
+ 
+
+ align:start position:0%
+renewable resource that can be generated
+if you want to see maps for pretty much
+
+ align:start position:0%
+if you want to see maps for pretty much
+ 
+
+ align:start position:0%
+if you want to see maps for pretty much
+every country in the world or globally
+
+ align:start position:0%
+every country in the world or globally
+ 
+
+ align:start position:0%
+every country in the world or globally
+you can see the international renewable
+
+ align:start position:0%
+you can see the international renewable
+ 
+
+ align:start position:0%
+you can see the international renewable
+energy agency uh Irena has a very good
+
+ align:start position:0%
+energy agency uh Irena has a very good
+ 
+
+ align:start position:0%
+energy agency uh Irena has a very good
+resource of renewable energy potential
+
+ align:start position:0%
+resource of renewable energy potential
+ 
+
+ align:start position:0%
+resource of renewable energy potential
+studies uh I already know it's found in
+
+ align:start position:0%
+studies uh I already know it's found in
+ 
+
+ align:start position:0%
+studies uh I already know it's found in
+2009 it's the agency specifically
+
+ align:start position:0%
+2009 it's the agency specifically
+ 
+
+ align:start position:0%
+2009 it's the agency specifically
+focused on Renewables if you go to this
+
+ align:start position:0%
+focused on Renewables if you go to this
+ 
+
+ align:start position:0%
+focused on Renewables if you go to this
+link you can see potential studies and
+
+ align:start position:0%
+link you can see potential studies and
+ 
+
+ align:start position:0%
+link you can see potential studies and
+they have 10 000 studies on five major
+
+ align:start position:0%
+they have 10 000 studies on five major
+ 
+
+ align:start position:0%
+they have 10 000 studies on five major
+categories of Renewables and I think you
+
+ align:start position:0%
+categories of Renewables and I think you
+ 
+
+ align:start position:0%
+categories of Renewables and I think you
+can see which countries have been
+
+ align:start position:0%
+can see which countries have been
+ 
+
+ align:start position:0%
+can see which countries have been
+studied for your papers for this class
+
+ align:start position:0%
+studied for your papers for this class
+ 
+
+ align:start position:0%
+studied for your papers for this class
+so getting back to this graph I touched
+
+ align:start position:0%
+so getting back to this graph I touched
+ 
+
+ align:start position:0%
+so getting back to this graph I touched
+on this a little bit I think in the last
+
+ align:start position:0%
+on this a little bit I think in the last
+ 
+
+ align:start position:0%
+on this a little bit I think in the last
+lecture the price of electricity from
+
+ align:start position:0%
+lecture the price of electricity from
+ 
+
+ align:start position:0%
+lecture the price of electricity from
+new power plants has drastically changed
+
+ align:start position:0%
+new power plants has drastically changed
+ 
+
+ align:start position:0%
+new power plants has drastically changed
+over time a lot of these arrows in 2009
+
+ align:start position:0%
+over time a lot of these arrows in 2009
+ 
+
+ align:start position:0%
+over time a lot of these arrows in 2009
+nuclear has gone more expensive solar
+
+ align:start position:0%
+nuclear has gone more expensive solar
+ 
+
+ align:start position:0%
+nuclear has gone more expensive solar
+thermal has decreased slightly full
+
+ align:start position:0%
+thermal has decreased slightly full
+ 
+
+ align:start position:0%
+thermal has decreased slightly full
+power has not changed at all natural gas
+
+ align:start position:0%
+power has not changed at all natural gas
+ 
+
+ align:start position:0%
+power has not changed at all natural gas
+peaking plants and combined cycle plants
+
+ align:start position:0%
+peaking plants and combined cycle plants
+ 
+
+ align:start position:0%
+peaking plants and combined cycle plants
+have both decreased in the cost of
+
+ align:start position:0%
+have both decreased in the cost of
+ 
+
+ align:start position:0%
+have both decreased in the cost of
+electricity of new power plants but of
+
+ align:start position:0%
+electricity of new power plants but of
+ 
+
+ align:start position:0%
+electricity of new power plants but of
+course the two most drastic lines or the
+
+ align:start position:0%
+course the two most drastic lines or the
+ 
+
+ align:start position:0%
+course the two most drastic lines or the
+steepest slopes on this chart
+
+ align:start position:0%
+steepest slopes on this chart
+ 
+
+ align:start position:0%
+steepest slopes on this chart
+is the price of electricity from solar
+
+ align:start position:0%
+is the price of electricity from solar
+ 
+
+ align:start position:0%
+is the price of electricity from solar
+declining by about 90 in the last 10
+
+ align:start position:0%
+declining by about 90 in the last 10
+ 
+
+ align:start position:0%
+declining by about 90 in the last 10
+years and the price of onshore wind
+
+ align:start position:0%
+years and the price of onshore wind
+ 
+
+ align:start position:0%
+years and the price of onshore wind
+electricity depending about 70 over the
+
+ align:start position:0%
+electricity depending about 70 over the
+ 
+
+ align:start position:0%
+electricity depending about 70 over the
+last 10 years
+
+ align:start position:0%
+last 10 years
+ 
+
+ align:start position:0%
+last 10 years
+just again highlight that the price of
+
+ align:start position:0%
+just again highlight that the price of
+ 
+
+ align:start position:0%
+just again highlight that the price of
+onshore with electricity is declined by
+
+ align:start position:0%
+onshore with electricity is declined by
+ 
+
+ align:start position:0%
+onshore with electricity is declined by
+70 in the past 10 years and we have a
+
+ align:start position:0%
+70 in the past 10 years and we have a
+ 
+
+ align:start position:0%
+70 in the past 10 years and we have a
+very large installed base of wind
+
+ align:start position:0%
+very large installed base of wind
+ 
+
+ align:start position:0%
+very large installed base of wind
+just to kind of look at our win Basics
+
+ align:start position:0%
+just to kind of look at our win Basics
+ 
+
+ align:start position:0%
+just to kind of look at our win Basics
+uh these are all graphs from The High
+
+ align:start position:0%
+uh these are all graphs from The High
+ 
+
+ align:start position:0%
+uh these are all graphs from The High
+chapter that you all read for this class
+
+ align:start position:0%
+chapter that you all read for this class
+ 
+
+ align:start position:0%
+chapter that you all read for this class
+wind power is essentially just picking a
+
+ align:start position:0%
+wind power is essentially just picking a
+ 
+
+ align:start position:0%
+wind power is essentially just picking a
+wind you have some kind of volume air
+
+ align:start position:0%
+wind you have some kind of volume air
+ 
+
+ align:start position:0%
+wind you have some kind of volume air
+hit your wind turbine it gets slightly
+
+ align:start position:0%
+hit your wind turbine it gets slightly
+ 
+
+ align:start position:0%
+hit your wind turbine it gets slightly
+displaced by the Obstacle of the wind
+
+ align:start position:0%
+displaced by the Obstacle of the wind
+ 
+
+ align:start position:0%
+displaced by the Obstacle of the wind
+turbine until it blows and you're taking
+
+ align:start position:0%
+turbine until it blows and you're taking
+ 
+
+ align:start position:0%
+turbine until it blows and you're taking
+some amount of energy off out of the
+
+ align:start position:0%
+some amount of energy off out of the
+ 
+
+ align:start position:0%
+some amount of energy off out of the
+wind this rule of thumb in makai's book
+
+ align:start position:0%
+wind this rule of thumb in makai's book
+ 
+
+ align:start position:0%
+wind this rule of thumb in makai's book
+is that the wind turbine should be about
+
+ align:start position:0%
+is that the wind turbine should be about
+ 
+
+ align:start position:0%
+is that the wind turbine should be about
+five diameters apart I think that's
+
+ align:start position:0%
+five diameters apart I think that's
+ 
+
+ align:start position:0%
+five diameters apart I think that's
+probably changed and it's gotten more
+
+ align:start position:0%
+probably changed and it's gotten more
+ 
+
+ align:start position:0%
+probably changed and it's gotten more
+sophisticated over time Michael Howland
+
+ align:start position:0%
+sophisticated over time Michael Howland
+ 
+
+ align:start position:0%
+sophisticated over time Michael Howland
+a new faculty member in the department
+
+ align:start position:0%
+a new faculty member in the department
+ 
+
+ align:start position:0%
+a new faculty member in the department
+of civil engineering studies uh the
+
+ align:start position:0%
+of civil engineering studies uh the
+ 
+
+ align:start position:0%
+of civil engineering studies uh the
+operation of wind turbine leaves on how
+
+ align:start position:0%
+operation of wind turbine leaves on how
+ 
+
+ align:start position:0%
+operation of wind turbine leaves on how
+to optimize them
+
+ align:start position:0%
+to optimize them
+ 
+
+ align:start position:0%
+to optimize them
+and of course the important point that
+
+ align:start position:0%
+and of course the important point that
+ 
+
+ align:start position:0%
+and of course the important point that
+Makai makes is that the wind speed
+
+ align:start position:0%
+Makai makes is that the wind speed
+ 
+
+ align:start position:0%
+Makai makes is that the wind speed
+changes versus the height off of the
+
+ align:start position:0%
+changes versus the height off of the
+ 
+
+ align:start position:0%
+changes versus the height off of the
+ground you can see that the wind speed
+
+ align:start position:0%
+ground you can see that the wind speed
+ 
+
+ align:start position:0%
+ground you can see that the wind speed
+comes quite a bit higher and the power
+
+ align:start position:0%
+comes quite a bit higher and the power
+ 
+
+ align:start position:0%
+comes quite a bit higher and the power
+density that you can extract from the
+
+ align:start position:0%
+density that you can extract from the
+ 
+
+ align:start position:0%
+density that you can extract from the
+wind goes up actually non-linearly off
+
+ align:start position:0%
+wind goes up actually non-linearly off
+ 
+
+ align:start position:0%
+wind goes up actually non-linearly off
+the ground so in other words the bigger
+
+ align:start position:0%
+the ground so in other words the bigger
+ 
+
+ align:start position:0%
+the ground so in other words the bigger
+you make the turbine the higher off the
+
+ align:start position:0%
+you make the turbine the higher off the
+ 
+
+ align:start position:0%
+you make the turbine the higher off the
+ground the more wind power is there the
+
+ align:start position:0%
+ground the more wind power is there the
+ 
+
+ align:start position:0%
+ground the more wind power is there the
+mowing speed is there and the power
+
+ align:start position:0%
+mowing speed is there and the power
+ 
+
+ align:start position:0%
+mowing speed is there and the power
+density goes at the nonlinear function
+
+ align:start position:0%
+density goes at the nonlinear function
+ 
+
+ align:start position:0%
+density goes at the nonlinear function
+of the wind speed the more power can be
+
+ align:start position:0%
+of the wind speed the more power can be
+ 
+
+ align:start position:0%
+of the wind speed the more power can be
+extracted from this volume of air
+
+ align:start position:0%
+extracted from this volume of air
+ 
+
+ align:start position:0%
+extracted from this volume of air
+that's going to be our occurring theme
+
+ align:start position:0%
+that's going to be our occurring theme
+ 
+
+ align:start position:0%
+that's going to be our occurring theme
+as we look at wind turbines and wind
+
+ align:start position:0%
+as we look at wind turbines and wind
+ 
+
+ align:start position:0%
+as we look at wind turbines and wind
+power and where might go
+
+ align:start position:0%
+power and where might go
+ 
+
+ align:start position:0%
+power and where might go
+uh looking the department of energy
+
+ align:start position:0%
+uh looking the department of energy
+ 
+
+ align:start position:0%
+uh looking the department of energy
+United States produces a land-based wind
+
+ align:start position:0%
+United States produces a land-based wind
+ 
+
+ align:start position:0%
+United States produces a land-based wind
+market report in 2022 here they just map
+
+ align:start position:0%
+market report in 2022 here they just map
+ 
+
+ align:start position:0%
+market report in 2022 here they just map
+the wind speed at 100 meters off the
+
+ align:start position:0%
+the wind speed at 100 meters off the
+ 
+
+ align:start position:0%
+the wind speed at 100 meters off the
+ground they map it against these
+
+ align:start position:0%
+ground they map it against these
+ 
+
+ align:start position:0%
+ground they map it against these
+different regions which are tracked
+
+ align:start position:0%
+different regions which are tracked
+ 
+
+ align:start position:0%
+different regions which are tracked
+along different Regional transmission or
+
+ align:start position:0%
+along different Regional transmission or
+ 
+
+ align:start position:0%
+along different Regional transmission or
+interest system interconnected system
+
+ align:start position:0%
+interest system interconnected system
+ 
+
+ align:start position:0%
+interest system interconnected system
+operators these are all different
+
+ align:start position:0%
+operators these are all different
+ 
+
+ align:start position:0%
+operators these are all different
+regions of the electric grid it's
+
+ align:start position:0%
+regions of the electric grid it's
+ 
+
+ align:start position:0%
+regions of the electric grid it's
+relevant because wind is going to plug
+
+ align:start position:0%
+relevant because wind is going to plug
+ 
+
+ align:start position:0%
+relevant because wind is going to plug
+into regions of electric grid that are
+
+ align:start position:0%
+into regions of electric grid that are
+ 
+
+ align:start position:0%
+into regions of electric grid that are
+governed in different ways but the most
+
+ align:start position:0%
+governed in different ways but the most
+ 
+
+ align:start position:0%
+governed in different ways but the most
+important thing is that you can see that
+
+ align:start position:0%
+important thing is that you can see that
+ 
+
+ align:start position:0%
+important thing is that you can see that
+most of the power wind power are the
+
+ align:start position:0%
+most of the power wind power are the
+ 
+
+ align:start position:0%
+most of the power wind power are the
+wind speed in the United States is
+
+ align:start position:0%
+wind speed in the United States is
+ 
+
+ align:start position:0%
+wind speed in the United States is
+concentrated here in the middle part of
+
+ align:start position:0%
+concentrated here in the middle part of
+ 
+
+ align:start position:0%
+concentrated here in the middle part of
+the country that's concentrated in exits
+
+ align:start position:0%
+the country that's concentrated in exits
+ 
+
+ align:start position:0%
+the country that's concentrated in exits
+this is the region of the electric
+
+ align:start position:0%
+this is the region of the electric
+ 
+
+ align:start position:0%
+this is the region of the electric
+reliability Council of Texas the
+
+ align:start position:0%
+reliability Council of Texas the
+ 
+
+ align:start position:0%
+reliability Council of Texas the
+Southwest power pool constitutes much of
+
+ align:start position:0%
+Southwest power pool constitutes much of
+ 
+
+ align:start position:0%
+Southwest power pool constitutes much of
+the Midwest here and the Mid-Continental
+
+ align:start position:0%
+the Midwest here and the Mid-Continental
+ 
+
+ align:start position:0%
+the Midwest here and the Mid-Continental
+inter-system operator operates much in
+
+ align:start position:0%
+inter-system operator operates much in
+ 
+
+ align:start position:0%
+inter-system operator operates much in
+this part of the Midwest so our wind
+
+ align:start position:0%
+this part of the Midwest so our wind
+ 
+
+ align:start position:0%
+this part of the Midwest so our wind
+power is clearly concentrated on land in
+
+ align:start position:0%
+power is clearly concentrated on land in
+ 
+
+ align:start position:0%
+power is clearly concentrated on land in
+the middle of our country
+
+ align:start position:0%
+the middle of our country
+ 
+
+ align:start position:0%
+the middle of our country
+and if you look at the win market report
+
+ align:start position:0%
+and if you look at the win market report
+ 
+
+ align:start position:0%
+and if you look at the win market report
+it's been exciting to pack it over the
+
+ align:start position:0%
+it's been exciting to pack it over the
+ 
+
+ align:start position:0%
+it's been exciting to pack it over the
+last few years because you can see over
+
+ align:start position:0%
+last few years because you can see over
+ 
+
+ align:start position:0%
+last few years because you can see over
+the last few years these are the
+
+ align:start position:0%
+the last few years these are the
+ 
+
+ align:start position:0%
+the last few years these are the
+cumulative total capacity added
+
+ align:start position:0%
+cumulative total capacity added
+ 
+
+ align:start position:0%
+cumulative total capacity added
+and the cumulative total capacity has of
+
+ align:start position:0%
+and the cumulative total capacity has of
+ 
+
+ align:start position:0%
+and the cumulative total capacity has of
+course gone steadily up over the last 22
+
+ align:start position:0%
+course gone steadily up over the last 22
+ 
+
+ align:start position:0%
+course gone steadily up over the last 22
+years but if you look at the capacity
+
+ align:start position:0%
+years but if you look at the capacity
+ 
+
+ align:start position:0%
+years but if you look at the capacity
+Edition additions you can see that every
+
+ align:start position:0%
+Edition additions you can see that every
+ 
+
+ align:start position:0%
+Edition additions you can see that every
+single year we're adding much more
+
+ align:start position:0%
+single year we're adding much more
+ 
+
+ align:start position:0%
+single year we're adding much more
+capacity of wind power in fact until
+
+ align:start position:0%
+capacity of wind power in fact until
+ 
+
+ align:start position:0%
+capacity of wind power in fact until
+this last year until 2020 for four
+
+ align:start position:0%
+this last year until 2020 for four
+ 
+
+ align:start position:0%
+this last year until 2020 for four
+straight years the capacity had
+
+ align:start position:0%
+straight years the capacity had
+ 
+
+ align:start position:0%
+straight years the capacity had
+increased and you can see that almost
+
+ align:start position:0%
+increased and you can see that almost
+ 
+
+ align:start position:0%
+increased and you can see that almost
+quite regularly we're starting to break
+
+ align:start position:0%
+quite regularly we're starting to break
+ 
+
+ align:start position:0%
+quite regularly we're starting to break
+records for how much past they were
+
+ align:start position:0%
+records for how much past they were
+ 
+
+ align:start position:0%
+records for how much past they were
+adding in any given year
+
+ align:start position:0%
+adding in any given year
+ 
+
+ align:start position:0%
+adding in any given year
+2021 slowed slightly
+
+ align:start position:0%
+2021 slowed slightly
+ 
+
+ align:start position:0%
+2021 slowed slightly
+but you can see that a lot of this
+
+ align:start position:0%
+but you can see that a lot of this
+ 
+
+ align:start position:0%
+but you can see that a lot of this
+capacity is being added in certain
+
+ align:start position:0%
+capacity is being added in certain
+ 
+
+ align:start position:0%
+capacity is being added in certain
+regions and those are those three
+
+ align:start position:0%
+regions and those are those three
+ 
+
+ align:start position:0%
+regions and those are those three
+regions I showed you the map before
+
+ align:start position:0%
+regions I showed you the map before
+ 
+
+ align:start position:0%
+regions I showed you the map before
+Texas the Southwest power pool and the
+
+ align:start position:0%
+Texas the Southwest power pool and the
+ 
+
+ align:start position:0%
+Texas the Southwest power pool and the
+Mid-Continental inter-system operator
+
+ align:start position:0%
+Mid-Continental inter-system operator
+ 
+
+ align:start position:0%
+Mid-Continental inter-system operator
+if you look at where wind stands in our
+
+ align:start position:0%
+if you look at where wind stands in our
+ 
+
+ align:start position:0%
+if you look at where wind stands in our
+capacity conditions another exciting
+
+ align:start position:0%
+capacity conditions another exciting
+ 
+
+ align:start position:0%
+capacity conditions another exciting
+part of the story is that this is from
+
+ align:start position:0%
+part of the story is that this is from
+ 
+
+ align:start position:0%
+part of the story is that this is from
+the weed market report it shows Uber
+
+ align:start position:0%
+the weed market report it shows Uber
+ 
+
+ align:start position:0%
+the weed market report it shows Uber
+years well how much capacity how much
+
+ align:start position:0%
+years well how much capacity how much
+ 
+
+ align:start position:0%
+years well how much capacity how much
+capacity are we adding to the grid to
+
+ align:start position:0%
+capacity are we adding to the grid to
+ 
+
+ align:start position:0%
+capacity are we adding to the grid to
+generate electric power you can see
+
+ align:start position:0%
+generate electric power you can see
+ 
+
+ align:start position:0%
+generate electric power you can see
+overwhelmingly it is coming from wind
+
+ align:start position:0%
+overwhelmingly it is coming from wind
+ 
+
+ align:start position:0%
+overwhelmingly it is coming from wind
+solar and storage over the last few
+
+ align:start position:0%
+solar and storage over the last few
+ 
+
+ align:start position:0%
+solar and storage over the last few
+years natural gas and light blue have
+
+ align:start position:0%
+years natural gas and light blue have
+ 
+
+ align:start position:0%
+years natural gas and light blue have
+had some years of growth but it's
+
+ align:start position:0%
+had some years of growth but it's
+ 
+
+ align:start position:0%
+had some years of growth but it's
+steadily becoming a smaller part of our
+
+ align:start position:0%
+steadily becoming a smaller part of our
+ 
+
+ align:start position:0%
+steadily becoming a smaller part of our
+capacity additions our capacity
+
+ align:start position:0%
+capacity additions our capacity
+ 
+
+ align:start position:0%
+capacity additions our capacity
+additions to our electricity system are
+
+ align:start position:0%
+additions to our electricity system are
+ 
+
+ align:start position:0%
+additions to our electricity system are
+almost entirely wind solar and storage
+
+ align:start position:0%
+almost entirely wind solar and storage
+ 
+
+ align:start position:0%
+almost entirely wind solar and storage
+wind for the first time has I think
+
+ align:start position:0%
+wind for the first time has I think
+ 
+
+ align:start position:0%
+wind for the first time has I think
+fallen in the second place from solar it
+
+ align:start position:0%
+fallen in the second place from solar it
+ 
+
+ align:start position:0%
+fallen in the second place from solar it
+used to be a few years here it looked
+
+ align:start position:0%
+used to be a few years here it looked
+ 
+
+ align:start position:0%
+used to be a few years here it looked
+like solar is actually larger but now
+
+ align:start position:0%
+like solar is actually larger but now
+ 
+
+ align:start position:0%
+like solar is actually larger but now
+swim is clearly in the second position
+
+ align:start position:0%
+swim is clearly in the second position
+ 
+
+ align:start position:0%
+swim is clearly in the second position
+solar is the biggest capacity Edition
+
+ align:start position:0%
+solar is the biggest capacity Edition
+ 
+
+ align:start position:0%
+solar is the biggest capacity Edition
+being added to the grid this is the
+
+ align:start position:0%
+being added to the grid this is the
+ 
+
+ align:start position:0%
+being added to the grid this is the
+capacity the ability to generate power
+
+ align:start position:0%
+capacity the ability to generate power
+ 
+
+ align:start position:0%
+capacity the ability to generate power
+in gigawatts that doesn't necessarily
+
+ align:start position:0%
+in gigawatts that doesn't necessarily
+ 
+
+ align:start position:0%
+in gigawatts that doesn't necessarily
+mean that capacity is being used all the
+
+ align:start position:0%
+mean that capacity is being used all the
+ 
+
+ align:start position:0%
+mean that capacity is being used all the
+time which we will talk about we talk
+
+ align:start position:0%
+time which we will talk about we talk
+ 
+
+ align:start position:0%
+time which we will talk about we talk
+about intermittency
+
+ align:start position:0%
+about intermittency
+ 
+
+ align:start position:0%
+about intermittency
+but finally if we look at the different
+
+ align:start position:0%
+but finally if we look at the different
+ 
+
+ align:start position:0%
+but finally if we look at the different
+regions again wind is quite dominant in
+
+ align:start position:0%
+regions again wind is quite dominant in
+ 
+
+ align:start position:0%
+regions again wind is quite dominant in
+the middle of the country in the
+
+ align:start position:0%
+the middle of the country in the
+ 
+
+ align:start position:0%
+the middle of the country in the
+southwest power pool in the electric
+
+ align:start position:0%
+southwest power pool in the electric
+ 
+
+ align:start position:0%
+southwest power pool in the electric
+reliability Council of Texas and the mid
+
+ align:start position:0%
+reliability Council of Texas and the mid
+ 
+
+ align:start position:0%
+reliability Council of Texas and the mid
+Continental inter-system operator you
+
+ align:start position:0%
+Continental inter-system operator you
+ 
+
+ align:start position:0%
+Continental inter-system operator you
+can see all these errors are quite
+
+ align:start position:0%
+can see all these errors are quite
+ 
+
+ align:start position:0%
+can see all these errors are quite
+dominated by wind other parts of the
+
+ align:start position:0%
+dominated by wind other parts of the
+ 
+
+ align:start position:0%
+dominated by wind other parts of the
+country are more dominated by solar and
+
+ align:start position:0%
+country are more dominated by solar and
+ 
+
+ align:start position:0%
+country are more dominated by solar and
+natural gas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to give you an example of what
+
+ align:start position:0%
+so just to give you an example of what
+ 
+
+ align:start position:0%
+so just to give you an example of what
+these optional wind turbines look like
+
+ align:start position:0%
+these optional wind turbines look like
+ 
+
+ align:start position:0%
+these optional wind turbines look like
+this is actually a plain uh picture I
+
+ align:start position:0%
+this is actually a plain uh picture I
+ 
+
+ align:start position:0%
+this is actually a plain uh picture I
+took out of a plane window and I was
+
+ align:start position:0%
+took out of a plane window and I was
+ 
+
+ align:start position:0%
+took out of a plane window and I was
+flying I think over the North Sea in
+
+ align:start position:0%
+flying I think over the North Sea in
+ 
+
+ align:start position:0%
+flying I think over the North Sea in
+Europe this is I think off the coast of
+
+ align:start position:0%
+Europe this is I think off the coast of
+ 
+
+ align:start position:0%
+Europe this is I think off the coast of
+Poland and this just gives you a sense
+
+ align:start position:0%
+Poland and this just gives you a sense
+ 
+
+ align:start position:0%
+Poland and this just gives you a sense
+of what you can see from a plane there's
+
+ align:start position:0%
+of what you can see from a plane there's
+ 
+
+ align:start position:0%
+of what you can see from a plane there's
+a little yep probably not a little ship
+
+ align:start position:0%
+a little yep probably not a little ship
+ 
+
+ align:start position:0%
+a little yep probably not a little ship
+sailing between these wind turbines but
+
+ align:start position:0%
+sailing between these wind turbines but
+ 
+
+ align:start position:0%
+sailing between these wind turbines but
+these wind turbines are simply off tour
+
+ align:start position:0%
+these wind turbines are simply off tour
+ 
+
+ align:start position:0%
+these wind turbines are simply off tour
+where we know more wind is flowing
+
+ align:start position:0%
+where we know more wind is flowing
+ 
+
+ align:start position:0%
+where we know more wind is flowing
+I have to give you another picture this
+
+ align:start position:0%
+I have to give you another picture this
+ 
+
+ align:start position:0%
+I have to give you another picture this
+is a picture of uh of officero wind
+
+ align:start position:0%
+is a picture of uh of officero wind
+ 
+
+ align:start position:0%
+is a picture of uh of officero wind
+turbines in Europe which tends to have
+
+ align:start position:0%
+turbines in Europe which tends to have
+ 
+
+ align:start position:0%
+turbines in Europe which tends to have
+shallower Waters in the U.S but you have
+
+ align:start position:0%
+shallower Waters in the U.S but you have
+ 
+
+ align:start position:0%
+shallower Waters in the U.S but you have
+it looks like a ferry and you have a
+
+ align:start position:0%
+it looks like a ferry and you have a
+ 
+
+ align:start position:0%
+it looks like a ferry and you have a
+sailboat sailing through
+
+ align:start position:0%
+sailboat sailing through
+ 
+
+ align:start position:0%
+sailboat sailing through
+and the reason why it's exciting to talk
+
+ align:start position:0%
+and the reason why it's exciting to talk
+ 
+
+ align:start position:0%
+and the reason why it's exciting to talk
+about uh wind offshore is that if you
+
+ align:start position:0%
+about uh wind offshore is that if you
+ 
+
+ align:start position:0%
+about uh wind offshore is that if you
+look at the average wind speed above
+
+ align:start position:0%
+look at the average wind speed above
+ 
+
+ align:start position:0%
+look at the average wind speed above
+North America you can see that there is
+
+ align:start position:0%
+North America you can see that there is
+ 
+
+ align:start position:0%
+North America you can see that there is
+this concentration of wind power in the
+
+ align:start position:0%
+this concentration of wind power in the
+ 
+
+ align:start position:0%
+this concentration of wind power in the
+center of the country but very
+
+ align:start position:0%
+center of the country but very
+ 
+
+ align:start position:0%
+center of the country but very
+importantly you actually have very high
+
+ align:start position:0%
+importantly you actually have very high
+ 
+
+ align:start position:0%
+importantly you actually have very high
+wind speeds off the coast of the U.S
+
+ align:start position:0%
+wind speeds off the coast of the U.S
+ 
+
+ align:start position:0%
+wind speeds off the coast of the U.S
+this probably doesn't go all the way
+
+ align:start position:0%
+this probably doesn't go all the way
+ 
+
+ align:start position:0%
+this probably doesn't go all the way
+out into the ocean this is probably just
+
+ align:start position:0%
+out into the ocean this is probably just
+ 
+
+ align:start position:0%
+out into the ocean this is probably just
+map long Continental Health but you can
+
+ align:start position:0%
+map long Continental Health but you can
+ 
+
+ align:start position:0%
+map long Continental Health but you can
+see the concentrations of wind are just
+
+ align:start position:0%
+see the concentrations of wind are just
+ 
+
+ align:start position:0%
+see the concentrations of wind are just
+as high if not higher than the middle of
+
+ align:start position:0%
+as high if not higher than the middle of
+ 
+
+ align:start position:0%
+as high if not higher than the middle of
+the country but also quite importantly
+
+ align:start position:0%
+the country but also quite importantly
+ 
+
+ align:start position:0%
+the country but also quite importantly
+there these wind powers or wind
+
+ align:start position:0%
+there these wind powers or wind
+ 
+
+ align:start position:0%
+there these wind powers or wind
+potential are located very close to the
+
+ align:start position:0%
+potential are located very close to the
+ 
+
+ align:start position:0%
+potential are located very close to the
+population center of the us we know most
+
+ align:start position:0%
+population center of the us we know most
+ 
+
+ align:start position:0%
+population center of the us we know most
+the population of the US is actually
+
+ align:start position:0%
+the population of the US is actually
+ 
+
+ align:start position:0%
+the population of the US is actually
+complicated along the coasts and so it's
+
+ align:start position:0%
+complicated along the coasts and so it's
+ 
+
+ align:start position:0%
+complicated along the coasts and so it's
+important to generate renewable energy
+
+ align:start position:0%
+important to generate renewable energy
+ 
+
+ align:start position:0%
+important to generate renewable energy
+close to the populations because it
+
+ align:start position:0%
+close to the populations because it
+ 
+
+ align:start position:0%
+close to the populations because it
+minimizes our need to transmit the power
+
+ align:start position:0%
+minimizes our need to transmit the power
+ 
+
+ align:start position:0%
+minimizes our need to transmit the power
+through the grid so we will need more
+
+ align:start position:0%
+through the grid so we will need more
+ 
+
+ align:start position:0%
+through the grid so we will need more
+transmission lines for the grid also
+
+ align:start position:0%
+transmission lines for the grid also
+ 
+
+ align:start position:0%
+transmission lines for the grid also
+so just to give you a sense of what
+
+ align:start position:0%
+so just to give you a sense of what
+ 
+
+ align:start position:0%
+so just to give you a sense of what
+these floating what floating wind
+
+ align:start position:0%
+these floating what floating wind
+ 
+
+ align:start position:0%
+these floating what floating wind
+turbines can look like off the shore of
+
+ align:start position:0%
+turbines can look like off the shore of
+ 
+
+ align:start position:0%
+turbines can look like off the shore of
+the U.S here's three different ways of
+
+ align:start position:0%
+the U.S here's three different ways of
+ 
+
+ align:start position:0%
+the U.S here's three different ways of
+anchoring and floating wind turbine to
+
+ align:start position:0%
+anchoring and floating wind turbine to
+ 
+
+ align:start position:0%
+anchoring and floating wind turbine to
+the ocean floor you have one that has
+
+ align:start position:0%
+the ocean floor you have one that has
+ 
+
+ align:start position:0%
+the ocean floor you have one that has
+this big kind of counterweight to keep
+
+ align:start position:0%
+this big kind of counterweight to keep
+ 
+
+ align:start position:0%
+this big kind of counterweight to keep
+it upright you have these this kind of
+
+ align:start position:0%
+it upright you have these this kind of
+ 
+
+ align:start position:0%
+it upright you have these this kind of
+tripod system with three anchors and you
+
+ align:start position:0%
+tripod system with three anchors and you
+ 
+
+ align:start position:0%
+tripod system with three anchors and you
+have a different tripod system all meant
+
+ align:start position:0%
+have a different tripod system all meant
+ 
+
+ align:start position:0%
+have a different tripod system all meant
+to Anchor wind turbines offshore
+
+ align:start position:0%
+to Anchor wind turbines offshore
+ 
+
+ align:start position:0%
+to Anchor wind turbines offshore
+of course just to give you a sense
+
+ align:start position:0%
+of course just to give you a sense
+ 
+
+ align:start position:0%
+of course just to give you a sense
+of where this technical potential is
+
+ align:start position:0%
+of where this technical potential is
+ 
+
+ align:start position:0%
+of where this technical potential is
+located if according to the end result
+
+ align:start position:0%
+located if according to the end result
+ 
+
+ align:start position:0%
+located if according to the end result
+study if you look a place to have
+
+ align:start position:0%
+study if you look a place to have
+ 
+
+ align:start position:0%
+study if you look a place to have
+greater than seven meters per second
+
+ align:start position:0%
+greater than seven meters per second
+ 
+
+ align:start position:0%
+greater than seven meters per second
+wind speed less than a thousand meters
+
+ align:start position:0%
+wind speed less than a thousand meters
+ 
+
+ align:start position:0%
+wind speed less than a thousand meters
+in depth less than 60 meters in depth
+
+ align:start position:0%
+in depth less than 60 meters in depth
+ 
+
+ align:start position:0%
+in depth less than 60 meters in depth
+the great lakes and if you try to avoid
+
+ align:start position:0%
+the great lakes and if you try to avoid
+ 
+
+ align:start position:0%
+the great lakes and if you try to avoid
+conflicting use and environmental
+
+ align:start position:0%
+conflicting use and environmental
+ 
+
+ align:start position:0%
+conflicting use and environmental
+extensions you can see that there they
+
+ align:start position:0%
+extensions you can see that there they
+ 
+
+ align:start position:0%
+extensions you can see that there they
+break each of these bars into the places
+
+ align:start position:0%
+break each of these bars into the places
+ 
+
+ align:start position:0%
+break each of these bars into the places
+where the water depth is greater than 60
+
+ align:start position:0%
+where the water depth is greater than 60
+ 
+
+ align:start position:0%
+where the water depth is greater than 60
+meters and less than 60 meters
+
+ align:start position:0%
+meters and less than 60 meters
+ 
+
+ align:start position:0%
+meters and less than 60 meters
+and you can see surprisingly that one of
+
+ align:start position:0%
+and you can see surprisingly that one of
+ 
+
+ align:start position:0%
+and you can see surprisingly that one of
+the largest states for technical energy
+
+ align:start position:0%
+the largest states for technical energy
+ 
+
+ align:start position:0%
+the largest states for technical energy
+potential is Massachusetts and then
+
+ align:start position:0%
+potential is Massachusetts and then
+ 
+
+ align:start position:0%
+potential is Massachusetts and then
+Florida and then Texas and so on so
+
+ align:start position:0%
+Florida and then Texas and so on so
+ 
+
+ align:start position:0%
+Florida and then Texas and so on so
+these are all offshore wind potentials
+
+ align:start position:0%
+these are all offshore wind potentials
+ 
+
+ align:start position:0%
+these are all offshore wind potentials
+for different states but this is also to
+
+ align:start position:0%
+for different states but this is also to
+ 
+
+ align:start position:0%
+for different states but this is also to
+give you a sense of why it's so
+
+ align:start position:0%
+give you a sense of why it's so
+ 
+
+ align:start position:0%
+give you a sense of why it's so
+important that Massachusetts is pursuing
+
+ align:start position:0%
+important that Massachusetts is pursuing
+ 
+
+ align:start position:0%
+important that Massachusetts is pursuing
+offshore wind energy this is the chance
+
+ align:start position:0%
+offshore wind energy this is the chance
+ 
+
+ align:start position:0%
+offshore wind energy this is the chance
+that Massachusetts has to develop a
+
+ align:start position:0%
+that Massachusetts has to develop a
+ 
+
+ align:start position:0%
+that Massachusetts has to develop a
+renewable energy resources in a highly
+
+ align:start position:0%
+renewable energy resources in a highly
+ 
+
+ align:start position:0%
+renewable energy resources in a highly
+dense area of the country a highly
+
+ align:start position:0%
+dense area of the country a highly
+ 
+
+ align:start position:0%
+dense area of the country a highly
+populated area of the country like
+
+ align:start position:0%
+populated area of the country like
+ 
+
+ align:start position:0%
+populated area of the country like
+Massachusetts we're not going to build
+
+ align:start position:0%
+Massachusetts we're not going to build
+ 
+
+ align:start position:0%
+Massachusetts we're not going to build
+we're not going to be able to build as
+
+ align:start position:0%
+we're not going to be able to build as
+ 
+
+ align:start position:0%
+we're not going to be able to build as
+much solar as other parts of the country
+
+ align:start position:0%
+much solar as other parts of the country
+ 
+
+ align:start position:0%
+much solar as other parts of the country
+and frankly it's not very sunny
+
+ align:start position:0%
+and frankly it's not very sunny
+ 
+
+ align:start position:0%
+and frankly it's not very sunny
+Massachusetts compared to Arizona or
+
+ align:start position:0%
+Massachusetts compared to Arizona or
+ 
+
+ align:start position:0%
+Massachusetts compared to Arizona or
+Hawaii so offshore wind is probably
+
+ align:start position:0%
+Hawaii so offshore wind is probably
+ 
+
+ align:start position:0%
+Hawaii so offshore wind is probably
+going to be our biggest opportunity for
+
+ align:start position:0%
+going to be our biggest opportunity for
+ 
+
+ align:start position:0%
+going to be our biggest opportunity for
+building renewable energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now what's really exciting is if you
+
+ align:start position:0%
+now what's really exciting is if you
+ 
+
+ align:start position:0%
+now what's really exciting is if you
+look at the Boe the usdoe also does an
+
+ align:start position:0%
+look at the Boe the usdoe also does an
+ 
+
+ align:start position:0%
+look at the Boe the usdoe also does an
+offshore Wing market report every year
+
+ align:start position:0%
+offshore Wing market report every year
+ 
+
+ align:start position:0%
+offshore Wing market report every year
+I've been updating this and so actually
+
+ align:start position:0%
+I've been updating this and so actually
+ 
+
+ align:start position:0%
+I've been updating this and so actually
+it's interesting when you look at the
+
+ align:start position:0%
+it's interesting when you look at the
+ 
+
+ align:start position:0%
+it's interesting when you look at the
+graphics in the report every year they
+
+ align:start position:0%
+graphics in the report every year they
+ 
+
+ align:start position:0%
+graphics in the report every year they
+change because austral win is growing in
+
+ align:start position:0%
+change because austral win is growing in
+ 
+
+ align:start position:0%
+change because austral win is growing in
+fact in fact basically exploding and its
+
+ align:start position:0%
+fact in fact basically exploding and its
+ 
+
+ align:start position:0%
+fact in fact basically exploding and its
+potential so uh last year I think when I
+
+ align:start position:0%
+potential so uh last year I think when I
+ 
+
+ align:start position:0%
+potential so uh last year I think when I
+looked at this map they had the entire
+
+ align:start position:0%
+looked at this map they had the entire
+ 
+
+ align:start position:0%
+looked at this map they had the entire
+Atlantic post was on one map and there
+
+ align:start position:0%
+Atlantic post was on one map and there
+ 
+
+ align:start position:0%
+Atlantic post was on one map and there
+was I think about 20 planned projects
+
+ align:start position:0%
+was I think about 20 planned projects
+ 
+
+ align:start position:0%
+was I think about 20 planned projects
+now there's about 20 31 planned projects
+
+ align:start position:0%
+now there's about 20 31 planned projects
+ 
+
+ align:start position:0%
+now there's about 20 31 planned projects
+in the North Atlantic alone they also
+
+ align:start position:0%
+in the North Atlantic alone they also
+ 
+
+ align:start position:0%
+in the North Atlantic alone they also
+actually sorry 32 because they show uh
+
+ align:start position:0%
+actually sorry 32 because they show uh
+ 
+
+ align:start position:0%
+actually sorry 32 because they show uh
+Lake Erie having a offshore wind project
+
+ align:start position:0%
+Lake Erie having a offshore wind project
+ 
+
+ align:start position:0%
+Lake Erie having a offshore wind project
+some fresh water wind projects there's
+
+ align:start position:0%
+some fresh water wind projects there's
+ 
+
+ align:start position:0%
+some fresh water wind projects there's
+one all the way up in off the coast of
+
+ align:start position:0%
+one all the way up in off the coast of
+ 
+
+ align:start position:0%
+one all the way up in off the coast of
+Maine and you can see this on this graph
+
+ align:start position:0%
+Maine and you can see this on this graph
+ 
+
+ align:start position:0%
+Maine and you can see this on this graph
+that there's about 32 planned win
+
+ align:start position:0%
+that there's about 32 planned win
+ 
+
+ align:start position:0%
+that there's about 32 planned win
+projects
+
+ align:start position:0%
+projects
+ 
+
+ align:start position:0%
+projects
+they all are in different areas off the
+
+ align:start position:0%
+they all are in different areas off the
+ 
+
+ align:start position:0%
+they all are in different areas off the
+coast you can see they occur at
+
+ align:start position:0%
+coast you can see they occur at
+ 
+
+ align:start position:0%
+coast you can see they occur at
+different bathymetric depths they are
+
+ align:start position:0%
+different bathymetric depths they are
+ 
+
+ align:start position:0%
+different bathymetric depths they are
+some of them are leased some of them are
+
+ align:start position:0%
+some of them are leased some of them are
+ 
+
+ align:start position:0%
+some of them are leased some of them are
+dormant areas but these are all areas
+
+ align:start position:0%
+dormant areas but these are all areas
+ 
+
+ align:start position:0%
+dormant areas but these are all areas
+that have explored for offshore wind
+
+ align:start position:0%
+that have explored for offshore wind
+ 
+
+ align:start position:0%
+that have explored for offshore wind
+if you look at the Pacific coast and the
+
+ align:start position:0%
+if you look at the Pacific coast and the
+ 
+
+ align:start position:0%
+if you look at the Pacific coast and the
+South Atlantic now they have separate
+
+ align:start position:0%
+South Atlantic now they have separate
+ 
+
+ align:start position:0%
+South Atlantic now they have separate
+Maps broken out just for these areas you
+
+ align:start position:0%
+Maps broken out just for these areas you
+ 
+
+ align:start position:0%
+Maps broken out just for these areas you
+can see that on the west coast off of
+
+ align:start position:0%
+can see that on the west coast off of
+ 
+
+ align:start position:0%
+can see that on the west coast off of
+Oregon and California there's a number
+
+ align:start position:0%
+Oregon and California there's a number
+ 
+
+ align:start position:0%
+Oregon and California there's a number
+of off-road wind projects planned
+
+ align:start position:0%
+of off-road wind projects planned
+ 
+
+ align:start position:0%
+of off-road wind projects planned
+there's officer when projects planned
+
+ align:start position:0%
+there's officer when projects planned
+ 
+
+ align:start position:0%
+there's officer when projects planned
+off in Hawaii now and leaving the south
+
+ align:start position:0%
+off in Hawaii now and leaving the south
+ 
+
+ align:start position:0%
+off in Hawaii now and leaving the south
+at Landing these are all areas in the
+
+ align:start position:0%
+at Landing these are all areas in the
+ 
+
+ align:start position:0%
+at Landing these are all areas in the
+Gulf of Mexico these are all areas that
+
+ align:start position:0%
+Gulf of Mexico these are all areas that
+ 
+
+ align:start position:0%
+Gulf of Mexico these are all areas that
+weren't even mapped in the last off-road
+
+ align:start position:0%
+weren't even mapped in the last off-road
+ 
+
+ align:start position:0%
+weren't even mapped in the last off-road
+we've marked a report from just last
+
+ align:start position:0%
+we've marked a report from just last
+ 
+
+ align:start position:0%
+we've marked a report from just last
+year so clearly this is an area that is
+
+ align:start position:0%
+year so clearly this is an area that is
+ 
+
+ align:start position:0%
+year so clearly this is an area that is
+growing very rapidly
+
+ align:start position:0%
+growing very rapidly
+ 
+
+ align:start position:0%
+growing very rapidly
+if we look at the pipeline for offshore
+
+ align:start position:0%
+if we look at the pipeline for offshore
+ 
+
+ align:start position:0%
+if we look at the pipeline for offshore
+wind the Striking thing about it to you
+
+ align:start position:0%
+wind the Striking thing about it to you
+ 
+
+ align:start position:0%
+wind the Striking thing about it to you
+should be this classification from what
+
+ align:start position:0%
+should be this classification from what
+ 
+
+ align:start position:0%
+should be this classification from what
+we actually have operating from what's
+
+ align:start position:0%
+we actually have operating from what's
+ 
+
+ align:start position:0%
+we actually have operating from what's
+under construction from what's financial
+
+ align:start position:0%
+under construction from what's financial
+ 
+
+ align:start position:0%
+under construction from what's financial
+opposed what's been approved what's
+
+ align:start position:0%
+opposed what's been approved what's
+ 
+
+ align:start position:0%
+opposed what's been approved what's
+waiting for permitting areas that are
+
+ align:start position:0%
+waiting for permitting areas that are
+ 
+
+ align:start position:0%
+waiting for permitting areas that are
+under site control and areas that are
+
+ align:start position:0%
+under site control and areas that are
+ 
+
+ align:start position:0%
+under site control and areas that are
+being planned if you add all these parts
+
+ align:start position:0%
+being planned if you add all these parts
+ 
+
+ align:start position:0%
+being planned if you add all these parts
+up you get the total pipeline of off
+
+ align:start position:0%
+up you get the total pipeline of off
+ 
+
+ align:start position:0%
+up you get the total pipeline of off
+throw wind expected what you should
+
+ align:start position:0%
+throw wind expected what you should
+ 
+
+ align:start position:0%
+throw wind expected what you should
+notice about this is that four we have
+
+ align:start position:0%
+notice about this is that four we have
+ 
+
+ align:start position:0%
+notice about this is that four we have
+about 40 000 megawatts of optimal wind
+
+ align:start position:0%
+about 40 000 megawatts of optimal wind
+ 
+
+ align:start position:0%
+about 40 000 megawatts of optimal wind
+that's in the pipeline
+
+ align:start position:0%
+that's in the pipeline
+ 
+
+ align:start position:0%
+that's in the pipeline
+that's up about 35
+
+ align:start position:0%
+that's up about 35
+ 
+
+ align:start position:0%
+that's up about 35
+000 megawatts just last year alone but
+
+ align:start position:0%
+000 megawatts just last year alone but
+ 
+
+ align:start position:0%
+000 megawatts just last year alone but
+they're really striking thing to you
+
+ align:start position:0%
+they're really striking thing to you
+ 
+
+ align:start position:0%
+they're really striking thing to you
+should be that of the 40 000 megawatts
+
+ align:start position:0%
+should be that of the 40 000 megawatts
+ 
+
+ align:start position:0%
+should be that of the 40 000 megawatts
+we have planned we only have 42
+
+ align:start position:0%
+we have planned we only have 42
+ 
+
+ align:start position:0%
+we have planned we only have 42
+megawatts operating that's actually I
+
+ align:start position:0%
+megawatts operating that's actually I
+ 
+
+ align:start position:0%
+megawatts operating that's actually I
+think exactly seven offshore wind
+
+ align:start position:0%
+think exactly seven offshore wind
+ 
+
+ align:start position:0%
+think exactly seven offshore wind
+turbines in the US right now
+
+ align:start position:0%
+turbines in the US right now
+ 
+
+ align:start position:0%
+turbines in the US right now
+five off of Rhode Island and two off of
+
+ align:start position:0%
+five off of Rhode Island and two off of
+ 
+
+ align:start position:0%
+five off of Rhode Island and two off of
+Virginia
+
+ align:start position:0%
+Virginia
+ 
+
+ align:start position:0%
+Virginia
+that's all we have operating when we go
+
+ align:start position:0%
+that's all we have operating when we go
+ 
+
+ align:start position:0%
+that's all we have operating when we go
+to under construction we're going to
+
+ align:start position:0%
+to under construction we're going to
+ 
+
+ align:start position:0%
+to under construction we're going to
+effectively I think increase that by a
+
+ align:start position:0%
+effectively I think increase that by a
+ 
+
+ align:start position:0%
+effectively I think increase that by a
+factor of 20. a lot of that is looks
+
+ align:start position:0%
+factor of 20. a lot of that is looks
+ 
+
+ align:start position:0%
+factor of 20. a lot of that is looks
+like in Massachusetts
+
+ align:start position:0%
+like in Massachusetts
+ 
+
+ align:start position:0%
+like in Massachusetts
+and we have very little that's their
+
+ align:start position:0%
+and we have very little that's their
+ 
+
+ align:start position:0%
+and we have very little that's their
+financially closed and financially
+
+ align:start position:0%
+financially closed and financially
+ 
+
+ align:start position:0%
+financially closed and financially
+approved but if you look at the states
+
+ align:start position:0%
+approved but if you look at the states
+ 
+
+ align:start position:0%
+approved but if you look at the states
+that are permitted off girl wind it's
+
+ align:start position:0%
+that are permitted off girl wind it's
+ 
+
+ align:start position:0%
+that are permitted off girl wind it's
+New York Massachusetts New Jersey North
+
+ align:start position:0%
+New York Massachusetts New Jersey North
+ 
+
+ align:start position:0%
+New York Massachusetts New Jersey North
+Carolina Virginia Maryland all up and
+
+ align:start position:0%
+Carolina Virginia Maryland all up and
+ 
+
+ align:start position:0%
+Carolina Virginia Maryland all up and
+down the East Coast we have a lot of
+
+ align:start position:0%
+down the East Coast we have a lot of
+ 
+
+ align:start position:0%
+down the East Coast we have a lot of
+Permitting a lot of permits that need to
+
+ align:start position:0%
+Permitting a lot of permits that need to
+ 
+
+ align:start position:0%
+Permitting a lot of permits that need to
+be extradited or need to be achieved or
+
+ align:start position:0%
+be extradited or need to be achieved or
+ 
+
+ align:start position:0%
+be extradited or need to be achieved or
+approved for these projects to go
+
+ align:start position:0%
+approved for these projects to go
+ 
+
+ align:start position:0%
+approved for these projects to go
+forward in terms of areas that have
+
+ align:start position:0%
+forward in terms of areas that have
+ 
+
+ align:start position:0%
+forward in terms of areas that have
+people developers have achieved psych
+
+ align:start position:0%
+people developers have achieved psych
+ 
+
+ align:start position:0%
+people developers have achieved psych
+control
+
+ align:start position:0%
+control
+ 
+
+ align:start position:0%
+control
+a large majority of that is in New York
+
+ align:start position:0%
+a large majority of that is in New York
+ 
+
+ align:start position:0%
+a large majority of that is in New York
+and Massachusetts
+
+ align:start position:0%
+and Massachusetts
+ 
+
+ align:start position:0%
+and Massachusetts
+and then in terms of planning we have
+
+ align:start position:0%
+and then in terms of planning we have
+ 
+
+ align:start position:0%
+and then in terms of planning we have
+quite a bit of planning for offshore
+
+ align:start position:0%
+quite a bit of planning for offshore
+ 
+
+ align:start position:0%
+quite a bit of planning for offshore
+wind in California but again if you add
+
+ align:start position:0%
+wind in California but again if you add
+ 
+
+ align:start position:0%
+wind in California but again if you add
+this whole pipeline together of the 40
+
+ align:start position:0%
+this whole pipeline together of the 40
+ 
+
+ align:start position:0%
+this whole pipeline together of the 40
+000 megawatts we have in our total
+
+ align:start position:0%
+000 megawatts we have in our total
+ 
+
+ align:start position:0%
+000 megawatts we have in our total
+pipeline we only have 42 megawatts
+
+ align:start position:0%
+pipeline we only have 42 megawatts
+ 
+
+ align:start position:0%
+pipeline we only have 42 megawatts
+operating which is 0.1 percent so we
+
+ align:start position:0%
+operating which is 0.1 percent so we
+ 
+
+ align:start position:0%
+operating which is 0.1 percent so we
+obviously have big Ambitions for
+
+ align:start position:0%
+obviously have big Ambitions for
+ 
+
+ align:start position:0%
+obviously have big Ambitions for
+offshore wind but we haven't realized
+
+ align:start position:0%
+offshore wind but we haven't realized
+ 
+
+ align:start position:0%
+offshore wind but we haven't realized
+99.9 of the actual wind capacity yet
+
+ align:start position:0%
+99.9 of the actual wind capacity yet
+ 
+
+ align:start position:0%
+99.9 of the actual wind capacity yet
+if you look at these states and the wind
+
+ align:start position:0%
+if you look at these states and the wind
+ 
+
+ align:start position:0%
+if you look at these states and the wind
+pipeline by state you can also think
+
+ align:start position:0%
+pipeline by state you can also think
+ 
+
+ align:start position:0%
+pipeline by state you can also think
+about how this fits into the energy
+
+ align:start position:0%
+about how this fits into the energy
+ 
+
+ align:start position:0%
+about how this fits into the energy
+policies currently quite a bit of New
+
+ align:start position:0%
+policies currently quite a bit of New
+ 
+
+ align:start position:0%
+policies currently quite a bit of New
+York's potential is under site control
+
+ align:start position:0%
+York's potential is under site control
+ 
+
+ align:start position:0%
+York's potential is under site control
+and quite a bit is being permitted and a
+
+ align:start position:0%
+and quite a bit is being permitted and a
+ 
+
+ align:start position:0%
+and quite a bit is being permitted and a
+very small course should be under
+
+ align:start position:0%
+very small course should be under
+ 
+
+ align:start position:0%
+very small course should be under
+construction a Massachusetts had less
+
+ align:start position:0%
+construction a Massachusetts had less
+ 
+
+ align:start position:0%
+construction a Massachusetts had less
+total wind offshore pipeline but has
+
+ align:start position:0%
+total wind offshore pipeline but has
+ 
+
+ align:start position:0%
+total wind offshore pipeline but has
+less Underside control more in
+
+ align:start position:0%
+less Underside control more in
+ 
+
+ align:start position:0%
+less Underside control more in
+permitting and more Under Construction
+
+ align:start position:0%
+permitting and more Under Construction
+ 
+
+ align:start position:0%
+permitting and more Under Construction
+New Jersey is almost entirely in the
+
+ align:start position:0%
+New Jersey is almost entirely in the
+ 
+
+ align:start position:0%
+New Jersey is almost entirely in the
+permitting phase and so on and so on
+
+ align:start position:0%
+permitting phase and so on and so on
+ 
+
+ align:start position:0%
+permitting phase and so on and so on
+but let's just to give you a sense of
+
+ align:start position:0%
+but let's just to give you a sense of
+ 
+
+ align:start position:0%
+but let's just to give you a sense of
+how big these wind turbine blades are
+
+ align:start position:0%
+how big these wind turbine blades are
+ 
+
+ align:start position:0%
+how big these wind turbine blades are
+this is a graphic of the heli X turbine
+
+ align:start position:0%
+this is a graphic of the heli X turbine
+ 
+
+ align:start position:0%
+this is a graphic of the heli X turbine
+a new turbine introduced by GE just a
+
+ align:start position:0%
+a new turbine introduced by GE just a
+ 
+
+ align:start position:0%
+a new turbine introduced by GE just a
+couple years ago
+
+ align:start position:0%
+couple years ago
+ 
+
+ align:start position:0%
+couple years ago
+and just to give you an example this is
+
+ align:start position:0%
+and just to give you an example this is
+ 
+
+ align:start position:0%
+and just to give you an example this is
+the Statue of Liberty of 305 feet the
+
+ align:start position:0%
+the Statue of Liberty of 305 feet the
+ 
+
+ align:start position:0%
+the Statue of Liberty of 305 feet the
+Empire State Building the Eiffel Tower
+
+ align:start position:0%
+Empire State Building the Eiffel Tower
+ 
+
+ align:start position:0%
+Empire State Building the Eiffel Tower
+the average onshore turbine is 466 feet
+
+ align:start position:0%
+the average onshore turbine is 466 feet
+ 
+
+ align:start position:0%
+the average onshore turbine is 466 feet
+tall the tallest U.S turbine the tallest
+
+ align:start position:0%
+tall the tallest U.S turbine the tallest
+ 
+
+ align:start position:0%
+tall the tallest U.S turbine the tallest
+turbine you've probably seen on Shore is
+
+ align:start position:0%
+turbine you've probably seen on Shore is
+ 
+
+ align:start position:0%
+turbine you've probably seen on Shore is
+574 feet tall the new GE heliight X is
+
+ align:start position:0%
+574 feet tall the new GE heliight X is
+ 
+
+ align:start position:0%
+574 feet tall the new GE heliight X is
+853 feet tall the current the five uh
+
+ align:start position:0%
+853 feet tall the current the five uh
+ 
+
+ align:start position:0%
+853 feet tall the current the five uh
+weed turbines we have operating in the
+
+ align:start position:0%
+weed turbines we have operating in the
+ 
+
+ align:start position:0%
+weed turbines we have operating in the
+US are off of Rhode Island are only 590
+
+ align:start position:0%
+US are off of Rhode Island are only 590
+ 
+
+ align:start position:0%
+US are off of Rhode Island are only 590
+feet tall so G can build these turbines
+
+ align:start position:0%
+feet tall so G can build these turbines
+ 
+
+ align:start position:0%
+feet tall so G can build these turbines
+they've introduced us as a product but
+
+ align:start position:0%
+they've introduced us as a product but
+ 
+
+ align:start position:0%
+they've introduced us as a product but
+clearly these turbines are very large I
+
+ align:start position:0%
+clearly these turbines are very large I
+ 
+
+ align:start position:0%
+clearly these turbines are very large I
+think each of those blades is one or two
+
+ align:start position:0%
+think each of those blades is one or two
+ 
+
+ align:start position:0%
+think each of those blades is one or two
+aircraft Wings long
+
+ align:start position:0%
+aircraft Wings long
+ 
+
+ align:start position:0%
+aircraft Wings long
+so you know just to give you a sense
+
+ align:start position:0%
+so you know just to give you a sense
+ 
+
+ align:start position:0%
+so you know just to give you a sense
+um the uh the total height of the new
+
+ align:start position:0%
+um the uh the total height of the new
+ 
+
+ align:start position:0%
+um the uh the total height of the new
+Helia X wind turbine is three times the
+
+ align:start position:0%
+Helia X wind turbine is three times the
+ 
+
+ align:start position:0%
+Helia X wind turbine is three times the
+flat iron building the diameter is
+
+ align:start position:0%
+flat iron building the diameter is
+ 
+
+ align:start position:0%
+flat iron building the diameter is
+equivalent to the Golden Gate Bridge
+
+ align:start position:0%
+equivalent to the Golden Gate Bridge
+ 
+
+ align:start position:0%
+equivalent to the Golden Gate Bridge
+tower height above the water and the
+
+ align:start position:0%
+tower height above the water and the
+ 
+
+ align:start position:0%
+tower height above the water and the
+surface of the blade sweep is equivalent
+
+ align:start position:0%
+surface of the blade sweep is equivalent
+ 
+
+ align:start position:0%
+surface of the blade sweep is equivalent
+to seven American football fields
+
+ align:start position:0%
+to seven American football fields
+ 
+
+ align:start position:0%
+to seven American football fields
+single one of these turbines can
+
+ align:start position:0%
+single one of these turbines can
+ 
+
+ align:start position:0%
+single one of these turbines can
+generate 67 gigawatt hours annually
+
+ align:start position:0%
+generate 67 gigawatt hours annually
+ 
+
+ align:start position:0%
+generate 67 gigawatt hours annually
+which is I guess if that's enough for 16
+
+ align:start position:0%
+which is I guess if that's enough for 16
+ 
+
+ align:start position:0%
+which is I guess if that's enough for 16
+000 European households for Turbine
+
+ align:start position:0%
+000 European households for Turbine
+ 
+
+ align:start position:0%
+000 European households for Turbine
+which I guess maybe by 8 000 American
+
+ align:start position:0%
+which I guess maybe by 8 000 American
+ 
+
+ align:start position:0%
+which I guess maybe by 8 000 American
+households the key point though is that
+
+ align:start position:0%
+households the key point though is that
+ 
+
+ align:start position:0%
+households the key point though is that
+how's the map I showed you before wind
+
+ align:start position:0%
+how's the map I showed you before wind
+ 
+
+ align:start position:0%
+how's the map I showed you before wind
+speeds are higher October the wind is
+
+ align:start position:0%
+speeds are higher October the wind is
+ 
+
+ align:start position:0%
+speeds are higher October the wind is
+steadier off the door if you put one of
+
+ align:start position:0%
+steadier off the door if you put one of
+ 
+
+ align:start position:0%
+steadier off the door if you put one of
+these turbines offshore it'll generate
+
+ align:start position:0%
+these turbines offshore it'll generate
+ 
+
+ align:start position:0%
+these turbines offshore it'll generate
+much more power than onshore provides
+
+ align:start position:0%
+much more power than onshore provides
+ 
+
+ align:start position:0%
+much more power than onshore provides
+but again we've yet to realize this
+
+ align:start position:0%
+but again we've yet to realize this
+ 
+
+ align:start position:0%
+but again we've yet to realize this
+technology American waters are deeper
+
+ align:start position:0%
+technology American waters are deeper
+ 
+
+ align:start position:0%
+technology American waters are deeper
+and stormier than European Waters
+
+ align:start position:0%
+and stormier than European Waters
+ 
+
+ align:start position:0%
+and stormier than European Waters
+Europeans I think have deployed some
+
+ align:start position:0%
+Europeans I think have deployed some
+ 
+
+ align:start position:0%
+Europeans I think have deployed some
+like five or six thousand offshore wind
+
+ align:start position:0%
+like five or six thousand offshore wind
+ 
+
+ align:start position:0%
+like five or six thousand offshore wind
+turbines we've only deployed seven of
+
+ align:start position:0%
+turbines we've only deployed seven of
+ 
+
+ align:start position:0%
+turbines we've only deployed seven of
+the us we have a lot of obstacles and
+
+ align:start position:0%
+the us we have a lot of obstacles and
+ 
+
+ align:start position:0%
+the us we have a lot of obstacles and
+bearish to overcome such as the right
+
+ align:start position:0%
+bearish to overcome such as the right
+ 
+
+ align:start position:0%
+bearish to overcome such as the right
+kinds of chips and the right kind of
+
+ align:start position:0%
+kinds of chips and the right kind of
+ 
+
+ align:start position:0%
+kinds of chips and the right kind of
+Workforce and the import capability that
+
+ align:start position:0%
+Workforce and the import capability that
+ 
+
+ align:start position:0%
+Workforce and the import capability that
+that are all necessary to build these
+
+ align:start position:0%
+that are all necessary to build these
+ 
+
+ align:start position:0%
+that are all necessary to build these
+offshore turbines let alone the undersea
+
+ align:start position:0%
+offshore turbines let alone the undersea
+ 
+
+ align:start position:0%
+offshore turbines let alone the undersea
+wiring required to transmit the powerful
+
+ align:start position:0%
+wiring required to transmit the powerful
+ 
+
+ align:start position:0%
+wiring required to transmit the powerful
+off your on to onshore and connected to
+
+ align:start position:0%
+off your on to onshore and connected to
+ 
+
+ align:start position:0%
+off your on to onshore and connected to
+our grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'll skip over more GE marketing
+
+ align:start position:0%
+I'll skip over more GE marketing
+ 
+
+ align:start position:0%
+I'll skip over more GE marketing
+literature one key point or kind of
+
+ align:start position:0%
+literature one key point or kind of
+ 
+
+ align:start position:0%
+literature one key point or kind of
+analytical concept I want to talk to you
+
+ align:start position:0%
+analytical concept I want to talk to you
+ 
+
+ align:start position:0%
+analytical concept I want to talk to you
+about is the idea of intermittency
+
+ align:start position:0%
+about is the idea of intermittency
+ 
+
+ align:start position:0%
+about is the idea of intermittency
+you've probably heard that Renewable
+
+ align:start position:0%
+you've probably heard that Renewable
+ 
+
+ align:start position:0%
+you've probably heard that Renewable
+Energy Technologies are intermittent and
+
+ align:start position:0%
+Energy Technologies are intermittent and
+ 
+
+ align:start position:0%
+Energy Technologies are intermittent and
+that the wind doesn't always blow the
+
+ align:start position:0%
+that the wind doesn't always blow the
+ 
+
+ align:start position:0%
+that the wind doesn't always blow the
+sun doesn't always shine but what we use
+
+ align:start position:0%
+sun doesn't always shine but what we use
+ 
+
+ align:start position:0%
+sun doesn't always shine but what we use
+to measure the output of these
+
+ align:start position:0%
+to measure the output of these
+ 
+
+ align:start position:0%
+to measure the output of these
+technology is a calculation called the
+
+ align:start position:0%
+technology is a calculation called the
+ 
+
+ align:start position:0%
+technology is a calculation called the
+capacity Factor the asciate factor is
+
+ align:start position:0%
+capacity Factor the asciate factor is
+ 
+
+ align:start position:0%
+capacity Factor the asciate factor is
+defined as the ratio of actual power
+
+ align:start position:0%
+defined as the ratio of actual power
+ 
+
+ align:start position:0%
+defined as the ratio of actual power
+produced divided by the maximum possible
+
+ align:start position:0%
+produced divided by the maximum possible
+ 
+
+ align:start position:0%
+produced divided by the maximum possible
+power over a period of time
+
+ align:start position:0%
+power over a period of time
+ 
+
+ align:start position:0%
+power over a period of time
+so the key points I want to make is that
+
+ align:start position:0%
+so the key points I want to make is that
+ 
+
+ align:start position:0%
+so the key points I want to make is that
+it's unitless it's a percentage this is
+
+ align:start position:0%
+it's unitless it's a percentage this is
+ 
+
+ align:start position:0%
+it's unitless it's a percentage this is
+the number or percentage that's
+
+ align:start position:0%
+the number or percentage that's
+ 
+
+ align:start position:0%
+the number or percentage that's
+empirically determined in real life
+
+ align:start position:0%
+empirically determined in real life
+ 
+
+ align:start position:0%
+empirically determined in real life
+operation and it changes seasonally the
+
+ align:start position:0%
+operation and it changes seasonally the
+ 
+
+ align:start position:0%
+operation and it changes seasonally the
+wind blows differently in different
+
+ align:start position:0%
+wind blows differently in different
+ 
+
+ align:start position:0%
+wind blows differently in different
+places in the summer than the winter
+
+ align:start position:0%
+places in the summer than the winter
+ 
+
+ align:start position:0%
+places in the summer than the winter
+obviously uh it's determined real life
+
+ align:start position:0%
+obviously uh it's determined real life
+ 
+
+ align:start position:0%
+obviously uh it's determined real life
+operation uh seasonally solar operates
+
+ align:start position:0%
+operation uh seasonally solar operates
+ 
+
+ align:start position:0%
+operation uh seasonally solar operates
+as different intermittency or different
+
+ align:start position:0%
+as different intermittency or different
+ 
+
+ align:start position:0%
+as different intermittency or different
+capacity in different times of the year
+
+ align:start position:0%
+capacity in different times of the year
+ 
+
+ align:start position:0%
+capacity in different times of the year
+so we measure the capacity factor and we
+
+ align:start position:0%
+so we measure the capacity factor and we
+ 
+
+ align:start position:0%
+so we measure the capacity factor and we
+use capacity Factor as kind of a general
+
+ align:start position:0%
+use capacity Factor as kind of a general
+ 
+
+ align:start position:0%
+use capacity Factor as kind of a general
+ratio that we can use to calculate how
+
+ align:start position:0%
+ratio that we can use to calculate how
+ 
+
+ align:start position:0%
+ratio that we can use to calculate how
+much energy we're going to produce from
+
+ align:start position:0%
+much energy we're going to produce from
+ 
+
+ align:start position:0%
+much energy we're going to produce from
+a given technology given that the
+
+ align:start position:0%
+a given technology given that the
+ 
+
+ align:start position:0%
+a given technology given that the
+resource that is harvesting the wind or
+
+ align:start position:0%
+resource that is harvesting the wind or
+ 
+
+ align:start position:0%
+resource that is harvesting the wind or
+the sun are not necessarily always there
+
+ align:start position:0%
+the sun are not necessarily always there
+ 
+
+ align:start position:0%
+the sun are not necessarily always there
+so just to give you a few other kind of
+
+ align:start position:0%
+so just to give you a few other kind of
+ 
+
+ align:start position:0%
+so just to give you a few other kind of
+key terms the nameplate generation
+
+ align:start position:0%
+key terms the nameplate generation
+ 
+
+ align:start position:0%
+key terms the nameplate generation
+capacity this is what the general the
+
+ align:start position:0%
+capacity this is what the general the
+ 
+
+ align:start position:0%
+capacity this is what the general the
+manufacturer says the technology can
+
+ align:start position:0%
+manufacturer says the technology can
+ 
+
+ align:start position:0%
+manufacturer says the technology can
+generate that's what the GE diagram the
+
+ align:start position:0%
+generate that's what the GE diagram the
+ 
+
+ align:start position:0%
+generate that's what the GE diagram the
+previous few slides showed you that the
+
+ align:start position:0%
+previous few slides showed you that the
+ 
+
+ align:start position:0%
+previous few slides showed you that the
+nameplate generation capacity and the
+
+ align:start position:0%
+nameplate generation capacity and the
+ 
+
+ align:start position:0%
+nameplate generation capacity and the
+nameplate generation capacity varies for
+
+ align:start position:0%
+nameplate generation capacity varies for
+ 
+
+ align:start position:0%
+nameplate generation capacity varies for
+different Technologies just to show you
+
+ align:start position:0%
+different Technologies just to show you
+ 
+
+ align:start position:0%
+different Technologies just to show you
+a two fossil fuel Technologies a coal
+
+ align:start position:0%
+a two fossil fuel Technologies a coal
+ 
+
+ align:start position:0%
+a two fossil fuel Technologies a coal
+fire power plant or a natural gas
+
+ align:start position:0%
+fire power plant or a natural gas
+ 
+
+ align:start position:0%
+fire power plant or a natural gas
+turbine
+
+ align:start position:0%
+turbine
+ 
+
+ align:start position:0%
+turbine
+if we skip
+
+ align:start position:0%
+if we skip
+ 
+
+ align:start position:0%
+if we skip
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+the tables put out by the U.S Energy
+
+ align:start position:0%
+the tables put out by the U.S Energy
+ 
+
+ align:start position:0%
+the tables put out by the U.S Energy
+Information and administration when I
+
+ align:start position:0%
+Information and administration when I
+ 
+
+ align:start position:0%
+Information and administration when I
+clicked on the link from the slides for
+
+ align:start position:0%
+clicked on the link from the slides for
+ 
+
+ align:start position:0%
+clicked on the link from the slides for
+the eia tables from the electric power
+
+ align:start position:0%
+the eia tables from the electric power
+ 
+
+ align:start position:0%
+the eia tables from the electric power
+monthly what you're looking at here is a
+
+ align:start position:0%
+monthly what you're looking at here is a
+ 
+
+ align:start position:0%
+monthly what you're looking at here is a
+table of capacity factors for utility
+
+ align:start position:0%
+table of capacity factors for utility
+ 
+
+ align:start position:0%
+table of capacity factors for utility
+scale generators primarily using fossil
+
+ align:start position:0%
+scale generators primarily using fossil
+ 
+
+ align:start position:0%
+scale generators primarily using fossil
+fuels so just look at the uh kind of
+
+ align:start position:0%
+fuels so just look at the uh kind of
+ 
+
+ align:start position:0%
+fuels so just look at the uh kind of
+aspects of this table you have the
+
+ align:start position:0%
+aspects of this table you have the
+ 
+
+ align:start position:0%
+aspects of this table you have the
+annual data this is annualized data you
+
+ align:start position:0%
+annual data this is annualized data you
+ 
+
+ align:start position:0%
+annual data this is annualized data you
+have the various fossil fuel generating
+
+ align:start position:0%
+have the various fossil fuel generating
+ 
+
+ align:start position:0%
+have the various fossil fuel generating
+Technologies to pull natural gas natural
+
+ align:start position:0%
+Technologies to pull natural gas natural
+ 
+
+ align:start position:0%
+Technologies to pull natural gas natural
+gas is broken into combined cycle gas
+
+ align:start position:0%
+gas is broken into combined cycle gas
+ 
+
+ align:start position:0%
+gas is broken into combined cycle gas
+turbines and peaking gas turbines annual
+
+ align:start position:0%
+turbines and peaking gas turbines annual
+ 
+
+ align:start position:0%
+turbines and peaking gas turbines annual
+petroleum steam turbine gas turbine the
+
+ align:start position:0%
+petroleum steam turbine gas turbine the
+ 
+
+ align:start position:0%
+petroleum steam turbine gas turbine the
+internal combustion and so on these are
+
+ align:start position:0%
+internal combustion and so on these are
+ 
+
+ align:start position:0%
+internal combustion and so on these are
+all categorized in different ways but
+
+ align:start position:0%
+all categorized in different ways but
+ 
+
+ align:start position:0%
+all categorized in different ways but
+then the important thing to notice is
+
+ align:start position:0%
+then the important thing to notice is
+ 
+
+ align:start position:0%
+then the important thing to notice is
+that there's a Time adjust capacity it
+
+ align:start position:0%
+that there's a Time adjust capacity it
+ 
+
+ align:start position:0%
+that there's a Time adjust capacity it
+varies across years and here's the
+
+ align:start position:0%
+varies across years and here's the
+ 
+
+ align:start position:0%
+varies across years and here's the
+capacity factor it's a percentage of the
+
+ align:start position:0%
+capacity factor it's a percentage of the
+ 
+
+ align:start position:0%
+capacity factor it's a percentage of the
+time that the resource is actually
+
+ align:start position:0%
+time that the resource is actually
+ 
+
+ align:start position:0%
+time that the resource is actually
+producing power so you can see that coal
+
+ align:start position:0%
+producing power so you can see that coal
+ 
+
+ align:start position:0%
+producing power so you can see that coal
+has a relatively high capacity factor I
+
+ align:start position:0%
+has a relatively high capacity factor I
+ 
+
+ align:start position:0%
+has a relatively high capacity factor I
+guess around 50 or 6 60 percent but
+
+ align:start position:0%
+guess around 50 or 6 60 percent but
+ 
+
+ align:start position:0%
+guess around 50 or 6 60 percent but
+that's still much lower when we talk
+
+ align:start position:0%
+that's still much lower when we talk
+ 
+
+ align:start position:0%
+that's still much lower when we talk
+about coal as a base load resource a lot
+
+ align:start position:0%
+about coal as a base load resource a lot
+ 
+
+ align:start position:0%
+about coal as a base load resource a lot
+of Advocates will say well we need coal
+
+ align:start position:0%
+of Advocates will say well we need coal
+ 
+
+ align:start position:0%
+of Advocates will say well we need coal
+as a base load resource because it's
+
+ align:start position:0%
+as a base load resource because it's
+ 
+
+ align:start position:0%
+as a base load resource because it's
+always providing power
+
+ align:start position:0%
+always providing power
+ 
+
+ align:start position:0%
+always providing power
+so this has the factor could be
+
+ align:start position:0%
+so this has the factor could be
+ 
+
+ align:start position:0%
+so this has the factor could be
+relatively low at 56 50 or 60 percent of
+
+ align:start position:0%
+relatively low at 56 50 or 60 percent of
+ 
+
+ align:start position:0%
+relatively low at 56 50 or 60 percent of
+the time it's only providing resources
+
+ align:start position:0%
+the time it's only providing resources
+ 
+
+ align:start position:0%
+the time it's only providing resources
+or energy
+
+ align:start position:0%
+or energy
+ 
+
+ align:start position:0%
+or energy
+for a couple of different reasons it
+
+ align:start position:0%
+for a couple of different reasons it
+ 
+
+ align:start position:0%
+for a couple of different reasons it
+could be because it's uh coal power
+
+ align:start position:0%
+could be because it's uh coal power
+ 
+
+ align:start position:0%
+could be because it's uh coal power
+plants are actually frequently down for
+
+ align:start position:0%
+plants are actually frequently down for
+ 
+
+ align:start position:0%
+plants are actually frequently down for
+maintenance it could also be that cool
+
+ align:start position:0%
+maintenance it could also be that cool
+ 
+
+ align:start position:0%
+maintenance it could also be that cool
+fire power plants are simply out
+
+ align:start position:0%
+fire power plants are simply out
+ 
+
+ align:start position:0%
+fire power plants are simply out
+competed in certain seasons of the year
+
+ align:start position:0%
+competed in certain seasons of the year
+ 
+
+ align:start position:0%
+competed in certain seasons of the year
+for example if you look at the year 2020
+
+ align:start position:0%
+for example if you look at the year 2020
+ 
+
+ align:start position:0%
+for example if you look at the year 2020
+you look at the capacity Factor
+
+ align:start position:0%
+you look at the capacity Factor
+ 
+
+ align:start position:0%
+you look at the capacity Factor
+coal-fired power plants look like they
+
+ align:start position:0%
+coal-fired power plants look like they
+ 
+
+ align:start position:0%
+coal-fired power plants look like they
+have a capacity Factor around 50 or 60
+
+ align:start position:0%
+have a capacity Factor around 50 or 60
+ 
+
+ align:start position:0%
+have a capacity Factor around 50 or 60
+percent still in the summer because in
+
+ align:start position:0%
+percent still in the summer because in
+ 
+
+ align:start position:0%
+percent still in the summer because in
+July and August we have Peak electric
+
+ align:start position:0%
+July and August we have Peak electric
+ 
+
+ align:start position:0%
+July and August we have Peak electric
+demand but the capacity Factor gets as
+
+ align:start position:0%
+demand but the capacity Factor gets as
+ 
+
+ align:start position:0%
+demand but the capacity Factor gets as
+low as 25 or 30 percent for these kind
+
+ align:start position:0%
+low as 25 or 30 percent for these kind
+ 
+
+ align:start position:0%
+low as 25 or 30 percent for these kind
+of shoulder seasons and winter seasons
+
+ align:start position:0%
+of shoulder seasons and winter seasons
+ 
+
+ align:start position:0%
+of shoulder seasons and winter seasons
+probably because coal is simply not as
+
+ align:start position:0%
+probably because coal is simply not as
+ 
+
+ align:start position:0%
+probably because coal is simply not as
+necessary as for quote unquote base load
+
+ align:start position:0%
+necessary as for quote unquote base load
+ 
+
+ align:start position:0%
+necessary as for quote unquote base load
+power in those seasons of the year and
+
+ align:start position:0%
+power in those seasons of the year and
+ 
+
+ align:start position:0%
+power in those seasons of the year and
+it's probably being out competed by
+
+ align:start position:0%
+it's probably being out competed by
+ 
+
+ align:start position:0%
+it's probably being out competed by
+natural gas power plants
+
+ align:start position:0%
+natural gas power plants
+ 
+
+ align:start position:0%
+natural gas power plants
+if you look at combined cycle of gas
+
+ align:start position:0%
+if you look at combined cycle of gas
+ 
+
+ align:start position:0%
+if you look at combined cycle of gas
+turbines capacity Factor has been
+
+ align:start position:0%
+turbines capacity Factor has been
+ 
+
+ align:start position:0%
+turbines capacity Factor has been
+relatively steady over the previous
+
+ align:start position:0%
+relatively steady over the previous
+ 
+
+ align:start position:0%
+relatively steady over the previous
+years let's say around 50 to 60 percent
+
+ align:start position:0%
+years let's say around 50 to 60 percent
+ 
+
+ align:start position:0%
+years let's say around 50 to 60 percent
+and you can see again that they're much
+
+ align:start position:0%
+and you can see again that they're much
+ 
+
+ align:start position:0%
+and you can see again that they're much
+more utilized in the summer when we had
+
+ align:start position:0%
+more utilized in the summer when we had
+ 
+
+ align:start position:0%
+more utilized in the summer when we had
+electricity demand grain High because
+
+ align:start position:0%
+electricity demand grain High because
+ 
+
+ align:start position:0%
+electricity demand grain High because
+air conditioners but it's actually dips
+
+ align:start position:0%
+air conditioners but it's actually dips
+ 
+
+ align:start position:0%
+air conditioners but it's actually dips
+also in the uh kind of spring and fall
+
+ align:start position:0%
+also in the uh kind of spring and fall
+ 
+
+ align:start position:0%
+also in the uh kind of spring and fall
+simply because there's not as much
+
+ align:start position:0%
+simply because there's not as much
+ 
+
+ align:start position:0%
+simply because there's not as much
+electricity demand when it's not very
+
+ align:start position:0%
+electricity demand when it's not very
+ 
+
+ align:start position:0%
+electricity demand when it's not very
+hot or very cold if you look at another
+
+ align:start position:0%
+hot or very cold if you look at another
+ 
+
+ align:start position:0%
+hot or very cold if you look at another
+kind of gas turbine natural gas gas
+
+ align:start position:0%
+kind of gas turbine natural gas gas
+ 
+
+ align:start position:0%
+kind of gas turbine natural gas gas
+turbines these are probably peaking
+
+ align:start position:0%
+turbines these are probably peaking
+ 
+
+ align:start position:0%
+turbines these are probably peaking
+plants that are used to meet electricity
+
+ align:start position:0%
+plants that are used to meet electricity
+ 
+
+ align:start position:0%
+plants that are used to meet electricity
+demand for certain Peaks or for
+
+ align:start position:0%
+demand for certain Peaks or for
+ 
+
+ align:start position:0%
+demand for certain Peaks or for
+regulation of the grid keeping the Grid
+
+ align:start position:0%
+regulation of the grid keeping the Grid
+ 
+
+ align:start position:0%
+regulation of the grid keeping the Grid
+at the right frequency you can see that
+
+ align:start position:0%
+at the right frequency you can see that
+ 
+
+ align:start position:0%
+at the right frequency you can see that
+the demand utilization for these
+
+ align:start position:0%
+the demand utilization for these
+ 
+
+ align:start position:0%
+the demand utilization for these
+Technologies is relatively low it's like
+
+ align:start position:0%
+Technologies is relatively low it's like
+ 
+
+ align:start position:0%
+Technologies is relatively low it's like
+15 16 in July and August it dips as low
+
+ align:start position:0%
+15 16 in July and August it dips as low
+ 
+
+ align:start position:0%
+15 16 in July and August it dips as low
+as about nine or ten percent in the rest
+
+ align:start position:0%
+as about nine or ten percent in the rest
+ 
+
+ align:start position:0%
+as about nine or ten percent in the rest
+of the year simply because these
+
+ align:start position:0%
+of the year simply because these
+ 
+
+ align:start position:0%
+of the year simply because these
+turbines are mostly used to meet kind of
+
+ align:start position:0%
+turbines are mostly used to meet kind of
+ 
+
+ align:start position:0%
+turbines are mostly used to meet kind of
+the Peaks or the reserve or the
+
+ align:start position:0%
+the Peaks or the reserve or the
+ 
+
+ align:start position:0%
+the Peaks or the reserve or the
+regulation of the grid itself
+
+ align:start position:0%
+regulation of the grid itself
+ 
+
+ align:start position:0%
+regulation of the grid itself
+now I'm going to show you a different
+
+ align:start position:0%
+now I'm going to show you a different
+ 
+
+ align:start position:0%
+now I'm going to show you a different
+slide one moment
+
+ align:start position:0%
+slide one moment
+ 
+
+ align:start position:0%
+slide one moment
+if we go back to the slides the handout
+
+ align:start position:0%
+if we go back to the slides the handout
+ 
+
+ align:start position:0%
+if we go back to the slides the handout
+and I click on this table for electric
+
+ align:start position:0%
+and I click on this table for electric
+ 
+
+ align:start position:0%
+and I click on this table for electric
+power monthly table 6.07 B for
+
+ align:start position:0%
+power monthly table 6.07 B for
+ 
+
+ align:start position:0%
+power monthly table 6.07 B for
+non-fossil resources
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+once you now see our capacity factors
+
+ align:start position:0%
+once you now see our capacity factors
+ 
+
+ align:start position:0%
+once you now see our capacity factors
+for utility scale generators primarily
+
+ align:start position:0%
+for utility scale generators primarily
+ 
+
+ align:start position:0%
+for utility scale generators primarily
+using non-fossil fuels so we should just
+
+ align:start position:0%
+using non-fossil fuels so we should just
+ 
+
+ align:start position:0%
+using non-fossil fuels so we should just
+note right off the bat this is for
+
+ align:start position:0%
+note right off the bat this is for
+ 
+
+ align:start position:0%
+note right off the bat this is for
+utility scale generators this is what
+
+ align:start position:0%
+utility scale generators this is what
+ 
+
+ align:start position:0%
+utility scale generators this is what
+the US to eia the Energy Information
+
+ align:start position:0%
+the US to eia the Energy Information
+ 
+
+ align:start position:0%
+the US to eia the Energy Information
+Administration collects this doesn't
+
+ align:start position:0%
+Administration collects this doesn't
+ 
+
+ align:start position:0%
+Administration collects this doesn't
+include necessarily a new out solar
+
+ align:start position:0%
+include necessarily a new out solar
+ 
+
+ align:start position:0%
+include necessarily a new out solar
+but if you look at the different types
+
+ align:start position:0%
+but if you look at the different types
+ 
+
+ align:start position:0%
+but if you look at the different types
+of Technologies geothermal hydroelectric
+
+ align:start position:0%
+of Technologies geothermal hydroelectric
+ 
+
+ align:start position:0%
+of Technologies geothermal hydroelectric
+nuclear biomass other kinds of gas solar
+
+ align:start position:0%
+nuclear biomass other kinds of gas solar
+ 
+
+ align:start position:0%
+nuclear biomass other kinds of gas solar
+photovoltaic and solar thermal and wind
+
+ align:start position:0%
+photovoltaic and solar thermal and wind
+ 
+
+ align:start position:0%
+photovoltaic and solar thermal and wind
+and wood these are kind of what I've
+
+ align:start position:0%
+and wood these are kind of what I've
+ 
+
+ align:start position:0%
+and wood these are kind of what I've
+refer to as a renewable toolkit if you
+
+ align:start position:0%
+refer to as a renewable toolkit if you
+ 
+
+ align:start position:0%
+refer to as a renewable toolkit if you
+look at the capacity factor for
+
+ align:start position:0%
+look at the capacity factor for
+ 
+
+ align:start position:0%
+look at the capacity factor for
+geothermal it's actually quite High
+
+ align:start position:0%
+geothermal it's actually quite High
+ 
+
+ align:start position:0%
+geothermal it's actually quite High
+looks around 70 percent geothermal
+
+ align:start position:0%
+looks around 70 percent geothermal
+ 
+
+ align:start position:0%
+looks around 70 percent geothermal
+because it comes from the heat from the
+
+ align:start position:0%
+because it comes from the heat from the
+ 
+
+ align:start position:0%
+because it comes from the heat from the
+earth is quite steady
+
+ align:start position:0%
+earth is quite steady
+ 
+
+ align:start position:0%
+earth is quite steady
+hydroelectric is actually a surprisingly
+
+ align:start position:0%
+hydroelectric is actually a surprisingly
+ 
+
+ align:start position:0%
+hydroelectric is actually a surprisingly
+low around 30 or 40 percent
+
+ align:start position:0%
+low around 30 or 40 percent
+ 
+
+ align:start position:0%
+low around 30 or 40 percent
+probably because hydroelectric
+
+ align:start position:0%
+probably because hydroelectric
+ 
+
+ align:start position:0%
+probably because hydroelectric
+Technologies often require water to be
+
+ align:start position:0%
+Technologies often require water to be
+ 
+
+ align:start position:0%
+Technologies often require water to be
+behind a reservoir and then it flows
+
+ align:start position:0%
+behind a reservoir and then it flows
+ 
+
+ align:start position:0%
+behind a reservoir and then it flows
+through a turbine and generates
+
+ align:start position:0%
+through a turbine and generates
+ 
+
+ align:start position:0%
+through a turbine and generates
+electricity so hydroelectric plants may
+
+ align:start position:0%
+electricity so hydroelectric plants may
+ 
+
+ align:start position:0%
+electricity so hydroelectric plants may
+not be run all a year or they may be
+
+ align:start position:0%
+not be run all a year or they may be
+ 
+
+ align:start position:0%
+not be run all a year or they may be
+around certain times of the year again
+
+ align:start position:0%
+around certain times of the year again
+ 
+
+ align:start position:0%
+around certain times of the year again
+let's say in July and August actually
+
+ align:start position:0%
+let's say in July and August actually
+ 
+
+ align:start position:0%
+let's say in July and August actually
+it's relatively low here but you might
+
+ align:start position:0%
+it's relatively low here but you might
+ 
+
+ align:start position:0%
+it's relatively low here but you might
+imagine
+
+ align:start position:0%
+imagine
+ 
+
+ align:start position:0%
+imagine
+um I'd love to power plants being run
+
+ align:start position:0%
+um I'd love to power plants being run
+ 
+
+ align:start position:0%
+um I'd love to power plants being run
+for various reasons in different times
+
+ align:start position:0%
+for various reasons in different times
+ 
+
+ align:start position:0%
+for various reasons in different times
+of the year for example where there's
+
+ align:start position:0%
+of the year for example where there's
+ 
+
+ align:start position:0%
+of the year for example where there's
+more spring runoff or snow melt in the
+
+ align:start position:0%
+more spring runoff or snow melt in the
+ 
+
+ align:start position:0%
+more spring runoff or snow melt in the
+spring it might actually have higher
+
+ align:start position:0%
+spring it might actually have higher
+ 
+
+ align:start position:0%
+spring it might actually have higher
+capacity factors
+
+ align:start position:0%
+capacity factors
+ 
+
+ align:start position:0%
+capacity factors
+nuclear power plants look like they have
+
+ align:start position:0%
+nuclear power plants look like they have
+ 
+
+ align:start position:0%
+nuclear power plants look like they have
+very high capacity factors around 90 and
+
+ align:start position:0%
+very high capacity factors around 90 and
+ 
+
+ align:start position:0%
+very high capacity factors around 90 and
+consistently
+
+ align:start position:0%
+consistently
+ 
+
+ align:start position:0%
+consistently
+and then solar portable take you can see
+
+ align:start position:0%
+and then solar portable take you can see
+ 
+
+ align:start position:0%
+and then solar portable take you can see
+only has a capacity factor of 25 over
+
+ align:start position:0%
+only has a capacity factor of 25 over
+ 
+
+ align:start position:0%
+only has a capacity factor of 25 over
+many years it doesn't seem to change a
+
+ align:start position:0%
+many years it doesn't seem to change a
+ 
+
+ align:start position:0%
+many years it doesn't seem to change a
+whole lot though you can tell in the 20
+
+ align:start position:0%
+whole lot though you can tell in the 20
+ 
+
+ align:start position:0%
+whole lot though you can tell in the 20
+year 2020 it does change throughout the
+
+ align:start position:0%
+year 2020 it does change throughout the
+ 
+
+ align:start position:0%
+year 2020 it does change throughout the
+year because obviously in some parts of
+
+ align:start position:0%
+year because obviously in some parts of
+ 
+
+ align:start position:0%
+year because obviously in some parts of
+the year the days are longer notably
+
+ align:start position:0%
+the year the days are longer notably
+ 
+
+ align:start position:0%
+the year the days are longer notably
+summer than they are winter
+
+ align:start position:0%
+summer than they are winter
+ 
+
+ align:start position:0%
+summer than they are winter
+wind you can see that the capacity
+
+ align:start position:0%
+wind you can see that the capacity
+ 
+
+ align:start position:0%
+wind you can see that the capacity
+factors are around 30 35 over the years
+
+ align:start position:0%
+factors are around 30 35 over the years
+ 
+
+ align:start position:0%
+factors are around 30 35 over the years
+and you can actually see the capacity
+
+ align:start position:0%
+and you can actually see the capacity
+ 
+
+ align:start position:0%
+and you can actually see the capacity
+factors go down slightly in the summer
+
+ align:start position:0%
+factors go down slightly in the summer
+ 
+
+ align:start position:0%
+factors go down slightly in the summer
+that are slightly higher in the spring
+
+ align:start position:0%
+that are slightly higher in the spring
+ 
+
+ align:start position:0%
+that are slightly higher in the spring
+and the winter and the fall so this is
+
+ align:start position:0%
+and the winter and the fall so this is
+ 
+
+ align:start position:0%
+and the winter and the fall so this is
+just to give you a sense of even though
+
+ align:start position:0%
+just to give you a sense of even though
+ 
+
+ align:start position:0%
+just to give you a sense of even though
+certain technologies have a name plate
+
+ align:start position:0%
+certain technologies have a name plate
+ 
+
+ align:start position:0%
+certain technologies have a name plate
+capacity like GE Mark and Sarah Haley
+
+ align:start position:0%
+capacity like GE Mark and Sarah Haley
+ 
+
+ align:start position:0%
+capacity like GE Mark and Sarah Haley
+turbines it's not necessarily the energy
+
+ align:start position:0%
+turbines it's not necessarily the energy
+ 
+
+ align:start position:0%
+turbines it's not necessarily the energy
+or the electricity that we derive from
+
+ align:start position:0%
+or the electricity that we derive from
+ 
+
+ align:start position:0%
+or the electricity that we derive from
+these Technologies that's a percentage
+
+ align:start position:0%
+these Technologies that's a percentage
+ 
+
+ align:start position:0%
+these Technologies that's a percentage
+of the possible capacity
+
+ align:start position:0%
+of the possible capacity
+ 
+
+ align:start position:0%
+of the possible capacity
+so going back to our slides uh just to
+
+ align:start position:0%
+so going back to our slides uh just to
+ 
+
+ align:start position:0%
+so going back to our slides uh just to
+show you again the capacity Factor
+
+ align:start position:0%
+show you again the capacity Factor
+ 
+
+ align:start position:0%
+show you again the capacity Factor
+changes you can see that nuclear has
+
+ align:start position:0%
+changes you can see that nuclear has
+ 
+
+ align:start position:0%
+changes you can see that nuclear has
+relatively high capacity hydropower wind
+
+ align:start position:0%
+relatively high capacity hydropower wind
+ 
+
+ align:start position:0%
+relatively high capacity hydropower wind
+solar PV solar thermal all have lower
+
+ align:start position:0%
+solar PV solar thermal all have lower
+ 
+
+ align:start position:0%
+solar PV solar thermal all have lower
+capacity factors and of course our
+
+ align:start position:0%
+capacity factors and of course our
+ 
+
+ align:start position:0%
+capacity factors and of course our
+landfill gaps our biomass pole and
+
+ align:start position:0%
+landfill gaps our biomass pole and
+ 
+
+ align:start position:0%
+landfill gaps our biomass pole and
+natural gas power plants have higher
+
+ align:start position:0%
+natural gas power plants have higher
+ 
+
+ align:start position:0%
+natural gas power plants have higher
+capacity factors so the geothermal is
+
+ align:start position:0%
+capacity factors so the geothermal is
+ 
+
+ align:start position:0%
+capacity factors so the geothermal is
+also quite High a noticeable thing I
+
+ align:start position:0%
+also quite High a noticeable thing I
+ 
+
+ align:start position:0%
+also quite High a noticeable thing I
+want you to observe in this graph is
+
+ align:start position:0%
+want you to observe in this graph is
+ 
+
+ align:start position:0%
+want you to observe in this graph is
+that offshore wind has no capacity
+
+ align:start position:0%
+that offshore wind has no capacity
+ 
+
+ align:start position:0%
+that offshore wind has no capacity
+Factor because we haven't empirically
+
+ align:start position:0%
+Factor because we haven't empirically
+ 
+
+ align:start position:0%
+Factor because we haven't empirically
+determined it yet we haven't observed
+
+ align:start position:0%
+determined it yet we haven't observed
+ 
+
+ align:start position:0%
+determined it yet we haven't observed
+this technology in action as I said to
+
+ align:start position:0%
+this technology in action as I said to
+ 
+
+ align:start position:0%
+this technology in action as I said to
+you on the earlier slides there's only
+
+ align:start position:0%
+you on the earlier slides there's only
+ 
+
+ align:start position:0%
+you on the earlier slides there's only
+seven offshore wind turbines operating
+
+ align:start position:0%
+seven offshore wind turbines operating
+ 
+
+ align:start position:0%
+seven offshore wind turbines operating
+in the U.S even though we are planning
+
+ align:start position:0%
+in the U.S even though we are planning
+ 
+
+ align:start position:0%
+in the U.S even though we are planning
+to build about a hundred percent or a
+
+ align:start position:0%
+to build about a hundred percent or a
+ 
+
+ align:start position:0%
+to build about a hundred percent or a
+thousand times more offshore capacity at
+
+ align:start position:0%
+thousand times more offshore capacity at
+ 
+
+ align:start position:0%
+thousand times more offshore capacity at
+the moment it's a unproven technology
+
+ align:start position:0%
+the moment it's a unproven technology
+ 
+
+ align:start position:0%
+the moment it's a unproven technology
+that we still need to understand or the
+
+ align:start position:0%
+that we still need to understand or the
+ 
+
+ align:start position:0%
+that we still need to understand or the
+actual capacity is going to be so we can
+
+ align:start position:0%
+actual capacity is going to be so we can
+ 
+
+ align:start position:0%
+actual capacity is going to be so we can
+plan to build our grid or forecast how
+
+ align:start position:0%
+plan to build our grid or forecast how
+ 
+
+ align:start position:0%
+plan to build our grid or forecast how
+effective this technology is going to be
+
+ align:start position:0%
+effective this technology is going to be
+ 
+
+ align:start position:0%
+effective this technology is going to be
+in the future
+
+ align:start position:0%
+in the future
+ 
+
+ align:start position:0%
+in the future
+so another key metric for
+
+ align:start position:0%
+so another key metric for
+ 
+
+ align:start position:0%
+so another key metric for
+um this uh these costs of these
+
+ align:start position:0%
+um this uh these costs of these
+ 
+
+ align:start position:0%
+um this uh these costs of these
+Technologies is the levelized cost of
+
+ align:start position:0%
+Technologies is the levelized cost of
+ 
+
+ align:start position:0%
+Technologies is the levelized cost of
+energy in a simple way I'm just called
+
+ align:start position:0%
+energy in a simple way I'm just called
+ 
+
+ align:start position:0%
+energy in a simple way I'm just called
+here these simple levelized of
+
+ align:start position:0%
+here these simple levelized of
+ 
+
+ align:start position:0%
+here these simple levelized of
+energy it's taking the fixed cost
+
+ align:start position:0%
+energy it's taking the fixed cost
+ 
+
+ align:start position:0%
+energy it's taking the fixed cost
+the fuel costs and the variable
+
+ align:start position:0%
+the fuel costs and the variable
+ 
+
+ align:start position:0%
+the fuel costs and the variable
+operations maintenance and dividing it
+
+ align:start position:0%
+operations maintenance and dividing it
+ 
+
+ align:start position:0%
+operations maintenance and dividing it
+all or amortizing it over the length of
+
+ align:start position:0%
+all or amortizing it over the length of
+ 
+
+ align:start position:0%
+all or amortizing it over the length of
+Life the technology in other words
+
+ align:start position:0%
+Life the technology in other words
+ 
+
+ align:start position:0%
+Life the technology in other words
+taking the average cost of Technology
+
+ align:start position:0%
+taking the average cost of Technology
+ 
+
+ align:start position:0%
+taking the average cost of Technology
+averaged over its whole lifetime
+
+ align:start position:0%
+averaged over its whole lifetime
+ 
+
+ align:start position:0%
+averaged over its whole lifetime
+to show you in another way you have the
+
+ align:start position:0%
+to show you in another way you have the
+ 
+
+ align:start position:0%
+to show you in another way you have the
+capital cost times the recovery Factor
+
+ align:start position:0%
+capital cost times the recovery Factor
+ 
+
+ align:start position:0%
+capital cost times the recovery Factor
+plus the fixed cost this is the fixed
+
+ align:start position:0%
+plus the fixed cost this is the fixed
+ 
+
+ align:start position:0%
+plus the fixed cost this is the fixed
+cost term you divide it by 8 760 hours
+
+ align:start position:0%
+cost term you divide it by 8 760 hours
+ 
+
+ align:start position:0%
+cost term you divide it by 8 760 hours
+in a year and multiply comes the
+
+ align:start position:0%
+in a year and multiply comes the
+ 
+
+ align:start position:0%
+in a year and multiply comes the
+capacity Factor because you're not
+
+ align:start position:0%
+capacity Factor because you're not
+ 
+
+ align:start position:0%
+capacity Factor because you're not
+getting the full capacity of the
+
+ align:start position:0%
+getting the full capacity of the
+ 
+
+ align:start position:0%
+getting the full capacity of the
+technology all the time
+
+ align:start position:0%
+technology all the time
+ 
+
+ align:start position:0%
+technology all the time
+you can add on this additional fuel cost
+
+ align:start position:0%
+you can add on this additional fuel cost
+ 
+
+ align:start position:0%
+you can add on this additional fuel cost
+this is kind of the posture incurring
+
+ align:start position:0%
+this is kind of the posture incurring
+ 
+
+ align:start position:0%
+this is kind of the posture incurring
+throughout the life of the technology so
+
+ align:start position:0%
+throughout the life of the technology so
+ 
+
+ align:start position:0%
+throughout the life of the technology so
+you take the fuel cost to average over
+
+ align:start position:0%
+you take the fuel cost to average over
+ 
+
+ align:start position:0%
+you take the fuel cost to average over
+time and multiply times the speed rate
+
+ align:start position:0%
+time and multiply times the speed rate
+ 
+
+ align:start position:0%
+time and multiply times the speed rate
+which is the exact amount of energy
+
+ align:start position:0%
+which is the exact amount of energy
+ 
+
+ align:start position:0%
+which is the exact amount of energy
+you're actually getting out of the heat
+
+ align:start position:0%
+you're actually getting out of the heat
+ 
+
+ align:start position:0%
+you're actually getting out of the heat
+energy of the technology for example
+
+ align:start position:0%
+energy of the technology for example
+ 
+
+ align:start position:0%
+energy of the technology for example
+with a coal-fired power plant if it has
+
+ align:start position:0%
+with a coal-fired power plant if it has
+ 
+
+ align:start position:0%
+with a coal-fired power plant if it has
+a low heat rate around like 30 or 40
+
+ align:start position:0%
+a low heat rate around like 30 or 40
+ 
+
+ align:start position:0%
+a low heat rate around like 30 or 40
+percent the heat of the technology may
+
+ align:start position:0%
+percent the heat of the technology may
+ 
+
+ align:start position:0%
+percent the heat of the technology may
+actually be going out the Smoke Stack
+
+ align:start position:0%
+actually be going out the Smoke Stack
+ 
+
+ align:start position:0%
+actually be going out the Smoke Stack
+and you wouldn't factor that into the
+
+ align:start position:0%
+and you wouldn't factor that into the
+ 
+
+ align:start position:0%
+and you wouldn't factor that into the
+energy of the fuel that you're getting
+
+ align:start position:0%
+energy of the fuel that you're getting
+ 
+
+ align:start position:0%
+energy of the fuel that you're getting
+and then you might add on some variable
+
+ align:start position:0%
+and then you might add on some variable
+ 
+
+ align:start position:0%
+and then you might add on some variable
+operations and maintenance costs I think
+
+ align:start position:0%
+operations and maintenance costs I think
+ 
+
+ align:start position:0%
+operations and maintenance costs I think
+a more exact way or better but more
+
+ align:start position:0%
+a more exact way or better but more
+ 
+
+ align:start position:0%
+a more exact way or better but more
+complicated formula
+
+ align:start position:0%
+complicated formula
+ 
+
+ align:start position:0%
+complicated formula
+for the level as constant energy
+
+ align:start position:0%
+for the level as constant energy
+ 
+
+ align:start position:0%
+for the level as constant energy
+Wikipedia actually has a surprisingly
+
+ align:start position:0%
+Wikipedia actually has a surprisingly
+ 
+
+ align:start position:0%
+Wikipedia actually has a surprisingly
+good article on this they call the
+
+ align:start position:0%
+good article on this they call the
+ 
+
+ align:start position:0%
+good article on this they call the
+levelized quantum energy be some of
+
+ align:start position:0%
+levelized quantum energy be some of
+ 
+
+ align:start position:0%
+levelized quantum energy be some of
+costs over the lifetime divided by the
+
+ align:start position:0%
+costs over the lifetime divided by the
+ 
+
+ align:start position:0%
+costs over the lifetime divided by the
+sum of electrical energy produced over
+
+ align:start position:0%
+sum of electrical energy produced over
+ 
+
+ align:start position:0%
+sum of electrical energy produced over
+the lifetime
+
+ align:start position:0%
+the lifetime
+ 
+
+ align:start position:0%
+the lifetime
+so you have various terms like the
+
+ align:start position:0%
+so you have various terms like the
+ 
+
+ align:start position:0%
+so you have various terms like the
+investment expenditures and year T
+
+ align:start position:0%
+investment expenditures and year T
+ 
+
+ align:start position:0%
+investment expenditures and year T
+that's this term here plus the
+
+ align:start position:0%
+that's this term here plus the
+ 
+
+ align:start position:0%
+that's this term here plus the
+operations and maintenance expenditures
+
+ align:start position:0%
+operations and maintenance expenditures
+ 
+
+ align:start position:0%
+operations and maintenance expenditures
+in year T that's the Mt here plus the
+
+ align:start position:0%
+in year T that's the Mt here plus the
+ 
+
+ align:start position:0%
+in year T that's the Mt here plus the
+fuel expenditures in the given year T
+
+ align:start position:0%
+fuel expenditures in the given year T
+ 
+
+ align:start position:0%
+fuel expenditures in the given year T
+here you add it up across all the years
+
+ align:start position:0%
+here you add it up across all the years
+ 
+
+ align:start position:0%
+here you add it up across all the years
+and starting at T equals one but the
+
+ align:start position:0%
+and starting at T equals one but the
+ 
+
+ align:start position:0%
+and starting at T equals one but the
+more complicated formula has a discount
+
+ align:start position:0%
+more complicated formula has a discount
+ 
+
+ align:start position:0%
+more complicated formula has a discount
+term 1 plus r over T where R is a
+
+ align:start position:0%
+term 1 plus r over T where R is a
+ 
+
+ align:start position:0%
+term 1 plus r over T where R is a
+discount rate that's a way of taking all
+
+ align:start position:0%
+discount rate that's a way of taking all
+ 
+
+ align:start position:0%
+discount rate that's a way of taking all
+the financial costs and discounting it
+
+ align:start position:0%
+the financial costs and discounting it
+ 
+
+ align:start position:0%
+the financial costs and discounting it
+over the discount rate
+
+ align:start position:0%
+over the discount rate
+ 
+
+ align:start position:0%
+over the discount rate
+and then what you do on the bottom is
+
+ align:start position:0%
+and then what you do on the bottom is
+ 
+
+ align:start position:0%
+and then what you do on the bottom is
+you have the energy so this is the cost
+
+ align:start position:0%
+you have the energy so this is the cost
+ 
+
+ align:start position:0%
+you have the energy so this is the cost
+per energy and you take all the energy
+
+ align:start position:0%
+per energy and you take all the energy
+ 
+
+ align:start position:0%
+per energy and you take all the energy
+over each of the periods T again sum it
+
+ align:start position:0%
+over each of the periods T again sum it
+ 
+
+ align:start position:0%
+over each of the periods T again sum it
+up over n terms and discount it so you
+
+ align:start position:0%
+up over n terms and discount it so you
+ 
+
+ align:start position:0%
+up over n terms and discount it so you
+discount it because the value of the
+
+ align:start position:0%
+discount it because the value of the
+ 
+
+ align:start position:0%
+discount it because the value of the
+energy or the cost Energy may not be the
+
+ align:start position:0%
+energy or the cost Energy may not be the
+ 
+
+ align:start position:0%
+energy or the cost Energy may not be the
+same the same in the future as it is now
+
+ align:start position:0%
+same the same in the future as it is now
+ 
+
+ align:start position:0%
+same the same in the future as it is now
+like the time value of money you're
+
+ align:start position:0%
+like the time value of money you're
+ 
+
+ align:start position:0%
+like the time value of money you're
+valuing the energy and the costs up
+
+ align:start position:0%
+valuing the energy and the costs up
+ 
+
+ align:start position:0%
+valuing the energy and the costs up
+front more than you are the energy and
+
+ align:start position:0%
+front more than you are the energy and
+ 
+
+ align:start position:0%
+front more than you are the energy and
+cost in the future
+
+ align:start position:0%
+cost in the future
+ 
+
+ align:start position:0%
+cost in the future
+and of course this note down here is
+
+ align:start position:0%
+and of course this note down here is
+ 
+
+ align:start position:0%
+and of course this note down here is
+useful some caution must be taken when
+
+ align:start position:0%
+useful some caution must be taken when
+ 
+
+ align:start position:0%
+useful some caution must be taken when
+using formulas for the levelized cost as
+
+ align:start position:0%
+using formulas for the levelized cost as
+ 
+
+ align:start position:0%
+using formulas for the levelized cost as
+they often embody unseen assumptions
+
+ align:start position:0%
+they often embody unseen assumptions
+ 
+
+ align:start position:0%
+they often embody unseen assumptions
+like neglecting the effects of cactus or
+
+ align:start position:0%
+like neglecting the effects of cactus or
+ 
+
+ align:start position:0%
+like neglecting the effects of cactus or
+maybe specified in real or nominal terms
+
+ align:start position:0%
+maybe specified in real or nominal terms
+ 
+
+ align:start position:0%
+maybe specified in real or nominal terms
+in other words other versions of the
+
+ align:start position:0%
+in other words other versions of the
+ 
+
+ align:start position:0%
+in other words other versions of the
+above formula like the previous slide do
+
+ align:start position:0%
+above formula like the previous slide do
+ 
+
+ align:start position:0%
+above formula like the previous slide do
+not discount the electricity stream in a
+
+ align:start position:0%
+not discount the electricity stream in a
+ 
+
+ align:start position:0%
+not discount the electricity stream in a
+way that the Wikipedia formula discounts
+
+ align:start position:0%
+way that the Wikipedia formula discounts
+ 
+
+ align:start position:0%
+way that the Wikipedia formula discounts
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+but this is uh why we look at the levard
+
+ align:start position:0%
+but this is uh why we look at the levard
+ 
+
+ align:start position:0%
+but this is uh why we look at the levard
+levelized cost of energy analysis I
+
+ align:start position:0%
+levelized cost of energy analysis I
+ 
+
+ align:start position:0%
+levelized cost of energy analysis I
+think all the assumptions are stated up
+
+ align:start position:0%
+think all the assumptions are stated up
+ 
+
+ align:start position:0%
+think all the assumptions are stated up
+front in the report this is a fairly
+
+ align:start position:0%
+front in the report this is a fairly
+ 
+
+ align:start position:0%
+front in the report this is a fairly
+industry standard report that gets
+
+ align:start position:0%
+industry standard report that gets
+ 
+
+ align:start position:0%
+industry standard report that gets
+supported every year last year it came
+
+ align:start position:0%
+supported every year last year it came
+ 
+
+ align:start position:0%
+supported every year last year it came
+out this week in October so we may get a
+
+ align:start position:0%
+out this week in October so we may get a
+ 
+
+ align:start position:0%
+out this week in October so we may get a
+new version this week you can see the
+
+ align:start position:0%
+new version this week you can see the
+ 
+
+ align:start position:0%
+new version this week you can see the
+ Renewal Energy up here in the top
+
+ align:start position:0%
+ Renewal Energy up here in the top
+ 
+
+ align:start position:0%
+ Renewal Energy up here in the top
+boxes and the cost of conventional
+
+ align:start position:0%
+boxes and the cost of conventional
+ 
+
+ align:start position:0%
+boxes and the cost of conventional
+quote-unquote conventional or fossil
+
+ align:start position:0%
+quote-unquote conventional or fossil
+ 
+
+ align:start position:0%
+quote-unquote conventional or fossil
+fuel Technologies in the bottom and the
+
+ align:start position:0%
+fuel Technologies in the bottom and the
+ 
+
+ align:start position:0%
+fuel Technologies in the bottom and the
+reason why I say your renewable toolkit
+
+ align:start position:0%
+reason why I say your renewable toolkit
+ 
+
+ align:start position:0%
+reason why I say your renewable toolkit
+is getting cheaper and cleaner all the
+
+ align:start position:0%
+is getting cheaper and cleaner all the
+ 
+
+ align:start position:0%
+is getting cheaper and cleaner all the
+time look at the relative costs of
+
+ align:start position:0%
+time look at the relative costs of
+ 
+
+ align:start position:0%
+time look at the relative costs of
+feature Technologies solar PV uh on a
+
+ align:start position:0%
+feature Technologies solar PV uh on a
+ 
+
+ align:start position:0%
+feature Technologies solar PV uh on a
+cost in dollars of a megawatt hour is
+
+ align:start position:0%
+cost in dollars of a megawatt hour is
+ 
+
+ align:start position:0%
+cost in dollars of a megawatt hour is
+the same thing as the cost of cents per
+
+ align:start position:0%
+the same thing as the cost of cents per
+ 
+
+ align:start position:0%
+the same thing as the cost of cents per
+kilowatt hour that's 147 dollars per
+
+ align:start position:0%
+kilowatt hour that's 147 dollars per
+ 
+
+ align:start position:0%
+kilowatt hour that's 147 dollars per
+megawatt hour at least for solar Eevee
+
+ align:start position:0%
+megawatt hour at least for solar Eevee
+ 
+
+ align:start position:0%
+megawatt hour at least for solar Eevee
+in the rooftop residential but it's much
+
+ align:start position:0%
+in the rooftop residential but it's much
+ 
+
+ align:start position:0%
+in the rooftop residential but it's much
+cheaper for a commercial industrial
+
+ align:start position:0%
+cheaper for a commercial industrial
+ 
+
+ align:start position:0%
+cheaper for a commercial industrial
+rooftop installation it's actually about
+
+ align:start position:0%
+rooftop installation it's actually about
+ 
+
+ align:start position:0%
+rooftop installation it's actually about
+about 2.5 times less
+
+ align:start position:0%
+about 2.5 times less
+ 
+
+ align:start position:0%
+about 2.5 times less
+a solar PV and a community solar
+
+ align:start position:0%
+a solar PV and a community solar
+ 
+
+ align:start position:0%
+a solar PV and a community solar
+installation is even lower but not none
+
+ align:start position:0%
+installation is even lower but not none
+ 
+
+ align:start position:0%
+installation is even lower but not none
+of these other solar installations are
+
+ align:start position:0%
+of these other solar installations are
+ 
+
+ align:start position:0%
+of these other solar installations are
+as cheap as solar installed at the
+
+ align:start position:0%
+as cheap as solar installed at the
+ 
+
+ align:start position:0%
+as cheap as solar installed at the
+utility scale using different
+
+ align:start position:0%
+utility scale using different
+ 
+
+ align:start position:0%
+utility scale using different
+Technologies like crystalline
+
+ align:start position:0%
+Technologies like crystalline
+ 
+
+ align:start position:0%
+Technologies like crystalline
+photovoltaic panels or thin film
+
+ align:start position:0%
+photovoltaic panels or thin film
+ 
+
+ align:start position:0%
+photovoltaic panels or thin film
+photovoltaic panels
+
+ align:start position:0%
+photovoltaic panels
+ 
+
+ align:start position:0%
+photovoltaic panels
+if you look at solar Thermal Tower
+
+ align:start position:0%
+if you look at solar Thermal Tower
+ 
+
+ align:start position:0%
+if you look at solar Thermal Tower
+that's also called a concentrating solar
+
+ align:start position:0%
+that's also called a concentrating solar
+ 
+
+ align:start position:0%
+that's also called a concentrating solar
+tower this is like out in the desert in
+
+ align:start position:0%
+tower this is like out in the desert in
+ 
+
+ align:start position:0%
+tower this is like out in the desert in
+California this is still relatively
+
+ align:start position:0%
+California this is still relatively
+ 
+
+ align:start position:0%
+California this is still relatively
+expensive and has not gotten cheaper
+
+ align:start position:0%
+expensive and has not gotten cheaper
+ 
+
+ align:start position:0%
+expensive and has not gotten cheaper
+over time solar PV is the technology
+
+ align:start position:0%
+over time solar PV is the technology
+ 
+
+ align:start position:0%
+over time solar PV is the technology
+that's gotten cheapest most quickly
+
+ align:start position:0%
+that's gotten cheapest most quickly
+ 
+
+ align:start position:0%
+that's gotten cheapest most quickly
+we'll talk more about that in the next
+
+ align:start position:0%
+we'll talk more about that in the next
+ 
+
+ align:start position:0%
+we'll talk more about that in the next
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+geothermal is relatively cheap
+
+ align:start position:0%
+geothermal is relatively cheap
+ 
+
+ align:start position:0%
+geothermal is relatively cheap
+but it's also important to note in the
+
+ align:start position:0%
+but it's also important to note in the
+ 
+
+ align:start position:0%
+but it's also important to note in the
+context of this class that wind is the
+
+ align:start position:0%
+context of this class that wind is the
+ 
+
+ align:start position:0%
+context of this class that wind is the
+cheapest resource among the renewable
+
+ align:start position:0%
+cheapest resource among the renewable
+ 
+
+ align:start position:0%
+cheapest resource among the renewable
+Technologies it's at least at lowest
+
+ align:start position:0%
+Technologies it's at least at lowest
+ 
+
+ align:start position:0%
+Technologies it's at least at lowest
+point twenty six dollars per megawatt
+
+ align:start position:0%
+point twenty six dollars per megawatt
+ 
+
+ align:start position:0%
+point twenty six dollars per megawatt
+hour that can vary and be as much as
+
+ align:start position:0%
+hour that can vary and be as much as
+ 
+
+ align:start position:0%
+hour that can vary and be as much as
+fifty dollars per megawatt hour probably
+
+ align:start position:0%
+fifty dollars per megawatt hour probably
+ 
+
+ align:start position:0%
+fifty dollars per megawatt hour probably
+for older wind farm that has smaller
+
+ align:start position:0%
+for older wind farm that has smaller
+ 
+
+ align:start position:0%
+for older wind farm that has smaller
+wind turbines now the important thing to
+
+ align:start position:0%
+wind turbines now the important thing to
+ 
+
+ align:start position:0%
+wind turbines now the important thing to
+note is that wind at 26 dollars per
+
+ align:start position:0%
+note is that wind at 26 dollars per
+ 
+
+ align:start position:0%
+note is that wind at 26 dollars per
+megawatt hour on the low end of the
+
+ align:start position:0%
+megawatt hour on the low end of the
+ 
+
+ align:start position:0%
+megawatt hour on the low end of the
+scale is actually much cheaper than our
+
+ align:start position:0%
+scale is actually much cheaper than our
+ 
+
+ align:start position:0%
+scale is actually much cheaper than our
+other technology it's cheaper than a gas
+
+ align:start position:0%
+other technology it's cheaper than a gas
+ 
+
+ align:start position:0%
+other technology it's cheaper than a gas
+peaking natural gas plant it's much
+
+ align:start position:0%
+peaking natural gas plant it's much
+ 
+
+ align:start position:0%
+peaking natural gas plant it's much
+cheaper than a nuclear power plant it's
+
+ align:start position:0%
+cheaper than a nuclear power plant it's
+ 
+
+ align:start position:0%
+cheaper than a nuclear power plant it's
+cheaper than a coal fire power plant and
+
+ align:start position:0%
+cheaper than a coal fire power plant and
+ 
+
+ align:start position:0%
+cheaper than a coal fire power plant and
+it's basically cheaper than a combined
+
+ align:start position:0%
+it's basically cheaper than a combined
+ 
+
+ align:start position:0%
+it's basically cheaper than a combined
+gas cycle turbine power plant
+
+ align:start position:0%
+gas cycle turbine power plant
+ 
+
+ align:start position:0%
+gas cycle turbine power plant
+if we look at that the sensitivity of
+
+ align:start position:0%
+if we look at that the sensitivity of
+ 
+
+ align:start position:0%
+if we look at that the sensitivity of
+these various costs to federal tax
+
+ align:start position:0%
+these various costs to federal tax
+ 
+
+ align:start position:0%
+these various costs to federal tax
+subsidies have been levelized costs
+
+ align:start position:0%
+subsidies have been levelized costs
+ 
+
+ align:start position:0%
+subsidies have been levelized costs
+estimates from Ozark really include
+
+ align:start position:0%
+estimates from Ozark really include
+ 
+
+ align:start position:0%
+estimates from Ozark really include
+federal tax subsidies and public
+
+ align:start position:0%
+federal tax subsidies and public
+ 
+
+ align:start position:0%
+federal tax subsidies and public
+calculations you can see that federal
+
+ align:start position:0%
+calculations you can see that federal
+ 
+
+ align:start position:0%
+calculations you can see that federal
+tax deficitors make solar PV have the
+
+ align:start position:0%
+tax deficitors make solar PV have the
+ 
+
+ align:start position:0%
+tax deficitors make solar PV have the
+rooftop cheaper and make solar PV on the
+
+ align:start position:0%
+rooftop cheaper and make solar PV on the
+ 
+
+ align:start position:0%
+rooftop cheaper and make solar PV on the
+commercial industrial buildings keeper
+
+ align:start position:0%
+commercial industrial buildings keeper
+ 
+
+ align:start position:0%
+commercial industrial buildings keeper
+it makes Community solar cheaper it
+
+ align:start position:0%
+it makes Community solar cheaper it
+ 
+
+ align:start position:0%
+it makes Community solar cheaper it
+makes utility scale Cheaper by about 25
+
+ align:start position:0%
+makes utility scale Cheaper by about 25
+ 
+
+ align:start position:0%
+makes utility scale Cheaper by about 25
+30 percent
+
+ align:start position:0%
+30 percent
+ 
+
+ align:start position:0%
+30 percent
+makes solar thermal Towers cheaper it
+
+ align:start position:0%
+makes solar thermal Towers cheaper it
+ 
+
+ align:start position:0%
+makes solar thermal Towers cheaper it
+makes geothermal Technologies cheaper
+
+ align:start position:0%
+makes geothermal Technologies cheaper
+ 
+
+ align:start position:0%
+makes geothermal Technologies cheaper
+and it makes wind much much cheaper at
+
+ align:start position:0%
+and it makes wind much much cheaper at
+ 
+
+ align:start position:0%
+and it makes wind much much cheaper at
+the low end from 26 megawatt hour we
+
+ align:start position:0%
+the low end from 26 megawatt hour we
+ 
+
+ align:start position:0%
+the low end from 26 megawatt hour we
+went to nine dollars per megawatt hour
+
+ align:start position:0%
+went to nine dollars per megawatt hour
+ 
+
+ align:start position:0%
+went to nine dollars per megawatt hour
+if you compare that to all these
+
+ align:start position:0%
+if you compare that to all these
+ 
+
+ align:start position:0%
+if you compare that to all these
+conventional or fossil Technologies in
+
+ align:start position:0%
+conventional or fossil Technologies in
+ 
+
+ align:start position:0%
+conventional or fossil Technologies in
+the previous slide and none of these
+
+ align:start position:0%
+the previous slide and none of these
+ 
+
+ align:start position:0%
+the previous slide and none of these
+things compete because we don't offer as
+
+ align:start position:0%
+things compete because we don't offer as
+ 
+
+ align:start position:0%
+things compete because we don't offer as
+many overt federal tax subsidies for
+
+ align:start position:0%
+many overt federal tax subsidies for
+ 
+
+ align:start position:0%
+many overt federal tax subsidies for
+these Technologies in terms of energy
+
+ align:start position:0%
+these Technologies in terms of energy
+ 
+
+ align:start position:0%
+these Technologies in terms of energy
+production even though these
+
+ align:start position:0%
+production even though these
+ 
+
+ align:start position:0%
+production even though these
+Technologies or these industries do
+
+ align:start position:0%
+Technologies or these industries do
+ 
+
+ align:start position:0%
+Technologies or these industries do
+receive a lot of subsidies in other ways
+
+ align:start position:0%
+receive a lot of subsidies in other ways
+ 
+
+ align:start position:0%
+receive a lot of subsidies in other ways
+but Lazar doesn't calculate those
+
+ align:start position:0%
+but Lazar doesn't calculate those
+ 
+
+ align:start position:0%
+but Lazar doesn't calculate those
+levelized costs just to show the
+
+ align:start position:0%
+levelized costs just to show the
+ 
+
+ align:start position:0%
+levelized costs just to show the
+sensitivity of this because the federal
+
+ align:start position:0%
+sensitivity of this because the federal
+ 
+
+ align:start position:0%
+sensitivity of this because the federal
+tax subsidy for renewable energy have
+
+ align:start position:0%
+tax subsidy for renewable energy have
+ 
+
+ align:start position:0%
+tax subsidy for renewable energy have
+been much more debated and are frankly
+
+ align:start position:0%
+been much more debated and are frankly
+ 
+
+ align:start position:0%
+been much more debated and are frankly
+sometimes a little less secure or less
+
+ align:start position:0%
+sometimes a little less secure or less
+ 
+
+ align:start position:0%
+sometimes a little less secure or less
+entrenched than the fossil fuel
+
+ align:start position:0%
+entrenched than the fossil fuel
+ 
+
+ align:start position:0%
+entrenched than the fossil fuel
+subsidies
+
+ align:start position:0%
+subsidies
+ 
+
+ align:start position:0%
+subsidies
+but if we do this comparison again the
+
+ align:start position:0%
+but if we do this comparison again the
+ 
+
+ align:start position:0%
+but if we do this comparison again the
+key point from a lot of energy analysts
+
+ align:start position:0%
+key point from a lot of energy analysts
+ 
+
+ align:start position:0%
+key point from a lot of energy analysts
+and a lot of renewable energy Advocates
+
+ align:start position:0%
+and a lot of renewable energy Advocates
+ 
+
+ align:start position:0%
+and a lot of renewable energy Advocates
+is that if you compare the levelized
+
+ align:start position:0%
+is that if you compare the levelized
+ 
+
+ align:start position:0%
+is that if you compare the levelized
+cost of new build wind and solar versus
+
+ align:start position:0%
+cost of new build wind and solar versus
+ 
+
+ align:start position:0%
+cost of new build wind and solar versus
+the marginal cost of selected existing
+
+ align:start position:0%
+the marginal cost of selected existing
+ 
+
+ align:start position:0%
+the marginal cost of selected existing
+conventional generation in other words
+
+ align:start position:0%
+conventional generation in other words
+ 
+
+ align:start position:0%
+conventional generation in other words
+the right hand side here for coal
+
+ align:start position:0%
+the right hand side here for coal
+ 
+
+ align:start position:0%
+the right hand side here for coal
+nuclear and combined and gas cycle
+
+ align:start position:0%
+nuclear and combined and gas cycle
+ 
+
+ align:start position:0%
+nuclear and combined and gas cycle
+turbines we already have that fossil
+
+ align:start position:0%
+turbines we already have that fossil
+ 
+
+ align:start position:0%
+turbines we already have that fossil
+fuel system and it's already built or
+
+ align:start position:0%
+fuel system and it's already built or
+ 
+
+ align:start position:0%
+fuel system and it's already built or
+private compare is should we continue to
+
+ align:start position:0%
+private compare is should we continue to
+ 
+
+ align:start position:0%
+private compare is should we continue to
+operate the fossil fuel system that we
+
+ align:start position:0%
+operate the fossil fuel system that we
+ 
+
+ align:start position:0%
+operate the fossil fuel system that we
+have or should we new build wind and
+
+ align:start position:0%
+have or should we new build wind and
+ 
+
+ align:start position:0%
+have or should we new build wind and
+solar and so the point of this graph is
+
+ align:start position:0%
+solar and so the point of this graph is
+ 
+
+ align:start position:0%
+solar and so the point of this graph is
+to show that onshore wind if you
+
+ align:start position:0%
+to show that onshore wind if you
+ 
+
+ align:start position:0%
+to show that onshore wind if you
+subsidize it it's cheaper to build a
+
+ align:start position:0%
+subsidize it it's cheaper to build a
+ 
+
+ align:start position:0%
+subsidize it it's cheaper to build a
+whole new onshore wind turbine or farm
+
+ align:start position:0%
+whole new onshore wind turbine or farm
+ 
+
+ align:start position:0%
+whole new onshore wind turbine or farm
+and provide Power that way subsidized
+
+ align:start position:0%
+and provide Power that way subsidized
+ 
+
+ align:start position:0%
+and provide Power that way subsidized
+wind out competes all these fossil
+
+ align:start position:0%
+wind out competes all these fossil
+ 
+
+ align:start position:0%
+wind out competes all these fossil
+generation Technologies and unsubsidized
+
+ align:start position:0%
+generation Technologies and unsubsidized
+ 
+
+ align:start position:0%
+generation Technologies and unsubsidized
+solar PV unsubsidized wind and
+
+ align:start position:0%
+solar PV unsubsidized wind and
+ 
+
+ align:start position:0%
+solar PV unsubsidized wind and
+subsidized solar PV are getting to the
+
+ align:start position:0%
+subsidized solar PV are getting to the
+ 
+
+ align:start position:0%
+subsidized solar PV are getting to the
+point where they're starting to
+
+ align:start position:0%
+point where they're starting to
+ 
+
+ align:start position:0%
+point where they're starting to
+outcompete coal and nuclear and will
+
+ align:start position:0%
+outcompete coal and nuclear and will
+ 
+
+ align:start position:0%
+outcompete coal and nuclear and will
+probably soon algae outcompete gas and
+
+ align:start position:0%
+probably soon algae outcompete gas and
+ 
+
+ align:start position:0%
+probably soon algae outcompete gas and
+combined vehicle with combines that gold
+
+ align:start position:0%
+combined vehicle with combines that gold
+ 
+
+ align:start position:0%
+combined vehicle with combines that gold
+gas turbines also thank you very much
\ No newline at end of file
diff --git a/JGCSdBMU1uA.txt b/JGCSdBMU1uA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b05f507e763fdffaf5c23c0d5b170d86a5bc0532
--- /dev/null
+++ b/JGCSdBMU1uA.txt
@@ -0,0 +1,746 @@
+Sarah Hansen:
+Today on the podcast, we're highlighting the
+
+power of open educational resources or OER.
+
+Elizabeth Siler:
+I love using OER.
+
+One thing I love about teaching OER is that
+I get to teach what I want to teach.
+
+What I think my students need to know, in
+the way they need to learn it.
+
+Instead of just defaulting to what the textbooks
+say.
+
+Sarah Hansen:
+In this episode, I invited two instructors
+
+in to talk about open educational resources.
+
+One of them teaches negotiation and management
+here at MIT and shares her course materials
+
+in MIT OpenCourseWare.
+
+The other recently adapted those materials
+for use in her own course at another university.
+
+An organizational ombudsperson at MIT for
+42 years, adjunct professor Mary Rowe was
+
+among the very first instructors to put her
+course materials on OpenCourseWare almost
+
+20 years ago.
+
+That course is titled 15.667, Negotiation
+and Conflict Management.
+
+Associate professor Elizabeth Siler has used
+and adapted the materials from this course
+
+inner teachings at Worcester State University.
+
+When we brought these two instructors together,
+something really special happened while much
+
+of the conversation did center on negotiation
+itself.
+
+Mary and Elizabeth simultaneously began a
+real time collaboration about how to teach
+
+negotiation with OER from Mary's course.
+
+Sarah Hansen:
+The conversation brought forward so much of
+
+what we at OCW hope OER can do for educators.
+
+Things like creating community, shared ownership
+of learning materials and fuel for inspired
+
+teaching, that we just really wanted to share
+it with you.
+
+We hope it will help you find new inspiration
+for using OER in your teaching.
+
+So without any further ado, let's jump into
+the conversation.
+
+You'll hear me talking with Elizabeth first
+and we start with one of my own insecurities
+
+about negotiation, an anxiety some of you
+may share.
+
+When I think about negotiation, I like freeze
+up.
+
+I'm like, Oh God, I have to negotiate a salary.
+
+I'm never going to get what I want.
+
+I can't ask for what I want.
+
+Elizabeth Siler:
+Well, that's one of the reasons that I really
+
+like this course learning it and teaching
+it.
+
+It's one of the things that...
+
+This is probably true for most students and
+most people, they don't really like to deal
+
+with conflict, but learning about negotiation
+as a way that you can learn that there are
+
+different ways to handle a conflict, or handle
+a negotiation without changing your personality,
+
+right.
+
+Without being something that you're not.
+
+It's their skills and their behaviors, but
+they're not personality traits.
+
+You can be shy and still be clear in what
+you want and ask questions.
+
+You can still be a successful negotiator and
+still not like speaking in public.
+
+Mary Rowe:
+I think that's a wonderful example of how
+
+negotiation specialists try to build options,
+which is that those who get into negotiations
+
+about anything, including bedtime for children,
+want to come up with options.
+
+Sarah Hansen:
+I'm taking that to heart as I think about
+
+my three-year-old tonight.
+
+So the course 15.667, the one we have on MIT,
+OpenCourseWare it involves a number of case
+
+studies and simulations, which you've made
+openly available Mary to the world.
+
+Tell us about the role of case studies in
+the course?
+
+Mary Rowe:
+So case studies and discussing real life is
+
+how you learn negotiations.
+
+It's absolutely essential.
+
+Elizabeth Siler:
+There's one of them called dealing with an
+
+aggressive competitive negotiator.
+
+And this was a case, the main character's
+named Mr. Canny.
+
+And he just wants what you're selling, but
+he won't admit it and he won't give in.
+
+He won't, he keeps asking for more and it,
+I mean, he's a real pain.
+
+But what I love about this is that the students
+read this and they're like, "Oh, what do I
+
+do this person?
+
+How do I deal with this person?
+
+What's going on?"
+
+And then they talk about it with each other
+and they start to see that, okay, there are
+
+some things we could do.
+
+And then we start to apply that process of,
+well, what are his interests?
+
+What does he want?
+
+What's going on behind the scenes?
+
+Elizabeth Siler:
+He's being very aggressive, but why is that?
+
+And what does he like?
+
+How might you talk to this person, so
+he'll be more likely to take you seriously.
+
+And so the two things I like about this is,
+one is that the teaching notes for some of
+
+these are really thorough and lovely and wonderful,
+is this list that's like two pages long of
+
+things that you could do to address this situation.
+
+But the other thing about it is that this
+is written so strongly that my students had
+
+some really visceral reactions to this.
+
+Some of them felt really angry.
+
+We did this at the end of the class, the end
+of the semester, so that they were comfortable
+
+talking about...
+
+They were more comfortable with self disclosure
+about how they were feeling and what went
+
+on.
+
+And some of them got really angry.
+
+Some of them got really scared.
+
+I was thrilled when this very articulate,
+very kind of cool hockey player guy in my
+
+class said, "I'll admit it.
+
+You know, I was a little nervous when I was
+reading this."
+
+Like, yes.
+
+Okay, good.
+
+Elizabeth Siler:
+And so they could talk about how you have
+
+to deal with your own emotions right before
+you can go on and negotiate, which in business,
+
+so much... emotions are treated like they are
+bad, or that people don't have emotions.
+
+But you can't really negotiate well if you're
+afraid.
+
+Or you can't negotiate well with somebody
+if you're angry.
+
+So one of the things we talked about at the
+end is, okay, here's how you felt about this.
+
+What are some things that you do?
+
+I mean, there was money involved in it, but
+the thing that was really important about
+
+that one to me was to get the students to
+acknowledge their emotions and figure out
+
+how to deal with them.
+
+And then to see that there's a whole lot more
+things they could do in the situation than
+
+they thought of, than they had thought about
+before.
+
+Mary Rowe:
+It's hard to imagine, Elizabeth, more skillful
+
+discussion of teaching that case.
+
+Listening to you, I notice two things.
+
+One of them is that you've illuminated perfectly,
+that we're all negotiating with ourselves
+
+and how we're dealing with our negotiation,
+with our, our dealing, with our emotions.
+
+We've got two different points of view.
+
+I've got to make this work and I'm panicked
+or I'm furious.
+
+So you're opening up a discussion at the end
+of the class about even not just how I noticed
+
+that negotiations are important, I guess they
+should have been.
+
+My first point is that emotions are important
+that after all relationships between people,
+
+are almost always the most important thing
+going on, even more so than money.
+
+But secondly, that in dealing with my emotions,
+that I might be negotiating with myself, I
+
+loved your description.
+
+Elizabeth Siler:
+And I love how you could tie that back to
+
+the theory.
+
+Right?
+
+negotiating with yourself because...
+
+Well, that's, frankly, that's one of the hardest
+things I find about teaching is until I really,
+
+really know, like until I've taught the course
+a lot or really know it, it takes me longer
+
+to make those connections from the student
+experience to the theory.
+
+So it's really helpful to see that.
+
+Mary Rowe:
+Well, and it's helpful to me to listen to
+
+you and see it.
+
+So always learning.
+
+Listening to Elizabeth again now reminded
+me of how every student who plays has a chance
+
+to learn their own strengths and their own
+vulnerabilities.
+
+And I think that could be elucidated better
+in the teaching.
+
+I used to say at the beginning of the course,
+that I have no idea whether we can teach people
+
+to negotiate better in the sense of getting
+more of what you want.
+
+I was pretty sure that we can teach how you
+and your team can lose less in working with
+
+other people.
+
+I'd like to think more about that in revising
+the course.
+
+Mary Rowe:
+We, haven't actually proven that we can teach
+
+people to negotiate better, in part because
+how well you negotiate is for you to decide.
+
+And I can't tell you how you would think of
+it.
+
+You might watch me negotiate and think I'd
+given up the store and I'm pretty happy about
+
+it because I've maintained the relationships
+that mattered to me.
+
+But I think we can teach people to defend
+themselves better and that we can prove that.
+
+Anyway, you're right on the fringe know of
+what I've been thinking about.
+
+Sarah Hansen:
+The case studies and 15.667 are designed for
+
+graduate students in the MIT Sloan School
+of Management.
+
+And many of these students come to the course
+with previous management and business experience.
+
+Elizabeth Siler:
+My students have not had the same kinds of
+
+work experience that a graduate student would
+have.
+
+So I would add some things in to explain,
+well, this is how a law firm works, or this
+
+is what a defense contractor does.
+
+And this is the way the organization is structured.
+
+So when you say this, this is what it means.
+
+It, when it says this, this is what it means.
+
+And it was just really helpful because that's
+the stuff that they would need to know to
+
+make a decision, but they don't need to know
+it to learn how to negotiate.
+
+I try to get the confusing things out of the
+way so they can concentrate on what are the
+
+interests, and what am I going to say?
+
+Mary Rowe:
+Very good ideas.
+
+Sarah Hansen:
+It seems like you're touching on an important
+
+aspect of what it means to teach with OER.
+
+What it means to really discover something
+and then to change it, to make it work for
+
+your students.
+
+Elizabeth Siler:
+Yeah.
+
+I love using OER.
+
+One thing I love about teaching OER is that
+I get to teach what I want to teach.
+
+What I think my students need to know in the
+way they need to learn it.
+
+Instead of just defaulting to what the texts
+books say.
+
+And sometimes that means using a textbook
+that's an open resource and just adding things
+
+in.
+
+Sometimes it means pulling from more than
+one textbook.
+
+Sometimes it means pulling things from...
+
+Writing things and pulling in podcasts and
+articles and-
+
+Mary Rowe:
+And the newspaper from yesterday.
+
+Elizabeth Siler:
+... Newspaper from yesterday.
+
+Right.
+
+Sarah Hansen:
+I asked Elizabeth if she had any tips for
+
+educators who wanted to begin teaching with
+OER.
+
+Elizabeth Siler:
+The first thing I would do is to talk to your
+
+librarian, because librarians are pretty much
+at the forefront of open education resources.
+
+The next thing I would say is to find somebody
+to work with find some community, which is,
+
+Mary's nodding.
+
+It's a lot easier if you were starting a course
+kind of from scratch the way I was with this
+
+course to find somebody to work with, because
+it helps split up the workload and it gives
+
+you somebody to bounce ideas off of.
+
+And the other thing is just to think about
+what's working and what's not working about
+
+your current course.
+
+Because if something's not working, you can
+probably find something else to replace it.
+
+It's not just about using a textbook that's
+free, so that your students will have it.
+
+It's also about being able to teach what you
+think they need to learn.
+
+Elizabeth Siler:
+The other thing is, if you're using open educational
+
+resources that you can mix and match.
+
+There are several meta search engines for
+OER materials right now.
+
+And the good news is the bad news that there
+are so many of them, you might have to dig
+
+through to find what you're looking for.
+
+But the good news is that there is a lot out
+there.
+
+And if there's not, then you can write it.
+
+Sarah Hansen:
+Elizabeth, what plans do you have to share
+
+the materials you've adapted from Mary's course
+with others?
+
+Elizabeth Siler:
+Right.
+
+That's part of open education resources overall
+is community again, and it's doing what you
+
+have and sharing it with other people.
+
+Once I finish, I'm probably going to work
+with the instructional designer at my school,
+
+actually to put things in a word document
+and PDF documents.
+
+So that they could be in a format that can
+be easily adapted by other professors and
+
+then find a platform for it.
+
+Sarah Hansen:
+Before we ended our conversation, I asked
+
+Mary and Elizabeth, if there was anything
+else, they wanted to ask each other about
+
+teaching with the OER in 15.667.
+
+Mary Rowe:
+
+Well I would like to ask, Elizabeth, did you
+use the task of writing a perceived injurious
+
+experience letter?
+
+Elizabeth Siler:
+Oh, yes I did.
+
+Mary Rowe:
+The reason I ask is that of everything that
+
+I ever stumbled into, of course, everything
+you've heard from me is hindsight.
+
+I never had the wit to plan it, but of everything
+that I ever came up with in teaching negotiations,
+
+the perceived injurious letter and various
+variations of it, flew by far the furthest.
+
+I would get requests, I remember one from
+Canada to reproduce the instructions in 500,000
+
+copies for school, for elementary school or
+something.
+
+And still on my website at Sloan, it's now
+called ideas to consider if you've been harassed,
+
+right.
+
+But basically the notion of how to deal with
+a situation where you have felt injured or
+
+hurt.
+
+So I'm very interested in your experience
+with it.
+
+Elizabeth Siler:
+Yeah.
+
+From one of the last assignments in this semester,
+the students could write the perceived injurious-
+
+Mary Rowe:
+Experience.
+
+Elizabeth Siler:
+... experience, right.
+
+They could write a PIE letter or they could
+write an apology letter.
+
+They could choose, and they could write about
+something from themselves and their own life.
+
+Or they could write about something from one
+of the cases, because not everybody has the
+
+same level of comfort and disclosing and that's
+fine.
+
+They can still learn.
+
+And what I found out was, first of all I was
+really surprised still, even with being around
+
+hundreds of undergraduates every day, just
+how much, how personal people were willing
+
+to get at this.
+
+I mean, it was clear I was the only person
+who was going to read this.
+
+Nobody was ever going to do it.
+
+They didn't have to send it.
+
+But people got really personal and I thought
+they would be getting personal more about
+
+how they'd been injured, but they got really
+personal and really explicit and really thoughtful
+
+about how they had hurt other people.
+
+Elizabeth Siler:
+And that was really powerful.
+
+I mean, I was kind of blown away by how willing
+they were to take this on and the things they
+
+said.
+
+And I wish I had done it earlier in the semester
+so that I could find out some more, how did
+
+they react to that?
+
+Like what did they get out of it?
+
+Going back to the beginning of this, I think
+that maybe why this spoke to me so much, it's
+
+because it was everything every day.
+
+And that there are a lot of things you can
+do in business classes with a very low amount
+
+of emotions involved, and that's great, but
+this isn't one of them.
+
+And we don't really talk about it much in
+any other business classes, but we're human.
+
+As my finance professor said, Annabel Burrell.
+
+And she said, we are more than rational beings.
+
+Right?
+
+And I think this is one of the places where
+that's incredibly clear.
+
+Mary Rowe:
+You remind me also that it's the basis for
+
+leadership.
+
+To the extent that management training includes
+a discussion of leadership, emotions had relationships
+
+are profoundly fundamental.
+
+Sarah Hansen:
+You two have completely changed my perspective
+
+on what negotiation is.
+
+I feel like you've created a pathway for me
+to explore this area more.
+
+I feel like it's accessible to me that I might
+actually be good at it.
+
+Mary Rowe:
+Oh, yeah.
+
+Sarah Hansen:
+That I might be doing it already without knowing
+
+it.
+
+If you're getting the same feeling that maybe
+you or your students might already be, or
+
+it could become good at negotiation with the
+right tools, and want to learn more, you can
+
+explore, download, reuse, and remix all of
+Mary's teaching materials from our MIT OpenCourseWare
+
+website.
+
+On our website and in the show notes, you'll
+find the case study about dealing with an
+
+aggressive competitive negotiator, like Mr.
+Canny and guidelines for writing a perceived
+
+injurious experience letter.
+
+If you, like Elizabeth use these or other
+OER from OpenCourseWare in your teaching,
+
+we'd love to hear about it because when you
+share your story of using OER, you inspire
+
+others.
+
+And that's what we're all about.
+
+Thank you for listening.
+
+And we hope you enjoyed season one of Chalk
+Radio.
+
+We're already hard at work on season two.
+
+If there's a professor you'd like to hear
+from reach out and let us know.
+
+Until next time I'm Sarah Hansen from MIT,
+OpenCourseWare.
\ No newline at end of file
diff --git a/JPkgJwJHYSc.txt b/JPkgJwJHYSc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b555856f942314437efd56c3c248d9b804e6ad77
--- /dev/null
+++ b/JPkgJwJHYSc.txt
@@ -0,0 +1,14603 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm excited because I'm gonna get the
+
+ align:start position:0%
+I'm excited because I'm gonna get the
+ 
+
+ align:start position:0%
+I'm excited because I'm gonna get the
+chance to co-teach today with I would
+
+ align:start position:0%
+chance to co-teach today with I would
+ 
+
+ align:start position:0%
+chance to co-teach today with I would
+say one of the students but it's not
+
+ align:start position:0%
+say one of the students but it's not
+ 
+
+ align:start position:0%
+say one of the students but it's not
+really one of the students but Larry
+
+ align:start position:0%
+really one of the students but Larry
+ 
+
+ align:start position:0%
+really one of the students but Larry
+Lessig is consented to join us in a in a
+
+ align:start position:0%
+Lessig is consented to join us in a in a
+ 
+
+ align:start position:0%
+Lessig is consented to join us in a in a
+few minutes so I'm going to be breezing
+
+ align:start position:0%
+few minutes so I'm going to be breezing
+ 
+
+ align:start position:0%
+few minutes so I'm going to be breezing
+through a little faster than usual and
+
+ align:start position:0%
+through a little faster than usual and
+ 
+
+ align:start position:0%
+through a little faster than usual and
+then we'll co-teach this blockchain and
+
+ align:start position:0%
+then we'll co-teach this blockchain and
+ 
+
+ align:start position:0%
+then we'll co-teach this blockchain and
+money here we are where it's smart
+
+ align:start position:0%
+money here we are where it's smart
+ 
+
+ align:start position:0%
+money here we are where it's smart
+contracts everybody seems to be coming
+
+ align:start position:0%
+contracts everybody seems to be coming
+ 
+
+ align:start position:0%
+contracts everybody seems to be coming
+back which is a sign of your interest
+
+ align:start position:0%
+back which is a sign of your interest
+ 
+
+ align:start position:0%
+back which is a sign of your interest
+more than it is in my teaching but I
+
+ align:start position:0%
+more than it is in my teaching but I
+ 
+
+ align:start position:0%
+more than it is in my teaching but I
+thank you for being here
+
+ align:start position:0%
+thank you for being here
+ 
+
+ align:start position:0%
+thank you for being here
+we made it through the last three
+
+ align:start position:0%
+we made it through the last three
+ 
+
+ align:start position:0%
+we made it through the last three
+classes together on Bitcoin in the
+
+ align:start position:0%
+classes together on Bitcoin in the
+ 
+
+ align:start position:0%
+classes together on Bitcoin in the
+basics of that technology and in one
+
+ align:start position:0%
+basics of that technology and in one
+ 
+
+ align:start position:0%
+basics of that technology and in one
+class we're gonna try to chew off a bit
+
+ align:start position:0%
+class we're gonna try to chew off a bit
+ 
+
+ align:start position:0%
+class we're gonna try to chew off a bit
+on smart contracts both the technology
+
+ align:start position:0%
+on smart contracts both the technology
+ 
+
+ align:start position:0%
+on smart contracts both the technology
+side a little bit on the market and then
+
+ align:start position:0%
+side a little bit on the market and then
+ 
+
+ align:start position:0%
+side a little bit on the market and then
+the law that Larry is going to take us
+
+ align:start position:0%
+the law that Larry is going to take us
+ 
+
+ align:start position:0%
+the law that Larry is going to take us
+through and so as I said I want to start
+
+ align:start position:0%
+through and so as I said I want to start
+ 
+
+ align:start position:0%
+through and so as I said I want to start
+with a little administrative because we
+
+ align:start position:0%
+with a little administrative because we
+ 
+
+ align:start position:0%
+with a little administrative because we
+are on the sixth class I'm gonna review
+
+ align:start position:0%
+are on the sixth class I'm gonna review
+ 
+
+ align:start position:0%
+are on the sixth class I'm gonna review
+a bit about the projects very quickly
+
+ align:start position:0%
+a bit about the projects very quickly
+ 
+
+ align:start position:0%
+a bit about the projects very quickly
+we're gonna do smart contracts the the
+
+ align:start position:0%
+we're gonna do smart contracts the the
+ 
+
+ align:start position:0%
+we're gonna do smart contracts the the
+design what what design features yes
+
+ align:start position:0%
+design what what design features yes
+ 
+
+ align:start position:0%
+design what what design features yes
+we're gonna go back a little bit about
+
+ align:start position:0%
+we're gonna go back a little bit about
+ 
+
+ align:start position:0%
+we're gonna go back a little bit about
+hash functions and Merkle trees but not
+
+ align:start position:0%
+hash functions and Merkle trees but not
+ 
+
+ align:start position:0%
+hash functions and Merkle trees but not
+too much
+
+ align:start position:0%
+too much
+ 
+
+ align:start position:0%
+too much
+DAP switch are basically decentralized
+
+ align:start position:0%
+DAP switch are basically decentralized
+ 
+
+ align:start position:0%
+DAP switch are basically decentralized
+applications and token sales Larry's
+
+ align:start position:0%
+applications and token sales Larry's
+ 
+
+ align:start position:0%
+applications and token sales Larry's
+going to take us through legal issues
+
+ align:start position:0%
+going to take us through legal issues
+ 
+
+ align:start position:0%
+going to take us through legal issues
+and then we'll sum it all up so let me
+
+ align:start position:0%
+and then we'll sum it all up so let me
+ 
+
+ align:start position:0%
+and then we'll sum it all up so let me
+just real fast on the administrative
+
+ align:start position:0%
+just real fast on the administrative
+ 
+
+ align:start position:0%
+just real fast on the administrative
+side again class participation 30%
+
+ align:start position:0%
+side again class participation 30%
+ 
+
+ align:start position:0%
+side again class participation 30%
+that's why we're all here together
+
+ align:start position:0%
+that's why we're all here together
+ 
+
+ align:start position:0%
+that's why we're all here together
+that means hopefully reading the
+
+ align:start position:0%
+that means hopefully reading the
+ 
+
+ align:start position:0%
+that means hopefully reading the
+assignments and participating about half
+
+ align:start position:0%
+assignments and participating about half
+ 
+
+ align:start position:0%
+assignments and participating about half
+of you have participated so I guess I'm
+
+ align:start position:0%
+of you have participated so I guess I'm
+ 
+
+ align:start position:0%
+of you have participated so I guess I'm
+gonna go with a little bit more cold
+
+ align:start position:0%
+gonna go with a little bit more cold
+ 
+
+ align:start position:0%
+gonna go with a little bit more cold
+calling starting Thursday I'm not gonna
+
+ align:start position:0%
+calling starting Thursday I'm not gonna
+ 
+
+ align:start position:0%
+calling starting Thursday I'm not gonna
+do a bunch of it today because Larry and
+
+ align:start position:0%
+do a bunch of it today because Larry and
+ 
+
+ align:start position:0%
+do a bunch of it today because Larry and
+I are joining so you can ease off but be
+
+ align:start position:0%
+I are joining so you can ease off but be
+ 
+
+ align:start position:0%
+I are joining so you can ease off but be
+really be conscious if you haven't been
+
+ align:start position:0%
+really be conscious if you haven't been
+ 
+
+ align:start position:0%
+really be conscious if you haven't been
+participating try to get in and join the
+
+ align:start position:0%
+participating try to get in and join the
+ 
+
+ align:start position:0%
+participating try to get in and join the
+conversation and discussion the two
+
+ align:start position:0%
+conversation and discussion the two
+ 
+
+ align:start position:0%
+conversation and discussion the two
+individual write-ups I think we have
+
+ align:start position:0%
+individual write-ups I think we have
+ 
+
+ align:start position:0%
+individual write-ups I think we have
+seven but it's quite possible some of
+
+ align:start position:0%
+seven but it's quite possible some of
+ 
+
+ align:start position:0%
+seven but it's quite possible some of
+you have submitted already it's just
+
+ align:start position:0%
+you have submitted already it's just
+ 
+
+ align:start position:0%
+you have submitted already it's just
+meant to be
+
+ align:start position:0%
+meant to be
+ 
+
+ align:start position:0%
+meant to be
+critical business reasoning we are in a
+
+ align:start position:0%
+critical business reasoning we are in a
+ 
+
+ align:start position:0%
+critical business reasoning we are in a
+business school mcc's tenth you just
+
+ align:start position:0%
+business school mcc's tenth you just
+ 
+
+ align:start position:0%
+business school mcc's tenth you just
+summarized some readings I'm sure will
+
+ align:start position:0%
+summarized some readings I'm sure will
+ 
+
+ align:start position:0%
+summarized some readings I'm sure will
+give you a you know a pass on that but
+
+ align:start position:0%
+give you a you know a pass on that but
+ 
+
+ align:start position:0%
+give you a you know a pass on that but
+that's not what I'm looking for I'm
+
+ align:start position:0%
+that's not what I'm looking for I'm
+ 
+
+ align:start position:0%
+that's not what I'm looking for I'm
+really looking for critical reasoning
+
+ align:start position:0%
+really looking for critical reasoning
+ 
+
+ align:start position:0%
+really looking for critical reasoning
+and thinking from a business perspective
+
+ align:start position:0%
+and thinking from a business perspective
+ 
+
+ align:start position:0%
+and thinking from a business perspective
+of why does this matter what are its
+
+ align:start position:0%
+of why does this matter what are its
+ 
+
+ align:start position:0%
+of why does this matter what are its
+strengths or its values in terms of
+
+ align:start position:0%
+strengths or its values in terms of
+ 
+
+ align:start position:0%
+strengths or its values in terms of
+business reasoning and critical
+
+ align:start position:0%
+business reasoning and critical
+ 
+
+ align:start position:0%
+business reasoning and critical
+reasoning one by the tenth class one by
+
+ align:start position:0%
+reasoning one by the tenth class one by
+ 
+
+ align:start position:0%
+reasoning one by the tenth class one by
+the 23rd always before class what it
+
+ align:start position:0%
+the 23rd always before class what it
+ 
+
+ align:start position:0%
+the 23rd always before class what it
+likely means this will be getting most
+
+ align:start position:0%
+likely means this will be getting most
+ 
+
+ align:start position:0%
+likely means this will be getting most
+of these on the 8th 9th and 10th class I
+
+ align:start position:0%
+of these on the 8th 9th and 10th class I
+ 
+
+ align:start position:0%
+of these on the 8th 9th and 10th class I
+know how that works and so forth and
+
+ align:start position:0%
+know how that works and so forth and
+ 
+
+ align:start position:0%
+know how that works and so forth and
+that's okay that's okay
+
+ align:start position:0%
+that's okay that's okay
+ 
+
+ align:start position:0%
+that's okay that's okay
+but I'm just reminding you of that in
+
+ align:start position:0%
+but I'm just reminding you of that in
+ 
+
+ align:start position:0%
+but I'm just reminding you of that in
+terms of the group research paper again
+
+ align:start position:0%
+terms of the group research paper again
+ 
+
+ align:start position:0%
+terms of the group research paper again
+Sabrina and talita stood up a Google app
+
+ align:start position:0%
+Sabrina and talita stood up a Google app
+ 
+
+ align:start position:0%
+Sabrina and talita stood up a Google app
+I think it's in Google but where you can
+
+ align:start position:0%
+I think it's in Google but where you can
+ 
+
+ align:start position:0%
+I think it's in Google but where you can
+go in and team up in teams of three or
+
+ align:start position:0%
+go in and team up in teams of three or
+ 
+
+ align:start position:0%
+go in and team up in teams of three or
+four it's not required to do this by the
+
+ align:start position:0%
+four it's not required to do this by the
+ 
+
+ align:start position:0%
+four it's not required to do this by the
+eighth class next Tuesday but I'm
+
+ align:start position:0%
+eighth class next Tuesday but I'm
+ 
+
+ align:start position:0%
+eighth class next Tuesday but I'm
+strongly suggesting it to figure out who
+
+ align:start position:0%
+strongly suggesting it to figure out who
+ 
+
+ align:start position:0%
+strongly suggesting it to figure out who
+your teams are and not sort of wait till
+
+ align:start position:0%
+your teams are and not sort of wait till
+ 
+
+ align:start position:0%
+your teams are and not sort of wait till
+the second half of the semester and I'd
+
+ align:start position:0%
+the second half of the semester and I'd
+ 
+
+ align:start position:0%
+the second half of the semester and I'd
+like to encourage everybody to choose an
+
+ align:start position:0%
+like to encourage everybody to choose an
+ 
+
+ align:start position:0%
+like to encourage everybody to choose an
+area for your use case by mid way again
+
+ align:start position:0%
+area for your use case by mid way again
+ 
+
+ align:start position:0%
+area for your use case by mid way again
+you're not going to get graded if it
+
+ align:start position:0%
+you're not going to get graded if it
+ 
+
+ align:start position:0%
+you're not going to get graded if it
+takes you another class or two to figure
+
+ align:start position:0%
+takes you another class or two to figure
+ 
+
+ align:start position:0%
+takes you another class or two to figure
+it out but I just think it's much better
+
+ align:start position:0%
+it out but I just think it's much better
+ 
+
+ align:start position:0%
+it out but I just think it's much better
+if you you know your teams you know what
+
+ align:start position:0%
+if you you know your teams you know what
+ 
+
+ align:start position:0%
+if you you know your teams you know what
+your use case will be if it's not about
+
+ align:start position:0%
+your use case will be if it's not about
+ 
+
+ align:start position:0%
+your use case will be if it's not about
+finance one one group was already asked
+
+ align:start position:0%
+finance one one group was already asked
+ 
+
+ align:start position:0%
+finance one one group was already asked
+me to if that's all right I just want to
+
+ align:start position:0%
+me to if that's all right I just want to
+ 
+
+ align:start position:0%
+me to if that's all right I just want to
+know more detailed what its gonna be I'm
+
+ align:start position:0%
+know more detailed what its gonna be I'm
+ 
+
+ align:start position:0%
+know more detailed what its gonna be I'm
+probably gonna say yes but it needs a
+
+ align:start position:0%
+probably gonna say yes but it needs a
+ 
+
+ align:start position:0%
+probably gonna say yes but it needs a
+little bit of pre-approval if it's
+
+ align:start position:0%
+little bit of pre-approval if it's
+ 
+
+ align:start position:0%
+little bit of pre-approval if it's
+outside of Finance so any questions
+
+ align:start position:0%
+outside of Finance so any questions
+ 
+
+ align:start position:0%
+outside of Finance so any questions
+about the requirements I just wanted a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the study questions today's smart
+
+ align:start position:0%
+so the study questions today's smart
+ 
+
+ align:start position:0%
+so the study questions today's smart
+contracts and and basically how they
+
+ align:start position:0%
+contracts and and basically how they
+ 
+
+ align:start position:0%
+contracts and and basically how they
+compared to regular contracts and what
+
+ align:start position:0%
+compared to regular contracts and what
+ 
+
+ align:start position:0%
+compared to regular contracts and what
+are the tokens that are used within that
+
+ align:start position:0%
+are the tokens that are used within that
+ 
+
+ align:start position:0%
+are the tokens that are used within that
+ecosystem and what are the platforms in
+
+ align:start position:0%
+ecosystem and what are the platforms in
+ 
+
+ align:start position:0%
+ecosystem and what are the platforms in
+a very similar sense to
+
+ align:start position:0%
+a very similar sense to
+ 
+
+ align:start position:0%
+a very similar sense to
+the Internet we have the Internet and
+
+ align:start position:0%
+the Internet we have the Internet and
+ 
+
+ align:start position:0%
+the Internet we have the Internet and
+then above the internet you have you
+
+ align:start position:0%
+then above the internet you have you
+ 
+
+ align:start position:0%
+then above the internet you have you
+would say applications Facebook and
+
+ align:start position:0%
+would say applications Facebook and
+ 
+
+ align:start position:0%
+would say applications Facebook and
+other applications well this too has a
+
+ align:start position:0%
+other applications well this too has a
+ 
+
+ align:start position:0%
+other applications well this too has a
+series of platforms and then
+
+ align:start position:0%
+series of platforms and then
+ 
+
+ align:start position:0%
+series of platforms and then
+decentralized applications potentially
+
+ align:start position:0%
+decentralized applications potentially
+ 
+
+ align:start position:0%
+decentralized applications potentially
+on top of that and basically a quick
+
+ align:start position:0%
+on top of that and basically a quick
+ 
+
+ align:start position:0%
+on top of that and basically a quick
+touch on decentralized applications
+
+ align:start position:0%
+touch on decentralized applications
+ 
+
+ align:start position:0%
+touch on decentralized applications
+later in the semester we're going to
+
+ align:start position:0%
+later in the semester we're going to
+ 
+
+ align:start position:0%
+later in the semester we're going to
+take two sessions on initial point
+
+ align:start position:0%
+take two sessions on initial point
+ 
+
+ align:start position:0%
+take two sessions on initial point
+offerings and thus we're going to talk a
+
+ align:start position:0%
+offerings and thus we're going to talk a
+ 
+
+ align:start position:0%
+offerings and thus we're going to talk a
+lot about token economics so this will
+
+ align:start position:0%
+lot about token economics so this will
+ 
+
+ align:start position:0%
+lot about token economics so this will
+be just the first taste test and then
+
+ align:start position:0%
+be just the first taste test and then
+ 
+
+ align:start position:0%
+be just the first taste test and then
+we'll come back to it later and then the
+
+ align:start position:0%
+we'll come back to it later and then the
+ 
+
+ align:start position:0%
+we'll come back to it later and then the
+readings I hopefully everybody read
+
+ align:start position:0%
+readings I hopefully everybody read
+ 
+
+ align:start position:0%
+readings I hopefully everybody read
+through smart contracts
+
+ align:start position:0%
+through smart contracts
+ 
+
+ align:start position:0%
+through smart contracts
+I thought the chamber of digital
+
+ align:start position:0%
+I thought the chamber of digital
+ 
+
+ align:start position:0%
+I thought the chamber of digital
+commerce even though this is almost two
+
+ align:start position:0%
+commerce even though this is almost two
+ 
+
+ align:start position:0%
+commerce even though this is almost two
+years ago this paper was a very helpful
+
+ align:start position:0%
+years ago this paper was a very helpful
+ 
+
+ align:start position:0%
+years ago this paper was a very helpful
+sort of flavor for what folks and
+
+ align:start position:0%
+sort of flavor for what folks and
+ 
+
+ align:start position:0%
+sort of flavor for what folks and
+commerce are thinking and what
+
+ align:start position:0%
+commerce are thinking and what
+ 
+
+ align:start position:0%
+commerce are thinking and what
+developers were thinking and I love that
+
+ align:start position:0%
+developers were thinking and I love that
+ 
+
+ align:start position:0%
+developers were thinking and I love that
+nick szabo sort of wrote the
+
+ align:start position:0%
+nick szabo sort of wrote the
+ 
+
+ align:start position:0%
+nick szabo sort of wrote the
+introduction to it and and and it's
+
+ align:start position:0%
+introduction to it and and and it's
+ 
+
+ align:start position:0%
+introduction to it and and and it's
+interesting to see in question why is it
+
+ align:start position:0%
+interesting to see in question why is it
+ 
+
+ align:start position:0%
+interesting to see in question why is it
+that it's two years later and many of
+
+ align:start position:0%
+that it's two years later and many of
+ 
+
+ align:start position:0%
+that it's two years later and many of
+those use cases are still being
+
+ align:start position:0%
+those use cases are still being
+ 
+
+ align:start position:0%
+those use cases are still being
+discussed but haven't fully been adopted
+
+ align:start position:0%
+discussed but haven't fully been adopted
+ 
+
+ align:start position:0%
+discussed but haven't fully been adopted
+and then the state of the daps and and
+
+ align:start position:0%
+and then the state of the daps and and
+ 
+
+ align:start position:0%
+and then the state of the daps and and
+then who are the competitors to eat
+
+ align:start position:0%
+then who are the competitors to eat
+ 
+
+ align:start position:0%
+then who are the competitors to eat
+theorem so you don't you feel good I
+
+ align:start position:0%
+theorem so you don't you feel good I
+ 
+
+ align:start position:0%
+theorem so you don't you feel good I
+haven't asked anybody a cold question
+
+ align:start position:0%
+haven't asked anybody a cold question
+ 
+
+ align:start position:0%
+haven't asked anybody a cold question
+yet and then the optional readings I
+
+ align:start position:0%
+yet and then the optional readings I
+ 
+
+ align:start position:0%
+yet and then the optional readings I
+don't know did anybody actually go back
+
+ align:start position:0%
+don't know did anybody actually go back
+ 
+
+ align:start position:0%
+don't know did anybody actually go back
+there optional did anybody go back and
+
+ align:start position:0%
+there optional did anybody go back and
+ 
+
+ align:start position:0%
+there optional did anybody go back and
+read either Sabo's original piece from
+
+ align:start position:0%
+read either Sabo's original piece from
+ 
+
+ align:start position:0%
+read either Sabo's original piece from
+20 years ago in smart contracts so few
+
+ align:start position:0%
+20 years ago in smart contracts so few
+ 
+
+ align:start position:0%
+20 years ago in smart contracts so few
+of you are kind of into that rabbit hole
+
+ align:start position:0%
+of you are kind of into that rabbit hole
+ 
+
+ align:start position:0%
+of you are kind of into that rabbit hole
+of blocks ay and an ether British what
+
+ align:start position:0%
+of blocks ay and an ether British what
+ 
+
+ align:start position:0%
+of blocks ay and an ether British what
+did you think of you know it's 20 years
+
+ align:start position:0%
+did you think of you know it's 20 years
+ 
+
+ align:start position:0%
+did you think of you know it's 20 years
+ago he wrote this thing on nick szabo
+
+ align:start position:0%
+ago he wrote this thing on nick szabo
+ 
+
+ align:start position:0%
+ago he wrote this thing on nick szabo
+wrote this think about the etherium
+
+ align:start position:0%
+wrote this think about the etherium
+ 
+
+ align:start position:0%
+wrote this think about the etherium
+white paper what's interesting is even
+
+ align:start position:0%
+white paper what's interesting is even
+ 
+
+ align:start position:0%
+white paper what's interesting is even
+if you didn't do it for the class and
+
+ align:start position:0%
+if you didn't do it for the class and
+ 
+
+ align:start position:0%
+if you didn't do it for the class and
+you find yourself more and more
+
+ align:start position:0%
+you find yourself more and more
+ 
+
+ align:start position:0%
+you find yourself more and more
+interested in this over the next couple
+
+ align:start position:0%
+interested in this over the next couple
+ 
+
+ align:start position:0%
+interested in this over the next couple
+of months or even later going back and
+
+ align:start position:0%
+of months or even later going back and
+ 
+
+ align:start position:0%
+of months or even later going back and
+read
+
+ align:start position:0%
+read
+ 
+
+ align:start position:0%
+read
+the etherium white paper it's not highly
+
+ align:start position:0%
+the etherium white paper it's not highly
+ 
+
+ align:start position:0%
+the etherium white paper it's not highly
+technical in the first I don't know 10
+
+ align:start position:0%
+technical in the first I don't know 10
+ 
+
+ align:start position:0%
+technical in the first I don't know 10
+or 15 pages it really gives a history of
+
+ align:start position:0%
+or 15 pages it really gives a history of
+ 
+
+ align:start position:0%
+or 15 pages it really gives a history of
+Bitcoin it talks about distributed
+
+ align:start position:0%
+Bitcoin it talks about distributed
+ 
+
+ align:start position:0%
+Bitcoin it talks about distributed
+applications and largely written at the
+
+ align:start position:0%
+applications and largely written at the
+ 
+
+ align:start position:0%
+applications and largely written at the
+time by a nineteen year old as well so
+
+ align:start position:0%
+time by a nineteen year old as well so
+ 
+
+ align:start position:0%
+time by a nineteen year old as well so
+it's it's a remarkable thing and then
+
+ align:start position:0%
+it's it's a remarkable thing and then
+ 
+
+ align:start position:0%
+it's it's a remarkable thing and then
+one of Larry's colleague or maybe it's
+
+ align:start position:0%
+one of Larry's colleague or maybe it's
+ 
+
+ align:start position:0%
+one of Larry's colleague or maybe it's
+two of them but deep philippi paper as
+
+ align:start position:0%
+two of them but deep philippi paper as
+ 
+
+ align:start position:0%
+two of them but deep philippi paper as
+well on the regulatory issues so let me
+
+ align:start position:0%
+well on the regulatory issues so let me
+ 
+
+ align:start position:0%
+well on the regulatory issues so let me
+talk a little bit about smart contracts
+
+ align:start position:0%
+talk a little bit about smart contracts
+ 
+
+ align:start position:0%
+talk a little bit about smart contracts
+and lay a groundwork before Larry gives
+
+ align:start position:0%
+and lay a groundwork before Larry gives
+ 
+
+ align:start position:0%
+and lay a groundwork before Larry gives
+us the law a smart contract is a set of
+
+ align:start position:0%
+us the law a smart contract is a set of
+ 
+
+ align:start position:0%
+us the law a smart contract is a set of
+promises specified in a digital form I'm
+
+ align:start position:0%
+promises specified in a digital form I'm
+ 
+
+ align:start position:0%
+promises specified in a digital form I'm
+gonna say four things it's just a set of
+
+ align:start position:0%
+gonna say four things it's just a set of
+ 
+
+ align:start position:0%
+gonna say four things it's just a set of
+promises and in digital form so it's not
+
+ align:start position:0%
+promises and in digital form so it's not
+ 
+
+ align:start position:0%
+promises and in digital form so it's not
+hand written out it includes protocols
+
+ align:start position:0%
+hand written out it includes protocols
+ 
+
+ align:start position:0%
+hand written out it includes protocols
+what's a protocol andrew operating
+
+ align:start position:0%
+what's a protocol andrew operating
+ 
+
+ align:start position:0%
+what's a protocol andrew operating
+procedure is anybody else give me
+
+ align:start position:0%
+procedure is anybody else give me
+ 
+
+ align:start position:0%
+procedure is anybody else give me
+another word for it maybe an algorithm
+
+ align:start position:0%
+another word for it maybe an algorithm
+ 
+
+ align:start position:0%
+another word for it maybe an algorithm
+so so a set of promises in digital form
+
+ align:start position:0%
+so so a set of promises in digital form
+ 
+
+ align:start position:0%
+so so a set of promises in digital form
+but it can include math basically if you
+
+ align:start position:0%
+but it can include math basically if you
+ 
+
+ align:start position:0%
+but it can include math basically if you
+wish or standard operating procedures
+
+ align:start position:0%
+wish or standard operating procedures
+ 
+
+ align:start position:0%
+wish or standard operating procedures
+if-then statements and so forth and it's
+
+ align:start position:0%
+if-then statements and so forth and it's
+ 
+
+ align:start position:0%
+if-then statements and so forth and it's
+innate the parties then perform against
+
+ align:start position:0%
+innate the parties then perform against
+ 
+
+ align:start position:0%
+innate the parties then perform against
+these promises and guess what nick szabo
+
+ align:start position:0%
+these promises and guess what nick szabo
+ 
+
+ align:start position:0%
+these promises and guess what nick szabo
+wrote that in 1996 and i thought it was
+
+ align:start position:0%
+wrote that in 1996 and i thought it was
+ 
+
+ align:start position:0%
+wrote that in 1996 and i thought it was
+still probably the best definition of
+
+ align:start position:0%
+still probably the best definition of
+ 
+
+ align:start position:0%
+still probably the best definition of
+smart contract he coined the phrase 22
+
+ align:start position:0%
+smart contract he coined the phrase 22
+ 
+
+ align:start position:0%
+smart contract he coined the phrase 22
+years ago he might actually be Satoshi
+
+ align:start position:0%
+years ago he might actually be Satoshi
+ 
+
+ align:start position:0%
+years ago he might actually be Satoshi
+Nakamoto three of the tables in here you
+
+ align:start position:0%
+Nakamoto three of the tables in here you
+ 
+
+ align:start position:0%
+Nakamoto three of the tables in here you
+all voted that it was Nick's mo so I
+
+ align:start position:0%
+all voted that it was Nick's mo so I
+ 
+
+ align:start position:0%
+all voted that it was Nick's mo so I
+thought that's kind of the best
+
+ align:start position:0%
+thought that's kind of the best
+ 
+
+ align:start position:0%
+thought that's kind of the best
+definition if you've got to just kind of
+
+ align:start position:0%
+definition if you've got to just kind of
+ 
+
+ align:start position:0%
+definition if you've got to just kind of
+a root you know now I would also say
+
+ align:start position:0%
+a root you know now I would also say
+ 
+
+ align:start position:0%
+a root you know now I would also say
+however that smart contracts may not be
+
+ align:start position:0%
+however that smart contracts may not be
+ 
+
+ align:start position:0%
+however that smart contracts may not be
+so smart a lot of people have come to be
+
+ align:start position:0%
+so smart a lot of people have come to be
+ 
+
+ align:start position:0%
+so smart a lot of people have come to be
+calling them dumb contracts they're just
+
+ align:start position:0%
+calling them dumb contracts they're just
+ 
+
+ align:start position:0%
+calling them dumb contracts they're just
+algorithms that perform a function so
+
+ align:start position:0%
+algorithms that perform a function so
+ 
+
+ align:start position:0%
+algorithms that perform a function so
+don't think of them as artificial
+
+ align:start position:0%
+don't think of them as artificial
+ 
+
+ align:start position:0%
+don't think of them as artificial
+intelligence that's another class
+
+ align:start position:0%
+intelligence that's another class
+ 
+
+ align:start position:0%
+intelligence that's another class
+provided next semester by Simon Johnson
+
+ align:start position:0%
+provided next semester by Simon Johnson
+ 
+
+ align:start position:0%
+provided next semester by Simon Johnson
+think of them almost as just dumb
+
+ align:start position:0%
+think of them almost as just dumb
+ 
+
+ align:start position:0%
+think of them almost as just dumb
+contracts and in a sense they're
+
+ align:start position:0%
+contracts and in a sense they're
+ 
+
+ align:start position:0%
+contracts and in a sense they're
+mechanizing what might otherwise be done
+
+ align:start position:0%
+mechanizing what might otherwise be done
+ 
+
+ align:start position:0%
+mechanizing what might otherwise be done
+amongst them between humans and smart
+
+ align:start position:0%
+amongst them between humans and smart
+ 
+
+ align:start position:0%
+amongst them between humans and smart
+contracts may or may not be really
+
+ align:start position:0%
+contracts may or may not be really
+ 
+
+ align:start position:0%
+contracts may or may not be really
+contracts and that's why Larry is going
+
+ align:start position:0%
+contracts and that's why Larry is going
+ 
+
+ align:start position:0%
+contracts and that's why Larry is going
+to speak to it so I just remember even
+
+ align:start position:0%
+to speak to it so I just remember even
+ 
+
+ align:start position:0%
+to speak to it so I just remember even
+though Nick Sabo's calls it smart
+
+ align:start position:0%
+though Nick Sabo's calls it smart
+ 
+
+ align:start position:0%
+though Nick Sabo's calls it smart
+contracts they may not be smart and they
+
+ align:start position:0%
+contracts they may not be smart and they
+ 
+
+ align:start position:0%
+contracts they may not be smart and they
+may not be contracts so a little bit
+
+ align:start position:0%
+may not be contracts so a little bit
+ 
+
+ align:start position:0%
+may not be contracts so a little bit
+about the technical features remember
+
+ align:start position:0%
+about the technical features remember
+ 
+
+ align:start position:0%
+about the technical features remember
+our three three ways we did this what
+
+ align:start position:0%
+our three three ways we did this what
+ 
+
+ align:start position:0%
+our three three ways we did this what
+what are the big technical features that
+
+ align:start position:0%
+what are the big technical features that
+ 
+
+ align:start position:0%
+what are the big technical features that
+we studied I'm sorry to do this Anton
+
+ align:start position:0%
+we studied I'm sorry to do this Anton
+ 
+
+ align:start position:0%
+we studied I'm sorry to do this Anton
+what are the three big buckets remember
+
+ align:start position:0%
+what are the three big buckets remember
+ 
+
+ align:start position:0%
+what are the three big buckets remember
+we took three classes and three buckets
+
+ align:start position:0%
+we took three classes and three buckets
+ 
+
+ align:start position:0%
+we took three classes and three buckets
+of information great you got what two
+
+ align:start position:0%
+of information great you got what two
+ 
+
+ align:start position:0%
+of information great you got what two
+other people give me the others so
+
+ align:start position:0%
+other people give me the others so
+ 
+
+ align:start position:0%
+other people give me the others so
+cryptography guess what bitcoin and
+
+ align:start position:0%
+cryptography guess what bitcoin and
+ 
+
+ align:start position:0%
+cryptography guess what bitcoin and
+etherium all have the same cryptography
+
+ align:start position:0%
+etherium all have the same cryptography
+ 
+
+ align:start position:0%
+etherium all have the same cryptography
+it's not identical but for the purposes
+
+ align:start position:0%
+it's not identical but for the purposes
+ 
+
+ align:start position:0%
+it's not identical but for the purposes
+of design features it has cryptographic
+
+ align:start position:0%
+of design features it has cryptographic
+ 
+
+ align:start position:0%
+of design features it has cryptographic
+hashes timestamps block headers Merkle
+
+ align:start position:0%
+hashes timestamps block headers Merkle
+ 
+
+ align:start position:0%
+hashes timestamps block headers Merkle
+trees the etherium has more than one
+
+ align:start position:0%
+trees the etherium has more than one
+ 
+
+ align:start position:0%
+trees the etherium has more than one
+Merkel tree and Bitcoin has one and it
+
+ align:start position:0%
+Merkel tree and Bitcoin has one and it
+ 
+
+ align:start position:0%
+Merkel tree and Bitcoin has one and it
+has digital signatures and addresses so
+
+ align:start position:0%
+has digital signatures and addresses so
+ 
+
+ align:start position:0%
+has digital signatures and addresses so
+everything we talked about three
+
+ align:start position:0%
+everything we talked about three
+ 
+
+ align:start position:0%
+everything we talked about three
+lectures ago about cryptography both
+
+ align:start position:0%
+lectures ago about cryptography both
+ 
+
+ align:start position:0%
+lectures ago about cryptography both
+forms of block chains anybody want to
+
+ align:start position:0%
+forms of block chains anybody want to
+ 
+
+ align:start position:0%
+forms of block chains anybody want to
+give me what our second bucket was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Jeremy's centralization what else did we
+
+ align:start position:0%
+Jeremy's centralization what else did we
+ 
+
+ align:start position:0%
+Jeremy's centralization what else did we
+talk about Elan consensus so again
+
+ align:start position:0%
+talk about Elan consensus so again
+ 
+
+ align:start position:0%
+talk about Elan consensus so again
+decentralized network consensus if
+
+ align:start position:0%
+decentralized network consensus if
+ 
+
+ align:start position:0%
+decentralized network consensus if
+theorem actually uses proof of work even
+
+ align:start position:0%
+theorem actually uses proof of work even
+ 
+
+ align:start position:0%
+theorem actually uses proof of work even
+though that some there's some talk that
+
+ align:start position:0%
+though that some there's some talk that
+ 
+
+ align:start position:0%
+though that some there's some talk that
+ether will move to proof of stake but
+
+ align:start position:0%
+ether will move to proof of stake but
+ 
+
+ align:start position:0%
+ether will move to proof of stake but
+it's currently proof of work there's a
+
+ align:start position:0%
+it's currently proof of work there's a
+ 
+
+ align:start position:0%
+it's currently proof of work there's a
+native currency it's eath or F or ETH or
+
+ align:start position:0%
+native currency it's eath or F or ETH or
+ 
+
+ align:start position:0%
+native currency it's eath or F or ETH or
+ether instead of Bitcoin
+
+ align:start position:0%
+ether instead of Bitcoin
+ 
+
+ align:start position:0%
+ether instead of Bitcoin
+and it has a network the third thing
+
+ align:start position:0%
+and it has a network the third thing
+ 
+
+ align:start position:0%
+and it has a network the third thing
+that we talked about transaction format
+
+ align:start position:0%
+that we talked about transaction format
+ 
+
+ align:start position:0%
+that we talked about transaction format
+so we talked about transactions and
+
+ align:start position:0%
+so we talked about transactions and
+ 
+
+ align:start position:0%
+so we talked about transactions and
+script well guess what a theorem does
+
+ align:start position:0%
+script well guess what a theorem does
+ 
+
+ align:start position:0%
+script well guess what a theorem does
+not have a transaction script or aut XO
+
+ align:start position:0%
+not have a transaction script or aut XO
+ 
+
+ align:start position:0%
+not have a transaction script or aut XO
+so that's the one place that Vitalik
+
+ align:start position:0%
+so that's the one place that Vitalik
+ 
+
+ align:start position:0%
+so that's the one place that Vitalik
+Butera and who designed all of this no
+
+ align:start position:0%
+Butera and who designed all of this no
+ 
+
+ align:start position:0%
+Butera and who designed all of this no
+had to go a different way instead of
+
+ align:start position:0%
+had to go a different way instead of
+ 
+
+ align:start position:0%
+had to go a different way instead of
+transaction inputs and outputs there's
+
+ align:start position:0%
+transaction inputs and outputs there's
+ 
+
+ align:start position:0%
+transaction inputs and outputs there's
+something called state transitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Isabella Ledger's what are the two
+
+ align:start position:0%
+Isabella Ledger's what are the two
+ 
+
+ align:start position:0%
+Isabella Ledger's what are the two
+different types of Ledger's that we
+
+ align:start position:0%
+different types of Ledger's that we
+ 
+
+ align:start position:0%
+different types of Ledger's that we
+talked about in class two permissioned
+
+ align:start position:0%
+talked about in class two permissioned
+ 
+
+ align:start position:0%
+talked about in class two permissioned
+and public are two different types of
+
+ align:start position:0%
+and public are two different types of
+ 
+
+ align:start position:0%
+and public are two different types of
+blockchains about remind me your name
+
+ align:start position:0%
+blockchains about remind me your name
+ 
+
+ align:start position:0%
+blockchains about remind me your name
+again Stephanie so balanced ledger and
+
+ align:start position:0%
+again Stephanie so balanced ledger and
+ 
+
+ align:start position:0%
+again Stephanie so balanced ledger and
+transaction ledger you can keep a list
+
+ align:start position:0%
+transaction ledger you can keep a list
+ 
+
+ align:start position:0%
+transaction ledger you can keep a list
+of transactions and this goes back
+
+ align:start position:0%
+of transactions and this goes back
+ 
+
+ align:start position:0%
+of transactions and this goes back
+thousands of years this is not
+
+ align:start position:0%
+thousands of years this is not
+ 
+
+ align:start position:0%
+thousands of years this is not
+blockchain or you can keep balances
+
+ align:start position:0%
+blockchain or you can keep balances
+ 
+
+ align:start position:0%
+blockchain or you can keep balances
+Bitcoin is in essence a transaction
+
+ align:start position:0%
+Bitcoin is in essence a transaction
+ 
+
+ align:start position:0%
+Bitcoin is in essence a transaction
+ledger the theorem and many of the other
+
+ align:start position:0%
+ledger the theorem and many of the other
+ 
+
+ align:start position:0%
+ledger the theorem and many of the other
+smart contract platforms are balance
+
+ align:start position:0%
+smart contract platforms are balance
+ 
+
+ align:start position:0%
+smart contract platforms are balance
+Ledger's there's a lot of technological
+
+ align:start position:0%
+Ledger's there's a lot of technological
+ 
+
+ align:start position:0%
+Ledger's there's a lot of technological
+and mathematical reasons why which I'd
+
+ align:start position:0%
+and mathematical reasons why which I'd
+ 
+
+ align:start position:0%
+and mathematical reasons why which I'd
+be glad to do in office hours but
+
+ align:start position:0%
+be glad to do in office hours but
+ 
+
+ align:start position:0%
+be glad to do in office hours but
+because of that when you're moving from
+
+ align:start position:0%
+because of that when you're moving from
+ 
+
+ align:start position:0%
+because of that when you're moving from
+one set of balances like is it buh buh
+
+ align:start position:0%
+one set of balances like is it buh buh
+ 
+
+ align:start position:0%
+one set of balances like is it buh buh
+has $100 at Bank of America - buh having
+
+ align:start position:0%
+has $100 at Bank of America - buh having
+ 
+
+ align:start position:0%
+has $100 at Bank of America - buh having
+a hundred and one dollars you need to
+
+ align:start position:0%
+a hundred and one dollars you need to
+ 
+
+ align:start position:0%
+a hundred and one dollars you need to
+have a transition it's called a state
+
+ align:start position:0%
+have a transition it's called a state
+ 
+
+ align:start position:0%
+have a transition it's called a state
+transition which would mean add one
+
+ align:start position:0%
+transition which would mean add one
+ 
+
+ align:start position:0%
+transition which would mean add one
+dollar but so aetherium is an account
+
+ align:start position:0%
+dollar but so aetherium is an account
+ 
+
+ align:start position:0%
+dollar but so aetherium is an account
+based and an in fact doesn't even have
+
+ align:start position:0%
+based and an in fact doesn't even have
+ 
+
+ align:start position:0%
+based and an in fact doesn't even have
+one programming language there's six or
+
+ align:start position:0%
+one programming language there's six or
+ 
+
+ align:start position:0%
+one programming language there's six or
+seven programming languages you can
+
+ align:start position:0%
+seven programming languages you can
+ 
+
+ align:start position:0%
+seven programming languages you can
+write in for those who are so inclined
+
+ align:start position:0%
+write in for those who are so inclined
+ 
+
+ align:start position:0%
+write in for those who are so inclined
+so I'm going to go through really
+
+ align:start position:0%
+so I'm going to go through really
+ 
+
+ align:start position:0%
+so I'm going to go through really
+quickly my analysis and many other
+
+ align:start position:0%
+quickly my analysis and many other
+ 
+
+ align:start position:0%
+quickly my analysis and many other
+people's put up my sort of rendition of
+
+ align:start position:0%
+people's put up my sort of rendition of
+ 
+
+ align:start position:0%
+people's put up my sort of rendition of
+the difference between aetherium in
+
+ align:start position:0%
+the difference between aetherium in
+ 
+
+ align:start position:0%
+the difference between aetherium in
+Bitcoin
+
+ align:start position:0%
+Bitcoin
+ 
+
+ align:start position:0%
+Bitcoin
+but stop me if there's a question so the
+
+ align:start position:0%
+but stop me if there's a question so the
+ 
+
+ align:start position:0%
+but stop me if there's a question so the
+founder there's actually a founder the
+
+ align:start position:0%
+founder there's actually a founder the
+ 
+
+ align:start position:0%
+founder there's actually a founder the
+the mythology around
+
+ align:start position:0%
+the mythology around
+ 
+
+ align:start position:0%
+the mythology around
+Vitalik bhooteriya might not be as great
+
+ align:start position:0%
+Vitalik bhooteriya might not be as great
+ 
+
+ align:start position:0%
+Vitalik bhooteriya might not be as great
+as Satoshi Nakamoto but a 19 year old
+
+ align:start position:0%
+as Satoshi Nakamoto but a 19 year old
+ 
+
+ align:start position:0%
+as Satoshi Nakamoto but a 19 year old
+journalist who was writing about Bitcoin
+
+ align:start position:0%
+journalist who was writing about Bitcoin
+ 
+
+ align:start position:0%
+journalist who was writing about Bitcoin
+for was a Bitcoin magazine if I remember
+
+ align:start position:0%
+for was a Bitcoin magazine if I remember
+ 
+
+ align:start position:0%
+for was a Bitcoin magazine if I remember
+that where he was writing said we can
+
+ align:start position:0%
+that where he was writing said we can
+ 
+
+ align:start position:0%
+that where he was writing said we can
+build something on top of it using Nick
+
+ align:start position:0%
+build something on top of it using Nick
+ 
+
+ align:start position:0%
+build something on top of it using Nick
+Sabo's thoughts about smart contracts
+
+ align:start position:0%
+Sabo's thoughts about smart contracts
+ 
+
+ align:start position:0%
+Sabo's thoughts about smart contracts
+about six years after Bitcoin he made a
+
+ align:start position:0%
+about six years after Bitcoin he made a
+ 
+
+ align:start position:0%
+about six years after Bitcoin he made a
+touring complete does anyone want to
+
+ align:start position:0%
+touring complete does anyone want to
+ 
+
+ align:start position:0%
+touring complete does anyone want to
+remind the class what touring complete
+
+ align:start position:0%
+remind the class what touring complete
+ 
+
+ align:start position:0%
+remind the class what touring complete
+is did I see a hand up yes
+
+ align:start position:0%
+is did I see a hand up yes
+ 
+
+ align:start position:0%
+is did I see a hand up yes
+bold of you what's your first name again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Alana says touring complete means you
+
+ align:start position:0%
+Alana says touring complete means you
+ 
+
+ align:start position:0%
+Alana says touring complete means you
+can write loops but what that really
+
+ align:start position:0%
+can write loops but what that really
+ 
+
+ align:start position:0%
+can write loops but what that really
+means for the the business crowd is it
+
+ align:start position:0%
+means for the the business crowd is it
+ 
+
+ align:start position:0%
+means for the the business crowd is it
+means you can write a program to do just
+
+ align:start position:0%
+means you can write a program to do just
+ 
+
+ align:start position:0%
+means you can write a program to do just
+about anything it's highly flexible
+
+ align:start position:0%
+about anything it's highly flexible
+ 
+
+ align:start position:0%
+about anything it's highly flexible
+I'm sure the technologists and here will
+
+ align:start position:0%
+I'm sure the technologists and here will
+ 
+
+ align:start position:0%
+I'm sure the technologists and here will
+say well maybe there's something you
+
+ align:start position:0%
+say well maybe there's something you
+ 
+
+ align:start position:0%
+say well maybe there's something you
+can't do with it but the the point and
+
+ align:start position:0%
+can't do with it but the the point and
+ 
+
+ align:start position:0%
+can't do with it but the the point and
+what vitalik said is we shouldn't just
+
+ align:start position:0%
+what vitalik said is we shouldn't just
+ 
+
+ align:start position:0%
+what vitalik said is we shouldn't just
+limit it to a scripting language that
+
+ align:start position:0%
+limit it to a scripting language that
+ 
+
+ align:start position:0%
+limit it to a scripting language that
+was non touring complete that can just
+
+ align:start position:0%
+was non touring complete that can just
+ 
+
+ align:start position:0%
+was non touring complete that can just
+move a little bit appear to peer value
+
+ align:start position:0%
+move a little bit appear to peer value
+ 
+
+ align:start position:0%
+move a little bit appear to peer value
+around that he wanted to do basically a
+
+ align:start position:0%
+around that he wanted to do basically a
+ 
+
+ align:start position:0%
+around that he wanted to do basically a
+peer-to-peer virtual computer that could
+
+ align:start position:0%
+peer-to-peer virtual computer that could
+ 
+
+ align:start position:0%
+peer-to-peer virtual computer that could
+move code and complete code and he in
+
+ align:start position:0%
+move code and complete code and he in
+ 
+
+ align:start position:0%
+move code and complete code and he in
+over the years it's being able to be
+
+ align:start position:0%
+over the years it's being able to be
+ 
+
+ align:start position:0%
+over the years it's being able to be
+written in a bunch of things but
+
+ align:start position:0%
+written in a bunch of things but
+ 
+
+ align:start position:0%
+written in a bunch of things but
+solidity is the main program language
+
+ align:start position:0%
+solidity is the main program language
+ 
+
+ align:start position:0%
+solidity is the main program language
+and thus its account based rather than
+
+ align:start position:0%
+and thus its account based rather than
+ 
+
+ align:start position:0%
+and thus its account based rather than
+transaction based because of the loops
+
+ align:start position:0%
+transaction based because of the loops
+ 
+
+ align:start position:0%
+transaction based because of the loops
+if you could loop and be tore and
+
+ align:start position:0%
+if you could loop and be tore and
+ 
+
+ align:start position:0%
+if you could loop and be tore and
+complete with transactions there was a
+
+ align:start position:0%
+complete with transactions there was a
+ 
+
+ align:start position:0%
+complete with transactions there was a
+vulnerability and attack vectors that he
+
+ align:start position:0%
+vulnerability and attack vectors that he
+ 
+
+ align:start position:0%
+vulnerability and attack vectors that he
+he made it account based the
+
+ align:start position:0%
+he made it account based the
+ 
+
+ align:start position:0%
+he made it account based the
+transactions are stored in merkel keys
+
+ align:start position:0%
+transactions are stored in merkel keys
+ 
+
+ align:start position:0%
+transactions are stored in merkel keys
+but guess what if you really interests
+
+ align:start position:0%
+but guess what if you really interests
+ 
+
+ align:start position:0%
+but guess what if you really interests
+and wanted to learn everything about
+
+ align:start position:0%
+and wanted to learn everything about
+ 
+
+ align:start position:0%
+and wanted to learn everything about
+aetherium there's at least four key
+
+ align:start position:0%
+aetherium there's at least four key
+ 
+
+ align:start position:0%
+aetherium there's at least four key
+Merkel trees that get summarized up into
+
+ align:start position:0%
+Merkel trees that get summarized up into
+ 
+
+ align:start position:0%
+Merkel trees that get summarized up into
+that block headers
+
+ align:start position:0%
+that block headers
+ 
+
+ align:start position:0%
+that block headers
+there's the transactions which in
+
+ align:start position:0%
+there's the transactions which in
+ 
+
+ align:start position:0%
+there's the transactions which in
+essence aren't transactions they call
+
+ align:start position:0%
+essence aren't transactions they call
+ 
+
+ align:start position:0%
+essence aren't transactions they call
+them state
+
+ align:start position:0%
+them state
+ 
+
+ align:start position:0%
+them state
+there's the state itself something
+
+ align:start position:0%
+there's the state itself something
+ 
+
+ align:start position:0%
+there's the state itself something
+called storage which is really related
+
+ align:start position:0%
+called storage which is really related
+ 
+
+ align:start position:0%
+called storage which is really related
+to each one of the individual aetherium
+
+ align:start position:0%
+to each one of the individual aetherium
+ 
+
+ align:start position:0%
+to each one of the individual aetherium
+accounts and that believe it or not
+
+ align:start position:0%
+accounts and that believe it or not
+ 
+
+ align:start position:0%
+accounts and that believe it or not
+actually receipts there's a written
+
+ align:start position:0%
+actually receipts there's a written
+ 
+
+ align:start position:0%
+actually receipts there's a written
+records of receipts from every state
+
+ align:start position:0%
+records of receipts from every state
+ 
+
+ align:start position:0%
+records of receipts from every state
+transition so there's a lot more
+
+ align:start position:0%
+transition so there's a lot more
+ 
+
+ align:start position:0%
+transition so there's a lot more
+complexity inside the etherium
+
+ align:start position:0%
+complexity inside the etherium
+ 
+
+ align:start position:0%
+complexity inside the etherium
+blockchain
+
+ align:start position:0%
+blockchain
+ 
+
+ align:start position:0%
+blockchain
+they write about fourteen seconds of
+
+ align:start position:0%
+they write about fourteen seconds of
+ 
+
+ align:start position:0%
+they write about fourteen seconds of
+block instead of ten minutes and that
+
+ align:start position:0%
+block instead of ten minutes and that
+ 
+
+ align:start position:0%
+block instead of ten minutes and that
+changes a bunch of the economics proof
+
+ align:start position:0%
+changes a bunch of the economics proof
+ 
+
+ align:start position:0%
+changes a bunch of the economics proof
+of work for some reason which others can
+
+ align:start position:0%
+of work for some reason which others can
+ 
+
+ align:start position:0%
+of work for some reason which others can
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+Vitalik decided to use a different hash
+
+ align:start position:0%
+Vitalik decided to use a different hash
+ 
+
+ align:start position:0%
+Vitalik decided to use a different hash
+function it's still based on elliptic
+
+ align:start position:0%
+function it's still based on elliptic
+ 
+
+ align:start position:0%
+function it's still based on elliptic
+curves I think but a different hash
+
+ align:start position:0%
+curves I think but a different hash
+ 
+
+ align:start position:0%
+curves I think but a different hash
+function what about the economics well
+
+ align:start position:0%
+function what about the economics well
+ 
+
+ align:start position:0%
+function what about the economics well
+it's called a third ETH it's programmed
+
+ align:start position:0%
+it's called a third ETH it's programmed
+ 
+
+ align:start position:0%
+it's called a third ETH it's programmed
+in such a way that you can't use a six
+
+ align:start position:0%
+in such a way that you can't use a six
+ 
+
+ align:start position:0%
+in such a way that you can't use a six
+purposely sort of it makes it that
+
+ align:start position:0%
+purposely sort of it makes it that
+ 
+
+ align:start position:0%
+purposely sort of it makes it that
+mining is more decentralized and you
+
+ align:start position:0%
+mining is more decentralized and you
+ 
+
+ align:start position:0%
+mining is more decentralized and you
+don't have the big factories the entire
+
+ align:start position:0%
+don't have the big factories the entire
+ 
+
+ align:start position:0%
+don't have the big factories the entire
+hash community the entire mining
+
+ align:start position:0%
+hash community the entire mining
+ 
+
+ align:start position:0%
+hash community the entire mining
+community is much smaller in fact I
+
+ align:start position:0%
+community is much smaller in fact I
+ 
+
+ align:start position:0%
+community is much smaller in fact I
+think it's about what would that be two
+
+ align:start position:0%
+think it's about what would that be two
+ 
+
+ align:start position:0%
+think it's about what would that be two
+hundred thousand times smaller there's
+
+ align:start position:0%
+hundred thousand times smaller there's
+ 
+
+ align:start position:0%
+hundred thousand times smaller there's
+two hundred and sixty tera hashes per
+
+ align:start position:0%
+two hundred and sixty tera hashes per
+ 
+
+ align:start position:0%
+two hundred and sixty tera hashes per
+second as of yesterday and the Bitcoin
+
+ align:start position:0%
+second as of yesterday and the Bitcoin
+ 
+
+ align:start position:0%
+second as of yesterday and the Bitcoin
+mining community has 54 EXA hashes that
+
+ align:start position:0%
+mining community has 54 EXA hashes that
+ 
+
+ align:start position:0%
+mining community has 54 EXA hashes that
+means lots more computers a lot more
+
+ align:start position:0%
+means lots more computers a lot more
+ 
+
+ align:start position:0%
+means lots more computers a lot more
+electricity a lot more nationally of
+
+ align:start position:0%
+electricity a lot more nationally of
+ 
+
+ align:start position:0%
+electricity a lot more nationally of
+teeth about resources Bitcoin started in
+
+ align:start position:0%
+teeth about resources Bitcoin started in
+ 
+
+ align:start position:0%
+teeth about resources Bitcoin started in
+January of 2009 and nobody owned any
+
+ align:start position:0%
+January of 2009 and nobody owned any
+ 
+
+ align:start position:0%
+January of 2009 and nobody owned any
+Bitcoin whereas aetherium started with a
+
+ align:start position:0%
+Bitcoin whereas aetherium started with a
+ 
+
+ align:start position:0%
+Bitcoin whereas aetherium started with a
+pre-sale and an IC o---- which we'll be
+
+ align:start position:0%
+pre-sale and an IC o---- which we'll be
+ 
+
+ align:start position:0%
+pre-sale and an IC o---- which we'll be
+talking about about 72 million aetherium
+
+ align:start position:0%
+talking about about 72 million aetherium
+ 
+
+ align:start position:0%
+talking about about 72 million aetherium
+the talaq wanted to raise money he was
+
+ align:start position:0%
+the talaq wanted to raise money he was
+ 
+
+ align:start position:0%
+the talaq wanted to raise money he was
+maybe 19 years old he looped in with a
+
+ align:start position:0%
+maybe 19 years old he looped in with a
+ 
+
+ align:start position:0%
+maybe 19 years old he looped in with a
+venture capitalist from Canada Joe Lubin
+
+ align:start position:0%
+venture capitalist from Canada Joe Lubin
+ 
+
+ align:start position:0%
+venture capitalist from Canada Joe Lubin
+who now runs Consensus lumen took about
+
+ align:start position:0%
+who now runs Consensus lumen took about
+ 
+
+ align:start position:0%
+who now runs Consensus lumen took about
+10% or nine and a half percent of the
+
+ align:start position:0%
+10% or nine and a half percent of the
+ 
+
+ align:start position:0%
+10% or nine and a half percent of the
+offering they put nine half percent in a
+
+ align:start position:0%
+offering they put nine half percent in a
+ 
+
+ align:start position:0%
+offering they put nine half percent in a
+foundation called the etherium
+
+ align:start position:0%
+foundation called the etherium
+ 
+
+ align:start position:0%
+foundation called the etherium
+foundation and the other 80% was sold to
+
+ align:start position:0%
+foundation and the other 80% was sold to
+ 
+
+ align:start position:0%
+foundation and the other 80% was sold to
+the public for 18 million dollars
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll talk later in the semester as to
+
+ align:start position:0%
+we'll talk later in the semester as to
+ 
+
+ align:start position:0%
+we'll talk later in the semester as to
+whether that was really a securities
+
+ align:start position:0%
+whether that was really a securities
+ 
+
+ align:start position:0%
+whether that was really a securities
+offering I publicly said I think so but
+
+ align:start position:0%
+offering I publicly said I think so but
+ 
+
+ align:start position:0%
+offering I publicly said I think so but
+that was in 2014 and in 2018 and the
+
+ align:start position:0%
+that was in 2014 and in 2018 and the
+ 
+
+ align:start position:0%
+that was in 2014 and in 2018 and the
+Securities and Exchange Commission has
+
+ align:start position:0%
+Securities and Exchange Commission has
+ 
+
+ align:start position:0%
+Securities and Exchange Commission has
+said regardless of what it might have
+
+ align:start position:0%
+said regardless of what it might have
+ 
+
+ align:start position:0%
+said regardless of what it might have
+been in 14 it's now sufficiently
+
+ align:start position:0%
+been in 14 it's now sufficiently
+ 
+
+ align:start position:0%
+been in 14 it's now sufficiently
+decentralized that we'll consider it not
+
+ align:start position:0%
+decentralized that we'll consider it not
+ 
+
+ align:start position:0%
+decentralized that we'll consider it not
+as security but in essence they raised
+
+ align:start position:0%
+as security but in essence they raised
+ 
+
+ align:start position:0%
+as security but in essence they raised
+18 million dollars and were off to the
+
+ align:start position:0%
+18 million dollars and were off to the
+ 
+
+ align:start position:0%
+18 million dollars and were off to the
+races
+
+ align:start position:0%
+races
+ 
+
+ align:start position:0%
+races
+oh and the 10% that Joe Lubin capped if
+
+ align:start position:0%
+oh and the 10% that Joe Lubin capped if
+ 
+
+ align:start position:0%
+oh and the 10% that Joe Lubin capped if
+he still owned it would be worth about
+
+ align:start position:0%
+he still owned it would be worth about
+ 
+
+ align:start position:0%
+he still owned it would be worth about
+two billion dollars now but he probably
+
+ align:start position:0%
+two billion dollars now but he probably
+ 
+
+ align:start position:0%
+two billion dollars now but he probably
+sold some of it along the way there
+
+ align:start position:0%
+sold some of it along the way there
+ 
+
+ align:start position:0%
+sold some of it along the way there
+block rewards the monetary policy in
+
+ align:start position:0%
+block rewards the monetary policy in
+ 
+
+ align:start position:0%
+block rewards the monetary policy in
+aetherium if you remember it splits
+
+ align:start position:0%
+aetherium if you remember it splits
+ 
+
+ align:start position:0%
+aetherium if you remember it splits
+every four years you know that there's a
+
+ align:start position:0%
+every four years you know that there's a
+ 
+
+ align:start position:0%
+every four years you know that there's a
+block reward splits
+
+ align:start position:0%
+block reward splits
+ 
+
+ align:start position:0%
+block reward splits
+etherium was set up that was five if the
+
+ align:start position:0%
+etherium was set up that was five if the
+ 
+
+ align:start position:0%
+etherium was set up that was five if the
+ether per block and then a year ago they
+
+ align:start position:0%
+ether per block and then a year ago they
+ 
+
+ align:start position:0%
+ether per block and then a year ago they
+just announced they were gonna change
+
+ align:start position:0%
+just announced they were gonna change
+ 
+
+ align:start position:0%
+just announced they were gonna change
+the software to three ether per block
+
+ align:start position:0%
+the software to three ether per block
+ 
+
+ align:start position:0%
+the software to three ether per block
+and a month ago they announced they're
+
+ align:start position:0%
+and a month ago they announced they're
+ 
+
+ align:start position:0%
+and a month ago they announced they're
+gonna change it to two ether per block
+
+ align:start position:0%
+gonna change it to two ether per block
+ 
+
+ align:start position:0%
+gonna change it to two ether per block
+so the monetary policy of Bitcoin is
+
+ align:start position:0%
+so the monetary policy of Bitcoin is
+ 
+
+ align:start position:0%
+so the monetary policy of Bitcoin is
+said to be immutable and fixed forever
+
+ align:start position:0%
+said to be immutable and fixed forever
+ 
+
+ align:start position:0%
+said to be immutable and fixed forever
+but I would say that because he theorem
+
+ align:start position:0%
+but I would say that because he theorem
+ 
+
+ align:start position:0%
+but I would say that because he theorem
+supposedly was fixed and now twice
+
+ align:start position:0%
+supposedly was fixed and now twice
+ 
+
+ align:start position:0%
+supposedly was fixed and now twice
+they've changed the monetary policy
+
+ align:start position:0%
+they've changed the monetary policy
+ 
+
+ align:start position:0%
+they've changed the monetary policy
+there is a form that if all the miners
+
+ align:start position:0%
+there is a form that if all the miners
+ 
+
+ align:start position:0%
+there is a form that if all the miners
+and all the computer nodes decide they
+
+ align:start position:0%
+and all the computer nodes decide they
+ 
+
+ align:start position:0%
+and all the computer nodes decide they
+can change the monetary policy and if
+
+ align:start position:0%
+can change the monetary policy and if
+ 
+
+ align:start position:0%
+can change the monetary policy and if
+the etherium is shown that I think
+
+ align:start position:0%
+the etherium is shown that I think
+ 
+
+ align:start position:0%
+the etherium is shown that I think
+aetherium was a bit more centralized and
+
+ align:start position:0%
+aetherium was a bit more centralized and
+ 
+
+ align:start position:0%
+aetherium was a bit more centralized and
+has more leadership because Vitalik
+
+ align:start position:0%
+has more leadership because Vitalik
+ 
+
+ align:start position:0%
+has more leadership because Vitalik
+bhooteriya is an actual human who's
+
+ align:start position:0%
+bhooteriya is an actual human who's
+ 
+
+ align:start position:0%
+bhooteriya is an actual human who's
+willing to disclose who he is and he
+
+ align:start position:0%
+willing to disclose who he is and he
+ 
+
+ align:start position:0%
+willing to disclose who he is and he
+still has the sort of founder following
+
+ align:start position:0%
+still has the sort of founder following
+ 
+
+ align:start position:0%
+still has the sort of founder following
+and Satoshi Nakamoto went he ghosted all
+
+ align:start position:0%
+and Satoshi Nakamoto went he ghosted all
+ 
+
+ align:start position:0%
+and Satoshi Nakamoto went he ghosted all
+of us in a sense and so thus it's it's
+
+ align:start position:0%
+of us in a sense and so thus it's it's
+ 
+
+ align:start position:0%
+of us in a sense and so thus it's it's
+in some ways socially just more set
+
+ align:start position:0%
+in some ways socially just more set
+ 
+
+ align:start position:0%
+in some ways socially just more set
+decentralized and then fees are
+
+ align:start position:0%
+decentralized and then fees are
+ 
+
+ align:start position:0%
+decentralized and then fees are
+voluntary in Bitcoin they're a necessary
+
+ align:start position:0%
+voluntary in Bitcoin they're a necessary
+ 
+
+ align:start position:0%
+voluntary in Bitcoin they're a necessary
+part to channel everything Emily policy
+
+ align:start position:0%
+part to channel everything Emily policy
+ 
+
+ align:start position:0%
+part to channel everything Emily policy
+in practice what does it actually mean
+
+ align:start position:0%
+in practice what does it actually mean
+ 
+
+ align:start position:0%
+in practice what does it actually mean
+for like a difference between Bitcoin
+
+ align:start position:0%
+for like a difference between Bitcoin
+ 
+
+ align:start position:0%
+for like a difference between Bitcoin
+and a cerium that it's fixed for
+
+ align:start position:0%
+and a cerium that it's fixed for
+ 
+
+ align:start position:0%
+and a cerium that it's fixed for
+changing
+
+ align:start position:0%
+changing
+ 
+
+ align:start position:0%
+changing
+staying at that tape so Emily asked what
+
+ align:start position:0%
+staying at that tape so Emily asked what
+ 
+
+ align:start position:0%
+staying at that tape so Emily asked what
+does it mean in practice in practice
+
+ align:start position:0%
+does it mean in practice in practice
+ 
+
+ align:start position:0%
+does it mean in practice in practice
+Bitcoin has a much slower growth rate or
+
+ align:start position:0%
+Bitcoin has a much slower growth rate or
+ 
+
+ align:start position:0%
+Bitcoin has a much slower growth rate or
+inflation rate which is currently if I'm
+
+ align:start position:0%
+inflation rate which is currently if I'm
+ 
+
+ align:start position:0%
+inflation rate which is currently if I'm
+not mistaken about half what's that for
+
+ align:start position:0%
+not mistaken about half what's that for
+ 
+
+ align:start position:0%
+not mistaken about half what's that for
+about 4% but it's about half of the
+
+ align:start position:0%
+about 4% but it's about half of the
+ 
+
+ align:start position:0%
+about 4% but it's about half of the
+inflation rate at a theorem which is
+
+ align:start position:0%
+inflation rate at a theorem which is
+ 
+
+ align:start position:0%
+inflation rate at a theorem which is
+running in the 7% range every one of the
+
+ align:start position:0%
+running in the 7% range every one of the
+ 
+
+ align:start position:0%
+running in the 7% range every one of the
+1600 live tokens that are right now all
+
+ align:start position:0%
+1600 live tokens that are right now all
+ 
+
+ align:start position:0%
+1600 live tokens that are right now all
+coins have separate monetary policies
+
+ align:start position:0%
+coins have separate monetary policies
+ 
+
+ align:start position:0%
+coins have separate monetary policies
+and one could do a complete economic
+
+ align:start position:0%
+and one could do a complete economic
+ 
+
+ align:start position:0%
+and one could do a complete economic
+study about what it means but in terms
+
+ align:start position:0%
+study about what it means but in terms
+ 
+
+ align:start position:0%
+study about what it means but in terms
+of aetherium versus Bitcoin aetherium
+
+ align:start position:0%
+of aetherium versus Bitcoin aetherium
+ 
+
+ align:start position:0%
+of aetherium versus Bitcoin aetherium
+has a higher inflation rate and secondly
+
+ align:start position:0%
+has a higher inflation rate and secondly
+ 
+
+ align:start position:0%
+has a higher inflation rate and secondly
+because they've shown that they can form
+
+ align:start position:0%
+because they've shown that they can form
+ 
+
+ align:start position:0%
+because they've shown that they can form
+some consensus and change it I think it
+
+ align:start position:0%
+some consensus and change it I think it
+ 
+
+ align:start position:0%
+some consensus and change it I think it
+sends an interesting question into that
+
+ align:start position:0%
+sends an interesting question into that
+ 
+
+ align:start position:0%
+sends an interesting question into that
+that ecosystem as to how hard a monetary
+
+ align:start position:0%
+that ecosystem as to how hard a monetary
+ 
+
+ align:start position:0%
+that ecosystem as to how hard a monetary
+policy versus more human based flexible
+
+ align:start position:0%
+policy versus more human based flexible
+ 
+
+ align:start position:0%
+policy versus more human based flexible
+monetary policy Hugo the ethereum
+
+ align:start position:0%
+monetary policy Hugo the ethereum
+ 
+
+ align:start position:0%
+monetary policy Hugo the ethereum
+blockchain decide or so the core
+
+ align:start position:0%
+blockchain decide or so the core
+ 
+
+ align:start position:0%
+blockchain decide or so the core
+developers of any coin can propose to
+
+ align:start position:0%
+developers of any coin can propose to
+ 
+
+ align:start position:0%
+developers of any coin can propose to
+the various mining and nodes to make a
+
+ align:start position:0%
+the various mining and nodes to make a
+ 
+
+ align:start position:0%
+the various mining and nodes to make a
+change including the monetary policy
+
+ align:start position:0%
+change including the monetary policy
+ 
+
+ align:start position:0%
+change including the monetary policy
+even in Bitcoin the monetary policy
+
+ align:start position:0%
+even in Bitcoin the monetary policy
+ 
+
+ align:start position:0%
+even in Bitcoin the monetary policy
+could change if there was a proposal
+
+ align:start position:0%
+could change if there was a proposal
+ 
+
+ align:start position:0%
+could change if there was a proposal
+from the core developers in the theory
+
+ align:start position:0%
+from the core developers in the theory
+ 
+
+ align:start position:0%
+from the core developers in the theory
+of case they have done that twice the
+
+ align:start position:0%
+of case they have done that twice the
+ 
+
+ align:start position:0%
+of case they have done that twice the
+core development of aetherium is highly
+
+ align:start position:0%
+core development of aetherium is highly
+ 
+
+ align:start position:0%
+core development of aetherium is highly
+concentrated around the etherium
+
+ align:start position:0%
+concentrated around the etherium
+ 
+
+ align:start position:0%
+concentrated around the etherium
+foundation consensus the company that
+
+ align:start position:0%
+foundation consensus the company that
+ 
+
+ align:start position:0%
+foundation consensus the company that
+joe Lubin ron's has some normative
+
+ align:start position:0%
+joe Lubin ron's has some normative
+ 
+
+ align:start position:0%
+joe Lubin ron's has some normative
+social standing in the community as well
+
+ align:start position:0%
+social standing in the community as well
+ 
+
+ align:start position:0%
+social standing in the community as well
+but it's been it's been part of
+
+ align:start position:0%
+but it's been it's been part of
+ 
+
+ align:start position:0%
+but it's been it's been part of
+proposals and in reading the proposals
+
+ align:start position:0%
+proposals and in reading the proposals
+ 
+
+ align:start position:0%
+proposals and in reading the proposals
+that goes back to Emily's question the
+
+ align:start position:0%
+that goes back to Emily's question the
+ 
+
+ align:start position:0%
+that goes back to Emily's question the
+court of ella pers have said we should
+
+ align:start position:0%
+court of ella pers have said we should
+ 
+
+ align:start position:0%
+court of ella pers have said we should
+bring down the inflation rate like
+
+ align:start position:0%
+bring down the inflation rate like
+ 
+
+ align:start position:0%
+bring down the inflation rate like
+there's an active advocacy to bring down
+
+ align:start position:0%
+there's an active advocacy to bring down
+ 
+
+ align:start position:0%
+there's an active advocacy to bring down
+no and software or yes in essence buy
+
+ align:start position:0%
+no and software or yes in essence buy
+ 
+
+ align:start position:0%
+no and software or yes in essence buy
+and it could lead to a hard fork
+
+ align:start position:0%
+and it could lead to a hard fork
+ 
+
+ align:start position:0%
+and it could lead to a hard fork
+I believe so that's the background let
+
+ align:start position:0%
+I believe so that's the background let
+ 
+
+ align:start position:0%
+I believe so that's the background let
+me just talk about the platforms we know
+
+ align:start position:0%
+me just talk about the platforms we know
+ 
+
+ align:start position:0%
+me just talk about the platforms we know
+about aetherium we've just chatted about
+
+ align:start position:0%
+about aetherium we've just chatted about
+ 
+
+ align:start position:0%
+about aetherium we've just chatted about
+it it's actual current market value was
+
+ align:start position:0%
+it it's actual current market value was
+ 
+
+ align:start position:0%
+it it's actual current market value was
+22 billion well we're not going to spend
+
+ align:start position:0%
+22 billion well we're not going to spend
+ 
+
+ align:start position:0%
+22 billion well we're not going to spend
+a lot of time in this this class this
+
+ align:start position:0%
+a lot of time in this this class this
+ 
+
+ align:start position:0%
+a lot of time in this this class this
+semester about market values I thought
+
+ align:start position:0%
+semester about market values I thought
+ 
+
+ align:start position:0%
+semester about market values I thought
+it would give you a sense of how people
+
+ align:start position:0%
+it would give you a sense of how people
+ 
+
+ align:start position:0%
+it would give you a sense of how people
+think about it the other five that you
+
+ align:start position:0%
+think about it the other five that you
+ 
+
+ align:start position:0%
+think about it the other five that you
+did some reading about EEO smark values
+
+ align:start position:0%
+did some reading about EEO smark values
+ 
+
+ align:start position:0%
+did some reading about EEO smark values
+about five billion is so new because
+
+ align:start position:0%
+about five billion is so new because
+ 
+
+ align:start position:0%
+about five billion is so new because
+they just finished a initial coin
+
+ align:start position:0%
+they just finished a initial coin
+ 
+
+ align:start position:0%
+they just finished a initial coin
+offering in july and they just went live
+
+ align:start position:0%
+offering in july and they just went live
+ 
+
+ align:start position:0%
+offering in july and they just went live
+in july but they raised 4.2 billion
+
+ align:start position:0%
+in july but they raised 4.2 billion
+ 
+
+ align:start position:0%
+in july but they raised 4.2 billion
+dollars so my my estimate my prediction
+
+ align:start position:0%
+dollars so my my estimate my prediction
+ 
+
+ align:start position:0%
+dollars so my my estimate my prediction
+is EOS is going to be real and going to
+
+ align:start position:0%
+is EOS is going to be real and going to
+ 
+
+ align:start position:0%
+is EOS is going to be real and going to
+be around
+
+ align:start position:0%
+be around
+ 
+
+ align:start position:0%
+be around
+they've taken 1 billion of that 4.2
+
+ align:start position:0%
+they've taken 1 billion of that 4.2
+ 
+
+ align:start position:0%
+they've taken 1 billion of that 4.2
+billion and set up a Kickstarter sort of
+
+ align:start position:0%
+billion and set up a Kickstarter sort of
+ 
+
+ align:start position:0%
+billion and set up a Kickstarter sort of
+venture firm literally so that they
+
+ align:start position:0%
+venture firm literally so that they
+ 
+
+ align:start position:0%
+venture firm literally so that they
+could maybe support some of you you
+
+ align:start position:0%
+could maybe support some of you you
+ 
+
+ align:start position:0%
+could maybe support some of you you
+could be knocking on the eos venture
+
+ align:start position:0%
+could be knocking on the eos venture
+ 
+
+ align:start position:0%
+could be knocking on the eos venture
+firms door and saying fund me I've got a
+
+ align:start position:0%
+firms door and saying fund me I've got a
+ 
+
+ align:start position:0%
+firms door and saying fund me I've got a
+great idea and they'd have one condition
+
+ align:start position:0%
+great idea and they'd have one condition
+ 
+
+ align:start position:0%
+great idea and they'd have one condition
+amongst others you'd have to use Geo's
+
+ align:start position:0%
+amongst others you'd have to use Geo's
+ 
+
+ align:start position:0%
+amongst others you'd have to use Geo's
+as the platform so you know it's it's a
+
+ align:start position:0%
+as the platform so you know it's it's a
+ 
+
+ align:start position:0%
+as the platform so you know it's it's a
+self-reinforcing business model neo is
+
+ align:start position:0%
+self-reinforcing business model neo is
+ 
+
+ align:start position:0%
+self-reinforcing business model neo is
+the other big one that I'd mentioned
+
+ align:start position:0%
+the other big one that I'd mentioned
+ 
+
+ align:start position:0%
+the other big one that I'd mentioned
+which was started two years ago out of
+
+ align:start position:0%
+which was started two years ago out of
+ 
+
+ align:start position:0%
+which was started two years ago out of
+China a lot of people think with the
+
+ align:start position:0%
+China a lot of people think with the
+ 
+
+ align:start position:0%
+China a lot of people think with the
+backing of the Chinese government even
+
+ align:start position:0%
+backing of the Chinese government even
+ 
+
+ align:start position:0%
+backing of the Chinese government even
+not officially certainly with the the
+
+ align:start position:0%
+not officially certainly with the the
+ 
+
+ align:start position:0%
+not officially certainly with the the
+verbal and help of their some people
+
+ align:start position:0%
+verbal and help of their some people
+ 
+
+ align:start position:0%
+verbal and help of their some people
+think of it as the etherium of China but
+
+ align:start position:0%
+think of it as the etherium of China but
+ 
+
+ align:start position:0%
+think of it as the etherium of China but
+it does use a different proof of work
+
+ align:start position:0%
+it does use a different proof of work
+ 
+
+ align:start position:0%
+it does use a different proof of work
+and those are the main ones aetherium
+
+ align:start position:0%
+and those are the main ones aetherium
+ 
+
+ align:start position:0%
+and those are the main ones aetherium
+classic is there because there was a
+
+ align:start position:0%
+classic is there because there was a
+ 
+
+ align:start position:0%
+classic is there because there was a
+hard fork off of aetherium after the Dow
+
+ align:start position:0%
+hard fork off of aetherium after the Dow
+ 
+
+ align:start position:0%
+hard fork off of aetherium after the Dow
+Dow
+
+ align:start position:0%
+Dow
+ 
+
+ align:start position:0%
+Dow
+circumstance any quick questions about
+
+ align:start position:0%
+circumstance any quick questions about
+ 
+
+ align:start position:0%
+circumstance any quick questions about
+the platforms and nee and neo and EEO
+
+ align:start position:0%
+the platforms and nee and neo and EEO
+ 
+
+ align:start position:0%
+the platforms and nee and neo and EEO
+Tsar thought to be a little bit higher
+
+ align:start position:0%
+Tsar thought to be a little bit higher
+ 
+
+ align:start position:0%
+Tsar thought to be a little bit higher
+throughput and faster because of the
+
+ align:start position:0%
+throughput and faster because of the
+ 
+
+ align:start position:0%
+throughput and faster because of the
+different proof of work that each of
+
+ align:start position:0%
+different proof of work that each of
+ 
+
+ align:start position:0%
+different proof of work that each of
+them have so maybe they're more scalable
+
+ align:start position:0%
+them have so maybe they're more scalable
+ 
+
+ align:start position:0%
+them have so maybe they're more scalable
+than aetherium long term
+
+ align:start position:0%
+than aetherium long term
+ 
+
+ align:start position:0%
+than aetherium long term
+what's that so Hugo is pointing out that
+
+ align:start position:0%
+what's that so Hugo is pointing out that
+ 
+
+ align:start position:0%
+what's that so Hugo is pointing out that
+neither one truly used neo and ia's and
+
+ align:start position:0%
+neither one truly used neo and ia's and
+ 
+
+ align:start position:0%
+neither one truly used neo and ia's and
+truly use decentralized proof-of-work
+
+ align:start position:0%
+truly use decentralized proof-of-work
+ 
+
+ align:start position:0%
+truly use decentralized proof-of-work
+they use a delegated Byzantine fault
+
+ align:start position:0%
+they use a delegated Byzantine fault
+ 
+
+ align:start position:0%
+they use a delegated Byzantine fault
+tolerance this was from the reading
+
+ align:start position:0%
+tolerance this was from the reading
+ 
+
+ align:start position:0%
+tolerance this was from the reading
+we're not going to spend time on it but
+
+ align:start position:0%
+we're not going to spend time on it but
+ 
+
+ align:start position:0%
+we're not going to spend time on it but
+there was there was 12 use cases that
+
+ align:start position:0%
+there was there was 12 use cases that
+ 
+
+ align:start position:0%
+there was there was 12 use cases that
+the digital Chamber of Commerce came up
+
+ align:start position:0%
+the digital Chamber of Commerce came up
+ 
+
+ align:start position:0%
+the digital Chamber of Commerce came up
+with and we're gonna study most of these
+
+ align:start position:0%
+with and we're gonna study most of these
+ 
+
+ align:start position:0%
+with and we're gonna study most of these
+not all of these later in the semester
+
+ align:start position:0%
+not all of these later in the semester
+ 
+
+ align:start position:0%
+not all of these later in the semester
+I'm please tell me the question is is
+
+ align:start position:0%
+I'm please tell me the question is is
+ 
+
+ align:start position:0%
+I'm please tell me the question is is
+two multi-language platforms have more
+
+ align:start position:0%
+two multi-language platforms have more
+ 
+
+ align:start position:0%
+two multi-language platforms have more
+potential or less than single language
+
+ align:start position:0%
+potential or less than single language
+ 
+
+ align:start position:0%
+potential or less than single language
+platforms I haven't done a real study
+
+ align:start position:0%
+platforms I haven't done a real study
+ 
+
+ align:start position:0%
+platforms I haven't done a real study
+Mike my gut tells me that there's some
+
+ align:start position:0%
+Mike my gut tells me that there's some
+ 
+
+ align:start position:0%
+Mike my gut tells me that there's some
+trade-offs a multi-language platform
+
+ align:start position:0%
+trade-offs a multi-language platform
+ 
+
+ align:start position:0%
+trade-offs a multi-language platform
+probably allows for more development of
+
+ align:start position:0%
+probably allows for more development of
+ 
+
+ align:start position:0%
+probably allows for more development of
+apps just like on the internet you know
+
+ align:start position:0%
+apps just like on the internet you know
+ 
+
+ align:start position:0%
+apps just like on the internet you know
+if you can have more app development
+
+ align:start position:0%
+if you can have more app development
+ 
+
+ align:start position:0%
+if you can have more app development
+though if you have only one single
+
+ align:start position:0%
+though if you have only one single
+ 
+
+ align:start position:0%
+though if you have only one single
+language you might have fewer
+
+ align:start position:0%
+language you might have fewer
+ 
+
+ align:start position:0%
+language you might have fewer
+vulnerabilities vulnerabilities either
+
+ align:start position:0%
+vulnerabilities vulnerabilities either
+ 
+
+ align:start position:0%
+vulnerabilities vulnerabilities either
+to attack or coming down so there's
+
+ align:start position:0%
+to attack or coming down so there's
+ 
+
+ align:start position:0%
+to attack or coming down so there's
+probably some trade-offs and I'm more
+
+ align:start position:0%
+probably some trade-offs and I'm more
+ 
+
+ align:start position:0%
+probably some trade-offs and I'm more
+into democratizing capital markets so I
+
+ align:start position:0%
+into democratizing capital markets so I
+ 
+
+ align:start position:0%
+into democratizing capital markets so I
+probably my biases would be to the ones
+
+ align:start position:0%
+probably my biases would be to the ones
+ 
+
+ align:start position:0%
+probably my biases would be to the ones
+that have multi-language potential but I
+
+ align:start position:0%
+that have multi-language potential but I
+ 
+
+ align:start position:0%
+that have multi-language potential but I
+can't say for sure whether that little
+
+ align:start position:0%
+can't say for sure whether that little
+ 
+
+ align:start position:0%
+can't say for sure whether that little
+necessarily win because there are some
+
+ align:start position:0%
+necessarily win because there are some
+ 
+
+ align:start position:0%
+necessarily win because there are some
+trade-offs if that helps
+
+ align:start position:0%
+trade-offs if that helps
+ 
+
+ align:start position:0%
+trade-offs if that helps
+so we'll take a view of all of these
+
+ align:start position:0%
+so we'll take a view of all of these
+ 
+
+ align:start position:0%
+so we'll take a view of all of these
+later in the semester but what's
+
+ align:start position:0%
+later in the semester but what's
+ 
+
+ align:start position:0%
+later in the semester but what's
+interesting is none of them have yet
+
+ align:start position:0%
+interesting is none of them have yet
+ 
+
+ align:start position:0%
+interesting is none of them have yet
+taken off and in fact if you look at the
+
+ align:start position:0%
+taken off and in fact if you look at the
+ 
+
+ align:start position:0%
+taken off and in fact if you look at the
+DAPs today the decentralized
+
+ align:start position:0%
+DAPs today the decentralized
+ 
+
+ align:start position:0%
+DAPs today the decentralized
+applications which run on a
+
+ align:start position:0%
+applications which run on a
+ 
+
+ align:start position:0%
+applications which run on a
+decentralized blockchain they generally
+
+ align:start position:0%
+decentralized blockchain they generally
+ 
+
+ align:start position:0%
+decentralized blockchain they generally
+have native tokens they don't have to
+
+ align:start position:0%
+have native tokens they don't have to
+ 
+
+ align:start position:0%
+have native tokens they don't have to
+have a native token by the way you could
+
+ align:start position:0%
+have a native token by the way you could
+ 
+
+ align:start position:0%
+have a native token by the way you could
+run a
+
+ align:start position:0%
+run a
+ 
+
+ align:start position:0%
+run a
+based on ether you could run a DAP on
+
+ align:start position:0%
+based on ether you could run a DAP on
+ 
+
+ align:start position:0%
+based on ether you could run a DAP on
+the underlying token but they all almost
+
+ align:start position:0%
+the underlying token but they all almost
+ 
+
+ align:start position:0%
+the underlying token but they all almost
+always have their own native token this
+
+ align:start position:0%
+always have their own native token this
+ 
+
+ align:start position:0%
+always have their own native token this
+is a list that I pulled off the internet
+
+ align:start position:0%
+is a list that I pulled off the internet
+ 
+
+ align:start position:0%
+is a list that I pulled off the internet
+yesterday similar to your reading these
+
+ align:start position:0%
+yesterday similar to your reading these
+ 
+
+ align:start position:0%
+yesterday similar to your reading these
+are the actual DAPs that are working the
+
+ align:start position:0%
+are the actual DAPs that are working the
+ 
+
+ align:start position:0%
+are the actual DAPs that are working the
+highest gaming gambling exchanges in
+
+ align:start position:0%
+highest gaming gambling exchanges in
+ 
+
+ align:start position:0%
+highest gaming gambling exchanges in
+finance the the most active gap is a
+
+ align:start position:0%
+finance the the most active gap is a
+ 
+
+ align:start position:0%
+finance the the most active gap is a
+adapt is a gambling site that only has
+
+ align:start position:0%
+adapt is a gambling site that only has
+ 
+
+ align:start position:0%
+adapt is a gambling site that only has
+1,500 users a day in the last 24 hours I
+
+ align:start position:0%
+1,500 users a day in the last 24 hours I
+ 
+
+ align:start position:0%
+1,500 users a day in the last 24 hours I
+pulled this down yesterday so that was a
+
+ align:start position:0%
+pulled this down yesterday so that was a
+ 
+
+ align:start position:0%
+pulled this down yesterday so that was a
+Monday so this would have been Sunday
+
+ align:start position:0%
+Monday so this would have been Sunday
+ 
+
+ align:start position:0%
+Monday so this would have been Sunday
+night to Monday night there was only
+
+ align:start position:0%
+night to Monday night there was only
+ 
+
+ align:start position:0%
+night to Monday night there was only
+1,500 users to the most active gambling
+
+ align:start position:0%
+1,500 users to the most active gambling
+ 
+
+ align:start position:0%
+1,500 users to the most active gambling
+site crypto kitties that some of you
+
+ align:start position:0%
+site crypto kitties that some of you
+ 
+
+ align:start position:0%
+site crypto kitties that some of you
+might know had 418 users in those 24
+
+ align:start position:0%
+might know had 418 users in those 24
+ 
+
+ align:start position:0%
+might know had 418 users in those 24
+hours these are not you know economy
+
+ align:start position:0%
+hours these are not you know economy
+ 
+
+ align:start position:0%
+hours these are not you know economy
+wise use case you know the these you
+
+ align:start position:0%
+wise use case you know the these you
+ 
+
+ align:start position:0%
+wise use case you know the these you
+would see numbers that were hundreds of
+
+ align:start position:0%
+would see numbers that were hundreds of
+ 
+
+ align:start position:0%
+would see numbers that were hundreds of
+thousands or if it's like Facebook
+
+ align:start position:0%
+thousands or if it's like Facebook
+ 
+
+ align:start position:0%
+thousands or if it's like Facebook
+there's two billion members and probably
+
+ align:start position:0%
+there's two billion members and probably
+ 
+
+ align:start position:0%
+there's two billion members and probably
+in any 24 hours there's a half a billion
+
+ align:start position:0%
+in any 24 hours there's a half a billion
+ 
+
+ align:start position:0%
+in any 24 hours there's a half a billion
+to a billion people that check in on
+
+ align:start position:0%
+to a billion people that check in on
+ 
+
+ align:start position:0%
+to a billion people that check in on
+Facebook so these are pretty limited at
+
+ align:start position:0%
+Facebook so these are pretty limited at
+ 
+
+ align:start position:0%
+Facebook so these are pretty limited at
+this stage but it has led to something
+
+ align:start position:0%
+this stage but it has led to something
+ 
+
+ align:start position:0%
+this stage but it has led to something
+called initial coin offerings which
+
+ align:start position:0%
+called initial coin offerings which
+ 
+
+ align:start position:0%
+called initial coin offerings which
+we're going to study a bunch later in
+
+ align:start position:0%
+we're going to study a bunch later in
+ 
+
+ align:start position:0%
+we're going to study a bunch later in
+the semester initial coin offerings
+
+ align:start position:0%
+the semester initial coin offerings
+ 
+
+ align:start position:0%
+the semester initial coin offerings
+raise money to build a network but the
+
+ align:start position:0%
+raise money to build a network but the
+ 
+
+ align:start position:0%
+raise money to build a network but the
+tokens are usually issued before they're
+
+ align:start position:0%
+tokens are usually issued before they're
+ 
+
+ align:start position:0%
+tokens are usually issued before they're
+usable and a token is some native
+
+ align:start position:0%
+usable and a token is some native
+ 
+
+ align:start position:0%
+usable and a token is some native
+currency to be used on a on a network
+
+ align:start position:0%
+currency to be used on a on a network
+ 
+
+ align:start position:0%
+currency to be used on a on a network
+the development is open but highly
+
+ align:start position:0%
+the development is open but highly
+ 
+
+ align:start position:0%
+the development is open but highly
+centralized the promoters usually give
+
+ align:start position:0%
+centralized the promoters usually give
+ 
+
+ align:start position:0%
+centralized the promoters usually give
+themselves some skin in the game or some
+
+ align:start position:0%
+themselves some skin in the game or some
+ 
+
+ align:start position:0%
+themselves some skin in the game or some
+Vig in in the theory of initial coin
+
+ align:start position:0%
+Vig in in the theory of initial coin
+ 
+
+ align:start position:0%
+Vig in in the theory of initial coin
+offering the foundation kept 10% Joe
+
+ align:start position:0%
+offering the foundation kept 10% Joe
+ 
+
+ align:start position:0%
+offering the foundation kept 10% Joe
+lube and kept 10% and the other 80% was
+
+ align:start position:0%
+lube and kept 10% and the other 80% was
+ 
+
+ align:start position:0%
+lube and kept 10% and the other 80% was
+sold to the public but some keeps sixty
+
+ align:start position:0%
+sold to the public but some keeps sixty
+ 
+
+ align:start position:0%
+sold to the public but some keeps sixty
+or eighty percent for themselves I mean
+
+ align:start position:0%
+or eighty percent for themselves I mean
+ 
+
+ align:start position:0%
+or eighty percent for themselves I mean
+it's a whole wide range of economic
+
+ align:start position:0%
+it's a whole wide range of economic
+ 
+
+ align:start position:0%
+it's a whole wide range of economic
+incentives and models and the tokens are
+
+ align:start position:0%
+incentives and models and the tokens are
+ 
+
+ align:start position:0%
+incentives and models and the tokens are
+usually fungible and transferable and
+
+ align:start position:0%
+usually fungible and transferable and
+ 
+
+ align:start position:0%
+usually fungible and transferable and
+thus you can sort of put them on an
+
+ align:start position:0%
+thus you can sort of put them on an
+ 
+
+ align:start position:0%
+thus you can sort of put them on an
+exchange and try to sell them and
+
+ align:start position:0%
+exchange and try to sell them and
+ 
+
+ align:start position:0%
+exchange and try to sell them and
+promote them and again we're going to
+
+ align:start position:0%
+promote them and again we're going to
+ 
+
+ align:start position:0%
+promote them and again we're going to
+come back but I thought if we're talking
+
+ align:start position:0%
+come back but I thought if we're talking
+ 
+
+ align:start position:0%
+come back but I thought if we're talking
+about smart contracts they
+
+ align:start position:0%
+about smart contracts they
+ 
+
+ align:start position:0%
+about smart contracts they
+I into initial coin offerings Daniel is
+
+ align:start position:0%
+I into initial coin offerings Daniel is
+ 
+
+ align:start position:0%
+I into initial coin offerings Daniel is
+an excellent question Daniel says what
+
+ align:start position:0%
+an excellent question Daniel says what
+ 
+
+ align:start position:0%
+an excellent question Daniel says what
+goes into the valuation of something
+
+ align:start position:0%
+goes into the valuation of something
+ 
+
+ align:start position:0%
+goes into the valuation of something
+that is not functional and there there
+
+ align:start position:0%
+that is not functional and there there
+ 
+
+ align:start position:0%
+that is not functional and there there
+are many things that go up and
+
+ align:start position:0%
+are many things that go up and
+ 
+
+ align:start position:0%
+are many things that go up and
+ultimately it's in the anticipation of
+
+ align:start position:0%
+ultimately it's in the anticipation of
+ 
+
+ align:start position:0%
+ultimately it's in the anticipation of
+the potential profit and appreciation in
+
+ align:start position:0%
+the potential profit and appreciation in
+ 
+
+ align:start position:0%
+the potential profit and appreciation in
+the future so if you were just to have a
+
+ align:start position:0%
+the future so if you were just to have a
+ 
+
+ align:start position:0%
+the future so if you were just to have a
+laundromat a corner laundromat here in
+
+ align:start position:0%
+laundromat a corner laundromat here in
+ 
+
+ align:start position:0%
+laundromat a corner laundromat here in
+Cambridge you probably would only pay
+
+ align:start position:0%
+Cambridge you probably would only pay
+ 
+
+ align:start position:0%
+Cambridge you probably would only pay
+for the laundromat token what you
+
+ align:start position:0%
+for the laundromat token what you
+ 
+
+ align:start position:0%
+for the laundromat token what you
+thought the value was to do your laundry
+
+ align:start position:0%
+thought the value was to do your laundry
+ 
+
+ align:start position:0%
+thought the value was to do your laundry
+whatever there's 75 cents or whatever
+
+ align:start position:0%
+whatever there's 75 cents or whatever
+ 
+
+ align:start position:0%
+whatever there's 75 cents or whatever
+that frankly I don't know what the
+
+ align:start position:0%
+that frankly I don't know what the
+ 
+
+ align:start position:0%
+that frankly I don't know what the
+tokens go for and Cameron is anyway
+
+ align:start position:0%
+tokens go for and Cameron is anyway
+ 
+
+ align:start position:0%
+tokens go for and Cameron is anyway
+you're gonna tell me what a laundromat
+
+ align:start position:0%
+you're gonna tell me what a laundromat
+ 
+
+ align:start position:0%
+you're gonna tell me what a laundromat
+token goes for but if it's pre-function
+
+ align:start position:0%
+token goes for but if it's pre-function
+ 
+
+ align:start position:0%
+token goes for but if it's pre-function
+on the laundromat has not been built yet
+
+ align:start position:0%
+on the laundromat has not been built yet
+ 
+
+ align:start position:0%
+on the laundromat has not been built yet
+you and you have confidence it will be
+
+ align:start position:0%
+you and you have confidence it will be
+ 
+
+ align:start position:0%
+you and you have confidence it will be
+built you'll probably discount back you
+
+ align:start position:0%
+built you'll probably discount back you
+ 
+
+ align:start position:0%
+built you'll probably discount back you
+might pay 50 cents instead of 75 cents
+
+ align:start position:0%
+might pay 50 cents instead of 75 cents
+ 
+
+ align:start position:0%
+might pay 50 cents instead of 75 cents
+ultimately if you think it's going to be
+
+ align:start position:0%
+ultimately if you think it's going to be
+ 
+
+ align:start position:0%
+ultimately if you think it's going to be
+a really popular laundromat and it's
+
+ align:start position:0%
+a really popular laundromat and it's
+ 
+
+ align:start position:0%
+a really popular laundromat and it's
+gonna be the place to be seen by all MIT
+
+ align:start position:0%
+gonna be the place to be seen by all MIT
+ 
+
+ align:start position:0%
+gonna be the place to be seen by all MIT
+students and you think that token might
+
+ align:start position:0%
+students and you think that token might
+ 
+
+ align:start position:0%
+students and you think that token might
+one day be worth five dollars then
+
+ align:start position:0%
+one day be worth five dollars then
+ 
+
+ align:start position:0%
+one day be worth five dollars then
+you're starting to speculate on on the
+
+ align:start position:0%
+you're starting to speculate on on the
+ 
+
+ align:start position:0%
+you're starting to speculate on on the
+Community Interest so these tokens if
+
+ align:start position:0%
+Community Interest so these tokens if
+ 
+
+ align:start position:0%
+Community Interest so these tokens if
+you really believe in them you're trying
+
+ align:start position:0%
+you really believe in them you're trying
+ 
+
+ align:start position:0%
+you really believe in them you're trying
+to pay for what others will pay for them
+
+ align:start position:0%
+to pay for what others will pay for them
+ 
+
+ align:start position:0%
+to pay for what others will pay for them
+in the future and the economic
+
+ align:start position:0%
+in the future and the economic
+ 
+
+ align:start position:0%
+in the future and the economic
+equilibrium would be discounted so thus
+
+ align:start position:0%
+equilibrium would be discounted so thus
+ 
+
+ align:start position:0%
+equilibrium would be discounted so thus
+you're buying it because you think
+
+ align:start position:0%
+you're buying it because you think
+ 
+
+ align:start position:0%
+you're buying it because you think
+they'll appreciate in value so - Isaac
+
+ align:start position:0%
+they'll appreciate in value so - Isaac
+ 
+
+ align:start position:0%
+they'll appreciate in value so - Isaac
+says but maybe there could be a news Miz
+
+ align:start position:0%
+says but maybe there could be a news Miz
+ 
+
+ align:start position:0%
+says but maybe there could be a news Miz
+Matic or or other value to it it's
+
+ align:start position:0%
+Matic or or other value to it it's
+ 
+
+ align:start position:0%
+Matic or or other value to it it's
+possible I mean certainly crypto Kitty's
+
+ align:start position:0%
+possible I mean certainly crypto Kitty's
+ 
+
+ align:start position:0%
+possible I mean certainly crypto Kitty's
+caught into the whole collectibles wave
+
+ align:start position:0%
+caught into the whole collectibles wave
+ 
+
+ align:start position:0%
+caught into the whole collectibles wave
+let me try to wrap up so that I can hand
+
+ align:start position:0%
+let me try to wrap up so that I can hand
+ 
+
+ align:start position:0%
+let me try to wrap up so that I can hand
+it off to to Larry so there's been
+
+ align:start position:0%
+it off to to Larry so there's been
+ 
+
+ align:start position:0%
+it off to to Larry so there's been
+twenty eight billion dollars raised per
+
+ align:start position:0%
+twenty eight billion dollars raised per
+ 
+
+ align:start position:0%
+twenty eight billion dollars raised per
+one website
+
+ align:start position:0%
+one website
+ 
+
+ align:start position:0%
+one website
+elementa see others the track it think
+
+ align:start position:0%
+elementa see others the track it think
+ 
+
+ align:start position:0%
+elementa see others the track it think
+it's only between 20 and 25 billion
+
+ align:start position:0%
+it's only between 20 and 25 billion
+ 
+
+ align:start position:0%
+it's only between 20 and 25 billion
+there are no official arithmetic and no
+
+ align:start position:0%
+there are no official arithmetic and no
+ 
+
+ align:start position:0%
+there are no official arithmetic and no
+official records but the twenty eight
+
+ align:start position:0%
+official records but the twenty eight
+ 
+
+ align:start position:0%
+official records but the twenty eight
+billion dollars raised in initial coin
+
+ align:start position:0%
+billion dollars raised in initial coin
+ 
+
+ align:start position:0%
+billion dollars raised in initial coin
+offerings this is a cut of a neat video
+
+ align:start position:0%
+offerings this is a cut of a neat video
+ 
+
+ align:start position:0%
+offerings this is a cut of a neat video
+that I just took the last slide of from
+
+ align:start position:0%
+that I just took the last slide of from
+ 
+
+ align:start position:0%
+that I just took the last slide of from
+elementa so you can watch it in a minute
+
+ align:start position:0%
+elementa so you can watch it in a minute
+ 
+
+ align:start position:0%
+elementa so you can watch it in a minute
+and a half and over the years it's
+
+ align:start position:0%
+and a half and over the years it's
+ 
+
+ align:start position:0%
+and a half and over the years it's
+geographically dispersed with blue being
+
+ align:start position:0%
+geographically dispersed with blue being
+ 
+
+ align:start position:0%
+geographically dispersed with blue being
+Oceania Australia and and so forth
+
+ align:start position:0%
+Oceania Australia and and so forth
+ 
+
+ align:start position:0%
+Oceania Australia and and so forth
+Green being Asia North America being
+
+ align:start position:0%
+Green being Asia North America being
+ 
+
+ align:start position:0%
+Green being Asia North America being
+orange but the biggest ones is race 4.2
+
+ align:start position:0%
+orange but the biggest ones is race 4.2
+ 
+
+ align:start position:0%
+orange but the biggest ones is race 4.2
+billion telegram 1.7 billion and the
+
+ align:start position:0%
+billion telegram 1.7 billion and the
+ 
+
+ align:start position:0%
+billion telegram 1.7 billion and the
+like these are not small figures there's
+
+ align:start position:0%
+like these are not small figures there's
+ 
+
+ align:start position:0%
+like these are not small figures there's
+been forty five hundred at least forty
+
+ align:start position:0%
+been forty five hundred at least forty
+ 
+
+ align:start position:0%
+been forty five hundred at least forty
+five hundred proposed initial quaint
+
+ align:start position:0%
+five hundred proposed initial quaint
+ 
+
+ align:start position:0%
+five hundred proposed initial quaint
+offerings many of them didn't raise any
+
+ align:start position:0%
+offerings many of them didn't raise any
+ 
+
+ align:start position:0%
+offerings many of them didn't raise any
+money but over 2,000 to 3,000 have
+
+ align:start position:0%
+money but over 2,000 to 3,000 have
+ 
+
+ align:start position:0%
+money but over 2,000 to 3,000 have
+raised money I'm gonna use the three
+
+ align:start position:0%
+raised money I'm gonna use the three
+ 
+
+ align:start position:0%
+raised money I'm gonna use the three
+thousand figure less than half of them
+
+ align:start position:0%
+thousand figure less than half of them
+ 
+
+ align:start position:0%
+thousand figure less than half of them
+are even live today about fifty there's
+
+ align:start position:0%
+are even live today about fifty there's
+ 
+
+ align:start position:0%
+are even live today about fifty there's
+one study that shows that 59 percent
+
+ align:start position:0%
+one study that shows that 59 percent
+ 
+
+ align:start position:0%
+one study that shows that 59 percent
+fail within the first nine months there
+
+ align:start position:0%
+fail within the first nine months there
+ 
+
+ align:start position:0%
+fail within the first nine months there
+are other studies that say between a
+
+ align:start position:0%
+are other studies that say between a
+ 
+
+ align:start position:0%
+are other studies that say between a
+quarter and three quarters or scams
+
+ align:start position:0%
+quarter and three quarters or scams
+ 
+
+ align:start position:0%
+quarter and three quarters or scams
+Christian Catalina here has a study
+
+ align:start position:0%
+Christian Catalina here has a study
+ 
+
+ align:start position:0%
+Christian Catalina here has a study
+which I think is probably the most valid
+
+ align:start position:0%
+which I think is probably the most valid
+ 
+
+ align:start position:0%
+which I think is probably the most valid
+and reliable which says 25 percent of
+
+ align:start position:0%
+and reliable which says 25 percent of
+ 
+
+ align:start position:0%
+and reliable which says 25 percent of
+scams or frauds status has one that says
+
+ align:start position:0%
+scams or frauds status has one that says
+ 
+
+ align:start position:0%
+scams or frauds status has one that says
+80 percent might be I mean it just goes
+
+ align:start position:0%
+80 percent might be I mean it just goes
+ 
+
+ align:start position:0%
+80 percent might be I mean it just goes
+to zero or there's hold that until later
+
+ align:start position:0%
+to zero or there's hold that until later
+ 
+
+ align:start position:0%
+to zero or there's hold that until later
+when we're gonna dig into these in in
+
+ align:start position:0%
+when we're gonna dig into these in in
+ 
+
+ align:start position:0%
+when we're gonna dig into these in in
+the class but broad definition of fails
+
+ align:start position:0%
+the class but broad definition of fails
+ 
+
+ align:start position:0%
+the class but broad definition of fails
+so it's not just technology it means
+
+ align:start position:0%
+so it's not just technology it means
+ 
+
+ align:start position:0%
+so it's not just technology it means
+that you can't even find the website
+
+ align:start position:0%
+that you can't even find the website
+ 
+
+ align:start position:0%
+that you can't even find the website
+anymore they took your money and they
+
+ align:start position:0%
+anymore they took your money and they
+ 
+
+ align:start position:0%
+anymore they took your money and they
+ran or they still have a website but
+
+ align:start position:0%
+ran or they still have a website but
+ 
+
+ align:start position:0%
+ran or they still have a website but
+it's it's it's it's not live there
+
+ align:start position:0%
+it's it's it's it's not live there
+ 
+
+ align:start position:0%
+it's it's it's it's not live there
+doesn't seem like there's a development
+
+ align:start position:0%
+doesn't seem like there's a development
+ 
+
+ align:start position:0%
+doesn't seem like there's a development
+team any longer so multiple definitions
+
+ align:start position:0%
+team any longer so multiple definitions
+ 
+
+ align:start position:0%
+team any longer so multiple definitions
+of failure so that brings us to legal
+
+ align:start position:0%
+of failure so that brings us to legal
+ 
+
+ align:start position:0%
+of failure so that brings us to legal
+issues and as is Larry brings up is his
+
+ align:start position:0%
+issues and as is Larry brings up is his
+ 
+
+ align:start position:0%
+issues and as is Larry brings up is his
+computer let me just introduce our guest
+
+ align:start position:0%
+computer let me just introduce our guest
+ 
+
+ align:start position:0%
+computer let me just introduce our guest
+lecture Larry Lessig who's esteemed
+
+ align:start position:0%
+lecture Larry Lessig who's esteemed
+ 
+
+ align:start position:0%
+lecture Larry Lessig who's esteemed
+Harvard professor
+
+ align:start position:0%
+Harvard professor
+ 
+
+ align:start position:0%
+Harvard professor
+of law he was at Stanford he started
+
+ align:start position:0%
+of law he was at Stanford he started
+ 
+
+ align:start position:0%
+of law he was at Stanford he started
+something called the Internet and a
+
+ align:start position:0%
+something called the Internet and a
+ 
+
+ align:start position:0%
+something called the Internet and a
+center for Internet and Society you
+
+ align:start position:0%
+center for Internet and Society you
+ 
+
+ align:start position:0%
+center for Internet and Society you
+clerked for Justice Scalia so you must
+
+ align:start position:0%
+clerked for Justice Scalia so you must
+ 
+
+ align:start position:0%
+clerked for Justice Scalia so you must
+you must have some real views on what's
+
+ align:start position:0%
+you must have some real views on what's
+ 
+
+ align:start position:0%
+you must have some real views on what's
+going on this week then and this
+
+ align:start position:0%
+going on this week then and this
+ 
+
+ align:start position:0%
+going on this week then and this
+incredible appellate court judge posner
+
+ align:start position:0%
+incredible appellate court judge posner
+ 
+
+ align:start position:0%
+incredible appellate court judge posner
+and Larry also his first of what have
+
+ align:start position:0%
+and Larry also his first of what have
+ 
+
+ align:start position:0%
+and Larry also his first of what have
+you up to 9 or 10 books now but his
+
+ align:start position:0%
+you up to 9 or 10 books now but his
+ 
+
+ align:start position:0%
+you up to 9 or 10 books now but his
+first was the code in the law that I
+
+ align:start position:0%
+first was the code in the law that I
+ 
+
+ align:start position:0%
+first was the code in the law that I
+referenced in our first lecture Larry's
+
+ align:start position:0%
+referenced in our first lecture Larry's
+ 
+
+ align:start position:0%
+referenced in our first lecture Larry's
+going to take it away ok great so I'm
+
+ align:start position:0%
+going to take it away ok great so I'm
+ 
+
+ align:start position:0%
+going to take it away ok great so I'm
+really happy to be able to say that I've
+
+ align:start position:0%
+really happy to be able to say that I've
+ 
+
+ align:start position:0%
+really happy to be able to say that I've
+taught Business School students at MIT I
+
+ align:start position:0%
+taught Business School students at MIT I
+ 
+
+ align:start position:0%
+taught Business School students at MIT I
+mean I you know I'm a tech wannabe but
+
+ align:start position:0%
+mean I you know I'm a tech wannabe but
+ 
+
+ align:start position:0%
+mean I you know I'm a tech wannabe but
+have never been allowed to be officially
+
+ align:start position:0%
+have never been allowed to be officially
+ 
+
+ align:start position:0%
+have never been allowed to be officially
+here so this is exciting
+
+ align:start position:0%
+here so this is exciting
+ 
+
+ align:start position:0%
+here so this is exciting
+um but what I want to do is really
+
+ align:start position:0%
+um but what I want to do is really
+ 
+
+ align:start position:0%
+um but what I want to do is really
+address what I've experienced as
+
+ align:start position:0%
+address what I've experienced as
+ 
+
+ align:start position:0%
+address what I've experienced as
+misperceptions about the nature of the
+
+ align:start position:0%
+misperceptions about the nature of the
+ 
+
+ align:start position:0%
+misperceptions about the nature of the
+law as it might interact with the issues
+
+ align:start position:0%
+law as it might interact with the issues
+ 
+
+ align:start position:0%
+law as it might interact with the issues
+around digital contracts
+
+ align:start position:0%
+around digital contracts
+ 
+
+ align:start position:0%
+around digital contracts
+so I teach contract contract law is one
+
+ align:start position:0%
+so I teach contract contract law is one
+ 
+
+ align:start position:0%
+so I teach contract contract law is one
+of the subjects which I've taught since
+
+ align:start position:0%
+of the subjects which I've taught since
+ 
+
+ align:start position:0%
+of the subjects which I've taught since
+I started teaching and so I want to
+
+ align:start position:0%
+I started teaching and so I want to
+ 
+
+ align:start position:0%
+I started teaching and so I want to
+frame four points for you about how to
+
+ align:start position:0%
+frame four points for you about how to
+ 
+
+ align:start position:0%
+frame four points for you about how to
+think about contract law as it relates
+
+ align:start position:0%
+think about contract law as it relates
+ 
+
+ align:start position:0%
+think about contract law as it relates
+to these potential digital contracts but
+
+ align:start position:0%
+to these potential digital contracts but
+ 
+
+ align:start position:0%
+to these potential digital contracts but
+the first thing to do is just to make
+
+ align:start position:0%
+the first thing to do is just to make
+ 
+
+ align:start position:0%
+the first thing to do is just to make
+sure we understand we're all talking
+
+ align:start position:0%
+sure we understand we're all talking
+ 
+
+ align:start position:0%
+sure we understand we're all talking
+about the same thing okay so here's what
+
+ align:start position:0%
+about the same thing okay so here's what
+ 
+
+ align:start position:0%
+about the same thing okay so here's what
+the core of contract law teaches us
+
+ align:start position:0%
+the core of contract law teaches us
+ 
+
+ align:start position:0%
+the core of contract law teaches us
+contracts our contract is a promise or
+
+ align:start position:0%
+contracts our contract is a promise or
+ 
+
+ align:start position:0%
+contracts our contract is a promise or
+performance given in exchange for a
+
+ align:start position:0%
+performance given in exchange for a
+ 
+
+ align:start position:0%
+performance given in exchange for a
+promise or performance the given in
+
+ align:start position:0%
+promise or performance the given in
+ 
+
+ align:start position:0%
+promise or performance the given in
+exchange for is really critical that's
+
+ align:start position:0%
+exchange for is really critical that's
+ 
+
+ align:start position:0%
+exchange for is really critical that's
+the quid pro quo that sometimes referred
+
+ align:start position:0%
+the quid pro quo that sometimes referred
+ 
+
+ align:start position:0%
+the quid pro quo that sometimes referred
+to as the consideration for the promise
+
+ align:start position:0%
+to as the consideration for the promise
+ 
+
+ align:start position:0%
+to as the consideration for the promise
+but notice here this is mapping out four
+
+ align:start position:0%
+but notice here this is mapping out four
+ 
+
+ align:start position:0%
+but notice here this is mapping out four
+different possibilities you can have a
+
+ align:start position:0%
+different possibilities you can have a
+ 
+
+ align:start position:0%
+different possibilities you can have a
+promise in exchange for a promise I
+
+ align:start position:0%
+promise in exchange for a promise I
+ 
+
+ align:start position:0%
+promise in exchange for a promise I
+promise to pay you $10,000 if you
+
+ align:start position:0%
+promise to pay you $10,000 if you
+ 
+
+ align:start position:0%
+promise to pay you $10,000 if you
+promise to sing an opera for me tomorrow
+
+ align:start position:0%
+promise to sing an opera for me tomorrow
+ 
+
+ align:start position:0%
+promise to sing an opera for me tomorrow
+or it can be promise for a performance I
+
+ align:start position:0%
+or it can be promise for a performance I
+ 
+
+ align:start position:0%
+or it can be promise for a performance I
+promise to pay you Indy five dollars if
+
+ align:start position:0%
+promise to pay you Indy five dollars if
+ 
+
+ align:start position:0%
+promise to pay you Indy five dollars if
+you sing a song for us now
+
+ align:start position:0%
+you sing a song for us now
+ 
+
+ align:start position:0%
+you sing a song for us now
+so it's the performance I want I don't
+
+ align:start position:0%
+so it's the performance I want I don't
+ 
+
+ align:start position:0%
+so it's the performance I want I don't
+want to promise from him because we know
+
+ align:start position:0%
+want to promise from him because we know
+ 
+
+ align:start position:0%
+want to promise from him because we know
+what Andy's promises are worth or it
+
+ align:start position:0%
+what Andy's promises are worth or it
+ 
+
+ align:start position:0%
+what Andy's promises are worth or it
+could be a performance for a promise
+
+ align:start position:0%
+could be a performance for a promise
+ 
+
+ align:start position:0%
+could be a performance for a promise
+I'll sing if you promise to pay me after
+
+ align:start position:0%
+I'll sing if you promise to pay me after
+ 
+
+ align:start position:0%
+I'll sing if you promise to pay me after
+I'm done or the really interesting one
+
+ align:start position:0%
+I'm done or the really interesting one
+ 
+
+ align:start position:0%
+I'm done or the really interesting one
+for our purposes is a performance for a
+
+ align:start position:0%
+for our purposes is a performance for a
+ 
+
+ align:start position:0%
+for our purposes is a performance for a
+performance I'll sing if you pay me
+
+ align:start position:0%
+performance I'll sing if you pay me
+ 
+
+ align:start position:0%
+performance I'll sing if you pay me
+$5,000 I didn't want to promise from you
+
+ align:start position:0%
+$5,000 I didn't want to promise from you
+ 
+
+ align:start position:0%
+$5,000 I didn't want to promise from you
+because I don't trust you your business
+
+ align:start position:0%
+because I don't trust you your business
+ 
+
+ align:start position:0%
+because I don't trust you your business
+school students right so I I just want
+
+ align:start position:0%
+school students right so I I just want
+ 
+
+ align:start position:0%
+school students right so I I just want
+the money but I'm not promising to do
+
+ align:start position:0%
+the money but I'm not promising to do
+ 
+
+ align:start position:0%
+the money but I'm not promising to do
+anything I'm actually going to do
+
+ align:start position:0%
+anything I'm actually going to do
+ 
+
+ align:start position:0%
+anything I'm actually going to do
+something for you now that's the one
+
+ align:start position:0%
+something for you now that's the one
+ 
+
+ align:start position:0%
+something for you now that's the one
+that we're gonna think about in the
+
+ align:start position:0%
+that we're gonna think about in the
+ 
+
+ align:start position:0%
+that we're gonna think about in the
+context of digital contracts and they're
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually what's gonna make three points
+
+ align:start position:0%
+actually what's gonna make three points
+ 
+
+ align:start position:0%
+actually what's gonna make three points
+but then I decided I was gonna make four
+
+ align:start position:0%
+but then I decided I was gonna make four
+ 
+
+ align:start position:0%
+but then I decided I was gonna make four
+so let me fix that for points about
+
+ align:start position:0%
+so let me fix that for points about
+ 
+
+ align:start position:0%
+so let me fix that for points about
+contracts so the first point about
+
+ align:start position:0%
+contracts so the first point about
+ 
+
+ align:start position:0%
+contracts so the first point about
+contracts to think about this case all
+
+ align:start position:0%
+contracts to think about this case all
+ 
+
+ align:start position:0%
+contracts to think about this case all
+right here's a it's not quite digital
+
+ align:start position:0%
+right here's a it's not quite digital
+ 
+
+ align:start position:0%
+right here's a it's not quite digital
+but it's a physical contract machine in
+
+ align:start position:0%
+but it's a physical contract machine in
+ 
+
+ align:start position:0%
+but it's a physical contract machine in
+the sense that it's a performance for a
+
+ align:start position:0%
+the sense that it's a performance for a
+ 
+
+ align:start position:0%
+the sense that it's a performance for a
+performance if you drop a dime into this
+
+ align:start position:0%
+performance if you drop a dime into this
+ 
+
+ align:start position:0%
+performance if you drop a dime into this
+machine then out will come dr. pepper or
+
+ align:start position:0%
+machine then out will come dr. pepper or
+ 
+
+ align:start position:0%
+machine then out will come dr. pepper or
+something else okay so there's no
+
+ align:start position:0%
+something else okay so there's no
+ 
+
+ align:start position:0%
+something else okay so there's no
+promises involved and we understand
+
+ align:start position:0%
+promises involved and we understand
+ 
+
+ align:start position:0%
+promises involved and we understand
+there's a mechanism that's to produce
+
+ align:start position:0%
+there's a mechanism that's to produce
+ 
+
+ align:start position:0%
+there's a mechanism that's to produce
+this result and obviously these have
+
+ align:start position:0%
+this result and obviously these have
+ 
+
+ align:start position:0%
+this result and obviously these have
+been here for a long time and these
+
+ align:start position:0%
+been here for a long time and these
+ 
+
+ align:start position:0%
+been here for a long time and these
+mechanisms provide real value because to
+
+ align:start position:0%
+mechanisms provide real value because to
+ 
+
+ align:start position:0%
+mechanisms provide real value because to
+the extent you don't have to hire
+
+ align:start position:0%
+the extent you don't have to hire
+ 
+
+ align:start position:0%
+the extent you don't have to hire
+somebody to stand there handing out dr.
+
+ align:start position:0%
+somebody to stand there handing out dr.
+ 
+
+ align:start position:0%
+somebody to stand there handing out dr.
+peppers you can lower the cost of
+
+ align:start position:0%
+peppers you can lower the cost of
+ 
+
+ align:start position:0%
+peppers you can lower the cost of
+delivering dr. peppers and increase the
+
+ align:start position:0%
+delivering dr. peppers and increase the
+ 
+
+ align:start position:0%
+delivering dr. peppers and increase the
+market for dr. peppers so this is the
+
+ align:start position:0%
+market for dr. peppers so this is the
+ 
+
+ align:start position:0%
+market for dr. peppers so this is the
+motivation lower the transaction cost of
+
+ align:start position:0%
+motivation lower the transaction cost of
+ 
+
+ align:start position:0%
+motivation lower the transaction cost of
+engaging in a particular kind of
+
+ align:start position:0%
+engaging in a particular kind of
+ 
+
+ align:start position:0%
+engaging in a particular kind of
+contract which is performance for
+
+ align:start position:0%
+contract which is performance for
+ 
+
+ align:start position:0%
+contract which is performance for
+performance now when you look at that
+
+ align:start position:0%
+performance now when you look at that
+ 
+
+ align:start position:0%
+performance now when you look at that
+contract you should ask yourself what
+
+ align:start position:0%
+contract you should ask yourself what
+ 
+
+ align:start position:0%
+contract you should ask yourself what
+are the terms of this contract right so
+
+ align:start position:0%
+are the terms of this contract right so
+ 
+
+ align:start position:0%
+are the terms of this contract right so
+some of them are expressed and they're
+
+ align:start position:0%
+some of them are expressed and they're
+ 
+
+ align:start position:0%
+some of them are expressed and they're
+pretty obvious so this says 10 cents it
+
+ align:start position:0%
+pretty obvious so this says 10 cents it
+ 
+
+ align:start position:0%
+pretty obvious so this says 10 cents it
+says if you pay 10 cents there you will
+
+ align:start position:0%
+says if you pay 10 cents there you will
+ 
+
+ align:start position:0%
+says if you pay 10 cents there you will
+get the dr. pepper well that's what you
+
+ align:start position:0%
+get the dr. pepper well that's what you
+ 
+
+ align:start position:0%
+get the dr. pepper well that's what you
+kind of expect is a great cartoon I
+
+ align:start position:0%
+kind of expect is a great cartoon I
+ 
+
+ align:start position:0%
+kind of expect is a great cartoon I
+couldn't find where you come to a
+
+ align:start position:0%
+couldn't find where you come to a
+ 
+
+ align:start position:0%
+couldn't find where you come to a
+machine it says deposit 50 cents
+
+ align:start position:0%
+machine it says deposit 50 cents
+ 
+
+ align:start position:0%
+machine it says deposit 50 cents
+positive 50 cents and the light comes on
+
+ align:start position:0%
+positive 50 cents and the light comes on
+ 
+
+ align:start position:0%
+positive 50 cents and the light comes on
+thank you very much right so you think
+
+ align:start position:0%
+thank you very much right so you think
+ 
+
+ align:start position:0%
+thank you very much right so you think
+you know what this contract is but you
+
+ align:start position:0%
+you know what this contract is but you
+ 
+
+ align:start position:0%
+you know what this contract is but you
+know that the joke is to Vince that
+
+ align:start position:0%
+know that the joke is to Vince that
+ 
+
+ align:start position:0%
+know that the joke is to Vince that
+maybe you don't know what that contract
+
+ align:start position:0%
+maybe you don't know what that contract
+ 
+
+ align:start position:0%
+maybe you don't know what that contract
+is but but the Express terms are the one
+
+ align:start position:0%
+is but but the Express terms are the one
+ 
+
+ align:start position:0%
+is but but the Express terms are the one
+we expect go with the statement to the
+
+ align:start position:0%
+we expect go with the statement to the
+ 
+
+ align:start position:0%
+we expect go with the statement to the
+machine but then there's a whole bunch
+
+ align:start position:0%
+machine but then there's a whole bunch
+ 
+
+ align:start position:0%
+machine but then there's a whole bunch
+of implied terms so one implied term if
+
+ align:start position:0%
+of implied terms so one implied term if
+ 
+
+ align:start position:0%
+of implied terms so one implied term if
+this machine is in the United States is
+
+ align:start position:0%
+this machine is in the United States is
+ 
+
+ align:start position:0%
+this machine is in the United States is
+that when you take the dr. pepper out
+
+ align:start position:0%
+that when you take the dr. pepper out
+ 
+
+ align:start position:0%
+that when you take the dr. pepper out
+and you drink it it's actually going to
+
+ align:start position:0%
+and you drink it it's actually going to
+ 
+
+ align:start position:0%
+and you drink it it's actually going to
+be safe to drink
+
+ align:start position:0%
+be safe to drink
+ 
+
+ align:start position:0%
+be safe to drink
+it's actually gonna be dr. pepper it's
+
+ align:start position:0%
+it's actually gonna be dr. pepper it's
+ 
+
+ align:start position:0%
+it's actually gonna be dr. pepper it's
+actually not going to make you sick and
+
+ align:start position:0%
+actually not going to make you sick and
+ 
+
+ align:start position:0%
+actually not going to make you sick and
+none of that is written on the dr.
+
+ align:start position:0%
+none of that is written on the dr.
+ 
+
+ align:start position:0%
+none of that is written on the dr.
+pepper machine that's instead a term a
+
+ align:start position:0%
+pepper machine that's instead a term a
+ 
+
+ align:start position:0%
+pepper machine that's instead a term a
+contract term that gets created by the
+
+ align:start position:0%
+contract term that gets created by the
+ 
+
+ align:start position:0%
+contract term that gets created by the
+law and gets imposed or wrapped around
+
+ align:start position:0%
+law and gets imposed or wrapped around
+ 
+
+ align:start position:0%
+law and gets imposed or wrapped around
+the delivery of that drink
+
+ align:start position:0%
+the delivery of that drink
+ 
+
+ align:start position:0%
+the delivery of that drink
+okay that's your first point the second
+
+ align:start position:0%
+okay that's your first point the second
+ 
+
+ align:start position:0%
+okay that's your first point the second
+point that is to think more about what
+
+ align:start position:0%
+point that is to think more about what
+ 
+
+ align:start position:0%
+point that is to think more about what
+these implied terms imply because if
+
+ align:start position:0%
+these implied terms imply because if
+ 
+
+ align:start position:0%
+these implied terms imply because if
+these implied terms are implied by a
+
+ align:start position:0%
+these implied terms are implied by a
+ 
+
+ align:start position:0%
+these implied terms are implied by a
+legal system then that means the legal
+
+ align:start position:0%
+legal system then that means the legal
+ 
+
+ align:start position:0%
+legal system then that means the legal
+system has an interest in your contract
+
+ align:start position:0%
+system has an interest in your contract
+ 
+
+ align:start position:0%
+system has an interest in your contract
+legal system is not on that
+
+ align:start position:0%
+legal system is not on that
+ 
+
+ align:start position:0%
+legal system is not on that
+disinterested in your contract so we
+
+ align:start position:0%
+disinterested in your contract so we
+ 
+
+ align:start position:0%
+disinterested in your contract so we
+should always think that our contract is
+
+ align:start position:0%
+should always think that our contract is
+ 
+
+ align:start position:0%
+should always think that our contract is
+going to have two parties we call them
+
+ align:start position:0%
+going to have two parties we call them
+ 
+
+ align:start position:0%
+going to have two parties we call them
+the promise or and the promisee you know
+
+ align:start position:0%
+the promise or and the promisee you know
+ 
+
+ align:start position:0%
+the promise or and the promisee you know
+I've told you we've had contracts it can
+
+ align:start position:0%
+I've told you we've had contracts it can
+ 
+
+ align:start position:0%
+I've told you we've had contracts it can
+be performance the performance or isn't
+
+ align:start position:0%
+be performance the performance or isn't
+ 
+
+ align:start position:0%
+be performance the performance or isn't
+really a word but let's just say promise
+
+ align:start position:0%
+really a word but let's just say promise
+ 
+
+ align:start position:0%
+really a word but let's just say promise
+Oram promise e but there's always a
+
+ align:start position:0%
+Oram promise e but there's always a
+ 
+
+ align:start position:0%
+Oram promise e but there's always a
+third party which is the state who is in
+
+ align:start position:0%
+third party which is the state who is in
+ 
+
+ align:start position:0%
+third party which is the state who is in
+the middle of the contract in the sense
+
+ align:start position:0%
+the middle of the contract in the sense
+ 
+
+ align:start position:0%
+the middle of the contract in the sense
+that the states will police many
+
+ align:start position:0%
+that the states will police many
+ 
+
+ align:start position:0%
+that the states will police many
+contracts and decide whether they lie to
+
+ align:start position:0%
+contracts and decide whether they lie to
+ 
+
+ align:start position:0%
+contracts and decide whether they lie to
+the state likes the contract or not I
+
+ align:start position:0%
+the state likes the contract or not I
+ 
+
+ align:start position:0%
+the state likes the contract or not I
+mean if the state doesn't like the
+
+ align:start position:0%
+mean if the state doesn't like the
+ 
+
+ align:start position:0%
+mean if the state doesn't like the
+contract then the state won't enforce
+
+ align:start position:0%
+contract then the state won't enforce
+ 
+
+ align:start position:0%
+contract then the state won't enforce
+the contract or the state might actually
+
+ align:start position:0%
+the contract or the state might actually
+ 
+
+ align:start position:0%
+the contract or the state might actually
+punish you because of the contract so
+
+ align:start position:0%
+punish you because of the contract so
+ 
+
+ align:start position:0%
+punish you because of the contract so
+for example the state cares about the
+
+ align:start position:0%
+for example the state cares about the
+ 
+
+ align:start position:0%
+for example the state cares about the
+kinds of contracts you can have
+
+ align:start position:0%
+kinds of contracts you can have
+ 
+
+ align:start position:0%
+kinds of contracts you can have
+contracts for the sale of tables you
+
+ align:start position:0%
+contracts for the sale of tables you
+ 
+
+ align:start position:0%
+contracts for the sale of tables you
+can't have contracts for the sale of the
+
+ align:start position:0%
+can't have contracts for the sale of the
+ 
+
+ align:start position:0%
+can't have contracts for the sale of the
+people though you can sell dogs for
+
+ align:start position:0%
+people though you can sell dogs for
+ 
+
+ align:start position:0%
+people though you can sell dogs for
+reasons I can't understand but you know
+
+ align:start position:0%
+reasons I can't understand but you know
+ 
+
+ align:start position:0%
+reasons I can't understand but you know
+the point is we are deciding which type
+
+ align:start position:0%
+the point is we are deciding which type
+ 
+
+ align:start position:0%
+the point is we are deciding which type
+of things can be sold and which kind of
+
+ align:start position:0%
+of things can be sold and which kind of
+ 
+
+ align:start position:0%
+of things can be sold and which kind of
+things can't be sold the state cares
+
+ align:start position:0%
+things can't be sold the state cares
+ 
+
+ align:start position:0%
+things can't be sold the state cares
+about the effect of the contract
+
+ align:start position:0%
+about the effect of the contract
+ 
+
+ align:start position:0%
+about the effect of the contract
+if the contract is to render your
+
+ align:start position:0%
+if the contract is to render your
+ 
+
+ align:start position:0%
+if the contract is to render your
+corporation vulnerable to bankruptcy the
+
+ align:start position:0%
+corporation vulnerable to bankruptcy the
+ 
+
+ align:start position:0%
+corporation vulnerable to bankruptcy the
+state might have an interest in deciding
+
+ align:start position:0%
+state might have an interest in deciding
+ 
+
+ align:start position:0%
+state might have an interest in deciding
+whether that contract will be enforced
+
+ align:start position:0%
+whether that contract will be enforced
+ 
+
+ align:start position:0%
+whether that contract will be enforced
+or not or whether it will be allowed or
+
+ align:start position:0%
+or not or whether it will be allowed or
+ 
+
+ align:start position:0%
+or not or whether it will be allowed or
+not whether it's permissible under
+
+ align:start position:0%
+not whether it's permissible under
+ 
+
+ align:start position:0%
+not whether it's permissible under
+bankruptcy laws to engage in that
+
+ align:start position:0%
+bankruptcy laws to engage in that
+ 
+
+ align:start position:0%
+bankruptcy laws to engage in that
+contract because of the risk that it's
+
+ align:start position:0%
+contract because of the risk that it's
+ 
+
+ align:start position:0%
+contract because of the risk that it's
+going to create it's going to care about
+
+ align:start position:0%
+going to create it's going to care about
+ 
+
+ align:start position:0%
+going to create it's going to care about
+the terms of the contract so if you're
+
+ align:start position:0%
+the terms of the contract so if you're
+ 
+
+ align:start position:0%
+the terms of the contract so if you're
+selling your labor in a state with a
+
+ align:start position:0%
+selling your labor in a state with a
+ 
+
+ align:start position:0%
+selling your labor in a state with a
+minimum wage law the state's gonna care
+
+ align:start position:0%
+minimum wage law the state's gonna care
+ 
+
+ align:start position:0%
+minimum wage law the state's gonna care
+does the term that specifies your wage
+
+ align:start position:0%
+does the term that specifies your wage
+ 
+
+ align:start position:0%
+does the term that specifies your wage
+equal or exceed the minimum wage and the
+
+ align:start position:0%
+equal or exceed the minimum wage and the
+ 
+
+ align:start position:0%
+equal or exceed the minimum wage and the
+state's gonna obviously care the most
+
+ align:start position:0%
+state's gonna obviously care the most
+ 
+
+ align:start position:0%
+state's gonna obviously care the most
+important thing for the state is whether
+
+ align:start position:0%
+important thing for the state is whether
+ 
+
+ align:start position:0%
+important thing for the state is whether
+and how the state tax is the transaction
+
+ align:start position:0%
+and how the state tax is the transaction
+ 
+
+ align:start position:0%
+and how the state tax is the transaction
+in the contract so when does it tax the
+
+ align:start position:0%
+in the contract so when does it tax the
+ 
+
+ align:start position:0%
+in the contract so when does it tax the
+transaction of the contract does it you
+
+ align:start position:0%
+transaction of the contract does it you
+ 
+
+ align:start position:0%
+transaction of the contract does it you
+know what is the event that's going to
+
+ align:start position:0%
+know what is the event that's going to
+ 
+
+ align:start position:0%
+know what is the event that's going to
+manifest it and of course the contract
+
+ align:start position:0%
+manifest it and of course the contract
+ 
+
+ align:start position:0%
+manifest it and of course the contract
+can try to play with that to sort of
+
+ align:start position:0%
+can try to play with that to sort of
+ 
+
+ align:start position:0%
+can try to play with that to sort of
+deal with whether it will be taxed in
+
+ align:start position:0%
+deal with whether it will be taxed in
+ 
+
+ align:start position:0%
+deal with whether it will be taxed in
+the state will care about how the
+
+ align:start position:0%
+the state will care about how the
+ 
+
+ align:start position:0%
+the state will care about how the
+contract deals with okay so the point is
+
+ align:start position:0%
+contract deals with okay so the point is
+ 
+
+ align:start position:0%
+contract deals with okay so the point is
+to to fight against the first real bias
+
+ align:start position:0%
+to to fight against the first real bias
+ 
+
+ align:start position:0%
+to to fight against the first real bias
+then especially non it was let's say
+
+ align:start position:0%
+then especially non it was let's say
+ 
+
+ align:start position:0%
+then especially non it was let's say
+tech people maybe business tech people
+
+ align:start position:0%
+tech people maybe business tech people
+ 
+
+ align:start position:0%
+tech people maybe business tech people
+bringing to the idea of contract law
+
+ align:start position:0%
+bringing to the idea of contract law
+ 
+
+ align:start position:0%
+bringing to the idea of contract law
+which is that contracts are not about
+
+ align:start position:0%
+which is that contracts are not about
+ 
+
+ align:start position:0%
+which is that contracts are not about
+the state they're about private parties
+
+ align:start position:0%
+the state they're about private parties
+ 
+
+ align:start position:0%
+the state they're about private parties
+that's not true they're about private
+
+ align:start position:0%
+that's not true they're about private
+ 
+
+ align:start position:0%
+that's not true they're about private
+parties and the state and the state is
+
+ align:start position:0%
+parties and the state and the state is
+ 
+
+ align:start position:0%
+parties and the state and the state is
+always going to be there now so if I say
+
+ align:start position:0%
+always going to be there now so if I say
+ 
+
+ align:start position:0%
+always going to be there now so if I say
+to you so I'm trying to sell my parents
+
+ align:start position:0%
+to you so I'm trying to sell my parents
+ 
+
+ align:start position:0%
+to you so I'm trying to sell my parents
+house I can't sell it so if they say to
+
+ align:start position:0%
+house I can't sell it so if they say to
+ 
+
+ align:start position:0%
+house I can't sell it so if they say to
+you I'll offer you $10,000 to anyone who
+
+ align:start position:0%
+you I'll offer you $10,000 to anyone who
+ 
+
+ align:start position:0%
+you I'll offer you $10,000 to anyone who
+will burn down my parents house you're
+
+ align:start position:0%
+will burn down my parents house you're
+ 
+
+ align:start position:0%
+will burn down my parents house you're
+trying to accept that contract yeah
+
+ align:start position:0%
+trying to accept that contract yeah
+ 
+
+ align:start position:0%
+trying to accept that contract yeah
+you're raising your hand so you're
+
+ align:start position:0%
+you're raising your hand so you're
+ 
+
+ align:start position:0%
+you're raising your hand so you're
+trying to accept I want to say
+
+ align:start position:0%
+trying to accept I want to say
+ 
+
+ align:start position:0%
+trying to accept I want to say
+officially it's a joke so nobody gets
+
+ align:start position:0%
+officially it's a joke so nobody gets
+ 
+
+ align:start position:0%
+officially it's a joke so nobody gets
+any uncertainty about this now you can
+
+ align:start position:0%
+any uncertainty about this now you can
+ 
+
+ align:start position:0%
+any uncertainty about this now you can
+ask a question because I didn't want you
+
+ align:start position:0%
+ask a question because I didn't want you
+ 
+
+ align:start position:0%
+ask a question because I didn't want you
+to accept because if you accepted my
+
+ align:start position:0%
+to accept because if you accepted my
+ 
+
+ align:start position:0%
+to accept because if you accepted my
+offer then that's it I'm stuck so now
+
+ align:start position:0%
+offer then that's it I'm stuck so now
+ 
+
+ align:start position:0%
+offer then that's it I'm stuck so now
+it's clear it's not really an offer and
+
+ align:start position:0%
+it's clear it's not really an offer and
+ 
+
+ align:start position:0%
+it's clear it's not really an offer and
+I can ask you a question
+
+ align:start position:0%
+I can ask you a question
+ 
+
+ align:start position:0%
+I can ask you a question
+so they said contracts cannot be between
+
+ align:start position:0%
+so they said contracts cannot be between
+ 
+
+ align:start position:0%
+so they said contracts cannot be between
+two parties they have to be between two
+
+ align:start position:0%
+two parties they have to be between two
+ 
+
+ align:start position:0%
+two parties they have to be between two
+parties in the state let me see it more
+
+ align:start position:0%
+parties in the state let me see it more
+ 
+
+ align:start position:0%
+parties in the state let me see it more
+clearly contracts always have the state
+
+ align:start position:0%
+clearly contracts always have the state
+ 
+
+ align:start position:0%
+clearly contracts always have the state
+present so it's always between two
+
+ align:start position:0%
+present so it's always between two
+ 
+
+ align:start position:0%
+present so it's always between two
+parties or three parties or four so you
+
+ align:start position:0%
+parties or three parties or four so you
+ 
+
+ align:start position:0%
+parties or three parties or four so you
+and I enter into a contract not this one
+
+ align:start position:0%
+and I enter into a contract not this one
+ 
+
+ align:start position:0%
+and I enter into a contract not this one
+but another one
+
+ align:start position:0%
+but another one
+ 
+
+ align:start position:0%
+but another one
+but the state is in the room and
+
+ align:start position:0%
+but the state is in the room and
+ 
+
+ align:start position:0%
+but the state is in the room and
+deciding whether the states you know in
+
+ align:start position:0%
+deciding whether the states you know in
+ 
+
+ align:start position:0%
+deciding whether the states you know in
+the states gonna allow the contract to
+
+ align:start position:0%
+the states gonna allow the contract to
+ 
+
+ align:start position:0%
+the states gonna allow the contract to
+happen so most contracts the state
+
+ align:start position:0%
+happen so most contracts the state
+ 
+
+ align:start position:0%
+happen so most contracts the state
+doesn't care about but some contracts
+
+ align:start position:0%
+doesn't care about but some contracts
+ 
+
+ align:start position:0%
+doesn't care about but some contracts
+gonna say hell no we're not gonna allow
+
+ align:start position:0%
+gonna say hell no we're not gonna allow
+ 
+
+ align:start position:0%
+gonna say hell no we're not gonna allow
+it like this one you know if you didn't
+
+ align:start position:0%
+it like this one you know if you didn't
+ 
+
+ align:start position:0%
+it like this one you know if you didn't
+get that noticed it was a joke and you
+
+ align:start position:0%
+get that noticed it was a joke and you
+ 
+
+ align:start position:0%
+get that noticed it was a joke and you
+thought I was serious and you went you
+
+ align:start position:0%
+thought I was serious and you went you
+ 
+
+ align:start position:0%
+thought I was serious and you went you
+burned down my parents house so that we
+
+ align:start position:0%
+burned down my parents house so that we
+ 
+
+ align:start position:0%
+burned down my parents house so that we
+could get the insurance and not have to
+
+ align:start position:0%
+could get the insurance and not have to
+ 
+
+ align:start position:0%
+could get the insurance and not have to
+worry about selling the house and then
+
+ align:start position:0%
+worry about selling the house and then
+ 
+
+ align:start position:0%
+worry about selling the house and then
+you came to me and you said okay pay the
+
+ align:start position:0%
+you came to me and you said okay pay the
+ 
+
+ align:start position:0%
+you came to me and you said okay pay the
+$10,000 and I said it was an obvious
+
+ align:start position:0%
+$10,000 and I said it was an obvious
+ 
+
+ align:start position:0%
+$10,000 and I said it was an obvious
+joke and you went to a court and you
+
+ align:start position:0%
+joke and you went to a court and you
+ 
+
+ align:start position:0%
+joke and you went to a court and you
+said force Lessig to pay the $10,000 the
+
+ align:start position:0%
+said force Lessig to pay the $10,000 the
+ 
+
+ align:start position:0%
+said force Lessig to pay the $10,000 the
+Corbis say this is an illegal contract I
+
+ align:start position:0%
+Corbis say this is an illegal contract I
+ 
+
+ align:start position:0%
+Corbis say this is an illegal contract I
+come enforce this contract so my point
+
+ align:start position:0%
+come enforce this contract so my point
+ 
+
+ align:start position:0%
+come enforce this contract so my point
+is the state in a certain sense is the
+
+ align:start position:0%
+is the state in a certain sense is the
+ 
+
+ align:start position:0%
+is the state in a certain sense is the
+sense sensor of this contract the state
+
+ align:start position:0%
+sense sensor of this contract the state
+ 
+
+ align:start position:0%
+sense sensor of this contract the state
+is in the room when we make this
+
+ align:start position:0%
+is in the room when we make this
+ 
+
+ align:start position:0%
+is in the room when we make this
+contract and the state's judgment about
+
+ align:start position:0%
+contract and the state's judgment about
+ 
+
+ align:start position:0%
+contract and the state's judgment about
+it will decide whether we enforce it or
+
+ align:start position:0%
+it will decide whether we enforce it or
+ 
+
+ align:start position:0%
+it will decide whether we enforce it or
+not is that clear I'm not saying the
+
+ align:start position:0%
+not is that clear I'm not saying the
+ 
+
+ align:start position:0%
+not is that clear I'm not saying the
+state is technically signing the
+
+ align:start position:0%
+state is technically signing the
+ 
+
+ align:start position:0%
+state is technically signing the
+document but I'm getting you to
+
+ align:start position:0%
+document but I'm getting you to
+ 
+
+ align:start position:0%
+document but I'm getting you to
+recognize the fact that the contract is
+
+ align:start position:0%
+recognize the fact that the contract is
+ 
+
+ align:start position:0%
+recognize the fact that the contract is
+valuable to the extent it's enforceable
+
+ align:start position:0%
+valuable to the extent it's enforceable
+ 
+
+ align:start position:0%
+valuable to the extent it's enforceable
+and the state is the essential agent in
+
+ align:start position:0%
+and the state is the essential agent in
+ 
+
+ align:start position:0%
+and the state is the essential agent in
+enforcement in the that's my question
+
+ align:start position:0%
+enforcement in the that's my question
+ 
+
+ align:start position:0%
+enforcement in the that's my question
+because it seems like nowadays we can
+
+ align:start position:0%
+because it seems like nowadays we can
+ 
+
+ align:start position:0%
+because it seems like nowadays we can
+have contracts where the enforcement is
+
+ align:start position:0%
+have contracts where the enforcement is
+ 
+
+ align:start position:0%
+have contracts where the enforcement is
+not a contract that says hey if you can
+
+ align:start position:0%
+not a contract that says hey if you can
+ 
+
+ align:start position:0%
+not a contract that says hey if you can
+factor this number I'll give you 10 and
+
+ align:start position:0%
+factor this number I'll give you 10 and
+ 
+
+ align:start position:0%
+factor this number I'll give you 10 and
+what I started with when I was showing
+
+ align:start position:0%
+what I started with when I was showing
+ 
+
+ align:start position:0%
+what I started with when I was showing
+you this picture was to say actually
+
+ align:start position:0%
+you this picture was to say actually
+ 
+
+ align:start position:0%
+you this picture was to say actually
+that's been true for a while right so in
+
+ align:start position:0%
+that's been true for a while right so in
+ 
+
+ align:start position:0%
+that's been true for a while right so in
+what sense is the state here well the
+
+ align:start position:0%
+what sense is the state here well the
+ 
+
+ align:start position:0%
+what sense is the state here well the
+state is here if you know when you put
+
+ align:start position:0%
+state is here if you know when you put
+ 
+
+ align:start position:0%
+state is here if you know when you put
+the dime in you get the drink out and
+
+ align:start position:0%
+the dime in you get the drink out and
+ 
+
+ align:start position:0%
+the dime in you get the drink out and
+the drink doesn't have dr. pepper but it
+
+ align:start position:0%
+the drink doesn't have dr. pepper but it
+ 
+
+ align:start position:0%
+the drink doesn't have dr. pepper but it
+has gasoline in it
+
+ align:start position:0%
+has gasoline in it
+ 
+
+ align:start position:0%
+has gasoline in it
+you know the state would come in and say
+
+ align:start position:0%
+you know the state would come in and say
+ 
+
+ align:start position:0%
+you know the state would come in and say
+well you've breached the implied term
+
+ align:start position:0%
+well you've breached the implied term
+ 
+
+ align:start position:0%
+well you've breached the implied term
+that said that this was safe to consume
+
+ align:start position:0%
+that said that this was safe to consume
+ 
+
+ align:start position:0%
+that said that this was safe to consume
+so the state is in this contract too and
+
+ align:start position:0%
+so the state is in this contract too and
+ 
+
+ align:start position:0%
+so the state is in this contract too and
+and so what I'm trying to lead to I'll
+
+ align:start position:0%
+and so what I'm trying to lead to I'll
+ 
+
+ align:start position:0%
+and so what I'm trying to lead to I'll
+get to the place where we say is there
+
+ align:start position:0%
+get to the place where we say is there
+ 
+
+ align:start position:0%
+get to the place where we say is there
+ever a place where the state is not
+
+ align:start position:0%
+ever a place where the state is not
+ 
+
+ align:start position:0%
+ever a place where the state is not
+there which is what I think your you
+
+ align:start position:0%
+there which is what I think your you
+ 
+
+ align:start position:0%
+there which is what I think your you
+know your blockchain like invocation is
+
+ align:start position:0%
+know your blockchain like invocation is
+ 
+
+ align:start position:0%
+know your blockchain like invocation is
+so that's that's a question we're going
+
+ align:start position:0%
+so that's that's a question we're going
+ 
+
+ align:start position:0%
+so that's that's a question we're going
+to get here's another contract
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we'll offer you $50,000 to lobby
+
+ align:start position:0%
+we'll offer you $50,000 to lobby
+ 
+
+ align:start position:0%
+we'll offer you $50,000 to lobby
+Congress to pass HR 102 this contract
+
+ align:start position:0%
+Congress to pass HR 102 this contract
+ 
+
+ align:start position:0%
+Congress to pass HR 102 this contract
+looks pretty normal to us can imagine
+
+ align:start position:0%
+looks pretty normal to us can imagine
+ 
+
+ align:start position:0%
+looks pretty normal to us can imagine
+lobbyists have a contract like this all
+
+ align:start position:0%
+lobbyists have a contract like this all
+ 
+
+ align:start position:0%
+lobbyists have a contract like this all
+the time in fact in the middle of the
+
+ align:start position:0%
+the time in fact in the middle of the
+ 
+
+ align:start position:0%
+the time in fact in the middle of the
+19th century the Supreme Court ruled
+
+ align:start position:0%
+19th century the Supreme Court ruled
+ 
+
+ align:start position:0%
+19th century the Supreme Court ruled
+this contract was an illegal contract
+
+ align:start position:0%
+this contract was an illegal contract
+ 
+
+ align:start position:0%
+this contract was an illegal contract
+you weren't allowed to hire people to
+
+ align:start position:0%
+you weren't allowed to hire people to
+ 
+
+ align:start position:0%
+you weren't allowed to hire people to
+lobby Congress right so again the
+
+ align:start position:0%
+lobby Congress right so again the
+ 
+
+ align:start position:0%
+lobby Congress right so again the
+background norm of what is appropriate
+
+ align:start position:0%
+background norm of what is appropriate
+ 
+
+ align:start position:0%
+background norm of what is appropriate
+or not for the contract controlled what
+
+ align:start position:0%
+or not for the contract controlled what
+ 
+
+ align:start position:0%
+or not for the contract controlled what
+type of contracting was allowed okay so
+
+ align:start position:0%
+type of contracting was allowed okay so
+ 
+
+ align:start position:0%
+type of contracting was allowed okay so
+so that's about the type of contracts
+
+ align:start position:0%
+so that's about the type of contracts
+ 
+
+ align:start position:0%
+so that's about the type of contracts
+but then think about the terms of
+
+ align:start position:0%
+but then think about the terms of
+ 
+
+ align:start position:0%
+but then think about the terms of
+contract and so I want to now I want to
+
+ align:start position:0%
+contract and so I want to now I want to
+ 
+
+ align:start position:0%
+contract and so I want to now I want to
+get you to recognize the way in which
+
+ align:start position:0%
+get you to recognize the way in which
+ 
+
+ align:start position:0%
+get you to recognize the way in which
+the terms that the law wants a contract
+
+ align:start position:0%
+the terms that the law wants a contract
+ 
+
+ align:start position:0%
+the terms that the law wants a contract
+to have can be defeated or not by
+
+ align:start position:0%
+to have can be defeated or not by
+ 
+
+ align:start position:0%
+to have can be defeated or not by
+technology and the way I'm going to get
+
+ align:start position:0%
+technology and the way I'm going to get
+ 
+
+ align:start position:0%
+technology and the way I'm going to get
+you to think about that is to think
+
+ align:start position:0%
+you to think about that is to think
+ 
+
+ align:start position:0%
+you to think about that is to think
+about not contract law but something
+
+ align:start position:0%
+about not contract law but something
+ 
+
+ align:start position:0%
+about not contract law but something
+that will create the intuitions I want
+
+ align:start position:0%
+that will create the intuitions I want
+ 
+
+ align:start position:0%
+that will create the intuitions I want
+you to think about copyright law
+
+ align:start position:0%
+you to think about copyright law
+ 
+
+ align:start position:0%
+you to think about copyright law
+everybody knows so copyright law is a
+
+ align:start position:0%
+everybody knows so copyright law is a
+ 
+
+ align:start position:0%
+everybody knows so copyright law is a
+basic contract with the state where the
+
+ align:start position:0%
+basic contract with the state where the
+ 
+
+ align:start position:0%
+basic contract with the state where the
+state says if you create something then
+
+ align:start position:0%
+state says if you create something then
+ 
+
+ align:start position:0%
+state says if you create something then
+you're gonna get an exclusive right to
+
+ align:start position:0%
+you're gonna get an exclusive right to
+ 
+
+ align:start position:0%
+you're gonna get an exclusive right to
+it or exclusive rights a set of Rights
+
+ align:start position:0%
+it or exclusive rights a set of Rights
+ 
+
+ align:start position:0%
+it or exclusive rights a set of Rights
+the occlusive right to copy is whose
+
+ align:start position:0%
+the occlusive right to copy is whose
+ 
+
+ align:start position:0%
+the occlusive right to copy is whose
+right to sell it skews the right to make
+
+ align:start position:0%
+right to sell it skews the right to make
+ 
+
+ align:start position:0%
+right to sell it skews the right to make
+derivative works of it for a period of
+
+ align:start position:0%
+derivative works of it for a period of
+ 
+
+ align:start position:0%
+derivative works of it for a period of
+time and in America right now that's
+
+ align:start position:0%
+time and in America right now that's
+ 
+
+ align:start position:0%
+time and in America right now that's
+your life Plus 70 years subject to fair
+
+ align:start position:0%
+your life Plus 70 years subject to fair
+ 
+
+ align:start position:0%
+your life Plus 70 years subject to fair
+use meaning the law says you can't
+
+ align:start position:0%
+use meaning the law says you can't
+ 
+
+ align:start position:0%
+use meaning the law says you can't
+control every use of my copyrighted work
+
+ align:start position:0%
+control every use of my copyrighted work
+ 
+
+ align:start position:0%
+control every use of my copyrighted work
+if you want to take a book of mine and
+
+ align:start position:0%
+if you want to take a book of mine and
+ 
+
+ align:start position:0%
+if you want to take a book of mine and
+quote a section and write a review that
+
+ align:start position:0%
+quote a section and write a review that
+ 
+
+ align:start position:0%
+quote a section and write a review that
+says see how idiotic Lessig is you can
+
+ align:start position:0%
+says see how idiotic Lessig is you can
+ 
+
+ align:start position:0%
+says see how idiotic Lessig is you can
+do that and I can't wrap the book in a
+
+ align:start position:0%
+do that and I can't wrap the book in a
+ 
+
+ align:start position:0%
+do that and I can't wrap the book in a
+contract that says you're not allowed to
+
+ align:start position:0%
+contract that says you're not allowed to
+ 
+
+ align:start position:0%
+contract that says you're not allowed to
+quote it for purposes of criticizing I'm
+
+ align:start position:0%
+quote it for purposes of criticizing I'm
+ 
+
+ align:start position:0%
+quote it for purposes of criticizing I'm
+just not allowed to do so copyright law
+
+ align:start position:0%
+just not allowed to do so copyright law
+ 
+
+ align:start position:0%
+just not allowed to do so copyright law
+kind of imagined this bundle of Rights
+
+ align:start position:0%
+kind of imagined this bundle of Rights
+ 
+
+ align:start position:0%
+kind of imagined this bundle of Rights
+that it was offering but now imagine
+
+ align:start position:0%
+that it was offering but now imagine
+ 
+
+ align:start position:0%
+that it was offering but now imagine
+something like called DRM digital rights
+
+ align:start position:0%
+something like called DRM digital rights
+ 
+
+ align:start position:0%
+something like called DRM digital rights
+management DRM is a set of code that we
+
+ align:start position:0%
+management DRM is a set of code that we
+ 
+
+ align:start position:0%
+management DRM is a set of code that we
+can wrap copyrighted material in in the
+
+ align:start position:0%
+can wrap copyrighted material in in the
+ 
+
+ align:start position:0%
+can wrap copyrighted material in in the
+process of making it available to others
+
+ align:start position:0%
+process of making it available to others
+ 
+
+ align:start position:0%
+process of making it available to others
+networks and whatever else it's pretty
+
+ align:start position:0%
+networks and whatever else it's pretty
+ 
+
+ align:start position:0%
+networks and whatever else it's pretty
+trivial to see the way DRM could in
+
+ align:start position:0%
+trivial to see the way DRM could in
+ 
+
+ align:start position:0%
+trivial to see the way DRM could in
+effect destroy the limitations on the
+
+ align:start position:0%
+effect destroy the limitations on the
+ 
+
+ align:start position:0%
+effect destroy the limitations on the
+term you know you can wrap it encrypt it
+
+ align:start position:0%
+term you know you can wrap it encrypt it
+ 
+
+ align:start position:0%
+term you know you can wrap it encrypt it
+make it so that my ability to control it
+
+ align:start position:0%
+make it so that my ability to control it
+ 
+
+ align:start position:0%
+make it so that my ability to control it
+will be my ability to control it you
+
+ align:start position:0%
+will be my ability to control it you
+ 
+
+ align:start position:0%
+will be my ability to control it you
+know concept can see Vuli as long as
+
+ align:start position:0%
+know concept can see Vuli as long as
+ 
+
+ align:start position:0%
+know concept can see Vuli as long as
+machines are running you know if it's a
+
+ align:start position:0%
+machines are running you know if it's a
+ 
+
+ align:start position:0%
+machines are running you know if it's a
+Microsoft based system four years later
+
+ align:start position:0%
+Microsoft based system four years later
+ 
+
+ align:start position:0%
+Microsoft based system four years later
+it won't be workable but the point is in
+
+ align:start position:0%
+it won't be workable but the point is in
+ 
+
+ align:start position:0%
+it won't be workable but the point is in
+principle it could be forever
+
+ align:start position:0%
+principle it could be forever
+ 
+
+ align:start position:0%
+principle it could be forever
+same thing with fair use you can imagine
+
+ align:start position:0%
+same thing with fair use you can imagine
+ 
+
+ align:start position:0%
+same thing with fair use you can imagine
+it being wrapped in a way that disables
+
+ align:start position:0%
+it being wrapped in a way that disables
+ 
+
+ align:start position:0%
+it being wrapped in a way that disables
+the capacity to engage in fair use so I
+
+ align:start position:0%
+the capacity to engage in fair use so I
+ 
+
+ align:start position:0%
+the capacity to engage in fair use so I
+was a stunt you know I make tons of
+
+ align:start position:0%
+was a stunt you know I make tons of
+ 
+
+ align:start position:0%
+was a stunt you know I make tons of
+presentations all the time where I need
+
+ align:start position:0%
+presentations all the time where I need
+ 
+
+ align:start position:0%
+presentations all the time where I need
+to capture video and I was astonished to
+
+ align:start position:0%
+to capture video and I was astonished to
+ 
+
+ align:start position:0%
+to capture video and I was astonished to
+discover the latest round of this
+
+ align:start position:0%
+discover the latest round of this
+ 
+
+ align:start position:0%
+discover the latest round of this
+operating system basically makes it
+
+ align:start position:0%
+operating system basically makes it
+ 
+
+ align:start position:0%
+operating system basically makes it
+incredibly difficult to rip video for
+
+ align:start position:0%
+incredibly difficult to rip video for
+ 
+
+ align:start position:0%
+incredibly difficult to rip video for
+the purpose of capturing even two
+
+ align:start position:0%
+the purpose of capturing even two
+ 
+
+ align:start position:0%
+the purpose of capturing even two
+seconds of it so if you have a video
+
+ align:start position:0%
+seconds of it so if you have a video
+ 
+
+ align:start position:0%
+seconds of it so if you have a video
+program that is capturing your screen
+
+ align:start position:0%
+program that is capturing your screen
+ 
+
+ align:start position:0%
+program that is capturing your screen
+that this operating system will now
+
+ align:start position:0%
+that this operating system will now
+ 
+
+ align:start position:0%
+that this operating system will now
+disable it for any period of time that
+
+ align:start position:0%
+disable it for any period of time that
+ 
+
+ align:start position:0%
+disable it for any period of time that
+you're trying to capture the screen like
+
+ align:start position:0%
+you're trying to capture the screen like
+ 
+
+ align:start position:0%
+you're trying to capture the screen like
+they've built the technology so that now
+
+ align:start position:0%
+they've built the technology so that now
+ 
+
+ align:start position:0%
+they've built the technology so that now
+there is no capacity technical capacity
+
+ align:start position:0%
+there is no capacity technical capacity
+ 
+
+ align:start position:0%
+there is no capacity technical capacity
+to engage in fair use of copyrighted
+
+ align:start position:0%
+to engage in fair use of copyrighted
+ 
+
+ align:start position:0%
+to engage in fair use of copyrighted
+material on the Apple platform now you
+
+ align:start position:0%
+material on the Apple platform now you
+ 
+
+ align:start position:0%
+material on the Apple platform now you
+might say why should they be allowed to
+
+ align:start position:0%
+might say why should they be allowed to
+ 
+
+ align:start position:0%
+might say why should they be allowed to
+do that if the law intended that the
+
+ align:start position:0%
+do that if the law intended that the
+ 
+
+ align:start position:0%
+do that if the law intended that the
+contract gives you the free use of fair
+
+ align:start position:0%
+contract gives you the free use of fair
+ 
+
+ align:start position:0%
+contract gives you the free use of fair
+use why should they be allowed to do
+
+ align:start position:0%
+use why should they be allowed to do
+ 
+
+ align:start position:0%
+use why should they be allowed to do
+that but that's the battle that's been
+
+ align:start position:0%
+that but that's the battle that's been
+ 
+
+ align:start position:0%
+that but that's the battle that's been
+going on about DRM ever since the
+
+ align:start position:0%
+going on about DRM ever since the
+ 
+
+ align:start position:0%
+going on about DRM ever since the
+beginning of the internet on the
+
+ align:start position:0%
+beginning of the internet on the
+ 
+
+ align:start position:0%
+beginning of the internet on the
+beginning of copyright at work on the
+
+ align:start position:0%
+beginning of copyright at work on the
+ 
+
+ align:start position:0%
+beginning of copyright at work on the
+internet so my point is to get you to
+
+ align:start position:0%
+internet so my point is to get you to
+ 
+
+ align:start position:0%
+internet so my point is to get you to
+realize the way the code becomes part of
+
+ align:start position:0%
+realize the way the code becomes part of
+ 
+
+ align:start position:0%
+realize the way the code becomes part of
+the law of this contract and you have to
+
+ align:start position:0%
+the law of this contract and you have to
+ 
+
+ align:start position:0%
+the law of this contract and you have to
+ask yourself the question whether that
+
+ align:start position:0%
+ask yourself the question whether that
+ 
+
+ align:start position:0%
+ask yourself the question whether that
+law is respecting the law of the
+
+ align:start position:0%
+law is respecting the law of the
+ 
+
+ align:start position:0%
+law is respecting the law of the
+sovereign the law of the jurisdiction so
+
+ align:start position:0%
+sovereign the law of the jurisdiction so
+ 
+
+ align:start position:0%
+sovereign the law of the jurisdiction so
+when Apple and Disney get together and
+
+ align:start position:0%
+when Apple and Disney get together and
+ 
+
+ align:start position:0%
+when Apple and Disney get together and
+they sell this technology and they sell
+
+ align:start position:0%
+they sell this technology and they sell
+ 
+
+ align:start position:0%
+they sell this technology and they sell
+movies across the i2 platform that make
+
+ align:start position:0%
+movies across the i2 platform that make
+ 
+
+ align:start position:0%
+movies across the i2 platform that make
+it practically impossible you know
+
+ align:start position:0%
+it practically impossible you know
+ 
+
+ align:start position:0%
+it practically impossible you know
+there's not even code I mean if you go
+
+ align:start position:0%
+there's not even code I mean if you go
+ 
+
+ align:start position:0%
+there's not even code I mean if you go
+out there and you look you
+
+ align:start position:0%
+out there and you look you
+ 
+
+ align:start position:0%
+out there and you look you
+find everybody who says yeah with this
+
+ align:start position:0%
+find everybody who says yeah with this
+ 
+
+ align:start position:0%
+find everybody who says yeah with this
+version nobody's yet found a way to
+
+ align:start position:0%
+version nobody's yet found a way to
+ 
+
+ align:start position:0%
+version nobody's yet found a way to
+break it okay so so right now we're in a
+
+ align:start position:0%
+break it okay so so right now we're in a
+ 
+
+ align:start position:0%
+break it okay so so right now we're in a
+world where right now it's not possible
+
+ align:start position:0%
+world where right now it's not possible
+ 
+
+ align:start position:0%
+world where right now it's not possible
+for me to capture three seconds to put
+
+ align:start position:0%
+for me to capture three seconds to put
+ 
+
+ align:start position:0%
+for me to capture three seconds to put
+into a presentation and the issue that
+
+ align:start position:0%
+into a presentation and the issue that
+ 
+
+ align:start position:0%
+into a presentation and the issue that
+raises is to what extent is that
+
+ align:start position:0%
+raises is to what extent is that
+ 
+
+ align:start position:0%
+raises is to what extent is that
+consistent with copyright law if the
+
+ align:start position:0%
+consistent with copyright law if the
+ 
+
+ align:start position:0%
+consistent with copyright law if the
+technology now disables you from doing
+
+ align:start position:0%
+technology now disables you from doing
+ 
+
+ align:start position:0%
+technology now disables you from doing
+exactly what copyright law wants so this
+
+ align:start position:0%
+exactly what copyright law wants so this
+ 
+
+ align:start position:0%
+exactly what copyright law wants so this
+is the trade-off to think about the
+
+ align:start position:0%
+is the trade-off to think about the
+ 
+
+ align:start position:0%
+is the trade-off to think about the
+relationship between the policy that the
+
+ align:start position:0%
+relationship between the policy that the
+ 
+
+ align:start position:0%
+relationship between the policy that the
+law wants and the policy of the
+
+ align:start position:0%
+law wants and the policy of the
+ 
+
+ align:start position:0%
+law wants and the policy of the
+technology and there's no reason to
+
+ align:start position:0%
+technology and there's no reason to
+ 
+
+ align:start position:0%
+technology and there's no reason to
+believe the policy of the technology
+
+ align:start position:0%
+believe the policy of the technology
+ 
+
+ align:start position:0%
+believe the policy of the technology
+will always be consistent with the law
+
+ align:start position:0%
+will always be consistent with the law
+ 
+
+ align:start position:0%
+will always be consistent with the law
+and to the extent that's not consistent
+
+ align:start position:0%
+and to the extent that's not consistent
+ 
+
+ align:start position:0%
+and to the extent that's not consistent
+with the law it challenges the law it
+
+ align:start position:0%
+with the law it challenges the law it
+ 
+
+ align:start position:0%
+with the law it challenges the law it
+says to the law okay come out and get me
+
+ align:start position:0%
+says to the law okay come out and get me
+ 
+
+ align:start position:0%
+says to the law okay come out and get me
+now that obviously is implicated in the
+
+ align:start position:0%
+now that obviously is implicated in the
+ 
+
+ align:start position:0%
+now that obviously is implicated in the
+context of smart contracts because the
+
+ align:start position:0%
+context of smart contracts because the
+ 
+
+ align:start position:0%
+context of smart contracts because the
+biggest fear about smart contracts is
+
+ align:start position:0%
+biggest fear about smart contracts is
+ 
+
+ align:start position:0%
+biggest fear about smart contracts is
+that they enable a kind of transaction
+
+ align:start position:0%
+that they enable a kind of transaction
+ 
+
+ align:start position:0%
+that they enable a kind of transaction
+that can hide from the policy of the law
+
+ align:start position:0%
+that can hide from the policy of the law
+ 
+
+ align:start position:0%
+that can hide from the policy of the law
+so that question for the law is what
+
+ align:start position:0%
+so that question for the law is what
+ 
+
+ align:start position:0%
+so that question for the law is what
+will you do to step in and this is I
+
+ align:start position:0%
+will you do to step in and this is I
+ 
+
+ align:start position:0%
+will you do to step in and this is I
+think that where your question is going
+
+ align:start position:0%
+think that where your question is going
+ 
+
+ align:start position:0%
+think that where your question is going
+how does the state appear in the middle
+
+ align:start position:0%
+how does the state appear in the middle
+ 
+
+ align:start position:0%
+how does the state appear in the middle
+of that contract to that okay that's the
+
+ align:start position:0%
+of that contract to that okay that's the
+ 
+
+ align:start position:0%
+of that contract to that okay that's the
+second second point here's a third point
+
+ align:start position:0%
+second second point here's a third point
+ 
+
+ align:start position:0%
+second second point here's a third point
+there's often this intuition that
+
+ align:start position:0%
+there's often this intuition that
+ 
+
+ align:start position:0%
+there's often this intuition that
+especially technologists people have
+
+ align:start position:0%
+especially technologists people have
+ 
+
+ align:start position:0%
+especially technologists people have
+about what the particular aim of
+
+ align:start position:0%
+about what the particular aim of
+ 
+
+ align:start position:0%
+about what the particular aim of
+contract law is so in the very beginning
+
+ align:start position:0%
+contract law is so in the very beginning
+ 
+
+ align:start position:0%
+contract law is so in the very beginning
+of me writing about the law of
+
+ align:start position:0%
+of me writing about the law of
+ 
+
+ align:start position:0%
+of me writing about the law of
+cyberspace somebody from MIT I won't
+
+ align:start position:0%
+cyberspace somebody from MIT I won't
+ 
+
+ align:start position:0%
+cyberspace somebody from MIT I won't
+name any names it wasn't Andy showed up
+
+ align:start position:0%
+name any names it wasn't Andy showed up
+ 
+
+ align:start position:0%
+name any names it wasn't Andy showed up
+at the Harvard Law School and said I've
+
+ align:start position:0%
+at the Harvard Law School and said I've
+ 
+
+ align:start position:0%
+at the Harvard Law School and said I've
+solved the problem of contract law I
+
+ align:start position:0%
+solved the problem of contract law I
+ 
+
+ align:start position:0%
+solved the problem of contract law I
+said what do you mean he said I have a
+
+ align:start position:0%
+said what do you mean he said I have a
+ 
+
+ align:start position:0%
+said what do you mean he said I have a
+system that will eliminate risks in
+
+ align:start position:0%
+system that will eliminate risks in
+ 
+
+ align:start position:0%
+system that will eliminate risks in
+contracts and he was really disappointed
+
+ align:start position:0%
+contracts and he was really disappointed
+ 
+
+ align:start position:0%
+contracts and he was really disappointed
+when I said you know the objective of
+
+ align:start position:0%
+when I said you know the objective of
+ 
+
+ align:start position:0%
+when I said you know the objective of
+contract law is not to eliminate risks
+
+ align:start position:0%
+contract law is not to eliminate risks
+ 
+
+ align:start position:0%
+contract law is not to eliminate risks
+the objective of contract law is just to
+
+ align:start position:0%
+the objective of contract law is just to
+ 
+
+ align:start position:0%
+the objective of contract law is just to
+allocate risk to figure out who has the
+
+ align:start position:0%
+allocate risk to figure out who has the
+ 
+
+ align:start position:0%
+allocate risk to figure out who has the
+risk so each of us can figure out what
+
+ align:start position:0%
+risk so each of us can figure out what
+ 
+
+ align:start position:0%
+risk so each of us can figure out what
+to do in light of the risk so if I say I
+
+ align:start position:0%
+to do in light of the risk so if I say I
+ 
+
+ align:start position:0%
+to do in light of the risk so if I say I
+will buy ten thousand bushels of corn
+
+ align:start position:0%
+will buy ten thousand bushels of corn
+ 
+
+ align:start position:0%
+will buy ten thousand bushels of corn
+from you at 350 a bushel turns out that
+
+ align:start position:0%
+from you at 350 a bushel turns out that
+ 
+
+ align:start position:0%
+from you at 350 a bushel turns out that
+is the price of corn right now um he
+
+ align:start position:0%
+is the price of corn right now um he
+ 
+
+ align:start position:0%
+is the price of corn right now um he
+always looks up things on the internet I
+
+ align:start position:0%
+always looks up things on the internet I
+ 
+
+ align:start position:0%
+always looks up things on the internet I
+figure I should look it up before I
+
+ align:start position:0%
+figure I should look it up before I
+ 
+
+ align:start position:0%
+figure I should look it up before I
+presented 350 is the price of a bushel
+
+ align:start position:0%
+presented 350 is the price of a bushel
+ 
+
+ align:start position:0%
+presented 350 is the price of a bushel
+of corn right now deliver September 1
+
+ align:start position:0%
+of corn right now deliver September 1
+ 
+
+ align:start position:0%
+of corn right now deliver September 1
+what that's basically doing is it
+
+ align:start position:0%
+what that's basically doing is it
+ 
+
+ align:start position:0%
+what that's basically doing is it
+allocating the risk of the price of corn
+
+ align:start position:0%
+allocating the risk of the price of corn
+ 
+
+ align:start position:0%
+allocating the risk of the price of corn
+so if you're a farmer and you don't want
+
+ align:start position:0%
+so if you're a farmer and you don't want
+ 
+
+ align:start position:0%
+so if you're a farmer and you don't want
+to face the risk the price of corn is
+
+ align:start position:0%
+to face the risk the price of corn is
+ 
+
+ align:start position:0%
+to face the risk the price of corn is
+gonna fall to $3 you enter into this
+
+ align:start position:0%
+gonna fall to $3 you enter into this
+ 
+
+ align:start position:0%
+gonna fall to $3 you enter into this
+contract if you're a buyer you accept
+
+ align:start position:0%
+contract if you're a buyer you accept
+ 
+
+ align:start position:0%
+contract if you're a buyer you accept
+this contract but if the price of corn
+
+ align:start position:0%
+this contract but if the price of corn
+ 
+
+ align:start position:0%
+this contract but if the price of corn
+falls to $3 well you're you're out of
+
+ align:start position:0%
+falls to $3 well you're you're out of
+ 
+
+ align:start position:0%
+falls to $3 well you're you're out of
+luck so the point is it relocates the
+
+ align:start position:0%
+luck so the point is it relocates the
+ 
+
+ align:start position:0%
+luck so the point is it relocates the
+price of price change reallocates the
+
+ align:start position:0%
+price of price change reallocates the
+ 
+
+ align:start position:0%
+price of price change reallocates the
+risk of price gauge also reallocates the
+
+ align:start position:0%
+risk of price gauge also reallocates the
+ 
+
+ align:start position:0%
+risk of price gauge also reallocates the
+risk of delivery so if I've got all this
+
+ align:start position:0%
+risk of delivery so if I've got all this
+ 
+
+ align:start position:0%
+risk of delivery so if I've got all this
+corn I can place it in a certain place
+
+ align:start position:0%
+corn I can place it in a certain place
+ 
+
+ align:start position:0%
+corn I can place it in a certain place
+to shift the risk of delivery so that
+
+ align:start position:0%
+to shift the risk of delivery so that
+ 
+
+ align:start position:0%
+to shift the risk of delivery so that
+once again I'm in deep I used the
+
+ align:start position:0%
+once again I'm in deep I used the
+ 
+
+ align:start position:0%
+once again I'm in deep I used the
+contract to shift my risk of storage or
+
+ align:start position:0%
+contract to shift my risk of storage or
+ 
+
+ align:start position:0%
+contract to shift my risk of storage or
+my risk of delivery and you on the other
+
+ align:start position:0%
+my risk of delivery and you on the other
+ 
+
+ align:start position:0%
+my risk of delivery and you on the other
+side so the objective of contract law
+
+ align:start position:0%
+side so the objective of contract law
+ 
+
+ align:start position:0%
+side so the objective of contract law
+number one is risk allocation number one
+
+ align:start position:0%
+number one is risk allocation number one
+ 
+
+ align:start position:0%
+number one is risk allocation number one
+but allocation matters only if come say
+
+ align:start position:0%
+but allocation matters only if come say
+ 
+
+ align:start position:0%
+but allocation matters only if come say
+olia for me only if there's a system to
+
+ align:start position:0%
+olia for me only if there's a system to
+ 
+
+ align:start position:0%
+olia for me only if there's a system to
+process the breach of a contract only if
+
+ align:start position:0%
+process the breach of a contract only if
+ 
+
+ align:start position:0%
+process the breach of a contract only if
+you've got a technology let's say for
+
+ align:start position:0%
+you've got a technology let's say for
+ 
+
+ align:start position:0%
+you've got a technology let's say for
+processing the brief so if I have a
+
+ align:start position:0%
+processing the brief so if I have a
+ 
+
+ align:start position:0%
+processing the brief so if I have a
+contract with you of ten thousand
+
+ align:start position:0%
+contract with you of ten thousand
+ 
+
+ align:start position:0%
+contract with you of ten thousand
+bushels of corn three dollars and fifty
+
+ align:start position:0%
+bushels of corn three dollars and fifty
+ 
+
+ align:start position:0%
+bushels of corn three dollars and fifty
+on September first and you don't deliver
+
+ align:start position:0%
+on September first and you don't deliver
+ 
+
+ align:start position:0%
+on September first and you don't deliver
+that's a breach my risk has only been
+
+ align:start position:0%
+that's a breach my risk has only been
+ 
+
+ align:start position:0%
+that's a breach my risk has only been
+reallocated if there's some way for me
+
+ align:start position:0%
+reallocated if there's some way for me
+ 
+
+ align:start position:0%
+reallocated if there's some way for me
+to enforce the contract at that point so
+
+ align:start position:0%
+to enforce the contract at that point so
+ 
+
+ align:start position:0%
+to enforce the contract at that point so
+it requires this system and the system
+
+ align:start position:0%
+it requires this system and the system
+ 
+
+ align:start position:0%
+it requires this system and the system
+we ordinarily take for granted as a
+
+ align:start position:0%
+we ordinarily take for granted as a
+ 
+
+ align:start position:0%
+we ordinarily take for granted as a
+legal system and I say we take it for
+
+ align:start position:0%
+legal system and I say we take it for
+ 
+
+ align:start position:0%
+legal system and I say we take it for
+granted meaning some people can take it
+
+ align:start position:0%
+granted meaning some people can take it
+ 
+
+ align:start position:0%
+granted meaning some people can take it
+for granted like people in
+
+ align:start position:0%
+for granted like people in
+ 
+
+ align:start position:0%
+for granted like people in
+well-developed legal contexts but that's
+
+ align:start position:0%
+well-developed legal contexts but that's
+ 
+
+ align:start position:0%
+well-developed legal contexts but that's
+also emphasized other people can't take
+
+ align:start position:0%
+also emphasized other people can't take
+ 
+
+ align:start position:0%
+also emphasized other people can't take
+it for granted so for example people in
+
+ align:start position:0%
+it for granted so for example people in
+ 
+
+ align:start position:0%
+it for granted so for example people in
+developing worlds they can't take the
+
+ align:start position:0%
+developing worlds they can't take the
+ 
+
+ align:start position:0%
+developing worlds they can't take the
+legal system for granted they can't
+
+ align:start position:0%
+legal system for granted they can't
+ 
+
+ align:start position:0%
+legal system for granted they can't
+assume that if the contracts breach they
+
+ align:start position:0%
+assume that if the contracts breach they
+ 
+
+ align:start position:0%
+assume that if the contracts breach they
+can go into a court and say enforce the
+
+ align:start position:0%
+can go into a court and say enforce the
+ 
+
+ align:start position:0%
+can go into a court and say enforce the
+contract where give me damages or if
+
+ align:start position:0%
+contract where give me damages or if
+ 
+
+ align:start position:0%
+contract where give me damages or if
+you've got our contract between someone
+
+ align:start position:0%
+you've got our contract between someone
+ 
+
+ align:start position:0%
+you've got our contract between someone
+in Rwanda and somebody in Alaska then
+
+ align:start position:0%
+in Rwanda and somebody in Alaska then
+ 
+
+ align:start position:0%
+in Rwanda and somebody in Alaska then
+there - there's a question of whether
+
+ align:start position:0%
+there - there's a question of whether
+ 
+
+ align:start position:0%
+there - there's a question of whether
+we've got sufficient infrastructure to
+
+ align:start position:0%
+we've got sufficient infrastructure to
+ 
+
+ align:start position:0%
+we've got sufficient infrastructure to
+development so so so the point I want to
+
+ align:start position:0%
+development so so so the point I want to
+ 
+
+ align:start position:0%
+development so so so the point I want to
+emphasize at the end of this little
+
+ align:start position:0%
+emphasize at the end of this little
+ 
+
+ align:start position:0%
+emphasize at the end of this little
+intervention is to suggest that this
+
+ align:start position:0%
+intervention is to suggest that this
+ 
+
+ align:start position:0%
+intervention is to suggest that this
+fact that it takes for granted the
+
+ align:start position:0%
+fact that it takes for granted the
+ 
+
+ align:start position:0%
+fact that it takes for granted the
+system of enforcement shows the real
+
+ align:start position:0%
+system of enforcement shows the real
+ 
+
+ align:start position:0%
+system of enforcement shows the real
+potential benefit
+
+ align:start position:0%
+potential benefit
+ 
+
+ align:start position:0%
+potential benefit
+of this class of contracting devices
+
+ align:start position:0%
+of this class of contracting devices
+ 
+
+ align:start position:0%
+of this class of contracting devices
+because if we think about this as
+
+ align:start position:0%
+because if we think about this as
+ 
+
+ align:start position:0%
+because if we think about this as
+representation of a well-developed legal
+
+ align:start position:0%
+representation of a well-developed legal
+ 
+
+ align:start position:0%
+representation of a well-developed legal
+system and we think of first world
+
+ align:start position:0%
+system and we think of first world
+ 
+
+ align:start position:0%
+system and we think of first world
+countries that's having those and we
+
+ align:start position:0%
+countries that's having those and we
+ 
+
+ align:start position:0%
+countries that's having those and we
+compare like third world or developing
+
+ align:start position:0%
+compare like third world or developing
+ 
+
+ align:start position:0%
+compare like third world or developing
+world countries don't have these
+
+ align:start position:0%
+world countries don't have these
+ 
+
+ align:start position:0%
+world countries don't have these
+well-developed legal systems you might
+
+ align:start position:0%
+well-developed legal systems you might
+ 
+
+ align:start position:0%
+well-developed legal systems you might
+say that first world countries are
+
+ align:start position:0%
+say that first world countries are
+ 
+
+ align:start position:0%
+say that first world countries are
+better off relative to third world
+
+ align:start position:0%
+better off relative to third world
+ 
+
+ align:start position:0%
+better off relative to third world
+countries because they have the legal
+
+ align:start position:0%
+countries because they have the legal
+ 
+
+ align:start position:0%
+countries because they have the legal
+infrastructure to enable this risk
+
+ align:start position:0%
+infrastructure to enable this risk
+ 
+
+ align:start position:0%
+infrastructure to enable this risk
+allocation that will enable all sorts of
+
+ align:start position:0%
+allocation that will enable all sorts of
+ 
+
+ align:start position:0%
+allocation that will enable all sorts of
+market transactions to happen which
+
+ align:start position:0%
+market transactions to happen which
+ 
+
+ align:start position:0%
+market transactions to happen which
+otherwise wouldn't happen but if we
+
+ align:start position:0%
+otherwise wouldn't happen but if we
+ 
+
+ align:start position:0%
+otherwise wouldn't happen but if we
+imagine infrastructure like blockchain
+
+ align:start position:0%
+imagine infrastructure like blockchain
+ 
+
+ align:start position:0%
+imagine infrastructure like blockchain
+like infrastructures or aetherium
+
+ align:start position:0%
+like infrastructures or aetherium
+ 
+
+ align:start position:0%
+like infrastructures or aetherium
+infrastructures to enter the mix
+
+ align:start position:0%
+infrastructures to enter the mix
+ 
+
+ align:start position:0%
+infrastructures to enter the mix
+providing a technical infrastructure
+
+ align:start position:0%
+providing a technical infrastructure
+ 
+
+ align:start position:0%
+providing a technical infrastructure
+that doesn't require judges and lawyers
+
+ align:start position:0%
+that doesn't require judges and lawyers
+ 
+
+ align:start position:0%
+that doesn't require judges and lawyers
+but just requires code then that can
+
+ align:start position:0%
+but just requires code then that can
+ 
+
+ align:start position:0%
+but just requires code then that can
+come that can supplement substitute for
+
+ align:start position:0%
+come that can supplement substitute for
+ 
+
+ align:start position:0%
+come that can supplement substitute for
+the legal infrastructure provide the
+
+ align:start position:0%
+the legal infrastructure provide the
+ 
+
+ align:start position:0%
+the legal infrastructure provide the
+infrastructure the contract needs at a
+
+ align:start position:0%
+infrastructure the contract needs at a
+ 
+
+ align:start position:0%
+infrastructure the contract needs at a
+much lower cost and thereby enable
+
+ align:start position:0%
+much lower cost and thereby enable
+ 
+
+ align:start position:0%
+much lower cost and thereby enable
+people to contract who otherwise
+
+ align:start position:0%
+people to contract who otherwise
+ 
+
+ align:start position:0%
+people to contract who otherwise
+wouldn't rationally contract because
+
+ align:start position:0%
+wouldn't rationally contract because
+ 
+
+ align:start position:0%
+wouldn't rationally contract because
+they could never count on the
+
+ align:start position:0%
+they could never count on the
+ 
+
+ align:start position:0%
+they could never count on the
+infrastructure of the legal system to
+
+ align:start position:0%
+infrastructure of the legal system to
+ 
+
+ align:start position:0%
+infrastructure of the legal system to
+deliver what they need okay so the point
+
+ align:start position:0%
+deliver what they need okay so the point
+ 
+
+ align:start position:0%
+deliver what they need okay so the point
+is this picture is trying to say that
+
+ align:start position:0%
+is this picture is trying to say that
+ 
+
+ align:start position:0%
+is this picture is trying to say that
+the key value one key value of these
+
+ align:start position:0%
+the key value one key value of these
+ 
+
+ align:start position:0%
+the key value one key value of these
+technologies is that they will be a
+
+ align:start position:0%
+technologies is that they will be a
+ 
+
+ align:start position:0%
+technologies is that they will be a
+substitute for a failed legal system or
+
+ align:start position:0%
+substitute for a failed legal system or
+ 
+
+ align:start position:0%
+substitute for a failed legal system or
+a legal system that's not yet developed
+
+ align:start position:0%
+a legal system that's not yet developed
+ 
+
+ align:start position:0%
+a legal system that's not yet developed
+they will provide the infrastructure of
+
+ align:start position:0%
+they will provide the infrastructure of
+ 
+
+ align:start position:0%
+they will provide the infrastructure of
+a legal system or the legal system do
+
+ align:start position:0%
+a legal system or the legal system do
+ 
+
+ align:start position:0%
+a legal system or the legal system do
+anything because you can't make that
+
+ align:start position:0%
+anything because you can't make that
+ 
+
+ align:start position:0%
+anything because you can't make that
+contract with I will pay you three point
+
+ align:start position:0%
+contract with I will pay you three point
+ 
+
+ align:start position:0%
+contract with I will pay you three point
+five dollars per bushel temple first
+
+ align:start position:0%
+five dollars per bushel temple first
+ 
+
+ align:start position:0%
+five dollars per bushel temple first
+immaterial because you're making a
+
+ align:start position:0%
+immaterial because you're making a
+ 
+
+ align:start position:0%
+immaterial because you're making a
+statement about the real world your
+
+ align:start position:0%
+statement about the real world your
+ 
+
+ align:start position:0%
+statement about the real world your
+theory of blockchain cannot verify that
+
+ align:start position:0%
+theory of blockchain cannot verify that
+ 
+
+ align:start position:0%
+theory of blockchain cannot verify that
+I gave you the bushes they're very risky
+
+ align:start position:0%
+I gave you the bushes they're very risky
+ 
+
+ align:start position:0%
+I gave you the bushes they're very risky
+I should say racket for just I think
+
+ align:start position:0%
+I should say racket for just I think
+ 
+
+ align:start position:0%
+I should say racket for just I think
+it's I'm not sure if it's to you but
+
+ align:start position:0%
+it's I'm not sure if it's to you but
+ 
+
+ align:start position:0%
+it's I'm not sure if it's to you but
+it's in slides but you know n is less
+
+ align:start position:0%
+it's in slides but you know n is less
+ 
+
+ align:start position:0%
+it's in slides but you know n is less
+than a hundred I promise
+
+ align:start position:0%
+than a hundred I promise
+ 
+
+ align:start position:0%
+than a hundred I promise
+so just hold one second okay so if you
+
+ align:start position:0%
+so just hold one second okay so if you
+ 
+
+ align:start position:0%
+so just hold one second okay so if you
+say that one function here is to
+
+ align:start position:0%
+say that one function here is to
+ 
+
+ align:start position:0%
+say that one function here is to
+substitute for a failed legal system
+
+ align:start position:0%
+substitute for a failed legal system
+ 
+
+ align:start position:0%
+substitute for a failed legal system
+um that suggests the other key
+
+ align:start position:0%
+um that suggests the other key
+ 
+
+ align:start position:0%
+um that suggests the other key
+opportunity here is to enable contracts
+
+ align:start position:0%
+opportunity here is to enable contracts
+ 
+
+ align:start position:0%
+opportunity here is to enable contracts
+where the transaction costs right now
+
+ align:start position:0%
+where the transaction costs right now
+ 
+
+ align:start position:0%
+where the transaction costs right now
+are otherwise too high so this is a key
+
+ align:start position:0%
+are otherwise too high so this is a key
+ 
+
+ align:start position:0%
+are otherwise too high so this is a key
+opportunity to think of places where you
+
+ align:start position:0%
+opportunity to think of places where you
+ 
+
+ align:start position:0%
+opportunity to think of places where you
+could lower the transaction costs of the
+
+ align:start position:0%
+could lower the transaction costs of the
+ 
+
+ align:start position:0%
+could lower the transaction costs of the
+contract you will enable a contract
+
+ align:start position:0%
+contract you will enable a contract
+ 
+
+ align:start position:0%
+contract you will enable a contract
+which otherwise exists right now so I'm
+
+ align:start position:0%
+which otherwise exists right now so I'm
+ 
+
+ align:start position:0%
+which otherwise exists right now so I'm
+on a bull a scientific board for an
+
+ align:start position:0%
+on a bull a scientific board for an
+ 
+
+ align:start position:0%
+on a bull a scientific board for an
+insurance company and insurance company
+
+ align:start position:0%
+insurance company and insurance company
+ 
+
+ align:start position:0%
+insurance company and insurance company
+I saw I was meeting the president this
+
+ align:start position:0%
+I saw I was meeting the president this
+ 
+
+ align:start position:0%
+I saw I was meeting the president this
+week last week and he was all excited
+
+ align:start position:0%
+week last week and he was all excited
+ 
+
+ align:start position:0%
+week last week and he was all excited
+about a new product which they were
+
+ align:start position:0%
+about a new product which they were
+ 
+
+ align:start position:0%
+about a new product which they were
+investing in which was going to provide
+
+ align:start position:0%
+investing in which was going to provide
+ 
+
+ align:start position:0%
+investing in which was going to provide
+flight delay insurance and this product
+
+ align:start position:0%
+flight delay insurance and this product
+ 
+
+ align:start position:0%
+flight delay insurance and this product
+was going to be completely blocked
+
+ align:start position:0%
+was going to be completely blocked
+ 
+
+ align:start position:0%
+was going to be completely blocked
+chain-driven and it would this is that
+
+ align:start position:0%
+chain-driven and it would this is that
+ 
+
+ align:start position:0%
+chain-driven and it would this is that
+I'm trying to get to your point it would
+
+ align:start position:0%
+I'm trying to get to your point it would
+ 
+
+ align:start position:0%
+I'm trying to get to your point it would
+trigger payments and a completely
+
+ align:start position:0%
+trigger payments and a completely
+ 
+
+ align:start position:0%
+trigger payments and a completely
+automatic way based on the information
+
+ align:start position:0%
+automatic way based on the information
+ 
+
+ align:start position:0%
+automatic way based on the information
+that's being reported from you know the
+
+ align:start position:0%
+that's being reported from you know the
+ 
+
+ align:start position:0%
+that's being reported from you know the
+end different sites that are reporting
+
+ align:start position:0%
+end different sites that are reporting
+ 
+
+ align:start position:0%
+end different sites that are reporting
+information about flight so I buy the
+
+ align:start position:0%
+information about flight so I buy the
+ 
+
+ align:start position:0%
+information about flight so I buy the
+contract it says if my flights delayed
+
+ align:start position:0%
+contract it says if my flights delayed
+ 
+
+ align:start position:0%
+contract it says if my flights delayed
+more than an hour
+
+ align:start position:0%
+more than an hour
+ 
+
+ align:start position:0%
+more than an hour
+I get paid $200 and automatically as as
+
+ align:start position:0%
+I get paid $200 and automatically as as
+ 
+
+ align:start position:0%
+I get paid $200 and automatically as as
+he put it it's a no touch product by
+
+ align:start position:0%
+he put it it's a no touch product by
+ 
+
+ align:start position:0%
+he put it it's a no touch product by
+which he meant no human needs to touch
+
+ align:start position:0%
+which he meant no human needs to touch
+ 
+
+ align:start position:0%
+which he meant no human needs to touch
+this product for this contract to be
+
+ align:start position:0%
+this product for this contract to be
+ 
+
+ align:start position:0%
+this product for this contract to be
+enabled it's a kind of product that
+
+ align:start position:0%
+enabled it's a kind of product that
+ 
+
+ align:start position:0%
+enabled it's a kind of product that
+never would have been available before
+
+ align:start position:0%
+never would have been available before
+ 
+
+ align:start position:0%
+never would have been available before
+because the transaction cost of engaging
+
+ align:start position:0%
+because the transaction cost of engaging
+ 
+
+ align:start position:0%
+because the transaction cost of engaging
+it were way too high but now that we've
+
+ align:start position:0%
+it were way too high but now that we've
+ 
+
+ align:start position:0%
+it were way too high but now that we've
+lowered the transaction cost and have an
+
+ align:start position:0%
+lowered the transaction cost and have an
+ 
+
+ align:start position:0%
+lowered the transaction cost and have an
+infrastructure of trust which is what
+
+ align:start position:0%
+infrastructure of trust which is what
+ 
+
+ align:start position:0%
+infrastructure of trust which is what
+the blockchain is providing here there's
+
+ align:start position:0%
+the blockchain is providing here there's
+ 
+
+ align:start position:0%
+the blockchain is providing here there's
+a huge market that now is out available
+
+ align:start position:0%
+a huge market that now is out available
+ 
+
+ align:start position:0%
+a huge market that now is out available
+for a contract that otherwise you know
+
+ align:start position:0%
+for a contract that otherwise you know
+ 
+
+ align:start position:0%
+for a contract that otherwise you know
+it just wasn't there before
+
+ align:start position:0%
+it just wasn't there before
+ 
+
+ align:start position:0%
+it just wasn't there before
+now that market depends on making a
+
+ align:start position:0%
+now that market depends on making a
+ 
+
+ align:start position:0%
+now that market depends on making a
+couple assumptions you're not saying
+
+ align:start position:0%
+couple assumptions you're not saying
+ 
+
+ align:start position:0%
+couple assumptions you're not saying
+that there's a hundred percent certainty
+
+ align:start position:0%
+that there's a hundred percent certainty
+ 
+
+ align:start position:0%
+that there's a hundred percent certainty
+that everything in that market is
+
+ align:start position:0%
+that everything in that market is
+ 
+
+ align:start position:0%
+that everything in that market is
+working the way it's supposed to work
+
+ align:start position:0%
+working the way it's supposed to work
+ 
+
+ align:start position:0%
+working the way it's supposed to work
+but the point is you don't need a
+
+ align:start position:0%
+but the point is you don't need a
+ 
+
+ align:start position:0%
+but the point is you don't need a
+hundred percent certainty for the vast
+
+ align:start position:0%
+hundred percent certainty for the vast
+ 
+
+ align:start position:0%
+hundred percent certainty for the vast
+majority of these kinds of contracts if
+
+ align:start position:0%
+majority of these kinds of contracts if
+ 
+
+ align:start position:0%
+majority of these kinds of contracts if
+it gets it wrong every once in a while
+
+ align:start position:0%
+it gets it wrong every once in a while
+ 
+
+ align:start position:0%
+it gets it wrong every once in a while
+you know that's good enough for
+
+ align:start position:0%
+you know that's good enough for
+ 
+
+ align:start position:0%
+you know that's good enough for
+government work or good enough for
+
+ align:start position:0%
+government work or good enough for
+ 
+
+ align:start position:0%
+government work or good enough for
+airplane work and so so that's gonna be
+
+ align:start position:0%
+airplane work and so so that's gonna be
+ 
+
+ align:start position:0%
+airplane work and so so that's gonna be
+sufficient to enable the market
+
+ align:start position:0%
+sufficient to enable the market
+ 
+
+ align:start position:0%
+sufficient to enable the market
+recognizing that even in the legal
+
+ align:start position:0%
+recognizing that even in the legal
+ 
+
+ align:start position:0%
+recognizing that even in the legal
+system market guess what it doesn't
+
+ align:start position:0%
+system market guess what it doesn't
+ 
+
+ align:start position:0%
+system market guess what it doesn't
+always get it right either well it
+
+ align:start position:0%
+always get it right either well it
+ 
+
+ align:start position:0%
+always get it right either well it
+doesn't always enforce the contract well
+
+ align:start position:0%
+doesn't always enforce the contract well
+ 
+
+ align:start position:0%
+doesn't always enforce the contract well
+either in fact the costs are much much
+
+ align:start position:0%
+either in fact the costs are much much
+ 
+
+ align:start position:0%
+either in fact the costs are much much
+higher to fail in
+
+ align:start position:0%
+higher to fail in
+ 
+
+ align:start position:0%
+higher to fail in
+okay so two kinds of transaction costs
+
+ align:start position:0%
+okay so two kinds of transaction costs
+ 
+
+ align:start position:0%
+okay so two kinds of transaction costs
+one system transaction cost suggests
+
+ align:start position:0%
+one system transaction cost suggests
+ 
+
+ align:start position:0%
+one system transaction cost suggests
+that where you have less developed legal
+
+ align:start position:0%
+that where you have less developed legal
+ 
+
+ align:start position:0%
+that where you have less developed legal
+systems the blockchain is going to
+
+ align:start position:0%
+systems the blockchain is going to
+ 
+
+ align:start position:0%
+systems the blockchain is going to
+provide a real opportunity because
+
+ align:start position:0%
+provide a real opportunity because
+ 
+
+ align:start position:0%
+provide a real opportunity because
+you're going to lower the transaction
+
+ align:start position:0%
+you're going to lower the transaction
+ 
+
+ align:start position:0%
+you're going to lower the transaction
+cost for those systems and the other is
+
+ align:start position:0%
+cost for those systems and the other is
+ 
+
+ align:start position:0%
+cost for those systems and the other is
+just contract transaction costs there'll
+
+ align:start position:0%
+just contract transaction costs there'll
+ 
+
+ align:start position:0%
+just contract transaction costs there'll
+be a huge explosion of markets where
+
+ align:start position:0%
+be a huge explosion of markets where
+ 
+
+ align:start position:0%
+be a huge explosion of markets where
+right now the contract transaction costs
+
+ align:start position:0%
+right now the contract transaction costs
+ 
+
+ align:start position:0%
+right now the contract transaction costs
+are so high and we can lower them and
+
+ align:start position:0%
+are so high and we can lower them and
+ 
+
+ align:start position:0%
+are so high and we can lower them and
+thereby enable a certain kind of
+
+ align:start position:0%
+thereby enable a certain kind of
+ 
+
+ align:start position:0%
+thereby enable a certain kind of
+transaction that otherwise wouldn't be
+
+ align:start position:0%
+transaction that otherwise wouldn't be
+ 
+
+ align:start position:0%
+transaction that otherwise wouldn't be
+there okay final point I want to make
+
+ align:start position:0%
+there okay final point I want to make
+ 
+
+ align:start position:0%
+there okay final point I want to make
+the other thing technologists always
+
+ align:start position:0%
+the other thing technologists always
+ 
+
+ align:start position:0%
+the other thing technologists always
+love to say is the great thing we will
+
+ align:start position:0%
+love to say is the great thing we will
+ 
+
+ align:start position:0%
+love to say is the great thing we will
+do when we do contracts technologies is
+
+ align:start position:0%
+do when we do contracts technologies is
+ 
+
+ align:start position:0%
+do when we do contracts technologies is
+they'll be solved the clarity problem
+
+ align:start position:0%
+they'll be solved the clarity problem
+ 
+
+ align:start position:0%
+they'll be solved the clarity problem
+every term will be perfectly clear could
+
+ align:start position:0%
+every term will be perfectly clear could
+ 
+
+ align:start position:0%
+every term will be perfectly clear could
+you write those contracts out and
+
+ align:start position:0%
+you write those contracts out and
+ 
+
+ align:start position:0%
+you write those contracts out and
+there's all sorts of ambiguity vagueness
+
+ align:start position:0%
+there's all sorts of ambiguity vagueness
+ 
+
+ align:start position:0%
+there's all sorts of ambiguity vagueness
+and it's a total mess but when we've
+
+ align:start position:0%
+and it's a total mess but when we've
+ 
+
+ align:start position:0%
+and it's a total mess but when we've
+coded all of our contracts our smart
+
+ align:start position:0%
+coded all of our contracts our smart
+ 
+
+ align:start position:0%
+coded all of our contracts our smart
+contracts then we'll have perfect
+
+ align:start position:0%
+contracts then we'll have perfect
+ 
+
+ align:start position:0%
+contracts then we'll have perfect
+certainty for every single outcome and
+
+ align:start position:0%
+certainty for every single outcome and
+ 
+
+ align:start position:0%
+certainty for every single outcome and
+that will be great and the point I want
+
+ align:start position:0%
+that will be great and the point I want
+ 
+
+ align:start position:0%
+that will be great and the point I want
+to suggest to you is the is that often
+
+ align:start position:0%
+to suggest to you is the is that often
+ 
+
+ align:start position:0%
+to suggest to you is the is that often
+obscurity is a real value obscurity is
+
+ align:start position:0%
+obscurity is a real value obscurity is
+ 
+
+ align:start position:0%
+obscurity is a real value obscurity is
+what you want because there's a way to
+
+ align:start position:0%
+what you want because there's a way to
+ 
+
+ align:start position:0%
+what you want because there's a way to
+see it so imagine this is a decision
+
+ align:start position:0%
+see it so imagine this is a decision
+ 
+
+ align:start position:0%
+see it so imagine this is a decision
+tree and it's really small because I
+
+ align:start position:0%
+tree and it's really small because I
+ 
+
+ align:start position:0%
+tree and it's really small because I
+just stole it from the internet
+
+ align:start position:0%
+just stole it from the internet
+ 
+
+ align:start position:0%
+just stole it from the internet
+it doesn't have anything to do really
+
+ align:start position:0%
+it doesn't have anything to do really
+ 
+
+ align:start position:0%
+it doesn't have anything to do really
+with what I'm talking about here but
+
+ align:start position:0%
+with what I'm talking about here but
+ 
+
+ align:start position:0%
+with what I'm talking about here but
+imagine a really complicated decision
+
+ align:start position:0%
+imagine a really complicated decision
+ 
+
+ align:start position:0%
+imagine a really complicated decision
+tree like this we just represent all the
+
+ align:start position:0%
+tree like this we just represent all the
+ 
+
+ align:start position:0%
+tree like this we just represent all the
+possible things that could happen with
+
+ align:start position:0%
+possible things that could happen with
+ 
+
+ align:start position:0%
+possible things that could happen with
+our deal so I want to buy the house but
+
+ align:start position:0%
+our deal so I want to buy the house but
+ 
+
+ align:start position:0%
+our deal so I want to buy the house but
+what happens that the house get hit by a
+
+ align:start position:0%
+what happens that the house get hit by a
+ 
+
+ align:start position:0%
+what happens that the house get hit by a
+meteor or what happens if you go
+
+ align:start position:0%
+meteor or what happens if you go
+ 
+
+ align:start position:0%
+meteor or what happens if you go
+bankrupt all of these possible outcomes
+
+ align:start position:0%
+bankrupt all of these possible outcomes
+ 
+
+ align:start position:0%
+bankrupt all of these possible outcomes
+and in principle we could say we should
+
+ align:start position:0%
+and in principle we could say we should
+ 
+
+ align:start position:0%
+and in principle we could say we should
+be negotiating every one of these blue
+
+ align:start position:0%
+be negotiating every one of these blue
+ 
+
+ align:start position:0%
+be negotiating every one of these blue
+dots we should be saying what happens if
+
+ align:start position:0%
+dots we should be saying what happens if
+ 
+
+ align:start position:0%
+dots we should be saying what happens if
+this happens okay then this is what you
+
+ align:start position:0%
+this happens okay then this is what you
+ 
+
+ align:start position:0%
+this happens okay then this is what you
+get in this good idea what happens if
+
+ align:start position:0%
+get in this good idea what happens if
+ 
+
+ align:start position:0%
+get in this good idea what happens if
+that house would you get rid of okay so
+
+ align:start position:0%
+that house would you get rid of okay so
+ 
+
+ align:start position:0%
+that house would you get rid of okay so
+it imagine this blue dot here has a
+
+ align:start position:0%
+it imagine this blue dot here has a
+ 
+
+ align:start position:0%
+it imagine this blue dot here has a
+point zero zero two percent chance of
+
+ align:start position:0%
+point zero zero two percent chance of
+ 
+
+ align:start position:0%
+point zero zero two percent chance of
+happening so you know the chance of that
+
+ align:start position:0%
+happening so you know the chance of that
+ 
+
+ align:start position:0%
+happening so you know the chance of that
+happening is practically zero and so
+
+ align:start position:0%
+happening is practically zero and so
+ 
+
+ align:start position:0%
+happening is practically zero and so
+what's the reasonable amount of time you
+
+ align:start position:0%
+what's the reasonable amount of time you
+ 
+
+ align:start position:0%
+what's the reasonable amount of time you
+should spend negotiating that term zero
+
+ align:start position:0%
+should spend negotiating that term zero
+ 
+
+ align:start position:0%
+should spend negotiating that term zero
+right especially because you know if you
+
+ align:start position:0%
+right especially because you know if you
+ 
+
+ align:start position:0%
+right especially because you know if you
+know if you this term is something you
+
+ align:start position:0%
+know if you this term is something you
+ 
+
+ align:start position:0%
+know if you this term is something you
+know he's really he's really
+
+ align:start position:0%
+know he's really he's really
+ 
+
+ align:start position:0%
+know he's really he's really
+worked up about and you could never come
+
+ align:start position:0%
+worked up about and you could never come
+ 
+
+ align:start position:0%
+worked up about and you could never come
+to an agreement about that term it would
+
+ align:start position:0%
+to an agreement about that term it would
+ 
+
+ align:start position:0%
+to an agreement about that term it would
+be ridiculous that the whole contract
+
+ align:start position:0%
+be ridiculous that the whole contract
+ 
+
+ align:start position:0%
+be ridiculous that the whole contract
+fall about because of this point zero
+
+ align:start position:0%
+fall about because of this point zero
+ 
+
+ align:start position:0%
+fall about because of this point zero
+zero two percent possibility
+
+ align:start position:0%
+zero two percent possibility
+ 
+
+ align:start position:0%
+zero two percent possibility
+so what contracts do all the time is
+
+ align:start position:0%
+so what contracts do all the time is
+ 
+
+ align:start position:0%
+so what contracts do all the time is
+they create these fuzzy or vague or
+
+ align:start position:0%
+they create these fuzzy or vague or
+ 
+
+ align:start position:0%
+they create these fuzzy or vague or
+ambiguous places as a gamble it's like
+
+ align:start position:0%
+ambiguous places as a gamble it's like
+ 
+
+ align:start position:0%
+ambiguous places as a gamble it's like
+okay we'll go forward we're gonna just
+
+ align:start position:0%
+okay we'll go forward we're gonna just
+ 
+
+ align:start position:0%
+okay we'll go forward we're gonna just
+gamble that this point zero zero two
+
+ align:start position:0%
+gamble that this point zero zero two
+ 
+
+ align:start position:0%
+gamble that this point zero zero two
+percent outcome won't happen most of the
+
+ align:start position:0%
+percent outcome won't happen most of the
+ 
+
+ align:start position:0%
+percent outcome won't happen most of the
+time in fact you can work out how often
+
+ align:start position:0%
+time in fact you can work out how often
+ 
+
+ align:start position:0%
+time in fact you can work out how often
+it doesn't happen right so most of the
+
+ align:start position:0%
+it doesn't happen right so most of the
+ 
+
+ align:start position:0%
+it doesn't happen right so most of the
+time that'll be just fine and if it
+
+ align:start position:0%
+time that'll be just fine and if it
+ 
+
+ align:start position:0%
+time that'll be just fine and if it
+turns out to happen then what we'll do
+
+ align:start position:0%
+turns out to happen then what we'll do
+ 
+
+ align:start position:0%
+turns out to happen then what we'll do
+is ask somebody namely a judge to figure
+
+ align:start position:0%
+is ask somebody namely a judge to figure
+ 
+
+ align:start position:0%
+is ask somebody namely a judge to figure
+that term out we'll say what should that
+
+ align:start position:0%
+that term out we'll say what should that
+ 
+
+ align:start position:0%
+that term out we'll say what should that
+term be interpreted as it was ambiguous
+
+ align:start position:0%
+term be interpreted as it was ambiguous
+ 
+
+ align:start position:0%
+term be interpreted as it was ambiguous
+so what should the answer be and the
+
+ align:start position:0%
+so what should the answer be and the
+ 
+
+ align:start position:0%
+so what should the answer be and the
+judge will look at in judges Li well
+
+ align:start position:0%
+judge will look at in judges Li well
+ 
+
+ align:start position:0%
+judge will look at in judges Li well
+it's fair that you win or he wins so the
+
+ align:start position:0%
+it's fair that you win or he wins so the
+ 
+
+ align:start position:0%
+it's fair that you win or he wins so the
+point is there are many times when you
+
+ align:start position:0%
+point is there are many times when you
+ 
+
+ align:start position:0%
+point is there are many times when you
+ask the question should you negotiate a
+
+ align:start position:0%
+ask the question should you negotiate a
+ 
+
+ align:start position:0%
+ask the question should you negotiate a
+term ex ante and the answer to that
+
+ align:start position:0%
+term ex ante and the answer to that
+ 
+
+ align:start position:0%
+term ex ante and the answer to that
+question is no and in those contexts and
+
+ align:start position:0%
+question is no and in those contexts and
+ 
+
+ align:start position:0%
+question is no and in those contexts and
+ambiguity is a way to negotiate it ex
+
+ align:start position:0%
+ambiguity is a way to negotiate it ex
+ 
+
+ align:start position:0%
+ambiguity is a way to negotiate it ex
+post meaning after the fact exposed by
+
+ align:start position:0%
+post meaning after the fact exposed by
+ 
+
+ align:start position:0%
+post meaning after the fact exposed by
+using the court so as we think about
+
+ align:start position:0%
+using the court so as we think about
+ 
+
+ align:start position:0%
+using the court so as we think about
+these digital smart contracts this is
+
+ align:start position:0%
+these digital smart contracts this is
+ 
+
+ align:start position:0%
+these digital smart contracts this is
+why smart contracts are referred to as
+
+ align:start position:0%
+why smart contracts are referred to as
+ 
+
+ align:start position:0%
+why smart contracts are referred to as
+dumb contracts they're smart contracts
+
+ align:start position:0%
+dumb contracts they're smart contracts
+ 
+
+ align:start position:0%
+dumb contracts they're smart contracts
+for the equivalent of dropping a dime in
+
+ align:start position:0%
+for the equivalent of dropping a dime in
+ 
+
+ align:start position:0%
+for the equivalent of dropping a dime in
+and getting a dr. pepper the sorts of
+
+ align:start position:0%
+and getting a dr. pepper the sorts of
+ 
+
+ align:start position:0%
+and getting a dr. pepper the sorts of
+things where the possibilities are
+
+ align:start position:0%
+things where the possibilities are
+ 
+
+ align:start position:0%
+things where the possibilities are
+really small and narrow or like my CEO
+
+ align:start position:0%
+really small and narrow or like my CEO
+ 
+
+ align:start position:0%
+really small and narrow or like my CEO
+was really excited is your plane late
+
+ align:start position:0%
+was really excited is your plane late
+ 
+
+ align:start position:0%
+was really excited is your plane late
+yes I get $50 no I don't things where
+
+ align:start position:0%
+yes I get $50 no I don't things where
+ 
+
+ align:start position:0%
+yes I get $50 no I don't things where
+it's relatively clear but there's a
+
+ align:start position:0%
+it's relatively clear but there's a
+ 
+
+ align:start position:0%
+it's relatively clear but there's a
+really important conceptual question
+
+ align:start position:0%
+really important conceptual question
+ 
+
+ align:start position:0%
+really important conceptual question
+about what happens when we're trying to
+
+ align:start position:0%
+about what happens when we're trying to
+ 
+
+ align:start position:0%
+about what happens when we're trying to
+use them for the kinds of contracts
+
+ align:start position:0%
+use them for the kinds of contracts
+ 
+
+ align:start position:0%
+use them for the kinds of contracts
+where what we want is ambiguity because
+
+ align:start position:0%
+where what we want is ambiguity because
+ 
+
+ align:start position:0%
+where what we want is ambiguity because
+if the way if the very terms of
+
+ align:start position:0%
+if the way if the very terms of
+ 
+
+ align:start position:0%
+if the way if the very terms of
+deployment the platform demands
+
+ align:start position:0%
+deployment the platform demands
+ 
+
+ align:start position:0%
+deployment the platform demands
+specifying all of the outcomes in this
+
+ align:start position:0%
+specifying all of the outcomes in this
+ 
+
+ align:start position:0%
+specifying all of the outcomes in this
+tree then your basic thing well there's
+
+ align:start position:0%
+tree then your basic thing well there's
+ 
+
+ align:start position:0%
+tree then your basic thing well there's
+a whole bunch of contracts you're just
+
+ align:start position:0%
+a whole bunch of contracts you're just
+ 
+
+ align:start position:0%
+a whole bunch of contracts you're just
+not going to be able to have in this
+
+ align:start position:0%
+not going to be able to have in this
+ 
+
+ align:start position:0%
+not going to be able to have in this
+space because the costs
+
+ align:start position:0%
+space because the costs
+ 
+
+ align:start position:0%
+space because the costs
+of specifying that tree will be higher
+
+ align:start position:0%
+of specifying that tree will be higher
+ 
+
+ align:start position:0%
+of specifying that tree will be higher
+than the benefit of those contracts so
+
+ align:start position:0%
+than the benefit of those contracts so
+ 
+
+ align:start position:0%
+than the benefit of those contracts so
+it's a weird sense in which on the one
+
+ align:start position:0%
+it's a weird sense in which on the one
+ 
+
+ align:start position:0%
+it's a weird sense in which on the one
+hand I've said to you that these tech
+
+ align:start position:0%
+hand I've said to you that these tech
+ 
+
+ align:start position:0%
+hand I've said to you that these tech
+this technology can lower the
+
+ align:start position:0%
+this technology can lower the
+ 
+
+ align:start position:0%
+this technology can lower the
+transaction cost of contracts but for
+
+ align:start position:0%
+transaction cost of contracts but for
+ 
+
+ align:start position:0%
+transaction cost of contracts but for
+this kind of contract it can actually
+
+ align:start position:0%
+this kind of contract it can actually
+ 
+
+ align:start position:0%
+this kind of contract it can actually
+increase the transaction costs of
+
+ align:start position:0%
+increase the transaction costs of
+ 
+
+ align:start position:0%
+increase the transaction costs of
+contracts because for this kind of
+
+ align:start position:0%
+contracts because for this kind of
+ 
+
+ align:start position:0%
+contracts because for this kind of
+contract if it reveals the ambiguities
+
+ align:start position:0%
+contract if it reveals the ambiguities
+ 
+
+ align:start position:0%
+contract if it reveals the ambiguities
+we need to negotiate about and those
+
+ align:start position:0%
+we need to negotiate about and those
+ 
+
+ align:start position:0%
+we need to negotiate about and those
+negotiated ambiguities are just too
+
+ align:start position:0%
+negotiated ambiguities are just too
+ 
+
+ align:start position:0%
+negotiated ambiguities are just too
+costly for us to negotiate then it's
+
+ align:start position:0%
+costly for us to negotiate then it's
+ 
+
+ align:start position:0%
+costly for us to negotiate then it's
+going to block us from having that
+
+ align:start position:0%
+going to block us from having that
+ 
+
+ align:start position:0%
+going to block us from having that
+contract that forces us to see the point
+
+ align:start position:0%
+contract that forces us to see the point
+ 
+
+ align:start position:0%
+contract that forces us to see the point
+zero zero two percent you and I have to
+
+ align:start position:0%
+zero zero two percent you and I have to
+ 
+
+ align:start position:0%
+zero zero two percent you and I have to
+come to terms on it and we don't get
+
+ align:start position:0%
+come to terms on it and we don't get
+ 
+
+ align:start position:0%
+come to terms on it and we don't get
+have a good way to fake ambiguity I mean
+
+ align:start position:0%
+have a good way to fake ambiguity I mean
+ 
+
+ align:start position:0%
+have a good way to fake ambiguity I mean
+the legal system takes ambiguity because
+
+ align:start position:0%
+the legal system takes ambiguity because
+ 
+
+ align:start position:0%
+the legal system takes ambiguity because
+we just say oh yeah we didn't see that
+
+ align:start position:0%
+we just say oh yeah we didn't see that
+ 
+
+ align:start position:0%
+we just say oh yeah we didn't see that
+they saw it he knew it when they wrote
+
+ align:start position:0%
+they saw it he knew it when they wrote
+ 
+
+ align:start position:0%
+they saw it he knew it when they wrote
+the contract but they don't have to
+
+ align:start position:0%
+the contract but they don't have to
+ 
+
+ align:start position:0%
+the contract but they don't have to
+admit they knew it but the but the code
+
+ align:start position:0%
+admit they knew it but the but the code
+ 
+
+ align:start position:0%
+admit they knew it but the but the code
+has to admit it knows there's an
+
+ align:start position:0%
+has to admit it knows there's an
+ 
+
+ align:start position:0%
+has to admit it knows there's an
+ambiguity and that's a hard thing to
+
+ align:start position:0%
+ambiguity and that's a hard thing to
+ 
+
+ align:start position:0%
+ambiguity and that's a hard thing to
+self-consciously okay so I've given you
+
+ align:start position:0%
+self-consciously okay so I've given you
+ 
+
+ align:start position:0%
+self-consciously okay so I've given you
+four ideas happy to take questions abuse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what if you can code into the
+
+ align:start position:0%
+so what if you can code into the
+ 
+
+ align:start position:0%
+so what if you can code into the
+contract like the the easy scenarios and
+
+ align:start position:0%
+contract like the the easy scenarios and
+ 
+
+ align:start position:0%
+contract like the the easy scenarios and
+then say like elsif or go to court
+
+ align:start position:0%
+then say like elsif or go to court
+ 
+
+ align:start position:0%
+then say like elsif or go to court
+or some like multinational court that is
+
+ align:start position:0%
+or some like multinational court that is
+ 
+
+ align:start position:0%
+or some like multinational court that is
+like very important and even the
+
+ align:start position:0%
+like very important and even the
+ 
+
+ align:start position:0%
+like very important and even the
+etherium court will have to have a court
+
+ align:start position:0%
+etherium court will have to have a court
+ 
+
+ align:start position:0%
+etherium court will have to have a court
+above it if it wants to avoid government
+
+ align:start position:0%
+above it if it wants to avoid government
+ 
+
+ align:start position:0%
+above it if it wants to avoid government
+saying if you have anything to do with
+
+ align:start position:0%
+saying if you have anything to do with
+ 
+
+ align:start position:0%
+saying if you have anything to do with
+the theory am we're gonna punish it
+
+ align:start position:0%
+the theory am we're gonna punish it
+ 
+
+ align:start position:0%
+the theory am we're gonna punish it
+right so this is the sense of which I
+
+ align:start position:0%
+right so this is the sense of which I
+ 
+
+ align:start position:0%
+right so this is the sense of which I
+wanted to suggest to go back to your
+
+ align:start position:0%
+wanted to suggest to go back to your
+ 
+
+ align:start position:0%
+wanted to suggest to go back to your
+first question that you know if you
+
+ align:start position:0%
+first question that you know if you
+ 
+
+ align:start position:0%
+first question that you know if you
+think about it as as layers of an onion
+
+ align:start position:0%
+think about it as as layers of an onion
+ 
+
+ align:start position:0%
+think about it as as layers of an onion
+peel the layers back enough and you're
+
+ align:start position:0%
+peel the layers back enough and you're
+ 
+
+ align:start position:0%
+peel the layers back enough and you're
+going to in the end have to get to a
+
+ align:start position:0%
+going to in the end have to get to a
+ 
+
+ align:start position:0%
+going to in the end have to get to a
+state in some sense you know state isn't
+
+ align:start position:0%
+state in some sense you know state isn't
+ 
+
+ align:start position:0%
+state in some sense you know state isn't
+as an enforceable mechanism and that
+
+ align:start position:0%
+as an enforceable mechanism and that
+ 
+
+ align:start position:0%
+as an enforceable mechanism and that
+enforceable mechanism I mean doesn't
+
+ align:start position:0%
+enforceable mechanism I mean doesn't
+ 
+
+ align:start position:0%
+enforceable mechanism I mean doesn't
+have to be for every case again 99% of
+
+ align:start position:0%
+have to be for every case again 99% of
+ 
+
+ align:start position:0%
+have to be for every case again 99% of
+the time you drop the diamond you get
+
+ align:start position:0%
+the time you drop the diamond you get
+ 
+
+ align:start position:0%
+the time you drop the diamond you get
+the dr. pepper but there's a contingency
+
+ align:start position:0%
+the dr. pepper but there's a contingency
+ 
+
+ align:start position:0%
+the dr. pepper but there's a contingency
+where you drop the diamond and out comes
+
+ align:start position:0%
+where you drop the diamond and out comes
+ 
+
+ align:start position:0%
+where you drop the diamond and out comes
+the bottle of gasoline and I need to go
+
+ align:start position:0%
+the bottle of gasoline and I need to go
+ 
+
+ align:start position:0%
+the bottle of gasoline and I need to go
+to somebody and say you've breached this
+
+ align:start position:0%
+to somebody and say you've breached this
+ 
+
+ align:start position:0%
+to somebody and say you've breached this
+contract and that person but if it's a
+
+ align:start position:0%
+contract and that person but if it's a
+ 
+
+ align:start position:0%
+contract and that person but if it's a
+contract between somebody and
+
+ align:start position:0%
+contract between somebody and
+ 
+
+ align:start position:0%
+contract between somebody and
+alaskan-style you know
+
+ align:start position:0%
+alaskan-style you know
+ 
+
+ align:start position:0%
+alaskan-style you know
+wit like you still have the question of
+
+ align:start position:0%
+wit like you still have the question of
+ 
+
+ align:start position:0%
+wit like you still have the question of
+which state to go to what's the
+
+ align:start position:0%
+which state to go to what's the
+ 
+
+ align:start position:0%
+which state to go to what's the
+jurisdiction so I feel like there would
+
+ align:start position:0%
+jurisdiction so I feel like there would
+ 
+
+ align:start position:0%
+jurisdiction so I feel like there would
+have to be some like extra national
+
+ align:start position:0%
+have to be some like extra national
+ 
+
+ align:start position:0%
+have to be some like extra national
+we'll see in these types of contracts is
+
+ align:start position:0%
+we'll see in these types of contracts is
+ 
+
+ align:start position:0%
+we'll see in these types of contracts is
+they'll be a whole bunch of boilerplate
+
+ align:start position:0%
+they'll be a whole bunch of boilerplate
+ 
+
+ align:start position:0%
+they'll be a whole bunch of boilerplate
+that specifies choice of law it turns
+
+ align:start position:0%
+that specifies choice of law it turns
+ 
+
+ align:start position:0%
+that specifies choice of law it turns
+out to be a relatively easy thing to do
+
+ align:start position:0%
+out to be a relatively easy thing to do
+ 
+
+ align:start position:0%
+out to be a relatively easy thing to do
+right now choice of jurisdictions for
+
+ align:start position:0%
+right now choice of jurisdictions for
+ 
+
+ align:start position:0%
+right now choice of jurisdictions for
+most countries is pretty user their
+
+ align:start position:0%
+most countries is pretty user their
+ 
+
+ align:start position:0%
+most countries is pretty user their
+standard ways to do that all that will
+
+ align:start position:0%
+standard ways to do that all that will
+ 
+
+ align:start position:0%
+standard ways to do that all that will
+plug in automatically but again all of
+
+ align:start position:0%
+plug in automatically but again all of
+ 
+
+ align:start position:0%
+plug in automatically but again all of
+those are outside of the code
+
+ align:start position:0%
+those are outside of the code
+ 
+
+ align:start position:0%
+those are outside of the code
+all of those are legally binding
+
+ align:start position:0%
+all of those are legally binding
+ 
+
+ align:start position:0%
+all of those are legally binding
+contracts so I government right trust
+
+ align:start position:0%
+contracts so I government right trust
+ 
+
+ align:start position:0%
+contracts so I government right trust
+the court I don't trust a software
+
+ align:start position:0%
+the court I don't trust a software
+ 
+
+ align:start position:0%
+the court I don't trust a software
+engineer to find a proper go protect me
+
+ align:start position:0%
+engineer to find a proper go protect me
+ 
+
+ align:start position:0%
+engineer to find a proper go protect me
+or my counterparty so like what do you
+
+ align:start position:0%
+or my counterparty so like what do you
+ 
+
+ align:start position:0%
+or my counterparty so like what do you
+think about that what is your take on
+
+ align:start position:0%
+think about that what is your take on
+ 
+
+ align:start position:0%
+think about that what is your take on
+those more contract not only your take
+
+ align:start position:0%
+those more contract not only your take
+ 
+
+ align:start position:0%
+those more contract not only your take
+on whether to trust but what the courts
+
+ align:start position:0%
+on whether to trust but what the courts
+ 
+
+ align:start position:0%
+on whether to trust but what the courts
+in Europe in the u.s. right now do if
+
+ align:start position:0%
+in Europe in the u.s. right now do if
+ 
+
+ align:start position:0%
+in Europe in the u.s. right now do if
+somebody says I wrote the contract and
+
+ align:start position:0%
+somebody says I wrote the contract and
+ 
+
+ align:start position:0%
+somebody says I wrote the contract and
+here's the code well so when you say let
+
+ align:start position:0%
+here's the code well so when you say let
+ 
+
+ align:start position:0%
+here's the code well so when you say let
+me just me understand a question better
+
+ align:start position:0%
+me just me understand a question better
+ 
+
+ align:start position:0%
+me just me understand a question better
+the way I'm sorry your name is dude the
+
+ align:start position:0%
+the way I'm sorry your name is dude the
+ 
+
+ align:start position:0%
+the way I'm sorry your name is dude the
+way Hugo described it I think is nice a
+
+ align:start position:0%
+way Hugo described it I think is nice a
+ 
+
+ align:start position:0%
+way Hugo described it I think is nice a
+whole bunch of conditional statements
+
+ align:start position:0%
+whole bunch of conditional statements
+ 
+
+ align:start position:0%
+whole bunch of conditional statements
+which is the code so the code says if
+
+ align:start position:0%
+which is the code so the code says if
+ 
+
+ align:start position:0%
+which is the code so the code says if
+the plane leaves more than 30 minutes
+
+ align:start position:0%
+the plane leaves more than 30 minutes
+ 
+
+ align:start position:0%
+the plane leaves more than 30 minutes
+late then transfer $100 to his account
+
+ align:start position:0%
+late then transfer $100 to his account
+ 
+
+ align:start position:0%
+late then transfer $100 to his account
+okay so you don't trust Vitale's system
+
+ align:start position:0%
+okay so you don't trust Vitale's system
+ 
+
+ align:start position:0%
+okay so you don't trust Vitale's system
+to be able to implement that conditional
+
+ align:start position:0%
+to be able to implement that conditional
+ 
+
+ align:start position:0%
+to be able to implement that conditional
+yep I mean I don't know the code I don't
+
+ align:start position:0%
+yep I mean I don't know the code I don't
+ 
+
+ align:start position:0%
+yep I mean I don't know the code I don't
+know if it's breakable I don't know if
+
+ align:start position:0%
+know if it's breakable I don't know if
+ 
+
+ align:start position:0%
+know if it's breakable I don't know if
+GE can log in and change it you know
+
+ align:start position:0%
+GE can log in and change it you know
+ 
+
+ align:start position:0%
+GE can log in and change it you know
+this is true of everything you know when
+
+ align:start position:0%
+this is true of everything you know when
+ 
+
+ align:start position:0%
+this is true of everything you know when
+I say to you I'm a lawyer I'm gonna
+
+ align:start position:0%
+I say to you I'm a lawyer I'm gonna
+ 
+
+ align:start position:0%
+I say to you I'm a lawyer I'm gonna
+write the contract so you can sell your
+
+ align:start position:0%
+write the contract so you can sell your
+ 
+
+ align:start position:0%
+write the contract so you can sell your
+car to Andy
+
+ align:start position:0%
+car to Andy
+ 
+
+ align:start position:0%
+car to Andy
+you know you can have the same questions
+
+ align:start position:0%
+you know you can have the same questions
+ 
+
+ align:start position:0%
+you know you can have the same questions
+or you can enter the question whether
+
+ align:start position:0%
+or you can enter the question whether
+ 
+
+ align:start position:0%
+or you can enter the question whether
+Andy's gonna you know have a way to flip
+
+ align:start position:0%
+Andy's gonna you know have a way to flip
+ 
+
+ align:start position:0%
+Andy's gonna you know have a way to flip
+the price so instead of a ten thousand
+
+ align:start position:0%
+the price so instead of a ten thousand
+ 
+
+ align:start position:0%
+the price so instead of a ten thousand
+it's fifteen thousand so this
+
+ align:start position:0%
+it's fifteen thousand so this
+ 
+
+ align:start position:0%
+it's fifteen thousand so this
+uncertainty is everywhere it might be
+
+ align:start position:0%
+uncertainty is everywhere it might be
+ 
+
+ align:start position:0%
+uncertainty is everywhere it might be
+Vitaly would say actually there's a more
+
+ align:start position:0%
+Vitaly would say actually there's a more
+ 
+
+ align:start position:0%
+Vitaly would say actually there's a more
+robust way to verify my code than
+
+ align:start position:0%
+robust way to verify my code than
+ 
+
+ align:start position:0%
+robust way to verify my code than
+Lessing's contract because lessons
+
+ align:start position:0%
+Lessing's contract because lessons
+ 
+
+ align:start position:0%
+Lessing's contract because lessons
+contract code is written in English we
+
+ align:start position:0%
+contract code is written in English we
+ 
+
+ align:start position:0%
+contract code is written in English we
+have all sorts of but my code you can
+
+ align:start position:0%
+have all sorts of but my code you can
+ 
+
+ align:start position:0%
+have all sorts of but my code you can
+have independent people who verify so at
+
+ align:start position:0%
+have independent people who verify so at
+ 
+
+ align:start position:0%
+have independent people who verify so at
+the level of conditionals I'm pretty
+
+ align:start position:0%
+the level of conditionals I'm pretty
+ 
+
+ align:start position:0%
+the level of conditionals I'm pretty
+confident what I'm not confident about
+
+ align:start position:0%
+confident what I'm not confident about
+ 
+
+ align:start position:0%
+confident what I'm not confident about
+is and I had the great pleasure in
+
+ align:start position:0%
+is and I had the great pleasure in
+ 
+
+ align:start position:0%
+is and I had the great pleasure in
+December of 2015
+
+ align:start position:0%
+December of 2015
+ 
+
+ align:start position:0%
+December of 2015
+spending a weekend with them like
+
+ align:start position:0%
+spending a weekend with them like
+ 
+
+ align:start position:0%
+spending a weekend with them like
+watching that group and you know it's
+
+ align:start position:0%
+watching that group and you know it's
+ 
+
+ align:start position:0%
+watching that group and you know it's
+this weird kind of you know he is like
+
+ align:start position:0%
+this weird kind of you know he is like
+ 
+
+ align:start position:0%
+this weird kind of you know he is like
+the Messiah figure and there's like
+
+ align:start position:0%
+the Messiah figure and there's like
+ 
+
+ align:start position:0%
+the Messiah figure and there's like
+twelve people sitting on the floor
+
+ align:start position:0%
+twelve people sitting on the floor
+ 
+
+ align:start position:0%
+twelve people sitting on the floor
+around him listening to his every bit of
+
+ align:start position:0%
+around him listening to his every bit of
+ 
+
+ align:start position:0%
+around him listening to his every bit of
+wisdom you know so it was inspirational
+
+ align:start position:0%
+wisdom you know so it was inspirational
+ 
+
+ align:start position:0%
+wisdom you know so it was inspirational
+and scary at the same time because you
+
+ align:start position:0%
+and scary at the same time because you
+ 
+
+ align:start position:0%
+and scary at the same time because you
+see how much money is resting on this
+
+ align:start position:0%
+see how much money is resting on this
+ 
+
+ align:start position:0%
+see how much money is resting on this
+Messiah structure but I have a lot of
+
+ align:start position:0%
+Messiah structure but I have a lot of
+ 
+
+ align:start position:0%
+Messiah structure but I have a lot of
+confidence in their ability to do the
+
+ align:start position:0%
+confidence in their ability to do the
+ 
+
+ align:start position:0%
+confidence in their ability to do the
+conditionals but I'm not so confident
+
+ align:start position:0%
+conditionals but I'm not so confident
+ 
+
+ align:start position:0%
+conditionals but I'm not so confident
+that they yet thought through how it
+
+ align:start position:0%
+that they yet thought through how it
+ 
+
+ align:start position:0%
+that they yet thought through how it
+plugs in to the bigger legal story and
+
+ align:start position:0%
+plugs in to the bigger legal story and
+ 
+
+ align:start position:0%
+plugs in to the bigger legal story and
+that's part of what I was trying to
+
+ align:start position:0%
+that's part of what I was trying to
+ 
+
+ align:start position:0%
+that's part of what I was trying to
+pitch to them is when I'm trying to him
+
+ align:start position:0%
+pitch to them is when I'm trying to him
+ 
+
+ align:start position:0%
+pitch to them is when I'm trying to him
+and that's what I'm trying to pitch to
+
+ align:start position:0%
+and that's what I'm trying to pitch to
+ 
+
+ align:start position:0%
+and that's what I'm trying to pitch to
+you that it's never gonna be the case
+
+ align:start position:0%
+you that it's never gonna be the case
+ 
+
+ align:start position:0%
+you that it's never gonna be the case
+it's not this conference in Australia
+
+ align:start position:0%
+it's not this conference in Australia
+ 
+
+ align:start position:0%
+it's not this conference in Australia
+where I met them and so many of the
+
+ align:start position:0%
+where I met them and so many of the
+ 
+
+ align:start position:0%
+where I met them and so many of the
+people there were speaking the way
+
+ align:start position:0%
+people there were speaking the way
+ 
+
+ align:start position:0%
+people there were speaking the way
+people spoke about the internet 20 years
+
+ align:start position:0%
+people spoke about the internet 20 years
+ 
+
+ align:start position:0%
+people spoke about the internet 20 years
+ago it's like oh there's like the real
+
+ align:start position:0%
+ago it's like oh there's like the real
+ 
+
+ align:start position:0%
+ago it's like oh there's like the real
+world we have the government's but we're
+
+ align:start position:0%
+world we have the government's but we're
+ 
+
+ align:start position:0%
+world we have the government's but we're
+gonna create like John Perry Barlow
+
+ align:start position:0%
+gonna create like John Perry Barlow
+ 
+
+ align:start position:0%
+gonna create like John Perry Barlow
+speak we're gonna trade this virtual
+
+ align:start position:0%
+speak we're gonna trade this virtual
+ 
+
+ align:start position:0%
+speak we're gonna trade this virtual
+world where there's no governments where
+
+ align:start position:0%
+world where there's no governments where
+ 
+
+ align:start position:0%
+world where there's no governments where
+we just live free of government and it's
+
+ align:start position:0%
+we just live free of government and it's
+ 
+
+ align:start position:0%
+we just live free of government and it's
+like so naive about the way this stuff
+
+ align:start position:0%
+like so naive about the way this stuff
+ 
+
+ align:start position:0%
+like so naive about the way this stuff
+works because it's always embedded in a
+
+ align:start position:0%
+works because it's always embedded in a
+ 
+
+ align:start position:0%
+works because it's always embedded in a
+real world which has a real government
+
+ align:start position:0%
+real world which has a real government
+ 
+
+ align:start position:0%
+real world which has a real government
+and that real government is not going to
+
+ align:start position:0%
+and that real government is not going to
+ 
+
+ align:start position:0%
+and that real government is not going to
+look the other way if you're you know
+
+ align:start position:0%
+look the other way if you're you know
+ 
+
+ align:start position:0%
+look the other way if you're you know
+doing lots of damage or not paying your
+
+ align:start position:0%
+doing lots of damage or not paying your
+ 
+
+ align:start position:0%
+doing lots of damage or not paying your
+taxes so the question isn't whether the
+
+ align:start position:0%
+taxes so the question isn't whether the
+ 
+
+ align:start position:0%
+taxes so the question isn't whether the
+question is just how and how much we go
+
+ align:start position:0%
+question is just how and how much we go
+ 
+
+ align:start position:0%
+question is just how and how much we go
+impact there what kind of implications
+
+ align:start position:0%
+impact there what kind of implications
+ 
+
+ align:start position:0%
+impact there what kind of implications
+you have do you think this technology
+
+ align:start position:0%
+you have do you think this technology
+ 
+
+ align:start position:0%
+you have do you think this technology
+has to broaden access to legal services
+
+ align:start position:0%
+has to broaden access to legal services
+ 
+
+ align:start position:0%
+has to broaden access to legal services
+and generally letting people know when
+
+ align:start position:0%
+and generally letting people know when
+ 
+
+ align:start position:0%
+and generally letting people know when
+they're being taken advantage or being
+
+ align:start position:0%
+they're being taken advantage or being
+ 
+
+ align:start position:0%
+they're being taken advantage or being
+able to like provide more standard
+
+ align:start position:0%
+able to like provide more standard
+ 
+
+ align:start position:0%
+able to like provide more standard
+versions of
+
+ align:start position:0%
+versions of
+ 
+
+ align:start position:0%
+versions of
+really call it contracts employment
+
+ align:start position:0%
+really call it contracts employment
+ 
+
+ align:start position:0%
+really call it contracts employment
+contracts or these contracts and things
+
+ align:start position:0%
+contracts or these contracts and things
+ 
+
+ align:start position:0%
+contracts or these contracts and things
+like that do you think that this is
+
+ align:start position:0%
+like that do you think that this is
+ 
+
+ align:start position:0%
+like that do you think that this is
+going to be a game-changer I mean you
+
+ align:start position:0%
+going to be a game-changer I mean you
+ 
+
+ align:start position:0%
+going to be a game-changer I mean you
+know you've got a muster the political
+
+ align:start position:0%
+know you've got a muster the political
+ 
+
+ align:start position:0%
+know you've got a muster the political
+will to break the monopoly lawyers have
+
+ align:start position:0%
+will to break the monopoly lawyers have
+ 
+
+ align:start position:0%
+will to break the monopoly lawyers have
+in this space and you know I'll tell you
+
+ align:start position:0%
+in this space and you know I'll tell you
+ 
+
+ align:start position:0%
+in this space and you know I'll tell you
+we're gonna fight hard against it but
+
+ align:start position:0%
+we're gonna fight hard against it but
+ 
+
+ align:start position:0%
+we're gonna fight hard against it but
+there is no reason for 90% of what
+
+ align:start position:0%
+there is no reason for 90% of what
+ 
+
+ align:start position:0%
+there is no reason for 90% of what
+lawyers do to be done by lawyers just
+
+ align:start position:0%
+lawyers do to be done by lawyers just
+ 
+
+ align:start position:0%
+lawyers do to be done by lawyers just
+like when you know go if you buy a house
+
+ align:start position:0%
+like when you know go if you buy a house
+ 
+
+ align:start position:0%
+like when you know go if you buy a house
+and you like have to have a lawyer who
+
+ align:start position:0%
+and you like have to have a lawyer who
+ 
+
+ align:start position:0%
+and you like have to have a lawyer who
+sits there and basically signs documents
+
+ align:start position:0%
+sits there and basically signs documents
+ 
+
+ align:start position:0%
+sits there and basically signs documents
+for you and you're like why and the
+
+ align:start position:0%
+for you and you're like why and the
+ 
+
+ align:start position:0%
+for you and you're like why and the
+answer is because the law has been
+
+ align:start position:0%
+answer is because the law has been
+ 
+
+ align:start position:0%
+answer is because the law has been
+written to require that person to sit
+
+ align:start position:0%
+written to require that person to sit
+ 
+
+ align:start position:0%
+written to require that person to sit
+there and sign documents and why because
+
+ align:start position:0%
+there and sign documents and why because
+ 
+
+ align:start position:0%
+there and sign documents and why because
+people get paid to sign documents have
+
+ align:start position:0%
+people get paid to sign documents have
+ 
+
+ align:start position:0%
+people get paid to sign documents have
+corrupted the law so so there's lots to
+
+ align:start position:0%
+corrupted the law so so there's lots to
+ 
+
+ align:start position:0%
+corrupted the law so so there's lots to
+clean up but if we could clean it up
+
+ align:start position:0%
+clean up but if we could clean it up
+ 
+
+ align:start position:0%
+clean up but if we could clean it up
+absolutely you know 99% of this stuff
+
+ align:start position:0%
+absolutely you know 99% of this stuff
+ 
+
+ align:start position:0%
+absolutely you know 99% of this stuff
+ought to be automatic and then let's get
+
+ align:start position:0%
+ought to be automatic and then let's get
+ 
+
+ align:start position:0%
+ought to be automatic and then let's get
+the lawyers to focus on the hard corner
+
+ align:start position:0%
+the lawyers to focus on the hard corner
+ 
+
+ align:start position:0%
+the lawyers to focus on the hard corner
+case it's not on the know everything
+
+ align:start position:0%
+case it's not on the know everything
+ 
+
+ align:start position:0%
+case it's not on the know everything
+should be automatic and that and that
+
+ align:start position:0%
+should be automatic and that and that
+ 
+
+ align:start position:0%
+should be automatic and that and that
+certainly should be true not just within
+
+ align:start position:0%
+certainly should be true not just within
+ 
+
+ align:start position:0%
+certainly should be true not just within
+a jurisdiction but across jurisdiction
+
+ align:start position:0%
+a jurisdiction but across jurisdiction
+ 
+
+ align:start position:0%
+a jurisdiction but across jurisdiction
+can I return to your insurance example I
+
+ align:start position:0%
+can I return to your insurance example I
+ 
+
+ align:start position:0%
+can I return to your insurance example I
+got the idea that you could write a
+
+ align:start position:0%
+got the idea that you could write a
+ 
+
+ align:start position:0%
+got the idea that you could write a
+smart contract that would pay you
+
+ align:start position:0%
+smart contract that would pay you
+ 
+
+ align:start position:0%
+smart contract that would pay you
+automatically planes just later but then
+
+ align:start position:0%
+automatically planes just later but then
+ 
+
+ align:start position:0%
+automatically planes just later but then
+you said it puts it on the clock that
+
+ align:start position:0%
+you said it puts it on the clock that
+ 
+
+ align:start position:0%
+you said it puts it on the clock that
+can you connect why he put it on a
+
+ align:start position:0%
+can you connect why he put it on a
+ 
+
+ align:start position:0%
+can you connect why he put it on a
+blockchain as opposed to just putting it
+
+ align:start position:0%
+blockchain as opposed to just putting it
+ 
+
+ align:start position:0%
+blockchain as opposed to just putting it
+on his disk and letting your credit card
+
+ align:start position:0%
+on his disk and letting your credit card
+ 
+
+ align:start position:0%
+on his disk and letting your credit card
+get credited I mean where did the
+
+ align:start position:0%
+get credited I mean where did the
+ 
+
+ align:start position:0%
+get credited I mean where did the
+blockchain
+
+ align:start position:0%
+blockchain
+ 
+
+ align:start position:0%
+blockchain
+enter into that and why did he need a
+
+ align:start position:0%
+enter into that and why did he need a
+ 
+
+ align:start position:0%
+enter into that and why did he need a
+blockchain in order to maintain that
+
+ align:start position:0%
+blockchain in order to maintain that
+ 
+
+ align:start position:0%
+blockchain in order to maintain that
+state thing that he thought he was
+
+ align:start position:0%
+state thing that he thought he was
+ 
+
+ align:start position:0%
+state thing that he thought he was
+getting out of the blockchain is to
+
+ align:start position:0%
+getting out of the blockchain is to
+ 
+
+ align:start position:0%
+getting out of the blockchain is to
+increase the verify ability of third
+
+ align:start position:0%
+increase the verify ability of third
+ 
+
+ align:start position:0%
+increase the verify ability of third
+parties of the actual payments according
+
+ align:start position:0%
+parties of the actual payments according
+ 
+
+ align:start position:0%
+parties of the actual payments according
+to the data so if I say to you I'm gonna
+
+ align:start position:0%
+to the data so if I say to you I'm gonna
+ 
+
+ align:start position:0%
+to the data so if I say to you I'm gonna
+be paying you 500 dollars if you're
+
+ align:start position:0%
+be paying you 500 dollars if you're
+ 
+
+ align:start position:0%
+be paying you 500 dollars if you're
+playing as an hour late and we have the
+
+ align:start position:0%
+playing as an hour late and we have the
+ 
+
+ align:start position:0%
+playing as an hour late and we have the
+data out there about the planes being
+
+ align:start position:0%
+data out there about the planes being
+ 
+
+ align:start position:0%
+data out there about the planes being
+late if he did it inside of his
+
+ align:start position:0%
+late if he did it inside of his
+ 
+
+ align:start position:0%
+late if he did it inside of his
+insurance company I wouldn't have any
+
+ align:start position:0%
+insurance company I wouldn't have any
+ 
+
+ align:start position:0%
+insurance company I wouldn't have any
+way to know that he paid you 500 dollars
+
+ align:start position:0%
+way to know that he paid you 500 dollars
+ 
+
+ align:start position:0%
+way to know that he paid you 500 dollars
+for the plane being late but if it's in
+
+ align:start position:0%
+for the plane being late but if it's in
+ 
+
+ align:start position:0%
+for the plane being late but if it's in
+a blog chain there's at least
+
+ align:start position:0%
+a blog chain there's at least
+ 
+
+ align:start position:0%
+a blog chain there's at least
+conceptually a way in which we could be
+
+ align:start position:0%
+conceptually a way in which we could be
+ 
+
+ align:start position:0%
+conceptually a way in which we could be
+doing this
+
+ align:start position:0%
+doing this
+ 
+
+ align:start position:0%
+doing this
+not that I'm revealing it to you but we
+
+ align:start position:0%
+not that I'm revealing it to you but we
+ 
+
+ align:start position:0%
+not that I'm revealing it to you but we
+could be signaling Apollo that depends
+
+ align:start position:0%
+could be signaling Apollo that depends
+ 
+
+ align:start position:0%
+could be signaling Apollo that depends
+on who maintains the knowledge chain and
+
+ align:start position:0%
+on who maintains the knowledge chain and
+ 
+
+ align:start position:0%
+on who maintains the knowledge chain and
+at the same time and return to that
+
+ align:start position:0%
+at the same time and return to that
+ 
+
+ align:start position:0%
+at the same time and return to that
+suddenly everybody knows the cash flow
+
+ align:start position:0%
+suddenly everybody knows the cash flow
+ 
+
+ align:start position:0%
+suddenly everybody knows the cash flow
+of that insurance company which is
+
+ align:start position:0%
+of that insurance company which is
+ 
+
+ align:start position:0%
+of that insurance company which is
+likely not something he wants to do
+
+ align:start position:0%
+likely not something he wants to do
+ 
+
+ align:start position:0%
+likely not something he wants to do
+companies bigger than authenticating the
+
+ align:start position:0%
+companies bigger than authenticating the
+ 
+
+ align:start position:0%
+companies bigger than authenticating the
+truth about certain types of my do not
+
+ align:start position:0%
+truth about certain types of my do not
+ 
+
+ align:start position:0%
+truth about certain types of my do not
+want everybody to know what planes I'm
+
+ align:start position:0%
+want everybody to know what planes I'm
+ 
+
+ align:start position:0%
+want everybody to know what planes I'm
+flying
+
+ align:start position:0%
+flying
+ 
+
+ align:start position:0%
+flying
+so you've implied that there's now a
+
+ align:start position:0%
+so you've implied that there's now a
+ 
+
+ align:start position:0%
+so you've implied that there's now a
+public no all I mean to all I need to
+
+ align:start position:0%
+public no all I mean to all I need to
+ 
+
+ align:start position:0%
+public no all I mean to all I need to
+argue and I didn't interrogate him far I
+
+ align:start position:0%
+argue and I didn't interrogate him far I
+ 
+
+ align:start position:0%
+argue and I didn't interrogate him far I
+was just taking his statement that he's
+
+ align:start position:0%
+was just taking his statement that he's
+ 
+
+ align:start position:0%
+was just taking his statement that he's
+doing so I'm trying to think why would
+
+ align:start position:0%
+doing so I'm trying to think why would
+ 
+
+ align:start position:0%
+doing so I'm trying to think why would
+he want to do it because I had the same
+
+ align:start position:0%
+he want to do it because I had the same
+ 
+
+ align:start position:0%
+he want to do it because I had the same
+kind of question you want to do you had
+
+ align:start position:0%
+kind of question you want to do you had
+ 
+
+ align:start position:0%
+kind of question you want to do you had
+and it's just that if you are trying to
+
+ align:start position:0%
+and it's just that if you are trying to
+ 
+
+ align:start position:0%
+and it's just that if you are trying to
+create credibility around your claim do
+
+ align:start position:0%
+create credibility around your claim do
+ 
+
+ align:start position:0%
+create credibility around your claim do
+I have a reason to trust this insurance
+
+ align:start position:0%
+I have a reason to trust this insurance
+ 
+
+ align:start position:0%
+I have a reason to trust this insurance
+company that in fact it's going to be
+
+ align:start position:0%
+company that in fact it's going to be
+ 
+
+ align:start position:0%
+company that in fact it's going to be
+doing this then there's some
+
+ align:start position:0%
+doing this then there's some
+ 
+
+ align:start position:0%
+doing this then there's some
+transparency that this enables not
+
+ align:start position:0%
+transparency that this enables not
+ 
+
+ align:start position:0%
+transparency that this enables not
+necessarily the transparency of your
+
+ align:start position:0%
+necessarily the transparency of your
+ 
+
+ align:start position:0%
+necessarily the transparency of your
+credit card number or your name or the
+
+ align:start position:0%
+credit card number or your name or the
+ 
+
+ align:start position:0%
+credit card number or your name or the
+flights that you're taking but that
+
+ align:start position:0%
+flights that you're taking but that
+ 
+
+ align:start position:0%
+flights that you're taking but that
+there was somebody who was on this who
+
+ align:start position:0%
+there was somebody who was on this who
+ 
+
+ align:start position:0%
+there was somebody who was on this who
+had a contract and we then made this
+
+ align:start position:0%
+had a contract and we then made this
+ 
+
+ align:start position:0%
+had a contract and we then made this
+kind of payment it might that would be a
+
+ align:start position:0%
+kind of payment it might that would be a
+ 
+
+ align:start position:0%
+kind of payment it might that would be a
+potential value that he has now if
+
+ align:start position:0%
+potential value that he has now if
+ 
+
+ align:start position:0%
+potential value that he has now if
+there's no value from that then you're
+
+ align:start position:0%
+there's no value from that then you're
+ 
+
+ align:start position:0%
+there's no value from that then you're
+right the overhead of the blockchain or
+
+ align:start position:0%
+right the overhead of the blockchain or
+ 
+
+ align:start position:0%
+right the overhead of the blockchain or
+public or private or whatever is too
+
+ align:start position:0%
+public or private or whatever is too
+ 
+
+ align:start position:0%
+public or private or whatever is too
+high and he just could do it inside and
+
+ align:start position:0%
+high and he just could do it inside and
+ 
+
+ align:start position:0%
+high and he just could do it inside and
+for certain companies like you know if
+
+ align:start position:0%
+for certain companies like you know if
+ 
+
+ align:start position:0%
+for certain companies like you know if
+you went to a credible insurance company
+
+ align:start position:0%
+you went to a credible insurance company
+ 
+
+ align:start position:0%
+you went to a credible insurance company
+the credible insurance company you know
+
+ align:start position:0%
+the credible insurance company you know
+ 
+
+ align:start position:0%
+the credible insurance company you know
+you probably trust that credible
+
+ align:start position:0%
+you probably trust that credible
+ 
+
+ align:start position:0%
+you probably trust that credible
+insurance company but again if you're a
+
+ align:start position:0%
+insurance company but again if you're a
+ 
+
+ align:start position:0%
+insurance company but again if you're a
+not credible insurance company if you're
+
+ align:start position:0%
+not credible insurance company if you're
+ 
+
+ align:start position:0%
+not credible insurance company if you're
+a startup and you are out there in the
+
+ align:start position:0%
+a startup and you are out there in the
+ 
+
+ align:start position:0%
+a startup and you are out there in the
+market and you're saying give me your
+
+ align:start position:0%
+market and you're saying give me your
+ 
+
+ align:start position:0%
+market and you're saying give me your
+money and I'll pay you if the planes
+
+ align:start position:0%
+money and I'll pay you if the planes
+ 
+
+ align:start position:0%
+money and I'll pay you if the planes
+late people are gonna say why should I
+
+ align:start position:0%
+late people are gonna say why should I
+ 
+
+ align:start position:0%
+late people are gonna say why should I
+trust you and you're like well here you
+
+ align:start position:0%
+trust you and you're like well here you
+ 
+
+ align:start position:0%
+trust you and you're like well here you
+don't really have to trust me here's the
+
+ align:start position:0%
+don't really have to trust me here's the
+ 
+
+ align:start position:0%
+don't really have to trust me here's the
+data to democratical way than if I just
+
+ align:start position:0%
+data to democratical way than if I just
+ 
+
+ align:start position:0%
+data to democratical way than if I just
+published a report on my website that
+
+ align:start position:0%
+published a report on my website that
+ 
+
+ align:start position:0%
+published a report on my website that
+I'm doing what I say on to it let me
+
+ align:start position:0%
+I'm doing what I say on to it let me
+ 
+
+ align:start position:0%
+I'm doing what I say on to it let me
+strut it Andy let's try to get a couple
+
+ align:start position:0%
+strut it Andy let's try to get a couple
+ 
+
+ align:start position:0%
+strut it Andy let's try to get a couple
+more questions but my hunch is that it's
+
+ align:start position:0%
+more questions but my hunch is that it's
+ 
+
+ align:start position:0%
+more questions but my hunch is that it's
+probably a permission rather than
+
+ align:start position:0%
+probably a permission rather than
+ 
+
+ align:start position:0%
+probably a permission rather than
+permission list blockchain and and it
+
+ align:start position:0%
+permission list blockchain and and it
+ 
+
+ align:start position:0%
+permission list blockchain and and it
+may be the insurance company wants to
+
+ align:start position:0%
+may be the insurance company wants to
+ 
+
+ align:start position:0%
+may be the insurance company wants to
+ride on the buzz of blockchain but it's
+
+ align:start position:0%
+ride on the buzz of blockchain but it's
+ 
+
+ align:start position:0%
+ride on the buzz of blockchain but it's
+possible also that he thinks that
+
+ align:start position:0%
+possible also that he thinks that
+ 
+
+ align:start position:0%
+possible also that he thinks that
+there'll be more trust that consumers
+
+ align:start position:0%
+there'll be more trust that consumers
+ 
+
+ align:start position:0%
+there'll be more trust that consumers
+will trust it if it's called a block J
+
+ align:start position:0%
+will trust it if it's called a block J
+ 
+
+ align:start position:0%
+will trust it if it's called a block J
+so it's but you didn't interview
+
+ align:start position:0%
+so it's but you didn't interview
+ 
+
+ align:start position:0%
+so it's but you didn't interview
+you can pick who you want to write this
+
+ align:start position:0%
+you can pick who you want to write this
+ 
+
+ align:start position:0%
+you can pick who you want to write this
+whole smart conscience solvent
+
+ align:start position:0%
+whole smart conscience solvent
+ 
+
+ align:start position:0%
+whole smart conscience solvent
+submarines in some countries would
+
+ align:start position:0%
+submarines in some countries would
+ 
+
+ align:start position:0%
+submarines in some countries would
+receive and I was talking to in context
+
+ align:start position:0%
+receive and I was talking to in context
+ 
+
+ align:start position:0%
+receive and I was talking to in context
+or something like that yeah if you have
+
+ align:start position:0%
+or something like that yeah if you have
+ 
+
+ align:start position:0%
+or something like that yeah if you have
+an alternative way to credibly represent
+
+ align:start position:0%
+an alternative way to credibly represent
+ 
+
+ align:start position:0%
+an alternative way to credibly represent
+a fact and again this is kind of
+
+ align:start position:0%
+a fact and again this is kind of
+ 
+
+ align:start position:0%
+a fact and again this is kind of
+connected to Andy's point like what is
+
+ align:start position:0%
+connected to Andy's point like what is
+ 
+
+ align:start position:0%
+connected to Andy's point like what is
+this and is there an alternative way and
+
+ align:start position:0%
+this and is there an alternative way and
+ 
+
+ align:start position:0%
+this and is there an alternative way and
+is this the alternative way then you
+
+ align:start position:0%
+is this the alternative way then you
+ 
+
+ align:start position:0%
+is this the alternative way then you
+lower the transaction cost of that kind
+
+ align:start position:0%
+lower the transaction cost of that kind
+ 
+
+ align:start position:0%
+lower the transaction cost of that kind
+of contract because I'm going to trust
+
+ align:start position:0%
+of contract because I'm going to trust
+ 
+
+ align:start position:0%
+of contract because I'm going to trust
+the contracting process more if I'm
+
+ align:start position:0%
+the contracting process more if I'm
+ 
+
+ align:start position:0%
+the contracting process more if I'm
+confident that in fact the the fact that
+
+ align:start position:0%
+confident that in fact the the fact that
+ 
+
+ align:start position:0%
+confident that in fact the the fact that
+I'm late I'm not late it doesn't
+
+ align:start position:0%
+I'm late I'm not late it doesn't
+ 
+
+ align:start position:0%
+I'm late I'm not late it doesn't
+penalize me or you don't penalize me
+
+ align:start position:0%
+penalize me or you don't penalize me
+ 
+
+ align:start position:0%
+penalize me or you don't penalize me
+claiming I'm late so to the extent you
+
+ align:start position:0%
+claiming I'm late so to the extent you
+ 
+
+ align:start position:0%
+claiming I'm late so to the extent you
+lower the cost of verifying facts in the
+
+ align:start position:0%
+lower the cost of verifying facts in the
+ 
+
+ align:start position:0%
+lower the cost of verifying facts in the
+world you increase the opportunity for
+
+ align:start position:0%
+world you increase the opportunity for
+ 
+
+ align:start position:0%
+world you increase the opportunity for
+certain contracts to happen who
+
+ align:start position:0%
+certain contracts to happen who
+ 
+
+ align:start position:0%
+certain contracts to happen who
+otherwise wouldn't have and and that's
+
+ align:start position:0%
+otherwise wouldn't have and and that's
+ 
+
+ align:start position:0%
+otherwise wouldn't have and and that's
+the only trade-off that I'm trying to
+
+ align:start position:0%
+the only trade-off that I'm trying to
+ 
+
+ align:start position:0%
+the only trade-off that I'm trying to
+emphasize by emphasizing the transaction
+
+ align:start position:0%
+emphasize by emphasizing the transaction
+ 
+
+ align:start position:0%
+emphasize by emphasizing the transaction
+cost apart from these contracts you had
+
+ align:start position:0%
+cost apart from these contracts you had
+ 
+
+ align:start position:0%
+cost apart from these contracts you had
+a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not for one-off transactions before the
+
+ align:start position:0%
+not for one-off transactions before the
+ 
+
+ align:start position:0%
+not for one-off transactions before the
+insurance company aggregate thousands of
+
+ align:start position:0%
+insurance company aggregate thousands of
+ 
+
+ align:start position:0%
+insurance company aggregate thousands of
+transactions where they've shown
+
+ align:start position:0%
+transactions where they've shown
+ 
+
+ align:start position:0%
+transactions where they've shown
+performance they can use this ethical or
+
+ align:start position:0%
+performance they can use this ethical or
+ 
+
+ align:start position:0%
+performance they can use this ethical or
+commercial reasons to show that yes
+
+ align:start position:0%
+commercial reasons to show that yes
+ 
+
+ align:start position:0%
+commercial reasons to show that yes
+people get paid when
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ridiculous yeah you would free that it
+
+ align:start position:0%
+ridiculous yeah you would free that it
+ 
+
+ align:start position:0%
+ridiculous yeah you would free that it
+would have to be that that would be a
+
+ align:start position:0%
+would have to be that that would be a
+ 
+
+ align:start position:0%
+would have to be that that would be a
+value it was providing otherwise to be
+
+ align:start position:0%
+value it was providing otherwise to be
+ 
+
+ align:start position:0%
+value it was providing otherwise to be
+Eddie's point there would be no reason
+
+ align:start position:0%
+Eddie's point there would be no reason
+ 
+
+ align:start position:0%
+Eddie's point there would be no reason
+to adopt that's gonna go on the back
+
+ align:start position:0%
+to adopt that's gonna go on the back
+ 
+
+ align:start position:0%
+to adopt that's gonna go on the back
+right I don't remember a name so with
+
+ align:start position:0%
+right I don't remember a name so with
+ 
+
+ align:start position:0%
+right I don't remember a name so with
+it's easier access to these kind of
+
+ align:start position:0%
+it's easier access to these kind of
+ 
+
+ align:start position:0%
+it's easier access to these kind of
+derivative contracts do you proceed a
+
+ align:start position:0%
+derivative contracts do you proceed a
+ 
+
+ align:start position:0%
+derivative contracts do you proceed a
+world where there's a lot more leverage
+
+ align:start position:0%
+world where there's a lot more leverage
+ 
+
+ align:start position:0%
+world where there's a lot more leverage
+and sort of any type of market outside
+
+ align:start position:0%
+and sort of any type of market outside
+ 
+
+ align:start position:0%
+and sort of any type of market outside
+of financial markets or see this
+
+ align:start position:0%
+of financial markets or see this
+ 
+
+ align:start position:0%
+of financial markets or see this
+creating risk this is your expertise
+
+ align:start position:0%
+creating risk this is your expertise
+ 
+
+ align:start position:0%
+creating risk this is your expertise
+right because I mean we already saw in
+
+ align:start position:0%
+right because I mean we already saw in
+ 
+
+ align:start position:0%
+right because I mean we already saw in
+the derivatives market the fact that the
+
+ align:start position:0%
+the derivatives market the fact that the
+ 
+
+ align:start position:0%
+the derivatives market the fact that the
+choice by policymakers was to allow it
+
+ align:start position:0%
+choice by policymakers was to allow it
+ 
+
+ align:start position:0%
+choice by policymakers was to allow it
+to be an invisible market and not to
+
+ align:start position:0%
+to be an invisible market and not to
+ 
+
+ align:start position:0%
+to be an invisible market and not to
+regulate that market created all sorts
+
+ align:start position:0%
+regulate that market created all sorts
+ 
+
+ align:start position:0%
+regulate that market created all sorts
+of risks that you know people might
+
+ align:start position:0%
+of risks that you know people might
+ 
+
+ align:start position:0%
+of risks that you know people might
+think shouldn't have been there and I
+
+ align:start position:0%
+think shouldn't have been there and I
+ 
+
+ align:start position:0%
+think shouldn't have been there and I
+think the same potential is here which
+
+ align:start position:0%
+think the same potential is here which
+ 
+
+ align:start position:0%
+think the same potential is here which
+is again to come back to the point don't
+
+ align:start position:0%
+is again to come back to the point don't
+ 
+
+ align:start position:0%
+is again to come back to the point don't
+expect there not to be government here I
+
+ align:start position:0%
+expect there not to be government here I
+ 
+
+ align:start position:0%
+expect there not to be government here I
+mean you know to the extent people
+
+ align:start position:0%
+mean you know to the extent people
+ 
+
+ align:start position:0%
+mean you know to the extent people
+realize this risk and don't have as much
+
+ align:start position:0%
+realize this risk and don't have as much
+ 
+
+ align:start position:0%
+realize this risk and don't have as much
+political corrupting power as Wall
+
+ align:start position:0%
+political corrupting power as Wall
+ 
+
+ align:start position:0%
+political corrupting power as Wall
+Street did in our system I would say yes
+
+ align:start position:0%
+Street did in our system I would say yes
+ 
+
+ align:start position:0%
+Street did in our system I would say yes
+even on Bitcoin you can create something
+
+ align:start position:0%
+even on Bitcoin you can create something
+ 
+
+ align:start position:0%
+even on Bitcoin you can create something
+called discrete log contracts to do
+
+ align:start position:0%
+called discrete log contracts to do
+ 
+
+ align:start position:0%
+called discrete log contracts to do
+contracts for differences or derivatives
+
+ align:start position:0%
+contracts for differences or derivatives
+ 
+
+ align:start position:0%
+contracts for differences or derivatives
+but with smart contracts you can put a
+
+ align:start position:0%
+but with smart contracts you can put a
+ 
+
+ align:start position:0%
+but with smart contracts you can put a
+lot of leverage into the system and
+
+ align:start position:0%
+lot of leverage into the system and
+ 
+
+ align:start position:0%
+lot of leverage into the system and
+transactions can move quickly so I think
+
+ align:start position:0%
+transactions can move quickly so I think
+ 
+
+ align:start position:0%
+transactions can move quickly so I think
+the state will have an interest
+
+ align:start position:0%
+the state will have an interest
+ 
+
+ align:start position:0%
+the state will have an interest
+particularly if it grows you probably
+
+ align:start position:0%
+particularly if it grows you probably
+ 
+
+ align:start position:0%
+particularly if it grows you probably
+only have time for two more questions
+
+ align:start position:0%
+only have time for two more questions
+ 
+
+ align:start position:0%
+only have time for two more questions
+and I'm still wondering how do courts
+
+ align:start position:0%
+and I'm still wondering how do courts
+ 
+
+ align:start position:0%
+and I'm still wondering how do courts
+currently look at these as a matter of
+
+ align:start position:0%
+currently look at these as a matter of
+ 
+
+ align:start position:0%
+currently look at these as a matter of
+law and the late 1990s I was honored to
+
+ align:start position:0%
+law and the late 1990s I was honored to
+ 
+
+ align:start position:0%
+law and the late 1990s I was honored to
+work with Senator John McCain on
+
+ align:start position:0%
+work with Senator John McCain on
+ 
+
+ align:start position:0%
+work with Senator John McCain on
+something which became the e-signature
+
+ align:start position:0%
+something which became the e-signature
+ 
+
+ align:start position:0%
+something which became the e-signature
+law I was just playing point for the US
+
+ align:start position:0%
+law I was just playing point for the US
+ 
+
+ align:start position:0%
+law I was just playing point for the US
+Department of Treasury it was really
+
+ align:start position:0%
+Department of Treasury it was really
+ 
+
+ align:start position:0%
+Department of Treasury it was really
+John McCain's law Congress was doing but
+
+ align:start position:0%
+John McCain's law Congress was doing but
+ 
+
+ align:start position:0%
+John McCain's law Congress was doing but
+I'm wondering how the courts today would
+
+ align:start position:0%
+I'm wondering how the courts today would
+ 
+
+ align:start position:0%
+I'm wondering how the courts today would
+see these contracts is it like do we
+
+ align:start position:0%
+see these contracts is it like do we
+ 
+
+ align:start position:0%
+see these contracts is it like do we
+need something like them a signature law
+
+ align:start position:0%
+need something like them a signature law
+ 
+
+ align:start position:0%
+need something like them a signature law
+to have code accepted beyond what ecig
+
+ align:start position:0%
+to have code accepted beyond what ecig
+ 
+
+ align:start position:0%
+to have code accepted beyond what ecig
+mature
+
+ align:start position:0%
+mature
+ 
+
+ align:start position:0%
+mature
+no I think easy I think the e-signature
+
+ align:start position:0%
+no I think easy I think the e-signature
+ 
+
+ align:start position:0%
+no I think easy I think the e-signature
+infrastructure is going to be 99 percent
+
+ align:start position:0%
+infrastructure is going to be 99 percent
+ 
+
+ align:start position:0%
+infrastructure is going to be 99 percent
+of what you mean that which I worked 120
+
+ align:start position:0%
+of what you mean that which I worked 120
+ 
+
+ align:start position:0%
+of what you mean that which I worked 120
+years ago little did I know - yeah I
+
+ align:start position:0%
+years ago little did I know - yeah I
+ 
+
+ align:start position:0%
+years ago little did I know - yeah I
+mean because there's no there's no
+
+ align:start position:0%
+mean because there's no there's no
+ 
+
+ align:start position:0%
+mean because there's no there's no
+that's why I wanted to wrap this around
+
+ align:start position:0%
+that's why I wanted to wrap this around
+ 
+
+ align:start position:0%
+that's why I wanted to wrap this around
+the idea of a soda pop it's like it's
+
+ align:start position:0%
+the idea of a soda pop it's like it's
+ 
+
+ align:start position:0%
+the idea of a soda pop it's like it's
+nothing new in some sense contract law
+
+ align:start position:0%
+nothing new in some sense contract law
+ 
+
+ align:start position:0%
+nothing new in some sense contract law
+has always dealt with machines that are
+
+ align:start position:0%
+has always dealt with machines that are
+ 
+
+ align:start position:0%
+has always dealt with machines that are
+delivering on obligations it's just a
+
+ align:start position:0%
+delivering on obligations it's just a
+ 
+
+ align:start position:0%
+delivering on obligations it's just a
+more sophisticated set of proves you're
+
+ align:start position:0%
+more sophisticated set of proves you're
+ 
+
+ align:start position:0%
+more sophisticated set of proves you're
+gonna have to make in the court but it's
+
+ align:start position:0%
+gonna have to make in the court but it's
+ 
+
+ align:start position:0%
+gonna have to make in the court but it's
+the same underlying one more question I
+
+ align:start position:0%
+the same underlying one more question I
+ 
+
+ align:start position:0%
+the same underlying one more question I
+mean it's just we're supposed to we
+
+ align:start position:0%
+mean it's just we're supposed to we
+ 
+
+ align:start position:0%
+mean it's just we're supposed to we
+always we're MIT we supposed to end five
+
+ align:start position:0%
+always we're MIT we supposed to end five
+ 
+
+ align:start position:0%
+always we're MIT we supposed to end five
+minutes early
+
+ align:start position:0%
+minutes early
+ 
+
+ align:start position:0%
+minutes early
+okay I don't know what you do it or I
+
+ align:start position:0%
+okay I don't know what you do it or I
+ 
+
+ align:start position:0%
+okay I don't know what you do it or I
+don't remember yeah it's Harvard Law you
+
+ align:start position:0%
+don't remember yeah it's Harvard Law you
+ 
+
+ align:start position:0%
+don't remember yeah it's Harvard Law you
+know question from Elan which is a lot
+
+ align:start position:0%
+know question from Elan which is a lot
+ 
+
+ align:start position:0%
+know question from Elan which is a lot
+of the contracts you're talking about
+
+ align:start position:0%
+of the contracts you're talking about
+ 
+
+ align:start position:0%
+of the contracts you're talking about
+simple contracts right you've got
+
+ align:start position:0%
+simple contracts right you've got
+ 
+
+ align:start position:0%
+simple contracts right you've got
+individuals on one side got large
+
+ align:start position:0%
+individuals on one side got large
+ 
+
+ align:start position:0%
+individuals on one side got large
+companies like your insurance company
+
+ align:start position:0%
+companies like your insurance company
+ 
+
+ align:start position:0%
+companies like your insurance company
+other the insurance company can't in
+
+ align:start position:0%
+other the insurance company can't in
+ 
+
+ align:start position:0%
+other the insurance company can't in
+fact go through the entire decision tree
+
+ align:start position:0%
+fact go through the entire decision tree
+ 
+
+ align:start position:0%
+fact go through the entire decision tree
+and decide what every term is in their
+
+ align:start position:0%
+and decide what every term is in their
+ 
+
+ align:start position:0%
+and decide what every term is in their
+favor and the law deals with that all
+
+ align:start position:0%
+favor and the law deals with that all
+ 
+
+ align:start position:0%
+favor and the law deals with that all
+the time but here you have another
+
+ align:start position:0%
+the time but here you have another
+ 
+
+ align:start position:0%
+the time but here you have another
+problem which is now it's going to be
+
+ align:start position:0%
+problem which is now it's going to be
+ 
+
+ align:start position:0%
+problem which is now it's going to be
+okay it's going to be written computer
+
+ align:start position:0%
+okay it's going to be written computer
+ 
+
+ align:start position:0%
+okay it's going to be written computer
+code how the judge is going to deal with
+
+ align:start position:0%
+code how the judge is going to deal with
+ 
+
+ align:start position:0%
+code how the judge is going to deal with
+that now it's in a language that is
+
+ align:start position:0%
+that now it's in a language that is
+ 
+
+ align:start position:0%
+that now it's in a language that is
+going to be even tougher to deal with
+
+ align:start position:0%
+going to be even tougher to deal with
+ 
+
+ align:start position:0%
+going to be even tougher to deal with
+that problem and the answer is so this
+
+ align:start position:0%
+that problem and the answer is so this
+ 
+
+ align:start position:0%
+that problem and the answer is so this
+is actually a another version of your
+
+ align:start position:0%
+is actually a another version of your
+ 
+
+ align:start position:0%
+is actually a another version of your
+question the answer to that is nobody
+
+ align:start position:0%
+question the answer to that is nobody
+ 
+
+ align:start position:0%
+question the answer to that is nobody
+knows right now and so this issue gets
+
+ align:start position:0%
+knows right now and so this issue gets
+ 
+
+ align:start position:0%
+knows right now and so this issue gets
+raised in a lot of parallel contexts for
+
+ align:start position:0%
+raised in a lot of parallel contexts for
+ 
+
+ align:start position:0%
+raised in a lot of parallel contexts for
+example there's a Supreme Court justice
+
+ align:start position:0%
+example there's a Supreme Court justice
+ 
+
+ align:start position:0%
+example there's a Supreme Court justice
+from California who's doing a lot of
+
+ align:start position:0%
+from California who's doing a lot of
+ 
+
+ align:start position:0%
+from California who's doing a lot of
+work about the question of black boxes
+
+ align:start position:0%
+work about the question of black boxes
+ 
+
+ align:start position:0%
+work about the question of black boxes
+that predict whether you are likely to
+
+ align:start position:0%
+that predict whether you are likely to
+ 
+
+ align:start position:0%
+that predict whether you are likely to
+commit a crime again so like if you're
+
+ align:start position:0%
+commit a crime again so like if you're
+ 
+
+ align:start position:0%
+commit a crime again so like if you're
+convicted of crime the question is well
+
+ align:start position:0%
+convicted of crime the question is well
+ 
+
+ align:start position:0%
+convicted of crime the question is well
+you're gonna have parole the parole juh
+
+ align:start position:0%
+you're gonna have parole the parole juh
+ 
+
+ align:start position:0%
+you're gonna have parole the parole juh
+the parole process is supposed to decide
+
+ align:start position:0%
+the parole process is supposed to decide
+ 
+
+ align:start position:0%
+the parole process is supposed to decide
+your likelihood of committing a crime so
+
+ align:start position:0%
+your likelihood of committing a crime so
+ 
+
+ align:start position:0%
+your likelihood of committing a crime so
+these companies have built these black
+
+ align:start position:0%
+these companies have built these black
+ 
+
+ align:start position:0%
+these companies have built these black
+boxes where you spit in every bit of
+
+ align:start position:0%
+boxes where you spit in every bit of
+ 
+
+ align:start position:0%
+boxes where you spit in every bit of
+data and it comes out and says yes
+
+ align:start position:0%
+data and it comes out and says yes
+ 
+
+ align:start position:0%
+data and it comes out and says yes
+you're a criminal or no you're not and
+
+ align:start position:0%
+you're a criminal or no you're not and
+ 
+
+ align:start position:0%
+you're a criminal or no you're not and
+then the lawyers come forward they say
+
+ align:start position:0%
+then the lawyers come forward they say
+ 
+
+ align:start position:0%
+then the lawyers come forward they say
+well I want to interrogate the black box
+
+ align:start position:0%
+well I want to interrogate the black box
+ 
+
+ align:start position:0%
+well I want to interrogate the black box
+I want to know what and the courts are
+
+ align:start position:0%
+I want to know what and the courts are
+ 
+
+ align:start position:0%
+I want to know what and the courts are
+come
+
+ align:start position:0%
+come
+ 
+
+ align:start position:0%
+come
+confused about this because on the one
+
+ align:start position:0%
+confused about this because on the one
+ 
+
+ align:start position:0%
+confused about this because on the one
+hand they say no no this is their trade
+
+ align:start position:0%
+hand they say no no this is their trade
+ 
+
+ align:start position:0%
+hand they say no no this is their trade
+secret but on the other hand they're
+
+ align:start position:0%
+secret but on the other hand they're
+ 
+
+ align:start position:0%
+secret but on the other hand they're
+like wait wait a minute you can't decide
+
+ align:start position:0%
+like wait wait a minute you can't decide
+ 
+
+ align:start position:0%
+like wait wait a minute you can't decide
+whether I have Liberty or not based on
+
+ align:start position:0%
+whether I have Liberty or not based on
+ 
+
+ align:start position:0%
+whether I have Liberty or not based on
+these black boxes that just spit out
+
+ align:start position:0%
+these black boxes that just spit out
+ 
+
+ align:start position:0%
+these black boxes that just spit out
+numbers right so I've got to be able to
+
+ align:start position:0%
+numbers right so I've got to be able to
+ 
+
+ align:start position:0%
+numbers right so I've got to be able to
+interrogate right so this is the most
+
+ align:start position:0%
+interrogate right so this is the most
+ 
+
+ align:start position:0%
+interrogate right so this is the most
+important innovation that's got to
+
+ align:start position:0%
+important innovation that's got to
+ 
+
+ align:start position:0%
+important innovation that's got to
+happen in law lawyers have to become
+
+ align:start position:0%
+happen in law lawyers have to become
+ 
+
+ align:start position:0%
+happen in law lawyers have to become
+technically sophisticated to be able to
+
+ align:start position:0%
+technically sophisticated to be able to
+ 
+
+ align:start position:0%
+technically sophisticated to be able to
+read code like they read legal contracts
+
+ align:start position:0%
+read code like they read legal contracts
+ 
+
+ align:start position:0%
+read code like they read legal contracts
+they have to have a conceptual
+
+ align:start position:0%
+they have to have a conceptual
+ 
+
+ align:start position:0%
+they have to have a conceptual
+understanding of what code can do so
+
+ align:start position:0%
+understanding of what code can do so
+ 
+
+ align:start position:0%
+understanding of what code can do so
+they can think creatively about code
+
+ align:start position:0%
+they can think creatively about code
+ 
+
+ align:start position:0%
+they can think creatively about code
+like they think creatively about
+
+ align:start position:0%
+like they think creatively about
+ 
+
+ align:start position:0%
+like they think creatively about
+language right and one of the most
+
+ align:start position:0%
+language right and one of the most
+ 
+
+ align:start position:0%
+language right and one of the most
+important innovations that we you know
+
+ align:start position:0%
+important innovations that we you know
+ 
+
+ align:start position:0%
+important innovations that we you know
+like we'd like the Berkman Center and
+
+ align:start position:0%
+like we'd like the Berkman Center and
+ 
+
+ align:start position:0%
+like we'd like the Berkman Center and
+people like that are trying to push into
+
+ align:start position:0%
+people like that are trying to push into
+ 
+
+ align:start position:0%
+people like that are trying to push into
+the legal environment is to insist that
+
+ align:start position:0%
+the legal environment is to insist that
+ 
+
+ align:start position:0%
+the legal environment is to insist that
+just like lawyers now all study
+
+ align:start position:0%
+just like lawyers now all study
+ 
+
+ align:start position:0%
+just like lawyers now all study
+economics because that's a core way of
+
+ align:start position:0%
+economics because that's a core way of
+ 
+
+ align:start position:0%
+economics because that's a core way of
+thinking about the law we also should
+
+ align:start position:0%
+thinking about the law we also should
+ 
+
+ align:start position:0%
+thinking about the law we also should
+study basic code so we should can think
+
+ align:start position:0%
+study basic code so we should can think
+ 
+
+ align:start position:0%
+study basic code so we should can think
+about this modality of regulation not to
+
+ align:start position:0%
+about this modality of regulation not to
+ 
+
+ align:start position:0%
+about this modality of regulation not to
+expect people to be writing code but at
+
+ align:start position:0%
+expect people to be writing code but at
+ 
+
+ align:start position:0%
+expect people to be writing code but at
+least that they can think through it so
+
+ align:start position:0%
+least that they can think through it so
+ 
+
+ align:start position:0%
+least that they can think through it so
+I completely agree that's a that's a you
+
+ align:start position:0%
+I completely agree that's a that's a you
+ 
+
+ align:start position:0%
+I completely agree that's a that's a you
+know a fudge States that I didn't talk
+
+ align:start position:0%
+know a fudge States that I didn't talk
+ 
+
+ align:start position:0%
+know a fudge States that I didn't talk
+about at all but I think it's a really
+
+ align:start position:0%
+about at all but I think it's a really
+ 
+
+ align:start position:0%
+about at all but I think it's a really
+important problem thinking about whether
+
+ align:start position:0%
+important problem thinking about whether
+ 
+
+ align:start position:0%
+important problem thinking about whether
+the legal system is gonna be able to
+
+ align:start position:0%
+the legal system is gonna be able to
+ 
+
+ align:start position:0%
+the legal system is gonna be able to
+deal with it because if none of the
+
+ align:start position:0%
+deal with it because if none of the
+ 
+
+ align:start position:0%
+deal with it because if none of the
+lawyers understand it I'm yeah let me
+
+ align:start position:0%
+lawyers understand it I'm yeah let me
+ 
+
+ align:start position:0%
+lawyers understand it I'm yeah let me
+just end with one story about that so
+
+ align:start position:0%
+just end with one story about that so
+ 
+
+ align:start position:0%
+just end with one story about that so
+when I first started doing this work
+
+ align:start position:0%
+when I first started doing this work
+ 
+
+ align:start position:0%
+when I first started doing this work
+talking about code and regular I went to
+
+ align:start position:0%
+talking about code and regular I went to
+ 
+
+ align:start position:0%
+talking about code and regular I went to
+Paris 20 years ago and I gave a speech
+
+ align:start position:0%
+Paris 20 years ago and I gave a speech
+ 
+
+ align:start position:0%
+Paris 20 years ago and I gave a speech
+to some lawyer group and I sat down
+
+ align:start position:0%
+to some lawyer group and I sat down
+ 
+
+ align:start position:0%
+to some lawyer group and I sat down
+after the speech and the chairman of
+
+ align:start position:0%
+after the speech and the chairman of
+ 
+
+ align:start position:0%
+after the speech and the chairman of
+this buccal group sat down next to me
+
+ align:start position:0%
+this buccal group sat down next to me
+ 
+
+ align:start position:0%
+this buccal group sat down next to me
+and I introduced myself and he stood up
+
+ align:start position:0%
+and I introduced myself and he stood up
+ 
+
+ align:start position:0%
+and I introduced myself and he stood up
+and he grabbed my card and he crushed it
+
+ align:start position:0%
+and he grabbed my card and he crushed it
+ 
+
+ align:start position:0%
+and he grabbed my card and he crushed it
+and he threw it to the ground and he
+
+ align:start position:0%
+and he threw it to the ground and he
+ 
+
+ align:start position:0%
+and he threw it to the ground and he
+said I am NOT a technician and his point
+
+ align:start position:0%
+said I am NOT a technician and his point
+ 
+
+ align:start position:0%
+said I am NOT a technician and his point
+was he is a lawyer could never accept
+
+ align:start position:0%
+was he is a lawyer could never accept
+ 
+
+ align:start position:0%
+was he is a lawyer could never accept
+the idea that what he needed to
+
+ align:start position:0%
+the idea that what he needed to
+ 
+
+ align:start position:0%
+the idea that what he needed to
+understand was code like that was
+
+ align:start position:0%
+understand was code like that was
+ 
+
+ align:start position:0%
+understand was code like that was
+forbidden it was beneath him and I think
+
+ align:start position:0%
+forbidden it was beneath him and I think
+ 
+
+ align:start position:0%
+forbidden it was beneath him and I think
+it's a you know it's a hugely important
+
+ align:start position:0%
+it's a you know it's a hugely important
+ 
+
+ align:start position:0%
+it's a you know it's a hugely important
+cultural problem - like integrate this
+
+ align:start position:0%
+cultural problem - like integrate this
+ 
+
+ align:start position:0%
+cultural problem - like integrate this
+form of knowledge because if we don't
+
+ align:start position:0%
+form of knowledge because if we don't
+ 
+
+ align:start position:0%
+form of knowledge because if we don't
+then the problem you're talking about is
+
+ align:start position:0%
+then the problem you're talking about is
+ 
+
+ align:start position:0%
+then the problem you're talking about is
+really a huge problem but I think we can
+
+ align:start position:0%
+really a huge problem but I think we can
+ 
+
+ align:start position:0%
+really a huge problem but I think we can
+because we've seen last
+
+ align:start position:0%
+because we've seen last
+ 
+
+ align:start position:0%
+because we've seen last
+so I want to thank you on behalf of the
+
+ align:start position:0%
+so I want to thank you on behalf of the
+ 
+
+ align:start position:0%
+so I want to thank you on behalf of the
+class blockchain money I also want to
+
+ align:start position:0%
+class blockchain money I also want to
+ 
+
+ align:start position:0%
+class blockchain money I also want to
+say you're much better than Christopher
+
+ align:start position:0%
+say you're much better than Christopher
+ 
+
+ align:start position:0%
+say you're much better than Christopher
+Lloyd if anybody wants to know the joke
+
+ align:start position:0%
+Lloyd if anybody wants to know the joke
+ 
+
+ align:start position:0%
+Lloyd if anybody wants to know the joke
+watch that West weaning episode that
+
+ align:start position:0%
+watch that West weaning episode that
+ 
+
+ align:start position:0%
+watch that West weaning episode that
+Christopher Lloyd plays Professor
+
+ align:start position:0%
+Christopher Lloyd plays Professor
+ 
+
+ align:start position:0%
+Christopher Lloyd plays Professor
+Lawrence Lessig so thank you see you on
+
+ align:start position:0%
+Lawrence Lessig so thank you see you on
+ 
+
+ align:start position:0%
+Lawrence Lessig so thank you see you on
+Thursday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/K1w2o5i0NGQ.txt b/K1w2o5i0NGQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..30ba702af931298ab6ff1f3f2f770eb7bb096efa
--- /dev/null
+++ b/K1w2o5i0NGQ.txt
@@ -0,0 +1,2077 @@
+III The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: All right.
+
+We'll back up and start again
+since I just turned on my
+
+microphone.
+
+I started with the observation
+that for most of recorded
+
+history people thought
+qualitatively, not
+
+quantitatively.
+
+They didn't know what
+statistics were.
+
+They must have had some
+intuitive sense, for example,
+
+that if you're old, you're
+more likely to have bad
+
+hearing than if you're young.
+
+If you're old you're
+more likely to die
+
+than if you're young.
+
+Things like that.
+
+But they were just anecdotes,
+and they had no careful way to
+
+go from statements about
+individuals to statements
+
+about populations
+or expectations.
+
+This changed in about the middle
+of the 17th century,
+
+changed fairly dramatically,
+when an Englishman named John
+
+Graunt published something
+called The Natural and
+
+Political Observations Made Upon
+the Bills of Mortality.
+
+This was the first work in
+recorded history that actually
+
+used statistics.
+
+And what he did is he looked
+at the fairly comprehensive
+
+statistics of when people died
+in the city of London.
+
+And from that, attempted to
+produce a model that could be
+
+used to predict the spread
+of the plague.
+
+And it turns out, he was
+pretty good at it.
+
+And that just changed the way
+people started to think.
+
+And since that time, people have
+used statistics both to
+
+inform and, unfortunately,
+to mislead.
+
+Some have willfully used
+statistics to mislead, others
+
+have merely been incompetent.
+
+And that gets me to what I
+want to talk about today,
+
+which is statistics.
+
+This is often attributed to Mark
+Twain but, in fact, he
+
+copied it from Benjamin
+Disraeli, who said, "There are
+
+three kinds of lies: lies,
+damned lies, and statistics."
+
+And there is, unfortunately,
+a lot of truth in that.
+
+More recently, in the '50s
+Darrell Huff wrote a wonderful
+
+book, I recommend it, called
+How to Lie with Statistics.
+
+Now here's a quote from the
+book, "If you can't prove what
+
+you want to prove, demonstrate
+something else and pretend
+
+that they're the same thing.
+
+In the daze that follows the
+collision of statistics with
+
+the human mind, hardly anyone
+will notice the difference."
+
+Alas, that seems to be true.
+
+So what I want to do today is
+talk about a few ways in which
+
+one can be fooled into drawing
+inappropriate conclusions from
+
+statistical data.
+
+Now I trust that you
+will use this
+
+information only for good.
+
+And it will make you a better
+consumer and purveyor of data
+
+rather than a better liar,
+but that's up to you.
+
+All right.
+
+So let's start with the
+first way out thing I
+
+want to talk about.
+
+And it's important to always
+remember that no matter how
+
+good your statistics are,
+statistical measures don't
+
+tell the whole story.
+
+We've seen examples of this
+already earlier in the term.
+
+There are an enormous set of
+statistics that can be
+
+extracted from a data set.
+
+And by carefully picking and
+choosing among them, it's
+
+possible to convey almost any
+impression you want about the
+
+same data set.
+
+The best antidote, of course, is
+to look at the data itself.
+
+In 1973, the statistician John
+Anscombe published a paper
+
+with this set of data.
+
+Four different examples where
+he gave values for x and y,
+
+nothing very sophisticated.
+
+The interesting thing is that
+in many ways, the statistics
+
+for these four data sets
+are very similar.
+
+They have the same mean, the
+same median, the same variance
+
+for x and y both, the same
+correlation between x and y.
+
+And even if we use linear
+regression to get a fit, we
+
+get very similar things.
+
+So let's look at it.
+
+I actually wrote some
+code to do that.
+
+So this just reads in the data
+set that we just had up, and
+
+then plots some things
+with it.
+
+And so let's look at it.
+
+So what you can see is, you have
+these in your hand out,
+
+we have four graphs,
+four plots.
+
+And I won't show you
+them all because
+
+they're all are identical.
+
+What they all give me is a mean
+of 7.5 and a whole bunch
+
+of things, same to 17 decimal
+places or so, the same median
+
+and the same linear fit,
+y equals 0.5x plus 3.
+
+So I might write a paper in
+which I would tell you that
+
+well, from a statistical
+sense, these data
+
+sets are all the same.
+
+Every statistical result I
+ran said these things are
+
+indistinguishable.
+
+Well, is it true that
+these data sets are
+
+indistinguishable?
+
+Well, one way to look at it is
+to actually plot the points.
+
+So we can run it with true,
+which says in addition to
+
+plotting the data, put points
+on them in addition to
+
+plotting the statistics.
+
+And now we see something
+fairly dramatic.
+
+So for example, figure (2) and
+figure (1) don't look a lot
+
+like each other, when we
+actually look at the data.
+
+Figure (3) looks quite different
+and figure (4) is
+
+remarkably different.
+
+Compare figure (4) to,
+say, figure (1).
+
+Again, these are all
+in your hand out.
+
+So the moral is pretty simple
+here, and it's one we looked
+
+at before, which is, don't
+ever ignore the data.
+
+Don't just look at statistics
+about the data, try and find a
+
+way to look at the
+data itself.
+
+Of course, it's easy enough to
+look at the data, but how do
+
+you look at it?
+
+And the next thing to
+remember is that
+
+pictures can be deceiving.
+
+There can be no doubt about the
+utility of graphics for
+
+quickly conveying information.
+
+However, when used carelessly or
+maliciously, a plot can be
+
+highly misleading.
+
+So let's look-- go back to the
+PowerPoint, and look at this
+
+plot of housing prices
+in the Midwest.
+
+So we've got a plot here, and
+we've got years 2006, 2007 and
+
+then in 2008 and 9,
+we have quarters.
+
+You may remember that there was
+an event in the housing
+
+market in 2008 precipitating the
+global financial crisis.
+
+And if we look at this, what
+impression do we get about
+
+housing prices in the mid
+west during this period?
+
+Well I would get the impression
+that they are
+
+remarkably stable.
+
+You publish this and you say,
+OK, look they really haven't
+
+changed very much.
+
+Maybe they've gone down
+a little, but
+
+nothing very serious.
+
+If we compare that to this plot,
+which is exactly the
+
+same data, and now I ask
+you about housing
+
+prices in the Midwest.
+
+Well, what you might
+tell me is it's--
+
+they're remarkably unstable.
+
+And in fact, there was
+clearly some sort of
+
+horrible event here.
+
+Exactly the same data, two
+plots both of which are
+
+truthful, but which give a
+radically different impression
+
+about what happened.
+
+The chart on the right
+was designed--
+
+on the right in your handout--
+
+was designed to show that they
+were highly unstable.
+
+So what's the difference?
+
+What trick did I use to produce
+these two plots?
+
+Yeah?
+
+AUDIENCE: In the more
+stable one, you used
+
+the logarithmic scale.
+
+And then here only has
+selected numbers so--
+
+PROFESSOR: So that
+was certainly one
+
+trick that I performed.
+
+That in the first chart,
+I plotted the y-axis
+
+logarithmically, which always
+make things look like they are
+
+changing less than if
+I plot it linearly.
+
+And in this chart, I
+used a linear plot.
+
+Go ahead.
+
+AUDIENCE: You see a much
+narrower scale
+
+on the second plot.
+
+So that the magnitude of the
+difference is much less
+
+compared to the magnitude of the
+whole graph of the scale.
+
+PROFESSOR: So that's the other
+thing I did is, if you look at
+
+it, I sort of cheated.
+
+I had full years here and
+then I went to quarters.
+
+So in part of my chart, the
+resolution on the x is pretty
+
+wide is a whole year, and then
+part of it's on a quarter.
+
+And, not surprisingly, since
+we know that housing prices
+
+change seasonally, they're
+different in the spring than
+
+in the winter, once I start
+plotting quarters, even if
+
+there had not been a crash, it
+would have looked much less
+
+stable in the out years,
+because I changed the
+
+resolution on the x-axis.
+
+I didn't lie.
+
+You can tell reading the
+legend that I did that.
+
+But I sure could have
+fooled a lot of
+
+people with these charts.
+
+Here's another nice example
+of statistics.
+
+So this plots--
+
+this is from a paper by two
+professors, I think from Yale,
+
+shows what you can do if you're
+in the Ivy league, that
+
+plots initials against GPA
+for students at Yale.
+
+And so you can see that if your
+first name starts with
+
+the letter A, I think it was
+first initials, your GPA is
+
+considerably higher than if it
+starts with C or D. And if
+
+your parents weren't nice enough
+to give you an A name,
+
+you could hope they at least
+gave you a B name.
+
+And you certainly don't
+want them to give
+
+you a C or a D name.
+
+So if you're Charlene or David
+you could have a real problem.
+
+I have to say my first child
+was named David.
+
+His GPA might have been
+somewhere in there.
+
+All right --
+
+clearly it matters.
+
+Well, what tricks did
+I perform here?
+
+AUDIENCE: There is very
+little disparity in x.
+
+You are going from 3.32 to--
+
+PROFESSOR: Right.
+
+So what I did here is I made the
+range on the y-axis very
+
+small, ranging from 3.32 to
+3.38, not a big difference.
+
+However, because that's the
+whole thing, it looks like
+
+it's a big difference.
+
+You will often see this when
+you, say, look at things in
+
+newspapers where, in fact,
+someone has manipulated one of
+
+the axes to make things
+look big or small.
+
+If I had ranged this from a GPA
+of 0.0 to a GPA of 4.0,
+
+the highest GPA at Yale,
+this difference would
+
+have looked very tiny.
+
+But I didn't --
+
+actually it wasn't I. I actually
+copied this from
+
+their paper.
+
+This was the way they presented
+it in their paper.
+
+Because they were trying to
+argue in the paper that your
+
+name had a big influence
+on your life.
+
+And they used many statistics
+including your grades.
+
+And so they actually formatted
+it kind of like this to try
+
+and give you this impression.
+
+Now later we'll see another
+statistical sin they committed
+
+in this paper, which, basically,
+was designed to
+
+show that in your name
+was destiny.
+
+And they had many
+other things.
+
+If you're a baseball player, and
+your name starts with K,
+
+you're more likely
+to strike out.
+
+Because K is the symbol for
+strikeouts in a baseball score
+
+book, a lot of implausible
+things.
+
+All right.
+
+Moving right along, probably
+the most serious and common
+
+statistical error is
+the one known as
+
+Garbage In Garbage Out.
+
+And it's so common that people
+typically refer to it by its
+
+acronym GIGO --
+
+Garbage In Garbage Out.
+
+A classic example of this
+occurred and, we could look at
+
+more recent examples,
+but I don't want to
+
+offend any of you.
+
+In 1840, United states census
+showed that insanity among
+
+free blacks and mulattoes was
+roughly 10 times more common
+
+than insanity among enslaved
+blacks or mulattoes.
+
+And the conclusion from this
+was obvious, I guess.
+
+US Senator, former Vice
+President, and later,
+
+Secretary of State John C.
+Calhoun concluded from the
+
+census and I quote, "The data
+on sanity revealed In this
+
+census is unimpeachable.
+
+From it, our nation must
+conclude that the abolition of
+
+slavery would be to the African,
+a curse." Because
+
+after all, if you freed them
+from slavery, they
+
+would all go insane.
+
+That's what the statistics
+reported, he said.
+
+Now never mind it was soon clear
+that in fact that census
+
+was riddled with errors.
+
+And John Quincy Adams, a former
+Vice President and
+
+Massachusetts resident responded
+to Calhoun and said,
+
+no that's a ridiculous
+conclusion.
+
+The census is full of errors.
+
+Calhoun, being a very patient
+person, explained to Adams the
+
+following, "There were so many
+errors, that they balanced one
+
+another out, and led to the same
+conclusion just as much
+
+as if they were all correct."
+There were just enough errors
+
+that you could be OK.
+
+Well, what was he relying on?
+
+What should he have said if he
+wanted to make this statement
+
+more mathematically precise?
+
+What he was basically implying
+is that the measurement errors
+
+are unbiased and independent of
+each other and, therefore,
+
+almost identically distributed
+on either side of the mean.
+
+I see a typo, I might
+as well fix it.
+
+Might as well make it big
+enough to fix it.
+
+That's interesting.
+
+If he had made this much more
+precise statement, then you
+
+could have had an meaningful
+discussion--
+
+assuming it was possible to have
+a meaningful discussion
+
+with John Calhoun, which
+is perhaps dubious--
+
+about whether or not, in fact,
+the errors are independent.
+
+Because if they're not, if, for
+example, they represent
+
+bias in the people compiling the
+data, then you cannot rely
+
+upon statistical methods
+to say that they'll
+
+balance each other out.
+
+You remember way back in Gauss'
+time, Gauss talked
+
+about this when he talked about
+the normal distribution.
+
+And said, well, if we take
+these astronomical
+
+measurements and we assume our
+errors are independent and
+
+normally distributed, then we
+can look at the mean and
+
+assume that that's close
+to the truth.
+
+Well, those are important
+assumptions which in this case
+
+turned out to be not correct.
+
+And, in fact, it was later shown
+that the errors did not
+
+balance each other out nicely.
+
+And in fact, today you can say
+that no statistical conclusion
+
+can be drawn from that.
+
+On the other hand recently,
+the US National Research
+
+Council, perhaps the most
+prestigious academic
+
+organization in the United
+states, published a ranking of
+
+all universities
+in the country.
+
+And it was later shown that it
+was full of garbagy input.
+
+And they did extensive
+statistical analysis and
+
+published it on data that turned
+out to be just wrong.
+
+And it was very embarrassing.
+
+Now the good news is
+MIT came out near
+
+the top of this analysis.
+
+And the bad news is we can't
+conclude that it actually
+
+should have been near the top
+because who knows about the
+
+quality of the data, but
+kind of embarrassing.
+
+All right.
+
+Moving right along, another very
+common way to lie with
+
+statistics is to exploit what's
+called the cum hoc ergo
+
+propter hoc fallacy.
+
+So anyone here study Latin?
+
+Bunch of techy--
+
+Oh OK.
+
+Well what does it mean?
+
+AUDIENCE: With this therefore,
+because of this?
+
+PROFESSOR: Boy, your
+Latin is good.
+
+Either that or you just
+know statistics.
+
+But I have to say that was the
+most fluent translation I've
+
+had it all the years I've
+asked this question.
+
+I hit the relay man-- the relay
+woman on the throw.
+
+All right.
+
+Yes, with this, therefore
+because of this.
+
+I don't know why but
+statisticians, like physicians
+
+and attorneys, like
+to show off by
+
+phrasing things in Latin.
+
+So for example, it is a
+statistical fact that college
+
+students, including MIT
+students, who regularly attend
+
+lectures have higher GPAs than
+students who attend lectures
+
+only sporadically.
+
+So that would tell us that those
+of you in the room are
+
+likely to have a higher GPA than
+the various students in
+
+6.00 who are not in this room.
+
+I hope it's true.
+
+Now if you're a professor who
+gives these lectures, what you
+
+want to believe it's because the
+lectures are so incredibly
+
+informative, that we make the
+students who come much smarter
+
+and, therefore, they
+do better.
+
+And so we'd like to
+assume causality.
+
+Because I give beautiful
+lectures and you choose to
+
+come, you will get a better
+grade in 6.00.
+
+Well, yes, there's
+a correlation.
+
+It's unquestionably true, but
+causation is hard to jump to.
+
+For example, maybe it's the
+point that students who bother
+
+to come to lecture also bother
+to do the problem sets, and
+
+are just more conscientious.
+
+And whether they came to lecture
+or not, the fact that
+
+they're more conscientious would
+give them better GPAs.
+
+There's no way I know to
+separate those two things,
+
+other than doing a controlled
+experiment, right?
+
+Maybe kicking half of you out of
+lecture every day and just
+
+see how it goes.
+
+But it's dangerous but again,
+you can read things like the
+
+faculty newsletter, which will
+talk about how important it is
+
+to come the lecture because
+you'll do better.
+
+Because whoever wrote that
+article for the faculty
+
+newsletter didn't understand
+this--
+
+this fallacy, or was just
+thinking wishfully.
+
+Another nice example, one that
+was in the news not too long
+
+ago, has to do with the flu.
+
+This was the cases of
+flu in New York
+
+State in recent years.
+
+And you'll notice that there was
+a peak in 2009, and that
+
+was the famous swine flu
+epidemic, which I'm sure you
+
+all remember.
+
+Now, if you look at this
+carefully, or even not too
+
+carefully, you'll notice a
+correlation between when
+
+schools are in session and
+when the flu occurs.
+
+That in fact, during those
+months when schools are in
+
+session, there are more cases of
+flu than in the months when
+
+school is not in session, high
+schools, colleges, whatever.
+
+Quite a strong correlation,
+in fact.
+
+This led many to conclude that
+going to school is an
+
+important causative factor
+in getting the flu.
+
+And so maybe you shouldn't
+have come to the lectures
+
+because you would have just
+gotten the flu by doing so.
+
+And in fact because of this,
+you had many parents not
+
+sending their kids to school
+during the swine flu epidemic.
+
+And in fact, you had many
+schools closing in some
+
+communities because of the
+swine flu epidemic.
+
+Well, let's think about it.
+
+Just as you could use this
+correlation to conclude that
+
+going to school causes the swine
+flu, you could have also
+
+used it to prove that the flu
+causes you to go to school.
+
+Because more people are in
+school when the flu season is
+
+at it's height.
+
+And therefore, it's the growth
+of flu that causes people to
+
+go to school.
+
+That's an equally valid
+statistical
+
+assumption from this data.
+
+Kind of a weird thing but
+it's true, right?
+
+Just as we could conclude that
+having a high GPA causes
+
+people to come to the lecture.
+
+You look at your GPA every
+morning, and if it's high
+
+enough, you come to lecture,
+otherwise, you don't.
+
+You could draw that conclusion
+from the data as well.
+
+The issue here that you have to
+think about is whether or
+
+not there is what's called a
+lurking variable, some other
+
+variable that's related to the
+other two, and maybe that's
+
+the causative one.
+
+So for example, a lurking
+variable here is that the
+
+school season coincides with
+or the non-school season,
+
+maybe I should say, coincides
+with the summer.
+
+And in fact, if you study the
+flu virus in a lab, you will
+
+discover that it survives longer
+in cold weather than in
+
+hot and humid weather.
+
+When it's cold and dry, the flu
+virus will survive for a
+
+longer time on a surface
+than it will when
+
+it's warm and humid.
+
+And so in fact, maybe it's the
+weather, not the presence of
+
+schools, that causes the flu
+to be more virulent during
+
+certain times of the year.
+
+In fact, it's probably
+likely true.
+
+So there is a lurking variable
+that we have to consider, and
+
+maybe that's the causative
+factor.
+
+Now, this can actually lead
+to some really bad
+
+decisions in the world.
+
+I'm particularly interested in
+issues related to health care
+
+and public health.
+
+In 2002, roughly 6 million
+American women were taking
+
+hormone replacement therapy, in
+the belief that this would
+
+substantially lower their risk
+of cardiovascular disease.
+
+It was argued that women over a
+certain age or of a certain
+
+age, if you took extra hormones,
+they were less
+
+likely to have a heart attack.
+
+This belief was supported by
+several published studies in
+
+highly reputable journals in
+which they showed a strong
+
+correlation between being on
+hormone replacement therapy
+
+and not having cardiovascular
+disease.
+
+And this data had been around
+a while and, as I said, by
+
+2002 in the US, roughly
+6 million women
+
+were on this therapy.
+
+Later that year, the Journal
+of the American Medical
+
+Society published an article
+asserting that in fact being
+
+on this therapy increased
+women's risk of
+
+cardiovascular disease.
+
+It made you more likely to
+have a heart attack.
+
+Well, how could this
+have happened?
+
+After the new study came out,
+people went back and
+
+reanalyzed the old study and
+discovered that the women in
+
+that study who'd been on hormone
+replacement therapy
+
+were more likely than the other
+women in the group to
+
+have also better diet and be on
+a better exercise regimen.
+
+In fact, they were women who
+were more health conscious.
+
+So there were the lurking
+variables of diet and exercise
+
+and other things that were, in
+fact, probably the causative
+
+factors in better health, not
+the replacement therapy.
+
+But there was this lurking
+variable that had not been
+
+discovered in the initial
+analysis of the data.
+
+So what we saw is that taking
+hormone replacement therapy
+
+and improved cardiac health were
+coincident effects of a
+
+common cause, that is to say
+being health conscious.
+
+Kind of a strange thing but
+a true and sad story.
+
+All right.
+
+Moving right along, another
+thing to be cautious of is
+
+non-response bias and
+related problem of a
+
+non-representative sample.
+
+You'll probably recall that when
+I first started talking
+
+about statistics and the use of
+randomness, I said that all
+
+statistical techniques are based
+upon the assumption that
+
+by sampling a subset of a
+population, we can infer
+
+things about the population
+as a whole.
+
+And that's true, typically,
+because if random sampling is
+
+used, you can make assumptions
+that the distribution of
+
+results from the random sample,
+if it's large enough,
+
+will be the same as a
+distribution of results from
+
+the whole population.
+
+And that's why we typically
+want to sample randomly.
+
+And so for all the simulations
+we looked at, we used random
+
+sampling to try and ensure that
+a small number of samples
+
+would give us something
+representative of the
+
+population.
+
+And then we use statistical
+techniques to answer the
+
+question about how many random
+samples we needed.
+
+But those techniques were only
+valid if the samples were
+
+indeed random.
+
+Otherwise, you can analyze it
+to your heart's content and
+
+any conclusions you've drawn are
+likely to be fallacious.
+
+Unfortunately, many studies,
+particularly in the social
+
+sciences, are based on
+what is often called
+
+a convenience sampling.
+
+So for example, if you look
+at psychological--
+
+psychology journals, you'll find
+that many psychological
+
+studies use populations of
+
+undergraduates for their studies.
+
+Why did they do this?
+
+Is it because they believe
+that undergraduates are
+
+representative of the population
+as a whole?
+
+No.
+
+It's because they're captive.
+
+They have to agree to
+participate, right?
+
+It's a convenience if you happen
+to be at a university
+
+to do your experiments
+on undergraduates.
+
+And so they do that and then
+they say, well, the
+
+undergraduates are just like
+the population as a whole.
+
+You may have observed that at
+least at this institution, the
+
+undergraduates are probably
+not representative of the
+
+population as a whole.
+
+A well-known example of what you
+can do with this occurred
+
+during World War II.
+
+Whenever an allied plane would
+return from a bombing run over
+
+Germany, the plane would be
+inspected to see where flak
+
+had hit it.
+
+So the planes would fly over
+to drop bombs, the Germans
+
+would shoot flak at the planes
+to try and knock
+
+them out the air.
+
+They'd come back to England,
+they'd get inspected, they'd
+
+say, well the flak hit this part
+of the plane more often
+
+than that part of the
+plane on average.
+
+And so they would reinforce the
+skin of those parts of the
+
+plane where they expected the
+flak to hit, to try and make
+
+the plane less likely to be
+damaged in future runs, or the
+
+planes in general.
+
+What's wrong with this?
+
+Yeah?
+
+AUDIENCE: They're not getting
+the planes that dropped?
+
+PROFESSOR: Exactly.
+
+What they're not sampling is the
+planes that never made it
+
+back from the bombing, ooh, that
+never made it back from
+
+the bombing runs because they
+weren't there to sample.
+
+And in fact maybe it's the case
+that what they were doing
+
+was reinforcing those parts of
+the planes where it didn't
+
+matter if you got hit by flak
+because it wouldn't cause a
+
+plane to crash, and not
+reinforcing those parts of the
+
+planes that were most
+vulnerable to
+
+being damaged by flak.
+
+They did a convenient
+sampling, they drew
+
+conclusions, and they probably
+did exactly the wrong thing in
+
+what they chose to reinforce
+in the airplanes.
+
+This particular error is called
+non-response bias where
+
+you do some sort of survey, for
+example, and some people
+
+don't respond and, therefore,
+you ignore what
+
+they would have said.
+
+It's perhaps something we see
+when we do the underground
+
+guide to Course 6.
+
+In fact I should point out
+that it's now online.
+
+And it would be good if each of
+you would go and rate this
+
+course, rate the lectures,
+rate the TAs, et cetera.
+
+We actually do read them and it
+makes a difference in how
+
+we teach the course in
+subsequent terms.
+
+But there's clearly a bias.
+
+You know, maybe only the
+people who really feel
+
+strongly about the course,
+either positively or
+
+negatively, bother to
+fill out the survey.
+
+And we draw the conclusions
+that there's a bimodal
+
+distribution, and nobody thinks
+it's kind of mediocre,
+
+because they don't bother
+responding.
+
+Or maybe only the people who
+hate the course respond, and
+
+we think everybody
+hates the course.
+
+Who knows.
+
+It's a big problem.
+
+We see it, it's a big problem
+today with telephone polls,
+
+where you get more convenient
+sampling and
+
+non-representative samples,
+where a lot of polls are done
+
+using telephones.
+
+By law, these pollsters cannot
+call cell phones, so they only
+
+call land lines.
+
+How many of you have
+a land line?
+
+Let the record show, nobody.
+
+How many of your parents
+have a land line?
+
+Let the record show, pretty
+much everybody.
+
+Well, that means your parents
+are more likely to get sampled
+
+than you when there's a poll
+of, say, who should be
+
+nominated for president.
+
+And so any of these polls
+that are based on
+
+telephones will be biased.
+
+And, unfortunately, their poll
+may just say, a telephone
+
+sample, and people may
+not realize the
+
+implication of that.
+
+That whole part of the
+population is under sampled.
+
+There are lots of examples
+of this.
+
+All right.
+
+Moving along, another problem
+we often see is data
+
+enhancement.
+
+It's easy to read much more
+into data than it actually
+
+implies, especially when
+viewed out of context.
+
+So on April 29, 2009, CNN
+reported that quote, "Mexican
+
+health officials suspect that
+the swine flu outbreak has
+
+caused more than 159 deaths and
+roughly 2,500 illnesses."
+
+It was pretty scary stuff at the
+time, and people got all
+
+worried about the swine flu.
+
+On the other hand, how many
+deaths a year do you think are
+
+attributable to the
+conventional
+
+seasonal flu in the US?
+
+Anyone want to hazard a guess?
+
+36,000.
+
+So 36,000 people a year, on
+average, will die from the
+
+seasonal flu, which sort of puts
+in prospective that 159
+
+deaths from the swine flu
+maybe shouldn't be so
+
+terrifying.
+
+But again, people typically did
+not report both of those.
+
+Another great statistic, and
+accurate, is that most auto
+
+accidents happen within
+10 miles of home.
+
+I'm sure many of you
+have heard that.
+
+So what does that mean?
+
+Almost nothing.
+
+Most driving is done
+with 10 miles--
+
+within 10 miles of home.
+
+And besides that, what does
+home mean in this context?
+
+What home means is
+the registration
+
+address of the car.
+
+So if I were to choose to
+register my car in Alaska,
+
+does that mean I'm less likely
+to have an accident driving
+
+around MIT?
+
+I don't think so.
+
+Again, it's a kind
+of a meaningless.
+
+Another aspect of this
+is people often
+
+extrapolate from data.
+
+So we can look at an example
+of internet usage.
+
+This is kind of a fun one too.
+
+So what I've plotted here is
+the internet usage in the
+
+United states as a percentage
+of population.
+
+And I plotted of this from--
+
+starting at 1994.
+
+And the green line, or actually,
+the blue line there
+
+are the points and the green
+line is a linear fit.
+
+If you looked at my code, you'd
+see I was using polyfit
+
+with a 1 to get a line to fit,
+and you can see it's a pretty
+
+darn good fit.
+
+So people actually looked at
+these things and used this to
+
+extrapolate internet usage
+going forward.
+
+So we can do that.
+
+Now, we'll run the same
+code with the
+
+extrapolation turned on.
+
+And so figure (1) is the same
+figure (1) as before, same
+
+data, same fit.
+
+And here's figure (2).
+
+And you'll notice that as of
+last year about 115% of the US
+
+population was using the
+internet, probably not true.
+
+It may be possible in sports
+to give 110%, but in
+
+statistics it's not.
+
+Again, you see this all the
+time when people are doing
+
+these projections.
+
+They'll say, fit some data,
+they extrapolate into the
+
+future without understanding
+why maybe that isn't a good
+
+thing to do.
+
+We saw that by when we were
+modeling springs, right?
+
+We could accurately project
+linearly until we exceeded the
+
+constant of elasticity at which
+point our linear model
+
+was totally broken.
+
+So you always need to have some
+reason other than just
+
+fitting the data to believe that
+what you're doing makes
+
+actual sense.
+
+All right.
+
+The final one I want to talk
+about is what is typically
+
+called in the literature the
+Texas sharpshooter fallacy.
+
+And this is a little bit tricky
+
+to understand sometimes.
+
+Actually, is there anyone
+here from Texas?
+
+Oh good, so no one will
+be offended by this.
+
+Well imagine that you're driving
+down some country road
+
+in Texas and that
+you see a barn.
+
+And that barn has six targets
+painted on it, and in the dead
+
+center of each target, you
+find a bullet hole.
+
+So you're driving, your pretty
+impressed, and you stop.
+
+And you see the owner of the
+barn and you say, you must be
+
+a damn good shot.
+
+And he says, absolutely,
+I never miss.
+
+At which point the farmer's
+wife walks out and says,
+
+that's right there ain't a man
+in the state of Texas who is
+
+more accurate with
+a paint gun.
+
+What did he do?
+
+He shot six bullets into
+the barn, and he
+
+was a terrible shot.
+
+They were all over the place.
+
+Then he went and painted a
+target around each of them.
+
+And it looked like he
+was a great shot.
+
+Now you might think that, well
+that's silly, no one would do
+
+that in practice.
+
+But in fact, it happens all
+of the time in practice.
+
+A classic of this genre appeared
+in the magazine New
+
+Scientist, in 2001.
+
+And it reported that a research
+team led by John
+
+Eagles of the Royal Cornhill
+Hospital in Aberdeen, had
+
+discovered that and I quote,
+"Anorexic women are most
+
+likely to have been born in
+the spring or early summer
+
+between March and June.
+
+In fact, there were
+more than--
+
+there were more than 13%--
+
+there were 13% more anorexics
+born on average in those
+
+months, and 30% more anorexics,
+on average, in
+
+June."
+
+Now, let's look at this
+worrisome statistic.
+
+Are any of you women
+here born in June?
+
+All right.
+
+Well, I won't ask about
+your health history.
+
+But maybe you should be
+worried, or maybe not.
+
+So let's look at how they
+did this study.
+
+You may wonder why so many of
+these studies are all studies
+
+about women's health.
+
+And then, perhaps, because
+they're all
+
+done by male doctors.
+
+Anyway, the team studied 446
+women who had been diagnosed
+
+as anorexic.
+
+So if you divide that by 12
+what you've discovered is
+
+that, on average, there should
+have been 37 women born in
+
+each of those months,
+of the 446.
+
+And in fact, in June, there were
+48 anorexic women born.
+
+So they said, well, how likely
+is this to have occurred
+
+simply by chance?
+
+Well as I am want to do in
+such occasions, I checked
+
+their analysis, and I
+wrote a little piece
+
+of code to do that.
+
+So trying to figure out what's
+the probability of 48 women
+
+being born in June, I ran
+a simulation in which I
+
+simulated 446 births and chose
+a month at random, and looked
+
+at the probability.
+
+And let's see what it
+was when we run it.
+
+Oops, well we didn't
+want these graphs.
+
+The probability of at least 48
+births in June was 0.042.
+
+So in fact, pretty low.
+
+You might say, well, what's
+the odds of this
+
+happening by accident?
+
+Pretty small.
+
+Therefore, maybe we are really
+on to something.
+
+Maybe it has to do with the
+conditions of the birth and
+
+the weather or who knows what.
+
+Well, what's wrong with
+this analysis?
+
+Well, one way to look at it is
+this analysis would have been
+
+perfectly valid if the
+researchers had started with a
+
+hypothesis that there are more
+babies born in June than in
+
+any other month-- more future
+anorexics born in June than in
+
+any other month, and then run
+this experiment to test it,
+
+and validated it.
+
+So if they had started with the
+hypothesis, and then from
+
+the hypothesis conducted what's
+called a prospective
+
+study then they would have,
+perhaps, valid reason to
+
+believe that the study supports
+the hypothesis.
+
+But that's not what they did.
+
+Instead what they did is they
+looked at the data and then
+
+chose a hypothesis that matched
+the data, the Texas
+
+sharpshooter fallacy.
+
+Given that that was the
+experiment they performed, the
+
+right question to ask is not
+what is the probability that
+
+you had 48 future anorexics born
+in June, but what was the
+
+probability that you have 48
+future anorexics born in at
+
+least one of the 12 months?
+
+Because that's what they were
+really doing, right?
+
+So therefore, we should really
+have run this simulation.
+
+Similar to the previous one,
+again, these are in your hand
+
+out, but is there at least
+one month in which
+
+there were 48 births?
+
+And if we run that we'll see
+that the probability is over
+
+40%, not so impressive as 4%.
+
+So in fact, we see that we
+probably shouldn't draw any
+
+conclusion.
+
+The probability of this
+happening by pure accident is
+
+almost 50%.
+
+So why should we believe that
+it's somehow meaningful.
+
+Again, an example of the Texas
+sharpshooter fallacy that
+
+appeared in the literature and
+a lot of people fell for it.
+
+And if we had more time, I
+would give you many more
+
+examples, but we don't.
+
+I'll see you on Thursday,
+on Tuesday, rather.
+
+Two more lectures to go.
+
+On Tuesday, I'm going to go over
+some code that I'll be
+
+asking you to look
+at in preparation
+
+for the final exam.
+
+And then on Thursday, we'll
+wrap things up.
\ No newline at end of file
diff --git a/K2Tlj27nkjs.txt b/K2Tlj27nkjs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d93961cb09cb32528fb8ff683099f16f4b28faad
--- /dev/null
+++ b/K2Tlj27nkjs.txt
@@ -0,0 +1,899 @@
+align:start position:0%
+ 
+in this segment we start a new topic we
+
+ align:start position:0%
+in this segment we start a new topic we
+ 
+
+ align:start position:0%
+in this segment we start a new topic we
+will talk about the covariance of two
+
+ align:start position:0%
+will talk about the covariance of two
+ 
+
+ align:start position:0%
+will talk about the covariance of two
+random variables which gives us useful
+
+ align:start position:0%
+random variables which gives us useful
+ 
+
+ align:start position:0%
+random variables which gives us useful
+information about the dependencies
+
+ align:start position:0%
+information about the dependencies
+ 
+
+ align:start position:0%
+information about the dependencies
+between these two random variables let
+
+ align:start position:0%
+between these two random variables let
+ 
+
+ align:start position:0%
+between these two random variables let
+us motivate the concept by looking first
+
+ align:start position:0%
+us motivate the concept by looking first
+ 
+
+ align:start position:0%
+us motivate the concept by looking first
+the special case suppose that x and y
+
+ align:start position:0%
+the special case suppose that x and y
+ 
+
+ align:start position:0%
+the special case suppose that x and y
+have zero means and that they are
+
+ align:start position:0%
+have zero means and that they are
+ 
+
+ align:start position:0%
+have zero means and that they are
+discrete random variables if x and y are
+
+ align:start position:0%
+discrete random variables if x and y are
+ 
+
+ align:start position:0%
+discrete random variables if x and y are
+independent then the expectation of the
+
+ align:start position:0%
+independent then the expectation of the
+ 
+
+ align:start position:0%
+independent then the expectation of the
+product is the product of the
+
+ align:start position:0%
+product is the product of the
+ 
+
+ align:start position:0%
+product is the product of the
+expectations and since we have assumed
+
+ align:start position:0%
+expectations and since we have assumed
+ 
+
+ align:start position:0%
+expectations and since we have assumed
+zero means this is going to be equal to
+
+ align:start position:0%
+zero means this is going to be equal to
+ 
+
+ align:start position:0%
+zero means this is going to be equal to
+zero but suppose instead that the joint
+
+ align:start position:0%
+zero but suppose instead that the joint
+ 
+
+ align:start position:0%
+zero but suppose instead that the joint
+PMF of the x and y is of the following
+
+ align:start position:0%
+PMF of the x and y is of the following
+ 
+
+ align:start position:0%
+PMF of the x and y is of the following
+kind each point in this diagram is
+
+ align:start position:0%
+kind each point in this diagram is
+ 
+
+ align:start position:0%
+kind each point in this diagram is
+equally likely so we have here a
+
+ align:start position:0%
+equally likely so we have here a
+ 
+
+ align:start position:0%
+equally likely so we have here a
+discrete uniform distribution on the
+
+ align:start position:0%
+discrete uniform distribution on the
+ 
+
+ align:start position:0%
+discrete uniform distribution on the
+discrete set which consists of the
+
+ align:start position:0%
+discrete set which consists of the
+ 
+
+ align:start position:0%
+discrete set which consists of the
+points shown in this diagram what we
+
+ align:start position:0%
+points shown in this diagram what we
+ 
+
+ align:start position:0%
+points shown in this diagram what we
+have in this particular example is that
+
+ align:start position:0%
+have in this particular example is that
+ 
+
+ align:start position:0%
+have in this particular example is that
+that most outcomes positive values of X
+
+ align:start position:0%
+that most outcomes positive values of X
+ 
+
+ align:start position:0%
+that most outcomes positive values of X
+tend to go together with positive values
+
+ align:start position:0%
+tend to go together with positive values
+ 
+
+ align:start position:0%
+tend to go together with positive values
+of Y and negative values of X tend to go
+
+ align:start position:0%
+of Y and negative values of X tend to go
+ 
+
+ align:start position:0%
+of Y and negative values of X tend to go
+together with negative values of Y so
+
+ align:start position:0%
+together with negative values of Y so
+ 
+
+ align:start position:0%
+together with negative values of Y so
+most of the time we have outcomes in
+
+ align:start position:0%
+most of the time we have outcomes in
+ 
+
+ align:start position:0%
+most of the time we have outcomes in
+this quadrant in which x times y is
+
+ align:start position:0%
+this quadrant in which x times y is
+ 
+
+ align:start position:0%
+this quadrant in which x times y is
+positive or in this quadrant where x
+
+ align:start position:0%
+positive or in this quadrant where x
+ 
+
+ align:start position:0%
+positive or in this quadrant where x
+times y is again positive but some of
+
+ align:start position:0%
+times y is again positive but some of
+ 
+
+ align:start position:0%
+times y is again positive but some of
+the time we fall in this quadrant when
+
+ align:start position:0%
+the time we fall in this quadrant when
+ 
+
+ align:start position:0%
+the time we fall in this quadrant when
+an x times y is negative or in this
+
+ align:start position:0%
+an x times y is negative or in this
+ 
+
+ align:start position:0%
+an x times y is negative or in this
+quadrant where x times y is negative
+
+ align:start position:0%
+quadrant where x times y is negative
+ 
+
+ align:start position:0%
+quadrant where x times y is negative
+since we have many more points here and
+
+ align:start position:0%
+since we have many more points here and
+ 
+
+ align:start position:0%
+since we have many more points here and
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+on the average the value of x times y is
+
+ align:start position:0%
+on the average the value of x times y is
+ 
+
+ align:start position:0%
+on the average the value of x times y is
+going to be positive on the other hand
+
+ align:start position:0%
+going to be positive on the other hand
+ 
+
+ align:start position:0%
+going to be positive on the other hand
+if the diagram takes this form then most
+
+ align:start position:0%
+if the diagram takes this form then most
+ 
+
+ align:start position:0%
+if the diagram takes this form then most
+of the time the pair XY lies in this
+
+ align:start position:0%
+of the time the pair XY lies in this
+ 
+
+ align:start position:0%
+of the time the pair XY lies in this
+quadrant or in that quadrant where the
+
+ align:start position:0%
+quadrant or in that quadrant where the
+ 
+
+ align:start position:0%
+quadrant or in that quadrant where the
+product of x times y is negative so the
+
+ align:start position:0%
+product of x times y is negative so the
+ 
+
+ align:start position:0%
+product of x times y is negative so the
+random variables x and y typically have
+
+ align:start position:0%
+random variables x and y typically have
+ 
+
+ align:start position:0%
+random variables x and y typically have
+opposite signs and on the average the
+
+ align:start position:0%
+opposite signs and on the average the
+ 
+
+ align:start position:0%
+opposite signs and on the average the
+expected value of x times y is going to
+
+ align:start position:0%
+expected value of x times y is going to
+ 
+
+ align:start position:0%
+expected value of x times y is going to
+be negative so here we have a positive
+
+ align:start position:0%
+be negative so here we have a positive
+ 
+
+ align:start position:0%
+be negative so here we have a positive
+expectation here we have a negative
+
+ align:start position:0%
+expectation here we have a negative
+ 
+
+ align:start position:0%
+expectation here we have a negative
+expectation of x times y this quantity
+
+ align:start position:0%
+expectation of x times y this quantity
+ 
+
+ align:start position:0%
+expectation of x times y this quantity
+the expected value of x times y tells us
+
+ align:start position:0%
+the expected value of x times y tells us
+ 
+
+ align:start position:0%
+the expected value of x times y tells us
+whether x and y tend to move in the same
+
+ align:start position:0%
+whether x and y tend to move in the same
+ 
+
+ align:start position:0%
+whether x and y tend to move in the same
+or in opposite directions and this
+
+ align:start position:0%
+or in opposite directions and this
+ 
+
+ align:start position:0%
+or in opposite directions and this
+quantity is what we call the covariance
+
+ align:start position:0%
+quantity is what we call the covariance
+ 
+
+ align:start position:0%
+quantity is what we call the covariance
+in the zero mean case let us now
+
+ align:start position:0%
+in the zero mean case let us now
+ 
+
+ align:start position:0%
+in the zero mean case let us now
+generalize the random variables do not
+
+ align:start position:0%
+generalize the random variables do not
+ 
+
+ align:start position:0%
+generalize the random variables do not
+have to be discrete
+
+ align:start position:0%
+have to be discrete
+ 
+
+ align:start position:0%
+have to be discrete
+this quantity is well defined for any
+
+ align:start position:0%
+this quantity is well defined for any
+ 
+
+ align:start position:0%
+this quantity is well defined for any
+kind of random variables and if we have
+
+ align:start position:0%
+kind of random variables and if we have
+ 
+
+ align:start position:0%
+kind of random variables and if we have
+non zero means the covariance is defined
+
+ align:start position:0%
+non zero means the covariance is defined
+ 
+
+ align:start position:0%
+non zero means the covariance is defined
+by this expression what we have here is
+
+ align:start position:0%
+by this expression what we have here is
+ 
+
+ align:start position:0%
+by this expression what we have here is
+that we look at the deviation of X from
+
+ align:start position:0%
+that we look at the deviation of X from
+ 
+
+ align:start position:0%
+that we look at the deviation of X from
+its mean value and the deviation of Y
+
+ align:start position:0%
+its mean value and the deviation of Y
+ 
+
+ align:start position:0%
+its mean value and the deviation of Y
+from its mean value and we are asking
+
+ align:start position:0%
+from its mean value and we are asking
+ 
+
+ align:start position:0%
+from its mean value and we are asking
+whether these two deviations tend to
+
+ align:start position:0%
+whether these two deviations tend to
+ 
+
+ align:start position:0%
+whether these two deviations tend to
+have the same sign or not whether they
+
+ align:start position:0%
+have the same sign or not whether they
+ 
+
+ align:start position:0%
+have the same sign or not whether they
+move in the same direction or not if the
+
+ align:start position:0%
+move in the same direction or not if the
+ 
+
+ align:start position:0%
+move in the same direction or not if the
+covariance is positive what it tells us
+
+ align:start position:0%
+covariance is positive what it tells us
+ 
+
+ align:start position:0%
+covariance is positive what it tells us
+is that whenever this quantity is
+
+ align:start position:0%
+is that whenever this quantity is
+ 
+
+ align:start position:0%
+is that whenever this quantity is
+positive so that X is above its mean
+
+ align:start position:0%
+positive so that X is above its mean
+ 
+
+ align:start position:0%
+positive so that X is above its mean
+then typically or usually the deviation
+
+ align:start position:0%
+then typically or usually the deviation
+ 
+
+ align:start position:0%
+then typically or usually the deviation
+of Y from its mean will also tend to be
+
+ align:start position:0%
+of Y from its mean will also tend to be
+ 
+
+ align:start position:0%
+of Y from its mean will also tend to be
+positive to summarize the covariance in
+
+ align:start position:0%
+positive to summarize the covariance in
+ 
+
+ align:start position:0%
+positive to summarize the covariance in
+general tells us whether two random
+
+ align:start position:0%
+general tells us whether two random
+ 
+
+ align:start position:0%
+general tells us whether two random
+variables tend to move together both
+
+ align:start position:0%
+variables tend to move together both
+ 
+
+ align:start position:0%
+variables tend to move together both
+being high or both being low in sum
+
+ align:start position:0%
+being high or both being low in sum
+ 
+
+ align:start position:0%
+being high or both being low in sum
+average or typical sense now if the two
+
+ align:start position:0%
+average or typical sense now if the two
+ 
+
+ align:start position:0%
+average or typical sense now if the two
+random variables are independent we
+
+ align:start position:0%
+random variables are independent we
+ 
+
+ align:start position:0%
+random variables are independent we
+already saw that in the zero mean case
+
+ align:start position:0%
+already saw that in the zero mean case
+ 
+
+ align:start position:0%
+already saw that in the zero mean case
+this quantity the covariance is going to
+
+ align:start position:0%
+this quantity the covariance is going to
+ 
+
+ align:start position:0%
+this quantity the covariance is going to
+be zero how about the case where we have
+
+ align:start position:0%
+be zero how about the case where we have
+ 
+
+ align:start position:0%
+be zero how about the case where we have
+nonzero means well if we have
+
+ align:start position:0%
+nonzero means well if we have
+ 
+
+ align:start position:0%
+nonzero means well if we have
+independence then we have the expected
+
+ align:start position:0%
+independence then we have the expected
+ 
+
+ align:start position:0%
+independence then we have the expected
+value of the product of two random
+
+ align:start position:0%
+value of the product of two random
+ 
+
+ align:start position:0%
+value of the product of two random
+variables x and y are independent so X
+
+ align:start position:0%
+variables x and y are independent so X
+ 
+
+ align:start position:0%
+variables x and y are independent so X
+minus the expected value which is a
+
+ align:start position:0%
+minus the expected value which is a
+ 
+
+ align:start position:0%
+minus the expected value which is a
+constant is going to be independent from
+
+ align:start position:0%
+constant is going to be independent from
+ 
+
+ align:start position:0%
+constant is going to be independent from
+Y minus its expected value and so the
+
+ align:start position:0%
+Y minus its expected value and so the
+ 
+
+ align:start position:0%
+Y minus its expected value and so the
+covariance is going to be the product of
+
+ align:start position:0%
+covariance is going to be the product of
+ 
+
+ align:start position:0%
+covariance is going to be the product of
+two expectations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but the expected value of X minus this
+
+ align:start position:0%
+but the expected value of X minus this
+ 
+
+ align:start position:0%
+but the expected value of X minus this
+constant is zero and the same is true
+
+ align:start position:0%
+constant is zero and the same is true
+ 
+
+ align:start position:0%
+constant is zero and the same is true
+for this term as well so the covariance
+
+ align:start position:0%
+for this term as well so the covariance
+ 
+
+ align:start position:0%
+for this term as well so the covariance
+in this case is going to be equal to
+
+ align:start position:0%
+in this case is going to be equal to
+ 
+
+ align:start position:0%
+in this case is going to be equal to
+zero so in the independent case we have
+
+ align:start position:0%
+zero so in the independent case we have
+ 
+
+ align:start position:0%
+zero so in the independent case we have
+zero covariances on the other hand the
+
+ align:start position:0%
+zero covariances on the other hand the
+ 
+
+ align:start position:0%
+zero covariances on the other hand the
+converse is not true there are examples
+
+ align:start position:0%
+converse is not true there are examples
+ 
+
+ align:start position:0%
+converse is not true there are examples
+in which we have dependence but zero
+
+ align:start position:0%
+in which we have dependence but zero
+ 
+
+ align:start position:0%
+in which we have dependence but zero
+covariance here is one example in this
+
+ align:start position:0%
+covariance here is one example in this
+ 
+
+ align:start position:0%
+covariance here is one example in this
+example there are four possible outcomes
+
+ align:start position:0%
+example there are four possible outcomes
+ 
+
+ align:start position:0%
+example there are four possible outcomes
+at at any particular outcome either X or
+
+ align:start position:0%
+at at any particular outcome either X or
+ 
+
+ align:start position:0%
+at at any particular outcome either X or
+Y is going to be zero so in this example
+
+ align:start position:0%
+Y is going to be zero so in this example
+ 
+
+ align:start position:0%
+Y is going to be zero so in this example
+the random variable x times y is
+
+ align:start position:0%
+the random variable x times y is
+ 
+
+ align:start position:0%
+the random variable x times y is
+identically equal to 0 the mean of X is
+
+ align:start position:0%
+identically equal to 0 the mean of X is
+ 
+
+ align:start position:0%
+identically equal to 0 the mean of X is
+also 0 the mean of Y is also 0 by
+
+ align:start position:0%
+also 0 the mean of Y is also 0 by
+ 
+
+ align:start position:0%
+also 0 the mean of Y is also 0 by
+symmetry so the covariance is the
+
+ align:start position:0%
+symmetry so the covariance is the
+ 
+
+ align:start position:0%
+symmetry so the covariance is the
+expected value of this quantity and so
+
+ align:start position:0%
+expected value of this quantity and so
+ 
+
+ align:start position:0%
+expected value of this quantity and so
+the covariance in this example is equal
+
+ align:start position:0%
+the covariance in this example is equal
+ 
+
+ align:start position:0%
+the covariance in this example is equal
+to 0 on the other hand the two random
+
+ align:start position:0%
+to 0 on the other hand the two random
+ 
+
+ align:start position:0%
+to 0 on the other hand the two random
+variables x and y are dependent if I
+
+ align:start position:0%
+variables x and y are dependent if I
+ 
+
+ align:start position:0%
+variables x and y are dependent if I
+tell you that X is equal to 1 then you
+
+ align:start position:0%
+tell you that X is equal to 1 then you
+ 
+
+ align:start position:0%
+tell you that X is equal to 1 then you
+know that this outcome has occurred and
+
+ align:start position:0%
+know that this outcome has occurred and
+ 
+
+ align:start position:0%
+know that this outcome has occurred and
+in that case you are certain that Y is
+
+ align:start position:0%
+in that case you are certain that Y is
+ 
+
+ align:start position:0%
+in that case you are certain that Y is
+equal to 0 so knowing the value of X
+
+ align:start position:0%
+equal to 0 so knowing the value of X
+ 
+
+ align:start position:0%
+equal to 0 so knowing the value of X
+tells you a lot about the value of Y and
+
+ align:start position:0%
+tells you a lot about the value of Y and
+ 
+
+ align:start position:0%
+tells you a lot about the value of Y and
+therefore we have dependence between
+
+ align:start position:0%
+therefore we have dependence between
+ 
+
+ align:start position:0%
+therefore we have dependence between
+these two random variables
\ No newline at end of file
diff --git a/MniYgsZSp30.txt b/MniYgsZSp30.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b2dc41267014ab0a50776ba7bf1eaea21a4b31f4
--- /dev/null
+++ b/MniYgsZSp30.txt
@@ -0,0 +1,3849 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: OK.
+
+Well hello, everyone.
+
+And welcome back to
+Computational Systems Biology.
+
+I am David Gifford and I
+am delighted to be back
+
+with you today.
+
+We're going to talk,
+today, about understanding
+
+transcription.
+
+Specifically, how we're going
+to understand transcription
+
+is a technique called RNA-seq.
+
+And RNA-seq is a methodology
+for characterizing RNA molecules
+
+through next
+generation sequencing.
+
+And we'll talk, first,
+about RNA-seq principles.
+
+We'll then talk
+about how to take
+
+the data we learn from RNA-seq
+and analyze it using tools
+
+for characterizing
+differential gene
+
+expression and principal
+component analysis.
+
+And finally, we'll talk about
+single cell RNA-seq, which
+
+is a very important and growing
+area of scientific inquiry.
+
+But first, let's
+talk about RNA-seq.
+
+How many people have
+heard of RNA-seq before?
+
+Fantastic.
+
+How many people
+have done it before?
+
+Some?
+
+Great.
+
+So RNA-seq is fairly
+simple in concept.
+
+What we're going to
+do is we're going
+
+to isolate RNA species from
+a cell or collection of cells
+
+in the desired condition.
+
+And note that we can choose
+which kind of RNA molecules
+
+to isolate.
+
+We can isolate molecules
+before any selection, which
+
+would include molecules that
+are precursor RNAs that have not
+
+been spliced yet,
+including non-coding RNAs.
+
+As you probably know, the
+study of non-coding RNAs
+
+is extraordinarily important.
+
+There are over 3,300
+so-called long non-coding RNAs
+
+that have been
+characterized so far.
+
+Those are non-coding
+RNAs over 200 bases long.
+
+We'll be talking about
+those later on, when
+
+we talk about chromatin
+function in the genome.
+
+And of course, there are
+the precursor messenger RNAs
+
+that are spliced, turned into
+messenger RNAs that are then
+
+translated into protein.
+
+And the specifics of
+the RNA-seq protocol
+
+will give you various
+of these species
+
+depending upon what kinds of
+purification methodologies
+
+you use.
+
+But as you're aware,
+there are many isoforms
+
+that are possible in
+most mammalian genes.
+
+This is a short summary,
+produced by the Burge
+
+Laboratory, of different
+kinds of splicing
+
+events that can occur.
+
+And the splicing
+events are often
+
+regulated by
+cis-regulatory sequences
+
+that live in the introns.
+
+And these introns contain
+recognition sequences
+
+for splicing factors where
+the splicing factors can
+
+be conditionally expressed.
+
+And so you get
+different combinations
+
+of these exons
+being glued together
+
+to produce variant
+forms of proteins.
+
+So we have to be
+mindful of the idea
+
+that the RNA
+molecules that we're
+
+going to be
+observing, typically,
+
+are going to be
+reverse transcribed.
+
+So we'll see entire
+transcripts that came, perhaps,
+
+from distinct exonic
+locations in the genome.
+
+And the essential
+idea of RNA-seq
+
+is that we take the RNA
+molecules we care about--
+
+in this case, we're
+going to purify
+
+the ones that have poly-A tails.
+
+We will take those molecules.
+
+We'll reverse transcribe them.
+
+We'll sequence fragments
+of them and then
+
+map them to the genome.
+
+Now if you don't purify
+for poly-A tails,
+
+you get a lot of things
+mapping to the genome that
+
+are intronic.
+
+And so you get a
+lot of data that
+
+is very difficult to analyze.
+
+So typically,
+people, when they're
+
+looking for gene
+expression data,
+
+will do poly-A purification.
+
+And when you do this-- when you
+sequence the result of doing
+
+the reverse transcription
+of these RNA molecules--
+
+and you map the results to
+the genome, what you find
+
+is data that looks like this.
+
+This is the SOX2 gene.
+
+This is typical expression data.
+
+You can see all of the
+individual reads mapping
+
+to the genome, the blue
+in the plus strand,
+
+the pink on the minus strand.
+
+And our job is to take data
+like this and to analyze it.
+
+Now we can take
+these data and we
+
+can summarize them
+in various formats.
+
+One way is to simply
+count the number of times
+
+that we see a read
+at a particular base,
+
+like here, for the SMUG1 gene.
+
+And here you see
+something else going on,
+
+which is that we have
+reads from-- the sequencing
+
+experiments have been
+polyadenylated and purified.
+
+So we're only seeing
+the reads that
+
+occur over the exonic
+sequences, more or less.
+
+There are a few intronic
+reads there, scattered about.
+
+The other thing that we see,
+which is very important,
+
+is that we see reads that
+are split across exons.
+
+Because the splicing
+event has occurred,
+
+the RNA molecule is
+a contiguous sequence
+
+of a collection of exons.
+
+And sometimes you'll
+get a read that
+
+spans an exon-exon boundary.
+
+And when we get
+this, you can see,
+
+in the bottom part of the
+slide that I'm showing you,
+
+these reads can map
+across the exons.
+
+Typically, in order to
+get good performance out
+
+of something like
+this, we want to use
+
+reads that are about
+100 bases long.
+
+And we'll use a mapper
+that is capable of mapping
+
+both ends of a read to
+account for split reads
+
+for these exon crossing events.
+
+So that gives you an idea of
+the kinds of data that we have.
+
+And part of the
+challenge now is looking
+
+at how we can determine which
+particular isoforms of a gene
+
+are being expressed by
+evaluating these data.
+
+So there are two principal
+ways of going about this.
+
+One way is we simply
+take our read data,
+
+and we use the ideas
+that we talked about
+
+in genome assembly, and
+we assemble the reads
+
+into transcripts.
+
+That's typically done de novo.
+
+There are reference
+guided assemblers.
+
+It has the benefit that you
+don't need a reference genome.
+
+So sometimes, when you're
+working with an organism that
+
+does not have a well
+characterized reference genome,
+
+you will de novo
+assemble the transcripts
+
+from an RNA-seq experiment.
+
+But it also has problems
+with correctness,
+
+as we saw when we
+talked about assembly.
+
+The other approach, which
+is more typically used,
+
+is to map reads, or aligned the
+reads, to a reference genome
+
+and identify the
+different isoforms that
+
+are being expressed
+using constraints.
+
+And ultimately, the goals
+is to identify the isoforms
+
+and quantitate them so we can
+do further downstream analysis.
+
+And you'll hear about
+two different metrics,
+
+sometimes, in the
+literature, for expression.
+
+One is the number of
+reads per kilobase
+
+of transcript per million reads.
+
+So you might have, for
+example, an RPKM metric
+
+of 1,000, which means that one
+out of every thousandth read
+
+is mapping to a particular gene.
+
+So it gives you a metric
+that's adjusted for the fact
+
+that longer genes will
+produce more reads.
+
+An alternative
+metric is fragments
+
+per kilobase per million.
+
+And that's sometimes
+used when we're
+
+talking about paired end data.
+
+And you're considering
+that you're
+
+sequencing both
+ends of a fragment.
+
+So here we're talking
+about how many fragments
+
+we see for a particular
+gene per 1,000
+
+bases of the gene per
+million fragments.
+
+OK.
+
+So the essential idea,
+then, is to take the reads
+
+that we have-- the basket of
+reads-- align it to the genome,
+
+both to exons and
+to exon crossings,
+
+and to determine, for a given
+gene, what isoforms we have
+
+and how they're being expressed.
+
+So from here on in,
+I'm going to assume
+
+that we're talking about
+a gene and its isoforms.
+
+And that's OK.
+
+Because typically, we can
+map reads uniquely to a gene.
+
+And there are
+details, of course,
+
+when you have genes
+there are paralogs that
+
+have identical sequences across
+the genome where this becomes
+
+more difficult.
+
+So if we consider
+this, once again,
+
+we're going to take
+our reads, we're
+
+going to map them to
+the genome, and we're
+
+going to look for all
+possible pairings of exons.
+
+What we would like
+to do is to enumerate
+
+all of the possible
+isoforms that are possible
+
+given the data that we have.
+
+And we can use junction crossing
+reads and other methodologies
+
+to enumerate all the
+possible isoforms.
+
+But what we're
+going to assume is
+
+that we've enumerated
+all the isoforms.
+
+And we're going to
+number them 1 through n.
+
+So we have isoform 1, isoform
+2, isoform 3 for a given gene.
+
+And what we want to
+compute for each isoform is
+
+its relative contribution
+to the read population
+
+we're seeing that
+maps to that gene.
+
+So in order to do
+that, what we could do
+
+is use some constraints.
+
+So if I show you
+this picture, which
+
+suggests that we have
+possible splice events here
+
+for the event C in the
+middle, if I told you
+
+that A, C, and E were very
+highly covered by reeds,
+
+you might think that
+A, C, and E represented
+
+one isoform that was
+highly expressed.
+
+And so if we think about
+how to use our read
+
+coverage as a guide to
+determining isoform prevalence,
+
+we'll be in good shape.
+
+And really, that's the
+best evidence we have.
+
+We have two sources
+of evidence, right?
+
+We have our junction
+crossing reads, which tell us
+
+which exons are being
+spliced together,
+
+that helps us both compute
+the set of possible isoforms
+
+and estimate their prevalence.
+
+The other thing we
+have is the reads
+
+that actually
+simply cover exons.
+
+And their relative
+prevalence can also
+
+help us compute the relative
+amounts of different isoforms.
+
+So in order to do this, we can
+think about what reads tell us.
+
+And some reads will
+exclude certain isoforms.
+
+So if we consider the
+reads that we have,
+
+we can think about reads that
+cross particular junctions that
+
+are inclusion reads
+saying that-- for example,
+
+in this case, the top
+reads are indicating
+
+that the middle white exon is
+being included in a transcript
+
+whereas the bottom
+reads are exclusion
+
+reads indicating that that
+white exon in the middle
+
+is being spliced out.
+
+So what we would
+like to do, then,
+
+is to build a
+probabilistic model that
+
+takes into account what we know
+about what a read tells us.
+
+Because each read is
+a piece of evidence.
+
+And we're going to use
+that read like detectives.
+
+We're going to go in and
+we're going to try and analyze
+
+all of the different
+reads we see for a gene
+
+and use it to
+weight what we think
+
+is happening with
+the different isoform
+
+expressions in the pool of
+reads that we're observing.
+
+And in order to do
+so, we will have
+
+to build a function
+that describes
+
+the probability of
+seeing a read given
+
+the expression of a
+particular isoform.
+
+So the essential idea is this--
+for the next three slides,
+
+I want to build a model of
+the probability of seeing
+
+a read conditioned upon a
+particular isoform being
+
+expressed.
+
+All right?
+
+So there are three
+ways to approach this.
+
+One is that I can
+see a read that I
+
+know is incompatible
+with a given isoform.
+
+And therefore, the
+probability of seeing that
+
+read given the isoform is 0.
+
+And that's perfectly fine.
+
+And this can either happen
+with a single ended read
+
+or with a paired end read.
+
+And it's a conditional
+probability.
+
+So the probability of seeing
+read i given and isoform j
+
+can be 0.
+
+Another possibility is that,
+if I have a transcript--
+
+now recall that the
+transcript has been spliced.
+
+So what we're looking at
+is the entire sequence
+
+of the spliced isoform.
+
+And we see a read.
+
+And the read can land anywhere
+within that transcript.
+
+Let's assume, for
+the time being,
+
+we're looking at
+single ended read.
+
+Then, the probability
+of seeing that read
+
+land in that transcript
+is 1 over the length
+
+of the transcript-- all
+right-- at a particular base.
+
+So this read is compatible
+with that transcript.
+
+And we can describe the
+probability in this fashion.
+
+It's also possible for us to
+consider paired end reads.
+
+And if we have
+paired end reads, we
+
+can describe a
+probability function
+
+that has two
+essential components.
+
+The denominator
+is still the same.
+
+That is, the likelihood
+of the read aligning
+
+at a particular
+position is going
+
+to be 1 over the length
+of the entire transcript.
+
+The numerator is
+different though.
+
+We're going to compute
+the length of the read
+
+that we have, or the implied
+length of the paired end read,
+
+and ask, what's the
+likelihood of seeing that.
+
+So we don't know the exact
+length, recall, of the insert.
+
+When we're looking
+at paired end reads,
+
+we can only estimate
+how long the fragment
+
+is that we're sequencing.
+
+And so we are going to have a
+probabilistic interpretation
+
+of how long the piece of RNA
+is that we actually wound up
+
+sequencing the ends of.
+
+And that is placed
+in the numerator,
+
+which scales the 1 over l sub j.
+
+So this gives us a
+probability for seeing
+
+a read in a particular
+transcript that
+
+accounts for the
+fact that we have
+
+to back both ends
+to that transcript.
+
+OK?
+
+So we have three possibilities
+that we've described,
+
+one, where a particular read is
+incompatible with an isoform,
+
+two, where we had
+a single end read
+
+mapping to an isoform,
+which is simply
+
+1 over the length
+of the isoform,
+
+and three, where
+we're mapping paired
+
+end reads to an isoform,
+which includes uncertainty
+
+about where it will map,
+which is the 1 over l sub j,
+
+and also uncertainty about the
+length of the fragment itself,
+
+which is encoded in
+the F function, which
+
+is a distribution
+over fragment lengths.
+
+OK.
+
+So once we have
+this structure, we
+
+can then estimate
+isoform expression.
+
+Now we talked before, when
+we talked about ChIP-seq
+
+last time, the idea of
+estimating proportions.
+
+And the essential idea
+here is that if we
+
+want to compute the
+probability of a read given,
+
+in this case, a mixture of
+isoforms, that's simply going
+
+to be-- let's see, what
+variable did I use?
+
+Yeah-- the estimated
+concentration
+
+of that isoform times the
+probability of the read as
+
+seen in that isoform.
+
+So for an individual read, we
+can estimate its likelihood
+
+given this mixture.
+
+And then the product
+around the outside
+
+describes how to
+estimate the probability
+
+of the entire basket of reads
+that we see for that gene.
+
+And what we would like to do
+is to pick psi, in this case,
+
+to maximize the likelihood
+of the observed reads.
+
+So what psi is
+going to do is it's
+
+going to give us the fraction
+of each isoform that we see.
+
+Are there any questions
+about the idea
+
+of isoform quantitation?
+
+Yes.
+
+AUDIENCE: I'm a little lost in--
+in the last full slide review,
+
+you were describing these three
+cases for excluded, single,
+
+and paired reads.
+
+So we're computing the
+different probabilities
+
+for both ends to happen in a
+transcript, of for just one,
+
+or--
+
+PROFESSOR: It depends.
+
+The second and third
+cases depend upon
+
+whether we're
+analyzing single ended
+
+reads or paired end reads.
+
+And so we wouldn't use both
+of them at the same time.
+
+In other words, if you only
+have single ended data,
+
+you would use the second
+case that we showed.
+
+And if you had
+paired end data, you
+
+would use the third
+case that we showed.
+
+AUDIENCE: OK.
+
+PROFESSOR: Question, yes.
+
+AUDIENCE: Sorry.
+
+I noticed that the single
+end reads case-- could you
+
+explain the intuition behind
+that probability [INAUDIBLE]?
+
+PROFESSOR: Sure.
+
+The intuition behind
+that probability
+
+is that we're asking--
+so here is a transcript.
+
+And we're assuming, what is
+the probability of a read given
+
+that it came from
+this transcript.
+
+OK?
+
+What's the probability of
+observing a particular read?
+
+And the probability of
+observing it lining up
+
+at a particular position
+is 1 over the length
+
+of this transcript.
+
+And so the probability actually
+includes the idea of alignment
+
+at a particular position
+in the transcript.
+
+OK?
+
+So obviously, the
+probability's 1
+
+if we assume it comes from here
+if we don't consider this fact.
+
+But if we want to ask where
+it lines up in the transcript,
+
+it's going to be 1 over l sub j.
+
+OK?
+
+AUDIENCE: So we assume that
+it's uniformly possible?
+
+PROFESSOR: That it's
+uniformly possible,
+
+which gets us to a good point.
+
+I'm glad you asked
+that question.
+
+Sometimes we would
+have more reads
+
+at the three prime end of
+a transcript than the five
+
+prime end.
+
+Can anybody imagine why?
+
+Yes.
+
+AUDIENCE: Because you're
+pulling on the poly-A tails.
+
+PROFESSOR: Yeah.
+
+So this actually was
+purified by the poly-A tail.
+
+And we're pulling on this.
+
+We're purifying by it.
+
+And if there's breakage
+of these transcripts
+
+as it goes through the
+biochemical processing,
+
+we can get shorter
+and shorter molecules.
+
+They all contain this bit.
+
+And the probability to contain
+that whole thing actually
+
+decreases.
+
+So oftentimes there
+is three prime bias
+
+in RNA-seq experiments one
+needs to be mindful of.
+
+But we're assuming, today,
+that there isn't such bias
+
+and that the probability's
+equal that it
+
+maps someplace in
+this transcript.
+
+OK?
+
+Does that answer your question?
+
+Yes.
+
+AUDIENCE: Sorry.
+
+I do have one more.
+
+Can you show us how
+that extends, then,
+
+to the paired end read and where
+the probability distribution--
+
+PROFESSOR: Right.
+
+So if we go to paired end
+reads, right, like this,
+
+this component is going to
+be where it aligns, right?
+
+And then, the probability of the
+length of this entire molecule
+
+is what I had up
+there before, which
+
+is-- exactly how did I do that?
+
+So this is going to be--
+this is this bit, which
+
+is the implied length of this.
+
+OK?
+
+So if I map the
+left and the right--
+
+this component is where
+the left end maps.
+
+OK?
+
+I take the left and the
+right ends of the read
+
+that I have from
+that transcript.
+
+And it has a particular
+length on this transcript.
+
+OK?
+
+I'll call that length
+l sub j of R sub i.
+
+Now remember, that
+is not the same
+
+as the length in the genome.
+
+That's the length in this
+transcript as it is spliced.
+
+OK?
+
+F is going to be the
+probability distribution
+
+of the length of the fragments.
+
+So let's just say that they're
+centered around 200 bases.
+
+OK?
+
+So if this is exactly 200 bases,
+it's going to be quite likely.
+
+OK?
+
+But imagine that when
+I map this fragment,
+
+this wound up being
+400 bases apart.
+
+Then, this
+distribution would tell
+
+is it's very unlikely that
+I would see a fragment that
+
+mapped here and
+mapped 400 bases up
+
+here, because my fragment
+with distribution defined by F
+
+is 200 bases.
+
+So it's going to discount
+that, the probability of that.
+
+So this term that the
+probability of the read
+
+given the transcript
+is the component
+
+of where it's aligning
+times the likelihood
+
+that the implied
+fragment length agrees
+
+with what we think
+we have empirically.
+
+OK?
+
+Does that make sense?
+
+OK.
+
+Those are good questions.
+
+OK.
+
+So given this
+framework, we can either
+
+use EM or other machine learning
+like frameworks to maximize psi
+
+and to learn the
+fraction of expression
+
+of each different isoform
+from the observed data given
+
+the functions that we have.
+
+And just to give
+you an idea, when
+
+this was done for
+myogenesis, a program
+
+called Cufflinks, which
+does this kind of process
+
+of identifying
+isoform prevalences,
+
+was able to identify a
+large number of transcripts.
+
+70% of the reads
+were in previously
+
+annotated transcripts.
+
+But it also found 643
+new isoforms of genes
+
+in this single time series.
+
+And I posted one
+of the papers that
+
+describes some this technology
+on the Stellar site.
+
+But note that certain of the
+genes have light coverage.
+
+And what we're seeing here is
+that for genes are expressed
+
+in low copy numbers,
+it's obviously
+
+more difficult to get
+reads out of them.
+
+And I'm presuming, in this
+particular experiment--
+
+although I can't recollect--
+that the reason they don't see
+
+that many intronic reads is
+they did poly-A purification.
+
+OK.
+
+So we've talked about
+how to take our reads,
+
+build a probabilistic model,
+estimate isoform prevalences.
+
+And we know how many reads
+are mapping to a given gene.
+
+The question now
+is whether or not
+
+we see differential
+expression of a gene
+
+in different conditions.
+
+So I'd like to turn to the
+analysis of differential
+
+expression unless there
+are any final questions
+
+about the details of RNA-seq
+and isoform estimation.
+
+This is your chance to
+ask those hard questions.
+
+Yes.
+
+AUDIENCE: OK.
+
+I have a really silly question.
+
+But can you explain, really
+quickly, what are isoforms?
+
+PROFESSOR: What an isoform is?
+
+AUDIENCE: Yeah.
+
+PROFESSOR: Sure.
+
+An isoform is a particular
+splice variant of a gene.
+
+So a gene that has a
+particular splicing pattern
+
+is called an isoform.
+
+So imagine we have three
+exons, one, two, and three.
+
+And a transcript that has all
+three would be one isoform.
+
+And another variant that omits
+two would be a second isoform.
+
+So just one in three
+would be an isoform.
+
+And each gene has a set
+of isoforms it exhibits.
+
+And that depends upon how it's
+regulated and whether or not
+
+any splicing is
+constitutive-- it always
+
+happens-- or whether
+or not it's regulated.
+
+And so in theory,
+a gene with n exons
+
+has how many potential isoforms?
+
+It's 2 to the n.
+
+Because you can consider each
+exon being included or omitted.
+
+All right.
+
+But that isn't
+typically the case--
+
+that there are many
+fewer isoforms than that.
+
+But in general, an isoform
+refers to a particular splice
+
+variant of a gene.
+
+Yes.
+
+AUDIENCE: I just want to
+make sure I have everything
+
+correctly.
+
+When you're using single
+legged or pair end reads,
+
+you can get excluded
+ends, right?
+
+So you can get that in both
+cases, whether or not you're--
+
+PROFESSOR: Well, it depends.
+
+Once again, it's
+somewhat probabilistic
+
+where the reads actually hit.
+
+Because if all the
+reads only hit exons,
+
+and you didn't
+get any junctions,
+
+and none of your paired end
+reads crossed junctions,
+
+then you wouldn't
+actually have exclusion.
+
+All right?
+
+AUDIENCE: But it's possible for
+using both types of sequencing?
+
+PROFESSOR: Yes, it's possible
+with both types of sequencing.
+
+In fact, oftentimes,
+what people do
+
+is that they will count
+junction crossing reads.
+
+If you have a large
+enough number of reads
+
+in your sequencing, say,
+100 base pairs at least,
+
+then a large number
+of your reads
+
+are going to be-- not a large,
+but a significant fraction--
+
+will be exon crossing.
+
+And you'll be able to count the
+number of exon-exon junctions
+
+you have of different types.
+
+And that will give
+you an estimate
+
+of how much splicing is going
+on and will help validate
+
+the kinds of conclusions
+that come out of programs
+
+like Cufflinks or MISO, which is
+another program from the Burge
+
+Laboratory that is used to
+estimate isoform prevalence.
+
+Yes.
+
+AUDIENCE: So even
+given this information,
+
+you can't say which exons go
+with which exons necessarily,
+
+except paralogs, right?
+
+Because the reads, in
+general, aren't long enough
+
+to span an exon.
+
+And therefore we wouldn't
+know, for example,
+
+that a given transcript is
+exons one, five, and six.
+
+You could only know that exons
+five and six went together.
+
+PROFESSOR: That is
+not strictly true
+
+if you have paired end
+reads and your fragments
+
+are long enough to span exons.
+
+But in general, you're correct.
+
+And that's why modern
+sequencing technologies that
+
+are coming down the pike
+that can do 25 kilobase reads
+
+are so important for doing
+things just like that.
+
+Yes.
+
+AUDIENCE: In your diagram
+of the read up there,
+
+are the boxes the actual genome
+or RNA sequence and the line
+
+in between the artificial linker
+that you added when you seq
+
+ref'd?
+
+PROFESSOR: Ah, that's
+a good question.
+
+The question is,
+is this the linker
+
+and these are the
+actual sequences.
+
+No.
+
+What I'm drawing here is
+that these are the bits
+
+that we actually get
+to see the sequence of.
+
+We sequence from both
+ends of a molecule.
+
+This is the part of the fragment
+that we haven't sequenced
+
+because our reads
+aren't long enough.
+
+And so the entire fragment
+might be 300 bases long.
+
+If this is 100 and this is
+100, then the unobserved part
+
+is 100 in the middle.
+
+OK?
+
+And that's called
+the insert length,
+
+the entire length
+of the molecule.
+
+And we get to choose how
+long these fragments are up
+
+to a maximum size.
+
+Contemporary
+sequencers don't really
+
+like fragments over 1,000 bases.
+
+And the performance
+starts falling off
+
+when you get close
+to that number.
+
+So people, typically,
+are operating
+
+in a more optimal
+range of fragments
+
+that are a few
+hundred bases long.
+
+Any other questions?
+
+OK.
+
+So I wanted to briefly talk
+about hypothesis testing.
+
+Because we're going
+to be needing it
+
+for determining when things
+are really differentially
+
+expressed.
+
+So I'm just going to
+show you some data
+
+and ask you a few
+questions about it.
+
+So here are two different
+scatters of data.
+
+Well, actually, it's
+exactly the same data.
+
+But we have two
+different bits to it.
+
+We have two
+independent Gaussians
+
+that are fit to the data,
+from gene one and gene two.
+
+And another fit
+uses two Gaussians
+
+that have a correlation
+structure between them.
+
+And the question
+is whether or not
+
+the null hypothesis or
+the alternative hypothesis
+
+is more reasonable.
+
+And typically, when
+we say reasonable,
+
+we want to judge whether
+or not it's significant.
+
+Significance
+typically talks about,
+
+what's the chance
+that the data we saw
+
+occurred at random given
+the null hypothesis.
+
+So what's the chance
+it was generated
+
+by the null hypothesis
+versus the chance
+
+that it was generated by
+the alternative hypothesis?
+
+Now the problem is that
+alternative hypotheses,
+
+typically, are more complex.
+
+And a more complex model will
+always explain data better.
+
+So we need to have
+a principled way
+
+of asking the question, given
+that the alternative hypothesis
+
+is always going to
+do a better job,
+
+does it do such a better
+job that it can exclude
+
+the null hypothesis at a
+particular probability level.
+
+OK?
+
+So here are two different
+models for these data.
+
+The null model, H0,
+is that they came
+
+from two independent Gaussians.
+
+The alternative model,
+H1, is that they
+
+came from two
+correlated Gaussians.
+
+And then we can
+ask whether or not
+
+H1 is sufficiently more likely
+to warrant our rejecting H0
+
+and accepting H1.
+
+Now as I said, H1 is always
+going to fit the data better.
+
+So the probability
+of that collection
+
+of points evaluated with the
+H1 model, fit to the data,
+
+is always going to be superior.
+
+So we need to have
+a way to compare
+
+the probability of the data
+given H1 versus the data
+
+given H0 in a way that
+allows us to judge
+
+the probability that the data
+via H0 occurred at random.
+
+In this particular case,
+the data supports H1.
+
+And let's see why.
+
+So this is a key idea here.
+
+How many people have heard of
+likelihood ratio statistics
+
+before?
+
+OK.
+
+About half the class.
+
+OK.
+
+So here's the idea.
+
+The idea is that what
+we're going to do
+
+is we're going to
+compute a test statistic.
+
+And the test statistic
+is going to be
+
+a function of the observed data.
+
+And it's 2 times the log of
+the probability of the observed
+
+data given H1 over the
+probability of the observed
+
+data given H0.
+
+OK?
+
+Now we know that
+this is always going
+
+to have a higher value than the
+probability in the denominator.
+
+So this is always going
+to be greater than 1.
+
+So the test statistic will
+always be greater than 0
+
+since we're operating
+in the log domain.
+
+OK?
+
+The question is-- we
+know that this is always
+
+going to be better, even when
+the data was generated from H0.
+
+But when is this
+sufficiently better
+
+for us to believe that H0 is not
+true and we should accept H1?
+
+What we need is a distribution
+for this test statistic
+
+that occurred if H0 was true.
+
+And that distribution allows
+us to compute the probability
+
+that an observed value
+for the test statistic
+
+occurred, even in the presence--
+assuming that H0 is true.
+
+OK.
+
+So this depends upon
+the number of degrees
+
+of freedom difference
+between H1 and H0.
+
+How many degrees of
+freedom are there
+
+in H1 in this model up here?
+
+How many parameters
+do we get to pick?
+
+AUDIENCE: Six.
+
+PROFESSOR: Hmm?
+
+AUDIENCE: Six.
+
+PROFESSOR: Six?
+
+AUDIENCE: Two means and four--
+
+PROFESSOR: Two means
+and four coherences.
+
+And for H0?
+
+AUDIENCE: Just four.
+
+PROFESSOR: Four.
+
+So what's the
+difference in the number
+
+of degrees of freedom
+between H1 and H0?
+
+It's two.
+
+So the test statistic
+is parametrized
+
+by the difference in number
+of degrees of freedom.
+
+And so what we see, then, is
+something that looks like this.
+
+We see a test statistic where
+this is the probability of it,
+
+on the y-axis, and the test
+statistic on the x-axis.
+
+But as the test statistic
+gets larger and larger,
+
+the probability that it
+occurred with H0 being true
+
+gets smaller and smaller.
+
+So let us just suppose that we
+took our data from our model
+
+that we observed.
+
+And we computed the test
+statistic at a particular value
+
+call T observed.
+
+So this is the actual
+value that we computed out
+
+of our likelihood ratio test.
+
+What we would like to ask
+is, what's the probability
+
+that our test statistic is
+greater than or equal to T
+
+observed given that
+H0 is true, which
+
+means that we're
+going to consider
+
+all the tail of
+this distribution.
+
+Because we want to also consider
+the case where T observed
+
+was even greater
+than what we saw.
+
+And this gives us a way of
+computing the probability
+
+that H0 is true given
+the test statistic.
+
+And this gives us our p-value.
+
+OK?
+
+So this is a way of,
+in general, comparing
+
+two probabilistic models and
+analyzing the significance
+
+of adding extra degrees
+of freedom to the model.
+
+Typically, what we'll be
+doing in today's lecture
+
+is asking whether or
+not-- if we let the means
+
+change, for example,
+between two conditions--
+
+we get a sufficient
+improvement in our ability
+
+to predict the data that our
+test statistic will allow
+
+us to reject the null hypothesis
+that the means are the same.
+
+OK.
+
+I'm going to stop
+here and see if there
+
+are any questions
+at all about this.
+
+AUDIENCE: Yes.
+
+Where did the degrees of
+freedom enter into the equation?
+
+PROFESSOR: Where did the degrees
+of freedom enter into this?
+
+Great question.
+
+The chi-square tables
+that you look up
+
+are indexed by the
+number of degrees
+
+of freedom of difference.
+
+OK?
+
+And so whenever you
+compute a chi-squared,
+
+you will compute
+it with the number
+
+of degrees of
+freedom difference.
+
+Any other questions?
+
+OK.
+
+So let's now turn to evaluating
+RNA-seq data once again.
+
+And I'm going to describe
+a method called DESeq
+
+for determining
+differential expression.
+
+And in our analysis,
+what we're going to do
+
+is we're going to let i range
+over a gene or an isoform.
+
+j is an experiment.
+
+And there may be
+multiple experiments
+
+in the same condition
+that are replicates.
+
+And Kij is the number of
+counts observed for i and j.
+
+So that's the expression of gene
+or isoform i in experiment j.
+
+Now what we need
+to do, however, is
+
+to normalize experiments
+against one another.
+
+And the normalization
+factor s sub j
+
+is computed for a
+particular experiment.
+
+And it's used to normalize
+all of the values
+
+in that experiment.
+
+And if all the experiments
+were completely identical--
+
+the read depth was identical
+and everything was the same--
+
+then all of the s
+sub js would be 1.
+
+If you had an experiment that
+had exactly twice as many reads
+
+as the other experiments,
+it's s sub j would be 2.
+
+So this scale factor is
+used to normalize things
+
+in our next slide, as we'll see.
+
+And the essential
+idea is that we're
+
+going to take the median
+value of this ratio.
+
+And the reason that the
+denominator is a geometric mean
+
+is so that no one experiment
+dominates the average.
+
+They all have equal
+weight for the average.
+
+But the geometric mean
+is simply the product
+
+of all of the expressions for
+a particular median gene taken
+
+to the root m power
+to get them back
+
+to the value for a
+single experiment.
+
+And that is the
+normalizing factor
+
+for the numerator, which
+is the number of counts
+
+for a particular gene.
+
+OK?
+
+So we're just doing
+median style normalization
+
+where s sub j is a scale factor.
+
+Once again, if all the
+experiments were the same,
+
+s sub j would be 1.
+
+If one particular experiment
+had twice as many counts
+
+as another experiment
+uniformly, s
+
+sub j would be 2, just
+for that experiment.
+
+Any questions about
+the scale factor?
+
+Yes.
+
+AUDIENCE: Sorry,
+what is the term
+
+on the bottom-- in
+the denominator?
+
+PROFESSOR: That's
+a normalizing term
+
+across-- that's the geometric
+mean of all the experiments put
+
+together.
+
+All right?
+
+So because it's the product
+of all the experiments-- m
+
+experiments-- then,
+rooted m, it's
+
+equal to the geometric mean
+of a single experiment.
+
+Any other questions?
+
+Yes.
+
+AUDIENCE: Are we normalizing
+different experiments
+
+to each other or
+different replicates
+
+of a single experiment?
+
+PROFESSOR: In this particular
+case, each one of these
+
+is a different replicate.
+
+OK?
+
+So j is ranging over
+different replicates,
+
+not over conditions, right now.
+
+So each replicate,
+each experiment,
+
+gets its own normalizing factor.
+
+We'll see, in a moment, how to
+put those replicates together
+
+to build statistical strength.
+
+But we need-- since each
+replicate has its own read
+
+depth, we have to normalize
+each one independently.
+
+OK?
+
+So what we then do is we compute
+an expression for a condition.
+
+Now a condition,
+we're going to call p.
+
+And q sub ip is the
+normalized expression
+
+for gene slash isoform
+i in condition p.
+
+So a condition may have
+multiple replicates in it.
+
+So we're going to
+average, over all
+
+of the replicates, the
+average expression,
+
+as you can see here.
+
+So we're summing over
+all the replicates
+
+for a given condition.
+
+We're going to take
+each replicate,
+
+normalize it by its scale
+factor we just computed,
+
+and then compute the normalized
+expression for a gene
+
+or an isoform in that
+particular condition.
+
+Is that clear to everybody,
+what's going on here?
+
+Now I'm describing this to
+you because the key fact is
+
+the next line, which
+is that we compute
+
+the mean for a
+particular replicate
+
+by taking the normalized
+expression for a gene
+
+and then reverse correcting
+it back to scaling it
+
+back up again for that
+particular replicate
+
+by multiplying by s sub j.
+
+But the most important
+thing is what's
+
+on the right hand side,
+which is that the variance is
+
+equal to the mean plus this
+function of the expression.
+
+And the reason this
+is important is
+
+that most other models for
+modeling expression data
+
+use Poisson models.
+
+And we've already seen,
+when we talked about library
+
+complexity, that Poisson
+models don't work that well
+
+all the time.
+
+So this is using a negative
+binomial function, once again.
+
+We saw negative
+binomials before.
+
+We're modelling both the
+mean and the variance.
+
+And the variance is a
+function, a linear function
+
+and a non-linear
+function, of the mean.
+
+So what's going to
+happen, then, is
+
+that we're going to use the
+negative binomial to compute
+
+the probability of observing
+the data in a given condition.
+
+And we can either combine
+conditions and ask,
+
+what's the probability of
+seeing the conditions combined
+
+with a single mean and variance,
+or we can separate them
+
+into a more complex
+H1 hypothesis and ask,
+
+what's the probability of
+seeing them with separate means
+
+and variances,
+and then do a test
+
+to see how significant the
+difference is to determine
+
+whether or not we can exclude
+the fact that the genes are
+
+expressed at the same level.
+
+And to give you an intuitive
+idea of what's going on,
+
+this is a plot from the paper
+showing the relationship
+
+between mean expression
+and variance.
+
+Recall, for Poisson, that
+variance is equal to mean.
+
+We only have one parameter
+to tune for Poisson,
+
+which is lambda.
+
+The purple line is Poisson.
+
+And you can check and
+see that the mean's
+
+equal to the variance
+in that case.
+
+What DESeq does is it fits the
+orange line to the observed
+
+data.
+
+Yes.
+
+AUDIENCE: I don't know where
+the v sub p comes from.
+
+Where is that, again?
+
+PROFESSOR: That's the function.
+
+V sub p, in that
+equation up there,
+
+is the function that
+we're fitting-- that's
+
+the solid orange
+line-- to the observed
+
+relationship between mean
+and variance in the data.
+
+OK?
+
+So DESeq fits that function.
+
+EdgeR is another technique that
+does not fit and instead uses
+
+the estimate that's the dotted
+line, which isn't as good.
+
+So a lot of people
+use DESeq these days
+
+for doing differential
+expression analysis
+
+because it allows the
+variance to change
+
+as the mean increases.
+
+And this is the case for
+these type of count data.
+
+Before I go on though,
+I'll pause and see
+
+if there are any questions at
+all about what's going on here.
+
+Yes.
+
+AUDIENCE: You said that mu sub
+p, then, is the [INAUDIBLE]
+
+to the data.
+
+I'm confused.
+
+How do we fit that function,
+or where does that come from?
+
+PROFESSOR: You
+mean the mu sub p?
+
+AUDIENCE: Yes.
+
+PROFESSOR: That function is fit.
+
+And the paper
+describes exactly how
+
+it's fit, which I posted
+on the Stellar site.
+
+But it's a nonlinear
+function of q, in this case.
+
+Good question.
+
+Any other questions?
+
+OK.
+
+So once again, we
+have two hypotheses,
+
+the null hypothesis that A and
+B are expressing identically,
+
+H1, A and B
+differentially express.
+
+We can compute the number
+of degrees of freedom.
+
+And we can do a likelihood
+ratio test, if we'd like,
+
+to compute the
+probability of H0.
+
+And our model in this case is
+the negative binomial model
+
+of the data, which
+fits the data better.
+
+And that's why DESeq
+does a better job
+
+than other methodologies.
+
+Because it provides a
+better approximation
+
+to the underlying noise.
+
+And the next slide
+shows what you get out
+
+of this kind of analysis,
+where the little red dots are
+
+the genes that have
+been called significant
+
+using Benjamini-Hochberg
+correction, which
+
+we talked about previously.
+
+And you can see how, as the mean
+increases, the required log 2
+
+fold change comes down
+to be significant.
+
+So oftentimes, you'll
+see plots like this
+
+in papers that describe how they
+actually computed what genes
+
+were differentially expressed.
+
+Any questions at all?
+
+Yes.
+
+AUDIENCE: Why is it
+that the significance is
+
+lower as the mean increases?
+
+PROFESSOR: Why the
+significance is lower?
+
+AUDIENCE: Or the threshold.
+
+PROFESSOR: Oh, because
+as you increase
+
+the number of observations,
+the mean value theorem
+
+is going to cause
+things to actually get
+
+closer and closer to 0.
+
+And so you need less of
+a fold change difference
+
+to be significant as you get
+more and more observations.
+
+And other questions?
+
+OK.
+
+So now we're going to
+delve into one other area.
+
+How many people have done
+hypergeometric tests before?
+
+OK.
+
+So we're going to talk
+about hypergeometric tests.
+
+So imagine that we have a
+universe, for simplicity,
+
+of 1,000 genes.
+
+OK?
+
+So we have this universe.
+
+And we have, B is a set of
+genes that there are 30 of them.
+
+And there's another set,
+A, of which there are 20.
+
+And the overlap between these
+two is a total of three genes.
+
+So it might be that
+A is the set of genes
+
+that are differentially
+expressed
+
+between two conditions.
+
+B is the set of genes
+that, you happen to know,
+
+have a particular annotation.
+
+For example, they're involved
+in stress response in the cell.
+
+And you'd like to
+know whether or not
+
+the genes that are
+differentially expressed
+
+have a significant component of
+stress response related genes
+
+or whether or not this
+occurred at random.
+
+OK?
+
+So we need to compute that.
+
+So how many ways
+could we choose B?
+
+Well, if we are going to use--
+this is n1, n2, this is big N,
+
+and this is k.
+
+All right?
+
+So the number of ways I can
+choose B is big N choose n2.
+
+That's the number of ways I can
+choose B. Is everybody with me
+
+on that?
+
+Yeah?
+
+OK.
+
+How many ways can I
+choose three elements out
+
+of A, these three that
+are going to overlap?
+
+Well, that's going
+to be n1 choose k.
+
+So that's how many ways I can
+choose these three elements.
+
+And then, how many ways could I
+choose the other elements of B?
+
+So once again, I'm figuring
+out how I can choose B. Well,
+
+how could I choose
+the rest of B?
+
+Well, how many elements do I
+have to choose, of B, here?
+
+Well, B is n too big.
+
+But I've already
+chosen k of them.
+
+Right?
+
+All right.
+
+Sorry, it's the
+other way around.
+
+The universe I can
+pick from is 1,000,
+
+which is all the elements, minus
+the elements of A that I've
+
+already chosen from
+to get those three.
+
+And then I need to pick the
+27 things they don't overlap
+
+with A. So 27 things
+that don't overlap with A
+
+would be n2 minus k.
+
+So this is the
+number ways to choose
+
+B given this set of constraints.
+
+This is the number of ways to
+choose B given no constraints.
+
+So the probability
+that I have overlap
+
+of exactly k is equal
+to this, which is,
+
+how many ways are there
+with no constraints
+
+and how many ways
+are there given
+
+that I have an overlap of k.
+
+All right?
+
+And typically, what
+I want to ask is,
+
+what is the probability
+that my observed overlap
+
+is greater than or equal to k.
+
+So this case, the
+overlap would be three.
+
+But I also would need
+to consider the fact
+
+that I might have four,
+or five, or six, which
+
+would be even more unlikely,
+but still significant.
+
+So if you look at the
+exact computation,
+
+the probability of
+three here is 0.017.
+
+And the probability that I
+have three or more is 0.02.
+
+So that's still
+pretty significant.
+
+Unlikely that would
+occur by chance.
+
+Right?
+
+That I have three or more genes
+overlapping in this situation
+
+could only happen
+two out of 100 times.
+
+Does everybody understand
+what's going on here?
+
+Any questions at all?
+
+So you're all now
+hypergeometric whizzes, right?
+
+All right?
+
+Fantastic.
+
+OK.
+
+Now we're going to turn to
+a final kind of analysis.
+
+How many people have heard of
+principal component analysis
+
+before?
+
+How many people know how to do
+principal component analysis?
+
+A few.
+
+OK.
+
+Great.
+
+Yes.
+
+AUDIENCE: Sorry,
+could you just briefly
+
+mention, again, where exactly do
+we use the hypergeometric test?
+
+What kinds of questions are
+we asking when we do that?
+
+PROFESSOR: Typically,
+they're overlap questions.
+
+So you're asking-- you have a
+universe of objects, right--
+
+like, in this case, genes.
+
+And you have a subset of
+20 and a subset of 30.
+
+Let's say these are the
+differentially expressed genes.
+
+These are genes in the
+stress response pathway.
+
+They overlap by three genes.
+
+Does that actually
+occur at random or not?
+
+All right?
+
+If I told you that there are
+a much smaller number of genes
+
+and the stress response
+genes were very much larger,
+
+it could be much easier for
+that overlap to occur at random.
+
+Good question.
+
+Any other questions?
+
+OK.
+
+So the next part of
+lecture is entitled
+
+"multivariate Gaussians
+are your friends."
+
+OK?
+
+They are friendly.
+
+They're like a puppy dog.
+
+They are just wonderful to
+play with and very friendly.
+
+And the reason most people get
+a little turned off by them
+
+is because they get this--
+the first thing they're shown
+
+is this very hairy
+looking exponential
+
+which describes what they are.
+
+And so I'm going to shy away
+from complicated looking
+
+exponentials and give you the
+puppy dog, my favorite way
+
+of looking at
+multivariate Gaussians.
+
+OK?
+
+Which, I think, is a
+great way to look at them.
+
+And the reason we need to
+look at multivariate Gaussians
+
+is that they help
+us understand what
+
+is going on with principal
+component analysis in a very
+
+straightforward way.
+
+And the reason that we want
+to use principal component
+
+analysis is that
+we're going to be
+
+able to reveal hidden factors
+and structures in our data.
+
+And they're also
+going to allow us
+
+to reduce the
+dimensionality of the data.
+
+And we'll see why in a moment.
+
+But here is the friendly version
+of multivariate Gaussians.
+
+And let me describe to you why
+I think this is so friendly.
+
+So we're all familiar with
+unidimensional Gaussians
+
+like this.
+
+Centered at zero.
+
+They have variance 1.
+
+Just very friendly
+univariate Gaussians, right?
+
+Everybody's familiar with those?
+
+Normal distributions?
+
+So let's suppose
+that we just take
+
+a whole collection of those.
+
+And we say that we
+have a vector z that
+
+is sampled from a collection
+of univariate Gaussians.
+
+And it can be as
+long as we like.
+
+OK?
+
+But they're all sampled
+from the same distribution.
+
+And what we're going to say is
+that our multivariate Gaussian,
+
+x, is going to be a matrix
+times z plus a mean.
+
+And so what this
+matrix is going to do
+
+is it's going to take all
+of our univariate Gaussians
+
+and combine them to produce
+our multivariate Gaussian.
+
+All right?
+
+So the structure
+of this matrix will
+
+describe how these single
+variate Gaussians are
+
+being mixed together to produce
+this multivariate distribution.
+
+And you can imagine
+various structures
+
+for this matrix A. Right?
+
+And the covariance
+matrix, sigma,
+
+which describes the structure
+of this multivariate Gaussian,
+
+is shown on this slide to
+be equal to A A transpose.
+
+And thus, if we knew this
+matrix A, which we may not know,
+
+we'd be able to compute the
+covariance matrix directly.
+
+OK?
+
+Let me take that one more time.
+
+We take a bunch of
+univariate Gaussians,
+
+make a vector z out of them.
+
+And just for
+clarity, right, we're
+
+going to talk about matrices and
+vectors as rows across columns.
+
+So this is n by 1.
+
+This is n by n.
+
+This is n by 1.
+
+And this is n by 1.
+
+OK?
+
+That's the dimensionality
+of these various objects
+
+we're dealing with here.
+
+So we get this vector
+of univariate Gaussians.
+
+We apply this matrix n
+to combine them together.
+
+We get out our multivariate
+Gaussian offset by some mean.
+
+Is everybody happy
+with that so far?
+
+Yes?
+
+No?
+
+You're suspending disbelief
+for the next slide.
+
+Is that-- OK.
+
+Well, here's the next
+thing I'd like to say,
+
+is that the variance of
+a vector-- we'll call it
+
+v-- times x, which
+is a random variable,
+
+is going to be equal
+to-- x is derived
+
+from this distribution--
+v transpose sigma
+
+v. And the demonstration of
+that is on the top of this page.
+
+So the variance of this
+vector-- sorry, the projection
+
+of this random variable
+onto this vector--
+
+is going to give you a
+variance in this direction
+
+as that product.
+
+So what we would
+like to do is this.
+
+We would like to find v
+sub i, which are vectors,
+
+to maximize variance
+of v sub i transpose x
+
+such that v sub i transpose
+v sub i is equal to 1.
+
+In other words, they're
+unit length vectors.
+
+So these are going to be
+called the eigenvectors.
+
+And if we think about the
+structure that we desire,
+
+what we'll find is that
+they satisfy the constraint
+
+that the covariance matrix
+times an eigenvector
+
+is equal to the
+eigenvalue associated
+
+with that vector times
+the vector itself.
+
+And with a little manipulation--
+if we multiply both sides by v
+
+sub i transpose-- v sub i equals
+v sub i transpose lambda sub i
+
+sigma squared v sub i-- and
+we move these guys around,
+
+v sub i transpose
+sigma v sub i is
+
+equal to-- these two
+guys, multiplied together,
+
+equal 1-- lambda sub i squared.
+
+This, we see up above,
+is equal to the variance
+
+when it's projected
+in the direction of v.
+
+And so lambda sub i squared is
+simply the variance associated
+
+with that direction.
+
+So the question then becomes,
+how do we find these things.
+
+And how do we discover
+these magic eigenvectors
+
+that are directions in which
+this multivariate Gaussian has
+
+its variance maximized?
+
+And we can do this by
+singular value decomposition.
+
+So we can compute this
+covariance matrix.
+
+So we compute sigma
+from the data.
+
+And then we do a singular
+value decomposition
+
+such that sigma is equal
+to U S U transpose.
+
+And that's what the singular
+value decomposition does
+
+for us is it
+decomposes the sigma
+
+matrix into these
+components where
+
+S is a diagonal matrix that
+contains the eigenvalues
+
+and U is a column.
+
+Each column is an eigenvector.
+
+So in doing a singular
+value decomposition,
+
+we get the eigenvalues
+and the eigenvectors.
+
+The other thing, you
+recall, was that sigma
+
+was equal to A A transpose
+when we started off.
+
+A was the matrix that we used to
+make our multivariate Gaussian
+
+out of our univariate Gaussians.
+
+And thus, what we can observe is
+that our multivariate Gaussian
+
+x is equal to U S to the
+1/2 times z plus a mean.
+
+So here is what's going when we
+make a multivariate Gaussian is
+
+we're taking a bunch of
+univariate Gaussians,
+
+we're scaling them, and
+we're rotating them.
+
+OK?
+
+And that makes a
+multivariate Gaussian.
+
+And then we offset this
+whole thing by a mean.
+
+Because we also have to do
+rotations around the origin.
+
+So the way I think about
+multivariate Gaussians
+
+is that it is a
+scaling and a rotation
+
+of univariate Gaussians.
+
+And implicit in that
+scaling and rotation
+
+is the discovery of the
+major directions of variance
+
+in the underlying
+data as represented
+
+by the eigenvectors.
+
+And the eigenvalues tell
+you how much of the variance
+
+is accounted for in each
+one of those dimensions.
+
+Are there any
+questions about that?
+
+I hope there are.
+
+Yes.
+
+AUDIENCE: How do you
+compute sigma from the data?
+
+Is it some magical process?
+
+PROFESSOR: The sigma of
+the value of decomposition?
+
+AUDIENCE: No.
+
+So--
+
+PROFESSOR: How do you
+compute sigma from the data?
+
+AUDIENCE: Yeah, the first step.
+
+PROFESSOR: That is
+shown in equation seven.
+
+So you can compute the means.
+
+And you know you have x,
+which are observed values.
+
+So you compute that expectation.
+
+And that is sigma.
+
+OK?
+
+Good question.
+
+Any other questions?
+
+OK.
+
+So we have these
+eigenvectors and eigenvalues,
+
+which represent the
+vectors of maximum variance
+
+in the underlying data.
+
+And we can use these to organize
+data by projecting observations
+
+onto these eigenvectors--
+or they're sometimes
+
+called principal components--
+defined dimensions
+
+of variability that help us
+organize our underlying data.
+
+We'll come back to
+that in a moment.
+
+OK.
+
+Any other questions about
+principal component analysis?
+
+Yes.
+
+AUDIENCE: [INAUDIBLE]
+e was expectation
+
+when you were
+calculating the second?
+
+PROFESSOR: Yes, e is the
+expectation is correct.
+
+AUDIENCE: And also
+what that means.
+
+PROFESSOR: It's the
+average expected value.
+
+So in the case of
+computing sigma,
+
+you would compute the expected
+value of that inner equation
+
+across all the data
+points that you see.
+
+So you'd sum up all
+the values and divide
+
+by the number of
+things that you had.
+
+Any other questions?
+
+OK.
+
+So just for calibration for
+next year, how many people
+
+think they've got a general
+idea of what principal component
+
+analysis is-- a general idea?
+
+Uh-oh.
+
+How many people who thought
+it was really interesting
+
+were sort of completely
+baffled about halfway through?
+
+OK.
+
+All right.
+
+Well, I think that
+recitation can
+
+help with some of
+those questions.
+
+But if anybody has a question
+they'd like to ask now-- No?
+
+It's that far gone?
+
+I mean, the thing with
+this sort of analysis
+
+is that if your matrix algebra
+is a little rusty, then,
+
+when you start looking
+at equations like that,
+
+you can get a little
+lost sometimes.
+
+All right.
+
+Well, let's turn, then-- if
+there aren't any brave souls
+
+who wish to ask
+a question, we'll
+
+turn to single cell
+RNA-seq analysis.
+
+So I'm a firm believer
+that single cell analysis
+
+of biological samples is
+the next big frontier.
+
+And it's being made possible
+through devices like this.
+
+This is a Fluidigm C1 chip,
+which has 96 different reaction
+
+wells, which allows
+you, in each well,
+
+to process a single
+cell independently.
+
+And the little winds are ways
+to get reagents into those cells
+
+to do things like produce
+RNA-seq ready materials.
+
+And when you do
+single cell analysis,
+
+you can take apart what's
+happening in a population.
+
+So an early paper asked some
+fairly fundamental but simple
+
+questions.
+
+For example, if you take
+two 10,000 cell aliquots
+
+of the same culture, and you
+profile them independently,
+
+and you ask how well to the
+expression values for each gene
+
+agree between sample
+A and sample B,
+
+you expect there to be a very
+good agreement between sample A
+
+and sample B in these
+10,000 cell cultures.
+
+A second question is, now,
+if you take, say, 14 cells
+
+from those cultures and you
+profile them independently,
+
+and you ask, how well
+do they correlate
+
+with what you saw in the
+10,000 cell experiment, that
+
+will tell you something about
+the population heterogeneity
+
+that you're observing.
+
+Because if they correlate
+perfectly with the 10,000 cell
+
+experiment, then you
+really know that there's
+
+no point in looking at
+individual cells in some sense,
+
+because they're all the same.
+
+Seen one, seem them all.
+
+Right?
+
+But if you find
+that each cell has
+
+its own particular
+expression fingerprint
+
+and what you're seeing in the
+10,000 cell average experiment
+
+wipes out those
+fingerprints, then you
+
+know it's very important to
+analyze each cell individually.
+
+So the analysis that was done
+asked exactly that question.
+
+So here's what I'll
+show you in these plots.
+
+So here is, on the upper left,
+the 10,000 cell experiment
+
+versus the 10,000
+cell experiment.
+
+And as you can see, the
+correlation coefficient
+
+is quite high-- 0.98--
+and looks very, very good
+
+of experiment one
+versus experiment two,
+
+or rep one, rep two.
+
+Here is a separate
+experiment which
+
+is looking at two
+individual cells
+
+and asking-- and
+plotting, for each gene,
+
+the expression in one
+cell versus the gene
+
+in the other cell.
+
+And you can see that the
+correlation coefficient's 0.54.
+
+And there's actually
+a fairly wide spread.
+
+In fact, there are genes that
+are expressed in one cell that
+
+are not expressed in the
+other cell, and vice versa.
+
+So the expression of
+these individual cells
+
+it's quite divergent.
+
+And the final panel
+shows how-- down here--
+
+how a single cell
+average on the y-axis
+
+relates to the 10,000
+cell experiment.
+
+But given the middle
+panel-- the panel B there--
+
+that is showing the fact that
+two single cells don't really
+
+relate that well to another,
+it bags other questions.
+
+For example, are the
+isoforms of the genes that
+
+are being expressed the same
+in those distinct cells?
+
+And so panel D
+shows isoforms that
+
+are the same across each one
+of the single cells being
+
+profiled, which is the
+solid bar at the top.
+
+And the bottom couple
+of rows in figure D
+
+are the 10,000 cell
+experiment average.
+
+But panel E is the
+most interesting,
+
+perhaps, which is that the
+isoforms for those four genes
+
+are being
+differentially expressed
+
+in different individual cells.
+
+And that's further supported
+by taking two of those genes
+
+and doing fluorescent in situ
+histochemistry and microscopy,
+
+and looking at the
+number of RNA molecules
+
+for each one of those, and
+noting that it corresponds
+
+to what's seen in the
+upper right hand panel.
+
+So we see that in
+individual cells,
+
+different isoforms
+are being expressed.
+
+Now these cells were
+derived from bone marrow.
+
+And they're exposed
+to lipopolysaccharide
+
+to activate an immune response.
+
+So they are clearly not all
+behaving exactly the same.
+
+And to further elucidate this,
+the authors of this paper
+
+took the gene
+expressions that they
+
+saw for a given cell
+as a large vector
+
+and computed the
+principal components,
+
+and then projected the cells
+into the first and second
+
+principal component
+or eigenvector space.
+
+And as you can see, there is
+a distinct separation of three
+
+of the cells from the
+rest of the cells, where
+
+three of the cells,
+which correlate well
+
+with principal component
+one, are thought
+
+to be mature cells that
+express certain cell surface
+
+proteins whereas the ones
+on the left-- the maturing
+
+cells-- the triangle
+depicted cells--
+
+express certain cytokines
+under the maturing legend
+
+there, on the clustergram
+on the right-hand side.
+
+And thus, the first
+principal component
+
+was able to separate those
+two different broad classes
+
+of cells.
+
+So it looks like there are
+at least two different kinds
+
+of cells in this population.
+
+And then, the authors
+asked another question,
+
+which is, can they take
+individual cell data
+
+and look at the relationship
+between pairs of genes
+
+to see which genes
+are co-expressed.
+
+And the hypothesis
+is that genes that
+
+are co-expressed
+in individual cells
+
+make up individual
+regulatory circuits.
+
+And so they hypothesize that
+the genes LRF7 and IFIT1
+
+and STAT2 and LRF7 are all in an
+anti-viral regulatory circuit.
+
+They then ask the question,
+if they knocked out
+
+LRF7, which is the second
+panel on the right-hand side,
+
+would they oblate
+downstream gene expression.
+
+And they partially did.
+
+And they thought that since
+STAT2 and LRF7 are both thought
+
+to be regulators of
+the circuit and they're
+
+both downstream of the
+interfering receptor,
+
+they thought if they knocked
+out the interfering receptor,
+
+they would oblate most of
+the anti-viral cluster,
+
+which, in fact, they did.
+
+So what this is suggesting
+is that, first, single cell
+
+analysis is
+extraordinarily important
+
+to understand what's going
+on in individual cells.
+
+Because in a cell culture, the
+cells can be quite different.
+
+And secondarily, it's
+possible, within the context
+
+of individual single
+cell analysis,
+
+to be able to pick out
+regulatory circuits that
+
+wouldn't be as
+evident when you're
+
+looking at cells en masse.
+
+And finally-- I'll thank Mike
+for the next two slides--
+
+I wanted to point
+out that quality
+
+metrics for RNA-seq data for
+single cells is very important.
+
+And we talked about library
+complexity earlier in the term.
+
+And here, you can see that as
+library complexity increases,
+
+expression of coefficient
+of variation, which
+
+is the standard
+deviation over the mean,
+
+comes down as you get
+sufficient library complexity.
+
+And furthermore, as library
+complexity increases,
+
+mean expression increases.
+
+And the cells that are in
+red were classified as bad
+
+by microscopy, from the Fluidigm
+instrument processing step.
+
+So I think you can see that
+single cell analysis is going
+
+to be extraordinarily
+important and can reveal
+
+a lot of information that is
+not present in these large batch
+
+experiments.
+
+And it's coming
+to a lab near you.
+
+So on that note, I'll thank
+you very much for today.
+
+And we'll see you
+later in the term.
+
+And Professor Burge will
+return at the next lecture.
+
+Thanks very much.
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index 0000000000000000000000000000000000000000..9f43c90df1c10bd487e7c665a5f5e3caf4eb66cc
--- /dev/null
+++ b/N9f0MIzNcmI.txt
@@ -0,0 +1,1083 @@
+align:start position:0%
+ 
+so case a wig Zeeman effect so what are
+
+ align:start position:0%
+so case a wig Zeeman effect so what are
+ 
+
+ align:start position:0%
+so case a wig Zeeman effect so what are
+our states here we discovered that and
+
+ align:start position:0%
+our states here we discovered that and
+ 
+
+ align:start position:0%
+our states here we discovered that and
+we know those are the couple basis
+
+ align:start position:0%
+we know those are the couple basis
+ 
+
+ align:start position:0%
+we know those are the couple basis
+states and the states of h 0 tilde
+
+ align:start position:0%
+states and the states of h 0 tilde
+ 
+
+ align:start position:0%
+states and the states of h 0 tilde
+eigenstates are eigenstates they're the
+
+ align:start position:0%
+eigenstates are eigenstates they're the
+ 
+
+ align:start position:0%
+eigenstates are eigenstates they're the
+approximate that eigenstates are the
+
+ align:start position:0%
+approximate that eigenstates are the
+ 
+
+ align:start position:0%
+approximate that eigenstates are the
+states n l j MJ and the energies were
+
+ align:start position:0%
+states n l j MJ and the energies were
+ 
+
+ align:start position:0%
+states n l j MJ and the energies were
+energies of dependent on N and J we had
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the 1 s 1/2 to s 1/2 to P 1/2 + 2 p3
+
+ align:start position:0%
+so the 1 s 1/2 to s 1/2 to P 1/2 + 2 p3
+ 
+
+ align:start position:0%
+so the 1 s 1/2 to s 1/2 to P 1/2 + 2 p3
+halves roughly to remind you of what
+
+ align:start position:0%
+halves roughly to remind you of what
+ 
+
+ align:start position:0%
+halves roughly to remind you of what
+happened the original states were
+
+ align:start position:0%
+happened the original states were
+ 
+
+ align:start position:0%
+happened the original states were
+shifted and we use the J quantum number
+
+ align:start position:0%
+shifted and we use the J quantum number
+ 
+
+ align:start position:0%
+shifted and we use the J quantum number
+in here and and those are our multiplets
+
+ align:start position:0%
+in here and and those are our multiplets
+ 
+
+ align:start position:0%
+in here and and those are our multiplets
+those are our multiplicity we have a lot
+
+ align:start position:0%
+those are our multiplicity we have a lot
+ 
+
+ align:start position:0%
+those are our multiplicity we have a lot
+of degeneracy as usual so this is the
+
+ align:start position:0%
+of degeneracy as usual so this is the
+ 
+
+ align:start position:0%
+of degeneracy as usual so this is the
+generous e here and the generous e here
+
+ align:start position:0%
+generous e here and the generous e here
+ 
+
+ align:start position:0%
+generous e here and the generous e here
+because a multiplet p3 halves is j equal
+
+ align:start position:0%
+because a multiplet p3 halves is j equal
+ 
+
+ align:start position:0%
+because a multiplet p3 halves is j equal
+three-halves and that's four states here
+
+ align:start position:0%
+three-halves and that's four states here
+ 
+
+ align:start position:0%
+three-halves and that's four states here
+you have two states and here you have
+
+ align:start position:0%
+you have two states and here you have
+ 
+
+ align:start position:0%
+you have two states and here you have
+two states as well so quite a bit of
+
+ align:start position:0%
+two states as well so quite a bit of
+ 
+
+ align:start position:0%
+two states as well so quite a bit of
+states that are degenerate
+
+ align:start position:0%
+states that are degenerate
+ 
+
+ align:start position:0%
+states that are degenerate
+so in principle when we do the Zeeman
+
+ align:start position:0%
+so in principle when we do the Zeeman
+ 
+
+ align:start position:0%
+so in principle when we do the Zeeman
+splitting we may
+
+ align:start position:0%
+splitting we may
+ 
+
+ align:start position:0%
+splitting we may
+have to consider the full matrix n LJ MJ
+
+ align:start position:0%
+have to consider the full matrix n LJ MJ
+ 
+
+ align:start position:0%
+have to consider the full matrix n LJ MJ
+Delta H demon and L prime J and prime J
+
+ align:start position:0%
+Delta H demon and L prime J and prime J
+ 
+
+ align:start position:0%
+Delta H demon and L prime J and prime J
+so what are our degeneracies our
+
+ align:start position:0%
+so what are our degeneracies our
+ 
+
+ align:start position:0%
+so what are our degeneracies our
+degeneracies are when you have a given
+
+ align:start position:0%
+degeneracies are when you have a given
+ 
+
+ align:start position:0%
+degeneracies are when you have a given
+value of J so they did a degenerate
+
+ align:start position:0%
+value of J so they did a degenerate
+ 
+
+ align:start position:0%
+value of J so they did a degenerate
+subspace can have different else for
+
+ align:start position:0%
+subspace can have different else for
+ 
+
+ align:start position:0%
+subspace can have different else for
+example here but the same J and
+
+ align:start position:0%
+example here but the same J and
+ 
+
+ align:start position:0%
+example here but the same J and
+therefore different MJ's or within a
+
+ align:start position:0%
+therefore different MJ's or within a
+ 
+
+ align:start position:0%
+therefore different MJ's or within a
+given J multiplet it might have
+
+ align:start position:0%
+given J multiplet it might have
+ 
+
+ align:start position:0%
+given J multiplet it might have
+different MJ's so this is the scope of
+
+ align:start position:0%
+different MJ's so this is the scope of
+ 
+
+ align:start position:0%
+different MJ's so this is the scope of
+the degeneracy and in principle we may
+
+ align:start position:0%
+the degeneracy and in principle we may
+ 
+
+ align:start position:0%
+the degeneracy and in principle we may
+have to diagonalize a matrix like that
+
+ align:start position:0%
+have to diagonalize a matrix like that
+ 
+
+ align:start position:0%
+have to diagonalize a matrix like that
+by looking at the degenerate spaces if
+
+ align:start position:0%
+by looking at the degenerate spaces if
+ 
+
+ align:start position:0%
+by looking at the degenerate spaces if
+you are doing the level 2 you would have
+
+ align:start position:0%
+you are doing the level 2 you would have
+ 
+
+ align:start position:0%
+you are doing the level 2 you would have
+to discuss this four states here you
+
+ align:start position:0%
+to discuss this four states here you
+ 
+
+ align:start position:0%
+to discuss this four states here you
+would have to discuss these other four
+
+ align:start position:0%
+would have to discuss these other four
+ 
+
+ align:start position:0%
+would have to discuss these other four
+states happily we don't have to do that
+
+ align:start position:0%
+states happily we don't have to do that
+ 
+
+ align:start position:0%
+states happily we don't have to do that
+much because as usual
+
+ align:start position:0%
+much because as usual
+ 
+
+ align:start position:0%
+much because as usual
+well Delta H diamond is proportional to
+
+ align:start position:0%
+well Delta H diamond is proportional to
+ 
+
+ align:start position:0%
+well Delta H diamond is proportional to
+L Z plus two s Z and this commutes with
+
+ align:start position:0%
+L Z plus two s Z and this commutes with
+ 
+
+ align:start position:0%
+L Z plus two s Z and this commutes with
+l squared with Delta H Zeeman l squared
+
+ align:start position:0%
+l squared with Delta H Zeeman l squared
+ 
+
+ align:start position:0%
+l squared with Delta H Zeeman l squared
+commutes with ne L operator is certainly
+
+ align:start position:0%
+commutes with ne L operator is certainly
+ 
+
+ align:start position:0%
+commutes with ne L operator is certainly
+commute with n es operator they don't
+
+ align:start position:0%
+commute with n es operator they don't
+ 
+
+ align:start position:0%
+commute with n es operator they don't
+even talk to each other and therefore l
+
+ align:start position:0%
+even talk to each other and therefore l
+ 
+
+ align:start position:0%
+even talk to each other and therefore l
+squared commutes with l cement which
+
+ align:start position:0%
+squared commutes with l cement which
+ 
+
+ align:start position:0%
+squared commutes with l cement which
+means that when L is different from L
+
+ align:start position:0%
+means that when L is different from L
+ 
+
+ align:start position:0%
+means that when L is different from L
+prime this matrix element has to vanish
+
+ align:start position:0%
+prime this matrix element has to vanish
+ 
+
+ align:start position:0%
+prime this matrix element has to vanish
+this is our remark from perturbation
+
+ align:start position:0%
+this is our remark from perturbation
+ 
+
+ align:start position:0%
+this is our remark from perturbation
+theory long long ago
+
+ align:start position:0%
+theory long long ago
+ 
+
+ align:start position:0%
+theory long long ago
+you have another operator for which the
+
+ align:start position:0%
+you have another operator for which the
+ 
+
+ align:start position:0%
+you have another operator for which the
+states have different eigenvalues
+
+ align:start position:0%
+states have different eigenvalues
+ 
+
+ align:start position:0%
+states have different eigenvalues
+commutes with your perturbation the
+
+ align:start position:0%
+commutes with your perturbation the
+ 
+
+ align:start position:0%
+commutes with your perturbation the
+matrix element of the perturbation must
+
+ align:start position:0%
+matrix element of the perturbation must
+ 
+
+ align:start position:0%
+matrix element of the perturbation must
+vanish between those states so we don't
+
+ align:start position:0%
+vanish between those states so we don't
+ 
+
+ align:start position:0%
+vanish between those states so we don't
+have Agins states like that and when L
+
+ align:start position:0%
+have Agins states like that and when L
+ 
+
+ align:start position:0%
+have Agins states like that and when L
+is equal to L prime are ready so we
+
+ align:start position:0%
+is equal to L prime are ready so we
+ 
+
+ align:start position:0%
+is equal to L prime are ready so we
+focus on L equals to L Prime
+
+ align:start position:0%
+focus on L equals to L Prime
+ 
+
+ align:start position:0%
+focus on L equals to L Prime
+so we only need to worry within
+
+ align:start position:0%
+so we only need to worry within
+ 
+
+ align:start position:0%
+so we only need to worry within
+multiplets so you have n LJ MJ Delta H
+
+ align:start position:0%
+multiplets so you have n LJ MJ Delta H
+ 
+
+ align:start position:0%
+multiplets so you have n LJ MJ Delta H
+demon now and LJ MJ prime is an issue of
+
+ align:start position:0%
+demon now and LJ MJ prime is an issue of
+ 
+
+ align:start position:0%
+demon now and LJ MJ prime is an issue of
+M J prime now but demon thing commutes
+
+ align:start position:0%
+M J prime now but demon thing commutes
+ 
+
+ align:start position:0%
+M J prime now but demon thing commutes
+with j z jz commute with delta h demon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+JZ is LZ plus s z and z components in
+
+ align:start position:0%
+JZ is LZ plus s z and z components in
+ 
+
+ align:start position:0%
+JZ is LZ plus s z and z components in
+angular momentum to identical components
+
+ align:start position:0%
+angular momentum to identical components
+ 
+
+ align:start position:0%
+angular momentum to identical components
+always commute of course
+
+ align:start position:0%
+always commute of course
+ 
+
+ align:start position:0%
+always commute of course
+so jz commute with delta h seaman so
+
+ align:start position:0%
+so jz commute with delta h seaman so
+ 
+
+ align:start position:0%
+so jz commute with delta h seaman so
+this thing will vanish and less M is
+
+ align:start position:0%
+this thing will vanish and less M is
+ 
+
+ align:start position:0%
+this thing will vanish and less M is
+equal to M Prime and that's great
+
+ align:start position:0%
+equal to M Prime and that's great
+ 
+
+ align:start position:0%
+equal to M Prime and that's great
+because you're back to non degenerate
+
+ align:start position:0%
+because you're back to non degenerate
+ 
+
+ align:start position:0%
+because you're back to non degenerate
+perturbation Theory Hall matrix this
+
+ align:start position:0%
+perturbation Theory Hall matrix this
+ 
+
+ align:start position:0%
+perturbation Theory Hall matrix this
+Zeeman thing could have turned out to be
+
+ align:start position:0%
+Zeeman thing could have turned out to be
+ 
+
+ align:start position:0%
+Zeeman thing could have turned out to be
+complicated matrices now it's perfectly
+
+ align:start position:0%
+complicated matrices now it's perfectly
+ 
+
+ align:start position:0%
+complicated matrices now it's perfectly
+diagonal in this basis there's nothing
+
+ align:start position:0%
+diagonal in this basis there's nothing
+ 
+
+ align:start position:0%
+diagonal in this basis there's nothing
+to worry about here except that it's
+
+ align:start position:0%
+to worry about here except that it's
+ 
+
+ align:start position:0%
+to worry about here except that it's
+still not easy to compute as we will see
+
+ align:start position:0%
+still not easy to compute as we will see
+ 
+
+ align:start position:0%
+still not easy to compute as we will see
+so what what do we need to compute we'll
+
+ align:start position:0%
+so what what do we need to compute we'll
+ 
+
+ align:start position:0%
+so what what do we need to compute we'll
+have the first order Corrections due to
+
+ align:start position:0%
+have the first order Corrections due to
+ 
+
+ align:start position:0%
+have the first order Corrections due to
+Zeeman on the m l j MJ basis is equal
+
+ align:start position:0%
+Zeeman on the m l j MJ basis is equal
+ 
+
+ align:start position:0%
+Zeeman on the m l j MJ basis is equal
+well the Zeeman Hamiltonian has an e
+
+ align:start position:0%
+well the Zeeman Hamiltonian has an e
+ 
+
+ align:start position:0%
+well the Zeeman Hamiltonian has an e
+over to MC so let's put it there e let's
+
+ align:start position:0%
+over to MC so let's put it there e let's
+ 
+
+ align:start position:0%
+over to MC so let's put it there e let's
+put the big close to the e to MC and now
+
+ align:start position:0%
+put the big close to the e to MC and now
+ 
+
+ align:start position:0%
+put the big close to the e to MC and now
+we have to do n LJ m j LZ plus 2 SZ + LJ
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy perfectly they either know and
+
+ align:start position:0%
+energy perfectly they either know and
+ 
+
+ align:start position:0%
+energy perfectly they either know and
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+non-degenerate perturbation theory is
+
+ align:start position:0%
+non-degenerate perturbation theory is
+ 
+
+ align:start position:0%
+non-degenerate perturbation theory is
+gonna give us all the energies we want
+
+ align:start position:0%
+gonna give us all the energies we want
+ 
+
+ align:start position:0%
+gonna give us all the energies we want
+all the splittings we want so basically
+
+ align:start position:0%
+all the splittings we want so basically
+ 
+
+ align:start position:0%
+all the splittings we want so basically
+what's going to happen as you didn't see
+
+ align:start position:0%
+what's going to happen as you didn't see
+ 
+
+ align:start position:0%
+what's going to happen as you didn't see
+here is that things don't mix everything
+
+ align:start position:0%
+here is that things don't mix everything
+ 
+
+ align:start position:0%
+here is that things don't mix everything
+is there honestly these two levels have
+
+ align:start position:0%
+is there honestly these two levels have
+ 
+
+ align:start position:0%
+is there honestly these two levels have
+been a split these two levels I'm going
+
+ align:start position:0%
+been a split these two levels I'm going
+ 
+
+ align:start position:0%
+been a split these two levels I'm going
+to split these four levels are going to
+
+ align:start position:0%
+to split these four levels are going to
+ 
+
+ align:start position:0%
+to split these four levels are going to
+split everything is gonna split here
+
+ align:start position:0%
+split everything is gonna split here
+ 
+
+ align:start position:0%
+split everything is gonna split here
+the remarkable thing of this formula and
+
+ align:start position:0%
+the remarkable thing of this formula and
+ 
+
+ align:start position:0%
+the remarkable thing of this formula and
+it's going to keep us busy for about 10
+
+ align:start position:0%
+it's going to keep us busy for about 10
+ 
+
+ align:start position:0%
+it's going to keep us busy for about 10
+15 more minutes is that this thing this
+
+ align:start position:0%
+15 more minutes is that this thing this
+ 
+
+ align:start position:0%
+15 more minutes is that this thing this
+matrix element is proportional to MJ so
+
+ align:start position:0%
+matrix element is proportional to MJ so
+ 
+
+ align:start position:0%
+matrix element is proportional to MJ so
+the state split proportional to the M
+
+ align:start position:0%
+the state split proportional to the M
+ 
+
+ align:start position:0%
+the state split proportional to the M
+quantum number the state with M equal
+
+ align:start position:0%
+quantum number the state with M equal
+ 
+
+ align:start position:0%
+quantum number the state with M equal
+three halves will split three times as
+
+ align:start position:0%
+three halves will split three times as
+ 
+
+ align:start position:0%
+three halves will split three times as
+much as the state with M equal 1/2 and
+
+ align:start position:0%
+much as the state with M equal 1/2 and
+ 
+
+ align:start position:0%
+much as the state with M equal 1/2 and
+that's not obvious here
+
+ align:start position:0%
+that's not obvious here
+ 
+
+ align:start position:0%
+that's not obvious here
+it's a remarkable result it's part of
+
+ align:start position:0%
+it's a remarkable result it's part of
+ 
+
+ align:start position:0%
+it's a remarkable result it's part of
+what's called the vintner Edward theorem
+
+ align:start position:0%
+what's called the vintner Edward theorem
+ 
+
+ align:start position:0%
+what's called the vintner Edward theorem
+something that you study in graduate
+
+ align:start position:0%
+something that you study in graduate
+ 
+
+ align:start position:0%
+something that you study in graduate
+quantum mechanics but we're going to see
+
+ align:start position:0%
+quantum mechanics but we're going to see
+ 
+
+ align:start position:0%
+quantum mechanics but we're going to see
+a bit of it the beginning of it in this
+
+ align:start position:0%
+a bit of it the beginning of it in this
+ 
+
+ align:start position:0%
+a bit of it the beginning of it in this
+computation and it's a fairly remarkable
+
+ align:start position:0%
+computation and it's a fairly remarkable
+ 
+
+ align:start position:0%
+computation and it's a fairly remarkable
+result so the remarkable result here
+
+ align:start position:0%
+result so the remarkable result here
+ 
+
+ align:start position:0%
+result so the remarkable result here
+markable is that e ones are proportional
+
+ align:start position:0%
+markable is that e ones are proportional
+ 
+
+ align:start position:0%
+markable is that e ones are proportional
+to MJ and that defines a linear
+
+ align:start position:0%
+to MJ and that defines a linear
+ 
+
+ align:start position:0%
+to MJ and that defines a linear
+splitting because it's linearly
+
+ align:start position:0%
+splitting because it's linearly
+ 
+
+ align:start position:0%
+splitting because it's linearly
+proportional to the magnitude of the
+
+ align:start position:0%
+proportional to the magnitude of the
+ 
+
+ align:start position:0%
+proportional to the magnitude of the
+magnetic field and divides the states
+
+ align:start position:0%
+magnetic field and divides the states
+ 
+
+ align:start position:0%
+magnetic field and divides the states
+nicely so we want to understand this
+
+ align:start position:0%
+nicely so we want to understand this
+ 
+
+ align:start position:0%
+nicely so we want to understand this
+matrix element and there's a little
+
+ align:start position:0%
+matrix element and there's a little
+ 
+
+ align:start position:0%
+matrix element and there's a little
+thing we can do notice that LZ plus 2's
+
+ align:start position:0%
+thing we can do notice that LZ plus 2's
+ 
+
+ align:start position:0%
+thing we can do notice that LZ plus 2's
+Z is equal to JZ + SZ you can take one
+
+ align:start position:0%
+Z is equal to JZ + SZ you can take one
+ 
+
+ align:start position:0%
+Z is equal to JZ + SZ you can take one
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+the SZ is and complete jz and you're
+
+ align:start position:0%
+the SZ is and complete jz and you're
+ 
+
+ align:start position:0%
+the SZ is and complete jz and you're
+left with that so the matrix element n
+
+ align:start position:0%
+left with that so the matrix element n
+ 
+
+ align:start position:0%
+left with that so the matrix element n
+LJ m LZ + 2 SZ m LJ MJ is equal if you
+
+ align:start position:0%
+LJ m LZ + 2 SZ m LJ MJ is equal if you
+ 
+
+ align:start position:0%
+LJ m LZ + 2 SZ m LJ MJ is equal if you
+have a jz that gives you just something
+
+ align:start position:0%
+have a jz that gives you just something
+ 
+
+ align:start position:0%
+have a jz that gives you just something
+proportional to H MJ plus m l j m j SZ +
+
+ align:start position:0%
+proportional to H MJ plus m l j m j SZ +
+ 
+
+ align:start position:0%
+proportional to H MJ plus m l j m j SZ +
+LJ m j so okay a little bit of the
+
+ align:start position:0%
+LJ m j so okay a little bit of the
+ 
+
+ align:start position:0%
+LJ m j so okay a little bit of the
+mystery baby seems to you at least
+
+ align:start position:0%
+mystery baby seems to you at least
+ 
+
+ align:start position:0%
+mystery baby seems to you at least
+consistent here I said this matrix
+
+ align:start position:0%
+consistent here I said this matrix
+ 
+
+ align:start position:0%
+consistent here I said this matrix
+element turns out to be proportional to
+
+ align:start position:0%
+element turns out to be proportional to
+ 
+
+ align:start position:0%
+element turns out to be proportional to
+M J and certainly this piece having to
+
+ align:start position:0%
+M J and certainly this piece having to
+ 
+
+ align:start position:0%
+M J and certainly this piece having to
+do with the J component here is
+
+ align:start position:0%
+do with the J component here is
+ 
+
+ align:start position:0%
+do with the J component here is
+proportional to M J the mystery that
+
+ align:start position:0%
+proportional to M J the mystery that
+ 
+
+ align:start position:0%
+proportional to M J the mystery that
+remains is why this matrix element would
+
+ align:start position:0%
+remains is why this matrix element would
+ 
+
+ align:start position:0%
+remains is why this matrix element would
+be proportional to M J
\ No newline at end of file
diff --git a/O06G95nJrQI.txt b/O06G95nJrQI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f89e755f53f03b559c48d1f15325e66a46c9656
--- /dev/null
+++ b/O06G95nJrQI.txt
@@ -0,0 +1,8024 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we are going to spend today
+
+ align:start position:0%
+so we are going to spend today
+ 
+
+ align:start position:0%
+so we are going to spend today
+mostly
+
+ align:start position:0%
+mostly
+ 
+
+ align:start position:0%
+mostly
+on the cloudiest clap around equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remember we're still in chapter
+
+ align:start position:0%
+and remember we're still in chapter
+ 
+
+ align:start position:0%
+and remember we're still in chapter
+seven
+
+ align:start position:0%
+seven
+ 
+
+ align:start position:0%
+seven
+of the text okay good so what is the CC
+
+ align:start position:0%
+of the text okay good so what is the CC
+ 
+
+ align:start position:0%
+of the text okay good so what is the CC
+equation the CC equation is the
+
+ align:start position:0%
+equation the CC equation is the
+ 
+
+ align:start position:0%
+equation the CC equation is the
+following
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have a phase diagram here I'm going
+
+ align:start position:0%
+we have a phase diagram here I'm going
+ 
+
+ align:start position:0%
+we have a phase diagram here I'm going
+to draw a little close-up section
+
+ align:start position:0%
+to draw a little close-up section
+ 
+
+ align:start position:0%
+to draw a little close-up section
+of a phase diagram and this is very
+
+ align:start position:0%
+of a phase diagram and this is very
+ 
+
+ align:start position:0%
+of a phase diagram and this is very
+generic
+
+ align:start position:0%
+generic
+ 
+
+ align:start position:0%
+generic
+and all right so let's say we have
+
+ align:start position:0%
+and all right so let's say we have
+ 
+
+ align:start position:0%
+and all right so let's say we have
+Alpha
+
+ align:start position:0%
+Alpha
+ 
+
+ align:start position:0%
+Alpha
+I like to use Colors Let's make alpha
+
+ align:start position:0%
+I like to use Colors Let's make alpha
+ 
+
+ align:start position:0%
+I like to use Colors Let's make alpha
+kind of teal
+
+ align:start position:0%
+kind of teal
+ 
+
+ align:start position:0%
+kind of teal
+and let's say we have beta
+
+ align:start position:0%
+and let's say we have beta
+ 
+
+ align:start position:0%
+and let's say we have beta
+and beta is going to be
+
+ align:start position:0%
+and beta is going to be
+ 
+
+ align:start position:0%
+and beta is going to be
+kind of purple
+
+ align:start position:0%
+kind of purple
+ 
+
+ align:start position:0%
+kind of purple
+and we have a coexistence line
+
+ align:start position:0%
+and we have a coexistence line
+ 
+
+ align:start position:0%
+and we have a coexistence line
+between them
+
+ align:start position:0%
+between them
+ 
+
+ align:start position:0%
+between them
+and at any point on that line we have a
+
+ align:start position:0%
+and at any point on that line we have a
+ 
+
+ align:start position:0%
+and at any point on that line we have a
+slope
+
+ align:start position:0%
+slope
+ 
+
+ align:start position:0%
+slope
+right we have rise over run
+
+ align:start position:0%
+right we have rise over run
+ 
+
+ align:start position:0%
+right we have rise over run
+so here's a little DP
+
+ align:start position:0%
+so here's a little DP
+ 
+
+ align:start position:0%
+so here's a little DP
+and here's a little DT
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what makes these phases
+
+ align:start position:0%
+okay what makes these phases
+ 
+
+ align:start position:0%
+okay what makes these phases
+stable well over here mu of alpha is
+
+ align:start position:0%
+stable well over here mu of alpha is
+ 
+
+ align:start position:0%
+stable well over here mu of alpha is
+less the MU of beta right that's that's
+
+ align:start position:0%
+less the MU of beta right that's that's
+ 
+
+ align:start position:0%
+less the MU of beta right that's that's
+the definition we developed
+
+ align:start position:0%
+the definition we developed
+ 
+
+ align:start position:0%
+the definition we developed
+last time and over here
+
+ align:start position:0%
+last time and over here
+ 
+
+ align:start position:0%
+last time and over here
+mu of beta is less than mu of alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the coexistence line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right last time we developed the
+
+ align:start position:0%
+all right last time we developed the
+ 
+
+ align:start position:0%
+all right last time we developed the
+conditions
+
+ align:start position:0%
+conditions
+ 
+
+ align:start position:0%
+conditions
+for two-phase equilibrium so on that
+
+ align:start position:0%
+for two-phase equilibrium so on that
+ 
+
+ align:start position:0%
+for two-phase equilibrium so on that
+coexistence line mu of alpha which is of
+
+ align:start position:0%
+coexistence line mu of alpha which is of
+ 
+
+ align:start position:0%
+coexistence line mu of alpha which is of
+course a function of temperature and
+
+ align:start position:0%
+course a function of temperature and
+ 
+
+ align:start position:0%
+course a function of temperature and
+pressure equals mu of theta which is a
+
+ align:start position:0%
+pressure equals mu of theta which is a
+ 
+
+ align:start position:0%
+pressure equals mu of theta which is a
+function of temperature and pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I take a little jog
+
+ align:start position:0%
+so if I take a little jog
+ 
+
+ align:start position:0%
+so if I take a little jog
+I take a little jog from here let's see
+
+ align:start position:0%
+I take a little jog from here let's see
+ 
+
+ align:start position:0%
+I take a little jog from here let's see
+and start running out of colors pretty
+
+ align:start position:0%
+and start running out of colors pretty
+ 
+
+ align:start position:0%
+and start running out of colors pretty
+soon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's take a little jog let's walk a
+
+ align:start position:0%
+let's take a little jog let's walk a
+ 
+
+ align:start position:0%
+let's take a little jog let's walk a
+little bit
+
+ align:start position:0%
+little bit
+ 
+
+ align:start position:0%
+little bit
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+if I'm going to stay on the line I need
+
+ align:start position:0%
+if I'm going to stay on the line I need
+ 
+
+ align:start position:0%
+if I'm going to stay on the line I need
+demu of alpha
+
+ align:start position:0%
+demu of alpha
+ 
+
+ align:start position:0%
+demu of alpha
+which is of course a function of
+
+ align:start position:0%
+which is of course a function of
+ 
+
+ align:start position:0%
+which is of course a function of
+temperature and pressure to be equal to
+
+ align:start position:0%
+temperature and pressure to be equal to
+ 
+
+ align:start position:0%
+temperature and pressure to be equal to
+D mu of beta
+
+ align:start position:0%
+D mu of beta
+ 
+
+ align:start position:0%
+D mu of beta
+as a function of temperature and
+
+ align:start position:0%
+as a function of temperature and
+ 
+
+ align:start position:0%
+as a function of temperature and
+pressure all right I want you to think
+
+ align:start position:0%
+pressure all right I want you to think
+ 
+
+ align:start position:0%
+pressure all right I want you to think
+about uh this line as a Mountain Ridge
+
+ align:start position:0%
+about uh this line as a Mountain Ridge
+ 
+
+ align:start position:0%
+about uh this line as a Mountain Ridge
+and you're walking along the Mountain
+
+ align:start position:0%
+and you're walking along the Mountain
+ 
+
+ align:start position:0%
+and you're walking along the Mountain
+Ridge
+
+ align:start position:0%
+Ridge
+ 
+
+ align:start position:0%
+Ridge
+and you want to stay on the ridge
+
+ align:start position:0%
+and you want to stay on the ridge
+ 
+
+ align:start position:0%
+and you want to stay on the ridge
+because if you fall off the ridge you
+
+ align:start position:0%
+because if you fall off the ridge you
+ 
+
+ align:start position:0%
+because if you fall off the ridge you
+you fall very far it hurts so and the
+
+ align:start position:0%
+you fall very far it hurts so and the
+ 
+
+ align:start position:0%
+you fall very far it hurts so and the
+ridge is a curvy line and so if you want
+
+ align:start position:0%
+ridge is a curvy line and so if you want
+ 
+
+ align:start position:0%
+ridge is a curvy line and so if you want
+to stay on the ridge right you just
+
+ align:start position:0%
+to stay on the ridge right you just
+ 
+
+ align:start position:0%
+to stay on the ridge right you just
+can't walk in any direction for as long
+
+ align:start position:0%
+can't walk in any direction for as long
+ 
+
+ align:start position:0%
+can't walk in any direction for as long
+as you like
+
+ align:start position:0%
+as you like
+ 
+
+ align:start position:0%
+as you like
+if you want to stay in the ridge you
+
+ align:start position:0%
+if you want to stay in the ridge you
+ 
+
+ align:start position:0%
+if you want to stay in the ridge you
+can't walk in X and Y as much as you
+
+ align:start position:0%
+can't walk in X and Y as much as you
+ 
+
+ align:start position:0%
+can't walk in X and Y as much as you
+like Northwest
+
+ align:start position:0%
+like Northwest
+ 
+
+ align:start position:0%
+like Northwest
+east and south you need to stay on the
+
+ align:start position:0%
+east and south you need to stay on the
+ 
+
+ align:start position:0%
+east and south you need to stay on the
+ridge so you only have one degree of
+
+ align:start position:0%
+ridge so you only have one degree of
+ 
+
+ align:start position:0%
+ridge so you only have one degree of
+Freedom right if you walk a little bit
+
+ align:start position:0%
+Freedom right if you walk a little bit
+ 
+
+ align:start position:0%
+Freedom right if you walk a little bit
+north you've got to adjust a little bit
+
+ align:start position:0%
+north you've got to adjust a little bit
+ 
+
+ align:start position:0%
+north you've got to adjust a little bit
+west or east to stay on the ridge
+
+ align:start position:0%
+west or east to stay on the ridge
+ 
+
+ align:start position:0%
+west or east to stay on the ridge
+that's pretty intuitive if you're on a
+
+ align:start position:0%
+that's pretty intuitive if you're on a
+ 
+
+ align:start position:0%
+that's pretty intuitive if you're on a
+Mountain Ridge you don't have to go
+
+ align:start position:0%
+Mountain Ridge you don't have to go
+ 
+
+ align:start position:0%
+Mountain Ridge you don't have to go
+through all that thinking and think
+
+ align:start position:0%
+through all that thinking and think
+ 
+
+ align:start position:0%
+through all that thinking and think
+about multivariable calculus you just
+
+ align:start position:0%
+about multivariable calculus you just
+ 
+
+ align:start position:0%
+about multivariable calculus you just
+don't want to fall off the ridge but
+
+ align:start position:0%
+don't want to fall off the ridge but
+ 
+
+ align:start position:0%
+don't want to fall off the ridge but
+that's what's going on here we want to
+
+ align:start position:0%
+that's what's going on here we want to
+ 
+
+ align:start position:0%
+that's what's going on here we want to
+stay on the coexistence line This is the
+
+ align:start position:0%
+stay on the coexistence line This is the
+ 
+
+ align:start position:0%
+stay on the coexistence line This is the
+condition to stay on the line
+
+ align:start position:0%
+condition to stay on the line
+ 
+
+ align:start position:0%
+condition to stay on the line
+right the potentials are equal and so if
+
+ align:start position:0%
+right the potentials are equal and so if
+ 
+
+ align:start position:0%
+right the potentials are equal and so if
+I take a little step I've got to stay
+
+ align:start position:0%
+I take a little step I've got to stay
+ 
+
+ align:start position:0%
+I take a little step I've got to stay
+take a step such that the changes of
+
+ align:start position:0%
+take a step such that the changes of
+ 
+
+ align:start position:0%
+take a step such that the changes of
+these chemical potentials are also equal
+
+ align:start position:0%
+these chemical potentials are also equal
+ 
+
+ align:start position:0%
+these chemical potentials are also equal
+so that I stay on the ridge
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay questions on this concept because
+
+ align:start position:0%
+okay questions on this concept because
+ 
+
+ align:start position:0%
+okay questions on this concept because
+we're going to start evaluating this
+
+ align:start position:0%
+we're going to start evaluating this
+ 
+
+ align:start position:0%
+we're going to start evaluating this
+condition now so it's going to get kind
+
+ align:start position:0%
+condition now so it's going to get kind
+ 
+
+ align:start position:0%
+condition now so it's going to get kind
+of mathy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so let's evaluate that condition that's
+
+ align:start position:0%
+so let's evaluate that condition that's
+ 
+
+ align:start position:0%
+so let's evaluate that condition that's
+the condition for the line
+
+ align:start position:0%
+the condition for the line
+ 
+
+ align:start position:0%
+the condition for the line
+all right so D Mu Alpha
+
+ align:start position:0%
+all right so D Mu Alpha
+ 
+
+ align:start position:0%
+all right so D Mu Alpha
+we know what this is who wants to give
+
+ align:start position:0%
+we know what this is who wants to give
+ 
+
+ align:start position:0%
+we know what this is who wants to give
+me an expression for D mu of alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's something times DT plus something
+
+ align:start position:0%
+it's something times DT plus something
+ 
+
+ align:start position:0%
+it's something times DT plus something
+times TP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus s DT plus VDP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you may recall that chemical
+
+ align:start position:0%
+right you may recall that chemical
+ 
+
+ align:start position:0%
+right you may recall that chemical
+potential is molar Gibbs free energy so
+
+ align:start position:0%
+potential is molar Gibbs free energy so
+ 
+
+ align:start position:0%
+potential is molar Gibbs free energy so
+we're seeing the same differential form
+
+ align:start position:0%
+we're seeing the same differential form
+ 
+
+ align:start position:0%
+we're seeing the same differential form
+here as we did
+
+ align:start position:0%
+here as we did
+ 
+
+ align:start position:0%
+here as we did
+a couple weeks ago now
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we developed a differential form
+
+ align:start position:0%
+when we developed a differential form
+ 
+
+ align:start position:0%
+when we developed a differential form
+for indeed Gibbs right so the only thing
+
+ align:start position:0%
+for indeed Gibbs right so the only thing
+ 
+
+ align:start position:0%
+for indeed Gibbs right so the only thing
+I've done here is I'm expressing the
+
+ align:start position:0%
+I've done here is I'm expressing the
+ 
+
+ align:start position:0%
+I've done here is I'm expressing the
+molar Gibbs free energy as chemical
+
+ align:start position:0%
+molar Gibbs free energy as chemical
+ 
+
+ align:start position:0%
+molar Gibbs free energy as chemical
+potential and I'm adding the phase
+
+ align:start position:0%
+potential and I'm adding the phase
+ 
+
+ align:start position:0%
+potential and I'm adding the phase
+labels right because now I have a
+
+ align:start position:0%
+labels right because now I have a
+ 
+
+ align:start position:0%
+labels right because now I have a
+heterogeneous system multiple phases so
+
+ align:start position:0%
+heterogeneous system multiple phases so
+ 
+
+ align:start position:0%
+heterogeneous system multiple phases so
+I have to keep track of the phase levels
+
+ align:start position:0%
+I have to keep track of the phase levels
+ 
+
+ align:start position:0%
+I have to keep track of the phase levels
+okay so thank you for that I didn't see
+
+ align:start position:0%
+okay so thank you for that I didn't see
+ 
+
+ align:start position:0%
+okay so thank you for that I didn't see
+which rectangle answered that question
+
+ align:start position:0%
+which rectangle answered that question
+ 
+
+ align:start position:0%
+which rectangle answered that question
+but thank you for that
+
+ align:start position:0%
+but thank you for that
+ 
+
+ align:start position:0%
+but thank you for that
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and likewise we have
+
+ align:start position:0%
+and likewise we have
+ 
+
+ align:start position:0%
+and likewise we have
+verbata
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is true right for Alpha and
+
+ align:start position:0%
+okay so this is true right for Alpha and
+ 
+
+ align:start position:0%
+okay so this is true right for Alpha and
+beta phase and I want the MU of alpha to
+
+ align:start position:0%
+beta phase and I want the MU of alpha to
+ 
+
+ align:start position:0%
+beta phase and I want the MU of alpha to
+be equal to D mu of beta so I'm going to
+
+ align:start position:0%
+be equal to D mu of beta so I'm going to
+ 
+
+ align:start position:0%
+be equal to D mu of beta so I'm going to
+combine these three lines
+
+ align:start position:0%
+combine these three lines
+ 
+
+ align:start position:0%
+combine these three lines
+right I'm going to plug in for D Mu
+
+ align:start position:0%
+right I'm going to plug in for D Mu
+ 
+
+ align:start position:0%
+right I'm going to plug in for D Mu
+Alpha I'm going to plug in for DBU beta
+
+ align:start position:0%
+Alpha I'm going to plug in for DBU beta
+ 
+
+ align:start position:0%
+Alpha I'm going to plug in for DBU beta
+I'm going to see what I get and so what
+
+ align:start position:0%
+I'm going to see what I get and so what
+ 
+
+ align:start position:0%
+I'm going to see what I get and so what
+I get is
+
+ align:start position:0%
+I get is
+ 
+
+ align:start position:0%
+I get is
+um what D Mu Alpha equals minus s Alpha
+
+ align:start position:0%
+um what D Mu Alpha equals minus s Alpha
+ 
+
+ align:start position:0%
+um what D Mu Alpha equals minus s Alpha
+DT plus v Alpha DP and that's going to
+
+ align:start position:0%
+DT plus v Alpha DP and that's going to
+ 
+
+ align:start position:0%
+DT plus v Alpha DP and that's going to
+be equal to minus s beta DT plus v beta
+
+ align:start position:0%
+be equal to minus s beta DT plus v beta
+ 
+
+ align:start position:0%
+be equal to minus s beta DT plus v beta
+DP I'm going to collect terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+collect terms and I get S of alpha minus
+
+ align:start position:0%
+collect terms and I get S of alpha minus
+ 
+
+ align:start position:0%
+collect terms and I get S of alpha minus
+s of beta
+
+ align:start position:0%
+s of beta
+ 
+
+ align:start position:0%
+s of beta
+DT
+
+ align:start position:0%
+DT
+ 
+
+ align:start position:0%
+DT
+equals V of alpha minus V of beta
+
+ align:start position:0%
+equals V of alpha minus V of beta
+ 
+
+ align:start position:0%
+equals V of alpha minus V of beta
+DP
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this here this is a transformation
+
+ align:start position:0%
+and this here this is a transformation
+ 
+
+ align:start position:0%
+and this here this is a transformation
+quantity
+
+ align:start position:0%
+quantity
+ 
+
+ align:start position:0%
+quantity
+I hope everyone watched the the three
+
+ align:start position:0%
+I hope everyone watched the the three
+ 
+
+ align:start position:0%
+I hope everyone watched the the three
+d's of thermodynamics uh
+
+ align:start position:0%
+d's of thermodynamics uh
+ 
+
+ align:start position:0%
+d's of thermodynamics uh
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+if you did I hope you found it useful
+
+ align:start position:0%
+if you did I hope you found it useful
+ 
+
+ align:start position:0%
+if you did I hope you found it useful
+so this is a transformation quantity
+
+ align:start position:0%
+so this is a transformation quantity
+ 
+
+ align:start position:0%
+so this is a transformation quantity
+this is Delta s and this is Delta V
+
+ align:start position:0%
+this is Delta s and this is Delta V
+ 
+
+ align:start position:0%
+this is Delta s and this is Delta V
+as we go between phases beta Alpha is
+
+ align:start position:0%
+as we go between phases beta Alpha is
+ 
+
+ align:start position:0%
+as we go between phases beta Alpha is
+your transformation quantities
+
+ align:start position:0%
+your transformation quantities
+ 
+
+ align:start position:0%
+your transformation quantities
+and we're going to then
+
+ align:start position:0%
+and we're going to then
+ 
+
+ align:start position:0%
+and we're going to then
+divide through
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divide through and we're going to get
+
+ align:start position:0%
+divide through and we're going to get
+ 
+
+ align:start position:0%
+divide through and we're going to get
+an expression for the slope DP DT equals
+
+ align:start position:0%
+an expression for the slope DP DT equals
+ 
+
+ align:start position:0%
+an expression for the slope DP DT equals
+Delta s over Delta V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+that's pretty useful
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now we have an expression for the
+
+ align:start position:0%
+so now we have an expression for the
+ 
+
+ align:start position:0%
+so now we have an expression for the
+slope the local slope of that coexist
+
+ align:start position:0%
+slope the local slope of that coexist
+ 
+
+ align:start position:0%
+slope the local slope of that coexist
+enzyme as a function of these
+
+ align:start position:0%
+enzyme as a function of these
+ 
+
+ align:start position:0%
+enzyme as a function of these
+transformation quantities
+
+ align:start position:0%
+transformation quantities
+ 
+
+ align:start position:0%
+transformation quantities
+and we have something else for an
+
+ align:start position:0%
+and we have something else for an
+ 
+
+ align:start position:0%
+and we have something else for an
+isothermal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equilibrium transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we know that Delta s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals Delta H over t
+
+ align:start position:0%
+equals Delta H over t
+ 
+
+ align:start position:0%
+equals Delta H over t
+so I can re-express this as
+
+ align:start position:0%
+so I can re-express this as
+ 
+
+ align:start position:0%
+so I can re-express this as
+g p DT
+
+ align:start position:0%
+g p DT
+ 
+
+ align:start position:0%
+g p DT
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+Delta H over t
+
+ align:start position:0%
+Delta H over t
+ 
+
+ align:start position:0%
+Delta H over t
+Delta V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these are equivalent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and these are called the cloud CS
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+relation or equation
+
+ align:start position:0%
+relation or equation
+ 
+
+ align:start position:0%
+relation or equation
+okay so that that's that's where these
+
+ align:start position:0%
+okay so that that's that's where these
+ 
+
+ align:start position:0%
+okay so that that's that's where these
+are these are very famous
+
+ align:start position:0%
+are these are very famous
+ 
+
+ align:start position:0%
+are these are very famous
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so it's it's a differential equation
+
+ align:start position:0%
+and so it's it's a differential equation
+ 
+
+ align:start position:0%
+and so it's it's a differential equation
+it's a differential equation for this
+
+ align:start position:0%
+it's a differential equation for this
+ 
+
+ align:start position:0%
+it's a differential equation for this
+line right it's not an equation for the
+
+ align:start position:0%
+line right it's not an equation for the
+ 
+
+ align:start position:0%
+line right it's not an equation for the
+line but it's giving the slope of the
+
+ align:start position:0%
+line but it's giving the slope of the
+ 
+
+ align:start position:0%
+line but it's giving the slope of the
+line as a function of temperature and
+
+ align:start position:0%
+line as a function of temperature and
+ 
+
+ align:start position:0%
+line as a function of temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where temperature and pressure
+
+ align:start position:0%
+where temperature and pressure
+ 
+
+ align:start position:0%
+where temperature and pressure
+parameterize these transformation
+
+ align:start position:0%
+parameterize these transformation
+ 
+
+ align:start position:0%
+parameterize these transformation
+quantities Delta seductively
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this is in general true for any
+
+ align:start position:0%
+okay so this is in general true for any
+ 
+
+ align:start position:0%
+okay so this is in general true for any
+two-phase coexistence line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to analyze it now for the
+
+ align:start position:0%
+we're going to analyze it now for the
+ 
+
+ align:start position:0%
+we're going to analyze it now for the
+case of vapor pressure
+
+ align:start position:0%
+case of vapor pressure
+ 
+
+ align:start position:0%
+case of vapor pressure
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+the equation simplify for vapor pressure
+
+ align:start position:0%
+the equation simplify for vapor pressure
+ 
+
+ align:start position:0%
+the equation simplify for vapor pressure
+and it's also a very useful
+
+ align:start position:0%
+and it's also a very useful
+ 
+
+ align:start position:0%
+and it's also a very useful
+result which is used in lots of
+
+ align:start position:0%
+result which is used in lots of
+ 
+
+ align:start position:0%
+result which is used in lots of
+different fields
+
+ align:start position:0%
+different fields
+ 
+
+ align:start position:0%
+different fields
+but before I move on to a specific case
+
+ align:start position:0%
+but before I move on to a specific case
+ 
+
+ align:start position:0%
+but before I move on to a specific case
+this should be a good time for questions
+
+ align:start position:0%
+this should be a good time for questions
+ 
+
+ align:start position:0%
+this should be a good time for questions
+on the general case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you explain when you
+
+ align:start position:0%
+can you explain when you
+ 
+
+ align:start position:0%
+can you explain when you
+um said like that for the isothermal
+
+ align:start position:0%
+um said like that for the isothermal
+ 
+
+ align:start position:0%
+um said like that for the isothermal
+equilibrium transformation why you
+
+ align:start position:0%
+equilibrium transformation why you
+ 
+
+ align:start position:0%
+equilibrium transformation why you
+specified that case sure I think that
+
+ align:start position:0%
+specified that case sure I think that
+ 
+
+ align:start position:0%
+specified that case sure I think that
+was Ryman but anyway thank you
+
+ align:start position:0%
+was Ryman but anyway thank you
+ 
+
+ align:start position:0%
+was Ryman but anyway thank you
+um so when we are having an isothermal
+
+ align:start position:0%
+um so when we are having an isothermal
+ 
+
+ align:start position:0%
+um so when we are having an isothermal
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+foreign
+
+ align:start position:0%
+foreign
+ 
+
+ align:start position:0%
+foreign
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+if Alpha
+
+ align:start position:0%
+if Alpha
+ 
+
+ align:start position:0%
+if Alpha
+and beta can transform through each
+
+ align:start position:0%
+and beta can transform through each
+ 
+
+ align:start position:0%
+and beta can transform through each
+other at equilibrium that's the that's
+
+ align:start position:0%
+other at equilibrium that's the that's
+ 
+
+ align:start position:0%
+other at equilibrium that's the that's
+almost the meaning of coexistence then
+
+ align:start position:0%
+almost the meaning of coexistence then
+ 
+
+ align:start position:0%
+almost the meaning of coexistence then
+Delta G has to be zero
+
+ align:start position:0%
+Delta G has to be zero
+ 
+
+ align:start position:0%
+Delta G has to be zero
+that again was our our requirement for
+
+ align:start position:0%
+that again was our our requirement for
+ 
+
+ align:start position:0%
+that again was our our requirement for
+equilibrium at constant temperature and
+
+ align:start position:0%
+equilibrium at constant temperature and
+ 
+
+ align:start position:0%
+equilibrium at constant temperature and
+pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to give free energy of the two
+
+ align:start position:0%
+and to give free energy of the two
+ 
+
+ align:start position:0%
+and to give free energy of the two
+phases is equal or in other words the
+
+ align:start position:0%
+phases is equal or in other words the
+ 
+
+ align:start position:0%
+phases is equal or in other words the
+chemical potentials are equal
+
+ align:start position:0%
+chemical potentials are equal
+ 
+
+ align:start position:0%
+chemical potentials are equal
+so Delta G
+
+ align:start position:0%
+so Delta G
+ 
+
+ align:start position:0%
+so Delta G
+equals Delta
+
+ align:start position:0%
+equals Delta
+ 
+
+ align:start position:0%
+equals Delta
+H minus TS all right that's just from
+
+ align:start position:0%
+H minus TS all right that's just from
+ 
+
+ align:start position:0%
+H minus TS all right that's just from
+the definition and if it's isothermal
+
+ align:start position:0%
+the definition and if it's isothermal
+ 
+
+ align:start position:0%
+the definition and if it's isothermal
+this is Delta H minus t Delta s because
+
+ align:start position:0%
+this is Delta H minus t Delta s because
+ 
+
+ align:start position:0%
+this is Delta H minus t Delta s because
+T here is a fixed number for an
+
+ align:start position:0%
+T here is a fixed number for an
+ 
+
+ align:start position:0%
+T here is a fixed number for an
+isochonal transformation
+
+ align:start position:0%
+isochonal transformation
+ 
+
+ align:start position:0%
+isochonal transformation
+so this has to equal zero if phases
+
+ align:start position:0%
+so this has to equal zero if phases
+ 
+
+ align:start position:0%
+so this has to equal zero if phases
+Alpha and beta are in equilibrium
+
+ align:start position:0%
+Alpha and beta are in equilibrium
+ 
+
+ align:start position:0%
+Alpha and beta are in equilibrium
+so this is um
+
+ align:start position:0%
+so this is um
+ 
+
+ align:start position:0%
+so this is um
+useful and I mentioned this in the last
+
+ align:start position:0%
+useful and I mentioned this in the last
+ 
+
+ align:start position:0%
+useful and I mentioned this in the last
+class that the fact that
+
+ align:start position:0%
+class that the fact that
+ 
+
+ align:start position:0%
+class that the fact that
+Delta H minus t Delta s is zero
+
+ align:start position:0%
+Delta H minus t Delta s is zero
+ 
+
+ align:start position:0%
+Delta H minus t Delta s is zero
+for two phase equilibrium is is um
+
+ align:start position:0%
+for two phase equilibrium is is um
+ 
+
+ align:start position:0%
+for two phase equilibrium is is um
+it's used for instance
+
+ align:start position:0%
+it's used for instance
+ 
+
+ align:start position:0%
+it's used for instance
+in databases for Transformations you
+
+ align:start position:0%
+in databases for Transformations you
+ 
+
+ align:start position:0%
+in databases for Transformations you
+might see temperature and you might see
+
+ align:start position:0%
+might see temperature and you might see
+ 
+
+ align:start position:0%
+might see temperature and you might see
+Delta s or you might see Delta H and you
+
+ align:start position:0%
+Delta s or you might see Delta H and you
+ 
+
+ align:start position:0%
+Delta s or you might see Delta H and you
+might see Delta s right you might see a
+
+ align:start position:0%
+might see Delta s right you might see a
+ 
+
+ align:start position:0%
+might see Delta s right you might see a
+pair of numbers but you might not see
+
+ align:start position:0%
+pair of numbers but you might not see
+ 
+
+ align:start position:0%
+pair of numbers but you might not see
+all three
+
+ align:start position:0%
+all three
+ 
+
+ align:start position:0%
+all three
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+um having all three is redundant because
+
+ align:start position:0%
+um having all three is redundant because
+ 
+
+ align:start position:0%
+um having all three is redundant because
+you have to have this condition
+
+ align:start position:0%
+you have to have this condition
+ 
+
+ align:start position:0%
+you have to have this condition
+satisfied and if you uh you can you can
+
+ align:start position:0%
+satisfied and if you uh you can you can
+ 
+
+ align:start position:0%
+satisfied and if you uh you can you can
+you know you can check that if you open
+
+ align:start position:0%
+you know you can check that if you open
+ 
+
+ align:start position:0%
+you know you can check that if you open
+the textbook and you go to
+
+ align:start position:0%
+the textbook and you go to
+ 
+
+ align:start position:0%
+the textbook and you go to
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+phase Transformations for the elements
+
+ align:start position:0%
+phase Transformations for the elements
+ 
+
+ align:start position:0%
+phase Transformations for the elements
+you know there's a bunch of data here
+
+ align:start position:0%
+you know there's a bunch of data here
+ 
+
+ align:start position:0%
+you know there's a bunch of data here
+and if you like to you can go and check
+
+ align:start position:0%
+and if you like to you can go and check
+ 
+
+ align:start position:0%
+and if you like to you can go and check
+in for example silver here silver melts
+
+ align:start position:0%
+in for example silver here silver melts
+ 
+
+ align:start position:0%
+in for example silver here silver melts
+from FCC to liquid at 1235 Kelvin I know
+
+ align:start position:0%
+from FCC to liquid at 1235 Kelvin I know
+ 
+
+ align:start position:0%
+from FCC to liquid at 1235 Kelvin I know
+you can't read the numbers but I'm just
+
+ align:start position:0%
+you can't read the numbers but I'm just
+ 
+
+ align:start position:0%
+you can't read the numbers but I'm just
+pointing out the structure of the
+
+ align:start position:0%
+pointing out the structure of the
+ 
+
+ align:start position:0%
+pointing out the structure of the
+database and there's Delta s of the
+
+ align:start position:0%
+database and there's Delta s of the
+ 
+
+ align:start position:0%
+database and there's Delta s of the
+transformation and the Delta h of the
+
+ align:start position:0%
+transformation and the Delta h of the
+ 
+
+ align:start position:0%
+transformation and the Delta h of the
+transformation
+
+ align:start position:0%
+transformation
+ 
+
+ align:start position:0%
+transformation
+and you can confirm that Delta H minus t
+
+ align:start position:0%
+and you can confirm that Delta H minus t
+ 
+
+ align:start position:0%
+and you can confirm that Delta H minus t
+times Delta s is going to be zero for
+
+ align:start position:0%
+times Delta s is going to be zero for
+ 
+
+ align:start position:0%
+times Delta s is going to be zero for
+every single set of these
+
+ align:start position:0%
+every single set of these
+ 
+
+ align:start position:0%
+every single set of these
+so the Hoff is nice and it gives you
+
+ align:start position:0%
+so the Hoff is nice and it gives you
+ 
+
+ align:start position:0%
+so the Hoff is nice and it gives you
+extra information right but he could for
+
+ align:start position:0%
+extra information right but he could for
+ 
+
+ align:start position:0%
+extra information right but he could for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+block out the temperature of the
+
+ align:start position:0%
+block out the temperature of the
+ 
+
+ align:start position:0%
+block out the temperature of the
+transformation and not list the melting
+
+ align:start position:0%
+transformation and not list the melting
+ 
+
+ align:start position:0%
+transformation and not list the melting
+temperature and you say what on Earth
+
+ align:start position:0%
+temperature and you say what on Earth
+ 
+
+ align:start position:0%
+temperature and you say what on Earth
+it's a table of melting temperatures and
+
+ align:start position:0%
+it's a table of melting temperatures and
+ 
+
+ align:start position:0%
+it's a table of melting temperatures and
+it doesn't lose the melting temperature
+
+ align:start position:0%
+it doesn't lose the melting temperature
+ 
+
+ align:start position:0%
+it doesn't lose the melting temperature
+what is he doing right well you can
+
+ align:start position:0%
+what is he doing right well you can
+ 
+
+ align:start position:0%
+what is he doing right well you can
+solve for the transformation temperature
+
+ align:start position:0%
+solve for the transformation temperature
+ 
+
+ align:start position:0%
+solve for the transformation temperature
+from Delta X and Delta h
+
+ align:start position:0%
+from Delta X and Delta h
+ 
+
+ align:start position:0%
+from Delta X and Delta h
+under the condition of the Delta G of
+
+ align:start position:0%
+under the condition of the Delta G of
+ 
+
+ align:start position:0%
+under the condition of the Delta G of
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+now I don't know if that answers your
+
+ align:start position:0%
+now I don't know if that answers your
+ 
+
+ align:start position:0%
+now I don't know if that answers your
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um if it's off page please try again
+
+ align:start position:0%
+um if it's off page please try again
+ 
+
+ align:start position:0%
+um if it's off page please try again
+no that was helpful thank you
+
+ align:start position:0%
+no that was helpful thank you
+ 
+
+ align:start position:0%
+no that was helpful thank you
+thank you all right so um
+
+ align:start position:0%
+thank you all right so um
+ 
+
+ align:start position:0%
+thank you all right so um
+let's move on right so let's use the
+
+ align:start position:0%
+let's move on right so let's use the
+ 
+
+ align:start position:0%
+let's move on right so let's use the
+kind of calcium equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using
+
+ align:start position:0%
+using
+ 
+
+ align:start position:0%
+using
+the c c
+
+ align:start position:0%
+the c c
+ 
+
+ align:start position:0%
+the c c
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+vapor pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so this is a very useful case
+
+ align:start position:0%
+so this is a very useful case
+ 
+
+ align:start position:0%
+so this is a very useful case
+and let's just remember what what we're
+
+ align:start position:0%
+and let's just remember what what we're
+ 
+
+ align:start position:0%
+and let's just remember what what we're
+doing here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right here is
+
+ align:start position:0%
+right here is
+ 
+
+ align:start position:0%
+right here is
+I have temperature here I have pressure
+
+ align:start position:0%
+I have temperature here I have pressure
+ 
+
+ align:start position:0%
+I have temperature here I have pressure
+here that's a typical way that vapor
+
+ align:start position:0%
+here that's a typical way that vapor
+ 
+
+ align:start position:0%
+here that's a typical way that vapor
+pressure curves are plotted
+
+ align:start position:0%
+pressure curves are plotted
+ 
+
+ align:start position:0%
+pressure curves are plotted
+and there's a typical curve and here's
+
+ align:start position:0%
+and there's a typical curve and here's
+ 
+
+ align:start position:0%
+and there's a typical curve and here's
+um solid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for instance
+
+ align:start position:0%
+for instance
+ 
+
+ align:start position:0%
+for instance
+and here is vapor
+
+ align:start position:0%
+and here is vapor
+ 
+
+ align:start position:0%
+and here is vapor
+I use green for both that's not very
+
+ align:start position:0%
+I use green for both that's not very
+ 
+
+ align:start position:0%
+I use green for both that's not very
+creative
+
+ align:start position:0%
+creative
+ 
+
+ align:start position:0%
+creative
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let me point out that everything we're
+
+ align:start position:0%
+let me point out that everything we're
+ 
+
+ align:start position:0%
+let me point out that everything we're
+about to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+also applies if that's liquid
+
+ align:start position:0%
+also applies if that's liquid
+ 
+
+ align:start position:0%
+also applies if that's liquid
+so it's vapor pressure over a condensed
+
+ align:start position:0%
+so it's vapor pressure over a condensed
+ 
+
+ align:start position:0%
+so it's vapor pressure over a condensed
+phase it doesn't have to be over the
+
+ align:start position:0%
+phase it doesn't have to be over the
+ 
+
+ align:start position:0%
+phase it doesn't have to be over the
+solid phase it could also be over liquid
+
+ align:start position:0%
+solid phase it could also be over liquid
+ 
+
+ align:start position:0%
+solid phase it could also be over liquid
+so here
+
+ align:start position:0%
+so here
+ 
+
+ align:start position:0%
+so here
+vapor
+
+ align:start position:0%
+vapor
+ 
+
+ align:start position:0%
+vapor
+condenses
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right on that side of the curve vapor
+
+ align:start position:0%
+right on that side of the curve vapor
+ 
+
+ align:start position:0%
+right on that side of the curve vapor
+condenses
+
+ align:start position:0%
+condenses
+ 
+
+ align:start position:0%
+condenses
+and here
+
+ align:start position:0%
+and here
+ 
+
+ align:start position:0%
+and here
+solid
+
+ align:start position:0%
+solid
+ 
+
+ align:start position:0%
+solid
+sublimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or liquid evaporates as the case may be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so that's the meaning of this
+
+ align:start position:0%
+right so that's the meaning of this
+ 
+
+ align:start position:0%
+right so that's the meaning of this
+phase diagram
+
+ align:start position:0%
+phase diagram
+ 
+
+ align:start position:0%
+phase diagram
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+Okay so
+
+ align:start position:0%
+Okay so
+ 
+
+ align:start position:0%
+Okay so
+on the coexistence line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the coexistence line
+
+ align:start position:0%
+on the coexistence line
+ 
+
+ align:start position:0%
+on the coexistence line
+vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saturated that's an important word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you need to be able to interpret that
+
+ align:start position:0%
+you need to be able to interpret that
+ 
+
+ align:start position:0%
+you need to be able to interpret that
+word when you see it in all sorts of
+
+ align:start position:0%
+word when you see it in all sorts of
+ 
+
+ align:start position:0%
+word when you see it in all sorts of
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+saturated
+
+ align:start position:0%
+saturated
+ 
+
+ align:start position:0%
+saturated
+that's a really important concept
+
+ align:start position:0%
+that's a really important concept
+ 
+
+ align:start position:0%
+that's a really important concept
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+saturation vapor pressure
+
+ align:start position:0%
+saturation vapor pressure
+ 
+
+ align:start position:0%
+saturation vapor pressure
+so these terms saturation saturation
+
+ align:start position:0%
+so these terms saturation saturation
+ 
+
+ align:start position:0%
+so these terms saturation saturation
+vapor pressure you're going to encounter
+
+ align:start position:0%
+vapor pressure you're going to encounter
+ 
+
+ align:start position:0%
+vapor pressure you're going to encounter
+these all over the place
+
+ align:start position:0%
+these all over the place
+ 
+
+ align:start position:0%
+these all over the place
+um even on your even on your weather
+
+ align:start position:0%
+um even on your even on your weather
+ 
+
+ align:start position:0%
+um even on your even on your weather
+forecast
+
+ align:start position:0%
+forecast
+ 
+
+ align:start position:0%
+forecast
+and it's nice to be able to connect it
+
+ align:start position:0%
+and it's nice to be able to connect it
+ 
+
+ align:start position:0%
+and it's nice to be able to connect it
+back to the thermodynamics Okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're on the curve let's say
+
+ align:start position:0%
+we're on the curve let's say
+ 
+
+ align:start position:0%
+we're on the curve let's say
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+excess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vapor pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is added
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what will happen imagine you have a
+
+ align:start position:0%
+what will happen imagine you have a
+ 
+
+ align:start position:0%
+what will happen imagine you have a
+system you have these two phases in a
+
+ align:start position:0%
+system you have these two phases in a
+ 
+
+ align:start position:0%
+system you have these two phases in a
+box
+
+ align:start position:0%
+box
+ 
+
+ align:start position:0%
+box
+and you turn up the vapor pressure
+
+ align:start position:0%
+and you turn up the vapor pressure
+ 
+
+ align:start position:0%
+and you turn up the vapor pressure
+what will spontaneously happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The Vapor will condense to decrease
+
+ align:start position:0%
+The Vapor will condense to decrease
+ 
+
+ align:start position:0%
+The Vapor will condense to decrease
+thank you will spontaneously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condense
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to let me put this in quotes
+
+ align:start position:0%
+to let me put this in quotes
+ 
+
+ align:start position:0%
+to let me put this in quotes
+to try to
+
+ align:start position:0%
+to try to
+ 
+
+ align:start position:0%
+to try to
+reapproach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right to try to reapproach PSAT likewise
+
+ align:start position:0%
+right to try to reapproach PSAT likewise
+ 
+
+ align:start position:0%
+right to try to reapproach PSAT likewise
+if vapor pressure
+
+ align:start position:0%
+if vapor pressure
+ 
+
+ align:start position:0%
+if vapor pressure
+is reduced let's say you hook it up to a
+
+ align:start position:0%
+is reduced let's say you hook it up to a
+ 
+
+ align:start position:0%
+is reduced let's say you hook it up to a
+vacuum pump
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what will happen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solid will thank you I'm going to use a
+
+ align:start position:0%
+solid will thank you I'm going to use a
+ 
+
+ align:start position:0%
+solid will thank you I'm going to use a
+case of the solid but you're right
+
+ align:start position:0%
+case of the solid but you're right
+ 
+
+ align:start position:0%
+case of the solid but you're right
+spontaneously
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sublime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to again in air quotes
+
+ align:start position:0%
+to again in air quotes
+ 
+
+ align:start position:0%
+to again in air quotes
+try to
+
+ align:start position:0%
+try to
+ 
+
+ align:start position:0%
+try to
+reapproach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+saturation vapor pressure
+
+ align:start position:0%
+saturation vapor pressure
+ 
+
+ align:start position:0%
+saturation vapor pressure
+okay so it seems that when you're on
+
+ align:start position:0%
+okay so it seems that when you're on
+ 
+
+ align:start position:0%
+okay so it seems that when you're on
+this coexistence line
+
+ align:start position:0%
+this coexistence line
+ 
+
+ align:start position:0%
+this coexistence line
+if you try to change the Intensive
+
+ align:start position:0%
+if you try to change the Intensive
+ 
+
+ align:start position:0%
+if you try to change the Intensive
+parameters of the system
+
+ align:start position:0%
+parameters of the system
+ 
+
+ align:start position:0%
+parameters of the system
+if you try to change the pressure say
+
+ align:start position:0%
+if you try to change the pressure say
+ 
+
+ align:start position:0%
+if you try to change the pressure say
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+the system will respond to try to
+
+ align:start position:0%
+the system will respond to try to
+ 
+
+ align:start position:0%
+the system will respond to try to
+counteract your change it will try to
+
+ align:start position:0%
+counteract your change it will try to
+ 
+
+ align:start position:0%
+counteract your change it will try to
+resist whatever you're trying to do if
+
+ align:start position:0%
+resist whatever you're trying to do if
+ 
+
+ align:start position:0%
+resist whatever you're trying to do if
+you try to increase the pressure it's
+
+ align:start position:0%
+you try to increase the pressure it's
+ 
+
+ align:start position:0%
+you try to increase the pressure it's
+got a way to try to
+
+ align:start position:0%
+got a way to try to
+ 
+
+ align:start position:0%
+got a way to try to
+pull it back down if you try to decrease
+
+ align:start position:0%
+pull it back down if you try to decrease
+ 
+
+ align:start position:0%
+pull it back down if you try to decrease
+the pressure it's got a way to try to
+
+ align:start position:0%
+the pressure it's got a way to try to
+ 
+
+ align:start position:0%
+the pressure it's got a way to try to
+push it back up
+
+ align:start position:0%
+push it back up
+ 
+
+ align:start position:0%
+push it back up
+right so it has a way to resist you
+
+ align:start position:0%
+right so it has a way to resist you
+ 
+
+ align:start position:0%
+right so it has a way to resist you
+what's the principle behind that and
+
+ align:start position:0%
+what's the principle behind that and
+ 
+
+ align:start position:0%
+what's the principle behind that and
+it's a french guy who remembers there's
+
+ align:start position:0%
+it's a french guy who remembers there's
+ 
+
+ align:start position:0%
+it's a french guy who remembers there's
+a general principle which explains this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is a really nice example of the
+
+ align:start position:0%
+this is a really nice example of the
+ 
+
+ align:start position:0%
+this is a really nice example of the
+shot to the ace principle
+
+ align:start position:0%
+shot to the ace principle
+ 
+
+ align:start position:0%
+shot to the ace principle
+that is nature reacts in such a way to
+
+ align:start position:0%
+that is nature reacts in such a way to
+ 
+
+ align:start position:0%
+that is nature reacts in such a way to
+counteract any external impulses
+
+ align:start position:0%
+counteract any external impulses
+ 
+
+ align:start position:0%
+counteract any external impulses
+or in other words it's stubborn it will
+
+ align:start position:0%
+or in other words it's stubborn it will
+ 
+
+ align:start position:0%
+or in other words it's stubborn it will
+resist you by any means possible so in
+
+ align:start position:0%
+resist you by any means possible so in
+ 
+
+ align:start position:0%
+resist you by any means possible so in
+this case you're on the coexistence line
+
+ align:start position:0%
+this case you're on the coexistence line
+ 
+
+ align:start position:0%
+this case you're on the coexistence line
+it has a means of resistance which is
+
+ align:start position:0%
+it has a means of resistance which is
+ 
+
+ align:start position:0%
+it has a means of resistance which is
+this phase transformation and it will
+
+ align:start position:0%
+this phase transformation and it will
+ 
+
+ align:start position:0%
+this phase transformation and it will
+use that phase transformation to try to
+
+ align:start position:0%
+use that phase transformation to try to
+ 
+
+ align:start position:0%
+use that phase transformation to try to
+resist the changes which you impose
+
+ align:start position:0%
+resist the changes which you impose
+ 
+
+ align:start position:0%
+resist the changes which you impose
+all right so I hope that's a little bit
+
+ align:start position:0%
+all right so I hope that's a little bit
+ 
+
+ align:start position:0%
+all right so I hope that's a little bit
+intuitive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do some math around that
+
+ align:start position:0%
+let's do some math around that
+ 
+
+ align:start position:0%
+let's do some math around that
+all right so let's calculate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's calculate the calculation the
+
+ align:start position:0%
+let's calculate the calculation the
+ 
+
+ align:start position:0%
+let's calculate the calculation the
+saturation vapor pressure
+
+ align:start position:0%
+saturation vapor pressure
+ 
+
+ align:start position:0%
+saturation vapor pressure
+how do we do that we have a a
+
+ align:start position:0%
+how do we do that we have a a
+ 
+
+ align:start position:0%
+how do we do that we have a a
+differential equation right
+
+ align:start position:0%
+differential equation right
+ 
+
+ align:start position:0%
+differential equation right
+so how do we get an equation from a
+
+ align:start position:0%
+so how do we get an equation from a
+ 
+
+ align:start position:0%
+so how do we get an equation from a
+differential equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right you have to solve it
+
+ align:start position:0%
+right you have to solve it
+ 
+
+ align:start position:0%
+right you have to solve it
+so we're going to do it by integrating
+
+ align:start position:0%
+so we're going to do it by integrating
+ 
+
+ align:start position:0%
+so we're going to do it by integrating
+the CC equation
+
+ align:start position:0%
+the CC equation
+ 
+
+ align:start position:0%
+the CC equation
+and as we'll see uh normally uh in
+
+ align:start position:0%
+and as we'll see uh normally uh in
+ 
+
+ align:start position:0%
+and as we'll see uh normally uh in
+general you can't do this
+
+ align:start position:0%
+general you can't do this
+ 
+
+ align:start position:0%
+general you can't do this
+because it can't you might not have
+
+ align:start position:0%
+because it can't you might not have
+ 
+
+ align:start position:0%
+because it can't you might not have
+closed form expressions for everything
+
+ align:start position:0%
+closed form expressions for everything
+ 
+
+ align:start position:0%
+closed form expressions for everything
+that you need but we're going to make
+
+ align:start position:0%
+that you need but we're going to make
+ 
+
+ align:start position:0%
+that you need but we're going to make
+some approximations
+
+ align:start position:0%
+some approximations
+ 
+
+ align:start position:0%
+some approximations
+so here's in general we have this DP
+
+ align:start position:0%
+so here's in general we have this DP
+ 
+
+ align:start position:0%
+so here's in general we have this DP
+Delta V
+
+ align:start position:0%
+Delta V
+ 
+
+ align:start position:0%
+Delta V
+equals DT
+
+ align:start position:0%
+equals DT
+ 
+
+ align:start position:0%
+equals DT
+Delta H over T right if we're going to
+
+ align:start position:0%
+Delta H over T right if we're going to
+ 
+
+ align:start position:0%
+Delta H over T right if we're going to
+integral integrate this thing in general
+
+ align:start position:0%
+integral integrate this thing in general
+ 
+
+ align:start position:0%
+integral integrate this thing in general
+we need
+
+ align:start position:0%
+we need
+ 
+
+ align:start position:0%
+we need
+what we need Delta H as a function of T
+
+ align:start position:0%
+what we need Delta H as a function of T
+ 
+
+ align:start position:0%
+what we need Delta H as a function of T
+and P and we need Delta v as a function
+
+ align:start position:0%
+and P and we need Delta v as a function
+ 
+
+ align:start position:0%
+and P and we need Delta v as a function
+of T and P right in general we're going
+
+ align:start position:0%
+of T and P right in general we're going
+ 
+
+ align:start position:0%
+of T and P right in general we're going
+to need these things and we have no even
+
+ align:start position:0%
+to need these things and we have no even
+ 
+
+ align:start position:0%
+to need these things and we have no even
+if these equations of State exist
+
+ align:start position:0%
+if these equations of State exist
+ 
+
+ align:start position:0%
+if these equations of State exist
+there's no guarantee that they're
+
+ align:start position:0%
+there's no guarantee that they're
+ 
+
+ align:start position:0%
+there's no guarantee that they're
+separable or that we know how to solve
+
+ align:start position:0%
+separable or that we know how to solve
+ 
+
+ align:start position:0%
+separable or that we know how to solve
+the equation
+
+ align:start position:0%
+the equation
+ 
+
+ align:start position:0%
+the equation
+um right this is why we use
+
+ align:start position:0%
+um right this is why we use
+ 
+
+ align:start position:0%
+um right this is why we use
+computers
+
+ align:start position:0%
+computers
+ 
+
+ align:start position:0%
+computers
+so in in general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these transformation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right as we saw last time
+
+ align:start position:0%
+right as we saw last time
+ 
+
+ align:start position:0%
+right as we saw last time
+in general
+
+ align:start position:0%
+in general
+ 
+
+ align:start position:0%
+in general
+let's say this is pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is temperature
+
+ align:start position:0%
+this is temperature
+ 
+
+ align:start position:0%
+this is temperature
+let's say there's
+
+ align:start position:0%
+let's say there's
+ 
+
+ align:start position:0%
+let's say there's
+a standard
+
+ align:start position:0%
+a standard
+ 
+
+ align:start position:0%
+a standard
+t-not peanut
+
+ align:start position:0%
+t-not peanut
+ 
+
+ align:start position:0%
+t-not peanut
+like standard temperature and pressure
+
+ align:start position:0%
+like standard temperature and pressure
+ 
+
+ align:start position:0%
+like standard temperature and pressure
+conditions right
+
+ align:start position:0%
+conditions right
+ 
+
+ align:start position:0%
+conditions right
+standard state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and someone gives us the transformation
+
+ align:start position:0%
+and someone gives us the transformation
+ 
+
+ align:start position:0%
+and someone gives us the transformation
+quantities there
+
+ align:start position:0%
+quantities there
+ 
+
+ align:start position:0%
+quantities there
+right and we actually need them over
+
+ align:start position:0%
+right and we actually need them over
+ 
+
+ align:start position:0%
+right and we actually need them over
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right at some other p
+
+ align:start position:0%
+right at some other p
+ 
+
+ align:start position:0%
+right at some other p
+and T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so in general in general we can
+
+ align:start position:0%
+right so in general in general we can
+ 
+
+ align:start position:0%
+right so in general in general we can
+integrate so for instance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculating Delta H as a function of t
+
+ align:start position:0%
+calculating Delta H as a function of t
+ 
+
+ align:start position:0%
+calculating Delta H as a function of t
+and P
+
+ align:start position:0%
+and P
+ 
+
+ align:start position:0%
+and P
+like DH equals c p d t minus plus v one
+
+ align:start position:0%
+like DH equals c p d t minus plus v one
+ 
+
+ align:start position:0%
+like DH equals c p d t minus plus v one
+minus t Alpha
+
+ align:start position:0%
+minus t Alpha
+ 
+
+ align:start position:0%
+minus t Alpha
+DP
+
+ align:start position:0%
+DP
+ 
+
+ align:start position:0%
+DP
+so it's Delta H at T and P
+
+ align:start position:0%
+so it's Delta H at T and P
+ 
+
+ align:start position:0%
+so it's Delta H at T and P
+equals Delta h
+
+ align:start position:0%
+equals Delta h
+ 
+
+ align:start position:0%
+equals Delta h
+x a t naught and P naught some standard
+
+ align:start position:0%
+x a t naught and P naught some standard
+ 
+
+ align:start position:0%
+x a t naught and P naught some standard
+data which I found maybe in a database
+
+ align:start position:0%
+data which I found maybe in a database
+ 
+
+ align:start position:0%
+data which I found maybe in a database
+plus from T naught to T
+
+ align:start position:0%
+plus from T naught to T
+ 
+
+ align:start position:0%
+plus from T naught to T
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+Delta h
+
+ align:start position:0%
+Delta h
+ 
+
+ align:start position:0%
+Delta h
+and fixed pressure
+
+ align:start position:0%
+and fixed pressure
+ 
+
+ align:start position:0%
+and fixed pressure
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+from P naught to p
+
+ align:start position:0%
+from P naught to p
+ 
+
+ align:start position:0%
+from P naught to p
+d
+
+ align:start position:0%
+d
+ 
+
+ align:start position:0%
+d
+Delta H at fixed temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which equals Delta h
+
+ align:start position:0%
+which equals Delta h
+ 
+
+ align:start position:0%
+which equals Delta h
+T naught T naught Plus
+
+ align:start position:0%
+T naught T naught Plus
+ 
+
+ align:start position:0%
+T naught T naught Plus
+T naught over t
+
+ align:start position:0%
+T naught over t
+ 
+
+ align:start position:0%
+T naught over t
+d t Prime dummy variable Delta CP so
+
+ align:start position:0%
+d t Prime dummy variable Delta CP so
+ 
+
+ align:start position:0%
+d t Prime dummy variable Delta CP so
+there's my heat capacity differences
+
+ align:start position:0%
+there's my heat capacity differences
+ 
+
+ align:start position:0%
+there's my heat capacity differences
+right so here's where that data comes in
+
+ align:start position:0%
+right so here's where that data comes in
+ 
+
+ align:start position:0%
+right so here's where that data comes in
+P naught to p d
+
+ align:start position:0%
+P naught to p d
+ 
+
+ align:start position:0%
+P naught to p d
+P Prime dummy variable
+
+ align:start position:0%
+P Prime dummy variable
+ 
+
+ align:start position:0%
+P Prime dummy variable
+and again a transformation quantity V
+
+ align:start position:0%
+and again a transformation quantity V
+ 
+
+ align:start position:0%
+and again a transformation quantity V
+one minus t Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transformation quantities
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right these characterize the change
+
+ align:start position:0%
+all right these characterize the change
+ 
+
+ align:start position:0%
+all right these characterize the change
+as you move between phases
+
+ align:start position:0%
+as you move between phases
+ 
+
+ align:start position:0%
+as you move between phases
+all right so I'm just I'm just laying
+
+ align:start position:0%
+all right so I'm just I'm just laying
+ 
+
+ align:start position:0%
+all right so I'm just I'm just laying
+this out in general you're very rare
+
+ align:start position:0%
+this out in general you're very rare
+ 
+
+ align:start position:0%
+this out in general you're very rare
+that you actually have to do
+
+ align:start position:0%
+that you actually have to do
+ 
+
+ align:start position:0%
+that you actually have to do
+calculations like this let me lay out
+
+ align:start position:0%
+calculations like this let me lay out
+ 
+
+ align:start position:0%
+calculations like this let me lay out
+how to calculate Delta V
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculating Delta V right that's the
+
+ align:start position:0%
+calculating Delta V right that's the
+ 
+
+ align:start position:0%
+calculating Delta V right that's the
+other part of the integral Delta V so we
+
+ align:start position:0%
+other part of the integral Delta V so we
+ 
+
+ align:start position:0%
+other part of the integral Delta V so we
+have DV equals V Alpha DT minus V beta
+
+ align:start position:0%
+have DV equals V Alpha DT minus V beta
+ 
+
+ align:start position:0%
+have DV equals V Alpha DT minus V beta
+DP that's the general form
+
+ align:start position:0%
+DP that's the general form
+ 
+
+ align:start position:0%
+DP that's the general form
+so Delta V
+
+ align:start position:0%
+so Delta V
+ 
+
+ align:start position:0%
+so Delta V
+at some temperature and pressure
+
+ align:start position:0%
+at some temperature and pressure
+ 
+
+ align:start position:0%
+at some temperature and pressure
+equals Delta V
+
+ align:start position:0%
+equals Delta V
+ 
+
+ align:start position:0%
+equals Delta V
+at a standard temperature and pressure
+
+ align:start position:0%
+at a standard temperature and pressure
+ 
+
+ align:start position:0%
+at a standard temperature and pressure
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+from standard temperature to my desired
+
+ align:start position:0%
+from standard temperature to my desired
+ 
+
+ align:start position:0%
+from standard temperature to my desired
+temperature D Delta V at fixed pressure
+
+ align:start position:0%
+temperature D Delta V at fixed pressure
+ 
+
+ align:start position:0%
+temperature D Delta V at fixed pressure
+plus from standard pressure to my
+
+ align:start position:0%
+plus from standard pressure to my
+ 
+
+ align:start position:0%
+plus from standard pressure to my
+pressure of Interest D Delta V at a
+
+ align:start position:0%
+pressure of Interest D Delta V at a
+ 
+
+ align:start position:0%
+pressure of Interest D Delta V at a
+fixed temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals Delta V
+
+ align:start position:0%
+equals Delta V
+ 
+
+ align:start position:0%
+equals Delta V
+at T naught P naught Plus
+
+ align:start position:0%
+at T naught P naught Plus
+ 
+
+ align:start position:0%
+at T naught P naught Plus
+T naught t
+
+ align:start position:0%
+T naught t
+ 
+
+ align:start position:0%
+T naught t
+D dummy variable
+
+ align:start position:0%
+D dummy variable
+ 
+
+ align:start position:0%
+D dummy variable
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+V Alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Plus
+
+ align:start position:0%
+Plus
+ 
+
+ align:start position:0%
+Plus
+P naught to P dummy variable
+
+ align:start position:0%
+P naught to P dummy variable
+ 
+
+ align:start position:0%
+P naught to P dummy variable
+Delta minus V beta and again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these are transformation quantities
+
+ align:start position:0%
+these are transformation quantities
+ 
+
+ align:start position:0%
+these are transformation quantities
+they're the differences
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between phases
+
+ align:start position:0%
+between phases
+ 
+
+ align:start position:0%
+between phases
+transformation quantities all right so
+
+ align:start position:0%
+transformation quantities all right so
+ 
+
+ align:start position:0%
+transformation quantities all right so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+why am I telling you this right uh
+
+ align:start position:0%
+why am I telling you this right uh
+ 
+
+ align:start position:0%
+why am I telling you this right uh
+I can hear that go live from Hamilton in
+
+ align:start position:0%
+I can hear that go live from Hamilton in
+ 
+
+ align:start position:0%
+I can hear that go live from Hamilton in
+my background why am I telling you this
+
+ align:start position:0%
+my background why am I telling you this
+ 
+
+ align:start position:0%
+my background why am I telling you this
+I'm telling you this because in general
+
+ align:start position:0%
+I'm telling you this because in general
+ 
+
+ align:start position:0%
+I'm telling you this because in general
+you need a lot of data to do these
+
+ align:start position:0%
+you need a lot of data to do these
+ 
+
+ align:start position:0%
+you need a lot of data to do these
+calculations you need to know the heat
+
+ align:start position:0%
+calculations you need to know the heat
+ 
+
+ align:start position:0%
+calculations you need to know the heat
+capacities of all the phases and their
+
+ align:start position:0%
+capacities of all the phases and their
+ 
+
+ align:start position:0%
+capacities of all the phases and their
+differences you need to know that
+
+ align:start position:0%
+differences you need to know that
+ 
+
+ align:start position:0%
+differences you need to know that
+thermal expansion coefficients of all
+
+ align:start position:0%
+thermal expansion coefficients of all
+ 
+
+ align:start position:0%
+thermal expansion coefficients of all
+the phases and their differences
+
+ align:start position:0%
+the phases and their differences
+ 
+
+ align:start position:0%
+the phases and their differences
+for this calculation you need to tell
+
+ align:start position:0%
+for this calculation you need to tell
+ 
+
+ align:start position:0%
+for this calculation you need to tell
+the volume of all the phases
+
+ align:start position:0%
+the volume of all the phases
+ 
+
+ align:start position:0%
+the volume of all the phases
+and you know
+
+ align:start position:0%
+and you know
+ 
+
+ align:start position:0%
+and you know
+here right we are calculating Delta V's
+
+ align:start position:0%
+here right we are calculating Delta V's
+ 
+
+ align:start position:0%
+here right we are calculating Delta V's
+you need to know the volume of all the
+
+ align:start position:0%
+you need to know the volume of all the
+ 
+
+ align:start position:0%
+you need to know the volume of all the
+phases
+
+ align:start position:0%
+phases
+ 
+
+ align:start position:0%
+phases
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+and if you don't know the volume of all
+
+ align:start position:0%
+and if you don't know the volume of all
+ 
+
+ align:start position:0%
+and if you don't know the volume of all
+the faces at all temperature and
+
+ align:start position:0%
+the faces at all temperature and
+ 
+
+ align:start position:0%
+the faces at all temperature and
+pressure you have to know it at some
+
+ align:start position:0%
+pressure you have to know it at some
+ 
+
+ align:start position:0%
+pressure you have to know it at some
+temperature and pressure then you need
+
+ align:start position:0%
+temperature and pressure then you need
+ 
+
+ align:start position:0%
+temperature and pressure then you need
+the thermal expansion coefficient of all
+
+ align:start position:0%
+the thermal expansion coefficient of all
+ 
+
+ align:start position:0%
+the thermal expansion coefficient of all
+the phases and you need the isothermal
+
+ align:start position:0%
+the phases and you need the isothermal
+ 
+
+ align:start position:0%
+the phases and you need the isothermal
+compressibility of other phases all
+
+ align:start position:0%
+compressibility of other phases all
+ 
+
+ align:start position:0%
+compressibility of other phases all
+right so again you can see why calcater
+
+ align:start position:0%
+right so again you can see why calcater
+ 
+
+ align:start position:0%
+right so again you can see why calcater
+computer you know calculation phase
+
+ align:start position:0%
+computer you know calculation phase
+ 
+
+ align:start position:0%
+computer you know calculation phase
+diagrams is so powerful because it
+
+ align:start position:0%
+diagrams is so powerful because it
+ 
+
+ align:start position:0%
+diagrams is so powerful because it
+integrates all this stuff for you
+
+ align:start position:0%
+integrates all this stuff for you
+ 
+
+ align:start position:0%
+integrates all this stuff for you
+automatically right
+
+ align:start position:0%
+automatically right
+ 
+
+ align:start position:0%
+automatically right
+so in general
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general this requires
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+knowing some writing's getting sloppy
+
+ align:start position:0%
+knowing some writing's getting sloppy
+ 
+
+ align:start position:0%
+knowing some writing's getting sloppy
+here this requires knowing
+
+ align:start position:0%
+here this requires knowing
+ 
+
+ align:start position:0%
+here this requires knowing
+CP as a function of temperature and
+
+ align:start position:0%
+CP as a function of temperature and
+ 
+
+ align:start position:0%
+CP as a function of temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+v as a function of temperature and
+
+ align:start position:0%
+v as a function of temperature and
+ 
+
+ align:start position:0%
+v as a function of temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+Alpha as a function of temperature and
+
+ align:start position:0%
+Alpha as a function of temperature and
+ 
+
+ align:start position:0%
+Alpha as a function of temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+and beta as a function of temperature
+
+ align:start position:0%
+and beta as a function of temperature
+ 
+
+ align:start position:0%
+and beta as a function of temperature
+and pressure
+
+ align:start position:0%
+and pressure
+ 
+
+ align:start position:0%
+and pressure
+for both phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's get phase labels here right
+
+ align:start position:0%
+so let's get phase labels here right
+ 
+
+ align:start position:0%
+so let's get phase labels here right
+there's a lot of information that we
+
+ align:start position:0%
+there's a lot of information that we
+ 
+
+ align:start position:0%
+there's a lot of information that we
+need to tabulate for both phases Kappa
+
+ align:start position:0%
+need to tabulate for both phases Kappa
+ 
+
+ align:start position:0%
+need to tabulate for both phases Kappa
+equals a of fan beta right
+
+ align:start position:0%
+equals a of fan beta right
+ 
+
+ align:start position:0%
+equals a of fan beta right
+however
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+vaporization
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of a condensed phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for vaporization of a condensed phase
+
+ align:start position:0%
+for vaporization of a condensed phase
+ 
+
+ align:start position:0%
+for vaporization of a condensed phase
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+a limited temperature range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can simplify
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+using three assumptions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+we're going to say Delta H is
+
+ align:start position:0%
+we're going to say Delta H is
+ 
+
+ align:start position:0%
+we're going to say Delta H is
+approximately equal
+
+ align:start position:0%
+approximately equal
+ 
+
+ align:start position:0%
+approximately equal
+to a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's probably the worst approximation
+
+ align:start position:0%
+that's probably the worst approximation
+ 
+
+ align:start position:0%
+that's probably the worst approximation
+we don't know if it's good or not we're
+
+ align:start position:0%
+we don't know if it's good or not we're
+ 
+
+ align:start position:0%
+we don't know if it's good or not we're
+just going to go with it
+
+ align:start position:0%
+just going to go with it
+ 
+
+ align:start position:0%
+just going to go with it
+if Delta H is a constant I don't need to
+
+ align:start position:0%
+if Delta H is a constant I don't need to
+ 
+
+ align:start position:0%
+if Delta H is a constant I don't need to
+do all that heat capacity integrating
+
+ align:start position:0%
+do all that heat capacity integrating
+ 
+
+ align:start position:0%
+do all that heat capacity integrating
+and so forth right it's just a number
+
+ align:start position:0%
+and so forth right it's just a number
+ 
+
+ align:start position:0%
+and so forth right it's just a number
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+volume of the gas is going to be much
+
+ align:start position:0%
+volume of the gas is going to be much
+ 
+
+ align:start position:0%
+volume of the gas is going to be much
+much greater than volume of the solid or
+
+ align:start position:0%
+much greater than volume of the solid or
+ 
+
+ align:start position:0%
+much greater than volume of the solid or
+volume of the liquid
+
+ align:start position:0%
+volume of the liquid
+ 
+
+ align:start position:0%
+volume of the liquid
+right if I assume the volume of the gas
+
+ align:start position:0%
+right if I assume the volume of the gas
+ 
+
+ align:start position:0%
+right if I assume the volume of the gas
+molar volume is much much greater than
+
+ align:start position:0%
+molar volume is much much greater than
+ 
+
+ align:start position:0%
+molar volume is much much greater than
+the solid of the liquid
+
+ align:start position:0%
+the solid of the liquid
+ 
+
+ align:start position:0%
+the solid of the liquid
+then Delta volume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is approximately equal to what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Delta volume this is a transformation
+
+ align:start position:0%
+Delta volume this is a transformation
+ 
+
+ align:start position:0%
+Delta volume this is a transformation
+quantity
+
+ align:start position:0%
+quantity
+ 
+
+ align:start position:0%
+quantity
+I am vaporizing
+
+ align:start position:0%
+I am vaporizing
+ 
+
+ align:start position:0%
+I am vaporizing
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+Delta volume is approximately equal to
+
+ align:start position:0%
+Delta volume is approximately equal to
+ 
+
+ align:start position:0%
+Delta volume is approximately equal to
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+the volume of the gas right exactly
+
+ align:start position:0%
+the volume of the gas right exactly
+ 
+
+ align:start position:0%
+the volume of the gas right exactly
+right Delta Delta V equals volume gas
+
+ align:start position:0%
+right Delta Delta V equals volume gas
+ 
+
+ align:start position:0%
+right Delta Delta V equals volume gas
+minus volume solid
+
+ align:start position:0%
+minus volume solid
+ 
+
+ align:start position:0%
+minus volume solid
+right and if the volume of gas is so
+
+ align:start position:0%
+right and if the volume of gas is so
+ 
+
+ align:start position:0%
+right and if the volume of gas is so
+much bigger
+
+ align:start position:0%
+much bigger
+ 
+
+ align:start position:0%
+much bigger
+uh right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can say it's basically equal to the
+
+ align:start position:0%
+we can say it's basically equal to the
+ 
+
+ align:start position:0%
+we can say it's basically equal to the
+volume of the vapor in and um you know
+
+ align:start position:0%
+volume of the vapor in and um you know
+ 
+
+ align:start position:0%
+volume of the vapor in and um you know
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+when when typical condensed phases
+
+ align:start position:0%
+when when typical condensed phases
+ 
+
+ align:start position:0%
+when when typical condensed phases
+sublime or evaporate you have factors of
+
+ align:start position:0%
+sublime or evaporate you have factors of
+ 
+
+ align:start position:0%
+sublime or evaporate you have factors of
+20 000 or more increase in volume molar
+
+ align:start position:0%
+20 000 or more increase in volume molar
+ 
+
+ align:start position:0%
+20 000 or more increase in volume molar
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+so you know that means you're making an
+
+ align:start position:0%
+so you know that means you're making an
+ 
+
+ align:start position:0%
+so you know that means you're making an
+error one part and twenty thousand it's
+
+ align:start position:0%
+error one part and twenty thousand it's
+ 
+
+ align:start position:0%
+error one part and twenty thousand it's
+it's a pretty good approximation so that
+
+ align:start position:0%
+it's a pretty good approximation so that
+ 
+
+ align:start position:0%
+it's a pretty good approximation so that
+would say that that this is um
+
+ align:start position:0%
+would say that that this is um
+ 
+
+ align:start position:0%
+would say that that this is um
+this is a good approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this one here is kind of a approximation
+
+ align:start position:0%
+this one here is kind of a approximation
+ 
+
+ align:start position:0%
+this one here is kind of a approximation
+it's okay it's not bad
+
+ align:start position:0%
+it's okay it's not bad
+ 
+
+ align:start position:0%
+it's okay it's not bad
+and here's
+
+ align:start position:0%
+and here's
+ 
+
+ align:start position:0%
+and here's
+the third approximation is that the gas
+
+ align:start position:0%
+the third approximation is that the gas
+ 
+
+ align:start position:0%
+the third approximation is that the gas
+the age ideally
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we can use the ideal gas equation of
+
+ align:start position:0%
+so we can use the ideal gas equation of
+ 
+
+ align:start position:0%
+so we can use the ideal gas equation of
+state and unless you're at high
+
+ align:start position:0%
+state and unless you're at high
+ 
+
+ align:start position:0%
+state and unless you're at high
+pressures that's also a pretty good
+
+ align:start position:0%
+pressures that's also a pretty good
+ 
+
+ align:start position:0%
+pressures that's also a pretty good
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+so what we're going to see next is how
+
+ align:start position:0%
+so what we're going to see next is how
+ 
+
+ align:start position:0%
+so what we're going to see next is how
+these three approximations
+
+ align:start position:0%
+these three approximations
+ 
+
+ align:start position:0%
+these three approximations
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+what I'm going to do I'm just going to
+
+ align:start position:0%
+what I'm going to do I'm just going to
+ 
+
+ align:start position:0%
+what I'm going to do I'm just going to
+outline the the way that this goes
+
+ align:start position:0%
+outline the the way that this goes
+ 
+
+ align:start position:0%
+outline the the way that this goes
+forward because
+
+ align:start position:0%
+forward because
+ 
+
+ align:start position:0%
+forward because
+um for on the pset if you need to use
+
+ align:start position:0%
+um for on the pset if you need to use
+ 
+
+ align:start position:0%
+um for on the pset if you need to use
+this a little bit so I want you to
+
+ align:start position:0%
+this a little bit so I want you to
+ 
+
+ align:start position:0%
+this a little bit so I want you to
+explore a little bit
+
+ align:start position:0%
+explore a little bit
+ 
+
+ align:start position:0%
+explore a little bit
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+right if the volume of the gas
+
+ align:start position:0%
+right if the volume of the gas
+ 
+
+ align:start position:0%
+right if the volume of the gas
+equals RT
+
+ align:start position:0%
+equals RT
+ 
+
+ align:start position:0%
+equals RT
+over p
+
+ align:start position:0%
+over p
+ 
+
+ align:start position:0%
+over p
+right that's PV equals nrt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's approximately equal to Delta
+
+ align:start position:0%
+and that's approximately equal to Delta
+ 
+
+ align:start position:0%
+and that's approximately equal to Delta
+V
+
+ align:start position:0%
+V
+ 
+
+ align:start position:0%
+V
+and Delta H is constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right let's remember what I'm trying to
+
+ align:start position:0%
+right let's remember what I'm trying to
+ 
+
+ align:start position:0%
+right let's remember what I'm trying to
+do here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right here I have DP
+
+ align:start position:0%
+right here I have DP
+ 
+
+ align:start position:0%
+right here I have DP
+Delta V equals z t Del's H over K so
+
+ align:start position:0%
+Delta V equals z t Del's H over K so
+ 
+
+ align:start position:0%
+Delta V equals z t Del's H over K so
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+DP
+
+ align:start position:0%
+DP
+ 
+
+ align:start position:0%
+DP
+Delta V equals
+
+ align:start position:0%
+Delta V equals
+ 
+
+ align:start position:0%
+Delta V equals
+DT Delta h
+
+ align:start position:0%
+DT Delta h
+ 
+
+ align:start position:0%
+DT Delta h
+over t
+
+ align:start position:0%
+over t
+ 
+
+ align:start position:0%
+over t
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+so what
+
+ align:start position:0%
+so what
+ 
+
+ align:start position:0%
+so what
+we have DP
+
+ align:start position:0%
+we have DP
+ 
+
+ align:start position:0%
+we have DP
+RT over p
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals DT Delta H over t
+
+ align:start position:0%
+equals DT Delta H over t
+ 
+
+ align:start position:0%
+equals DT Delta H over t
+right so so this is a constant now the
+
+ align:start position:0%
+right so so this is a constant now the
+ 
+
+ align:start position:0%
+right so so this is a constant now the
+the H is a constant that's our
+
+ align:start position:0%
+the H is a constant that's our
+ 
+
+ align:start position:0%
+the H is a constant that's our
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+we have temperature
+
+ align:start position:0%
+we have temperature
+ 
+
+ align:start position:0%
+we have temperature
+and temperature so it's separable I can
+
+ align:start position:0%
+and temperature so it's separable I can
+ 
+
+ align:start position:0%
+and temperature so it's separable I can
+take this temperature over here
+
+ align:start position:0%
+take this temperature over here
+ 
+
+ align:start position:0%
+take this temperature over here
+right so I'm going to have DT over t
+
+ align:start position:0%
+right so I'm going to have DT over t
+ 
+
+ align:start position:0%
+right so I'm going to have DT over t
+squared on the right hand side where the
+
+ align:start position:0%
+squared on the right hand side where the
+ 
+
+ align:start position:0%
+squared on the right hand side where the
+constant factor and the left hand side
+
+ align:start position:0%
+constant factor and the left hand side
+ 
+
+ align:start position:0%
+constant factor and the left hand side
+I'm going to have DP over p
+
+ align:start position:0%
+I'm going to have DP over p
+ 
+
+ align:start position:0%
+I'm going to have DP over p
+with a constant Factor so this is this
+
+ align:start position:0%
+with a constant Factor so this is this
+ 
+
+ align:start position:0%
+with a constant Factor so this is this
+is now a separable and easy differential
+
+ align:start position:0%
+is now a separable and easy differential
+ 
+
+ align:start position:0%
+is now a separable and easy differential
+equation to solve
+
+ align:start position:0%
+equation to solve
+ 
+
+ align:start position:0%
+equation to solve
+and as you can see already you're going
+
+ align:start position:0%
+and as you can see already you're going
+ 
+
+ align:start position:0%
+and as you can see already you're going
+to get logarithms
+
+ align:start position:0%
+to get logarithms
+ 
+
+ align:start position:0%
+to get logarithms
+uh from from the DP over P term okay so
+
+ align:start position:0%
+uh from from the DP over P term okay so
+ 
+
+ align:start position:0%
+uh from from the DP over P term okay so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I'm going to leave it here for you to
+
+ align:start position:0%
+I'm going to leave it here for you to
+ 
+
+ align:start position:0%
+I'm going to leave it here for you to
+finish this calculation
+
+ align:start position:0%
+finish this calculation
+ 
+
+ align:start position:0%
+finish this calculation
+um and you'll use the result
+
+ align:start position:0%
+um and you'll use the result
+ 
+
+ align:start position:0%
+um and you'll use the result
+on the uh in the P set
+
+ align:start position:0%
+on the uh in the P set
+ 
+
+ align:start position:0%
+on the uh in the P set
+and this is very well described in the
+
+ align:start position:0%
+and this is very well described in the
+ 
+
+ align:start position:0%
+and this is very well described in the
+textbook so you can step through it's a
+
+ align:start position:0%
+textbook so you can step through it's a
+ 
+
+ align:start position:0%
+textbook so you can step through it's a
+nice calculation to finish
+
+ align:start position:0%
+nice calculation to finish
+ 
+
+ align:start position:0%
+nice calculation to finish
+um I'm going to move on to Gibbs phase
+
+ align:start position:0%
+um I'm going to move on to Gibbs phase
+ 
+
+ align:start position:0%
+um I'm going to move on to Gibbs phase
+rule so so we're going to leave this
+
+ align:start position:0%
+rule so so we're going to leave this
+ 
+
+ align:start position:0%
+rule so so we're going to leave this
+here on questions on saturation vapor
+
+ align:start position:0%
+here on questions on saturation vapor
+ 
+
+ align:start position:0%
+here on questions on saturation vapor
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+um this is a good time for them I will
+
+ align:start position:0%
+um this is a good time for them I will
+ 
+
+ align:start position:0%
+um this is a good time for them I will
+note that we're going to return to the
+
+ align:start position:0%
+note that we're going to return to the
+ 
+
+ align:start position:0%
+note that we're going to return to the
+concept of saturation vapor pressure on
+
+ align:start position:0%
+concept of saturation vapor pressure on
+ 
+
+ align:start position:0%
+concept of saturation vapor pressure on
+Wednesday when we're going to do an
+
+ align:start position:0%
+Wednesday when we're going to do an
+ 
+
+ align:start position:0%
+Wednesday when we're going to do an
+extended example
+
+ align:start position:0%
+extended example
+ 
+
+ align:start position:0%
+extended example
+so this isn't the last you'll see
+
+ align:start position:0%
+so this isn't the last you'll see
+ 
+
+ align:start position:0%
+so this isn't the last you'll see
+saturation vapor pressure
+
+ align:start position:0%
+saturation vapor pressure
+ 
+
+ align:start position:0%
+saturation vapor pressure
+and we'll come back with a vengeance
+
+ align:start position:0%
+and we'll come back with a vengeance
+ 
+
+ align:start position:0%
+and we'll come back with a vengeance
+um in a couple weeks from now when we do
+
+ align:start position:0%
+um in a couple weeks from now when we do
+ 
+
+ align:start position:0%
+um in a couple weeks from now when we do
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+multi-phase multi-component reacting
+
+ align:start position:0%
+multi-phase multi-component reacting
+ 
+
+ align:start position:0%
+multi-phase multi-component reacting
+systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well I do have a quick question so
+
+ align:start position:0%
+well I do have a quick question so
+ 
+
+ align:start position:0%
+well I do have a quick question so
+in order to assume like DP over DT
+
+ align:start position:0%
+in order to assume like DP over DT
+ 
+
+ align:start position:0%
+in order to assume like DP over DT
+equals Delta H over T Delta V we said
+
+ align:start position:0%
+equals Delta H over T Delta V we said
+ 
+
+ align:start position:0%
+equals Delta H over T Delta V we said
+that it had to be isothermal
+
+ align:start position:0%
+that it had to be isothermal
+ 
+
+ align:start position:0%
+that it had to be isothermal
+yes I did this was um I'm sorry you're
+
+ align:start position:0%
+yes I did this was um I'm sorry you're
+ 
+
+ align:start position:0%
+yes I did this was um I'm sorry you're
+referring back to Delta at the end of
+
+ align:start position:0%
+referring back to Delta at the end of
+ 
+
+ align:start position:0%
+referring back to Delta at the end of
+the cost of Delta H minus t Delta s
+
+ align:start position:0%
+the cost of Delta H minus t Delta s
+ 
+
+ align:start position:0%
+the cost of Delta H minus t Delta s
+yeah and then we said like when
+
+ align:start position:0%
+yeah and then we said like when
+ 
+
+ align:start position:0%
+yeah and then we said like when
+we wrote the second form of like the
+
+ align:start position:0%
+we wrote the second form of like the
+ 
+
+ align:start position:0%
+we wrote the second form of like the
+clausius cap clap around equation like
+
+ align:start position:0%
+clausius cap clap around equation like
+ 
+
+ align:start position:0%
+clausius cap clap around equation like
+that it had to be isothermal for that
+
+ align:start position:0%
+that it had to be isothermal for that
+ 
+
+ align:start position:0%
+that it had to be isothermal for that
+right so then why is DT not zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good question
+
+ align:start position:0%
+good question
+ 
+
+ align:start position:0%
+good question
+this is a consistent question of
+
+ align:start position:0%
+this is a consistent question of
+ 
+
+ align:start position:0%
+this is a consistent question of
+confusion
+
+ align:start position:0%
+confusion
+ 
+
+ align:start position:0%
+confusion
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+these and and again
+
+ align:start position:0%
+these and and again
+ 
+
+ align:start position:0%
+these and and again
+um I won't put you on the spot and ask
+
+ align:start position:0%
+um I won't put you on the spot and ask
+ 
+
+ align:start position:0%
+um I won't put you on the spot and ask
+you whether you've
+
+ align:start position:0%
+you whether you've
+ 
+
+ align:start position:0%
+you whether you've
+watched and spent time thinking about
+
+ align:start position:0%
+watched and spent time thinking about
+ 
+
+ align:start position:0%
+watched and spent time thinking about
+the 3DS of thermodynamics video I don't
+
+ align:start position:0%
+the 3DS of thermodynamics video I don't
+ 
+
+ align:start position:0%
+the 3DS of thermodynamics video I don't
+mean to for suggest upset a Panacea but
+
+ align:start position:0%
+mean to for suggest upset a Panacea but
+ 
+
+ align:start position:0%
+mean to for suggest upset a Panacea but
+um this is a very confusing point
+
+ align:start position:0%
+um this is a very confusing point
+ 
+
+ align:start position:0%
+um this is a very confusing point
+these are transformation quantities
+
+ align:start position:0%
+these are transformation quantities
+ 
+
+ align:start position:0%
+these are transformation quantities
+these are functions of temperature and
+
+ align:start position:0%
+these are functions of temperature and
+ 
+
+ align:start position:0%
+these are functions of temperature and
+pressure at any given temperature and
+
+ align:start position:0%
+pressure at any given temperature and
+ 
+
+ align:start position:0%
+pressure at any given temperature and
+pressure they're numbers
+
+ align:start position:0%
+pressure they're numbers
+ 
+
+ align:start position:0%
+pressure they're numbers
+so for instance Delta s Delta V Delta H
+
+ align:start position:0%
+so for instance Delta s Delta V Delta H
+ 
+
+ align:start position:0%
+so for instance Delta s Delta V Delta H
+Delta V and any given temperature and
+
+ align:start position:0%
+Delta V and any given temperature and
+ 
+
+ align:start position:0%
+Delta V and any given temperature and
+pressure they're numbers they
+
+ align:start position:0%
+pressure they're numbers they
+ 
+
+ align:start position:0%
+pressure they're numbers they
+characterize the change in state
+
+ align:start position:0%
+characterize the change in state
+ 
+
+ align:start position:0%
+characterize the change in state
+variables As you move between phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+being functions of temperature and
+
+ align:start position:0%
+being functions of temperature and
+ 
+
+ align:start position:0%
+being functions of temperature and
+pressure they depend on temperature and
+
+ align:start position:0%
+pressure they depend on temperature and
+ 
+
+ align:start position:0%
+pressure they depend on temperature and
+pressure so I want you to think of these
+
+ align:start position:0%
+pressure so I want you to think of these
+ 
+
+ align:start position:0%
+pressure so I want you to think of these
+capital D Deltas as the distances
+
+ align:start position:0%
+capital D Deltas as the distances
+ 
+
+ align:start position:0%
+capital D Deltas as the distances
+between these surfaces and I'm sort of
+
+ align:start position:0%
+between these surfaces and I'm sort of
+ 
+
+ align:start position:0%
+between these surfaces and I'm sort of
+drawing surfaces here but it was I drew
+
+ align:start position:0%
+drawing surfaces here but it was I drew
+ 
+
+ align:start position:0%
+drawing surfaces here but it was I drew
+it in the last lecture and it's really
+
+ align:start position:0%
+it in the last lecture and it's really
+ 
+
+ align:start position:0%
+it in the last lecture and it's really
+well Illustrated in a textbook so each
+
+ align:start position:0%
+well Illustrated in a textbook so each
+ 
+
+ align:start position:0%
+well Illustrated in a textbook so each
+of these quantities Delta s Delta V is
+
+ align:start position:0%
+of these quantities Delta s Delta V is
+ 
+
+ align:start position:0%
+of these quantities Delta s Delta V is
+the distance between let's say the
+
+ align:start position:0%
+the distance between let's say the
+ 
+
+ align:start position:0%
+the distance between let's say the
+surface s for phase vapor and S for
+
+ align:start position:0%
+surface s for phase vapor and S for
+ 
+
+ align:start position:0%
+surface s for phase vapor and S for
+phase solid as as drawing the last
+
+ align:start position:0%
+phase solid as as drawing the last
+ 
+
+ align:start position:0%
+phase solid as as drawing the last
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since they're functions of
+
+ align:start position:0%
+and since they're functions of
+ 
+
+ align:start position:0%
+and since they're functions of
+temperature and pressure they vary with
+
+ align:start position:0%
+temperature and pressure they vary with
+ 
+
+ align:start position:0%
+temperature and pressure they vary with
+temperature and pressure
+
+ align:start position:0%
+temperature and pressure
+ 
+
+ align:start position:0%
+temperature and pressure
+so for example you have volume oh that's
+
+ align:start position:0%
+so for example you have volume oh that's
+ 
+
+ align:start position:0%
+so for example you have volume oh that's
+a really fat pen that's not helping
+
+ align:start position:0%
+a really fat pen that's not helping
+ 
+
+ align:start position:0%
+a really fat pen that's not helping
+let me find a page where I have some
+
+ align:start position:0%
+let me find a page where I have some
+ 
+
+ align:start position:0%
+let me find a page where I have some
+white space this there I have my space
+
+ align:start position:0%
+white space this there I have my space
+ 
+
+ align:start position:0%
+white space this there I have my space
+on this page
+
+ align:start position:0%
+on this page
+ 
+
+ align:start position:0%
+on this page
+let me grab a pen that's not too worn
+
+ align:start position:0%
+let me grab a pen that's not too worn
+ 
+
+ align:start position:0%
+let me grab a pen that's not too worn
+out yet so let's say I have
+
+ align:start position:0%
+out yet so let's say I have
+ 
+
+ align:start position:0%
+out yet so let's say I have
+volume of phase Alpha that of course
+
+ align:start position:0%
+volume of phase Alpha that of course
+ 
+
+ align:start position:0%
+volume of phase Alpha that of course
+depends on temperature and pressure
+
+ align:start position:0%
+depends on temperature and pressure
+ 
+
+ align:start position:0%
+depends on temperature and pressure
+volume of phase beta that of course
+
+ align:start position:0%
+volume of phase beta that of course
+ 
+
+ align:start position:0%
+volume of phase beta that of course
+depends on pressure and temperature
+
+ align:start position:0%
+depends on pressure and temperature
+ 
+
+ align:start position:0%
+depends on pressure and temperature
+and so I might have a transformation
+
+ align:start position:0%
+and so I might have a transformation
+ 
+
+ align:start position:0%
+and so I might have a transformation
+quantity the change in volume as I
+
+ align:start position:0%
+quantity the change in volume as I
+ 
+
+ align:start position:0%
+quantity the change in volume as I
+transform from alpha to Beta this equals
+
+ align:start position:0%
+transform from alpha to Beta this equals
+ 
+
+ align:start position:0%
+transform from alpha to Beta this equals
+volume of beta temperature and pressure
+
+ align:start position:0%
+volume of beta temperature and pressure
+ 
+
+ align:start position:0%
+volume of beta temperature and pressure
+minus volume of alpha temperature and
+
+ align:start position:0%
+minus volume of alpha temperature and
+ 
+
+ align:start position:0%
+minus volume of alpha temperature and
+pressure and so this explicitly depends
+
+ align:start position:0%
+pressure and so this explicitly depends
+ 
+
+ align:start position:0%
+pressure and so this explicitly depends
+on temperature and pressure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+right that means that even though I can
+
+ align:start position:0%
+right that means that even though I can
+ 
+
+ align:start position:0%
+right that means that even though I can
+consider an isothermal transformation
+
+ align:start position:0%
+consider an isothermal transformation
+ 
+
+ align:start position:0%
+consider an isothermal transformation
+between Alpha and beta I can also ask
+
+ align:start position:0%
+between Alpha and beta I can also ask
+ 
+
+ align:start position:0%
+between Alpha and beta I can also ask
+how that quantity varies
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say with temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right that's the slope of that surface
+
+ align:start position:0%
+right that's the slope of that surface
+ 
+
+ align:start position:0%
+right that's the slope of that surface
+for varying temperature with fixed
+
+ align:start position:0%
+for varying temperature with fixed
+ 
+
+ align:start position:0%
+for varying temperature with fixed
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+and and I'm hesitating to launch into
+
+ align:start position:0%
+and and I'm hesitating to launch into
+ 
+
+ align:start position:0%
+and and I'm hesitating to launch into
+redrawing all those surfaces that I did
+
+ align:start position:0%
+redrawing all those surfaces that I did
+ 
+
+ align:start position:0%
+redrawing all those surfaces that I did
+the last time because it just if I do it
+
+ align:start position:0%
+the last time because it just if I do it
+ 
+
+ align:start position:0%
+the last time because it just if I do it
+quickly it'll be too messy to be useful
+
+ align:start position:0%
+quickly it'll be too messy to be useful
+ 
+
+ align:start position:0%
+quickly it'll be too messy to be useful
+and if I take my time I'll be repeating
+
+ align:start position:0%
+and if I take my time I'll be repeating
+ 
+
+ align:start position:0%
+and if I take my time I'll be repeating
+myself and we'll run out of time with
+
+ align:start position:0%
+myself and we'll run out of time with
+ 
+
+ align:start position:0%
+myself and we'll run out of time with
+today's lecture
+
+ align:start position:0%
+today's lecture
+ 
+
+ align:start position:0%
+today's lecture
+another way to think about it is that at
+
+ align:start position:0%
+another way to think about it is that at
+ 
+
+ align:start position:0%
+another way to think about it is that at
+any given temperature and pressure a
+
+ align:start position:0%
+any given temperature and pressure a
+ 
+
+ align:start position:0%
+any given temperature and pressure a
+fixed temperature and a fixed pressure I
+
+ align:start position:0%
+fixed temperature and a fixed pressure I
+ 
+
+ align:start position:0%
+fixed temperature and a fixed pressure I
+have these equilibrium conditions
+
+ align:start position:0%
+have these equilibrium conditions
+ 
+
+ align:start position:0%
+have these equilibrium conditions
+between the two phases
+
+ align:start position:0%
+between the two phases
+ 
+
+ align:start position:0%
+between the two phases
+and now I'm going to take a little I'm
+
+ align:start position:0%
+and now I'm going to take a little I'm
+ 
+
+ align:start position:0%
+and now I'm going to take a little I'm
+going to take a little trip
+
+ align:start position:0%
+going to take a little trip
+ 
+
+ align:start position:0%
+going to take a little trip
+I'm gonna go from one temperature and
+
+ align:start position:0%
+I'm gonna go from one temperature and
+ 
+
+ align:start position:0%
+I'm gonna go from one temperature and
+pressure to another temperature and
+
+ align:start position:0%
+pressure to another temperature and
+ 
+
+ align:start position:0%
+pressure to another temperature and
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+and causes claparon is about making sure
+
+ align:start position:0%
+and causes claparon is about making sure
+ 
+
+ align:start position:0%
+and causes claparon is about making sure
+that I stay on that equilibrium
+
+ align:start position:0%
+that I stay on that equilibrium
+ 
+
+ align:start position:0%
+that I stay on that equilibrium
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+okay I don't know if that was helpful
+
+ align:start position:0%
+okay I don't know if that was helpful
+ 
+
+ align:start position:0%
+okay I don't know if that was helpful
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+let's let's move on and then and then as
+
+ align:start position:0%
+let's let's move on and then and then as
+ 
+
+ align:start position:0%
+let's let's move on and then and then as
+time allows um come back to that
+
+ align:start position:0%
+time allows um come back to that
+ 
+
+ align:start position:0%
+time allows um come back to that
+question at the end of the lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but again transformation quantities
+
+ align:start position:0%
+but again transformation quantities
+ 
+
+ align:start position:0%
+but again transformation quantities
+they're super important
+
+ align:start position:0%
+they're super important
+ 
+
+ align:start position:0%
+they're super important
+Gibbs phase rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to go over this a little bit
+
+ align:start position:0%
+we're going to go over this a little bit
+ 
+
+ align:start position:0%
+we're going to go over this a little bit
+quickly
+
+ align:start position:0%
+quickly
+ 
+
+ align:start position:0%
+quickly
+gives phase rule is the answer to the
+
+ align:start position:0%
+gives phase rule is the answer to the
+ 
+
+ align:start position:0%
+gives phase rule is the answer to the
+following question how many phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can coexist
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+at equilibrium how many phases goes acid
+
+ align:start position:0%
+at equilibrium how many phases goes acid
+ 
+
+ align:start position:0%
+at equilibrium how many phases goes acid
+equilibrium so Gibbs phase rule is a
+
+ align:start position:0%
+equilibrium so Gibbs phase rule is a
+ 
+
+ align:start position:0%
+equilibrium so Gibbs phase rule is a
+linear algebra problem it's like this
+
+ align:start position:0%
+linear algebra problem it's like this
+ 
+
+ align:start position:0%
+linear algebra problem it's like this
+number of degrees of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equals number of variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus number of independent
+
+ align:start position:0%
+minus number of independent
+ 
+
+ align:start position:0%
+minus number of independent
+constraints
+
+ align:start position:0%
+constraints
+ 
+
+ align:start position:0%
+constraints
+so hopefully this is um familiar from
+
+ align:start position:0%
+so hopefully this is um familiar from
+ 
+
+ align:start position:0%
+so hopefully this is um familiar from
+linear algebra so let's count variables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I just have to go through this in order
+
+ align:start position:0%
+I just have to go through this in order
+ 
+
+ align:start position:0%
+I just have to go through this in order
+to for it to make any sense
+
+ align:start position:0%
+to for it to make any sense
+ 
+
+ align:start position:0%
+to for it to make any sense
+all right so I have
+
+ align:start position:0%
+all right so I have
+ 
+
+ align:start position:0%
+all right so I have
+let's see
+
+ align:start position:0%
+let's see
+ 
+
+ align:start position:0%
+let's see
+for phase Alpha I have a temperature and
+
+ align:start position:0%
+for phase Alpha I have a temperature and
+ 
+
+ align:start position:0%
+for phase Alpha I have a temperature and
+a pressure
+
+ align:start position:0%
+a pressure
+ 
+
+ align:start position:0%
+a pressure
+sorry bro let's say that was drawn for
+
+ align:start position:0%
+sorry bro let's say that was drawn for
+ 
+
+ align:start position:0%
+sorry bro let's say that was drawn for
+face beta I apologize for temperature
+
+ align:start position:0%
+face beta I apologize for temperature
+ 
+
+ align:start position:0%
+face beta I apologize for temperature
+temperature and pressure for Alpha
+
+ align:start position:0%
+temperature and pressure for Alpha
+ 
+
+ align:start position:0%
+temperature and pressure for Alpha
+temperature and pressure for phase gamma
+
+ align:start position:0%
+temperature and pressure for phase gamma
+ 
+
+ align:start position:0%
+temperature and pressure for phase gamma
+and so forth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for each of pH phases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have
+
+ align:start position:0%
+I have
+ 
+
+ align:start position:0%
+I have
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+variables that's what I mean to set up I
+
+ align:start position:0%
+variables that's what I mean to set up I
+ 
+
+ align:start position:0%
+variables that's what I mean to set up I
+mean to suggest an array
+
+ align:start position:0%
+mean to suggest an array
+ 
+
+ align:start position:0%
+mean to suggest an array
+of phases and two variables so in this
+
+ align:start position:0%
+of phases and two variables so in this
+ 
+
+ align:start position:0%
+of phases and two variables so in this
+approach
+
+ align:start position:0%
+approach
+ 
+
+ align:start position:0%
+approach
+the number of variables
+
+ align:start position:0%
+the number of variables
+ 
+
+ align:start position:0%
+the number of variables
+in my system
+
+ align:start position:0%
+in my system
+ 
+
+ align:start position:0%
+in my system
+equals two
+
+ align:start position:0%
+equals two
+ 
+
+ align:start position:0%
+equals two
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+F and I use fa because the textbook uses
+
+ align:start position:0%
+F and I use fa because the textbook uses
+ 
+
+ align:start position:0%
+F and I use fa because the textbook uses
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+um whereas in every other page of the
+
+ align:start position:0%
+um whereas in every other page of the
+ 
+
+ align:start position:0%
+um whereas in every other page of the
+textbook p means pressure
+
+ align:start position:0%
+textbook p means pressure
+ 
+
+ align:start position:0%
+textbook p means pressure
+so I don't like what they do so I use
+
+ align:start position:0%
+so I don't like what they do so I use
+ 
+
+ align:start position:0%
+so I don't like what they do so I use
+ all right so that's that's okay now
+
+ align:start position:0%
+ all right so that's that's okay now
+ 
+
+ align:start position:0%
+ all right so that's that's okay now
+let's do um
+
+ align:start position:0%
+let's do um
+ 
+
+ align:start position:0%
+let's do um
+let's do uh number of degrees of freedom
+
+ align:start position:0%
+let's do uh number of degrees of freedom
+ 
+
+ align:start position:0%
+let's do uh number of degrees of freedom
+the number of variables number of
+
+ align:start position:0%
+the number of variables number of
+ 
+
+ align:start position:0%
+the number of variables number of
+independent constraints
+
+ align:start position:0%
+independent constraints
+ 
+
+ align:start position:0%
+independent constraints
+number of constraints
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number of constraints I'm not going to
+
+ align:start position:0%
+number of constraints I'm not going to
+ 
+
+ align:start position:0%
+number of constraints I'm not going to
+write this out because it's very well
+
+ align:start position:0%
+write this out because it's very well
+ 
+
+ align:start position:0%
+write this out because it's very well
+presented in the text but my constraints
+
+ align:start position:0%
+presented in the text but my constraints
+ 
+
+ align:start position:0%
+presented in the text but my constraints
+are my equilibrium conditions such as
+
+ align:start position:0%
+are my equilibrium conditions such as
+ 
+
+ align:start position:0%
+are my equilibrium conditions such as
+T of alpha
+
+ align:start position:0%
+T of alpha
+ 
+
+ align:start position:0%
+T of alpha
+equals T of beta equals T of gamma
+
+ align:start position:0%
+equals T of beta equals T of gamma
+ 
+
+ align:start position:0%
+equals T of beta equals T of gamma
+equals T of all the other phases
+
+ align:start position:0%
+equals T of all the other phases
+ 
+
+ align:start position:0%
+equals T of all the other phases
+and for example P of alpha equals P of
+
+ align:start position:0%
+and for example P of alpha equals P of
+ 
+
+ align:start position:0%
+and for example P of alpha equals P of
+beta equals P of gamma equals and so
+
+ align:start position:0%
+beta equals P of gamma equals and so
+ 
+
+ align:start position:0%
+beta equals P of gamma equals and so
+forth so I have my variables and I have
+
+ align:start position:0%
+forth so I have my variables and I have
+ 
+
+ align:start position:0%
+forth so I have my variables and I have
+my constraints the variables come from
+
+ align:start position:0%
+my constraints the variables come from
+ 
+
+ align:start position:0%
+my constraints the variables come from
+counting the constraints come from the
+
+ align:start position:0%
+counting the constraints come from the
+ 
+
+ align:start position:0%
+counting the constraints come from the
+equilibrium conditions which we've
+
+ align:start position:0%
+equilibrium conditions which we've
+ 
+
+ align:start position:0%
+equilibrium conditions which we've
+already derived and let me skip straight
+
+ align:start position:0%
+already derived and let me skip straight
+ 
+
+ align:start position:0%
+already derived and let me skip straight
+to the answer
+
+ align:start position:0%
+to the answer
+ 
+
+ align:start position:0%
+to the answer
+the answer
+
+ align:start position:0%
+the answer
+ 
+
+ align:start position:0%
+the answer
+is that my number of degree of Freedom
+
+ align:start position:0%
+is that my number of degree of Freedom
+ 
+
+ align:start position:0%
+is that my number of degree of Freedom
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+times phases
+
+ align:start position:0%
+times phases
+ 
+
+ align:start position:0%
+times phases
+minus three
+
+ align:start position:0%
+minus three
+ 
+
+ align:start position:0%
+minus three
+times phases minus one
+
+ align:start position:0%
+times phases minus one
+ 
+
+ align:start position:0%
+times phases minus one
+equals 3
+
+ align:start position:0%
+equals 3
+ 
+
+ align:start position:0%
+equals 3
+minus the number of phases this is gives
+
+ align:start position:0%
+minus the number of phases this is gives
+ 
+
+ align:start position:0%
+minus the number of phases this is gives
+phase rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for unitary systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so this is this is um
+
+ align:start position:0%
+right so this is this is um
+ 
+
+ align:start position:0%
+right so this is this is um
+skipping straight to the answer it's
+
+ align:start position:0%
+skipping straight to the answer it's
+ 
+
+ align:start position:0%
+skipping straight to the answer it's
+more thoroughly developed than the text
+
+ align:start position:0%
+more thoroughly developed than the text
+ 
+
+ align:start position:0%
+more thoroughly developed than the text
+what does this mean that's what I want
+
+ align:start position:0%
+what does this mean that's what I want
+ 
+
+ align:start position:0%
+what does this mean that's what I want
+to get to that's why I'm rushing ahead
+
+ align:start position:0%
+to get to that's why I'm rushing ahead
+ 
+
+ align:start position:0%
+to get to that's why I'm rushing ahead
+a one phase region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one phase
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+phase equals one
+
+ align:start position:0%
+phase equals one
+ 
+
+ align:start position:0%
+phase equals one
+through gria Freedom equals two
+
+ align:start position:0%
+through gria Freedom equals two
+ 
+
+ align:start position:0%
+through gria Freedom equals two
+for example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the TP plane
+
+ align:start position:0%
+the TP plane
+ 
+
+ align:start position:0%
+the TP plane
+right so this is getting back to what we
+
+ align:start position:0%
+right so this is getting back to what we
+ 
+
+ align:start position:0%
+right so this is getting back to what we
+know to be true which is that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a unary phase diagram in general I'm
+
+ align:start position:0%
+in a unary phase diagram in general I'm
+ 
+
+ align:start position:0%
+in a unary phase diagram in general I'm
+going to draw the one for water here
+
+ align:start position:0%
+going to draw the one for water here
+ 
+
+ align:start position:0%
+going to draw the one for water here
+because it's pretty familiar
+
+ align:start position:0%
+because it's pretty familiar
+ 
+
+ align:start position:0%
+because it's pretty familiar
+let's see this is temperature this is
+
+ align:start position:0%
+let's see this is temperature this is
+ 
+
+ align:start position:0%
+let's see this is temperature this is
+pressure
+
+ align:start position:0%
+pressure
+ 
+
+ align:start position:0%
+pressure
+this is liquid solid and a vapor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in general in a urinary phase diagram
+
+ align:start position:0%
+in general in a urinary phase diagram
+ 
+
+ align:start position:0%
+in general in a urinary phase diagram
+I can stick in one phase region and I
+
+ align:start position:0%
+I can stick in one phase region and I
+ 
+
+ align:start position:0%
+I can stick in one phase region and I
+can wander around randomly in
+
+ align:start position:0%
+can wander around randomly in
+ 
+
+ align:start position:0%
+can wander around randomly in
+temperature and pressure and remain in
+
+ align:start position:0%
+temperature and pressure and remain in
+ 
+
+ align:start position:0%
+temperature and pressure and remain in
+that one phase region
+
+ align:start position:0%
+that one phase region
+ 
+
+ align:start position:0%
+that one phase region
+that's the meaning of having two degrees
+
+ align:start position:0%
+that's the meaning of having two degrees
+ 
+
+ align:start position:0%
+that's the meaning of having two degrees
+of freedom I can wander at random in
+
+ align:start position:0%
+of freedom I can wander at random in
+ 
+
+ align:start position:0%
+of freedom I can wander at random in
+temperature and pressure independently
+
+ align:start position:0%
+temperature and pressure independently
+ 
+
+ align:start position:0%
+temperature and pressure independently
+while remaining in my one phase region
+
+ align:start position:0%
+while remaining in my one phase region
+ 
+
+ align:start position:0%
+while remaining in my one phase region
+now it's considered two-phase region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two-phase region
+
+ align:start position:0%
+two-phase region
+ 
+
+ align:start position:0%
+two-phase region
+front equals two so what's my degrees of
+
+ align:start position:0%
+front equals two so what's my degrees of
+ 
+
+ align:start position:0%
+front equals two so what's my degrees of
+freedom anybody
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one one right
+
+ align:start position:0%
+one one right
+ 
+
+ align:start position:0%
+one one right
+so what does that mean if I am
+
+ align:start position:0%
+so what does that mean if I am
+ 
+
+ align:start position:0%
+so what does that mean if I am
+in a two-phase region let's say on that
+
+ align:start position:0%
+in a two-phase region let's say on that
+ 
+
+ align:start position:0%
+in a two-phase region let's say on that
+coexistence line
+
+ align:start position:0%
+coexistence line
+ 
+
+ align:start position:0%
+coexistence line
+I can move along the line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and maintain my two-phase coexistence
+
+ align:start position:0%
+and maintain my two-phase coexistence
+ 
+
+ align:start position:0%
+and maintain my two-phase coexistence
+condition
+
+ align:start position:0%
+condition
+ 
+
+ align:start position:0%
+condition
+that's one degree of freedom right if I
+
+ align:start position:0%
+that's one degree of freedom right if I
+ 
+
+ align:start position:0%
+that's one degree of freedom right if I
+move in temperature the move in pressure
+
+ align:start position:0%
+move in temperature the move in pressure
+ 
+
+ align:start position:0%
+move in temperature the move in pressure
+is prescribed
+
+ align:start position:0%
+is prescribed
+ 
+
+ align:start position:0%
+is prescribed
+I can't move independently in both
+
+ align:start position:0%
+I can't move independently in both
+ 
+
+ align:start position:0%
+I can't move independently in both
+pressure and temperature
+
+ align:start position:0%
+pressure and temperature
+ 
+
+ align:start position:0%
+pressure and temperature
+and it's prescribed by the cloud 6
+
+ align:start position:0%
+and it's prescribed by the cloud 6
+ 
+
+ align:start position:0%
+and it's prescribed by the cloud 6
+collaboron equation we just derived that
+
+ align:start position:0%
+collaboron equation we just derived that
+ 
+
+ align:start position:0%
+collaboron equation we just derived that
+right so that's one degree of freedom
+
+ align:start position:0%
+right so that's one degree of freedom
+ 
+
+ align:start position:0%
+right so that's one degree of freedom
+is a line
+
+ align:start position:0%
+is a line
+ 
+
+ align:start position:0%
+is a line
+right this is a coexistence line
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally
+
+ align:start position:0%
+and finally
+ 
+
+ align:start position:0%
+and finally
+a three-phase region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number phases equals three
+
+ align:start position:0%
+number phases equals three
+ 
+
+ align:start position:0%
+number phases equals three
+so my degrees of freedom equals zero
+
+ align:start position:0%
+so my degrees of freedom equals zero
+ 
+
+ align:start position:0%
+so my degrees of freedom equals zero
+what's a geometrical object with zero
+
+ align:start position:0%
+what's a geometrical object with zero
+ 
+
+ align:start position:0%
+what's a geometrical object with zero
+degrees of freedom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a point what
+
+ align:start position:0%
+a point what
+ 
+
+ align:start position:0%
+a point what
+so we have in unitary phase diagrams
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so-called triple points
+
+ align:start position:0%
+so-called triple points
+ 
+
+ align:start position:0%
+so-called triple points
+these are points where
+
+ align:start position:0%
+these are points where
+ 
+
+ align:start position:0%
+these are points where
+three phases can exist at equilibrium
+
+ align:start position:0%
+three phases can exist at equilibrium
+ 
+
+ align:start position:0%
+three phases can exist at equilibrium
+can coexist at equilibrium
+
+ align:start position:0%
+can coexist at equilibrium
+ 
+
+ align:start position:0%
+can coexist at equilibrium
+however
+
+ align:start position:0%
+however
+ 
+
+ align:start position:0%
+however
+there are special points if I change
+
+ align:start position:0%
+there are special points if I change
+ 
+
+ align:start position:0%
+there are special points if I change
+temperature or pressure away from those
+
+ align:start position:0%
+temperature or pressure away from those
+ 
+
+ align:start position:0%
+temperature or pressure away from those
+points I fall out of that three-phase
+
+ align:start position:0%
+points I fall out of that three-phase
+ 
+
+ align:start position:0%
+points I fall out of that three-phase
+coexistence condition
+
+ align:start position:0%
+coexistence condition
+ 
+
+ align:start position:0%
+coexistence condition
+so for example my triple point here of
+
+ align:start position:0%
+so for example my triple point here of
+ 
+
+ align:start position:0%
+so for example my triple point here of
+water
+
+ align:start position:0%
+water
+ 
+
+ align:start position:0%
+water
+is um
+
+ align:start position:0%
+is um
+ 
+
+ align:start position:0%
+is um
+gosh what is it it's like 10 Tor and
+
+ align:start position:0%
+gosh what is it it's like 10 Tor and
+ 
+
+ align:start position:0%
+gosh what is it it's like 10 Tor and
+right around 273 see I forget exactly
+
+ align:start position:0%
+right around 273 see I forget exactly
+ 
+
+ align:start position:0%
+right around 273 see I forget exactly
+the number
+
+ align:start position:0%
+the number
+ 
+
+ align:start position:0%
+the number
+if I'm in any temperature and pressure
+
+ align:start position:0%
+if I'm in any temperature and pressure
+ 
+
+ align:start position:0%
+if I'm in any temperature and pressure
+other than that special triple point I
+
+ align:start position:0%
+other than that special triple point I
+ 
+
+ align:start position:0%
+other than that special triple point I
+cannot have all three phases coexisting
+
+ align:start position:0%
+cannot have all three phases coexisting
+ 
+
+ align:start position:0%
+cannot have all three phases coexisting
+in equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it comes out of of this uh
+
+ align:start position:0%
+it comes out of of this uh
+ 
+
+ align:start position:0%
+it comes out of of this uh
+relatively simple linear algebra
+
+ align:start position:0%
+relatively simple linear algebra
+ 
+
+ align:start position:0%
+relatively simple linear algebra
+approach and four-phase region
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not allowed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so from thinking about the number of
+
+ align:start position:0%
+so from thinking about the number of
+ 
+
+ align:start position:0%
+so from thinking about the number of
+independent variables in a unary system
+
+ align:start position:0%
+independent variables in a unary system
+ 
+
+ align:start position:0%
+independent variables in a unary system
+that is pressure and temperature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and deriving the conditions for
+
+ align:start position:0%
+and deriving the conditions for
+ 
+
+ align:start position:0%
+and deriving the conditions for
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+right which you'll recall came from
+
+ align:start position:0%
+right which you'll recall came from
+ 
+
+ align:start position:0%
+right which you'll recall came from
+entropy Max condition
+
+ align:start position:0%
+entropy Max condition
+ 
+
+ align:start position:0%
+entropy Max condition
+and thinking about those things we have
+
+ align:start position:0%
+and thinking about those things we have
+ 
+
+ align:start position:0%
+and thinking about those things we have
+arrived at
+
+ align:start position:0%
+arrived at
+ 
+
+ align:start position:0%
+arrived at
+a pretty strict set of rules
+
+ align:start position:0%
+a pretty strict set of rules
+ 
+
+ align:start position:0%
+a pretty strict set of rules
+and they're fully consistent with
+
+ align:start position:0%
+and they're fully consistent with
+ 
+
+ align:start position:0%
+and they're fully consistent with
+everything we know nature does
+
+ align:start position:0%
+everything we know nature does
+ 
+
+ align:start position:0%
+everything we know nature does
+so I think that's kind of cool
+
+ align:start position:0%
+so I think that's kind of cool
+ 
+
+ align:start position:0%
+so I think that's kind of cool
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+it's an example of the deductive power
+
+ align:start position:0%
+it's an example of the deductive power
+ 
+
+ align:start position:0%
+it's an example of the deductive power
+of thermodynamics you start with these
+
+ align:start position:0%
+of thermodynamics you start with these
+ 
+
+ align:start position:0%
+of thermodynamics you start with these
+abstract principles and some math
+
+ align:start position:0%
+abstract principles and some math
+ 
+
+ align:start position:0%
+abstract principles and some math
+and you get very practical real world
+
+ align:start position:0%
+and you get very practical real world
+ 
+
+ align:start position:0%
+and you get very practical real world
+predictions that are borne out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what happens how do I get a four-phase
+
+ align:start position:0%
+what happens how do I get a four-phase
+ 
+
+ align:start position:0%
+what happens how do I get a four-phase
+region does anyone know there are four
+
+ align:start position:0%
+region does anyone know there are four
+ 
+
+ align:start position:0%
+region does anyone know there are four
+phase equilibria in nature they're
+
+ align:start position:0%
+phase equilibria in nature they're
+ 
+
+ align:start position:0%
+phase equilibria in nature they're
+allowed but they're not allowed in unary
+
+ align:start position:0%
+allowed but they're not allowed in unary
+ 
+
+ align:start position:0%
+allowed but they're not allowed in unary
+systems how do I get a four-phase
+
+ align:start position:0%
+systems how do I get a four-phase
+ 
+
+ align:start position:0%
+systems how do I get a four-phase
+coexistence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it happens if I somehow increase
+
+ align:start position:0%
+right it happens if I somehow increase
+ 
+
+ align:start position:0%
+right it happens if I somehow increase
+my number of variables faster than
+
+ align:start position:0%
+my number of variables faster than
+ 
+
+ align:start position:0%
+my number of variables faster than
+increase my independent constraints and
+
+ align:start position:0%
+increase my independent constraints and
+ 
+
+ align:start position:0%
+increase my independent constraints and
+that's what happens when you add
+
+ align:start position:0%
+that's what happens when you add
+ 
+
+ align:start position:0%
+that's what happens when you add
+multiple components to a system so we're
+
+ align:start position:0%
+multiple components to a system so we're
+ 
+
+ align:start position:0%
+multiple components to a system so we're
+going to revisit Gibbs phase rule when
+
+ align:start position:0%
+going to revisit Gibbs phase rule when
+ 
+
+ align:start position:0%
+going to revisit Gibbs phase rule when
+we do uh
+
+ align:start position:0%
+we do uh
+ 
+
+ align:start position:0%
+we do uh
+multi-component systems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+except
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if multi-components
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+okay so
+ 
+
+ align:start position:0%
+okay so
+um this is the end of our treatment of
+
+ align:start position:0%
+um this is the end of our treatment of
+ 
+
+ align:start position:0%
+um this is the end of our treatment of
+urinary phase diagrams
+
+ align:start position:0%
+urinary phase diagrams
+ 
+
+ align:start position:0%
+urinary phase diagrams
+um in terms of new material on Wednesday
+
+ align:start position:0%
+um in terms of new material on Wednesday
+ 
+
+ align:start position:0%
+um in terms of new material on Wednesday
+we're going to study saturation vapor
+
+ align:start position:0%
+we're going to study saturation vapor
+ 
+
+ align:start position:0%
+we're going to study saturation vapor
+pressure in some detail
+
+ align:start position:0%
+pressure in some detail
+ 
+
+ align:start position:0%
+pressure in some detail
+uh I hope this does give you a little
+
+ align:start position:0%
+uh I hope this does give you a little
+ 
+
+ align:start position:0%
+uh I hope this does give you a little
+bit of a flavor of the pace of this
+
+ align:start position:0%
+bit of a flavor of the pace of this
+ 
+
+ align:start position:0%
+bit of a flavor of the pace of this
+class there's no way that I could cover
+
+ align:start position:0%
+class there's no way that I could cover
+ 
+
+ align:start position:0%
+class there's no way that I could cover
+all the material and work examples
+
+ align:start position:0%
+all the material and work examples
+ 
+
+ align:start position:0%
+all the material and work examples
+um in lecture and so we rely also on on
+
+ align:start position:0%
+um in lecture and so we rely also on on
+ 
+
+ align:start position:0%
+um in lecture and so we rely also on on
+the textbooks on the reading so please
+
+ align:start position:0%
+the textbooks on the reading so please
+ 
+
+ align:start position:0%
+the textbooks on the reading so please
+do keep up
\ No newline at end of file
diff --git a/O7AoQhYEdLA.txt b/O7AoQhYEdLA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18efa83d5564ee08c22cea1d251e698567ec2be3
--- /dev/null
+++ b/O7AoQhYEdLA.txt
@@ -0,0 +1,603 @@
+align:start position:0%
+ 
+in this lecture would describe the
+
+ align:start position:0%
+in this lecture would describe the
+ 
+
+ align:start position:0%
+in this lecture would describe the
+Framingham Heart Study one of the most
+
+ align:start position:0%
+Framingham Heart Study one of the most
+ 
+
+ align:start position:0%
+Framingham Heart Study one of the most
+important epidemiological studies ever
+
+ align:start position:0%
+important epidemiological studies ever
+ 
+
+ align:start position:0%
+important epidemiological studies ever
+conducted and the underlying analytics
+
+ align:start position:0%
+conducted and the underlying analytics
+ 
+
+ align:start position:0%
+conducted and the underlying analytics
+that led to our current understanding of
+
+ align:start position:0%
+that led to our current understanding of
+ 
+
+ align:start position:0%
+that led to our current understanding of
+cardiovascular disease to motivate how
+
+ align:start position:0%
+cardiovascular disease to motivate how
+ 
+
+ align:start position:0%
+cardiovascular disease to motivate how
+the study affected our understanding of
+
+ align:start position:0%
+the study affected our understanding of
+ 
+
+ align:start position:0%
+the study affected our understanding of
+blood pressure today we described the
+
+ align:start position:0%
+blood pressure today we described the
+ 
+
+ align:start position:0%
+blood pressure today we described the
+case of Franklin Delano Roosevelt FDR
+
+ align:start position:0%
+case of Franklin Delano Roosevelt FDR
+ 
+
+ align:start position:0%
+case of Franklin Delano Roosevelt FDR
+for short who is the President of the
+
+ align:start position:0%
+for short who is the President of the
+ 
+
+ align:start position:0%
+for short who is the President of the
+United States from 1933 to 1945 he was
+
+ align:start position:0%
+United States from 1933 to 1945 he was
+ 
+
+ align:start position:0%
+United States from 1933 to 1945 he was
+the longest-serving president of the
+
+ align:start position:0%
+the longest-serving president of the
+ 
+
+ align:start position:0%
+the longest-serving president of the
+United States and he led the country
+
+ align:start position:0%
+United States and he led the country
+ 
+
+ align:start position:0%
+United States and he led the country
+during difficult times the Great
+
+ align:start position:0%
+during difficult times the Great
+ 
+
+ align:start position:0%
+during difficult times the Great
+Depression and World War two he died
+
+ align:start position:0%
+Depression and World War two he died
+ 
+
+ align:start position:0%
+Depression and World War two he died
+while a president on April 12 1945
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before the president before the
+
+ align:start position:0%
+before the president before the
+ 
+
+ align:start position:0%
+before the president before the
+presidency
+
+ align:start position:0%
+presidency
+ 
+
+ align:start position:0%
+presidency
+FDR's blood pressure was 140 over 100
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today healthy blood pressure is
+
+ align:start position:0%
+today healthy blood pressure is
+ 
+
+ align:start position:0%
+today healthy blood pressure is
+considered to be less than 120 over 80
+
+ align:start position:0%
+considered to be less than 120 over 80
+ 
+
+ align:start position:0%
+considered to be less than 120 over 80
+so therefore 140 over 100 is today
+
+ align:start position:0%
+so therefore 140 over 100 is today
+ 
+
+ align:start position:0%
+so therefore 140 over 100 is today
+considered high blood pressure one year
+
+ align:start position:0%
+considered high blood pressure one year
+ 
+
+ align:start position:0%
+considered high blood pressure one year
+before his death his blood pressure was
+
+ align:start position:0%
+before his death his blood pressure was
+ 
+
+ align:start position:0%
+before his death his blood pressure was
+210 over 120 today this is called
+
+ align:start position:0%
+210 over 120 today this is called
+ 
+
+ align:start position:0%
+210 over 120 today this is called
+hypertensive crisis an emergency care is
+
+ align:start position:0%
+hypertensive crisis an emergency care is
+ 
+
+ align:start position:0%
+hypertensive crisis an emergency care is
+needed on the other hand
+
+ align:start position:0%
+needed on the other hand
+ 
+
+ align:start position:0%
+needed on the other hand
+FDR's personal physician said a moderate
+
+ align:start position:0%
+FDR's personal physician said a moderate
+ 
+
+ align:start position:0%
+FDR's personal physician said a moderate
+degree of arteriosus although no more
+
+ align:start position:0%
+degree of arteriosus although no more
+ 
+
+ align:start position:0%
+degree of arteriosus although no more
+than normal for a man of his age two
+
+ align:start position:0%
+than normal for a man of his age two
+ 
+
+ align:start position:0%
+than normal for a man of his age two
+months before his death his blood
+
+ align:start position:0%
+months before his death his blood
+ 
+
+ align:start position:0%
+months before his death his blood
+pressure was 260 over 150 and the day of
+
+ align:start position:0%
+pressure was 260 over 150 and the day of
+ 
+
+ align:start position:0%
+pressure was 260 over 150 and the day of
+his death was 300 over 190 there were
+
+ align:start position:0%
+his death was 300 over 190 there were
+ 
+
+ align:start position:0%
+his death was 300 over 190 there were
+early misconceptions in the first half
+
+ align:start position:0%
+early misconceptions in the first half
+ 
+
+ align:start position:0%
+early misconceptions in the first half
+of the 20th century about blood pressure
+
+ align:start position:0%
+of the 20th century about blood pressure
+ 
+
+ align:start position:0%
+of the 20th century about blood pressure
+high blood pressure dubbed essential
+
+ align:start position:0%
+high blood pressure dubbed essential
+ 
+
+ align:start position:0%
+high blood pressure dubbed essential
+hypertension was considered important to
+
+ align:start position:0%
+hypertension was considered important to
+ 
+
+ align:start position:0%
+hypertension was considered important to
+force blood through arteries and is
+
+ align:start position:0%
+force blood through arteries and is
+ 
+
+ align:start position:0%
+force blood through arteries and is
+considered harmful to lower blood
+
+ align:start position:0%
+considered harmful to lower blood
+ 
+
+ align:start position:0%
+considered harmful to lower blood
+pressure today of course we know better
+
+ align:start position:0%
+pressure today of course we know better
+ 
+
+ align:start position:0%
+pressure today of course we know better
+in the words of Daniel Levy the
+
+ align:start position:0%
+in the words of Daniel Levy the
+ 
+
+ align:start position:0%
+in the words of Daniel Levy the
+Framingham Heart Study director where he
+
+ align:start position:0%
+Framingham Heart Study director where he
+ 
+
+ align:start position:0%
+Framingham Heart Study director where he
+says today presidential blood
+
+ align:start position:0%
+says today presidential blood
+ 
+
+ align:start position:0%
+says today presidential blood
+numbers like FDR's would send the
+
+ align:start position:0%
+numbers like FDR's would send the
+ 
+
+ align:start position:0%
+numbers like FDR's would send the
+country's leading doctors racing down
+
+ align:start position:0%
+country's leading doctors racing down
+ 
+
+ align:start position:0%
+country's leading doctors racing down
+hallways whisking the nation's leader in
+
+ align:start position:0%
+hallways whisking the nation's leader in
+ 
+
+ align:start position:0%
+hallways whisking the nation's leader in
+to the cardia care unit of this Bethesda
+
+ align:start position:0%
+to the cardia care unit of this Bethesda
+ 
+
+ align:start position:0%
+to the cardia care unit of this Bethesda
+Naval Hospital so how do we learn in the
+
+ align:start position:0%
+Naval Hospital so how do we learn in the
+ 
+
+ align:start position:0%
+Naval Hospital so how do we learn in the
+1940s in the late 1940s the US
+
+ align:start position:0%
+1940s in the late 1940s the US
+ 
+
+ align:start position:0%
+1940s in the late 1940s the US
+government set out to better understand
+
+ align:start position:0%
+government set out to better understand
+ 
+
+ align:start position:0%
+government set out to better understand
+cardiovascular disease the plan was to
+
+ align:start position:0%
+cardiovascular disease the plan was to
+ 
+
+ align:start position:0%
+cardiovascular disease the plan was to
+track a large cohort of initially
+
+ align:start position:0%
+track a large cohort of initially
+ 
+
+ align:start position:0%
+track a large cohort of initially
+healthy patients over their lifetimes a
+
+ align:start position:0%
+healthy patients over their lifetimes a
+ 
+
+ align:start position:0%
+healthy patients over their lifetimes a
+city was chosen the city of Framingham
+
+ align:start position:0%
+city was chosen the city of Framingham
+ 
+
+ align:start position:0%
+city was chosen the city of Framingham
+Massachusetts to be the site for the
+
+ align:start position:0%
+Massachusetts to be the site for the
+ 
+
+ align:start position:0%
+Massachusetts to be the site for the
+study
+
+ align:start position:0%
+study
+ 
+
+ align:start position:0%
+study
+Framingham has an appropriate size it's
+
+ align:start position:0%
+Framingham has an appropriate size it's
+ 
+
+ align:start position:0%
+Framingham has an appropriate size it's
+not too large it's not too small it has
+
+ align:start position:0%
+not too large it's not too small it has
+ 
+
+ align:start position:0%
+not too large it's not too small it has
+a stable population that doesn't move
+
+ align:start position:0%
+a stable population that doesn't move
+ 
+
+ align:start position:0%
+a stable population that doesn't move
+too much and the doctors and residents
+
+ align:start position:0%
+too much and the doctors and residents
+ 
+
+ align:start position:0%
+too much and the doctors and residents
+were quite cooperative so in 1948 the
+
+ align:start position:0%
+were quite cooperative so in 1948 the
+ 
+
+ align:start position:0%
+were quite cooperative so in 1948 the
+Framingham starting Heart Study started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the study included 5,000 209 patients
+
+ align:start position:0%
+the study included 5,000 209 patients
+ 
+
+ align:start position:0%
+the study included 5,000 209 patients
+aged 30 to 59 patients were given a
+
+ align:start position:0%
+aged 30 to 59 patients were given a
+ 
+
+ align:start position:0%
+aged 30 to 59 patients were given a
+questionnaire and an examination every
+
+ align:start position:0%
+questionnaire and an examination every
+ 
+
+ align:start position:0%
+questionnaire and an examination every
+two years during this examination their
+
+ align:start position:0%
+two years during this examination their
+ 
+
+ align:start position:0%
+two years during this examination their
+physical characteristics were recorded
+
+ align:start position:0%
+physical characteristics were recorded
+ 
+
+ align:start position:0%
+physical characteristics were recorded
+the behavioral characteristics as well
+
+ align:start position:0%
+the behavioral characteristics as well
+ 
+
+ align:start position:0%
+the behavioral characteristics as well
+as test results exams and questions
+
+ align:start position:0%
+as test results exams and questions
+ 
+
+ align:start position:0%
+as test results exams and questions
+expanded over time but the key in the
+
+ align:start position:0%
+expanded over time but the key in the
+ 
+
+ align:start position:0%
+expanded over time but the key in the
+study was that the trajectory of the
+
+ align:start position:0%
+study was that the trajectory of the
+ 
+
+ align:start position:0%
+study was that the trajectory of the
+health of the patients was followed
+
+ align:start position:0%
+health of the patients was followed
+ 
+
+ align:start position:0%
+health of the patients was followed
+during the entire life span in this
+
+ align:start position:0%
+during the entire life span in this
+ 
+
+ align:start position:0%
+during the entire life span in this
+class we'll be we will build models
+
+ align:start position:0%
+class we'll be we will build models
+ 
+
+ align:start position:0%
+class we'll be we will build models
+using the Framingham data to predict and
+
+ align:start position:0%
+using the Framingham data to predict and
+ 
+
+ align:start position:0%
+using the Framingham data to predict and
+prevent
\ No newline at end of file
diff --git a/OK7_ReXhVaQ.txt b/OK7_ReXhVaQ.txt
new file mode 100644
index 0000000000000000000000000000000000000000..86073aea87de497dc5c46dfc6db65f56c369eb49
--- /dev/null
+++ b/OK7_ReXhVaQ.txt
@@ -0,0 +1,357 @@
+PROFESSOR ROBERT DORKIN:Hi, and
+welcome to a help session
+
+on recombinant DNA.
+
+Today we will be talking about
+the polymerase chain reaction
+
+as well as DNA sequencing.
+
+The polymerase chain reaction,
+also known as
+
+PCR, has many uses.
+
+One of the most common
+uses is to amplify a
+
+desired section of DNA.
+
+What you need for the reaction
+is your DNA sequence of
+
+interest, DNA polymerase, DNA
+primers, and then four
+
+different nucleotides.
+
+You combine all these together,
+and the first thing
+
+that you do is you heat
+the reaction up.
+
+What this does is that by adding
+heat to the system, you
+
+break the hydrogen bonds
+between the two
+
+different DNA strands.
+
+This results in two separate
+DNA sequences.
+
+Now what happens is that you
+allow the system to cool.
+
+As it cools, the DNA primers are
+able to hybridize to this
+
+separate strands.
+
+Now as you remember from
+lecture, when you're
+
+synthesizing DNA, you synthesize
+from the five prime
+
+to three prime direction.
+
+This means that the primers you
+design have to match the
+
+three prime end of your
+sequences of interest.
+
+So for example, if we were
+designing primers for these
+
+two sequences, one of them would
+be GGTA and the other
+
+one would be AGCT.
+
+Now, I've written four here.
+
+In actuality, these primers are
+generally longer, around
+
+16 or so, 16 to 27.
+
+However, they can be a whole
+different variety of lengths
+
+dependent on numerous
+different factors.
+
+The next thing that happens is
+that the DNA polymerase is
+
+going to bind to the DNA
+sequence with the primer.
+
+Once the DNA polymerase is
+bound, it's going to take some
+
+of the free nucleotides in the
+surrounding area and slowly
+
+add them to finish
+up the strand.
+
+And so on and so forth.
+
+Once it's completed, we are
+going to have now doubled our
+
+original DNA sequence.
+
+We're going to have two strands
+that are identical to
+
+the first one.
+
+As you can see, by repeating
+the steps, heating it,
+
+allowing it to cool, allowing
+more primers to bond, and then
+
+allowing the DNA polymerase to
+elongate, we can double the
+
+number of sequences
+every round.
+
+And you can rapidly
+get a large amount
+
+of the desired sequence.
+
+PCR has other uses though
+besides simply increasing the
+
+total amount of DNA
+that you have.
+
+One of the uses of PCR
+is to sequence DNA.
+
+Now, if we look over here,
+normally DNA is form of
+
+deoxyribonucleic acids.
+
+You have the phosphate group
+on the five prime end.
+
+You have a hydroxyl group
+on the three prime end.
+
+This hydroxyl group
+is very important.
+
+That's because when a new
+nucleotide is added, this
+
+hydroxyl group undergoes a
+covalent bond with the
+
+phosphate on the new nucleotide
+and then adds a new
+
+nucleotide that way.
+
+So you can see you're adding
+the five prime
+
+the three prime direction.
+
+However, it is possible
+to create a
+
+dideoxyribonucleic acid.
+
+The dideoxyribonucleic acid,
+instead of having a three
+
+prime hydroxyl group, has
+a three prime hydrogen.
+
+This three prime hydrogen is no
+longer capable of forming a
+
+covalent bond with
+a phosphate.
+
+That means as soon as the
+dideoxyribonucleic acid is
+
+added to DNA, no further
+nucleotides can be added in
+
+the series.
+
+Let's go back to our example
+with the primers.
+
+What does that mean for here?
+
+Well, let's say you have a
+normal PCR reaction, but in
+
+addition to the four
+deoxyribonucleic acids you
+
+have, you also take a little
+bit of dideoxyribonucleic
+
+acids of one of the types.
+
+So let's say we add
+in some ddTTP.
+
+Now what happens is that your
+DNA polymerase will go along
+
+adding nucleotides as normal,
+but if it ever adds a
+
+dideoxyribonucleic acid, the
+polymerase will stop.
+
+So if it adds, say
+a normal T here--
+
+continues down, continues
+down.
+
+If it adds a dideoxyribonucleic
+acid here,
+
+it's going to stop,
+and we're going to
+
+get a truncated sequence.
+
+And so you can see that at any
+position that we have an A,
+
+it's going to be possible to
+have a truncated sequence of
+
+that length.
+
+What this means that we're now
+going to, once the PCR is
+
+complete, have different DNA
+sequences of numerous
+
+different lengths.
+
+But the one thing they're all
+going to have in common is
+
+that they're all going to end
+with a T. So you can imagine
+
+doing this now for each of the
+four different letters.
+
+Then we can take them and
+run them out of a gel.
+
+Let's go look at such
+a gel over here.
+
+Here we have a gel.
+
+Each of these letters
+represents which
+
+dideoxyribonucleic acid was
+used for that experiment.
+
+And then the PCR was
+run out on the gel.
+
+As you remember, the strands
+close to the bottom are the
+
+shorter strands, and the strands
+close to the top are
+
+the longer strands.
+
+So if we look at this gel, we
+know that the shortest strand
+
+ends with a G. The next shortest
+strand ends in a T.
+
+Oh, sorry, ends in
+an A, excuse me.
+
+Then the next short strand ends
+in a T, then two A's,
+
+then a G, then a C, then a T. So
+as you can see, this is one
+
+way to determine the
+sequence of DNA.
+
+Another way has been devised,
+which is even faster.
+
+Instead of running the sequences
+all out in different
+
+polymerase chain reactions, what
+they do is they have some
+
+of each of the
+dideoxynucleotides together.
+
+But now, they fluorescently
+label them, such that you have
+
+a different fluorescent
+label on each
+
+dideoxyribonucleic acid.
+
+Now what happens is that
+you can run it
+
+out all on one column.
+
+And then by just looking at the
+colors, you can determine
+
+what the sequence is.
+
+So once again, the sequence
+would be GATAAGCT.
+
+And so this way, you can more
+efficiently, more rapidly,
+
+determine what the
+DNA sequence is.
+
+This has been two examples of
+polymerase chain reactions and
+
+their uses.
+
+This has been another help
+session on recombinant DNA.
+
+We hope you join us
+again next time.
+
+Thank you.
\ No newline at end of file
diff --git a/OznepAivkkg.txt b/OznepAivkkg.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b211be1ef23aa78b2bf149d27cde56ebdedb577c
--- /dev/null
+++ b/OznepAivkkg.txt
@@ -0,0 +1,2222 @@
+PROFESSOR: All right.
+
+Lecture 17 was about folding
+polygons into polyhedra,
+
+and today we will do it
+with real pieces of paper.
+
+But before we get
+there, I want to talk
+
+about some things we could make.
+
+In lecture, I demonstrated
+this perimeter having technique
+
+where you take
+any convex polygon
+
+and you pick any point
+on the perimeter.
+
+Then you measure out the
+perimeter halfway on each side.
+
+You get the antipodal point, y.
+
+And then just
+glue-- locally, you
+
+glue everything
+around x and around y.
+
+So I mean, you just start.
+
+We call this zipping where you
+don't glue any extra material
+
+in here, you just start
+zipping these guys together.
+
+I guess these circles or when
+you happen to hit this vertex,
+
+well, then you just keep
+going-- zip, zip, zip, zip, zip.
+
+So that's one thing we could
+make with convex polygons.
+
+Slightly more general
+is called a pita form.
+
+This is defined in the textbook.
+
+And the idea is instead
+of a convex polygon,
+
+you could take any convex body.
+
+It could have some corners
+or it could be smooth.
+
+So this is what
+we call a convex,
+
+or what I'm going to call
+today a convex 2D body, meaning
+
+it can be smooth in
+addition to polygonal.
+
+And then you pick any
+point on the boundary
+
+and you measure out the
+perimeter halfway, x and y,
+
+and you glue in
+exactly the same way.
+
+Now, it does not follow
+from Alexandrov's theorem
+
+that this will make
+a convex thing,
+
+but it follows from a
+slightly more general form
+
+of Alexandrov's theorem called
+Alexandrov-Pogorelov theorem.
+
+So Pogorelov was a
+student of Alexandrov
+
+and he edited some things
+that Alexandrov wrote,
+
+but then also Pogorelov
+wrote his own papers
+
+and proved some
+stronger versions
+
+of Alexandrov's theorem that
+hold for smooth bodies, not
+
+just polygonal folding.
+
+So Alexandrov's
+theorem, you recall,
+
+if you have a convex
+polyhedral metric homeomorphic
+
+to a sphere, then it's realized
+by a unique convex polyhedron.
+
+So the Pogorelov's extension
+is that if you have everything
+
+except the polyhedral
+part-- so if you
+
+have a convex metric
+homeomorphic to a sphere-- so
+
+topologically it's a sphere,
+but we omit the polyhedral part.
+
+So polyhedral was that you
+have finitely many vertices.
+
+In some sense, I have
+infinitely many vertices,
+
+infinitesimal curvature
+at every point here.
+
+Then it's realized by a
+unique convex 3D body.
+
+So same concept of
+a convex object.
+
+Well, I should say this
+is really the surface of.
+
+So a convex body, I should
+probably define that.
+
+Convex body is one where
+you take any two points
+
+and you draw a
+straight line and you
+
+stay within the body for
+the entire straight line.
+
+So that's convex.
+
+You take any two points,
+like this one and this one,
+
+draw a line between them,
+and you stay inside.
+
+The body is the piece of
+paper we're gluing up.
+
+Here we have a 3D
+body, but then we
+
+just look at the surface
+of it, the boundary.
+
+And that's going to be
+the surface we make.
+
+Technically, that
+surface is not convex.
+
+It's the interior that's convex
+because you can draw lines
+
+through it and you stay inside.
+
+This is exactly the same thing,
+but instead of polyhedron here,
+
+we have body because we didn't
+have finitely many vertices.
+
+And I'm not going to
+prove this theorem.
+
+But existence is
+basically the same proof.
+
+You just take a limit.
+
+So you can polygonalize
+with lots of little edges
+
+here, add little points,
+and take the limit
+
+as that approximation gets very,
+very close to the actual curve.
+
+At all times you
+have a polyhedron,
+
+it's easy to show you will
+converge to a convex body.
+
+The uniqueness is the
+harder part, I believe.
+
+I haven't read the proof,
+but it was more challenging.
+
+I think that took 20 years
+or so to settle uniqueness.
+
+Alexandrov's like 1950.
+
+This theorem I think is
+1973 the final version.
+
+But the version without unique
+was proved back in 1950.
+
+So that's something
+else we can do.
+
+Instead of cutting
+out a polygon,
+
+we can cut out a nice smooth
+thing or you can add some kinks
+
+and be smooth elsewhere.
+
+As long as it's
+convex, then you're
+
+guaranteed that-- we're
+only gluing together
+
+two convex points.
+
+It could be flat or it
+could be strictly convex,
+
+which means we'll have at most
+360 degrees of material at any
+
+point because it's always
+doing two at most 180's.
+
+And so we will have
+a convex metric,
+
+meaning always at most 360
+of material everywhere.
+
+So then this theorem applies
+so we'll get a unique thing.
+
+Another thing we could
+make is called a D-form.
+
+And I have some examples
+of D-forms here.
+
+So the idea with the D-form is
+you take two convex 2D bodies--
+
+so here they have some
+straight parts and some curve
+
+parts-- of the same perimeter.
+
+I pick one point from one
+body and I pick another point
+
+from the other body.
+
+I attach them there.
+
+And then I zip.
+
+So it would be zip,
+zip, zip, zip, zip.
+
+Wherever my fingers
+were at the same time,
+
+those are points that
+get glued together.
+
+And this is with the
+convex body you get.
+
+Again, Alexandrov-Pogorelov
+applies because we're still
+
+only gluing two convex
+points together at any point.
+
+As long as these guys
+have matching perimeter,
+
+we'll be OK.
+
+And so we will get a
+unique convex 3D body.
+
+In this case, we get
+this fun kind of shape.
+
+So this is what I
+suggest you make.
+
+D-forms tend to look a
+little bit cooler somehow
+
+because they have two polygons.
+
+And the one that's
+particularly easy to build
+
+is two copies of the
+same shape, but then you
+
+don't want to glue
+corresponding points.
+
+Like if I glued this
+point to that point,
+
+I would just get a flat,
+doubly covered thing
+
+and that's boring.
+
+But you just pick
+some other point
+
+and glue it to
+non-matching points,
+
+then it acts like you have
+two very different convex
+
+bodies which is kind of cool.
+
+I have some images
+of D-forms here.
+
+There's actually a whole book
+on D-forms by John Sharp.
+
+They're invented by this guy
+Tony Wills who's an artist.
+
+At the top, the
+quote is, "there is
+
+no such thing as
+an ugly D-form."
+
+So we are guaranteed
+success here.
+
+And also it says, "they
+surprise, confuse,
+
+can be addictive.
+
+They're an intellectual virus.
+
+Beware."
+
+So you've been warned.
+
+This is Tony Wills,
+the inventor.
+
+Now, from the
+artistic perspective,
+
+you don't have to start
+from convex polygons.
+
+We're going to start
+from convex bodies
+
+because they're
+guaranteed to work.
+
+If you're careful to satisfy
+Alexandrov-Pogorelov,
+
+you can have a convex
+metric even though you
+
+start from nonconvex bodies,
+although in this case,
+
+he's actually getting
+nonconvex shapes as well.
+
+More typical D-form is
+something like this.
+
+This is made from two ellipses
+and he builds them out
+
+of metal.
+
+This is a simulation by
+this guy Kenneth Brakke
+
+who has this software
+called Surface Evolver.
+
+And it's usually used for
+computing minimal services,
+
+soap bundles and
+things like that.
+
+But here it's computing
+what D-forms look like,
+
+approximately.
+
+And so this is an example
+of taking two ellipses
+
+and instead of-- if you
+glue at matching points,
+
+they would be flat-- but
+then you change the rotation.
+
+So here, they're rotated by 22.5
+degrees, rotated by 45 degrees,
+
+rotated by 90 degrees, so
+you get this nice continuum
+
+of different things that
+you could zip together.
+
+So I propose we make some.
+
+And so you have your
+scissors and tape.
+
+If you don't have two sheets of
+paper, get some from the front.
+
+And so everyone have
+scissors, tape, everything?
+
+We're going to have
+to share a bit.
+
+So what we want to do is make
+two identical convex shapes.
+
+So you have some here.
+
+Two rectangles are
+valid convex shapes.
+
+You could cut not all.
+
+Everyone should do
+something different.
+
+I'm just going to make sure
+they're nicely aligned.
+
+Hold on tight because you
+don't want them to let go,
+
+and then just cut.
+
+Always turn left
+with your cutting.
+
+You can be smooth.
+
+You can have some corners,
+what you want to do.
+
+Just always turn left.
+
+And once you have your two
+shapes, you pull them apart.
+
+Make sure you do not glue
+corresponding points.
+
+Pick some other points and
+attach them together with tape.
+
+Here's where it gets a
+little bit challenging.
+
+With smooth curves, it's little
+harder to tape them together,
+
+so you're probably going to
+have to use a bunch of points
+
+of tape, so to speak,
+not literal points.
+
+And I just tape, tape, tape.
+
+Before you get all
+the way, you want
+
+to make sure you can still
+pop it up and be convex.
+
+I think we'll be able to
+do that by [INAUDIBLE]
+
+inside the limit.
+
+Give me some scissors.
+
+All right.
+
+There's my D-form.
+
+Mostly convex, kind of fun.
+
+So a funny thing you'll
+notice about D-forms,
+
+if you made yours
+smooth-- so if you don't
+
+have any kinks on the
+outer boundary-- then
+
+the surface looks smooth,
+which is kind of nice.
+
+The other thing is there's
+this noticeable seam where
+
+you taped things.
+
+There, you're not
+smooth, obviously.
+
+You've got a crease
+along the seam.
+
+But also it looks like all
+that the surface is doing
+
+is kind of taking
+the convex hull,
+
+the envelope of that seam.
+
+So there's two
+properties we observe.
+
+One is that it looks
+smooth, except at the seam.
+
+And the other is
+that the hull surface
+
+is the convex hull
+of the 3D seam.
+
+And I want to prove
+both of those things.
+
+Those are both true facts.
+
+But first I need to
+define some things.
+
+So we're going to
+prove that D-forms
+
+are smooth and
+other good things.
+
+This is a paper
+that was originally
+
+a class project in this
+class, I think in 2007.
+
+Sounds about right.
+
+Submitted during class, it looks
+like, or just after semester
+
+with Greg Price.
+
+D-form have no spurious creases.
+
+So what's a D-form?
+
+You take two, for
+us, it's going to be
+
+two convex shapes
+of equal perimeter.
+
+You glue two points, two
+corresponding points P and Q
+
+together, and then
+you zip from there.
+
+We can actually talk about
+something even more general
+
+which we'll call a seam form.
+
+A seam form, you can have
+multiple convex shapes.
+
+It's a little harder
+to imagine, but you
+
+can join multiple
+points together.
+
+Maybe you join all three
+of those corners together.
+
+As long as you have at most
+360 of material everywhere,
+
+it'll be fine.
+
+Maybe do some zipping.
+
+I'm not going to try to figure
+out exactly how this gluing
+
+pattern works, but you
+find a gluing pattern
+
+where you don't
+violate anything.
+
+So it looks like
+if I do this one,
+
+I better have these
+guys also a little bit
+
+sharp so that they don't add
+up to too much angle there.
+
+So these three points
+would also join together.
+
+This would be like three
+petals in like a seed pod
+
+or something, like those leaves
+that wrap around little fruits
+
+or something.
+
+I won't try to draw it but--
+I guess I will try to draw it.
+
+Something like this.
+
+So that's a thing.
+
+This could even fold
+not exactly a sphere,
+
+but something like a sphere.
+
+So seam forms, you could have
+any number of convex shapes
+
+and glue them together
+however you want,
+
+provided at all points you
+satisfy Alexandrov-Pogorelov,
+
+so you only have at most
+360 degrees of material
+
+and you are
+topologically a sphere.
+
+Then you have a seam form.
+
+So most of the theorems I'm
+going to talk about apply
+
+to general seam forms, but we're
+interested in D-forms and pita
+
+forms in particular.
+
+So let me tell you some
+theorems about seam forms.
+
+Theorem 1 is that
+a seam form equals
+
+convex hull of its seams.
+
+So the seams in
+general are these parts
+
+where you did gluing,
+wherever you taped stuff.
+
+The boundaries of the convex
+polygons, those are the seams.
+
+They map to some curves in 3D.
+
+If you take the
+convex hull, the claim
+
+is you get the entire seam form.
+
+That's actually
+pretty easy to prove.
+
+Then the second
+claim is there aren't
+
+many creases other than
+the seams of course.
+
+The seams are usually
+going to be creased.
+
+And these creases are
+going to be line segments.
+
+And not just any line
+segments, but their endpoints
+
+are pretty special.
+
+So the claim is that
+the creases have
+
+to be line segments basically
+connecting strict vertices.
+
+What do I mean by strict vertex?
+
+Something like these three
+points which come together,
+
+provided the total angle here
+is strictly less than 360.
+
+I call that a strict vertex.
+
+Whereas these points
+connecting from here to here,
+
+those don't count
+as strict vertices.
+
+They do have curvature, but
+only infinitesimal curvature.
+
+Because this is essentially
+180 degrees of material,
+
+just slightly less
+because it's curved.
+
+So only where I have
+kinks can I potentially
+
+have strictly less than 180.
+
+And if I join them together
+to be strictly less than 360,
+
+that's a strict vertex.
+
+So potentially, I have a
+seam coming from here, also
+
+at the other endpoint.
+
+So in this picture, I might
+have a crease like this,
+
+I might have a
+crease like this, I
+
+might have a crease
+like this, potentially.
+
+But in something like a D-form,
+there are no strict vertices.
+
+If these are smooth-- so I'll
+assume here these are smooth.
+
+We could call it a smooth
+D-form if you like.
+
+Then there's no vertices,
+no strict vertices,
+
+only these sort of
+barely vertices.
+
+So there could be no creases.
+
+There's one other
+situation which
+
+is creases could be
+tangent to seams.
+
+This should seem
+impossible because the way
+
+I've defined things
+it is impossible.
+
+You're tangent to a seam, that
+would be you're like this.
+
+How am I supposed to have
+a crease inside that's
+
+tangent to the seam?
+
+The answer is you can't.
+
+If these regions are
+convex, you can't have them.
+
+This statement is actually
+about a more general form
+
+of seam forms where you
+can have a nonconvex piece.
+
+So in general seam form, you
+have a bunch of flat pieces
+
+and you somehow search
+for them together so
+
+that you satisfy
+Alexandrov-Pogorelov.
+
+And now you could
+have a tangent.
+
+I could, for example, have a
+crease that emanates from there
+
+or have a crease that
+emanates from there.
+
+But right now, it
+has nowhere to stop.
+
+The only way for these
+creases to actually exist
+
+is if there's a
+kink here, then this
+
+could go from there to there.
+
+So this is starting at a
+vertex and ending tangent.
+
+You could, of course, also
+start tangent and end tangent
+
+if there's another bend.
+
+But the claim is,
+all crease look
+
+like that, which
+means if you carefully
+
+designed your thing
+or vaguely carefully
+
+such as a smooth
+D-form, then you're
+
+guaranteed there are no creases
+which is what we observe.
+
+So this is justifying our
+intuition from these examples.
+
+One other case is the pita form.
+
+So pita form does
+actually make vertices.
+
+This point x is going to be
+a strict vertex because it
+
+has less than 180 of
+material, so definitely
+
+strictly less than 360.
+
+Same with y.
+
+So pita form is
+potentially going
+
+to have a seam from x
+to y, but that's it.
+
+Sorry, a crease from x to y.
+
+It has at most one crease.
+
+I think most examples
+we've made do
+
+have such a crease from x to y.
+
+Let's prove these theorems,
+or at least sketch the proofs.
+
+Don't want to get
+too technical here.
+
+So to prove the first
+part that the seam form is
+
+convex hull of its seams, it's
+helpful to have a tool here
+
+which is a theorem by Minkowski.
+
+We'll call it
+Minkowski's theorem,
+
+although he has a bunch.
+
+Hermann Minkowski.
+
+It relates convex
+things to convex hulls.
+
+It says, any convex
+body is the convex hull
+
+of its extreme points.
+
+What are extreme points?
+
+Extreme points are points
+on the surface where
+
+you can touch just that
+point with a tangent plane.
+
+So if you think of
+polyhedra, these
+
+are vertices of the polyhedra.
+
+But I want to handle
+things that are smooth,
+
+so they may might not
+really have any vertices.
+
+In general, I have
+some convex body.
+
+If I can draw-- imagine
+this is in two dimensions--
+
+if I can draw a
+tangent plane that just
+
+touches at a single point,
+then I call that point extreme.
+
+Let's look at an example here.
+
+Here I believe
+every seam point is
+
+going to be an extreme
+point because I
+
+can put a tangent plane.
+
+It just touches at that point.
+
+What am I distinguishing from?
+
+Well, for example, this point,
+this surface is developable.
+
+We know it's ruled.
+
+So there's a straight line here.
+
+You can see it in the
+shadow, in the silhouette.
+
+If I said, is this
+point extreme?
+
+I try to put a tangent
+plane on, the only way
+
+to get a tangent plane is
+to include this entire line.
+
+So it's impossible to
+just hit this point
+
+or any point along that line.
+
+In fact, every interior
+point, I claim,
+
+you cannot just hit that point.
+
+You've got to hit
+an entire line.
+
+Whereas at the
+seam, I can do it.
+
+I can angle between
+this and this.
+
+There's a tangent
+plane, because this
+
+is curving, that only
+hits at one point.
+
+If I had a straight
+segment, then
+
+the endpoints of the
+straight segment of the seam
+
+would be extreme, but the points
+in the middle of the segment
+
+would not be extreme.
+
+So that's the
+meaning of extreme.
+
+And we're going to
+use this because I
+
+claim that these interior
+points can never be extreme.
+
+It can only be the seam
+points that are extreme.
+
+And therefore, we are the
+convex hull of the seam points
+
+because we are the convex
+hull of the extreme points.
+
+How do we argue that?
+
+So I claim an extreme
+point can't be locally flat
+
+and at the same time be convex,
+because convex in 3D, that's
+
+what we need.
+
+If you had a point and it
+just meets a tangent plane
+
+at that single point,
+that means locally
+
+you're kind of going
+down from that plane,
+
+if you think of that
+plane as vertical.
+
+So this is a situation.
+
+I want to prove this.
+
+To prove it, I need to
+introduce another tool which
+
+is a generally good
+thing for you guys
+
+to know about, so
+kind of an excuse
+
+to tell you about the Gauss
+sphere, which I don't think we
+
+actually cover in lectures,
+but might come up again.
+
+Gauss sphere is a simple idea.
+
+For every tangent
+plane-- let's just think
+
+of this single point.
+
+I want to look at the-- it's
+called the tangent space.
+
+Look at all the tangent
+planes that touch this point.
+
+Because this
+particular tangent plan
+
+I drew only touches that one
+point, it has some wiggle room.
+
+I can pick any direction
+and just wiggle
+
+and rotate the plane
+around this point
+
+and it won't immediately
+hit the surface.
+
+I've got a little bit of time
+before it hits the surface.
+
+So there's a two-dimensional
+space of tangent planes
+
+that touch just this point.
+
+Because there's
+at least one, I've
+
+got to have some wiggle room.
+
+So I want to draw that space.
+
+And a clean way to draw the
+space is for every such plane
+
+to draw a normal vector
+perpendicular to the plane,
+
+take the direction of
+that normal vector,
+
+and draw it on a sphere.
+
+It's a unit sphere.
+
+So this is a sphere.
+
+This one looks pretty vertical
+so that would correspond
+
+to the north pole of the sphere.
+
+So that direction becomes
+a point on the sphere.
+
+Think of it as this vector
+from the center of the sphere
+
+to the north pole.
+
+But we'll just
+draw it as a point.
+
+And because I've got a
+two-dimensional space
+
+of maneuverability or
+rotatability of this plane,
+
+I'm going to get some
+region-- which maybe I
+
+should draw like
+this-- of the sphere.
+
+Those are all the
+possible normal vectors
+
+of tangent planes at that point.
+
+So this is called the Gauss map
+where you map all these normals
+
+to the Gauss sphere, which Gauss
+sphere is just a unit sphere.
+
+Fun fact.
+
+The area of that thing,
+which is the map of all
+
+the tangent normal directions,
+equals the curvature
+
+at that point.
+
+You may recall at
+some point curvature
+
+is actually Gaussian
+curvature, so that's
+
+why Gauss is all
+over the place here.
+
+Now because I claim this
+is a two-dimensional space,
+
+this thing will
+have positive area.
+
+Therefore, at this
+point, that vertex
+
+has positive curvature
+on the surface.
+
+And yet, it was supposed
+to be in the middle of one
+
+of these flat shapes.
+
+That's supposed to
+have zero curvature.
+
+Contradiction.
+
+Or stated more
+positively, if I have
+
+a point that is
+an extreme point,
+
+it's only touched by
+one of these planes,
+
+I have this flexibility.
+
+Therefore, I get area.
+
+Therefore, it is
+not locally flat,
+
+so it must be a seam point.
+
+It could be one like this
+where I'm barely non-flat,
+
+but I am non-flat.
+
+There's kind of
+infinitesimal curvature here.
+
+Or it could be one of these
+points where I'm very non-flat,
+
+or I guess X and Y here
+are other examples of here
+
+I'm very not flat.
+
+I've only got 180 degrees
+of curvature roughly.
+
+So it's got to be one
+of those if you're
+
+going to be an extreme point.
+
+Therefore, all the extreme
+points are seam points.
+
+Therefore, convex hull
+of the extreme points
+
+is the convex hull of the seams,
+and that is your seam form.
+
+So that's part one.
+
+It's pretty easy.
+
+Let me tell you about part two.
+
+Part two builds on part one.
+
+It's one reason
+why we care about.
+
+So part two is that there
+are no spurious creases.
+
+Unless you have strict
+vertices, then you
+
+could connect those up.
+
+So let's look at a
+locally flat crease point.
+
+Actually, at this point,
+I should probably mention.
+
+This paper, I think of as a
+forerunner to the "How Paper
+
+Folds Between
+Creases" paper which
+
+is that hyperbolic
+parabolas don't exist.
+
+You may recall there were
+theorems about what creases
+
+look like, what ruled
+surfaces look like,
+
+and so on between creases.
+
+In that setting, we've proved
+things like straight creases
+
+stay straight and all
+these good things.
+
+Here, it's a little
+bit different
+
+because we have kind of
+two levels of creases.
+
+There's the seam
+which is special.
+
+And then we're imagining
+hypothetical creases
+
+between the seam.
+
+And could you have
+a curved crease?
+
+Claim is no.
+
+Claim is all the creases
+in between the seams
+
+have to be straight.
+
+And in fact, they
+can't look like this.
+
+They have to be at
+corners somehow.
+
+So that's what we're
+going to prove.
+
+But a lot of the
+same techniques,
+
+most of the same definitions.
+
+This paper was
+kind of a warm up,
+
+I feel like, for
+the nonexistence
+
+of hyperbolic parabolas.
+
+Although they use a
+lot of the same tools.
+
+They have two of
+the same authors,
+
+but there's no
+theorem that really
+
+is shared between the two.
+
+They're not identical.
+
+So we're looking
+inside a flat region.
+
+We're imagining, let's
+look at a crease point.
+
+It lies on some crease locally.
+
+And it's a fold crease.
+
+So I'm going to wave
+my hands a little bit.
+
+But imagine a folded crease.
+
+Maybe it's a curve.
+
+We don't know.
+
+It's folded by some
+angle, some nonzero angle.
+
+Otherwise, it's not a crease.
+
+So locally, it looks like
+two kind of planes, at least
+
+to the first order they're
+going to be planes.
+
+Maybe something like this.
+
+I'm going to draw
+the creases straight
+
+because to the first
+order, it is straight.
+
+But it might be slightly curved.
+
+So we're looking
+at a point here.
+
+And my point is, it's
+bent by some angle.
+
+So I'm going to draw
+the two tangent planes.
+
+There's a tangent
+plane on the right.
+
+Whatever the surface
+is doing on the right,
+
+there's a tangent
+plane over there.
+
+Whatever the surface is doing
+on the left of the crease,
+
+there's a tangent plane there.
+
+They're not the same plane
+because we are creased.
+
+Whatever the crease
+angle is, that's
+
+the angle between
+these two planes.
+
+I want to look at this tangent
+space again a little bit.
+
+You can think of it,
+the tangent space
+
+at the least it has
+this tangent plane.
+
+For this point, you have
+at least this tangent plane
+
+and at least this
+other tangent plane.
+
+And so in particular, you have
+to have the sweep between them.
+
+So you get at least a
+one-dimensional set there.
+
+Now, this can happen.
+
+So we're not going to
+get a contradiction.
+
+We're not going to
+suddenly discover
+
+there's a two-dimensional area
+and get that it wasn't flat.
+
+But at least we've got
+a one-dimensional arc.
+
+On the Gaussian sphere here,
+we've got something like this
+
+so far.
+
+This is one extreme
+tangent plane on the left.
+
+This is extreme tangent
+plane on the right.
+
+These two points
+correspond to those two.
+
+And then we've got
+the arc of-- you
+
+can sweep the tangent
+plane around and still
+
+stay outside the surface,
+
+Well, that's interesting.
+
+It's interesting because
+all of those tangent planes
+
+share a line, which is going to
+be this line that I drew here.
+
+I mean, you look at
+these two planes,
+
+there's a line that they share.
+
+And if you rotate the
+plane through that line,
+
+you'll still pass
+through this point
+
+and you won't hit the surface.
+
+So in fact, all those tangent
+planes share this line.
+
+I think we actually
+just need these two.
+
+So if you don't see
+that, don't worry.
+
+There are these two planes.
+
+There's a line there.
+
+They're tangent,
+which means that line
+
+is on or outside the surface
+because tangent planes don't
+
+hit the surface.
+
+I mean, they touch
+the surface barely,
+
+but they don't go interior.
+
+Well, I claim that in fact the
+surface must touch this line.
+
+I claim the surface,
+at least locally,
+
+has got to follow
+along that intersection
+
+line of the left and
+right tangent planes.
+
+Why?
+
+It comes down to this
+Gaussian sphere thing.
+
+We know that the surface
+lies inside these two planes.
+
+There's this wedge here.
+
+The surface must be below.
+
+We also know the surface comes
+and touches it at this point.
+
+Could it, from here, kind of
+dip down away from this line?
+
+I claim no.
+
+If it dipped down, then there'd
+be a third tangent plane.
+
+The tangent plane could
+follow and dip down as well.
+
+And then we've got not
+just a one-dimensional arc,
+
+but we're actually going to get
+a whole triangle in the Gauss
+
+sphere.
+
+Once you have a whole triangle,
+that means you weren't flat.
+
+You have positive curvature.
+
+So we're looking at a
+locally flat crease point
+
+somewhere in the middle
+of one of these polygons.
+
+So in fact, you can't afford
+to dip down because then you'd
+
+have at least a little
+bit of curvature there.
+
+Because you have zero curvature,
+you've got to stay straight.
+
+So that means that
+the surface locally
+
+has to exist along the
+segment in both directions
+
+until something happens.
+
+Now, we assumed
+that our point was
+
+locally flat and a crease point.
+
+So the surface must
+continue in this direction
+
+until we reach a point that
+is either not locally flat
+
+or not a crease point.
+
+I claim it's got to
+remain a crease point.
+
+Because look, you're following
+along this intersection
+
+line of these two
+tangent planes.
+
+These remain tangent planes.
+
+These are not only tangent
+planes at this point.
+
+They're also tangent
+planes at this point
+
+and potentially any
+point along this segment.
+
+As long as the surface is
+here, they are tangent planes.
+
+Therefore, you are creased here.
+
+I mean, you can't be
+smooth if you're butting up
+
+against these two
+tangent planes.
+
+So crease must be preserved, so
+the only issue is locally flat.
+
+It could be at some point
+you become not locally flat.
+
+And that indeed happens.
+
+That's when you hit the seam.
+
+When you hit the seam, then
+you're no longer locally flat.
+
+So this proves the
+creases must be
+
+line segments between
+two points on the seam.
+
+There's a little bit more to
+prove which is it either hits
+
+a strict vertex or
+it's tangent to seams.
+
+And this basically
+follows the same argument
+
+that if you hit something other
+than a strict vertex or a seam,
+
+you would have positive
+curvature where
+
+you shouldn't, basically.
+
+So I'll just leave it at that.
+
+I think that's
+enough for the proof.
+
+You get the idea why
+creases can't exist.
+
+Any questions about that?
+
+I have few more questions.
+
+One question is, can we see
+more examples of rolling belts?
+
+And in some sense,
+this example is
+
+an example of a rolling belt.
+
+So D-forms, you take
+two, say, ellipses.
+
+And the seam that connects
+them is a rolling belt.
+
+And this is an illustration
+of the rolling action.
+
+As you change, which point
+glues to which point?
+
+Let's say I fix this point.
+
+I can glue to this one or
+to this one or to this one
+
+or to this one.
+
+And then I zip around.
+
+That's the rolling of the belt.
+
+More generally,
+I'll draw a picture.
+
+More generally, a rolling
+belt from the viewpoint
+
+of a gluing tree is that
+you have basically it's
+
+like a conveyor belt
+like at the airport
+
+or on a tank or something.
+
+You've got treads here
+and it's going to roll.
+
+So if I mark a point, let's
+say I mark this point.
+
+And I roll it around
+this way a little bit,
+
+this point maybe
+stays stationary
+
+and I end up with
+something like this.
+
+And what that means is whatever
+this guy glued to over here
+
+is now over here.
+
+So we're changing the gluing.
+
+This guy's now getting glued
+to some point like this
+
+because it kind of rolls around.
+
+So in general,
+you're rolling this,
+
+but then you're always just
+gluing across this path.
+
+For this to work, every angle
+out here must be less than
+
+or equal to 180,
+like the material
+
+that's out on the outside.
+
+Remember, the gluing
+tree has the outside
+
+of the polygon in here.
+
+The inside of
+polygon's out here.
+
+So all the material's
+on the outside here.
+
+All of these things must be
+less than or equal to 180.
+
+If you can find a path
+in your gluing tree
+
+where you've got less than
+180 material all around you,
+
+then you can do this rolling.
+
+And no matter how you roll,
+and then just glue across,
+
+you will still have a valid
+gluing, a valid Alexandrov
+
+gluing.
+
+So that's what rolling
+belts look like in general.
+
+We see them all over the
+place with these D-forms.
+
+The simple example
+I showed in class
+
+was when you take a rectangle,
+you glue into a cylinder.
+
+And now up here, I've
+got a rolling belt.
+
+Because if you look
+at the sides here,
+
+I've got actually exactly
+180 degrees of material
+
+all around the belt.
+
+And so I could
+collapse it like this
+
+or I could collapse
+it-- let me tape it.
+
+A little hard to
+hold everything.
+
+If you look at this belt, I
+could collapse it like this.
+
+Or I could roll it a little
+bit and classify like that.
+
+Or I could roll it a little
+bit, collapse it like that.
+
+Roll it a little more.
+
+Collapse it like that.
+
+All of these are valid
+gluing because they're always
+
+gluing 180 to 180.
+
+And that's what
+rolling belts are.
+
+Does the broken applet work now?
+
+I don't know why
+it wasn't working.
+
+Probably some conflict
+with suspension
+
+or just the Java
+installation was bad.
+
+But here it is.
+
+It's freely available online.
+
+You draw your graph.
+
+It's a little hard to just use.
+
+It's hard to draw
+an exciting example.
+
+Here I'll a draw a tetrahedron
+because that's simple.
+
+In this case, it's abstract,
+so all of these edges
+
+are unit lengths.
+
+It's kind of like TreeMaker.
+
+You separately
+specify the lengths.
+
+Then you say Compute.
+
+And it will find, in this
+case, it's a tetrahedron,
+
+an equilateral.
+
+A regular tetrahedron
+is a little hard
+
+to see because we've got
+either a weird field of view
+
+or a lot of perspective here.
+
+But this is a
+regular tetrahedron.
+
+You can verify that by say
+making some of these lengths
+
+longer.
+
+I'll make three of them five.
+
+So then this is like a pyramid.
+
+Of course, we're just
+essentially applying
+
+Cauchy's rigidity theorem here
+and say, oh, this uniquely
+
+assembles into this
+spiky tetrahedron.
+
+You could, in principle,
+drawn an across here
+
+with the appropriate gluing.
+
+It's a little tricky
+to draw in because you
+
+have to also triangulate.
+
+It'd be hard to do from
+scratch to compute gluings.
+
+But in theory, especially
+if you use software
+
+to compute the gluings
+and compute shortest
+
+path in a glued
+polygon-- which we'll
+
+be getting more to next class.
+
+Next lecture is about
+algorithms for finding gluings.
+
+Then computing shortest paths.
+
+Then you could use that as
+input to this software which
+
+will then compute what
+the 3D polyhedron is.
+
+So that's the Alexandrov
+implementation.
+
+This is by, I think, a student
+of Bobenko and Izmestiev.
+
+One quick question
+about-- running out
+
+of time-- about
+the nonconvex case.
+
+So we're doing all this work
+about making convex surfaces.
+
+I said nonconvex
+case is trivial.
+
+In a sense, the decision
+problem is trivial.
+
+It's not an easy
+theorem to prove.
+
+And aha, taped it up.
+
+It follows from what's called
+the Burago-Zalgaller theorem.
+
+And it says that if you tap
+any polyhedral metric-- so that
+
+means you take a polygon,
+you glue it however you want.
+
+You could even add boundary.
+
+Pick any polyhedron metrics, so
+you take any polygon and glue
+
+it however you want.
+
+It could have handles.
+
+It could be a doughnut.
+
+It could be whatever.
+
+Then it has an isometric
+polyhedral realization in 3D.
+
+So there is a way-- so
+we're doing it abstractly.
+
+We're gluing stuff together.
+
+It's kind of topologically.
+
+We don't know what we're doing.
+
+But then there is a way
+to actually embed it
+
+as a polyhedral surface
+in 3D without stretching
+
+any of the lengths.
+
+So it's a folding of
+the piece of paper.
+
+It could have creases in
+it, will have actually
+
+tons of creases in it.
+
+And it has exactly the
+right-- it connects
+
+all the things you want
+it to connect together.
+
+It's kind of crazy.
+
+Furthermore, it could
+be self-crossing.
+
+But if your surface
+is either orientable--
+
+so it doesn't have any cross
+caps or Mobius strips in it--
+
+or it has boundary,
+then there's even
+
+a way to do without crossings.
+
+So that's basically all
+the cases we care about.
+
+You could glue this together
+into a sphere or into a disk
+
+or into a torus or
+two-handled torus or whatever.
+
+No matter what you
+do, there is a way
+
+to embed it in 3D as a
+presumably nonconvex very
+
+creased surface.
+
+This is a hard to prove.
+
+If you're familiar
+with Nash's embedding
+
+theorem about embedding
+Riemannian surfaces,
+
+it uses a bunch of techniques
+from there called spiraling
+
+perturbations,
+which I don't know.
+
+And one description I read
+calls the resulting surfaces
+
+"strongly corrugated," which
+I think means tons of creases.
+
+It is finitely many creases.
+
+That's the theorem.
+
+There's no bound on them.
+
+As far as I know,
+there's no algorithm
+
+to compute this thing.
+
+I've never seen a picture
+of them, otherwise,
+
+I'd show it to you.
+
+So lots of open problems
+in making this real.
+
+But at least the decision
+problem is kind of boring.
+
+You do any gluing.
+
+It will make a nonconvex thing.
+
+To find that thing is
+still pretty interesting
+
+question though.
+
+That's it.
\ No newline at end of file
diff --git a/P5Ce9tbK86M.txt b/P5Ce9tbK86M.txt
new file mode 100644
index 0000000000000000000000000000000000000000..eedb1f03928ebf3592b06b00397cf9fe03eb637e
--- /dev/null
+++ b/P5Ce9tbK86M.txt
@@ -0,0 +1,1854 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: In discussing
+the continuous-time and
+
+discrete-time Fourier
+transforms, we developed a
+
+number of important
+properties.
+
+Two particularly significant
+ones, as I mentioned at the
+
+time, are the modulation
+property and
+
+the convolution property.
+
+Starting with the next lecture,
+the one after this
+
+one, we'll be developing and
+exploiting some of the
+
+consequences of the modulation
+property.
+
+In today's lecture though, I'd
+like to review and expand on
+
+the notion of filtering, which,
+as I had mentioned,
+
+flows more or less directly from
+the convolution property.
+
+To begin, let me just quickly
+review what the convolution
+
+property is.
+
+Both for continuous-time and
+for discrete-time, the
+
+convolution property tells us
+that the Fourier transform of
+
+the convolution of two time
+functions is the product of
+
+the Fourier transforms.
+
+Now, what this means in terms
+of linear time-invariant
+
+filters, since we know that in
+the time domain the output of
+
+a linear time-invariant filter
+is the convolution of the
+
+input and the impulse response,
+it says essentially
+
+then in the frequency domain
+that the Fourier transform of
+
+the output is the product the
+Fourier transform of the
+
+impulse response, namely the
+frequency response, and the
+
+Fourier transform
+of the input.
+
+So the output is described
+through that product.
+
+Now, recall also that in
+developing the Fourier
+
+transform, I interpreted the
+Fourier transform as the
+
+complex amplitude of a
+decomposition of the signal in
+
+terms of a set of complex
+exponentials.
+
+And the frequency response or
+the convolution property, in
+
+effect, tells us how to modify
+the amplitudes of each of
+
+those complex exponentials as
+they go through the system.
+
+Now, this led to the notion of
+filtering, where the basic
+
+concept was that since we can
+modify the amplitudes of each
+
+of the complex exponential
+components separately, we can,
+
+for example, retain
+some of them and
+
+totally eliminate others.
+
+And this is the basic
+notion of filtering.
+
+So we have, as you recall, first
+of all the notion in
+
+continuous-time of an ideal
+filter, for example, I
+
+illustrate here an ideal lowpass
+filter where we pass
+
+exactly frequency components in
+one band and reject totally
+
+frequency components
+in another band.
+
+The band being passed, of
+course, referred to as the
+
+passband, and the band rejected
+as the stopband.
+
+I illustrated here
+a lowpass filter.
+
+We can, of course, reject the
+low frequencies and retain the
+
+high frequencies.
+
+And that then corresponds to
+an ideal highpass filter.
+
+Or we can just retain
+frequencies within a band.
+
+And so I show below what is
+referred to commonly as a
+
+bandpass filter.
+
+Now, this is what the ideal
+filters looked like for
+
+continuous-time.
+
+For discrete-time, we have
+exactly the same situation.
+
+Namely, we have an ideal
+discrete-time lowpass filter,
+
+which passes exactly frequencies
+which are the low
+
+frequencies.
+
+Low frequencies, of course,
+being around 0, and because of
+
+the periodicity, also
+around 2pi.
+
+We show also an ideal
+highpass filter.
+
+And a highpass filter, as I
+indicated last time, passes
+
+frequencies around pi.
+
+And finally, below that, I show
+an ideal bandpass filter
+
+passing frequencies someplace in
+the range between 0 and pi.
+
+And recall also that the basic
+difference between
+
+continuous-time a discrete-time
+for these
+
+filters is that the
+discrete-time versions are, of
+
+course, periodic in frequency.
+
+Now, let's look at these ideal
+filters, and in particular the
+
+ideal lowpass filter
+in the time domain.
+
+We have the frequency response
+of the ideal lowpass filter.
+
+And shown below it is the
+impulse response.
+
+So here is the frequency
+response and below it the
+
+impulse response of the
+ideal lowpass filter.
+
+And this, of course,
+is a sine x over x
+
+form of impulse response.
+
+And recognize also or recall
+that since this frequency
+
+response is real-valued, the
+impulse response, in other
+
+words, the inverse transform is
+an even function of time.
+
+And notice also, since I want
+to refer back to this, that
+
+the impulse response of an ideal
+lowpass filter, in fact,
+
+is non-causal.
+
+That follows, from among other
+things, from the fact that
+
+it's an even function.
+
+But keep in mind, in fact, that
+a sine x over x function
+
+goes off to infinity
+in both directions.
+
+So the impulse response of the
+ideal lowpass filter is
+
+symmetric and continues to have
+tails off to plus and
+
+minus infinity.
+
+Now, the situation is basically
+the same in the
+
+discrete-time case.
+
+Let's look at the frequency
+response and associated
+
+impulse response for an ideal
+discrete-time lowpass filter.
+
+So once again, here is the
+frequency response of the
+
+ideal lowpass filter.
+
+And below what I show the
+impulse response.
+
+Again, it's a sine x over x
+type of impulse response.
+
+And again, we recognize that
+since in the frequency domain,
+
+this frequency response
+is real-valued.
+
+That means, as a consequence
+of the properties of the
+
+Fourier transform and inverse
+Fourier transform, that the
+
+impulse response is an even
+function in the time domain.
+
+And also, incidentally, the sine
+x over x function goes
+
+off to infinity, again,
+in both directions.
+
+Now, we've talked about ideal
+filters in this discussion.
+
+And ideal filters all
+are, in fact, ideal
+
+in a certain sense.
+
+What they do ideally is they
+pass a certain band of
+
+frequencies exactly and
+they reject a band
+
+of frequencies exactly.
+
+On the other hand, there are
+many filtering problems in
+
+which, generally, we don't
+have a sharp distinction
+
+between the frequencies we
+want to pass and the
+
+frequencies we want to reject.
+
+One example of this that's
+elaborated on in the text is
+
+the design of an automotive
+suspension system, which, in
+
+fact, is the design of
+a lowpass filter.
+
+And basically what you want to
+do in a case like that is
+
+filter out or attenuate very
+rapid road variations and keep
+
+the lower variations in, of
+course, elevation of the
+
+highway or road.
+
+And what you can see intuitively
+is that there
+
+isn't really a very sharp
+distinction or sharp cut-off
+
+between what you would logically
+call the low
+
+frequencies and what you would
+call the high frequencies.
+
+Now, also somewhat related to
+this is the fact that as we've
+
+seen in the time domain, these
+ideal filters have a very
+
+particular kind of character.
+
+For example, let's look back at
+the ideal lowpass filter.
+
+And we saw the impulse
+response.
+
+The impulse response is what
+we had shown here.
+
+Let's now look at the step
+response of the discrete-time
+
+ideal lowpass filter.
+
+And notice the fact that it has
+a tail that oscillates.
+
+And when the step hits,
+in fact, it has
+
+an oscillatory behavior.
+
+Now, exactly the same
+situation occurs in
+
+continuous-time.
+
+Let's look at the step
+response of the
+
+continuous-time ideal
+lowpass filter.
+
+And what we see is that when a
+step hits then, in fact, we
+
+get an oscillation.
+
+And very often, that oscillation
+is something
+
+that's undesirable.
+
+For example, if you were
+designing an automotive
+
+suspension system and you hit
+a curve, which is a step
+
+input, in fact, you probably
+would not like to have the
+
+automobile oscillating, dying
+down in oscillation.
+
+Now there's another very
+important point, which again,
+
+we can see either in
+continuous-time or
+
+discrete-time, which is that
+even if we want it to have an
+
+ideal filter, the ideal filter
+has another problem if we want
+
+to attempt to implement
+it in real time.
+
+What's the problem?
+
+The problem is that since the
+impulse response is even and,
+
+in fact, has tails that go off
+to plus and minus infinity,
+
+it's non-causal.
+
+So if, in fact, we want to build
+a filter and the filter
+
+is restricted to operate in real
+time, then, in fact, we
+
+can't build an ideal filter.
+
+So what that says is that, in
+practice, although ideal
+
+filters are nice to think about
+and perhaps relate to
+
+practical problems, more
+typically what we consider are
+
+nonideal filters and in the
+discrete-time case, a nonideal
+
+filter then we would have a
+characteristic somewhat like
+
+I've indicated here.
+
+Where instead of a very rapid
+transition from passband to
+
+stopband, there would be a more
+gradual transition with a
+
+passband cutoff frequency and
+a stopband cutoff frequency.
+
+And perhaps also instead of
+having an exactly flat
+
+characteristic in the stopband
+in the passband, we would
+
+allow a certain amount
+of ripple.
+
+We also have exactly the same
+situation in continuous-time,
+
+where here we'll just simply
+change our frequency axis to a
+
+continuous frequency axis
+instead of the discrete
+
+frequency axis.
+
+Again, we would think in terms
+of an allowable passband
+
+ripple, a transition from
+passband to stopband with a
+
+passband cutoff frequency and
+a stopband cutoff frequency.
+
+So the notion here is that,
+again, ideal filters are ideal
+
+in some respects, not ideal
+in other respects.
+
+And for many practical
+problems, we
+
+may not want them.
+
+And even if we did want them,
+we may not be able to get
+
+them, perhaps because of this
+issue of causality.
+
+Even if causality is not an
+issue, what happens in filter
+
+design and implementation, in
+fact, is that the sharper you
+
+attempt to make the cutoff, the
+more expensive, in some
+
+sense, the filter becomes,
+either in terms of components,
+
+in continuous-time, or in
+terms of computation in
+
+discrete-time.
+
+And so there are these whole
+variety of issues that really
+
+make it important to
+understand the
+
+notion nonideal filters.
+
+Now, just to illustrate as an
+example, let me remind you of
+
+one example of what, in fact, is
+a nonideal lowpass filter.
+
+And we have looked previously
+at the associated
+
+differential equation.
+
+Let me now, in fact, relate
+it to a circuit, and in
+
+particular an RC circuit, where
+the output could either
+
+be across the capacitor
+or the output can
+
+be across the resistor.
+
+So in effect, we have
+two systems here.
+
+We have a system, which is the
+system function from the
+
+voltage source input to the
+capacitor output, the system
+
+from the voltage source input
+to the resistor output.
+
+And, in fact, just applying
+Kirchhoff's Voltage Law to
+
+this, we can relate those in
+a very straightforward way.
+
+It's very straightforward to
+verify that the system from
+
+input to resistor output is
+simply the identity system
+
+with the capacitor output
+subtracted from it.
+
+Now, we can write the
+differential equation for
+
+either of these systems and, as
+we talked about last time
+
+in the last several lectures,
+solve that equation using and
+
+exploiting the properties of
+the Fourier transform.
+
+And in fact, if we look at the
+differential equation relating
+
+the capacitor output to the
+voltage source input, we
+
+recognize that this is an
+example that, in effect, we've
+
+solved previously.
+
+And so just working our way
+down, applying the Fourier
+
+transform to the differential
+equation and generating the
+
+system function by taking the
+ratio of the capacitor voltage
+
+or its Fourier transform to the
+Fourier transform of the
+
+source, we then have the system
+function associated
+
+with the system for which
+the output is
+
+the capacitor voltage.
+
+Or if we solve instead for the
+system function associated
+
+with the resistor output,
+we can simply
+
+subtract H1 from unity.
+
+And the system function that
+we get in that case is the
+
+system function that
+I show here.
+
+So we have, now, two system
+functions, one for the
+
+capacitor output, the other
+for the resistor output.
+
+And one, the first,
+corresponding to the capacitor
+
+output, in fact, if we plot it
+on a linear amplitude scale,
+
+looks like this.
+
+And as you can see, and as
+we saw last time, is an
+
+approximation to a
+lowpass filter.
+
+It is, in fact, and nonideal
+lowpass filter, whereas the
+
+resistor output is an
+approximation to a highpass
+
+filter, or in effect, a nonideal
+highpass filter.
+
+So in one case, just comparing
+the two, we have a lowpass
+
+filter as the capacitor output
+associated with the capacitor
+
+output, and a highpass filter
+associated with
+
+the resistor output.
+
+Let's just quickly look at that
+example now, looking on a
+
+Bode plot, instead of
+on the linear scale
+
+that we showed before.
+
+And recall incidentally, and be
+aware incidentally, of the
+
+fact that we can, of course,
+cascade several filters of
+
+this type and improve
+the characteristics.
+
+So I have shown at the top
+a Bode plot of the system
+
+function associated with
+the capacitor output.
+
+It's flat out to a frequency
+corresponding to 1 over the
+
+time constant, RC.
+
+And then it falls off at 10 dB
+per decade, a decade being a
+
+factor of 10.
+
+Or if instead we look at the
+system function associated
+
+with the resistor output, that
+corresponds to a 10 dB per
+
+decade increase in frequency
+up to approximately the
+
+reciprocal of the time constant,
+and then approaching
+
+a flat characteristic
+after that.
+
+And if we consider either one
+of these, looking back again
+
+at the lowpass filter, if we
+were to cascade several
+
+filters with this frequency
+response, then because we have
+
+things plotted on a Bode plot,
+the Bode plot for the cascade
+
+would simply be summing these.
+
+And so if we cascaded, for
+example, two stages instead of
+
+a roll-off at 10 dB per decade,
+it would roll off at
+
+20 dB per decade.
+
+Now, filters in this type, RC
+filters, perhaps several of
+
+them in cascade, are in
+fact very prevalent.
+
+And in fact, in an environment
+like this, where we're, in
+
+fact, doing recording, we see
+there are filters of that type
+
+that show up very commonly
+both in the audio and the
+
+video portion of the signal
+processing that's associated
+
+with making this set of tapes.
+
+In fact, let's take a look
+in the control room.
+
+And what I'll be able to show
+you in the control room is the
+
+audio portion of the processing
+that's done and the
+
+kinds of filters, very much of
+the type we just talked about,
+
+that are associated with the
+signal processing that's done
+
+in preparing the audio
+for the tapes.
+
+So let's just take a walk
+into the control room
+
+and see what we see.
+
+This is the control room that's
+
+used for camera switching.
+
+It's used for computer editing
+and also audio control.
+
+You can see the monitors,
+and these are used
+
+for the camera switching.
+
+And this is the computer editing
+console that's used
+
+for online and offline
+computer editing.
+
+What I really want to
+demonstrate though, in the
+
+context of the lecture is the
+audio control panel, which
+
+contains, among other things, a
+variety of filters for high
+
+frequency, low frequencies,
+et cetera, basically
+
+equalization filters.
+
+And what we have in the way of
+filtering is, first of all,
+
+what's referred to as a graphic
+equalizer, which
+
+consists of a set of bandpass
+filters, which I'll describe a
+
+little more carefully
+in a minute.
+
+And then also, an audio control
+panel, which is down
+
+here and which contains separate
+equalizer circuits
+
+for each of a whole set of
+channels and also lots of
+
+controls on them.
+
+Well, let me begin in the
+demonstration by demonstrating
+
+a little bit of what the
+graphic equalizer does.
+
+Well, what we have is a set
+of bandpass filters.
+
+And what's indicated up here are
+the center frequencies of
+
+the filters, and then a slider
+switch for each one that lets
+
+us attenuate or amplify.
+
+And this is a dB scale.
+
+So essentially, if you look
+across this bank of filters
+
+with the total output of the
+equalizer just being the sum
+
+of the outputs from each of
+these filters, interestingly
+
+the position of the slider
+switches as you move across
+
+here, in effect, shows you what
+the frequency response of
+
+the equalizer is.
+
+So you can change the overall
+shaping of the filter by
+
+moving the switches
+up and down.
+
+Right now the equalizer
+is out.
+
+Let's put the equalizer
+into the circuit.
+
+And now I put in this filtering
+characteristic.
+
+And what I'd like to demonstrate
+is filtering with
+
+this, when we do things that
+are a little more dramatic
+
+than what would normally be
+done in a typical audio
+
+recording setting.
+
+And to do this, let's add to my
+voice some music to make it
+
+more interesting.
+
+Not that my voice isn't
+interesting as it is.
+
+But in any case, let's
+bring some music up.
+
+[MUSIC PLAYING]
+
+And now what I'll do is set
+the low frequencies flat.
+
+And let me take out the high
+frequencies above 800 cycles.
+
+And so now what we have,
+effectively,
+
+is a lowpass filter.
+
+And now with the lowpass filter,
+let me now bring the
+
+highs back up.
+
+And so I'm bringing up those
+bandpass filters.
+
+And now let me cut
+out the lows.
+
+And you'll hear the lows
+disappearing and, in effect,
+
+keeping the highs in effectively
+crispens the
+
+sound, either my voice
+or the music.
+
+And finally, let me go back to
+0 dB equalization on each of
+
+the filters.
+
+And what I'll also do now is
+take the equalizer out of the
+
+circuit totally.
+
+Now, let's take a look at the
+audio master control panel.
+
+And this panel has, of course,
+for each channel and, for
+
+example, the channel
+that we're working
+
+on, of a volume control.
+
+I can turn the volume down, and
+I can turn the volume up.
+
+And it also has, for this
+particular equalizer circuit,
+
+it has a set of three bandpass
+filters and knobs which let us
+
+either put in up to 12 dB gain
+or 12 dB attenuation in each
+
+of the bands, and also a
+selector switch that lets us
+
+select the center the band.
+
+So let me just again
+demonstrate a
+
+little bit with this.
+
+And let's get a close
+up of this panel.
+
+So what we have, as
+I indicated, is
+
+three bandpass filters.
+
+And these knobs that I'm
+pointing to here are controls
+
+that allow us for each of the
+filters to put in up to 12 dB
+
+gain or 12 dB attenuation.
+
+There are also with each of the
+filters a selector switch
+
+that lets us adjust the center
+frequency of the filter.
+
+Basically it's a two-position
+switch.
+
+There also, as you can see, is
+a button that let's us either
+
+put the equalization
+in or out.
+
+Currently the equalization
+is out.
+
+Let's put the equalization in.
+
+We won't hear any effect from
+that, because the gain
+
+controls are all set at 0 dB.
+
+And I'll want to illustrate
+shortly the effect of these.
+
+But before I do, let me draw
+your attention to one other
+
+filter, which is this
+white switch.
+
+And this switch is a highpass
+filter that essentially cuts
+
+out frequencies below
+about 100 cycles.
+
+So what it means is that if I
+put this switch in, everything
+
+is more or less flat
+above 100 cycles.
+
+And what that's used for,
+basically, is to eliminate
+
+perhaps 60 cycle noise, if
+that's present, or some low
+
+frequency hum or whatever.
+
+Well, we won't really
+demonstrate
+
+anything with that.
+
+Let's [? go ?] now with the
+equalization in, demonstrate
+
+the effect of boosting or
+attenuating the low and high
+
+frequencies.
+
+And again, I think to
+demonstrate this, it
+
+illustrates the point the
+best if we have a
+
+little background music.
+
+So maestro, if you can
+bring that up.
+
+[MUSIC PLAYING]
+
+And so now what I'm going to
+do is first boost the low
+
+frequencies.
+
+And that's what this
+potentiometer knob will do.
+
+So now, increasing the low
+frequency gain and, in fact,
+
+all the way up to 12 dB when I
+have the knob over as far as
+
+I've gone here.
+
+And so that has a very
+bassy sound.
+
+And in fact, we can make it
+even bassier by taking the
+
+high frequencies and attenuating
+those by 12 dB.
+
+OK well, let's put some of the
+high frequencies back in.
+
+And now let's turn the
+low-frequency gain first
+
+back down to 0.
+
+And now we're back to
+flat equalization.
+
+And now I can turn the low
+frequency gain down so that I
+
+attenuate the low frequencies
+by much as 12 dB.
+
+And that's where we are now.
+
+And so this has, of course,
+a much crisper sound.
+
+And to enhance the highs even
+more, I can, in addition to
+
+cutting out the lows, boost
+the highs by putting in,
+
+again, as much as 12 dB.
+
+OK well, let's turn down the
+music now and go back to no
+
+equalization by setting
+these knobs to 0 dB.
+
+And in fact, we can take
+the equalizer out.
+
+Well, that's a quick look at
+some real-world filters.
+
+Now let's stop having so
+much fun, and let's
+
+go back to the lecture.
+
+OK well, that's a little
+behind-the-scenes look.
+
+What I'd like to do now is
+turn our attention to
+
+discrete-time filters.
+
+And as I've meant in previous
+lectures, there are basically
+
+two classes of discrete-time
+filters or discrete-time
+
+difference equations.
+
+One class is referred to a
+non-recursive or moving
+
+average filter.
+
+And the basic idea with a
+moving average filter is
+
+something that perhaps you're
+somewhat familiar with
+
+intuitively.
+
+Think of the notion of taking
+a data sequence, and let's
+
+suppose that what we wanted to
+do was apply some smoothing to
+
+the data sequence.
+
+We could, for example, think
+of taking adjacent points,
+
+averaging them together, and
+then moving that average along
+
+the data sequence.
+
+And what you can kind of see
+intuitively is that that would
+
+apply some smoothing.
+
+So in fact, the difference
+equation, let's say, for
+
+three-point moving average
+would be the difference
+
+equation that I indicate here,
+just simply taking a data
+
+point and the two data points
+adjacent to it and forming an
+
+average of those three.
+
+So if we thought of the
+processing involved, if we're
+
+forming an output sequence
+value, we would take three
+
+adjacent points and
+average them.
+
+That would give us the output
+add the associated time.
+
+And then to compute the next
+output point, we would just
+
+simply slide this by one point,
+average these together,
+
+and that would give us the
+next output point.
+
+And we would continue along,
+just simply sliding and
+
+averaging to form the output
+data sequence.
+
+Now, that's an example of what's
+commonly referred to a
+
+three-point moving average.
+
+In fact, we can generalize
+that notion
+
+in a number of ways.
+
+One way of generalizing the
+notion of a moving average
+
+from the three-point moving
+average, which I summarize
+
+again here, is to think of
+extending that to a larger
+
+number of points, and in fact
+applying weights to that as I
+
+indicated here, so that, in
+addition to just summing up
+
+the points and dividing by the
+number of points summed, we
+
+can, in fact, apply individual
+weights to the points so that
+
+it's what is often referred to
+as a weighting moving average.
+
+And I show below one possible
+curve that might result, where
+
+these would be essentially the
+weights associated with this
+
+weighted moving average.
+
+And in fact, it's easy to
+verify that this indeed
+
+corresponds to the impulse
+response of the filter.
+
+Well, just to cement this
+notion, let me show you an
+
+example or two.
+
+Here is an example of a
+five-point moving average.
+
+A five-point moving average
+would have an impulse response
+
+that just consists of a
+rectangle of length five.
+
+And if this is convolved with
+a data sequence, that would
+
+correspond to taking five
+adjacent points and, in
+
+effect, averaging them.
+
+We've looked previously at the
+Fourier transform of this
+
+rectangular sequence.
+
+And the Fourier transform of
+that, in fact, is of the form
+
+of a sine n x over
+sine x curve.
+
+And as you can see, that is
+some approximation to a
+
+lowpass filter.
+
+And so this, again, is the
+impulse response and frequency
+
+response of a nonideal
+lowpass filter.
+
+Now, there are a variety of
+algorithms that, in fact, tell
+
+you how to choose the weights
+associated with a weighted
+
+moving average to, in some
+sense, design better
+
+approximations and without going
+into the details of any
+
+of those algorithms.
+
+Let me just show the result of
+choosing the weights for the
+
+design of a 251-point moving
+average filter, where the
+
+weights are chosen using an
+optimum algorithm to generate
+
+as sharp a cutoff as can
+possibly be generated.
+
+And so what I show here is the
+frequency response of the
+
+resulting filter on a
+logarithmic amplitude scale
+
+and a linear frequency scale.
+
+Notice that on this scale, the
+passband is very flat.
+
+Although here is an expanded
+view of it.
+
+And in fact, it has what's
+referred to as an equal-ripple
+
+characteristic.
+
+And then here is the
+transition band.
+
+And here we have to stopband,
+which in fact is down somewhat
+
+more than 80 dB and, again, has
+what's referred to as an
+
+equal-ripple characteristic.
+
+Now, the notion of a moving
+average for filtering is
+
+something that is very
+commonly used.
+
+I had shown last time actually
+the result of some filtering
+
+on a particular data
+sequence, the Dow
+
+Jones Industrial Average.
+
+And very often, in looking at
+various kinds of stock market
+
+publications, what you will see
+is the Dow Jones average
+
+shown in its raw form
+as a data sequence.
+
+And then very typically, you'll
+see also the result of
+
+a moving average, where the
+moving average might be on the
+
+order of day, or it might be
+on the order of months.
+
+The whole notion being to take
+some of the random high
+
+frequency fluctuations out of
+the average and show the low
+
+frequency, or trends, over
+some period of time.
+
+So let's, in fact, go back
+to the Dow Jones average.
+
+And let me now show you what the
+result of filtering with a
+
+moving average filter would
+look like on the same Dow
+
+Jones industrial average
+sequence that
+
+I showed last time.
+
+So once again, we have the Dow
+Jones average from 1927 to
+
+roughly 1932.
+
+At the top, we see the
+impulse response
+
+for the moving average.
+
+Again, I remind you on an
+expanded time scale, and
+
+what's shown here is
+the moving average
+
+with just one point.
+
+So the output on the bottom
+trace is just simply identical
+
+to the input.
+
+Now, let's increase the
+length of the moving
+
+average to two points.
+
+And we see that there is a small
+amount of smoothing,
+
+three points and just
+a little more
+
+smoothing, that gets inserted.
+
+Now a four-point moving
+average, and next the
+
+five-point moving average,
+and a six-point
+
+moving average next.
+
+And we see that the smoothing
+increases.
+
+Now, let's increase the length
+of the moving average filter
+
+much more rapidly and watch
+how the output is more and
+
+more smooth in relation
+to the input.
+
+Again, I emphasize that the
+time scale for the impulse
+
+response is significantly
+expanded in relationship to
+
+the time scale for both the
+input and the output.
+
+And once again, through the
+magic of filtering, we've been
+
+able to eliminate the 1929
+Stock Market Crash.
+
+All right, so we've seen moving
+average filters, or
+
+what are sometimes referred to
+as non-recursive filters.
+
+And they are, as I stressed,
+a very important class of
+
+discrete-time filters.
+
+Another very important class of
+discrete-time filters are
+
+what are referred to as
+recursive filters.
+
+Recursive filters are filters
+for which the difference
+
+equation has feedback from the
+output back into the input.
+
+In other words, the output
+depends not only on the input,
+
+but also on previous values
+of the output.
+
+So for example, as I've
+stressed previously, a
+
+recursive difference equation
+has the general form that I
+
+indicate here, a linear
+combination of weighted
+
+outputs on the left-hand side
+and linear combination of
+
+weighted inputs on the
+right-hand side.
+
+And as we've talked about, we
+can solve this equation for
+
+the current output y of n in
+terms of current and past
+
+inputs and past outputs.
+
+For example, just to interpret
+this, focus on the
+
+interpretation of this as a
+filter, let's look at a first
+
+order difference equation, which
+we've talked about and
+
+generated the solution
+to previously.
+
+So the first order difference
+equation would be as I
+
+indicated here.
+
+And imposing causality on this,
+so that we assume that
+
+we are running this as a
+recursive forward in time, we
+
+can solve this for y of n in
+terms of x of n and y of n
+
+minus 1 weighted by
+the factor a.
+
+And I simply indicate the
+block diagram for this.
+
+But what we want to examine
+now for this first order
+
+recursion is the frequency
+response and see its
+
+interpretation as a filter.
+
+Well in fact, again, the
+mathematics for this we've
+
+gone through in the
+last lecture.
+
+And so interpreting the first
+order difference equation as a
+
+system, what we're attempting
+to generate is the frequency
+
+response, which is the
+Fourier transform
+
+of the impulse response.
+
+And from the difference
+equation, we can, of course,
+
+solve for either one of those
+by using the properties,
+
+exploiting the properties,
+of Fourier transform.
+
+Applying the Fourier transform
+to the difference equation, we
+
+will end up with the Fourier
+transform of the output equal
+
+to the Fourier transform of the
+input times this factor,
+
+which we know from the
+convolution property, in fact,
+
+is the frequency response
+of the system.
+
+So this is the frequency
+response.
+
+And of course, the inverse
+Fourier transform of that,
+
+which I indicate below, is the
+system impulse response.
+
+So we have the frequency
+response obtained by applying
+
+the Fourier transform to the
+difference equation, the
+
+impulse response.
+
+And, as we did last time, we can
+look at that in terms of a
+
+frequency response
+characteristic.
+
+And recall that, depending on
+whether the factor a is
+
+positive or negative, we either
+get a lowpass filter or
+
+a highpass filter.
+
+And if, in fact, we look at the
+frequency response for the
+
+factor a being positive, then
+we see that this is an
+
+approximation to a lowpass
+filter, whereas below it I
+
+show the frequency response
+for a negative.
+
+And there this corresponds to
+a highpass filter, because
+
+we're attenuating low
+frequencies and retaining the
+
+high frequencies.
+
+And recall also that
+we illustrated this
+
+characteristic as a lowpass or
+highpass filter for the first
+
+order recursion by looking at
+how it worked as a filter in
+
+both cases when the input was
+the Dow Jones average.
+
+And indeed, we saw that it
+generated both lowpass and
+
+highpass filtering in the
+appropriate cases.
+
+So for discrete-time, we have
+the two classes, moving
+
+average and recursive filters.
+
+And there are a variety of
+issues discussed in the text
+
+about why, in certain contexts,
+one might want to
+
+use one of the other.
+
+Basically, what happens is that
+for the moving average
+
+filter, for a given set a filter
+specifications, there
+
+are many more multiplications
+required than
+
+for a recursive filter.
+
+But there are, in certain
+contexts, some very important
+
+compensating benefits for the
+moving average filter.
+
+Now, this concludes, pretty
+much, what I want to say in
+
+detail about filtering, the
+concept of filtering, in the
+
+set of lectures.
+
+This is only a very quick
+glimpse into a very important
+
+and very rich topic, and one, of
+course, that can be studied
+
+on its own in an considerable
+amount of detail.
+
+As the lectures go on, what
+we'll find is that the basic
+
+concept of filtering, both ideal
+and nonideal filtering,
+
+will be a very important
+part of what we do.
+
+And in particular, beginning
+with the next lecture, we'll
+
+turn to a discussion of
+modulation, exploiting the
+
+property of modulation
+as it relates to
+
+some practical problems.
+
+And what we'll find when we do
+that is that a very important
+
+part of that discussion and, in
+fact, a very important part
+
+of the use of modulation also
+just naturally incorporates
+
+the concept and properties
+of filtering.
+
+Thank you.
\ No newline at end of file
diff --git a/PkpRIStmfrE.txt b/PkpRIStmfrE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18f0e0cdbd9f85079a3b76113fe0c6841146deed
--- /dev/null
+++ b/PkpRIStmfrE.txt
@@ -0,0 +1,7099 @@
+align:start position:0%
+ 
+okay so let's get
+
+ align:start position:0%
+okay so let's get
+ 
+
+ align:start position:0%
+okay so let's get
+started
+
+ align:start position:0%
+started
+ 
+
+ align:start position:0%
+started
+so as I said I I I'm going to do second
+
+ align:start position:0%
+so as I said I I I'm going to do second
+ 
+
+ align:start position:0%
+so as I said I I I'm going to do second
+derivatives which is just going to be
+
+ align:start position:0%
+derivatives which is just going to be
+ 
+
+ align:start position:0%
+derivatives which is just going to be
+the derivative of the
+
+ align:start position:0%
+the derivative of the
+ 
+
+ align:start position:0%
+the derivative of the
+derivative but you know when you have um
+
+ align:start position:0%
+derivative but you know when you have um
+ 
+
+ align:start position:0%
+derivative but you know when you have um
+functions from you know matrices to
+
+ align:start position:0%
+functions from you know matrices to
+ 
+
+ align:start position:0%
+functions from you know matrices to
+matrices or something like that you have
+
+ align:start position:0%
+matrices or something like that you have
+ 
+
+ align:start position:0%
+matrices or something like that you have
+to think a little bit
+
+ align:start position:0%
+to think a little bit
+ 
+
+ align:start position:0%
+to think a little bit
+carefully just to make sure we
+
+ align:start position:0%
+carefully just to make sure we
+ 
+
+ align:start position:0%
+carefully just to make sure we
+understand what kind of thing the second
+
+ align:start position:0%
+understand what kind of thing the second
+ 
+
+ align:start position:0%
+understand what kind of thing the second
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+is so remember when we take basically
+
+ align:start position:0%
+is so remember when we take basically
+ 
+
+ align:start position:0%
+is so remember when we take basically
+the the first
+
+ align:start position:0%
+the the first
+ 
+
+ align:start position:0%
+the the first
+derivative right what what we have is
+
+ align:start position:0%
+derivative right what what we have is
+ 
+
+ align:start position:0%
+derivative right what what we have is
+this this linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator F primed of X that takes in uh
+
+ align:start position:0%
+operator F primed of X that takes in uh
+ 
+
+ align:start position:0%
+operator F primed of X that takes in uh
+a little
+
+ align:start position:0%
+a little
+ 
+
+ align:start position:0%
+a little
+change right and gives us you know a DF
+
+ align:start position:0%
+change right and gives us you know a DF
+ 
+
+ align:start position:0%
+change right and gives us you know a DF
+which is the the the f of x plus DX
+
+ align:start position:0%
+which is the the the f of x plus DX
+ 
+
+ align:start position:0%
+which is the the the f of x plus DX
+minus F ofx to first order right they
+
+ align:start position:0%
+minus F ofx to first order right they
+ 
+
+ align:start position:0%
+minus F ofx to first order right they
+dropping higher order
+
+ align:start position:0%
+dropping higher order
+ 
+
+ align:start position:0%
+dropping higher order
+terms and so it's really natural you
+
+ align:start position:0%
+terms and so it's really natural you
+ 
+
+ align:start position:0%
+terms and so it's really natural you
+know to define the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative say derive as the derivative
+
+ align:start position:0%
+derivative say derive as the derivative
+ 
+
+ align:start position:0%
+derivative say derive as the derivative
+of that so what
+
+ align:start position:0%
+of that so what
+ 
+
+ align:start position:0%
+of that so what
+should what what should uh uh um
+
+ align:start position:0%
+should what what should uh uh um
+ 
+
+ align:start position:0%
+should what what should uh uh um
+F Prim
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+B right F
+
+ align:start position:0%
+B right F
+ 
+
+ align:start position:0%
+B right F
+primed of uh of
+
+ align:start position:0%
+primed of uh of
+ 
+
+ align:start position:0%
+primed of uh of
+X should take in a that's called let me
+
+ align:start position:0%
+X should take in a that's called let me
+ 
+
+ align:start position:0%
+X should take in a that's called let me
+call it DX Prime that means that's not a
+
+ align:start position:0%
+call it DX Prime that means that's not a
+ 
+
+ align:start position:0%
+call it DX Prime that means that's not a
+derivative just means a different uh let
+
+ align:start position:0%
+derivative just means a different uh let
+ 
+
+ align:start position:0%
+derivative just means a different uh let
+me put it in here a red is it's going to
+
+ align:start position:0%
+me put it in here a red is it's going to
+ 
+
+ align:start position:0%
+me put it in here a red is it's going to
+be a a
+
+ align:start position:0%
+be a a
+ 
+
+ align:start position:0%
+be a a
+different small
+
+ align:start position:0%
+different small
+ 
+
+ align:start position:0%
+different small
+change right so Prime here is not
+
+ align:start position:0%
+change right so Prime here is not
+ 
+
+ align:start position:0%
+change right so Prime here is not
+derivative it's just different okay call
+
+ align:start position:0%
+derivative it's just different okay call
+ 
+
+ align:start position:0%
+derivative it's just different okay call
+it Tilda or something like that but we
+
+ align:start position:0%
+it Tilda or something like that but we
+ 
+
+ align:start position:0%
+it Tilda or something like that but we
+overload the prime a lot in mathematics
+
+ align:start position:0%
+overload the prime a lot in mathematics
+ 
+
+ align:start position:0%
+overload the prime a lot in mathematics
+right so what should it be well it
+
+ align:start position:0%
+right so what should it be well it
+ 
+
+ align:start position:0%
+right so what should it be well it
+should be the derivative I mean it
+
+ align:start position:0%
+should be the derivative I mean it
+ 
+
+ align:start position:0%
+should be the derivative I mean it
+should be exactly the same thing it
+
+ align:start position:0%
+should be exactly the same thing it
+ 
+
+ align:start position:0%
+should be exactly the same thing it
+should be it should be
+
+ align:start position:0%
+should be it should be
+ 
+
+ align:start position:0%
+should be it should be
+DF primed right so it should be FR Prim
+
+ align:start position:0%
+DF primed right so it should be FR Prim
+ 
+
+ align:start position:0%
+DF primed right so it should be FR Prim
+of x uh plus DXE
+
+ align:start position:0%
+of x uh plus DXE
+ 
+
+ align:start position:0%
+of x uh plus DXE
+primed
+
+ align:start position:0%
+primed
+ 
+
+ align:start position:0%
+primed
+minus F primed of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X it should look exactly the same but
+
+ align:start position:0%
+X it should look exactly the same but
+ 
+
+ align:start position:0%
+X it should look exactly the same but
+now let's think about what this means so
+
+ align:start position:0%
+now let's think about what this means so
+ 
+
+ align:start position:0%
+now let's think about what this means so
+this F Prime here is not a number
+
+ align:start position:0%
+this F Prime here is not a number
+ 
+
+ align:start position:0%
+this F Prime here is not a number
+anymore this is it could be a number but
+
+ align:start position:0%
+anymore this is it could be a number but
+ 
+
+ align:start position:0%
+anymore this is it could be a number but
+in general it's a linear operator right
+
+ align:start position:0%
+in general it's a linear operator right
+ 
+
+ align:start position:0%
+in general it's a linear operator right
+so this
+
+ align:start position:0%
+so this
+ 
+
+ align:start position:0%
+so this
+here is the difference of two linear
+
+ align:start position:0%
+here is the difference of two linear
+ 
+
+ align:start position:0%
+here is the difference of two linear
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right and what does it mean to to add
+
+ align:start position:0%
+right and what does it mean to to add
+ 
+
+ align:start position:0%
+right and what does it mean to to add
+and subtract and and take differences of
+
+ align:start position:0%
+and subtract and and take differences of
+ 
+
+ align:start position:0%
+and subtract and and take differences of
+linear operators right and we did a
+
+ align:start position:0%
+linear operators right and we did a
+ 
+
+ align:start position:0%
+linear operators right and we did a
+little bit of this in problem set one
+
+ align:start position:0%
+little bit of this in problem set one
+ 
+
+ align:start position:0%
+little bit of this in problem set one
+you can think of linear operators
+
+ align:start position:0%
+you can think of linear operators
+ 
+
+ align:start position:0%
+you can think of linear operators
+themselves as a vector space right you
+
+ align:start position:0%
+themselves as a vector space right you
+ 
+
+ align:start position:0%
+themselves as a vector space right you
+can just like we can take functions you
+
+ align:start position:0%
+can just like we can take functions you
+ 
+
+ align:start position:0%
+can just like we can take functions you
+know sinx plus cosine X is another
+
+ align:start position:0%
+know sinx plus cosine X is another
+ 
+
+ align:start position:0%
+know sinx plus cosine X is another
+function right so so we can take think
+
+ align:start position:0%
+function right so so we can take think
+ 
+
+ align:start position:0%
+function right so so we can take think
+of linear operators as as as a vector
+
+ align:start position:0%
+of linear operators as as as a vector
+ 
+
+ align:start position:0%
+of linear operators as as as a vector
+space as well so if you have if we have
+
+ align:start position:0%
+space as well so if you have if we have
+ 
+
+ align:start position:0%
+space as well so if you have if we have
+linear
+
+ align:start position:0%
+linear
+ 
+
+ align:start position:0%
+linear
+operators
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh operators
+
+ align:start position:0%
+uh operators
+ 
+
+ align:start position:0%
+uh operators
+operators uh L1 and
+
+ align:start position:0%
+operators uh L1 and
+ 
+
+ align:start position:0%
+operators uh L1 and
+L2 then what we mean by their addition
+
+ align:start position:0%
+L2 then what we mean by their addition
+ 
+
+ align:start position:0%
+L2 then what we mean by their addition
+L1 plus L2 or plus or minus
+
+ align:start position:0%
+L1 plus L2 or plus or minus
+ 
+
+ align:start position:0%
+L1 plus L2 or plus or minus
+is the linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator that takes a vector
+
+ align:start position:0%
+operator that takes a vector
+ 
+
+ align:start position:0%
+operator that takes a vector
+v and gives you L1 of
+
+ align:start position:0%
+v and gives you L1 of
+ 
+
+ align:start position:0%
+v and gives you L1 of
+V plus L2 of
+
+ align:start position:0%
+V plus L2 of
+ 
+
+ align:start position:0%
+V plus L2 of
+V right and the same thing if you if you
+
+ align:start position:0%
+V right and the same thing if you if you
+ 
+
+ align:start position:0%
+V right and the same thing if you if you
+multiply a linear Operator by a
+
+ align:start position:0%
+multiply a linear Operator by a
+ 
+
+ align:start position:0%
+multiply a linear Operator by a
+scalar that's the linear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator that sends a vector v to Alpha
+
+ align:start position:0%
+operator that sends a vector v to Alpha
+ 
+
+ align:start position:0%
+operator that sends a vector v to Alpha
+time L1 one of
+
+ align:start position:0%
+time L1 one of
+ 
+
+ align:start position:0%
+time L1 one of
+V right so so and this this should be
+
+ align:start position:0%
+V right so so and this this should be
+ 
+
+ align:start position:0%
+V right so so and this this should be
+familiar right so if I take two matrices
+
+ align:start position:0%
+familiar right so if I take two matrices
+ 
+
+ align:start position:0%
+familiar right so if I take two matrices
+and I add them you actually know what
+
+ align:start position:0%
+and I add them you actually know what
+ 
+
+ align:start position:0%
+and I add them you actually know what
+that mean you say oh that means you add
+
+ align:start position:0%
+that mean you say oh that means you add
+ 
+
+ align:start position:0%
+that mean you say oh that means you add
+the elements up element wise but where
+
+ align:start position:0%
+the elements up element wise but where
+ 
+
+ align:start position:0%
+the elements up element wise but where
+does that rule come from that adding up
+
+ align:start position:0%
+does that rule come from that adding up
+ 
+
+ align:start position:0%
+does that rule come from that adding up
+two matrices element wise is exactly the
+
+ align:start position:0%
+two matrices element wise is exactly the
+ 
+
+ align:start position:0%
+two matrices element wise is exactly the
+new Matrix that acting on a vector gives
+
+ align:start position:0%
+new Matrix that acting on a vector gives
+ 
+
+ align:start position:0%
+new Matrix that acting on a vector gives
+you the first Matrix times the vector
+
+ align:start position:0%
+you the first Matrix times the vector
+ 
+
+ align:start position:0%
+you the first Matrix times the vector
+plus the second Matrix times a vector
+
+ align:start position:0%
+plus the second Matrix times a vector
+ 
+
+ align:start position:0%
+plus the second Matrix times a vector
+right if I take a matrix and multiply it
+
+ align:start position:0%
+right if I take a matrix and multiply it
+ 
+
+ align:start position:0%
+right if I take a matrix and multiply it
+by three you can say oh you multiply all
+
+ align:start position:0%
+by three you can say oh you multiply all
+ 
+
+ align:start position:0%
+by three you can say oh you multiply all
+the entries by three but why it's
+
+ align:start position:0%
+the entries by three but why it's
+ 
+
+ align:start position:0%
+the entries by three but why it's
+because if I take that's the the linear
+
+ align:start position:0%
+because if I take that's the the linear
+ 
+
+ align:start position:0%
+because if I take that's the the linear
+operator that taking a takes a vector
+
+ align:start position:0%
+operator that taking a takes a vector
+ 
+
+ align:start position:0%
+operator that taking a takes a vector
+it's equivalent to multiplying it by
+
+ align:start position:0%
+it's equivalent to multiplying it by
+ 
+
+ align:start position:0%
+it's equivalent to multiplying it by
+that M original Matrix and then
+
+ align:start position:0%
+that M original Matrix and then
+ 
+
+ align:start position:0%
+that M original Matrix and then
+multiplying by three right so that's
+
+ align:start position:0%
+multiplying by three right so that's
+ 
+
+ align:start position:0%
+multiplying by three right so that's
+where those rules Come From just like
+
+ align:start position:0%
+where those rules Come From just like
+ 
+
+ align:start position:0%
+where those rules Come From just like
+the rule for multiplying two matrices oh
+
+ align:start position:0%
+the rule for multiplying two matrices oh
+ 
+
+ align:start position:0%
+the rule for multiplying two matrices oh
+rows times columns why because that's
+
+ align:start position:0%
+rows times columns why because that's
+ 
+
+ align:start position:0%
+rows times columns why because that's
+the new M that's the new linear operator
+
+ align:start position:0%
+the new M that's the new linear operator
+ 
+
+ align:start position:0%
+the new M that's the new linear operator
+that equivalent to multiplying by the
+
+ align:start position:0%
+that equivalent to multiplying by the
+ 
+
+ align:start position:0%
+that equivalent to multiplying by the
+first Matrix by the right Matrix and
+
+ align:start position:0%
+first Matrix by the right Matrix and
+ 
+
+ align:start position:0%
+first Matrix by the right Matrix and
+then by the left Matrix right that's
+
+ align:start position:0%
+then by the left Matrix right that's
+ 
+
+ align:start position:0%
+then by the left Matrix right that's
+where these rules Come From right so
+
+ align:start position:0%
+where these rules Come From right so
+ 
+
+ align:start position:0%
+where these rules Come From right so
+this thing here
+
+ align:start position:0%
+this thing here
+ 
+
+ align:start position:0%
+this thing here
+is is now so what we really mean by this
+
+ align:start position:0%
+is is now so what we really mean by this
+ 
+
+ align:start position:0%
+is is now so what we really mean by this
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+this is a linear
+
+ align:start position:0%
+this is a linear
+ 
+
+ align:start position:0%
+this is a linear
+operator right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so right that this is the difference of
+
+ align:start position:0%
+so right that this is the difference of
+ 
+
+ align:start position:0%
+so right that this is the difference of
+two linear operators this is these are
+
+ align:start position:0%
+two linear operators this is these are
+ 
+
+ align:start position:0%
+two linear operators this is these are
+linear operators that take in a DX and
+
+ align:start position:0%
+linear operators that take in a DX and
+ 
+
+ align:start position:0%
+linear operators that take in a DX and
+give you something else give you a DF
+
+ align:start position:0%
+give you something else give you a DF
+ 
+
+ align:start position:0%
+give you something else give you a DF
+right so the difference of these two
+
+ align:start position:0%
+right so the difference of these two
+ 
+
+ align:start position:0%
+right so the difference of these two
+things is a linear operator that takes
+
+ align:start position:0%
+things is a linear operator that takes
+ 
+
+ align:start position:0%
+things is a linear operator that takes
+in a DX not a DX prime a DX and gives
+
+ align:start position:0%
+in a DX not a DX prime a DX and gives
+ 
+
+ align:start position:0%
+in a DX not a DX prime a DX and gives
+you uh and gives you something else so
+
+ align:start position:0%
+you uh and gives you something else so
+ 
+
+ align:start position:0%
+you uh and gives you something else so
+this is this is a linear operator that
+
+ align:start position:0%
+this is this is a linear operator that
+ 
+
+ align:start position:0%
+this is this is a linear operator that
+takes in we can call it uh F Prim right
+
+ align:start position:0%
+takes in we can call it uh F Prim right
+ 
+
+ align:start position:0%
+takes in we can call it uh F Prim right
+uh of X it takes in a DX
+
+ align:start position:0%
+uh of X it takes in a DX
+ 
+
+ align:start position:0%
+uh of X it takes in a DX
+Prime that takes in so another input we
+
+ align:start position:0%
+Prime that takes in so another input we
+ 
+
+ align:start position:0%
+Prime that takes in so another input we
+can take it write it as it takes in an
+
+ align:start position:0%
+can take it write it as it takes in an
+ 
+
+ align:start position:0%
+can take it write it as it takes in an
+input
+
+ align:start position:0%
+input
+ 
+
+ align:start position:0%
+input
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+oops and what it gives you is frim of x
+
+ align:start position:0%
+oops and what it gives you is frim of x
+ 
+
+ align:start position:0%
+oops and what it gives you is frim of x
++ DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prim uh acting
+
+ align:start position:0%
+Prim uh acting
+ 
+
+ align:start position:0%
+Prim uh acting
+on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+minus minus fime of X acting on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX does everyone see so so so this F
+
+ align:start position:0%
+DX does everyone see so so so this F
+ 
+
+ align:start position:0%
+DX does everyone see so so so this F
+Prime is going to be it's just copying
+
+ align:start position:0%
+Prime is going to be it's just copying
+ 
+
+ align:start position:0%
+Prime is going to be it's just copying
+down the formula for the for the
+
+ align:start position:0%
+down the formula for the for the
+ 
+
+ align:start position:0%
+down the formula for the for the
+derivative except applying it to F Prime
+
+ align:start position:0%
+derivative except applying it to F Prime
+ 
+
+ align:start position:0%
+derivative except applying it to F Prime
+but then so this is the the linear
+
+ align:start position:0%
+but then so this is the the linear
+ 
+
+ align:start position:0%
+but then so this is the the linear
+operator you get when you take the
+
+ align:start position:0%
+operator you get when you take the
+ 
+
+ align:start position:0%
+operator you get when you take the
+original linear operator at F at a
+
+ align:start position:0%
+original linear operator at F at a
+ 
+
+ align:start position:0%
+original linear operator at F at a
+slightly shifted x minus minus frime of
+
+ align:start position:0%
+slightly shifted x minus minus frime of
+ 
+
+ align:start position:0%
+slightly shifted x minus minus frime of
+X so this is a linear operator that X on
+
+ align:start position:0%
+X so this is a linear operator that X on
+ 
+
+ align:start position:0%
+X so this is a linear operator that X on
+DX and what it does is it's just the
+
+ align:start position:0%
+DX and what it does is it's just the
+ 
+
+ align:start position:0%
+DX and what it does is it's just the
+linear operator that takes this on DX
+
+ align:start position:0%
+linear operator that takes this on DX
+ 
+
+ align:start position:0%
+linear operator that takes this on DX
+minus this on DX but then if you think
+
+ align:start position:0%
+minus this on DX but then if you think
+ 
+
+ align:start position:0%
+minus this on DX but then if you think
+about this object now this object now
+
+ align:start position:0%
+about this object now this object now
+ 
+
+ align:start position:0%
+about this object now this object now
+takes two
+
+ align:start position:0%
+takes two
+ 
+
+ align:start position:0%
+takes two
+inputs right it takes the change it
+
+ align:start position:0%
+inputs right it takes the change it
+ 
+
+ align:start position:0%
+inputs right it takes the change it
+takes the change in X you know where DX
+
+ align:start position:0%
+takes the change in X you know where DX
+ 
+
+ align:start position:0%
+takes the change in X you know where DX
+Prime is a change in where you're taking
+
+ align:start position:0%
+Prime is a change in where you're taking
+ 
+
+ align:start position:0%
+Prime is a change in where you're taking
+the derivative right and then the second
+
+ align:start position:0%
+the derivative right and then the second
+ 
+
+ align:start position:0%
+the derivative right and then the second
+one DX is the change you know in X that
+
+ align:start position:0%
+one DX is the change you know in X that
+ 
+
+ align:start position:0%
+one DX is the change you know in X that
+you're acting the derivative f primed on
+
+ align:start position:0%
+you're acting the derivative f primed on
+ 
+
+ align:start position:0%
+you're acting the derivative f primed on
+right so this is called a bilinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+form right so we have we're going to
+
+ align:start position:0%
+form right so we have we're going to
+ 
+
+ align:start position:0%
+form right so we have we're going to
+have F
+
+ align:start position:0%
+have F
+ 
+
+ align:start position:0%
+have F
+primed that's taking of X that takes two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inputs DX
+
+ align:start position:0%
+inputs DX
+ 
+
+ align:start position:0%
+inputs DX
+Prime and
+
+ align:start position:0%
+Prime and
+ 
+
+ align:start position:0%
+Prime and
+DX but writing those two pairs of
+
+ align:start position:0%
+DX but writing those two pairs of
+ 
+
+ align:start position:0%
+DX but writing those two pairs of
+brackets is a little bit annoying so let
+
+ align:start position:0%
+brackets is a little bit annoying so let
+ 
+
+ align:start position:0%
+brackets is a little bit annoying so let
+me just write one pair of brackets and
+
+ align:start position:0%
+me just write one pair of brackets and
+ 
+
+ align:start position:0%
+me just write one pair of brackets and
+just give it two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arguments right and so it acts on two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors and it's linear in
+
+ align:start position:0%
+vectors and it's linear in
+ 
+
+ align:start position:0%
+vectors and it's linear in
+both right so in general uh you know
+
+ align:start position:0%
+both right so in general uh you know
+ 
+
+ align:start position:0%
+both right so in general uh you know
+bilinear form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right it say let me just remind you of
+
+ align:start position:0%
+right it say let me just remind you of
+ 
+
+ align:start position:0%
+right it say let me just remind you of
+linearity right you have a bilinear
+
+ align:start position:0%
+linearity right you have a bilinear
+ 
+
+ align:start position:0%
+linearity right you have a bilinear
+form form you know call it B that takes
+
+ align:start position:0%
+form form you know call it B that takes
+ 
+
+ align:start position:0%
+form form you know call it B that takes
+in a vector U and it takes in a vector v
+
+ align:start position:0%
+in a vector U and it takes in a vector v
+ 
+
+ align:start position:0%
+in a vector U and it takes in a vector v
+right with and and
+
+ align:start position:0%
+right with and and
+ 
+
+ align:start position:0%
+right with and and
+linearity means if you take like B of U1
+
+ align:start position:0%
+linearity means if you take like B of U1
+ 
+
+ align:start position:0%
+linearity means if you take like B of U1
++ U2 that had oops comma V that had
+
+ align:start position:0%
++ U2 that had oops comma V that had
+ 
+
+ align:start position:0%
++ U2 that had oops comma V that had
+better equal
+
+ align:start position:0%
+better equal
+ 
+
+ align:start position:0%
+better equal
+B of U1
+
+ align:start position:0%
+B of U1
+ 
+
+ align:start position:0%
+B of U1
+V plus b of U2 V but it also has to be
+
+ align:start position:0%
+V plus b of U2 V but it also has to be
+ 
+
+ align:start position:0%
+V plus b of U2 V but it also has to be
+linear in the second argument B of U V1
+
+ align:start position:0%
+linear in the second argument B of U V1
+ 
+
+ align:start position:0%
+linear in the second argument B of U V1
+plus
+
+ align:start position:0%
+plus
+ 
+
+ align:start position:0%
+plus
+V2 has to equal B of U V1 plus b of U
+
+ align:start position:0%
+V2 has to equal B of U V1 plus b of U
+ 
+
+ align:start position:0%
+V2 has to equal B of U V1 plus b of U
+V2 Etc right you can also scale the and
+
+ align:start position:0%
+V2 Etc right you can also scale the and
+ 
+
+ align:start position:0%
+V2 Etc right you can also scale the and
+multiply one of the arguments by two and
+
+ align:start position:0%
+multiply one of the arguments by two and
+ 
+
+ align:start position:0%
+multiply one of the arguments by two and
+so forth right if I multiply both of the
+
+ align:start position:0%
+so forth right if I multiply both of the
+ 
+
+ align:start position:0%
+so forth right if I multiply both of the
+arguments by two if I I do
+
+ align:start position:0%
+arguments by two if I I do
+ 
+
+ align:start position:0%
+arguments by two if I I do
+B uh if I do B of like 2 U * 3 V right
+
+ align:start position:0%
+B uh if I do B of like 2 U * 3 V right
+ 
+
+ align:start position:0%
+B uh if I do B of like 2 U * 3 V right
+that had better be 2 * 3 uh B of UV
+
+ align:start position:0%
+that had better be 2 * 3 uh B of UV
+ 
+
+ align:start position:0%
+that had better be 2 * 3 uh B of UV
+right so if I multiply both arguments by
+
+ align:start position:0%
+right so if I multiply both arguments by
+ 
+
+ align:start position:0%
+right so if I multiply both arguments by
+two it doesn't multiply the output by
+
+ align:start position:0%
+two it doesn't multiply the output by
+ 
+
+ align:start position:0%
+two it doesn't multiply the output by
+two it multiplies it by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+so so that's what this second derivative
+
+ align:start position:0%
+so so that's what this second derivative
+ 
+
+ align:start position:0%
+so so that's what this second derivative
+is it takes in a change a two changes
+
+ align:start position:0%
+is it takes in a change a two changes
+ 
+
+ align:start position:0%
+is it takes in a change a two changes
+right A change in where you're taking
+
+ align:start position:0%
+right A change in where you're taking
+ 
+
+ align:start position:0%
+right A change in where you're taking
+the derivative and a change in the thing
+
+ align:start position:0%
+the derivative and a change in the thing
+ 
+
+ align:start position:0%
+the derivative and a change in the thing
+that you're taking the derivative
+
+ align:start position:0%
+that you're taking the derivative
+ 
+
+ align:start position:0%
+that you're taking the derivative
+on and you might wonder if it if it if
+
+ align:start position:0%
+on and you might wonder if it if it if
+ 
+
+ align:start position:0%
+on and you might wonder if it if it if
+it matters like the order oops and I
+
+ align:start position:0%
+it matters like the order oops and I
+ 
+
+ align:start position:0%
+it matters like the order oops and I
+this should not have been a
+
+ align:start position:0%
+this should not have been a
+ 
+
+ align:start position:0%
+this should not have been a
+prime okay if it matters does the order
+
+ align:start position:0%
+prime okay if it matters does the order
+ 
+
+ align:start position:0%
+prime okay if it matters does the order
+of these two things matter and in
+
+ align:start position:0%
+of these two things matter and in
+ 
+
+ align:start position:0%
+of these two things matter and in
+general for bilinear forms the order
+
+ align:start position:0%
+general for bilinear forms the order
+ 
+
+ align:start position:0%
+general for bilinear forms the order
+matters in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+general for bilinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forms um
+
+ align:start position:0%
+forms um
+ 
+
+ align:start position:0%
+forms um
+you know B of u v is not equal to B of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+v
+
+ align:start position:0%
+v
+ 
+
+ align:start position:0%
+v
+v and and in fact it may not even make
+
+ align:start position:0%
+v and and in fact it may not even make
+ 
+
+ align:start position:0%
+v and and in fact it may not even make
+sense to swap the arguments like you can
+
+ align:start position:0%
+sense to swap the arguments like you can
+ 
+
+ align:start position:0%
+sense to swap the arguments like you can
+have a bilinear form where U lives in
+
+ align:start position:0%
+have a bilinear form where U lives in
+ 
+
+ align:start position:0%
+have a bilinear form where U lives in
+one vector space and V lives in
+
+ align:start position:0%
+one vector space and V lives in
+ 
+
+ align:start position:0%
+one vector space and V lives in
+completely different Vector space like
+
+ align:start position:0%
+completely different Vector space like
+ 
+
+ align:start position:0%
+completely different Vector space like
+so U is a scalar and V is a column
+
+ align:start position:0%
+so U is a scalar and V is a column
+ 
+
+ align:start position:0%
+so U is a scalar and V is a column
+Vector like it doesn't even you can't
+
+ align:start position:0%
+Vector like it doesn't even you can't
+ 
+
+ align:start position:0%
+Vector like it doesn't even you can't
+even uh swap them so I it
+
+ align:start position:0%
+even uh swap them so I it
+ 
+
+ align:start position:0%
+even uh swap them so I it
+this may not even makes
+
+ align:start position:0%
+this may not even makes
+ 
+
+ align:start position:0%
+this may not even makes
+sense but here you know DX and DX Prime
+
+ align:start position:0%
+sense but here you know DX and DX Prime
+ 
+
+ align:start position:0%
+sense but here you know DX and DX Prime
+they clearly live in the same Vector
+
+ align:start position:0%
+they clearly live in the same Vector
+ 
+
+ align:start position:0%
+they clearly live in the same Vector
+space it both changes to X and so it do
+
+ align:start position:0%
+space it both changes to X and so it do
+ 
+
+ align:start position:0%
+space it both changes to X and so it do
+you could swap them and ask what's the
+
+ align:start position:0%
+you could swap them and ask what's the
+ 
+
+ align:start position:0%
+you could swap them and ask what's the
+change and in fact but here it turns out
+
+ align:start position:0%
+change and in fact but here it turns out
+ 
+
+ align:start position:0%
+change and in fact but here it turns out
+they are the same so here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for uh
+
+ align:start position:0%
+for uh
+ 
+
+ align:start position:0%
+for uh
+here um it turns out that F primed
+
+ align:start position:0%
+here um it turns out that F primed
+ 
+
+ align:start position:0%
+here um it turns out that F primed
+of DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+primed my color came right fouble I was
+
+ align:start position:0%
+primed my color came right fouble I was
+ 
+
+ align:start position:0%
+primed my color came right fouble I was
+using black right F primed of X right
+
+ align:start position:0%
+using black right F primed of X right
+ 
+
+ align:start position:0%
+using black right F primed of X right
+there's a point at which you're valuing
+
+ align:start position:0%
+there's a point at which you're valuing
+ 
+
+ align:start position:0%
+there's a point at which you're valuing
+the second derivative of DX Prime comma
+
+ align:start position:0%
+the second derivative of DX Prime comma
+ 
+
+ align:start position:0%
+the second derivative of DX Prime comma
+DX always in fact equals F primed of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X DX
+
+ align:start position:0%
+X DX
+ 
+
+ align:start position:0%
+X DX
+comma DX Prime and so this is what's
+
+ align:start position:0%
+comma DX Prime and so this is what's
+ 
+
+ align:start position:0%
+comma DX Prime and so this is what's
+called a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+and we can show it pretty easily just
+
+ align:start position:0%
+and we can show it pretty easily just
+ 
+
+ align:start position:0%
+and we can show it pretty easily just
+from the definition right so so in fact
+
+ align:start position:0%
+from the definition right so so in fact
+ 
+
+ align:start position:0%
+from the definition right so so in fact
+you as I'll show in a minute this is
+
+ align:start position:0%
+you as I'll show in a minute this is
+ 
+
+ align:start position:0%
+you as I'll show in a minute this is
+actually you've seen this kind of thing
+
+ align:start position:0%
+actually you've seen this kind of thing
+ 
+
+ align:start position:0%
+actually you've seen this kind of thing
+before you didn't realize it so you
+
+ align:start position:0%
+before you didn't realize it so you
+ 
+
+ align:start position:0%
+before you didn't realize it so you
+learned in 1802 monly variable calculus
+
+ align:start position:0%
+learned in 1802 monly variable calculus
+ 
+
+ align:start position:0%
+learned in 1802 monly variable calculus
+then when I take a partial derivative
+
+ align:start position:0%
+then when I take a partial derivative
+ 
+
+ align:start position:0%
+then when I take a partial derivative
+like partial F partial X partial y like
+
+ align:start position:0%
+like partial F partial X partial y like
+ 
+
+ align:start position:0%
+like partial F partial X partial y like
+two and I can swap them it doesn't
+
+ align:start position:0%
+two and I can swap them it doesn't
+ 
+
+ align:start position:0%
+two and I can swap them it doesn't
+matter and it turns out that is is going
+
+ align:start position:0%
+matter and it turns out that is is going
+ 
+
+ align:start position:0%
+matter and it turns out that is is going
+to be a special case of this right so so
+
+ align:start position:0%
+to be a special case of this right so so
+ 
+
+ align:start position:0%
+to be a special case of this right so so
+let me let me show it in general from
+
+ align:start position:0%
+let me let me show it in general from
+ 
+
+ align:start position:0%
+let me let me show it in general from
+just from the definition so so why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this okay why so y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric and so we just we just need to
+
+ align:start position:0%
+symmetric and so we just we just need to
+ 
+
+ align:start position:0%
+symmetric and so we just we just need to
+write out the definition a little bit so
+
+ align:start position:0%
+write out the definition a little bit so
+ 
+
+ align:start position:0%
+write out the definition a little bit so
+just write out FP Prim of
+
+ align:start position:0%
+just write out FP Prim of
+ 
+
+ align:start position:0%
+just write out FP Prim of
+X of DX Prim DX I'm not going to use
+
+ align:start position:0%
+X of DX Prim DX I'm not going to use
+ 
+
+ align:start position:0%
+X of DX Prim DX I'm not going to use
+colors here because it gets too annoying
+
+ align:start position:0%
+colors here because it gets too annoying
+ 
+
+ align:start position:0%
+colors here because it gets too annoying
+to swap swap pens back and forth
+
+ align:start position:0%
+to swap swap pens back and forth
+ 
+
+ align:start position:0%
+to swap swap pens back and forth
+okay so there's there's two terms here
+
+ align:start position:0%
+okay so there's there's two terms here
+ 
+
+ align:start position:0%
+okay so there's there's two terms here
+so there's a term that comes from um FR
+
+ align:start position:0%
+so there's a term that comes from um FR
+ 
+
+ align:start position:0%
+so there's a term that comes from um FR
+Prime of x + DX
+
+ align:start position:0%
+Prime of x + DX
+ 
+
+ align:start position:0%
+Prime of x + DX
+Prime acting on
+
+ align:start position:0%
+Prime acting on
+ 
+
+ align:start position:0%
+Prime acting on
+DX
+
+ align:start position:0%
+DX
+ 
+
+ align:start position:0%
+DX
+minus F
+
+ align:start position:0%
+minus F
+ 
+
+ align:start position:0%
+minus F
+ofx FR Prime of X acting on DX right
+
+ align:start position:0%
+ofx FR Prime of X acting on DX right
+ 
+
+ align:start position:0%
+ofx FR Prime of X acting on DX right
+that's just the definition I did before
+
+ align:start position:0%
+that's just the definition I did before
+ 
+
+ align:start position:0%
+that's just the definition I did before
+right that's the it's it's the F Prime
+
+ align:start position:0%
+right that's the it's it's the F Prime
+ 
+
+ align:start position:0%
+right that's the it's it's the F Prime
+is the difference of these two linear
+
+ align:start position:0%
+is the difference of these two linear
+ 
+
+ align:start position:0%
+is the difference of these two linear
+operators so acting on DX is the
+
+ align:start position:0%
+operators so acting on DX is the
+ 
+
+ align:start position:0%
+operators so acting on DX is the
+difference of what they do on the
+
+ align:start position:0%
+difference of what they do on the
+ 
+
+ align:start position:0%
+difference of what they do on the
+DX but now let's take it one step
+
+ align:start position:0%
+DX but now let's take it one step
+ 
+
+ align:start position:0%
+DX but now let's take it one step
+further I'm going to expand out what's
+
+ align:start position:0%
+further I'm going to expand out what's
+ 
+
+ align:start position:0%
+further I'm going to expand out what's
+the definition of f primed let's go back
+
+ align:start position:0%
+the definition of f primed let's go back
+ 
+
+ align:start position:0%
+the definition of f primed let's go back
+to that frime of of X fim let's do the
+
+ align:start position:0%
+to that frime of of X fim let's do the
+ 
+
+ align:start position:0%
+to that frime of of X fim let's do the
+second one that's easier
+
+ align:start position:0%
+second one that's easier
+ 
+
+ align:start position:0%
+second one that's easier
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+um so the second
+
+ align:start position:0%
+um so the second
+ 
+
+ align:start position:0%
+um so the second
+term what's F Prime of X DX we
+
+ align:start position:0%
+term what's F Prime of X DX we
+ 
+
+ align:start position:0%
+term what's F Prime of X DX we
+said you know very in the very first
+
+ align:start position:0%
+said you know very in the very first
+ 
+
+ align:start position:0%
+said you know very in the very first
+lecture that's the same thing as f ofx
+
+ align:start position:0%
+lecture that's the same thing as f ofx
+ 
+
+ align:start position:0%
+lecture that's the same thing as f ofx
+plus DX minus F ofx right that's what
+
+ align:start position:0%
+plus DX minus F ofx right that's what
+ 
+
+ align:start position:0%
+plus DX minus F ofx right that's what
+that's what that is so
+
+ align:start position:0%
+that's what that is so
+ 
+
+ align:start position:0%
+that's what that is so
+what's what's F Prime of X Plus DX Prime
+
+ align:start position:0%
+what's what's F Prime of X Plus DX Prime
+ 
+
+ align:start position:0%
+what's what's F Prime of X Plus DX Prime
+DX it's f
+
+ align:start position:0%
+DX it's f
+ 
+
+ align:start position:0%
+DX it's f
+of x + DX Prim + DX minus F ofx +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+dxr now let me just regroup these terms
+
+ align:start position:0%
+dxr now let me just regroup these terms
+ 
+
+ align:start position:0%
+dxr now let me just regroup these terms
+a little bit so I have one term that
+
+ align:start position:0%
+a little bit so I have one term that
+ 
+
+ align:start position:0%
+a little bit so I have one term that
+looks like f ofx + DX prime plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX and I have another term that looks
+
+ align:start position:0%
+DX and I have another term that looks
+ 
+
+ align:start position:0%
+DX and I have another term that looks
+like just a A plus F ofx that's not very
+
+ align:start position:0%
+like just a A plus F ofx that's not very
+ 
+
+ align:start position:0%
+like just a A plus F ofx that's not very
+interesting and then I have another term
+
+ align:start position:0%
+interesting and then I have another term
+ 
+
+ align:start position:0%
+interesting and then I have another term
+that looks like f ofx uh plus DX with
+
+ align:start position:0%
+that looks like f ofx uh plus DX with
+ 
+
+ align:start position:0%
+that looks like f ofx uh plus DX with
+the minus sign and I have another term
+
+ align:start position:0%
+the minus sign and I have another term
+ 
+
+ align:start position:0%
+the minus sign and I have another term
+that looks like f ofx plus DX
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+but now if you stare at this
+
+ align:start position:0%
+but now if you stare at this
+ 
+
+ align:start position:0%
+but now if you stare at this
+clearly vector addition is commutative
+
+ align:start position:0%
+clearly vector addition is commutative
+ 
+
+ align:start position:0%
+clearly vector addition is commutative
+right I can swap those I can swap
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+these these two two terms so this is
+
+ align:start position:0%
+these these two two terms so this is
+ 
+
+ align:start position:0%
+these these two two terms so this is
+this is I can I can swap the addition in
+
+ align:start position:0%
+this is I can I can swap the addition in
+ 
+
+ align:start position:0%
+this is I can I can swap the addition in
+the input I can also swap the addition
+
+ align:start position:0%
+the input I can also swap the addition
+ 
+
+ align:start position:0%
+the input I can also swap the addition
+of the output I can just arrange these
+
+ align:start position:0%
+of the output I can just arrange these
+ 
+
+ align:start position:0%
+of the output I can just arrange these
+two terms right and so this whole thing
+
+ align:start position:0%
+two terms right and so this whole thing
+ 
+
+ align:start position:0%
+two terms right and so this whole thing
+is exactly what you the same as what you
+
+ align:start position:0%
+is exactly what you the same as what you
+ 
+
+ align:start position:0%
+is exactly what you the same as what you
+would get is if I took F Prime of X and
+
+ align:start position:0%
+would get is if I took F Prime of X and
+ 
+
+ align:start position:0%
+would get is if I took F Prime of X and
+evaluated it at and I swapped the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+outputs so it's just just writing out
+
+ align:start position:0%
+outputs so it's just just writing out
+ 
+
+ align:start position:0%
+outputs so it's just just writing out
+the definition
+
+ align:start position:0%
+the definition
+ 
+
+ align:start position:0%
+the definition
+this this does not look symmetric
+
+ align:start position:0%
+this this does not look symmetric
+ 
+
+ align:start position:0%
+this this does not look symmetric
+because here the DX Prime is in in the
+
+ align:start position:0%
+because here the DX Prime is in in the
+ 
+
+ align:start position:0%
+because here the DX Prime is in in the
+argument and DX is what f is acting on
+
+ align:start position:0%
+argument and DX is what f is acting on
+ 
+
+ align:start position:0%
+argument and DX is what f is acting on
+but when you write out the derivative
+
+ align:start position:0%
+but when you write out the derivative
+ 
+
+ align:start position:0%
+but when you write out the derivative
+the definition the derivative then you
+
+ align:start position:0%
+the definition the derivative then you
+ 
+
+ align:start position:0%
+the definition the derivative then you
+see that both DX and DX Prime appear in
+
+ align:start position:0%
+see that both DX and DX Prime appear in
+ 
+
+ align:start position:0%
+see that both DX and DX Prime appear in
+the same way
+
+ align:start position:0%
+the same way
+ 
+
+ align:start position:0%
+the same way
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's
+
+ align:start position:0%
+so let's
+ 
+
+ align:start position:0%
+so let's
+do uh you know uh so the 181 example is
+
+ align:start position:0%
+do uh you know uh so the 181 example is
+ 
+
+ align:start position:0%
+do uh you know uh so the 181 example is
+is very easy the the first derivative is
+
+ align:start position:0%
+is very easy the the first derivative is
+ 
+
+ align:start position:0%
+is very easy the the first derivative is
+a number the second derivative is also a
+
+ align:start position:0%
+a number the second derivative is also a
+ 
+
+ align:start position:0%
+a number the second derivative is also a
+number that that's kind of boring so
+
+ align:start position:0%
+number that that's kind of boring so
+ 
+
+ align:start position:0%
+number that that's kind of boring so
+that so it's it's The Familiar this is
+
+ align:start position:0%
+that so it's it's The Familiar this is
+ 
+
+ align:start position:0%
+that so it's it's The Familiar this is
+this is a strict generalization of what
+
+ align:start position:0%
+this is a strict generalization of what
+ 
+
+ align:start position:0%
+this is a strict generalization of what
+you learned before it's nothing new um
+
+ align:start position:0%
+you learned before it's nothing new um
+ 
+
+ align:start position:0%
+you learned before it's nothing new um
+but let's do an
+
+ align:start position:0%
+but let's do an
+ 
+
+ align:start position:0%
+but let's do an
+1802 you know multivariable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+calculus right so suppose we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scalar function f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ofx right so the output is a
+
+ align:start position:0%
+ofx right so the output is a
+ 
+
+ align:start position:0%
+ofx right so the output is a
+scalar
+
+ align:start position:0%
+scalar
+ 
+
+ align:start position:0%
+scalar
+but the input uh is going to be uh this
+
+ align:start position:0%
+but the input uh is going to be uh this
+ 
+
+ align:start position:0%
+but the input uh is going to be uh this
+this is going to be in RN so this is an
+
+ align:start position:0%
+this is going to be in RN so this is an
+ 
+
+ align:start position:0%
+this is going to be in RN so this is an
+N component
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Vector you could think of it as a column
+
+ align:start position:0%
+Vector you could think of it as a column
+ 
+
+ align:start position:0%
+Vector you could think of it as a column
+Vector if you if you if you
+
+ align:start position:0%
+Vector if you if you if you
+ 
+
+ align:start position:0%
+Vector if you if you if you
+want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so then what do we know so we know
+
+ align:start position:0%
+right so then what do we know so we know
+ 
+
+ align:start position:0%
+right so then what do we know so we know
+that FR
+
+ align:start position:0%
+that FR
+ 
+
+ align:start position:0%
+that FR
+Prim of x X is a row Vector it's the
+
+ align:start position:0%
+Prim of x X is a row Vector it's the
+ 
+
+ align:start position:0%
+Prim of x X is a row Vector it's the
+transpose of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gradient right so that that way um fime
+
+ align:start position:0%
+gradient right so that that way um fime
+ 
+
+ align:start position:0%
+gradient right so that that way um fime
+of x times DX is a
+
+ align:start position:0%
+of x times DX is a
+ 
+
+ align:start position:0%
+of x times DX is a
+scalar right that's the only way to get
+
+ align:start position:0%
+scalar right that's the only way to get
+ 
+
+ align:start position:0%
+scalar right that's the only way to get
+that's the only linear operator that
+
+ align:start position:0%
+that's the only linear operator that
+ 
+
+ align:start position:0%
+that's the only linear operator that
+takes a vector in and scalar out so then
+
+ align:start position:0%
+takes a vector in and scalar out so then
+ 
+
+ align:start position:0%
+takes a vector in and scalar out so then
+now let's think about what is um what is
+
+ align:start position:0%
+now let's think about what is um what is
+ 
+
+ align:start position:0%
+now let's think about what is um what is
+our our second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative our fime X it has to take in
+
+ align:start position:0%
+derivative our fime X it has to take in
+ 
+
+ align:start position:0%
+derivative our fime X it has to take in
+two vectors DX Prime and DX so that now
+
+ align:start position:0%
+two vectors DX Prime and DX so that now
+ 
+
+ align:start position:0%
+two vectors DX Prime and DX so that now
+it doesn't really matter which order I
+
+ align:start position:0%
+it doesn't really matter which order I
+ 
+
+ align:start position:0%
+it doesn't really matter which order I
+put the the
+
+ align:start position:0%
+put the the
+ 
+
+ align:start position:0%
+put the the
+prime okay but it has to give a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scalar right in the end right that that
+
+ align:start position:0%
+scalar right in the end right that that
+ 
+
+ align:start position:0%
+scalar right in the end right that that
+that's that the output is this has to
+
+ align:start position:0%
+that's that the output is this has to
+ 
+
+ align:start position:0%
+that's that the output is this has to
+match if you plug in both these things
+
+ align:start position:0%
+match if you plug in both these things
+ 
+
+ align:start position:0%
+match if you plug in both these things
+matches F right just again just go back
+
+ align:start position:0%
+matches F right just again just go back
+ 
+
+ align:start position:0%
+matches F right just again just go back
+to the definition uh uh um that you know
+
+ align:start position:0%
+to the definition uh uh um that you know
+ 
+
+ align:start position:0%
+to the definition uh uh um that you know
+you know uh uh um f Prime takes in a
+
+ align:start position:0%
+you know uh uh um f Prime takes in a
+ 
+
+ align:start position:0%
+you know uh uh um f Prime takes in a
+vector and gives you the the same output
+
+ align:start position:0%
+vector and gives you the the same output
+ 
+
+ align:start position:0%
+vector and gives you the the same output
+as F because it gives it gives you the
+
+ align:start position:0%
+as F because it gives it gives you the
+ 
+
+ align:start position:0%
+as F because it gives it gives you the
+the DF so F primed when you plug in your
+
+ align:start position:0%
+the DF so F primed when you plug in your
+ 
+
+ align:start position:0%
+the DF so F primed when you plug in your
+both vectors your DX DX Prime and DX and
+
+ align:start position:0%
+both vectors your DX DX Prime and DX and
+ 
+
+ align:start position:0%
+both vectors your DX DX Prime and DX and
+DX it has to give the same output as
+
+ align:start position:0%
+DX it has to give the same output as
+ 
+
+ align:start position:0%
+DX it has to give the same output as
+frime of DX right so it has to give this
+
+ align:start position:0%
+frime of DX right so it has to give this
+ 
+
+ align:start position:0%
+frime of DX right so it has to give this
+something the same shape as F so this
+
+ align:start position:0%
+something the same shape as F so this
+ 
+
+ align:start position:0%
+something the same shape as F so this
+this takes
+
+ align:start position:0%
+this takes
+ 
+
+ align:start position:0%
+this takes
+in two vectors and gives you a scalar
+
+ align:start position:0%
+in two vectors and gives you a scalar
+ 
+
+ align:start position:0%
+in two vectors and gives you a scalar
+right and and there's only there turns
+
+ align:start position:0%
+right and and there's only there turns
+ 
+
+ align:start position:0%
+right and and there's only there turns
+out there's only one kind of linear of
+
+ align:start position:0%
+out there's only one kind of linear of
+ 
+
+ align:start position:0%
+out there's only one kind of linear of
+way to write down an operation that
+
+ align:start position:0%
+way to write down an operation that
+ 
+
+ align:start position:0%
+way to write down an operation that
+takes in two column vectors and outputs
+
+ align:start position:0%
+takes in two column vectors and outputs
+ 
+
+ align:start position:0%
+takes in two column vectors and outputs
+a scalar and is linear in both of the
+
+ align:start position:0%
+a scalar and is linear in both of the
+ 
+
+ align:start position:0%
+a scalar and is linear in both of the
+vectors and that
+
+ align:start position:0%
+vectors and that
+ 
+
+ align:start position:0%
+vectors and that
+is to put a matrix
+
+ align:start position:0%
+is to put a matrix
+ 
+
+ align:start position:0%
+is to put a matrix
+here um and put a a DX here and a DX
+
+ align:start position:0%
+here um and put a a DX here and a DX
+ 
+
+ align:start position:0%
+here um and put a a DX here and a DX
+primed transpose over there
+
+ align:start position:0%
+primed transpose over there
+ 
+
+ align:start position:0%
+primed transpose over there
+and it has to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric we know it has to be the same
+
+ align:start position:0%
+symmetric we know it has to be the same
+ 
+
+ align:start position:0%
+symmetric we know it has to be the same
+thing if you
+
+ align:start position:0%
+thing if you
+ 
+
+ align:start position:0%
+thing if you
+swap
+
+ align:start position:0%
+swap
+ 
+
+ align:start position:0%
+swap
+the the DX and DX
+
+ align:start position:0%
+the the DX and DX
+ 
+
+ align:start position:0%
+the the DX and DX
+Prime
+
+ align:start position:0%
+Prime
+ 
+
+ align:start position:0%
+Prime
+so um but that that that means actually
+
+ align:start position:0%
+so um but that that that means actually
+ 
+
+ align:start position:0%
+so um but that that that means actually
+it has to be a symmetric Matrix because
+
+ align:start position:0%
+it has to be a symmetric Matrix because
+ 
+
+ align:start position:0%
+it has to be a symmetric Matrix because
+this is this is also a
+
+ align:start position:0%
+this is this is also a
+ 
+
+ align:start position:0%
+this is this is also a
+number so it equals the transpose of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself
+
+ align:start position:0%
+itself
+ 
+
+ align:start position:0%
+itself
+right this is true for any number you
+
+ align:start position:0%
+right this is true for any number you
+ 
+
+ align:start position:0%
+right this is true for any number you
+can always equal to the transpose itself
+
+ align:start position:0%
+can always equal to the transpose itself
+ 
+
+ align:start position:0%
+can always equal to the transpose itself
+so that equals DX transpose H transpose
+
+ align:start position:0%
+so that equals DX transpose H transpose
+ 
+
+ align:start position:0%
+so that equals DX transpose H transpose
+uh uh um DX Prime so these two have to
+
+ align:start position:0%
+uh uh um DX Prime so these two have to
+ 
+
+ align:start position:0%
+uh uh um DX Prime so these two have to
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+equal right so we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric n byn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix h which is called The hessan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix how many of you have heard of
+
+ align:start position:0%
+Matrix how many of you have heard of
+ 
+
+ align:start position:0%
+Matrix how many of you have heard of
+Hessian matrices before yeah it's a fair
+
+ align:start position:0%
+Hessian matrices before yeah it's a fair
+ 
+
+ align:start position:0%
+Hessian matrices before yeah it's a fair
+number of you right so yeah so that's
+
+ align:start position:0%
+number of you right so yeah so that's
+ 
+
+ align:start position:0%
+number of you right so yeah so that's
+that's what a bilinear form looks like
+
+ align:start position:0%
+that's what a bilinear form looks like
+ 
+
+ align:start position:0%
+that's what a bilinear form looks like
+acting on column vectors it's it's a
+
+ align:start position:0%
+acting on column vectors it's it's a
+ 
+
+ align:start position:0%
+acting on column vectors it's it's a
+matrix right
+
+ align:start position:0%
+matrix right
+ 
+
+ align:start position:0%
+matrix right
+and but it's it's it's it's it's nice to
+
+ align:start position:0%
+and but it's it's it's it's it's nice to
+ 
+
+ align:start position:0%
+and but it's it's it's it's it's nice to
+write it in in 1802 terms sort of more
+
+ align:start position:0%
+write it in in 1802 terms sort of more
+ 
+
+ align:start position:0%
+write it in in 1802 terms sort of more
+explicitly like component wise right
+
+ align:start position:0%
+explicitly like component wise right
+ 
+
+ align:start position:0%
+explicitly like component wise right
+just like the gradient and 18 know in
+
+ align:start position:0%
+just like the gradient and 18 know in
+ 
+
+ align:start position:0%
+just like the gradient and 18 know in
+when you first learn it it's partial F
+
+ align:start position:0%
+when you first learn it it's partial F
+ 
+
+ align:start position:0%
+when you first learn it it's partial F
+partial X1 partial F partial X2 and so
+
+ align:start position:0%
+partial X1 partial F partial X2 and so
+ 
+
+ align:start position:0%
+partial X1 partial F partial X2 and so
+forth like H is is going to be the same
+
+ align:start position:0%
+forth like H is is going to be the same
+ 
+
+ align:start position:0%
+forth like H is is going to be the same
+thing so same kind of thing so so now if
+
+ align:start position:0%
+thing so same kind of thing so so now if
+ 
+
+ align:start position:0%
+thing so same kind of thing so so now if
+we do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+explicitly let's just sort of write out
+
+ align:start position:0%
+explicitly let's just sort of write out
+ 
+
+ align:start position:0%
+explicitly let's just sort of write out
+slowly right so we know that the
+
+ align:start position:0%
+slowly right so we know that the
+ 
+
+ align:start position:0%
+slowly right so we know that the
+gradient of f is the vector that has
+
+ align:start position:0%
+gradient of f is the vector that has
+ 
+
+ align:start position:0%
+gradient of f is the vector that has
+partial F parti
+
+ align:start position:0%
+partial F parti
+ 
+
+ align:start position:0%
+partial F parti
+X1 to partial F partial
+
+ align:start position:0%
+X1 to partial F partial
+ 
+
+ align:start position:0%
+X1 to partial F partial
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+right so that means what is what is
+
+ align:start position:0%
+right so that means what is what is
+ 
+
+ align:start position:0%
+right so that means what is what is
+um what we want to take is the change D
+
+ align:start position:0%
+um what we want to take is the change D
+ 
+
+ align:start position:0%
+um what we want to take is the change D
+of of
+
+ align:start position:0%
+of of
+ 
+
+ align:start position:0%
+of of
+uh of uh gradient
+
+ align:start position:0%
+uh of uh gradient
+ 
+
+ align:start position:0%
+uh of uh gradient
+F right uh say transposed I guess uh um
+
+ align:start position:0%
+F right uh say transposed I guess uh um
+ 
+
+ align:start position:0%
+F right uh say transposed I guess uh um
+yeah um you so what's yeah what's What's
+
+ align:start position:0%
+yeah um you so what's yeah what's What's
+ 
+
+ align:start position:0%
+yeah um you so what's yeah what's What's
+d of uh of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh of this for example so well it's the
+
+ align:start position:0%
+uh of this for example so well it's the
+ 
+
+ align:start position:0%
+uh of this for example so well it's the
+same thing
+
+ align:start position:0%
+same thing
+ 
+
+ align:start position:0%
+same thing
+as D of partial F partial
+
+ align:start position:0%
+as D of partial F partial
+ 
+
+ align:start position:0%
+as D of partial F partial
+X1 to d d of partial F partial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+xn
+
+ align:start position:0%
+xn
+ 
+
+ align:start position:0%
+xn
+but partial F partial X1 is a scalar
+
+ align:start position:0%
+but partial F partial X1 is a scalar
+ 
+
+ align:start position:0%
+but partial F partial X1 is a scalar
+function right that take for of of X of
+
+ align:start position:0%
+function right that take for of of X of
+ 
+
+ align:start position:0%
+function right that take for of of X of
+all the comp depends on all the
+
+ align:start position:0%
+all the comp depends on all the
+ 
+
+ align:start position:0%
+all the comp depends on all the
+components X and you spit that a number
+
+ align:start position:0%
+components X and you spit that a number
+ 
+
+ align:start position:0%
+components X and you spit that a number
+which is partial F partial X1 so we know
+
+ align:start position:0%
+which is partial F partial X1 so we know
+ 
+
+ align:start position:0%
+which is partial F partial X1 so we know
+what the D of that looks like the D of
+
+ align:start position:0%
+what the D of that looks like the D of
+ 
+
+ align:start position:0%
+what the D of that looks like the D of
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+gradient right of partial F partial X1
+
+ align:start position:0%
+gradient right of partial F partial X1
+ 
+
+ align:start position:0%
+gradient right of partial F partial X1
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+DX say all the way to gradient
+
+ align:start position:0%
+DX say all the way to gradient
+ 
+
+ align:start position:0%
+DX say all the way to gradient
+of partial F partial xn transpose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX but we can write that out
+
+ align:start position:0%
+DX but we can write that out
+ 
+
+ align:start position:0%
+DX but we can write that out
+as we can pull out the DX column vector
+
+ align:start position:0%
+as we can pull out the DX column vector
+ 
+
+ align:start position:0%
+as we can pull out the DX column vector
+and that's gradient of partial F partial
+
+ align:start position:0%
+and that's gradient of partial F partial
+ 
+
+ align:start position:0%
+and that's gradient of partial F partial
+X1
+
+ align:start position:0%
+X1
+ 
+
+ align:start position:0%
+X1
+transpose all the way to par gradient of
+
+ align:start position:0%
+transpose all the way to par gradient of
+ 
+
+ align:start position:0%
+transpose all the way to par gradient of
+partial F partial xn
+
+ align:start position:0%
+partial F partial xn
+ 
+
+ align:start position:0%
+partial F partial xn
+transpose but that Matrix
+
+ align:start position:0%
+transpose but that Matrix
+ 
+
+ align:start position:0%
+transpose but that Matrix
+that what is the gradient that's that's
+
+ align:start position:0%
+that what is the gradient that's that's
+ 
+
+ align:start position:0%
+that what is the gradient that's that's
+the that's partial F that's partial
+
+ align:start position:0%
+the that's partial F that's partial
+ 
+
+ align:start position:0%
+the that's partial F that's partial
+squared of f partial X1 partial X1
+
+ align:start position:0%
+squared of f partial X1 partial X1
+ 
+
+ align:start position:0%
+squared of f partial X1 partial X1
+to partial F partial X1 partial xn
+
+ align:start position:0%
+to partial F partial X1 partial xn
+ 
+
+ align:start position:0%
+to partial F partial X1 partial xn
+that's what the gradient transpose looks
+
+ align:start position:0%
+that's what the gradient transpose looks
+ 
+
+ align:start position:0%
+that's what the gradient transpose looks
+like I take partial partial F X1 and
+
+ align:start position:0%
+like I take partial partial F X1 and
+ 
+
+ align:start position:0%
+like I take partial partial F X1 and
+take this derivative respect to X1 to xn
+
+ align:start position:0%
+take this derivative respect to X1 to xn
+ 
+
+ align:start position:0%
+take this derivative respect to X1 to xn
+so that's a mixed second
+
+ align:start position:0%
+so that's a mixed second
+ 
+
+ align:start position:0%
+so that's a mixed second
+derivative and then the last row is the
+
+ align:start position:0%
+derivative and then the last row is the
+ 
+
+ align:start position:0%
+derivative and then the last row is the
+same thing partial squared partial F par
+
+ align:start position:0%
+same thing partial squared partial F par
+ 
+
+ align:start position:0%
+same thing partial squared partial F par
+I xn and I take its derivative respect
+
+ align:start position:0%
+I xn and I take its derivative respect
+ 
+
+ align:start position:0%
+I xn and I take its derivative respect
+to X1 all the way to its derivative with
+
+ align:start position:0%
+to X1 all the way to its derivative with
+ 
+
+ align:start position:0%
+to X1 all the way to its derivative with
+respect
+
+ align:start position:0%
+respect
+ 
+
+ align:start position:0%
+respect
+to xn derivatives xn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+DX right and this is uh this is this is
+
+ align:start position:0%
+DX right and this is uh this is this is
+ 
+
+ align:start position:0%
+DX right and this is uh this is this is
+a matrix of second derivatives this is
+
+ align:start position:0%
+a matrix of second derivatives this is
+ 
+
+ align:start position:0%
+a matrix of second derivatives this is
+this is exactly going to be um I guess
+
+ align:start position:0%
+this is exactly going to be um I guess
+ 
+
+ align:start position:0%
+this is exactly going to be um I guess
+this was
+
+ align:start position:0%
+this was
+ 
+
+ align:start position:0%
+this was
+um uh
+
+ align:start position:0%
+um uh
+ 
+
+ align:start position:0%
+um uh
+this this is this is I guess H uh or
+
+ align:start position:0%
+this this is this is I guess H uh or
+ 
+
+ align:start position:0%
+this this is this is I guess H uh or
+it's equal to I guess it's h transpose
+
+ align:start position:0%
+it's equal to I guess it's h transpose
+ 
+
+ align:start position:0%
+it's equal to I guess it's h transpose
+because gr gr F was the transpose of the
+
+ align:start position:0%
+because gr gr F was the transpose of the
+ 
+
+ align:start position:0%
+because gr gr F was the transpose of the
+derivative right so this gives you the
+
+ align:start position:0%
+derivative right so this gives you the
+ 
+
+ align:start position:0%
+derivative right so this gives you the
+change this is this is the D of frime
+
+ align:start position:0%
+change this is this is the D of frime
+ 
+
+ align:start position:0%
+change this is this is the D of frime
+transpose right so it's h transpose but
+
+ align:start position:0%
+transpose right so it's h transpose but
+ 
+
+ align:start position:0%
+transpose right so it's h transpose but
+we know that that equals H so it doesn't
+
+ align:start position:0%
+we know that that equals H so it doesn't
+ 
+
+ align:start position:0%
+we know that that equals H so it doesn't
+really matter and so now so then we get
+
+ align:start position:0%
+really matter and so now so then we get
+ 
+
+ align:start position:0%
+really matter and so now so then we get
+that the H the IJ
+
+ align:start position:0%
+that the H the IJ
+ 
+
+ align:start position:0%
+that the H the IJ
+element is just part
+
+ align:start position:0%
+element is just part
+ 
+
+ align:start position:0%
+element is just part
+F partial x i partial
+
+ align:start position:0%
+F partial x i partial
+ 
+
+ align:start position:0%
+F partial x i partial
+XJ but that equals hji because we know
+
+ align:start position:0%
+XJ but that equals hji because we know
+ 
+
+ align:start position:0%
+XJ but that equals hji because we know
+in general that the pesan is a symmetric
+
+ align:start position:0%
+in general that the pesan is a symmetric
+ 
+
+ align:start position:0%
+in general that the pesan is a symmetric
+Matrix is is a symmetric bilinear form
+
+ align:start position:0%
+Matrix is is a symmetric bilinear form
+ 
+
+ align:start position:0%
+Matrix is is a symmetric bilinear form
+which means it's a symmetric Matrix so
+
+ align:start position:0%
+which means it's a symmetric Matrix so
+ 
+
+ align:start position:0%
+which means it's a symmetric Matrix so
+that gives you this relationship you
+
+ align:start position:0%
+that gives you this relationship you
+ 
+
+ align:start position:0%
+that gives you this relationship you
+learned in multivariable calculus that I
+
+ align:start position:0%
+learned in multivariable calculus that I
+ 
+
+ align:start position:0%
+learned in multivariable calculus that I
+when I take partial derivatives I can
+
+ align:start position:0%
+when I take partial derivatives I can
+ 
+
+ align:start position:0%
+when I take partial derivatives I can
+swap the
+
+ align:start position:0%
+swap the
+ 
+
+ align:start position:0%
+swap the
+order it just comes from the definition
+
+ align:start position:0%
+order it just comes from the definition
+ 
+
+ align:start position:0%
+order it just comes from the definition
+the derivative but the point is that
+
+ align:start position:0%
+the derivative but the point is that
+ 
+
+ align:start position:0%
+the derivative but the point is that
+that extends to more when you extend
+
+ align:start position:0%
+that extends to more when you extend
+ 
+
+ align:start position:0%
+that extends to more when you extend
+that to more General objects it turns
+
+ align:start position:0%
+that to more General objects it turns
+ 
+
+ align:start position:0%
+that to more General objects it turns
+turns into this symmetric par your form
+
+ align:start position:0%
+turns into this symmetric par your form
+ 
+
+ align:start position:0%
+turns into this symmetric par your form
+business any questions
+
+ align:start position:0%
+business any questions
+ 
+
+ align:start position:0%
+business any questions
+yeah this should be n one like they
+
+ align:start position:0%
+yeah this should be n one like they
+ 
+
+ align:start position:0%
+yeah this should be n one like they
+should be reversed right just in the
+
+ align:start position:0%
+should be reversed right just in the
+ 
+
+ align:start position:0%
+should be reversed right just in the
+Matrix
+
+ align:start position:0%
+Matrix
+ 
+
+ align:start position:0%
+Matrix
+itself which the partial div these
+
+ align:start position:0%
+itself which the partial div these
+ 
+
+ align:start position:0%
+itself which the partial div these
+should be reversed yeah te I guess it
+
+ align:start position:0%
+should be reversed yeah te I guess it
+ 
+
+ align:start position:0%
+should be reversed yeah te I guess it
+depends on yes it depends on what you
+
+ align:start position:0%
+depends on yes it depends on what you
+ 
+
+ align:start position:0%
+depends on yes it depends on what you
+mean by part because because we're so
+
+ align:start position:0%
+mean by part because because we're so
+ 
+
+ align:start position:0%
+mean by part because because we're so
+used to the fact that this this you can
+
+ align:start position:0%
+used to the fact that this this you can
+ 
+
+ align:start position:0%
+used to the fact that this this you can
+take the derivative in either order so
+
+ align:start position:0%
+take the derivative in either order so
+ 
+
+ align:start position:0%
+take the derivative in either order so
+actually I don't know like does it mean
+
+ align:start position:0%
+actually I don't know like does it mean
+ 
+
+ align:start position:0%
+actually I don't know like does it mean
+you take the this derivative then this
+
+ align:start position:0%
+you take the this derivative then this
+ 
+
+ align:start position:0%
+you take the this derivative then this
+derivative or the other way around
+
+ align:start position:0%
+derivative or the other way around
+ 
+
+ align:start position:0%
+derivative or the other way around
+like if I put parentheses here I think
+
+ align:start position:0%
+like if I put parentheses here I think
+ 
+
+ align:start position:0%
+like if I put parentheses here I think
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+right okay yeah because
+
+ align:start position:0%
+right okay yeah because
+ 
+
+ align:start position:0%
+right okay yeah because
+but the notation is kind of ambiguous
+
+ align:start position:0%
+but the notation is kind of ambiguous
+ 
+
+ align:start position:0%
+but the notation is kind of ambiguous
+because it doesn't need to be explicit
+
+ align:start position:0%
+because it doesn't need to be explicit
+ 
+
+ align:start position:0%
+because it doesn't need to be explicit
+because you can you can swap the order
+
+ align:start position:0%
+because you can you can swap the order
+ 
+
+ align:start position:0%
+because you can you can swap the order
+but yeah so I think I think yeah if I
+
+ align:start position:0%
+but yeah so I think I think yeah if I
+ 
+
+ align:start position:0%
+but yeah so I think I think yeah if I
+put derivative parentheses here that's
+
+ align:start position:0%
+put derivative parentheses here that's
+ 
+
+ align:start position:0%
+put derivative parentheses here that's
+sort of the the explicit thing I take
+
+ align:start position:0%
+sort of the the explicit thing I take
+ 
+
+ align:start position:0%
+sort of the the explicit thing I take
+partial F partial X1 I take it dtive
+
+ align:start position:0%
+partial F partial X1 I take it dtive
+ 
+
+ align:start position:0%
+partial F partial X1 I take it dtive
+respect to X1 and all the way to xn but
+
+ align:start position:0%
+respect to X1 and all the way to xn but
+ 
+
+ align:start position:0%
+respect to X1 and all the way to xn but
+if you put parentheses there then it's
+
+ align:start position:0%
+if you put parentheses there then it's
+ 
+
+ align:start position:0%
+if you put parentheses there then it's
+the opposite right but at the end of the
+
+ align:start position:0%
+the opposite right but at the end of the
+ 
+
+ align:start position:0%
+the opposite right but at the end of the
+day it's not going to matter because
+
+ align:start position:0%
+day it's not going to matter because
+ 
+
+ align:start position:0%
+day it's not going to matter because
+because this is
+
+ align:start position:0%
+because this is
+ 
+
+ align:start position:0%
+because this is
+symmetric yeah okay so so that's what
+
+ align:start position:0%
+symmetric yeah okay so so that's what
+ 
+
+ align:start position:0%
+symmetric yeah okay so so that's what
+you know you know how many learn the H
+
+ align:start position:0%
+you know you know how many learn the H
+ 
+
+ align:start position:0%
+you know you know how many learn the H
+Matrix this way it's basically it's the
+
+ align:start position:0%
+Matrix this way it's basically it's the
+ 
+
+ align:start position:0%
+Matrix this way it's basically it's the
+Matrix of all the mixed second
+
+ align:start position:0%
+Matrix of all the mixed second
+ 
+
+ align:start position:0%
+Matrix of all the mixed second
+derivative you have so that's that's
+
+ align:start position:0%
+derivative you have so that's that's
+ 
+
+ align:start position:0%
+derivative you have so that's that's
+usually how it's presented right so and
+
+ align:start position:0%
+usually how it's presented right so and
+ 
+
+ align:start position:0%
+usually how it's presented right so and
+that's yes that it's the Jacobian of the
+
+ align:start position:0%
+that's yes that it's the Jacobian of the
+ 
+
+ align:start position:0%
+that's yes that it's the Jacobian of the
+gradient in a way yeah it's exactly the
+
+ align:start position:0%
+gradient in a way yeah it's exactly the
+ 
+
+ align:start position:0%
+gradient in a way yeah it's exactly the
+Jacobian of the gradient yes good good
+
+ align:start position:0%
+Jacobian of the gradient yes good good
+ 
+
+ align:start position:0%
+Jacobian of the gradient yes good good
+good good let me me write that down so
+
+ align:start position:0%
+good good let me me write that down so
+ 
+
+ align:start position:0%
+good good let me me write that down so
+this is this is the
+
+ align:start position:0%
+this is this is the
+ 
+
+ align:start position:0%
+this is this is the
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so um yeah so but but now we
+
+ align:start position:0%
+exactly so um yeah so but but now we
+ 
+
+ align:start position:0%
+exactly so um yeah so but but now we
+have it in a much more general setting
+
+ align:start position:0%
+have it in a much more general setting
+ 
+
+ align:start position:0%
+have it in a much more general setting
+right so it's it's I think it's it's
+
+ align:start position:0%
+right so it's it's I think it's it's
+ 
+
+ align:start position:0%
+right so it's it's I think it's it's
+it's nice to do let's do a let's do a
+
+ align:start position:0%
+it's nice to do let's do a let's do a
+ 
+
+ align:start position:0%
+it's nice to do let's do a let's do a
+more General
+
+ align:start position:0%
+more General
+ 
+
+ align:start position:0%
+more General
+example an example that you that it's
+
+ align:start position:0%
+example an example that you that it's
+ 
+
+ align:start position:0%
+example an example that you that it's
+not so easy to
+
+ align:start position:0%
+not so easy to
+ 
+
+ align:start position:0%
+not so easy to
+do with 1801
+
+ align:start position:0%
+do with 1801
+ 
+
+ align:start position:0%
+do with 1801
+let's do 1802 even let's take our
+
+ align:start position:0%
+let's do 1802 even let's take our
+ 
+
+ align:start position:0%
+let's do 1802 even let's take our
+favorite function our new favorite
+
+ align:start position:0%
+favorite function our new favorite
+ 
+
+ align:start position:0%
+favorite function our new favorite
+function that takes in a matrix and
+
+ align:start position:0%
+function that takes in a matrix and
+ 
+
+ align:start position:0%
+function that takes in a matrix and
+gives you a
+
+ align:start position:0%
+gives you a
+ 
+
+ align:start position:0%
+gives you a
+scalar right so uh from previous from
+
+ align:start position:0%
+scalar right so uh from previous from
+ 
+
+ align:start position:0%
+scalar right so uh from previous from
+the previous lecture we we learn what
+
+ align:start position:0%
+the previous lecture we we learn what
+ 
+
+ align:start position:0%
+the previous lecture we we learn what
+the derivative of this
+
+ align:start position:0%
+the derivative of this
+ 
+
+ align:start position:0%
+the derivative of this
+is so if you take FR primed of
+
+ align:start position:0%
+is so if you take FR primed of
+ 
+
+ align:start position:0%
+is so if you take FR primed of
+a that's that's the linear operator act
+
+ align:start position:0%
+a that's that's the linear operator act
+ 
+
+ align:start position:0%
+a that's that's the linear operator act
+that acting on da what it gives you is
+
+ align:start position:0%
+that acting on da what it gives you is
+ 
+
+ align:start position:0%
+that acting on da what it gives you is
+deter terminant
+
+ align:start position:0%
+deter terminant
+ 
+
+ align:start position:0%
+deter terminant
+a times the trace of a inverse
+
+ align:start position:0%
+a times the trace of a inverse
+ 
+
+ align:start position:0%
+a times the trace of a inverse
+da right so or equivalently we showed
+
+ align:start position:0%
+da right so or equivalently we showed
+ 
+
+ align:start position:0%
+da right so or equivalently we showed
+that the the gradient of f was the
+
+ align:start position:0%
+that the the gradient of f was the
+ 
+
+ align:start position:0%
+that the the gradient of f was the
+determinant of a times the transpose of
+
+ align:start position:0%
+determinant of a times the transpose of
+ 
+
+ align:start position:0%
+determinant of a times the transpose of
+this a inverse transpose which is called
+
+ align:start position:0%
+this a inverse transpose which is called
+ 
+
+ align:start position:0%
+this a inverse transpose which is called
+the The adjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix yeah the adjugate of the
+
+ align:start position:0%
+Matrix yeah the adjugate of the
+ 
+
+ align:start position:0%
+Matrix yeah the adjugate of the
+transpose of the ugate sorry the
+
+ align:start position:0%
+transpose of the ugate sorry the
+ 
+
+ align:start position:0%
+transpose of the ugate sorry the
+adjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transposed I always forget which is
+
+ align:start position:0%
+transposed I always forget which is
+ 
+
+ align:start position:0%
+transposed I always forget which is
+which um it's the co-actor Matrix of a
+
+ align:start position:0%
+which um it's the co-actor Matrix of a
+ 
+
+ align:start position:0%
+which um it's the co-actor Matrix of a
+um so yes so we saw this and and there's
+
+ align:start position:0%
+um so yes so we saw this and and there's
+ 
+
+ align:start position:0%
+um so yes so we saw this and and there's
+various ways you can you can you can
+
+ align:start position:0%
+various ways you can you can you can
+ 
+
+ align:start position:0%
+various ways you can you can you can
+show this so Professor adman looked at a
+
+ align:start position:0%
+show this so Professor adman looked at a
+ 
+
+ align:start position:0%
+show this so Professor adman looked at a
+couple different ways so now let's go
+
+ align:start position:0%
+couple different ways so now let's go
+ 
+
+ align:start position:0%
+couple different ways so now let's go
+one step further and now let's let's
+
+ align:start position:0%
+one step further and now let's let's
+ 
+
+ align:start position:0%
+one step further and now let's let's
+take the second derivative and whenever
+
+ align:start position:0%
+take the second derivative and whenever
+ 
+
+ align:start position:0%
+take the second derivative and whenever
+we faces something new and confusing
+
+ align:start position:0%
+we faces something new and confusing
+ 
+
+ align:start position:0%
+we faces something new and confusing
+it's it's always good to fall back on
+
+ align:start position:0%
+it's it's always good to fall back on
+ 
+
+ align:start position:0%
+it's it's always good to fall back on
+the definition right so all we're doing
+
+ align:start position:0%
+the definition right so all we're doing
+ 
+
+ align:start position:0%
+the definition right so all we're doing
+is just uh I'm going to take um we're
+
+ align:start position:0%
+is just uh I'm going to take um we're
+ 
+
+ align:start position:0%
+is just uh I'm going to take um we're
+going to take uh D of this right d
+
+ align:start position:0%
+going to take uh D of this right d
+ 
+
+ align:start position:0%
+going to take uh D of this right d
+of of of uh of uh of this whole
+
+ align:start position:0%
+of of of uh of uh of this whole
+ 
+
+ align:start position:0%
+of of of uh of uh of this whole
+formula determinant a trace a a
+
+ align:start position:0%
+formula determinant a trace a a
+ 
+
+ align:start position:0%
+formula determinant a trace a a
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+da
+
+ align:start position:0%
+da
+ 
+
+ align:start position:0%
+da
+I'm going to put a prime here here just
+
+ align:start position:0%
+I'm going to put a prime here here just
+ 
+
+ align:start position:0%
+I'm going to put a prime here here just
+just to make it clear that what I'm
+
+ align:start position:0%
+just to make it clear that what I'm
+ 
+
+ align:start position:0%
+just to make it clear that what I'm
+changing is a not da I'm going to use a
+
+ align:start position:0%
+changing is a not da I'm going to use a
+ 
+
+ align:start position:0%
+changing is a not da I'm going to use a
+DA Prime so da D
+
+ align:start position:0%
+DA Prime so da D
+ 
+
+ align:start position:0%
+DA Prime so da D
+primed so this what this is going to be
+
+ align:start position:0%
+primed so this what this is going to be
+ 
+
+ align:start position:0%
+primed so this what this is going to be
+is this is going to be
+
+ align:start position:0%
+is this is going to be
+ 
+
+ align:start position:0%
+is this is going to be
+our F primed of a plus da
+
+ align:start position:0%
+our F primed of a plus da
+ 
+
+ align:start position:0%
+our F primed of a plus da
+primed acting on
+
+ align:start position:0%
+primed acting on
+ 
+
+ align:start position:0%
+primed acting on
+da let me give myself a little more
+
+ align:start position:0%
+da let me give myself a little more
+ 
+
+ align:start position:0%
+da let me give myself a little more
+space
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus frime of
+
+ align:start position:0%
+minus frime of
+ 
+
+ align:start position:0%
+minus frime of
+a On Da right so the prime here is just
+
+ align:start position:0%
+a On Da right so the prime here is just
+ 
+
+ align:start position:0%
+a On Da right so the prime here is just
+it's not another derivative I'm
+
+ align:start position:0%
+it's not another derivative I'm
+ 
+
+ align:start position:0%
+it's not another derivative I'm
+overloading my primes a little bit but
+
+ align:start position:0%
+overloading my primes a little bit but
+ 
+
+ align:start position:0%
+overloading my primes a little bit but
+it's just it just means I'm using I'm
+
+ align:start position:0%
+it's just it just means I'm using I'm
+ 
+
+ align:start position:0%
+it's just it just means I'm using I'm
+Chang I'm changing a by da
+
+ align:start position:0%
+Chang I'm changing a by da
+ 
+
+ align:start position:0%
+Chang I'm changing a by da
+Prime okay and and da is going to be
+
+ align:start position:0%
+Prime okay and and da is going to be
+ 
+
+ align:start position:0%
+Prime okay and and da is going to be
+fixed yes in the previous example as
+
+ align:start position:0%
+fixed yes in the previous example as
+ 
+
+ align:start position:0%
+fixed yes in the previous example as
+well that was technically DX right just
+
+ align:start position:0%
+well that was technically DX right just
+ 
+
+ align:start position:0%
+well that was technically DX right just
+clarify
+
+ align:start position:0%
+clarify
+ 
+
+ align:start position:0%
+clarify
+yeah um yeah well I didn't have any DXs
+
+ align:start position:0%
+yeah um yeah well I didn't have any DXs
+ 
+
+ align:start position:0%
+yeah um yeah well I didn't have any DXs
+here so I didn't need a a d Prime right
+
+ align:start position:0%
+here so I didn't need a a d Prime right
+ 
+
+ align:start position:0%
+here so I didn't need a a d Prime right
+so yeah yeah I but I could have used a d
+
+ align:start position:0%
+so yeah yeah I but I could have used a d
+ 
+
+ align:start position:0%
+so yeah yeah I but I could have used a d
+Prime there if I wanted but it's really
+
+ align:start position:0%
+Prime there if I wanted but it's really
+ 
+
+ align:start position:0%
+Prime there if I wanted but it's really
+the same kind of thing it's just I I
+
+ align:start position:0%
+the same kind of thing it's just I I
+ 
+
+ align:start position:0%
+the same kind of thing it's just I I
+already have a DA here and I want to be
+
+ align:start position:0%
+already have a DA here and I want to be
+ 
+
+ align:start position:0%
+already have a DA here and I want to be
+careful that I'm not changing this this
+
+ align:start position:0%
+careful that I'm not changing this this
+ 
+
+ align:start position:0%
+careful that I'm not changing this this
+is this is now going to be this is
+
+ align:start position:0%
+is this is now going to be this is
+ 
+
+ align:start position:0%
+is this is now going to be this is
+actually let me put this in blue here
+
+ align:start position:0%
+actually let me put this in blue here
+ 
+
+ align:start position:0%
+actually let me put this in blue here
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+is um so this
+
+ align:start position:0%
+is um so this
+ 
+
+ align:start position:0%
+is um so this
+is da da
+
+ align:start position:0%
+is da da
+ 
+
+ align:start position:0%
+is da da
+da this is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed okay so da is Da is not changing
+
+ align:start position:0%
+fixed okay so da is Da is not changing
+ 
+
+ align:start position:0%
+fixed okay so da is Da is not changing
+we can think of as a a
+
+ align:start position:0%
+we can think of as a a
+ 
+
+ align:start position:0%
+we can think of as a a
+constant so when I when I change things
+
+ align:start position:0%
+constant so when I when I change things
+ 
+
+ align:start position:0%
+constant so when I when I change things
+I'm changing a by da Prime okay and so
+
+ align:start position:0%
+I'm changing a by da Prime okay and so
+ 
+
+ align:start position:0%
+I'm changing a by da Prime okay and so
+now I can just use the by the product
+
+ align:start position:0%
+now I can just use the by the product
+ 
+
+ align:start position:0%
+now I can just use the by the product
+use the uh um our derivative
+
+ align:start position:0%
+use the uh um our derivative
+ 
+
+ align:start position:0%
+use the uh um our derivative
+rules our
+
+ align:start position:0%
+rules our
+ 
+
+ align:start position:0%
+rules our
+product uh and our chain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rules dot dot dot right and what do I
+
+ align:start position:0%
+rules dot dot dot right and what do I
+ 
+
+ align:start position:0%
+rules dot dot dot right and what do I
+get right
+
+ align:start position:0%
+get right
+ 
+
+ align:start position:0%
+get right
+so so so now I'm just treating da as
+
+ align:start position:0%
+so so so now I'm just treating da as
+ 
+
+ align:start position:0%
+so so so now I'm just treating da as
+just a constant Matrix I'm sticking in
+
+ align:start position:0%
+just a constant Matrix I'm sticking in
+ 
+
+ align:start position:0%
+just a constant Matrix I'm sticking in
+there and then I'm taking the derivative
+
+ align:start position:0%
+there and then I'm taking the derivative
+ 
+
+ align:start position:0%
+there and then I'm taking the derivative
+the same way as before well I have the
+
+ align:start position:0%
+the same way as before well I have the
+ 
+
+ align:start position:0%
+the same way as before well I have the
+derivative of this term times this plus
+
+ align:start position:0%
+derivative of this term times this plus
+ 
+
+ align:start position:0%
+derivative of this term times this plus
+this times the derivative of that term
+
+ align:start position:0%
+this times the derivative of that term
+ 
+
+ align:start position:0%
+this times the derivative of that term
+right and the Der of this term we just
+
+ align:start position:0%
+right and the Der of this term we just
+ 
+
+ align:start position:0%
+right and the Der of this term we just
+we just or the differential sorry of
+
+ align:start position:0%
+we just or the differential sorry of
+ 
+
+ align:start position:0%
+we just or the differential sorry of
+that term we just saw what it was right
+
+ align:start position:0%
+that term we just saw what it was right
+ 
+
+ align:start position:0%
+that term we just saw what it was right
+this is our this is our CH oops it's
+
+ align:start position:0%
+this is our this is our CH oops it's
+ 
+
+ align:start position:0%
+this is our this is our CH oops it's
+this ah it's this right so the first
+
+ align:start position:0%
+this ah it's this right so the first
+ 
+
+ align:start position:0%
+this ah it's this right so the first
+term
+
+ align:start position:0%
+term
+ 
+
+ align:start position:0%
+term
+is uh determinant of a
+
+ align:start position:0%
+is uh determinant of a
+ 
+
+ align:start position:0%
+is uh determinant of a
+times uh so so the D of the determinant
+
+ align:start position:0%
+times uh so so the D of the determinant
+ 
+
+ align:start position:0%
+times uh so so the D of the determinant
+is the determinant of a times the trace
+
+ align:start position:0%
+is the determinant of a times the trace
+ 
+
+ align:start position:0%
+is the determinant of a times the trace
+of a prime not a prime a
+
+ align:start position:0%
+of a prime not a prime a
+ 
+
+ align:start position:0%
+of a prime not a prime a
+inverse da
+
+ align:start position:0%
+inverse da
+ 
+
+ align:start position:0%
+inverse da
+primed right so this came
+
+ align:start position:0%
+primed right so this came
+ 
+
+ align:start position:0%
+primed right so this came
+from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that term right times times the other
+
+ align:start position:0%
+that term right times times the other
+ 
+
+ align:start position:0%
+that term right times times the other
+term trace of a
+
+ align:start position:0%
+term trace of a
+ 
+
+ align:start position:0%
+term trace of a
+inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+da
+
+ align:start position:0%
+da
+ 
+
+ align:start position:0%
+da
+plus I have my still have my determinant
+
+ align:start position:0%
+plus I have my still have my determinant
+ 
+
+ align:start position:0%
+plus I have my still have my determinant
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a times the derivative of the other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term and Trace is a linear operator so I
+
+ align:start position:0%
+term and Trace is a linear operator so I
+ 
+
+ align:start position:0%
+term and Trace is a linear operator so I
+can just take the derivative
+
+ align:start position:0%
+can just take the derivative
+ 
+
+ align:start position:0%
+can just take the derivative
+inside and so now I or the differential
+
+ align:start position:0%
+inside and so now I or the differential
+ 
+
+ align:start position:0%
+inside and so now I or the differential
+inside and now I need da inverse and we
+
+ align:start position:0%
+inside and now I need da inverse and we
+ 
+
+ align:start position:0%
+inside and now I need da inverse and we
+know what da inverse that was a minus
+
+ align:start position:0%
+know what da inverse that was a minus
+ 
+
+ align:start position:0%
+know what da inverse that was a minus
+sign so let me change this to a minus
+
+ align:start position:0%
+sign so let me change this to a minus
+ 
+
+ align:start position:0%
+sign so let me change this to a minus
+sign okay of a
+
+ align:start position:0%
+sign okay of a
+ 
+
+ align:start position:0%
+sign okay of a
+inverse d a primed a
+
+ align:start position:0%
+inverse d a primed a
+ 
+
+ align:start position:0%
+inverse d a primed a
+inverse and then there's still a
+
+ align:start position:0%
+inverse and then there's still a
+ 
+
+ align:start position:0%
+inverse and then there's still a
+DA everyone see that so This this term
+
+ align:start position:0%
+DA everyone see that so This this term
+ 
+
+ align:start position:0%
+DA everyone see that so This this term
+here is exactly D
+
+ align:start position:0%
+here is exactly D
+ 
+
+ align:start position:0%
+here is exactly D
+primed of a
+
+ align:start position:0%
+primed of a
+ 
+
+ align:start position:0%
+primed of a
+inverse well with the minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now the question is is this this
+
+ align:start position:0%
+and now the question is is this this
+ 
+
+ align:start position:0%
+and now the question is is this this
+this is it this is this is a bi it's not
+
+ align:start position:0%
+this is it this is this is a bi it's not
+ 
+
+ align:start position:0%
+this is it this is this is a bi it's not
+going to get much simpler than this this
+
+ align:start position:0%
+going to get much simpler than this this
+ 
+
+ align:start position:0%
+going to get much simpler than this this
+this is our bilinear form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bilinear and you know in da primed and
+
+ align:start position:0%
+bilinear and you know in da primed and
+ 
+
+ align:start position:0%
+bilinear and you know in da primed and
+uh and uh
+
+ align:start position:0%
+uh and uh
+ 
+
+ align:start position:0%
+uh and uh
+da right so I stick in any da Prime any
+
+ align:start position:0%
+da right so I stick in any da Prime any
+ 
+
+ align:start position:0%
+da right so I stick in any da Prime any
+da clearly this is linear in each one of
+
+ align:start position:0%
+da clearly this is linear in each one of
+ 
+
+ align:start position:0%
+da clearly this is linear in each one of
+them individually right there's I never
+
+ align:start position:0%
+them individually right there's I never
+ 
+
+ align:start position:0%
+them individually right there's I never
+I never multip I can multiply da by da
+
+ align:start position:0%
+I never multip I can multiply da by da
+ 
+
+ align:start position:0%
+I never multip I can multiply da by da
+Prime it's
+
+ align:start position:0%
+Prime it's
+ 
+
+ align:start position:0%
+Prime it's
+quadratic but it's but but it's uh
+
+ align:start position:0%
+quadratic but it's but but it's uh
+ 
+
+ align:start position:0%
+quadratic but it's but but it's uh
+but I can't multiply um d da by itself
+
+ align:start position:0%
+but I can't multiply um d da by itself
+ 
+
+ align:start position:0%
+but I can't multiply um d da by itself
+okay and is it
+
+ align:start position:0%
+okay and is it
+ 
+
+ align:start position:0%
+okay and is it
+symmetric well let's look this term is
+
+ align:start position:0%
+symmetric well let's look this term is
+ 
+
+ align:start position:0%
+symmetric well let's look this term is
+the same as
+
+ align:start position:0%
+the same as
+ 
+
+ align:start position:0%
+the same as
+this right so if I swap and these are
+
+ align:start position:0%
+this right so if I swap and these are
+ 
+
+ align:start position:0%
+this right so if I swap and these are
+just Trace is just number so I can swap
+
+ align:start position:0%
+just Trace is just number so I can swap
+ 
+
+ align:start position:0%
+just Trace is just number so I can swap
+these two terms and that's that's that's
+
+ align:start position:0%
+these two terms and that's that's that's
+ 
+
+ align:start position:0%
+these two terms and that's that's that's
+fine this is and this is also a number
+
+ align:start position:0%
+fine this is and this is also a number
+ 
+
+ align:start position:0%
+fine this is and this is also a number
+right what about this if I swap D and D
+
+ align:start position:0%
+right what about this if I swap D and D
+ 
+
+ align:start position:0%
+right what about this if I swap D and D
+prime it looks it looks a little bit
+
+ align:start position:0%
+prime it looks it looks a little bit
+ 
+
+ align:start position:0%
+prime it looks it looks a little bit
+different but remember the trace has the
+
+ align:start position:0%
+different but remember the trace has the
+ 
+
+ align:start position:0%
+different but remember the trace has the
+cyclic property I can I can move the
+
+ align:start position:0%
+cyclic property I can I can move the
+ 
+
+ align:start position:0%
+cyclic property I can I can move the
+like the a inverse da over to the
+
+ align:start position:0%
+like the a inverse da over to the
+ 
+
+ align:start position:0%
+like the a inverse da over to the
+beginning and then it looks like trace
+
+ align:start position:0%
+beginning and then it looks like trace
+ 
+
+ align:start position:0%
+beginning and then it looks like trace
+of a inverse da a inverse da
+
+ align:start position:0%
+of a inverse da a inverse da
+ 
+
+ align:start position:0%
+of a inverse da a inverse da
+Prime right so this
+
+ align:start position:0%
+Prime right so this
+ 
+
+ align:start position:0%
+Prime right so this
+is this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+symmetric uh
+
+ align:start position:0%
+symmetric uh
+ 
+
+ align:start position:0%
+symmetric uh
+using this cyclic property of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+trace
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's it this is this this doesn't
+
+ align:start position:0%
+that's it this is this this doesn't
+ 
+
+ align:start position:0%
+that's it this is this this doesn't
+simplify into we can't write it as a
+
+ align:start position:0%
+simplify into we can't write it as a
+ 
+
+ align:start position:0%
+simplify into we can't write it as a
+Hessian matrix unless I vectorize things
+
+ align:start position:0%
+Hessian matrix unless I vectorize things
+ 
+
+ align:start position:0%
+Hessian matrix unless I vectorize things
+okay so if I if I if I do VC of d da
+
+ align:start position:0%
+okay so if I if I if I do VC of d da
+ 
+
+ align:start position:0%
+okay so if I if I if I do VC of d da
+right this this could be some big Matrix
+
+ align:start position:0%
+right this this could be some big Matrix
+ 
+
+ align:start position:0%
+right this this could be some big Matrix
+and and squ by yeah it's n s by n s
+
+ align:start position:0%
+and and squ by yeah it's n s by n s
+ 
+
+ align:start position:0%
+and and squ by yeah it's n s by n s
+Matrix right that has a VEC of Da on one
+
+ align:start position:0%
+Matrix right that has a VEC of Da on one
+ 
+
+ align:start position:0%
+Matrix right that has a VEC of Da on one
+side and VEC of Da Prime on the other
+
+ align:start position:0%
+side and VEC of Da Prime on the other
+ 
+
+ align:start position:0%
+side and VEC of Da Prime on the other
+side but it's it's not very natural to
+
+ align:start position:0%
+side but it's it's not very natural to
+ 
+
+ align:start position:0%
+side but it's it's not very natural to
+do that and see in some ways it's easier
+
+ align:start position:0%
+do that and see in some ways it's easier
+ 
+
+ align:start position:0%
+do that and see in some ways it's easier
+to do this okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so so let's I want to talk a little bit
+
+ align:start position:0%
+so so let's I want to talk a little bit
+ 
+
+ align:start position:0%
+so so let's I want to talk a little bit
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um now why second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivatives and of course they come up
+
+ align:start position:0%
+derivatives and of course they come up
+ 
+
+ align:start position:0%
+derivatives and of course they come up
+in lots of cases right but but let me
+
+ align:start position:0%
+in lots of cases right but but let me
+ 
+
+ align:start position:0%
+in lots of cases right but but let me
+just mention a few Salient things so
+
+ align:start position:0%
+just mention a few Salient things so
+ 
+
+ align:start position:0%
+just mention a few Salient things so
+first of all they give you the the the
+
+ align:start position:0%
+first of all they give you the the the
+ 
+
+ align:start position:0%
+first of all they give you the the the
+first Der of give you a linear
+
+ align:start position:0%
+first Der of give you a linear
+ 
+
+ align:start position:0%
+first Der of give you a linear
+approximation of a function
+
+ align:start position:0%
+approximation of a function
+ 
+
+ align:start position:0%
+approximation of a function
+linearization this the second
+
+ align:start position:0%
+linearization this the second
+ 
+
+ align:start position:0%
+linearization this the second
+derivatives give you quadratic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximations right so if you have
+
+ align:start position:0%
+approximations right so if you have
+ 
+
+ align:start position:0%
+approximations right so if you have
+f of x plus little a little change let's
+
+ align:start position:0%
+f of x plus little a little change let's
+ 
+
+ align:start position:0%
+f of x plus little a little change let's
+call it Delta X that's not it's not
+
+ align:start position:0%
+call it Delta X that's not it's not
+ 
+
+ align:start position:0%
+call it Delta X that's not it's not
+infinite decimal anymore so this is
+
+ align:start position:0%
+infinite decimal anymore so this is
+ 
+
+ align:start position:0%
+infinite decimal anymore so this is
+going to be an
+
+ align:start position:0%
+going to be an
+ 
+
+ align:start position:0%
+going to be an
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+this is approximately f
+
+ align:start position:0%
+this is approximately f
+ 
+
+ align:start position:0%
+this is approximately f
+ofx plus frime of X Delta X that's our
+
+ align:start position:0%
+ofx plus frime of X Delta X that's our
+ 
+
+ align:start position:0%
+ofx plus frime of X Delta X that's our
+linear approximation from the first
+
+ align:start position:0%
+linear approximation from the first
+ 
+
+ align:start position:0%
+linear approximation from the first
+derivative or finite difference
+
+ align:start position:0%
+derivative or finite difference
+ 
+
+ align:start position:0%
+derivative or finite difference
+approximation if you think of it and now
+
+ align:start position:0%
+approximation if you think of it and now
+ 
+
+ align:start position:0%
+approximation if you think of it and now
+there'll be a new
+
+ align:start position:0%
+there'll be a new
+ 
+
+ align:start position:0%
+there'll be a new
+term that'll look like f Prim of X with
+
+ align:start position:0%
+term that'll look like f Prim of X with
+ 
+
+ align:start position:0%
+term that'll look like f Prim of X with
+a Delta x a Delta
+
+ align:start position:0%
+a Delta x a Delta
+ 
+
+ align:start position:0%
+a Delta x a Delta
+X and I'm missing something what am I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+missing
+
+ align:start position:0%
+missing
+ 
+
+ align:start position:0%
+missing
+just think of 1801 Taylor
+
+ align:start position:0%
+just think of 1801 Taylor
+ 
+
+ align:start position:0%
+just think of 1801 Taylor
+series there's a half yeah right and
+
+ align:start position:0%
+series there's a half yeah right and
+ 
+
+ align:start position:0%
+series there's a half yeah right and
+then and then and then and then there's
+
+ align:start position:0%
+then and then and then and then there's
+ 
+
+ align:start position:0%
+then and then and then and then there's
+higher order terms little low of Delta
+
+ align:start position:0%
+higher order terms little low of Delta
+ 
+
+ align:start position:0%
+higher order terms little low of Delta
+X squar right we're dropping terms so
+
+ align:start position:0%
+X squar right we're dropping terms so
+ 
+
+ align:start position:0%
+X squar right we're dropping terms so
+we're dropping terms that are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+smaller than
+
+ align:start position:0%
+smaller than
+ 
+
+ align:start position:0%
+smaller than
+quadratic all right so if it's if it's
+
+ align:start position:0%
+quadratic all right so if it's if it's
+ 
+
+ align:start position:0%
+quadratic all right so if it's if it's
+three times differentiable we're
+
+ align:start position:0%
+three times differentiable we're
+ 
+
+ align:start position:0%
+three times differentiable we're
+dropping cubic terms but maybe the
+
+ align:start position:0%
+dropping cubic terms but maybe the
+ 
+
+ align:start position:0%
+dropping cubic terms but maybe the
+function doesn't have at their
+
+ align:start position:0%
+function doesn't have at their
+ 
+
+ align:start position:0%
+function doesn't have at their
+derivative but definitely what we're
+
+ align:start position:0%
+derivative but definitely what we're
+ 
+
+ align:start position:0%
+derivative but definitely what we're
+dropping are are terms that are higher
+
+ align:start position:0%
+dropping are are terms that are higher
+ 
+
+ align:start position:0%
+dropping are are terms that are higher
+than quadratic so the
+
+ align:start position:0%
+than quadratic so the
+ 
+
+ align:start position:0%
+than quadratic so the
+1/2 you can you can derive this pretty
+
+ align:start position:0%
+1/2 you can you can derive this pretty
+ 
+
+ align:start position:0%
+1/2 you can you can derive this pretty
+easily by just just if you if if you
+
+ align:start position:0%
+easily by just just if you if if you
+ 
+
+ align:start position:0%
+easily by just just if you if if you
+take two derivatives of this you'd
+
+ align:start position:0%
+take two derivatives of this you'd
+ 
+
+ align:start position:0%
+take two derivatives of this you'd
+better get back to F Prime F Prime right
+
+ align:start position:0%
+better get back to F Prime F Prime right
+ 
+
+ align:start position:0%
+better get back to F Prime F Prime right
+it's better had a better match the
+
+ align:start position:0%
+it's better had a better match the
+ 
+
+ align:start position:0%
+it's better had a better match the
+second derivative but because DX appears
+
+ align:start position:0%
+second derivative but because DX appears
+ 
+
+ align:start position:0%
+second derivative but because DX appears
+twice in this then uh if you take two
+
+ align:start position:0%
+twice in this then uh if you take two
+ 
+
+ align:start position:0%
+twice in this then uh if you take two
+der to Delta X sorry you should get you
+
+ align:start position:0%
+der to Delta X sorry you should get you
+ 
+
+ align:start position:0%
+der to Delta X sorry you should get you
+should get back to f F Prim and but
+
+ align:start position:0%
+should get back to f F Prim and but
+ 
+
+ align:start position:0%
+should get back to f F Prim and but
+because Delta X appears twice in this
+
+ align:start position:0%
+because Delta X appears twice in this
+ 
+
+ align:start position:0%
+because Delta X appears twice in this
+you need to have a half there um in
+
+ align:start position:0%
+you need to have a half there um in
+ 
+
+ align:start position:0%
+you need to have a half there um in
+order to get back to F Prime so if we
+
+ align:start position:0%
+order to get back to F Prime so if we
+ 
+
+ align:start position:0%
+order to get back to F Prime so if we
+take let me just write that in so if we
+
+ align:start position:0%
+take let me just write that in so if we
+ 
+
+ align:start position:0%
+take let me just write that in so if we
+take okay the second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+derivative with
+
+ align:start position:0%
+derivative with
+ 
+
+ align:start position:0%
+derivative with
+respect to Delta X you had better get
+
+ align:start position:0%
+respect to Delta X you had better get
+ 
+
+ align:start position:0%
+respect to Delta X you had better get
+back to fpre of X and that 1/ half
+
+ align:start position:0%
+back to fpre of X and that 1/ half
+ 
+
+ align:start position:0%
+back to fpre of X and that 1/ half
+factor is is is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+necessary because it appears twice so
+
+ align:start position:0%
+necessary because it appears twice so
+ 
+
+ align:start position:0%
+necessary because it appears twice so
+otherwise you you'd see it get twice
+
+ align:start position:0%
+otherwise you you'd see it get twice
+ 
+
+ align:start position:0%
+otherwise you you'd see it get twice
+just like if you you know for the same
+
+ align:start position:0%
+just like if you you know for the same
+ 
+
+ align:start position:0%
+just like if you you know for the same
+same reason you have it in the Taylor
+
+ align:start position:0%
+same reason you have it in the Taylor
+ 
+
+ align:start position:0%
+same reason you have it in the Taylor
+series right if these are just scalers
+
+ align:start position:0%
+series right if these are just scalers
+ 
+
+ align:start position:0%
+series right if these are just scalers
+right when I take this this is a Delta x
+
+ align:start position:0%
+right when I take this this is a Delta x
+ 
+
+ align:start position:0%
+right when I take this this is a Delta x
+squared when I take the second
+
+ align:start position:0%
+squared when I take the second
+ 
+
+ align:start position:0%
+squared when I take the second
+derivative I'm going to get a two and if
+
+ align:start position:0%
+derivative I'm going to get a two and if
+ 
+
+ align:start position:0%
+derivative I'm going to get a two and if
+I really wanted to match the second
+
+ align:start position:0%
+I really wanted to match the second
+ 
+
+ align:start position:0%
+I really wanted to match the second
+derivative if you know of my function at
+
+ align:start position:0%
+derivative if you know of my function at
+ 
+
+ align:start position:0%
+derivative if you know of my function at
+that point so okay so you know linear
+
+ align:start position:0%
+that point so okay so you know linear
+ 
+
+ align:start position:0%
+that point so okay so you know linear
+approximating things by the things is
+
+ align:start position:0%
+approximating things by the things is
+ 
+
+ align:start position:0%
+approximating things by the things is
+useful approxim things like quadratic
+
+ align:start position:0%
+useful approxim things like quadratic
+ 
+
+ align:start position:0%
+useful approxim things like quadratic
+functions is useful so for example um if
+
+ align:start position:0%
+functions is useful so for example um if
+ 
+
+ align:start position:0%
+functions is useful so for example um if
+you're doing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+optimization right we approximate uh
+
+ align:start position:0%
+optimization right we approximate uh
+ 
+
+ align:start position:0%
+optimization right we approximate uh
+f f uh by approximately a
+
+ align:start position:0%
+f f uh by approximately a
+ 
+
+ align:start position:0%
+f f uh by approximately a
+quadratic and then optimiz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quadratic to get a
+
+ align:start position:0%
+quadratic to get a
+ 
+
+ align:start position:0%
+quadratic to get a
+step a
+
+ align:start position:0%
+step a
+ 
+
+ align:start position:0%
+step a
+step this is sometimes called this has a
+
+ align:start position:0%
+step this is sometimes called this has a
+ 
+
+ align:start position:0%
+step this is sometimes called this has a
+variety of names it's sometimes called
+
+ align:start position:0%
+variety of names it's sometimes called
+ 
+
+ align:start position:0%
+variety of names it's sometimes called
+sequential quadratic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+programming or or
+
+ align:start position:0%
+programming or or
+ 
+
+ align:start position:0%
+programming or or
+sqp technically you you should also if
+
+ align:start position:0%
+sqp technically you you should also if
+ 
+
+ align:start position:0%
+sqp technically you you should also if
+you if you have constraints you
+
+ align:start position:0%
+you if you have constraints you
+ 
+
+ align:start position:0%
+you if you have constraints you
+take you you make linear approximations
+
+ align:start position:0%
+take you you make linear approximations
+ 
+
+ align:start position:0%
+take you you make linear approximations
+of the
+
+ align:start position:0%
+of the
+ 
+
+ align:start position:0%
+of the
+constraints or I guess uh aine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximations but it's colloquially
+
+ align:start position:0%
+approximations but it's colloquially
+ 
+
+ align:start position:0%
+approximations but it's colloquially
+it's called linear
+
+ align:start position:0%
+it's called linear
+ 
+
+ align:start position:0%
+it's called linear
+approximations a
+
+ align:start position:0%
+approximations a
+ 
+
+ align:start position:0%
+approximations a
+prod of
+
+ align:start position:0%
+prod of
+ 
+
+ align:start position:0%
+prod of
+constraints so if you have a arbit
+
+ align:start position:0%
+constraints so if you have a arbit
+ 
+
+ align:start position:0%
+constraints so if you have a arbit
+minimizing an arbitrary nonlinear
+
+ align:start position:0%
+minimizing an arbitrary nonlinear
+ 
+
+ align:start position:0%
+minimizing an arbitrary nonlinear
+function arbitrary con nonlinear
+
+ align:start position:0%
+function arbitrary con nonlinear
+ 
+
+ align:start position:0%
+function arbitrary con nonlinear
+constraints right um that's hard but if
+
+ align:start position:0%
+constraints right um that's hard but if
+ 
+
+ align:start position:0%
+constraints right um that's hard but if
+you approximate the function by a
+
+ align:start position:0%
+you approximate the function by a
+ 
+
+ align:start position:0%
+you approximate the function by a
+quadratic function using a second
+
+ align:start position:0%
+quadratic function using a second
+ 
+
+ align:start position:0%
+quadratic function using a second
+derivative approximate the constraints
+
+ align:start position:0%
+derivative approximate the constraints
+ 
+
+ align:start position:0%
+derivative approximate the constraints
+by linear that's called a QP or
+
+ align:start position:0%
+by linear that's called a QP or
+ 
+
+ align:start position:0%
+by linear that's called a QP or
+quadratic program and there are there
+
+ align:start position:0%
+quadratic program and there are there
+ 
+
+ align:start position:0%
+quadratic program and there are there
+are you know good methods to solve those
+
+ align:start position:0%
+are you know good methods to solve those
+ 
+
+ align:start position:0%
+are you know good methods to solve those
+kinds of things right
+
+ align:start position:0%
+kinds of things right
+ 
+
+ align:start position:0%
+kinds of things right
+um another equivalent
+
+ align:start position:0%
+um another equivalent
+ 
+
+ align:start position:0%
+um another equivalent
+equivalently optimizing a quadratic
+
+ align:start position:0%
+equivalently optimizing a quadratic
+ 
+
+ align:start position:0%
+equivalently optimizing a quadratic
+function is the same thing is uh you
+
+ align:start position:0%
+function is the same thing is uh you
+ 
+
+ align:start position:0%
+function is the same thing is uh you
+know so optimizing a function is equal
+
+ align:start position:0%
+know so optimizing a function is equal
+ 
+
+ align:start position:0%
+know so optimizing a function is equal
+to finding locally to finding you know a
+
+ align:start position:0%
+to finding locally to finding you know a
+ 
+
+ align:start position:0%
+to finding locally to finding you know a
+root of the gradient right so we're
+
+ align:start position:0%
+root of the gradient right so we're
+ 
+
+ align:start position:0%
+root of the gradient right so we're
+equivalently
+
+ align:start position:0%
+equivalently
+ 
+
+ align:start position:0%
+equivalently
+finding a root of the gradient of F and
+
+ align:start position:0%
+finding a root of the gradient of F and
+ 
+
+ align:start position:0%
+finding a root of the gradient of F and
+you're going to approximate it by a
+
+ align:start position:0%
+you're going to approximate it by a
+ 
+
+ align:start position:0%
+you're going to approximate it by a
+linear you know by an
+
+ align:start position:0%
+linear you know by an
+ 
+
+ align:start position:0%
+linear you know by an
+Aline by
+
+ align:start position:0%
+Aline by
+ 
+
+ align:start position:0%
+Aline by
+by right because if I but you know or
+
+ align:start position:0%
+by right because if I but you know or
+ 
+
+ align:start position:0%
+by right because if I but you know or
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+linear colloquially linear right right
+
+ align:start position:0%
+linear colloquially linear right right
+ 
+
+ align:start position:0%
+linear colloquially linear right right
+because because you equivalently you're
+
+ align:start position:0%
+because because you equivalently you're
+ 
+
+ align:start position:0%
+because because you equivalently you're
+approximating it by FR Prime of X Plus
+
+ align:start position:0%
+approximating it by FR Prime of X Plus
+ 
+
+ align:start position:0%
+approximating it by FR Prime of X Plus
+um plus your F primed of x uh you know
+
+ align:start position:0%
+um plus your F primed of x uh you know
+ 
+
+ align:start position:0%
+um plus your F primed of x uh you know
+Delta
+
+ align:start position:0%
+Delta
+ 
+
+ align:start position:0%
+Delta
+X
+
+ align:start position:0%
+X
+ 
+
+ align:start position:0%
+X
+right and so if you're finding a root of
+
+ align:start position:0%
+right and so if you're finding a root of
+ 
+
+ align:start position:0%
+right and so if you're finding a root of
+a linear
+
+ align:start position:0%
+a linear
+ 
+
+ align:start position:0%
+a linear
+function you have non trying to find the
+
+ align:start position:0%
+function you have non trying to find the
+ 
+
+ align:start position:0%
+function you have non trying to find the
+root of a nonlinear function grad F and
+
+ align:start position:0%
+root of a nonlinear function grad F and
+ 
+
+ align:start position:0%
+root of a nonlinear function grad F and
+you approximate it by a linear thing and
+
+ align:start position:0%
+you approximate it by a linear thing and
+ 
+
+ align:start position:0%
+you approximate it by a linear thing and
+you find a root of that what's the name
+
+ align:start position:0%
+you find a root of that what's the name
+ 
+
+ align:start position:0%
+you find a root of that what's the name
+for that
+
+ align:start position:0%
+for that
+ 
+
+ align:start position:0%
+for that
+method Newton's method so this is just
+
+ align:start position:0%
+method Newton's method so this is just
+ 
+
+ align:start position:0%
+method Newton's method so this is just
+Newton's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method right and uh so in in
+
+ align:start position:0%
+method right and uh so in in
+ 
+
+ align:start position:0%
+method right and uh so in in
+practice uh finding the
+
+ align:start position:0%
+practice uh finding the
+ 
+
+ align:start position:0%
+practice uh finding the
+Hessian or finding the the F Prime uh um
+
+ align:start position:0%
+Hessian or finding the the F Prime uh um
+ 
+
+ align:start position:0%
+Hessian or finding the the F Prime uh um
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+or or the Hessian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix is is often
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expensive if you have if F ofx again
+
+ align:start position:0%
+expensive if you have if F ofx again
+ 
+
+ align:start position:0%
+expensive if you have if F ofx again
+takes a a a a RN to a
+
+ align:start position:0%
+takes a a a a RN to a
+ 
+
+ align:start position:0%
+takes a a a a RN to a
+scaler then um H is an N byn
+
+ align:start position:0%
+scaler then um H is an N byn
+ 
+
+ align:start position:0%
+scaler then um H is an N byn
+Matrix and this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+huge if n is large l so if you have a
+
+ align:start position:0%
+huge if n is large l so if you have a
+ 
+
+ align:start position:0%
+huge if n is large l so if you have a
+neural network with aill is a billion
+
+ align:start position:0%
+neural network with aill is a billion
+ 
+
+ align:start position:0%
+neural network with aill is a billion
+the Hassan is a billion by million
+
+ align:start position:0%
+the Hassan is a billion by million
+ 
+
+ align:start position:0%
+the Hassan is a billion by million
+Matrix you can't even store this Matrix
+
+ align:start position:0%
+Matrix you can't even store this Matrix
+ 
+
+ align:start position:0%
+Matrix you can't even store this Matrix
+much less comput it so it's it's it's
+
+ align:start position:0%
+much less comput it so it's it's it's
+ 
+
+ align:start position:0%
+much less comput it so it's it's it's
+it's hard to get exactly for in in I
+
+ align:start position:0%
+it's hard to get exactly for in in I
+ 
+
+ align:start position:0%
+it's hard to get exactly for in in I
+guess say in high
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dimensions so often what you try and do
+
+ align:start position:0%
+Dimensions so often what you try and do
+ 
+
+ align:start position:0%
+Dimensions so often what you try and do
+is you try and
+
+ align:start position:0%
+is you try and
+ 
+
+ align:start position:0%
+is you try and
+approximate if you don't want to give up
+
+ align:start position:0%
+approximate if you don't want to give up
+ 
+
+ align:start position:0%
+approximate if you don't want to give up
+on it entirely you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+approximate the
+
+ align:start position:0%
+approximate the
+ 
+
+ align:start position:0%
+approximate the
+Hessian uh uh in various
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ways
+
+ align:start position:0%
+ways
+ 
+
+ align:start position:0%
+ways
+and so these these give you rise to a
+
+ align:start position:0%
+and so these these give you rise to a
+ 
+
+ align:start position:0%
+and so these these give you rise to a
+variety of methods called quasi Newton
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methods uh
+
+ align:start position:0%
+methods uh
+ 
+
+ align:start position:0%
+methods uh
+methods that the most famous of which is
+
+ align:start position:0%
+methods that the most famous of which is
+ 
+
+ align:start position:0%
+methods that the most famous of which is
+called the bfgs method which is like
+
+ align:start position:0%
+called the bfgs method which is like
+ 
+
+ align:start position:0%
+called the bfgs method which is like
+Bren Fletcher goldb and Shannon I think
+
+ align:start position:0%
+Bren Fletcher goldb and Shannon I think
+ 
+
+ align:start position:0%
+Bren Fletcher goldb and Shannon I think
+it's named after four people who
+
+ align:start position:0%
+it's named after four people who
+ 
+
+ align:start position:0%
+it's named after four people who
+amusingly discovered the same thing in
+
+ align:start position:0%
+amusingly discovered the same thing in
+ 
+
+ align:start position:0%
+amusingly discovered the same thing in
+the same year independently like there's
+
+ align:start position:0%
+the same year independently like there's
+ 
+
+ align:start position:0%
+the same year independently like there's
+like there's three three or four
+
+ align:start position:0%
+like there's three three or four
+ 
+
+ align:start position:0%
+like there's three three or four
+separate
+
+ align:start position:0%
+separate
+ 
+
+ align:start position:0%
+separate
+papers on the same thing there there's
+
+ align:start position:0%
+papers on the same thing there there's
+ 
+
+ align:start position:0%
+papers on the same thing there there's
+also a closely related method called uh
+
+ align:start position:0%
+also a closely related method called uh
+ 
+
+ align:start position:0%
+also a closely related method called uh
+Newton kroff
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+methods
+
+ align:start position:0%
+methods
+ 
+
+ align:start position:0%
+methods
+right and so forth so you know I don't
+
+ align:start position:0%
+right and so forth so you know I don't
+ 
+
+ align:start position:0%
+right and so forth so you know I don't
+don't have time to explain all these
+
+ align:start position:0%
+don't have time to explain all these
+ 
+
+ align:start position:0%
+don't have time to explain all these
+things but you know this
+
+ align:start position:0%
+things but you know this
+ 
+
+ align:start position:0%
+things but you know this
+is these are some key wordss if you ever
+
+ align:start position:0%
+is these are some key wordss if you ever
+ 
+
+ align:start position:0%
+is these are some key wordss if you ever
+need to do this so you know Hessians are
+
+ align:start position:0%
+need to do this so you know Hessians are
+ 
+
+ align:start position:0%
+need to do this so you know Hessians are
+useful for small n you can compute them
+
+ align:start position:0%
+useful for small n you can compute them
+ 
+
+ align:start position:0%
+useful for small n you can compute them
+explicitly by even automatic
+
+ align:start position:0%
+explicitly by even automatic
+ 
+
+ align:start position:0%
+explicitly by even automatic
+differentiation can get hens for you but
+
+ align:start position:0%
+differentiation can get hens for you but
+ 
+
+ align:start position:0%
+differentiation can get hens for you but
+for big ends you can't even store it
+
+ align:start position:0%
+for big ends you can't even store it
+ 
+
+ align:start position:0%
+for big ends you can't even store it
+much less compute it so then there are
+
+ align:start position:0%
+much less compute it so then there are
+ 
+
+ align:start position:0%
+much less compute it so then there are
+ways to kind of and it's a really
+
+ align:start position:0%
+ways to kind of and it's a really
+ 
+
+ align:start position:0%
+ways to kind of and it's a really
+intricate problem to approximate
+
+ align:start position:0%
+intricate problem to approximate
+ 
+
+ align:start position:0%
+intricate problem to approximate
+Hessians or you can you can compute the
+
+ align:start position:0%
+Hessians or you can you can compute the
+ 
+
+ align:start position:0%
+Hessians or you can you can compute the
+hessan times in a particular direction
+
+ align:start position:0%
+hessan times in a particular direction
+ 
+
+ align:start position:0%
+hessan times in a particular direction
+quickly like aian times a operated on a
+
+ align:start position:0%
+quickly like aian times a operated on a
+ 
+
+ align:start position:0%
+quickly like aian times a operated on a
+DX that that you can get quickly
+
+ align:start position:0%
+DX that that you can get quickly
+ 
+
+ align:start position:0%
+DX that that you can get quickly
+um but um yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
\ No newline at end of file
diff --git a/QcUUGlsSXmY.txt b/QcUUGlsSXmY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..66dd7ef174430a66150d86f2a1ffb67f47db569f
--- /dev/null
+++ b/QcUUGlsSXmY.txt
@@ -0,0 +1,11675 @@
+align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's get started today first of all
+
+ align:start position:0%
+so let's get started today first of all
+ 
+
+ align:start position:0%
+so let's get started today first of all
+are there any questions from last time
+
+ align:start position:0%
+are there any questions from last time
+ 
+
+ align:start position:0%
+are there any questions from last time
+all right so please feel free to ask
+
+ align:start position:0%
+all right so please feel free to ask
+ 
+
+ align:start position:0%
+all right so please feel free to ask
+questions along the way in terms of the
+
+ align:start position:0%
+questions along the way in terms of the
+ 
+
+ align:start position:0%
+questions along the way in terms of the
+reading list for up to lecture nine
+
+ align:start position:0%
+reading list for up to lecture nine
+ 
+
+ align:start position:0%
+reading list for up to lecture nine
+today we're sharing with production it's
+
+ align:start position:0%
+today we're sharing with production it's
+ 
+
+ align:start position:0%
+today we're sharing with production it's
+our second lecture on applications there
+
+ align:start position:0%
+our second lecture on applications there
+ 
+
+ align:start position:0%
+our second lecture on applications there
+are two starred papers and we're going
+
+ align:start position:0%
+are two starred papers and we're going
+ 
+
+ align:start position:0%
+are two starred papers and we're going
+to be going through the first one with
+
+ align:start position:0%
+to be going through the first one with
+ 
+
+ align:start position:0%
+to be going through the first one with
+some Panther Rock and some detail and
+
+ align:start position:0%
+some Panther Rock and some detail and
+ 
+
+ align:start position:0%
+some Panther Rock and some detail and
+then a few selected slides on the Canon
+
+ align:start position:0%
+then a few selected slides on the Canon
+ 
+
+ align:start position:0%
+then a few selected slides on the Canon
+at Al paper but like all starred papers
+
+ align:start position:0%
+at Al paper but like all starred papers
+ 
+
+ align:start position:0%
+at Al paper but like all starred papers
+I hope you will be reading them because
+
+ align:start position:0%
+I hope you will be reading them because
+ 
+
+ align:start position:0%
+I hope you will be reading them because
+I know you're very well trained now and
+
+ align:start position:0%
+I know you're very well trained now and
+ 
+
+ align:start position:0%
+I know you're very well trained now and
+you will be able to read those articles
+
+ align:start position:0%
+you will be able to read those articles
+ 
+
+ align:start position:0%
+you will be able to read those articles
+so think you would get a lot out of it
+
+ align:start position:0%
+so think you would get a lot out of it
+ 
+
+ align:start position:0%
+so think you would get a lot out of it
+but we will cover most of it today
+
+ align:start position:0%
+but we will cover most of it today
+ 
+
+ align:start position:0%
+but we will cover most of it today
+the other thing
+
+ align:start position:0%
+the other thing
+ 
+
+ align:start position:0%
+the other thing
+for the study guide
+
+ align:start position:0%
+for the study guide
+ 
+
+ align:start position:0%
+for the study guide
+so let me ask you guys some
+
+ align:start position:0%
+so let me ask you guys some
+ 
+
+ align:start position:0%
+so let me ask you guys some
+questions
+
+ align:start position:0%
+questions
+ 
+
+ align:start position:0%
+questions
+last time was our first applied lecture
+
+ align:start position:0%
+last time was our first applied lecture
+ 
+
+ align:start position:0%
+last time was our first applied lecture
+on resharing we did it in both Village
+
+ align:start position:0%
+on resharing we did it in both Village
+ 
+
+ align:start position:0%
+on resharing we did it in both Village
+India and medieval villages
+
+ align:start position:0%
+India and medieval villages
+ 
+
+ align:start position:0%
+India and medieval villages
+and today I want to
+
+ align:start position:0%
+and today I want to
+ 
+
+ align:start position:0%
+and today I want to
+give a little bit more emphasis to the
+
+ align:start position:0%
+give a little bit more emphasis to the
+ 
+
+ align:start position:0%
+give a little bit more emphasis to the
+economics combined with the analysis
+
+ align:start position:0%
+economics combined with the analysis
+ 
+
+ align:start position:0%
+economics combined with the analysis
+more than I usually do but it seems like
+
+ align:start position:0%
+more than I usually do but it seems like
+ 
+
+ align:start position:0%
+more than I usually do but it seems like
+the time to do that since we're talking
+
+ align:start position:0%
+the time to do that since we're talking
+ 
+
+ align:start position:0%
+the time to do that since we're talking
+about applications
+
+ align:start position:0%
+about applications
+ 
+
+ align:start position:0%
+about applications
+so the first one I picked here
+
+ align:start position:0%
+so the first one I picked here
+ 
+
+ align:start position:0%
+so the first one I picked here
+describing words why villages in India
+
+ align:start position:0%
+describing words why villages in India
+ 
+
+ align:start position:0%
+describing words why villages in India
+are a risky place
+
+ align:start position:0%
+are a risky place
+ 
+
+ align:start position:0%
+are a risky place
+how to quantify that risk and its
+
+ align:start position:0%
+how to quantify that risk and its
+ 
+
+ align:start position:0%
+how to quantify that risk and its
+sources
+
+ align:start position:0%
+sources
+ 
+
+ align:start position:0%
+sources
+and how that risk might be mitigated or
+
+ align:start position:0%
+and how that risk might be mitigated or
+ 
+
+ align:start position:0%
+and how that risk might be mitigated or
+potentially
+
+ align:start position:0%
+potentially
+ 
+
+ align:start position:0%
+potentially
+well mitigated via individual or social
+
+ align:start position:0%
+well mitigated via individual or social
+ 
+
+ align:start position:0%
+well mitigated via individual or social
+diversification
+
+ align:start position:0%
+diversification
+ 
+
+ align:start position:0%
+diversification
+so I have lately been taking
+
+ align:start position:0%
+so I have lately been taking
+ 
+
+ align:start position:0%
+so I have lately been taking
+volunteers uh but let me ask Dixon do
+
+ align:start position:0%
+volunteers uh but let me ask Dixon do
+ 
+
+ align:start position:0%
+volunteers uh but let me ask Dixon do
+you want to take a stab at that
+
+ align:start position:0%
+you want to take a stab at that
+ 
+
+ align:start position:0%
+you want to take a stab at that
+yeah sure uh so Villages are a risky
+
+ align:start position:0%
+yeah sure uh so Villages are a risky
+ 
+
+ align:start position:0%
+yeah sure uh so Villages are a risky
+place because
+
+ align:start position:0%
+place because
+ 
+
+ align:start position:0%
+place because
+um it's mostly Agriculture and it's not
+
+ align:start position:0%
+um it's mostly Agriculture and it's not
+ 
+
+ align:start position:0%
+um it's mostly Agriculture and it's not
+a stable source of income
+
+ align:start position:0%
+a stable source of income
+ 
+
+ align:start position:0%
+a stable source of income
+and I think we can quantify that risk by
+
+ align:start position:0%
+and I think we can quantify that risk by
+ 
+
+ align:start position:0%
+and I think we can quantify that risk by
+just looking at like the variation
+
+ align:start position:0%
+just looking at like the variation
+ 
+
+ align:start position:0%
+just looking at like the variation
+through the years and how it like really
+
+ align:start position:0%
+through the years and how it like really
+ 
+
+ align:start position:0%
+through the years and how it like really
+changes
+
+ align:start position:0%
+changes
+ 
+
+ align:start position:0%
+changes
+um and how a lot of things are like
+
+ align:start position:0%
+um and how a lot of things are like
+ 
+
+ align:start position:0%
+um and how a lot of things are like
+linked with each other in terms of their
+
+ align:start position:0%
+linked with each other in terms of their
+ 
+
+ align:start position:0%
+linked with each other in terms of their
+risk and it can be mitigated by
+
+ align:start position:0%
+risk and it can be mitigated by
+ 
+
+ align:start position:0%
+risk and it can be mitigated by
+um like
+
+ align:start position:0%
+um like
+ 
+
+ align:start position:0%
+um like
+planting different kinds of like plants
+
+ align:start position:0%
+planting different kinds of like plants
+ 
+
+ align:start position:0%
+planting different kinds of like plants
+or like
+
+ align:start position:0%
+or like
+ 
+
+ align:start position:0%
+or like
+um planting like far apart that's
+
+ align:start position:0%
+um planting like far apart that's
+ 
+
+ align:start position:0%
+um planting like far apart that's
+individually in Social diversification
+
+ align:start position:0%
+individually in Social diversification
+ 
+
+ align:start position:0%
+individually in Social diversification
+like giving gifts or transfers
+
+ align:start position:0%
+like giving gifts or transfers
+ 
+
+ align:start position:0%
+like giving gifts or transfers
+come on yeah
+
+ align:start position:0%
+come on yeah
+ 
+
+ align:start position:0%
+come on yeah
+very very good answer
+
+ align:start position:0%
+very very good answer
+ 
+
+ align:start position:0%
+very very good answer
+thank you so
+
+ align:start position:0%
+thank you so
+ 
+
+ align:start position:0%
+thank you so
+yeah we Quantified the risk by the
+
+ align:start position:0%
+yeah we Quantified the risk by the
+ 
+
+ align:start position:0%
+yeah we Quantified the risk by the
+coefficient of variation of a given crop
+
+ align:start position:0%
+coefficient of variation of a given crop
+ 
+
+ align:start position:0%
+coefficient of variation of a given crop
+or a given crop in a certain soil type
+
+ align:start position:0%
+or a given crop in a certain soil type
+ 
+
+ align:start position:0%
+or a given crop in a certain soil type
+or a certain
+
+ align:start position:0%
+or a certain
+ 
+
+ align:start position:0%
+or a certain
+income source
+
+ align:start position:0%
+income source
+ 
+
+ align:start position:0%
+income source
+just to add a few more details your
+
+ align:start position:0%
+just to add a few more details your
+ 
+
+ align:start position:0%
+just to add a few more details your
+answer was fine
+
+ align:start position:0%
+answer was fine
+ 
+
+ align:start position:0%
+answer was fine
+the the covariance across those things
+
+ align:start position:0%
+the the covariance across those things
+ 
+
+ align:start position:0%
+the the covariance across those things
+actually helps mitigate the risk and
+
+ align:start position:0%
+actually helps mitigate the risk and
+ 
+
+ align:start position:0%
+actually helps mitigate the risk and
+that's what you're saying when you to
+
+ align:start position:0%
+that's what you're saying when you to
+ 
+
+ align:start position:0%
+that's what you're saying when you to
+different crops or different spots on
+
+ align:start position:0%
+different crops or different spots on
+ 
+
+ align:start position:0%
+different crops or different spots on
+the field
+
+ align:start position:0%
+the field
+ 
+
+ align:start position:0%
+the field
+those are ex-antees so there's like
+
+ align:start position:0%
+those are ex-antees so there's like
+ 
+
+ align:start position:0%
+those are ex-antees so there's like
+individual
+
+ align:start position:0%
+individual
+ 
+
+ align:start position:0%
+individual
+things that people can do and the expose
+
+ align:start position:0%
+things that people can do and the expose
+ 
+
+ align:start position:0%
+things that people can do and the expose
+social diversification is the gifts
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+next one comparing incomes over
+
+ align:start position:0%
+next one comparing incomes over
+ 
+
+ align:start position:0%
+next one comparing incomes over
+households and time
+
+ align:start position:0%
+households and time
+ 
+
+ align:start position:0%
+households and time
+with consumption over households in time
+
+ align:start position:0%
+with consumption over households in time
+ 
+
+ align:start position:0%
+with consumption over households in time
+what can you infer from the data alone
+
+ align:start position:0%
+what can you infer from the data alone
+ 
+
+ align:start position:0%
+what can you infer from the data alone
+so let me stop there and not read the
+
+ align:start position:0%
+so let me stop there and not read the
+ 
+
+ align:start position:0%
+so let me stop there and not read the
+second part
+
+ align:start position:0%
+second part
+ 
+
+ align:start position:0%
+second part
+let's see who would like to
+
+ align:start position:0%
+let's see who would like to
+ 
+
+ align:start position:0%
+let's see who would like to
+Charles do you want to take a stab at
+
+ align:start position:0%
+Charles do you want to take a stab at
+ 
+
+ align:start position:0%
+Charles do you want to take a stab at
+that are you there yeah
+
+ align:start position:0%
+that are you there yeah
+ 
+
+ align:start position:0%
+that are you there yeah
+um let me think remember correctly is
+
+ align:start position:0%
+um let me think remember correctly is
+ 
+
+ align:start position:0%
+um let me think remember correctly is
+this something like uh you could sort of
+
+ align:start position:0%
+this something like uh you could sort of
+ 
+
+ align:start position:0%
+this something like uh you could sort of
+like compare like the incomes which is
+
+ align:start position:0%
+like compare like the incomes which is
+ 
+
+ align:start position:0%
+like compare like the incomes which is
+basically the part risk and what you end
+
+ align:start position:0%
+basically the part risk and what you end
+ 
+
+ align:start position:0%
+basically the part risk and what you end
+up end of the way you end up receiving
+
+ align:start position:0%
+up end of the way you end up receiving
+ 
+
+ align:start position:0%
+up end of the way you end up receiving
+and like I remember there's like you can
+
+ align:start position:0%
+and like I remember there's like you can
+ 
+
+ align:start position:0%
+and like I remember there's like you can
+you can infer from you can see that it's
+
+ align:start position:0%
+you can infer from you can see that it's
+ 
+
+ align:start position:0%
+you can infer from you can see that it's
+definitely much the the what you end up
+
+ align:start position:0%
+definitely much the the what you end up
+ 
+
+ align:start position:0%
+definitely much the the what you end up
+getting it's much flatter within what
+
+ align:start position:0%
+getting it's much flatter within what
+ 
+
+ align:start position:0%
+getting it's much flatter within what
+then was produced so there's so I guess
+
+ align:start position:0%
+then was produced so there's so I guess
+ 
+
+ align:start position:0%
+then was produced so there's so I guess
+I'm trying to answer the second part of
+
+ align:start position:0%
+I'm trying to answer the second part of
+ 
+
+ align:start position:0%
+I'm trying to answer the second part of
+the question like now but like that that
+
+ align:start position:0%
+the question like now but like that that
+ 
+
+ align:start position:0%
+the question like now but like that that
+sort of like is data that suggested with
+
+ align:start position:0%
+sort of like is data that suggested with
+ 
+
+ align:start position:0%
+sort of like is data that suggested with
+sharing I don't
+
+ align:start position:0%
+sharing I don't
+ 
+
+ align:start position:0%
+sharing I don't
+I don't think that's enough to prove
+
+ align:start position:0%
+I don't think that's enough to prove
+ 
+
+ align:start position:0%
+I don't think that's enough to prove
+causation it was definitely suggestive
+
+ align:start position:0%
+causation it was definitely suggestive
+ 
+
+ align:start position:0%
+causation it was definitely suggestive
+yeah that's good the second part
+
+ align:start position:0%
+yeah that's good the second part
+ 
+
+ align:start position:0%
+yeah that's good the second part
+uh maybe the second sentence helps
+
+ align:start position:0%
+uh maybe the second sentence helps
+ 
+
+ align:start position:0%
+uh maybe the second sentence helps
+if average consumption of households
+
+ align:start position:0%
+if average consumption of households
+ 
+
+ align:start position:0%
+if average consumption of households
+increased when average income of
+
+ align:start position:0%
+increased when average income of
+ 
+
+ align:start position:0%
+increased when average income of
+households increased
+
+ align:start position:0%
+households increased
+ 
+
+ align:start position:0%
+households increased
+would that be consistent with resharing
+
+ align:start position:0%
+would that be consistent with resharing
+ 
+
+ align:start position:0%
+would that be consistent with resharing
+or not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh for me yeah for you
+
+ align:start position:0%
+uh for me yeah for you
+ 
+
+ align:start position:0%
+uh for me yeah for you
+so okay so if so okay average exception
+
+ align:start position:0%
+so okay so if so okay average exception
+ 
+
+ align:start position:0%
+so okay so if so okay average exception
+of how to increase but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I wouldn't like completely like
+
+ align:start position:0%
+I wouldn't like completely like
+ 
+
+ align:start position:0%
+I wouldn't like completely like
+annihilate everything but so like I
+
+ align:start position:0%
+annihilate everything but so like I
+ 
+
+ align:start position:0%
+annihilate everything but so like I
+don't think that would be enough that
+
+ align:start position:0%
+don't think that would be enough that
+ 
+
+ align:start position:0%
+don't think that would be enough that
+would I think that would still be
+
+ align:start position:0%
+would I think that would still be
+ 
+
+ align:start position:0%
+would I think that would still be
+consistent with some level right
+
+ align:start position:0%
+consistent with some level right
+ 
+
+ align:start position:0%
+consistent with some level right
+yeah it's not uh it's actually a
+
+ align:start position:0%
+yeah it's not uh it's actually a
+ 
+
+ align:start position:0%
+yeah it's not uh it's actually a
+sentence is not terribly well worded but
+
+ align:start position:0%
+sentence is not terribly well worded but
+ 
+
+ align:start position:0%
+sentence is not terribly well worded but
+it is
+
+ align:start position:0%
+it is
+ 
+
+ align:start position:0%
+it is
+you know worthwhile to clarify
+
+ align:start position:0%
+you know worthwhile to clarify
+ 
+
+ align:start position:0%
+you know worthwhile to clarify
+you know so the first part that we
+
+ align:start position:0%
+you know so the first part that we
+ 
+
+ align:start position:0%
+you know so the first part that we
+looked at is just the levels of stuff
+
+ align:start position:0%
+looked at is just the levels of stuff
+ 
+
+ align:start position:0%
+looked at is just the levels of stuff
+over households and over time
+
+ align:start position:0%
+over households and over time
+ 
+
+ align:start position:0%
+over households and over time
+we referred to the Rocky Mountain
+
+ align:start position:0%
+we referred to the Rocky Mountain
+ 
+
+ align:start position:0%
+we referred to the Rocky Mountain
+picture as
+
+ align:start position:0%
+picture as
+ 
+
+ align:start position:0%
+picture as
+incomes going up concealing the valley
+
+ align:start position:0%
+incomes going up concealing the valley
+ 
+
+ align:start position:0%
+incomes going up concealing the valley
+behind
+
+ align:start position:0%
+behind
+ 
+
+ align:start position:0%
+behind
+and very uh very Jagged Rocky pictures
+
+ align:start position:0%
+and very uh very Jagged Rocky pictures
+ 
+
+ align:start position:0%
+and very uh very Jagged Rocky pictures
+as opposed to consumption
+
+ align:start position:0%
+as opposed to consumption
+ 
+
+ align:start position:0%
+as opposed to consumption
+which was very flat and we were even
+
+ align:start position:0%
+which was very flat and we were even
+ 
+
+ align:start position:0%
+which was very flat and we were even
+joking around a bit you know very boring
+
+ align:start position:0%
+joking around a bit you know very boring
+ 
+
+ align:start position:0%
+joking around a bit you know very boring
+as in Kansas
+
+ align:start position:0%
+as in Kansas
+ 
+
+ align:start position:0%
+as in Kansas
+so then the issue would be with the
+
+ align:start position:0%
+so then the issue would be with the
+ 
+
+ align:start position:0%
+so then the issue would be with the
+theory that we're about to look at apart
+
+ align:start position:0%
+theory that we're about to look at apart
+ 
+
+ align:start position:0%
+theory that we're about to look at apart
+from the data alone
+
+ align:start position:0%
+from the data alone
+ 
+
+ align:start position:0%
+from the data alone
+would you think household consumption
+
+ align:start position:0%
+would you think household consumption
+ 
+
+ align:start position:0%
+would you think household consumption
+ought to move with household income
+
+ align:start position:0%
+ought to move with household income
+ 
+
+ align:start position:0%
+ought to move with household income
+actually I think there's a question
+
+ align:start position:0%
+actually I think there's a question
+ 
+
+ align:start position:0%
+actually I think there's a question
+below and what's ambiguous about that
+
+ align:start position:0%
+below and what's ambiguous about that
+ 
+
+ align:start position:0%
+below and what's ambiguous about that
+sentence is household consumptions
+
+ align:start position:0%
+sentence is household consumptions
+ 
+
+ align:start position:0%
+sentence is household consumptions
+increase with average household average
+
+ align:start position:0%
+increase with average household average
+ 
+
+ align:start position:0%
+increase with average household average
+income of households
+
+ align:start position:0%
+income of households
+ 
+
+ align:start position:0%
+income of households
+yeah that's very treacherously worded I
+
+ align:start position:0%
+yeah that's very treacherously worded I
+ 
+
+ align:start position:0%
+yeah that's very treacherously worded I
+mean average income meaning overall the
+
+ align:start position:0%
+mean average income meaning overall the
+ 
+
+ align:start position:0%
+mean average income meaning overall the
+dates of a given household that kind of
+
+ align:start position:0%
+dates of a given household that kind of
+ 
+
+ align:start position:0%
+dates of a given household that kind of
+sets the levels of things and maybe you
+
+ align:start position:0%
+sets the levels of things and maybe you
+ 
+
+ align:start position:0%
+sets the levels of things and maybe you
+know that uh my household will hire
+
+ align:start position:0%
+know that uh my household will hire
+ 
+
+ align:start position:0%
+know that uh my household will hire
+average
+
+ align:start position:0%
+average
+ 
+
+ align:start position:0%
+average
+income over time has a higher average
+
+ align:start position:0%
+income over time has a higher average
+ 
+
+ align:start position:0%
+income over time has a higher average
+consumption over time
+
+ align:start position:0%
+consumption over time
+ 
+
+ align:start position:0%
+consumption over time
+and I'll I'll ask for volunteers
+
+ align:start position:0%
+and I'll I'll ask for volunteers
+ 
+
+ align:start position:0%
+and I'll I'll ask for volunteers
+if we we have this regression where we
+
+ align:start position:0%
+if we we have this regression where we
+ 
+
+ align:start position:0%
+if we we have this regression where we
+run household consumption on the left as
+
+ align:start position:0%
+run household consumption on the left as
+ 
+
+ align:start position:0%
+run household consumption on the left as
+a dependent variable onto aggregate
+
+ align:start position:0%
+a dependent variable onto aggregate
+ 
+
+ align:start position:0%
+a dependent variable onto aggregate
+consumption and individual income on the
+
+ align:start position:0%
+consumption and individual income on the
+ 
+
+ align:start position:0%
+consumption and individual income on the
+right throwing in some intercepts so
+
+ align:start position:0%
+right throwing in some intercepts so
+ 
+
+ align:start position:0%
+right throwing in some intercepts so
+what restrictions from the theory are
+
+ align:start position:0%
+what restrictions from the theory are
+ 
+
+ align:start position:0%
+what restrictions from the theory are
+placed on the coefficient
+
+ align:start position:0%
+placed on the coefficient
+ 
+
+ align:start position:0%
+placed on the coefficient
+of individual income
+
+ align:start position:0%
+of individual income
+ 
+
+ align:start position:0%
+of individual income
+and I'll take a volunteer for that
+
+ align:start position:0%
+and I'll take a volunteer for that
+ 
+
+ align:start position:0%
+and I'll take a volunteer for that
+I think the the coefficient individual
+
+ align:start position:0%
+I think the the coefficient individual
+ 
+
+ align:start position:0%
+I think the the coefficient individual
+come should be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggested really
+
+ align:start position:0%
+suggested really
+ 
+
+ align:start position:0%
+suggested really
+really aggregate consumption aggregate
+
+ align:start position:0%
+really aggregate consumption aggregate
+ 
+
+ align:start position:0%
+really aggregate consumption aggregate
+in average income of the household
+
+ align:start position:0%
+in average income of the household
+ 
+
+ align:start position:0%
+in average income of the household
+and I have a question here is that I
+
+ align:start position:0%
+and I have a question here is that I
+ 
+
+ align:start position:0%
+and I have a question here is that I
+remember in these slides I say that when
+
+ align:start position:0%
+remember in these slides I say that when
+ 
+
+ align:start position:0%
+remember in these slides I say that when
+all the household held the same risk
+
+ align:start position:0%
+all the household held the same risk
+ 
+
+ align:start position:0%
+all the household held the same risk
+aversion then the coefficient between
+
+ align:start position:0%
+aversion then the coefficient between
+ 
+
+ align:start position:0%
+aversion then the coefficient between
+the aggregate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+between the aggregate consumption should
+
+ align:start position:0%
+between the aggregate consumption should
+ 
+
+ align:start position:0%
+between the aggregate consumption should
+be one
+
+ align:start position:0%
+be one
+ 
+
+ align:start position:0%
+be one
+yeah but but I why
+
+ align:start position:0%
+yeah but but I why
+ 
+
+ align:start position:0%
+yeah but but I why
+I think the coefficient on the average
+
+ align:start position:0%
+I think the coefficient on the average
+ 
+
+ align:start position:0%
+I think the coefficient on the average
+consumption should be when not the
+
+ align:start position:0%
+consumption should be when not the
+ 
+
+ align:start position:0%
+consumption should be when not the
+aggregate consumption
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh well there's a say a fixed number of
+
+ align:start position:0%
+oh well there's a say a fixed number of
+ 
+
+ align:start position:0%
+oh well there's a say a fixed number of
+households or taking
+
+ align:start position:0%
+households or taking
+ 
+
+ align:start position:0%
+households or taking
+the Aggregate and dividing by the number
+
+ align:start position:0%
+the Aggregate and dividing by the number
+ 
+
+ align:start position:0%
+the Aggregate and dividing by the number
+of households gives you the average
+
+ align:start position:0%
+of households gives you the average
+ 
+
+ align:start position:0%
+of households gives you the average
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+it's just a re-normalization of the
+
+ align:start position:0%
+it's just a re-normalization of the
+ 
+
+ align:start position:0%
+it's just a re-normalization of the
+units that's all but it's you're right
+
+ align:start position:0%
+units that's all but it's you're right
+ 
+
+ align:start position:0%
+units that's all but it's you're right
+that it's meant to represent the
+
+ align:start position:0%
+that it's meant to represent the
+ 
+
+ align:start position:0%
+that it's meant to represent the
+aggregate
+
+ align:start position:0%
+aggregate
+ 
+
+ align:start position:0%
+aggregate
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so so you can think of it that way
+
+ align:start position:0%
+so so you can think of it that way
+ 
+
+ align:start position:0%
+so so you can think of it that way
+because the economics makes more sense
+
+ align:start position:0%
+because the economics makes more sense
+ 
+
+ align:start position:0%
+because the economics makes more sense
+the aggregate
+
+ align:start position:0%
+the aggregate
+ 
+
+ align:start position:0%
+the aggregate
+is going up
+
+ align:start position:0%
+is going up
+ 
+
+ align:start position:0%
+is going up
+coming up over all the individuals
+
+ align:start position:0%
+coming up over all the individuals
+ 
+
+ align:start position:0%
+coming up over all the individuals
+and if there's
+
+ align:start position:0%
+and if there's
+ 
+
+ align:start position:0%
+and if there's
+constant absolute risk conversion and
+
+ align:start position:0%
+constant absolute risk conversion and
+ 
+
+ align:start position:0%
+constant absolute risk conversion and
+the same risk aversion for all the
+
+ align:start position:0%
+the same risk aversion for all the
+ 
+
+ align:start position:0%
+the same risk aversion for all the
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+and whenever the aggregate goes up every
+
+ align:start position:0%
+and whenever the aggregate goes up every
+ 
+
+ align:start position:0%
+and whenever the aggregate goes up every
+individual household consumption goes up
+
+ align:start position:0%
+individual household consumption goes up
+ 
+
+ align:start position:0%
+individual household consumption goes up
+one to one yeah yeah which is what you
+
+ align:start position:0%
+one to one yeah yeah which is what you
+ 
+
+ align:start position:0%
+one to one yeah yeah which is what you
+said okay
+
+ align:start position:0%
+said okay
+ 
+
+ align:start position:0%
+said okay
+thank you
+
+ align:start position:0%
+thank you
+ 
+
+ align:start position:0%
+thank you
+yeah and the emphasis here is the
+
+ align:start position:0%
+yeah and the emphasis here is the
+ 
+
+ align:start position:0%
+yeah and the emphasis here is the
+household specific income
+
+ align:start position:0%
+household specific income
+ 
+
+ align:start position:0%
+household specific income
+it has a coefficient of zero that's the
+
+ align:start position:0%
+it has a coefficient of zero that's the
+ 
+
+ align:start position:0%
+it has a coefficient of zero that's the
+kind of salient
+
+ align:start position:0%
+kind of salient
+ 
+
+ align:start position:0%
+kind of salient
+restriction that the theory places on
+
+ align:start position:0%
+restriction that the theory places on
+ 
+
+ align:start position:0%
+restriction that the theory places on
+the data
+
+ align:start position:0%
+the data
+ 
+
+ align:start position:0%
+the data
+as well
+
+ align:start position:0%
+as well
+ 
+
+ align:start position:0%
+as well
+okay and then finally
+
+ align:start position:0%
+okay and then finally
+ 
+
+ align:start position:0%
+okay and then finally
+he looked at the division of land
+
+ align:start position:0%
+he looked at the division of land
+ 
+
+ align:start position:0%
+he looked at the division of land
+in these medieval village
+
+ align:start position:0%
+in these medieval village
+ 
+
+ align:start position:0%
+in these medieval village
+and the question is
+
+ align:start position:0%
+and the question is
+ 
+
+ align:start position:0%
+and the question is
+with scattering of an individual
+
+ align:start position:0%
+with scattering of an individual
+ 
+
+ align:start position:0%
+with scattering of an individual
+households plots across the different
+
+ align:start position:0%
+households plots across the different
+ 
+
+ align:start position:0%
+households plots across the different
+fields
+
+ align:start position:0%
+fields
+ 
+
+ align:start position:0%
+fields
+be enough to achieve an optimal
+
+ align:start position:0%
+be enough to achieve an optimal
+ 
+
+ align:start position:0%
+be enough to achieve an optimal
+allocation of risk bearing Paolo do you
+
+ align:start position:0%
+allocation of risk bearing Paolo do you
+ 
+
+ align:start position:0%
+allocation of risk bearing Paolo do you
+want to take a crack at that
+
+ align:start position:0%
+want to take a crack at that
+ 
+
+ align:start position:0%
+want to take a crack at that
+um sure I think the answer is no just
+
+ align:start position:0%
+um sure I think the answer is no just
+ 
+
+ align:start position:0%
+um sure I think the answer is no just
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+um it's not necessarily that each field
+
+ align:start position:0%
+um it's not necessarily that each field
+ 
+
+ align:start position:0%
+um it's not necessarily that each field
+is a random
+
+ align:start position:0%
+is a random
+ 
+
+ align:start position:0%
+is a random
+um draw you can have correlations like
+
+ align:start position:0%
+um draw you can have correlations like
+ 
+
+ align:start position:0%
+um draw you can have correlations like
+it's just like a trappier and there's
+
+ align:start position:0%
+it's just like a trappier and there's
+ 
+
+ align:start position:0%
+it's just like a trappier and there's
+like no ring anywhere that's a like Risk
+
+ align:start position:0%
+like no ring anywhere that's a like Risk
+ 
+
+ align:start position:0%
+like no ring anywhere that's a like Risk
+which would like be a shock to all of
+
+ align:start position:0%
+which would like be a shock to all of
+ 
+
+ align:start position:0%
+which would like be a shock to all of
+your crops essentially
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+um so it's correct that it's not
+
+ align:start position:0%
+um so it's correct that it's not
+ 
+
+ align:start position:0%
+um so it's correct that it's not
+necessarily enough unless you have very
+
+ align:start position:0%
+necessarily enough unless you have very
+ 
+
+ align:start position:0%
+necessarily enough unless you have very
+special
+
+ align:start position:0%
+special
+ 
+
+ align:start position:0%
+special
+characteristics of those of those plots
+
+ align:start position:0%
+characteristics of those of those plots
+ 
+
+ align:start position:0%
+characteristics of those of those plots
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+how they move with various states of the
+
+ align:start position:0%
+how they move with various states of the
+ 
+
+ align:start position:0%
+how they move with various states of the
+world
+
+ align:start position:0%
+world
+ 
+
+ align:start position:0%
+world
+in the lecture we gave an example
+
+ align:start position:0%
+in the lecture we gave an example
+ 
+
+ align:start position:0%
+in the lecture we gave an example
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+two examples really
+
+ align:start position:0%
+two examples really
+ 
+
+ align:start position:0%
+two examples really
+uh one where there are two types of land
+
+ align:start position:0%
+uh one where there are two types of land
+ 
+
+ align:start position:0%
+uh one where there are two types of land
+and um
+
+ align:start position:0%
+and um
+ 
+
+ align:start position:0%
+and um
+both are increasing as the states
+
+ align:start position:0%
+both are increasing as the states
+ 
+
+ align:start position:0%
+both are increasing as the states
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+it would be enough to kind of have each
+
+ align:start position:0%
+it would be enough to kind of have each
+ 
+
+ align:start position:0%
+it would be enough to kind of have each
+household have
+
+ align:start position:0%
+household have
+ 
+
+ align:start position:0%
+household have
+uh a share a constant share over the two
+
+ align:start position:0%
+uh a share a constant share over the two
+ 
+
+ align:start position:0%
+uh a share a constant share over the two
+types of land
+
+ align:start position:0%
+types of land
+ 
+
+ align:start position:0%
+types of land
+that would result in a linear risk
+
+ align:start position:0%
+that would result in a linear risk
+ 
+
+ align:start position:0%
+that would result in a linear risk
+sharing schedule
+
+ align:start position:0%
+sharing schedule
+ 
+
+ align:start position:0%
+sharing schedule
+so for certain utility functions
+
+ align:start position:0%
+so for certain utility functions
+ 
+
+ align:start position:0%
+so for certain utility functions
+including you know
+
+ align:start position:0%
+including you know
+ 
+
+ align:start position:0%
+including you know
+an examination of the slope in the
+
+ align:start position:0%
+an examination of the slope in the
+ 
+
+ align:start position:0%
+an examination of the slope in the
+intercepts that would be enough
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in special cases it might work
+
+ align:start position:0%
+so in special cases it might work
+ 
+
+ align:start position:0%
+so in special cases it might work
+but in general you have two different
+
+ align:start position:0%
+but in general you have two different
+ 
+
+ align:start position:0%
+but in general you have two different
+types of land and output goes up in one
+
+ align:start position:0%
+types of land and output goes up in one
+ 
+
+ align:start position:0%
+types of land and output goes up in one
+it may go down in the other depending on
+
+ align:start position:0%
+it may go down in the other depending on
+ 
+
+ align:start position:0%
+it may go down in the other depending on
+the state of the world
+
+ align:start position:0%
+the state of the world
+ 
+
+ align:start position:0%
+the state of the world
+in which case you know handing out
+
+ align:start position:0%
+in which case you know handing out
+ 
+
+ align:start position:0%
+in which case you know handing out
+shares of each type
+
+ align:start position:0%
+shares of each type
+ 
+
+ align:start position:0%
+shares of each type
+uh is is not going to work necessarily
+
+ align:start position:0%
+uh is is not going to work necessarily
+ 
+
+ align:start position:0%
+uh is is not going to work necessarily
+and we explore that further in the
+
+ align:start position:0%
+and we explore that further in the
+ 
+
+ align:start position:0%
+and we explore that further in the
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+so that whole lecture kind of culminated
+
+ align:start position:0%
+so that whole lecture kind of culminated
+ 
+
+ align:start position:0%
+so that whole lecture kind of culminated
+at the end
+
+ align:start position:0%
+at the end
+ 
+
+ align:start position:0%
+at the end
+with an example where we had
+
+ align:start position:0%
+with an example where we had
+ 
+
+ align:start position:0%
+with an example where we had
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+more states of the world than we had
+
+ align:start position:0%
+more states of the world than we had
+ 
+
+ align:start position:0%
+more states of the world than we had
+land types
+
+ align:start position:0%
+land types
+ 
+
+ align:start position:0%
+land types
+and uh restricted them to
+
+ align:start position:0%
+and uh restricted them to
+ 
+
+ align:start position:0%
+and uh restricted them to
+having shares of each type
+
+ align:start position:0%
+having shares of each type
+ 
+
+ align:start position:0%
+having shares of each type
+as if they could not transfer stuff
+
+ align:start position:0%
+as if they could not transfer stuff
+ 
+
+ align:start position:0%
+as if they could not transfer stuff
+around and
+
+ align:start position:0%
+around and
+ 
+
+ align:start position:0%
+around and
+it was clear that it was constrained
+
+ align:start position:0%
+it was clear that it was constrained
+ 
+
+ align:start position:0%
+it was clear that it was constrained
+optimal
+
+ align:start position:0%
+optimal
+ 
+
+ align:start position:0%
+optimal
+so taking that allocation of land with
+
+ align:start position:0%
+so taking that allocation of land with
+ 
+
+ align:start position:0%
+so taking that allocation of land with
+the Harvest as given we could do better
+
+ align:start position:0%
+the Harvest as given we could do better
+ 
+
+ align:start position:0%
+the Harvest as given we could do better
+by add to Welfare by having exposed
+
+ align:start position:0%
+by add to Welfare by having exposed
+ 
+
+ align:start position:0%
+by add to Welfare by having exposed
+redistribution of the grain via
+
+ align:start position:0%
+redistribution of the grain via
+ 
+
+ align:start position:0%
+redistribution of the grain via
+transfers okay so that's probably enough
+
+ align:start position:0%
+transfers okay so that's probably enough
+ 
+
+ align:start position:0%
+transfers okay so that's probably enough
+of a review as always there are many
+
+ align:start position:0%
+of a review as always there are many
+ 
+
+ align:start position:0%
+of a review as always there are many
+more questions in the study guide and
+
+ align:start position:0%
+more questions in the study guide and
+ 
+
+ align:start position:0%
+more questions in the study guide and
+probably spent quite a lot of time just
+
+ align:start position:0%
+probably spent quite a lot of time just
+ 
+
+ align:start position:0%
+probably spent quite a lot of time just
+deciding which ones to ask in class you
+
+ align:start position:0%
+deciding which ones to ask in class you
+ 
+
+ align:start position:0%
+deciding which ones to ask in class you
+should look at all of them
+
+ align:start position:0%
+should look at all of them
+ 
+
+ align:start position:0%
+should look at all of them
+and let's get to lecture nine
+
+ align:start position:0%
+and let's get to lecture nine
+ 
+
+ align:start position:0%
+and let's get to lecture nine
+is what we're doing today and this is
+
+ align:start position:0%
+is what we're doing today and this is
+ 
+
+ align:start position:0%
+is what we're doing today and this is
+risk sharing with production three main
+
+ align:start position:0%
+risk sharing with production three main
+ 
+
+ align:start position:0%
+risk sharing with production three main
+topics really risk and return in
+
+ align:start position:0%
+topics really risk and return in
+ 
+
+ align:start position:0%
+topics really risk and return in
+production and that part is continuation
+
+ align:start position:0%
+production and that part is continuation
+ 
+
+ align:start position:0%
+production and that part is continuation
+of some of the themes although we didn't
+
+ align:start position:0%
+of some of the themes although we didn't
+ 
+
+ align:start position:0%
+of some of the themes although we didn't
+really put all the pieces together we
+
+ align:start position:0%
+really put all the pieces together we
+ 
+
+ align:start position:0%
+really put all the pieces together we
+had production in the Dynamics lecture
+
+ align:start position:0%
+had production in the Dynamics lecture
+ 
+
+ align:start position:0%
+had production in the Dynamics lecture
+we had risk as in yields coming from
+
+ align:start position:0%
+we had risk as in yields coming from
+ 
+
+ align:start position:0%
+we had risk as in yields coming from
+land plots but we never talked about
+
+ align:start position:0%
+land plots but we never talked about
+ 
+
+ align:start position:0%
+land plots but we never talked about
+inputs into land plots and Associated
+
+ align:start position:0%
+inputs into land plots and Associated
+ 
+
+ align:start position:0%
+inputs into land plots and Associated
+outputs and so on so we'll put those two
+
+ align:start position:0%
+outputs and so on so we'll put those two
+ 
+
+ align:start position:0%
+outputs and so on so we'll put those two
+pieces together another feature of this
+
+ align:start position:0%
+pieces together another feature of this
+ 
+
+ align:start position:0%
+pieces together another feature of this
+lecture is that we're going to use data
+
+ align:start position:0%
+lecture is that we're going to use data
+ 
+
+ align:start position:0%
+lecture is that we're going to use data
+on production but also on consumption so
+
+ align:start position:0%
+on production but also on consumption so
+ 
+
+ align:start position:0%
+on production but also on consumption so
+both things will be there and this is
+
+ align:start position:0%
+both things will be there and this is
+ 
+
+ align:start position:0%
+both things will be there and this is
+illustrative of how powerful this risk
+
+ align:start position:0%
+illustrative of how powerful this risk
+ 
+
+ align:start position:0%
+illustrative of how powerful this risk
+sharing framework is it extends to more
+
+ align:start position:0%
+sharing framework is it extends to more
+ 
+
+ align:start position:0%
+sharing framework is it extends to more
+and more complicated situations we're
+
+ align:start position:0%
+and more complicated situations we're
+ 
+
+ align:start position:0%
+and more complicated situations we're
+able to do more and more with it and
+
+ align:start position:0%
+able to do more and more with it and
+ 
+
+ align:start position:0%
+able to do more and more with it and
+finally I have some words at the end
+
+ align:start position:0%
+finally I have some words at the end
+ 
+
+ align:start position:0%
+finally I have some words at the end
+about social networks and sharing risk
+
+ align:start position:0%
+about social networks and sharing risk
+ 
+
+ align:start position:0%
+about social networks and sharing risk
+and in particular an example that will
+
+ align:start position:0%
+and in particular an example that will
+ 
+
+ align:start position:0%
+and in particular an example that will
+remind you for better or worse of covid
+
+ align:start position:0%
+remind you for better or worse of covid
+ 
+
+ align:start position:0%
+remind you for better or worse of covid
+and what's going on or when people get
+
+ align:start position:0%
+and what's going on or when people get
+ 
+
+ align:start position:0%
+and what's going on or when people get
+sick with the economics okay so this
+
+ align:start position:0%
+sick with the economics okay so this
+ 
+
+ align:start position:0%
+sick with the economics okay so this
+first starred paper on the reading list
+
+ align:start position:0%
+first starred paper on the reading list
+ 
+
+ align:start position:0%
+first starred paper on the reading list
+with could its alert some pantalach it
+
+ align:start position:0%
+with could its alert some pantalach it
+ 
+
+ align:start position:0%
+with could its alert some pantalach it
+was Thai if you haven't guessed
+
+ align:start position:0%
+was Thai if you haven't guessed
+ 
+
+ align:start position:0%
+was Thai if you haven't guessed
+extensions of the theory project
+
+ align:start position:0%
+extensions of the theory project
+ 
+
+ align:start position:0%
+extensions of the theory project
+selection so we studied a model with
+
+ align:start position:0%
+selection so we studied a model with
+ 
+
+ align:start position:0%
+selection so we studied a model with
+risk and return in productive Assets in
+
+ align:start position:0%
+risk and return in productive Assets in
+ 
+
+ align:start position:0%
+risk and return in productive Assets in
+developing economies namely Thailand
+
+ align:start position:0%
+developing economies namely Thailand
+ 
+
+ align:start position:0%
+developing economies namely Thailand
+we're going to measure idiosyncratic and
+
+ align:start position:0%
+we're going to measure idiosyncratic and
+ 
+
+ align:start position:0%
+we're going to measure idiosyncratic and
+aggregate risk Premia those words
+
+ align:start position:0%
+aggregate risk Premia those words
+ 
+
+ align:start position:0%
+aggregate risk Premia those words
+probably don't make a whole lot of sense
+
+ align:start position:0%
+probably don't make a whole lot of sense
+ 
+
+ align:start position:0%
+probably don't make a whole lot of sense
+although we've been talking about
+
+ align:start position:0%
+although we've been talking about
+ 
+
+ align:start position:0%
+although we've been talking about
+related things just now with the risk
+
+ align:start position:0%
+related things just now with the risk
+ 
+
+ align:start position:0%
+related things just now with the risk
+sharing regression
+
+ align:start position:0%
+sharing regression
+ 
+
+ align:start position:0%
+sharing regression
+idiosyncratic being household specific
+
+ align:start position:0%
+idiosyncratic being household specific
+ 
+
+ align:start position:0%
+idiosyncratic being household specific
+income and aggregate being aggregate
+
+ align:start position:0%
+income and aggregate being aggregate
+ 
+
+ align:start position:0%
+income and aggregate being aggregate
+consumption and we're going to use we're
+
+ align:start position:0%
+consumption and we're going to use we're
+ 
+
+ align:start position:0%
+consumption and we're going to use we're
+going to be able to quantify those two
+
+ align:start position:0%
+going to be able to quantify those two
+ 
+
+ align:start position:0%
+going to be able to quantify those two
+different Premia and analyze what
+
+ align:start position:0%
+different Premia and analyze what
+ 
+
+ align:start position:0%
+different Premia and analyze what
+households are doing how exposed they
+
+ align:start position:0%
+households are doing how exposed they
+ 
+
+ align:start position:0%
+households are doing how exposed they
+are to risk and finally in principle one
+
+ align:start position:0%
+are to risk and finally in principle one
+ 
+
+ align:start position:0%
+are to risk and finally in principle one
+could take not just the straight out
+
+ align:start position:0%
+could take not just the straight out
+ 
+
+ align:start position:0%
+could take not just the straight out
+returns but risk-adjusted returns and
+
+ align:start position:0%
+returns but risk-adjusted returns and
+ 
+
+ align:start position:0%
+returns but risk-adjusted returns and
+look for patterns across households like
+
+ align:start position:0%
+look for patterns across households like
+ 
+
+ align:start position:0%
+look for patterns across households like
+whether poor households are more
+
+ align:start position:0%
+whether poor households are more
+ 
+
+ align:start position:0%
+whether poor households are more
+vulnerable or less vulnerable as
+
+ align:start position:0%
+vulnerable or less vulnerable as
+ 
+
+ align:start position:0%
+vulnerable or less vulnerable as
+education matter and so on so here's the
+
+ align:start position:0%
+education matter and so on so here's the
+ 
+
+ align:start position:0%
+education matter and so on so here's the
+model there are capital J households
+
+ align:start position:0%
+model there are capital J households
+ 
+
+ align:start position:0%
+model there are capital J households
+indexed by J Little J for an individual
+
+ align:start position:0%
+indexed by J Little J for an individual
+ 
+
+ align:start position:0%
+indexed by J Little J for an individual
+J is the number for the aggregate their
+
+ align:start position:0%
+J is the number for the aggregate their
+ 
+
+ align:start position:0%
+J is the number for the aggregate their
+eye production activities little I big I
+
+ align:start position:0%
+eye production activities little I big I
+ 
+
+ align:start position:0%
+eye production activities little I big I
+and you can think of those production
+
+ align:start position:0%
+and you can think of those production
+ 
+
+ align:start position:0%
+and you can think of those production
+activities as production sets or
+
+ align:start position:0%
+activities as production sets or
+ 
+
+ align:start position:0%
+activities as production sets or
+Production Technologies the inputs are
+
+ align:start position:0%
+Production Technologies the inputs are
+ 
+
+ align:start position:0%
+Production Technologies the inputs are
+capital and now say some words in a bit
+
+ align:start position:0%
+capital and now say some words in a bit
+ 
+
+ align:start position:0%
+capital and now say some words in a bit
+later about where labor and materials
+
+ align:start position:0%
+later about where labor and materials
+ 
+
+ align:start position:0%
+later about where labor and materials
+and seed and other things went but for
+
+ align:start position:0%
+and seed and other things went but for
+ 
+
+ align:start position:0%
+and seed and other things went but for
+now just think of being of there being a
+
+ align:start position:0%
+now just think of being of there being a
+ 
+
+ align:start position:0%
+now just think of being of there being a
+single input called capital and the
+
+ align:start position:0%
+single input called capital and the
+ 
+
+ align:start position:0%
+single input called capital and the
+outputs are in the same units of a
+
+ align:start position:0%
+outputs are in the same units of a
+ 
+
+ align:start position:0%
+outputs are in the same units of a
+single consumption good
+
+ align:start position:0%
+single consumption good
+ 
+
+ align:start position:0%
+single consumption good
+so we're going to be looking at a
+
+ align:start position:0%
+so we're going to be looking at a
+ 
+
+ align:start position:0%
+so we're going to be looking at a
+household running a portfolio of Assets
+
+ align:start position:0%
+household running a portfolio of Assets
+ 
+
+ align:start position:0%
+household running a portfolio of Assets
+Now actually the way you think about
+
+ align:start position:0%
+Now actually the way you think about
+ 
+
+ align:start position:0%
+Now actually the way you think about
+this in finance is you want to engage in
+
+ align:start position:0%
+this in finance is you want to engage in
+ 
+
+ align:start position:0%
+this in finance is you want to engage in
+a certain activity you require the
+
+ align:start position:0%
+a certain activity you require the
+ 
+
+ align:start position:0%
+a certain activity you require the
+assets necessary to do that activity and
+
+ align:start position:0%
+assets necessary to do that activity and
+ 
+
+ align:start position:0%
+assets necessary to do that activity and
+a household could be doing one or
+
+ align:start position:0%
+a household could be doing one or
+ 
+
+ align:start position:0%
+a household could be doing one or
+multiple activities this will generate a
+
+ align:start position:0%
+multiple activities this will generate a
+ 
+
+ align:start position:0%
+multiple activities this will generate a
+return so we want to know how well the
+
+ align:start position:0%
+return so we want to know how well the
+ 
+
+ align:start position:0%
+return so we want to know how well the
+project is doing and whether it was
+
+ align:start position:0%
+project is doing and whether it was
+ 
+
+ align:start position:0%
+project is doing and whether it was
+selected properly so you want to compare
+
+ align:start position:0%
+selected properly so you want to compare
+ 
+
+ align:start position:0%
+selected properly so you want to compare
+the rate of return to the best
+
+ align:start position:0%
+the rate of return to the best
+ 
+
+ align:start position:0%
+the rate of return to the best
+alternative use of funds
+
+ align:start position:0%
+alternative use of funds
+ 
+
+ align:start position:0%
+alternative use of funds
+except that here we're going to put risk
+
+ align:start position:0%
+except that here we're going to put risk
+ 
+
+ align:start position:0%
+except that here we're going to put risk
+in so it makes it much more interesting
+
+ align:start position:0%
+in so it makes it much more interesting
+ 
+
+ align:start position:0%
+in so it makes it much more interesting
+in particular these asset returns are
+
+ align:start position:0%
+in particular these asset returns are
+ 
+
+ align:start position:0%
+in particular these asset returns are
+stochastic and they can be correlated
+
+ align:start position:0%
+stochastic and they can be correlated
+ 
+
+ align:start position:0%
+stochastic and they can be correlated
+over activities and correlated over
+
+ align:start position:0%
+over activities and correlated over
+ 
+
+ align:start position:0%
+over activities and correlated over
+households
+
+ align:start position:0%
+households
+ 
+
+ align:start position:0%
+households
+so again you can think about the
+
+ align:start position:0%
+so again you can think about the
+ 
+
+ align:start position:0%
+so again you can think about the
+previous lecture with Village India
+
+ align:start position:0%
+previous lecture with Village India
+ 
+
+ align:start position:0%
+previous lecture with Village India
+although this happens to be Village
+
+ align:start position:0%
+although this happens to be Village
+ 
+
+ align:start position:0%
+although this happens to be Village
+Thailand that is different kinds of
+
+ align:start position:0%
+Thailand that is different kinds of
+ 
+
+ align:start position:0%
+Thailand that is different kinds of
+crops and different soils different
+
+ align:start position:0%
+crops and different soils different
+ 
+
+ align:start position:0%
+crops and different soils different
+income sources and so on so I mentioned
+
+ align:start position:0%
+income sources and so on so I mentioned
+ 
+
+ align:start position:0%
+income sources and so on so I mentioned
+early on in lecture one that we were
+
+ align:start position:0%
+early on in lecture one that we were
+ 
+
+ align:start position:0%
+early on in lecture one that we were
+going to go back and forth between uh
+
+ align:start position:0%
+going to go back and forth between uh
+ 
+
+ align:start position:0%
+going to go back and forth between uh
+actual real agrarian economies and
+
+ align:start position:0%
+actual real agrarian economies and
+ 
+
+ align:start position:0%
+actual real agrarian economies and
+Associated metaphors so we can talk
+
+ align:start position:0%
+Associated metaphors so we can talk
+ 
+
+ align:start position:0%
+Associated metaphors so we can talk
+about trees bearing fruit literally in
+
+ align:start position:0%
+about trees bearing fruit literally in
+ 
+
+ align:start position:0%
+about trees bearing fruit literally in
+the data but we can also talk about a
+
+ align:start position:0%
+the data but we can also talk about a
+ 
+
+ align:start position:0%
+the data but we can also talk about a
+tree as an asset in financial markets
+
+ align:start position:0%
+tree as an asset in financial markets
+ 
+
+ align:start position:0%
+tree as an asset in financial markets
+household sole assets and they pay
+
+ align:start position:0%
+household sole assets and they pay
+ 
+
+ align:start position:0%
+household sole assets and they pay
+dividends and there may be correlations
+
+ align:start position:0%
+dividends and there may be correlations
+ 
+
+ align:start position:0%
+dividends and there may be correlations
+in stock returns so exactly the same
+
+ align:start position:0%
+in stock returns so exactly the same
+ 
+
+ align:start position:0%
+in stock returns so exactly the same
+theory is being applied to two very
+
+ align:start position:0%
+theory is being applied to two very
+ 
+
+ align:start position:0%
+theory is being applied to two very
+different settings and in fact we're
+
+ align:start position:0%
+different settings and in fact we're
+ 
+
+ align:start position:0%
+different settings and in fact we're
+kind of reverse engineering in this
+
+ align:start position:0%
+kind of reverse engineering in this
+ 
+
+ align:start position:0%
+kind of reverse engineering in this
+paper we're taking measures of risk
+
+ align:start position:0%
+paper we're taking measures of risk
+ 
+
+ align:start position:0%
+paper we're taking measures of risk
+reduction and risk Premia that have been
+
+ align:start position:0%
+reduction and risk Premia that have been
+ 
+
+ align:start position:0%
+reduction and risk Premia that have been
+applied to stocks in the New York Stock
+
+ align:start position:0%
+applied to stocks in the New York Stock
+ 
+
+ align:start position:0%
+applied to stocks in the New York Stock
+Exchange and applying it to all these
+
+ align:start position:0%
+Exchange and applying it to all these
+ 
+
+ align:start position:0%
+Exchange and applying it to all these
+activities across various households in
+
+ align:start position:0%
+activities across various households in
+ 
+
+ align:start position:0%
+activities across various households in
+a in a typical Thai Village
+
+ align:start position:0%
+a in a typical Thai Village
+ 
+
+ align:start position:0%
+a in a typical Thai Village
+okay so a little bit more in notation we
+
+ align:start position:0%
+okay so a little bit more in notation we
+ 
+
+ align:start position:0%
+okay so a little bit more in notation we
+have F production function for activity
+
+ align:start position:0%
+have F production function for activity
+ 
+
+ align:start position:0%
+have F production function for activity
+I run by household J and it has as this
+
+ align:start position:0%
+I run by household J and it has as this
+ 
+
+ align:start position:0%
+I run by household J and it has as this
+single input the level at which it's
+
+ align:start position:0%
+single input the level at which it's
+ 
+
+ align:start position:0%
+single input the level at which it's
+capitalized the capital input inactivity
+
+ align:start position:0%
+capitalized the capital input inactivity
+ 
+
+ align:start position:0%
+capitalized the capital input inactivity
+I run by household J so we can sum over
+
+ align:start position:0%
+I run by household J so we can sum over
+ 
+
+ align:start position:0%
+I run by household J so we can sum over
+all activities in some overall
+
+ align:start position:0%
+all activities in some overall
+ 
+
+ align:start position:0%
+all activities in some overall
+households and get an aggregate
+
+ align:start position:0%
+households and get an aggregate
+ 
+
+ align:start position:0%
+households and get an aggregate
+production function so again early on in
+
+ align:start position:0%
+production function so again early on in
+ 
+
+ align:start position:0%
+production function so again early on in
+one of those lectures on production we
+
+ align:start position:0%
+one of those lectures on production we
+ 
+
+ align:start position:0%
+one of those lectures on production we
+talked about aggregating two example
+
+ align:start position:0%
+talked about aggregating two example
+ 
+
+ align:start position:0%
+talked about aggregating two example
+production sets into one so this is a
+
+ align:start position:0%
+production sets into one so this is a
+ 
+
+ align:start position:0%
+production sets into one so this is a
+version of that so the economy starts
+
+ align:start position:0%
+version of that so the economy starts
+ 
+
+ align:start position:0%
+version of that so the economy starts
+out with an aggregate amount of wealth
+
+ align:start position:0%
+out with an aggregate amount of wealth
+ 
+
+ align:start position:0%
+out with an aggregate amount of wealth
+which is coming from two sources
+
+ align:start position:0%
+which is coming from two sources
+ 
+
+ align:start position:0%
+which is coming from two sources
+one the trees and two the fruit now let
+
+ align:start position:0%
+one the trees and two the fruit now let
+ 
+
+ align:start position:0%
+one the trees and two the fruit now let
+me just say that as is standard in a lot
+
+ align:start position:0%
+me just say that as is standard in a lot
+ 
+
+ align:start position:0%
+me just say that as is standard in a lot
+not all but a lot of economic models
+
+ align:start position:0%
+not all but a lot of economic models
+ 
+
+ align:start position:0%
+not all but a lot of economic models
+we're gonna have we're going to call uh
+
+ align:start position:0%
+we're gonna have we're going to call uh
+ 
+
+ align:start position:0%
+we're gonna have we're going to call uh
+Putty Putty meaning that you take the
+
+ align:start position:0%
+Putty Putty meaning that you take the
+ 
+
+ align:start position:0%
+Putty Putty meaning that you take the
+putty in terms of very malleable
+
+ align:start position:0%
+putty in terms of very malleable
+ 
+
+ align:start position:0%
+putty in terms of very malleable
+consumption what could be consumption
+
+ align:start position:0%
+consumption what could be consumption
+ 
+
+ align:start position:0%
+consumption what could be consumption
+and invested into capital and then that
+
+ align:start position:0%
+and invested into capital and then that
+ 
+
+ align:start position:0%
+and invested into capital and then that
+yields a return you can certainly eat
+
+ align:start position:0%
+yields a return you can certainly eat
+ 
+
+ align:start position:0%
+yields a return you can certainly eat
+the fruit but you can also eat the tree
+
+ align:start position:0%
+the fruit but you can also eat the tree
+ 
+
+ align:start position:0%
+the fruit but you can also eat the tree
+so the Putty Putty part you know comes
+
+ align:start position:0%
+so the Putty Putty part you know comes
+ 
+
+ align:start position:0%
+so the Putty Putty part you know comes
+from undoing the tree of course in many
+
+ align:start position:0%
+from undoing the tree of course in many
+ 
+
+ align:start position:0%
+from undoing the tree of course in many
+actual situations you can't eat the
+
+ align:start position:0%
+actual situations you can't eat the
+ 
+
+ align:start position:0%
+actual situations you can't eat the
+machine but it's as if you could sell
+
+ align:start position:0%
+machine but it's as if you could sell
+ 
+
+ align:start position:0%
+machine but it's as if you could sell
+the machine and get the consumption
+
+ align:start position:0%
+the machine and get the consumption
+ 
+
+ align:start position:0%
+the machine and get the consumption
+equivalent if you wanted to eat all of
+
+ align:start position:0%
+equivalent if you wanted to eat all of
+ 
+
+ align:start position:0%
+equivalent if you wanted to eat all of
+it you could and you'll see that right
+
+ align:start position:0%
+it you could and you'll see that right
+ 
+
+ align:start position:0%
+it you could and you'll see that right
+now in the notation
+
+ align:start position:0%
+now in the notation
+ 
+
+ align:start position:0%
+now in the notation
+we're going to have quote unquote a
+
+ align:start position:0%
+we're going to have quote unquote a
+ 
+
+ align:start position:0%
+we're going to have quote unquote a
+social planner but of course you know
+
+ align:start position:0%
+social planner but of course you know
+ 
+
+ align:start position:0%
+social planner but of course you know
+now that's just means that we're going
+
+ align:start position:0%
+now that's just means that we're going
+ 
+
+ align:start position:0%
+now that's just means that we're going
+to have these programming problems for
+
+ align:start position:0%
+to have these programming problems for
+ 
+
+ align:start position:0%
+to have these programming problems for
+the determination of Pareto optimal
+
+ align:start position:0%
+the determination of Pareto optimal
+ 
+
+ align:start position:0%
+the determination of Pareto optimal
+allocation and we're going to act as if
+
+ align:start position:0%
+allocation and we're going to act as if
+ 
+
+ align:start position:0%
+allocation and we're going to act as if
+the planner is doing it but it's really
+
+ align:start position:0%
+the planner is doing it but it's really
+ 
+
+ align:start position:0%
+the planner is doing it but it's really
+a math problem that we can solve to go
+
+ align:start position:0%
+a math problem that we can solve to go
+ 
+
+ align:start position:0%
+a math problem that we can solve to go
+back and forth between solutions to the
+
+ align:start position:0%
+back and forth between solutions to the
+ 
+
+ align:start position:0%
+back and forth between solutions to the
+math problem
+
+ align:start position:0%
+math problem
+ 
+
+ align:start position:0%
+math problem
+and various Pareto optimal allocations
+
+ align:start position:0%
+and various Pareto optimal allocations
+ 
+
+ align:start position:0%
+and various Pareto optimal allocations
+so consumption of household J at a given
+
+ align:start position:0%
+so consumption of household J at a given
+ 
+
+ align:start position:0%
+so consumption of household J at a given
+moment say a year the sources of
+
+ align:start position:0%
+moment say a year the sources of
+ 
+
+ align:start position:0%
+moment say a year the sources of
+potential consumption would be the fruit
+
+ align:start position:0%
+potential consumption would be the fruit
+ 
+
+ align:start position:0%
+potential consumption would be the fruit
+how much activity I is yielding a fruit
+
+ align:start position:0%
+how much activity I is yielding a fruit
+ 
+
+ align:start position:0%
+how much activity I is yielding a fruit
+run by household J as a function of
+
+ align:start position:0%
+run by household J as a function of
+ 
+
+ align:start position:0%
+run by household J as a function of
+previously determined capitalization
+
+ align:start position:0%
+previously determined capitalization
+ 
+
+ align:start position:0%
+previously determined capitalization
+k i j we sum over all I and we have the
+
+ align:start position:0%
+k i j we sum over all I and we have the
+ 
+
+ align:start position:0%
+k i j we sum over all I and we have the
+tree itself which as I've said now would
+
+ align:start position:0%
+tree itself which as I've said now would
+ 
+
+ align:start position:0%
+tree itself which as I've said now would
+be potentially eaten but from these
+
+ align:start position:0%
+be potentially eaten but from these
+ 
+
+ align:start position:0%
+be potentially eaten but from these
+available resources we can subtract off
+
+ align:start position:0%
+available resources we can subtract off
+ 
+
+ align:start position:0%
+available resources we can subtract off
+the capitalization for Next Period Prime
+
+ align:start position:0%
+the capitalization for Next Period Prime
+ 
+
+ align:start position:0%
+the capitalization for Next Period Prime
+means tomorrow or next year and kij is
+
+ align:start position:0%
+means tomorrow or next year and kij is
+ 
+
+ align:start position:0%
+means tomorrow or next year and kij is
+the level of capital carried out from
+
+ align:start position:0%
+the level of capital carried out from
+ 
+
+ align:start position:0%
+the level of capital carried out from
+this year into next year so this is like
+
+ align:start position:0%
+this year into next year so this is like
+ 
+
+ align:start position:0%
+this year into next year so this is like
+storage in that Dynamic medieval village
+
+ align:start position:0%
+storage in that Dynamic medieval village
+ 
+
+ align:start position:0%
+storage in that Dynamic medieval village
+economy it's also like that's one
+
+ align:start position:0%
+economy it's also like that's one
+ 
+
+ align:start position:0%
+economy it's also like that's one
+activity seed planted in the ground is
+
+ align:start position:0%
+activity seed planted in the ground is
+ 
+
+ align:start position:0%
+activity seed planted in the ground is
+another type of activity this is a
+
+ align:start position:0%
+another type of activity this is a
+ 
+
+ align:start position:0%
+another type of activity this is a
+generalization
+
+ align:start position:0%
+generalization
+ 
+
+ align:start position:0%
+generalization
+and finally we have these transfers Tau
+
+ align:start position:0%
+and finally we have these transfers Tau
+ 
+
+ align:start position:0%
+and finally we have these transfers Tau
+these are going to be among other things
+
+ align:start position:0%
+these are going to be among other things
+ 
+
+ align:start position:0%
+these are going to be among other things
+key control variables of the so-called
+
+ align:start position:0%
+key control variables of the so-called
+ 
+
+ align:start position:0%
+key control variables of the so-called
+planner adding potentially to the
+
+ align:start position:0%
+planner adding potentially to the
+ 
+
+ align:start position:0%
+planner adding potentially to the
+resources of the household or if
+
+ align:start position:0%
+resources of the household or if
+ 
+
+ align:start position:0%
+resources of the household or if
+negative taking away
+
+ align:start position:0%
+negative taking away
+ 
+
+ align:start position:0%
+negative taking away
+so then we come to this programming
+
+ align:start position:0%
+so then we come to this programming
+ 
+
+ align:start position:0%
+so then we come to this programming
+problem for the determination of
+
+ align:start position:0%
+problem for the determination of
+ 
+
+ align:start position:0%
+problem for the determination of
+Pareto optimal allocations
+
+ align:start position:0%
+Pareto optimal allocations
+ 
+
+ align:start position:0%
+Pareto optimal allocations
+and despite some heavy looking notation
+
+ align:start position:0%
+and despite some heavy looking notation
+ 
+
+ align:start position:0%
+and despite some heavy looking notation
+you'll probably understand this pretty
+
+ align:start position:0%
+you'll probably understand this pretty
+ 
+
+ align:start position:0%
+you'll probably understand this pretty
+readily first of all here's the utility
+
+ align:start position:0%
+readily first of all here's the utility
+ 
+
+ align:start position:0%
+readily first of all here's the utility
+function of household J
+
+ align:start position:0%
+function of household J
+ 
+
+ align:start position:0%
+function of household J
+and all the slide does is stick into
+
+ align:start position:0%
+and all the slide does is stick into
+ 
+
+ align:start position:0%
+and all the slide does is stick into
+what would be consumption the
+
+ align:start position:0%
+what would be consumption the
+ 
+
+ align:start position:0%
+what would be consumption the
+consumption is defined at the bottom of
+
+ align:start position:0%
+consumption is defined at the bottom of
+ 
+
+ align:start position:0%
+consumption is defined at the bottom of
+the previous slide sort of resources
+
+ align:start position:0%
+the previous slide sort of resources
+ 
+
+ align:start position:0%
+the previous slide sort of resources
+available minus resources utilized for
+
+ align:start position:0%
+available minus resources utilized for
+ 
+
+ align:start position:0%
+available minus resources utilized for
+Next Period here plus the transfer these
+
+ align:start position:0%
+Next Period here plus the transfer these
+ 
+
+ align:start position:0%
+Next Period here plus the transfer these
+lambdas are the Pareto weights we're
+
+ align:start position:0%
+lambdas are the Pareto weights we're
+ 
+
+ align:start position:0%
+lambdas are the Pareto weights we're
+maximizing a Lambda weighted sum of
+
+ align:start position:0%
+maximizing a Lambda weighted sum of
+ 
+
+ align:start position:0%
+maximizing a Lambda weighted sum of
+utilities today
+
+ align:start position:0%
+utilities today
+ 
+
+ align:start position:0%
+utilities today
+and the control variables for the
+
+ align:start position:0%
+and the control variables for the
+ 
+
+ align:start position:0%
+and the control variables for the
+planter are these transfers as I've
+
+ align:start position:0%
+planter are these transfers as I've
+ 
+
+ align:start position:0%
+planter are these transfers as I've
+already said plus the level of
+
+ align:start position:0%
+already said plus the level of
+ 
+
+ align:start position:0%
+already said plus the level of
+capitalization of all the projects so
+
+ align:start position:0%
+capitalization of all the projects so
+ 
+
+ align:start position:0%
+capitalization of all the projects so
+we're trying to find an optimal
+
+ align:start position:0%
+we're trying to find an optimal
+ 
+
+ align:start position:0%
+we're trying to find an optimal
+allocation of capital as well as an
+
+ align:start position:0%
+allocation of capital as well as an
+ 
+
+ align:start position:0%
+allocation of capital as well as an
+optimal allocation of the transfers
+
+ align:start position:0%
+optimal allocation of the transfers
+ 
+
+ align:start position:0%
+optimal allocation of the transfers
+small apology the this apostrophe
+
+ align:start position:0%
+small apology the this apostrophe
+ 
+
+ align:start position:0%
+small apology the this apostrophe
+looking object shouldn't be there and on
+
+ align:start position:0%
+looking object shouldn't be there and on
+ 
+
+ align:start position:0%
+looking object shouldn't be there and on
+top of the towels it's not a prime
+
+ align:start position:0%
+top of the towels it's not a prime
+ 
+
+ align:start position:0%
+top of the towels it's not a prime
+because the transfers are decided today
+
+ align:start position:0%
+because the transfers are decided today
+ 
+
+ align:start position:0%
+because the transfers are decided today
+not next period but there's definitely a
+
+ align:start position:0%
+not next period but there's definitely a
+ 
+
+ align:start position:0%
+not next period but there's definitely a
+Prime on this Capital because the
+
+ align:start position:0%
+Prime on this Capital because the
+ 
+
+ align:start position:0%
+Prime on this Capital because the
+current state is already given the
+
+ align:start position:0%
+current state is already given the
+ 
+
+ align:start position:0%
+current state is already given the
+projects with their capitalizations the
+
+ align:start position:0%
+projects with their capitalizations the
+ 
+
+ align:start position:0%
+projects with their capitalizations the
+thing to be decided upon is how much
+
+ align:start position:0%
+thing to be decided upon is how much
+ 
+
+ align:start position:0%
+thing to be decided upon is how much
+Capital you want to invest in all the
+
+ align:start position:0%
+Capital you want to invest in all the
+ 
+
+ align:start position:0%
+Capital you want to invest in all the
+various possible projects for tomorrow
+
+ align:start position:0%
+various possible projects for tomorrow
+ 
+
+ align:start position:0%
+various possible projects for tomorrow
+um is it is it better to add a
+
+ align:start position:0%
+um is it is it better to add a
+ 
+
+ align:start position:0%
+um is it is it better to add a
+depreciation here because if you if you
+
+ align:start position:0%
+depreciation here because if you if you
+ 
+
+ align:start position:0%
+depreciation here because if you if you
+instead of a tree if you think of a
+
+ align:start position:0%
+instead of a tree if you think of a
+ 
+
+ align:start position:0%
+instead of a tree if you think of a
+machine
+
+ align:start position:0%
+machine
+ 
+
+ align:start position:0%
+machine
+yeah it will definitely depreciate yeah
+
+ align:start position:0%
+yeah it will definitely depreciate yeah
+ 
+
+ align:start position:0%
+yeah it will definitely depreciate yeah
+it's kind of loaded into this uh output
+
+ align:start position:0%
+it's kind of loaded into this uh output
+ 
+
+ align:start position:0%
+it's kind of loaded into this uh output
+so and you'll see this in the data you
+
+ align:start position:0%
+so and you'll see this in the data you
+ 
+
+ align:start position:0%
+so and you'll see this in the data you
+take net profits but you subtract off as
+
+ align:start position:0%
+take net profits but you subtract off as
+ 
+
+ align:start position:0%
+take net profits but you subtract off as
+an expense the depreciation but I mean
+
+ align:start position:0%
+an expense the depreciation but I mean
+ 
+
+ align:start position:0%
+an expense the depreciation but I mean
+it's true it's not there explicitly but
+
+ align:start position:0%
+it's true it's not there explicitly but
+ 
+
+ align:start position:0%
+it's true it's not there explicitly but
+that's where it is
+
+ align:start position:0%
+that's where it is
+ 
+
+ align:start position:0%
+that's where it is
+so yeah it should be and it is included
+
+ align:start position:0%
+so yeah it should be and it is included
+ 
+
+ align:start position:0%
+so yeah it should be and it is included
+okay okay now the other thing that makes
+
+ align:start position:0%
+okay okay now the other thing that makes
+ 
+
+ align:start position:0%
+okay okay now the other thing that makes
+this thing complicated but again you're
+
+ align:start position:0%
+this thing complicated but again you're
+ 
+
+ align:start position:0%
+this thing complicated but again you're
+already tooled up to get this right away
+
+ align:start position:0%
+already tooled up to get this right away
+ 
+
+ align:start position:0%
+already tooled up to get this right away
+these are these value functions
+
+ align:start position:0%
+these are these value functions
+ 
+
+ align:start position:0%
+these are these value functions
+so what what is the state of the world
+
+ align:start position:0%
+so what what is the state of the world
+ 
+
+ align:start position:0%
+so what what is the state of the world
+today it's total wealth that's available
+
+ align:start position:0%
+today it's total wealth that's available
+ 
+
+ align:start position:0%
+today it's total wealth that's available
+at the bottom of the slide summing
+
+ align:start position:0%
+at the bottom of the slide summing
+ 
+
+ align:start position:0%
+at the bottom of the slide summing
+overall activities in households all
+
+ align:start position:0%
+overall activities in households all
+ 
+
+ align:start position:0%
+overall activities in households all
+fruit and all trees this Capital Lambda
+
+ align:start position:0%
+fruit and all trees this Capital Lambda
+ 
+
+ align:start position:0%
+fruit and all trees this Capital Lambda
+is just the individual Pareto weights
+
+ align:start position:0%
+is just the individual Pareto weights
+ 
+
+ align:start position:0%
+is just the individual Pareto weights
+and they're fixed for all time and then
+
+ align:start position:0%
+and they're fixed for all time and then
+ 
+
+ align:start position:0%
+and they're fixed for all time and then
+you decide on these control variables
+
+ align:start position:0%
+you decide on these control variables
+ 
+
+ align:start position:0%
+you decide on these control variables
+how much to eat and how much to save in
+
+ align:start position:0%
+how much to eat and how much to save in
+ 
+
+ align:start position:0%
+how much to eat and how much to save in
+the various Technologies that's going to
+
+ align:start position:0%
+the various Technologies that's going to
+ 
+
+ align:start position:0%
+the various Technologies that's going to
+deliver a state for tomorrow which is
+
+ align:start position:0%
+deliver a state for tomorrow which is
+ 
+
+ align:start position:0%
+deliver a state for tomorrow which is
+wealth tomorrow W it would be W Prime
+
+ align:start position:0%
+wealth tomorrow W it would be W Prime
+ 
+
+ align:start position:0%
+wealth tomorrow W it would be W Prime
+just like w is this period W Prime would
+
+ align:start position:0%
+just like w is this period W Prime would
+ 
+
+ align:start position:0%
+just like w is this period W Prime would
+be for Next Period and you would have a
+
+ align:start position:0%
+be for Next Period and you would have a
+ 
+
+ align:start position:0%
+be for Next Period and you would have a
+Prime on all of these objects you'd have
+
+ align:start position:0%
+Prime on all of these objects you'd have
+ 
+
+ align:start position:0%
+Prime on all of these objects you'd have
+the fruit in the trees Next Period at
+
+ align:start position:0%
+the fruit in the trees Next Period at
+ 
+
+ align:start position:0%
+the fruit in the trees Next Period at
+Prime that's the W Prime this value
+
+ align:start position:0%
+Prime that's the W Prime this value
+ 
+
+ align:start position:0%
+Prime that's the W Prime this value
+function is as if they lived in a
+
+ align:start position:0%
+function is as if they lived in a
+ 
+
+ align:start position:0%
+function is as if they lived in a
+infinite Horizon economy they're
+
+ align:start position:0%
+infinite Horizon economy they're
+ 
+
+ align:start position:0%
+infinite Horizon economy they're
+discounting Next Period by this fee
+
+ align:start position:0%
+discounting Next Period by this fee
+ 
+
+ align:start position:0%
+discounting Next Period by this fee
+usually we use beta but beta in this
+
+ align:start position:0%
+usually we use beta but beta in this
+ 
+
+ align:start position:0%
+usually we use beta but beta in this
+lecture is reserved for something adults
+
+ align:start position:0%
+lecture is reserved for something adults
+ 
+
+ align:start position:0%
+lecture is reserved for something adults
+like a regression coefficient so Phi is
+
+ align:start position:0%
+like a regression coefficient so Phi is
+ 
+
+ align:start position:0%
+like a regression coefficient so Phi is
+the common discount rate across all the
+
+ align:start position:0%
+the common discount rate across all the
+ 
+
+ align:start position:0%
+the common discount rate across all the
+households and you remember how we got
+
+ align:start position:0%
+households and you remember how we got
+ 
+
+ align:start position:0%
+households and you remember how we got
+these V's right we had a slide at the
+
+ align:start position:0%
+these V's right we had a slide at the
+ 
+
+ align:start position:0%
+these V's right we had a slide at the
+end of one of the at the dynamic lecture
+
+ align:start position:0%
+end of one of the at the dynamic lecture
+ 
+
+ align:start position:0%
+end of one of the at the dynamic lecture
+you know act like it's a finite period
+
+ align:start position:0%
+you know act like it's a finite period
+ 
+
+ align:start position:0%
+you know act like it's a finite period
+solve for the optimum which would be you
+
+ align:start position:0%
+solve for the optimum which would be you
+ 
+
+ align:start position:0%
+solve for the optimum which would be you
+know don't fund everything eat
+
+ align:start position:0%
+know don't fund everything eat
+ 
+
+ align:start position:0%
+know don't fund everything eat
+everything in sight and then go to the
+
+ align:start position:0%
+everything in sight and then go to the
+ 
+
+ align:start position:0%
+everything in sight and then go to the
+next to last period and third to last
+
+ align:start position:0%
+next to last period and third to last
+ 
+
+ align:start position:0%
+next to last period and third to last
+period and then keep iterating as far
+
+ align:start position:0%
+period and then keep iterating as far
+ 
+
+ align:start position:0%
+period and then keep iterating as far
+back into the present as possible and
+
+ align:start position:0%
+back into the present as possible and
+ 
+
+ align:start position:0%
+back into the present as possible and
+this value function which would have a t
+
+ align:start position:0%
+this value function which would have a t
+ 
+
+ align:start position:0%
+this value function which would have a t
+on it for the length of the Horizon will
+
+ align:start position:0%
+on it for the length of the Horizon will
+ 
+
+ align:start position:0%
+on it for the length of the Horizon will
+go to something stable as if we had
+
+ align:start position:0%
+go to something stable as if we had
+ 
+
+ align:start position:0%
+go to something stable as if we had
+solved the infinite Horizon problem so
+
+ align:start position:0%
+solved the infinite Horizon problem so
+ 
+
+ align:start position:0%
+solved the infinite Horizon problem so
+that's all loaded up in here too
+
+ align:start position:0%
+that's all loaded up in here too
+ 
+
+ align:start position:0%
+that's all loaded up in here too
+questions about this slide
+
+ align:start position:0%
+questions about this slide
+ 
+
+ align:start position:0%
+questions about this slide
+oh one last thing you can't put negative
+
+ align:start position:0%
+oh one last thing you can't put negative
+ 
+
+ align:start position:0%
+oh one last thing you can't put negative
+Capital into the ground I mean Capital
+
+ align:start position:0%
+Capital into the ground I mean Capital
+ 
+
+ align:start position:0%
+Capital into the ground I mean Capital
+could be zero but in which case you're
+
+ align:start position:0%
+could be zero but in which case you're
+ 
+
+ align:start position:0%
+could be zero but in which case you're
+not doing that activity or it's positive
+
+ align:start position:0%
+not doing that activity or it's positive
+ 
+
+ align:start position:0%
+not doing that activity or it's positive
+in which case you are doing the activity
+
+ align:start position:0%
+in which case you are doing the activity
+ 
+
+ align:start position:0%
+in which case you are doing the activity
+this is true over all projects I and all
+
+ align:start position:0%
+this is true over all projects I and all
+ 
+
+ align:start position:0%
+this is true over all projects I and all
+households J
+
+ align:start position:0%
+households J
+ 
+
+ align:start position:0%
+households J
+you can set that thing up as a
+
+ align:start position:0%
+you can set that thing up as a
+ 
+
+ align:start position:0%
+you can set that thing up as a
+lagrangian with the Shadow prices and
+
+ align:start position:0%
+lagrangian with the Shadow prices and
+ 
+
+ align:start position:0%
+lagrangian with the Shadow prices and
+solve and you'll get kind of a familiar
+
+ align:start position:0%
+solve and you'll get kind of a familiar
+ 
+
+ align:start position:0%
+solve and you'll get kind of a familiar
+condition if you differentiate with
+
+ align:start position:0%
+condition if you differentiate with
+ 
+
+ align:start position:0%
+condition if you differentiate with
+respect to consumptions or the transfers
+
+ align:start position:0%
+respect to consumptions or the transfers
+ 
+
+ align:start position:0%
+respect to consumptions or the transfers
+for that matter uh you will get that
+
+ align:start position:0%
+for that matter uh you will get that
+ 
+
+ align:start position:0%
+for that matter uh you will get that
+these Lambda weighted margin utilities
+
+ align:start position:0%
+these Lambda weighted margin utilities
+ 
+
+ align:start position:0%
+these Lambda weighted margin utilities
+should be the same overall households
+
+ align:start position:0%
+should be the same overall households
+ 
+
+ align:start position:0%
+should be the same overall households
+and equal to a common LaGrange
+
+ align:start position:0%
+and equal to a common LaGrange
+ 
+
+ align:start position:0%
+and equal to a common LaGrange
+multiplier on the current resource
+
+ align:start position:0%
+multiplier on the current resource
+ 
+
+ align:start position:0%
+multiplier on the current resource
+constraint mu so you've actually seen
+
+ align:start position:0%
+constraint mu so you've actually seen
+ 
+
+ align:start position:0%
+constraint mu so you've actually seen
+this before
+
+ align:start position:0%
+this before
+ 
+
+ align:start position:0%
+this before
+it's exactly equal to what we had before
+
+ align:start position:0%
+it's exactly equal to what we had before
+ 
+
+ align:start position:0%
+it's exactly equal to what we had before
+in Village India without consideration
+
+ align:start position:0%
+in Village India without consideration
+ 
+
+ align:start position:0%
+in Village India without consideration
+of production
+
+ align:start position:0%
+of production
+ 
+
+ align:start position:0%
+of production
+but we're going to get something else
+
+ align:start position:0%
+but we're going to get something else
+ 
+
+ align:start position:0%
+but we're going to get something else
+namely when we look at the control
+
+ align:start position:0%
+namely when we look at the control
+ 
+
+ align:start position:0%
+namely when we look at the control
+variable the capital control variables
+
+ align:start position:0%
+variable the capital control variables
+ 
+
+ align:start position:0%
+variable the capital control variables
+we're going to get something that links
+
+ align:start position:0%
+we're going to get something that links
+ 
+
+ align:start position:0%
+we're going to get something that links
+marginal utility today to effectively to
+
+ align:start position:0%
+marginal utility today to effectively to
+ 
+
+ align:start position:0%
+marginal utility today to effectively to
+marginal utility Next Period and that is
+
+ align:start position:0%
+marginal utility Next Period and that is
+ 
+
+ align:start position:0%
+marginal utility Next Period and that is
+that the Lambda weighted margin utility
+
+ align:start position:0%
+that the Lambda weighted margin utility
+ 
+
+ align:start position:0%
+that the Lambda weighted margin utility
+of consumption today for household J If
+
+ align:start position:0%
+of consumption today for household J If
+ 
+
+ align:start position:0%
+of consumption today for household J If
+This Were said equal should be equal to
+
+ align:start position:0%
+This Were said equal should be equal to
+ 
+
+ align:start position:0%
+This Were said equal should be equal to
+the Future margin utility well if you
+
+ align:start position:0%
+the Future margin utility well if you
+ 
+
+ align:start position:0%
+the Future margin utility well if you
+take a unit of resource today
+
+ align:start position:0%
+take a unit of resource today
+ 
+
+ align:start position:0%
+take a unit of resource today
+infinitesimally small and instead of
+
+ align:start position:0%
+infinitesimally small and instead of
+ 
+
+ align:start position:0%
+infinitesimally small and instead of
+eating it you invest it what you'll get
+
+ align:start position:0%
+eating it you invest it what you'll get
+ 
+
+ align:start position:0%
+eating it you invest it what you'll get
+tomorrow would be the derivative of the
+
+ align:start position:0%
+tomorrow would be the derivative of the
+ 
+
+ align:start position:0%
+tomorrow would be the derivative of the
+production function of that investment
+
+ align:start position:0%
+production function of that investment
+ 
+
+ align:start position:0%
+production function of that investment
+plus you get the tree back that one unit
+
+ align:start position:0%
+plus you get the tree back that one unit
+ 
+
+ align:start position:0%
+plus you get the tree back that one unit
+back and that return stream is going to
+
+ align:start position:0%
+back and that return stream is going to
+ 
+
+ align:start position:0%
+back and that return stream is going to
+be evaluated at the margin utility of
+
+ align:start position:0%
+be evaluated at the margin utility of
+ 
+
+ align:start position:0%
+be evaluated at the margin utility of
+wealth which is the derivative of this
+
+ align:start position:0%
+wealth which is the derivative of this
+ 
+
+ align:start position:0%
+wealth which is the derivative of this
+value function at tomorrow's wealth so
+
+ align:start position:0%
+value function at tomorrow's wealth so
+ 
+
+ align:start position:0%
+value function at tomorrow's wealth so
+again we're just taking a derivative of
+
+ align:start position:0%
+again we're just taking a derivative of
+ 
+
+ align:start position:0%
+again we're just taking a derivative of
+this right hand side term
+
+ align:start position:0%
+this right hand side term
+ 
+
+ align:start position:0%
+this right hand side term
+questions so it's written as a weak
+
+ align:start position:0%
+questions so it's written as a weak
+ 
+
+ align:start position:0%
+questions so it's written as a weak
+inequality it could be less than zero if
+
+ align:start position:0%
+inequality it could be less than zero if
+ 
+
+ align:start position:0%
+inequality it could be less than zero if
+it's less than zero let's take the
+
+ align:start position:0%
+it's less than zero let's take the
+ 
+
+ align:start position:0%
+it's less than zero let's take the
+margin utility of consumption today
+
+ align:start position:0%
+margin utility of consumption today
+ 
+
+ align:start position:0%
+margin utility of consumption today
+which is minus on and on the left hand
+
+ align:start position:0%
+which is minus on and on the left hand
+ 
+
+ align:start position:0%
+which is minus on and on the left hand
+side and put it on the right hand side
+
+ align:start position:0%
+side and put it on the right hand side
+ 
+
+ align:start position:0%
+side and put it on the right hand side
+and that would say the weighted margin
+
+ align:start position:0%
+and that would say the weighted margin
+ 
+
+ align:start position:0%
+and that would say the weighted margin
+utility of consumption today is strictly
+
+ align:start position:0%
+utility of consumption today is strictly
+ 
+
+ align:start position:0%
+utility of consumption today is strictly
+greater than the margin utility you
+
+ align:start position:0%
+greater than the margin utility you
+ 
+
+ align:start position:0%
+greater than the margin utility you
+would get tomorrow so they're going to
+
+ align:start position:0%
+would get tomorrow so they're going to
+ 
+
+ align:start position:0%
+would get tomorrow so they're going to
+hit a corner they would like actually
+
+ align:start position:0%
+hit a corner they would like actually
+ 
+
+ align:start position:0%
+hit a corner they would like actually
+the capital level to go negative because
+
+ align:start position:0%
+the capital level to go negative because
+ 
+
+ align:start position:0%
+the capital level to go negative because
+they're kind of desperate to eat today
+
+ align:start position:0%
+they're kind of desperate to eat today
+ 
+
+ align:start position:0%
+they're kind of desperate to eat today
+the marginal utility return today is
+
+ align:start position:0%
+the marginal utility return today is
+ 
+
+ align:start position:0%
+the marginal utility return today is
+higher than it will be next period but
+
+ align:start position:0%
+higher than it will be next period but
+ 
+
+ align:start position:0%
+higher than it will be next period but
+of course we're not allowing them to go
+
+ align:start position:0%
+of course we're not allowing them to go
+ 
+
+ align:start position:0%
+of course we're not allowing them to go
+negative so hence the inequality if if
+
+ align:start position:0%
+negative so hence the inequality if if
+ 
+
+ align:start position:0%
+negative so hence the inequality if if
+to remind you in other contexts we write
+
+ align:start position:0%
+to remind you in other contexts we write
+ 
+
+ align:start position:0%
+to remind you in other contexts we write
+out the full lagrangian program we put
+
+ align:start position:0%
+out the full lagrangian program we put
+ 
+
+ align:start position:0%
+out the full lagrangian program we put
+an extra LaGrange multiplier on these
+
+ align:start position:0%
+an extra LaGrange multiplier on these
+ 
+
+ align:start position:0%
+an extra LaGrange multiplier on these
+non-negativity constraints then this
+
+ align:start position:0%
+non-negativity constraints then this
+ 
+
+ align:start position:0%
+non-negativity constraints then this
+whole thing would be at an equality but
+
+ align:start position:0%
+whole thing would be at an equality but
+ 
+
+ align:start position:0%
+whole thing would be at an equality but
+it would have as well the potentially
+
+ align:start position:0%
+it would have as well the potentially
+ 
+
+ align:start position:0%
+it would have as well the potentially
+positive LaGrange multiplier
+
+ align:start position:0%
+positive LaGrange multiplier
+ 
+
+ align:start position:0%
+positive LaGrange multiplier
+anyway the conclusion is not all
+
+ align:start position:0%
+anyway the conclusion is not all
+ 
+
+ align:start position:0%
+anyway the conclusion is not all
+activities need to be funded you might
+
+ align:start position:0%
+activities need to be funded you might
+ 
+
+ align:start position:0%
+activities need to be funded you might
+actually want to unfund them and draw
+
+ align:start position:0%
+actually want to unfund them and draw
+ 
+
+ align:start position:0%
+actually want to unfund them and draw
+resources out of them that aren't there
+
+ align:start position:0%
+resources out of them that aren't there
+ 
+
+ align:start position:0%
+resources out of them that aren't there
+you can't do that so you set them equal
+
+ align:start position:0%
+you can't do that so you set them equal
+ 
+
+ align:start position:0%
+you can't do that so you set them equal
+to zero others get funded at a positive
+
+ align:start position:0%
+to zero others get funded at a positive
+ 
+
+ align:start position:0%
+to zero others get funded at a positive
+level we will be focusing a lot on the
+
+ align:start position:0%
+level we will be focusing a lot on the
+ 
+
+ align:start position:0%
+level we will be focusing a lot on the
+set of activities over households for
+
+ align:start position:0%
+set of activities over households for
+ 
+
+ align:start position:0%
+set of activities over households for
+which this is equal to zero and those
+
+ align:start position:0%
+which this is equal to zero and those
+ 
+
+ align:start position:0%
+which this is equal to zero and those
+are funded projects okay so it looks
+
+ align:start position:0%
+are funded projects okay so it looks
+ 
+
+ align:start position:0%
+are funded projects okay so it looks
+like this is entirely closed economy but
+
+ align:start position:0%
+like this is entirely closed economy but
+ 
+
+ align:start position:0%
+like this is entirely closed economy but
+as I said these techniques generalize so
+
+ align:start position:0%
+as I said these techniques generalize so
+ 
+
+ align:start position:0%
+as I said these techniques generalize so
+we can think of a village as a small
+
+ align:start position:0%
+we can think of a village as a small
+ 
+
+ align:start position:0%
+we can think of a village as a small
+open economy and maybe they can go to an
+
+ align:start position:0%
+open economy and maybe they can go to an
+ 
+
+ align:start position:0%
+open economy and maybe they can go to an
+outside bank and borrow money in which
+
+ align:start position:0%
+outside bank and borrow money in which
+ 
+
+ align:start position:0%
+outside bank and borrow money in which
+case we'd have to change the wealth
+
+ align:start position:0%
+case we'd have to change the wealth
+ 
+
+ align:start position:0%
+case we'd have to change the wealth
+variable to subtract off the principal
+
+ align:start position:0%
+variable to subtract off the principal
+ 
+
+ align:start position:0%
+variable to subtract off the principal
+and interest that's coming due today but
+
+ align:start position:0%
+and interest that's coming due today but
+ 
+
+ align:start position:0%
+and interest that's coming due today but
+add in the debt that they enter into
+
+ align:start position:0%
+add in the debt that they enter into
+ 
+
+ align:start position:0%
+add in the debt that they enter into
+today that will come due the next period
+
+ align:start position:0%
+today that will come due the next period
+ 
+
+ align:start position:0%
+today that will come due the next period
+nothing changes these first order
+
+ align:start position:0%
+nothing changes these first order
+ 
+
+ align:start position:0%
+nothing changes these first order
+conditions don't change oh it's good for
+
+ align:start position:0%
+conditions don't change oh it's good for
+ 
+
+ align:start position:0%
+conditions don't change oh it's good for
+them in terms of smoothing if the
+
+ align:start position:0%
+them in terms of smoothing if the
+ 
+
+ align:start position:0%
+them in terms of smoothing if the
+village wealth is low The Village as a
+
+ align:start position:0%
+village wealth is low The Village as a
+ 
+
+ align:start position:0%
+village wealth is low The Village as a
+whole might want to borrow that's fine
+
+ align:start position:0%
+whole might want to borrow that's fine
+ 
+
+ align:start position:0%
+whole might want to borrow that's fine
+so the quantitative solution can change
+
+ align:start position:0%
+so the quantitative solution can change
+ 
+
+ align:start position:0%
+so the quantitative solution can change
+but our characterization in terms of
+
+ align:start position:0%
+but our characterization in terms of
+ 
+
+ align:start position:0%
+but our characterization in terms of
+these first order conditions will not
+
+ align:start position:0%
+these first order conditions will not
+ 
+
+ align:start position:0%
+these first order conditions will not
+change but we do not need to assume a
+
+ align:start position:0%
+change but we do not need to assume a
+ 
+
+ align:start position:0%
+change but we do not need to assume a
+closed economy all right so what the
+
+ align:start position:0%
+closed economy all right so what the
+ 
+
+ align:start position:0%
+closed economy all right so what the
+heck is this well
+
+ align:start position:0%
+heck is this well
+ 
+
+ align:start position:0%
+heck is this well
+this mu is the land awaited marketing
+
+ align:start position:0%
+this mu is the land awaited marketing
+ 
+
+ align:start position:0%
+this mu is the land awaited marketing
+utility I substituted that into this
+
+ align:start position:0%
+utility I substituted that into this
+ 
+
+ align:start position:0%
+utility I substituted that into this
+left-hand side of the second expression
+
+ align:start position:0%
+left-hand side of the second expression
+ 
+
+ align:start position:0%
+left-hand side of the second expression
+set it equal to zero
+
+ align:start position:0%
+set it equal to zero
+ 
+
+ align:start position:0%
+set it equal to zero
+and then you've got two terms dividing
+
+ align:start position:0%
+and then you've got two terms dividing
+ 
+
+ align:start position:0%
+and then you've got two terms dividing
+through by this
+
+ align:start position:0%
+through by this
+ 
+
+ align:start position:0%
+through by this
+you would set everything equal to one so
+
+ align:start position:0%
+you would set everything equal to one so
+ 
+
+ align:start position:0%
+you would set everything equal to one so
+it's actually easier to look at the
+
+ align:start position:0%
+it's actually easier to look at the
+ 
+
+ align:start position:0%
+it's actually easier to look at the
+algebra than it is to to say it in words
+
+ align:start position:0%
+algebra than it is to to say it in words
+ 
+
+ align:start position:0%
+algebra than it is to to say it in words
+we take mu here and divide this term by
+
+ align:start position:0%
+we take mu here and divide this term by
+ 
+
+ align:start position:0%
+we take mu here and divide this term by
+mu which makes it equal to Unity and the
+
+ align:start position:0%
+mu which makes it equal to Unity and the
+ 
+
+ align:start position:0%
+mu which makes it equal to Unity and the
+second term by mu which is what is being
+
+ align:start position:0%
+second term by mu which is what is being
+ 
+
+ align:start position:0%
+second term by mu which is what is being
+displayed here
+
+ align:start position:0%
+displayed here
+ 
+
+ align:start position:0%
+displayed here
+and then the rest is algebra although
+
+ align:start position:0%
+and then the rest is algebra although
+ 
+
+ align:start position:0%
+and then the rest is algebra although
+it's kind of revealing that we can take
+
+ align:start position:0%
+it's kind of revealing that we can take
+ 
+
+ align:start position:0%
+it's kind of revealing that we can take
+this expectation operator outside the
+
+ align:start position:0%
+this expectation operator outside the
+ 
+
+ align:start position:0%
+this expectation operator outside the
+whole expression because these returns
+
+ align:start position:0%
+whole expression because these returns
+ 
+
+ align:start position:0%
+whole expression because these returns
+are random I'm not sure I've been
+
+ align:start position:0%
+are random I'm not sure I've been
+ 
+
+ align:start position:0%
+are random I'm not sure I've been
+emphasizing that enough
+
+ align:start position:0%
+emphasizing that enough
+ 
+
+ align:start position:0%
+emphasizing that enough
+it looked like constants because you
+
+ align:start position:0%
+it looked like constants because you
+ 
+
+ align:start position:0%
+it looked like constants because you
+just have the level of capital but the
+
+ align:start position:0%
+just have the level of capital but the
+ 
+
+ align:start position:0%
+just have the level of capital but the
+the return on a unit of capital is
+
+ align:start position:0%
+the return on a unit of capital is
+ 
+
+ align:start position:0%
+the return on a unit of capital is
+random where did that first start to
+
+ align:start position:0%
+random where did that first start to
+ 
+
+ align:start position:0%
+random where did that first start to
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+I should have said it right here when we
+
+ align:start position:0%
+I should have said it right here when we
+ 
+
+ align:start position:0%
+I should have said it right here when we
+had that expectation operator so anyway
+
+ align:start position:0%
+had that expectation operator so anyway
+ 
+
+ align:start position:0%
+had that expectation operator so anyway
+bring the expectation operator out in
+
+ align:start position:0%
+bring the expectation operator out in
+ 
+
+ align:start position:0%
+bring the expectation operator out in
+front of everything and then adopt some
+
+ align:start position:0%
+front of everything and then adopt some
+ 
+
+ align:start position:0%
+front of everything and then adopt some
+very cryptic notation M actually M Prime
+
+ align:start position:0%
+very cryptic notation M actually M Prime
+ 
+
+ align:start position:0%
+very cryptic notation M actually M Prime
+for for this term which is essentially
+
+ align:start position:0%
+for for this term which is essentially
+ 
+
+ align:start position:0%
+for for this term which is essentially
+the discounted LaGrange multiplier Next
+
+ align:start position:0%
+the discounted LaGrange multiplier Next
+ 
+
+ align:start position:0%
+the discounted LaGrange multiplier Next
+Period divided by the LaGrange
+
+ align:start position:0%
+Period divided by the LaGrange
+ 
+
+ align:start position:0%
+Period divided by the LaGrange
+multiplier today
+
+ align:start position:0%
+multiplier today
+ 
+
+ align:start position:0%
+multiplier today
+so that that's like a discount Factor
+
+ align:start position:0%
+so that that's like a discount Factor
+ 
+
+ align:start position:0%
+so that that's like a discount Factor
+call it m Prime and this r capital r is
+
+ align:start position:0%
+call it m Prime and this r capital r is
+ 
+
+ align:start position:0%
+call it m Prime and this r capital r is
+the total return on the project being
+
+ align:start position:0%
+the total return on the project being
+ 
+
+ align:start position:0%
+the total return on the project being
+run the activity I run by household J
+
+ align:start position:0%
+run the activity I run by household J
+ 
+
+ align:start position:0%
+run the activity I run by household J
+the return you get the tree back plus
+
+ align:start position:0%
+the return you get the tree back plus
+ 
+
+ align:start position:0%
+the return you get the tree back plus
+the fruit and this this is a prime here
+
+ align:start position:0%
+the fruit and this this is a prime here
+ 
+
+ align:start position:0%
+the fruit and this this is a prime here
+it's the marginal return obviously
+
+ align:start position:0%
+it's the marginal return obviously
+ 
+
+ align:start position:0%
+it's the marginal return obviously
+because when we looked at the first
+
+ align:start position:0%
+because when we looked at the first
+ 
+
+ align:start position:0%
+because when we looked at the first
+order condition we were varying the
+
+ align:start position:0%
+order condition we were varying the
+ 
+
+ align:start position:0%
+order condition we were varying the
+level of capital so we picked up a
+
+ align:start position:0%
+level of capital so we picked up a
+ 
+
+ align:start position:0%
+level of capital so we picked up a
+derivative in the production function so
+
+ align:start position:0%
+derivative in the production function so
+ 
+
+ align:start position:0%
+derivative in the production function so
+this is just notation but it's very
+
+ align:start position:0%
+this is just notation but it's very
+ 
+
+ align:start position:0%
+this is just notation but it's very
+convenient notation
+
+ align:start position:0%
+convenient notation
+ 
+
+ align:start position:0%
+convenient notation
+so it's saying that for all activities I
+
+ align:start position:0%
+so it's saying that for all activities I
+ 
+
+ align:start position:0%
+so it's saying that for all activities I
+run by households J this product the
+
+ align:start position:0%
+run by households J this product the
+ 
+
+ align:start position:0%
+run by households J this product the
+this expected product is equal to one
+
+ align:start position:0%
+this expected product is equal to one
+ 
+
+ align:start position:0%
+this expected product is equal to one
+furthermore looking at that expected
+
+ align:start position:0%
+furthermore looking at that expected
+ 
+
+ align:start position:0%
+furthermore looking at that expected
+product there's a result in statistics
+
+ align:start position:0%
+product there's a result in statistics
+ 
+
+ align:start position:0%
+product there's a result in statistics
+that we didn't put into the lecture on
+
+ align:start position:0%
+that we didn't put into the lecture on
+ 
+
+ align:start position:0%
+that we didn't put into the lecture on
+uncertainty but it's easy enough to
+
+ align:start position:0%
+uncertainty but it's easy enough to
+ 
+
+ align:start position:0%
+uncertainty but it's easy enough to
+state which is expectation of two random
+
+ align:start position:0%
+state which is expectation of two random
+ 
+
+ align:start position:0%
+state which is expectation of two random
+variables is equal to the product of the
+
+ align:start position:0%
+variables is equal to the product of the
+ 
+
+ align:start position:0%
+variables is equal to the product of the
+expectations adjusted by the covariance
+
+ align:start position:0%
+expectations adjusted by the covariance
+ 
+
+ align:start position:0%
+expectations adjusted by the covariance
+of the two variables if the covariance
+
+ align:start position:0%
+of the two variables if the covariance
+ 
+
+ align:start position:0%
+of the two variables if the covariance
+is zero then these variants these
+
+ align:start position:0%
+is zero then these variants these
+ 
+
+ align:start position:0%
+is zero then these variants these
+individual variables are independent and
+
+ align:start position:0%
+individual variables are independent and
+ 
+
+ align:start position:0%
+individual variables are independent and
+it's just a product of the expectations
+
+ align:start position:0%
+it's just a product of the expectations
+ 
+
+ align:start position:0%
+it's just a product of the expectations
+but the covariance is an easy way to
+
+ align:start position:0%
+but the covariance is an easy way to
+ 
+
+ align:start position:0%
+but the covariance is an easy way to
+adjust if they're not independent so now
+
+ align:start position:0%
+adjust if they're not independent so now
+ 
+
+ align:start position:0%
+adjust if they're not independent so now
+we just substitute in that formula in
+
+ align:start position:0%
+we just substitute in that formula in
+ 
+
+ align:start position:0%
+we just substitute in that formula in
+the previous slide which had this
+
+ align:start position:0%
+the previous slide which had this
+ 
+
+ align:start position:0%
+the previous slide which had this
+expression on the left we now substitute
+
+ align:start position:0%
+expression on the left we now substitute
+ 
+
+ align:start position:0%
+expression on the left we now substitute
+in the expression on the right and
+
+ align:start position:0%
+in the expression on the right and
+ 
+
+ align:start position:0%
+in the expression on the right and
+manipulate by dividing through this
+
+ align:start position:0%
+manipulate by dividing through this
+ 
+
+ align:start position:0%
+manipulate by dividing through this
+expectation of M Prime and we get this
+
+ align:start position:0%
+expectation of M Prime and we get this
+ 
+
+ align:start position:0%
+expectation of M Prime and we get this
+object here so the expected return on
+
+ align:start position:0%
+object here so the expected return on
+ 
+
+ align:start position:0%
+object here so the expected return on
+activity I run by household J
+
+ align:start position:0%
+activity I run by household J
+ 
+
+ align:start position:0%
+activity I run by household J
+expect to return next period as an
+
+ align:start position:0%
+expect to return next period as an
+ 
+
+ align:start position:0%
+expect to return next period as an
+Intercept in some kind of product term
+
+ align:start position:0%
+Intercept in some kind of product term
+ 
+
+ align:start position:0%
+Intercept in some kind of product term
+and I'm about to give you an
+
+ align:start position:0%
+and I'm about to give you an
+ 
+
+ align:start position:0%
+and I'm about to give you an
+interpretation of what these are and in
+
+ align:start position:0%
+interpretation of what these are and in
+ 
+
+ align:start position:0%
+interpretation of what these are and in
+some respects this beta is going to be a
+
+ align:start position:0%
+some respects this beta is going to be a
+ 
+
+ align:start position:0%
+some respects this beta is going to be a
+regression coefficient and the Lambda is
+
+ align:start position:0%
+regression coefficient and the Lambda is
+ 
+
+ align:start position:0%
+regression coefficient and the Lambda is
+going to be a measure of social risk
+
+ align:start position:0%
+going to be a measure of social risk
+ 
+
+ align:start position:0%
+going to be a measure of social risk
+in particular finally
+
+ align:start position:0%
+in particular finally
+ 
+
+ align:start position:0%
+in particular finally
+if we imagine those production functions
+
+ align:start position:0%
+if we imagine those production functions
+ 
+
+ align:start position:0%
+if we imagine those production functions
+are linear
+
+ align:start position:0%
+are linear
+ 
+
+ align:start position:0%
+are linear
+then the return on activity I run by
+
+ align:start position:0%
+then the return on activity I run by
+ 
+
+ align:start position:0%
+then the return on activity I run by
+household J is linear in the capital
+
+ align:start position:0%
+household J is linear in the capital
+ 
+
+ align:start position:0%
+household J is linear in the capital
+constant returns to scale however as I
+
+ align:start position:0%
+constant returns to scale however as I
+ 
+
+ align:start position:0%
+constant returns to scale however as I
+have been trying to say this return this
+
+ align:start position:0%
+have been trying to say this return this
+ 
+
+ align:start position:0%
+have been trying to say this return this
+little r thing is a random variable
+
+ align:start position:0%
+little r thing is a random variable
+ 
+
+ align:start position:0%
+little r thing is a random variable
+anyway the marginal return is that
+
+ align:start position:0%
+anyway the marginal return is that
+ 
+
+ align:start position:0%
+anyway the marginal return is that
+little r so also is the average return
+
+ align:start position:0%
+little r so also is the average return
+ 
+
+ align:start position:0%
+little r so also is the average return
+for that matter and we can talk about
+
+ align:start position:0%
+for that matter and we can talk about
+ 
+
+ align:start position:0%
+for that matter and we can talk about
+the growth rate of return equal one plus
+
+ align:start position:0%
+the growth rate of return equal one plus
+ 
+
+ align:start position:0%
+the growth rate of return equal one plus
+the net rate of return as a definition
+
+ align:start position:0%
+the net rate of return as a definition
+ 
+
+ align:start position:0%
+the net rate of return as a definition
+of capital r just so you might feel a
+
+ align:start position:0%
+of capital r just so you might feel a
+ 
+
+ align:start position:0%
+of capital r just so you might feel a
+bit more comfortable if we have a
+
+ align:start position:0%
+bit more comfortable if we have a
+ 
+
+ align:start position:0%
+bit more comfortable if we have a
+constant returns to scale production
+
+ align:start position:0%
+constant returns to scale production
+ 
+
+ align:start position:0%
+constant returns to scale production
+function actually finally modeling other
+
+ align:start position:0%
+function actually finally modeling other
+ 
+
+ align:start position:0%
+function actually finally modeling other
+inputs like labor and materials and so
+
+ align:start position:0%
+inputs like labor and materials and so
+ 
+
+ align:start position:0%
+inputs like labor and materials and so
+on if you optimize that and put the
+
+ align:start position:0%
+on if you optimize that and put the
+ 
+
+ align:start position:0%
+on if you optimize that and put the
+optimized inputs back into the function
+
+ align:start position:0%
+optimized inputs back into the function
+ 
+
+ align:start position:0%
+optimized inputs back into the function
+you would get this derived function
+
+ align:start position:0%
+you would get this derived function
+ 
+
+ align:start position:0%
+you would get this derived function
+which is linear in the Capital stock so
+
+ align:start position:0%
+which is linear in the Capital stock so
+ 
+
+ align:start position:0%
+which is linear in the Capital stock so
+that's where it's coming from but I
+
+ align:start position:0%
+that's where it's coming from but I
+ 
+
+ align:start position:0%
+that's where it's coming from but I
+didn't give you that algebra secondly
+
+ align:start position:0%
+didn't give you that algebra secondly
+ 
+
+ align:start position:0%
+didn't give you that algebra secondly
+what about preferences let's let the
+
+ align:start position:0%
+what about preferences let's let the
+ 
+
+ align:start position:0%
+what about preferences let's let the
+value function be quadratic so you've
+
+ align:start position:0%
+value function be quadratic so you've
+ 
+
+ align:start position:0%
+value function be quadratic so you've
+seen these before W star is kind of a
+
+ align:start position:0%
+seen these before W star is kind of a
+ 
+
+ align:start position:0%
+seen these before W star is kind of a
+bliss point and W less than W star so
+
+ align:start position:0%
+bliss point and W less than W star so
+ 
+
+ align:start position:0%
+bliss point and W less than W star so
+that the margin utility of wealth is
+
+ align:start position:0%
+that the margin utility of wealth is
+ 
+
+ align:start position:0%
+that the margin utility of wealth is
+always strictly positive so if we go
+
+ align:start position:0%
+always strictly positive so if we go
+ 
+
+ align:start position:0%
+always strictly positive so if we go
+back to this guy here and start
+
+ align:start position:0%
+back to this guy here and start
+ 
+
+ align:start position:0%
+back to this guy here and start
+substituting in what we know about
+
+ align:start position:0%
+substituting in what we know about
+ 
+
+ align:start position:0%
+substituting in what we know about
+assumed about the production function
+
+ align:start position:0%
+assumed about the production function
+ 
+
+ align:start position:0%
+assumed about the production function
+and utility function now we're actually
+
+ align:start position:0%
+and utility function now we're actually
+ 
+
+ align:start position:0%
+and utility function now we're actually
+going to get an expression which says
+
+ align:start position:0%
+going to get an expression which says
+ 
+
+ align:start position:0%
+going to get an expression which says
+the average or expected return on
+
+ align:start position:0%
+the average or expected return on
+ 
+
+ align:start position:0%
+the average or expected return on
+household J's activities less the
+
+ align:start position:0%
+household J's activities less the
+ 
+
+ align:start position:0%
+household J's activities less the
+risk-free rate is equal to Beta J for
+
+ align:start position:0%
+risk-free rate is equal to Beta J for
+ 
+
+ align:start position:0%
+risk-free rate is equal to Beta J for
+household J times the expected return in
+
+ align:start position:0%
+household J times the expected return in
+ 
+
+ align:start position:0%
+household J times the expected return in
+the whole village minus the risk-free
+
+ align:start position:0%
+the whole village minus the risk-free
+ 
+
+ align:start position:0%
+the whole village minus the risk-free
+rate in fact you can put this R Prime F
+
+ align:start position:0%
+rate in fact you can put this R Prime F
+ 
+
+ align:start position:0%
+rate in fact you can put this R Prime F
+the risk-free rate on the right hand
+
+ align:start position:0%
+the risk-free rate on the right hand
+ 
+
+ align:start position:0%
+the risk-free rate on the right hand
+side so that would be the constant so
+
+ align:start position:0%
+side so that would be the constant so
+ 
+
+ align:start position:0%
+side so that would be the constant so
+it's constant plus Theta times this guy
+
+ align:start position:0%
+it's constant plus Theta times this guy
+ 
+
+ align:start position:0%
+it's constant plus Theta times this guy
+and let me Define these terms a little
+
+ align:start position:0%
+and let me Define these terms a little
+ 
+
+ align:start position:0%
+and let me Define these terms a little
+bit R Prime J no longer has an I on it
+
+ align:start position:0%
+bit R Prime J no longer has an I on it
+ 
+
+ align:start position:0%
+bit R Prime J no longer has an I on it
+because it's the weighted return over
+
+ align:start position:0%
+because it's the weighted return over
+ 
+
+ align:start position:0%
+because it's the weighted return over
+all the activities run by household J
+
+ align:start position:0%
+all the activities run by household J
+ 
+
+ align:start position:0%
+all the activities run by household J
+likewise the return for the whole
+
+ align:start position:0%
+likewise the return for the whole
+ 
+
+ align:start position:0%
+likewise the return for the whole
+Village Market if you like m is the
+
+ align:start position:0%
+Village Market if you like m is the
+ 
+
+ align:start position:0%
+Village Market if you like m is the
+weighted average return over all
+
+ align:start position:0%
+weighted average return over all
+ 
+
+ align:start position:0%
+weighted average return over all
+activities and all households so you
+
+ align:start position:0%
+activities and all households so you
+ 
+
+ align:start position:0%
+activities and all households so you
+take the capitalization of activity I
+
+ align:start position:0%
+take the capitalization of activity I
+ 
+
+ align:start position:0%
+take the capitalization of activity I
+run by household Jay look at the return
+
+ align:start position:0%
+run by household Jay look at the return
+ 
+
+ align:start position:0%
+run by household Jay look at the return
+on that as up here activity I run by
+
+ align:start position:0%
+on that as up here activity I run by
+ 
+
+ align:start position:0%
+on that as up here activity I run by
+household J some over for the household
+
+ align:start position:0%
+household J some over for the household
+ 
+
+ align:start position:0%
+household J some over for the household
+all activities I some over all
+
+ align:start position:0%
+all activities I some over all
+ 
+
+ align:start position:0%
+all activities I some over all
+households J you're getting a total
+
+ align:start position:0%
+households J you're getting a total
+ 
+
+ align:start position:0%
+households J you're getting a total
+return over all activities in all
+
+ align:start position:0%
+return over all activities in all
+ 
+
+ align:start position:0%
+return over all activities in all
+households and to get a rate of return
+
+ align:start position:0%
+households and to get a rate of return
+ 
+
+ align:start position:0%
+households and to get a rate of return
+you divide by the level of
+
+ align:start position:0%
+you divide by the level of
+ 
+
+ align:start position:0%
+you divide by the level of
+capitalization and the total level of
+
+ align:start position:0%
+capitalization and the total level of
+ 
+
+ align:start position:0%
+capitalization and the total level of
+capitalization is just the sum of the
+
+ align:start position:0%
+capitalization is just the sum of the
+ 
+
+ align:start position:0%
+capitalization is just the sum of the
+capitals over all activities and
+
+ align:start position:0%
+capitals over all activities and
+ 
+
+ align:start position:0%
+capitals over all activities and
+projects and what is this beta this beta
+
+ align:start position:0%
+projects and what is this beta this beta
+ 
+
+ align:start position:0%
+projects and what is this beta this beta
+is just a covariance divided by a
+
+ align:start position:0%
+is just a covariance divided by a
+ 
+
+ align:start position:0%
+is just a covariance divided by a
+variance as I've said it's going to be a
+
+ align:start position:0%
+variance as I've said it's going to be a
+ 
+
+ align:start position:0%
+variance as I've said it's going to be a
+regression coefficient if you're used to
+
+ align:start position:0%
+regression coefficient if you're used to
+ 
+
+ align:start position:0%
+regression coefficient if you're used to
+ordinary least squares you know that a
+
+ align:start position:0%
+ordinary least squares you know that a
+ 
+
+ align:start position:0%
+ordinary least squares you know that a
+regression coefficient is X Prime X
+
+ align:start position:0%
+regression coefficient is X Prime X
+ 
+
+ align:start position:0%
+regression coefficient is X Prime X
+inverse X Prime y so X must be in the
+
+ align:start position:0%
+inverse X Prime y so X must be in the
+ 
+
+ align:start position:0%
+inverse X Prime y so X must be in the
+denominator here which means that we're
+
+ align:start position:0%
+denominator here which means that we're
+ 
+
+ align:start position:0%
+denominator here which means that we're
+running on the right hand side the total
+
+ align:start position:0%
+running on the right hand side the total
+ 
+
+ align:start position:0%
+running on the right hand side the total
+Market Village return and on the left
+
+ align:start position:0%
+Market Village return and on the left
+ 
+
+ align:start position:0%
+Market Village return and on the left
+hand side the dependent variable is
+
+ align:start position:0%
+hand side the dependent variable is
+ 
+
+ align:start position:0%
+hand side the dependent variable is
+going to be the return of household
+
+ align:start position:0%
+going to be the return of household
+ 
+
+ align:start position:0%
+going to be the return of household
+chain so we're going to regress the
+
+ align:start position:0%
+chain so we're going to regress the
+ 
+
+ align:start position:0%
+chain so we're going to regress the
+return of household J over all the
+
+ align:start position:0%
+return of household J over all the
+ 
+
+ align:start position:0%
+return of household J over all the
+periods of the sample onto the
+
+ align:start position:0%
+periods of the sample onto the
+ 
+
+ align:start position:0%
+periods of the sample onto the
+aggregated village level return and get
+
+ align:start position:0%
+aggregated village level return and get
+ 
+
+ align:start position:0%
+aggregated village level return and get
+a regression coefficient and that's
+
+ align:start position:0%
+a regression coefficient and that's
+ 
+
+ align:start position:0%
+a regression coefficient and that's
+going to be beta J and that's going to
+
+ align:start position:0%
+going to be beta J and that's going to
+ 
+
+ align:start position:0%
+going to be beta J and that's going to
+capture how much the activities run by
+
+ align:start position:0%
+capture how much the activities run by
+ 
+
+ align:start position:0%
+capture how much the activities run by
+household J are covarying with what the
+
+ align:start position:0%
+household J are covarying with what the
+ 
+
+ align:start position:0%
+household J are covarying with what the
+village is doing as a whole
+
+ align:start position:0%
+village is doing as a whole
+ 
+
+ align:start position:0%
+village is doing as a whole
+now this as I think I explained to you
+
+ align:start position:0%
+now this as I think I explained to you
+ 
+
+ align:start position:0%
+now this as I think I explained to you
+last time I could go from here to here
+
+ align:start position:0%
+last time I could go from here to here
+ 
+
+ align:start position:0%
+last time I could go from here to here
+and it would all just look like some
+
+ align:start position:0%
+and it would all just look like some
+ 
+
+ align:start position:0%
+and it would all just look like some
+kind of claim go see the paper if you
+
+ align:start position:0%
+kind of claim go see the paper if you
+ 
+
+ align:start position:0%
+kind of claim go see the paper if you
+don't read the paper it remains
+
+ align:start position:0%
+don't read the paper it remains
+ 
+
+ align:start position:0%
+don't read the paper it remains
+mysterious you have an extra level of
+
+ align:start position:0%
+mysterious you have an extra level of
+ 
+
+ align:start position:0%
+mysterious you have an extra level of
+abstraction you don't believe the
+
+ align:start position:0%
+abstraction you don't believe the
+ 
+
+ align:start position:0%
+abstraction you don't believe the
+results so I actually wrote in the
+
+ align:start position:0%
+results so I actually wrote in the
+ 
+
+ align:start position:0%
+results so I actually wrote in the
+algebra I am not going to go through it
+
+ align:start position:0%
+algebra I am not going to go through it
+ 
+
+ align:start position:0%
+algebra I am not going to go through it
+today because it is nothing other than
+
+ align:start position:0%
+today because it is nothing other than
+ 
+
+ align:start position:0%
+today because it is nothing other than
+algebra
+
+ align:start position:0%
+algebra
+ 
+
+ align:start position:0%
+algebra
+but it's how to take those two
+
+ align:start position:0%
+but it's how to take those two
+ 
+
+ align:start position:0%
+but it's how to take those two
+assumptions about quadratic utility and
+
+ align:start position:0%
+assumptions about quadratic utility and
+ 
+
+ align:start position:0%
+assumptions about quadratic utility and
+production functions and actually
+
+ align:start position:0%
+production functions and actually
+ 
+
+ align:start position:0%
+production functions and actually
+manipulate the equations we already had
+
+ align:start position:0%
+manipulate the equations we already had
+ 
+
+ align:start position:0%
+manipulate the equations we already had
+substituting in these particular
+
+ align:start position:0%
+substituting in these particular
+ 
+
+ align:start position:0%
+substituting in these particular
+expressions and getting at the bottom
+
+ align:start position:0%
+expressions and getting at the bottom
+ 
+
+ align:start position:0%
+expressions and getting at the bottom
+the expression that corresponds to to
+
+ align:start position:0%
+the expression that corresponds to to
+ 
+
+ align:start position:0%
+the expression that corresponds to to
+this okay but I'm going to skip that so
+
+ align:start position:0%
+this okay but I'm going to skip that so
+ 
+
+ align:start position:0%
+this okay but I'm going to skip that so
+again mechanically take the return of
+
+ align:start position:0%
+again mechanically take the return of
+ 
+
+ align:start position:0%
+again mechanically take the return of
+household J at date at er T regress it
+
+ align:start position:0%
+household J at date at er T regress it
+ 
+
+ align:start position:0%
+household J at date at er T regress it
+on to constant and on to the time series
+
+ align:start position:0%
+on to constant and on to the time series
+ 
+
+ align:start position:0%
+on to constant and on to the time series
+of the market return
+
+ align:start position:0%
+of the market return
+ 
+
+ align:start position:0%
+of the market return
+yeah this is actually a prime here we're
+
+ align:start position:0%
+yeah this is actually a prime here we're
+ 
+
+ align:start position:0%
+yeah this is actually a prime here we're
+having trouble editing you know these
+
+ align:start position:0%
+having trouble editing you know these
+ 
+
+ align:start position:0%
+having trouble editing you know these
+latex files I guess so this is a prime
+
+ align:start position:0%
+latex files I guess so this is a prime
+ 
+
+ align:start position:0%
+latex files I guess so this is a prime
+so we have Prime this could be all today
+
+ align:start position:0%
+so we have Prime this could be all today
+ 
+
+ align:start position:0%
+so we have Prime this could be all today
+today or it could be next period next
+
+ align:start position:0%
+today or it could be next period next
+ 
+
+ align:start position:0%
+today or it could be next period next
+period just be consistent about it so
+
+ align:start position:0%
+period just be consistent about it so
+ 
+
+ align:start position:0%
+period just be consistent about it so
+the return of household J at day t
+
+ align:start position:0%
+the return of household J at day t
+ 
+
+ align:start position:0%
+the return of household J at day t
+regressed on to the reach the village
+
+ align:start position:0%
+regressed on to the reach the village
+ 
+
+ align:start position:0%
+regressed on to the reach the village
+level return at dates T running over all
+
+ align:start position:0%
+level return at dates T running over all
+ 
+
+ align:start position:0%
+level return at dates T running over all
+T so the sample could you know I'll show
+
+ align:start position:0%
+T so the sample could you know I'll show
+ 
+
+ align:start position:0%
+T so the sample could you know I'll show
+you in a minute something like 10 years
+
+ align:start position:0%
+you in a minute something like 10 years
+ 
+
+ align:start position:0%
+you in a minute something like 10 years
+of data a bit more
+
+ align:start position:0%
+of data a bit more
+ 
+
+ align:start position:0%
+of data a bit more
+plus an Epsilon is like the error term
+
+ align:start position:0%
+plus an Epsilon is like the error term
+ 
+
+ align:start position:0%
+plus an Epsilon is like the error term
+after you run this regression using the
+
+ align:start position:0%
+after you run this regression using the
+ 
+
+ align:start position:0%
+after you run this regression using the
+time series for each household one at a
+
+ align:start position:0%
+time series for each household one at a
+ 
+
+ align:start position:0%
+time series for each household one at a
+time and having estimated these beta J's
+
+ align:start position:0%
+time and having estimated these beta J's
+ 
+
+ align:start position:0%
+time and having estimated these beta J's
+we now run the next regression which is
+
+ align:start position:0%
+we now run the next regression which is
+ 
+
+ align:start position:0%
+we now run the next regression which is
+entirely cross-sectional regression we
+
+ align:start position:0%
+entirely cross-sectional regression we
+ 
+
+ align:start position:0%
+entirely cross-sectional regression we
+compute for each household the average
+
+ align:start position:0%
+compute for each household the average
+ 
+
+ align:start position:0%
+compute for each household the average
+return over the entire sample which is a
+
+ align:start position:0%
+return over the entire sample which is a
+ 
+
+ align:start position:0%
+return over the entire sample which is a
+proxy for the household's expected
+
+ align:start position:0%
+proxy for the household's expected
+ 
+
+ align:start position:0%
+proxy for the household's expected
+return the data analog to that and we
+
+ align:start position:0%
+return the data analog to that and we
+ 
+
+ align:start position:0%
+return the data analog to that and we
+regress that for each household J onto
+
+ align:start position:0%
+regress that for each household J onto
+ 
+
+ align:start position:0%
+regress that for each household J onto
+its beta J as derived in the first
+
+ align:start position:0%
+its beta J as derived in the first
+ 
+
+ align:start position:0%
+its beta J as derived in the first
+equation step one so the economics here
+
+ align:start position:0%
+equation step one so the economics here
+ 
+
+ align:start position:0%
+equation step one so the economics here
+is the return on the project run by
+
+ align:start position:0%
+is the return on the project run by
+ 
+
+ align:start position:0%
+is the return on the project run by
+household J the expected return should
+
+ align:start position:0%
+household J the expected return should
+ 
+
+ align:start position:0%
+household J the expected return should
+equal say roughly the risk-free rate but
+
+ align:start position:0%
+equal say roughly the risk-free rate but
+ 
+
+ align:start position:0%
+equal say roughly the risk-free rate but
+it has a risk premium first time I've
+
+ align:start position:0%
+it has a risk premium first time I've
+ 
+
+ align:start position:0%
+it has a risk premium first time I've
+used that now with the notation and the
+
+ align:start position:0%
+used that now with the notation and the
+ 
+
+ align:start position:0%
+used that now with the notation and the
+risk premium has to do with the
+
+ align:start position:0%
+risk premium has to do with the
+ 
+
+ align:start position:0%
+risk premium has to do with the
+co-movement of household Jay's activity
+
+ align:start position:0%
+co-movement of household Jay's activity
+ 
+
+ align:start position:0%
+co-movement of household Jay's activity
+with the village aggregate
+
+ align:start position:0%
+with the village aggregate
+ 
+
+ align:start position:0%
+with the village aggregate
+so we talked about diversification at
+
+ align:start position:0%
+so we talked about diversification at
+ 
+
+ align:start position:0%
+so we talked about diversification at
+the beginning of class and the idea here
+
+ align:start position:0%
+the beginning of class and the idea here
+ 
+
+ align:start position:0%
+the beginning of class and the idea here
+is if the things household J is doing
+
+ align:start position:0%
+is if the things household J is doing
+ 
+
+ align:start position:0%
+is if the things household J is doing
+are highly correlated with returns on
+
+ align:start position:0%
+are highly correlated with returns on
+ 
+
+ align:start position:0%
+are highly correlated with returns on
+what other people are doing then
+
+ align:start position:0%
+what other people are doing then
+ 
+
+ align:start position:0%
+what other people are doing then
+household J isn't doing very much
+
+ align:start position:0%
+household J isn't doing very much
+ 
+
+ align:start position:0%
+household J isn't doing very much
+worthwhile Council J is not diversifying
+
+ align:start position:0%
+worthwhile Council J is not diversifying
+ 
+
+ align:start position:0%
+worthwhile Council J is not diversifying
+The Village level risk so in order to
+
+ align:start position:0%
+The Village level risk so in order to
+ 
+
+ align:start position:0%
+The Village level risk so in order to
+justify a set of activities that
+
+ align:start position:0%
+justify a set of activities that
+ 
+
+ align:start position:0%
+justify a set of activities that
+household J is doing we have to bump up
+
+ align:start position:0%
+household J is doing we have to bump up
+ 
+
+ align:start position:0%
+household J is doing we have to bump up
+its expected rate of return in some
+
+ align:start position:0%
+its expected rate of return in some
+ 
+
+ align:start position:0%
+its expected rate of return in some
+sense we use the word risk premium
+
+ align:start position:0%
+sense we use the word risk premium
+ 
+
+ align:start position:0%
+sense we use the word risk premium
+meaning household Jazz activities are
+
+ align:start position:0%
+meaning household Jazz activities are
+ 
+
+ align:start position:0%
+meaning household Jazz activities are
+pretty risky why because they're
+
+ align:start position:0%
+pretty risky why because they're
+ 
+
+ align:start position:0%
+pretty risky why because they're
+correlated with the village average so
+
+ align:start position:0%
+correlated with the village average so
+ 
+
+ align:start position:0%
+correlated with the village average so
+diversification is not and we need to
+
+ align:start position:0%
+diversification is not and we need to
+ 
+
+ align:start position:0%
+diversification is not and we need to
+compensate for that lack of
+
+ align:start position:0%
+compensate for that lack of
+ 
+
+ align:start position:0%
+compensate for that lack of
+diversification the opposite is more
+
+ align:start position:0%
+diversification the opposite is more
+ 
+
+ align:start position:0%
+diversification the opposite is more
+revealing perhaps which is if this
+
+ align:start position:0%
+revealing perhaps which is if this
+ 
+
+ align:start position:0%
+revealing perhaps which is if this
+correlation is low or even zero It's a
+
+ align:start position:0%
+correlation is low or even zero It's a
+ 
+
+ align:start position:0%
+correlation is low or even zero It's a
+Wonderful hedge even if not many
+
+ align:start position:0%
+Wonderful hedge even if not many
+ 
+
+ align:start position:0%
+Wonderful hedge even if not many
+households are doing those things if
+
+ align:start position:0%
+households are doing those things if
+ 
+
+ align:start position:0%
+households are doing those things if
+household J does them and manages to
+
+ align:start position:0%
+household J does them and manages to
+ 
+
+ align:start position:0%
+household J does them and manages to
+produce a return stream which is not so
+
+ align:start position:0%
+produce a return stream which is not so
+ 
+
+ align:start position:0%
+produce a return stream which is not so
+correlated with the return streams of
+
+ align:start position:0%
+correlated with the return streams of
+ 
+
+ align:start position:0%
+correlated with the return streams of
+the other households that's great in
+
+ align:start position:0%
+the other households that's great in
+ 
+
+ align:start position:0%
+the other households that's great in
+which case we don't need to have a high
+
+ align:start position:0%
+which case we don't need to have a high
+ 
+
+ align:start position:0%
+which case we don't need to have a high
+risk premium because actually it's
+
+ align:start position:0%
+risk premium because actually it's
+ 
+
+ align:start position:0%
+risk premium because actually it's
+reducing risk so that's the economics of
+
+ align:start position:0%
+reducing risk so that's the economics of
+ 
+
+ align:start position:0%
+reducing risk so that's the economics of
+it it's all also entirely here in terms
+
+ align:start position:0%
+it it's all also entirely here in terms
+ 
+
+ align:start position:0%
+it it's all also entirely here in terms
+of the equations all right I'm sorry I
+
+ align:start position:0%
+of the equations all right I'm sorry I
+ 
+
+ align:start position:0%
+of the equations all right I'm sorry I
+have a I have a question about a
+
+ align:start position:0%
+have a I have a question about a
+ 
+
+ align:start position:0%
+have a I have a question about a
+previous slide
+
+ align:start position:0%
+previous slide
+ 
+
+ align:start position:0%
+previous slide
+yeah so um is no uh it's more like a
+
+ align:start position:0%
+yeah so um is no uh it's more like a
+ 
+
+ align:start position:0%
+yeah so um is no uh it's more like a
+econometric stuff because um I think
+
+ align:start position:0%
+econometric stuff because um I think
+ 
+
+ align:start position:0%
+econometric stuff because um I think
+there should be some estimation error
+
+ align:start position:0%
+there should be some estimation error
+ 
+
+ align:start position:0%
+there should be some estimation error
+here because
+
+ align:start position:0%
+here because
+ 
+
+ align:start position:0%
+here because
+um the beta is estimated and in step two
+
+ align:start position:0%
+um the beta is estimated and in step two
+ 
+
+ align:start position:0%
+um the beta is estimated and in step two
+you just request you regressive return
+
+ align:start position:0%
+you just request you regressive return
+ 
+
+ align:start position:0%
+you just request you regressive return
+on some estimated beta right
+
+ align:start position:0%
+on some estimated beta right
+ 
+
+ align:start position:0%
+on some estimated beta right
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+I mean
+
+ align:start position:0%
+I mean
+ 
+
+ align:start position:0%
+I mean
+you you just really regrets some some
+
+ align:start position:0%
+you you just really regrets some some
+ 
+
+ align:start position:0%
+you you just really regrets some some
+some true data on some estimated data
+
+ align:start position:0%
+some true data on some estimated data
+ 
+
+ align:start position:0%
+some true data on some estimated data
+and I think the Lambda here will have
+
+ align:start position:0%
+and I think the Lambda here will have
+ 
+
+ align:start position:0%
+and I think the Lambda here will have
+some error right
+
+ align:start position:0%
+some error right
+ 
+
+ align:start position:0%
+some error right
+well there are two things
+
+ align:start position:0%
+well there are two things
+ 
+
+ align:start position:0%
+well there are two things
+to adjust for one this is a a regression
+
+ align:start position:0%
+to adjust for one this is a a regression
+ 
+
+ align:start position:0%
+to adjust for one this is a a regression
+coefficient so it is measured with error
+
+ align:start position:0%
+coefficient so it is measured with error
+ 
+
+ align:start position:0%
+coefficient so it is measured with error
+it has a standard error and we do adjust
+
+ align:start position:0%
+it has a standard error and we do adjust
+ 
+
+ align:start position:0%
+it has a standard error and we do adjust
+the beta that we're using to allow for
+
+ align:start position:0%
+the beta that we're using to allow for
+ 
+
+ align:start position:0%
+the beta that we're using to allow for
+that uncertainty if that's part of what
+
+ align:start position:0%
+that uncertainty if that's part of what
+ 
+
+ align:start position:0%
+that uncertainty if that's part of what
+you're asking
+
+ align:start position:0%
+you're asking
+ 
+
+ align:start position:0%
+you're asking
+is that what you're asking about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+yeah probably but yeah okay okay yeah
+
+ align:start position:0%
+yeah probably but yeah okay okay yeah
+ 
+
+ align:start position:0%
+yeah probably but yeah okay okay yeah
+I mean the other thing is
+
+ align:start position:0%
+I mean the other thing is
+ 
+
+ align:start position:0%
+I mean the other thing is
+that you know
+
+ align:start position:0%
+that you know
+ 
+
+ align:start position:0%
+that you know
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here we're regressing an individual J
+
+ align:start position:0%
+here we're regressing an individual J
+ 
+
+ align:start position:0%
+here we're regressing an individual J
+return on the village average so you do
+
+ align:start position:0%
+return on the village average so you do
+ 
+
+ align:start position:0%
+return on the village average so you do
+have to be worried about regressing
+
+ align:start position:0%
+have to be worried about regressing
+ 
+
+ align:start position:0%
+have to be worried about regressing
+dependent variables on the left with
+
+ align:start position:0%
+dependent variables on the left with
+ 
+
+ align:start position:0%
+dependent variables on the left with
+their average on the right
+
+ align:start position:0%
+their average on the right
+ 
+
+ align:start position:0%
+their average on the right
+you know that tends to bias this beta
+
+ align:start position:0%
+you know that tends to bias this beta
+ 
+
+ align:start position:0%
+you know that tends to bias this beta
+toward one
+
+ align:start position:0%
+toward one
+ 
+
+ align:start position:0%
+toward one
+that's another econometric problem
+
+ align:start position:0%
+that's another econometric problem
+ 
+
+ align:start position:0%
+that's another econometric problem
+except that here
+
+ align:start position:0%
+except that here
+ 
+
+ align:start position:0%
+except that here
+we're actually interested in dispersion
+
+ align:start position:0%
+we're actually interested in dispersion
+ 
+
+ align:start position:0%
+we're actually interested in dispersion
+across the different betas
+
+ align:start position:0%
+across the different betas
+ 
+
+ align:start position:0%
+across the different betas
+and so we're okay
+
+ align:start position:0%
+and so we're okay
+ 
+
+ align:start position:0%
+and so we're okay
+uh and this
+
+ align:start position:0%
+uh and this
+ 
+
+ align:start position:0%
+uh and this
+is Fama French
+
+ align:start position:0%
+is Fama French
+ 
+
+ align:start position:0%
+is Fama French
+which I suspect you know
+
+ align:start position:0%
+which I suspect you know
+ 
+
+ align:start position:0%
+which I suspect you know
+yeah I know that yeah yeah so we're just
+
+ align:start position:0%
+yeah I know that yeah yeah so we're just
+ 
+
+ align:start position:0%
+yeah I know that yeah yeah so we're just
+doing
+
+ align:start position:0%
+doing
+ 
+
+ align:start position:0%
+doing
+what they did with the New York stocks
+
+ align:start position:0%
+what they did with the New York stocks
+ 
+
+ align:start position:0%
+what they did with the New York stocks
+we're doing it here in the five villages
+
+ align:start position:0%
+we're doing it here in the five villages
+ 
+
+ align:start position:0%
+we're doing it here in the five villages
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+we started our survey in 1998 with a big
+
+ align:start position:0%
+we started our survey in 1998 with a big
+ 
+
+ align:start position:0%
+we started our survey in 1998 with a big
+Baseline we updated every month
+
+ align:start position:0%
+Baseline we updated every month
+ 
+
+ align:start position:0%
+Baseline we updated every month
+uh thereafter this said at the time we
+
+ align:start position:0%
+uh thereafter this said at the time we
+ 
+
+ align:start position:0%
+uh thereafter this said at the time we
+were writing the paper the survey was
+
+ align:start position:0%
+were writing the paper the survey was
+ 
+
+ align:start position:0%
+were writing the paper the survey was
+still ongoing
+
+ align:start position:0%
+still ongoing
+ 
+
+ align:start position:0%
+still ongoing
+although even then the later months were
+
+ align:start position:0%
+although even then the later months were
+ 
+
+ align:start position:0%
+although even then the later months were
+not ready so we ended up using monthly
+
+ align:start position:0%
+not ready so we ended up using monthly
+ 
+
+ align:start position:0%
+not ready so we ended up using monthly
+data from month five to month 160 of the
+
+ align:start position:0%
+data from month five to month 160 of the
+ 
+
+ align:start position:0%
+data from month five to month 160 of the
+survey now the other thing is misleading
+
+ align:start position:0%
+survey now the other thing is misleading
+ 
+
+ align:start position:0%
+survey now the other thing is misleading
+is not ongoing anymore the project ended
+
+ align:start position:0%
+is not ongoing anymore the project ended
+ 
+
+ align:start position:0%
+is not ongoing anymore the project ended
+about 18 months ago
+
+ align:start position:0%
+about 18 months ago
+ 
+
+ align:start position:0%
+about 18 months ago
+but we did end up with almost 20 years
+
+ align:start position:0%
+but we did end up with almost 20 years
+ 
+
+ align:start position:0%
+but we did end up with almost 20 years
+of monthly data so it's a vast Warehouse
+
+ align:start position:0%
+of monthly data so it's a vast Warehouse
+ 
+
+ align:start position:0%
+of monthly data so it's a vast Warehouse
+of you know potential projects that can
+
+ align:start position:0%
+of you know potential projects that can
+ 
+
+ align:start position:0%
+of you know potential projects that can
+be done with it and I'm happy to tell
+
+ align:start position:0%
+be done with it and I'm happy to tell
+ 
+
+ align:start position:0%
+be done with it and I'm happy to tell
+you more but today I want to focus on
+
+ align:start position:0%
+you more but today I want to focus on
+ 
+
+ align:start position:0%
+you more but today I want to focus on
+this paper so we only included the
+
+ align:start position:0%
+this paper so we only included the
+ 
+
+ align:start position:0%
+this paper so we only included the
+households that were actually in the
+
+ align:start position:0%
+households that were actually in the
+ 
+
+ align:start position:0%
+households that were actually in the
+village for the whole period sometimes
+
+ align:start position:0%
+village for the whole period sometimes
+ 
+
+ align:start position:0%
+village for the whole period sometimes
+entire households pick up stakes and
+
+ align:start position:0%
+entire households pick up stakes and
+ 
+
+ align:start position:0%
+entire households pick up stakes and
+leave
+
+ align:start position:0%
+leave
+ 
+
+ align:start position:0%
+leave
+we excluded them we also are looking
+
+ align:start position:0%
+we excluded them we also are looking
+ 
+
+ align:start position:0%
+we excluded them we also are looking
+only at households with production
+
+ align:start position:0%
+only at households with production
+ 
+
+ align:start position:0%
+only at households with production
+activities Farm is included but also
+
+ align:start position:0%
+activities Farm is included but also
+ 
+
+ align:start position:0%
+activities Farm is included but also
+fish shrimp livestock trade-in
+
+ align:start position:0%
+fish shrimp livestock trade-in
+ 
+
+ align:start position:0%
+fish shrimp livestock trade-in
+handicrafts but not just wage earnings
+
+ align:start position:0%
+handicrafts but not just wage earnings
+ 
+
+ align:start position:0%
+handicrafts but not just wage earnings
+why because with wage earnings they're
+
+ align:start position:0%
+why because with wage earnings they're
+ 
+
+ align:start position:0%
+why because with wage earnings they're
+not really producing anything they're
+
+ align:start position:0%
+not really producing anything they're
+ 
+
+ align:start position:0%
+not really producing anything they're
+earning something by working for others
+
+ align:start position:0%
+earning something by working for others
+ 
+
+ align:start position:0%
+earning something by working for others
+so they're not entrepreneurs so we did
+
+ align:start position:0%
+so they're not entrepreneurs so we did
+ 
+
+ align:start position:0%
+so they're not entrepreneurs so we did
+not include them
+
+ align:start position:0%
+not include them
+ 
+
+ align:start position:0%
+not include them
+and there are extensive networks of
+
+ align:start position:0%
+and there are extensive networks of
+ 
+
+ align:start position:0%
+and there are extensive networks of
+family in these Villages and I'm going
+
+ align:start position:0%
+family in these Villages and I'm going
+ 
+
+ align:start position:0%
+family in these Villages and I'm going
+to come back to that a little bit later
+
+ align:start position:0%
+to come back to that a little bit later
+ 
+
+ align:start position:0%
+to come back to that a little bit later
+toward the end so just to give you a
+
+ align:start position:0%
+toward the end so just to give you a
+ 
+
+ align:start position:0%
+toward the end so just to give you a
+feeling of the the data we've got net
+
+ align:start position:0%
+feeling of the the data we've got net
+ 
+
+ align:start position:0%
+feeling of the the data we've got net
+income which means
+
+ align:start position:0%
+income which means
+ 
+
+ align:start position:0%
+income which means
+income from household Enterprise it's
+
+ align:start position:0%
+income from household Enterprise it's
+ 
+
+ align:start position:0%
+income from household Enterprise it's
+the difference between revenue and costs
+
+ align:start position:0%
+the difference between revenue and costs
+ 
+
+ align:start position:0%
+the difference between revenue and costs
+of all the inputs revenue is realized at
+
+ align:start position:0%
+of all the inputs revenue is realized at
+ 
+
+ align:start position:0%
+of all the inputs revenue is realized at
+the time of sale or it could be if it's
+
+ align:start position:0%
+the time of sale or it could be if it's
+ 
+
+ align:start position:0%
+the time of sale or it could be if it's
+a crop it could be eaten it could be
+
+ align:start position:0%
+a crop it could be eaten it could be
+ 
+
+ align:start position:0%
+a crop it could be eaten it could be
+given as a gift from to others it all
+
+ align:start position:0%
+given as a gift from to others it all
+ 
+
+ align:start position:0%
+given as a gift from to others it all
+counts
+
+ align:start position:0%
+counts
+ 
+
+ align:start position:0%
+counts
+we add them all up uh Revenue even comes
+
+ align:start position:0%
+we add them all up uh Revenue even comes
+ 
+
+ align:start position:0%
+we add them all up uh Revenue even comes
+from renting out assets we include that
+
+ align:start position:0%
+from renting out assets we include that
+ 
+
+ align:start position:0%
+from renting out assets we include that
+costs are all the inputs used in
+
+ align:start position:0%
+costs are all the inputs used in
+ 
+
+ align:start position:0%
+costs are all the inputs used in
+production whether they're acquired in
+
+ align:start position:0%
+production whether they're acquired in
+ 
+
+ align:start position:0%
+production whether they're acquired in
+cash or in kind with credit or gifts
+
+ align:start position:0%
+cash or in kind with credit or gifts
+ 
+
+ align:start position:0%
+cash or in kind with credit or gifts
+we count them all we put a valuation on
+
+ align:start position:0%
+we count them all we put a valuation on
+ 
+
+ align:start position:0%
+we count them all we put a valuation on
+them if it's not acquired in the market
+
+ align:start position:0%
+them if it's not acquired in the market
+ 
+
+ align:start position:0%
+them if it's not acquired in the market
+so we take Revenue minus costs include
+
+ align:start position:0%
+so we take Revenue minus costs include
+ 
+
+ align:start position:0%
+so we take Revenue minus costs include
+depreciation that came up earlier
+
+ align:start position:0%
+depreciation that came up earlier
+ 
+
+ align:start position:0%
+depreciation that came up earlier
+subtracted and we get net income
+
+ align:start position:0%
+subtracted and we get net income
+ 
+
+ align:start position:0%
+subtracted and we get net income
+and these assets we're talking about you
+
+ align:start position:0%
+and these assets we're talking about you
+ 
+
+ align:start position:0%
+and these assets we're talking about you
+know we have agricultural business
+
+ align:start position:0%
+know we have agricultural business
+ 
+
+ align:start position:0%
+know we have agricultural business
+livestock assets we've also got land and
+
+ align:start position:0%
+livestock assets we've also got land and
+ 
+
+ align:start position:0%
+livestock assets we've also got land and
+household assets the agricultural assets
+
+ align:start position:0%
+household assets the agricultural assets
+ 
+
+ align:start position:0%
+household assets the agricultural assets
+to give you an example includes walking
+
+ align:start position:0%
+to give you an example includes walking
+ 
+
+ align:start position:0%
+to give you an example includes walking
+tractors you might remember in the
+
+ align:start position:0%
+tractors you might remember in the
+ 
+
+ align:start position:0%
+tractors you might remember in the
+production lecture I showed you a
+
+ align:start position:0%
+production lecture I showed you a
+ 
+
+ align:start position:0%
+production lecture I showed you a
+picture of that guy walking around with
+
+ align:start position:0%
+picture of that guy walking around with
+ 
+
+ align:start position:0%
+picture of that guy walking around with
+the tractor or larger four-wheel
+
+ align:start position:0%
+the tractor or larger four-wheel
+ 
+
+ align:start position:0%
+the tractor or larger four-wheel
+tractors aerators for ponds machines to
+
+ align:start position:0%
+tractors aerators for ponds machines to
+ 
+
+ align:start position:0%
+tractors aerators for ponds machines to
+put seeds in the ground machines like
+
+ align:start position:0%
+put seeds in the ground machines like
+ 
+
+ align:start position:0%
+put seeds in the ground machines like
+sprinklers
+
+ align:start position:0%
+sprinklers
+ 
+
+ align:start position:0%
+sprinklers
+Etc so you know you're in the village
+
+ align:start position:0%
+Etc so you know you're in the village
+ 
+
+ align:start position:0%
+Etc so you know you're in the village
+now you can imagine living there I think
+
+ align:start position:0%
+now you can imagine living there I think
+ 
+
+ align:start position:0%
+now you can imagine living there I think
+this is the level of detail that we have
+
+ align:start position:0%
+this is the level of detail that we have
+ 
+
+ align:start position:0%
+this is the level of detail that we have
+we did put household assets in that's a
+
+ align:start position:0%
+we did put household assets in that's a
+ 
+
+ align:start position:0%
+we did put household assets in that's a
+decision because some of the things that
+
+ align:start position:0%
+decision because some of the things that
+ 
+
+ align:start position:0%
+decision because some of the things that
+look like a durable good end up being
+
+ align:start position:0%
+look like a durable good end up being
+ 
+
+ align:start position:0%
+look like a durable good end up being
+used in farming like a pickup truck you
+
+ align:start position:0%
+used in farming like a pickup truck you
+ 
+
+ align:start position:0%
+used in farming like a pickup truck you
+know they use it so rather than include
+
+ align:start position:0%
+know they use it so rather than include
+ 
+
+ align:start position:0%
+know they use it so rather than include
+but we've done robustness checks but
+
+ align:start position:0%
+but we've done robustness checks but
+ 
+
+ align:start position:0%
+but we've done robustness checks but
+here we included them all okay so let me
+
+ align:start position:0%
+here we included them all okay so let me
+ 
+
+ align:start position:0%
+here we included them all okay so let me
+just jump here if we look at that beta
+
+ align:start position:0%
+just jump here if we look at that beta
+ 
+
+ align:start position:0%
+just jump here if we look at that beta
+this is the return on assets the
+
+ align:start position:0%
+this is the return on assets the
+ 
+
+ align:start position:0%
+this is the return on assets the
+expected return on household J
+
+ align:start position:0%
+expected return on household J
+ 
+
+ align:start position:0%
+expected return on household J
+each J corresponds to a DOT here and
+
+ align:start position:0%
+each J corresponds to a DOT here and
+ 
+
+ align:start position:0%
+each J corresponds to a DOT here and
+it's just the average return for
+
+ align:start position:0%
+it's just the average return for
+ 
+
+ align:start position:0%
+it's just the average return for
+household J on the y-axis and the beta
+
+ align:start position:0%
+household J on the y-axis and the beta
+ 
+
+ align:start position:0%
+household J on the y-axis and the beta
+the regression coefficient on the
+
+ align:start position:0%
+the regression coefficient on the
+ 
+
+ align:start position:0%
+the regression coefficient on the
+village average is on the x-axis
+
+ align:start position:0%
+village average is on the x-axis
+ 
+
+ align:start position:0%
+village average is on the x-axis
+so you can see that households have that
+
+ align:start position:0%
+so you can see that households have that
+ 
+
+ align:start position:0%
+so you can see that households have that
+have higher returns are households that
+
+ align:start position:0%
+have higher returns are households that
+ 
+
+ align:start position:0%
+have higher returns are households that
+have higher betas
+
+ align:start position:0%
+have higher betas
+ 
+
+ align:start position:0%
+have higher betas
+for three of the four
+
+ align:start position:0%
+for three of the four
+ 
+
+ align:start position:0%
+for three of the four
+potentially all four although Bergeron
+
+ align:start position:0%
+potentially all four although Bergeron
+ 
+
+ align:start position:0%
+potentially all four although Bergeron
+is not not the greatest example
+
+ align:start position:0%
+is not not the greatest example
+ 
+
+ align:start position:0%
+is not not the greatest example
+and I have shown this picture to guys
+
+ align:start position:0%
+and I have shown this picture to guys
+ 
+
+ align:start position:0%
+and I have shown this picture to guys
+working in finance with New York Stock
+
+ align:start position:0%
+working in finance with New York Stock
+ 
+
+ align:start position:0%
+working in finance with New York Stock
+Exchange or Swedish data and they see
+
+ align:start position:0%
+Exchange or Swedish data and they see
+ 
+
+ align:start position:0%
+Exchange or Swedish data and they see
+this degree of correlation and they're
+
+ align:start position:0%
+this degree of correlation and they're
+ 
+
+ align:start position:0%
+this degree of correlation and they're
+like wow that's really amazing so the
+
+ align:start position:0%
+like wow that's really amazing so the
+ 
+
+ align:start position:0%
+like wow that's really amazing so the
+theory is working pretty well
+
+ align:start position:0%
+theory is working pretty well
+ 
+
+ align:start position:0%
+theory is working pretty well
+and this is the regression doesn't
+
+ align:start position:0%
+and this is the regression doesn't
+ 
+
+ align:start position:0%
+and this is the regression doesn't
+really add more this is the regression
+
+ align:start position:0%
+really add more this is the regression
+ 
+
+ align:start position:0%
+really add more this is the regression
+from that step one with the
+
+ align:start position:0%
+from that step one with the
+ 
+
+ align:start position:0%
+from that step one with the
+corresponding sorry step two it is with
+
+ align:start position:0%
+corresponding sorry step two it is with
+ 
+
+ align:start position:0%
+corresponding sorry step two it is with
+the corresponding betas and it's not
+
+ align:start position:0%
+the corresponding betas and it's not
+ 
+
+ align:start position:0%
+the corresponding betas and it's not
+significant number around but it is in
+
+ align:start position:0%
+significant number around but it is in
+ 
+
+ align:start position:0%
+significant number around but it is in
+the other three provinces not sure if
+
+ align:start position:0%
+the other three provinces not sure if
+ 
+
+ align:start position:0%
+the other three provinces not sure if
+I've shown you this map I don't think we
+
+ align:start position:0%
+I've shown you this map I don't think we
+ 
+
+ align:start position:0%
+I've shown you this map I don't think we
+did chachang Sao and lopuri are
+
+ align:start position:0%
+did chachang Sao and lopuri are
+ 
+
+ align:start position:0%
+did chachang Sao and lopuri are
+relatively near to Bangkok
+
+ align:start position:0%
+relatively near to Bangkok
+ 
+
+ align:start position:0%
+relatively near to Bangkok
+and birder rum and sitsakata are out in
+
+ align:start position:0%
+and birder rum and sitsakata are out in
+ 
+
+ align:start position:0%
+and birder rum and sitsakata are out in
+The Agrarian regions of the Northeast so
+
+ align:start position:0%
+The Agrarian regions of the Northeast so
+ 
+
+ align:start position:0%
+The Agrarian regions of the Northeast so
+very different types of sample okay so
+
+ align:start position:0%
+very different types of sample okay so
+ 
+
+ align:start position:0%
+very different types of sample okay so
+let's talk about idiosyncratic risk the
+
+ align:start position:0%
+let's talk about idiosyncratic risk the
+ 
+
+ align:start position:0%
+let's talk about idiosyncratic risk the
+return on household J is determined by
+
+ align:start position:0%
+return on household J is determined by
+ 
+
+ align:start position:0%
+return on household J is determined by
+Beta J that we've been talking about X
+
+ align:start position:0%
+Beta J that we've been talking about X
+ 
+
+ align:start position:0%
+Beta J that we've been talking about X
+is to make the argument more General so
+
+ align:start position:0%
+is to make the argument more General so
+ 
+
+ align:start position:0%
+is to make the argument more General so
+bait regression coefficients times the
+
+ align:start position:0%
+bait regression coefficients times the
+ 
+
+ align:start position:0%
+bait regression coefficients times the
+object
+
+ align:start position:0%
+object
+ 
+
+ align:start position:0%
+object
+and then an error term so if you take
+
+ align:start position:0%
+and then an error term so if you take
+ 
+
+ align:start position:0%
+and then an error term so if you take
+the variance of both sides doing a
+
+ align:start position:0%
+the variance of both sides doing a
+ 
+
+ align:start position:0%
+the variance of both sides doing a
+variance decomposition the variance of
+
+ align:start position:0%
+variance decomposition the variance of
+ 
+
+ align:start position:0%
+variance decomposition the variance of
+the return is the variance explained by
+
+ align:start position:0%
+the return is the variance explained by
+ 
+
+ align:start position:0%
+the return is the variance explained by
+the dependent variable with its
+
+ align:start position:0%
+the dependent variable with its
+ 
+
+ align:start position:0%
+the dependent variable with its
+coefficient plus the variance of the
+
+ align:start position:0%
+coefficient plus the variance of the
+ 
+
+ align:start position:0%
+coefficient plus the variance of the
+error term so when we talk about
+
+ align:start position:0%
+error term so when we talk about
+ 
+
+ align:start position:0%
+error term so when we talk about
+idiosyncratic risk we're talking about
+
+ align:start position:0%
+idiosyncratic risk we're talking about
+ 
+
+ align:start position:0%
+idiosyncratic risk we're talking about
+the error term here
+
+ align:start position:0%
+the error term here
+ 
+
+ align:start position:0%
+the error term here
+as opposed to how much of the variance
+
+ align:start position:0%
+as opposed to how much of the variance
+ 
+
+ align:start position:0%
+as opposed to how much of the variance
+is determined by The Village aggregate
+
+ align:start position:0%
+is determined by The Village aggregate
+ 
+
+ align:start position:0%
+is determined by The Village aggregate
+and so you could just imagine taking
+
+ align:start position:0%
+and so you could just imagine taking
+ 
+
+ align:start position:0%
+and so you could just imagine taking
+this variance term and dividing it
+
+ align:start position:0%
+this variance term and dividing it
+ 
+
+ align:start position:0%
+this variance term and dividing it
+through both sides and then you'll have
+
+ align:start position:0%
+through both sides and then you'll have
+ 
+
+ align:start position:0%
+through both sides and then you'll have
+one like 100 percent is equal to the
+
+ align:start position:0%
+one like 100 percent is equal to the
+ 
+
+ align:start position:0%
+one like 100 percent is equal to the
+contribution of the of the village
+
+ align:start position:0%
+contribution of the of the village
+ 
+
+ align:start position:0%
+contribution of the of the village
+return plus the contribution of the
+
+ align:start position:0%
+return plus the contribution of the
+ 
+
+ align:start position:0%
+return plus the contribution of the
+idiosyncratic variance to the total so
+
+ align:start position:0%
+idiosyncratic variance to the total so
+ 
+
+ align:start position:0%
+idiosyncratic variance to the total so
+this is not a theory this is a way of
+
+ align:start position:0%
+this is not a theory this is a way of
+ 
+
+ align:start position:0%
+this is not a theory this is a way of
+quantifying how much aggregate Village
+
+ align:start position:0%
+quantifying how much aggregate Village
+ 
+
+ align:start position:0%
+quantifying how much aggregate Village
+average risk there is and how much
+
+ align:start position:0%
+average risk there is and how much
+ 
+
+ align:start position:0%
+average risk there is and how much
+idiosyncratic risk there is in an
+
+ align:start position:0%
+idiosyncratic risk there is in an
+ 
+
+ align:start position:0%
+idiosyncratic risk there is in an
+individual J's return
+
+ align:start position:0%
+individual J's return
+ 
+
+ align:start position:0%
+individual J's return
+now the next thing back to the
+
+ align:start position:0%
+now the next thing back to the
+ 
+
+ align:start position:0%
+now the next thing back to the
+regression as I have been saying in the
+
+ align:start position:0%
+regression as I have been saying in the
+ 
+
+ align:start position:0%
+regression as I have been saying in the
+Baseline we're running the average
+
+ align:start position:0%
+Baseline we're running the average
+ 
+
+ align:start position:0%
+Baseline we're running the average
+return on household J onto a constant
+
+ align:start position:0%
+return on household J onto a constant
+ 
+
+ align:start position:0%
+return on household J onto a constant
+plus the beta J coefficient times beta J
+
+ align:start position:0%
+plus the beta J coefficient times beta J
+ 
+
+ align:start position:0%
+plus the beta J coefficient times beta J
+and now we do something extra
+
+ align:start position:0%
+and now we do something extra
+ 
+
+ align:start position:0%
+and now we do something extra
+we add in Sigma J where Sigma J here is
+
+ align:start position:0%
+we add in Sigma J where Sigma J here is
+ 
+
+ align:start position:0%
+we add in Sigma J where Sigma J here is
+the variance of this Epsilon term how
+
+ align:start position:0%
+the variance of this Epsilon term how
+ 
+
+ align:start position:0%
+the variance of this Epsilon term how
+much is it moving well it's right here
+
+ align:start position:0%
+much is it moving well it's right here
+ 
+
+ align:start position:0%
+much is it moving well it's right here
+except that I didn't call it Sigma J
+
+ align:start position:0%
+except that I didn't call it Sigma J
+ 
+
+ align:start position:0%
+except that I didn't call it Sigma J
+here the variance of Epsilon J is Sigma
+
+ align:start position:0%
+here the variance of Epsilon J is Sigma
+ 
+
+ align:start position:0%
+here the variance of Epsilon J is Sigma
+J stick that into this cross-sectional
+
+ align:start position:0%
+J stick that into this cross-sectional
+ 
+
+ align:start position:0%
+J stick that into this cross-sectional
+regression as an extra right-hand side
+
+ align:start position:0%
+regression as an extra right-hand side
+ 
+
+ align:start position:0%
+regression as an extra right-hand side
+variable and get a coefficient on it so
+
+ align:start position:0%
+variable and get a coefficient on it so
+ 
+
+ align:start position:0%
+variable and get a coefficient on it so
+now we can do a similar calculation we
+
+ align:start position:0%
+now we can do a similar calculation we
+ 
+
+ align:start position:0%
+now we can do a similar calculation we
+can take the risk premium which is the
+
+ align:start position:0%
+can take the risk premium which is the
+ 
+
+ align:start position:0%
+can take the risk premium which is the
+sum of both the return over and above
+
+ align:start position:0%
+sum of both the return over and above
+ 
+
+ align:start position:0%
+sum of both the return over and above
+the risk-free rate that's due to the
+
+ align:start position:0%
+the risk-free rate that's due to the
+ 
+
+ align:start position:0%
+the risk-free rate that's due to the
+aggregate return and also due to the
+
+ align:start position:0%
+aggregate return and also due to the
+ 
+
+ align:start position:0%
+aggregate return and also due to the
+idiosyncratic risk and so we can
+
+ align:start position:0%
+idiosyncratic risk and so we can
+ 
+
+ align:start position:0%
+idiosyncratic risk and so we can
+decompose the aggregate risk as a
+
+ align:start position:0%
+decompose the aggregate risk as a
+ 
+
+ align:start position:0%
+decompose the aggregate risk as a
+proportion of the total and likewise the
+
+ align:start position:0%
+proportion of the total and likewise the
+ 
+
+ align:start position:0%
+proportion of the total and likewise the
+idiosyncratic risk as the proportion of
+
+ align:start position:0%
+idiosyncratic risk as the proportion of
+ 
+
+ align:start position:0%
+idiosyncratic risk as the proportion of
+the total
+
+ align:start position:0%
+the total
+ 
+
+ align:start position:0%
+the total
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+so doing that we
+
+ align:start position:0%
+so doing that we
+ 
+
+ align:start position:0%
+so doing that we
+summarize the results the contribution
+
+ align:start position:0%
+summarize the results the contribution
+ 
+
+ align:start position:0%
+summarize the results the contribution
+of idiosyncratic risk to Total risk and
+
+ align:start position:0%
+of idiosyncratic risk to Total risk and
+ 
+
+ align:start position:0%
+of idiosyncratic risk to Total risk and
+the contribution of idiosyncratic risk
+
+ align:start position:0%
+the contribution of idiosyncratic risk
+ 
+
+ align:start position:0%
+the contribution of idiosyncratic risk
+to the risk premium the contribution of
+
+ align:start position:0%
+to the risk premium the contribution of
+ 
+
+ align:start position:0%
+to the risk premium the contribution of
+idiosyncratic risk to the total variance
+
+ align:start position:0%
+idiosyncratic risk to the total variance
+ 
+
+ align:start position:0%
+idiosyncratic risk to the total variance
+is huge
+
+ align:start position:0%
+is huge
+ 
+
+ align:start position:0%
+is huge
+this row here
+
+ align:start position:0%
+this row here
+ 
+
+ align:start position:0%
+this row here
+running across the villages and looking
+
+ align:start position:0%
+running across the villages and looking
+ 
+
+ align:start position:0%
+running across the villages and looking
+at the quartiles including the median he
+
+ align:start position:0%
+at the quartiles including the median he
+ 
+
+ align:start position:0%
+at the quartiles including the median he
+got 98 of it 97 of it 94 of it 65
+
+ align:start position:0%
+got 98 of it 97 of it 94 of it 65
+ 
+
+ align:start position:0%
+got 98 of it 97 of it 94 of it 65
+percent of the risk is coming from the
+
+ align:start position:0%
+percent of the risk is coming from the
+ 
+
+ align:start position:0%
+percent of the risk is coming from the
+idiosyncratic component coming from this
+
+ align:start position:0%
+idiosyncratic component coming from this
+ 
+
+ align:start position:0%
+idiosyncratic component coming from this
+guy
+
+ align:start position:0%
+guy
+ 
+
+ align:start position:0%
+guy
+let me back up coming from this guy
+
+ align:start position:0%
+let me back up coming from this guy
+ 
+
+ align:start position:0%
+let me back up coming from this guy
+second row of this table is the
+
+ align:start position:0%
+second row of this table is the
+ 
+
+ align:start position:0%
+second row of this table is the
+contribution to the risk premium of the
+
+ align:start position:0%
+contribution to the risk premium of the
+ 
+
+ align:start position:0%
+contribution to the risk premium of the
+idiosyncratic risk and it's pretty small
+
+ align:start position:0%
+idiosyncratic risk and it's pretty small
+ 
+
+ align:start position:0%
+idiosyncratic risk and it's pretty small
+two things to note it's almost always
+
+ align:start position:0%
+two things to note it's almost always
+ 
+
+ align:start position:0%
+two things to note it's almost always
+lower than the quantity so the risk
+
+ align:start position:0%
+lower than the quantity so the risk
+ 
+
+ align:start position:0%
+lower than the quantity so the risk
+premium here it's also small here it's
+
+ align:start position:0%
+premium here it's also small here it's
+ 
+
+ align:start position:0%
+premium here it's also small here it's
+21 percent which isn't trivial or even
+
+ align:start position:0%
+21 percent which isn't trivial or even
+ 
+
+ align:start position:0%
+21 percent which isn't trivial or even
+here 45 percent but the 45 percent is
+
+ align:start position:0%
+here 45 percent but the 45 percent is
+ 
+
+ align:start position:0%
+here 45 percent but the 45 percent is
+still less than the 99 so the
+
+ align:start position:0%
+still less than the 99 so the
+ 
+
+ align:start position:0%
+still less than the 99 so the
+contribution to the risk premium in
+
+ align:start position:0%
+contribution to the risk premium in
+ 
+
+ align:start position:0%
+contribution to the risk premium in
+terms of the compensating returns
+
+ align:start position:0%
+terms of the compensating returns
+ 
+
+ align:start position:0%
+terms of the compensating returns
+required for the household to run that
+
+ align:start position:0%
+required for the household to run that
+ 
+
+ align:start position:0%
+required for the household to run that
+those Technologies is always the
+
+ align:start position:0%
+those Technologies is always the
+ 
+
+ align:start position:0%
+those Technologies is always the
+contribution to the total risk is always
+
+ align:start position:0%
+contribution to the total risk is always
+ 
+
+ align:start position:0%
+contribution to the total risk is always
+greater than the risk premium
+
+ align:start position:0%
+greater than the risk premium
+ 
+
+ align:start position:0%
+greater than the risk premium
+except for Iran kind of screws up over
+
+ align:start position:0%
+except for Iran kind of screws up over
+ 
+
+ align:start position:0%
+except for Iran kind of screws up over
+here but as you've seen pretty rum
+
+ align:start position:0%
+here but as you've seen pretty rum
+ 
+
+ align:start position:0%
+here but as you've seen pretty rum
+screws up in other ways and then we do a
+
+ align:start position:0%
+screws up in other ways and then we do a
+ 
+
+ align:start position:0%
+screws up in other ways and then we do a
+robustness check
+
+ align:start position:0%
+robustness check
+ 
+
+ align:start position:0%
+robustness check
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay back to the economics
+
+ align:start position:0%
+okay back to the economics
+ 
+
+ align:start position:0%
+okay back to the economics
+plan the medieval Villages scattered
+
+ align:start position:0%
+plan the medieval Villages scattered
+ 
+
+ align:start position:0%
+plan the medieval Villages scattered
+around random returns
+
+ align:start position:0%
+around random returns
+ 
+
+ align:start position:0%
+around random returns
+you know should they diversify do they
+
+ align:start position:0%
+you know should they diversify do they
+ 
+
+ align:start position:0%
+you know should they diversify do they
+do different activities Etc
+
+ align:start position:0%
+do different activities Etc
+ 
+
+ align:start position:0%
+do different activities Etc
+well that depends on the level of risk
+
+ align:start position:0%
+well that depends on the level of risk
+ 
+
+ align:start position:0%
+well that depends on the level of risk
+and it turns out there's a lot of risk
+
+ align:start position:0%
+and it turns out there's a lot of risk
+ 
+
+ align:start position:0%
+and it turns out there's a lot of risk
+but a lot of it is plot specific or
+
+ align:start position:0%
+but a lot of it is plot specific or
+ 
+
+ align:start position:0%
+but a lot of it is plot specific or
+activity specific
+
+ align:start position:0%
+activity specific
+ 
+
+ align:start position:0%
+activity specific
+most of it is idiosyncratic and not
+
+ align:start position:0%
+most of it is idiosyncratic and not
+ 
+
+ align:start position:0%
+most of it is idiosyncratic and not
+aggregate it is not true that the
+
+ align:start position:0%
+aggregate it is not true that the
+ 
+
+ align:start position:0%
+aggregate it is not true that the
+returns are co-moving much across all
+
+ align:start position:0%
+returns are co-moving much across all
+ 
+
+ align:start position:0%
+returns are co-moving much across all
+these activities
+
+ align:start position:0%
+these activities
+ 
+
+ align:start position:0%
+these activities
+so it's a very risky place as in India
+
+ align:start position:0%
+so it's a very risky place as in India
+ 
+
+ align:start position:0%
+so it's a very risky place as in India
+but there are plenty of diversification
+
+ align:start position:0%
+but there are plenty of diversification
+ 
+
+ align:start position:0%
+but there are plenty of diversification
+possibilities by holding multiple
+
+ align:start position:0%
+possibilities by holding multiple
+ 
+
+ align:start position:0%
+possibilities by holding multiple
+activities
+
+ align:start position:0%
+activities
+ 
+
+ align:start position:0%
+activities
+Etc so we're back to a version of what
+
+ align:start position:0%
+Etc so we're back to a version of what
+ 
+
+ align:start position:0%
+Etc so we're back to a version of what
+we did in medieval Villages right how
+
+ align:start position:0%
+we did in medieval Villages right how
+ 
+
+ align:start position:0%
+we did in medieval Villages right how
+much did they hold different plots here
+
+ align:start position:0%
+much did they hold different plots here
+ 
+
+ align:start position:0%
+much did they hold different plots here
+we are asking how much do they hold
+
+ align:start position:0%
+we are asking how much do they hold
+ 
+
+ align:start position:0%
+we are asking how much do they hold
+different activities and what can be
+
+ align:start position:0%
+different activities and what can be
+ 
+
+ align:start position:0%
+different activities and what can be
+accomplished by doing that and moreover
+
+ align:start position:0%
+accomplished by doing that and moreover
+ 
+
+ align:start position:0%
+accomplished by doing that and moreover
+since it's idiosyncratic you can kind of
+
+ align:start position:0%
+since it's idiosyncratic you can kind of
+ 
+
+ align:start position:0%
+since it's idiosyncratic you can kind of
+hope that it might get the risk premium
+
+ align:start position:0%
+hope that it might get the risk premium
+ 
+
+ align:start position:0%
+hope that it might get the risk premium
+for the idiosyncratic stuff might get
+
+ align:start position:0%
+for the idiosyncratic stuff might get
+ 
+
+ align:start position:0%
+for the idiosyncratic stuff might get
+small anyway all of this is from the
+
+ align:start position:0%
+small anyway all of this is from the
+ 
+
+ align:start position:0%
+small anyway all of this is from the
+production data let's look at the
+
+ align:start position:0%
+production data let's look at the
+ 
+
+ align:start position:0%
+production data let's look at the
+consumption data and in particular look
+
+ align:start position:0%
+consumption data and in particular look
+ 
+
+ align:start position:0%
+consumption data and in particular look
+at the gifts so now we're going from
+
+ align:start position:0%
+at the gifts so now we're going from
+ 
+
+ align:start position:0%
+at the gifts so now we're going from
+medieval Villages so to speak in terms
+
+ align:start position:0%
+medieval Villages so to speak in terms
+ 
+
+ align:start position:0%
+medieval Villages so to speak in terms
+of plots and production to India in
+
+ align:start position:0%
+of plots and production to India in
+ 
+
+ align:start position:0%
+of plots and production to India in
+terms of exposed consumption smoothing
+
+ align:start position:0%
+terms of exposed consumption smoothing
+ 
+
+ align:start position:0%
+terms of exposed consumption smoothing
+the gifts and transfers are the x-post
+
+ align:start position:0%
+the gifts and transfers are the x-post
+ 
+
+ align:start position:0%
+the gifts and transfers are the x-post
+part
+
+ align:start position:0%
+part
+ 
+
+ align:start position:0%
+part
+it's how much they would give money to
+
+ align:start position:0%
+it's how much they would give money to
+ 
+
+ align:start position:0%
+it's how much they would give money to
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+starting from do actually give money to
+
+ align:start position:0%
+starting from do actually give money to
+ 
+
+ align:start position:0%
+starting from do actually give money to
+each other
+
+ align:start position:0%
+each other
+ 
+
+ align:start position:0%
+each other
+starting from the yields on their
+
+ align:start position:0%
+starting from the yields on their
+ 
+
+ align:start position:0%
+starting from the yields on their
+production activities
+
+ align:start position:0%
+production activities
+ 
+
+ align:start position:0%
+production activities
+so if you look back here again
+
+ align:start position:0%
+so if you look back here again
+ 
+
+ align:start position:0%
+so if you look back here again
+you would see these Epsilon so this
+
+ align:start position:0%
+you would see these Epsilon so this
+ 
+
+ align:start position:0%
+you would see these Epsilon so this
+could be high this could be low it's the
+
+ align:start position:0%
+could be high this could be low it's the
+ 
+
+ align:start position:0%
+could be high this could be low it's the
+variance is Big it's moving the returns
+
+ align:start position:0%
+variance is Big it's moving the returns
+ 
+
+ align:start position:0%
+variance is Big it's moving the returns
+around what happens when it's really big
+
+ align:start position:0%
+around what happens when it's really big
+ 
+
+ align:start position:0%
+around what happens when it's really big
+then this household got lucky it had a
+
+ align:start position:0%
+then this household got lucky it had a
+ 
+
+ align:start position:0%
+then this household got lucky it had a
+high return just lucky what does it do
+
+ align:start position:0%
+high return just lucky what does it do
+ 
+
+ align:start position:0%
+high return just lucky what does it do
+it gives stuff away
+
+ align:start position:0%
+it gives stuff away
+ 
+
+ align:start position:0%
+it gives stuff away
+or another version they get unlucky the
+
+ align:start position:0%
+or another version they get unlucky the
+ 
+
+ align:start position:0%
+or another version they get unlucky the
+Epsilon is low what do they do people
+
+ align:start position:0%
+Epsilon is low what do they do people
+ 
+
+ align:start position:0%
+Epsilon is low what do they do people
+give them gifts
+
+ align:start position:0%
+give them gifts
+ 
+
+ align:start position:0%
+give them gifts
+well I haven't actually shown your
+
+ align:start position:0%
+well I haven't actually shown your
+ 
+
+ align:start position:0%
+well I haven't actually shown your
+result but that's exactly what is going
+
+ align:start position:0%
+result but that's exactly what is going
+ 
+
+ align:start position:0%
+result but that's exactly what is going
+on in the data
+
+ align:start position:0%
+on in the data
+ 
+
+ align:start position:0%
+on in the data
+so if you regress those shocks those
+
+ align:start position:0%
+so if you regress those shocks those
+ 
+
+ align:start position:0%
+so if you regress those shocks those
+idiosyncratic shocks and on the right
+
+ align:start position:0%
+idiosyncratic shocks and on the right
+ 
+
+ align:start position:0%
+idiosyncratic shocks and on the right
+hand side onto gifts and net lending Etc
+
+ align:start position:0%
+hand side onto gifts and net lending Etc
+ 
+
+ align:start position:0%
+hand side onto gifts and net lending Etc
+you can see both there is an ultimate
+
+ align:start position:0%
+you can see both there is an ultimate
+ 
+
+ align:start position:0%
+you can see both there is an ultimate
+impact on consumption yes but it's small
+
+ align:start position:0%
+impact on consumption yes but it's small
+ 
+
+ align:start position:0%
+impact on consumption yes but it's small
+relative to the way they're mitigating
+
+ align:start position:0%
+relative to the way they're mitigating
+ 
+
+ align:start position:0%
+relative to the way they're mitigating
+the risk namely when the shock is high
+
+ align:start position:0%
+the risk namely when the shock is high
+ 
+
+ align:start position:0%
+the risk namely when the shock is high
+they're giving stuff away and lending it
+
+ align:start position:0%
+they're giving stuff away and lending it
+ 
+
+ align:start position:0%
+they're giving stuff away and lending it
+out and conversely when the shock is low
+
+ align:start position:0%
+out and conversely when the shock is low
+ 
+
+ align:start position:0%
+out and conversely when the shock is low
+they're getting this stuff in it depends
+
+ align:start position:0%
+they're getting this stuff in it depends
+ 
+
+ align:start position:0%
+they're getting this stuff in it depends
+on the sign this is net gift outflow
+
+ align:start position:0%
+on the sign this is net gift outflow
+ 
+
+ align:start position:0%
+on the sign this is net gift outflow
+when the shock is high it's positive
+
+ align:start position:0%
+when the shock is high it's positive
+ 
+
+ align:start position:0%
+when the shock is high it's positive
+it's statistically significant you can
+
+ align:start position:0%
+it's statistically significant you can
+ 
+
+ align:start position:0%
+it's statistically significant you can
+add up both gifts and borrowing and
+
+ align:start position:0%
+add up both gifts and borrowing and
+ 
+
+ align:start position:0%
+add up both gifts and borrowing and
+lending and get a bigger coefficient
+
+ align:start position:0%
+lending and get a bigger coefficient
+ 
+
+ align:start position:0%
+lending and get a bigger coefficient
+here it's 40. the 40 relative to the
+
+ align:start position:0%
+here it's 40. the 40 relative to the
+ 
+
+ align:start position:0%
+here it's 40. the 40 relative to the
+impact on consumption which is four in
+
+ align:start position:0%
+impact on consumption which is four in
+ 
+
+ align:start position:0%
+impact on consumption which is four in
+other words for every unit of
+
+ align:start position:0%
+other words for every unit of
+ 
+
+ align:start position:0%
+other words for every unit of
+idiosyncratic shock roughly 10 percent
+
+ align:start position:0%
+idiosyncratic shock roughly 10 percent
+ 
+
+ align:start position:0%
+idiosyncratic shock roughly 10 percent
+of it is making its way into consumption
+
+ align:start position:0%
+of it is making its way into consumption
+ 
+
+ align:start position:0%
+of it is making its way into consumption
+which it shouldn't it violates the
+
+ align:start position:0%
+which it shouldn't it violates the
+ 
+
+ align:start position:0%
+which it shouldn't it violates the
+resharing theory but 90 10 of it is
+
+ align:start position:0%
+resharing theory but 90 10 of it is
+ 
+
+ align:start position:0%
+resharing theory but 90 10 of it is
+being pulled away by this Village gift
+
+ align:start position:0%
+being pulled away by this Village gift
+ 
+
+ align:start position:0%
+being pulled away by this Village gift
+giving mechanism
+
+ align:start position:0%
+giving mechanism
+ 
+
+ align:start position:0%
+giving mechanism
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in economics we call this The Smoking
+
+ align:start position:0%
+in economics we call this The Smoking
+ 
+
+ align:start position:0%
+in economics we call this The Smoking
+Gun you kind of theorize a lot you think
+
+ align:start position:0%
+Gun you kind of theorize a lot you think
+ 
+
+ align:start position:0%
+Gun you kind of theorize a lot you think
+you know what happened but what's the
+
+ align:start position:0%
+you know what happened but what's the
+ 
+
+ align:start position:0%
+you know what happened but what's the
+evidence oh they smooth a lot must be
+
+ align:start position:0%
+evidence oh they smooth a lot must be
+ 
+
+ align:start position:0%
+evidence oh they smooth a lot must be
+the gifts okay fine if you think so well
+
+ align:start position:0%
+the gifts okay fine if you think so well
+ 
+
+ align:start position:0%
+the gifts okay fine if you think so well
+here's the evidence they're actually
+
+ align:start position:0%
+here's the evidence they're actually
+ 
+
+ align:start position:0%
+here's the evidence they're actually
+doing it and not only that they openly
+
+ align:start position:0%
+doing it and not only that they openly
+ 
+
+ align:start position:0%
+doing it and not only that they openly
+tell us they're doing it they they are
+
+ align:start position:0%
+tell us they're doing it they they are
+ 
+
+ align:start position:0%
+tell us they're doing it they they are
+very aware that they help each other I I
+
+ align:start position:0%
+very aware that they help each other I I
+ 
+
+ align:start position:0%
+very aware that they help each other I I
+think you might have seen the video by
+
+ align:start position:0%
+think you might have seen the video by
+ 
+
+ align:start position:0%
+think you might have seen the video by
+now my movie so to speak if not take a
+
+ align:start position:0%
+now my movie so to speak if not take a
+ 
+
+ align:start position:0%
+now my movie so to speak if not take a
+look at it because it describes you'll
+
+ align:start position:0%
+look at it because it describes you'll
+ 
+
+ align:start position:0%
+look at it because it describes you'll
+actually see the setting of these Thai
+
+ align:start position:0%
+actually see the setting of these Thai
+ 
+
+ align:start position:0%
+actually see the setting of these Thai
+Villages and how we've gathered the data
+
+ align:start position:0%
+Villages and how we've gathered the data
+ 
+
+ align:start position:0%
+Villages and how we've gathered the data
+and so on Michael is planning to show
+
+ align:start position:0%
+and so on Michael is planning to show
+ 
+
+ align:start position:0%
+and so on Michael is planning to show
+that at one point but it's available
+
+ align:start position:0%
+that at one point but it's available
+ 
+
+ align:start position:0%
+that at one point but it's available
+the 32-minute movie it's not so much of
+
+ align:start position:0%
+the 32-minute movie it's not so much of
+ 
+
+ align:start position:0%
+the 32-minute movie it's not so much of
+a burden
+
+ align:start position:0%
+a burden
+ 
+
+ align:start position:0%
+a burden
+and you'll see how I spend 20 years of
+
+ align:start position:0%
+and you'll see how I spend 20 years of
+ 
+
+ align:start position:0%
+and you'll see how I spend 20 years of
+my life okay
+
+ align:start position:0%
+my life okay
+ 
+
+ align:start position:0%
+my life okay
+so we've talked about this now let's
+
+ align:start position:0%
+so we've talked about this now let's
+ 
+
+ align:start position:0%
+so we've talked about this now let's
+come back to health shocks
+
+ align:start position:0%
+come back to health shocks
+ 
+
+ align:start position:0%
+come back to health shocks
+no it's not covered but it is an illness
+
+ align:start position:0%
+no it's not covered but it is an illness
+ 
+
+ align:start position:0%
+no it's not covered but it is an illness
+experienced by the household and it's
+
+ align:start position:0%
+experienced by the household and it's
+ 
+
+ align:start position:0%
+experienced by the household and it's
+not covered by insurance and the
+
+ align:start position:0%
+not covered by insurance and the
+ 
+
+ align:start position:0%
+not covered by insurance and the
+expenditures go up so this is normalized
+
+ align:start position:0%
+expenditures go up so this is normalized
+ 
+
+ align:start position:0%
+expenditures go up so this is normalized
+so that the event happens here and
+
+ align:start position:0%
+so that the event happens here and
+ 
+
+ align:start position:0%
+so that the event happens here and
+health spending is big and other things
+
+ align:start position:0%
+health spending is big and other things
+ 
+
+ align:start position:0%
+health spending is big and other things
+like they say they're sick they're
+
+ align:start position:0%
+like they say they're sick they're
+ 
+
+ align:start position:0%
+like they say they're sick they're
+reporting symptoms to us we also
+
+ align:start position:0%
+reporting symptoms to us we also
+ 
+
+ align:start position:0%
+reporting symptoms to us we also
+measured that so we're pretty much sure
+
+ align:start position:0%
+measured that so we're pretty much sure
+ 
+
+ align:start position:0%
+measured that so we're pretty much sure
+that we nailed the episode Etc and sick
+
+ align:start position:0%
+that we nailed the episode Etc and sick
+ 
+
+ align:start position:0%
+that we nailed the episode Etc and sick
+days you know it goes up and kind of
+
+ align:start position:0%
+days you know it goes up and kind of
+ 
+
+ align:start position:0%
+days you know it goes up and kind of
+stays up for a while before it comes
+
+ align:start position:0%
+stays up for a while before it comes
+ 
+
+ align:start position:0%
+stays up for a while before it comes
+back down again okay and what happens
+
+ align:start position:0%
+back down again okay and what happens
+ 
+
+ align:start position:0%
+back down again okay and what happens
+there come the gifts
+
+ align:start position:0%
+there come the gifts
+ 
+
+ align:start position:0%
+there come the gifts
+again centered around
+
+ align:start position:0%
+again centered around
+ 
+
+ align:start position:0%
+again centered around
+you know the episode the event as soon
+
+ align:start position:0%
+you know the episode the event as soon
+ 
+
+ align:start position:0%
+you know the episode the event as soon
+as the event happens it's actually minus
+
+ align:start position:0%
+as the event happens it's actually minus
+ 
+
+ align:start position:0%
+as the event happens it's actually minus
+one as soon as the event happens the
+
+ align:start position:0%
+one as soon as the event happens the
+ 
+
+ align:start position:0%
+one as soon as the event happens the
+gifts are positive and statistically
+
+ align:start position:0%
+gifts are positive and statistically
+ 
+
+ align:start position:0%
+gifts are positive and statistically
+different than for households that did
+
+ align:start position:0%
+different than for households that did
+ 
+
+ align:start position:0%
+different than for households that did
+not experience those cell shocks
+
+ align:start position:0%
+not experience those cell shocks
+ 
+
+ align:start position:0%
+not experience those cell shocks
+here we're comparing Placebo households
+
+ align:start position:0%
+here we're comparing Placebo households
+ 
+
+ align:start position:0%
+here we're comparing Placebo households
+if you like which is a dangerous
+
+ align:start position:0%
+if you like which is a dangerous
+ 
+
+ align:start position:0%
+if you like which is a dangerous
+metaphor given the illness part of it
+
+ align:start position:0%
+metaphor given the illness part of it
+ 
+
+ align:start position:0%
+metaphor given the illness part of it
+and the covet we're taking households
+
+ align:start position:0%
+and the covet we're taking households
+ 
+
+ align:start position:0%
+and the covet we're taking households
+pairwise conceptually ones that have
+
+ align:start position:0%
+pairwise conceptually ones that have
+ 
+
+ align:start position:0%
+pairwise conceptually ones that have
+experienced T Cell shocks to ones that
+
+ align:start position:0%
+experienced T Cell shocks to ones that
+ 
+
+ align:start position:0%
+experienced T Cell shocks to ones that
+have not
+
+ align:start position:0%
+have not
+ 
+
+ align:start position:0%
+have not
+and looking at the difference in the
+
+ align:start position:0%
+and looking at the difference in the
+ 
+
+ align:start position:0%
+and looking at the difference in the
+gifts that they get
+
+ align:start position:0%
+gifts that they get
+ 
+
+ align:start position:0%
+gifts that they get
+so if they're sick they're much more
+
+ align:start position:0%
+so if they're sick they're much more
+ 
+
+ align:start position:0%
+so if they're sick they're much more
+likely to be getting gifts than the
+
+ align:start position:0%
+likely to be getting gifts than the
+ 
+
+ align:start position:0%
+likely to be getting gifts than the
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+this is the same setting as what I
+
+ align:start position:0%
+this is the same setting as what I
+ 
+
+ align:start position:0%
+this is the same setting as what I
+showed you when rates of return except
+
+ align:start position:0%
+showed you when rates of return except
+ 
+
+ align:start position:0%
+showed you when rates of return except
+we've changed the subject from shocks to
+
+ align:start position:0%
+we've changed the subject from shocks to
+ 
+
+ align:start position:0%
+we've changed the subject from shocks to
+production to illness shocks now
+
+ align:start position:0%
+production to illness shocks now
+ 
+
+ align:start position:0%
+production to illness shocks now
+actually related they're still producing
+
+ align:start position:0%
+actually related they're still producing
+ 
+
+ align:start position:0%
+actually related they're still producing
+or trying to and the fact that they've
+
+ align:start position:0%
+or trying to and the fact that they've
+ 
+
+ align:start position:0%
+or trying to and the fact that they've
+doubled say their health expenditure is
+
+ align:start position:0%
+doubled say their health expenditure is
+ 
+
+ align:start position:0%
+doubled say their health expenditure is
+a big problem for them because they have
+
+ align:start position:0%
+a big problem for them because they have
+ 
+
+ align:start position:0%
+a big problem for them because they have
+only so much liquidity and they're
+
+ align:start position:0%
+only so much liquidity and they're
+ 
+
+ align:start position:0%
+only so much liquidity and they're
+supposed to be buying inputs and so on
+
+ align:start position:0%
+supposed to be buying inputs and so on
+ 
+
+ align:start position:0%
+supposed to be buying inputs and so on
+to fund their Agriculture and so on so
+
+ align:start position:0%
+to fund their Agriculture and so on so
+ 
+
+ align:start position:0%
+to fund their Agriculture and so on so
+this is a liquidity shock it's not just
+
+ align:start position:0%
+this is a liquidity shock it's not just
+ 
+
+ align:start position:0%
+this is a liquidity shock it's not just
+a health shock in fact sometimes it's an
+
+ align:start position:0%
+a health shock in fact sometimes it's an
+ 
+
+ align:start position:0%
+a health shock in fact sometimes it's an
+elderly person in the household that is
+
+ align:start position:0%
+elderly person in the household that is
+ 
+
+ align:start position:0%
+elderly person in the household that is
+not even contributing to production
+
+ align:start position:0%
+not even contributing to production
+ 
+
+ align:start position:0%
+not even contributing to production
+so we're looking at the economic impact
+
+ align:start position:0%
+so we're looking at the economic impact
+ 
+
+ align:start position:0%
+so we're looking at the economic impact
+of someone taking money away from their
+
+ align:start position:0%
+of someone taking money away from their
+ 
+
+ align:start position:0%
+of someone taking money away from their
+budget essentially
+
+ align:start position:0%
+budget essentially
+ 
+
+ align:start position:0%
+budget essentially
+okay there are various kinds of networks
+
+ align:start position:0%
+okay there are various kinds of networks
+ 
+
+ align:start position:0%
+okay there are various kinds of networks
+in these villages
+
+ align:start position:0%
+in these villages
+ 
+
+ align:start position:0%
+in these villages
+this is the kinship Network who's
+
+ align:start position:0%
+this is the kinship Network who's
+ 
+
+ align:start position:0%
+this is the kinship Network who's
+related to whom this is the financial
+
+ align:start position:0%
+related to whom this is the financial
+ 
+
+ align:start position:0%
+related to whom this is the financial
+Network
+
+ align:start position:0%
+Network
+ 
+
+ align:start position:0%
+Network
+terms of giving gifts to one another
+
+ align:start position:0%
+terms of giving gifts to one another
+ 
+
+ align:start position:0%
+terms of giving gifts to one another
+this is the sales network who they sell
+
+ align:start position:0%
+this is the sales network who they sell
+ 
+
+ align:start position:0%
+this is the sales network who they sell
+to in the village
+
+ align:start position:0%
+to in the village
+ 
+
+ align:start position:0%
+to in the village
+and this is who they hire from
+
+ align:start position:0%
+and this is who they hire from
+ 
+
+ align:start position:0%
+and this is who they hire from
+you know so the way these pictures are
+
+ align:start position:0%
+you know so the way these pictures are
+ 
+
+ align:start position:0%
+you know so the way these pictures are
+produced with the software roughly
+
+ align:start position:0%
+produced with the software roughly
+ 
+
+ align:start position:0%
+produced with the software roughly
+speaking households in the middle you
+
+ align:start position:0%
+speaking households in the middle you
+ 
+
+ align:start position:0%
+speaking households in the middle you
+know are connected to other many other
+
+ align:start position:0%
+know are connected to other many other
+ 
+
+ align:start position:0%
+know are connected to other many other
+households households On The Fringe
+
+ align:start position:0%
+households households On The Fringe
+ 
+
+ align:start position:0%
+households households On The Fringe
+don't have that many connections
+
+ align:start position:0%
+don't have that many connections
+ 
+
+ align:start position:0%
+don't have that many connections
+depending on the variable
+
+ align:start position:0%
+depending on the variable
+ 
+
+ align:start position:0%
+depending on the variable
+and the gift-giving financial network is
+
+ align:start position:0%
+and the gift-giving financial network is
+ 
+
+ align:start position:0%
+and the gift-giving financial network is
+different from the sales and production
+
+ align:start position:0%
+different from the sales and production
+ 
+
+ align:start position:0%
+different from the sales and production
+Network and I'm going to show you what
+
+ align:start position:0%
+Network and I'm going to show you what
+ 
+
+ align:start position:0%
+Network and I'm going to show you what
+happens because of that
+
+ align:start position:0%
+happens because of that
+ 
+
+ align:start position:0%
+happens because of that
+I don't have a slide to show you this
+
+ align:start position:0%
+I don't have a slide to show you this
+ 
+
+ align:start position:0%
+I don't have a slide to show you this
+but if they're in this gift giving
+
+ align:start position:0%
+but if they're in this gift giving
+ 
+
+ align:start position:0%
+but if they're in this gift giving
+Network
+
+ align:start position:0%
+Network
+ 
+
+ align:start position:0%
+Network
+measured by how many times they got
+
+ align:start position:0%
+measured by how many times they got
+ 
+
+ align:start position:0%
+measured by how many times they got
+gifts before the health shock happened
+
+ align:start position:0%
+gifts before the health shock happened
+ 
+
+ align:start position:0%
+gifts before the health shock happened
+then most of the impact of the shock is
+
+ align:start position:0%
+then most of the impact of the shock is
+ 
+
+ align:start position:0%
+then most of the impact of the shock is
+covered by incoming gifts
+
+ align:start position:0%
+covered by incoming gifts
+ 
+
+ align:start position:0%
+covered by incoming gifts
+but what do we have in the U.S you know
+
+ align:start position:0%
+but what do we have in the U.S you know
+ 
+
+ align:start position:0%
+but what do we have in the U.S you know
+this is an issue a household gets sick
+
+ align:start position:0%
+this is an issue a household gets sick
+ 
+
+ align:start position:0%
+this is an issue a household gets sick
+is the government going to be able to
+
+ align:start position:0%
+is the government going to be able to
+ 
+
+ align:start position:0%
+is the government going to be able to
+help them
+
+ align:start position:0%
+help them
+ 
+
+ align:start position:0%
+help them
+we have these PPP paycheck protection
+
+ align:start position:0%
+we have these PPP paycheck protection
+ 
+
+ align:start position:0%
+we have these PPP paycheck protection
+programs and so on
+
+ align:start position:0%
+programs and so on
+ 
+
+ align:start position:0%
+programs and so on
+our relatives helping probably so we
+
+ align:start position:0%
+our relatives helping probably so we
+ 
+
+ align:start position:0%
+our relatives helping probably so we
+don't know the extent of it it's not
+
+ align:start position:0%
+don't know the extent of it it's not
+ 
+
+ align:start position:0%
+don't know the extent of it it's not
+measured we tend to think households are
+
+ align:start position:0%
+measured we tend to think households are
+ 
+
+ align:start position:0%
+measured we tend to think households are
+our Standalone they're vulnerable
+
+ align:start position:0%
+our Standalone they're vulnerable
+ 
+
+ align:start position:0%
+our Standalone they're vulnerable
+households running businesses in
+
+ align:start position:0%
+households running businesses in
+ 
+
+ align:start position:0%
+households running businesses in
+particular get a liquidity shock and
+
+ align:start position:0%
+particular get a liquidity shock and
+ 
+
+ align:start position:0%
+particular get a liquidity shock and
+mainly they don't have sales with covet
+
+ align:start position:0%
+mainly they don't have sales with covet
+ 
+
+ align:start position:0%
+mainly they don't have sales with covet
+or their employees aren't you know able
+
+ align:start position:0%
+or their employees aren't you know able
+ 
+
+ align:start position:0%
+or their employees aren't you know able
+to work
+
+ align:start position:0%
+to work
+ 
+
+ align:start position:0%
+to work
+so they're not generating Revenue
+
+ align:start position:0%
+so they're not generating Revenue
+ 
+
+ align:start position:0%
+so they're not generating Revenue
+well if it were covered with gifts as it
+
+ align:start position:0%
+well if it were covered with gifts as it
+ 
+
+ align:start position:0%
+well if it were covered with gifts as it
+is for some people in Thailand then they
+
+ align:start position:0%
+is for some people in Thailand then they
+ 
+
+ align:start position:0%
+is for some people in Thailand then they
+pool that risk away
+
+ align:start position:0%
+pool that risk away
+ 
+
+ align:start position:0%
+pool that risk away
+great system
+
+ align:start position:0%
+great system
+ 
+
+ align:start position:0%
+great system
+if they're not there are other
+
+ align:start position:0%
+if they're not there are other
+ 
+
+ align:start position:0%
+if they're not there are other
+consequences
+
+ align:start position:0%
+consequences
+ 
+
+ align:start position:0%
+consequences
+so in particular
+
+ align:start position:0%
+so in particular
+ 
+
+ align:start position:0%
+so in particular
+we can look at who's connected to whom
+
+ align:start position:0%
+we can look at who's connected to whom
+ 
+
+ align:start position:0%
+we can look at who's connected to whom
+in terms of the network
+
+ align:start position:0%
+in terms of the network
+ 
+
+ align:start position:0%
+in terms of the network
+households who experience shocks and
+
+ align:start position:0%
+households who experience shocks and
+ 
+
+ align:start position:0%
+households who experience shocks and
+were selling to other households their
+
+ align:start position:0%
+were selling to other households their
+ 
+
+ align:start position:0%
+were selling to other households their
+sales go down
+
+ align:start position:0%
+sales go down
+ 
+
+ align:start position:0%
+sales go down
+it's a bit counterintuitive because you
+
+ align:start position:0%
+it's a bit counterintuitive because you
+ 
+
+ align:start position:0%
+it's a bit counterintuitive because you
+would think they would want the money
+
+ align:start position:0%
+would think they would want the money
+ 
+
+ align:start position:0%
+would think they would want the money
+from the sales
+
+ align:start position:0%
+from the sales
+ 
+
+ align:start position:0%
+from the sales
+but the problem is they had to reduce
+
+ align:start position:0%
+but the problem is they had to reduce
+ 
+
+ align:start position:0%
+but the problem is they had to reduce
+the inputs they had the scale production
+
+ align:start position:0%
+the inputs they had the scale production
+ 
+
+ align:start position:0%
+the inputs they had the scale production
+down and so they have less Revenue as a
+
+ align:start position:0%
+down and so they have less Revenue as a
+ 
+
+ align:start position:0%
+down and so they have less Revenue as a
+result
+
+ align:start position:0%
+result
+ 
+
+ align:start position:0%
+result
+sales are down inventories are up
+
+ align:start position:0%
+sales are down inventories are up
+ 
+
+ align:start position:0%
+sales are down inventories are up
+well I should let me come back and
+
+ align:start position:0%
+well I should let me come back and
+ 
+
+ align:start position:0%
+well I should let me come back and
+clarify these are
+
+ align:start position:0%
+clarify these are
+ 
+
+ align:start position:0%
+clarify these are
+households connected to the household
+
+ align:start position:0%
+households connected to the household
+ 
+
+ align:start position:0%
+households connected to the household
+that has experienced the shock
+
+ align:start position:0%
+that has experienced the shock
+ 
+
+ align:start position:0%
+that has experienced the shock
+these guys were selling I said it wrong
+
+ align:start position:0%
+these guys were selling I said it wrong
+ 
+
+ align:start position:0%
+these guys were selling I said it wrong
+I'm sorry these guys were selling
+
+ align:start position:0%
+I'm sorry these guys were selling
+ 
+
+ align:start position:0%
+I'm sorry these guys were selling
+Revenue to the household that had the
+
+ align:start position:0%
+Revenue to the household that had the
+ 
+
+ align:start position:0%
+Revenue to the household that had the
+shock now they sell less likewise
+
+ align:start position:0%
+shock now they sell less likewise
+ 
+
+ align:start position:0%
+shock now they sell less likewise
+because they sell less they're
+
+ align:start position:0%
+because they sell less they're
+ 
+
+ align:start position:0%
+because they sell less they're
+accumulating inventory and they're
+
+ align:start position:0%
+accumulating inventory and they're
+ 
+
+ align:start position:0%
+accumulating inventory and they're
+holding on to inventory longer this is
+
+ align:start position:0%
+holding on to inventory longer this is
+ 
+
+ align:start position:0%
+holding on to inventory longer this is
+for this inventory turnover ratio
+
+ align:start position:0%
+for this inventory turnover ratio
+ 
+
+ align:start position:0%
+for this inventory turnover ratio
+it's a measure of and when it's high
+
+ align:start position:0%
+it's a measure of and when it's high
+ 
+
+ align:start position:0%
+it's a measure of and when it's high
+it's a measure of inefficiency it's also
+
+ align:start position:0%
+it's a measure of inefficiency it's also
+ 
+
+ align:start position:0%
+it's a measure of inefficiency it's also
+negative with an adverse effect
+
+ align:start position:0%
+negative with an adverse effect
+ 
+
+ align:start position:0%
+negative with an adverse effect
+we do this for all the shocks and do it
+
+ align:start position:0%
+we do this for all the shocks and do it
+ 
+
+ align:start position:0%
+we do this for all the shocks and do it
+for the large shock so now we see the
+
+ align:start position:0%
+for the large shock so now we see the
+ 
+
+ align:start position:0%
+for the large shock so now we see the
+covet connection right which is you know
+
+ align:start position:0%
+covet connection right which is you know
+ 
+
+ align:start position:0%
+covet connection right which is you know
+a household experiences expenses
+
+ align:start position:0%
+a household experiences expenses
+ 
+
+ align:start position:0%
+a household experiences expenses
+associated with the illness even if it's
+
+ align:start position:0%
+associated with the illness even if it's
+ 
+
+ align:start position:0%
+associated with the illness even if it's
+not a working member how do they cover
+
+ align:start position:0%
+not a working member how do they cover
+ 
+
+ align:start position:0%
+not a working member how do they cover
+those expenses they they try to cut back
+
+ align:start position:0%
+those expenses they they try to cut back
+ 
+
+ align:start position:0%
+those expenses they they try to cut back
+they cut back on spending in these
+
+ align:start position:0%
+they cut back on spending in these
+ 
+
+ align:start position:0%
+they cut back on spending in these
+Village economies businesses are
+
+ align:start position:0%
+Village economies businesses are
+ 
+
+ align:start position:0%
+Village economies businesses are
+connected
+
+ align:start position:0%
+connected
+ 
+
+ align:start position:0%
+connected
+they're buying and selling inputs from
+
+ align:start position:0%
+they're buying and selling inputs from
+ 
+
+ align:start position:0%
+they're buying and selling inputs from
+one another and selling output so if
+
+ align:start position:0%
+one another and selling output so if
+ 
+
+ align:start position:0%
+one another and selling output so if
+they have to cut back and they don't
+
+ align:start position:0%
+they have to cut back and they don't
+ 
+
+ align:start position:0%
+they have to cut back and they don't
+have the revenue that they had before
+
+ align:start position:0%
+have the revenue that they had before
+ 
+
+ align:start position:0%
+have the revenue that they had before
+the people who had been buying have been
+
+ align:start position:0%
+the people who had been buying have been
+ 
+
+ align:start position:0%
+the people who had been buying have been
+selling to them you know no longer have
+
+ align:start position:0%
+selling to them you know no longer have
+ 
+
+ align:start position:0%
+selling to them you know no longer have
+the sales just like you know one
+
+ align:start position:0%
+the sales just like you know one
+ 
+
+ align:start position:0%
+the sales just like you know one
+business is connected to another they
+
+ align:start position:0%
+business is connected to another they
+ 
+
+ align:start position:0%
+business is connected to another they
+all go down the supply chain because
+
+ align:start position:0%
+all go down the supply chain because
+ 
+
+ align:start position:0%
+all go down the supply chain because
+they're connected we had a lecture at
+
+ align:start position:0%
+they're connected we had a lecture at
+ 
+
+ align:start position:0%
+they're connected we had a lecture at
+the end on interconnections among
+
+ align:start position:0%
+the end on interconnections among
+ 
+
+ align:start position:0%
+the end on interconnections among
+households we did leonte up we did the
+
+ align:start position:0%
+households we did leonte up we did the
+ 
+
+ align:start position:0%
+households we did leonte up we did the
+input output Matrix I showed you
+
+ align:start position:0%
+input output Matrix I showed you
+ 
+
+ align:start position:0%
+input output Matrix I showed you
+fukujima Shima and the effect of the
+
+ align:start position:0%
+fukujima Shima and the effect of the
+ 
+
+ align:start position:0%
+fukujima Shima and the effect of the
+earthquake there and those were all
+
+ align:start position:0%
+earthquake there and those were all
+ 
+
+ align:start position:0%
+earthquake there and those were all
+Supply chains you know one sector is
+
+ align:start position:0%
+Supply chains you know one sector is
+ 
+
+ align:start position:0%
+Supply chains you know one sector is
+connected to another one firms connected
+
+ align:start position:0%
+connected to another one firms connected
+ 
+
+ align:start position:0%
+connected to another one firms connected
+to another these Thai households are
+
+ align:start position:0%
+to another these Thai households are
+ 
+
+ align:start position:0%
+to another these Thai households are
+connected to another and the more the
+
+ align:start position:0%
+connected to another and the more the
+ 
+
+ align:start position:0%
+connected to another and the more the
+point of this I guess I haven't said
+
+ align:start position:0%
+point of this I guess I haven't said
+ 
+
+ align:start position:0%
+point of this I guess I haven't said
+that is yet the closer they are to the
+
+ align:start position:0%
+that is yet the closer they are to the
+ 
+
+ align:start position:0%
+that is yet the closer they are to the
+adversely impacted household the more
+
+ align:start position:0%
+adversely impacted household the more
+ 
+
+ align:start position:0%
+adversely impacted household the more
+they suffer so you think networks are a
+
+ align:start position:0%
+they suffer so you think networks are a
+ 
+
+ align:start position:0%
+they suffer so you think networks are a
+good thing networks are a good thing
+
+ align:start position:0%
+good thing networks are a good thing
+ 
+
+ align:start position:0%
+good thing networks are a good thing
+when it comes to financial gift giving
+
+ align:start position:0%
+when it comes to financial gift giving
+ 
+
+ align:start position:0%
+when it comes to financial gift giving
+but if gift giving doesn't cover the
+
+ align:start position:0%
+but if gift giving doesn't cover the
+ 
+
+ align:start position:0%
+but if gift giving doesn't cover the
+adverse shock we're actually getting an
+
+ align:start position:0%
+adverse shock we're actually getting an
+ 
+
+ align:start position:0%
+adverse shock we're actually getting an
+amplification in this economy that's
+
+ align:start position:0%
+amplification in this economy that's
+ 
+
+ align:start position:0%
+amplification in this economy that's
+showing up in terms of lost wages and
+
+ align:start position:0%
+showing up in terms of lost wages and
+ 
+
+ align:start position:0%
+showing up in terms of lost wages and
+less production unless sales and finally
+
+ align:start position:0%
+less production unless sales and finally
+ 
+
+ align:start position:0%
+less production unless sales and finally
+this distinction which I've been pushing
+
+ align:start position:0%
+this distinction which I've been pushing
+ 
+
+ align:start position:0%
+this distinction which I've been pushing
+today about Aggregate and idiosyncratic
+
+ align:start position:0%
+today about Aggregate and idiosyncratic
+ 
+
+ align:start position:0%
+today about Aggregate and idiosyncratic
+shocks
+
+ align:start position:0%
+shocks
+ 
+
+ align:start position:0%
+shocks
+go to one of the areas where they have
+
+ align:start position:0%
+go to one of the areas where they have
+ 
+
+ align:start position:0%
+go to one of the areas where they have
+fish ponds shrimp ponds in particular
+
+ align:start position:0%
+fish ponds shrimp ponds in particular
+ 
+
+ align:start position:0%
+fish ponds shrimp ponds in particular
+and it's pretty polluted and they didn't
+
+ align:start position:0%
+and it's pretty polluted and they didn't
+ 
+
+ align:start position:0%
+and it's pretty polluted and they didn't
+have you know Green agriculture so to
+
+ align:start position:0%
+have you know Green agriculture so to
+ 
+
+ align:start position:0%
+have you know Green agriculture so to
+speak and the EU put a ban on the shrimp
+
+ align:start position:0%
+speak and the EU put a ban on the shrimp
+ 
+
+ align:start position:0%
+speak and the EU put a ban on the shrimp
+by the way if you go to Walmart you know
+
+ align:start position:0%
+by the way if you go to Walmart you know
+ 
+
+ align:start position:0%
+by the way if you go to Walmart you know
+you say villagers who cares well anyway
+
+ align:start position:0%
+you say villagers who cares well anyway
+ 
+
+ align:start position:0%
+you say villagers who cares well anyway
+they produce the shrimp that you buy in
+
+ align:start position:0%
+they produce the shrimp that you buy in
+ 
+
+ align:start position:0%
+they produce the shrimp that you buy in
+Walmart but the EU put a ban
+
+ align:start position:0%
+Walmart but the EU put a ban
+ 
+
+ align:start position:0%
+Walmart but the EU put a ban
+on the on the shrimp because they say it
+
+ align:start position:0%
+on the on the shrimp because they say it
+ 
+
+ align:start position:0%
+on the on the shrimp because they say it
+wasn't clean which it wasn't now the
+
+ align:start position:0%
+wasn't clean which it wasn't now the
+ 
+
+ align:start position:0%
+wasn't clean which it wasn't now the
+point is most but not all households are
+
+ align:start position:0%
+point is most but not all households are
+ 
+
+ align:start position:0%
+point is most but not all households are
+doing those shrimp ponds and the ban is
+
+ align:start position:0%
+doing those shrimp ponds and the ban is
+ 
+
+ align:start position:0%
+doing those shrimp ponds and the ban is
+like an aggregate shock so we can
+
+ align:start position:0%
+like an aggregate shock so we can
+ 
+
+ align:start position:0%
+like an aggregate shock so we can
+compare the aggregate shock which is
+
+ align:start position:0%
+compare the aggregate shock which is
+ 
+
+ align:start position:0%
+compare the aggregate shock which is
+most of the households to the
+
+ align:start position:0%
+most of the households to the
+ 
+
+ align:start position:0%
+most of the households to the
+idiosyncratic illness shocks and you can
+
+ align:start position:0%
+idiosyncratic illness shocks and you can
+ 
+
+ align:start position:0%
+idiosyncratic illness shocks and you can
+see that although gifts go up I already
+
+ align:start position:0%
+see that although gifts go up I already
+ 
+
+ align:start position:0%
+see that although gifts go up I already
+showed you that for the idiosyncratic
+
+ align:start position:0%
+showed you that for the idiosyncratic
+ 
+
+ align:start position:0%
+showed you that for the idiosyncratic
+shocks including in this Village there's
+
+ align:start position:0%
+shocks including in this Village there's
+ 
+
+ align:start position:0%
+shocks including in this Village there's
+not that clear picture when it comes to
+
+ align:start position:0%
+not that clear picture when it comes to
+ 
+
+ align:start position:0%
+not that clear picture when it comes to
+the trim shock because it's an aggregate
+
+ align:start position:0%
+the trim shock because it's an aggregate
+ 
+
+ align:start position:0%
+the trim shock because it's an aggregate
+shock there's not a lot of weight excuse
+
+ align:start position:0%
+shock there's not a lot of weight excuse
+ 
+
+ align:start position:0%
+shock there's not a lot of weight excuse
+me to reallocate that risk
+
+ align:start position:0%
+me to reallocate that risk
+ 
+
+ align:start position:0%
+me to reallocate that risk
+and this is the associated decline in
+
+ align:start position:0%
+and this is the associated decline in
+ 
+
+ align:start position:0%
+and this is the associated decline in
+employment which is bigger under the
+
+ align:start position:0%
+employment which is bigger under the
+ 
+
+ align:start position:0%
+employment which is bigger under the
+aggregate shock
+
+ align:start position:0%
+aggregate shock
+ 
+
+ align:start position:0%
+aggregate shock
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what I have for today and
+
+ align:start position:0%
+okay so that's what I have for today and
+ 
+
+ align:start position:0%
+okay so that's what I have for today and
+we'll continue on Thursday thank you for
+
+ align:start position:0%
+we'll continue on Thursday thank you for
+ 
+
+ align:start position:0%
+we'll continue on Thursday thank you for
+coming today talk to you soon
\ No newline at end of file
diff --git a/RUz-DJz3--I.txt b/RUz-DJz3--I.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69f2040e12cc8407c69be9984c5ae39d01c5521e
--- /dev/null
+++ b/RUz-DJz3--I.txt
@@ -0,0 +1,2030 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So.
+
+In the meantime, you've started
+looking at two phase
+
+equilibrium.
+
+So now we're starting
+to look at mixtures.
+
+And so now we have more
+than one constituent.
+
+And we have more than
+one phase present.
+
+Right?
+
+So you've started to look at
+things that look like this,
+
+where you've got, let's
+say, two components.
+
+Both in the gas phase.
+
+And now to try to figure
+out what the phase
+
+equilibria look like.
+
+Of course it's now a little bit
+more complicated than what
+
+you went through before, where
+you can get pressure
+
+temperature phase diagrams with
+just a single component.
+
+Now we want to worry about
+what's the composition.
+
+Of each of the components.
+
+In each of the phases.
+
+And what's the temperature
+and the pressure.
+
+Total and partial pressures
+and all of that.
+
+So you can really figure out
+everything about both phases.
+
+And there are all sorts of
+important reasons to do that,
+
+obviously lots of chemistry
+happens in liquid mixtures.
+
+Some in gas mixtures.
+
+Some where they're
+in equilibrium.
+
+All sorts of chemical
+processes.
+
+Distillation, for example,
+takes advantage of the
+
+properties of liquid
+and gas mixtures.
+
+Where one of them might be
+richer, will be richer, and
+
+the more volatile of
+the components.
+
+That can be used as a basis
+for purification.
+
+You mix ethanol and water
+together so you've got a
+
+liquid with a certain
+composition of each.
+
+The gas is going to be richer
+and the more volatile of the
+
+two, the ethanol.
+
+So in a distillation, where you
+put things up in the gas,
+
+more of the ethanol comes up.
+
+You could then collect
+that gas, right?
+
+And re-condense it, and
+make a new liquid.
+
+Which is much richer in ethanol
+than the original
+
+liquid was.
+
+Then you could make, then you
+could put some of them up into
+
+the gas phase.
+
+Where it will be still
+richer in ethanol.
+
+And then you could collect that
+and repeat the process.
+
+So the point is that properties
+of liquid gas,
+
+two-component or multi-component
+mixtures like
+
+this can be exploited.
+
+Basically, the different
+volatilities of the different
+
+components can be exploited for
+things like purification.
+
+Also if you want to calculate
+chemical equilibria in the
+
+liquid and gas phase, of
+course, now you've seen
+
+chemical equilibrium, so the
+amount of reaction depends on
+
+the composition.
+
+So of course if you want
+reactions to go, then this
+
+also can be exploited by looking
+at which phase might
+
+be richer in one reactant
+or another.
+
+And thereby pushing the
+equilibrium toward one
+
+direction or the other.
+
+OK.
+
+So. we've got some total
+temperature and pressure.
+
+And we have compositions.
+
+So in the gas phase, we've got
+mole fractions yA and yB.
+
+In the liquid phase we've got
+mole fractions xA and xB.
+
+So that's our system.
+
+One of the things that you
+established last time is that,
+
+so there are the total number
+of variables including the
+
+temperature and the pressure.
+
+And let's say the mole fraction
+of A in each of the
+
+liquid and gas phases, right?
+
+But then there are
+constraints.
+
+Because the chemical
+potentials have
+
+to be equal, right?
+
+Chemical potential of
+A has to be equal in
+
+the liquid and gas.
+
+Same with B. Those two
+constraints reduce the number
+
+of independent variables.
+
+So there'll be two in this
+case rather than four
+
+independent variables.
+
+If you control those, then
+everything else will follow.
+
+What that means is if you've got
+a, if you control, if you
+
+fix the temperature and the
+total pressure, everything
+
+else should be determinable.
+
+No more free variables.
+
+And then, what you saw is that
+in simple or ideal liquid
+
+mixtures, a result called
+Raoult's law would hold.
+
+Which just says that the partial
+pressure of A is equal
+
+to the mole fraction of A in the
+liquid times the pressure
+
+of pure A over the liquid.
+
+And so what this gives
+you is a diagram
+
+that looks like this.
+
+If we plot this versus xB, this
+is mole fraction of B in
+
+the liquid going from
+zero to one.
+
+Then we could construct a
+diagram of this sort.
+
+So this is the total pressure
+of A and B. The partial
+
+pressures are given
+by these lines.
+
+So this is our pA star
+and pB star.
+
+The pressures over the pure
+liquid A and B at the limits
+
+of mole fraction of B
+being zero and one.
+
+So in this situation, for
+example, A is the more
+
+volatile of the components.
+
+So it's partial pressure
+over its pure liquid.
+
+At this temperature.
+
+Is higher than the partial
+pressure of B
+
+over its pure liquid.
+
+A would be the ethanol, for
+example and B the water in
+
+that mixture.
+
+OK.
+
+Then you started looking at both
+the gas and the liquid
+
+phase in the same diagram.
+
+So this is the mole fraction
+of the liquid.
+
+If you look and see, well, OK
+now we should be able to
+
+determine the mole fraction
+in the gas as well.
+
+Again, if we note total
+temperature and pressure,
+
+everything else must follow.
+
+And so, you saw this
+worked out.
+
+Relation between p and
+yA, for example.
+
+The result was p is pA star
+times pB star over pA star
+
+plus pB star minus
+pA star times yA.
+
+And the point here is that
+unlike this case, where you
+
+have a linear relationship, the
+relationship between the
+
+pressure and the liquid mole
+fraction isn't linear.
+
+We can still plot
+it, of course.
+
+So if we do that, then we end
+up with a diagram that looks
+
+like the following.
+
+Now I'm going to keep both mole
+fractions, xB and yB,
+
+I've got some total pressure.
+
+I still have my linear
+relationship.
+
+And then I have a non-linear
+relationship between the
+
+pressure and the mole fraction
+in the gas phase.
+
+So let's just fill this in.
+
+Here is pA star still.
+
+Here's pB star.
+
+Of course, at the limits they're
+still, both mole
+
+fractions they're zero and one.
+
+OK.
+
+I believe this is this is where
+you ended up at the end
+
+of the last lecture.
+
+But it's probably not so clear
+exactly how you read
+
+something like this.
+
+And use it.
+
+It's extremely useful.
+
+You just have to kind of learn
+how to follow what happens in
+
+a diagram like this.
+
+And that's what I want to spend
+some of today doing.
+
+Is just, walking through what's
+happening physically,
+
+with a container with a
+mixture of the two.
+
+And how does that correspond
+to what gets read off the
+
+diagram under different
+conditions.
+
+So.
+
+Let's just start somewhere on
+a phase diagram like this.
+
+Let's start up here at some
+point one, so we're in the
+
+pure - well, not pure, you're
+in the all liquid phase.
+
+It's still a mixture.
+
+It's not a pure substance.
+pA star, pB star.
+
+There's the gas phase.
+
+So, if we start at one, and now
+
+there's some total pressure.
+
+And now we're going
+to reduce it.
+
+What happens?
+
+We start with a pure - with
+an all-liquid mixture.
+
+No gas.
+
+And now we're going to bring
+down the pressure.
+
+Allowing some of the liquid to
+go up into the gas phase.
+
+So, we can do that.
+
+And once we reach point
+two, then we find
+
+a coexistence curve.
+
+Now the liquid and gas
+are going to coexist.
+
+So this is the liquid phase.
+
+And that means that
+this must be xB.
+
+And it's xB at one, but it's
+also xB at two, and I want to
+
+emphasize that.
+
+So let's put our pressure
+for two.
+
+And if we go over here, this is
+telling us about the mole
+
+fraction in the gas phase.
+
+That's what these curves
+are, remember.
+
+So this is the one that's
+showing us the mole fraction
+
+in the liquid phase.
+
+This nonlinear one
+in the gas phase.
+
+So that means just reading off
+it, this is xB, that's the
+
+liquid mole fraction.
+
+Here's yB.
+
+The gas mole fraction.
+
+They're not the same, right,
+because of course the
+
+components have different
+volatility.
+
+A's more volatile.
+
+So that means that the mole
+fraction of B in the liquid
+
+phase is higher than the
+mole fraction of
+
+B in the gas phase.
+
+Because A is the more
+volatile component.
+
+So more, relatively more, of A,
+the mole fraction of A is
+
+going to be higher up
+in the gas phase.
+
+Which means the mole
+fraction of B is
+
+lower in the gas phase.
+
+So, yB less than xB if
+A is more volatile.
+
+OK, so now what's happening
+physically?
+
+Well, we started at a
+point where we only
+
+had the liquid present.
+
+So at our initial pressure,
+we just have all liquid.
+
+There's some xB at one.
+
+That's all there is, there
+isn't any gas yet.
+
+Now, what happened here?
+
+Well, now we lowered
+the pressure.
+
+So you could imagine, well,
+we made the box bigger.
+
+Now, if the liquid was under
+pressure, being squeezed by
+
+the box, right then you
+could make the box
+
+a little bit bigger.
+
+And there's still no gas.
+
+That's moving down like this.
+
+But then you get to a point
+where there's just barely any
+
+pressure on top of the liquid.
+
+And then you keep expanding
+the box.
+
+Now some gas is going to form.
+
+So now we're going to
+go to our case two.
+
+We've got a bigger box.
+
+And now, right around
+where this was, this
+
+is going to be liquid.
+
+And there's gas up here.
+
+So up here is yB at
+pressure two.
+
+Here's xB at pressure two.
+
+Liquid and gas.
+
+So that's where we are
+at point two here.
+
+Now, what happens if
+we keep going?
+
+Let's lower the pressure
+some more.
+
+Well, we can lower
+it and do this.
+
+But really if we want to see
+what's happening in each of
+
+the phases, we have to stay
+on the coexistence curves.
+
+Those are what tell us what
+the pressures are.
+
+What the partial pressure
+are going to be
+
+in each of the phases.
+
+In each of the two, in the
+liquid and the gas phases.
+
+So let's say we lower the
+pressure a little more.
+
+What's going to happen
+is, then we'll end up
+
+somewhere over here.
+
+In the liquid, and that'll
+correspond to something over
+
+here in the gas.
+
+So here's three.
+
+So now we're going to have,
+that's going to be xB at
+
+pressure three.
+
+And over here is going to
+be yB at pressure three.
+
+And all we've done, of
+course, is we've just
+
+expanded this further.
+
+So now we've got a
+still taller box.
+
+And the liquid is going to be a
+little lower because some of
+
+it has evaporated, formed
+the gas phase.
+
+So here's xB at three.
+
+Here's yB at three, here's
+our gas phase.
+
+Now we could decrease
+even further.
+
+And this is the sort of
+thing that you maybe
+
+can't do in real life.
+
+But I can do on a blackboard.
+
+I'm going to give myself more
+room on this curve, to finish
+
+this illustration.
+
+There.
+
+Beautiful.
+
+So now we can lower a little bit
+further, and what I want
+
+to illustrate is, if we keep
+going down, eventually we get
+
+to a pressure where now if we
+look over in the gas phase,
+
+we're at the same pressure,
+mole fraction that we had
+
+originally in the
+liquid phase.
+
+So let's make four even
+lower pressure.
+
+What does that mean?
+
+What it means is, we're
+running out of liquid.
+
+So what's supposed to
+happen is A is the
+
+more volatile component.
+
+So as we start opening up some
+room for gas to form, you get
+
+more of A in the gas phase.
+
+But of course, and the liquid is
+richer in B. But of course,
+
+eventually you run
+out of liquid.
+
+You make the box pretty big, and
+you run out, or you have
+
+the very last drop of liquid.
+
+So what's the mole fraction
+of B in the gas phase?
+
+It has to be the same as
+what it started in
+
+in the liquid phase.
+
+Because after all the total
+number of moles of A and B
+
+hasn't changed any.
+
+So if you take them all from the
+liquid and put them all up
+
+into the gas phase, it
+must be the same.
+
+So yB of four.
+
+Once you just have
+the last drop.
+
+So then yB of four is basically
+equal to xB of one.
+
+Because everything's now
+up in the gas phase.
+
+So in principle, there's still
+a tiny, tiny bit of xB at
+
+pressure four.
+
+Well, we could keep lowering
+the pressure.
+
+We could make the box
+a little bigger.
+
+Then the very last of the liquid
+is going to be gone.
+
+And what'll happen then
+is, we're all here.
+
+There's no more liquid.
+
+We're not going down on the
+coexistence curve any more.
+
+We don't have a liquid gas
+coexistence any more.
+
+We just have a gas phase.
+
+Of course, we can continue
+to lower the pressure.
+
+And then what we're doing
+is just going down here.
+
+So there's five.
+
+And five is the same as
+this only bigger.
+
+And so forth.
+
+OK, any questions about
+how this works?
+
+It's really important to just
+gain facility in reading these
+
+things and seeing, OK, what is
+it that this is telling you.
+
+And you can see it's not
+complicated to do it, but it
+
+takes a little bit of practice.
+
+OK.
+
+Now, of course, we could do
+exactly the same thing
+
+starting from the gas phase.
+
+And raising the pressure.
+
+And although you may anticipate
+that it's kind of
+
+pedantic, I really do want to
+illustrate something by it.
+
+So let me just imagine that
+we're going to do that.
+
+Let's start all in
+the gas phase.
+
+Up here's the liquid.
+pA star, pB star.
+
+And now let's start
+somewhere here.
+
+So we're down somewhere in
+the gas phase with some
+
+composition.
+
+So it's the same story, except
+now we're starting here.
+
+It's all gas.
+
+And we're going to
+start squeezing.
+
+We're increasing the pressure.
+
+And eventually here's one, will
+reach two, so of course
+
+here's our yB.
+
+We started with all
+gas, no liquid.
+
+So this is yB of one.
+
+It's the same as yB of two, I'm
+just raising the pressure
+
+enough to just reach the
+coexistence curve.
+
+And of course, out here tells
+us xB of two, right?
+
+So what is it saying?
+
+We've squeezed and started
+to form some liquid.
+
+And the liquid is richer in
+component B. Maybe it's
+
+ethanol water again.
+
+And we squeeze, and now we've
+got more water in the liquid
+
+phase than in the gas phase.
+
+Because water's the less
+volatile component.
+
+It's what's going to
+condense first.
+
+So the liquid is rich in the
+less volatile of the
+
+components.
+
+Now, obviously, we can continue
+in doing exactly the
+
+reverse of what I showed you.
+
+But all I want to really
+illustrate is, this is a
+
+strategy for purification of the
+less volatile component.
+
+Once you've done this, well now
+you've got some liquid.
+
+Now you could collect that
+liquid in a separate vessel.
+
+So let's collect the liquid
+mixture with xB of two.
+
+So it's got some mole fraction
+of B. So we've purified that.
+
+But now we're going to start,
+we've got pure liquid.
+
+Now let's make the vessel big.
+
+So it all goes into
+the gas phase.
+
+Then lower p.
+
+All gas.
+
+So we start with yB of three,
+which equals xB of two.
+
+In other words, it's the
+same mole fraction.
+
+So let's reconstruct that.
+
+So here's p of two.
+
+And now we're going to go
+to some new pressure.
+
+And the point is, now we're
+going to start, since the mole
+
+fraction in the gas phase that
+we're starting from is the
+
+same number as this was.
+
+So it's around here somewhere.
+
+That's yB of three
+equals xB of two.
+
+And we're down here.
+
+In other words, all we've done
+is make the container big
+
+enough so the pressure's low and
+it's all in the gas phase.
+
+That's all we have,
+is the gas.
+
+But the composition is whatever
+the composition is
+
+that we extracted here
+from the liquid.
+
+So this xB, which is the liquid
+mole fraction, is now
+
+yB, the gas mole fraction.
+
+Of course, the pressure
+is different.
+
+Lower than it was before.
+
+Great.
+
+Now let's increase.
+
+So here's three.
+
+And now let's increase
+the pressure to four.
+
+And of course what happens,
+now we've got coexistence.
+
+So here's liquid.
+
+Here's gas.
+
+So, now we're over here again.
+
+There's xB at pressure four.
+
+Pure still in component B. We
+can repeat the same procedure.
+
+Collect it.
+
+All liquid, put it
+in a new vessel.
+
+Expand it, lower the pressure,
+all goes back
+
+into the gas phase.
+
+Do it all again.
+
+And the point is, what you're
+doing is walking along here.
+
+Here to here.
+
+Then you start down here, and
+go from here to here.
+
+From here to here.
+
+And you can purify.
+
+Now, of course, the optimal
+procedure, you have to think a
+
+little bit.
+
+Because if you really do
+precisely what I said, you're
+
+going to have a mighty little
+bit of material
+
+each time you do that.
+
+So yes it'll be the little bit
+you've gotten at the end is
+
+going to be really pure, but
+there's not a whole lot of it.
+
+Because, remember, what we
+said is let's raise the
+
+pressure until we just
+start being on
+
+the coexistence curve.
+
+So we've still got mostly gas.
+
+Little bit of liquid.
+
+Now, I could raise the pressure
+a bit higher.
+
+So that in the interest of
+having more of the liquid,
+
+when I do that, though, the
+liquid that I have at this
+
+higher pressure won't be as
+enriched as it was down here.
+
+Now, I could still do
+this procedure.
+
+I could just do more of them.
+
+So it takes a little bit of
+judiciousness to figure out
+
+how to optimize that.
+
+In the end, though, you can
+continue to walk your way down
+
+through these coexistence curves
+and purify repeatedly
+
+the component B, the less
+volatile of them, and end up
+
+with some amount of it.
+
+And there'll be some balance
+between the amount that you
+
+feel like you need to end
+up with and how pure
+
+you need it to be.
+
+Any questions about
+how this works?
+
+So purification of less
+volatile components.
+
+Now, how much of each of
+these quantities in
+
+each of these phases?
+
+So, pertinent to this
+discussion, of course we need
+
+to know that.
+
+If you want to try to optimize
+a procedure like that, of
+
+course it's going to be
+crucial to be able to
+
+understand and calculate for any
+pressure that you decide
+
+to raise to, just how many moles
+do you have in each of
+
+the phases?
+
+So at the end of the day, you
+can figure out, OK, now when I
+
+reach a certain degree of
+purification, here's how much
+
+of the stuff I end up with.
+
+Well, that turns out
+to be reasonably
+
+straightforward to do.
+
+And so what I'll go through
+is a simple mathematical
+
+derivation.
+
+And it turns out that it allows
+you to just read right
+
+off the diagram how much of each
+material you're going to
+
+end up with.
+
+So, here's what happens.
+
+This is something called
+the lever rule.
+
+How much of each component
+is there in each phase?
+
+So let's consider a
+case like this.
+
+Let me draw yet once again,
+just to get the numbering
+
+consistent.
+
+With how we'll treat this.
+
+So we're going to start here.
+
+And I want to draw it right
+in the middle, so I've
+
+got plenty of room.
+
+And we're going to go
+up to some pressure.
+
+And somewhere out there,
+now I can go to
+
+my coexistence curves.
+
+Liquid.
+
+And gas.
+
+And I can read off my values.
+
+So this is the liquid xB.
+
+So I'm going to go up to some
+point two, here's xB of two.
+
+Here's yB of two.
+
+Great.
+
+Now let's get these
+written in.
+
+So let's just define terms
+a little bit. nA, nB.
+
+Or just our total number of
+moles. ng and n liquid, of
+
+course, total number of moles.
+
+In the gas and liquid phases.
+
+So let's just do the calculation
+for each
+
+of these two cases.
+
+We'll start with one.
+
+That's the easier case.
+
+Because then we have
+only the gas.
+
+So at one, all gas.
+
+It says pure gas in the notes,
+but of course that
+
+isn't the pure gas.
+
+It's the mixture of the
+two components.
+
+So.
+
+How many moles of A?
+
+Well it's the mole fraction
+of A in the gas.
+
+Times the total number
+of moles in the gas.
+
+Let me put one in here.
+
+Just to be clear.
+
+And since we have all gas, the
+number of moles in the gas is
+
+just the total number
+of moles.
+
+So this is just yA at
+one times n total.
+
+Let's just write that in.
+
+And of course n total is
+equal to nA plus nB.
+
+So now let's look at
+condition two.
+
+Now we have to look a little
+more carefully.
+
+Because we have a liquid
+gas mixture.
+
+So nA is equal to yA
+at pressure two.
+
+Times the number of moles
+of gas at pressure two.
+
+Plus xA, at pressure two, times
+the number of moles of
+
+liquid at pressure two.
+
+Now, of course, these things
+have to be equal.
+
+The total number of moles of
+A didn't change, right?
+
+So those are equal.
+
+Then yA of two times
+ng of two.
+
+Plus xA of two times n liquid of
+two, that's equal to yA of
+
+one times n total.
+
+Which is of course equal to yA
+of one times n gas at two plus
+
+n liquid at two.
+
+I suppose I could be,
+add that equality.
+
+Of course, it's an
+obvious one.
+
+But let me do it anyway.
+
+The total number of moles
+is equal to nA plus nB.
+
+But it's also equal to
+n liquid plus n gas.
+
+And that's all I'm taking
+advantage of here.
+
+And now I'm just going to
+rearrange the terms.
+
+So I'm going to write yA at one
+minus yA at two, times ng
+
+at two, is equal to, and I'm
+going to take the other terms,
+
+the xA term. xA of two
+minus yA of one
+
+times n liquid at two.
+
+So I've just rearranged
+the terms.
+
+And I've done that because
+now, I think I omitted
+
+something here. yA
+of one times ng.
+
+No, I forgot a bracket, is what
+I did. yA of one there.
+
+And I did this because now I
+want to do is look at the
+
+ratio of liquid to gas
+at pressure two.
+
+So, ratio of I'll put it gas
+to liquid, that's ng of two
+
+over n liquid at two.
+
+And that's just equal to xA of
+two minus yA at one minus yA
+
+at one minus yA at two.
+
+So what does it mean?
+
+It's the ratio of these
+lever arms.
+
+That's what it's telling me.
+
+I can look, so I raise the
+pressure up to two.
+
+And so here's xB at two,
+here's yB at two.
+
+And I'm here somewhere.
+
+And this little amount and this
+little amount, that's
+
+that difference.
+
+And it's just telling me that
+ratio of those arms is the
+
+ratio of the total number of
+moles of gas to liquid.
+
+And that's great.
+
+Because now when I go back to
+the problem that we were just
+
+looking at, where I say, well
+I'm going to purify the less
+
+volatile component by raising
+the pressure until I'm at
+
+coexistence starting
+in the gas phase.
+
+Raise the pressure, I've
+got some liquid.
+
+But I also want some finite
+amount of liquid.
+
+But I don't want to just, when
+I get the very, very first
+
+drop of liquid now collected, of
+course it's enriched in the
+
+less volatile component.
+
+But there may be a minuscule
+amount, right?
+
+So I'll raise the pressure
+a bit more.
+
+I'll go up in pressure.
+
+And now, of course, when I do
+that the amount of enrichment
+
+of the liquid isn't as big as it
+was if I just raised it up
+
+enough to barely have
+any liquid.
+
+Then I'd be out here.
+
+But I've got more material in
+the liquid phase to collect.
+
+And that's what this allows
+me to calculate.
+
+Is how much do I
+get in the end.
+
+So it's very handy.
+
+You can also see, if I go all
+the way to the limit where the
+
+mole fraction in the liquid at
+the end is equal to what it
+
+was in the gas when I started,
+what that says is that there's
+
+no more gas left any more.
+
+In other words, these two
+things are equal.
+
+If I go all the way to the point
+where I've got all the,
+
+this is the amount I started
+with, in the pure gas phase,
+
+now I keep raising
+it all the way.
+
+Until I've got the same mole
+fraction in the liquid.
+
+Of course, we know what
+that really means.
+
+That means that I've gone
+all the way from
+
+pure gas to pure liquid.
+
+And the mole fraction in that
+case has to be the same.
+
+And what this is just telling
+us mathematically is, when
+
+that happens this is zero.
+
+That means I don't have
+any gas left.
+
+Yeah.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: No.
+
+Because, so it's the mole
+fraction in the gas phase.
+
+But you've started with some
+amount that it's only going to
+
+go down from there.
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+Yeah.
+
+Any other questions?
+
+OK.
+
+Well, now what I want to do
+is just put up a slightly
+
+different kind of diagram, but
+different in an important way.
+
+Namely, instead of showing the
+mole fractions as a function
+
+of the pressure.
+
+And I haven't written it in,
+but all of these are at
+
+constant temperature, right?
+
+I've assumed the temperature
+is constant
+
+in all these things.
+
+Now let's consider the other
+possibility, the other simple
+
+possibility, which is, let's
+hold the pressure constant and
+
+vary the temperature.
+
+Of course, you know in the lab,
+that's usually what's
+
+easiest to do.
+
+Now, unfortunately, the
+arithmetic gets more
+
+complicated.
+
+It's not monumentally
+complicated, but here in this
+
+case, where you have one linear
+relationship, which is
+
+very convenient.
+
+From Raoult's law.
+
+And then you have one non-linear
+relationship there
+
+for the mole fraction
+of the gas.
+
+In the case of temperature,
+they're both,
+
+neither one is linear.
+
+Nevertheless, we can just
+sketch what the
+
+diagram looks like.
+
+And of course it's very useful
+to do that, and see how to
+
+read off it.
+
+And I should say the derivation
+of the curves isn't
+
+particularly complicated.
+
+It's not particularly more
+complicated than what I think
+
+you saw last time
+to derive this.
+
+There's no complicated
+math involved.
+
+But the point is, the derivation
+doesn't yield a
+
+linear relationship for either
+the gas or the liquid part of
+
+the coexistence curve.
+
+OK, so we're going to look at
+temperature and mole fraction
+
+phase diagrams.
+
+Again, a little more complicated
+mathematically but
+
+more practical in real use.
+
+And this is T. And here is the,
+sort of, form that these
+
+things take.
+
+So again, neither
+one is linear.
+
+Up here, now, of course if you
+raise the temperatures, that's
+
+where you end up with gas.
+
+If you lower the temperature,
+you
+
+condense and get the liquid.
+
+So, this is TA star.
+
+TB star.
+
+So now I want to stick
+with A as the
+
+more volatile component.
+
+At constant temperature, that
+meant that pA star is bigger
+
+than pB star.
+
+In other words, the vapor
+pressure over pure liquid A is
+
+higher than the vapor pressure
+over pure liquid B. Similarly,
+
+now I've got constant pressure
+and really what I'm looking
+
+at, let's say I'm at the
+limit where I've
+
+got the pure liquid.
+
+Or the pure A. And now I'm going
+to, let's say, raise the
+
+temperature until I'm at the
+liquid-gas equilibrium.
+
+That's just the boiling point.
+
+So if A is the more volatile
+component, it has the lower
+
+boiling point.
+
+And that's what this reflects.
+
+So higher pB star A corresponds
+to lower TA star
+
+A. Which is just the boiling
+point of pure A.
+
+So, this is called
+the bubble line.
+
+That's called the dew line.
+
+All that means is, let's say
+I'm at high temperature.
+
+I've got all gas.
+
+Right no coexistence,
+no liquid yet.
+
+And I start to cool
+things off.
+
+Just to where I just barely
+start to get liquid.
+
+What you see that as is,
+dew starts forming.
+
+A little bit of condensation.
+
+If you're outside, it means on
+the grass a little bit of dew
+
+is forming.
+
+Similarly, if I start at low
+temperature, all liquid now I
+
+start raising the temperature
+until I just start to boil.
+
+I just start to see the
+first bubbles forming.
+
+And so that's why these things
+have those names.
+
+So now let's just follow along
+what happens when I do the
+
+same sort of thing that
+I illustrated there.
+
+I want to start at one point
+in this phase diagram.
+
+And then start changing
+the conditions.
+
+So let's start here.
+
+So I'm going to start all
+in the liquid phase.
+
+That is, the temperature
+is low.
+
+Here's xB.
+
+And my original temperature.
+
+Now I'm going to raise it.
+
+So if I raise it a little bit,
+I reach a point at which I
+
+first start to boil.
+
+Start to find some gas
+above the liquid.
+
+And if I look right here,
+that'll be my composition.
+
+Let me raise it a little
+farther, now that we've
+
+already seen the lever
+rule and so forth.
+
+I'll raise it up to here.
+
+And that means that out here,
+I suppose I should do here.
+
+So, here is the liquid mole
+fraction at temperature two.
+
+xB at temperature two.
+
+This is yB at temperature two.
+
+The gas mole fraction.
+
+So as you should expect, what's
+going to happen here is
+
+that the gas, this is going to
+be lower in B. A, that means
+
+that the mole fraction
+of A must be
+
+higher in the gas phase.
+
+That's one minus yB.
+
+So xA is one minus -- yA, which
+is one minus yB higher
+
+in gas phase.
+
+Than xA, which is
+one minus xB.
+
+In other words, the less
+volatile component is enriched
+
+up in the gas phase.
+
+Now, what does that mean?
+
+That means I could follow the
+same sort of procedure that I
+
+indicated before when we looked
+at the pressure mole
+
+fraction phase diagram.
+
+Namely, I could do this
+and now I could
+
+take the gas phase.
+
+Which has less of B. It
+has more of A. And
+
+I can collect it.
+
+And then I can reduce
+the temperature.
+
+So it liquefies.
+
+So I can condense it,
+in other words.
+
+So now I'm going to start with,
+let's say I lower the
+
+temperature enough so I've got
+basically pure liquid.
+
+But its composition is the
+same as the gas here.
+
+Because of course that's what
+that liquid is formed from.
+
+I collected the gas
+and separated it.
+
+So now I could start
+all over again.
+
+Except instead of being here,
+I'll be down here.
+
+And then I can raise the
+temperature again.
+
+To some place where I choose.
+
+I could choose here, and
+go all the way to hear.
+
+A great amount of enrichment.
+
+But I know from the lever rule
+that if I do that, I'm going
+
+to have precious little
+material over here.
+
+So I might prefer to raise the
+temperature a little more.
+
+Still get a substantial
+amount of enrichment.
+
+And now I've got, in the gas
+phase, I'll further enriched
+
+in component A. And again
+I can collect the gas.
+
+Condense it.
+
+Now I'm out here somewhere, I've
+got all liquid and I'll
+
+raise the temperature again.
+
+And I can again keep walking
+my way over.
+
+And that's what happens during
+an ordinary distillation.
+
+Each step of the distillation
+walks along in the phase
+
+diagram at some selected
+point.
+
+And of course what you're
+doing is, you're always
+
+condensing the gas.
+
+And starting with fresh liquid
+that now is enriched in more
+
+volatile of the components.
+
+So of course if you're really
+purifying, say, ethanol from
+
+an ethanol water mixture,
+that's how you do it.
+
+Ethanol is the more volatile
+component.
+
+So a still is set up.
+
+It will boil the stuff and
+collect the gas and and
+
+condense it.
+
+And boil it again,
+and so forth.
+
+And the whole thing can be set
+up in a very efficient way.
+
+So you have essentially
+continuous distillation.
+
+Where you have a whole sequence
+of collection and
+
+condensation and reheating
+and so forth events.
+
+So then, in a practical way,
+it's possible to walk quite
+
+far along the distillation,
+the coexistence curve, and
+
+distill to really a high
+degree of purification.
+
+Any questions about
+how that works?
+
+OK.
+
+I'll leave till next time the
+discussion of the chemical
+
+potentials.
+
+But what we'll do, just to
+foreshadow a little bit, what
+
+I'll do at the beginning of the
+next lecture is what's at
+
+the end of your notes here.
+
+Which is just to say OK, now
+if we look at Raoult's law,
+
+it's straightforward to say what
+is the chemical potential
+
+for each of the substances in
+the liquid and the gas phase.
+
+Of course, it has to be equal.
+
+Given that, that's for
+an ideal solution.
+
+We can gain some insight
+from that.
+
+And then look at real
+solutions, non-ideal
+
+solutions, and understand a lot
+of their behavior as well.
+
+Just from starting from our
+understanding of what the
+
+chemical potential does even
+in a simple ideal mixture.
+
+So we'll look at the chemical
+potentials.
+
+And then we'll look at
+non-ideal solution
+
+mixtures next time.
+
+See you then.
\ No newline at end of file
diff --git a/RWvi4Vx4CDc.txt b/RWvi4Vx4CDc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..68924e3d80fea985ca682959ddf20dd57f6321f2
--- /dev/null
+++ b/RWvi4Vx4CDc.txt
@@ -0,0 +1,6355 @@
+align:start position:0%
+ 
+okay good the final class in linear
+
+ align:start position:0%
+okay good the final class in linear
+ 
+
+ align:start position:0%
+okay good the final class in linear
+algebra at MIT this fall is to review
+
+ align:start position:0%
+algebra at MIT this fall is to review
+ 
+
+ align:start position:0%
+algebra at MIT this fall is to review
+the whole course and uh you know the
+
+ align:start position:0%
+the whole course and uh you know the
+ 
+
+ align:start position:0%
+the whole course and uh you know the
+best way I know how to review is to take
+
+ align:start position:0%
+best way I know how to review is to take
+ 
+
+ align:start position:0%
+best way I know how to review is to take
+old
+
+ align:start position:0%
+old
+ 
+
+ align:start position:0%
+old
+exams and just think through the proc
+
+ align:start position:0%
+exams and just think through the proc
+ 
+
+ align:start position:0%
+exams and just think through the proc
+problems so it'll be a three-hour exam
+
+ align:start position:0%
+problems so it'll be a three-hour exam
+ 
+
+ align:start position:0%
+problems so it'll be a three-hour exam
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+Thursday uh anybody who's got I mean
+
+ align:start position:0%
+Thursday uh anybody who's got I mean
+ 
+
+ align:start position:0%
+Thursday uh anybody who's got I mean
+nobody will be able to take an exam
+
+ align:start position:0%
+nobody will be able to take an exam
+ 
+
+ align:start position:0%
+nobody will be able to take an exam
+before Thursday anybody who needs to
+
+ align:start position:0%
+before Thursday anybody who needs to
+ 
+
+ align:start position:0%
+before Thursday anybody who needs to
+take it in some different way after
+
+ align:start position:0%
+take it in some different way after
+ 
+
+ align:start position:0%
+take it in some different way after
+Thursday should see me next Monday I'll
+
+ align:start position:0%
+Thursday should see me next Monday I'll
+ 
+
+ align:start position:0%
+Thursday should see me next Monday I'll
+be in my office Monday
+
+ align:start position:0%
+be in my office Monday
+ 
+
+ align:start position:0%
+be in my office Monday
+okay so may I just read out some
+
+ align:start position:0%
+okay so may I just read out some
+ 
+
+ align:start position:0%
+okay so may I just read out some
+problems and uh I'll let me bring the
+
+ align:start position:0%
+problems and uh I'll let me bring the
+ 
+
+ align:start position:0%
+problems and uh I'll let me bring the
+board down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's start
+
+ align:start position:0%
+and let's start
+ 
+
+ align:start position:0%
+and let's start
+okay here's a
+
+ align:start position:0%
+okay here's a
+ 
+
+ align:start position:0%
+okay here's a
+question this is a this is about an a 3
+
+ align:start position:0%
+question this is a this is about an a 3
+ 
+
+ align:start position:0%
+question this is a this is about an a 3
+byn
+
+ align:start position:0%
+byn
+ 
+
+ align:start position:0%
+byn
+Matrix and we're given so we're
+
+ align:start position:0%
+Matrix and we're given so we're
+ 
+
+ align:start position:0%
+Matrix and we're given so we're
+given
+
+ align:start position:0%
+given
+ 
+
+ align:start position:0%
+given
+given ax
+
+ align:start position:0%
+given ax
+ 
+
+ align:start position:0%
+given ax
+= 1 0 has no
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution and we're also given ax = 0 one
+
+ align:start position:0%
+solution and we're also given ax = 0 one
+ 
+
+ align:start position:0%
+solution and we're also given ax = 0 one
+Z has exactly one
+
+ align:start position:0%
+Z has exactly one
+ 
+
+ align:start position:0%
+Z has exactly one
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+okay so you can you can probably
+
+ align:start position:0%
+okay so you can you can probably
+ 
+
+ align:start position:0%
+okay so you can you can probably
+anticipate my first question what can
+
+ align:start position:0%
+anticipate my first question what can
+ 
+
+ align:start position:0%
+anticipate my first question what can
+you tell me about M it's it's an M byn
+
+ align:start position:0%
+you tell me about M it's it's an M byn
+ 
+
+ align:start position:0%
+you tell me about M it's it's an M byn
+Matrix of rank r as always what can you
+
+ align:start position:0%
+Matrix of rank r as always what can you
+ 
+
+ align:start position:0%
+Matrix of rank r as always what can you
+tell me about those three numbers so
+
+ align:start position:0%
+tell me about those three numbers so
+ 
+
+ align:start position:0%
+tell me about those three numbers so
+what can we tell me about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M the number of
+
+ align:start position:0%
+M the number of
+ 
+
+ align:start position:0%
+M the number of
+rows n the number of columns and R the
+
+ align:start position:0%
+rows n the number of columns and R the
+ 
+
+ align:start position:0%
+rows n the number of columns and R the
+rank
+
+ align:start position:0%
+rank
+ 
+
+ align:start position:0%
+rank
+okay see do you want to tell me first
+
+ align:start position:0%
+okay see do you want to tell me first
+ 
+
+ align:start position:0%
+okay see do you want to tell me first
+what m is how many rows in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix must be
+
+ align:start position:0%
+Matrix must be
+ 
+
+ align:start position:0%
+Matrix must be
+three right we can't tell what n is but
+
+ align:start position:0%
+three right we can't tell what n is but
+ 
+
+ align:start position:0%
+three right we can't tell what n is but
+we can certainly tell that m is three
+
+ align:start position:0%
+we can certainly tell that m is three
+ 
+
+ align:start position:0%
+we can certainly tell that m is three
+okay and what do we know
+
+ align:start position:0%
+okay and what do we know
+ 
+
+ align:start position:0%
+okay and what do we know
+about um so what do these things tell us
+
+ align:start position:0%
+about um so what do these things tell us
+ 
+
+ align:start position:0%
+about um so what do these things tell us
+let's take them one at a time when when
+
+ align:start position:0%
+let's take them one at a time when when
+ 
+
+ align:start position:0%
+let's take them one at a time when when
+this when I discover that some equation
+
+ align:start position:0%
+this when I discover that some equation
+ 
+
+ align:start position:0%
+this when I discover that some equation
+has no solution that there's some right
+
+ align:start position:0%
+has no solution that there's some right
+ 
+
+ align:start position:0%
+has no solution that there's some right
+hand side with no answer what does that
+
+ align:start position:0%
+hand side with no answer what does that
+ 
+
+ align:start position:0%
+hand side with no answer what does that
+tell me about the rank
+
+ align:start position:0%
+tell me about the rank
+ 
+
+ align:start position:0%
+tell me about the rank
+rank of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrix it's smaller than it's smaller
+
+ align:start position:0%
+matrix it's smaller than it's smaller
+ 
+
+ align:start position:0%
+matrix it's smaller than it's smaller
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+than m is that right that this if if
+
+ align:start position:0%
+than m is that right that this if if
+ 
+
+ align:start position:0%
+than m is that right that this if if
+there's no solution that tells me that
+
+ align:start position:0%
+there's no solution that tells me that
+ 
+
+ align:start position:0%
+there's no solution that tells me that
+the rank that the that some rows of the
+
+ align:start position:0%
+the rank that the that some rows of the
+ 
+
+ align:start position:0%
+the rank that the that some rows of the
+Matrix are combinations of other
+
+ align:start position:0%
+Matrix are combinations of other
+ 
+
+ align:start position:0%
+Matrix are combinations of other
+rows because if if if I had a pivot in
+
+ align:start position:0%
+rows because if if if I had a pivot in
+ 
+
+ align:start position:0%
+rows because if if if I had a pivot in
+every row
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I would certainly be able to solve
+
+ align:start position:0%
+then I would certainly be able to solve
+ 
+
+ align:start position:0%
+then I would certainly be able to solve
+the system I would have particular
+
+ align:start position:0%
+the system I would have particular
+ 
+
+ align:start position:0%
+the system I would have particular
+Solutions and all all the good stuff so
+
+ align:start position:0%
+Solutions and all all the good stuff so
+ 
+
+ align:start position:0%
+Solutions and all all the good stuff so
+if if anytime that there's a system that
+
+ align:start position:0%
+if if anytime that there's a system that
+ 
+
+ align:start position:0%
+if if anytime that there's a system that
+has with no solutions that tells me that
+
+ align:start position:0%
+has with no solutions that tells me that
+ 
+
+ align:start position:0%
+has with no solutions that tells me that
+R must be below M what about uh the fact
+
+ align:start position:0%
+R must be below M what about uh the fact
+ 
+
+ align:start position:0%
+R must be below M what about uh the fact
+that if when there is a solution there's
+
+ align:start position:0%
+that if when there is a solution there's
+ 
+
+ align:start position:0%
+that if when there is a solution there's
+only one what does that tell
+
+ align:start position:0%
+only one what does that tell
+ 
+
+ align:start position:0%
+only one what does that tell
+me Well normally there'd be one solution
+
+ align:start position:0%
+me Well normally there'd be one solution
+ 
+
+ align:start position:0%
+me Well normally there'd be one solution
+and then we could add in anything in the
+
+ align:start position:0%
+and then we could add in anything in the
+ 
+
+ align:start position:0%
+and then we could add in anything in the
+null space so this is telling me the
+
+ align:start position:0%
+null space so this is telling me the
+ 
+
+ align:start position:0%
+null space so this is telling me the
+null space only has the zero Vector in
+
+ align:start position:0%
+null space only has the zero Vector in
+ 
+
+ align:start position:0%
+null space only has the zero Vector in
+it there's just that there's just one
+
+ align:start position:0%
+it there's just that there's just one
+ 
+
+ align:start position:0%
+it there's just that there's just one
+solution period so what does that tell
+
+ align:start position:0%
+solution period so what does that tell
+ 
+
+ align:start position:0%
+solution period so what does that tell
+me the null space has only the zero
+
+ align:start position:0%
+me the null space has only the zero
+ 
+
+ align:start position:0%
+me the null space has only the zero
+Vector in it that tells me what does
+
+ align:start position:0%
+Vector in it that tells me what does
+ 
+
+ align:start position:0%
+Vector in it that tells me what does
+that tell me about the relation of R to
+
+ align:start position:0%
+that tell me about the relation of R to
+ 
+
+ align:start position:0%
+that tell me about the relation of R to
+n so this is one solution only that
+
+ align:start position:0%
+n so this is one solution only that
+ 
+
+ align:start position:0%
+n so this is one solution only that
+means the null space of the Matrix must
+
+ align:start position:0%
+means the null space of the Matrix must
+ 
+
+ align:start position:0%
+means the null space of the Matrix must
+be just the zero vector and what what
+
+ align:start position:0%
+be just the zero vector and what what
+ 
+
+ align:start position:0%
+be just the zero vector and what what
+does that tell me about R and
+
+ align:start position:0%
+does that tell me about R and
+ 
+
+ align:start position:0%
+does that tell me about R and
+N they're equal The Columns are
+
+ align:start position:0%
+N they're equal The Columns are
+ 
+
+ align:start position:0%
+N they're equal The Columns are
+independent so I've got now r equal n
+
+ align:start position:0%
+independent so I've got now r equal n
+ 
+
+ align:start position:0%
+independent so I've got now r equal n
+and R less than M and now I and I also
+
+ align:start position:0%
+and R less than M and now I and I also
+ 
+
+ align:start position:0%
+and R less than M and now I and I also
+know m is three so those are really the
+
+ align:start position:0%
+know m is three so those are really the
+ 
+
+ align:start position:0%
+know m is three so those are really the
+facts I know n equals
+
+ align:start position:0%
+facts I know n equals
+ 
+
+ align:start position:0%
+facts I know n equals
+R and those numbers are smaller than
+
+ align:start position:0%
+R and those numbers are smaller than
+ 
+
+ align:start position:0%
+R and those numbers are smaller than
+three uh sorry yeah yeah R is smaller
+
+ align:start position:0%
+three uh sorry yeah yeah R is smaller
+ 
+
+ align:start position:0%
+three uh sorry yeah yeah R is smaller
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+M and N of course is also so I guess
+
+ align:start position:0%
+M and N of course is also so I guess
+ 
+
+ align:start position:0%
+M and N of course is also so I guess
+this summarizes what what we can
+
+ align:start position:0%
+this summarizes what what we can
+ 
+
+ align:start position:0%
+this summarizes what what we can
+tell in fact why not give me a
+
+ align:start position:0%
+tell in fact why not give me a
+ 
+
+ align:start position:0%
+tell in fact why not give me a
+matrix because I would often ask for an
+
+ align:start position:0%
+matrix because I would often ask for an
+ 
+
+ align:start position:0%
+matrix because I would often ask for an
+example of such a matrix can you give me
+
+ align:start position:0%
+example of such a matrix can you give me
+ 
+
+ align:start position:0%
+example of such a matrix can you give me
+a matrix a that that's an example that
+
+ align:start position:0%
+a matrix a that that's an example that
+ 
+
+ align:start position:0%
+a matrix a that that's an example that
+shows this shows this possibility that
+
+ align:start position:0%
+shows this shows this possibility that
+ 
+
+ align:start position:0%
+shows this shows this possibility that
+exactly that that that there's no
+
+ align:start position:0%
+exactly that that that there's no
+ 
+
+ align:start position:0%
+exactly that that that there's no
+solution with uh with that right hand
+
+ align:start position:0%
+solution with uh with that right hand
+ 
+
+ align:start position:0%
+solution with uh with that right hand
+side but there's there's exactly one
+
+ align:start position:0%
+side but there's there's exactly one
+ 
+
+ align:start position:0%
+side but there's there's exactly one
+solution with this right hand side
+
+ align:start position:0%
+solution with this right hand side
+ 
+
+ align:start position:0%
+solution with this right hand side
+anybody want to suggest a Matrix that
+
+ align:start position:0%
+anybody want to suggest a Matrix that
+ 
+
+ align:start position:0%
+anybody want to suggest a Matrix that
+that that does
+
+ align:start position:0%
+that that does
+ 
+
+ align:start position:0%
+that that does
+that let's see what do I what Vector do
+
+ align:start position:0%
+that let's see what do I what Vector do
+ 
+
+ align:start position:0%
+that let's see what do I what Vector do
+I want in in the column
+
+ align:start position:0%
+I want in in the column
+ 
+
+ align:start position:0%
+I want in in the column
+space I want 0 one 0 to be in the column
+
+ align:start position:0%
+space I want 0 one 0 to be in the column
+ 
+
+ align:start position:0%
+space I want 0 one 0 to be in the column
+space because I'm I'm able to solve for
+
+ align:start position:0%
+space because I'm I'm able to solve for
+ 
+
+ align:start position:0%
+space because I'm I'm able to solve for
+that so let's put 0 one 0 in the column
+
+ align:start position:0%
+that so let's put 0 one 0 in the column
+ 
+
+ align:start position:0%
+that so let's put 0 one 0 in the column
+space actually I could stop right
+
+ align:start position:0%
+space actually I could stop right
+ 
+
+ align:start position:0%
+space actually I could stop right
+there that would be a matrix with m
+
+ align:start position:0%
+there that would be a matrix with m
+ 
+
+ align:start position:0%
+there that would be a matrix with m
+equal 3 three rows and n and R are both
+
+ align:start position:0%
+equal 3 three rows and n and R are both
+ 
+
+ align:start position:0%
+equal 3 three rows and n and R are both
+both one rank
+
+ align:start position:0%
+both one rank
+ 
+
+ align:start position:0%
+both one rank
+one one
+
+ align:start position:0%
+one one
+ 
+
+ align:start position:0%
+one one
+column
+
+ align:start position:0%
+column
+ 
+
+ align:start position:0%
+column
+and of course there's no solution to
+
+ align:start position:0%
+and of course there's no solution to
+ 
+
+ align:start position:0%
+and of course there's no solution to
+that one so that's perfectly good as it
+
+ align:start position:0%
+that one so that's perfectly good as it
+ 
+
+ align:start position:0%
+that one so that's perfectly good as it
+is or if you kind of have a prejudice
+
+ align:start position:0%
+is or if you kind of have a prejudice
+ 
+
+ align:start position:0%
+is or if you kind of have a prejudice
+against matrices that only have one
+
+ align:start position:0%
+against matrices that only have one
+ 
+
+ align:start position:0%
+against matrices that only have one
+column I'll I'll accept a second column
+
+ align:start position:0%
+column I'll I'll accept a second column
+ 
+
+ align:start position:0%
+column I'll I'll accept a second column
+so what could I include as a second
+
+ align:start position:0%
+so what could I include as a second
+ 
+
+ align:start position:0%
+so what could I include as a second
+column that would just be a different
+
+ align:start position:0%
+column that would just be a different
+ 
+
+ align:start position:0%
+column that would just be a different
+answer but equally good uh I could put
+
+ align:start position:0%
+answer but equally good uh I could put
+ 
+
+ align:start position:0%
+answer but equally good uh I could put
+this Vector in the column space too if I
+
+ align:start position:0%
+this Vector in the column space too if I
+ 
+
+ align:start position:0%
+this Vector in the column space too if I
+wanted that would now be a case with Ral
+
+ align:start position:0%
+wanted that would now be a case with Ral
+ 
+
+ align:start position:0%
+wanted that would now be a case with Ral
+Nal
+
+ align:start position:0%
+Nal
+ 
+
+ align:start position:0%
+Nal
+2 but of course three m m is still three
+
+ align:start position:0%
+2 but of course three m m is still three
+ 
+
+ align:start position:0%
+2 but of course three m m is still three
+and this Vector is not in the column
+
+ align:start position:0%
+and this Vector is not in the column
+ 
+
+ align:start position:0%
+and this Vector is not in the column
+space so you're this is just like
+
+ align:start position:0%
+space so you're this is just like
+ 
+
+ align:start position:0%
+space so you're this is just like
+prompting us to remember all those
+
+ align:start position:0%
+prompting us to remember all those
+ 
+
+ align:start position:0%
+prompting us to remember all those
+things column space null space all that
+
+ align:start position:0%
+things column space null space all that
+ 
+
+ align:start position:0%
+things column space null space all that
+stuff now I probably asked a second
+
+ align:start position:0%
+stuff now I probably asked a second
+ 
+
+ align:start position:0%
+stuff now I probably asked a second
+question about this type of thing
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay oh I even asked write down an
+
+ align:start position:0%
+okay oh I even asked write down an
+ 
+
+ align:start position:0%
+okay oh I even asked write down an
+example of a matrix that fits the
+
+ align:start position:0%
+example of a matrix that fits the
+ 
+
+ align:start position:0%
+example of a matrix that fits the
+description um
+
+ align:start position:0%
+description um
+ 
+
+ align:start position:0%
+description um
+H I guess I haven't learned anything in
+
+ align:start position:0%
+H I guess I haven't learned anything in
+ 
+
+ align:start position:0%
+H I guess I haven't learned anything in
+uh 26 years okay uh cross out all
+
+ align:start position:0%
+uh 26 years okay uh cross out all
+ 
+
+ align:start position:0%
+uh 26 years okay uh cross out all
+statements that are false about any
+
+ align:start position:0%
+statements that are false about any
+ 
+
+ align:start position:0%
+statements that are false about any
+Matrix with these so again these are
+
+ align:start position:0%
+Matrix with these so again these are
+ 
+
+ align:start position:0%
+Matrix with these so again these are
+this is the preliminary State these are
+
+ align:start position:0%
+this is the preliminary State these are
+ 
+
+ align:start position:0%
+this is the preliminary State these are
+the facts about my Matrix this is one
+
+ align:start position:0%
+the facts about my Matrix this is one
+ 
+
+ align:start position:0%
+the facts about my Matrix this is one
+example but of course by having an
+
+ align:start position:0%
+example but of course by having an
+ 
+
+ align:start position:0%
+example but of course by having an
+example it'll be easy to check some of
+
+ align:start position:0%
+example it'll be easy to check some of
+ 
+
+ align:start position:0%
+example it'll be easy to check some of
+these facts or nonfacts let me uh let me
+
+ align:start position:0%
+these facts or nonfacts let me uh let me
+ 
+
+ align:start position:0%
+these facts or nonfacts let me uh let me
+write
+
+ align:start position:0%
+write
+ 
+
+ align:start position:0%
+write
+down some uh facts some some possible
+
+ align:start position:0%
+down some uh facts some some possible
+ 
+
+ align:start position:0%
+down some uh facts some some possible
+facts true so this is really true or
+
+ align:start position:0%
+facts true so this is really true or
+ 
+
+ align:start position:0%
+facts true so this is really true or
+false the
+
+ align:start position:0%
+false the
+ 
+
+ align:start position:0%
+false the
+determinant of this is part one the
+
+ align:start position:0%
+determinant of this is part one the
+ 
+
+ align:start position:0%
+determinant of this is part one the
+determinant of a transpose a is the same
+
+ align:start position:0%
+determinant of a transpose a is the same
+ 
+
+ align:start position:0%
+determinant of a transpose a is the same
+as the determinant of AA transpose is
+
+ align:start position:0%
+as the determinant of AA transpose is
+ 
+
+ align:start position:0%
+as the determinant of AA transpose is
+that true or not second
+
+ align:start position:0%
+that true or not second
+ 
+
+ align:start position:0%
+that true or not second
+one a transpose a is
+
+ align:start position:0%
+one a transpose a is
+ 
+
+ align:start position:0%
+one a transpose a is
+invertible is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invertible third possible fact a a
+
+ align:start position:0%
+invertible third possible fact a a
+ 
+
+ align:start position:0%
+invertible third possible fact a a
+transpose is positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite so you see how on an exam
+
+ align:start position:0%
+definite so you see how on an exam
+ 
+
+ align:start position:0%
+definite so you see how on an exam
+question I try to connect the different
+
+ align:start position:0%
+question I try to connect the different
+ 
+
+ align:start position:0%
+question I try to connect the different
+parts of the course so
+
+ align:start position:0%
+parts of the course so
+ 
+
+ align:start position:0%
+parts of the course so
+well I mean the simplest way would be to
+
+ align:start position:0%
+well I mean the simplest way would be to
+ 
+
+ align:start position:0%
+well I mean the simplest way would be to
+try it with that Matrix a as a as a as a
+
+ align:start position:0%
+try it with that Matrix a as a as a as a
+ 
+
+ align:start position:0%
+try it with that Matrix a as a as a as a
+good example uh but maybe we can answer
+
+ align:start position:0%
+good example uh but maybe we can answer
+ 
+
+ align:start position:0%
+good example uh but maybe we can answer
+uh even directly let let me take number
+
+ align:start position:0%
+uh even directly let let me take number
+ 
+
+ align:start position:0%
+uh even directly let let me take number
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+first because
+
+ align:start position:0%
+first because
+ 
+
+ align:start position:0%
+first because
+I'm you know I'm very very fond of that
+
+ align:start position:0%
+I'm you know I'm very very fond of that
+ 
+
+ align:start position:0%
+I'm you know I'm very very fond of that
+Matrix a transpose
+
+ align:start position:0%
+Matrix a transpose
+ 
+
+ align:start position:0%
+Matrix a transpose
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+and when is it invertible
+
+ align:start position:0%
+and when is it invertible
+ 
+
+ align:start position:0%
+and when is it invertible
+when is the Matrix a transpose a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+invertible the the great thing is that I
+
+ align:start position:0%
+invertible the the great thing is that I
+ 
+
+ align:start position:0%
+invertible the the great thing is that I
+can tell from the from the rank of a
+
+ align:start position:0%
+can tell from the from the rank of a
+ 
+
+ align:start position:0%
+can tell from the from the rank of a
+that I don't have to multiply out a
+
+ align:start position:0%
+that I don't have to multiply out a
+ 
+
+ align:start position:0%
+that I don't have to multiply out a
+transpose a a transpose a is
+
+ align:start position:0%
+transpose a a transpose a is
+ 
+
+ align:start position:0%
+transpose a a transpose a is
+invertible well if a has a null space
+
+ align:start position:0%
+invertible well if a has a null space
+ 
+
+ align:start position:0%
+invertible well if a has a null space
+other than the zero Vector then it it's
+
+ align:start position:0%
+other than the zero Vector then it it's
+ 
+
+ align:start position:0%
+other than the zero Vector then it it's
+no way it's going to be invertible but
+
+ align:start position:0%
+no way it's going to be invertible but
+ 
+
+ align:start position:0%
+no way it's going to be invertible but
+the beauty is if the null space of a is
+
+ align:start position:0%
+the beauty is if the null space of a is
+ 
+
+ align:start position:0%
+the beauty is if the null space of a is
+just the zero Vector so the fact the key
+
+ align:start position:0%
+just the zero Vector so the fact the key
+ 
+
+ align:start position:0%
+just the zero Vector so the fact the key
+fact is this is invertible if R equals n
+
+ align:start position:0%
+fact is this is invertible if R equals n
+ 
+
+ align:start position:0%
+fact is this is invertible if R equals n
+by which I mean independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Columns of a in a in The Matrix a if R
+
+ align:start position:0%
+Columns of a in a in The Matrix a if R
+ 
+
+ align:start position:0%
+Columns of a in a in The Matrix a if R
+equals n if the Matrix a has independent
+
+ align:start position:0%
+equals n if the Matrix a has independent
+ 
+
+ align:start position:0%
+equals n if the Matrix a has independent
+columns then this combination a
+
+ align:start position:0%
+columns then this combination a
+ 
+
+ align:start position:0%
+columns then this combination a
+transpose a is square and still that
+
+ align:start position:0%
+transpose a is square and still that
+ 
+
+ align:start position:0%
+transpose a is square and still that
+same space only the zero Vector
+
+ align:start position:0%
+same space only the zero Vector
+ 
+
+ align:start position:0%
+same space only the zero Vector
+independent columns all good and so
+
+ align:start position:0%
+independent columns all good and so
+ 
+
+ align:start position:0%
+independent columns all good and so
+what's the what's the true false is it
+
+ align:start position:0%
+what's the what's the true false is it
+ 
+
+ align:start position:0%
+what's the what's the true false is it
+is this middle one t or F for this in
+
+ align:start position:0%
+is this middle one t or F for this in
+ 
+
+ align:start position:0%
+is this middle one t or F for this in
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+setup well we discovered that we
+
+ align:start position:0%
+setup well we discovered that we
+ 
+
+ align:start position:0%
+setup well we discovered that we
+discovered that that R was n from that
+
+ align:start position:0%
+discovered that that R was n from that
+ 
+
+ align:start position:0%
+discovered that that R was n from that
+second fact so this is a true that's a
+
+ align:start position:0%
+second fact so this is a true that's a
+ 
+
+ align:start position:0%
+second fact so this is a true that's a
+true and of course a transpose a in this
+
+ align:start position:0%
+true and of course a transpose a in this
+ 
+
+ align:start position:0%
+true and of course a transpose a in this
+example would probably be what would a
+
+ align:start position:0%
+example would probably be what would a
+ 
+
+ align:start position:0%
+example would probably be what would a
+transpose a be for that
+
+ align:start position:0%
+transpose a be for that
+ 
+
+ align:start position:0%
+transpose a be for that
+Matrix can you multiply a transpose a
+
+ align:start position:0%
+Matrix can you multiply a transpose a
+ 
+
+ align:start position:0%
+Matrix can you multiply a transpose a
+and see what it looks like for that
+
+ align:start position:0%
+and see what it looks like for that
+ 
+
+ align:start position:0%
+and see what it looks like for that
+Matrix what shape would it
+
+ align:start position:0%
+Matrix what shape would it
+ 
+
+ align:start position:0%
+Matrix what shape would it
+be it'll be 2x two and what Matrix will
+
+ align:start position:0%
+be it'll be 2x two and what Matrix will
+ 
+
+ align:start position:0%
+be it'll be 2x two and what Matrix will
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+be the identity so checks out okay what
+
+ align:start position:0%
+be the identity so checks out okay what
+ 
+
+ align:start position:0%
+be the identity so checks out okay what
+about AA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+well depending on the shape of a it
+
+ align:start position:0%
+well depending on the shape of a it
+ 
+
+ align:start position:0%
+well depending on the shape of a it
+could be good or not so good it's always
+
+ align:start position:0%
+could be good or not so good it's always
+ 
+
+ align:start position:0%
+could be good or not so good it's always
+symmetric it's always square but what's
+
+ align:start position:0%
+symmetric it's always square but what's
+ 
+
+ align:start position:0%
+symmetric it's always square but what's
+the size now this is 3 by n and this is
+
+ align:start position:0%
+the size now this is 3 by n and this is
+ 
+
+ align:start position:0%
+the size now this is 3 by n and this is
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+by3 so the result is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3x3 is it positive
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+definite I don't think so
+
+ align:start position:0%
+definite I don't think so
+ 
+
+ align:start position:0%
+definite I don't think so
+false If I multiply that by a transpose
+
+ align:start position:0%
+false If I multiply that by a transpose
+ 
+
+ align:start position:0%
+false If I multiply that by a transpose
+a a transpose
+
+ align:start position:0%
+a a transpose
+ 
+
+ align:start position:0%
+a a transpose
+what would the rank
+
+ align:start position:0%
+what would the rank
+ 
+
+ align:start position:0%
+what would the rank
+be it would be the same as the rank of a
+
+ align:start position:0%
+be it would be the same as the rank of a
+ 
+
+ align:start position:0%
+be it would be the same as the rank of a
+that's that's it would be just rank
+
+ align:start position:0%
+that's that's it would be just rank
+ 
+
+ align:start position:0%
+that's that's it would be just rank
+two and if it's 3x3 and it's only rank
+
+ align:start position:0%
+two and if it's 3x3 and it's only rank
+ 
+
+ align:start position:0%
+two and if it's 3x3 and it's only rank
+two it's certainly not positive definite
+
+ align:start position:0%
+two it's certainly not positive definite
+ 
+
+ align:start position:0%
+two it's certainly not positive definite
+so what's what could I say about AA
+
+ align:start position:0%
+so what's what could I say about AA
+ 
+
+ align:start position:0%
+so what's what could I say about AA
+transpose if I wanted to like say
+
+ align:start position:0%
+transpose if I wanted to like say
+ 
+
+ align:start position:0%
+transpose if I wanted to like say
+something true about
+
+ align:start position:0%
+something true about
+ 
+
+ align:start position:0%
+something true about
+it it's true that it is
+
+ align:start position:0%
+it it's true that it is
+ 
+
+ align:start position:0%
+it it's true that it is
+positive semi-definite if I made this
+
+ align:start position:0%
+positive semi-definite if I made this
+ 
+
+ align:start position:0%
+positive semi-definite if I made this
+semi-definite it would always always be
+
+ align:start position:0%
+semi-definite it would always always be
+ 
+
+ align:start position:0%
+semi-definite it would always always be
+true always but if I'm looking for
+
+ align:start position:0%
+true always but if I'm looking for
+ 
+
+ align:start position:0%
+true always but if I'm looking for
+positive definite then I'm looking at
+
+ align:start position:0%
+positive definite then I'm looking at
+ 
+
+ align:start position:0%
+positive definite then I'm looking at
+the null space of whatever is here and
+
+ align:start position:0%
+the null space of whatever is here and
+ 
+
+ align:start position:0%
+the null space of whatever is here and
+in this case uh it's got a null
+
+ align:start position:0%
+in this case uh it's got a null
+ 
+
+ align:start position:0%
+in this case uh it's got a null
+space so AA so we just figure it out
+
+ align:start position:0%
+space so AA so we just figure it out
+ 
+
+ align:start position:0%
+space so AA so we just figure it out
+here A A transposed for that Matrix will
+
+ align:start position:0%
+here A A transposed for that Matrix will
+ 
+
+ align:start position:0%
+here A A transposed for that Matrix will
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+3x3 if I multiplied a by a transpose
+
+ align:start position:0%
+3x3 if I multiplied a by a transpose
+ 
+
+ align:start position:0%
+3x3 if I multiplied a by a transpose
+what would the first row be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all zeros right first row of AA
+
+ align:start position:0%
+all zeros right first row of AA
+ 
+
+ align:start position:0%
+all zeros right first row of AA
+transposed could only be all
+
+ align:start position:0%
+transposed could only be all
+ 
+
+ align:start position:0%
+transposed could only be all
+zeros so it's probably a one there and a
+
+ align:start position:0%
+zeros so it's probably a one there and a
+ 
+
+ align:start position:0%
+zeros so it's probably a one there and a
+one there something like that but uh I I
+
+ align:start position:0%
+one there something like that but uh I I
+ 
+
+ align:start position:0%
+one there something like that but uh I I
+don't even know if that's right but it's
+
+ align:start position:0%
+don't even know if that's right but it's
+ 
+
+ align:start position:0%
+don't even know if that's right but it's
+all zeros there so it's certainly not
+
+ align:start position:0%
+all zeros there so it's certainly not
+ 
+
+ align:start position:0%
+all zeros there so it's certainly not
+positive definite let me not put up
+
+ align:start position:0%
+positive definite let me not put up
+ 
+
+ align:start position:0%
+positive definite let me not put up
+anything I'm not don't check what about
+
+ align:start position:0%
+anything I'm not don't check what about
+ 
+
+ align:start position:0%
+anything I'm not don't check what about
+this determinant oh well I
+
+ align:start position:0%
+this determinant oh well I
+ 
+
+ align:start position:0%
+this determinant oh well I
+guess that's a sort of tricky
+
+ align:start position:0%
+guess that's a sort of tricky
+ 
+
+ align:start position:0%
+guess that's a sort of tricky
+question is it true or false in this
+
+ align:start position:0%
+question is it true or false in this
+ 
+
+ align:start position:0%
+question is it true or false in this
+case it's false
+
+ align:start position:0%
+case it's false
+ 
+
+ align:start position:0%
+case it's false
+apparently because a transpose a is
+
+ align:start position:0%
+apparently because a transpose a is
+ 
+
+ align:start position:0%
+apparently because a transpose a is
+invertible we just got a true for this
+
+ align:start position:0%
+invertible we just got a true for this
+ 
+
+ align:start position:0%
+invertible we just got a true for this
+one and we got a false we got a we got a
+
+ align:start position:0%
+one and we got a false we got a we got a
+ 
+
+ align:start position:0%
+one and we got a false we got a we got a
+non-invertible one for this one so
+
+ align:start position:0%
+non-invertible one for this one so
+ 
+
+ align:start position:0%
+non-invertible one for this one so
+actually this one is false number
+
+ align:start position:0%
+actually this one is false number
+ 
+
+ align:start position:0%
+actually this one is false number
+one that surprises us actually because
+
+ align:start position:0%
+one that surprises us actually because
+ 
+
+ align:start position:0%
+one that surprises us actually because
+it's I mean why was it tricky because
+
+ align:start position:0%
+it's I mean why was it tricky because
+ 
+
+ align:start position:0%
+it's I mean why was it tricky because
+what is true about determinants
+
+ align:start position:0%
+what is true about determinants
+ 
+
+ align:start position:0%
+what is true about determinants
+this would be true if those matrices
+
+ align:start position:0%
+this would be true if those matrices
+ 
+
+ align:start position:0%
+this would be true if those matrices
+were square if I have two square
+
+ align:start position:0%
+were square if I have two square
+ 
+
+ align:start position:0%
+were square if I have two square
+matrices a and any other Matrix B could
+
+ align:start position:0%
+matrices a and any other Matrix B could
+ 
+
+ align:start position:0%
+matrices a and any other Matrix B could
+be a transpose could be somebody else's
+
+ align:start position:0%
+be a transpose could be somebody else's
+ 
+
+ align:start position:0%
+be a transpose could be somebody else's
+Matrix then it would be true that the
+
+ align:start position:0%
+Matrix then it would be true that the
+ 
+
+ align:start position:0%
+Matrix then it would be true that the
+determinant of ba would equal the
+
+ align:start position:0%
+determinant of ba would equal the
+ 
+
+ align:start position:0%
+determinant of ba would equal the
+determinant of ab but if the matrices
+
+ align:start position:0%
+determinant of ab but if the matrices
+ 
+
+ align:start position:0%
+determinant of ab but if the matrices
+are not
+
+ align:start position:0%
+are not
+ 
+
+ align:start position:0%
+are not
+square and it would actually be true
+
+ align:start position:0%
+square and it would actually be true
+ 
+
+ align:start position:0%
+square and it would actually be true
+that it would be that would equal that
+
+ align:start position:0%
+that it would be that would equal that
+ 
+
+ align:start position:0%
+that it would be that would equal that
+this would equal the determinant of a
+
+ align:start position:0%
+this would equal the determinant of a
+ 
+
+ align:start position:0%
+this would equal the determinant of a
+times the determinant of a transpose we
+
+ align:start position:0%
+times the determinant of a transpose we
+ 
+
+ align:start position:0%
+times the determinant of a transpose we
+could even split up those two separate
+
+ align:start position:0%
+could even split up those two separate
+ 
+
+ align:start position:0%
+could even split up those two separate
+determinants and of course those would
+
+ align:start position:0%
+determinants and of course those would
+ 
+
+ align:start position:0%
+determinants and of course those would
+be equal but only when a is
+
+ align:start position:0%
+be equal but only when a is
+ 
+
+ align:start position:0%
+be equal but only when a is
+square so that's just uh that's a
+
+ align:start position:0%
+square so that's just uh that's a
+ 
+
+ align:start position:0%
+square so that's just uh that's a
+question that rests on the the falseness
+
+ align:start position:0%
+question that rests on the the falseness
+ 
+
+ align:start position:0%
+question that rests on the the falseness
+rests on the fact that the Matrix isn't
+
+ align:start position:0%
+rests on the fact that the Matrix isn't
+ 
+
+ align:start position:0%
+rests on the fact that the Matrix isn't
+Square in the first place okay good um
+
+ align:start position:0%
+Square in the first place okay good um
+ 
+
+ align:start position:0%
+Square in the first place okay good um
+let's
+
+ align:start position:0%
+let's
+ 
+
+ align:start position:0%
+let's
+see uh oh now even asks more prove prove
+
+ align:start position:0%
+see uh oh now even asks more prove prove
+ 
+
+ align:start position:0%
+see uh oh now even asks more prove prove
+that a transpose y equal
+
+ align:start position:0%
+that a transpose y equal
+ 
+
+ align:start position:0%
+that a transpose y equal
+c h God it's this question goes on and
+
+ align:start position:0%
+c h God it's this question goes on and
+ 
+
+ align:start position:0%
+c h God it's this question goes on and
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+um now I ask you about a transpose yals
+
+ align:start position:0%
+um now I ask you about a transpose yals
+ 
+
+ align:start position:0%
+um now I ask you about a transpose yals
+C so I'm asking you about the equation
+
+ align:start position:0%
+C so I'm asking you about the equation
+ 
+
+ align:start position:0%
+C so I'm asking you about the equation
+about the Matrix a transpose and I want
+
+ align:start position:0%
+about the Matrix a transpose and I want
+ 
+
+ align:start position:0%
+about the Matrix a transpose and I want
+you to prove that it has at least one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution one solution
+
+ align:start position:0%
+solution one solution
+ 
+
+ align:start position:0%
+solution one solution
+for every C every right hand side C and
+
+ align:start position:0%
+for every C every right hand side C and
+ 
+
+ align:start position:0%
+for every C every right hand side C and
+in fact in
+
+ align:start position:0%
+in fact in
+ 
+
+ align:start position:0%
+in fact in
+fact infinitely many
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solutions for every
+
+ align:start position:0%
+solutions for every
+ 
+
+ align:start position:0%
+solutions for every
+C okay well none of this is difficult
+
+ align:start position:0%
+C okay well none of this is difficult
+ 
+
+ align:start position:0%
+C okay well none of this is difficult
+but it's been
+
+ align:start position:0%
+but it's been
+ 
+
+ align:start position:0%
+but it's been
+uh a little
+
+ align:start position:0%
+uh a little
+ 
+
+ align:start position:0%
+uh a little
+while so we just have to think again
+
+ align:start position:0%
+while so we just have to think again
+ 
+
+ align:start position:0%
+while so we just have to think again
+when I have a system of
+
+ align:start position:0%
+when I have a system of
+ 
+
+ align:start position:0%
+when I have a system of
+equations this is this Matrix a
+
+ align:start position:0%
+equations this is this Matrix a
+ 
+
+ align:start position:0%
+equations this is this Matrix a
+transposes now instead of
+
+ align:start position:0%
+transposes now instead of
+ 
+
+ align:start position:0%
+transposes now instead of
+being 3x n it's n by3 it's it's n by m
+
+ align:start position:0%
+being 3x n it's n by3 it's it's n by m
+ 
+
+ align:start position:0%
+being 3x n it's n by3 it's it's n by m
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course to show that a that a system has
+
+ align:start position:0%
+course to show that a that a system has
+ 
+
+ align:start position:0%
+course to show that a that a system has
+at least one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution when does this when does the
+
+ align:start position:0%
+solution when does this when does the
+ 
+
+ align:start position:0%
+solution when does this when does the
+system when is the system always
+
+ align:start position:0%
+system when is the system always
+ 
+
+ align:start position:0%
+system when is the system always
+solvable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when it has full row rank when the rows
+
+ align:start position:0%
+when it has full row rank when the rows
+ 
+
+ align:start position:0%
+when it has full row rank when the rows
+are independent here we have n
+
+ align:start position:0%
+are independent here we have n
+ 
+
+ align:start position:0%
+are independent here we have n
+rows and that's the rank so at least one
+
+ align:start position:0%
+rows and that's the rank so at least one
+ 
+
+ align:start position:0%
+rows and that's the rank so at least one
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+because the number of rows which is n
+
+ align:start position:0%
+because the number of rows which is n
+ 
+
+ align:start position:0%
+because the number of rows which is n
+for the transpose is equal to R the
+
+ align:start position:0%
+for the transpose is equal to R the
+ 
+
+ align:start position:0%
+for the transpose is equal to R the
+rank this this has this a transpose has
+
+ align:start position:0%
+rank this this has this a transpose has
+ 
+
+ align:start position:0%
+rank this this has this a transpose has
+has independent rows because a had
+
+ align:start position:0%
+has independent rows because a had
+ 
+
+ align:start position:0%
+has independent rows because a had
+independent columns
+
+ align:start position:0%
+independent columns
+ 
+
+ align:start position:0%
+independent columns
+right the original a had
+
+ align:start position:0%
+right the original a had
+ 
+
+ align:start position:0%
+right the original a had
+independent
+
+ align:start position:0%
+independent
+ 
+
+ align:start position:0%
+independent
+columns when we transpose it it has
+
+ align:start position:0%
+columns when we transpose it it has
+ 
+
+ align:start position:0%
+columns when we transpose it it has
+independent rows so there's at least one
+
+ align:start position:0%
+independent rows so there's at least one
+ 
+
+ align:start position:0%
+independent rows so there's at least one
+solution but now how do I even know that
+
+ align:start position:0%
+solution but now how do I even know that
+ 
+
+ align:start position:0%
+solution but now how do I even know that
+there are infinitely many solutions oh I
+
+ align:start position:0%
+there are infinitely many solutions oh I
+ 
+
+ align:start position:0%
+there are infinitely many solutions oh I
+I what do I I want to know something
+
+ align:start position:0%
+I what do I I want to know something
+ 
+
+ align:start position:0%
+I what do I I want to know something
+about the null space what's the
+
+ align:start position:0%
+about the null space what's the
+ 
+
+ align:start position:0%
+about the null space what's the
+dimension of the null space of a
+
+ align:start position:0%
+dimension of the null space of a
+ 
+
+ align:start position:0%
+dimension of the null space of a
+transpose so so the answer has got to be
+
+ align:start position:0%
+transpose so so the answer has got to be
+ 
+
+ align:start position:0%
+transpose so so the answer has got to be
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+dimension of the null space of a
+
+ align:start position:0%
+dimension of the null space of a
+ 
+
+ align:start position:0%
+dimension of the null space of a
+transpose what's the general fact if if
+
+ align:start position:0%
+transpose what's the general fact if if
+ 
+
+ align:start position:0%
+transpose what's the general fact if if
+it's an if I have if a is an M byn
+
+ align:start position:0%
+it's an if I have if a is an M byn
+ 
+
+ align:start position:0%
+it's an if I have if a is an M byn
+Matrix of rank R what's the dimension of
+
+ align:start position:0%
+Matrix of rank R what's the dimension of
+ 
+
+ align:start position:0%
+Matrix of rank R what's the dimension of
+a transpose of the null space of a
+
+ align:start position:0%
+a transpose of the null space of a
+ 
+
+ align:start position:0%
+a transpose of the null space of a
+transpose you remember that little
+
+ align:start position:0%
+transpose you remember that little
+ 
+
+ align:start position:0%
+transpose you remember that little
+fourth Subspace that's tagging along
+
+ align:start position:0%
+fourth Subspace that's tagging along
+ 
+
+ align:start position:0%
+fourth Subspace that's tagging along
+down in our big picture its Dimension
+
+ align:start position:0%
+down in our big picture its Dimension
+ 
+
+ align:start position:0%
+down in our big picture its Dimension
+was M minus r
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's bigger than zero m is bigger
+
+ align:start position:0%
+and that's bigger than zero m is bigger
+ 
+
+ align:start position:0%
+and that's bigger than zero m is bigger
+than
+
+ align:start position:0%
+than
+ 
+
+ align:start position:0%
+than
+R so there's a lot in that n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space so there's always one solution
+
+ align:start position:0%
+space so there's always one solution
+ 
+
+ align:start position:0%
+space so there's always one solution
+because and this is speaking about a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transpose so for a transposed the roles
+
+ align:start position:0%
+transpose so for a transposed the roles
+ 
+
+ align:start position:0%
+transpose so for a transposed the roles
+of M and N are reversed of course so I'm
+
+ align:start position:0%
+of M and N are reversed of course so I'm
+ 
+
+ align:start position:0%
+of M and N are reversed of course so I'm
+keep keep in mind that that this board
+
+ align:start position:0%
+keep keep in mind that that this board
+ 
+
+ align:start position:0%
+keep keep in mind that that this board
+was about a transposed so the rules so
+
+ align:start position:0%
+was about a transposed so the rules so
+ 
+
+ align:start position:0%
+was about a transposed so the rules so
+it's the null space of a transposed and
+
+ align:start position:0%
+it's the null space of a transposed and
+ 
+
+ align:start position:0%
+it's the null space of a transposed and
+there are M minus r free
+
+ align:start position:0%
+there are M minus r free
+ 
+
+ align:start position:0%
+there are M minus r free
+variables okay that's like just some
+
+ align:start position:0%
+variables okay that's like just some
+ 
+
+ align:start position:0%
+variables okay that's like just some
+uh review can I take another problem
+
+ align:start position:0%
+uh review can I take another problem
+ 
+
+ align:start position:0%
+uh review can I take another problem
+that's also sort of
+
+ align:start position:0%
+that's also sort of
+ 
+
+ align:start position:0%
+that's also sort of
+suppose The Matrix a has three columns
+
+ align:start position:0%
+suppose The Matrix a has three columns
+ 
+
+ align:start position:0%
+suppose The Matrix a has three columns
+V1 V2
+
+ align:start position:0%
+V1 V2
+ 
+
+ align:start position:0%
+V1 V2
+V3 those are The Columns of The Matrix
+
+ align:start position:0%
+V3 those are The Columns of The Matrix
+ 
+
+ align:start position:0%
+V3 those are The Columns of The Matrix
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right question
+
+ align:start position:0%
+right question
+ 
+
+ align:start position:0%
+right question
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+solve a x = V1 - V2 +
+
+ align:start position:0%
+solve a x = V1 - V2 +
+ 
+
+ align:start position:0%
+solve a x = V1 - V2 +
+V3 tell me what x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+well there you're seeing the most the
+
+ align:start position:0%
+well there you're seeing the most the
+ 
+
+ align:start position:0%
+well there you're seeing the most the
+one absolutely
+
+ align:start position:0%
+one absolutely
+ 
+
+ align:start position:0%
+one absolutely
+essential
+
+ align:start position:0%
+essential
+ 
+
+ align:start position:0%
+essential
+fact about matrix multiplication how
+
+ align:start position:0%
+fact about matrix multiplication how
+ 
+
+ align:start position:0%
+fact about matrix multiplication how
+does it work when it when we do it a
+
+ align:start position:0%
+does it work when it when we do it a
+ 
+
+ align:start position:0%
+does it work when it when we do it a
+column at a time the very very first day
+
+ align:start position:0%
+column at a time the very very first day
+ 
+
+ align:start position:0%
+column at a time the very very first day
+way back in September we did
+
+ align:start position:0%
+way back in September we did
+ 
+
+ align:start position:0%
+way back in September we did
+multiplication a column at a time so
+
+ align:start position:0%
+multiplication a column at a time so
+ 
+
+ align:start position:0%
+multiplication a column at a time so
+what's what's X just tell me one minus
+
+ align:start position:0%
+what's what's X just tell me one minus
+ 
+
+ align:start position:0%
+what's what's X just tell me one minus
+one one thanks okay everybody's got that
+
+ align:start position:0%
+one one thanks okay everybody's got that
+ 
+
+ align:start position:0%
+one one thanks okay everybody's got that
+okay then the next question is suppose
+
+ align:start position:0%
+okay then the next question is suppose
+ 
+
+ align:start position:0%
+okay then the next question is suppose
+that combination is zero oh yeah okay
+
+ align:start position:0%
+that combination is zero oh yeah okay
+ 
+
+ align:start position:0%
+that combination is zero oh yeah okay
+okay so question B
+
+ align:start position:0%
+okay so question B
+ 
+
+ align:start position:0%
+okay so question B
+says Part B
+
+ align:start position:0%
+says Part B
+ 
+
+ align:start position:0%
+says Part B
+says
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suppose this
+
+ align:start position:0%
+suppose this
+ 
+
+ align:start position:0%
+suppose this
+thing is
+
+ align:start position:0%
+thing is
+ 
+
+ align:start position:0%
+thing is
+zero suppose that's
+
+ align:start position:0%
+zero suppose that's
+ 
+
+ align:start position:0%
+zero suppose that's
+zero then the solution is not
+
+ align:start position:0%
+zero then the solution is not
+ 
+
+ align:start position:0%
+zero then the solution is not
+unique suppose no so I want true or
+
+ align:start position:0%
+unique suppose no so I want true or
+ 
+
+ align:start position:0%
+unique suppose no so I want true or
+false and and a reason suppose this this
+
+ align:start position:0%
+false and and a reason suppose this this
+ 
+
+ align:start position:0%
+false and and a reason suppose this this
+combination is zero
+
+ align:start position:0%
+combination is zero
+ 
+
+ align:start position:0%
+combination is zero
+V1 minus V2
+
+ align:start position:0%
+V1 minus V2
+ 
+
+ align:start position:0%
+V1 minus V2
+V3 show
+
+ align:start position:0%
+V3 show
+ 
+
+ align:start position:0%
+V3 show
+that what can what does that tell me so
+
+ align:start position:0%
+that what can what does that tell me so
+ 
+
+ align:start position:0%
+that what can what does that tell me so
+it's a separate question maybe I I sort
+
+ align:start position:0%
+it's a separate question maybe I I sort
+ 
+
+ align:start position:0%
+it's a separate question maybe I I sort
+of save time by writing it that way but
+
+ align:start position:0%
+of save time by writing it that way but
+ 
+
+ align:start position:0%
+of save time by writing it that way but
+it's a separate totally separate
+
+ align:start position:0%
+it's a separate totally separate
+ 
+
+ align:start position:0%
+it's a separate totally separate
+question if I know if I have a matrix
+
+ align:start position:0%
+question if I know if I have a matrix
+ 
+
+ align:start position:0%
+question if I know if I have a matrix
+and I know that column 1 minus column 2
+
+ align:start position:0%
+and I know that column 1 minus column 2
+ 
+
+ align:start position:0%
+and I know that column 1 minus column 2
+plus column 3 is
+
+ align:start position:0%
+plus column 3 is
+ 
+
+ align:start position:0%
+plus column 3 is
+zero what does that tell me
+
+ align:start position:0%
+zero what does that tell me
+ 
+
+ align:start position:0%
+zero what does that tell me
+about whether the solution is unique or
+
+ align:start position:0%
+about whether the solution is unique or
+ 
+
+ align:start position:0%
+about whether the solution is unique or
+not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could if is there are there are there is
+
+ align:start position:0%
+could if is there are there are there is
+ 
+
+ align:start position:0%
+could if is there are there are there is
+there more than one
+
+ align:start position:0%
+there more than one
+ 
+
+ align:start position:0%
+there more than one
+solution what what's uniqueness
+
+ align:start position:0%
+solution what what's uniqueness
+ 
+
+ align:start position:0%
+solution what what's uniqueness
+about uniqueness is about is there
+
+ align:start position:0%
+about uniqueness is about is there
+ 
+
+ align:start position:0%
+about uniqueness is about is there
+anything in the null space right the
+
+ align:start position:0%
+anything in the null space right the
+ 
+
+ align:start position:0%
+anything in the null space right the
+solution is unique when there's nobody
+
+ align:start position:0%
+solution is unique when there's nobody
+ 
+
+ align:start position:0%
+solution is unique when there's nobody
+in the null space except the zero vector
+
+ align:start position:0%
+in the null space except the zero vector
+ 
+
+ align:start position:0%
+in the null space except the zero vector
+and if that's
+
+ align:start position:0%
+and if that's
+ 
+
+ align:start position:0%
+and if that's
+zero then this guy would be in the null
+
+ align:start position:0%
+zero then this guy would be in the null
+ 
+
+ align:start position:0%
+zero then this guy would be in the null
+space so so then so if this were zero
+
+ align:start position:0%
+space so so then so if this were zero
+ 
+
+ align:start position:0%
+space so so then so if this were zero
+then then this x is in the null space of
+
+ align:start position:0%
+then then this x is in the null space of
+ 
+
+ align:start position:0%
+then then this x is in the null space of
+a so
+
+ align:start position:0%
+a so
+ 
+
+ align:start position:0%
+a so
+Solutions are
+
+ align:start position:0%
+Solutions are
+ 
+
+ align:start position:0%
+Solutions are
+never
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique because I could always add that
+
+ align:start position:0%
+unique because I could always add that
+ 
+
+ align:start position:0%
+unique because I could always add that
+to any
+
+ align:start position:0%
+to any
+ 
+
+ align:start position:0%
+to any
+solution and it it and ax would wouldn't
+
+ align:start position:0%
+solution and it it and ax would wouldn't
+ 
+
+ align:start position:0%
+solution and it it and ax would wouldn't
+change so uh so always that question is
+
+ align:start position:0%
+change so uh so always that question is
+ 
+
+ align:start position:0%
+change so uh so always that question is
+there somebody in the null space okay
+
+ align:start position:0%
+there somebody in the null space okay
+ 
+
+ align:start position:0%
+there somebody in the null space okay
+third oh now here's a totally different
+
+ align:start position:0%
+third oh now here's a totally different
+ 
+
+ align:start position:0%
+third oh now here's a totally different
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+suppose those three vectors V1 V2 V3 are
+
+ align:start position:0%
+suppose those three vectors V1 V2 V3 are
+ 
+
+ align:start position:0%
+suppose those three vectors V1 V2 V3 are
+orthonormal so that's I mean they this
+
+ align:start position:0%
+orthonormal so that's I mean they this
+ 
+
+ align:start position:0%
+orthonormal so that's I mean they this
+isn't going to happen for orthonormal
+
+ align:start position:0%
+isn't going to happen for orthonormal
+ 
+
+ align:start position:0%
+isn't going to happen for orthonormal
+vectors okay so part C forget Part B C
+
+ align:start position:0%
+vectors okay so part C forget Part B C
+ 
+
+ align:start position:0%
+vectors okay so part C forget Part B C
+if V1 V2 V3 are orth
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+normal
+
+ align:start position:0%
+normal
+ 
+
+ align:start position:0%
+normal
+orthonormal so that I would usually have
+
+ align:start position:0%
+orthonormal so that I would usually have
+ 
+
+ align:start position:0%
+orthonormal so that I would usually have
+called them q1 Q2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Q3 now what combination oh here's a nice
+
+ align:start position:0%
+Q3 now what combination oh here's a nice
+ 
+
+ align:start position:0%
+Q3 now what combination oh here's a nice
+question if I say so myself what
+
+ align:start position:0%
+question if I say so myself what
+ 
+
+ align:start position:0%
+question if I say so myself what
+combination of V1 and V2 is closest to
+
+ align:start position:0%
+combination of V1 and V2 is closest to
+ 
+
+ align:start position:0%
+combination of V1 and V2 is closest to
+V3 what point on the plane of V1 and V2
+
+ align:start position:0%
+V3 what point on the plane of V1 and V2
+ 
+
+ align:start position:0%
+V3 what point on the plane of V1 and V2
+is the closest point to V3 if these
+
+ align:start position:0%
+is the closest point to V3 if these
+ 
+
+ align:start position:0%
+is the closest point to V3 if these
+vectors are orthonormal so let me I'll
+
+ align:start position:0%
+vectors are orthonormal so let me I'll
+ 
+
+ align:start position:0%
+vectors are orthonormal so let me I'll
+start the sentence then
+
+ align:start position:0%
+start the sentence then
+ 
+
+ align:start position:0%
+start the sentence then
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+combination something time V1 plus
+
+ align:start position:0%
+combination something time V1 plus
+ 
+
+ align:start position:0%
+combination something time V1 plus
+something * V2 is
+
+ align:start position:0%
+something * V2 is
+ 
+
+ align:start position:0%
+something * V2 is
+closest is the closest combination to
+
+ align:start position:0%
+closest is the closest combination to
+ 
+
+ align:start position:0%
+closest is the closest combination to
+V3 and what's the answer what's the
+
+ align:start position:0%
+V3 and what's the answer what's the
+ 
+
+ align:start position:0%
+V3 and what's the answer what's the
+what's the closest Vector on that plane
+
+ align:start position:0%
+what's the closest Vector on that plane
+ 
+
+ align:start position:0%
+what's the closest Vector on that plane
+to V3
+
+ align:start position:0%
+to V3
+ 
+
+ align:start position:0%
+to V3
+zeros right we just imagine the
+
+ align:start position:0%
+zeros right we just imagine the
+ 
+
+ align:start position:0%
+zeros right we just imagine the
+XYZ X the V V1 V2 V3 could be the
+
+ align:start position:0%
+XYZ X the V V1 V2 V3 could be the
+ 
+
+ align:start position:0%
+XYZ X the V V1 V2 V3 could be the
+standard basis the
+
+ align:start position:0%
+standard basis the
+ 
+
+ align:start position:0%
+standard basis the
+XYZ vectors and of course the point on
+
+ align:start position:0%
+XYZ vectors and of course the point on
+ 
+
+ align:start position:0%
+XYZ vectors and of course the point on
+the XY plane that's closest to the to V3
+
+ align:start position:0%
+the XY plane that's closest to the to V3
+ 
+
+ align:start position:0%
+the XY plane that's closest to the to V3
+on the z-axis is zero so so I if we're
+
+ align:start position:0%
+on the z-axis is zero so so I if we're
+ 
+
+ align:start position:0%
+on the z-axis is zero so so I if we're
+orthonormal then the projection
+
+ align:start position:0%
+orthonormal then the projection
+ 
+
+ align:start position:0%
+orthonormal then the projection
+of V3 onto that plane is it's it's
+
+ align:start position:0%
+of V3 onto that plane is it's it's
+ 
+
+ align:start position:0%
+of V3 onto that plane is it's it's
+perpendicular it hits right at zero okay
+
+ align:start position:0%
+perpendicular it hits right at zero okay
+ 
+
+ align:start position:0%
+perpendicular it hits right at zero okay
+so that's that's like a quick qu you
+
+ align:start position:0%
+so that's that's like a quick qu you
+ 
+
+ align:start position:0%
+so that's that's like a quick qu you
+know easy question but still brings it
+
+ align:start position:0%
+know easy question but still brings it
+ 
+
+ align:start position:0%
+know easy question but still brings it
+out okay um let let me see
+
+ align:start position:0%
+out okay um let let me see
+ 
+
+ align:start position:0%
+out okay um let let me see
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+um shall I write down
+
+ align:start position:0%
+um shall I write down
+ 
+
+ align:start position:0%
+um shall I write down
+a a yeah a Markoff Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tell and I'll I'll ask you for its igen
+
+ align:start position:0%
+tell and I'll I'll ask you for its igen
+ 
+
+ align:start position:0%
+tell and I'll I'll ask you for its igen
+values okay here's a Markoff
+
+ align:start position:0%
+values okay here's a Markoff
+ 
+
+ align:start position:0%
+values okay here's a Markoff
+Matrix this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this and uh tell me it's ion
+
+ align:start position:0%
+this and uh tell me it's ion
+ 
+
+ align:start position:0%
+this and uh tell me it's ion
+values so here I'll call the Matrix a
+
+ align:start position:0%
+values so here I'll call the Matrix a
+ 
+
+ align:start position:0%
+values so here I'll call the Matrix a
+and I'll call the this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2.4.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4.24 3.3.4
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's see it helps out by to notice
+
+ align:start position:0%
+okay let's see it helps out by to notice
+ 
+
+ align:start position:0%
+okay let's see it helps out by to notice
+that column
+
+ align:start position:0%
+that column
+ 
+
+ align:start position:0%
+that column
+1 plus column
+
+ align:start position:0%
+1 plus column
+ 
+
+ align:start position:0%
+1 plus column
+2 what's what what's interesting about
+
+ align:start position:0%
+2 what's what what's interesting about
+ 
+
+ align:start position:0%
+2 what's what what's interesting about
+column 1 plus column
+
+ align:start position:0%
+column 1 plus column
+ 
+
+ align:start position:0%
+column 1 plus column
+2 it's twice as much as column
+
+ align:start position:0%
+2 it's twice as much as column
+ 
+
+ align:start position:0%
+2 it's twice as much as column
+3 so column 1 plus column 2 equals 2 *
+
+ align:start position:0%
+3 so column 1 plus column 2 equals 2 *
+ 
+
+ align:start position:0%
+3 so column 1 plus column 2 equals 2 *
+column 3 I I put that in there column 1
+
+ align:start position:0%
+column 3 I I put that in there column 1
+ 
+
+ align:start position:0%
+column 3 I I put that in there column 1
++ column 2 equal twice column three
+
+ align:start position:0%
++ column 2 equal twice column three
+ 
+
+ align:start position:0%
++ column 2 equal twice column three
+that's a observation okay I want to tell
+
+ align:start position:0%
+that's a observation okay I want to tell
+ 
+
+ align:start position:0%
+that's a observation okay I want to tell
+me the IG values of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix okay tell me one I
+
+ align:start position:0%
+Matrix okay tell me one I
+ 
+
+ align:start position:0%
+Matrix okay tell me one I
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+zero because the Matrix is singular tell
+
+ align:start position:0%
+zero because the Matrix is singular tell
+ 
+
+ align:start position:0%
+zero because the Matrix is singular tell
+me another ion value one because it's a
+
+ align:start position:0%
+me another ion value one because it's a
+ 
+
+ align:start position:0%
+me another ion value one because it's a
+Markoff
+
+ align:start position:0%
+Markoff
+ 
+
+ align:start position:0%
+Markoff
+Matrix The Columns add to the all ones
+
+ align:start position:0%
+Matrix The Columns add to the all ones
+ 
+
+ align:start position:0%
+Matrix The Columns add to the all ones
+vector and uh that will be a
+
+ align:start position:0%
+vector and uh that will be a
+ 
+
+ align:start position:0%
+vector and uh that will be a
+igen Vector of a transpose and tell me
+
+ align:start position:0%
+igen Vector of a transpose and tell me
+ 
+
+ align:start position:0%
+igen Vector of a transpose and tell me
+the third igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value let's see to make the trace come
+
+ align:start position:0%
+value let's see to make the trace come
+ 
+
+ align:start position:0%
+value let's see to make the trace come
+out right which is 8 we need minus
+
+ align:start position:0%
+out right which is 8 we need minus
+ 
+
+ align:start position:0%
+out right which is 8 we need minus
+point2
+
+ align:start position:0%
+point2
+ 
+
+ align:start position:0%
+point2
+okay okay and
+
+ align:start position:0%
+okay okay and
+ 
+
+ align:start position:0%
+okay okay and
+now suppose I start the markof
+
+ align:start position:0%
+now suppose I start the markof
+ 
+
+ align:start position:0%
+now suppose I start the markof
+process suppose I start with a a mate
+
+ align:start position:0%
+process suppose I start with a a mate
+ 
+
+ align:start position:0%
+process suppose I start with a a mate
+with U of zero so I'm going to look at
+
+ align:start position:0%
+with U of zero so I'm going to look at
+ 
+
+ align:start position:0%
+with U of zero so I'm going to look at
+the I'm going to look at the powers of a
+
+ align:start position:0%
+the I'm going to look at the powers of a
+ 
+
+ align:start position:0%
+the I'm going to look at the powers of a
+applied to U of Z this is this is UK
+
+ align:start position:0%
+applied to U of Z this is this is UK
+ 
+
+ align:start position:0%
+applied to U of Z this is this is UK
+K and there's my Matrix and I'm going to
+
+ align:start position:0%
+K and there's my Matrix and I'm going to
+ 
+
+ align:start position:0%
+K and there's my Matrix and I'm going to
+let U of0 be this is going to be 010
+
+ align:start position:0%
+let U of0 be this is going to be 010
+ 
+
+ align:start position:0%
+let U of0 be this is going to be 010
+0 and I I want to my question is what
+
+ align:start position:0%
+0 and I I want to my question is what
+ 
+
+ align:start position:0%
+0 and I I want to my question is what
+does that
+
+ align:start position:0%
+does that
+ 
+
+ align:start position:0%
+does that
+approach if if U of zero is equal to
+
+ align:start position:0%
+approach if if U of zero is equal to
+ 
+
+ align:start position:0%
+approach if if U of zero is equal to
+this if there's U of Z shall I write it
+
+ align:start position:0%
+this if there's U of Z shall I write it
+ 
+
+ align:start position:0%
+this if there's U of Z shall I write it
+in maybe I'll just write in U of Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a to the K starting with
+
+ align:start position:0%
+a to the K starting with
+ 
+
+ align:start position:0%
+a to the K starting with
+10 people in state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+and every step follows the Markoff rule
+
+ align:start position:0%
+and every step follows the Markoff rule
+ 
+
+ align:start position:0%
+and every step follows the Markoff rule
+what's the what's the what what does the
+
+ align:start position:0%
+what's the what's the what what does the
+ 
+
+ align:start position:0%
+what's the what's the what what does the
+solution look like after K steps let me
+
+ align:start position:0%
+solution look like after K steps let me
+ 
+
+ align:start position:0%
+solution look like after K steps let me
+just ask you that and then what happens
+
+ align:start position:0%
+just ask you that and then what happens
+ 
+
+ align:start position:0%
+just ask you that and then what happens
+as K goes to Infinity this is a steady
+
+ align:start position:0%
+as K goes to Infinity this is a steady
+ 
+
+ align:start position:0%
+as K goes to Infinity this is a steady
+state question right I'm looking for the
+
+ align:start position:0%
+state question right I'm looking for the
+ 
+
+ align:start position:0%
+state question right I'm looking for the
+steady state actually the question
+
+ align:start position:0%
+steady state actually the question
+ 
+
+ align:start position:0%
+steady state actually the question
+doesn't ask for the kstep answer it just
+
+ align:start position:0%
+doesn't ask for the kstep answer it just
+ 
+
+ align:start position:0%
+doesn't ask for the kstep answer it just
+jumps right away to Infinity but how
+
+ align:start position:0%
+jumps right away to Infinity but how
+ 
+
+ align:start position:0%
+jumps right away to Infinity but how
+would I express the solution after K
+
+ align:start position:0%
+would I express the solution after K
+ 
+
+ align:start position:0%
+would I express the solution after K
+steps it would be some
+
+ align:start position:0%
+steps it would be some
+ 
+
+ align:start position:0%
+steps it would be some
+multiple of the first igon
+
+ align:start position:0%
+multiple of the first igon
+ 
+
+ align:start position:0%
+multiple of the first igon
+value times the first to the case power
+
+ align:start position:0%
+value times the first to the case power
+ 
+
+ align:start position:0%
+value times the first to the case power
+times the first igon Vector plus some
+
+ align:start position:0%
+times the first igon Vector plus some
+ 
+
+ align:start position:0%
+times the first igon Vector plus some
+other multip Le of the second IG value
+
+ align:start position:0%
+other multip Le of the second IG value
+ 
+
+ align:start position:0%
+other multip Le of the second IG value
+times its IG vector and some multiple of
+
+ align:start position:0%
+times its IG vector and some multiple of
+ 
+
+ align:start position:0%
+times its IG vector and some multiple of
+the third IG value time its igen
+
+ align:start position:0%
+the third IG value time its igen
+ 
+
+ align:start position:0%
+the third IG value time its igen
+Vector okay
+
+ align:start position:0%
+Vector okay
+ 
+
+ align:start position:0%
+Vector okay
+good and these igen values are
+
+ align:start position:0%
+good and these igen values are
+ 
+
+ align:start position:0%
+good and these igen values are
+0 1 and minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point2 so what happens as K goes to
+
+ align:start position:0%
+point2 so what happens as K goes to
+ 
+
+ align:start position:0%
+point2 so what happens as K goes to
+Infinity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the only thing that survives the steady
+
+ align:start position:0%
+the only thing that survives the steady
+ 
+
+ align:start position:0%
+the only thing that survives the steady
+state so at at U
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Infinity this is gone this is gone all
+
+ align:start position:0%
+Infinity this is gone this is gone all
+ 
+
+ align:start position:0%
+Infinity this is gone this is gone all
+that's left is C2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 so I better find
+
+ align:start position:0%
+X2 so I better find
+ 
+
+ align:start position:0%
+X2 so I better find
+X2 I've got to find that igen Vector to
+
+ align:start position:0%
+X2 I've got to find that igen Vector to
+ 
+
+ align:start position:0%
+X2 I've got to find that igen Vector to
+complete the answer what's the IG Vector
+
+ align:start position:0%
+complete the answer what's the IG Vector
+ 
+
+ align:start position:0%
+complete the answer what's the IG Vector
+that corresponds to Lambda equal 1
+
+ align:start position:0%
+that corresponds to Lambda equal 1
+ 
+
+ align:start position:0%
+that corresponds to Lambda equal 1
+that's the the key IG vector in any
+
+ align:start position:0%
+that's the the key IG vector in any
+ 
+
+ align:start position:0%
+that's the the key IG vector in any
+markof process is that igen
+
+ align:start position:0%
+markof process is that igen
+ 
+
+ align:start position:0%
+markof process is that igen
+Vector Lambda equal 1 is an igen value I
+
+ align:start position:0%
+Vector Lambda equal 1 is an igen value I
+ 
+
+ align:start position:0%
+Vector Lambda equal 1 is an igen value I
+need its igen Vector
+
+ align:start position:0%
+need its igen Vector
+ 
+
+ align:start position:0%
+need its igen Vector
+X2 and then I need to know how much of
+
+ align:start position:0%
+X2 and then I need to know how much of
+ 
+
+ align:start position:0%
+X2 and then I need to know how much of
+it is in the starting Vector
+
+ align:start position:0%
+it is in the starting Vector
+ 
+
+ align:start position:0%
+it is in the starting Vector
+U okay so how do I find that igen Vector
+
+ align:start position:0%
+U okay so how do I find that igen Vector
+ 
+
+ align:start position:0%
+U okay so how do I find that igen Vector
+I guess I subtract one from the diagonal
+
+ align:start position:0%
+I guess I subtract one from the diagonal
+ 
+
+ align:start position:0%
+I guess I subtract one from the diagonal
+right so I have
+
+ align:start position:0%
+right so I have
+ 
+
+ align:start position:0%
+right so I have
+minus8
+
+ align:start position:0%
+minus8
+ 
+
+ align:start position:0%
+minus8
+-8
+
+ align:start position:0%
+-8
+ 
+
+ align:start position:0%
+-8
+-.6 and the rest of course is just still
+
+ align:start position:0%
+-.6 and the rest of course is just still
+ 
+
+ align:start position:0%
+-.6 and the rest of course is just still
+4.4
+
+ align:start position:0%
+4.4
+ 
+
+ align:start position:0%
+4.4
+4.4
+
+ align:start position:0%
+4.4
+ 
+
+ align:start position:0%
+4.4
+3.3 and hopefully that's a singular
+
+ align:start position:0%
+3.3 and hopefully that's a singular
+ 
+
+ align:start position:0%
+3.3 and hopefully that's a singular
+Matrix so I'm looking to
+
+ align:start position:0%
+Matrix so I'm looking to
+ 
+
+ align:start position:0%
+Matrix so I'm looking to
+solve a minus I equal
+
+ align:start position:0%
+solve a minus I equal
+ 
+
+ align:start position:0%
+solve a minus I equal
+the a minus i x equals z let's see can
+
+ align:start position:0%
+the a minus i x equals z let's see can
+ 
+
+ align:start position:0%
+the a minus i x equals z let's see can
+anybody spot the solution here I don't
+
+ align:start position:0%
+anybody spot the solution here I don't
+ 
+
+ align:start position:0%
+anybody spot the solution here I don't
+know I didn't make it easy for
+
+ align:start position:0%
+know I didn't make it easy for
+ 
+
+ align:start position:0%
+know I didn't make it easy for
+myself um what do you think
+
+ align:start position:0%
+myself um what do you think
+ 
+
+ align:start position:0%
+myself um what do you think
+there maybe those since those I'm just
+
+ align:start position:0%
+there maybe those since those I'm just
+ 
+
+ align:start position:0%
+there maybe those since those I'm just
+thinking aloud here those first let me
+
+ align:start position:0%
+thinking aloud here those first let me
+ 
+
+ align:start position:0%
+thinking aloud here those first let me
+let me guess those first two entries
+
+ align:start position:0%
+let me guess those first two entries
+ 
+
+ align:start position:0%
+let me guess those first two entries
+might be oh no what do you think any
+
+ align:start position:0%
+might be oh no what do you think any
+ 
+
+ align:start position:0%
+might be oh no what do you think any
+anybody see
+
+ align:start position:0%
+anybody see
+ 
+
+ align:start position:0%
+anybody see
+it we could use elimination if we were
+
+ align:start position:0%
+it we could use elimination if we were
+ 
+
+ align:start position:0%
+it we could use elimination if we were
+desperate are we that
+
+ align:start position:0%
+desperate are we that
+ 
+
+ align:start position:0%
+desperate are we that
+desperate anybody just call out if you
+
+ align:start position:0%
+desperate anybody just call out if you
+ 
+
+ align:start position:0%
+desperate anybody just call out if you
+see the vector here that's in that null
+
+ align:start position:0%
+see the vector here that's in that null
+ 
+
+ align:start position:0%
+see the vector here that's in that null
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+there better be a vector in that null
+
+ align:start position:0%
+there better be a vector in that null
+ 
+
+ align:start position:0%
+there better be a vector in that null
+space or I'm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quitting
+
+ align:start position:0%
+quitting
+ 
+
+ align:start position:0%
+quitting
+uh okay well I guess we could use
+
+ align:start position:0%
+uh okay well I guess we could use
+ 
+
+ align:start position:0%
+uh okay well I guess we could use
+elimination
+
+ align:start position:0%
+elimination
+ 
+
+ align:start position:0%
+elimination
+seems I thought maybe somebody might see
+
+ align:start position:0%
+seems I thought maybe somebody might see
+ 
+
+ align:start position:0%
+seems I thought maybe somebody might see
+it from further away
+
+ align:start position:0%
+it from further away
+ 
+
+ align:start position:0%
+it from further away
+uh you think is there a chance that
+
+ align:start position:0%
+uh you think is there a chance that
+ 
+
+ align:start position:0%
+uh you think is there a chance that
+these guys are could it be that these
+
+ align:start position:0%
+these guys are could it be that these
+ 
+
+ align:start position:0%
+these guys are could it be that these
+these two are equal and this is whatever
+
+ align:start position:0%
+these two are equal and this is whatever
+ 
+
+ align:start position:0%
+these two are equal and this is whatever
+it takes like something like
+
+ align:start position:0%
+it takes like something like
+ 
+
+ align:start position:0%
+it takes like something like
+332 would that possibly work I mean
+
+ align:start position:0%
+332 would that possibly work I mean
+ 
+
+ align:start position:0%
+332 would that possibly work I mean
+that's great for this no it's not that
+
+ align:start position:0%
+that's great for this no it's not that
+ 
+
+ align:start position:0%
+that's great for this no it's not that
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+334 this is uh deeper mathematics you're
+
+ align:start position:0%
+334 this is uh deeper mathematics you're
+ 
+
+ align:start position:0%
+334 this is uh deeper mathematics you're
+watching now 334 that is
+
+ align:start position:0%
+watching now 334 that is
+ 
+
+ align:start position:0%
+watching now 334 that is
+that it works don't don't mess with it
+
+ align:start position:0%
+that it works don't don't mess with it
+ 
+
+ align:start position:0%
+that it works don't don't mess with it
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+works yeah okay it works all right and
+
+ align:start position:0%
+works yeah okay it works all right and
+ 
+
+ align:start position:0%
+works yeah okay it works all right and
+yes okay and uh so that 6 2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+334 and uh how much of that Vector is
+
+ align:start position:0%
+334 and uh how much of that Vector is
+ 
+
+ align:start position:0%
+334 and uh how much of that Vector is
+in is in the starting
+
+ align:start position:0%
+in is in the starting
+ 
+
+ align:start position:0%
+in is in the starting
+Vector well we could go we could go
+
+ align:start position:0%
+Vector well we could go we could go
+ 
+
+ align:start position:0%
+Vector well we could go we could go
+through a complicated process but what's
+
+ align:start position:0%
+through a complicated process but what's
+ 
+
+ align:start position:0%
+through a complicated process but what's
+the beauty of markof things that that
+
+ align:start position:0%
+the beauty of markof things that that
+ 
+
+ align:start position:0%
+the beauty of markof things that that
+the total number of the total population
+
+ align:start position:0%
+the total number of the total population
+ 
+
+ align:start position:0%
+the total number of the total population
+that the the the sum of these doesn't
+
+ align:start position:0%
+that the the the sum of these doesn't
+ 
+
+ align:start position:0%
+that the the the sum of these doesn't
+change the the total number of people
+
+ align:start position:0%
+change the the total number of people
+ 
+
+ align:start position:0%
+change the the total number of people
+they're moving around but they
+
+ align:start position:0%
+they're moving around but they
+ 
+
+ align:start position:0%
+they're moving around but they
+don't get born or or or or get dead so
+
+ align:start position:0%
+don't get born or or or or get dead so
+ 
+
+ align:start position:0%
+don't get born or or or or get dead so
+so there's 10 of them at the start so
+
+ align:start position:0%
+so there's 10 of them at the start so
+ 
+
+ align:start position:0%
+so there's 10 of them at the start so
+there's 10 of them there so C2 is
+
+ align:start position:0%
+there's 10 of them there so C2 is
+ 
+
+ align:start position:0%
+there's 10 of them there so C2 is
+actually one yeah so that would be the
+
+ align:start position:0%
+actually one yeah so that would be the
+ 
+
+ align:start position:0%
+actually one yeah so that would be the
+the correct correct solution okay that
+
+ align:start position:0%
+the correct correct solution okay that
+ 
+
+ align:start position:0%
+the correct correct solution okay that
+would be the U
+
+ align:start position:0%
+would be the U
+ 
+
+ align:start position:0%
+would be the U
+Infinity okay so I use there in that
+
+ align:start position:0%
+Infinity okay so I use there in that
+ 
+
+ align:start position:0%
+Infinity okay so I use there in that
+process sort of the main facts about
+
+ align:start position:0%
+process sort of the main facts about
+ 
+
+ align:start position:0%
+process sort of the main facts about
+Markoff matrices to uh to get a jump on
+
+ align:start position:0%
+Markoff matrices to uh to get a jump on
+ 
+
+ align:start position:0%
+Markoff matrices to uh to get a jump on
+the uh answer
+
+ align:start position:0%
+the uh answer
+ 
+
+ align:start position:0%
+the uh answer
+okay um let's see okay here's some uh
+
+ align:start position:0%
+okay um let's see okay here's some uh
+ 
+
+ align:start position:0%
+okay um let's see okay here's some uh
+kind of quick short
+
+ align:start position:0%
+kind of quick short
+ 
+
+ align:start position:0%
+kind of quick short
+questions uh maybe I I'll move over to
+
+ align:start position:0%
+questions uh maybe I I'll move over to
+ 
+
+ align:start position:0%
+questions uh maybe I I'll move over to
+this board and leave that for the
+
+ align:start position:0%
+this board and leave that for the
+ 
+
+ align:start position:0%
+this board and leave that for the
+moment I'm looking for 2 by two
+
+ align:start position:0%
+moment I'm looking for 2 by two
+ 
+
+ align:start position:0%
+moment I'm looking for 2 by two
+matrices and I'll read out the property
+
+ align:start position:0%
+matrices and I'll read out the property
+ 
+
+ align:start position:0%
+matrices and I'll read out the property
+I want and you give me an example or
+
+ align:start position:0%
+I want and you give me an example or
+ 
+
+ align:start position:0%
+I want and you give me an example or
+tell me there isn't such a
+
+ align:start position:0%
+tell me there isn't such a
+ 
+
+ align:start position:0%
+tell me there isn't such a
+matrix all right here we go first so 2
+
+ align:start position:0%
+matrix all right here we go first so 2
+ 
+
+ align:start position:0%
+matrix all right here we go first so 2
+by tws
+
+ align:start position:0%
+by tws
+ 
+
+ align:start position:0%
+by tws
+first I want to project I want the
+
+ align:start position:0%
+first I want to project I want the
+ 
+
+ align:start position:0%
+first I want to project I want the
+projection projection onto the line
+
+ align:start position:0%
+projection projection onto the line
+ 
+
+ align:start position:0%
+projection projection onto the line
+through a = 4 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+3 so it's a one 1D a one-dimensional
+
+ align:start position:0%
+3 so it's a one 1D a one-dimensional
+ 
+
+ align:start position:0%
+3 so it's a one 1D a one-dimensional
+projection Matrix I'm looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for and what's the formula for it for
+
+ align:start position:0%
+for and what's the formula for it for
+ 
+
+ align:start position:0%
+for and what's the formula for it for
+what's the formula for the projection
+
+ align:start position:0%
+what's the formula for the projection
+ 
+
+ align:start position:0%
+what's the formula for the projection
+ction Matrix P onto a line through a and
+
+ align:start position:0%
+ction Matrix P onto a line through a and
+ 
+
+ align:start position:0%
+ction Matrix P onto a line through a and
+then we'll just plug in this particular
+
+ align:start position:0%
+then we'll just plug in this particular
+ 
+
+ align:start position:0%
+then we'll just plug in this particular
+a you remember that
+
+ align:start position:0%
+a you remember that
+ 
+
+ align:start position:0%
+a you remember that
+formula there's an A and an a
+
+ align:start position:0%
+formula there's an A and an a
+ 
+
+ align:start position:0%
+formula there's an A and an a
+transpose and we can normally we would
+
+ align:start position:0%
+transpose and we can normally we would
+ 
+
+ align:start position:0%
+transpose and we can normally we would
+have an A transpose a inverse in the
+
+ align:start position:0%
+have an A transpose a inverse in the
+ 
+
+ align:start position:0%
+have an A transpose a inverse in the
+middle but here we just got numbers so
+
+ align:start position:0%
+middle but here we just got numbers so
+ 
+
+ align:start position:0%
+middle but here we just got numbers so
+we just divide by
+
+ align:start position:0%
+we just divide by
+ 
+
+ align:start position:0%
+we just divide by
+it and then plug in a and we've got
+
+ align:start position:0%
+it and then plug in a and we've got
+ 
+
+ align:start position:0%
+it and then plug in a and we've got
+it okay so equals
+
+ align:start position:0%
+it okay so equals
+ 
+
+ align:start position:0%
+it okay so equals
+you can put in the numbers trivial right
+
+ align:start position:0%
+you can put in the numbers trivial right
+ 
+
+ align:start position:0%
+you can put in the numbers trivial right
+okay number two the Matrix
+
+ align:start position:0%
+okay number two the Matrix
+ 
+
+ align:start position:0%
+okay number two the Matrix
+that has igen value zero so this is a
+
+ align:start position:0%
+that has igen value zero so this is a
+ 
+
+ align:start position:0%
+that has igen value zero so this is a
+new problem The Matrix with igen value 0
+
+ align:start position:0%
+new problem The Matrix with igen value 0
+ 
+
+ align:start position:0%
+new problem The Matrix with igen value 0
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+three and I vectors well let me write
+
+ align:start position:0%
+three and I vectors well let me write
+ 
+
+ align:start position:0%
+three and I vectors well let me write
+these down I value zero I Vector one
+
+ align:start position:0%
+these down I value zero I Vector one
+ 
+
+ align:start position:0%
+these down I value zero I Vector one
+two I value three I Vector 2 one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm giving you the igen values and IG
+
+ align:start position:0%
+I'm giving you the igen values and IG
+ 
+
+ align:start position:0%
+I'm giving you the igen values and IG
+vectors instead of asking for them now
+
+ align:start position:0%
+vectors instead of asking for them now
+ 
+
+ align:start position:0%
+vectors instead of asking for them now
+I'm asking for the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix what's what's the Matrix then
+
+ align:start position:0%
+Matrix what's what's the Matrix then
+ 
+
+ align:start position:0%
+Matrix what's what's the Matrix then
+what's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+a what's here was a formula then we just
+
+ align:start position:0%
+a what's here was a formula then we just
+ 
+
+ align:start position:0%
+a what's here was a formula then we just
+put in some numbers what's the formula
+
+ align:start position:0%
+put in some numbers what's the formula
+ 
+
+ align:start position:0%
+put in some numbers what's the formula
+here into which we'll just put the given
+
+ align:start position:0%
+here into which we'll just put the given
+ 
+
+ align:start position:0%
+here into which we'll just put the given
+numbers it's the s Lambda s inverse
+
+ align:start position:0%
+numbers it's the s Lambda s inverse
+ 
+
+ align:start position:0%
+numbers it's the s Lambda s inverse
+right so it's s which is this IG Vector
+
+ align:start position:0%
+right so it's s which is this IG Vector
+ 
+
+ align:start position:0%
+right so it's s which is this IG Vector
+matrix it's the Lambda which is the IG
+
+ align:start position:0%
+matrix it's the Lambda which is the IG
+ 
+
+ align:start position:0%
+matrix it's the Lambda which is the IG
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+matrix it's the S inverse whatever that
+
+ align:start position:0%
+matrix it's the S inverse whatever that
+ 
+
+ align:start position:0%
+matrix it's the S inverse whatever that
+turns out to be let me just leave it as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse that has to be it
+
+ align:start position:0%
+inverse that has to be it
+ 
+
+ align:start position:0%
+inverse that has to be it
+right because if we went in the other
+
+ align:start position:0%
+right because if we went in the other
+ 
+
+ align:start position:0%
+right because if we went in the other
+direction that Matrix S would
+
+ align:start position:0%
+direction that Matrix S would
+ 
+
+ align:start position:0%
+direction that Matrix S would
+diagonalize a to produce Lambda so it's
+
+ align:start position:0%
+diagonalize a to produce Lambda so it's
+ 
+
+ align:start position:0%
+diagonalize a to produce Lambda so it's
+s Lambda s inverse good okay ready for
+
+ align:start position:0%
+s Lambda s inverse good okay ready for
+ 
+
+ align:start position:0%
+s Lambda s inverse good okay ready for
+number three a real Matrix that cannot
+
+ align:start position:0%
+number three a real Matrix that cannot
+ 
+
+ align:start position:0%
+number three a real Matrix that cannot
+be factored
+
+ align:start position:0%
+be factored
+ 
+
+ align:start position:0%
+be factored
+into a I'm looking for a matrix a that
+
+ align:start position:0%
+into a I'm looking for a matrix a that
+ 
+
+ align:start position:0%
+into a I'm looking for a matrix a that
+doesn't that never could equal B
+
+ align:start position:0%
+doesn't that never could equal B
+ 
+
+ align:start position:0%
+doesn't that never could equal B
+transpose B for any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+b a 2X two Matrix that could not be
+
+ align:start position:0%
+b a 2X two Matrix that could not be
+ 
+
+ align:start position:0%
+b a 2X two Matrix that could not be
+factored in the form B transpose
+
+ align:start position:0%
+factored in the form B transpose
+ 
+
+ align:start position:0%
+factored in the form B transpose
+B so all you have to do is think well
+
+ align:start position:0%
+B so all you have to do is think well
+ 
+
+ align:start position:0%
+B so all you have to do is think well
+what does B transpose B look like and
+
+ align:start position:0%
+what does B transpose B look like and
+ 
+
+ align:start position:0%
+what does B transpose B look like and
+then pick something
+
+ align:start position:0%
+then pick something
+ 
+
+ align:start position:0%
+then pick something
+different what what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggest uh let's see what what what
+
+ align:start position:0%
+suggest uh let's see what what what
+ 
+
+ align:start position:0%
+suggest uh let's see what what what
+should we take for a matrix that could
+
+ align:start position:0%
+should we take for a matrix that could
+ 
+
+ align:start position:0%
+should we take for a matrix that could
+not be could not have this Form bpos B
+
+ align:start position:0%
+not be could not have this Form bpos B
+ 
+
+ align:start position:0%
+not be could not have this Form bpos B
+well what do we know about bpos B it's
+
+ align:start position:0%
+well what do we know about bpos B it's
+ 
+
+ align:start position:0%
+well what do we know about bpos B it's
+always symmetric so just give me any
+
+ align:start position:0%
+always symmetric so just give me any
+ 
+
+ align:start position:0%
+always symmetric so just give me any
+non-symmetric Matrix it couldn't
+
+ align:start position:0%
+non-symmetric Matrix it couldn't
+ 
+
+ align:start position:0%
+non-symmetric Matrix it couldn't
+possibly have that for form okay and let
+
+ align:start position:0%
+possibly have that for form okay and let
+ 
+
+ align:start position:0%
+possibly have that for form okay and let
+me ask the fourth part of this question
+
+ align:start position:0%
+me ask the fourth part of this question
+ 
+
+ align:start position:0%
+me ask the fourth part of this question
+a matrix that
+
+ align:start position:0%
+a matrix that
+ 
+
+ align:start position:0%
+a matrix that
+has orthogonal igen vectors but it's not
+
+ align:start position:0%
+has orthogonal igen vectors but it's not
+ 
+
+ align:start position:0%
+has orthogonal igen vectors but it's not
+symmetric tell me a matrix How could a
+
+ align:start position:0%
+symmetric tell me a matrix How could a
+ 
+
+ align:start position:0%
+symmetric tell me a matrix How could a
+matrix what matrices have orthogonal ion
+
+ align:start position:0%
+matrix what matrices have orthogonal ion
+ 
+
+ align:start position:0%
+matrix what matrices have orthogonal ion
+vectors but they're not symmetric
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matrices what other matrices tell me a
+
+ align:start position:0%
+matrices what other matrices tell me a
+ 
+
+ align:start position:0%
+matrices what other matrices tell me a
+different other families of matrices
+
+ align:start position:0%
+different other families of matrices
+ 
+
+ align:start position:0%
+different other families of matrices
+that have orthogonal ien vectors
+
+ align:start position:0%
+that have orthogonal ien vectors
+ 
+
+ align:start position:0%
+that have orthogonal ien vectors
+we know symmetric matrices do but but
+
+ align:start position:0%
+we know symmetric matrices do but but
+ 
+
+ align:start position:0%
+we know symmetric matrices do but but
+others
+
+ align:start position:0%
+others
+ 
+
+ align:start position:0%
+others
+also so so I'm looking for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orthogonal I can
+
+ align:start position:0%
+orthogonal I can
+ 
+
+ align:start position:0%
+orthogonal I can
+vectors and what do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+suggest uh The Matrix could be skew
+
+ align:start position:0%
+suggest uh The Matrix could be skew
+ 
+
+ align:start position:0%
+suggest uh The Matrix could be skew
+symmetric it could be an orthogonal
+
+ align:start position:0%
+symmetric it could be an orthogonal
+ 
+
+ align:start position:0%
+symmetric it could be an orthogonal
+Matrix so I I it it could be symmetric
+
+ align:start position:0%
+Matrix so I I it it could be symmetric
+ 
+
+ align:start position:0%
+Matrix so I I it it could be symmetric
+but but that was too easy so I Ruled
+
+ align:start position:0%
+but but that was too easy so I Ruled
+ 
+
+ align:start position:0%
+but but that was too easy so I Ruled
+that out it could be skew
+
+ align:start position:0%
+that out it could be skew
+ 
+
+ align:start position:0%
+that out it could be skew
+symmetric
+
+ align:start position:0%
+symmetric
+ 
+
+ align:start position:0%
+symmetric
+like like uh 1 minus one like
+
+ align:start position:0%
+like like uh 1 minus one like
+ 
+
+ align:start position:0%
+like like uh 1 minus one like
+that or it could be an orthogonal
+
+ align:start position:0%
+that or it could be an orthogonal
+ 
+
+ align:start position:0%
+that or it could be an orthogonal
+Matrix it could be an orthogonal Matrix
+
+ align:start position:0%
+Matrix it could be an orthogonal Matrix
+ 
+
+ align:start position:0%
+Matrix it could be an orthogonal Matrix
+like cosine s minus sin cosine all those
+
+ align:start position:0%
+like cosine s minus sin cosine all those
+ 
+
+ align:start position:0%
+like cosine s minus sin cosine all those
+matrices would have
+
+ align:start position:0%
+matrices would have
+ 
+
+ align:start position:0%
+matrices would have
+complex orthogonal
+
+ align:start position:0%
+complex orthogonal
+ 
+
+ align:start position:0%
+complex orthogonal
+igen
+
+ align:start position:0%
+igen
+ 
+
+ align:start position:0%
+igen
+vectors but they would be
+
+ align:start position:0%
+vectors but they would be
+ 
+
+ align:start position:0%
+vectors but they would be
+orthogonal and so those those examples
+
+ align:start position:0%
+orthogonal and so those those examples
+ 
+
+ align:start position:0%
+orthogonal and so those those examples
+are fine okay we can continue a little
+
+ align:start position:0%
+are fine okay we can continue a little
+ 
+
+ align:start position:0%
+are fine okay we can continue a little
+longer if you would like to uh um with
+
+ align:start position:0%
+longer if you would like to uh um with
+ 
+
+ align:start position:0%
+longer if you would like to uh um with
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+um these from this from this exam from
+
+ align:start position:0%
+um these from this from this exam from
+ 
+
+ align:start position:0%
+um these from this from this exam from
+these exams least
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squares okay here's a least squares
+
+ align:start position:0%
+squares okay here's a least squares
+ 
+
+ align:start position:0%
+squares okay here's a least squares
+problem in which to make life quick
+
+ align:start position:0%
+problem in which to make life quick
+ 
+
+ align:start position:0%
+problem in which to make life quick
+I've given the answer it's it's like
+
+ align:start position:0%
+I've given the answer it's it's like
+ 
+
+ align:start position:0%
+I've given the answer it's it's like
+Jeopardy right uh I I just give the
+
+ align:start position:0%
+Jeopardy right uh I I just give the
+ 
+
+ align:start position:0%
+Jeopardy right uh I I just give the
+answer and you give the question
+
+ align:start position:0%
+answer and you give the question
+ 
+
+ align:start position:0%
+answer and you give the question
+okay oops
+
+ align:start position:0%
+okay oops
+ 
+
+ align:start position:0%
+okay oops
+we've sorry I'll let's see can I stay
+
+ align:start position:0%
+we've sorry I'll let's see can I stay
+ 
+
+ align:start position:0%
+we've sorry I'll let's see can I stay
+over here for the for the uh next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question okay least Square so I'm I'm
+
+ align:start position:0%
+question okay least Square so I'm I'm
+ 
+
+ align:start position:0%
+question okay least Square so I'm I'm
+giving you the problem 11 1 012 2
+
+ align:start position:0%
+giving you the problem 11 1 012 2
+ 
+
+ align:start position:0%
+giving you the problem 11 1 012 2
+CD equal
+
+ align:start position:0%
+CD equal
+ 
+
+ align:start position:0%
+CD equal
+341 and that's B of course this is axal
+
+ align:start position:0%
+341 and that's B of course this is axal
+ 
+
+ align:start position:0%
+341 and that's B of course this is axal
+B and the least Square solution so may I
+
+ align:start position:0%
+B and the least Square solution so may I
+ 
+
+ align:start position:0%
+B and the least Square solution so may I
+put C hat D hat to emphasize it's not
+
+ align:start position:0%
+put C hat D hat to emphasize it's not
+ 
+
+ align:start position:0%
+put C hat D hat to emphasize it's not
+the true solution has Le so the least
+
+ align:start position:0%
+the true solution has Le so the least
+ 
+
+ align:start position:0%
+the true solution has Le so the least
+Square solution maybe I should the hats
+
+ align:start position:0%
+Square solution maybe I should the hats
+ 
+
+ align:start position:0%
+Square solution maybe I should the hats
+really go here is 11/3 and minus1
+
+ align:start position:0%
+really go here is 11/3 and minus1
+ 
+
+ align:start position:0%
+really go here is 11/3 and minus1
+of course you could have figured that
+
+ align:start position:0%
+of course you could have figured that
+ 
+
+ align:start position:0%
+of course you could have figured that
+out in no time so this year I'll ask you
+
+ align:start position:0%
+out in no time so this year I'll ask you
+ 
+
+ align:start position:0%
+out in no time so this year I'll ask you
+to do it probably but suppose we're
+
+ align:start position:0%
+to do it probably but suppose we're
+ 
+
+ align:start position:0%
+to do it probably but suppose we're
+given the
+
+ align:start position:0%
+given the
+ 
+
+ align:start position:0%
+given the
+answer then let's just remember what
+
+ align:start position:0%
+answer then let's just remember what
+ 
+
+ align:start position:0%
+answer then let's just remember what
+what happened what is the pro okay good
+
+ align:start position:0%
+what happened what is the pro okay good
+ 
+
+ align:start position:0%
+what happened what is the pro okay good
+question what's the projection P of this
+
+ align:start position:0%
+question what's the projection P of this
+ 
+
+ align:start position:0%
+question what's the projection P of this
+Vector onto the column space of that
+
+ align:start position:0%
+Vector onto the column space of that
+ 
+
+ align:start position:0%
+Vector onto the column space of that
+Matrix what's so so I write that
+
+ align:start position:0%
+Matrix what's so so I write that
+ 
+
+ align:start position:0%
+Matrix what's so so I write that
+question down
+
+ align:start position:0%
+question down
+ 
+
+ align:start position:0%
+question down
+one what is p the
+
+ align:start position:0%
+one what is p the
+ 
+
+ align:start position:0%
+one what is p the
+projection the projection of
+
+ align:start position:0%
+projection the projection of
+ 
+
+ align:start position:0%
+projection the projection of
+B
+
+ align:start position:0%
+B
+ 
+
+ align:start position:0%
+B
+onto the column space of
+
+ align:start position:0%
+onto the column space of
+ 
+
+ align:start position:0%
+onto the column space of
+a is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what hopefully that's what the least
+
+ align:start position:0%
+what hopefully that's what the least
+ 
+
+ align:start position:0%
+what hopefully that's what the least
+squares problem
+
+ align:start position:0%
+squares problem
+ 
+
+ align:start position:0%
+squares problem
+solved what is
+
+ align:start position:0%
+solved what is
+ 
+
+ align:start position:0%
+solved what is
+it it's this was the best solution this
+
+ align:start position:0%
+it it's this was the best solution this
+ 
+
+ align:start position:0%
+it it's this was the best solution this
+it it's
+
+ align:start position:0%
+it it's
+ 
+
+ align:start position:0%
+it it's
+11/3 time * column
+
+ align:start position:0%
+11/3 time * column
+ 
+
+ align:start position:0%
+11/3 time * column
+1 plus or rather minus one time column 2
+
+ align:start position:0%
+1 plus or rather minus one time column 2
+ 
+
+ align:start position:0%
+1 plus or rather minus one time column 2
+right that's what these squares did it
+
+ align:start position:0%
+right that's what these squares did it
+ 
+
+ align:start position:0%
+right that's what these squares did it
+found the combination of the columns
+
+ align:start position:0%
+found the combination of the columns
+ 
+
+ align:start position:0%
+found the combination of the columns
+that was as close as possible to be
+
+ align:start position:0%
+that was as close as possible to be
+ 
+
+ align:start position:0%
+that was as close as possible to be
+that's what Le squares was doing it
+
+ align:start position:0%
+that's what Le squares was doing it
+ 
+
+ align:start position:0%
+that's what Le squares was doing it
+found the projection okay
+
+ align:start position:0%
+found the projection okay
+ 
+
+ align:start position:0%
+found the projection okay
+secondly draw the straight line problem
+
+ align:start position:0%
+secondly draw the straight line problem
+ 
+
+ align:start position:0%
+secondly draw the straight line problem
+that corresponds to this system
+
+ align:start position:0%
+that corresponds to this system
+ 
+
+ align:start position:0%
+that corresponds to this system
+so I guess that the straight line
+
+ align:start position:0%
+so I guess that the straight line
+ 
+
+ align:start position:0%
+so I guess that the straight line
+straight line fitting a straight line
+
+ align:start position:0%
+straight line fitting a straight line
+ 
+
+ align:start position:0%
+straight line fitting a straight line
+problem uh we kind of recognize we
+
+ align:start position:0%
+problem uh we kind of recognize we
+ 
+
+ align:start position:0%
+problem uh we kind of recognize we
+recognize these are the Heights and
+
+ align:start position:0%
+recognize these are the Heights and
+ 
+
+ align:start position:0%
+recognize these are the Heights and
+these are the points so at 012 the
+
+ align:start position:0%
+these are the points so at 012 the
+ 
+
+ align:start position:0%
+these are the points so at 012 the
+heights are
+
+ align:start position:0%
+heights are
+ 
+
+ align:start position:0%
+heights are
+three and at at t equal to one the
+
+ align:start position:0%
+three and at at t equal to one the
+ 
+
+ align:start position:0%
+three and at at t equal to one the
+height is 4 1 2 3 4 and tal to 2 the
+
+ align:start position:0%
+height is 4 1 2 3 4 and tal to 2 the
+ 
+
+ align:start position:0%
+height is 4 1 2 3 4 and tal to 2 the
+height is
+
+ align:start position:0%
+height is
+ 
+
+ align:start position:0%
+height is
+one so I'm trying to fix the
+
+ align:start position:0%
+one so I'm trying to fix the
+ 
+
+ align:start position:0%
+one so I'm trying to fix the
+best straight line through those
+
+ align:start position:0%
+best straight line through those
+ 
+
+ align:start position:0%
+best straight line through those
+points
+
+ align:start position:0%
+points
+ 
+
+ align:start position:0%
+points
+God uh I could fit a triangle very well
+
+ align:start position:0%
+God uh I could fit a triangle very well
+ 
+
+ align:start position:0%
+God uh I could fit a triangle very well
+but uh uh where's the best I don't even
+
+ align:start position:0%
+but uh uh where's the best I don't even
+ 
+
+ align:start position:0%
+but uh uh where's the best I don't even
+know which way the best straight line
+
+ align:start position:0%
+know which way the best straight line
+ 
+
+ align:start position:0%
+know which way the best straight line
+goes maybe it goes oh I do know how it
+
+ align:start position:0%
+goes maybe it goes oh I do know how it
+ 
+
+ align:start position:0%
+goes maybe it goes oh I do know how it
+goes because there's the answer yes uh
+
+ align:start position:0%
+goes because there's the answer yes uh
+ 
+
+ align:start position:0%
+goes because there's the answer yes uh
+it it has it has a height
+
+ align:start position:0%
+it it has it has a height
+ 
+
+ align:start position:0%
+it it has it has a height
+11/3 and it has slope minus one so it's
+
+ align:start position:0%
+11/3 and it has slope minus one so it's
+ 
+
+ align:start position:0%
+11/3 and it has slope minus one so it's
+something like that okay great now
+
+ align:start position:0%
+something like that okay great now
+ 
+
+ align:start position:0%
+something like that okay great now
+finally and this completes the
+
+ align:start position:0%
+finally and this completes the
+ 
+
+ align:start position:0%
+finally and this completes the
+course find a vector a different Vector
+
+ align:start position:0%
+course find a vector a different Vector
+ 
+
+ align:start position:0%
+course find a vector a different Vector
+B not all zeros for which the least
+
+ align:start position:0%
+B not all zeros for which the least
+ 
+
+ align:start position:0%
+B not all zeros for which the least
+Square solution would be zero so I want
+
+ align:start position:0%
+Square solution would be zero so I want
+ 
+
+ align:start position:0%
+Square solution would be zero so I want
+you to find a different
+
+ align:start position:0%
+you to find a different
+ 
+
+ align:start position:0%
+you to find a different
+B so that the least Square solution
+
+ align:start position:0%
+B so that the least Square solution
+ 
+
+ align:start position:0%
+B so that the least Square solution
+changes to all zeros
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so tell me what I'm really looking for
+
+ align:start position:0%
+so tell me what I'm really looking for
+ 
+
+ align:start position:0%
+so tell me what I'm really looking for
+here I'm looking for a b where the best
+
+ align:start position:0%
+here I'm looking for a b where the best
+ 
+
+ align:start position:0%
+here I'm looking for a b where the best
+combination of these two columns is the
+
+ align:start position:0%
+combination of these two columns is the
+ 
+
+ align:start position:0%
+combination of these two columns is the
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+combination so what kind of a vector B
+
+ align:start position:0%
+combination so what kind of a vector B
+ 
+
+ align:start position:0%
+combination so what kind of a vector B
+am I looking for I'm looking for a
+
+ align:start position:0%
+am I looking for I'm looking for a
+ 
+
+ align:start position:0%
+am I looking for I'm looking for a
+vector B that's orthogonal to those
+
+ align:start position:0%
+vector B that's orthogonal to those
+ 
+
+ align:start position:0%
+vector B that's orthogonal to those
+columns it's orthogonal to those columns
+
+ align:start position:0%
+columns it's orthogonal to those columns
+ 
+
+ align:start position:0%
+columns it's orthogonal to those columns
+it's orthogonal to the column space the
+
+ align:start position:0%
+it's orthogonal to the column space the
+ 
+
+ align:start position:0%
+it's orthogonal to the column space the
+best possible answer is zero so a vector
+
+ align:start position:0%
+best possible answer is zero so a vector
+ 
+
+ align:start position:0%
+best possible answer is zero so a vector
+B that's orth to those columns let's see
+
+ align:start position:0%
+B that's orth to those columns let's see
+ 
+
+ align:start position:0%
+B that's orth to those columns let's see
+maybe maybe uh one of those minus two of
+
+ align:start position:0%
+maybe maybe uh one of those minus two of
+ 
+
+ align:start position:0%
+maybe maybe uh one of those minus two of
+those and one of those that would be
+
+ align:start position:0%
+those and one of those that would be
+ 
+
+ align:start position:0%
+those and one of those that would be
+orthogonal to those columns and the best
+
+ align:start position:0%
+orthogonal to those columns and the best
+ 
+
+ align:start position:0%
+orthogonal to those columns and the best
+Vector would be 0
+
+ align:start position:0%
+Vector would be 0
+ 
+
+ align:start position:0%
+Vector would be 0
+0 okay so that's as many questions as I
+
+ align:start position:0%
+0 okay so that's as many questions as I
+ 
+
+ align:start position:0%
+0 okay so that's as many questions as I
+can do in an hour but you get three
+
+ align:start position:0%
+can do in an hour but you get three
+ 
+
+ align:start position:0%
+can do in an hour but you get three
+hours and uh let me just say as I've
+
+ align:start position:0%
+hours and uh let me just say as I've
+ 
+
+ align:start position:0%
+hours and uh let me just say as I've
+said by
+
+ align:start position:0%
+said by
+ 
+
+ align:start position:0%
+said by
+email um thanks very much for your
+
+ align:start position:0%
+email um thanks very much for your
+ 
+
+ align:start position:0%
+email um thanks very much for your
+patience as this series of lectures was
+
+ align:start position:0%
+patience as this series of lectures was
+ 
+
+ align:start position:0%
+patience as this series of lectures was
+videotaped and um thanks for filling out
+
+ align:start position:0%
+videotaped and um thanks for filling out
+ 
+
+ align:start position:0%
+videotaped and um thanks for filling out
+these forms maybe just leave them on the
+
+ align:start position:0%
+these forms maybe just leave them on the
+ 
+
+ align:start position:0%
+these forms maybe just leave them on the
+table up there as you go out and above
+
+ align:start position:0%
+table up there as you go out and above
+ 
+
+ align:start position:0%
+table up there as you go out and above
+all thanks for taking the course thank
+
+ align:start position:0%
+all thanks for taking the course thank
+ 
+
+ align:start position:0%
+all thanks for taking the course thank
+you thanks
\ No newline at end of file
diff --git a/RhMdeFIw1rM.txt b/RhMdeFIw1rM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..68eca16e4549d0b42b4ab762c2c4061474e3b82c
--- /dev/null
+++ b/RhMdeFIw1rM.txt
@@ -0,0 +1,1299 @@
+align:start position:0%
+ 
+so um
+
+ align:start position:0%
+so um
+ 
+
+ align:start position:0%
+so um
+the thing about an expected value value
+
+ align:start position:0%
+the thing about an expected value value
+ 
+
+ align:start position:0%
+the thing about an expected value value
+of information it's an expected value
+
+ align:start position:0%
+of information it's an expected value
+ 
+
+ align:start position:0%
+of information it's an expected value
+that is
+
+ align:start position:0%
+that is
+ 
+
+ align:start position:0%
+that is
+we're we're always dealing expectations
+
+ align:start position:0%
+we're we're always dealing expectations
+ 
+
+ align:start position:0%
+we're we're always dealing expectations
+here in the world of uncertainty so you
+
+ align:start position:0%
+here in the world of uncertainty so you
+ 
+
+ align:start position:0%
+here in the world of uncertainty so you
+may have the information that says it's
+
+ align:start position:0%
+may have the information that says it's
+ 
+
+ align:start position:0%
+may have the information that says it's
+really good and it turns out that it's
+
+ align:start position:0%
+really good and it turns out that it's
+ 
+
+ align:start position:0%
+really good and it turns out that it's
+not so good so you you're you're not
+
+ align:start position:0%
+not so good so you you're you're not
+ 
+
+ align:start position:0%
+not so good so you you're you're not
+something that it's
+
+ align:start position:0%
+something that it's
+ 
+
+ align:start position:0%
+something that it's
+uh absolutely sure but it's an expected
+
+ align:start position:0%
+uh absolutely sure but it's an expected
+ 
+
+ align:start position:0%
+uh absolutely sure but it's an expected
+value
+
+ align:start position:0%
+value
+ 
+
+ align:start position:0%
+value
+so now let me talk about
+
+ align:start position:0%
+so now let me talk about
+ 
+
+ align:start position:0%
+so now let me talk about
+uh the way when we do this in a full
+
+ align:start position:0%
+uh the way when we do this in a full
+ 
+
+ align:start position:0%
+uh the way when we do this in a full
+analysis
+
+ align:start position:0%
+analysis
+ 
+
+ align:start position:0%
+analysis
+and i think it's important as a baseline
+
+ align:start position:0%
+and i think it's important as a baseline
+ 
+
+ align:start position:0%
+and i think it's important as a baseline
+thank you for the uh word it's a
+
+ align:start position:0%
+thank you for the uh word it's a
+ 
+
+ align:start position:0%
+thank you for the uh word it's a
+baseline
+
+ align:start position:0%
+baseline
+ 
+
+ align:start position:0%
+baseline
+for how we think about it so
+
+ align:start position:0%
+for how we think about it so
+ 
+
+ align:start position:0%
+for how we think about it so
+the calculations are complex
+
+ align:start position:0%
+the calculations are complex
+ 
+
+ align:start position:0%
+the calculations are complex
+first of all any test you can have can
+
+ align:start position:0%
+first of all any test you can have can
+ 
+
+ align:start position:0%
+first of all any test you can have can
+many results had to have many different
+
+ align:start position:0%
+many results had to have many different
+ 
+
+ align:start position:0%
+many results had to have many different
+results for example a prototype plan
+
+ align:start position:0%
+results for example a prototype plan
+ 
+
+ align:start position:0%
+results for example a prototype plan
+might work very well well so so poorly
+
+ align:start position:0%
+might work very well well so so poorly
+ 
+
+ align:start position:0%
+might work very well well so so poorly
+failed
+
+ align:start position:0%
+failed
+ 
+
+ align:start position:0%
+failed
+so you don't get necessarily a yes no
+
+ align:start position:0%
+so you don't get necessarily a yes no
+ 
+
+ align:start position:0%
+so you don't get necessarily a yes no
+answer you get a range of answers
+
+ align:start position:0%
+answer you get a range of answers
+ 
+
+ align:start position:0%
+answer you get a range of answers
+now these answers don't prove what will
+
+ align:start position:0%
+now these answers don't prove what will
+ 
+
+ align:start position:0%
+now these answers don't prove what will
+happen
+
+ align:start position:0%
+happen
+ 
+
+ align:start position:0%
+happen
+why is that i've run it i've got a
+
+ align:start position:0%
+why is that i've run it i've got a
+ 
+
+ align:start position:0%
+why is that i've run it i've got a
+result it works well
+
+ align:start position:0%
+result it works well
+ 
+
+ align:start position:0%
+result it works well
+do i know that it's going to work well
+
+ align:start position:0%
+do i know that it's going to work well
+ 
+
+ align:start position:0%
+do i know that it's going to work well
+or don't i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the test results will not prove what
+
+ align:start position:0%
+the test results will not prove what
+ 
+
+ align:start position:0%
+the test results will not prove what
+happens they are samples just like if i
+
+ align:start position:0%
+happens they are samples just like if i
+ 
+
+ align:start position:0%
+happens they are samples just like if i
+go through a
+
+ align:start position:0%
+go through a
+ 
+
+ align:start position:0%
+go through a
+test for tb or
+
+ align:start position:0%
+test for tb or
+ 
+
+ align:start position:0%
+test for tb or
+contemporaneously if i go through a test
+
+ align:start position:0%
+contemporaneously if i go through a test
+ 
+
+ align:start position:0%
+contemporaneously if i go through a test
+for covid and i have a negative result
+
+ align:start position:0%
+for covid and i have a negative result
+ 
+
+ align:start position:0%
+for covid and i have a negative result
+it doesn't necessarily mean
+
+ align:start position:0%
+it doesn't necessarily mean
+ 
+
+ align:start position:0%
+it doesn't necessarily mean
+that the
+
+ align:start position:0%
+that the
+ 
+
+ align:start position:0%
+that the
+uh that i am i'm negative it might be
+
+ align:start position:0%
+uh that i am i'm negative it might be
+ 
+
+ align:start position:0%
+uh that i am i'm negative it might be
+there's a false negative or contrarily
+
+ align:start position:0%
+there's a false negative or contrarily
+ 
+
+ align:start position:0%
+there's a false negative or contrarily
+that's a false positive they thought
+
+ align:start position:0%
+that's a false positive they thought
+ 
+
+ align:start position:0%
+that's a false positive they thought
+they saw something but it's not there
+
+ align:start position:0%
+they saw something but it's not there
+ 
+
+ align:start position:0%
+they saw something but it's not there
+so what the new information does is not
+
+ align:start position:0%
+so what the new information does is not
+ 
+
+ align:start position:0%
+so what the new information does is not
+tell you what was happening you knew
+
+ align:start position:0%
+tell you what was happening you knew
+ 
+
+ align:start position:0%
+tell you what was happening you knew
+this already but i'm emphasizing it
+
+ align:start position:0%
+this already but i'm emphasizing it
+ 
+
+ align:start position:0%
+this already but i'm emphasizing it
+but it says okay
+
+ align:start position:0%
+but it says okay
+ 
+
+ align:start position:0%
+but it says okay
+you thought it was like this you got
+
+ align:start position:0%
+you thought it was like this you got
+ 
+
+ align:start position:0%
+you thought it was like this you got
+some new information
+
+ align:start position:0%
+some new information
+ 
+
+ align:start position:0%
+some new information
+it made you think that it might be
+
+ align:start position:0%
+it made you think that it might be
+ 
+
+ align:start position:0%
+it made you think that it might be
+different so each
+
+ align:start position:0%
+different so each
+ 
+
+ align:start position:0%
+different so each
+piece of new information whether it
+
+ align:start position:0%
+piece of new information whether it
+ 
+
+ align:start position:0%
+piece of new information whether it
+performs well very well poorly so so and
+
+ align:start position:0%
+performs well very well poorly so so and
+ 
+
+ align:start position:0%
+performs well very well poorly so so and
+so on
+
+ align:start position:0%
+so on
+ 
+
+ align:start position:0%
+so on
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+updates the prior estimates
+
+ align:start position:0%
+updates the prior estimates
+ 
+
+ align:start position:0%
+updates the prior estimates
+the technical way to do that is using
+
+ align:start position:0%
+the technical way to do that is using
+ 
+
+ align:start position:0%
+the technical way to do that is using
+something called bayes theorem
+
+ align:start position:0%
+something called bayes theorem
+ 
+
+ align:start position:0%
+something called bayes theorem
+now this is not a particularly uh simple
+
+ align:start position:0%
+now this is not a particularly uh simple
+ 
+
+ align:start position:0%
+now this is not a particularly uh simple
+topic we get to because if i have say
+
+ align:start position:0%
+topic we get to because if i have say
+ 
+
+ align:start position:0%
+topic we get to because if i have say
+five results as i listed before
+
+ align:start position:0%
+five results as i listed before
+ 
+
+ align:start position:0%
+five results as i listed before
+and each test result implies a different
+
+ align:start position:0%
+and each test result implies a different
+ 
+
+ align:start position:0%
+and each test result implies a different
+value of the project each with a
+
+ align:start position:0%
+value of the project each with a
+ 
+
+ align:start position:0%
+value of the project each with a
+different probability that five test
+
+ align:start position:0%
+different probability that five test
+ 
+
+ align:start position:0%
+different probability that five test
+results will give you five different
+
+ align:start position:0%
+results will give you five different
+ 
+
+ align:start position:0%
+results will give you five different
+updates
+
+ align:start position:0%
+updates
+ 
+
+ align:start position:0%
+updates
+for your system and
+
+ align:start position:0%
+for your system and
+ 
+
+ align:start position:0%
+for your system and
+each will have a different set of prior
+
+ align:start position:0%
+each will have a different set of prior
+ 
+
+ align:start position:0%
+each will have a different set of prior
+probabilities that you updated from the
+
+ align:start position:0%
+probabilities that you updated from the
+ 
+
+ align:start position:0%
+probabilities that you updated from the
+priors to the posteriors
+
+ align:start position:0%
+priors to the posteriors
+ 
+
+ align:start position:0%
+priors to the posteriors
+and you have five different solutions so
+
+ align:start position:0%
+and you have five different solutions so
+ 
+
+ align:start position:0%
+and you have five different solutions so
+each
+
+ align:start position:0%
+each
+ 
+
+ align:start position:0%
+each
+so the
+
+ align:start position:0%
+so the
+ 
+
+ align:start position:0%
+so the
+calculation of this
+
+ align:start position:0%
+calculation of this
+ 
+
+ align:start position:0%
+calculation of this
+uh process that is the expected value of
+
+ align:start position:0%
+uh process that is the expected value of
+ 
+
+ align:start position:0%
+uh process that is the expected value of
+sample information is complicated
+
+ align:start position:0%
+sample information is complicated
+ 
+
+ align:start position:0%
+sample information is complicated
+so first of all
+
+ align:start position:0%
+so first of all
+ 
+
+ align:start position:0%
+so first of all
+what's bayes theorem i imagine that many
+
+ align:start position:0%
+what's bayes theorem i imagine that many
+ 
+
+ align:start position:0%
+what's bayes theorem i imagine that many
+of you if not most of you who have
+
+ align:start position:0%
+of you if not most of you who have
+ 
+
+ align:start position:0%
+of you if not most of you who have
+already dealt with this maybe you had in
+
+ align:start position:0%
+already dealt with this maybe you had in
+ 
+
+ align:start position:0%
+already dealt with this maybe you had in
+a course and had to pass quizzes on it
+
+ align:start position:0%
+a course and had to pass quizzes on it
+ 
+
+ align:start position:0%
+a course and had to pass quizzes on it
+and so forth but this is a recall
+
+ align:start position:0%
+and so forth but this is a recall
+ 
+
+ align:start position:0%
+and so forth but this is a recall
+let me
+
+ align:start position:0%
+let me
+ 
+
+ align:start position:0%
+let me
+remind everybody or introduce the others
+
+ align:start position:0%
+remind everybody or introduce the others
+ 
+
+ align:start position:0%
+remind everybody or introduce the others
+to uh what it is
+
+ align:start position:0%
+to uh what it is
+ 
+
+ align:start position:0%
+to uh what it is
+the formula is very simple
+
+ align:start position:0%
+the formula is very simple
+ 
+
+ align:start position:0%
+the formula is very simple
+but i'm arguing for you this is what i'm
+
+ align:start position:0%
+but i'm arguing for you this is what i'm
+ 
+
+ align:start position:0%
+but i'm arguing for you this is what i'm
+talking about because it comes up
+
+ align:start position:0%
+talking about because it comes up
+ 
+
+ align:start position:0%
+talking about because it comes up
+is it's impractical use for a system
+
+ align:start position:0%
+is it's impractical use for a system
+ 
+
+ align:start position:0%
+is it's impractical use for a system
+designed on a regular basis
+
+ align:start position:0%
+designed on a regular basis
+ 
+
+ align:start position:0%
+designed on a regular basis
+but let me tell you what it is and we'll
+
+ align:start position:0%
+but let me tell you what it is and we'll
+ 
+
+ align:start position:0%
+but let me tell you what it is and we'll
+you'll see what i'm i hope you'll see
+
+ align:start position:0%
+you'll see what i'm i hope you'll see
+ 
+
+ align:start position:0%
+you'll see what i'm i hope you'll see
+what i'm coming to
+
+ align:start position:0%
+what i'm coming to
+ 
+
+ align:start position:0%
+what i'm coming to
+so the probability the posterior
+
+ align:start position:0%
+so the probability the posterior
+ 
+
+ align:start position:0%
+so the probability the posterior
+probability of something
+
+ align:start position:0%
+probability of something
+ 
+
+ align:start position:0%
+probability of something
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+say that the market will sell that the
+
+ align:start position:0%
+say that the market will sell that the
+ 
+
+ align:start position:0%
+say that the market will sell that the
+product will sell well
+
+ align:start position:0%
+product will sell well
+ 
+
+ align:start position:0%
+product will sell well
+after the observation b
+
+ align:start position:0%
+after the observation b
+ 
+
+ align:start position:0%
+after the observation b
+call basically called a probability of a
+
+ align:start position:0%
+call basically called a probability of a
+ 
+
+ align:start position:0%
+call basically called a probability of a
+given b that is
+
+ align:start position:0%
+given b that is
+ 
+
+ align:start position:0%
+given b that is
+i had a prior probability maybe 50
+
+ align:start position:0%
+i had a prior probability maybe 50
+ 
+
+ align:start position:0%
+i had a prior probability maybe 50
+percent is going to sell well
+
+ align:start position:0%
+percent is going to sell well
+ 
+
+ align:start position:0%
+percent is going to sell well
+i took my tractor to the state fair
+
+ align:start position:0%
+i took my tractor to the state fair
+ 
+
+ align:start position:0%
+i took my tractor to the state fair
+they gushed over it and made me think ah
+
+ align:start position:0%
+they gushed over it and made me think ah
+ 
+
+ align:start position:0%
+they gushed over it and made me think ah
+it will probably it's more than 50 50
+
+ align:start position:0%
+it will probably it's more than 50 50
+ 
+
+ align:start position:0%
+it will probably it's more than 50 50
+chance it'll maybe a 70 30 chance it'll
+
+ align:start position:0%
+chance it'll maybe a 70 30 chance it'll
+ 
+
+ align:start position:0%
+chance it'll maybe a 70 30 chance it'll
+sell well
+
+ align:start position:0%
+sell well
+ 
+
+ align:start position:0%
+sell well
+so my posterior probability my revised
+
+ align:start position:0%
+so my posterior probability my revised
+ 
+
+ align:start position:0%
+so my posterior probability my revised
+probability
+
+ align:start position:0%
+probability
+ 
+
+ align:start position:0%
+probability
+is a simple formula
+
+ align:start position:0%
+is a simple formula
+ 
+
+ align:start position:0%
+is a simple formula
+it is equal to the probability you had
+
+ align:start position:0%
+it is equal to the probability you had
+ 
+
+ align:start position:0%
+it is equal to the probability you had
+in the beginning
+
+ align:start position:0%
+in the beginning
+ 
+
+ align:start position:0%
+in the beginning
+times a factor
+
+ align:start position:0%
+times a factor
+ 
+
+ align:start position:0%
+times a factor
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+all the devil is under these details
+
+ align:start position:0%
+all the devil is under these details
+ 
+
+ align:start position:0%
+all the devil is under these details
+the factor is
+
+ align:start position:0%
+the factor is
+ 
+
+ align:start position:0%
+the factor is
+the probability that b is correlated
+
+ align:start position:0%
+the probability that b is correlated
+ 
+
+ align:start position:0%
+the probability that b is correlated
+with a that these kinds of responses
+
+ align:start position:0%
+with a that these kinds of responses
+ 
+
+ align:start position:0%
+with a that these kinds of responses
+actually lead to uh the market results
+
+ align:start position:0%
+actually lead to uh the market results
+ 
+
+ align:start position:0%
+actually lead to uh the market results
+divided by the probability of b the
+
+ align:start position:0%
+divided by the probability of b the
+ 
+
+ align:start position:0%
+divided by the probability of b the
+prior probability of b
+
+ align:start position:0%
+prior probability of b
+ 
+
+ align:start position:0%
+prior probability of b
+now
+
+ align:start position:0%
+now
+ 
+
+ align:start position:0%
+now
+the issue is
+
+ align:start position:0%
+the issue is
+ 
+
+ align:start position:0%
+the issue is
+that although the formula is really
+
+ align:start position:0%
+that although the formula is really
+ 
+
+ align:start position:0%
+that although the formula is really
+simple you know it's uh uh
+
+ align:start position:0%
+simple you know it's uh uh
+ 
+
+ align:start position:0%
+simple you know it's uh uh
+your probability times a factor and i
+
+ align:start position:0%
+your probability times a factor and i
+ 
+
+ align:start position:0%
+your probability times a factor and i
+can state the factor is
+
+ align:start position:0%
+can state the factor is
+ 
+
+ align:start position:0%
+can state the factor is
+that the these elements are
+
+ align:start position:0%
+that the these elements are
+ 
+
+ align:start position:0%
+that the these elements are
+unavailable in practice
+
+ align:start position:0%
+unavailable in practice
+ 
+
+ align:start position:0%
+unavailable in practice
+that is how if you're thinking about how
+
+ align:start position:0%
+that is how if you're thinking about how
+ 
+
+ align:start position:0%
+that is how if you're thinking about how
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+folks at the state fair are responding
+
+ align:start position:0%
+folks at the state fair are responding
+ 
+
+ align:start position:0%
+folks at the state fair are responding
+to my new tractor
+
+ align:start position:0%
+to my new tractor
+ 
+
+ align:start position:0%
+to my new tractor
+um and how does that correlate with the
+
+ align:start position:0%
+um and how does that correlate with the
+ 
+
+ align:start position:0%
+um and how does that correlate with the
+actual sales well that's something you
+
+ align:start position:0%
+actual sales well that's something you
+ 
+
+ align:start position:0%
+actual sales well that's something you
+don't have data on
+
+ align:start position:0%
+don't have data on
+ 
+
+ align:start position:0%
+don't have data on
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+what's the probability of b well you
+
+ align:start position:0%
+what's the probability of b well you
+ 
+
+ align:start position:0%
+what's the probability of b well you
+could think that you you might imagine
+
+ align:start position:0%
+could think that you you might imagine
+ 
+
+ align:start position:0%
+could think that you you might imagine
+some ways of doing this but you don't
+
+ align:start position:0%
+some ways of doing this but you don't
+ 
+
+ align:start position:0%
+some ways of doing this but you don't
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+now if you're doing a repetitive test
+
+ align:start position:0%
+now if you're doing a repetitive test
+ 
+
+ align:start position:0%
+now if you're doing a repetitive test
+and have been doing this
+
+ align:start position:0%
+and have been doing this
+ 
+
+ align:start position:0%
+and have been doing this
+say agricultural sampling or test fields
+
+ align:start position:0%
+say agricultural sampling or test fields
+ 
+
+ align:start position:0%
+say agricultural sampling or test fields
+if you have lots of data and so forth
+
+ align:start position:0%
+if you have lots of data and so forth
+ 
+
+ align:start position:0%
+if you have lots of data and so forth
+you can get these conditional
+
+ align:start position:0%
+you can get these conditional
+ 
+
+ align:start position:0%
+you can get these conditional
+probabilities as they're called
+
+ align:start position:0%
+probabilities as they're called
+ 
+
+ align:start position:0%
+probabilities as they're called
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+you can run the analysis but in general
+
+ align:start position:0%
+you can run the analysis but in general
+ 
+
+ align:start position:0%
+you can run the analysis but in general
+you won't have them
+
+ align:start position:0%
+you won't have them
+ 
+
+ align:start position:0%
+you won't have them
+so that although the formula is really
+
+ align:start position:0%
+so that although the formula is really
+ 
+
+ align:start position:0%
+so that although the formula is really
+simple
+
+ align:start position:0%
+simple
+ 
+
+ align:start position:0%
+simple
+from the point of view of system design
+
+ align:start position:0%
+from the point of view of system design
+ 
+
+ align:start position:0%
+from the point of view of system design
+and management they're really not
+
+ align:start position:0%
+and management they're really not
+ 
+
+ align:start position:0%
+and management they're really not
+available but i want to
+
+ align:start position:0%
+available but i want to
+ 
+
+ align:start position:0%
+available but i want to
+show you how the thing works so that you
+
+ align:start position:0%
+show you how the thing works so that you
+ 
+
+ align:start position:0%
+show you how the thing works so that you
+can appreciate what's going on and why
+
+ align:start position:0%
+can appreciate what's going on and why
+ 
+
+ align:start position:0%
+can appreciate what's going on and why
+there's a another approach
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/Rn9zldxtZko.txt b/Rn9zldxtZko.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ee53c0bd4bd153154eb0bf3b72b0119bf0d9f27b
--- /dev/null
+++ b/Rn9zldxtZko.txt
@@ -0,0 +1,82 @@
+PROFESSOR: Hi.
+
+In this clip, we're going to
+discuss the numbering and
+
+labeling conventions of
+RNA and of protein.
+
+Here we have a nucleoside
+triphosphate or NTP.
+
+This NTP is numbered
+on each carbon.
+
+And we're going to start here
+to the right of this oxygen
+
+and label one prime and proceed
+two prime, three
+
+prime, four prime, and this
+last, five prime carbon.
+
+This means that when we
+polymerize two or more of
+
+these NTP's to get an RNA chain,
+it becomes apparent why
+
+one end is labeled five prime
+and the other end is labeled
+
+three prime.
+
+On this end, the extending atom
+is the five prime carbon.
+
+And on this side, the other end,
+the extending atom is the
+
+three prime carbon attached
+to this oxygen.
+
+This three prime carbon is where
+you would attach another
+
+NTP if you would wish to
+extend this chain.
+
+And so we label the ends of RNA
+five prime to three prime.
+
+And RNA is always polymerized in
+the five prime to the three
+
+prime direction.
+
+Now with our amino acid, we
+label this end, which is our
+
+amino terminus, as N and this
+end which is our carboxy
+
+terminus as C. As before, when
+we polymerize three amino
+
+acids into this short protein
+chain, I'm going to label this
+
+end which has a protruding amino
+terminus as N and this
+
+end which has a protruding
+carboxy terminus as C.
+
+So that's how the conventions
+are in science to label and
+
+number amino acids
+and proteins.
+
+Thanks for watching.
\ No newline at end of file
diff --git a/RsJ1eg7XNVs.txt b/RsJ1eg7XNVs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..52ef5f9f8b7dd1ba97e7019c5b0efdb39e766c3d
--- /dev/null
+++ b/RsJ1eg7XNVs.txt
@@ -0,0 +1,1914 @@
+Let's get started.
+
+Can you hear me back there?
+Loud and clear.
+
+OK.
+Let's get started.
+
+Before I begin,
+just a couple of announcements.
+
+Brad Buren is one of our
+students here and he needs a
+
+note-taker.
+It's a paid position.
+
+So if you are interested you
+can stop by after class and see
+
+him.
+He's sitting right here out
+
+there, OK?
+Second, just a reminder that
+
+6.002 does have prerequisites.
+And the prerequisites are 8.02
+
+and 18.03.
+So with that let me start off
+
+with the usual.
+Do a quick review of what we've
+
+done so far.
+So we started out life looking
+
+at the laws of physics and
+Maxwell's equations and so on.
+
+And those were way too hard so
+we said let's make life easy for
+
+ourselves.
+So we chose to play in this
+
+playground in which we said we
+shall adhere to the lumped
+
+matter discipline.
+OK?
+
+The LMD.
+So we are in that playground.
+
+So this entire course,
+and for that matter large parts
+
+of EECS are within that
+playground, within which the
+
+lumped matter discipline
+applies.
+
+So as soon as we jumped into
+the playground,
+
+the LMD playground,
+we could take Maxwell's
+
+equations and abstract them out
+into two very,
+
+very simple rules.
+And the very simple rules were
+
+KVL and KCL.
+KVL simply said that I can sum
+
+the voltages in any loop in a
+circuit and the result then
+
+would be zero.
+Similarly, I can sum the
+
+currents that enter or exit any
+node and the sum will also be
+
+zero.
+So what you can now do is,
+
+if you feel like,
+you can go around and brag.
+
+Oh, yeah, we use Maxwell's
+equations in everyday life and,
+
+yeah, it's good stuff.
+And the key is that this is
+
+really an encapsulation of
+Maxwell's equations within this
+
+playground that we are in.
+So I talked about the first
+
+method of circuit analysis in
+the last lecture.
+
+And that method simply took
+the, wrote KVL for all the
+
+loops, wrote KCL for all the
+nodes and wrote element vi
+
+relationships.
+And together gave you a big
+
+bunch of equations.
+And you sat down and grunged
+
+through the equations and you
+solved for branch voltages and
+
+currents.
+So we reviewed a second method
+
+of circuit analysis.
+And I'll simply call it circuit
+
+composition.
+The basic idea behind this
+
+method was to learn some simple
+rules of how resistors add and
+
+conductances add and so on and
+so forth and look at a circuit
+
+and simplify the circuit by
+making series simplifications
+
+when the resistors are in series
+and so on and so forth,
+
+and compose it and play around
+with it till we end up with the
+
+current, the voltages that we
+are looking for.
+
+This is the intuitive method.
+And so a section in Chapter 2,
+
+I believe, of the course notes
+discusses several examples using
+
+this method and attempts to make
+a little bit formal the
+
+intuitive approach that is
+applied in this method.
+
+So we then looked at the node
+method.
+
+And the node method was simply
+a particular way of applying KVL
+
+and KCL.
+Node method,
+
+remember?
+We took a ground node.
+
+Then we labeled the nodes of
+the remaining voltages with
+
+respect to that ground.
+Then we wrote KCL for each of
+
+the nodes.
+And when we wrote KCL for each
+
+of the nodes,
+remember, KVL was implicit in
+
+this expression that we used for
+each of the currents that were
+
+exiting each node.
+So if Ej was a node voltage,
+
+then Ej minus Ei multiplied by
+the conductance Gi was the
+
+current that was going through
+one of those,
+
+I should call it Gij.
+This is a conductance that
+
+connects nodes i and j.
+That gave us the KVL that fed
+
+into the same system.
+So these are three methods.
+
+The node method,
+by the way, is sort of the
+
+workhorse of the 6.002 industry.
+And for that matter for all of
+
+the circuits industry.
+When in doubt,
+
+apply the mode method,
+you'll be OK.
+
+That applies to linear
+circuits, nonlinear circuits,
+
+what have you.
+What I'm going to do today is
+
+go through two more methods.
+So notice that the first few
+
+lectures of this course,
+the first three lectures simply
+
+comprise transitioning you from
+the world of physics to the
+
+world of EECS.
+And then two lectures on giving
+
+you a bag of tricks.
+So we start you off with the
+
+sort of tools,
+your mallets and chisels and so
+
+on and so forth.
+And these five methods are your
+
+tools.
+We'll look at two methods
+
+today.
+One method is called the method
+
+of superposition and the second
+method is called the Thevenin
+
+method.
+And these methods apply only to
+
+linear circuits.
+So we look at the subset of
+
+circuits that are linear,
+and these two methods apply to
+
+only those circuits.
+These are methods that combined
+
+with intuition really enables
+you to solve very interesting
+
+circuits very,
+very quickly.
+
+So let me do an example using a
+usual node method.
+
+And then jump into introducing
+the superposition methods and
+
+Thevenin methods using that same
+example.
+
+So let me draw you an example
+circuit here.
+
+So, again, I'm using this
+example, I will use this example
+
+to introduce the method of
+superposition and the Thevenin
+
+method.
+So what I'm going to do is
+
+start off the usual way and
+analyze the circuit using a
+
+method that you know now,
+the node method.
+
+And what I'll do is write down
+the node equations for this by
+
+applying the node method.
+So if you recall the node
+
+method.
+I choose a ground node.
+
+I'm going to choose this node.
+It's got both the voltage
+
+source connected to it,
+and it's also got many other
+
+edges impinging on it.
+So I'm going to choose that as
+
+my ground node and I'm going to
+label the other nodes with their
+
+voltages.
+So this is an unknown.
+
+I'll label it as e.
+I guess we just have one
+
+unknown e.
+And I know the voltage of this
+
+node, and that is simply V.
+Since it's V,
+
+there's a voltage source
+between the ground node and that
+
+node.
+So what I can do next is that I
+
+can write down the node equation
+for this node and then go from
+
+there.
+So let me go ahead and do that.
+
+So let me sum up the currents
+going outside,
+
+going outwards.
+So I have e minus v divide by
+
+R1, I have e minus zero divide
+by R2, and I have minus i equals
+
+zero.
+This is a node equation.
+
+The first thing I want you to
+observe is that this equation is
+
+linear in V and i.
+What I mean by linear is that
+
+you don't see terms like Vi or
+V-squared and things like that.
+
+It's some constant times V plus
+some constant times i equals
+
+some other constant.
+So that's quite nice.
+
+So I'm going to rearrange the
+terms in the following manner.
+
+I'll move the known sources to
+the right-hand side and collect
+
+the coefficients of e on this
+side, so I get one by R1 plus
+
+one by R2 over here.
+
+So stare at this for a moment
+and notice again here I have e,
+
+my unknown node voltage,
+there is some constant
+
+multiplier, and that equals some
+function of V summed up with
+
+some function of i.
+And, again, notice that this is
+
+a linear combination of V and i.
+No multiplication terms and so
+
+on and so forth.
+This is a pretty standard form
+
+in which we will represent
+equations quite often.
+
+And just to label it,
+this is often labeled G as the
+
+conductance matrix.
+Of course this is e,
+
+our unknown node voltages,
+and this is a linear sum of
+
+sources.
+So this is a very standard way
+
+that we will represent
+equations.
+
+We did that last week as well,
+or rather on Tuesday where I
+
+took a conductance matrix,
+multiplied that by a column
+
+vector of unknown node voltages
+and equated that to some linear
+
+combination of my source
+voltages.
+
+The reason the circuit is
+linear is that I have only
+
+linear elements in the circuit.
+I don't have any nonlinear
+
+elements.
+And because of that I can
+
+rewrite this in the following
+manner.
+
+I'm just going to express e as
+a function of V and i and bring
+
+it over to this side.
+So it's some function of i.
+
+So I get R1 R2 divide by R1
+plus R2.
+
+And I bring R1 R2 to this side.
+That's what I get.
+
+So stare at this for a few
+seconds, very common form.
+
+My unknown node voltage is
+equal to this stuff on the
+
+right-hand side.
+The stuff on the right-hand
+
+side has a term multiplying the
+source voltage V and some other
+
+term multiplying the current I.
+And if I were to put this in
+
+sort of symbol-like form my
+unknown node voltage is some
+
+constant times V1 plus some
+constant times,
+
+is of the form constant times
+the source current,
+
+constant times the source
+voltage and so on.
+
+The units of As and Vs are
+different because in this case A
+
+has no units because V is a
+voltage.
+
+And so is e.
+In this case V has units of
+
+resistance.
+So that V times i gives me a
+
+voltage.
+So stare at this equation for a
+
+few seconds and this should help
+us build up some insight that
+
+will allow us to write down the
+answer almost by inspection.
+
+I'm going to show you a method
+now, in a few minutes,
+
+which will allow you to write
+down the answer e just by
+
+starring at the circuit without
+having to go through node
+
+equations and so on.
+The more and more methods I
+
+teach you, the more you will be
+able to do a lot of this
+
+completely by yourselves.
+In this particular example it's
+
+a relatively simple circuit but
+these methods would be
+
+particularly useful when you
+have more complicated
+
+situations.
+But before I go on let me spend
+
+a few minutes pontificating on
+linearity.
+
+So that's a linear circuit.
+And this equation gives me the
+
+unknown node voltage e as a
+linear sum of source voltages
+
+and source currents.
+Linearity implies two
+
+properties, the property of
+homogeneity and also gives vice
+
+to the property of
+superposition.
+
+Let's do homogeneity first.
+What this says is if I have a
+
+circuit, some circuit and I feed
+it some sort of inputs,
+
+A, then let's say my output is
+S.
+
+If you're feeling hungry think
+of these as apples and the
+
+circuit converts them into
+applesauce.
+
+So what homogeneity says is
+that what I can do is if I take
+
+each of my apples and instead of
+feeding it an entire apple what
+
+if I give it three-quarters of
+an apple?
+
+Say I multiple all my inputs by
+some constant alpha,
+
+three-quarters.
+What that says is that at the
+
+output instead of getting one
+full bottle of applesauce I'm
+
+going to get three-quarters of a
+bottle of apple sauce.
+
+So if I proportionately reduce
+all the inputs and if this is a
+
+linear circuit then so shall my
+output be reduced in the same
+
+proportion.
+So that's homogeneity.
+
+Next, let's look at
+superposition.
+
+The property of superposition
+says the following.
+
+The same kind of circuit.
+If I feed it apples then I get
+
+applesauce.
+I take the same circuit,
+
+and this time around if I feed
+the circuit a different set of
+
+inputs, say blueberries.
+And let's say my output,
+
+oops, let me do it this way.
+So as my output I get blueberry
+
+sauce, if such exists.
+So apples applesauce,
+
+blueberries give me blueberry
+sauce.
+
+Then what I'm going to get if I
+mix up the two,
+
+so let's say I take my circuit,
+the same circuit with a set of
+
+inputs and in this example one
+output.
+
+Let's say I mix up my inputs
+and some of my inputs in the
+
+following way,
+here I feed an A1 plus B1 and
+
+here A2 plus B2 and so on then
+at the output I am going to get
+
+a mush of apple sauce and
+blueberry sauce.
+
+All this says is that if I
+apply just apples I get
+
+applesauce.
+If I apply just blueberries I
+
+get blueberry sauce.
+Then if I were to figure out
+
+how this blender would have
+worked had I fed in the
+
+combinations of apples and
+blueberries, then for the
+
+purposes of understanding that
+blender all I could have done
+
+was taken by two outputs and
+just mixed them up together
+
+myself and that's exactly what
+I'd get.
+
+So if I sum up the inputs my
+outputs would also be the sum of
+
+the outputs with the inputs
+applied by themselves.
+
+So let me take this here and
+munge around with hit for a few
+
+seconds and get something
+interesting out of it.
+
+So notice two inputs,
+two inputs, outputs.
+
+In your notes I've given you
+another template for the next
+
+set of scribbles I'm going to
+make here.
+
+So use the next set of
+templates on page three.
+
+What I'm going to do here is
+something very simple,
+
+set one output to zero and feed
+a voltage V1.
+
+So that's feed a voltage V1 and
+set the other output to zero.
+
+And let's say I get Y1 as an
+output.
+
+And in this case I set the
+first voltage to zero and feed a
+
+different voltage V2 on the
+second input.
+
+And let's say my output is Y2.
+This is just a particular
+
+application of the superposition
+principle I just outlined.
+
+Apply V1 set one output to
+zero.
+
+Apply V2 set the original
+output to zero.
+
+Then what I'm going to find is
+that the answer will simply look
+
+like this, just replace for As
+and Bs what I just did and we
+
+get V1 and zero here and we get
+zero and V2 here.
+
+And as my output I'm going to
+get exactly the sum Y1 plus Y2.
+
+This is simply a particular
+application of superposition
+
+where what I'm saying is the
+following.
+
+If you look at this circuit
+here effectively what have I
+
+done?
+Effectively what I've done is
+
+apply the voltage V1 on one
+input and a voltage V2 on the
+
+other input.
+V1 here.
+
+V2 here.
+And the output is Y1 plus Y2.
+
+What I'm saying is look
+backwards now.
+
+What I'm saying is that the
+whole components of the output
+
+Y1 plus Y2 could individually be
+derived in the following manner.
+
+I could get the component Y1 by
+simply applying one of the
+
+voltages and setting the other
+to zero.
+
+I can get the other component
+Y2 by setting yet another input
+
+to zero and applying the voltage
+V2 to get Y2.
+
+And sum then up and that's my
+answer.
+
+This will become a lot clearer
+with an example.
+
+Again, remember if I have a
+bunch of inputs applied to a
+
+circuit, V1, V2 and so on,
+and I get some output then what
+
+this is saying is that I can
+alternatively find out the
+
+answer by applying just one
+voltage, setting all the others
+
+to zero, measuring the output,
+apply a second voltage,
+
+set all inputs to zero,
+measure the output and sum of
+
+applesauce and blueberry sauce
+and there you get the answer.
+
+Let's do an example.
+And before we go into that I
+
+talked about setting voltage
+sources and current sources to
+
+zero.
+First of all,
+
+what does it mean to set a
+voltage source to zero?
+
+This is the same as this.
+Setting a voltage source to
+
+zero is simply replacing the
+voltage source with a short,
+
+and setting a current source to
+zero simply implies an open
+
+circuit.
+So when I say zero that source,
+
+if it's a voltage source short
+it, if it's a current source
+
+open it.
+
+I can take any two nodes in the
+world and measure the potential
+
+difference across them.
+So there may be some potential
+
+difference across these set by
+the circuit that I haven't shown
+
+you on this side.
+There might be some other
+
+circuit that is controlling the
+voltage of these two nodes.
+
+The same with the short.
+What's V going to be?
+
+But there is a V.
+It's zero.
+
+So that's method four,
+method of superposition.
+
+And this method says that the
+output of a circuit --
+
+Again, remember I'm focusing on
+linear circuits.
+
+Remember, I have this
+playground where LMD applies.
+
+And within that playground I'm
+playing in the south goal area.
+
+In the south goal area,
+in that subset of the
+
+playground circuits are linear.
+So in that part of the
+
+playground superposition applies
+because there circuits are
+
+linear.
+So the output of a circuit is
+
+determined by summing up the
+responses to each source acting
+
+alone.
+
+Now, in this statement here
+this source stands for
+
+independent source.
+I haven't talked about
+
+independent versus dependent
+sources.
+
+We'll talk about dependent
+sources a few weeks from today.
+
+And just so you don't get
+confused, for dependent sources
+
+you will be looking at Section
+3.3.3 of your course notes to
+
+see how superposition works with
+dependent sources.
+
+But remember we haven't covered
+dependent sources yet.
+
+We will be covering them about
+two weeks from now.
+
+So let's go back to our example
+and apply the method of
+
+superposition to an example.
+So the method says sum up the
+
+outputs of each of the
+sub-circuits where I'm applying
+
+one source acting alone.
+So let me just do this here.
+
+Let me start with the circuit.
+And let me start with shutting
+
+I off.
+So I have voltage V --
+
+I have R2.
+And I'm shutting I off.
+
+So I have replaced this with an
+open circuit.
+
+So I is zero.
+Let me call the node voltage eV
+
+to reflect that component of the
+node voltage that arises due to
+
+V acting alone.
+And you should look at this
+
+pattern here and very quickly be
+able to write the answer for
+
+patterns like this voltage,
+the two resistors.
+
+That's called a resistive
+divider.
+
+It will appear again and again
+and again.
+
+And eV is simply V times R2
+divided by R1 plus R2.
+
+That's still my ground node.
+So the voltage here is simply
+
+this voltage divided by the two
+resistors to give you the
+
+current multiplied by R2 to give
+you the voltage across this R.
+
+Remember this pattern.
+You apply voltage divider
+
+patterns probably more times
+than any other pattern that you
+
+might imagine.
+So that's with the V acting
+
+alone.
+Now, let me do I acting alone.
+
+So for I acting alone --
+
+And what I do this time around
+is replace this with a short,
+
+replace the voltage source to
+the short.
+
+And let me call this voltage eI
+for the component of the voltage
+
+due to the current I.
+And eI, in this case,
+
+is simply given by yet another
+pattern here,
+
+the current across a pair or
+resistors is simply the
+
+effective resistance multiplied
+by the current so it's i and the
+
+effective resistance is R1,
+R2 or R1 plus R2.
+
+That's eI.
+That's a component that node
+
+due to the current I.
+Now, so the method says that.
+
+Then take these components,
+sum them up and there you have
+
+the answer.
+So E is simply ev plus ei.
+
+The components of V and I
+acting alone,
+
+just simply V times R2 divided
+by R1 plus R2 plus R1,
+
+R2.
+There we go.
+
+Fortunately,
+the fates have been kind to us
+
+and the answer is the same as
+the answer we obtained with the
+
+node method.
+No surprise here.
+
+So this is actually an
+incredibly simple method.
+
+So you can take a very complex
+circuit.
+
+What have you really done here?
+You can take a very complex
+
+circuit and you can solve a very
+complex circuit by breaking it
+
+down into many simple individual
+sub problems.
+
+You will do this in EECS time
+and time and time again.
+
+Whether it's in software
+systems or hardware systems or
+
+what have you,
+you're often times building
+
+complicated systems.
+Remember doom on this side?
+
+And the way and when you put
+these things together,
+
+let's say a large software
+system, is you don't write the
+
+whole piece of software starting
+main and grunge down.
+
+You build a lot of little
+components and tie the
+
+components together.
+In the same manner here you
+
+take a big circuit and you find
+its behavior for each source
+
+acting alone.
+Lots of little inky dinky
+
+simple little circuits.
+And you will see examples in
+
+your homework where you're given
+a big circuit or because it set
+
+all the Is to zero and the other
+Vs to zero the whole circuit
+
+almost vanishes and all that
+you're left with is a little
+
+resistor or two.
+So this is the very,
+
+very powerful method.
+I'd like to do a little
+
+demonstration for you.
+And what I'm going to show you
+
+is the demo is a vat of water.
+Actually, I'll tell you what it
+
+is in a second.
+But assume it is salt water for
+
+now.
+I'll apply two voltages.
+
+In this case I'm going to apply
+a sinusoid.
+
+That's not very good.
+A sinusoid and a triangular
+
+wave.
+And what I'm going to do is
+
+measure the response at this
+site.
+
+Now, this is a vat of salt
+water.
+
+And I'm going to tell you it
+behaves like a linear system.
+
+If you view each little
+particle, or each little
+
+cubic-centimeter or whatever of
+water, it'll behave like little
+
+resistor.
+So this vat of salt water
+
+behaves like big distributed
+resistor in the following
+
+manner.
+
+And so on.
+This of this big mesh of little
+
+resistors, but it's all
+resistors.
+
+It's a linear circuit.
+So I'm going to apply two
+
+voltages, a triangular and a
+sinusoid, and we're going to
+
+observe the output.
+And what do you expect to see
+
+there?
+You will see the superposition
+
+of the two, which is you'll see
+a sinusoid.
+
+And then you'll see the jagged
+triangular thing articulating
+
+the sinusoid pattern.
+What I'm going to do right now,
+
+don't put any water yet.
+This is the vat of nothing
+
+right now.
+It's all empty.
+
+Can we show the screen on this
+side?
+
+The oscilloscope screen?
+
+OK.
+Oh, there you go.
+
+So this is the screen of the
+oscilloscope now.
+
+Notice that I have a sinusoid
+and I have a triangular wave and
+
+the output is zero.
+And the reason is there is
+
+nothing in this vat.
+It's empty.
+
+So previously when I taught
+this course I would get
+
+saltwater and pour saltwater.
+Then we discovered a much
+
+better source of water that
+conducted electricity like one
+
+real mean fluid.
+Cambridge water.
+
+It just works very pleasantly.
+It just conducts electricity
+
+like nothing at all.
+And I've been thinking of using
+
+Charles River water next time
+and see what happens,
+
+although there we'd probably
+get some biological organisms
+
+doing strange things at you.
+But go ahead.
+
+Our friendly demonstration
+expert, Lorenzo,
+
+will pour some water into the
+vat.
+
+And you should begin seeing the
+output being a superposition of
+
+the two.
+So as he pours,
+
+there you go,
+do you see that?
+
+So you do see the sinusoidal
+articulation and the jagged wave
+
+form.
+And just to have some more fun,
+
+what I can do is increase one
+of the voltages.
+
+And you'll see --
+
+Now you know what would have
+happened if I had used Charles
+
+River water.
+So my output keeps increasing
+
+as I increase the corresponding
+wave form.
+
+I could do this,
+this is fun.
+
+So let me pause there and go
+onto the next topic.
+
+So that little demonstration
+showed you that even something
+
+as simple as this physical
+entity vat of water behaves like
+
+a linear system,
+and we can model that linear
+
+system as a set of resistors.
+Unbeknownst to you,
+
+right now, in the past ten
+seconds I introduced a new
+
+concept.
+It's called subliminal
+
+advertising.
+So one of the things we do in
+
+EE a lot is model real systems.
+So often times if I wanted to
+
+look at the behavior of salt,
+behavior of a vat of water,
+
+I can model it as a set of
+resistors for certain kinds of
+
+activities.
+Just hold that thought for some
+
+time later in your careers.
+All right.
+
+That's method four,
+the superposition method.
+
+Remember, it is methods like
+this that will make your life
+
+really, really,
+really easy.
+
+If you find that you are having
+to do a lot of grunging homework
+
+or something,
+just step back and think
+
+superposition,
+think Thevenin or think
+
+composition rule.
+There must be a simpler way
+
+usually.
+Let's do the next method.
+
+This is called the Thevenin
+method.
+
+To derive this method let me
+start by applying superposition
+
+to some circuit.
+So let's say I have some
+
+arbitrary network N.
+Assume it's a linear network
+
+and the network has a whole
+bunch of goodies in it.
+
+It has a bunch of resistors,
+it has a bunch of voltage
+
+sources, and it has a bunch of
+current sources.
+
+Many current sources.
+Many voltage sources.
+
+Many resistors.
+Some jumbled voltage sources,
+
+current sources and resistors.
+And I look at two nodes in this
+
+network.
+Here are two nodes in the
+
+network, two points in the
+network were elements connect.
+
+I'm looking at those two nodes
+and all I want to do is the
+
+following.
+I want to figure out if I take
+
+a rinky-dinky little current
+source and apply it there,
+
+all I want to figure out is
+what is V and what is I.
+
+There is this mongo box out
+here, a black box of resistors,
+
+voltage source and current
+sources, too many to count.
+
+I pick two nodes,
+apply a current source,
+
+and all I care about is what is
+the voltage that I will measure
+
+by applying it here.
+Notice the current here will be
+
+I because the current here is I.
+And I apply it here.
+
+I want to measure what the
+voltage is.
+
+Now, with the insight you've
+obtained from superposition,
+
+you should be able to jump up
+and state the form of the
+
+answer.
+So by superposition we know the
+
+following.
+We know that the effect of the
+
+circuit will be the same as the
+sum of components being added
+
+up.
+Sum of component,
+
+sum of component,
+a bunch of components added up.
+
+Each component will be the
+response of one source acting
+
+alone.
+So if I can figure out the
+
+effect of one source acting
+alone and put that down here,
+
+and do the same thing for all
+the sources, that's what I will
+
+get.
+So for the source Vm it's a
+
+linear circuit.
+So I know that my answer is
+
+going to be, in the final answer
+is going to be a Vm term and
+
+it's going to be multiplied by
+some alpha M term.
+
+I know that.
+It's a linear circuit so I know
+
+that the answer shall have a
+term Vm multiplied by some
+
+constant.
+Simple, I know that.
+
+Similarly, the same is true
+for, oh, this is the term Vm.
+
+And what I can do is I can
+measure just this effect by
+
+setting all the other sources to
+zero.
+
+So I can set all the other
+current sources to zero and all
+
+voltage sources,
+except for this one,
+
+and I can get that answer.
+So, similarly,
+
+for every voltage source I am
+going to get a term.
+
+So for every single voltage
+source, M1, M2,
+
+M3 and so on I'm going to get
+such a term and they're all
+
+going to sum up.
+Similarly, I'm going to get a
+
+term for In.
+And I know there will be an In
+
+term, and I know it's going to
+be some constant beta
+
+multiplying In.
+In this example of ours here,
+
+in this example,
+remember alpha was this and
+
+beta was this constant here.
+There's some constant beta,
+
+some constant alpha.
+And because I have a whole
+
+bunch of current sources there's
+going to be such a term for each
+
+one of them.
+And each one of these terms,
+
+Vm, In will be the voltage I
+would see here if I set all the
+
+other Vms to zero and I set all
+the other current sources,
+
+except for that one to zero.
+What am I missing?
+
+Is that it?
+The response here,
+
+V here.
+Am I missing anything here?
+
+Is that it?
+Now, don't all yell at once.
+
+What am I missing?
+Current source i,
+
+exactly.
+So if I have a current source i
+
+then there's an effect of this
+current as well.
+
+And so I write down i there,
+too.
+
+It's going to be some constant
+multiplying I.
+
+And that constant is going to
+look like a resistor,
+
+right, because this circuit
+contains current sources,
+
+voltage sources and resistors.
+If I've shorted all my voltage
+
+sources and opened all my
+current sources,
+
+what's left in here?
+Just a whole caboodle full of
+
+Rs.
+It's just going to look like
+
+some resistance R.
+And that's what I get here.
+
+So this is what V is going to
+look like and that's a form.
+
+So let's take a look at these
+components.
+
+Let's focus on the easy part
+first.
+
+What does this look like?
+This component looks like an I,
+
+it looks like a current and has
+some resistance.
+
+What is that resistance given
+by?
+
+Supposing I gave you this
+network and this currency source
+
+and I asked you tell me R.
+How would you measure R?
+
+What you would do is open all
+the current sources,
+
+short all the voltage sources,
+put a ohmmeter in there and
+
+measure the resistance R.
+That's R.
+
+OK, so we understand this term.
+What about this term here?
+
+Can someone tell me the units
+of this term here,
+
+this big thing here?
+Voltage.
+
+This is a voltage.
+This is a voltage.
+
+iR is a voltage.
+So this does behave like a
+
+voltage.
+And it behaves like some
+
+voltage V.
+So notice that as far as this
+
+current I is concerned the rest
+of the universe looks like a
+
+resistor and a voltage source
+behaving in some manner.
+
+And let me just call it Vth for
+now, and you'll know why in a
+
+second.
+
+The voltage has a form,
+some voltage plus Ri.
+
+So, in other words,
+as far as this I is concerned
+
+this whole network here N full
+of all the nice stuff is
+
+indistinguishable to this I
+here.
+
+So my I is sitting out there
+injecting a current into two
+
+nodes.
+If I am i, I'm looking at this,
+
+this network looks no different
+than a voltage source in series
+
+with the resistor R.
+Notice that the equation for
+
+this simple circuit is this,
+so I is given by V minus Vth
+
+divided by R.
+Just remember.
+
+It's a circuit.
+In other words,
+
+Agarwal sitting here cannot
+tell the difference if I'm
+
+measuring the voltage here
+between a circuit that looks
+
+like a Vth in series to the
+resistor or this huge mess of
+
+voltage sources and current
+sources and so on.
+
+Now, we will talk about Vth and
+R.
+
+R is called the resistance of
+the network as seen from the
+
+port with all the sources shut
+off.
+
+And similarly Vth,
+what is Vth?
+
+Vth is the open circuit
+voltage.
+
+In other words,
+if I apply the voltage here
+
+this is the response of all the
+current sources and all the
+
+voltage sources acting together.
+So it's as if I took this out
+
+and simply measured my V here as
+if I didn't exist,
+
+correct?
+Because this is the component
+
+of i.
+So if I opened i and measured
+
+V, I would get that big term on
+the left-hand side.
+
+That's my Vth.
+So that inspires the next
+
+method called the Thevenin
+method.
+
+In this method what I'm going
+to do is take some circuit,
+
+I'm on Page 9,
+with a mess of stuff.
+
+It's a big mess of stuff.
+And if I care to look at its
+
+impact on something else that I
+add from the outside then as far
+
+as the outside world is
+concerned this is
+
+indistinguishable from a circuit
+that looks like this.
+
+So what I can do is if I want
+to figure out what's happening
+
+here then, for the purpose of my
+analysis, this simple network
+
+here with R and Vth becomes a
+surrogate for this entire mess.
+
+So for the purpose of finding
+out the behavior at this point,
+
+I can take this huge mess and
+replace it with its Thevenin
+
+surrogate or Thevenin
+equivalent.
+
+This is called the Thevenin
+equivalent of this big network.
+
+Let me do an example that will
+make the method completely
+
+clear.
+Again, remember in EECS,
+
+most of our lives are about how
+can we make things so simple as
+
+being able to be analyzed by
+inspection?
+
+And so this is a method that
+takes you further down that
+
+path.
+So let me use the same circuit
+
+that I've been using before,
+my voltage V,
+
+R1, R2.
+This is an R.
+
+I'm 55 minutes fast so we have
+another three or four minutes.
+
+So this is my circuit.
+And let's say all I care about
+
+is finding out i1.
+That's all I care about.
+
+And what I'm going to do is I'm
+going to box this up and see if
+
+I can replace that with its
+Thevenin equivalent.
+
+So I'm going to box that up.
+
+What I'm saying is that I'm
+going to box it up and replace
+
+it with this Thevenin
+equivalent.
+
+I don't know what Vth and R are
+at this point.
+
+I'm just calling it Rth for
+fun.
+
+I don't know what these two
+values are, but if I knew what
+
+these two values were I can
+determine I really trivially as
+
+follows.
+I can get i1 as simply V minus
+
+Vth divided by R1 plus Rth.
+So if I knew Vth and Rth,
+
+I can write down i1 by
+inspection in that manner.
+
+So next, finally,
+how do I get Vth and Rth?
+
+You get Rth by looking at this
+network and shutting off all the
+
+voltage sources and measuring
+the resistance there.
+
+So I short my voltage source,
+that's R1.
+
+Oops, wrong way.
+I need to look this way.
+
+So looking this way,
+that's what I get.
+
+So what's Rth?
+Rth is simply R2.
+
+So I have opened my current
+source.
+
+Similarly, for Vth,
+remember all I want to do is
+
+look at the two nodes,
+step back, put a voltmeter
+
+there, measure the voltage,
+that's my open circuit voltage.
+
+So the way I do it is I take
+the circuit and simply measure
+
+the voltage there.
+That's R2.
+
+That's my current capital I.
+And I simply want to measure
+
+the open circuit voltage here,
+which is what?
+
+Just simply if I stand back and
+I kind of gingerly measure the
+
+voltage here without disturbing
+anything, I simply get IR2.
+
+So Vth is IR2 and Rth is R2 and
+here is the formula for the
+
+current in this branch when I
+apply a voltage source and a
+
+resistor R1 to this little
+circuit here.
+
+OK, let's pause and let me
+summarize this in about ten
+
+seconds.
+I had this circuit here.
+
+I wanted to find out i1.
+So what I said I'd do is take
+
+this complicated mess,
+well, it's not a complicated
+
+mess but assume it is,
+and replace with it a
+
+resistance Rth got by turning
+off all the sources.
+
+And the voltage in series,
+Vth, which I get simply by
+
+pulling this thing out,
+taking my input,
+
+this part out and simply
+measuring the open circuit
+
+voltage out there,
+Vth.
+
+And then I replaced the whole
+network with this new network
+
+that they call the Thevenin
+network, and voila,
+
+I get the answer in a second.
\ No newline at end of file
diff --git a/SFXxjejtsCI.txt b/SFXxjejtsCI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5001d7a0043a0697bb443dc61de7ca43628c141d
--- /dev/null
+++ b/SFXxjejtsCI.txt
@@ -0,0 +1,12587 @@
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+
+ align:start position:0%
+who has a a well-regarded Blog kino.com
+ 
+
+ align:start position:0%
+who has a a well-regarded Blog kino.com
+uh he's a graduate of uh mit's media lab
+
+ align:start position:0%
+uh he's a graduate of uh mit's media lab
+ 
+
+ align:start position:0%
+uh he's a graduate of uh mit's media lab
+and currently an instructor at Mass art
+
+ align:start position:0%
+and currently an instructor at Mass art
+ 
+
+ align:start position:0%
+and currently an instructor at Mass art
+and he's going to take us through some
+
+ align:start position:0%
+and he's going to take us through some
+ 
+
+ align:start position:0%
+and he's going to take us through some
+of the basics of lighting uh and we're
+
+ align:start position:0%
+of the basics of lighting uh and we're
+ 
+
+ align:start position:0%
+of the basics of lighting uh and we're
+then going to do a demonstration of
+
+ align:start position:0%
+then going to do a demonstration of
+ 
+
+ align:start position:0%
+then going to do a demonstration of
+basic interview three-point lighting
+
+ align:start position:0%
+basic interview three-point lighting
+ 
+
+ align:start position:0%
+basic interview three-point lighting
+which should be a lot of fun so take it
+
+ align:start position:0%
+which should be a lot of fun so take it
+ 
+
+ align:start position:0%
+which should be a lot of fun so take it
+away David well glad to be here thanks
+
+ align:start position:0%
+away David well glad to be here thanks
+ 
+
+ align:start position:0%
+away David well glad to be here thanks
+Chris so as Chris said we're going to
+
+ align:start position:0%
+Chris so as Chris said we're going to
+ 
+
+ align:start position:0%
+Chris so as Chris said we're going to
+talk about basic lighting and we're
+
+ align:start position:0%
+talk about basic lighting and we're
+ 
+
+ align:start position:0%
+talk about basic lighting and we're
+going to use um a simple straightforward
+
+ align:start position:0%
+going to use um a simple straightforward
+ 
+
+ align:start position:0%
+going to use um a simple straightforward
+interview uh as the subject uh of our
+
+ align:start position:0%
+interview uh as the subject uh of our
+ 
+
+ align:start position:0%
+interview uh as the subject uh of our
+lighting discussion um today of course
+
+ align:start position:0%
+lighting discussion um today of course
+ 
+
+ align:start position:0%
+lighting discussion um today of course
+there's a lot of things that we can
+
+ align:start position:0%
+there's a lot of things that we can
+ 
+
+ align:start position:0%
+there's a lot of things that we can
+light uh but basically interview
+
+ align:start position:0%
+light uh but basically interview
+ 
+
+ align:start position:0%
+light uh but basically interview
+lighting um will be will be our
+
+ align:start position:0%
+lighting um will be will be our
+ 
+
+ align:start position:0%
+lighting um will be will be our
+Focus um just just since we're at MIT we
+
+ align:start position:0%
+Focus um just just since we're at MIT we
+ 
+
+ align:start position:0%
+Focus um just just since we're at MIT we
+need to talk a little bit about what
+
+ align:start position:0%
+need to talk a little bit about what
+ 
+
+ align:start position:0%
+need to talk a little bit about what
+light is um it's a tiny sliver of the
+
+ align:start position:0%
+light is um it's a tiny sliver of the
+ 
+
+ align:start position:0%
+light is um it's a tiny sliver of the
+electromagnetic spectrum that our eyes
+
+ align:start position:0%
+electromagnetic spectrum that our eyes
+ 
+
+ align:start position:0%
+electromagnetic spectrum that our eyes
+are sensitive to um as the wavelengths
+
+ align:start position:0%
+are sensitive to um as the wavelengths
+ 
+
+ align:start position:0%
+are sensitive to um as the wavelengths
+get shorter you end up with things like
+
+ align:start position:0%
+get shorter you end up with things like
+ 
+
+ align:start position:0%
+get shorter you end up with things like
+X-rays and gamma rays and um and as the
+
+ align:start position:0%
+X-rays and gamma rays and um and as the
+ 
+
+ align:start position:0%
+X-rays and gamma rays and um and as the
+wavelengths get longer we end up with
+
+ align:start position:0%
+wavelengths get longer we end up with
+ 
+
+ align:start position:0%
+wavelengths get longer we end up with
+radio waves uh just like this wireless
+
+ align:start position:0%
+radio waves uh just like this wireless
+ 
+
+ align:start position:0%
+radio waves uh just like this wireless
+mic um going on here uh but this tiny
+
+ align:start position:0%
+mic um going on here uh but this tiny
+ 
+
+ align:start position:0%
+mic um going on here uh but this tiny
+tiny tiny sliver of the electromagnetic
+
+ align:start position:0%
+tiny tiny sliver of the electromagnetic
+ 
+
+ align:start position:0%
+tiny tiny sliver of the electromagnetic
+spectrum is what our eyes um happen to
+
+ align:start position:0%
+spectrum is what our eyes um happen to
+ 
+
+ align:start position:0%
+spectrum is what our eyes um happen to
+be sensitive to and this is the medium
+
+ align:start position:0%
+be sensitive to and this is the medium
+ 
+
+ align:start position:0%
+be sensitive to and this is the medium
+that we are working with these are our
+
+ align:start position:0%
+that we are working with these are our
+ 
+
+ align:start position:0%
+that we are working with these are our
+materials uh that we work with uh in
+
+ align:start position:0%
+materials uh that we work with uh in
+ 
+
+ align:start position:0%
+materials uh that we work with uh in
+film and video um and of course you know
+
+ align:start position:0%
+film and video um and of course you know
+ 
+
+ align:start position:0%
+film and video um and of course you know
+there's that classic experiment that um
+
+ align:start position:0%
+there's that classic experiment that um
+ 
+
+ align:start position:0%
+there's that classic experiment that um
+Newton did in his I guess it was his
+
+ align:start position:0%
+Newton did in his I guess it was his
+ 
+
+ align:start position:0%
+Newton did in his I guess it was his
+grandmother's barn or something um not
+
+ align:start position:0%
+grandmother's barn or something um not
+ 
+
+ align:start position:0%
+grandmother's barn or something um not
+only did he it was well known at his
+
+ align:start position:0%
+only did he it was well known at his
+ 
+
+ align:start position:0%
+only did he it was well known at his
+time you know that light you could um
+
+ align:start position:0%
+time you know that light you could um
+ 
+
+ align:start position:0%
+time you know that light you could um
+break white light into the constituency
+
+ align:start position:0%
+break white light into the constituency
+ 
+
+ align:start position:0%
+break white light into the constituency
+of the various colors uh of the rainbow
+
+ align:start position:0%
+of the various colors uh of the rainbow
+ 
+
+ align:start position:0%
+of the various colors uh of the rainbow
+uh but he also showed that once you
+
+ align:start position:0%
+uh but he also showed that once you
+ 
+
+ align:start position:0%
+uh but he also showed that once you
+broke it down to those colors you
+
+ align:start position:0%
+broke it down to those colors you
+ 
+
+ align:start position:0%
+broke it down to those colors you
+couldn't break it down any further and
+
+ align:start position:0%
+couldn't break it down any further and
+ 
+
+ align:start position:0%
+couldn't break it down any further and
+that with a second prism you could
+
+ align:start position:0%
+that with a second prism you could
+ 
+
+ align:start position:0%
+that with a second prism you could
+recombine that light back into white
+
+ align:start position:0%
+recombine that light back into white
+ 
+
+ align:start position:0%
+recombine that light back into white
+light so it turns out that working with
+
+ align:start position:0%
+light so it turns out that working with
+ 
+
+ align:start position:0%
+light so it turns out that working with
+any combination of red green and blue
+
+ align:start position:0%
+any combination of red green and blue
+ 
+
+ align:start position:0%
+any combination of red green and blue
+light we can create any of the colors
+
+ align:start position:0%
+light we can create any of the colors
+ 
+
+ align:start position:0%
+light we can create any of the colors
+that we're sensitive to and so
+
+ align:start position:0%
+that we're sensitive to and so
+ 
+
+ align:start position:0%
+that we're sensitive to and so
+interestingly enough uh most of our
+
+ align:start position:0%
+interestingly enough uh most of our
+ 
+
+ align:start position:0%
+interestingly enough uh most of our
+Imaging systems today uh basically work
+
+ align:start position:0%
+Imaging systems today uh basically work
+ 
+
+ align:start position:0%
+Imaging systems today uh basically work
+with red green and blue uh receptors
+
+ align:start position:0%
+with red green and blue uh receptors
+ 
+
+ align:start position:0%
+with red green and blue uh receptors
+which we uh will talk about why red
+
+ align:start position:0%
+which we uh will talk about why red
+ 
+
+ align:start position:0%
+which we uh will talk about why red
+green and blue happens to be sort of the
+
+ align:start position:0%
+green and blue happens to be sort of the
+ 
+
+ align:start position:0%
+green and blue happens to be sort of the
+star colors from which all other colors
+
+ align:start position:0%
+star colors from which all other colors
+ 
+
+ align:start position:0%
+star colors from which all other colors
+uh can be derived and it turns out that
+
+ align:start position:0%
+uh can be derived and it turns out that
+ 
+
+ align:start position:0%
+uh can be derived and it turns out that
+our eyes have receptors sensitive in the
+
+ align:start position:0%
+our eyes have receptors sensitive in the
+ 
+
+ align:start position:0%
+our eyes have receptors sensitive in the
+blue range the green range and the uh
+
+ align:start position:0%
+blue range the green range and the uh
+ 
+
+ align:start position:0%
+blue range the green range and the uh
+red range and we are most sensitive to
+
+ align:start position:0%
+red range and we are most sensitive to
+ 
+
+ align:start position:0%
+red range and we are most sensitive to
+those in the green range perhaps our
+
+ align:start position:0%
+those in the green range perhaps our
+ 
+
+ align:start position:0%
+those in the green range perhaps our
+ancestors um who could see green were
+
+ align:start position:0%
+ancestors um who could see green were
+ 
+
+ align:start position:0%
+ancestors um who could see green were
+more successful uh than our ancestors
+
+ align:start position:0%
+more successful uh than our ancestors
+ 
+
+ align:start position:0%
+more successful uh than our ancestors
+who were primarily sensitive to other
+
+ align:start position:0%
+who were primarily sensitive to other
+ 
+
+ align:start position:0%
+who were primarily sensitive to other
+uh uh frequencies of light who knows
+
+ align:start position:0%
+uh uh frequencies of light who knows
+ 
+
+ align:start position:0%
+uh uh frequencies of light who knows
+about that but enough technical stuff uh
+
+ align:start position:0%
+about that but enough technical stuff uh
+ 
+
+ align:start position:0%
+about that but enough technical stuff uh
+when we talk about light creatively
+
+ align:start position:0%
+when we talk about light creatively
+ 
+
+ align:start position:0%
+when we talk about light creatively
+we're not thinking about wavelengths and
+
+ align:start position:0%
+we're not thinking about wavelengths and
+ 
+
+ align:start position:0%
+we're not thinking about wavelengths and
+and and uh the individual colors that
+
+ align:start position:0%
+and and uh the individual colors that
+ 
+
+ align:start position:0%
+and and uh the individual colors that
+much but we're thinking about certain
+
+ align:start position:0%
+much but we're thinking about certain
+ 
+
+ align:start position:0%
+much but we're thinking about certain
+characteristics um we often talk about
+
+ align:start position:0%
+characteristics um we often talk about
+ 
+
+ align:start position:0%
+characteristics um we often talk about
+intensity how bright is the light and it
+
+ align:start position:0%
+intensity how bright is the light and it
+ 
+
+ align:start position:0%
+intensity how bright is the light and it
+turns out that since most um light
+
+ align:start position:0%
+turns out that since most um light
+ 
+
+ align:start position:0%
+turns out that since most um light
+sources radiate in all directions
+
+ align:start position:0%
+sources radiate in all directions
+ 
+
+ align:start position:0%
+sources radiate in all directions
+there's very very rapid falloff of light
+
+ align:start position:0%
+there's very very rapid falloff of light
+ 
+
+ align:start position:0%
+there's very very rapid falloff of light
+so we call that the inverse Square law
+
+ align:start position:0%
+so we call that the inverse Square law
+ 
+
+ align:start position:0%
+so we call that the inverse Square law
+so if you're by a window and you have a
+
+ align:start position:0%
+so if you're by a window and you have a
+ 
+
+ align:start position:0%
+so if you're by a window and you have a
+really really nice exposure walking away
+
+ align:start position:0%
+really really nice exposure walking away
+ 
+
+ align:start position:0%
+really really nice exposure walking away
+from the window just a little bit is
+
+ align:start position:0%
+from the window just a little bit is
+ 
+
+ align:start position:0%
+from the window just a little bit is
+enough to end up in in in darkness
+
+ align:start position:0%
+enough to end up in in in darkness
+ 
+
+ align:start position:0%
+enough to end up in in in darkness
+because if you double the distance
+
+ align:start position:0%
+because if you double the distance
+ 
+
+ align:start position:0%
+because if you double the distance
+between the light and the subject you
+
+ align:start position:0%
+between the light and the subject you
+ 
+
+ align:start position:0%
+between the light and the subject you
+only have 1/4 of the intensity as before
+
+ align:start position:0%
+only have 1/4 of the intensity as before
+ 
+
+ align:start position:0%
+only have 1/4 of the intensity as before
+so you're always working against the
+
+ align:start position:0%
+so you're always working against the
+ 
+
+ align:start position:0%
+so you're always working against the
+inverse Square law um in terms of the
+
+ align:start position:0%
+inverse Square law um in terms of the
+ 
+
+ align:start position:0%
+inverse Square law um in terms of the
+intensity so if you need your light to
+
+ align:start position:0%
+intensity so if you need your light to
+ 
+
+ align:start position:0%
+intensity so if you need your light to
+be brighter you can always uh move it
+
+ align:start position:0%
+be brighter you can always uh move it
+ 
+
+ align:start position:0%
+be brighter you can always uh move it
+closer to your subject or get a bigger
+
+ align:start position:0%
+closer to your subject or get a bigger
+ 
+
+ align:start position:0%
+closer to your subject or get a bigger
+light we also talk about the quality of
+
+ align:start position:0%
+light we also talk about the quality of
+ 
+
+ align:start position:0%
+light we also talk about the quality of
+light whether it's hard or soft hard
+
+ align:start position:0%
+light whether it's hard or soft hard
+ 
+
+ align:start position:0%
+light whether it's hard or soft hard
+light has bold Shadows crisp textures
+
+ align:start position:0%
+light has bold Shadows crisp textures
+ 
+
+ align:start position:0%
+light has bold Shadows crisp textures
+we'll look at an example in just a
+
+ align:start position:0%
+we'll look at an example in just a
+ 
+
+ align:start position:0%
+we'll look at an example in just a
+moment and soft light has gentle
+
+ align:start position:0%
+moment and soft light has gentle
+ 
+
+ align:start position:0%
+moment and soft light has gentle
+contrast it's more diffused typically
+
+ align:start position:0%
+contrast it's more diffused typically
+ 
+
+ align:start position:0%
+contrast it's more diffused typically
+very soft or or no Shadows we often talk
+
+ align:start position:0%
+very soft or or no Shadows we often talk
+ 
+
+ align:start position:0%
+very soft or or no Shadows we often talk
+about the direction of light where is it
+
+ align:start position:0%
+about the direction of light where is it
+ 
+
+ align:start position:0%
+about the direction of light where is it
+coming from it refers to the path of the
+
+ align:start position:0%
+coming from it refers to the path of the
+ 
+
+ align:start position:0%
+coming from it refers to the path of the
+light from the source of the light to
+
+ align:start position:0%
+light from the source of the light to
+ 
+
+ align:start position:0%
+light from the source of the light to
+our subject is it coming from the front
+
+ align:start position:0%
+our subject is it coming from the front
+ 
+
+ align:start position:0%
+our subject is it coming from the front
+the side the back under light top light
+
+ align:start position:0%
+the side the back under light top light
+ 
+
+ align:start position:0%
+the side the back under light top light
+and we use these terms to describe where
+
+ align:start position:0%
+and we use these terms to describe where
+ 
+
+ align:start position:0%
+and we use these terms to describe where
+the light uh comes from and of course
+
+ align:start position:0%
+the light uh comes from and of course
+ 
+
+ align:start position:0%
+the light uh comes from and of course
+color like we just saw in the previous
+
+ align:start position:0%
+color like we just saw in the previous
+ 
+
+ align:start position:0%
+color like we just saw in the previous
+slide it's the relative mix of
+
+ align:start position:0%
+slide it's the relative mix of
+ 
+
+ align:start position:0%
+slide it's the relative mix of
+wavelengths and color is often motivated
+
+ align:start position:0%
+wavelengths and color is often motivated
+ 
+
+ align:start position:0%
+wavelengths and color is often motivated
+by the light source so if we want to
+
+ align:start position:0%
+by the light source so if we want to
+ 
+
+ align:start position:0%
+by the light source so if we want to
+depict a sunny day we have sort of
+
+ align:start position:0%
+depict a sunny day we have sort of
+ 
+
+ align:start position:0%
+depict a sunny day we have sort of
+we use yellows and and very very light
+
+ align:start position:0%
+we use yellows and and very very light
+ 
+
+ align:start position:0%
+we use yellows and and very very light
+blues and and white uh it can establish
+
+ align:start position:0%
+blues and and white uh it can establish
+ 
+
+ align:start position:0%
+blues and and white uh it can establish
+mood so if we're going to you know
+
+ align:start position:0%
+mood so if we're going to you know
+ 
+
+ align:start position:0%
+mood so if we're going to you know
+typically period pieces that take places
+
+ align:start position:0%
+typically period pieces that take places
+ 
+
+ align:start position:0%
+typically period pieces that take places
+during the Renaissance happen to have
+
+ align:start position:0%
+during the Renaissance happen to have
+ 
+
+ align:start position:0%
+during the Renaissance happen to have
+sort of a kind of an orange glow about
+
+ align:start position:0%
+sort of a kind of an orange glow about
+ 
+
+ align:start position:0%
+sort of a kind of an orange glow about
+them I just just last night I saw goya's
+
+ align:start position:0%
+them I just just last night I saw goya's
+ 
+
+ align:start position:0%
+them I just just last night I saw goya's
+ghost and was reminded of of how we seem
+
+ align:start position:0%
+ghost and was reminded of of how we seem
+ 
+
+ align:start position:0%
+ghost and was reminded of of how we seem
+to depict certain time periods with
+
+ align:start position:0%
+to depict certain time periods with
+ 
+
+ align:start position:0%
+to depict certain time periods with
+certain color pets and perhaps since the
+
+ align:start position:0%
+certain color pets and perhaps since the
+ 
+
+ align:start position:0%
+certain color pets and perhaps since the
+primary light source uh during the
+
+ align:start position:0%
+primary light source uh during the
+ 
+
+ align:start position:0%
+primary light source uh during the
+Renaissance was candles uh instead of uh
+
+ align:start position:0%
+Renaissance was candles uh instead of uh
+ 
+
+ align:start position:0%
+Renaissance was candles uh instead of uh
+HMI daylight balanced lights like we
+
+ align:start position:0%
+HMI daylight balanced lights like we
+ 
+
+ align:start position:0%
+HMI daylight balanced lights like we
+have on film sets today it it makes a
+
+ align:start position:0%
+have on film sets today it it makes a
+ 
+
+ align:start position:0%
+have on film sets today it it makes a
+lot of a lot of sense that you know in
+
+ align:start position:0%
+lot of a lot of sense that you know in
+ 
+
+ align:start position:0%
+lot of a lot of sense that you know in
+the evenings the world was predominantly
+
+ align:start position:0%
+the evenings the world was predominantly
+ 
+
+ align:start position:0%
+the evenings the world was predominantly
+sort of this golden golden yellow just
+
+ align:start position:0%
+sort of this golden golden yellow just
+ 
+
+ align:start position:0%
+sort of this golden golden yellow just
+want to add one quick thing about that
+
+ align:start position:0%
+want to add one quick thing about that
+ 
+
+ align:start position:0%
+want to add one quick thing about that
+as a documentary filmmaker uh who's
+
+ align:start position:0%
+as a documentary filmmaker uh who's
+ 
+
+ align:start position:0%
+as a documentary filmmaker uh who's
+often working in available light just
+
+ align:start position:0%
+often working in available light just
+ 
+
+ align:start position:0%
+often working in available light just
+remember that those uh qualities that
+
+ align:start position:0%
+remember that those uh qualities that
+ 
+
+ align:start position:0%
+remember that those uh qualities that
+David just talked about apply to
+
+ align:start position:0%
+David just talked about apply to
+ 
+
+ align:start position:0%
+David just talked about apply to
+available light just as much as to
+
+ align:start position:0%
+available light just as much as to
+ 
+
+ align:start position:0%
+available light just as much as to
+lights that you might set up so if you
+
+ align:start position:0%
+lights that you might set up so if you
+ 
+
+ align:start position:0%
+lights that you might set up so if you
+think about the lighting in this room
+
+ align:start position:0%
+think about the lighting in this room
+ 
+
+ align:start position:0%
+think about the lighting in this room
+you know it it's really important to get
+
+ align:start position:0%
+you know it it's really important to get
+ 
+
+ align:start position:0%
+you know it it's really important to get
+start getting getting sensitive to those
+
+ align:start position:0%
+start getting getting sensitive to those
+ 
+
+ align:start position:0%
+start getting getting sensitive to those
+exact same situations where's the light
+
+ align:start position:0%
+exact same situations where's the light
+ 
+
+ align:start position:0%
+exact same situations where's the light
+coming from it's coming from overhead
+
+ align:start position:0%
+coming from it's coming from overhead
+ 
+
+ align:start position:0%
+coming from it's coming from overhead
+lights so what does that mean for the
+
+ align:start position:0%
+lights so what does that mean for the
+ 
+
+ align:start position:0%
+lights so what does that mean for the
+way things look what are the colors of
+
+ align:start position:0%
+way things look what are the colors of
+ 
+
+ align:start position:0%
+way things look what are the colors of
+those lights well they're were
+
+ align:start position:0%
+those lights well they're were
+ 
+
+ align:start position:0%
+those lights well they're were
+fluorescent but if you actually look at
+
+ align:start position:0%
+fluorescent but if you actually look at
+ 
+
+ align:start position:0%
+fluorescent but if you actually look at
+the bulbs you see that there are they
+
+ align:start position:0%
+the bulbs you see that there are they
+ 
+
+ align:start position:0%
+the bulbs you see that there are they
+don't even match from from fixture to
+
+ align:start position:0%
+don't even match from from fixture to
+ 
+
+ align:start position:0%
+don't even match from from fixture to
+fix yeah some of these over here are
+
+ align:start position:0%
+fix yeah some of these over here are
+ 
+
+ align:start position:0%
+fix yeah some of these over here are
+yellow and some of these over here are
+
+ align:start position:0%
+yellow and some of these over here are
+ 
+
+ align:start position:0%
+yellow and some of these over here are
+more towards the white white yeah so so
+
+ align:start position:0%
+more towards the white white yeah so so
+ 
+
+ align:start position:0%
+more towards the white white yeah so so
+those are the kinds of things that you
+
+ align:start position:0%
+those are the kinds of things that you
+ 
+
+ align:start position:0%
+those are the kinds of things that you
+start to become sensitive to uh even as
+
+ align:start position:0%
+start to become sensitive to uh even as
+ 
+
+ align:start position:0%
+start to become sensitive to uh even as
+a documentary filmmaker working without
+
+ align:start position:0%
+a documentary filmmaker working without
+ 
+
+ align:start position:0%
+a documentary filmmaker working without
+lights and all of those things whe the
+
+ align:start position:0%
+lights and all of those things whe the
+ 
+
+ align:start position:0%
+lights and all of those things whe the
+heart
+
+ align:start position:0%
+heart
+ 
+
+ align:start position:0%
+heart
+theity of the theity of the light the
+
+ align:start position:0%
+theity of the theity of the light the
+ 
+
+ align:start position:0%
+theity of the theity of the light the
+dire the color are assessments that you
+
+ align:start position:0%
+dire the color are assessments that you
+ 
+
+ align:start position:0%
+dire the color are assessments that you
+need to make even in situations where
+
+ align:start position:0%
+need to make even in situations where
+ 
+
+ align:start position:0%
+need to make even in situations where
+you're not actually controlling the
+
+ align:start position:0%
+you're not actually controlling the
+ 
+
+ align:start position:0%
+you're not actually controlling the
+light with artificial light producing
+
+ align:start position:0%
+light with artificial light producing
+ 
+
+ align:start position:0%
+light with artificial light producing
+instruments like we're going to work
+
+ align:start position:0%
+instruments like we're going to work
+ 
+
+ align:start position:0%
+instruments like we're going to work
+with later yeah I mean even when I go to
+
+ align:start position:0%
+with later yeah I mean even when I go to
+ 
+
+ align:start position:0%
+with later yeah I mean even when I go to
+do an interview and I'm doing sort of a
+
+ align:start position:0%
+do an interview and I'm doing sort of a
+ 
+
+ align:start position:0%
+do an interview and I'm doing sort of a
+prein and talking to the subject I
+
+ align:start position:0%
+prein and talking to the subject I
+ 
+
+ align:start position:0%
+prein and talking to the subject I
+always say can we talk while we're
+
+ align:start position:0%
+always say can we talk while we're
+ 
+
+ align:start position:0%
+always say can we talk while we're
+walking around because I want to sort of
+
+ align:start position:0%
+walking around because I want to sort of
+ 
+
+ align:start position:0%
+walking around because I want to sort of
+look at the light in the environment and
+
+ align:start position:0%
+look at the light in the environment and
+ 
+
+ align:start position:0%
+look at the light in the environment and
+try to start with something natural
+
+ align:start position:0%
+try to start with something natural
+ 
+
+ align:start position:0%
+try to start with something natural
+exactly I mean just this weekend we were
+
+ align:start position:0%
+exactly I mean just this weekend we were
+ 
+
+ align:start position:0%
+exactly I mean just this weekend we were
+on Martha's Vineyard doing an interview
+
+ align:start position:0%
+on Martha's Vineyard doing an interview
+ 
+
+ align:start position:0%
+on Martha's Vineyard doing an interview
+and we we carted the lighting kit you
+
+ align:start position:0%
+and we we carted the lighting kit you
+ 
+
+ align:start position:0%
+and we we carted the lighting kit you
+know in the trunk of the car we carried
+
+ align:start position:0%
+know in the trunk of the car we carried
+ 
+
+ align:start position:0%
+know in the trunk of the car we carried
+it around we took it across the ferry we
+
+ align:start position:0%
+it around we took it across the ferry we
+ 
+
+ align:start position:0%
+it around we took it across the ferry we
+carried this big huge lighting kit with
+
+ align:start position:0%
+carried this big huge lighting kit with
+ 
+
+ align:start position:0%
+carried this big huge lighting kit with
+us wherever we went and I never cracked
+
+ align:start position:0%
+us wherever we went and I never cracked
+ 
+
+ align:start position:0%
+us wherever we went and I never cracked
+it open because we were able to find
+
+ align:start position:0%
+it open because we were able to find
+ 
+
+ align:start position:0%
+it open because we were able to find
+several positions um to do our
+
+ align:start position:0%
+several positions um to do our
+ 
+
+ align:start position:0%
+several positions um to do our
+interviews where the lighting was
+
+ align:start position:0%
+interviews where the lighting was
+ 
+
+ align:start position:0%
+interviews where the lighting was
+perfect and natural however it was very
+
+ align:start position:0%
+perfect and natural however it was very
+ 
+
+ align:start position:0%
+perfect and natural however it was very
+important for me to know that if we
+
+ align:start position:0%
+important for me to know that if we
+ 
+
+ align:start position:0%
+important for me to know that if we
+didn't find a beautiful spot um we could
+
+ align:start position:0%
+didn't find a beautiful spot um we could
+ 
+
+ align:start position:0%
+didn't find a beautiful spot um we could
+accent uh what we had and supplement
+
+ align:start position:0%
+accent uh what we had and supplement
+ 
+
+ align:start position:0%
+accent uh what we had and supplement
+with with additional light so one of the
+
+ align:start position:0%
+with with additional light so one of the
+ 
+
+ align:start position:0%
+with with additional light so one of the
+big takeaways from this uh lecture today
+
+ align:start position:0%
+big takeaways from this uh lecture today
+ 
+
+ align:start position:0%
+big takeaways from this uh lecture today
+isn't just how to set up lights although
+
+ align:start position:0%
+isn't just how to set up lights although
+ 
+
+ align:start position:0%
+isn't just how to set up lights although
+that's very important but it's also how
+
+ align:start position:0%
+that's very important but it's also how
+ 
+
+ align:start position:0%
+that's very important but it's also how
+to assess the light that you have and
+
+ align:start position:0%
+to assess the light that you have and
+ 
+
+ align:start position:0%
+to assess the light that you have and
+how to make choices about where you
+
+ align:start position:0%
+how to make choices about where you
+ 
+
+ align:start position:0%
+how to make choices about where you
+shoot Things based on those that
+
+ align:start position:0%
+shoot Things based on those that
+ 
+
+ align:start position:0%
+shoot Things based on those that
+assessment that's a very important
+
+ align:start position:0%
+assessment that's a very important
+ 
+
+ align:start position:0%
+assessment that's a very important
+Insight
+
+ align:start position:0%
+Insight
+ 
+
+ align:start position:0%
+Insight
+um so uh very briefly and and and by the
+
+ align:start position:0%
+um so uh very briefly and and and by the
+ 
+
+ align:start position:0%
+um so uh very briefly and and and by the
+way um a PDF with the slides and a PDF
+
+ align:start position:0%
+way um a PDF with the slides and a PDF
+ 
+
+ align:start position:0%
+way um a PDF with the slides and a PDF
+with a uh written note to go with each
+
+ align:start position:0%
+with a uh written note to go with each
+ 
+
+ align:start position:0%
+with a uh written note to go with each
+of the slides will be available as part
+
+ align:start position:0%
+of the slides will be available as part
+ 
+
+ align:start position:0%
+of the slides will be available as part
+of this package um so I don't want to go
+
+ align:start position:0%
+of this package um so I don't want to go
+ 
+
+ align:start position:0%
+of this package um so I don't want to go
+into too much detail here but there are
+
+ align:start position:0%
+into too much detail here but there are
+ 
+
+ align:start position:0%
+into too much detail here but there are
+two primary light models that we use
+
+ align:start position:0%
+two primary light models that we use
+ 
+
+ align:start position:0%
+two primary light models that we use
+when we're talking about light um we
+
+ align:start position:0%
+when we're talking about light um we
+ 
+
+ align:start position:0%
+when we're talking about light um we
+often talk about the additive model so
+
+ align:start position:0%
+often talk about the additive model so
+ 
+
+ align:start position:0%
+often talk about the additive model so
+if we I don't know if you've been to the
+
+ align:start position:0%
+if we I don't know if you've been to the
+ 
+
+ align:start position:0%
+if we I don't know if you've been to the
+Museum of Science but they have this
+
+ align:start position:0%
+Museum of Science but they have this
+ 
+
+ align:start position:0%
+Museum of Science but they have this
+great exhibit where they show a three
+
+ align:start position:0%
+great exhibit where they show a three
+ 
+
+ align:start position:0%
+great exhibit where they show a three
+projectors blue red and green light and
+
+ align:start position:0%
+projectors blue red and green light and
+ 
+
+ align:start position:0%
+projectors blue red and green light and
+where those three uh projected light
+
+ align:start position:0%
+where those three uh projected light
+ 
+
+ align:start position:0%
+where those three uh projected light
+beams intersect you end up with white
+
+ align:start position:0%
+beams intersect you end up with white
+ 
+
+ align:start position:0%
+beams intersect you end up with white
+light which I remember at being around 5
+
+ align:start position:0%
+light which I remember at being around 5
+ 
+
+ align:start position:0%
+light which I remember at being around 5
+years old and seeing this for the first
+
+ align:start position:0%
+years old and seeing this for the first
+ 
+
+ align:start position:0%
+years old and seeing this for the first
+time and I just thought that was
+
+ align:start position:0%
+time and I just thought that was
+ 
+
+ align:start position:0%
+time and I just thought that was
+miraculous like how can those three
+
+ align:start position:0%
+miraculous like how can those three
+ 
+
+ align:start position:0%
+miraculous like how can those three
+colors become white because my
+
+ align:start position:0%
+colors become white because my
+ 
+
+ align:start position:0%
+colors become white because my
+experience with paints was so different
+
+ align:start position:0%
+experience with paints was so different
+ 
+
+ align:start position:0%
+experience with paints was so different
+but that's because my real world
+
+ align:start position:0%
+but that's because my real world
+ 
+
+ align:start position:0%
+but that's because my real world
+experience was the other lighting model
+
+ align:start position:0%
+experience was the other lighting model
+ 
+
+ align:start position:0%
+experience was the other lighting model
+which we'll get to in a moment but that
+
+ align:start position:0%
+which we'll get to in a moment but that
+ 
+
+ align:start position:0%
+which we'll get to in a moment but that
+was sort of magical that you could
+
+ align:start position:0%
+was sort of magical that you could
+ 
+
+ align:start position:0%
+was sort of magical that you could
+combine these colors it turns out if you
+
+ align:start position:0%
+combine these colors it turns out if you
+ 
+
+ align:start position:0%
+combine these colors it turns out if you
+combine red light and its complement
+
+ align:start position:0%
+combine red light and its complement
+ 
+
+ align:start position:0%
+combine red light and its complement
+cyan um you end up with white light as
+
+ align:start position:0%
+cyan um you end up with white light as
+ 
+
+ align:start position:0%
+cyan um you end up with white light as
+well because as long as if you have
+
+ align:start position:0%
+well because as long as if you have
+ 
+
+ align:start position:0%
+well because as long as if you have
+equal amounts of red green and blue
+
+ align:start position:0%
+equal amounts of red green and blue
+ 
+
+ align:start position:0%
+equal amounts of red green and blue
+light then we see what we call White uh
+
+ align:start position:0%
+light then we see what we call White uh
+ 
+
+ align:start position:0%
+light then we see what we call White uh
+and so you can I would suggest uh
+
+ align:start position:0%
+and so you can I would suggest uh
+ 
+
+ align:start position:0%
+and so you can I would suggest uh
+visiting the PDF documents for the Gory
+
+ align:start position:0%
+visiting the PDF documents for the Gory
+ 
+
+ align:start position:0%
+visiting the PDF documents for the Gory
+details now when we're working with uh
+
+ align:start position:0%
+details now when we're working with uh
+ 
+
+ align:start position:0%
+details now when we're working with uh
+often we want to change the color of a
+
+ align:start position:0%
+often we want to change the color of a
+ 
+
+ align:start position:0%
+often we want to change the color of a
+light source and we'll put something
+
+ align:start position:0%
+light source and we'll put something
+ 
+
+ align:start position:0%
+light source and we'll put something
+called a gel over that light and when
+
+ align:start position:0%
+called a gel over that light and when
+ 
+
+ align:start position:0%
+called a gel over that light and when
+we're doing that we're using what we
+
+ align:start position:0%
+we're doing that we're using what we
+ 
+
+ align:start position:0%
+we're doing that we're using what we
+call the subtractive light model in
+
+ align:start position:0%
+call the subtractive light model in
+ 
+
+ align:start position:0%
+call the subtractive light model in
+other words we're filtering out some of
+
+ align:start position:0%
+other words we're filtering out some of
+ 
+
+ align:start position:0%
+other words we're filtering out some of
+the wavelengths and not others so it
+
+ align:start position:0%
+the wavelengths and not others so it
+ 
+
+ align:start position:0%
+the wavelengths and not others so it
+turns out that if you put yellow cyan
+
+ align:start position:0%
+turns out that if you put yellow cyan
+ 
+
+ align:start position:0%
+turns out that if you put yellow cyan
+and magenta gels which happen to be the
+
+ align:start position:0%
+and magenta gels which happen to be the
+ 
+
+ align:start position:0%
+and magenta gels which happen to be the
+complements of red green and blue but if
+
+ align:start position:0%
+complements of red green and blue but if
+ 
+
+ align:start position:0%
+complements of red green and blue but if
+you put those three gels over a light
+
+ align:start position:0%
+you put those three gels over a light
+ 
+
+ align:start position:0%
+you put those three gels over a light
+table for example you will see that you
+
+ align:start position:0%
+table for example you will see that you
+ 
+
+ align:start position:0%
+table for example you will see that you
+end up with this muddy Brown Darkness
+
+ align:start position:0%
+end up with this muddy Brown Darkness
+ 
+
+ align:start position:0%
+end up with this muddy Brown Darkness
+where they overlap because you have
+
+ align:start position:0%
+where they overlap because you have
+ 
+
+ align:start position:0%
+where they overlap because you have
+pretty much filtered out all of uh the
+
+ align:start position:0%
+pretty much filtered out all of uh the
+ 
+
+ align:start position:0%
+pretty much filtered out all of uh the
+light sources um they're not perfect
+
+ align:start position:0%
+light sources um they're not perfect
+ 
+
+ align:start position:0%
+light sources um they're not perfect
+filters so that black will never be
+
+ align:start position:0%
+filters so that black will never be
+ 
+
+ align:start position:0%
+filters so that black will never be
+totally black this is why in like fourcc
+
+ align:start position:0%
+totally black this is why in like fourcc
+ 
+
+ align:start position:0%
+totally black this is why in like fourcc
+color printing of like magazines and
+
+ align:start position:0%
+color printing of like magazines and
+ 
+
+ align:start position:0%
+color printing of like magazines and
+newspapers they use Canan magenta um
+
+ align:start position:0%
+newspapers they use Canan magenta um
+ 
+
+ align:start position:0%
+newspapers they use Canan magenta um
+yellow and black ink for that extra
+
+ align:start position:0%
+yellow and black ink for that extra
+ 
+
+ align:start position:0%
+yellow and black ink for that extra
+Blackness so that's also uses the
+
+ align:start position:0%
+Blackness so that's also uses the
+ 
+
+ align:start position:0%
+Blackness so that's also uses the
+subtractive system so you can either use
+
+ align:start position:0%
+subtractive system so you can either use
+ 
+
+ align:start position:0%
+subtractive system so you can either use
+pigments or you can use gels to subtract
+
+ align:start position:0%
+pigments or you can use gels to subtract
+ 
+
+ align:start position:0%
+pigments or you can use gels to subtract
+particular wavelengths so for example if
+
+ align:start position:0%
+particular wavelengths so for example if
+ 
+
+ align:start position:0%
+particular wavelengths so for example if
+my scene was a little too orangey and I
+
+ align:start position:0%
+my scene was a little too orangey and I
+ 
+
+ align:start position:0%
+my scene was a little too orangey and I
+wanted my light sources to be a little
+
+ align:start position:0%
+wanted my light sources to be a little
+ 
+
+ align:start position:0%
+wanted my light sources to be a little
+less orangey I would be putting
+
+ align:start position:0%
+less orangey I would be putting
+ 
+
+ align:start position:0%
+less orangey I would be putting
+different gradiation of blue gels over
+
+ align:start position:0%
+different gradiation of blue gels over
+ 
+
+ align:start position:0%
+different gradiation of blue gels over
+those lights for example so that's the
+
+ align:start position:0%
+those lights for example so that's the
+ 
+
+ align:start position:0%
+those lights for example so that's the
+subtractive model and it's once you uh
+
+ align:start position:0%
+subtractive model and it's once you uh
+ 
+
+ align:start position:0%
+subtractive model and it's once you uh
+get to know this it makes perfect sense
+
+ align:start position:0%
+get to know this it makes perfect sense
+ 
+
+ align:start position:0%
+get to know this it makes perfect sense
+um and we'll talk a little more about
+
+ align:start position:0%
+um and we'll talk a little more about
+ 
+
+ align:start position:0%
+um and we'll talk a little more about
+blue and and orangey correction gels
+
+ align:start position:0%
+blue and and orangey correction gels
+ 
+
+ align:start position:0%
+blue and and orangey correction gels
+which we have a tendency to use a lot in
+
+ align:start position:0%
+which we have a tendency to use a lot in
+ 
+
+ align:start position:0%
+which we have a tendency to use a lot in
+film video work because we're often
+
+ align:start position:0%
+film video work because we're often
+ 
+
+ align:start position:0%
+film video work because we're often
+correcting or changing the light from
+
+ align:start position:0%
+correcting or changing the light from
+ 
+
+ align:start position:0%
+correcting or changing the light from
+the Cool Blues to the warmer orangey
+
+ align:start position:0%
+the Cool Blues to the warmer orangey
+ 
+
+ align:start position:0%
+the Cool Blues to the warmer orangey
+lights but that's the subtractive model
+
+ align:start position:0%
+lights but that's the subtractive model
+ 
+
+ align:start position:0%
+lights but that's the subtractive model
+at
+
+ align:start position:0%
+at
+ 
+
+ align:start position:0%
+at
+work so um it turns out that video
+
+ align:start position:0%
+work so um it turns out that video
+ 
+
+ align:start position:0%
+work so um it turns out that video
+cameras being technical devices um they
+
+ align:start position:0%
+cameras being technical devices um they
+ 
+
+ align:start position:0%
+cameras being technical devices um they
+don't really know what white is some
+
+ align:start position:0%
+don't really know what white is some
+ 
+
+ align:start position:0%
+don't really know what white is some
+combination of red green and blue
+
+ align:start position:0%
+combination of red green and blue
+ 
+
+ align:start position:0%
+combination of red green and blue
+wavelengths is white but your white
+
+ align:start position:0%
+wavelengths is white but your white
+ 
+
+ align:start position:0%
+wavelengths is white but your white
+might be different than my white might
+
+ align:start position:0%
+might be different than my white might
+ 
+
+ align:start position:0%
+might be different than my white might
+be different than that Sony camera's
+
+ align:start position:0%
+be different than that Sony camera's
+ 
+
+ align:start position:0%
+be different than that Sony camera's
+white so what we typically do when we
+
+ align:start position:0%
+white so what we typically do when we
+ 
+
+ align:start position:0%
+white so what we typically do when we
+white balance the camera is we point the
+
+ align:start position:0%
+white balance the camera is we point the
+ 
+
+ align:start position:0%
+white balance the camera is we point the
+camera and hold up a white card and we
+
+ align:start position:0%
+camera and hold up a white card and we
+ 
+
+ align:start position:0%
+camera and hold up a white card and we
+push the white balance button and we're
+
+ align:start position:0%
+push the white balance button and we're
+ 
+
+ align:start position:0%
+push the white balance button and we're
+telling the camera that particular
+
+ align:start position:0%
+telling the camera that particular
+ 
+
+ align:start position:0%
+telling the camera that particular
+combination of red green and blue
+
+ align:start position:0%
+combination of red green and blue
+ 
+
+ align:start position:0%
+combination of red green and blue
+whatever it happens to be that's my
+
+ align:start position:0%
+whatever it happens to be that's my
+ 
+
+ align:start position:0%
+whatever it happens to be that's my
+white reference and now the camera will
+
+ align:start position:0%
+white reference and now the camera will
+ 
+
+ align:start position:0%
+white reference and now the camera will
+display whatever that card is uh as pure
+
+ align:start position:0%
+display whatever that card is uh as pure
+ 
+
+ align:start position:0%
+display whatever that card is uh as pure
+white well it turns out that
+
+ align:start position:0%
+white well it turns out that
+ 
+
+ align:start position:0%
+white well it turns out that
+um the this sort of relative B balance
+
+ align:start position:0%
+um the this sort of relative B balance
+ 
+
+ align:start position:0%
+um the this sort of relative B balance
+of red green and blue uh the camera sees
+
+ align:start position:0%
+of red green and blue uh the camera sees
+ 
+
+ align:start position:0%
+of red green and blue uh the camera sees
+it as a technical problem to solve and
+
+ align:start position:0%
+it as a technical problem to solve and
+ 
+
+ align:start position:0%
+it as a technical problem to solve and
+very often the perfect white balance of
+
+ align:start position:0%
+very often the perfect white balance of
+ 
+
+ align:start position:0%
+very often the perfect white balance of
+a camera is often maybe a little too too
+
+ align:start position:0%
+a camera is often maybe a little too too
+ 
+
+ align:start position:0%
+a camera is often maybe a little too too
+clean too dry too perfect so a trick
+
+ align:start position:0%
+clean too dry too perfect so a trick
+ 
+
+ align:start position:0%
+clean too dry too perfect so a trick
+that I do is I get something called an
+
+ align:start position:0%
+that I do is I get something called an
+ 
+
+ align:start position:0%
+that I do is I get something called an
+eighth blue gel which is like a pale
+
+ align:start position:0%
+eighth blue gel which is like a pale
+ 
+
+ align:start position:0%
+eighth blue gel which is like a pale
+very pale blue gel and when I white
+
+ align:start position:0%
+very pale blue gel and when I white
+ 
+
+ align:start position:0%
+very pale blue gel and when I white
+balance my camera I hold that pale blue
+
+ align:start position:0%
+balance my camera I hold that pale blue
+ 
+
+ align:start position:0%
+balance my camera I hold that pale blue
+gel over the camera lens I press the
+
+ align:start position:0%
+gel over the camera lens I press the
+ 
+
+ align:start position:0%
+gel over the camera lens I press the
+white balance button and I push away the
+
+ align:start position:0%
+white balance button and I push away the
+ 
+
+ align:start position:0%
+white balance button and I push away the
+G gel and what have I
+
+ align:start position:0%
+G gel and what have I
+ 
+
+ align:start position:0%
+G gel and what have I
+done I have fooled the camera into
+
+ align:start position:0%
+done I have fooled the camera into
+ 
+
+ align:start position:0%
+done I have fooled the camera into
+thinking that there's more blue in the
+
+ align:start position:0%
+thinking that there's more blue in the
+ 
+
+ align:start position:0%
+thinking that there's more blue in the
+world and it compensates by making the
+
+ align:start position:0%
+world and it compensates by making the
+ 
+
+ align:start position:0%
+world and it compensates by making the
+image a teeny bit warmer a little more
+
+ align:start position:0%
+image a teeny bit warmer a little more
+ 
+
+ align:start position:0%
+image a teeny bit warmer a little more
+orangey and flesh tones uh look a lot
+
+ align:start position:0%
+orangey and flesh tones uh look a lot
+ 
+
+ align:start position:0%
+orangey and flesh tones uh look a lot
+better with just a little bit of warmth
+
+ align:start position:0%
+better with just a little bit of warmth
+ 
+
+ align:start position:0%
+better with just a little bit of warmth
+added so this is sort of my like you
+
+ align:start position:0%
+added so this is sort of my like you
+ 
+
+ align:start position:0%
+added so this is sort of my like you
+know little bit of Basil in the sauce uh
+
+ align:start position:0%
+know little bit of Basil in the sauce uh
+ 
+
+ align:start position:0%
+know little bit of Basil in the sauce uh
+for a slightly uh tastier
+
+ align:start position:0%
+for a slightly uh tastier
+ 
+
+ align:start position:0%
+for a slightly uh tastier
+image um you will hear a lot of people
+
+ align:start position:0%
+image um you will hear a lot of people
+ 
+
+ align:start position:0%
+image um you will hear a lot of people
+talk about color temperature this is a
+
+ align:start position:0%
+talk about color temperature this is a
+ 
+
+ align:start position:0%
+talk about color temperature this is a
+method that is used to
+
+ align:start position:0%
+method that is used to
+ 
+
+ align:start position:0%
+method that is used to
+describe what the color of a light
+
+ align:start position:0%
+describe what the color of a light
+ 
+
+ align:start position:0%
+describe what the color of a light
+source is we work so often in this sort
+
+ align:start position:0%
+source is we work so often in this sort
+ 
+
+ align:start position:0%
+source is we work so often in this sort
+of orange to Blue to White Dimension uh
+
+ align:start position:0%
+of orange to Blue to White Dimension uh
+ 
+
+ align:start position:0%
+of orange to Blue to White Dimension uh
+simply because so many of our artificial
+
+ align:start position:0%
+simply because so many of our artificial
+ 
+
+ align:start position:0%
+simply because so many of our artificial
+and natural light sources are in that
+
+ align:start position:0%
+and natural light sources are in that
+ 
+
+ align:start position:0%
+and natural light sources are in that
+range for example fire candle matches
+
+ align:start position:0%
+range for example fire candle matches
+ 
+
+ align:start position:0%
+range for example fire candle matches
+they're all kind of orange sunlight is
+
+ align:start position:0%
+they're all kind of orange sunlight is
+ 
+
+ align:start position:0%
+they're all kind of orange sunlight is
+very
+
+ align:start position:0%
+very
+ 
+
+ align:start position:0%
+very
+blue and so it turns out that um color
+
+ align:start position:0%
+blue and so it turns out that um color
+ 
+
+ align:start position:0%
+blue and so it turns out that um color
+temperature is basically
+
+ align:start position:0%
+temperature is basically
+ 
+
+ align:start position:0%
+temperature is basically
+what temperature do you need to heat up
+
+ align:start position:0%
+what temperature do you need to heat up
+ 
+
+ align:start position:0%
+what temperature do you need to heat up
+this theoretical black body Radiator in
+
+ align:start position:0%
+this theoretical black body Radiator in
+ 
+
+ align:start position:0%
+this theoretical black body Radiator in
+order to get that color well it turns
+
+ align:start position:0%
+order to get that color well it turns
+ 
+
+ align:start position:0%
+order to get that color well it turns
+out in in Practical everyday world uh
+
+ align:start position:0%
+out in in Practical everyday world uh
+ 
+
+ align:start position:0%
+out in in Practical everyday world uh
+that black body radiator that you've
+
+ align:start position:0%
+that black body radiator that you've
+ 
+
+ align:start position:0%
+that black body radiator that you've
+read in cinematography books the
+
+ align:start position:0%
+read in cinematography books the
+ 
+
+ align:start position:0%
+read in cinematography books the
+equivalent think of it as a Tungsten
+
+ align:start position:0%
+equivalent think of it as a Tungsten
+ 
+
+ align:start position:0%
+equivalent think of it as a Tungsten
+filament as a light filament the more
+
+ align:start position:0%
+filament as a light filament the more
+ 
+
+ align:start position:0%
+filament as a light filament the more
+juice you put through that filament the
+
+ align:start position:0%
+juice you put through that filament the
+ 
+
+ align:start position:0%
+juice you put through that filament the
+less orangey it is and the more white it
+
+ align:start position:0%
+less orangey it is and the more white it
+ 
+
+ align:start position:0%
+less orangey it is and the more white it
+becomes of course at some point it
+
+ align:start position:0%
+becomes of course at some point it
+ 
+
+ align:start position:0%
+becomes of course at some point it
+explodes because it's handling too much
+
+ align:start position:0%
+explodes because it's handling too much
+ 
+
+ align:start position:0%
+explodes because it's handling too much
+current but in theory if you heated it
+
+ align:start position:0%
+current but in theory if you heated it
+ 
+
+ align:start position:0%
+current but in theory if you heated it
+up to 9,000
+
+ align:start position:0%
+up to 9,000
+ 
+
+ align:start position:0%
+up to 9,000
+uh degrees you would have the same color
+
+ align:start position:0%
+uh degrees you would have the same color
+ 
+
+ align:start position:0%
+uh degrees you would have the same color
+as hazy sunlight which is very very pale
+
+ align:start position:0%
+as hazy sunlight which is very very pale
+ 
+
+ align:start position:0%
+as hazy sunlight which is very very pale
+blue almost white but if you bring the
+
+ align:start position:0%
+blue almost white but if you bring the
+ 
+
+ align:start position:0%
+blue almost white but if you bring the
+temperature down to 1,700 de Kelvin you
+
+ align:start position:0%
+temperature down to 1,700 de Kelvin you
+ 
+
+ align:start position:0%
+temperature down to 1,700 de Kelvin you
+would have the nice orangey color of a
+
+ align:start position:0%
+would have the nice orangey color of a
+ 
+
+ align:start position:0%
+would have the nice orangey color of a
+match flame so this is sort of this
+
+ align:start position:0%
+match flame so this is sort of this
+ 
+
+ align:start position:0%
+match flame so this is sort of this
+temperature scale from orangey on the
+
+ align:start position:0%
+temperature scale from orangey on the
+ 
+
+ align:start position:0%
+temperature scale from orangey on the
+low temperature end to like almost
+
+ align:start position:0%
+low temperature end to like almost
+ 
+
+ align:start position:0%
+low temperature end to like almost
+perfect white with a slight tinge of
+
+ align:start position:0%
+perfect white with a slight tinge of
+ 
+
+ align:start position:0%
+perfect white with a slight tinge of
+blue on the high end there are two magic
+
+ align:start position:0%
+blue on the high end there are two magic
+ 
+
+ align:start position:0%
+blue on the high end there are two magic
+numbers that you hear in the world of
+
+ align:start position:0%
+numbers that you hear in the world of
+ 
+
+ align:start position:0%
+numbers that you hear in the world of
+white balance 3200 de Kelvin which is
+
+ align:start position:0%
+white balance 3200 de Kelvin which is
+ 
+
+ align:start position:0%
+white balance 3200 de Kelvin which is
+the industry standard for Tungsten
+
+ align:start position:0%
+the industry standard for Tungsten
+ 
+
+ align:start position:0%
+the industry standard for Tungsten
+filament incandescent lights it is the
+
+ align:start position:0%
+filament incandescent lights it is the
+ 
+
+ align:start position:0%
+filament incandescent lights it is the
+standard that for almost 100 years well
+
+ align:start position:0%
+standard that for almost 100 years well
+ 
+
+ align:start position:0%
+standard that for almost 100 years well
+maybe 80 years um film emulsions were
+
+ align:start position:0%
+maybe 80 years um film emulsions were
+ 
+
+ align:start position:0%
+maybe 80 years um film emulsions were
+matched to that color temperature so
+
+ align:start position:0%
+matched to that color temperature so
+ 
+
+ align:start position:0%
+matched to that color temperature so
+that something lit under 3200 de Kelvin
+
+ align:start position:0%
+that something lit under 3200 de Kelvin
+ 
+
+ align:start position:0%
+that something lit under 3200 de Kelvin
+light would look white um there's also
+
+ align:start position:0%
+light would look white um there's also
+ 
+
+ align:start position:0%
+light would look white um there's also
+daylight balanced film so consumer film
+
+ align:start position:0%
+daylight balanced film so consumer film
+ 
+
+ align:start position:0%
+daylight balanced film so consumer film
+was usually uh Balan to 5,500 de Kelvin
+
+ align:start position:0%
+was usually uh Balan to 5,500 de Kelvin
+ 
+
+ align:start position:0%
+was usually uh Balan to 5,500 de Kelvin
+and that's called daylight balance so
+
+ align:start position:0%
+and that's called daylight balance so
+ 
+
+ align:start position:0%
+and that's called daylight balance so
+most electronic Flash
+
+ align:start position:0%
+most electronic Flash
+ 
+
+ align:start position:0%
+most electronic Flash
+um is balanced for daylight and consumer
+
+ align:start position:0%
+um is balanced for daylight and consumer
+ 
+
+ align:start position:0%
+um is balanced for daylight and consumer
+film was always mostly balanced for
+
+ align:start position:0%
+film was always mostly balanced for
+ 
+
+ align:start position:0%
+film was always mostly balanced for
+daylight um and of course now in the era
+
+ align:start position:0%
+daylight um and of course now in the era
+ 
+
+ align:start position:0%
+daylight um and of course now in the era
+of video and digital imaging it's sort
+
+ align:start position:0%
+of video and digital imaging it's sort
+ 
+
+ align:start position:0%
+of video and digital imaging it's sort
+of kind of a little bit of a holdover
+
+ align:start position:0%
+of kind of a little bit of a holdover
+ 
+
+ align:start position:0%
+of kind of a little bit of a holdover
+but we still use these terms because
+
+ align:start position:0%
+but we still use these terms because
+ 
+
+ align:start position:0%
+but we still use these terms because
+film lighting is still um comes
+
+ align:start position:0%
+film lighting is still um comes
+ 
+
+ align:start position:0%
+film lighting is still um comes
+primarily in two flavors tungsten
+
+ align:start position:0%
+primarily in two flavors tungsten
+ 
+
+ align:start position:0%
+primarily in two flavors tungsten
+balanced quartz hallogen lamps LED lamps
+
+ align:start position:0%
+balanced quartz hallogen lamps LED lamps
+ 
+
+ align:start position:0%
+balanced quartz hallogen lamps LED lamps
+fluorescent lamps Etc they're all
+
+ align:start position:0%
+fluorescent lamps Etc they're all
+ 
+
+ align:start position:0%
+fluorescent lamps Etc they're all
+available matched perfectly 3200 de
+
+ align:start position:0%
+available matched perfectly 3200 de
+ 
+
+ align:start position:0%
+available matched perfectly 3200 de
+Kelvin and a new generation of HMI
+
+ align:start position:0%
+Kelvin and a new generation of HMI
+ 
+
+ align:start position:0%
+Kelvin and a new generation of HMI
+daylight balance lights daylight Balan
+
+ align:start position:0%
+daylight balance lights daylight Balan
+ 
+
+ align:start position:0%
+daylight balance lights daylight Balan
+fluorescence daylight balanced LEDs
+
+ align:start position:0%
+fluorescence daylight balanced LEDs
+ 
+
+ align:start position:0%
+fluorescence daylight balanced LEDs
+they're available matched perfectly to
+
+ align:start position:0%
+they're available matched perfectly to
+ 
+
+ align:start position:0%
+they're available matched perfectly to
+5,500 de Kelvin and also many cameras uh
+
+ align:start position:0%
+5,500 de Kelvin and also many cameras uh
+ 
+
+ align:start position:0%
+5,500 de Kelvin and also many cameras uh
+that you may use uh have preset white
+
+ align:start position:0%
+that you may use uh have preset white
+ 
+
+ align:start position:0%
+that you may use uh have preset white
+balance settings so there may be one for
+
+ align:start position:0%
+balance settings so there may be one for
+ 
+
+ align:start position:0%
+balance settings so there may be one for
+daylight there may be one for Tungsten
+
+ align:start position:0%
+daylight there may be one for Tungsten
+ 
+
+ align:start position:0%
+daylight there may be one for Tungsten
+and when you click it to one of those
+
+ align:start position:0%
+and when you click it to one of those
+ 
+
+ align:start position:0%
+and when you click it to one of those
+settings rather than create the white
+
+ align:start position:0%
+settings rather than create the white
+ 
+
+ align:start position:0%
+settings rather than create the white
+balance yourself as David just described
+
+ align:start position:0%
+balance yourself as David just described
+ 
+
+ align:start position:0%
+balance yourself as David just described
+essentially what you're doing is the
+
+ align:start position:0%
+essentially what you're doing is the
+ 
+
+ align:start position:0%
+essentially what you're doing is the
+equivalent of of loading your camera
+
+ align:start position:0%
+equivalent of of loading your camera
+ 
+
+ align:start position:0%
+equivalent of of loading your camera
+with an Emulsion that's balanced to one
+
+ align:start position:0%
+with an Emulsion that's balanced to one
+ 
+
+ align:start position:0%
+with an Emulsion that's balanced to one
+of those presets so 3200 is is in theory
+
+ align:start position:0%
+of those presets so 3200 is is in theory
+ 
+
+ align:start position:0%
+of those presets so 3200 is is in theory
+perfectly balanced for Tungsten light
+
+ align:start position:0%
+perfectly balanced for Tungsten light
+ 
+
+ align:start position:0%
+perfectly balanced for Tungsten light
+and the daylight balance is perfectly
+
+ align:start position:0%
+and the daylight balance is perfectly
+ 
+
+ align:start position:0%
+and the daylight balance is perfectly
+balanced in theory for about 5,500
+
+ align:start position:0%
+balanced in theory for about 5,500
+ 
+
+ align:start position:0%
+balanced in theory for about 5,500
+5600 yeah and it's handy right when you
+
+ align:start position:0%
+5600 yeah and it's handy right when you
+ 
+
+ align:start position:0%
+5600 yeah and it's handy right when you
+buy lighting instruments it's kind of
+
+ align:start position:0%
+buy lighting instruments it's kind of
+ 
+
+ align:start position:0%
+buy lighting instruments it's kind of
+nice that they all sort of match for the
+
+ align:start position:0%
+nice that they all sort of match for the
+ 
+
+ align:start position:0%
+nice that they all sort of match for the
+most part right now if we look at these
+
+ align:start position:0%
+most part right now if we look at these
+ 
+
+ align:start position:0%
+most part right now if we look at these
+three little pictures here something to
+
+ align:start position:0%
+three little pictures here something to
+ 
+
+ align:start position:0%
+three little pictures here something to
+think about outdoor Shadows are
+
+ align:start position:0%
+think about outdoor Shadows are
+ 
+
+ align:start position:0%
+think about outdoor Shadows are
+predominant
+
+ align:start position:0%
+predominant
+ 
+
+ align:start position:0%
+predominant
+blue like if you shoot in in Shadow you
+
+ align:start position:0%
+blue like if you shoot in in Shadow you
+ 
+
+ align:start position:0%
+blue like if you shoot in in Shadow you
+get really really bluish images to our
+
+ align:start position:0%
+get really really bluish images to our
+ 
+
+ align:start position:0%
+get really really bluish images to our
+eyes it may look perfectly neutral but
+
+ align:start position:0%
+eyes it may look perfectly neutral but
+ 
+
+ align:start position:0%
+eyes it may look perfectly neutral but
+to the camera it looks really blue why
+
+ align:start position:0%
+to the camera it looks really blue why
+ 
+
+ align:start position:0%
+to the camera it looks really blue why
+because Shadows doesn't have any direct
+
+ align:start position:0%
+because Shadows doesn't have any direct
+ 
+
+ align:start position:0%
+because Shadows doesn't have any direct
+sun all the lighting in the shadow is
+
+ align:start position:0%
+sun all the lighting in the shadow is
+ 
+
+ align:start position:0%
+sun all the lighting in the shadow is
+coming from the sky which is
+
+ align:start position:0%
+coming from the sky which is
+ 
+
+ align:start position:0%
+coming from the sky which is
+predominantly blue due to the way that
+
+ align:start position:0%
+predominantly blue due to the way that
+ 
+
+ align:start position:0%
+predominantly blue due to the way that
+the light waves are scattered the
+
+ align:start position:0%
+the light waves are scattered the
+ 
+
+ align:start position:0%
+the light waves are scattered the
+different wavelengths are scattered a
+
+ align:start position:0%
+different wavelengths are scattered a
+ 
+
+ align:start position:0%
+different wavelengths are scattered a
+different amount and so sky has a
+
+ align:start position:0%
+different amount and so sky has a
+ 
+
+ align:start position:0%
+different amount and so sky has a
+tendency to be very blue in the middle
+
+ align:start position:0%
+tendency to be very blue in the middle
+ 
+
+ align:start position:0%
+tendency to be very blue in the middle
+picture you see here a mixed environment
+
+ align:start position:0%
+picture you see here a mixed environment
+ 
+
+ align:start position:0%
+picture you see here a mixed environment
+the interior lighting in this museum is
+
+ align:start position:0%
+the interior lighting in this museum is
+ 
+
+ align:start position:0%
+the interior lighting in this museum is
+tungsten incandescent lighting but you
+
+ align:start position:0%
+tungsten incandescent lighting but you
+ 
+
+ align:start position:0%
+tungsten incandescent lighting but you
+have blue daylight streaming through the
+
+ align:start position:0%
+have blue daylight streaming through the
+ 
+
+ align:start position:0%
+have blue daylight streaming through the
+Skylight these are the most difficult
+
+ align:start position:0%
+Skylight these are the most difficult
+ 
+
+ align:start position:0%
+Skylight these are the most difficult
+situations to shoot because you
+
+ align:start position:0%
+situations to shoot because you
+ 
+
+ align:start position:0%
+situations to shoot because you
+basically have to split the difference
+
+ align:start position:0%
+basically have to split the difference
+ 
+
+ align:start position:0%
+basically have to split the difference
+or find some happy medium between the
+
+ align:start position:0%
+or find some happy medium between the
+ 
+
+ align:start position:0%
+or find some happy medium between the
+tungsten lighting and the daylight
+
+ align:start position:0%
+tungsten lighting and the daylight
+ 
+
+ align:start position:0%
+tungsten lighting and the daylight
+lighting because there's no way to
+
+ align:start position:0%
+lighting because there's no way to
+ 
+
+ align:start position:0%
+lighting because there's no way to
+reproduce that the way the eye sees it
+
+ align:start position:0%
+reproduce that the way the eye sees it
+ 
+
+ align:start position:0%
+reproduce that the way the eye sees it
+unless you do some trickery in post-
+
+ align:start position:0%
+unless you do some trickery in post-
+ 
+
+ align:start position:0%
+unless you do some trickery in post-
+production so often we're kind of
+
+ align:start position:0%
+production so often we're kind of
+ 
+
+ align:start position:0%
+production so often we're kind of
+splitting the difference between
+
+ align:start position:0%
+splitting the difference between
+ 
+
+ align:start position:0%
+splitting the difference between
+tungsten interior lighting and and
+
+ align:start position:0%
+tungsten interior lighting and and
+ 
+
+ align:start position:0%
+tungsten interior lighting and and
+daylight streaming through Windows um on
+
+ align:start position:0%
+daylight streaming through Windows um on
+ 
+
+ align:start position:0%
+daylight streaming through Windows um on
+a big b you know big Hollywood budget
+
+ align:start position:0%
+a big b you know big Hollywood budget
+ 
+
+ align:start position:0%
+a big b you know big Hollywood budget
+you know you you'd send a crew to maybe
+
+ align:start position:0%
+you know you you'd send a crew to maybe
+ 
+
+ align:start position:0%
+you know you you'd send a crew to maybe
+gel those windows and put orange gel
+
+ align:start position:0%
+gel those windows and put orange gel
+ 
+
+ align:start position:0%
+gel those windows and put orange gel
+over the windows so that now everything
+
+ align:start position:0%
+over the windows so that now everything
+ 
+
+ align:start position:0%
+over the windows so that now everything
+is is perfectly is perfectly balanced uh
+
+ align:start position:0%
+is is perfectly is perfectly balanced uh
+ 
+
+ align:start position:0%
+is is perfectly is perfectly balanced uh
+as documentary makers we typically don't
+
+ align:start position:0%
+as documentary makers we typically don't
+ 
+
+ align:start position:0%
+as documentary makers we typically don't
+have a crew um that can gel windows and
+
+ align:start position:0%
+have a crew um that can gel windows and
+ 
+
+ align:start position:0%
+have a crew um that can gel windows and
+things like that and so we're in some
+
+ align:start position:0%
+things like that and so we're in some
+ 
+
+ align:start position:0%
+things like that and so we're in some
+ways we have to be much more creative in
+
+ align:start position:0%
+ways we have to be much more creative in
+ 
+
+ align:start position:0%
+ways we have to be much more creative in
+terms of how we choose where we're going
+
+ align:start position:0%
+terms of how we choose where we're going
+ 
+
+ align:start position:0%
+terms of how we choose where we're going
+to set the white balance um for our
+
+ align:start position:0%
+to set the white balance um for our
+ 
+
+ align:start position:0%
+to set the white balance um for our
+scene and of course sunsets are
+
+ align:start position:0%
+scene and of course sunsets are
+ 
+
+ align:start position:0%
+scene and of course sunsets are
+extremely warm due to the scattering
+
+ align:start position:0%
+extremely warm due to the scattering
+ 
+
+ align:start position:0%
+extremely warm due to the scattering
+again the way the light rays are
+
+ align:start position:0%
+again the way the light rays are
+ 
+
+ align:start position:0%
+again the way the light rays are
+scattered and they have a tendency to be
+
+ align:start position:0%
+scattered and they have a tendency to be
+ 
+
+ align:start position:0%
+scattered and they have a tendency to be
+very very warm very very orangey uh and
+
+ align:start position:0%
+very very warm very very orangey uh and
+ 
+
+ align:start position:0%
+very very warm very very orangey uh and
+the more you know crap that we put in
+
+ align:start position:0%
+the more you know crap that we put in
+ 
+
+ align:start position:0%
+the more you know crap that we put in
+the atmosphere the more gorgeous sunsets
+
+ align:start position:0%
+the atmosphere the more gorgeous sunsets
+ 
+
+ align:start position:0%
+the atmosphere the more gorgeous sunsets
+we get which is the one thing I do miss
+
+ align:start position:0%
+we get which is the one thing I do miss
+ 
+
+ align:start position:0%
+we get which is the one thing I do miss
+about living in Los Angeles we had
+
+ align:start position:0%
+about living in Los Angeles we had
+ 
+
+ align:start position:0%
+about living in Los Angeles we had
+intense beautiful orange sunsets so the
+
+ align:start position:0%
+intense beautiful orange sunsets so the
+ 
+
+ align:start position:0%
+intense beautiful orange sunsets so the
+smog is good for
+
+ align:start position:0%
+smog is good for
+ 
+
+ align:start position:0%
+smog is good for
+something um let me relate this to the
+
+ align:start position:0%
+something um let me relate this to the
+ 
+
+ align:start position:0%
+something um let me relate this to the
+color correction that you're going to
+
+ align:start position:0%
+color correction that you're going to
+ 
+
+ align:start position:0%
+color correction that you're going to
+see in post we talked about the green
+
+ align:start position:0%
+see in post we talked about the green
+ 
+
+ align:start position:0%
+see in post we talked about the green
+cyan Dimension and the green magenta
+
+ align:start position:0%
+cyan Dimension and the green magenta
+ 
+
+ align:start position:0%
+cyan Dimension and the green magenta
+Dimension and the blue yellow which is
+
+ align:start position:0%
+Dimension and the blue yellow which is
+ 
+
+ align:start position:0%
+Dimension and the blue yellow which is
+the dimension that we're usually working
+
+ align:start position:0%
+the dimension that we're usually working
+ 
+
+ align:start position:0%
+the dimension that we're usually working
+with and when you're correcting images
+
+ align:start position:0%
+with and when you're correcting images
+ 
+
+ align:start position:0%
+with and when you're correcting images
+in post- production it turns out that
+
+ align:start position:0%
+in post- production it turns out that
+ 
+
+ align:start position:0%
+in post- production it turns out that
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+same the same dimensions that we saw in
+
+ align:start position:0%
+same the same dimensions that we saw in
+ 
+
+ align:start position:0%
+same the same dimensions that we saw in
+the additive uh color model uh come come
+
+ align:start position:0%
+the additive uh color model uh come come
+ 
+
+ align:start position:0%
+the additive uh color model uh come come
+to work here as well right because our
+
+ align:start position:0%
+to work here as well right because our
+ 
+
+ align:start position:0%
+to work here as well right because our
+our LCD monitors were looking at red
+
+ align:start position:0%
+our LCD monitors were looking at red
+ 
+
+ align:start position:0%
+our LCD monitors were looking at red
+green and blue pixels with our cameras
+
+ align:start position:0%
+green and blue pixels with our cameras
+ 
+
+ align:start position:0%
+green and blue pixels with our cameras
+we have red green and blue uh sensitive
+
+ align:start position:0%
+we have red green and blue uh sensitive
+ 
+
+ align:start position:0%
+we have red green and blue uh sensitive
+sensors so if our scene is a little too
+
+ align:start position:0%
+sensors so if our scene is a little too
+ 
+
+ align:start position:0%
+sensors so if our scene is a little too
+yellow or a little too blue we can
+
+ align:start position:0%
+yellow or a little too blue we can
+ 
+
+ align:start position:0%
+yellow or a little too blue we can
+simply adjust in our color correction
+
+ align:start position:0%
+simply adjust in our color correction
+ 
+
+ align:start position:0%
+simply adjust in our color correction
+dial so if you can correct in post-
+
+ align:start position:0%
+dial so if you can correct in post-
+ 
+
+ align:start position:0%
+dial so if you can correct in post-
+production these problems with white
+
+ align:start position:0%
+production these problems with white
+ 
+
+ align:start position:0%
+production these problems with white
+balance why do we worry so much about it
+
+ align:start position:0%
+balance why do we worry so much about it
+ 
+
+ align:start position:0%
+balance why do we worry so much about it
+while we're
+
+ align:start position:0%
+while we're
+ 
+
+ align:start position:0%
+while we're
+shooting the reason is you want to get
+
+ align:start position:0%
+shooting the reason is you want to get
+ 
+
+ align:start position:0%
+shooting the reason is you want to get
+the right the white balance right the
+
+ align:start position:0%
+the right the white balance right the
+ 
+
+ align:start position:0%
+the right the white balance right the
+first time when you shoot because if the
+
+ align:start position:0%
+first time when you shoot because if the
+ 
+
+ align:start position:0%
+first time when you shoot because if the
+scene is excessively blue or the scene
+
+ align:start position:0%
+scene is excessively blue or the scene
+ 
+
+ align:start position:0%
+scene is excessively blue or the scene
+is excessively orange what happens is
+
+ align:start position:0%
+is excessively orange what happens is
+ 
+
+ align:start position:0%
+is excessively orange what happens is
+you're going to overexpose the red
+
+ align:start position:0%
+you're going to overexpose the red
+ 
+
+ align:start position:0%
+you're going to overexpose the red
+Channel or overexpose the blue Channel
+
+ align:start position:0%
+Channel or overexpose the blue Channel
+ 
+
+ align:start position:0%
+Channel or overexpose the blue Channel
+um and what happens is once you
+
+ align:start position:0%
+um and what happens is once you
+ 
+
+ align:start position:0%
+um and what happens is once you
+overexpose that color Channel there's no
+
+ align:start position:0%
+overexpose that color Channel there's no
+ 
+
+ align:start position:0%
+overexpose that color Channel there's no
+information or detail to bring back when
+
+ align:start position:0%
+information or detail to bring back when
+ 
+
+ align:start position:0%
+information or detail to bring back when
+you correct so you will always notice
+
+ align:start position:0%
+you correct so you will always notice
+ 
+
+ align:start position:0%
+you correct so you will always notice
+that a properly white balanced scene you
+
+ align:start position:0%
+that a properly white balanced scene you
+ 
+
+ align:start position:0%
+that a properly white balanced scene you
+can fine-tune the color and get a very
+
+ align:start position:0%
+can fine-tune the color and get a very
+ 
+
+ align:start position:0%
+can fine-tune the color and get a very
+rich sensual image but if you shoot the
+
+ align:start position:0%
+rich sensual image but if you shoot the
+ 
+
+ align:start position:0%
+rich sensual image but if you shoot the
+wrong white balance and you go into
+
+ align:start position:0%
+wrong white balance and you go into
+ 
+
+ align:start position:0%
+wrong white balance and you go into
+correct you're going to notice that your
+
+ align:start position:0%
+correct you're going to notice that your
+ 
+
+ align:start position:0%
+correct you're going to notice that your
+detail looks different and your
+
+ align:start position:0%
+detail looks different and your
+ 
+
+ align:start position:0%
+detail looks different and your
+highlights don't have the same texture
+
+ align:start position:0%
+highlights don't have the same texture
+ 
+
+ align:start position:0%
+highlights don't have the same texture
+and detail because if you shot for
+
+ align:start position:0%
+and detail because if you shot for
+ 
+
+ align:start position:0%
+and detail because if you shot for
+example daylight balanced in a Tungsten
+
+ align:start position:0%
+example daylight balanced in a Tungsten
+ 
+
+ align:start position:0%
+example daylight balanced in a Tungsten
+environment you have completely whacked
+
+ align:start position:0%
+environment you have completely whacked
+ 
+
+ align:start position:0%
+environment you have completely whacked
+out the red Channel relative to the
+
+ align:start position:0%
+out the red Channel relative to the
+ 
+
+ align:start position:0%
+out the red Channel relative to the
+green and uh blue channels right so you
+
+ align:start position:0%
+green and uh blue channels right so you
+ 
+
+ align:start position:0%
+green and uh blue channels right so you
+do want to get it right because having
+
+ align:start position:0%
+do want to get it right because having
+ 
+
+ align:start position:0%
+do want to get it right because having
+one channel way
+
+ align:start position:0%
+one channel way
+ 
+
+ align:start position:0%
+one channel way
+Overexposed you that detail is lost
+
+ align:start position:0%
+Overexposed you that detail is lost
+ 
+
+ align:start position:0%
+Overexposed you that detail is lost
+forever so yes you can correct in post
+
+ align:start position:0%
+forever so yes you can correct in post
+ 
+
+ align:start position:0%
+forever so yes you can correct in post
+but get it right the get at least a good
+
+ align:start position:0%
+but get it right the get at least a good
+ 
+
+ align:start position:0%
+but get it right the get at least a good
+middle of the road starting point in in
+
+ align:start position:0%
+middle of the road starting point in in
+ 
+
+ align:start position:0%
+middle of the road starting point in in
+production I want to revisit quality of
+
+ align:start position:0%
+production I want to revisit quality of
+ 
+
+ align:start position:0%
+production I want to revisit quality of
+light um so on the left we have a scene
+
+ align:start position:0%
+light um so on the left we have a scene
+ 
+
+ align:start position:0%
+light um so on the left we have a scene
+that was shot uh on a cloudy day and
+
+ align:start position:0%
+that was shot uh on a cloudy day and
+ 
+
+ align:start position:0%
+that was shot uh on a cloudy day and
+it's raining um and by the way a little
+
+ align:start position:0%
+it's raining um and by the way a little
+ 
+
+ align:start position:0%
+it's raining um and by the way a little
+trick uh on a cloudy day you would never
+
+ align:start position:0%
+trick uh on a cloudy day you would never
+ 
+
+ align:start position:0%
+trick uh on a cloudy day you would never
+see the raindrops on film so we cheated
+
+ align:start position:0%
+see the raindrops on film so we cheated
+ 
+
+ align:start position:0%
+see the raindrops on film so we cheated
+and we put a very bright HMI backlight
+
+ align:start position:0%
+and we put a very bright HMI backlight
+ 
+
+ align:start position:0%
+and we put a very bright HMI backlight
+daylight balance backlight uh behind the
+
+ align:start position:0%
+daylight balance backlight uh behind the
+ 
+
+ align:start position:0%
+daylight balance backlight uh behind the
+actors so that you would see the
+
+ align:start position:0%
+actors so that you would see the
+ 
+
+ align:start position:0%
+actors so that you would see the
+raindrops so otherwise the lighting is
+
+ align:start position:0%
+raindrops so otherwise the lighting is
+ 
+
+ align:start position:0%
+raindrops so otherwise the lighting is
+completely flat and diffused but we
+
+ align:start position:0%
+completely flat and diffused but we
+ 
+
+ align:start position:0%
+completely flat and diffused but we
+cheated by having a little hard hard
+
+ align:start position:0%
+cheated by having a little hard hard
+ 
+
+ align:start position:0%
+cheated by having a little hard hard
+hard backlight that you don't actually
+
+ align:start position:0%
+hard backlight that you don't actually
+ 
+
+ align:start position:0%
+hard backlight that you don't actually
+see and then the raindrops show up but a
+
+ align:start position:0%
+see and then the raindrops show up but a
+ 
+
+ align:start position:0%
+see and then the raindrops show up but a
+typical overcast day has very very soft
+
+ align:start position:0%
+typical overcast day has very very soft
+ 
+
+ align:start position:0%
+typical overcast day has very very soft
+light the light is coming from many many
+
+ align:start position:0%
+light the light is coming from many many
+ 
+
+ align:start position:0%
+light the light is coming from many many
+different directions and so you don't
+
+ align:start position:0%
+different directions and so you don't
+ 
+
+ align:start position:0%
+different directions and so you don't
+see distinct shadows and it has a
+
+ align:start position:0%
+see distinct shadows and it has a
+ 
+
+ align:start position:0%
+see distinct shadows and it has a
+particular uh maybe soft or even maybe
+
+ align:start position:0%
+particular uh maybe soft or even maybe
+ 
+
+ align:start position:0%
+particular uh maybe soft or even maybe
+even a gloomy feel depending on on the
+
+ align:start position:0%
+even a gloomy feel depending on on the
+ 
+
+ align:start position:0%
+even a gloomy feel depending on on the
+context of the scene um notice on the
+
+ align:start position:0%
+context of the scene um notice on the
+ 
+
+ align:start position:0%
+context of the scene um notice on the
+right in with direct sunlight you get
+
+ align:start position:0%
+right in with direct sunlight you get
+ 
+
+ align:start position:0%
+right in with direct sunlight you get
+very very hard crisp distinct Shadows so
+
+ align:start position:0%
+very very hard crisp distinct Shadows so
+ 
+
+ align:start position:0%
+very very hard crisp distinct Shadows so
+it turns out that what determines the
+
+ align:start position:0%
+it turns out that what determines the
+ 
+
+ align:start position:0%
+it turns out that what determines the
+quality of hard light versus soft light
+
+ align:start position:0%
+quality of hard light versus soft light
+ 
+
+ align:start position:0%
+quality of hard light versus soft light
+has a lot to do with the size of the
+
+ align:start position:0%
+has a lot to do with the size of the
+ 
+
+ align:start position:0%
+has a lot to do with the size of the
+light source so even though the sun is
+
+ align:start position:0%
+light source so even though the sun is
+ 
+
+ align:start position:0%
+light source so even though the sun is
+many times larger than the earth because
+
+ align:start position:0%
+many times larger than the earth because
+ 
+
+ align:start position:0%
+many times larger than the earth because
+it's so far away it's effectively a
+
+ align:start position:0%
+it's so far away it's effectively a
+ 
+
+ align:start position:0%
+it's so far away it's effectively a
+point source and a teeny tiny point
+
+ align:start position:0%
+point source and a teeny tiny point
+ 
+
+ align:start position:0%
+point source and a teeny tiny point
+source is going to give us crisp clean
+
+ align:start position:0%
+source is going to give us crisp clean
+ 
+
+ align:start position:0%
+source is going to give us crisp clean
+Shadows whereas on an overcast day the
+
+ align:start position:0%
+Shadows whereas on an overcast day the
+ 
+
+ align:start position:0%
+Shadows whereas on an overcast day the
+entire cloud cover is like Mother
+
+ align:start position:0%
+entire cloud cover is like Mother
+ 
+
+ align:start position:0%
+entire cloud cover is like Mother
+Nature's beautiful silk it's all light
+
+ align:start position:0%
+Nature's beautiful silk it's all light
+ 
+
+ align:start position:0%
+Nature's beautiful silk it's all light
+coming from all sorts of different
+
+ align:start position:0%
+coming from all sorts of different
+ 
+
+ align:start position:0%
+coming from all sorts of different
+directions and it's soft um and you know
+
+ align:start position:0%
+directions and it's soft um and you know
+ 
+
+ align:start position:0%
+directions and it's soft um and you know
+you can't beat the beautiful quality of
+
+ align:start position:0%
+you can't beat the beautiful quality of
+ 
+
+ align:start position:0%
+you can't beat the beautiful quality of
+of light on a cloudy day and then you
+
+ align:start position:0%
+of light on a cloudy day and then you
+ 
+
+ align:start position:0%
+of light on a cloudy day and then you
+can add a small accent light for a
+
+ align:start position:0%
+can add a small accent light for a
+ 
+
+ align:start position:0%
+can add a small accent light for a
+little bit of Dimension and you'll get
+
+ align:start position:0%
+little bit of Dimension and you'll get
+ 
+
+ align:start position:0%
+little bit of Dimension and you'll get
+Beautiful video images but harsh
+
+ align:start position:0%
+Beautiful video images but harsh
+ 
+
+ align:start position:0%
+Beautiful video images but harsh
+sunlight is pretty hard to deal with
+
+ align:start position:0%
+sunlight is pretty hard to deal with
+ 
+
+ align:start position:0%
+sunlight is pretty hard to deal with
+especially with faces but we'll talk
+
+ align:start position:0%
+especially with faces but we'll talk
+ 
+
+ align:start position:0%
+especially with faces but we'll talk
+about when we do the on Hands-On demo
+
+ align:start position:0%
+about when we do the on Hands-On demo
+ 
+
+ align:start position:0%
+about when we do the on Hands-On demo
+we'll talk about how we can deal with
+
+ align:start position:0%
+we'll talk about how we can deal with
+ 
+
+ align:start position:0%
+we'll talk about how we can deal with
+those issues in bright direct
+
+ align:start position:0%
+those issues in bright direct
+ 
+
+ align:start position:0%
+those issues in bright direct
+sunlight so this is sort of a summary in
+
+ align:start position:0%
+sunlight so this is sort of a summary in
+ 
+
+ align:start position:0%
+sunlight so this is sort of a summary in
+in more detail of what I've just talked
+
+ align:start position:0%
+in more detail of what I've just talked
+ 
+
+ align:start position:0%
+in more detail of what I've just talked
+about but I want to point out that in
+
+ align:start position:0%
+about but I want to point out that in
+ 
+
+ align:start position:0%
+about but I want to point out that in
+terms of soft light sources we're
+
+ align:start position:0%
+terms of soft light sources we're
+ 
+
+ align:start position:0%
+terms of soft light sources we're
+looking at things like soft boxes which
+
+ align:start position:0%
+looking at things like soft boxes which
+ 
+
+ align:start position:0%
+looking at things like soft boxes which
+have a large diffusion material in front
+
+ align:start position:0%
+have a large diffusion material in front
+ 
+
+ align:start position:0%
+have a large diffusion material in front
+of a a hard light um or light bouncing
+
+ align:start position:0%
+of a a hard light um or light bouncing
+ 
+
+ align:start position:0%
+of a a hard light um or light bouncing
+off of a white surface this is how you
+
+ align:start position:0%
+off of a white surface this is how you
+ 
+
+ align:start position:0%
+off of a white surface this is how you
+create soft light um because you can't
+
+ align:start position:0%
+create soft light um because you can't
+ 
+
+ align:start position:0%
+create soft light um because you can't
+always order in a cloudy day and cloudy
+
+ align:start position:0%
+always order in a cloudy day and cloudy
+ 
+
+ align:start position:0%
+always order in a cloudy day and cloudy
+days don't always walk into the building
+
+ align:start position:0%
+days don't always walk into the building
+ 
+
+ align:start position:0%
+days don't always walk into the building
+with you so you may have to create that
+
+ align:start position:0%
+with you so you may have to create that
+ 
+
+ align:start position:0%
+with you so you may have to create that
+soft light with an artificial uh unit um
+
+ align:start position:0%
+soft light with an artificial uh unit um
+ 
+
+ align:start position:0%
+soft light with an artificial uh unit um
+hard light typically Al a a direct
+
+ align:start position:0%
+hard light typically Al a a direct
+ 
+
+ align:start position:0%
+hard light typically Al a a direct
+sunlight a Fel instrument uh any kind of
+
+ align:start position:0%
+sunlight a Fel instrument uh any kind of
+ 
+
+ align:start position:0%
+sunlight a Fel instrument uh any kind of
+open face light with a reflector is
+
+ align:start position:0%
+open face light with a reflector is
+ 
+
+ align:start position:0%
+open face light with a reflector is
+going to give you hard light what's nice
+
+ align:start position:0%
+going to give you hard light what's nice
+ 
+
+ align:start position:0%
+going to give you hard light what's nice
+though is you can always soften a hard
+
+ align:start position:0%
+though is you can always soften a hard
+ 
+
+ align:start position:0%
+though is you can always soften a hard
+light by throwing diffusion material in
+
+ align:start position:0%
+light by throwing diffusion material in
+ 
+
+ align:start position:0%
+light by throwing diffusion material in
+front of it which spreads the beam so
+
+ align:start position:0%
+front of it which spreads the beam so
+ 
+
+ align:start position:0%
+front of it which spreads the beam so
+it's always great to have hard lights in
+
+ align:start position:0%
+it's always great to have hard lights in
+ 
+
+ align:start position:0%
+it's always great to have hard lights in
+your kit because you can always soften
+
+ align:start position:0%
+your kit because you can always soften
+ 
+
+ align:start position:0%
+your kit because you can always soften
+them but once a soft light unit there's
+
+ align:start position:0%
+them but once a soft light unit there's
+ 
+
+ align:start position:0%
+them but once a soft light unit there's
+really no practical way to make it hard
+
+ align:start position:0%
+really no practical way to make it hard
+ 
+
+ align:start position:0%
+really no practical way to make it hard
+again now something that we are you know
+
+ align:start position:0%
+again now something that we are you know
+ 
+
+ align:start position:0%
+again now something that we are you know
+we are entering this world of 3D
+
+ align:start position:0%
+we are entering this world of 3D
+ 
+
+ align:start position:0%
+we are entering this world of 3D
+cinematography and and all of that great
+
+ align:start position:0%
+cinematography and and all of that great
+ 
+
+ align:start position:0%
+cinematography and and all of that great
+stuff um but it turns out that for a
+
+ align:start position:0%
+stuff um but it turns out that for a
+ 
+
+ align:start position:0%
+stuff um but it turns out that for a
+zillion years uh photographers
+
+ align:start position:0%
+zillion years uh photographers
+ 
+
+ align:start position:0%
+zillion years uh photographers
+painters um cinematographers have been
+
+ align:start position:0%
+painters um cinematographers have been
+ 
+
+ align:start position:0%
+painters um cinematographers have been
+creating a sense of three dimensions uh
+
+ align:start position:0%
+creating a sense of three dimensions uh
+ 
+
+ align:start position:0%
+creating a sense of three dimensions uh
+without two cameras and two lenses uh
+
+ align:start position:0%
+without two cameras and two lenses uh
+ 
+
+ align:start position:0%
+without two cameras and two lenses uh
+but using light to do it and the trick
+
+ align:start position:0%
+but using light to do it and the trick
+ 
+
+ align:start position:0%
+but using light to do it and the trick
+is to create these alternating areas of
+
+ align:start position:0%
+is to create these alternating areas of
+ 
+
+ align:start position:0%
+is to create these alternating areas of
+light and dark and light and dark in a
+
+ align:start position:0%
+light and dark and light and dark in a
+ 
+
+ align:start position:0%
+light and dark and light and dark in a
+scene and the great great Prince of
+
+ align:start position:0%
+scene and the great great Prince of
+ 
+
+ align:start position:0%
+scene and the great great Prince of
+Karas skuro was Caravaggio Caravaggio
+
+ align:start position:0%
+Karas skuro was Caravaggio Caravaggio
+ 
+
+ align:start position:0%
+Karas skuro was Caravaggio Caravaggio
+basically introduced black into the
+
+ align:start position:0%
+basically introduced black into the
+ 
+
+ align:start position:0%
+basically introduced black into the
+painter's palet um and created these
+
+ align:start position:0%
+painter's palet um and created these
+ 
+
+ align:start position:0%
+painter's palet um and created these
+really dramatic three-dimensional
+
+ align:start position:0%
+really dramatic three-dimensional
+ 
+
+ align:start position:0%
+really dramatic three-dimensional
+Effects by alternating light and dark
+
+ align:start position:0%
+Effects by alternating light and dark
+ 
+
+ align:start position:0%
+Effects by alternating light and dark
+and light and dark um and we often talk
+
+ align:start position:0%
+and light and dark um and we often talk
+ 
+
+ align:start position:0%
+and light and dark um and we often talk
+about rembrand lighting in in
+
+ align:start position:0%
+about rembrand lighting in in
+ 
+
+ align:start position:0%
+about rembrand lighting in in
+portraiture and that little trademark
+
+ align:start position:0%
+portraiture and that little trademark
+ 
+
+ align:start position:0%
+portraiture and that little trademark
+Little Triangle in the opposite in the
+
+ align:start position:0%
+Little Triangle in the opposite in the
+ 
+
+ align:start position:0%
+Little Triangle in the opposite in the
+cheek opposite the light source um is
+
+ align:start position:0%
+cheek opposite the light source um is
+ 
+
+ align:start position:0%
+cheek opposite the light source um is
+one of the trademarks of of rbrand
+
+ align:start position:0%
+one of the trademarks of of rbrand
+ 
+
+ align:start position:0%
+one of the trademarks of of rbrand
+lighting and it's it's not really about
+
+ align:start position:0%
+lighting and it's it's not really about
+ 
+
+ align:start position:0%
+lighting and it's it's not really about
+the triangle but what the triangle means
+
+ align:start position:0%
+the triangle but what the triangle means
+ 
+
+ align:start position:0%
+the triangle but what the triangle means
+is that once again we've created the
+
+ align:start position:0%
+is that once again we've created the
+ 
+
+ align:start position:0%
+is that once again we've created the
+sense of light on the side of the face
+
+ align:start position:0%
+sense of light on the side of the face
+ 
+
+ align:start position:0%
+sense of light on the side of the face
+and then Darkness behind the nose and
+
+ align:start position:0%
+and then Darkness behind the nose and
+ 
+
+ align:start position:0%
+and then Darkness behind the nose and
+then another area of light and then
+
+ align:start position:0%
+then another area of light and then
+ 
+
+ align:start position:0%
+then another area of light and then
+another area of darkness and that sort
+
+ align:start position:0%
+another area of darkness and that sort
+ 
+
+ align:start position:0%
+another area of darkness and that sort
+of those sort of alternating areas of
+
+ align:start position:0%
+of those sort of alternating areas of
+ 
+
+ align:start position:0%
+of those sort of alternating areas of
+light and dark create this sense of
+
+ align:start position:0%
+light and dark create this sense of
+ 
+
+ align:start position:0%
+light and dark create this sense of
+Dimension so by simply moving the
+
+ align:start position:0%
+Dimension so by simply moving the
+ 
+
+ align:start position:0%
+Dimension so by simply moving the
+direction and the quality of your
+
+ align:start position:0%
+direction and the quality of your
+ 
+
+ align:start position:0%
+direction and the quality of your
+primary light source you can go from
+
+ align:start position:0%
+primary light source you can go from
+ 
+
+ align:start position:0%
+primary light source you can go from
+Flat daytime soap opera lighting to
+
+ align:start position:0%
+Flat daytime soap opera lighting to
+ 
+
+ align:start position:0%
+Flat daytime soap opera lighting to
+dimensional dramatic Frontline interview
+
+ align:start position:0%
+dimensional dramatic Frontline interview
+ 
+
+ align:start position:0%
+dimensional dramatic Frontline interview
+or R Brandt portrait um kind of lighting
+
+ align:start position:0%
+or R Brandt portrait um kind of lighting
+ 
+
+ align:start position:0%
+or R Brandt portrait um kind of lighting
+and it's all about the quality of light
+
+ align:start position:0%
+and it's all about the quality of light
+ 
+
+ align:start position:0%
+and it's all about the quality of light
+and what direction it's coming from and
+
+ align:start position:0%
+and what direction it's coming from and
+ 
+
+ align:start position:0%
+and what direction it's coming from and
+rembrand and carvaggio offer a wonderful
+
+ align:start position:0%
+rembrand and carvaggio offer a wonderful
+ 
+
+ align:start position:0%
+rembrand and carvaggio offer a wonderful
+study um in classic Kos guro
+
+ align:start position:0%
+study um in classic Kos guro
+ 
+
+ align:start position:0%
+study um in classic Kos guro
+lighting so let's talk about uh a few
+
+ align:start position:0%
+lighting so let's talk about uh a few
+ 
+
+ align:start position:0%
+lighting so let's talk about uh a few
+practical real world almost run in gun
+
+ align:start position:0%
+practical real world almost run in gun
+ 
+
+ align:start position:0%
+practical real world almost run in gun
+but not quite carrying three lights uh
+
+ align:start position:0%
+but not quite carrying three lights uh
+ 
+
+ align:start position:0%
+but not quite carrying three lights uh
+sort of
+
+ align:start position:0%
+sort of
+ 
+
+ align:start position:0%
+sort of
+interviews um so
+
+ align:start position:0%
+interviews um so
+ 
+
+ align:start position:0%
+interviews um so
+here here's a here's a frame from a film
+
+ align:start position:0%
+here here's a here's a frame from a film
+ 
+
+ align:start position:0%
+here here's a here's a frame from a film
+uh the lighting is a little more
+
+ align:start position:0%
+uh the lighting is a little more
+ 
+
+ align:start position:0%
+uh the lighting is a little more
+dramatic than you usually see I have a
+
+ align:start position:0%
+dramatic than you usually see I have a
+ 
+
+ align:start position:0%
+dramatic than you usually see I have a
+tendency to air on the side of drama uh
+
+ align:start position:0%
+tendency to air on the side of drama uh
+ 
+
+ align:start position:0%
+tendency to air on the side of drama uh
+we sort of have that little rembrand
+
+ align:start position:0%
+we sort of have that little rembrand
+ 
+
+ align:start position:0%
+we sort of have that little rembrand
+triangle on on her cheek and we can see
+
+ align:start position:0%
+triangle on on her cheek and we can see
+ 
+
+ align:start position:0%
+triangle on on her cheek and we can see
+that there's alternating areas of Light
+
+ align:start position:0%
+that there's alternating areas of Light
+ 
+
+ align:start position:0%
+that there's alternating areas of Light
+Dark Light Dark um in this
+
+ align:start position:0%
+Dark Light Dark um in this
+ 
+
+ align:start position:0%
+Dark Light Dark um in this
+Frame so how did we create this what did
+
+ align:start position:0%
+Frame so how did we create this what did
+ 
+
+ align:start position:0%
+Frame so how did we create this what did
+we do so if we look behind the scenes we
+
+ align:start position:0%
+we do so if we look behind the scenes we
+ 
+
+ align:start position:0%
+we do so if we look behind the scenes we
+see that we have a primary light source
+
+ align:start position:0%
+see that we have a primary light source
+ 
+
+ align:start position:0%
+see that we have a primary light source
+a soft box um the primary light source
+
+ align:start position:0%
+a soft box um the primary light source
+ 
+
+ align:start position:0%
+a soft box um the primary light source
+is typically called the key light our
+
+ align:start position:0%
+is typically called the key light our
+ 
+
+ align:start position:0%
+is typically called the key light our
+primary light source it's off to the
+
+ align:start position:0%
+primary light source it's off to the
+ 
+
+ align:start position:0%
+primary light source it's off to the
+side it's creating that sense of
+
+ align:start position:0%
+side it's creating that sense of
+ 
+
+ align:start position:0%
+side it's creating that sense of
+Dimension
+
+ align:start position:0%
+Dimension
+ 
+
+ align:start position:0%
+Dimension
+um we uh to the right we have what's
+
+ align:start position:0%
+um we uh to the right we have what's
+ 
+
+ align:start position:0%
+um we uh to the right we have what's
+called The Fill light whatever light is
+
+ align:start position:0%
+called The Fill light whatever light is
+ 
+
+ align:start position:0%
+called The Fill light whatever light is
+filling in the shadows created by the
+
+ align:start position:0%
+filling in the shadows created by the
+ 
+
+ align:start position:0%
+filling in the shadows created by the
+key light we call that the fill light
+
+ align:start position:0%
+key light we call that the fill light
+ 
+
+ align:start position:0%
+key light we call that the fill light
+and in the case of this example we're
+
+ align:start position:0%
+and in the case of this example we're
+ 
+
+ align:start position:0%
+and in the case of this example we're
+using a reflector it's called a flex
+
+ align:start position:0%
+using a reflector it's called a flex
+ 
+
+ align:start position:0%
+using a reflector it's called a flex
+fill which you'll see in the live demo
+
+ align:start position:0%
+fill which you'll see in the live demo
+ 
+
+ align:start position:0%
+fill which you'll see in the live demo
+portion of our show um we're using a
+
+ align:start position:0%
+portion of our show um we're using a
+ 
+
+ align:start position:0%
+portion of our show um we're using a
+flex fill to reflect some of that key
+
+ align:start position:0%
+flex fill to reflect some of that key
+ 
+
+ align:start position:0%
+flex fill to reflect some of that key
+light back onto the subject so that the
+
+ align:start position:0%
+light back onto the subject so that the
+ 
+
+ align:start position:0%
+light back onto the subject so that the
+dark side of the face doesn't become
+
+ align:start position:0%
+dark side of the face doesn't become
+ 
+
+ align:start position:0%
+dark side of the face doesn't become
+totally dark um and then slightly off
+
+ align:start position:0%
+totally dark um and then slightly off
+ 
+
+ align:start position:0%
+totally dark um and then slightly off
+the top of the frame there we have a
+
+ align:start position:0%
+the top of the frame there we have a
+ 
+
+ align:start position:0%
+the top of the frame there we have a
+backlight and we're using the backlight
+
+ align:start position:0%
+backlight and we're using the backlight
+ 
+
+ align:start position:0%
+backlight and we're using the backlight
+to create a little bit if we go back to
+
+ align:start position:0%
+to create a little bit if we go back to
+ 
+
+ align:start position:0%
+to create a little bit if we go back to
+this image there's a little bit of light
+
+ align:start position:0%
+this image there's a little bit of light
+ 
+
+ align:start position:0%
+this image there's a little bit of light
+on her shoulder and there's a little bit
+
+ align:start position:0%
+on her shoulder and there's a little bit
+ 
+
+ align:start position:0%
+on her shoulder and there's a little bit
+of light on on her hair that's coming
+
+ align:start position:0%
+of light on on her hair that's coming
+ 
+
+ align:start position:0%
+of light on on her hair that's coming
+from behind her so what we did is we
+
+ align:start position:0%
+from behind her so what we did is we
+ 
+
+ align:start position:0%
+from behind her so what we did is we
+have a 300 watt Fel we'll talk a little
+
+ align:start position:0%
+have a 300 watt Fel we'll talk a little
+ 
+
+ align:start position:0%
+have a 300 watt Fel we'll talk a little
+more about frels
+
+ align:start position:0%
+more about frels
+ 
+
+ align:start position:0%
+more about frels
+later um behind her that's just giving a
+
+ align:start position:0%
+later um behind her that's just giving a
+ 
+
+ align:start position:0%
+later um behind her that's just giving a
+little bit of light coming from the back
+
+ align:start position:0%
+little bit of light coming from the back
+ 
+
+ align:start position:0%
+little bit of light coming from the back
+which creates a little bit of additional
+
+ align:start position:0%
+which creates a little bit of additional
+ 
+
+ align:start position:0%
+which creates a little bit of additional
+dimensionality and separation from the
+
+ align:start position:0%
+dimensionality and separation from the
+ 
+
+ align:start position:0%
+dimensionality and separation from the
+background but in this particular frame
+
+ align:start position:0%
+background but in this particular frame
+ 
+
+ align:start position:0%
+background but in this particular frame
+it's very subtle if you overdo the
+
+ align:start position:0%
+it's very subtle if you overdo the
+ 
+
+ align:start position:0%
+it's very subtle if you overdo the
+backlight all of a sudden things start
+
+ align:start position:0%
+backlight all of a sudden things start
+ 
+
+ align:start position:0%
+backlight all of a sudden things start
+to look theatrical we're in the middle
+
+ align:start position:0%
+to look theatrical we're in the middle
+ 
+
+ align:start position:0%
+to look theatrical we're in the middle
+of a play we're not in the middle of a
+
+ align:start position:0%
+of a play we're not in the middle of a
+ 
+
+ align:start position:0%
+of a play we're not in the middle of a
+documentary anymore so you have to be
+
+ align:start position:0%
+documentary anymore so you have to be
+ 
+
+ align:start position:0%
+documentary anymore so you have to be
+careful because the backlight is a very
+
+ align:start position:0%
+careful because the backlight is a very
+ 
+
+ align:start position:0%
+careful because the backlight is a very
+artificial element um but if done subtly
+
+ align:start position:0%
+artificial element um but if done subtly
+ 
+
+ align:start position:0%
+artificial element um but if done subtly
+it can be it can look very much like a
+
+ align:start position:0%
+it can be it can look very much like a
+ 
+
+ align:start position:0%
+it can be it can look very much like a
+natural element and give a little bit of
+
+ align:start position:0%
+natural element and give a little bit of
+ 
+
+ align:start position:0%
+natural element and give a little bit of
+separation and we can see a little bit
+
+ align:start position:0%
+separation and we can see a little bit
+ 
+
+ align:start position:0%
+separation and we can see a little bit
+of shine in the hair uh and then we have
+
+ align:start position:0%
+of shine in the hair uh and then we have
+ 
+
+ align:start position:0%
+of shine in the hair uh and then we have
+a fourth light because remember we've
+
+ align:start position:0%
+a fourth light because remember we've
+ 
+
+ align:start position:0%
+a fourth light because remember we've
+got the key light The Fill light filling
+
+ align:start position:0%
+got the key light The Fill light filling
+ 
+
+ align:start position:0%
+got the key light The Fill light filling
+in the shadows caused by the key light a
+
+ align:start position:0%
+in the shadows caused by the key light a
+ 
+
+ align:start position:0%
+in the shadows caused by the key light a
+back light coming from behind the
+
+ align:start position:0%
+back light coming from behind the
+ 
+
+ align:start position:0%
+back light coming from behind the
+subject offering a little bit of
+
+ align:start position:0%
+subject offering a little bit of
+ 
+
+ align:start position:0%
+subject offering a little bit of
+Dimension and there's a fourth light
+
+ align:start position:0%
+Dimension and there's a fourth light
+ 
+
+ align:start position:0%
+Dimension and there's a fourth light
+that we often talk about and that's the
+
+ align:start position:0%
+that we often talk about and that's the
+ 
+
+ align:start position:0%
+that we often talk about and that's the
+background light not to be confused with
+
+ align:start position:0%
+background light not to be confused with
+ 
+
+ align:start position:0%
+background light not to be confused with
+the backl now the background light in
+
+ align:start position:0%
+the backl now the background light in
+ 
+
+ align:start position:0%
+the backl now the background light in
+this particular scene is being provided
+
+ align:start position:0%
+this particular scene is being provided
+ 
+
+ align:start position:0%
+this particular scene is being provided
+by the window in the upper right hand
+
+ align:start position:0%
+by the window in the upper right hand
+ 
+
+ align:start position:0%
+by the window in the upper right hand
+corner I've covered up part of the
+
+ align:start position:0%
+corner I've covered up part of the
+ 
+
+ align:start position:0%
+corner I've covered up part of the
+window with foam core um but I've left
+
+ align:start position:0%
+window with foam core um but I've left
+ 
+
+ align:start position:0%
+window with foam core um but I've left
+the rest of the window open to kind of
+
+ align:start position:0%
+the rest of the window open to kind of
+ 
+
+ align:start position:0%
+the rest of the window open to kind of
+add this sort of overall light so if we
+
+ align:start position:0%
+add this sort of overall light so if we
+ 
+
+ align:start position:0%
+add this sort of overall light so if we
+go oops if we go back
+
+ align:start position:0%
+go oops if we go back
+ 
+
+ align:start position:0%
+go oops if we go back
+here the overall ambient light that's
+
+ align:start position:0%
+here the overall ambient light that's
+ 
+
+ align:start position:0%
+here the overall ambient light that's
+lighting the back wall is a mixture of
+
+ align:start position:0%
+lighting the back wall is a mixture of
+ 
+
+ align:start position:0%
+lighting the back wall is a mixture of
+what's coming in from the window and
+
+ align:start position:0%
+what's coming in from the window and
+ 
+
+ align:start position:0%
+what's coming in from the window and
+what's coming in from the key light cuz
+
+ align:start position:0%
+what's coming in from the key light cuz
+ 
+
+ align:start position:0%
+what's coming in from the key light cuz
+we don't want the background we want the
+
+ align:start position:0%
+we don't want the background we want the
+ 
+
+ align:start position:0%
+we don't want the background we want the
+background to be a little bit darker
+
+ align:start position:0%
+background to be a little bit darker
+ 
+
+ align:start position:0%
+background to be a little bit darker
+than the subject so the subject kind of
+
+ align:start position:0%
+than the subject so the subject kind of
+ 
+
+ align:start position:0%
+than the subject so the subject kind of
+um pops out as the main element CU you
+
+ align:start position:0%
+um pops out as the main element CU you
+ 
+
+ align:start position:0%
+um pops out as the main element CU you
+know one of the things that we're
+
+ align:start position:0%
+know one of the things that we're
+ 
+
+ align:start position:0%
+know one of the things that we're
+thinking about when we're lighting is
+
+ align:start position:0%
+thinking about when we're lighting is
+ 
+
+ align:start position:0%
+thinking about when we're lighting is
+we're drawing attention we're using
+
+ align:start position:0%
+we're drawing attention we're using
+ 
+
+ align:start position:0%
+we're drawing attention we're using
+lighting to draw the viewer's attention
+
+ align:start position:0%
+lighting to draw the viewer's attention
+ 
+
+ align:start position:0%
+lighting to draw the viewer's attention
+to what the important things are in the
+
+ align:start position:0%
+to what the important things are in the
+ 
+
+ align:start position:0%
+to what the important things are in the
+frame but we don't want to completely
+
+ align:start position:0%
+frame but we don't want to completely
+ 
+
+ align:start position:0%
+frame but we don't want to completely
+obscure the background because while the
+
+ align:start position:0%
+obscure the background because while the
+ 
+
+ align:start position:0%
+obscure the background because while the
+interview subject may be the subject of
+
+ align:start position:0%
+interview subject may be the subject of
+ 
+
+ align:start position:0%
+interview subject may be the subject of
+our image there's also a predicate just
+
+ align:start position:0%
+our image there's also a predicate just
+ 
+
+ align:start position:0%
+our image there's also a predicate just
+like any good sentence and so the
+
+ align:start position:0%
+like any good sentence and so the
+ 
+
+ align:start position:0%
+like any good sentence and so the
+context here is the editing room is the
+
+ align:start position:0%
+context here is the editing room is the
+ 
+
+ align:start position:0%
+context here is the editing room is the
+equipment that's in the room so we want
+
+ align:start position:0%
+equipment that's in the room so we want
+ 
+
+ align:start position:0%
+equipment that's in the room so we want
+to feature that too but we want it to
+
+ align:start position:0%
+to feature that too but we want it to
+ 
+
+ align:start position:0%
+to feature that too but we want it to
+feel like it's part of the background
+
+ align:start position:0%
+feel like it's part of the background
+ 
+
+ align:start position:0%
+feel like it's part of the background
+both in terms of intensity and in terms
+
+ align:start position:0%
+both in terms of intensity and in terms
+ 
+
+ align:start position:0%
+both in terms of intensity and in terms
+of of placement um so a little bit of
+
+ align:start position:0%
+of of placement um so a little bit of
+ 
+
+ align:start position:0%
+of of placement um so a little bit of
+background light is being provided by
+
+ align:start position:0%
+background light is being provided by
+ 
+
+ align:start position:0%
+background light is being provided by
+both spill from the key as well as some
+
+ align:start position:0%
+both spill from the key as well as some
+ 
+
+ align:start position:0%
+both spill from the key as well as some
+of the windows so what we did is we
+
+ align:start position:0%
+of the windows so what we did is we
+ 
+
+ align:start position:0%
+of the windows so what we did is we
+varied that foam core until we had just
+
+ align:start position:0%
+varied that foam core until we had just
+ 
+
+ align:start position:0%
+varied that foam core until we had just
+the right amount of ambient light in the
+
+ align:start position:0%
+the right amount of ambient light in the
+ 
+
+ align:start position:0%
+the right amount of ambient light in the
+room and that's where we placed it so
+
+ align:start position:0%
+room and that's where we placed it so
+ 
+
+ align:start position:0%
+room and that's where we placed it so
+very often you can use nature natural
+
+ align:start position:0%
+very often you can use nature natural
+ 
+
+ align:start position:0%
+very often you can use nature natural
+light as as as one of your light units I
+
+ align:start position:0%
+light as as as one of your light units I
+ 
+
+ align:start position:0%
+light as as as one of your light units I
+like to work with what's natural I knew
+
+ align:start position:0%
+like to work with what's natural I knew
+ 
+
+ align:start position:0%
+like to work with what's natural I knew
+that that was facing in a direction that
+
+ align:start position:0%
+that that was facing in a direction that
+ 
+
+ align:start position:0%
+that that was facing in a direction that
+we wouldn't have direct sun shining in
+
+ align:start position:0%
+we wouldn't have direct sun shining in
+ 
+
+ align:start position:0%
+we wouldn't have direct sun shining in
+the room anytime during the interview so
+
+ align:start position:0%
+the room anytime during the interview so
+ 
+
+ align:start position:0%
+the room anytime during the interview so
+it's always good to know what direction
+
+ align:start position:0%
+it's always good to know what direction
+ 
+
+ align:start position:0%
+it's always good to know what direction
+the sun's going in so we could rely for
+
+ align:start position:0%
+the sun's going in so we could rely for
+ 
+
+ align:start position:0%
+the sun's going in so we could rely for
+two hours that we would have Skylight
+
+ align:start position:0%
+two hours that we would have Skylight
+ 
+
+ align:start position:0%
+two hours that we would have Skylight
+but no direct sunlight to kind of mess
+
+ align:start position:0%
+but no direct sunlight to kind of mess
+ 
+
+ align:start position:0%
+but no direct sunlight to kind of mess
+up our scene so if I can bring Mother
+
+ align:start position:0%
+up our scene so if I can bring Mother
+ 
+
+ align:start position:0%
+up our scene so if I can bring Mother
+Nature into the lighting equation that's
+
+ align:start position:0%
+Nature into the lighting equation that's
+ 
+
+ align:start position:0%
+Nature into the lighting equation that's
+great if I could do this whole setup
+
+ align:start position:0%
+great if I could do this whole setup
+ 
+
+ align:start position:0%
+great if I could do this whole setup
+without any artificial light that would
+
+ align:start position:0%
+without any artificial light that would
+ 
+
+ align:start position:0%
+without any artificial light that would
+be even better um but that doesn't
+
+ align:start position:0%
+be even better um but that doesn't
+ 
+
+ align:start position:0%
+be even better um but that doesn't
+always work out that
+
+ align:start position:0%
+always work out that
+ 
+
+ align:start position:0%
+always work out that
+way so I'm going to basically kind of
+
+ align:start position:0%
+way so I'm going to basically kind of
+ 
+
+ align:start position:0%
+way so I'm going to basically kind of
+review what we just talked about in in
+
+ align:start position:0%
+review what we just talked about in in
+ 
+
+ align:start position:0%
+review what we just talked about in in
+four different environments so a typical
+
+ align:start position:0%
+four different environments so a typical
+ 
+
+ align:start position:0%
+four different environments so a typical
+formal interview is what you just saw in
+
+ align:start position:0%
+formal interview is what you just saw in
+ 
+
+ align:start position:0%
+formal interview is what you just saw in
+this particular uh situation um I saw
+
+ align:start position:0%
+this particular uh situation um I saw
+ 
+
+ align:start position:0%
+this particular uh situation um I saw
+that there were these beautiful French
+
+ align:start position:0%
+that there were these beautiful French
+ 
+
+ align:start position:0%
+that there were these beautiful French
+doors in the room I said aha we're going
+
+ align:start position:0%
+doors in the room I said aha we're going
+ 
+
+ align:start position:0%
+doors in the room I said aha we're going
+to use that um as our background because
+
+ align:start position:0%
+to use that um as our background because
+ 
+
+ align:start position:0%
+to use that um as our background because
+it kind of you know it looks nice it
+
+ align:start position:0%
+it kind of you know it looks nice it
+ 
+
+ align:start position:0%
+it kind of you know it looks nice it
+adds a little bit of Dimension um but I
+
+ align:start position:0%
+adds a little bit of Dimension um but I
+ 
+
+ align:start position:0%
+adds a little bit of Dimension um but I
+want the background to recede and I want
+
+ align:start position:0%
+want the background to recede and I want
+ 
+
+ align:start position:0%
+want the background to recede and I want
+the foreground to move forward well it
+
+ align:start position:0%
+the foreground to move forward well it
+ 
+
+ align:start position:0%
+the foreground to move forward well it
+turns out that your warmer colors have a
+
+ align:start position:0%
+turns out that your warmer colors have a
+ 
+
+ align:start position:0%
+turns out that your warmer colors have a
+tendency to move forward and your cooler
+
+ align:start position:0%
+tendency to move forward and your cooler
+ 
+
+ align:start position:0%
+tendency to move forward and your cooler
+colors like your Blues have a tendency
+
+ align:start position:0%
+colors like your Blues have a tendency
+ 
+
+ align:start position:0%
+colors like your Blues have a tendency
+to kind of fall into the background so
+
+ align:start position:0%
+to kind of fall into the background so
+ 
+
+ align:start position:0%
+to kind of fall into the background so
+what did I do is I put a background
+
+ align:start position:0%
+what did I do is I put a background
+ 
+
+ align:start position:0%
+what did I do is I put a background
+light behind the lace curtains behind
+
+ align:start position:0%
+light behind the lace curtains behind
+ 
+
+ align:start position:0%
+light behind the lace curtains behind
+those French doors with a half blue gel
+
+ align:start position:0%
+those French doors with a half blue gel
+ 
+
+ align:start position:0%
+those French doors with a half blue gel
+so that's giving me the kind of the
+
+ align:start position:0%
+so that's giving me the kind of the
+ 
+
+ align:start position:0%
+so that's giving me the kind of the
+bluish background and of course she's
+
+ align:start position:0%
+bluish background and of course she's
+ 
+
+ align:start position:0%
+bluish background and of course she's
+being lit by a soft box something called
+
+ align:start position:0%
+being lit by a soft box something called
+ 
+
+ align:start position:0%
+being lit by a soft box something called
+a Rea light from l so the primary key in
+
+ align:start position:0%
+a Rea light from l so the primary key in
+ 
+
+ align:start position:0%
+a Rea light from l so the primary key in
+this case is is a you know it's a soft
+
+ align:start position:0%
+this case is is a you know it's a soft
+ 
+
+ align:start position:0%
+this case is is a you know it's a soft
+LGE relatively mediumsized I guess soft
+
+ align:start position:0%
+LGE relatively mediumsized I guess soft
+ 
+
+ align:start position:0%
+LGE relatively mediumsized I guess soft
+light and once again we're using the
+
+ align:start position:0%
+light and once again we're using the
+ 
+
+ align:start position:0%
+light and once again we're using the
+reflector flexfill as our full light
+
+ align:start position:0%
+reflector flexfill as our full light
+ 
+
+ align:start position:0%
+reflector flexfill as our full light
+because you know the less wires and the
+
+ align:start position:0%
+because you know the less wires and the
+ 
+
+ align:start position:0%
+because you know the less wires and the
+less light that I can travel with the
+
+ align:start position:0%
+less light that I can travel with the
+ 
+
+ align:start position:0%
+less light that I can travel with the
+better so we we basically lit this
+
+ align:start position:0%
+better so we we basically lit this
+ 
+
+ align:start position:0%
+better so we we basically lit this
+situation with two lights plus the
+
+ align:start position:0%
+situation with two lights plus the
+ 
+
+ align:start position:0%
+situation with two lights plus the
+ambient spill that was coming from the
+
+ align:start position:0%
+ambient spill that was coming from the
+ 
+
+ align:start position:0%
+ambient spill that was coming from the
+windows in the middle of the day so this
+
+ align:start position:0%
+windows in the middle of the day so this
+ 
+
+ align:start position:0%
+windows in the middle of the day so this
+was once again um a 3point lighting
+
+ align:start position:0%
+was once again um a 3point lighting
+ 
+
+ align:start position:0%
+was once again um a 3point lighting
+setup but we're only using two fixtures
+
+ align:start position:0%
+setup but we're only using two fixtures
+ 
+
+ align:start position:0%
+setup but we're only using two fixtures
+because we're making use of the natural
+
+ align:start position:0%
+because we're making use of the natural
+ 
+
+ align:start position:0%
+because we're making use of the natural
+light that was available in this living
+
+ align:start position:0%
+light that was available in this living
+ 
+
+ align:start position:0%
+light that was available in this living
+room uh at at the time and the key is
+
+ align:start position:0%
+room uh at at the time and the key is
+ 
+
+ align:start position:0%
+room uh at at the time and the key is
+relatively soft and you can tell that by
+
+ align:start position:0%
+relatively soft and you can tell that by
+ 
+
+ align:start position:0%
+relatively soft and you can tell that by
+the way the light wraps around the face
+
+ align:start position:0%
+the way the light wraps around the face
+ 
+
+ align:start position:0%
+the way the light wraps around the face
+so notice how even though that there's a
+
+ align:start position:0%
+so notice how even though that there's a
+ 
+
+ align:start position:0%
+so notice how even though that there's a
+shadow uh where her nose is and there's
+
+ align:start position:0%
+shadow uh where her nose is and there's
+ 
+
+ align:start position:0%
+shadow uh where her nose is and there's
+a shadow on the right hand side of her
+
+ align:start position:0%
+a shadow on the right hand side of her
+ 
+
+ align:start position:0%
+a shadow on the right hand side of her
+face there is a smooth gradient from the
+
+ align:start position:0%
+face there is a smooth gradient from the
+ 
+
+ align:start position:0%
+face there is a smooth gradient from the
+light to the dark area and we call that
+
+ align:start position:0%
+light to the dark area and we call that
+ 
+
+ align:start position:0%
+light to the dark area and we call that
+the way the light wraps around the face
+
+ align:start position:0%
+the way the light wraps around the face
+ 
+
+ align:start position:0%
+the way the light wraps around the face
+um if we had a we'll see now in this
+
+ align:start position:0%
+um if we had a we'll see now in this
+ 
+
+ align:start position:0%
+um if we had a we'll see now in this
+other interview we have a harsh overhead
+
+ align:start position:0%
+other interview we have a harsh overhead
+ 
+
+ align:start position:0%
+other interview we have a harsh overhead
+standard Edison based light bulb 150 W
+
+ align:start position:0%
+standard Edison based light bulb 150 W
+ 
+
+ align:start position:0%
+standard Edison based light bulb 150 W
+screw light bulb in the top of the room
+
+ align:start position:0%
+screw light bulb in the top of the room
+ 
+
+ align:start position:0%
+screw light bulb in the top of the room
+there's also a couple of small quartz
+
+ align:start position:0%
+there's also a couple of small quartz
+ 
+
+ align:start position:0%
+there's also a couple of small quartz
+lights that are lighting the uh the toy
+
+ align:start position:0%
+lights that are lighting the uh the toy
+ 
+
+ align:start position:0%
+lights that are lighting the uh the toy
+collection cabinet behind her um but
+
+ align:start position:0%
+collection cabinet behind her um but
+ 
+
+ align:start position:0%
+collection cabinet behind her um but
+this is basically working under very
+
+ align:start position:0%
+this is basically working under very
+ 
+
+ align:start position:0%
+this is basically working under very
+harsh um nonoptimal lighting conditions
+
+ align:start position:0%
+harsh um nonoptimal lighting conditions
+ 
+
+ align:start position:0%
+harsh um nonoptimal lighting conditions
+um and so it's not at all
+
+ align:start position:0%
+um and so it's not at all
+ 
+
+ align:start position:0%
+um and so it's not at all
+flattering in in some ways um
+
+ align:start position:0%
+flattering in in some ways um
+ 
+
+ align:start position:0%
+flattering in in some ways um
+we're we're not doing our subject
+
+ align:start position:0%
+we're we're not doing our subject
+ 
+
+ align:start position:0%
+we're we're not doing our subject
+justice of course in this film she was
+
+ align:start position:0%
+justice of course in this film she was
+ 
+
+ align:start position:0%
+justice of course in this film she was
+sort of playfully playing the role of
+
+ align:start position:0%
+sort of playfully playing the role of
+ 
+
+ align:start position:0%
+sort of playfully playing the role of
+the bad guy um so the lighting kind of
+
+ align:start position:0%
+the bad guy um so the lighting kind of
+ 
+
+ align:start position:0%
+the bad guy um so the lighting kind of
+worked dramatically for those purposes
+
+ align:start position:0%
+worked dramatically for those purposes
+ 
+
+ align:start position:0%
+worked dramatically for those purposes
+um so I decided to go with it rather
+
+ align:start position:0%
+um so I decided to go with it rather
+ 
+
+ align:start position:0%
+um so I decided to go with it rather
+than bringing the lighting kit out uh
+
+ align:start position:0%
+than bringing the lighting kit out uh
+ 
+
+ align:start position:0%
+than bringing the lighting kit out uh
+because we said it looks okay we want
+
+ align:start position:0%
+because we said it looks okay we want
+ 
+
+ align:start position:0%
+because we said it looks okay we want
+this to kind of be raw and harsh uh once
+
+ align:start position:0%
+this to kind of be raw and harsh uh once
+ 
+
+ align:start position:0%
+this to kind of be raw and harsh uh once
+again it's all about context what does
+
+ align:start position:0%
+again it's all about context what does
+ 
+
+ align:start position:0%
+again it's all about context what does
+the lighting do for your storytelling uh
+
+ align:start position:0%
+the lighting do for your storytelling uh
+ 
+
+ align:start position:0%
+the lighting do for your storytelling uh
+it it was okay uh for a character making
+
+ align:start position:0%
+it it was okay uh for a character making
+ 
+
+ align:start position:0%
+it it was okay uh for a character making
+certain harsh comments to be kind of in
+
+ align:start position:0%
+certain harsh comments to be kind of in
+ 
+
+ align:start position:0%
+certain harsh comments to be kind of in
+slightly harsh uh light at least it
+
+ align:start position:0%
+slightly harsh uh light at least it
+ 
+
+ align:start position:0%
+slightly harsh uh light at least it
+worked uh for me uh creatively in this
+
+ align:start position:0%
+worked uh for me uh creatively in this
+ 
+
+ align:start position:0%
+worked uh for me uh creatively in this
+particular scene but most of the time
+
+ align:start position:0%
+particular scene but most of the time
+ 
+
+ align:start position:0%
+particular scene but most of the time
+that's not what I want here's another
+
+ align:start position:0%
+that's not what I want here's another
+ 
+
+ align:start position:0%
+that's not what I want here's another
+situation which is not at all optimal
+
+ align:start position:0%
+situation which is not at all optimal
+ 
+
+ align:start position:0%
+situation which is not at all optimal
+this is
+
+ align:start position:0%
+this is
+ 
+
+ align:start position:0%
+this is
+handheld um
+
+ align:start position:0%
+handheld um
+ 
+
+ align:start position:0%
+handheld um
+impromptu uh conversation with a
+
+ align:start position:0%
+impromptu uh conversation with a
+ 
+
+ align:start position:0%
+impromptu uh conversation with a
+character in the middle of an art
+
+ align:start position:0%
+character in the middle of an art
+ 
+
+ align:start position:0%
+character in the middle of an art
+opening um it the the the lighting was
+
+ align:start position:0%
+opening um it the the the lighting was
+ 
+
+ align:start position:0%
+opening um it the the the lighting was
+mixed window light dark Corners
+
+ align:start position:0%
+mixed window light dark Corners
+ 
+
+ align:start position:0%
+mixed window light dark Corners
+incandescent lights harsh really really
+
+ align:start position:0%
+incandescent lights harsh really really
+ 
+
+ align:start position:0%
+incandescent lights harsh really really
+difficult I looked around the room and I
+
+ align:start position:0%
+difficult I looked around the room and I
+ 
+
+ align:start position:0%
+difficult I looked around the room and I
+go oh my God what are we going to do um
+
+ align:start position:0%
+go oh my God what are we going to do um
+ 
+
+ align:start position:0%
+go oh my God what are we going to do um
+and then I saw this big window and I
+
+ align:start position:0%
+and then I saw this big window and I
+ 
+
+ align:start position:0%
+and then I saw this big window and I
+said do you mind standing next to the
+
+ align:start position:0%
+said do you mind standing next to the
+ 
+
+ align:start position:0%
+said do you mind standing next to the
+big window so out of the darkness I was
+
+ align:start position:0%
+big window so out of the darkness I was
+ 
+
+ align:start position:0%
+big window so out of the darkness I was
+able to move the subject so that uh she
+
+ align:start position:0%
+able to move the subject so that uh she
+ 
+
+ align:start position:0%
+able to move the subject so that uh she
+was being lit by um window
+
+ align:start position:0%
+was being lit by um window
+ 
+
+ align:start position:0%
+was being lit by um window
+light so here's me no lights no kit
+
+ align:start position:0%
+light so here's me no lights no kit
+ 
+
+ align:start position:0%
+light so here's me no lights no kit
+camera in my right hand microphone in
+
+ align:start position:0%
+camera in my right hand microphone in
+ 
+
+ align:start position:0%
+camera in my right hand microphone in
+the left hand um let's move by the
+
+ align:start position:0%
+the left hand um let's move by the
+ 
+
+ align:start position:0%
+the left hand um let's move by the
+window so sometimes you just got to look
+
+ align:start position:0%
+window so sometimes you just got to look
+ 
+
+ align:start position:0%
+window so sometimes you just got to look
+around and see where the light looks
+
+ align:start position:0%
+around and see where the light looks
+ 
+
+ align:start position:0%
+around and see where the light looks
+best and move your subject into um that
+
+ align:start position:0%
+best and move your subject into um that
+ 
+
+ align:start position:0%
+best and move your subject into um that
+area and it's remembering again to apply
+
+ align:start position:0%
+area and it's remembering again to apply
+ 
+
+ align:start position:0%
+area and it's remembering again to apply
+some of the principles that you're
+
+ align:start position:0%
+some of the principles that you're
+ 
+
+ align:start position:0%
+some of the principles that you're
+talking about in a situation where you
+
+ align:start position:0%
+talking about in a situation where you
+ 
+
+ align:start position:0%
+talking about in a situation where you
+don't have lights uh but still keeping
+
+ align:start position:0%
+don't have lights uh but still keeping
+ 
+
+ align:start position:0%
+don't have lights uh but still keeping
+in mind all of the things that that that
+
+ align:start position:0%
+in mind all of the things that that that
+ 
+
+ align:start position:0%
+in mind all of the things that that that
+were discussing the intensity of the
+
+ align:start position:0%
+were discussing the intensity of the
+ 
+
+ align:start position:0%
+were discussing the intensity of the
+light the direction of the light the the
+
+ align:start position:0%
+light the direction of the light the the
+ 
+
+ align:start position:0%
+light the direction of the light the the
+quality of the light the the
+
+ align:start position:0%
+quality of the light the the
+ 
+
+ align:start position:0%
+quality of the light the the
+um mhm uh color of the light and and
+
+ align:start position:0%
+um mhm uh color of the light and and
+ 
+
+ align:start position:0%
+um mhm uh color of the light and and
+making choices on on where you conduct
+
+ align:start position:0%
+making choices on on where you conduct
+ 
+
+ align:start position:0%
+making choices on on where you conduct
+your interviews or do your shooting
+
+ align:start position:0%
+your interviews or do your shooting
+ 
+
+ align:start position:0%
+your interviews or do your shooting
+exactly based on those principles uh you
+
+ align:start position:0%
+exactly based on those principles uh you
+ 
+
+ align:start position:0%
+exactly based on those principles uh you
+know in fact in this case I didn't even
+
+ align:start position:0%
+know in fact in this case I didn't even
+ 
+
+ align:start position:0%
+know in fact in this case I didn't even
+even have time to do my eighth blue
+
+ align:start position:0%
+even have time to do my eighth blue
+ 
+
+ align:start position:0%
+even have time to do my eighth blue
+trick I just set the preset to Daylight
+
+ align:start position:0%
+trick I just set the preset to Daylight
+ 
+
+ align:start position:0%
+trick I just set the preset to Daylight
+because I knew that
+
+ align:start position:0%
+because I knew that
+ 
+
+ align:start position:0%
+because I knew that
+the window was pretty much daylight and
+
+ align:start position:0%
+the window was pretty much daylight and
+ 
+
+ align:start position:0%
+the window was pretty much daylight and
+of course you're getting the little bit
+
+ align:start position:0%
+of course you're getting the little bit
+ 
+
+ align:start position:0%
+of course you're getting the little bit
+of triangle on the cheek because of her
+
+ align:start position:0%
+of triangle on the cheek because of her
+ 
+
+ align:start position:0%
+of triangle on the cheek because of her
+position relative relative to the light
+
+ align:start position:0%
+position relative relative to the light
+ 
+
+ align:start position:0%
+position relative relative to the light
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh that is what I'm always paying
+
+ align:start position:0%
+uh that is what I'm always paying
+ 
+
+ align:start position:0%
+uh that is what I'm always paying
+attention to I watch somebody talking
+
+ align:start position:0%
+attention to I watch somebody talking
+ 
+
+ align:start position:0%
+attention to I watch somebody talking
+and I go am I am I seeing that
+
+ align:start position:0%
+and I go am I am I seeing that
+ 
+
+ align:start position:0%
+and I go am I am I seeing that
+dimensional light sometimes I just and
+
+ align:start position:0%
+dimensional light sometimes I just and
+ 
+
+ align:start position:0%
+dimensional light sometimes I just and
+in fact when I'm doing an impromptu
+
+ align:start position:0%
+in fact when I'm doing an impromptu
+ 
+
+ align:start position:0%
+in fact when I'm doing an impromptu
+interview like this I won't ask the
+
+ align:start position:0%
+interview like this I won't ask the
+ 
+
+ align:start position:0%
+interview like this I won't ask the
+subject to change very often I will
+
+ align:start position:0%
+subject to change very often I will
+ 
+
+ align:start position:0%
+subject to change very often I will
+move and watch how the lighting changes
+
+ align:start position:0%
+move and watch how the lighting changes
+ 
+
+ align:start position:0%
+move and watch how the lighting changes
+on their face because sometimes just
+
+ align:start position:0%
+on their face because sometimes just
+ 
+
+ align:start position:0%
+on their face because sometimes just
+moving to the left a foot and a half or
+
+ align:start position:0%
+moving to the left a foot and a half or
+ 
+
+ align:start position:0%
+moving to the left a foot and a half or
+to the right a foot and a half will
+
+ align:start position:0%
+to the right a foot and a half will
+ 
+
+ align:start position:0%
+to the right a foot and a half will
+completely change the lighting when
+
+ align:start position:0%
+completely change the lighting when
+ 
+
+ align:start position:0%
+completely change the lighting when
+somebody moves their face like this to
+
+ align:start position:0%
+somebody moves their face like this to
+ 
+
+ align:start position:0%
+somebody moves their face like this to
+look at you or like this to look at you
+
+ align:start position:0%
+look at you or like this to look at you
+ 
+
+ align:start position:0%
+look at you or like this to look at you
+so those are the things that you want to
+
+ align:start position:0%
+so those are the things that you want to
+ 
+
+ align:start position:0%
+so those are the things that you want to
+get get in the habit of like always
+
+ align:start position:0%
+get get in the habit of like always
+ 
+
+ align:start position:0%
+get get in the habit of like always
+thinking about it becomes this automatic
+
+ align:start position:0%
+thinking about it becomes this automatic
+ 
+
+ align:start position:0%
+thinking about it becomes this automatic
+background process sort of like you know
+
+ align:start position:0%
+background process sort of like you know
+ 
+
+ align:start position:0%
+background process sort of like you know
+background rendering or whatever um and
+
+ align:start position:0%
+background rendering or whatever um and
+ 
+
+ align:start position:0%
+background rendering or whatever um and
+and of course I I do like dramatic kiar
+
+ align:start position:0%
+and of course I I do like dramatic kiar
+ 
+
+ align:start position:0%
+and of course I I do like dramatic kiar
+skuro sometimes um this was a particular
+
+ align:start position:0%
+skuro sometimes um this was a particular
+ 
+
+ align:start position:0%
+skuro sometimes um this was a particular
+moment where the character is talking
+
+ align:start position:0%
+moment where the character is talking
+ 
+
+ align:start position:0%
+moment where the character is talking
+about how he first came to Boston and he
+
+ align:start position:0%
+about how he first came to Boston and he
+ 
+
+ align:start position:0%
+about how he first came to Boston and he
+found it to be a cool and uninviting
+
+ align:start position:0%
+found it to be a cool and uninviting
+ 
+
+ align:start position:0%
+found it to be a cool and uninviting
+place and people weren't very friendly
+
+ align:start position:0%
+place and people weren't very friendly
+ 
+
+ align:start position:0%
+place and people weren't very friendly
+um and so even though most of the
+
+ align:start position:0%
+um and so even though most of the
+ 
+
+ align:start position:0%
+um and so even though most of the
+interviews in this film are shot in
+
+ align:start position:0%
+interviews in this film are shot in
+ 
+
+ align:start position:0%
+interviews in this film are shot in
+natural light I decided to to to shoot
+
+ align:start position:0%
+natural light I decided to to to shoot
+ 
+
+ align:start position:0%
+natural light I decided to to to shoot
+this one kind of dramatic and dark this
+
+ align:start position:0%
+this one kind of dramatic and dark this
+ 
+
+ align:start position:0%
+this one kind of dramatic and dark this
+is sort of the the this is where the
+
+ align:start position:0%
+is sort of the the this is where the
+ 
+
+ align:start position:0%
+is sort of the the this is where the
+character starts to realize um certain
+
+ align:start position:0%
+character starts to realize um certain
+ 
+
+ align:start position:0%
+character starts to realize um certain
+things and it's a very sort of kind of
+
+ align:start position:0%
+things and it's a very sort of kind of
+ 
+
+ align:start position:0%
+things and it's a very sort of kind of
+personal intimate moment so we said okay
+
+ align:start position:0%
+personal intimate moment so we said okay
+ 
+
+ align:start position:0%
+personal intimate moment so we said okay
+let's let's kind of light uh do the more
+
+ align:start position:0%
+let's let's kind of light uh do the more
+ 
+
+ align:start position:0%
+let's let's kind of light uh do the more
+Kos skuro thing so you have the the
+
+ align:start position:0%
+Kos skuro thing so you have the the
+ 
+
+ align:start position:0%
+Kos skuro thing so you have the the
+light coming from from the side and
+
+ align:start position:0%
+light coming from from the side and
+ 
+
+ align:start position:0%
+light coming from from the side and
+we're using actually pretty relatively
+
+ align:start position:0%
+we're using actually pretty relatively
+ 
+
+ align:start position:0%
+we're using actually pretty relatively
+intense blue backlights U for the
+
+ align:start position:0%
+intense blue backlights U for the
+ 
+
+ align:start position:0%
+intense blue backlights U for the
+background so that the background
+
+ align:start position:0%
+background so that the background
+ 
+
+ align:start position:0%
+background so that the background
+doesn't go totally black but it's it's
+
+ align:start position:0%
+doesn't go totally black but it's it's
+ 
+
+ align:start position:0%
+doesn't go totally black but it's it's
+relatively dark so this is a little more
+
+ align:start position:0%
+relatively dark so this is a little more
+ 
+
+ align:start position:0%
+relatively dark so this is a little more
+along the lines of carvaggio versus
+
+ align:start position:0%
+along the lines of carvaggio versus
+ 
+
+ align:start position:0%
+along the lines of carvaggio versus
+verir and you can also you can also see
+
+ align:start position:0%
+verir and you can also you can also see
+ 
+
+ align:start position:0%
+verir and you can also you can also see
+kind of the theatricality that you were
+
+ align:start position:0%
+kind of the theatricality that you were
+ 
+
+ align:start position:0%
+kind of the theatricality that you were
+talking about before I mean it might
+
+ align:start position:0%
+talking about before I mean it might
+ 
+
+ align:start position:0%
+talking about before I mean it might
+work for the subject in this case it
+
+ align:start position:0%
+work for the subject in this case it
+ 
+
+ align:start position:0%
+work for the subject in this case it
+worked in this case and it's really the
+
+ align:start position:0%
+worked in this case and it's really the
+ 
+
+ align:start position:0%
+worked in this case and it's really the
+only interview in the entire film that's
+
+ align:start position:0%
+only interview in the entire film that's
+ 
+
+ align:start position:0%
+only interview in the entire film that's
+lit this way this was was kind of a
+
+ align:start position:0%
+lit this way this was was kind of a
+ 
+
+ align:start position:0%
+lit this way this was was kind of a
+brief theatrical moment in some respects
+
+ align:start position:0%
+brief theatrical moment in some respects
+ 
+
+ align:start position:0%
+brief theatrical moment in some respects
+but yeah it has that theatricality it's
+
+ align:start position:0%
+but yeah it has that theatricality it's
+ 
+
+ align:start position:0%
+but yeah it has that theatricality it's
+not at all
+
+ align:start position:0%
+not at all
+ 
+
+ align:start position:0%
+not at all
+natural right this was of somebody
+
+ align:start position:0%
+natural right this was of somebody
+ 
+
+ align:start position:0%
+natural right this was of somebody
+feeling like a fish out of water I
+
+ align:start position:0%
+feeling like a fish out of water I
+ 
+
+ align:start position:0%
+feeling like a fish out of water I
+wanted to create an image that didn't
+
+ align:start position:0%
+wanted to create an image that didn't
+ 
+
+ align:start position:0%
+wanted to create an image that didn't
+feel like it fit with the rest of the
+
+ align:start position:0%
+feel like it fit with the rest of the
+ 
+
+ align:start position:0%
+feel like it fit with the rest of the
+film uh
+
+ align:start position:0%
+film uh
+ 
+
+ align:start position:0%
+film uh
+so so these are four different
+
+ align:start position:0%
+so so these are four different
+ 
+
+ align:start position:0%
+so so these are four different
+approaches um to an interview situation
+
+ align:start position:0%
+approaches um to an interview situation
+ 
+
+ align:start position:0%
+approaches um to an interview situation
+and if you take a look at the PDF uh
+
+ align:start position:0%
+and if you take a look at the PDF uh
+ 
+
+ align:start position:0%
+and if you take a look at the PDF uh
+I've kind of synthesized what I have
+
+ align:start position:0%
+I've kind of synthesized what I have
+ 
+
+ align:start position:0%
+I've kind of synthesized what I have
+found from seven or eight different
+
+ align:start position:0%
+found from seven or eight different
+ 
+
+ align:start position:0%
+found from seven or eight different
+sources um there are
+
+ align:start position:0%
+sources um there are
+ 
+
+ align:start position:0%
+sources um there are
+basically as you change the key
+
+ align:start position:0%
+basically as you change the key
+ 
+
+ align:start position:0%
+basically as you change the key
+light as you change the position of the
+
+ align:start position:0%
+light as you change the position of the
+ 
+
+ align:start position:0%
+light as you change the position of the
+key light relative to the subject you
+
+ align:start position:0%
+key light relative to the subject you
+ 
+
+ align:start position:0%
+key light relative to the subject you
+you change you go from this Continuum
+
+ align:start position:0%
+you change you go from this Continuum
+ 
+
+ align:start position:0%
+you change you go from this Continuum
+from glamour Lighting on the left where
+
+ align:start position:0%
+from glamour Lighting on the left where
+ 
+
+ align:start position:0%
+from glamour Lighting on the left where
+the key light and the fill light are
+
+ align:start position:0%
+the key light and the fill light are
+ 
+
+ align:start position:0%
+the key light and the fill light are
+actually directly overhead there's a
+
+ align:start position:0%
+actually directly overhead there's a
+ 
+
+ align:start position:0%
+actually directly overhead there's a
+small little butterfly Shadow under the
+
+ align:start position:0%
+small little butterfly Shadow under the
+ 
+
+ align:start position:0%
+small little butterfly Shadow under the
+nose and there's a fill light filling
+
+ align:start position:0%
+nose and there's a fill light filling
+ 
+
+ align:start position:0%
+nose and there's a fill light filling
+that in so it's not a harsh Shadow under
+
+ align:start position:0%
+that in so it's not a harsh Shadow under
+ 
+
+ align:start position:0%
+that in so it's not a harsh Shadow under
+the nose and it and this kind of
+
+ align:start position:0%
+the nose and it and this kind of
+ 
+
+ align:start position:0%
+the nose and it and this kind of
+Hollywood lighting where the key is
+
+ align:start position:0%
+Hollywood lighting where the key is
+ 
+
+ align:start position:0%
+Hollywood lighting where the key is
+almost in front of the subject gives you
+
+ align:start position:0%
+almost in front of the subject gives you
+ 
+
+ align:start position:0%
+almost in front of the subject gives you
+this very glamorous look especially if
+
+ align:start position:0%
+this very glamorous look especially if
+ 
+
+ align:start position:0%
+this very glamorous look especially if
+you have high
+
+ align:start position:0%
+you have high
+ 
+
+ align:start position:0%
+you have high
+cheekbones uh but it's not at all
+
+ align:start position:0%
+cheekbones uh but it's not at all
+ 
+
+ align:start position:0%
+cheekbones uh but it's not at all
+natural but it is very glamorous um and
+
+ align:start position:0%
+natural but it is very glamorous um and
+ 
+
+ align:start position:0%
+natural but it is very glamorous um and
+then as you move the fill light to the
+
+ align:start position:0%
+then as you move the fill light to the
+ 
+
+ align:start position:0%
+then as you move the fill light to the
+left in the middle here you get to the
+
+ align:start position:0%
+left in the middle here you get to the
+ 
+
+ align:start position:0%
+left in the middle here you get to the
+rembrand style which is kind of my
+
+ align:start position:0%
+rembrand style which is kind of my
+ 
+
+ align:start position:0%
+rembrand style which is kind of my
+tendency I like the light coming from
+
+ align:start position:0%
+tendency I like the light coming from
+ 
+
+ align:start position:0%
+tendency I like the light coming from
+the left I also find in situations where
+
+ align:start position:0%
+the left I also find in situations where
+ 
+
+ align:start position:0%
+the left I also find in situations where
+I'm like using a small handheld LED
+
+ align:start position:0%
+I'm like using a small handheld LED
+ 
+
+ align:start position:0%
+I'm like using a small handheld LED
+light to give a little bit of
+
+ align:start position:0%
+light to give a little bit of
+ 
+
+ align:start position:0%
+light to give a little bit of
+supplemental Lighting in a otherwise
+
+ align:start position:0%
+supplemental Lighting in a otherwise
+ 
+
+ align:start position:0%
+supplemental Lighting in a otherwise
+verit situation if I put light to the
+
+ align:start position:0%
+verit situation if I put light to the
+ 
+
+ align:start position:0%
+verit situation if I put light to the
+left of the subject not only do they
+
+ align:start position:0%
+left of the subject not only do they
+ 
+
+ align:start position:0%
+left of the subject not only do they
+look better and more dimensional but
+
+ align:start position:0%
+look better and more dimensional but
+ 
+
+ align:start position:0%
+look better and more dimensional but
+it's not glaring in their eye and that's
+
+ align:start position:0%
+it's not glaring in their eye and that's
+ 
+
+ align:start position:0%
+it's not glaring in their eye and that's
+actually more
+
+ align:start position:0%
+actually more
+ 
+
+ align:start position:0%
+actually more
+comfortable and then of course profile
+
+ align:start position:0%
+comfortable and then of course profile
+ 
+
+ align:start position:0%
+comfortable and then of course profile
+lighting where you basically the key is
+
+ align:start position:0%
+lighting where you basically the key is
+ 
+
+ align:start position:0%
+lighting where you basically the key is
+is behind the
+
+ align:start position:0%
+is behind the
+ 
+
+ align:start position:0%
+is behind the
+subject and you're emphasizing their
+
+ align:start position:0%
+subject and you're emphasizing their
+ 
+
+ align:start position:0%
+subject and you're emphasizing their
+profile I mean that's really dramatic
+
+ align:start position:0%
+profile I mean that's really dramatic
+ 
+
+ align:start position:0%
+profile I mean that's really dramatic
+you would do that for sort of you know
+
+ align:start position:0%
+you would do that for sort of you know
+ 
+
+ align:start position:0%
+you would do that for sort of you know
+interview with somebody whose identity
+
+ align:start position:0%
+interview with somebody whose identity
+ 
+
+ align:start position:0%
+interview with somebody whose identity
+you want to obscure you kill the you
+
+ align:start position:0%
+you want to obscure you kill the you
+ 
+
+ align:start position:0%
+you want to obscure you kill the you
+kill the fillite
+
+ align:start position:0%
+kill the fillite
+ 
+
+ align:start position:0%
+kill the fillite
+and you have a backlight coming from the
+
+ align:start position:0%
+and you have a backlight coming from the
+ 
+
+ align:start position:0%
+and you have a backlight coming from the
+back and you just see this outline rim
+
+ align:start position:0%
+back and you just see this outline rim
+ 
+
+ align:start position:0%
+back and you just see this outline rim
+of a person so as you you know what this
+
+ align:start position:0%
+of a person so as you you know what this
+ 
+
+ align:start position:0%
+of a person so as you you know what this
+slide is about is to encourage you when
+
+ align:start position:0%
+slide is about is to encourage you when
+ 
+
+ align:start position:0%
+slide is about is to encourage you when
+I've like taught a detailed
+
+ align:start position:0%
+I've like taught a detailed
+ 
+
+ align:start position:0%
+I've like taught a detailed
+cinematography class I actually have the
+
+ align:start position:0%
+cinematography class I actually have the
+ 
+
+ align:start position:0%
+cinematography class I actually have the
+students set all of these up and shoot
+
+ align:start position:0%
+students set all of these up and shoot
+ 
+
+ align:start position:0%
+students set all of these up and shoot
+all these different setups and reflect
+
+ align:start position:0%
+all these different setups and reflect
+ 
+
+ align:start position:0%
+all these different setups and reflect
+on how the how the lighting changes as
+
+ align:start position:0%
+on how the how the lighting changes as
+ 
+
+ align:start position:0%
+on how the how the lighting changes as
+you move the key light around you know
+
+ align:start position:0%
+you move the key light around you know
+ 
+
+ align:start position:0%
+you move the key light around you know
+it' be cool to have like a 3D simulator
+
+ align:start position:0%
+it' be cool to have like a 3D simulator
+ 
+
+ align:start position:0%
+it' be cool to have like a 3D simulator
+environment to kind of try these things
+
+ align:start position:0%
+environment to kind of try these things
+ 
+
+ align:start position:0%
+environment to kind of try these things
+out but there's nothing like going out
+
+ align:start position:0%
+out but there's nothing like going out
+ 
+
+ align:start position:0%
+out but there's nothing like going out
+into the real world with your lighting
+
+ align:start position:0%
+into the real world with your lighting
+ 
+
+ align:start position:0%
+into the real world with your lighting
+kit um and trying these different setups
+
+ align:start position:0%
+kit um and trying these different setups
+ 
+
+ align:start position:0%
+kit um and trying these different setups
+so um we've talked about soft light
+
+ align:start position:0%
+so um we've talked about soft light
+ 
+
+ align:start position:0%
+so um we've talked about soft light
+we've talked about hard lights some
+
+ align:start position:0%
+we've talked about hard lights some
+ 
+
+ align:start position:0%
+we've talked about hard lights some
+common lights that you find available in
+
+ align:start position:0%
+common lights that you find available in
+ 
+
+ align:start position:0%
+common lights that you find available in
+the market today um there's a variety of
+
+ align:start position:0%
+the market today um there's a variety of
+ 
+
+ align:start position:0%
+the market today um there's a variety of
+soft lights they're very popular since
+
+ align:start position:0%
+soft lights they're very popular since
+ 
+
+ align:start position:0%
+soft lights they're very popular since
+if you're going to have if you're going
+
+ align:start position:0%
+if you're going to have if you're going
+ 
+
+ align:start position:0%
+if you're going to have if you're going
+to do a simple quick and dirty interview
+
+ align:start position:0%
+to do a simple quick and dirty interview
+ 
+
+ align:start position:0%
+to do a simple quick and dirty interview
+with a single light typically you'll
+
+ align:start position:0%
+with a single light typically you'll
+ 
+
+ align:start position:0%
+with a single light typically you'll
+just pull out a soft light um a popular
+
+ align:start position:0%
+just pull out a soft light um a popular
+ 
+
+ align:start position:0%
+just pull out a soft light um a popular
+soft light is something called the low
+
+ align:start position:0%
+soft light is something called the low
+ 
+
+ align:start position:0%
+soft light is something called the low
+Rea it kind of Pops open like an
+
+ align:start position:0%
+Rea it kind of Pops open like an
+ 
+
+ align:start position:0%
+Rea it kind of Pops open like an
+umbrella you throw a diffus user on the
+
+ align:start position:0%
+umbrella you throw a diffus user on the
+ 
+
+ align:start position:0%
+umbrella you throw a diffus user on the
+front you hook it up to the stand and it
+
+ align:start position:0%
+front you hook it up to the stand and it
+ 
+
+ align:start position:0%
+front you hook it up to the stand and it
+sets up very quickly and instant soft
+
+ align:start position:0%
+sets up very quickly and instant soft
+ 
+
+ align:start position:0%
+sets up very quickly and instant soft
+light um I prefer although they're a
+
+ align:start position:0%
+light um I prefer although they're a
+ 
+
+ align:start position:0%
+light um I prefer although they're a
+little more expensive I love the kinof
+
+ align:start position:0%
+little more expensive I love the kinof
+ 
+
+ align:start position:0%
+little more expensive I love the kinof
+flow Diva light this is a a fluorescent
+
+ align:start position:0%
+flow Diva light this is a a fluorescent
+ 
+
+ align:start position:0%
+flow Diva light this is a a fluorescent
+lights light fixture that has four or
+
+ align:start position:0%
+lights light fixture that has four or
+ 
+
+ align:start position:0%
+lights light fixture that has four or
+two depending on the size fluorescent
+
+ align:start position:0%
+two depending on the size fluorescent
+ 
+
+ align:start position:0%
+two depending on the size fluorescent
+bulbs and you can pop in either daylight
+
+ align:start position:0%
+bulbs and you can pop in either daylight
+ 
+
+ align:start position:0%
+bulbs and you can pop in either daylight
+balance fluorescent or tungsten balance
+
+ align:start position:0%
+balance fluorescent or tungsten balance
+ 
+
+ align:start position:0%
+balance fluorescent or tungsten balance
+fluoresence I've done a lot of
+
+ align:start position:0%
+fluoresence I've done a lot of
+ 
+
+ align:start position:0%
+fluoresence I've done a lot of
+interviews Outdoors under a tree in the
+
+ align:start position:0%
+interviews Outdoors under a tree in the
+ 
+
+ align:start position:0%
+interviews Outdoors under a tree in the
+shade and brought in the diva with the
+
+ align:start position:0%
+shade and brought in the diva with the
+ 
+
+ align:start position:0%
+shade and brought in the diva with the
+daylight balance light just for a little
+
+ align:start position:0%
+daylight balance light just for a little
+ 
+
+ align:start position:0%
+daylight balance light just for a little
+bit of Sparkle in the eyes just for a
+
+ align:start position:0%
+bit of Sparkle in the eyes just for a
+ 
+
+ align:start position:0%
+bit of Sparkle in the eyes just for a
+little bit of extra definition and all
+
+ align:start position:0%
+little bit of extra definition and all
+ 
+
+ align:start position:0%
+little bit of extra definition and all
+of a sudden it takes something in the
+
+ align:start position:0%
+of a sudden it takes something in the
+ 
+
+ align:start position:0%
+of a sudden it takes something in the
+shade and soft and gives it just a
+
+ align:start position:0%
+shade and soft and gives it just a
+ 
+
+ align:start position:0%
+shade and soft and gives it just a
+little bit of dimensionality and you
+
+ align:start position:0%
+little bit of dimensionality and you
+ 
+
+ align:start position:0%
+little bit of dimensionality and you
+can't do that unless your light source
+
+ align:start position:0%
+can't do that unless your light source
+ 
+
+ align:start position:0%
+can't do that unless your light source
+is daylight balanced and the diva is
+
+ align:start position:0%
+is daylight balanced and the diva is
+ 
+
+ align:start position:0%
+is daylight balanced and the diva is
+just barely bright enough to use in the
+
+ align:start position:0%
+just barely bright enough to use in the
+ 
+
+ align:start position:0%
+just barely bright enough to use in the
+shade no light source is going to work
+
+ align:start position:0%
+shade no light source is going to work
+ 
+
+ align:start position:0%
+shade no light source is going to work
+in the sun unless you have a Hollywood
+
+ align:start position:0%
+in the sun unless you have a Hollywood
+ 
+
+ align:start position:0%
+in the sun unless you have a Hollywood
+grip truck um but for indoor interviews
+
+ align:start position:0%
+grip truck um but for indoor interviews
+ 
+
+ align:start position:0%
+grip truck um but for indoor interviews
+the diva a couple of Divas is just
+
+ align:start position:0%
+the diva a couple of Divas is just
+ 
+
+ align:start position:0%
+the diva a couple of Divas is just
+spectacular in terms of soft light with
+
+ align:start position:0%
+spectacular in terms of soft light with
+ 
+
+ align:start position:0%
+spectacular in terms of soft light with
+just a little bit of
+
+ align:start position:0%
+just a little bit of
+ 
+
+ align:start position:0%
+just a little bit of
+directionality um and the fact that you
+
+ align:start position:0%
+directionality um and the fact that you
+ 
+
+ align:start position:0%
+directionality um and the fact that you
+can pop in and out the fluorescent light
+
+ align:start position:0%
+can pop in and out the fluorescent light
+ 
+
+ align:start position:0%
+can pop in and out the fluorescent light
+tubes for either daylight or tungsten is
+
+ align:start position:0%
+tubes for either daylight or tungsten is
+ 
+
+ align:start position:0%
+tubes for either daylight or tungsten is
+really awesome it comes in a little
+
+ align:start position:0%
+really awesome it comes in a little
+ 
+
+ align:start position:0%
+really awesome it comes in a little
+suitcase with both sets of bulbs um and
+
+ align:start position:0%
+suitcase with both sets of bulbs um and
+ 
+
+ align:start position:0%
+suitcase with both sets of bulbs um and
+off you go uh open face lights are much
+
+ align:start position:0%
+off you go uh open face lights are much
+ 
+
+ align:start position:0%
+off you go uh open face lights are much
+less expensive they're they're they're
+
+ align:start position:0%
+less expensive they're they're they're
+ 
+
+ align:start position:0%
+less expensive they're they're they're
+relatively cheap anything from a $30
+
+ align:start position:0%
+relatively cheap anything from a $30
+ 
+
+ align:start position:0%
+relatively cheap anything from a $30
+work light at Home Depot to a loyal a
+
+ align:start position:0%
+work light at Home Depot to a loyal a
+ 
+
+ align:start position:0%
+work light at Home Depot to a loyal a
+low omn light they come in all sorts of
+
+ align:start position:0%
+low omn light they come in all sorts of
+ 
+
+ align:start position:0%
+low omn light they come in all sorts of
+shapes and sizes typically they have a
+
+ align:start position:0%
+shapes and sizes typically they have a
+ 
+
+ align:start position:0%
+shapes and sizes typically they have a
+parabolic
+
+ align:start position:0%
+parabolic
+ 
+
+ align:start position:0%
+parabolic
+reflector and then we'll talk in a
+
+ align:start position:0%
+reflector and then we'll talk in a
+ 
+
+ align:start position:0%
+reflector and then we'll talk in a
+moment about Fels Fels are a little
+
+ align:start position:0%
+moment about Fels Fels are a little
+ 
+
+ align:start position:0%
+moment about Fels Fels are a little
+fancier they actually have a lens
+
+ align:start position:0%
+fancier they actually have a lens
+ 
+
+ align:start position:0%
+fancier they actually have a lens
+system uh pars and of course what you
+
+ align:start position:0%
+system uh pars and of course what you
+ 
+
+ align:start position:0%
+system uh pars and of course what you
+see here in the picture is a par with a
+
+ align:start position:0%
+see here in the picture is a par with a
+ 
+
+ align:start position:0%
+see here in the picture is a par with a
+soft box on top of it pars are very
+
+ align:start position:0%
+soft box on top of it pars are very
+ 
+
+ align:start position:0%
+soft box on top of it pars are very
+efficient light sources because they
+
+ align:start position:0%
+efficient light sources because they
+ 
+
+ align:start position:0%
+efficient light sources because they
+have this parabolic reflector built into
+
+ align:start position:0%
+have this parabolic reflector built into
+ 
+
+ align:start position:0%
+have this parabolic reflector built into
+the light unit um and they're often
+
+ align:start position:0%
+the light unit um and they're often
+ 
+
+ align:start position:0%
+the light unit um and they're often
+available in this high technology
+
+ align:start position:0%
+available in this high technology
+ 
+
+ align:start position:0%
+available in this high technology
+daylight balanced light called an HMI um
+
+ align:start position:0%
+daylight balanced light called an HMI um
+ 
+
+ align:start position:0%
+daylight balanced light called an HMI um
+small Pars in the 300 watt range are
+
+ align:start position:0%
+small Pars in the 300 watt range are
+ 
+
+ align:start position:0%
+small Pars in the 300 watt range are
+very popular am with documentary Crews
+
+ align:start position:0%
+very popular am with documentary Crews
+ 
+
+ align:start position:0%
+very popular am with documentary Crews
+because you can power them off a small
+
+ align:start position:0%
+because you can power them off a small
+ 
+
+ align:start position:0%
+because you can power them off a small
+battery um they're daylight balance so
+
+ align:start position:0%
+battery um they're daylight balance so
+ 
+
+ align:start position:0%
+battery um they're daylight balance so
+you can use them Outdoors to get rid of
+
+ align:start position:0%
+you can use them Outdoors to get rid of
+ 
+
+ align:start position:0%
+you can use them Outdoors to get rid of
+Shadows and stuff like that uh and then
+
+ align:start position:0%
+Shadows and stuff like that uh and then
+ 
+
+ align:start position:0%
+Shadows and stuff like that uh and then
+if you need to soften them you can
+
+ align:start position:0%
+if you need to soften them you can
+ 
+
+ align:start position:0%
+if you need to soften them you can
+always pop a soft box in the front or if
+
+ align:start position:0%
+always pop a soft box in the front or if
+ 
+
+ align:start position:0%
+always pop a soft box in the front or if
+you need that hard intensity efficiency
+
+ align:start position:0%
+you need that hard intensity efficiency
+ 
+
+ align:start position:0%
+you need that hard intensity efficiency
+of the par unit you can just pull the
+
+ align:start position:0%
+of the par unit you can just pull the
+ 
+
+ align:start position:0%
+of the par unit you can just pull the
+soft box off so they're very versatile
+
+ align:start position:0%
+soft box off so they're very versatile
+ 
+
+ align:start position:0%
+soft box off so they're very versatile
+in that respect and in fact here in
+
+ align:start position:0%
+in that respect and in fact here in
+ 
+
+ align:start position:0%
+in that respect and in fact here in
+Boston um
+
+ align:start position:0%
+Boston um
+ 
+
+ align:start position:0%
+Boston um
+the local rental house rents something
+
+ align:start position:0%
+the local rental house rents something
+ 
+
+ align:start position:0%
+the local rental house rents something
+called the cobal did I say that right
+
+ align:start position:0%
+called the cobal did I say that right
+ 
+
+ align:start position:0%
+called the cobal did I say that right
+cobal um small HMI par uh which is
+
+ align:start position:0%
+cobal um small HMI par uh which is
+ 
+
+ align:start position:0%
+cobal um small HMI par uh which is
+really useful
+
+ align:start position:0%
+really useful
+ 
+
+ align:start position:0%
+really useful
+um but if you're on a tight budget you
+
+ align:start position:0%
+um but if you're on a tight budget you
+ 
+
+ align:start position:0%
+um but if you're on a tight budget you
+don't necessarily have to go out and
+
+ align:start position:0%
+don't necessarily have to go out and
+ 
+
+ align:start position:0%
+don't necessarily have to go out and
+spend thousands of dollars on
+
+ align:start position:0%
+spend thousands of dollars on
+ 
+
+ align:start position:0%
+spend thousands of dollars on
+professional lighting Mother Nature
+
+ align:start position:0%
+professional lighting Mother Nature
+ 
+
+ align:start position:0%
+professional lighting Mother Nature
+usually provides her services for free
+
+ align:start position:0%
+usually provides her services for free
+ 
+
+ align:start position:0%
+usually provides her services for free
+you can use practical household bulbs uh
+
+ align:start position:0%
+you can use practical household bulbs uh
+ 
+
+ align:start position:0%
+you can use practical household bulbs uh
+popular among um some folks or S you
+
+ align:start position:0%
+popular among um some folks or S you
+ 
+
+ align:start position:0%
+popular among um some folks or S you
+know simple photo flood lamps which are
+
+ align:start position:0%
+know simple photo flood lamps which are
+ 
+
+ align:start position:0%
+know simple photo flood lamps which are
+very bright incandescent lamps that you
+
+ align:start position:0%
+very bright incandescent lamps that you
+ 
+
+ align:start position:0%
+very bright incandescent lamps that you
+can put in inexpensive fixtures it turns
+
+ align:start position:0%
+can put in inexpensive fixtures it turns
+ 
+
+ align:start position:0%
+can put in inexpensive fixtures it turns
+out fluorescent utility lights ordinary
+
+ align:start position:0%
+out fluorescent utility lights ordinary
+ 
+
+ align:start position:0%
+out fluorescent utility lights ordinary
+fluorescent lights you can actually go
+
+ align:start position:0%
+fluorescent lights you can actually go
+ 
+
+ align:start position:0%
+fluorescent lights you can actually go
+to your local hardware supply store and
+
+ align:start position:0%
+to your local hardware supply store and
+ 
+
+ align:start position:0%
+to your local hardware supply store and
+buy daylight balanced or um tungsten
+
+ align:start position:0%
+buy daylight balanced or um tungsten
+ 
+
+ align:start position:0%
+buy daylight balanced or um tungsten
+balanced uh fluorescent uh tubes chroma
+
+ align:start position:0%
+balanced uh fluorescent uh tubes chroma
+ 
+
+ align:start position:0%
+balanced uh fluorescent uh tubes chroma
+50s and Ultra 32s I think they're called
+
+ align:start position:0%
+50s and Ultra 32s I think they're called
+ 
+
+ align:start position:0%
+50s and Ultra 32s I think they're called
+um and you can put them in ordinary
+
+ align:start position:0%
+um and you can put them in ordinary
+ 
+
+ align:start position:0%
+um and you can put them in ordinary
+florescent fixtures uh Chinese lanterns
+
+ align:start position:0%
+florescent fixtures uh Chinese lanterns
+ 
+
+ align:start position:0%
+florescent fixtures uh Chinese lanterns
+are awesome these paper little lanterns
+
+ align:start position:0%
+are awesome these paper little lanterns
+ 
+
+ align:start position:0%
+are awesome these paper little lanterns
+but I wouldn't use more than a 60 or
+
+ align:start position:0%
+but I wouldn't use more than a 60 or
+ 
+
+ align:start position:0%
+but I wouldn't use more than a 60 or
+pushing it 100 watt bulb in these paper
+
+ align:start position:0%
+pushing it 100 watt bulb in these paper
+ 
+
+ align:start position:0%
+pushing it 100 watt bulb in these paper
+lanterns and never leave them unattended
+
+ align:start position:0%
+lanterns and never leave them unattended
+ 
+
+ align:start position:0%
+lanterns and never leave them unattended
+um regardless of how flame retardant the
+
+ align:start position:0%
+um regardless of how flame retardant the
+ 
+
+ align:start position:0%
+um regardless of how flame retardant the
+manufacturers say they are I wouldn't
+
+ align:start position:0%
+manufacturers say they are I wouldn't
+ 
+
+ align:start position:0%
+manufacturers say they are I wouldn't
+leave them alone um but they give you
+
+ align:start position:0%
+leave them alone um but they give you
+ 
+
+ align:start position:0%
+leave them alone um but they give you
+this beautiful soft light now there's a
+
+ align:start position:0%
+this beautiful soft light now there's a
+ 
+
+ align:start position:0%
+this beautiful soft light now there's a
+professional version of these lanterns
+
+ align:start position:0%
+professional version of these lanterns
+ 
+
+ align:start position:0%
+professional version of these lanterns
+called Chima lanterns and they're made
+
+ align:start position:0%
+called Chima lanterns and they're made
+ 
+
+ align:start position:0%
+called Chima lanterns and they're made
+of a you know special high heat
+
+ align:start position:0%
+of a you know special high heat
+ 
+
+ align:start position:0%
+of a you know special high heat
+resistant material and you can put a
+
+ align:start position:0%
+resistant material and you can put a
+ 
+
+ align:start position:0%
+resistant material and you can put a
+pretty powerful thousand watt lamp
+
+ align:start position:0%
+pretty powerful thousand watt lamp
+ 
+
+ align:start position:0%
+pretty powerful thousand watt lamp
+inside one of those and get this
+
+ align:start position:0%
+inside one of those and get this
+ 
+
+ align:start position:0%
+inside one of those and get this
+beautiful beautiful soft light um but
+
+ align:start position:0%
+beautiful beautiful soft light um but
+ 
+
+ align:start position:0%
+beautiful beautiful soft light um but
+I've seen a lot of people get a lot of
+
+ align:start position:0%
+I've seen a lot of people get a lot of
+ 
+
+ align:start position:0%
+I've seen a lot of people get a lot of
+mileage out of ordinary um work lights I
+
+ align:start position:0%
+mileage out of ordinary um work lights I
+ 
+
+ align:start position:0%
+mileage out of ordinary um work lights I
+know a lot of Animation folks use
+
+ align:start position:0%
+know a lot of Animation folks use
+ 
+
+ align:start position:0%
+know a lot of Animation folks use
+ordinary hardware store work lights for
+
+ align:start position:0%
+ordinary hardware store work lights for
+ 
+
+ align:start position:0%
+ordinary hardware store work lights for
+their lighting Source you can clip a
+
+ align:start position:0%
+their lighting Source you can clip a
+ 
+
+ align:start position:0%
+their lighting Source you can clip a
+little diffusion in the front if you
+
+ align:start position:0%
+little diffusion in the front if you
+ 
+
+ align:start position:0%
+little diffusion in the front if you
+need to they're cheap the only downside
+
+ align:start position:0%
+need to they're cheap the only downside
+ 
+
+ align:start position:0%
+need to they're cheap the only downside
+is that they don't fold up nicely for
+
+ align:start position:0%
+is that they don't fold up nicely for
+ 
+
+ align:start position:0%
+is that they don't fold up nicely for
+for travel um but if you're doing like
+
+ align:start position:0%
+for travel um but if you're doing like
+ 
+
+ align:start position:0%
+for travel um but if you're doing like
+animation work at home uh those
+
+ align:start position:0%
+animation work at home uh those
+ 
+
+ align:start position:0%
+animation work at home uh those
+inexpensive work lights uh work great
+
+ align:start position:0%
+inexpensive work lights uh work great
+ 
+
+ align:start position:0%
+inexpensive work lights uh work great
+and you can actually buy you know Tong
+
+ align:start position:0%
+and you can actually buy you know Tong
+ 
+
+ align:start position:0%
+and you can actually buy you know Tong
+inbalance 3200 de Kelvin bulbs for them
+
+ align:start position:0%
+inbalance 3200 de Kelvin bulbs for them
+ 
+
+ align:start position:0%
+inbalance 3200 de Kelvin bulbs for them
+so uh on camera lights some people like
+
+ align:start position:0%
+so uh on camera lights some people like
+ 
+
+ align:start position:0%
+so uh on camera lights some people like
+them I personally don't like on camera
+
+ align:start position:0%
+them I personally don't like on camera
+ 
+
+ align:start position:0%
+them I personally don't like on camera
+lights um because I really don't like
+
+ align:start position:0%
+lights um because I really don't like
+ 
+
+ align:start position:0%
+lights um because I really don't like
+the flat look that they create um I
+
+ align:start position:0%
+the flat look that they create um I
+ 
+
+ align:start position:0%
+the flat look that they create um I
+prefer to hold a camera off to the side
+
+ align:start position:0%
+prefer to hold a camera off to the side
+ 
+
+ align:start position:0%
+prefer to hold a camera off to the side
+find an assistant find somebody um to
+
+ align:start position:0%
+find an assistant find somebody um to
+ 
+
+ align:start position:0%
+find an assistant find somebody um to
+kind of hold the light off to the side
+
+ align:start position:0%
+kind of hold the light off to the side
+ 
+
+ align:start position:0%
+kind of hold the light off to the side
+I've even done it myself it you your arm
+
+ align:start position:0%
+I've even done it myself it you your arm
+ 
+
+ align:start position:0%
+I've even done it myself it you your arm
+gets really really really tired but um
+
+ align:start position:0%
+gets really really really tired but um
+ 
+
+ align:start position:0%
+gets really really really tired but um
+it pays off by not having that deer Cott
+
+ align:start position:0%
+it pays off by not having that deer Cott
+ 
+
+ align:start position:0%
+it pays off by not having that deer Cott
+in the headlights look of the light
+
+ align:start position:0%
+in the headlights look of the light
+ 
+
+ align:start position:0%
+in the headlights look of the light
+directly on the camera people don't like
+
+ align:start position:0%
+directly on the camera people don't like
+ 
+
+ align:start position:0%
+directly on the camera people don't like
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+blinded get the light off to the side is
+
+ align:start position:0%
+blinded get the light off to the side is
+ 
+
+ align:start position:0%
+blinded get the light off to the side is
+the moral of the story but these small
+
+ align:start position:0%
+the moral of the story but these small
+ 
+
+ align:start position:0%
+the moral of the story but these small
+battery powered lights especially the
+
+ align:start position:0%
+battery powered lights especially the
+ 
+
+ align:start position:0%
+battery powered lights especially the
+new generation of light emitting diode
+
+ align:start position:0%
+new generation of light emitting diode
+ 
+
+ align:start position:0%
+new generation of light emitting diode
+LED lights are spectacular because I've
+
+ align:start position:0%
+LED lights are spectacular because I've
+ 
+
+ align:start position:0%
+LED lights are spectacular because I've
+been able to like shoot all day with
+
+ align:start position:0%
+been able to like shoot all day with
+ 
+
+ align:start position:0%
+been able to like shoot all day with
+like four camera batteries and a couple
+
+ align:start position:0%
+like four camera batteries and a couple
+ 
+
+ align:start position:0%
+like four camera batteries and a couple
+of LED lights uh not on continuously but
+
+ align:start position:0%
+of LED lights uh not on continuously but
+ 
+
+ align:start position:0%
+of LED lights uh not on continuously but
+it can work um I have a thing for frels
+
+ align:start position:0%
+it can work um I have a thing for frels
+ 
+
+ align:start position:0%
+it can work um I have a thing for frels
+I really like the quality of their light
+
+ align:start position:0%
+I really like the quality of their light
+ 
+
+ align:start position:0%
+I really like the quality of their light
+um they were originally developed by
+
+ align:start position:0%
+um they were originally developed by
+ 
+
+ align:start position:0%
+um they were originally developed by
+Austine Fel who contributed to the
+
+ align:start position:0%
+Austine Fel who contributed to the
+ 
+
+ align:start position:0%
+Austine Fel who contributed to the
+theory of color and Optics and the
+
+ align:start position:0%
+theory of color and Optics and the
+ 
+
+ align:start position:0%
+theory of color and Optics and the
+French Lighthouse commission had a
+
+ align:start position:0%
+French Lighthouse commission had a
+ 
+
+ align:start position:0%
+French Lighthouse commission had a
+problem you know in the early 1800s
+
+ align:start position:0%
+problem you know in the early 1800s
+ 
+
+ align:start position:0%
+problem you know in the early 1800s
+those whale oil lamps weren't very
+
+ align:start position:0%
+those whale oil lamps weren't very
+ 
+
+ align:start position:0%
+those whale oil lamps weren't very
+bright ships are going into rocks a lot
+
+ align:start position:0%
+bright ships are going into rocks a lot
+ 
+
+ align:start position:0%
+bright ships are going into rocks a lot
+of sailors and merchandise was being
+
+ align:start position:0%
+of sailors and merchandise was being
+ 
+
+ align:start position:0%
+of sailors and merchandise was being
+lost at sea um and they commissioned Fel
+
+ align:start position:0%
+lost at sea um and they commissioned Fel
+ 
+
+ align:start position:0%
+lost at sea um and they commissioned Fel
+to solve the lighthouse problem well he
+
+ align:start position:0%
+to solve the lighthouse problem well he
+ 
+
+ align:start position:0%
+to solve the lighthouse problem well he
+realized you know what if we put a whole
+
+ align:start position:0%
+realized you know what if we put a whole
+ 
+
+ align:start position:0%
+realized you know what if we put a whole
+bunch of these triangular pieces of
+
+ align:start position:0%
+bunch of these triangular pieces of
+ 
+
+ align:start position:0%
+bunch of these triangular pieces of
+glass
+
+ align:start position:0%
+glass
+ 
+
+ align:start position:0%
+glass
+in the right arrangement we can take all
+
+ align:start position:0%
+in the right arrangement we can take all
+ 
+
+ align:start position:0%
+in the right arrangement we can take all
+of those light rays that are going
+
+ align:start position:0%
+of those light rays that are going
+ 
+
+ align:start position:0%
+of those light rays that are going
+astray and send them all off single line
+
+ align:start position:0%
+astray and send them all off single line
+ 
+
+ align:start position:0%
+astray and send them all off single line
+out to see and all of a sudden these
+
+ align:start position:0%
+out to see and all of a sudden these
+ 
+
+ align:start position:0%
+out to see and all of a sudden these
+teeny tiny little whale oil powered um
+
+ align:start position:0%
+teeny tiny little whale oil powered um
+ 
+
+ align:start position:0%
+teeny tiny little whale oil powered um
+lamps were super bright CU all of the
+
+ align:start position:0%
+lamps were super bright CU all of the
+ 
+
+ align:start position:0%
+lamps were super bright CU all of the
+light rays are going single file where
+
+ align:start position:0%
+light rays are going single file where
+ 
+
+ align:start position:0%
+light rays are going single file where
+they're supposed to be out to seea
+
+ align:start position:0%
+they're supposed to be out to seea
+ 
+
+ align:start position:0%
+they're supposed to be out to seea
+instead of you know lighting the side of
+
+ align:start position:0%
+instead of you know lighting the side of
+ 
+
+ align:start position:0%
+instead of you know lighting the side of
+the lighthouse who cares about that
+
+ align:start position:0%
+the lighthouse who cares about that
+ 
+
+ align:start position:0%
+the lighthouse who cares about that
+right so what's interesting about Fels
+
+ align:start position:0%
+right so what's interesting about Fels
+ 
+
+ align:start position:0%
+right so what's interesting about Fels
+is that they're very crisp clean Focus
+
+ align:start position:0%
+is that they're very crisp clean Focus
+ 
+
+ align:start position:0%
+is that they're very crisp clean Focus
+lights that cast perfectly clean Shadows
+
+ align:start position:0%
+lights that cast perfectly clean Shadows
+ 
+
+ align:start position:0%
+lights that cast perfectly clean Shadows
+they have the same quality of light as
+
+ align:start position:0%
+they have the same quality of light as
+ 
+
+ align:start position:0%
+they have the same quality of light as
+direct sunlight they're great for back
+
+ align:start position:0%
+direct sunlight they're great for back
+ 
+
+ align:start position:0%
+direct sunlight they're great for back
+lights they're great for when you want
+
+ align:start position:0%
+lights they're great for when you want
+ 
+
+ align:start position:0%
+lights they're great for when you want
+that sort of quality of light coming
+
+ align:start position:0%
+that sort of quality of light coming
+ 
+
+ align:start position:0%
+that sort of quality of light coming
+through window they're a little heavier
+
+ align:start position:0%
+through window they're a little heavier
+ 
+
+ align:start position:0%
+through window they're a little heavier
+and more expensive because they have
+
+ align:start position:0%
+and more expensive because they have
+ 
+
+ align:start position:0%
+and more expensive because they have
+this scalloped Glass lens which you
+
+ align:start position:0%
+this scalloped Glass lens which you
+ 
+
+ align:start position:0%
+this scalloped Glass lens which you
+might recognize the pattern from
+
+ align:start position:0%
+might recognize the pattern from
+ 
+
+ align:start position:0%
+might recognize the pattern from
+lighthouses which we have a lot of here
+
+ align:start position:0%
+lighthouses which we have a lot of here
+ 
+
+ align:start position:0%
+lighthouses which we have a lot of here
+in New England um and so the units are a
+
+ align:start position:0%
+in New England um and so the units are a
+ 
+
+ align:start position:0%
+in New England um and so the units are a
+little heavier but they have a little
+
+ align:start position:0%
+little heavier but they have a little
+ 
+
+ align:start position:0%
+little heavier but they have a little
+knob where you can focus them and uh
+
+ align:start position:0%
+knob where you can focus them and uh
+ 
+
+ align:start position:0%
+knob where you can focus them and uh
+they have that nice crisp quality of
+
+ align:start position:0%
+they have that nice crisp quality of
+ 
+
+ align:start position:0%
+they have that nice crisp quality of
+light so I have a thing for frels I
+
+ align:start position:0%
+light so I have a thing for frels I
+ 
+
+ align:start position:0%
+light so I have a thing for frels I
+really like them I own five myself um
+
+ align:start position:0%
+really like them I own five myself um
+ 
+
+ align:start position:0%
+really like them I own five myself um
+but they are heavy to carry around
+
+ align:start position:0%
+but they are heavy to carry around
+ 
+
+ align:start position:0%
+but they are heavy to carry around
+that's the price you pay they they are
+
+ align:start position:0%
+that's the price you pay they they are
+ 
+
+ align:start position:0%
+that's the price you pay they they are
+physically bigger and physically heavier
+
+ align:start position:0%
+physically bigger and physically heavier
+ 
+
+ align:start position:0%
+physically bigger and physically heavier
+um here's a chart sort of comparing
+
+ align:start position:0%
+um here's a chart sort of comparing
+ 
+
+ align:start position:0%
+um here's a chart sort of comparing
+different lighting technologies because
+
+ align:start position:0%
+different lighting technologies because
+ 
+
+ align:start position:0%
+different lighting technologies because
+not only do we have different
+
+ align:start position:0%
+not only do we have different
+ 
+
+ align:start position:0%
+not only do we have different
+configuration of Lights like openface
+
+ align:start position:0%
+configuration of Lights like openface
+ 
+
+ align:start position:0%
+configuration of Lights like openface
+soft light soft
+
+ align:start position:0%
+soft light soft
+ 
+
+ align:start position:0%
+soft light soft
+um open face Fel soft light Etc in terms
+
+ align:start position:0%
+um open face Fel soft light Etc in terms
+ 
+
+ align:start position:0%
+um open face Fel soft light Etc in terms
+of the physical configuration of the
+
+ align:start position:0%
+of the physical configuration of the
+ 
+
+ align:start position:0%
+of the physical configuration of the
+light source versus you know the lens
+
+ align:start position:0%
+light source versus you know the lens
+ 
+
+ align:start position:0%
+light source versus you know the lens
+unit and things like that but there's
+
+ align:start position:0%
+unit and things like that but there's
+ 
+
+ align:start position:0%
+unit and things like that but there's
+basically four technologies that we use
+
+ align:start position:0%
+basically four technologies that we use
+ 
+
+ align:start position:0%
+basically four technologies that we use
+today in professional lighting uh for
+
+ align:start position:0%
+today in professional lighting uh for
+ 
+
+ align:start position:0%
+today in professional lighting uh for
+providing the source of light typical
+
+ align:start position:0%
+providing the source of light typical
+ 
+
+ align:start position:0%
+providing the source of light typical
+tungston incandescent lamps are the
+
+ align:start position:0%
+tungston incandescent lamps are the
+ 
+
+ align:start position:0%
+tungston incandescent lamps are the
+least expensive but they use up a lot of
+
+ align:start position:0%
+least expensive but they use up a lot of
+ 
+
+ align:start position:0%
+least expensive but they use up a lot of
+energy unfortunately incandescent lights
+
+ align:start position:0%
+energy unfortunately incandescent lights
+ 
+
+ align:start position:0%
+energy unfortunately incandescent lights
+they're actually space heaters that
+
+ align:start position:0%
+they're actually space heaters that
+ 
+
+ align:start position:0%
+they're actually space heaters that
+happen to give a small percentage of
+
+ align:start position:0%
+happen to give a small percentage of
+ 
+
+ align:start position:0%
+happen to give a small percentage of
+their energy out in the light range but
+
+ align:start position:0%
+their energy out in the light range but
+ 
+
+ align:start position:0%
+their energy out in the light range but
+they're you know maybe 30% is light and
+
+ align:start position:0%
+they're you know maybe 30% is light and
+ 
+
+ align:start position:0%
+they're you know maybe 30% is light and
+the rest of the energy is is is heat
+
+ align:start position:0%
+the rest of the energy is is is heat
+ 
+
+ align:start position:0%
+the rest of the energy is is is heat
+they're very hot and on a hot summer day
+
+ align:start position:0%
+they're very hot and on a hot summer day
+ 
+
+ align:start position:0%
+they're very hot and on a hot summer day
+they're just really uncomfortable to be
+
+ align:start position:0%
+they're just really uncomfortable to be
+ 
+
+ align:start position:0%
+they're just really uncomfortable to be
+close to hmis is newer technology
+
+ align:start position:0%
+close to hmis is newer technology
+ 
+
+ align:start position:0%
+close to hmis is newer technology
+daylight balanced very high tech um
+
+ align:start position:0%
+daylight balanced very high tech um
+ 
+
+ align:start position:0%
+daylight balanced very high tech um
+units but they're expensive they require
+
+ align:start position:0%
+units but they're expensive they require
+ 
+
+ align:start position:0%
+units but they're expensive they require
+a lot of electronics they require very
+
+ align:start position:0%
+a lot of electronics they require very
+ 
+
+ align:start position:0%
+a lot of electronics they require very
+sophisticated lamps with rare earth
+
+ align:start position:0%
+sophisticated lamps with rare earth
+ 
+
+ align:start position:0%
+sophisticated lamps with rare earth
+gases and all kinds of fancy stuff uh
+
+ align:start position:0%
+gases and all kinds of fancy stuff uh
+ 
+
+ align:start position:0%
+gases and all kinds of fancy stuff uh
+but they're daylight balanced and
+
+ align:start position:0%
+but they're daylight balanced and
+ 
+
+ align:start position:0%
+but they're daylight balanced and
+they're very bright and very efficient
+
+ align:start position:0%
+they're very bright and very efficient
+ 
+
+ align:start position:0%
+they're very bright and very efficient
+um kind of halfway in between are
+
+ align:start position:0%
+um kind of halfway in between are
+ 
+
+ align:start position:0%
+um kind of halfway in between are
+fluorescents um they make great soft
+
+ align:start position:0%
+fluorescents um they make great soft
+ 
+
+ align:start position:0%
+fluorescents um they make great soft
+lights um they're they run very cool um
+
+ align:start position:0%
+lights um they're they run very cool um
+ 
+
+ align:start position:0%
+lights um they're they run very cool um
+they're not necessarily the best thing
+
+ align:start position:0%
+they're not necessarily the best thing
+ 
+
+ align:start position:0%
+they're not necessarily the best thing
+for the environment but neither are the
+
+ align:start position:0%
+for the environment but neither are the
+ 
+
+ align:start position:0%
+for the environment but neither are the
+other lighting sources uh but they run
+
+ align:start position:0%
+other lighting sources uh but they run
+ 
+
+ align:start position:0%
+other lighting sources uh but they run
+cool and they use less power and the
+
+ align:start position:0%
+cool and they use less power and the
+ 
+
+ align:start position:0%
+cool and they use less power and the
+kinof flow fluorescent lights are just
+
+ align:start position:0%
+kinof flow fluorescent lights are just
+ 
+
+ align:start position:0%
+kinof flow fluorescent lights are just
+awesome and up and coming are LEDs LEDs
+
+ align:start position:0%
+awesome and up and coming are LEDs LEDs
+ 
+
+ align:start position:0%
+awesome and up and coming are LEDs LEDs
+have uh have come a long way in the last
+
+ align:start position:0%
+have uh have come a long way in the last
+ 
+
+ align:start position:0%
+have uh have come a long way in the last
+few years they're available in these
+
+ align:start position:0%
+few years they're available in these
+ 
+
+ align:start position:0%
+few years they're available in these
+like panels of either daylight balanced
+
+ align:start position:0%
+like panels of either daylight balanced
+ 
+
+ align:start position:0%
+like panels of either daylight balanced
+or tungsten balanced uh in fact light
+
+ align:start position:0%
+or tungsten balanced uh in fact light
+ 
+
+ align:start position:0%
+or tungsten balanced uh in fact light
+panels has a really nice grid that's a
+
+ align:start position:0%
+panels has a really nice grid that's a
+ 
+
+ align:start position:0%
+panels has a really nice grid that's a
+by color panel it's a grid of both
+
+ align:start position:0%
+by color panel it's a grid of both
+ 
+
+ align:start position:0%
+by color panel it's a grid of both
+daylight and tungsten balanced uh LEDs
+
+ align:start position:0%
+daylight and tungsten balanced uh LEDs
+ 
+
+ align:start position:0%
+daylight and tungsten balanced uh LEDs
+and you can dial in how much you want of
+
+ align:start position:0%
+and you can dial in how much you want of
+ 
+
+ align:start position:0%
+and you can dial in how much you want of
+each there's also a small version uh
+
+ align:start position:0%
+each there's also a small version uh
+ 
+
+ align:start position:0%
+each there's also a small version uh
+called the blender which actually has a
+
+ align:start position:0%
+called the blender which actually has a
+ 
+
+ align:start position:0%
+called the blender which actually has a
+grid of LED of of daylight and tungsten
+
+ align:start position:0%
+grid of LED of of daylight and tungsten
+ 
+
+ align:start position:0%
+grid of LED of of daylight and tungsten
+balanced LEDs and you can dial in the
+
+ align:start position:0%
+balanced LEDs and you can dial in the
+ 
+
+ align:start position:0%
+balanced LEDs and you can dial in the
+color temperature you want so they're
+
+ align:start position:0%
+color temperature you want so they're
+ 
+
+ align:start position:0%
+color temperature you want so they're
+very expensive compared to other light
+
+ align:start position:0%
+very expensive compared to other light
+ 
+
+ align:start position:0%
+very expensive compared to other light
+sources but they're very versatile the
+
+ align:start position:0%
+sources but they're very versatile the
+ 
+
+ align:start position:0%
+sources but they're very versatile the
+zylight is a model of LED light that you
+
+ align:start position:0%
+zylight is a model of LED light that you
+ 
+
+ align:start position:0%
+zylight is a model of LED light that you
+can dial in any color because it uses a
+
+ align:start position:0%
+can dial in any color because it uses a
+ 
+
+ align:start position:0%
+can dial in any color because it uses a
+red green blue grid of LEDs there's some
+
+ align:start position:0%
+red green blue grid of LEDs there's some
+ 
+
+ align:start position:0%
+red green blue grid of LEDs there's some
+really nice new products in the LED
+
+ align:start position:0%
+really nice new products in the LED
+ 
+
+ align:start position:0%
+really nice new products in the LED
+department and while they're expensive
+
+ align:start position:0%
+department and while they're expensive
+ 
+
+ align:start position:0%
+department and while they're expensive
+their lightness is just awesome you can
+
+ align:start position:0%
+their lightness is just awesome you can
+ 
+
+ align:start position:0%
+their lightness is just awesome you can
+pretty much if you go all LEDs you can
+
+ align:start position:0%
+pretty much if you go all LEDs you can
+ 
+
+ align:start position:0%
+pretty much if you go all LEDs you can
+cut the weight uh and size of your
+
+ align:start position:0%
+cut the weight uh and size of your
+ 
+
+ align:start position:0%
+cut the weight uh and size of your
+lighting kit in half so there's
+
+ align:start position:0%
+lighting kit in half so there's
+ 
+
+ align:start position:0%
+lighting kit in half so there's
+something to be said for for
+
+ align:start position:0%
+something to be said for for
+ 
+
+ align:start position:0%
+something to be said for for
+High-Tech uh if you're just starting out
+
+ align:start position:0%
+High-Tech uh if you're just starting out
+ 
+
+ align:start position:0%
+High-Tech uh if you're just starting out
+you don't have any lighting at all and
+
+ align:start position:0%
+you don't have any lighting at all and
+ 
+
+ align:start position:0%
+you don't have any lighting at all and
+you'd like a little something to start
+
+ align:start position:0%
+you'd like a little something to start
+ 
+
+ align:start position:0%
+you'd like a little something to start
+with uh one suggestion is um an open
+
+ align:start position:0%
+with uh one suggestion is um an open
+ 
+
+ align:start position:0%
+with uh one suggestion is um an open
+face light with an umbrella uh L makes
+
+ align:start position:0%
+face light with an umbrella uh L makes
+ 
+
+ align:start position:0%
+face light with an umbrella uh L makes
+this light called the toal light and
+
+ align:start position:0%
+this light called the toal light and
+ 
+
+ align:start position:0%
+this light called the toal light and
+they also have a newer version called
+
+ align:start position:0%
+they also have a newer version called
+ 
+
+ align:start position:0%
+they also have a newer version called
+The V light which is a little safer uh
+
+ align:start position:0%
+The V light which is a little safer uh
+ 
+
+ align:start position:0%
+The V light which is a little safer uh
+but this is basically just an open face
+
+ align:start position:0%
+but this is basically just an open face
+ 
+
+ align:start position:0%
+but this is basically just an open face
+light unit um and used with an umbrella
+
+ align:start position:0%
+light unit um and used with an umbrella
+ 
+
+ align:start position:0%
+light unit um and used with an umbrella
+bouncing the light you can now have a
+
+ align:start position:0%
+bouncing the light you can now have a
+ 
+
+ align:start position:0%
+bouncing the light you can now have a
+choice between a hard light or a soft
+
+ align:start position:0%
+choice between a hard light or a soft
+ 
+
+ align:start position:0%
+choice between a hard light or a soft
+light and so you can get a very quick
+
+ align:start position:0%
+light and so you can get a very quick
+ 
+
+ align:start position:0%
+light and so you can get a very quick
+and easy lightweight soft Source by
+
+ align:start position:0%
+and easy lightweight soft Source by
+ 
+
+ align:start position:0%
+and easy lightweight soft Source by
+bouncing the TOA off the umbrella and
+
+ align:start position:0%
+bouncing the TOA off the umbrella and
+ 
+
+ align:start position:0%
+bouncing the TOA off the umbrella and
+there's your soft light and you can put
+
+ align:start position:0%
+there's your soft light and you can put
+ 
+
+ align:start position:0%
+there's your soft light and you can put
+this kit together including a small
+
+ align:start position:0%
+this kit together including a small
+ 
+
+ align:start position:0%
+this kit together including a small
+light stand for less than $250 from your
+
+ align:start position:0%
+light stand for less than $250 from your
+ 
+
+ align:start position:0%
+light stand for less than $250 from your
+favorite online equipment retailer or
+
+ align:start position:0%
+favorite online equipment retailer or
+ 
+
+ align:start position:0%
+favorite online equipment retailer or
+your local
+
+ align:start position:0%
+your local
+ 
+
+ align:start position:0%
+your local
+Photoshop um set that sells video and
+
+ align:start position:0%
+Photoshop um set that sells video and
+ 
+
+ align:start position:0%
+Photoshop um set that sells video and
+and lighting equipment uh so this is the
+
+ align:start position:0%
+and lighting equipment uh so this is the
+ 
+
+ align:start position:0%
+and lighting equipment uh so this is the
+low todal or the low V light um as as a
+
+ align:start position:0%
+low todal or the low V light um as as a
+ 
+
+ align:start position:0%
+low todal or the low V light um as as a
+great starter kit you can put this in a
+
+ align:start position:0%
+great starter kit you can put this in a
+ 
+
+ align:start position:0%
+great starter kit you can put this in a
+teeny duffel bag I've often taken
+
+ align:start position:0%
+teeny duffel bag I've often taken
+ 
+
+ align:start position:0%
+teeny duffel bag I've often taken
+something like this with me on the train
+
+ align:start position:0%
+something like this with me on the train
+ 
+
+ align:start position:0%
+something like this with me on the train
+down to New York camera on one shoulder
+
+ align:start position:0%
+down to New York camera on one shoulder
+ 
+
+ align:start position:0%
+down to New York camera on one shoulder
+with sound gear and this in a on the
+
+ align:start position:0%
+with sound gear and this in a on the
+ 
+
+ align:start position:0%
+with sound gear and this in a on the
+other shoulder very light simple
+
+ align:start position:0%
+other shoulder very light simple
+ 
+
+ align:start position:0%
+other shoulder very light simple
+effective then you know over time you
+
+ align:start position:0%
+effective then you know over time you
+ 
+
+ align:start position:0%
+effective then you know over time you
+might want to add you know additional
+
+ align:start position:0%
+might want to add you know additional
+ 
+
+ align:start position:0%
+might want to add you know additional
+units depending on your particular
+
+ align:start position:0%
+units depending on your particular
+ 
+
+ align:start position:0%
+units depending on your particular
+lighting style you know a lot of people
+
+ align:start position:0%
+lighting style you know a lot of people
+ 
+
+ align:start position:0%
+lighting style you know a lot of people
+ask me what lighting kit do you
+
+ align:start position:0%
+ask me what lighting kit do you
+ 
+
+ align:start position:0%
+ask me what lighting kit do you
+recommend well it's really hard for me
+
+ align:start position:0%
+recommend well it's really hard for me
+ 
+
+ align:start position:0%
+recommend well it's really hard for me
+to recommend a lighting kit because it
+
+ align:start position:0%
+to recommend a lighting kit because it
+ 
+
+ align:start position:0%
+to recommend a lighting kit because it
+really depends on what your preferences
+
+ align:start position:0%
+really depends on what your preferences
+ 
+
+ align:start position:0%
+really depends on what your preferences
+are and what you want to accomplish so I
+
+ align:start position:0%
+are and what you want to accomplish so I
+ 
+
+ align:start position:0%
+are and what you want to accomplish so I
+would suggest you know buy one light at
+
+ align:start position:0%
+would suggest you know buy one light at
+ 
+
+ align:start position:0%
+would suggest you know buy one light at
+a time learn it get to know it and
+
+ align:start position:0%
+a time learn it get to know it and
+ 
+
+ align:start position:0%
+a time learn it get to know it and
+figure out what you want next start with
+
+ align:start position:0%
+figure out what you want next start with
+ 
+
+ align:start position:0%
+figure out what you want next start with
+a basic soft light and go from there you
+
+ align:start position:0%
+a basic soft light and go from there you
+ 
+
+ align:start position:0%
+a basic soft light and go from there you
+might want to add some Fels you might
+
+ align:start position:0%
+might want to add some Fels you might
+ 
+
+ align:start position:0%
+might want to add some Fels you might
+want to add some LED lights you might
+
+ align:start position:0%
+want to add some LED lights you might
+ 
+
+ align:start position:0%
+want to add some LED lights you might
+want to add a flex fill reflector which
+
+ align:start position:0%
+want to add a flex fill reflector which
+ 
+
+ align:start position:0%
+want to add a flex fill reflector which
+you'll see in the live demo portion um
+
+ align:start position:0%
+you'll see in the live demo portion um
+ 
+
+ align:start position:0%
+you'll see in the live demo portion um
+so these are various things that you
+
+ align:start position:0%
+so these are various things that you
+ 
+
+ align:start position:0%
+so these are various things that you
+might want to add but you know explore
+
+ align:start position:0%
+might want to add but you know explore
+ 
+
+ align:start position:0%
+might want to add but you know explore
+use it and figure out what you need a
+
+ align:start position:0%
+use it and figure out what you need a
+ 
+
+ align:start position:0%
+use it and figure out what you need a
+lot of a lot of uh towns have rental
+
+ align:start position:0%
+lot of a lot of uh towns have rental
+ 
+
+ align:start position:0%
+lot of a lot of uh towns have rental
+houses that you can rent light kits rent
+
+ align:start position:0%
+houses that you can rent light kits rent
+ 
+
+ align:start position:0%
+houses that you can rent light kits rent
+a kit for a weekend get to know it
+
+ align:start position:0%
+a kit for a weekend get to know it
+ 
+
+ align:start position:0%
+a kit for a weekend get to know it
+decide what you like what works for you
+
+ align:start position:0%
+decide what you like what works for you
+ 
+
+ align:start position:0%
+decide what you like what works for you
+what doesn't work for
+
+ align:start position:0%
+what doesn't work for
+ 
+
+ align:start position:0%
+what doesn't work for
+you um just remember it all starts with
+
+ align:start position:0%
+you um just remember it all starts with
+ 
+
+ align:start position:0%
+you um just remember it all starts with
+a good key light so definitely at some
+
+ align:start position:0%
+a good key light so definitely at some
+ 
+
+ align:start position:0%
+a good key light so definitely at some
+point you want to have something like a
+
+ align:start position:0%
+point you want to have something like a
+ 
+
+ align:start position:0%
+point you want to have something like a
+low Rea light or a diva kinof flow Diva
+
+ align:start position:0%
+low Rea light or a diva kinof flow Diva
+ 
+
+ align:start position:0%
+low Rea light or a diva kinof flow Diva
+light um as as your staple um soft light
+
+ align:start position:0%
+light um as as your staple um soft light
+ 
+
+ align:start position:0%
+light um as as your staple um soft light
+and then we talked about diffusion
+
+ align:start position:0%
+and then we talked about diffusion
+ 
+
+ align:start position:0%
+and then we talked about diffusion
+material that you can get this it sort
+
+ align:start position:0%
+material that you can get this it sort
+ 
+
+ align:start position:0%
+material that you can get this it sort
+of looks like opaque kind of gel that
+
+ align:start position:0%
+of looks like opaque kind of gel that
+ 
+
+ align:start position:0%
+of looks like opaque kind of gel that
+will soften any light that's why it's
+
+ align:start position:0%
+will soften any light that's why it's
+ 
+
+ align:start position:0%
+will soften any light that's why it's
+nice to have a few hard lights because
+
+ align:start position:0%
+nice to have a few hard lights because
+ 
+
+ align:start position:0%
+nice to have a few hard lights because
+you can always soften them with gels uh
+
+ align:start position:0%
+you can always soften them with gels uh
+ 
+
+ align:start position:0%
+you can always soften them with gels uh
+color changing gels there's this whole
+
+ align:start position:0%
+color changing gels there's this whole
+ 
+
+ align:start position:0%
+color changing gels there's this whole
+series called CTB for color temperature
+
+ align:start position:0%
+series called CTB for color temperature
+ 
+
+ align:start position:0%
+series called CTB for color temperature
+blue CTO for color temperature orange
+
+ align:start position:0%
+blue CTO for color temperature orange
+ 
+
+ align:start position:0%
+blue CTO for color temperature orange
+you can use these gels for changing the
+
+ align:start position:0%
+you can use these gels for changing the
+ 
+
+ align:start position:0%
+you can use these gels for changing the
+color of light sources black wrap is an
+
+ align:start position:0%
+color of light sources black wrap is an
+ 
+
+ align:start position:0%
+color of light sources black wrap is an
+interesting material it's aluminum foil
+
+ align:start position:0%
+interesting material it's aluminum foil
+ 
+
+ align:start position:0%
+interesting material it's aluminum foil
+with flame retardant black paint you can
+
+ align:start position:0%
+with flame retardant black paint you can
+ 
+
+ align:start position:0%
+with flame retardant black paint you can
+use that that if if light is spilling
+
+ align:start position:0%
+use that that if if light is spilling
+ 
+
+ align:start position:0%
+use that that if if light is spilling
+from a light unit you use the black wrap
+
+ align:start position:0%
+from a light unit you use the black wrap
+ 
+
+ align:start position:0%
+from a light unit you use the black wrap
+to kind of Kill The Spill off the light
+
+ align:start position:0%
+to kind of Kill The Spill off the light
+ 
+
+ align:start position:0%
+to kind of Kill The Spill off the light
+and you won't start any fires because
+
+ align:start position:0%
+and you won't start any fires because
+ 
+
+ align:start position:0%
+and you won't start any fires because
+it's flame retardant and it's metal foil
+
+ align:start position:0%
+it's flame retardant and it's metal foil
+ 
+
+ align:start position:0%
+it's flame retardant and it's metal foil
+does get hot though and uh several
+
+ align:start position:0%
+does get hot though and uh several
+ 
+
+ align:start position:0%
+does get hot though and uh several
+manufacturers make these great little
+
+ align:start position:0%
+manufacturers make these great little
+ 
+
+ align:start position:0%
+manufacturers make these great little
+wrapping things called jelly rolls that
+
+ align:start position:0%
+wrapping things called jelly rolls that
+ 
+
+ align:start position:0%
+wrapping things called jelly rolls that
+you can roll up your gels in and they
+
+ align:start position:0%
+you can roll up your gels in and they
+ 
+
+ align:start position:0%
+you can roll up your gels in and they
+come in both small and large sizes
+
+ align:start position:0%
+come in both small and large sizes
+ 
+
+ align:start position:0%
+come in both small and large sizes
+dimmers are handy for dimming lights but
+
+ align:start position:0%
+dimmers are handy for dimming lights but
+ 
+
+ align:start position:0%
+dimmers are handy for dimming lights but
+I'll warn you now that they create cycle
+
+ align:start position:0%
+I'll warn you now that they create cycle
+ 
+
+ align:start position:0%
+I'll warn you now that they create cycle
+hum and Buzz and very often light lights
+
+ align:start position:0%
+hum and Buzz and very often light lights
+ 
+
+ align:start position:0%
+hum and Buzz and very often light lights
+will the filament of lights will buzz so
+
+ align:start position:0%
+will the filament of lights will buzz so
+ 
+
+ align:start position:0%
+will the filament of lights will buzz so
+if you carry dimmers on the set uh if
+
+ align:start position:0%
+if you carry dimmers on the set uh if
+ 
+
+ align:start position:0%
+if you carry dimmers on the set uh if
+you're working with a sound person they
+
+ align:start position:0%
+you're working with a sound person they
+ 
+
+ align:start position:0%
+you're working with a sound person they
+will talk to you about it so dimmers are
+
+ align:start position:0%
+will talk to you about it so dimmers are
+ 
+
+ align:start position:0%
+will talk to you about it so dimmers are
+useful but they're tricky because of the
+
+ align:start position:0%
+useful but they're tricky because of the
+ 
+
+ align:start position:0%
+useful but they're tricky because of the
+uh interference problems uh but they can
+
+ align:start position:0%
+uh interference problems uh but they can
+ 
+
+ align:start position:0%
+uh interference problems uh but they can
+you know in some cases they can be
+
+ align:start position:0%
+you know in some cases they can be
+ 
+
+ align:start position:0%
+you know in some cases they can be
+used Cube Taps are useful for turning
+
+ align:start position:0%
+used Cube Taps are useful for turning
+ 
+
+ align:start position:0%
+used Cube Taps are useful for turning
+one Outlet into three want to be careful
+
+ align:start position:0%
+one Outlet into three want to be careful
+ 
+
+ align:start position:0%
+one Outlet into three want to be careful
+with those two prong to three-prong
+
+ align:start position:0%
+with those two prong to three-prong
+ 
+
+ align:start position:0%
+with those two prong to three-prong
+adapters but in a lot of older houses
+
+ align:start position:0%
+adapters but in a lot of older houses
+ 
+
+ align:start position:0%
+adapters but in a lot of older houses
+they don't have three prong plugs my own
+
+ align:start position:0%
+they don't have three prong plugs my own
+ 
+
+ align:start position:0%
+they don't have three prong plugs my own
+included um gloves are handy if you um I
+
+ align:start position:0%
+included um gloves are handy if you um I
+ 
+
+ align:start position:0%
+included um gloves are handy if you um I
+usually handle uh lights without gloves
+
+ align:start position:0%
+usually handle uh lights without gloves
+ 
+
+ align:start position:0%
+usually handle uh lights without gloves
+because I know exactly where the hot
+
+ align:start position:0%
+because I know exactly where the hot
+ 
+
+ align:start position:0%
+because I know exactly where the hot
+parts are and where the hot Parts aren't
+
+ align:start position:0%
+parts are and where the hot Parts aren't
+ 
+
+ align:start position:0%
+parts are and where the hot Parts aren't
+from years of experience but when you're
+
+ align:start position:0%
+from years of experience but when you're
+ 
+
+ align:start position:0%
+from years of experience but when you're
+starting out you might want to use
+
+ align:start position:0%
+starting out you might want to use
+ 
+
+ align:start position:0%
+starting out you might want to use
+gloves um and be careful gaffer tape is
+
+ align:start position:0%
+gloves um and be careful gaffer tape is
+ 
+
+ align:start position:0%
+gloves um and be careful gaffer tape is
+the will solve any problem that the
+
+ align:start position:0%
+the will solve any problem that the
+ 
+
+ align:start position:0%
+the will solve any problem that the
+lighting instruments can't solve in most
+
+ align:start position:0%
+lighting instruments can't solve in most
+ 
+
+ align:start position:0%
+lighting instruments can't solve in most
+cases and I won't go into detail but as
+
+ align:start position:0%
+cases and I won't go into detail but as
+ 
+
+ align:start position:0%
+cases and I won't go into detail but as
+you expand your uh lighting work you
+
+ align:start position:0%
+you expand your uh lighting work you
+ 
+
+ align:start position:0%
+you expand your uh lighting work you
+might want to add things like flags and
+
+ align:start position:0%
+might want to add things like flags and
+ 
+
+ align:start position:0%
+might want to add things like flags and
+Nets for for sculpting light but that's
+
+ align:start position:0%
+Nets for for sculpting light but that's
+ 
+
+ align:start position:0%
+Nets for for sculpting light but that's
+beyond the scope of this talk if you
+
+ align:start position:0%
+beyond the scope of this talk if you
+ 
+
+ align:start position:0%
+beyond the scope of this talk if you
+ever have larger lights you're going to
+
+ align:start position:0%
+ever have larger lights you're going to
+ 
+
+ align:start position:0%
+ever have larger lights you're going to
+need to put sandbags on the stands so
+
+ align:start position:0%
+need to put sandbags on the stands so
+ 
+
+ align:start position:0%
+need to put sandbags on the stands so
+having some portable Beach is very very
+
+ align:start position:0%
+having some portable Beach is very very
+ 
+
+ align:start position:0%
+having some portable Beach is very very
+handy and there's the universal sea
+
+ align:start position:0%
+handy and there's the universal sea
+ 
+
+ align:start position:0%
+handy and there's the universal sea
+stand that's uh can you be used for all
+
+ align:start position:0%
+stand that's uh can you be used for all
+ 
+
+ align:start position:0%
+stand that's uh can you be used for all
+sorts of things hanging sound blankets
+
+ align:start position:0%
+sorts of things hanging sound blankets
+ 
+
+ align:start position:0%
+sorts of things hanging sound blankets
+in addition to holding lights and stuff
+
+ align:start position:0%
+in addition to holding lights and stuff
+ 
+
+ align:start position:0%
+in addition to holding lights and stuff
+and there's a lot of gripy that we're
+
+ align:start position:0%
+and there's a lot of gripy that we're
+ 
+
+ align:start position:0%
+and there's a lot of gripy that we're
+not going to get into today but it's
+
+ align:start position:0%
+not going to get into today but it's
+ 
+
+ align:start position:0%
+not going to get into today but it's
+good to know that there is this whole um
+
+ align:start position:0%
+good to know that there is this whole um
+ 
+
+ align:start position:0%
+good to know that there is this whole um
+collection of gear out
+
+ align:start position:0%
+collection of gear out
+ 
+
+ align:start position:0%
+collection of gear out
+there but some that are useful is if
+
+ align:start position:0%
+there but some that are useful is if
+ 
+
+ align:start position:0%
+there but some that are useful is if
+you're working in an environment with uh
+
+ align:start position:0%
+you're working in an environment with uh
+ 
+
+ align:start position:0%
+you're working in an environment with uh
+drop ceilings these little scissor
+
+ align:start position:0%
+drop ceilings these little scissor
+ 
+
+ align:start position:0%
+drop ceilings these little scissor
+clamps are great which will give you a
+
+ align:start position:0%
+clamps are great which will give you a
+ 
+
+ align:start position:0%
+clamps are great which will give you a
+standard 5/8 inch stud for hanging a
+
+ align:start position:0%
+standard 5/8 inch stud for hanging a
+ 
+
+ align:start position:0%
+standard 5/8 inch stud for hanging a
+small light it's good to have a couple
+
+ align:start position:0%
+small light it's good to have a couple
+ 
+
+ align:start position:0%
+small light it's good to have a couple
+of those in your kit mayfer clamps are
+
+ align:start position:0%
+of those in your kit mayfer clamps are
+ 
+
+ align:start position:0%
+of those in your kit mayfer clamps are
+very handy also known as photo clamps
+
+ align:start position:0%
+very handy also known as photo clamps
+ 
+
+ align:start position:0%
+very handy also known as photo clamps
+depending on who you ask um these are
+
+ align:start position:0%
+depending on who you ask um these are
+ 
+
+ align:start position:0%
+depending on who you ask um these are
+great clamps that you can attach to
+
+ align:start position:0%
+great clamps that you can attach to
+ 
+
+ align:start position:0%
+great clamps that you can attach to
+pipes and all sorts of conduit and
+
+ align:start position:0%
+pipes and all sorts of conduit and
+ 
+
+ align:start position:0%
+pipes and all sorts of conduit and
+things if you need um you'll notice that
+
+ align:start position:0%
+things if you need um you'll notice that
+ 
+
+ align:start position:0%
+things if you need um you'll notice that
+for all small lights the industry
+
+ align:start position:0%
+for all small lights the industry
+ 
+
+ align:start position:0%
+for all small lights the industry
+standard is a 5/8 inch stud it's also
+
+ align:start position:0%
+standard is a 5/8 inch stud it's also
+ 
+
+ align:start position:0%
+standard is a 5/8 inch stud it's also
+known as a baby stud grip Clips are
+
+ align:start position:0%
+known as a baby stud grip Clips are
+ 
+
+ align:start position:0%
+known as a baby stud grip Clips are
+great um you can buy official grip Clips
+
+ align:start position:0%
+great um you can buy official grip Clips
+ 
+
+ align:start position:0%
+great um you can buy official grip Clips
+you can go to the hardware store and buy
+
+ align:start position:0%
+you can go to the hardware store and buy
+ 
+
+ align:start position:0%
+you can go to the hardware store and buy
+the equivalent for a fraction of the
+
+ align:start position:0%
+the equivalent for a fraction of the
+ 
+
+ align:start position:0%
+the equivalent for a fraction of the
+price um I still use a light meter
+
+ align:start position:0%
+price um I still use a light meter
+ 
+
+ align:start position:0%
+price um I still use a light meter
+sometimes when I'm setting up lights but
+
+ align:start position:0%
+sometimes when I'm setting up lights but
+ 
+
+ align:start position:0%
+sometimes when I'm setting up lights but
+that's probably an
+
+ align:start position:0%
+that's probably an
+ 
+
+ align:start position:0%
+that's probably an
+anachronism though it is Handy to have
+
+ align:start position:0%
+anachronism though it is Handy to have
+ 
+
+ align:start position:0%
+anachronism though it is Handy to have
+an 18% gray card white on one side for
+
+ align:start position:0%
+an 18% gray card white on one side for
+ 
+
+ align:start position:0%
+an 18% gray card white on one side for
+white balance gray on the other side uh
+
+ align:start position:0%
+white balance gray on the other side uh
+ 
+
+ align:start position:0%
+white balance gray on the other side uh
+very often if you're color correcting a
+
+ align:start position:0%
+very often if you're color correcting a
+ 
+
+ align:start position:0%
+very often if you're color correcting a
+scene and you put that gray card in the
+
+ align:start position:0%
+scene and you put that gray card in the
+ 
+
+ align:start position:0%
+scene and you put that gray card in the
+scene and now you have a gray reference
+
+ align:start position:0%
+scene and now you have a gray reference
+ 
+
+ align:start position:0%
+scene and now you have a gray reference
+so if you're color obsessed like myself
+
+ align:start position:0%
+so if you're color obsessed like myself
+ 
+
+ align:start position:0%
+so if you're color obsessed like myself
+you might want to carry a gray card in
+
+ align:start position:0%
+you might want to carry a gray card in
+ 
+
+ align:start position:0%
+you might want to carry a gray card in
+your kit but um and there's a list here
+
+ align:start position:0%
+your kit but um and there's a list here
+ 
+
+ align:start position:0%
+your kit but um and there's a list here
+of other things um this is sort of a
+
+ align:start position:0%
+of other things um this is sort of a
+ 
+
+ align:start position:0%
+of other things um this is sort of a
+homework assignment figure out what all
+
+ align:start position:0%
+homework assignment figure out what all
+ 
+
+ align:start position:0%
+homework assignment figure out what all
+these things are it's a good good thing
+
+ align:start position:0%
+these things are it's a good good thing
+ 
+
+ align:start position:0%
+these things are it's a good good thing
+to learn um you know at the end of the
+
+ align:start position:0%
+to learn um you know at the end of the
+ 
+
+ align:start position:0%
+to learn um you know at the end of the
+day just remember there are no rules
+
+ align:start position:0%
+day just remember there are no rules
+ 
+
+ align:start position:0%
+day just remember there are no rules
+about what is good lighting and bad
+
+ align:start position:0%
+about what is good lighting and bad
+ 
+
+ align:start position:0%
+about what is good lighting and bad
+lighting um because one person's bad
+
+ align:start position:0%
+lighting um because one person's bad
+ 
+
+ align:start position:0%
+lighting um because one person's bad
+lighting is another person's dramatic
+
+ align:start position:0%
+lighting is another person's dramatic
+ 
+
+ align:start position:0%
+lighting is another person's dramatic
+lighting um it might be bad if it
+
+ align:start position:0%
+lighting um it might be bad if it
+ 
+
+ align:start position:0%
+lighting um it might be bad if it
+creates the wrong Ambience for the scene
+
+ align:start position:0%
+creates the wrong Ambience for the scene
+ 
+
+ align:start position:0%
+creates the wrong Ambience for the scene
+or produces an unintended unflattering
+
+ align:start position:0%
+or produces an unintended unflattering
+ 
+
+ align:start position:0%
+or produces an unintended unflattering
+effect or it distracts the viewer's
+
+ align:start position:0%
+effect or it distracts the viewer's
+ 
+
+ align:start position:0%
+effect or it distracts the viewer's
+attention remember we were talking about
+
+ align:start position:0%
+attention remember we were talking about
+ 
+
+ align:start position:0%
+attention remember we were talking about
+we use light
+
+ align:start position:0%
+we use light
+ 
+
+ align:start position:0%
+we use light
+to drive the viewer's attention in the
+
+ align:start position:0%
+to drive the viewer's attention in the
+ 
+
+ align:start position:0%
+to drive the viewer's attention in the
+scene but if it's not doing that then
+
+ align:start position:0%
+scene but if it's not doing that then
+ 
+
+ align:start position:0%
+scene but if it's not doing that then
+maybe it is bad lighting does it prevent
+
+ align:start position:0%
+maybe it is bad lighting does it prevent
+ 
+
+ align:start position:0%
+maybe it is bad lighting does it prevent
+the viewer from seeing what's
+
+ align:start position:0%
+the viewer from seeing what's
+ 
+
+ align:start position:0%
+the viewer from seeing what's
+important or is it showing things that
+
+ align:start position:0%
+important or is it showing things that
+ 
+
+ align:start position:0%
+important or is it showing things that
+are irrelevant so one of the biggest
+
+ align:start position:0%
+are irrelevant so one of the biggest
+ 
+
+ align:start position:0%
+are irrelevant so one of the biggest
+problems with point and shoot video is
+
+ align:start position:0%
+problems with point and shoot video is
+ 
+
+ align:start position:0%
+problems with point and shoot video is
+that often times our subject is obscured
+
+ align:start position:0%
+that often times our subject is obscured
+ 
+
+ align:start position:0%
+that often times our subject is obscured
+and something that's completely
+
+ align:start position:0%
+and something that's completely
+ 
+
+ align:start position:0%
+and something that's completely
+unimportant is is staring at you know
+
+ align:start position:0%
+unimportant is is staring at you know
+ 
+
+ align:start position:0%
+unimportant is is staring at you know
+staring us right at the face so think
+
+ align:start position:0%
+staring us right at the face so think
+ 
+
+ align:start position:0%
+staring us right at the face so think
+about what is it doing for you and your
+
+ align:start position:0%
+about what is it doing for you and your
+ 
+
+ align:start position:0%
+about what is it doing for you and your
+own storytelling good lighting allows us
+
+ align:start position:0%
+own storytelling good lighting allows us
+ 
+
+ align:start position:0%
+own storytelling good lighting allows us
+to do many many things I'm not going to
+
+ align:start position:0%
+to do many many things I'm not going to
+ 
+
+ align:start position:0%
+to do many many things I'm not going to
+go through this whole list but once
+
+ align:start position:0%
+go through this whole list but once
+ 
+
+ align:start position:0%
+go through this whole list but once
+again it can help us draw attention to
+
+ align:start position:0%
+again it can help us draw attention to
+ 
+
+ align:start position:0%
+again it can help us draw attention to
+what's important in the scene it can
+
+ align:start position:0%
+what's important in the scene it can
+ 
+
+ align:start position:0%
+what's important in the scene it can
+help isolate the subject it could imply
+
+ align:start position:0%
+help isolate the subject it could imply
+ 
+
+ align:start position:0%
+help isolate the subject it could imply
+a season it could establish a local it
+
+ align:start position:0%
+a season it could establish a local it
+ 
+
+ align:start position:0%
+a season it could establish a local it
+can concentrate attention to a
+
+ align:start position:0%
+can concentrate attention to a
+ 
+
+ align:start position:0%
+can concentrate attention to a
+particular part of the scene it can
+
+ align:start position:0%
+particular part of the scene it can
+ 
+
+ align:start position:0%
+particular part of the scene it can
+emphasize form like we talked about with
+
+ align:start position:0%
+emphasize form like we talked about with
+ 
+
+ align:start position:0%
+emphasize form like we talked about with
+Kos skuro or we can deemphasize form
+
+ align:start position:0%
+Kos skuro or we can deemphasize form
+ 
+
+ align:start position:0%
+Kos skuro or we can deemphasize form
+with flat lighting at the end of the day
+
+ align:start position:0%
+with flat lighting at the end of the day
+ 
+
+ align:start position:0%
+with flat lighting at the end of the day
+it's about altering the viewer's
+
+ align:start position:0%
+it's about altering the viewer's
+ 
+
+ align:start position:0%
+it's about altering the viewer's
+emotional response um and establishing a
+
+ align:start position:0%
+emotional response um and establishing a
+ 
+
+ align:start position:0%
+emotional response um and establishing a
+mood and so here's kind of my laundry
+
+ align:start position:0%
+mood and so here's kind of my laundry
+ 
+
+ align:start position:0%
+mood and so here's kind of my laundry
+list of all the things that lighting can
+
+ align:start position:0%
+list of all the things that lighting can
+ 
+
+ align:start position:0%
+list of all the things that lighting can
+do for you and through experience and
+
+ align:start position:0%
+do for you and through experience and
+ 
+
+ align:start position:0%
+do for you and through experience and
+through practice you will see how what
+
+ align:start position:0%
+through practice you will see how what
+ 
+
+ align:start position:0%
+through practice you will see how what
+you do with lighting has an impact in
+
+ align:start position:0%
+you do with lighting has an impact in
+ 
+
+ align:start position:0%
+you do with lighting has an impact in
+your storytelling um so that's kind of a
+
+ align:start position:0%
+your storytelling um so that's kind of a
+ 
+
+ align:start position:0%
+your storytelling um so that's kind of a
+list of all the things that lighting
+
+ align:start position:0%
+list of all the things that lighting
+ 
+
+ align:start position:0%
+list of all the things that lighting
+lighting can do for you and at the end
+
+ align:start position:0%
+lighting can do for you and at the end
+ 
+
+ align:start position:0%
+lighting can do for you and at the end
+here um there's a there's a a brief
+
+ align:start position:0%
+here um there's a there's a a brief
+ 
+
+ align:start position:0%
+here um there's a there's a a brief
+glossery of terms of Enlightenment uh
+
+ align:start position:0%
+glossery of terms of Enlightenment uh
+ 
+
+ align:start position:0%
+glossery of terms of Enlightenment uh
+which is a word I borrowed from Ross LEL
+
+ align:start position:0%
+which is a word I borrowed from Ross LEL
+ 
+
+ align:start position:0%
+which is a word I borrowed from Ross LEL
+who wrote a wonderful book called
+
+ align:start position:0%
+who wrote a wonderful book called
+ 
+
+ align:start position:0%
+who wrote a wonderful book called
+matters of light and depth which I
+
+ align:start position:0%
+matters of light and depth which I
+ 
+
+ align:start position:0%
+matters of light and depth which I
+highly
+
+ align:start position:0%
+highly
+ 
+
+ align:start position:0%
+highly
+recommend um there's electricity
+
+ align:start position:0%
+recommend um there's electricity
+ 
+
+ align:start position:0%
+recommend um there's electricity
+involved in lighting and you want to be
+
+ align:start position:0%
+involved in lighting and you want to be
+ 
+
+ align:start position:0%
+involved in lighting and you want to be
+very careful
+
+ align:start position:0%
+very careful
+ 
+
+ align:start position:0%
+very careful
+um and treat it with respect and if you
+
+ align:start position:0%
+um and treat it with respect and if you
+ 
+
+ align:start position:0%
+um and treat it with respect and if you
+have frayed wires or anything damaged in
+
+ align:start position:0%
+have frayed wires or anything damaged in
+ 
+
+ align:start position:0%
+have frayed wires or anything damaged in
+your lighting equipment you want to fix
+
+ align:start position:0%
+your lighting equipment you want to fix
+ 
+
+ align:start position:0%
+your lighting equipment you want to fix
+it before you plug it into the wall uh
+
+ align:start position:0%
+it before you plug it into the wall uh
+ 
+
+ align:start position:0%
+it before you plug it into the wall uh
+what you what you have here is a simple
+
+ align:start position:0%
+what you what you have here is a simple
+ 
+
+ align:start position:0%
+what you what you have here is a simple
+calculator for determining do you have
+
+ align:start position:0%
+calculator for determining do you have
+ 
+
+ align:start position:0%
+calculator for determining do you have
+enough power to light to provide the
+
+ align:start position:0%
+enough power to light to provide the
+ 
+
+ align:start position:0%
+enough power to light to provide the
+power for your lighting units so the way
+
+ align:start position:0%
+power for your lighting units so the way
+ 
+
+ align:start position:0%
+power for your lighting units so the way
+to remember it is a 20 amp circuit a 20
+
+ align:start position:0%
+to remember it is a 20 amp circuit a 20
+ 
+
+ align:start position:0%
+to remember it is a 20 amp circuit a 20
+amp household circuit which is pretty
+
+ align:start position:0%
+amp household circuit which is pretty
+ 
+
+ align:start position:0%
+amp household circuit which is pretty
+standard in bathrooms and kitchens in
+
+ align:start position:0%
+standard in bathrooms and kitchens in
+ 
+
+ align:start position:0%
+standard in bathrooms and kitchens in
+contemporary Construction in a lot of
+
+ align:start position:0%
+contemporary Construction in a lot of
+ 
+
+ align:start position:0%
+contemporary Construction in a lot of
+older houses you will find 15 amp
+
+ align:start position:0%
+older houses you will find 15 amp
+ 
+
+ align:start position:0%
+older houses you will find 15 amp
+circuits but the thing to remember a 20
+
+ align:start position:0%
+circuits but the thing to remember a 20
+ 
+
+ align:start position:0%
+circuits but the thing to remember a 20
+amp circuit can support 2,000 Watts
+
+ align:start position:0%
+amp circuit can support 2,000 Watts
+ 
+
+ align:start position:0%
+amp circuit can support 2,000 Watts
+that's the only number you need to
+
+ align:start position:0%
+that's the only number you need to
+ 
+
+ align:start position:0%
+that's the only number you need to
+remember and you can extrapolate from
+
+ align:start position:0%
+remember and you can extrapolate from
+ 
+
+ align:start position:0%
+remember and you can extrapolate from
+there a 20 amp circuit gives you can
+
+ align:start position:0%
+there a 20 amp circuit gives you can
+ 
+
+ align:start position:0%
+there a 20 amp circuit gives you can
+feed two 2,000 Watts because you just
+
+ align:start position:0%
+feed two 2,000 Watts because you just
+ 
+
+ align:start position:0%
+feed two 2,000 Watts because you just
+basically take the amps and
+
+ align:start position:0%
+basically take the amps and
+ 
+
+ align:start position:0%
+basically take the amps and
+multiply by uh 100 right amps
+
+ align:start position:0%
+multiply by uh 100 right amps
+ 
+
+ align:start position:0%
+multiply by uh 100 right amps
+um are basically a measure of how much
+
+ align:start position:0%
+um are basically a measure of how much
+ 
+
+ align:start position:0%
+um are basically a measure of how much
+current how much oomph you're drawing
+
+ align:start position:0%
+current how much oomph you're drawing
+ 
+
+ align:start position:0%
+current how much oomph you're drawing
+from that circuit and the wattage of a
+
+ align:start position:0%
+from that circuit and the wattage of a
+ 
+
+ align:start position:0%
+from that circuit and the wattage of a
+lamp 2,000 Watts 100 watt watts is how
+
+ align:start position:0%
+lamp 2,000 Watts 100 watt watts is how
+ 
+
+ align:start position:0%
+lamp 2,000 Watts 100 watt watts is how
+much energy that lamp is putting to work
+
+ align:start position:0%
+much energy that lamp is putting to work
+ 
+
+ align:start position:0%
+much energy that lamp is putting to work
+so the important thing is is that you
+
+ align:start position:0%
+so the important thing is is that you
+ 
+
+ align:start position:0%
+so the important thing is is that you
+don't want to draw more current from the
+
+ align:start position:0%
+don't want to draw more current from the
+ 
+
+ align:start position:0%
+don't want to draw more current from the
+circuit than it can take because then
+
+ align:start position:0%
+circuit than it can take because then
+ 
+
+ align:start position:0%
+circuit than it can take because then
+you'll pop the circuit breaker so
+
+ align:start position:0%
+you'll pop the circuit breaker so
+ 
+
+ align:start position:0%
+you'll pop the circuit breaker so
+whenever you set up a lighting kit um if
+
+ align:start position:0%
+whenever you set up a lighting kit um if
+ 
+
+ align:start position:0%
+whenever you set up a lighting kit um if
+your total lighting kit uses only uses
+
+ align:start position:0%
+your total lighting kit uses only uses
+ 
+
+ align:start position:0%
+your total lighting kit uses only uses
+1,500 Watts you probably don't have to
+
+ align:start position:0%
+1,500 Watts you probably don't have to
+ 
+
+ align:start position:0%
+1,500 Watts you probably don't have to
+worry about popping an ordinary breaker
+
+ align:start position:0%
+worry about popping an ordinary breaker
+ 
+
+ align:start position:0%
+worry about popping an ordinary breaker
+but you want to know where the breaker
+
+ align:start position:0%
+but you want to know where the breaker
+ 
+
+ align:start position:0%
+but you want to know where the breaker
+box is just in case and whenever I go
+
+ align:start position:0%
+box is just in case and whenever I go
+ 
+
+ align:start position:0%
+box is just in case and whenever I go
+into somebody's home to do an interview
+
+ align:start position:0%
+into somebody's home to do an interview
+ 
+
+ align:start position:0%
+into somebody's home to do an interview
+or whatever I always ask them do you
+
+ align:start position:0%
+or whatever I always ask them do you
+ 
+
+ align:start position:0%
+or whatever I always ask them do you
+have anything plugged in that if the
+
+ align:start position:0%
+have anything plugged in that if the
+ 
+
+ align:start position:0%
+have anything plugged in that if the
+power went out would cause some sort of
+
+ align:start position:0%
+power went out would cause some sort of
+ 
+
+ align:start position:0%
+power went out would cause some sort of
+disaster always ask um there are times
+
+ align:start position:0%
+disaster always ask um there are times
+ 
+
+ align:start position:0%
+disaster always ask um there are times
+for example when I've run extension
+
+ align:start position:0%
+for example when I've run extension
+ 
+
+ align:start position:0%
+for example when I've run extension
+cords into a kitchen to power an
+
+ align:start position:0%
+cords into a kitchen to power an
+ 
+
+ align:start position:0%
+cords into a kitchen to power an
+interview in a living room because
+
+ align:start position:0%
+interview in a living room because
+ 
+
+ align:start position:0%
+interview in a living room because
+somebody had their computer set up and
+
+ align:start position:0%
+somebody had their computer set up and
+ 
+
+ align:start position:0%
+somebody had their computer set up and
+they didn't want to turn it off and
+
+ align:start position:0%
+they didn't want to turn it off and
+ 
+
+ align:start position:0%
+they didn't want to turn it off and
+whatever you just don't want to mess
+
+ align:start position:0%
+whatever you just don't want to mess
+ 
+
+ align:start position:0%
+whatever you just don't want to mess
+with it but the thing is you can in
+
+ align:start position:0%
+with it but the thing is you can in
+ 
+
+ align:start position:0%
+with it but the thing is you can in
+modern construction you can always count
+
+ align:start position:0%
+modern construction you can always count
+ 
+
+ align:start position:0%
+modern construction you can always count
+on a solid 20 amp circuit in a kitchen
+
+ align:start position:0%
+on a solid 20 amp circuit in a kitchen
+ 
+
+ align:start position:0%
+on a solid 20 amp circuit in a kitchen
+or a
+
+ align:start position:0%
+or a
+ 
+
+ align:start position:0%
+or a
+bathroom and usually there's nothing
+
+ align:start position:0%
+bathroom and usually there's nothing
+ 
+
+ align:start position:0%
+bathroom and usually there's nothing
+else plugged into that
+
+ align:start position:0%
+else plugged into that
+ 
+
+ align:start position:0%
+else plugged into that
+circuit um so this will go into some
+
+ align:start position:0%
+circuit um so this will go into some
+ 
+
+ align:start position:0%
+circuit um so this will go into some
+safety tips um common sense that you
+
+ align:start position:0%
+safety tips um common sense that you
+ 
+
+ align:start position:0%
+safety tips um common sense that you
+should
+
+ align:start position:0%
+should
+ 
+
+ align:start position:0%
+should
+read and I mentioned uh a good resource
+
+ align:start position:0%
+read and I mentioned uh a good resource
+ 
+
+ align:start position:0%
+read and I mentioned uh a good resource
+for further study is Ross lel's
+
+ align:start position:0%
+for further study is Ross lel's
+ 
+
+ align:start position:0%
+for further study is Ross lel's
+wonderful book matters of of of light
+
+ align:start position:0%
+wonderful book matters of of of light
+ 
+
+ align:start position:0%
+wonderful book matters of of of light
+and depth to date it's the best book
+
+ align:start position:0%
+and depth to date it's the best book
+ 
+
+ align:start position:0%
+and depth to date it's the best book
+ever written about lighting it's written
+
+ align:start position:0%
+ever written about lighting it's written
+ 
+
+ align:start position:0%
+ever written about lighting it's written
+from the point of view of a lot of
+
+ align:start position:0%
+from the point of view of a lot of
+ 
+
+ align:start position:0%
+from the point of view of a lot of
+experience and what's interesting about
+
+ align:start position:0%
+experience and what's interesting about
+ 
+
+ align:start position:0%
+experience and what's interesting about
+Ross LEL is he has done a lot of
+
+ align:start position:0%
+Ross LEL is he has done a lot of
+ 
+
+ align:start position:0%
+Ross LEL is he has done a lot of
+shooting with a minimal amount of gear
+
+ align:start position:0%
+shooting with a minimal amount of gear
+ 
+
+ align:start position:0%
+shooting with a minimal amount of gear
+and it's written from the point of view
+
+ align:start position:0%
+and it's written from the point of view
+ 
+
+ align:start position:0%
+and it's written from the point of view
+of getting the most out of the least
+
+ align:start position:0%
+of getting the most out of the least
+ 
+
+ align:start position:0%
+of getting the most out of the least
+amount of gear uh in terms of lighting
+
+ align:start position:0%
+amount of gear uh in terms of lighting
+ 
+
+ align:start position:0%
+amount of gear uh in terms of lighting
+and Ross LEL developed a company uh LEL
+
+ align:start position:0%
+and Ross LEL developed a company uh LEL
+ 
+
+ align:start position:0%
+and Ross LEL developed a company uh LEL
+lights um to sell his at the time he
+
+ align:start position:0%
+lights um to sell his at the time he
+ 
+
+ align:start position:0%
+lights um to sell his at the time he
+developed a whole new generation of
+
+ align:start position:0%
+developed a whole new generation of
+ 
+
+ align:start position:0%
+developed a whole new generation of
+lightweight lighting units which were
+
+ align:start position:0%
+lightweight lighting units which were
+ 
+
+ align:start position:0%
+lightweight lighting units which were
+very popular among documentarian who
+
+ align:start position:0%
+very popular among documentarian who
+ 
+
+ align:start position:0%
+very popular among documentarian who
+didn't want to carry around big
+
+ align:start position:0%
+didn't want to carry around big
+ 
+
+ align:start position:0%
+didn't want to carry around big
+equipment cases they wanted to carry
+
+ align:start position:0%
+equipment cases they wanted to carry
+ 
+
+ align:start position:0%
+equipment cases they wanted to carry
+around small equipment cases and it's
+
+ align:start position:0%
+around small equipment cases and it's
+ 
+
+ align:start position:0%
+around small equipment cases and it's
+also written with a wonderful sense of
+
+ align:start position:0%
+also written with a wonderful sense of
+ 
+
+ align:start position:0%
+also written with a wonderful sense of
+humor you will chuckle while you read
+
+ align:start position:0%
+humor you will chuckle while you read
+ 
+
+ align:start position:0%
+humor you will chuckle while you read
+this book so matters of life and death
+
+ align:start position:0%
+this book so matters of life and death
+ 
+
+ align:start position:0%
+this book so matters of life and death
+highly recommended and there's also a
+
+ align:start position:0%
+highly recommended and there's also a
+ 
+
+ align:start position:0%
+highly recommended and there's also a
+lot of wonderful resources online um DV
+
+ align:start position:0%
+lot of wonderful resources online um DV
+ 
+
+ align:start position:0%
+lot of wonderful resources online um DV
+info.net is a wonderful discussion group
+
+ align:start position:0%
+info.net is a wonderful discussion group
+ 
+
+ align:start position:0%
+info.net is a wonderful discussion group
+for matters of of a technical nature and
+
+ align:start position:0%
+for matters of of a technical nature and
+ 
+
+ align:start position:0%
+for matters of of a technical nature and
+self-reliant film.com is a wonderful
+
+ align:start position:0%
+self-reliant film.com is a wonderful
+ 
+
+ align:start position:0%
+self-reliant film.com is a wonderful
+blog about making films do it yourself
+
+ align:start position:0%
+blog about making films do it yourself
+ 
+
+ align:start position:0%
+blog about making films do it yourself
+style which I highly
+
+ align:start position:0%
+style which I highly
+ 
+
+ align:start position:0%
+style which I highly
+recommend and that's
+
+ align:start position:0%
+recommend and that's
+ 
+
+ align:start position:0%
+recommend and that's
+it so just to to wrap up uh the second
+
+ align:start position:0%
+it so just to to wrap up uh the second
+ 
+
+ align:start position:0%
+it so just to to wrap up uh the second
+half after a short break is going to be
+
+ align:start position:0%
+half after a short break is going to be
+ 
+
+ align:start position:0%
+half after a short break is going to be
+uh the demo and a lot of the things that
+
+ align:start position:0%
+uh the demo and a lot of the things that
+ 
+
+ align:start position:0%
+uh the demo and a lot of the things that
+David talked about and showed in the the
+
+ align:start position:0%
+David talked about and showed in the the
+ 
+
+ align:start position:0%
+David talked about and showed in the the
+the PowerPoint will become a little bit
+
+ align:start position:0%
+the PowerPoint will become a little bit
+ 
+
+ align:start position:0%
+the PowerPoint will become a little bit
+clearer as we go through the demo um but
+
+ align:start position:0%
+clearer as we go through the demo um but
+ 
+
+ align:start position:0%
+clearer as we go through the demo um but
+just to to sort of wrap up a a lot of
+
+ align:start position:0%
+just to to sort of wrap up a a lot of
+ 
+
+ align:start position:0%
+just to to sort of wrap up a a lot of
+lighting especially Lighting on on our
+
+ align:start position:0%
+lighting especially Lighting on on our
+ 
+
+ align:start position:0%
+lighting especially Lighting on on our
+level beginning and sort of low no
+
+ align:start position:0%
+level beginning and sort of low no
+ 
+
+ align:start position:0%
+level beginning and sort of low no
+instrument lighting uh boils down to
+
+ align:start position:0%
+instrument lighting uh boils down to
+ 
+
+ align:start position:0%
+instrument lighting uh boils down to
+just learning how to see things and it's
+
+ align:start position:0%
+just learning how to see things and it's
+ 
+
+ align:start position:0%
+just learning how to see things and it's
+so much like other things in in shooting
+
+ align:start position:0%
+so much like other things in in shooting
+ 
+
+ align:start position:0%
+so much like other things in in shooting
+framing learning how to shoot for an
+
+ align:start position:0%
+framing learning how to shoot for an
+ 
+
+ align:start position:0%
+framing learning how to shoot for an
+edit you you really need to practice
+
+ align:start position:0%
+edit you you really need to practice
+ 
+
+ align:start position:0%
+edit you you really need to practice
+seeing what's actually there and
+
+ align:start position:0%
+seeing what's actually there and
+ 
+
+ align:start position:0%
+seeing what's actually there and
+thinking about how that is going to
+
+ align:start position:0%
+thinking about how that is going to
+ 
+
+ align:start position:0%
+thinking about how that is going to
+affect your audience you know you're the
+
+ align:start position:0%
+affect your audience you know you're the
+ 
+
+ align:start position:0%
+affect your audience you know you're the
+first audience for your film so all of
+
+ align:start position:0%
+first audience for your film so all of
+ 
+
+ align:start position:0%
+first audience for your film so all of
+the things that David talked about at
+
+ align:start position:0%
+the things that David talked about at
+ 
+
+ align:start position:0%
+the things that David talked about at
+the end really boil down to seeing
+
+ align:start position:0%
+the end really boil down to seeing
+ 
+
+ align:start position:0%
+the end really boil down to seeing
+what's there and learning how to make a
+
+ align:start position:0%
+what's there and learning how to make a
+ 
+
+ align:start position:0%
+what's there and learning how to make a
+determination about what needs to be
+
+ align:start position:0%
+determination about what needs to be
+ 
+
+ align:start position:0%
+determination about what needs to be
+changed in order to get the image that's
+
+ align:start position:0%
+changed in order to get the image that's
+ 
+
+ align:start position:0%
+changed in order to get the image that's
+going to have the impact that it needs
+
+ align:start position:0%
+going to have the impact that it needs
+ 
+
+ align:start position:0%
+going to have the impact that it needs
+to have
+
+ align:start position:0%
+to have
+ 
+
+ align:start position:0%
+to have
+uh so often and I I think I've said this
+
+ align:start position:0%
+uh so often and I I think I've said this
+ 
+
+ align:start position:0%
+uh so often and I I think I've said this
+before but so often um even people who
+
+ align:start position:0%
+before but so often um even people who
+ 
+
+ align:start position:0%
+before but so often um even people who
+have been doing film for a long time
+
+ align:start position:0%
+have been doing film for a long time
+ 
+
+ align:start position:0%
+have been doing film for a long time
+sometimes fall into the Trap of
+
+ align:start position:0%
+sometimes fall into the Trap of
+ 
+
+ align:start position:0%
+sometimes fall into the Trap of
+forgetting that you can actually make a
+
+ align:start position:0%
+forgetting that you can actually make a
+ 
+
+ align:start position:0%
+forgetting that you can actually make a
+change because it's difficult or you
+
+ align:start position:0%
+change because it's difficult or you
+ 
+
+ align:start position:0%
+change because it's difficult or you
+know it's in position it's problematic
+
+ align:start position:0%
+know it's in position it's problematic
+ 
+
+ align:start position:0%
+know it's in position it's problematic
+for somebody but if it really is
+
+ align:start position:0%
+for somebody but if it really is
+ 
+
+ align:start position:0%
+for somebody but if it really is
+necessary to make some kind of change
+
+ align:start position:0%
+necessary to make some kind of change
+ 
+
+ align:start position:0%
+necessary to make some kind of change
+it's really up to you to do it so if
+
+ align:start position:0%
+it's really up to you to do it so if
+ 
+
+ align:start position:0%
+it's really up to you to do it so if
+you're shooting in a room doing an inter
+
+ align:start position:0%
+you're shooting in a room doing an inter
+ 
+
+ align:start position:0%
+you're shooting in a room doing an inter
+interview in a room or in a location
+
+ align:start position:0%
+interview in a room or in a location
+ 
+
+ align:start position:0%
+interview in a room or in a location
+that's not going to work because the
+
+ align:start position:0%
+that's not going to work because the
+ 
+
+ align:start position:0%
+that's not going to work because the
+lighting just is impossible to to do if
+
+ align:start position:0%
+lighting just is impossible to to do if
+ 
+
+ align:start position:0%
+lighting just is impossible to to do if
+the person standing in a place that it's
+
+ align:start position:0%
+the person standing in a place that it's
+ 
+
+ align:start position:0%
+the person standing in a place that it's
+just going to be a disaster you need to
+
+ align:start position:0%
+just going to be a disaster you need to
+ 
+
+ align:start position:0%
+just going to be a disaster you need to
+make a change you need to ask them to
+
+ align:start position:0%
+make a change you need to ask them to
+ 
+
+ align:start position:0%
+make a change you need to ask them to
+move somewhere else and determining you
+
+ align:start position:0%
+move somewhere else and determining you
+ 
+
+ align:start position:0%
+move somewhere else and determining you
+know using your your experience and your
+
+ align:start position:0%
+know using your your experience and your
+ 
+
+ align:start position:0%
+know using your your experience and your
+sensitivity to what the situation is
+
+ align:start position:0%
+sensitivity to what the situation is
+ 
+
+ align:start position:0%
+sensitivity to what the situation is
+based on some of these things Davis
+
+ align:start position:0%
+based on some of these things Davis
+ 
+
+ align:start position:0%
+based on some of these things Davis
+talked about these basic principles then
+
+ align:start position:0%
+talked about these basic principles then
+ 
+
+ align:start position:0%
+talked about these basic principles then
+determines where you get them to move to
+
+ align:start position:0%
+determines where you get them to move to
+ 
+
+ align:start position:0%
+determines where you get them to move to
+what you actually what change you
+
+ align:start position:0%
+what you actually what change you
+ 
+
+ align:start position:0%
+what you actually what change you
+actually affect in order to get the
+
+ align:start position:0%
+actually affect in order to get the
+ 
+
+ align:start position:0%
+actually affect in order to get the
+image that you need to get um so that's
+
+ align:start position:0%
+image that you need to get um so that's
+ 
+
+ align:start position:0%
+image that you need to get um so that's
+it um I think the second part of this is
+
+ align:start position:0%
+it um I think the second part of this is
+ 
+
+ align:start position:0%
+it um I think the second part of this is
+going to be really fun because we're
+
+ align:start position:0%
+going to be really fun because we're
+ 
+
+ align:start position:0%
+going to be really fun because we're
+going to see some of these principles in
+
+ align:start position:0%
+going to see some of these principles in
+ 
+
+ align:start position:0%
+going to see some of these principles in
+action so thanks a lot
\ No newline at end of file
diff --git a/Sn-5Dwt_1qw.txt b/Sn-5Dwt_1qw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f4027bf7847641b10c5519f4060dec85d76a32d7
--- /dev/null
+++ b/Sn-5Dwt_1qw.txt
@@ -0,0 +1,36 @@
+Hello, this is Dimitris.
+
+This week, our lectures focus
+on applications of analytics
+
+into interesting areas.
+
+In the first lecture,
+we'll describe
+
+how a Princeton professor
+used linear regression
+
+to predict the quality of wine.
+
+In the second lecture,
+we'll discuss the story
+
+of Moneyball, and how
+data and analytics was
+
+used to create a
+championship team.
+
+Through these examples,
+we will teach you
+
+the method of linear regression.
+
+In both lectures, we'll use
+data to replicate the models in
+
+R, and so how simple analytics
+can create a significant edge.
+
+Let's get started.
\ No newline at end of file
diff --git a/SuOIpJnn888.txt b/SuOIpJnn888.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9a35a133a71b4638af13b96827f14ffa965793f0
--- /dev/null
+++ b/SuOIpJnn888.txt
@@ -0,0 +1,1911 @@
+OPERATOR: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So let's start.
+
+I have written a number
+on the board here.
+
+Anyone want to speculate what
+that number represents?
+
+Well, you may recall at the end
+of the last lecture, we
+
+were simulating pi, and I
+started up running it with a
+
+billion darts.
+
+And when it finally terminated,
+this was the
+
+estimate of pi it gave
+me with a billion.
+
+Not bad, not quite perfect,
+but still pretty good.
+
+In fact when I later ran it with
+10 billion darts, which
+
+took a rather long time to run,
+didn't do much better.
+
+So it's converging very slowly
+now near the end.
+
+When we use an algorithm like
+that one to perform a Monte
+
+Carlo simulation, we're
+trusting, as I said, that fate
+
+will give us an unbiased sample,
+a sample that would be
+
+representative of true
+random throws.
+
+And, indeed in this case,
+that's a pretty good
+
+assumption.
+
+The random number generator is
+not truly random, it's what's
+
+called pseudo-random, in that if
+you start it with the same
+
+initial conditions, it will
+give you the same results.
+
+But it's close enough for, at
+least for government work, and
+
+other useful projects.
+
+We do have to think about the
+question, how many samples
+
+should we run?
+
+Was a billion darts enough?
+
+Now since we sort of all started
+knowing what pi was,
+
+we could look at it and say,
+yeah, pretty good.
+
+But suppose we had no clue about
+the actual value of pi.
+
+We still have to
+think about the
+
+question of how many samples?
+
+And also, how accurate do we
+believe our result is, given
+
+the number of samples?
+
+As you might guess, these two
+questions are closely related.
+
+That, if we know in advance how
+much accuracy we want, we
+
+can sometimes use that
+to calculate how
+
+many samples we need.
+
+But there's still always
+the issue.
+
+It's never possible
+to achieve perfect
+
+accuracy through sampling.
+
+Unless you sample the
+entire population.
+
+No matter how many samples you
+take, you can never be sure
+
+that the sample set is typical
+until you've checked every
+
+last element.
+
+So if I went around MIT and
+sampled 100 students to try
+
+and, for example, guess the
+fraction of students at MIT
+
+who are of Chinese descent.
+
+Maybe 100 students would be
+enough, but maybe I would get
+
+unlucky and draw
+the wrong 100.
+
+In the sense of, by accident,
+100 Chinese descent, or 100
+
+non-Chinese descent,
+which would give
+
+me the wrong answer.
+
+And there would be no way I
+could be sure that I had not
+
+drawn a biased sample, unless
+I really did have the whole
+
+population to look at.
+
+So we can never know that
+our estimate is correct.
+
+Now maybe I took a billion
+darts, and for some reason got
+
+really unlucky and they
+all ended up inside
+
+or outside the circle.
+
+But what we can know, is how
+likely it is that our answer
+
+is correct, given
+the assumptions.
+
+And that's the topic we'll spend
+the next few lectures
+
+on, at least one
+of the topics.
+
+It's saying, how can we know
+how likely it is that our
+
+answer is good.
+
+But it's always given some set
+of assumptions, and we have to
+
+worry a lot about those
+assumptions.
+
+Now in the case of our pi
+example, our assumption was
+
+that the random number generator
+was indeed giving us
+
+random numbers in the
+interval 0 to 1.
+
+So that was our underlying
+assumption.
+
+Then using that, we looked at a
+plot, and we saw that after
+
+time the answer wasn't
+changing very much.
+
+And we use that to say, OK, it
+looks like we're actually
+
+converging on an answer.
+
+And then I ran it again, with
+another trial, and it
+
+converged again at
+the same place.
+
+And the fact that that happened
+several times led me
+
+to at least have some reason to
+believe that I was actually
+
+finding a good approximation
+of pi.
+
+That's a good thing to do.
+
+It's a necessary thing to do.
+
+But it is not sufficient.
+
+Because errors can creep
+into many places.
+
+So that kind of technique,
+and in fact, almost all
+
+statistical techniques, are good
+at establishing, in some
+
+sense, the reproduce-ability of
+the result, and that it is
+
+statistically valid, and that
+there's no error, for example,
+
+in the way I'm generating
+the numbers.
+
+Or I didn't get very unlucky.
+
+However, they're other places
+other than bad luck where
+
+errors can creep in.
+
+So let's look at an
+example here.
+
+I've taken the algorithm we
+looked at last time for
+
+finding pi, and I've
+made a change.
+
+You'll remember that we were
+before using 4 as our
+
+multiplier, and here what I've
+done is, just gone in and
+
+replaced 4 by 2.
+
+Assuming that I made a
+programming error.
+
+Now let's see what happens
+when we run it.
+
+Well, a bad thing
+has happened.
+
+Sure enough, we ran it and
+it converged, started to
+
+converge, and if I ran 100
+trials each one would converge
+
+at roughly the same place.
+
+Any statistical test I would
+do, would say that my
+
+statistics are sound, I've
+chosen enough samples, and for
+
+some accuracy, it's
+converting.
+
+Everything is perfect,
+except for what?
+
+It's the wrong answer.
+
+The moral here, is that just
+because an answer is
+
+statistically valid, does not
+mean it's the right answer.
+
+And that's really important to
+understand, because you see
+
+this, and we'll see more
+examples later, not today, but
+
+after Thanksgiving, comes
+up all the time in the
+
+newspapers, in scientific
+articles, where people do a
+
+million tests, do all the
+statistics right, say here's
+
+the answer, and it turns out
+to be completely wrong.
+
+And that's because it was some
+underlying assumption that
+
+went into the decision,
+that was not true.
+
+So here, the assumption is,
+that I've done my algebra
+
+right for computing pi based
+upon where the darts land.
+
+And it turns out, if I put 2
+here, my algebra is wrong.
+
+Now how could I discover this?
+
+Since I've already told you
+no statistical test is
+
+going to help me.
+
+What's the obvious thing I
+should be doing when I get
+
+this answer?
+
+Somebody?
+
+Yeah?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Exactly.
+
+Checking against reality.
+
+I started with the notion that
+pi had some relation to the
+
+area of a circle.
+
+So I could use this value
+of pi, draw a
+
+circle with a radius.
+
+Do my best to measure
+the area.
+
+I wouldn't need to get a very
+good, accurate measurement,
+
+and I would say, whoa, this
+isn't even close.
+
+And that would tell me
+I have a problem.
+
+So the moral here is,
+to check results
+
+against physical reality.
+
+So for example, the current
+problem set, you're doing a
+
+simulation about what
+happens to viruses
+
+when drugs are applied.
+
+If you were doing this for a
+pharmaceutical company, in
+
+addition to the simulation,
+you'd want to run some real
+
+experiments.
+
+And make sure that
+things matched.
+
+OK, what this suggests, is that
+we often use simulation,
+
+and other computational
+techniques, to try and model
+
+the real world, or the
+physical world, in
+
+which we all live.
+
+And we can use data
+to do that.
+
+I now want to go through another
+set of examples, and
+
+we're going to look at the
+interplay of three things:
+
+what happens when you have data,
+say from measurements,
+
+and models that at least claim
+to explain the data.
+
+And then, consequences that
+follow from the models.
+
+This is often the way science
+works, its the way engineering
+
+works, we have some
+measurements, we have a theory
+
+that explains the measurements,
+and then we
+
+write software to explore the
+consequences of that theory.
+
+Including, is it plausible
+that it's really true?
+
+So I want to start, as
+an example, with a
+
+classic chosen from 8.01.
+
+So I presume, everyone
+here has taken 8.01?
+
+Or in 8.01?
+
+Anyone here who's not had
+an experience with 801?
+
+All right, well.
+
+I hope you know about springs,
+because we're going to talk
+
+about springs.
+
+So if you think about it, I'm
+now just talking not about
+
+springs that have water in them,
+but springs that you
+
+compress, you know, and expand,
+and things like that.
+
+And there's typically something
+called the spring
+
+constant that tells us how stiff
+the spring is, how much
+
+energy it takes to compress
+this spring.
+
+Or equivalently, how much pop
+the spring has when you're no
+
+longer holding it down.
+
+Some springs are easy to
+stretch, they have a small
+
+spring constant.
+
+Some strings, for example,
+the ones that hold up an
+
+automobile, suspension,
+are much harder
+
+to stretch and compress.
+
+There's a theory about them
+called Hooke's Law.
+
+And it's quite simple.
+
+Force, the amount of force
+exerted by a spring, is equal
+
+to minus some constant times
+the distance you have
+
+compressed the spring.
+
+It's minus, because the force
+is exerted in an opposite
+
+direction, trying
+to spring up.
+
+So for example, we could
+look at it this way.
+
+We've got a spring, excuse
+my art here.
+
+And we put some weight on the
+spring, which has therefore
+
+compressed it a little bit.
+
+And the spring is exerting
+some upward force.
+
+And the amount of force it's
+exerting is proportional to
+
+the distance x.
+
+So, if we believe Hooke's Law,
+and I give you a spring, how
+
+can we find out what
+this constant is?
+
+Well, we can do it by putting a
+weight on top of the spring.
+
+It will compress the spring a
+certain amount, and then the
+
+spring will stop moving.
+
+Now gravity would normally have
+had this weight go all
+
+the way down to the bottom,
+if there was no spring.
+
+So clearly the spring is
+exerting some force in the
+
+upward direction, to keep that
+mass from going down to the
+
+table, right?
+
+So we know what that
+force is there.
+
+If we compress the spring to a
+bunch of different distances,
+
+by putting, say, different size
+weights on it, we can
+
+then solve for the spring
+constant, just the way,
+
+before, we solved for pi.
+
+So it just so happens, not quite
+by accident, that I've
+
+got some data from a spring.
+
+So let's look at it.
+
+So here's some data taken
+from measuring a spring.
+
+This is distance and force,
+force computed from the mass,
+
+basically, right?
+
+Because we know that these
+have to be in balance.
+
+And I'm not going to ask you to
+in your head estimate the
+
+constant from these, but what
+you'll see is, the format is,
+
+there's a distance, and then a
+colon, and then the force.
+
+Yeah?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Ok, right,
+yes, thank you.
+
+All right, want to repeat that
+more loudly for everyone?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Right, right, because
+the x in the equation
+
+-- right, here we're getting
+an equilibrium.
+
+OK, so let's look at what
+happens when we try and
+
+examine this.
+
+We'll look at spring dot pi.
+
+So it's pretty simple.
+
+First thing is, I've got a
+function that reads in the
+
+data and parses it.
+
+You've all done more complicated
+parsing of data
+
+files than this.
+
+So I won't belabor
+the details.
+
+I called it get data rather than
+get spring data, because
+
+I'm going to use the same
+thing for a lot of
+
+other kinds of data.
+
+And the only thing I want you
+to notice, is that it's
+
+returning a pair of arrays.
+
+OK, not lists.
+
+The usual thing is, I'm building
+them up using lists,
+
+because lists have append and
+arrays don't, and then I'm
+
+converting them to arrays so
+I can do matrix kinds of
+
+operations on them.
+
+So I'll get the distances
+and the forces.
+
+And then I'm just going to plot
+them, and we'll see what
+
+they look like.
+
+So let's do that.
+
+There they are.
+
+Now, if you believe Hooke's Law,
+you could look at this
+
+data, and maybe you
+wouldn't like it.
+
+Because Hooke's Law implies
+that, in fact, these points
+
+should lie in a straight
+line, right?
+
+If I just plug in values here,
+what am I going to get?
+
+A straight line, right?
+
+I'm just multiplying
+k times x.
+
+But I don't have a straight
+line, I have a little scatter
+
+of points, kind of it looks
+like a straight
+
+line, but it's not.
+
+And why do you think
+that's true?
+
+What's going on here?
+
+What could cause this line
+not to be straight?
+
+Have any you ever done
+a physics experiment?
+
+And when you did it, did your
+results actually match the
+
+theory that your high
+school teacher, say,
+
+explained to you.
+
+No, and why not.
+
+Yeah, you have various kinds of
+experimental or measurement
+
+error, right?
+
+Because, when you're doing these
+experiments, at least
+
+I'm not perfect, and I suspect
+at least most of you are not
+
+perfect, you get mistakes.
+
+A little bit of error creeps
+in inevitably.
+
+And so, when we acquired this
+data, sure enough there was
+
+measurement error.
+
+And so the points are
+scattered around.
+
+This is something
+to be expected.
+
+Real data almost never matches
+the theory precisely.
+
+Because there usually is some
+sort of experimental error
+
+that creeps into things.
+
+So what should we
+do about that?
+
+Well, what usually people do,
+when they think about this, is
+
+they would look at this data
+and say, well, let me fit a
+
+line to this.
+
+Somehow, say, what would
+be the line that best
+
+approximates these points?
+
+And then the slope of
+that line would give
+
+me the spring constant.
+
+So that raises the next
+question, what do I mean by
+
+finding a line that best
+fits these points?
+
+How do we, fit, in this case,
+a line, to the data?
+
+First of all, I should ask the
+question, why did I say let's
+
+fit a line?
+
+Maybe I should have said, let's
+fit a parabola, or let's
+
+fit a circle?
+
+Why should I had said
+let's fit a line.
+
+Yeah?
+
+STUDENT: [INAUDIBLE]
+
+PROFESSOR: Well, how
+do I know that the
+
+plot is a linear function?
+
+Pardon?
+
+Well, so, two things.
+
+One is, I had a theory.
+
+You know, I had up there a
+model, and my model suggested
+
+that I expected it
+to be linear.
+
+And so if I'm testing my model,
+I should and fit a
+
+line, my theory, if you will.
+
+But also when I look at it, it
+looks kind of like a line.
+
+So you know, if I looked at it,
+and it didn't look like a
+
+line, I might have said, well,
+my model must be badly broken.
+
+So let's try and see
+if we can fit it.
+
+Whenever we try and fit
+something, we need some sort
+
+of an objective function
+that captures the
+
+goodness of a fit.
+
+I'm trying to find, this is an
+optimization problem of the
+
+sort that we've looked
+at before.
+
+I'm trying to find a
+line that optimizes
+
+some objective function.
+
+So a very simple objective
+function here, is called the
+
+least squares fit.
+
+I want to find the line that
+minimizes the sum of
+
+observation sub i, the i'th data
+point I have, minus what
+
+the line, the model, predicts
+that point should have been,
+
+and then I'll square it.
+
+So I want to minimize
+this value.
+
+I want to find the line
+that gives me the
+
+smallest value for this.
+
+Why do you think I'm squaring
+the difference?
+
+What would happen if I didn't
+square the difference?
+
+Yeah?
+
+Positive and negative errors
+might cancel each other out.
+
+And in judging the quality of
+the fit, I don't really care
+
+deeply -- you're going to get
+very fat the way you're
+
+collecting candy here --
+
+I don't care deeply whether the
+error is, which side, it
+
+is, just that it's wrong.
+
+And so by squaring it, it's
+kind of like taking the
+
+absolute value of the error,
+among other things.
+
+All right, so if we look
+at our example here,
+
+what would this be?
+
+I want to minimize, want to find
+a line that minimizes it.
+
+So how do I do that?
+
+I could easily do it
+using successive
+
+approximation, right?
+
+I could choose a line, basically
+what I am, is I'm
+
+choosing a slope, here, right?
+
+And, I could, just like Newton
+Raphson, do successive
+
+approximation for awhile,
+and get the best fit.
+
+That's one way to do
+the optimization.
+
+It turns out that for this
+particular optimization
+
+there's something
+more efficient.
+
+You can actually, there is a
+closed form way of attacking
+
+this, and I could explain
+that, but in fact, I'll
+
+explain something even better.
+
+It's built into Pylab.
+
+So Pylab has a function built-in
+called polyfit.
+
+Which, given a set of points,
+finds the polynomial that
+
+gives you the best
+least squares
+
+approximation to those points.
+
+It's called polynomial because
+it isn't necessarily going to
+
+be first order, that
+is to say, a line.
+
+It can find polynomials
+of arbitrary degree.
+
+So let's look at the example
+here, we'll see how it works.
+
+So let me uncomment it.
+
+So I'm going to get k and b
+equals Pylab dot polyfit here.
+
+What it's going to do is, think
+about a polynomial.
+
+I give you a polynomial of
+degree one, you have all
+
+learned that it's a x plus b,
+b is the constant, and x is
+
+the single variable.
+
+And so I multiply a by x and I
+add b to it, and as I vary x I
+
+get new values.
+
+And so polyfit, in this case,
+will take the set of points
+
+defined by these two arrays and
+return me a value for a
+
+and a value for b.
+
+Now here I've assigned a to k,
+but don't worry about that.
+
+And then, I'm gonna now generate
+the predictions that
+
+I would get from this k
+and b, and plot those.
+
+So let's look at it.
+
+So here it said the k is 31.475,
+etc., and it's plotted
+
+the line that it's found.
+
+Or I've plotted the line.
+
+You'll note, a lot of the points
+don't lie on the line,
+
+in fact, most of the points
+don't lie on the line.
+
+But it's asserting that
+this is the best it
+
+can do with the line.
+
+And there's some points, for
+example, up here, that are
+
+kind of outliers, that are
+pretty far from the line.
+
+But it has minimized the error,
+if you will, for all of
+
+the points it has.
+
+That's quite different from,
+say, finding the line that
+
+touches the most
+points, right?
+
+It's minimizing the
+sum of the errors.
+
+Now, given that I was just
+looking for a constant to
+
+start with, why did I bother
+even plotting the data?
+
+I happen to have known before
+I did this that polyfit
+
+existed, and what I was really
+looking for was this line.
+
+So maybe I should have just
+done the polyfit and said
+
+here's k and I'm done.
+
+Would that have been
+a good idea?
+
+Yeah?
+
+STUDENT: You can't know without
+seeing the actual data
+
+how well it's actually
+fitting it.
+
+PROFESSOR: Right.
+
+Exactly right.
+
+That says, well how would I know
+that it was fitting it
+
+badly or well, and in fact,
+how would I know that my
+
+notion of the model is sound,
+or that my experiment isn't
+
+completely broken?
+
+So always, I think, always
+look at the real data.
+
+Don't just, I've seen too many
+papers where people show me
+
+the curve that fits the data,
+and don't show me the data,
+
+and it always makes
+me very nervous.
+
+So always look at the data,
+as well as however you're
+
+choosing to fit it.
+
+As an example of that, let's
+look at another set of inputs.
+
+This is not a spring.
+
+It's the same get data function
+as before, ignore
+
+that thing at the top.
+
+I'm going to analyze it
+and we'll look at it.
+
+So here I'm plotting the speed
+of something over time.
+
+So I plotted it, and I've done
+a least squares fit using
+
+polyfit just as before to get a
+line, and I put the line vs.
+
+the data, and here I'm
+a little suspicious.
+
+Right, I fit a line, but when
+I look at it, I don't think
+
+it's a real good fit
+for the data.
+
+Somehow modeling this data as a
+line is probably not right.
+
+A linear model is not
+good for this data.
+
+This data is derived
+from something, a
+
+more complex process.
+
+So take a look at it, and tell
+me what order were calling of
+
+polynomial do you think
+might fit this data?
+
+What shape does this
+look like to you?
+
+Pardon?
+
+STUDENT: Quadratic.
+
+PROFESSOR: Quadratic, because
+the shape is a what?
+
+It's a parabola.
+
+Well, I don't know if I
+dare try this one all
+
+the way to the back.
+
+Ooh, at least I didn't
+hurt anybody.
+
+All right, fortunately it's just
+as easy to fit a ravel
+
+parabola as a line.
+
+So let's look down here.
+
+I've done the same thing, but
+instead of passing it one, as
+
+I did up here as the argument,
+I'm passing it two.
+
+Saying, instead of fitting a
+polynomial of degree one, fit
+
+a polynomial of degree two.
+
+And now let's see what
+it looks like.
+
+Well, my eyes tell me this
+is a much better
+
+fit than the line.
+
+So again, that's why I wanted
+to see the scatter plot, so
+
+that I could at least look at
+it with my eyes, and say,
+
+yeah, this looks like
+a better fit.
+
+All right, any question about
+what's going on here?
+
+What we've been looking at is
+something called linear
+
+regression.
+
+It's called linear because the
+relationship of the dependent
+
+variable y to the independent
+variables is assumed to be a
+
+linear function of
+the parameters.
+
+It's not because it has to
+be a linear function of
+
+the value of x, OK?
+
+Because as you can see, we're
+not getting a line, we're
+
+getting a parabola.
+
+Don't worry about the details,
+the point I want to make is,
+
+people sometimes see the word
+linear regression and think it
+
+can only be used
+to find lines.
+
+It's not so.
+
+So when, for example, we did the
+quadratic, what we had is
+
+y equals a x squared
+plus b x plus c.
+
+The graph vs. x will not be a
+straight line, right, because
+
+I'm squaring x.
+
+But it is, just about, in this
+case, the single variable x.
+
+Now, when I looked at this, I
+said, all right, it's clear
+
+that the yellow curve is a
+better fit than the red.
+
+It's a red line.
+
+But that was a pretty
+informal statement.
+
+I can actually look at this
+much more formally.
+
+And we're going to look at
+something that's the
+
+statisticians call r squared.
+
+Which in the case of a linear
+regression is the coefficient
+
+of determination.
+
+Now, this is a big fancy word
+for something that's actually
+
+pretty simple.
+
+So what r squared its going
+to be, and this is on your
+
+handout, is 1 minus e e over d
+v. So e e is going to be the
+
+errors in the estimation.
+
+So I've got some estimated
+values, some predicted values,
+
+if you will, given to me by the
+model, either the line or
+
+the parabola in this case.
+
+And I've got some real values,
+corresponding to each of those
+
+points, and I can look at the
+difference between the 2 And
+
+that will tell me how much
+difference there is between
+
+the estimated data and the,
+well, between the predicted
+
+data and the measured
+data, in this case.
+
+And then I want to divide that
+by the variance in the
+
+measured data.
+
+The data variance.
+
+How broadly scattered the
+measured points are.
+
+And I'll do that by comparing
+the mean of the measured data,
+
+to the measured data.
+
+So I get the average value of
+the measured data, and I look
+
+at how different the points
+I measure are.
+
+So I just want to give to you,
+informally, because I really
+
+don't care if you understand
+all the math.
+
+What I do want you to
+understand, when someone tells
+
+you, here's the r squared value,
+is, informally what it
+
+really is saying.
+
+It's attempting to capture the
+proportion of the response
+
+variation explained by the
+variables in the model.
+
+In this case, x.
+
+So you'll have some amount of
+variation that is explained by
+
+changing the values
+of the variables.
+
+So if, actually, I'm going to
+give an example and then come
+
+back to it more informally.
+
+So if, for example, r squared
+were to equal 0.9, that would
+
+mean that approximately 90
+percent of the variation in
+
+the variables can be explained
+by the model.
+
+OK, so we have some amount of
+variation in the measured
+
+data, and if r squared is 0.9,
+it says that 90 percent can be
+
+explained by the models, and the
+other 10 percent cannot.
+
+Now, that other 10 percent could
+be experimental error,
+
+or it could be that, in
+fact, you need more
+
+variables in the model.
+
+That there are what are called
+lurking variables.
+
+I love this term.
+
+A lurking variable is something
+that actually
+
+effects the result, but is not
+reflected in the model.
+
+As we'll see a little bit
+later, this is a very
+
+important thing to worry about,
+when you're looking at
+
+experimental data and you're
+building models.
+
+So we see this, for example,
+in the medical literature,
+
+that they will do some
+experiment, and they'll say
+
+that this drug explains
+x, or has this affect.
+
+And the variables they are
+looking at are, say, the
+
+disease the patient has, and
+the age of the patient.
+
+Well, maybe the gender of the
+patient is also important, but
+
+it doesn't happen to
+be in the model.
+
+Now, if when they did a fit,
+it came out with 0.9, that
+
+says at worst case, the
+variables we didn't consider
+
+could cause a 10
+percent error.
+
+But, that could be big, that
+could matter a lot.
+
+And so as you get farther from
+1, you ought to get very
+
+worried about whether
+you actually have
+
+all the right variables.
+
+Now you might have the right
+variables, and just experiment
+
+was not conducted well, But it's
+usually the case that the
+
+problem is not that, but that
+there are lurking variables.
+
+And we'll see examples
+of that.
+
+So, easier to read than the
+math, at least by me, easier
+
+to read than the math, is the
+implementation of r square.
+
+So it's measured and estimated
+values, I get the diffs, the
+
+differences, between the
+estimated and the measured.
+
+These are both arrays, so I
+subtract 1 array from the
+
+other, and then I square it.
+
+Remember, this'll do an
+element-wise subtraction, and
+
+then square each element.
+
+Then I can get the mean, by
+dividing the sum of the array
+
+measured by the length of it.
+
+I can get the variance, which is
+the measured mean minus the
+
+measured value, again squared.
+
+And then I'll return
+1 minus this.
+
+All right?
+
+So, just to make sure we sort
+of understand the code, and
+
+the theory here as well, what
+would we get if we had
+
+absolutely perfect prediction?
+
+So if every measured point
+actually fit on the curb
+
+predicted by our model, what
+would r square return?
+
+So in this case, measured and
+estimated would be identical.
+
+What gets return by this?
+
+Yeah, 1.
+
+Exactly right.
+
+Because when I compute it, it
+will turn out that these two
+
+numbers will be the, I'll get
+0, 1 minus 0 is 0, right?
+
+Because the differences
+will be zero.
+
+OK?
+
+So I can use this, now, to
+actually get a notion of how
+
+good my fit is.
+
+So let's look at speed dot pi
+again here, and now I'm going
+
+to uncomment these two things,
+where I'm going to, after I
+
+compute the fit, I'm going
+to then measure it.
+
+And you'll see here that the r
+squared error for the linear
+
+fit is 0.896, and for the
+quadratic fit is 0.973.
+
+So indeed, we get a much
+better fit here.
+
+So not only does our eye tell
+us we have a better fit, our
+
+more formal statistical measure
+tells us we have a
+
+better fit, and it tells
+us how good it is.
+
+It's not a perfect fit,
+but it's a pretty
+
+good fit, for sure.
+
+Now, interestingly enough, it
+isn't surprising that the
+
+quadratic fit is better
+than the linear fit.
+
+In fact, the mathematics of
+this should tell us it can
+
+never be worse.
+
+How do I know it can
+never be worse?
+
+That's just, never is a
+really strong word.
+
+How do I know that?
+
+Because, when I do the quadratic
+fit, if I had
+
+perfectly linear data, then this
+coefficient, whoops, not
+
+that coefficient, wrong, this
+coefficient, could be 0.
+
+So if I ask it to do a quadratic
+fit to linear data,
+
+and the a is truly perfectly
+linear, this coefficient will
+
+be 0, and my model will turn
+out to be the same as the
+
+linear model.
+
+So I will always get at
+least as good a fit.
+
+Now, does this mean that it's
+always better to use a higher
+
+order polynomial?
+
+The answer is no, and
+let's look at why.
+
+So here what I've done is, I've
+taken seven points, and
+
+I've generated, if you look at
+this line here, the y-values,
+
+for x in x vals, points
+dot append x
+
+plus some random number.
+
+So basically I've got something
+linear in x, but I'm
+
+perturbing, if you will, my
+data by some random value.
+
+Something between 0 and 1 is
+getting added to things.
+
+And I'm doing this so my
+points won't lie on a
+
+perfectly straight line.
+
+And then we'll try and
+fit a line to it.
+
+And also, just for fun, we'll
+try and fit a fifth order
+
+polynomial to it.
+
+And let's see what we get.
+
+Well, there's my line, and
+there's my fifth order
+
+polynomial.
+
+Neither is quite perfect, but
+which do you think looks like
+
+a closer fit?
+
+With your eye.
+
+Well, I would say the red line,
+the red curve, if you
+
+will, is a better fit, and sure
+enough if we look at the
+
+statistics, we'll see it's 0.99,
+as opposed to 0.978.
+
+So it's clearly a closer fit.
+
+But that raises the very
+important question: does
+
+closer equal better, or tighter,
+which is another word
+
+for closer?
+
+And the answer is no.
+
+It's a tighter fit, but it's not
+necessarily better, in the
+
+sense of more useful.
+
+Because one of the things I
+want to do when I build a
+
+model like this, is
+have something
+
+with predictive power.
+
+I don't really necessarily need
+a model to tell me where
+
+the points I've measured lie,
+because I have them.
+
+The whole purpose of the model
+is to give me some way to
+
+predict where unmeasured points
+would lie, where future
+
+points would lie.
+
+OK, I understand how the spring
+works, and I can guess
+
+where it would be if things
+I haven't had the time to
+
+measure, or the ability
+to measure.
+
+So let's look at that.
+
+Let's see, where'd
+that figure go.
+
+It's lurking somewhere.
+
+All right, we'll just
+kill this for now.
+
+So let's generate some more
+points, and I'm going to use
+
+exactly the same algorithm.
+
+But I'm going to generate
+twice as many points.
+
+But I'm only fitting it
+to the first half.
+
+So if I run this one,
+figure one is what
+
+we looked at before.
+
+The red line is fitting
+them a little better.
+
+But here's figure two.
+
+What happens when I extrapolate
+the curve to the
+
+new points?
+
+Well, you can see, it's
+a terrible fit.
+
+And you would expect that,
+because my data was basically
+
+linear, and I fit in non-linear
+curve to it.
+
+And if you look at it you can
+see that, OK, look at this, to
+
+get from here to here, it
+thought I had to take off
+
+pretty sharply.
+
+And so sure enough, as I get
+new points, the prediction
+
+will postulate that it's still
+going up, much more steeply
+
+than it really does.
+
+So you can see it's a
+terrible prediction.
+
+And that's because what I've
+done is, I over-fit the data.
+
+I've taken a very high degree
+polynomial, which has given me
+
+a good close fit, and I can
+always get a fit, by the way.
+
+If I choose a high enough degree
+polynomial, I can fit
+
+lots and lots of data sets.
+
+But I have reason to
+be very suspicious.
+
+The fact that I took a fifth
+order polynomial to get six
+
+points should make
+me very nervous.
+
+And it's a very important
+moral.
+
+Beware of over-fitting.
+
+If you have a very complex
+model, there's a good chance
+
+that it's over-fit.
+
+The larger moral is, beware of
+statistics without any theory.
+
+You're just cranking away, you
+get a great r squared, you say
+
+it's a beautiful fit.
+
+But there was no real
+theory there.
+
+You can always find a fit.
+
+As Disraeli is alleged to have
+said, there are three kinds of
+
+lies: lies, damned lies,
+and statistics.
+
+And we'll spend some more time
+when we get back from
+
+Thanksgiving looking at how
+to lie with statistics.
+
+Have a great holiday,
+everybody.
\ No newline at end of file
diff --git a/UCc9q_cAhho.txt b/UCc9q_cAhho.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c2fd1f6cc544e4884563911a8dab9f4b9836a7c2
--- /dev/null
+++ b/UCc9q_cAhho.txt
@@ -0,0 +1,5595 @@
+align:start position:0%
+ 
+one and the lecture on symmetric
+
+ align:start position:0%
+one and the lecture on symmetric
+ 
+
+ align:start position:0%
+one and the lecture on symmetric
+matrices so that's the most important
+
+ align:start position:0%
+matrices so that's the most important
+ 
+
+ align:start position:0%
+matrices so that's the most important
+class of matrices symmetric matrices a
+
+ align:start position:0%
+class of matrices symmetric matrices a
+ 
+
+ align:start position:0%
+class of matrices symmetric matrices a
+equals a transpose so the first points
+
+ align:start position:0%
+equals a transpose so the first points
+ 
+
+ align:start position:0%
+equals a transpose so the first points
+the main points of the lecture I'll tell
+
+ align:start position:0%
+the main points of the lecture I'll tell
+ 
+
+ align:start position:0%
+the main points of the lecture I'll tell
+you right away what's special about the
+
+ align:start position:0%
+you right away what's special about the
+ 
+
+ align:start position:0%
+you right away what's special about the
+eigenvalues what's special about the
+
+ align:start position:0%
+eigenvalues what's special about the
+ 
+
+ align:start position:0%
+eigenvalues what's special about the
+eigenvectors this is now that this is
+
+ align:start position:0%
+eigenvectors this is now that this is
+ 
+
+ align:start position:0%
+eigenvectors this is now that this is
+the way we now look at a matrix we want
+
+ align:start position:0%
+the way we now look at a matrix we want
+ 
+
+ align:start position:0%
+the way we now look at a matrix we want
+to know about its eigenvalues and
+
+ align:start position:0%
+to know about its eigenvalues and
+ 
+
+ align:start position:0%
+to know about its eigenvalues and
+eigenvectors and if we have a special
+
+ align:start position:0%
+eigenvectors and if we have a special
+ 
+
+ align:start position:0%
+eigenvectors and if we have a special
+type of matrix that should tell us
+
+ align:start position:0%
+type of matrix that should tell us
+ 
+
+ align:start position:0%
+type of matrix that should tell us
+something about eigenvalues and
+
+ align:start position:0%
+something about eigenvalues and
+ 
+
+ align:start position:0%
+something about eigenvalues and
+eigenvectors like markov matrices they
+
+ align:start position:0%
+eigenvectors like markov matrices they
+ 
+
+ align:start position:0%
+eigenvectors like markov matrices they
+have an eigenvalue equal 1 now symmetric
+
+ align:start position:0%
+have an eigenvalue equal 1 now symmetric
+ 
+
+ align:start position:0%
+have an eigenvalue equal 1 now symmetric
+matrices can I just tell you right off
+
+ align:start position:0%
+matrices can I just tell you right off
+ 
+
+ align:start position:0%
+matrices can I just tell you right off
+what the main facts the two main facts
+
+ align:start position:0%
+what the main facts the two main facts
+ 
+
+ align:start position:0%
+what the main facts the two main facts
+are the eigenvalues of a symmetric
+
+ align:start position:0%
+are the eigenvalues of a symmetric
+ 
+
+ align:start position:0%
+are the eigenvalues of a symmetric
+matrix real this is a real symmetric
+
+ align:start position:0%
+matrix real this is a real symmetric
+ 
+
+ align:start position:0%
+matrix real this is a real symmetric
+matrix we're talking mostly about real
+
+ align:start position:0%
+matrix we're talking mostly about real
+ 
+
+ align:start position:0%
+matrix we're talking mostly about real
+matrices the eigen values are also real
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our examples of rotation matrices
+
+ align:start position:0%
+so our examples of rotation matrices
+ 
+
+ align:start position:0%
+so our examples of rotation matrices
+where where we got I can values that
+
+ align:start position:0%
+where where we got I can values that
+ 
+
+ align:start position:0%
+where where we got I can values that
+were complex that won't happen now for a
+
+ align:start position:0%
+were complex that won't happen now for a
+ 
+
+ align:start position:0%
+were complex that won't happen now for a
+symmetric matrices the eigen values are
+
+ align:start position:0%
+symmetric matrices the eigen values are
+ 
+
+ align:start position:0%
+symmetric matrices the eigen values are
+real and the eigen vectors are also very
+
+ align:start position:0%
+real and the eigen vectors are also very
+ 
+
+ align:start position:0%
+real and the eigen vectors are also very
+special the eigen vectors are
+
+ align:start position:0%
+special the eigen vectors are
+ 
+
+ align:start position:0%
+special the eigen vectors are
+perpendicular orthogonal so which do you
+
+ align:start position:0%
+perpendicular orthogonal so which do you
+ 
+
+ align:start position:0%
+perpendicular orthogonal so which do you
+prefer I'll say perpendicular perp well
+
+ align:start position:0%
+prefer I'll say perpendicular perp well
+ 
+
+ align:start position:0%
+prefer I'll say perpendicular perp well
+they're both long words perp and dick
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay right so I you should say why and
+
+ align:start position:0%
+okay right so I you should say why and
+ 
+
+ align:start position:0%
+okay right so I you should say why and
+I'll at least answer why for case one
+
+ align:start position:0%
+I'll at least answer why for case one
+ 
+
+ align:start position:0%
+I'll at least answer why for case one
+maybe case to the checking the eigen
+
+ align:start position:0%
+maybe case to the checking the eigen
+ 
+
+ align:start position:0%
+maybe case to the checking the eigen
+that the eigen vectors are perpendicular
+
+ align:start position:0%
+that the eigen vectors are perpendicular
+ 
+
+ align:start position:0%
+that the eigen vectors are perpendicular
+I'll leave to the book but let's just
+
+ align:start position:0%
+I'll leave to the book but let's just
+ 
+
+ align:start position:0%
+I'll leave to the book but let's just
+realize what well first I have to say it
+
+ align:start position:0%
+realize what well first I have to say it
+ 
+
+ align:start position:0%
+realize what well first I have to say it
+it could happen like for the identity
+
+ align:start position:0%
+it could happen like for the identity
+ 
+
+ align:start position:0%
+it could happen like for the identity
+matrix there's a symmetric matrix its
+
+ align:start position:0%
+matrix there's a symmetric matrix its
+ 
+
+ align:start position:0%
+matrix there's a symmetric matrix its
+eigenvalues are certainly all real
+
+ align:start position:0%
+eigenvalues are certainly all real
+ 
+
+ align:start position:0%
+eigenvalues are certainly all real
+they're all one for the identity matrix
+
+ align:start position:0%
+they're all one for the identity matrix
+ 
+
+ align:start position:0%
+they're all one for the identity matrix
+what about the eigenvectors well for the
+
+ align:start position:0%
+what about the eigenvectors well for the
+ 
+
+ align:start position:0%
+what about the eigenvectors well for the
+identity every vector is an eigenvector
+
+ align:start position:0%
+identity every vector is an eigenvector
+ 
+
+ align:start position:0%
+identity every vector is an eigenvector
+so how can i say they're perpendicular
+
+ align:start position:0%
+so how can i say they're perpendicular
+ 
+
+ align:start position:0%
+so how can i say they're perpendicular
+what I really mean is the this word are
+
+ align:start position:0%
+what I really mean is the this word are
+ 
+
+ align:start position:0%
+what I really mean is the this word are
+should really be written can be chosen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+perpendicular that is if we have it's
+
+ align:start position:0%
+perpendicular that is if we have it's
+ 
+
+ align:start position:0%
+perpendicular that is if we have it's
+the usual case if the eigenvalues are
+
+ align:start position:0%
+the usual case if the eigenvalues are
+ 
+
+ align:start position:0%
+the usual case if the eigenvalues are
+all different then each eigenvalue as
+
+ align:start position:0%
+all different then each eigenvalue as
+ 
+
+ align:start position:0%
+all different then each eigenvalue as
+one line of eigenvectors and those lines
+
+ align:start position:0%
+one line of eigenvectors and those lines
+ 
+
+ align:start position:0%
+one line of eigenvectors and those lines
+are perpendicular here but if an
+
+ align:start position:0%
+are perpendicular here but if an
+ 
+
+ align:start position:0%
+are perpendicular here but if an
+eigenvalue is repeated then there's a
+
+ align:start position:0%
+eigenvalue is repeated then there's a
+ 
+
+ align:start position:0%
+eigenvalue is repeated then there's a
+whole plane of eigenvectors and all I'm
+
+ align:start position:0%
+whole plane of eigenvectors and all I'm
+ 
+
+ align:start position:0%
+whole plane of eigenvectors and all I'm
+saying is that in that plane we can
+
+ align:start position:0%
+saying is that in that plane we can
+ 
+
+ align:start position:0%
+saying is that in that plane we can
+choose perpendicular ones so that's why
+
+ align:start position:0%
+choose perpendicular ones so that's why
+ 
+
+ align:start position:0%
+choose perpendicular ones so that's why
+it's a can be chosen part if this is in
+
+ align:start position:0%
+it's a can be chosen part if this is in
+ 
+
+ align:start position:0%
+it's a can be chosen part if this is in
+the case of a repeated eigenvalue where
+
+ align:start position:0%
+the case of a repeated eigenvalue where
+ 
+
+ align:start position:0%
+the case of a repeated eigenvalue where
+there's some real substantial freedom
+
+ align:start position:0%
+there's some real substantial freedom
+ 
+
+ align:start position:0%
+there's some real substantial freedom
+but the typical case is different
+
+ align:start position:0%
+but the typical case is different
+ 
+
+ align:start position:0%
+but the typical case is different
+eigenvalues all real one-dimensional
+
+ align:start position:0%
+eigenvalues all real one-dimensional
+ 
+
+ align:start position:0%
+eigenvalues all real one-dimensional
+eigen vector spaces eigenspaces and all
+
+ align:start position:0%
+eigen vector spaces eigenspaces and all
+ 
+
+ align:start position:0%
+eigen vector spaces eigenspaces and all
+perpendicular so just let's just see the
+
+ align:start position:0%
+perpendicular so just let's just see the
+ 
+
+ align:start position:0%
+perpendicular so just let's just see the
+conclusion if we accept those as correct
+
+ align:start position:0%
+conclusion if we accept those as correct
+ 
+
+ align:start position:0%
+conclusion if we accept those as correct
+what happens and i also mean that
+
+ align:start position:0%
+what happens and i also mean that
+ 
+
+ align:start position:0%
+what happens and i also mean that
+there's a full set of them i
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's part of this picture here that
+
+ align:start position:0%
+so that's part of this picture here that
+ 
+
+ align:start position:0%
+so that's part of this picture here that
+there's a complete set of eigenvectors
+
+ align:start position:0%
+there's a complete set of eigenvectors
+ 
+
+ align:start position:0%
+there's a complete set of eigenvectors
+perpendicular ones so having a complete
+
+ align:start position:0%
+perpendicular ones so having a complete
+ 
+
+ align:start position:0%
+perpendicular ones so having a complete
+set of eigenvectors means so normal so
+
+ align:start position:0%
+set of eigenvectors means so normal so
+ 
+
+ align:start position:0%
+set of eigenvectors means so normal so
+the usual maybe I put the usually usual
+
+ align:start position:0%
+the usual maybe I put the usually usual
+ 
+
+ align:start position:0%
+the usual maybe I put the usually usual
+usual case is that the matrix a we can
+
+ align:start position:0%
+usual case is that the matrix a we can
+ 
+
+ align:start position:0%
+usual case is that the matrix a we can
+write in terms of its eigen value matrix
+
+ align:start position:0%
+write in terms of its eigen value matrix
+ 
+
+ align:start position:0%
+write in terms of its eigen value matrix
+and its eigenvector matrix this way
+
+ align:start position:0%
+and its eigenvector matrix this way
+ 
+
+ align:start position:0%
+and its eigenvector matrix this way
+right we can do that in the usual case
+
+ align:start position:0%
+right we can do that in the usual case
+ 
+
+ align:start position:0%
+right we can do that in the usual case
+but now what's special when the matrix
+
+ align:start position:0%
+but now what's special when the matrix
+ 
+
+ align:start position:0%
+but now what's special when the matrix
+is symmetric so this is the usual case
+
+ align:start position:0%
+is symmetric so this is the usual case
+ 
+
+ align:start position:0%
+is symmetric so this is the usual case
+and now let me go to the symmetric case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in the symmetric case a this this
+
+ align:start position:0%
+so in the symmetric case a this this
+ 
+
+ align:start position:0%
+so in the symmetric case a this this
+should become somehow a little special
+
+ align:start position:0%
+should become somehow a little special
+ 
+
+ align:start position:0%
+should become somehow a little special
+well the lambdas on the diagonal are
+
+ align:start position:0%
+well the lambdas on the diagonal are
+ 
+
+ align:start position:0%
+well the lambdas on the diagonal are
+still on the diagonal there they're real
+
+ align:start position:0%
+still on the diagonal there they're real
+ 
+
+ align:start position:0%
+still on the diagonal there they're real
+but that's where they are what about the
+
+ align:start position:0%
+but that's where they are what about the
+ 
+
+ align:start position:0%
+but that's where they are what about the
+eigenvector matrix so what can I do now
+
+ align:start position:0%
+eigenvector matrix so what can I do now
+ 
+
+ align:start position:0%
+eigenvector matrix so what can I do now
+special about the eigenvector matrix
+
+ align:start position:0%
+special about the eigenvector matrix
+ 
+
+ align:start position:0%
+special about the eigenvector matrix
+when when the a itself is symmetric that
+
+ align:start position:0%
+when when the a itself is symmetric that
+ 
+
+ align:start position:0%
+when when the a itself is symmetric that
+says something good about the
+
+ align:start position:0%
+says something good about the
+ 
+
+ align:start position:0%
+says something good about the
+eigenvector matrix so what is this what
+
+ align:start position:0%
+eigenvector matrix so what is this what
+ 
+
+ align:start position:0%
+eigenvector matrix so what is this what
+does this lead to this these
+
+ align:start position:0%
+does this lead to this these
+ 
+
+ align:start position:0%
+does this lead to this these
+perpendicular eigenvectors I can only I
+
+ align:start position:0%
+perpendicular eigenvectors I can only I
+ 
+
+ align:start position:0%
+perpendicular eigenvectors I can only I
+can not only guarantee they're
+
+ align:start position:0%
+can not only guarantee they're
+ 
+
+ align:start position:0%
+can not only guarantee they're
+perpendicular I could also make them
+
+ align:start position:0%
+perpendicular I could also make them
+ 
+
+ align:start position:0%
+perpendicular I could also make them
+unit vectors no problem just scale their
+
+ align:start position:0%
+unit vectors no problem just scale their
+ 
+
+ align:start position:0%
+unit vectors no problem just scale their
+lengths to one so what do I have I have
+
+ align:start position:0%
+lengths to one so what do I have I have
+ 
+
+ align:start position:0%
+lengths to one so what do I have I have
+orthonormal eigenvectors and what does
+
+ align:start position:0%
+orthonormal eigenvectors and what does
+ 
+
+ align:start position:0%
+orthonormal eigenvectors and what does
+that tell me about the eigenvector
+
+ align:start position:0%
+that tell me about the eigenvector
+ 
+
+ align:start position:0%
+that tell me about the eigenvector
+matrix what what letter should I now use
+
+ align:start position:0%
+matrix what what letter should I now use
+ 
+
+ align:start position:0%
+matrix what what letter should I now use
+in place of s remember s has the
+
+ align:start position:0%
+in place of s remember s has the
+ 
+
+ align:start position:0%
+in place of s remember s has the
+eigenvectors in its columns but now
+
+ align:start position:0%
+eigenvectors in its columns but now
+ 
+
+ align:start position:0%
+eigenvectors in its columns but now
+those columns are orthonormal so the
+
+ align:start position:0%
+those columns are orthonormal so the
+ 
+
+ align:start position:0%
+those columns are orthonormal so the
+right letter to use is q so that's where
+
+ align:start position:0%
+right letter to use is q so that's where
+ 
+
+ align:start position:0%
+right letter to use is q so that's where
+so we've got the letter all set up so
+
+ align:start position:0%
+so we've got the letter all set up so
+ 
+
+ align:start position:0%
+so we've got the letter all set up so
+this should
+
+ align:start position:0%
+this should
+ 
+
+ align:start position:0%
+this should
+Q lambda Q inverse Q standing in our
+
+ align:start position:0%
+Q lambda Q inverse Q standing in our
+ 
+
+ align:start position:0%
+Q lambda Q inverse Q standing in our
+minds always for this matrix in this
+
+ align:start position:0%
+minds always for this matrix in this
+ 
+
+ align:start position:0%
+minds always for this matrix in this
+case its square its its so these are the
+
+ align:start position:0%
+case its square its its so these are the
+ 
+
+ align:start position:0%
+case its square its its so these are the
+columns of Q of course and one more
+
+ align:start position:0%
+columns of Q of course and one more
+ 
+
+ align:start position:0%
+columns of Q of course and one more
+thing what's Q inverse for an
+
+ align:start position:0%
+thing what's Q inverse for an
+ 
+
+ align:start position:0%
+thing what's Q inverse for an
+orthonormal for a matrix that has these
+
+ align:start position:0%
+orthonormal for a matrix that has these
+ 
+
+ align:start position:0%
+orthonormal for a matrix that has these
+orthonormal columns we know that the
+
+ align:start position:0%
+orthonormal columns we know that the
+ 
+
+ align:start position:0%
+orthonormal columns we know that the
+inverse is the same as the transpose so
+
+ align:start position:0%
+inverse is the same as the transpose so
+ 
+
+ align:start position:0%
+inverse is the same as the transpose so
+here is the beautiful there's the the
+
+ align:start position:0%
+here is the beautiful there's the the
+ 
+
+ align:start position:0%
+here is the beautiful there's the the
+great description the factorization of a
+
+ align:start position:0%
+great description the factorization of a
+ 
+
+ align:start position:0%
+great description the factorization of a
+symmetric matrix and this is like one of
+
+ align:start position:0%
+symmetric matrix and this is like one of
+ 
+
+ align:start position:0%
+symmetric matrix and this is like one of
+the famous theorems of linear algebra
+
+ align:start position:0%
+the famous theorems of linear algebra
+ 
+
+ align:start position:0%
+the famous theorems of linear algebra
+that if I have a symmetric matrix it can
+
+ align:start position:0%
+that if I have a symmetric matrix it can
+ 
+
+ align:start position:0%
+that if I have a symmetric matrix it can
+be factored in this form an orthogonal
+
+ align:start position:0%
+be factored in this form an orthogonal
+ 
+
+ align:start position:0%
+be factored in this form an orthogonal
+matrix times diagonal times the
+
+ align:start position:0%
+matrix times diagonal times the
+ 
+
+ align:start position:0%
+matrix times diagonal times the
+transpose of that orthogonal matrix and
+
+ align:start position:0%
+transpose of that orthogonal matrix and
+ 
+
+ align:start position:0%
+transpose of that orthogonal matrix and
+of course everybody immediately says yes
+
+ align:start position:0%
+of course everybody immediately says yes
+ 
+
+ align:start position:0%
+of course everybody immediately says yes
+and if this is possible then that's
+
+ align:start position:0%
+and if this is possible then that's
+ 
+
+ align:start position:0%
+and if this is possible then that's
+clearly symmetric right that take we've
+
+ align:start position:0%
+clearly symmetric right that take we've
+ 
+
+ align:start position:0%
+clearly symmetric right that take we've
+looked at products of three guys like
+
+ align:start position:0%
+looked at products of three guys like
+ 
+
+ align:start position:0%
+looked at products of three guys like
+that and taken their transpose and we
+
+ align:start position:0%
+that and taken their transpose and we
+ 
+
+ align:start position:0%
+that and taken their transpose and we
+got it back again so do you see the
+
+ align:start position:0%
+got it back again so do you see the
+ 
+
+ align:start position:0%
+got it back again so do you see the
+beauty of this of this factorization
+
+ align:start position:0%
+beauty of this of this factorization
+ 
+
+ align:start position:0%
+beauty of this of this factorization
+then it completely displays the
+
+ align:start position:0%
+then it completely displays the
+ 
+
+ align:start position:0%
+then it completely displays the
+eigenvalues and eigenvectors and the
+
+ align:start position:0%
+eigenvalues and eigenvectors and the
+ 
+
+ align:start position:0%
+eigenvalues and eigenvectors and the
+symmetry of the of the whole thing
+
+ align:start position:0%
+symmetry of the of the whole thing
+ 
+
+ align:start position:0%
+symmetry of the of the whole thing
+because that product q times lambda
+
+ align:start position:0%
+because that product q times lambda
+ 
+
+ align:start position:0%
+because that product q times lambda
+times q transpose if I transpose it it
+
+ align:start position:0%
+times q transpose if I transpose it it
+ 
+
+ align:start position:0%
+times q transpose if I transpose it it
+just comes in this position and we get
+
+ align:start position:0%
+just comes in this position and we get
+ 
+
+ align:start position:0%
+just comes in this position and we get
+that matrix back again so that's in
+
+ align:start position:0%
+that matrix back again so that's in
+ 
+
+ align:start position:0%
+that matrix back again so that's in
+mathematics that's called the spectral
+
+ align:start position:0%
+mathematics that's called the spectral
+ 
+
+ align:start position:0%
+mathematics that's called the spectral
+theorem spectrum is the set of
+
+ align:start position:0%
+theorem spectrum is the set of
+ 
+
+ align:start position:0%
+theorem spectrum is the set of
+eigenvalues of a matrix spec
+
+ align:start position:0%
+eigenvalues of a matrix spec
+ 
+
+ align:start position:0%
+eigenvalues of a matrix spec
+it somehow comes from the idea of the
+
+ align:start position:0%
+it somehow comes from the idea of the
+ 
+
+ align:start position:0%
+it somehow comes from the idea of the
+spectrum of light as a combination of
+
+ align:start position:0%
+spectrum of light as a combination of
+ 
+
+ align:start position:0%
+spectrum of light as a combination of
+pure things where our matrix is broken
+
+ align:start position:0%
+pure things where our matrix is broken
+ 
+
+ align:start position:0%
+pure things where our matrix is broken
+down into pure eigenvalues and
+
+ align:start position:0%
+down into pure eigenvalues and
+ 
+
+ align:start position:0%
+down into pure eigenvalues and
+eigenvectors
+
+ align:start position:0%
+eigenvectors
+ 
+
+ align:start position:0%
+eigenvectors
+in mechanic's it's often called the
+
+ align:start position:0%
+in mechanic's it's often called the
+ 
+
+ align:start position:0%
+in mechanic's it's often called the
+principal axis theorem it's very useful
+
+ align:start position:0%
+principal axis theorem it's very useful
+ 
+
+ align:start position:0%
+principal axis theorem it's very useful
+it means that if you have we'll see it
+
+ align:start position:0%
+it means that if you have we'll see it
+ 
+
+ align:start position:0%
+it means that if you have we'll see it
+geometrically it means that if I have
+
+ align:start position:0%
+geometrically it means that if I have
+ 
+
+ align:start position:0%
+geometrically it means that if I have
+some material if I look at the right
+
+ align:start position:0%
+some material if I look at the right
+ 
+
+ align:start position:0%
+some material if I look at the right
+axes it becomes diagonal it becomes the
+
+ align:start position:0%
+axes it becomes diagonal it becomes the
+ 
+
+ align:start position:0%
+axes it becomes diagonal it becomes the
+the directions don't couple together
+
+ align:start position:0%
+the directions don't couple together
+ 
+
+ align:start position:0%
+the directions don't couple together
+okay so that's that's what to remember
+
+ align:start position:0%
+okay so that's that's what to remember
+ 
+
+ align:start position:0%
+okay so that's that's what to remember
+from this lecture now I would like to
+
+ align:start position:0%
+from this lecture now I would like to
+ 
+
+ align:start position:0%
+from this lecture now I would like to
+say why are the eigenvalues real can I
+
+ align:start position:0%
+say why are the eigenvalues real can I
+ 
+
+ align:start position:0%
+say why are the eigenvalues real can I
+do that
+
+ align:start position:0%
+do that
+ 
+
+ align:start position:0%
+do that
+so because something useful comes out so
+
+ align:start position:0%
+so because something useful comes out so
+ 
+
+ align:start position:0%
+so because something useful comes out so
+I'll just come back come to that
+
+ align:start position:0%
+I'll just come back come to that
+ 
+
+ align:start position:0%
+I'll just come back come to that
+question why real eigenvalues okay so I
+
+ align:start position:0%
+question why real eigenvalues okay so I
+ 
+
+ align:start position:0%
+question why real eigenvalues okay so I
+have to start from the only thing we
+
+ align:start position:0%
+have to start from the only thing we
+ 
+
+ align:start position:0%
+have to start from the only thing we
+know ax equal lambda X okay but as far
+
+ align:start position:0%
+know ax equal lambda X okay but as far
+ 
+
+ align:start position:0%
+know ax equal lambda X okay but as far
+as I know at this moment lambda could be
+
+ align:start position:0%
+as I know at this moment lambda could be
+ 
+
+ align:start position:0%
+as I know at this moment lambda could be
+complex I'm going to prove it's not and
+
+ align:start position:0%
+complex I'm going to prove it's not and
+ 
+
+ align:start position:0%
+complex I'm going to prove it's not and
+X could be complex in fact for the
+
+ align:start position:0%
+X could be complex in fact for the
+ 
+
+ align:start position:0%
+X could be complex in fact for the
+moment even a could be we could even
+
+ align:start position:0%
+moment even a could be we could even
+ 
+
+ align:start position:0%
+moment even a could be we could even
+think well what happens if a is complex
+
+ align:start position:0%
+think well what happens if a is complex
+ 
+
+ align:start position:0%
+think well what happens if a is complex
+well one thing we can always do this is
+
+ align:start position:0%
+well one thing we can always do this is
+ 
+
+ align:start position:0%
+well one thing we can always do this is
+this is like always always okay I can if
+
+ align:start position:0%
+this is like always always okay I can if
+ 
+
+ align:start position:0%
+this is like always always okay I can if
+I have an equation I can take the
+
+ align:start position:0%
+I have an equation I can take the
+ 
+
+ align:start position:0%
+I have an equation I can take the
+complex conjugate of everything that's
+
+ align:start position:0%
+complex conjugate of everything that's
+ 
+
+ align:start position:0%
+complex conjugate of everything that's
+no so a conjugate X conjugate equal
+
+ align:start position:0%
+no so a conjugate X conjugate equal
+ 
+
+ align:start position:0%
+no so a conjugate X conjugate equal
+lambda conjugate X conjugate it just
+
+ align:start position:0%
+lambda conjugate X conjugate it just
+ 
+
+ align:start position:0%
+lambda conjugate X conjugate it just
+means that everywhere over here that
+
+ align:start position:0%
+means that everywhere over here that
+ 
+
+ align:start position:0%
+means that everywhere over here that
+there was a an I then here I changed it
+
+ align:start position:0%
+there was a an I then here I changed it
+ 
+
+ align:start position:0%
+there was a an I then here I changed it
+to a minus I that that you know that
+
+ align:start position:0%
+to a minus I that that you know that
+ 
+
+ align:start position:0%
+to a minus I that that you know that
+that step that conjugate business that a
+
+ align:start position:0%
+that step that conjugate business that a
+ 
+
+ align:start position:0%
+that step that conjugate business that a
+plus IB if I conjugated it's a minus IB
+
+ align:start position:0%
+plus IB if I conjugated it's a minus IB
+ 
+
+ align:start position:0%
+plus IB if I conjugated it's a minus IB
+that's the meaning of conjugate and
+
+ align:start position:0%
+that's the meaning of conjugate and
+ 
+
+ align:start position:0%
+that's the meaning of conjugate and
+products behave right I can conjugate
+
+ align:start position:0%
+products behave right I can conjugate
+ 
+
+ align:start position:0%
+products behave right I can conjugate
+every factor so I haven't done anything
+
+ align:start position:0%
+every factor so I haven't done anything
+ 
+
+ align:start position:0%
+every factor so I haven't done anything
+yet except to say what
+
+ align:start position:0%
+yet except to say what
+ 
+
+ align:start position:0%
+yet except to say what
+would be true if X in any case even if X
+
+ align:start position:0%
+would be true if X in any case even if X
+ 
+
+ align:start position:0%
+would be true if X in any case even if X
+and lambda were complex of course our
+
+ align:start position:0%
+and lambda were complex of course our
+ 
+
+ align:start position:0%
+and lambda were complex of course our
+and we're speaking about real matrices a
+
+ align:start position:0%
+and we're speaking about real matrices a
+ 
+
+ align:start position:0%
+and we're speaking about real matrices a
+so I can take that out actually this
+
+ align:start position:0%
+so I can take that out actually this
+ 
+
+ align:start position:0%
+so I can take that out actually this
+already tells me something about real
+
+ align:start position:0%
+already tells me something about real
+ 
+
+ align:start position:0%
+already tells me something about real
+matrices I haven't used any assumption
+
+ align:start position:0%
+matrices I haven't used any assumption
+ 
+
+ align:start position:0%
+matrices I haven't used any assumption
+of a equal a transpose yet symmetry is
+
+ align:start position:0%
+of a equal a transpose yet symmetry is
+ 
+
+ align:start position:0%
+of a equal a transpose yet symmetry is
+waiting in the wings to be used this
+
+ align:start position:0%
+waiting in the wings to be used this
+ 
+
+ align:start position:0%
+waiting in the wings to be used this
+tells me that if a real matrix has an
+
+ align:start position:0%
+tells me that if a real matrix has an
+ 
+
+ align:start position:0%
+tells me that if a real matrix has an
+eigenvalue lambda and an eigenvector x
+
+ align:start position:0%
+eigenvalue lambda and an eigenvector x
+ 
+
+ align:start position:0%
+eigenvalue lambda and an eigenvector x
+it also has another of its eigenvalues
+
+ align:start position:0%
+it also has another of its eigenvalues
+ 
+
+ align:start position:0%
+it also has another of its eigenvalues
+is lambda bar with eigenvector x bar
+
+ align:start position:0%
+is lambda bar with eigenvector x bar
+ 
+
+ align:start position:0%
+is lambda bar with eigenvector x bar
+real matrices the eigen values come in
+
+ align:start position:0%
+real matrices the eigen values come in
+ 
+
+ align:start position:0%
+real matrices the eigen values come in
+lambda lambda bar the complex
+
+ align:start position:0%
+lambda lambda bar the complex
+ 
+
+ align:start position:0%
+lambda lambda bar the complex
+eigenvalues come in lambda and lambda
+
+ align:start position:0%
+eigenvalues come in lambda and lambda
+ 
+
+ align:start position:0%
+eigenvalues come in lambda and lambda
+bar pairs but of course I'm aiming to
+
+ align:start position:0%
+bar pairs but of course I'm aiming to
+ 
+
+ align:start position:0%
+bar pairs but of course I'm aiming to
+show that they're not complex at all
+
+ align:start position:0%
+show that they're not complex at all
+ 
+
+ align:start position:0%
+show that they're not complex at all
+here by getting symmetry in so how am I
+
+ align:start position:0%
+here by getting symmetry in so how am I
+ 
+
+ align:start position:0%
+here by getting symmetry in so how am I
+going to use symmetry I'm going to
+
+ align:start position:0%
+going to use symmetry I'm going to
+ 
+
+ align:start position:0%
+going to use symmetry I'm going to
+transpose this equation to X bar
+
+ align:start position:0%
+transpose this equation to X bar
+ 
+
+ align:start position:0%
+transpose this equation to X bar
+transpose a transpose equals X bar
+
+ align:start position:0%
+transpose a transpose equals X bar
+ 
+
+ align:start position:0%
+transpose a transpose equals X bar
+transpose lambda bar that's just a
+
+ align:start position:0%
+transpose lambda bar that's just a
+ 
+
+ align:start position:0%
+transpose lambda bar that's just a
+number so I don't mind where I put that
+
+ align:start position:0%
+number so I don't mind where I put that
+ 
+
+ align:start position:0%
+number so I don't mind where I put that
+number this is this is then again okay
+
+ align:start position:0%
+number this is this is then again okay
+ 
+
+ align:start position:0%
+number this is this is then again okay
+but now I'm ready to use symmetry I'm
+
+ align:start position:0%
+but now I'm ready to use symmetry I'm
+ 
+
+ align:start position:0%
+but now I'm ready to use symmetry I'm
+ready so this was all just mechanics now
+
+ align:start position:0%
+ready so this was all just mechanics now
+ 
+
+ align:start position:0%
+ready so this was all just mechanics now
+now comes the moment to say okay if the
+
+ align:start position:0%
+now comes the moment to say okay if the
+ 
+
+ align:start position:0%
+now comes the moment to say okay if the
+matrix is symmetric then this a
+
+ align:start position:0%
+matrix is symmetric then this a
+ 
+
+ align:start position:0%
+matrix is symmetric then this a
+transpose is the same as a you see at
+
+ align:start position:0%
+transpose is the same as a you see at
+ 
+
+ align:start position:0%
+transpose is the same as a you see at
+that moment I use the assumption now let
+
+ align:start position:0%
+that moment I use the assumption now let
+ 
+
+ align:start position:0%
+that moment I use the assumption now let
+me finish the discussion here's the way
+
+ align:start position:0%
+me finish the discussion here's the way
+ 
+
+ align:start position:0%
+me finish the discussion here's the way
+I finish I look at this original
+
+ align:start position:0%
+I finish I look at this original
+ 
+
+ align:start position:0%
+I finish I look at this original
+equation and I take the inner product I
+
+ align:start position:0%
+equation and I take the inner product I
+ 
+
+ align:start position:0%
+equation and I take the inner product I
+multiply both sides by oh maybe I'll do
+
+ align:start position:0%
+multiply both sides by oh maybe I'll do
+ 
+
+ align:start position:0%
+multiply both sides by oh maybe I'll do
+it with this one I take I multiply both
+
+ align:start position:0%
+it with this one I take I multiply both
+ 
+
+ align:start position:0%
+it with this one I take I multiply both
+sides by X bar transpose X bar transpose
+
+ align:start position:0%
+sides by X bar transpose X bar transpose
+ 
+
+ align:start position:0%
+sides by X bar transpose X bar transpose
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+spar equals lambda bar X bar transpose X
+
+ align:start position:0%
+spar equals lambda bar X bar transpose X
+ 
+
+ align:start position:0%
+spar equals lambda bar X bar transpose X
+bar okay fine all right now what's the
+
+ align:start position:0%
+bar okay fine all right now what's the
+ 
+
+ align:start position:0%
+bar okay fine all right now what's the
+other one oh the other one I'll probably
+
+ align:start position:0%
+other one oh the other one I'll probably
+ 
+
+ align:start position:0%
+other one oh the other one I'll probably
+use this guy am i happy about this no
+
+ align:start position:0%
+use this guy am i happy about this no
+ 
+
+ align:start position:0%
+use this guy am i happy about this no
+for some reason I'm not I'm I want to
+
+ align:start position:0%
+for some reason I'm not I'm I want to
+ 
+
+ align:start position:0%
+for some reason I'm not I'm I want to
+yeah if I take the inner product of this
+
+ align:start position:0%
+yeah if I take the inner product of this
+ 
+
+ align:start position:0%
+yeah if I take the inner product of this
+from the right with X bar I get X bar
+
+ align:start position:0%
+from the right with X bar I get X bar
+ 
+
+ align:start position:0%
+from the right with X bar I get X bar
+transpose a X bar equals x bar transpose
+
+ align:start position:0%
+transpose a X bar equals x bar transpose
+ 
+
+ align:start position:0%
+transpose a X bar equals x bar transpose
+lambda bar X bar I've done something
+
+ align:start position:0%
+lambda bar X bar I've done something
+ 
+
+ align:start position:0%
+lambda bar X bar I've done something
+dumb because I've got the I haven't
+
+ align:start position:0%
+dumb because I've got the I haven't
+ 
+
+ align:start position:0%
+dumb because I've got the I haven't
+learned anything I've got those two
+
+ align:start position:0%
+learned anything I've got those two
+ 
+
+ align:start position:0%
+learned anything I've got those two
+equations are identical so forgive me
+
+ align:start position:0%
+equations are identical so forgive me
+ 
+
+ align:start position:0%
+equations are identical so forgive me
+for doing such a thing
+
+ align:start position:0%
+for doing such a thing
+ 
+
+ align:start position:0%
+for doing such a thing
+but a look at the book okay so I took
+
+ align:start position:0%
+but a look at the book okay so I took
+ 
+
+ align:start position:0%
+but a look at the book okay so I took
+the dot product yeah somehow it didn't I
+
+ align:start position:0%
+the dot product yeah somehow it didn't I
+ 
+
+ align:start position:0%
+the dot product yeah somehow it didn't I
+should have taken the dot product of
+
+ align:start position:0%
+should have taken the dot product of
+ 
+
+ align:start position:0%
+should have taken the dot product of
+this guy here with that's what I was
+
+ align:start position:0%
+this guy here with that's what I was
+ 
+
+ align:start position:0%
+this guy here with that's what I was
+gonna do a x equals lambda X bar
+
+ align:start position:0%
+gonna do a x equals lambda X bar
+ 
+
+ align:start position:0%
+gonna do a x equals lambda X bar
+transpose X right okay so that that was
+
+ align:start position:0%
+transpose X right okay so that that was
+ 
+
+ align:start position:0%
+transpose X right okay so that that was
+that's fine that comes directly from
+
+ align:start position:0%
+that's fine that comes directly from
+ 
+
+ align:start position:0%
+that's fine that comes directly from
+that multiplying both sides by X bar
+
+ align:start position:0%
+that multiplying both sides by X bar
+ 
+
+ align:start position:0%
+that multiplying both sides by X bar
+transpose but now I'd like to get why do
+
+ align:start position:0%
+transpose but now I'd like to get why do
+ 
+
+ align:start position:0%
+transpose but now I'd like to get why do
+I have X bars over there oh yes forget
+
+ align:start position:0%
+I have X bars over there oh yes forget
+ 
+
+ align:start position:0%
+I have X bars over there oh yes forget
+this okay on this one right on this one
+
+ align:start position:0%
+this okay on this one right on this one
+ 
+
+ align:start position:0%
+this okay on this one right on this one
+I took it like that I multiply on the
+
+ align:start position:0%
+I took it like that I multiply on the
+ 
+
+ align:start position:0%
+I took it like that I multiply on the
+right by X that's the idea okay now why
+
+ align:start position:0%
+right by X that's the idea okay now why
+ 
+
+ align:start position:0%
+right by X that's the idea okay now why
+am i happier with this situation now the
+
+ align:start position:0%
+am i happier with this situation now the
+ 
+
+ align:start position:0%
+am i happier with this situation now the
+proof is coming here because I compare
+
+ align:start position:0%
+proof is coming here because I compare
+ 
+
+ align:start position:0%
+proof is coming here because I compare
+this guy
+
+ align:start position:0%
+this guy
+ 
+
+ align:start position:0%
+this guy
+with this one and they have the same
+
+ align:start position:0%
+with this one and they have the same
+ 
+
+ align:start position:0%
+with this one and they have the same
+left-hand side so they have the same
+
+ align:start position:0%
+left-hand side so they have the same
+ 
+
+ align:start position:0%
+left-hand side so they have the same
+right-hand side so comparing those two
+
+ align:start position:0%
+right-hand side so comparing those two
+ 
+
+ align:start position:0%
+right-hand side so comparing those two
+can I'll raise the board to do this
+
+ align:start position:0%
+can I'll raise the board to do this
+ 
+
+ align:start position:0%
+can I'll raise the board to do this
+comparison this thing lambda X bar
+
+ align:start position:0%
+comparison this thing lambda X bar
+ 
+
+ align:start position:0%
+comparison this thing lambda X bar
+transpose X is equal to lambda bar X bar
+
+ align:start position:0%
+transpose X is equal to lambda bar X bar
+ 
+
+ align:start position:0%
+transpose X is equal to lambda bar X bar
+transpose X okay and the conclusion I'm
+
+ align:start position:0%
+transpose X okay and the conclusion I'm
+ 
+
+ align:start position:0%
+transpose X okay and the conclusion I'm
+going to reach am I am I on the right
+
+ align:start position:0%
+going to reach am I am I on the right
+ 
+
+ align:start position:0%
+going to reach am I am I on the right
+track here the conclusion I'm going to
+
+ align:start position:0%
+track here the conclusion I'm going to
+ 
+
+ align:start position:0%
+track here the conclusion I'm going to
+reach is lambda equal lambda bar I would
+
+ align:start position:0%
+reach is lambda equal lambda bar I would
+ 
+
+ align:start position:0%
+reach is lambda equal lambda bar I would
+have to track down the other possibility
+
+ align:start position:0%
+have to track down the other possibility
+ 
+
+ align:start position:0%
+have to track down the other possibility
+that this this thing is zero but let me
+
+ align:start position:0%
+that this this thing is zero but let me
+ 
+
+ align:start position:0%
+that this this thing is zero but let me
+oh oh yeah that's important it's not
+
+ align:start position:0%
+oh oh yeah that's important it's not
+ 
+
+ align:start position:0%
+oh oh yeah that's important it's not
+zero so once I know that this isn't zero
+
+ align:start position:0%
+zero so once I know that this isn't zero
+ 
+
+ align:start position:0%
+zero so once I know that this isn't zero
+I just cancel it and I learned that
+
+ align:start position:0%
+I just cancel it and I learned that
+ 
+
+ align:start position:0%
+I just cancel it and I learned that
+lambda equals lambda bar and so what can
+
+ align:start position:0%
+lambda equals lambda bar and so what can
+ 
+
+ align:start position:0%
+lambda equals lambda bar and so what can
+you do have you got the reasoning
+
+ align:start position:0%
+you do have you got the reasoning
+ 
+
+ align:start position:0%
+you do have you got the reasoning
+altogether what does this tell us
+
+ align:start position:0%
+altogether what does this tell us
+ 
+
+ align:start position:0%
+altogether what does this tell us
+lambda is an eigenvalue of this
+
+ align:start position:0%
+lambda is an eigenvalue of this
+ 
+
+ align:start position:0%
+lambda is an eigenvalue of this
+symmetric matrix we've just proved that
+
+ align:start position:0%
+symmetric matrix we've just proved that
+ 
+
+ align:start position:0%
+symmetric matrix we've just proved that
+an equaled lambda bar so we have just
+
+ align:start position:0%
+an equaled lambda bar so we have just
+ 
+
+ align:start position:0%
+an equaled lambda bar so we have just
+proved that lambda is real right if if a
+
+ align:start position:0%
+proved that lambda is real right if if a
+ 
+
+ align:start position:0%
+proved that lambda is real right if if a
+number is equal to its own complex
+
+ align:start position:0%
+number is equal to its own complex
+ 
+
+ align:start position:0%
+number is equal to its own complex
+conjugate then there's no imaginary part
+
+ align:start position:0%
+conjugate then there's no imaginary part
+ 
+
+ align:start position:0%
+conjugate then there's no imaginary part
+at all the number is real so lambda is
+
+ align:start position:0%
+at all the number is real so lambda is
+ 
+
+ align:start position:0%
+at all the number is real so lambda is
+real good good
+
+ align:start position:0%
+real good good
+ 
+
+ align:start position:0%
+real good good
+now what but it depended on this little
+
+ align:start position:0%
+now what but it depended on this little
+ 
+
+ align:start position:0%
+now what but it depended on this little
+expression on knowing that that wasn't
+
+ align:start position:0%
+expression on knowing that that wasn't
+ 
+
+ align:start position:0%
+expression on knowing that that wasn't
+zero so that I could cancel it out so
+
+ align:start position:0%
+zero so that I could cancel it out so
+ 
+
+ align:start position:0%
+zero so that I could cancel it out so
+can we just take a second on that one
+
+ align:start position:0%
+can we just take a second on that one
+ 
+
+ align:start position:0%
+can we just take a second on that one
+because it's an important quantity X bar
+
+ align:start position:0%
+because it's an important quantity X bar
+ 
+
+ align:start position:0%
+because it's an important quantity X bar
+transpose X okay now remember as far as
+
+ align:start position:0%
+transpose X okay now remember as far as
+ 
+
+ align:start position:0%
+transpose X okay now remember as far as
+we know X is complex so this is
+
+ align:start position:0%
+we know X is complex so this is
+ 
+
+ align:start position:0%
+we know X is complex so this is
+here X is complex X has these components
+
+ align:start position:0%
+here X is complex X has these components
+ 
+
+ align:start position:0%
+here X is complex X has these components
+X 1 X 2 down 2 X n and X bar transpose
+
+ align:start position:0%
+X 1 X 2 down 2 X n and X bar transpose
+ 
+
+ align:start position:0%
+X 1 X 2 down 2 X n and X bar transpose
+well it's transposed and it's conjugated
+
+ align:start position:0%
+well it's transposed and it's conjugated
+ 
+
+ align:start position:0%
+well it's transposed and it's conjugated
+so that's X 1 conjugated X 2 conjugated
+
+ align:start position:0%
+so that's X 1 conjugated X 2 conjugated
+ 
+
+ align:start position:0%
+so that's X 1 conjugated X 2 conjugated
+up to X and conjugate it I'm really
+
+ align:start position:0%
+up to X and conjugate it I'm really
+ 
+
+ align:start position:0%
+up to X and conjugate it I'm really
+reminding you of crucial facts about
+
+ align:start position:0%
+reminding you of crucial facts about
+ 
+
+ align:start position:0%
+reminding you of crucial facts about
+complex numbers that are going to come
+
+ align:start position:0%
+complex numbers that are going to come
+ 
+
+ align:start position:0%
+complex numbers that are going to come
+into the next lecture as well as this
+
+ align:start position:0%
+into the next lecture as well as this
+ 
+
+ align:start position:0%
+into the next lecture as well as this
+one so what can you tell me about that
+
+ align:start position:0%
+one so what can you tell me about that
+ 
+
+ align:start position:0%
+one so what can you tell me about that
+product I guess what I'm trying to say
+
+ align:start position:0%
+product I guess what I'm trying to say
+ 
+
+ align:start position:0%
+product I guess what I'm trying to say
+is if I had a complex vector this would
+
+ align:start position:0%
+is if I had a complex vector this would
+ 
+
+ align:start position:0%
+is if I had a complex vector this would
+be the quantity I would I would like
+
+ align:start position:0%
+be the quantity I would I would like
+ 
+
+ align:start position:0%
+be the quantity I would I would like
+this is the quantity I like I would take
+
+ align:start position:0%
+this is the quantity I like I would take
+ 
+
+ align:start position:0%
+this is the quantity I like I would take
+the vector times its transpose now what
+
+ align:start position:0%
+the vector times its transpose now what
+ 
+
+ align:start position:0%
+the vector times its transpose now what
+what happens usually if I take a vector
+
+ align:start position:0%
+what happens usually if I take a vector
+ 
+
+ align:start position:0%
+what happens usually if I take a vector
+X transpose X I mean that's a quantity
+
+ align:start position:0%
+X transpose X I mean that's a quantity
+ 
+
+ align:start position:0%
+X transpose X I mean that's a quantity
+we see all the time X transpose X that's
+
+ align:start position:0%
+we see all the time X transpose X that's
+ 
+
+ align:start position:0%
+we see all the time X transpose X that's
+the length of x squared right
+
+ align:start position:0%
+the length of x squared right
+ 
+
+ align:start position:0%
+the length of x squared right
+that's this positive length squared it's
+
+ align:start position:0%
+that's this positive length squared it's
+ 
+
+ align:start position:0%
+that's this positive length squared it's
+Pythagoras it's x1 squared plus x2
+
+ align:start position:0%
+Pythagoras it's x1 squared plus x2
+ 
+
+ align:start position:0%
+Pythagoras it's x1 squared plus x2
+squared and so on
+
+ align:start position:0%
+squared and so on
+ 
+
+ align:start position:0%
+squared and so on
+now our vectors complex and you see the
+
+ align:start position:0%
+now our vectors complex and you see the
+ 
+
+ align:start position:0%
+now our vectors complex and you see the
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+I'm conjugating one of these guys so now
+
+ align:start position:0%
+I'm conjugating one of these guys so now
+ 
+
+ align:start position:0%
+I'm conjugating one of these guys so now
+when I do this multiplication
+
+ align:start position:0%
+when I do this multiplication
+ 
+
+ align:start position:0%
+when I do this multiplication
+I have x1 bar times x1 and x2 bar times
+
+ align:start position:0%
+I have x1 bar times x1 and x2 bar times
+ 
+
+ align:start position:0%
+I have x1 bar times x1 and x2 bar times
+x2 and so on so this is an this is some
+
+ align:start position:0%
+x2 and so on so this is an this is some
+ 
+
+ align:start position:0%
+x2 and so on so this is an this is some
+a plus IB and this is some a minus IB I
+
+ align:start position:0%
+a plus IB and this is some a minus IB I
+ 
+
+ align:start position:0%
+a plus IB and this is some a minus IB I
+mean what's the point here
+
+ align:start position:0%
+mean what's the point here
+ 
+
+ align:start position:0%
+mean what's the point here
+what's the point when I multiply a
+
+ align:start position:0%
+what's the point when I multiply a
+ 
+
+ align:start position:0%
+what's the point when I multiply a
+number by its conjugate a complex number
+
+ align:start position:0%
+number by its conjugate a complex number
+ 
+
+ align:start position:0%
+number by its conjugate a complex number
+by its conjugate what do I get I get up
+
+ align:start position:0%
+by its conjugate what do I get I get up
+ 
+
+ align:start position:0%
+by its conjugate what do I get I get up
+the the imaginary part is gone when I
+
+ align:start position:0%
+the the imaginary part is gone when I
+ 
+
+ align:start position:0%
+the the imaginary part is gone when I
+multiply a plus IB by its conjugate
+
+ align:start position:0%
+multiply a plus IB by its conjugate
+ 
+
+ align:start position:0%
+multiply a plus IB by its conjugate
+what's what's the result of that of each
+
+ align:start position:0%
+what's what's the result of that of each
+ 
+
+ align:start position:0%
+what's what's the result of that of each
+of those separate little multiplications
+
+ align:start position:0%
+of those separate little multiplications
+ 
+
+ align:start position:0%
+of those separate little multiplications
+there's an a squared and and what how
+
+ align:start position:0%
+there's an a squared and and what how
+ 
+
+ align:start position:0%
+there's an a squared and and what how
+many what's B squared it comes in with a
+
+ align:start position:0%
+many what's B squared it comes in with a
+ 
+
+ align:start position:0%
+many what's B squared it comes in with a
+plus or a minus a plus
+
+ align:start position:0%
+plus or a minus a plus
+ 
+
+ align:start position:0%
+plus or a minus a plus
+I times minus I is a plus B squared and
+
+ align:start position:0%
+I times minus I is a plus B squared and
+ 
+
+ align:start position:0%
+I times minus I is a plus B squared and
+what about the imaginary part gone right
+
+ align:start position:0%
+what about the imaginary part gone right
+ 
+
+ align:start position:0%
+what about the imaginary part gone right
+and I a B and a minus I a B so this this
+
+ align:start position:0%
+and I a B and a minus I a B so this this
+ 
+
+ align:start position:0%
+and I a B and a minus I a B so this this
+is the right thing to do if you want a
+
+ align:start position:0%
+is the right thing to do if you want a
+ 
+
+ align:start position:0%
+is the right thing to do if you want a
+decent answer then multiply numbers by
+
+ align:start position:0%
+decent answer then multiply numbers by
+ 
+
+ align:start position:0%
+decent answer then multiply numbers by
+their conjugates multiply vectors by the
+
+ align:start position:0%
+their conjugates multiply vectors by the
+ 
+
+ align:start position:0%
+their conjugates multiply vectors by the
+conjugates of X transpose so this
+
+ align:start position:0%
+conjugates of X transpose so this
+ 
+
+ align:start position:0%
+conjugates of X transpose so this
+quantity is positive this quantity is
+
+ align:start position:0%
+quantity is positive this quantity is
+ 
+
+ align:start position:0%
+quantity is positive this quantity is
+positive the whole thing is positive
+
+ align:start position:0%
+positive the whole thing is positive
+ 
+
+ align:start position:0%
+positive the whole thing is positive
+except for the zero vector and that
+
+ align:start position:0%
+except for the zero vector and that
+ 
+
+ align:start position:0%
+except for the zero vector and that
+allows me to know that this is a
+
+ align:start position:0%
+allows me to know that this is a
+ 
+
+ align:start position:0%
+allows me to know that this is a
+positive number which I safely cancel
+
+ align:start position:0%
+positive number which I safely cancel
+ 
+
+ align:start position:0%
+positive number which I safely cancel
+out and I reach the conclusion so
+
+ align:start position:0%
+out and I reach the conclusion so
+ 
+
+ align:start position:0%
+out and I reach the conclusion so
+actually in this discussion here I've
+
+ align:start position:0%
+actually in this discussion here I've
+ 
+
+ align:start position:0%
+actually in this discussion here I've
+done two things I've reached the
+
+ align:start position:0%
+done two things I've reached the
+ 
+
+ align:start position:0%
+done two things I've reached the
+conclusion that lambdas real which I
+
+ align:start position:0%
+conclusion that lambdas real which I
+ 
+
+ align:start position:0%
+conclusion that lambdas real which I
+wanted to do but at the same time we
+
+ align:start position:0%
+wanted to do but at the same time we
+ 
+
+ align:start position:0%
+wanted to do but at the same time we
+sort of saw what to do if things were
+
+ align:start position:0%
+sort of saw what to do if things were
+ 
+
+ align:start position:0%
+sort of saw what to do if things were
+complex if a vector is complex then it's
+
+ align:start position:0%
+complex if a vector is complex then it's
+ 
+
+ align:start position:0%
+complex if a vector is complex then it's
+X bar transpose X this is its length
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+squared and as I said the next lecture
+
+ align:start position:0%
+squared and as I said the next lecture
+ 
+
+ align:start position:0%
+squared and as I said the next lecture
+Monday will will repeat that this is the
+
+ align:start position:0%
+Monday will will repeat that this is the
+ 
+
+ align:start position:0%
+Monday will will repeat that this is the
+right thing and then do the right thing
+
+ align:start position:0%
+right thing and then do the right thing
+ 
+
+ align:start position:0%
+right thing and then do the right thing
+for matrices and all other all other
+
+ align:start position:0%
+for matrices and all other all other
+ 
+
+ align:start position:0%
+for matrices and all other all other
+complex possibilities okay but the main
+
+ align:start position:0%
+complex possibilities okay but the main
+ 
+
+ align:start position:0%
+complex possibilities okay but the main
+point then is that the eigenvalues of a
+
+ align:start position:0%
+point then is that the eigenvalues of a
+ 
+
+ align:start position:0%
+point then is that the eigenvalues of a
+symmetric matrix it just where did we
+
+ align:start position:0%
+symmetric matrix it just where did we
+ 
+
+ align:start position:0%
+symmetric matrix it just where did we
+use symmetry by the way we use it here
+
+ align:start position:0%
+use symmetry by the way we use it here
+ 
+
+ align:start position:0%
+use symmetry by the way we use it here
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+can I just suppose a was a complex
+
+ align:start position:0%
+can I just suppose a was a complex
+ 
+
+ align:start position:0%
+can I just suppose a was a complex
+suppose I had been a complex number
+
+ align:start position:0%
+suppose I had been a complex number
+ 
+
+ align:start position:0%
+suppose I had been a complex number
+could could I have made all this work if
+
+ align:start position:0%
+could could I have made all this work if
+ 
+
+ align:start position:0%
+could could I have made all this work if
+a was a complex number but complex
+
+ align:start position:0%
+a was a complex number but complex
+ 
+
+ align:start position:0%
+a was a complex number but complex
+matrix then here I should have written a
+
+ align:start position:0%
+matrix then here I should have written a
+ 
+
+ align:start position:0%
+matrix then here I should have written a
+bar I erased the bar because I assumed a
+
+ align:start position:0%
+bar I erased the bar because I assumed a
+ 
+
+ align:start position:0%
+bar I erased the bar because I assumed a
+was real but now let's
+
+ align:start position:0%
+was real but now let's
+ 
+
+ align:start position:0%
+was real but now let's
+suppose for a moment it's not then when
+
+ align:start position:0%
+suppose for a moment it's not then when
+ 
+
+ align:start position:0%
+suppose for a moment it's not then when
+I took this step what should I have what
+
+ align:start position:0%
+I took this step what should I have what
+ 
+
+ align:start position:0%
+I took this step what should I have what
+did i do on that step I transposed so I
+
+ align:start position:0%
+did i do on that step I transposed so I
+ 
+
+ align:start position:0%
+did i do on that step I transposed so I
+should have a bar transpose in the
+
+ align:start position:0%
+should have a bar transpose in the
+ 
+
+ align:start position:0%
+should have a bar transpose in the
+symmetric case that was a and that's
+
+ align:start position:0%
+symmetric case that was a and that's
+ 
+
+ align:start position:0%
+symmetric case that was a and that's
+what made everything work right this
+
+ align:start position:0%
+what made everything work right this
+ 
+
+ align:start position:0%
+what made everything work right this
+this led immediately to that this one
+
+ align:start position:0%
+this led immediately to that this one
+ 
+
+ align:start position:0%
+this led immediately to that this one
+that immediately to this when the matrix
+
+ align:start position:0%
+that immediately to this when the matrix
+ 
+
+ align:start position:0%
+that immediately to this when the matrix
+was real so that didn't matter
+
+ align:start position:0%
+was real so that didn't matter
+ 
+
+ align:start position:0%
+was real so that didn't matter
+and it was symmetric so that didn't
+
+ align:start position:0%
+and it was symmetric so that didn't
+ 
+
+ align:start position:0%
+and it was symmetric so that didn't
+matter then I got a but so now I just
+
+ align:start position:0%
+matter then I got a but so now I just
+ 
+
+ align:start position:0%
+matter then I got a but so now I just
+get to ask you suppose the matrix had
+
+ align:start position:0%
+get to ask you suppose the matrix had
+ 
+
+ align:start position:0%
+get to ask you suppose the matrix had
+been complex what's the right equivalent
+
+ align:start position:0%
+been complex what's the right equivalent
+ 
+
+ align:start position:0%
+been complex what's the right equivalent
+of symmetry so so so the good matrix so
+
+ align:start position:0%
+of symmetry so so so the good matrix so
+ 
+
+ align:start position:0%
+of symmetry so so so the good matrix so
+here let me say good matrices by good I
+
+ align:start position:0%
+here let me say good matrices by good I
+ 
+
+ align:start position:0%
+here let me say good matrices by good I
+mean real lambdas and perpendicular X's
+
+ align:start position:0%
+mean real lambdas and perpendicular X's
+ 
+
+ align:start position:0%
+mean real lambdas and perpendicular X's
+and tell me now which matrices are good
+
+ align:start position:0%
+and tell me now which matrices are good
+ 
+
+ align:start position:0%
+and tell me now which matrices are good
+if they're submit if they're if they're
+
+ align:start position:0%
+if they're submit if they're if they're
+ 
+
+ align:start position:0%
+if they're submit if they're if they're
+real matrices the good ones are
+
+ align:start position:0%
+real matrices the good ones are
+ 
+
+ align:start position:0%
+real matrices the good ones are
+symmetric because then everything went
+
+ align:start position:0%
+symmetric because then everything went
+ 
+
+ align:start position:0%
+symmetric because then everything went
+through so the so the good the I'm
+
+ align:start position:0%
+through so the so the good the I'm
+ 
+
+ align:start position:0%
+through so the so the good the I'm
+saying now what's good this is this is
+
+ align:start position:0%
+saying now what's good this is this is
+ 
+
+ align:start position:0%
+saying now what's good this is this is
+these are the good matrices they have
+
+ align:start position:0%
+these are the good matrices they have
+ 
+
+ align:start position:0%
+these are the good matrices they have
+real eigenvalues perpendicular
+
+ align:start position:0%
+real eigenvalues perpendicular
+ 
+
+ align:start position:0%
+real eigenvalues perpendicular
+eigenvectors good means a equal a
+
+ align:start position:0%
+eigenvectors good means a equal a
+ 
+
+ align:start position:0%
+eigenvectors good means a equal a
+transpose if real then then that was
+
+ align:start position:0%
+transpose if real then then that was
+ 
+
+ align:start position:0%
+transpose if real then then that was
+what our proof worked but if a is
+
+ align:start position:0%
+what our proof worked but if a is
+ 
+
+ align:start position:0%
+what our proof worked but if a is
+complex all our proof will still work
+
+ align:start position:0%
+complex all our proof will still work
+ 
+
+ align:start position:0%
+complex all our proof will still work
+provided a bar transpose is a do you see
+
+ align:start position:0%
+provided a bar transpose is a do you see
+ 
+
+ align:start position:0%
+provided a bar transpose is a do you see
+that I'm saying
+
+ align:start position:0%
+that I'm saying
+ 
+
+ align:start position:0%
+that I'm saying
+I'm saying if we have complex matrices
+
+ align:start position:0%
+I'm saying if we have complex matrices
+ 
+
+ align:start position:0%
+I'm saying if we have complex matrices
+and we want to say are they are they as
+
+ align:start position:0%
+and we want to say are they are they as
+ 
+
+ align:start position:0%
+and we want to say are they are they as
+good as symmetric matrices then we
+
+ align:start position:0%
+good as symmetric matrices then we
+ 
+
+ align:start position:0%
+good as symmetric matrices then we
+should not only transpose the thing but
+
+ align:start position:0%
+should not only transpose the thing but
+ 
+
+ align:start position:0%
+should not only transpose the thing but
+conjugate it
+
+ align:start position:0%
+conjugate it
+ 
+
+ align:start position:0%
+conjugate it
+those are good matrices and of course
+
+ align:start position:0%
+those are good matrices and of course
+ 
+
+ align:start position:0%
+those are good matrices and of course
+the most
+
+ align:start position:0%
+the most
+ 
+
+ align:start position:0%
+the most
+importance the most important case is
+
+ align:start position:0%
+importance the most important case is
+ 
+
+ align:start position:0%
+importance the most important case is
+when they're real this part doesn't
+
+ align:start position:0%
+when they're real this part doesn't
+ 
+
+ align:start position:0%
+when they're real this part doesn't
+matter and I just have a equal a
+
+ align:start position:0%
+matter and I just have a equal a
+ 
+
+ align:start position:0%
+matter and I just have a equal a
+transpose symmetric I'll just repeat
+
+ align:start position:0%
+transpose symmetric I'll just repeat
+ 
+
+ align:start position:0%
+transpose symmetric I'll just repeat
+that the good matrices if complex are
+
+ align:start position:0%
+that the good matrices if complex are
+ 
+
+ align:start position:0%
+that the good matrices if complex are
+these if real that doesn't make any
+
+ align:start position:0%
+these if real that doesn't make any
+ 
+
+ align:start position:0%
+these if real that doesn't make any
+difference so I'm just saying symmetric
+
+ align:start position:0%
+difference so I'm just saying symmetric
+ 
+
+ align:start position:0%
+difference so I'm just saying symmetric
+and of course 99% of examples and
+
+ align:start position:0%
+and of course 99% of examples and
+ 
+
+ align:start position:0%
+and of course 99% of examples and
+applications the matrices are real and
+
+ align:start position:0%
+applications the matrices are real and
+ 
+
+ align:start position:0%
+applications the matrices are real and
+we don't have that and then symmetric is
+
+ align:start position:0%
+we don't have that and then symmetric is
+ 
+
+ align:start position:0%
+we don't have that and then symmetric is
+the key property ok so that that's these
+
+ align:start position:0%
+the key property ok so that that's these
+ 
+
+ align:start position:0%
+the key property ok so that that's these
+main facts and now let me just let me
+
+ align:start position:0%
+main facts and now let me just let me
+ 
+
+ align:start position:0%
+main facts and now let me just let me
+just so that's this X bar transpose X ok
+
+ align:start position:0%
+just so that's this X bar transpose X ok
+ 
+
+ align:start position:0%
+just so that's this X bar transpose X ok
+so I'll just write it once more in this
+
+ align:start position:0%
+so I'll just write it once more in this
+ 
+
+ align:start position:0%
+so I'll just write it once more in this
+form so perpendicular orthonormal
+
+ align:start position:0%
+form so perpendicular orthonormal
+ 
+
+ align:start position:0%
+form so perpendicular orthonormal
+eigenvectors real eigenvalues transposes
+
+ align:start position:0%
+eigenvectors real eigenvalues transposes
+ 
+
+ align:start position:0%
+eigenvectors real eigenvalues transposes
+of orthonormal eigenvectors
+
+ align:start position:0%
+of orthonormal eigenvectors
+ 
+
+ align:start position:0%
+of orthonormal eigenvectors
+that's the symmetric case a equal a
+
+ align:start position:0%
+that's the symmetric case a equal a
+ 
+
+ align:start position:0%
+that's the symmetric case a equal a
+transpose oh good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually I'll even take one more step
+
+ align:start position:0%
+actually I'll even take one more step
+ 
+
+ align:start position:0%
+actually I'll even take one more step
+here suppose I can break this down to
+
+ align:start position:0%
+here suppose I can break this down to
+ 
+
+ align:start position:0%
+here suppose I can break this down to
+show you really what that says about a
+
+ align:start position:0%
+show you really what that says about a
+ 
+
+ align:start position:0%
+show you really what that says about a
+symmetric matrix I can break that down
+
+ align:start position:0%
+symmetric matrix I can break that down
+ 
+
+ align:start position:0%
+symmetric matrix I can break that down
+let me here go these eigenvectors i here
+
+ align:start position:0%
+let me here go these eigenvectors i here
+ 
+
+ align:start position:0%
+let me here go these eigenvectors i here
+go these eigenvalues lambda 1 lambda 2
+
+ align:start position:0%
+go these eigenvalues lambda 1 lambda 2
+ 
+
+ align:start position:0%
+go these eigenvalues lambda 1 lambda 2
+and so on here go these eigenvectors
+
+ align:start position:0%
+and so on here go these eigenvectors
+ 
+
+ align:start position:0%
+and so on here go these eigenvectors
+transposed and what happens if i
+
+ align:start position:0%
+transposed and what happens if i
+ 
+
+ align:start position:0%
+transposed and what happens if i
+actually do out that multiplication do
+
+ align:start position:0%
+actually do out that multiplication do
+ 
+
+ align:start position:0%
+actually do out that multiplication do
+you see what will happen
+
+ align:start position:0%
+you see what will happen
+ 
+
+ align:start position:0%
+you see what will happen
+there's lambda 1 times q1 transpose so
+
+ align:start position:0%
+there's lambda 1 times q1 transpose so
+ 
+
+ align:start position:0%
+there's lambda 1 times q1 transpose so
+the first row here is just lambda 1 Q 1
+
+ align:start position:0%
+the first row here is just lambda 1 Q 1
+ 
+
+ align:start position:0%
+the first row here is just lambda 1 Q 1
+transpose if I multiply column times row
+
+ align:start position:0%
+transpose if I multiply column times row
+ 
+
+ align:start position:0%
+transpose if I multiply column times row
+you remember I could do
+
+ align:start position:0%
+you remember I could do
+ 
+
+ align:start position:0%
+you remember I could do
+that when I multiply matrices I can
+
+ align:start position:0%
+that when I multiply matrices I can
+ 
+
+ align:start position:0%
+that when I multiply matrices I can
+multiply columns times rows so what I do
+
+ align:start position:0%
+multiply columns times rows so what I do
+ 
+
+ align:start position:0%
+multiply columns times rows so what I do
+that I get lambda 1 and then the column
+
+ align:start position:0%
+that I get lambda 1 and then the column
+ 
+
+ align:start position:0%
+that I get lambda 1 and then the column
+and then the row and then lambda 2 and
+
+ align:start position:0%
+and then the row and then lambda 2 and
+ 
+
+ align:start position:0%
+and then the row and then lambda 2 and
+the column and the row every symmetric
+
+ align:start position:0%
+the column and the row every symmetric
+ 
+
+ align:start position:0%
+the column and the row every symmetric
+matrix breaks up into these pieces so
+
+ align:start position:0%
+matrix breaks up into these pieces so
+ 
+
+ align:start position:0%
+matrix breaks up into these pieces so
+these pieces have real lambdas and they
+
+ align:start position:0%
+these pieces have real lambdas and they
+ 
+
+ align:start position:0%
+these pieces have real lambdas and they
+have these eigen these orthonormal
+
+ align:start position:0%
+have these eigen these orthonormal
+ 
+
+ align:start position:0%
+have these eigen these orthonormal
+eigenvectors and maybe you even could
+
+ align:start position:0%
+eigenvectors and maybe you even could
+ 
+
+ align:start position:0%
+eigenvectors and maybe you even could
+tell me what kind of a matrix have I got
+
+ align:start position:0%
+tell me what kind of a matrix have I got
+ 
+
+ align:start position:0%
+tell me what kind of a matrix have I got
+there suppose I take a unit vector times
+
+ align:start position:0%
+there suppose I take a unit vector times
+ 
+
+ align:start position:0%
+there suppose I take a unit vector times
+its transpose so column times row I'm
+
+ align:start position:0%
+its transpose so column times row I'm
+ 
+
+ align:start position:0%
+its transpose so column times row I'm
+getting a matrix that's a matrix with a
+
+ align:start position:0%
+getting a matrix that's a matrix with a
+ 
+
+ align:start position:0%
+getting a matrix that's a matrix with a
+special old name what's its what kind of
+
+ align:start position:0%
+special old name what's its what kind of
+ 
+
+ align:start position:0%
+special old name what's its what kind of
+a matrix is it we've seen those matrices
+
+ align:start position:0%
+a matrix is it we've seen those matrices
+ 
+
+ align:start position:0%
+a matrix is it we've seen those matrices
+now in Chapter four it's is a a
+
+ align:start position:0%
+now in Chapter four it's is a a
+ 
+
+ align:start position:0%
+now in Chapter four it's is a a
+transpose with a unit vector so I don't
+
+ align:start position:0%
+transpose with a unit vector so I don't
+ 
+
+ align:start position:0%
+transpose with a unit vector so I don't
+have to divide by a transpose a that
+
+ align:start position:0%
+have to divide by a transpose a that
+ 
+
+ align:start position:0%
+have to divide by a transpose a that
+matrix is a projection matrix that's a
+
+ align:start position:0%
+matrix is a projection matrix that's a
+ 
+
+ align:start position:0%
+matrix is a projection matrix that's a
+projection matrix it's symmetric and if
+
+ align:start position:0%
+projection matrix it's symmetric and if
+ 
+
+ align:start position:0%
+projection matrix it's symmetric and if
+I square it there'll be another there be
+
+ align:start position:0%
+I square it there'll be another there be
+ 
+
+ align:start position:0%
+I square it there'll be another there be
+a q1 transpose Q 1 which is 1 so I'll
+
+ align:start position:0%
+a q1 transpose Q 1 which is 1 so I'll
+ 
+
+ align:start position:0%
+a q1 transpose Q 1 which is 1 so I'll
+get that matrix back again every so
+
+ align:start position:0%
+get that matrix back again every so
+ 
+
+ align:start position:0%
+get that matrix back again every so
+every symmetric matrix every symmetric
+
+ align:start position:0%
+every symmetric matrix every symmetric
+ 
+
+ align:start position:0%
+every symmetric matrix every symmetric
+matrix is a combination of mutually
+
+ align:start position:0%
+matrix is a combination of mutually
+ 
+
+ align:start position:0%
+matrix is a combination of mutually
+perpendicular so perpendicular
+
+ align:start position:0%
+perpendicular so perpendicular
+ 
+
+ align:start position:0%
+perpendicular so perpendicular
+projection matrices projection matrices
+
+ align:start position:0%
+projection matrices projection matrices
+ 
+
+ align:start position:0%
+projection matrices projection matrices
+ok that's another way that people like
+
+ align:start position:0%
+ok that's another way that people like
+ 
+
+ align:start position:0%
+ok that's another way that people like
+to think of the spectral theorem that
+
+ align:start position:0%
+to think of the spectral theorem that
+ 
+
+ align:start position:0%
+to think of the spectral theorem that
+every symmetric matrix can be
+
+ align:start position:0%
+every symmetric matrix can be
+ 
+
+ align:start position:0%
+every symmetric matrix can be
+broken up that way that I guess at this
+
+ align:start position:0%
+broken up that way that I guess at this
+ 
+
+ align:start position:0%
+broken up that way that I guess at this
+moment first I haven't done an example I
+
+ align:start position:0%
+moment first I haven't done an example I
+ 
+
+ align:start position:0%
+moment first I haven't done an example I
+could create a symmetric matrix check
+
+ align:start position:0%
+could create a symmetric matrix check
+ 
+
+ align:start position:0%
+could create a symmetric matrix check
+that it's a find its eigenvalues they
+
+ align:start position:0%
+that it's a find its eigenvalues they
+ 
+
+ align:start position:0%
+that it's a find its eigenvalues they
+would come out real find its
+
+ align:start position:0%
+would come out real find its
+ 
+
+ align:start position:0%
+would come out real find its
+eigenvectors they would come out
+
+ align:start position:0%
+eigenvectors they would come out
+ 
+
+ align:start position:0%
+eigenvectors they would come out
+perpendicular and you would see it in
+
+ align:start position:0%
+perpendicular and you would see it in
+ 
+
+ align:start position:0%
+perpendicular and you would see it in
+numbers but maybe I'll leave it here for
+
+ align:start position:0%
+numbers but maybe I'll leave it here for
+ 
+
+ align:start position:0%
+numbers but maybe I'll leave it here for
+the moment in letters oh maybe I will do
+
+ align:start position:0%
+the moment in letters oh maybe I will do
+ 
+
+ align:start position:0%
+the moment in letters oh maybe I will do
+it with numbers for this reason because
+
+ align:start position:0%
+it with numbers for this reason because
+ 
+
+ align:start position:0%
+it with numbers for this reason because
+there's one more remarkable fact can I
+
+ align:start position:0%
+there's one more remarkable fact can I
+ 
+
+ align:start position:0%
+there's one more remarkable fact can I
+just put this further great fact about
+
+ align:start position:0%
+just put this further great fact about
+ 
+
+ align:start position:0%
+just put this further great fact about
+symmetric matrices on the board when I
+
+ align:start position:0%
+symmetric matrices on the board when I
+ 
+
+ align:start position:0%
+symmetric matrices on the board when I
+have symmetric matrices I know their
+
+ align:start position:0%
+have symmetric matrices I know their
+ 
+
+ align:start position:0%
+have symmetric matrices I know their
+eigenvalues are real so then I can get
+
+ align:start position:0%
+eigenvalues are real so then I can get
+ 
+
+ align:start position:0%
+eigenvalues are real so then I can get
+interested in the question are they
+
+ align:start position:0%
+interested in the question are they
+ 
+
+ align:start position:0%
+interested in the question are they
+positive or negative and you remember
+
+ align:start position:0%
+positive or negative and you remember
+ 
+
+ align:start position:0%
+positive or negative and you remember
+why that's important for differential
+
+ align:start position:0%
+why that's important for differential
+ 
+
+ align:start position:0%
+why that's important for differential
+equations that decides between
+
+ align:start position:0%
+equations that decides between
+ 
+
+ align:start position:0%
+equations that decides between
+instability and stability so I'm after I
+
+ align:start position:0%
+instability and stability so I'm after I
+ 
+
+ align:start position:0%
+instability and stability so I'm after I
+know they're real then the next question
+
+ align:start position:0%
+know they're real then the next question
+ 
+
+ align:start position:0%
+know they're real then the next question
+is are they positive are they negative
+
+ align:start position:0%
+is are they positive are they negative
+ 
+
+ align:start position:0%
+is are they positive are they negative
+and I hate to have to compute those
+
+ align:start position:0%
+and I hate to have to compute those
+ 
+
+ align:start position:0%
+and I hate to have to compute those
+eigenvalues to answer that question
+
+ align:start position:0%
+eigenvalues to answer that question
+ 
+
+ align:start position:0%
+eigenvalues to answer that question
+right because computing the eigenvalues
+
+ align:start position:0%
+right because computing the eigenvalues
+ 
+
+ align:start position:0%
+right because computing the eigenvalues
+of a symmetric matrix of order let's say
+
+ align:start position:0%
+of a symmetric matrix of order let's say
+ 
+
+ align:start position:0%
+of a symmetric matrix of order let's say
+50 compute its 50 eigenvalues is a job I
+
+ align:start position:0%
+50 compute its 50 eigenvalues is a job I
+ 
+
+ align:start position:0%
+50 compute its 50 eigenvalues is a job I
+mean by pencil and paper it's a
+
+ align:start position:0%
+mean by pencil and paper it's a
+ 
+
+ align:start position:0%
+mean by pencil and paper it's a
+lifetime's job I mean which and in fact
+
+ align:start position:0%
+lifetime's job I mean which and in fact
+ 
+
+ align:start position:0%
+lifetime's job I mean which and in fact
+a few years ago well say 20 years ago or
+
+ align:start position:0%
+a few years ago well say 20 years ago or
+ 
+
+ align:start position:0%
+a few years ago well say 20 years ago or
+30 nobody really knew how to do it I
+
+ align:start position:0%
+30 nobody really knew how to do it I
+ 
+
+ align:start position:0%
+30 nobody really knew how to do it I
+mean so like science was stuck on this
+
+ align:start position:0%
+mean so like science was stuck on this
+ 
+
+ align:start position:0%
+mean so like science was stuck on this
+problem if you have a matrix of order 50
+
+ align:start position:0%
+problem if you have a matrix of order 50
+ 
+
+ align:start position:0%
+problem if you have a matrix of order 50
+or 100 how do you find its eigenvalues
+
+ align:start position:0%
+or 100 how do you find its eigenvalues
+ 
+
+ align:start position:0%
+or 100 how do you find its eigenvalues
+numerically now I'm just saying because
+
+ align:start position:0%
+numerically now I'm just saying because
+ 
+
+ align:start position:0%
+numerically now I'm just saying because
+pencil and paper is we're going to run
+
+ align:start position:0%
+pencil and paper is we're going to run
+ 
+
+ align:start position:0%
+pencil and paper is we're going to run
+out of time or paper or something before
+
+ align:start position:0%
+out of time or paper or something before
+ 
+
+ align:start position:0%
+out of time or paper or something before
+we get it well and you might think okay
+
+ align:start position:0%
+we get it well and you might think okay
+ 
+
+ align:start position:0%
+we get it well and you might think okay
+get the get get MATLAB
+
+ align:start position:0%
+get the get get MATLAB
+ 
+
+ align:start position:0%
+get the get get MATLAB
+to compute the determinant of lambda
+
+ align:start position:0%
+to compute the determinant of lambda
+ 
+
+ align:start position:0%
+to compute the determinant of lambda
+minus a a a minus lambda I this
+
+ align:start position:0%
+minus a a a minus lambda I this
+ 
+
+ align:start position:0%
+minus a a a minus lambda I this
+polynomial of 50th degree and then find
+
+ align:start position:0%
+polynomial of 50th degree and then find
+ 
+
+ align:start position:0%
+polynomial of 50th degree and then find
+the roots MATLAB will do it but it will
+
+ align:start position:0%
+the roots MATLAB will do it but it will
+ 
+
+ align:start position:0%
+the roots MATLAB will do it but it will
+complain because it's a very bad way to
+
+ align:start position:0%
+complain because it's a very bad way to
+ 
+
+ align:start position:0%
+complain because it's a very bad way to
+find the eigenvalues I'm sorry to be
+
+ align:start position:0%
+find the eigenvalues I'm sorry to be
+ 
+
+ align:start position:0%
+find the eigenvalues I'm sorry to be
+saying this because it's the way I
+
+ align:start position:0%
+saying this because it's the way I
+ 
+
+ align:start position:0%
+saying this because it's the way I
+taught you to do it right I taught you
+
+ align:start position:0%
+taught you to do it right I taught you
+ 
+
+ align:start position:0%
+taught you to do it right I taught you
+to find the eigenvalues by doing that
+
+ align:start position:0%
+to find the eigenvalues by doing that
+ 
+
+ align:start position:0%
+to find the eigenvalues by doing that
+determinant and taking the roots of that
+
+ align:start position:0%
+determinant and taking the roots of that
+ 
+
+ align:start position:0%
+determinant and taking the roots of that
+polynomial but now I'm saying okay I
+
+ align:start position:0%
+polynomial but now I'm saying okay I
+ 
+
+ align:start position:0%
+polynomial but now I'm saying okay I
+really meant that for two by twos and
+
+ align:start position:0%
+really meant that for two by twos and
+ 
+
+ align:start position:0%
+really meant that for two by twos and
+three by threes but I didn't mean you to
+
+ align:start position:0%
+three by threes but I didn't mean you to
+ 
+
+ align:start position:0%
+three by threes but I didn't mean you to
+do it on a 50 by 50 and you're not too
+
+ align:start position:0%
+do it on a 50 by 50 and you're not too
+ 
+
+ align:start position:0%
+do it on a 50 by 50 and you're not too
+unhappy probably because you didn't want
+
+ align:start position:0%
+unhappy probably because you didn't want
+ 
+
+ align:start position:0%
+unhappy probably because you didn't want
+to do it but good because it would be
+
+ align:start position:0%
+to do it but good because it would be
+ 
+
+ align:start position:0%
+to do it but good because it would be
+very unstable way the aunt the 50
+
+ align:start position:0%
+very unstable way the aunt the 50
+ 
+
+ align:start position:0%
+very unstable way the aunt the 50
+answers that would come out would be
+
+ align:start position:0%
+answers that would come out would be
+ 
+
+ align:start position:0%
+answers that would come out would be
+highly unreliable so new ways are are
+
+ align:start position:0%
+highly unreliable so new ways are are
+ 
+
+ align:start position:0%
+highly unreliable so new ways are are
+much better to find those 50 eigenvalues
+
+ align:start position:0%
+much better to find those 50 eigenvalues
+ 
+
+ align:start position:0%
+much better to find those 50 eigenvalues
+that's a that's a part of numerical
+
+ align:start position:0%
+that's a that's a part of numerical
+ 
+
+ align:start position:0%
+that's a that's a part of numerical
+linear algebra but here's the remarkable
+
+ align:start position:0%
+linear algebra but here's the remarkable
+ 
+
+ align:start position:0%
+linear algebra but here's the remarkable
+fact that MATLAB would quite happily
+
+ align:start position:0%
+fact that MATLAB would quite happily
+ 
+
+ align:start position:0%
+fact that MATLAB would quite happily
+find the 50 pivots right now the pivots
+
+ align:start position:0%
+find the 50 pivots right now the pivots
+ 
+
+ align:start position:0%
+find the 50 pivots right now the pivots
+are not the same as the eigenvalues but
+
+ align:start position:0%
+are not the same as the eigenvalues but
+ 
+
+ align:start position:0%
+are not the same as the eigenvalues but
+here's the great thing if if I had a
+
+ align:start position:0%
+here's the great thing if if I had a
+ 
+
+ align:start position:0%
+here's the great thing if if I had a
+real matrix I could find those 50 pivots
+
+ align:start position:0%
+real matrix I could find those 50 pivots
+ 
+
+ align:start position:0%
+real matrix I could find those 50 pivots
+and I could see maybe 28 of them are
+
+ align:start position:0%
+and I could see maybe 28 of them are
+ 
+
+ align:start position:0%
+and I could see maybe 28 of them are
+positive and 22 or negative pivots and I
+
+ align:start position:0%
+positive and 22 or negative pivots and I
+ 
+
+ align:start position:0%
+positive and 22 or negative pivots and I
+can compute those safely and quickly and
+
+ align:start position:0%
+can compute those safely and quickly and
+ 
+
+ align:start position:0%
+can compute those safely and quickly and
+the great fact is that 28 of the
+
+ align:start position:0%
+the great fact is that 28 of the
+ 
+
+ align:start position:0%
+the great fact is that 28 of the
+eigenvalues would be positive and 22
+
+ align:start position:0%
+eigenvalues would be positive and 22
+ 
+
+ align:start position:0%
+eigenvalues would be positive and 22
+would be negative that the signs of the
+
+ align:start position:0%
+would be negative that the signs of the
+ 
+
+ align:start position:0%
+would be negative that the signs of the
+pivots so this is like just I hope you
+
+ align:start position:0%
+pivots so this is like just I hope you
+ 
+
+ align:start position:0%
+pivots so this is like just I hope you
+think this this is kind of a nice thing
+
+ align:start position:0%
+think this this is kind of a nice thing
+ 
+
+ align:start position:0%
+think this this is kind of a nice thing
+that the signs of the pivots for
+
+ align:start position:0%
+that the signs of the pivots for
+ 
+
+ align:start position:0%
+that the signs of the pivots for
+symmetric I'm always talking about
+
+ align:start position:0%
+symmetric I'm always talking about
+ 
+
+ align:start position:0%
+symmetric I'm always talking about
+symmetric matrices so I really like
+
+ align:start position:0%
+symmetric matrices so I really like
+ 
+
+ align:start position:0%
+symmetric matrices so I really like
+trying to convince you that symmetric
+
+ align:start position:0%
+trying to convince you that symmetric
+ 
+
+ align:start position:0%
+trying to convince you that symmetric
+matrices are better than the rest so the
+
+ align:start position:0%
+matrices are better than the rest so the
+ 
+
+ align:start position:0%
+matrices are better than the rest so the
+signs of the pivots are same as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the signs of the eigenvalues the same
+
+ align:start position:0%
+the signs of the eigenvalues the same
+ 
+
+ align:start position:0%
+the signs of the eigenvalues the same
+number the number of pivots greater than
+
+ align:start position:0%
+number the number of pivots greater than
+ 
+
+ align:start position:0%
+number the number of pivots greater than
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+the number of positive pivots is equal
+
+ align:start position:0%
+the number of positive pivots is equal
+ 
+
+ align:start position:0%
+the number of positive pivots is equal
+to the number of positive eigenvalues so
+
+ align:start position:0%
+to the number of positive eigenvalues so
+ 
+
+ align:start position:0%
+to the number of positive eigenvalues so
+that actually is a very useful that
+
+ align:start position:0%
+that actually is a very useful that
+ 
+
+ align:start position:0%
+that actually is a very useful that
+gives you a good start on a decent way
+
+ align:start position:0%
+gives you a good start on a decent way
+ 
+
+ align:start position:0%
+gives you a good start on a decent way
+to compute eigenvalues because you can
+
+ align:start position:0%
+to compute eigenvalues because you can
+ 
+
+ align:start position:0%
+to compute eigenvalues because you can
+narrow them down you can find out how
+
+ align:start position:0%
+narrow them down you can find out how
+ 
+
+ align:start position:0%
+narrow them down you can find out how
+many are positive how many are negative
+
+ align:start position:0%
+many are positive how many are negative
+ 
+
+ align:start position:0%
+many are positive how many are negative
+then you could shift the matrix by seven
+
+ align:start position:0%
+then you could shift the matrix by seven
+ 
+
+ align:start position:0%
+then you could shift the matrix by seven
+times the identity that would shift all
+
+ align:start position:0%
+times the identity that would shift all
+ 
+
+ align:start position:0%
+times the identity that would shift all
+the eigenvalues by seven then you could
+
+ align:start position:0%
+the eigenvalues by seven then you could
+ 
+
+ align:start position:0%
+the eigenvalues by seven then you could
+take the pivots of that matrix and you
+
+ align:start position:0%
+take the pivots of that matrix and you
+ 
+
+ align:start position:0%
+take the pivots of that matrix and you
+would know how many eigen values of the
+
+ align:start position:0%
+would know how many eigen values of the
+ 
+
+ align:start position:0%
+would know how many eigen values of the
+original were above seven and below
+
+ align:start position:0%
+original were above seven and below
+ 
+
+ align:start position:0%
+original were above seven and below
+seven so this this neat little theorem
+
+ align:start position:0%
+seven so this this neat little theorem
+ 
+
+ align:start position:0%
+seven so this this neat little theorem
+that the symmetric matrices have this
+
+ align:start position:0%
+that the symmetric matrices have this
+ 
+
+ align:start position:0%
+that the symmetric matrices have this
+connection between nobody's mixing up in
+
+ align:start position:0%
+connection between nobody's mixing up in
+ 
+
+ align:start position:0%
+connection between nobody's mixing up in
+thinking the pivots are the eigenvalues
+
+ align:start position:0%
+thinking the pivots are the eigenvalues
+ 
+
+ align:start position:0%
+thinking the pivots are the eigenvalues
+I mean the only thing I can think of is
+
+ align:start position:0%
+I mean the only thing I can think of is
+ 
+
+ align:start position:0%
+I mean the only thing I can think of is
+the product of the pivots equals the
+
+ align:start position:0%
+the product of the pivots equals the
+ 
+
+ align:start position:0%
+the product of the pivots equals the
+product of the eigenvalues why is that
+
+ align:start position:0%
+product of the eigenvalues why is that
+ 
+
+ align:start position:0%
+product of the eigenvalues why is that
+so if I asked you for the reason on that
+
+ align:start position:0%
+so if I asked you for the reason on that
+ 
+
+ align:start position:0%
+so if I asked you for the reason on that
+why is the product of the pivots for a
+
+ align:start position:0%
+why is the product of the pivots for a
+ 
+
+ align:start position:0%
+why is the product of the pivots for a
+symmetric matrix the same as the product
+
+ align:start position:0%
+symmetric matrix the same as the product
+ 
+
+ align:start position:0%
+symmetric matrix the same as the product
+of the eigenvalues because they both
+
+ align:start position:0%
+of the eigenvalues because they both
+ 
+
+ align:start position:0%
+of the eigenvalues because they both
+equal the determinant right the product
+
+ align:start position:0%
+equal the determinant right the product
+ 
+
+ align:start position:0%
+equal the determinant right the product
+of the pivots gives the determinant if
+
+ align:start position:0%
+of the pivots gives the determinant if
+ 
+
+ align:start position:0%
+of the pivots gives the determinant if
+no row exchanges the product of the
+
+ align:start position:0%
+no row exchanges the product of the
+ 
+
+ align:start position:0%
+no row exchanges the product of the
+eigenvalues always gives the determinant
+
+ align:start position:0%
+eigenvalues always gives the determinant
+ 
+
+ align:start position:0%
+eigenvalues always gives the determinant
+so so that products but that doesn't
+
+ align:start position:0%
+so so that products but that doesn't
+ 
+
+ align:start position:0%
+so so that products but that doesn't
+tell you anything about the 50
+
+ align:start position:0%
+tell you anything about the 50
+ 
+
+ align:start position:0%
+tell you anything about the 50
+individual ones which this does okay so
+
+ align:start position:0%
+individual ones which this does okay so
+ 
+
+ align:start position:0%
+individual ones which this does okay so
+that's those are essential facts about
+
+ align:start position:0%
+that's those are essential facts about
+ 
+
+ align:start position:0%
+that's those are essential facts about
+symmetric matrices okay now I said in
+
+ align:start position:0%
+symmetric matrices okay now I said in
+ 
+
+ align:start position:0%
+symmetric matrices okay now I said in
+the in the lecture description that I
+
+ align:start position:0%
+the in the lecture description that I
+ 
+
+ align:start position:0%
+the in the lecture description that I
+would take the last minute
+
+ align:start position:0%
+would take the last minute
+ 
+
+ align:start position:0%
+would take the last minute
+to start on positive definite matrices
+
+ align:start position:0%
+to start on positive definite matrices
+ 
+
+ align:start position:0%
+to start on positive definite matrices
+because we're right there where we're
+
+ align:start position:0%
+because we're right there where we're
+ 
+
+ align:start position:0%
+because we're right there where we're
+we're ready to say what's a positive
+
+ align:start position:0%
+we're ready to say what's a positive
+ 
+
+ align:start position:0%
+we're ready to say what's a positive
+definite matrix it's symmetric first of
+
+ align:start position:0%
+definite matrix it's symmetric first of
+ 
+
+ align:start position:0%
+definite matrix it's symmetric first of
+all I always I will mean symmetric so
+
+ align:start position:0%
+all I always I will mean symmetric so
+ 
+
+ align:start position:0%
+all I always I will mean symmetric so
+this is the this is the next section of
+
+ align:start position:0%
+this is the this is the next section of
+ 
+
+ align:start position:0%
+this is the this is the next section of
+the book it's about this if symmetric
+
+ align:start position:0%
+the book it's about this if symmetric
+ 
+
+ align:start position:0%
+the book it's about this if symmetric
+matrices are good which is like the
+
+ align:start position:0%
+matrices are good which is like the
+ 
+
+ align:start position:0%
+matrices are good which is like the
+point of my lecture so far then positive
+
+ align:start position:0%
+point of my lecture so far then positive
+ 
+
+ align:start position:0%
+point of my lecture so far then positive
+definite matrices are a subclass that
+
+ align:start position:0%
+definite matrices are a subclass that
+ 
+
+ align:start position:0%
+definite matrices are a subclass that
+are excellent ok just the greatest oh so
+
+ align:start position:0%
+are excellent ok just the greatest oh so
+ 
+
+ align:start position:0%
+are excellent ok just the greatest oh so
+what are they they're matrices they're
+
+ align:start position:0%
+what are they they're matrices they're
+ 
+
+ align:start position:0%
+what are they they're matrices they're
+symmetric matrices so all their
+
+ align:start position:0%
+symmetric matrices so all their
+ 
+
+ align:start position:0%
+symmetric matrices so all their
+eigenvalues are real you can guess what
+
+ align:start position:0%
+eigenvalues are real you can guess what
+ 
+
+ align:start position:0%
+eigenvalues are real you can guess what
+they are these are symmetric matrices
+
+ align:start position:0%
+they are these are symmetric matrices
+ 
+
+ align:start position:0%
+they are these are symmetric matrices
+with all the eigenvalues are ok tell me
+
+ align:start position:0%
+with all the eigenvalues are ok tell me
+ 
+
+ align:start position:0%
+with all the eigenvalues are ok tell me
+what to write what well it it's hinted
+
+ align:start position:0%
+what to write what well it it's hinted
+ 
+
+ align:start position:0%
+what to write what well it it's hinted
+of course by the name for these things
+
+ align:start position:0%
+of course by the name for these things
+ 
+
+ align:start position:0%
+of course by the name for these things
+all the eigenvalues are positive ok tell
+
+ align:start position:0%
+all the eigenvalues are positive ok tell
+ 
+
+ align:start position:0%
+all the eigenvalues are positive ok tell
+me about the pivots we can check the
+
+ align:start position:0%
+me about the pivots we can check the
+ 
+
+ align:start position:0%
+me about the pivots we can check the
+eigenvalues or we can check the pivots
+
+ align:start position:0%
+eigenvalues or we can check the pivots
+ 
+
+ align:start position:0%
+eigenvalues or we can check the pivots
+all the pivots are what and then I'll
+
+ align:start position:0%
+all the pivots are what and then I'll
+ 
+
+ align:start position:0%
+all the pivots are what and then I'll
+then I'll finally give an example I feel
+
+ align:start position:0%
+then I'll finally give an example I feel
+ 
+
+ align:start position:0%
+then I'll finally give an example I feel
+awful that I have got to this point in
+
+ align:start position:0%
+awful that I have got to this point in
+ 
+
+ align:start position:0%
+awful that I have got to this point in
+the lecture and I haven't given you a
+
+ align:start position:0%
+the lecture and I haven't given you a
+ 
+
+ align:start position:0%
+the lecture and I haven't given you a
+single example so let me give you 1 5 3
+
+ align:start position:0%
+single example so let me give you 1 5 3
+ 
+
+ align:start position:0%
+single example so let me give you 1 5 3
+2 2 at symmetric fine its eigenvalues
+
+ align:start position:0%
+2 2 at symmetric fine its eigenvalues
+ 
+
+ align:start position:0%
+2 2 at symmetric fine its eigenvalues
+are real for sure but more than that
+
+ align:start position:0%
+are real for sure but more than that
+ 
+
+ align:start position:0%
+are real for sure but more than that
+I know the signs of those eigenvalues
+
+ align:start position:0%
+I know the signs of those eigenvalues
+ 
+
+ align:start position:0%
+I know the signs of those eigenvalues
+and also I know the signs of those
+
+ align:start position:0%
+and also I know the signs of those
+ 
+
+ align:start position:0%
+and also I know the signs of those
+pivots so what's the deal with the
+
+ align:start position:0%
+pivots so what's the deal with the
+ 
+
+ align:start position:0%
+pivots so what's the deal with the
+pivots yeah if the eigenvalues are all
+
+ align:start position:0%
+pivots yeah if the eigenvalues are all
+ 
+
+ align:start position:0%
+pivots yeah if the eigenvalues are all
+positive and if this little fact is true
+
+ align:start position:0%
+positive and if this little fact is true
+ 
+
+ align:start position:0%
+positive and if this little fact is true
+that the pivots and eigenvalues have the
+
+ align:start position:0%
+that the pivots and eigenvalues have the
+ 
+
+ align:start position:0%
+that the pivots and eigenvalues have the
+same signs then this must be true all
+
+ align:start position:0%
+same signs then this must be true all
+ 
+
+ align:start position:0%
+same signs then this must be true all
+the pivots are positive and that's the
+
+ align:start position:0%
+the pivots are positive and that's the
+ 
+
+ align:start position:0%
+the pivots are positive and that's the
+good way to test this is the good test
+
+ align:start position:0%
+good way to test this is the good test
+ 
+
+ align:start position:0%
+good way to test this is the good test
+because I could what are the pivots for
+
+ align:start position:0%
+because I could what are the pivots for
+ 
+
+ align:start position:0%
+because I could what are the pivots for
+that matrix the pivots for that matrix
+
+ align:start position:0%
+that matrix the pivots for that matrix
+ 
+
+ align:start position:0%
+that matrix the pivots for that matrix
+are five so pivots are five and what's
+
+ align:start position:0%
+are five so pivots are five and what's
+ 
+
+ align:start position:0%
+are five so pivots are five and what's
+the second pivot have we like notice the
+
+ align:start position:0%
+the second pivot have we like notice the
+ 
+
+ align:start position:0%
+the second pivot have we like notice the
+formula for the second pivot in a matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it doesn't necessarily you know it may
+
+ align:start position:0%
+it doesn't necessarily you know it may
+ 
+
+ align:start position:0%
+it doesn't necessarily you know it may
+come out of fraction for sure but what
+
+ align:start position:0%
+come out of fraction for sure but what
+ 
+
+ align:start position:0%
+come out of fraction for sure but what
+is that fraction can you tell me well
+
+ align:start position:0%
+is that fraction can you tell me well
+ 
+
+ align:start position:0%
+is that fraction can you tell me well
+here the product of the pivots is the
+
+ align:start position:0%
+here the product of the pivots is the
+ 
+
+ align:start position:0%
+here the product of the pivots is the
+determinant what's the determinant of
+
+ align:start position:0%
+determinant what's the determinant of
+ 
+
+ align:start position:0%
+determinant what's the determinant of
+this matrix eleven so the second pivot
+
+ align:start position:0%
+this matrix eleven so the second pivot
+ 
+
+ align:start position:0%
+this matrix eleven so the second pivot
+must be eleven over five so that the
+
+ align:start position:0%
+must be eleven over five so that the
+ 
+
+ align:start position:0%
+must be eleven over five so that the
+product is eleven they're both positive
+
+ align:start position:0%
+product is eleven they're both positive
+ 
+
+ align:start position:0%
+product is eleven they're both positive
+then I know that the eigenvalues of that
+
+ align:start position:0%
+then I know that the eigenvalues of that
+ 
+
+ align:start position:0%
+then I know that the eigenvalues of that
+matrix are both positive what are the
+
+ align:start position:0%
+matrix are both positive what are the
+ 
+
+ align:start position:0%
+matrix are both positive what are the
+eigenvalues well I've got to take the
+
+ align:start position:0%
+eigenvalues well I've got to take the
+ 
+
+ align:start position:0%
+eigenvalues well I've got to take the
+roots of you know do I put in a minus
+
+ align:start position:0%
+roots of you know do I put in a minus
+ 
+
+ align:start position:0%
+roots of you know do I put in a minus
+lambda you mentally do this lambda
+
+ align:start position:0%
+lambda you mentally do this lambda
+ 
+
+ align:start position:0%
+lambda you mentally do this lambda
+squared
+
+ align:start position:0%
+squared
+ 
+
+ align:start position:0%
+squared
+- how many lambdas eight right five and
+
+ align:start position:0%
+- how many lambdas eight right five and
+ 
+
+ align:start position:0%
+- how many lambdas eight right five and
+three the trace comes in there plus what
+
+ align:start position:0%
+three the trace comes in there plus what
+ 
+
+ align:start position:0%
+three the trace comes in there plus what
+number comes here they determinant the
+
+ align:start position:0%
+number comes here they determinant the
+ 
+
+ align:start position:0%
+number comes here they determinant the
+eleven so I set that to zero so the
+
+ align:start position:0%
+eleven so I set that to zero so the
+ 
+
+ align:start position:0%
+eleven so I set that to zero so the
+eigenvalues are let's see half of that
+
+ align:start position:0%
+eigenvalues are let's see half of that
+ 
+
+ align:start position:0%
+eigenvalues are let's see half of that
+is four look at that positive number
+
+ align:start position:0%
+is four look at that positive number
+ 
+
+ align:start position:0%
+is four look at that positive number
+plus or minus the square root of 16
+
+ align:start position:0%
+plus or minus the square root of 16
+ 
+
+ align:start position:0%
+plus or minus the square root of 16
+minus eleven I think five the
+
+ align:start position:0%
+minus eleven I think five the
+ 
+
+ align:start position:0%
+minus eleven I think five the
+eigenvalues well
+
+ align:start position:0%
+eigenvalues well
+ 
+
+ align:start position:0%
+eigenvalues well
+- by - they're not so terrible but
+
+ align:start position:0%
+- by - they're not so terrible but
+ 
+
+ align:start position:0%
+- by - they're not so terrible but
+they're not so
+
+ align:start position:0%
+they're not so
+ 
+
+ align:start position:0%
+they're not so
+perfect pivots are really simple and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is this is the family of matrices
+
+ align:start position:0%
+this is this is the family of matrices
+ 
+
+ align:start position:0%
+this is this is the family of matrices
+that you really want in differential
+
+ align:start position:0%
+that you really want in differential
+ 
+
+ align:start position:0%
+that you really want in differential
+equations because you know the signs of
+
+ align:start position:0%
+equations because you know the signs of
+ 
+
+ align:start position:0%
+equations because you know the signs of
+the eigenvalues so you know the
+
+ align:start position:0%
+the eigenvalues so you know the
+ 
+
+ align:start position:0%
+the eigenvalues so you know the
+stability or not okay there's one other
+
+ align:start position:0%
+stability or not okay there's one other
+ 
+
+ align:start position:0%
+stability or not okay there's one other
+related fact I can pop in here and in
+
+ align:start position:0%
+related fact I can pop in here and in
+ 
+
+ align:start position:0%
+related fact I can pop in here and in
+the time available for positive definite
+
+ align:start position:0%
+the time available for positive definite
+ 
+
+ align:start position:0%
+the time available for positive definite
+matrices the the related fact is to ask
+
+ align:start position:0%
+matrices the the related fact is to ask
+ 
+
+ align:start position:0%
+matrices the the related fact is to ask
+you about determinants so what's the
+
+ align:start position:0%
+you about determinants so what's the
+ 
+
+ align:start position:0%
+you about determinants so what's the
+determinant what can you tell me if I
+
+ align:start position:0%
+determinant what can you tell me if I
+ 
+
+ align:start position:0%
+determinant what can you tell me if I
+remember positive definite means all
+
+ align:start position:0%
+remember positive definite means all
+ 
+
+ align:start position:0%
+remember positive definite means all
+eigenvalues are positive all pivots are
+
+ align:start position:0%
+eigenvalues are positive all pivots are
+ 
+
+ align:start position:0%
+eigenvalues are positive all pivots are
+positive so what can you tell me about
+
+ align:start position:0%
+positive so what can you tell me about
+ 
+
+ align:start position:0%
+positive so what can you tell me about
+the determinant it's positive too but
+
+ align:start position:0%
+the determinant it's positive too but
+ 
+
+ align:start position:0%
+the determinant it's positive too but
+somehow that that's not quite enough
+
+ align:start position:0%
+somehow that that's not quite enough
+ 
+
+ align:start position:0%
+somehow that that's not quite enough
+here's a matrix minus 1 minus 3 what's
+
+ align:start position:0%
+here's a matrix minus 1 minus 3 what's
+ 
+
+ align:start position:0%
+here's a matrix minus 1 minus 3 what's
+the determinant of that guy it's
+
+ align:start position:0%
+the determinant of that guy it's
+ 
+
+ align:start position:0%
+the determinant of that guy it's
+positive right is this a positive
+
+ align:start position:0%
+positive right is this a positive
+ 
+
+ align:start position:0%
+positive right is this a positive
+definite matrix are the pivots what are
+
+ align:start position:0%
+definite matrix are the pivots what are
+ 
+
+ align:start position:0%
+definite matrix are the pivots what are
+the pivots well negative what are the
+
+ align:start position:0%
+the pivots well negative what are the
+ 
+
+ align:start position:0%
+the pivots well negative what are the
+eigenvalues well they're also the same
+
+ align:start position:0%
+eigenvalues well they're also the same
+ 
+
+ align:start position:0%
+eigenvalues well they're also the same
+so somehow I don't just want the
+
+ align:start position:0%
+so somehow I don't just want the
+ 
+
+ align:start position:0%
+so somehow I don't just want the
+determinant of the whole matrix here is
+
+ align:start position:0%
+determinant of the whole matrix here is
+ 
+
+ align:start position:0%
+determinant of the whole matrix here is
+11 that's great
+
+ align:start position:0%
+11 that's great
+ 
+
+ align:start position:0%
+11 that's great
+here the determinate of the whole matrix
+
+ align:start position:0%
+here the determinate of the whole matrix
+ 
+
+ align:start position:0%
+here the determinate of the whole matrix
+is 3 that's positive I also I've got to
+
+ align:start position:0%
+is 3 that's positive I also I've got to
+ 
+
+ align:start position:0%
+is 3 that's positive I also I've got to
+check like little sub determinants say
+
+ align:start position:0%
+check like little sub determinants say
+ 
+
+ align:start position:0%
+check like little sub determinants say
+maybe coming down from the left so the 1
+
+ align:start position:0%
+maybe coming down from the left so the 1
+ 
+
+ align:start position:0%
+maybe coming down from the left so the 1
+by 1 and the 2 by 2 have to be positive
+
+ align:start position:0%
+by 1 and the 2 by 2 have to be positive
+ 
+
+ align:start position:0%
+by 1 and the 2 by 2 have to be positive
+so there that's where I get the all all
+
+ align:start position:0%
+so there that's where I get the all all
+ 
+
+ align:start position:0%
+so there that's where I get the all all
+can I call them sub determinants or see
+
+ align:start position:0%
+can I call them sub determinants or see
+ 
+
+ align:start position:0%
+can I call them sub determinants or see
+I have to I need to make the thing
+
+ align:start position:0%
+I have to I need to make the thing
+ 
+
+ align:start position:0%
+I have to I need to make the thing
+plural I need to test end things not
+
+ align:start position:0%
+plural I need to test end things not
+ 
+
+ align:start position:0%
+plural I need to test end things not
+just the big determine
+
+ align:start position:0%
+just the big determine
+ 
+
+ align:start position:0%
+just the big determine
+all sub determinants are positive then
+
+ align:start position:0%
+all sub determinants are positive then
+ 
+
+ align:start position:0%
+all sub determinants are positive then
+I'm okay then I'm okay this passes the
+
+ align:start position:0%
+I'm okay then I'm okay this passes the
+ 
+
+ align:start position:0%
+I'm okay then I'm okay this passes the
+test five is positive and eleven is
+
+ align:start position:0%
+test five is positive and eleven is
+ 
+
+ align:start position:0%
+test five is positive and eleven is
+positive this fails the test because
+
+ align:start position:0%
+positive this fails the test because
+ 
+
+ align:start position:0%
+positive this fails the test because
+that minus one there is negative and
+
+ align:start position:0%
+that minus one there is negative and
+ 
+
+ align:start position:0%
+that minus one there is negative and
+then the big determinant is positive
+
+ align:start position:0%
+then the big determinant is positive
+ 
+
+ align:start position:0%
+then the big determinant is positive
+three so this these this fact you see
+
+ align:start position:0%
+three so this these this fact you see
+ 
+
+ align:start position:0%
+three so this these this fact you see
+that actually the course like coming
+
+ align:start position:0%
+that actually the course like coming
+ 
+
+ align:start position:0%
+that actually the course like coming
+together and that's really my point now
+
+ align:start position:0%
+together and that's really my point now
+ 
+
+ align:start position:0%
+together and that's really my point now
+in the next in this lecture and
+
+ align:start position:0%
+in the next in this lecture and
+ 
+
+ align:start position:0%
+in the next in this lecture and
+particularly next Wednesday and Friday
+
+ align:start position:0%
+particularly next Wednesday and Friday
+ 
+
+ align:start position:0%
+particularly next Wednesday and Friday
+the course comes together these pivots
+
+ align:start position:0%
+the course comes together these pivots
+ 
+
+ align:start position:0%
+the course comes together these pivots
+that we met in the first week these
+
+ align:start position:0%
+that we met in the first week these
+ 
+
+ align:start position:0%
+that we met in the first week these
+determinants that we met in the middle
+
+ align:start position:0%
+determinants that we met in the middle
+ 
+
+ align:start position:0%
+determinants that we met in the middle
+of the course these eigenvalues that we
+
+ align:start position:0%
+of the course these eigenvalues that we
+ 
+
+ align:start position:0%
+of the course these eigenvalues that we
+met most recently all matrices are
+
+ align:start position:0%
+met most recently all matrices are
+ 
+
+ align:start position:0%
+met most recently all matrices are
+square here so coming together for
+
+ align:start position:0%
+square here so coming together for
+ 
+
+ align:start position:0%
+square here so coming together for
+square matrices means these three pieces
+
+ align:start position:0%
+square matrices means these three pieces
+ 
+
+ align:start position:0%
+square matrices means these three pieces
+come together and they come together in
+
+ align:start position:0%
+come together and they come together in
+ 
+
+ align:start position:0%
+come together and they come together in
+that beautiful fact that if that all
+
+ align:start position:0%
+that beautiful fact that if that all
+ 
+
+ align:start position:0%
+that beautiful fact that if that all
+that if I have one of these I have the
+
+ align:start position:0%
+that if I have one of these I have the
+ 
+
+ align:start position:0%
+that if I have one of these I have the
+others that if I have but for symmetric
+
+ align:start position:0%
+others that if I have but for symmetric
+ 
+
+ align:start position:0%
+others that if I have but for symmetric
+matrices so that this will be the
+
+ align:start position:0%
+matrices so that this will be the
+ 
+
+ align:start position:0%
+matrices so that this will be the
+positive definite section and then the
+
+ align:start position:0%
+positive definite section and then the
+ 
+
+ align:start position:0%
+positive definite section and then the
+real climax of the course is to make
+
+ align:start position:0%
+real climax of the course is to make
+ 
+
+ align:start position:0%
+real climax of the course is to make
+everything come together for M by n
+
+ align:start position:0%
+everything come together for M by n
+ 
+
+ align:start position:0%
+everything come together for M by n
+matrices not necessarily symmetric bring
+
+ align:start position:0%
+matrices not necessarily symmetric bring
+ 
+
+ align:start position:0%
+matrices not necessarily symmetric bring
+bring everything together there and that
+
+ align:start position:0%
+bring everything together there and that
+ 
+
+ align:start position:0%
+bring everything together there and that
+will be the final thing ok so have a
+
+ align:start position:0%
+will be the final thing ok so have a
+ 
+
+ align:start position:0%
+will be the final thing ok so have a
+great weekend and don't forget symmetric
+
+ align:start position:0%
+great weekend and don't forget symmetric
+ 
+
+ align:start position:0%
+great weekend and don't forget symmetric
+matrices Thanks
\ No newline at end of file
diff --git a/UGKL1wHouho.txt b/UGKL1wHouho.txt
new file mode 100644
index 0000000000000000000000000000000000000000..301736f5aea5fd4990c3398091c023941f1983f5
--- /dev/null
+++ b/UGKL1wHouho.txt
@@ -0,0 +1,6243 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi today we would like to begin our
+
+ align:start position:0%
+hi today we would like to begin our
+ 
+
+ align:start position:0%
+hi today we would like to begin our
+study of calculus of several real
+
+ align:start position:0%
+study of calculus of several real
+ 
+
+ align:start position:0%
+study of calculus of several real
+variables and as I mentioned in our last
+
+ align:start position:0%
+variables and as I mentioned in our last
+ 
+
+ align:start position:0%
+variables and as I mentioned in our last
+lecture I would like to begin it from
+
+ align:start position:0%
+lecture I would like to begin it from
+ 
+
+ align:start position:0%
+lecture I would like to begin it from
+the traditional point of view and I
+
+ align:start position:0%
+the traditional point of view and I
+ 
+
+ align:start position:0%
+the traditional point of view and I
+guess I'd like to make a little bit of a
+
+ align:start position:0%
+guess I'd like to make a little bit of a
+ 
+
+ align:start position:0%
+guess I'd like to make a little bit of a
+short speech even before we begin that
+
+ align:start position:0%
+short speech even before we begin that
+ 
+
+ align:start position:0%
+short speech even before we begin that
+there may be a little bit of danger that
+
+ align:start position:0%
+there may be a little bit of danger that
+ 
+
+ align:start position:0%
+there may be a little bit of danger that
+in the way I've been emphasizing ing the
+
+ align:start position:0%
+in the way I've been emphasizing ing the
+ 
+
+ align:start position:0%
+in the way I've been emphasizing ing the
+modern approach to mathematics that one
+
+ align:start position:0%
+modern approach to mathematics that one
+ 
+
+ align:start position:0%
+modern approach to mathematics that one
+may actually believe that the the
+
+ align:start position:0%
+may actually believe that the the
+ 
+
+ align:start position:0%
+may actually believe that the the
+traditional approach to mathematics left
+
+ align:start position:0%
+traditional approach to mathematics left
+ 
+
+ align:start position:0%
+traditional approach to mathematics left
+very very much to be desired the answer
+
+ align:start position:0%
+very very much to be desired the answer
+ 
+
+ align:start position:0%
+very very much to be desired the answer
+is it didn't really that the role of
+
+ align:start position:0%
+is it didn't really that the role of
+ 
+
+ align:start position:0%
+is it didn't really that the role of
+logic in good traditional mathematics
+
+ align:start position:0%
+logic in good traditional mathematics
+ 
+
+ align:start position:0%
+logic in good traditional mathematics
+was about the same as it is in good
+
+ align:start position:0%
+was about the same as it is in good
+ 
+
+ align:start position:0%
+was about the same as it is in good
+modern mathematics that in fact if we
+
+ align:start position:0%
+modern mathematics that in fact if we
+ 
+
+ align:start position:0%
+modern mathematics that in fact if we
+Define new mathematics as meaning
+
+ align:start position:0%
+Define new mathematics as meaning
+ 
+
+ align:start position:0%
+Define new mathematics as meaning
+meaningful mathematics there really was
+
+ align:start position:0%
+meaningful mathematics there really was
+ 
+
+ align:start position:0%
+meaningful mathematics there really was
+no difference between the two approaches
+
+ align:start position:0%
+no difference between the two approaches
+ 
+
+ align:start position:0%
+no difference between the two approaches
+except for the fact that after you have
+
+ align:start position:0%
+except for the fact that after you have
+ 
+
+ align:start position:0%
+except for the fact that after you have
+a couple of hundred years of hindsight
+
+ align:start position:0%
+a couple of hundred years of hindsight
+ 
+
+ align:start position:0%
+a couple of hundred years of hindsight
+and can take a subject apart from a
+
+ align:start position:0%
+and can take a subject apart from a
+ 
+
+ align:start position:0%
+and can take a subject apart from a
+different point of view then obviously
+
+ align:start position:0%
+different point of view then obviously
+ 
+
+ align:start position:0%
+different point of view then obviously
+it's no great surprise that you can find
+
+ align:start position:0%
+it's no great surprise that you can find
+ 
+
+ align:start position:0%
+it's no great surprise that you can find
+cleaner ways of really presenting the
+
+ align:start position:0%
+cleaner ways of really presenting the
+ 
+
+ align:start position:0%
+cleaner ways of really presenting the
+topic it's the old cliche of hindsight
+
+ align:start position:0%
+topic it's the old cliche of hindsight
+ 
+
+ align:start position:0%
+topic it's the old cliche of hindsight
+being better than foresight by a Don
+
+ align:start position:0%
+being better than foresight by a Don
+ 
+
+ align:start position:0%
+being better than foresight by a Don
+site or some such thing but at any rate
+
+ align:start position:0%
+site or some such thing but at any rate
+ 
+
+ align:start position:0%
+site or some such thing but at any rate
+without further Ado let's actually look
+
+ align:start position:0%
+without further Ado let's actually look
+ 
+
+ align:start position:0%
+without further Ado let's actually look
+at the introduction to calculus of
+
+ align:start position:0%
+at the introduction to calculus of
+ 
+
+ align:start position:0%
+at the introduction to calculus of
+several real variables from a
+
+ align:start position:0%
+several real variables from a
+ 
+
+ align:start position:0%
+several real variables from a
+traditional point of view and I've
+
+ align:start position:0%
+traditional point of view and I've
+ 
+
+ align:start position:0%
+traditional point of view and I've
+abbreviated that title to Simply say
+
+ align:start position:0%
+abbreviated that title to Simply say
+ 
+
+ align:start position:0%
+abbreviated that title to Simply say
+calculus of several variables whereas I
+
+ align:start position:0%
+calculus of several variables whereas I
+ 
+
+ align:start position:0%
+calculus of several variables whereas I
+say that think of two things first of
+
+ align:start position:0%
+say that think of two things first of
+ 
+
+ align:start position:0%
+say that think of two things first of
+all it's an introduction and second of
+
+ align:start position:0%
+all it's an introduction and second of
+ 
+
+ align:start position:0%
+all it's an introduction and second of
+all we're going to be doing this from
+
+ align:start position:0%
+all we're going to be doing this from
+ 
+
+ align:start position:0%
+all we're going to be doing this from
+the traditional point of view now what
+
+ align:start position:0%
+the traditional point of view now what
+ 
+
+ align:start position:0%
+the traditional point of view now what
+we're assuming is remember last time we
+
+ align:start position:0%
+we're assuming is remember last time we
+ 
+
+ align:start position:0%
+we're assuming is remember last time we
+talked about functions of several real
+
+ align:start position:0%
+talked about functions of several real
+ 
+
+ align:start position:0%
+talked about functions of several real
+variables we talked about the limit
+
+ align:start position:0%
+variables we talked about the limit
+ 
+
+ align:start position:0%
+variables we talked about the limit
+concept gave you exercises that drilled
+
+ align:start position:0%
+concept gave you exercises that drilled
+ 
+
+ align:start position:0%
+concept gave you exercises that drilled
+you on what limits meant and the like
+
+ align:start position:0%
+you on what limits meant and the like
+ 
+
+ align:start position:0%
+you on what limits meant and the like
+and as a result it now makes sense to
+
+ align:start position:0%
+and as a result it now makes sense to
+ 
+
+ align:start position:0%
+and as a result it now makes sense to
+talk about uh the calculus the
+
+ align:start position:0%
+talk about uh the calculus the
+ 
+
+ align:start position:0%
+talk about uh the calculus the
+instantaneous rate of change except that
+
+ align:start position:0%
+instantaneous rate of change except that
+ 
+
+ align:start position:0%
+instantaneous rate of change except that
+you have an awful lot of variables in
+
+ align:start position:0%
+you have an awful lot of variables in
+ 
+
+ align:start position:0%
+you have an awful lot of variables in
+here in other words the general case
+
+ align:start position:0%
+here in other words the general case
+ 
+
+ align:start position:0%
+here in other words the general case
+that we'd like to tackle is the case
+
+ align:start position:0%
+that we'd like to tackle is the case
+ 
+
+ align:start position:0%
+that we'd like to tackle is the case
+where we have W being some real number
+
+ align:start position:0%
+where we have W being some real number
+ 
+
+ align:start position:0%
+where we have W being some real number
+being a function of the N independent
+
+ align:start position:0%
+being a function of the N independent
+ 
+
+ align:start position:0%
+being a function of the N independent
+variables X1 up to xn and of course you
+
+ align:start position:0%
+variables X1 up to xn and of course you
+ 
+
+ align:start position:0%
+variables X1 up to xn and of course you
+see the calculus applies to the F the W
+
+ align:start position:0%
+see the calculus applies to the F the W
+ 
+
+ align:start position:0%
+see the calculus applies to the F the W
+Used here is to indicate the fact that
+
+ align:start position:0%
+Used here is to indicate the fact that
+ 
+
+ align:start position:0%
+Used here is to indicate the fact that
+the output is a real number I it's like
+
+ align:start position:0%
+the output is a real number I it's like
+ 
+
+ align:start position:0%
+the output is a real number I it's like
+talking about F ofx versus y equal F ofx
+
+ align:start position:0%
+talking about F ofx versus y equal F ofx
+ 
+
+ align:start position:0%
+talking about F ofx versus y equal F ofx
+in a manner of speaking it's the F ofx
+
+ align:start position:0%
+in a manner of speaking it's the F ofx
+ 
+
+ align:start position:0%
+in a manner of speaking it's the F ofx
+that's important we won't get into that
+
+ align:start position:0%
+that's important we won't get into that
+ 
+
+ align:start position:0%
+that's important we won't get into that
+right now what was important though
+
+ align:start position:0%
+right now what was important though
+ 
+
+ align:start position:0%
+right now what was important though
+about y equals f ofx it indicated a
+
+ align:start position:0%
+about y equals f ofx it indicated a
+ 
+
+ align:start position:0%
+about y equals f ofx it indicated a
+graph graph and because it was a graph
+
+ align:start position:0%
+graph graph and because it was a graph
+ 
+
+ align:start position:0%
+graph graph and because it was a graph
+we could visualize things pictorially
+
+ align:start position:0%
+we could visualize things pictorially
+ 
+
+ align:start position:0%
+we could visualize things pictorially
+that might have been harder to
+
+ align:start position:0%
+that might have been harder to
+ 
+
+ align:start position:0%
+that might have been harder to
+understand analytically for this reason
+
+ align:start position:0%
+understand analytically for this reason
+ 
+
+ align:start position:0%
+understand analytically for this reason
+even though n may be any positive
+
+ align:start position:0%
+even though n may be any positive
+ 
+
+ align:start position:0%
+even though n may be any positive
+integer whatsoever preferably of course
+
+ align:start position:0%
+integer whatsoever preferably of course
+ 
+
+ align:start position:0%
+integer whatsoever preferably of course
+greater than one otherwise we wouldn't
+
+ align:start position:0%
+greater than one otherwise we wouldn't
+ 
+
+ align:start position:0%
+greater than one otherwise we wouldn't
+have a function of several variables
+
+ align:start position:0%
+have a function of several variables
+ 
+
+ align:start position:0%
+have a function of several variables
+fact that's a defition of a function of
+
+ align:start position:0%
+fact that's a defition of a function of
+ 
+
+ align:start position:0%
+fact that's a defition of a function of
+several variables it's an expression of
+
+ align:start position:0%
+several variables it's an expression of
+ 
+
+ align:start position:0%
+several variables it's an expression of
+this type where n is greater than one
+
+ align:start position:0%
+this type where n is greater than one
+ 
+
+ align:start position:0%
+this type where n is greater than one
+but in general and you'll notice this in
+
+ align:start position:0%
+but in general and you'll notice this in
+ 
+
+ align:start position:0%
+but in general and you'll notice this in
+the text as well we begin with the
+
+ align:start position:0%
+the text as well we begin with the
+ 
+
+ align:start position:0%
+the text as well we begin with the
+special case that n equals 2 because you
+
+ align:start position:0%
+special case that n equals 2 because you
+ 
+
+ align:start position:0%
+special case that n equals 2 because you
+see if n is two we need what two degrees
+
+ align:start position:0%
+see if n is two we need what two degrees
+ 
+
+ align:start position:0%
+see if n is two we need what two degrees
+of freedom to plot the independent
+
+ align:start position:0%
+of freedom to plot the independent
+ 
+
+ align:start position:0%
+of freedom to plot the independent
+variables that would be the XY plane for
+
+ align:start position:0%
+variables that would be the XY plane for
+ 
+
+ align:start position:0%
+variables that would be the XY plane for
+example a third degree of Freedom say
+
+ align:start position:0%
+example a third degree of Freedom say
+ 
+
+ align:start position:0%
+example a third degree of Freedom say
+the z-axis often called The W axis
+
+ align:start position:0%
+the z-axis often called The W axis
+ 
+
+ align:start position:0%
+the z-axis often called The W axis
+because of this symbolism in other it in
+
+ align:start position:0%
+because of this symbolism in other it in
+ 
+
+ align:start position:0%
+because of this symbolism in other it in
+the same way that I could graph a real
+
+ align:start position:0%
+the same way that I could graph a real
+ 
+
+ align:start position:0%
+the same way that I could graph a real
+valued function of a single real
+
+ align:start position:0%
+valued function of a single real
+ 
+
+ align:start position:0%
+valued function of a single real
+variable as a curve in the plane I can
+
+ align:start position:0%
+variable as a curve in the plane I can
+ 
+
+ align:start position:0%
+variable as a curve in the plane I can
+graph a real valued function of two real
+
+ align:start position:0%
+graph a real valued function of two real
+ 
+
+ align:start position:0%
+graph a real valued function of two real
+variables as a surface in
+
+ align:start position:0%
+variables as a surface in
+ 
+
+ align:start position:0%
+variables as a surface in
+three-dimensional space and as a result
+
+ align:start position:0%
+three-dimensional space and as a result
+ 
+
+ align:start position:0%
+three-dimensional space and as a result
+when one is adjusting to new language
+
+ align:start position:0%
+when one is adjusting to new language
+ 
+
+ align:start position:0%
+when one is adjusting to new language
+it's nice to take the case n equals 2
+
+ align:start position:0%
+it's nice to take the case n equals 2
+ 
+
+ align:start position:0%
+it's nice to take the case n equals 2
+simply because you can view things
+
+ align:start position:0%
+simply because you can view things
+ 
+
+ align:start position:0%
+simply because you can view things
+pictorially the danger of course with n
+
+ align:start position:0%
+pictorially the danger of course with n
+ 
+
+ align:start position:0%
+pictorially the danger of course with n
+equals 2 is you get so used to the
+
+ align:start position:0%
+equals 2 is you get so used to the
+ 
+
+ align:start position:0%
+equals 2 is you get so used to the
+picture that after a while you forget
+
+ align:start position:0%
+picture that after a while you forget
+ 
+
+ align:start position:0%
+picture that after a while you forget
+that n could have been more than two so
+
+ align:start position:0%
+that n could have been more than two so
+ 
+
+ align:start position:0%
+that n could have been more than two so
+I will try to pay uh homage to both
+
+ align:start position:0%
+I will try to pay uh homage to both
+ 
+
+ align:start position:0%
+I will try to pay uh homage to both
+points of view I will simply mention
+
+ align:start position:0%
+points of view I will simply mention
+ 
+
+ align:start position:0%
+points of view I will simply mention
+here that we will often let N equal 2 to
+
+ align:start position:0%
+here that we will often let N equal 2 to
+ 
+
+ align:start position:0%
+here that we will often let N equal 2 to
+take advantage of geometry when we do
+
+ align:start position:0%
+take advantage of geometry when we do
+ 
+
+ align:start position:0%
+take advantage of geometry when we do
+this the usual notation is to let W
+
+ align:start position:0%
+this the usual notation is to let W
+ 
+
+ align:start position:0%
+this the usual notation is to let W
+equal F of XY where X and Y are
+
+ align:start position:0%
+equal F of XY where X and Y are
+ 
+
+ align:start position:0%
+equal F of XY where X and Y are
+independent and I should mention why
+
+ align:start position:0%
+independent and I should mention why
+ 
+
+ align:start position:0%
+independent and I should mention why
+it's so important to talk about
+
+ align:start position:0%
+it's so important to talk about
+ 
+
+ align:start position:0%
+it's so important to talk about
+independent variables the it'll become
+
+ align:start position:0%
+independent variables the it'll become
+ 
+
+ align:start position:0%
+independent variables the it'll become
+clear in a moment let me just tell you
+
+ align:start position:0%
+clear in a moment let me just tell you
+ 
+
+ align:start position:0%
+clear in a moment let me just tell you
+what independent means and then I'll
+
+ align:start position:0%
+what independent means and then I'll
+ 
+
+ align:start position:0%
+what independent means and then I'll
+show you why it becomes clear in a
+
+ align:start position:0%
+show you why it becomes clear in a
+ 
+
+ align:start position:0%
+show you why it becomes clear in a
+moment to say that X and Y are
+
+ align:start position:0%
+moment to say that X and Y are
+ 
+
+ align:start position:0%
+moment to say that X and Y are
+independent simply means that you can
+
+ align:start position:0%
+independent simply means that you can
+ 
+
+ align:start position:0%
+independent simply means that you can
+choose one of the two variables without
+
+ align:start position:0%
+choose one of the two variables without
+ 
+
+ align:start position:0%
+choose one of the two variables without
+determining the other for example if I
+
+ align:start position:0%
+determining the other for example if I
+ 
+
+ align:start position:0%
+determining the other for example if I
+were to say let y equal 2x then
+
+ align:start position:0%
+were to say let y equal 2x then
+ 
+
+ align:start position:0%
+were to say let y equal 2x then
+certainly Y and X are not independent
+
+ align:start position:0%
+certainly Y and X are not independent
+ 
+
+ align:start position:0%
+certainly Y and X are not independent
+because the choice of X determines the
+
+ align:start position:0%
+because the choice of X determines the
+ 
+
+ align:start position:0%
+because the choice of X determines the
+choice of Y but to say that X and Y are
+
+ align:start position:0%
+choice of Y but to say that X and Y are
+ 
+
+ align:start position:0%
+choice of Y but to say that X and Y are
+independent and that's what we mean by
+
+ align:start position:0%
+independent and that's what we mean by
+ 
+
+ align:start position:0%
+independent and that's what we mean by
+two degrees of freedom is I can take any
+
+ align:start position:0%
+two degrees of freedom is I can take any
+ 
+
+ align:start position:0%
+two degrees of freedom is I can take any
+value of x that I want and not be
+
+ align:start position:0%
+value of x that I want and not be
+ 
+
+ align:start position:0%
+value of x that I want and not be
+impeded as to the choice of Y that I
+
+ align:start position:0%
+impeded as to the choice of Y that I
+ 
+
+ align:start position:0%
+impeded as to the choice of Y that I
+want and that's why we say the domain is
+
+ align:start position:0%
+want and that's why we say the domain is
+ 
+
+ align:start position:0%
+want and that's why we say the domain is
+the XY plane I have two degrees of
+
+ align:start position:0%
+the XY plane I have two degrees of
+ 
+
+ align:start position:0%
+the XY plane I have two degrees of
+freedom I can roam anywhere through the
+
+ align:start position:0%
+freedom I can roam anywhere through the
+ 
+
+ align:start position:0%
+freedom I can roam anywhere through the
+plane this way but the reason that we
+
+ align:start position:0%
+plane this way but the reason that we
+ 
+
+ align:start position:0%
+plane this way but the reason that we
+want this is as follows and this is
+
+ align:start position:0%
+want this is as follows and this is
+ 
+
+ align:start position:0%
+want this is as follows and this is
+where the the traditional mathematics
+
+ align:start position:0%
+where the the traditional mathematics
+ 
+
+ align:start position:0%
+where the the traditional mathematics
+was every bit as logical as the modern
+
+ align:start position:0%
+was every bit as logical as the modern
+ 
+
+ align:start position:0%
+was every bit as logical as the modern
+mathematics let's keep in mind that
+
+ align:start position:0%
+mathematics let's keep in mind that
+ 
+
+ align:start position:0%
+mathematics let's keep in mind that
+logic is the art of taking known
+
+ align:start position:0%
+logic is the art of taking known
+ 
+
+ align:start position:0%
+logic is the art of taking known
+situations that we know how to handle
+
+ align:start position:0%
+situations that we know how to handle
+ 
+
+ align:start position:0%
+situations that we know how to handle
+you see and reducing unfamiliar
+
+ align:start position:0%
+you see and reducing unfamiliar
+ 
+
+ align:start position:0%
+you see and reducing unfamiliar
+situations to these more familiar
+
+ align:start position:0%
+situations to these more familiar
+ 
+
+ align:start position:0%
+situations to these more familiar
+situations the point is that that even
+
+ align:start position:0%
+situations the point is that that even
+ 
+
+ align:start position:0%
+situations the point is that that even
+in traditional mathematics one knew how
+
+ align:start position:0%
+in traditional mathematics one knew how
+ 
+
+ align:start position:0%
+in traditional mathematics one knew how
+to handle the calculus of a single real
+
+ align:start position:0%
+to handle the calculus of a single real
+ 
+
+ align:start position:0%
+to handle the calculus of a single real
+variable so what one said was this given
+
+ align:start position:0%
+variable so what one said was this given
+ 
+
+ align:start position:0%
+variable so what one said was this given
+that W is a function of both X and Y
+
+ align:start position:0%
+that W is a function of both X and Y
+ 
+
+ align:start position:0%
+that W is a function of both X and Y
+let's hold y fixed for example and let X
+
+ align:start position:0%
+let's hold y fixed for example and let X
+ 
+
+ align:start position:0%
+let's hold y fixed for example and let X
+vary you see if I fix Y at some
+
+ align:start position:0%
+vary you see if I fix Y at some
+ 
+
+ align:start position:0%
+vary you see if I fix Y at some
+particular value and let X vary once
+
+ align:start position:0%
+particular value and let X vary once
+ 
+
+ align:start position:0%
+particular value and let X vary once
+I've made that fixed choice of Y I have
+
+ align:start position:0%
+I've made that fixed choice of Y I have
+ 
+
+ align:start position:0%
+I've made that fixed choice of Y I have
+W as a function of X alone and as long
+
+ align:start position:0%
+W as a function of X alone and as long
+ 
+
+ align:start position:0%
+W as a function of X alone and as long
+as W is a function of X alone I already
+
+ align:start position:0%
+as W is a function of X alone I already
+ 
+
+ align:start position:0%
+as W is a function of X alone I already
+know how to take the derivative of w
+
+ align:start position:0%
+know how to take the derivative of w
+ 
+
+ align:start position:0%
+know how to take the derivative of w
+with respect to x and by the way there's
+
+ align:start position:0%
+with respect to x and by the way there's
+ 
+
+ align:start position:0%
+with respect to x and by the way there's
+no favoritism here between X and Y in a
+
+ align:start position:0%
+no favoritism here between X and Y in a
+ 
+
+ align:start position:0%
+no favoritism here between X and Y in a
+similar way if I hold x constant and let
+
+ align:start position:0%
+similar way if I hold x constant and let
+ 
+
+ align:start position:0%
+similar way if I hold x constant and let
+y vary then W is a function of Y alone
+
+ align:start position:0%
+y vary then W is a function of Y alone
+ 
+
+ align:start position:0%
+y vary then W is a function of Y alone
+and I can then find the derivative of w
+
+ align:start position:0%
+and I can then find the derivative of w
+ 
+
+ align:start position:0%
+and I can then find the derivative of w
+with respect to Y and these things were
+
+ align:start position:0%
+with respect to Y and these things were
+ 
+
+ align:start position:0%
+with respect to Y and these things were
+called partial derivatives you see
+
+ align:start position:0%
+called partial derivatives you see
+ 
+
+ align:start position:0%
+called partial derivatives you see
+because it involved holding what all but
+
+ align:start position:0%
+because it involved holding what all but
+ 
+
+ align:start position:0%
+because it involved holding what all but
+one of the variables constant we'll go
+
+ align:start position:0%
+one of the variables constant we'll go
+ 
+
+ align:start position:0%
+one of the variables constant we'll go
+into that in more detail as we go along
+
+ align:start position:0%
+into that in more detail as we go along
+ 
+
+ align:start position:0%
+into that in more detail as we go along
+but the whole idea is what by choosing
+
+ align:start position:0%
+but the whole idea is what by choosing
+ 
+
+ align:start position:0%
+but the whole idea is what by choosing
+the VAR to be independent we can hold
+
+ align:start position:0%
+the VAR to be independent we can hold
+ 
+
+ align:start position:0%
+the VAR to be independent we can hold
+all of them but one at a time constant
+
+ align:start position:0%
+all of them but one at a time constant
+ 
+
+ align:start position:0%
+all of them but one at a time constant
+and as long as we're doing that the
+
+ align:start position:0%
+and as long as we're doing that the
+ 
+
+ align:start position:0%
+and as long as we're doing that the
+resulting function is a function of a
+
+ align:start position:0%
+resulting function is a function of a
+ 
+
+ align:start position:0%
+resulting function is a function of a
+single real variable and this reduces us
+
+ align:start position:0%
+single real variable and this reduces us
+ 
+
+ align:start position:0%
+single real variable and this reduces us
+to part one of our course so at any rate
+
+ align:start position:0%
+to part one of our course so at any rate
+ 
+
+ align:start position:0%
+to part one of our course so at any rate
+what we're saying is fix Y at some
+
+ align:start position:0%
+what we're saying is fix Y at some
+ 
+
+ align:start position:0%
+what we're saying is fix Y at some
+constant value say yal y Sub 0 and we
+
+ align:start position:0%
+constant value say yal y Sub 0 and we
+ 
+
+ align:start position:0%
+constant value say yal y Sub 0 and we
+then let X vary as an ordinary
+
+ align:start position:0%
+then let X vary as an ordinary
+ 
+
+ align:start position:0%
+then let X vary as an ordinary
+one-dimensional calculus between x0
+
+ align:start position:0%
+one-dimensional calculus between x0
+ 
+
+ align:start position:0%
+one-dimensional calculus between x0
+minus the magnitude of Delta X and x0
+
+ align:start position:0%
+minus the magnitude of Delta X and x0
+ 
+
+ align:start position:0%
+minus the magnitude of Delta X and x0
+plus the magnitude of Delta X in other
+
+ align:start position:0%
+plus the magnitude of Delta X in other
+ 
+
+ align:start position:0%
+plus the magnitude of Delta X in other
+words we mark off an interval of
+
+ align:start position:0%
+words we mark off an interval of
+ 
+
+ align:start position:0%
+words we mark off an interval of
+magnitude Delta X on either side of x0
+
+ align:start position:0%
+magnitude Delta X on either side of x0
+ 
+
+ align:start position:0%
+magnitude Delta X on either side of x0
+and let X be any place in here then what
+
+ align:start position:0%
+and let X be any place in here then what
+ 
+
+ align:start position:0%
+and let X be any place in here then what
+we do is remembering that y0 is a
+
+ align:start position:0%
+we do is remembering that y0 is a
+ 
+
+ align:start position:0%
+we do is remembering that y0 is a
+constant and that this function no
+
+ align:start position:0%
+constant and that this function no
+ 
+
+ align:start position:0%
+constant and that this function no
+matter how complicated it looks like is
+
+ align:start position:0%
+matter how complicated it looks like is
+ 
+
+ align:start position:0%
+matter how complicated it looks like is
+a function of just Delta X alone we
+
+ align:start position:0%
+a function of just Delta X alone we
+ 
+
+ align:start position:0%
+a function of just Delta X alone we
+mimic the definition of an ordinary
+
+ align:start position:0%
+mimic the definition of an ordinary
+ 
+
+ align:start position:0%
+mimic the definition of an ordinary
+derivative in other words we take the
+
+ align:start position:0%
+derivative in other words we take the
+ 
+
+ align:start position:0%
+derivative in other words we take the
+limit as Delta X approaches 0 of f of x0
+
+ align:start position:0%
+limit as Delta X approaches 0 of f of x0
+ 
+
+ align:start position:0%
+limit as Delta X approaches 0 of f of x0
++ Delta X comma y0 minus F of x0 comma
+
+ align:start position:0%
++ Delta X comma y0 minus F of x0 comma
+ 
+
+ align:start position:0%
++ Delta X comma y0 minus F of x0 comma
+y0 and divide that by Delta X in other
+
+ align:start position:0%
+y0 and divide that by Delta X in other
+ 
+
+ align:start position:0%
+y0 and divide that by Delta X in other
+words with y0 being treated as a
+
+ align:start position:0%
+words with y0 being treated as a
+ 
+
+ align:start position:0%
+words with y0 being treated as a
+constant notice that essentially this is
+
+ align:start position:0%
+constant notice that essentially this is
+ 
+
+ align:start position:0%
+constant notice that essentially this is
+the change in f as X varies between x0
+
+ align:start position:0%
+the change in f as X varies between x0
+ 
+
+ align:start position:0%
+the change in f as X varies between x0
+and x0 plus Delta x divided by the
+
+ align:start position:0%
+and x0 plus Delta x divided by the
+ 
+
+ align:start position:0%
+and x0 plus Delta x divided by the
+change in X in other words it's the
+
+ align:start position:0%
+change in X in other words it's the
+ 
+
+ align:start position:0%
+change in X in other words it's the
+limit of an average rate of change of f
+
+ align:start position:0%
+limit of an average rate of change of f
+ 
+
+ align:start position:0%
+limit of an average rate of change of f
+ofx with respect to X for a fixed value
+
+ align:start position:0%
+ofx with respect to X for a fixed value
+ 
+
+ align:start position:0%
+ofx with respect to X for a fixed value
+of y0 and to indicate that we write this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analogously I would say to how we write
+
+ align:start position:0%
+analogously I would say to how we write
+ 
+
+ align:start position:0%
+analogously I would say to how we write
+functions of a single real variable in
+
+ align:start position:0%
+functions of a single real variable in
+ 
+
+ align:start position:0%
+functions of a single real variable in
+other words we write F Prime instead of
+
+ align:start position:0%
+other words we write F Prime instead of
+ 
+
+ align:start position:0%
+other words we write F Prime instead of
+f Prime we indicate let me put this way
+
+ align:start position:0%
+f Prime we indicate let me put this way
+ 
+
+ align:start position:0%
+f Prime we indicate let me put this way
+when you had only one real variable was
+
+ align:start position:0%
+when you had only one real variable was
+ 
+
+ align:start position:0%
+when you had only one real variable was
+there any danger of misinterpreting the
+
+ align:start position:0%
+there any danger of misinterpreting the
+ 
+
+ align:start position:0%
+there any danger of misinterpreting the
+prime after all with only one
+
+ align:start position:0%
+prime after all with only one
+ 
+
+ align:start position:0%
+prime after all with only one
+independent variable when you said
+
+ align:start position:0%
+independent variable when you said
+ 
+
+ align:start position:0%
+independent variable when you said
+derivative it was obvious what variable
+
+ align:start position:0%
+derivative it was obvious what variable
+ 
+
+ align:start position:0%
+derivative it was obvious what variable
+you were differentiating with respect to
+
+ align:start position:0%
+you were differentiating with respect to
+ 
+
+ align:start position:0%
+you were differentiating with respect to
+here there are two variables X and Y so
+
+ align:start position:0%
+here there are two variables X and Y so
+ 
+
+ align:start position:0%
+here there are two variables X and Y so
+instead of the Prime as a subscript we
+
+ align:start position:0%
+instead of the Prime as a subscript we
+ 
+
+ align:start position:0%
+instead of the Prime as a subscript we
+write down the variable with respect to
+
+ align:start position:0%
+write down the variable with respect to
+ 
+
+ align:start position:0%
+write down the variable with respect to
+which we're taking the derivative and
+
+ align:start position:0%
+which we're taking the derivative and
+ 
+
+ align:start position:0%
+which we're taking the derivative and
+then we put in the point at which the
+
+ align:start position:0%
+then we put in the point at which the
+ 
+
+ align:start position:0%
+then we put in the point at which the
+derivative is being evaluated you see in
+
+ align:start position:0%
+derivative is being evaluated you see in
+ 
+
+ align:start position:0%
+derivative is being evaluated you see in
+a similar way to have defined F suby of
+
+ align:start position:0%
+a similar way to have defined F suby of
+ 
+
+ align:start position:0%
+a similar way to have defined F suby of
+x0 y0 that would have meant what we hold
+
+ align:start position:0%
+x0 y0 that would have meant what we hold
+ 
+
+ align:start position:0%
+x0 y0 that would have meant what we hold
+x constant at some value
+
+ align:start position:0%
+x constant at some value
+ 
+
+ align:start position:0%
+x constant at some value
+x0 let y vary between y0 and y0 + Delta
+
+ align:start position:0%
+x0 let y vary between y0 and y0 + Delta
+ 
+
+ align:start position:0%
+x0 let y vary between y0 and y0 + Delta
+Y and take the limit of this expression
+
+ align:start position:0%
+Y and take the limit of this expression
+ 
+
+ align:start position:0%
+Y and take the limit of this expression
+F ofx 0a y0 + Delta Yus F of x0 y0 over
+
+ align:start position:0%
+F ofx 0a y0 + Delta Yus F of x0 y0 over
+ 
+
+ align:start position:0%
+F ofx 0a y0 + Delta Yus F of x0 y0 over
+Delta y take the limit of that
+
+ align:start position:0%
+Delta y take the limit of that
+ 
+
+ align:start position:0%
+Delta y take the limit of that
+expression as Delta y approaches zero
+
+ align:start position:0%
+expression as Delta y approaches zero
+ 
+
+ align:start position:0%
+expression as Delta y approaches zero
+you see and we're going to show this
+
+ align:start position:0%
+you see and we're going to show this
+ 
+
+ align:start position:0%
+you see and we're going to show this
+pictorially in a while after all that's
+
+ align:start position:0%
+pictorially in a while after all that's
+ 
+
+ align:start position:0%
+pictorially in a while after all that's
+why we chose the case n equals 2 was so
+
+ align:start position:0%
+why we chose the case n equals 2 was so
+ 
+
+ align:start position:0%
+why we chose the case n equals 2 was so
+that we could eventually illustrate this
+
+ align:start position:0%
+that we could eventually illustrate this
+ 
+
+ align:start position:0%
+that we could eventually illustrate this
+thing pictorially but for the time being
+
+ align:start position:0%
+thing pictorially but for the time being
+ 
+
+ align:start position:0%
+thing pictorially but for the time being
+I prefer not to introduce the picture
+
+ align:start position:0%
+I prefer not to introduce the picture
+ 
+
+ align:start position:0%
+I prefer not to introduce the picture
+because I want you to see that even in
+
+ align:start position:0%
+because I want you to see that even in
+ 
+
+ align:start position:0%
+because I want you to see that even in
+the case where my input consists of an
+
+ align:start position:0%
+the case where my input consists of an
+ 
+
+ align:start position:0%
+the case where my input consists of an
+npple where n is greater than two or
+
+ align:start position:0%
+npple where n is greater than two or
+ 
+
+ align:start position:0%
+npple where n is greater than two or
+three or four whatever you want that do
+
+ align:start position:0%
+three or four whatever you want that do
+ 
+
+ align:start position:0%
+three or four whatever you want that do
+this thing still make sense in other
+
+ align:start position:0%
+this thing still make sense in other
+ 
+
+ align:start position:0%
+this thing still make sense in other
+words in general suppose W is a function
+
+ align:start position:0%
+words in general suppose W is a function
+ 
+
+ align:start position:0%
+words in general suppose W is a function
+of the N independent variables x sub 1
+
+ align:start position:0%
+of the N independent variables x sub 1
+ 
+
+ align:start position:0%
+of the N independent variables x sub 1
+up to X subn and I want to compute f of
+
+ align:start position:0%
+up to X subn and I want to compute f of
+ 
+
+ align:start position:0%
+up to X subn and I want to compute f of
+x sub1 at the point X1 = A1 Etc xn = a n
+
+ align:start position:0%
+x sub1 at the point X1 = A1 Etc xn = a n
+ 
+
+ align:start position:0%
+x sub1 at the point X1 = A1 Etc xn = a n
+by definition what I do is I hold A2 up
+
+ align:start position:0%
+by definition what I do is I hold A2 up
+ 
+
+ align:start position:0%
+by definition what I do is I hold A2 up
+to a n
+
+ align:start position:0%
+to a n
+ 
+
+ align:start position:0%
+to a n
+constant I let X1 vary from A1 to A1 +
+
+ align:start position:0%
+constant I let X1 vary from A1 to A1 +
+ 
+
+ align:start position:0%
+constant I let X1 vary from A1 to A1 +
+Delta x i compute what f F of A1 + Delta
+
+ align:start position:0%
+Delta x i compute what f F of A1 + Delta
+ 
+
+ align:start position:0%
+Delta x i compute what f F of A1 + Delta
+X comma A2 Etc comma a n minus F of A1
+
+ align:start position:0%
+X comma A2 Etc comma a n minus F of A1
+ 
+
+ align:start position:0%
+X comma A2 Etc comma a n minus F of A1
+up to a n noticing that that numerator
+
+ align:start position:0%
+up to a n noticing that that numerator
+ 
+
+ align:start position:0%
+up to a n noticing that that numerator
+is simply the change in
+
+ align:start position:0%
+is simply the change in
+ 
+
+ align:start position:0%
+is simply the change in
+f as X1 varies from A1 to A1 Plus Delta
+
+ align:start position:0%
+f as X1 varies from A1 to A1 Plus Delta
+ 
+
+ align:start position:0%
+f as X1 varies from A1 to A1 Plus Delta
+X1 while all the other variables are
+
+ align:start position:0%
+X1 while all the other variables are
+ 
+
+ align:start position:0%
+X1 while all the other variables are
+being held constant which of course I
+
+ align:start position:0%
+being held constant which of course I
+ 
+
+ align:start position:0%
+being held constant which of course I
+can do if the variables are independent
+
+ align:start position:0%
+can do if the variables are independent
+ 
+
+ align:start position:0%
+can do if the variables are independent
+I then divide that by Delta X1 that's
+
+ align:start position:0%
+I then divide that by Delta X1 that's
+ 
+
+ align:start position:0%
+I then divide that by Delta X1 that's
+the average rate of change then I take
+
+ align:start position:0%
+the average rate of change then I take
+ 
+
+ align:start position:0%
+the average rate of change then I take
+the limit as Delta X1 approaches zero
+
+ align:start position:0%
+the limit as Delta X1 approaches zero
+ 
+
+ align:start position:0%
+the limit as Delta X1 approaches zero
+and this I can do for any number of
+
+ align:start position:0%
+and this I can do for any number of
+ 
+
+ align:start position:0%
+and this I can do for any number of
+variables provided that they're
+
+ align:start position:0%
+variables provided that they're
+ 
+
+ align:start position:0%
+variables provided that they're
+independent keep that in mind if x subn
+
+ align:start position:0%
+independent keep that in mind if x subn
+ 
+
+ align:start position:0%
+independent keep that in mind if x subn
+could be expressed in terms of the
+
+ align:start position:0%
+could be expressed in terms of the
+ 
+
+ align:start position:0%
+could be expressed in terms of the
+remaining X's how can I hold a subn
+
+ align:start position:0%
+remaining X's how can I hold a subn
+ 
+
+ align:start position:0%
+remaining X's how can I hold a subn
+constant while or how can I vary a subn
+
+ align:start position:0%
+constant while or how can I vary a subn
+ 
+
+ align:start position:0%
+constant while or how can I vary a subn
+while I hold the other ones constant in
+
+ align:start position:0%
+while I hold the other ones constant in
+ 
+
+ align:start position:0%
+while I hold the other ones constant in
+other words if the a ends if if one of
+
+ align:start position:0%
+other words if the a ends if if one of
+ 
+
+ align:start position:0%
+other words if the a ends if if one of
+the variables depends on the others they
+
+ align:start position:0%
+the variables depends on the others they
+ 
+
+ align:start position:0%
+the variables depends on the others they
+are related in terms of their motion
+
+ align:start position:0%
+are related in terms of their motion
+ 
+
+ align:start position:0%
+are related in terms of their motion
+keep in mind here I just chose Delta X1
+
+ align:start position:0%
+keep in mind here I just chose Delta X1
+ 
+
+ align:start position:0%
+keep in mind here I just chose Delta X1
+analogous definitions held for f subx
+
+ align:start position:0%
+analogous definitions held for f subx
+ 
+
+ align:start position:0%
+analogous definitions held for f subx
+sub 2 FX sub3 Etc okay I think again
+
+ align:start position:0%
+sub 2 FX sub3 Etc okay I think again
+ 
+
+ align:start position:0%
+sub 2 FX sub3 Etc okay I think again
+that once you see a few examples the
+
+ align:start position:0%
+that once you see a few examples the
+ 
+
+ align:start position:0%
+that once you see a few examples the
+mystery vanishes what this thing says in
+
+ align:start position:0%
+mystery vanishes what this thing says in
+ 
+
+ align:start position:0%
+mystery vanishes what this thing says in
+plain English is that when you have a
+
+ align:start position:0%
+plain English is that when you have a
+ 
+
+ align:start position:0%
+plain English is that when you have a
+function of several variables and you
+
+ align:start position:0%
+function of several variables and you
+ 
+
+ align:start position:0%
+function of several variables and you
+want to take the derivative with respect
+
+ align:start position:0%
+want to take the derivative with respect
+ 
+
+ align:start position:0%
+want to take the derivative with respect
+to one of those variables pretend that
+
+ align:start position:0%
+to one of those variables pretend that
+ 
+
+ align:start position:0%
+to one of those variables pretend that
+every one of the other variables was
+
+ align:start position:0%
+every one of the other variables was
+ 
+
+ align:start position:0%
+every one of the other variables was
+being held constant let me give you an
+
+ align:start position:0%
+being held constant let me give you an
+ 
+
+ align:start position:0%
+being held constant let me give you an
+example let W be F of X1 X2 X3 where
+
+ align:start position:0%
+example let W be F of X1 X2 X3 where
+ 
+
+ align:start position:0%
+example let W be F of X1 X2 X3 where
+where the specific F that I have in mind
+
+ align:start position:0%
+where the specific F that I have in mind
+ 
+
+ align:start position:0%
+where the specific F that I have in mind
+is obtained as follows it's X1 * X2 * X3
+
+ align:start position:0%
+is obtained as follows it's X1 * X2 * X3
+ 
+
+ align:start position:0%
+is obtained as follows it's X1 * X2 * X3
+plus e to the X1 power now to take the
+
+ align:start position:0%
+plus e to the X1 power now to take the
+ 
+
+ align:start position:0%
+plus e to the X1 power now to take the
+derivative of this with respect to X1
+
+ align:start position:0%
+derivative of this with respect to X1
+ 
+
+ align:start position:0%
+derivative of this with respect to X1
+all this says is treat X2 and X3 as if
+
+ align:start position:0%
+all this says is treat X2 and X3 as if
+ 
+
+ align:start position:0%
+all this says is treat X2 and X3 as if
+they were constants well look at if I
+
+ align:start position:0%
+they were constants well look at if I
+ 
+
+ align:start position:0%
+they were constants well look at if I
+treat X2 and X3 as if they were
+
+ align:start position:0%
+treat X2 and X3 as if they were
+ 
+
+ align:start position:0%
+treat X2 and X3 as if they were
+constants if I differentiate this with
+
+ align:start position:0%
+constants if I differentiate this with
+ 
+
+ align:start position:0%
+constants if I differentiate this with
+respect to X1 all I have left is what
+
+ align:start position:0%
+respect to X1 all I have left is what
+ 
+
+ align:start position:0%
+respect to X1 all I have left is what
+this particular constant which is X2 *
+
+ align:start position:0%
+this particular constant which is X2 *
+ 
+
+ align:start position:0%
+this particular constant which is X2 *
+X3 and a derivative of e the X1 is with
+
+ align:start position:0%
+X3 and a derivative of e the X1 is with
+ 
+
+ align:start position:0%
+X3 and a derivative of e the X1 is with
+respect to X1 is e to the X1 therefore F
+
+ align:start position:0%
+respect to X1 is e to the X1 therefore F
+ 
+
+ align:start position:0%
+respect to X1 is e to the X1 therefore F
+subx1 in this case is X2 X3 plus e to
+
+ align:start position:0%
+subx1 in this case is X2 X3 plus e to
+ 
+
+ align:start position:0%
+subx1 in this case is X2 X3 plus e to
+the X1 in particular if I evaluate F
+
+ align:start position:0%
+the X1 in particular if I evaluate F
+ 
+
+ align:start position:0%
+the X1 in particular if I evaluate F
+subx sub1 at the 3le 1 2 3 namely I
+
+ align:start position:0%
+subx sub1 at the 3le 1 2 3 namely I
+ 
+
+ align:start position:0%
+subx sub1 at the 3le 1 2 3 namely I
+replace X1 by 1 X2 by 2 X3 by 3 I obtain
+
+ align:start position:0%
+replace X1 by 1 X2 by 2 X3 by 3 I obtain
+ 
+
+ align:start position:0%
+replace X1 by 1 X2 by 2 X3 by 3 I obtain
+what 2 * 3 + e to the first Power in
+
+ align:start position:0%
+what 2 * 3 + e to the first Power in
+ 
+
+ align:start position:0%
+what 2 * 3 + e to the first Power in
+other words this is just a number 6 + 8
+
+ align:start position:0%
+other words this is just a number 6 + 8
+ 
+
+ align:start position:0%
+other words this is just a number 6 + 8
+on the other hand if I had decided to
+
+ align:start position:0%
+on the other hand if I had decided to
+ 
+
+ align:start position:0%
+on the other hand if I had decided to
+differentiate this with respect to X2 I
+
+ align:start position:0%
+differentiate this with respect to X2 I
+ 
+
+ align:start position:0%
+differentiate this with respect to X2 I
+would have treated X1 and X3 as
+
+ align:start position:0%
+would have treated X1 and X3 as
+ 
+
+ align:start position:0%
+would have treated X1 and X3 as
+constants with X1 and X3 as constants
+
+ align:start position:0%
+constants with X1 and X3 as constants
+ 
+
+ align:start position:0%
+constants with X1 and X3 as constants
+the derivative of this with respect to
+
+ align:start position:0%
+the derivative of this with respect to
+ 
+
+ align:start position:0%
+the derivative of this with respect to
+X2 is just X1
+
+ align:start position:0%
+X2 is just X1
+ 
+
+ align:start position:0%
+X2 is just X1
+X3 treating X1 as a constant the
+
+ align:start position:0%
+X3 treating X1 as a constant the
+ 
+
+ align:start position:0%
+X3 treating X1 as a constant the
+derivative of e to the X1 with respect
+
+ align:start position:0%
+derivative of e to the X1 with respect
+ 
+
+ align:start position:0%
+derivative of e to the X1 with respect
+to the variable X3 is zero because the
+
+ align:start position:0%
+to the variable X3 is zero because the
+ 
+
+ align:start position:0%
+to the variable X3 is zero because the
+derivative of any constant is zero
+
+ align:start position:0%
+derivative of any constant is zero
+ 
+
+ align:start position:0%
+derivative of any constant is zero
+notice that this is not really a
+
+ align:start position:0%
+notice that this is not really a
+ 
+
+ align:start position:0%
+notice that this is not really a
+constant it's a constant once I fixed X1
+
+ align:start position:0%
+constant it's a constant once I fixed X1
+ 
+
+ align:start position:0%
+constant it's a constant once I fixed X1
+at a particular value which is what this
+
+ align:start position:0%
+at a particular value which is what this
+ 
+
+ align:start position:0%
+at a particular value which is what this
+particular definition
+
+ align:start position:0%
+particular definition
+ 
+
+ align:start position:0%
+particular definition
+says in particular F subx sub 2 of 1 2 3
+
+ align:start position:0%
+says in particular F subx sub 2 of 1 2 3
+ 
+
+ align:start position:0%
+says in particular F subx sub 2 of 1 2 3
+is 1 * 3 or three I should also mention
+
+ align:start position:0%
+is 1 * 3 or three I should also mention
+ 
+
+ align:start position:0%
+is 1 * 3 or three I should also mention
+that sometimes instead of writing F ofx
+
+ align:start position:0%
+that sometimes instead of writing F ofx
+ 
+
+ align:start position:0%
+that sometimes instead of writing F ofx
+sub one we write something that looks
+
+ align:start position:0%
+sub one we write something that looks
+ 
+
+ align:start position:0%
+sub one we write something that looks
+like the regular derivative only we make
+
+ align:start position:0%
+like the regular derivative only we make
+ 
+
+ align:start position:0%
+like the regular derivative only we make
+a funny kind of script D instead of an
+
+ align:start position:0%
+a funny kind of script D instead of an
+ 
+
+ align:start position:0%
+a funny kind of script D instead of an
+ordinary D this is read the partial
+
+ align:start position:0%
+ordinary D this is read the partial
+ 
+
+ align:start position:0%
+ordinary D this is read the partial
+derivative of w with respect to X1 and
+
+ align:start position:0%
+derivative of w with respect to X1 and
+ 
+
+ align:start position:0%
+derivative of w with respect to X1 and
+the relationship between these two
+
+ align:start position:0%
+the relationship between these two
+ 
+
+ align:start position:0%
+the relationship between these two
+notations is rather similar to the
+
+ align:start position:0%
+notations is rather similar to the
+ 
+
+ align:start position:0%
+notations is rather similar to the
+relationship that exists between the
+
+ align:start position:0%
+relationship that exists between the
+ 
+
+ align:start position:0%
+relationship that exists between the
+notations Dy DX and frime of X at any
+
+ align:start position:0%
+notations Dy DX and frime of X at any
+ 
+
+ align:start position:0%
+notations Dy DX and frime of X at any
+rate if we have the N independent
+
+ align:start position:0%
+rate if we have the N independent
+ 
+
+ align:start position:0%
+rate if we have the N independent
+variables X1 up to xn and F is a
+
+ align:start position:0%
+variables X1 up to xn and F is a
+ 
+
+ align:start position:0%
+variables X1 up to xn and F is a
+function of those variables F subx sub1
+
+ align:start position:0%
+function of those variables F subx sub1
+ 
+
+ align:start position:0%
+function of those variables F subx sub1
+Etc f subx subn are called the partial
+
+ align:start position:0%
+Etc f subx subn are called the partial
+ 
+
+ align:start position:0%
+Etc f subx subn are called the partial
+derivatives of f with respect to X1 up
+
+ align:start position:0%
+derivatives of f with respect to X1 up
+ 
+
+ align:start position:0%
+derivatives of f with respect to X1 up
+to xn respectively in other words this
+
+ align:start position:0%
+to xn respectively in other words this
+ 
+
+ align:start position:0%
+to xn respectively in other words this
+means what the partial derivative of
+
+ align:start position:0%
+means what the partial derivative of
+ 
+
+ align:start position:0%
+means what the partial derivative of
+with respect to X1 that means what take
+
+ align:start position:0%
+with respect to X1 that means what take
+ 
+
+ align:start position:0%
+with respect to X1 that means what take
+the ordinary derivative as if X1 were
+
+ align:start position:0%
+the ordinary derivative as if X1 were
+ 
+
+ align:start position:0%
+the ordinary derivative as if X1 were
+the only variable this is the partial of
+
+ align:start position:0%
+the only variable this is the partial of
+ 
+
+ align:start position:0%
+the only variable this is the partial of
+f with respect to X subn that means take
+
+ align:start position:0%
+f with respect to X subn that means take
+ 
+
+ align:start position:0%
+f with respect to X subn that means take
+the ordinary derivative of f as if x
+
+ align:start position:0%
+the ordinary derivative of f as if x
+ 
+
+ align:start position:0%
+the ordinary derivative of f as if x
+subn were the only variable and you can
+
+ align:start position:0%
+subn were the only variable and you can
+ 
+
+ align:start position:0%
+subn were the only variable and you can
+always do this provided that your
+
+ align:start position:0%
+always do this provided that your
+ 
+
+ align:start position:0%
+always do this provided that your
+variables are
+
+ align:start position:0%
+variables are
+ 
+
+ align:start position:0%
+variables are
+independent because our definition so
+
+ align:start position:0%
+independent because our definition so
+ 
+
+ align:start position:0%
+independent because our definition so
+closely parallel the structure for what
+
+ align:start position:0%
+closely parallel the structure for what
+ 
+
+ align:start position:0%
+closely parallel the structure for what
+happened in the case of one independent
+
+ align:start position:0%
+happened in the case of one independent
+ 
+
+ align:start position:0%
+happened in the case of one independent
+variable including the limit theorems
+
+ align:start position:0%
+variable including the limit theorems
+ 
+
+ align:start position:0%
+variable including the limit theorems
+the distance formulas and what have you
+
+ align:start position:0%
+the distance formulas and what have you
+ 
+
+ align:start position:0%
+the distance formulas and what have you
+it turns out that the usual derivative
+
+ align:start position:0%
+it turns out that the usual derivative
+ 
+
+ align:start position:0%
+it turns out that the usual derivative
+properties still hold for example if W
+
+ align:start position:0%
+properties still hold for example if W
+ 
+
+ align:start position:0%
+properties still hold for example if W
+happens to be the function of the two
+
+ align:start position:0%
+happens to be the function of the two
+ 
+
+ align:start position:0%
+happens to be the function of the two
+independent variables e to 3x + y * sin
+
+ align:start position:0%
+independent variables e to 3x + y * sin
+ 
+
+ align:start position:0%
+independent variables e to 3x + y * sin
+2x - Y and I want to take the derivative
+
+ align:start position:0%
+2x - Y and I want to take the derivative
+ 
+
+ align:start position:0%
+2x - Y and I want to take the derivative
+of w with respect to X meaning
+
+ align:start position:0%
+of w with respect to X meaning
+ 
+
+ align:start position:0%
+of w with respect to X meaning
+differentiate this treating y as a
+
+ align:start position:0%
+differentiate this treating y as a
+ 
+
+ align:start position:0%
+differentiate this treating y as a
+constant notice that treating y as a
+
+ align:start position:0%
+constant notice that treating y as a
+ 
+
+ align:start position:0%
+constant notice that treating y as a
+constant gives me two
+
+ align:start position:0%
+constant gives me two
+ 
+
+ align:start position:0%
+constant gives me two
+functions of what x in other words I my
+
+ align:start position:0%
+functions of what x in other words I my
+ 
+
+ align:start position:0%
+functions of what x in other words I my
+function is a product of two functions
+
+ align:start position:0%
+function is a product of two functions
+ 
+
+ align:start position:0%
+function is a product of two functions
+Each of which depends on X so I use the
+
+ align:start position:0%
+Each of which depends on X so I use the
+ 
+
+ align:start position:0%
+Each of which depends on X so I use the
+ordinary product rule to differentiate
+
+ align:start position:0%
+ordinary product rule to differentiate
+ 
+
+ align:start position:0%
+ordinary product rule to differentiate
+this namely how do I use the product
+
+ align:start position:0%
+this namely how do I use the product
+ 
+
+ align:start position:0%
+this namely how do I use the product
+rule to take the partial of w respect to
+
+ align:start position:0%
+rule to take the partial of w respect to
+ 
+
+ align:start position:0%
+rule to take the partial of w respect to
+X I treat y as a constant and I
+
+ align:start position:0%
+X I treat y as a constant and I
+ 
+
+ align:start position:0%
+X I treat y as a constant and I
+differentiate as if x is the only
+
+ align:start position:0%
+differentiate as if x is the only
+ 
+
+ align:start position:0%
+differentiate as if x is the only
+variable I say what it's the first
+
+ align:start position:0%
+variable I say what it's the first
+ 
+
+ align:start position:0%
+variable I say what it's the first
+Factor e to 3x + y times the derivative
+
+ align:start position:0%
+Factor e to 3x + y times the derivative
+ 
+
+ align:start position:0%
+Factor e to 3x + y times the derivative
+of the second with respect to X treating
+
+ align:start position:0%
+of the second with respect to X treating
+ 
+
+ align:start position:0%
+of the second with respect to X treating
+y as a constant if I treat y as a
+
+ align:start position:0%
+y as a constant if I treat y as a
+ 
+
+ align:start position:0%
+y as a constant if I treat y as a
+constant the derivative of s of 2x - Y
+
+ align:start position:0%
+constant the derivative of s of 2x - Y
+ 
+
+ align:start position:0%
+constant the derivative of s of 2x - Y
+is cosine 2x - y times the derivative of
+
+ align:start position:0%
+is cosine 2x - y times the derivative of
+ 
+
+ align:start position:0%
+is cosine 2x - y times the derivative of
+what's inside with respect to X and
+
+ align:start position:0%
+what's inside with respect to X and
+ 
+
+ align:start position:0%
+what's inside with respect to X and
+that's just
+
+ align:start position:0%
+that's just
+ 
+
+ align:start position:0%
+that's just
+two plus what the second term times the
+
+ align:start position:0%
+two plus what the second term times the
+ 
+
+ align:start position:0%
+two plus what the second term times the
+derivative of the first and the
+
+ align:start position:0%
+derivative of the first and the
+ 
+
+ align:start position:0%
+derivative of the first and the
+derivative of e to 3x + y with respect
+
+ align:start position:0%
+derivative of e to 3x + y with respect
+ 
+
+ align:start position:0%
+derivative of e to 3x + y with respect
+to X treating y as a constant is e to 3x
+
+ align:start position:0%
+to X treating y as a constant is e to 3x
+ 
+
+ align:start position:0%
+to X treating y as a constant is e to 3x
++ y times the derivative of 3x + y with
+
+ align:start position:0%
++ y times the derivative of 3x + y with
+ 
+
+ align:start position:0%
++ y times the derivative of 3x + y with
+respect to X which is just three and so
+
+ align:start position:0%
+respect to X which is just three and so
+ 
+
+ align:start position:0%
+respect to X which is just three and so
+I have the partial of w with respect to
+
+ align:start position:0%
+I have the partial of w with respect to
+ 
+
+ align:start position:0%
+I have the partial of w with respect to
+X in a similar way I could have found
+
+ align:start position:0%
+X in a similar way I could have found
+ 
+
+ align:start position:0%
+X in a similar way I could have found
+the partial of w with respect to Y
+
+ align:start position:0%
+the partial of w with respect to Y
+ 
+
+ align:start position:0%
+the partial of w with respect to Y
+Etc I should now introduce one little
+
+ align:start position:0%
+Etc I should now introduce one little
+ 
+
+ align:start position:0%
+Etc I should now introduce one little
+problem that will bother you maybe even
+
+ align:start position:0%
+problem that will bother you maybe even
+ 
+
+ align:start position:0%
+problem that will bother you maybe even
+after I help you with this in fact I
+
+ align:start position:0%
+after I help you with this in fact I
+ 
+
+ align:start position:0%
+after I help you with this in fact I
+guess what really crushes me is the
+
+ align:start position:0%
+guess what really crushes me is the
+ 
+
+ align:start position:0%
+guess what really crushes me is the
+student who comes up in a live class you
+
+ align:start position:0%
+student who comes up in a live class you
+ 
+
+ align:start position:0%
+student who comes up in a live class you
+know after class and says I understood
+
+ align:start position:0%
+know after class and says I understood
+ 
+
+ align:start position:0%
+know after class and says I understood
+it until I heard you lecture on it I
+
+ align:start position:0%
+it until I heard you lecture on it I
+ 
+
+ align:start position:0%
+it until I heard you lecture on it I
+hope this doesn't cause that problem but
+
+ align:start position:0%
+hope this doesn't cause that problem but
+ 
+
+ align:start position:0%
+hope this doesn't cause that problem but
+the danger is I tell you look it
+
+ align:start position:0%
+the danger is I tell you look it
+ 
+
+ align:start position:0%
+the danger is I tell you look it
+everything that happened for calculus of
+
+ align:start position:0%
+everything that happened for calculus of
+ 
+
+ align:start position:0%
+everything that happened for calculus of
+a single variable happens for calculus
+
+ align:start position:0%
+a single variable happens for calculus
+ 
+
+ align:start position:0%
+a single variable happens for calculus
+of several variables then all of a
+
+ align:start position:0%
+of several variables then all of a
+ 
+
+ align:start position:0%
+of several variables then all of a
+sudden you'll find in our textbook in
+
+ align:start position:0%
+sudden you'll find in our textbook in
+ 
+
+ align:start position:0%
+sudden you'll find in our textbook in
+every textbook just about they'll say
+
+ align:start position:0%
+every textbook just about they'll say
+ 
+
+ align:start position:0%
+every textbook just about they'll say
+things like look at if you take the
+
+ align:start position:0%
+things like look at if you take the
+ 
+
+ align:start position:0%
+things like look at if you take the
+partial of the variable U with respect
+
+ align:start position:0%
+partial of the variable U with respect
+ 
+
+ align:start position:0%
+partial of the variable U with respect
+to X you do not get the reciprocal of
+
+ align:start position:0%
+to X you do not get the reciprocal of
+ 
+
+ align:start position:0%
+to X you do not get the reciprocal of
+the partial of X with respect to you in
+
+ align:start position:0%
+the partial of X with respect to you in
+ 
+
+ align:start position:0%
+the partial of X with respect to you in
+other words remember for one variable
+
+ align:start position:0%
+other words remember for one variable
+ 
+
+ align:start position:0%
+other words remember for one variable
+dydx right was the reciprocal of DX Dy
+
+ align:start position:0%
+dydx right was the reciprocal of DX Dy
+ 
+
+ align:start position:0%
+dydx right was the reciprocal of DX Dy
+they say it's not true in several
+
+ align:start position:0%
+they say it's not true in several
+ 
+
+ align:start position:0%
+they say it's not true in several
+variables I have written in an
+
+ align:start position:0%
+variables I have written in an
+ 
+
+ align:start position:0%
+variables I have written in an
+accentuated question mark here because I
+
+ align:start position:0%
+accentuated question mark here because I
+ 
+
+ align:start position:0%
+accentuated question mark here because I
+want to explain something very important
+
+ align:start position:0%
+want to explain something very important
+ 
+
+ align:start position:0%
+want to explain something very important
+to you you and by the way if you
+
+ align:start position:0%
+to you you and by the way if you
+ 
+
+ align:start position:0%
+to you you and by the way if you
+understand this you're 90% of the way
+
+ align:start position:0%
+understand this you're 90% of the way
+ 
+
+ align:start position:0%
+understand this you're 90% of the way
+home free as far as understanding how
+
+ align:start position:0%
+home free as far as understanding how
+ 
+
+ align:start position:0%
+home free as far as understanding how
+calculus of several variables is used in
+
+ align:start position:0%
+calculus of several variables is used in
+ 
+
+ align:start position:0%
+calculus of several variables is used in
+most important applications let me take
+
+ align:start position:0%
+most important applications let me take
+ 
+
+ align:start position:0%
+most important applications let me take
+a very simple case let U equal x + y and
+
+ align:start position:0%
+a very simple case let U equal x + y and
+ 
+
+ align:start position:0%
+a very simple case let U equal x + y and
+let V equal xus y now obviously if U
+
+ align:start position:0%
+let V equal xus y now obviously if U
+ 
+
+ align:start position:0%
+let V equal xus y now obviously if U
+equal x + y the partial of U respect to
+
+ align:start position:0%
+equal x + y the partial of U respect to
+ 
+
+ align:start position:0%
+equal x + y the partial of U respect to
+X If We Hold y constant which read X is
+
+ align:start position:0%
+X If We Hold y constant which read X is
+ 
+
+ align:start position:0%
+X If We Hold y constant which read X is
+the only variable is one right the
+
+ align:start position:0%
+the only variable is one right the
+ 
+
+ align:start position:0%
+the only variable is one right the
+partial of view respect to X is one on
+
+ align:start position:0%
+partial of view respect to X is one on
+ 
+
+ align:start position:0%
+partial of view respect to X is one on
+the other hand notice that if I add
+
+ align:start position:0%
+the other hand notice that if I add
+ 
+
+ align:start position:0%
+the other hand notice that if I add
+these two equations the Y term drops out
+
+ align:start position:0%
+these two equations the Y term drops out
+ 
+
+ align:start position:0%
+these two equations the Y term drops out
+I get what 2x = U + V divide through by
+
+ align:start position:0%
+I get what 2x = U + V divide through by
+ 
+
+ align:start position:0%
+I get what 2x = U + V divide through by
+2 that says X is equal to 12 U + 12 V
+
+ align:start position:0%
+2 that says X is equal to 12 U + 12 V
+ 
+
+ align:start position:0%
+2 that says X is equal to 12 U + 12 V
+let me now take the partial of X with
+
+ align:start position:0%
+let me now take the partial of X with
+ 
+
+ align:start position:0%
+let me now take the partial of X with
+respect to U holding V constant treating
+
+ align:start position:0%
+respect to U holding V constant treating
+ 
+
+ align:start position:0%
+respect to U holding V constant treating
+U as the only variable it's easy for me
+
+ align:start position:0%
+U as the only variable it's easy for me
+ 
+
+ align:start position:0%
+U as the only variable it's easy for me
+to see that the partial of X with
+
+ align:start position:0%
+to see that the partial of X with
+ 
+
+ align:start position:0%
+to see that the partial of X with
+respect to U is2 and certainly if I now
+
+ align:start position:0%
+respect to U is2 and certainly if I now
+ 
+
+ align:start position:0%
+respect to U is2 and certainly if I now
+compare these two it should be clear
+
+ align:start position:0%
+compare these two it should be clear
+ 
+
+ align:start position:0%
+compare these two it should be clear
+that this is not the reciprocal of this
+
+ align:start position:0%
+that this is not the reciprocal of this
+ 
+
+ align:start position:0%
+that this is not the reciprocal of this
+or vice versa the point that I wanted to
+
+ align:start position:0%
+or vice versa the point that I wanted to
+ 
+
+ align:start position:0%
+or vice versa the point that I wanted to
+mention though was the following that
+
+ align:start position:0%
+mention though was the following that
+ 
+
+ align:start position:0%
+mention though was the following that
+when here we said take the partial of
+
+ align:start position:0%
+when here we said take the partial of
+ 
+
+ align:start position:0%
+when here we said take the partial of
+you with respect to X we were assuming
+
+ align:start position:0%
+you with respect to X we were assuming
+ 
+
+ align:start position:0%
+you with respect to X we were assuming
+that the independent variables were X
+
+ align:start position:0%
+that the independent variables were X
+ 
+
+ align:start position:0%
+that the independent variables were X
+and Y and when we said here take the
+
+ align:start position:0%
+and Y and when we said here take the
+ 
+
+ align:start position:0%
+and Y and when we said here take the
+partial of X with respect to U what did
+
+ align:start position:0%
+partial of X with respect to U what did
+ 
+
+ align:start position:0%
+partial of X with respect to U what did
+we hold constant we held the constant in
+
+ align:start position:0%
+we hold constant we held the constant in
+ 
+
+ align:start position:0%
+we hold constant we held the constant in
+other words I'm not going to keep this
+
+ align:start position:0%
+other words I'm not going to keep this
+ 
+
+ align:start position:0%
+other words I'm not going to keep this
+habit up very long but just for the time
+
+ align:start position:0%
+habit up very long but just for the time
+ 
+
+ align:start position:0%
+habit up very long but just for the time
+being I would like you to get used to
+
+ align:start position:0%
+being I would like you to get used to
+ 
+
+ align:start position:0%
+being I would like you to get used to
+the idea of putting in as a subscript
+
+ align:start position:0%
+the idea of putting in as a subscript
+ 
+
+ align:start position:0%
+the idea of putting in as a subscript
+the variables that are being held
+
+ align:start position:0%
+the variables that are being held
+ 
+
+ align:start position:0%
+the variables that are being held
+constant you see in the textbook when
+
+ align:start position:0%
+constant you see in the textbook when
+ 
+
+ align:start position:0%
+constant you see in the textbook when
+they say this is the case what they
+
+ align:start position:0%
+they say this is the case what they
+ 
+
+ align:start position:0%
+they say this is the case what they
+really mean is if you differentiate U
+
+ align:start position:0%
+really mean is if you differentiate U
+ 
+
+ align:start position:0%
+really mean is if you differentiate U
+with respect to X holding y constant
+
+ align:start position:0%
+with respect to X holding y constant
+ 
+
+ align:start position:0%
+with respect to X holding y constant
+that in general will not be the
+
+ align:start position:0%
+that in general will not be the
+ 
+
+ align:start position:0%
+that in general will not be the
+reciprocal of the derivative of x with
+
+ align:start position:0%
+reciprocal of the derivative of x with
+ 
+
+ align:start position:0%
+reciprocal of the derivative of x with
+respect to U holding V constant so I can
+
+ align:start position:0%
+respect to U holding V constant so I can
+ 
+
+ align:start position:0%
+respect to U holding V constant so I can
+cross out the the question mark now but
+
+ align:start position:0%
+cross out the the question mark now but
+ 
+
+ align:start position:0%
+cross out the the question mark now but
+the point is notice that the variables
+
+ align:start position:0%
+the point is notice that the variables
+ 
+
+ align:start position:0%
+the point is notice that the variables
+that you're holding constant here are
+
+ align:start position:0%
+that you're holding constant here are
+ 
+
+ align:start position:0%
+that you're holding constant here are
+different you see suppose instead I took
+
+ align:start position:0%
+different you see suppose instead I took
+ 
+
+ align:start position:0%
+different you see suppose instead I took
+the partial of X with respect to U
+
+ align:start position:0%
+the partial of X with respect to U
+ 
+
+ align:start position:0%
+the partial of X with respect to U
+holding y constant in other words
+
+ align:start position:0%
+holding y constant in other words
+ 
+
+ align:start position:0%
+holding y constant in other words
+suppose I solve for x in terms of U and
+
+ align:start position:0%
+suppose I solve for x in terms of U and
+ 
+
+ align:start position:0%
+suppose I solve for x in terms of U and
+Y that happens to be very easy to do
+
+ align:start position:0%
+Y that happens to be very easy to do
+ 
+
+ align:start position:0%
+Y that happens to be very easy to do
+here if given that U equal x + y it
+
+ align:start position:0%
+here if given that U equal x + y it
+ 
+
+ align:start position:0%
+here if given that U equal x + y it
+follows immediately that X is equal to
+
+ align:start position:0%
+follows immediately that X is equal to
+ 
+
+ align:start position:0%
+follows immediately that X is equal to
+uus Y now if I take the partial of X
+
+ align:start position:0%
+uus Y now if I take the partial of X
+ 
+
+ align:start position:0%
+uus Y now if I take the partial of X
+with respect to U treating y as a
+
+ align:start position:0%
+with respect to U treating y as a
+ 
+
+ align:start position:0%
+with respect to U treating y as a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+so let me do that what do I get for an
+
+ align:start position:0%
+so let me do that what do I get for an
+ 
+
+ align:start position:0%
+so let me do that what do I get for an
+answer I get one for an answer in other
+
+ align:start position:0%
+answer I get one for an answer in other
+ 
+
+ align:start position:0%
+answer I get one for an answer in other
+words the reciprocal of the partial of X
+
+ align:start position:0%
+words the reciprocal of the partial of X
+ 
+
+ align:start position:0%
+words the reciprocal of the partial of X
+with respect to you treating y as a
+
+ align:start position:0%
+with respect to you treating y as a
+ 
+
+ align:start position:0%
+with respect to you treating y as a
+constant as as the other independent
+
+ align:start position:0%
+constant as as the other independent
+ 
+
+ align:start position:0%
+constant as as the other independent
+variable is equal to the partial of U
+
+ align:start position:0%
+variable is equal to the partial of U
+ 
+
+ align:start position:0%
+variable is equal to the partial of U
+respect to X when it's also y That's
+
+ align:start position:0%
+respect to X when it's also y That's
+ 
+
+ align:start position:0%
+respect to X when it's also y That's
+being considered as the other variable
+
+ align:start position:0%
+being considered as the other variable
+ 
+
+ align:start position:0%
+being considered as the other variable
+when the variables outside here match up
+
+ align:start position:0%
+when the variables outside here match up
+ 
+
+ align:start position:0%
+when the variables outside here match up
+the recipes work course that leads to
+
+ align:start position:0%
+the recipes work course that leads to
+ 
+
+ align:start position:0%
+the recipes work course that leads to
+the question then why do the textbooks
+
+ align:start position:0%
+the question then why do the textbooks
+ 
+
+ align:start position:0%
+the question then why do the textbooks
+tell you that this isn't true why do
+
+ align:start position:0%
+tell you that this isn't true why do
+ 
+
+ align:start position:0%
+tell you that this isn't true why do
+they pick this particular representation
+
+ align:start position:0%
+they pick this particular representation
+ 
+
+ align:start position:0%
+they pick this particular representation
+rather than this one and I have a
+
+ align:start position:0%
+rather than this one and I have a
+ 
+
+ align:start position:0%
+rather than this one and I have a
+combination example and explanation here
+
+ align:start position:0%
+combination example and explanation here
+ 
+
+ align:start position:0%
+combination example and explanation here
+and it's simply this let's suppose I was
+
+ align:start position:0%
+and it's simply this let's suppose I was
+ 
+
+ align:start position:0%
+and it's simply this let's suppose I was
+given that wal e to x + y * cosine x - y
+
+ align:start position:0%
+given that wal e to x + y * cosine x - y
+ 
+
+ align:start position:0%
+given that wal e to x + y * cosine x - y
+it seems that since the only way the
+
+ align:start position:0%
+it seems that since the only way the
+ 
+
+ align:start position:0%
+it seems that since the only way the
+variable appears in the first factor is
+
+ align:start position:0%
+variable appears in the first factor is
+ 
+
+ align:start position:0%
+variable appears in the first factor is
+is as x + y and the only way it appears
+
+ align:start position:0%
+is as x + y and the only way it appears
+ 
+
+ align:start position:0%
+is as x + y and the only way it appears
+in the second factor is in the form xus
+
+ align:start position:0%
+in the second factor is in the form xus
+ 
+
+ align:start position:0%
+in the second factor is in the form xus
+y a very natural substitution might be
+
+ align:start position:0%
+y a very natural substitution might be
+ 
+
+ align:start position:0%
+y a very natural substitution might be
+to say let U equal x + y and v = xus y
+
+ align:start position:0%
+to say let U equal x + y and v = xus y
+ 
+
+ align:start position:0%
+to say let U equal x + y and v = xus y
+in other words I could either visualize
+
+ align:start position:0%
+in other words I could either visualize
+ 
+
+ align:start position:0%
+in other words I could either visualize
+W as being a function of X and Y in
+
+ align:start position:0%
+W as being a function of X and Y in
+ 
+
+ align:start position:0%
+W as being a function of X and Y in
+which case it would be e to x + y *
+
+ align:start position:0%
+which case it would be e to x + y *
+ 
+
+ align:start position:0%
+which case it would be e to x + y *
+cosine x - y or I could visualize W as
+
+ align:start position:0%
+cosine x - y or I could visualize W as
+ 
+
+ align:start position:0%
+cosine x - y or I could visualize W as
+being a simpler function of the two new
+
+ align:start position:0%
+being a simpler function of the two new
+ 
+
+ align:start position:0%
+being a simpler function of the two new
+variables u and v with W is then just
+
+ align:start position:0%
+variables u and v with W is then just
+ 
+
+ align:start position:0%
+variables u and v with W is then just
+what e to U * cosine V notice again that
+
+ align:start position:0%
+what e to U * cosine V notice again that
+ 
+
+ align:start position:0%
+what e to U * cosine V notice again that
+this formula here is much simpler than
+
+ align:start position:0%
+this formula here is much simpler than
+ 
+
+ align:start position:0%
+this formula here is much simpler than
+this one this one says what take e to
+
+ align:start position:0%
+this one this one says what take e to
+ 
+
+ align:start position:0%
+this one this one says what take e to
+the sum of these two multipli by the
+
+ align:start position:0%
+the sum of these two multipli by the
+ 
+
+ align:start position:0%
+the sum of these two multipli by the
+cosine of the difference of these two
+
+ align:start position:0%
+cosine of the difference of these two
+ 
+
+ align:start position:0%
+cosine of the difference of these two
+and this one just says what take e to
+
+ align:start position:0%
+and this one just says what take e to
+ 
+
+ align:start position:0%
+and this one just says what take e to
+the 1 times the cosine of the second but
+
+ align:start position:0%
+the 1 times the cosine of the second but
+ 
+
+ align:start position:0%
+the 1 times the cosine of the second but
+the point is that you might make this
+
+ align:start position:0%
+the point is that you might make this
+ 
+
+ align:start position:0%
+the point is that you might make this
+change of variables to simplify your
+
+ align:start position:0%
+change of variables to simplify your
+ 
+
+ align:start position:0%
+change of variables to simplify your
+computations the point is that either we
+
+ align:start position:0%
+computations the point is that either we
+ 
+
+ align:start position:0%
+computations the point is that either we
+would treat W as a function of X and Y
+
+ align:start position:0%
+would treat W as a function of X and Y
+ 
+
+ align:start position:0%
+would treat W as a function of X and Y
+or we would have treated W as a function
+
+ align:start position:0%
+or we would have treated W as a function
+ 
+
+ align:start position:0%
+or we would have treated W as a function
+of u and v and by way notice here my use
+
+ align:start position:0%
+of u and v and by way notice here my use
+ 
+
+ align:start position:0%
+of u and v and by way notice here my use
+of f and g notice that f is a that W is
+
+ align:start position:0%
+of f and g notice that f is a that W is
+ 
+
+ align:start position:0%
+of f and g notice that f is a that W is
+a different function of X and Y than it
+
+ align:start position:0%
+a different function of X and Y than it
+ 
+
+ align:start position:0%
+a different function of X and Y than it
+is of u and v but this notation says
+
+ align:start position:0%
+is of u and v but this notation says
+ 
+
+ align:start position:0%
+is of u and v but this notation says
+what we can consider W either in terms
+
+ align:start position:0%
+what we can consider W either in terms
+ 
+
+ align:start position:0%
+what we can consider W either in terms
+of X and Y or in terms of u and v hardly
+
+ align:start position:0%
+of X and Y or in terms of u and v hardly
+ 
+
+ align:start position:0%
+of X and Y or in terms of u and v hardly
+ever would we consider W as a function
+
+ align:start position:0%
+ever would we consider W as a function
+ 
+
+ align:start position:0%
+ever would we consider W as a function
+of U and Y in other words either we
+
+ align:start position:0%
+of U and Y in other words either we
+ 
+
+ align:start position:0%
+of U and Y in other words either we
+would change the variables or we don't
+
+ align:start position:0%
+would change the variables or we don't
+ 
+
+ align:start position:0%
+would change the variables or we don't
+oh for example in terms of polar versus
+
+ align:start position:0%
+oh for example in terms of polar versus
+ 
+
+ align:start position:0%
+oh for example in terms of polar versus
+cartisian coordinates either we use X
+
+ align:start position:0%
+cartisian coordinates either we use X
+ 
+
+ align:start position:0%
+cartisian coordinates either we use X
+and Y or we use R in Theta we don't
+
+ align:start position:0%
+and Y or we use R in Theta we don't
+ 
+
+ align:start position:0%
+and Y or we use R in Theta we don't
+usually use R in X other words going
+
+ align:start position:0%
+usually use R in X other words going
+ 
+
+ align:start position:0%
+usually use R in X other words going
+back to the textbook example again if we
+
+ align:start position:0%
+back to the textbook example again if we
+ 
+
+ align:start position:0%
+back to the textbook example again if we
+look at this particular situation here
+
+ align:start position:0%
+look at this particular situation here
+ 
+
+ align:start position:0%
+look at this particular situation here
+all the book is saying is look at when
+
+ align:start position:0%
+all the book is saying is look at when
+ 
+
+ align:start position:0%
+all the book is saying is look at when
+you're differentiating with respect to X
+
+ align:start position:0%
+you're differentiating with respect to X
+ 
+
+ align:start position:0%
+you're differentiating with respect to X
+you usually mean that Y is the variable
+
+ align:start position:0%
+you usually mean that Y is the variable
+ 
+
+ align:start position:0%
+you usually mean that Y is the variable
+being held constant when we
+
+ align:start position:0%
+being held constant when we
+ 
+
+ align:start position:0%
+being held constant when we
+differentiate with respect to U you
+
+ align:start position:0%
+differentiate with respect to U you
+ 
+
+ align:start position:0%
+differentiate with respect to U you
+usually mean that V is the variable
+
+ align:start position:0%
+usually mean that V is the variable
+ 
+
+ align:start position:0%
+usually mean that V is the variable
+that's being held constant again more of
+
+ align:start position:0%
+that's being held constant again more of
+ 
+
+ align:start position:0%
+that's being held constant again more of
+this is said in our exercises but for
+
+ align:start position:0%
+this is said in our exercises but for
+ 
+
+ align:start position:0%
+this is said in our exercises but for
+the time being I want you to see how
+
+ align:start position:0%
+the time being I want you to see how
+ 
+
+ align:start position:0%
+the time being I want you to see how
+important it is when you have several
+
+ align:start position:0%
+important it is when you have several
+ 
+
+ align:start position:0%
+important it is when you have several
+variables to keep track of which are the
+
+ align:start position:0%
+variables to keep track of which are the
+ 
+
+ align:start position:0%
+variables to keep track of which are the
+dependent variables which are the
+
+ align:start position:0%
+dependent variables which are the
+ 
+
+ align:start position:0%
+dependent variables which are the
+independent variables and how they're
+
+ align:start position:0%
+independent variables and how they're
+ 
+
+ align:start position:0%
+independent variables and how they're
+coupled I said earlier that one of the
+
+ align:start position:0%
+coupled I said earlier that one of the
+ 
+
+ align:start position:0%
+coupled I said earlier that one of the
+nice things about picking n equals 2 is
+
+ align:start position:0%
+nice things about picking n equals 2 is
+ 
+
+ align:start position:0%
+nice things about picking n equals 2 is
+that you can draw a nice picture of the
+
+ align:start position:0%
+that you can draw a nice picture of the
+ 
+
+ align:start position:0%
+that you can draw a nice picture of the
+situation and what I thought you might
+
+ align:start position:0%
+situation and what I thought you might
+ 
+
+ align:start position:0%
+situation and what I thought you might
+like to see is the following let's
+
+ align:start position:0%
+like to see is the following let's
+ 
+
+ align:start position:0%
+like to see is the following let's
+suppose you have the W is some function
+
+ align:start position:0%
+suppose you have the W is some function
+ 
+
+ align:start position:0%
+suppose you have the W is some function
+of X and Y what that means is we can
+
+ align:start position:0%
+of X and Y what that means is we can
+ 
+
+ align:start position:0%
+of X and Y what that means is we can
+locate for a given value of x and a
+
+ align:start position:0%
+locate for a given value of x and a
+ 
+
+ align:start position:0%
+locate for a given value of x and a
+given value of y in other words for xal
+
+ align:start position:0%
+given value of y in other words for xal
+ 
+
+ align:start position:0%
+given value of y in other words for xal
+x0 yal y0 we you can think of the point
+
+ align:start position:0%
+x0 yal y0 we you can think of the point
+ 
+
+ align:start position:0%
+x0 yal y0 we you can think of the point
+x0 y0 as being in the XY plane W which
+
+ align:start position:0%
+x0 y0 as being in the XY plane W which
+ 
+
+ align:start position:0%
+x0 y0 as being in the XY plane W which
+is f of x0 y0 is just the height to this
+
+ align:start position:0%
+is f of x0 y0 is just the height to this
+ 
+
+ align:start position:0%
+is f of x0 y0 is just the height to this
+particular surface in other words if I
+
+ align:start position:0%
+particular surface in other words if I
+ 
+
+ align:start position:0%
+particular surface in other words if I
+let F of x0 y0 be called w0 notice that
+
+ align:start position:0%
+let F of x0 y0 be called w0 notice that
+ 
+
+ align:start position:0%
+let F of x0 y0 be called w0 notice that
+the function f ofx y at the point x = x0
+
+ align:start position:0%
+the function f ofx y at the point x = x0
+ 
+
+ align:start position:0%
+the function f ofx y at the point x = x0
+y = y0 graphically corresponds to the
+
+ align:start position:0%
+y = y0 graphically corresponds to the
+ 
+
+ align:start position:0%
+y = y0 graphically corresponds to the
+point whose coordinates are x0 y Z and
+
+ align:start position:0%
+point whose coordinates are x0 y Z and
+ 
+
+ align:start position:0%
+point whose coordinates are x0 y Z and
+w0 okay this is now a surface and in the
+
+ align:start position:0%
+w0 okay this is now a surface and in the
+ 
+
+ align:start position:0%
+w0 okay this is now a surface and in the
+same way that we use tangent lines to
+
+ align:start position:0%
+same way that we use tangent lines to
+ 
+
+ align:start position:0%
+same way that we use tangent lines to
+replace curves when we had one
+
+ align:start position:0%
+replace curves when we had one
+ 
+
+ align:start position:0%
+replace curves when we had one
+independent variable in two independent
+
+ align:start position:0%
+independent variable in two independent
+ 
+
+ align:start position:0%
+independent variable in two independent
+variables we use tangent planes to in to
+
+ align:start position:0%
+variables we use tangent planes to in to
+ 
+
+ align:start position:0%
+variables we use tangent planes to in to
+replace surfaces the question that comes
+
+ align:start position:0%
+replace surfaces the question that comes
+ 
+
+ align:start position:0%
+replace surfaces the question that comes
+up is how do you get a tangent plane and
+
+ align:start position:0%
+up is how do you get a tangent plane and
+ 
+
+ align:start position:0%
+up is how do you get a tangent plane and
+what does this have to do with the
+
+ align:start position:0%
+what does this have to do with the
+ 
+
+ align:start position:0%
+what does this have to do with the
+partial derivatives and what I'd like to
+
+ align:start position:0%
+partial derivatives and what I'd like to
+ 
+
+ align:start position:0%
+partial derivatives and what I'd like to
+show you was the following first of all
+
+ align:start position:0%
+show you was the following first of all
+ 
+
+ align:start position:0%
+show you was the following first of all
+one very natural way of intersecting
+
+ align:start position:0%
+one very natural way of intersecting
+ 
+
+ align:start position:0%
+one very natural way of intersecting
+this surface with a plane in other words
+
+ align:start position:0%
+this surface with a plane in other words
+ 
+
+ align:start position:0%
+this surface with a plane in other words
+when you take the partial of w with
+
+ align:start position:0%
+when you take the partial of w with
+ 
+
+ align:start position:0%
+when you take the partial of w with
+respect to Y you holding x constant
+
+ align:start position:0%
+respect to Y you holding x constant
+ 
+
+ align:start position:0%
+respect to Y you holding x constant
+you're saying let x equal x0 notice that
+
+ align:start position:0%
+you're saying let x equal x0 notice that
+ 
+
+ align:start position:0%
+you're saying let x equal x0 notice that
+in three-dimensional space xal x0 is the
+
+ align:start position:0%
+in three-dimensional space xal x0 is the
+ 
+
+ align:start position:0%
+in three-dimensional space xal x0 is the
+equation of this plane and this plane
+
+ align:start position:0%
+equation of this plane and this plane
+ 
+
+ align:start position:0%
+equation of this plane and this plane
+see what is the the plane xal x0 it's
+
+ align:start position:0%
+see what is the the plane xal x0 it's
+ 
+
+ align:start position:0%
+see what is the the plane xal x0 it's
+the plane that goes through the line X =
+
+ align:start position:0%
+the plane that goes through the line X =
+ 
+
+ align:start position:0%
+the plane that goes through the line X =
+x0 parallel to the Wy plane This Plane
+
+ align:start position:0%
+x0 parallel to the Wy plane This Plane
+ 
+
+ align:start position:0%
+x0 parallel to the Wy plane This Plane
+intersects my Surface in a particular
+
+ align:start position:0%
+intersects my Surface in a particular
+ 
+
+ align:start position:0%
+intersects my Surface in a particular
+curve that curve passes through P0 I can
+
+ align:start position:0%
+curve that curve passes through P0 I can
+ 
+
+ align:start position:0%
+curve that curve passes through P0 I can
+talk about the slope of the curve at
+
+ align:start position:0%
+talk about the slope of the curve at
+ 
+
+ align:start position:0%
+talk about the slope of the curve at
+that particular Point okay in a similar
+
+ align:start position:0%
+that particular Point okay in a similar
+ 
+
+ align:start position:0%
+that particular Point okay in a similar
+way I could have sliced this Surface by
+
+ align:start position:0%
+way I could have sliced this Surface by
+ 
+
+ align:start position:0%
+way I could have sliced this Surface by
+a the plane yal y0 in other words hold y
+
+ align:start position:0%
+a the plane yal y0 in other words hold y
+ 
+
+ align:start position:0%
+a the plane yal y0 in other words hold y
+constant where you see to hold y
+
+ align:start position:0%
+constant where you see to hold y
+ 
+
+ align:start position:0%
+constant where you see to hold y
+constant that means I again draw my
+
+ align:start position:0%
+constant that means I again draw my
+ 
+
+ align:start position:0%
+constant that means I again draw my
+plane it intersects the surface in a
+
+ align:start position:0%
+plane it intersects the surface in a
+ 
+
+ align:start position:0%
+plane it intersects the surface in a
+different curve but that curve must also
+
+ align:start position:0%
+different curve but that curve must also
+ 
+
+ align:start position:0%
+different curve but that curve must also
+go through the point p 0 this this the
+
+ align:start position:0%
+go through the point p 0 this this the
+ 
+
+ align:start position:0%
+go through the point p 0 this this the
+same p 0 that's over here because after
+
+ align:start position:0%
+same p 0 that's over here because after
+ 
+
+ align:start position:0%
+same p 0 that's over here because after
+all the point on the surface that is
+
+ align:start position:0%
+all the point on the surface that is
+ 
+
+ align:start position:0%
+all the point on the surface that is
+directly above x0 y0 is p 0 and that
+
+ align:start position:0%
+directly above x0 y0 is p 0 and that
+ 
+
+ align:start position:0%
+directly above x0 y0 is p 0 and that
+point doesn't change no matter what
+
+ align:start position:0%
+point doesn't change no matter what
+ 
+
+ align:start position:0%
+point doesn't change no matter what
+plane you slice this thing with okay and
+
+ align:start position:0%
+plane you slice this thing with okay and
+ 
+
+ align:start position:0%
+plane you slice this thing with okay and
+so again I can talk about the slope of
+
+ align:start position:0%
+so again I can talk about the slope of
+ 
+
+ align:start position:0%
+so again I can talk about the slope of
+the tangent to this particular curve of
+
+ align:start position:0%
+the tangent to this particular curve of
+ 
+
+ align:start position:0%
+the tangent to this particular curve of
+intersection by the way one very brief
+
+ align:start position:0%
+intersection by the way one very brief
+ 
+
+ align:start position:0%
+intersection by the way one very brief
+aside before I continue on with this one
+
+ align:start position:0%
+aside before I continue on with this one
+ 
+
+ align:start position:0%
+aside before I continue on with this one
+of the things that makes functions of
+
+ align:start position:0%
+of the things that makes functions of
+ 
+
+ align:start position:0%
+of the things that makes functions of
+several variables so difficult is I
+
+ align:start position:0%
+several variables so difficult is I
+ 
+
+ align:start position:0%
+several variables so difficult is I
+would like you to observe because this
+
+ align:start position:0%
+would like you to observe because this
+ 
+
+ align:start position:0%
+would like you to observe because this
+will become the backbone of our future
+
+ align:start position:0%
+will become the backbone of our future
+ 
+
+ align:start position:0%
+will become the backbone of our future
+investigations that these two particular
+
+ align:start position:0%
+investigations that these two particular
+ 
+
+ align:start position:0%
+investigations that these two particular
+planes that I drew to intersect my
+
+ align:start position:0%
+planes that I drew to intersect my
+ 
+
+ align:start position:0%
+planes that I drew to intersect my
+Surface were very special planes one of
+
+ align:start position:0%
+Surface were very special planes one of
+ 
+
+ align:start position:0%
+Surface were very special planes one of
+them was par they both went through the
+
+ align:start position:0%
+them was par they both went through the
+ 
+
+ align:start position:0%
+them was par they both went through the
+point x0 y0 but one happened to be
+
+ align:start position:0%
+point x0 y0 but one happened to be
+ 
+
+ align:start position:0%
+point x0 y0 but one happened to be
+parallel to the Wy plane and the other
+
+ align:start position:0%
+parallel to the Wy plane and the other
+ 
+
+ align:start position:0%
+parallel to the Wy plane and the other
+one happened to be parallel to the WX
+
+ align:start position:0%
+one happened to be parallel to the WX
+ 
+
+ align:start position:0%
+one happened to be parallel to the WX
+plane notice that in
+
+ align:start position:0%
+plane notice that in
+ 
+
+ align:start position:0%
+plane notice that in
+general I could have passed infinitely
+
+ align:start position:0%
+general I could have passed infinitely
+ 
+
+ align:start position:0%
+general I could have passed infinitely
+many different planes through x0 y0 Each
+
+ align:start position:0%
+many different planes through x0 y0 Each
+ 
+
+ align:start position:0%
+many different planes through x0 y0 Each
+of which would have intersected the
+
+ align:start position:0%
+of which would have intersected the
+ 
+
+ align:start position:0%
+of which would have intersected the
+surface at a in a different curve and
+
+ align:start position:0%
+surface at a in a different curve and
+ 
+
+ align:start position:0%
+surface at a in a different curve and
+this is what leads later to the more
+
+ align:start position:0%
+this is what leads later to the more
+ 
+
+ align:start position:0%
+this is what leads later to the more
+generalized concept of directional
+
+ align:start position:0%
+generalized concept of directional
+ 
+
+ align:start position:0%
+generalized concept of directional
+derivatives that we will talk about in
+
+ align:start position:0%
+derivatives that we will talk about in
+ 
+
+ align:start position:0%
+derivatives that we will talk about in
+more detail in our future lectures but I
+
+ align:start position:0%
+more detail in our future lectures but I
+ 
+
+ align:start position:0%
+more detail in our future lectures but I
+simply mention the wood now because in
+
+ align:start position:0%
+simply mention the wood now because in
+ 
+
+ align:start position:0%
+simply mention the wood now because in
+the reading material in this assignment
+
+ align:start position:0%
+the reading material in this assignment
+ 
+
+ align:start position:0%
+the reading material in this assignment
+some mention is made of directional
+
+ align:start position:0%
+some mention is made of directional
+ 
+
+ align:start position:0%
+some mention is made of directional
+derivatives in other words uh I want to
+
+ align:start position:0%
+derivatives in other words uh I want to
+ 
+
+ align:start position:0%
+derivatives in other words uh I want to
+point out that to take partial
+
+ align:start position:0%
+point out that to take partial
+ 
+
+ align:start position:0%
+point out that to take partial
+derivatives we are interested in two
+
+ align:start position:0%
+derivatives we are interested in two
+ 
+
+ align:start position:0%
+derivatives we are interested in two
+special directions even though there are
+
+ align:start position:0%
+special directions even though there are
+ 
+
+ align:start position:0%
+special directions even though there are
+other directions the question that comes
+
+ align:start position:0%
+other directions the question that comes
+ 
+
+ align:start position:0%
+other directions the question that comes
+up of course is where do the partials
+
+ align:start position:0%
+up of course is where do the partials
+ 
+
+ align:start position:0%
+up of course is where do the partials
+come in here and secondly knowing where
+
+ align:start position:0%
+come in here and secondly knowing where
+ 
+
+ align:start position:0%
+come in here and secondly knowing where
+the partials come up in here where do
+
+ align:start position:0%
+the partials come up in here where do
+ 
+
+ align:start position:0%
+the partials come up in here where do
+they uh use C how do we find the
+
+ align:start position:0%
+they uh use C how do we find the
+ 
+
+ align:start position:0%
+they uh use C how do we find the
+equation of a tangent plane and all I
+
+ align:start position:0%
+equation of a tangent plane and all I
+ 
+
+ align:start position:0%
+equation of a tangent plane and all I
+would like you to see from here is that
+
+ align:start position:0%
+would like you to see from here is that
+ 
+
+ align:start position:0%
+would like you to see from here is that
+I'm going to use the same old technique
+
+ align:start position:0%
+I'm going to use the same old technique
+ 
+
+ align:start position:0%
+I'm going to use the same old technique
+as always given these two tangent lines
+
+ align:start position:0%
+as always given these two tangent lines
+ 
+
+ align:start position:0%
+as always given these two tangent lines
+I am going to vectorize them I am then
+
+ align:start position:0%
+I am going to vectorize them I am then
+ 
+
+ align:start position:0%
+I am going to vectorize them I am then
+going to find the equation of the plane
+
+ align:start position:0%
+going to find the equation of the plane
+ 
+
+ align:start position:0%
+going to find the equation of the plane
+that passes through those two vectors to
+
+ align:start position:0%
+that passes through those two vectors to
+ 
+
+ align:start position:0%
+that passes through those two vectors to
+do that I'm going to have to find the
+
+ align:start position:0%
+do that I'm going to have to find the
+ 
+
+ align:start position:0%
+do that I'm going to have to find the
+normal to that plane Etc and I'm going
+
+ align:start position:0%
+normal to that plane Etc and I'm going
+ 
+
+ align:start position:0%
+normal to that plane Etc and I'm going
+to wind up with the equation of a
+
+ align:start position:0%
+to wind up with the equation of a
+ 
+
+ align:start position:0%
+to wind up with the equation of a
+tangent plane in more slow motion all
+
+ align:start position:0%
+tangent plane in more slow motion all
+ 
+
+ align:start position:0%
+tangent plane in more slow motion all
+I'm saying is if I now take this picture
+
+ align:start position:0%
+I'm saying is if I now take this picture
+ 
+
+ align:start position:0%
+I'm saying is if I now take this picture
+and draw it over here notice the
+
+ align:start position:0%
+and draw it over here notice the
+ 
+
+ align:start position:0%
+and draw it over here notice the
+representation it looks as if the curve
+
+ align:start position:0%
+representation it looks as if the curve
+ 
+
+ align:start position:0%
+representation it looks as if the curve
+that I get is in the Wy plane it's
+
+ align:start position:0%
+that I get is in the Wy plane it's
+ 
+
+ align:start position:0%
+that I get is in the Wy plane it's
+actually in a plane parallel to the W y
+
+ align:start position:0%
+actually in a plane parallel to the W y
+ 
+
+ align:start position:0%
+actually in a plane parallel to the W y
+plane characterized by x = x Sub 0 and
+
+ align:start position:0%
+plane characterized by x = x Sub 0 and
+ 
+
+ align:start position:0%
+plane characterized by x = x Sub 0 and
+by the way notice even though X = x0 was
+
+ align:start position:0%
+by the way notice even though X = x0 was
+ 
+
+ align:start position:0%
+by the way notice even though X = x0 was
+chosen so that x0 was fixed I hope it's
+
+ align:start position:0%
+chosen so that x0 was fixed I hope it's
+ 
+
+ align:start position:0%
+chosen so that x0 was fixed I hope it's
+clear to you that if I let x sub Z vary
+
+ align:start position:0%
+clear to you that if I let x sub Z vary
+ 
+
+ align:start position:0%
+clear to you that if I let x sub Z vary
+and I pick different values of X Sub 0
+
+ align:start position:0%
+and I pick different values of X Sub 0
+ 
+
+ align:start position:0%
+and I pick different values of X Sub 0
+the curve that I get here will in
+
+ align:start position:0%
+the curve that I get here will in
+ 
+
+ align:start position:0%
+the curve that I get here will in
+general differ you see what I'm saying
+
+ align:start position:0%
+general differ you see what I'm saying
+ 
+
+ align:start position:0%
+general differ you see what I'm saying
+is if I take slices parallel to the Wy
+
+ align:start position:0%
+is if I take slices parallel to the Wy
+ 
+
+ align:start position:0%
+is if I take slices parallel to the Wy
+plane for a particular surface the
+
+ align:start position:0%
+plane for a particular surface the
+ 
+
+ align:start position:0%
+plane for a particular surface the
+slices that I get the shape will depend
+
+ align:start position:0%
+slices that I get the shape will depend
+ 
+
+ align:start position:0%
+slices that I get the shape will depend
+on what the particular value of x0 is
+
+ align:start position:0%
+on what the particular value of x0 is
+ 
+
+ align:start position:0%
+on what the particular value of x0 is
+but that's not the crucial issue right
+
+ align:start position:0%
+but that's not the crucial issue right
+ 
+
+ align:start position:0%
+but that's not the crucial issue right
+now the point that I'm driving at is if
+
+ align:start position:0%
+now the point that I'm driving at is if
+ 
+
+ align:start position:0%
+now the point that I'm driving at is if
+I now call this tangent if I vectorize
+
+ align:start position:0%
+I now call this tangent if I vectorize
+ 
+
+ align:start position:0%
+I now call this tangent if I vectorize
+the tangent line and call that V1 what
+
+ align:start position:0%
+the tangent line and call that V1 what
+ 
+
+ align:start position:0%
+the tangent line and call that V1 what
+does that tangent line look like first
+
+ align:start position:0%
+does that tangent line look like first
+ 
+
+ align:start position:0%
+does that tangent line look like first
+of all let's see what its slope is now
+
+ align:start position:0%
+of all let's see what its slope is now
+ 
+
+ align:start position:0%
+of all let's see what its slope is now
+again if you didn't see this over here
+
+ align:start position:0%
+again if you didn't see this over here
+ 
+
+ align:start position:0%
+again if you didn't see this over here
+and all I showed you was this diagram
+
+ align:start position:0%
+and all I showed you was this diagram
+ 
+
+ align:start position:0%
+and all I showed you was this diagram
+you would say hey that slope is just the
+
+ align:start position:0%
+you would say hey that slope is just the
+ 
+
+ align:start position:0%
+you would say hey that slope is just the
+derivative of w with respect to y but we
+
+ align:start position:0%
+derivative of w with respect to y but we
+ 
+
+ align:start position:0%
+derivative of w with respect to y but we
+write that the partial of w with respect
+
+ align:start position:0%
+write that the partial of w with respect
+ 
+
+ align:start position:0%
+write that the partial of w with respect
+to Y in deference to the fact that W is
+
+ align:start position:0%
+to Y in deference to the fact that W is
+ 
+
+ align:start position:0%
+to Y in deference to the fact that W is
+not a function of Y alone the W depends
+
+ align:start position:0%
+not a function of Y alone the W depends
+ 
+
+ align:start position:0%
+not a function of Y alone the W depends
+on both X and Y and the reason that we
+
+ align:start position:0%
+on both X and Y and the reason that we
+ 
+
+ align:start position:0%
+on both X and Y and the reason that we
+got this curve was that we fixed X at
+
+ align:start position:0%
+got this curve was that we fixed X at
+ 
+
+ align:start position:0%
+got this curve was that we fixed X at
+some particular value so this is really
+
+ align:start position:0%
+some particular value so this is really
+ 
+
+ align:start position:0%
+some particular value so this is really
+what not the not the derivative of w
+
+ align:start position:0%
+what not the not the derivative of w
+ 
+
+ align:start position:0%
+what not the not the derivative of w
+with respect to Y evaluated at yal y0
+
+ align:start position:0%
+with respect to Y evaluated at yal y0
+ 
+
+ align:start position:0%
+with respect to Y evaluated at yal y0
+it's the partial of w with respect to Y
+
+ align:start position:0%
+it's the partial of w with respect to Y
+ 
+
+ align:start position:0%
+it's the partial of w with respect to Y
+evaluated at what x0 comma y0
+
+ align:start position:0%
+evaluated at what x0 comma y0
+ 
+
+ align:start position:0%
+evaluated at what x0 comma y0
+all right at any rate now that we have
+
+ align:start position:0%
+all right at any rate now that we have
+ 
+
+ align:start position:0%
+all right at any rate now that we have
+the slope notice that the slope of a
+
+ align:start position:0%
+the slope notice that the slope of a
+ 
+
+ align:start position:0%
+the slope notice that the slope of a
+vector can always be viewed as the K
+
+ align:start position:0%
+vector can always be viewed as the K
+ 
+
+ align:start position:0%
+vector can always be viewed as the K
+component in this case the K component
+
+ align:start position:0%
+component in this case the K component
+ 
+
+ align:start position:0%
+component in this case the K component
+divided by the J component if I make the
+
+ align:start position:0%
+divided by the J component if I make the
+ 
+
+ align:start position:0%
+divided by the J component if I make the
+J component one the slope will just be
+
+ align:start position:0%
+J component one the slope will just be
+ 
+
+ align:start position:0%
+J component one the slope will just be
+the K component in other words a vector
+
+ align:start position:0%
+the K component in other words a vector
+ 
+
+ align:start position:0%
+the K component in other words a vector
+which is tangent to the curve and one
+
+ align:start position:0%
+which is tangent to the curve and one
+ 
+
+ align:start position:0%
+which is tangent to the curve and one
+that's easy to write down is J plus the
+
+ align:start position:0%
+that's easy to write down is J plus the
+ 
+
+ align:start position:0%
+that's easy to write down is J plus the
+partial of w with respect to Y evaluated
+
+ align:start position:0%
+partial of w with respect to Y evaluated
+ 
+
+ align:start position:0%
+partial of w with respect to Y evaluated
+x0 y0 time K and notice by the way that
+
+ align:start position:0%
+x0 y0 time K and notice by the way that
+ 
+
+ align:start position:0%
+x0 y0 time K and notice by the way that
+this is a
+
+ align:start position:0%
+this is a
+ 
+
+ align:start position:0%
+this is a
+number that once I take the partial
+
+ align:start position:0%
+number that once I take the partial
+ 
+
+ align:start position:0%
+number that once I take the partial
+derivative and evaluated at a point I
+
+ align:start position:0%
+derivative and evaluated at a point I
+ 
+
+ align:start position:0%
+derivative and evaluated at a point I
+have a number so this is what a constant
+
+ align:start position:0%
+have a number so this is what a constant
+ 
+
+ align:start position:0%
+have a number so this is what a constant
+Vector once x0 and y0 are fixed in a
+
+ align:start position:0%
+Vector once x0 and y0 are fixed in a
+ 
+
+ align:start position:0%
+Vector once x0 and y0 are fixed in a
+similar
+
+ align:start position:0%
+similar
+ 
+
+ align:start position:0%
+similar
+way my Vector V2 which is for my curve
+
+ align:start position:0%
+way my Vector V2 which is for my curve
+ 
+
+ align:start position:0%
+way my Vector V2 which is for my curve
+parallel to the WX plane the slope of
+
+ align:start position:0%
+parallel to the WX plane the slope of
+ 
+
+ align:start position:0%
+parallel to the WX plane the slope of
+that curve at the point p 0 is not D wdx
+
+ align:start position:0%
+that curve at the point p 0 is not D wdx
+ 
+
+ align:start position:0%
+that curve at the point p 0 is not D wdx
+it's the partial of w with respect to X
+
+ align:start position:0%
+it's the partial of w with respect to X
+ 
+
+ align:start position:0%
+it's the partial of w with respect to X
+evaluated x0 y0 again why because even
+
+ align:start position:0%
+evaluated x0 y0 again why because even
+ 
+
+ align:start position:0%
+evaluated x0 y0 again why because even
+though this looks like w is a function
+
+ align:start position:0%
+though this looks like w is a function
+ 
+
+ align:start position:0%
+though this looks like w is a function
+of X alone here it was only that way
+
+ align:start position:0%
+of X alone here it was only that way
+ 
+
+ align:start position:0%
+of X alone here it was only that way
+because we took the second variable and
+
+ align:start position:0%
+because we took the second variable and
+ 
+
+ align:start position:0%
+because we took the second variable and
+in a sense froze it at the value y0 at
+
+ align:start position:0%
+in a sense froze it at the value y0 at
+ 
+
+ align:start position:0%
+in a sense froze it at the value y0 at
+any rate in in analogous manner V2 turns
+
+ align:start position:0%
+any rate in in analogous manner V2 turns
+ 
+
+ align:start position:0%
+any rate in in analogous manner V2 turns
+out to be what Vector it's I plus the
+
+ align:start position:0%
+out to be what Vector it's I plus the
+ 
+
+ align:start position:0%
+out to be what Vector it's I plus the
+partial of w respect to X evaluated x0 y
+
+ align:start position:0%
+partial of w respect to X evaluated x0 y
+ 
+
+ align:start position:0%
+partial of w respect to X evaluated x0 y
+z time K in other words the slope is the
+
+ align:start position:0%
+z time K in other words the slope is the
+ 
+
+ align:start position:0%
+z time K in other words the slope is the
+partial of w with respect to X and it's
+
+ align:start position:0%
+partial of w with respect to X and it's
+ 
+
+ align:start position:0%
+partial of w with respect to X and it's
+in the ik plane in other words the xw
+
+ align:start position:0%
+in the ik plane in other words the xw
+ 
+
+ align:start position:0%
+in the ik plane in other words the xw
+plane now that I have my two vectors to
+
+ align:start position:0%
+plane now that I have my two vectors to
+ 
+
+ align:start position:0%
+plane now that I have my two vectors to
+find the plane that passes through them
+
+ align:start position:0%
+find the plane that passes through them
+ 
+
+ align:start position:0%
+find the plane that passes through them
+all I need is what the normal vector and
+
+ align:start position:0%
+all I need is what the normal vector and
+ 
+
+ align:start position:0%
+all I need is what the normal vector and
+a point in the plane well one of the
+
+ align:start position:0%
+a point in the plane well one of the
+ 
+
+ align:start position:0%
+a point in the plane well one of the
+nice things about having studied
+
+ align:start position:0%
+nice things about having studied
+ 
+
+ align:start position:0%
+nice things about having studied
+cartisian the cross product here is that
+
+ align:start position:0%
+cartisian the cross product here is that
+ 
+
+ align:start position:0%
+cartisian the cross product here is that
+I can now take the cross product of V1
+
+ align:start position:0%
+I can now take the cross product of V1
+ 
+
+ align:start position:0%
+I can now take the cross product of V1
+and V2 sparing you the details remember
+
+ align:start position:0%
+and V2 sparing you the details remember
+ 
+
+ align:start position:0%
+and V2 sparing you the details remember
+what I do here I just write down I J K
+
+ align:start position:0%
+what I do here I just write down I J K
+ 
+
+ align:start position:0%
+what I do here I just write down I J K
+V1 has these components V2 has these
+
+ align:start position:0%
+V1 has these components V2 has these
+ 
+
+ align:start position:0%
+V1 has these components V2 has these
+these components I now expand this
+
+ align:start position:0%
+these components I now expand this
+ 
+
+ align:start position:0%
+these components I now expand this
+determinant in the usual way and I get
+
+ align:start position:0%
+determinant in the usual way and I get
+ 
+
+ align:start position:0%
+determinant in the usual way and I get
+what this particular Vector in other
+
+ align:start position:0%
+what this particular Vector in other
+ 
+
+ align:start position:0%
+what this particular Vector in other
+words the I component is the partial of
+
+ align:start position:0%
+words the I component is the partial of
+ 
+
+ align:start position:0%
+words the I component is the partial of
+w respect to X the J component is the
+
+ align:start position:0%
+w respect to X the J component is the
+ 
+
+ align:start position:0%
+w respect to X the J component is the
+partial of w respect to Y both evaluated
+
+ align:start position:0%
+partial of w respect to Y both evaluated
+ 
+
+ align:start position:0%
+partial of w respect to Y both evaluated
+at the point x0 y0 and the K component
+
+ align:start position:0%
+at the point x0 y0 and the K component
+ 
+
+ align:start position:0%
+at the point x0 y0 and the K component
+is minus one now to find the equation of
+
+ align:start position:0%
+is minus one now to find the equation of
+ 
+
+ align:start position:0%
+is minus one now to find the equation of
+a tangent plane all I have to do is what
+
+ align:start position:0%
+a tangent plane all I have to do is what
+ 
+
+ align:start position:0%
+a tangent plane all I have to do is what
+take the standard form of the plane in
+
+ align:start position:0%
+take the standard form of the plane in
+ 
+
+ align:start position:0%
+take the standard form of the plane in
+other words the coefficients will be the
+
+ align:start position:0%
+other words the coefficients will be the
+ 
+
+ align:start position:0%
+other words the coefficients will be the
+and then I take x0 y0 w0 which is a
+
+ align:start position:0%
+and then I take x0 y0 w0 which is a
+ 
+
+ align:start position:0%
+and then I take x0 y0 w0 which is a
+point in my plane and then the equation
+
+ align:start position:0%
+point in my plane and then the equation
+ 
+
+ align:start position:0%
+point in my plane and then the equation
+of the tangent plane becomes quite
+
+ align:start position:0%
+of the tangent plane becomes quite
+ 
+
+ align:start position:0%
+of the tangent plane becomes quite
+simply this expression here and in fact
+
+ align:start position:0%
+simply this expression here and in fact
+ 
+
+ align:start position:0%
+simply this expression here and in fact
+if I rewrite that notice I can transpose
+
+ align:start position:0%
+if I rewrite that notice I can transpose
+ 
+
+ align:start position:0%
+if I rewrite that notice I can transpose
+the wus w0 term that is the change in W
+
+ align:start position:0%
+the wus w0 term that is the change in W
+ 
+
+ align:start position:0%
+the wus w0 term that is the change in W
+but to remind us that we're in a tangent
+
+ align:start position:0%
+but to remind us that we're in a tangent
+ 
+
+ align:start position:0%
+but to remind us that we're in a tangent
+plane we don't write this as Delta w we
+
+ align:start position:0%
+plane we don't write this as Delta w we
+ 
+
+ align:start position:0%
+plane we don't write this as Delta w we
+write it as Delta W sub tan and notice
+
+ align:start position:0%
+write it as Delta W sub tan and notice
+ 
+
+ align:start position:0%
+write it as Delta W sub tan and notice
+that the ch in W to the tangent plane is
+
+ align:start position:0%
+that the ch in W to the tangent plane is
+ 
+
+ align:start position:0%
+that the ch in W to the tangent plane is
+just the partial of w respect to x *
+
+ align:start position:0%
+just the partial of w respect to x *
+ 
+
+ align:start position:0%
+just the partial of w respect to x *
+Delta X plus the partial of w respect to
+
+ align:start position:0%
+Delta X plus the partial of w respect to
+ 
+
+ align:start position:0%
+Delta X plus the partial of w respect to
+y * Delta Y and hopefully this starts to
+
+ align:start position:0%
+y * Delta Y and hopefully this starts to
+ 
+
+ align:start position:0%
+y * Delta Y and hopefully this starts to
+seem familiar to you this should almost
+
+ align:start position:0%
+seem familiar to you this should almost
+ 
+
+ align:start position:0%
+seem familiar to you this should almost
+look like the equation of Delta y tan
+
+ align:start position:0%
+look like the equation of Delta y tan
+ 
+
+ align:start position:0%
+look like the equation of Delta y tan
+only in two Dimensions remember we had
+
+ align:start position:0%
+only in two Dimensions remember we had
+ 
+
+ align:start position:0%
+only in two Dimensions remember we had
+Delta y Tan in part one of the course
+
+ align:start position:0%
+Delta y Tan in part one of the course
+ 
+
+ align:start position:0%
+Delta y Tan in part one of the course
+see what this really says is what this
+
+ align:start position:0%
+see what this really says is what this
+ 
+
+ align:start position:0%
+see what this really says is what this
+is the change in W with respect to X
+
+ align:start position:0%
+is the change in W with respect to X
+ 
+
+ align:start position:0%
+is the change in W with respect to X
+multiplied by the total change in X in
+
+ align:start position:0%
+multiplied by the total change in X in
+ 
+
+ align:start position:0%
+multiplied by the total change in X in
+other words this term is what it's the
+
+ align:start position:0%
+other words this term is what it's the
+ 
+
+ align:start position:0%
+other words this term is what it's the
+change in W due to the change in X alone
+
+ align:start position:0%
+change in W due to the change in X alone
+ 
+
+ align:start position:0%
+change in W due to the change in X alone
+this term is the change in W with
+
+ align:start position:0%
+this term is the change in W with
+ 
+
+ align:start position:0%
+this term is the change in W with
+respect to Y times the total change in y
+
+ align:start position:0%
+respect to Y times the total change in y
+ 
+
+ align:start position:0%
+respect to Y times the total change in y
+so this term tells you the change in W
+
+ align:start position:0%
+so this term tells you the change in W
+ 
+
+ align:start position:0%
+so this term tells you the change in W
+due to the change in y alone and if you
+
+ align:start position:0%
+due to the change in y alone and if you
+ 
+
+ align:start position:0%
+due to the change in y alone and if you
+add these two up since X and Y are
+
+ align:start position:0%
+add these two up since X and Y are
+ 
+
+ align:start position:0%
+add these two up since X and Y are
+independent this should give you the
+
+ align:start position:0%
+independent this should give you the
+ 
+
+ align:start position:0%
+independent this should give you the
+total change in W the reason of course
+
+ align:start position:0%
+total change in W the reason of course
+ 
+
+ align:start position:0%
+total change in W the reason of course
+that you don't get the total change in W
+
+ align:start position:0%
+that you don't get the total change in W
+ 
+
+ align:start position:0%
+that you don't get the total change in W
+but rather Delta W tan is the fact that
+
+ align:start position:0%
+but rather Delta W tan is the fact that
+ 
+
+ align:start position:0%
+but rather Delta W tan is the fact that
+if you if these Expressions here are not
+
+ align:start position:0%
+if you if these Expressions here are not
+ 
+
+ align:start position:0%
+if you if these Expressions here are not
+constant num numbers as Delta X and
+
+ align:start position:0%
+constant num numbers as Delta X and
+ 
+
+ align:start position:0%
+constant num numbers as Delta X and
+Delta y are varying these numbers here
+
+ align:start position:0%
+Delta y are varying these numbers here
+ 
+
+ align:start position:0%
+Delta y are varying these numbers here
+are varying these are variables but you
+
+ align:start position:0%
+are varying these are variables but you
+ 
+
+ align:start position:0%
+are varying these are variables but you
+see once you fix these at these values
+
+ align:start position:0%
+see once you fix these at these values
+ 
+
+ align:start position:0%
+see once you fix these at these values
+these become numbers and now you know
+
+ align:start position:0%
+these become numbers and now you know
+ 
+
+ align:start position:0%
+these become numbers and now you know
+what Delta wtan is now look at in some
+
+ align:start position:0%
+what Delta wtan is now look at in some
+ 
+
+ align:start position:0%
+what Delta wtan is now look at in some
+of the homework problems in the text
+
+ align:start position:0%
+of the homework problems in the text
+ 
+
+ align:start position:0%
+of the homework problems in the text
+what we're going to do is just practice
+
+ align:start position:0%
+what we're going to do is just practice
+ 
+
+ align:start position:0%
+what we're going to do is just practice
+the geometry itself we're going to find
+
+ align:start position:0%
+the geometry itself we're going to find
+ 
+
+ align:start position:0%
+the geometry itself we're going to find
+equations of tangent planes the thing
+
+ align:start position:0%
+equations of tangent planes the thing
+ 
+
+ align:start position:0%
+equations of tangent planes the thing
+that's very important to us in future
+
+ align:start position:0%
+that's very important to us in future
+ 
+
+ align:start position:0%
+that's very important to us in future
+lectures from a structural point of view
+
+ align:start position:0%
+lectures from a structural point of view
+ 
+
+ align:start position:0%
+lectures from a structural point of view
+is that the equation of the tangent
+
+ align:start position:0%
+is that the equation of the tangent
+ 
+
+ align:start position:0%
+is that the equation of the tangent
+plane in other words the equation for
+
+ align:start position:0%
+plane in other words the equation for
+ 
+
+ align:start position:0%
+plane in other words the equation for
+Delta W tan is far more simple to handle
+
+ align:start position:0%
+Delta W tan is far more simple to handle
+ 
+
+ align:start position:0%
+Delta W tan is far more simple to handle
+than the equation for the true Delta W
+
+ align:start position:0%
+than the equation for the true Delta W
+ 
+
+ align:start position:0%
+than the equation for the true Delta W
+you see the equation for Delta W tan
+
+ align:start position:0%
+you see the equation for Delta W tan
+ 
+
+ align:start position:0%
+you see the equation for Delta W tan
+just has Delta X and Delta y appearing
+
+ align:start position:0%
+just has Delta X and Delta y appearing
+ 
+
+ align:start position:0%
+just has Delta X and Delta y appearing
+to the first Power whereas if you try to
+
+ align:start position:0%
+to the first Power whereas if you try to
+ 
+
+ align:start position:0%
+to the first Power whereas if you try to
+find Delta W exactly for an arbitrary
+
+ align:start position:0%
+find Delta W exactly for an arbitrary
+ 
+
+ align:start position:0%
+find Delta W exactly for an arbitrary
+function of X and Y this be can become a
+
+ align:start position:0%
+function of X and Y this be can become a
+ 
+
+ align:start position:0%
+function of X and Y this be can become a
+very very messy thing in short Delta W10
+
+ align:start position:0%
+very very messy thing in short Delta W10
+ 
+
+ align:start position:0%
+very very messy thing in short Delta W10
+will play for two and more independent
+
+ align:start position:0%
+will play for two and more independent
+ 
+
+ align:start position:0%
+will play for two and more independent
+variables the same role that Delta y
+
+ align:start position:0%
+variables the same role that Delta y
+ 
+
+ align:start position:0%
+variables the same role that Delta y
+suban played for us in part one of this
+
+ align:start position:0%
+suban played for us in part one of this
+ 
+
+ align:start position:0%
+suban played for us in part one of this
+course as a
+
+ align:start position:0%
+course as a
+ 
+
+ align:start position:0%
+course as a
+differential and what we'll be
+
+ align:start position:0%
+differential and what we'll be
+ 
+
+ align:start position:0%
+differential and what we'll be
+discussing next or at least trying to
+
+ align:start position:0%
+discussing next or at least trying to
+ 
+
+ align:start position:0%
+discussing next or at least trying to
+get at the root of is just what does
+
+ align:start position:0%
+get at the root of is just what does
+ 
+
+ align:start position:0%
+get at the root of is just what does
+play the role of a differential when
+
+ align:start position:0%
+play the role of a differential when
+ 
+
+ align:start position:0%
+play the role of a differential when
+you're dealing with Calculus of several
+
+ align:start position:0%
+you're dealing with Calculus of several
+ 
+
+ align:start position:0%
+you're dealing with Calculus of several
+variables and what we're going to find
+
+ align:start position:0%
+variables and what we're going to find
+ 
+
+ align:start position:0%
+variables and what we're going to find
+is that again the computations become
+
+ align:start position:0%
+is that again the computations become
+ 
+
+ align:start position:0%
+is that again the computations become
+messy enough so that even though the
+
+ align:start position:0%
+messy enough so that even though the
+ 
+
+ align:start position:0%
+messy enough so that even though the
+structure stays fairly nice there are
+
+ align:start position:0%
+structure stays fairly nice there are
+ 
+
+ align:start position:0%
+structure stays fairly nice there are
+some wrinkles that come out that will
+
+ align:start position:0%
+some wrinkles that come out that will
+ 
+
+ align:start position:0%
+some wrinkles that come out that will
+take us a considerable amount of time to
+
+ align:start position:0%
+take us a considerable amount of time to
+ 
+
+ align:start position:0%
+take us a considerable amount of time to
+untangle but we'll worry about that when
+
+ align:start position:0%
+untangle but we'll worry about that when
+ 
+
+ align:start position:0%
+untangle but we'll worry about that when
+the time comes and so until that time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goodbye funding for the publication of
+
+ align:start position:0%
+goodbye funding for the publication of
+ 
+
+ align:start position:0%
+goodbye funding for the publication of
+this video was provided by the Gabriella
+
+ align:start position:0%
+this video was provided by the Gabriella
+ 
+
+ align:start position:0%
+this video was provided by the Gabriella
+and Paul rosenbom
+
+ align:start position:0%
+and Paul rosenbom
+ 
+
+ align:start position:0%
+and Paul rosenbom
+foundation help ocw continue to provide
+
+ align:start position:0%
+foundation help ocw continue to provide
+ 
+
+ align:start position:0%
+foundation help ocw continue to provide
+free and open access to MIT courses by
+
+ align:start position:0%
+free and open access to MIT courses by
+ 
+
+ align:start position:0%
+free and open access to MIT courses by
+making a donation at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+edu donate
\ No newline at end of file
diff --git a/VSqpYPgxcps.txt b/VSqpYPgxcps.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c450d00a2e47f81f5d7ffa88e292609f984d8730
--- /dev/null
+++ b/VSqpYPgxcps.txt
@@ -0,0 +1,12483 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or to view additional
+
+ align:start position:0%
+to make a donation or to view additional
+ 
+
+ align:start position:0%
+to make a donation or to view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hi everyone I'm in a very good mood
+
+ align:start position:0%
+hi everyone I'm in a very good mood
+ 
+
+ align:start position:0%
+hi everyone I'm in a very good mood
+today I nothing to do with the class but
+
+ align:start position:0%
+today I nothing to do with the class but
+ 
+
+ align:start position:0%
+today I nothing to do with the class but
+I'm having a baby so so that's kind of
+
+ align:start position:0%
+I'm having a baby so so that's kind of
+ 
+
+ align:start position:0%
+I'm having a baby so so that's kind of
+exciting
+
+ align:start position:0%
+exciting
+ 
+
+ align:start position:0%
+exciting
+so if I just start giggling you'll know
+
+ align:start position:0%
+so if I just start giggling you'll know
+ 
+
+ align:start position:0%
+so if I just start giggling you'll know
+why and then six months if I just
+
+ align:start position:0%
+why and then six months if I just
+ 
+
+ align:start position:0%
+why and then six months if I just
+weeping it on the ground you'll also
+
+ align:start position:0%
+weeping it on the ground you'll also
+ 
+
+ align:start position:0%
+weeping it on the ground you'll also
+know why so so today we're gonna do two
+
+ align:start position:0%
+know why so so today we're gonna do two
+ 
+
+ align:start position:0%
+know why so so today we're gonna do two
+things the first is we're going I'm
+
+ align:start position:0%
+things the first is we're going I'm
+ 
+
+ align:start position:0%
+things the first is we're going I'm
+gonna give you well the first is review
+
+ align:start position:0%
+gonna give you well the first is review
+ 
+
+ align:start position:0%
+gonna give you well the first is review
+a little bit of practice for the exam
+
+ align:start position:0%
+a little bit of practice for the exam
+ 
+
+ align:start position:0%
+a little bit of practice for the exam
+we're gonna have on Thursday let me tell
+
+ align:start position:0%
+we're gonna have on Thursday let me tell
+ 
+
+ align:start position:0%
+we're gonna have on Thursday let me tell
+you a little bit more about the exam the
+
+ align:start position:0%
+you a little bit more about the exam the
+ 
+
+ align:start position:0%
+you a little bit more about the exam the
+exam by the way has been rescheduled to
+
+ align:start position:0%
+exam by the way has been rescheduled to
+ 
+
+ align:start position:0%
+exam by the way has been rescheduled to
+be in six one twenty not in Walker gym
+
+ align:start position:0%
+be in six one twenty not in Walker gym
+ 
+
+ align:start position:0%
+be in six one twenty not in Walker gym
+so it's gonna be the usual place we're
+
+ align:start position:0%
+so it's gonna be the usual place we're
+ 
+
+ align:start position:0%
+so it's gonna be the usual place we're
+not moving and the reason is I'm
+
+ align:start position:0%
+not moving and the reason is I'm
+ 
+
+ align:start position:0%
+not moving and the reason is I'm
+changing the format on this exam in part
+
+ align:start position:0%
+changing the format on this exam in part
+ 
+
+ align:start position:0%
+changing the format on this exam in part
+to make it a little less of a burden to
+
+ align:start position:0%
+to make it a little less of a burden to
+ 
+
+ align:start position:0%
+to make it a little less of a burden to
+everyone but also in part because I've
+
+ align:start position:0%
+everyone but also in part because I've
+ 
+
+ align:start position:0%
+everyone but also in part because I've
+been struggling with the question of how
+
+ align:start position:0%
+been struggling with the question of how
+ 
+
+ align:start position:0%
+been struggling with the question of how
+to make the exam most useful the purpose
+
+ align:start position:0%
+to make the exam most useful the purpose
+ 
+
+ align:start position:0%
+to make the exam most useful the purpose
+of an exam like this is not to get get
+
+ align:start position:0%
+of an exam like this is not to get get
+ 
+
+ align:start position:0%
+of an exam like this is not to get get
+grades for you guys although that's an
+
+ align:start position:0%
+grades for you guys although that's an
+ 
+
+ align:start position:0%
+grades for you guys although that's an
+incidental by-product the purpose is to
+
+ align:start position:0%
+incidental by-product the purpose is to
+ 
+
+ align:start position:0%
+incidental by-product the purpose is to
+give you some feedback on how you're
+
+ align:start position:0%
+give you some feedback on how you're
+ 
+
+ align:start position:0%
+give you some feedback on how you're
+doing how you're command of the material
+
+ align:start position:0%
+doing how you're command of the material
+ 
+
+ align:start position:0%
+doing how you're command of the material
+has evolved and also to to help you sort
+
+ align:start position:0%
+has evolved and also to to help you sort
+ 
+
+ align:start position:0%
+has evolved and also to to help you sort
+of learn some of the things that you
+
+ align:start position:0%
+of learn some of the things that you
+ 
+
+ align:start position:0%
+of learn some of the things that you
+might not have mastered so the way the
+
+ align:start position:0%
+might not have mastered so the way the
+ 
+
+ align:start position:0%
+might not have mastered so the way the
+exam is gonna be structured it's gonna
+
+ align:start position:0%
+exam is gonna be structured it's gonna
+ 
+
+ align:start position:0%
+exam is gonna be structured it's gonna
+be about 50 minutes of short answer
+
+ align:start position:0%
+be about 50 minutes of short answer
+ 
+
+ align:start position:0%
+be about 50 minutes of short answer
+questions a couple of very short
+
+ align:start position:0%
+questions a couple of very short
+ 
+
+ align:start position:0%
+questions a couple of very short
+computations but mostly short answer
+
+ align:start position:0%
+computations but mostly short answer
+ 
+
+ align:start position:0%
+computations but mostly short answer
+questions on paper you'll hand those
+
+ align:start position:0%
+questions on paper you'll hand those
+ 
+
+ align:start position:0%
+questions on paper you'll hand those
+back and then we'll go over those
+
+ align:start position:0%
+back and then we'll go over those
+ 
+
+ align:start position:0%
+back and then we'll go over those
+questions in class afterwards okay so
+
+ align:start position:0%
+questions in class afterwards okay so
+ 
+
+ align:start position:0%
+questions in class afterwards okay so
+it's a relatively low pressure exam and
+
+ align:start position:0%
+it's a relatively low pressure exam and
+ 
+
+ align:start position:0%
+it's a relatively low pressure exam and
+it's mostly conceptual it will cover
+
+ align:start position:0%
+it's mostly conceptual it will cover
+ 
+
+ align:start position:0%
+it's mostly conceptual it will cover
+everything we've done through this last
+
+ align:start position:0%
+everything we've done through this last
+ 
+
+ align:start position:0%
+everything we've done through this last
+problem set today's the to the degree
+
+ align:start position:0%
+problem set today's the to the degree
+ 
+
+ align:start position:0%
+problem set today's the to the degree
+that we get to the lecture part of today
+
+ align:start position:0%
+that we get to the lecture part of today
+ 
+
+ align:start position:0%
+that we get to the lecture part of today
+after questions today's lecture will not
+
+ align:start position:0%
+after questions today's lecture will not
+ 
+
+ align:start position:0%
+after questions today's lecture will not
+be directly covered however it will be a
+
+ align:start position:0%
+be directly covered however it will be a
+ 
+
+ align:start position:0%
+be directly covered however it will be a
+fair game for the next midterm which
+
+ align:start position:0%
+fair game for the next midterm which
+ 
+
+ align:start position:0%
+fair game for the next midterm which
+would be more of a traditional midterm
+
+ align:start position:0%
+would be more of a traditional midterm
+ 
+
+ align:start position:0%
+would be more of a traditional midterm
+and that's coming in April so the
+
+ align:start position:0%
+and that's coming in April so the
+ 
+
+ align:start position:0%
+and that's coming in April so the
+structure of today is I'm going to give
+
+ align:start position:0%
+structure of today is I'm going to give
+ 
+
+ align:start position:0%
+structure of today is I'm going to give
+you a whole bunch of clicker questions
+
+ align:start position:0%
+you a whole bunch of clicker questions
+ 
+
+ align:start position:0%
+you a whole bunch of clicker questions
+so make sure you've got your clickers
+
+ align:start position:0%
+so make sure you've got your clickers
+ 
+
+ align:start position:0%
+so make sure you've got your clickers
+out and those clicker questions are
+
+ align:start position:0%
+out and those clicker questions are
+ 
+
+ align:start position:0%
+out and those clicker questions are
+going to give you a sense for the level
+
+ align:start position:0%
+going to give you a sense for the level
+ 
+
+ align:start position:0%
+going to give you a sense for the level
+and scope of the exam
+
+ align:start position:0%
+and scope of the exam
+ 
+
+ align:start position:0%
+and scope of the exam
+the exam will be a little harder than
+
+ align:start position:0%
+the exam will be a little harder than
+ 
+
+ align:start position:0%
+the exam will be a little harder than
+the clicker questions but not a whole
+
+ align:start position:0%
+the clicker questions but not a whole
+ 
+
+ align:start position:0%
+the clicker questions but not a whole
+lot and the difference is just that it's
+
+ align:start position:0%
+lot and the difference is just that it's
+ 
+
+ align:start position:0%
+lot and the difference is just that it's
+going to be on paper in front of you
+
+ align:start position:0%
+going to be on paper in front of you
+ 
+
+ align:start position:0%
+going to be on paper in front of you
+instead of you know clicker and thus
+
+ align:start position:0%
+instead of you know clicker and thus
+ 
+
+ align:start position:0%
+instead of you know clicker and thus
+that gives you a little more room to do
+
+ align:start position:0%
+that gives you a little more room to do
+ 
+
+ align:start position:0%
+that gives you a little more room to do
+calculations on a piece of paper short
+
+ align:start position:0%
+calculations on a piece of paper short
+ 
+
+ align:start position:0%
+calculations on a piece of paper short
+short calculations and then after that
+
+ align:start position:0%
+short calculations and then after that
+ 
+
+ align:start position:0%
+short calculations and then after that
+we'll we'll come on to some in some
+
+ align:start position:0%
+we'll we'll come on to some in some
+ 
+
+ align:start position:0%
+we'll we'll come on to some in some
+sense of a review but also an
+
+ align:start position:0%
+sense of a review but also an
+ 
+
+ align:start position:0%
+sense of a review but also an
+introduction to the Drakh bra ket
+
+ align:start position:0%
+introduction to the Drakh bra ket
+ 
+
+ align:start position:0%
+introduction to the Drakh bra ket
+notation that many of our textbooks use
+
+ align:start position:0%
+notation that many of our textbooks use
+ 
+
+ align:start position:0%
+notation that many of our textbooks use
+but that we haven't introduced in
+
+ align:start position:0%
+but that we haven't introduced in
+ 
+
+ align:start position:0%
+but that we haven't introduced in
+lecture so far okay any questions before
+
+ align:start position:0%
+lecture so far okay any questions before
+ 
+
+ align:start position:0%
+lecture so far okay any questions before
+you get started
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+41 other questions I think there will
+
+ align:start position:0%
+41 other questions I think there will
+ 
+
+ align:start position:0%
+41 other questions I think there will
+probably not be a practice exam because
+
+ align:start position:0%
+probably not be a practice exam because
+ 
+
+ align:start position:0%
+probably not be a practice exam because
+of the shift in format today will
+
+ align:start position:0%
+of the shift in format today will
+ 
+
+ align:start position:0%
+of the shift in format today will
+basically be your practice exam okay if
+
+ align:start position:0%
+basically be your practice exam okay if
+ 
+
+ align:start position:0%
+basically be your practice exam okay if
+I can get my work together and get you
+
+ align:start position:0%
+I can get my work together and get you
+ 
+
+ align:start position:0%
+I can get my work together and get you
+guys a practice exam of the right format
+
+ align:start position:0%
+guys a practice exam of the right format
+ 
+
+ align:start position:0%
+guys a practice exam of the right format
+then maybe but it wouldn't even be all
+
+ align:start position:0%
+then maybe but it wouldn't even be all
+ 
+
+ align:start position:0%
+then maybe but it wouldn't even be all
+that useful is the problem so watch what
+
+ align:start position:0%
+that useful is the problem so watch what
+ 
+
+ align:start position:0%
+that useful is the problem so watch what
+happens today yep I will post the
+
+ align:start position:0%
+happens today yep I will post the
+ 
+
+ align:start position:0%
+happens today yep I will post the
+questions from today on the website yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can tell you that but it's not gonna
+
+ align:start position:0%
+I can tell you that but it's not gonna
+ 
+
+ align:start position:0%
+I can tell you that but it's not gonna
+be a time trial okay you're not gonna be
+
+ align:start position:0%
+be a time trial okay you're not gonna be
+ 
+
+ align:start position:0%
+be a time trial okay you're not gonna be
+racing to get the you know it will
+
+ align:start position:0%
+racing to get the you know it will
+ 
+
+ align:start position:0%
+racing to get the you know it will
+because it to my mind part of the reason
+
+ align:start position:0%
+because it to my mind part of the reason
+ 
+
+ align:start position:0%
+because it to my mind part of the reason
+to or to design the exam this way is
+
+ align:start position:0%
+to or to design the exam this way is
+ 
+
+ align:start position:0%
+to or to design the exam this way is
+that it's testing your conceptual
+
+ align:start position:0%
+that it's testing your conceptual
+ 
+
+ align:start position:0%
+that it's testing your conceptual
+understanding which is the important
+
+ align:start position:0%
+understanding which is the important
+ 
+
+ align:start position:0%
+understanding which is the important
+thing so yeah it will be the questions
+
+ align:start position:0%
+thing so yeah it will be the questions
+ 
+
+ align:start position:0%
+thing so yeah it will be the questions
+alright so let's get started with the
+
+ align:start position:0%
+alright so let's get started with the
+ 
+
+ align:start position:0%
+alright so let's get started with the
+clicker part of today so do do we're on
+
+ align:start position:0%
+clicker part of today so do do we're on
+ 
+
+ align:start position:0%
+clicker part of today so do do we're on
+channel 41 okay
+
+ align:start position:0%
+channel 41 okay
+ 
+
+ align:start position:0%
+channel 41 okay
+so consider this eigenvalue equation two
+
+ align:start position:0%
+so consider this eigenvalue equation two
+ 
+
+ align:start position:0%
+so consider this eigenvalue equation two
+derivatives on f it's constant times f
+
+ align:start position:0%
+derivatives on f it's constant times f
+ 
+
+ align:start position:0%
+derivatives on f it's constant times f
+of X how many of these are eigen
+
+ align:start position:0%
+of X how many of these are eigen
+ 
+
+ align:start position:0%
+of X how many of these are eigen
+functions with the corresponding
+
+ align:start position:0%
+functions with the corresponding
+ 
+
+ align:start position:0%
+functions with the corresponding
+eigenvalue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I've got about 10 seconds let's go
+
+ align:start position:0%
+okay I've got about 10 seconds let's go
+ 
+
+ align:start position:0%
+okay I've got about 10 seconds let's go
+ahead and put in your clicks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and so your whoops oh sorry that
+
+ align:start position:0%
+okay and so your whoops oh sorry that
+ 
+
+ align:start position:0%
+okay and so your whoops oh sorry that
+just cleared your responses
+
+ align:start position:0%
+just cleared your responses
+ 
+
+ align:start position:0%
+just cleared your responses
+unfortunately the durian they're saved
+
+ align:start position:0%
+unfortunately the durian they're saved
+ 
+
+ align:start position:0%
+unfortunately the durian they're saved
+in memory just clear them off my screen
+
+ align:start position:0%
+in memory just clear them off my screen
+ 
+
+ align:start position:0%
+in memory just clear them off my screen
+so the response is here we go that
+
+ align:start position:0%
+so the response is here we go that
+ 
+
+ align:start position:0%
+so the response is here we go that
+didn't work
+
+ align:start position:0%
+didn't work
+ 
+
+ align:start position:0%
+didn't work
+Wow it just totally disappeared how did
+
+ align:start position:0%
+Wow it just totally disappeared how did
+ 
+
+ align:start position:0%
+Wow it just totally disappeared how did
+that happen
+
+ align:start position:0%
+that happen
+ 
+
+ align:start position:0%
+that happen
+wow that's so weird oh no that didn't
+
+ align:start position:0%
+wow that's so weird oh no that didn't
+ 
+
+ align:start position:0%
+wow that's so weird oh no that didn't
+work let's try this
+
+ align:start position:0%
+work let's try this
+ 
+
+ align:start position:0%
+work let's try this
+where did it go ah there it is
+
+ align:start position:0%
+where did it go ah there it is
+ 
+
+ align:start position:0%
+where did it go ah there it is
+whoa this is all very confusing okay
+
+ align:start position:0%
+whoa this is all very confusing okay
+ 
+
+ align:start position:0%
+whoa this is all very confusing okay
+this one so that that was your response
+
+ align:start position:0%
+this one so that that was your response
+ 
+
+ align:start position:0%
+this one so that that was your response
+B and C 63 and 38% so let's go back to
+
+ align:start position:0%
+B and C 63 and 38% so let's go back to
+ 
+
+ align:start position:0%
+B and C 63 and 38% so let's go back to
+this so quickly discuss this with your
+
+ align:start position:0%
+this so quickly discuss this with your
+ 
+
+ align:start position:0%
+this so quickly discuss this with your
+neighbor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and now go ahead and click in your
+
+ align:start position:0%
+okay and now go ahead and click in your
+ 
+
+ align:start position:0%
+okay and now go ahead and click in your
+new answers if you you can keep talking
+
+ align:start position:0%
+new answers if you you can keep talking
+ 
+
+ align:start position:0%
+new answers if you you can keep talking
+that's fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay another five seconds awesome
+
+ align:start position:0%
+okay another five seconds awesome
+ 
+
+ align:start position:0%
+okay another five seconds awesome
+okay that's it so the answer is B and
+
+ align:start position:0%
+okay that's it so the answer is B and
+ 
+
+ align:start position:0%
+okay that's it so the answer is B and
+99% of y'all got that I suspect someone
+
+ align:start position:0%
+99% of y'all got that I suspect someone
+ 
+
+ align:start position:0%
+99% of y'all got that I suspect someone
+didn't click okay good
+
+ align:start position:0%
+didn't click okay good
+ 
+
+ align:start position:0%
+didn't click okay good
+next question so I want insight to our
+
+ align:start position:0%
+next question so I want insight to our
+ 
+
+ align:start position:0%
+next question so I want insight to our
+two solutions of the Schrodinger
+
+ align:start position:0%
+two solutions of the Schrodinger
+ 
+
+ align:start position:0%
+two solutions of the Schrodinger
+equation is the sum of the two of them
+
+ align:start position:0%
+equation is the sum of the two of them
+ 
+
+ align:start position:0%
+equation is the sum of the two of them
+with coefficients a and B also a
+
+ align:start position:0%
+with coefficients a and B also a
+ 
+
+ align:start position:0%
+with coefficients a and B also a
+solution of the Schrodinger equation oh
+
+ align:start position:0%
+solution of the Schrodinger equation oh
+ 
+
+ align:start position:0%
+solution of the Schrodinger equation oh
+and I forgot to start the clicky thingy
+
+ align:start position:0%
+and I forgot to start the clicky thingy
+ 
+
+ align:start position:0%
+and I forgot to start the clicky thingy
+so click now oh yeah it is supposed to
+
+ align:start position:0%
+so click now oh yeah it is supposed to
+ 
+
+ align:start position:0%
+so click now oh yeah it is supposed to
+say psi 2 it says B Saito on the next
+
+ align:start position:0%
+say psi 2 it says B Saito on the next
+ 
+
+ align:start position:0%
+say psi 2 it says B Saito on the next
+sorry it's a Sai 1 plus psi 1 it should
+
+ align:start position:0%
+sorry it's a Sai 1 plus psi 1 it should
+ 
+
+ align:start position:0%
+sorry it's a Sai 1 plus psi 1 it should
+say Sai 1 plus psi 2 thank you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah with the same potential yeah yeah
+
+ align:start position:0%
+yeah with the same potential yeah yeah
+ 
+
+ align:start position:0%
+yeah with the same potential yeah yeah
+[Laughter]
+
+ align:start position:0%
+[Laughter]
+ 
+
+ align:start position:0%
+[Laughter]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Wow
+
+ align:start position:0%
+Wow
+ 
+
+ align:start position:0%
+Wow
+yeah so you know Einstein said God
+
+ align:start position:0%
+yeah so you know Einstein said God
+ 
+
+ align:start position:0%
+yeah so you know Einstein said God
+didn't play dice and let me paraphrase
+
+ align:start position:0%
+didn't play dice and let me paraphrase
+ 
+
+ align:start position:0%
+didn't play dice and let me paraphrase
+that is God doesn't mess with you and
+
+ align:start position:0%
+that is God doesn't mess with you and
+ 
+
+ align:start position:0%
+that is God doesn't mess with you and
+clicker question yeah okay and and you
+
+ align:start position:0%
+clicker question yeah okay and and you
+ 
+
+ align:start position:0%
+clicker question yeah okay and and you
+guys have effectively universally that
+
+ align:start position:0%
+guys have effectively universally that
+ 
+
+ align:start position:0%
+guys have effectively universally that
+the answer is a yes the superposition
+
+ align:start position:0%
+the answer is a yes the superposition
+ 
+
+ align:start position:0%
+the answer is a yes the superposition
+principle okay next question is going to
+
+ align:start position:0%
+principle okay next question is going to
+ 
+
+ align:start position:0%
+principle okay next question is going to
+be for answer here we go
+
+ align:start position:0%
+be for answer here we go
+ 
+
+ align:start position:0%
+be for answer here we go
+consider an infinite square well with
+
+ align:start position:0%
+consider an infinite square well with
+ 
+
+ align:start position:0%
+consider an infinite square well with
+with a and compared to the infinite
+
+ align:start position:0%
+with a and compared to the infinite
+ 
+
+ align:start position:0%
+with a and compared to the infinite
+square well with with a the ground state
+
+ align:start position:0%
+square well with with a the ground state
+ 
+
+ align:start position:0%
+square well with with a the ground state
+of a finite well is lower higher same
+
+ align:start position:0%
+of a finite well is lower higher same
+ 
+
+ align:start position:0%
+of a finite well is lower higher same
+energy or undetermined
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you've got ten seconds so continue
+
+ align:start position:0%
+you've got ten seconds so continue
+ 
+
+ align:start position:0%
+you've got ten seconds so continue
+thinking through this five seconds okay
+
+ align:start position:0%
+thinking through this five seconds okay
+ 
+
+ align:start position:0%
+thinking through this five seconds okay
+and you mostly got it but have a quick
+
+ align:start position:0%
+and you mostly got it but have a quick
+ 
+
+ align:start position:0%
+and you mostly got it but have a quick
+chat with the person next to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right let's try again it's such a
+
+ align:start position:0%
+all right let's try again it's such a
+ 
+
+ align:start position:0%
+all right let's try again it's such a
+good technique um I read another five
+
+ align:start position:0%
+good technique um I read another five
+ 
+
+ align:start position:0%
+good technique um I read another five
+seconds to put in your answer four three
+
+ align:start position:0%
+seconds to put in your answer four three
+ 
+
+ align:start position:0%
+seconds to put in your answer four three
+two one okay and you virtually all got
+
+ align:start position:0%
+two one okay and you virtually all got
+ 
+
+ align:start position:0%
+two one okay and you virtually all got
+it right they lower energy and let's
+
+ align:start position:0%
+it right they lower energy and let's
+ 
+
+ align:start position:0%
+it right they lower energy and let's
+just think about this intuitively
+
+ align:start position:0%
+just think about this intuitively
+ 
+
+ align:start position:0%
+just think about this intuitively
+intuitively the the gradient of the
+
+ align:start position:0%
+intuitively the the gradient of the
+ 
+
+ align:start position:0%
+intuitively the the gradient of the
+potential is a force right so in the
+
+ align:start position:0%
+potential is a force right so in the
+ 
+
+ align:start position:0%
+potential is a force right so in the
+second case you've got less force
+
+ align:start position:0%
+second case you've got less force
+ 
+
+ align:start position:0%
+second case you've got less force
+cramming the particle inside the box so
+
+ align:start position:0%
+cramming the particle inside the box so
+ 
+
+ align:start position:0%
+cramming the particle inside the box so
+it's being squeezed less tightly more
+
+ align:start position:0%
+it's being squeezed less tightly more
+ 
+
+ align:start position:0%
+it's being squeezed less tightly more
+physically you see that there was an
+
+ align:start position:0%
+physically you see that there was an
+ 
+
+ align:start position:0%
+physically you see that there was an
+evanescent tail on the outside what that
+
+ align:start position:0%
+evanescent tail on the outside what that
+ 
+
+ align:start position:0%
+evanescent tail on the outside what that
+tells you is the wave flux you didn't
+
+ align:start position:0%
+tells you is the wave flux you didn't
+ 
+
+ align:start position:0%
+tells you is the wave flux you didn't
+have to go to zero at the end it just
+
+ align:start position:0%
+have to go to zero at the end it just
+ 
+
+ align:start position:0%
+have to go to zero at the end it just
+had to get small and match on to a dying
+
+ align:start position:0%
+had to get small and match on to a dying
+ 
+
+ align:start position:0%
+had to get small and match on to a dying
+exponential right that's from the
+
+ align:start position:0%
+exponential right that's from the
+ 
+
+ align:start position:0%
+exponential right that's from the
+qualitative analysis of wave functions
+
+ align:start position:0%
+qualitative analysis of wave functions
+ 
+
+ align:start position:0%
+qualitative analysis of wave functions
+but meanwhile what that tells you is it
+
+ align:start position:0%
+but meanwhile what that tells you is it
+ 
+
+ align:start position:0%
+but meanwhile what that tells you is it
+has to curve less inside in order to
+
+ align:start position:0%
+has to curve less inside in order to
+ 
+
+ align:start position:0%
+has to curve less inside in order to
+have to get to zero it just has to get
+
+ align:start position:0%
+have to get to zero it just has to get
+ 
+
+ align:start position:0%
+have to get to zero it just has to get
+to a small value where matches to the
+
+ align:start position:0%
+to a small value where matches to the
+ 
+
+ align:start position:0%
+to a small value where matches to the
+decaying exponential so if the curvature
+
+ align:start position:0%
+decaying exponential so if the curvature
+ 
+
+ align:start position:0%
+decaying exponential so if the curvature
+is less than the energy is less cool
+
+ align:start position:0%
+is less than the energy is less cool
+ 
+
+ align:start position:0%
+is less than the energy is less cool
+okay next question
+
+ align:start position:0%
+okay next question
+ 
+
+ align:start position:0%
+okay next question
+or so any questions on that okay good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+time zero wavefunction infinite well
+
+ align:start position:0%
+time zero wavefunction infinite well
+ 
+
+ align:start position:0%
+time zero wavefunction infinite well
+with a is this sine squared with the
+
+ align:start position:0%
+with a is this sine squared with the
+ 
+
+ align:start position:0%
+with a is this sine squared with the
+normalization what's the wave function
+
+ align:start position:0%
+normalization what's the wave function
+ 
+
+ align:start position:0%
+normalization what's the wave function
+at a subsequent time T
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and will remind you that you have solved
+
+ align:start position:0%
+and will remind you that you have solved
+ 
+
+ align:start position:0%
+and will remind you that you have solved
+the problem of the infinite square well
+
+ align:start position:0%
+the problem of the infinite square well
+ 
+
+ align:start position:0%
+the problem of the infinite square well
+and you know what the energies the
+
+ align:start position:0%
+and you know what the energies the
+ 
+
+ align:start position:0%
+and you know what the energies the
+eigenenergies and eigenfunctions are of
+
+ align:start position:0%
+eigenenergies and eigenfunctions are of
+ 
+
+ align:start position:0%
+eigenenergies and eigenfunctions are of
+the energy operators energy operator in
+
+ align:start position:0%
+the energy operators energy operator in
+ 
+
+ align:start position:0%
+the energy operators energy operator in
+the infinite square well so remember
+
+ align:start position:0%
+the infinite square well so remember
+ 
+
+ align:start position:0%
+the infinite square well so remember
+back to what those are all right and you
+
+ align:start position:0%
+back to what those are all right and you
+ 
+
+ align:start position:0%
+back to what those are all right and you
+have five seconds okay we are at about
+
+ align:start position:0%
+have five seconds okay we are at about
+ 
+
+ align:start position:0%
+have five seconds okay we are at about
+50/50 correct
+
+ align:start position:0%
+50/50 correct
+ 
+
+ align:start position:0%
+50/50 correct
+so chat with the person next to you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and now any moments go ahead
+
+ align:start position:0%
+all right and now any moments go ahead
+ 
+
+ align:start position:0%
+all right and now any moments go ahead
+and vote again good five more seconds
+
+ align:start position:0%
+and vote again good five more seconds
+ 
+
+ align:start position:0%
+and vote again good five more seconds
+and then put in your final vote okay
+
+ align:start position:0%
+and then put in your final vote okay
+ 
+
+ align:start position:0%
+and then put in your final vote okay
+that's it for now so what's the answer D
+
+ align:start position:0%
+that's it for now so what's the answer D
+ 
+
+ align:start position:0%
+that's it for now so what's the answer D
+is the answer but a lot of people so
+
+ align:start position:0%
+is the answer but a lot of people so
+ 
+
+ align:start position:0%
+is the answer but a lot of people so
+it's in doubt so who wants to give an
+
+ align:start position:0%
+it's in doubt so who wants to give an
+ 
+
+ align:start position:0%
+it's in doubt so who wants to give an
+explanation for why it's D excellent
+
+ align:start position:0%
+explanation for why it's D excellent
+ 
+
+ align:start position:0%
+explanation for why it's D excellent
+excellent really okay so I'm gonna
+
+ align:start position:0%
+excellent really okay so I'm gonna
+ 
+
+ align:start position:0%
+excellent really okay so I'm gonna
+restate that that was exactly correct in
+
+ align:start position:0%
+restate that that was exactly correct in
+ 
+
+ align:start position:0%
+restate that that was exactly correct in
+every step so the first thing is that
+
+ align:start position:0%
+every step so the first thing is that
+ 
+
+ align:start position:0%
+every step so the first thing is that
+wave function at time 0 sine squared of
+
+ align:start position:0%
+wave function at time 0 sine squared of
+ 
+
+ align:start position:0%
+wave function at time 0 sine squared of
+X is not an eigenfunction of the energy
+
+ align:start position:0%
+X is not an eigenfunction of the energy
+ 
+
+ align:start position:0%
+X is not an eigenfunction of the energy
+operator for the system in fact we
+
+ align:start position:0%
+operator for the system in fact we
+ 
+
+ align:start position:0%
+operator for the system in fact we
+computed the eigenfunctions for the
+
+ align:start position:0%
+computed the eigenfunctions for the
+ 
+
+ align:start position:0%
+computed the eigenfunctions for the
+energy operator in the infinite square
+
+ align:start position:0%
+energy operator in the infinite square
+ 
+
+ align:start position:0%
+energy operator in the infinite square
+well and their signs where they get a
+
+ align:start position:0%
+well and their signs where they get a
+ 
+
+ align:start position:0%
+well and their signs where they get a
+zero at the ends on the other hand any
+
+ align:start position:0%
+zero at the ends on the other hand any
+ 
+
+ align:start position:0%
+zero at the ends on the other hand any
+function with which satisfying the
+
+ align:start position:0%
+function with which satisfying the
+ 
+
+ align:start position:0%
+function with which satisfying the
+boundary conditions normalizable hits
+
+ align:start position:0%
+boundary conditions normalizable hits
+ 
+
+ align:start position:0%
+boundary conditions normalizable hits
+zero at the boundaries is a
+
+ align:start position:0%
+zero at the boundaries is a
+ 
+
+ align:start position:0%
+zero at the boundaries is a
+superposition of energy eigenfunctions
+
+ align:start position:0%
+superposition of energy eigenfunctions
+ 
+
+ align:start position:0%
+superposition of energy eigenfunctions
+and we can use that to determine the
+
+ align:start position:0%
+and we can use that to determine the
+ 
+
+ align:start position:0%
+and we can use that to determine the
+time evolution we take that
+
+ align:start position:0%
+time evolution we take that
+ 
+
+ align:start position:0%
+time evolution we take that
+superposition and and add on a phase e
+
+ align:start position:0%
+superposition and and add on a phase e
+ 
+
+ align:start position:0%
+superposition and and add on a phase e
+to the minus IET upon h-bar for each of
+
+ align:start position:0%
+to the minus IET upon h-bar for each of
+ 
+
+ align:start position:0%
+to the minus IET upon h-bar for each of
+the energy eigenfunctions and in Part D
+
+ align:start position:0%
+the energy eigenfunctions and in Part D
+ 
+
+ align:start position:0%
+the energy eigenfunctions and in Part D
+we express that wave function as a
+
+ align:start position:0%
+we express that wave function as a
+ 
+
+ align:start position:0%
+we express that wave function as a
+superposition with the coefficient cn
+
+ align:start position:0%
+superposition with the coefficient cn
+ 
+
+ align:start position:0%
+superposition with the coefficient cn
+determined from the overlap of our
+
+ align:start position:0%
+determined from the overlap of our
+ 
+
+ align:start position:0%
+determined from the overlap of our
+original function and the energy
+
+ align:start position:0%
+original function and the energy
+ 
+
+ align:start position:0%
+original function and the energy
+eigenfunctions everyone cool that so
+
+ align:start position:0%
+eigenfunctions everyone cool that so
+ 
+
+ align:start position:0%
+eigenfunctions everyone cool that so
+this is literally just a transcription
+
+ align:start position:0%
+this is literally just a transcription
+ 
+
+ align:start position:0%
+this is literally just a transcription
+of one of our postulates
+
+ align:start position:0%
+of one of our postulates
+ 
+
+ align:start position:0%
+of one of our postulates
+ok questions if you have any questions
+
+ align:start position:0%
+ok questions if you have any questions
+ 
+
+ align:start position:0%
+ok questions if you have any questions
+at all ask them this is the time to ask
+
+ align:start position:0%
+at all ask them this is the time to ask
+ 
+
+ align:start position:0%
+at all ask them this is the time to ask
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly so the way you get CN is by
+
+ align:start position:0%
+exactly so the way you get CN is by
+ 
+
+ align:start position:0%
+exactly so the way you get CN is by
+saying look I have my wave function Phi
+
+ align:start position:0%
+saying look I have my wave function Phi
+ 
+
+ align:start position:0%
+saying look I have my wave function Phi
+of X is equal to sum over n CN Phi n of
+
+ align:start position:0%
+of X is equal to sum over n CN Phi n of
+ 
+
+ align:start position:0%
+of X is equal to sum over n CN Phi n of
+X where these fans are energy
+
+ align:start position:0%
+X where these fans are energy
+ 
+
+ align:start position:0%
+X where these fans are energy
+eigenfunctions e Phi n is equal to e n
+
+ align:start position:0%
+eigenfunctions e Phi n is equal to e n
+ 
+
+ align:start position:0%
+eigenfunctions e Phi n is equal to e n
+Phi n right of X and we also know that
+
+ align:start position:0%
+Phi n right of X and we also know that
+ 
+
+ align:start position:0%
+Phi n right of X and we also know that
+the integral of Phi n complex conjugate
+
+ align:start position:0%
+the integral of Phi n complex conjugate
+ 
+
+ align:start position:0%
+the integral of Phi n complex conjugate
+Phi M is equal to Delta MN right this is
+
+ align:start position:0%
+Phi M is equal to Delta MN right this is
+ 
+
+ align:start position:0%
+Phi M is equal to Delta MN right this is
+the statement that they're orthogonal
+
+ align:start position:0%
+the statement that they're orthogonal
+ 
+
+ align:start position:0%
+the statement that they're orthogonal
+and properly normalized we also write
+
+ align:start position:0%
+and properly normalized we also write
+ 
+
+ align:start position:0%
+and properly normalized we also write
+this as equal to Phi n Phi M and we can
+
+ align:start position:0%
+this as equal to Phi n Phi M and we can
+ 
+
+ align:start position:0%
+this as equal to Phi n Phi M and we can
+use this to determine the CNS the CN is
+
+ align:start position:0%
+use this to determine the CNS the CN is
+ 
+
+ align:start position:0%
+use this to determine the CNS the CN is
+equal to the inner product of Phi n with
+
+ align:start position:0%
+equal to the inner product of Phi n with
+ 
+
+ align:start position:0%
+equal to the inner product of Phi n with
+our wave function this is equal to the
+
+ align:start position:0%
+our wave function this is equal to the
+ 
+
+ align:start position:0%
+our wave function this is equal to the
+integral DX Phi star Phi n star sign
+
+ align:start position:0%
+integral DX Phi star Phi n star sign
+ 
+
+ align:start position:0%
+integral DX Phi star Phi n star sign
+which is equal to the integral DX Phi n
+
+ align:start position:0%
+which is equal to the integral DX Phi n
+ 
+
+ align:start position:0%
+which is equal to the integral DX Phi n
+star sum over m of C M by M but this sum
+
+ align:start position:0%
+star sum over m of C M by M but this sum
+ 
+
+ align:start position:0%
+star sum over m of C M by M but this sum
+over m of C M can be pulled out because
+
+ align:start position:0%
+over m of C M can be pulled out because
+ 
+
+ align:start position:0%
+over m of C M can be pulled out because
+this is just an integral over a sum of
+
+ align:start position:0%
+this is just an integral over a sum of
+ 
+
+ align:start position:0%
+this is just an integral over a sum of
+terms which is the same as a sum over m
+
+ align:start position:0%
+terms which is the same as a sum over m
+ 
+
+ align:start position:0%
+terms which is the same as a sum over m
+cm integral Phi n complex conjugate to
+
+ align:start position:0%
+cm integral Phi n complex conjugate to
+ 
+
+ align:start position:0%
+cm integral Phi n complex conjugate to
+Phi M and that's Delta MN which is 0
+
+ align:start position:0%
+Phi M and that's Delta MN which is 0
+ 
+
+ align:start position:0%
+Phi M and that's Delta MN which is 0
+unless n is equal to M because these
+
+ align:start position:0%
+unless n is equal to M because these
+ 
+
+ align:start position:0%
+unless n is equal to M because these
+guys are orthogonal and properly
+
+ align:start position:0%
+guys are orthogonal and properly
+ 
+
+ align:start position:0%
+guys are orthogonal and properly
+normalized so this is zero unless n is
+
+ align:start position:0%
+normalized so this is zero unless n is
+ 
+
+ align:start position:0%
+normalized so this is zero unless n is
+equal to M so in this sum the only term
+
+ align:start position:0%
+equal to M so in this sum the only term
+ 
+
+ align:start position:0%
+equal to M so in this sum the only term
+that contributes is when M is equal to n
+
+ align:start position:0%
+that contributes is when M is equal to n
+ 
+
+ align:start position:0%
+that contributes is when M is equal to n
+this is equal to CN so CN is given by
+
+ align:start position:0%
+this is equal to CN so CN is given by
+ 
+
+ align:start position:0%
+this is equal to CN so CN is given by
+the overlap of our wave function with
+
+ align:start position:0%
+the overlap of our wave function with
+ 
+
+ align:start position:0%
+the overlap of our wave function with
+the corresponding eigen function this
+
+ align:start position:0%
+the corresponding eigen function this
+ 
+
+ align:start position:0%
+the corresponding eigen function this
+allows us to take our function a known
+
+ align:start position:0%
+allows us to take our function a known
+ 
+
+ align:start position:0%
+allows us to take our function a known
+function for example sine squared and
+
+ align:start position:0%
+function for example sine squared and
+ 
+
+ align:start position:0%
+function for example sine squared and
+express the coefficients in terms of an
+
+ align:start position:0%
+express the coefficients in terms of an
+ 
+
+ align:start position:0%
+express the coefficients in terms of an
+overlap of our wave function sine
+
+ align:start position:0%
+overlap of our wave function sine
+ 
+
+ align:start position:0%
+overlap of our wave function sine
+squared with the wave functions sign and
+
+ align:start position:0%
+squared with the wave functions sign and
+ 
+
+ align:start position:0%
+squared with the wave functions sign and
+that's exactly the expression you see
+
+ align:start position:0%
+that's exactly the expression you see
+ 
+
+ align:start position:0%
+that's exactly the expression you see
+below CN is equal to the integral of
+
+ align:start position:0%
+below CN is equal to the integral of
+ 
+
+ align:start position:0%
+below CN is equal to the integral of
+sine squared our wave function and sine
+
+ align:start position:0%
+sine squared our wave function and sine
+ 
+
+ align:start position:0%
+sine squared our wave function and sine
+which is the energy eigenfunction cool
+
+ align:start position:0%
+which is the energy eigenfunction cool
+ 
+
+ align:start position:0%
+which is the energy eigenfunction cool
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+questions okay great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next problem come to me a computer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I can't it should be written in Python
+
+ align:start position:0%
+I can't it should be written in Python
+ 
+
+ align:start position:0%
+I can't it should be written in Python
+okay I'm good yeah eigenstates Phi n
+
+ align:start position:0%
+okay I'm good yeah eigenstates Phi n
+ 
+
+ align:start position:0%
+okay I'm good yeah eigenstates Phi n
+which we usually call sign but there it
+
+ align:start position:0%
+which we usually call sign but there it
+ 
+
+ align:start position:0%
+which we usually call sign but there it
+is form an orthonormal set meaning
+
+ align:start position:0%
+is form an orthonormal set meaning
+ 
+
+ align:start position:0%
+is form an orthonormal set meaning
+integral of Phi M star Phi n is Delta MN
+
+ align:start position:0%
+integral of Phi M star Phi n is Delta MN
+ 
+
+ align:start position:0%
+integral of Phi M star Phi n is Delta MN
+what is the value of integral Siam
+
+ align:start position:0%
+what is the value of integral Siam
+ 
+
+ align:start position:0%
+what is the value of integral Siam
+against the sum CN Phi n okay you got
+
+ align:start position:0%
+against the sum CN Phi n okay you got
+ 
+
+ align:start position:0%
+against the sum CN Phi n okay you got
+five seconds give you a little extra
+
+ align:start position:0%
+five seconds give you a little extra
+ 
+
+ align:start position:0%
+five seconds give you a little extra
+time because people are clicking away
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+you now have seven seconds because time
+
+ align:start position:0%
+you now have seven seconds because time
+ 
+
+ align:start position:0%
+you now have seven seconds because time
+is nonlinear okay so quickly discuss
+
+ align:start position:0%
+is nonlinear okay so quickly discuss
+ 
+
+ align:start position:0%
+is nonlinear okay so quickly discuss
+because there's still some ambiguity
+
+ align:start position:0%
+because there's still some ambiguity
+ 
+
+ align:start position:0%
+because there's still some ambiguity
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right you have 10 seconds to modify
+
+ align:start position:0%
+all right you have 10 seconds to modify
+ 
+
+ align:start position:0%
+all right you have 10 seconds to modify
+your clicks click alright yes and the
+
+ align:start position:0%
+your clicks click alright yes and the
+ 
+
+ align:start position:0%
+your clicks click alright yes and the
+answer is C excellent okay good right
+
+ align:start position:0%
+answer is C excellent okay good right
+ 
+
+ align:start position:0%
+answer is C excellent okay good right
+because in fact we just did that okay
+
+ align:start position:0%
+because in fact we just did that okay
+ 
+
+ align:start position:0%
+because in fact we just did that okay
+that one happened on the actual exam so
+
+ align:start position:0%
+that one happened on the actual exam so
+ 
+
+ align:start position:0%
+that one happened on the actual exam so
+here's the next question
+
+ align:start position:0%
+here's the next question
+ 
+
+ align:start position:0%
+here's the next question
+let the Hamiltonian on a dagger u n
+
+ align:start position:0%
+let the Hamiltonian on a dagger u n
+ 
+
+ align:start position:0%
+let the Hamiltonian on a dagger u n
+equals y n plus H Omega that should be
+
+ align:start position:0%
+equals y n plus H Omega that should be
+ 
+
+ align:start position:0%
+equals y n plus H Omega that should be
+an H bar a dagger u n what can you say
+
+ align:start position:0%
+an H bar a dagger u n what can you say
+ 
+
+ align:start position:0%
+an H bar a dagger u n what can you say
+about a dagger u n here what we should
+
+ align:start position:0%
+about a dagger u n here what we should
+ 
+
+ align:start position:0%
+about a dagger u n here what we should
+probably say what can one say you know
+
+ align:start position:0%
+probably say what can one say you know
+ 
+
+ align:start position:0%
+probably say what can one say you know
+possible okay what could one say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here the assumption just to say it out
+
+ align:start position:0%
+here the assumption just to say it out
+ 
+
+ align:start position:0%
+here the assumption just to say it out
+loud the assumption is that UN is an
+
+ align:start position:0%
+loud the assumption is that UN is an
+ 
+
+ align:start position:0%
+loud the assumption is that UN is an
+eigenfunction of the energy operator H
+
+ align:start position:0%
+eigenfunction of the energy operator H
+ 
+
+ align:start position:0%
+eigenfunction of the energy operator H
+with eigenvalue en okay you've got five
+
+ align:start position:0%
+with eigenvalue en okay you've got five
+ 
+
+ align:start position:0%
+with eigenvalue en okay you've got five
+seconds all right we are at 5050 so
+
+ align:start position:0%
+seconds all right we are at 5050 so
+ 
+
+ align:start position:0%
+seconds all right we are at 5050 so
+discuss amongst yourselves
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right you have okay go ahead and
+
+ align:start position:0%
+all right you have okay go ahead and
+ 
+
+ align:start position:0%
+all right you have okay go ahead and
+enter again enter your modified guesses
+
+ align:start position:0%
+enter again enter your modified guesses
+ 
+
+ align:start position:0%
+enter again enter your modified guesses
+and you have ten seconds to do so wow
+
+ align:start position:0%
+and you have ten seconds to do so wow
+ 
+
+ align:start position:0%
+and you have ten seconds to do so wow
+this is a lot better okay this is great
+
+ align:start position:0%
+this is a lot better okay this is great
+ 
+
+ align:start position:0%
+this is a lot better okay this is great
+so this is one of those really
+
+ align:start position:0%
+so this is one of those really
+ 
+
+ align:start position:0%
+so this is one of those really
+satisfying moments it's improved but
+
+ align:start position:0%
+satisfying moments it's improved but
+ 
+
+ align:start position:0%
+satisfying moments it's improved but
+there's still some real doubt here so I
+
+ align:start position:0%
+there's still some real doubt here so I
+ 
+
+ align:start position:0%
+there's still some real doubt here so I
+would like to get one person to argue
+
+ align:start position:0%
+would like to get one person to argue
+ 
+
+ align:start position:0%
+would like to get one person to argue
+for B and one person to argue for C's
+
+ align:start position:0%
+for B and one person to argue for C's
+ 
+
+ align:start position:0%
+for B and one person to argue for C's
+who who wants to volunteer for each of
+
+ align:start position:0%
+who who wants to volunteer for each of
+ 
+
+ align:start position:0%
+who who wants to volunteer for each of
+those which one you want who's gonna
+
+ align:start position:0%
+those which one you want who's gonna
+ 
+
+ align:start position:0%
+those which one you want who's gonna
+argue for be someone's gonna argue for
+
+ align:start position:0%
+argue for be someone's gonna argue for
+ 
+
+ align:start position:0%
+argue for be someone's gonna argue for
+me come on I'm not gonna argue for you
+
+ align:start position:0%
+me come on I'm not gonna argue for you
+ 
+
+ align:start position:0%
+me come on I'm not gonna argue for you
+I'm not gonna argue for C either that
+
+ align:start position:0%
+I'm not gonna argue for C either that
+ 
+
+ align:start position:0%
+I'm not gonna argue for C either that
+defeat surprised me I have to see this
+
+ align:start position:0%
+defeat surprised me I have to see this
+ 
+
+ align:start position:0%
+defeat surprised me I have to see this
+all the time so who's gonna intervene
+
+ align:start position:0%
+all the time so who's gonna intervene
+ 
+
+ align:start position:0%
+all the time so who's gonna intervene
+okay you argue for me who's gonna argue
+
+ align:start position:0%
+okay you argue for me who's gonna argue
+ 
+
+ align:start position:0%
+okay you argue for me who's gonna argue
+for C all right yeah that worked out
+
+ align:start position:0%
+for C all right yeah that worked out
+ 
+
+ align:start position:0%
+for C all right yeah that worked out
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+great beat are you for me you can do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I guess I can do this so originally I
+
+ align:start position:0%
+so I guess I can do this so originally I
+ 
+
+ align:start position:0%
+so I guess I can do this so originally I
+just kind of didn't read the question
+
+ align:start position:0%
+just kind of didn't read the question
+ 
+
+ align:start position:0%
+just kind of didn't read the question
+and I thought since you're acting the
+
+ align:start position:0%
+and I thought since you're acting the
+ 
+
+ align:start position:0%
+and I thought since you're acting the
+ladder operator on the I can say that
+
+ align:start position:0%
+ladder operator on the I can say that
+ 
+
+ align:start position:0%
+ladder operator on the I can say that
+you get a proportionality constant sign
+
+ align:start position:0%
+you get a proportionality constant sign
+ 
+
+ align:start position:0%
+you get a proportionality constant sign
+some eigenstate so that's why that's not
+
+ align:start position:0%
+some eigenstate so that's why that's not
+ 
+
+ align:start position:0%
+some eigenstate so that's why that's not
+the best argument imaginable for B but
+
+ align:start position:0%
+the best argument imaginable for B but
+ 
+
+ align:start position:0%
+the best argument imaginable for B but
+we'll take it we'll take it so you can
+
+ align:start position:0%
+we'll take it we'll take it so you can
+ 
+
+ align:start position:0%
+we'll take it we'll take it so you can
+thank you so I yeah when I put someone
+
+ align:start position:0%
+thank you so I yeah when I put someone
+ 
+
+ align:start position:0%
+thank you so I yeah when I put someone
+in an impossible position to see
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fantastic that's exactly right so let me
+
+ align:start position:0%
+fantastic that's exactly right so let me
+ 
+
+ align:start position:0%
+fantastic that's exactly right so let me
+walk through that let me say that out
+
+ align:start position:0%
+walk through that let me say that out
+ 
+
+ align:start position:0%
+walk through that let me say that out
+loud
+
+ align:start position:0%
+loud
+ 
+
+ align:start position:0%
+loud
+so from the first line it is clear that
+
+ align:start position:0%
+so from the first line it is clear that
+ 
+
+ align:start position:0%
+so from the first line it is clear that
+the object a UN is an eigenfunction of
+
+ align:start position:0%
+the object a UN is an eigenfunction of
+ 
+
+ align:start position:0%
+the object a UN is an eigenfunction of
+the energy operator right and it's got
+
+ align:start position:0%
+the energy operator right and it's got
+ 
+
+ align:start position:0%
+the energy operator right and it's got
+egg in value en plus h Omega so it is a
+
+ align:start position:0%
+egg in value en plus h Omega so it is a
+ 
+
+ align:start position:0%
+egg in value en plus h Omega so it is a
+stationary States an eigenfunction of
+
+ align:start position:0%
+stationary States an eigenfunction of
+ 
+
+ align:start position:0%
+stationary States an eigenfunction of
+the energy it is not the same one
+
+ align:start position:0%
+the energy it is not the same one
+ 
+
+ align:start position:0%
+the energy it is not the same one
+because it has a different eigen value
+
+ align:start position:0%
+because it has a different eigen value
+ 
+
+ align:start position:0%
+because it has a different eigen value
+so if what it means to be the same
+
+ align:start position:0%
+so if what it means to be the same
+ 
+
+ align:start position:0%
+so if what it means to be the same
+energy eigenstate as it has the same
+
+ align:start position:0%
+energy eigenstate as it has the same
+ 
+
+ align:start position:0%
+energy eigenstate as it has the same
+eigen value it has a different energy
+
+ align:start position:0%
+eigen value it has a different energy
+ 
+
+ align:start position:0%
+eigen value it has a different energy
+eigenvalue it is a different state and
+
+ align:start position:0%
+eigenvalue it is a different state and
+ 
+
+ align:start position:0%
+eigenvalue it is a different state and
+they're orthogonal we proved this before
+
+ align:start position:0%
+they're orthogonal we proved this before
+ 
+
+ align:start position:0%
+they're orthogonal we proved this before
+two states with different energy
+
+ align:start position:0%
+two states with different energy
+ 
+
+ align:start position:0%
+two states with different energy
+orthogonal so they don't even not only
+
+ align:start position:0%
+orthogonal so they don't even not only
+ 
+
+ align:start position:0%
+orthogonal so they don't even not only
+are they not the same they don't even
+
+ align:start position:0%
+are they not the same they don't even
+ 
+
+ align:start position:0%
+are they not the same they don't even
+have any overlap okay so it is a
+
+ align:start position:0%
+have any overlap okay so it is a
+ 
+
+ align:start position:0%
+have any overlap okay so it is a
+stationary state but it's not
+
+ align:start position:0%
+stationary state but it's not
+ 
+
+ align:start position:0%
+stationary state but it's not
+proportional with the state UN it's an
+
+ align:start position:0%
+proportional with the state UN it's an
+ 
+
+ align:start position:0%
+proportional with the state UN it's an
+important one okay
+
+ align:start position:0%
+important one okay
+ 
+
+ align:start position:0%
+important one okay
+questions about that one before we move
+
+ align:start position:0%
+questions about that one before we move
+ 
+
+ align:start position:0%
+questions about that one before we move
+on to the next if it were proportional
+
+ align:start position:0%
+on to the next if it were proportional
+ 
+
+ align:start position:0%
+on to the next if it were proportional
+to the state UN then it would be some
+
+ align:start position:0%
+to the state UN then it would be some
+ 
+
+ align:start position:0%
+to the state UN then it would be some
+constant times UN that's what we mean by
+
+ align:start position:0%
+constant times UN that's what we mean by
+ 
+
+ align:start position:0%
+constant times UN that's what we mean by
+saying it's proportional but then if we
+
+ align:start position:0%
+saying it's proportional but then if we
+ 
+
+ align:start position:0%
+saying it's proportional but then if we
+acted on it with the energy operator
+
+ align:start position:0%
+acted on it with the energy operator
+ 
+
+ align:start position:0%
+acted on it with the energy operator
+what would the eigenvalue be so let me
+
+ align:start position:0%
+what would the eigenvalue be so let me
+ 
+
+ align:start position:0%
+what would the eigenvalue be so let me
+say this again suppose I have a state UN
+
+ align:start position:0%
+say this again suppose I have a state UN
+ 
+
+ align:start position:0%
+say this again suppose I have a state UN
+which I know that if I act with the
+
+ align:start position:0%
+which I know that if I act with the
+ 
+
+ align:start position:0%
+which I know that if I act with the
+energy operator on it or this is
+
+ align:start position:0%
+energy operator on it or this is
+ 
+
+ align:start position:0%
+energy operator on it or this is
+sometimes called H UN is equal to en un
+
+ align:start position:0%
+sometimes called H UN is equal to en un
+ 
+
+ align:start position:0%
+sometimes called H UN is equal to en un
+okay if I act with e on alpha UN where
+
+ align:start position:0%
+okay if I act with e on alpha UN where
+ 
+
+ align:start position:0%
+okay if I act with e on alpha UN where
+alpha is a constant what is this equal
+
+ align:start position:0%
+alpha is a constant what is this equal
+ 
+
+ align:start position:0%
+alpha is a constant what is this equal
+to alpha en un right so the eigenvalue
+
+ align:start position:0%
+to alpha en un right so the eigenvalue
+ 
+
+ align:start position:0%
+to alpha en un right so the eigenvalue
+is the same it's en right because they
+
+ align:start position:0%
+is the same it's en right because they
+ 
+
+ align:start position:0%
+is the same it's en right because they
+can't divide through by L so so if you
+
+ align:start position:0%
+can't divide through by L so so if you
+ 
+
+ align:start position:0%
+can't divide through by L so so if you
+have the same state meaning proportional
+
+ align:start position:0%
+have the same state meaning proportional
+ 
+
+ align:start position:0%
+have the same state meaning proportional
+to it then will have the same eigen
+
+ align:start position:0%
+to it then will have the same eigen
+ 
+
+ align:start position:0%
+to it then will have the same eigen
+value but this manifestly has a
+
+ align:start position:0%
+value but this manifestly has a
+ 
+
+ align:start position:0%
+value but this manifestly has a
+different eigen value cool awesome
+
+ align:start position:0%
+different eigen value cool awesome
+ 
+
+ align:start position:0%
+different eigen value cool awesome
+okay other questions yeah
+
+ align:start position:0%
+okay other questions yeah
+ 
+
+ align:start position:0%
+okay other questions yeah
+ah good okay so H is another name so
+
+ align:start position:0%
+ah good okay so H is another name so
+ 
+
+ align:start position:0%
+ah good okay so H is another name so
+some books use H and some books use E
+
+ align:start position:0%
+some books use H and some books use E
+ 
+
+ align:start position:0%
+some books use H and some books use E
+and the reason goes back to classical
+
+ align:start position:0%
+and the reason goes back to classical
+ 
+
+ align:start position:0%
+and the reason goes back to classical
+mechanics there's a there's an object
+
+ align:start position:0%
+mechanics there's a there's an object
+ 
+
+ align:start position:0%
+mechanics there's a there's an object
+called the Hamiltonian which it's sort
+
+ align:start position:0%
+called the Hamiltonian which it's sort
+ 
+
+ align:start position:0%
+called the Hamiltonian which it's sort
+of like saying I don't know it's like
+
+ align:start position:0%
+of like saying I don't know it's like
+ 
+
+ align:start position:0%
+of like saying I don't know it's like
+saying look bread and bond are the same
+
+ align:start position:0%
+saying look bread and bond are the same
+ 
+
+ align:start position:0%
+saying look bread and bond are the same
+thing but they evoke different things
+
+ align:start position:0%
+thing but they evoke different things
+ 
+
+ align:start position:0%
+thing but they evoke different things
+right you say bread and you think like
+
+ align:start position:0%
+right you say bread and you think like
+ 
+
+ align:start position:0%
+right you say bread and you think like
+Dixie and you say Ben and you think you
+
+ align:start position:0%
+Dixie and you say Ben and you think you
+ 
+
+ align:start position:0%
+Dixie and you say Ben and you think you
+know the me of some gorgeous baguette
+
+ align:start position:0%
+know the me of some gorgeous baguette
+ 
+
+ align:start position:0%
+know the me of some gorgeous baguette
+right okay it has a different feel it
+
+ align:start position:0%
+right okay it has a different feel it
+ 
+
+ align:start position:0%
+right okay it has a different feel it
+has a different feel so this invokes
+
+ align:start position:0%
+has a different feel so this invokes
+ 
+
+ align:start position:0%
+has a different feel so this invokes
+different things a particular to a
+
+ align:start position:0%
+different things a particular to a
+ 
+
+ align:start position:0%
+different things a particular to a
+classical mechanic the Hamiltonian is
+
+ align:start position:0%
+classical mechanic the Hamiltonian is
+ 
+
+ align:start position:0%
+classical mechanic the Hamiltonian is
+the generator of time translations now
+
+ align:start position:0%
+the generator of time translations now
+ 
+
+ align:start position:0%
+the generator of time translations now
+we don't usually that wasn't the classic
+
+ align:start position:0%
+we don't usually that wasn't the classic
+ 
+
+ align:start position:0%
+we don't usually that wasn't the classic
+way of thinking about the energy
+
+ align:start position:0%
+way of thinking about the energy
+ 
+
+ align:start position:0%
+way of thinking about the energy
+operator in you know say Newton's time
+
+ align:start position:0%
+operator in you know say Newton's time
+ 
+
+ align:start position:0%
+operator in you know say Newton's time
+okay but it is how we think about energy
+
+ align:start position:0%
+okay but it is how we think about energy
+ 
+
+ align:start position:0%
+okay but it is how we think about energy
+now so that's just this is just
+
+ align:start position:0%
+now so that's just this is just
+ 
+
+ align:start position:0%
+now so that's just this is just
+terminology for anyone who didn't get
+
+ align:start position:0%
+terminology for anyone who didn't get
+ 
+
+ align:start position:0%
+terminology for anyone who didn't get
+that sorry about that this is something
+
+ align:start position:0%
+that sorry about that this is something
+ 
+
+ align:start position:0%
+that sorry about that this is something
+that we've run across before but I
+
+ align:start position:0%
+that we've run across before but I
+ 
+
+ align:start position:0%
+that we've run across before but I
+should emphasize so when you hear people
+
+ align:start position:0%
+should emphasize so when you hear people
+ 
+
+ align:start position:0%
+should emphasize so when you hear people
+say the Hamiltonian that means the
+
+ align:start position:0%
+say the Hamiltonian that means the
+ 
+
+ align:start position:0%
+say the Hamiltonian that means the
+energy operator the reason I say energy
+
+ align:start position:0%
+energy operator the reason I say energy
+ 
+
+ align:start position:0%
+energy operator the reason I say energy
+operator rather than saying Hamiltonian
+
+ align:start position:0%
+operator rather than saying Hamiltonian
+ 
+
+ align:start position:0%
+operator rather than saying Hamiltonian
+which is the more common thing in the
+
+ align:start position:0%
+which is the more common thing in the
+ 
+
+ align:start position:0%
+which is the more common thing in the
+lingua franca of quantum mechanics
+
+ align:start position:0%
+lingua franca of quantum mechanics
+ 
+
+ align:start position:0%
+lingua franca of quantum mechanics
+because I want to impress upon you guys
+
+ align:start position:0%
+because I want to impress upon you guys
+ 
+
+ align:start position:0%
+because I want to impress upon you guys
+that it's just energy it is the energy
+
+ align:start position:0%
+that it's just energy it is the energy
+ 
+
+ align:start position:0%
+that it's just energy it is the energy
+it's nothing else it's not some strange
+
+ align:start position:0%
+it's nothing else it's not some strange
+ 
+
+ align:start position:0%
+it's nothing else it's not some strange
+beast it's just energy okay other
+
+ align:start position:0%
+beast it's just energy okay other
+ 
+
+ align:start position:0%
+beast it's just energy okay other
+questions bread
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+other questions okay for next question
+
+ align:start position:0%
+other questions okay for next question
+ 
+
+ align:start position:0%
+other questions okay for next question
+which of these graphs shows the
+
+ align:start position:0%
+which of these graphs shows the
+ 
+
+ align:start position:0%
+which of these graphs shows the
+curvature of the wave function in a
+
+ align:start position:0%
+curvature of the wave function in a
+ 
+
+ align:start position:0%
+curvature of the wave function in a
+classically allowed region okay five
+
+ align:start position:0%
+classically allowed region okay five
+ 
+
+ align:start position:0%
+classically allowed region okay five
+seconds left all right
+
+ align:start position:0%
+seconds left all right
+ 
+
+ align:start position:0%
+seconds left all right
+fantastic and the answer is a because
+
+ align:start position:0%
+fantastic and the answer is a because
+ 
+
+ align:start position:0%
+fantastic and the answer is a because
+the curvature has to be towards the axis
+
+ align:start position:0%
+the curvature has to be towards the axis
+ 
+
+ align:start position:0%
+the curvature has to be towards the axis
+in a classically allowed reason the wave
+
+ align:start position:0%
+in a classically allowed reason the wave
+ 
+
+ align:start position:0%
+in a classically allowed reason the wave
+function is sinusoidal
+
+ align:start position:0%
+function is sinusoidal
+ 
+
+ align:start position:0%
+function is sinusoidal
+it's oscillatory alright and oops and
+
+ align:start position:0%
+it's oscillatory alright and oops and
+ 
+
+ align:start position:0%
+it's oscillatory alright and oops and
+the partner of that question is what
+
+ align:start position:0%
+the partner of that question is what
+ 
+
+ align:start position:0%
+the partner of that question is what
+about in the classically disallowed
+
+ align:start position:0%
+about in the classically disallowed
+ 
+
+ align:start position:0%
+about in the classically disallowed
+region okay five seconds okay awesome
+
+ align:start position:0%
+region okay five seconds okay awesome
+ 
+
+ align:start position:0%
+region okay five seconds okay awesome
+and basically everyone got this be great
+
+ align:start position:0%
+and basically everyone got this be great
+ 
+
+ align:start position:0%
+and basically everyone got this be great
+questions all right oh yeah sorry
+
+ align:start position:0%
+questions all right oh yeah sorry
+ 
+
+ align:start position:0%
+questions all right oh yeah sorry
+nope no that's a very good question so C
+
+ align:start position:0%
+nope no that's a very good question so C
+ 
+
+ align:start position:0%
+nope no that's a very good question so C
+and D I should say I should let me be a
+
+ align:start position:0%
+and D I should say I should let me be a
+ 
+
+ align:start position:0%
+and D I should say I should let me be a
+little more precise but it's a very
+
+ align:start position:0%
+little more precise but it's a very
+ 
+
+ align:start position:0%
+little more precise but it's a very
+reasonable question so let me give you
+
+ align:start position:0%
+reasonable question so let me give you
+ 
+
+ align:start position:0%
+reasonable question so let me give you
+an answer suppose you saw a wave
+
+ align:start position:0%
+an answer suppose you saw a wave
+ 
+
+ align:start position:0%
+an answer suppose you saw a wave
+function that had the curvature
+
+ align:start position:0%
+function that had the curvature
+ 
+
+ align:start position:0%
+function that had the curvature
+structure of C it was curved oscillatory
+
+ align:start position:0%
+structure of C it was curved oscillatory
+ 
+
+ align:start position:0%
+structure of C it was curved oscillatory
+over there and curved exponential over
+
+ align:start position:0%
+over there and curved exponential over
+ 
+
+ align:start position:0%
+over there and curved exponential over
+there on the right what would you say
+
+ align:start position:0%
+there on the right what would you say
+ 
+
+ align:start position:0%
+there on the right what would you say
+about the potential relative to the
+
+ align:start position:0%
+about the potential relative to the
+ 
+
+ align:start position:0%
+about the potential relative to the
+energy sagan yeah good so on one side
+
+ align:start position:0%
+energy sagan yeah good so on one side
+ 
+
+ align:start position:0%
+energy sagan yeah good so on one side
+were allowed and on the other side were
+
+ align:start position:0%
+were allowed and on the other side were
+ 
+
+ align:start position:0%
+were allowed and on the other side were
+disallowed so if you saw a wave function
+
+ align:start position:0%
+disallowed so if you saw a wave function
+ 
+
+ align:start position:0%
+disallowed so if you saw a wave function
+that had that curvature structure you'd
+
+ align:start position:0%
+that had that curvature structure you'd
+ 
+
+ align:start position:0%
+that had that curvature structure you'd
+immediately know that it was in the loud
+
+ align:start position:0%
+immediately know that it was in the loud
+ 
+
+ align:start position:0%
+immediately know that it was in the loud
+region on the left but then on the right
+
+ align:start position:0%
+region on the left but then on the right
+ 
+
+ align:start position:0%
+region on the left but then on the right
+it was disallowed classically just
+
+ align:start position:0%
+it was disallowed classically just
+ 
+
+ align:start position:0%
+it was disallowed classically just
+because it had curvature away from the
+
+ align:start position:0%
+because it had curvature away from the
+ 
+
+ align:start position:0%
+because it had curvature away from the
+axis that cool so that's something you
+
+ align:start position:0%
+axis that cool so that's something you
+ 
+
+ align:start position:0%
+axis that cool so that's something you
+if you saw a wave function so for
+
+ align:start position:0%
+if you saw a wave function so for
+ 
+
+ align:start position:0%
+if you saw a wave function so for
+example you might say well look you
+
+ align:start position:0%
+example you might say well look you
+ 
+
+ align:start position:0%
+example you might say well look you
+never get a wave function that does this
+
+ align:start position:0%
+never get a wave function that does this
+ 
+
+ align:start position:0%
+never get a wave function that does this
+and and that's not true right you could
+
+ align:start position:0%
+and and that's not true right you could
+ 
+
+ align:start position:0%
+and and that's not true right you could
+do that so this would be classically
+
+ align:start position:0%
+do that so this would be classically
+ 
+
+ align:start position:0%
+do that so this would be classically
+disallowed because it's curvature down
+
+ align:start position:0%
+disallowed because it's curvature down
+ 
+
+ align:start position:0%
+disallowed because it's curvature down
+this would be
+
+ align:start position:0%
+this would be
+ 
+
+ align:start position:0%
+this would be
+classically loud so the potential for
+
+ align:start position:0%
+classically loud so the potential for
+ 
+
+ align:start position:0%
+classically loud so the potential for
+example if this is the energy the
+
+ align:start position:0%
+example if this is the energy the
+ 
+
+ align:start position:0%
+example if this is the energy the
+potential could be do do okay so a
+
+ align:start position:0%
+potential could be do do okay so a
+ 
+
+ align:start position:0%
+potential could be do do okay so a
+potential like this could lead to a wave
+
+ align:start position:0%
+potential like this could lead to a wave
+ 
+
+ align:start position:0%
+potential like this could lead to a wave
+function like this that cool okay so
+
+ align:start position:0%
+function like this that cool okay so
+ 
+
+ align:start position:0%
+function like this that cool okay so
+it's a very good question I'm sorry I
+
+ align:start position:0%
+it's a very good question I'm sorry I
+ 
+
+ align:start position:0%
+it's a very good question I'm sorry I
+should have seen what you were asking
+
+ align:start position:0%
+should have seen what you were asking
+ 
+
+ align:start position:0%
+should have seen what you were asking
+more immediately okay other questions is
+
+ align:start position:0%
+more immediately okay other questions is
+ 
+
+ align:start position:0%
+more immediately okay other questions is
+following up on that anything okay cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no one ever asked that question before
+
+ align:start position:0%
+no one ever asked that question before
+ 
+
+ align:start position:0%
+no one ever asked that question before
+and I just want to emphasize that you
+
+ align:start position:0%
+and I just want to emphasize that you
+ 
+
+ align:start position:0%
+and I just want to emphasize that you
+guys should just ask questions when you
+
+ align:start position:0%
+guys should just ask questions when you
+ 
+
+ align:start position:0%
+guys should just ask questions when you
+don't when you're confused by something
+
+ align:start position:0%
+don't when you're confused by something
+ 
+
+ align:start position:0%
+don't when you're confused by something
+someone else is gonna be confused by it
+
+ align:start position:0%
+someone else is gonna be confused by it
+ 
+
+ align:start position:0%
+someone else is gonna be confused by it
+I wouldn't even necessarily know that
+
+ align:start position:0%
+I wouldn't even necessarily know that
+ 
+
+ align:start position:0%
+I wouldn't even necessarily know that
+the question is a meaningful question I
+
+ align:start position:0%
+the question is a meaningful question I
+ 
+
+ align:start position:0%
+the question is a meaningful question I
+get questions I've never heard before
+
+ align:start position:0%
+get questions I've never heard before
+ 
+
+ align:start position:0%
+get questions I've never heard before
+all the time in this class just don't
+
+ align:start position:0%
+all the time in this class just don't
+ 
+
+ align:start position:0%
+all the time in this class just don't
+hesitate to ask it's always a good idea
+
+ align:start position:0%
+hesitate to ask it's always a good idea
+ 
+
+ align:start position:0%
+hesitate to ask it's always a good idea
+okay next one wave function Phi has been
+
+ align:start position:0%
+okay next one wave function Phi has been
+ 
+
+ align:start position:0%
+okay next one wave function Phi has been
+expressed as a sum over energy
+
+ align:start position:0%
+expressed as a sum over energy
+ 
+
+ align:start position:0%
+expressed as a sum over energy
+eigenfunctions UN compared to the
+
+ align:start position:0%
+eigenfunctions UN compared to the
+ 
+
+ align:start position:0%
+eigenfunctions UN compared to the
+original wave function as a function of
+
+ align:start position:0%
+original wave function as a function of
+ 
+
+ align:start position:0%
+original wave function as a function of
+X a set of coefficients C 1 dot dot
+
+ align:start position:0%
+X a set of coefficients C 1 dot dot
+ 
+
+ align:start position:0%
+X a set of coefficients C 1 dot dot
+contains more or less same information
+
+ align:start position:0%
+contains more or less same information
+ 
+
+ align:start position:0%
+contains more or less same information
+or cannot be determined or depends
+
+ align:start position:0%
+or cannot be determined or depends
+ 
+
+ align:start position:0%
+or cannot be determined or depends
+all right 5 seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right and the answer is same
+
+ align:start position:0%
+all right and the answer is same
+ 
+
+ align:start position:0%
+all right and the answer is same
+information
+
+ align:start position:0%
+information
+ 
+
+ align:start position:0%
+information
+good questions okay good some of these
+
+ align:start position:0%
+good questions okay good some of these
+ 
+
+ align:start position:0%
+good questions okay good some of these
+you've seen before F and G are wave
+
+ align:start position:0%
+you've seen before F and G are wave
+ 
+
+ align:start position:0%
+you've seen before F and G are wave
+functions and C is a constant then the
+
+ align:start position:0%
+functions and C is a constant then the
+ 
+
+ align:start position:0%
+functions and C is a constant then the
+inner product C F with G is equal to
+
+ align:start position:0%
+inner product C F with G is equal to
+ 
+
+ align:start position:0%
+inner product C F with G is equal to
+click away ten seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you've got about five seconds still
+
+ align:start position:0%
+okay you've got about five seconds still
+ 
+
+ align:start position:0%
+okay you've got about five seconds still
+a lot of fluctuations here wow I'm
+
+ align:start position:0%
+a lot of fluctuations here wow I'm
+ 
+
+ align:start position:0%
+a lot of fluctuations here wow I'm
+surprised by this one all right
+
+ align:start position:0%
+surprised by this one all right
+ 
+
+ align:start position:0%
+surprised by this one all right
+uh yeah question let's come back the
+
+ align:start position:0%
+uh yeah question let's come back the
+ 
+
+ align:start position:0%
+uh yeah question let's come back the
+previous one I have to redo this sir
+
+ align:start position:0%
+previous one I have to redo this sir
+ 
+
+ align:start position:0%
+previous one I have to redo this sir
+thanks but remind me to after we move on
+
+ align:start position:0%
+thanks but remind me to after we move on
+ 
+
+ align:start position:0%
+thanks but remind me to after we move on
+okay so discuss because about a third of
+
+ align:start position:0%
+okay so discuss because about a third of
+ 
+
+ align:start position:0%
+okay so discuss because about a third of
+you got this one wrong
+
+ align:start position:0%
+you got this one wrong
+ 
+
+ align:start position:0%
+you got this one wrong
+so discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so go ahead and put in your
+
+ align:start position:0%
+all right so go ahead and put in your
+ 
+
+ align:start position:0%
+all right so go ahead and put in your
+answers again good all right another
+
+ align:start position:0%
+answers again good all right another
+ 
+
+ align:start position:0%
+answers again good all right another
+five seconds great okay and the answer
+
+ align:start position:0%
+five seconds great okay and the answer
+ 
+
+ align:start position:0%
+five seconds great okay and the answer
+is good get that complex conjugation
+
+ align:start position:0%
+is good get that complex conjugation
+ 
+
+ align:start position:0%
+is good get that complex conjugation
+right little things like that can cause
+
+ align:start position:0%
+right little things like that can cause
+ 
+
+ align:start position:0%
+right little things like that can cause
+you an infinite amount of trouble
+
+ align:start position:0%
+you an infinite amount of trouble
+ 
+
+ align:start position:0%
+you an infinite amount of trouble
+especially as you'll notice on the
+
+ align:start position:0%
+especially as you'll notice on the
+ 
+
+ align:start position:0%
+especially as you'll notice on the
+problem set when you're computing time
+
+ align:start position:0%
+problem set when you're computing time
+ 
+
+ align:start position:0%
+problem set when you're computing time
+dependence of expectation values getting
+
+ align:start position:0%
+dependence of expectation values getting
+ 
+
+ align:start position:0%
+dependence of expectation values getting
+that complex conjugation right is
+
+ align:start position:0%
+that complex conjugation right is
+ 
+
+ align:start position:0%
+that complex conjugation right is
+essential because you need to see
+
+ align:start position:0%
+essential because you need to see
+ 
+
+ align:start position:0%
+essential because you need to see
+interference terms and without the
+
+ align:start position:0%
+interference terms and without the
+ 
+
+ align:start position:0%
+interference terms and without the
+complex conjugation you will not get the
+
+ align:start position:0%
+complex conjugation you will not get the
+ 
+
+ align:start position:0%
+complex conjugation you will not get the
+right interference terms okay question
+
+ align:start position:0%
+right interference terms okay question
+ 
+
+ align:start position:0%
+right interference terms okay question
+oh yeah it's question from previous
+
+ align:start position:0%
+oh yeah it's question from previous
+ 
+
+ align:start position:0%
+oh yeah it's question from previous
+problem thank you the norm squared gives
+
+ align:start position:0%
+problem thank you the norm squared gives
+ 
+
+ align:start position:0%
+problem thank you the norm squared gives
+you the probabilities but if you know
+
+ align:start position:0%
+you the probabilities but if you know
+ 
+
+ align:start position:0%
+you the probabilities but if you know
+the coefficient so good this is a good
+
+ align:start position:0%
+the coefficient so good this is a good
+ 
+
+ align:start position:0%
+the coefficient so good this is a good
+question so let me rephrase the question
+
+ align:start position:0%
+question so let me rephrase the question
+ 
+
+ align:start position:0%
+question so let me rephrase the question
+so the question is look in the previous
+
+ align:start position:0%
+so the question is look in the previous
+ 
+
+ align:start position:0%
+so the question is look in the previous
+question we said look our wave function
+
+ align:start position:0%
+question we said look our wave function
+ 
+
+ align:start position:0%
+question we said look our wave function
+Phi of X is some function which we could
+
+ align:start position:0%
+Phi of X is some function which we could
+ 
+
+ align:start position:0%
+Phi of X is some function which we could
+draw right so I could represent this in
+
+ align:start position:0%
+draw right so I could represent this in
+ 
+
+ align:start position:0%
+draw right so I could represent this in
+two ways I could have there draw it or I
+
+ align:start position:0%
+two ways I could have there draw it or I
+ 
+
+ align:start position:0%
+two ways I could have there draw it or I
+could represent it as equal the sum over
+
+ align:start position:0%
+could represent it as equal the sum over
+ 
+
+ align:start position:0%
+could represent it as equal the sum over
+n of C n Phi n where Phi n are the known
+
+ align:start position:0%
+n of C n Phi n where Phi n are the known
+ 
+
+ align:start position:0%
+n of C n Phi n where Phi n are the known
+energy eigenfunctions right and the
+
+ align:start position:0%
+energy eigenfunctions right and the
+ 
+
+ align:start position:0%
+energy eigenfunctions right and the
+question is did the CN contain the same
+
+ align:start position:0%
+question is did the CN contain the same
+ 
+
+ align:start position:0%
+question is did the CN contain the same
+information so that's that was a
+
+ align:start position:0%
+information so that's that was a
+ 
+
+ align:start position:0%
+information so that's that was a
+question and the point that's being
+
+ align:start position:0%
+question and the point that's being
+ 
+
+ align:start position:0%
+question and the point that's being
+asked about here is a very good question
+
+ align:start position:0%
+asked about here is a very good question
+ 
+
+ align:start position:0%
+asked about here is a very good question
+the question is look we know what the C
+
+ align:start position:0%
+the question is look we know what the C
+ 
+
+ align:start position:0%
+the question is look we know what the C
+NS mean what the C ends mean is the
+
+ align:start position:0%
+NS mean what the C ends mean is the
+ 
+
+ align:start position:0%
+NS mean what the C ends mean is the
+probability that you measure the energy
+
+ align:start position:0%
+probability that you measure the energy
+ 
+
+ align:start position:0%
+probability that you measure the energy
+given that the state is signed the
+
+ align:start position:0%
+given that the state is signed the
+ 
+
+ align:start position:0%
+given that the state is signed the
+probability usually measure the energy B
+
+ align:start position:0%
+probability usually measure the energy B
+ 
+
+ align:start position:0%
+probability usually measure the energy B
+n is equal to norm CN squared right and
+
+ align:start position:0%
+n is equal to norm CN squared right and
+ 
+
+ align:start position:0%
+n is equal to norm CN squared right and
+so the CNS tell you about probabilities
+
+ align:start position:0%
+so the CNS tell you about probabilities
+ 
+
+ align:start position:0%
+so the CNS tell you about probabilities
+they don't tell you what the state is
+
+ align:start position:0%
+they don't tell you what the state is
+ 
+
+ align:start position:0%
+they don't tell you what the state is
+they just tell you what probability is
+
+ align:start position:0%
+they just tell you what probability is
+ 
+
+ align:start position:0%
+they just tell you what probability is
+that you'll measure a particular energy
+
+ align:start position:0%
+that you'll measure a particular energy
+ 
+
+ align:start position:0%
+that you'll measure a particular energy
+is that right so how can it contain the
+
+ align:start position:0%
+is that right so how can it contain the
+ 
+
+ align:start position:0%
+is that right so how can it contain the
+same information and the there are two
+
+ align:start position:0%
+same information and the there are two
+ 
+
+ align:start position:0%
+same information and the there are two
+important things to say about this first
+
+ align:start position:0%
+important things to say about this first
+ 
+
+ align:start position:0%
+important things to say about this first
+off this is of course true and this does
+
+ align:start position:0%
+off this is of course true and this does
+ 
+
+ align:start position:0%
+off this is of course true and this does
+give you the probability and the
+
+ align:start position:0%
+give you the probability and the
+ 
+
+ align:start position:0%
+give you the probability and the
+probability comes from the norm squared
+
+ align:start position:0%
+probability comes from the norm squared
+ 
+
+ align:start position:0%
+probability comes from the norm squared
+so the co if the phase of CN doesn't
+
+ align:start position:0%
+so the co if the phase of CN doesn't
+ 
+
+ align:start position:0%
+so the co if the phase of CN doesn't
+particularly matter for that however the
+
+ align:start position:0%
+particularly matter for that however the
+ 
+
+ align:start position:0%
+particularly matter for that however the
+claim that I can expand this function at
+
+ align:start position:0%
+claim that I can expand this function at
+ 
+
+ align:start position:0%
+claim that I can expand this function at
+in in a
+
+ align:start position:0%
+in in a
+ 
+
+ align:start position:0%
+in in a
+basis of the energy eigenfunctions in a
+
+ align:start position:0%
+basis of the energy eigenfunctions in a
+ 
+
+ align:start position:0%
+basis of the energy eigenfunctions in a
+basis of other functions is this
+
+ align:start position:0%
+basis of other functions is this
+ 
+
+ align:start position:0%
+basis of other functions is this
+statement if I know these CNS then I
+
+ align:start position:0%
+statement if I know these CNS then I
+ 
+
+ align:start position:0%
+statement if I know these CNS then I
+take C 1 multiplied by Phi 1 C 2
+
+ align:start position:0%
+take C 1 multiplied by Phi 1 C 2
+ 
+
+ align:start position:0%
+take C 1 multiplied by Phi 1 C 2
+multiplied by Phi Q add them all back up
+
+ align:start position:0%
+multiplied by Phi Q add them all back up
+ 
+
+ align:start position:0%
+multiplied by Phi Q add them all back up
+and they get nothing other than this
+
+ align:start position:0%
+and they get nothing other than this
+ 
+
+ align:start position:0%
+and they get nothing other than this
+original function okay so if I know the
+
+ align:start position:0%
+original function okay so if I know the
+ 
+
+ align:start position:0%
+original function okay so if I know the
+C ends I can just construct that
+
+ align:start position:0%
+C ends I can just construct that
+ 
+
+ align:start position:0%
+C ends I can just construct that
+original function explicitly so this
+
+ align:start position:0%
+original function explicitly so this
+ 
+
+ align:start position:0%
+original function explicitly so this
+can't contain any more or any less
+
+ align:start position:0%
+can't contain any more or any less
+ 
+
+ align:start position:0%
+can't contain any more or any less
+information than the list of C NS as
+
+ align:start position:0%
+information than the list of C NS as
+ 
+
+ align:start position:0%
+information than the list of C NS as
+long as I know what basis I'm talking
+
+ align:start position:0%
+long as I know what basis I'm talking
+ 
+
+ align:start position:0%
+long as I know what basis I'm talking
+about okay so here's the disturbing
+
+ align:start position:0%
+about okay so here's the disturbing
+ 
+
+ align:start position:0%
+about okay so here's the disturbing
+thing about that when we say the wave
+
+ align:start position:0%
+thing about that when we say the wave
+ 
+
+ align:start position:0%
+thing about that when we say the wave
+function is the state of the system it
+
+ align:start position:0%
+function is the state of the system it
+ 
+
+ align:start position:0%
+function is the state of the system it
+contains all knowledge you could
+
+ align:start position:0%
+contains all knowledge you could
+ 
+
+ align:start position:0%
+contains all knowledge you could
+possibly have access to and not just
+
+ align:start position:0%
+possibly have access to and not just
+ 
+
+ align:start position:0%
+possibly have access to and not just
+knowledge that you could have access to
+
+ align:start position:0%
+knowledge that you could have access to
+ 
+
+ align:start position:0%
+knowledge that you could have access to
+it contains all of the information of
+
+ align:start position:0%
+it contains all of the information of
+ 
+
+ align:start position:0%
+it contains all of the information of
+the state and then we look at this and
+
+ align:start position:0%
+the state and then we look at this and
+ 
+
+ align:start position:0%
+the state and then we look at this and
+say well look it doesn't give us
+
+ align:start position:0%
+say well look it doesn't give us
+ 
+
+ align:start position:0%
+say well look it doesn't give us
+something deterministic because of
+
+ align:start position:0%
+something deterministic because of
+ 
+
+ align:start position:0%
+something deterministic because of
+something probabilistic it tells us the
+
+ align:start position:0%
+something probabilistic it tells us the
+ 
+
+ align:start position:0%
+something probabilistic it tells us the
+probability distribution for measuring
+
+ align:start position:0%
+probability distribution for measuring
+ 
+
+ align:start position:0%
+probability distribution for measuring
+the various different energies what does
+
+ align:start position:0%
+the various different energies what does
+ 
+
+ align:start position:0%
+the various different energies what does
+that immediately tell you since they're
+
+ align:start position:0%
+that immediately tell you since they're
+ 
+
+ align:start position:0%
+that immediately tell you since they're
+equivalent information this guy tells
+
+ align:start position:0%
+equivalent information this guy tells
+ 
+
+ align:start position:0%
+equivalent information this guy tells
+you nothing more than the probabilities
+
+ align:start position:0%
+you nothing more than the probabilities
+ 
+
+ align:start position:0%
+you nothing more than the probabilities
+I'm imagining it doesn't tell you what
+
+ align:start position:0%
+I'm imagining it doesn't tell you what
+ 
+
+ align:start position:0%
+I'm imagining it doesn't tell you what
+energies you'll measure it tells you the
+
+ align:start position:0%
+energies you'll measure it tells you the
+ 
+
+ align:start position:0%
+energies you'll measure it tells you the
+probabilities with which you will
+
+ align:start position:0%
+probabilities with which you will
+ 
+
+ align:start position:0%
+probabilities with which you will
+measure energies so they're the same
+
+ align:start position:0%
+measure energies so they're the same
+ 
+
+ align:start position:0%
+measure energies so they're the same
+thing it's a very it's a very good
+
+ align:start position:0%
+thing it's a very it's a very good
+ 
+
+ align:start position:0%
+thing it's a very it's a very good
+question and I think the way to take the
+
+ align:start position:0%
+question and I think the way to take the
+ 
+
+ align:start position:0%
+question and I think the way to take the
+sort of discomfort that that I don't
+
+ align:start position:0%
+sort of discomfort that that I don't
+ 
+
+ align:start position:0%
+sort of discomfort that that I don't
+know about you that causes me is just to
+
+ align:start position:0%
+know about you that causes me is just to
+ 
+
+ align:start position:0%
+know about you that causes me is just to
+read that as saying look the wave
+
+ align:start position:0%
+read that as saying look the wave
+ 
+
+ align:start position:0%
+read that as saying look the wave
+function is giving you probabilistic
+
+ align:start position:0%
+function is giving you probabilistic
+ 
+
+ align:start position:0%
+function is giving you probabilistic
+information about measurements
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent excellent
+
+ align:start position:0%
+excellent excellent
+ 
+
+ align:start position:0%
+excellent excellent
+okay so let me turn this around let me
+
+ align:start position:0%
+okay so let me turn this around let me
+ 
+
+ align:start position:0%
+okay so let me turn this around let me
+phrase it slightly different tell me if
+
+ align:start position:0%
+phrase it slightly different tell me if
+ 
+
+ align:start position:0%
+phrase it slightly different tell me if
+this is getting at the same point if I
+
+ align:start position:0%
+this is getting at the same point if I
+ 
+
+ align:start position:0%
+this is getting at the same point if I
+gave you a list of numbers one fourteen
+
+ align:start position:0%
+gave you a list of numbers one fourteen
+ 
+
+ align:start position:0%
+gave you a list of numbers one fourteen
+twelve does that tell you what function
+
+ align:start position:0%
+twelve does that tell you what function
+ 
+
+ align:start position:0%
+twelve does that tell you what function
+I'm talking about no I have to tell you
+
+ align:start position:0%
+I'm talking about no I have to tell you
+ 
+
+ align:start position:0%
+I'm talking about no I have to tell you
+that there are the expansion
+
+ align:start position:0%
+that there are the expansion
+ 
+
+ align:start position:0%
+that there are the expansion
+coefficients in say sine waves of a
+
+ align:start position:0%
+coefficients in say sine waves of a
+ 
+
+ align:start position:0%
+coefficients in say sine waves of a
+particular wavelength or energy
+
+ align:start position:0%
+particular wavelength or energy
+ 
+
+ align:start position:0%
+particular wavelength or energy
+eigenfunctions in some particular energy
+
+ align:start position:0%
+eigenfunctions in some particular energy
+ 
+
+ align:start position:0%
+eigenfunctions in some particular energy
+operator if I just give you a list of
+
+ align:start position:0%
+operator if I just give you a list of
+ 
+
+ align:start position:0%
+operator if I just give you a list of
+numbers it doesn't tell you what
+
+ align:start position:0%
+numbers it doesn't tell you what
+ 
+
+ align:start position:0%
+numbers it doesn't tell you what
+function is I have to give you a list of
+
+ align:start position:0%
+function is I have to give you a list of
+ 
+
+ align:start position:0%
+function is I have to give you a list of
+numbers and I have to tell you what
+
+ align:start position:0%
+numbers and I have to tell you what
+ 
+
+ align:start position:0%
+numbers and I have to tell you what
+basis I'm talking about if you have the
+
+ align:start position:0%
+basis I'm talking about if you have the
+ 
+
+ align:start position:0%
+basis I'm talking about if you have the
+wave function you don't need to know
+
+ align:start position:0%
+wave function you don't need to know
+ 
+
+ align:start position:0%
+wave function you don't need to know
+what basis you're talking about the wave
+
+ align:start position:0%
+what basis you're talking about the wave
+ 
+
+ align:start position:0%
+what basis you're talking about the wave
+function is basis independent right it's
+
+ align:start position:0%
+function is basis independent right it's
+ 
+
+ align:start position:0%
+function is basis independent right it's
+just a function in a few minutes I'm
+
+ align:start position:0%
+just a function in a few minutes I'm
+ 
+
+ align:start position:0%
+just a function in a few minutes I'm
+gonna come back and subvert what I just
+
+ align:start position:0%
+gonna come back and subvert what I just
+ 
+
+ align:start position:0%
+gonna come back and subvert what I just
+said but so the wave function is just
+
+ align:start position:0%
+said but so the wave function is just
+ 
+
+ align:start position:0%
+said but so the wave function is just
+what the wave function is and if I give
+
+ align:start position:0%
+what the wave function is and if I give
+ 
+
+ align:start position:0%
+what the wave function is and if I give
+you a list of numbers they're only
+
+ align:start position:0%
+you a list of numbers they're only
+ 
+
+ align:start position:0%
+you a list of numbers they're only
+equivalent when you also know the wave
+
+ align:start position:0%
+equivalent when you also know the wave
+ 
+
+ align:start position:0%
+equivalent when you also know the wave
+function so in order for these two
+
+ align:start position:0%
+function so in order for these two
+ 
+
+ align:start position:0%
+function so in order for these two
+things to be equivalent it's important
+
+ align:start position:0%
+things to be equivalent it's important
+ 
+
+ align:start position:0%
+things to be equivalent it's important
+that you know what basis you're talking
+
+ align:start position:0%
+that you know what basis you're talking
+ 
+
+ align:start position:0%
+that you know what basis you're talking
+about in particular it's important that
+
+ align:start position:0%
+about in particular it's important that
+ 
+
+ align:start position:0%
+about in particular it's important that
+you know the energy eigenfunctions is
+
+ align:start position:0%
+you know the energy eigenfunctions is
+ 
+
+ align:start position:0%
+you know the energy eigenfunctions is
+that is that getting it what what's the
+
+ align:start position:0%
+that is that getting it what what's the
+ 
+
+ align:start position:0%
+that is that getting it what what's the
+distinction you're making
+
+ align:start position:0%
+distinction you're making
+ 
+
+ align:start position:0%
+distinction you're making
+okay think more about it and and and and
+
+ align:start position:0%
+okay think more about it and and and and
+ 
+
+ align:start position:0%
+okay think more about it and and and and
+when when the question becomes more
+
+ align:start position:0%
+when when the question becomes more
+ 
+
+ align:start position:0%
+when when the question becomes more
+sharp ask okay other questions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you know the end are we supposed to do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah usually I I've I try on
+
+ align:start position:0%
+yeah yeah usually I I've I try on
+ 
+
+ align:start position:0%
+yeah yeah usually I I've I try on
+problem sets and exams to make that
+
+ align:start position:0%
+problem sets and exams to make that
+ 
+
+ align:start position:0%
+problem sets and exams to make that
+distinction clear but that will
+
+ align:start position:0%
+distinction clear but that will
+ 
+
+ align:start position:0%
+distinction clear but that will
+generally be assumed other questions all
+
+ align:start position:0%
+generally be assumed other questions all
+ 
+
+ align:start position:0%
+generally be assumed other questions all
+right I'm gonna come back to this but
+
+ align:start position:0%
+right I'm gonna come back to this but
+ 
+
+ align:start position:0%
+right I'm gonna come back to this but
+well I'm gonna come back to this when we
+
+ align:start position:0%
+well I'm gonna come back to this when we
+ 
+
+ align:start position:0%
+well I'm gonna come back to this when we
+finish with the clicker questions okay
+
+ align:start position:0%
+finish with the clicker questions okay
+ 
+
+ align:start position:0%
+finish with the clicker questions okay
+the next question in the simple harmonic
+
+ align:start position:0%
+the next question in the simple harmonic
+ 
+
+ align:start position:0%
+the next question in the simple harmonic
+oscillator the eigenvalues as we've just
+
+ align:start position:0%
+oscillator the eigenvalues as we've just
+ 
+
+ align:start position:0%
+oscillator the eigenvalues as we've just
+derived twice are en is h-bar n Rho
+
+ align:start position:0%
+derived twice are en is h-bar n Rho
+ 
+
+ align:start position:0%
+derived twice are en is h-bar n Rho
+Omega times n plus 1/2 for an integer N
+
+ align:start position:0%
+Omega times n plus 1/2 for an integer N
+ 
+
+ align:start position:0%
+Omega times n plus 1/2 for an integer N
+and a measurement of energy will always
+
+ align:start position:0%
+and a measurement of energy will always
+ 
+
+ align:start position:0%
+and a measurement of energy will always
+observe one of these values that's from
+
+ align:start position:0%
+observe one of these values that's from
+ 
+
+ align:start position:0%
+observe one of these values that's from
+postulate four three three what can we
+
+ align:start position:0%
+postulate four three three what can we
+ 
+
+ align:start position:0%
+postulate four three three what can we
+say about the expectation value of the
+
+ align:start position:0%
+say about the expectation value of the
+ 
+
+ align:start position:0%
+say about the expectation value of the
+energy in some arbitrary state okay
+
+ align:start position:0%
+energy in some arbitrary state okay
+ 
+
+ align:start position:0%
+energy in some arbitrary state okay
+this one isn't tricky but it's not
+
+ align:start position:0%
+this one isn't tricky but it's not
+ 
+
+ align:start position:0%
+this one isn't tricky but it's not
+trivial so think carefully about it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right you have five seconds enter
+
+ align:start position:0%
+all right you have five seconds enter
+ 
+
+ align:start position:0%
+all right you have five seconds enter
+your your best guess all right and you
+
+ align:start position:0%
+your your best guess all right and you
+ 
+
+ align:start position:0%
+your your best guess all right and you
+are at complete chance I think we've
+
+ align:start position:0%
+are at complete chance I think we've
+ 
+
+ align:start position:0%
+are at complete chance I think we've
+just put you through a hardness box so
+
+ align:start position:0%
+just put you through a hardness box so
+ 
+
+ align:start position:0%
+just put you through a hardness box so
+so discuss
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and okay go ahead and start put in your
+
+ align:start position:0%
+and okay go ahead and start put in your
+ 
+
+ align:start position:0%
+and okay go ahead and start put in your
+modified response all right another five
+
+ align:start position:0%
+modified response all right another five
+ 
+
+ align:start position:0%
+modified response all right another five
+seconds or so okay click okay you're
+
+ align:start position:0%
+seconds or so okay click okay you're
+ 
+
+ align:start position:0%
+seconds or so okay click okay you're
+still there's still a lot of
+
+ align:start position:0%
+still there's still a lot of
+ 
+
+ align:start position:0%
+still there's still a lot of
+disagreement here so let's see so who
+
+ align:start position:0%
+disagreement here so let's see so who
+ 
+
+ align:start position:0%
+disagreement here so let's see so who
+would like to argue for C would like to
+
+ align:start position:0%
+would like to argue for C would like to
+ 
+
+ align:start position:0%
+would like to argue for C would like to
+argue for D go ahead excellent excellent
+
+ align:start position:0%
+argue for D go ahead excellent excellent
+ 
+
+ align:start position:0%
+argue for D go ahead excellent excellent
+okay so let me let me restate that so
+
+ align:start position:0%
+okay so let me let me restate that so
+ 
+
+ align:start position:0%
+okay so let me let me restate that so
+the statement if I'm following your
+
+ align:start position:0%
+the statement if I'm following your
+ 
+
+ align:start position:0%
+the statement if I'm following your
+logic thank you so the same uniform your
+
+ align:start position:0%
+logic thank you so the same uniform your
+ 
+
+ align:start position:0%
+logic thank you so the same uniform your
+logic goes something like this
+
+ align:start position:0%
+logic goes something like this
+ 
+
+ align:start position:0%
+logic goes something like this
+look if we had the wave function which
+
+ align:start position:0%
+look if we had the wave function which
+ 
+
+ align:start position:0%
+look if we had the wave function which
+was Phi sub n times some phase some
+
+ align:start position:0%
+was Phi sub n times some phase some
+ 
+
+ align:start position:0%
+was Phi sub n times some phase some
+ridiculous phase let's say the phase is
+
+ align:start position:0%
+ridiculous phase let's say the phase is
+ 
+
+ align:start position:0%
+ridiculous phase let's say the phase is
+one if we had the wave functions Phi sub
+
+ align:start position:0%
+one if we had the wave functions Phi sub
+ 
+
+ align:start position:0%
+one if we had the wave functions Phi sub
+n what will the expectation value of the
+
+ align:start position:0%
+n what will the expectation value of the
+ 
+
+ align:start position:0%
+n what will the expectation value of the
+energy operator be in this state en
+
+ align:start position:0%
+energy operator be in this state en
+ 
+
+ align:start position:0%
+energy operator be in this state en
+right because it's the energy it's the
+
+ align:start position:0%
+right because it's the energy it's the
+ 
+
+ align:start position:0%
+right because it's the energy it's the
+sum over all possible ends of en times
+
+ align:start position:0%
+sum over all possible ends of en times
+ 
+
+ align:start position:0%
+sum over all possible ends of en times
+the probability that we measure en by
+
+ align:start position:0%
+the probability that we measure en by
+ 
+
+ align:start position:0%
+the probability that we measure en by
+definition but this is equal to sum over
+
+ align:start position:0%
+definition but this is equal to sum over
+ 
+
+ align:start position:0%
+definition but this is equal to sum over
+N of en times the expansion coefficient
+
+ align:start position:0%
+N of en times the expansion coefficient
+ 
+
+ align:start position:0%
+N of en times the expansion coefficient
+of our wave function
+
+ align:start position:0%
+of our wave function
+ 
+
+ align:start position:0%
+of our wave function
+in the energy eigenstate basis C N
+
+ align:start position:0%
+in the energy eigenstate basis C N
+ 
+
+ align:start position:0%
+in the energy eigenstate basis C N
+squared now what's the what's the
+
+ align:start position:0%
+squared now what's the what's the
+ 
+
+ align:start position:0%
+squared now what's the what's the
+expansion coefficient in our energy
+
+ align:start position:0%
+expansion coefficient in our energy
+ 
+
+ align:start position:0%
+expansion coefficient in our energy
+eigenbasis here it's one for a
+
+ align:start position:0%
+eigenbasis here it's one for a
+ 
+
+ align:start position:0%
+eigenbasis here it's one for a
+particular value of n and zero for
+
+ align:start position:0%
+particular value of n and zero for
+ 
+
+ align:start position:0%
+particular value of n and zero for
+everything else right so what will our
+
+ align:start position:0%
+everything else right so what will our
+ 
+
+ align:start position:0%
+everything else right so what will our
+answer be it will be zero for everything
+
+ align:start position:0%
+answer be it will be zero for everything
+ 
+
+ align:start position:0%
+answer be it will be zero for everything
+except one for a particular value yen
+
+ align:start position:0%
+except one for a particular value yen
+ 
+
+ align:start position:0%
+except one for a particular value yen
+corresponding to little n I should
+
+ align:start position:0%
+corresponding to little n I should
+ 
+
+ align:start position:0%
+corresponding to little n I should
+really call this mm so you know dummy
+
+ align:start position:0%
+really call this mm so you know dummy
+ 
+
+ align:start position:0%
+really call this mm so you know dummy
+variables that were summing over don't
+
+ align:start position:0%
+variables that were summing over don't
+ 
+
+ align:start position:0%
+variables that were summing over don't
+matter so for this particular case the
+
+ align:start position:0%
+matter so for this particular case the
+ 
+
+ align:start position:0%
+matter so for this particular case the
+expectation value of E is equal to en
+
+ align:start position:0%
+expectation value of E is equal to en
+ 
+
+ align:start position:0%
+expectation value of E is equal to en
+everyone call that so it certainly can
+
+ align:start position:0%
+everyone call that so it certainly can
+ 
+
+ align:start position:0%
+everyone call that so it certainly can
+be en but is this the only way to get in
+
+ align:start position:0%
+be en but is this the only way to get in
+ 
+
+ align:start position:0%
+be en but is this the only way to get in
+no so for example suppose we have Alpha
+
+ align:start position:0%
+no so for example suppose we have Alpha
+ 
+
+ align:start position:0%
+no so for example suppose we have Alpha
+Phi n or v 1 Phi 1 plus beta Phi 3 okay
+
+ align:start position:0%
+Phi n or v 1 Phi 1 plus beta Phi 3 okay
+ 
+
+ align:start position:0%
+Phi n or v 1 Phi 1 plus beta Phi 3 okay
+what will the answer be now first off in
+
+ align:start position:0%
+what will the answer be now first off in
+ 
+
+ align:start position:0%
+what will the answer be now first off in
+order to make this normalizable what is
+
+ align:start position:0%
+order to make this normalizable what is
+ 
+
+ align:start position:0%
+order to make this normalizable what is
+beta have to be it needs to be square of
+
+ align:start position:0%
+beta have to be it needs to be square of
+ 
+
+ align:start position:0%
+beta have to be it needs to be square of
+1 minus alpha norm squared right just so
+
+ align:start position:0%
+1 minus alpha norm squared right just so
+ 
+
+ align:start position:0%
+1 minus alpha norm squared right just so
+that they sum to 1 1 norm squared so
+
+ align:start position:0%
+that they sum to 1 1 norm squared so
+ 
+
+ align:start position:0%
+that they sum to 1 1 norm squared so
+what I want to plot now the expectation
+
+ align:start position:0%
+what I want to plot now the expectation
+ 
+
+ align:start position:0%
+what I want to plot now the expectation
+value of the energy as a function of
+
+ align:start position:0%
+value of the energy as a function of
+ 
+
+ align:start position:0%
+value of the energy as a function of
+alpha when alpha is zero what is the
+
+ align:start position:0%
+alpha when alpha is zero what is the
+ 
+
+ align:start position:0%
+alpha when alpha is zero what is the
+expectation value of the energy III when
+
+ align:start position:0%
+expectation value of the energy III when
+ 
+
+ align:start position:0%
+expectation value of the energy III when
+alpha is 1 which it can't be anything
+
+ align:start position:0%
+alpha is 1 which it can't be anything
+ 
+
+ align:start position:0%
+alpha is 1 which it can't be anything
+greater than well if alpha is 1 what is
+
+ align:start position:0%
+greater than well if alpha is 1 what is
+ 
+
+ align:start position:0%
+greater than well if alpha is 1 what is
+the expectation value of the energy e1
+
+ align:start position:0%
+the expectation value of the energy e1
+ 
+
+ align:start position:0%
+the expectation value of the energy e1
+and how does the expectation value of
+
+ align:start position:0%
+and how does the expectation value of
+ 
+
+ align:start position:0%
+and how does the expectation value of
+the energy vary between these two as a
+
+ align:start position:0%
+the energy vary between these two as a
+ 
+
+ align:start position:0%
+the energy vary between these two as a
+function of alpha
+
+ align:start position:0%
+function of alpha
+ 
+
+ align:start position:0%
+function of alpha
+well it's smooth right and in particular
+
+ align:start position:0%
+well it's smooth right and in particular
+ 
+
+ align:start position:0%
+well it's smooth right and in particular
+it's in particular it's quadratic
+
+ align:start position:0%
+it's in particular it's quadratic
+ 
+
+ align:start position:0%
+it's in particular it's quadratic
+because goes like the square of these
+
+ align:start position:0%
+because goes like the square of these
+ 
+
+ align:start position:0%
+because goes like the square of these
+coefficients so it's something smooth
+
+ align:start position:0%
+coefficients so it's something smooth
+ 
+
+ align:start position:0%
+coefficients so it's something smooth
+that does this and have slope zero at
+
+ align:start position:0%
+that does this and have slope zero at
+ 
+
+ align:start position:0%
+that does this and have slope zero at
+the end ok and somewhere in between it
+
+ align:start position:0%
+the end ok and somewhere in between it
+ 
+
+ align:start position:0%
+the end ok and somewhere in between it
+will hit e to but there is not only is
+
+ align:start position:0%
+will hit e to but there is not only is
+ 
+
+ align:start position:0%
+will hit e to but there is not only is
+this not equal to two it doesn't even
+
+ align:start position:0%
+this not equal to two it doesn't even
+ 
+
+ align:start position:0%
+this not equal to two it doesn't even
+contain e2 as an element of the
+
+ align:start position:0%
+contain e2 as an element of the
+ 
+
+ align:start position:0%
+contain e2 as an element of the
+superposition right so this is a counter
+
+ align:start position:0%
+superposition right so this is a counter
+ 
+
+ align:start position:0%
+superposition right so this is a counter
+example to see every cool this is an
+
+ align:start position:0%
+example to see every cool this is an
+ 
+
+ align:start position:0%
+example to see every cool this is an
+important point now if I let the system
+
+ align:start position:0%
+important point now if I let the system
+ 
+
+ align:start position:0%
+important point now if I let the system
+if I know that at some moment in time
+
+ align:start position:0%
+if I know that at some moment in time
+ 
+
+ align:start position:0%
+if I know that at some moment in time
+the energy expectation value is this
+
+ align:start position:0%
+the energy expectation value is this
+ 
+
+ align:start position:0%
+the energy expectation value is this
+value corresponding say to some
+
+ align:start position:0%
+value corresponding say to some
+ 
+
+ align:start position:0%
+value corresponding say to some
+particular alpha and I let the system
+
+ align:start position:0%
+particular alpha and I let the system
+ 
+
+ align:start position:0%
+particular alpha and I let the system
+evolve in time how does that expectation
+
+ align:start position:0%
+evolve in time how does that expectation
+ 
+
+ align:start position:0%
+evolve in time how does that expectation
+value evolving
+
+ align:start position:0%
+value evolving
+ 
+
+ align:start position:0%
+value evolving
+time how does the expectation value of
+
+ align:start position:0%
+time how does the expectation value of
+ 
+
+ align:start position:0%
+time how does the expectation value of
+the energy change over time it doesn't
+
+ align:start position:0%
+the energy change over time it doesn't
+ 
+
+ align:start position:0%
+the energy change over time it doesn't
+the expectation value of energy is
+
+ align:start position:0%
+the expectation value of energy is
+ 
+
+ align:start position:0%
+the expectation value of energy is
+always time independent yeah
+
+ align:start position:0%
+always time independent yeah
+ 
+
+ align:start position:0%
+always time independent yeah
+does the expectation value of position
+
+ align:start position:0%
+does the expectation value of position
+ 
+
+ align:start position:0%
+does the expectation value of position
+change over time in general yes
+
+ align:start position:0%
+change over time in general yes
+ 
+
+ align:start position:0%
+change over time in general yes
+when does it not change over time in a
+
+ align:start position:0%
+when does it not change over time in a
+ 
+
+ align:start position:0%
+when does it not change over time in a
+stationary state right so this is
+
+ align:start position:0%
+stationary state right so this is
+ 
+
+ align:start position:0%
+stationary state right so this is
+exactly what this is working through
+
+ align:start position:0%
+exactly what this is working through
+ 
+
+ align:start position:0%
+exactly what this is working through
+this is what's on your previous problem
+
+ align:start position:0%
+this is what's on your previous problem
+ 
+
+ align:start position:0%
+this is what's on your previous problem
+set as well as on your current problem
+
+ align:start position:0%
+set as well as on your current problem
+ 
+
+ align:start position:0%
+set as well as on your current problem
+set yeah is this anything like
+
+ align:start position:0%
+set yeah is this anything like
+ 
+
+ align:start position:0%
+set yeah is this anything like
+conservation of energy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent it sort of sounds like that
+
+ align:start position:0%
+excellent it sort of sounds like that
+ 
+
+ align:start position:0%
+excellent it sort of sounds like that
+will make a sharp version of that later
+
+ align:start position:0%
+will make a sharp version of that later
+ 
+
+ align:start position:0%
+will make a sharp version of that later
+so you should have that tinkling in the
+
+ align:start position:0%
+so you should have that tinkling in the
+ 
+
+ align:start position:0%
+so you should have that tinkling in the
+back of your head is like oh look we
+
+ align:start position:0%
+back of your head is like oh look we
+ 
+
+ align:start position:0%
+back of your head is like oh look we
+have a time independent potential energy
+
+ align:start position:0%
+have a time independent potential energy
+ 
+
+ align:start position:0%
+have a time independent potential energy
+is conserved that sounds kind of like
+
+ align:start position:0%
+is conserved that sounds kind of like
+ 
+
+ align:start position:0%
+is conserved that sounds kind of like
+the expectation value is constant but we
+
+ align:start position:0%
+the expectation value is constant but we
+ 
+
+ align:start position:0%
+the expectation value is constant but we
+need to make that more precise and we'll
+
+ align:start position:0%
+need to make that more precise and we'll
+ 
+
+ align:start position:0%
+need to make that more precise and we'll
+find a precise version of that statement
+
+ align:start position:0%
+find a precise version of that statement
+ 
+
+ align:start position:0%
+find a precise version of that statement
+later in the semester but it's a very
+
+ align:start position:0%
+later in the semester but it's a very
+ 
+
+ align:start position:0%
+later in the semester but it's a very
+good intuition to have other questions
+
+ align:start position:0%
+good intuition to have other questions
+ 
+
+ align:start position:0%
+good intuition to have other questions
+okay so the answer is D and you guys
+
+ align:start position:0%
+okay so the answer is D and you guys
+ 
+
+ align:start position:0%
+okay so the answer is D and you guys
+were about 4/5 on that at the end but
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that was not right okay next one this is
+
+ align:start position:0%
+that was not right okay next one this is
+ 
+
+ align:start position:0%
+that was not right okay next one this is
+a three step question we have observable
+
+ align:start position:0%
+a three step question we have observable
+ 
+
+ align:start position:0%
+a three step question we have observable
+a and B with eigen States i1 its IQ and
+
+ align:start position:0%
+a and B with eigen States i1 its IQ and
+ 
+
+ align:start position:0%
+a and B with eigen States i1 its IQ and
+phi1 and phi2 of a and b and eigen
+
+ align:start position:0%
+phi1 and phi2 of a and b and eigen
+ 
+
+ align:start position:0%
+phi1 and phi2 of a and b and eigen
+values a1 a2 and b1 b2 the eigen states
+
+ align:start position:0%
+values a1 a2 and b1 b2 the eigen states
+ 
+
+ align:start position:0%
+values a1 a2 and b1 b2 the eigen states
+are related in this linear fashion I
+
+ align:start position:0%
+are related in this linear fashion I
+ 
+
+ align:start position:0%
+are related in this linear fashion I
+measure observable a and get the value a
+
+ align:start position:0%
+measure observable a and get the value a
+ 
+
+ align:start position:0%
+measure observable a and get the value a
+1 what's the state immediately after
+
+ align:start position:0%
+1 what's the state immediately after
+ 
+
+ align:start position:0%
+1 what's the state immediately after
+that measurement what is the wave
+
+ align:start position:0%
+that measurement what is the wave
+ 
+
+ align:start position:0%
+that measurement what is the wave
+function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright five seconds to one-click ways
+
+ align:start position:0%
+alright five seconds to one-click ways
+ 
+
+ align:start position:0%
+alright five seconds to one-click ways
+okay great so there's pretty strong
+
+ align:start position:0%
+okay great so there's pretty strong
+ 
+
+ align:start position:0%
+okay great so there's pretty strong
+agreement among y'all that the answer is
+
+ align:start position:0%
+agreement among y'all that the answer is
+ 
+
+ align:start position:0%
+agreement among y'all that the answer is
+a and that is indeed the answer okay
+
+ align:start position:0%
+a and that is indeed the answer okay
+ 
+
+ align:start position:0%
+a and that is indeed the answer okay
+questions okay good so a slightly less
+
+ align:start position:0%
+questions okay good so a slightly less
+ 
+
+ align:start position:0%
+questions okay good so a slightly less
+obvious one immediately after this
+
+ align:start position:0%
+obvious one immediately after this
+ 
+
+ align:start position:0%
+obvious one immediately after this
+measurement of a the observable B is
+
+ align:start position:0%
+measurement of a the observable B is
+ 
+
+ align:start position:0%
+measurement of a the observable B is
+measured what's the probability that B 1
+
+ align:start position:0%
+measured what's the probability that B 1
+ 
+
+ align:start position:0%
+measured what's the probability that B 1
+is found
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well there's some amazing initial
+
+ align:start position:0%
+well there's some amazing initial
+ 
+
+ align:start position:0%
+well there's some amazing initial
+transients there I could use this that
+
+ align:start position:0%
+transients there I could use this that
+ 
+
+ align:start position:0%
+transients there I could use this that
+could use the first couple of seconds as
+
+ align:start position:0%
+could use the first couple of seconds as
+ 
+
+ align:start position:0%
+could use the first couple of seconds as
+a random number generator move around
+
+ align:start position:0%
+a random number generator move around
+ 
+
+ align:start position:0%
+a random number generator move around
+okay that's it and and there's actually
+
+ align:start position:0%
+okay that's it and and there's actually
+ 
+
+ align:start position:0%
+okay that's it and and there's actually
+a third of you disagree with the correct
+
+ align:start position:0%
+a third of you disagree with the correct
+ 
+
+ align:start position:0%
+a third of you disagree with the correct
+answer so I'm gonna invite you to chat
+
+ align:start position:0%
+answer so I'm gonna invite you to chat
+ 
+
+ align:start position:0%
+answer so I'm gonna invite you to chat
+with each other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go ahead and update your answers good
+
+ align:start position:0%
+go ahead and update your answers good
+ 
+
+ align:start position:0%
+go ahead and update your answers good
+okay five more seconds one second okay
+
+ align:start position:0%
+okay five more seconds one second okay
+ 
+
+ align:start position:0%
+okay five more seconds one second okay
+nice excellent you guys went from about
+
+ align:start position:0%
+nice excellent you guys went from about
+ 
+
+ align:start position:0%
+nice excellent you guys went from about
+65 percent to 90 percent so that was
+
+ align:start position:0%
+65 percent to 90 percent so that was
+ 
+
+ align:start position:0%
+65 percent to 90 percent so that was
+great the answer is e it's the norm
+
+ align:start position:0%
+great the answer is e it's the norm
+ 
+
+ align:start position:0%
+great the answer is e it's the norm
+squared of the coefficient of the the
+
+ align:start position:0%
+squared of the coefficient of the the
+ 
+
+ align:start position:0%
+squared of the coefficient of the the
+eigen value or eigen function
+
+ align:start position:0%
+eigen value or eigen function
+ 
+
+ align:start position:0%
+eigen value or eigen function
+corresponding to be one in the original
+
+ align:start position:0%
+corresponding to be one in the original
+ 
+
+ align:start position:0%
+corresponding to be one in the original
+state which was silent
+
+ align:start position:0%
+state which was silent
+ 
+
+ align:start position:0%
+state which was silent
+okay now imagine on the other hand that
+
+ align:start position:0%
+okay now imagine on the other hand that
+ 
+
+ align:start position:0%
+okay now imagine on the other hand that
+the grad student doing the measurement
+
+ align:start position:0%
+the grad student doing the measurement
+ 
+
+ align:start position:0%
+the grad student doing the measurement
+failed to in fact measure the observer
+
+ align:start position:0%
+failed to in fact measure the observer
+ 
+
+ align:start position:0%
+failed to in fact measure the observer
+will be it was a bad day but instead
+
+ align:start position:0%
+will be it was a bad day but instead
+ 
+
+ align:start position:0%
+will be it was a bad day but instead
+measure day again what's the probability
+
+ align:start position:0%
+measure day again what's the probability
+ 
+
+ align:start position:0%
+measure day again what's the probability
+that the second measurement will yield a
+
+ align:start position:0%
+that the second measurement will yield a
+ 
+
+ align:start position:0%
+that the second measurement will yield a
+one trust me on this one there's so many
+
+ align:start position:0%
+one trust me on this one there's so many
+ 
+
+ align:start position:0%
+one trust me on this one there's so many
+ways you know they read the package
+
+ align:start position:0%
+ways you know they read the package
+ 
+
+ align:start position:0%
+ways you know they read the package
+wrong you know they did the wrong
+
+ align:start position:0%
+wrong you know they did the wrong
+ 
+
+ align:start position:0%
+wrong you know they did the wrong
+measurement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry thank you thank you thank you no
+
+ align:start position:0%
+sorry thank you thank you thank you no
+ 
+
+ align:start position:0%
+sorry thank you thank you thank you no
+no very good question
+
+ align:start position:0%
+no very good question
+ 
+
+ align:start position:0%
+no very good question
+he accidentally measured thee instead of
+
+ align:start position:0%
+he accidentally measured thee instead of
+ 
+
+ align:start position:0%
+he accidentally measured thee instead of
+a are you need a MBA into the be
+
+ align:start position:0%
+a are you need a MBA into the be
+ 
+
+ align:start position:0%
+a are you need a MBA into the be
+actually live today and see how easy it
+
+ align:start position:0%
+actually live today and see how easy it
+ 
+
+ align:start position:0%
+actually live today and see how easy it
+is to make that mistake the accidentally
+
+ align:start position:0%
+is to make that mistake the accidentally
+ 
+
+ align:start position:0%
+is to make that mistake the accidentally
+measured a instead of B I preached that
+
+ align:start position:0%
+measured a instead of B I preached that
+ 
+
+ align:start position:0%
+measured a instead of B I preached that
+was intentional okay so and we get a
+
+ align:start position:0%
+was intentional okay so and we get a
+ 
+
+ align:start position:0%
+was intentional okay so and we get a
+almost total unanimity the answer is B
+
+ align:start position:0%
+almost total unanimity the answer is B
+ 
+
+ align:start position:0%
+almost total unanimity the answer is B
+yes question great question let's just
+
+ align:start position:0%
+yes question great question let's just
+ 
+
+ align:start position:0%
+yes question great question let's just
+assume it's instantaneous
+
+ align:start position:0%
+assume it's instantaneous
+ 
+
+ align:start position:0%
+assume it's instantaneous
+maybe sloppy but he's very quick okay
+
+ align:start position:0%
+maybe sloppy but he's very quick okay
+ 
+
+ align:start position:0%
+maybe sloppy but he's very quick okay
+next question a system is in a state
+
+ align:start position:0%
+next question a system is in a state
+ 
+
+ align:start position:0%
+next question a system is in a state
+which is a linear superposition of N
+
+ align:start position:0%
+which is a linear superposition of N
+ 
+
+ align:start position:0%
+which is a linear superposition of N
+equals 1 and N equals 2 energy
+
+ align:start position:0%
+equals 1 and N equals 2 energy
+ 
+
+ align:start position:0%
+equals 1 and N equals 2 energy
+eigenstates bla what's the probability
+
+ align:start position:0%
+eigenstates bla what's the probability
+ 
+
+ align:start position:0%
+eigenstates bla what's the probability
+that measurement of the energy will
+
+ align:start position:0%
+that measurement of the energy will
+ 
+
+ align:start position:0%
+that measurement of the energy will
+yield the first energy eigenvalue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another 5 seconds 5 great you guys
+
+ align:start position:0%
+another 5 seconds 5 great you guys
+ 
+
+ align:start position:0%
+another 5 seconds 5 great you guys
+totally agree that the answer is C ok
+
+ align:start position:0%
+totally agree that the answer is C ok
+ 
+
+ align:start position:0%
+totally agree that the answer is C ok
+great ok that's it that's it for that
+
+ align:start position:0%
+great ok that's it that's it for that
+ 
+
+ align:start position:0%
+great ok that's it that's it for that
+clicker questions for today um so here's
+
+ align:start position:0%
+clicker questions for today um so here's
+ 
+
+ align:start position:0%
+clicker questions for today um so here's
+the thing I want to emphasize the first
+
+ align:start position:0%
+the thing I want to emphasize the first
+ 
+
+ align:start position:0%
+the thing I want to emphasize the first
+is that these were totally conceptual
+
+ align:start position:0%
+is that these were totally conceptual
+ 
+
+ align:start position:0%
+is that these were totally conceptual
+they did not involve any computations
+
+ align:start position:0%
+they did not involve any computations
+ 
+
+ align:start position:0%
+they did not involve any computations
+and yet and yet they're they're not
+
+ align:start position:0%
+and yet and yet they're they're not
+ 
+
+ align:start position:0%
+and yet and yet they're they're not
+trivial some of them were really not
+
+ align:start position:0%
+trivial some of them were really not
+ 
+
+ align:start position:0%
+trivial some of them were really not
+some of them got you know 50 percent
+
+ align:start position:0%
+some of them got you know 50 percent
+ 
+
+ align:start position:0%
+some of them got you know 50 percent
+consistently across the class so it's
+
+ align:start position:0%
+consistently across the class so it's
+ 
+
+ align:start position:0%
+consistently across the class so it's
+not just the calculations that are hard
+
+ align:start position:0%
+not just the calculations that are hard
+ 
+
+ align:start position:0%
+not just the calculations that are hard
+just thinking through the the basic
+
+ align:start position:0%
+just thinking through the the basic
+ 
+
+ align:start position:0%
+just thinking through the the basic
+premises the basic postulates is really
+
+ align:start position:0%
+premises the basic postulates is really
+ 
+
+ align:start position:0%
+premises the basic postulates is really
+essential at this point it's more
+
+ align:start position:0%
+essential at this point it's more
+ 
+
+ align:start position:0%
+essential at this point it's more
+important than the computation yeah I
+
+ align:start position:0%
+important than the computation yeah I
+ 
+
+ align:start position:0%
+important than the computation yeah I
+will post these I will post these ok any
+
+ align:start position:0%
+will post these I will post these ok any
+ 
+
+ align:start position:0%
+will post these I will post these ok any
+questions remaining from after this
+
+ align:start position:0%
+questions remaining from after this
+ 
+
+ align:start position:0%
+questions remaining from after this
+little oh shoot you know I missed out on
+
+ align:start position:0%
+little oh shoot you know I missed out on
+ 
+
+ align:start position:0%
+little oh shoot you know I missed out on
+a whole opportunity um I'll do it next
+
+ align:start position:0%
+a whole opportunity um I'll do it next
+ 
+
+ align:start position:0%
+a whole opportunity um I'll do it next
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+whoo any other questions before we move
+
+ align:start position:0%
+whoo any other questions before we move
+ 
+
+ align:start position:0%
+whoo any other questions before we move
+on to the lecture part oh you totally
+
+ align:start position:0%
+on to the lecture part oh you totally
+ 
+
+ align:start position:0%
+on to the lecture part oh you totally
+have to wait
+
+ align:start position:0%
+have to wait
+ 
+
+ align:start position:0%
+have to wait
+and you totally have to wait okay any
+
+ align:start position:0%
+and you totally have to wait okay any
+ 
+
+ align:start position:0%
+and you totally have to wait okay any
+any other questions yeah well that's a
+
+ align:start position:0%
+any other questions yeah well that's a
+ 
+
+ align:start position:0%
+any other questions yeah well that's a
+very good question so the question is
+
+ align:start position:0%
+very good question so the question is
+ 
+
+ align:start position:0%
+very good question so the question is
+can you ever have a potential function
+
+ align:start position:0%
+can you ever have a potential function
+ 
+
+ align:start position:0%
+can you ever have a potential function
+that is odd so for example so let me
+
+ align:start position:0%
+that is odd so for example so let me
+ 
+
+ align:start position:0%
+that is odd so for example so let me
+you're actually asking two questions and
+
+ align:start position:0%
+you're actually asking two questions and
+ 
+
+ align:start position:0%
+you're actually asking two questions and
+let me disentangle them so one question
+
+ align:start position:0%
+let me disentangle them so one question
+ 
+
+ align:start position:0%
+let me disentangle them so one question
+is can I have an energy and then a
+
+ align:start position:0%
+is can I have an energy and then a
+ 
+
+ align:start position:0%
+is can I have an energy and then a
+potential function which is odd in and
+
+ align:start position:0%
+potential function which is odd in and
+ 
+
+ align:start position:0%
+potential function which is odd in and
+linear right
+
+ align:start position:0%
+linear right
+ 
+
+ align:start position:0%
+linear right
+so it just ramps all the way down so
+
+ align:start position:0%
+so it just ramps all the way down so
+ 
+
+ align:start position:0%
+so it just ramps all the way down so
+does that seem physical is the energy
+
+ align:start position:0%
+does that seem physical is the energy
+ 
+
+ align:start position:0%
+does that seem physical is the energy
+bounded from below no okay well that's
+
+ align:start position:0%
+bounded from below no okay well that's
+ 
+
+ align:start position:0%
+bounded from below no okay well that's
+not a terribly good criterion because
+
+ align:start position:0%
+not a terribly good criterion because
+ 
+
+ align:start position:0%
+not a terribly good criterion because
+it's not bounded from below for the
+
+ align:start position:0%
+it's not bounded from below for the
+ 
+
+ align:start position:0%
+it's not bounded from below for the
+Coulomb potential either all right but
+
+ align:start position:0%
+Coulomb potential either all right but
+ 
+
+ align:start position:0%
+Coulomb potential either all right but
+in the case of the Coulomb potential
+
+ align:start position:0%
+in the case of the Coulomb potential
+ 
+
+ align:start position:0%
+in the case of the Coulomb potential
+it's not bounded from below in a little
+
+ align:start position:0%
+it's not bounded from below in a little
+ 
+
+ align:start position:0%
+it's not bounded from below in a little
+tiny region right not you know in a huge
+
+ align:start position:0%
+tiny region right not you know in a huge
+ 
+
+ align:start position:0%
+tiny region right not you know in a huge
+swath so we're gonna need a better
+
+ align:start position:0%
+swath so we're gonna need a better
+ 
+
+ align:start position:0%
+swath so we're gonna need a better
+definition of this but the short answer
+
+ align:start position:0%
+definition of this but the short answer
+ 
+
+ align:start position:0%
+definition of this but the short answer
+to this one is no this is not good okay
+
+ align:start position:0%
+to this one is no this is not good okay
+ 
+
+ align:start position:0%
+to this one is no this is not good okay
+on the other hand it's not the oddness
+
+ align:start position:0%
+on the other hand it's not the oddness
+ 
+
+ align:start position:0%
+on the other hand it's not the oddness
+that's bad it's that the energy is
+
+ align:start position:0%
+that's bad it's that the energy is
+ 
+
+ align:start position:0%
+that's bad it's that the energy is
+continuing to be unbounded from below
+
+ align:start position:0%
+continuing to be unbounded from below
+ 
+
+ align:start position:0%
+continuing to be unbounded from below
+and here's what here so let me be more
+
+ align:start position:0%
+and here's what here so let me be more
+ 
+
+ align:start position:0%
+and here's what here so let me be more
+precise than saying it's not happy what
+
+ align:start position:0%
+precise than saying it's not happy what
+ 
+
+ align:start position:0%
+precise than saying it's not happy what
+is it what's important for an observable
+
+ align:start position:0%
+is it what's important for an observable
+ 
+
+ align:start position:0%
+is it what's important for an observable
+what's important for an observable the
+
+ align:start position:0%
+what's important for an observable the
+ 
+
+ align:start position:0%
+what's important for an observable the
+operator corresponding to an observable
+
+ align:start position:0%
+operator corresponding to an observable
+ 
+
+ align:start position:0%
+operator corresponding to an observable
+in quantum mechanics what property must
+
+ align:start position:0%
+in quantum mechanics what property must
+ 
+
+ align:start position:0%
+in quantum mechanics what property must
+that operator have it has to be
+
+ align:start position:0%
+that operator have it has to be
+ 
+
+ align:start position:0%
+that operator have it has to be
+hermitian right and empty oh that
+
+ align:start position:0%
+hermitian right and empty oh that
+ 
+
+ align:start position:0%
+hermitian right and empty oh that
+implies real eigenvalues it implies that
+
+ align:start position:0%
+implies real eigenvalues it implies that
+ 
+
+ align:start position:0%
+implies real eigenvalues it implies that
+there's a basis of its eigenfunctions
+
+ align:start position:0%
+there's a basis of its eigenfunctions
+ 
+
+ align:start position:0%
+there's a basis of its eigenfunctions
+all these nice things what we will find
+
+ align:start position:0%
+all these nice things what we will find
+ 
+
+ align:start position:0%
+all these nice things what we will find
+is that the Coulomb potential
+
+ align:start position:0%
+is that the Coulomb potential
+ 
+
+ align:start position:0%
+is that the Coulomb potential
+the hydrogen potential gives us a nice
+
+ align:start position:0%
+the hydrogen potential gives us a nice
+ 
+
+ align:start position:0%
+the hydrogen potential gives us a nice
+hermitian energy operator will prove
+
+ align:start position:0%
+hermitian energy operator will prove
+ 
+
+ align:start position:0%
+hermitian energy operator will prove
+that the energy operator self the joint
+
+ align:start position:0%
+that the energy operator self the joint
+ 
+
+ align:start position:0%
+that the energy operator self the joint
+on a problem set however this guy will
+
+ align:start position:0%
+on a problem set however this guy will
+ 
+
+ align:start position:0%
+on a problem set however this guy will
+not okay so we're gonna have a one that
+
+ align:start position:0%
+not okay so we're gonna have a one that
+ 
+
+ align:start position:0%
+not okay so we're gonna have a one that
+is not bounded from below and so while
+
+ align:start position:0%
+is not bounded from below and so while
+ 
+
+ align:start position:0%
+is not bounded from below and so while
+it's there's a sense in which its
+
+ align:start position:0%
+it's there's a sense in which its
+ 
+
+ align:start position:0%
+it's there's a sense in which its
+hermitian there's not a good sense in
+
+ align:start position:0%
+hermitian there's not a good sense in
+ 
+
+ align:start position:0%
+hermitian there's not a good sense in
+which it's it's got problems so but
+
+ align:start position:0%
+which it's it's got problems so but
+ 
+
+ align:start position:0%
+which it's it's got problems so but
+that's a more technical detail however
+
+ align:start position:0%
+that's a more technical detail however
+ 
+
+ align:start position:0%
+that's a more technical detail however
+there's a second part of your question
+
+ align:start position:0%
+there's a second part of your question
+ 
+
+ align:start position:0%
+there's a second part of your question
+which is you could have been asking a
+
+ align:start position:0%
+which is you could have been asking a
+ 
+
+ align:start position:0%
+which is you could have been asking a
+look can you have a potential that's odd
+
+ align:start position:0%
+look can you have a potential that's odd
+ 
+
+ align:start position:0%
+look can you have a potential that's odd
+but literally decide the diverging it
+
+ align:start position:0%
+but literally decide the diverging it
+ 
+
+ align:start position:0%
+but literally decide the diverging it
+and infinity so for example cuz you have
+
+ align:start position:0%
+and infinity so for example cuz you have
+ 
+
+ align:start position:0%
+and infinity so for example cuz you have
+a potential that does this so that it's
+
+ align:start position:0%
+a potential that does this so that it's
+ 
+
+ align:start position:0%
+a potential that does this so that it's
+odd but it it's bounded and that's fine
+
+ align:start position:0%
+odd but it it's bounded and that's fine
+ 
+
+ align:start position:0%
+odd but it it's bounded and that's fine
+nothing wrong with that so odd isn't the
+
+ align:start position:0%
+nothing wrong with that so odd isn't the
+ 
+
+ align:start position:0%
+nothing wrong with that so odd isn't the
+problem the problem is certain ways of
+
+ align:start position:0%
+problem the problem is certain ways of
+ 
+
+ align:start position:0%
+problem the problem is certain ways of
+diverging
+
+ align:start position:0%
+diverging
+ 
+
+ align:start position:0%
+diverging
+yeah so later does that mean so what
+
+ align:start position:0%
+yeah so later does that mean so what
+ 
+
+ align:start position:0%
+yeah so later does that mean so what
+would happen in the case where you did
+
+ align:start position:0%
+would happen in the case where you did
+ 
+
+ align:start position:0%
+would happen in the case where you did
+have some kind of linear potentially get
+
+ align:start position:0%
+have some kind of linear potentially get
+ 
+
+ align:start position:0%
+have some kind of linear potentially get
+a uniform electric field and something
+
+ align:start position:0%
+a uniform electric field and something
+ 
+
+ align:start position:0%
+a uniform electric field and something
+was moving is that like just is it is
+
+ align:start position:0%
+was moving is that like just is it is
+ 
+
+ align:start position:0%
+was moving is that like just is it is
+the problem that that potential
+
+ align:start position:0%
+the problem that that potential
+ 
+
+ align:start position:0%
+the problem that that potential
+technically isn't like a physical
+
+ align:start position:0%
+technically isn't like a physical
+ 
+
+ align:start position:0%
+technically isn't like a physical
+potential because it doesn't go away or
+
+ align:start position:0%
+potential because it doesn't go away or
+ 
+
+ align:start position:0%
+potential because it doesn't go away or
+well how would you ever build a linear
+
+ align:start position:0%
+well how would you ever build a linear
+ 
+
+ align:start position:0%
+well how would you ever build a linear
+potential right so the question here is
+
+ align:start position:0%
+potential right so the question here is
+ 
+
+ align:start position:0%
+potential right so the question here is
+looks I know how to build a linear
+
+ align:start position:0%
+looks I know how to build a linear
+ 
+
+ align:start position:0%
+looks I know how to build a linear
+potential turn on a uniform electric
+
+ align:start position:0%
+potential turn on a uniform electric
+ 
+
+ align:start position:0%
+potential turn on a uniform electric
+field and the electric field is a
+
+ align:start position:0%
+field and the electric field is a
+ 
+
+ align:start position:0%
+field and the electric field is a
+gradient to the electrostatic potential
+
+ align:start position:0%
+gradient to the electrostatic potential
+ 
+
+ align:start position:0%
+gradient to the electrostatic potential
+so that means the electrostatic
+
+ align:start position:0%
+so that means the electrostatic
+ 
+
+ align:start position:0%
+so that means the electrostatic
+potential is linear and the potential
+
+ align:start position:0%
+potential is linear and the potential
+ 
+
+ align:start position:0%
+potential is linear and the potential
+energy of a charged particle with charge
+
+ align:start position:0%
+energy of a charged particle with charge
+ 
+
+ align:start position:0%
+energy of a charged particle with charge
+Q in an electrostatic potential is Q
+
+ align:start position:0%
+Q in an electrostatic potential is Q
+ 
+
+ align:start position:0%
+Q in an electrostatic potential is Q
+times the electrostatic potential so the
+
+ align:start position:0%
+times the electrostatic potential so the
+ 
+
+ align:start position:0%
+times the electrostatic potential so the
+potential energy for that charged
+
+ align:start position:0%
+potential energy for that charged
+ 
+
+ align:start position:0%
+potential energy for that charged
+particle is a linear function so how do
+
+ align:start position:0%
+particle is a linear function so how do
+ 
+
+ align:start position:0%
+particle is a linear function so how do
+I build such thing well I take two
+
+ align:start position:0%
+I build such thing well I take two
+ 
+
+ align:start position:0%
+I build such thing well I take two
+capacitor plates and I dump some charge
+
+ align:start position:0%
+capacitor plates and I dump some charge
+ 
+
+ align:start position:0%
+capacitor plates and I dump some charge
+on this one in the opposite charge on
+
+ align:start position:0%
+on this one in the opposite charge on
+ 
+
+ align:start position:0%
+on this one in the opposite charge on
+this guy and I build up a linear
+
+ align:start position:0%
+this guy and I build up a linear
+ 
+
+ align:start position:0%
+this guy and I build up a linear
+potential well yeah exactly so that's
+
+ align:start position:0%
+potential well yeah exactly so that's
+ 
+
+ align:start position:0%
+potential well yeah exactly so that's
+the problem so can I build make this
+
+ align:start position:0%
+the problem so can I build make this
+ 
+
+ align:start position:0%
+the problem so can I build make this
+linear over an arbitrarily large domain
+
+ align:start position:0%
+linear over an arbitrarily large domain
+ 
+
+ align:start position:0%
+linear over an arbitrarily large domain
+no I need an arbitrarily large amount of
+
+ align:start position:0%
+no I need an arbitrarily large amount of
+ 
+
+ align:start position:0%
+no I need an arbitrarily large amount of
+charge and I need to push them apart
+
+ align:start position:0%
+charge and I need to push them apart
+ 
+
+ align:start position:0%
+charge and I need to push them apart
+from each other arbitrarily far which
+
+ align:start position:0%
+from each other arbitrarily far which
+ 
+
+ align:start position:0%
+from each other arbitrarily far which
+takes an arbitrarily large amount of
+
+ align:start position:0%
+takes an arbitrarily large amount of
+ 
+
+ align:start position:0%
+takes an arbitrarily large amount of
+work that's not terribly physical right
+
+ align:start position:0%
+work that's not terribly physical right
+ 
+
+ align:start position:0%
+work that's not terribly physical right
+your arms are only so big right so so at
+
+ align:start position:0%
+your arms are only so big right so so at
+ 
+
+ align:start position:0%
+your arms are only so big right so so at
+the end of the day we're always going to
+
+ align:start position:0%
+the end of the day we're always going to
+ 
+
+ align:start position:0%
+the end of the day we're always going to
+discover that the pathologies that show
+
+ align:start position:0%
+discover that the pathologies that show
+ 
+
+ align:start position:0%
+discover that the pathologies that show
+up in a potential like is like the
+
+ align:start position:0%
+up in a potential like is like the
+ 
+
+ align:start position:0%
+up in a potential like is like the
+Hamiltonian is not self adjoint and
+
+ align:start position:0%
+Hamiltonian is not self adjoint and
+ 
+
+ align:start position:0%
+Hamiltonian is not self adjoint and
+compactly supported space of complex
+
+ align:start position:0%
+compactly supported space of complex
+ 
+
+ align:start position:0%
+compactly supported space of complex
+supported l2 continuous functions then
+
+ align:start position:0%
+supported l2 continuous functions then
+ 
+
+ align:start position:0%
+supported l2 continuous functions then
+okay that's that's going to always be
+
+ align:start position:0%
+okay that's that's going to always be
+ 
+
+ align:start position:0%
+okay that's that's going to always be
+some mathematical version of your arms
+
+ align:start position:0%
+some mathematical version of your arms
+ 
+
+ align:start position:0%
+some mathematical version of your arms
+are only so big you cannot build an
+
+ align:start position:0%
+are only so big you cannot build an
+ 
+
+ align:start position:0%
+are only so big you cannot build an
+infinitely large apparatus like this so
+
+ align:start position:0%
+infinitely large apparatus like this so
+ 
+
+ align:start position:0%
+infinitely large apparatus like this so
+yes you're exactly right it is not
+
+ align:start position:0%
+yes you're exactly right it is not
+ 
+
+ align:start position:0%
+yes you're exactly right it is not
+physical is it a mathematical problem
+
+ align:start position:0%
+physical is it a mathematical problem
+ 
+
+ align:start position:0%
+physical is it a mathematical problem
+one could analyze yes one could write a
+
+ align:start position:0%
+one could analyze yes one could write a
+ 
+
+ align:start position:0%
+one could analyze yes one could write a
+dissertation on the celerity structure
+
+ align:start position:0%
+dissertation on the celerity structure
+ 
+
+ align:start position:0%
+dissertation on the celerity structure
+of these differential equations but that
+
+ align:start position:0%
+of these differential equations but that
+ 
+
+ align:start position:0%
+of these differential equations but that
+dissertation would never be read by a
+
+ align:start position:0%
+dissertation would never be read by a
+ 
+
+ align:start position:0%
+dissertation would never be read by a
+physicist other questions yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excellent question no no so here's what
+
+ align:start position:0%
+excellent question no no so here's what
+ 
+
+ align:start position:0%
+excellent question no no so here's what
+you can do
+
+ align:start position:0%
+you can do
+ 
+
+ align:start position:0%
+you can do
+suppose I have a bunch of energy
+
+ align:start position:0%
+suppose I have a bunch of energy
+ 
+
+ align:start position:0%
+suppose I have a bunch of energy
+eigenstates I have some potential at
+
+ align:start position:0%
+eigenstates I have some potential at
+ 
+
+ align:start position:0%
+eigenstates I have some potential at
+some crease this is the potential
+
+ align:start position:0%
+some crease this is the potential
+ 
+
+ align:start position:0%
+some crease this is the potential
+it's a crazy potential right and it has
+
+ align:start position:0%
+it's a crazy potential right and it has
+ 
+
+ align:start position:0%
+it's a crazy potential right and it has
+some definite energy eigenvalues as
+
+ align:start position:0%
+some definite energy eigenvalues as
+ 
+
+ align:start position:0%
+some definite energy eigenvalues as
+we've shown in 1d we don't her as I've
+
+ align:start position:0%
+we've shown in 1d we don't her as I've
+ 
+
+ align:start position:0%
+we've shown in 1d we don't her as I've
+mentioned and proved in office hours we
+
+ align:start position:0%
+mentioned and proved in office hours we
+ 
+
+ align:start position:0%
+mentioned and proved in office hours we
+can't find degenerate eigen functions in
+
+ align:start position:0%
+can't find degenerate eigen functions in
+ 
+
+ align:start position:0%
+can't find degenerate eigen functions in
+a one dimensional potential so they're
+
+ align:start position:0%
+a one dimensional potential so they're
+ 
+
+ align:start position:0%
+a one dimensional potential so they're
+just they're not degenerate their space
+
+ align:start position:0%
+just they're not degenerate their space
+ 
+
+ align:start position:0%
+just they're not degenerate their space
+to find a distance part four four states
+
+ align:start position:0%
+to find a distance part four four states
+ 
+
+ align:start position:0%
+to find a distance part four four states
+for wave functions that converge it to
+
+ align:start position:0%
+for wave functions that converge it to
+ 
+
+ align:start position:0%
+for wave functions that converge it to
+zero at infinity for a bound States so I
+
+ align:start position:0%
+zero at infinity for a bound States so I
+ 
+
+ align:start position:0%
+zero at infinity for a bound States so I
+could always construct an operator which
+
+ align:start position:0%
+could always construct an operator which
+ 
+
+ align:start position:0%
+could always construct an operator which
+I will simply define in this way a and
+
+ align:start position:0%
+I will simply define in this way a and
+ 
+
+ align:start position:0%
+I will simply define in this way a and
+just for flourish I will put a dagger on
+
+ align:start position:0%
+just for flourish I will put a dagger on
+ 
+
+ align:start position:0%
+just for flourish I will put a dagger on
+it which does the following a dagger is
+
+ align:start position:0%
+it which does the following a dagger is
+ 
+
+ align:start position:0%
+it which does the following a dagger is
+the is defined as the operator that
+
+ align:start position:0%
+the is defined as the operator that
+ 
+
+ align:start position:0%
+the is defined as the operator that
+map's Phi n to Phi M and plus one right
+
+ align:start position:0%
+map's Phi n to Phi M and plus one right
+ 
+
+ align:start position:0%
+map's Phi n to Phi M and plus one right
+so what's the rule it takes this state
+
+ align:start position:0%
+so what's the rule it takes this state
+ 
+
+ align:start position:0%
+so what's the rule it takes this state
+to this state this state to this state
+
+ align:start position:0%
+to this state this state to this state
+ 
+
+ align:start position:0%
+to this state this state to this state
+this state to this a and since we can
+
+ align:start position:0%
+this state to this a and since we can
+ 
+
+ align:start position:0%
+this state to this a and since we can
+extend since these are a basis then that
+
+ align:start position:0%
+extend since these are a basis then that
+ 
+
+ align:start position:0%
+extend since these are a basis then that
+tells us how this acts on an arbitrary
+
+ align:start position:0%
+tells us how this acts on an arbitrary
+ 
+
+ align:start position:0%
+tells us how this acts on an arbitrary
+function because it acts on the
+
+ align:start position:0%
+function because it acts on the
+ 
+
+ align:start position:0%
+function because it acts on the
+superposition as acting on each term so
+
+ align:start position:0%
+superposition as acting on each term so
+ 
+
+ align:start position:0%
+superposition as acting on each term so
+we can define it in this way but here's
+
+ align:start position:0%
+we can define it in this way but here's
+ 
+
+ align:start position:0%
+we can define it in this way but here's
+the question what does it mean for the
+
+ align:start position:0%
+the question what does it mean for the
+ 
+
+ align:start position:0%
+the question what does it mean for the
+raising operator to be the raising
+
+ align:start position:0%
+raising operator to be the raising
+ 
+
+ align:start position:0%
+raising operator to be the raising
+operator it wasn't that it lifted the
+
+ align:start position:0%
+operator it wasn't that it lifted the
+ 
+
+ align:start position:0%
+operator it wasn't that it lifted the
+raise the operator that's not what
+
+ align:start position:0%
+raise the operator that's not what
+ 
+
+ align:start position:0%
+raise the operator that's not what
+started out the whole machinery where
+
+ align:start position:0%
+started out the whole machinery where
+ 
+
+ align:start position:0%
+started out the whole machinery where
+the raising operator got its juice was
+
+ align:start position:0%
+the raising operator got its juice was
+ 
+
+ align:start position:0%
+the raising operator got its juice was
+from this commutation relation a dagger
+
+ align:start position:0%
+from this commutation relation a dagger
+ 
+
+ align:start position:0%
+from this commutation relation a dagger
+with E was equal to H bar Omega a dagger
+
+ align:start position:0%
+with E was equal to H bar Omega a dagger
+ 
+
+ align:start position:0%
+with E was equal to H bar Omega a dagger
+right so can we build an operator a
+
+ align:start position:0%
+right so can we build an operator a
+ 
+
+ align:start position:0%
+right so can we build an operator a
+dagger that raises States and commutes
+
+ align:start position:0%
+dagger that raises States and commutes
+ 
+
+ align:start position:0%
+dagger that raises States and commutes
+with the energy operator in this fashion
+
+ align:start position:0%
+with the energy operator in this fashion
+ 
+
+ align:start position:0%
+with the energy operator in this fashion
+no that depends on the energy operator
+
+ align:start position:0%
+no that depends on the energy operator
+ 
+
+ align:start position:0%
+no that depends on the energy operator
+this is not a general property this is
+
+ align:start position:0%
+this is not a general property this is
+ 
+
+ align:start position:0%
+this is not a general property this is
+not always something we can do okay if
+
+ align:start position:0%
+not always something we can do okay if
+ 
+
+ align:start position:0%
+not always something we can do okay if
+we could then that energy operator would
+
+ align:start position:0%
+we could then that energy operator would
+ 
+
+ align:start position:0%
+we could then that energy operator would
+have evenly spaced energy eigenfunctions
+
+ align:start position:0%
+have evenly spaced energy eigenfunctions
+ 
+
+ align:start position:0%
+have evenly spaced energy eigenfunctions
+on the other hand it's not like it's
+
+ align:start position:0%
+on the other hand it's not like it's
+ 
+
+ align:start position:0%
+on the other hand it's not like it's
+never useful so consider the following
+
+ align:start position:0%
+never useful so consider the following
+ 
+
+ align:start position:0%
+never useful so consider the following
+example and I think this was on your
+
+ align:start position:0%
+example and I think this was on your
+ 
+
+ align:start position:0%
+example and I think this was on your
+promise up in our number so let me just
+
+ align:start position:0%
+promise up in our number so let me just
+ 
+
+ align:start position:0%
+promise up in our number so let me just
+say it
+
+ align:start position:0%
+say it
+ 
+
+ align:start position:0%
+say it
+consider the what if we write um a
+
+ align:start position:0%
+consider the what if we write um a
+ 
+
+ align:start position:0%
+consider the what if we write um a
+dagger a is equal to n right then the
+
+ align:start position:0%
+dagger a is equal to n right then the
+ 
+
+ align:start position:0%
+dagger a is equal to n right then the
+commutation relation for this so the
+
+ align:start position:0%
+commutation relation for this so the
+ 
+
+ align:start position:0%
+commutation relation for this so the
+energy operator for the harmonic
+
+ align:start position:0%
+energy operator for the harmonic
+ 
+
+ align:start position:0%
+energy operator for the harmonic
+oscillator was equal to H bar Omega n
+
+ align:start position:0%
+oscillator was equal to H bar Omega n
+ 
+
+ align:start position:0%
+oscillator was equal to H bar Omega n
+plus 1/2 right that's what we derived
+
+ align:start position:0%
+plus 1/2 right that's what we derived
+ 
+
+ align:start position:0%
+plus 1/2 right that's what we derived
+last time if we drive define a dagger a
+
+ align:start position:0%
+last time if we drive define a dagger a
+ 
+
+ align:start position:0%
+last time if we drive define a dagger a
+is n
+
+ align:start position:0%
+is n
+ 
+
+ align:start position:0%
+is n
+then commutator of n with a dagger is a
+
+ align:start position:0%
+then commutator of n with a dagger is a
+ 
+
+ align:start position:0%
+then commutator of n with a dagger is a
+dagger and the commutator of n with a is
+
+ align:start position:0%
+dagger and the commutator of n with a is
+ 
+
+ align:start position:0%
+dagger and the commutator of n with a is
+equal to minus a suppose the Hamiltonian
+
+ align:start position:0%
+equal to minus a suppose the Hamiltonian
+ 
+
+ align:start position:0%
+equal to minus a suppose the Hamiltonian
+or suppose the energy operator sorry
+
+ align:start position:0%
+or suppose the energy operator sorry
+ 
+
+ align:start position:0%
+or suppose the energy operator sorry
+the French suppose the energy operator
+
+ align:start position:0%
+the French suppose the energy operator
+ 
+
+ align:start position:0%
+the French suppose the energy operator
+is is equal to H bar Omega n plus and
+
+ align:start position:0%
+is is equal to H bar Omega n plus and
+ 
+
+ align:start position:0%
+is is equal to H bar Omega n plus and
+cubed okay does the raising operator
+
+ align:start position:0%
+cubed okay does the raising operator
+ 
+
+ align:start position:0%
+cubed okay does the raising operator
+commute with the energy operator to give
+
+ align:start position:0%
+commute with the energy operator to give
+ 
+
+ align:start position:0%
+commute with the energy operator to give
+you a dagger again no because it's going
+
+ align:start position:0%
+you a dagger again no because it's going
+ 
+
+ align:start position:0%
+you a dagger again no because it's going
+to give you a commutes to give you an a
+
+ align:start position:0%
+to give you a commutes to give you an a
+ 
+
+ align:start position:0%
+to give you a commutes to give you an a
+dagger and commutes with this guy to
+
+ align:start position:0%
+dagger and commutes with this guy to
+ 
+
+ align:start position:0%
+dagger and commutes with this guy to
+give you well a constant times n squared
+
+ align:start position:0%
+give you well a constant times n squared
+ 
+
+ align:start position:0%
+give you well a constant times n squared
+a dagger which is a slightly funny Beast
+
+ align:start position:0%
+a dagger which is a slightly funny Beast
+ 
+
+ align:start position:0%
+a dagger which is a slightly funny Beast
+so this doesn't have the same
+
+ align:start position:0%
+so this doesn't have the same
+ 
+
+ align:start position:0%
+so this doesn't have the same
+commutation relations on the other hand
+
+ align:start position:0%
+commutation relations on the other hand
+ 
+
+ align:start position:0%
+commutation relations on the other hand
+we know how to build the eigenfunctions
+
+ align:start position:0%
+we know how to build the eigenfunctions
+ 
+
+ align:start position:0%
+we know how to build the eigenfunctions
+of the ennop rater because they live in
+
+ align:start position:0%
+of the ennop rater because they live in
+ 
+
+ align:start position:0%
+of the ennop rater because they live in
+a tower by this algebra by this
+
+ align:start position:0%
+a tower by this algebra by this
+ 
+
+ align:start position:0%
+a tower by this algebra by this
+commutator relation they live in a tower
+
+ align:start position:0%
+commutator relation they live in a tower
+ 
+
+ align:start position:0%
+commutator relation they live in a tower
+so I can build the eigenfunctions of n
+
+ align:start position:0%
+so I can build the eigenfunctions of n
+ 
+
+ align:start position:0%
+so I can build the eigenfunctions of n
+and then I can take those eigenfunctions
+
+ align:start position:0%
+and then I can take those eigenfunctions
+ 
+
+ align:start position:0%
+and then I can take those eigenfunctions
+of n act on them with E and we'll
+
+ align:start position:0%
+of n act on them with E and we'll
+ 
+
+ align:start position:0%
+of n act on them with E and we'll
+discover that they're also eigen
+
+ align:start position:0%
+discover that they're also eigen
+ 
+
+ align:start position:0%
+discover that they're also eigen
+functions of e because yakking on them
+
+ align:start position:0%
+functions of e because yakking on them
+ 
+
+ align:start position:0%
+functions of e because yakking on them
+is just n and then cube backing on the
+
+ align:start position:0%
+is just n and then cube backing on the
+ 
+
+ align:start position:0%
+is just n and then cube backing on the
+eigenfunctions of n and then so they're
+
+ align:start position:0%
+eigenfunctions of n and then so they're
+ 
+
+ align:start position:0%
+eigenfunctions of n and then so they're
+high interest so the states with
+
+ align:start position:0%
+high interest so the states with
+ 
+
+ align:start position:0%
+high interest so the states with
+definite n are still eigenfunctions of
+
+ align:start position:0%
+definite n are still eigenfunctions of
+ 
+
+ align:start position:0%
+definite n are still eigenfunctions of
+the energy operator but they're not
+
+ align:start position:0%
+the energy operator but they're not
+ 
+
+ align:start position:0%
+the energy operator but they're not
+evenly spaced now can every potential be
+
+ align:start position:0%
+evenly spaced now can every potential be
+ 
+
+ align:start position:0%
+evenly spaced now can every potential be
+written in terms of this n operator so I
+
+ align:start position:0%
+written in terms of this n operator so I
+ 
+
+ align:start position:0%
+written in terms of this n operator so I
+leave that to you as an exercise the
+
+ align:start position:0%
+leave that to you as an exercise the
+ 
+
+ align:start position:0%
+leave that to you as an exercise the
+answer is no try it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah exactly so if there's there's
+
+ align:start position:0%
+yeah exactly so if there's there's
+ 
+
+ align:start position:0%
+yeah exactly so if there's there's
+always something that you can formally
+
+ align:start position:0%
+always something that you can formally
+ 
+
+ align:start position:0%
+always something that you can formally
+define in this fashion it's not always
+
+ align:start position:0%
+define in this fashion it's not always
+ 
+
+ align:start position:0%
+define in this fashion it's not always
+useful to you because it doesn't always
+
+ align:start position:0%
+useful to you because it doesn't always
+ 
+
+ align:start position:0%
+useful to you because it doesn't always
+commute with the energy operator in some
+
+ align:start position:0%
+commute with the energy operator in some
+ 
+
+ align:start position:0%
+commute with the energy operator in some
+nice way right so now you can ask are
+
+ align:start position:0%
+nice way right so now you can ask are
+ 
+
+ align:start position:0%
+nice way right so now you can ask are
+there think properties that are nice
+
+ align:start position:0%
+there think properties that are nice
+ 
+
+ align:start position:0%
+there think properties that are nice
+about this well there's something called
+
+ align:start position:0%
+about this well there's something called
+ 
+
+ align:start position:0%
+about this well there's something called
+the super symmetric method in 1d quantum
+
+ align:start position:0%
+the super symmetric method in 1d quantum
+ 
+
+ align:start position:0%
+the super symmetric method in 1d quantum
+mechanics but that's sort of beyond the
+
+ align:start position:0%
+mechanics but that's sort of beyond the
+ 
+
+ align:start position:0%
+mechanics but that's sort of beyond the
+scope come to my office hours and ask me
+
+ align:start position:0%
+scope come to my office hours and ask me
+ 
+
+ align:start position:0%
+scope come to my office hours and ask me
+this question again this is a miracle of
+
+ align:start position:0%
+this question again this is a miracle of
+ 
+
+ align:start position:0%
+this question again this is a miracle of
+the harmonic oscillator other questions
+
+ align:start position:0%
+the harmonic oscillator other questions
+ 
+
+ align:start position:0%
+the harmonic oscillator other questions
+yeah to construct the ground state we
+
+ align:start position:0%
+yeah to construct the ground state we
+ 
+
+ align:start position:0%
+yeah to construct the ground state we
+use a condition that a five zero is zero
+
+ align:start position:0%
+use a condition that a five zero is zero
+ 
+
+ align:start position:0%
+use a condition that a five zero is zero
+yes did we like so how did we call them
+
+ align:start position:0%
+yes did we like so how did we call them
+ 
+
+ align:start position:0%
+yes did we like so how did we call them
+did we demand that on physical grounds
+
+ align:start position:0%
+did we demand that on physical grounds
+ 
+
+ align:start position:0%
+did we demand that on physical grounds
+that it had to be zero yes we did so
+
+ align:start position:0%
+that it had to be zero yes we did so
+ 
+
+ align:start position:0%
+that it had to be zero yes we did so
+excellent question so the question is
+
+ align:start position:0%
+excellent question so the question is
+ 
+
+ align:start position:0%
+excellent question so the question is
+this when we constructed using the
+
+ align:start position:0%
+this when we constructed using the
+ 
+
+ align:start position:0%
+this when we constructed using the
+operator method for the harmonic
+
+ align:start position:0%
+operator method for the harmonic
+ 
+
+ align:start position:0%
+operator method for the harmonic
+oscillator when we constructed the
+
+ align:start position:0%
+oscillator when we constructed the
+ 
+
+ align:start position:0%
+oscillator when we constructed the
+ground state we said the ground state by
+
+ align:start position:0%
+ground state we said the ground state by
+ 
+
+ align:start position:0%
+ground state we said the ground state by
+zero is that state which is annihilated
+
+ align:start position:0%
+zero is that state which is annihilated
+ 
+
+ align:start position:0%
+zero is that state which is annihilated
+by the lowering operator AFI zero is
+
+ align:start position:0%
+by the lowering operator AFI zero is
+ 
+
+ align:start position:0%
+by the lowering operator AFI zero is
+equal to zero so where did that come
+
+ align:start position:0%
+equal to zero so where did that come
+ 
+
+ align:start position:0%
+equal to zero so where did that come
+from why were we fortunate enough for
+
+ align:start position:0%
+from why were we fortunate enough for
+ 
+
+ align:start position:0%
+from why were we fortunate enough for
+physical reasons for mathematical
+
+ align:start position:0%
+physical reasons for mathematical
+ 
+
+ align:start position:0%
+physical reasons for mathematical
+reasons what was it what was the reason
+
+ align:start position:0%
+reasons what was it what was the reason
+ 
+
+ align:start position:0%
+reasons what was it what was the reason
+so this was room this was very important
+
+ align:start position:0%
+so this was room this was very important
+ 
+
+ align:start position:0%
+so this was room this was very important
+so let's go through it slowly so
+
+ align:start position:0%
+so let's go through it slowly so
+ 
+
+ align:start position:0%
+so let's go through it slowly so
+remember the step that came immediately
+
+ align:start position:0%
+remember the step that came immediately
+ 
+
+ align:start position:0%
+remember the step that came immediately
+before this step immediately before this
+
+ align:start position:0%
+before this step immediately before this
+ 
+
+ align:start position:0%
+before this step immediately before this
+step we said look the expectation value
+
+ align:start position:0%
+step we said look the expectation value
+ 
+
+ align:start position:0%
+step we said look the expectation value
+of energy can always be written as a
+
+ align:start position:0%
+of energy can always be written as a
+ 
+
+ align:start position:0%
+of energy can always be written as a
+strictly positive thing it's equal to
+
+ align:start position:0%
+strictly positive thing it's equal to
+ 
+
+ align:start position:0%
+strictly positive thing it's equal to
+the integral and you should derive this
+
+ align:start position:0%
+the integral and you should derive this
+ 
+
+ align:start position:0%
+the integral and you should derive this
+for yourself I didn't derive it but this
+
+ align:start position:0%
+for yourself I didn't derive it but this
+ 
+
+ align:start position:0%
+for yourself I didn't derive it but this
+is a good thing to derive for yourself
+
+ align:start position:0%
+is a good thing to derive for yourself
+ 
+
+ align:start position:0%
+is a good thing to derive for yourself
+it takes only a couple of steps integral
+
+ align:start position:0%
+it takes only a couple of steps integral
+ 
+
+ align:start position:0%
+it takes only a couple of steps integral
+over all momentum of sigh tilde of P
+
+ align:start position:0%
+over all momentum of sigh tilde of P
+ 
+
+ align:start position:0%
+over all momentum of sigh tilde of P
+before ei transformed norm squared this
+
+ align:start position:0%
+before ei transformed norm squared this
+ 
+
+ align:start position:0%
+before ei transformed norm squared this
+is the probability that you have given
+
+ align:start position:0%
+is the probability that you have given
+ 
+
+ align:start position:0%
+is the probability that you have given
+the state sign this is the probability
+
+ align:start position:0%
+the state sign this is the probability
+ 
+
+ align:start position:0%
+the state sign this is the probability
+density that you have momentum P P
+
+ align:start position:0%
+density that you have momentum P P
+ 
+
+ align:start position:0%
+density that you have momentum P P
+squared upon 2m plus the integral of DX
+
+ align:start position:0%
+squared upon 2m plus the integral of DX
+ 
+
+ align:start position:0%
+squared upon 2m plus the integral of DX
+Phi of X norm squared M Omega squared
+
+ align:start position:0%
+Phi of X norm squared M Omega squared
+ 
+
+ align:start position:0%
+Phi of X norm squared M Omega squared
+upon 2 x squared right it's the
+
+ align:start position:0%
+upon 2 x squared right it's the
+ 
+
+ align:start position:0%
+upon 2 x squared right it's the
+probability that you're at position x
+
+ align:start position:0%
+probability that you're at position x
+ 
+
+ align:start position:0%
+probability that you're at position x
+given the wave function X movements the
+
+ align:start position:0%
+given the wave function X movements the
+ 
+
+ align:start position:0%
+given the wave function X movements the
+value of the potential now this is a
+
+ align:start position:0%
+value of the potential now this is a
+ 
+
+ align:start position:0%
+value of the potential now this is a
+strictly positive quantity as is this
+
+ align:start position:0%
+strictly positive quantity as is this
+ 
+
+ align:start position:0%
+strictly positive quantity as is this
+strictly positive as is this that is a
+
+ align:start position:0%
+strictly positive as is this that is a
+ 
+
+ align:start position:0%
+strictly positive as is this that is a
+plus this quantity must always be
+
+ align:start position:0%
+plus this quantity must always be
+ 
+
+ align:start position:0%
+plus this quantity must always be
+greater than or equal to zero correct
+
+ align:start position:0%
+greater than or equal to zero correct
+ 
+
+ align:start position:0%
+greater than or equal to zero correct
+however we derive from the operator
+
+ align:start position:0%
+however we derive from the operator
+ 
+
+ align:start position:0%
+however we derive from the operator
+relations that if we take a wave
+
+ align:start position:0%
+relations that if we take a wave
+ 
+
+ align:start position:0%
+relations that if we take a wave
+function Phi sub n sorry Phi sub E and
+
+ align:start position:0%
+function Phi sub n sorry Phi sub E and
+ 
+
+ align:start position:0%
+function Phi sub n sorry Phi sub E and
+we act on it with the lowering operator
+
+ align:start position:0%
+we act on it with the lowering operator
+ 
+
+ align:start position:0%
+we act on it with the lowering operator
+a this defines a new state which up to
+
+ align:start position:0%
+a this defines a new state which up to
+ 
+
+ align:start position:0%
+a this defines a new state which up to
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+Malaysian is is an eigenfunction of the
+
+ align:start position:0%
+Malaysian is is an eigenfunction of the
+ 
+
+ align:start position:0%
+Malaysian is is an eigenfunction of the
+energy operator with energy e minus
+
+ align:start position:0%
+energy operator with energy e minus
+ 
+
+ align:start position:0%
+energy operator with energy e minus
+h-bar Omega and we show this by showing
+
+ align:start position:0%
+h-bar Omega and we show this by showing
+ 
+
+ align:start position:0%
+h-bar Omega and we show this by showing
+that the energy eigenfunction acting on
+
+ align:start position:0%
+that the energy eigenfunction acting on
+ 
+
+ align:start position:0%
+that the energy eigenfunction acting on
+this gives exactly this coefficient
+
+ align:start position:0%
+this gives exactly this coefficient
+ 
+
+ align:start position:0%
+this gives exactly this coefficient
+times this back
+
+ align:start position:0%
+times this back
+ 
+
+ align:start position:0%
+times this back
+it's an eigenfunction we just showed
+
+ align:start position:0%
+it's an eigenfunction we just showed
+ 
+
+ align:start position:0%
+it's an eigenfunction we just showed
+explicit it's an eigenfunction so this
+
+ align:start position:0%
+explicit it's an eigenfunction so this
+ 
+
+ align:start position:0%
+explicit it's an eigenfunction so this
+suggests that if you have a state with
+
+ align:start position:0%
+suggests that if you have a state with
+ 
+
+ align:start position:0%
+suggests that if you have a state with
+energy e you can also build a state with
+
+ align:start position:0%
+energy e you can also build a state with
+ 
+
+ align:start position:0%
+energy e you can also build a state with
+energy e minus h-bar Omega and thus we
+
+ align:start position:0%
+energy e minus h-bar Omega and thus we
+ 
+
+ align:start position:0%
+energy e minus h-bar Omega and thus we
+can repeat a minus 2 H bar Omega and
+
+ align:start position:0%
+can repeat a minus 2 H bar Omega and
+ 
+
+ align:start position:0%
+can repeat a minus 2 H bar Omega and
+it's Turtles all the way down the
+
+ align:start position:0%
+it's Turtles all the way down the
+ 
+
+ align:start position:0%
+it's Turtles all the way down the
+problem is for any finite value of e
+
+ align:start position:0%
+problem is for any finite value of e
+ 
+
+ align:start position:0%
+problem is for any finite value of e
+eventually this tower will get negative
+
+ align:start position:0%
+eventually this tower will get negative
+ 
+
+ align:start position:0%
+eventually this tower will get negative
+here zero but the energy expectation
+
+ align:start position:0%
+here zero but the energy expectation
+ 
+
+ align:start position:0%
+here zero but the energy expectation
+value cannot be less than zero it's got
+
+ align:start position:0%
+value cannot be less than zero it's got
+ 
+
+ align:start position:0%
+value cannot be less than zero it's got
+to be strictly greater than zero but if
+
+ align:start position:0%
+to be strictly greater than zero but if
+ 
+
+ align:start position:0%
+to be strictly greater than zero but if
+we were in this energy eigenstate and we
+
+ align:start position:0%
+we were in this energy eigenstate and we
+ 
+
+ align:start position:0%
+we were in this energy eigenstate and we
+measured the expectation value of energy
+
+ align:start position:0%
+measured the expectation value of energy
+ 
+
+ align:start position:0%
+measured the expectation value of energy
+this is the value we would get which
+
+ align:start position:0%
+this is the value we would get which
+ 
+
+ align:start position:0%
+this is the value we would get which
+would be negative
+
+ align:start position:0%
+would be negative
+ 
+
+ align:start position:0%
+would be negative
+oops that's a 2 so something is amiss
+
+ align:start position:0%
+oops that's a 2 so something is amiss
+ 
+
+ align:start position:0%
+oops that's a 2 so something is amiss
+how can this possibly make sense and the
+
+ align:start position:0%
+how can this possibly make sense and the
+ 
+
+ align:start position:0%
+how can this possibly make sense and the
+answer we came up with was well look
+
+ align:start position:0%
+answer we came up with was well look
+ 
+
+ align:start position:0%
+answer we came up with was well look
+it's inescapable that acting was a on
+
+ align:start position:0%
+it's inescapable that acting was a on
+ 
+
+ align:start position:0%
+it's inescapable that acting was a on
+Phi gives us something that's an
+
+ align:start position:0%
+Phi gives us something that's an
+ 
+
+ align:start position:0%
+Phi gives us something that's an
+eigenfunction of the energy
+
+ align:start position:0%
+eigenfunction of the energy
+ 
+
+ align:start position:0%
+eigenfunction of the energy
+it's possible that this I can that this
+
+ align:start position:0%
+it's possible that this I can that this
+ 
+
+ align:start position:0%
+it's possible that this I can that this
+function happens to be the zero function
+
+ align:start position:0%
+function happens to be the zero function
+ 
+
+ align:start position:0%
+function happens to be the zero function
+non zero energy just zero not a function
+
+ align:start position:0%
+non zero energy just zero not a function
+ 
+
+ align:start position:0%
+non zero energy just zero not a function
+is zero normalizable no the integral of
+
+ align:start position:0%
+is zero normalizable no the integral of
+ 
+
+ align:start position:0%
+is zero normalizable no the integral of
+zero squared is zero no coefficient
+
+ align:start position:0%
+zero squared is zero no coefficient
+ 
+
+ align:start position:0%
+zero squared is zero no coefficient
+times that is a finite number is one so
+
+ align:start position:0%
+times that is a finite number is one so
+ 
+
+ align:start position:0%
+times that is a finite number is one so
+the only way so what must happen is it
+
+ align:start position:0%
+the only way so what must happen is it
+ 
+
+ align:start position:0%
+the only way so what must happen is it
+must be true that at some point we can't
+
+ align:start position:0%
+must be true that at some point we can't
+ 
+
+ align:start position:0%
+must be true that at some point we can't
+lower anymore but we can always act with
+
+ align:start position:0%
+lower anymore but we can always act with
+ 
+
+ align:start position:0%
+lower anymore but we can always act with
+a so we can always try to lower the only
+
+ align:start position:0%
+a so we can always try to lower the only
+ 
+
+ align:start position:0%
+a so we can always try to lower the only
+out is if when we lower one particular
+
+ align:start position:0%
+out is if when we lower one particular
+ 
+
+ align:start position:0%
+out is if when we lower one particular
+guy which I will call Phi zero the only
+
+ align:start position:0%
+guy which I will call Phi zero the only
+ 
+
+ align:start position:0%
+guy which I will call Phi zero the only
+out is if we try to lower Phi zero we
+
+ align:start position:0%
+out is if we try to lower Phi zero we
+ 
+
+ align:start position:0%
+out is if we try to lower Phi zero we
+don't get another state which we assumed
+
+ align:start position:0%
+don't get another state which we assumed
+ 
+
+ align:start position:0%
+don't get another state which we assumed
+we did here we don't get another state
+
+ align:start position:0%
+we did here we don't get another state
+ 
+
+ align:start position:0%
+we did here we don't get another state
+instead we just get zero we get no state
+
+ align:start position:0%
+instead we just get zero we get no state
+ 
+
+ align:start position:0%
+instead we just get zero we get no state
+not energy zero zero the function is 0
+
+ align:start position:0%
+not energy zero zero the function is 0
+ 
+
+ align:start position:0%
+not energy zero zero the function is 0
+identically vanishing this does not
+
+ align:start position:0%
+identically vanishing this does not
+ 
+
+ align:start position:0%
+identically vanishing this does not
+describe the configuration of a particle
+
+ align:start position:0%
+describe the configuration of a particle
+ 
+
+ align:start position:0%
+describe the configuration of a particle
+probability of it being anywhere is zero
+
+ align:start position:0%
+probability of it being anywhere is zero
+ 
+
+ align:start position:0%
+probability of it being anywhere is zero
+that's bad
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so in order for the tower to end in
+
+ align:start position:0%
+so in order for the tower to end in
+ 
+
+ align:start position:0%
+so in order for the tower to end in
+order for the energy to be bounded from
+
+ align:start position:0%
+order for the energy to be bounded from
+ 
+
+ align:start position:0%
+order for the energy to be bounded from
+below as the potential is we need that
+
+ align:start position:0%
+below as the potential is we need that
+ 
+
+ align:start position:0%
+below as the potential is we need that
+there's a lowest state in the tower that
+
+ align:start position:0%
+there's a lowest state in the tower that
+ 
+
+ align:start position:0%
+there's a lowest state in the tower that
+answer your question
+
+ align:start position:0%
+answer your question
+ 
+
+ align:start position:0%
+answer your question
+great yeah very good question you're
+
+ align:start position:0%
+great yeah very good question you're
+ 
+
+ align:start position:0%
+great yeah very good question you're
+gonna show this on the problem set if
+
+ align:start position:0%
+gonna show this on the problem set if
+ 
+
+ align:start position:0%
+gonna show this on the problem set if
+you haven't already I thought you did
+
+ align:start position:0%
+you haven't already I thought you did
+ 
+
+ align:start position:0%
+you haven't already I thought you did
+but maybe not um the energy
+
+ align:start position:0%
+but maybe not um the energy
+ 
+
+ align:start position:0%
+but maybe not um the energy
+eigenfunctions for the energy
+
+ align:start position:0%
+eigenfunctions for the energy
+ 
+
+ align:start position:0%
+eigenfunctions for the energy
+eigenfunctions cannot wait for for
+
+ align:start position:0%
+eigenfunctions cannot wait for for
+ 
+
+ align:start position:0%
+eigenfunctions cannot wait for for
+potentials with only bound states can
+
+ align:start position:0%
+potentials with only bound states can
+ 
+
+ align:start position:0%
+potentials with only bound states can
+always be expressed as purely real or a
+
+ align:start position:0%
+always be expressed as purely real or a
+ 
+
+ align:start position:0%
+always be expressed as purely real or a
+purely imaginary you can always
+
+ align:start position:0%
+purely imaginary you can always
+ 
+
+ align:start position:0%
+purely imaginary you can always
+decompose them in terms of purely real
+
+ align:start position:0%
+decompose them in terms of purely real
+ 
+
+ align:start position:0%
+decompose them in terms of purely real
+and purely imaginary proving that will
+
+ align:start position:0%
+and purely imaginary proving that will
+ 
+
+ align:start position:0%
+and purely imaginary proving that will
+be a problem on one of your problem sets
+
+ align:start position:0%
+be a problem on one of your problem sets
+ 
+
+ align:start position:0%
+be a problem on one of your problem sets
+but for the moment let me just say that
+
+ align:start position:0%
+but for the moment let me just say that
+ 
+
+ align:start position:0%
+but for the moment let me just say that
+yes you can always show that the the
+
+ align:start position:0%
+yes you can always show that the the
+ 
+
+ align:start position:0%
+yes you can always show that the the
+energy eigenfunctions and for 1d
+
+ align:start position:0%
+energy eigenfunctions and for 1d
+ 
+
+ align:start position:0%
+energy eigenfunctions and for 1d
+potential can always be expressed as
+
+ align:start position:0%
+potential can always be expressed as
+ 
+
+ align:start position:0%
+potential can always be expressed as
+purely real loop I need that bound state
+
+ align:start position:0%
+purely real loop I need that bound state
+ 
+
+ align:start position:0%
+purely real loop I need that bound state
+condition as we'll see later in the
+
+ align:start position:0%
+condition as we'll see later in the
+ 
+
+ align:start position:0%
+condition as we'll see later in the
+course yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hu make it sorry no no no this sorry no
+
+ align:start position:0%
+hu make it sorry no no no this sorry no
+ 
+
+ align:start position:0%
+hu make it sorry no no no this sorry no
+good good good so what this says is
+
+ align:start position:0%
+good good good so what this says is
+ 
+
+ align:start position:0%
+good good good so what this says is
+given some state with energy e when we
+
+ align:start position:0%
+given some state with energy e when we
+ 
+
+ align:start position:0%
+given some state with energy e when we
+lower we get h-bar Omega less that
+
+ align:start position:0%
+lower we get h-bar Omega less that
+ 
+
+ align:start position:0%
+lower we get h-bar Omega less that
+doesn't tell you what he is good other
+
+ align:start position:0%
+doesn't tell you what he is good other
+ 
+
+ align:start position:0%
+doesn't tell you what he is good other
+questions yeah expand on that slowly if
+
+ align:start position:0%
+questions yeah expand on that slowly if
+ 
+
+ align:start position:0%
+questions yeah expand on that slowly if
+you get this zero function that doesn't
+
+ align:start position:0%
+you get this zero function that doesn't
+ 
+
+ align:start position:0%
+you get this zero function that doesn't
+actually correspond to any energy
+
+ align:start position:0%
+actually correspond to any energy
+ 
+
+ align:start position:0%
+actually correspond to any energy
+eigenvalue current little on zero
+
+ align:start position:0%
+eigenvalue current little on zero
+ 
+
+ align:start position:0%
+eigenvalue current little on zero
+Cranky's say any correct zero the
+
+ align:start position:0%
+Cranky's say any correct zero the
+ 
+
+ align:start position:0%
+Cranky's say any correct zero the
+function zero is an eigenfunction of
+
+ align:start position:0%
+function zero is an eigenfunction of
+ 
+
+ align:start position:0%
+function zero is an eigenfunction of
+every operator but it's a stupid
+
+ align:start position:0%
+every operator but it's a stupid
+ 
+
+ align:start position:0%
+every operator but it's a stupid
+eigenfunction of every operator in
+
+ align:start position:0%
+eigenfunction of every operator in
+ 
+
+ align:start position:0%
+eigenfunction of every operator in
+particular it has nothing to do with the
+
+ align:start position:0%
+particular it has nothing to do with the
+ 
+
+ align:start position:0%
+particular it has nothing to do with the
+states we're interested in we are
+
+ align:start position:0%
+states we're interested in we are
+ 
+
+ align:start position:0%
+states we're interested in we are
+interested in normalizable states right
+
+ align:start position:0%
+interested in normalizable states right
+ 
+
+ align:start position:0%
+interested in normalizable states right
+and that is an auto normalizable state
+
+ align:start position:0%
+and that is an auto normalizable state
+ 
+
+ align:start position:0%
+and that is an auto normalizable state
+you can't multiply by any finite
+
+ align:start position:0%
+you can't multiply by any finite
+ 
+
+ align:start position:0%
+you can't multiply by any finite
+coefficient and get one when you square
+
+ align:start position:0%
+coefficient and get one when you square
+ 
+
+ align:start position:0%
+coefficient and get one when you square
+integrate it okay yep one last question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well you we need to add more words that
+
+ align:start position:0%
+well you we need to add more words that
+ 
+
+ align:start position:0%
+well you we need to add more words that
+so the question is does that mean that
+
+ align:start position:0%
+so the question is does that mean that
+ 
+
+ align:start position:0%
+so the question is does that mean that
+the that the only particle that could
+
+ align:start position:0%
+the that the only particle that could
+ 
+
+ align:start position:0%
+the that the only particle that could
+really have zero energy is some
+
+ align:start position:0%
+really have zero energy is some
+ 
+
+ align:start position:0%
+really have zero energy is some
+imaginary particle that doesn't exist
+
+ align:start position:0%
+imaginary particle that doesn't exist
+ 
+
+ align:start position:0%
+imaginary particle that doesn't exist
+first off imaginary particles may exist
+
+ align:start position:0%
+first off imaginary particles may exist
+ 
+
+ align:start position:0%
+first off imaginary particles may exist
+and we just haven't seen them I mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right okay so so I need to say two
+
+ align:start position:0%
+right okay so so I need to say two
+ 
+
+ align:start position:0%
+right okay so so I need to say two
+things about this so there's a technical
+
+ align:start position:0%
+things about this so there's a technical
+ 
+
+ align:start position:0%
+things about this so there's a technical
+complaint I need to make about your
+
+ align:start position:0%
+complaint I need to make about your
+ 
+
+ align:start position:0%
+complaint I need to make about your
+question which is a very fair question
+
+ align:start position:0%
+question which is a very fair question
+ 
+
+ align:start position:0%
+question which is a very fair question
+but I need to make it all the same and
+
+ align:start position:0%
+but I need to make it all the same and
+ 
+
+ align:start position:0%
+but I need to make it all the same and
+the second is a more physical answer so
+
+ align:start position:0%
+the second is a more physical answer so
+ 
+
+ align:start position:0%
+the second is a more physical answer so
+the technical complaint is what do you
+
+ align:start position:0%
+the technical complaint is what do you
+ 
+
+ align:start position:0%
+the technical complaint is what do you
+mean by zero energy
+
+ align:start position:0%
+mean by zero energy
+ 
+
+ align:start position:0%
+mean by zero energy
+do you ever measure an energy directly
+
+ align:start position:0%
+do you ever measure an energy directly
+ 
+
+ align:start position:0%
+do you ever measure an energy directly
+and you measure energy differences right
+
+ align:start position:0%
+and you measure energy differences right
+ 
+
+ align:start position:0%
+and you measure energy differences right
+so relative to what we have to decide
+
+ align:start position:0%
+so relative to what we have to decide
+ 
+
+ align:start position:0%
+so relative to what we have to decide
+relative to what so for example in the
+
+ align:start position:0%
+relative to what so for example in the
+ 
+
+ align:start position:0%
+relative to what so for example in the
+harmonic oscillator what we mean when we
+
+ align:start position:0%
+harmonic oscillator what we mean when we
+ 
+
+ align:start position:0%
+harmonic oscillator what we mean when we
+say that grad student energy is nonzero
+
+ align:start position:0%
+say that grad student energy is nonzero
+ 
+
+ align:start position:0%
+say that grad student energy is nonzero
+is if we draw the potential and we call
+
+ align:start position:0%
+is if we draw the potential and we call
+ 
+
+ align:start position:0%
+is if we draw the potential and we call
+the minimum of the potential is zero
+
+ align:start position:0%
+the minimum of the potential is zero
+ 
+
+ align:start position:0%
+the minimum of the potential is zero
+classically a zero then what we discover
+
+ align:start position:0%
+classically a zero then what we discover
+ 
+
+ align:start position:0%
+classically a zero then what we discover
+is that the energy of the quantum
+
+ align:start position:0%
+is that the energy of the quantum
+ 
+
+ align:start position:0%
+is that the energy of the quantum
+mechanical ground state is one-half H
+
+ align:start position:0%
+mechanical ground state is one-half H
+ 
+
+ align:start position:0%
+mechanical ground state is one-half H
+bar Omega right above zero so is there
+
+ align:start position:0%
+bar Omega right above zero so is there
+ 
+
+ align:start position:0%
+bar Omega right above zero so is there
+any state of the harmonic oscillator
+
+ align:start position:0%
+any state of the harmonic oscillator
+ 
+
+ align:start position:0%
+any state of the harmonic oscillator
+with energy zero no okay now if we have
+
+ align:start position:0%
+with energy zero no okay now if we have
+ 
+
+ align:start position:0%
+with energy zero no okay now if we have
+a free particle is there is there a
+
+ align:start position:0%
+a free particle is there is there a
+ 
+
+ align:start position:0%
+a free particle is there is there a
+configuration with energy zero wow
+
+ align:start position:0%
+configuration with energy zero wow
+ 
+
+ align:start position:0%
+configuration with energy zero wow
+that's an interesting question so what
+
+ align:start position:0%
+that's an interesting question so what
+ 
+
+ align:start position:0%
+that's an interesting question so what
+are the ground what are the eigenstates
+
+ align:start position:0%
+are the ground what are the eigenstates
+ 
+
+ align:start position:0%
+are the ground what are the eigenstates
+e to the ikx okay when the energy is
+
+ align:start position:0%
+e to the ikx okay when the energy is
+ 
+
+ align:start position:0%
+e to the ikx okay when the energy is
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+so and the energy is because it's just P
+
+ align:start position:0%
+so and the energy is because it's just P
+ 
+
+ align:start position:0%
+so and the energy is because it's just P
+squared upon 2m which is H bar squared K
+
+ align:start position:0%
+squared upon 2m which is H bar squared K
+ 
+
+ align:start position:0%
+squared upon 2m which is H bar squared K
+squared upon 2m the energy is H bar
+
+ align:start position:0%
+squared upon 2m the energy is H bar
+ 
+
+ align:start position:0%
+squared upon 2m the energy is H bar
+squared K squared upon 2m for a free
+
+ align:start position:0%
+squared K squared upon 2m for a free
+ 
+
+ align:start position:0%
+squared K squared upon 2m for a free
+particle no potential and by zeroing the
+
+ align:start position:0%
+particle no potential and by zeroing the
+ 
+
+ align:start position:0%
+particle no potential and by zeroing the
+asymptotic energy u equals zero can you
+
+ align:start position:0%
+asymptotic energy u equals zero can you
+ 
+
+ align:start position:0%
+asymptotic energy u equals zero can you
+have a state with energy zero this one's
+
+ align:start position:0%
+have a state with energy zero this one's
+ 
+
+ align:start position:0%
+have a state with energy zero this one's
+a little subtle because if we take the
+
+ align:start position:0%
+a little subtle because if we take the
+ 
+
+ align:start position:0%
+a little subtle because if we take the
+energy zero what must K be zero okay
+
+ align:start position:0%
+energy zero what must K be zero okay
+ 
+
+ align:start position:0%
+energy zero what must K be zero okay
+great so what's the wave function
+
+ align:start position:0%
+great so what's the wave function
+ 
+
+ align:start position:0%
+great so what's the wave function
+constant is that normalizable not so
+
+ align:start position:0%
+constant is that normalizable not so
+ 
+
+ align:start position:0%
+constant is that normalizable not so
+much so can you build a wave packet with
+
+ align:start position:0%
+much so can you build a wave packet with
+ 
+
+ align:start position:0%
+much so can you build a wave packet with
+energy zero carica sorry let me not say
+
+ align:start position:0%
+energy zero carica sorry let me not say
+ 
+
+ align:start position:0%
+energy zero carica sorry let me not say
+that can you put a single particle in a
+
+ align:start position:0%
+that can you put a single particle in a
+ 
+
+ align:start position:0%
+that can you put a single particle in a
+state with energy zero no that would not
+
+ align:start position:0%
+state with energy zero no that would not
+ 
+
+ align:start position:0%
+state with energy zero no that would not
+seem to be possible because that would
+
+ align:start position:0%
+seem to be possible because that would
+ 
+
+ align:start position:0%
+seem to be possible because that would
+be non-normalizable state well you say
+
+ align:start position:0%
+be non-normalizable state well you say
+ 
+
+ align:start position:0%
+be non-normalizable state well you say
+we deal with these Exponential's all the
+
+ align:start position:0%
+we deal with these Exponential's all the
+ 
+
+ align:start position:0%
+we deal with these Exponential's all the
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+we know how to deal with that we don't
+
+ align:start position:0%
+we know how to deal with that we don't
+ 
+
+ align:start position:0%
+we know how to deal with that we don't
+use a single wave plane wave we use a
+
+ align:start position:0%
+use a single wave plane wave we use a
+ 
+
+ align:start position:0%
+use a single wave plane wave we use a
+wave packet with some width right so I
+
+ align:start position:0%
+wave packet with some width right so I
+ 
+
+ align:start position:0%
+wave packet with some width right so I
+can build a wave packet with you know
+
+ align:start position:0%
+can build a wave packet with you know
+ 
+
+ align:start position:0%
+can build a wave packet with you know
+some average width but will that average
+
+ align:start position:0%
+some average width but will that average
+ 
+
+ align:start position:0%
+some average width but will that average
+width ever have expectation value of K
+
+ align:start position:0%
+width ever have expectation value of K
+ 
+
+ align:start position:0%
+width ever have expectation value of K
+equals zero
+
+ align:start position:0%
+equals zero
+ 
+
+ align:start position:0%
+equals zero
+no because we'll always have
+
+ align:start position:0%
+no because we'll always have
+ 
+
+ align:start position:0%
+no because we'll always have
+contributions from K naught equals zero
+
+ align:start position:0%
+contributions from K naught equals zero
+ 
+
+ align:start position:0%
+contributions from K naught equals zero
+so that it's localized so that it
+
+ align:start position:0%
+so that it's localized so that it
+ 
+
+ align:start position:0%
+so that it's localized so that it
+spatially localized so can you build a
+
+ align:start position:0%
+spatially localized so can you build a
+ 
+
+ align:start position:0%
+spatially localized so can you build a
+normalizable state with energies here
+
+ align:start position:0%
+normalizable state with energies here
+ 
+
+ align:start position:0%
+normalizable state with energies here
+which is an eigenfunction of the energy
+
+ align:start position:0%
+which is an eigenfunction of the energy
+ 
+
+ align:start position:0%
+which is an eigenfunction of the energy
+theorem no not in this case either so
+
+ align:start position:0%
+theorem no not in this case either so
+ 
+
+ align:start position:0%
+theorem no not in this case either so
+there's the technical complaint that you
+
+ align:start position:0%
+there's the technical complaint that you
+ 
+
+ align:start position:0%
+there's the technical complaint that you
+need to talk about what you mean
+
+ align:start position:0%
+need to talk about what you mean
+ 
+
+ align:start position:0%
+need to talk about what you mean
+relative to what that was about your
+
+ align:start position:0%
+relative to what that was about your
+ 
+
+ align:start position:0%
+relative to what that was about your
+question and the second of can you ever
+
+ align:start position:0%
+question and the second of can you ever
+ 
+
+ align:start position:0%
+question and the second of can you ever
+have an energy eigenstate which is that
+
+ align:start position:0%
+have an energy eigenstate which is that
+ 
+
+ align:start position:0%
+have an energy eigenstate which is that
+the minimum of the potential and that's
+
+ align:start position:0%
+the minimum of the potential and that's
+ 
+
+ align:start position:0%
+the minimum of the potential and that's
+also zero that's also no you'll actually
+
+ align:start position:0%
+also zero that's also no you'll actually
+ 
+
+ align:start position:0%
+also zero that's also no you'll actually
+prove that on a later problem set okay
+
+ align:start position:0%
+prove that on a later problem set okay
+ 
+
+ align:start position:0%
+prove that on a later problem set okay
+so um with all that said we now have a
+
+ align:start position:0%
+so um with all that said we now have a
+ 
+
+ align:start position:0%
+so um with all that said we now have a
+mirror that's awesome 15 minutes for a
+
+ align:start position:0%
+mirror that's awesome 15 minutes for a
+ 
+
+ align:start position:0%
+mirror that's awesome 15 minutes for a
+14 page lecture so can I do this fast no
+
+ align:start position:0%
+14 page lecture so can I do this fast no
+ 
+
+ align:start position:0%
+14 page lecture so can I do this fast no
+I'm kidding um I won't do that to you so
+
+ align:start position:0%
+I'm kidding um I won't do that to you so
+ 
+
+ align:start position:0%
+I'm kidding um I won't do that to you so
+I want to just instead of going through
+
+ align:start position:0%
+I want to just instead of going through
+ 
+
+ align:start position:0%
+I want to just instead of going through
+so this was not directly relevant for
+
+ align:start position:0%
+so this was not directly relevant for
+ 
+
+ align:start position:0%
+so this was not directly relevant for
+the exam and it's also um yeah this can
+
+ align:start position:0%
+the exam and it's also um yeah this can
+ 
+
+ align:start position:0%
+the exam and it's also um yeah this can
+come a little bit later so let me let me
+
+ align:start position:0%
+come a little bit later so let me let me
+ 
+
+ align:start position:0%
+come a little bit later so let me let me
+just do a couple let me show you a
+
+ align:start position:0%
+just do a couple let me show you a
+ 
+
+ align:start position:0%
+just do a couple let me show you a
+couple of quick things so the notes are
+
+ align:start position:0%
+couple of quick things so the notes are
+ 
+
+ align:start position:0%
+couple of quick things so the notes are
+posted online look at them I'll go over
+
+ align:start position:0%
+posted online look at them I'll go over
+ 
+
+ align:start position:0%
+posted online look at them I'll go over
+them again in the future what do I want
+
+ align:start position:0%
+them again in the future what do I want
+ 
+
+ align:start position:0%
+them again in the future what do I want
+to do so I want to introduce to you two
+
+ align:start position:0%
+to do so I want to introduce to you two
+ 
+
+ align:start position:0%
+to do so I want to introduce to you two
+ideas one is direct notation and this is
+
+ align:start position:0%
+ideas one is direct notation and this is
+ 
+
+ align:start position:0%
+ideas one is direct notation and this is
+harkening back to basics of vector
+
+ align:start position:0%
+harkening back to basics of vector
+ 
+
+ align:start position:0%
+harkening back to basics of vector
+spaces and the second is i want to tell
+
+ align:start position:0%
+spaces and the second is i want to tell
+ 
+
+ align:start position:0%
+spaces and the second is i want to tell
+you something about what the commutator
+
+ align:start position:0%
+you something about what the commutator
+ 
+
+ align:start position:0%
+you something about what the commutator
+means so first off let me ask you guys a
+
+ align:start position:0%
+means so first off let me ask you guys a
+ 
+
+ align:start position:0%
+means so first off let me ask you guys a
+question now I can use I have one more
+
+ align:start position:0%
+question now I can use I have one more
+ 
+
+ align:start position:0%
+question now I can use I have one more
+clicker question for you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right y'all ready everyone up with
+
+ align:start position:0%
+all right y'all ready everyone up with
+ 
+
+ align:start position:0%
+all right y'all ready everyone up with
+ya okay everyone everyone up with the
+
+ align:start position:0%
+ya okay everyone everyone up with the
+ 
+
+ align:start position:0%
+ya okay everyone everyone up with the
+clickers okay here is a question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+when you go ahead and start clicking now
+
+ align:start position:0%
+when you go ahead and start clicking now
+ 
+
+ align:start position:0%
+when you go ahead and start clicking now
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sigma is the uncertainty sorry Sigma is
+
+ align:start position:0%
+Sigma is the uncertainty sorry Sigma is
+ 
+
+ align:start position:0%
+Sigma is the uncertainty sorry Sigma is
+young certainty this is awesome I swear
+
+ align:start position:0%
+young certainty this is awesome I swear
+ 
+
+ align:start position:0%
+young certainty this is awesome I swear
+the clicks are going in beat with the
+
+ align:start position:0%
+the clicks are going in beat with the
+ 
+
+ align:start position:0%
+the clicks are going in beat with the
+music okay so at the moment so let me
+
+ align:start position:0%
+music okay so at the moment so let me
+ 
+
+ align:start position:0%
+music okay so at the moment so let me
+give you three more seconds one two
+
+ align:start position:0%
+give you three more seconds one two
+ 
+
+ align:start position:0%
+give you three more seconds one two
+three okay this is awesome you guys are
+
+ align:start position:0%
+three okay this is awesome you guys are
+ 
+
+ align:start position:0%
+three okay this is awesome you guys are
+totally at chance you have even
+
+ align:start position:0%
+totally at chance you have even
+ 
+
+ align:start position:0%
+totally at chance you have even
+probability distribution across the
+
+ align:start position:0%
+probability distribution across the
+ 
+
+ align:start position:0%
+probability distribution across the
+three so this is good because we haven't
+
+ align:start position:0%
+three so this is good because we haven't
+ 
+
+ align:start position:0%
+three so this is good because we haven't
+actually introduced this idea yet in a
+
+ align:start position:0%
+actually introduced this idea yet in a
+ 
+
+ align:start position:0%
+actually introduced this idea yet in a
+you know four so let me quickly talk you
+
+ align:start position:0%
+you know four so let me quickly talk you
+ 
+
+ align:start position:0%
+you know four so let me quickly talk you
+through this okay so yeah we've it off
+
+ align:start position:0%
+through this okay so yeah we've it off
+ 
+
+ align:start position:0%
+through this okay so yeah we've it off
+so so let me quickly quickly talk you
+
+ align:start position:0%
+so so let me quickly quickly talk you
+ 
+
+ align:start position:0%
+so so let me quickly quickly talk you
+through this and this is important this
+
+ align:start position:0%
+through this and this is important this
+ 
+
+ align:start position:0%
+through this and this is important this
+is going to give you some intuition for
+
+ align:start position:0%
+is going to give you some intuition for
+ 
+
+ align:start position:0%
+is going to give you some intuition for
+what on what uncertainty means and it's
+
+ align:start position:0%
+what on what uncertainty means and it's
+ 
+
+ align:start position:0%
+what on what uncertainty means and it's
+also going to give you some intuition
+
+ align:start position:0%
+also going to give you some intuition
+ 
+
+ align:start position:0%
+also going to give you some intuition
+for what the commutator means okay so
+
+ align:start position:0%
+for what the commutator means okay so
+ 
+
+ align:start position:0%
+for what the commutator means okay so
+this is a little more experience a
+
+ align:start position:0%
+this is a little more experience a
+ 
+
+ align:start position:0%
+this is a little more experience a
+little more practice with operators and
+
+ align:start position:0%
+little more practice with operators and
+ 
+
+ align:start position:0%
+little more practice with operators and
+we'll pick up on the direct notation and
+
+ align:start position:0%
+we'll pick up on the direct notation and
+ 
+
+ align:start position:0%
+we'll pick up on the direct notation and
+everything I think next time because I
+
+ align:start position:0%
+everything I think next time because I
+ 
+
+ align:start position:0%
+everything I think next time because I
+just want to get through this physics so
+
+ align:start position:0%
+just want to get through this physics so
+ 
+
+ align:start position:0%
+just want to get through this physics so
+consider two operators a and B so a and
+
+ align:start position:0%
+consider two operators a and B so a and
+ 
+
+ align:start position:0%
+consider two operators a and B so a and
+B are my two operators they have hats he
+
+ align:start position:0%
+B are my two operators they have hats he
+ 
+
+ align:start position:0%
+B are my two operators they have hats he
+has a top hat so we have you've got to
+
+ align:start position:0%
+has a top hat so we have you've got to
+ 
+
+ align:start position:0%
+has a top hat so we have you've got to
+make this stuff a little more
+
+ align:start position:0%
+make this stuff a little more
+ 
+
+ align:start position:0%
+make this stuff a little more
+lighthearted so we have two operators a
+
+ align:start position:0%
+lighthearted so we have two operators a
+ 
+
+ align:start position:0%
+lighthearted so we have two operators a
+and B and I want to ask is it possible
+
+ align:start position:0%
+and B and I want to ask is it possible
+ 
+
+ align:start position:0%
+and B and I want to ask is it possible
+for there to be a function by little a
+
+ align:start position:0%
+for there to be a function by little a
+ 
+
+ align:start position:0%
+for there to be a function by little a
+little B which is simultaneously an
+
+ align:start position:0%
+little B which is simultaneously an
+ 
+
+ align:start position:0%
+little B which is simultaneously an
+eigenfunction of a and an eigenfunction
+
+ align:start position:0%
+eigenfunction of a and an eigenfunction
+ 
+
+ align:start position:0%
+eigenfunction of a and an eigenfunction
+of B so now we're just this is a pure
+
+ align:start position:0%
+of B so now we're just this is a pure
+ 
+
+ align:start position:0%
+of B so now we're just this is a pure
+math question given two operators a and
+
+ align:start position:0%
+math question given two operators a and
+ 
+
+ align:start position:0%
+math question given two operators a and
+B can you build a function which is
+
+ align:start position:0%
+B can you build a function which is
+ 
+
+ align:start position:0%
+B can you build a function which is
+simultaneously an eigenfunction of a and
+
+ align:start position:0%
+simultaneously an eigenfunction of a and
+ 
+
+ align:start position:0%
+simultaneously an eigenfunction of a and
+an eigenfunction of b I will call this
+
+ align:start position:0%
+an eigenfunction of b I will call this
+ 
+
+ align:start position:0%
+an eigenfunction of b I will call this
+Phi baby yo why not okay so Phi sub a B
+
+ align:start position:0%
+Phi baby yo why not okay so Phi sub a B
+ 
+
+ align:start position:0%
+Phi baby yo why not okay so Phi sub a B
+has this property a on Phi a B is equal
+
+ align:start position:0%
+has this property a on Phi a B is equal
+ 
+
+ align:start position:0%
+has this property a on Phi a B is equal
+to a Phi B why not and B on Phi a B is a
+
+ align:start position:0%
+to a Phi B why not and B on Phi a B is a
+ 
+
+ align:start position:0%
+to a Phi B why not and B on Phi a B is a
+little beyond Phi B you can't stop me I
+
+ align:start position:0%
+little beyond Phi B you can't stop me I
+ 
+
+ align:start position:0%
+little beyond Phi B you can't stop me I
+have now created this OP this object
+
+ align:start position:0%
+have now created this OP this object
+ 
+
+ align:start position:0%
+have now created this OP this object
+what from the existence of this state
+
+ align:start position:0%
+what from the existence of this state
+ 
+
+ align:start position:0%
+what from the existence of this state
+what can you deduce about the operators
+
+ align:start position:0%
+what can you deduce about the operators
+ 
+
+ align:start position:0%
+what can you deduce about the operators
+a and B and if you've already seen this
+
+ align:start position:0%
+a and B and if you've already seen this
+ 
+
+ align:start position:0%
+a and B and if you've already seen this
+before that's cheating so don't raise
+
+ align:start position:0%
+before that's cheating so don't raise
+ 
+
+ align:start position:0%
+before that's cheating so don't raise
+your hand but if you haven't seen this
+
+ align:start position:0%
+your hand but if you haven't seen this
+ 
+
+ align:start position:0%
+your hand but if you haven't seen this
+before just think through what what what
+
+ align:start position:0%
+before just think through what what what
+ 
+
+ align:start position:0%
+before just think through what what what
+does this tell you about the operators a
+
+ align:start position:0%
+does this tell you about the operators a
+ 
+
+ align:start position:0%
+does this tell you about the operators a
+and B
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+great
+
+ align:start position:0%
+great
+ 
+
+ align:start position:0%
+great
+that's a nice guess I like that guess so
+
+ align:start position:0%
+that's a nice guess I like that guess so
+ 
+
+ align:start position:0%
+that's a nice guess I like that guess so
+so let's check okay so what would it
+
+ align:start position:0%
+so let's check okay so what would it
+ 
+
+ align:start position:0%
+so let's check okay so what would it
+mean for the commutator of a and B to be
+
+ align:start position:0%
+mean for the commutator of a and B to be
+ 
+
+ align:start position:0%
+mean for the commutator of a and B to be
+0 so if so a B is some so this is equal
+
+ align:start position:0%
+0 so if so a B is some so this is equal
+ 
+
+ align:start position:0%
+0 so if so a B is some so this is equal
+to a B minus B a and what the commutator
+
+ align:start position:0%
+to a B minus B a and what the commutator
+ 
+
+ align:start position:0%
+to a B minus B a and what the commutator
+does is it takes two operators and it
+
+ align:start position:0%
+does is it takes two operators and it
+ 
+
+ align:start position:0%
+does is it takes two operators and it
+gives you a new operator called bracket
+
+ align:start position:0%
+gives you a new operator called bracket
+ 
+
+ align:start position:0%
+gives you a new operator called bracket
+a B sometimes it's useful to call it C
+
+ align:start position:0%
+a B sometimes it's useful to call it C
+ 
+
+ align:start position:0%
+a B sometimes it's useful to call it C
+for commutator so it gives you a new
+
+ align:start position:0%
+for commutator so it gives you a new
+ 
+
+ align:start position:0%
+for commutator so it gives you a new
+operator giving two operators you build
+
+ align:start position:0%
+operator giving two operators you build
+ 
+
+ align:start position:0%
+operator giving two operators you build
+a new operator and saying that this so
+
+ align:start position:0%
+a new operator and saying that this so
+ 
+
+ align:start position:0%
+a new operator and saying that this so
+good and suppose now that we have a
+
+ align:start position:0%
+good and suppose now that we have a
+ 
+
+ align:start position:0%
+good and suppose now that we have a
+common eigen function of a and B what
+
+ align:start position:0%
+common eigen function of a and B what
+ 
+
+ align:start position:0%
+common eigen function of a and B what
+does it tell you well let's take the
+
+ align:start position:0%
+does it tell you well let's take the
+ 
+
+ align:start position:0%
+does it tell you well let's take the
+commutator a B and let's take it and act
+
+ align:start position:0%
+commutator a B and let's take it and act
+ 
+
+ align:start position:0%
+commutator a B and let's take it and act
+on five sub a B on this common
+
+ align:start position:0%
+on five sub a B on this common
+ 
+
+ align:start position:0%
+on five sub a B on this common
+eigenstate so what is this equal to this
+
+ align:start position:0%
+eigenstate so what is this equal to this
+ 
+
+ align:start position:0%
+eigenstate so what is this equal to this
+is equal to a B minus B a 5e which I can
+
+ align:start position:0%
+is equal to a B minus B a 5e which I can
+ 
+
+ align:start position:0%
+is equal to a B minus B a 5e which I can
+write as a B by B minus B a 5e by
+
+ align:start position:0%
+write as a B by B minus B a 5e by
+ 
+
+ align:start position:0%
+write as a B by B minus B a 5e by
+linearity by addition really okay but be
+
+ align:start position:0%
+linearity by addition really okay but be
+ 
+
+ align:start position:0%
+linearity by addition really okay but be
+acting on Phi B gives me by hypothesis
+
+ align:start position:0%
+acting on Phi B gives me by hypothesis
+ 
+
+ align:start position:0%
+acting on Phi B gives me by hypothesis
+little B Phi V and then a acting on a
+
+ align:start position:0%
+little B Phi V and then a acting on a
+ 
+
+ align:start position:0%
+little B Phi V and then a acting on a
+constant times Phi B gives me a little a
+
+ align:start position:0%
+constant times Phi B gives me a little a
+ 
+
+ align:start position:0%
+constant times Phi B gives me a little a
+times that constant okay - now here a
+
+ align:start position:0%
+times that constant okay - now here a
+ 
+
+ align:start position:0%
+times that constant okay - now here a
+acting on Phi B gives me a little a Phi
+
+ align:start position:0%
+acting on Phi B gives me a little a Phi
+ 
+
+ align:start position:0%
+acting on Phi B gives me a little a Phi
+B and then B acting are constant times
+
+ align:start position:0%
+B and then B acting are constant times
+ 
+
+ align:start position:0%
+B and then B acting are constant times
+Phi B gives me a little B and now I can
+
+ align:start position:0%
+Phi B gives me a little B and now I can
+ 
+
+ align:start position:0%
+Phi B gives me a little B and now I can
+join these together this is equal to
+
+ align:start position:0%
+join these together this is equal to
+ 
+
+ align:start position:0%
+join these together this is equal to
+good a B little a B minus B a Phi B but
+
+ align:start position:0%
+good a B little a B minus B a Phi B but
+ 
+
+ align:start position:0%
+good a B little a B minus B a Phi B but
+little a and little B our numbers if you
+
+ align:start position:0%
+little a and little B our numbers if you
+ 
+
+ align:start position:0%
+little a and little B our numbers if you
+take seven times five and five times
+
+ align:start position:0%
+take seven times five and five times
+ 
+
+ align:start position:0%
+take seven times five and five times
+seven and you subtract them what do you
+
+ align:start position:0%
+seven and you subtract them what do you
+ 
+
+ align:start position:0%
+seven and you subtract them what do you
+get zero so in order for a and B to
+
+ align:start position:0%
+get zero so in order for a and B to
+ 
+
+ align:start position:0%
+get zero so in order for a and B to
+share a single eigenfunction phi a be
+
+ align:start position:0%
+share a single eigenfunction phi a be
+ 
+
+ align:start position:0%
+share a single eigenfunction phi a be
+what must be true of their commutator
+
+ align:start position:0%
+what must be true of their commutator
+ 
+
+ align:start position:0%
+ 
+it must have a nonzero kernel exactly it
+
+ align:start position:0%
+it must have a nonzero kernel exactly it
+ 
+
+ align:start position:0%
+it must have a nonzero kernel exactly it
+must the commutator must annihilate that
+
+ align:start position:0%
+must the commutator must annihilate that
+ 
+
+ align:start position:0%
+must the commutator must annihilate that
+particular function that common
+
+ align:start position:0%
+particular function that common
+ 
+
+ align:start position:0%
+particular function that common
+eigenfunction okay does it tell you that
+
+ align:start position:0%
+eigenfunction okay does it tell you that
+ 
+
+ align:start position:0%
+eigenfunction okay does it tell you that
+it kills every eigenfunction no but it
+
+ align:start position:0%
+it kills every eigenfunction no but it
+ 
+
+ align:start position:0%
+it kills every eigenfunction no but it
+must at the very least annihilate the
+
+ align:start position:0%
+must at the very least annihilate the
+ 
+
+ align:start position:0%
+must at the very least annihilate the
+shared eigenfunction true consider two
+
+ align:start position:0%
+shared eigenfunction true consider two
+ 
+
+ align:start position:0%
+shared eigenfunction true consider two
+operators of the following form consider
+
+ align:start position:0%
+operators of the following form consider
+ 
+
+ align:start position:0%
+operators of the following form consider
+two operators who commutator a b is
+
+ align:start position:0%
+two operators who commutator a b is
+ 
+
+ align:start position:0%
+two operators who commutator a b is
+equal to the identity times a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay do these operators share any common
+
+ align:start position:0%
+okay do these operators share any common
+ 
+
+ align:start position:0%
+okay do these operators share any common
+eigenfunctions they can't because the
+
+ align:start position:0%
+eigenfunctions they can't because the
+ 
+
+ align:start position:0%
+eigenfunctions they can't because the
+commutator the identity doesn't
+
+ align:start position:0%
+commutator the identity doesn't
+ 
+
+ align:start position:0%
+commutator the identity doesn't
+annihilate any wave functions any
+
+ align:start position:0%
+annihilate any wave functions any
+ 
+
+ align:start position:0%
+annihilate any wave functions any
+functions nothing is 0 when acted upon
+
+ align:start position:0%
+functions nothing is 0 when acted upon
+ 
+
+ align:start position:0%
+functions nothing is 0 when acted upon
+by the identity that's the definition of
+
+ align:start position:0%
+by the identity that's the definition of
+ 
+
+ align:start position:0%
+by the identity that's the definition of
+the identity right the identity takes
+
+ align:start position:0%
+the identity right the identity takes
+ 
+
+ align:start position:0%
+the identity right the identity takes
+any function gives it that function back
+
+ align:start position:0%
+any function gives it that function back
+ 
+
+ align:start position:0%
+any function gives it that function back
+cool do a and B share any common
+
+ align:start position:0%
+cool do a and B share any common
+ 
+
+ align:start position:0%
+cool do a and B share any common
+eigenfunctions now let's think about
+
+ align:start position:0%
+eigenfunctions now let's think about
+ 
+
+ align:start position:0%
+eigenfunctions now let's think about
+what that means in terms of what single
+
+ align:start position:0%
+what that means in terms of what single
+ 
+
+ align:start position:0%
+what that means in terms of what single
+with that term but what that means in
+
+ align:start position:0%
+with that term but what that means in
+ 
+
+ align:start position:0%
+with that term but what that means in
+terms of observables observables are
+
+ align:start position:0%
+terms of observables observables are
+ 
+
+ align:start position:0%
+terms of observables observables are
+represented by operators what are the
+
+ align:start position:0%
+represented by operators what are the
+ 
+
+ align:start position:0%
+represented by operators what are the
+eigen function what is the meaning of
+
+ align:start position:0%
+eigen function what is the meaning of
+ 
+
+ align:start position:0%
+eigen function what is the meaning of
+the eigenfunctions of those operators it
+
+ align:start position:0%
+the eigenfunctions of those operators it
+ 
+
+ align:start position:0%
+the eigenfunctions of those operators it
+corresponds to the state with a definite
+
+ align:start position:0%
+corresponds to the state with a definite
+ 
+
+ align:start position:0%
+corresponds to the state with a definite
+value of that observable and the value
+
+ align:start position:0%
+value of that observable and the value
+ 
+
+ align:start position:0%
+value of that observable and the value
+is the corresponding eigen function I
+
+ align:start position:0%
+is the corresponding eigen function I
+ 
+
+ align:start position:0%
+is the corresponding eigen function I
+can value yeah so the eigen function of
+
+ align:start position:0%
+can value yeah so the eigen function of
+ 
+
+ align:start position:0%
+can value yeah so the eigen function of
+an operator of an observable operator is
+
+ align:start position:0%
+an operator of an observable operator is
+ 
+
+ align:start position:0%
+an operator of an observable operator is
+a possible state with a definite value
+
+ align:start position:0%
+a possible state with a definite value
+ 
+
+ align:start position:0%
+a possible state with a definite value
+of that operator if I tell you that I
+
+ align:start position:0%
+of that operator if I tell you that I
+ 
+
+ align:start position:0%
+of that operator if I tell you that I
+have a state which is an energy
+
+ align:start position:0%
+have a state which is an energy
+ 
+
+ align:start position:0%
+have a state which is an energy
+eigenfunction then that means it is a
+
+ align:start position:0%
+eigenfunction then that means it is a
+ 
+
+ align:start position:0%
+eigenfunction then that means it is a
+state with a definite value of the
+
+ align:start position:0%
+state with a definite value of the
+ 
+
+ align:start position:0%
+state with a definite value of the
+energy if I measure that under general
+
+ align:start position:0%
+energy if I measure that under general
+ 
+
+ align:start position:0%
+energy if I measure that under general
+exactly what I will get cool if these
+
+ align:start position:0%
+exactly what I will get cool if these
+ 
+
+ align:start position:0%
+exactly what I will get cool if these
+are two observables that a and B are two
+
+ align:start position:0%
+are two observables that a and B are two
+ 
+
+ align:start position:0%
+are two observables that a and B are two
+observables and their commutator is
+
+ align:start position:0%
+observables and their commutator is
+ 
+
+ align:start position:0%
+observables and their commutator is
+proportional to the identity is it
+
+ align:start position:0%
+proportional to the identity is it
+ 
+
+ align:start position:0%
+proportional to the identity is it
+possible that there is a state with a
+
+ align:start position:0%
+possible that there is a state with a
+ 
+
+ align:start position:0%
+possible that there is a state with a
+definite value of a and a definite value
+
+ align:start position:0%
+definite value of a and a definite value
+ 
+
+ align:start position:0%
+definite value of a and a definite value
+of B simultaneously no because I stay
+
+ align:start position:0%
+of B simultaneously no because I stay
+ 
+
+ align:start position:0%
+of B simultaneously no because I stay
+with the definite value of an a would be
+
+ align:start position:0%
+with the definite value of an a would be
+ 
+
+ align:start position:0%
+with the definite value of an a would be
+an eigenfunction of a
+
+ align:start position:0%
+an eigenfunction of a
+ 
+
+ align:start position:0%
+an eigenfunction of a
+the state with the definite value of B
+
+ align:start position:0%
+the state with the definite value of B
+ 
+
+ align:start position:0%
+the state with the definite value of B
+would be a eigenfunction of B and there
+
+ align:start position:0%
+would be a eigenfunction of B and there
+ 
+
+ align:start position:0%
+would be a eigenfunction of B and there
+are no common States no common
+
+ align:start position:0%
+are no common States no common
+ 
+
+ align:start position:0%
+are no common States no common
+eigenfunctions of a and B because the
+
+ align:start position:0%
+eigenfunctions of a and B because the
+ 
+
+ align:start position:0%
+eigenfunctions of a and B because the
+commutator never kills a state and it
+
+ align:start position:0%
+commutator never kills a state and it
+ 
+
+ align:start position:0%
+commutator never kills a state and it
+has no zeros what is the commutator of X
+
+ align:start position:0%
+has no zeros what is the commutator of X
+ 
+
+ align:start position:0%
+has no zeros what is the commutator of X
+and P commit this memory IH bar now when
+
+ align:start position:0%
+and P commit this memory IH bar now when
+ 
+
+ align:start position:0%
+and P commit this memory IH bar now when
+we write a H bar this is not really an
+
+ align:start position:0%
+we write a H bar this is not really an
+ 
+
+ align:start position:0%
+we write a H bar this is not really an
+opera that's a number what's the
+
+ align:start position:0%
+opera that's a number what's the
+ 
+
+ align:start position:0%
+opera that's a number what's the
+operator the identity are there any
+
+ align:start position:0%
+operator the identity are there any
+ 
+
+ align:start position:0%
+operator the identity are there any
+states which are simultaneously
+
+ align:start position:0%
+states which are simultaneously
+ 
+
+ align:start position:0%
+states which are simultaneously
+eigenfunctions of X the operator X
+
+ align:start position:0%
+eigenfunctions of X the operator X
+ 
+
+ align:start position:0%
+eigenfunctions of X the operator X
+intimate and eigenfunctions of P are
+
+ align:start position:0%
+intimate and eigenfunctions of P are
+ 
+
+ align:start position:0%
+intimate and eigenfunctions of P are
+there any states that have a definite
+
+ align:start position:0%
+there any states that have a definite
+ 
+
+ align:start position:0%
+there any states that have a definite
+position and a definite momentum
+
+ align:start position:0%
+position and a definite momentum
+ 
+
+ align:start position:0%
+position and a definite momentum
+simultaneously is that because we're
+
+ align:start position:0%
+simultaneously is that because we're
+ 
+
+ align:start position:0%
+simultaneously is that because we're
+ignorant are we ignorant yes okay good
+
+ align:start position:0%
+ignorant are we ignorant yes okay good
+ 
+
+ align:start position:0%
+ignorant are we ignorant yes okay good
+so it is not it is because the kinds of
+
+ align:start position:0%
+so it is not it is because the kinds of
+ 
+
+ align:start position:0%
+so it is not it is because the kinds of
+things that position and momentum are
+
+ align:start position:0%
+things that position and momentum are
+ 
+
+ align:start position:0%
+things that position and momentum are
+forbid the existence of a state with a
+
+ align:start position:0%
+forbid the existence of a state with a
+ 
+
+ align:start position:0%
+forbid the existence of a state with a
+definite value of x and with a definite
+
+ align:start position:0%
+definite value of x and with a definite
+ 
+
+ align:start position:0%
+definite value of x and with a definite
+value of P simultaneously there's veter
+
+ align:start position:0%
+value of P simultaneously there's veter
+ 
+
+ align:start position:0%
+value of P simultaneously there's veter
+here and we're there nor pose nor
+
+ align:start position:0%
+here and we're there nor pose nor
+ 
+
+ align:start position:0%
+here and we're there nor pose nor
+neither okay so this tells us something
+
+ align:start position:0%
+neither okay so this tells us something
+ 
+
+ align:start position:0%
+neither okay so this tells us something
+very lovely this tells us that if we're
+
+ align:start position:0%
+very lovely this tells us that if we're
+ 
+
+ align:start position:0%
+very lovely this tells us that if we're
+in a state with a definite value of X
+
+ align:start position:0%
+in a state with a definite value of X
+ 
+
+ align:start position:0%
+in a state with a definite value of X
+what must be true of our uncertainty in
+
+ align:start position:0%
+what must be true of our uncertainty in
+ 
+
+ align:start position:0%
+what must be true of our uncertainty in
+the value of P it can't be zero
+
+ align:start position:0%
+the value of P it can't be zero
+ 
+
+ align:start position:0%
+the value of P it can't be zero
+because if it were zero for uncertainty
+
+ align:start position:0%
+because if it were zero for uncertainty
+ 
+
+ align:start position:0%
+because if it were zero for uncertainty
+in the knowledge P were zero that would
+
+ align:start position:0%
+in the knowledge P were zero that would
+ 
+
+ align:start position:0%
+in the knowledge P were zero that would
+mean we're in a P I can say we would
+
+ align:start position:0%
+mean we're in a P I can say we would
+ 
+
+ align:start position:0%
+mean we're in a P I can say we would
+have a definite value of P so if Delta X
+
+ align:start position:0%
+have a definite value of P so if Delta X
+ 
+
+ align:start position:0%
+have a definite value of P so if Delta X
+is zero Delta P cannot be zero for sure
+
+ align:start position:0%
+is zero Delta P cannot be zero for sure
+ 
+
+ align:start position:0%
+is zero Delta P cannot be zero for sure
+now how big does it have to be could it
+
+ align:start position:0%
+now how big does it have to be could it
+ 
+
+ align:start position:0%
+now how big does it have to be could it
+be arbitrarily small so here's a
+
+ align:start position:0%
+be arbitrarily small so here's a
+ 
+
+ align:start position:0%
+be arbitrarily small so here's a
+commutation relation you will prove the
+
+ align:start position:0%
+commutation relation you will prove the
+ 
+
+ align:start position:0%
+commutation relation you will prove the
+following relation later on in the
+
+ align:start position:0%
+following relation later on in the
+ 
+
+ align:start position:0%
+following relation later on in the
+course but I want to tell you now
+
+ align:start position:0%
+course but I want to tell you now
+ 
+
+ align:start position:0%
+course but I want to tell you now
+because I want to give you some
+
+ align:start position:0%
+because I want to give you some
+ 
+
+ align:start position:0%
+because I want to give you some
+intuition for what the commutator is
+
+ align:start position:0%
+intuition for what the commutator is
+ 
+
+ align:start position:0%
+intuition for what the commutator is
+what it means what the physics of it is
+
+ align:start position:0%
+what it means what the physics of it is
+ 
+
+ align:start position:0%
+what it means what the physics of it is
+if I take two operators a and B with
+
+ align:start position:0%
+if I take two operators a and B with
+ 
+
+ align:start position:0%
+if I take two operators a and B with
+which have a commutator which is a
+
+ align:start position:0%
+which have a commutator which is a
+ 
+
+ align:start position:0%
+which have a commutator which is a
+constant times the identity then the
+
+ align:start position:0%
+constant times the identity then the
+ 
+
+ align:start position:0%
+constant times the identity then the
+uncertainty in any state a sasai of a
+
+ align:start position:0%
+uncertainty in any state a sasai of a
+ 
+
+ align:start position:0%
+uncertainty in any state a sasai of a
+times the uncertainty in a States I the
+
+ align:start position:0%
+times the uncertainty in a States I the
+ 
+
+ align:start position:0%
+times the uncertainty in a States I the
+same States I of B must be greater than
+
+ align:start position:0%
+same States I of B must be greater than
+ 
+
+ align:start position:0%
+same States I of B must be greater than
+or equal to one-half
+
+ align:start position:0%
+or equal to one-half
+ 
+
+ align:start position:0%
+or equal to one-half
+the absolute value of the expectation
+
+ align:start position:0%
+the absolute value of the expectation
+ 
+
+ align:start position:0%
+the absolute value of the expectation
+value of the commutator that's an
+
+ align:start position:0%
+value of the commutator that's an
+ 
+
+ align:start position:0%
+value of the commutator that's an
+amazing set of symbols of a with B okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+square root I gotta take a squirt thank
+
+ align:start position:0%
+square root I gotta take a squirt thank
+ 
+
+ align:start position:0%
+square root I gotta take a squirt thank
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+so the easier way through these are file
+
+ align:start position:0%
+so the easier way through these are file
+ 
+
+ align:start position:0%
+so the easier way through these are file
+let's see a B let's just make sure I'm
+
+ align:start position:0%
+let's see a B let's just make sure I'm
+ 
+
+ align:start position:0%
+let's see a B let's just make sure I'm
+getting this right
+
+ align:start position:0%
+getting this right
+ 
+
+ align:start position:0%
+getting this right
+I'm commentator of a and B it's oh no no
+
+ align:start position:0%
+I'm commentator of a and B it's oh no no
+ 
+
+ align:start position:0%
+I'm commentator of a and B it's oh no no
+there's no square root sorry why are you
+
+ align:start position:0%
+there's no square root sorry why are you
+ 
+
+ align:start position:0%
+there's no square root sorry why are you
+messing with me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+expectation value of a and B Delta a
+
+ align:start position:0%
+expectation value of a and B Delta a
+ 
+
+ align:start position:0%
+expectation value of a and B Delta a
+delta P H bar um yes good okay so in
+
+ align:start position:0%
+delta P H bar um yes good okay so in
+ 
+
+ align:start position:0%
+delta P H bar um yes good okay so in
+particular this expectation value should
+
+ align:start position:0%
+particular this expectation value should
+ 
+
+ align:start position:0%
+particular this expectation value should
+be taken with the states I sorry late
+
+ align:start position:0%
+be taken with the states I sorry late
+ 
+
+ align:start position:0%
+be taken with the states I sorry late
+and I'm tired
+
+ align:start position:0%
+and I'm tired
+ 
+
+ align:start position:0%
+and I'm tired
+sorry and this should be taken in the
+
+ align:start position:0%
+sorry and this should be taken in the
+ 
+
+ align:start position:0%
+sorry and this should be taken in the
+states I okay so we compute the
+
+ align:start position:0%
+states I okay so we compute the
+ 
+
+ align:start position:0%
+states I okay so we compute the
+commutator we take the expectation value
+
+ align:start position:0%
+commutator we take the expectation value
+ 
+
+ align:start position:0%
+commutator we take the expectation value
+in our state we take the norm multiplied
+
+ align:start position:0%
+in our state we take the norm multiplied
+ 
+
+ align:start position:0%
+in our state we take the norm multiplied
+by 1/2 and this is the bound this is the
+
+ align:start position:0%
+by 1/2 and this is the bound this is the
+ 
+
+ align:start position:0%
+by 1/2 and this is the bound this is the
+claim so let's check this in the case of
+
+ align:start position:0%
+claim so let's check this in the case of
+ 
+
+ align:start position:0%
+claim so let's check this in the case of
+X and P and we'll derive this using just
+
+ align:start position:0%
+X and P and we'll derive this using just
+ 
+
+ align:start position:0%
+X and P and we'll derive this using just
+math this will come from just linear
+
+ align:start position:0%
+math this will come from just linear
+ 
+
+ align:start position:0%
+math this will come from just linear
+algebra so let's check this in the case
+
+ align:start position:0%
+algebra so let's check this in the case
+ 
+
+ align:start position:0%
+algebra so let's check this in the case
+of X in P and X and P what's the
+
+ align:start position:0%
+of X in P and X and P what's the
+ 
+
+ align:start position:0%
+of X in P and X and P what's the
+expectation so what's the expectation
+
+ align:start position:0%
+expectation so what's the expectation
+ 
+
+ align:start position:0%
+expectation so what's the expectation
+value in a state sigh of I h-bar times
+
+ align:start position:0%
+value in a state sigh of I h-bar times
+ 
+
+ align:start position:0%
+value in a state sigh of I h-bar times
+the operator one saw its IH bar IH bar
+
+ align:start position:0%
+the operator one saw its IH bar IH bar
+ 
+
+ align:start position:0%
+the operator one saw its IH bar IH bar
+great so what happens over here what do
+
+ align:start position:0%
+great so what happens over here what do
+ 
+
+ align:start position:0%
+great so what happens over here what do
+we get for Delta X into the states I
+
+ align:start position:0%
+we get for Delta X into the states I
+ 
+
+ align:start position:0%
+we get for Delta X into the states I
+times Delta P in the state's I whoops in
+
+ align:start position:0%
+times Delta P in the state's I whoops in
+ 
+
+ align:start position:0%
+times Delta P in the state's I whoops in
+the states I P this must be greater than
+
+ align:start position:0%
+the states I P this must be greater than
+ 
+
+ align:start position:0%
+the states I P this must be greater than
+or equal to 1/2 times the act of the
+
+ align:start position:0%
+or equal to 1/2 times the act of the
+ 
+
+ align:start position:0%
+or equal to 1/2 times the act of the
+absolute value of the expectation value
+
+ align:start position:0%
+absolute value of the expectation value
+ 
+
+ align:start position:0%
+absolute value of the expectation value
+of the commutator but the expectation
+
+ align:start position:0%
+of the commutator but the expectation
+ 
+
+ align:start position:0%
+of the commutator but the expectation
+value of the commutator is IH bar and
+
+ align:start position:0%
+value of the commutator is IH bar and
+ 
+
+ align:start position:0%
+value of the commutator is IH bar and
+the norm of that is just H bar this is
+
+ align:start position:0%
+the norm of that is just H bar this is
+ 
+
+ align:start position:0%
+the norm of that is just H bar this is
+the uncertainty relation so given some
+
+ align:start position:0%
+the uncertainty relation so given some
+ 
+
+ align:start position:0%
+the uncertainty relation so given some
+uncertainty in Delta X this tells us how
+
+ align:start position:0%
+uncertainty in Delta X this tells us how
+ 
+
+ align:start position:0%
+uncertainty in Delta X this tells us how
+much Delta P is now how does this
+
+ align:start position:0%
+much Delta P is now how does this
+ 
+
+ align:start position:0%
+much Delta P is now how does this
+right-hand side depend on the weight
+
+ align:start position:0%
+right-hand side depend on the weight
+ 
+
+ align:start position:0%
+right-hand side depend on the weight
+and sigh well it turns out it doesn't
+
+ align:start position:0%
+and sigh well it turns out it doesn't
+ 
+
+ align:start position:0%
+and sigh well it turns out it doesn't
+right it's explicitly independent of the
+
+ align:start position:0%
+right it's explicitly independent of the
+ 
+
+ align:start position:0%
+right it's explicitly independent of the
+particular wavefunction we're interested
+
+ align:start position:0%
+particular wavefunction we're interested
+ 
+
+ align:start position:0%
+particular wavefunction we're interested
+in for any wave function mm-hmm
+
+ align:start position:0%
+in for any wave function mm-hmm
+ 
+
+ align:start position:0%
+in for any wave function mm-hmm
+for any wave function whatsoever the
+
+ align:start position:0%
+for any wave function whatsoever the
+ 
+
+ align:start position:0%
+for any wave function whatsoever the
+uncertainty in X times the uncertainty
+
+ align:start position:0%
+uncertainty in X times the uncertainty
+ 
+
+ align:start position:0%
+uncertainty in X times the uncertainty
+in P must be greater than or equal to
+
+ align:start position:0%
+in P must be greater than or equal to
+ 
+
+ align:start position:0%
+in P must be greater than or equal to
+1/2 H bar and this is a consequence of
+
+ align:start position:0%
+1/2 H bar and this is a consequence of
+ 
+
+ align:start position:0%
+1/2 H bar and this is a consequence of
+the commutation and more importantly the
+
+ align:start position:0%
+the commutation and more importantly the
+ 
+
+ align:start position:0%
+the commutation and more importantly the
+failure of X and P to commute because
+
+ align:start position:0%
+failure of X and P to commute because
+ 
+
+ align:start position:0%
+failure of X and P to commute because
+the ability to commute and get 0 is
+
+ align:start position:0%
+the ability to commute and get 0 is
+ 
+
+ align:start position:0%
+the ability to commute and get 0 is
+necessary for there to be common
+
+ align:start position:0%
+necessary for there to be common
+ 
+
+ align:start position:0%
+necessary for there to be common
+eigenstates now imagine in this case a
+
+ align:start position:0%
+eigenstates now imagine in this case a
+ 
+
+ align:start position:0%
+eigenstates now imagine in this case a
+and B are that a and B that in fact do
+
+ align:start position:0%
+and B are that a and B that in fact do
+ 
+
+ align:start position:0%
+and B are that a and B that in fact do
+share a common eigenstate so let's take
+
+ align:start position:0%
+share a common eigenstate so let's take
+ 
+
+ align:start position:0%
+share a common eigenstate so let's take
+compute the expectation value R the
+
+ align:start position:0%
+compute the expectation value R the
+ 
+
+ align:start position:0%
+compute the expectation value R the
+uncertainty of a in the state Phi so
+
+ align:start position:0%
+uncertainty of a in the state Phi so
+ 
+
+ align:start position:0%
+uncertainty of a in the state Phi so
+maybe by some baby
+
+ align:start position:0%
+maybe by some baby
+ 
+
+ align:start position:0%
+maybe by some baby
+Phi baby vise baby and what is this
+
+ align:start position:0%
+Phi baby vise baby and what is this
+ 
+
+ align:start position:0%
+Phi baby vise baby and what is this
+equal to well what's the commutator
+
+ align:start position:0%
+equal to well what's the commutator
+ 
+
+ align:start position:0%
+equal to well what's the commutator
+acting on the state Phi sub a B 0 so
+
+ align:start position:0%
+acting on the state Phi sub a B 0 so
+ 
+
+ align:start position:0%
+acting on the state Phi sub a B 0 so
+this is greater than or equal to 0
+
+ align:start position:0%
+this is greater than or equal to 0
+ 
+
+ align:start position:0%
+this is greater than or equal to 0
+and in fact you can just check by going
+
+ align:start position:0%
+and in fact you can just check by going
+ 
+
+ align:start position:0%
+and in fact you can just check by going
+through the proof of this that is just
+
+ align:start position:0%
+through the proof of this that is just
+ 
+
+ align:start position:0%
+through the proof of this that is just
+equal to 0 so what's the uncertainty of
+
+ align:start position:0%
+equal to 0 so what's the uncertainty of
+ 
+
+ align:start position:0%
+equal to 0 so what's the uncertainty of
+a well we know it's in the state with
+
+ align:start position:0%
+a well we know it's in the state with
+ 
+
+ align:start position:0%
+a well we know it's in the state with
+definite value of a it's 0 uncertainty
+
+ align:start position:0%
+definite value of a it's 0 uncertainty
+ 
+
+ align:start position:0%
+definite value of a it's 0 uncertainty
+and B in the state what's the
+
+ align:start position:0%
+and B in the state what's the
+ 
+
+ align:start position:0%
+and B in the state what's the
+uncertainty 0 we know that it's in an
+
+ align:start position:0%
+uncertainty 0 we know that it's in an
+ 
+
+ align:start position:0%
+uncertainty 0 we know that it's in an
+eigenstate of B so 0 is indeed greater
+
+ align:start position:0%
+eigenstate of B so 0 is indeed greater
+ 
+
+ align:start position:0%
+eigenstate of B so 0 is indeed greater
+than or equal to 0 so it satisfies the
+
+ align:start position:0%
+than or equal to 0 so it satisfies the
+ 
+
+ align:start position:0%
+than or equal to 0 so it satisfies the
+uncertainty relation commuting is
+
+ align:start position:0%
+uncertainty relation commuting is
+ 
+
+ align:start position:0%
+uncertainty relation commuting is
+telling you about the possibility of the
+
+ align:start position:0%
+telling you about the possibility of the
+ 
+
+ align:start position:0%
+telling you about the possibility of the
+state having definite values of both
+
+ align:start position:0%
+state having definite values of both
+ 
+
+ align:start position:0%
+state having definite values of both
+operators simultaneously and this is
+
+ align:start position:0%
+operators simultaneously and this is
+ 
+
+ align:start position:0%
+operators simultaneously and this is
+going to turn out to be enormously
+
+ align:start position:0%
+going to turn out to be enormously
+ 
+
+ align:start position:0%
+going to turn out to be enormously
+valuable when we talk about angular
+
+ align:start position:0%
+valuable when we talk about angular
+ 
+
+ align:start position:0%
+valuable when we talk about angular
+momentum which is coming in a couple of
+
+ align:start position:0%
+momentum which is coming in a couple of
+ 
+
+ align:start position:0%
+momentum which is coming in a couple of
+weeks ok see you guys on Thursday here
+
+ align:start position:0%
+weeks ok see you guys on Thursday here
+ 
+
+ align:start position:0%
+weeks ok see you guys on Thursday here
+for the midterm
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/WaCXmcVVduI.txt b/WaCXmcVVduI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..de9d42f122391fec5026b60c3e1fcc0f0c8bd673
--- /dev/null
+++ b/WaCXmcVVduI.txt
@@ -0,0 +1,4507 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu uh chemical properties so
+
+ align:start position:0%
+ocw.mit.edu uh chemical properties so
+ 
+
+ align:start position:0%
+ocw.mit.edu uh chemical properties so
+let's uh let's put something up as a
+
+ align:start position:0%
+let's uh let's put something up as a
+ 
+
+ align:start position:0%
+let's uh let's put something up as a
+hypothesis let's say well uh maybe it
+
+ align:start position:0%
+hypothesis let's say well uh maybe it
+ 
+
+ align:start position:0%
+hypothesis let's say well uh maybe it
+has to do with the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy that it takes to remove electrons
+
+ align:start position:0%
+energy that it takes to remove electrons
+ 
+
+ align:start position:0%
+energy that it takes to remove electrons
+and note one other thing that I
+
+ align:start position:0%
+and note one other thing that I
+ 
+
+ align:start position:0%
+and note one other thing that I
+uh failed to point out if you take a
+
+ align:start position:0%
+uh failed to point out if you take a
+ 
+
+ align:start position:0%
+uh failed to point out if you take a
+look at the energies associated with the
+
+ align:start position:0%
+look at the energies associated with the
+ 
+
+ align:start position:0%
+look at the energies associated with the
+outermost electrons in this case lithium
+
+ align:start position:0%
+outermost electrons in this case lithium
+ 
+
+ align:start position:0%
+outermost electrons in this case lithium
+you see it's um .5 megga per mole and
+
+ align:start position:0%
+you see it's um .5 megga per mole and
+ 
+
+ align:start position:0%
+you see it's um .5 megga per mole and
+then what's the 6.26 that's associated
+
+ align:start position:0%
+then what's the 6.26 that's associated
+ 
+
+ align:start position:0%
+then what's the 6.26 that's associated
+with one n equals 1 inner shell there's
+
+ align:start position:0%
+with one n equals 1 inner shell there's
+ 
+
+ align:start position:0%
+with one n equals 1 inner shell there's
+a huge difference between the energies
+
+ align:start position:0%
+a huge difference between the energies
+ 
+
+ align:start position:0%
+a huge difference between the energies
+and the outermost shell shell and the
+
+ align:start position:0%
+and the outermost shell shell and the
+ 
+
+ align:start position:0%
+and the outermost shell shell and the
+inner shells which tells you that it's
+
+ align:start position:0%
+inner shells which tells you that it's
+ 
+
+ align:start position:0%
+inner shells which tells you that it's
+unlikely that any electrons except those
+
+ align:start position:0%
+unlikely that any electrons except those
+ 
+
+ align:start position:0%
+unlikely that any electrons except those
+in the outermost shell are going to be
+
+ align:start position:0%
+in the outermost shell are going to be
+ 
+
+ align:start position:0%
+in the outermost shell are going to be
+active the inner electrons are so
+
+ align:start position:0%
+active the inner electrons are so
+ 
+
+ align:start position:0%
+active the inner electrons are so
+tightly bound that they're for
+
+ align:start position:0%
+tightly bound that they're for
+ 
+
+ align:start position:0%
+tightly bound that they're for
+all intents and purposes immobilized
+
+ align:start position:0%
+all intents and purposes immobilized
+ 
+
+ align:start position:0%
+all intents and purposes immobilized
+when it comes to reactivity again Boron
+
+ align:start position:0%
+when it comes to reactivity again Boron
+ 
+
+ align:start position:0%
+when it comes to reactivity again Boron
+is a good example look 8 1.36 this is 2p
+
+ align:start position:0%
+is a good example look 8 1.36 this is 2p
+ 
+
+ align:start position:0%
+is a good example look 8 1.36 this is 2p
+this is 2s yeah they're different but
+
+ align:start position:0%
+this is 2s yeah they're different but
+ 
+
+ align:start position:0%
+this is 2s yeah they're different but
+they're roughly on the order of about 1
+
+ align:start position:0%
+they're roughly on the order of about 1
+ 
+
+ align:start position:0%
+they're roughly on the order of about 1
+megga per mole if you go down to 1s it's
+
+ align:start position:0%
+megga per mole if you go down to 1s it's
+ 
+
+ align:start position:0%
+megga per mole if you go down to 1s it's
+20 Mega per mole so the chances of
+
+ align:start position:0%
+20 Mega per mole so the chances of
+ 
+
+ align:start position:0%
+20 Mega per mole so the chances of
+getting any activity from these inner
+
+ align:start position:0%
+getting any activity from these inner
+ 
+
+ align:start position:0%
+getting any activity from these inner
+shell electrons are vanishingly small so
+
+ align:start position:0%
+shell electrons are vanishingly small so
+ 
+
+ align:start position:0%
+shell electrons are vanishingly small so
+let's focus on the outer shell electrons
+
+ align:start position:0%
+let's focus on the outer shell electrons
+ 
+
+ align:start position:0%
+let's focus on the outer shell electrons
+and these outer shell electrons are
+
+ align:start position:0%
+and these outer shell electrons are
+ 
+
+ align:start position:0%
+and these outer shell electrons are
+termed veence electrons so let's
+
+ align:start position:0%
+termed veence electrons so let's
+ 
+
+ align:start position:0%
+termed veence electrons so let's
+construct let's construct a uh a model
+
+ align:start position:0%
+construct let's construct a uh a model
+ 
+
+ align:start position:0%
+construct let's construct a uh a model
+here that suggests that chemical
+
+ align:start position:0%
+here that suggests that chemical
+ 
+
+ align:start position:0%
+here that suggests that chemical
+reactivity is somehow related
+
+ align:start position:0%
+reactivity is somehow related
+ 
+
+ align:start position:0%
+reactivity is somehow related
+to chemical
+
+ align:start position:0%
+to chemical
+ 
+
+ align:start position:0%
+to chemical
+reactivity is somehow related to the
+
+ align:start position:0%
+reactivity is somehow related to the
+ 
+
+ align:start position:0%
+reactivity is somehow related to the
+electron binding energies electron
+
+ align:start position:0%
+electron binding energies electron
+ 
+
+ align:start position:0%
+electron binding energies electron
+binding
+
+ align:start position:0%
+binding
+ 
+
+ align:start position:0%
+binding
+energies of the outermost
+
+ align:start position:0%
+energies of the outermost
+ 
+
+ align:start position:0%
+energies of the outermost
+electrons of the outermost
+
+ align:start position:0%
+electrons of the outermost
+ 
+
+ align:start position:0%
+electrons of the outermost
+shell and this outermost shell is termed
+
+ align:start position:0%
+shell and this outermost shell is termed
+ 
+
+ align:start position:0%
+shell and this outermost shell is termed
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+veence the veence shell so in a first
+
+ align:start position:0%
+veence the veence shell so in a first
+ 
+
+ align:start position:0%
+veence the veence shell so in a first
+blush you might say well why don't we
+
+ align:start position:0%
+blush you might say well why don't we
+ 
+
+ align:start position:0%
+blush you might say well why don't we
+just take the first ionization energy
+
+ align:start position:0%
+just take the first ionization energy
+ 
+
+ align:start position:0%
+just take the first ionization energy
+and that's not a bad first guess but we
+
+ align:start position:0%
+and that's not a bad first guess but we
+ 
+
+ align:start position:0%
+and that's not a bad first guess but we
+know for example that magnesium when it
+
+ align:start position:0%
+know for example that magnesium when it
+ 
+
+ align:start position:0%
+know for example that magnesium when it
+reacts it reacts with both of its
+
+ align:start position:0%
+reacts it reacts with both of its
+ 
+
+ align:start position:0%
+reacts it reacts with both of its
+electrons not just one of its electrons
+
+ align:start position:0%
+electrons not just one of its electrons
+ 
+
+ align:start position:0%
+electrons not just one of its electrons
+so taking just the outermost electron
+
+ align:start position:0%
+so taking just the outermost electron
+ 
+
+ align:start position:0%
+so taking just the outermost electron
+might give us um some false reading so
+
+ align:start position:0%
+might give us um some false reading so
+ 
+
+ align:start position:0%
+might give us um some false reading so
+what if we capture all of the veence
+
+ align:start position:0%
+what if we capture all of the veence
+ 
+
+ align:start position:0%
+what if we capture all of the veence
+electrons is there some way of of
+
+ align:start position:0%
+electrons is there some way of of
+ 
+
+ align:start position:0%
+electrons is there some way of of
+handling that because that'll take care
+
+ align:start position:0%
+handling that because that'll take care
+ 
+
+ align:start position:0%
+handling that because that'll take care
+of all of the electrons that are capable
+
+ align:start position:0%
+of all of the electrons that are capable
+ 
+
+ align:start position:0%
+of all of the electrons that are capable
+of reacting none of the inner shell
+
+ align:start position:0%
+of reacting none of the inner shell
+ 
+
+ align:start position:0%
+of reacting none of the inner shell
+electrons and we do so by a
+
+ align:start position:0%
+electrons and we do so by a
+ 
+
+ align:start position:0%
+electrons and we do so by a
+uh a quantity called the
+
+ align:start position:0%
+uh a quantity called the
+ 
+
+ align:start position:0%
+uh a quantity called the
+average veence electron energy it's in
+
+ align:start position:0%
+average veence electron energy it's in
+ 
+
+ align:start position:0%
+average veence electron energy it's in
+other words it's the average energy of
+
+ align:start position:0%
+other words it's the average energy of
+ 
+
+ align:start position:0%
+other words it's the average energy of
+all the veence
+
+ align:start position:0%
+all the veence
+ 
+
+ align:start position:0%
+all the veence
+electrons so let's take a look at a an
+
+ align:start position:0%
+electrons so let's take a look at a an
+ 
+
+ align:start position:0%
+electrons so let's take a look at a an
+example an example of that might be um
+
+ align:start position:0%
+example an example of that might be um
+ 
+
+ align:start position:0%
+example an example of that might be um
+oh let's look at something
+
+ align:start position:0%
+oh let's look at something
+ 
+
+ align:start position:0%
+oh let's look at something
+like oxygen if you look at oxygen oxygen
+
+ align:start position:0%
+like oxygen if you look at oxygen oxygen
+ 
+
+ align:start position:0%
+like oxygen if you look at oxygen oxygen
+is 1 S2 which is an inshell electron I'm
+
+ align:start position:0%
+is 1 S2 which is an inshell electron I'm
+ 
+
+ align:start position:0%
+is 1 S2 which is an inshell electron I'm
+just putting it up for completeness 2s2
+
+ align:start position:0%
+just putting it up for completeness 2s2
+ 
+
+ align:start position:0%
+just putting it up for completeness 2s2
+and 2
+
+ align:start position:0%
+and 2
+ 
+
+ align:start position:0%
+and 2
+P4 and um so here's the veent shell if I
+
+ align:start position:0%
+P4 and um so here's the veent shell if I
+ 
+
+ align:start position:0%
+P4 and um so here's the veent shell if I
+want to take the average energy of all
+
+ align:start position:0%
+want to take the average energy of all
+ 
+
+ align:start position:0%
+want to take the average energy of all
+of those what I can do is go over to my
+
+ align:start position:0%
+of those what I can do is go over to my
+ 
+
+ align:start position:0%
+of those what I can do is go over to my
+data set here's a data set there's
+
+ align:start position:0%
+data set here's a data set there's
+ 
+
+ align:start position:0%
+data set here's a data set there's
+oxygen the 2p is 1.31 the 2s is
+
+ align:start position:0%
+oxygen the 2p is 1.31 the 2s is
+ 
+
+ align:start position:0%
+oxygen the 2p is 1.31 the 2s is
+3.12 so then I could say that the
+
+ align:start position:0%
+3.12 so then I could say that the
+ 
+
+ align:start position:0%
+3.12 so then I could say that the
+average veence electron energy for
+
+ align:start position:0%
+average veence electron energy for
+ 
+
+ align:start position:0%
+average veence electron energy for
+oxygen would then be I've got two uh s
+
+ align:start position:0%
+oxygen would then be I've got two uh s
+ 
+
+ align:start position:0%
+oxygen would then be I've got two uh s
+electrons so it's 2 *
+
+ align:start position:0%
+electrons so it's 2 *
+ 
+
+ align:start position:0%
+electrons so it's 2 *
+3.12 plus 4 *
+
+ align:start position:0%
+3.12 plus 4 *
+ 
+
+ align:start position:0%
+3.12 plus 4 *
+what is it uh
+
+ align:start position:0%
+what is it uh
+ 
+
+ align:start position:0%
+what is it uh
+1.31 all divided by six I'm averaging it
+
+ align:start position:0%
+1.31 all divided by six I'm averaging it
+ 
+
+ align:start position:0%
+1.31 all divided by six I'm averaging it
+over the entire set of valence electrons
+
+ align:start position:0%
+over the entire set of valence electrons
+ 
+
+ align:start position:0%
+over the entire set of valence electrons
+which gives me
+
+ align:start position:0%
+which gives me
+ 
+
+ align:start position:0%
+which gives me
+1.91 megga per mole or uh in my favorite
+
+ align:start position:0%
+1.91 megga per mole or uh in my favorite
+ 
+
+ align:start position:0%
+1.91 megga per mole or uh in my favorite
+unit 19.8 electron volts this is
+
+ align:start position:0%
+unit 19.8 electron volts this is
+ 
+
+ align:start position:0%
+unit 19.8 electron volts this is
+electron volts per per
+
+ align:start position:0%
+electron volts per per
+ 
+
+ align:start position:0%
+electron volts per per
+atom so how does average veence electron
+
+ align:start position:0%
+atom so how does average veence electron
+ 
+
+ align:start position:0%
+atom so how does average veence electron
+energy uh vary across the periodic table
+
+ align:start position:0%
+energy uh vary across the periodic table
+ 
+
+ align:start position:0%
+energy uh vary across the periodic table
+let's take a look at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so we see it here we see that it
+
+ align:start position:0%
+that so we see it here we see that it
+ 
+
+ align:start position:0%
+that so we see it here we see that it
+varies uh monotonically from left to
+
+ align:start position:0%
+varies uh monotonically from left to
+ 
+
+ align:start position:0%
+varies uh monotonically from left to
+right as we move along a row so this is
+
+ align:start position:0%
+right as we move along a row so this is
+ 
+
+ align:start position:0%
+right as we move along a row so this is
+a constant n number within a constant
+
+ align:start position:0%
+a constant n number within a constant
+ 
+
+ align:start position:0%
+a constant n number within a constant
+shell it varies from left to right
+
+ align:start position:0%
+shell it varies from left to right
+ 
+
+ align:start position:0%
+shell it varies from left to right
+maximally uh taking value at the right
+
+ align:start position:0%
+maximally uh taking value at the right
+ 
+
+ align:start position:0%
+maximally uh taking value at the right
+extreme and within a column it decreases
+
+ align:start position:0%
+extreme and within a column it decreases
+ 
+
+ align:start position:0%
+extreme and within a column it decreases
+down a column it rises up a row it
+
+ align:start position:0%
+down a column it rises up a row it
+ 
+
+ align:start position:0%
+down a column it rises up a row it
+decreases down a
+
+ align:start position:0%
+decreases down a
+ 
+
+ align:start position:0%
+decreases down a
+column and the values that it takes uh
+
+ align:start position:0%
+column and the values that it takes uh
+ 
+
+ align:start position:0%
+column and the values that it takes uh
+can be broken into three groups over
+
+ align:start position:0%
+can be broken into three groups over
+ 
+
+ align:start position:0%
+can be broken into three groups over
+here in the uh in the lower left corner
+
+ align:start position:0%
+here in the uh in the lower left corner
+ 
+
+ align:start position:0%
+here in the uh in the lower left corner
+we have elements that as a group have
+
+ align:start position:0%
+we have elements that as a group have
+ 
+
+ align:start position:0%
+we have elements that as a group have
+very low values of average veence
+
+ align:start position:0%
+very low values of average veence
+ 
+
+ align:start position:0%
+very low values of average veence
+electron energy these are elements
+
+ align:start position:0%
+electron energy these are elements
+ 
+
+ align:start position:0%
+electron energy these are elements
+that are good electron donors they're
+
+ align:start position:0%
+that are good electron donors they're
+ 
+
+ align:start position:0%
+that are good electron donors they're
+good electron donors because the
+
+ align:start position:0%
+good electron donors because the
+ 
+
+ align:start position:0%
+good electron donors because the
+electrons aren't tightly baled
+
+ align:start position:0%
+electrons aren't tightly baled
+ 
+
+ align:start position:0%
+electrons aren't tightly baled
+okay elements with low average valence
+
+ align:start position:0%
+okay elements with low average valence
+ 
+
+ align:start position:0%
+okay elements with low average valence
+electron energy and here I'm
+
+ align:start position:0%
+electron energy and here I'm
+ 
+
+ align:start position:0%
+electron energy and here I'm
+saying below 11 electron volts these are
+
+ align:start position:0%
+saying below 11 electron volts these are
+ 
+
+ align:start position:0%
+saying below 11 electron volts these are
+good electron
+
+ align:start position:0%
+good electron
+ 
+
+ align:start position:0%
+good electron
+donors good electron donors and we call
+
+ align:start position:0%
+donors good electron donors and we call
+ 
+
+ align:start position:0%
+donors good electron donors and we call
+these in simple English Metals these are
+
+ align:start position:0%
+these in simple English Metals these are
+ 
+
+ align:start position:0%
+these in simple English Metals these are
+metals and it turns out that about 75%
+
+ align:start position:0%
+metals and it turns out that about 75%
+ 
+
+ align:start position:0%
+metals and it turns out that about 75%
+of the periodic table 75% of the
+
+ align:start position:0%
+of the periodic table 75% of the
+ 
+
+ align:start position:0%
+of the periodic table 75% of the
+periodic table falls into this C
+
+ align:start position:0%
+periodic table falls into this C
+ 
+
+ align:start position:0%
+periodic table falls into this C
+category so the vast majority of
+
+ align:start position:0%
+category so the vast majority of
+ 
+
+ align:start position:0%
+category so the vast majority of
+elements on the periodic table are uh
+
+ align:start position:0%
+elements on the periodic table are uh
+ 
+
+ align:start position:0%
+elements on the periodic table are uh
+metals and at The Other Extreme we have
+
+ align:start position:0%
+metals and at The Other Extreme we have
+ 
+
+ align:start position:0%
+metals and at The Other Extreme we have
+elements with very high
+
+ align:start position:0%
+elements with very high
+ 
+
+ align:start position:0%
+elements with very high
+value elements with high average veence
+
+ align:start position:0%
+value elements with high average veence
+ 
+
+ align:start position:0%
+value elements with high average veence
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+energy we just did the calculation for
+
+ align:start position:0%
+energy we just did the calculation for
+ 
+
+ align:start position:0%
+energy we just did the calculation for
+oxygen this almost 20 EV High average
+
+ align:start position:0%
+oxygen this almost 20 EV High average
+ 
+
+ align:start position:0%
+oxygen this almost 20 EV High average
+veence electron energy greater than 13
+
+ align:start position:0%
+veence electron energy greater than 13
+ 
+
+ align:start position:0%
+veence electron energy greater than 13
+electron volts so that means the
+
+ align:start position:0%
+electron volts so that means the
+ 
+
+ align:start position:0%
+electron volts so that means the
+electrons are tightly bound so these are
+
+ align:start position:0%
+electrons are tightly bound so these are
+ 
+
+ align:start position:0%
+electrons are tightly bound so these are
+poor electron donors and in fact if any
+
+ align:start position:0%
+poor electron donors and in fact if any
+ 
+
+ align:start position:0%
+poor electron donors and in fact if any
+electron comes in their midst they'll
+
+ align:start position:0%
+electron comes in their midst they'll
+ 
+
+ align:start position:0%
+electron comes in their midst they'll
+capture it because the binding energy is
+
+ align:start position:0%
+capture it because the binding energy is
+ 
+
+ align:start position:0%
+capture it because the binding energy is
+so high so these are
+
+ align:start position:0%
+so high so these are
+ 
+
+ align:start position:0%
+so high so these are
+poor electron donors but also good
+
+ align:start position:0%
+poor electron donors but also good
+ 
+
+ align:start position:0%
+poor electron donors but also good
+electron
+
+ align:start position:0%
+electron
+ 
+
+ align:start position:0%
+electron
+acceptors
+
+ align:start position:0%
+acceptors
+ 
+
+ align:start position:0%
+acceptors
+good electronic
+
+ align:start position:0%
+good electronic
+ 
+
+ align:start position:0%
+good electronic
+acceptors and we call these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+non-metals and you see those and then
+
+ align:start position:0%
+non-metals and you see those and then
+ 
+
+ align:start position:0%
+non-metals and you see those and then
+there's this group of about a half a
+
+ align:start position:0%
+there's this group of about a half a
+ 
+
+ align:start position:0%
+there's this group of about a half a
+dozen right down the diagonal middle and
+
+ align:start position:0%
+dozen right down the diagonal middle and
+ 
+
+ align:start position:0%
+dozen right down the diagonal middle and
+they have intermediate values so when
+
+ align:start position:0%
+they have intermediate values so when
+ 
+
+ align:start position:0%
+they have intermediate values so when
+the when the value of the average veence
+
+ align:start position:0%
+the when the value of the average veence
+ 
+
+ align:start position:0%
+the when the value of the average veence
+electron energy lies
+
+ align:start position:0%
+electron energy lies
+ 
+
+ align:start position:0%
+electron energy lies
+between 11 EV and 13 EV we have these
+
+ align:start position:0%
+between 11 EV and 13 EV we have these
+ 
+
+ align:start position:0%
+between 11 EV and 13 EV we have these
+elements that are neither fish or foul
+
+ align:start position:0%
+elements that are neither fish or foul
+ 
+
+ align:start position:0%
+elements that are neither fish or foul
+and you'll see a a little bit they're uh
+
+ align:start position:0%
+and you'll see a a little bit they're uh
+ 
+
+ align:start position:0%
+and you'll see a a little bit they're uh
+unique uh electrical properties and
+
+ align:start position:0%
+unique uh electrical properties and
+ 
+
+ align:start position:0%
+unique uh electrical properties and
+these are called semi
+
+ align:start position:0%
+these are called semi
+ 
+
+ align:start position:0%
+these are called semi
+Metals semi metals or
+
+ align:start position:0%
+Metals semi metals or
+ 
+
+ align:start position:0%
+Metals semi metals or
+metalloids and in some instan es they
+
+ align:start position:0%
+metalloids and in some instan es they
+ 
+
+ align:start position:0%
+metalloids and in some instan es they
+can be made to behave more nearly
+
+ align:start position:0%
+can be made to behave more nearly
+ 
+
+ align:start position:0%
+can be made to behave more nearly
+metallic and in other cases they behave
+
+ align:start position:0%
+metallic and in other cases they behave
+ 
+
+ align:start position:0%
+metallic and in other cases they behave
+more nearly uh as
+
+ align:start position:0%
+more nearly uh as
+ 
+
+ align:start position:0%
+more nearly uh as
+insulators so now with this framework I
+
+ align:start position:0%
+insulators so now with this framework I
+ 
+
+ align:start position:0%
+insulators so now with this framework I
+said that talking about these veence
+
+ align:start position:0%
+said that talking about these veence
+ 
+
+ align:start position:0%
+said that talking about these veence
+electrons might give us some insight
+
+ align:start position:0%
+electrons might give us some insight
+ 
+
+ align:start position:0%
+electrons might give us some insight
+into uh chemical reactivity what can we
+
+ align:start position:0%
+into uh chemical reactivity what can we
+ 
+
+ align:start position:0%
+into uh chemical reactivity what can we
+say about chemical reactivity well um
+
+ align:start position:0%
+say about chemical reactivity well um
+ 
+
+ align:start position:0%
+say about chemical reactivity well um
+what do we know about extremes of
+
+ align:start position:0%
+what do we know about extremes of
+ 
+
+ align:start position:0%
+what do we know about extremes of
+chemical reactivity see if we can grab
+
+ align:start position:0%
+chemical reactivity see if we can grab
+ 
+
+ align:start position:0%
+chemical reactivity see if we can grab
+on to something we know that um at one
+
+ align:start position:0%
+on to something we know that um at one
+ 
+
+ align:start position:0%
+on to something we know that um at one
+extreme we have no chemical reactivity
+
+ align:start position:0%
+extreme we have no chemical reactivity
+ 
+
+ align:start position:0%
+extreme we have no chemical reactivity
+we have elements that are totally inert
+
+ align:start position:0%
+we have elements that are totally inert
+ 
+
+ align:start position:0%
+we have elements that are totally inert
+and we have examples of this the noble
+
+ align:start position:0%
+and we have examples of this the noble
+ 
+
+ align:start position:0%
+and we have examples of this the noble
+gases dominantly inert once I know
+
+ align:start position:0%
+gases dominantly inert once I know
+ 
+
+ align:start position:0%
+gases dominantly inert once I know
+there's it's possible to induce chemical
+
+ align:start position:0%
+there's it's possible to induce chemical
+ 
+
+ align:start position:0%
+there's it's possible to induce chemical
+reactions but these are exceptions this
+
+ align:start position:0%
+reactions but these are exceptions this
+ 
+
+ align:start position:0%
+reactions but these are exceptions this
+is not the norm so we have inertness and
+
+ align:start position:0%
+is not the norm so we have inertness and
+ 
+
+ align:start position:0%
+is not the norm so we have inertness and
+at the other end we have
+
+ align:start position:0%
+at the other end we have
+ 
+
+ align:start position:0%
+at the other end we have
+explosive explosive reaction okay so do
+
+ align:start position:0%
+explosive explosive reaction okay so do
+ 
+
+ align:start position:0%
+explosive explosive reaction okay so do
+we know anything so far that we can p
+
+ align:start position:0%
+we know anything so far that we can p
+ 
+
+ align:start position:0%
+we know anything so far that we can p
+point to that would give us uh a
+
+ align:start position:0%
+point to that would give us uh a
+ 
+
+ align:start position:0%
+point to that would give us uh a
+departure and the answer is yes we know
+
+ align:start position:0%
+departure and the answer is yes we know
+ 
+
+ align:start position:0%
+departure and the answer is yes we know
+something about the noble gases we know
+
+ align:start position:0%
+something about the noble gases we know
+ 
+
+ align:start position:0%
+something about the noble gases we know
+something about the noble gases what do
+
+ align:start position:0%
+something about the noble gases what do
+ 
+
+ align:start position:0%
+something about the noble gases what do
+we know about the noble gases they're
+
+ align:start position:0%
+we know about the noble gases they're
+ 
+
+ align:start position:0%
+we know about the noble gases they're
+chemically inert they have the highest
+
+ align:start position:0%
+chemically inert they have the highest
+ 
+
+ align:start position:0%
+chemically inert they have the highest
+values they have the highest average
+
+ align:start position:0%
+values they have the highest average
+ 
+
+ align:start position:0%
+values they have the highest average
+veence electron energy in any
+
+ align:start position:0%
+veence electron energy in any
+ 
+
+ align:start position:0%
+veence electron energy in any
+shell and the electron configuration is
+
+ align:start position:0%
+shell and the electron configuration is
+ 
+
+ align:start position:0%
+shell and the electron configuration is
+always n
+
+ align:start position:0%
+always n
+ 
+
+ align:start position:0%
+always n
+S2
+
+ align:start position:0%
+S2
+ 
+
+ align:start position:0%
+S2
+P6 whatever the N number is with the
+
+ align:start position:0%
+P6 whatever the N number is with the
+ 
+
+ align:start position:0%
+P6 whatever the N number is with the
+exception of helium helium is the Oddity
+
+ align:start position:0%
+exception of helium helium is the Oddity
+ 
+
+ align:start position:0%
+exception of helium helium is the Oddity
+because there's only two uh elements in
+
+ align:start position:0%
+because there's only two uh elements in
+ 
+
+ align:start position:0%
+because there's only two uh elements in
+n equals one shell but once you get
+
+ align:start position:0%
+n equals one shell but once you get
+ 
+
+ align:start position:0%
+n equals one shell but once you get
+Beyond n equals 1 it's always 2 S2 2 P6
+
+ align:start position:0%
+Beyond n equals 1 it's always 2 S2 2 P6
+ 
+
+ align:start position:0%
+Beyond n equals 1 it's always 2 S2 2 P6
+3 S2 3 P6 so we have an octet an octet
+
+ align:start position:0%
+3 S2 3 P6 so we have an octet an octet
+ 
+
+ align:start position:0%
+3 S2 3 P6 so we have an octet an octet
+of electrons that seems to be associated
+
+ align:start position:0%
+of electrons that seems to be associated
+ 
+
+ align:start position:0%
+of electrons that seems to be associated
+with chemical
+
+ align:start position:0%
+with chemical
+ 
+
+ align:start position:0%
+with chemical
+inertness
+
+ align:start position:0%
+inertness
+ 
+
+ align:start position:0%
+inertness
+octet stability is the term applied to
+
+ align:start position:0%
+octet stability is the term applied to
+ 
+
+ align:start position:0%
+octet stability is the term applied to
+this feature so all right so let's go
+
+ align:start position:0%
+this feature so all right so let's go
+ 
+
+ align:start position:0%
+this feature so all right so let's go
+with this let's say well um suppose
+
+ align:start position:0%
+with this let's say well um suppose
+ 
+
+ align:start position:0%
+with this let's say well um suppose
+we hypothesize that an octet of
+
+ align:start position:0%
+we hypothesize that an octet of
+ 
+
+ align:start position:0%
+we hypothesize that an octet of
+electrons is going to lead to stability
+
+ align:start position:0%
+electrons is going to lead to stability
+ 
+
+ align:start position:0%
+electrons is going to lead to stability
+is is there someplace we can go next
+
+ align:start position:0%
+is is there someplace we can go next
+ 
+
+ align:start position:0%
+is is there someplace we can go next
+with this and I say well let's look at
+
+ align:start position:0%
+with this and I say well let's look at
+ 
+
+ align:start position:0%
+with this and I say well let's look at
+something like sodium let's look at
+
+ align:start position:0%
+something like sodium let's look at
+ 
+
+ align:start position:0%
+something like sodium let's look at
+sodium sodium has the electronic
+
+ align:start position:0%
+sodium sodium has the electronic
+ 
+
+ align:start position:0%
+sodium sodium has the electronic
+structure 1 S2 uh 2 S2 2 P6 3 S1 now
+
+ align:start position:0%
+structure 1 S2 uh 2 S2 2 P6 3 S1 now
+ 
+
+ align:start position:0%
+structure 1 S2 uh 2 S2 2 P6 3 S1 now
+that's not an Octan set but it's not
+
+ align:start position:0%
+that's not an Octan set but it's not
+ 
+
+ align:start position:0%
+that's not an Octan set but it's not
+far this is the electronic structure of
+
+ align:start position:0%
+far this is the electronic structure of
+ 
+
+ align:start position:0%
+far this is the electronic structure of
+neon so it's really sodium you can think
+
+ align:start position:0%
+neon so it's really sodium you can think
+ 
+
+ align:start position:0%
+neon so it's really sodium you can think
+of electronically as neon plus the 3s1
+
+ align:start position:0%
+of electronically as neon plus the 3s1
+ 
+
+ align:start position:0%
+of electronically as neon plus the 3s1
+electron it's so close and I also know
+
+ align:start position:0%
+electron it's so close and I also know
+ 
+
+ align:start position:0%
+electron it's so close and I also know
+something else about sodium it's got a
+
+ align:start position:0%
+something else about sodium it's got a
+ 
+
+ align:start position:0%
+something else about sodium it's got a
+very low average veence electron energy
+
+ align:start position:0%
+very low average veence electron energy
+ 
+
+ align:start position:0%
+very low average veence electron energy
+its average veence electron energy is
+
+ align:start position:0%
+its average veence electron energy is
+ 
+
+ align:start position:0%
+its average veence electron energy is
+5.2 electron volts which is a heck of a
+
+ align:start position:0%
+5.2 electron volts which is a heck of a
+ 
+
+ align:start position:0%
+5.2 electron volts which is a heck of a
+lot less than 11 so this is a good metal
+
+ align:start position:0%
+lot less than 11 so this is a good metal
+ 
+
+ align:start position:0%
+lot less than 11 so this is a good metal
+it's a good electron
+
+ align:start position:0%
+it's a good electron
+ 
+
+ align:start position:0%
+it's a good electron
+donor Okay so so I've got something
+
+ align:start position:0%
+donor Okay so so I've got something
+ 
+
+ align:start position:0%
+donor Okay so so I've got something
+that's one electron away from the
+
+ align:start position:0%
+that's one electron away from the
+ 
+
+ align:start position:0%
+that's one electron away from the
+electronic structure of neon it's a good
+
+ align:start position:0%
+electronic structure of neon it's a good
+ 
+
+ align:start position:0%
+electronic structure of neon it's a good
+electron donor if it could only ditch
+
+ align:start position:0%
+electron donor if it could only ditch
+ 
+
+ align:start position:0%
+electron donor if it could only ditch
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+electron it could have the same
+
+ align:start position:0%
+electron it could have the same
+ 
+
+ align:start position:0%
+electron it could have the same
+electronic structure as neon but you
+
+ align:start position:0%
+electronic structure as neon but you
+ 
+
+ align:start position:0%
+electronic structure as neon but you
+can't just ditch an electron charge
+
+ align:start position:0%
+can't just ditch an electron charge
+ 
+
+ align:start position:0%
+can't just ditch an electron charge
+neutrality won't allow for it if you
+
+ align:start position:0%
+neutrality won't allow for it if you
+ 
+
+ align:start position:0%
+neutrality won't allow for it if you
+want to lose an electron you have to
+
+ align:start position:0%
+want to lose an electron you have to
+ 
+
+ align:start position:0%
+want to lose an electron you have to
+find some place for that electron to go
+
+ align:start position:0%
+find some place for that electron to go
+ 
+
+ align:start position:0%
+find some place for that electron to go
+another words for an electron donor to
+
+ align:start position:0%
+another words for an electron donor to
+ 
+
+ align:start position:0%
+another words for an electron donor to
+give up its electron the electron donor
+
+ align:start position:0%
+give up its electron the electron donor
+ 
+
+ align:start position:0%
+give up its electron the electron donor
+needs to have an electron sceptor so
+
+ align:start position:0%
+needs to have an electron sceptor so
+ 
+
+ align:start position:0%
+needs to have an electron sceptor so
+that's sort of half the story now let's
+
+ align:start position:0%
+that's sort of half the story now let's
+ 
+
+ align:start position:0%
+that's sort of half the story now let's
+go over to the other side let's look at
+
+ align:start position:0%
+go over to the other side let's look at
+ 
+
+ align:start position:0%
+go over to the other side let's look at
+chlorine chlorine is S2 2 S2 2
+
+ align:start position:0%
+chlorine chlorine is S2 2 S2 2
+ 
+
+ align:start position:0%
+chlorine chlorine is S2 2 S2 2
+P6 3 S2 3
+
+ align:start position:0%
+P6 3 S2 3
+ 
+
+ align:start position:0%
+P6 3 S2 3
+P5 and
+
+ align:start position:0%
+P5 and
+ 
+
+ align:start position:0%
+P5 and
+chlorine it's uh it's not an octet here
+
+ align:start position:0%
+chlorine it's uh it's not an octet here
+ 
+
+ align:start position:0%
+chlorine it's uh it's not an octet here
+this is 5 + 2 is seven but when I went
+
+ align:start position:0%
+this is 5 + 2 is seven but when I went
+ 
+
+ align:start position:0%
+this is 5 + 2 is seven but when I went
+to school seven was only one less than
+
+ align:start position:0%
+to school seven was only one less than
+ 
+
+ align:start position:0%
+to school seven was only one less than
+eight so this needs only one more
+
+ align:start position:0%
+eight so this needs only one more
+ 
+
+ align:start position:0%
+eight so this needs only one more
+electron if it could gain one more
+
+ align:start position:0%
+electron if it could gain one more
+ 
+
+ align:start position:0%
+electron if it could gain one more
+electron then chlorine would be ISO
+
+ align:start position:0%
+electron then chlorine would be ISO
+ 
+
+ align:start position:0%
+electron then chlorine would be ISO
+electronic with argon so it would
+
+ align:start position:0%
+electronic with argon so it would
+ 
+
+ align:start position:0%
+electronic with argon so it would
+achieve octet
+
+ align:start position:0%
+achieve octet
+ 
+
+ align:start position:0%
+achieve octet
+stability and we know that chlorine is
+
+ align:start position:0%
+stability and we know that chlorine is
+ 
+
+ align:start position:0%
+stability and we know that chlorine is
+very aggressive when it comes to
+
+ align:start position:0%
+very aggressive when it comes to
+ 
+
+ align:start position:0%
+very aggressive when it comes to
+electrons it's got an average veence
+
+ align:start position:0%
+electrons it's got an average veence
+ 
+
+ align:start position:0%
+electrons it's got an average veence
+electron energy of about 16
+
+ align:start position:0%
+electron energy of about 16
+ 
+
+ align:start position:0%
+electron energy of about 16
+EV 16.5 EV which is a lot greater than
+
+ align:start position:0%
+EV 16.5 EV which is a lot greater than
+ 
+
+ align:start position:0%
+EV 16.5 EV which is a lot greater than
+11 so what if we were to put the two of
+
+ align:start position:0%
+11 so what if we were to put the two of
+ 
+
+ align:start position:0%
+11 so what if we were to put the two of
+these in the same room you've got an
+
+ align:start position:0%
+these in the same room you've got an
+ 
+
+ align:start position:0%
+these in the same room you've got an
+electron donor with a powerful urge to
+
+ align:start position:0%
+electron donor with a powerful urge to
+ 
+
+ align:start position:0%
+electron donor with a powerful urge to
+become neon likee you got an electronic
+
+ align:start position:0%
+become neon likee you got an electronic
+ 
+
+ align:start position:0%
+become neon likee you got an electronic
+sepor with a powerful urge to become
+
+ align:start position:0%
+sepor with a powerful urge to become
+ 
+
+ align:start position:0%
+sepor with a powerful urge to become
+argon likee what if we were to take this
+
+ align:start position:0%
+argon likee what if we were to take this
+ 
+
+ align:start position:0%
+argon likee what if we were to take this
+electron and send it over to
+
+ align:start position:0%
+electron and send it over to
+ 
+
+ align:start position:0%
+electron and send it over to
+here in other words engage in electron
+
+ align:start position:0%
+here in other words engage in electron
+ 
+
+ align:start position:0%
+here in other words engage in electron
+transfer electron transfer what would we
+
+ align:start position:0%
+transfer electron transfer what would we
+ 
+
+ align:start position:0%
+transfer electron transfer what would we
+achieve sodium would become sodium plus
+
+ align:start position:0%
+achieve sodium would become sodium plus
+ 
+
+ align:start position:0%
+achieve sodium would become sodium plus
+chlorine would become chlorine
+
+ align:start position:0%
+chlorine would become chlorine
+ 
+
+ align:start position:0%
+chlorine would become chlorine
+minus so I've got ion pair formation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I've got a huge decrease in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+energy because a donor is able to
+
+ align:start position:0%
+energy because a donor is able to
+ 
+
+ align:start position:0%
+energy because a donor is able to
+express that urge an acceptor is able to
+
+ align:start position:0%
+express that urge an acceptor is able to
+ 
+
+ align:start position:0%
+express that urge an acceptor is able to
+express that urge and I've achieved
+
+ align:start position:0%
+express that urge and I've achieved
+ 
+
+ align:start position:0%
+express that urge and I've achieved
+octet stability in a new way but there's
+
+ align:start position:0%
+octet stability in a new way but there's
+ 
+
+ align:start position:0%
+octet stability in a new way but there's
+more because now I've got pluses and
+
+ align:start position:0%
+more because now I've got pluses and
+ 
+
+ align:start position:0%
+more because now I've got pluses and
+minuses this is all gas phase all right
+
+ align:start position:0%
+minuses this is all gas phase all right
+ 
+
+ align:start position:0%
+minuses this is all gas phase all right
+it's all gas phase so what happens if I
+
+ align:start position:0%
+it's all gas phase so what happens if I
+ 
+
+ align:start position:0%
+it's all gas phase so what happens if I
+put pluses and minuses in a gas phase
+
+ align:start position:0%
+put pluses and minuses in a gas phase
+ 
+
+ align:start position:0%
+put pluses and minuses in a gas phase
+face there's a colic force of attraction
+
+ align:start position:0%
+face there's a colic force of attraction
+ 
+
+ align:start position:0%
+face there's a colic force of attraction
+there's a colic force of attraction so
+
+ align:start position:0%
+there's a colic force of attraction so
+ 
+
+ align:start position:0%
+there's a colic force of attraction so
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sodium over here and the chlorine over
+
+ align:start position:0%
+sodium over here and the chlorine over
+ 
+
+ align:start position:0%
+sodium over here and the chlorine over
+here they'll be attracted to one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another so let's start so
+
+ align:start position:0%
+another so let's start so
+ 
+
+ align:start position:0%
+another so let's start so
+sodium chlorine
+
+ align:start position:0%
+sodium chlorine
+ 
+
+ align:start position:0%
+sodium chlorine
+attaches um but there's more sodiums
+
+ align:start position:0%
+attaches um but there's more sodiums
+ 
+
+ align:start position:0%
+attaches um but there's more sodiums
+there's more chlorine so maybe another
+
+ align:start position:0%
+there's more chlorine so maybe another
+ 
+
+ align:start position:0%
+there's more chlorine so maybe another
+sodium will
+
+ align:start position:0%
+sodium will
+ 
+
+ align:start position:0%
+sodium will
+attach maybe another chlorine will
+
+ align:start position:0%
+attach maybe another chlorine will
+ 
+
+ align:start position:0%
+attach maybe another chlorine will
+attach and then this will go on and on
+
+ align:start position:0%
+attach and then this will go on and on
+ 
+
+ align:start position:0%
+attach and then this will go on and on
+and on without limit so what's the
+
+ align:start position:0%
+and on without limit so what's the
+ 
+
+ align:start position:0%
+and on without limit so what's the
+consequence of forming these gas ions
+
+ align:start position:0%
+consequence of forming these gas ions
+ 
+
+ align:start position:0%
+consequence of forming these gas ions
+these gas ions if you take gas
+
+ align:start position:0%
+these gas ions if you take gas
+ 
+
+ align:start position:0%
+these gas ions if you take gas
+ions gas ions of opposite
+
+ align:start position:0%
+ions gas ions of opposite
+ 
+
+ align:start position:0%
+ions gas ions of opposite
+charge will
+
+ align:start position:0%
+charge will
+ 
+
+ align:start position:0%
+charge will
+necessarily agglomerate without
+
+ align:start position:0%
+necessarily agglomerate without
+ 
+
+ align:start position:0%
+necessarily agglomerate without
+limit agglomerate without limit and what
+
+ align:start position:0%
+limit agglomerate without limit and what
+ 
+
+ align:start position:0%
+limit agglomerate without limit and what
+happens if I put a gazillion of these
+
+ align:start position:0%
+happens if I put a gazillion of these
+ 
+
+ align:start position:0%
+happens if I put a gazillion of these
+things together what's the what's the
+
+ align:start position:0%
+things together what's the what's the
+ 
+
+ align:start position:0%
+things together what's the what's the
+resulting form the resulting form is is
+
+ align:start position:0%
+resulting form the resulting form is is
+ 
+
+ align:start position:0%
+resulting form the resulting form is is
+a solid a solid will form so if you
+
+ align:start position:0%
+a solid a solid will form so if you
+ 
+
+ align:start position:0%
+a solid a solid will form so if you
+start with sodium vapor and chlorine gas
+
+ align:start position:0%
+start with sodium vapor and chlorine gas
+ 
+
+ align:start position:0%
+start with sodium vapor and chlorine gas
+electron transfer will occur and you
+
+ align:start position:0%
+electron transfer will occur and you
+ 
+
+ align:start position:0%
+electron transfer will occur and you
+will form a crystal of sodium chloride
+
+ align:start position:0%
+will form a crystal of sodium chloride
+ 
+
+ align:start position:0%
+will form a crystal of sodium chloride
+as a result of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this need to
+
+ align:start position:0%
+this need to
+ 
+
+ align:start position:0%
+this need to
+form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh Crystal expressed through the kulms
+
+ align:start position:0%
+uh Crystal expressed through the kulms
+ 
+
+ align:start position:0%
+uh Crystal expressed through the kulms
+law so now I want to take a look at the
+
+ align:start position:0%
+law so now I want to take a look at the
+ 
+
+ align:start position:0%
+law so now I want to take a look at the
+energetics of that let's look at the
+
+ align:start position:0%
+energetics of that let's look at the
+ 
+
+ align:start position:0%
+energetics of that let's look at the
+energetics of uh kum's law I want to
+
+ align:start position:0%
+energetics of uh kum's law I want to
+ 
+
+ align:start position:0%
+energetics of uh kum's law I want to
+talk a little bit uh sort of at a
+
+ align:start position:0%
+talk a little bit uh sort of at a
+ 
+
+ align:start position:0%
+talk a little bit uh sort of at a
+general level about modeling how would I
+
+ align:start position:0%
+general level about modeling how would I
+ 
+
+ align:start position:0%
+general level about modeling how would I
+model this system well there's levels of
+
+ align:start position:0%
+model this system well there's levels of
+ 
+
+ align:start position:0%
+model this system well there's levels of
+models and the bottom line in modeling
+
+ align:start position:0%
+models and the bottom line in modeling
+ 
+
+ align:start position:0%
+models and the bottom line in modeling
+is make it as only as complex as you
+
+ align:start position:0%
+is make it as only as complex as you
+ 
+
+ align:start position:0%
+is make it as only as complex as you
+need to don't put in extra bells and
+
+ align:start position:0%
+need to don't put in extra bells and
+ 
+
+ align:start position:0%
+need to don't put in extra bells and
+whistles if it's not necessary so for
+
+ align:start position:0%
+whistles if it's not necessary so for
+ 
+
+ align:start position:0%
+whistles if it's not necessary so for
+example if I have a sodium ion over here
+
+ align:start position:0%
+example if I have a sodium ion over here
+ 
+
+ align:start position:0%
+example if I have a sodium ion over here
+and I have a chloride ion over
+
+ align:start position:0%
+and I have a chloride ion over
+ 
+
+ align:start position:0%
+and I have a chloride ion over
+here where the distance the distance
+
+ align:start position:0%
+here where the distance the distance
+ 
+
+ align:start position:0%
+here where the distance the distance
+from Center to
+
+ align:start position:0%
+from Center to
+ 
+
+ align:start position:0%
+from Center to
+Center I'm denoting as R this is a
+
+ align:start position:0%
+Center I'm denoting as R this is a
+ 
+
+ align:start position:0%
+Center I'm denoting as R this is a
+nucleus to nucleus separation and let's
+
+ align:start position:0%
+nucleus to nucleus separation and let's
+ 
+
+ align:start position:0%
+nucleus to nucleus separation and let's
+say that sodium
+
+ align:start position:0%
+say that sodium
+ 
+
+ align:start position:0%
+say that sodium
+has a radius
+
+ align:start position:0%
+has a radius
+ 
+
+ align:start position:0%
+has a radius
+r+ and chlorine has a radius R minus
+
+ align:start position:0%
+r+ and chlorine has a radius R minus
+ 
+
+ align:start position:0%
+r+ and chlorine has a radius R minus
+when R when R is very large in
+
+ align:start position:0%
+when R when R is very large in
+ 
+
+ align:start position:0%
+when R when R is very large in
+comparison to the radi of
+
+ align:start position:0%
+comparison to the radi of
+ 
+
+ align:start position:0%
+comparison to the radi of
+the ions I don't need to draw them this
+
+ align:start position:0%
+the ions I don't need to draw them this
+ 
+
+ align:start position:0%
+the ions I don't need to draw them this
+way I can model this whole thing it's
+
+ align:start position:0%
+way I can model this whole thing it's
+ 
+
+ align:start position:0%
+way I can model this whole thing it's
+point charges I could model it as point
+
+ align:start position:0%
+point charges I could model it as point
+ 
+
+ align:start position:0%
+point charges I could model it as point
+charges this is a point that's negative
+
+ align:start position:0%
+charges this is a point that's negative
+ 
+
+ align:start position:0%
+charges this is a point that's negative
+and this is a point that's positive and
+
+ align:start position:0%
+and this is a point that's positive and
+ 
+
+ align:start position:0%
+and this is a point that's positive and
+that's all we need to do and a lot of
+
+ align:start position:0%
+that's all we need to do and a lot of
+ 
+
+ align:start position:0%
+that's all we need to do and a lot of
+the derivations you'll see in physics
+
+ align:start position:0%
+the derivations you'll see in physics
+ 
+
+ align:start position:0%
+the derivations you'll see in physics
+rely on this being able to model as
+
+ align:start position:0%
+rely on this being able to model as
+ 
+
+ align:start position:0%
+rely on this being able to model as
+point charges but what happens when
+
+ align:start position:0%
+point charges but what happens when
+ 
+
+ align:start position:0%
+point charges but what happens when
+these two start to get really close
+
+ align:start position:0%
+these two start to get really close
+ 
+
+ align:start position:0%
+these two start to get really close
+together when they start getting close
+
+ align:start position:0%
+together when they start getting close
+ 
+
+ align:start position:0%
+together when they start getting close
+together there's more
+
+ align:start position:0%
+together there's more
+ 
+
+ align:start position:0%
+together there's more
+complexity complexity takes on this form
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so now let's get a
+
+ align:start position:0%
+so now let's get a
+ 
+
+ align:start position:0%
+so now let's get a
+sodium here and the chloride ion next to
+
+ align:start position:0%
+sodium here and the chloride ion next to
+ 
+
+ align:start position:0%
+sodium here and the chloride ion next to
+it to the point where they're touching
+
+ align:start position:0%
+it to the point where they're touching
+ 
+
+ align:start position:0%
+it to the point where they're touching
+so now I'm going to show some fine
+
+ align:start position:0%
+so now I'm going to show some fine
+ 
+
+ align:start position:0%
+so now I'm going to show some fine
+structure yeah this is net
+
+ align:start position:0%
+structure yeah this is net
+ 
+
+ align:start position:0%
+structure yeah this is net
+positive the sodium is net
+
+ align:start position:0%
+positive the sodium is net
+ 
+
+ align:start position:0%
+positive the sodium is net
+positive and the
+
+ align:start position:0%
+positive and the
+ 
+
+ align:start position:0%
+positive and the
+chloride is net
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative and so there's an attractive
+
+ align:start position:0%
+negative and so there's an attractive
+ 
+
+ align:start position:0%
+negative and so there's an attractive
+force between the two of them positive
+
+ align:start position:0%
+force between the two of them positive
+ 
+
+ align:start position:0%
+force between the two of them positive
+and the negative but let's look more
+
+ align:start position:0%
+and the negative but let's look more
+ 
+
+ align:start position:0%
+and the negative but let's look more
+carefully this is uh sodium is net
+
+ align:start position:0%
+carefully this is uh sodium is net
+ 
+
+ align:start position:0%
+carefully this is uh sodium is net
+positive but I've got a nucleus with 11
+
+ align:start position:0%
+positive but I've got a nucleus with 11
+ 
+
+ align:start position:0%
+positive but I've got a nucleus with 11
+protons in it and I've got 10 electrons
+
+ align:start position:0%
+protons in it and I've got 10 electrons
+ 
+
+ align:start position:0%
+protons in it and I've got 10 electrons
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+it and here I've got 17 protons in the
+
+ align:start position:0%
+it and here I've got 17 protons in the
+ 
+
+ align:start position:0%
+it and here I've got 17 protons in the
+nucleus and I've got 18 electrons around
+
+ align:start position:0%
+nucleus and I've got 18 electrons around
+ 
+
+ align:start position:0%
+nucleus and I've got 18 electrons around
+it so when we get really close together
+
+ align:start position:0%
+it so when we get really close together
+ 
+
+ align:start position:0%
+it so when we get really close together
+granted there's a net positive negative
+
+ align:start position:0%
+granted there's a net positive negative
+ 
+
+ align:start position:0%
+granted there's a net positive negative
+charge with a colic Force of Attraction
+
+ align:start position:0%
+charge with a colic Force of Attraction
+ 
+
+ align:start position:0%
+charge with a colic Force of Attraction
+but can you see that as you get really
+
+ align:start position:0%
+but can you see that as you get really
+ 
+
+ align:start position:0%
+but can you see that as you get really
+close together the negative electronic
+
+ align:start position:0%
+close together the negative electronic
+ 
+
+ align:start position:0%
+close together the negative electronic
+clouds surrounding the two ions start to
+
+ align:start position:0%
+clouds surrounding the two ions start to
+ 
+
+ align:start position:0%
+clouds surrounding the two ions start to
+sense one another and there's a mutual
+
+ align:start position:0%
+sense one another and there's a mutual
+ 
+
+ align:start position:0%
+sense one another and there's a mutual
+repulsive Force here there's a repulsive
+
+ align:start position:0%
+repulsive Force here there's a repulsive
+ 
+
+ align:start position:0%
+repulsive Force here there's a repulsive
+Force the attractive force between ions
+
+ align:start position:0%
+Force the attractive force between ions
+ 
+
+ align:start position:0%
+Force the attractive force between ions
+of opposite charge is offset by a
+
+ align:start position:0%
+of opposite charge is offset by a
+ 
+
+ align:start position:0%
+of opposite charge is offset by a
+repulsive repulsive force due to
+
+ align:start position:0%
+repulsive repulsive force due to
+ 
+
+ align:start position:0%
+repulsive repulsive force due to
+electron cloud
+
+ align:start position:0%
+electron cloud
+ 
+
+ align:start position:0%
+electron cloud
+interactions this is the clouds are the
+
+ align:start position:0%
+interactions this is the clouds are the
+ 
+
+ align:start position:0%
+interactions this is the clouds are the
+orbitals electron cloud
+
+ align:start position:0%
+orbitals electron cloud
+ 
+
+ align:start position:0%
+orbitals electron cloud
+interactions and this is what prevents
+
+ align:start position:0%
+interactions and this is what prevents
+ 
+
+ align:start position:0%
+interactions and this is what prevents
+them from collapsing into one another
+
+ align:start position:0%
+them from collapsing into one another
+ 
+
+ align:start position:0%
+them from collapsing into one another
+they reach a certain
+
+ align:start position:0%
+they reach a certain
+ 
+
+ align:start position:0%
+they reach a certain
+equilibrium so what we're going to do
+
+ align:start position:0%
+equilibrium so what we're going to do
+ 
+
+ align:start position:0%
+equilibrium so what we're going to do
+now is look at the energetics associated
+
+ align:start position:0%
+now is look at the energetics associated
+ 
+
+ align:start position:0%
+now is look at the energetics associated
+with that that's given as follows I want
+
+ align:start position:0%
+with that that's given as follows I want
+ 
+
+ align:start position:0%
+with that that's given as follows I want
+to plot energy in this system as a
+
+ align:start position:0%
+to plot energy in this system as a
+ 
+
+ align:start position:0%
+to plot energy in this system as a
+function of interatomic
+
+ align:start position:0%
+function of interatomic
+ 
+
+ align:start position:0%
+function of interatomic
+spacing
+
+ align:start position:0%
+spacing
+ 
+
+ align:start position:0%
+spacing
+so the xaxis is inter Atomic spacing and
+
+ align:start position:0%
+so the xaxis is inter Atomic spacing and
+ 
+
+ align:start position:0%
+so the xaxis is inter Atomic spacing and
+the Y AIS is
+
+ align:start position:0%
+the Y AIS is
+ 
+
+ align:start position:0%
+the Y AIS is
+energy positive energy is
+
+ align:start position:0%
+energy positive energy is
+ 
+
+ align:start position:0%
+energy positive energy is
+repulsive and negative energy is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+attractive and I'm going to put the
+
+ align:start position:0%
+attractive and I'm going to put the
+ 
+
+ align:start position:0%
+attractive and I'm going to put the
+sodium atom at the uh at the
+
+ align:start position:0%
+sodium atom at the uh at the
+ 
+
+ align:start position:0%
+sodium atom at the uh at the
+center so here's
+
+ align:start position:0%
+center so here's
+ 
+
+ align:start position:0%
+center so here's
+sodium and I'm going to ask what happens
+
+ align:start position:0%
+sodium and I'm going to ask what happens
+ 
+
+ align:start position:0%
+sodium and I'm going to ask what happens
+when when chlorine comes in so I'll put
+
+ align:start position:0%
+when when chlorine comes in so I'll put
+ 
+
+ align:start position:0%
+when when chlorine comes in so I'll put
+chlorine over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this the chloride ion it's over here
+
+ align:start position:0%
+so this the chloride ion it's over here
+ 
+
+ align:start position:0%
+so this the chloride ion it's over here
+and we're going to look at what happens
+
+ align:start position:0%
+and we're going to look at what happens
+ 
+
+ align:start position:0%
+and we're going to look at what happens
+as the chloride ion moves from Infinity
+
+ align:start position:0%
+as the chloride ion moves from Infinity
+ 
+
+ align:start position:0%
+as the chloride ion moves from Infinity
+in towards the positive ion so let's
+
+ align:start position:0%
+in towards the positive ion so let's
+ 
+
+ align:start position:0%
+in towards the positive ion so let's
+first go with the attractive because you
+
+ align:start position:0%
+first go with the attractive because you
+ 
+
+ align:start position:0%
+first go with the attractive because you
+know this already the attractive uh
+
+ align:start position:0%
+know this already the attractive uh
+ 
+
+ align:start position:0%
+know this already the attractive uh
+energy is just a potential energy cumic
+
+ align:start position:0%
+energy is just a potential energy cumic
+ 
+
+ align:start position:0%
+energy is just a potential energy cumic
+potential that's simply q1 Q2 over 4 Pi
+
+ align:start position:0%
+potential that's simply q1 Q2 over 4 Pi
+ 
+
+ align:start position:0%
+potential that's simply q1 Q2 over 4 Pi
+Epsilon 0r and q1 is equal to the charge
+
+ align:start position:0%
+Epsilon 0r and q1 is equal to the charge
+ 
+
+ align:start position:0%
+Epsilon 0r and q1 is equal to the charge
+on sodium Q2 is the charge on chlorine
+
+ align:start position:0%
+on sodium Q2 is the charge on chlorine
+ 
+
+ align:start position:0%
+on sodium Q2 is the charge on chlorine
+so this is uh positive e on the sodium
+
+ align:start position:0%
+so this is uh positive e on the sodium
+ 
+
+ align:start position:0%
+so this is uh positive e on the sodium
+negative e on the chlorine over 4 pi
+
+ align:start position:0%
+negative e on the chlorine over 4 pi
+ 
+
+ align:start position:0%
+negative e on the chlorine over 4 pi
+epsilon0 r which is going to give us
+
+ align:start position:0%
+epsilon0 r which is going to give us
+ 
+
+ align:start position:0%
+epsilon0 r which is going to give us
+minus e^2 over 4 pi epsilon0 r and this
+
+ align:start position:0%
+minus e^2 over 4 pi epsilon0 r and this
+ 
+
+ align:start position:0%
+minus e^2 over 4 pi epsilon0 r and this
+is just a uh
+
+ align:start position:0%
+is just a uh
+ 
+
+ align:start position:0%
+is just a uh
+rectangular uh hyperbola and it's going
+
+ align:start position:0%
+rectangular uh hyperbola and it's going
+ 
+
+ align:start position:0%
+rectangular uh hyperbola and it's going
+to look like
+
+ align:start position:0%
+to look like
+ 
+
+ align:start position:0%
+to look like
+this so this is the E
+
+ align:start position:0%
+this so this is the E
+ 
+
+ align:start position:0%
+this so this is the E
+attractive and infinity there's no
+
+ align:start position:0%
+attractive and infinity there's no
+ 
+
+ align:start position:0%
+attractive and infinity there's no
+stored potential energy and it drops off
+
+ align:start position:0%
+stored potential energy and it drops off
+ 
+
+ align:start position:0%
+stored potential energy and it drops off
+more and more negative as 1 /
+
+ align:start position:0%
+more and more negative as 1 /
+ 
+
+ align:start position:0%
+more and more negative as 1 /
+R now how about this repulsion between
+
+ align:start position:0%
+R now how about this repulsion between
+ 
+
+ align:start position:0%
+R now how about this repulsion between
+electrons this is not a cumic force it's
+
+ align:start position:0%
+electrons this is not a cumic force it's
+ 
+
+ align:start position:0%
+electrons this is not a cumic force it's
+very different the repulsive term the
+
+ align:start position:0%
+very different the repulsive term the
+ 
+
+ align:start position:0%
+very different the repulsive term the
+repulsive term goes as some constant
+
+ align:start position:0%
+repulsive term goes as some constant
+ 
+
+ align:start position:0%
+repulsive term goes as some constant
+lowercase b divided by R to the n n is
+
+ align:start position:0%
+lowercase b divided by R to the n n is
+ 
+
+ align:start position:0%
+lowercase b divided by R to the n n is
+not the quantum number N is a is a power
+
+ align:start position:0%
+not the quantum number N is a is a power
+ 
+
+ align:start position:0%
+not the quantum number N is a is a power
+law factor in here and it's given by
+
+ align:start position:0%
+law factor in here and it's given by
+ 
+
+ align:start position:0%
+law factor in here and it's given by
+what is called the born exponent the
+
+ align:start position:0%
+what is called the born exponent the
+ 
+
+ align:start position:0%
+what is called the born exponent the
+born exponent and it's a very high
+
+ align:start position:0%
+born exponent and it's a very high
+ 
+
+ align:start position:0%
+born exponent and it's a very high
+number why is it a high number because
+
+ align:start position:0%
+number why is it a high number because
+ 
+
+ align:start position:0%
+number why is it a high number because
+it has to drop off precipitously when
+
+ align:start position:0%
+it has to drop off precipitously when
+ 
+
+ align:start position:0%
+it has to drop off precipitously when
+you get one over R you get a gradual
+
+ align:start position:0%
+you get one over R you get a gradual
+ 
+
+ align:start position:0%
+you get one over R you get a gradual
+fall if you get one over R squar it'll
+
+ align:start position:0%
+fall if you get one over R squar it'll
+ 
+
+ align:start position:0%
+fall if you get one over R squar it'll
+be a little steeper 1 / R to the 6 will
+
+ align:start position:0%
+be a little steeper 1 / R to the 6 will
+ 
+
+ align:start position:0%
+be a little steeper 1 / R to the 6 will
+come in and then jump off precipitously
+
+ align:start position:0%
+come in and then jump off precipitously
+ 
+
+ align:start position:0%
+come in and then jump off precipitously
+and that's what you want because the
+
+ align:start position:0%
+and that's what you want because the
+ 
+
+ align:start position:0%
+and that's what you want because the
+electron electron repulsion is only felt
+
+ align:start position:0%
+electron electron repulsion is only felt
+ 
+
+ align:start position:0%
+electron electron repulsion is only felt
+which you when you're in really really
+
+ align:start position:0%
+which you when you're in really really
+ 
+
+ align:start position:0%
+which you when you're in really really
+close and then it for all intents and
+
+ align:start position:0%
+close and then it for all intents and
+ 
+
+ align:start position:0%
+close and then it for all intents and
+purposes Falls to zero so the born
+
+ align:start position:0%
+purposes Falls to zero so the born
+ 
+
+ align:start position:0%
+purposes Falls to zero so the born
+exponent typically takes values of
+
+ align:start position:0%
+exponent typically takes values of
+ 
+
+ align:start position:0%
+exponent typically takes values of
+between 6 and 12 and B is some constant
+
+ align:start position:0%
+between 6 and 12 and B is some constant
+ 
+
+ align:start position:0%
+between 6 and 12 and B is some constant
+that we have to determine so what's uh 1
+
+ align:start position:0%
+that we have to determine so what's uh 1
+ 
+
+ align:start position:0%
+that we have to determine so what's uh 1
+/ R to the 8th going to look like on
+
+ align:start position:0%
+/ R to the 8th going to look like on
+ 
+
+ align:start position:0%
+/ R to the 8th going to look like on
+this scale it's going to look like this
+
+ align:start position:0%
+this scale it's going to look like this
+ 
+
+ align:start position:0%
+this scale it's going to look like this
+it's going to hug the x axis until it
+
+ align:start position:0%
+it's going to hug the x axis until it
+ 
+
+ align:start position:0%
+it's going to hug the x axis until it
+gets in very very close and then it's
+
+ align:start position:0%
+gets in very very close and then it's
+ 
+
+ align:start position:0%
+gets in very very close and then it's
+going to take off like a shot so this is
+
+ align:start position:0%
+going to take off like a shot so this is
+ 
+
+ align:start position:0%
+going to take off like a shot so this is
+the the repulsive energy turn and so
+
+ align:start position:0%
+the the repulsive energy turn and so
+ 
+
+ align:start position:0%
+the the repulsive energy turn and so
+what's the net energy the net energy is
+
+ align:start position:0%
+what's the net energy the net energy is
+ 
+
+ align:start position:0%
+what's the net energy the net energy is
+the sum of the repulsive and the
+
+ align:start position:0%
+the sum of the repulsive and the
+ 
+
+ align:start position:0%
+the sum of the repulsive and the
+attractive and see out at very very high
+
+ align:start position:0%
+attractive and see out at very very high
+ 
+
+ align:start position:0%
+attractive and see out at very very high
+separation ation it's essentially all
+
+ align:start position:0%
+separation ation it's essentially all
+ 
+
+ align:start position:0%
+separation ation it's essentially all
+repulsive excuse me all attractive and
+
+ align:start position:0%
+repulsive excuse me all attractive and
+ 
+
+ align:start position:0%
+repulsive excuse me all attractive and
+at very very low separations it's all
+
+ align:start position:0%
+at very very low separations it's all
+ 
+
+ align:start position:0%
+at very very low separations it's all
+repulsive and in between it goes through
+
+ align:start position:0%
+repulsive and in between it goes through
+ 
+
+ align:start position:0%
+repulsive and in between it goes through
+a minimum and this minimum here is what
+
+ align:start position:0%
+a minimum and this minimum here is what
+ 
+
+ align:start position:0%
+a minimum and this minimum here is what
+gives us the value of the inter
+
+ align:start position:0%
+gives us the value of the inter
+ 
+
+ align:start position:0%
+gives us the value of the inter
+electrode separation the inter ion
+
+ align:start position:0%
+electrode separation the inter ion
+ 
+
+ align:start position:0%
+electrode separation the inter ion
+separation and so I need to I need to
+
+ align:start position:0%
+separation and so I need to I need to
+ 
+
+ align:start position:0%
+separation and so I need to I need to
+cheat a little bit on the drawing and
+
+ align:start position:0%
+cheat a little bit on the drawing and
+ 
+
+ align:start position:0%
+cheat a little bit on the drawing and
+make sure that this minimum
+
+ align:start position:0%
+make sure that this minimum
+ 
+
+ align:start position:0%
+make sure that this minimum
+occurs right
+
+ align:start position:0%
+occurs right
+ 
+
+ align:start position:0%
+occurs right
+here okay so our minimum
+
+ align:start position:0%
+here okay so our minimum
+ 
+
+ align:start position:0%
+here okay so our minimum
+the minimum uh separation occurs when
+
+ align:start position:0%
+the minimum uh separation occurs when
+ 
+
+ align:start position:0%
+the minimum uh separation occurs when
+the energy is at its minimum and that's
+
+ align:start position:0%
+the energy is at its minimum and that's
+ 
+
+ align:start position:0%
+the energy is at its minimum and that's
+given by the balance between the
+
+ align:start position:0%
+given by the balance between the
+ 
+
+ align:start position:0%
+given by the balance between the
+attractive force of the ions offset by
+
+ align:start position:0%
+attractive force of the ions offset by
+ 
+
+ align:start position:0%
+attractive force of the ions offset by
+the repulsive force in the electronic
+
+ align:start position:0%
+the repulsive force in the electronic
+ 
+
+ align:start position:0%
+the repulsive force in the electronic
+shells and what we'll do next day is
+
+ align:start position:0%
+shells and what we'll do next day is
+ 
+
+ align:start position:0%
+shells and what we'll do next day is
+we'll uh look at the consequences of
+
+ align:start position:0%
+we'll uh look at the consequences of
+ 
+
+ align:start position:0%
+we'll uh look at the consequences of
+such an energetic uh setup and
+
+ align:start position:0%
+such an energetic uh setup and
+ 
+
+ align:start position:0%
+such an energetic uh setup and
+rationalize that when ions form
+
+ align:start position:0%
+rationalize that when ions form
+ 
+
+ align:start position:0%
+rationalize that when ions form
+by necessity we must form ionic
+
+ align:start position:0%
+by necessity we must form ionic
+ 
+
+ align:start position:0%
+by necessity we must form ionic
+crystals so I think with that I'll shift
+
+ align:start position:0%
+crystals so I think with that I'll shift
+ 
+
+ align:start position:0%
+crystals so I think with that I'll shift
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+to uh some external matters uh we've
+
+ align:start position:0%
+to uh some external matters uh we've
+ 
+
+ align:start position:0%
+to uh some external matters uh we've
+seen so far that we can have a neutral
+
+ align:start position:0%
+seen so far that we can have a neutral
+ 
+
+ align:start position:0%
+seen so far that we can have a neutral
+plus neutral sodium plus chlorine goes
+
+ align:start position:0%
+plus neutral sodium plus chlorine goes
+ 
+
+ align:start position:0%
+plus neutral sodium plus chlorine goes
+to cation plus anion that's what we've
+
+ align:start position:0%
+to cation plus anion that's what we've
+ 
+
+ align:start position:0%
+to cation plus anion that's what we've
+just been looking at and this occurs in
+
+ align:start position:0%
+just been looking at and this occurs in
+ 
+
+ align:start position:0%
+just been looking at and this occurs in
+order to achieve octet stability well
+
+ align:start position:0%
+order to achieve octet stability well
+ 
+
+ align:start position:0%
+order to achieve octet stability well
+it's possible to reverse this it's Poss
+
+ align:start position:0%
+it's possible to reverse this it's Poss
+ 
+
+ align:start position:0%
+it's possible to reverse this it's Poss
+possible to take the cation and anion
+
+ align:start position:0%
+possible to take the cation and anion
+ 
+
+ align:start position:0%
+possible to take the cation and anion
+and restore them to their neutral States
+
+ align:start position:0%
+and restore them to their neutral States
+ 
+
+ align:start position:0%
+and restore them to their neutral States
+so for example in an electrochemical
+
+ align:start position:0%
+so for example in an electrochemical
+ 
+
+ align:start position:0%
+so for example in an electrochemical
+cell it would be possible to take the
+
+ align:start position:0%
+cell it would be possible to take the
+ 
+
+ align:start position:0%
+cell it would be possible to take the
+sodium ion give back its electron and
+
+ align:start position:0%
+sodium ion give back its electron and
+ 
+
+ align:start position:0%
+sodium ion give back its electron and
+convert it into metallic sodium take the
+
+ align:start position:0%
+convert it into metallic sodium take the
+ 
+
+ align:start position:0%
+convert it into metallic sodium take the
+chloride ion remove its electron and
+
+ align:start position:0%
+chloride ion remove its electron and
+ 
+
+ align:start position:0%
+chloride ion remove its electron and
+restore chlorine gas so this is what
+
+ align:start position:0%
+restore chlorine gas so this is what
+ 
+
+ align:start position:0%
+restore chlorine gas so this is what
+goes on in electrolysis cell and it
+
+ align:start position:0%
+goes on in electrolysis cell and it
+ 
+
+ align:start position:0%
+goes on in electrolysis cell and it
+works thanks to input energy from a
+
+ align:start position:0%
+works thanks to input energy from a
+ 
+
+ align:start position:0%
+works thanks to input energy from a
+power supply shown here so that's Point
+
+ align:start position:0%
+power supply shown here so that's Point
+ 
+
+ align:start position:0%
+power supply shown here so that's Point
+number one point number two is that
+
+ align:start position:0%
+number one point number two is that
+ 
+
+ align:start position:0%
+number one point number two is that
+ionic solids at high temperatures make
+
+ align:start position:0%
+ionic solids at high temperatures make
+ 
+
+ align:start position:0%
+ionic solids at high temperatures make
+ionic liquids so one such ionic liquid
+
+ align:start position:0%
+ionic liquids so one such ionic liquid
+ 
+
+ align:start position:0%
+ionic liquids so one such ionic liquid
+is magnesium chloride magnesium chloride
+
+ align:start position:0%
+is magnesium chloride magnesium chloride
+ 
+
+ align:start position:0%
+is magnesium chloride magnesium chloride
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the raw material for the production of
+
+ align:start position:0%
+the raw material for the production of
+ 
+
+ align:start position:0%
+the raw material for the production of
+magnesium this is Magnesium it's the
+
+ align:start position:0%
+magnesium this is Magnesium it's the
+ 
+
+ align:start position:0%
+magnesium this is Magnesium it's the
+lightest of the con structural Metals
+
+ align:start position:0%
+lightest of the con structural Metals
+ 
+
+ align:start position:0%
+lightest of the con structural Metals
+it's got a density of about 1.76 at room
+
+ align:start position:0%
+it's got a density of about 1.76 at room
+ 
+
+ align:start position:0%
+it's got a density of about 1.76 at room
+temperature uh for comparison aluminum
+
+ align:start position:0%
+temperature uh for comparison aluminum
+ 
+
+ align:start position:0%
+temperature uh for comparison aluminum
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+2.7 so this is about aluminum is about
+
+ align:start position:0%
+2.7 so this is about aluminum is about
+ 
+
+ align:start position:0%
+2.7 so this is about aluminum is about
+50% denser than magnesium steel is 7.87
+
+ align:start position:0%
+50% denser than magnesium steel is 7.87
+ 
+
+ align:start position:0%
+50% denser than magnesium steel is 7.87
+so this is about a quarter the density
+
+ align:start position:0%
+so this is about a quarter the density
+ 
+
+ align:start position:0%
+so this is about a quarter the density
+of Steel so if you could make
+
+ align:start position:0%
+of Steel so if you could make
+ 
+
+ align:start position:0%
+of Steel so if you could make
+automobiles with a high magnesium
+
+ align:start position:0%
+automobiles with a high magnesium
+ 
+
+ align:start position:0%
+automobiles with a high magnesium
+content you would reduce the mass reduce
+
+ align:start position:0%
+content you would reduce the mass reduce
+ 
+
+ align:start position:0%
+content you would reduce the mass reduce
+the energy required and thereby reduce
+
+ align:start position:0%
+the energy required and thereby reduce
+ 
+
+ align:start position:0%
+the energy required and thereby reduce
+the environmental impact clearly if I
+
+ align:start position:0%
+the environmental impact clearly if I
+ 
+
+ align:start position:0%
+the environmental impact clearly if I
+did nothing more but I took every car
+
+ align:start position:0%
+did nothing more but I took every car
+ 
+
+ align:start position:0%
+did nothing more but I took every car
+doubled its fuel economy its emissions
+
+ align:start position:0%
+doubled its fuel economy its emissions
+ 
+
+ align:start position:0%
+doubled its fuel economy its emissions
+would go to 50% of what they are now no
+
+ align:start position:0%
+would go to 50% of what they are now no
+ 
+
+ align:start position:0%
+would go to 50% of what they are now no
+other changes being made so fuel economy
+
+ align:start position:0%
+other changes being made so fuel economy
+ 
+
+ align:start position:0%
+other changes being made so fuel economy
+and environmental Conservancy make a lot
+
+ align:start position:0%
+and environmental Conservancy make a lot
+ 
+
+ align:start position:0%
+and environmental Conservancy make a lot
+of sense if you care about such things
+
+ align:start position:0%
+of sense if you care about such things
+ 
+
+ align:start position:0%
+of sense if you care about such things
+of course so here's magnesium it's very
+
+ align:start position:0%
+of course so here's magnesium it's very
+ 
+
+ align:start position:0%
+of course so here's magnesium it's very
+light takes energy and this is how it's
+
+ align:start position:0%
+light takes energy and this is how it's
+ 
+
+ align:start position:0%
+light takes energy and this is how it's
+made electrolysis of of magnesium
+
+ align:start position:0%
+made electrolysis of of magnesium
+ 
+
+ align:start position:0%
+made electrolysis of of magnesium
+chloride in a Cell where the one
+
+ align:start position:0%
+chloride in a Cell where the one
+ 
+
+ align:start position:0%
+chloride in a Cell where the one
+electrode we make magnesium the other
+
+ align:start position:0%
+electrode we make magnesium the other
+ 
+
+ align:start position:0%
+electrode we make magnesium the other
+electrode we make chlorine gas and so
+
+ align:start position:0%
+electrode we make chlorine gas and so
+ 
+
+ align:start position:0%
+electrode we make chlorine gas and so
+the question becomes well what are the
+
+ align:start position:0%
+the question becomes well what are the
+ 
+
+ align:start position:0%
+the question becomes well what are the
+resources for magnesium do we have
+
+ align:start position:0%
+resources for magnesium do we have
+ 
+
+ align:start position:0%
+resources for magnesium do we have
+magnesium to do this so I went to the
+
+ align:start position:0%
+magnesium to do this so I went to the
+ 
+
+ align:start position:0%
+magnesium to do this so I went to the
+library and I looked up uh advances in
+
+ align:start position:0%
+library and I looked up uh advances in
+ 
+
+ align:start position:0%
+library and I looked up uh advances in
+molten salt chemistry volume 6 because
+
+ align:start position:0%
+molten salt chemistry volume 6 because
+ 
+
+ align:start position:0%
+molten salt chemistry volume 6 because
+there's an article in there about the
+
+ align:start position:0%
+there's an article in there about the
+ 
+
+ align:start position:0%
+there's an article in there about the
+chemistry and electrochemistry of
+
+ align:start position:0%
+chemistry and electrochemistry of
+ 
+
+ align:start position:0%
+chemistry and electrochemistry of
+magnesium production so I went I went to
+
+ align:start position:0%
+magnesium production so I went I went to
+ 
+
+ align:start position:0%
+magnesium production so I went I went to
+look up the the authoritative Source on
+
+ align:start position:0%
+look up the the authoritative Source on
+ 
+
+ align:start position:0%
+look up the the authoritative Source on
+this and uh so I uh I looked at I looked
+
+ align:start position:0%
+this and uh so I uh I looked at I looked
+ 
+
+ align:start position:0%
+this and uh so I uh I looked at I looked
+this up and and I want to give you a
+
+ align:start position:0%
+this up and and I want to give you a
+ 
+
+ align:start position:0%
+this up and and I want to give you a
+sense of of what the truth is people
+
+ align:start position:0%
+sense of of what the truth is people
+ 
+
+ align:start position:0%
+sense of of what the truth is people
+tell you that we're resource
+
+ align:start position:0%
+tell you that we're resource
+ 
+
+ align:start position:0%
+tell you that we're resource
+constrainted that we're running out of
+
+ align:start position:0%
+constrainted that we're running out of
+ 
+
+ align:start position:0%
+constrainted that we're running out of
+resources well think about this where
+
+ align:start position:0%
+resources well think about this where
+ 
+
+ align:start position:0%
+resources well think about this where
+are the data a cubic kilometer of
+
+ align:start position:0%
+are the data a cubic kilometer of
+ 
+
+ align:start position:0%
+are the data a cubic kilometer of
+seawater that's a go into the ocean and
+
+ align:start position:0%
+seawater that's a go into the ocean and
+ 
+
+ align:start position:0%
+seawater that's a go into the ocean and
+imagine a box 1 kilometer by 1 kilm by 1
+
+ align:start position:0%
+imagine a box 1 kilometer by 1 kilm by 1
+ 
+
+ align:start position:0%
+imagine a box 1 kilometer by 1 kilm by 1
+kilm that's a cubic kilometer contains a
+
+ align:start position:0%
+kilm that's a cubic kilometer contains a
+ 
+
+ align:start position:0%
+kilm that's a cubic kilometer contains a
+million tons of magnesium a million tons
+
+ align:start position:0%
+million tons of magnesium a million tons
+ 
+
+ align:start position:0%
+million tons of magnesium a million tons
+which is more than has ever been
+
+ align:start position:0%
+which is more than has ever been
+ 
+
+ align:start position:0%
+which is more than has ever been
+produced in one year by all the
+
+ align:start position:0%
+produced in one year by all the
+ 
+
+ align:start position:0%
+produced in one year by all the
+Magnesium plants in the world annual
+
+ align:start position:0%
+Magnesium plants in the world annual
+ 
+
+ align:start position:0%
+Magnesium plants in the world annual
+production of magnesium is about 600,000
+
+ align:start position:0%
+production of magnesium is about 600,000
+ 
+
+ align:start position:0%
+production of magnesium is about 600,000
+tons per year you get that out of 1
+
+ align:start position:0%
+tons per year you get that out of 1
+ 
+
+ align:start position:0%
+tons per year you get that out of 1
+cubic kilometer of
+
+ align:start position:0%
+cubic kilometer of
+ 
+
+ align:start position:0%
+cubic kilometer of
+seawater and seawat contains only 3.7%
+
+ align:start position:0%
+seawater and seawat contains only 3.7%
+ 
+
+ align:start position:0%
+seawater and seawat contains only 3.7%
+of the total magnesium present in the
+
+ align:start position:0%
+of the total magnesium present in the
+ 
+
+ align:start position:0%
+of the total magnesium present in the
+Earth's
+
+ align:start position:0%
+Earth's
+ 
+
+ align:start position:0%
+Earth's
+crust so clearly magnesium resource are
+
+ align:start position:0%
+crust so clearly magnesium resource are
+ 
+
+ align:start position:0%
+crust so clearly magnesium resource are
+ubiquitous and virtually inexhaustible
+
+ align:start position:0%
+ubiquitous and virtually inexhaustible
+ 
+
+ align:start position:0%
+ubiquitous and virtually inexhaustible
+there's lots of
+
+ align:start position:0%
+there's lots of
+ 
+
+ align:start position:0%
+there's lots of
+magnesium there's lots of magnesium so
+
+ align:start position:0%
+magnesium there's lots of magnesium so
+ 
+
+ align:start position:0%
+magnesium there's lots of magnesium so
+if magnesium is so
+
+ align:start position:0%
+if magnesium is so
+ 
+
+ align:start position:0%
+if magnesium is so
+abundant why is it so expensive steel is
+
+ align:start position:0%
+abundant why is it so expensive steel is
+ 
+
+ align:start position:0%
+abundant why is it so expensive steel is
+about 10 cents a pound aluminum is about
+
+ align:start position:0%
+about 10 cents a pound aluminum is about
+ 
+
+ align:start position:0%
+about 10 cents a pound aluminum is about
+70 cents a pound and magnesium is over a
+
+ align:start position:0%
+70 cents a pound and magnesium is over a
+ 
+
+ align:start position:0%
+70 cents a pound and magnesium is over a
+dollar a pound why is it so expensive
+
+ align:start position:0%
+dollar a pound why is it so expensive
+ 
+
+ align:start position:0%
+dollar a pound why is it so expensive
+it's not because of scarcity it's
+
+ align:start position:0%
+it's not because of scarcity it's
+ 
+
+ align:start position:0%
+it's not because of scarcity it's
+expensive because the process by which
+
+ align:start position:0%
+expensive because the process by which
+ 
+
+ align:start position:0%
+expensive because the process by which
+we produce it is energy intensive and
+
+ align:start position:0%
+we produce it is energy intensive and
+ 
+
+ align:start position:0%
+we produce it is energy intensive and
+resource intensive so if we want to get
+
+ align:start position:0%
+resource intensive so if we want to get
+ 
+
+ align:start position:0%
+resource intensive so if we want to get
+more magnesium into the marketplace at
+
+ align:start position:0%
+more magnesium into the marketplace at
+ 
+
+ align:start position:0%
+more magnesium into the marketplace at
+an affordable price not by government
+
+ align:start position:0%
+an affordable price not by government
+ 
+
+ align:start position:0%
+an affordable price not by government
+edict what do we have to do we have to
+
+ align:start position:0%
+edict what do we have to do we have to
+ 
+
+ align:start position:0%
+edict what do we have to do we have to
+invent a process a chemical extraction
+
+ align:start position:0%
+invent a process a chemical extraction
+ 
+
+ align:start position:0%
+invent a process a chemical extraction
+process that will make the production of
+
+ align:start position:0%
+process that will make the production of
+ 
+
+ align:start position:0%
+process that will make the production of
+magnesium cheaper so that we will have
+
+ align:start position:0%
+magnesium cheaper so that we will have
+ 
+
+ align:start position:0%
+magnesium cheaper so that we will have
+the opportunity to Avail ourselves of
+
+ align:start position:0%
+the opportunity to Avail ourselves of
+ 
+
+ align:start position:0%
+the opportunity to Avail ourselves of
+energy efficient materials and so maybe
+
+ align:start position:0%
+energy efficient materials and so maybe
+ 
+
+ align:start position:0%
+energy efficient materials and so maybe
+somebody in this room
+
+ align:start position:0%
+somebody in this room
+ 
+
+ align:start position:0%
+somebody in this room
+working with me will invent such a
+
+ align:start position:0%
+working with me will invent such a
+ 
+
+ align:start position:0%
+working with me will invent such a
+process all right I'll see you on Friday
\ No newline at end of file
diff --git a/WacNWdXhvVM.txt b/WacNWdXhvVM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c459c94a034a8e8322f5a3bf3a842ecef1508865
--- /dev/null
+++ b/WacNWdXhvVM.txt
@@ -0,0 +1,995 @@
+align:start position:0%
+ 
+today's lecture is a story of Moneyball
+
+ align:start position:0%
+today's lecture is a story of Moneyball
+ 
+
+ align:start position:0%
+today's lecture is a story of Moneyball
+a book my Michael Lewis in 2003 and a
+
+ align:start position:0%
+a book my Michael Lewis in 2003 and a
+ 
+
+ align:start position:0%
+a book my Michael Lewis in 2003 and a
+movie in 2011 starring Brad Pitt
+
+ align:start position:0%
+movie in 2011 starring Brad Pitt
+ 
+
+ align:start position:0%
+movie in 2011 starring Brad Pitt
+Moneyball discusses how Sports analytics
+
+ align:start position:0%
+Moneyball discusses how Sports analytics
+ 
+
+ align:start position:0%
+Moneyball discusses how Sports analytics
+changed baseball Moneyball tells the
+
+ align:start position:0%
+changed baseball Moneyball tells the
+ 
+
+ align:start position:0%
+changed baseball Moneyball tells the
+story of the oakland a's the a's is a
+
+ align:start position:0%
+story of the oakland a's the a's is a
+ 
+
+ align:start position:0%
+story of the oakland a's the a's is a
+team near san francisco california they
+
+ align:start position:0%
+team near san francisco california they
+ 
+
+ align:start position:0%
+team near san francisco california they
+were once a rich team but the team was
+
+ align:start position:0%
+were once a rich team but the team was
+ 
+
+ align:start position:0%
+were once a rich team but the team was
+purchased in 1995 by owners who enforce
+
+ align:start position:0%
+purchased in 1995 by owners who enforce
+ 
+
+ align:start position:0%
+purchased in 1995 by owners who enforce
+strict budget cuts despite this they
+
+ align:start position:0%
+strict budget cuts despite this they
+ 
+
+ align:start position:0%
+strict budget cuts despite this they
+were improving over the years 1997 to
+
+ align:start position:0%
+were improving over the years 1997 to
+ 
+
+ align:start position:0%
+were improving over the years 1997 to
+2001 in the table you can see that the
+
+ align:start position:0%
+2001 in the table you can see that the
+ 
+
+ align:start position:0%
+2001 in the table you can see that the
+percentage of wins was increasing in
+
+ align:start position:0%
+percentage of wins was increasing in
+ 
+
+ align:start position:0%
+percentage of wins was increasing in
+each and every year this was puzzling
+
+ align:start position:0%
+each and every year this was puzzling
+ 
+
+ align:start position:0%
+each and every year this was puzzling
+and many baseball experts thought it was
+
+ align:start position:0%
+and many baseball experts thought it was
+ 
+
+ align:start position:0%
+and many baseball experts thought it was
+just luck in 2002 the A's lost three key
+
+ align:start position:0%
+just luck in 2002 the A's lost three key
+ 
+
+ align:start position:0%
+just luck in 2002 the A's lost three key
+players the key question could they
+
+ align:start position:0%
+players the key question could they
+ 
+
+ align:start position:0%
+players the key question could they
+continue winning without them so what is
+
+ align:start position:0%
+continue winning without them so what is
+ 
+
+ align:start position:0%
+continue winning without them so what is
+the key problem let us discuss the graph
+
+ align:start position:0%
+the key problem let us discuss the graph
+ 
+
+ align:start position:0%
+the key problem let us discuss the graph
+on the left of the screen the horizontal
+
+ align:start position:0%
+on the left of the screen the horizontal
+ 
+
+ align:start position:0%
+on the left of the screen the horizontal
+axis so the average payroll during the
+
+ align:start position:0%
+axis so the average payroll during the
+ 
+
+ align:start position:0%
+axis so the average payroll during the
+years 1998 to 2001 the vertical axis
+
+ align:start position:0%
+years 1998 to 2001 the vertical axis
+ 
+
+ align:start position:0%
+years 1998 to 2001 the vertical axis
+shows the average yearly wins over the
+
+ align:start position:0%
+shows the average yearly wins over the
+ 
+
+ align:start position:0%
+shows the average yearly wins over the
+same years so let's look at some of the
+
+ align:start position:0%
+same years so let's look at some of the
+ 
+
+ align:start position:0%
+same years so let's look at some of the
+teams in this graph so which one is this
+
+ align:start position:0%
+teams in this graph so which one is this
+ 
+
+ align:start position:0%
+teams in this graph so which one is this
+team this is a team that won about a
+
+ align:start position:0%
+team this is a team that won about a
+ 
+
+ align:start position:0%
+team this is a team that won about a
+hundred games and spent roughly ninety
+
+ align:start position:0%
+hundred games and spent roughly ninety
+ 
+
+ align:start position:0%
+hundred games and spent roughly ninety
+million during this period so this is
+
+ align:start position:0%
+million during this period so this is
+ 
+
+ align:start position:0%
+million during this period so this is
+the New York Yankees let's look at this
+
+ align:start position:0%
+the New York Yankees let's look at this
+ 
+
+ align:start position:0%
+the New York Yankees let's look at this
+team this team spent about eighty
+
+ align:start position:0%
+team this team spent about eighty
+ 
+
+ align:start position:0%
+team this team spent about eighty
+million and and won about 90 games this
+
+ align:start position:0%
+million and and won about 90 games this
+ 
+
+ align:start position:0%
+million and and won about 90 games this
+is the Red Sox
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where are the oakland a's the a's are
+
+ align:start position:0%
+where are the oakland a's the a's are
+ 
+
+ align:start position:0%
+where are the oakland a's the a's are
+here they won about 90 games and they
+
+ align:start position:0%
+here they won about 90 games and they
+ 
+
+ align:start position:0%
+here they won about 90 games and they
+spend under 30 million if you compare it
+
+ align:start position:0%
+spend under 30 million if you compare it
+ 
+
+ align:start position:0%
+spend under 30 million if you compare it
+with the Red Sox they won about the same
+
+ align:start position:0%
+with the Red Sox they won about the same
+ 
+
+ align:start position:0%
+with the Red Sox they won about the same
+number of games during this period but
+
+ align:start position:0%
+number of games during this period but
+ 
+
+ align:start position:0%
+number of games during this period but
+the Red Sox spent about 50 million more
+
+ align:start position:0%
+the Red Sox spent about 50 million more
+ 
+
+ align:start position:0%
+the Red Sox spent about 50 million more
+per year than the A's clearly rich teams
+
+ align:start position:0%
+per year than the A's clearly rich teams
+ 
+
+ align:start position:0%
+per year than the A's clearly rich teams
+like the Yankees and the Red Sox can
+
+ align:start position:0%
+like the Yankees and the Red Sox can
+ 
+
+ align:start position:0%
+like the Yankees and the Red Sox can
+afford the all-star players but please
+
+ align:start position:0%
+afford the all-star players but please
+ 
+
+ align:start position:0%
+afford the all-star players but please
+observe how efficient the A's are as I
+
+ align:start position:0%
+observe how efficient the A's are as I
+ 
+
+ align:start position:0%
+observe how efficient the A's are as I
+mentioned they won 90 games and their
+
+ align:start position:0%
+mentioned they won 90 games and their
+ 
+
+ align:start position:0%
+mentioned they won 90 games and their
+payroll was under 30 million compared to
+
+ align:start position:0%
+payroll was under 30 million compared to
+ 
+
+ align:start position:0%
+payroll was under 30 million compared to
+the Yankees who spent almost three to
+
+ align:start position:0%
+the Yankees who spent almost three to
+ 
+
+ align:start position:0%
+the Yankees who spent almost three to
+four times as much and they won of
+
+ align:start position:0%
+four times as much and they won of
+ 
+
+ align:start position:0%
+four times as much and they won of
+course more than more games but not that
+
+ align:start position:0%
+course more than more games but not that
+ 
+
+ align:start position:0%
+course more than more games but not that
+much more so rich teams as I mentioned
+
+ align:start position:0%
+much more so rich teams as I mentioned
+ 
+
+ align:start position:0%
+much more so rich teams as I mentioned
+have three to four times the payroll of
+
+ align:start position:0%
+have three to four times the payroll of
+ 
+
+ align:start position:0%
+have three to four times the payroll of
+poor teams yet the aides made the
+
+ align:start position:0%
+poor teams yet the aides made the
+ 
+
+ align:start position:0%
+poor teams yet the aides made the
+payroll every year made the play of
+
+ align:start position:0%
+payroll every year made the play of
+ 
+
+ align:start position:0%
+payroll every year made the play of
+cement every year how do they do this
+
+ align:start position:0%
+cement every year how do they do this
+ 
+
+ align:start position:0%
+cement every year how do they do this
+and what we will see in this lecture is
+
+ align:start position:0%
+and what we will see in this lecture is
+ 
+
+ align:start position:0%
+and what we will see in this lecture is
+that by taking a quantitative approach
+
+ align:start position:0%
+that by taking a quantitative approach
+ 
+
+ align:start position:0%
+that by taking a quantitative approach
+an analytics approach they were able to
+
+ align:start position:0%
+an analytics approach they were able to
+ 
+
+ align:start position:0%
+an analytics approach they were able to
+find undervalued players and form teams
+
+ align:start position:0%
+find undervalued players and form teams
+ 
+
+ align:start position:0%
+find undervalued players and form teams
+that were very efficient so V Hayes
+
+ align:start position:0%
+that were very efficient so V Hayes
+ 
+
+ align:start position:0%
+that were very efficient so V Hayes
+started using a different method to
+
+ align:start position:0%
+started using a different method to
+ 
+
+ align:start position:0%
+started using a different method to
+select players the traditional way of
+
+ align:start position:0%
+select players the traditional way of
+ 
+
+ align:start position:0%
+select players the traditional way of
+selecting players was through scouting
+
+ align:start position:0%
+selecting players was through scouting
+ 
+
+ align:start position:0%
+selecting players was through scouting
+Scouts would watch high school and
+
+ align:start position:0%
+Scouts would watch high school and
+ 
+
+ align:start position:0%
+Scouts would watch high school and
+college players and they would report
+
+ align:start position:0%
+college players and they would report
+ 
+
+ align:start position:0%
+college players and they would report
+back about their skills especially
+
+ align:start position:0%
+back about their skills especially
+ 
+
+ align:start position:0%
+back about their skills especially
+discussing their speed and their
+
+ align:start position:0%
+discussing their speed and their
+ 
+
+ align:start position:0%
+discussing their speed and their
+athletic build the ACE however selected
+
+ align:start position:0%
+athletic build the ACE however selected
+ 
+
+ align:start position:0%
+athletic build the ACE however selected
+players based on their statistics not on
+
+ align:start position:0%
+players based on their statistics not on
+ 
+
+ align:start position:0%
+players based on their statistics not on
+their looks
+
+ align:start position:0%
+their looks
+ 
+
+ align:start position:0%
+their looks
+the following are quotes from the book
+
+ align:start position:0%
+the following are quotes from the book
+ 
+
+ align:start position:0%
+the following are quotes from the book
+Moneyball the statistics enable you to
+
+ align:start position:0%
+Moneyball the statistics enable you to
+ 
+
+ align:start position:0%
+Moneyball the statistics enable you to
+find your way past all sorts of site
+
+ align:start position:0%
+find your way past all sorts of site
+ 
+
+ align:start position:0%
+find your way past all sorts of site
+based scouting prejudiced in a direct
+
+ align:start position:0%
+based scouting prejudiced in a direct
+ 
+
+ align:start position:0%
+based scouting prejudiced in a direct
+quote from Billy Beane the manager
+
+ align:start position:0%
+quote from Billy Beane the manager
+ 
+
+ align:start position:0%
+quote from Billy Beane the manager
+of the Oakland A's in the architect of
+
+ align:start position:0%
+of the Oakland A's in the architect of
+ 
+
+ align:start position:0%
+of the Oakland A's in the architect of
+this approach with we are not selling
+
+ align:start position:0%
+this approach with we are not selling
+ 
+
+ align:start position:0%
+this approach with we are not selling
+jeans here let us construct contrast how
+
+ align:start position:0%
+jeans here let us construct contrast how
+ 
+
+ align:start position:0%
+jeans here let us construct contrast how
+the aides selected players versus the
+
+ align:start position:0%
+the aides selected players versus the
+ 
+
+ align:start position:0%
+the aides selected players versus the
+Yankees on the left you see a catcher
+
+ align:start position:0%
+Yankees on the left you see a catcher
+ 
+
+ align:start position:0%
+Yankees on the left you see a catcher
+Scott Hatteberg that he a selected who
+
+ align:start position:0%
+Scott Hatteberg that he a selected who
+ 
+
+ align:start position:0%
+Scott Hatteberg that he a selected who
+would not throw particularly well but
+
+ align:start position:0%
+would not throw particularly well but
+ 
+
+ align:start position:0%
+would not throw particularly well but
+got on base a lot on the right you see
+
+ align:start position:0%
+got on base a lot on the right you see
+ 
+
+ align:start position:0%
+got on base a lot on the right you see
+Derek Jeter one of the top players in
+
+ align:start position:0%
+Derek Jeter one of the top players in
+ 
+
+ align:start position:0%
+Derek Jeter one of the top players in
+baseball a consistent sore top shortstop
+
+ align:start position:0%
+baseball a consistent sore top shortstop
+ 
+
+ align:start position:0%
+baseball a consistent sore top shortstop
+and the leader in hits and stolen bases
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let us look into pictures on the left
+
+ align:start position:0%
+let us look into pictures on the left
+ 
+
+ align:start position:0%
+let us look into pictures on the left
+you see Chad Bradford a pitcher for the
+
+ align:start position:0%
+you see Chad Bradford a pitcher for the
+ 
+
+ align:start position:0%
+you see Chad Bradford a pitcher for the
+A's a submariner who used the
+
+ align:start position:0%
+A's a submariner who used the
+ 
+
+ align:start position:0%
+A's a submariner who used the
+non-conventional delivery and slow speed
+
+ align:start position:0%
+non-conventional delivery and slow speed
+ 
+
+ align:start position:0%
+non-conventional delivery and slow speed
+on the right you see Roger Clemens one
+
+ align:start position:0%
+on the right you see Roger Clemens one
+ 
+
+ align:start position:0%
+on the right you see Roger Clemens one
+of the best pitchers in the game that
+
+ align:start position:0%
+of the best pitchers in the game that
+ 
+
+ align:start position:0%
+of the best pitchers in the game that
+use conventional delivery and fast speed
+
+ align:start position:0%
+use conventional delivery and fast speed
+ 
+
+ align:start position:0%
+use conventional delivery and fast speed
+Billy Beane was the manager of the
+
+ align:start position:0%
+Billy Beane was the manager of the
+ 
+
+ align:start position:0%
+Billy Beane was the manager of the
+Oakland A's since 1997 he played major
+
+ align:start position:0%
+Oakland A's since 1997 he played major
+ 
+
+ align:start position:0%
+Oakland A's since 1997 he played major
+league baseball but he was not a great
+
+ align:start position:0%
+league baseball but he was not a great
+ 
+
+ align:start position:0%
+league baseball but he was not a great
+player in fact he sees himself as a
+
+ align:start position:0%
+player in fact he sees himself as a
+ 
+
+ align:start position:0%
+player in fact he sees himself as a
+typical scouting error in the 1980s and
+
+ align:start position:0%
+typical scouting error in the 1980s and
+ 
+
+ align:start position:0%
+typical scouting error in the 1980s and
+1990s analysts were hired by baseball
+
+ align:start position:0%
+1990s analysts were hired by baseball
+ 
+
+ align:start position:0%
+1990s analysts were hired by baseball
+teams but none of them had enough power
+
+ align:start position:0%
+teams but none of them had enough power
+ 
+
+ align:start position:0%
+teams but none of them had enough power
+to affect anything important as I
+
+ align:start position:0%
+to affect anything important as I
+ 
+
+ align:start position:0%
+to affect anything important as I
+mentioned Billy Beane became the general
+
+ align:start position:0%
+mentioned Billy Beane became the general
+ 
+
+ align:start position:0%
+mentioned Billy Beane became the general
+manager of the Oakland A's in 1997 and
+
+ align:start position:0%
+manager of the Oakland A's in 1997 and
+ 
+
+ align:start position:0%
+manager of the Oakland A's in 1997 and
+he was given another small budget he
+
+ align:start position:0%
+he was given another small budget he
+ 
+
+ align:start position:0%
+he was given another small budget he
+understood the importance of analytics
+
+ align:start position:0%
+understood the importance of analytics
+ 
+
+ align:start position:0%
+understood the importance of analytics
+but during this period most general
+
+ align:start position:0%
+but during this period most general
+ 
+
+ align:start position:0%
+but during this period most general
+managers knew little about statistics
+
+ align:start position:0%
+managers knew little about statistics
+ 
+
+ align:start position:0%
+managers knew little about statistics
+and based decisions primarily on
+
+ align:start position:0%
+and based decisions primarily on
+ 
+
+ align:start position:0%
+and based decisions primarily on
+feelings
+
+ align:start position:0%
+feelings
+ 
+
+ align:start position:0%
+feelings
+in contrast Billy Beane hired Paul
+
+ align:start position:0%
+in contrast Billy Beane hired Paul
+ 
+
+ align:start position:0%
+in contrast Billy Beane hired Paul
+DePodesta a - gradual as his assistant
+
+ align:start position:0%
+DePodesta a - gradual as his assistant
+ 
+
+ align:start position:0%
+DePodesta a - gradual as his assistant
+furthermore he was not afraid to
+
+ align:start position:0%
+furthermore he was not afraid to
+ 
+
+ align:start position:0%
+furthermore he was not afraid to
+eliminate Scouts managers and players if
+
+ align:start position:0%
+eliminate Scouts managers and players if
+ 
+
+ align:start position:0%
+eliminate Scouts managers and players if
+the quantity
+
+ align:start position:0%
+the quantity
+ 
+
+ align:start position:0%
+the quantity
+approach suggested decisions that were
+
+ align:start position:0%
+approach suggested decisions that were
+ 
+
+ align:start position:0%
+approach suggested decisions that were
+different than the scouts or the
+
+ align:start position:0%
+different than the scouts or the
+ 
+
+ align:start position:0%
+different than the scouts or the
+managers or the players suggested an
+
+ align:start position:0%
+managers or the players suggested an
+ 
+
+ align:start position:0%
+managers or the players suggested an
+important player and an important player
+
+ align:start position:0%
+important player and an important player
+ 
+
+ align:start position:0%
+important player and an important player
+in this in a story in spaulder Podesta a
+
+ align:start position:0%
+in this in a story in spaulder Podesta a
+ 
+
+ align:start position:0%
+in this in a story in spaulder Podesta a
+Harvard graduate Paul spent a lot of
+
+ align:start position:0%
+Harvard graduate Paul spent a lot of
+ 
+
+ align:start position:0%
+Harvard graduate Paul spent a lot of
+time looking at the data the analysis
+
+ align:start position:0%
+time looking at the data the analysis
+ 
+
+ align:start position:0%
+time looking at the data the analysis
+suggested that some skills were
+
+ align:start position:0%
+suggested that some skills were
+ 
+
+ align:start position:0%
+suggested that some skills were
+undervalued and some skills were
+
+ align:start position:0%
+undervalued and some skills were
+ 
+
+ align:start position:0%
+undervalued and some skills were
+overvalued the key premise of the
+
+ align:start position:0%
+overvalued the key premise of the
+ 
+
+ align:start position:0%
+overvalued the key premise of the
+Oakland A's is that if they could detect
+
+ align:start position:0%
+Oakland A's is that if they could detect
+ 
+
+ align:start position:0%
+Oakland A's is that if they could detect
+the undervalued skills they could find
+
+ align:start position:0%
+the undervalued skills they could find
+ 
+
+ align:start position:0%
+the undervalued skills they could find
+players at a bargain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/WsEPhUu8kKU.txt b/WsEPhUu8kKU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ae5a63c76c179895d7aceabc0aa4f6b53dbb442
--- /dev/null
+++ b/WsEPhUu8kKU.txt
@@ -0,0 +1,8371 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit mitop courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu we make a transition now to
+
+ align:start position:0%
+ocw.mit.edu we make a transition now to
+ 
+
+ align:start position:0%
+ocw.mit.edu we make a transition now to
+the final segment of our course in which
+
+ align:start position:0%
+the final segment of our course in which
+ 
+
+ align:start position:0%
+the final segment of our course in which
+we uh and and and this transition always
+
+ align:start position:0%
+we uh and and and this transition always
+ 
+
+ align:start position:0%
+we uh and and and this transition always
+induces uh a a kind of guilt in me a
+
+ align:start position:0%
+induces uh a a kind of guilt in me a
+ 
+
+ align:start position:0%
+induces uh a a kind of guilt in me a
+kind of deep ambivalence and
+
+ align:start position:0%
+kind of deep ambivalence and
+ 
+
+ align:start position:0%
+kind of deep ambivalence and
+disappointment and awareness of the
+
+ align:start position:0%
+disappointment and awareness of the
+ 
+
+ align:start position:0%
+disappointment and awareness of the
+simplifications and reductions that are
+
+ align:start position:0%
+simplifications and reductions that are
+ 
+
+ align:start position:0%
+simplifications and reductions that are
+embedded in all syllabi and in all
+
+ align:start position:0%
+embedded in all syllabi and in all
+ 
+
+ align:start position:0%
+embedded in all syllabi and in all
+curricula and it's a good opportunity
+
+ align:start position:0%
+curricula and it's a good opportunity
+ 
+
+ align:start position:0%
+curricula and it's a good opportunity
+for me to remind you that even the
+
+ align:start position:0%
+for me to remind you that even the
+ 
+
+ align:start position:0%
+for me to remind you that even the
+primary emphasis of our course which is
+
+ align:start position:0%
+primary emphasis of our course which is
+ 
+
+ align:start position:0%
+primary emphasis of our course which is
+on certain forms of American Film is
+
+ align:start position:0%
+on certain forms of American Film is
+ 
+
+ align:start position:0%
+on certain forms of American Film is
+itself highly selective and simplified
+
+ align:start position:0%
+itself highly selective and simplified
+ 
+
+ align:start position:0%
+itself highly selective and simplified
+and reductive as you as told you they
+
+ align:start position:0%
+and reductive as you as told you they
+ 
+
+ align:start position:0%
+and reductive as you as told you they
+were in the Hollywood System they were
+
+ align:start position:0%
+were in the Hollywood System they were
+ 
+
+ align:start position:0%
+were in the Hollywood System they were
+making 500 films a year think of the
+
+ align:start position:0%
+making 500 films a year think of the
+ 
+
+ align:start position:0%
+making 500 films a year think of the
+small number we've actually seen right
+
+ align:start position:0%
+small number we've actually seen right
+ 
+
+ align:start position:0%
+small number we've actually seen right
+it's the tinest sampling of what's
+
+ align:start position:0%
+it's the tinest sampling of what's
+ 
+
+ align:start position:0%
+it's the tinest sampling of what's
+actually available and what I've tried
+
+ align:start position:0%
+actually available and what I've tried
+ 
+
+ align:start position:0%
+actually available and what I've tried
+to do is give you a kind of taste of
+
+ align:start position:0%
+to do is give you a kind of taste of
+ 
+
+ align:start position:0%
+to do is give you a kind of taste of
+what that uh U uh phenomenon of the
+
+ align:start position:0%
+what that uh U uh phenomenon of the
+ 
+
+ align:start position:0%
+what that uh U uh phenomenon of the
+Hollywood film was like without trying
+
+ align:start position:0%
+Hollywood film was like without trying
+ 
+
+ align:start position:0%
+Hollywood film was like without trying
+to pretend at all that I was coming
+
+ align:start position:0%
+to pretend at all that I was coming
+ 
+
+ align:start position:0%
+to pretend at all that I was coming
+anything close to not not just couldn't
+
+ align:start position:0%
+anything close to not not just couldn't
+ 
+
+ align:start position:0%
+anything close to not not just couldn't
+be exhaustive we couldn't even be uh uh
+
+ align:start position:0%
+be exhaustive we couldn't even be uh uh
+ 
+
+ align:start position:0%
+be exhaustive we couldn't even be uh uh
+extensive or or mildly serious ious
+
+ align:start position:0%
+extensive or or mildly serious ious
+ 
+
+ align:start position:0%
+extensive or or mildly serious ious
+about about trying to do justice to the
+
+ align:start position:0%
+about about trying to do justice to the
+ 
+
+ align:start position:0%
+about about trying to do justice to the
+complexity of that body of material uh
+
+ align:start position:0%
+complexity of that body of material uh
+ 
+
+ align:start position:0%
+complexity of that body of material uh
+and that's even truer of course in this
+
+ align:start position:0%
+and that's even truer of course in this
+ 
+
+ align:start position:0%
+and that's even truer of course in this
+moment uh in this Final in these final
+
+ align:start position:0%
+moment uh in this Final in these final
+ 
+
+ align:start position:0%
+moment uh in this Final in these final
+moments of the course where I try to do
+
+ align:start position:0%
+moments of the course where I try to do
+ 
+
+ align:start position:0%
+moments of the course where I try to do
+sort of a a brief acknowledgement of the
+
+ align:start position:0%
+sort of a a brief acknowledgement of the
+ 
+
+ align:start position:0%
+sort of a a brief acknowledgement of the
+fact that there are profound and
+
+ align:start position:0%
+fact that there are profound and
+ 
+
+ align:start position:0%
+fact that there are profound and
+Powerful traditions of Cinema outside
+
+ align:start position:0%
+Powerful traditions of Cinema outside
+ 
+
+ align:start position:0%
+Powerful traditions of Cinema outside
+the United States in fact some more
+
+ align:start position:0%
+the United States in fact some more
+ 
+
+ align:start position:0%
+the United States in fact some more
+profound or at least as profound and
+
+ align:start position:0%
+profound or at least as profound and
+ 
+
+ align:start position:0%
+profound or at least as profound and
+some more powerful on many people would
+
+ align:start position:0%
+some more powerful on many people would
+ 
+
+ align:start position:0%
+some more powerful on many people would
+say than than the achievement of
+
+ align:start position:0%
+say than than the achievement of
+ 
+
+ align:start position:0%
+say than than the achievement of
+American Cinema the achievements of
+
+ align:start position:0%
+American Cinema the achievements of
+ 
+
+ align:start position:0%
+American Cinema the achievements of
+American Cinema and perhaps the
+
+ align:start position:0%
+American Cinema and perhaps the
+ 
+
+ align:start position:0%
+American Cinema and perhaps the
+strongest example of that the most
+
+ align:start position:0%
+strongest example of that the most
+ 
+
+ align:start position:0%
+strongest example of that the most
+dramatic example of that is French film
+
+ align:start position:0%
+dramatic example of that is French film
+ 
+
+ align:start position:0%
+dramatic example of that is French film
+it has a kind of parallel history at
+
+ align:start position:0%
+it has a kind of parallel history at
+ 
+
+ align:start position:0%
+it has a kind of parallel history at
+virtually every stage of the history of
+
+ align:start position:0%
+virtually every stage of the history of
+ 
+
+ align:start position:0%
+virtually every stage of the history of
+French of American Film you can find a
+
+ align:start position:0%
+French of American Film you can find a
+ 
+
+ align:start position:0%
+French of American Film you can find a
+kind of counterpart story in French film
+
+ align:start position:0%
+kind of counterpart story in French film
+ 
+
+ align:start position:0%
+kind of counterpart story in French film
+as if it's almost as it and in fact
+
+ align:start position:0%
+as if it's almost as it and in fact
+ 
+
+ align:start position:0%
+as if it's almost as it and in fact
+there have been historians who have
+
+ align:start position:0%
+there have been historians who have
+ 
+
+ align:start position:0%
+there have been historians who have
+tried to argue about the priority who
+
+ align:start position:0%
+tried to argue about the priority who
+ 
+
+ align:start position:0%
+tried to argue about the priority who
+invented film were were the French more
+
+ align:start position:0%
+invented film were were the French more
+ 
+
+ align:start position:0%
+invented film were were the French more
+advanced than the Americans uh who first
+
+ align:start position:0%
+advanced than the Americans uh who first
+ 
+
+ align:start position:0%
+advanced than the Americans uh who first
+developed forms of serial movies who
+
+ align:start position:0%
+developed forms of serial movies who
+ 
+
+ align:start position:0%
+developed forms of serial movies who
+first developed forms of of of of the of
+
+ align:start position:0%
+first developed forms of of of of the of
+ 
+
+ align:start position:0%
+first developed forms of of of of the of
+the chase of the comic chase film in the
+
+ align:start position:0%
+the chase of the comic chase film in the
+ 
+
+ align:start position:0%
+the chase of the comic chase film in the
+early silent era and so forth and and uh
+
+ align:start position:0%
+early silent era and so forth and and uh
+ 
+
+ align:start position:0%
+early silent era and so forth and and uh
+I think these arguments are not very
+
+ align:start position:0%
+I think these arguments are not very
+ 
+
+ align:start position:0%
+I think these arguments are not very
+helpful about priority but it is very
+
+ align:start position:0%
+helpful about priority but it is very
+ 
+
+ align:start position:0%
+helpful about priority but it is very
+important to remind you that the uh
+
+ align:start position:0%
+important to remind you that the uh
+ 
+
+ align:start position:0%
+important to remind you that the uh
+history of of of uh other National
+
+ align:start position:0%
+history of of of uh other National
+ 
+
+ align:start position:0%
+history of of of uh other National
+Cinemas and most especially the
+
+ align:start position:0%
+Cinemas and most especially the
+ 
+
+ align:start position:0%
+Cinemas and most especially the
+histories of the history of French
+
+ align:start position:0%
+histories of the history of French
+ 
+
+ align:start position:0%
+histories of the history of French
+Cinema has the same complexity Nuance
+
+ align:start position:0%
+Cinema has the same complexity Nuance
+ 
+
+ align:start position:0%
+Cinema has the same complexity Nuance
+detail that American that American film
+
+ align:start position:0%
+detail that American that American film
+ 
+
+ align:start position:0%
+detail that American that American film
+has we can speak and just let me very
+
+ align:start position:0%
+has we can speak and just let me very
+ 
+
+ align:start position:0%
+has we can speak and just let me very
+quickly remind you uh I I've asked I
+
+ align:start position:0%
+quickly remind you uh I I've asked I
+ 
+
+ align:start position:0%
+quickly remind you uh I I've asked I
+asked you to read a chapter from David
+
+ align:start position:0%
+asked you to read a chapter from David
+ 
+
+ align:start position:0%
+asked you to read a chapter from David
+Cook's history of narrative film that
+
+ align:start position:0%
+Cook's history of narrative film that
+ 
+
+ align:start position:0%
+Cook's history of narrative film that
+deals with the complex achievements of
+
+ align:start position:0%
+deals with the complex achievements of
+ 
+
+ align:start position:0%
+deals with the complex achievements of
+French film in both the silent and in
+
+ align:start position:0%
+French film in both the silent and in
+ 
+
+ align:start position:0%
+French film in both the silent and in
+the sound era and I hope you read those
+
+ align:start position:0%
+the sound era and I hope you read those
+ 
+
+ align:start position:0%
+the sound era and I hope you read those
+chapters and reread those chapters
+
+ align:start position:0%
+chapters and reread those chapters
+ 
+
+ align:start position:0%
+chapters and reread those chapters
+closely and think about them just as a
+
+ align:start position:0%
+closely and think about them just as a
+ 
+
+ align:start position:0%
+closely and think about them just as a
+reminder however uh we you know there
+
+ align:start position:0%
+reminder however uh we you know there
+ 
+
+ align:start position:0%
+reminder however uh we you know there
+are arguments just as just as Edison and
+
+ align:start position:0%
+are arguments just as just as Edison and
+ 
+
+ align:start position:0%
+are arguments just as just as Edison and
+and the um the uh earliest films that
+
+ align:start position:0%
+and the um the uh earliest films that
+ 
+
+ align:start position:0%
+and the um the uh earliest films that
+were made in the United States are
+
+ align:start position:0%
+were made in the United States are
+ 
+
+ align:start position:0%
+were made in the United States are
+associated with the Edison Company so
+
+ align:start position:0%
+associated with the Edison Company so
+ 
+
+ align:start position:0%
+associated with the Edison Company so
+the same kind of thing is true for the
+
+ align:start position:0%
+the same kind of thing is true for the
+ 
+
+ align:start position:0%
+the same kind of thing is true for the
+Lumiere films that were developed in the
+
+ align:start position:0%
+Lumiere films that were developed in the
+ 
+
+ align:start position:0%
+Lumiere films that were developed in the
+1890s in France and of course just as
+
+ align:start position:0%
+1890s in France and of course just as
+ 
+
+ align:start position:0%
+1890s in France and of course just as
+there were pioneering uh directors who
+
+ align:start position:0%
+there were pioneering uh directors who
+ 
+
+ align:start position:0%
+there were pioneering uh directors who
+explored and the nature of Cinema the
+
+ align:start position:0%
+explored and the nature of Cinema the
+ 
+
+ align:start position:0%
+explored and the nature of Cinema the
+possibilities of of this new of this new
+
+ align:start position:0%
+possibilities of of this new of this new
+ 
+
+ align:start position:0%
+possibilities of of this new of this new
+medium in the United States an identical
+
+ align:start position:0%
+medium in the United States an identical
+ 
+
+ align:start position:0%
+medium in the United States an identical
+uh activity was taking place in France
+
+ align:start position:0%
+uh activity was taking place in France
+ 
+
+ align:start position:0%
+uh activity was taking place in France
+and some of you of course know about the
+
+ align:start position:0%
+and some of you of course know about the
+ 
+
+ align:start position:0%
+and some of you of course know about the
+entral contribution of the uh early
+
+ align:start position:0%
+entral contribution of the uh early
+ 
+
+ align:start position:0%
+entral contribution of the uh early
+pioneering director meler uh um who cook
+
+ align:start position:0%
+pioneering director meler uh um who cook
+ 
+
+ align:start position:0%
+pioneering director meler uh um who cook
+talks extensive ly about him in in the
+
+ align:start position:0%
+talks extensive ly about him in in the
+ 
+
+ align:start position:0%
+talks extensive ly about him in in the
+chapter I asked you to read the the man
+
+ align:start position:0%
+chapter I asked you to read the the man
+ 
+
+ align:start position:0%
+chapter I asked you to read the the man
+who in effect invented the science
+
+ align:start position:0%
+who in effect invented the science
+ 
+
+ align:start position:0%
+who in effect invented the science
+fiction movie in the film a trip to the
+
+ align:start position:0%
+fiction movie in the film a trip to the
+ 
+
+ align:start position:0%
+fiction movie in the film a trip to the
+moon and did so many other uh uh uh
+
+ align:start position:0%
+moon and did so many other uh uh uh
+ 
+
+ align:start position:0%
+moon and did so many other uh uh uh
+early uh experiments with for with with
+
+ align:start position:0%
+early uh experiments with for with with
+ 
+
+ align:start position:0%
+early uh experiments with for with with
+combining uh uh the reality of film with
+
+ align:start position:0%
+combining uh uh the reality of film with
+ 
+
+ align:start position:0%
+combining uh uh the reality of film with
+certain forms of surrealist imagination
+
+ align:start position:0%
+certain forms of surrealist imagination
+ 
+
+ align:start position:0%
+certain forms of surrealist imagination
+the tradition of discourse about film in
+
+ align:start position:0%
+the tradition of discourse about film in
+ 
+
+ align:start position:0%
+the tradition of discourse about film in
+France probably is deeper and has a
+
+ align:start position:0%
+France probably is deeper and has a
+ 
+
+ align:start position:0%
+France probably is deeper and has a
+longer life than in any other society
+
+ align:start position:0%
+longer life than in any other society
+ 
+
+ align:start position:0%
+longer life than in any other society
+and many people would say that along
+
+ align:start position:0%
+and many people would say that along
+ 
+
+ align:start position:0%
+and many people would say that along
+with eisenstein the great Russian
+
+ align:start position:0%
+with eisenstein the great Russian
+ 
+
+ align:start position:0%
+with eisenstein the great Russian
+director it's the French who elaborated
+
+ align:start position:0%
+director it's the French who elaborated
+ 
+
+ align:start position:0%
+director it's the French who elaborated
+the first systematic forms of film
+
+ align:start position:0%
+the first systematic forms of film
+ 
+
+ align:start position:0%
+the first systematic forms of film
+Theory uh and there were in the in the
+
+ align:start position:0%
+Theory uh and there were in the in the
+ 
+
+ align:start position:0%
+Theory uh and there were in the in the
+in the in the in the silent era and in
+
+ align:start position:0%
+in the in the in the silent era and in
+ 
+
+ align:start position:0%
+in the in the in the silent era and in
+the 20s uh uh in France uh a series of
+
+ align:start position:0%
+the 20s uh uh in France uh a series of
+ 
+
+ align:start position:0%
+the 20s uh uh in France uh a series of
+developments that encouraged a
+
+ align:start position:0%
+developments that encouraged a
+ 
+
+ align:start position:0%
+developments that encouraged a
+systematic kind of theoretical approach
+
+ align:start position:0%
+systematic kind of theoretical approach
+ 
+
+ align:start position:0%
+systematic kind of theoretical approach
+to film I won't mention names here or
+
+ align:start position:0%
+to film I won't mention names here or
+ 
+
+ align:start position:0%
+to film I won't mention names here or
+particular or particular uh uh theorists
+
+ align:start position:0%
+particular or particular uh uh theorists
+ 
+
+ align:start position:0%
+particular or particular uh uh theorists
+simply acknowledging the fact that that
+
+ align:start position:0%
+simply acknowledging the fact that that
+ 
+
+ align:start position:0%
+simply acknowledging the fact that that
+the French tradition of of discussion
+
+ align:start position:0%
+the French tradition of of discussion
+ 
+
+ align:start position:0%
+the French tradition of of discussion
+about film and in the creation of film
+
+ align:start position:0%
+about film and in the creation of film
+ 
+
+ align:start position:0%
+about film and in the creation of film
+is at least as rich as that of any other
+
+ align:start position:0%
+is at least as rich as that of any other
+ 
+
+ align:start position:0%
+is at least as rich as that of any other
+Society I say this because making uh um
+
+ align:start position:0%
+Society I say this because making uh um
+ 
+
+ align:start position:0%
+Society I say this because making uh um
+je Renoir stand for this whole Rich
+
+ align:start position:0%
+je Renoir stand for this whole Rich
+ 
+
+ align:start position:0%
+je Renoir stand for this whole Rich
+tradition is unfair even to so
+
+ align:start position:0%
+tradition is unfair even to so
+ 
+
+ align:start position:0%
+tradition is unfair even to so
+remarkable and influential director as
+
+ align:start position:0%
+remarkable and influential director as
+ 
+
+ align:start position:0%
+remarkable and influential director as
+Jean Renoir but having made that basic
+
+ align:start position:0%
+Jean Renoir but having made that basic
+ 
+
+ align:start position:0%
+Jean Renoir but having made that basic
+apology let me now make my transition to
+
+ align:start position:0%
+apology let me now make my transition to
+ 
+
+ align:start position:0%
+apology let me now make my transition to
+Renoir himself um um some of you will
+
+ align:start position:0%
+Renoir himself um um some of you will
+ 
+
+ align:start position:0%
+Renoir himself um um some of you will
+recognize of of uh renoir's name I hope
+
+ align:start position:0%
+recognize of of uh renoir's name I hope
+ 
+
+ align:start position:0%
+recognize of of uh renoir's name I hope
+he's the Second Son of the great U uh um
+
+ align:start position:0%
+he's the Second Son of the great U uh um
+ 
+
+ align:start position:0%
+he's the Second Son of the great U uh um
+impressionist painter August Renoir and
+
+ align:start position:0%
+impressionist painter August Renoir and
+ 
+
+ align:start position:0%
+impressionist painter August Renoir and
+in fact you can uh he was himself a uh a
+
+ align:start position:0%
+in fact you can uh he was himself a uh a
+ 
+
+ align:start position:0%
+in fact you can uh he was himself a uh a
+a subject of his father's paintings
+
+ align:start position:0%
+a subject of his father's paintings
+ 
+
+ align:start position:0%
+a subject of his father's paintings
+there's the there there's the young
+
+ align:start position:0%
+there's the there there's the young
+ 
+
+ align:start position:0%
+there's the there there's the young
+Renoir with blonde reddish hair as he
+
+ align:start position:0%
+Renoir with blonde reddish hair as he
+ 
+
+ align:start position:0%
+Renoir with blonde reddish hair as he
+appears in one of his father's paintings
+
+ align:start position:0%
+appears in one of his father's paintings
+ 
+
+ align:start position:0%
+appears in one of his father's paintings
+in the period 1895 to 1899 when the when
+
+ align:start position:0%
+in the period 1895 to 1899 when the when
+ 
+
+ align:start position:0%
+in the period 1895 to 1899 when the when
+young Jean appeared in a series of
+
+ align:start position:0%
+young Jean appeared in a series of
+ 
+
+ align:start position:0%
+young Jean appeared in a series of
+paintings in some of the p in some of
+
+ align:start position:0%
+paintings in some of the p in some of
+ 
+
+ align:start position:0%
+paintings in some of the p in some of
+the paintings his his tier is very
+
+ align:start position:0%
+the paintings his his tier is very
+ 
+
+ align:start position:0%
+the paintings his his tier is very
+ambiguous he looks not just that he has
+
+ align:start position:0%
+ambiguous he looks not just that he has
+ 
+
+ align:start position:0%
+ambiguous he looks not just that he has
+long hair but even seems dressed in a in
+
+ align:start position:0%
+long hair but even seems dressed in a in
+ 
+
+ align:start position:0%
+long hair but even seems dressed in a in
+a kind of girly way and he's sometimes
+
+ align:start position:0%
+a kind of girly way and he's sometimes
+ 
+
+ align:start position:0%
+a kind of girly way and he's sometimes
+mistaken for a girl when people look at
+
+ align:start position:0%
+mistaken for a girl when people look at
+ 
+
+ align:start position:0%
+mistaken for a girl when people look at
+the at the images but isn't it
+
+ align:start position:0%
+the at the images but isn't it
+ 
+
+ align:start position:0%
+the at the images but isn't it
+interesting that this great film artist
+
+ align:start position:0%
+interesting that this great film artist
+ 
+
+ align:start position:0%
+interesting that this great film artist
+is himself uh in a series of or is is
+
+ align:start position:0%
+is himself uh in a series of or is is
+ 
+
+ align:start position:0%
+is himself uh in a series of or is is
+already in a series of IM Immortal works
+
+ align:start position:0%
+already in a series of IM Immortal works
+ 
+
+ align:start position:0%
+already in a series of IM Immortal works
+of art created created by his father
+
+ align:start position:0%
+of art created created by his father
+ 
+
+ align:start position:0%
+of art created created by his father
+Jean Renoir grew up in a in in an
+
+ align:start position:0%
+Jean Renoir grew up in a in in an
+ 
+
+ align:start position:0%
+Jean Renoir grew up in a in in an
+atmosphere of avanguard uh almost
+
+ align:start position:0%
+atmosphere of avanguard uh almost
+ 
+
+ align:start position:0%
+atmosphere of avanguard uh almost
+avangard frenzy in a a uh uh many of the
+
+ align:start position:0%
+avangard frenzy in a a uh uh many of the
+ 
+
+ align:start position:0%
+avangard frenzy in a a uh uh many of the
+most distinguished artists and
+
+ align:start position:0%
+most distinguished artists and
+ 
+
+ align:start position:0%
+most distinguished artists and
+performers of the day were regulars in
+
+ align:start position:0%
+performers of the day were regulars in
+ 
+
+ align:start position:0%
+performers of the day were regulars in
+his household because his father by the
+
+ align:start position:0%
+his household because his father by the
+ 
+
+ align:start position:0%
+his household because his father by the
+he was born late in his very late in his
+
+ align:start position:0%
+he was born late in his very late in his
+ 
+
+ align:start position:0%
+he was born late in his very late in his
+father's life and his father was already
+
+ align:start position:0%
+father's life and his father was already
+ 
+
+ align:start position:0%
+father's life and his father was already
+a very famous painter by the time uh U
+
+ align:start position:0%
+a very famous painter by the time uh U
+ 
+
+ align:start position:0%
+a very famous painter by the time uh U
+Jean was born when he grew to adulthood
+
+ align:start position:0%
+Jean was born when he grew to adulthood
+ 
+
+ align:start position:0%
+Jean was born when he grew to adulthood
+he uh uh around the time of the first
+
+ align:start position:0%
+he uh uh around the time of the first
+ 
+
+ align:start position:0%
+he uh uh around the time of the first
+World War uh he served first in the
+
+ align:start position:0%
+World War uh he served first in the
+ 
+
+ align:start position:0%
+World War uh he served first in the
+Cavalry in 1913 uh very briefly uh um
+
+ align:start position:0%
+Cavalry in 1913 uh very briefly uh um
+ 
+
+ align:start position:0%
+Cavalry in 1913 uh very briefly uh um
+was actually injured he was kicked by an
+
+ align:start position:0%
+was actually injured he was kicked by an
+ 
+
+ align:start position:0%
+was actually injured he was kicked by an
+animal I think a horse or a mule kicked
+
+ align:start position:0%
+animal I think a horse or a mule kicked
+ 
+
+ align:start position:0%
+animal I think a horse or a mule kicked
+him and he was laid up then he
+
+ align:start position:0%
+him and he was laid up then he
+ 
+
+ align:start position:0%
+him and he was laid up then he
+reenlisted in the Infantry where he was
+
+ align:start position:0%
+reenlisted in the Infantry where he was
+ 
+
+ align:start position:0%
+reenlisted in the Infantry where he was
+wounded and he and finally this is very
+
+ align:start position:0%
+wounded and he and finally this is very
+ 
+
+ align:start position:0%
+wounded and he and finally this is very
+rare in the first World War uh uh he
+
+ align:start position:0%
+rare in the first World War uh uh he
+ 
+
+ align:start position:0%
+rare in the first World War uh uh he
+ended up serving also in the Air Force
+
+ align:start position:0%
+ended up serving also in the Air Force
+ 
+
+ align:start position:0%
+ended up serving also in the Air Force
+and he was briefly a pilot in the French
+
+ align:start position:0%
+and he was briefly a pilot in the French
+ 
+
+ align:start position:0%
+and he was briefly a pilot in the French
+Air Force so he served in all three
+
+ align:start position:0%
+Air Force so he served in all three
+ 
+
+ align:start position:0%
+Air Force so he served in all three
+branches of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+French first world war and the film
+
+ align:start position:0%
+French first world war and the film
+ 
+
+ align:start position:0%
+French first world war and the film
+you're going to see tonight The Great
+
+ align:start position:0%
+you're going to see tonight The Great
+ 
+
+ align:start position:0%
+you're going to see tonight The Great
+Masterpiece so such the great
+
+ align:start position:0%
+Masterpiece so such the great
+ 
+
+ align:start position:0%
+Masterpiece so such the great
+influential deeply influential film
+
+ align:start position:0%
+influential deeply influential film
+ 
+
+ align:start position:0%
+influential deeply influential film
+Grand Illusion is a war film of a
+
+ align:start position:0%
+Grand Illusion is a war film of a
+ 
+
+ align:start position:0%
+Grand Illusion is a war film of a
+certain Renoir sort as you'll see this
+
+ align:start position:0%
+certain Renoir sort as you'll see this
+ 
+
+ align:start position:0%
+certain Renoir sort as you'll see this
+evening um uh
+
+ align:start position:0%
+evening um uh
+ 
+
+ align:start position:0%
+evening um uh
+he uh was he also served briefly uh in
+
+ align:start position:0%
+he uh was he also served briefly uh in
+ 
+
+ align:start position:0%
+he uh was he also served briefly uh in
+as a prisoner of war during the uh first
+
+ align:start position:0%
+as a prisoner of war during the uh first
+ 
+
+ align:start position:0%
+as a prisoner of war during the uh first
+world war and and uh that experience of
+
+ align:start position:0%
+world war and and uh that experience of
+ 
+
+ align:start position:0%
+world war and and uh that experience of
+course in some degree in in some Central
+
+ align:start position:0%
+course in some degree in in some Central
+ 
+
+ align:start position:0%
+course in some degree in in some Central
+Way informs the story and the experience
+
+ align:start position:0%
+Way informs the story and the experience
+ 
+
+ align:start position:0%
+Way informs the story and the experience
+of grand delusion which is also a story
+
+ align:start position:0%
+of grand delusion which is also a story
+ 
+
+ align:start position:0%
+of grand delusion which is also a story
+about a film about prisoners of War
+
+ align:start position:0%
+about a film about prisoners of War
+ 
+
+ align:start position:0%
+about a film about prisoners of War
+during wartime
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh you can get some sense of of do we
+
+ align:start position:0%
+uh you can get some sense of of do we
+ 
+
+ align:start position:0%
+uh you can get some sense of of do we
+have some pictures of of his of his
+
+ align:start position:0%
+have some pictures of of his of his
+ 
+
+ align:start position:0%
+have some pictures of of his of his
+father's paintings let me just get these
+
+ align:start position:0%
+father's paintings let me just get these
+ 
+
+ align:start position:0%
+father's paintings let me just get these
+are just of course among some of uh uh
+
+ align:start position:0%
+are just of course among some of uh uh
+ 
+
+ align:start position:0%
+are just of course among some of uh uh
+uh Renoir pe's most famous paintings I
+
+ align:start position:0%
+uh Renoir pe's most famous paintings I
+ 
+
+ align:start position:0%
+uh Renoir pe's most famous paintings I
+thought that it would be you would be
+
+ align:start position:0%
+thought that it would be you would be
+ 
+
+ align:start position:0%
+thought that it would be you would be
+interested to see them to get some sense
+
+ align:start position:0%
+interested to see them to get some sense
+ 
+
+ align:start position:0%
+interested to see them to get some sense
+of of of of uh uh to remind you of what
+
+ align:start position:0%
+of of of of uh uh to remind you of what
+ 
+
+ align:start position:0%
+of of of of uh uh to remind you of what
+of of of the importance of his father's
+
+ align:start position:0%
+of of of the importance of his father's
+ 
+
+ align:start position:0%
+of of of the importance of his father's
+art uh and of the the uh asking you and
+
+ align:start position:0%
+art uh and of the the uh asking you and
+ 
+
+ align:start position:0%
+art uh and of the the uh asking you and
+also as a way of encouraging you to
+
+ align:start position:0%
+also as a way of encouraging you to
+ 
+
+ align:start position:0%
+also as a way of encouraging you to
+imagine what the impact might have been
+
+ align:start position:0%
+imagine what the impact might have been
+ 
+
+ align:start position:0%
+imagine what the impact might have been
+on the Young on the young boy to have
+
+ align:start position:0%
+on the Young on the young boy to have
+ 
+
+ align:start position:0%
+on the Young on the young boy to have
+grown up in an environment in an
+
+ align:start position:0%
+grown up in an environment in an
+ 
+
+ align:start position:0%
+grown up in an environment in an
+environment like this I don't know that
+
+ align:start position:0%
+environment like this I don't know that
+ 
+
+ align:start position:0%
+environment like this I don't know that
+that does look like Jean maybe it is
+
+ align:start position:0%
+that does look like Jean maybe it is
+ 
+
+ align:start position:0%
+that does look like Jean maybe it is
+another picture of Jean uh um he had
+
+ align:start position:0%
+another picture of Jean uh um he had
+ 
+
+ align:start position:0%
+another picture of Jean uh um he had
+kind of a jowly face and that may be
+
+ align:start position:0%
+kind of a jowly face and that may be
+ 
+
+ align:start position:0%
+kind of a jowly face and that may be
+among the oldest images of him
+
+ align:start position:0%
+among the oldest images of him
+ 
+
+ align:start position:0%
+among the oldest images of him
+that him at the oldest age that his
+
+ align:start position:0%
+that him at the oldest age that his
+ 
+
+ align:start position:0%
+that him at the oldest age that his
+father painted him
+
+ align:start position:0%
+father painted him
+ 
+
+ align:start position:0%
+father painted him
+um he
+
+ align:start position:0%
+um he
+ 
+
+ align:start position:0%
+um he
+um worked on his first after he emerged
+
+ align:start position:0%
+um worked on his first after he emerged
+ 
+
+ align:start position:0%
+um worked on his first after he emerged
+from the first World War War he he had
+
+ align:start position:0%
+from the first World War War he he had
+ 
+
+ align:start position:0%
+from the first World War War he he had
+uh uh conflicting Ambitions but he moved
+
+ align:start position:0%
+uh uh conflicting Ambitions but he moved
+ 
+
+ align:start position:0%
+uh uh conflicting Ambitions but he moved
+into into film uh fairly soon he wrote a
+
+ align:start position:0%
+into into film uh fairly soon he wrote a
+ 
+
+ align:start position:0%
+into into film uh fairly soon he wrote a
+script in
+
+ align:start position:0%
+script in
+ 
+
+ align:start position:0%
+script in
+1924 uh he began to make uh uh his own
+
+ align:start position:0%
+1924 uh he began to make uh uh his own
+ 
+
+ align:start position:0%
+1924 uh he began to make uh uh his own
+movies around the same time I have a
+
+ align:start position:0%
+movies around the same time I have a
+ 
+
+ align:start position:0%
+movies around the same time I have a
+very brief list of some of his films
+
+ align:start position:0%
+very brief list of some of his films
+ 
+
+ align:start position:0%
+very brief list of some of his films
+would you put those up uh I want to talk
+
+ align:start position:0%
+would you put those up uh I want to talk
+ 
+
+ align:start position:0%
+would you put those up uh I want to talk
+very quickly about a couple of his films
+
+ align:start position:0%
+very quickly about a couple of his films
+ 
+
+ align:start position:0%
+very quickly about a couple of his films
+and then turn to certain other uh
+
+ align:start position:0%
+and then turn to certain other uh
+ 
+
+ align:start position:0%
+and then turn to certain other uh
+important matters but the most important
+
+ align:start position:0%
+important matters but the most important
+ 
+
+ align:start position:0%
+important matters but the most important
+thing to say about renoir's gen renoir's
+
+ align:start position:0%
+thing to say about renoir's gen renoir's
+ 
+
+ align:start position:0%
+thing to say about renoir's gen renoir's
+career is that like some important
+
+ align:start position:0%
+career is that like some important
+ 
+
+ align:start position:0%
+career is that like some important
+American directors his career spans both
+
+ align:start position:0%
+American directors his career spans both
+ 
+
+ align:start position:0%
+American directors his career spans both
+the silent and the sound era uh uh and
+
+ align:start position:0%
+the silent and the sound era uh uh and
+ 
+
+ align:start position:0%
+the silent and the sound era uh uh and
+he made some significant experimental
+
+ align:start position:0%
+he made some significant experimental
+ 
+
+ align:start position:0%
+he made some significant experimental
+silent films of which um uh the most
+
+ align:start position:0%
+silent films of which um uh the most
+ 
+
+ align:start position:0%
+silent films of which um uh the most
+wellknown in in terms of experiment is
+
+ align:start position:0%
+wellknown in in terms of experiment is
+ 
+
+ align:start position:0%
+wellknown in in terms of experiment is
+the film The Little Match Girl based on
+
+ align:start position:0%
+the film The Little Match Girl based on
+ 
+
+ align:start position:0%
+the film The Little Match Girl based on
+a Hans Christian Anderson story and it
+
+ align:start position:0%
+a Hans Christian Anderson story and it
+ 
+
+ align:start position:0%
+a Hans Christian Anderson story and it
+uses certain kinds of surreal imagery
+
+ align:start position:0%
+uses certain kinds of surreal imagery
+ 
+
+ align:start position:0%
+uses certain kinds of surreal imagery
+that's very surprising especially in a
+
+ align:start position:0%
+that's very surprising especially in a
+ 
+
+ align:start position:0%
+that's very surprising especially in a
+in a silent film and uh and I I
+
+ align:start position:0%
+in a silent film and uh and I I
+ 
+
+ align:start position:0%
+in a silent film and uh and I I
+mentioned
+
+ align:start position:0%
+mentioned
+ 
+
+ align:start position:0%
+mentioned
+the that he made a silent version of a
+
+ align:start position:0%
+the that he made a silent version of a
+ 
+
+ align:start position:0%
+the that he made a silent version of a
+novel by zolah Nana Nana as a way of
+
+ align:start position:0%
+novel by zolah Nana Nana as a way of
+ 
+
+ align:start position:0%
+novel by zolah Nana Nana as a way of
+simply also reminding you from a very
+
+ align:start position:0%
+simply also reminding you from a very
+ 
+
+ align:start position:0%
+simply also reminding you from a very
+early stage Renoir understood that the
+
+ align:start position:0%
+early stage Renoir understood that the
+ 
+
+ align:start position:0%
+early stage Renoir understood that the
+movies were were a form that could
+
+ align:start position:0%
+movies were were a form that could
+ 
+
+ align:start position:0%
+movies were were a form that could
+sustain the most ambitious kind of
+
+ align:start position:0%
+sustain the most ambitious kind of
+ 
+
+ align:start position:0%
+sustain the most ambitious kind of
+artistic act um uh uh aims and and uh um
+
+ align:start position:0%
+artistic act um uh uh aims and and uh um
+ 
+
+ align:start position:0%
+artistic act um uh uh aims and and uh um
+in uh it's a measure of his sense of
+
+ align:start position:0%
+in uh it's a measure of his sense of
+ 
+
+ align:start position:0%
+in uh it's a measure of his sense of
+that that he would adapt even during the
+
+ align:start position:0%
+that that he would adapt even during the
+ 
+
+ align:start position:0%
+that that he would adapt even during the
+silent era a film by one of France by
+
+ align:start position:0%
+silent era a film by one of France by
+ 
+
+ align:start position:0%
+silent era a film by one of France by
+one by a classic French author um but
+
+ align:start position:0%
+one by a classic French author um but
+ 
+
+ align:start position:0%
+one by a classic French author um but
+his most but his really significant work
+
+ align:start position:0%
+his most but his really significant work
+ 
+
+ align:start position:0%
+his most but his really significant work
+begins in the sound era and in what's
+
+ align:start position:0%
+begins in the sound era and in what's
+ 
+
+ align:start position:0%
+begins in the sound era and in what's
+often called his French period and the
+
+ align:start position:0%
+often called his French period and the
+ 
+
+ align:start position:0%
+often called his French period and the
+films I've listed between 31 and 39 not
+
+ align:start position:0%
+films I've listed between 31 and 39 not
+ 
+
+ align:start position:0%
+films I've listed between 31 and 39 not
+a complete list of his films this is a
+
+ align:start position:0%
+a complete list of his films this is a
+ 
+
+ align:start position:0%
+a complete list of his films this is a
+very selected list but it's a list of
+
+ align:start position:0%
+very selected list but it's a list of
+ 
+
+ align:start position:0%
+very selected list but it's a list of
+his Mo of some of his most significant
+
+ align:start position:0%
+his Mo of some of his most significant
+ 
+
+ align:start position:0%
+his Mo of some of his most significant
+all of his most among his most
+
+ align:start position:0%
+all of his most among his most
+ 
+
+ align:start position:0%
+all of his most among his most
+significant films for sure no really
+
+ align:start position:0%
+significant films for sure no really
+ 
+
+ align:start position:0%
+significant films for sure no really
+important title is missing although
+
+ align:start position:0%
+important title is missing although
+ 
+
+ align:start position:0%
+important title is missing although
+there are many other interesting films
+
+ align:start position:0%
+there are many other interesting films
+ 
+
+ align:start position:0%
+there are many other interesting films
+that he made and it's the period between
+
+ align:start position:0%
+that he made and it's the period between
+ 
+
+ align:start position:0%
+that he made and it's the period between
+31 and 39 he left France after rules of
+
+ align:start position:0%
+31 and 39 he left France after rules of
+ 
+
+ align:start position:0%
+31 and 39 he left France after rules of
+the game while when the second world war
+
+ align:start position:0%
+the game while when the second world war
+ 
+
+ align:start position:0%
+the game while when the second world war
+was imminent came to the United States
+
+ align:start position:0%
+was imminent came to the United States
+ 
+
+ align:start position:0%
+was imminent came to the United States
+the films of the 40s that I've listed
+
+ align:start position:0%
+the films of the 40s that I've listed
+ 
+
+ align:start position:0%
+the films of the 40s that I've listed
+there were made in Hollywood and he was
+
+ align:start position:0%
+there were made in Hollywood and he was
+ 
+
+ align:start position:0%
+there were made in Hollywood and he was
+very welcomed in Hollywood and there are
+
+ align:start position:0%
+very welcomed in Hollywood and there are
+ 
+
+ align:start position:0%
+very welcomed in Hollywood and there are
+people who uh film Scholars who are
+
+ align:start position:0%
+people who uh film Scholars who are
+ 
+
+ align:start position:0%
+people who uh film Scholars who are
+great fans of these three films these
+
+ align:start position:0%
+great fans of these three films these
+ 
+
+ align:start position:0%
+great fans of these three films these
+three titles that he made in the United
+
+ align:start position:0%
+three titles that he made in the United
+ 
+
+ align:start position:0%
+three titles that he made in the United
+States uh then he left the United States
+
+ align:start position:0%
+States uh then he left the United States
+ 
+
+ align:start position:0%
+States uh then he left the United States
+the the film The River which many uh uh
+
+ align:start position:0%
+the the film The River which many uh uh
+ 
+
+ align:start position:0%
+the the film The River which many uh uh
+Renoir Buffs love as much as his primary
+
+ align:start position:0%
+Renoir Buffs love as much as his primary
+ 
+
+ align:start position:0%
+Renoir Buffs love as much as his primary
+films although I find it a much slower
+
+ align:start position:0%
+films although I find it a much slower
+ 
+
+ align:start position:0%
+films although I find it a much slower
+less powerful film although visually
+
+ align:start position:0%
+less powerful film although visually
+ 
+
+ align:start position:0%
+less powerful film although visually
+incredibly beautiful it's set in India
+
+ align:start position:0%
+incredibly beautiful it's set in India
+ 
+
+ align:start position:0%
+incredibly beautiful it's set in India
+and and the river is the Ganges uh and
+
+ align:start position:0%
+and and the river is the Ganges uh and
+ 
+
+ align:start position:0%
+and and the river is the Ganges uh and
+it's a very very remarkable uh uh
+
+ align:start position:0%
+it's a very very remarkable uh uh
+ 
+
+ align:start position:0%
+it's a very very remarkable uh uh
+meditation on the power of place uh in
+
+ align:start position:0%
+meditation on the power of place uh in
+ 
+
+ align:start position:0%
+meditation on the power of place uh in
+in societ but his Central achievement
+
+ align:start position:0%
+in societ but his Central achievement
+ 
+
+ align:start position:0%
+in societ but his Central achievement
+are the films of his French period uh
+
+ align:start position:0%
+are the films of his French period uh
+ 
+
+ align:start position:0%
+are the films of his French period uh
+running through the 1930s uh and I I
+
+ align:start position:0%
+running through the 1930s uh and I I
+ 
+
+ align:start position:0%
+running through the 1930s uh and I I
+want to say a word about some of these
+
+ align:start position:0%
+want to say a word about some of these
+ 
+
+ align:start position:0%
+want to say a word about some of these
+uh uh um one of them lashen uh Stars
+
+ align:start position:0%
+uh uh um one of them lashen uh Stars
+ 
+
+ align:start position:0%
+uh uh um one of them lashen uh Stars
+the same character who stars in budoo
+
+ align:start position:0%
+the same character who stars in budoo
+ 
+
+ align:start position:0%
+the same character who stars in budoo
+save from drowning and you're going to
+
+ align:start position:0%
+save from drowning and you're going to
+ 
+
+ align:start position:0%
+save from drowning and you're going to
+see a clip from that uh uh U film in a
+
+ align:start position:0%
+see a clip from that uh uh U film in a
+ 
+
+ align:start position:0%
+see a clip from that uh uh U film in a
+moment uh uh Michelle Simone uh and uh
+
+ align:start position:0%
+moment uh uh Michelle Simone uh and uh
+ 
+
+ align:start position:0%
+moment uh uh Michelle Simone uh and uh
+lashen announced a kind of complexity
+
+ align:start position:0%
+lashen announced a kind of complexity
+ 
+
+ align:start position:0%
+lashen announced a kind of complexity
+and ambitiousness in in uh uh renoir's
+
+ align:start position:0%
+and ambitiousness in in uh uh renoir's
+ 
+
+ align:start position:0%
+and ambitiousness in in uh uh renoir's
+work that that uh was deeply significant
+
+ align:start position:0%
+work that that uh was deeply significant
+ 
+
+ align:start position:0%
+work that that uh was deeply significant
+it it had a kind of moral or political
+
+ align:start position:0%
+it it had a kind of moral or political
+ 
+
+ align:start position:0%
+it it had a kind of moral or political
+uh uh claim it was a film uh set in the
+
+ align:start position:0%
+uh uh claim it was a film uh set in the
+ 
+
+ align:start position:0%
+uh uh claim it was a film uh set in the
+in the slums and it was about a uh a an
+
+ align:start position:0%
+in the slums and it was about a uh a an
+ 
+
+ align:start position:0%
+in the slums and it was about a uh a an
+aborted or an abortive or tragic love
+
+ align:start position:0%
+aborted or an abortive or tragic love
+ 
+
+ align:start position:0%
+aborted or an abortive or tragic love
+affair between a working a working man
+
+ align:start position:0%
+affair between a working a working man
+ 
+
+ align:start position:0%
+affair between a working a working man
+played by a proletarian played by
+
+ align:start position:0%
+played by a proletarian played by
+ 
+
+ align:start position:0%
+played by a proletarian played by
+Michelle Simone and a prostitute who is
+
+ align:start position:0%
+Michelle Simone and a prostitute who is
+ 
+
+ align:start position:0%
+Michelle Simone and a prostitute who is
+unkind to him at the end and and and and
+
+ align:start position:0%
+unkind to him at the end and and and and
+ 
+
+ align:start position:0%
+unkind to him at the end and and and and
+uh throws him over at the end uh and uh
+
+ align:start position:0%
+uh throws him over at the end uh and uh
+ 
+
+ align:start position:0%
+uh throws him over at the end uh and uh
+the the film's in the film's interest in
+
+ align:start position:0%
+the the film's in the film's interest in
+ 
+
+ align:start position:0%
+the the film's in the film's interest in
+the life of the low in the lives and
+
+ align:start position:0%
+the life of the low in the lives and
+ 
+
+ align:start position:0%
+the life of the low in the lives and
+circumstances of the lower social orders
+
+ align:start position:0%
+circumstances of the lower social orders
+ 
+
+ align:start position:0%
+circumstances of the lower social orders
+was a was was especially significant
+
+ align:start position:0%
+was a was was especially significant
+ 
+
+ align:start position:0%
+was a was was especially significant
+significant and Michelle Simone's uh
+
+ align:start position:0%
+significant and Michelle Simone's uh
+ 
+
+ align:start position:0%
+significant and Michelle Simone's uh
+mely powerful uh uh uh physical
+
+ align:start position:0%
+mely powerful uh uh uh physical
+ 
+
+ align:start position:0%
+mely powerful uh uh uh physical
+performance uh was uh also memorable and
+
+ align:start position:0%
+performance uh was uh also memorable and
+ 
+
+ align:start position:0%
+performance uh was uh also memorable and
+you'll see a version of that in a moment
+
+ align:start position:0%
+you'll see a version of that in a moment
+ 
+
+ align:start position:0%
+you'll see a version of that in a moment
+in in the following year he made what
+
+ align:start position:0%
+in in the following year he made what
+ 
+
+ align:start position:0%
+in in the following year he made what
+many people call his first Great
+
+ align:start position:0%
+many people call his first Great
+ 
+
+ align:start position:0%
+many people call his first Great
+Masterpiece a film called budoo save
+
+ align:start position:0%
+Masterpiece a film called budoo save
+ 
+
+ align:start position:0%
+Masterpiece a film called budoo save
+from drowning it's the French title is
+
+ align:start position:0%
+from drowning it's the French title is
+ 
+
+ align:start position:0%
+from drowning it's the French title is
+budo so Deo saved from the waters Deo
+
+ align:start position:0%
+budo so Deo saved from the waters Deo
+ 
+
+ align:start position:0%
+budo so Deo saved from the waters Deo
+the the waters plural uh and the French
+
+ align:start position:0%
+the the waters plural uh and the French
+ 
+
+ align:start position:0%
+the the waters plural uh and the French
+title is a little better as I'll try to
+
+ align:start position:0%
+title is a little better as I'll try to
+ 
+
+ align:start position:0%
+title is a little better as I'll try to
+say in a moment U uh he made I mentioned
+
+ align:start position:0%
+say in a moment U uh he made I mentioned
+ 
+
+ align:start position:0%
+say in a moment U uh he made I mentioned
+The Madame Bou partly again to show you
+
+ align:start position:0%
+The Madame Bou partly again to show you
+ 
+
+ align:start position:0%
+The Madame Bou partly again to show you
+something about his ambition he's trying
+
+ align:start position:0%
+something about his ambition he's trying
+ 
+
+ align:start position:0%
+something about his ambition he's trying
+to say in effect look the film is an
+
+ align:start position:0%
+to say in effect look the film is an
+ 
+
+ align:start position:0%
+to say in effect look the film is an
+equivalent art form to the great novels
+
+ align:start position:0%
+equivalent art form to the great novels
+ 
+
+ align:start position:0%
+equivalent art form to the great novels
+of our past uh uh in 1935 he made a film
+
+ align:start position:0%
+of our past uh uh in 1935 he made a film
+ 
+
+ align:start position:0%
+of our past uh uh in 1935 he made a film
+that many uh identify as a
+
+ align:start position:0%
+that many uh identify as a
+ 
+
+ align:start position:0%
+that many uh identify as a
+forerunner of of uh Italian neorealism
+
+ align:start position:0%
+forerunner of of uh Italian neorealism
+ 
+
+ align:start position:0%
+forerunner of of uh Italian neorealism
+the movement we'll be studying next week
+
+ align:start position:0%
+the movement we'll be studying next week
+ 
+
+ align:start position:0%
+the movement we'll be studying next week
+and I talk a bit about Tony in next
+
+ align:start position:0%
+and I talk a bit about Tony in next
+ 
+
+ align:start position:0%
+and I talk a bit about Tony in next
+week's lecture uh it's a film uh uh very
+
+ align:start position:0%
+week's lecture uh it's a film uh uh very
+ 
+
+ align:start position:0%
+week's lecture uh it's a film uh uh very
+experimental in certain ways it uses a
+
+ align:start position:0%
+experimental in certain ways it uses a
+ 
+
+ align:start position:0%
+experimental in certain ways it uses a
+lot of nonprofessional actors uh um uh
+
+ align:start position:0%
+lot of nonprofessional actors uh um uh
+ 
+
+ align:start position:0%
+lot of nonprofessional actors uh um uh
+and and again it's
+
+ align:start position:0%
+and and again it's
+ 
+
+ align:start position:0%
+and and again it's
+about the circumstances of of the
+
+ align:start position:0%
+about the circumstances of of the
+ 
+
+ align:start position:0%
+about the circumstances of of the
+working class in some way it's about
+
+ align:start position:0%
+working class in some way it's about
+ 
+
+ align:start position:0%
+working class in some way it's about
+it's about uh um French Quarry worker
+
+ align:start position:0%
+it's about uh um French Quarry worker
+ 
+
+ align:start position:0%
+it's about uh um French Quarry worker
+workers who are treated with a kind of
+
+ align:start position:0%
+workers who are treated with a kind of
+ 
+
+ align:start position:0%
+workers who are treated with a kind of
+with with a kind of with a kind of
+
+ align:start position:0%
+with with a kind of with a kind of
+ 
+
+ align:start position:0%
+with with a kind of with a kind of
+clarity and and attentiveness that that
+
+ align:start position:0%
+clarity and and attentiveness that that
+ 
+
+ align:start position:0%
+clarity and and attentiveness that that
+uh previous films had had not had had
+
+ align:start position:0%
+uh previous films had had not had had
+ 
+
+ align:start position:0%
+uh previous films had had not had had
+rarely granted to members of the uh not
+
+ align:start position:0%
+rarely granted to members of the uh not
+ 
+
+ align:start position:0%
+rarely granted to members of the uh not
+only the lower social orders but here
+
+ align:start position:0%
+only the lower social orders but here
+ 
+
+ align:start position:0%
+only the lower social orders but here
+immigrants not even not not not even
+
+ align:start position:0%
+immigrants not even not not not even
+ 
+
+ align:start position:0%
+immigrants not even not not not even
+natives uh his two masterpieces come uh
+
+ align:start position:0%
+natives uh his two masterpieces come uh
+ 
+
+ align:start position:0%
+natives uh his two masterpieces come uh
+in 37 and 39 n again remember I've left
+
+ align:start position:0%
+in 37 and 39 n again remember I've left
+ 
+
+ align:start position:0%
+in 37 and 39 n again remember I've left
+out a number of titles here this is a
+
+ align:start position:0%
+out a number of titles here this is a
+ 
+
+ align:start position:0%
+out a number of titles here this is a
+selected list uh the film you'll see
+
+ align:start position:0%
+selected list uh the film you'll see
+ 
+
+ align:start position:0%
+selected list uh the film you'll see
+tonight Grand Illusion and uh what many
+
+ align:start position:0%
+tonight Grand Illusion and uh what many
+ 
+
+ align:start position:0%
+tonight Grand Illusion and uh what many
+people think of as his greatest film a
+
+ align:start position:0%
+people think of as his greatest film a
+ 
+
+ align:start position:0%
+people think of as his greatest film a
+deep complex satire on contemporary
+
+ align:start position:0%
+deep complex satire on contemporary
+ 
+
+ align:start position:0%
+deep complex satire on contemporary
+French life in the pre in just before
+
+ align:start position:0%
+French life in the pre in just before
+ 
+
+ align:start position:0%
+French life in the pre in just before
+the war called rules of the game the
+
+ align:start position:0%
+the war called rules of the game the
+ 
+
+ align:start position:0%
+the war called rules of the game the
+primary label that's attached to Jean
+
+ align:start position:0%
+primary label that's attached to Jean
+ 
+
+ align:start position:0%
+primary label that's attached to Jean
+renoir's work is that of poetic realism
+
+ align:start position:0%
+renoir's work is that of poetic realism
+ 
+
+ align:start position:0%
+renoir's work is that of poetic realism
+and it's a it's a way of trying to
+
+ align:start position:0%
+and it's a it's a way of trying to
+ 
+
+ align:start position:0%
+and it's a it's a way of trying to
+distinguish a form of movie making that
+
+ align:start position:0%
+distinguish a form of movie making that
+ 
+
+ align:start position:0%
+distinguish a form of movie making that
+emerges of which uh Renoir is the most
+
+ align:start position:0%
+emerges of which uh Renoir is the most
+ 
+
+ align:start position:0%
+emerges of which uh Renoir is the most
+dramatic and Powerful Exemplar but there
+
+ align:start position:0%
+dramatic and Powerful Exemplar but there
+ 
+
+ align:start position:0%
+dramatic and Powerful Exemplar but there
+were many other examples in in in in in
+
+ align:start position:0%
+were many other examples in in in in in
+ 
+
+ align:start position:0%
+were many other examples in in in in in
+uh in French Cinema and and it's worth
+
+ align:start position:0%
+uh in French Cinema and and it's worth
+ 
+
+ align:start position:0%
+uh in French Cinema and and it's worth
+talking a little bit about a t
+
+ align:start position:0%
+talking a little bit about a t
+ 
+
+ align:start position:0%
+talking a little bit about a t
+Forerunner to the tradition of poetic
+
+ align:start position:0%
+Forerunner to the tradition of poetic
+ 
+
+ align:start position:0%
+Forerunner to the tradition of poetic
+realism a director named Jean Vio who
+
+ align:start position:0%
+realism a director named Jean Vio who
+ 
+
+ align:start position:0%
+realism a director named Jean Vio who
+died tragically young as you can see
+
+ align:start position:0%
+died tragically young as you can see
+ 
+
+ align:start position:0%
+died tragically young as you can see
+from his dates who made uh uh the three
+
+ align:start position:0%
+from his dates who made uh uh the three
+ 
+
+ align:start position:0%
+from his dates who made uh uh the three
+films three titles I've listed there uh
+
+ align:start position:0%
+films three titles I've listed there uh
+ 
+
+ align:start position:0%
+films three titles I've listed there uh
+and these these films had an immense uh
+
+ align:start position:0%
+and these these films had an immense uh
+ 
+
+ align:start position:0%
+and these these films had an immense uh
+uh influence on later filmmakers uh zero
+
+ align:start position:0%
+uh influence on later filmmakers uh zero
+ 
+
+ align:start position:0%
+uh influence on later filmmakers uh zero
+for conduct is a is a a film set in a it
+
+ align:start position:0%
+for conduct is a is a a film set in a it
+ 
+
+ align:start position:0%
+for conduct is a is a a film set in a it
+has surreal elements and it's it's it's
+
+ align:start position:0%
+has surreal elements and it's it's it's
+ 
+
+ align:start position:0%
+has surreal elements and it's it's it's
+it's plot it's hard to follow but it
+
+ align:start position:0%
+it's plot it's hard to follow but it
+ 
+
+ align:start position:0%
+it's plot it's hard to follow but it
+essentially it tells the story of
+
+ align:start position:0%
+essentially it tells the story of
+ 
+
+ align:start position:0%
+essentially it tells the story of
+children going back to school it's a
+
+ align:start position:0%
+children going back to school it's a
+ 
+
+ align:start position:0%
+children going back to school it's a
+it's a it's a and following them once
+
+ align:start position:0%
+it's a it's a and following them once
+ 
+
+ align:start position:0%
+it's a it's a and following them once
+they get into a kind of boarding school
+
+ align:start position:0%
+they get into a kind of boarding school
+ 
+
+ align:start position:0%
+they get into a kind of boarding school
+and rebel against their house masters
+
+ align:start position:0%
+and rebel against their house masters
+ 
+
+ align:start position:0%
+and rebel against their house masters
+and the there's a sort of comic element
+
+ align:start position:0%
+and the there's a sort of comic element
+ 
+
+ align:start position:0%
+and the there's a sort of comic element
+in the film and there's also an element
+
+ align:start position:0%
+in the film and there's also an element
+ 
+
+ align:start position:0%
+in the film and there's also an element
+that might be called an Impulse toward
+
+ align:start position:0%
+that might be called an Impulse toward
+ 
+
+ align:start position:0%
+that might be called an Impulse toward
+lyric retardation by which I mean the
+
+ align:start position:0%
+lyric retardation by which I mean the
+ 
+
+ align:start position:0%
+lyric retardation by which I mean the
+the retarding is the retarding of the
+
+ align:start position:0%
+the retarding is the retarding of the
+ 
+
+ align:start position:0%
+the retarding is the retarding of the
+plot I don't mean mental right
+
+ align:start position:0%
+plot I don't mean mental right
+ 
+
+ align:start position:0%
+plot I don't mean mental right
+there's a kind of lyric impulse to
+
+ align:start position:0%
+there's a kind of lyric impulse to
+ 
+
+ align:start position:0%
+there's a kind of lyric impulse to
+celebrate what's going on right in front
+
+ align:start position:0%
+celebrate what's going on right in front
+ 
+
+ align:start position:0%
+celebrate what's going on right in front
+of you at the expense of the plot as if
+
+ align:start position:0%
+of you at the expense of the plot as if
+ 
+
+ align:start position:0%
+of you at the expense of the plot as if
+as if as if the story almost stops
+
+ align:start position:0%
+as if as if the story almost stops
+ 
+
+ align:start position:0%
+as if as if the story almost stops
+moving at a certain point while the
+
+ align:start position:0%
+moving at a certain point while the
+ 
+
+ align:start position:0%
+moving at a certain point while the
+camera and the and the and the and the
+
+ align:start position:0%
+camera and the and the and the and the
+ 
+
+ align:start position:0%
+camera and the and the and the and the
+uh well the camera itself sort of
+
+ align:start position:0%
+uh well the camera itself sort of
+ 
+
+ align:start position:0%
+uh well the camera itself sort of
+indulges in in a in in in in witnessing
+
+ align:start position:0%
+indulges in in a in in in in witnessing
+ 
+
+ align:start position:0%
+indulges in in a in in in in witnessing
+a spectacle so intrinsically interesting
+
+ align:start position:0%
+a spectacle so intrinsically interesting
+ 
+
+ align:start position:0%
+a spectacle so intrinsically interesting
+in itself that it seems to lose interest
+
+ align:start position:0%
+in itself that it seems to lose interest
+ 
+
+ align:start position:0%
+in itself that it seems to lose interest
+in the ongoing story so there's this
+
+ align:start position:0%
+in the ongoing story so there's this
+ 
+
+ align:start position:0%
+in the ongoing story so there's this
+tension in vigo's films from the very
+
+ align:start position:0%
+tension in vigo's films from the very
+ 
+
+ align:start position:0%
+tension in vigo's films from the very
+beginning in what some Scholars have
+
+ align:start position:0%
+beginning in what some Scholars have
+ 
+
+ align:start position:0%
+beginning in what some Scholars have
+seen a tension between denotation and
+
+ align:start position:0%
+seen a tension between denotation and
+ 
+
+ align:start position:0%
+seen a tension between denotation and
+connotation between the denotation being
+
+ align:start position:0%
+connotation between the denotation being
+ 
+
+ align:start position:0%
+connotation between the denotation being
+the simple realism the ongoing story
+
+ align:start position:0%
+the simple realism the ongoing story
+ 
+
+ align:start position:0%
+the simple realism the ongoing story
+right and the connotation being the
+
+ align:start position:0%
+right and the connotation being the
+ 
+
+ align:start position:0%
+right and the connotation being the
+poetic or lyrical impulse of the film to
+
+ align:start position:0%
+poetic or lyrical impulse of the film to
+ 
+
+ align:start position:0%
+poetic or lyrical impulse of the film to
+sort of Celebrate life in its complexity
+
+ align:start position:0%
+sort of Celebrate life in its complexity
+ 
+
+ align:start position:0%
+sort of Celebrate life in its complexity
+and its Nuance without any interference
+
+ align:start position:0%
+and its Nuance without any interference
+ 
+
+ align:start position:0%
+and its Nuance without any interference
+from the demand that you follow a story
+
+ align:start position:0%
+from the demand that you follow a story
+ 
+
+ align:start position:0%
+from the demand that you follow a story
+and this tension uh is is a fundamental
+
+ align:start position:0%
+and this tension uh is is a fundamental
+ 
+
+ align:start position:0%
+and this tension uh is is a fundamental
+element not only in in uh uh po realism
+
+ align:start position:0%
+element not only in in uh uh po realism
+ 
+
+ align:start position:0%
+element not only in in uh uh po realism
+but as you'll see in the Italian form of
+
+ align:start position:0%
+but as you'll see in the Italian form of
+ 
+
+ align:start position:0%
+but as you'll see in the Italian form of
+this called neorealism that emerges out
+
+ align:start position:0%
+this called neorealism that emerges out
+ 
+
+ align:start position:0%
+this called neorealism that emerges out
+of it and is somewhat of a grittier and
+
+ align:start position:0%
+of it and is somewhat of a grittier and
+ 
+
+ align:start position:0%
+of it and is somewhat of a grittier and
+more historically um um uh politically
+
+ align:start position:0%
+more historically um um uh politically
+ 
+
+ align:start position:0%
+more historically um um uh politically
+engaged kind of kind of uh drama even
+
+ align:start position:0%
+engaged kind of kind of uh drama even
+ 
+
+ align:start position:0%
+engaged kind of kind of uh drama even
+kind of kind of film even though it's a
+
+ align:start position:0%
+kind of kind of film even though it's a
+ 
+
+ align:start position:0%
+kind of kind of film even though it's a
+direct outgrowth of the kind of thing
+
+ align:start position:0%
+direct outgrowth of the kind of thing
+ 
+
+ align:start position:0%
+direct outgrowth of the kind of thing
+we're saying about poetic realism and in
+
+ align:start position:0%
+we're saying about poetic realism and in
+ 
+
+ align:start position:0%
+we're saying about poetic realism and in
+both forms in both kinds of film there
+
+ align:start position:0%
+both forms in both kinds of film there
+ 
+
+ align:start position:0%
+both forms in both kinds of film there
+is this retarding impulse this lyric
+
+ align:start position:0%
+is this retarding impulse this lyric
+ 
+
+ align:start position:0%
+is this retarding impulse this lyric
+impulse in which in which the story's
+
+ align:start position:0%
+impulse in which in which the story's
+ 
+
+ align:start position:0%
+impulse in which in which the story's
+desire to get on with itself is
+
+ align:start position:0%
+desire to get on with itself is
+ 
+
+ align:start position:0%
+desire to get on with itself is
+sometimes in conflict with the Cam's
+
+ align:start position:0%
+sometimes in conflict with the Cam's
+ 
+
+ align:start position:0%
+sometimes in conflict with the Cam's
+desire to look at what it sees to to to
+
+ align:start position:0%
+desire to look at what it sees to to to
+ 
+
+ align:start position:0%
+desire to look at what it sees to to to
+to to to Riel in what it in what it
+
+ align:start position:0%
+to to to Riel in what it in what it
+ 
+
+ align:start position:0%
+to to to Riel in what it in what it
+wants to look at um and uh uh um so so
+
+ align:start position:0%
+wants to look at um and uh uh um so so
+ 
+
+ align:start position:0%
+wants to look at um and uh uh um so so
+Jean Vigo uh partly indeed because of
+
+ align:start position:0%
+Jean Vigo uh partly indeed because of
+ 
+
+ align:start position:0%
+Jean Vigo uh partly indeed because of
+his tragic life short life uh and and
+
+ align:start position:0%
+his tragic life short life uh and and
+ 
+
+ align:start position:0%
+his tragic life short life uh and and
+partly because of he was the son of an
+
+ align:start position:0%
+partly because of he was the son of an
+ 
+
+ align:start position:0%
+partly because of he was the son of an
+anarchist of a political Anarchist a
+
+ align:start position:0%
+anarchist of a political Anarchist a
+ 
+
+ align:start position:0%
+anarchist of a political Anarchist a
+serious Anarchist who who wrote about
+
+ align:start position:0%
+serious Anarchist who who wrote about
+ 
+
+ align:start position:0%
+serious Anarchist who who wrote about
+theories of an of of Anar anarchism as a
+
+ align:start position:0%
+theories of an of of Anar anarchism as a
+ 
+
+ align:start position:0%
+theories of an of of Anar anarchism as a
+political movement and he himself was
+
+ align:start position:0%
+political movement and he himself was
+ 
+
+ align:start position:0%
+political movement and he himself was
+very very hostile to Authority Jean Vio
+
+ align:start position:0%
+very very hostile to Authority Jean Vio
+ 
+
+ align:start position:0%
+very very hostile to Authority Jean Vio
+and his films animate a kind of uh
+
+ align:start position:0%
+and his films animate a kind of uh
+ 
+
+ align:start position:0%
+and his films animate a kind of uh
+anarchic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+antiestablishmentarianism uh that is
+
+ align:start position:0%
+antiestablishmentarianism uh that is
+ 
+
+ align:start position:0%
+antiestablishmentarianism uh that is
+that is that is very distinctive he's
+
+ align:start position:0%
+that is that is very distinctive he's
+ 
+
+ align:start position:0%
+that is that is very distinctive he's
+almost always on the side of the of the
+
+ align:start position:0%
+almost always on the side of the of the
+ 
+
+ align:start position:0%
+almost always on the side of the of the
+weak and the
+
+ align:start position:0%
+weak and the
+ 
+
+ align:start position:0%
+weak and the
+powerless um let me say a few words
+
+ align:start position:0%
+powerless um let me say a few words
+ 
+
+ align:start position:0%
+powerless um let me say a few words
+about the key what we might call the key
+
+ align:start position:0%
+about the key what we might call the key
+ 
+
+ align:start position:0%
+about the key what we might call the key
+features of neorealism one of the most
+
+ align:start position:0%
+features of neorealism one of the most
+ 
+
+ align:start position:0%
+features of neorealism one of the most
+fundamental elements of neorealism is
+
+ align:start position:0%
+fundamental elements of neorealism is
+ 
+
+ align:start position:0%
+fundamental elements of neorealism is
+what could be called a Misa nonsense
+
+ align:start position:0%
+what could be called a Misa nonsense
+ 
+
+ align:start position:0%
+what could be called a Misa nonsense
+style that is to say it's committed to
+
+ align:start position:0%
+style that is to say it's committed to
+ 
+
+ align:start position:0%
+style that is to say it's committed to
+long takes the poetic realism is
+
+ align:start position:0%
+long takes the poetic realism is
+ 
+
+ align:start position:0%
+long takes the poetic realism is
+interested in the external world and in
+
+ align:start position:0%
+interested in the external world and in
+ 
+
+ align:start position:0%
+interested in the external world and in
+the relation between characters and the
+
+ align:start position:0%
+the relation between characters and the
+ 
+
+ align:start position:0%
+the relation between characters and the
+outer world and and and although it will
+
+ align:start position:0%
+outer world and and and although it will
+ 
+
+ align:start position:0%
+outer world and and and although it will
+use abrupt cuts of various kinds it
+
+ align:start position:0%
+use abrupt cuts of various kinds it
+ 
+
+ align:start position:0%
+use abrupt cuts of various kinds it
+won't do so at the expense of your
+
+ align:start position:0%
+won't do so at the expense of your
+ 
+
+ align:start position:0%
+won't do so at the expense of your
+experience of the outer World it wants
+
+ align:start position:0%
+experience of the outer World it wants
+ 
+
+ align:start position:0%
+experience of the outer World it wants
+the audience to take in uh what it sees
+
+ align:start position:0%
+the audience to take in uh what it sees
+ 
+
+ align:start position:0%
+the audience to take in uh what it sees
+and to make judgments about it it
+
+ align:start position:0%
+and to make judgments about it it
+ 
+
+ align:start position:0%
+and to make judgments about it it
+doesn't try to in the in the way that
+
+ align:start position:0%
+doesn't try to in the in the way that
+ 
+
+ align:start position:0%
+doesn't try to in the in the way that
+certain other kinds of styles might do
+
+ align:start position:0%
+certain other kinds of styles might do
+ 
+
+ align:start position:0%
+certain other kinds of styles might do
+to manipulate your respon in quite the
+
+ align:start position:0%
+to manipulate your respon in quite the
+ 
+
+ align:start position:0%
+to manipulate your respon in quite the
+in in in in so dramatic a way uh and
+
+ align:start position:0%
+in in in in so dramatic a way uh and
+ 
+
+ align:start position:0%
+in in in in so dramatic a way uh and
+what follows from this Mison sense style
+
+ align:start position:0%
+what follows from this Mison sense style
+ 
+
+ align:start position:0%
+what follows from this Mison sense style
+is what some Scholars have called in
+
+ align:start position:0%
+is what some Scholars have called in
+ 
+
+ align:start position:0%
+is what some Scholars have called in
+camera editing because what's going on
+
+ align:start position:0%
+camera editing because what's going on
+ 
+
+ align:start position:0%
+camera editing because what's going on
+is because the camera the T because the
+
+ align:start position:0%
+is because the camera the T because the
+ 
+
+ align:start position:0%
+is because the camera the T because the
+camera uh is the style is committed to
+
+ align:start position:0%
+camera uh is the style is committed to
+ 
+
+ align:start position:0%
+camera uh is the style is committed to
+long takes what will happen is the
+
+ align:start position:0%
+long takes what will happen is the
+ 
+
+ align:start position:0%
+long takes what will happen is the
+camera will alter its focal length its
+
+ align:start position:0%
+camera will alter its focal length its
+ 
+
+ align:start position:0%
+camera will alter its focal length its
+depth of field uh or it will simply move
+
+ align:start position:0%
+depth of field uh or it will simply move
+ 
+
+ align:start position:0%
+depth of field uh or it will simply move
+and change its it's uh the the the um
+
+ align:start position:0%
+and change its it's uh the the the um
+ 
+
+ align:start position:0%
+and change its it's uh the the the um
+object of its gaze uh while it is in
+
+ align:start position:0%
+object of its gaze uh while it is in
+ 
+
+ align:start position:0%
+object of its gaze uh while it is in
+operation so that it's instead of a
+
+ align:start position:0%
+operation so that it's instead of a
+ 
+
+ align:start position:0%
+operation so that it's instead of a
+series of cuts that are made in the
+
+ align:start position:0%
+series of cuts that are made in the
+ 
+
+ align:start position:0%
+series of cuts that are made in the
+editing room in it's the cameraman
+
+ align:start position:0%
+editing room in it's the cameraman
+ 
+
+ align:start position:0%
+editing room in it's the cameraman
+working the camera who's making certain
+
+ align:start position:0%
+working the camera who's making certain
+ 
+
+ align:start position:0%
+working the camera who's making certain
+decisions that in another kind of film
+
+ align:start position:0%
+decisions that in another kind of film
+ 
+
+ align:start position:0%
+decisions that in another kind of film
+would be made by a film editor after the
+
+ align:start position:0%
+would be made by a film editor after the
+ 
+
+ align:start position:0%
+would be made by a film editor after the
+fact and this creates an effect of not
+
+ align:start position:0%
+fact and this creates an effect of not
+ 
+
+ align:start position:0%
+fact and this creates an effect of not
+exactly improvisation but an effect of
+
+ align:start position:0%
+exactly improvisation but an effect of
+ 
+
+ align:start position:0%
+exactly improvisation but an effect of
+uh an effect that creates the impression
+
+ align:start position:0%
+uh an effect that creates the impression
+ 
+
+ align:start position:0%
+uh an effect that creates the impression
+that there's a sometimes that it's most
+
+ align:start position:0%
+that there's a sometimes that it's most
+ 
+
+ align:start position:0%
+that there's a sometimes that it's most
+powerful or compelling moments as if the
+
+ align:start position:0%
+powerful or compelling moments as if the
+ 
+
+ align:start position:0%
+powerful or compelling moments as if the
+camera is actually uh almost a living
+
+ align:start position:0%
+camera is actually uh almost a living
+ 
+
+ align:start position:0%
+camera is actually uh almost a living
+witness to what seeing and it's and
+
+ align:start position:0%
+witness to what seeing and it's and
+ 
+
+ align:start position:0%
+witness to what seeing and it's and
+responding in very nuanced and sometimes
+
+ align:start position:0%
+responding in very nuanced and sometimes
+ 
+
+ align:start position:0%
+responding in very nuanced and sometimes
+very uh uh abrupt ways to what it sees
+
+ align:start position:0%
+very uh uh abrupt ways to what it sees
+ 
+
+ align:start position:0%
+very uh uh abrupt ways to what it sees
+and hears so there's sometimes moments
+
+ align:start position:0%
+and hears so there's sometimes moments
+ 
+
+ align:start position:0%
+and hears so there's sometimes moments
+in in in both poetic realist films and
+
+ align:start position:0%
+in in in both poetic realist films and
+ 
+
+ align:start position:0%
+in in in both poetic realist films and
+in Italian neorealist films in which a
+
+ align:start position:0%
+in Italian neorealist films in which a
+ 
+
+ align:start position:0%
+in Italian neorealist films in which a
+noise will occur and you'll suddenly see
+
+ align:start position:0%
+noise will occur and you'll suddenly see
+ 
+
+ align:start position:0%
+noise will occur and you'll suddenly see
+the camera turn to find out what the
+
+ align:start position:0%
+the camera turn to find out what the
+ 
+
+ align:start position:0%
+the camera turn to find out what the
+noise is as if it as if the camera is
+
+ align:start position:0%
+noise is as if it as if the camera is
+ 
+
+ align:start position:0%
+noise is as if it as if the camera is
+humanized in this kind of and what
+
+ align:start position:0%
+humanized in this kind of and what
+ 
+
+ align:start position:0%
+humanized in this kind of and what
+follows from that is the camera is all
+
+ align:start position:0%
+follows from that is the camera is all
+ 
+
+ align:start position:0%
+follows from that is the camera is all
+not always but usually set at eye level
+
+ align:start position:0%
+not always but usually set at eye level
+ 
+
+ align:start position:0%
+not always but usually set at eye level
+it does not give a lot of fantastic uh
+
+ align:start position:0%
+it does not give a lot of fantastic uh
+ 
+
+ align:start position:0%
+it does not give a lot of fantastic uh
+distorting uh angle a vision because
+
+ align:start position:0%
+distorting uh angle a vision because
+ 
+
+ align:start position:0%
+distorting uh angle a vision because
+it's not interested in that kind of uh U
+
+ align:start position:0%
+it's not interested in that kind of uh U
+ 
+
+ align:start position:0%
+it's not interested in that kind of uh U
+surreal or expressionist uh
+
+ align:start position:0%
+surreal or expressionist uh
+ 
+
+ align:start position:0%
+surreal or expressionist uh
+representation um uh so misen style in
+
+ align:start position:0%
+representation um uh so misen style in
+ 
+
+ align:start position:0%
+representation um uh so misen style in
+camera editing a second fundamental
+
+ align:start position:0%
+camera editing a second fundamental
+ 
+
+ align:start position:0%
+camera editing a second fundamental
+feature would be filming on location
+
+ align:start position:0%
+feature would be filming on location
+ 
+
+ align:start position:0%
+feature would be filming on location
+right no more in studio there's a kind
+
+ align:start position:0%
+right no more in studio there's a kind
+ 
+
+ align:start position:0%
+right no more in studio there's a kind
+of there's a kind of gross fundamental
+
+ align:start position:0%
+of there's a kind of gross fundamental
+ 
+
+ align:start position:0%
+of there's a kind of gross fundamental
+realism to these kinds of films because
+
+ align:start position:0%
+realism to these kinds of films because
+ 
+
+ align:start position:0%
+realism to these kinds of films because
+they because they use natural lighting
+
+ align:start position:0%
+they because they use natural lighting
+ 
+
+ align:start position:0%
+they because they use natural lighting
+they they in they in they insist or try
+
+ align:start position:0%
+they they in they in they insist or try
+ 
+
+ align:start position:0%
+they they in they in they insist or try
+to insist on them on themselves as as
+
+ align:start position:0%
+to insist on them on themselves as as
+ 
+
+ align:start position:0%
+to insist on them on themselves as as
+actual photographing a world you
+
+ align:start position:0%
+actual photographing a world you
+ 
+
+ align:start position:0%
+actual photographing a world you
+recognize as real not a world that has
+
+ align:start position:0%
+recognize as real not a world that has
+ 
+
+ align:start position:0%
+recognize as real not a world that has
+been artificially constructed in a
+
+ align:start position:0%
+been artificially constructed in a
+ 
+
+ align:start position:0%
+been artificially constructed in a
+studio uh in a studio space um uh uh
+
+ align:start position:0%
+studio uh in a studio space um uh uh
+ 
+
+ align:start position:0%
+studio uh in a studio space um uh uh
+what follows also from the location
+
+ align:start position:0%
+what follows also from the location
+ 
+
+ align:start position:0%
+what follows also from the location
+filming is a commitment to what might be
+
+ align:start position:0%
+filming is a commitment to what might be
+ 
+
+ align:start position:0%
+filming is a commitment to what might be
+called True light and sound right it's
+
+ align:start position:0%
+called True light and sound right it's
+ 
+
+ align:start position:0%
+called True light and sound right it's
+very rare in these kinds of films to
+
+ align:start position:0%
+very rare in these kinds of films to
+ 
+
+ align:start position:0%
+very rare in these kinds of films to
+have external sound the sound even the
+
+ align:start position:0%
+have external sound the sound even the
+ 
+
+ align:start position:0%
+have external sound the sound even the
+music that comes up in many of these in
+
+ align:start position:0%
+music that comes up in many of these in
+ 
+
+ align:start position:0%
+music that comes up in many of these in
+most of these films this is a wonderful
+
+ align:start position:0%
+most of these films this is a wonderful
+ 
+
+ align:start position:0%
+most of these films this is a wonderful
+habit of uh Renoir himself uh the
+
+ align:start position:0%
+habit of uh Renoir himself uh the
+ 
+
+ align:start position:0%
+habit of uh Renoir himself uh the
+sometimes you actually think the music
+
+ align:start position:0%
+sometimes you actually think the music
+ 
+
+ align:start position:0%
+sometimes you actually think the music
+is not a part of the drama but then you
+
+ align:start position:0%
+is not a part of the drama but then you
+ 
+
+ align:start position:0%
+is not a part of the drama but then you
+discover it is almost all the music in
+
+ align:start position:0%
+discover it is almost all the music in
+ 
+
+ align:start position:0%
+discover it is almost all the music in
+renoir's films is is part of the
+
+ align:start position:0%
+renoir's films is is part of the
+ 
+
+ align:start position:0%
+renoir's films is is part of the
+dramatic texture it's not imposed from
+
+ align:start position:0%
+dramatic texture it's not imposed from
+ 
+
+ align:start position:0%
+dramatic texture it's not imposed from
+the outside it's not it's not a
+
+ align:start position:0%
+the outside it's not it's not a
+ 
+
+ align:start position:0%
+the outside it's not it's not a
+soundtrack that doesn't grow out of the
+
+ align:start position:0%
+soundtrack that doesn't grow out of the
+ 
+
+ align:start position:0%
+soundtrack that doesn't grow out of the
+action so if you hear music in a Run
+
+ align:start position:0%
+action so if you hear music in a Run
+ 
+
+ align:start position:0%
+action so if you hear music in a Run
+film I'll show you an example of it in a
+
+ align:start position:0%
+film I'll show you an example of it in a
+ 
+
+ align:start position:0%
+film I'll show you an example of it in a
+moment from budoo uh it turns out that
+
+ align:start position:0%
+moment from budoo uh it turns out that
+ 
+
+ align:start position:0%
+moment from budoo uh it turns out that
+the music is being played by characters
+
+ align:start position:0%
+the music is being played by characters
+ 
+
+ align:start position:0%
+the music is being played by characters
+in the film and you actually end up
+
+ align:start position:0%
+in the film and you actually end up
+ 
+
+ align:start position:0%
+in the film and you actually end up
+seeing them with their instruments uh so
+
+ align:start position:0%
+seeing them with their instruments uh so
+ 
+
+ align:start position:0%
+seeing them with their instruments uh so
+true light and sound and and and and
+
+ align:start position:0%
+true light and sound and and and and
+ 
+
+ align:start position:0%
+true light and sound and and and and
+that what that also means is sometimes
+
+ align:start position:0%
+that what that also means is sometimes
+ 
+
+ align:start position:0%
+that what that also means is sometimes
+sound is obscure
+
+ align:start position:0%
+sound is obscure
+ 
+
+ align:start position:0%
+sound is obscure
+sometimes sound is is uh is overlapped
+
+ align:start position:0%
+sometimes sound is is uh is overlapped
+ 
+
+ align:start position:0%
+sometimes sound is is uh is overlapped
+with other noises sometimes dialogue is
+
+ align:start position:0%
+with other noises sometimes dialogue is
+ 
+
+ align:start position:0%
+with other noises sometimes dialogue is
+hard to hear because there are noises in
+
+ align:start position:0%
+hard to hear because there are noises in
+ 
+
+ align:start position:0%
+hard to hear because there are noises in
+in in in the real world we I I noted
+
+ align:start position:0%
+in in in the real world we I I noted
+ 
+
+ align:start position:0%
+in in in the real world we I I noted
+that this was an aspect of a number of
+
+ align:start position:0%
+that this was an aspect of a number of
+ 
+
+ align:start position:0%
+that this was an aspect of a number of
+American directors in the in the post
+
+ align:start position:0%
+American directors in the in the post
+ 
+
+ align:start position:0%
+American directors in the in the post
+Studio era uh and especially in a film
+
+ align:start position:0%
+Studio era uh and especially in a film
+ 
+
+ align:start position:0%
+Studio era uh and especially in a film
+like mcab where ultman does this kind of
+
+ align:start position:0%
+like mcab where ultman does this kind of
+ 
+
+ align:start position:0%
+like mcab where ultman does this kind of
+thing and I think I think that it uh
+
+ align:start position:0%
+thing and I think I think that it uh
+ 
+
+ align:start position:0%
+thing and I think I think that it uh
+it's it's it's very probable even though
+
+ align:start position:0%
+it's it's it's very probable even though
+ 
+
+ align:start position:0%
+it's it's it's very probable even though
+I don't know this for certain that Alman
+
+ align:start position:0%
+I don't know this for certain that Alman
+ 
+
+ align:start position:0%
+I don't know this for certain that Alman
+himself went to school on these films
+
+ align:start position:0%
+himself went to school on these films
+ 
+
+ align:start position:0%
+himself went to school on these films
+and knew uh the experiments with sound
+
+ align:start position:0%
+and knew uh the experiments with sound
+ 
+
+ align:start position:0%
+and knew uh the experiments with sound
+or the treat M of sound that was
+
+ align:start position:0%
+or the treat M of sound that was
+ 
+
+ align:start position:0%
+or the treat M of sound that was
+characteristic of renoir's U uh of
+
+ align:start position:0%
+characteristic of renoir's U uh of
+ 
+
+ align:start position:0%
+characteristic of renoir's U uh of
+renoir's films and other forms of it of
+
+ align:start position:0%
+renoir's films and other forms of it of
+ 
+
+ align:start position:0%
+renoir's films and other forms of it of
+both French and uh and Italian forms of
+
+ align:start position:0%
+both French and uh and Italian forms of
+ 
+
+ align:start position:0%
+both French and uh and Italian forms of
+of realism what what was called realism
+
+ align:start position:0%
+of realism what what was called realism
+ 
+
+ align:start position:0%
+of realism what what was called realism
+so uh uh and then and then uh two other
+
+ align:start position:0%
+so uh uh and then and then uh two other
+ 
+
+ align:start position:0%
+so uh uh and then and then uh two other
+features one already implied in what I
+
+ align:start position:0%
+features one already implied in what I
+ 
+
+ align:start position:0%
+features one already implied in what I
+was saying a camera that's very fluid in
+
+ align:start position:0%
+was saying a camera that's very fluid in
+ 
+
+ align:start position:0%
+was saying a camera that's very fluid in
+MO in motion uh not in gigantic motion
+
+ align:start position:0%
+MO in motion uh not in gigantic motion
+ 
+
+ align:start position:0%
+MO in motion uh not in gigantic motion
+but very subtle kinds of motions and if
+
+ align:start position:0%
+but very subtle kinds of motions and if
+ 
+
+ align:start position:0%
+but very subtle kinds of motions and if
+you watch Ren War's camera you'll see
+
+ align:start position:0%
+you watch Ren War's camera you'll see
+ 
+
+ align:start position:0%
+you watch Ren War's camera you'll see
+that it's almost constantly making these
+
+ align:start position:0%
+that it's almost constantly making these
+ 
+
+ align:start position:0%
+that it's almost constantly making these
+minute adjustments to what it's looking
+
+ align:start position:0%
+minute adjustments to what it's looking
+ 
+
+ align:start position:0%
+minute adjustments to what it's looking
+at or to what it to or to what it wants
+
+ align:start position:0%
+at or to what it to or to what it wants
+ 
+
+ align:start position:0%
+at or to what it to or to what it wants
+to see and then and then finally
+
+ align:start position:0%
+to see and then and then finally
+ 
+
+ align:start position:0%
+to see and then and then finally
+something I've already said uh there's a
+
+ align:start position:0%
+something I've already said uh there's a
+ 
+
+ align:start position:0%
+something I've already said uh there's a
+great emphasis on what could be called
+
+ align:start position:0%
+great emphasis on what could be called
+ 
+
+ align:start position:0%
+great emphasis on what could be called
+depth of field that is to say you're
+
+ align:start position:0%
+depth of field that is to say you're
+ 
+
+ align:start position:0%
+depth of field that is to say you're
+aware of the dimensionality of the
+
+ align:start position:0%
+aware of the dimensionality of the
+ 
+
+ align:start position:0%
+aware of the dimensionality of the
+images you're looking at so there's a
+
+ align:start position:0%
+images you're looking at so there's a
+ 
+
+ align:start position:0%
+images you're looking at so there's a
+background a middle ground and a
+
+ align:start position:0%
+background a middle ground and a
+ 
+
+ align:start position:0%
+background a middle ground and a
+foreground and uh um very often you'll
+
+ align:start position:0%
+foreground and uh um very often you'll
+ 
+
+ align:start position:0%
+foreground and uh um very often you'll
+see the camera change its focal uh uh
+
+ align:start position:0%
+see the camera change its focal uh uh
+ 
+
+ align:start position:0%
+see the camera change its focal uh uh
+length uh and what will if the
+
+ align:start position:0%
+length uh and what will if the
+ 
+
+ align:start position:0%
+length uh and what will if the
+foreground was in in in Focus you you'll
+
+ align:start position:0%
+foreground was in in in Focus you you'll
+ 
+
+ align:start position:0%
+foreground was in in in Focus you you'll
+actually experience the camera shifting
+
+ align:start position:0%
+actually experience the camera shifting
+ 
+
+ align:start position:0%
+actually experience the camera shifting
+its uh its focus bringing in the
+
+ align:start position:0%
+its uh its focus bringing in the
+ 
+
+ align:start position:0%
+its uh its focus bringing in the
+background that had been out of focus
+
+ align:start position:0%
+background that had been out of focus
+ 
+
+ align:start position:0%
+background that had been out of focus
+before and the effect of this while it
+
+ align:start position:0%
+before and the effect of this while it
+ 
+
+ align:start position:0%
+before and the effect of this while it
+because it takes place within your
+
+ align:start position:0%
+because it takes place within your
+ 
+
+ align:start position:0%
+because it takes place within your
+experience of viewing it doesn't take
+
+ align:start position:0%
+experience of viewing it doesn't take
+ 
+
+ align:start position:0%
+experience of viewing it doesn't take
+place hidden behind behind edits is to
+
+ align:start position:0%
+place hidden behind behind edits is to
+ 
+
+ align:start position:0%
+place hidden behind behind edits is to
+make you part of the process in some
+
+ align:start position:0%
+make you part of the process in some
+ 
+
+ align:start position:0%
+make you part of the process in some
+sense again to make you feel that the
+
+ align:start position:0%
+sense again to make you feel that the
+ 
+
+ align:start position:0%
+sense again to make you feel that the
+camera's behavior is a uh is a part of
+
+ align:start position:0%
+camera's behavior is a uh is a part of
+ 
+
+ align:start position:0%
+camera's behavior is a uh is a part of
+your experience of the film that you're
+
+ align:start position:0%
+your experience of the film that you're
+ 
+
+ align:start position:0%
+your experience of the film that you're
+experiencing the film through a a medium
+
+ align:start position:0%
+experiencing the film through a a medium
+ 
+
+ align:start position:0%
+experiencing the film through a a medium
+that has a kind of immense sensitivity
+
+ align:start position:0%
+that has a kind of immense sensitivity
+ 
+
+ align:start position:0%
+that has a kind of immense sensitivity
+to what it's looking at an immense
+
+ align:start position:0%
+to what it's looking at an immense
+ 
+
+ align:start position:0%
+to what it's looking at an immense
+respect for what it's looking at well uh
+
+ align:start position:0%
+respect for what it's looking at well uh
+ 
+
+ align:start position:0%
+respect for what it's looking at well uh
+so key features let me just summarize
+
+ align:start position:0%
+so key features let me just summarize
+ 
+
+ align:start position:0%
+so key features let me just summarize
+them again amen style which means in
+
+ align:start position:0%
+them again amen style which means in
+ 
+
+ align:start position:0%
+them again amen style which means in
+camera editing uh especially uh filming
+
+ align:start position:0%
+camera editing uh especially uh filming
+ 
+
+ align:start position:0%
+camera editing uh especially uh filming
+on location commitment to True light and
+
+ align:start position:0%
+on location commitment to True light and
+ 
+
+ align:start position:0%
+on location commitment to True light and
+sound a fluid moving camera commitment
+
+ align:start position:0%
+sound a fluid moving camera commitment
+ 
+
+ align:start position:0%
+sound a fluid moving camera commitment
+to depth of field what we might call
+
+ align:start position:0%
+to depth of field what we might call
+ 
+
+ align:start position:0%
+to depth of field what we might call
+again creating this tension between a
+
+ align:start position:0%
+again creating this tension between a
+ 
+
+ align:start position:0%
+again creating this tension between a
+kind of lyrical impulse uh a kind of a
+
+ align:start position:0%
+kind of lyrical impulse uh a kind of a
+ 
+
+ align:start position:0%
+kind of lyrical impulse uh a kind of a
+kind of celebratory or a poetic impulse
+
+ align:start position:0%
+kind of celebratory or a poetic impulse
+ 
+
+ align:start position:0%
+kind of celebratory or a poetic impulse
+as some people have said uh and a and an
+
+ align:start position:0%
+as some people have said uh and a and an
+ 
+
+ align:start position:0%
+as some people have said uh and a and an
+Impulse simply to to denote the world to
+
+ align:start position:0%
+Impulse simply to to denote the world to
+ 
+
+ align:start position:0%
+Impulse simply to to denote the world to
+capture the world to describe or to to
+
+ align:start position:0%
+capture the world to describe or to to
+ 
+
+ align:start position:0%
+capture the world to describe or to to
+dramatize the world fully well I I think
+
+ align:start position:0%
+dramatize the world fully well I I think
+ 
+
+ align:start position:0%
+dramatize the world fully well I I think
+I can show you or or dramatize these
+
+ align:start position:0%
+I can show you or or dramatize these
+ 
+
+ align:start position:0%
+I can show you or or dramatize these
+principles uh more fully for you um uh
+
+ align:start position:0%
+principles uh more fully for you um uh
+ 
+
+ align:start position:0%
+principles uh more fully for you um uh
+if I give you some examples but uh as a
+
+ align:start position:0%
+if I give you some examples but uh as a
+ 
+
+ align:start position:0%
+if I give you some examples but uh as a
+as a way of introducing this I want to
+
+ align:start position:0%
+as a way of introducing this I want to
+ 
+
+ align:start position:0%
+as a way of introducing this I want to
+talk uh very
+
+ align:start position:0%
+talk uh very
+ 
+
+ align:start position:0%
+talk uh very
+quickly about one formulation uh
+
+ align:start position:0%
+quickly about one formulation uh
+ 
+
+ align:start position:0%
+quickly about one formulation uh
+immensely influential formulation about
+
+ align:start position:0%
+immensely influential formulation about
+ 
+
+ align:start position:0%
+immensely influential formulation about
+Renoir that I think you'll find helpful
+
+ align:start position:0%
+Renoir that I think you'll find helpful
+ 
+
+ align:start position:0%
+Renoir that I think you'll find helpful
+and interesting and these are lines that
+
+ align:start position:0%
+and interesting and these are lines that
+ 
+
+ align:start position:0%
+and interesting and these are lines that
+have been written about by the great uh
+
+ align:start position:0%
+have been written about by the great uh
+ 
+
+ align:start position:0%
+have been written about by the great uh
+uh critic Andre Baza who was a great
+
+ align:start position:0%
+uh critic Andre Baza who was a great
+ 
+
+ align:start position:0%
+uh critic Andre Baza who was a great
+champion of renoir's work also a great
+
+ align:start position:0%
+champion of renoir's work also a great
+ 
+
+ align:start position:0%
+champion of renoir's work also a great
+champion of Italian neoism and one of
+
+ align:start position:0%
+champion of Italian neoism and one of
+ 
+
+ align:start position:0%
+champion of Italian neoism and one of
+the great theorists of of the of of the
+
+ align:start position:0%
+the great theorists of of the of of the
+ 
+
+ align:start position:0%
+the great theorists of of the of of the
+cinema uh and uh um we can capture I
+
+ align:start position:0%
+cinema uh and uh um we can capture I
+ 
+
+ align:start position:0%
+cinema uh and uh um we can capture I
+think Ren I think that bazan captured
+
+ align:start position:0%
+think Ren I think that bazan captured
+ 
+
+ align:start position:0%
+think Ren I think that bazan captured
+something of renoir's importance in
+
+ align:start position:0%
+something of renoir's importance in
+ 
+
+ align:start position:0%
+something of renoir's importance in
+these passages from his book titled Jean
+
+ align:start position:0%
+these passages from his book titled Jean
+ 
+
+ align:start position:0%
+these passages from his book titled Jean
+Renoir published in 1971 no one has
+
+ align:start position:0%
+Renoir published in 1971 no one has
+ 
+
+ align:start position:0%
+Renoir published in 1971 no one has
+grasped the true nature of the screen
+
+ align:start position:0%
+grasped the true nature of the screen
+ 
+
+ align:start position:0%
+grasped the true nature of the screen
+better than Ren are so wrote bazan no
+
+ align:start position:0%
+better than Ren are so wrote bazan no
+ 
+
+ align:start position:0%
+better than Ren are so wrote bazan no
+one has more successfully rid it of the
+
+ align:start position:0%
+one has more successfully rid it of the
+ 
+
+ align:start position:0%
+one has more successfully rid it of the
+equivocal of equivocal analogies with
+
+ align:start position:0%
+equivocal of equivocal analogies with
+ 
+
+ align:start position:0%
+equivocal of equivocal analogies with
+painting and the theater plastically the
+
+ align:start position:0%
+painting and the theater plastically the
+ 
+
+ align:start position:0%
+painting and the theater plastically the
+screen is most often made to conform to
+
+ align:start position:0%
+screen is most often made to conform to
+ 
+
+ align:start position:0%
+screen is most often made to conform to
+the limits of the canvas and
+
+ align:start position:0%
+the limits of the canvas and
+ 
+
+ align:start position:0%
+the limits of the canvas and
+dramatically it's modeled on the stage
+
+ align:start position:0%
+dramatically it's modeled on the stage
+ 
+
+ align:start position:0%
+dramatically it's modeled on the stage
+you see what he what bazan is saying is
+
+ align:start position:0%
+you see what he what bazan is saying is
+ 
+
+ align:start position:0%
+you see what he what bazan is saying is
+he's reminding us that when a new
+
+ align:start position:0%
+he's reminding us that when a new
+ 
+
+ align:start position:0%
+he's reminding us that when a new
+technology emerges uh old habits are so
+
+ align:start position:0%
+technology emerges uh old habits are so
+ 
+
+ align:start position:0%
+technology emerges uh old habits are so
+deeply embedded that it's very hard to
+
+ align:start position:0%
+deeply embedded that it's very hard to
+ 
+
+ align:start position:0%
+deeply embedded that it's very hard to
+free oneself from them even though
+
+ align:start position:0%
+free oneself from them even though
+ 
+
+ align:start position:0%
+free oneself from them even though
+there's nothing inherent in the new
+
+ align:start position:0%
+there's nothing inherent in the new
+ 
+
+ align:start position:0%
+there's nothing inherent in the new
+technology that requires you to see the
+
+ align:start position:0%
+technology that requires you to see the
+ 
+
+ align:start position:0%
+technology that requires you to see the
+world in the ways that the older systems
+
+ align:start position:0%
+world in the ways that the older systems
+ 
+
+ align:start position:0%
+world in the ways that the older systems
+did and then there's a period of
+
+ align:start position:0%
+did and then there's a period of
+ 
+
+ align:start position:0%
+did and then there's a period of
+transition that's involved period of
+
+ align:start position:0%
+transition that's involved period of
+ 
+
+ align:start position:0%
+transition that's involved period of
+experiment and Discovery what bazan is
+
+ align:start position:0%
+experiment and Discovery what bazan is
+ 
+
+ align:start position:0%
+experiment and Discovery what bazan is
+saying here is that Renoir is one of the
+
+ align:start position:0%
+saying here is that Renoir is one of the
+ 
+
+ align:start position:0%
+saying here is that Renoir is one of the
+great pioneering discoverers right
+
+ align:start position:0%
+great pioneering discoverers right
+ 
+
+ align:start position:0%
+great pioneering discoverers right
+because with these two traditional
+
+ align:start position:0%
+because with these two traditional
+ 
+
+ align:start position:0%
+because with these two traditional
+references in mind directors have
+
+ align:start position:0%
+references in mind directors have
+ 
+
+ align:start position:0%
+references in mind directors have
+conceived their images as boxed within a
+
+ align:start position:0%
+conceived their images as boxed within a
+ 
+
+ align:start position:0%
+conceived their images as boxed within a
+rectangle as do the painter and the
+
+ align:start position:0%
+rectangle as do the painter and the
+ 
+
+ align:start position:0%
+rectangle as do the painter and the
+stage director and in fact this still
+
+ align:start position:0%
+stage director and in fact this still
+ 
+
+ align:start position:0%
+stage director and in fact this still
+happens today with lazy or foolish
+
+ align:start position:0%
+happens today with lazy or foolish
+ 
+
+ align:start position:0%
+happens today with lazy or foolish
+directors right
+
+ align:start position:0%
+directors right
+ 
+
+ align:start position:0%
+directors right
+war on the other hand understands that
+
+ align:start position:0%
+war on the other hand understands that
+ 
+
+ align:start position:0%
+war on the other hand understands that
+the screen is not a simple rectangle but
+
+ align:start position:0%
+the screen is not a simple rectangle but
+ 
+
+ align:start position:0%
+the screen is not a simple rectangle but
+rather the surface of the viewfinder of
+
+ align:start position:0%
+rather the surface of the viewfinder of
+ 
+
+ align:start position:0%
+rather the surface of the viewfinder of
+his camera it is the opposite of a frame
+
+ align:start position:0%
+his camera it is the opposite of a frame
+ 
+
+ align:start position:0%
+his camera it is the opposite of a frame
+right there's stuff that goes on outside
+
+ align:start position:0%
+right there's stuff that goes on outside
+ 
+
+ align:start position:0%
+right there's stuff that goes on outside
+the frame if it's look right this is a
+
+ align:start position:0%
+the frame if it's look right this is a
+ 
+
+ align:start position:0%
+the frame if it's look right this is a
+brilliant piece of writing I think
+
+ align:start position:0%
+brilliant piece of writing I think
+ 
+
+ align:start position:0%
+brilliant piece of writing I think
+technically this conception of the
+
+ align:start position:0%
+technically this conception of the
+ 
+
+ align:start position:0%
+technically this conception of the
+screen assumes what I bazan shall call
+
+ align:start position:0%
+screen assumes what I bazan shall call
+ 
+
+ align:start position:0%
+screen assumes what I bazan shall call
+lateral depth of field lateral depth of
+
+ align:start position:0%
+lateral depth of field lateral depth of
+ 
+
+ align:start position:0%
+lateral depth of field lateral depth of
+field that is but it's a oxoboron i gu
+
+ align:start position:0%
+field that is but it's a oxoboron i gu
+ 
+
+ align:start position:0%
+field that is but it's a oxoboron i gu
+or a contradiction but right how could
+
+ align:start position:0%
+or a contradiction but right how could
+ 
+
+ align:start position:0%
+or a contradiction but right how could
+there be a lateral but what he means is
+
+ align:start position:0%
+there be a lateral but what he means is
+ 
+
+ align:start position:0%
+there be a lateral but what he means is
+that you become aware of things going on
+
+ align:start position:0%
+that you become aware of things going on
+ 
+
+ align:start position:0%
+that you become aware of things going on
+on the margins of the of the of the
+
+ align:start position:0%
+on the margins of the of the of the
+ 
+
+ align:start position:0%
+on the margins of the of the of the
+visual of the visual field even outside
+
+ align:start position:0%
+visual of the visual field even outside
+ 
+
+ align:start position:0%
+visual of the visual field even outside
+of what you can actually see um um since
+
+ align:start position:0%
+of what you can actually see um um since
+ 
+
+ align:start position:0%
+of what you can actually see um um since
+what we are shown is only significant in
+
+ align:start position:0%
+what we are shown is only significant in
+ 
+
+ align:start position:0%
+what we are shown is only significant in
+terms of what is hidden from us and
+
+ align:start position:0%
+terms of what is hidden from us and
+ 
+
+ align:start position:0%
+terms of what is hidden from us and
+since the value of what we see is
+
+ align:start position:0%
+since the value of what we see is
+ 
+
+ align:start position:0%
+since the value of what we see is
+therefore continually threatened the
+
+ align:start position:0%
+therefore continually threatened the
+ 
+
+ align:start position:0%
+therefore continually threatened the
+misen right what is put in the scene
+
+ align:start position:0%
+misen right what is put in the scene
+ 
+
+ align:start position:0%
+misen right what is put in the scene
+right the Misan sen cannot Li limit
+
+ align:start position:0%
+right the Misan sen cannot Li limit
+ 
+
+ align:start position:0%
+right the Misan sen cannot Li limit
+itself to what is presented on the
+
+ align:start position:0%
+itself to what is presented on the
+ 
+
+ align:start position:0%
+itself to what is presented on the
+screen the rest of the scene while
+
+ align:start position:0%
+screen the rest of the scene while
+ 
+
+ align:start position:0%
+screen the rest of the scene while
+effectively hidden should not cease to
+
+ align:start position:0%
+effectively hidden should not cease to
+ 
+
+ align:start position:0%
+effectively hidden should not cease to
+exist the action is not bounded by the
+
+ align:start position:0%
+exist the action is not bounded by the
+ 
+
+ align:start position:0%
+exist the action is not bounded by the
+screen but merely passes through it and
+
+ align:start position:0%
+screen but merely passes through it and
+ 
+
+ align:start position:0%
+screen but merely passes through it and
+a person who enters the camera's field
+
+ align:start position:0%
+a person who enters the camera's field
+ 
+
+ align:start position:0%
+a person who enters the camera's field
+of vision is coming from other areas of
+
+ align:start position:0%
+of vision is coming from other areas of
+ 
+
+ align:start position:0%
+of vision is coming from other areas of
+the action and not from some limbo or
+
+ align:start position:0%
+the action and not from some limbo or
+ 
+
+ align:start position:0%
+the action and not from some limbo or
+some from imaginary backstage you get
+
+ align:start position:0%
+some from imaginary backstage you get
+ 
+
+ align:start position:0%
+some from imaginary backstage you get
+this think how exciting this is what a
+
+ align:start position:0%
+this think how exciting this is what a
+ 
+
+ align:start position:0%
+this think how exciting this is what a
+what a fundamental Insight it is into
+
+ align:start position:0%
+what a fundamental Insight it is into
+ 
+
+ align:start position:0%
+what a fundamental Insight it is into
+the way a film can become compelling and
+
+ align:start position:0%
+the way a film can become compelling and
+ 
+
+ align:start position:0%
+the way a film can become compelling and
+why it is that so many films might seem
+
+ align:start position:0%
+why it is that so many films might seem
+ 
+
+ align:start position:0%
+why it is that so many films might seem
+factitious to us despite the gross
+
+ align:start position:0%
+factitious to us despite the gross
+ 
+
+ align:start position:0%
+factitious to us despite the gross
+reality of the Cinematic image likewise
+
+ align:start position:0%
+reality of the Cinematic image likewise
+ 
+
+ align:start position:0%
+reality of the Cinematic image likewise
+the camera should be able to spin
+
+ align:start position:0%
+the camera should be able to spin
+ 
+
+ align:start position:0%
+the camera should be able to spin
+suddenly Renoir is full of moments in
+
+ align:start position:0%
+suddenly Renoir is full of moments in
+ 
+
+ align:start position:0%
+suddenly Renoir is full of moments in
+which the camera will make wide SWAT
+
+ align:start position:0%
+which the camera will make wide SWAT
+ 
+
+ align:start position:0%
+which the camera will make wide SWAT
+sometimes sometimes 360 degree uh uh
+
+ align:start position:0%
+sometimes sometimes 360 degree uh uh
+ 
+
+ align:start position:0%
+sometimes sometimes 360 degree uh uh
+circles sometimes 180 degree turns in
+
+ align:start position:0%
+circles sometimes 180 degree turns in
+ 
+
+ align:start position:0%
+circles sometimes 180 degree turns in
+order to remind us of what has not been
+
+ align:start position:0%
+order to remind us of what has not been
+ 
+
+ align:start position:0%
+order to remind us of what has not been
+in the frame of what is on the margins
+
+ align:start position:0%
+in the frame of what is on the margins
+ 
+
+ align:start position:0%
+in the frame of what is on the margins
+of the frame so the camera should be
+
+ align:start position:0%
+of the frame so the camera should be
+ 
+
+ align:start position:0%
+of the frame so the camera should be
+able to spin suddenly without picking up
+
+ align:start position:0%
+able to spin suddenly without picking up
+ 
+
+ align:start position:0%
+able to spin suddenly without picking up
+any holes or dead spots in the action
+
+ align:start position:0%
+any holes or dead spots in the action
+ 
+
+ align:start position:0%
+any holes or dead spots in the action
+well I want to give you two examples of
+
+ align:start position:0%
+well I want to give you two examples of
+ 
+
+ align:start position:0%
+well I want to give you two examples of
+this which are among other things
+
+ align:start position:0%
+this which are among other things
+ 
+
+ align:start position:0%
+this which are among other things
+instances of what I call put my outline
+
+ align:start position:0%
+instances of what I call put my outline
+ 
+
+ align:start position:0%
+instances of what I call put my outline
+back up uh instance of instances of what
+
+ align:start position:0%
+back up uh instance of instances of what
+ 
+
+ align:start position:0%
+back up uh instance of instances of what
+I call Visual style as moral vision and
+
+ align:start position:0%
+I call Visual style as moral vision and
+ 
+
+ align:start position:0%
+I call Visual style as moral vision and
+I'll hopefully be explaining that uh
+
+ align:start position:0%
+I'll hopefully be explaining that uh
+ 
+
+ align:start position:0%
+I'll hopefully be explaining that uh
+term as we as we look at it so so the
+
+ align:start position:0%
+term as we as we look at it so so the
+ 
+
+ align:start position:0%
+term as we as we look at it so so the
+first clip I want to show you uh is from
+
+ align:start position:0%
+first clip I want to show you uh is from
+ 
+
+ align:start position:0%
+first clip I want to show you uh is from
+the film you're going to see tonight and
+
+ align:start position:0%
+the film you're going to see tonight and
+ 
+
+ align:start position:0%
+the film you're going to see tonight and
+it's a way of alerting you to qualities
+
+ align:start position:0%
+it's a way of alerting you to qualities
+ 
+
+ align:start position:0%
+it's a way of alerting you to qualities
+not just in this scene but elsewhere in
+
+ align:start position:0%
+not just in this scene but elsewhere in
+ 
+
+ align:start position:0%
+not just in this scene but elsewhere in
+the film that I hope you'll become much
+
+ align:start position:0%
+the film that I hope you'll become much
+ 
+
+ align:start position:0%
+the film that I hope you'll become much
+more attentive to because we're taking
+
+ align:start position:0%
+more attentive to because we're taking
+ 
+
+ align:start position:0%
+more attentive to because we're taking
+the time to single them out now so here
+
+ align:start position:0%
+the time to single them out now so here
+ 
+
+ align:start position:0%
+the time to single them out now so here
+is a a scene from are we ready grandus
+
+ align:start position:0%
+is a a scene from are we ready grandus
+ 
+
+ align:start position:0%
+is a a scene from are we ready grandus
+uh from from uh um
+
+ align:start position:0%
+uh from from uh um
+ 
+
+ align:start position:0%
+uh from from uh um
+um Grand Illusion uh from relatively
+
+ align:start position:0%
+um Grand Illusion uh from relatively
+ 
+
+ align:start position:0%
+um Grand Illusion uh from relatively
+early in this in the in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+film now U as I've told you this the
+
+ align:start position:0%
+film now U as I've told you this the
+ 
+
+ align:start position:0%
+film now U as I've told you this the
+film is about prisoner French prisoners
+
+ align:start position:0%
+film is about prisoner French prisoners
+ 
+
+ align:start position:0%
+film is about prisoner French prisoners
+of War so here's a scene uh the French
+
+ align:start position:0%
+of War so here's a scene uh the French
+ 
+
+ align:start position:0%
+of War so here's a scene uh the French
+they these are prisoners but it's first
+
+ align:start position:0%
+they these are prisoners but it's first
+ 
+
+ align:start position:0%
+they these are prisoners but it's first
+world war they're allowed to receive
+
+ align:start position:0%
+world war they're allowed to receive
+ 
+
+ align:start position:0%
+world war they're allowed to receive
+packages from their from from from uh in
+
+ align:start position:0%
+packages from their from from from uh in
+ 
+
+ align:start position:0%
+packages from their from from from uh in
+the mail and what and what people in
+
+ align:start position:0%
+the mail and what and what people in
+ 
+
+ align:start position:0%
+the mail and what and what people in
+what people their relatives and friends
+
+ align:start position:0%
+what people their relatives and friends
+ 
+
+ align:start position:0%
+what people their relatives and friends
+send them is food very often all right
+
+ align:start position:0%
+send them is food very often all right
+ 
+
+ align:start position:0%
+send them is food very often all right
+all
+
+ align:start position:0%
+all
+ 
+
+ align:start position:0%
+all
+right can you make it a little louder
+
+ align:start position:0%
+right can you make it a little louder
+ 
+
+ align:start position:0%
+right can you make it a little louder
+not that it really
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+matters now watch the camera's Behavior
+
+ align:start position:0%
+matters now watch the camera's Behavior
+ 
+
+ align:start position:0%
+matters now watch the camera's Behavior
+what can you freeze it one second look
+
+ align:start position:0%
+what can you freeze it one second look
+ 
+
+ align:start position:0%
+what can you freeze it one second look
+at look at the window there why is that
+
+ align:start position:0%
+at look at the window there why is that
+ 
+
+ align:start position:0%
+at look at the window there why is that
+significant what do you notice in the
+
+ align:start position:0%
+significant what do you notice in the
+ 
+
+ align:start position:0%
+significant what do you notice in the
+window already movement right right and
+
+ align:start position:0%
+window already movement right right and
+ 
+
+ align:start position:0%
+window already movement right right and
+do you see how and and the way the scene
+
+ align:start position:0%
+do you see how and and the way the scene
+ 
+
+ align:start position:0%
+do you see how and and the way the scene
+began we know where that character has
+
+ align:start position:0%
+began we know where that character has
+ 
+
+ align:start position:0%
+began we know where that character has
+come from even though these two
+
+ align:start position:0%
+come from even though these two
+ 
+
+ align:start position:0%
+come from even though these two
+characters are in confrontation and
+
+ align:start position:0%
+characters are in confrontation and
+ 
+
+ align:start position:0%
+characters are in confrontation and
+talking to each other we're aware of
+
+ align:start position:0%
+talking to each other we're aware of
+ 
+
+ align:start position:0%
+talking to each other we're aware of
+activity in the window behind them we're
+
+ align:start position:0%
+activity in the window behind them we're
+ 
+
+ align:start position:0%
+activity in the window behind them we're
+aware of other people in the room it
+
+ align:start position:0%
+aware of other people in the room it
+ 
+
+ align:start position:0%
+aware of other people in the room it
+actually may seem as if it's very easy
+
+ align:start position:0%
+actually may seem as if it's very easy
+ 
+
+ align:start position:0%
+actually may seem as if it's very easy
+to create this effect but of course it's
+
+ align:start position:0%
+to create this effect but of course it's
+ 
+
+ align:start position:0%
+to create this effect but of course it's
+profoundly difficult and and Renoir is
+
+ align:start position:0%
+profoundly difficult and and Renoir is
+ 
+
+ align:start position:0%
+profoundly difficult and and Renoir is
+the Pioneer uh in creating these these
+
+ align:start position:0%
+the Pioneer uh in creating these these
+ 
+
+ align:start position:0%
+the Pioneer uh in creating these these
+kinds of effects how fluid the camera is
+
+ align:start position:0%
+kinds of effects how fluid the camera is
+ 
+
+ align:start position:0%
+kinds of effects how fluid the camera is
+how that's what I want you to watch for
+
+ align:start position:0%
+how that's what I want you to watch for
+ 
+
+ align:start position:0%
+how that's what I want you to watch for
+your awareness of the fact of action
+
+ align:start position:0%
+your awareness of the fact of action
+ 
+
+ align:start position:0%
+your awareness of the fact of action
+that's going on partly outside the
+
+ align:start position:0%
+that's going on partly outside the
+ 
+
+ align:start position:0%
+that's going on partly outside the
+frame all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+continue the man at the head table is
+
+ align:start position:0%
+continue the man at the head table is
+ 
+
+ align:start position:0%
+continue the man at the head table is
+the wealthiest of the prisoners and he
+
+ align:start position:0%
+the wealthiest of the prisoners and he
+ 
+
+ align:start position:0%
+the wealthiest of the prisoners and he
+gets the best food so he shares it with
+
+ align:start position:0%
+gets the best food so he shares it with
+ 
+
+ align:start position:0%
+gets the best food so he shares it with
+his
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+comrades it's a tremendously good meal
+
+ align:start position:0%
+comrades it's a tremendously good meal
+ 
+
+ align:start position:0%
+comrades it's a tremendously good meal
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+prisoners this is the least violent war
+
+ align:start position:0%
+prisoners this is the least violent war
+ 
+
+ align:start position:0%
+prisoners this is the least violent war
+movie ever made
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+are you beginning to notice how each of
+
+ align:start position:0%
+are you beginning to notice how each of
+ 
+
+ align:start position:0%
+are you beginning to notice how each of
+the characters is individuated in this
+
+ align:start position:0%
+the characters is individuated in this
+ 
+
+ align:start position:0%
+the characters is individuated in this
+scene I don't have time to talk about
+
+ align:start position:0%
+scene I don't have time to talk about
+ 
+
+ align:start position:0%
+scene I don't have time to talk about
+this watch it tonight maybe I'll say a
+
+ align:start position:0%
+this watch it tonight maybe I'll say a
+ 
+
+ align:start position:0%
+this watch it tonight maybe I'll say a
+bit about it tonight when I introduced
+
+ align:start position:0%
+bit about it tonight when I introduced
+ 
+
+ align:start position:0%
+bit about it tonight when I introduced
+the fil but each one of them we can
+
+ align:start position:0%
+the fil but each one of them we can
+ 
+
+ align:start position:0%
+the fil but each one of them we can
+almost we can tell what social class
+
+ align:start position:0%
+almost we can tell what social class
+ 
+
+ align:start position:0%
+almost we can tell what social class
+they belong to from their dress from
+
+ align:start position:0%
+they belong to from their dress from
+ 
+
+ align:start position:0%
+they belong to from their dress from
+their mode of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+speech you see how quietly but complexly
+
+ align:start position:0%
+speech you see how quietly but complexly
+ 
+
+ align:start position:0%
+speech you see how quietly but complexly
+the camera
+
+ align:start position:0%
+the camera
+ 
+
+ align:start position:0%
+the camera
+examines the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space and that's J gaban one of the
+
+ align:start position:0%
+space and that's J gaban one of the
+ 
+
+ align:start position:0%
+space and that's J gaban one of the
+great one of the central
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characters and one of the great French
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actors all right we have to stop this
+
+ align:start position:0%
+actors all right we have to stop this
+ 
+
+ align:start position:0%
+actors all right we have to stop this
+because I'm sorry I have to cut this
+
+ align:start position:0%
+because I'm sorry I have to cut this
+ 
+
+ align:start position:0%
+because I'm sorry I have to cut this
+short it's a brilliant scene watch for
+
+ align:start position:0%
+short it's a brilliant scene watch for
+ 
+
+ align:start position:0%
+short it's a brilliant scene watch for
+it tonight comes fairly early in the
+
+ align:start position:0%
+it tonight comes fairly early in the
+ 
+
+ align:start position:0%
+it tonight comes fairly early in the
+film watch how each of the characters is
+
+ align:start position:0%
+film watch how each of the characters is
+ 
+
+ align:start position:0%
+film watch how each of the characters is
+individuated as the scene goes on how
+
+ align:start position:0%
+individuated as the scene goes on how
+ 
+
+ align:start position:0%
+individuated as the scene goes on how
+crowded the scene is in one sense how
+
+ align:start position:0%
+crowded the scene is in one sense how
+ 
+
+ align:start position:0%
+crowded the scene is in one sense how
+how how you're aware of activities and
+
+ align:start position:0%
+how how you're aware of activities and
+ 
+
+ align:start position:0%
+how how you're aware of activities and
+even conversations that are taking place
+
+ align:start position:0%
+even conversations that are taking place
+ 
+
+ align:start position:0%
+even conversations that are taking place
+outside the uh uh frame of the of the of
+
+ align:start position:0%
+outside the uh uh frame of the of the of
+ 
+
+ align:start position:0%
+outside the uh uh frame of the of the of
+the camera itself and when the camera
+
+ align:start position:0%
+the camera itself and when the camera
+ 
+
+ align:start position:0%
+the camera itself and when the camera
+shifts over to one set of characters
+
+ align:start position:0%
+shifts over to one set of characters
+ 
+
+ align:start position:0%
+shifts over to one set of characters
+you're aware of other conversations that
+
+ align:start position:0%
+you're aware of other conversations that
+ 
+
+ align:start position:0%
+you're aware of other conversations that
+that are ongoing other words the sense
+
+ align:start position:0%
+that are ongoing other words the sense
+ 
+
+ align:start position:0%
+that are ongoing other words the sense
+of reality that this style creates is
+
+ align:start position:0%
+of reality that this style creates is
+ 
+
+ align:start position:0%
+of reality that this style creates is
+profound and compelling it seems to me
+
+ align:start position:0%
+profound and compelling it seems to me
+ 
+
+ align:start position:0%
+profound and compelling it seems to me
+um powerful but I want to show you
+
+ align:start position:0%
+um powerful but I want to show you
+ 
+
+ align:start position:0%
+um powerful but I want to show you
+another and even more dramatic clip uh
+
+ align:start position:0%
+another and even more dramatic clip uh
+ 
+
+ align:start position:0%
+another and even more dramatic clip uh
+because partly because it comes from a
+
+ align:start position:0%
+because partly because it comes from a
+ 
+
+ align:start position:0%
+because partly because it comes from a
+film you've not seen because and because
+
+ align:start position:0%
+film you've not seen because and because
+ 
+
+ align:start position:0%
+film you've not seen because and because
+it captures certain other qualities in
+
+ align:start position:0%
+it captures certain other qualities in
+ 
+
+ align:start position:0%
+it captures certain other qualities in
+in uh renoir's R in renoir's work and
+
+ align:start position:0%
+in uh renoir's R in renoir's work and
+ 
+
+ align:start position:0%
+in uh renoir's R in renoir's work and
+this is this is the famous ending of
+
+ align:start position:0%
+this is this is the famous ending of
+ 
+
+ align:start position:0%
+this is this is the famous ending of
+budo save from drowning let me set the
+
+ align:start position:0%
+budo save from drowning let me set the
+ 
+
+ align:start position:0%
+budo save from drowning let me set the
+scene for you while uh Kristen's getting
+
+ align:start position:0%
+scene for you while uh Kristen's getting
+ 
+
+ align:start position:0%
+scene for you while uh Kristen's getting
+it up uh in this scene uh this comes at
+
+ align:start position:0%
+it up uh in this scene uh this comes at
+ 
+
+ align:start position:0%
+it up uh in this scene uh this comes at
+the very end of the film uh it's a the
+
+ align:start position:0%
+the very end of the film uh it's a the
+ 
+
+ align:start position:0%
+the very end of the film uh it's a the
+film is a satire and budoo is a bum a
+
+ align:start position:0%
+film is a satire and budoo is a bum a
+ 
+
+ align:start position:0%
+film is a satire and budoo is a bum a
+clar of whom there were tens of there
+
+ align:start position:0%
+clar of whom there were tens of there
+ 
+
+ align:start position:0%
+clar of whom there were tens of there
+were thousands if not tens of thousands
+
+ align:start position:0%
+were thousands if not tens of thousands
+ 
+
+ align:start position:0%
+were thousands if not tens of thousands
+living in Paris during the era when the
+
+ align:start position:0%
+living in Paris during the era when the
+ 
+
+ align:start position:0%
+living in Paris during the era when the
+film was made uh a kind of uh uh
+
+ align:start position:0%
+film was made uh a kind of uh uh
+ 
+
+ align:start position:0%
+film was made uh a kind of uh uh
+like like like the character that the
+
+ align:start position:0%
+like like like the character that the
+ 
+
+ align:start position:0%
+like like like the character that the
+chaplain figure plays in the American
+
+ align:start position:0%
+chaplain figure plays in the American
+ 
+
+ align:start position:0%
+chaplain figure plays in the American
+films although Michelle Simone is a much
+
+ align:start position:0%
+films although Michelle Simone is a much
+ 
+
+ align:start position:0%
+films although Michelle Simone is a much
+more massive figure than chaplain and uh
+
+ align:start position:0%
+more massive figure than chaplain and uh
+ 
+
+ align:start position:0%
+more massive figure than chaplain and uh
+in the very beginning of the film he
+
+ align:start position:0%
+in the very beginning of the film he
+ 
+
+ align:start position:0%
+in the very beginning of the film he
+plays this he seems to try he jumps into
+
+ align:start position:0%
+plays this he seems to try he jumps into
+ 
+
+ align:start position:0%
+plays this he seems to try he jumps into
+the river to try to commit suicide
+
+ align:start position:0%
+the river to try to commit suicide
+ 
+
+ align:start position:0%
+the river to try to commit suicide
+because he's lost his beloved dog he's a
+
+ align:start position:0%
+because he's lost his beloved dog he's a
+ 
+
+ align:start position:0%
+because he's lost his beloved dog he's a
+figure of Despair and a middle class
+
+ align:start position:0%
+figure of Despair and a middle class
+ 
+
+ align:start position:0%
+figure of Despair and a middle class
+book seller named leting Gua spying him
+
+ align:start position:0%
+book seller named leting Gua spying him
+ 
+
+ align:start position:0%
+book seller named leting Gua spying him
+through his spy glasses he's looking out
+
+ align:start position:0%
+through his spy glasses he's looking out
+ 
+
+ align:start position:0%
+through his spy glasses he's looking out
+of the out of his uh book out of the
+
+ align:start position:0%
+of the out of his uh book out of the
+ 
+
+ align:start position:0%
+of the out of his uh book out of the
+windows of his book of his book shop
+
+ align:start position:0%
+windows of his book of his book shop
+ 
+
+ align:start position:0%
+windows of his book of his book shop
+sees this bum at first he look Oh What A
+
+ align:start position:0%
+sees this bum at first he look Oh What A
+ 
+
+ align:start position:0%
+sees this bum at first he look Oh What A
+Perfect Bum he thinks to himself what a
+
+ align:start position:0%
+Perfect Bum he thinks to himself what a
+ 
+
+ align:start position:0%
+Perfect Bum he thinks to himself what a
+perfect embodiment of what a is
+
+ align:start position:0%
+perfect embodiment of what a is
+ 
+
+ align:start position:0%
+perfect embodiment of what a is
+and then he becomes upset when he sees
+
+ align:start position:0%
+and then he becomes upset when he sees
+ 
+
+ align:start position:0%
+and then he becomes upset when he sees
+the guy jump into the river and he runs
+
+ align:start position:0%
+the guy jump into the river and he runs
+ 
+
+ align:start position:0%
+the guy jump into the river and he runs
+out he dives into the river to save him
+
+ align:start position:0%
+out he dives into the river to save him
+ 
+
+ align:start position:0%
+out he dives into the river to save him
+and it turns into a kind of comic scene
+
+ align:start position:0%
+and it turns into a kind of comic scene
+ 
+
+ align:start position:0%
+and it turns into a kind of comic scene
+of saving people gather on the bridge
+
+ align:start position:0%
+of saving people gather on the bridge
+ 
+
+ align:start position:0%
+of saving people gather on the bridge
+and look down and so forth he pulls him
+
+ align:start position:0%
+and look down and so forth he pulls him
+ 
+
+ align:start position:0%
+and look down and so forth he pulls him
+out brings him into his home his wife is
+
+ align:start position:0%
+out brings him into his home his wife is
+ 
+
+ align:start position:0%
+out brings him into his home his wife is
+is very resentful of it but eventually
+
+ align:start position:0%
+is very resentful of it but eventually
+ 
+
+ align:start position:0%
+is very resentful of it but eventually
+she adapts and he moves into the uh
+
+ align:start position:0%
+she adapts and he moves into the uh
+ 
+
+ align:start position:0%
+she adapts and he moves into the uh
+middle class book seller's home and of
+
+ align:start position:0%
+middle class book seller's home and of
+ 
+
+ align:start position:0%
+middle class book seller's home and of
+course he WS Havoc there because he
+
+ align:start position:0%
+course he WS Havoc there because he
+ 
+
+ align:start position:0%
+course he WS Havoc there because he
+stands for nature itself he can't be
+
+ align:start position:0%
+stands for nature itself he can't be
+ 
+
+ align:start position:0%
+stands for nature itself he can't be
+civilized or tamed right he's buddo so
+
+ align:start position:0%
+civilized or tamed right he's buddo so
+ 
+
+ align:start position:0%
+civilized or tamed right he's buddo so
+saved from the waters right so he saved
+
+ align:start position:0%
+saved from the waters right so he saved
+ 
+
+ align:start position:0%
+saved from the waters right so he saved
+from The Waters at the end but as you'll
+
+ align:start position:0%
+from The Waters at the end but as you'll
+ 
+
+ align:start position:0%
+from The Waters at the end but as you'll
+see at the at the beginning but as
+
+ align:start position:0%
+see at the at the beginning but as
+ 
+
+ align:start position:0%
+see at the at the beginning but as
+you'll see at the end of the film he's
+
+ align:start position:0%
+you'll see at the end of the film he's
+ 
+
+ align:start position:0%
+you'll see at the end of the film he's
+back to the waters so here so what
+
+ align:start position:0%
+back to the waters so here so what
+ 
+
+ align:start position:0%
+back to the waters so here so what
+happens essentially is among other
+
+ align:start position:0%
+happens essentially is among other
+ 
+
+ align:start position:0%
+happens essentially is among other
+things in the course of the story this
+
+ align:start position:0%
+things in the course of the story this
+ 
+
+ align:start position:0%
+things in the course of the story this
+this uh figure of raw nature turns out
+
+ align:start position:0%
+this uh figure of raw nature turns out
+ 
+
+ align:start position:0%
+this uh figure of raw nature turns out
+that he can't quite be civilized one of
+
+ align:start position:0%
+that he can't quite be civilized one of
+ 
+
+ align:start position:0%
+that he can't quite be civilized one of
+the things he does is he manages to have
+
+ align:start position:0%
+the things he does is he manages to have
+ 
+
+ align:start position:0%
+the things he does is he manages to have
+a love affair or to or to seduce I could
+
+ align:start position:0%
+a love affair or to or to seduce I could
+ 
+
+ align:start position:0%
+a love affair or to or to seduce I could
+shouldn't call it a love affair both
+
+ align:start position:0%
+shouldn't call it a love affair both
+ 
+
+ align:start position:0%
+shouldn't call it a love affair both
+leting gu's mistress a young maid who
+
+ align:start position:0%
+leting gu's mistress a young maid who
+ 
+
+ align:start position:0%
+leting gu's mistress a young maid who
+works in his house and his
+
+ align:start position:0%
+works in his house and his
+ 
+
+ align:start position:0%
+works in his house and his
+wife and a kind of semis Scandal occurs
+
+ align:start position:0%
+wife and a kind of semis Scandal occurs
+ 
+
+ align:start position:0%
+wife and a kind of semis Scandal occurs
+in which F uh in which the uh uh um in
+
+ align:start position:0%
+in which F uh in which the uh uh um in
+ 
+
+ align:start position:0%
+in which F uh in which the uh uh um in
+which the character play played by
+
+ align:start position:0%
+which the character play played by
+ 
+
+ align:start position:0%
+which the character play played by
+Michelle Simon wins the lottery and
+
+ align:start position:0%
+Michelle Simon wins the lottery and
+ 
+
+ align:start position:0%
+Michelle Simon wins the lottery and
+becomes very rich so he then very a
+
+ align:start position:0%
+becomes very rich so he then very a
+ 
+
+ align:start position:0%
+becomes very rich so he then very a
+marriage of convenience is arranged and
+
+ align:start position:0%
+marriage of convenience is arranged and
+ 
+
+ align:start position:0%
+marriage of convenience is arranged and
+he's going to marry the maid that had
+
+ align:start position:0%
+he's going to marry the maid that had
+ 
+
+ align:start position:0%
+he's going to marry the maid that had
+been the book seller's mistress and this
+
+ align:start position:0%
+been the book seller's mistress and this
+ 
+
+ align:start position:0%
+been the book seller's mistress and this
+sort of straightens everything out
+
+ align:start position:0%
+sort of straightens everything out
+ 
+
+ align:start position:0%
+sort of straightens everything out
+because there had been a kind of Scandal
+
+ align:start position:0%
+because there had been a kind of Scandal
+ 
+
+ align:start position:0%
+because there had been a kind of Scandal
+brewing and in the and the final scene
+
+ align:start position:0%
+brewing and in the and the final scene
+ 
+
+ align:start position:0%
+brewing and in the and the final scene
+of the film is the wedding party in
+
+ align:start position:0%
+of the film is the wedding party in
+ 
+
+ align:start position:0%
+of the film is the wedding party in
+which in which in which uh budo his new
+
+ align:start position:0%
+which in which in which uh budo his new
+ 
+
+ align:start position:0%
+which in which in which uh budo his new
+bride the book seller and his wife are
+
+ align:start position:0%
+bride the book seller and his wife are
+ 
+
+ align:start position:0%
+bride the book seller and his wife are
+in a boat together celebrating the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wedding and and of course these images
+
+ align:start position:0%
+wedding and and of course these images
+ 
+
+ align:start position:0%
+wedding and and of course these images
+would have invoked Renoir Pear's films
+
+ align:start position:0%
+would have invoked Renoir Pear's films
+ 
+
+ align:start position:0%
+would have invoked Renoir Pear's films
+paintings very powerfully as
+
+ align:start position:0%
+paintings very powerfully as
+ 
+
+ align:start position:0%
+paintings very powerfully as
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well many of Jean renoir's treatment uh
+
+ align:start position:0%
+well many of Jean renoir's treatment uh
+ 
+
+ align:start position:0%
+well many of Jean renoir's treatment uh
+films said in nature are said to have
+
+ align:start position:0%
+films said in nature are said to have
+ 
+
+ align:start position:0%
+films said in nature are said to have
+been influenced in some ways by his
+
+ align:start position:0%
+been influenced in some ways by his
+ 
+
+ align:start position:0%
+been influenced in some ways by his
+father's paintings there's Michelle
+
+ align:start position:0%
+father's paintings there's Michelle
+ 
+
+ align:start position:0%
+father's paintings there's Michelle
+Simone in his new
+
+ align:start position:0%
+Simone in his new
+ 
+
+ align:start position:0%
+Simone in his new
+bride you see how there's music but it's
+
+ align:start position:0%
+bride you see how there's music but it's
+ 
+
+ align:start position:0%
+bride you see how there's music but it's
+coming from Source inside the story
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's the book seller in the back with
+
+ align:start position:0%
+that's the book seller in the back with
+ 
+
+ align:start position:0%
+that's the book seller in the back with
+a white hat everything looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+wonderful one thing I think one reason I
+
+ align:start position:0%
+wonderful one thing I think one reason I
+ 
+
+ align:start position:0%
+wonderful one thing I think one reason I
+wanted you to see this is look how
+
+ align:start position:0%
+wanted you to see this is look how
+ 
+
+ align:start position:0%
+wanted you to see this is look how
+leisurely this is even I mean it was
+
+ align:start position:0%
+leisurely this is even I mean it was
+ 
+
+ align:start position:0%
+leisurely this is even I mean it was
+where is it going we're at the end of
+
+ align:start position:0%
+where is it going we're at the end of
+ 
+
+ align:start position:0%
+where is it going we're at the end of
+the movie yet now and yet look how how
+
+ align:start position:0%
+the movie yet now and yet look how how
+ 
+
+ align:start position:0%
+the movie yet now and yet look how how
+the film sort of almost as if it doesn't
+
+ align:start position:0%
+the film sort of almost as if it doesn't
+ 
+
+ align:start position:0%
+the film sort of almost as if it doesn't
+even at this stage doesn't want to end
+
+ align:start position:0%
+even at this stage doesn't want to end
+ 
+
+ align:start position:0%
+even at this stage doesn't want to end
+doesn't want to move
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forward all right he reaches for the
+
+ align:start position:0%
+forward all right he reaches for the
+ 
+
+ align:start position:0%
+forward all right he reaches for the
+flower
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+he
+
+ align:start position:0%
+he
+ 
+
+ align:start position:0%
+he
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now remember he's just been married
+
+ align:start position:0%
+now remember he's just been married
+ 
+
+ align:start position:0%
+now remember he's just been married
+what's happening to him where's he
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+going you know often when I show this to
+
+ align:start position:0%
+going you know often when I show this to
+ 
+
+ align:start position:0%
+going you know often when I show this to
+my classes because I'm always worried
+
+ align:start position:0%
+my classes because I'm always worried
+ 
+
+ align:start position:0%
+my classes because I'm always worried
+about time I get impatient here but in
+
+ align:start position:0%
+about time I get impatient here but in
+ 
+
+ align:start position:0%
+about time I get impatient here but in
+fact it's a bad reaction because the
+
+ align:start position:0%
+fact it's a bad reaction because the
+ 
+
+ align:start position:0%
+fact it's a bad reaction because the
+film wants us to savor what it's doing
+
+ align:start position:0%
+film wants us to savor what it's doing
+ 
+
+ align:start position:0%
+film wants us to savor what it's doing
+right it can you feel the sort of
+
+ align:start position:0%
+right it can you feel the sort of
+ 
+
+ align:start position:0%
+right it can you feel the sort of
+lyrical tendency just to sort of look at
+
+ align:start position:0%
+lyrical tendency just to sort of look at
+ 
+
+ align:start position:0%
+lyrical tendency just to sort of look at
+the world in its beauty
+
+ align:start position:0%
+the world in its beauty
+ 
+
+ align:start position:0%
+the world in its beauty
+as if the impulse to tell a story and
+
+ align:start position:0%
+as if the impulse to tell a story and
+ 
+
+ align:start position:0%
+as if the impulse to tell a story and
+the impulse to photograph the world are
+
+ align:start position:0%
+the impulse to photograph the world are
+ 
+
+ align:start position:0%
+the impulse to photograph the world are
+in some degree in conflict because the
+
+ align:start position:0%
+in some degree in conflict because the
+ 
+
+ align:start position:0%
+in some degree in conflict because the
+world keeps resisting the categories you
+
+ align:start position:0%
+world keeps resisting the categories you
+ 
+
+ align:start position:0%
+world keeps resisting the categories you
+put it in the camera keeps discovering
+
+ align:start position:0%
+put it in the camera keeps discovering
+ 
+
+ align:start position:0%
+put it in the camera keeps discovering
+new things to look at so here budo comes
+
+ align:start position:0%
+new things to look at so here budo comes
+ 
+
+ align:start position:0%
+new things to look at so here budo comes
+ashore think of how anarchic this vision
+
+ align:start position:0%
+ashore think of how anarchic this vision
+ 
+
+ align:start position:0%
+ashore think of how anarchic this vision
+of life is because he's just deserted
+
+ align:start position:0%
+of life is because he's just deserted
+ 
+
+ align:start position:0%
+of life is because he's just deserted
+his new bride and his new wedding and
+
+ align:start position:0%
+his new bride and his new wedding and
+ 
+
+ align:start position:0%
+his new bride and his new wedding and
+all the right doesn't seem to matter he
+
+ align:start position:0%
+all the right doesn't seem to matter he
+ 
+
+ align:start position:0%
+all the right doesn't seem to matter he
+gets up on
+
+ align:start position:0%
+gets up on
+ 
+
+ align:start position:0%
+gets up on
+shore he's still wearing his wet clothes
+
+ align:start position:0%
+shore he's still wearing his wet clothes
+ 
+
+ align:start position:0%
+shore he's still wearing his wet clothes
+and this becomes then a highly symbolic
+
+ align:start position:0%
+and this becomes then a highly symbolic
+ 
+
+ align:start position:0%
+and this becomes then a highly symbolic
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moment he sees a
+
+ align:start position:0%
+moment he sees a
+ 
+
+ align:start position:0%
+moment he sees a
+scarecrow now he's going to shed his
+
+ align:start position:0%
+scarecrow now he's going to shed his
+ 
+
+ align:start position:0%
+scarecrow now he's going to shed his
+middle class
+
+ align:start position:0%
+middle class
+ 
+
+ align:start position:0%
+middle class
+identity by changing clothes with it
+
+ align:start position:0%
+identity by changing clothes with it
+ 
+
+ align:start position:0%
+identity by changing clothes with it
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I suppose one fundamental aspect of the
+
+ align:start position:0%
+I suppose one fundamental aspect of the
+ 
+
+ align:start position:0%
+I suppose one fundamental aspect of the
+satire is what the film is saying is
+
+ align:start position:0%
+satire is what the film is saying is
+ 
+
+ align:start position:0%
+satire is what the film is saying is
+look nature is always more untamed and
+
+ align:start position:0%
+look nature is always more untamed and
+ 
+
+ align:start position:0%
+look nature is always more untamed and
+difficult than middle class uh Romantics
+
+ align:start position:0%
+difficult than middle class uh Romantics
+ 
+
+ align:start position:0%
+difficult than middle class uh Romantics
+imagine right it's not a table thing
+
+ align:start position:0%
+imagine right it's not a table thing
+ 
+
+ align:start position:0%
+imagine right it's not a table thing
+well here he comes eating his bread
+
+ align:start position:0%
+well here he comes eating his bread
+ 
+
+ align:start position:0%
+well here he comes eating his bread
+newly free again
+
+ align:start position:0%
+newly free again
+ 
+
+ align:start position:0%
+newly free again
+right identifies with the goat shares
+
+ align:start position:0%
+right identifies with the goat shares
+ 
+
+ align:start position:0%
+right identifies with the goat shares
+his food with the goat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pay attention to the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+camera for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay shut it off at one point in his
+
+ align:start position:0%
+okay shut it off at one point in his
+ 
+
+ align:start position:0%
+okay shut it off at one point in his
+book on bazan bazan's book on Renoir he
+
+ align:start position:0%
+book on bazan bazan's book on Renoir he
+ 
+
+ align:start position:0%
+book on bazan bazan's book on Renoir he
+talks about this sequence and I want to
+
+ align:start position:0%
+talks about this sequence and I want to
+ 
+
+ align:start position:0%
+talks about this sequence and I want to
+remind you that he talks about this
+
+ align:start position:0%
+remind you that he talks about this
+ 
+
+ align:start position:0%
+remind you that he talks about this
+sequence in an era before it was
+
+ align:start position:0%
+sequence in an era before it was
+ 
+
+ align:start position:0%
+sequence in an era before it was
+possible to easily repl movies right it
+
+ align:start position:0%
+possible to easily repl movies right it
+ 
+
+ align:start position:0%
+possible to easily repl movies right it
+was an ERA long before videotape long
+
+ align:start position:0%
+was an ERA long before videotape long
+ 
+
+ align:start position:0%
+was an ERA long before videotape long
+before television actually uh and when
+
+ align:start position:0%
+before television actually uh and when
+ 
+
+ align:start position:0%
+before television actually uh and when
+when you wanted to watch a movie again
+
+ align:start position:0%
+when you wanted to watch a movie again
+ 
+
+ align:start position:0%
+when you wanted to watch a movie again
+you had to get projectors and show them
+
+ align:start position:0%
+you had to get projectors and show them
+ 
+
+ align:start position:0%
+you had to get projectors and show them
+so very often when bazan was writing
+
+ align:start position:0%
+so very often when bazan was writing
+ 
+
+ align:start position:0%
+so very often when bazan was writing
+about his films he was working for
+
+ align:start position:0%
+about his films he was working for
+ 
+
+ align:start position:0%
+about his films he was working for
+memory and he makes some technical
+
+ align:start position:0%
+memory and he makes some technical
+ 
+
+ align:start position:0%
+memory and he makes some technical
+mistakes but he gets the essence of the
+
+ align:start position:0%
+mistakes but he gets the essence of the
+ 
+
+ align:start position:0%
+mistakes but he gets the essence of the
+scene right listen to this he says
+
+ align:start position:0%
+scene right listen to this he says
+ 
+
+ align:start position:0%
+scene right listen to this he says
+Renoir the moralist is also the most
+
+ align:start position:0%
+Renoir the moralist is also the most
+ 
+
+ align:start position:0%
+Renoir the moralist is also the most
+realistic of filmmakers sacrificing
+
+ align:start position:0%
+realistic of filmmakers sacrificing
+ 
+
+ align:start position:0%
+realistic of filmmakers sacrificing
+reality as little as possible to the
+
+ align:start position:0%
+reality as little as possible to the
+ 
+
+ align:start position:0%
+reality as little as possible to the
+thrust of his message the last scenes
+
+ align:start position:0%
+thrust of his message the last scenes
+ 
+
+ align:start position:0%
+thrust of his message the last scenes
+from budo could serve as an epigraph to
+
+ align:start position:0%
+from budo could serve as an epigraph to
+ 
+
+ align:start position:0%
+from budo could serve as an epigraph to
+all of renoir's French work budo newly
+
+ align:start position:0%
+all of renoir's French work budo newly
+ 
+
+ align:start position:0%
+all of renoir's French work budo newly
+wed throws himself into the water not
+
+ align:start position:0%
+wed throws himself into the water not
+ 
+
+ align:start position:0%
+wed throws himself into the water not
+exactly it's an accident it's important
+
+ align:start position:0%
+exactly it's an accident it's important
+ 
+
+ align:start position:0%
+exactly it's an accident it's important
+that it's an accident it's not like he
+
+ align:start position:0%
+that it's an accident it's not like he
+ 
+
+ align:start position:0%
+that it's an accident it's not like he
+was planning his Escape right because
+
+ align:start position:0%
+was planning his Escape right because
+ 
+
+ align:start position:0%
+was planning his Escape right because
+he's nature he doesn't he doesn't think
+
+ align:start position:0%
+he's nature he doesn't he doesn't think
+ 
+
+ align:start position:0%
+he's nature he doesn't he doesn't think
+he stands for the natural right uh but
+
+ align:start position:0%
+he stands for the natural right uh but
+ 
+
+ align:start position:0%
+he stands for the natural right uh but
+but by accident the book the the the
+
+ align:start position:0%
+but by accident the book the the the
+ 
+
+ align:start position:0%
+but by accident the book the the the
+boat overturns and budo makes his his
+
+ align:start position:0%
+boat overturns and budo makes his his
+ 
+
+ align:start position:0%
+boat overturns and budo makes his his
+Escape because it's possible to do so
+
+ align:start position:0%
+Escape because it's possible to do so
+ 
+
+ align:start position:0%
+Escape because it's possible to do so
+it's not as if it's premeditated that's
+
+ align:start position:0%
+it's not as if it's premeditated that's
+ 
+
+ align:start position:0%
+it's not as if it's premeditated that's
+important and um uh dramatic or
+
+ align:start position:0%
+important and um uh dramatic or
+ 
+
+ align:start position:0%
+important and um uh dramatic or
+psychological logic would demand that
+
+ align:start position:0%
+psychological logic would demand that
+ 
+
+ align:start position:0%
+psychological logic would demand that
+such an act have a precise meaning is it
+
+ align:start position:0%
+such an act have a precise meaning is it
+ 
+
+ align:start position:0%
+such an act have a precise meaning is it
+despair or suicide no it's not at all in
+
+ align:start position:0%
+despair or suicide no it's not at all in
+ 
+
+ align:start position:0%
+despair or suicide no it's not at all in
+fact it's just an accident uh um budo is
+
+ align:start position:0%
+fact it's just an accident uh um budo is
+ 
+
+ align:start position:0%
+fact it's just an accident uh um budo is
+uh budo without maybe even fully
+
+ align:start position:0%
+uh budo without maybe even fully
+ 
+
+ align:start position:0%
+uh budo without maybe even fully
+realizing it is trying to flee the
+
+ align:start position:0%
+realizing it is trying to flee the
+ 
+
+ align:start position:0%
+realizing it is trying to flee the
+chains of a Bourgeois marriage
+
+ align:start position:0%
+chains of a Bourgeois marriage
+ 
+
+ align:start position:0%
+chains of a Bourgeois marriage
+um Renoir like his character forgets the
+
+ align:start position:0%
+um Renoir like his character forgets the
+ 
+
+ align:start position:0%
+um Renoir like his character forgets the
+act in favor of the fact and the true
+
+ align:start position:0%
+act in favor of the fact and the true
+ 
+
+ align:start position:0%
+act in favor of the fact and the true
+object of the scene ceases gradually to
+
+ align:start position:0%
+object of the scene ceases gradually to
+ 
+
+ align:start position:0%
+object of the scene ceases gradually to
+be what budo intends right what is budo
+
+ align:start position:0%
+be what budo intends right what is budo
+ 
+
+ align:start position:0%
+be what budo intends right what is budo
+up to why is he doing this I don't even
+
+ align:start position:0%
+up to why is he doing this I don't even
+ 
+
+ align:start position:0%
+up to why is he doing this I don't even
+think he's bazan is right to even raise
+
+ align:start position:0%
+think he's bazan is right to even raise
+ 
+
+ align:start position:0%
+think he's bazan is right to even raise
+the question because what we think he's
+
+ align:start position:0%
+the question because what we think he's
+ 
+
+ align:start position:0%
+the question because what we think he's
+doing is just enjoying himself self
+
+ align:start position:0%
+doing is just enjoying himself self
+ 
+
+ align:start position:0%
+doing is just enjoying himself self
+right then it occurs to him when he gets
+
+ align:start position:0%
+right then it occurs to him when he gets
+ 
+
+ align:start position:0%
+right then it occurs to him when he gets
+on land that he's free of his marriage
+
+ align:start position:0%
+on land that he's free of his marriage
+ 
+
+ align:start position:0%
+on land that he's free of his marriage
+right um uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um Renoir like his character forgets the
+
+ align:start position:0%
+um Renoir like his character forgets the
+ 
+
+ align:start position:0%
+um Renoir like his character forgets the
+act in favor of the fact and the true
+
+ align:start position:0%
+act in favor of the fact and the true
+ 
+
+ align:start position:0%
+act in favor of the fact and the true
+object of the scene ceases to be Bud's
+
+ align:start position:0%
+object of the scene ceases to be Bud's
+ 
+
+ align:start position:0%
+object of the scene ceases to be Bud's
+intentions and becomes the spectacle of
+
+ align:start position:0%
+intentions and becomes the spectacle of
+ 
+
+ align:start position:0%
+intentions and becomes the spectacle of
+his pleasure and by extension the
+
+ align:start position:0%
+his pleasure and by extension the
+ 
+
+ align:start position:0%
+his pleasure and by extension the
+enjoyment that Renoir derives or we as
+
+ align:start position:0%
+enjoyment that Renoir derives or we as
+ 
+
+ align:start position:0%
+enjoyment that Renoir derives or we as
+viewers derive from the antics of his
+
+ align:start position:0%
+viewers derive from the antics of his
+ 
+
+ align:start position:0%
+viewers derive from the antics of his
+hero the water is no longer water but
+
+ align:start position:0%
+hero the water is no longer water but
+ 
+
+ align:start position:0%
+hero the water is no longer water but
+more specifically the water of the marn
+
+ align:start position:0%
+more specifically the water of the marn
+ 
+
+ align:start position:0%
+more specifically the water of the marn
+a tributary of the sen in in uh August
+
+ align:start position:0%
+a tributary of the sen in in uh August
+ 
+
+ align:start position:0%
+a tributary of the sen in in uh August
+Michelle Simone floats on it turns over
+
+ align:start position:0%
+Michelle Simone floats on it turns over
+ 
+
+ align:start position:0%
+Michelle Simone floats on it turns over
+sprays like a seal and as he plays we
+
+ align:start position:0%
+sprays like a seal and as he plays we
+ 
+
+ align:start position:0%
+sprays like a seal and as he plays we
+begin to perceive the depth quality and
+
+ align:start position:0%
+begin to perceive the depth quality and
+ 
+
+ align:start position:0%
+begin to perceive the depth quality and
+even the tepid warmth of the water when
+
+ align:start position:0%
+even the tepid warmth of the water when
+ 
+
+ align:start position:0%
+even the tepid warmth of the water when
+he comes up on the bank an extraordinary
+
+ align:start position:0%
+he comes up on the bank an extraordinary
+ 
+
+ align:start position:0%
+he comes up on the bank an extraordinary
+slow he calls it a 360 degree pan
+
+ align:start position:0%
+slow he calls it a 360 degree pan
+ 
+
+ align:start position:0%
+slow he calls it a 360 degree pan
+remember that final move the camera but
+
+ align:start position:0%
+remember that final move the camera but
+ 
+
+ align:start position:0%
+remember that final move the camera but
+it's probably 180° he's remembering it
+
+ align:start position:0%
+it's probably 180° he's remembering it
+ 
+
+ align:start position:0%
+it's probably 180° he's remembering it
+imperfectly shows us the countryside he
+
+ align:start position:0%
+imperfectly shows us the countryside he
+ 
+
+ align:start position:0%
+imperfectly shows us the countryside he
+sees before him the world he sees before
+
+ align:start position:0%
+sees before him the world he sees before
+ 
+
+ align:start position:0%
+sees before him the world he sees before
+him but this effect by Nature
+
+ align:start position:0%
+him but this effect by Nature
+ 
+
+ align:start position:0%
+him but this effect by Nature
+descriptive which could indicate space
+
+ align:start position:0%
+descriptive which could indicate space
+ 
+
+ align:start position:0%
+descriptive which could indicate space
+and Liberty regained is of unequal
+
+ align:start position:0%
+and Liberty regained is of unequal
+ 
+
+ align:start position:0%
+and Liberty regained is of unequal
+poetry because what moves us is not the
+
+ align:start position:0%
+poetry because what moves us is not the
+ 
+
+ align:start position:0%
+poetry because what moves us is not the
+fact that this Countryside is once more
+
+ align:start position:0%
+fact that this Countryside is once more
+ 
+
+ align:start position:0%
+fact that this Countryside is once more
+again bdo's domain although that is one
+
+ align:start position:0%
+again bdo's domain although that is one
+ 
+
+ align:start position:0%
+again bdo's domain although that is one
+effect of it budoo is free and the
+
+ align:start position:0%
+effect of it budoo is free and the
+ 
+
+ align:start position:0%
+effect of it budoo is free and the
+camera shows the beauty and freedom of
+
+ align:start position:0%
+camera shows the beauty and freedom of
+ 
+
+ align:start position:0%
+camera shows the beauty and freedom of
+the world in that in that 180 degree pan
+
+ align:start position:0%
+the world in that in that 180 degree pan
+ 
+
+ align:start position:0%
+the world in that in that 180 degree pan
+but that the banks of the m and all
+
+ align:start position:0%
+but that the banks of the m and all
+ 
+
+ align:start position:0%
+but that the banks of the m and all
+their richness of detail are
+
+ align:start position:0%
+their richness of detail are
+ 
+
+ align:start position:0%
+their richness of detail are
+intrinsically beautiful and you're aware
+
+ align:start position:0%
+intrinsically beautiful and you're aware
+ 
+
+ align:start position:0%
+intrinsically beautiful and you're aware
+of that aren't you at the end of the pan
+
+ align:start position:0%
+of that aren't you at the end of the pan
+ 
+
+ align:start position:0%
+of that aren't you at the end of the pan
+the camera picks up a bit of grass or
+
+ align:start position:0%
+the camera picks up a bit of grass or
+ 
+
+ align:start position:0%
+the camera picks up a bit of grass or
+where in closeup one one can see the
+
+ align:start position:0%
+where in closeup one one can see the
+ 
+
+ align:start position:0%
+where in closeup one one can see the
+dust uh that the Heat and the wind have
+
+ align:start position:0%
+dust uh that the Heat and the wind have
+ 
+
+ align:start position:0%
+dust uh that the Heat and the wind have
+lifted From the Path one can almost feel
+
+ align:start position:0%
+lifted From the Path one can almost feel
+ 
+
+ align:start position:0%
+lifted From the Path one can almost feel
+it between one's fingers if I were
+
+ align:start position:0%
+it between one's fingers if I were
+ 
+
+ align:start position:0%
+it between one's fingers if I were
+deprived of the pleasure of seeing budo
+
+ align:start position:0%
+deprived of the pleasure of seeing budo
+ 
+
+ align:start position:0%
+deprived of the pleasure of seeing budo
+again for the rest of my days I remember
+
+ align:start position:0%
+again for the rest of my days I remember
+ 
+
+ align:start position:0%
+again for the rest of my days I remember
+the first time I read those lines and I
+
+ align:start position:0%
+the first time I read those lines and I
+ 
+
+ align:start position:0%
+the first time I read those lines and I
+realized what it meant to be a movie
+
+ align:start position:0%
+realized what it meant to be a movie
+ 
+
+ align:start position:0%
+realized what it meant to be a movie
+critic or a literary critic think of
+
+ align:start position:0%
+critic or a literary critic think of
+ 
+
+ align:start position:0%
+critic or a literary critic think of
+what what what's implied by that if I
+
+ align:start position:0%
+what what what's implied by that if I
+ 
+
+ align:start position:0%
+what what what's implied by that if I
+were deprived
+
+ align:start position:0%
+were deprived
+ 
+
+ align:start position:0%
+were deprived
+of the pleasure of seeing budoo again
+
+ align:start position:0%
+of the pleasure of seeing budoo again
+ 
+
+ align:start position:0%
+of the pleasure of seeing budoo again
+for the rest of my life as if this would
+
+ align:start position:0%
+for the rest of my life as if this would
+ 
+
+ align:start position:0%
+for the rest of my life as if this would
+be a deprivation too horrible to
+
+ align:start position:0%
+be a deprivation too horrible to
+ 
+
+ align:start position:0%
+be a deprivation too horrible to
+contemplate right it made me realize my
+
+ align:start position:0%
+contemplate right it made me realize my
+ 
+
+ align:start position:0%
+contemplate right it made me realize my
+own vocation in a way uh if I were
+
+ align:start position:0%
+own vocation in a way uh if I were
+ 
+
+ align:start position:0%
+own vocation in a way uh if I were
+deprived of the pleasure of seeing budoo
+
+ align:start position:0%
+deprived of the pleasure of seeing budoo
+ 
+
+ align:start position:0%
+deprived of the pleasure of seeing budoo
+again for the rest of my days I would
+
+ align:start position:0%
+again for the rest of my days I would
+ 
+
+ align:start position:0%
+again for the rest of my days I would
+never forget that grass that dust and
+
+ align:start position:0%
+never forget that grass that dust and
+ 
+
+ align:start position:0%
+never forget that grass that dust and
+their relationship to the liberty of a
+
+ align:start position:0%
+their relationship to the liberty of a
+ 
+
+ align:start position:0%
+their relationship to the liberty of a
+ the point of this exercise is to
+
+ align:start position:0%
+ the point of this exercise is to
+ 
+
+ align:start position:0%
+ the point of this exercise is to
+remind you of the immense power the
+
+ align:start position:0%
+remind you of the immense power the
+ 
+
+ align:start position:0%
+remind you of the immense power the
+potency of even a single camera move
+
+ align:start position:0%
+potency of even a single camera move
+ 
+
+ align:start position:0%
+potency of even a single camera move
+think what that 180 degree pan suggests
+
+ align:start position:0%
+think what that 180 degree pan suggests
+ 
+
+ align:start position:0%
+think what that 180 degree pan suggests
+as bazan brilliantly uh uh argues for us
+
+ align:start position:0%
+as bazan brilliantly uh uh argues for us
+ 
+
+ align:start position:0%
+as bazan brilliantly uh uh argues for us
+so the conclusion then is that the
+
+ align:start position:0%
+so the conclusion then is that the
+ 
+
+ align:start position:0%
+so the conclusion then is that the
+visual style of a film over certain
+
+ align:start position:0%
+visual style of a film over certain
+ 
+
+ align:start position:0%
+visual style of a film over certain
+films anyway can express a moral vision
+
+ align:start position:0%
+films anyway can express a moral vision
+ 
+
+ align:start position:0%
+films anyway can express a moral vision
+and by moral Vision I don't mean
+
+ align:start position:0%
+and by moral Vision I don't mean
+ 
+
+ align:start position:0%
+and by moral Vision I don't mean
+moralistic what's Mo what's what's
+
+ align:start position:0%
+moralistic what's Mo what's what's
+ 
+
+ align:start position:0%
+moralistic what's Mo what's what's
+didactically right and wrong but a
+
+ align:start position:0%
+didactically right and wrong but a
+ 
+
+ align:start position:0%
+didactically right and wrong but a
+vision having to do with the values and
+
+ align:start position:0%
+vision having to do with the values and
+ 
+
+ align:start position:0%
+vision having to do with the values and
+assumptions you make about the nature of
+
+ align:start position:0%
+assumptions you make about the nature of
+ 
+
+ align:start position:0%
+assumptions you make about the nature of
+the world there's a moral Vision
+
+ align:start position:0%
+the world there's a moral Vision
+ 
+
+ align:start position:0%
+the world there's a moral Vision
+implicit in the tentativeness the
+
+ align:start position:0%
+implicit in the tentativeness the
+ 
+
+ align:start position:0%
+implicit in the tentativeness the
+hesitancy the retarding impulse to to
+
+ align:start position:0%
+hesitancy the retarding impulse to to
+ 
+
+ align:start position:0%
+hesitancy the retarding impulse to to
+dwell and Linger on things in in the in
+
+ align:start position:0%
+dwell and Linger on things in in the in
+ 
+
+ align:start position:0%
+dwell and Linger on things in in the in
+renoir's camera and in the basic habits
+
+ align:start position:0%
+renoir's camera and in the basic habits
+ 
+
+ align:start position:0%
+renoir's camera and in the basic habits
+of of poetic realism that you will see
+
+ align:start position:0%
+of of poetic realism that you will see
+ 
+
+ align:start position:0%
+of of poetic realism that you will see
+brilliantly embodied in the film you're
+
+ align:start position:0%
+brilliantly embodied in the film you're
+ 
+
+ align:start position:0%
+brilliantly embodied in the film you're
+going to watch tonight Grand delusion
\ No newline at end of file
diff --git a/X2GJVlLC8bc.txt b/X2GJVlLC8bc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a94d5a1f80c0011112b0113f48627aa3d633d95
--- /dev/null
+++ b/X2GJVlLC8bc.txt
@@ -0,0 +1,219 @@
+align:start position:0%
+ 
+this in mind What technological
+
+ align:start position:0%
+this in mind What technological
+ 
+
+ align:start position:0%
+this in mind What technological
+responses do we have as Hughes mentioned
+
+ align:start position:0%
+responses do we have as Hughes mentioned
+ 
+
+ align:start position:0%
+responses do we have as Hughes mentioned
+um they're fairly limited um I have my
+
+ align:start position:0%
+um they're fairly limited um I have my
+ 
+
+ align:start position:0%
+um they're fairly limited um I have my
+research has been on vaccines and I've
+
+ align:start position:0%
+research has been on vaccines and I've
+ 
+
+ align:start position:0%
+research has been on vaccines and I've
+determined that they are not a first
+
+ align:start position:0%
+determined that they are not a first
+ 
+
+ align:start position:0%
+determined that they are not a first
+line of defense particularly for
+
+ align:start position:0%
+line of defense particularly for
+ 
+
+ align:start position:0%
+line of defense particularly for
+civilian populations they are useful uh
+
+ align:start position:0%
+civilian populations they are useful uh
+ 
+
+ align:start position:0%
+civilian populations they are useful uh
+to stabilize a situation after a attack
+
+ align:start position:0%
+to stabilize a situation after a attack
+ 
+
+ align:start position:0%
+to stabilize a situation after a attack
+has occurred for example once an agent
+
+ align:start position:0%
+has occurred for example once an agent
+ 
+
+ align:start position:0%
+has occurred for example once an agent
+has been identified it can be used a
+
+ align:start position:0%
+has been identified it can be used a
+ 
+
+ align:start position:0%
+has been identified it can be used a
+vaccine can be used to stem SE second
+
+ align:start position:0%
+vaccine can be used to stem SE second
+ 
+
+ align:start position:0%
+vaccine can be used to stem SE second
+waves of infection vaccines can be used
+
+ align:start position:0%
+waves of infection vaccines can be used
+ 
+
+ align:start position:0%
+waves of infection vaccines can be used
+to protect First Responders such as
+
+ align:start position:0%
+to protect First Responders such as
+ 
+
+ align:start position:0%
+to protect First Responders such as
+doctors nurses and emergency EMTs um
+
+ align:start position:0%
+doctors nurses and emergency EMTs um
+ 
+
+ align:start position:0%
+doctors nurses and emergency EMTs um
+this will allow the medical system to
+
+ align:start position:0%
+this will allow the medical system to
+ 
+
+ align:start position:0%
+this will allow the medical system to
+continue to function uh vaccines can
+
+ align:start position:0%
+continue to function uh vaccines can
+ 
+
+ align:start position:0%
+continue to function uh vaccines can
+also be used to permit re-entry of
+
+ align:start position:0%
+also be used to permit re-entry of
+ 
+
+ align:start position:0%
+also be used to permit re-entry of
+residents into an infected city um of
+
+ align:start position:0%
+residents into an infected city um of
+ 
+
+ align:start position:0%
+residents into an infected city um of
+course a successful biod defense program
+
+ align:start position:0%
+course a successful biod defense program
+ 
+
+ align:start position:0%
+course a successful biod defense program
+using vaccines is predicated on the
+
+ align:start position:0%
+using vaccines is predicated on the
+ 
+
+ align:start position:0%
+using vaccines is predicated on the
+availability of vaccines um and my
+
+ align:start position:0%
+availability of vaccines um and my
+ 
+
+ align:start position:0%
+availability of vaccines um and my
+research has demonstrated that we've had
+
+ align:start position:0%
+research has demonstrated that we've had
+ 
+
+ align:start position:0%
+research has demonstrated that we've had
+a lot of problems with vaccine Supply
+
+ align:start position:0%
+a lot of problems with vaccine Supply
+ 
+
+ align:start position:0%
+a lot of problems with vaccine Supply
+and Innovation particularly over the
+
+ align:start position:0%
+and Innovation particularly over the
+ 
+
+ align:start position:0%
+and Innovation particularly over the
+past 20 years and particularly for
+
+ align:start position:0%
+past 20 years and particularly for
+ 
+
+ align:start position:0%
+past 20 years and particularly for
+limited use vaccines which would be such
+
+ align:start position:0%
+limited use vaccines which would be such
+ 
+
+ align:start position:0%
+limited use vaccines which would be such
+as Anthrax and smallpox which is what we
+
+ align:start position:0%
+as Anthrax and smallpox which is what we
+ 
+
+ align:start position:0%
+as Anthrax and smallpox which is what we
+would need to mitigate an attack
\ No newline at end of file
diff --git a/X_HvnH9Mlwc.txt b/X_HvnH9Mlwc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..10e754d2be1484e42ed45cbc7a4bc37f5fe3cc7b
--- /dev/null
+++ b/X_HvnH9Mlwc.txt
@@ -0,0 +1,7603 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+open courseware under a Creative Commons
+
+ align:start position:0%
+open courseware under a Creative Commons
+ 
+
+ align:start position:0%
+open courseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu all right so uh we're in the
+
+ align:start position:0%
+ocw.mit.edu all right so uh we're in the
+ 
+
+ align:start position:0%
+ocw.mit.edu all right so uh we're in the
+middle of acids and
+
+ align:start position:0%
+middle of acids and
+ 
+
+ align:start position:0%
+middle of acids and
+bases and we're going to just finish up
+
+ align:start position:0%
+bases and we're going to just finish up
+ 
+
+ align:start position:0%
+bases and we're going to just finish up
+the handout from Monday starting uh
+
+ align:start position:0%
+the handout from Monday starting uh
+ 
+
+ align:start position:0%
+the handout from Monday starting uh
+first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we're talking about relative
+
+ align:start position:0%
+and we're talking about relative
+ 
+
+ align:start position:0%
+and we're talking about relative
+strengths of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acids so if you have an equation such as
+
+ align:start position:0%
+acids so if you have an equation such as
+ 
+
+ align:start position:0%
+acids so if you have an equation such as
+this there is acid base chemistry going
+
+ align:start position:0%
+this there is acid base chemistry going
+ 
+
+ align:start position:0%
+this there is acid base chemistry going
+on in both
+
+ align:start position:0%
+on in both
+ 
+
+ align:start position:0%
+on in both
+directions so in the forward direction
+
+ align:start position:0%
+directions so in the forward direction
+ 
+
+ align:start position:0%
+directions so in the forward direction
+hno3 is acting as the acid it's giving
+
+ align:start position:0%
+hno3 is acting as the acid it's giving
+ 
+
+ align:start position:0%
+hno3 is acting as the acid it's giving
+up its hydrogen ion or proton to
+
+ align:start position:0%
+up its hydrogen ion or proton to
+ 
+
+ align:start position:0%
+up its hydrogen ion or proton to
+NH3 and when it gives it up it's forming
+
+ align:start position:0%
+NH3 and when it gives it up it's forming
+ 
+
+ align:start position:0%
+NH3 and when it gives it up it's forming
+its conjugate NH3 minus and when NH3
+
+ align:start position:0%
+its conjugate NH3 minus and when NH3
+ 
+
+ align:start position:0%
+its conjugate NH3 minus and when NH3
+accepts a hydrogen atom or proton it's
+
+ align:start position:0%
+accepts a hydrogen atom or proton it's
+ 
+
+ align:start position:0%
+accepts a hydrogen atom or proton it's
+forming its conjugate acid
+
+ align:start position:0%
+forming its conjugate acid
+ 
+
+ align:start position:0%
+forming its conjugate acid
+nh4+ so that's what's happening in the
+
+ align:start position:0%
+nh4+ so that's what's happening in the
+ 
+
+ align:start position:0%
+nh4+ so that's what's happening in the
+forward direction of this reaction in
+
+ align:start position:0%
+forward direction of this reaction in
+ 
+
+ align:start position:0%
+forward direction of this reaction in
+the reverse direction of this reaction
+
+ align:start position:0%
+the reverse direction of this reaction
+ 
+
+ align:start position:0%
+the reverse direction of this reaction
+nh4+ is acting as the acid it's giving
+
+ align:start position:0%
+nh4+ is acting as the acid it's giving
+ 
+
+ align:start position:0%
+nh4+ is acting as the acid it's giving
+up a proton to NH3 minus when it gives
+
+ align:start position:0%
+up a proton to NH3 minus when it gives
+ 
+
+ align:start position:0%
+up a proton to NH3 minus when it gives
+up the proton it's forming NH3 the
+
+ align:start position:0%
+up the proton it's forming NH3 the
+ 
+
+ align:start position:0%
+up the proton it's forming NH3 the
+conjugate and when this accepts the
+
+ align:start position:0%
+conjugate and when this accepts the
+ 
+
+ align:start position:0%
+conjugate and when this accepts the
+hydrogen ion or proton it's forming its
+
+ align:start position:0%
+hydrogen ion or proton it's forming its
+ 
+
+ align:start position:0%
+hydrogen ion or proton it's forming its
+conjugate acid so in this direction this
+
+ align:start position:0%
+conjugate acid so in this direction this
+ 
+
+ align:start position:0%
+conjugate acid so in this direction this
+is the acid and in the reverse Direction
+
+ align:start position:0%
+is the acid and in the reverse Direction
+ 
+
+ align:start position:0%
+is the acid and in the reverse Direction
+This is the acid so you can predict
+
+ align:start position:0%
+This is the acid so you can predict
+ 
+
+ align:start position:0%
+This is the acid so you can predict
+something about the where the
+
+ align:start position:0%
+something about the where the
+ 
+
+ align:start position:0%
+something about the where the
+equilibrium lies whether it's to the
+
+ align:start position:0%
+equilibrium lies whether it's to the
+ 
+
+ align:start position:0%
+equilibrium lies whether it's to the
+right or the left if you have a big k or
+
+ align:start position:0%
+right or the left if you have a big k or
+ 
+
+ align:start position:0%
+right or the left if you have a big k or
+a small k for this reaction based on
+
+ align:start position:0%
+a small k for this reaction based on
+ 
+
+ align:start position:0%
+a small k for this reaction based on
+whether this is the stronger acid or
+
+ align:start position:0%
+whether this is the stronger acid or
+ 
+
+ align:start position:0%
+whether this is the stronger acid or
+this is the stronger acid so if this is
+
+ align:start position:0%
+this is the stronger acid so if this is
+ 
+
+ align:start position:0%
+this is the stronger acid so if this is
+a stronger acid the equilibrium will lie
+
+ align:start position:0%
+a stronger acid the equilibrium will lie
+ 
+
+ align:start position:0%
+a stronger acid the equilibrium will lie
+to the right if this is a stronger acid
+
+ align:start position:0%
+to the right if this is a stronger acid
+ 
+
+ align:start position:0%
+to the right if this is a stronger acid
+the equilibrium will lie to the left and
+
+ align:start position:0%
+the equilibrium will lie to the left and
+ 
+
+ align:start position:0%
+the equilibrium will lie to the left and
+so we can take a look at this and work
+
+ align:start position:0%
+so we can take a look at this and work
+ 
+
+ align:start position:0%
+so we can take a look at this and work
+out which is the stronger acid and where
+
+ align:start position:0%
+out which is the stronger acid and where
+ 
+
+ align:start position:0%
+out which is the stronger acid and where
+the equilibrium
+
+ align:start position:0%
+the equilibrium
+ 
+
+ align:start position:0%
+the equilibrium
+lies so here's the equilibrium constant
+
+ align:start position:0%
+lies so here's the equilibrium constant
+ 
+
+ align:start position:0%
+lies so here's the equilibrium constant
+for this reaction again it would be
+
+ align:start position:0%
+for this reaction again it would be
+ 
+
+ align:start position:0%
+for this reaction again it would be
+product
+
+ align:start position:0%
+product
+ 
+
+ align:start position:0%
+product
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+reactants and so to find this number we
+
+ align:start position:0%
+reactants and so to find this number we
+ 
+
+ align:start position:0%
+reactants and so to find this number we
+can work through it by getting
+
+ align:start position:0%
+can work through it by getting
+ 
+
+ align:start position:0%
+can work through it by getting
+information about the KA or acid
+
+ align:start position:0%
+information about the KA or acid
+ 
+
+ align:start position:0%
+information about the KA or acid
+ionization constant for this acid and
+
+ align:start position:0%
+ionization constant for this acid and
+ 
+
+ align:start position:0%
+ionization constant for this acid and
+for this
+
+ align:start position:0%
+for this
+ 
+
+ align:start position:0%
+for this
+acid so we can consider the reaction
+
+ align:start position:0%
+acid so we can consider the reaction
+ 
+
+ align:start position:0%
+acid so we can consider the reaction
+separately we can consider this acting
+
+ align:start position:0%
+separately we can consider this acting
+ 
+
+ align:start position:0%
+separately we can consider this acting
+as an acid and also this one so let's
+
+ align:start position:0%
+as an acid and also this one so let's
+ 
+
+ align:start position:0%
+as an acid and also this one so let's
+start here and consider the forward
+
+ align:start position:0%
+start here and consider the forward
+ 
+
+ align:start position:0%
+start here and consider the forward
+direction of the of the reaction and
+
+ align:start position:0%
+direction of the of the reaction and
+ 
+
+ align:start position:0%
+direction of the of the reaction and
+consider how good an acid NH uh n hno3
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is so you all should be able to write
+
+ align:start position:0%
+is so you all should be able to write
+ 
+
+ align:start position:0%
+is so you all should be able to write
+reactions of acid in water or bases in
+
+ align:start position:0%
+reactions of acid in water or bases in
+ 
+
+ align:start position:0%
+reactions of acid in water or bases in
+water and figure out what the products
+
+ align:start position:0%
+water and figure out what the products
+ 
+
+ align:start position:0%
+water and figure out what the products
+are going to be of that so if we have
+
+ align:start position:0%
+are going to be of that so if we have
+ 
+
+ align:start position:0%
+are going to be of that so if we have
+NH3 in
+
+ align:start position:0%
+NH3 in
+ 
+
+ align:start position:0%
+NH3 in
+water then we're going to be forming
+
+ align:start position:0%
+water then we're going to be forming
+ 
+
+ align:start position:0%
+water then we're going to be forming
+hydronium ion and the conjugate base of
+
+ align:start position:0%
+hydronium ion and the conjugate base of
+ 
+
+ align:start position:0%
+hydronium ion and the conjugate base of
+this conjugate acid here
+
+ align:start position:0%
+this conjugate acid here
+ 
+
+ align:start position:0%
+this conjugate acid here
+and then we can write a Ka and it's a Ka
+
+ align:start position:0%
+and then we can write a Ka and it's a Ka
+ 
+
+ align:start position:0%
+and then we can write a Ka and it's a Ka
+because we're talking about an acid in
+
+ align:start position:0%
+because we're talking about an acid in
+ 
+
+ align:start position:0%
+because we're talking about an acid in
+water so the KA is going to be equal to
+
+ align:start position:0%
+water so the KA is going to be equal to
+ 
+
+ align:start position:0%
+water so the KA is going to be equal to
+the products over the reactants and here
+
+ align:start position:0%
+the products over the reactants and here
+ 
+
+ align:start position:0%
+the products over the reactants and here
+water isn't included because it's the
+
+ align:start position:0%
+water isn't included because it's the
+ 
+
+ align:start position:0%
+water isn't included because it's the
+solvent and its concentration really
+
+ align:start position:0%
+solvent and its concentration really
+ 
+
+ align:start position:0%
+solvent and its concentration really
+isn't changing through the course of
+
+ align:start position:0%
+isn't changing through the course of
+ 
+
+ align:start position:0%
+isn't changing through the course of
+this reaction and we can look up uh an
+
+ align:start position:0%
+this reaction and we can look up uh an
+ 
+
+ align:start position:0%
+this reaction and we can look up uh an
+equilibrium uh constant for this acid
+
+ align:start position:0%
+equilibrium uh constant for this acid
+ 
+
+ align:start position:0%
+equilibrium uh constant for this acid
+and that's 20 so is that a strong acid
+
+ align:start position:0%
+and that's 20 so is that a strong acid
+ 
+
+ align:start position:0%
+and that's 20 so is that a strong acid
+or a weak acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how did we Define strong acid last
+
+ align:start position:0%
+how did we Define strong acid last
+ 
+
+ align:start position:0%
+how did we Define strong acid last
+time it was a Ka if is greater than one
+
+ align:start position:0%
+time it was a Ka if is greater than one
+ 
+
+ align:start position:0%
+time it was a Ka if is greater than one
+so 20 is greater than one so this is a
+
+ align:start position:0%
+so 20 is greater than one so this is a
+ 
+
+ align:start position:0%
+so 20 is greater than one so this is a
+strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid now we can do the same thing for
+
+ align:start position:0%
+acid now we can do the same thing for
+ 
+
+ align:start position:0%
+acid now we can do the same thing for
+the reverse Direction in the reverse
+
+ align:start position:0%
+the reverse Direction in the reverse
+ 
+
+ align:start position:0%
+the reverse Direction in the reverse
+Direction the acid is
+
+ align:start position:0%
+Direction the acid is
+ 
+
+ align:start position:0%
+Direction the acid is
+nh4+ so we can write
+
+ align:start position:0%
+nh4+ so we can write
+ 
+
+ align:start position:0%
+nh4+ so we can write
+nh4+ in water and that would go to
+
+ align:start position:0%
+nh4+ in water and that would go to
+ 
+
+ align:start position:0%
+nh4+ in water and that would go to
+hydronium ions and the conjugate of this
+
+ align:start position:0%
+hydronium ions and the conjugate of this
+ 
+
+ align:start position:0%
+hydronium ions and the conjugate of this
+acid which is
+
+ align:start position:0%
+acid which is
+ 
+
+ align:start position:0%
+acid which is
+NH3 we can write out a Ka expression for
+
+ align:start position:0%
+NH3 we can write out a Ka expression for
+ 
+
+ align:start position:0%
+NH3 we can write out a Ka expression for
+this again it would be pro products over
+
+ align:start position:0%
+this again it would be pro products over
+ 
+
+ align:start position:0%
+this again it would be pro products over
+reactants and here the KA which could be
+
+ align:start position:0%
+reactants and here the KA which could be
+ 
+
+ align:start position:0%
+reactants and here the KA which could be
+looked up is 5.6 * 10us 10 so is that a
+
+ align:start position:0%
+looked up is 5.6 * 10us 10 so is that a
+ 
+
+ align:start position:0%
+looked up is 5.6 * 10us 10 so is that a
+strong or weak
+
+ align:start position:0%
+strong or weak
+ 
+
+ align:start position:0%
+strong or weak
+acid that's a weak acid so the KA is
+
+ align:start position:0%
+acid that's a weak acid so the KA is
+ 
+
+ align:start position:0%
+acid that's a weak acid so the KA is
+quite a bit less than one so already we
+
+ align:start position:0%
+quite a bit less than one so already we
+ 
+
+ align:start position:0%
+quite a bit less than one so already we
+can predict that for this over all
+
+ align:start position:0%
+can predict that for this over all
+ 
+
+ align:start position:0%
+can predict that for this over all
+reaction it will lie to the right this
+
+ align:start position:0%
+reaction it will lie to the right this
+ 
+
+ align:start position:0%
+reaction it will lie to the right this
+is a much stronger acid than this one
+
+ align:start position:0%
+is a much stronger acid than this one
+ 
+
+ align:start position:0%
+is a much stronger acid than this one
+but we can prove that that's true by
+
+ align:start position:0%
+but we can prove that that's true by
+ 
+
+ align:start position:0%
+but we can prove that that's true by
+using these two Ka values to get the
+
+ align:start position:0%
+using these two Ka values to get the
+ 
+
+ align:start position:0%
+using these two Ka values to get the
+overall equilibrium constant for this
+
+ align:start position:0%
+overall equilibrium constant for this
+ 
+
+ align:start position:0%
+overall equilibrium constant for this
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+here so if we took those two individual
+
+ align:start position:0%
+here so if we took those two individual
+ 
+
+ align:start position:0%
+here so if we took those two individual
+reactions that we wrote out and uh
+
+ align:start position:0%
+reactions that we wrote out and uh
+ 
+
+ align:start position:0%
+reactions that we wrote out and uh
+subtract them we can get our overall
+
+ align:start position:0%
+subtract them we can get our overall
+ 
+
+ align:start position:0%
+subtract them we can get our overall
+expression uh for the reaction and if we
+
+ align:start position:0%
+expression uh for the reaction and if we
+ 
+
+ align:start position:0%
+expression uh for the reaction and if we
+subtract them then we can come up with
+
+ align:start position:0%
+subtract them then we can come up with
+ 
+
+ align:start position:0%
+subtract them then we can come up with
+the K by dividing the uh the KA from
+
+ align:start position:0%
+the K by dividing the uh the KA from
+ 
+
+ align:start position:0%
+the K by dividing the uh the KA from
+each other so remember we talked about K
+
+ align:start position:0%
+each other so remember we talked about K
+ 
+
+ align:start position:0%
+each other so remember we talked about K
+if you add together you multiply if you
+
+ align:start position:0%
+if you add together you multiply if you
+ 
+
+ align:start position:0%
+if you add together you multiply if you
+subtract reactions you can divide and so
+
+ align:start position:0%
+subtract reactions you can divide and so
+ 
+
+ align:start position:0%
+subtract reactions you can divide and so
+we can prove that this is true that if
+
+ align:start position:0%
+we can prove that this is true that if
+ 
+
+ align:start position:0%
+we can prove that this is true that if
+we have the KA up here and the K down
+
+ align:start position:0%
+we have the KA up here and the K down
+ 
+
+ align:start position:0%
+we have the KA up here and the K down
+here it will cancel to form uh the
+
+ align:start position:0%
+here it will cancel to form uh the
+ 
+
+ align:start position:0%
+here it will cancel to form uh the
+equilibrium expression for the overall
+
+ align:start position:0%
+equilibrium expression for the overall
+ 
+
+ align:start position:0%
+equilibrium expression for the overall
+reaction and we can substitute our ka's
+
+ align:start position:0%
+reaction and we can substitute our ka's
+ 
+
+ align:start position:0%
+reaction and we can substitute our ka's
+in 20 over 5.6 *
+
+ align:start position:0%
+in 20 over 5.6 *
+ 
+
+ align:start position:0%
+in 20 over 5.6 *
+10-10 and we get a k for the overall
+
+ align:start position:0%
+10-10 and we get a k for the overall
+ 
+
+ align:start position:0%
+10-10 and we get a k for the overall
+reaction of 3.6 * 10 10 which is an
+
+ align:start position:0%
+reaction of 3.6 * 10 10 which is an
+ 
+
+ align:start position:0%
+reaction of 3.6 * 10 10 which is an
+enormous number and so this would lie
+
+ align:start position:0%
+enormous number and so this would lie
+ 
+
+ align:start position:0%
+enormous number and so this would lie
+very very far to the right this is a
+
+ align:start position:0%
+very very far to the right this is a
+ 
+
+ align:start position:0%
+very very far to the right this is a
+much much stronger acid than
+
+ align:start position:0%
+much much stronger acid than
+ 
+
+ align:start position:0%
+much much stronger acid than
+nh4+ so if you know something if you
+
+ align:start position:0%
+nh4+ so if you know something if you
+ 
+
+ align:start position:0%
+nh4+ so if you know something if you
+have acid base on both sides of the
+
+ align:start position:0%
+have acid base on both sides of the
+ 
+
+ align:start position:0%
+have acid base on both sides of the
+equilibrium you know about the strengths
+
+ align:start position:0%
+equilibrium you know about the strengths
+ 
+
+ align:start position:0%
+equilibrium you know about the strengths
+you could predict where the equilibrium
+
+ align:start position:0%
+you could predict where the equilibrium
+ 
+
+ align:start position:0%
+you could predict where the equilibrium
+of an overall reaction is going to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lie all right
+
+ align:start position:0%
+lie all right
+ 
+
+ align:start position:0%
+lie all right
+so this is still on the handout from
+
+ align:start position:0%
+so this is still on the handout from
+ 
+
+ align:start position:0%
+so this is still on the handout from
+from Monday and mentioned that there are
+
+ align:start position:0%
+from Monday and mentioned that there are
+ 
+
+ align:start position:0%
+from Monday and mentioned that there are
+five different types of acid-based
+
+ align:start position:0%
+five different types of acid-based
+ 
+
+ align:start position:0%
+five different types of acid-based
+problems that you're going to encounter
+
+ align:start position:0%
+problems that you're going to encounter
+ 
+
+ align:start position:0%
+problems that you're going to encounter
+in this unit and there uh there's
+
+ align:start position:0%
+in this unit and there uh there's
+ 
+
+ align:start position:0%
+in this unit and there uh there's
+problems of salt and water which we're
+
+ align:start position:0%
+problems of salt and water which we're
+ 
+
+ align:start position:0%
+problems of salt and water which we're
+going to see today break down to a weak
+
+ align:start position:0%
+going to see today break down to a weak
+ 
+
+ align:start position:0%
+going to see today break down to a weak
+acid or a weak base in water problem so
+
+ align:start position:0%
+acid or a weak base in water problem so
+ 
+
+ align:start position:0%
+acid or a weak base in water problem so
+it's really not a different type of
+
+ align:start position:0%
+it's really not a different type of
+ 
+
+ align:start position:0%
+it's really not a different type of
+problem at all so there's weak acid and
+
+ align:start position:0%
+problem at all so there's weak acid and
+ 
+
+ align:start position:0%
+problem at all so there's weak acid and
+water weak base strong acid strong base
+
+ align:start position:0%
+water weak base strong acid strong base
+ 
+
+ align:start position:0%
+water weak base strong acid strong base
+and they're buffer problems and when we
+
+ align:start position:0%
+and they're buffer problems and when we
+ 
+
+ align:start position:0%
+and they're buffer problems and when we
+do titrations it'll seem like that's a
+
+ align:start position:0%
+do titrations it'll seem like that's a
+ 
+
+ align:start position:0%
+do titrations it'll seem like that's a
+different kind but it also breaks down
+
+ align:start position:0%
+different kind but it also breaks down
+ 
+
+ align:start position:0%
+different kind but it also breaks down
+into these categories so one trick that
+
+ align:start position:0%
+into these categories so one trick that
+ 
+
+ align:start position:0%
+into these categories so one trick that
+I've learned from teaching this a number
+
+ align:start position:0%
+I've learned from teaching this a number
+ 
+
+ align:start position:0%
+I've learned from teaching this a number
+of years is to get people starting to
+
+ align:start position:0%
+of years is to get people starting to
+ 
+
+ align:start position:0%
+of years is to get people starting to
+think about what type of problem it is
+
+ align:start position:0%
+think about what type of problem it is
+ 
+
+ align:start position:0%
+think about what type of problem it is
+whenever they see it and figuring out
+
+ align:start position:0%
+whenever they see it and figuring out
+ 
+
+ align:start position:0%
+whenever they see it and figuring out
+then they know how to address that
+
+ align:start position:0%
+then they know how to address that
+ 
+
+ align:start position:0%
+then they know how to address that
+problem so always be thinking about what
+
+ align:start position:0%
+problem so always be thinking about what
+ 
+
+ align:start position:0%
+problem so always be thinking about what
+type of problem is this and so how do I
+
+ align:start position:0%
+type of problem is this and so how do I
+ 
+
+ align:start position:0%
+type of problem is this and so how do I
+go about solving it so we're going to
+
+ align:start position:0%
+go about solving it so we're going to
+ 
+
+ align:start position:0%
+go about solving it so we're going to
+look at the first number one here a week
+
+ align:start position:0%
+look at the first number one here a week
+ 
+
+ align:start position:0%
+look at the first number one here a week
+acid and water
+
+ align:start position:0%
+acid and water
+ 
+
+ align:start position:0%
+acid and water
+problem and the weak acid that I pick to
+
+ align:start position:0%
+problem and the weak acid that I pick to
+ 
+
+ align:start position:0%
+problem and the weak acid that I pick to
+look at is Vitamin C so in this
+
+ align:start position:0%
+look at is Vitamin C so in this
+ 
+
+ align:start position:0%
+look at is Vitamin C so in this
+particular problem we are going to ask
+
+ align:start position:0%
+particular problem we are going to ask
+ 
+
+ align:start position:0%
+particular problem we are going to ask
+um what the pH would be if I take this
+
+ align:start position:0%
+um what the pH would be if I take this
+ 
+
+ align:start position:0%
+um what the pH would be if I take this
+vitamin C tablet and it's a 50 mgram
+
+ align:start position:0%
+vitamin C tablet and it's a 50 mgram
+ 
+
+ align:start position:0%
+vitamin C tablet and it's a 50 mgram
+tablet and put it into uh 100
+
+ align:start position:0%
+tablet and put it into uh 100
+ 
+
+ align:start position:0%
+tablet and put it into uh 100
+milliliters uh of water
+
+ align:start position:0%
+milliliters uh of water
+ 
+
+ align:start position:0%
+milliliters uh of water
+and usually when you try to swallow
+
+ align:start position:0%
+and usually when you try to swallow
+ 
+
+ align:start position:0%
+and usually when you try to swallow
+vitamin tablets you try not to dissolve
+
+ align:start position:0%
+vitamin tablets you try not to dissolve
+ 
+
+ align:start position:0%
+vitamin tablets you try not to dissolve
+them um but if we did then we could look
+
+ align:start position:0%
+them um but if we did then we could look
+ 
+
+ align:start position:0%
+them um but if we did then we could look
+at the pH I've discovered though I
+
+ align:start position:0%
+at the pH I've discovered though I
+ 
+
+ align:start position:0%
+at the pH I've discovered though I
+actually tried to do the calculations
+
+ align:start position:0%
+actually tried to do the calculations
+ 
+
+ align:start position:0%
+actually tried to do the calculations
+and do the actual experiment one year
+
+ align:start position:0%
+and do the actual experiment one year
+ 
+
+ align:start position:0%
+and do the actual experiment one year
+and discovered that these vitamin C
+
+ align:start position:0%
+and discovered that these vitamin C
+ 
+
+ align:start position:0%
+and discovered that these vitamin C
+tablets are coated really well you
+
+ align:start position:0%
+tablets are coated really well you
+ 
+
+ align:start position:0%
+tablets are coated really well you
+cannot get them to dissolve very easily
+
+ align:start position:0%
+cannot get them to dissolve very easily
+ 
+
+ align:start position:0%
+cannot get them to dissolve very easily
+and so uh that's because you don't want
+
+ align:start position:0%
+and so uh that's because you don't want
+ 
+
+ align:start position:0%
+and so uh that's because you don't want
+the bad taste in your mouth so Nature's
+
+ align:start position:0%
+the bad taste in your mouth so Nature's
+ 
+
+ align:start position:0%
+the bad taste in your mouth so Nature's
+Bounty if you don't want this tablet to
+
+ align:start position:0%
+Bounty if you don't want this tablet to
+ 
+
+ align:start position:0%
+Bounty if you don't want this tablet to
+dissolve in your mouth before you
+
+ align:start position:0%
+dissolve in your mouth before you
+ 
+
+ align:start position:0%
+dissolve in your mouth before you
+swallow it I guarantee it won't you have
+
+ align:start position:0%
+swallow it I guarantee it won't you have
+ 
+
+ align:start position:0%
+swallow it I guarantee it won't you have
+to go to extreme lengths to get this to
+
+ align:start position:0%
+to go to extreme lengths to get this to
+ 
+
+ align:start position:0%
+to go to extreme lengths to get this to
+dissolve in your mouth so we can't
+
+ align:start position:0%
+dissolve in your mouth so we can't
+ 
+
+ align:start position:0%
+dissolve in your mouth so we can't
+actually measure the pH of this because
+
+ align:start position:0%
+actually measure the pH of this because
+ 
+
+ align:start position:0%
+actually measure the pH of this because
+it's not going to uh dissolve the cating
+
+ align:start position:0%
+it's not going to uh dissolve the cating
+ 
+
+ align:start position:0%
+it's not going to uh dissolve the cating
+is pretty good but we can do the
+
+ align:start position:0%
+is pretty good but we can do the
+ 
+
+ align:start position:0%
+is pretty good but we can do the
+calculations if the coding was less good
+
+ align:start position:0%
+calculations if the coding was less good
+ 
+
+ align:start position:0%
+calculations if the coding was less good
+uh What the pH of that would be all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so the first thing we need to know
+
+ align:start position:0%
+right so the first thing we need to know
+ 
+
+ align:start position:0%
+right so the first thing we need to know
+is marity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so you can do this uh
+
+ align:start position:0%
+and so you can do this uh
+ 
+
+ align:start position:0%
+and so you can do this uh
+calculation you uh know the number of
+
+ align:start position:0%
+calculation you uh know the number of
+ 
+
+ align:start position:0%
+calculation you uh know the number of
+milligrams convert to grams look up the
+
+ align:start position:0%
+milligrams convert to grams look up the
+ 
+
+ align:start position:0%
+milligrams convert to grams look up the
+molecular weight uh calculate how many
+
+ align:start position:0%
+molecular weight uh calculate how many
+ 
+
+ align:start position:0%
+molecular weight uh calculate how many
+moles that is and then that number of
+
+ align:start position:0%
+moles that is and then that number of
+ 
+
+ align:start position:0%
+moles that is and then that number of
+moles in your uh 0.1 lers or 100
+
+ align:start position:0%
+moles in your uh 0.1 lers or 100
+ 
+
+ align:start position:0%
+moles in your uh 0.1 lers or 100
+milligrams and you can get the marity of
+
+ align:start position:0%
+milligrams and you can get the marity of
+ 
+
+ align:start position:0%
+milligrams and you can get the marity of
+a vitamin C tablet in uh in 100
+
+ align:start position:0%
+a vitamin C tablet in uh in 100
+ 
+
+ align:start position:0%
+a vitamin C tablet in uh in 100
+milliliters of
+
+ align:start position:0%
+milliliters of
+ 
+
+ align:start position:0%
+milliliters of
+water then you would need to write the
+
+ align:start position:0%
+water then you would need to write the
+ 
+
+ align:start position:0%
+water then you would need to write the
+equation for a weak acid in water
+
+ align:start position:0%
+equation for a weak acid in water
+ 
+
+ align:start position:0%
+equation for a weak acid in water
+problem and so here's our weak acid in
+
+ align:start position:0%
+problem and so here's our weak acid in
+ 
+
+ align:start position:0%
+problem and so here's our weak acid in
+water it's forming hydronium ions and a
+
+ align:start position:0%
+water it's forming hydronium ions and a
+ 
+
+ align:start position:0%
+water it's forming hydronium ions and a
+conjugate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base so then you can set this up and
+
+ align:start position:0%
+base so then you can set this up and
+ 
+
+ align:start position:0%
+base so then you can set this up and
+figure out what happens as uh initially
+
+ align:start position:0%
+figure out what happens as uh initially
+ 
+
+ align:start position:0%
+figure out what happens as uh initially
+the change and then what the
+
+ align:start position:0%
+the change and then what the
+ 
+
+ align:start position:0%
+the change and then what the
+concentration would be at equilibrium so
+
+ align:start position:0%
+concentration would be at equilibrium so
+ 
+
+ align:start position:0%
+concentration would be at equilibrium so
+in the beginning you just have this
+
+ align:start position:0%
+in the beginning you just have this
+ 
+
+ align:start position:0%
+in the beginning you just have this
+marity the point
+
+ align:start position:0%
+marity the point
+ 
+
+ align:start position:0%
+marity the point
+0284 molar solution and you don't have
+
+ align:start position:0%
+0284 molar solution and you don't have
+ 
+
+ align:start position:0%
+0284 molar solution and you don't have
+any of these initially the change would
+
+ align:start position:0%
+any of these initially the change would
+ 
+
+ align:start position:0%
+any of these initially the change would
+be minus X and then plus X Plus X so at
+
+ align:start position:0%
+be minus X and then plus X Plus X so at
+ 
+
+ align:start position:0%
+be minus X and then plus X Plus X so at
+equilibrium we're
+
+ align:start position:0%
+equilibrium we're
+ 
+
+ align:start position:0%
+equilibrium we're
+0284 - x and again plus
+
+ align:start position:0%
+0284 - x and again plus
+ 
+
+ align:start position:0%
+0284 - x and again plus
+X so now to solve for x which is what we
+
+ align:start position:0%
+X so now to solve for x which is what we
+ 
+
+ align:start position:0%
+X so now to solve for x which is what we
+want to solve we want to find out pH and
+
+ align:start position:0%
+want to solve we want to find out pH and
+ 
+
+ align:start position:0%
+want to solve we want to find out pH and
+pH is the minus log of the hydronium ion
+
+ align:start position:0%
+pH is the minus log of the hydronium ion
+ 
+
+ align:start position:0%
+pH is the minus log of the hydronium ion
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+so we need to find X to be able to find
+
+ align:start position:0%
+so we need to find X to be able to find
+ 
+
+ align:start position:0%
+so we need to find X to be able to find
+pH and to get X we can do that if we
+
+ align:start position:0%
+pH and to get X we can do that if we
+ 
+
+ align:start position:0%
+pH and to get X we can do that if we
+know the KA for the solution write out
+
+ align:start position:0%
+know the KA for the solution write out
+ 
+
+ align:start position:0%
+know the KA for the solution write out
+the expression hydronium ion conjugate
+
+ align:start position:0%
+the expression hydronium ion conjugate
+ 
+
+ align:start position:0%
+the expression hydronium ion conjugate
+base over acid we're leaving out the
+
+ align:start position:0%
+base over acid we're leaving out the
+ 
+
+ align:start position:0%
+base over acid we're leaving out the
+water again so that would be equal to
+
+ align:start position:0%
+water again so that would be equal to
+ 
+
+ align:start position:0%
+water again so that would be equal to
+x^2
+
+ align:start position:0%
+x^2
+ 
+
+ align:start position:0%
+x^2
+0284 -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x so now we can try an assumption and
+
+ align:start position:0%
+x so now we can try an assumption and
+ 
+
+ align:start position:0%
+x so now we can try an assumption and
+and this will be useful to you on exams
+
+ align:start position:0%
+and this will be useful to you on exams
+ 
+
+ align:start position:0%
+and this will be useful to you on exams
+so first you can try to say what if x
+
+ align:start position:0%
+so first you can try to say what if x
+ 
+
+ align:start position:0%
+so first you can try to say what if x
+was really small what if x was much much
+
+ align:start position:0%
+was really small what if x was much much
+ 
+
+ align:start position:0%
+was really small what if x was much much
+smaller than this
+
+ align:start position:0%
+smaller than this
+ 
+
+ align:start position:0%
+smaller than this
+0284 then this term just collapses into
+
+ align:start position:0%
+0284 then this term just collapses into
+ 
+
+ align:start position:0%
+0284 then this term just collapses into
+the number so you can make that
+
+ align:start position:0%
+the number so you can make that
+ 
+
+ align:start position:0%
+the number so you can make that
+assumption and try it and see if it
+
+ align:start position:0%
+assumption and try it and see if it
+ 
+
+ align:start position:0%
+assumption and try it and see if it
+works and I'll tell you what the rule
+
+ align:start position:0%
+works and I'll tell you what the rule
+ 
+
+ align:start position:0%
+works and I'll tell you what the rule
+will be to check that out so if we try
+
+ align:start position:0%
+will be to check that out so if we try
+ 
+
+ align:start position:0%
+will be to check that out so if we try
+the Assumption then uh we have just X
+
+ align:start position:0%
+the Assumption then uh we have just X
+ 
+
+ align:start position:0%
+the Assumption then uh we have just X
+squar over this number that's easier to
+
+ align:start position:0%
+squar over this number that's easier to
+ 
+
+ align:start position:0%
+squar over this number that's easier to
+solve
+
+ align:start position:0%
+solve
+ 
+
+ align:start position:0%
+solve
+and we can solve for
+
+ align:start position:0%
+and we can solve for
+ 
+
+ align:start position:0%
+and we can solve for
+x and here x is
+
+ align:start position:0%
+x and here x is
+ 
+
+ align:start position:0%
+x and here x is
+0.151 and I'm carrying an extra
+
+ align:start position:0%
+0.151 and I'm carrying an extra
+ 
+
+ align:start position:0%
+0.151 and I'm carrying an extra
+significant
+
+ align:start position:0%
+significant
+ 
+
+ align:start position:0%
+significant
+figure and then we can go and check is
+
+ align:start position:0%
+figure and then we can go and check is
+ 
+
+ align:start position:0%
+figure and then we can go and check is
+this true that that is in fact much
+
+ align:start position:0%
+this true that that is in fact much
+ 
+
+ align:start position:0%
+this true that that is in fact much
+smaller than this and the rule that
+
+ align:start position:0%
+smaller than this and the rule that
+ 
+
+ align:start position:0%
+smaller than this and the rule that
+we'll use is 5% so you can uh calculate
+
+ align:start position:0%
+we'll use is 5% so you can uh calculate
+ 
+
+ align:start position:0%
+we'll use is 5% so you can uh calculate
+whether the number is 5% take X over
+
+ align:start position:0%
+whether the number is 5% take X over
+ 
+
+ align:start position:0%
+whether the number is 5% take X over
+your initial number times 100 % in this
+
+ align:start position:0%
+your initial number times 100 % in this
+ 
+
+ align:start position:0%
+your initial number times 100 % in this
+case it was
+
+ align:start position:0%
+case it was
+ 
+
+ align:start position:0%
+case it was
+5.3% which is more than five and so you
+
+ align:start position:0%
+5.3% which is more than five and so you
+ 
+
+ align:start position:0%
+5.3% which is more than five and so you
+should use the quadratic equation to
+
+ align:start position:0%
+should use the quadratic equation to
+ 
+
+ align:start position:0%
+should use the quadratic equation to
+solve for x so most of you normally use
+
+ align:start position:0%
+solve for x so most of you normally use
+ 
+
+ align:start position:0%
+solve for x so most of you normally use
+calculators which there's no problem in
+
+ align:start position:0%
+calculators which there's no problem in
+ 
+
+ align:start position:0%
+calculators which there's no problem in
+doing quadratic but of course the
+
+ align:start position:0%
+doing quadratic but of course the
+ 
+
+ align:start position:0%
+doing quadratic but of course the
+calculators we use on the exams uh are
+
+ align:start position:0%
+calculators we use on the exams uh are
+ 
+
+ align:start position:0%
+calculators we use on the exams uh are
+not so amenable to doing this so I
+
+ align:start position:0%
+not so amenable to doing this so I
+ 
+
+ align:start position:0%
+not so amenable to doing this so I
+suggest on an exam you always try the
+
+ align:start position:0%
+suggest on an exam you always try the
+ 
+
+ align:start position:0%
+suggest on an exam you always try the
+assumption that you can make it a
+
+ align:start position:0%
+assumption that you can make it a
+ 
+
+ align:start position:0%
+assumption that you can make it a
+simpler problem to save yourself time
+
+ align:start position:0%
+simpler problem to save yourself time
+ 
+
+ align:start position:0%
+simpler problem to save yourself time
+so the rule is 5% has to be less than
+
+ align:start position:0%
+so the rule is 5% has to be less than
+ 
+
+ align:start position:0%
+so the rule is 5% has to be less than
+5% so I'll just mention that the book
+
+ align:start position:0%
+5% so I'll just mention that the book
+ 
+
+ align:start position:0%
+5% so I'll just mention that the book
+talks about this expression and refers
+
+ align:start position:0%
+talks about this expression and refers
+ 
+
+ align:start position:0%
+talks about this expression and refers
+to a percent ionized or percent T
+
+ align:start position:0%
+to a percent ionized or percent T
+ 
+
+ align:start position:0%
+to a percent ionized or percent T
+protonated So this equation which is
+
+ align:start position:0%
+protonated So this equation which is
+ 
+
+ align:start position:0%
+protonated So this equation which is
+really X over the uh the number minus
+
+ align:start position:0%
+really X over the uh the number minus
+ 
+
+ align:start position:0%
+really X over the uh the number minus
+the initial marity minus X is how much
+
+ align:start position:0%
+the initial marity minus X is how much
+ 
+
+ align:start position:0%
+the initial marity minus X is how much
+you've gone to that side of the equation
+
+ align:start position:0%
+you've gone to that side of the equation
+ 
+
+ align:start position:0%
+you've gone to that side of the equation
+how much you've deprotonated what the
+
+ align:start position:0%
+how much you've deprotonated what the
+ 
+
+ align:start position:0%
+how much you've deprotonated what the
+percent ionization is so you'll see
+
+ align:start position:0%
+percent ionization is so you'll see
+ 
+
+ align:start position:0%
+percent ionization is so you'll see
+those terms uh in the problem set and
+
+ align:start position:0%
+those terms uh in the problem set and
+ 
+
+ align:start position:0%
+those terms uh in the problem set and
+and in the
+
+ align:start position:0%
+and in the
+ 
+
+ align:start position:0%
+and in the
+book so if you use the quadratic
+
+ align:start position:0%
+book so if you use the quadratic
+ 
+
+ align:start position:0%
+book so if you use the quadratic
+equation then you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.147 and uh we're still carrying an
+
+ align:start position:0%
+0.147 and uh we're still carrying an
+ 
+
+ align:start position:0%
+0.147 and uh we're still carrying an
+extra significant figure that's really
+
+ align:start position:0%
+extra significant figure that's really
+ 
+
+ align:start position:0%
+extra significant figure that's really
+two significant figures the KA just had
+
+ align:start position:0%
+two significant figures the KA just had
+ 
+
+ align:start position:0%
+two significant figures the KA just had
+two significant figures that was given
+
+ align:start position:0%
+two significant figures that was given
+ 
+
+ align:start position:0%
+two significant figures that was given
+and so if we uh now solve so this is x
+
+ align:start position:0%
+and so if we uh now solve so this is x
+ 
+
+ align:start position:0%
+and so if we uh now solve so this is x
+when X was the hydronium ion
+
+ align:start position:0%
+when X was the hydronium ion
+ 
+
+ align:start position:0%
+when X was the hydronium ion
+concentration so pH is minus log of the
+
+ align:start position:0%
+concentration so pH is minus log of the
+ 
+
+ align:start position:0%
+concentration so pH is minus log of the
+hydronium ion concentration which would
+
+ align:start position:0%
+hydronium ion concentration which would
+ 
+
+ align:start position:0%
+hydronium ion concentration which would
+be 2. uh
+
+ align:start position:0%
+be 2. uh
+ 
+
+ align:start position:0%
+be 2. uh
+83 and since this was really two
+
+ align:start position:0%
+83 and since this was really two
+ 
+
+ align:start position:0%
+83 and since this was really two
+significant figures now you have two
+
+ align:start position:0%
+significant figures now you have two
+ 
+
+ align:start position:0%
+significant figures now you have two
+significant figures after the decimal
+
+ align:start position:0%
+significant figures after the decimal
+ 
+
+ align:start position:0%
+significant figures after the decimal
+point so uh that would be the correct
+
+ align:start position:0%
+point so uh that would be the correct
+ 
+
+ align:start position:0%
+point so uh that would be the correct
+significant figure uh number for this so
+
+ align:start position:0%
+significant figure uh number for this so
+ 
+
+ align:start position:0%
+significant figure uh number for this so
+remember this 5% rule to make your life
+
+ align:start position:0%
+remember this 5% rule to make your life
+ 
+
+ align:start position:0%
+remember this 5% rule to make your life
+easier and also in all of these problems
+
+ align:start position:0%
+easier and also in all of these problems
+ 
+
+ align:start position:0%
+easier and also in all of these problems
+you want to pay attention to the
+
+ align:start position:0%
+you want to pay attention to the
+ 
+
+ align:start position:0%
+you want to pay attention to the
+significant figures again the rules for
+
+ align:start position:0%
+significant figures again the rules for
+ 
+
+ align:start position:0%
+significant figures again the rules for
+logs and significant figures
+
+ align:start position:0%
+logs and significant figures
+ 
+
+ align:start position:0%
+logs and significant figures
+uh are are a little complicated and and
+
+ align:start position:0%
+uh are are a little complicated and and
+ 
+
+ align:start position:0%
+uh are are a little complicated and and
+require some some
+
+ align:start position:0%
+require some some
+ 
+
+ align:start position:0%
+require some some
+thought all right so that's that's weak
+
+ align:start position:0%
+thought all right so that's that's weak
+ 
+
+ align:start position:0%
+thought all right so that's that's weak
+acid in water type problem and the weak
+
+ align:start position:0%
+acid in water type problem and the weak
+ 
+
+ align:start position:0%
+acid in water type problem and the weak
+base is going to be very very similar to
+
+ align:start position:0%
+base is going to be very very similar to
+ 
+
+ align:start position:0%
+base is going to be very very similar to
+that and so today we're going to be
+
+ align:start position:0%
+that and so today we're going to be
+ 
+
+ align:start position:0%
+that and so today we're going to be
+going on and talking about weak bases
+
+ align:start position:0%
+going on and talking about weak bases
+ 
+
+ align:start position:0%
+going on and talking about weak bases
+we're going to talk about Salt Solutions
+
+ align:start position:0%
+we're going to talk about Salt Solutions
+ 
+
+ align:start position:0%
+we're going to talk about Salt Solutions
+and I'll try to prove to you that salt
+
+ align:start position:0%
+and I'll try to prove to you that salt
+ 
+
+ align:start position:0%
+and I'll try to prove to you that salt
+solution problems just break down to
+
+ align:start position:0%
+solution problems just break down to
+ 
+
+ align:start position:0%
+solution problems just break down to
+weak acid problems and weak base
+
+ align:start position:0%
+weak acid problems and weak base
+ 
+
+ align:start position:0%
+weak acid problems and weak base
+problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+C no that's the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X it's just smaller than it's just a
+
+ align:start position:0%
+X it's just smaller than it's just a
+ 
+
+ align:start position:0%
+X it's just smaller than it's just a
+question of is it's smaller than the
+
+ align:start position:0%
+question of is it's smaller than the
+ 
+
+ align:start position:0%
+question of is it's smaller than the
+number so back here it's not that it's
+
+ align:start position:0%
+number so back here it's not that it's
+ 
+
+ align:start position:0%
+number so back here it's not that it's
+it's incredibly small number it's just
+
+ align:start position:0%
+it's incredibly small number it's just
+ 
+
+ align:start position:0%
+it's incredibly small number it's just
+within the significant figures smaller
+
+ align:start position:0%
+within the significant figures smaller
+ 
+
+ align:start position:0%
+within the significant figures smaller
+than this number so that if you
+
+ align:start position:0%
+than this number so that if you
+ 
+
+ align:start position:0%
+than this number so that if you
+subtracted it from that number it
+
+ align:start position:0%
+subtracted it from that number it
+ 
+
+ align:start position:0%
+subtracted it from that number it
+wouldn't really make any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+difference this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one yeah so th this is the the
+
+ align:start position:0%
+one yeah so th this is the the
+ 
+
+ align:start position:0%
+one yeah so th this is the the
+assumption that X the number X is going
+
+ align:start position:0%
+assumption that X the number X is going
+ 
+
+ align:start position:0%
+assumption that X the number X is going
+to be enough smaller than 028
+
+ align:start position:0%
+to be enough smaller than 028
+ 
+
+ align:start position:0%
+to be enough smaller than 028
+that if you subtracted X from that
+
+ align:start position:0%
+that if you subtracted X from that
+ 
+
+ align:start position:0%
+that if you subtracted X from that
+number you'd still get that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number yeah so here you're getting plus
+
+ align:start position:0%
+number yeah so here you're getting plus
+ 
+
+ align:start position:0%
+number yeah so here you're getting plus
+X you're forming this amount of
+
+ align:start position:0%
+X you're forming this amount of
+ 
+
+ align:start position:0%
+X you're forming this amount of
+hydronium ion this amount of the
+
+ align:start position:0%
+hydronium ion this amount of the
+ 
+
+ align:start position:0%
+hydronium ion this amount of the
+conjugate and that's the same amount
+
+ align:start position:0%
+conjugate and that's the same amount
+ 
+
+ align:start position:0%
+conjugate and that's the same amount
+that's forming here that what you're
+
+ align:start position:0%
+that's forming here that what you're
+ 
+
+ align:start position:0%
+that's forming here that what you're
+taking away from your initial over here
+
+ align:start position:0%
+taking away from your initial over here
+ 
+
+ align:start position:0%
+taking away from your initial over here
+so it is the same X so you're not you're
+
+ align:start position:0%
+so it is the same X so you're not you're
+ 
+
+ align:start position:0%
+so it is the same X so you're not you're
+not really saying that this is infantes
+
+ align:start position:0%
+not really saying that this is infantes
+ 
+
+ align:start position:0%
+not really saying that this is infantes
+small number you're just saying that
+
+ align:start position:0%
+small number you're just saying that
+ 
+
+ align:start position:0%
+small number you're just saying that
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+smaller than this to to the degree that
+
+ align:start position:0%
+smaller than this to to the degree that
+ 
+
+ align:start position:0%
+smaller than this to to the degree that
+it's not playing a big it's not changing
+
+ align:start position:0%
+it's not playing a big it's not changing
+ 
+
+ align:start position:0%
+it's not playing a big it's not changing
+this very much so you don't have to
+
+ align:start position:0%
+this very much so you don't have to
+ 
+
+ align:start position:0%
+this very much so you don't have to
+actually do that subtraction and so the
+
+ align:start position:0%
+actually do that subtraction and so the
+ 
+
+ align:start position:0%
+actually do that subtraction and so the
+rule we use for that is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+5% okay so again there are these types
+
+ align:start position:0%
+5% okay so again there are these types
+ 
+
+ align:start position:0%
+5% okay so again there are these types
+of problems and now we're going to look
+
+ align:start position:0%
+of problems and now we're going to look
+ 
+
+ align:start position:0%
+of problems and now we're going to look
+at a weak base
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem okay so let's look at a weak
+
+ align:start position:0%
+problem okay so let's look at a weak
+ 
+
+ align:start position:0%
+problem okay so let's look at a weak
+based problem I need better chalk than
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that all right so weak base in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+water so if we have
+
+ align:start position:0%
+water so if we have
+ 
+
+ align:start position:0%
+water so if we have
+NH3 plus
+
+ align:start position:0%
+NH3 plus
+ 
+
+ align:start position:0%
+NH3 plus
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+water it will go to the conjugate of NH3
+
+ align:start position:0%
+water it will go to the conjugate of NH3
+ 
+
+ align:start position:0%
+water it will go to the conjugate of NH3
+which is NH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+4+ and hydroxide
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ion so if you're talking about a weak
+
+ align:start position:0%
+ion so if you're talking about a weak
+ 
+
+ align:start position:0%
+ion so if you're talking about a weak
+base in water
+
+ align:start position:0%
+base in water
+ 
+
+ align:start position:0%
+base in water
+problem you're going to expect to see
+
+ align:start position:0%
+problem you're going to expect to see
+ 
+
+ align:start position:0%
+problem you're going to expect to see
+hydronium ion on the other side and this
+
+ align:start position:0%
+hydronium ion on the other side and this
+ 
+
+ align:start position:0%
+hydronium ion on the other side and this
+is just a check that you want to make
+
+ align:start position:0%
+is just a check that you want to make
+ 
+
+ align:start position:0%
+is just a check that you want to make
+sure you're asking yourself as you're
+
+ align:start position:0%
+sure you're asking yourself as you're
+ 
+
+ align:start position:0%
+sure you're asking yourself as you're
+doing these problems if you write the
+
+ align:start position:0%
+doing these problems if you write the
+ 
+
+ align:start position:0%
+doing these problems if you write the
+equation wrong you're going to be in a
+
+ align:start position:0%
+equation wrong you're going to be in a
+ 
+
+ align:start position:0%
+equation wrong you're going to be in a
+lot of trouble weak base should yield a
+
+ align:start position:0%
+lot of trouble weak base should yield a
+ 
+
+ align:start position:0%
+lot of trouble weak base should yield a
+basic solution so you should be getting
+
+ align:start position:0%
+basic solution so you should be getting
+ 
+
+ align:start position:0%
+basic solution so you should be getting
+hydroxide ions
+
+ align:start position:0%
+hydroxide ions
+ 
+
+ align:start position:0%
+hydroxide ions
+out all right so if we look at this
+
+ align:start position:0%
+out all right so if we look at this
+ 
+
+ align:start position:0%
+out all right so if we look at this
+problem we have an initial
+
+ align:start position:0%
+problem we have an initial
+ 
+
+ align:start position:0%
+problem we have an initial
+concentration of
+
+ align:start position:0%
+concentration of
+ 
+
+ align:start position:0%
+concentration of
+.15
+
+ align:start position:0%
+.15
+ 
+
+ align:start position:0%
+.15
+molar and we don't have any of this and
+
+ align:start position:0%
+molar and we don't have any of this and
+ 
+
+ align:start position:0%
+molar and we don't have any of this and
+we don't have any of
+
+ align:start position:0%
+we don't have any of
+ 
+
+ align:start position:0%
+we don't have any of
+that the change is going to be -
+
+ align:start position:0%
+that the change is going to be -
+ 
+
+ align:start position:0%
+that the change is going to be -
+X Plus
+
+ align:start position:0%
+X Plus
+ 
+
+ align:start position:0%
+X Plus
+X and plus X
+
+ align:start position:0%
+X and plus X
+ 
+
+ align:start position:0%
+X and plus X
+then at
+
+ align:start position:0%
+then at
+ 
+
+ align:start position:0%
+then at
+equilibrium we'll have 05 - x and we'll
+
+ align:start position:0%
+equilibrium we'll have 05 - x and we'll
+ 
+
+ align:start position:0%
+equilibrium we'll have 05 - x and we'll
+have x and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x so now it's a weak base in water so
+
+ align:start position:0%
+x so now it's a weak base in water so
+ 
+
+ align:start position:0%
+x so now it's a weak base in water so
+we're going to talk about a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KB and so KB is the base ionization
+
+ align:start position:0%
+KB and so KB is the base ionization
+ 
+
+ align:start position:0%
+KB and so KB is the base ionization
+constant so KB is also going to be equal
+
+ align:start position:0%
+constant so KB is also going to be equal
+ 
+
+ align:start position:0%
+constant so KB is also going to be equal
+to the products because it is an
+
+ align:start position:0%
+to the products because it is an
+ 
+
+ align:start position:0%
+to the products because it is an
+equilibrium constant
+
+ align:start position:0%
+equilibrium constant
+ 
+
+ align:start position:0%
+equilibrium constant
+products over
+
+ align:start position:0%
+products over
+ 
+
+ align:start position:0%
+products over
+reactants and we're not including water
+
+ align:start position:0%
+reactants and we're not including water
+ 
+
+ align:start position:0%
+reactants and we're not including water
+because it's the
+
+ align:start position:0%
+because it's the
+ 
+
+ align:start position:0%
+because it's the
+solvent so this will be equal
+
+ align:start position:0%
+solvent so this will be equal
+ 
+
+ align:start position:0%
+solvent so this will be equal
+to X2 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1.15 minus
+
+ align:start position:0%
+1.15 minus
+ 
+
+ align:start position:0%
+1.15 minus
+X and we can try try this assumption
+
+ align:start position:0%
+X and we can try try this assumption
+ 
+
+ align:start position:0%
+X and we can try try this assumption
+again that that might be equal to x^2
+
+ align:start position:0%
+again that that might be equal to x^2
+ 
+
+ align:start position:0%
+again that that might be equal to x^2
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+.15 so the
+
+ align:start position:0%
+.15 so the
+ 
+
+ align:start position:0%
+.15 so the
+KB is given and for a lot of the
+
+ align:start position:0%
+KB is given and for a lot of the
+ 
+
+ align:start position:0%
+KB is given and for a lot of the
+problems you'll be able to look this up
+
+ align:start position:0%
+problems you'll be able to look this up
+ 
+
+ align:start position:0%
+problems you'll be able to look this up
+in your book of 1.8 * 10us 5 so again
+
+ align:start position:0%
+in your book of 1.8 * 10us 5 so again
+ 
+
+ align:start position:0%
+in your book of 1.8 * 10us 5 so again
+it's a weak base it's less than one it
+
+ align:start position:0%
+it's a weak base it's less than one it
+ 
+
+ align:start position:0%
+it's a weak base it's less than one it
+has a a KB less uh a KB that's less than
+
+ align:start position:0%
+has a a KB less uh a KB that's less than
+ 
+
+ align:start position:0%
+has a a KB less uh a KB that's less than
+one one and so if we solve for x here we
+
+ align:start position:0%
+one one and so if we solve for x here we
+ 
+
+ align:start position:0%
+one one and so if we solve for x here we
+get X as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.164 and now we can check our
+
+ align:start position:0%
+0.164 and now we can check our
+ 
+
+ align:start position:0%
+0.164 and now we can check our
+assumption that that is okay using the
+
+ align:start position:0%
+assumption that that is okay using the
+ 
+
+ align:start position:0%
+assumption that that is okay using the
+5% rule
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+164 over
+
+ align:start position:0%
+164 over
+ 
+
+ align:start position:0%
+164 over
+.15 * 100 gives you
+
+ align:start position:0%
+.15 * 100 gives you
+ 
+
+ align:start position:0%
+.15 * 100 gives you
+1.1% so you are checking the Assumption
+
+ align:start position:0%
+1.1% so you are checking the Assumption
+ 
+
+ align:start position:0%
+1.1% so you are checking the Assumption
+and the assumption is okay it's less
+
+ align:start position:0%
+and the assumption is okay it's less
+ 
+
+ align:start position:0%
+and the assumption is okay it's less
+than five so we can use use that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+number all right so now we want to find
+
+ align:start position:0%
+number all right so now we want to find
+ 
+
+ align:start position:0%
+number all right so now we want to find
+out the pH of of this mixture at
+
+ align:start position:0%
+out the pH of of this mixture at
+ 
+
+ align:start position:0%
+out the pH of of this mixture at
+equilibrium and we have x x is equal to
+
+ align:start position:0%
+equilibrium and we have x x is equal to
+ 
+
+ align:start position:0%
+equilibrium and we have x x is equal to
+the hydroxide ion concentration
+
+ align:start position:0%
+the hydroxide ion concentration
+ 
+
+ align:start position:0%
+the hydroxide ion concentration
+so we can calculate first
+
+ align:start position:0%
+so we can calculate first
+ 
+
+ align:start position:0%
+so we can calculate first
+P minus log of the hydroxide ion
+
+ align:start position:0%
+P minus log of the hydroxide ion
+ 
+
+ align:start position:0%
+P minus log of the hydroxide ion
+concentration and so we have minus log
+
+ align:start position:0%
+concentration and so we have minus log
+ 
+
+ align:start position:0%
+concentration and so we have minus log
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0.164 and we get
+
+ align:start position:0%
+0.164 and we get
+ 
+
+ align:start position:0%
+0.164 and we get
+2.79 so this only had two real
+
+ align:start position:0%
+2.79 so this only had two real
+ 
+
+ align:start position:0%
+2.79 so this only had two real
+significant figures we're carrying an
+
+ align:start position:0%
+significant figures we're carrying an
+ 
+
+ align:start position:0%
+significant figures we're carrying an
+extra one we only had 0.15 we only had
+
+ align:start position:0%
+extra one we only had 0.15 we only had
+ 
+
+ align:start position:0%
+extra one we only had 0.15 we only had
+had two significant figures here so this
+
+ align:start position:0%
+had two significant figures here so this
+ 
+
+ align:start position:0%
+had two significant figures here so this
+is going to get two after the decimal
+
+ align:start position:0%
+is going to get two after the decimal
+ 
+
+ align:start position:0%
+is going to get two after the decimal
+point so our number would since we have
+
+ align:start position:0%
+point so our number would since we have
+ 
+
+ align:start position:0%
+point so our number would since we have
+two
+
+ align:start position:0%
+two
+ 
+
+ align:start position:0%
+two
+here we get two sigfigs after
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decimal so now we have P how do we get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pH yeah we we can subtract from 14 so
+
+ align:start position:0%
+pH yeah we we can subtract from 14 so
+ 
+
+ align:start position:0%
+pH yeah we we can subtract from 14 so
+the pH is going to equal
+
+ align:start position:0%
+the pH is going to equal
+ 
+
+ align:start position:0%
+the pH is going to equal
+14.00 minus
+
+ align:start position:0%
+14.00 minus
+ 
+
+ align:start position:0%
+14.00 minus
+2.79 and it'll be
+
+ align:start position:0%
+2.79 and it'll be
+ 
+
+ align:start position:0%
+2.79 and it'll be
+11.21 will be the
+
+ align:start position:0%
+11.21 will be the
+ 
+
+ align:start position:0%
+11.21 will be the
+ph and I just want to remind people
+
+ align:start position:0%
+ph and I just want to remind people
+ 
+
+ align:start position:0%
+ph and I just want to remind people
+sometimes when you're in a hurry on a
+
+ align:start position:0%
+sometimes when you're in a hurry on a
+ 
+
+ align:start position:0%
+sometimes when you're in a hurry on a
+test and you get to this point and have
+
+ align:start position:0%
+test and you get to this point and have
+ 
+
+ align:start position:0%
+test and you get to this point and have
+this number of 2.79 and you say oh I'm
+
+ align:start position:0%
+this number of 2.79 and you say oh I'm
+ 
+
+ align:start position:0%
+this number of 2.79 and you say oh I'm
+done but that's the p and if you think
+
+ align:start position:0%
+done but that's the p and if you think
+ 
+
+ align:start position:0%
+done but that's the p and if you think
+about it for a minute a weak base in
+
+ align:start position:0%
+about it for a minute a weak base in
+ 
+
+ align:start position:0%
+about it for a minute a weak base in
+water a base in water should give rise
+
+ align:start position:0%
+water a base in water should give rise
+ 
+
+ align:start position:0%
+water a base in water should give rise
+to a basic pH I.E a pH greater than
+
+ align:start position:0%
+to a basic pH I.E a pH greater than
+ 
+
+ align:start position:0%
+to a basic pH I.E a pH greater than
+seven so below seven is acidic above
+
+ align:start position:0%
+seven so below seven is acidic above
+ 
+
+ align:start position:0%
+seven so below seven is acidic above
+seven is basic so you have to remember
+
+ align:start position:0%
+seven is basic so you have to remember
+ 
+
+ align:start position:0%
+seven is basic so you have to remember
+to convert to pH the pH should be a
+
+ align:start position:0%
+to convert to pH the pH should be a
+ 
+
+ align:start position:0%
+to convert to pH the pH should be a
+basic number so just keep it in mind as
+
+ align:start position:0%
+basic number so just keep it in mind as
+ 
+
+ align:start position:0%
+basic number so just keep it in mind as
+you're doing these problems think about
+
+ align:start position:0%
+you're doing these problems think about
+ 
+
+ align:start position:0%
+you're doing these problems think about
+what the problem was oh it's a weak base
+
+ align:start position:0%
+what the problem was oh it's a weak base
+ 
+
+ align:start position:0%
+what the problem was oh it's a weak base
+in water does my answer make sense to
+
+ align:start position:0%
+in water does my answer make sense to
+ 
+
+ align:start position:0%
+in water does my answer make sense to
+kind of double check that you've gone
+
+ align:start position:0%
+kind of double check that you've gone
+ 
+
+ align:start position:0%
+kind of double check that you've gone
+you've gone the full Direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's weak base now we're going
+
+ align:start position:0%
+okay so that's weak base now we're going
+ 
+
+ align:start position:0%
+okay so that's weak base now we're going
+to talk about uh salts in in solution
+
+ align:start position:0%
+to talk about uh salts in in solution
+ 
+
+ align:start position:0%
+to talk about uh salts in in solution
+for a minute and salts and solution are
+
+ align:start position:0%
+for a minute and salts and solution are
+ 
+
+ align:start position:0%
+for a minute and salts and solution are
+going to break down into weak acid and
+
+ align:start position:0%
+going to break down into weak acid and
+ 
+
+ align:start position:0%
+going to break down into weak acid and
+weak base
+
+ align:start position:0%
+weak base
+ 
+
+ align:start position:0%
+weak base
+problems so if you have a a salt a salt
+
+ align:start position:0%
+problems so if you have a a salt a salt
+ 
+
+ align:start position:0%
+problems so if you have a a salt a salt
+can be formed by mixing an acid and a
+
+ align:start position:0%
+can be formed by mixing an acid and a
+ 
+
+ align:start position:0%
+can be formed by mixing an acid and a
+base as shown up here but the pH of salt
+
+ align:start position:0%
+base as shown up here but the pH of salt
+ 
+
+ align:start position:0%
+base as shown up here but the pH of salt
+water is not always going to be
+
+ align:start position:0%
+water is not always going to be
+ 
+
+ align:start position:0%
+water is not always going to be
+neutral so if if the salt
+
+ align:start position:0%
+neutral so if if the salt
+ 
+
+ align:start position:0%
+neutral so if if the salt
+contains for example the conjugate acid
+
+ align:start position:0%
+contains for example the conjugate acid
+ 
+
+ align:start position:0%
+contains for example the conjugate acid
+of a weak base then it contains a
+
+ align:start position:0%
+of a weak base then it contains a
+ 
+
+ align:start position:0%
+of a weak base then it contains a
+conjugate acid so it'll produce an
+
+ align:start position:0%
+conjugate acid so it'll produce an
+ 
+
+ align:start position:0%
+conjugate acid so it'll produce an
+acidic solution also salts that contain
+
+ align:start position:0%
+acidic solution also salts that contain
+ 
+
+ align:start position:0%
+acidic solution also salts that contain
+uh High some small highly charged metals
+
+ align:start position:0%
+uh High some small highly charged metals
+ 
+
+ align:start position:0%
+uh High some small highly charged metals
+like iron uh 3+ will also affect the
+
+ align:start position:0%
+like iron uh 3+ will also affect the
+ 
+
+ align:start position:0%
+like iron uh 3+ will also affect the
+pH this is something that that you
+
+ align:start position:0%
+pH this is something that that you
+ 
+
+ align:start position:0%
+pH this is something that that you
+should remember group one and group two
+
+ align:start position:0%
+should remember group one and group two
+ 
+
+ align:start position:0%
+should remember group one and group two
+metals um or metal cations with charges
+
+ align:start position:0%
+metals um or metal cations with charges
+ 
+
+ align:start position:0%
+metals um or metal cations with charges
+of plus one and we have Li I calcium
+
+ align:start position:0%
+of plus one and we have Li I calcium
+ 
+
+ align:start position:0%
+of plus one and we have Li I calcium
+plus 2 a silver what plus one these are
+
+ align:start position:0%
+plus 2 a silver what plus one these are
+ 
+
+ align:start position:0%
+plus 2 a silver what plus one these are
+all going to be neutral but other things
+
+ align:start position:0%
+all going to be neutral but other things
+ 
+
+ align:start position:0%
+all going to be neutral but other things
+like iron 3+ will not be or if you have
+
+ align:start position:0%
+like iron 3+ will not be or if you have
+ 
+
+ align:start position:0%
+like iron 3+ will not be or if you have
+a salt that contains a conjugate base of
+
+ align:start position:0%
+a salt that contains a conjugate base of
+ 
+
+ align:start position:0%
+a salt that contains a conjugate base of
+a weak acid it's a conjugate base so it
+
+ align:start position:0%
+a weak acid it's a conjugate base so it
+ 
+
+ align:start position:0%
+a weak acid it's a conjugate base so it
+can produce a basic
+
+ align:start position:0%
+can produce a basic
+ 
+
+ align:start position:0%
+can produce a basic
+solution so uh if you remember on Monday
+
+ align:start position:0%
+solution so uh if you remember on Monday
+ 
+
+ align:start position:0%
+solution so uh if you remember on Monday
+we measured the pH of MIT tap water and
+
+ align:start position:0%
+we measured the pH of MIT tap water and
+ 
+
+ align:start position:0%
+we measured the pH of MIT tap water and
+found that it was not neutral it was ph6
+
+ align:start position:0%
+found that it was not neutral it was ph6
+ 
+
+ align:start position:0%
+found that it was not neutral it was ph6
+rather than seven so that would suggest
+
+ align:start position:0%
+rather than seven so that would suggest
+ 
+
+ align:start position:0%
+rather than seven so that would suggest
+that there was some salt in that tap
+
+ align:start position:0%
+that there was some salt in that tap
+ 
+
+ align:start position:0%
+that there was some salt in that tap
+water that was giving rise to a
+
+ align:start position:0%
+water that was giving rise to a
+ 
+
+ align:start position:0%
+water that was giving rise to a
+non-neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pH so in terms this is also a review
+
+ align:start position:0%
+pH so in terms this is also a review
+ 
+
+ align:start position:0%
+pH so in terms this is also a review
+from last
+
+ align:start position:0%
+from last
+ 
+
+ align:start position:0%
+from last
+time there's this relationship between
+
+ align:start position:0%
+time there's this relationship between
+ 
+
+ align:start position:0%
+time there's this relationship between
+the conjugate acids and bases this isn't
+
+ align:start position:0%
+the conjugate acids and bases this isn't
+ 
+
+ align:start position:0%
+the conjugate acids and bases this isn't
+in your handout but uh just to to remind
+
+ align:start position:0%
+in your handout but uh just to to remind
+ 
+
+ align:start position:0%
+in your handout but uh just to to remind
+you what we were talking about if you
+
+ align:start position:0%
+you what we were talking about if you
+ 
+
+ align:start position:0%
+you what we were talking about if you
+have a strong acid its conjugate is
+
+ align:start position:0%
+have a strong acid its conjugate is
+ 
+
+ align:start position:0%
+have a strong acid its conjugate is
+ineffective as a base if you have an
+
+ align:start position:0%
+ineffective as a base if you have an
+ 
+
+ align:start position:0%
+ineffective as a base if you have an
+acid that's moderately weak to weak then
+
+ align:start position:0%
+acid that's moderately weak to weak then
+ 
+
+ align:start position:0%
+acid that's moderately weak to weak then
+it will have a conjugate base that's
+
+ align:start position:0%
+it will have a conjugate base that's
+ 
+
+ align:start position:0%
+it will have a conjugate base that's
+also moderately weak to very weak and if
+
+ align:start position:0%
+also moderately weak to very weak and if
+ 
+
+ align:start position:0%
+also moderately weak to very weak and if
+you have a really strong base then its
+
+ align:start position:0%
+you have a really strong base then its
+ 
+
+ align:start position:0%
+you have a really strong base then its
+conjugate will be ineffective as an acid
+
+ align:start position:0%
+conjugate will be ineffective as an acid
+ 
+
+ align:start position:0%
+conjugate will be ineffective as an acid
+so there's this uh this
+
+ align:start position:0%
+so there's this uh this
+ 
+
+ align:start position:0%
+so there's this uh this
+relationship all right so let's take a
+
+ align:start position:0%
+relationship all right so let's take a
+ 
+
+ align:start position:0%
+relationship all right so let's take a
+look at some examples of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+salts so if we have uh
+
+ align:start position:0%
+salts so if we have uh
+ 
+
+ align:start position:0%
+salts so if we have uh
+nh4 CL
+
+ align:start position:0%
+nh4 CL
+ 
+
+ align:start position:0%
+nh4 CL
+if you're asked whether putting some
+
+ align:start position:0%
+if you're asked whether putting some
+ 
+
+ align:start position:0%
+if you're asked whether putting some
+amount of this in water will lead to an
+
+ align:start position:0%
+amount of this in water will lead to an
+ 
+
+ align:start position:0%
+amount of this in water will lead to an
+acidic solution or a basic solution or a
+
+ align:start position:0%
+acidic solution or a basic solution or a
+ 
+
+ align:start position:0%
+acidic solution or a basic solution or a
+neutral solution this is how you would
+
+ align:start position:0%
+neutral solution this is how you would
+ 
+
+ align:start position:0%
+neutral solution this is how you would
+approach the problem first you're going
+
+ align:start position:0%
+approach the problem first you're going
+ 
+
+ align:start position:0%
+approach the problem first you're going
+to break this compound through the
+
+ align:start position:0%
+to break this compound through the
+ 
+
+ align:start position:0%
+to break this compound through the
+middle and consider two
+
+ align:start position:0%
+middle and consider two
+ 
+
+ align:start position:0%
+middle and consider two
+sides you'll say this salt would be
+
+ align:start position:0%
+sides you'll say this salt would be
+ 
+
+ align:start position:0%
+sides you'll say this salt would be
+composed of nh4
+
+ align:start position:0%
+composed of nh4
+ 
+
+ align:start position:0%
+composed of nh4
+plus and cl
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus then you're going to ask whether
+
+ align:start position:0%
+minus then you're going to ask whether
+ 
+
+ align:start position:0%
+minus then you're going to ask whether
+this is a conjugate acid of a weak
+
+ align:start position:0%
+this is a conjugate acid of a weak
+ 
+
+ align:start position:0%
+this is a conjugate acid of a weak
+base so is this a conjugate acid
+
+ align:start position:0%
+base so is this a conjugate acid
+ 
+
+ align:start position:0%
+base so is this a conjugate acid
+of a weak base if it is a conjugate acid
+
+ align:start position:0%
+of a weak base if it is a conjugate acid
+ 
+
+ align:start position:0%
+of a weak base if it is a conjugate acid
+of a weak base then that will affect the
+
+ align:start position:0%
+of a weak base then that will affect the
+ 
+
+ align:start position:0%
+of a weak base then that will affect the
+pH of the
+
+ align:start position:0%
+pH of the
+ 
+
+ align:start position:0%
+pH of the
+solution so what's the conjugate of
+
+ align:start position:0%
+solution so what's the conjugate of
+ 
+
+ align:start position:0%
+solution so what's the conjugate of
+Na
+
+ align:start position:0%
+Na
+ 
+
+ align:start position:0%
+Na
+nh4 Plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the conjugate of this is
+
+ align:start position:0%
+so the conjugate of this is
+ 
+
+ align:start position:0%
+so the conjugate of this is
+ammonia so the con the weak base if you
+
+ align:start position:0%
+ammonia so the con the weak base if you
+ 
+
+ align:start position:0%
+ammonia so the con the weak base if you
+take the weak base so the conjugate the
+
+ align:start position:0%
+take the weak base so the conjugate the
+ 
+
+ align:start position:0%
+take the weak base so the conjugate the
+weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base is
+
+ align:start position:0%
+base is
+ 
+
+ align:start position:0%
+base is
+NH3 and if you added a proton to this
+
+ align:start position:0%
+NH3 and if you added a proton to this
+ 
+
+ align:start position:0%
+NH3 and if you added a proton to this
+you get the conjugate acid NH H4 plus so
+
+ align:start position:0%
+you get the conjugate acid NH H4 plus so
+ 
+
+ align:start position:0%
+you get the conjugate acid NH H4 plus so
+this is a weak base so the answer to
+
+ align:start position:0%
+this is a weak base so the answer to
+ 
+
+ align:start position:0%
+this is a weak base so the answer to
+that question was yes you could look it
+
+ align:start position:0%
+that question was yes you could look it
+ 
+
+ align:start position:0%
+that question was yes you could look it
+up in the table here's ammonia it has a
+
+ align:start position:0%
+up in the table here's ammonia it has a
+ 
+
+ align:start position:0%
+up in the table here's ammonia it has a
+KB
+
+ align:start position:0%
+KB
+ 
+
+ align:start position:0%
+KB
+that's uh fairly small so it is a weak
+
+ align:start position:0%
+that's uh fairly small so it is a weak
+ 
+
+ align:start position:0%
+that's uh fairly small so it is a weak
+base and we also had it on this this
+
+ align:start position:0%
+base and we also had it on this this
+ 
+
+ align:start position:0%
+base and we also had it on this this
+chart you had NH uh
+
+ align:start position:0%
+chart you had NH uh
+ 
+
+ align:start position:0%
+chart you had NH uh
+3 over here and so you could see that it
+
+ align:start position:0%
+3 over here and so you could see that it
+ 
+
+ align:start position:0%
+3 over here and so you could see that it
+is in fact a weak a weak
+
+ align:start position:0%
+is in fact a weak a weak
+ 
+
+ align:start position:0%
+is in fact a weak a weak
+base and we can look up the uh the KB
+
+ align:start position:0%
+base and we can look up the uh the KB
+ 
+
+ align:start position:0%
+base and we can look up the uh the KB
+for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and so the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KB is 1 Point 8 *
+
+ align:start position:0%
+KB is 1 Point 8 *
+ 
+
+ align:start position:0%
+KB is 1 Point 8 *
+10-5 so that's a weak base so because
+
+ align:start position:0%
+10-5 so that's a weak base so because
+ 
+
+ align:start position:0%
+10-5 so that's a weak base so because
+the conjugate is a weak base that means
+
+ align:start position:0%
+the conjugate is a weak base that means
+ 
+
+ align:start position:0%
+the conjugate is a weak base that means
+that the conjugate acid is also a weak
+
+ align:start position:0%
+that the conjugate acid is also a weak
+ 
+
+ align:start position:0%
+that the conjugate acid is also a weak
+acid and so this should be acidic in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution so that should be acidic in
+
+ align:start position:0%
+solution so that should be acidic in
+ 
+
+ align:start position:0%
+solution so that should be acidic in
+solution and let's just write that out
+
+ align:start position:0%
+solution and let's just write that out
+ 
+
+ align:start position:0%
+solution and let's just write that out
+over here so if we have
+
+ align:start position:0%
+over here so if we have
+ 
+
+ align:start position:0%
+over here so if we have
+nh4+ and that's got to be a weak acid
+
+ align:start position:0%
+nh4+ and that's got to be a weak acid
+ 
+
+ align:start position:0%
+nh4+ and that's got to be a weak acid
+because its conjugate is a weak base and
+
+ align:start position:0%
+because its conjugate is a weak base and
+ 
+
+ align:start position:0%
+because its conjugate is a weak base and
+we put the weak acid in
+
+ align:start position:0%
+we put the weak acid in
+ 
+
+ align:start position:0%
+we put the weak acid in
+water we should get the conjugate base
+
+ align:start position:0%
+water we should get the conjugate base
+ 
+
+ align:start position:0%
+water we should get the conjugate base
+back plus hydronium ion and the presence
+
+ align:start position:0%
+back plus hydronium ion and the presence
+ 
+
+ align:start position:0%
+back plus hydronium ion and the presence
+of the hydronium ion is going to make
+
+ align:start position:0%
+of the hydronium ion is going to make
+ 
+
+ align:start position:0%
+of the hydronium ion is going to make
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+acidic and so this is a weak weak base
+
+ align:start position:0%
+acidic and so this is a weak weak base
+ 
+
+ align:start position:0%
+acidic and so this is a weak weak base
+over here it's conjugate is a weak base
+
+ align:start position:0%
+over here it's conjugate is a weak base
+ 
+
+ align:start position:0%
+over here it's conjugate is a weak base
+and we can look up a Ka number for it
+
+ align:start position:0%
+and we can look up a Ka number for it
+ 
+
+ align:start position:0%
+and we can look up a Ka number for it
+5.6 *
+
+ align:start position:0%
+5.6 *
+ 
+
+ align:start position:0%
+5.6 *
+10-1 so that is in fact a weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid and so here it is on this table we
+
+ align:start position:0%
+acid and so here it is on this table we
+ 
+
+ align:start position:0%
+acid and so here it is on this table we
+can look it up and it is a weak it's
+
+ align:start position:0%
+can look it up and it is a weak it's
+ 
+
+ align:start position:0%
+can look it up and it is a weak it's
+less than one it's definitely a weak
+
+ align:start position:0%
+less than one it's definitely a weak
+ 
+
+ align:start position:0%
+less than one it's definitely a weak
+acid so this part on this side of the uh
+
+ align:start position:0%
+acid so this part on this side of the uh
+ 
+
+ align:start position:0%
+acid so this part on this side of the uh
+compound we have something that's going
+
+ align:start position:0%
+compound we have something that's going
+ 
+
+ align:start position:0%
+compound we have something that's going
+to produce an acidic solution U so now
+
+ align:start position:0%
+to produce an acidic solution U so now
+ 
+
+ align:start position:0%
+to produce an acidic solution U so now
+we have to ask what about this side over
+
+ align:start position:0%
+we have to ask what about this side over
+ 
+
+ align:start position:0%
+we have to ask what about this side over
+here and so we would ask is this a
+
+ align:start position:0%
+here and so we would ask is this a
+ 
+
+ align:start position:0%
+here and so we would ask is this a
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+base of a
+
+ align:start position:0%
+base of a
+ 
+
+ align:start position:0%
+base of a
+weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid is CL minus a conjugate base of a
+
+ align:start position:0%
+acid is CL minus a conjugate base of a
+ 
+
+ align:start position:0%
+acid is CL minus a conjugate base of a
+weak acid what would be the acid the
+
+ align:start position:0%
+weak acid what would be the acid the
+ 
+
+ align:start position:0%
+weak acid what would be the acid the
+conjugate acid of Cl
+
+ align:start position:0%
+conjugate acid of Cl
+ 
+
+ align:start position:0%
+conjugate acid of Cl
+minus HCL
+
+ align:start position:0%
+minus HCL
+ 
+
+ align:start position:0%
+minus HCL
+so the conjugate is HCl is that
+
+ align:start position:0%
+so the conjugate is HCl is that
+ 
+
+ align:start position:0%
+so the conjugate is HCl is that
+weak no so this is a
+
+ align:start position:0%
+weak no so this is a
+ 
+
+ align:start position:0%
+weak no so this is a
+strong a strong acid and that's one that
+
+ align:start position:0%
+strong a strong acid and that's one that
+ 
+
+ align:start position:0%
+strong a strong acid and that's one that
+you'll encounter a bunch so you'll
+
+ align:start position:0%
+you'll encounter a bunch so you'll
+ 
+
+ align:start position:0%
+you'll encounter a bunch so you'll
+definitely have uh that that memorized
+
+ align:start position:0%
+definitely have uh that that memorized
+ 
+
+ align:start position:0%
+definitely have uh that that memorized
+by the time you get through the problems
+
+ align:start position:0%
+by the time you get through the problems
+ 
+
+ align:start position:0%
+by the time you get through the problems
+so it has a Ka over here of 10 to the
+
+ align:start position:0%
+so it has a Ka over here of 10 to the
+ 
+
+ align:start position:0%
+so it has a Ka over here of 10 to the
+7th so if you put that in in water if
+
+ align:start position:0%
+7th so if you put that in in water if
+ 
+
+ align:start position:0%
+7th so if you put that in in water if
+you had
+
+ align:start position:0%
+you had
+ 
+
+ align:start position:0%
+you had
+HCL in water it's a really strong
+
+ align:start position:0%
+HCL in water it's a really strong
+ 
+
+ align:start position:0%
+HCL in water it's a really strong
+acid Ka 10 the 7th and
+
+ align:start position:0%
+acid Ka 10 the 7th and
+ 
+
+ align:start position:0%
+acid Ka 10 the 7th and
+so it would go pretty much all the way
+
+ align:start position:0%
+so it would go pretty much all the way
+ 
+
+ align:start position:0%
+so it would go pretty much all the way
+to completion so that means that this
+
+ align:start position:0%
+to completion so that means that this
+ 
+
+ align:start position:0%
+to completion so that means that this
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+ineffective as a
+
+ align:start position:0%
+ineffective as a
+ 
+
+ align:start position:0%
+ineffective as a
+base if you have a strong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid again there's these relationships
+
+ align:start position:0%
+acid again there's these relationships
+ 
+
+ align:start position:0%
+acid again there's these relationships
+that we talked about um if something is
+
+ align:start position:0%
+that we talked about um if something is
+ 
+
+ align:start position:0%
+that we talked about um if something is
+a really strong acid up here then its
+
+ align:start position:0%
+a really strong acid up here then its
+ 
+
+ align:start position:0%
+a really strong acid up here then its
+conjugate is completely ineffective as a
+
+ align:start position:0%
+conjugate is completely ineffective as a
+ 
+
+ align:start position:0%
+conjugate is completely ineffective as a
+base so this then is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+neutral so because this is not going to
+
+ align:start position:0%
+neutral so because this is not going to
+ 
+
+ align:start position:0%
+neutral so because this is not going to
+change the pH anymore it's ineffective
+
+ align:start position:0%
+change the pH anymore it's ineffective
+ 
+
+ align:start position:0%
+change the pH anymore it's ineffective
+it is base it's not going to make the
+
+ align:start position:0%
+it is base it's not going to make the
+ 
+
+ align:start position:0%
+it is base it's not going to make the
+solution basic at all whereas on the
+
+ align:start position:0%
+solution basic at all whereas on the
+ 
+
+ align:start position:0%
+solution basic at all whereas on the
+other side nh4 plus is a conjugate acid
+
+ align:start position:0%
+other side nh4 plus is a conjugate acid
+ 
+
+ align:start position:0%
+other side nh4 plus is a conjugate acid
+of a weak base so it will produce an
+
+ align:start position:0%
+of a weak base so it will produce an
+ 
+
+ align:start position:0%
+of a weak base so it will produce an
+acidic solution so the answer is that
+
+ align:start position:0%
+acidic solution so the answer is that
+ 
+
+ align:start position:0%
+acidic solution so the answer is that
+this salt in water will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acidic so if you were given an amount of
+
+ align:start position:0%
+acidic so if you were given an amount of
+ 
+
+ align:start position:0%
+acidic so if you were given an amount of
+this compound if you
+
+ align:start position:0%
+this compound if you
+ 
+
+ align:start position:0%
+this compound if you
+said5 molar for example what is the pH
+
+ align:start position:0%
+said5 molar for example what is the pH
+ 
+
+ align:start position:0%
+said5 molar for example what is the pH
+you could work that out by just doing a
+
+ align:start position:0%
+you could work that out by just doing a
+ 
+
+ align:start position:0%
+you could work that out by just doing a
+weak acid type problem and solving for x
+
+ align:start position:0%
+weak acid type problem and solving for x
+ 
+
+ align:start position:0%
+weak acid type problem and solving for x
+here and calculating pH so this
+
+ align:start position:0%
+here and calculating pH so this
+ 
+
+ align:start position:0%
+here and calculating pH so this
+particular salt in water problem is just
+
+ align:start position:0%
+particular salt in water problem is just
+ 
+
+ align:start position:0%
+particular salt in water problem is just
+a weak acid in water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem okay let's look at another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example okay again we're going to take
+
+ align:start position:0%
+example okay again we're going to take
+ 
+
+ align:start position:0%
+example okay again we're going to take
+take this compound and break it
+
+ align:start position:0%
+take this compound and break it
+ 
+
+ align:start position:0%
+take this compound and break it
+up and we form
+
+ align:start position:0%
+up and we form
+ 
+
+ align:start position:0%
+up and we form
+na+ and ch3
+
+ align:start position:0%
+na+ and ch3
+ 
+
+ align:start position:0%
+na+ and ch3
+Co
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus so then we ask is
+
+ align:start position:0%
+minus so then we ask is
+ 
+
+ align:start position:0%
+minus so then we ask is
+this a conjugate
+
+ align:start position:0%
+this a conjugate
+ 
+
+ align:start position:0%
+this a conjugate
+acid of a
+
+ align:start position:0%
+acid of a
+ 
+
+ align:start position:0%
+acid of a
+weak
+
+ align:start position:0%
+weak
+ 
+
+ align:start position:0%
+weak
+base and what's the
+
+ align:start position:0%
+base and what's the
+ 
+
+ align:start position:0%
+base and what's the
+answer where do you think it probably
+
+ align:start position:0%
+answer where do you think it probably
+ 
+
+ align:start position:0%
+answer where do you think it probably
+came
+
+ align:start position:0%
+came
+ 
+
+ align:start position:0%
+came
+from yeah it probably came from NaOH so
+
+ align:start position:0%
+from yeah it probably came from NaOH so
+ 
+
+ align:start position:0%
+from yeah it probably came from NaOH so
+this one the answer here is
+
+ align:start position:0%
+this one the answer here is
+ 
+
+ align:start position:0%
+this one the answer here is
+no and we talked about rules that all
+
+ align:start position:0%
+no and we talked about rules that all
+ 
+
+ align:start position:0%
+no and we talked about rules that all
+group one and group two um are
+
+ align:start position:0%
+group one and group two um are
+ 
+
+ align:start position:0%
+group one and group two um are
+neutral group one ions are neutral group
+
+ align:start position:0%
+neutral group one ions are neutral group
+ 
+
+ align:start position:0%
+neutral group one ions are neutral group
+one and group two are
+
+ align:start position:0%
+one and group two are
+ 
+
+ align:start position:0%
+one and group two are
+neutral so this in
+
+ align:start position:0%
+neutral so this in
+ 
+
+ align:start position:0%
+neutral so this in
+solution will be neutral
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's look at the other
+
+ align:start position:0%
+all right so let's look at the other
+ 
+
+ align:start position:0%
+all right so let's look at the other
+side and ask so is this the conjugate
+
+ align:start position:0%
+side and ask so is this the conjugate
+ 
+
+ align:start position:0%
+side and ask so is this the conjugate
+base of a
+
+ align:start position:0%
+base of a
+ 
+
+ align:start position:0%
+base of a
+weak
+
+ align:start position:0%
+weak
+ 
+
+ align:start position:0%
+weak
+acid and what would be the acid
+
+ align:start position:0%
+acid and what would be the acid
+ 
+
+ align:start position:0%
+acid and what would be the acid
+here yeah atic acid so we have ch3
+
+ align:start position:0%
+here yeah atic acid so we have ch3
+ 
+
+ align:start position:0%
+here yeah atic acid so we have ch3
+Co and we can look to see if that is a
+
+ align:start position:0%
+Co and we can look to see if that is a
+ 
+
+ align:start position:0%
+Co and we can look to see if that is a
+weak
+
+ align:start position:0%
+weak
+ 
+
+ align:start position:0%
+weak
+acid and we can look it up here here and
+
+ align:start position:0%
+acid and we can look it up here here and
+ 
+
+ align:start position:0%
+acid and we can look it up here here and
+so we have um you get the right get the
+
+ align:start position:0%
+so we have um you get the right get the
+ 
+
+ align:start position:0%
+so we have um you get the right get the
+right line 1.76 * 10us 5 so is that a
+
+ align:start position:0%
+right line 1.76 * 10us 5 so is that a
+ 
+
+ align:start position:0%
+right line 1.76 * 10us 5 so is that a
+weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+acid is that a weak acid
+
+ align:start position:0%
+acid is that a weak acid
+ 
+
+ align:start position:0%
+acid is that a weak acid
+yes so if it's a conjugate base of a
+
+ align:start position:0%
+yes so if it's a conjugate base of a
+ 
+
+ align:start position:0%
+yes so if it's a conjugate base of a
+weak acid then in
+
+ align:start position:0%
+weak acid then in
+ 
+
+ align:start position:0%
+weak acid then in
+solution it's going to be basic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we can work that out if we wrote it
+
+ align:start position:0%
+and we can work that out if we wrote it
+ 
+
+ align:start position:0%
+and we can work that out if we wrote it
+out we have ch3 Co minus in
+
+ align:start position:0%
+out we have ch3 Co minus in
+ 
+
+ align:start position:0%
+out we have ch3 Co minus in
+water is going to yield hydroxide
+
+ align:start position:0%
+water is going to yield hydroxide
+ 
+
+ align:start position:0%
+water is going to yield hydroxide
+ions and the conjugate acid over here
+
+ align:start position:0%
+ions and the conjugate acid over here
+ 
+
+ align:start position:0%
+ions and the conjugate acid over here
+and the presence of this will make of
+
+ align:start position:0%
+and the presence of this will make of
+ 
+
+ align:start position:0%
+and the presence of this will make of
+the hydroxide ion will make the solution
+
+ align:start position:0%
+the hydroxide ion will make the solution
+ 
+
+ align:start position:0%
+the hydroxide ion will make the solution
+basic so this is a weak a weak base on
+
+ align:start position:0%
+basic so this is a weak a weak base on
+ 
+
+ align:start position:0%
+basic so this is a weak a weak base on
+this side and so if if you were asked
+
+ align:start position:0%
+this side and so if if you were asked
+ 
+
+ align:start position:0%
+this side and so if if you were asked
+given an amount you could solve the
+
+ align:start position:0%
+given an amount you could solve the
+ 
+
+ align:start position:0%
+given an amount you could solve the
+problem using the KB of the weak base
+
+ align:start position:0%
+problem using the KB of the weak base
+ 
+
+ align:start position:0%
+problem using the KB of the weak base
+solving for o minus finding Po and then
+
+ align:start position:0%
+solving for o minus finding Po and then
+ 
+
+ align:start position:0%
+solving for o minus finding Po and then
+pH so overall this salt in solution will
+
+ align:start position:0%
+pH so overall this salt in solution will
+ 
+
+ align:start position:0%
+pH so overall this salt in solution will
+give rise
+
+ align:start position:0%
+give rise
+ 
+
+ align:start position:0%
+give rise
+to a basic solution so you'd have a
+
+ align:start position:0%
+to a basic solution so you'd have a
+ 
+
+ align:start position:0%
+to a basic solution so you'd have a
+should have a pH greater than seven so
+
+ align:start position:0%
+should have a pH greater than seven so
+ 
+
+ align:start position:0%
+should have a pH greater than seven so
+this salt and water would give rise to a
+
+ align:start position:0%
+this salt and water would give rise to a
+ 
+
+ align:start position:0%
+this salt and water would give rise to a
+basic solution and this salt and water
+
+ align:start position:0%
+basic solution and this salt and water
+ 
+
+ align:start position:0%
+basic solution and this salt and water
+problem breaks down into a weak base in
+
+ align:start position:0%
+problem breaks down into a weak base in
+ 
+
+ align:start position:0%
+problem breaks down into a weak base in
+water
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+problem so let's just do the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+generic the generic type of problem so
+
+ align:start position:0%
+generic the generic type of problem so
+ 
+
+ align:start position:0%
+generic the generic type of problem so
+in the
+
+ align:start position:0%
+in the
+ 
+
+ align:start position:0%
+in the
+general the general
+
+ align:start position:0%
+general the general
+ 
+
+ align:start position:0%
+general the general
+case if we have made up compound
+
+ align:start position:0%
+case if we have made up compound
+ 
+
+ align:start position:0%
+case if we have made up compound
+XZ madeup compound XZ will break down
+
+ align:start position:0%
+XZ madeup compound XZ will break down
+ 
+
+ align:start position:0%
+XZ madeup compound XZ will break down
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+X+ and Z
+
+ align:start position:0%
+X+ and Z
+ 
+
+ align:start position:0%
+X+ and Z
+minus and you're going to
+
+ align:start position:0%
+minus and you're going to
+ 
+
+ align:start position:0%
+minus and you're going to
+ask is this a
+
+ align:start position:0%
+ask is this a
+ 
+
+ align:start position:0%
+ask is this a
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+acid of weak
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+base and
+
+ align:start position:0%
+base and
+ 
+
+ align:start position:0%
+base and
+um or you're asking basically is this
+
+ align:start position:0%
+um or you're asking basically is this
+ 
+
+ align:start position:0%
+um or you're asking basically is this
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+acidic so if the answer is yes if you
+
+ align:start position:0%
+acidic so if the answer is yes if you
+ 
+
+ align:start position:0%
+acidic so if the answer is yes if you
+have a conjugate of a weak base which is
+
+ align:start position:0%
+have a conjugate of a weak base which is
+ 
+
+ align:start position:0%
+have a conjugate of a weak base which is
+a weak acid you will have an acidic
+
+ align:start position:0%
+a weak acid you will have an acidic
+ 
+
+ align:start position:0%
+a weak acid you will have an acidic
+solution if the answer is no you will
+
+ align:start position:0%
+solution if the answer is no you will
+ 
+
+ align:start position:0%
+solution if the answer is no you will
+have a neutral at least in terms of the
+
+ align:start position:0%
+have a neutral at least in terms of the
+ 
+
+ align:start position:0%
+have a neutral at least in terms of the
+X on the other side for the Z minus
+
+ align:start position:0%
+X on the other side for the Z minus
+ 
+
+ align:start position:0%
+X on the other side for the Z minus
+you're asking the
+
+ align:start position:0%
+you're asking the
+ 
+
+ align:start position:0%
+you're asking the
+question is this a
+
+ align:start position:0%
+question is this a
+ 
+
+ align:start position:0%
+question is this a
+conjugate
+
+ align:start position:0%
+conjugate
+ 
+
+ align:start position:0%
+conjugate
+base of a weak acid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it is a conjugate base of a weak acid
+
+ align:start position:0%
+if it is a conjugate base of a weak acid
+ 
+
+ align:start position:0%
+if it is a conjugate base of a weak acid
+then it's going to be basic it will be a
+
+ align:start position:0%
+then it's going to be basic it will be a
+ 
+
+ align:start position:0%
+then it's going to be basic it will be a
+weak base and so the answer is yes
+
+ align:start position:0%
+weak base and so the answer is yes
+ 
+
+ align:start position:0%
+weak base and so the answer is yes
+you're going to get a basic solution if
+
+ align:start position:0%
+you're going to get a basic solution if
+ 
+
+ align:start position:0%
+you're going to get a basic solution if
+the answer is no here it will be
+
+ align:start position:0%
+the answer is no here it will be
+ 
+
+ align:start position:0%
+the answer is no here it will be
+neutral and in these problems in the
+
+ align:start position:0%
+neutral and in these problems in the
+ 
+
+ align:start position:0%
+neutral and in these problems in the
+short answer type format here you're not
+
+ align:start position:0%
+short answer type format here you're not
+ 
+
+ align:start position:0%
+short answer type format here you're not
+going to be given a case where one side
+
+ align:start position:0%
+going to be given a case where one side
+ 
+
+ align:start position:0%
+going to be given a case where one side
+will be acidic and the other side will
+
+ align:start position:0%
+will be acidic and the other side will
+ 
+
+ align:start position:0%
+will be acidic and the other side will
+be basic because then you can't give a
+
+ align:start position:0%
+be basic because then you can't give a
+ 
+
+ align:start position:0%
+be basic because then you can't give a
+short answer to that problem you'd have
+
+ align:start position:0%
+short answer to that problem you'd have
+ 
+
+ align:start position:0%
+short answer to that problem you'd have
+to figure out which one is more acidic
+
+ align:start position:0%
+to figure out which one is more acidic
+ 
+
+ align:start position:0%
+to figure out which one is more acidic
+and which one was more basic uh so in
+
+ align:start position:0%
+and which one was more basic uh so in
+ 
+
+ align:start position:0%
+and which one was more basic uh so in
+these types of problems one side will
+
+ align:start position:0%
+these types of problems one side will
+ 
+
+ align:start position:0%
+these types of problems one side will
+always be neutral or they could both be
+
+ align:start position:0%
+always be neutral or they could both be
+ 
+
+ align:start position:0%
+always be neutral or they could both be
+neutral you will see examples where both
+
+ align:start position:0%
+neutral you will see examples where both
+ 
+
+ align:start position:0%
+neutral you will see examples where both
+of them are neutral but you're looking
+
+ align:start position:0%
+of them are neutral but you're looking
+ 
+
+ align:start position:0%
+of them are neutral but you're looking
+at each side and asking a question about
+
+ align:start position:0%
+at each side and asking a question about
+ 
+
+ align:start position:0%
+at each side and asking a question about
+it so that's how you go about doing
+
+ align:start position:0%
+it so that's how you go about doing
+ 
+
+ align:start position:0%
+it so that's how you go about doing
+these salt and and water problems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so this leads us right into
+
+ align:start position:0%
+all right so this leads us right into
+ 
+
+ align:start position:0%
+all right so this leads us right into
+buffers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so buffers this is another type of
+
+ align:start position:0%
+so buffers this is another type of
+ 
+
+ align:start position:0%
+so buffers this is another type of
+problem that that we will have and again
+
+ align:start position:0%
+problem that that we will have and again
+ 
+
+ align:start position:0%
+problem that that we will have and again
+you're talking about weak acids and weak
+
+ align:start position:0%
+you're talking about weak acids and weak
+ 
+
+ align:start position:0%
+you're talking about weak acids and weak
+bases here so a buffer is any solution
+
+ align:start position:0%
+bases here so a buffer is any solution
+ 
+
+ align:start position:0%
+bases here so a buffer is any solution
+that maintains pretty much a constant pH
+
+ align:start position:0%
+that maintains pretty much a constant pH
+ 
+
+ align:start position:0%
+that maintains pretty much a constant pH
+despite the addition of small amount of
+
+ align:start position:0%
+despite the addition of small amount of
+ 
+
+ align:start position:0%
+despite the addition of small amount of
+acids and bases so buffering is all
+
+ align:start position:0%
+acids and bases so buffering is all
+ 
+
+ align:start position:0%
+acids and bases so buffering is all
+about about constant
+
+ align:start position:0%
+about about constant
+ 
+
+ align:start position:0%
+about about constant
+pH an acidic buffer is just a buffer
+
+ align:start position:0%
+pH an acidic buffer is just a buffer
+ 
+
+ align:start position:0%
+pH an acidic buffer is just a buffer
+that's going to pH or stay sort of a
+
+ align:start position:0%
+that's going to pH or stay sort of a
+ 
+
+ align:start position:0%
+that's going to pH or stay sort of a
+constant pH in the acidic range so the
+
+ align:start position:0%
+constant pH in the acidic range so the
+ 
+
+ align:start position:0%
+constant pH in the acidic range so the
+acidic side of neutral and it would
+
+ align:start position:0%
+acidic side of neutral and it would
+ 
+
+ align:start position:0%
+acidic side of neutral and it would
+consist of a weak acid and its conjugate
+
+ align:start position:0%
+consist of a weak acid and its conjugate
+ 
+
+ align:start position:0%
+consist of a weak acid and its conjugate
+base supplied as a salt a basic buffer
+
+ align:start position:0%
+base supplied as a salt a basic buffer
+ 
+
+ align:start position:0%
+base supplied as a salt a basic buffer
+will have a weak base and its conjugate
+
+ align:start position:0%
+will have a weak base and its conjugate
+ 
+
+ align:start position:0%
+will have a weak base and its conjugate
+acid supplied as a salt and it's going
+
+ align:start position:0%
+acid supplied as a salt and it's going
+ 
+
+ align:start position:0%
+acid supplied as a salt and it's going
+to buffer on the basic side of neutral
+
+ align:start position:0%
+to buffer on the basic side of neutral
+ 
+
+ align:start position:0%
+to buffer on the basic side of neutral
+so that that Mak makes a lot of
+
+ align:start position:0%
+so that that Mak makes a lot of
+ 
+
+ align:start position:0%
+so that that Mak makes a lot of
+sense all right so let's look at a
+
+ align:start position:0%
+sense all right so let's look at a
+ 
+
+ align:start position:0%
+sense all right so let's look at a
+buffer example so in all buffers you're
+
+ align:start position:0%
+buffer example so in all buffers you're
+ 
+
+ align:start position:0%
+buffer example so in all buffers you're
+going to have an acid mixed with its
+
+ align:start position:0%
+going to have an acid mixed with its
+ 
+
+ align:start position:0%
+going to have an acid mixed with its
+conjugate as in the form of a salt to
+
+ align:start position:0%
+conjugate as in the form of a salt to
+ 
+
+ align:start position:0%
+conjugate as in the form of a salt to
+get a dynamic
+
+ align:start position:0%
+get a dynamic
+ 
+
+ align:start position:0%
+get a dynamic
+equilibrium and so if we have this we
+
+ align:start position:0%
+equilibrium and so if we have this we
+ 
+
+ align:start position:0%
+equilibrium and so if we have this we
+have the acid and it's conjugate added
+
+ align:start position:0%
+have the acid and it's conjugate added
+ 
+
+ align:start position:0%
+have the acid and it's conjugate added
+here and we ask what happens if you add
+
+ align:start position:0%
+here and we ask what happens if you add
+ 
+
+ align:start position:0%
+here and we ask what happens if you add
+a strong acid to this
+
+ align:start position:0%
+a strong acid to this
+ 
+
+ align:start position:0%
+a strong acid to this
+solution and because again what we want
+
+ align:start position:0%
+solution and because again what we want
+ 
+
+ align:start position:0%
+solution and because again what we want
+to have a buffer do is maintain a
+
+ align:start position:0%
+to have a buffer do is maintain a
+ 
+
+ align:start position:0%
+to have a buffer do is maintain a
+constant
+
+ align:start position:0%
+constant
+ 
+
+ align:start position:0%
+constant
+pH so you need to have about the same
+
+ align:start position:0%
+pH so you need to have about the same
+ 
+
+ align:start position:0%
+pH so you need to have about the same
+amount of this guy as this guy for that
+
+ align:start position:0%
+amount of this guy as this guy for that
+ 
+
+ align:start position:0%
+amount of this guy as this guy for that
+to be
+
+ align:start position:0%
+to be
+ 
+
+ align:start position:0%
+to be
+true so if you added strong acid and you
+
+ align:start position:0%
+true so if you added strong acid and you
+ 
+
+ align:start position:0%
+true so if you added strong acid and you
+had some of this and some of this the
+
+ align:start position:0%
+had some of this and some of this the
+ 
+
+ align:start position:0%
+had some of this and some of this the
+acid is going to react with the
+
+ align:start position:0%
+acid is going to react with the
+ 
+
+ align:start position:0%
+acid is going to react with the
+conjugate base and drive it in this
+
+ align:start position:0%
+conjugate base and drive it in this
+ 
+
+ align:start position:0%
+conjugate base and drive it in this
+direction using up the amount of strong
+
+ align:start position:0%
+direction using up the amount of strong
+ 
+
+ align:start position:0%
+direction using up the amount of strong
+acid that was added so the added uh acid
+
+ align:start position:0%
+acid that was added so the added uh acid
+ 
+
+ align:start position:0%
+acid that was added so the added uh acid
+hydronium ions are affective itively
+
+ align:start position:0%
+hydronium ions are affective itively
+ 
+
+ align:start position:0%
+hydronium ions are affective itively
+removed and the pH stays pretty much
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant now what happens if you add a
+
+ align:start position:0%
+constant now what happens if you add a
+ 
+
+ align:start position:0%
+constant now what happens if you add a
+strong base well strong base is going to
+
+ align:start position:0%
+strong base well strong base is going to
+ 
+
+ align:start position:0%
+strong base well strong base is going to
+react with the weak acid over here and
+
+ align:start position:0%
+react with the weak acid over here and
+ 
+
+ align:start position:0%
+react with the weak acid over here and
+it will also be
+
+ align:start position:0%
+it will also be
+ 
+
+ align:start position:0%
+it will also be
+consumed and so you you are taking uh
+
+ align:start position:0%
+consumed and so you you are taking uh
+ 
+
+ align:start position:0%
+consumed and so you you are taking uh
+the uh the O here is removing a proton
+
+ align:start position:0%
+the uh the O here is removing a proton
+ 
+
+ align:start position:0%
+the uh the O here is removing a proton
+it's reacting with the weak acid and
+
+ align:start position:0%
+it's reacting with the weak acid and
+ 
+
+ align:start position:0%
+it's reacting with the weak acid and
+it'll form more conjugate base and it'll
+
+ align:start position:0%
+it'll form more conjugate base and it'll
+ 
+
+ align:start position:0%
+it'll form more conjugate base and it'll
+also form water so again it's
+
+ align:start position:0%
+also form water so again it's
+ 
+
+ align:start position:0%
+also form water so again it's
+effectively removed and the pH stays
+
+ align:start position:0%
+effectively removed and the pH stays
+ 
+
+ align:start position:0%
+effectively removed and the pH stays
+pretty much constant so a buffer should
+
+ align:start position:0%
+pretty much constant so a buffer should
+ 
+
+ align:start position:0%
+pretty much constant so a buffer should
+be a source uh a source in a sync for um
+
+ align:start position:0%
+be a source uh a source in a sync for um
+ 
+
+ align:start position:0%
+be a source uh a source in a sync for um
+added uh problems to the reaction it's
+
+ align:start position:0%
+added uh problems to the reaction it's
+ 
+
+ align:start position:0%
+added uh problems to the reaction it's
+going to use up either the acid or the
+
+ align:start position:0%
+going to use up either the acid or the
+ 
+
+ align:start position:0%
+going to use up either the acid or the
+base that's added and keep keep the uh
+
+ align:start position:0%
+base that's added and keep keep the uh
+ 
+
+ align:start position:0%
+base that's added and keep keep the uh
+pH pretty much constant so again what's
+
+ align:start position:0%
+pH pretty much constant so again what's
+ 
+
+ align:start position:0%
+pH pretty much constant so again what's
+happening is that the weak acid that you
+
+ align:start position:0%
+happening is that the weak acid that you
+ 
+
+ align:start position:0%
+happening is that the weak acid that you
+use and you can have anyone there is
+
+ align:start position:0%
+use and you can have anyone there is
+ 
+
+ align:start position:0%
+use and you can have anyone there is
+going to transfer protons to this and
+
+ align:start position:0%
+going to transfer protons to this and
+ 
+
+ align:start position:0%
+going to transfer protons to this and
+that will uh cause the reaction to
+
+ align:start position:0%
+that will uh cause the reaction to
+ 
+
+ align:start position:0%
+that will uh cause the reaction to
+happen use up the H hydroxide ion a
+
+ align:start position:0%
+happen use up the H hydroxide ion a
+ 
+
+ align:start position:0%
+happen use up the H hydroxide ion a
+conjugate base that's added to the as a
+
+ align:start position:0%
+conjugate base that's added to the as a
+ 
+
+ align:start position:0%
+conjugate base that's added to the as a
+form of a salt um it would would then be
+
+ align:start position:0%
+form of a salt um it would would then be
+ 
+
+ align:start position:0%
+form of a salt um it would would then be
+able to accept protons from any acid
+
+ align:start position:0%
+able to accept protons from any acid
+ 
+
+ align:start position:0%
+able to accept protons from any acid
+that's used so you need both the weak
+
+ align:start position:0%
+that's used so you need both the weak
+ 
+
+ align:start position:0%
+that's used so you need both the weak
+acid and the conjugate base added in the
+
+ align:start position:0%
+acid and the conjugate base added in the
+ 
+
+ align:start position:0%
+acid and the conjugate base added in the
+form of salt one will react if you add
+
+ align:start position:0%
+form of salt one will react if you add
+ 
+
+ align:start position:0%
+form of salt one will react if you add
+extra acid one will react if you add
+
+ align:start position:0%
+extra acid one will react if you add
+ 
+
+ align:start position:0%
+extra acid one will react if you add
+excess
+
+ align:start position:0%
+excess
+ 
+
+ align:start position:0%
+excess
+base so why wouldn't a strong strong
+
+ align:start position:0%
+base so why wouldn't a strong strong
+ 
+
+ align:start position:0%
+base so why wouldn't a strong strong
+acid and the conjugate base of that
+
+ align:start position:0%
+acid and the conjugate base of that
+ 
+
+ align:start position:0%
+acid and the conjugate base of that
+strong acid why wouldn't that make a
+
+ align:start position:0%
+strong acid why wouldn't that make a
+ 
+
+ align:start position:0%
+strong acid why wouldn't that make a
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buffer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yeah right because the conjugate
+
+ align:start position:0%
+yeah yeah right because the conjugate
+ 
+
+ align:start position:0%
+yeah yeah right because the conjugate
+base would be ineffective as a base and
+
+ align:start position:0%
+base would be ineffective as a base and
+ 
+
+ align:start position:0%
+base would be ineffective as a base and
+so the strong acid would go to
+
+ align:start position:0%
+so the strong acid would go to
+ 
+
+ align:start position:0%
+so the strong acid would go to
+completion will drive to the right this
+
+ align:start position:0%
+completion will drive to the right this
+ 
+
+ align:start position:0%
+completion will drive to the right this
+is ineffective as a base you're not
+
+ align:start position:0%
+is ineffective as a base you're not
+ 
+
+ align:start position:0%
+is ineffective as a base you're not
+going to push it back the other way so
+
+ align:start position:0%
+going to push it back the other way so
+ 
+
+ align:start position:0%
+going to push it back the other way so
+you're only going to have a good
+
+ align:start position:0%
+you're only going to have a good
+ 
+
+ align:start position:0%
+you're only going to have a good
+buffering system with a weak something
+
+ align:start position:0%
+buffering system with a weak something
+ 
+
+ align:start position:0%
+buffering system with a weak something
+and it's conjugate that's also a weak
+
+ align:start position:0%
+and it's conjugate that's also a weak
+ 
+
+ align:start position:0%
+and it's conjugate that's also a weak
+something so a weak acid and it's
+
+ align:start position:0%
+something so a weak acid and it's
+ 
+
+ align:start position:0%
+something so a weak acid and it's
+conjugate weak base a weak base and it's
+
+ align:start position:0%
+conjugate weak base a weak base and it's
+ 
+
+ align:start position:0%
+conjugate weak base a weak base and it's
+conjugate weak acid that will buffer
+
+ align:start position:0%
+conjugate weak acid that will buffer
+ 
+
+ align:start position:0%
+conjugate weak acid that will buffer
+because it'll go both directions so both
+
+ align:start position:0%
+because it'll go both directions so both
+ 
+
+ align:start position:0%
+because it'll go both directions so both
+conjugates have to work as an acid or a
+
+ align:start position:0%
+conjugates have to work as an acid or a
+ 
+
+ align:start position:0%
+conjugates have to work as an acid or a
+base if you have a strong acid then its
+
+ align:start position:0%
+base if you have a strong acid then its
+ 
+
+ align:start position:0%
+base if you have a strong acid then its
+conjugate is ineffective as a base it
+
+ align:start position:0%
+conjugate is ineffective as a base it
+ 
+
+ align:start position:0%
+conjugate is ineffective as a base it
+won't work if you have a strong base
+
+ align:start position:0%
+won't work if you have a strong base
+ 
+
+ align:start position:0%
+won't work if you have a strong base
+then its conjugate is ineffective as an
+
+ align:start position:0%
+then its conjugate is ineffective as an
+ 
+
+ align:start position:0%
+then its conjugate is ineffective as an
+acid and it won't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+work all right so base buffering example
+
+ align:start position:0%
+work all right so base buffering example
+ 
+
+ align:start position:0%
+work all right so base buffering example
+same same stuff applies here so um if
+
+ align:start position:0%
+same same stuff applies here so um if
+ 
+
+ align:start position:0%
+same same stuff applies here so um if
+you add a strong acid it will react with
+
+ align:start position:0%
+you add a strong acid it will react with
+ 
+
+ align:start position:0%
+you add a strong acid it will react with
+the base the base will accept the
+
+ align:start position:0%
+the base the base will accept the
+ 
+
+ align:start position:0%
+the base the base will accept the
+protons and uh make more of the nh4 and
+
+ align:start position:0%
+protons and uh make more of the nh4 and
+ 
+
+ align:start position:0%
+protons and uh make more of the nh4 and
+it'll use up the strong
+
+ align:start position:0%
+it'll use up the strong
+ 
+
+ align:start position:0%
+it'll use up the strong
+acid when a strong base is added it'll
+
+ align:start position:0%
+acid when a strong base is added it'll
+ 
+
+ align:start position:0%
+acid when a strong base is added it'll
+react with a conjugate acid and go the
+
+ align:start position:0%
+react with a conjugate acid and go the
+ 
+
+ align:start position:0%
+react with a conjugate acid and go the
+other direction and so you'll form more
+
+ align:start position:0%
+other direction and so you'll form more
+ 
+
+ align:start position:0%
+other direction and so you'll form more
+of the conjugate base in water again the
+
+ align:start position:0%
+of the conjugate base in water again the
+ 
+
+ align:start position:0%
+of the conjugate base in water again the
+pH is staying the same you're using up
+
+ align:start position:0%
+pH is staying the same you're using up
+ 
+
+ align:start position:0%
+pH is staying the same you're using up
+the strong base that's that's
+
+ align:start position:0%
+the strong base that's that's
+ 
+
+ align:start position:0%
+the strong base that's that's
+added so in a in a buffer action you
+
+ align:start position:0%
+added so in a in a buffer action you
+ 
+
+ align:start position:0%
+added so in a in a buffer action you
+have a weak base accepting protons
+
+ align:start position:0%
+have a weak base accepting protons
+ 
+
+ align:start position:0%
+have a weak base accepting protons
+supplied by the strong acid and you have
+
+ align:start position:0%
+supplied by the strong acid and you have
+ 
+
+ align:start position:0%
+supplied by the strong acid and you have
+the conjugate acid of the weak base
+
+ align:start position:0%
+the conjugate acid of the weak base
+ 
+
+ align:start position:0%
+the conjugate acid of the weak base
+transferring protons to the hydroxide
+
+ align:start position:0%
+transferring protons to the hydroxide
+ 
+
+ align:start position:0%
+transferring protons to the hydroxide
+the strong base that's added using that
+
+ align:start position:0%
+the strong base that's added using that
+ 
+
+ align:start position:0%
+the strong base that's added using that
+up as well so again it's about going
+
+ align:start position:0%
+up as well so again it's about going
+ 
+
+ align:start position:0%
+up as well so again it's about going
+both directions of the reaction that
+
+ align:start position:0%
+both directions of the reaction that
+ 
+
+ align:start position:0%
+both directions of the reaction that
+makes something a good buffer so a
+
+ align:start position:0%
+makes something a good buffer so a
+ 
+
+ align:start position:0%
+makes something a good buffer so a
+buffer mixture of weak conjugate acids
+
+ align:start position:0%
+buffer mixture of weak conjugate acids
+ 
+
+ align:start position:0%
+buffer mixture of weak conjugate acids
+and base stabilize the pH of a solution
+
+ align:start position:0%
+and base stabilize the pH of a solution
+ 
+
+ align:start position:0%
+and base stabilize the pH of a solution
+by providing a source or sync for the
+
+ align:start position:0%
+by providing a source or sync for the
+ 
+
+ align:start position:0%
+by providing a source or sync for the
+protons so either um they're they're
+
+ align:start position:0%
+protons so either um they're they're
+ 
+
+ align:start position:0%
+protons so either um they're they're
+providing a source to neutralize the O
+
+ align:start position:0%
+providing a source to neutralize the O
+ 
+
+ align:start position:0%
+providing a source to neutralize the O
+that's minus or a zinc for the protons
+
+ align:start position:0%
+that's minus or a zinc for the protons
+ 
+
+ align:start position:0%
+that's minus or a zinc for the protons
+that are added in the form of acid so
+
+ align:start position:0%
+that are added in the form of acid so
+ 
+
+ align:start position:0%
+that are added in the form of acid so
+the pH stays pretty much the same so you
+
+ align:start position:0%
+the pH stays pretty much the same so you
+ 
+
+ align:start position:0%
+the pH stays pretty much the same so you
+need something that can do this dynamic
+
+ align:start position:0%
+need something that can do this dynamic
+ 
+
+ align:start position:0%
+need something that can do this dynamic
+equilibrium to be a good buffer all
+
+ align:start position:0%
+equilibrium to be a good buffer all
+ 
+
+ align:start position:0%
+equilibrium to be a good buffer all
+right so let me just give you um last
+
+ align:start position:0%
+right so let me just give you um last
+ 
+
+ align:start position:0%
+right so let me just give you um last
+couple minutes an example
+
+ align:start position:0%
+couple minutes an example
+ 
+
+ align:start position:0%
+couple minutes an example
+of why buffering is important from a
+
+ align:start position:0%
+of why buffering is important from a
+ 
+
+ align:start position:0%
+of why buffering is important from a
+human health
+
+ align:start position:0%
+human health
+ 
+
+ align:start position:0%
+human health
+perspective all right so your blood is
+
+ align:start position:0%
+perspective all right so your blood is
+ 
+
+ align:start position:0%
+perspective all right so your blood is
+buffered around a neutral
+
+ align:start position:0%
+buffered around a neutral
+ 
+
+ align:start position:0%
+buffered around a neutral
+range and the buffering agents are shown
+
+ align:start position:0%
+range and the buffering agents are shown
+ 
+
+ align:start position:0%
+range and the buffering agents are shown
+here carbonic acid and bicarbonate are
+
+ align:start position:0%
+here carbonic acid and bicarbonate are
+ 
+
+ align:start position:0%
+here carbonic acid and bicarbonate are
+effective as buffering agents so they
+
+ align:start position:0%
+effective as buffering agents so they
+ 
+
+ align:start position:0%
+effective as buffering agents so they
+can be provide the source or sink for
+
+ align:start position:0%
+can be provide the source or sink for
+ 
+
+ align:start position:0%
+can be provide the source or sink for
+added uh added stress to the system for
+
+ align:start position:0%
+added uh added stress to the system for
+ 
+
+ align:start position:0%
+added uh added stress to the system for
+added acid or added added base so your
+
+ align:start position:0%
+added acid or added added base so your
+ 
+
+ align:start position:0%
+added acid or added added base so your
+blood is buffered and this is really
+
+ align:start position:0%
+blood is buffered and this is really
+ 
+
+ align:start position:0%
+blood is buffered and this is really
+important if your blood if your blood pH
+
+ align:start position:0%
+important if your blood if your blood pH
+ 
+
+ align:start position:0%
+important if your blood if your blood pH
+changes enzymes are designed to work at
+
+ align:start position:0%
+changes enzymes are designed to work at
+ 
+
+ align:start position:0%
+changes enzymes are designed to work at
+particular ph's molecules are not
+
+ align:start position:0%
+particular ph's molecules are not
+ 
+
+ align:start position:0%
+particular ph's molecules are not
+necessarily stable at certain phes so
+
+ align:start position:0%
+necessarily stable at certain phes so
+ 
+
+ align:start position:0%
+necessarily stable at certain phes so
+our body would not work well if it was
+
+ align:start position:0%
+our body would not work well if it was
+ 
+
+ align:start position:0%
+our body would not work well if it was
+not appropriately appropriately buffered
+
+ align:start position:0%
+not appropriately appropriately buffered
+ 
+
+ align:start position:0%
+not appropriately appropriately buffered
+so let me give you an example of a
+
+ align:start position:0%
+so let me give you an example of a
+ 
+
+ align:start position:0%
+so let me give you an example of a
+genetic defect that leads it overwhelms
+
+ align:start position:0%
+genetic defect that leads it overwhelms
+ 
+
+ align:start position:0%
+genetic defect that leads it overwhelms
+the buffering capacity of the blood and
+
+ align:start position:0%
+the buffering capacity of the blood and
+ 
+
+ align:start position:0%
+the buffering capacity of the blood and
+leads to a condition so this is uh an
+
+ align:start position:0%
+leads to a condition so this is uh an
+ 
+
+ align:start position:0%
+leads to a condition so this is uh an
+enzyme that you have in your body it's
+
+ align:start position:0%
+enzyme that you have in your body it's
+ 
+
+ align:start position:0%
+enzyme that you have in your body it's
+in your
+
+ align:start position:0%
+in your
+ 
+
+ align:start position:0%
+in your
+mitochondria and it requires vitamin
+
+ align:start position:0%
+mitochondria and it requires vitamin
+ 
+
+ align:start position:0%
+mitochondria and it requires vitamin
+B12 and this is what the enzyme is
+
+ align:start position:0%
+B12 and this is what the enzyme is
+ 
+
+ align:start position:0%
+B12 and this is what the enzyme is
+involved in it's involved in breaking
+
+ align:start position:0%
+involved in it's involved in breaking
+ 
+
+ align:start position:0%
+involved in it's involved in breaking
+down fatty acids to form energy so most
+
+ align:start position:0%
+down fatty acids to form energy so most
+ 
+
+ align:start position:0%
+down fatty acids to form energy so most
+people like this enzyme they're very
+
+ align:start position:0%
+people like this enzyme they're very
+ 
+
+ align:start position:0%
+people like this enzyme they're very
+happy with this enzyme most people want
+
+ align:start position:0%
+happy with this enzyme most people want
+ 
+
+ align:start position:0%
+happy with this enzyme most people want
+their fat converted to energy and so
+
+ align:start position:0%
+their fat converted to energy and so
+ 
+
+ align:start position:0%
+their fat converted to energy and so
+this enzyme helps out with that going on
+
+ align:start position:0%
+this enzyme helps out with that going on
+ 
+
+ align:start position:0%
+this enzyme helps out with that going on
+all right so what happens if you have a
+
+ align:start position:0%
+all right so what happens if you have a
+ 
+
+ align:start position:0%
+all right so what happens if you have a
+genetic defect or if you don't have
+
+ align:start position:0%
+genetic defect or if you don't have
+ 
+
+ align:start position:0%
+genetic defect or if you don't have
+enough vitamin B12 but in this case
+
+ align:start position:0%
+enough vitamin B12 but in this case
+ 
+
+ align:start position:0%
+enough vitamin B12 but in this case
+we're talking about a genetic defect
+
+ align:start position:0%
+we're talking about a genetic defect
+ 
+
+ align:start position:0%
+we're talking about a genetic defect
+this step is blocked so your body is
+
+ align:start position:0%
+this step is blocked so your body is
+ 
+
+ align:start position:0%
+this step is blocked so your body is
+making a lot of methyl malinal COA and
+
+ align:start position:0%
+making a lot of methyl malinal COA and
+ 
+
+ align:start position:0%
+making a lot of methyl malinal COA and
+it doesn't know what to do with it it's
+
+ align:start position:0%
+it doesn't know what to do with it it's
+ 
+
+ align:start position:0%
+it doesn't know what to do with it it's
+a huge amount and so it actually gets
+
+ align:start position:0%
+a huge amount and so it actually gets
+ 
+
+ align:start position:0%
+a huge amount and so it actually gets
+excreted from the body in the form of an
+
+ align:start position:0%
+excreted from the body in the form of an
+ 
+
+ align:start position:0%
+excreted from the body in the form of an
+acid and so this leads to a condition
+
+ align:start position:0%
+acid and so this leads to a condition
+ 
+
+ align:start position:0%
+acid and so this leads to a condition
+known as methylmalonic aciduria so
+
+ align:start position:0%
+known as methylmalonic aciduria so
+ 
+
+ align:start position:0%
+known as methylmalonic aciduria so
+there's so much of this made you're
+
+ align:start position:0%
+there's so much of this made you're
+ 
+
+ align:start position:0%
+there's so much of this made you're
+excreting like a gram of this acid every
+
+ align:start position:0%
+excreting like a gram of this acid every
+ 
+
+ align:start position:0%
+excreting like a gram of this acid every
+day the blood is overwhelmed it can't
+
+ align:start position:0%
+day the blood is overwhelmed it can't
+ 
+
+ align:start position:0%
+day the blood is overwhelmed it can't
+handle that much acid it's buffering
+
+ align:start position:0%
+handle that much acid it's buffering
+ 
+
+ align:start position:0%
+handle that much acid it's buffering
+capacity isn't that that good all right
+
+ align:start position:0%
+capacity isn't that that good all right
+ 
+
+ align:start position:0%
+capacity isn't that that good all right
+so what causes this problem um so I'll
+
+ align:start position:0%
+so what causes this problem um so I'll
+ 
+
+ align:start position:0%
+so what causes this problem um so I'll
+tell you that this now is the amino acid
+
+ align:start position:0%
+tell you that this now is the amino acid
+ 
+
+ align:start position:0%
+tell you that this now is the amino acid
+sequence of the enzyme so enzymes are
+
+ align:start position:0%
+sequence of the enzyme so enzymes are
+ 
+
+ align:start position:0%
+sequence of the enzyme so enzymes are
+made up of multiple amino acids strung
+
+ align:start position:0%
+made up of multiple amino acids strung
+ 
+
+ align:start position:0%
+made up of multiple amino acids strung
+together in a polypeptide chain and down
+
+ align:start position:0%
+together in a polypeptide chain and down
+ 
+
+ align:start position:0%
+together in a polypeptide chain and down
+here's the number
+
+ align:start position:0%
+here's the number
+ 
+
+ align:start position:0%
+here's the number
+721 so this is a lot of amino acids and
+
+ align:start position:0%
+721 so this is a lot of amino acids and
+ 
+
+ align:start position:0%
+721 so this is a lot of amino acids and
+at the time there were these babies born
+
+ align:start position:0%
+at the time there were these babies born
+ 
+
+ align:start position:0%
+at the time there were these babies born
+with this condition and the doctors
+
+ align:start position:0%
+with this condition and the doctors
+ 
+
+ align:start position:0%
+with this condition and the doctors
+didn't know what to do to treat them and
+
+ align:start position:0%
+didn't know what to do to treat them and
+ 
+
+ align:start position:0%
+didn't know what to do to treat them and
+a lot of the babies died so a number of
+
+ align:start position:0%
+a lot of the babies died so a number of
+ 
+
+ align:start position:0%
+a lot of the babies died so a number of
+them got together and they tried to
+
+ align:start position:0%
+them got together and they tried to
+ 
+
+ align:start position:0%
+them got together and they tried to
+sequence the gene now of course there's
+
+ align:start position:0%
+sequence the gene now of course there's
+ 
+
+ align:start position:0%
+sequence the gene now of course there's
+a Human Genome Project so we know a lot
+
+ align:start position:0%
+a Human Genome Project so we know a lot
+ 
+
+ align:start position:0%
+a Human Genome Project so we know a lot
+of the sequences of genes but the
+
+ align:start position:0%
+of the sequences of genes but the
+ 
+
+ align:start position:0%
+of the sequences of genes but the
+doctors sequenced this Gene and they sat
+
+ align:start position:0%
+doctors sequenced this Gene and they sat
+ 
+
+ align:start position:0%
+doctors sequenced this Gene and they sat
+down with the parents and said okay
+
+ align:start position:0%
+down with the parents and said okay
+ 
+
+ align:start position:0%
+down with the parents and said okay
+there's a mistake right here where that
+
+ align:start position:0%
+there's a mistake right here where that
+ 
+
+ align:start position:0%
+there's a mistake right here where that
+red arrow is it should be a glycine
+
+ align:start position:0%
+red arrow is it should be a glycine
+ 
+
+ align:start position:0%
+red arrow is it should be a glycine
+residue but it's something else all
+
+ align:start position:0%
+residue but it's something else all
+ 
+
+ align:start position:0%
+residue but it's something else all
+right so imagine you're a parent you
+
+ align:start position:0%
+right so imagine you're a parent you
+ 
+
+ align:start position:0%
+right so imagine you're a parent you
+have a kid and the doctor tells you ah
+
+ align:start position:0%
+have a kid and the doctor tells you ah
+ 
+
+ align:start position:0%
+have a kid and the doctor tells you ah
+there's a mistake right here
+
+ align:start position:0%
+there's a mistake right here
+ 
+
+ align:start position:0%
+there's a mistake right here
+okay well that's fantastic what are you
+
+ align:start position:0%
+okay well that's fantastic what are you
+ 
+
+ align:start position:0%
+okay well that's fantastic what are you
+going to do about it well at the time
+
+ align:start position:0%
+going to do about it well at the time
+ 
+
+ align:start position:0%
+going to do about it well at the time
+the doctors had no idea what to do about
+
+ align:start position:0%
+the doctors had no idea what to do about
+ 
+
+ align:start position:0%
+the doctors had no idea what to do about
+it because they didn't really know what
+
+ align:start position:0%
+it because they didn't really know what
+ 
+
+ align:start position:0%
+it because they didn't really know what
+was going on here so um this answer
+
+ align:start position:0%
+was going on here so um this answer
+ 
+
+ align:start position:0%
+was going on here so um this answer
+partly came uh through uh structure
+
+ align:start position:0%
+partly came uh through uh structure
+ 
+
+ align:start position:0%
+partly came uh through uh structure
+determination and they found that
+
+ align:start position:0%
+determination and they found that
+ 
+
+ align:start position:0%
+determination and they found that
+vitamin B12 changes shape when it binds
+
+ align:start position:0%
+vitamin B12 changes shape when it binds
+ 
+
+ align:start position:0%
+vitamin B12 changes shape when it binds
+to a protein so here's vitamin B12 it
+
+ align:start position:0%
+to a protein so here's vitamin B12 it
+ 
+
+ align:start position:0%
+to a protein so here's vitamin B12 it
+has this group uh up attached to the
+
+ align:start position:0%
+has this group uh up attached to the
+ 
+
+ align:start position:0%
+has this group uh up attached to the
+Cobalt when it's free uh when it's bound
+
+ align:start position:0%
+Cobalt when it's free uh when it's bound
+ 
+
+ align:start position:0%
+Cobalt when it's free uh when it's bound
+to the protein it looks like this this
+
+ align:start position:0%
+to the protein it looks like this this
+ 
+
+ align:start position:0%
+to the protein it looks like this this
+long group is extended into the core of
+
+ align:start position:0%
+long group is extended into the core of
+ 
+
+ align:start position:0%
+long group is extended into the core of
+the protein so the protein needs a big
+
+ align:start position:0%
+the protein so the protein needs a big
+ 
+
+ align:start position:0%
+the protein so the protein needs a big
+hole to put this group and so this is a
+
+ align:start position:0%
+hole to put this group and so this is a
+ 
+
+ align:start position:0%
+hole to put this group and so this is a
+model of what the protein looked like
+
+ align:start position:0%
+model of what the protein looked like
+ 
+
+ align:start position:0%
+model of what the protein looked like
+and here's a model of vitamin B12 so we
+
+ align:start position:0%
+and here's a model of vitamin B12 so we
+ 
+
+ align:start position:0%
+and here's a model of vitamin B12 so we
+discovered that it fits like this it's
+
+ align:start position:0%
+discovered that it fits like this it's
+ 
+
+ align:start position:0%
+discovered that it fits like this it's
+fantastic there's a huge hole in the
+
+ align:start position:0%
+fantastic there's a huge hole in the
+ 
+
+ align:start position:0%
+fantastic there's a huge hole in the
+protein into which you can put the
+
+ align:start position:0%
+protein into which you can put the
+ 
+
+ align:start position:0%
+protein into which you can put the
+vitamin so how did nature create a hole
+
+ align:start position:0%
+vitamin so how did nature create a hole
+ 
+
+ align:start position:0%
+vitamin so how did nature create a hole
+how did it make this space for the
+
+ align:start position:0%
+how did it make this space for the
+ 
+
+ align:start position:0%
+how did it make this space for the
+Vitamin to fit and then with the vitamin
+
+ align:start position:0%
+Vitamin to fit and then with the vitamin
+ 
+
+ align:start position:0%
+Vitamin to fit and then with the vitamin
+Bal it's active so what it did was it
+
+ align:start position:0%
+Bal it's active so what it did was it
+ 
+
+ align:start position:0%
+Bal it's active so what it did was it
+put the smallest amino acids it could
+
+ align:start position:0%
+put the smallest amino acids it could
+ 
+
+ align:start position:0%
+put the smallest amino acids it could
+find over
+
+ align:start position:0%
+find over
+ 
+
+ align:start position:0%
+find over
+here now what happens in this mutant
+
+ align:start position:0%
+here now what happens in this mutant
+ 
+
+ align:start position:0%
+here now what happens in this mutant
+protein is that one of those small amino
+
+ align:start position:0%
+protein is that one of those small amino
+ 
+
+ align:start position:0%
+protein is that one of those small amino
+acids was converted to something larger
+
+ align:start position:0%
+acids was converted to something larger
+ 
+
+ align:start position:0%
+acids was converted to something larger
+in the dark blue so this was the protein
+
+ align:start position:0%
+in the dark blue so this was the protein
+ 
+
+ align:start position:0%
+in the dark blue so this was the protein
+that these babies had and the doctors
+
+ align:start position:0%
+that these babies had and the doctors
+ 
+
+ align:start position:0%
+that these babies had and the doctors
+kept giving them more B12 more B12 more
+
+ align:start position:0%
+kept giving them more B12 more B12 more
+ 
+
+ align:start position:0%
+kept giving them more B12 more B12 more
+B12 and it didn't do any good at all
+
+ align:start position:0%
+B12 and it didn't do any good at all
+ 
+
+ align:start position:0%
+B12 and it didn't do any good at all
+because no matter how much you gave you
+
+ align:start position:0%
+because no matter how much you gave you
+ 
+
+ align:start position:0%
+because no matter how much you gave you
+it couldn't bump it was blocked The
+
+ align:start position:0%
+it couldn't bump it was blocked The
+ 
+
+ align:start position:0%
+it couldn't bump it was blocked The
+Binding was blocked so this suggested to
+
+ align:start position:0%
+Binding was blocked so this suggested to
+ 
+
+ align:start position:0%
+Binding was blocked so this suggested to
+doctors that instead of giving them the
+
+ align:start position:0%
+doctors that instead of giving them the
+ 
+
+ align:start position:0%
+doctors that instead of giving them the
+full vitamin B12 and basically take a
+
+ align:start position:0%
+full vitamin B12 and basically take a
+ 
+
+ align:start position:0%
+full vitamin B12 and basically take a
+pair of scissors and chop off part of it
+
+ align:start position:0%
+pair of scissors and chop off part of it
+ 
+
+ align:start position:0%
+pair of scissors and chop off part of it
+and create something that looked more
+
+ align:start position:0%
+and create something that looked more
+ 
+
+ align:start position:0%
+and create something that looked more
+like this and then uh try to see if that
+
+ align:start position:0%
+like this and then uh try to see if that
+ 
+
+ align:start position:0%
+like this and then uh try to see if that
+would then bind to the mutated protein
+
+ align:start position:0%
+would then bind to the mutated protein
+ 
+
+ align:start position:0%
+would then bind to the mutated protein
+so that's the kind of thing that they
+
+ align:start position:0%
+so that's the kind of thing that they
+ 
+
+ align:start position:0%
+so that's the kind of thing that they
+were were looking at trying to alleviate
+
+ align:start position:0%
+were were looking at trying to alleviate
+ 
+
+ align:start position:0%
+were were looking at trying to alleviate
+this particular condition because the
+
+ align:start position:0%
+this particular condition because the
+ 
+
+ align:start position:0%
+this particular condition because the
+buffering of the blood is pretty good if
+
+ align:start position:0%
+buffering of the blood is pretty good if
+ 
+
+ align:start position:0%
+buffering of the blood is pretty good if
+you could restore some activity get rid
+
+ align:start position:0%
+you could restore some activity get rid
+ 
+
+ align:start position:0%
+you could restore some activity get rid
+of some of the acid you might be able to
+
+ align:start position:0%
+of some of the acid you might be able to
+ 
+
+ align:start position:0%
+of some of the acid you might be able to
+have a more normal pH okay have a good
+
+ align:start position:0%
+have a more normal pH okay have a good
+ 
+
+ align:start position:0%
+have a more normal pH okay have a good
+weekend
\ No newline at end of file
diff --git a/YulNobAZgkA.txt b/YulNobAZgkA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..800c328b0f627253a8512e5ac1e10cf41fa5bbfe
--- /dev/null
+++ b/YulNobAZgkA.txt
@@ -0,0 +1,1123 @@
+align:start position:0%
+ 
+so Adam light interactions so we will
+
+ align:start position:0%
+so Adam light interactions so we will
+ 
+
+ align:start position:0%
+so Adam light interactions so we will
+focus just on the electric field e field
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magnetic field effects are suppressed by
+
+ align:start position:0%
+magnetic field effects are suppressed by
+ 
+
+ align:start position:0%
+magnetic field effects are suppressed by
+the velocity of the electrons divided by
+
+ align:start position:0%
+the velocity of the electrons divided by
+ 
+
+ align:start position:0%
+the velocity of the electrons divided by
+C and that you know is the
+
+ align:start position:0%
+C and that you know is the
+ 
+
+ align:start position:0%
+C and that you know is the
+fine-structure constant so magnetic
+
+ align:start position:0%
+fine-structure constant so magnetic
+ 
+
+ align:start position:0%
+fine-structure constant so magnetic
+field effects are suppressed ignore
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+magnetic v over c Corrections with v
+
+ align:start position:0%
+magnetic v over c Corrections with v
+ 
+
+ align:start position:0%
+magnetic v over c Corrections with v
+over c again of the order of the
+
+ align:start position:0%
+over c again of the order of the
+ 
+
+ align:start position:0%
+over c again of the order of the
+fine-structure constant we will also
+
+ align:start position:0%
+fine-structure constant we will also
+ 
+
+ align:start position:0%
+fine-structure constant we will also
+think of optical typically optical
+
+ align:start position:0%
+think of optical typically optical
+ 
+
+ align:start position:0%
+think of optical typically optical
+frequencies lambda in the optical range
+
+ align:start position:0%
+frequencies lambda in the optical range
+ 
+
+ align:start position:0%
+frequencies lambda in the optical range
+so from about 4,000 to 8,000 angstroms
+
+ align:start position:0%
+so from about 4,000 to 8,000 angstroms
+ 
+
+ align:start position:0%
+so from about 4,000 to 8,000 angstroms
+and that's much much bigger than a zero
+
+ align:start position:0%
+and that's much much bigger than a zero
+ 
+
+ align:start position:0%
+and that's much much bigger than a zero
+which is about 0.5 angstroms and that's
+
+ align:start position:0%
+which is about 0.5 angstroms and that's
+ 
+
+ align:start position:0%
+which is about 0.5 angstroms and that's
+good for our approximation that the wave
+
+ align:start position:0%
+good for our approximation that the wave
+ 
+
+ align:start position:0%
+good for our approximation that the wave
+is relatively constant being the
+
+ align:start position:0%
+is relatively constant being the
+ 
+
+ align:start position:0%
+is relatively constant being the
+wavelength so large is constant over the
+
+ align:start position:0%
+wavelength so large is constant over the
+ 
+
+ align:start position:0%
+wavelength so large is constant over the
+extent of the atom so we will think of
+
+ align:start position:0%
+extent of the atom so we will think of
+ 
+
+ align:start position:0%
+extent of the atom so we will think of
+the electric field at the atom II at the
+
+ align:start position:0%
+the electric field at the atom II at the
+ 
+
+ align:start position:0%
+the electric field at the atom II at the
+atom
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our electric field a lot a bit of
+
+ align:start position:0%
+our electric field a lot a bit of
+ 
+
+ align:start position:0%
+our electric field a lot a bit of
+notation will depend on time and it will
+
+ align:start position:0%
+notation will depend on time and it will
+ 
+
+ align:start position:0%
+notation will depend on time and it will
+be a real function of time times a unit
+
+ align:start position:0%
+be a real function of time times a unit
+ 
+
+ align:start position:0%
+be a real function of time times a unit
+vector to begin with this will get more
+
+ align:start position:0%
+vector to begin with this will get more
+ 
+
+ align:start position:0%
+vector to begin with this will get more
+interesting because we're going to be
+
+ align:start position:0%
+interesting because we're going to be
+ 
+
+ align:start position:0%
+interesting because we're going to be
+dealing with thermal radiation so
+
+ align:start position:0%
+dealing with thermal radiation so
+ 
+
+ align:start position:0%
+dealing with thermal radiation so
+eventually this vector n will be
+
+ align:start position:0%
+eventually this vector n will be
+ 
+
+ align:start position:0%
+eventually this vector n will be
+pointing I will average it over all
+
+ align:start position:0%
+pointing I will average it over all
+ 
+
+ align:start position:0%
+pointing I will average it over all
+directions because thermal radiation
+
+ align:start position:0%
+directions because thermal radiation
+ 
+
+ align:start position:0%
+directions because thermal radiation
+comes with all polarizations and in all
+
+ align:start position:0%
+comes with all polarizations and in all
+ 
+
+ align:start position:0%
+comes with all polarizations and in all
+directions so there will be a little bit
+
+ align:start position:0%
+directions so there will be a little bit
+ 
+
+ align:start position:0%
+directions so there will be a little bit
+of averaging necessary for that that
+
+ align:start position:0%
+of averaging necessary for that that
+ 
+
+ align:start position:0%
+of averaging necessary for that that
+will happen next time as we wrap up this
+
+ align:start position:0%
+will happen next time as we wrap up this
+ 
+
+ align:start position:0%
+will happen next time as we wrap up this
+discussion so this picture is of an atom
+
+ align:start position:0%
+discussion so this picture is of an atom
+ 
+
+ align:start position:0%
+discussion so this picture is of an atom
+sitting here in particular its electron
+
+ align:start position:0%
+sitting here in particular its electron
+ 
+
+ align:start position:0%
+sitting here in particular its electron
+which is the particle that reacts the
+
+ align:start position:0%
+which is the particle that reacts the
+ 
+
+ align:start position:0%
+which is the particle that reacts the
+most of the electric field and there's a
+
+ align:start position:0%
+most of the electric field and there's a
+ 
+
+ align:start position:0%
+most of the electric field and there's a
+unit vector and and there's P of T here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the electric field E of T is - e not
+
+ align:start position:0%
+so the electric field E of T is - e not
+ 
+
+ align:start position:0%
+so the electric field E of T is - e not
+in our conventions cosine Omega T times
+
+ align:start position:0%
+in our conventions cosine Omega T times
+ 
+
+ align:start position:0%
+in our conventions cosine Omega T times
+the vector n so what is the vector and
+
+ align:start position:0%
+the vector n so what is the vector and
+ 
+
+ align:start position:0%
+the vector n so what is the vector and
+the scalar potential RT is minus R times
+
+ align:start position:0%
+the scalar potential RT is minus R times
+ 
+
+ align:start position:0%
+the scalar potential RT is minus R times
+e of T this is the formula that gives
+
+ align:start position:0%
+e of T this is the formula that gives
+ 
+
+ align:start position:0%
+e of T this is the formula that gives
+you a as minus the gradient of Phi this
+
+ align:start position:0%
+you a as minus the gradient of Phi this
+ 
+
+ align:start position:0%
+you a as minus the gradient of Phi this
+formula is not true in the presence of
+
+ align:start position:0%
+formula is not true in the presence of
+ 
+
+ align:start position:0%
+formula is not true in the presence of
+magnetic fields in general there's a
+
+ align:start position:0%
+magnetic fields in general there's a
+ 
+
+ align:start position:0%
+magnetic fields in general there's a
+time derivative of the vector potential
+
+ align:start position:0%
+time derivative of the vector potential
+ 
+
+ align:start position:0%
+time derivative of the vector potential
+but again we're ignoring magnetic
+
+ align:start position:0%
+but again we're ignoring magnetic
+ 
+
+ align:start position:0%
+but again we're ignoring magnetic
+effects so this is good enough for us if
+
+ align:start position:0%
+effects so this is good enough for us if
+ 
+
+ align:start position:0%
+effects so this is good enough for us if
+you take the gradient of this formula
+
+ align:start position:0%
+you take the gradient of this formula
+ 
+
+ align:start position:0%
+you take the gradient of this formula
+the only are the pen
+
+ align:start position:0%
+the only are the pen
+ 
+
+ align:start position:0%
+the only are the pen
+is here there's no our dependence in
+
+ align:start position:0%
+is here there's no our dependence in
+ 
+
+ align:start position:0%
+is here there's no our dependence in
+this electric field and particular we
+
+ align:start position:0%
+this electric field and particular we
+ 
+
+ align:start position:0%
+this electric field and particular we
+considered the wavelengths to be very
+
+ align:start position:0%
+considered the wavelengths to be very
+ 
+
+ align:start position:0%
+considered the wavelengths to be very
+big and this is good enough so what is
+
+ align:start position:0%
+big and this is good enough so what is
+ 
+
+ align:start position:0%
+big and this is good enough so what is
+the perturbing Hamiltonian due to the
+
+ align:start position:0%
+the perturbing Hamiltonian due to the
+ 
+
+ align:start position:0%
+the perturbing Hamiltonian due to the
+coupling of the electric field to the
+
+ align:start position:0%
+coupling of the electric field to the
+ 
+
+ align:start position:0%
+coupling of the electric field to the
+charge particle and we'll say atom and
+
+ align:start position:0%
+charge particle and we'll say atom and
+ 
+
+ align:start position:0%
+charge particle and we'll say atom and
+we'll put an electron or something and
+
+ align:start position:0%
+we'll put an electron or something and
+ 
+
+ align:start position:0%
+we'll put an electron or something and
+we'll say the charge is Q eventually it
+
+ align:start position:0%
+we'll say the charge is Q eventually it
+ 
+
+ align:start position:0%
+we'll say the charge is Q eventually it
+will be minus e for the electron but
+
+ align:start position:0%
+will be minus e for the electron but
+ 
+
+ align:start position:0%
+will be minus e for the electron but
+let's keep it at Q Delta H is Q times
+
+ align:start position:0%
+let's keep it at Q Delta H is Q times
+ 
+
+ align:start position:0%
+let's keep it at Q Delta H is Q times
+Phi of R and T so this is minus Q times
+
+ align:start position:0%
+Phi of R and T so this is minus Q times
+ 
+
+ align:start position:0%
+Phi of R and T so this is minus Q times
+R times T of T vector or minus Q times R
+
+ align:start position:0%
+R times T of T vector or minus Q times R
+ 
+
+ align:start position:0%
+R times T of T vector or minus Q times R
+times n times e of T so so far simple
+
+ align:start position:0%
+times n times e of T so so far simple
+ 
+
+ align:start position:0%
+times n times e of T so so far simple
+things we're just considering the
+
+ align:start position:0%
+things we're just considering the
+ 
+
+ align:start position:0%
+things we're just considering the
+electric field and how it acts on a
+
+ align:start position:0%
+electric field and how it acts on a
+ 
+
+ align:start position:0%
+electric field and how it acts on a
+charged particle this is of course the
+
+ align:start position:0%
+charged particle this is of course the
+ 
+
+ align:start position:0%
+charged particle this is of course the
+simplest situation we will be
+
+ align:start position:0%
+simplest situation we will be
+ 
+
+ align:start position:0%
+simplest situation we will be
+considering in this course soon in fact
+
+ align:start position:0%
+considering in this course soon in fact
+ 
+
+ align:start position:0%
+considering in this course soon in fact
+starting next lecture the general
+
+ align:start position:0%
+starting next lecture the general
+ 
+
+ align:start position:0%
+starting next lecture the general
+interaction of charged particles with
+
+ align:start position:0%
+interaction of charged particles with
+ 
+
+ align:start position:0%
+interaction of charged particles with
+electromagnetic fields but for the time
+
+ align:start position:0%
+electromagnetic fields but for the time
+ 
+
+ align:start position:0%
+electromagnetic fields but for the time
+being and in this approximation this is
+
+ align:start position:0%
+being and in this approximation this is
+ 
+
+ align:start position:0%
+being and in this approximation this is
+enough and we will define now a dipole
+
+ align:start position:0%
+enough and we will define now a dipole
+ 
+
+ align:start position:0%
+enough and we will define now a dipole
+operator it's something you should keep
+
+ align:start position:0%
+operator it's something you should keep
+ 
+
+ align:start position:0%
+operator it's something you should keep
+in mind it's a the usual thing when you
+
+ align:start position:0%
+in mind it's a the usual thing when you
+ 
+
+ align:start position:0%
+in mind it's a the usual thing when you
+define dipoles if you sum or integrate
+
+ align:start position:0%
+define dipoles if you sum or integrate
+ 
+
+ align:start position:0%
+define dipoles if you sum or integrate
+over charges and position vectors so
+
+ align:start position:0%
+over charges and position vectors so
+ 
+
+ align:start position:0%
+over charges and position vectors so
+this is a dipole operator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operator and emphasize the operator
+
+ align:start position:0%
+operator and emphasize the operator
+ 
+
+ align:start position:0%
+operator and emphasize the operator
+because of the are when you have matrix
+
+ align:start position:0%
+because of the are when you have matrix
+ 
+
+ align:start position:0%
+because of the are when you have matrix
+elements transitions between states
+
+ align:start position:0%
+elements transitions between states
+ 
+
+ align:start position:0%
+elements transitions between states
+everything we will have to deal with
+
+ align:start position:0%
+everything we will have to deal with
+ 
+
+ align:start position:0%
+everything we will have to deal with
+those matrix elements of our and that's
+
+ align:start position:0%
+those matrix elements of our and that's
+ 
+
+ align:start position:0%
+those matrix elements of our and that's
+why we'll have a dipole term there so
+
+ align:start position:0%
+why we'll have a dipole term there so
+ 
+
+ align:start position:0%
+why we'll have a dipole term there so
+Delta H at this moment has become what -
+
+ align:start position:0%
+Delta H at this moment has become what -
+ 
+
+ align:start position:0%
+Delta H at this moment has become what -
+the dipole times the electric field so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's do this - the dipole I'll do it
+
+ align:start position:0%
+so let's do this - the dipole I'll do it
+ 
+
+ align:start position:0%
+so let's do this - the dipole I'll do it
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mine is the dipole dotted with the
+
+ align:start position:0%
+mine is the dipole dotted with the
+ 
+
+ align:start position:0%
+mine is the dipole dotted with the
+electric field vector or minus B dot and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with - in times the magnitude of the
+
+ align:start position:0%
+with - in times the magnitude of the
+ 
+
+ align:start position:0%
+with - in times the magnitude of the
+electric field or minus B dot and x 2 e
+
+ align:start position:0%
+electric field or minus B dot and x 2 e
+ 
+
+ align:start position:0%
+electric field or minus B dot and x 2 e
+naught cosine of Omega T you know
+
+ align:start position:0%
+naught cosine of Omega T you know
+ 
+
+ align:start position:0%
+naught cosine of Omega T you know
+factors of 2 keep us busy always and we
+
+ align:start position:0%
+factors of 2 keep us busy always and we
+ 
+
+ align:start position:0%
+factors of 2 keep us busy always and we
+have to get them right remember when we
+
+ align:start position:0%
+have to get them right remember when we
+ 
+
+ align:start position:0%
+have to get them right remember when we
+did our definition of perturbed
+
+ align:start position:0%
+did our definition of perturbed
+ 
+
+ align:start position:0%
+did our definition of perturbed
+hamiltonians we said that Delta H was
+
+ align:start position:0%
+hamiltonians we said that Delta H was
+ 
+
+ align:start position:0%
+hamiltonians we said that Delta H was
+going to be equal to 2 H prime cosine of
+
+ align:start position:0%
+going to be equal to 2 H prime cosine of
+ 
+
+ align:start position:0%
+going to be equal to 2 H prime cosine of
+Omega T and our transition amplitude and
+
+ align:start position:0%
+Omega T and our transition amplitude and
+ 
+
+ align:start position:0%
+Omega T and our transition amplitude and
+everything were written in terms of H
+
+ align:start position:0%
+everything were written in terms of H
+ 
+
+ align:start position:0%
+everything were written in terms of H
+prime so this was our definition so at
+
+ align:start position:0%
+prime so this was our definition so at
+ 
+
+ align:start position:0%
+prime so this was our definition so at
+this moment we can isolate H prime here
+
+ align:start position:0%
+this moment we can isolate H prime here
+ 
+
+ align:start position:0%
+this moment we can isolate H prime here
+so H prime is everything except for the
+
+ align:start position:0%
+so H prime is everything except for the
+ 
+
+ align:start position:0%
+so H prime is everything except for the
+2 and the cosine of Omega T so H prime
+
+ align:start position:0%
+2 and the cosine of Omega T so H prime
+ 
+
+ align:start position:0%
+2 and the cosine of Omega T so H prime
+for our problem of atoms in
+
+ align:start position:0%
+for our problem of atoms in
+ 
+
+ align:start position:0%
+for our problem of atoms in
+acting with electromagnetic fields is a
+
+ align:start position:0%
+acting with electromagnetic fields is a
+ 
+
+ align:start position:0%
+acting with electromagnetic fields is a
+dipole interaction and it's given by
+
+ align:start position:0%
+dipole interaction and it's given by
+ 
+
+ align:start position:0%
+dipole interaction and it's given by
+this nice simple formula that's our kind
+
+ align:start position:0%
+this nice simple formula that's our kind
+ 
+
+ align:start position:0%
+this nice simple formula that's our kind
+of important and result so if we have
+
+ align:start position:0%
+of important and result so if we have
+ 
+
+ align:start position:0%
+of important and result so if we have
+this Hamiltonian we have calculated the
+
+ align:start position:0%
+this Hamiltonian we have calculated the
+ 
+
+ align:start position:0%
+this Hamiltonian we have calculated the
+transition rates for or actually more
+
+ align:start position:0%
+transition rates for or actually more
+ 
+
+ align:start position:0%
+transition rates for or actually more
+not the transition rates the probability
+
+ align:start position:0%
+not the transition rates the probability
+ 
+
+ align:start position:0%
+not the transition rates the probability
+for transitions for example from B to a
+
+ align:start position:0%
+for transitions for example from B to a
+ 
+
+ align:start position:0%
+for transitions for example from B to a
+as a function of time when we have a
+
+ align:start position:0%
+as a function of time when we have a
+ 
+
+ align:start position:0%
+as a function of time when we have a
+harmonic perturbation coupled to a
+
+ align:start position:0%
+harmonic perturbation coupled to a
+ 
+
+ align:start position:0%
+harmonic perturbation coupled to a
+two-level system we have a probability
+
+ align:start position:0%
+two-level system we have a probability
+ 
+
+ align:start position:0%
+two-level system we have a probability
+we don't have yet a rate we just have a
+
+ align:start position:0%
+we don't have yet a rate we just have a
+ 
+
+ align:start position:0%
+we don't have yet a rate we just have a
+probability and this is equal to the
+
+ align:start position:0%
+probability and this is equal to the
+ 
+
+ align:start position:0%
+probability and this is equal to the
+other one - the reverse one its 4-h a B
+
+ align:start position:0%
+other one - the reverse one its 4-h a B
+ 
+
+ align:start position:0%
+other one - the reverse one its 4-h a B
+prime squared over H squared sine
+
+ align:start position:0%
+prime squared over H squared sine
+ 
+
+ align:start position:0%
+prime squared over H squared sine
+squared of Omega B a minus Omega over 2t
+
+ align:start position:0%
+squared of Omega B a minus Omega over 2t
+ 
+
+ align:start position:0%
+squared of Omega B a minus Omega over 2t
+over Omega B a minus Omega squared that
+
+ align:start position:0%
+over Omega B a minus Omega squared that
+ 
+
+ align:start position:0%
+over Omega B a minus Omega squared that
+was the formula we had in our case now H
+
+ align:start position:0%
+was the formula we had in our case now H
+ 
+
+ align:start position:0%
+was the formula we had in our case now H
+prime a/b is that so we'll get the
+
+ align:start position:0%
+prime a/b is that so we'll get the
+ 
+
+ align:start position:0%
+prime a/b is that so we'll get the
+following for e zero squared the e zero
+
+ align:start position:0%
+following for e zero squared the e zero
+ 
+
+ align:start position:0%
+following for e zero squared the e zero
+factor here goes out and then we will
+
+ align:start position:0%
+factor here goes out and then we will
+ 
+
+ align:start position:0%
+factor here goes out and then we will
+have the matrix elements of the dipole
+
+ align:start position:0%
+have the matrix elements of the dipole
+ 
+
+ align:start position:0%
+have the matrix elements of the dipole
+operator V dot n a B so it will all be
+
+ align:start position:0%
+operator V dot n a B so it will all be
+ 
+
+ align:start position:0%
+operator V dot n a B so it will all be
+matter of the dipole operator H squared
+
+ align:start position:0%
+matter of the dipole operator H squared
+ 
+
+ align:start position:0%
+matter of the dipole operator H squared
+and the same factor sine squared Omega B
+
+ align:start position:0%
+and the same factor sine squared Omega B
+ 
+
+ align:start position:0%
+and the same factor sine squared Omega B
+a minus Omega over 2t over Omega B a
+
+ align:start position:0%
+a minus Omega over 2t over Omega B a
+ 
+
+ align:start position:0%
+a minus Omega over 2t over Omega B a
+minus Omega squared so this is the
+
+ align:start position:0%
+minus Omega squared so this is the
+ 
+
+ align:start position:0%
+minus Omega squared so this is the
+transition probability
+
+ align:start position:0%
+transition probability
+ 
+
+ align:start position:0%
+transition probability
+don't have a rate but the rate will come
+
+ align:start position:0%
+don't have a rate but the rate will come
+ 
+
+ align:start position:0%
+don't have a rate but the rate will come
+when we integrate over all the photons
+
+ align:start position:0%
+when we integrate over all the photons
+ 
+
+ align:start position:0%
+when we integrate over all the photons
+that contribute to this process and
+
+ align:start position:0%
+that contribute to this process and
+ 
+
+ align:start position:0%
+that contribute to this process and
+we'll get an exact analog of a Fermi
+
+ align:start position:0%
+we'll get an exact analog of a Fermi
+ 
+
+ align:start position:0%
+we'll get an exact analog of a Fermi
+golden rule so that will be next time
\ No newline at end of file
diff --git a/_62YvNU_yOM.txt b/_62YvNU_yOM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..160063ae1cacb1a417d0454ef373fede1087d5ed
--- /dev/null
+++ b/_62YvNU_yOM.txt
@@ -0,0 +1,291 @@
+align:start position:0%
+ 
+advice that I would give to educators
+
+ align:start position:0%
+advice that I would give to educators
+ 
+
+ align:start position:0%
+advice that I would give to educators
+also planning or hoping to teach the
+
+ align:start position:0%
+also planning or hoping to teach the
+ 
+
+ align:start position:0%
+also planning or hoping to teach the
+same kind of course material or subject
+
+ align:start position:0%
+same kind of course material or subject
+ 
+
+ align:start position:0%
+same kind of course material or subject
+would be to have somebody of the
+
+ align:start position:0%
+would be to have somebody of the
+ 
+
+ align:start position:0%
+would be to have somebody of the
+diaspora or somebody who can relate to
+
+ align:start position:0%
+diaspora or somebody who can relate to
+ 
+
+ align:start position:0%
+diaspora or somebody who can relate to
+the diaspora teach it it's important to
+
+ align:start position:0%
+the diaspora teach it it's important to
+ 
+
+ align:start position:0%
+the diaspora teach it it's important to
+have people of the background or of the
+
+ align:start position:0%
+have people of the background or of the
+ 
+
+ align:start position:0%
+have people of the background or of the
+diaspora educating it's like who better
+
+ align:start position:0%
+diaspora educating it's like who better
+ 
+
+ align:start position:0%
+diaspora educating it's like who better
+to educate than those that have
+
+ align:start position:0%
+to educate than those that have
+ 
+
+ align:start position:0%
+to educate than those that have
+experienced it themselves or those that
+
+ align:start position:0%
+experienced it themselves or those that
+ 
+
+ align:start position:0%
+experienced it themselves or those that
+you know like come from that area so I
+
+ align:start position:0%
+you know like come from that area so I
+ 
+
+ align:start position:0%
+you know like come from that area so I
+feel like that's probably the biggest
+
+ align:start position:0%
+feel like that's probably the biggest
+ 
+
+ align:start position:0%
+feel like that's probably the biggest
+advice I would give I think maybe other
+
+ align:start position:0%
+advice I would give I think maybe other
+ 
+
+ align:start position:0%
+advice I would give I think maybe other
+advice would be really making sure to
+
+ align:start position:0%
+advice would be really making sure to
+ 
+
+ align:start position:0%
+advice would be really making sure to
+create safe spaces for students to have
+
+ align:start position:0%
+create safe spaces for students to have
+ 
+
+ align:start position:0%
+create safe spaces for students to have
+conversations because I feel like we had
+
+ align:start position:0%
+conversations because I feel like we had
+ 
+
+ align:start position:0%
+conversations because I feel like we had
+that in this class and that you can have
+
+ align:start position:0%
+that in this class and that you can have
+ 
+
+ align:start position:0%
+that in this class and that you can have
+a curriculum that can be very diverse
+
+ align:start position:0%
+a curriculum that can be very diverse
+ 
+
+ align:start position:0%
+a curriculum that can be very diverse
+and like can be very open but if you
+
+ align:start position:0%
+and like can be very open but if you
+ 
+
+ align:start position:0%
+and like can be very open but if you
+don't create an environment and we're
+
+ align:start position:0%
+don't create an environment and we're
+ 
+
+ align:start position:0%
+don't create an environment and we're
+like in which students can like openly
+
+ align:start position:0%
+like in which students can like openly
+ 
+
+ align:start position:0%
+like in which students can like openly
+speak about things and openly talk about
+
+ align:start position:0%
+speak about things and openly talk about
+ 
+
+ align:start position:0%
+speak about things and openly talk about
+things like it's not gonna matter and I
+
+ align:start position:0%
+things like it's not gonna matter and I
+ 
+
+ align:start position:0%
+things like it's not gonna matter and I
+feel like it limits the kinds of
+
+ align:start position:0%
+feel like it limits the kinds of
+ 
+
+ align:start position:0%
+feel like it limits the kinds of
+discussions you have and I feel like
+
+ align:start position:0%
+discussions you have and I feel like
+ 
+
+ align:start position:0%
+discussions you have and I feel like
+we've had a lot of great discussions in
+
+ align:start position:0%
+we've had a lot of great discussions in
+ 
+
+ align:start position:0%
+we've had a lot of great discussions in
+this class because the environment has
+
+ align:start position:0%
+this class because the environment has
+ 
+
+ align:start position:0%
+this class because the environment has
+been it's been a safe environment you
+
+ align:start position:0%
+been it's been a safe environment you
+ 
+
+ align:start position:0%
+been it's been a safe environment you
+know when people can voice their
+
+ align:start position:0%
+know when people can voice their
+ 
+
+ align:start position:0%
+know when people can voice their
+opinions and things have gotten very
+
+ align:start position:0%
+opinions and things have gotten very
+ 
+
+ align:start position:0%
+opinions and things have gotten very
+personal in this class sometimes you
+
+ align:start position:0%
+personal in this class sometimes you
+ 
+
+ align:start position:0%
+personal in this class sometimes you
+know there have been one or two
+
+ align:start position:0%
+know there have been one or two
+ 
+
+ align:start position:0%
+know there have been one or two
+instances where students that have been
+
+ align:start position:0%
+instances where students that have been
+ 
+
+ align:start position:0%
+instances where students that have been
+left you know because they were so
+
+ align:start position:0%
+left you know because they were so
+ 
+
+ align:start position:0%
+left you know because they were so
+emotional and so like yeah it's not it's
+
+ align:start position:0%
+emotional and so like yeah it's not it's
+ 
+
+ align:start position:0%
+emotional and so like yeah it's not it's
+not just about the curriculum - it's
+
+ align:start position:0%
+not just about the curriculum - it's
+ 
+
+ align:start position:0%
+not just about the curriculum - it's
+also about the space that you create
\ No newline at end of file
diff --git a/_jz3HWBmruo.txt b/_jz3HWBmruo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6a07b44aa470a30105423491c5bcf43b96f09dea
--- /dev/null
+++ b/_jz3HWBmruo.txt
@@ -0,0 +1,2531 @@
+align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+in most of our calculations of safety
+
+ align:start position:0%
+in most of our calculations of safety
+ 
+
+ align:start position:0%
+in most of our calculations of safety
+we're going to be interested in the
+
+ align:start position:0%
+we're going to be interested in the
+ 
+
+ align:start position:0%
+we're going to be interested in the
+steady state average transmission rate
+
+ align:start position:0%
+steady state average transmission rate
+ 
+
+ align:start position:0%
+steady state average transmission rate
+between individuals in a room
+
+ align:start position:0%
+between individuals in a room
+ 
+
+ align:start position:0%
+between individuals in a room
+after the aerosol particles have built
+
+ align:start position:0%
+after the aerosol particles have built
+ 
+
+ align:start position:0%
+after the aerosol particles have built
+up to a steady state
+
+ align:start position:0%
+up to a steady state
+ 
+
+ align:start position:0%
+up to a steady state
+but let's briefly talk about the
+
+ align:start position:0%
+but let's briefly talk about the
+ 
+
+ align:start position:0%
+but let's briefly talk about the
+transient buildup and how to take that
+
+ align:start position:0%
+transient buildup and how to take that
+ 
+
+ align:start position:0%
+transient buildup and how to take that
+into account
+
+ align:start position:0%
+into account
+ 
+
+ align:start position:0%
+into account
+just as an aside in this board here so
+
+ align:start position:0%
+just as an aside in this board here so
+ 
+
+ align:start position:0%
+just as an aside in this board here so
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is the general expression for the
+
+ align:start position:0%
+is the general expression for the
+ 
+
+ align:start position:0%
+is the general expression for the
+transmission rate that we described
+
+ align:start position:0%
+transmission rate that we described
+ 
+
+ align:start position:0%
+transmission rate that we described
+which depends on the breathing rate
+
+ align:start position:0%
+which depends on the breathing rate
+ 
+
+ align:start position:0%
+which depends on the breathing rate
+squared uh the
+
+ align:start position:0%
+squared uh the
+ 
+
+ align:start position:0%
+squared uh the
+the volume of the room it's an integral
+
+ align:start position:0%
+the volume of the room it's an integral
+ 
+
+ align:start position:0%
+the volume of the room it's an integral
+over all the different drop sizes
+
+ align:start position:0%
+over all the different drop sizes
+ 
+
+ align:start position:0%
+over all the different drop sizes
+where nq is a lumped distribution
+
+ align:start position:0%
+where nq is a lumped distribution
+ 
+
+ align:start position:0%
+where nq is a lumped distribution
+of the number of infection quanta per
+
+ align:start position:0%
+of the number of infection quanta per
+ 
+
+ align:start position:0%
+of the number of infection quanta per
+volume
+
+ align:start position:0%
+volume
+ 
+
+ align:start position:0%
+volume
+per per radius
+
+ align:start position:0%
+per per radius
+ 
+
+ align:start position:0%
+per per radius
+and then pm is the mass transmission
+
+ align:start position:0%
+and then pm is the mass transmission
+ 
+
+ align:start position:0%
+and then pm is the mass transmission
+factor which depends on radius
+
+ align:start position:0%
+factor which depends on radius
+ 
+
+ align:start position:0%
+factor which depends on radius
+and lambda c is the total relaxation
+
+ align:start position:0%
+and lambda c is the total relaxation
+ 
+
+ align:start position:0%
+and lambda c is the total relaxation
+rate involving sedimentation
+
+ align:start position:0%
+rate involving sedimentation
+ 
+
+ align:start position:0%
+rate involving sedimentation
+and or settling and
+
+ align:start position:0%
+and or settling and
+ 
+
+ align:start position:0%
+and or settling and
+viral deactivation and filtration and
+
+ align:start position:0%
+viral deactivation and filtration and
+ 
+
+ align:start position:0%
+viral deactivation and filtration and
+that also depends of course on r and
+
+ align:start position:0%
+that also depends of course on r and
+ 
+
+ align:start position:0%
+that also depends of course on r and
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+lambda c of r also ends up in the
+
+ align:start position:0%
+lambda c of r also ends up in the
+ 
+
+ align:start position:0%
+lambda c of r also ends up in the
+exponent here so that actually
+
+ align:start position:0%
+exponent here so that actually
+ 
+
+ align:start position:0%
+exponent here so that actually
+that that rate of relaxation of the
+
+ align:start position:0%
+that that rate of relaxation of the
+ 
+
+ align:start position:0%
+that that rate of relaxation of the
+concentration in the air
+
+ align:start position:0%
+concentration in the air
+ 
+
+ align:start position:0%
+concentration in the air
+is also setting the time scale lambda c
+
+ align:start position:0%
+is also setting the time scale lambda c
+ 
+
+ align:start position:0%
+is also setting the time scale lambda c
+inverse for the buildup of those aerosol
+
+ align:start position:0%
+inverse for the buildup of those aerosol
+ 
+
+ align:start position:0%
+inverse for the buildup of those aerosol
+droplets in the air and so that's this
+
+ align:start position:0%
+droplets in the air and so that's this
+ 
+
+ align:start position:0%
+droplets in the air and so that's this
+factor here this is basically the
+
+ align:start position:0%
+factor here this is basically the
+ 
+
+ align:start position:0%
+factor here this is basically the
+the transient term
+
+ align:start position:0%
+the transient term
+ 
+
+ align:start position:0%
+the transient term
+is this term and then this term
+
+ align:start position:0%
+is this term and then this term
+ 
+
+ align:start position:0%
+is this term and then this term
+the one is the steady term okay
+
+ align:start position:0%
+the one is the steady term okay
+ 
+
+ align:start position:0%
+the one is the steady term okay
+so we're interested now what's the
+
+ align:start position:0%
+so we're interested now what's the
+ 
+
+ align:start position:0%
+so we're interested now what's the
+effect of the transient now before we
+
+ align:start position:0%
+effect of the transient now before we
+ 
+
+ align:start position:0%
+effect of the transient now before we
+get to that
+
+ align:start position:0%
+get to that
+ 
+
+ align:start position:0%
+get to that
+if we forget about the transient now we
+
+ align:start position:0%
+if we forget about the transient now we
+ 
+
+ align:start position:0%
+if we forget about the transient now we
+just have the steady state
+
+ align:start position:0%
+just have the steady state
+ 
+
+ align:start position:0%
+just have the steady state
+then we have introduced beta bar as the
+
+ align:start position:0%
+then we have introduced beta bar as the
+ 
+
+ align:start position:0%
+then we have introduced beta bar as the
+sort of constant
+
+ align:start position:0%
+sort of constant
+ 
+
+ align:start position:0%
+sort of constant
+steady state value transmission and
+
+ align:start position:0%
+steady state value transmission and
+ 
+
+ align:start position:0%
+steady state value transmission and
+through this definition here by doing
+
+ align:start position:0%
+through this definition here by doing
+ 
+
+ align:start position:0%
+through this definition here by doing
+these integrals we have defined an
+
+ align:start position:0%
+these integrals we have defined an
+ 
+
+ align:start position:0%
+these integrals we have defined an
+effective
+
+ align:start position:0%
+effective
+ 
+
+ align:start position:0%
+effective
+radius r bar which is sort of
+
+ align:start position:0%
+radius r bar which is sort of
+ 
+
+ align:start position:0%
+radius r bar which is sort of
+where you evaluate the mass transmission
+
+ align:start position:0%
+where you evaluate the mass transmission
+ 
+
+ align:start position:0%
+where you evaluate the mass transmission
+factor and also the
+
+ align:start position:0%
+factor and also the
+ 
+
+ align:start position:0%
+factor and also the
+filtration or the relaxation rate in
+
+ align:start position:0%
+filtration or the relaxation rate in
+ 
+
+ align:start position:0%
+filtration or the relaxation rate in
+order to make these two
+
+ align:start position:0%
+order to make these two
+ 
+
+ align:start position:0%
+order to make these two
+uh values equal so that's actually our
+
+ align:start position:0%
+uh values equal so that's actually our
+ 
+
+ align:start position:0%
+uh values equal so that's actually our
+definition of effective radius
+
+ align:start position:0%
+definition of effective radius
+ 
+
+ align:start position:0%
+definition of effective radius
+and so now looking at the uh at the
+
+ align:start position:0%
+and so now looking at the uh at the
+ 
+
+ align:start position:0%
+and so now looking at the uh at the
+transient term
+
+ align:start position:0%
+transient term
+ 
+
+ align:start position:0%
+transient term
+uh let's ask ourselves what is the
+
+ align:start position:0%
+uh let's ask ourselves what is the
+ 
+
+ align:start position:0%
+uh let's ask ourselves what is the
+average transmission rate up to a
+
+ align:start position:0%
+average transmission rate up to a
+ 
+
+ align:start position:0%
+average transmission rate up to a
+certain time
+
+ align:start position:0%
+certain time
+ 
+
+ align:start position:0%
+certain time
+tau so that would be we divide by a time
+
+ align:start position:0%
+tau so that would be we divide by a time
+ 
+
+ align:start position:0%
+tau so that would be we divide by a time
+tau
+
+ align:start position:0%
+tau
+ 
+
+ align:start position:0%
+tau
+and we ask ourselves up to that time you
+
+ align:start position:0%
+and we ask ourselves up to that time you
+ 
+
+ align:start position:0%
+and we ask ourselves up to that time you
+know what is the
+
+ align:start position:0%
+know what is the
+ 
+
+ align:start position:0%
+know what is the
+average transmission rate so we
+
+ align:start position:0%
+average transmission rate so we
+ 
+
+ align:start position:0%
+average transmission rate so we
+integrate beta dt from 0 to tau
+
+ align:start position:0%
+integrate beta dt from 0 to tau
+ 
+
+ align:start position:0%
+integrate beta dt from 0 to tau
+and then divide by divide by tau so what
+
+ align:start position:0%
+and then divide by divide by tau so what
+ 
+
+ align:start position:0%
+and then divide by divide by tau so what
+would that be
+
+ align:start position:0%
+would that be
+ 
+
+ align:start position:0%
+would that be
+well we can take this time integral and
+
+ align:start position:0%
+well we can take this time integral and
+ 
+
+ align:start position:0%
+well we can take this time integral and
+bring it inside the
+
+ align:start position:0%
+bring it inside the
+ 
+
+ align:start position:0%
+bring it inside the
+radius integral and write this as
+
+ align:start position:0%
+radius integral and write this as
+ 
+
+ align:start position:0%
+radius integral and write this as
+qb squared over v integral
+
+ align:start position:0%
+qb squared over v integral
+ 
+
+ align:start position:0%
+qb squared over v integral
+0 to infinity of pm
+
+ align:start position:0%
+0 to infinity of pm
+ 
+
+ align:start position:0%
+0 to infinity of pm
+squared and q of lambda c keep in mind
+
+ align:start position:0%
+squared and q of lambda c keep in mind
+ 
+
+ align:start position:0%
+squared and q of lambda c keep in mind
+all those
+
+ align:start position:0%
+all those
+ 
+
+ align:start position:0%
+all those
+factors depend on r times
+
+ align:start position:0%
+factors depend on r times
+ 
+
+ align:start position:0%
+factors depend on r times
+now an integral from 0 to tau and i'll
+
+ align:start position:0%
+now an integral from 0 to tau and i'll
+ 
+
+ align:start position:0%
+now an integral from 0 to tau and i'll
+put this in brackets
+
+ align:start position:0%
+put this in brackets
+ 
+
+ align:start position:0%
+put this in brackets
+of 1 minus e to the minus lambda c
+
+ align:start position:0%
+of 1 minus e to the minus lambda c
+ 
+
+ align:start position:0%
+of 1 minus e to the minus lambda c
+which depends on r times t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by divided by
+
+ align:start position:0%
+divided by divided by
+ 
+
+ align:start position:0%
+divided by divided by
+tau dt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then dr so switching the order of
+
+ align:start position:0%
+and then dr so switching the order of
+ 
+
+ align:start position:0%
+and then dr so switching the order of
+integration where we're going to do
+
+ align:start position:0%
+integration where we're going to do
+ 
+
+ align:start position:0%
+integration where we're going to do
+the time integral first okay
+
+ align:start position:0%
+the time integral first okay
+ 
+
+ align:start position:0%
+the time integral first okay
+and so what we have here if we just look
+
+ align:start position:0%
+and so what we have here if we just look
+ 
+
+ align:start position:0%
+and so what we have here if we just look
+only at this expression right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we can write this as a sum of a steady
+
+ align:start position:0%
+we can write this as a sum of a steady
+ 
+
+ align:start position:0%
+we can write this as a sum of a steady
+state term
+
+ align:start position:0%
+state term
+ 
+
+ align:start position:0%
+state term
+so when it's just one this is the
+
+ align:start position:0%
+so when it's just one this is the
+ 
+
+ align:start position:0%
+so when it's just one this is the
+integral of one over tau you know from
+
+ align:start position:0%
+integral of one over tau you know from
+ 
+
+ align:start position:0%
+integral of one over tau you know from
+zero to tau so that's just
+
+ align:start position:0%
+zero to tau so that's just
+ 
+
+ align:start position:0%
+zero to tau so that's just
+one so that's the steady state
+
+ align:start position:0%
+one so that's the steady state
+ 
+
+ align:start position:0%
+one so that's the steady state
+contribution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one plus and there's a transient
+
+ align:start position:0%
+one plus and there's a transient
+ 
+
+ align:start position:0%
+one plus and there's a transient
+contribution we have to do this integral
+
+ align:start position:0%
+contribution we have to do this integral
+ 
+
+ align:start position:0%
+contribution we have to do this integral
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so that's e to the minus lambda c
+
+ align:start position:0%
+so that's e to the minus lambda c
+ 
+
+ align:start position:0%
+so that's e to the minus lambda c
+of t over lambda c
+
+ align:start position:0%
+of t over lambda c
+ 
+
+ align:start position:0%
+of t over lambda c
+tau evaluated from zero
+
+ align:start position:0%
+tau evaluated from zero
+ 
+
+ align:start position:0%
+tau evaluated from zero
+to tau and so we'll come back to this in
+
+ align:start position:0%
+to tau and so we'll come back to this in
+ 
+
+ align:start position:0%
+to tau and so we'll come back to this in
+just a moment and evaluate that
+
+ align:start position:0%
+just a moment and evaluate that
+ 
+
+ align:start position:0%
+just a moment and evaluate that
+but just to draw a picture maybe first
+
+ align:start position:0%
+but just to draw a picture maybe first
+ 
+
+ align:start position:0%
+but just to draw a picture maybe first
+of what we're looking at here
+
+ align:start position:0%
+of what we're looking at here
+ 
+
+ align:start position:0%
+of what we're looking at here
+the average transmission rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as a function of this averaging time tau
+
+ align:start position:0%
+as a function of this averaging time tau
+ 
+
+ align:start position:0%
+as a function of this averaging time tau
+well eventually of course it tends to
+
+ align:start position:0%
+well eventually of course it tends to
+ 
+
+ align:start position:0%
+well eventually of course it tends to
+the steady state value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but it does so in a certain way we're
+
+ align:start position:0%
+but it does so in a certain way we're
+ 
+
+ align:start position:0%
+but it does so in a certain way we're
+going to calculate like that
+
+ align:start position:0%
+going to calculate like that
+ 
+
+ align:start position:0%
+going to calculate like that
+where the time for that transmission or
+
+ align:start position:0%
+where the time for that transmission or
+ 
+
+ align:start position:0%
+where the time for that transmission or
+for that transition is the inverse of
+
+ align:start position:0%
+for that transition is the inverse of
+ 
+
+ align:start position:0%
+for that transition is the inverse of
+the relaxation time
+
+ align:start position:0%
+the relaxation time
+ 
+
+ align:start position:0%
+the relaxation time
+although there's not a precise value of
+
+ align:start position:0%
+although there's not a precise value of
+ 
+
+ align:start position:0%
+although there's not a precise value of
+that but if we want to keep actually a
+
+ align:start position:0%
+that but if we want to keep actually a
+ 
+
+ align:start position:0%
+that but if we want to keep actually a
+scale for it it's going to be evaluate
+
+ align:start position:0%
+scale for it it's going to be evaluate
+ 
+
+ align:start position:0%
+scale for it it's going to be evaluate
+that value
+
+ align:start position:0%
+that value
+ 
+
+ align:start position:0%
+that value
+r bar that i mentioned that gives you a
+
+ align:start position:0%
+r bar that i mentioned that gives you a
+ 
+
+ align:start position:0%
+r bar that i mentioned that gives you a
+rough sense of the overall location so
+
+ align:start position:0%
+rough sense of the overall location so
+ 
+
+ align:start position:0%
+rough sense of the overall location so
+this is this build up of the aerosol
+
+ align:start position:0%
+this is this build up of the aerosol
+ 
+
+ align:start position:0%
+this is this build up of the aerosol
+concentration in the room once the
+
+ align:start position:0%
+concentration in the room once the
+ 
+
+ align:start position:0%
+concentration in the room once the
+infected person is entered and
+
+ align:start position:0%
+infected person is entered and
+ 
+
+ align:start position:0%
+infected person is entered and
+eventually they serve a steady
+
+ align:start position:0%
+eventually they serve a steady
+ 
+
+ align:start position:0%
+eventually they serve a steady
+transmission rate to everyone else in
+
+ align:start position:0%
+transmission rate to everyone else in
+ 
+
+ align:start position:0%
+transmission rate to everyone else in
+the room
+
+ align:start position:0%
+the room
+ 
+
+ align:start position:0%
+the room
+so let's let's continue calculating this
+
+ align:start position:0%
+so let's let's continue calculating this
+ 
+
+ align:start position:0%
+so let's let's continue calculating this
+right here now
+
+ align:start position:0%
+right here now
+ 
+
+ align:start position:0%
+right here now
+so this is the transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i can write this as 1
+
+ align:start position:0%
+and i can write this as 1
+ 
+
+ align:start position:0%
+and i can write this as 1
+um and if i evaluate here i can put it
+
+ align:start position:0%
+um and if i evaluate here i can put it
+ 
+
+ align:start position:0%
+um and if i evaluate here i can put it
+this way as minus and then i evaluate
+
+ align:start position:0%
+this way as minus and then i evaluate
+ 
+
+ align:start position:0%
+this way as minus and then i evaluate
+first to the lower limit which gives me
+
+ align:start position:0%
+first to the lower limit which gives me
+ 
+
+ align:start position:0%
+first to the lower limit which gives me
+another one
+
+ align:start position:0%
+another one
+ 
+
+ align:start position:0%
+another one
+minus and then evaluate the upper limit
+
+ align:start position:0%
+minus and then evaluate the upper limit
+ 
+
+ align:start position:0%
+minus and then evaluate the upper limit
+is tau e to the minus
+
+ align:start position:0%
+is tau e to the minus
+ 
+
+ align:start position:0%
+is tau e to the minus
+lambda c tau over lambda c
+
+ align:start position:0%
+lambda c tau over lambda c
+ 
+
+ align:start position:0%
+lambda c tau over lambda c
+tau okay and now i'll use
+
+ align:start position:0%
+tau okay and now i'll use
+ 
+
+ align:start position:0%
+tau okay and now i'll use
+an approximation that helps me get a
+
+ align:start position:0%
+an approximation that helps me get a
+ 
+
+ align:start position:0%
+an approximation that helps me get a
+simple analytical result so i should
+
+ align:start position:0%
+simple analytical result so i should
+ 
+
+ align:start position:0%
+simple analytical result so i should
+mention
+
+ align:start position:0%
+mention
+ 
+
+ align:start position:0%
+mention
+as soon as we have exponentials and
+
+ align:start position:0%
+as soon as we have exponentials and
+ 
+
+ align:start position:0%
+as soon as we have exponentials and
+polynomial factors it can be difficult
+
+ align:start position:0%
+polynomial factors it can be difficult
+ 
+
+ align:start position:0%
+polynomial factors it can be difficult
+to solve equations for for example what
+
+ align:start position:0%
+to solve equations for for example what
+ 
+
+ align:start position:0%
+to solve equations for for example what
+is the bound
+
+ align:start position:0%
+is the bound
+ 
+
+ align:start position:0%
+is the bound
+on the occupancy or the time in the room
+
+ align:start position:0%
+on the occupancy or the time in the room
+ 
+
+ align:start position:0%
+on the occupancy or the time in the room
+you know or the ventilation
+
+ align:start position:0%
+you know or the ventilation
+ 
+
+ align:start position:0%
+you know or the ventilation
+we'd like to get a simple formula and so
+
+ align:start position:0%
+we'd like to get a simple formula and so
+ 
+
+ align:start position:0%
+we'd like to get a simple formula and so
+uh there's a nice approximation i can
+
+ align:start position:0%
+uh there's a nice approximation i can
+ 
+
+ align:start position:0%
+uh there's a nice approximation i can
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+which is that 1 minus e to the minus
+
+ align:start position:0%
+which is that 1 minus e to the minus
+ 
+
+ align:start position:0%
+which is that 1 minus e to the minus
+x over x is not
+
+ align:start position:0%
+x over x is not
+ 
+
+ align:start position:0%
+x over x is not
+too far off from 1 over 1 plus
+
+ align:start position:0%
+too far off from 1 over 1 plus
+ 
+
+ align:start position:0%
+too far off from 1 over 1 plus
+x it turns out so it's not a perfect
+
+ align:start position:0%
+x it turns out so it's not a perfect
+ 
+
+ align:start position:0%
+x it turns out so it's not a perfect
+match you can try plotting these two
+
+ align:start position:0%
+match you can try plotting these two
+ 
+
+ align:start position:0%
+match you can try plotting these two
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+but it's it's it's a reasonable
+
+ align:start position:0%
+but it's it's it's a reasonable
+ 
+
+ align:start position:0%
+but it's it's it's a reasonable
+approximation given that everything
+
+ align:start position:0%
+approximation given that everything
+ 
+
+ align:start position:0%
+approximation given that everything
+we're doing in this calculation
+
+ align:start position:0%
+we're doing in this calculation
+ 
+
+ align:start position:0%
+we're doing in this calculation
+when applied to a real situation is
+
+ align:start position:0%
+when applied to a real situation is
+ 
+
+ align:start position:0%
+when applied to a real situation is
+going to be off you know by some
+
+ align:start position:0%
+going to be off you know by some
+ 
+
+ align:start position:0%
+going to be off you know by some
+uh uncertainty which could be you know
+
+ align:start position:0%
+uh uncertainty which could be you know
+ 
+
+ align:start position:0%
+uh uncertainty which could be you know
+factor of two or three
+
+ align:start position:0%
+factor of two or three
+ 
+
+ align:start position:0%
+factor of two or three
+uh this is actually going to be more
+
+ align:start position:0%
+uh this is actually going to be more
+ 
+
+ align:start position:0%
+uh this is actually going to be more
+than good enough of our approximation
+
+ align:start position:0%
+than good enough of our approximation
+ 
+
+ align:start position:0%
+than good enough of our approximation
+for us
+
+ align:start position:0%
+for us
+ 
+
+ align:start position:0%
+for us
+so if i make that approximation then
+
+ align:start position:0%
+so if i make that approximation then
+ 
+
+ align:start position:0%
+so if i make that approximation then
+what i have here
+
+ align:start position:0%
+what i have here
+ 
+
+ align:start position:0%
+what i have here
+is that this thing is 1 over 1
+
+ align:start position:0%
+is that this thing is 1 over 1
+ 
+
+ align:start position:0%
+is that this thing is 1 over 1
+plus 1 plus
+
+ align:start position:0%
+plus 1 plus
+ 
+
+ align:start position:0%
+plus 1 plus
+x here and so we end up with
+
+ align:start position:0%
+x here and so we end up with
+ 
+
+ align:start position:0%
+x here and so we end up with
+1 minus 1 over 1 plus lambda c
+
+ align:start position:0%
+1 minus 1 over 1 plus lambda c
+ 
+
+ align:start position:0%
+1 minus 1 over 1 plus lambda c
+tau and when i combine those two terms i
+
+ align:start position:0%
+tau and when i combine those two terms i
+ 
+
+ align:start position:0%
+tau and when i combine those two terms i
+end up with lambda c
+
+ align:start position:0%
+end up with lambda c
+ 
+
+ align:start position:0%
+end up with lambda c
+tau over one plus lambda c
+
+ align:start position:0%
+tau over one plus lambda c
+ 
+
+ align:start position:0%
+tau over one plus lambda c
+tau okay so that's
+
+ align:start position:0%
+tau okay so that's
+ 
+
+ align:start position:0%
+tau okay so that's
+uh this is my approximation in fact i
+
+ align:start position:0%
+uh this is my approximation in fact i
+ 
+
+ align:start position:0%
+uh this is my approximation in fact i
+can further then
+
+ align:start position:0%
+can further then
+ 
+
+ align:start position:0%
+can further then
+write that as 1 over 1 plus
+
+ align:start position:0%
+write that as 1 over 1 plus
+ 
+
+ align:start position:0%
+write that as 1 over 1 plus
+lambda c tau inverse dividing the
+
+ align:start position:0%
+lambda c tau inverse dividing the
+ 
+
+ align:start position:0%
+lambda c tau inverse dividing the
+numerator denominator by lambda c
+
+ align:start position:0%
+numerator denominator by lambda c
+ 
+
+ align:start position:0%
+numerator denominator by lambda c
+tau okay so i'm just making some
+
+ align:start position:0%
+tau okay so i'm just making some
+ 
+
+ align:start position:0%
+tau okay so i'm just making some
+approximations here that allow me to get
+
+ align:start position:0%
+approximations here that allow me to get
+ 
+
+ align:start position:0%
+approximations here that allow me to get
+a very simple expression in the end
+
+ align:start position:0%
+a very simple expression in the end
+ 
+
+ align:start position:0%
+a very simple expression in the end
+for my my safety guideline
+
+ align:start position:0%
+for my my safety guideline
+ 
+
+ align:start position:0%
+for my my safety guideline
+taking into account this transient build
+
+ align:start position:0%
+taking into account this transient build
+ 
+
+ align:start position:0%
+taking into account this transient build
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+so remember that the bound we have is
+
+ align:start position:0%
+so remember that the bound we have is
+ 
+
+ align:start position:0%
+so remember that the bound we have is
+on the indoor reproductive number which
+
+ align:start position:0%
+on the indoor reproductive number which
+ 
+
+ align:start position:0%
+on the indoor reproductive number which
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+n minus 1 times the integral
+
+ align:start position:0%
+n minus 1 times the integral
+ 
+
+ align:start position:0%
+n minus 1 times the integral
+of to tau of beta
+
+ align:start position:0%
+of to tau of beta
+ 
+
+ align:start position:0%
+of to tau of beta
+dt so what is that that's just
+
+ align:start position:0%
+dt so what is that that's just
+ 
+
+ align:start position:0%
+dt so what is that that's just
+the sort of time average beta times
+
+ align:start position:0%
+the sort of time average beta times
+ 
+
+ align:start position:0%
+the sort of time average beta times
+tau okay so this bound is actually n
+
+ align:start position:0%
+tau okay so this bound is actually n
+ 
+
+ align:start position:0%
+tau okay so this bound is actually n
+minus one time average beta times tau
+
+ align:start position:0%
+minus one time average beta times tau
+ 
+
+ align:start position:0%
+minus one time average beta times tau
+and then our guideline of course is to
+
+ align:start position:0%
+and then our guideline of course is to
+ 
+
+ align:start position:0%
+and then our guideline of course is to
+make this less
+
+ align:start position:0%
+make this less
+ 
+
+ align:start position:0%
+make this less
+than our tolerance epsilon okay
+
+ align:start position:0%
+than our tolerance epsilon okay
+ 
+
+ align:start position:0%
+than our tolerance epsilon okay
+and so what that means then is using
+
+ align:start position:0%
+and so what that means then is using
+ 
+
+ align:start position:0%
+and so what that means then is using
+this result you can see that
+
+ align:start position:0%
+this result you can see that
+ 
+
+ align:start position:0%
+this result you can see that
+i just get the rest so if i look at the
+
+ align:start position:0%
+i just get the rest so if i look at the
+ 
+
+ align:start position:0%
+i just get the rest so if i look at the
+expression for beta
+
+ align:start position:0%
+expression for beta
+ 
+
+ align:start position:0%
+expression for beta
+bracket is just the steady state
+
+ align:start position:0%
+bracket is just the steady state
+ 
+
+ align:start position:0%
+bracket is just the steady state
+expression
+
+ align:start position:0%
+expression
+ 
+
+ align:start position:0%
+expression
+times this factor so basically this is
+
+ align:start position:0%
+times this factor so basically this is
+ 
+
+ align:start position:0%
+times this factor so basically this is
+kind of the the factor that corrects for
+
+ align:start position:0%
+kind of the the factor that corrects for
+ 
+
+ align:start position:0%
+kind of the the factor that corrects for
+transient effects
+
+ align:start position:0%
+transient effects
+ 
+
+ align:start position:0%
+transient effects
+again with just a simple approximation
+
+ align:start position:0%
+again with just a simple approximation
+ 
+
+ align:start position:0%
+again with just a simple approximation
+so i can then write that my guideline
+
+ align:start position:0%
+so i can then write that my guideline
+ 
+
+ align:start position:0%
+so i can then write that my guideline
+now has a modified form which is that
+
+ align:start position:0%
+now has a modified form which is that
+ 
+
+ align:start position:0%
+now has a modified form which is that
+n minus 1 times tau
+
+ align:start position:0%
+n minus 1 times tau
+ 
+
+ align:start position:0%
+n minus 1 times tau
+is less than epsilon over the
+
+ align:start position:0%
+is less than epsilon over the
+ 
+
+ align:start position:0%
+is less than epsilon over the
+time average beta up to time tau
+
+ align:start position:0%
+time average beta up to time tau
+ 
+
+ align:start position:0%
+time average beta up to time tau
+and this is approximately equal to
+
+ align:start position:0%
+and this is approximately equal to
+ 
+
+ align:start position:0%
+and this is approximately equal to
+epsilon over beta steady state
+
+ align:start position:0%
+epsilon over beta steady state
+ 
+
+ align:start position:0%
+epsilon over beta steady state
+times this factor here if i multiply
+
+ align:start position:0%
+times this factor here if i multiply
+ 
+
+ align:start position:0%
+times this factor here if i multiply
+that to the other side
+
+ align:start position:0%
+that to the other side
+ 
+
+ align:start position:0%
+that to the other side
+um i just get 1 plus 1
+
+ align:start position:0%
+um i just get 1 plus 1
+ 
+
+ align:start position:0%
+um i just get 1 plus 1
+over is lambda c of r bar tau
+
+ align:start position:0%
+over is lambda c of r bar tau
+ 
+
+ align:start position:0%
+over is lambda c of r bar tau
+so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so basically this right here
+
+ align:start position:0%
+so basically this right here
+ 
+
+ align:start position:0%
+so basically this right here
+is the transient
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correction or modification
+
+ align:start position:0%
+correction or modification
+ 
+
+ align:start position:0%
+correction or modification
+and this
+
+ align:start position:0%
+and this
+ 
+
+ align:start position:0%
+and this
+is the steady state formula which we
+
+ align:start position:0%
+is the steady state formula which we
+ 
+
+ align:start position:0%
+is the steady state formula which we
+will more typically
+
+ align:start position:0%
+will more typically
+ 
+
+ align:start position:0%
+will more typically
+be using now why do we care about the
+
+ align:start position:0%
+be using now why do we care about the
+ 
+
+ align:start position:0%
+be using now why do we care about the
+transient
+
+ align:start position:0%
+transient
+ 
+
+ align:start position:0%
+transient
+well first of all you can see that the
+
+ align:start position:0%
+well first of all you can see that the
+ 
+
+ align:start position:0%
+well first of all you can see that the
+by using the transient we are being
+
+ align:start position:0%
+by using the transient we are being
+ 
+
+ align:start position:0%
+by using the transient we are being
+uh less conservative so if we want to be
+
+ align:start position:0%
+uh less conservative so if we want to be
+ 
+
+ align:start position:0%
+uh less conservative so if we want to be
+very conservative we can say you know
+
+ align:start position:0%
+very conservative we can say you know
+ 
+
+ align:start position:0%
+very conservative we can say you know
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+let's just assume the second that the
+
+ align:start position:0%
+let's just assume the second that the
+ 
+
+ align:start position:0%
+let's just assume the second that the
+affected person enters the room
+
+ align:start position:0%
+affected person enters the room
+ 
+
+ align:start position:0%
+affected person enters the room
+boom the transition rate goes right to
+
+ align:start position:0%
+boom the transition rate goes right to
+ 
+
+ align:start position:0%
+boom the transition rate goes right to
+the maximum value
+
+ align:start position:0%
+the maximum value
+ 
+
+ align:start position:0%
+the maximum value
+that's the most conservative so
+
+ align:start position:0%
+that's the most conservative so
+ 
+
+ align:start position:0%
+that's the most conservative so
+generally using the steady state
+
+ align:start position:0%
+generally using the steady state
+ 
+
+ align:start position:0%
+generally using the steady state
+is more conservative
+
+ align:start position:0%
+is more conservative
+ 
+
+ align:start position:0%
+is more conservative
+so that's one reason we like to use it
+
+ align:start position:0%
+so that's one reason we like to use it
+ 
+
+ align:start position:0%
+so that's one reason we like to use it
+also it gives you a simpler formula why
+
+ align:start position:0%
+also it gives you a simpler formula why
+ 
+
+ align:start position:0%
+also it gives you a simpler formula why
+add a bunch of factors to a formula that
+
+ align:start position:0%
+add a bunch of factors to a formula that
+ 
+
+ align:start position:0%
+add a bunch of factors to a formula that
+only make it less conservative
+
+ align:start position:0%
+only make it less conservative
+ 
+
+ align:start position:0%
+only make it less conservative
+and you know we've made a lot of
+
+ align:start position:0%
+and you know we've made a lot of
+ 
+
+ align:start position:0%
+and you know we've made a lot of
+assumptions in this model so it makes
+
+ align:start position:0%
+assumptions in this model so it makes
+ 
+
+ align:start position:0%
+assumptions in this model so it makes
+sense maybe let's not worry about it
+
+ align:start position:0%
+sense maybe let's not worry about it
+ 
+
+ align:start position:0%
+sense maybe let's not worry about it
+however i do actually like to include it
+
+ align:start position:0%
+however i do actually like to include it
+ 
+
+ align:start position:0%
+however i do actually like to include it
+for certain examples
+
+ align:start position:0%
+for certain examples
+ 
+
+ align:start position:0%
+for certain examples
+because it allows you to capture the
+
+ align:start position:0%
+because it allows you to capture the
+ 
+
+ align:start position:0%
+because it allows you to capture the
+intuition we all have
+
+ align:start position:0%
+intuition we all have
+ 
+
+ align:start position:0%
+intuition we all have
+that when the time goes to zero the risk
+
+ align:start position:0%
+that when the time goes to zero the risk
+ 
+
+ align:start position:0%
+that when the time goes to zero the risk
+also has to go to zero
+
+ align:start position:0%
+also has to go to zero
+ 
+
+ align:start position:0%
+also has to go to zero
+which you don't get from steady state
+
+ align:start position:0%
+which you don't get from steady state
+ 
+
+ align:start position:0%
+which you don't get from steady state
+right if this bumps up right away then
+
+ align:start position:0%
+right if this bumps up right away then
+ 
+
+ align:start position:0%
+right if this bumps up right away then
+you could be spending like two seconds
+
+ align:start position:0%
+you could be spending like two seconds
+ 
+
+ align:start position:0%
+you could be spending like two seconds
+in a room and you have
+
+ align:start position:0%
+in a room and you have
+ 
+
+ align:start position:0%
+in a room and you have
+a chance in fact a chance of getting
+
+ align:start position:0%
+a chance in fact a chance of getting
+ 
+
+ align:start position:0%
+a chance in fact a chance of getting
+infected right away which is actually
+
+ align:start position:0%
+infected right away which is actually
+ 
+
+ align:start position:0%
+infected right away which is actually
+not right there has to be some time
+
+ align:start position:0%
+not right there has to be some time
+ 
+
+ align:start position:0%
+not right there has to be some time
+physically for transmission to happen
+
+ align:start position:0%
+physically for transmission to happen
+ 
+
+ align:start position:0%
+physically for transmission to happen
+through these droplets from one person
+
+ align:start position:0%
+through these droplets from one person
+ 
+
+ align:start position:0%
+through these droplets from one person
+to another
+
+ align:start position:0%
+to another
+ 
+
+ align:start position:0%
+to another
+so the effect of the transient
+
+ align:start position:0%
+so the effect of the transient
+ 
+
+ align:start position:0%
+so the effect of the transient
+correction as you can see here is
+
+ align:start position:0%
+correction as you can see here is
+ 
+
+ align:start position:0%
+correction as you can see here is
+when when lambda c tau is
+
+ align:start position:0%
+when when lambda c tau is
+ 
+
+ align:start position:0%
+when when lambda c tau is
+larger than one so that's times that are
+
+ align:start position:0%
+larger than one so that's times that are
+ 
+
+ align:start position:0%
+larger than one so that's times that are
+kind of out here that term is gone
+
+ align:start position:0%
+kind of out here that term is gone
+ 
+
+ align:start position:0%
+kind of out here that term is gone
+but when you get to these earlier times
+
+ align:start position:0%
+but when you get to these earlier times
+ 
+
+ align:start position:0%
+but when you get to these earlier times
+or very short times where there hasn't
+
+ align:start position:0%
+or very short times where there hasn't
+ 
+
+ align:start position:0%
+or very short times where there hasn't
+been time yet for the build up
+
+ align:start position:0%
+been time yet for the build up
+ 
+
+ align:start position:0%
+been time yet for the build up
+of the airborne concentration
+
+ align:start position:0%
+of the airborne concentration
+ 
+
+ align:start position:0%
+of the airborne concentration
+then as you see as tau goes to zero
+
+ align:start position:0%
+then as you see as tau goes to zero
+ 
+
+ align:start position:0%
+then as you see as tau goes to zero
+actually this term diverges
+
+ align:start position:0%
+actually this term diverges
+ 
+
+ align:start position:0%
+actually this term diverges
+so what actually happens is that if i
+
+ align:start position:0%
+so what actually happens is that if i
+ 
+
+ align:start position:0%
+so what actually happens is that if i
+calculate sort of you know
+
+ align:start position:0%
+calculate sort of you know
+ 
+
+ align:start position:0%
+calculate sort of you know
+for example what they get from this
+
+ align:start position:0%
+for example what they get from this
+ 
+
+ align:start position:0%
+for example what they get from this
+guideline is
+
+ align:start position:0%
+guideline is
+ 
+
+ align:start position:0%
+guideline is
+what is the uh
+
+ align:start position:0%
+what is the uh
+ 
+
+ align:start position:0%
+what is the uh
+sort of sort of maximum occupancy
+
+ align:start position:0%
+sort of sort of maximum occupancy
+ 
+
+ align:start position:0%
+sort of sort of maximum occupancy
+or versus time or it's sort of the
+
+ align:start position:0%
+or versus time or it's sort of the
+ 
+
+ align:start position:0%
+or versus time or it's sort of the
+maximum time in the room for a given
+
+ align:start position:0%
+maximum time in the room for a given
+ 
+
+ align:start position:0%
+maximum time in the room for a given
+occupancy we're going to be looking at
+
+ align:start position:0%
+occupancy we're going to be looking at
+ 
+
+ align:start position:0%
+occupancy we're going to be looking at
+lots of plots like this
+
+ align:start position:0%
+lots of plots like this
+ 
+
+ align:start position:0%
+lots of plots like this
+um i would have something that might
+
+ align:start position:0%
+um i would have something that might
+ 
+
+ align:start position:0%
+um i would have something that might
+look
+
+ align:start position:0%
+look
+ 
+
+ align:start position:0%
+look
+like this for steady transmission
+
+ align:start position:0%
+like this for steady transmission
+ 
+
+ align:start position:0%
+like this for steady transmission
+okay and when this time
+
+ align:start position:0%
+okay and when this time
+ 
+
+ align:start position:0%
+okay and when this time
+gets larger than
+
+ align:start position:0%
+gets larger than
+ 
+
+ align:start position:0%
+gets larger than
+lambda c of r bar inverse
+
+ align:start position:0%
+lambda c of r bar inverse
+ 
+
+ align:start position:0%
+lambda c of r bar inverse
+okay there's some critical time scale
+
+ align:start position:0%
+okay there's some critical time scale
+ 
+
+ align:start position:0%
+okay there's some critical time scale
+there which is this one right here
+
+ align:start position:0%
+there which is this one right here
+ 
+
+ align:start position:0%
+there which is this one right here
+then when you're past that time so
+
+ align:start position:0%
+then when you're past that time so
+ 
+
+ align:start position:0%
+then when you're past that time so
+you've got the steady state but if you
+
+ align:start position:0%
+you've got the steady state but if you
+ 
+
+ align:start position:0%
+you've got the steady state but if you
+go to smaller times
+
+ align:start position:0%
+go to smaller times
+ 
+
+ align:start position:0%
+go to smaller times
+then what happens that this thing can
+
+ align:start position:0%
+then what happens that this thing can
+ 
+
+ align:start position:0%
+then what happens that this thing can
+sort of blow up a lot
+
+ align:start position:0%
+sort of blow up a lot
+ 
+
+ align:start position:0%
+sort of blow up a lot
+faster so so what it kind of
+
+ align:start position:0%
+faster so so what it kind of
+ 
+
+ align:start position:0%
+faster so so what it kind of
+helps to capture is again this intuition
+
+ align:start position:0%
+helps to capture is again this intuition
+ 
+
+ align:start position:0%
+helps to capture is again this intuition
+that if i put in like tau is
+
+ align:start position:0%
+that if i put in like tau is
+ 
+
+ align:start position:0%
+that if i put in like tau is
+you know extremely small then of course
+
+ align:start position:0%
+you know extremely small then of course
+ 
+
+ align:start position:0%
+you know extremely small then of course
+the risk goes away and i can have larger
+
+ align:start position:0%
+the risk goes away and i can have larger
+ 
+
+ align:start position:0%
+the risk goes away and i can have larger
+numbers of people in the room or i can
+
+ align:start position:0%
+numbers of people in the room or i can
+ 
+
+ align:start position:0%
+numbers of people in the room or i can
+tolerate smaller times and actually be
+
+ align:start position:0%
+tolerate smaller times and actually be
+ 
+
+ align:start position:0%
+tolerate smaller times and actually be
+safe
+
+ align:start position:0%
+safe
+ 
+
+ align:start position:0%
+safe
+so anyway that's one reason
+
+ align:start position:0%
+so anyway that's one reason
+ 
+
+ align:start position:0%
+so anyway that's one reason
+we do that on the other hand for a
+
+ align:start position:0%
+we do that on the other hand for a
+ 
+
+ align:start position:0%
+we do that on the other hand for a
+conservative guideline and the most
+
+ align:start position:0%
+conservative guideline and the most
+ 
+
+ align:start position:0%
+conservative guideline and the most
+important message of this course
+
+ align:start position:0%
+important message of this course
+ 
+
+ align:start position:0%
+important message of this course
+really is to think about that steady
+
+ align:start position:0%
+really is to think about that steady
+ 
+
+ align:start position:0%
+really is to think about that steady
+state transmission rate which we will
+
+ align:start position:0%
+state transmission rate which we will
+ 
+
+ align:start position:0%
+state transmission rate which we will
+mainly be focusing on in all of our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples
\ No newline at end of file
diff --git a/_qTVDxXBK5A.txt b/_qTVDxXBK5A.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df2c4c12b920d3258dd4abb87c4fcf92684e56a0
--- /dev/null
+++ b/_qTVDxXBK5A.txt
@@ -0,0 +1,635 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I'm Nick chinii I'm finishing my PhD in
+
+ align:start position:0%
+I'm Nick chinii I'm finishing my PhD in
+ 
+
+ align:start position:0%
+I'm Nick chinii I'm finishing my PhD in
+computational biology at Cornell
+
+ align:start position:0%
+computational biology at Cornell
+ 
+
+ align:start position:0%
+computational biology at Cornell
+University Gabriel criman and I are
+
+ align:start position:0%
+University Gabriel criman and I are
+ 
+
+ align:start position:0%
+University Gabriel criman and I are
+interested in seeing how deep networks
+
+ align:start position:0%
+interested in seeing how deep networks
+ 
+
+ align:start position:0%
+interested in seeing how deep networks
+respond to neuroplasticity so in the
+
+ align:start position:0%
+respond to neuroplasticity so in the
+ 
+
+ align:start position:0%
+respond to neuroplasticity so in the
+brain we know that the brain's
+
+ align:start position:0%
+brain we know that the brain's
+ 
+
+ align:start position:0%
+brain we know that the brain's
+constantly in flux and neurons are
+
+ align:start position:0%
+constantly in flux and neurons are
+ 
+
+ align:start position:0%
+constantly in flux and neurons are
+growing and dying weights are changing
+
+ align:start position:0%
+growing and dying weights are changing
+ 
+
+ align:start position:0%
+growing and dying weights are changing
+in response to stimuli but most of the
+
+ align:start position:0%
+in response to stimuli but most of the
+ 
+
+ align:start position:0%
+in response to stimuli but most of the
+time in machine learning what we do is
+
+ align:start position:0%
+time in machine learning what we do is
+ 
+
+ align:start position:0%
+time in machine learning what we do is
+pre-train a network on some training set
+
+ align:start position:0%
+pre-train a network on some training set
+ 
+
+ align:start position:0%
+pre-train a network on some training set
+but then we want to use it for real we
+
+ align:start position:0%
+but then we want to use it for real we
+ 
+
+ align:start position:0%
+but then we want to use it for real we
+freeze it um and keep it in some static
+
+ align:start position:0%
+freeze it um and keep it in some static
+ 
+
+ align:start position:0%
+freeze it um and keep it in some static
+form there's been a lot more emphasis
+
+ align:start position:0%
+form there's been a lot more emphasis
+ 
+
+ align:start position:0%
+form there's been a lot more emphasis
+lately on more online learning so that
+
+ align:start position:0%
+lately on more online learning so that
+ 
+
+ align:start position:0%
+lately on more online learning so that
+you learn as you're working on a data
+
+ align:start position:0%
+you learn as you're working on a data
+ 
+
+ align:start position:0%
+you learn as you're working on a data
+set and in those kind of environments we
+
+ align:start position:0%
+set and in those kind of environments we
+ 
+
+ align:start position:0%
+set and in those kind of environments we
+think that the network will be changing
+
+ align:start position:0%
+think that the network will be changing
+ 
+
+ align:start position:0%
+think that the network will be changing
+quite a bit so we're looking at how uh
+
+ align:start position:0%
+quite a bit so we're looking at how uh
+ 
+
+ align:start position:0%
+quite a bit so we're looking at how uh
+that Network could be robust to those
+
+ align:start position:0%
+that Network could be robust to those
+ 
+
+ align:start position:0%
+that Network could be robust to those
+kind of changes uh much like the bra is
+
+ align:start position:0%
+kind of changes uh much like the bra is
+ 
+
+ align:start position:0%
+kind of changes uh much like the bra is
+to Everyday stimuli and actions and sees
+
+ align:start position:0%
+to Everyday stimuli and actions and sees
+ 
+
+ align:start position:0%
+to Everyday stimuli and actions and sees
+to start out um just doing a a very
+
+ align:start position:0%
+to start out um just doing a a very
+ 
+
+ align:start position:0%
+to start out um just doing a a very
+simple test uh looking at perturbations
+
+ align:start position:0%
+simple test uh looking at perturbations
+ 
+
+ align:start position:0%
+simple test uh looking at perturbations
+of the network so just throwing random
+
+ align:start position:0%
+of the network so just throwing random
+ 
+
+ align:start position:0%
+of the network so just throwing random
+changes at the weights uh that make up
+
+ align:start position:0%
+changes at the weights uh that make up
+ 
+
+ align:start position:0%
+changes at the weights uh that make up
+this network um and seeing how that
+
+ align:start position:0%
+this network um and seeing how that
+ 
+
+ align:start position:0%
+this network um and seeing how that
+affects its ability to classify images
+
+ align:start position:0%
+affects its ability to classify images
+ 
+
+ align:start position:0%
+affects its ability to classify images
+after that we're looking at how
+
+ align:start position:0%
+after that we're looking at how
+ 
+
+ align:start position:0%
+after that we're looking at how
+different parts of the network respond
+
+ align:start position:0%
+different parts of the network respond
+ 
+
+ align:start position:0%
+different parts of the network respond
+differently to these kind of changes and
+
+ align:start position:0%
+differently to these kind of changes and
+ 
+
+ align:start position:0%
+differently to these kind of changes and
+then ideally we'd like to have some kind
+
+ align:start position:0%
+then ideally we'd like to have some kind
+ 
+
+ align:start position:0%
+then ideally we'd like to have some kind
+of rule that uh doesn't affect the
+
+ align:start position:0%
+of rule that uh doesn't affect the
+ 
+
+ align:start position:0%
+of rule that uh doesn't affect the
+performance of the network that much and
+
+ align:start position:0%
+performance of the network that much and
+ 
+
+ align:start position:0%
+performance of the network that much and
+it's able to maintain its ability to
+
+ align:start position:0%
+it's able to maintain its ability to
+ 
+
+ align:start position:0%
+it's able to maintain its ability to
+classify throughout seeing a number of
+
+ align:start position:0%
+classify throughout seeing a number of
+ 
+
+ align:start position:0%
+classify throughout seeing a number of
+stimuli so we know that the brain has
+
+ align:start position:0%
+stimuli so we know that the brain has
+ 
+
+ align:start position:0%
+stimuli so we know that the brain has
+certain learning rules like tb's rule um
+
+ align:start position:0%
+certain learning rules like tb's rule um
+ 
+
+ align:start position:0%
+certain learning rules like tb's rule um
+in which neurons that fire one after
+
+ align:start position:0%
+in which neurons that fire one after
+ 
+
+ align:start position:0%
+in which neurons that fire one after
+another end up strengthening their
+
+ align:start position:0%
+another end up strengthening their
+ 
+
+ align:start position:0%
+another end up strengthening their
+connections or uh conversely weakening
+
+ align:start position:0%
+connections or uh conversely weakening
+ 
+
+ align:start position:0%
+connections or uh conversely weakening
+their reactions and we're see going to
+
+ align:start position:0%
+their reactions and we're see going to
+ 
+
+ align:start position:0%
+their reactions and we're see going to
+see if rules like that uh end up
+
+ align:start position:0%
+see if rules like that uh end up
+ 
+
+ align:start position:0%
+see if rules like that uh end up
+providing stable perturbations where the
+
+ align:start position:0%
+providing stable perturbations where the
+ 
+
+ align:start position:0%
+providing stable perturbations where the
+network can easily recover um and
+
+ align:start position:0%
+network can easily recover um and
+ 
+
+ align:start position:0%
+network can easily recover um and
+maintain what it's doing or unstable
+
+ align:start position:0%
+maintain what it's doing or unstable
+ 
+
+ align:start position:0%
+maintain what it's doing or unstable
+ones where we're going to go down on
+
+ align:start position:0%
+ones where we're going to go down on
+ 
+
+ align:start position:0%
+ones where we're going to go down on
+track or we know that deep networks act
+
+ align:start position:0%
+track or we know that deep networks act
+ 
+
+ align:start position:0%
+track or we know that deep networks act
+uh similar to how the brain works uh Jim
+
+ align:start position:0%
+uh similar to how the brain works uh Jim
+ 
+
+ align:start position:0%
+uh similar to how the brain works uh Jim
+D Carlo came great gave a great talk
+
+ align:start position:0%
+D Carlo came great gave a great talk
+ 
+
+ align:start position:0%
+D Carlo came great gave a great talk
+about um how the features we see in deep
+
+ align:start position:0%
+about um how the features we see in deep
+ 
+
+ align:start position:0%
+about um how the features we see in deep
+networks are similar to the features in
+
+ align:start position:0%
+networks are similar to the features in
+ 
+
+ align:start position:0%
+networks are similar to the features in
+the brain we know that the brain's
+
+ align:start position:0%
+the brain we know that the brain's
+ 
+
+ align:start position:0%
+the brain we know that the brain's
+constantly undergoing these kind of
+
+ align:start position:0%
+constantly undergoing these kind of
+ 
+
+ align:start position:0%
+constantly undergoing these kind of
+changes so uh it's we're curious
+
+ align:start position:0%
+changes so uh it's we're curious
+ 
+
+ align:start position:0%
+changes so uh it's we're curious
+scientifically to see how these computer
+
+ align:start position:0%
+scientifically to see how these computer
+ 
+
+ align:start position:0%
+scientifically to see how these computer
+models respond um in understanding how
+
+ align:start position:0%
+models respond um in understanding how
+ 
+
+ align:start position:0%
+models respond um in understanding how
+these two systems are the same or
+
+ align:start position:0%
+these two systems are the same or
+ 
+
+ align:start position:0%
+these two systems are the same or
+different uh but also from an
+
+ align:start position:0%
+different uh but also from an
+ 
+
+ align:start position:0%
+different uh but also from an
+engineering context uh online learning
+
+ align:start position:0%
+engineering context uh online learning
+ 
+
+ align:start position:0%
+engineering context uh online learning
+where the network is changing uh while
+
+ align:start position:0%
+where the network is changing uh while
+ 
+
+ align:start position:0%
+where the network is changing uh while
+it's learning is going to be I think a
+
+ align:start position:0%
+it's learning is going to be I think a
+ 
+
+ align:start position:0%
+it's learning is going to be I think a
+much larger part of the use of machine
+
+ align:start position:0%
+much larger part of the use of machine
+ 
+
+ align:start position:0%
+much larger part of the use of machine
+learning going forward so understanding
+
+ align:start position:0%
+learning going forward so understanding
+ 
+
+ align:start position:0%
+learning going forward so understanding
+how stable these things are uh to
+
+ align:start position:0%
+how stable these things are uh to
+ 
+
+ align:start position:0%
+how stable these things are uh to
+constantly changing parameters I think
+
+ align:start position:0%
+constantly changing parameters I think
+ 
+
+ align:start position:0%
+constantly changing parameters I think
+will be quite informative for those kind
+
+ align:start position:0%
+will be quite informative for those kind
+ 
+
+ align:start position:0%
+will be quite informative for those kind
+of studies being able to
+
+ align:start position:0%
+of studies being able to
+ 
+
+ align:start position:0%
+of studies being able to
+explore uh new types of M materials and
+
+ align:start position:0%
+explore uh new types of M materials and
+ 
+
+ align:start position:0%
+explore uh new types of M materials and
+uh learn a lot about both computer
+
+ align:start position:0%
+uh learn a lot about both computer
+ 
+
+ align:start position:0%
+uh learn a lot about both computer
+vision and Neuroscience has been a lot
+
+ align:start position:0%
+vision and Neuroscience has been a lot
+ 
+
+ align:start position:0%
+vision and Neuroscience has been a lot
+of fun um and certainly informative deep
+
+ align:start position:0%
+of fun um and certainly informative deep
+ 
+
+ align:start position:0%
+of fun um and certainly informative deep
+learning is is a very hot topic right
+
+ align:start position:0%
+learning is is a very hot topic right
+ 
+
+ align:start position:0%
+learning is is a very hot topic right
+now so being able to dive hands in a
+
+ align:start position:0%
+now so being able to dive hands in a
+ 
+
+ align:start position:0%
+now so being able to dive hands in a
+little bit um and get some experience
+
+ align:start position:0%
+little bit um and get some experience
+ 
+
+ align:start position:0%
+little bit um and get some experience
+working with these models and some of
+
+ align:start position:0%
+working with these models and some of
+ 
+
+ align:start position:0%
+working with these models and some of
+the the latest uh software packages I
+
+ align:start position:0%
+the the latest uh software packages I
+ 
+
+ align:start position:0%
+the the latest uh software packages I
+think will be useful going forwards too
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Music]
\ No newline at end of file
diff --git a/bAkuNXtgrLA.txt b/bAkuNXtgrLA.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5598e2f7413d14cd914c2fa5d24ee68f94a37378
--- /dev/null
+++ b/bAkuNXtgrLA.txt
@@ -0,0 +1,11619 @@
+align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+seeing where animals are going so you
+
+ align:start position:0%
+seeing where animals are going so you
+ 
+
+ align:start position:0%
+seeing where animals are going so you
+can avoid them if they're coming after
+
+ align:start position:0%
+can avoid them if they're coming after
+ 
+
+ align:start position:0%
+can avoid them if they're coming after
+you or if you can catch them if you're
+
+ align:start position:0%
+you or if you can catch them if you're
+ 
+
+ align:start position:0%
+you or if you can catch them if you're
+going after them right one of the
+
+ align:start position:0%
+going after them right one of the
+ 
+
+ align:start position:0%
+going after them right one of the
+arguably
+
+ align:start position:0%
+arguably
+ 
+
+ align:start position:0%
+arguably
+uniquely human abilities is precision
+
+ align:start position:0%
+uniquely human abilities is precision
+ 
+
+ align:start position:0%
+uniquely human abilities is precision
+throwing right no other animal can do
+
+ align:start position:0%
+throwing right no other animal can do
+ 
+
+ align:start position:0%
+throwing right no other animal can do
+that that's a very human thing
+
+ align:start position:0%
+that that's a very human thing
+ 
+
+ align:start position:0%
+that that's a very human thing
+although visual motion is shared with
+
+ align:start position:0%
+although visual motion is shared with
+ 
+
+ align:start position:0%
+although visual motion is shared with
+lots of ability to see motion is shared
+
+ align:start position:0%
+lots of ability to see motion is shared
+ 
+
+ align:start position:0%
+lots of ability to see motion is shared
+with lots of animals what else did you
+
+ align:start position:0%
+with lots of animals what else did you
+ 
+
+ align:start position:0%
+with lots of animals what else did you
+notice
+
+ align:start position:0%
+notice
+ 
+
+ align:start position:0%
+notice
+what else seemed funny or or
+
+ align:start position:0%
+what else seemed funny or or
+ 
+
+ align:start position:0%
+what else seemed funny or or
+you know harder to discern with stop
+
+ align:start position:0%
+you know harder to discern with stop
+ 
+
+ align:start position:0%
+you know harder to discern with stop
+motion yeah
+
+ align:start position:0%
+motion yeah
+ 
+
+ align:start position:0%
+motion yeah
+we care about small details like the
+
+ align:start position:0%
+we care about small details like the
+ 
+
+ align:start position:0%
+we care about small details like the
+movement to
+
+ align:start position:0%
+movement to
+ 
+
+ align:start position:0%
+movement to
+understand what your person is saying
+
+ align:start position:0%
+understand what your person is saying
+ 
+
+ align:start position:0%
+understand what your person is saying
+yeah yeah so
+
+ align:start position:0%
+yeah yeah so
+ 
+
+ align:start position:0%
+yeah yeah so
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+i was making notes to self i haven't
+
+ align:start position:0%
+i was making notes to self i haven't
+ 
+
+ align:start position:0%
+i was making notes to self i haven't
+done that demo before but in future it
+
+ align:start position:0%
+done that demo before but in future it
+ 
+
+ align:start position:0%
+done that demo before but in future it
+would be really good to have the audio
+
+ align:start position:0%
+would be really good to have the audio
+ 
+
+ align:start position:0%
+would be really good to have the audio
+quality terrible because if the audio
+
+ align:start position:0%
+quality terrible because if the audio
+ 
+
+ align:start position:0%
+quality terrible because if the audio
+quality is terrible you would lean more
+
+ align:start position:0%
+quality is terrible you would lean more
+ 
+
+ align:start position:0%
+quality is terrible you would lean more
+on lip reading and we might have noticed
+
+ align:start position:0%
+on lip reading and we might have noticed
+ 
+
+ align:start position:0%
+on lip reading and we might have noticed
+more that it's really hard to do that
+
+ align:start position:0%
+more that it's really hard to do that
+ 
+
+ align:start position:0%
+more that it's really hard to do that
+probably even at relatively fast flicker
+
+ align:start position:0%
+probably even at relatively fast flicker
+ 
+
+ align:start position:0%
+probably even at relatively fast flicker
+rates because that motion information is
+
+ align:start position:0%
+rates because that motion information is
+ 
+
+ align:start position:0%
+rates because that motion information is
+important absolutely what else
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how about beyond just lip reading what
+
+ align:start position:0%
+how about beyond just lip reading what
+ 
+
+ align:start position:0%
+how about beyond just lip reading what
+else did you notice about the faces mine
+
+ align:start position:0%
+else did you notice about the faces mine
+ 
+
+ align:start position:0%
+else did you notice about the faces mine
+or gems
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+could you yeah they were static so it
+
+ align:start position:0%
+could you yeah they were static so it
+ 
+
+ align:start position:0%
+could you yeah they were static so it
+was kind of hard to tell like emotion
+
+ align:start position:0%
+was kind of hard to tell like emotion
+ 
+
+ align:start position:0%
+was kind of hard to tell like emotion
+because like a lot of our um the ways we
+
+ align:start position:0%
+because like a lot of our um the ways we
+ 
+
+ align:start position:0%
+because like a lot of our um the ways we
+express emotion is very nuanced exactly
+
+ align:start position:0%
+express emotion is very nuanced exactly
+ 
+
+ align:start position:0%
+express emotion is very nuanced exactly
+exactly facial expressions are
+
+ align:start position:0%
+exactly facial expressions are
+ 
+
+ align:start position:0%
+exactly facial expressions are
+incredibly subtle like little micro
+
+ align:start position:0%
+incredibly subtle like little micro
+ 
+
+ align:start position:0%
+incredibly subtle like little micro
+expressions flicker across the face in a
+
+ align:start position:0%
+expressions flicker across the face in a
+ 
+
+ align:start position:0%
+expressions flicker across the face in a
+tenth of a second and go away and you
+
+ align:start position:0%
+tenth of a second and go away and you
+ 
+
+ align:start position:0%
+tenth of a second and go away and you
+guys detect them like we're we're very
+
+ align:start position:0%
+guys detect them like we're we're very
+ 
+
+ align:start position:0%
+guys detect them like we're we're very
+very sensitive to those things you know
+
+ align:start position:0%
+very sensitive to those things you know
+ 
+
+ align:start position:0%
+very sensitive to those things you know
+if somebody you know sometimes if you
+
+ align:start position:0%
+if somebody you know sometimes if you
+ 
+
+ align:start position:0%
+if somebody you know sometimes if you
+see somebody in a hallway and
+
+ align:start position:0%
+see somebody in a hallway and
+ 
+
+ align:start position:0%
+see somebody in a hallway and
+for a moment there's an expression that
+
+ align:start position:0%
+for a moment there's an expression that
+ 
+
+ align:start position:0%
+for a moment there's an expression that
+flickers across their face and then they
+
+ align:start position:0%
+flickers across their face and then they
+ 
+
+ align:start position:0%
+flickers across their face and then they
+give you like a normal smile but you can
+
+ align:start position:0%
+give you like a normal smile but you can
+ 
+
+ align:start position:0%
+give you like a normal smile but you can
+tell from that expression that actually
+
+ align:start position:0%
+tell from that expression that actually
+ 
+
+ align:start position:0%
+tell from that expression that actually
+they didn't want to see you for whatever
+
+ align:start position:0%
+they didn't want to see you for whatever
+ 
+
+ align:start position:0%
+they didn't want to see you for whatever
+reason right we catch those things we're
+
+ align:start position:0%
+reason right we catch those things we're
+ 
+
+ align:start position:0%
+reason right we catch those things we're
+really really good at catching those
+
+ align:start position:0%
+really really good at catching those
+ 
+
+ align:start position:0%
+really really good at catching those
+little fleeting expressions and those
+
+ align:start position:0%
+little fleeting expressions and those
+ 
+
+ align:start position:0%
+little fleeting expressions and those
+probably have to do with not just
+
+ align:start position:0%
+probably have to do with not just
+ 
+
+ align:start position:0%
+probably have to do with not just
+sampling with fine temporal frequency
+
+ align:start position:0%
+sampling with fine temporal frequency
+ 
+
+ align:start position:0%
+sampling with fine temporal frequency
+but probably seeing the direction of
+
+ align:start position:0%
+but probably seeing the direction of
+ 
+
+ align:start position:0%
+but probably seeing the direction of
+motion of each little part of the face
+
+ align:start position:0%
+motion of each little part of the face
+ 
+
+ align:start position:0%
+motion of each little part of the face
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+okay so this is just common sense
+
+ align:start position:0%
+okay so this is just common sense
+ 
+
+ align:start position:0%
+okay so this is just common sense
+reasoning about what we might have
+
+ align:start position:0%
+reasoning about what we might have
+ 
+
+ align:start position:0%
+reasoning about what we might have
+motion for okay and so you guys got all
+
+ align:start position:0%
+motion for okay and so you guys got all
+ 
+
+ align:start position:0%
+motion for okay and so you guys got all
+the things that i had in mind okay so
+
+ align:start position:0%
+the things that i had in mind okay so
+ 
+
+ align:start position:0%
+the things that i had in mind okay so
+now next question just kind of thought a
+
+ align:start position:0%
+now next question just kind of thought a
+ 
+
+ align:start position:0%
+now next question just kind of thought a
+thought question speculation question
+
+ align:start position:0%
+thought question speculation question
+ 
+
+ align:start position:0%
+thought question speculation question
+given the these many different things
+
+ align:start position:0%
+given the these many different things
+ 
+
+ align:start position:0%
+given the these many different things
+that make motion important to us uh
+
+ align:start position:0%
+that make motion important to us uh
+ 
+
+ align:start position:0%
+that make motion important to us uh
+biologically ecologically in our daily
+
+ align:start position:0%
+biologically ecologically in our daily
+ 
+
+ align:start position:0%
+biologically ecologically in our daily
+lives
+
+ align:start position:0%
+lives
+ 
+
+ align:start position:0%
+lives
+maybe that's important enough that we
+
+ align:start position:0%
+maybe that's important enough that we
+ 
+
+ align:start position:0%
+maybe that's important enough that we
+might allocate special brain machinery
+
+ align:start position:0%
+might allocate special brain machinery
+ 
+
+ align:start position:0%
+might allocate special brain machinery
+to processing motion
+
+ align:start position:0%
+to processing motion
+ 
+
+ align:start position:0%
+to processing motion
+what do you think
+
+ align:start position:0%
+what do you think
+ 
+
+ align:start position:0%
+what do you think
+important enough could you get by if you
+
+ align:start position:0%
+important enough could you get by if you
+ 
+
+ align:start position:0%
+important enough could you get by if you
+lived in a strobe world all the time
+
+ align:start position:0%
+lived in a strobe world all the time
+ 
+
+ align:start position:0%
+lived in a strobe world all the time
+could you survive just fine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+hard to say right might be hard i mean
+
+ align:start position:0%
+hard to say right might be hard i mean
+ 
+
+ align:start position:0%
+hard to say right might be hard i mean
+we probably don't need to go hunting
+
+ align:start position:0%
+we probably don't need to go hunting
+ 
+
+ align:start position:0%
+we probably don't need to go hunting
+down predators but um you know you walk
+
+ align:start position:0%
+down predators but um you know you walk
+ 
+
+ align:start position:0%
+down predators but um you know you walk
+across vassar street and there's some
+
+ align:start position:0%
+across vassar street and there's some
+ 
+
+ align:start position:0%
+across vassar street and there's some
+pretty dangerous predators coming down
+
+ align:start position:0%
+pretty dangerous predators coming down
+ 
+
+ align:start position:0%
+pretty dangerous predators coming down
+vassar street in the way of cars right
+
+ align:start position:0%
+vassar street in the way of cars right
+ 
+
+ align:start position:0%
+vassar street in the way of cars right
+you need to know where they're going and
+
+ align:start position:0%
+you need to know where they're going and
+ 
+
+ align:start position:0%
+you need to know where they're going and
+whether you can cross in front of them
+
+ align:start position:0%
+whether you can cross in front of them
+ 
+
+ align:start position:0%
+whether you can cross in front of them
+so it's actually pretty hard
+
+ align:start position:0%
+so it's actually pretty hard
+ 
+
+ align:start position:0%
+so it's actually pretty hard
+to live life without being able to see
+
+ align:start position:0%
+to live life without being able to see
+ 
+
+ align:start position:0%
+to live life without being able to see
+motion and i'll tell you about a woman
+
+ align:start position:0%
+motion and i'll tell you about a woman
+ 
+
+ align:start position:0%
+motion and i'll tell you about a woman
+who has that experience later in the
+
+ align:start position:0%
+who has that experience later in the
+ 
+
+ align:start position:0%
+who has that experience later in the
+lecture
+
+ align:start position:0%
+lecture
+ 
+
+ align:start position:0%
+lecture
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+next question
+
+ align:start position:0%
+next question
+ 
+
+ align:start position:0%
+next question
+just think about this i'm not going to
+
+ align:start position:0%
+just think about this i'm not going to
+ 
+
+ align:start position:0%
+just think about this i'm not going to
+test you on it or anything it's not the
+
+ align:start position:0%
+test you on it or anything it's not the
+ 
+
+ align:start position:0%
+test you on it or anything it's not the
+topic of this course but it's a
+
+ align:start position:0%
+topic of this course but it's a
+ 
+
+ align:start position:0%
+topic of this course but it's a
+perspective you should take imagine
+
+ align:start position:0%
+perspective you should take imagine
+ 
+
+ align:start position:0%
+perspective you should take imagine
+that this were a cs course and i gave
+
+ align:start position:0%
+that this were a cs course and i gave
+ 
+
+ align:start position:0%
+that this were a cs course and i gave
+you a segment of video
+
+ align:start position:0%
+you a segment of video
+ 
+
+ align:start position:0%
+you a segment of video
+and your task was to take some to write
+
+ align:start position:0%
+and your task was to take some to write
+ 
+
+ align:start position:0%
+and your task was to take some to write
+some code that takes that video input
+
+ align:start position:0%
+some code that takes that video input
+ 
+
+ align:start position:0%
+some code that takes that video input
+and says whether objects are moving in
+
+ align:start position:0%
+and says whether objects are moving in
+ 
+
+ align:start position:0%
+and says whether objects are moving in
+that movie or says which objects are
+
+ align:start position:0%
+that movie or says which objects are
+ 
+
+ align:start position:0%
+that movie or says which objects are
+moving or how much they're moving or
+
+ align:start position:0%
+moving or how much they're moving or
+ 
+
+ align:start position:0%
+moving or how much they're moving or
+what direction they're moving what kind
+
+ align:start position:0%
+what direction they're moving what kind
+ 
+
+ align:start position:0%
+what direction they're moving what kind
+of code would you have to write to take
+
+ align:start position:0%
+of code would you have to write to take
+ 
+
+ align:start position:0%
+of code would you have to write to take
+that video input to try to figure that
+
+ align:start position:0%
+that video input to try to figure that
+ 
+
+ align:start position:0%
+that video input to try to figure that
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay so just think about that we're not
+
+ align:start position:0%
+okay so just think about that we're not
+ 
+
+ align:start position:0%
+okay so just think about that we're not
+going to be writing code in this class
+
+ align:start position:0%
+going to be writing code in this class
+ 
+
+ align:start position:0%
+going to be writing code in this class
+but a lot of what we're going to be
+
+ align:start position:0%
+but a lot of what we're going to be
+ 
+
+ align:start position:0%
+but a lot of what we're going to be
+doing is thinking about
+
+ align:start position:0%
+doing is thinking about
+ 
+
+ align:start position:0%
+doing is thinking about
+how do you
+
+ align:start position:0%
+how do you
+ 
+
+ align:start position:0%
+how do you
+take this kind of perceptual input and
+
+ align:start position:0%
+take this kind of perceptual input and
+ 
+
+ align:start position:0%
+take this kind of perceptual input and
+come out with that kind of perceptual
+
+ align:start position:0%
+come out with that kind of perceptual
+ 
+
+ align:start position:0%
+come out with that kind of perceptual
+inference
+
+ align:start position:0%
+inference
+ 
+
+ align:start position:0%
+inference
+and what kinds of computations would
+
+ align:start position:0%
+and what kinds of computations would
+ 
+
+ align:start position:0%
+and what kinds of computations would
+have to go on in between
+
+ align:start position:0%
+have to go on in between
+ 
+
+ align:start position:0%
+have to go on in between
+whether those computations are going on
+
+ align:start position:0%
+whether those computations are going on
+ 
+
+ align:start position:0%
+whether those computations are going on
+in code that you guys write or in a
+
+ align:start position:0%
+in code that you guys write or in a
+ 
+
+ align:start position:0%
+in code that you guys write or in a
+piece of brain that's doing that
+
+ align:start position:0%
+piece of brain that's doing that
+ 
+
+ align:start position:0%
+piece of brain that's doing that
+computation
+
+ align:start position:0%
+computation
+ 
+
+ align:start position:0%
+computation
+and thinking about how you might might
+
+ align:start position:0%
+and thinking about how you might might
+ 
+
+ align:start position:0%
+and thinking about how you might might
+write the code gives you really
+
+ align:start position:0%
+write the code gives you really
+ 
+
+ align:start position:0%
+write the code gives you really
+important insights about what the brain
+
+ align:start position:0%
+important insights about what the brain
+ 
+
+ align:start position:0%
+important insights about what the brain
+might be doing okay
+
+ align:start position:0%
+might be doing okay
+ 
+
+ align:start position:0%
+might be doing okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so that's the point of all of that the
+
+ align:start position:0%
+so that's the point of all of that the
+ 
+
+ align:start position:0%
+so that's the point of all of that the
+the mar reading talks about all of this
+
+ align:start position:0%
+the mar reading talks about all of this
+ 
+
+ align:start position:0%
+the mar reading talks about all of this
+and the key point we're trying to get
+
+ align:start position:0%
+and the key point we're trying to get
+ 
+
+ align:start position:0%
+and the key point we're trying to get
+here is that you can't understand
+
+ align:start position:0%
+here is that you can't understand
+ 
+
+ align:start position:0%
+here is that you can't understand
+perception
+
+ align:start position:0%
+perception
+ 
+
+ align:start position:0%
+perception
+without thinking about what each
+
+ align:start position:0%
+without thinking about what each
+ 
+
+ align:start position:0%
+without thinking about what each
+perceptual inference is necessary for
+
+ align:start position:0%
+perceptual inference is necessary for
+ 
+
+ align:start position:0%
+perceptual inference is necessary for
+ecologically in daily lives
+
+ align:start position:0%
+ecologically in daily lives
+ 
+
+ align:start position:0%
+ecologically in daily lives
+and about the computational challenges
+
+ align:start position:0%
+and about the computational challenges
+ 
+
+ align:start position:0%
+and about the computational challenges
+involved in making that inference okay
+
+ align:start position:0%
+involved in making that inference okay
+ 
+
+ align:start position:0%
+involved in making that inference okay
+so we'll get back to all that
+
+ align:start position:0%
+so we'll get back to all that
+ 
+
+ align:start position:0%
+so we'll get back to all that
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+next week and beyond but meanwhile
+
+ align:start position:0%
+next week and beyond but meanwhile
+ 
+
+ align:start position:0%
+next week and beyond but meanwhile
+here's the agenda for today so here's
+
+ align:start position:0%
+here's the agenda for today so here's
+ 
+
+ align:start position:0%
+here's the agenda for today so here's
+the agenda we just did the demo we're
+
+ align:start position:0%
+the agenda we just did the demo we're
+ 
+
+ align:start position:0%
+the agenda we just did the demo we're
+now going to skip and do some
+
+ align:start position:0%
+now going to skip and do some
+ 
+
+ align:start position:0%
+now going to skip and do some
+neuroanatomy absolutely bear basics
+
+ align:start position:0%
+neuroanatomy absolutely bear basics
+ 
+
+ align:start position:0%
+neuroanatomy absolutely bear basics
+because on wednesday we have this
+
+ align:start position:0%
+because on wednesday we have this
+ 
+
+ align:start position:0%
+because on wednesday we have this
+amazing opportunity to have one of the
+
+ align:start position:0%
+amazing opportunity to have one of the
+ 
+
+ align:start position:0%
+amazing opportunity to have one of the
+most kind of famous neuroscientists in
+
+ align:start position:0%
+most kind of famous neuroscientists in
+ 
+
+ align:start position:0%
+most kind of famous neuroscientists in
+the world do a dissection of a real
+
+ align:start position:0%
+the world do a dissection of a real
+ 
+
+ align:start position:0%
+the world do a dissection of a real
+human brain right here right in front of
+
+ align:start position:0%
+human brain right here right in front of
+ 
+
+ align:start position:0%
+human brain right here right in front of
+you it's going to be awesome
+
+ align:start position:0%
+you it's going to be awesome
+ 
+
+ align:start position:0%
+you it's going to be awesome
+and i don't want to
+
+ align:start position:0%
+and i don't want to
+ 
+
+ align:start position:0%
+and i don't want to
+waste that opportunity
+
+ align:start position:0%
+waste that opportunity
+ 
+
+ align:start position:0%
+waste that opportunity
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+embarrass ourselves by having people not
+
+ align:start position:0%
+embarrass ourselves by having people not
+ 
+
+ align:start position:0%
+embarrass ourselves by having people not
+know the bare basics so we're going to
+
+ align:start position:0%
+know the bare basics so we're going to
+ 
+
+ align:start position:0%
+know the bare basics so we're going to
+do the bare basics it's all stuff you
+
+ align:start position:0%
+do the bare basics it's all stuff you
+ 
+
+ align:start position:0%
+do the bare basics it's all stuff you
+should know from 900 and 901 and i'm
+
+ align:start position:0%
+should know from 900 and 901 and i'm
+ 
+
+ align:start position:0%
+should know from 900 and 901 and i'm
+going to whip through it fast so we can
+
+ align:start position:0%
+going to whip through it fast so we can
+ 
+
+ align:start position:0%
+going to whip through it fast so we can
+get to more interesting stuff and get
+
+ align:start position:0%
+get to more interesting stuff and get
+ 
+
+ align:start position:0%
+get to more interesting stuff and get
+back to visual motion okay
+
+ align:start position:0%
+back to visual motion okay
+ 
+
+ align:start position:0%
+back to visual motion okay
+that's the agenda
+
+ align:start position:0%
+that's the agenda
+ 
+
+ align:start position:0%
+that's the agenda
+all right so some absolute bare basics
+
+ align:start position:0%
+all right so some absolute bare basics
+ 
+
+ align:start position:0%
+all right so some absolute bare basics
+of the brain
+
+ align:start position:0%
+of the brain
+ 
+
+ align:start position:0%
+of the brain
+the human brain contains about 100
+
+ align:start position:0%
+the human brain contains about 100
+ 
+
+ align:start position:0%
+the human brain contains about 100
+billion 10 to the 11th neurons and
+
+ align:start position:0%
+billion 10 to the 11th neurons and
+ 
+
+ align:start position:0%
+billion 10 to the 11th neurons and
+that's a very big number that's such a
+
+ align:start position:0%
+that's a very big number that's such a
+ 
+
+ align:start position:0%
+that's a very big number that's such a
+big number it's approximately jeff bezos
+
+ align:start position:0%
+big number it's approximately jeff bezos
+ 
+
+ align:start position:0%
+big number it's approximately jeff bezos
+is worth well it was until mackenzie got
+
+ align:start position:0%
+is worth well it was until mackenzie got
+ 
+
+ align:start position:0%
+is worth well it was until mackenzie got
+into the picture so we'll see
+
+ align:start position:0%
+into the picture so we'll see
+ 
+
+ align:start position:0%
+into the picture so we'll see
+no you don't need to remember this
+
+ align:start position:0%
+no you don't need to remember this
+ 
+
+ align:start position:0%
+no you don't need to remember this
+number just know it's a really big
+
+ align:start position:0%
+number just know it's a really big
+ 
+
+ align:start position:0%
+number just know it's a really big
+number
+
+ align:start position:0%
+number
+ 
+
+ align:start position:0%
+number
+basics of a neuron here's a neuron a
+
+ align:start position:0%
+basics of a neuron here's a neuron a
+ 
+
+ align:start position:0%
+basics of a neuron here's a neuron a
+neuron is a cell like any other cell in
+
+ align:start position:0%
+neuron is a cell like any other cell in
+ 
+
+ align:start position:0%
+neuron is a cell like any other cell in
+the body it's got a cell body and a
+
+ align:start position:0%
+the body it's got a cell body and a
+ 
+
+ align:start position:0%
+the body it's got a cell body and a
+nucleus just like any other cell in your
+
+ align:start position:0%
+nucleus just like any other cell in your
+ 
+
+ align:start position:0%
+nucleus just like any other cell in your
+body but the thing that's distinctive
+
+ align:start position:0%
+body but the thing that's distinctive
+ 
+
+ align:start position:0%
+body but the thing that's distinctive
+about a neuron is has a big long process
+
+ align:start position:0%
+about a neuron is has a big long process
+ 
+
+ align:start position:0%
+about a neuron is has a big long process
+called an axon it's got a bunch of
+
+ align:start position:0%
+called an axon it's got a bunch of
+ 
+
+ align:start position:0%
+called an axon it's got a bunch of
+dendrites the little processes little
+
+ align:start position:0%
+dendrites the little processes little
+ 
+
+ align:start position:0%
+dendrites the little processes little
+thingies
+
+ align:start position:0%
+thingies
+ 
+
+ align:start position:0%
+thingies
+near the cell body and out at the tip of
+
+ align:start position:0%
+near the cell body and out at the tip of
+ 
+
+ align:start position:0%
+near the cell body and out at the tip of
+the axon
+
+ align:start position:0%
+the axon
+ 
+
+ align:start position:0%
+the axon
+that's your classic neuron many neurons
+
+ align:start position:0%
+that's your classic neuron many neurons
+ 
+
+ align:start position:0%
+that's your classic neuron many neurons
+have a myelin sheath a layer of rolled
+
+ align:start position:0%
+have a myelin sheath a layer of rolled
+ 
+
+ align:start position:0%
+have a myelin sheath a layer of rolled
+up fat around the axon
+
+ align:start position:0%
+up fat around the axon
+ 
+
+ align:start position:0%
+up fat around the axon
+made up of other cells that makes axon
+
+ align:start position:0%
+made up of other cells that makes axon
+ 
+
+ align:start position:0%
+made up of other cells that makes axon
+conduct neural signals faster okay you
+
+ align:start position:0%
+conduct neural signals faster okay you
+ 
+
+ align:start position:0%
+conduct neural signals faster okay you
+should know all that i'm not trying to
+
+ align:start position:0%
+should know all that i'm not trying to
+ 
+
+ align:start position:0%
+should know all that i'm not trying to
+insult your intelligence i'm just trying
+
+ align:start position:0%
+insult your intelligence i'm just trying
+ 
+
+ align:start position:0%
+insult your intelligence i'm just trying
+to make sure everybody's with the
+
+ align:start position:0%
+to make sure everybody's with the
+ 
+
+ align:start position:0%
+to make sure everybody's with the
+program here okay so you have thousands
+
+ align:start position:0%
+program here okay so you have thousands
+ 
+
+ align:start position:0%
+program here okay so you have thousands
+of synapses on each neuron and that
+
+ align:start position:0%
+of synapses on each neuron and that
+ 
+
+ align:start position:0%
+of synapses on each neuron and that
+means you have to put a technically a
+
+ align:start position:0%
+means you have to put a technically a
+ 
+
+ align:start position:0%
+means you have to put a technically a
+shitload of synapses in your brain okay
+
+ align:start position:0%
+shitload of synapses in your brain okay
+ 
+
+ align:start position:0%
+shitload of synapses in your brain okay
+another important point um the brain
+
+ align:start position:0%
+another important point um the brain
+ 
+
+ align:start position:0%
+another important point um the brain
+runs on a mere 20 watts and if you're
+
+ align:start position:0%
+runs on a mere 20 watts and if you're
+ 
+
+ align:start position:0%
+runs on a mere 20 watts and if you're
+not impressed with that
+
+ align:start position:0%
+not impressed with that
+ 
+
+ align:start position:0%
+not impressed with that
+reflect on the fact that ibm's watson
+
+ align:start position:0%
+reflect on the fact that ibm's watson
+ 
+
+ align:start position:0%
+reflect on the fact that ibm's watson
+runs on 20 000 watts so one of the cool
+
+ align:start position:0%
+runs on 20 000 watts so one of the cool
+ 
+
+ align:start position:0%
+runs on 20 000 watts so one of the cool
+things about the human brain is not just
+
+ align:start position:0%
+things about the human brain is not just
+ 
+
+ align:start position:0%
+things about the human brain is not just
+all the awesome stuff that we can do
+
+ align:start position:0%
+all the awesome stuff that we can do
+ 
+
+ align:start position:0%
+all the awesome stuff that we can do
+that still no computer can do that i
+
+ align:start position:0%
+that still no computer can do that i
+ 
+
+ align:start position:0%
+that still no computer can do that i
+talked about last time but also how
+
+ align:start position:0%
+talked about last time but also how
+ 
+
+ align:start position:0%
+talked about last time but also how
+incredibly energetically efficiently we
+
+ align:start position:0%
+incredibly energetically efficiently we
+ 
+
+ align:start position:0%
+incredibly energetically efficiently we
+do it with our human brains
+
+ align:start position:0%
+do it with our human brains
+ 
+
+ align:start position:0%
+do it with our human brains
+so most of this course is going to talk
+
+ align:start position:0%
+so most of this course is going to talk
+ 
+
+ align:start position:0%
+so most of this course is going to talk
+about the cortex that's all the stuff on
+
+ align:start position:0%
+about the cortex that's all the stuff on
+ 
+
+ align:start position:0%
+about the cortex that's all the stuff on
+the outside of the brain it's a sheet
+
+ align:start position:0%
+the outside of the brain it's a sheet
+ 
+
+ align:start position:0%
+the outside of the brain it's a sheet
+wrapping around the outside of the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that folded outer surface
+
+ align:start position:0%
+that folded outer surface
+ 
+
+ align:start position:0%
+that folded outer surface
+it's approx approximately the size and
+
+ align:start position:0%
+it's approx approximately the size and
+ 
+
+ align:start position:0%
+it's approx approximately the size and
+area of a large pizza
+
+ align:start position:0%
+area of a large pizza
+ 
+
+ align:start position:0%
+area of a large pizza
+but there are lots of other important
+
+ align:start position:0%
+but there are lots of other important
+ 
+
+ align:start position:0%
+but there are lots of other important
+bits too and i'm going to just do
+
+ align:start position:0%
+bits too and i'm going to just do
+ 
+
+ align:start position:0%
+bits too and i'm going to just do
+whirlwind tour of those other bits
+
+ align:start position:0%
+whirlwind tour of those other bits
+ 
+
+ align:start position:0%
+whirlwind tour of those other bits
+now okay so you can think of the brain
+
+ align:start position:0%
+now okay so you can think of the brain
+ 
+
+ align:start position:0%
+now okay so you can think of the brain
+as composed of four major kinds of
+
+ align:start position:0%
+as composed of four major kinds of
+ 
+
+ align:start position:0%
+as composed of four major kinds of
+components
+
+ align:start position:0%
+components
+ 
+
+ align:start position:0%
+components
+deep down in the bottom of the brain you
+
+ align:start position:0%
+deep down in the bottom of the brain you
+ 
+
+ align:start position:0%
+deep down in the bottom of the brain you
+have the brain stem where the spinal
+
+ align:start position:0%
+have the brain stem where the spinal
+ 
+
+ align:start position:0%
+have the brain stem where the spinal
+cord comes in here and the rest of the
+
+ align:start position:0%
+cord comes in here and the rest of the
+ 
+
+ align:start position:0%
+cord comes in here and the rest of the
+brain is up there and the brain stem is
+
+ align:start position:0%
+brain is up there and the brain stem is
+ 
+
+ align:start position:0%
+brain is up there and the brain stem is
+right down here and the cerebellum this
+
+ align:start position:0%
+right down here and the cerebellum this
+ 
+
+ align:start position:0%
+right down here and the cerebellum this
+little cauliflower-like thing that sits
+
+ align:start position:0%
+little cauliflower-like thing that sits
+ 
+
+ align:start position:0%
+little cauliflower-like thing that sits
+out right back there
+
+ align:start position:0%
+out right back there
+ 
+
+ align:start position:0%
+out right back there
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+in the middle of the brain you have the
+
+ align:start position:0%
+in the middle of the brain you have the
+ 
+
+ align:start position:0%
+in the middle of the brain you have the
+limbic system with a whole bunch of
+
+ align:start position:0%
+limbic system with a whole bunch of
+ 
+
+ align:start position:0%
+limbic system with a whole bunch of
+subcortical regions and we'll talk about
+
+ align:start position:0%
+subcortical regions and we'll talk about
+ 
+
+ align:start position:0%
+subcortical regions and we'll talk about
+a few of those in a moment
+
+ align:start position:0%
+a few of those in a moment
+ 
+
+ align:start position:0%
+a few of those in a moment
+and you have white matter all the cables
+
+ align:start position:0%
+and you have white matter all the cables
+ 
+
+ align:start position:0%
+and you have white matter all the cables
+and connections that go from one part of
+
+ align:start position:0%
+and connections that go from one part of
+ 
+
+ align:start position:0%
+and connections that go from one part of
+the brain to another part this is an
+
+ align:start position:0%
+the brain to another part this is an
+ 
+
+ align:start position:0%
+the brain to another part this is an
+actual dissected human brain and all
+
+ align:start position:0%
+actual dissected human brain and all
+ 
+
+ align:start position:0%
+actual dissected human brain and all
+those kind of weird fibrous things are
+
+ align:start position:0%
+those kind of weird fibrous things are
+ 
+
+ align:start position:0%
+those kind of weird fibrous things are
+bundles of axons connecting remote parts
+
+ align:start position:0%
+bundles of axons connecting remote parts
+ 
+
+ align:start position:0%
+bundles of axons connecting remote parts
+of the brain to each other you can see
+
+ align:start position:0%
+of the brain to each other you can see
+ 
+
+ align:start position:0%
+of the brain to each other you can see
+them in gross dissection okay
+
+ align:start position:0%
+them in gross dissection okay
+ 
+
+ align:start position:0%
+them in gross dissection okay
+and of course you have the cortex okay
+
+ align:start position:0%
+and of course you have the cortex okay
+ 
+
+ align:start position:0%
+and of course you have the cortex okay
+so these are just four major things to
+
+ align:start position:0%
+so these are just four major things to
+ 
+
+ align:start position:0%
+so these are just four major things to
+think about and before we spend the rest
+
+ align:start position:0%
+think about and before we spend the rest
+ 
+
+ align:start position:0%
+think about and before we spend the rest
+of the course on that we're going to do
+
+ align:start position:0%
+of the course on that we're going to do
+ 
+
+ align:start position:0%
+of the course on that we're going to do
+just a teeny little bit on the other
+
+ align:start position:0%
+just a teeny little bit on the other
+ 
+
+ align:start position:0%
+just a teeny little bit on the other
+major bits
+
+ align:start position:0%
+major bits
+ 
+
+ align:start position:0%
+major bits
+okay and i'm going fast so just stop me
+
+ align:start position:0%
+okay and i'm going fast so just stop me
+ 
+
+ align:start position:0%
+okay and i'm going fast so just stop me
+if any of this isn't clear
+
+ align:start position:0%
+if any of this isn't clear
+ 
+
+ align:start position:0%
+if any of this isn't clear
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+so the reason we're doing this in part
+
+ align:start position:0%
+so the reason we're doing this in part
+ 
+
+ align:start position:0%
+so the reason we're doing this in part
+is that with a dissection of a brain
+
+ align:start position:0%
+is that with a dissection of a brain
+ 
+
+ align:start position:0%
+is that with a dissection of a brain
+some of the main things you see are
+
+ align:start position:0%
+some of the main things you see are
+ 
+
+ align:start position:0%
+some of the main things you see are
+those subcortical structures right and
+
+ align:start position:0%
+those subcortical structures right and
+ 
+
+ align:start position:0%
+those subcortical structures right and
+so even though the course is going to
+
+ align:start position:0%
+so even though the course is going to
+ 
+
+ align:start position:0%
+so even though the course is going to
+focus on the cortex each little
+
+ align:start position:0%
+focus on the cortex each little
+ 
+
+ align:start position:0%
+focus on the cortex each little
+different bit of the cortex to the naked
+
+ align:start position:0%
+different bit of the cortex to the naked
+ 
+
+ align:start position:0%
+different bit of the cortex to the naked
+eye looks like any other bit of the
+
+ align:start position:0%
+eye looks like any other bit of the
+ 
+
+ align:start position:0%
+eye looks like any other bit of the
+cortex it's the subcortical stuff that
+
+ align:start position:0%
+cortex it's the subcortical stuff that
+ 
+
+ align:start position:0%
+cortex it's the subcortical stuff that
+looks different right
+
+ align:start position:0%
+looks different right
+ 
+
+ align:start position:0%
+looks different right
+so that's why we're doing this okay bear
+
+ align:start position:0%
+so that's why we're doing this okay bear
+ 
+
+ align:start position:0%
+so that's why we're doing this okay bear
+basics on the brain stem
+
+ align:start position:0%
+basics on the brain stem
+ 
+
+ align:start position:0%
+basics on the brain stem
+you can think of it as a bunch of relays
+
+ align:start position:0%
+you can think of it as a bunch of relays
+ 
+
+ align:start position:0%
+you can think of it as a bunch of relays
+in here different uh centers that
+
+ align:start position:0%
+in here different uh centers that
+ 
+
+ align:start position:0%
+in here different uh centers that
+connect information coming up from the
+
+ align:start position:0%
+connect information coming up from the
+ 
+
+ align:start position:0%
+connect information coming up from the
+spinal cord and send it through into the
+
+ align:start position:0%
+spinal cord and send it through into the
+ 
+
+ align:start position:0%
+spinal cord and send it through into the
+cerebellum
+
+ align:start position:0%
+cerebellum
+ 
+
+ align:start position:0%
+cerebellum
+so it's in many ways the most primitive
+
+ align:start position:0%
+so it's in many ways the most primitive
+ 
+
+ align:start position:0%
+so it's in many ways the most primitive
+part of the brain that means it's shared
+
+ align:start position:0%
+part of the brain that means it's shared
+ 
+
+ align:start position:0%
+part of the brain that means it's shared
+with animals very that branched off from
+
+ align:start position:0%
+with animals very that branched off from
+ 
+
+ align:start position:0%
+with animals very that branched off from
+us very far back in in mammalian
+
+ align:start position:0%
+us very far back in in mammalian
+ 
+
+ align:start position:0%
+us very far back in in mammalian
+evolution
+
+ align:start position:0%
+evolution
+ 
+
+ align:start position:0%
+evolution
+but it's also essential to life okay so
+
+ align:start position:0%
+but it's also essential to life okay so
+ 
+
+ align:start position:0%
+but it's also essential to life okay so
+you can get by with most of your cortex
+
+ align:start position:0%
+you can get by with most of your cortex
+ 
+
+ align:start position:0%
+you can get by with most of your cortex
+gone like you may not have a lot of fun
+
+ align:start position:0%
+gone like you may not have a lot of fun
+ 
+
+ align:start position:0%
+gone like you may not have a lot of fun
+you may not really know what's going on
+
+ align:start position:0%
+you may not really know what's going on
+ 
+
+ align:start position:0%
+you may not really know what's going on
+but you will stay alive but you can't
+
+ align:start position:0%
+but you will stay alive but you can't
+ 
+
+ align:start position:0%
+but you will stay alive but you can't
+get by without your brain stem right
+
+ align:start position:0%
+get by without your brain stem right
+ 
+
+ align:start position:0%
+get by without your brain stem right
+it's a it controls all kinds of basic
+
+ align:start position:0%
+it's a it controls all kinds of basic
+ 
+
+ align:start position:0%
+it's a it controls all kinds of basic
+crucial bodily functions like breathing
+
+ align:start position:0%
+crucial bodily functions like breathing
+ 
+
+ align:start position:0%
+crucial bodily functions like breathing
+consciousness temporary temperature
+
+ align:start position:0%
+consciousness temporary temperature
+ 
+
+ align:start position:0%
+consciousness temporary temperature
+regulation etc so it's not interesting
+
+ align:start position:0%
+regulation etc so it's not interesting
+ 
+
+ align:start position:0%
+regulation etc so it's not interesting
+cognitively but it's crucial for life
+
+ align:start position:0%
+cognitively but it's crucial for life
+ 
+
+ align:start position:0%
+cognitively but it's crucial for life
+cerebellum this beautiful thing here
+
+ align:start position:0%
+cerebellum this beautiful thing here
+ 
+
+ align:start position:0%
+cerebellum this beautiful thing here
+it's basically involved in motor
+
+ align:start position:0%
+it's basically involved in motor
+ 
+
+ align:start position:0%
+it's basically involved in motor
+coordination
+
+ align:start position:0%
+coordination
+ 
+
+ align:start position:0%
+coordination
+but from there on out there's a huge
+
+ align:start position:0%
+but from there on out there's a huge
+ 
+
+ align:start position:0%
+but from there on out there's a huge
+debate about its possible role in
+
+ align:start position:0%
+debate about its possible role in
+ 
+
+ align:start position:0%
+debate about its possible role in
+cognition and so there's lots of brain
+
+ align:start position:0%
+cognition and so there's lots of brain
+ 
+
+ align:start position:0%
+cognition and so there's lots of brain
+imaging studies where people find that
+
+ align:start position:0%
+imaging studies where people find that
+ 
+
+ align:start position:0%
+imaging studies where people find that
+the cerebellum is engaged in all kinds
+
+ align:start position:0%
+the cerebellum is engaged in all kinds
+ 
+
+ align:start position:0%
+the cerebellum is engaged in all kinds
+of things from aspects of perception up
+
+ align:start position:0%
+of things from aspects of perception up
+ 
+
+ align:start position:0%
+of things from aspects of perception up
+through aspects of language
+
+ align:start position:0%
+through aspects of language
+ 
+
+ align:start position:0%
+through aspects of language
+understanding you can find activations
+
+ align:start position:0%
+understanding you can find activations
+ 
+
+ align:start position:0%
+understanding you can find activations
+um in brain imaging studies
+
+ align:start position:0%
+um in brain imaging studies
+ 
+
+ align:start position:0%
+um in brain imaging studies
+nonetheless the best guess is that you
+
+ align:start position:0%
+nonetheless the best guess is that you
+ 
+
+ align:start position:0%
+nonetheless the best guess is that you
+actually don't need a cerebellum uh for
+
+ align:start position:0%
+actually don't need a cerebellum uh for
+ 
+
+ align:start position:0%
+actually don't need a cerebellum uh for
+any of this
+
+ align:start position:0%
+any of this
+ 
+
+ align:start position:0%
+any of this
+so there's if anybody's interested i'm
+
+ align:start position:0%
+so there's if anybody's interested i'm
+ 
+
+ align:start position:0%
+so there's if anybody's interested i'm
+going to actually try to remember to put
+
+ align:start position:0%
+going to actually try to remember to put
+ 
+
+ align:start position:0%
+going to actually try to remember to put
+it up as an optional reading on the site
+
+ align:start position:0%
+it up as an optional reading on the site
+ 
+
+ align:start position:0%
+it up as an optional reading on the site
+there's a recent article in the atlantic
+
+ align:start position:0%
+there's a recent article in the atlantic
+ 
+
+ align:start position:0%
+there's a recent article in the atlantic
+or the new yorker
+
+ align:start position:0%
+or the new yorker
+ 
+
+ align:start position:0%
+or the new yorker
+about a kid who had no cerebellum
+
+ align:start position:0%
+about a kid who had no cerebellum
+ 
+
+ align:start position:0%
+about a kid who had no cerebellum
+and he learned to walk late and slow
+
+ align:start position:0%
+and he learned to walk late and slow
+ 
+
+ align:start position:0%
+and he learned to walk late and slow
+nobody knew what his problem was but he
+
+ align:start position:0%
+nobody knew what his problem was but he
+ 
+
+ align:start position:0%
+nobody knew what his problem was but he
+learned to do pretty much everything
+
+ align:start position:0%
+learned to do pretty much everything
+ 
+
+ align:start position:0%
+learned to do pretty much everything
+like he's pretty much fine his motor
+
+ align:start position:0%
+like he's pretty much fine his motor
+ 
+
+ align:start position:0%
+like he's pretty much fine his motor
+coordination isn't great but he's fine
+
+ align:start position:0%
+coordination isn't great but he's fine
+ 
+
+ align:start position:0%
+coordination isn't great but he's fine
+yeah how are you defining consciousness
+
+ align:start position:0%
+yeah how are you defining consciousness
+ 
+
+ align:start position:0%
+yeah how are you defining consciousness
+in this context oh that's a good
+
+ align:start position:0%
+in this context oh that's a good
+ 
+
+ align:start position:0%
+in this context oh that's a good
+question and it's a big question and
+
+ align:start position:0%
+question and it's a big question and
+ 
+
+ align:start position:0%
+question and it's a big question and
+it's a question that nobody knows how to
+
+ align:start position:0%
+it's a question that nobody knows how to
+ 
+
+ align:start position:0%
+it's a question that nobody knows how to
+answer not just me
+
+ align:start position:0%
+answer not just me
+ 
+
+ align:start position:0%
+answer not just me
+so christoph koh who does more of work
+
+ align:start position:0%
+so christoph koh who does more of work
+ 
+
+ align:start position:0%
+so christoph koh who does more of work
+on the neural basis of consciousness
+
+ align:start position:0%
+on the neural basis of consciousness
+ 
+
+ align:start position:0%
+on the neural basis of consciousness
+than just about anybody has been going
+
+ align:start position:0%
+than just about anybody has been going
+ 
+
+ align:start position:0%
+than just about anybody has been going
+around saying for about 15 years
+
+ align:start position:0%
+around saying for about 15 years
+ 
+
+ align:start position:0%
+around saying for about 15 years
+we must not get stuck on a premature
+
+ align:start position:0%
+we must not get stuck on a premature
+ 
+
+ align:start position:0%
+we must not get stuck on a premature
+definition of consciousness because we
+
+ align:start position:0%
+definition of consciousness because we
+ 
+
+ align:start position:0%
+definition of consciousness because we
+don't know what that thing is that we're
+
+ align:start position:0%
+don't know what that thing is that we're
+ 
+
+ align:start position:0%
+don't know what that thing is that we're
+trying to understand so i'll hide behind
+
+ align:start position:0%
+trying to understand so i'll hide behind
+ 
+
+ align:start position:0%
+trying to understand so i'll hide behind
+kristoff's uh perry of that question
+
+ align:start position:0%
+kristoff's uh perry of that question
+ 
+
+ align:start position:0%
+kristoff's uh perry of that question
+and say we'll talk about it later in the
+
+ align:start position:0%
+and say we'll talk about it later in the
+ 
+
+ align:start position:0%
+and say we'll talk about it later in the
+course but it's there are many different
+
+ align:start position:0%
+course but it's there are many different
+ 
+
+ align:start position:0%
+course but it's there are many different
+kind of ways of defining it from the
+
+ align:start position:0%
+kind of ways of defining it from the
+ 
+
+ align:start position:0%
+kind of ways of defining it from the
+difference of difference between being
+
+ align:start position:0%
+difference of difference between being
+ 
+
+ align:start position:0%
+difference of difference between being
+awake versus asleep which is some of the
+
+ align:start position:0%
+awake versus asleep which is some of the
+ 
+
+ align:start position:0%
+awake versus asleep which is some of the
+functions that go on here the difference
+
+ align:start position:0%
+functions that go on here the difference
+ 
+
+ align:start position:0%
+functions that go on here the difference
+between
+
+ align:start position:0%
+between
+ 
+
+ align:start position:0%
+between
+being kind of knocked out and completely
+
+ align:start position:0%
+being kind of knocked out and completely
+ 
+
+ align:start position:0%
+being kind of knocked out and completely
+unconscious under general anesthesia
+
+ align:start position:0%
+unconscious under general anesthesia
+ 
+
+ align:start position:0%
+unconscious under general anesthesia
+which is different from being asleep
+
+ align:start position:0%
+which is different from being asleep
+ 
+
+ align:start position:0%
+which is different from being asleep
+those kind of states of consciousness
+
+ align:start position:0%
+those kind of states of consciousness
+ 
+
+ align:start position:0%
+those kind of states of consciousness
+are regulated in part in here yeah
+
+ align:start position:0%
+are regulated in part in here yeah
+ 
+
+ align:start position:0%
+are regulated in part in here yeah
+okay so you can get by without a
+
+ align:start position:0%
+okay so you can get by without a
+ 
+
+ align:start position:0%
+okay so you can get by without a
+cerebellum but it's not recommended
+
+ align:start position:0%
+cerebellum but it's not recommended
+ 
+
+ align:start position:0%
+cerebellum but it's not recommended
+um moving right along all those
+
+ align:start position:0%
+um moving right along all those
+ 
+
+ align:start position:0%
+um moving right along all those
+subcortical bits we're just going to
+
+ align:start position:0%
+subcortical bits we're just going to
+ 
+
+ align:start position:0%
+subcortical bits we're just going to
+talk about three of the most important
+
+ align:start position:0%
+talk about three of the most important
+ 
+
+ align:start position:0%
+talk about three of the most important
+ones the thalamus this big guy right
+
+ align:start position:0%
+ones the thalamus this big guy right
+ 
+
+ align:start position:0%
+ones the thalamus this big guy right
+smack in the middle of the brain very
+
+ align:start position:0%
+smack in the middle of the brain very
+ 
+
+ align:start position:0%
+smack in the middle of the brain very
+large structure
+
+ align:start position:0%
+large structure
+ 
+
+ align:start position:0%
+large structure
+the hippocampus and the amygdala okay
+
+ align:start position:0%
+the hippocampus and the amygdala okay
+ 
+
+ align:start position:0%
+the hippocampus and the amygdala okay
+let's talk about the thalamus
+
+ align:start position:0%
+let's talk about the thalamus
+ 
+
+ align:start position:0%
+let's talk about the thalamus
+think about the thalamus as a grand
+
+ align:start position:0%
+think about the thalamus as a grand
+ 
+
+ align:start position:0%
+think about the thalamus as a grand
+central station of the brain okay with
+
+ align:start position:0%
+central station of the brain okay with
+ 
+
+ align:start position:0%
+central station of the brain okay with
+all of these connections going to all
+
+ align:start position:0%
+all of these connections going to all
+ 
+
+ align:start position:0%
+all of these connections going to all
+those parts of cortex coming in and out
+
+ align:start position:0%
+those parts of cortex coming in and out
+ 
+
+ align:start position:0%
+those parts of cortex coming in and out
+of the thalamus like that okay
+
+ align:start position:0%
+of the thalamus like that okay
+ 
+
+ align:start position:0%
+of the thalamus like that okay
+so one of the key things about the
+
+ align:start position:0%
+so one of the key things about the
+ 
+
+ align:start position:0%
+so one of the key things about the
+thalamus
+
+ align:start position:0%
+thalamus
+ 
+
+ align:start position:0%
+thalamus
+is that most of the incoming sensory
+
+ align:start position:0%
+is that most of the incoming sensory
+ 
+
+ align:start position:0%
+is that most of the incoming sensory
+information goes by way of the thalamus
+
+ align:start position:0%
+information goes by way of the thalamus
+ 
+
+ align:start position:0%
+information goes by way of the thalamus
+on route to the cortex
+
+ align:start position:0%
+on route to the cortex
+ 
+
+ align:start position:0%
+on route to the cortex
+okay so if you start with your ear
+
+ align:start position:0%
+okay so if you start with your ear
+ 
+
+ align:start position:0%
+okay so if you start with your ear
+there's sensory endings in your ear that
+
+ align:start position:0%
+there's sensory endings in your ear that
+ 
+
+ align:start position:0%
+there's sensory endings in your ear that
+we'll talk about later in the term and
+
+ align:start position:0%
+we'll talk about later in the term and
+ 
+
+ align:start position:0%
+we'll talk about later in the term and
+they send
+
+ align:start position:0%
+they send
+ 
+
+ align:start position:0%
+they send
+neurons into this thalamus here this
+
+ align:start position:0%
+neurons into this thalamus here this
+ 
+
+ align:start position:0%
+neurons into this thalamus here this
+yellow thing
+
+ align:start position:0%
+yellow thing
+ 
+
+ align:start position:0%
+yellow thing
+through a bunch of different stages they
+
+ align:start position:0%
+through a bunch of different stages they
+ 
+
+ align:start position:0%
+through a bunch of different stages they
+make a stop in the thalamus and then
+
+ align:start position:0%
+make a stop in the thalamus and then
+ 
+
+ align:start position:0%
+make a stop in the thalamus and then
+they come up here to this green patch
+
+ align:start position:0%
+they come up here to this green patch
+ 
+
+ align:start position:0%
+they come up here to this green patch
+which is auditory cortex
+
+ align:start position:0%
+which is auditory cortex
+ 
+
+ align:start position:0%
+which is auditory cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+similarly
+
+ align:start position:0%
+similarly
+ 
+
+ align:start position:0%
+similarly
+somatosensory endings touch sensors in
+
+ align:start position:0%
+somatosensory endings touch sensors in
+ 
+
+ align:start position:0%
+somatosensory endings touch sensors in
+your skin that enable you to feel when
+
+ align:start position:0%
+your skin that enable you to feel when
+ 
+
+ align:start position:0%
+your skin that enable you to feel when
+you're being touched
+
+ align:start position:0%
+you're being touched
+ 
+
+ align:start position:0%
+you're being touched
+come in through the skin
+
+ align:start position:0%
+come in through the skin
+ 
+
+ align:start position:0%
+come in through the skin
+and they make a stop in the thalamus and
+
+ align:start position:0%
+and they make a stop in the thalamus and
+ 
+
+ align:start position:0%
+and they make a stop in the thalamus and
+then they go up to somatosensory cortex
+
+ align:start position:0%
+then they go up to somatosensory cortex
+ 
+
+ align:start position:0%
+then they go up to somatosensory cortex
+up there
+
+ align:start position:0%
+up there
+ 
+
+ align:start position:0%
+up there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+similarly
+
+ align:start position:0%
+similarly
+ 
+
+ align:start position:0%
+similarly
+signals that come in from your eyes
+
+ align:start position:0%
+signals that come in from your eyes
+ 
+
+ align:start position:0%
+signals that come in from your eyes
+make a stop in the thalamus
+
+ align:start position:0%
+make a stop in the thalamus
+ 
+
+ align:start position:0%
+make a stop in the thalamus
+and then go up to visual cortex
+
+ align:start position:0%
+and then go up to visual cortex
+ 
+
+ align:start position:0%
+and then go up to visual cortex
+okay what's the name of the structure in
+
+ align:start position:0%
+okay what's the name of the structure in
+ 
+
+ align:start position:0%
+okay what's the name of the structure in
+the thalamus that those axons make a
+
+ align:start position:0%
+the thalamus that those axons make a
+ 
+
+ align:start position:0%
+the thalamus that those axons make a
+synapse in coming up from the eyes you
+
+ align:start position:0%
+synapse in coming up from the eyes you
+ 
+
+ align:start position:0%
+synapse in coming up from the eyes you
+make a synapse here and you go up oops
+
+ align:start position:0%
+make a synapse here and you go up oops
+ 
+
+ align:start position:0%
+make a synapse here and you go up oops
+you go up to visual cortex
+
+ align:start position:0%
+you go up to visual cortex
+ 
+
+ align:start position:0%
+you go up to visual cortex
+lgn perfect what does it stand for
+
+ align:start position:0%
+lgn perfect what does it stand for
+ 
+
+ align:start position:0%
+lgn perfect what does it stand for
+perfect okay you should know that it's
+
+ align:start position:0%
+perfect okay you should know that it's
+ 
+
+ align:start position:0%
+perfect okay you should know that it's
+this is review from
+
+ align:start position:0%
+this is review from
+ 
+
+ align:start position:0%
+this is review from
+900 901 okay
+
+ align:start position:0%
+900 901 okay
+ 
+
+ align:start position:0%
+900 901 okay
+um yes sorry okay
+
+ align:start position:0%
+um yes sorry okay
+ 
+
+ align:start position:0%
+um yes sorry okay
+which sensory modality does not go
+
+ align:start position:0%
+which sensory modality does not go
+ 
+
+ align:start position:0%
+which sensory modality does not go
+through the thalamus on route to cortex
+
+ align:start position:0%
+through the thalamus on route to cortex
+ 
+
+ align:start position:0%
+through the thalamus on route to cortex
+between the sensory nerve endings and
+
+ align:start position:0%
+between the sensory nerve endings and
+ 
+
+ align:start position:0%
+between the sensory nerve endings and
+the cortex
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry
+
+ align:start position:0%
+sorry
+ 
+
+ align:start position:0%
+sorry
+yes yes you guys are on the ball yes
+
+ align:start position:0%
+yes yes you guys are on the ball yes
+ 
+
+ align:start position:0%
+yes yes you guys are on the ball yes
+olfactory system is the one sensory
+
+ align:start position:0%
+olfactory system is the one sensory
+ 
+
+ align:start position:0%
+olfactory system is the one sensory
+modality that doesn't make a stop in the
+
+ align:start position:0%
+modality that doesn't make a stop in the
+ 
+
+ align:start position:0%
+modality that doesn't make a stop in the
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+you can sort of see that here from the
+
+ align:start position:0%
+you can sort of see that here from the
+ 
+
+ align:start position:0%
+you can sort of see that here from the
+nose it goes straight up into
+
+ align:start position:0%
+nose it goes straight up into
+ 
+
+ align:start position:0%
+nose it goes straight up into
+olfactory cortex right there
+
+ align:start position:0%
+olfactory cortex right there
+ 
+
+ align:start position:0%
+olfactory cortex right there
+all right so that's the um
+
+ align:start position:0%
+all right so that's the um
+ 
+
+ align:start position:0%
+all right so that's the um
+standard view of the thalamus as this
+
+ align:start position:0%
+standard view of the thalamus as this
+ 
+
+ align:start position:0%
+standard view of the thalamus as this
+kind of like relay station where all the
+
+ align:start position:0%
+kind of like relay station where all the
+ 
+
+ align:start position:0%
+kind of like relay station where all the
+external sensory information comes in
+
+ align:start position:0%
+external sensory information comes in
+ 
+
+ align:start position:0%
+external sensory information comes in
+there makes a stop and then goes up to
+
+ align:start position:0%
+there makes a stop and then goes up to
+ 
+
+ align:start position:0%
+there makes a stop and then goes up to
+cortex okay
+
+ align:start position:0%
+cortex okay
+ 
+
+ align:start position:0%
+cortex okay
+that's my thalamus act boom like that
+
+ align:start position:0%
+that's my thalamus act boom like that
+ 
+
+ align:start position:0%
+that's my thalamus act boom like that
+right okay
+
+ align:start position:0%
+right okay
+ 
+
+ align:start position:0%
+right okay
+but
+
+ align:start position:0%
+but
+ 
+
+ align:start position:0%
+but
+uh increasingly there's evidence that
+
+ align:start position:0%
+uh increasingly there's evidence that
+ 
+
+ align:start position:0%
+uh increasingly there's evidence that
+the thalamus is much more than a relay
+
+ align:start position:0%
+the thalamus is much more than a relay
+ 
+
+ align:start position:0%
+the thalamus is much more than a relay
+station and why would you bother with a
+
+ align:start position:0%
+station and why would you bother with a
+ 
+
+ align:start position:0%
+station and why would you bother with a
+relay anyway kind of doesn't mean
+
+ align:start position:0%
+relay anyway kind of doesn't mean
+ 
+
+ align:start position:0%
+relay anyway kind of doesn't mean
+anything kind of means like we don't
+
+ align:start position:0%
+anything kind of means like we don't
+ 
+
+ align:start position:0%
+anything kind of means like we don't
+know what's going on here because you
+
+ align:start position:0%
+know what's going on here because you
+ 
+
+ align:start position:0%
+know what's going on here because you
+wouldn't just make a synapse for no
+
+ align:start position:0%
+wouldn't just make a synapse for no
+ 
+
+ align:start position:0%
+wouldn't just make a synapse for no
+reason right um okay and so the first
+
+ align:start position:0%
+reason right um okay and so the first
+ 
+
+ align:start position:0%
+reason right um okay and so the first
+thing to note is there are lots of
+
+ align:start position:0%
+thing to note is there are lots of
+ 
+
+ align:start position:0%
+thing to note is there are lots of
+connections that go back down the other
+
+ align:start position:0%
+connections that go back down the other
+ 
+
+ align:start position:0%
+connections that go back down the other
+way there are ten times as many
+
+ align:start position:0%
+way there are ten times as many
+ 
+
+ align:start position:0%
+way there are ten times as many
+connections that go from primary visual
+
+ align:start position:0%
+connections that go from primary visual
+ 
+
+ align:start position:0%
+connections that go from primary visual
+cortex right here in me
+
+ align:start position:0%
+cortex right here in me
+ 
+
+ align:start position:0%
+cortex right here in me
+right here in the sky in red there are
+
+ align:start position:0%
+right here in the sky in red there are
+ 
+
+ align:start position:0%
+right here in the sky in red there are
+ten times as many that go backwards
+
+ align:start position:0%
+ten times as many that go backwards
+ 
+
+ align:start position:0%
+ten times as many that go backwards
+down to the thalamus
+
+ align:start position:0%
+down to the thalamus
+ 
+
+ align:start position:0%
+down to the thalamus
+as go forwards
+
+ align:start position:0%
+as go forwards
+ 
+
+ align:start position:0%
+as go forwards
+that's mind-blowing right information
+
+ align:start position:0%
+that's mind-blowing right information
+ 
+
+ align:start position:0%
+that's mind-blowing right information
+comes from the eyes up into the brain
+
+ align:start position:0%
+comes from the eyes up into the brain
+ 
+
+ align:start position:0%
+comes from the eyes up into the brain
+what the hell are those things doing
+
+ align:start position:0%
+what the hell are those things doing
+ 
+
+ align:start position:0%
+what the hell are those things doing
+going backwards okay
+
+ align:start position:0%
+going backwards okay
+ 
+
+ align:start position:0%
+going backwards okay
+well they're doing all kinds of
+
+ align:start position:0%
+well they're doing all kinds of
+ 
+
+ align:start position:0%
+well they're doing all kinds of
+interesting things so that's the first
+
+ align:start position:0%
+interesting things so that's the first
+ 
+
+ align:start position:0%
+interesting things so that's the first
+indication that the thalamus isn't just
+
+ align:start position:0%
+indication that the thalamus isn't just
+ 
+
+ align:start position:0%
+indication that the thalamus isn't just
+relaying stuff in a stupid passive way
+
+ align:start position:0%
+relaying stuff in a stupid passive way
+ 
+
+ align:start position:0%
+relaying stuff in a stupid passive way
+and the second whole line of work which
+
+ align:start position:0%
+and the second whole line of work which
+ 
+
+ align:start position:0%
+and the second whole line of work which
+many people are working on but i think
+
+ align:start position:0%
+many people are working on but i think
+ 
+
+ align:start position:0%
+many people are working on but i think
+some of the most awesome work on this
+
+ align:start position:0%
+some of the most awesome work on this
+ 
+
+ align:start position:0%
+some of the most awesome work on this
+topic is done by our own mike halasa in
+
+ align:start position:0%
+topic is done by our own mike halasa in
+ 
+
+ align:start position:0%
+topic is done by our own mike halasa in
+this department
+
+ align:start position:0%
+this department
+ 
+
+ align:start position:0%
+this department
+and he does these incredible studies
+
+ align:start position:0%
+and he does these incredible studies
+ 
+
+ align:start position:0%
+and he does these incredible studies
+that you can do in mice with these
+
+ align:start position:0%
+that you can do in mice with these
+ 
+
+ align:start position:0%
+that you can do in mice with these
+spectacular methods that we can't use in
+
+ align:start position:0%
+spectacular methods that we can't use in
+ 
+
+ align:start position:0%
+spectacular methods that we can't use in
+humans
+
+ align:start position:0%
+humans
+ 
+
+ align:start position:0%
+humans
+where he can really take apart the
+
+ align:start position:0%
+where he can really take apart the
+ 
+
+ align:start position:0%
+where he can really take apart the
+circuit in magnificent detail
+
+ align:start position:0%
+circuit in magnificent detail
+ 
+
+ align:start position:0%
+circuit in magnificent detail
+and he's showing that the thalamus is
+
+ align:start position:0%
+and he's showing that the thalamus is
+ 
+
+ align:start position:0%
+and he's showing that the thalamus is
+involved in all kinds of high-level
+
+ align:start position:0%
+involved in all kinds of high-level
+ 
+
+ align:start position:0%
+involved in all kinds of high-level
+cognitive computations in mice it's
+
+ align:start position:0%
+cognitive computations in mice it's
+ 
+
+ align:start position:0%
+cognitive computations in mice it's
+really stunning work when the mice have
+
+ align:start position:0%
+really stunning work when the mice have
+ 
+
+ align:start position:0%
+really stunning work when the mice have
+to switch from doing one task to another
+
+ align:start position:0%
+to switch from doing one task to another
+ 
+
+ align:start position:0%
+to switch from doing one task to another
+the thalamus plays a key role in gating
+
+ align:start position:0%
+the thalamus plays a key role in gating
+ 
+
+ align:start position:0%
+the thalamus plays a key role in gating
+the flow of information from one
+
+ align:start position:0%
+the flow of information from one
+ 
+
+ align:start position:0%
+the flow of information from one
+cortical region to another
+
+ align:start position:0%
+cortical region to another
+ 
+
+ align:start position:0%
+cortical region to another
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right moving along they hit the
+
+ align:start position:0%
+all right moving along they hit the
+ 
+
+ align:start position:0%
+all right moving along they hit the
+campus i know you guys all learn about
+
+ align:start position:0%
+campus i know you guys all learn about
+ 
+
+ align:start position:0%
+campus i know you guys all learn about
+this the number one gripe in this
+
+ align:start position:0%
+this the number one gripe in this
+ 
+
+ align:start position:0%
+this the number one gripe in this
+department is we learn about hm in every
+
+ align:start position:0%
+department is we learn about hm in every
+ 
+
+ align:start position:0%
+department is we learn about hm in every
+course so that's going to happen here
+
+ align:start position:0%
+course so that's going to happen here
+ 
+
+ align:start position:0%
+course so that's going to happen here
+but it's going to last about 20 seconds
+
+ align:start position:0%
+but it's going to last about 20 seconds
+ 
+
+ align:start position:0%
+but it's going to last about 20 seconds
+so here it goes that's a normal slice of
+
+ align:start position:0%
+so here it goes that's a normal slice of
+ 
+
+ align:start position:0%
+so here it goes that's a normal slice of
+the brain like this here's the
+
+ align:start position:0%
+the brain like this here's the
+ 
+
+ align:start position:0%
+the brain like this here's the
+hippocampus on either side it's like a
+
+ align:start position:0%
+hippocampus on either side it's like a
+ 
+
+ align:start position:0%
+hippocampus on either side it's like a
+whole curled up deal right there and
+
+ align:start position:0%
+whole curled up deal right there and
+ 
+
+ align:start position:0%
+whole curled up deal right there and
+right there
+
+ align:start position:0%
+right there
+ 
+
+ align:start position:0%
+right there
+and here is hm's brain the famous hm who
+
+ align:start position:0%
+and here is hm's brain the famous hm who
+ 
+
+ align:start position:0%
+and here is hm's brain the famous hm who
+had surgery to remove his hippocampus on
+
+ align:start position:0%
+had surgery to remove his hippocampus on
+ 
+
+ align:start position:0%
+had surgery to remove his hippocampus on
+both sides and completely lost his
+
+ align:start position:0%
+both sides and completely lost his
+ 
+
+ align:start position:0%
+both sides and completely lost his
+episodic memory for anything that
+
+ align:start position:0%
+episodic memory for anything that
+ 
+
+ align:start position:0%
+episodic memory for anything that
+happened after his surgery okay you all
+
+ align:start position:0%
+happened after his surgery okay you all
+ 
+
+ align:start position:0%
+happened after his surgery okay you all
+remember that right
+
+ align:start position:0%
+remember that right
+ 
+
+ align:start position:0%
+remember that right
+if anybody hasn't heard of hm send me an
+
+ align:start position:0%
+if anybody hasn't heard of hm send me an
+ 
+
+ align:start position:0%
+if anybody hasn't heard of hm send me an
+email i'll give you some background
+
+ align:start position:0%
+email i'll give you some background
+ 
+
+ align:start position:0%
+email i'll give you some background
+reading
+
+ align:start position:0%
+reading
+ 
+
+ align:start position:0%
+reading
+okay so very loosely the hippocampus
+
+ align:start position:0%
+okay so very loosely the hippocampus
+ 
+
+ align:start position:0%
+okay so very loosely the hippocampus
+involved both in this kind of long-term
+
+ align:start position:0%
+involved both in this kind of long-term
+ 
+
+ align:start position:0%
+involved both in this kind of long-term
+episodic memory that hm lost and it also
+
+ align:start position:0%
+episodic memory that hm lost and it also
+ 
+
+ align:start position:0%
+episodic memory that hm lost and it also
+plays a key role in navigation which
+
+ align:start position:0%
+plays a key role in navigation which
+ 
+
+ align:start position:0%
+plays a key role in navigation which
+we'll talk about in
+
+ align:start position:0%
+we'll talk about in
+ 
+
+ align:start position:0%
+we'll talk about in
+great detail in a few weeks
+
+ align:start position:0%
+great detail in a few weeks
+ 
+
+ align:start position:0%
+great detail in a few weeks
+and i just want to say that some cases
+
+ align:start position:0%
+and i just want to say that some cases
+ 
+
+ align:start position:0%
+and i just want to say that some cases
+are even more extreme than hm
+
+ align:start position:0%
+are even more extreme than hm
+ 
+
+ align:start position:0%
+are even more extreme than hm
+so there's a case of lonnie sue johnson
+
+ align:start position:0%
+so there's a case of lonnie sue johnson
+ 
+
+ align:start position:0%
+so there's a case of lonnie sue johnson
+and i am trying to get you guys a video
+
+ align:start position:0%
+and i am trying to get you guys a video
+ 
+
+ align:start position:0%
+and i am trying to get you guys a video
+and i didn't get it in time but i'll
+
+ align:start position:0%
+and i didn't get it in time but i'll
+ 
+
+ align:start position:0%
+and i didn't get it in time but i'll
+show it to you later in the term if
+
+ align:start position:0%
+show it to you later in the term if
+ 
+
+ align:start position:0%
+show it to you later in the term if
+you're interested
+
+ align:start position:0%
+you're interested
+ 
+
+ align:start position:0%
+you're interested
+lonnie sue johnson had a viral infection
+
+ align:start position:0%
+lonnie sue johnson had a viral infection
+ 
+
+ align:start position:0%
+lonnie sue johnson had a viral infection
+that went up into her brain she was an
+
+ align:start position:0%
+that went up into her brain she was an
+ 
+
+ align:start position:0%
+that went up into her brain she was an
+extremely accomplished person she did
+
+ align:start position:0%
+extremely accomplished person she did
+ 
+
+ align:start position:0%
+extremely accomplished person she did
+illustrations on the cover of the new
+
+ align:start position:0%
+illustrations on the cover of the new
+ 
+
+ align:start position:0%
+illustrations on the cover of the new
+yorker she was a pilot she had her own
+
+ align:start position:0%
+yorker she was a pilot she had her own
+ 
+
+ align:start position:0%
+yorker she was a pilot she had her own
+farm when she raised you know lots of
+
+ align:start position:0%
+farm when she raised you know lots of
+ 
+
+ align:start position:0%
+farm when she raised you know lots of
+lots of stuff
+
+ align:start position:0%
+lots of stuff
+ 
+
+ align:start position:0%
+lots of stuff
+a very smart interesting multi-talented
+
+ align:start position:0%
+a very smart interesting multi-talented
+ 
+
+ align:start position:0%
+a very smart interesting multi-talented
+woman who had this
+
+ align:start position:0%
+woman who had this
+ 
+
+ align:start position:0%
+woman who had this
+terrible tragedy of getting viral
+
+ align:start position:0%
+terrible tragedy of getting viral
+ 
+
+ align:start position:0%
+terrible tragedy of getting viral
+encephalitis at i don't know what age
+
+ align:start position:0%
+encephalitis at i don't know what age
+ 
+
+ align:start position:0%
+encephalitis at i don't know what age
+but middle age
+
+ align:start position:0%
+but middle age
+ 
+
+ align:start position:0%
+but middle age
+and she now does not remember a single
+
+ align:start position:0%
+and she now does not remember a single
+ 
+
+ align:start position:0%
+and she now does not remember a single
+event in her life
+
+ align:start position:0%
+event in her life
+ 
+
+ align:start position:0%
+event in her life
+she's smart she's funny her personality
+
+ align:start position:0%
+she's smart she's funny her personality
+ 
+
+ align:start position:0%
+she's smart she's funny her personality
+is totally intact
+
+ align:start position:0%
+is totally intact
+ 
+
+ align:start position:0%
+is totally intact
+she can answer questions she can paint
+
+ align:start position:0%
+she can answer questions she can paint
+ 
+
+ align:start position:0%
+she can answer questions she can paint
+she can do all kinds of things but she
+
+ align:start position:0%
+she can do all kinds of things but she
+ 
+
+ align:start position:0%
+she can do all kinds of things but she
+does not remember a single event in her
+
+ align:start position:0%
+does not remember a single event in her
+ 
+
+ align:start position:0%
+does not remember a single event in her
+life
+
+ align:start position:0%
+life
+ 
+
+ align:start position:0%
+life
+that's pretty astonishing
+
+ align:start position:0%
+that's pretty astonishing
+ 
+
+ align:start position:0%
+that's pretty astonishing
+reflect on what it means to have a sense
+
+ align:start position:0%
+reflect on what it means to have a sense
+ 
+
+ align:start position:0%
+reflect on what it means to have a sense
+of self if you don't remember anything
+
+ align:start position:0%
+of self if you don't remember anything
+ 
+
+ align:start position:0%
+of self if you don't remember anything
+in your life yeah she remember her again
+
+ align:start position:0%
+in your life yeah she remember her again
+ 
+
+ align:start position:0%
+in your life yeah she remember her again
+that's a good question i'm not sure she
+
+ align:start position:0%
+that's a good question i'm not sure she
+ 
+
+ align:start position:0%
+that's a good question i'm not sure she
+might know her yes she does know her
+
+ align:start position:0%
+might know her yes she does know her
+ 
+
+ align:start position:0%
+might know her yes she does know her
+name actually it is evident in this
+
+ align:start position:0%
+name actually it is evident in this
+ 
+
+ align:start position:0%
+name actually it is evident in this
+video but the video well so you know she
+
+ align:start position:0%
+video but the video well so you know she
+ 
+
+ align:start position:0%
+video but the video well so you know she
+doesn't remember at one point in this
+
+ align:start position:0%
+doesn't remember at one point in this
+ 
+
+ align:start position:0%
+doesn't remember at one point in this
+video she's asked were you ever married
+
+ align:start position:0%
+video she's asked were you ever married
+ 
+
+ align:start position:0%
+video she's asked were you ever married
+and she's lovely and sweet and gentle
+
+ align:start position:0%
+and she's lovely and sweet and gentle
+ 
+
+ align:start position:0%
+and she's lovely and sweet and gentle
+and kind of low-key and she's like you
+
+ align:start position:0%
+and kind of low-key and she's like you
+ 
+
+ align:start position:0%
+and kind of low-key and she's like you
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+just don't remember i might have been i
+
+ align:start position:0%
+just don't remember i might have been i
+ 
+
+ align:start position:0%
+just don't remember i might have been i
+might have been she was married for 10
+
+ align:start position:0%
+might have been she was married for 10
+ 
+
+ align:start position:0%
+might have been she was married for 10
+years
+
+ align:start position:0%
+years
+ 
+
+ align:start position:0%
+years
+so uh that's the hippocampus important
+
+ align:start position:0%
+so uh that's the hippocampus important
+ 
+
+ align:start position:0%
+so uh that's the hippocampus important
+you don't want to lose that one yeah
+
+ align:start position:0%
+you don't want to lose that one yeah
+ 
+
+ align:start position:0%
+you don't want to lose that one yeah
+about each other if the campus is using
+
+ align:start position:0%
+about each other if the campus is using
+ 
+
+ align:start position:0%
+about each other if the campus is using
+long-term memory why is it that it being
+
+ align:start position:0%
+long-term memory why is it that it being
+ 
+
+ align:start position:0%
+long-term memory why is it that it being
+removed causing to not form new memories
+
+ align:start position:0%
+removed causing to not form new memories
+ 
+
+ align:start position:0%
+removed causing to not form new memories
+well so long-term memory means you know
+
+ align:start position:0%
+well so long-term memory means you know
+ 
+
+ align:start position:0%
+well so long-term memory means you know
+it's a vague term it means the formation
+
+ align:start position:0%
+it's a vague term it means the formation
+ 
+
+ align:start position:0%
+it's a vague term it means the formation
+rich and retrieval of memories that are
+
+ align:start position:0%
+rich and retrieval of memories that are
+ 
+
+ align:start position:0%
+rich and retrieval of memories that are
+going to last a long time
+
+ align:start position:0%
+going to last a long time
+ 
+
+ align:start position:0%
+going to last a long time
+so in hm's case he can access a lot of
+
+ align:start position:0%
+so in hm's case he can access a lot of
+ 
+
+ align:start position:0%
+so in hm's case he can access a lot of
+the memories from before his injury
+
+ align:start position:0%
+the memories from before his injury
+ 
+
+ align:start position:0%
+the memories from before his injury
+in lonnie sue's case she can't do even
+
+ align:start position:0%
+in lonnie sue's case she can't do even
+ 
+
+ align:start position:0%
+in lonnie sue's case she can't do even
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+amygdala
+
+ align:start position:0%
+amygdala
+ 
+
+ align:start position:0%
+amygdala
+okay amygdala is a greek word that means
+
+ align:start position:0%
+okay amygdala is a greek word that means
+ 
+
+ align:start position:0%
+okay amygdala is a greek word that means
+almond because the amygdala is the size
+
+ align:start position:0%
+almond because the amygdala is the size
+ 
+
+ align:start position:0%
+almond because the amygdala is the size
+and shape of an almond
+
+ align:start position:0%
+and shape of an almond
+ 
+
+ align:start position:0%
+and shape of an almond
+and so
+
+ align:start position:0%
+and so
+ 
+
+ align:start position:0%
+and so
+just for fun we're passing on her own my
+
+ align:start position:0%
+just for fun we're passing on her own my
+ 
+
+ align:start position:0%
+just for fun we're passing on her own my
+favorite kind have some almonds and pass
+
+ align:start position:0%
+favorite kind have some almonds and pass
+ 
+
+ align:start position:0%
+favorite kind have some almonds and pass
+them around all right
+
+ align:start position:0%
+them around all right
+ 
+
+ align:start position:0%
+them around all right
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+okay so the amygdala is involved in
+
+ align:start position:0%
+okay so the amygdala is involved in
+ 
+
+ align:start position:0%
+okay so the amygdala is involved in
+experiencing and recognizing emotions
+
+ align:start position:0%
+experiencing and recognizing emotions
+ 
+
+ align:start position:0%
+experiencing and recognizing emotions
+especially fear
+
+ align:start position:0%
+especially fear
+ 
+
+ align:start position:0%
+especially fear
+the simple statement that you should
+
+ align:start position:0%
+the simple statement that you should
+ 
+
+ align:start position:0%
+the simple statement that you should
+remember about what the amygdala does
+
+ align:start position:0%
+remember about what the amygdala does
+ 
+
+ align:start position:0%
+remember about what the amygdala does
+is just remember the four f's you guys
+
+ align:start position:0%
+is just remember the four f's you guys
+ 
+
+ align:start position:0%
+is just remember the four f's you guys
+all know about the four f's
+
+ align:start position:0%
+all know about the four f's
+ 
+
+ align:start position:0%
+all know about the four f's
+fighting fleeing feeding and mating
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+patient sm
+
+ align:start position:0%
+patient sm
+ 
+
+ align:start position:0%
+patient sm
+lost her amygdala on both sides
+
+ align:start position:0%
+lost her amygdala on both sides
+ 
+
+ align:start position:0%
+lost her amygdala on both sides
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+she cannot experience fear
+
+ align:start position:0%
+she cannot experience fear
+ 
+
+ align:start position:0%
+she cannot experience fear
+she doesn't recognize fear on facial
+
+ align:start position:0%
+she doesn't recognize fear on facial
+ 
+
+ align:start position:0%
+she doesn't recognize fear on facial
+expressions of other people and she
+
+ align:start position:0%
+expressions of other people and she
+ 
+
+ align:start position:0%
+expressions of other people and she
+doesn't experience fear herself
+
+ align:start position:0%
+doesn't experience fear herself
+ 
+
+ align:start position:0%
+doesn't experience fear herself
+okay and so that's a the striking um
+
+ align:start position:0%
+okay and so that's a the striking um
+ 
+
+ align:start position:0%
+okay and so that's a the striking um
+piece of evidence on what the amygdala
+
+ align:start position:0%
+piece of evidence on what the amygdala
+ 
+
+ align:start position:0%
+piece of evidence on what the amygdala
+does her face recognition is normal
+
+ align:start position:0%
+does her face recognition is normal
+ 
+
+ align:start position:0%
+does her face recognition is normal
+recognizing identities
+
+ align:start position:0%
+recognizing identities
+ 
+
+ align:start position:0%
+recognizing identities
+her iq is normal
+
+ align:start position:0%
+her iq is normal
+ 
+
+ align:start position:0%
+her iq is normal
+she's overly trusting of other people
+
+ align:start position:0%
+she's overly trusting of other people
+ 
+
+ align:start position:0%
+she's overly trusting of other people
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um okay so that's all you need to know
+
+ align:start position:0%
+um okay so that's all you need to know
+ 
+
+ align:start position:0%
+um okay so that's all you need to know
+about the amygdala for now
+
+ align:start position:0%
+about the amygdala for now
+ 
+
+ align:start position:0%
+about the amygdala for now
+um okay let's talk about white matter
+
+ align:start position:0%
+um okay let's talk about white matter
+ 
+
+ align:start position:0%
+um okay let's talk about white matter
+just brief review here's a here's a kind
+
+ align:start position:0%
+just brief review here's a here's a kind
+ 
+
+ align:start position:0%
+just brief review here's a here's a kind
+of tunnel through a piece of cortex okay
+
+ align:start position:0%
+of tunnel through a piece of cortex okay
+ 
+
+ align:start position:0%
+of tunnel through a piece of cortex okay
+so my brain cortex is wrapping around
+
+ align:start position:0%
+so my brain cortex is wrapping around
+ 
+
+ align:start position:0%
+so my brain cortex is wrapping around
+like that if we took a piece like this
+
+ align:start position:0%
+like that if we took a piece like this
+ 
+
+ align:start position:0%
+like that if we took a piece like this
+just took a segment out like that this
+
+ align:start position:0%
+just took a segment out like that this
+ 
+
+ align:start position:0%
+just took a segment out like that this
+is the outside of the brain up there
+
+ align:start position:0%
+is the outside of the brain up there
+ 
+
+ align:start position:0%
+is the outside of the brain up there
+cortex runs like this
+
+ align:start position:0%
+cortex runs like this
+ 
+
+ align:start position:0%
+cortex runs like this
+and gray matter is the stuff on the
+
+ align:start position:0%
+and gray matter is the stuff on the
+ 
+
+ align:start position:0%
+and gray matter is the stuff on the
+outer surface that's full of cell bodies
+
+ align:start position:0%
+outer surface that's full of cell bodies
+ 
+
+ align:start position:0%
+outer surface that's full of cell bodies
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+white matter
+
+ align:start position:0%
+white matter
+ 
+
+ align:start position:0%
+white matter
+are the axons the processes that come
+
+ align:start position:0%
+are the axons the processes that come
+ 
+
+ align:start position:0%
+are the axons the processes that come
+out of those cell bodies and travel
+
+ align:start position:0%
+out of those cell bodies and travel
+ 
+
+ align:start position:0%
+out of those cell bodies and travel
+elsewhere in the brain
+
+ align:start position:0%
+elsewhere in the brain
+ 
+
+ align:start position:0%
+elsewhere in the brain
+okay everybody clear on that okay so
+
+ align:start position:0%
+okay everybody clear on that okay so
+ 
+
+ align:start position:0%
+okay everybody clear on that okay so
+we've got gray matter up here and white
+
+ align:start position:0%
+we've got gray matter up here and white
+ 
+
+ align:start position:0%
+we've got gray matter up here and white
+matter down there
+
+ align:start position:0%
+matter down there
+ 
+
+ align:start position:0%
+matter down there
+mostly myelinated axons that have that
+
+ align:start position:0%
+mostly myelinated axons that have that
+ 
+
+ align:start position:0%
+mostly myelinated axons that have that
+layer of fat to make them conduct fast
+
+ align:start position:0%
+layer of fat to make them conduct fast
+ 
+
+ align:start position:0%
+layer of fat to make them conduct fast
+and so you'll see bundles of white
+
+ align:start position:0%
+and so you'll see bundles of white
+ 
+
+ align:start position:0%
+and so you'll see bundles of white
+matter in the dissection
+
+ align:start position:0%
+matter in the dissection
+ 
+
+ align:start position:0%
+matter in the dissection
+and so here's an actual picture
+
+ align:start position:0%
+and so here's an actual picture
+ 
+
+ align:start position:0%
+and so here's an actual picture
+photograph of the slice through a brain
+
+ align:start position:0%
+photograph of the slice through a brain
+ 
+
+ align:start position:0%
+photograph of the slice through a brain
+so all that white stuff up there is
+
+ align:start position:0%
+so all that white stuff up there is
+ 
+
+ align:start position:0%
+so all that white stuff up there is
+white matter okay
+
+ align:start position:0%
+white matter okay
+ 
+
+ align:start position:0%
+white matter okay
+and so you might say well it's just a
+
+ align:start position:0%
+and so you might say well it's just a
+ 
+
+ align:start position:0%
+and so you might say well it's just a
+big bunch of wires
+
+ align:start position:0%
+big bunch of wires
+ 
+
+ align:start position:0%
+big bunch of wires
+who cares about that
+
+ align:start position:0%
+who cares about that
+ 
+
+ align:start position:0%
+who cares about that
+it's a good question but actually the
+
+ align:start position:0%
+it's a good question but actually the
+ 
+
+ align:start position:0%
+it's a good question but actually the
+wires are pretty damn interesting and
+
+ align:start position:0%
+wires are pretty damn interesting and
+ 
+
+ align:start position:0%
+wires are pretty damn interesting and
+pretty fundamental
+
+ align:start position:0%
+pretty fundamental
+ 
+
+ align:start position:0%
+pretty fundamental
+and so i'll just give you a few reasons
+
+ align:start position:0%
+and so i'll just give you a few reasons
+ 
+
+ align:start position:0%
+and so i'll just give you a few reasons
+and you don't need to memorize every one
+
+ align:start position:0%
+and you don't need to memorize every one
+ 
+
+ align:start position:0%
+and you don't need to memorize every one
+of these i'm just trying to give you a
+
+ align:start position:0%
+of these i'm just trying to give you a
+ 
+
+ align:start position:0%
+of these i'm just trying to give you a
+gist of why we might care about this and
+
+ align:start position:0%
+gist of why we might care about this and
+ 
+
+ align:start position:0%
+gist of why we might care about this and
+there will be a whole other lecture on
+
+ align:start position:0%
+there will be a whole other lecture on
+ 
+
+ align:start position:0%
+there will be a whole other lecture on
+networks and connectivity later in the
+
+ align:start position:0%
+networks and connectivity later in the
+ 
+
+ align:start position:0%
+networks and connectivity later in the
+course well first of all white matter is
+
+ align:start position:0%
+course well first of all white matter is
+ 
+
+ align:start position:0%
+course well first of all white matter is
+45 of the human brain
+
+ align:start position:0%
+45 of the human brain
+ 
+
+ align:start position:0%
+45 of the human brain
+okay so takes up a lot of space all
+
+ align:start position:0%
+okay so takes up a lot of space all
+ 
+
+ align:start position:0%
+okay so takes up a lot of space all
+those wires connecting one bit to
+
+ align:start position:0%
+those wires connecting one bit to
+ 
+
+ align:start position:0%
+those wires connecting one bit to
+another bit
+
+ align:start position:0%
+another bit
+ 
+
+ align:start position:0%
+another bit
+and i would say we cannot possibly
+
+ align:start position:0%
+and i would say we cannot possibly
+ 
+
+ align:start position:0%
+and i would say we cannot possibly
+understand the cortex and how it works
+
+ align:start position:0%
+understand the cortex and how it works
+ 
+
+ align:start position:0%
+understand the cortex and how it works
+or any little piece of it without
+
+ align:start position:0%
+or any little piece of it without
+ 
+
+ align:start position:0%
+or any little piece of it without
+knowing the connectivity of each piece
+
+ align:start position:0%
+knowing the connectivity of each piece
+ 
+
+ align:start position:0%
+knowing the connectivity of each piece
+to each other bit of the cortex right
+
+ align:start position:0%
+to each other bit of the cortex right
+ 
+
+ align:start position:0%
+to each other bit of the cortex right
+imagine trying to understand a computer
+
+ align:start position:0%
+imagine trying to understand a computer
+ 
+
+ align:start position:0%
+imagine trying to understand a computer
+or a circuit without being able to see
+
+ align:start position:0%
+or a circuit without being able to see
+ 
+
+ align:start position:0%
+or a circuit without being able to see
+the connections between the bits like it
+
+ align:start position:0%
+the connections between the bits like it
+ 
+
+ align:start position:0%
+the connections between the bits like it
+would drive you crazy that's a situation
+
+ align:start position:0%
+would drive you crazy that's a situation
+ 
+
+ align:start position:0%
+would drive you crazy that's a situation
+we're in now in human cognitive
+
+ align:start position:0%
+we're in now in human cognitive
+ 
+
+ align:start position:0%
+we're in now in human cognitive
+neuroscience it frankly drives me insane
+
+ align:start position:0%
+neuroscience it frankly drives me insane
+ 
+
+ align:start position:0%
+neuroscience it frankly drives me insane
+but that's where we are
+
+ align:start position:0%
+but that's where we are
+ 
+
+ align:start position:0%
+but that's where we are
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+next thing
+
+ align:start position:0%
+next thing
+ 
+
+ align:start position:0%
+next thing
+the long-range connectivity of each
+
+ align:start position:0%
+the long-range connectivity of each
+ 
+
+ align:start position:0%
+the long-range connectivity of each
+little bit of cortex some little bit
+
+ align:start position:0%
+little bit of cortex some little bit
+ 
+
+ align:start position:0%
+little bit of cortex some little bit
+right there in my brain is connected to
+
+ align:start position:0%
+right there in my brain is connected to
+ 
+
+ align:start position:0%
+right there in my brain is connected to
+some bunch of other remote regions in my
+
+ align:start position:0%
+some bunch of other remote regions in my
+ 
+
+ align:start position:0%
+some bunch of other remote regions in my
+brain and that particular set of
+
+ align:start position:0%
+brain and that particular set of
+ 
+
+ align:start position:0%
+brain and that particular set of
+connections is distinctive for that
+
+ align:start position:0%
+connections is distinctive for that
+ 
+
+ align:start position:0%
+connections is distinctive for that
+patch of cortex
+
+ align:start position:0%
+patch of cortex
+ 
+
+ align:start position:0%
+patch of cortex
+so you can think of it as a connectivity
+
+ align:start position:0%
+so you can think of it as a connectivity
+ 
+
+ align:start position:0%
+so you can think of it as a connectivity
+fingerprint of a patch of cortex
+
+ align:start position:0%
+fingerprint of a patch of cortex
+ 
+
+ align:start position:0%
+fingerprint of a patch of cortex
+okay so one of the ways that the
+
+ align:start position:0%
+okay so one of the ways that the
+ 
+
+ align:start position:0%
+okay so one of the ways that the
+different bits differ from each other is
+
+ align:start position:0%
+different bits differ from each other is
+ 
+
+ align:start position:0%
+different bits differ from each other is
+by way of their connectivity
+
+ align:start position:0%
+by way of their connectivity
+ 
+
+ align:start position:0%
+by way of their connectivity
+fingerprints
+
+ align:start position:0%
+fingerprints
+ 
+
+ align:start position:0%
+fingerprints
+and i'm going to skip the rest of these
+
+ align:start position:0%
+and i'm going to skip the rest of these
+ 
+
+ align:start position:0%
+and i'm going to skip the rest of these
+because we're going to get back to them
+
+ align:start position:0%
+because we're going to get back to them
+ 
+
+ align:start position:0%
+because we're going to get back to them
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+and i'm going to run out of time i'm
+
+ align:start position:0%
+and i'm going to run out of time i'm
+ 
+
+ align:start position:0%
+and i'm going to run out of time i'm
+going to assign the tas to sound the
+
+ align:start position:0%
+going to assign the tas to sound the
+ 
+
+ align:start position:0%
+going to assign the tas to sound the
+gong at 12 15. okay good
+
+ align:start position:0%
+gong at 12 15. okay good
+ 
+
+ align:start position:0%
+gong at 12 15. okay good
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+now we're up to the cortex this is
+
+ align:start position:0%
+now we're up to the cortex this is
+ 
+
+ align:start position:0%
+now we're up to the cortex this is
+really laughably
+
+ align:start position:0%
+really laughably
+ 
+
+ align:start position:0%
+really laughably
+shallow but whatever that's what we're
+
+ align:start position:0%
+shallow but whatever that's what we're
+ 
+
+ align:start position:0%
+shallow but whatever that's what we're
+doing here
+
+ align:start position:0%
+doing here
+ 
+
+ align:start position:0%
+doing here
+so here's this cortex and as i mentioned
+
+ align:start position:0%
+so here's this cortex and as i mentioned
+ 
+
+ align:start position:0%
+so here's this cortex and as i mentioned
+it's a whole big sheet and the different
+
+ align:start position:0%
+it's a whole big sheet and the different
+ 
+
+ align:start position:0%
+it's a whole big sheet and the different
+bits look really similar if you just
+
+ align:start position:0%
+bits look really similar if you just
+ 
+
+ align:start position:0%
+bits look really similar if you just
+look at them or slice them up
+
+ align:start position:0%
+look at them or slice them up
+ 
+
+ align:start position:0%
+look at them or slice them up
+so how are we going to figure out how
+
+ align:start position:0%
+so how are we going to figure out how
+ 
+
+ align:start position:0%
+so how are we going to figure out how
+this thing is organized
+
+ align:start position:0%
+this thing is organized
+ 
+
+ align:start position:0%
+this thing is organized
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+okay now we're up here talking about
+
+ align:start position:0%
+okay now we're up here talking about
+ 
+
+ align:start position:0%
+okay now we're up here talking about
+cortex all right let's start with the
+
+ align:start position:0%
+cortex all right let's start with the
+ 
+
+ align:start position:0%
+cortex all right let's start with the
+easy parts which you've already seen
+
+ align:start position:0%
+easy parts which you've already seen
+ 
+
+ align:start position:0%
+easy parts which you've already seen
+you've already seen this up here these
+
+ align:start position:0%
+you've already seen this up here these
+ 
+
+ align:start position:0%
+you've already seen this up here these
+colored bits visual cortex auditory
+
+ align:start position:0%
+colored bits visual cortex auditory
+ 
+
+ align:start position:0%
+colored bits visual cortex auditory
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+somatosensory cortex
+
+ align:start position:0%
+somatosensory cortex
+ 
+
+ align:start position:0%
+somatosensory cortex
+gustatory taste cortex
+
+ align:start position:0%
+gustatory taste cortex
+ 
+
+ align:start position:0%
+gustatory taste cortex
+those bits
+
+ align:start position:0%
+those bits
+ 
+
+ align:start position:0%
+those bits
+are like the easy parts of cortex those
+
+ align:start position:0%
+are like the easy parts of cortex those
+ 
+
+ align:start position:0%
+are like the easy parts of cortex those
+are called primary sensory regions
+
+ align:start position:0%
+are called primary sensory regions
+ 
+
+ align:start position:0%
+are called primary sensory regions
+there's also motor cortex right in front
+
+ align:start position:0%
+there's also motor cortex right in front
+ 
+
+ align:start position:0%
+there's also motor cortex right in front
+of sensory cortex so those are the
+
+ align:start position:0%
+of sensory cortex so those are the
+ 
+
+ align:start position:0%
+of sensory cortex so those are the
+primary regions
+
+ align:start position:0%
+primary regions
+ 
+
+ align:start position:0%
+primary regions
+their primary in the sense of this is
+
+ align:start position:0%
+their primary in the sense of this is
+ 
+
+ align:start position:0%
+their primary in the sense of this is
+the first place that sensory information
+
+ align:start position:0%
+the first place that sensory information
+ 
+
+ align:start position:0%
+the first place that sensory information
+lands up at the cortex coming up from
+
+ align:start position:0%
+lands up at the cortex coming up from
+ 
+
+ align:start position:0%
+lands up at the cortex coming up from
+the senses right
+
+ align:start position:0%
+the senses right
+ 
+
+ align:start position:0%
+the senses right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and all of that input is wired through
+
+ align:start position:0%
+and all of that input is wired through
+ 
+
+ align:start position:0%
+and all of that input is wired through
+what structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes thank you
+
+ align:start position:0%
+yes thank you
+ 
+
+ align:start position:0%
+yes thank you
+um so how are these regions organized
+
+ align:start position:0%
+um so how are these regions organized
+ 
+
+ align:start position:0%
+um so how are these regions organized
+um well they have maps every one of
+
+ align:start position:0%
+um well they have maps every one of
+ 
+
+ align:start position:0%
+um well they have maps every one of
+these regions has a map
+
+ align:start position:0%
+these regions has a map
+ 
+
+ align:start position:0%
+these regions has a map
+and each of them has a map of a
+
+ align:start position:0%
+and each of them has a map of a
+ 
+
+ align:start position:0%
+and each of them has a map of a
+different thing so let's start with
+
+ align:start position:0%
+different thing so let's start with
+ 
+
+ align:start position:0%
+different thing so let's start with
+visual cortex
+
+ align:start position:0%
+visual cortex
+ 
+
+ align:start position:0%
+visual cortex
+and we're going to talk about the map
+
+ align:start position:0%
+and we're going to talk about the map
+ 
+
+ align:start position:0%
+and we're going to talk about the map
+that lives in visual cortex but the
+
+ align:start position:0%
+that lives in visual cortex but the
+ 
+
+ align:start position:0%
+that lives in visual cortex but the
+prior condition for understanding that
+
+ align:start position:0%
+prior condition for understanding that
+ 
+
+ align:start position:0%
+prior condition for understanding that
+map is to understand the concept of
+
+ align:start position:0%
+map is to understand the concept of
+ 
+
+ align:start position:0%
+map is to understand the concept of
+receptive field which you should know so
+
+ align:start position:0%
+receptive field which you should know so
+ 
+
+ align:start position:0%
+receptive field which you should know so
+i'm going to whip through it quickly
+
+ align:start position:0%
+i'm going to whip through it quickly
+ 
+
+ align:start position:0%
+i'm going to whip through it quickly
+okay so here is how you map the
+
+ align:start position:0%
+okay so here is how you map the
+ 
+
+ align:start position:0%
+okay so here is how you map the
+receptive field as a property of an
+
+ align:start position:0%
+receptive field as a property of an
+ 
+
+ align:start position:0%
+receptive field as a property of an
+individual cell
+
+ align:start position:0%
+individual cell
+ 
+
+ align:start position:0%
+individual cell
+in a brain okay so the classic way in
+
+ align:start position:0%
+in a brain okay so the classic way in
+ 
+
+ align:start position:0%
+in a brain okay so the classic way in
+animal neuroscience is you place an
+
+ align:start position:0%
+animal neuroscience is you place an
+ 
+
+ align:start position:0%
+animal neuroscience is you place an
+electrode in the brain next to a neuron
+
+ align:start position:0%
+electrode in the brain next to a neuron
+ 
+
+ align:start position:0%
+electrode in the brain next to a neuron
+in monkey visual cortex
+
+ align:start position:0%
+in monkey visual cortex
+ 
+
+ align:start position:0%
+in monkey visual cortex
+okay so here's this monkey's gun
+
+ align:start position:0%
+okay so here's this monkey's gun
+ 
+
+ align:start position:0%
+okay so here's this monkey's gun
+electrode right in his brain right next
+
+ align:start position:0%
+electrode right in his brain right next
+ 
+
+ align:start position:0%
+electrode right in his brain right next
+to a neuron and visual cortex and every
+
+ align:start position:0%
+to a neuron and visual cortex and every
+ 
+
+ align:start position:0%
+to a neuron and visual cortex and every
+time that neuron fires
+
+ align:start position:0%
+time that neuron fires
+ 
+
+ align:start position:0%
+time that neuron fires
+you get a spike you hear a spike okay
+
+ align:start position:0%
+you get a spike you hear a spike okay
+ 
+
+ align:start position:0%
+you get a spike you hear a spike okay
+now you train the monkey to stare at a
+
+ align:start position:0%
+now you train the monkey to stare at a
+ 
+
+ align:start position:0%
+now you train the monkey to stare at a
+fixation spot without moving its eyes
+
+ align:start position:0%
+fixation spot without moving its eyes
+ 
+
+ align:start position:0%
+fixation spot without moving its eyes
+okay i can do this with humans without
+
+ align:start position:0%
+okay i can do this with humans without
+ 
+
+ align:start position:0%
+okay i can do this with humans without
+training you i can just tell you look at
+
+ align:start position:0%
+training you i can just tell you look at
+ 
+
+ align:start position:0%
+training you i can just tell you look at
+the tip of my nose okay so keep your
+
+ align:start position:0%
+the tip of my nose okay so keep your
+ 
+
+ align:start position:0%
+the tip of my nose okay so keep your
+eyes on the tip of my nose i can see if
+
+ align:start position:0%
+eyes on the tip of my nose i can see if
+ 
+
+ align:start position:0%
+eyes on the tip of my nose i can see if
+you're looking elsewhere so look at the
+
+ align:start position:0%
+you're looking elsewhere so look at the
+ 
+
+ align:start position:0%
+you're looking elsewhere so look at the
+tip of my nose okay okay so you train a
+
+ align:start position:0%
+tip of my nose okay okay so you train a
+ 
+
+ align:start position:0%
+tip of my nose okay okay so you train a
+monkey to do that that takes a few
+
+ align:start position:0%
+monkey to do that that takes a few
+ 
+
+ align:start position:0%
+monkey to do that that takes a few
+months and then they can do that
+
+ align:start position:0%
+months and then they can do that
+ 
+
+ align:start position:0%
+months and then they can do that
+and then while recording from neurons in
+
+ align:start position:0%
+and then while recording from neurons in
+ 
+
+ align:start position:0%
+and then while recording from neurons in
+his brain you put stimuli over here put
+
+ align:start position:0%
+his brain you put stimuli over here put
+ 
+
+ align:start position:0%
+his brain you put stimuli over here put
+a flash over there or a flash over here
+
+ align:start position:0%
+a flash over there or a flash over here
+ 
+
+ align:start position:0%
+a flash over there or a flash over here
+or a flash over here or flash over here
+
+ align:start position:0%
+or a flash over here or flash over here
+ 
+
+ align:start position:0%
+or a flash over here or flash over here
+okay you can stop looking at my nose
+
+ align:start position:0%
+okay you can stop looking at my nose
+ 
+
+ align:start position:0%
+okay you can stop looking at my nose
+it's not all that fabulous knows i
+
+ align:start position:0%
+it's not all that fabulous knows i
+ 
+
+ align:start position:0%
+it's not all that fabulous knows i
+realize okay
+
+ align:start position:0%
+realize okay
+ 
+
+ align:start position:0%
+realize okay
+so a receptive field
+
+ align:start position:0%
+so a receptive field
+ 
+
+ align:start position:0%
+so a receptive field
+is the place in the visual world that
+
+ align:start position:0%
+is the place in the visual world that
+ 
+
+ align:start position:0%
+is the place in the visual world that
+makes a given neuron fire
+
+ align:start position:0%
+makes a given neuron fire
+ 
+
+ align:start position:0%
+makes a given neuron fire
+okay so if there's a neuron in your
+
+ align:start position:0%
+okay so if there's a neuron in your
+ 
+
+ align:start position:0%
+okay so if there's a neuron in your
+brain that responds to a flash here but
+
+ align:start position:0%
+brain that responds to a flash here but
+ 
+
+ align:start position:0%
+brain that responds to a flash here but
+not a flash here or here or here or here
+
+ align:start position:0%
+not a flash here or here or here or here
+ 
+
+ align:start position:0%
+not a flash here or here or here or here
+the receptive field of that neuron is
+
+ align:start position:0%
+the receptive field of that neuron is
+ 
+
+ align:start position:0%
+the receptive field of that neuron is
+right there everybody got that idea
+
+ align:start position:0%
+right there everybody got that idea
+ 
+
+ align:start position:0%
+right there everybody got that idea
+okay so in visual cortex neurons have
+
+ align:start position:0%
+okay so in visual cortex neurons have
+ 
+
+ align:start position:0%
+okay so in visual cortex neurons have
+restricted receptive fields they don't
+
+ align:start position:0%
+restricted receptive fields they don't
+ 
+
+ align:start position:0%
+restricted receptive fields they don't
+respond to anything anywhere in the
+
+ align:start position:0%
+respond to anything anywhere in the
+ 
+
+ align:start position:0%
+respond to anything anywhere in the
+visual field they respond to a
+
+ align:start position:0%
+visual field they respond to a
+ 
+
+ align:start position:0%
+visual field they respond to a
+particular place in space
+
+ align:start position:0%
+particular place in space
+ 
+
+ align:start position:0%
+particular place in space
+okay if that's confusing at all ask a
+
+ align:start position:0%
+okay if that's confusing at all ask a
+ 
+
+ align:start position:0%
+okay if that's confusing at all ask a
+question because it will come up again
+
+ align:start position:0%
+question because it will come up again
+ 
+
+ align:start position:0%
+question because it will come up again
+and again
+
+ align:start position:0%
+and again
+ 
+
+ align:start position:0%
+and again
+all right so that's what the rest of
+
+ align:start position:0%
+all right so that's what the rest of
+ 
+
+ align:start position:0%
+all right so that's what the rest of
+this slide says what i just said blah
+
+ align:start position:0%
+this slide says what i just said blah
+ 
+
+ align:start position:0%
+this slide says what i just said blah
+blah blah doesn't matter that's a
+
+ align:start position:0%
+blah blah doesn't matter that's a
+ 
+
+ align:start position:0%
+blah blah doesn't matter that's a
+receptive field different visual neurons
+
+ align:start position:0%
+receptive field different visual neurons
+ 
+
+ align:start position:0%
+receptive field different visual neurons
+have different receptive fields
+
+ align:start position:0%
+have different receptive fields
+ 
+
+ align:start position:0%
+have different receptive fields
+for different parts of space
+
+ align:start position:0%
+for different parts of space
+ 
+
+ align:start position:0%
+for different parts of space
+now here comes the important idea in
+
+ align:start position:0%
+now here comes the important idea in
+ 
+
+ align:start position:0%
+now here comes the important idea in
+visual cortex two neurons that are next
+
+ align:start position:0%
+visual cortex two neurons that are next
+ 
+
+ align:start position:0%
+visual cortex two neurons that are next
+to each other in visual cortex have
+
+ align:start position:0%
+to each other in visual cortex have
+ 
+
+ align:start position:0%
+to each other in visual cortex have
+nearby receptive fields
+
+ align:start position:0%
+nearby receptive fields
+ 
+
+ align:start position:0%
+nearby receptive fields
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's the concept of retina topi
+
+ align:start position:0%
+so that's the concept of retina topi
+ 
+
+ align:start position:0%
+so that's the concept of retina topi
+or the map in visual cortex so you
+
+ align:start position:0%
+or the map in visual cortex so you
+ 
+
+ align:start position:0%
+or the map in visual cortex so you
+basically have a map of the visual world
+
+ align:start position:0%
+basically have a map of the visual world
+ 
+
+ align:start position:0%
+basically have a map of the visual world
+in your visual cortex because there's
+
+ align:start position:0%
+in your visual cortex because there's
+ 
+
+ align:start position:0%
+in your visual cortex because there's
+this systematic layout just like you
+
+ align:start position:0%
+this systematic layout just like you
+ 
+
+ align:start position:0%
+this systematic layout just like you
+have in your retina in your retina
+
+ align:start position:0%
+have in your retina in your retina
+ 
+
+ align:start position:0%
+have in your retina in your retina
+visual information comes in and because
+
+ align:start position:0%
+visual information comes in and because
+ 
+
+ align:start position:0%
+visual information comes in and because
+of optics different parts of your retina
+
+ align:start position:0%
+of optics different parts of your retina
+ 
+
+ align:start position:0%
+of optics different parts of your retina
+respond to different parts of the image
+
+ align:start position:0%
+respond to different parts of the image
+ 
+
+ align:start position:0%
+respond to different parts of the image
+but that information is propagated back
+
+ align:start position:0%
+but that information is propagated back
+ 
+
+ align:start position:0%
+but that information is propagated back
+through the lgn up to primary visual
+
+ align:start position:0%
+through the lgn up to primary visual
+ 
+
+ align:start position:0%
+through the lgn up to primary visual
+cortex where you still have a map of the
+
+ align:start position:0%
+cortex where you still have a map of the
+ 
+
+ align:start position:0%
+cortex where you still have a map of the
+visual space up in primary visual cortex
+
+ align:start position:0%
+visual space up in primary visual cortex
+ 
+
+ align:start position:0%
+visual space up in primary visual cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that map is called retinotopic in
+
+ align:start position:0%
+so that map is called retinotopic in
+ 
+
+ align:start position:0%
+so that map is called retinotopic in
+visual cortex because it's
+
+ align:start position:0%
+visual cortex because it's
+ 
+
+ align:start position:0%
+visual cortex because it's
+oriented like the retina
+
+ align:start position:0%
+oriented like the retina
+ 
+
+ align:start position:0%
+oriented like the retina
+and so here's a particularly kind of
+
+ align:start position:0%
+and so here's a particularly kind of
+ 
+
+ align:start position:0%
+and so here's a particularly kind of
+gruesome but very literal depiction of
+
+ align:start position:0%
+gruesome but very literal depiction of
+ 
+
+ align:start position:0%
+gruesome but very literal depiction of
+this property of retina topi
+
+ align:start position:0%
+this property of retina topi
+ 
+
+ align:start position:0%
+this property of retina topi
+in a monkey brain this is an experiment
+
+ align:start position:0%
+in a monkey brain this is an experiment
+ 
+
+ align:start position:0%
+in a monkey brain this is an experiment
+done very long ago by roger tutel
+
+ align:start position:0%
+done very long ago by roger tutel
+ 
+
+ align:start position:0%
+done very long ago by roger tutel
+and what he did was um
+
+ align:start position:0%
+and what he did was um
+ 
+
+ align:start position:0%
+and what he did was um
+he used a method called deoxyglucose and
+
+ align:start position:0%
+he used a method called deoxyglucose and
+ 
+
+ align:start position:0%
+he used a method called deoxyglucose and
+so what deoxyglucose
+
+ align:start position:0%
+so what deoxyglucose
+ 
+
+ align:start position:0%
+so what deoxyglucose
+is a molecule that's a whole lot like
+
+ align:start position:0%
+is a molecule that's a whole lot like
+ 
+
+ align:start position:0%
+is a molecule that's a whole lot like
+glucose
+
+ align:start position:0%
+glucose
+ 
+
+ align:start position:0%
+glucose
+but it's got one little change in the
+
+ align:start position:0%
+but it's got one little change in the
+ 
+
+ align:start position:0%
+but it's got one little change in the
+molecule which means it gets stuck on
+
+ align:start position:0%
+molecule which means it gets stuck on
+ 
+
+ align:start position:0%
+molecule which means it gets stuck on
+the metabolic chain and so it gets taken
+
+ align:start position:0%
+the metabolic chain and so it gets taken
+ 
+
+ align:start position:0%
+the metabolic chain and so it gets taken
+up by cells that want to take up glucose
+
+ align:start position:0%
+up by cells that want to take up glucose
+ 
+
+ align:start position:0%
+up by cells that want to take up glucose
+and then it gets stuck in there and
+
+ align:start position:0%
+and then it gets stuck in there and
+ 
+
+ align:start position:0%
+and then it gets stuck in there and
+can't be broken down so it builds up in
+
+ align:start position:0%
+can't be broken down so it builds up in
+ 
+
+ align:start position:0%
+can't be broken down so it builds up in
+cells that are metabolically active
+
+ align:start position:0%
+cells that are metabolically active
+ 
+
+ align:start position:0%
+cells that are metabolically active
+okay so you can put a little radioactive
+
+ align:start position:0%
+okay so you can put a little radioactive
+ 
+
+ align:start position:0%
+okay so you can put a little radioactive
+tracer on deoxyglucose
+
+ align:start position:0%
+tracer on deoxyglucose
+ 
+
+ align:start position:0%
+tracer on deoxyglucose
+inject it into a person or an animal and
+
+ align:start position:0%
+inject it into a person or an animal and
+ 
+
+ align:start position:0%
+inject it into a person or an animal and
+what happens is it builds up with this
+
+ align:start position:0%
+what happens is it builds up with this
+ 
+
+ align:start position:0%
+what happens is it builds up with this
+radioactive tag on all the cells that
+
+ align:start position:0%
+radioactive tag on all the cells that
+ 
+
+ align:start position:0%
+radioactive tag on all the cells that
+were active makes sense
+
+ align:start position:0%
+were active makes sense
+ 
+
+ align:start position:0%
+were active makes sense
+okay so tutel did an experiment where
+
+ align:start position:0%
+okay so tutel did an experiment where
+ 
+
+ align:start position:0%
+okay so tutel did an experiment where
+he had the monkey fixate on a spot
+
+ align:start position:0%
+he had the monkey fixate on a spot
+ 
+
+ align:start position:0%
+he had the monkey fixate on a spot
+and he presented this stimulus here so
+
+ align:start position:0%
+and he presented this stimulus here so
+ 
+
+ align:start position:0%
+and he presented this stimulus here so
+the monkey's fixating right there and
+
+ align:start position:0%
+the monkey's fixating right there and
+ 
+
+ align:start position:0%
+the monkey's fixating right there and
+the stimulus is flashing on and off
+
+ align:start position:0%
+the stimulus is flashing on and off
+ 
+
+ align:start position:0%
+the stimulus is flashing on and off
+he injects the radioactive deoxyglucose
+
+ align:start position:0%
+he injects the radioactive deoxyglucose
+ 
+
+ align:start position:0%
+he injects the radioactive deoxyglucose
+into the monkey while the monkey's
+
+ align:start position:0%
+into the monkey while the monkey's
+ 
+
+ align:start position:0%
+into the monkey while the monkey's
+looking at this
+
+ align:start position:0%
+looking at this
+ 
+
+ align:start position:0%
+looking at this
+and then i'm sorry to say he killed the
+
+ align:start position:0%
+and then i'm sorry to say he killed the
+ 
+
+ align:start position:0%
+and then i'm sorry to say he killed the
+monkey
+
+ align:start position:0%
+monkey
+ 
+
+ align:start position:0%
+monkey
+rolled out visual cortex into a sheet
+
+ align:start position:0%
+rolled out visual cortex into a sheet
+ 
+
+ align:start position:0%
+rolled out visual cortex into a sheet
+and there it is
+
+ align:start position:0%
+and there it is
+ 
+
+ align:start position:0%
+and there it is
+and you can see the bullseye pattern
+
+ align:start position:0%
+and you can see the bullseye pattern
+ 
+
+ align:start position:0%
+and you can see the bullseye pattern
+that the monkey was looking at across
+
+ align:start position:0%
+that the monkey was looking at across
+ 
+
+ align:start position:0%
+that the monkey was looking at across
+the surface of visual cortex
+
+ align:start position:0%
+the surface of visual cortex
+ 
+
+ align:start position:0%
+the surface of visual cortex
+does everybody get that
+
+ align:start position:0%
+does everybody get that
+ 
+
+ align:start position:0%
+does everybody get that
+okay so that shows you very literally
+
+ align:start position:0%
+okay so that shows you very literally
+ 
+
+ align:start position:0%
+okay so that shows you very literally
+what a retinotopic map is in the brain
+
+ align:start position:0%
+what a retinotopic map is in the brain
+ 
+
+ align:start position:0%
+what a retinotopic map is in the brain
+it's just like the map of the visual
+
+ align:start position:0%
+it's just like the map of the visual
+ 
+
+ align:start position:0%
+it's just like the map of the visual
+world in the retina but there it is up
+
+ align:start position:0%
+world in the retina but there it is up
+ 
+
+ align:start position:0%
+world in the retina but there it is up
+in the back of the brain and humans have
+
+ align:start position:0%
+in the back of the brain and humans have
+ 
+
+ align:start position:0%
+in the back of the brain and humans have
+this too
+
+ align:start position:0%
+this too
+ 
+
+ align:start position:0%
+this too
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and so this can be shown in humans with
+
+ align:start position:0%
+and so this can be shown in humans with
+ 
+
+ align:start position:0%
+and so this can be shown in humans with
+functional mri we'll talk later more
+
+ align:start position:0%
+functional mri we'll talk later more
+ 
+
+ align:start position:0%
+functional mri we'll talk later more
+about the methods of functional mri but
+
+ align:start position:0%
+about the methods of functional mri but
+ 
+
+ align:start position:0%
+about the methods of functional mri but
+here's a very high resolution functional
+
+ align:start position:0%
+here's a very high resolution functional
+ 
+
+ align:start position:0%
+here's a very high resolution functional
+mri experiment done by some people over
+
+ align:start position:0%
+mri experiment done by some people over
+ 
+
+ align:start position:0%
+mri experiment done by some people over
+at mgh charlestown by the way when i
+
+ align:start position:0%
+at mgh charlestown by the way when i
+ 
+
+ align:start position:0%
+at mgh charlestown by the way when i
+have names on slides
+
+ align:start position:0%
+have names on slides
+ 
+
+ align:start position:0%
+have names on slides
+it's just because in science we don't
+
+ align:start position:0%
+it's just because in science we don't
+ 
+
+ align:start position:0%
+it's just because in science we don't
+get paid that much and so our credit for
+
+ align:start position:0%
+get paid that much and so our credit for
+ 
+
+ align:start position:0%
+get paid that much and so our credit for
+our cool data is kind of all we have and
+
+ align:start position:0%
+our cool data is kind of all we have and
+ 
+
+ align:start position:0%
+our cool data is kind of all we have and
+so i can't stand to talk about other
+
+ align:start position:0%
+so i can't stand to talk about other
+ 
+
+ align:start position:0%
+so i can't stand to talk about other
+people's cool experiments without giving
+
+ align:start position:0%
+people's cool experiments without giving
+ 
+
+ align:start position:0%
+people's cool experiments without giving
+them credit i do not expect you to learn
+
+ align:start position:0%
+them credit i do not expect you to learn
+ 
+
+ align:start position:0%
+them credit i do not expect you to learn
+the names it's just my little personal
+
+ align:start position:0%
+the names it's just my little personal
+ 
+
+ align:start position:0%
+the names it's just my little personal
+tic that i need to have their name there
+
+ align:start position:0%
+tic that i need to have their name there
+ 
+
+ align:start position:0%
+tic that i need to have their name there
+to give them credit even though you
+
+ align:start position:0%
+to give them credit even though you
+ 
+
+ align:start position:0%
+to give them credit even though you
+don't know who they are okay
+
+ align:start position:0%
+don't know who they are okay
+ 
+
+ align:start position:0%
+don't know who they are okay
+okay so what this guy john palomani did
+
+ align:start position:0%
+okay so what this guy john palomani did
+ 
+
+ align:start position:0%
+okay so what this guy john palomani did
+was show human subjects this stimulus
+
+ align:start position:0%
+was show human subjects this stimulus
+ 
+
+ align:start position:0%
+was show human subjects this stimulus
+here they were fixating right there and
+
+ align:start position:0%
+here they were fixating right there and
+ 
+
+ align:start position:0%
+here they were fixating right there and
+the stimulus is flickering with the dots
+
+ align:start position:0%
+the stimulus is flickering with the dots
+ 
+
+ align:start position:0%
+the stimulus is flickering with the dots
+kind of dancing around
+
+ align:start position:0%
+kind of dancing around
+ 
+
+ align:start position:0%
+kind of dancing around
+and then he looked on the back in visual
+
+ align:start position:0%
+and then he looked on the back in visual
+ 
+
+ align:start position:0%
+and then he looked on the back in visual
+cortex on the surface of the brain
+
+ align:start position:0%
+cortex on the surface of the brain
+ 
+
+ align:start position:0%
+cortex on the surface of the brain
+and he sees an n there
+
+ align:start position:0%
+and he sees an n there
+ 
+
+ align:start position:0%
+and he sees an n there
+it's the same stimulus it's just flipped
+
+ align:start position:0%
+it's the same stimulus it's just flipped
+ 
+
+ align:start position:0%
+it's the same stimulus it's just flipped
+upside down which is not deeper
+
+ align:start position:0%
+upside down which is not deeper
+ 
+
+ align:start position:0%
+upside down which is not deeper
+interesting the cortex has to be
+
+ align:start position:0%
+interesting the cortex has to be
+ 
+
+ align:start position:0%
+interesting the cortex has to be
+oriented one way or another the brain
+
+ align:start position:0%
+oriented one way or another the brain
+ 
+
+ align:start position:0%
+oriented one way or another the brain
+doesn't care whether you turn it around
+
+ align:start position:0%
+doesn't care whether you turn it around
+ 
+
+ align:start position:0%
+doesn't care whether you turn it around
+right and your map of visual space is
+
+ align:start position:0%
+right and your map of visual space is
+ 
+
+ align:start position:0%
+right and your map of visual space is
+upside down in the back of the head
+
+ align:start position:0%
+upside down in the back of the head
+ 
+
+ align:start position:0%
+upside down in the back of the head
+and you see that m
+
+ align:start position:0%
+and you see that m
+ 
+
+ align:start position:0%
+and you see that m
+does everybody get how that also shows
+
+ align:start position:0%
+does everybody get how that also shows
+ 
+
+ align:start position:0%
+does everybody get how that also shows
+retinotopic properties in the brain
+
+ align:start position:0%
+retinotopic properties in the brain
+ 
+
+ align:start position:0%
+retinotopic properties in the brain
+in human visual cortex
+
+ align:start position:0%
+in human visual cortex
+ 
+
+ align:start position:0%
+in human visual cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right so the key idea of retina
+
+ align:start position:0%
+all right so the key idea of retina
+ 
+
+ align:start position:0%
+all right so the key idea of retina
+toppy is that adjacent parts of the
+
+ align:start position:0%
+toppy is that adjacent parts of the
+ 
+
+ align:start position:0%
+toppy is that adjacent parts of the
+visual seal field are mapped to adjacent
+
+ align:start position:0%
+visual seal field are mapped to adjacent
+ 
+
+ align:start position:0%
+visual seal field are mapped to adjacent
+parts of the cortex
+
+ align:start position:0%
+parts of the cortex
+ 
+
+ align:start position:0%
+parts of the cortex
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+okay a little bit of terminology just
+
+ align:start position:0%
+okay a little bit of terminology just
+ 
+
+ align:start position:0%
+okay a little bit of terminology just
+because
+
+ align:start position:0%
+because
+ 
+
+ align:start position:0%
+because
+people are fast and loose with these
+
+ align:start position:0%
+people are fast and loose with these
+ 
+
+ align:start position:0%
+people are fast and loose with these
+things i've already referred to v1 and
+
+ align:start position:0%
+things i've already referred to v1 and
+ 
+
+ align:start position:0%
+things i've already referred to v1 and
+primary visual cortex it's also
+
+ align:start position:0%
+primary visual cortex it's also
+ 
+
+ align:start position:0%
+primary visual cortex it's also
+sometimes called striat cortex it's all
+
+ align:start position:0%
+sometimes called striat cortex it's all
+ 
+
+ align:start position:0%
+sometimes called striat cortex it's all
+the same thing it's the part of the
+
+ align:start position:0%
+the same thing it's the part of the
+ 
+
+ align:start position:0%
+the same thing it's the part of the
+visual cortex where the information
+
+ align:start position:0%
+visual cortex where the information
+ 
+
+ align:start position:0%
+visual cortex where the information
+first comes up from the lgn right back
+
+ align:start position:0%
+first comes up from the lgn right back
+ 
+
+ align:start position:0%
+first comes up from the lgn right back
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+so in me it's right there most of it is
+
+ align:start position:0%
+so in me it's right there most of it is
+ 
+
+ align:start position:0%
+so in me it's right there most of it is
+in the space between the two hemispheres
+
+ align:start position:0%
+in the space between the two hemispheres
+ 
+
+ align:start position:0%
+in the space between the two hemispheres
+but a little bit sticks out on the side
+
+ align:start position:0%
+but a little bit sticks out on the side
+ 
+
+ align:start position:0%
+but a little bit sticks out on the side
+so in this person that yellowy orange
+
+ align:start position:0%
+so in this person that yellowy orange
+ 
+
+ align:start position:0%
+so in this person that yellowy orange
+stuff that's primary visual cortex which
+
+ align:start position:0%
+stuff that's primary visual cortex which
+ 
+
+ align:start position:0%
+stuff that's primary visual cortex which
+is the same as v1 and striat cortex okay
+
+ align:start position:0%
+is the same as v1 and striat cortex okay
+ 
+
+ align:start position:0%
+is the same as v1 and striat cortex okay
+that's just terminology
+
+ align:start position:0%
+that's just terminology
+ 
+
+ align:start position:0%
+that's just terminology
+all right just as we have maps for
+
+ align:start position:0%
+all right just as we have maps for
+ 
+
+ align:start position:0%
+all right just as we have maps for
+visual space we have maps for touch
+
+ align:start position:0%
+visual space we have maps for touch
+ 
+
+ align:start position:0%
+visual space we have maps for touch
+space and so you've probably seen this
+
+ align:start position:0%
+space and so you've probably seen this
+ 
+
+ align:start position:0%
+space and so you've probably seen this
+diagram here of the map of touch space
+
+ align:start position:0%
+diagram here of the map of touch space
+ 
+
+ align:start position:0%
+diagram here of the map of touch space
+going across somatosensory cortex like
+
+ align:start position:0%
+going across somatosensory cortex like
+ 
+
+ align:start position:0%
+going across somatosensory cortex like
+this so this is a picture of a slice
+
+ align:start position:0%
+this so this is a picture of a slice
+ 
+
+ align:start position:0%
+this so this is a picture of a slice
+like that showing you which parts of the
+
+ align:start position:0%
+like that showing you which parts of the
+ 
+
+ align:start position:0%
+like that showing you which parts of the
+body are mapped out to which parts of
+
+ align:start position:0%
+body are mapped out to which parts of
+ 
+
+ align:start position:0%
+body are mapped out to which parts of
+space
+
+ align:start position:0%
+space
+ 
+
+ align:start position:0%
+space
+and you can see that particularly
+
+ align:start position:0%
+and you can see that particularly
+ 
+
+ align:start position:0%
+and you can see that particularly
+important parts of the body get bigger
+
+ align:start position:0%
+important parts of the body get bigger
+ 
+
+ align:start position:0%
+important parts of the body get bigger
+bits of cortex
+
+ align:start position:0%
+bits of cortex
+ 
+
+ align:start position:0%
+bits of cortex
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+just as we have visual maps and touch
+
+ align:start position:0%
+just as we have visual maps and touch
+ 
+
+ align:start position:0%
+just as we have visual maps and touch
+maps we have auditory maps in auditory
+
+ align:start position:0%
+maps we have auditory maps in auditory
+ 
+
+ align:start position:0%
+maps we have auditory maps in auditory
+cortex which is right on the top of the
+
+ align:start position:0%
+cortex which is right on the top of the
+ 
+
+ align:start position:0%
+cortex which is right on the top of the
+temporal lobe right in here
+
+ align:start position:0%
+temporal lobe right in here
+ 
+
+ align:start position:0%
+temporal lobe right in here
+and which is what's mapped out in
+
+ align:start position:0%
+and which is what's mapped out in
+ 
+
+ align:start position:0%
+and which is what's mapped out in
+auditory cortex is auditory frequency
+
+ align:start position:0%
+auditory cortex is auditory frequency
+ 
+
+ align:start position:0%
+auditory cortex is auditory frequency
+high versus low versus high
+
+ align:start position:0%
+high versus low versus high
+ 
+
+ align:start position:0%
+high versus low versus high
+frequencies of sound and so you see that
+
+ align:start position:0%
+frequencies of sound and so you see that
+ 
+
+ align:start position:0%
+frequencies of sound and so you see that
+here's a piece of auditory cortex in one
+
+ align:start position:0%
+here's a piece of auditory cortex in one
+ 
+
+ align:start position:0%
+here's a piece of auditory cortex in one
+subject showing you
+
+ align:start position:0%
+subject showing you
+ 
+
+ align:start position:0%
+subject showing you
+regions that respond to high frequencies
+
+ align:start position:0%
+regions that respond to high frequencies
+ 
+
+ align:start position:0%
+regions that respond to high frequencies
+low frequencies high frequencies here it
+
+ align:start position:0%
+low frequencies high frequencies here it
+ 
+
+ align:start position:0%
+low frequencies high frequencies here it
+is another subject high low high another
+
+ align:start position:0%
+is another subject high low high another
+ 
+
+ align:start position:0%
+is another subject high low high another
+subject high low high
+
+ align:start position:0%
+subject high low high
+ 
+
+ align:start position:0%
+subject high low high
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so the point of all of this
+
+ align:start position:0%
+so the point of all of this
+ 
+
+ align:start position:0%
+so the point of all of this
+is that primary sensory cortex has maps
+
+ align:start position:0%
+is that primary sensory cortex has maps
+ 
+
+ align:start position:0%
+is that primary sensory cortex has maps
+everybody clear on this the different
+
+ align:start position:0%
+everybody clear on this the different
+ 
+
+ align:start position:0%
+everybody clear on this the different
+sensory modalities map different
+
+ align:start position:0%
+sensory modalities map different
+ 
+
+ align:start position:0%
+sensory modalities map different
+dimensions
+
+ align:start position:0%
+dimensions
+ 
+
+ align:start position:0%
+dimensions
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so what about the rest of cortex like
+
+ align:start position:0%
+so what about the rest of cortex like
+ 
+
+ align:start position:0%
+so what about the rest of cortex like
+you can see most of the cortex is not
+
+ align:start position:0%
+you can see most of the cortex is not
+ 
+
+ align:start position:0%
+you can see most of the cortex is not
+primary sensory cortex
+
+ align:start position:0%
+primary sensory cortex
+ 
+
+ align:start position:0%
+primary sensory cortex
+is the rest of cortex just mush or are
+
+ align:start position:0%
+is the rest of cortex just mush or are
+ 
+
+ align:start position:0%
+is the rest of cortex just mush or are
+there separate bits like primary sensory
+
+ align:start position:0%
+there separate bits like primary sensory
+ 
+
+ align:start position:0%
+there separate bits like primary sensory
+areas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if so do those other bits have maps
+
+ align:start position:0%
+and if so do those other bits have maps
+ 
+
+ align:start position:0%
+and if so do those other bits have maps
+and if so
+
+ align:start position:0%
+and if so
+ 
+
+ align:start position:0%
+and if so
+what are those maps of
+
+ align:start position:0%
+what are those maps of
+ 
+
+ align:start position:0%
+what are those maps of
+okay we just took you from 100 years ago
+
+ align:start position:0%
+okay we just took you from 100 years ago
+ 
+
+ align:start position:0%
+okay we just took you from 100 years ago
+to the cutting edge of the field is
+
+ align:start position:0%
+to the cutting edge of the field is
+ 
+
+ align:start position:0%
+to the cutting edge of the field is
+asking this question in lots of
+
+ align:start position:0%
+asking this question in lots of
+ 
+
+ align:start position:0%
+asking this question in lots of
+different ways right now
+
+ align:start position:0%
+different ways right now
+ 
+
+ align:start position:0%
+different ways right now
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's back up and ask what counts
+
+ align:start position:0%
+okay let's back up and ask what counts
+ 
+
+ align:start position:0%
+okay let's back up and ask what counts
+as a cortical area anyway i just posited
+
+ align:start position:0%
+as a cortical area anyway i just posited
+ 
+
+ align:start position:0%
+as a cortical area anyway i just posited
+that these primary sensory regions count
+
+ align:start position:0%
+that these primary sensory regions count
+ 
+
+ align:start position:0%
+that these primary sensory regions count
+as distinct things they're like the
+
+ align:start position:0%
+as distinct things they're like the
+ 
+
+ align:start position:0%
+as distinct things they're like the
+things right they're separate things in
+
+ align:start position:0%
+things right they're separate things in
+ 
+
+ align:start position:0%
+things right they're separate things in
+the brain okay and if for no other
+
+ align:start position:0%
+the brain okay and if for no other
+ 
+
+ align:start position:0%
+the brain okay and if for no other
+reason then they get direct input from
+
+ align:start position:0%
+reason then they get direct input from
+ 
+
+ align:start position:0%
+reason then they get direct input from
+the thalamus
+
+ align:start position:0%
+the thalamus
+ 
+
+ align:start position:0%
+the thalamus
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+but let's back up and ask what exactly
+
+ align:start position:0%
+but let's back up and ask what exactly
+ 
+
+ align:start position:0%
+but let's back up and ask what exactly
+is a cortical area
+
+ align:start position:0%
+is a cortical area
+ 
+
+ align:start position:0%
+is a cortical area
+and we're going to consider this
+
+ align:start position:0%
+and we're going to consider this
+ 
+
+ align:start position:0%
+and we're going to consider this
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+by considering the three key criteria
+
+ align:start position:0%
+by considering the three key criteria
+ 
+
+ align:start position:0%
+by considering the three key criteria
+for what counts as a cortical area
+
+ align:start position:0%
+for what counts as a cortical area
+ 
+
+ align:start position:0%
+for what counts as a cortical area
+okay the first one
+
+ align:start position:0%
+okay the first one
+ 
+
+ align:start position:0%
+okay the first one
+is that that region of cortex is
+
+ align:start position:0%
+is that that region of cortex is
+ 
+
+ align:start position:0%
+is that that region of cortex is
+distinct from its neighbors in function
+
+ align:start position:0%
+distinct from its neighbors in function
+ 
+
+ align:start position:0%
+distinct from its neighbors in function
+neurons their fire in response to
+
+ align:start position:0%
+neurons their fire in response to
+ 
+
+ align:start position:0%
+neurons their fire in response to
+something different from the neurons in
+
+ align:start position:0%
+something different from the neurons in
+ 
+
+ align:start position:0%
+something different from the neurons in
+the neighboring region okay that's very
+
+ align:start position:0%
+the neighboring region okay that's very
+ 
+
+ align:start position:0%
+the neighboring region okay that's very
+vague right now but we'll illustrate
+
+ align:start position:0%
+vague right now but we'll illustrate
+ 
+
+ align:start position:0%
+vague right now but we'll illustrate
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+the next one as i mentioned this before
+
+ align:start position:0%
+the next one as i mentioned this before
+ 
+
+ align:start position:0%
+the next one as i mentioned this before
+each distinct
+
+ align:start position:0%
+each distinct
+ 
+
+ align:start position:0%
+each distinct
+region of cortex has a different set of
+
+ align:start position:0%
+region of cortex has a different set of
+ 
+
+ align:start position:0%
+region of cortex has a different set of
+connections to other parts of the brain
+
+ align:start position:0%
+connections to other parts of the brain
+ 
+
+ align:start position:0%
+connections to other parts of the brain
+it has a distinct connectivity
+
+ align:start position:0%
+it has a distinct connectivity
+ 
+
+ align:start position:0%
+it has a distinct connectivity
+fingerprint
+
+ align:start position:0%
+fingerprint
+ 
+
+ align:start position:0%
+fingerprint
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the third thing is
+
+ align:start position:0%
+and the third thing is
+ 
+
+ align:start position:0%
+and the third thing is
+for at least some regions of the cortex
+
+ align:start position:0%
+for at least some regions of the cortex
+ 
+
+ align:start position:0%
+for at least some regions of the cortex
+they're physically different if you
+
+ align:start position:0%
+they're physically different if you
+ 
+
+ align:start position:0%
+they're physically different if you
+slice them up and stain them and look at
+
+ align:start position:0%
+slice them up and stain them and look at
+ 
+
+ align:start position:0%
+slice them up and stain them and look at
+them really carefully they might look a
+
+ align:start position:0%
+them really carefully they might look a
+ 
+
+ align:start position:0%
+them really carefully they might look a
+little different than other bits of the
+
+ align:start position:0%
+little different than other bits of the
+ 
+
+ align:start position:0%
+little different than other bits of the
+cortex
+
+ align:start position:0%
+cortex
+ 
+
+ align:start position:0%
+cortex
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so those are three of the key criteria
+
+ align:start position:0%
+so those are three of the key criteria
+ 
+
+ align:start position:0%
+so those are three of the key criteria
+that have been used to say this bit of
+
+ align:start position:0%
+that have been used to say this bit of
+ 
+
+ align:start position:0%
+that have been used to say this bit of
+cortex it's a thing right it's distinct
+
+ align:start position:0%
+cortex it's a thing right it's distinct
+ 
+
+ align:start position:0%
+cortex it's a thing right it's distinct
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so let's look at the classic example
+
+ align:start position:0%
+so let's look at the classic example
+ 
+
+ align:start position:0%
+so let's look at the classic example
+beyond those primary regions those are
+
+ align:start position:0%
+beyond those primary regions those are
+ 
+
+ align:start position:0%
+beyond those primary regions those are
+the most classic regions the primary
+
+ align:start position:0%
+the most classic regions the primary
+ 
+
+ align:start position:0%
+the most classic regions the primary
+regions we've already talked about those
+
+ align:start position:0%
+regions we've already talked about those
+ 
+
+ align:start position:0%
+regions we've already talked about those
+are the ones nobody would fight you on
+
+ align:start position:0%
+are the ones nobody would fight you on
+ 
+
+ align:start position:0%
+are the ones nobody would fight you on
+that this one is next in line nobody
+
+ align:start position:0%
+that this one is next in line nobody
+ 
+
+ align:start position:0%
+that this one is next in line nobody
+will fight you of say if you say visual
+
+ align:start position:0%
+will fight you of say if you say visual
+ 
+
+ align:start position:0%
+will fight you of say if you say visual
+area mt
+
+ align:start position:0%
+area mt
+ 
+
+ align:start position:0%
+area mt
+that's an area well they might but most
+
+ align:start position:0%
+that's an area well they might but most
+ 
+
+ align:start position:0%
+that's an area well they might but most
+people wouldn't okay and then from there
+
+ align:start position:0%
+people wouldn't okay and then from there
+ 
+
+ align:start position:0%
+people wouldn't okay and then from there
+on out it's all fighting all the time
+
+ align:start position:0%
+on out it's all fighting all the time
+ 
+
+ align:start position:0%
+on out it's all fighting all the time
+okay so let's talk about visual area mt
+
+ align:start position:0%
+okay so let's talk about visual area mt
+ 
+
+ align:start position:0%
+okay so let's talk about visual area mt
+it's a little patch of the cortex and a
+
+ align:start position:0%
+it's a little patch of the cortex and a
+ 
+
+ align:start position:0%
+it's a little patch of the cortex and a
+monkey brain this is a side view of a
+
+ align:start position:0%
+monkey brain this is a side view of a
+ 
+
+ align:start position:0%
+monkey brain this is a side view of a
+monkey brain
+
+ align:start position:0%
+monkey brain
+ 
+
+ align:start position:0%
+monkey brain
+and in this human brain it's that little
+
+ align:start position:0%
+and in this human brain it's that little
+ 
+
+ align:start position:0%
+and in this human brain it's that little
+patch right there
+
+ align:start position:0%
+patch right there
+ 
+
+ align:start position:0%
+patch right there
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+this region meets all the criteria to be
+
+ align:start position:0%
+this region meets all the criteria to be
+ 
+
+ align:start position:0%
+this region meets all the criteria to be
+a distinct visual area
+
+ align:start position:0%
+a distinct visual area
+ 
+
+ align:start position:0%
+a distinct visual area
+so how do we know this
+
+ align:start position:0%
+so how do we know this
+ 
+
+ align:start position:0%
+so how do we know this
+well we know this from lots and lots of
+
+ align:start position:0%
+well we know this from lots and lots of
+ 
+
+ align:start position:0%
+well we know this from lots and lots of
+different methods so i'm going to whip
+
+ align:start position:0%
+different methods so i'm going to whip
+ 
+
+ align:start position:0%
+different methods so i'm going to whip
+through a few of those to give you a
+
+ align:start position:0%
+through a few of those to give you a
+ 
+
+ align:start position:0%
+through a few of those to give you a
+gist of how we can find evidence that
+
+ align:start position:0%
+gist of how we can find evidence that
+ 
+
+ align:start position:0%
+gist of how we can find evidence that
+that region is distinct in function
+
+ align:start position:0%
+that region is distinct in function
+ 
+
+ align:start position:0%
+that region is distinct in function
+connectivity and
+
+ align:start position:0%
+connectivity and
+ 
+
+ align:start position:0%
+connectivity and
+the physical stuff sometimes called cyto
+
+ align:start position:0%
+the physical stuff sometimes called cyto
+ 
+
+ align:start position:0%
+the physical stuff sometimes called cyto
+architecture
+
+ align:start position:0%
+architecture
+ 
+
+ align:start position:0%
+architecture
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+all right
+
+ align:start position:0%
+all right
+ 
+
+ align:start position:0%
+all right
+function how would we know that region
+
+ align:start position:0%
+function how would we know that region
+ 
+
+ align:start position:0%
+function how would we know that region
+respon has a different function
+
+ align:start position:0%
+respon has a different function
+ 
+
+ align:start position:0%
+respon has a different function
+well one way the classic way is to
+
+ align:start position:0%
+well one way the classic way is to
+ 
+
+ align:start position:0%
+well one way the classic way is to
+record from individual neurons in monkey
+
+ align:start position:0%
+record from individual neurons in monkey
+ 
+
+ align:start position:0%
+record from individual neurons in monkey
+brains
+
+ align:start position:0%
+brains
+ 
+
+ align:start position:0%
+brains
+so if you stick a neuron into monkey
+
+ align:start position:0%
+so if you stick a neuron into monkey
+ 
+
+ align:start position:0%
+so if you stick a neuron into monkey
+visual cortex while the monkey is
+
+ align:start position:0%
+visual cortex while the monkey is
+ 
+
+ align:start position:0%
+visual cortex while the monkey is
+looking at the stimulus
+
+ align:start position:0%
+looking at the stimulus
+ 
+
+ align:start position:0%
+looking at the stimulus
+that i'll show you in a second you'll
+
+ align:start position:0%
+that i'll show you in a second you'll
+ 
+
+ align:start position:0%
+that i'll show you in a second you'll
+hear the responses of an individual
+
+ align:start position:0%
+hear the responses of an individual
+ 
+
+ align:start position:0%
+hear the responses of an individual
+neuron each clique will be the response
+
+ align:start position:0%
+neuron each clique will be the response
+ 
+
+ align:start position:0%
+neuron each clique will be the response
+of an individual neuron to the stimulus
+
+ align:start position:0%
+of an individual neuron to the stimulus
+ 
+
+ align:start position:0%
+of an individual neuron to the stimulus
+so let's play this thing
+
+ align:start position:0%
+so let's play this thing
+ 
+
+ align:start position:0%
+so let's play this thing
+except it's not making any sound chris
+
+ align:start position:0%
+except it's not making any sound chris
+ 
+
+ align:start position:0%
+except it's not making any sound chris
+can you help me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh right
+
+ align:start position:0%
+oh right
+ 
+
+ align:start position:0%
+oh right
+duh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that part
+
+ align:start position:0%
+that part
+ 
+
+ align:start position:0%
+that part
+okay see when the bar of light moves
+
+ align:start position:0%
+okay see when the bar of light moves
+ 
+
+ align:start position:0%
+okay see when the bar of light moves
+this way it makes a lot of firing
+
+ align:start position:0%
+this way it makes a lot of firing
+ 
+
+ align:start position:0%
+this way it makes a lot of firing
+and not when it moves the other way
+
+ align:start position:0%
+and not when it moves the other way
+ 
+
+ align:start position:0%
+and not when it moves the other way
+let's watch it for a second watch the
+
+ align:start position:0%
+let's watch it for a second watch the
+ 
+
+ align:start position:0%
+let's watch it for a second watch the
+bar move again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so he responds less when it's moving in
+
+ align:start position:0%
+so he responds less when it's moving in
+ 
+
+ align:start position:0%
+so he responds less when it's moving in
+a different direction ready got that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is this area right there called
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah this area right here in the middle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+exactly that's a receptive field that's
+
+ align:start position:0%
+exactly that's a receptive field that's
+ 
+
+ align:start position:0%
+exactly that's a receptive field that's
+a part of visual space that makes this
+
+ align:start position:0%
+a part of visual space that makes this
+ 
+
+ align:start position:0%
+a part of visual space that makes this
+neuron fire
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay this neuron also has a property
+
+ align:start position:0%
+okay this neuron also has a property
+ 
+
+ align:start position:0%
+okay this neuron also has a property
+called direction it's sensitive to
+
+ align:start position:0%
+called direction it's sensitive to
+ 
+
+ align:start position:0%
+called direction it's sensitive to
+motion as you see but it's also
+
+ align:start position:0%
+motion as you see but it's also
+ 
+
+ align:start position:0%
+motion as you see but it's also
+specific to specific directions of
+
+ align:start position:0%
+specific to specific directions of
+ 
+
+ align:start position:0%
+specific to specific directions of
+motion everybody see that
+
+ align:start position:0%
+motion everybody see that
+ 
+
+ align:start position:0%
+motion everybody see that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's a direction selective neuron
+
+ align:start position:0%
+so that's a direction selective neuron
+ 
+
+ align:start position:0%
+so that's a direction selective neuron
+in monkey area mt
+
+ align:start position:0%
+in monkey area mt
+ 
+
+ align:start position:0%
+in monkey area mt
+and here's a way of showing with data
+
+ align:start position:0%
+and here's a way of showing with data
+ 
+
+ align:start position:0%
+and here's a way of showing with data
+what you guys just saw
+
+ align:start position:0%
+what you guys just saw
+ 
+
+ align:start position:0%
+what you guys just saw
+this is a map of different directions in
+
+ align:start position:0%
+this is a map of different directions in
+ 
+
+ align:start position:0%
+this is a map of different directions in
+polar coordinates and this shows you how
+
+ align:start position:0%
+polar coordinates and this shows you how
+ 
+
+ align:start position:0%
+polar coordinates and this shows you how
+much
+
+ align:start position:0%
+much
+ 
+
+ align:start position:0%
+much
+this is a this is a single cell being
+
+ align:start position:0%
+this is a this is a single cell being
+ 
+
+ align:start position:0%
+this is a this is a single cell being
+described here this is the direction
+
+ align:start position:0%
+described here this is the direction
+ 
+
+ align:start position:0%
+described here this is the direction
+selectivity of that cell showing you
+
+ align:start position:0%
+selectivity of that cell showing you
+ 
+
+ align:start position:0%
+selectivity of that cell showing you
+that when motion moves when the stimulus
+
+ align:start position:0%
+that when motion moves when the stimulus
+ 
+
+ align:start position:0%
+that when motion moves when the stimulus
+moves in this direction you get a lot of
+
+ align:start position:0%
+moves in this direction you get a lot of
+ 
+
+ align:start position:0%
+moves in this direction you get a lot of
+firing when it moves in this direction
+
+ align:start position:0%
+firing when it moves in this direction
+ 
+
+ align:start position:0%
+firing when it moves in this direction
+you get less firing and can everybody
+
+ align:start position:0%
+you get less firing and can everybody
+ 
+
+ align:start position:0%
+you get less firing and can everybody
+see how this plot shows you the
+
+ align:start position:0%
+see how this plot shows you the
+ 
+
+ align:start position:0%
+see how this plot shows you the
+direction selectivity of that cell makes
+
+ align:start position:0%
+direction selectivity of that cell makes
+ 
+
+ align:start position:0%
+direction selectivity of that cell makes
+sense
+
+ align:start position:0%
+sense
+ 
+
+ align:start position:0%
+sense
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+okay so that shows you what you just saw
+
+ align:start position:0%
+okay so that shows you what you just saw
+ 
+
+ align:start position:0%
+okay so that shows you what you just saw
+in the movie
+
+ align:start position:0%
+in the movie
+ 
+
+ align:start position:0%
+in the movie
+so this is one way to establish the
+
+ align:start position:0%
+so this is one way to establish the
+ 
+
+ align:start position:0%
+so this is one way to establish the
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+of visual area mt is stick electrodes in
+
+ align:start position:0%
+of visual area mt is stick electrodes in
+ 
+
+ align:start position:0%
+of visual area mt is stick electrodes in
+there and record directly from them
+
+ align:start position:0%
+there and record directly from them
+ 
+
+ align:start position:0%
+there and record directly from them
+when a monkey looks at different kinds
+
+ align:start position:0%
+when a monkey looks at different kinds
+ 
+
+ align:start position:0%
+when a monkey looks at different kinds
+of stimuli and you see direction
+
+ align:start position:0%
+of stimuli and you see direction
+ 
+
+ align:start position:0%
+of stimuli and you see direction
+selectivity when you do that
+
+ align:start position:0%
+selectivity when you do that
+ 
+
+ align:start position:0%
+selectivity when you do that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+further
+
+ align:start position:0%
+further
+ 
+
+ align:start position:0%
+further
+if you actually do this systematically
+
+ align:start position:0%
+if you actually do this systematically
+ 
+
+ align:start position:0%
+if you actually do this systematically
+moving across next door bits
+
+ align:start position:0%
+moving across next door bits
+ 
+
+ align:start position:0%
+moving across next door bits
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+monkey area mt
+
+ align:start position:0%
+monkey area mt
+ 
+
+ align:start position:0%
+monkey area mt
+what you find is that as we said before
+
+ align:start position:0%
+what you find is that as we said before
+ 
+
+ align:start position:0%
+what you find is that as we said before
+nearby bits of cortex respond to similar
+
+ align:start position:0%
+nearby bits of cortex respond to similar
+ 
+
+ align:start position:0%
+nearby bits of cortex respond to similar
+things in this case to similar
+
+ align:start position:0%
+things in this case to similar
+ 
+
+ align:start position:0%
+things in this case to similar
+directions of motion so here's a little
+
+ align:start position:0%
+directions of motion so here's a little
+ 
+
+ align:start position:0%
+directions of motion so here's a little
+diagram as you move across the cortex
+
+ align:start position:0%
+diagram as you move across the cortex
+ 
+
+ align:start position:0%
+diagram as you move across the cortex
+you see a systematic change in the
+
+ align:start position:0%
+you see a systematic change in the
+ 
+
+ align:start position:0%
+you see a systematic change in the
+direction selectivity of neurons as you
+
+ align:start position:0%
+direction selectivity of neurons as you
+ 
+
+ align:start position:0%
+direction selectivity of neurons as you
+move across the cortex
+
+ align:start position:0%
+move across the cortex
+ 
+
+ align:start position:0%
+move across the cortex
+so in mt
+
+ align:start position:0%
+so in mt
+ 
+
+ align:start position:0%
+so in mt
+we have a map of direction preference
+
+ align:start position:0%
+we have a map of direction preference
+ 
+
+ align:start position:0%
+we have a map of direction preference
+just as we had a map of
+
+ align:start position:0%
+just as we had a map of
+ 
+
+ align:start position:0%
+just as we had a map of
+spatial location in primary visual
+
+ align:start position:0%
+spatial location in primary visual
+ 
+
+ align:start position:0%
+spatial location in primary visual
+cortex make sense
+
+ align:start position:0%
+cortex make sense
+ 
+
+ align:start position:0%
+cortex make sense
+okay now because those neurons are
+
+ align:start position:0%
+okay now because those neurons are
+ 
+
+ align:start position:0%
+okay now because those neurons are
+clustered like that
+
+ align:start position:0%
+clustered like that
+ 
+
+ align:start position:0%
+clustered like that
+i forget what my next point was no never
+
+ align:start position:0%
+i forget what my next point was no never
+ 
+
+ align:start position:0%
+i forget what my next point was no never
+mind we'll get that in a second okay
+
+ align:start position:0%
+mind we'll get that in a second okay
+ 
+
+ align:start position:0%
+mind we'll get that in a second okay
+what about humans okay so here's a
+
+ align:start position:0%
+what about humans okay so here's a
+ 
+
+ align:start position:0%
+what about humans okay so here's a
+monkey brain here's a neuron and a
+
+ align:start position:0%
+monkey brain here's a neuron and a
+ 
+
+ align:start position:0%
+monkey brain here's a neuron and a
+monkey brain what about humans can we
+
+ align:start position:0%
+monkey brain what about humans can we
+ 
+
+ align:start position:0%
+monkey brain what about humans can we
+record from single neurons in humans
+
+ align:start position:0%
+record from single neurons in humans
+ 
+
+ align:start position:0%
+record from single neurons in humans
+what do you think
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+do we ever get to do that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+neurosurgeons very occasionally enable
+
+ align:start position:0%
+neurosurgeons very occasionally enable
+ 
+
+ align:start position:0%
+neurosurgeons very occasionally enable
+us to record from individual neurons in
+
+ align:start position:0%
+us to record from individual neurons in
+ 
+
+ align:start position:0%
+us to record from individual neurons in
+human brains it's the most awesome data
+
+ align:start position:0%
+human brains it's the most awesome data
+ 
+
+ align:start position:0%
+human brains it's the most awesome data
+ever
+
+ align:start position:0%
+ever
+ 
+
+ align:start position:0%
+ever
+of course we only do it when the
+
+ align:start position:0%
+of course we only do it when the
+ 
+
+ align:start position:0%
+of course we only do it when the
+neurosurgeons have decided for clinical
+
+ align:start position:0%
+neurosurgeons have decided for clinical
+ 
+
+ align:start position:0%
+neurosurgeons have decided for clinical
+reasons to put electrodes in human
+
+ align:start position:0%
+reasons to put electrodes in human
+ 
+
+ align:start position:0%
+reasons to put electrodes in human
+brains they need to do this to map out
+
+ align:start position:0%
+brains they need to do this to map out
+ 
+
+ align:start position:0%
+brains they need to do this to map out
+epilepsy before surgery and sometimes
+
+ align:start position:0%
+epilepsy before surgery and sometimes
+ 
+
+ align:start position:0%
+epilepsy before surgery and sometimes
+those patients are super nice and say
+
+ align:start position:0%
+those patients are super nice and say
+ 
+
+ align:start position:0%
+those patients are super nice and say
+yes i'll look at your stimuli or listen
+
+ align:start position:0%
+yes i'll look at your stimuli or listen
+ 
+
+ align:start position:0%
+yes i'll look at your stimuli or listen
+to your stimuli while you record from my
+
+ align:start position:0%
+to your stimuli while you record from my
+ 
+
+ align:start position:0%
+to your stimuli while you record from my
+neurons and then we get the most awesome
+
+ align:start position:0%
+neurons and then we get the most awesome
+ 
+
+ align:start position:0%
+neurons and then we get the most awesome
+data ever but it's very very rare i
+
+ align:start position:0%
+data ever but it's very very rare i
+ 
+
+ align:start position:0%
+data ever but it's very very rare i
+don't know of any data where people have
+
+ align:start position:0%
+don't know of any data where people have
+ 
+
+ align:start position:0%
+don't know of any data where people have
+reported individual neurons in area mt
+
+ align:start position:0%
+reported individual neurons in area mt
+ 
+
+ align:start position:0%
+reported individual neurons in area mt
+in humans yeah so how powerful should an
+
+ align:start position:0%
+in humans yeah so how powerful should an
+ 
+
+ align:start position:0%
+in humans yeah so how powerful should an
+fmri be to be able to ignore such
+
+ align:start position:0%
+fmri be to be able to ignore such
+ 
+
+ align:start position:0%
+fmri be to be able to ignore such
+information oh we're getting there
+
+ align:start position:0%
+information oh we're getting there
+ 
+
+ align:start position:0%
+information oh we're getting there
+okay so given that we very rarely
+
+ align:start position:0%
+okay so given that we very rarely
+ 
+
+ align:start position:0%
+okay so given that we very rarely
+uh get uh get to record from individual
+
+ align:start position:0%
+uh get uh get to record from individual
+ 
+
+ align:start position:0%
+uh get uh get to record from individual
+neurons in humans and we want to know
+
+ align:start position:0%
+neurons in humans and we want to know
+ 
+
+ align:start position:0%
+neurons in humans and we want to know
+more generally
+
+ align:start position:0%
+more generally
+ 
+
+ align:start position:0%
+more generally
+if there is an mt in humans what do we
+
+ align:start position:0%
+if there is an mt in humans what do we
+ 
+
+ align:start position:0%
+if there is an mt in humans what do we
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+we pop subjects in an mri scanner
+
+ align:start position:0%
+we pop subjects in an mri scanner
+ 
+
+ align:start position:0%
+we pop subjects in an mri scanner
+and we show them moving dots or
+
+ align:start position:0%
+and we show them moving dots or
+ 
+
+ align:start position:0%
+and we show them moving dots or
+stationary dots
+
+ align:start position:0%
+stationary dots
+ 
+
+ align:start position:0%
+stationary dots
+and we scan them with functional mri
+
+ align:start position:0%
+and we scan them with functional mri
+ 
+
+ align:start position:0%
+and we scan them with functional mri
+we'll go through the details of how this
+
+ align:start position:0%
+we'll go through the details of how this
+ 
+
+ align:start position:0%
+we'll go through the details of how this
+works more in future lectures but what
+
+ align:start position:0%
+works more in future lectures but what
+ 
+
+ align:start position:0%
+works more in future lectures but what
+you see basically is this is a slice
+
+ align:start position:0%
+you see basically is this is a slice
+ 
+
+ align:start position:0%
+you see basically is this is a slice
+through the brain like this
+
+ align:start position:0%
+through the brain like this
+ 
+
+ align:start position:0%
+through the brain like this
+and you see this region right here
+
+ align:start position:0%
+and you see this region right here
+ 
+
+ align:start position:0%
+and you see this region right here
+responds more
+
+ align:start position:0%
+responds more
+ 
+
+ align:start position:0%
+responds more
+to the moving dots this is the response
+
+ align:start position:0%
+to the moving dots this is the response
+ 
+
+ align:start position:0%
+to the moving dots this is the response
+to the time here this is when the moving
+
+ align:start position:0%
+to the time here this is when the moving
+ 
+
+ align:start position:0%
+to the time here this is when the moving
+dots are on high response and then what
+
+ align:start position:0%
+dots are on high response and then what
+ 
+
+ align:start position:0%
+dots are on high response and then what
+switches to stationary dots
+
+ align:start position:0%
+switches to stationary dots
+ 
+
+ align:start position:0%
+switches to stationary dots
+the response drops
+
+ align:start position:0%
+the response drops
+ 
+
+ align:start position:0%
+the response drops
+okay so with functional mri you can also
+
+ align:start position:0%
+okay so with functional mri you can also
+ 
+
+ align:start position:0%
+okay so with functional mri you can also
+find visual area mt by the higher
+
+ align:start position:0%
+find visual area mt by the higher
+ 
+
+ align:start position:0%
+find visual area mt by the higher
+response to moving than stationary dots
+
+ align:start position:0%
+response to moving than stationary dots
+ 
+
+ align:start position:0%
+response to moving than stationary dots
+does that make sense more or less i mean
+
+ align:start position:0%
+does that make sense more or less i mean
+ 
+
+ align:start position:0%
+does that make sense more or less i mean
+i'm not giving you any of the details
+
+ align:start position:0%
+i'm not giving you any of the details
+ 
+
+ align:start position:0%
+i'm not giving you any of the details
+but for now they don't really matter
+
+ align:start position:0%
+but for now they don't really matter
+ 
+
+ align:start position:0%
+but for now they don't really matter
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so that's cool
+
+ align:start position:0%
+so that's cool
+ 
+
+ align:start position:0%
+so that's cool
+but does that tell us
+
+ align:start position:0%
+but does that tell us
+ 
+
+ align:start position:0%
+but does that tell us
+that neurons in human mt are specific
+
+ align:start position:0%
+that neurons in human mt are specific
+ 
+
+ align:start position:0%
+that neurons in human mt are specific
+for the direction of motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes
+
+ align:start position:0%
+yes
+ 
+
+ align:start position:0%
+yes
+moving in a specific motion removing in
+
+ align:start position:0%
+moving in a specific motion removing in
+ 
+
+ align:start position:0%
+moving in a specific motion removing in
+all the directions you see here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it doesn't
+
+ align:start position:0%
+no it doesn't
+ 
+
+ align:start position:0%
+no it doesn't
+it tells us it's sensitive to the
+
+ align:start position:0%
+it tells us it's sensitive to the
+ 
+
+ align:start position:0%
+it tells us it's sensitive to the
+presence of motion but not the direction
+
+ align:start position:0%
+presence of motion but not the direction
+ 
+
+ align:start position:0%
+presence of motion but not the direction
+of motion
+
+ align:start position:0%
+of motion
+ 
+
+ align:start position:0%
+of motion
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so if if we want to really know is human
+
+ align:start position:0%
+so if if we want to really know is human
+ 
+
+ align:start position:0%
+so if if we want to really know is human
+mt like monkey empty or is this really
+
+ align:start position:0%
+mt like monkey empty or is this really
+ 
+
+ align:start position:0%
+mt like monkey empty or is this really
+human empty we want to know are the
+
+ align:start position:0%
+human empty we want to know are the
+ 
+
+ align:start position:0%
+human empty we want to know are the
+neurons in there not just responsive to
+
+ align:start position:0%
+neurons in there not just responsive to
+ 
+
+ align:start position:0%
+neurons in there not just responsive to
+motion but are neurons specific for
+
+ align:start position:0%
+motion but are neurons specific for
+ 
+
+ align:start position:0%
+motion but are neurons specific for
+particular directions of motion
+
+ align:start position:0%
+particular directions of motion
+ 
+
+ align:start position:0%
+particular directions of motion
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+how would we do that okay
+
+ align:start position:0%
+how would we do that okay
+ 
+
+ align:start position:0%
+how would we do that okay
+uh well there's lots of ways of doing
+
+ align:start position:0%
+uh well there's lots of ways of doing
+ 
+
+ align:start position:0%
+uh well there's lots of ways of doing
+that but actually one of the charming
+
+ align:start position:0%
+that but actually one of the charming
+ 
+
+ align:start position:0%
+that but actually one of the charming
+things is you can do that without an mri
+
+ align:start position:0%
+things is you can do that without an mri
+ 
+
+ align:start position:0%
+things is you can do that without an mri
+scanner that is it won't tell you
+
+ align:start position:0%
+scanner that is it won't tell you
+ 
+
+ align:start position:0%
+scanner that is it won't tell you
+whether it's empty you're looking at but
+
+ align:start position:0%
+whether it's empty you're looking at but
+ 
+
+ align:start position:0%
+whether it's empty you're looking at but
+we can ask the question of whether your
+
+ align:start position:0%
+we can ask the question of whether your
+ 
+
+ align:start position:0%
+we can ask the question of whether your
+brains have neurons that are tuned for
+
+ align:start position:0%
+brains have neurons that are tuned for
+ 
+
+ align:start position:0%
+brains have neurons that are tuned for
+particular directions
+
+ align:start position:0%
+particular directions
+ 
+
+ align:start position:0%
+particular directions
+so for this demo i want you to
+
+ align:start position:0%
+so for this demo i want you to
+ 
+
+ align:start position:0%
+so for this demo i want you to
+fixate right in the center and do not
+
+ align:start position:0%
+fixate right in the center and do not
+ 
+
+ align:start position:0%
+fixate right in the center and do not
+move your eyes from that dot
+
+ align:start position:0%
+move your eyes from that dot
+ 
+
+ align:start position:0%
+move your eyes from that dot
+and i'm going to keep talking for a
+
+ align:start position:0%
+and i'm going to keep talking for a
+ 
+
+ align:start position:0%
+and i'm going to keep talking for a
+while while you keep fixating right on
+
+ align:start position:0%
+while while you keep fixating right on
+ 
+
+ align:start position:0%
+while while you keep fixating right on
+that dot
+
+ align:start position:0%
+that dot
+ 
+
+ align:start position:0%
+that dot
+and so what we're going to what i'm
+
+ align:start position:0%
+and so what we're going to what i'm
+ 
+
+ align:start position:0%
+and so what we're going to what i'm
+going to show you is something called an
+
+ align:start position:0%
+going to show you is something called an
+ 
+
+ align:start position:0%
+going to show you is something called an
+after effect this is also known as the
+
+ align:start position:0%
+after effect this is also known as the
+ 
+
+ align:start position:0%
+after effect this is also known as the
+psychophysicist's electrode
+
+ align:start position:0%
+psychophysicist's electrode
+ 
+
+ align:start position:0%
+psychophysicist's electrode
+psychophysicists are people who just
+
+ align:start position:0%
+psychophysicists are people who just
+ 
+
+ align:start position:0%
+psychophysicists are people who just
+measure behavior and from behavior they
+
+ align:start position:0%
+measure behavior and from behavior they
+ 
+
+ align:start position:0%
+measure behavior and from behavior they
+can infer how individual neurons work
+
+ align:start position:0%
+can infer how individual neurons work
+ 
+
+ align:start position:0%
+can infer how individual neurons work
+and that is about as awesome as it gets
+
+ align:start position:0%
+and that is about as awesome as it gets
+ 
+
+ align:start position:0%
+and that is about as awesome as it gets
+that's much more impressive than just
+
+ align:start position:0%
+that's much more impressive than just
+ 
+
+ align:start position:0%
+that's much more impressive than just
+recording from the damn neuron inferring
+
+ align:start position:0%
+recording from the damn neuron inferring
+ 
+
+ align:start position:0%
+recording from the damn neuron inferring
+from very indirect data how the neuron
+
+ align:start position:0%
+from very indirect data how the neuron
+ 
+
+ align:start position:0%
+from very indirect data how the neuron
+works from behavior now that is pretty
+
+ align:start position:0%
+works from behavior now that is pretty
+ 
+
+ align:start position:0%
+works from behavior now that is pretty
+oops okay sorry look directly at my face
+
+ align:start position:0%
+oops okay sorry look directly at my face
+ 
+
+ align:start position:0%
+oops okay sorry look directly at my face
+you see anything i didn't see it stop oh
+
+ align:start position:0%
+you see anything i didn't see it stop oh
+ 
+
+ align:start position:0%
+you see anything i didn't see it stop oh
+crap we're gonna oh here we go
+
+ align:start position:0%
+crap we're gonna oh here we go
+ 
+
+ align:start position:0%
+crap we're gonna oh here we go
+uh oh right okay just fixate on the
+
+ align:start position:0%
+uh oh right okay just fixate on the
+ 
+
+ align:start position:0%
+uh oh right okay just fixate on the
+center again sorry i forgot this guy was
+
+ align:start position:0%
+center again sorry i forgot this guy was
+ 
+
+ align:start position:0%
+center again sorry i forgot this guy was
+going to stop
+
+ align:start position:0%
+going to stop
+ 
+
+ align:start position:0%
+going to stop
+so keep looking at the center
+
+ align:start position:0%
+so keep looking at the center
+ 
+
+ align:start position:0%
+so keep looking at the center
+and then when it stops in a little bit
+
+ align:start position:0%
+and then when it stops in a little bit
+ 
+
+ align:start position:0%
+and then when it stops in a little bit
+then keep your eyes right on that dot
+
+ align:start position:0%
+then keep your eyes right on that dot
+ 
+
+ align:start position:0%
+then keep your eyes right on that dot
+and you can see what happens
+
+ align:start position:0%
+and you can see what happens
+ 
+
+ align:start position:0%
+and you can see what happens
+oh that's right good point yes right now
+
+ align:start position:0%
+oh that's right good point yes right now
+ 
+
+ align:start position:0%
+oh that's right good point yes right now
+it's alternating nothing's gonna happen
+
+ align:start position:0%
+it's alternating nothing's gonna happen
+ 
+
+ align:start position:0%
+it's alternating nothing's gonna happen
+but that's okay we're gonna have the
+
+ align:start position:0%
+but that's okay we're gonna have the
+ 
+
+ align:start position:0%
+but that's okay we're gonna have the
+whole experience keep fixating on the
+
+ align:start position:0%
+whole experience keep fixating on the
+ 
+
+ align:start position:0%
+whole experience keep fixating on the
+dot
+
+ align:start position:0%
+dot
+ 
+
+ align:start position:0%
+dot
+it's good the tas are on the ball
+
+ align:start position:0%
+it's good the tas are on the ball
+ 
+
+ align:start position:0%
+it's good the tas are on the ball
+okay fix it on the dot
+
+ align:start position:0%
+okay fix it on the dot
+ 
+
+ align:start position:0%
+okay fix it on the dot
+anybody see anything
+
+ align:start position:0%
+anybody see anything
+ 
+
+ align:start position:0%
+anybody see anything
+not really
+
+ align:start position:0%
+not really
+ 
+
+ align:start position:0%
+not really
+that's okay you're not supposed to
+
+ align:start position:0%
+that's okay you're not supposed to
+ 
+
+ align:start position:0%
+that's okay you're not supposed to
+that's the control condition it was
+
+ align:start position:0%
+that's the control condition it was
+ 
+
+ align:start position:0%
+that's the control condition it was
+alternating directions okay so i think
+
+ align:start position:0%
+alternating directions okay so i think
+ 
+
+ align:start position:0%
+alternating directions okay so i think
+it's going to start moving again
+
+ align:start position:0%
+it's going to start moving again
+ 
+
+ align:start position:0%
+it's going to start moving again
+i'm not sure let's go back let's just
+
+ align:start position:0%
+i'm not sure let's go back let's just
+ 
+
+ align:start position:0%
+i'm not sure let's go back let's just
+start it again okay sorry i blew it the
+
+ align:start position:0%
+start it again okay sorry i blew it the
+ 
+
+ align:start position:0%
+start it again okay sorry i blew it the
+first time but let's just get this right
+
+ align:start position:0%
+first time but let's just get this right
+ 
+
+ align:start position:0%
+first time but let's just get this right
+okay fixate on the center
+
+ align:start position:0%
+okay fixate on the center
+ 
+
+ align:start position:0%
+okay fixate on the center
+and just keep your eyes right on that
+
+ align:start position:0%
+and just keep your eyes right on that
+ 
+
+ align:start position:0%
+and just keep your eyes right on that
+center
+
+ align:start position:0%
+center
+ 
+
+ align:start position:0%
+center
+so this one it's not alternating
+
+ align:start position:0%
+so this one it's not alternating
+ 
+
+ align:start position:0%
+so this one it's not alternating
+and it's going to do this for around 30
+
+ align:start position:0%
+and it's going to do this for around 30
+ 
+
+ align:start position:0%
+and it's going to do this for around 30
+seconds
+
+ align:start position:0%
+seconds
+ 
+
+ align:start position:0%
+seconds
+and so the whole point of this is this
+
+ align:start position:0%
+and so the whole point of this is this
+ 
+
+ align:start position:0%
+and so the whole point of this is this
+is a way with behavior to ask the
+
+ align:start position:0%
+is a way with behavior to ask the
+ 
+
+ align:start position:0%
+is a way with behavior to ask the
+question of whether you have neurons in
+
+ align:start position:0%
+question of whether you have neurons in
+ 
+
+ align:start position:0%
+question of whether you have neurons in
+your brain tuned to specific directions
+
+ align:start position:0%
+your brain tuned to specific directions
+ 
+
+ align:start position:0%
+your brain tuned to specific directions
+of motion
+
+ align:start position:0%
+of motion
+ 
+
+ align:start position:0%
+of motion
+and something as low-tech and simple as
+
+ align:start position:0%
+and something as low-tech and simple as
+ 
+
+ align:start position:0%
+and something as low-tech and simple as
+an after effect can tell you that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+keep looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did you guys see anything
+
+ align:start position:0%
+did you guys see anything
+ 
+
+ align:start position:0%
+did you guys see anything
+what'd you see
+
+ align:start position:0%
+what'd you see
+ 
+
+ align:start position:0%
+what'd you see
+what happened
+
+ align:start position:0%
+what happened
+ 
+
+ align:start position:0%
+what happened
+it wasn't even exactly something they
+
+ align:start position:0%
+it wasn't even exactly something they
+ 
+
+ align:start position:0%
+it wasn't even exactly something they
+kind of like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+did it well it actually should
+
+ align:start position:0%
+did it well it actually should
+ 
+
+ align:start position:0%
+did it well it actually should
+well now it's doing something else but
+
+ align:start position:0%
+well now it's doing something else but
+ 
+
+ align:start position:0%
+well now it's doing something else but
+it should shrink at the end did you guys
+
+ align:start position:0%
+it should shrink at the end did you guys
+ 
+
+ align:start position:0%
+it should shrink at the end did you guys
+see it shrink
+
+ align:start position:0%
+see it shrink
+ 
+
+ align:start position:0%
+see it shrink
+okay so that's an after effect and the
+
+ align:start position:0%
+okay so that's an after effect and the
+ 
+
+ align:start position:0%
+okay so that's an after effect and the
+simple version of the story is that you
+
+ align:start position:0%
+simple version of the story is that you
+ 
+
+ align:start position:0%
+simple version of the story is that you
+are tiring out your neurons that are
+
+ align:start position:0%
+are tiring out your neurons that are
+ 
+
+ align:start position:0%
+are tiring out your neurons that are
+sensitive to outward motion while you
+
+ align:start position:0%
+sensitive to outward motion while you
+ 
+
+ align:start position:0%
+sensitive to outward motion while you
+stare at all that outward motion and
+
+ align:start position:0%
+stare at all that outward motion and
+ 
+
+ align:start position:0%
+stare at all that outward motion and
+after you kind of burn them out and
+
+ align:start position:0%
+after you kind of burn them out and
+ 
+
+ align:start position:0%
+after you kind of burn them out and
+exhaust them
+
+ align:start position:0%
+exhaust them
+ 
+
+ align:start position:0%
+exhaust them
+then when you look at something
+
+ align:start position:0%
+then when you look at something
+ 
+
+ align:start position:0%
+then when you look at something
+stationary it looks like it's going
+
+ align:start position:0%
+stationary it looks like it's going
+ 
+
+ align:start position:0%
+stationary it looks like it's going
+inward
+
+ align:start position:0%
+inward
+ 
+
+ align:start position:0%
+inward
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+and the general idea is you have pools
+
+ align:start position:0%
+and the general idea is you have pools
+ 
+
+ align:start position:0%
+and the general idea is you have pools
+of neurons that the the easiest way to
+
+ align:start position:0%
+of neurons that the the easiest way to
+ 
+
+ align:start position:0%
+of neurons that the the easiest way to
+account for that is you have pools of
+
+ align:start position:0%
+account for that is you have pools of
+ 
+
+ align:start position:0%
+account for that is you have pools of
+neurons tuned for different directions
+
+ align:start position:0%
+neurons tuned for different directions
+ 
+
+ align:start position:0%
+neurons tuned for different directions
+and that's why if you tire out one batch
+
+ align:start position:0%
+and that's why if you tire out one batch
+ 
+
+ align:start position:0%
+and that's why if you tire out one batch
+you have a net signal in the other
+
+ align:start position:0%
+you have a net signal in the other
+ 
+
+ align:start position:0%
+you have a net signal in the other
+direction does that make sense
+
+ align:start position:0%
+direction does that make sense
+ 
+
+ align:start position:0%
+direction does that make sense
+this is all very relevant to your
+
+ align:start position:0%
+this is all very relevant to your
+ 
+
+ align:start position:0%
+this is all very relevant to your
+assignment which is due tomorrow night
+
+ align:start position:0%
+assignment which is due tomorrow night
+ 
+
+ align:start position:0%
+assignment which is due tomorrow night
+at 6.
+
+ align:start position:0%
+at 6.
+ 
+
+ align:start position:0%
+at 6.
+this phenomenon was used in the scanner
+
+ align:start position:0%
+this phenomenon was used in the scanner
+ 
+
+ align:start position:0%
+this phenomenon was used in the scanner
+for that experiment and you can think
+
+ align:start position:0%
+for that experiment and you can think
+ 
+
+ align:start position:0%
+for that experiment and you can think
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+um how you would use this phenomenon
+
+ align:start position:0%
+um how you would use this phenomenon
+ 
+
+ align:start position:0%
+um how you would use this phenomenon
+um to ask whether there's direction
+
+ align:start position:0%
+um to ask whether there's direction
+ 
+
+ align:start position:0%
+um to ask whether there's direction
+selectivity not just responses to motion
+
+ align:start position:0%
+selectivity not just responses to motion
+ 
+
+ align:start position:0%
+selectivity not just responses to motion
+in human mt
+
+ align:start position:0%
+in human mt
+ 
+
+ align:start position:0%
+in human mt
+yeah wait uh i'm just a little bit
+
+ align:start position:0%
+yeah wait uh i'm just a little bit
+ 
+
+ align:start position:0%
+yeah wait uh i'm just a little bit
+confused so even when an image is like
+
+ align:start position:0%
+confused so even when an image is like
+ 
+
+ align:start position:0%
+confused so even when an image is like
+completely still like even if you're not
+
+ align:start position:0%
+completely still like even if you're not
+ 
+
+ align:start position:0%
+completely still like even if you're not
+detecting motion those neurons are still
+
+ align:start position:0%
+detecting motion those neurons are still
+ 
+
+ align:start position:0%
+detecting motion those neurons are still
+firing
+
+ align:start position:0%
+firing
+ 
+
+ align:start position:0%
+firing
+ah
+
+ align:start position:0%
+ah
+ 
+
+ align:start position:0%
+ah
+um that's a good question but but most
+
+ align:start position:0%
+um that's a good question but but most
+ 
+
+ align:start position:0%
+um that's a good question but but most
+likely it's the simple cases
+
+ align:start position:0%
+likely it's the simple cases
+ 
+
+ align:start position:0%
+likely it's the simple cases
+if this may have not worked beautifully
+
+ align:start position:0%
+if this may have not worked beautifully
+ 
+
+ align:start position:0%
+if this may have not worked beautifully
+in part because i screwed it up and
+
+ align:start position:0%
+in part because i screwed it up and
+ 
+
+ align:start position:0%
+in part because i screwed it up and
+didn't notice when it stopped
+
+ align:start position:0%
+didn't notice when it stopped
+ 
+
+ align:start position:0%
+didn't notice when it stopped
+but if it works well you should get a
+
+ align:start position:0%
+but if it works well you should get a
+ 
+
+ align:start position:0%
+but if it works well you should get a
+pretty powerful sense that after you see
+
+ align:start position:0%
+pretty powerful sense that after you see
+ 
+
+ align:start position:0%
+pretty powerful sense that after you see
+it expanding then when it's still it
+
+ align:start position:0%
+it expanding then when it's still it
+ 
+
+ align:start position:0%
+it expanding then when it's still it
+should seem to be contracting
+
+ align:start position:0%
+should seem to be contracting
+ 
+
+ align:start position:0%
+should seem to be contracting
+so when that happens
+
+ align:start position:0%
+so when that happens
+ 
+
+ align:start position:0%
+so when that happens
+the reading assigned for today tomorrow
+
+ align:start position:0%
+the reading assigned for today tomorrow
+ 
+
+ align:start position:0%
+the reading assigned for today tomorrow
+tomorrow night tells you what happens in
+
+ align:start position:0%
+tomorrow night tells you what happens in
+ 
+
+ align:start position:0%
+tomorrow night tells you what happens in
+your brain during that time when you are
+
+ align:start position:0%
+your brain during that time when you are
+ 
+
+ align:start position:0%
+your brain during that time when you are
+looking at stationary stimuli but
+
+ align:start position:0%
+looking at stationary stimuli but
+ 
+
+ align:start position:0%
+looking at stationary stimuli but
+experiencing motion
+
+ align:start position:0%
+experiencing motion
+ 
+
+ align:start position:0%
+experiencing motion
+so there's no motion in the stimulus but
+
+ align:start position:0%
+so there's no motion in the stimulus but
+ 
+
+ align:start position:0%
+so there's no motion in the stimulus but
+there's motion in your percept
+
+ align:start position:0%
+there's motion in your percept
+ 
+
+ align:start position:0%
+there's motion in your percept
+okay so that's the question
+
+ align:start position:0%
+okay so that's the question
+ 
+
+ align:start position:0%
+okay so that's the question
+right so read the paper and find out
+
+ align:start position:0%
+right so read the paper and find out
+ 
+
+ align:start position:0%
+right so read the paper and find out
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so all of that
+
+ align:start position:0%
+all right so all of that
+ 
+
+ align:start position:0%
+all right so all of that
+tells us just that there are neurons
+
+ align:start position:0%
+tells us just that there are neurons
+ 
+
+ align:start position:0%
+tells us just that there are neurons
+some place in your brain that are
+
+ align:start position:0%
+some place in your brain that are
+ 
+
+ align:start position:0%
+some place in your brain that are
+sensitive to the direction of motion
+
+ align:start position:0%
+sensitive to the direction of motion
+ 
+
+ align:start position:0%
+sensitive to the direction of motion
+it doesn't tell us that they're in mt in
+
+ align:start position:0%
+it doesn't tell us that they're in mt in
+ 
+
+ align:start position:0%
+it doesn't tell us that they're in mt in
+particular
+
+ align:start position:0%
+particular
+ 
+
+ align:start position:0%
+particular
+but the assigned reading will talk about
+
+ align:start position:0%
+but the assigned reading will talk about
+ 
+
+ align:start position:0%
+but the assigned reading will talk about
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+right a further bit of evidence
+
+ align:start position:0%
+right a further bit of evidence
+ 
+
+ align:start position:0%
+right a further bit of evidence
+is remember i said how in monkeys next
+
+ align:start position:0%
+is remember i said how in monkeys next
+ 
+
+ align:start position:0%
+is remember i said how in monkeys next
+door bits in mt have have have similar
+
+ align:start position:0%
+door bits in mt have have have similar
+ 
+
+ align:start position:0%
+door bits in mt have have have similar
+direction selectivity
+
+ align:start position:0%
+direction selectivity
+ 
+
+ align:start position:0%
+direction selectivity
+that means you can also inject an
+
+ align:start position:0%
+that means you can also inject an
+ 
+
+ align:start position:0%
+that means you can also inject an
+electrical signal in a little patch of
+
+ align:start position:0%
+electrical signal in a little patch of
+ 
+
+ align:start position:0%
+electrical signal in a little patch of
+mt
+
+ align:start position:0%
+mt
+ 
+
+ align:start position:0%
+mt
+and give the monkey a net percept of a
+
+ align:start position:0%
+and give the monkey a net percept of a
+ 
+
+ align:start position:0%
+and give the monkey a net percept of a
+direction of motion
+
+ align:start position:0%
+direction of motion
+ 
+
+ align:start position:0%
+direction of motion
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+if all the neurons were scrambled around
+
+ align:start position:0%
+if all the neurons were scrambled around
+ 
+
+ align:start position:0%
+if all the neurons were scrambled around
+spatially so that there was no
+
+ align:start position:0%
+spatially so that there was no
+ 
+
+ align:start position:0%
+spatially so that there was no
+clustering of neurons sensitive to say
+
+ align:start position:0%
+clustering of neurons sensitive to say
+ 
+
+ align:start position:0%
+clustering of neurons sensitive to say
+this direction of motion then
+
+ align:start position:0%
+this direction of motion then
+ 
+
+ align:start position:0%
+this direction of motion then
+stimulation wouldn't do anything
+
+ align:start position:0%
+stimulation wouldn't do anything
+ 
+
+ align:start position:0%
+stimulation wouldn't do anything
+but if you train a monkey to tell you
+
+ align:start position:0%
+but if you train a monkey to tell you
+ 
+
+ align:start position:0%
+but if you train a monkey to tell you
+what direction of motion he's seeing and
+
+ align:start position:0%
+what direction of motion he's seeing and
+ 
+
+ align:start position:0%
+what direction of motion he's seeing and
+you show them just random dots that
+
+ align:start position:0%
+you show them just random dots that
+ 
+
+ align:start position:0%
+you show them just random dots that
+aren't moving in any direction and you
+
+ align:start position:0%
+aren't moving in any direction and you
+ 
+
+ align:start position:0%
+aren't moving in any direction and you
+stimulate one little patch
+
+ align:start position:0%
+stimulate one little patch
+ 
+
+ align:start position:0%
+stimulate one little patch
+it'll tell you the direction of motion
+
+ align:start position:0%
+it'll tell you the direction of motion
+ 
+
+ align:start position:0%
+it'll tell you the direction of motion
+of the neurons in that little patch
+
+ align:start position:0%
+of the neurons in that little patch
+ 
+
+ align:start position:0%
+of the neurons in that little patch
+and that is much more powerful evidence
+
+ align:start position:0%
+and that is much more powerful evidence
+ 
+
+ align:start position:0%
+and that is much more powerful evidence
+that that region
+
+ align:start position:0%
+that that region
+ 
+
+ align:start position:0%
+that that region
+is not only responsive to motion but
+
+ align:start position:0%
+is not only responsive to motion but
+ 
+
+ align:start position:0%
+is not only responsive to motion but
+causally involved in your perception of
+
+ align:start position:0%
+causally involved in your perception of
+ 
+
+ align:start position:0%
+causally involved in your perception of
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+okay i'm a little obsessed with this
+
+ align:start position:0%
+okay i'm a little obsessed with this
+ 
+
+ align:start position:0%
+okay i'm a little obsessed with this
+distinction between
+
+ align:start position:0%
+distinction between
+ 
+
+ align:start position:0%
+distinction between
+you know recording responses and
+
+ align:start position:0%
+you know recording responses and
+ 
+
+ align:start position:0%
+you know recording responses and
+establishing causality so we'll go over
+
+ align:start position:0%
+establishing causality so we'll go over
+ 
+
+ align:start position:0%
+establishing causality so we'll go over
+this in more detail later but i want you
+
+ align:start position:0%
+this in more detail later but i want you
+ 
+
+ align:start position:0%
+this in more detail later but i want you
+to start getting used to that idea
+
+ align:start position:0%
+to start getting used to that idea
+ 
+
+ align:start position:0%
+to start getting used to that idea
+another way to test the causal role of
+
+ align:start position:0%
+another way to test the causal role of
+ 
+
+ align:start position:0%
+another way to test the causal role of
+area mt
+
+ align:start position:0%
+area mt
+ 
+
+ align:start position:0%
+area mt
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+motion is
+
+ align:start position:0%
+motion is
+ 
+
+ align:start position:0%
+motion is
+with patients with brain damage and area
+
+ align:start position:0%
+with patients with brain damage and area
+ 
+
+ align:start position:0%
+with patients with brain damage and area
+mt
+
+ align:start position:0%
+mt
+ 
+
+ align:start position:0%
+mt
+so there's one famous patient who had
+
+ align:start position:0%
+so there's one famous patient who had
+ 
+
+ align:start position:0%
+so there's one famous patient who had
+brain damage right there
+
+ align:start position:0%
+brain damage right there
+ 
+
+ align:start position:0%
+brain damage right there
+which is right where mt usually is
+
+ align:start position:0%
+which is right where mt usually is
+ 
+
+ align:start position:0%
+which is right where mt usually is
+and she could not see motion and she
+
+ align:start position:0%
+and she could not see motion and she
+ 
+
+ align:start position:0%
+and she could not see motion and she
+reports all kinds of things like
+
+ align:start position:0%
+reports all kinds of things like
+ 
+
+ align:start position:0%
+reports all kinds of things like
+difficulty crossing the street
+
+ align:start position:0%
+difficulty crossing the street
+ 
+
+ align:start position:0%
+difficulty crossing the street
+difficulty catching balls
+
+ align:start position:0%
+difficulty catching balls
+ 
+
+ align:start position:0%
+difficulty catching balls
+difficulty pouring water into a cup
+
+ align:start position:0%
+difficulty pouring water into a cup
+ 
+
+ align:start position:0%
+difficulty pouring water into a cup
+okay just as you guys saw earlier that's
+
+ align:start position:0%
+okay just as you guys saw earlier that's
+ 
+
+ align:start position:0%
+okay just as you guys saw earlier that's
+called akinatopsia
+
+ align:start position:0%
+called akinatopsia
+ 
+
+ align:start position:0%
+called akinatopsia
+right can it like kinetics motion a not
+
+ align:start position:0%
+right can it like kinetics motion a not
+ 
+
+ align:start position:0%
+right can it like kinetics motion a not
+motion right opsia eyes
+
+ align:start position:0%
+motion right opsia eyes
+ 
+
+ align:start position:0%
+motion right opsia eyes
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+all right so i started with these
+
+ align:start position:0%
+all right so i started with these
+ 
+
+ align:start position:0%
+all right so i started with these
+criteria for what makes something a
+
+ align:start position:0%
+criteria for what makes something a
+ 
+
+ align:start position:0%
+criteria for what makes something a
+visual a
+
+ align:start position:0%
+visual a
+ 
+
+ align:start position:0%
+visual a
+distinct area and one piece of evidence
+
+ align:start position:0%
+distinct area and one piece of evidence
+ 
+
+ align:start position:0%
+distinct area and one piece of evidence
+is function and i just gave you a whole
+
+ align:start position:0%
+is function and i just gave you a whole
+ 
+
+ align:start position:0%
+is function and i just gave you a whole
+bunch of different kinds of evidence for
+
+ align:start position:0%
+bunch of different kinds of evidence for
+ 
+
+ align:start position:0%
+bunch of different kinds of evidence for
+distinct function and visual area mt
+
+ align:start position:0%
+distinct function and visual area mt
+ 
+
+ align:start position:0%
+distinct function and visual area mt
+that it's specifically involved in
+
+ align:start position:0%
+that it's specifically involved in
+ 
+
+ align:start position:0%
+that it's specifically involved in
+motion
+
+ align:start position:0%
+motion
+ 
+
+ align:start position:0%
+motion
+processing
+
+ align:start position:0%
+processing
+ 
+
+ align:start position:0%
+processing
+and the two other criteria which are
+
+ align:start position:0%
+and the two other criteria which are
+ 
+
+ align:start position:0%
+and the two other criteria which are
+getting short shrift but i'll just toss
+
+ align:start position:0%
+getting short shrift but i'll just toss
+ 
+
+ align:start position:0%
+getting short shrift but i'll just toss
+them off and we'll return to them
+
+ align:start position:0%
+them off and we'll return to them
+ 
+
+ align:start position:0%
+them off and we'll return to them
+one is the distinct connectivity of that
+
+ align:start position:0%
+one is the distinct connectivity of that
+ 
+
+ align:start position:0%
+one is the distinct connectivity of that
+region
+
+ align:start position:0%
+region
+ 
+
+ align:start position:0%
+region
+okay so you may have seen this horrific
+
+ align:start position:0%
+okay so you may have seen this horrific
+ 
+
+ align:start position:0%
+okay so you may have seen this horrific
+wiring diagram of visual cortex in
+
+ align:start position:0%
+wiring diagram of visual cortex in
+ 
+
+ align:start position:0%
+wiring diagram of visual cortex in
+monkeys i think it comes up in like half
+
+ align:start position:0%
+monkeys i think it comes up in like half
+ 
+
+ align:start position:0%
+monkeys i think it comes up in like half
+the talks and classes in in my field
+
+ align:start position:0%
+the talks and classes in in my field
+ 
+
+ align:start position:0%
+the talks and classes in in my field
+this is the one down here and so there's
+
+ align:start position:0%
+this is the one down here and so there's
+ 
+
+ align:start position:0%
+this is the one down here and so there's
+lots and lots of different visual areas
+
+ align:start position:0%
+lots and lots of different visual areas
+ 
+
+ align:start position:0%
+lots and lots of different visual areas
+and there's a whole fancy wiring diagram
+
+ align:start position:0%
+and there's a whole fancy wiring diagram
+ 
+
+ align:start position:0%
+and there's a whole fancy wiring diagram
+and smack in the middle of this diagram
+
+ align:start position:0%
+and smack in the middle of this diagram
+ 
+
+ align:start position:0%
+and smack in the middle of this diagram
+that's visual area mt and if you blow
+
+ align:start position:0%
+that's visual area mt and if you blow
+ 
+
+ align:start position:0%
+that's visual area mt and if you blow
+this up and stare at it you'll see that
+
+ align:start position:0%
+this up and stare at it you'll see that
+ 
+
+ align:start position:0%
+this up and stare at it you'll see that
+mt has a particular set of connections
+
+ align:start position:0%
+mt has a particular set of connections
+ 
+
+ align:start position:0%
+mt has a particular set of connections
+to other visual regions and cortex and
+
+ align:start position:0%
+to other visual regions and cortex and
+ 
+
+ align:start position:0%
+to other visual regions and cortex and
+its particular set of connections are
+
+ align:start position:0%
+its particular set of connections are
+ 
+
+ align:start position:0%
+its particular set of connections are
+different from the connections of any of
+
+ align:start position:0%
+different from the connections of any of
+ 
+
+ align:start position:0%
+different from the connections of any of
+those other regions it's part of its
+
+ align:start position:0%
+those other regions it's part of its
+ 
+
+ align:start position:0%
+those other regions it's part of its
+connectivity fingerprint or signature
+
+ align:start position:0%
+connectivity fingerprint or signature
+ 
+
+ align:start position:0%
+connectivity fingerprint or signature
+and that's another piece of evidence
+
+ align:start position:0%
+and that's another piece of evidence
+ 
+
+ align:start position:0%
+and that's another piece of evidence
+that it's a thing
+
+ align:start position:0%
+that it's a thing
+ 
+
+ align:start position:0%
+that it's a thing
+okay it's not just another like
+
+ align:start position:0%
+okay it's not just another like
+ 
+
+ align:start position:0%
+okay it's not just another like
+amorphous bit of cortex it's a
+
+ align:start position:0%
+amorphous bit of cortex it's a
+ 
+
+ align:start position:0%
+amorphous bit of cortex it's a
+particular thing in the brain
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and finally you might wonder is that bit
+
+ align:start position:0%
+and finally you might wonder is that bit
+ 
+
+ align:start position:0%
+and finally you might wonder is that bit
+of cortex physically different are the
+
+ align:start position:0%
+of cortex physically different are the
+ 
+
+ align:start position:0%
+of cortex physically different are the
+cells in there different are the layers
+
+ align:start position:0%
+cells in there different are the layers
+ 
+
+ align:start position:0%
+cells in there different are the layers
+of cortex different
+
+ align:start position:0%
+of cortex different
+ 
+
+ align:start position:0%
+of cortex different
+um in any way
+
+ align:start position:0%
+um in any way
+ 
+
+ align:start position:0%
+um in any way
+and from
+
+ align:start position:0%
+and from
+ 
+
+ align:start position:0%
+and from
+and you may remember from probably 900
+
+ align:start position:0%
+and you may remember from probably 900
+ 
+
+ align:start position:0%
+and you may remember from probably 900
+about brodman areas like this dude
+
+ align:start position:0%
+about brodman areas like this dude
+ 
+
+ align:start position:0%
+about brodman areas like this dude
+corbinian brodeman
+
+ align:start position:0%
+corbinian brodeman
+ 
+
+ align:start position:0%
+corbinian brodeman
+sliced up lots of dead brains looked at
+
+ align:start position:0%
+sliced up lots of dead brains looked at
+ 
+
+ align:start position:0%
+sliced up lots of dead brains looked at
+them under a microscope and argued that
+
+ align:start position:0%
+them under a microscope and argued that
+ 
+
+ align:start position:0%
+them under a microscope and argued that
+were there were 52 different parts just
+
+ align:start position:0%
+were there were 52 different parts just
+ 
+
+ align:start position:0%
+were there were 52 different parts just
+from what it looked like if you slice
+
+ align:start position:0%
+from what it looked like if you slice
+ 
+
+ align:start position:0%
+from what it looked like if you slice
+them up under a microscope okay so we
+
+ align:start position:0%
+them up under a microscope okay so we
+ 
+
+ align:start position:0%
+them up under a microscope okay so we
+called those brodman areas and area 17
+
+ align:start position:0%
+called those brodman areas and area 17
+ 
+
+ align:start position:0%
+called those brodman areas and area 17
+this primary visual cortex comes from
+
+ align:start position:0%
+this primary visual cortex comes from
+ 
+
+ align:start position:0%
+this primary visual cortex comes from
+brodman's terminology
+
+ align:start position:0%
+brodman's terminology
+ 
+
+ align:start position:0%
+brodman's terminology
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+and so he argued that there he thought
+
+ align:start position:0%
+and so he argued that there he thought
+ 
+
+ align:start position:0%
+and so he argued that there he thought
+these were distinct organs in the brain
+
+ align:start position:0%
+these were distinct organs in the brain
+ 
+
+ align:start position:0%
+these were distinct organs in the brain
+and he even inferred the specific
+
+ align:start position:0%
+and he even inferred the specific
+ 
+
+ align:start position:0%
+and he even inferred the specific
+histological differentiation of the
+
+ align:start position:0%
+histological differentiation of the
+ 
+
+ align:start position:0%
+histological differentiation of the
+cortical areas proves irrefutably their
+
+ align:start position:0%
+cortical areas proves irrefutably their
+ 
+
+ align:start position:0%
+cortical areas proves irrefutably their
+specific functional differentiation well
+
+ align:start position:0%
+specific functional differentiation well
+ 
+
+ align:start position:0%
+specific functional differentiation well
+it doesn't but never mind kind of
+
+ align:start position:0%
+it doesn't but never mind kind of
+ 
+
+ align:start position:0%
+it doesn't but never mind kind of
+sounded good
+
+ align:start position:0%
+sounded good
+ 
+
+ align:start position:0%
+sounded good
+anyway that was his idea
+
+ align:start position:0%
+anyway that was his idea
+ 
+
+ align:start position:0%
+anyway that was his idea
+and these kinds of distinct
+
+ align:start position:0%
+and these kinds of distinct
+ 
+
+ align:start position:0%
+and these kinds of distinct
+kind of cellular physical anatomical
+
+ align:start position:0%
+kind of cellular physical anatomical
+ 
+
+ align:start position:0%
+kind of cellular physical anatomical
+differences are very salient for primary
+
+ align:start position:0%
+differences are very salient for primary
+ 
+
+ align:start position:0%
+differences are very salient for primary
+cortical areas
+
+ align:start position:0%
+cortical areas
+ 
+
+ align:start position:0%
+cortical areas
+for vision and audition and touch
+
+ align:start position:0%
+for vision and audition and touch
+ 
+
+ align:start position:0%
+for vision and audition and touch
+and motor cortex but they're much
+
+ align:start position:0%
+and motor cortex but they're much
+ 
+
+ align:start position:0%
+and motor cortex but they're much
+muckier for lots of other areas
+
+ align:start position:0%
+muckier for lots of other areas
+ 
+
+ align:start position:0%
+muckier for lots of other areas
+one important exception which is why we
+
+ align:start position:0%
+one important exception which is why we
+ 
+
+ align:start position:0%
+one important exception which is why we
+chose this is area mt
+
+ align:start position:0%
+chose this is area mt
+ 
+
+ align:start position:0%
+chose this is area mt
+and so i'll end in one minute but just
+
+ align:start position:0%
+and so i'll end in one minute but just
+ 
+
+ align:start position:0%
+and so i'll end in one minute but just
+to tell you where this is going this is
+
+ align:start position:0%
+to tell you where this is going this is
+ 
+
+ align:start position:0%
+to tell you where this is going this is
+a flattened piece of monkey cortex
+
+ align:start position:0%
+a flattened piece of monkey cortex
+ 
+
+ align:start position:0%
+a flattened piece of monkey cortex
+rolled out like with a baking roller no
+
+ align:start position:0%
+rolled out like with a baking roller no
+ 
+
+ align:start position:0%
+rolled out like with a baking roller no
+i don't know some something like that so
+
+ align:start position:0%
+i don't know some something like that so
+ 
+
+ align:start position:0%
+i don't know some something like that so
+here's monkey cortex and there's v1 and
+
+ align:start position:0%
+here's monkey cortex and there's v1 and
+ 
+
+ align:start position:0%
+here's monkey cortex and there's v1 and
+v2 and it's a big mess but that big dark
+
+ align:start position:0%
+v2 and it's a big mess but that big dark
+ 
+
+ align:start position:0%
+v2 and it's a big mess but that big dark
+blob this bit of cortex is stained with
+
+ align:start position:0%
+blob this bit of cortex is stained with
+ 
+
+ align:start position:0%
+blob this bit of cortex is stained with
+something called cytochrome oxidase
+
+ align:start position:0%
+something called cytochrome oxidase
+ 
+
+ align:start position:0%
+something called cytochrome oxidase
+and that indicates metabolic activity
+
+ align:start position:0%
+and that indicates metabolic activity
+ 
+
+ align:start position:0%
+and that indicates metabolic activity
+mt neurons are very highly metabolically
+
+ align:start position:0%
+mt neurons are very highly metabolically
+ 
+
+ align:start position:0%
+mt neurons are very highly metabolically
+active and so here's a map
+
+ align:start position:0%
+active and so here's a map
+ 
+
+ align:start position:0%
+active and so here's a map
+of visual cortex and that exactly is
+
+ align:start position:0%
+of visual cortex and that exactly is
+ 
+
+ align:start position:0%
+of visual cortex and that exactly is
+area mt
+
+ align:start position:0%
+area mt
+ 
+
+ align:start position:0%
+area mt
+so area mt actually is
+
+ align:start position:0%
+so area mt actually is
+ 
+
+ align:start position:0%
+so area mt actually is
+histologically or
+
+ align:start position:0%
+histologically or
+ 
+
+ align:start position:0%
+histologically or
+psychoarchitectonically
+
+ align:start position:0%
+psychoarchitectonically
+ 
+
+ align:start position:0%
+psychoarchitectonically
+different from its neighbors
+
+ align:start position:0%
+different from its neighbors
+ 
+
+ align:start position:0%
+different from its neighbors
+and hence fits all of the criteria for a
+
+ align:start position:0%
+and hence fits all of the criteria for a
+ 
+
+ align:start position:0%
+and hence fits all of the criteria for a
+cortical area
+
+ align:start position:0%
+cortical area
+ 
+
+ align:start position:0%
+cortical area
+okay i went one minute over i realize i
+
+ align:start position:0%
+okay i went one minute over i realize i
+ 
+
+ align:start position:0%
+okay i went one minute over i realize i
+threw out a lot of terminology i don't
+
+ align:start position:0%
+threw out a lot of terminology i don't
+ 
+
+ align:start position:0%
+threw out a lot of terminology i don't
+want you to memorize too much so i made
+
+ align:start position:0%
+want you to memorize too much so i made
+ 
+
+ align:start position:0%
+want you to memorize too much so i made
+a list of the kinds of things that you
+
+ align:start position:0%
+a list of the kinds of things that you
+ 
+
+ align:start position:0%
+a list of the kinds of things that you
+should understand from this lecture the
+
+ align:start position:0%
+should understand from this lecture the
+ 
+
+ align:start position:0%
+should understand from this lecture the
+things that i think are important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/bbh5AQTX8r4.txt b/bbh5AQTX8r4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1a78074bf646cd48a5a797a01cea4db109981978
--- /dev/null
+++ b/bbh5AQTX8r4.txt
@@ -0,0 +1,10187 @@
+align:start position:0%
+ 
+the following content is provided by MIT
+
+ align:start position:0%
+the following content is provided by MIT
+ 
+
+ align:start position:0%
+the following content is provided by MIT
+opencourseware under a Creative Commons
+
+ align:start position:0%
+opencourseware under a Creative Commons
+ 
+
+ align:start position:0%
+opencourseware under a Creative Commons
+license additional information about our
+
+ align:start position:0%
+license additional information about our
+ 
+
+ align:start position:0%
+license additional information about our
+license and MIT open courseware in
+
+ align:start position:0%
+license and MIT open courseware in
+ 
+
+ align:start position:0%
+license and MIT open courseware in
+general is available at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good morning class nice to see you again
+
+ align:start position:0%
+good morning class nice to see you again
+ 
+
+ align:start position:0%
+good morning class nice to see you again
+hope you had a a great weekend
+
+ align:start position:0%
+hope you had a a great weekend
+ 
+
+ align:start position:0%
+hope you had a a great weekend
+if you didn't it wasn't because of the
+
+ align:start position:0%
+if you didn't it wasn't because of the
+ 
+
+ align:start position:0%
+if you didn't it wasn't because of the
+weather
+
+ align:start position:0%
+weather
+ 
+
+ align:start position:0%
+weather
+so here I am once again a member of the
+
+ align:start position:0%
+so here I am once again a member of the
+ 
+
+ align:start position:0%
+so here I am once again a member of the
+walking wounded and we're talking about
+
+ align:start position:0%
+walking wounded and we're talking about
+ 
+
+ align:start position:0%
+walking wounded and we're talking about
+carbohydrates today as you may recall at
+
+ align:start position:0%
+carbohydrates today as you may recall at
+ 
+
+ align:start position:0%
+carbohydrates today as you may recall at
+least we were at the end of our
+
+ align:start position:0%
+least we were at the end of our
+ 
+
+ align:start position:0%
+least we were at the end of our
+discussion last time
+
+ align:start position:0%
+discussion last time
+ 
+
+ align:start position:0%
+discussion last time
+and we made the point that uh
+
+ align:start position:0%
+and we made the point that uh
+ 
+
+ align:start position:0%
+and we made the point that uh
+these multiple hydroxyl groups on the
+
+ align:start position:0%
+these multiple hydroxyl groups on the
+ 
+
+ align:start position:0%
+these multiple hydroxyl groups on the
+carbohydrates on the one hand determine
+
+ align:start position:0%
+carbohydrates on the one hand determine
+ 
+
+ align:start position:0%
+carbohydrates on the one hand determine
+the identity of a various kinds of uh
+
+ align:start position:0%
+the identity of a various kinds of uh
+ 
+
+ align:start position:0%
+the identity of a various kinds of uh
+sugars just the orientation the
+
+ align:start position:0%
+sugars just the orientation the
+ 
+
+ align:start position:0%
+sugars just the orientation the
+three-dimensional orientation of them
+
+ align:start position:0%
+three-dimensional orientation of them
+ 
+
+ align:start position:0%
+three-dimensional orientation of them
+uh for one thing and uh for another that
+
+ align:start position:0%
+uh for one thing and uh for another that
+ 
+
+ align:start position:0%
+uh for one thing and uh for another that
+these multiple hydroxyl groups
+
+ align:start position:0%
+these multiple hydroxyl groups
+ 
+
+ align:start position:0%
+these multiple hydroxyl groups
+represented the opportunity for forming
+
+ align:start position:0%
+represented the opportunity for forming
+ 
+
+ align:start position:0%
+represented the opportunity for forming
+covalent bonds with other
+
+ align:start position:0%
+covalent bonds with other
+ 
+
+ align:start position:0%
+covalent bonds with other
+monosaccharides as is indicated here in
+
+ align:start position:0%
+monosaccharides as is indicated here in
+ 
+
+ align:start position:0%
+monosaccharides as is indicated here in
+these disaccharides or covalent bonds
+
+ align:start position:0%
+these disaccharides or covalent bonds
+ 
+
+ align:start position:0%
+these disaccharides or covalent bonds
+end to end to create large molecules
+
+ align:start position:0%
+end to end to create large molecules
+ 
+
+ align:start position:0%
+end to end to create large molecules
+which will increasingly be the theme of
+
+ align:start position:0%
+which will increasingly be the theme of
+ 
+
+ align:start position:0%
+which will increasingly be the theme of
+our discussion today
+
+ align:start position:0%
+our discussion today
+ 
+
+ align:start position:0%
+our discussion today
+I.E when I talk about large molecules we
+
+ align:start position:0%
+I.E when I talk about large molecules we
+ 
+
+ align:start position:0%
+I.E when I talk about large molecules we
+just use the phrase generically of
+
+ align:start position:0%
+just use the phrase generically of
+ 
+
+ align:start position:0%
+just use the phrase generically of
+macromolecules
+
+ align:start position:0%
+macromolecules
+ 
+
+ align:start position:0%
+macromolecules
+since in principle uh these end-to-end
+
+ align:start position:0%
+since in principle uh these end-to-end
+ 
+
+ align:start position:0%
+since in principle uh these end-to-end
+joinings of molecules which involve the
+
+ align:start position:0%
+joinings of molecules which involve the
+ 
+
+ align:start position:0%
+joinings of molecules which involve the
+dehydration and the formation of these
+
+ align:start position:0%
+dehydration and the formation of these
+ 
+
+ align:start position:0%
+dehydration and the formation of these
+covalent bonds like right here can
+
+ align:start position:0%
+covalent bonds like right here can
+ 
+
+ align:start position:0%
+covalent bonds like right here can
+create molecules that are hundreds
+
+ align:start position:0%
+create molecules that are hundreds
+ 
+
+ align:start position:0%
+create molecules that are hundreds
+indeed even thousands of subunits long
+
+ align:start position:0%
+indeed even thousands of subunits long
+ 
+
+ align:start position:0%
+indeed even thousands of subunits long
+so here if we're talking about a polymer
+
+ align:start position:0%
+so here if we're talking about a polymer
+ 
+
+ align:start position:0%
+so here if we're talking about a polymer
+we refer to each one of these uh
+
+ align:start position:0%
+we refer to each one of these uh
+ 
+
+ align:start position:0%
+we refer to each one of these uh
+subunits of the polymer as being a
+
+ align:start position:0%
+subunits of the polymer as being a
+ 
+
+ align:start position:0%
+subunits of the polymer as being a
+monomer and the aggregate as a whole as
+
+ align:start position:0%
+monomer and the aggregate as a whole as
+ 
+
+ align:start position:0%
+monomer and the aggregate as a whole as
+being a polymer
+
+ align:start position:0%
+being a polymer
+ 
+
+ align:start position:0%
+being a polymer
+here we uh uh we touched upon the fact
+
+ align:start position:0%
+here we uh uh we touched upon the fact
+ 
+
+ align:start position:0%
+here we uh uh we touched upon the fact
+toward the end of last lecture in fact
+
+ align:start position:0%
+toward the end of last lecture in fact
+ 
+
+ align:start position:0%
+toward the end of last lecture in fact
+at the very end
+
+ align:start position:0%
+at the very end
+ 
+
+ align:start position:0%
+at the very end
+that um one can array one can cross-link
+
+ align:start position:0%
+that um one can array one can cross-link
+ 
+
+ align:start position:0%
+that um one can array one can cross-link
+these long linear chains of
+
+ align:start position:0%
+these long linear chains of
+ 
+
+ align:start position:0%
+these long linear chains of
+carbohydrates and here we see the fact
+
+ align:start position:0%
+carbohydrates and here we see the fact
+ 
+
+ align:start position:0%
+carbohydrates and here we see the fact
+that glycogen which is a form
+
+ align:start position:0%
+that glycogen which is a form
+ 
+
+ align:start position:0%
+that glycogen which is a form
+of glucose that is stored in our liver
+
+ align:start position:0%
+of glucose that is stored in our liver
+ 
+
+ align:start position:0%
+of glucose that is stored in our liver
+largely into a small extent in the
+
+ align:start position:0%
+largely into a small extent in the
+ 
+
+ align:start position:0%
+largely into a small extent in the
+muscles actually is is um
+
+ align:start position:0%
+muscles actually is is um
+ 
+
+ align:start position:0%
+muscles actually is is um
+it's cross Branch so if one looks at a
+
+ align:start position:0%
+it's cross Branch so if one looks at a
+ 
+
+ align:start position:0%
+it's cross Branch so if one looks at a
+if one draws on a much smaller scale a
+
+ align:start position:0%
+if one draws on a much smaller scale a
+ 
+
+ align:start position:0%
+if one draws on a much smaller scale a
+glycogen molecule one might draw a
+
+ align:start position:0%
+glycogen molecule one might draw a
+ 
+
+ align:start position:0%
+glycogen molecule one might draw a
+picture that looks like this
+
+ align:start position:0%
+picture that looks like this
+ 
+
+ align:start position:0%
+picture that looks like this
+then it looks almost like a Christmas
+
+ align:start position:0%
+then it looks almost like a Christmas
+ 
+
+ align:start position:0%
+then it looks almost like a Christmas
+tree with multiple branches and the
+
+ align:start position:0%
+tree with multiple branches and the
+ 
+
+ align:start position:0%
+tree with multiple branches and the
+purpose of this is actually to sequester
+
+ align:start position:0%
+purpose of this is actually to sequester
+ 
+
+ align:start position:0%
+purpose of this is actually to sequester
+the glucose to store the glucose in a
+
+ align:start position:0%
+the glucose to store the glucose in a
+ 
+
+ align:start position:0%
+the glucose to store the glucose in a
+metabolically inactive form until the
+
+ align:start position:0%
+metabolically inactive form until the
+ 
+
+ align:start position:0%
+metabolically inactive form until the
+time comes that the organism needs once
+
+ align:start position:0%
+time comes that the organism needs once
+ 
+
+ align:start position:0%
+time comes that the organism needs once
+again the energy that is stored in the
+
+ align:start position:0%
+again the energy that is stored in the
+ 
+
+ align:start position:0%
+again the energy that is stored in the
+glucose upon which occasion these bonds
+
+ align:start position:0%
+glucose upon which occasion these bonds
+ 
+
+ align:start position:0%
+glucose upon which occasion these bonds
+are rapidly broken down and the glucose
+
+ align:start position:0%
+are rapidly broken down and the glucose
+ 
+
+ align:start position:0%
+are rapidly broken down and the glucose
+is mobilized and put into the
+
+ align:start position:0%
+is mobilized and put into the
+ 
+
+ align:start position:0%
+is mobilized and put into the
+circulation for eventual disposition and
+
+ align:start position:0%
+circulation for eventual disposition and
+ 
+
+ align:start position:0%
+circulation for eventual disposition and
+use in certain specific tissues
+
+ align:start position:0%
+use in certain specific tissues
+ 
+
+ align:start position:0%
+use in certain specific tissues
+while it's encumbered in these high
+
+ align:start position:0%
+while it's encumbered in these high
+ 
+
+ align:start position:0%
+while it's encumbered in these high
+molecular weight polymers the glucose is
+
+ align:start position:0%
+molecular weight polymers the glucose is
+ 
+
+ align:start position:0%
+molecular weight polymers the glucose is
+essentially metabolically inactive the
+
+ align:start position:0%
+essentially metabolically inactive the
+ 
+
+ align:start position:0%
+essentially metabolically inactive the
+body doesn't realize it's there
+
+ align:start position:0%
+body doesn't realize it's there
+ 
+
+ align:start position:0%
+body doesn't realize it's there
+and we can as a consequence store large
+
+ align:start position:0%
+and we can as a consequence store large
+ 
+
+ align:start position:0%
+and we can as a consequence store large
+amounts of energy in these glycogen
+
+ align:start position:0%
+amounts of energy in these glycogen
+ 
+
+ align:start position:0%
+amounts of energy in these glycogen
+molecules and it can be stored there
+
+ align:start position:0%
+molecules and it can be stored there
+ 
+
+ align:start position:0%
+molecules and it can be stored there
+indefinitely
+
+ align:start position:0%
+indefinitely
+ 
+
+ align:start position:0%
+indefinitely
+now the fact is that uh this this idea
+
+ align:start position:0%
+now the fact is that uh this this idea
+ 
+
+ align:start position:0%
+now the fact is that uh this this idea
+of end-to-end polymerization that I just
+
+ align:start position:0%
+of end-to-end polymerization that I just
+ 
+
+ align:start position:0%
+of end-to-end polymerization that I just
+mentioned can be extended to other
+
+ align:start position:0%
+mentioned can be extended to other
+ 
+
+ align:start position:0%
+mentioned can be extended to other
+macromolecules which also become linked
+
+ align:start position:0%
+macromolecules which also become linked
+ 
+
+ align:start position:0%
+macromolecules which also become linked
+end to end in specific kinds of polymers
+
+ align:start position:0%
+end to end in specific kinds of polymers
+ 
+
+ align:start position:0%
+end to end in specific kinds of polymers
+and here we are moving now into the into
+
+ align:start position:0%
+and here we are moving now into the into
+ 
+
+ align:start position:0%
+and here we are moving now into the into
+the notion of talking about amino acids
+
+ align:start position:0%
+the notion of talking about amino acids
+ 
+
+ align:start position:0%
+the notion of talking about amino acids
+and we're talking about proteins if we
+
+ align:start position:0%
+and we're talking about proteins if we
+ 
+
+ align:start position:0%
+and we're talking about proteins if we
+look at an amino acid what we see is it
+
+ align:start position:0%
+look at an amino acid what we see is it
+ 
+
+ align:start position:0%
+look at an amino acid what we see is it
+has an important
+
+ align:start position:0%
+has an important
+ 
+
+ align:start position:0%
+has an important
+structure like this here's a central
+
+ align:start position:0%
+structure like this here's a central
+ 
+
+ align:start position:0%
+structure like this here's a central
+carbon and for in principle distinct
+
+ align:start position:0%
+carbon and for in principle distinct
+ 
+
+ align:start position:0%
+carbon and for in principle distinct
+side chains where R represents some side
+
+ align:start position:0%
+side chains where R represents some side
+ 
+
+ align:start position:0%
+side chains where R represents some side
+chain that can be any one of as we'll
+
+ align:start position:0%
+chain that can be any one of as we'll
+ 
+
+ align:start position:0%
+chain that can be any one of as we'll
+see shortly any one of 20 distinct
+
+ align:start position:0%
+see shortly any one of 20 distinct
+ 
+
+ align:start position:0%
+see shortly any one of 20 distinct
+identities
+
+ align:start position:0%
+identities
+ 
+
+ align:start position:0%
+identities
+but the old amino acids share in common
+
+ align:start position:0%
+but the old amino acids share in common
+ 
+
+ align:start position:0%
+but the old amino acids share in common
+the property that they have this overall
+
+ align:start position:0%
+the property that they have this overall
+ 
+
+ align:start position:0%
+the property that they have this overall
+structure and as you may recall from our
+
+ align:start position:0%
+structure and as you may recall from our
+ 
+
+ align:start position:0%
+structure and as you may recall from our
+discussion
+
+ align:start position:0%
+discussion
+ 
+
+ align:start position:0%
+discussion
+of discussions of last week at neutral
+
+ align:start position:0%
+of discussions of last week at neutral
+ 
+
+ align:start position:0%
+of discussions of last week at neutral
+pH it wouldn't a an amino acid of this
+
+ align:start position:0%
+pH it wouldn't a an amino acid of this
+ 
+
+ align:start position:0%
+pH it wouldn't a an amino acid of this
+sort whatever Aries wouldn't look like
+
+ align:start position:0%
+sort whatever Aries wouldn't look like
+ 
+
+ align:start position:0%
+sort whatever Aries wouldn't look like
+this at all
+
+ align:start position:0%
+this at all
+ 
+
+ align:start position:0%
+this at all
+because the amine group would attract an
+
+ align:start position:0%
+because the amine group would attract an
+ 
+
+ align:start position:0%
+because the amine group would attract an
+extra proton causing it to become
+
+ align:start position:0%
+extra proton causing it to become
+ 
+
+ align:start position:0%
+extra proton causing it to become
+positively charged and the carboxyl
+
+ align:start position:0%
+positively charged and the carboxyl
+ 
+
+ align:start position:0%
+positively charged and the carboxyl
+group would release a proton causing it
+
+ align:start position:0%
+group would release a proton causing it
+ 
+
+ align:start position:0%
+group would release a proton causing it
+to become negatively charged
+
+ align:start position:0%
+to become negatively charged
+ 
+
+ align:start position:0%
+to become negatively charged
+and as you might deduce from this at
+
+ align:start position:0%
+and as you might deduce from this at
+ 
+
+ align:start position:0%
+and as you might deduce from this at
+very low PH due to the greatly increased
+
+ align:start position:0%
+very low PH due to the greatly increased
+ 
+
+ align:start position:0%
+very low PH due to the greatly increased
+concentration of protons free protons in
+
+ align:start position:0%
+concentration of protons free protons in
+ 
+
+ align:start position:0%
+concentration of protons free protons in
+the solution the equilibrium will be
+
+ align:start position:0%
+the solution the equilibrium will be
+ 
+
+ align:start position:0%
+the solution the equilibrium will be
+would be driven more in favor of
+
+ align:start position:0%
+would be driven more in favor of
+ 
+
+ align:start position:0%
+would be driven more in favor of
+reattaching a proton to the carboxyl
+
+ align:start position:0%
+reattaching a proton to the carboxyl
+ 
+
+ align:start position:0%
+reattaching a proton to the carboxyl
+group just because there are so many of
+
+ align:start position:0%
+group just because there are so many of
+ 
+
+ align:start position:0%
+group just because there are so many of
+these protons around
+
+ align:start position:0%
+these protons around
+ 
+
+ align:start position:0%
+these protons around
+conversely at very high pH where the
+
+ align:start position:0%
+conversely at very high pH where the
+ 
+
+ align:start position:0%
+conversely at very high pH where the
+hydroxyl ions are in in the predominance
+
+ align:start position:0%
+hydroxyl ions are in in the predominance
+ 
+
+ align:start position:0%
+hydroxyl ions are in in the predominance
+they obviously tend to scavenge protons
+
+ align:start position:0%
+they obviously tend to scavenge protons
+ 
+
+ align:start position:0%
+they obviously tend to scavenge protons
+reducing the level of protons to very
+
+ align:start position:0%
+reducing the level of protons to very
+ 
+
+ align:start position:0%
+reducing the level of protons to very
+low level in in the water and under very
+
+ align:start position:0%
+low level in in the water and under very
+ 
+
+ align:start position:0%
+low level in in the water and under very
+high pH conditions this proton would be
+
+ align:start position:0%
+high pH conditions this proton would be
+ 
+
+ align:start position:0%
+high pH conditions this proton would be
+released and pulled away by the hydroxyl
+
+ align:start position:0%
+released and pulled away by the hydroxyl
+ 
+
+ align:start position:0%
+released and pulled away by the hydroxyl
+ions causing this amine group once again
+
+ align:start position:0%
+ions causing this amine group once again
+ 
+
+ align:start position:0%
+ions causing this amine group once again
+to return to its negative charge state
+
+ align:start position:0%
+to return to its negative charge state
+ 
+
+ align:start position:0%
+to return to its negative charge state
+now the fact of the matter is that uh
+
+ align:start position:0%
+now the fact of the matter is that uh
+ 
+
+ align:start position:0%
+now the fact of the matter is that uh
+these amino acids are
+
+ align:start position:0%
+these amino acids are
+ 
+
+ align:start position:0%
+these amino acids are
+exist in a very specific
+
+ align:start position:0%
+exist in a very specific
+ 
+
+ align:start position:0%
+exist in a very specific
+three-dimensional configuration and
+
+ align:start position:0%
+three-dimensional configuration and
+ 
+
+ align:start position:0%
+three-dimensional configuration and
+that's Illustrated much more nicely here
+
+ align:start position:0%
+that's Illustrated much more nicely here
+ 
+
+ align:start position:0%
+that's Illustrated much more nicely here
+than I could possibly draw on the board
+
+ align:start position:0%
+than I could possibly draw on the board
+ 
+
+ align:start position:0%
+than I could possibly draw on the board
+which in any case would be hopeless
+
+ align:start position:0%
+which in any case would be hopeless
+ 
+
+ align:start position:0%
+which in any case would be hopeless
+um which is that you can see in
+
+ align:start position:0%
+um which is that you can see in
+ 
+
+ align:start position:0%
+um which is that you can see in
+principle that once you have four
+
+ align:start position:0%
+principle that once you have four
+ 
+
+ align:start position:0%
+principle that once you have four
+distinct
+
+ align:start position:0%
+distinct
+ 
+
+ align:start position:0%
+distinct
+side groups coming off of a carbon that
+
+ align:start position:0%
+side groups coming off of a carbon that
+ 
+
+ align:start position:0%
+side groups coming off of a carbon that
+there is in principle two different ways
+
+ align:start position:0%
+there is in principle two different ways
+ 
+
+ align:start position:0%
+there is in principle two different ways
+to um to create them and this is
+
+ align:start position:0%
+to um to create them and this is
+ 
+
+ align:start position:0%
+to um to create them and this is
+sometimes called chirality chiral you
+
+ align:start position:0%
+sometimes called chirality chiral you
+ 
+
+ align:start position:0%
+sometimes called chirality chiral you
+see is the form right here the hands are
+
+ align:start position:0%
+see is the form right here the hands are
+ 
+
+ align:start position:0%
+see is the form right here the hands are
+chiral if I try as much as I will to
+
+ align:start position:0%
+chiral if I try as much as I will to
+ 
+
+ align:start position:0%
+chiral if I try as much as I will to
+superimpose one hand on top of another
+
+ align:start position:0%
+superimpose one hand on top of another
+ 
+
+ align:start position:0%
+superimpose one hand on top of another
+it doesn't work because there are mirror
+
+ align:start position:0%
+it doesn't work because there are mirror
+ 
+
+ align:start position:0%
+it doesn't work because there are mirror
+images of one another which are
+
+ align:start position:0%
+images of one another which are
+ 
+
+ align:start position:0%
+images of one another which are
+asymmetrical and as a consequence we see
+
+ align:start position:0%
+asymmetrical and as a consequence we see
+ 
+
+ align:start position:0%
+asymmetrical and as a consequence we see
+a similar kind of relationship occurring
+
+ align:start position:0%
+a similar kind of relationship occurring
+ 
+
+ align:start position:0%
+a similar kind of relationship occurring
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+where we see that these two forms of
+
+ align:start position:0%
+where we see that these two forms of
+ 
+
+ align:start position:0%
+where we see that these two forms of
+amino acids could in principle exist and
+
+ align:start position:0%
+amino acids could in principle exist and
+ 
+
+ align:start position:0%
+amino acids could in principle exist and
+they're not interchangeable unless one
+
+ align:start position:0%
+they're not interchangeable unless one
+ 
+
+ align:start position:0%
+they're not interchangeable unless one
+breaks one of the bonds and reforms it
+
+ align:start position:0%
+breaks one of the bonds and reforms it
+ 
+
+ align:start position:0%
+breaks one of the bonds and reforms it
+these two forms are called the L and the
+
+ align:start position:0%
+these two forms are called the L and the
+ 
+
+ align:start position:0%
+these two forms are called the L and the
+D and it turns out that the L form is
+
+ align:start position:0%
+D and it turns out that the L form is
+ 
+
+ align:start position:0%
+D and it turns out that the L form is
+the one that's uh used by virtually all
+
+ align:start position:0%
+the one that's uh used by virtually all
+ 
+
+ align:start position:0%
+the one that's uh used by virtually all
+life forms on the planet I.E there was
+
+ align:start position:0%
+life forms on the planet I.E there was
+ 
+
+ align:start position:0%
+life forms on the planet I.E there was
+an arbitrary Choice made sometime about
+
+ align:start position:0%
+an arbitrary Choice made sometime about
+ 
+
+ align:start position:0%
+an arbitrary Choice made sometime about
+three billion years ago and more to use
+
+ align:start position:0%
+three billion years ago and more to use
+ 
+
+ align:start position:0%
+three billion years ago and more to use
+one of the two
+
+ align:start position:0%
+one of the two
+ 
+
+ align:start position:0%
+one of the two
+um three-dimensional configurations and
+
+ align:start position:0%
+um three-dimensional configurations and
+ 
+
+ align:start position:0%
+um three-dimensional configurations and
+not to use the other the other is found
+
+ align:start position:0%
+not to use the other the other is found
+ 
+
+ align:start position:0%
+not to use the other the other is found
+in certain rare exceptions but virtually
+
+ align:start position:0%
+in certain rare exceptions but virtually
+ 
+
+ align:start position:0%
+in certain rare exceptions but virtually
+I all life forms on this planet use the
+
+ align:start position:0%
+I all life forms on this planet use the
+ 
+
+ align:start position:0%
+I all life forms on this planet use the
+L form that said by the way this begins
+
+ align:start position:0%
+L form that said by the way this begins
+ 
+
+ align:start position:0%
+L form that said by the way this begins
+to indicate some of the arbitrary
+
+ align:start position:0%
+to indicate some of the arbitrary
+ 
+
+ align:start position:0%
+to indicate some of the arbitrary
+decisions that were made early during
+
+ align:start position:0%
+decisions that were made early during
+ 
+
+ align:start position:0%
+decisions that were made early during
+Evolution because we could imagine on
+
+ align:start position:0%
+Evolution because we could imagine on
+ 
+
+ align:start position:0%
+Evolution because we could imagine on
+another planet if life were to exist
+
+ align:start position:0%
+another planet if life were to exist
+ 
+
+ align:start position:0%
+another planet if life were to exist
+there and if it were to depend on amino
+
+ align:start position:0%
+there and if it were to depend on amino
+ 
+
+ align:start position:0%
+there and if it were to depend on amino
+acids that that evolutionary system
+
+ align:start position:0%
+acids that that evolutionary system
+ 
+
+ align:start position:0%
+acids that that evolutionary system
+might have chosen the D form so this is
+
+ align:start position:0%
+might have chosen the D form so this is
+ 
+
+ align:start position:0%
+might have chosen the D form so this is
+sort of a luck of the draw this is
+
+ align:start position:0%
+sort of a luck of the draw this is
+ 
+
+ align:start position:0%
+sort of a luck of the draw this is
+actually the way things evolved here
+
+ align:start position:0%
+actually the way things evolved here
+ 
+
+ align:start position:0%
+actually the way things evolved here
+and what we begin to see now is if we
+
+ align:start position:0%
+and what we begin to see now is if we
+ 
+
+ align:start position:0%
+and what we begin to see now is if we
+talk about proteins or uh if we want to
+
+ align:start position:0%
+talk about proteins or uh if we want to
+ 
+
+ align:start position:0%
+talk about proteins or uh if we want to
+be more specific and use the more
+
+ align:start position:0%
+be more specific and use the more
+ 
+
+ align:start position:0%
+be more specific and use the more
+biochemical term polypeptide
+
+ align:start position:0%
+biochemical term polypeptide
+ 
+
+ align:start position:0%
+biochemical term polypeptide
+we see once again we have an end-to-end
+
+ align:start position:0%
+we see once again we have an end-to-end
+ 
+
+ align:start position:0%
+we see once again we have an end-to-end
+joining system
+
+ align:start position:0%
+joining system
+ 
+
+ align:start position:0%
+joining system
+which is a bit different from that which
+
+ align:start position:0%
+which is a bit different from that which
+ 
+
+ align:start position:0%
+which is a bit different from that which
+the mono saccharides employee to create
+
+ align:start position:0%
+the mono saccharides employee to create
+ 
+
+ align:start position:0%
+the mono saccharides employee to create
+long chains of of glycogen or of starch
+
+ align:start position:0%
+long chains of of glycogen or of starch
+ 
+
+ align:start position:0%
+long chains of of glycogen or of starch
+because here we see once again a
+
+ align:start position:0%
+because here we see once again a
+ 
+
+ align:start position:0%
+because here we see once again a
+dehydration reaction
+
+ align:start position:0%
+dehydration reaction
+ 
+
+ align:start position:0%
+dehydration reaction
+where in a mean group and a carboxyl
+
+ align:start position:0%
+where in a mean group and a carboxyl
+ 
+
+ align:start position:0%
+where in a mean group and a carboxyl
+group are caused to uh shed the hydroxyl
+
+ align:start position:0%
+group are caused to uh shed the hydroxyl
+ 
+
+ align:start position:0%
+group are caused to uh shed the hydroxyl
+and the proton
+
+ align:start position:0%
+and the proton
+ 
+
+ align:start position:0%
+and the proton
+causing the formation of a peptide bond
+
+ align:start position:0%
+causing the formation of a peptide bond
+ 
+
+ align:start position:0%
+causing the formation of a peptide bond
+and here we see this important very
+
+ align:start position:0%
+and here we see this important very
+ 
+
+ align:start position:0%
+and here we see this important very
+important biochemical entity a peptide
+
+ align:start position:0%
+important biochemical entity a peptide
+ 
+
+ align:start position:0%
+important biochemical entity a peptide
+bond consisting here of this carbonyl
+
+ align:start position:0%
+bond consisting here of this carbonyl
+ 
+
+ align:start position:0%
+bond consisting here of this carbonyl
+and this nitrogen
+
+ align:start position:0%
+and this nitrogen
+ 
+
+ align:start position:0%
+and this nitrogen
+fused in this specific way
+
+ align:start position:0%
+fused in this specific way
+ 
+
+ align:start position:0%
+fused in this specific way
+and of course if you recognize this as
+
+ align:start position:0%
+and of course if you recognize this as
+ 
+
+ align:start position:0%
+and of course if you recognize this as
+being a peptide bond then you can
+
+ align:start position:0%
+being a peptide bond then you can
+ 
+
+ align:start position:0%
+being a peptide bond then you can
+understand why proteins are sometimes
+
+ align:start position:0%
+understand why proteins are sometimes
+ 
+
+ align:start position:0%
+understand why proteins are sometimes
+given the term polypeptide
+
+ align:start position:0%
+given the term polypeptide
+ 
+
+ align:start position:0%
+given the term polypeptide
+in some cases if one has very short
+
+ align:start position:0%
+in some cases if one has very short
+ 
+
+ align:start position:0%
+in some cases if one has very short
+stretches of amino acids linked end to
+
+ align:start position:0%
+stretches of amino acids linked end to
+ 
+
+ align:start position:0%
+stretches of amino acids linked end to
+end like this we talk about these being
+
+ align:start position:0%
+end like this we talk about these being
+ 
+
+ align:start position:0%
+end like this we talk about these being
+oligopeptides where oligo is the general
+
+ align:start position:0%
+oligopeptides where oligo is the general
+ 
+
+ align:start position:0%
+oligopeptides where oligo is the general
+term used in biology to refer to a small
+
+ align:start position:0%
+term used in biology to refer to a small
+ 
+
+ align:start position:0%
+term used in biology to refer to a small
+number of things rather than a large
+
+ align:start position:0%
+number of things rather than a large
+ 
+
+ align:start position:0%
+number of things rather than a large
+number of of things
+
+ align:start position:0%
+number of of things
+ 
+
+ align:start position:0%
+number of of things
+and once again we have here the
+
+ align:start position:0%
+and once again we have here the
+ 
+
+ align:start position:0%
+and once again we have here the
+possibility
+
+ align:start position:0%
+possibility
+ 
+
+ align:start position:0%
+possibility
+infinitely there are no constraints in
+
+ align:start position:0%
+infinitely there are no constraints in
+ 
+
+ align:start position:0%
+infinitely there are no constraints in
+principle on making this 500 a thousand
+
+ align:start position:0%
+principle on making this 500 a thousand
+ 
+
+ align:start position:0%
+principle on making this 500 a thousand
+even two thousand amino acids long
+
+ align:start position:0%
+even two thousand amino acids long
+ 
+
+ align:start position:0%
+even two thousand amino acids long
+where each of these once again is an
+
+ align:start position:0%
+where each of these once again is an
+ 
+
+ align:start position:0%
+where each of these once again is an
+amino acid and we're once again I'm
+
+ align:start position:0%
+amino acid and we're once again I'm
+ 
+
+ align:start position:0%
+amino acid and we're once again I'm
+being very Coy about the identities of
+
+ align:start position:0%
+being very Coy about the identities of
+ 
+
+ align:start position:0%
+being very Coy about the identities of
+R1 and R2 which as I will indicate very
+
+ align:start position:0%
+R1 and R2 which as I will indicate very
+ 
+
+ align:start position:0%
+R1 and R2 which as I will indicate very
+shortly can be one of 20 distinct
+
+ align:start position:0%
+shortly can be one of 20 distinct
+ 
+
+ align:start position:0%
+shortly can be one of 20 distinct
+alternatives here you see uh that we're
+
+ align:start position:0%
+alternatives here you see uh that we're
+ 
+
+ align:start position:0%
+alternatives here you see uh that we're
+continuing this process of peptide bond
+
+ align:start position:0%
+continuing this process of peptide bond
+ 
+
+ align:start position:0%
+continuing this process of peptide bond
+formation
+
+ align:start position:0%
+formation
+ 
+
+ align:start position:0%
+formation
+and most importantly here is the
+
+ align:start position:0%
+and most importantly here is the
+ 
+
+ align:start position:0%
+and most importantly here is the
+realization that there is a polarity of
+
+ align:start position:0%
+realization that there is a polarity of
+ 
+
+ align:start position:0%
+realization that there is a polarity of
+elongation here it doesn't move with
+
+ align:start position:0%
+elongation here it doesn't move with
+ 
+
+ align:start position:0%
+elongation here it doesn't move with
+equal probability left to right or right
+
+ align:start position:0%
+equal probability left to right or right
+ 
+
+ align:start position:0%
+equal probability left to right or right
+to left we start at the amino end here
+
+ align:start position:0%
+to left we start at the amino end here
+ 
+
+ align:start position:0%
+to left we start at the amino end here
+this is the amino end and this is the
+
+ align:start position:0%
+this is the amino end and this is the
+ 
+
+ align:start position:0%
+this is the amino end and this is the
+carboxyl end the amino end and the
+
+ align:start position:0%
+carboxyl end the amino end and the
+ 
+
+ align:start position:0%
+carboxyl end the amino end and the
+carboxyl end and invariably again
+
+ align:start position:0%
+carboxyl end and invariably again
+ 
+
+ align:start position:0%
+carboxyl end and invariably again
+because of the way life has evolved on
+
+ align:start position:0%
+because of the way life has evolved on
+ 
+
+ align:start position:0%
+because of the way life has evolved on
+this planet
+
+ align:start position:0%
+this planet
+ 
+
+ align:start position:0%
+this planet
+the new amino acid is added on the
+
+ align:start position:0%
+the new amino acid is added on the
+ 
+
+ align:start position:0%
+the new amino acid is added on the
+carboxyl end and so when one often talks
+
+ align:start position:0%
+carboxyl end and so when one often talks
+ 
+
+ align:start position:0%
+carboxyl end and so when one often talks
+about uh proteins one refers to their
+
+ align:start position:0%
+about uh proteins one refers to their
+ 
+
+ align:start position:0%
+about uh proteins one refers to their
+n-terminal
+
+ align:start position:0%
+n-terminal
+ 
+
+ align:start position:0%
+n-terminal
+and to their C terminal ends
+
+ align:start position:0%
+and to their C terminal ends
+ 
+
+ align:start position:0%
+and to their C terminal ends
+these referring obviously to the amino
+
+ align:start position:0%
+these referring obviously to the amino
+ 
+
+ align:start position:0%
+these referring obviously to the amino
+group at one end and the carboxyl in at
+
+ align:start position:0%
+group at one end and the carboxyl in at
+ 
+
+ align:start position:0%
+group at one end and the carboxyl in at
+the other end so the polarity is always
+
+ align:start position:0%
+the other end so the polarity is always
+ 
+
+ align:start position:0%
+the other end so the polarity is always
+a a directed synthesis adding it on the
+
+ align:start position:0%
+a a directed synthesis adding it on the
+ 
+
+ align:start position:0%
+a a directed synthesis adding it on the
+c-terminal end in other words to use a a
+
+ align:start position:0%
+c-terminal end in other words to use a a
+ 
+
+ align:start position:0%
+c-terminal end in other words to use a a
+shorthand notation we think about
+
+ align:start position:0%
+shorthand notation we think about
+ 
+
+ align:start position:0%
+shorthand notation we think about
+um proteins is going in this with this
+
+ align:start position:0%
+um proteins is going in this with this
+ 
+
+ align:start position:0%
+um proteins is going in this with this
+polarity and towards C things are
+
+ align:start position:0%
+polarity and towards C things are
+ 
+
+ align:start position:0%
+polarity and towards C things are
+growing at the c-terminal and
+
+ align:start position:0%
+growing at the c-terminal and
+ 
+
+ align:start position:0%
+growing at the c-terminal and
+progressively
+
+ align:start position:0%
+progressively
+ 
+
+ align:start position:0%
+progressively
+and each time
+
+ align:start position:0%
+and each time
+ 
+
+ align:start position:0%
+and each time
+one can imagine the addition of an amino
+
+ align:start position:0%
+one can imagine the addition of an amino
+ 
+
+ align:start position:0%
+one can imagine the addition of an amino
+acid on the end of it so again it can be
+
+ align:start position:0%
+acid on the end of it so again it can be
+ 
+
+ align:start position:0%
+acid on the end of it so again it can be
+extended in principle indefinitely
+
+ align:start position:0%
+extended in principle indefinitely
+ 
+
+ align:start position:0%
+extended in principle indefinitely
+keep in mind as well something that's
+
+ align:start position:0%
+keep in mind as well something that's
+ 
+
+ align:start position:0%
+keep in mind as well something that's
+implicit in everything I'm telling you
+
+ align:start position:0%
+implicit in everything I'm telling you
+ 
+
+ align:start position:0%
+implicit in everything I'm telling you
+but I won't always mention it explicitly
+
+ align:start position:0%
+but I won't always mention it explicitly
+ 
+
+ align:start position:0%
+but I won't always mention it explicitly
+and that is virtually every biochemical
+
+ align:start position:0%
+and that is virtually every biochemical
+ 
+
+ align:start position:0%
+and that is virtually every biochemical
+reaction is reversible
+
+ align:start position:0%
+reaction is reversible
+ 
+
+ align:start position:0%
+reaction is reversible
+and therefore if one is able to form a
+
+ align:start position:0%
+and therefore if one is able to form a
+ 
+
+ align:start position:0%
+and therefore if one is able to form a
+peptide bond
+
+ align:start position:0%
+peptide bond
+ 
+
+ align:start position:0%
+peptide bond
+one is able to break it down by
+
+ align:start position:0%
+one is able to break it down by
+ 
+
+ align:start position:0%
+one is able to break it down by
+biological means as well I.E by
+
+ align:start position:0%
+biological means as well I.E by
+ 
+
+ align:start position:0%
+biological means as well I.E by
+introducing a water molecule back in and
+
+ align:start position:0%
+introducing a water molecule back in and
+ 
+
+ align:start position:0%
+introducing a water molecule back in and
+thereby using the process of hydrolysis
+
+ align:start position:0%
+thereby using the process of hydrolysis
+ 
+
+ align:start position:0%
+thereby using the process of hydrolysis
+which is the breakdown of a bond through
+
+ align:start position:0%
+which is the breakdown of a bond through
+ 
+
+ align:start position:0%
+which is the breakdown of a bond through
+the introduction of a water molecule
+
+ align:start position:0%
+the introduction of a water molecule
+ 
+
+ align:start position:0%
+the introduction of a water molecule
+to destroy the previously created Bond
+
+ align:start position:0%
+to destroy the previously created Bond
+ 
+
+ align:start position:0%
+to destroy the previously created Bond
+to use an MIT phrase the reversibility
+
+ align:start position:0%
+to use an MIT phrase the reversibility
+ 
+
+ align:start position:0%
+to use an MIT phrase the reversibility
+is intuitively obvious because if you
+
+ align:start position:0%
+is intuitively obvious because if you
+ 
+
+ align:start position:0%
+is intuitively obvious because if you
+were able to make a
+
+ align:start position:0%
+were able to make a
+ 
+
+ align:start position:0%
+were able to make a
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+I don't know it's still used but it was
+
+ align:start position:0%
+I don't know it's still used but it was
+ 
+
+ align:start position:0%
+I don't know it's still used but it was
+used in the late Stone Age around here
+
+ align:start position:0%
+used in the late Stone Age around here
+ 
+
+ align:start position:0%
+used in the late Stone Age around here
+anyhow so
+
+ align:start position:0%
+anyhow so
+ 
+
+ align:start position:0%
+anyhow so
+any biochemical action must be
+
+ align:start position:0%
+any biochemical action must be
+ 
+
+ align:start position:0%
+any biochemical action must be
+reversible because if for example this
+
+ align:start position:0%
+reversible because if for example this
+ 
+
+ align:start position:0%
+reversible because if for example this
+polymerization were irreversible
+
+ align:start position:0%
+polymerization were irreversible
+ 
+
+ align:start position:0%
+polymerization were irreversible
+then all the protein that was ever
+
+ align:start position:0%
+then all the protein that was ever
+ 
+
+ align:start position:0%
+then all the protein that was ever
+synthesized on the surface of the planet
+
+ align:start position:0%
+synthesized on the surface of the planet
+ 
+
+ align:start position:0%
+synthesized on the surface of the planet
+over the last three and a half billion
+
+ align:start position:0%
+over the last three and a half billion
+ 
+
+ align:start position:0%
+over the last three and a half billion
+years would accumulate progressively and
+
+ align:start position:0%
+years would accumulate progressively and
+ 
+
+ align:start position:0%
+years would accumulate progressively and
+obviously that doesn't happen and
+
+ align:start position:0%
+obviously that doesn't happen and
+ 
+
+ align:start position:0%
+obviously that doesn't happen and
+therefore macromolecular synthesis do
+
+ align:start position:0%
+therefore macromolecular synthesis do
+ 
+
+ align:start position:0%
+therefore macromolecular synthesis do
+the excessive proceeds forward obviously
+
+ align:start position:0%
+the excessive proceeds forward obviously
+ 
+
+ align:start position:0%
+the excessive proceeds forward obviously
+must go in the other direction as well
+
+ align:start position:0%
+must go in the other direction as well
+ 
+
+ align:start position:0%
+must go in the other direction as well
+and the resulting concentration of a
+
+ align:start position:0%
+and the resulting concentration of a
+ 
+
+ align:start position:0%
+and the resulting concentration of a
+complete protein is known as its steady
+
+ align:start position:0%
+complete protein is known as its steady
+ 
+
+ align:start position:0%
+complete protein is known as its steady
+state so we might make a protein
+
+ align:start position:0%
+state so we might make a protein
+ 
+
+ align:start position:0%
+state so we might make a protein
+at at one rate and break it down at the
+
+ align:start position:0%
+at at one rate and break it down at the
+ 
+
+ align:start position:0%
+at at one rate and break it down at the
+same rate and it's steady state
+
+ align:start position:0%
+same rate and it's steady state
+ 
+
+ align:start position:0%
+same rate and it's steady state
+concentration represents the compromise
+
+ align:start position:0%
+concentration represents the compromise
+ 
+
+ align:start position:0%
+concentration represents the compromise
+between these two I.E the concentration
+
+ align:start position:0%
+between these two I.E the concentration
+ 
+
+ align:start position:0%
+between these two I.E the concentration
+of such a protein that we might observe
+
+ align:start position:0%
+of such a protein that we might observe
+ 
+
+ align:start position:0%
+of such a protein that we might observe
+at any one point in time
+
+ align:start position:0%
+at any one point in time
+ 
+
+ align:start position:0%
+at any one point in time
+indeed the term steady state could be
+
+ align:start position:0%
+indeed the term steady state could be
+ 
+
+ align:start position:0%
+indeed the term steady state could be
+expanded to you to any process in which
+
+ align:start position:0%
+expanded to you to any process in which
+ 
+
+ align:start position:0%
+expanded to you to any process in which
+there's a synthesis and there's a
+
+ align:start position:0%
+there's a synthesis and there's a
+ 
+
+ align:start position:0%
+there's a synthesis and there's a
+breakdown of something and the
+
+ align:start position:0%
+breakdown of something and the
+ 
+
+ align:start position:0%
+breakdown of something and the
+equilibrium concentration which results
+
+ align:start position:0%
+equilibrium concentration which results
+ 
+
+ align:start position:0%
+equilibrium concentration which results
+is once again called the steady state
+
+ align:start position:0%
+is once again called the steady state
+ 
+
+ align:start position:0%
+is once again called the steady state
+um of that molecule now let's get down
+
+ align:start position:0%
+um of that molecule now let's get down
+ 
+
+ align:start position:0%
+um of that molecule now let's get down
+to the nitty-gritty which is obviously
+
+ align:start position:0%
+to the nitty-gritty which is obviously
+ 
+
+ align:start position:0%
+to the nitty-gritty which is obviously
+something which we can't avoid for very
+
+ align:start position:0%
+something which we can't avoid for very
+ 
+
+ align:start position:0%
+something which we can't avoid for very
+long which is to say the R's I.E the
+
+ align:start position:0%
+long which is to say the R's I.E the
+ 
+
+ align:start position:0%
+long which is to say the R's I.E the
+side chains
+
+ align:start position:0%
+side chains
+ 
+
+ align:start position:0%
+side chains
+once again here we see an arbitrary
+
+ align:start position:0%
+once again here we see an arbitrary
+ 
+
+ align:start position:0%
+once again here we see an arbitrary
+artifact of very early evolution in the
+
+ align:start position:0%
+artifact of very early evolution in the
+ 
+
+ align:start position:0%
+artifact of very early evolution in the
+biosphere because there are in effect 20
+
+ align:start position:0%
+biosphere because there are in effect 20
+ 
+
+ align:start position:0%
+biosphere because there are in effect 20
+different side chains creating set 20
+
+ align:start position:0%
+different side chains creating set 20
+ 
+
+ align:start position:0%
+different side chains creating set 20
+distinct amino acids
+
+ align:start position:0%
+distinct amino acids
+ 
+
+ align:start position:0%
+distinct amino acids
+which are used in proteins by all
+
+ align:start position:0%
+which are used in proteins by all
+ 
+
+ align:start position:0%
+which are used in proteins by all
+organisms on this planet
+
+ align:start position:0%
+organisms on this planet
+ 
+
+ align:start position:0%
+organisms on this planet
+again there are rare exceptions certain
+
+ align:start position:0%
+again there are rare exceptions certain
+ 
+
+ align:start position:0%
+again there are rare exceptions certain
+uh fungi and certain bacteria are able
+
+ align:start position:0%
+uh fungi and certain bacteria are able
+ 
+
+ align:start position:0%
+uh fungi and certain bacteria are able
+to make unusual amino acids but these
+
+ align:start position:0%
+to make unusual amino acids but these
+ 
+
+ align:start position:0%
+to make unusual amino acids but these
+are the basic building blocks of
+
+ align:start position:0%
+are the basic building blocks of
+ 
+
+ align:start position:0%
+are the basic building blocks of
+virtually all life forms on the planet
+
+ align:start position:0%
+virtually all life forms on the planet
+ 
+
+ align:start position:0%
+virtually all life forms on the planet
+99.99 of all the protein that is created
+
+ align:start position:0%
+99.99 of all the protein that is created
+ 
+
+ align:start position:0%
+99.99 of all the protein that is created
+is is synthesized through the
+
+ align:start position:0%
+is is synthesized through the
+ 
+
+ align:start position:0%
+is is synthesized through the
+polymerization of these 20 amino acids
+
+ align:start position:0%
+polymerization of these 20 amino acids
+ 
+
+ align:start position:0%
+polymerization of these 20 amino acids
+um and by the way uh one of the amino
+
+ align:start position:0%
+um and by the way uh one of the amino
+ 
+
+ align:start position:0%
+um and by the way uh one of the amino
+acids glycine over here you see it right
+
+ align:start position:0%
+acids glycine over here you see it right
+ 
+
+ align:start position:0%
+acids glycine over here you see it right
+here violates this rule of chirality and
+
+ align:start position:0%
+here violates this rule of chirality and
+ 
+
+ align:start position:0%
+here violates this rule of chirality and
+and you will recall before I said that
+
+ align:start position:0%
+and you will recall before I said that
+ 
+
+ align:start position:0%
+and you will recall before I said that
+because there are four distinct amino
+
+ align:start position:0%
+because there are four distinct amino
+ 
+
+ align:start position:0%
+because there are four distinct amino
+acids um
+
+ align:start position:0%
+acids um
+ 
+
+ align:start position:0%
+acids um
+uh four distinct side chains around a
+
+ align:start position:0%
+uh four distinct side chains around a
+ 
+
+ align:start position:0%
+uh four distinct side chains around a
+central carbon sometimes called the
+
+ align:start position:0%
+central carbon sometimes called the
+ 
+
+ align:start position:0%
+central carbon sometimes called the
+alpha carbon you always have a
+
+ align:start position:0%
+alpha carbon you always have a
+ 
+
+ align:start position:0%
+alpha carbon you always have a
+handedness of amino acids but in the
+
+ align:start position:0%
+handedness of amino acids but in the
+ 
+
+ align:start position:0%
+handedness of amino acids but in the
+case this cannot this uh notion cannot
+
+ align:start position:0%
+case this cannot this uh notion cannot
+ 
+
+ align:start position:0%
+case this cannot this uh notion cannot
+be respected in the case of glycine seen
+
+ align:start position:0%
+be respected in the case of glycine seen
+ 
+
+ align:start position:0%
+be respected in the case of glycine seen
+up here
+
+ align:start position:0%
+up here
+ 
+
+ align:start position:0%
+up here
+simply because we don't have four
+
+ align:start position:0%
+simply because we don't have four
+ 
+
+ align:start position:0%
+simply because we don't have four
+distinct here's the central carbon where
+
+ align:start position:0%
+distinct here's the central carbon where
+ 
+
+ align:start position:0%
+distinct here's the central carbon where
+I'm pointing with the red and here these
+
+ align:start position:0%
+I'm pointing with the red and here these
+ 
+
+ align:start position:0%
+I'm pointing with the red and here these
+two hydrogens are equivalent to one
+
+ align:start position:0%
+two hydrogens are equivalent to one
+ 
+
+ align:start position:0%
+two hydrogens are equivalent to one
+another they're not four distinct chains
+
+ align:start position:0%
+another they're not four distinct chains
+ 
+
+ align:start position:0%
+another they're not four distinct chains
+there's only three distinct chains here
+
+ align:start position:0%
+there's only three distinct chains here
+ 
+
+ align:start position:0%
+there's only three distinct chains here
+so glycine violates this rule of
+
+ align:start position:0%
+so glycine violates this rule of
+ 
+
+ align:start position:0%
+so glycine violates this rule of
+chirality of left and right handedness
+
+ align:start position:0%
+chirality of left and right handedness
+ 
+
+ align:start position:0%
+chirality of left and right handedness
+and here by the way the side chain which
+
+ align:start position:0%
+and here by the way the side chain which
+ 
+
+ align:start position:0%
+and here by the way the side chain which
+in all of these cases is depicted as
+
+ align:start position:0%
+in all of these cases is depicted as
+ 
+
+ align:start position:0%
+in all of these cases is depicted as
+extending off to the right of each amino
+
+ align:start position:0%
+extending off to the right of each amino
+ 
+
+ align:start position:0%
+extending off to the right of each amino
+acid the side chain is simply an H
+
+ align:start position:0%
+acid the side chain is simply an H
+ 
+
+ align:start position:0%
+acid the side chain is simply an H
+simply a proton a hydrogen atom
+
+ align:start position:0%
+simply a proton a hydrogen atom
+ 
+
+ align:start position:0%
+simply a proton a hydrogen atom
+in fact what we see about these um amino
+
+ align:start position:0%
+in fact what we see about these um amino
+ 
+
+ align:start position:0%
+in fact what we see about these um amino
+acids is is that the side chains have
+
+ align:start position:0%
+acids is is that the side chains have
+ 
+
+ align:start position:0%
+acids is is that the side chains have
+quite distinct biochemical properties
+
+ align:start position:0%
+quite distinct biochemical properties
+ 
+
+ align:start position:0%
+quite distinct biochemical properties
+and that begins to impress us with the
+
+ align:start position:0%
+and that begins to impress us with the
+ 
+
+ align:start position:0%
+and that begins to impress us with the
+notion that proteins and their
+
+ align:start position:0%
+notion that proteins and their
+ 
+
+ align:start position:0%
+notion that proteins and their
+biochemical attributes can be dictated
+
+ align:start position:0%
+biochemical attributes can be dictated
+ 
+
+ align:start position:0%
+biochemical attributes can be dictated
+by the identities of the amino acids
+
+ align:start position:0%
+by the identities of the amino acids
+ 
+
+ align:start position:0%
+by the identities of the amino acids
+that are used to construct them
+
+ align:start position:0%
+that are used to construct them
+ 
+
+ align:start position:0%
+that are used to construct them
+we can talk about the notion of nonpolar
+
+ align:start position:0%
+we can talk about the notion of nonpolar
+ 
+
+ align:start position:0%
+we can talk about the notion of nonpolar
+versus polar amino acids I.E amino acids
+
+ align:start position:0%
+versus polar amino acids I.E amino acids
+ 
+
+ align:start position:0%
+versus polar amino acids I.E amino acids
+which have poor affinity for water they
+
+ align:start position:0%
+which have poor affinity for water they
+ 
+
+ align:start position:0%
+which have poor affinity for water they
+don't have a separation of plus and
+
+ align:start position:0%
+don't have a separation of plus and
+ 
+
+ align:start position:0%
+don't have a separation of plus and
+minus uh charges
+
+ align:start position:0%
+minus uh charges
+ 
+
+ align:start position:0%
+minus uh charges
+and as a consequence they're they're a
+
+ align:start position:0%
+and as a consequence they're they're a
+ 
+
+ align:start position:0%
+and as a consequence they're they're a
+little bit or quite a bit hydrophobic
+
+ align:start position:0%
+little bit or quite a bit hydrophobic
+ 
+
+ align:start position:0%
+little bit or quite a bit hydrophobic
+now you will say well how can they be
+
+ align:start position:0%
+now you will say well how can they be
+ 
+
+ align:start position:0%
+now you will say well how can they be
+hydrophobic because here this oxygen is
+
+ align:start position:0%
+hydrophobic because here this oxygen is
+ 
+
+ align:start position:0%
+hydrophobic because here this oxygen is
+charged and here this Amino this amine
+
+ align:start position:0%
+charged and here this Amino this amine
+ 
+
+ align:start position:0%
+charged and here this Amino this amine
+group is charged that would make it
+
+ align:start position:0%
+group is charged that would make it
+ 
+
+ align:start position:0%
+group is charged that would make it
+highly hydrophilic
+
+ align:start position:0%
+highly hydrophilic
+ 
+
+ align:start position:0%
+highly hydrophilic
+but keep in mind when I'm talking about
+
+ align:start position:0%
+but keep in mind when I'm talking about
+ 
+
+ align:start position:0%
+but keep in mind when I'm talking about
+these amino acids I'm not talking about
+
+ align:start position:0%
+these amino acids I'm not talking about
+ 
+
+ align:start position:0%
+these amino acids I'm not talking about
+them when they're in a single amino acid
+
+ align:start position:0%
+them when they're in a single amino acid
+ 
+
+ align:start position:0%
+them when they're in a single amino acid
+form I'm talking about their properties
+
+ align:start position:0%
+form I'm talking about their properties
+ 
+
+ align:start position:0%
+form I'm talking about their properties
+once they have been polymerized into a
+
+ align:start position:0%
+once they have been polymerized into a
+ 
+
+ align:start position:0%
+once they have been polymerized into a
+state like this and once they're
+
+ align:start position:0%
+state like this and once they're
+ 
+
+ align:start position:0%
+state like this and once they're
+polymerized into a state like this
+
+ align:start position:0%
+polymerized into a state like this
+ 
+
+ align:start position:0%
+polymerized into a state like this
+the the nh2 and Co charging that is the
+
+ align:start position:0%
+the the nh2 and Co charging that is the
+ 
+
+ align:start position:0%
+the the nh2 and Co charging that is the
+charge here and the charge here become
+
+ align:start position:0%
+charge here and the charge here become
+ 
+
+ align:start position:0%
+charge here and the charge here become
+irrelevant because this oxygen and this
+
+ align:start position:0%
+irrelevant because this oxygen and this
+ 
+
+ align:start position:0%
+irrelevant because this oxygen and this
+amine group are both tied up in covalent
+
+ align:start position:0%
+amine group are both tied up in covalent
+ 
+
+ align:start position:0%
+amine group are both tied up in covalent
+bonds and this acquisition of a proton
+
+ align:start position:0%
+bonds and this acquisition of a proton
+ 
+
+ align:start position:0%
+bonds and this acquisition of a proton
+and this shedding of an elect of a
+
+ align:start position:0%
+and this shedding of an elect of a
+ 
+
+ align:start position:0%
+and this shedding of an elect of a
+proton over here cannot occur because
+
+ align:start position:0%
+proton over here cannot occur because
+ 
+
+ align:start position:0%
+proton over here cannot occur because
+both of these atoms o and and N are
+
+ align:start position:0%
+both of these atoms o and and N are
+ 
+
+ align:start position:0%
+both of these atoms o and and N are
+involved in covalent bonds so therefore
+
+ align:start position:0%
+involved in covalent bonds so therefore
+ 
+
+ align:start position:0%
+involved in covalent bonds so therefore
+when we talk about uh um nonpolar and
+
+ align:start position:0%
+when we talk about uh um nonpolar and
+ 
+
+ align:start position:0%
+when we talk about uh um nonpolar and
+and polar amino acids keep in mind we're
+
+ align:start position:0%
+and polar amino acids keep in mind we're
+ 
+
+ align:start position:0%
+and polar amino acids keep in mind we're
+focusing on the biochemical properties
+
+ align:start position:0%
+focusing on the biochemical properties
+ 
+
+ align:start position:0%
+focusing on the biochemical properties
+of the side chain because the central
+
+ align:start position:0%
+of the side chain because the central
+ 
+
+ align:start position:0%
+of the side chain because the central
+backbone of the of the polypeptide and
+
+ align:start position:0%
+backbone of the of the polypeptide and
+ 
+
+ align:start position:0%
+backbone of the of the polypeptide and
+the central backbone is defined quite
+
+ align:start position:0%
+the central backbone is defined quite
+ 
+
+ align:start position:0%
+the central backbone is defined quite
+clearly here here's the central backbone
+
+ align:start position:0%
+clearly here here's the central backbone
+ 
+
+ align:start position:0%
+clearly here here's the central backbone
+and you see it has a a quite repeating
+
+ align:start position:0%
+and you see it has a a quite repeating
+ 
+
+ align:start position:0%
+and you see it has a a quite repeating
+structure NCC
+
+ align:start position:0%
+structure NCC
+ 
+
+ align:start position:0%
+structure NCC
+nccncc this is invariant
+
+ align:start position:0%
+nccncc this is invariant
+ 
+
+ align:start position:0%
+nccncc this is invariant
+what what changes and what defines the
+
+ align:start position:0%
+what what changes and what defines the
+ 
+
+ align:start position:0%
+what what changes and what defines the
+biochemical attributes of this
+
+ align:start position:0%
+biochemical attributes of this
+ 
+
+ align:start position:0%
+biochemical attributes of this
+oligopeptide or a polypeptide are the
+
+ align:start position:0%
+oligopeptide or a polypeptide are the
+ 
+
+ align:start position:0%
+oligopeptide or a polypeptide are the
+identities of these Sky chains which
+
+ align:start position:0%
+identities of these Sky chains which
+ 
+
+ align:start position:0%
+identities of these Sky chains which
+again are are plotted on this particular
+
+ align:start position:0%
+again are are plotted on this particular
+ 
+
+ align:start position:0%
+again are are plotted on this particular
+graph and you have a different version
+
+ align:start position:0%
+graph and you have a different version
+ 
+
+ align:start position:0%
+graph and you have a different version
+in your book off to the right
+
+ align:start position:0%
+in your book off to the right
+ 
+
+ align:start position:0%
+in your book off to the right
+here you see we have a proton a methyl
+
+ align:start position:0%
+here you see we have a proton a methyl
+ 
+
+ align:start position:0%
+here you see we have a proton a methyl
+group a valine
+
+ align:start position:0%
+group a valine
+ 
+
+ align:start position:0%
+group a valine
+a leucine and isoleucine and the
+
+ align:start position:0%
+a leucine and isoleucine and the
+ 
+
+ align:start position:0%
+a leucine and isoleucine and the
+differences between this suggests these
+
+ align:start position:0%
+differences between this suggests these
+ 
+
+ align:start position:0%
+differences between this suggests these
+are all quite
+
+ align:start position:0%
+are all quite
+ 
+
+ align:start position:0%
+are all quite
+aliphatic uh
+
+ align:start position:0%
+aliphatic uh
+ 
+
+ align:start position:0%
+aliphatic uh
+quite similar to the propane and and the
+
+ align:start position:0%
+quite similar to the propane and and the
+ 
+
+ align:start position:0%
+quite similar to the propane and and the
+um that we talked about last time or the
+
+ align:start position:0%
+um that we talked about last time or the
+ 
+
+ align:start position:0%
+um that we talked about last time or the
+hexane that is to say these are quite
+
+ align:start position:0%
+hexane that is to say these are quite
+ 
+
+ align:start position:0%
+hexane that is to say these are quite
+hydrophobic side groups and as such if
+
+ align:start position:0%
+hydrophobic side groups and as such if
+ 
+
+ align:start position:0%
+hydrophobic side groups and as such if
+there were a polypeptide we can imagine
+
+ align:start position:0%
+there were a polypeptide we can imagine
+ 
+
+ align:start position:0%
+there were a polypeptide we can imagine
+and you put the polypeptide in water you
+
+ align:start position:0%
+and you put the polypeptide in water you
+ 
+
+ align:start position:0%
+and you put the polypeptide in water you
+can imagine that these amino acids would
+
+ align:start position:0%
+can imagine that these amino acids would
+ 
+
+ align:start position:0%
+can imagine that these amino acids would
+not like to be directly confronting the
+
+ align:start position:0%
+not like to be directly confronting the
+ 
+
+ align:start position:0%
+not like to be directly confronting the
+water because of the fact that they're
+
+ align:start position:0%
+water because of the fact that they're
+ 
+
+ align:start position:0%
+water because of the fact that they're
+hydrophobic
+
+ align:start position:0%
+hydrophobic
+ 
+
+ align:start position:0%
+hydrophobic
+methionine is also a bit hydrophobic
+
+ align:start position:0%
+methionine is also a bit hydrophobic
+ 
+
+ align:start position:0%
+methionine is also a bit hydrophobic
+it's I I I'm I'm
+
+ align:start position:0%
+it's I I I'm I'm
+ 
+
+ align:start position:0%
+it's I I I'm I'm
+equivocating there because the S has a
+
+ align:start position:0%
+equivocating there because the S has a
+ 
+
+ align:start position:0%
+equivocating there because the S has a
+slight degree of hydrophilicity uh has a
+
+ align:start position:0%
+slight degree of hydrophilicity uh has a
+ 
+
+ align:start position:0%
+slight degree of hydrophilicity uh has a
+slight uh degree of polarity but not
+
+ align:start position:0%
+slight uh degree of polarity but not
+ 
+
+ align:start position:0%
+slight uh degree of polarity but not
+really that much and these aromatic side
+
+ align:start position:0%
+really that much and these aromatic side
+ 
+
+ align:start position:0%
+really that much and these aromatic side
+chains here because they have these
+
+ align:start position:0%
+chains here because they have these
+ 
+
+ align:start position:0%
+chains here because they have these
+Benzene rings and then they're
+
+ align:start position:0%
+Benzene rings and then they're
+ 
+
+ align:start position:0%
+Benzene rings and then they're
+consequently called aromatic these are
+
+ align:start position:0%
+consequently called aromatic these are
+ 
+
+ align:start position:0%
+consequently called aromatic these are
+quite High strongly hydrophobic so they
+
+ align:start position:0%
+quite High strongly hydrophobic so they
+ 
+
+ align:start position:0%
+quite High strongly hydrophobic so they
+really hate to be in the uh in Intimate
+
+ align:start position:0%
+really hate to be in the uh in Intimate
+ 
+
+ align:start position:0%
+really hate to be in the uh in Intimate
+contact with water
+
+ align:start position:0%
+contact with water
+ 
+
+ align:start position:0%
+contact with water
+here on the other hand let's look at
+
+ align:start position:0%
+here on the other hand let's look at
+ 
+
+ align:start position:0%
+here on the other hand let's look at
+these side chains because
+
+ align:start position:0%
+these side chains because
+ 
+
+ align:start position:0%
+these side chains because
+here we have uh strongly uh polar
+
+ align:start position:0%
+here we have uh strongly uh polar
+ 
+
+ align:start position:0%
+here we have uh strongly uh polar
+molecules side chains again keep in mind
+
+ align:start position:0%
+molecules side chains again keep in mind
+ 
+
+ align:start position:0%
+molecules side chains again keep in mind
+we're focusing on the side chains here
+
+ align:start position:0%
+we're focusing on the side chains here
+ 
+
+ align:start position:0%
+we're focusing on the side chains here
+we see searing with a hydroxyl group
+
+ align:start position:0%
+we see searing with a hydroxyl group
+ 
+
+ align:start position:0%
+we see searing with a hydroxyl group
+that can form hydrogen bonds with the
+
+ align:start position:0%
+that can form hydrogen bonds with the
+ 
+
+ align:start position:0%
+that can form hydrogen bonds with the
+water threonine which has its own
+
+ align:start position:0%
+water threonine which has its own
+ 
+
+ align:start position:0%
+water threonine which has its own
+hydroxyl group
+
+ align:start position:0%
+hydroxyl group
+ 
+
+ align:start position:0%
+hydroxyl group
+asparagine which has two atoms here this
+
+ align:start position:0%
+asparagine which has two atoms here this
+ 
+
+ align:start position:0%
+asparagine which has two atoms here this
+carbonyl and the nh2 both of which can
+
+ align:start position:0%
+carbonyl and the nh2 both of which can
+ 
+
+ align:start position:0%
+carbonyl and the nh2 both of which can
+form hydrogen bonds uh to the with the
+
+ align:start position:0%
+form hydrogen bonds uh to the with the
+ 
+
+ align:start position:0%
+form hydrogen bonds uh to the with the
+water as can glutamine
+
+ align:start position:0%
+water as can glutamine
+ 
+
+ align:start position:0%
+water as can glutamine
+so these are quite hydrophilic they're
+
+ align:start position:0%
+so these are quite hydrophilic they're
+ 
+
+ align:start position:0%
+so these are quite hydrophilic they're
+not as
+
+ align:start position:0%
+not as
+ 
+
+ align:start position:0%
+not as
+fanatically hydrophilic as these charge
+
+ align:start position:0%
+fanatically hydrophilic as these charge
+ 
+
+ align:start position:0%
+fanatically hydrophilic as these charge
+molecules where the side chains are not
+
+ align:start position:0%
+molecules where the side chains are not
+ 
+
+ align:start position:0%
+molecules where the side chains are not
+just capable of forming hydrogen bonds
+
+ align:start position:0%
+just capable of forming hydrogen bonds
+ 
+
+ align:start position:0%
+just capable of forming hydrogen bonds
+in this lower group here the side chains
+
+ align:start position:0%
+in this lower group here the side chains
+ 
+
+ align:start position:0%
+in this lower group here the side chains
+are capable of undergoing ionization so
+
+ align:start position:0%
+are capable of undergoing ionization so
+ 
+
+ align:start position:0%
+are capable of undergoing ionization so
+they're actually strongly charged and
+
+ align:start position:0%
+they're actually strongly charged and
+ 
+
+ align:start position:0%
+they're actually strongly charged and
+here we see uh here the carboxyl group
+
+ align:start position:0%
+here we see uh here the carboxyl group
+ 
+
+ align:start position:0%
+here we see uh here the carboxyl group
+and the glue in this group in our
+
+ align:start position:0%
+and the glue in this group in our
+ 
+
+ align:start position:0%
+and the glue in this group in our
+spartic and glutamic acid has actually
+
+ align:start position:0%
+spartic and glutamic acid has actually
+ 
+
+ align:start position:0%
+spartic and glutamic acid has actually
+discharged its proton becoming
+
+ align:start position:0%
+discharged its proton becoming
+ 
+
+ align:start position:0%
+discharged its proton becoming
+negatively charged
+
+ align:start position:0%
+negatively charged
+ 
+
+ align:start position:0%
+negatively charged
+these are acidic amino acids by virtue
+
+ align:start position:0%
+these are acidic amino acids by virtue
+ 
+
+ align:start position:0%
+these are acidic amino acids by virtue
+of the carboxyl groups they have basic
+
+ align:start position:0%
+of the carboxyl groups they have basic
+ 
+
+ align:start position:0%
+of the carboxyl groups they have basic
+amino acids here um arginine lysine and
+
+ align:start position:0%
+amino acids here um arginine lysine and
+ 
+
+ align:start position:0%
+amino acids here um arginine lysine and
+histidine all acquire a positively
+
+ align:start position:0%
+histidine all acquire a positively
+ 
+
+ align:start position:0%
+histidine all acquire a positively
+charged side Chain by virtue of these
+
+ align:start position:0%
+charged side Chain by virtue of these
+ 
+
+ align:start position:0%
+charged side Chain by virtue of these
+nitrogens here which have a strong
+
+ align:start position:0%
+nitrogens here which have a strong
+ 
+
+ align:start position:0%
+nitrogens here which have a strong
+affinity for pulling away protons for
+
+ align:start position:0%
+affinity for pulling away protons for
+ 
+
+ align:start position:0%
+affinity for pulling away protons for
+abstracting protons from the aqueous
+
+ align:start position:0%
+abstracting protons from the aqueous
+ 
+
+ align:start position:0%
+abstracting protons from the aqueous
+solvent
+
+ align:start position:0%
+solvent
+ 
+
+ align:start position:0%
+solvent
+and so we have a whole gradient of
+
+ align:start position:0%
+and so we have a whole gradient of
+ 
+
+ align:start position:0%
+and so we have a whole gradient of
+of hydrophilicity down to
+
+ align:start position:0%
+of hydrophilicity down to
+ 
+
+ align:start position:0%
+of hydrophilicity down to
+hydrophobicity and here we have
+
+ align:start position:0%
+hydrophobicity and here we have
+ 
+
+ align:start position:0%
+hydrophobicity and here we have
+intermediate structures
+
+ align:start position:0%
+intermediate structures
+ 
+
+ align:start position:0%
+intermediate structures
+we also have some very special
+
+ align:start position:0%
+we also have some very special
+ 
+
+ align:start position:0%
+we also have some very special
+idiosyncratic kinds of amino acids here
+
+ align:start position:0%
+idiosyncratic kinds of amino acids here
+ 
+
+ align:start position:0%
+idiosyncratic kinds of amino acids here
+is tyrosine and tyrosine is a little bit
+
+ align:start position:0%
+is tyrosine and tyrosine is a little bit
+ 
+
+ align:start position:0%
+is tyrosine and tyrosine is a little bit
+schizophrenic again it has this highly
+
+ align:start position:0%
+schizophrenic again it has this highly
+ 
+
+ align:start position:0%
+schizophrenic again it has this highly
+hydrophobic aromatic group here the
+
+ align:start position:0%
+hydrophobic aromatic group here the
+ 
+
+ align:start position:0%
+hydrophobic aromatic group here the
+Benzene ring which hates to be in water
+
+ align:start position:0%
+Benzene ring which hates to be in water
+ 
+
+ align:start position:0%
+Benzene ring which hates to be in water
+and the hydroxyl group which actually is
+
+ align:start position:0%
+and the hydroxyl group which actually is
+ 
+
+ align:start position:0%
+and the hydroxyl group which actually is
+a friend of water so here we have
+
+ align:start position:0%
+a friend of water so here we have
+ 
+
+ align:start position:0%
+a friend of water so here we have
+something where its role is is quite
+
+ align:start position:0%
+something where its role is is quite
+ 
+
+ align:start position:0%
+something where its role is is quite
+equivocal
+
+ align:start position:0%
+equivocal
+ 
+
+ align:start position:0%
+equivocal
+here we have cysteine as indicated here
+
+ align:start position:0%
+here we have cysteine as indicated here
+ 
+
+ align:start position:0%
+here we have cysteine as indicated here
+and what's interesting about the
+
+ align:start position:0%
+and what's interesting about the
+ 
+
+ align:start position:0%
+and what's interesting about the
+cysteine group in this case is the sh
+
+ align:start position:0%
+cysteine group in this case is the sh
+ 
+
+ align:start position:0%
+cysteine group in this case is the sh
+group the side chain the sh group
+
+ align:start position:0%
+group the side chain the sh group
+ 
+
+ align:start position:0%
+group the side chain the sh group
+because this sh group is able to form uh
+
+ align:start position:0%
+because this sh group is able to form uh
+ 
+
+ align:start position:0%
+because this sh group is able to form uh
+bonds with yet other sh groups from
+
+ align:start position:0%
+bonds with yet other sh groups from
+ 
+
+ align:start position:0%
+bonds with yet other sh groups from
+other cysteines
+
+ align:start position:0%
+other cysteines
+ 
+
+ align:start position:0%
+other cysteines
+so let's just look at this cysteine here
+
+ align:start position:0%
+so let's just look at this cysteine here
+ 
+
+ align:start position:0%
+so let's just look at this cysteine here
+for a moment you see there's a ch2 and
+
+ align:start position:0%
+for a moment you see there's a ch2 and
+ 
+
+ align:start position:0%
+for a moment you see there's a ch2 and
+then there's an sh so let's imagine I'm
+
+ align:start position:0%
+then there's an sh so let's imagine I'm
+ 
+
+ align:start position:0%
+then there's an sh so let's imagine I'm
+not going to draw all the atoms here but
+
+ align:start position:0%
+not going to draw all the atoms here but
+ 
+
+ align:start position:0%
+not going to draw all the atoms here but
+let's imagine here we have the ch2 group
+
+ align:start position:0%
+let's imagine here we have the ch2 group
+ 
+
+ align:start position:0%
+let's imagine here we have the ch2 group
+I'm not drawing the backbone sh over
+
+ align:start position:0%
+I'm not drawing the backbone sh over
+ 
+
+ align:start position:0%
+I'm not drawing the backbone sh over
+here and we could imagine another
+
+ align:start position:0%
+here and we could imagine another
+ 
+
+ align:start position:0%
+here and we could imagine another
+protein chain another polypeptide chain
+
+ align:start position:0%
+protein chain another polypeptide chain
+ 
+
+ align:start position:0%
+protein chain another polypeptide chain
+down here again I'm not drawing the
+
+ align:start position:0%
+down here again I'm not drawing the
+ 
+
+ align:start position:0%
+down here again I'm not drawing the
+backbone
+
+ align:start position:0%
+backbone
+ 
+
+ align:start position:0%
+backbone
+but I'm drawing another sh like this
+
+ align:start position:0%
+but I'm drawing another sh like this
+ 
+
+ align:start position:0%
+but I'm drawing another sh like this
+and the fact is under the conditions of
+
+ align:start position:0%
+and the fact is under the conditions of
+ 
+
+ align:start position:0%
+and the fact is under the conditions of
+oxidation and reduction that operate in
+
+ align:start position:0%
+oxidation and reduction that operate in
+ 
+
+ align:start position:0%
+oxidation and reduction that operate in
+the at least in the extracellular space
+
+ align:start position:0%
+the at least in the extracellular space
+ 
+
+ align:start position:0%
+the at least in the extracellular space
+one can oxidize this these two resulting
+
+ align:start position:0%
+one can oxidize this these two resulting
+ 
+
+ align:start position:0%
+one can oxidize this these two resulting
+in the formation of what is known as a
+
+ align:start position:0%
+in the formation of what is known as a
+ 
+
+ align:start position:0%
+in the formation of what is known as a
+disulfide bond
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here we have now for the first notion
+
+ align:start position:0%
+so here we have now for the first notion
+ 
+
+ align:start position:0%
+so here we have now for the first notion
+uh idea at the time the notion that
+
+ align:start position:0%
+uh idea at the time the notion that
+ 
+
+ align:start position:0%
+uh idea at the time the notion that
+polypeptide chains can be covalently
+
+ align:start position:0%
+polypeptide chains can be covalently
+ 
+
+ align:start position:0%
+polypeptide chains can be covalently
+linked one another through these
+
+ align:start position:0%
+linked one another through these
+ 
+
+ align:start position:0%
+linked one another through these
+cross-linked crosslinks as indicated
+
+ align:start position:0%
+cross-linked crosslinks as indicated
+ 
+
+ align:start position:0%
+cross-linked crosslinks as indicated
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+conversely if you add a reducing agent
+
+ align:start position:0%
+conversely if you add a reducing agent
+ 
+
+ align:start position:0%
+conversely if you add a reducing agent
+that will add protons back to this and
+
+ align:start position:0%
+that will add protons back to this and
+ 
+
+ align:start position:0%
+that will add protons back to this and
+reduce the oxidation state of the
+
+ align:start position:0%
+reduce the oxidation state of the
+ 
+
+ align:start position:0%
+reduce the oxidation state of the
+sulfurs once again causing the disulfide
+
+ align:start position:0%
+sulfurs once again causing the disulfide
+ 
+
+ align:start position:0%
+sulfurs once again causing the disulfide
+bond to fall apart
+
+ align:start position:0%
+bond to fall apart
+ 
+
+ align:start position:0%
+bond to fall apart
+now in principle these disulfide bonds
+
+ align:start position:0%
+now in principle these disulfide bonds
+ 
+
+ align:start position:0%
+now in principle these disulfide bonds
+could be used to link two proteins
+
+ align:start position:0%
+could be used to link two proteins
+ 
+
+ align:start position:0%
+could be used to link two proteins
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+but more often than not if you look at
+
+ align:start position:0%
+but more often than not if you look at
+ 
+
+ align:start position:0%
+but more often than not if you look at
+the structure of a of a single protein
+
+ align:start position:0%
+the structure of a of a single protein
+ 
+
+ align:start position:0%
+the structure of a of a single protein
+protein here's the structure of a single
+
+ align:start position:0%
+protein here's the structure of a single
+ 
+
+ align:start position:0%
+protein here's the structure of a single
+protein and often there are
+
+ align:start position:0%
+protein and often there are
+ 
+
+ align:start position:0%
+protein and often there are
+intramolecular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bonds disulfide bonds High e bonds from
+
+ align:start position:0%
+bonds disulfide bonds High e bonds from
+ 
+
+ align:start position:0%
+bonds disulfide bonds High e bonds from
+one domain of the protein to another
+
+ align:start position:0%
+one domain of the protein to another
+ 
+
+ align:start position:0%
+one domain of the protein to another
+from one part of the protein to the
+
+ align:start position:0%
+from one part of the protein to the
+ 
+
+ align:start position:0%
+from one part of the protein to the
+other I'll draw them in right here here
+
+ align:start position:0%
+other I'll draw them in right here here
+ 
+
+ align:start position:0%
+other I'll draw them in right here here
+might be a disulfide bond here might be
+
+ align:start position:0%
+might be a disulfide bond here might be
+ 
+
+ align:start position:0%
+might be a disulfide bond here might be
+adult sulfide Bond and I could go on and
+
+ align:start position:0%
+adult sulfide Bond and I could go on and
+ 
+
+ align:start position:0%
+adult sulfide Bond and I could go on and
+on there might be another one over here
+
+ align:start position:0%
+on there might be another one over here
+ 
+
+ align:start position:0%
+on there might be another one over here
+why do we have these disulfide bonds
+
+ align:start position:0%
+why do we have these disulfide bonds
+ 
+
+ align:start position:0%
+why do we have these disulfide bonds
+because as we'll indicate very shortly
+
+ align:start position:0%
+because as we'll indicate very shortly
+ 
+
+ align:start position:0%
+because as we'll indicate very shortly
+the three-dimensional structure of a
+
+ align:start position:0%
+the three-dimensional structure of a
+ 
+
+ align:start position:0%
+the three-dimensional structure of a
+protein is very specifically determined
+
+ align:start position:0%
+protein is very specifically determined
+ 
+
+ align:start position:0%
+protein is very specifically determined
+a protein can only function when it
+
+ align:start position:0%
+a protein can only function when it
+ 
+
+ align:start position:0%
+a protein can only function when it
+assumes a certain three-dimensional
+
+ align:start position:0%
+assumes a certain three-dimensional
+ 
+
+ align:start position:0%
+assumes a certain three-dimensional
+configuration when it assumes assumes a
+
+ align:start position:0%
+configuration when it assumes assumes a
+ 
+
+ align:start position:0%
+configuration when it assumes assumes a
+certain three-dimensional uh
+
+ align:start position:0%
+certain three-dimensional uh
+ 
+
+ align:start position:0%
+certain three-dimensional uh
+stereochemical
+
+ align:start position:0%
+stereochemical
+ 
+
+ align:start position:0%
+stereochemical
+configuration
+
+ align:start position:0%
+configuration
+ 
+
+ align:start position:0%
+configuration
+when we talk about stereochemistry we're
+
+ align:start position:0%
+when we talk about stereochemistry we're
+ 
+
+ align:start position:0%
+when we talk about stereochemistry we're
+talking about the three-dimensional
+
+ align:start position:0%
+talking about the three-dimensional
+ 
+
+ align:start position:0%
+talking about the three-dimensional
+structures of molecules small and large
+
+ align:start position:0%
+structures of molecules small and large
+ 
+
+ align:start position:0%
+structures of molecules small and large
+and here we begin to touch on a theme of
+
+ align:start position:0%
+and here we begin to touch on a theme of
+ 
+
+ align:start position:0%
+and here we begin to touch on a theme of
+how these complex polypeptide chains are
+
+ align:start position:0%
+how these complex polypeptide chains are
+ 
+
+ align:start position:0%
+how these complex polypeptide chains are
+able to create proteins that have very
+
+ align:start position:0%
+able to create proteins that have very
+ 
+
+ align:start position:0%
+able to create proteins that have very
+specific often very rigid structures in
+
+ align:start position:0%
+specific often very rigid structures in
+ 
+
+ align:start position:0%
+specific often very rigid structures in
+three-dimensional space
+
+ align:start position:0%
+three-dimensional space
+ 
+
+ align:start position:0%
+three-dimensional space
+part of this structural rigidity is
+
+ align:start position:0%
+part of this structural rigidity is
+ 
+
+ align:start position:0%
+part of this structural rigidity is
+maintained by these covalent
+
+ align:start position:0%
+maintained by these covalent
+ 
+
+ align:start position:0%
+maintained by these covalent
+disulfide bonds which link tightly link
+
+ align:start position:0%
+disulfide bonds which link tightly link
+ 
+
+ align:start position:0%
+disulfide bonds which link tightly link
+neighboring regions or even not so
+
+ align:start position:0%
+neighboring regions or even not so
+ 
+
+ align:start position:0%
+neighboring regions or even not so
+neighboring regions of a single
+
+ align:start position:0%
+neighboring regions of a single
+ 
+
+ align:start position:0%
+neighboring regions of a single
+polypeptide chain these intramolecular
+
+ align:start position:0%
+polypeptide chain these intramolecular
+ 
+
+ align:start position:0%
+polypeptide chain these intramolecular
+links this doesn't preclude they're
+
+ align:start position:0%
+links this doesn't preclude they're
+ 
+
+ align:start position:0%
+links this doesn't preclude they're
+being intermolecular links between two
+
+ align:start position:0%
+being intermolecular links between two
+ 
+
+ align:start position:0%
+being intermolecular links between two
+polypeptide chains that are mediated as
+
+ align:start position:0%
+polypeptide chains that are mediated as
+ 
+
+ align:start position:0%
+polypeptide chains that are mediated as
+well by the disulfide bonds here's
+
+ align:start position:0%
+well by the disulfide bonds here's
+ 
+
+ align:start position:0%
+well by the disulfide bonds here's
+another very peculiar amino acid
+
+ align:start position:0%
+another very peculiar amino acid
+ 
+
+ align:start position:0%
+another very peculiar amino acid
+because what you see here is that the
+
+ align:start position:0%
+because what you see here is that the
+ 
+
+ align:start position:0%
+because what you see here is that the
+side chain which is ch2 ch2ch2 is
+
+ align:start position:0%
+side chain which is ch2 ch2ch2 is
+ 
+
+ align:start position:0%
+side chain which is ch2 ch2ch2 is
+hydrogen bonded here to the amine group
+
+ align:start position:0%
+hydrogen bonded here to the amine group
+ 
+
+ align:start position:0%
+hydrogen bonded here to the amine group
+it's not swinging out in free space it's
+
+ align:start position:0%
+it's not swinging out in free space it's
+ 
+
+ align:start position:0%
+it's not swinging out in free space it's
+I'm
+
+ align:start position:0%
+I'm
+ 
+
+ align:start position:0%
+I'm
+I misspoke
+
+ align:start position:0%
+I misspoke
+ 
+
+ align:start position:0%
+I misspoke
+what we see here is ch2ch2a is
+
+ align:start position:0%
+what we see here is ch2ch2a is
+ 
+
+ align:start position:0%
+what we see here is ch2ch2a is
+covalently bonded to the amine group you
+
+ align:start position:0%
+covalently bonded to the amine group you
+ 
+
+ align:start position:0%
+covalently bonded to the amine group you
+pick that up right
+
+ align:start position:0%
+pick that up right
+ 
+
+ align:start position:0%
+pick that up right
+I was just testing you sure I was okay
+
+ align:start position:0%
+I was just testing you sure I was okay
+ 
+
+ align:start position:0%
+I was just testing you sure I was okay
+so here we see a five-membered ring
+
+ align:start position:0%
+so here we see a five-membered ring
+ 
+
+ align:start position:0%
+so here we see a five-membered ring
+that's created
+
+ align:start position:0%
+that's created
+ 
+
+ align:start position:0%
+that's created
+so here this thing is not free swing out
+
+ align:start position:0%
+so here this thing is not free swing out
+ 
+
+ align:start position:0%
+so here this thing is not free swing out
+in free space it creates a five-membered
+
+ align:start position:0%
+in free space it creates a five-membered
+ 
+
+ align:start position:0%
+in free space it creates a five-membered
+ring coat where the end of the side
+
+ align:start position:0%
+ring coat where the end of the side
+ 
+
+ align:start position:0%
+ring coat where the end of the side
+chain is actually covalently linked to
+
+ align:start position:0%
+chain is actually covalently linked to
+ 
+
+ align:start position:0%
+chain is actually covalently linked to
+the amino group and that also has
+
+ align:start position:0%
+the amino group and that also has
+ 
+
+ align:start position:0%
+the amino group and that also has
+implications for the structure of
+
+ align:start position:0%
+implications for the structure of
+ 
+
+ align:start position:0%
+implications for the structure of
+proteins because this particular amino
+
+ align:start position:0%
+proteins because this particular amino
+ 
+
+ align:start position:0%
+proteins because this particular amino
+acid whenever it occurs within a
+
+ align:start position:0%
+acid whenever it occurs within a
+ 
+
+ align:start position:0%
+acid whenever it occurs within a
+polypeptide chain doesn't have the
+
+ align:start position:0%
+polypeptide chain doesn't have the
+ 
+
+ align:start position:0%
+polypeptide chain doesn't have the
+flexibility of assuming certain
+
+ align:start position:0%
+flexibility of assuming certain
+ 
+
+ align:start position:0%
+flexibility of assuming certain
+configurations that the other ones have
+
+ align:start position:0%
+configurations that the other ones have
+ 
+
+ align:start position:0%
+configurations that the other ones have
+who's whose four side chains are not so
+
+ align:start position:0%
+who's whose four side chains are not so
+ 
+
+ align:start position:0%
+who's whose four side chains are not so
+encumbered
+
+ align:start position:0%
+encumbered
+ 
+
+ align:start position:0%
+encumbered
+none of them has total flexibility but
+
+ align:start position:0%
+none of them has total flexibility but
+ 
+
+ align:start position:0%
+none of them has total flexibility but
+this one is far more encumbered in the
+
+ align:start position:0%
+this one is far more encumbered in the
+ 
+
+ align:start position:0%
+this one is far more encumbered in the
+in the kinds of three-dimensional
+
+ align:start position:0%
+in the kinds of three-dimensional
+ 
+
+ align:start position:0%
+in the kinds of three-dimensional
+structures that it can assume
+
+ align:start position:0%
+structures that it can assume
+ 
+
+ align:start position:0%
+structures that it can assume
+and um with that in mind we begin to ask
+
+ align:start position:0%
+and um with that in mind we begin to ask
+ 
+
+ align:start position:0%
+and um with that in mind we begin to ask
+questions about how uh polypeptide
+
+ align:start position:0%
+questions about how uh polypeptide
+ 
+
+ align:start position:0%
+questions about how uh polypeptide
+chains assume three-dimensional
+
+ align:start position:0%
+chains assume three-dimensional
+ 
+
+ align:start position:0%
+chains assume three-dimensional
+structure uh if we talk about a
+
+ align:start position:0%
+structure uh if we talk about a
+ 
+
+ align:start position:0%
+structure uh if we talk about a
+polypeptide chain
+
+ align:start position:0%
+polypeptide chain
+ 
+
+ align:start position:0%
+polypeptide chain
+in our minds
+
+ align:start position:0%
+in our minds
+ 
+
+ align:start position:0%
+in our minds
+hopefully
+
+ align:start position:0%
+hopefully
+ 
+
+ align:start position:0%
+hopefully
+there's only 28 combinations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+oh am I good or what okay anyhow
+
+ align:start position:0%
+oh am I good or what okay anyhow
+ 
+
+ align:start position:0%
+oh am I good or what okay anyhow
+all right so look here and here you see
+
+ align:start position:0%
+all right so look here and here you see
+ 
+
+ align:start position:0%
+all right so look here and here you see
+this is a typical polypeptide chain
+
+ align:start position:0%
+this is a typical polypeptide chain
+ 
+
+ align:start position:0%
+this is a typical polypeptide chain
+here we have a three a three letter code
+
+ align:start position:0%
+here we have a three a three letter code
+ 
+
+ align:start position:0%
+here we have a three a three letter code
+in truth there's a there's a single
+
+ align:start position:0%
+in truth there's a there's a single
+ 
+
+ align:start position:0%
+in truth there's a there's a single
+letter code which was introduced around
+
+ align:start position:0%
+letter code which was introduced around
+ 
+
+ align:start position:0%
+letter code which was introduced around
+1965 so each each of the 20 amino acids
+
+ align:start position:0%
+1965 so each each of the 20 amino acids
+ 
+
+ align:start position:0%
+1965 so each each of the 20 amino acids
+has its own single letter code
+
+ align:start position:0%
+has its own single letter code
+ 
+
+ align:start position:0%
+has its own single letter code
+and to make a Frank
+
+ align:start position:0%
+and to make a Frank
+ 
+
+ align:start position:0%
+and to make a Frank
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+depressing admission
+
+ align:start position:0%
+depressing admission
+ 
+
+ align:start position:0%
+depressing admission
+35 years 40 years after the single amino
+
+ align:start position:0%
+35 years 40 years after the single amino
+ 
+
+ align:start position:0%
+35 years 40 years after the single amino
+acid letter code was instituted I still
+
+ align:start position:0%
+acid letter code was instituted I still
+ 
+
+ align:start position:0%
+acid letter code was instituted I still
+haven't learned it
+
+ align:start position:0%
+haven't learned it
+ 
+
+ align:start position:0%
+haven't learned it
+but we can learn these three letter
+
+ align:start position:0%
+but we can learn these three letter
+ 
+
+ align:start position:0%
+but we can learn these three letter
+codes which fortunately are present here
+
+ align:start position:0%
+codes which fortunately are present here
+ 
+
+ align:start position:0%
+codes which fortunately are present here
+where in the single letter code L is
+
+ align:start position:0%
+where in the single letter code L is
+ 
+
+ align:start position:0%
+where in the single letter code L is
+leucine and uh a is art a is alanine see
+
+ align:start position:0%
+leucine and uh a is art a is alanine see
+ 
+
+ align:start position:0%
+leucine and uh a is art a is alanine see
+they know it
+
+ align:start position:0%
+they know it
+ 
+
+ align:start position:0%
+they know it
+this is another example of not being
+
+ align:start position:0%
+this is another example of not being
+ 
+
+ align:start position:0%
+this is another example of not being
+able to teach Old Dogs new tricks anyhow
+
+ align:start position:0%
+able to teach Old Dogs new tricks anyhow
+ 
+
+ align:start position:0%
+able to teach Old Dogs new tricks anyhow
+so here we see uh the way One Way by
+
+ align:start position:0%
+so here we see uh the way One Way by
+ 
+
+ align:start position:0%
+so here we see uh the way One Way by
+which one might depict enemies or amino
+
+ align:start position:0%
+which one might depict enemies or amino
+ 
+
+ align:start position:0%
+which one might depict enemies or amino
+acid and keeping amino acid chain a
+
+ align:start position:0%
+acid and keeping amino acid chain a
+ 
+
+ align:start position:0%
+acid and keeping amino acid chain a
+polypeptide chain and keep in mind this
+
+ align:start position:0%
+polypeptide chain and keep in mind this
+ 
+
+ align:start position:0%
+polypeptide chain and keep in mind this
+can go on indefinitely
+
+ align:start position:0%
+can go on indefinitely
+ 
+
+ align:start position:0%
+can go on indefinitely
+as we begin to wrestle with the
+
+ align:start position:0%
+as we begin to wrestle with the
+ 
+
+ align:start position:0%
+as we begin to wrestle with the
+three-dimensional structure of the chain
+
+ align:start position:0%
+three-dimensional structure of the chain
+ 
+
+ align:start position:0%
+three-dimensional structure of the chain
+we begin to realize the following and
+
+ align:start position:0%
+we begin to realize the following and
+ 
+
+ align:start position:0%
+we begin to realize the following and
+that is that after the chain is
+
+ align:start position:0%
+that is that after the chain is
+ 
+
+ align:start position:0%
+that is that after the chain is
+initially synthesized it's initially
+
+ align:start position:0%
+initially synthesized it's initially
+ 
+
+ align:start position:0%
+initially synthesized it's initially
+chaotic and as it extends it
+
+ align:start position:0%
+chaotic and as it extends it
+ 
+
+ align:start position:0%
+chaotic and as it extends it
+increasingly begins to assume a very
+
+ align:start position:0%
+increasingly begins to assume a very
+ 
+
+ align:start position:0%
+increasingly begins to assume a very
+specific
+
+ align:start position:0%
+specific
+ 
+
+ align:start position:0%
+specific
+uh molecular three-dimensional molecular
+
+ align:start position:0%
+uh molecular three-dimensional molecular
+ 
+
+ align:start position:0%
+uh molecular three-dimensional molecular
+configuration which is indicated down
+
+ align:start position:0%
+configuration which is indicated down
+ 
+
+ align:start position:0%
+configuration which is indicated down
+here so the chaos that operates uh
+
+ align:start position:0%
+here so the chaos that operates uh
+ 
+
+ align:start position:0%
+here so the chaos that operates uh
+initially will eventually result in a a
+
+ align:start position:0%
+initially will eventually result in a a
+ 
+
+ align:start position:0%
+initially will eventually result in a a
+native configuration over here which in
+
+ align:start position:0%
+native configuration over here which in
+ 
+
+ align:start position:0%
+native configuration over here which in
+many respects often represents the
+
+ align:start position:0%
+many respects often represents the
+ 
+
+ align:start position:0%
+many respects often represents the
+lowest free energy state
+
+ align:start position:0%
+lowest free energy state
+ 
+
+ align:start position:0%
+lowest free energy state
+since for the last 40 years people have
+
+ align:start position:0%
+since for the last 40 years people have
+ 
+
+ align:start position:0%
+since for the last 40 years people have
+been able to have been trying to figure
+
+ align:start position:0%
+been able to have been trying to figure
+ 
+
+ align:start position:0%
+been able to have been trying to figure
+out if you knew the amino acid sequence
+
+ align:start position:0%
+out if you knew the amino acid sequence
+ 
+
+ align:start position:0%
+out if you knew the amino acid sequence
+of this primary polypeptide here if you
+
+ align:start position:0%
+of this primary polypeptide here if you
+ 
+
+ align:start position:0%
+of this primary polypeptide here if you
+knew its primary structure and when I
+
+ align:start position:0%
+knew its primary structure and when I
+ 
+
+ align:start position:0%
+knew its primary structure and when I
+say primary structure what I mean is the
+
+ align:start position:0%
+say primary structure what I mean is the
+ 
+
+ align:start position:0%
+say primary structure what I mean is the
+sequence of the amino acids so if you
+
+ align:start position:0%
+sequence of the amino acids so if you
+ 
+
+ align:start position:0%
+sequence of the amino acids so if you
+knew the primary structure of the amino
+
+ align:start position:0%
+knew the primary structure of the amino
+ 
+
+ align:start position:0%
+knew the primary structure of the amino
+acids you should in principle be able to
+
+ align:start position:0%
+acids you should in principle be able to
+ 
+
+ align:start position:0%
+acids you should in principle be able to
+develop a computer algorithm that would
+
+ align:start position:0%
+develop a computer algorithm that would
+ 
+
+ align:start position:0%
+develop a computer algorithm that would
+predict the three-dimensional
+
+ align:start position:0%
+predict the three-dimensional
+ 
+
+ align:start position:0%
+predict the three-dimensional
+configuration which is shown here in a
+
+ align:start position:0%
+configuration which is shown here in a
+ 
+
+ align:start position:0%
+configuration which is shown here in a
+very schematic way and which we'll
+
+ align:start position:0%
+very schematic way and which we'll
+ 
+
+ align:start position:0%
+very schematic way and which we'll
+discuss in much greater detail shortly
+
+ align:start position:0%
+discuss in much greater detail shortly
+ 
+
+ align:start position:0%
+discuss in much greater detail shortly
+and the fact is after 40 Years of trying
+
+ align:start position:0%
+and the fact is after 40 Years of trying
+ 
+
+ align:start position:0%
+and the fact is after 40 Years of trying
+one still is unable to do that I.E if I
+
+ align:start position:0%
+one still is unable to do that I.E if I
+ 
+
+ align:start position:0%
+one still is unable to do that I.E if I
+were to give the three the primary amino
+
+ align:start position:0%
+were to give the three the primary amino
+ 
+
+ align:start position:0%
+were to give the three the primary amino
+acid sequence of a polypeptide to the
+
+ align:start position:0%
+acid sequence of a polypeptide to the
+ 
+
+ align:start position:0%
+acid sequence of a polypeptide to the
+smartest biochemist in the world and
+
+ align:start position:0%
+smartest biochemist in the world and
+ 
+
+ align:start position:0%
+smartest biochemist in the world and
+there are some very smart ones he or she
+
+ align:start position:0%
+there are some very smart ones he or she
+ 
+
+ align:start position:0%
+there are some very smart ones he or she
+could still not tell me what the
+
+ align:start position:0%
+could still not tell me what the
+ 
+
+ align:start position:0%
+could still not tell me what the
+three-dimensional structure of this
+
+ align:start position:0%
+three-dimensional structure of this
+ 
+
+ align:start position:0%
+three-dimensional structure of this
+protein with uh total certainly would be
+
+ align:start position:0%
+protein with uh total certainly would be
+ 
+
+ align:start position:0%
+protein with uh total certainly would be
+uh why because there's an almost
+
+ align:start position:0%
+uh why because there's an almost
+ 
+
+ align:start position:0%
+uh why because there's an almost
+infinite number of intramolecular
+
+ align:start position:0%
+infinite number of intramolecular
+ 
+
+ align:start position:0%
+infinite number of intramolecular
+interactions that greatly complicate
+
+ align:start position:0%
+interactions that greatly complicate
+ 
+
+ align:start position:0%
+interactions that greatly complicate
+how the protein assumes this structure
+
+ align:start position:0%
+how the protein assumes this structure
+ 
+
+ align:start position:0%
+how the protein assumes this structure
+moreover if we talk at this as the
+
+ align:start position:0%
+moreover if we talk at this as the
+ 
+
+ align:start position:0%
+moreover if we talk at this as the
+native state of the protein we can
+
+ align:start position:0%
+native state of the protein we can
+ 
+
+ align:start position:0%
+native state of the protein we can
+imagine that there's ways of disrupting
+
+ align:start position:0%
+imagine that there's ways of disrupting
+ 
+
+ align:start position:0%
+imagine that there's ways of disrupting
+that because much of this native state
+
+ align:start position:0%
+that because much of this native state
+ 
+
+ align:start position:0%
+that because much of this native state
+is created by intramolecular hydrogen
+
+ align:start position:0%
+is created by intramolecular hydrogen
+ 
+
+ align:start position:0%
+is created by intramolecular hydrogen
+bonds remember the hydrogen bonds are
+
+ align:start position:0%
+bonds remember the hydrogen bonds are
+ 
+
+ align:start position:0%
+bonds remember the hydrogen bonds are
+relatively weak and if we heat up the um
+
+ align:start position:0%
+relatively weak and if we heat up the um
+ 
+
+ align:start position:0%
+relatively weak and if we heat up the um
+the the temperature then we can break
+
+ align:start position:0%
+the the temperature then we can break
+ 
+
+ align:start position:0%
+the the temperature then we can break
+hydrogen bonds and therefore every time
+
+ align:start position:0%
+hydrogen bonds and therefore every time
+ 
+
+ align:start position:0%
+hydrogen bonds and therefore every time
+we uh we fry an egg for example if we
+
+ align:start position:0%
+we uh we fry an egg for example if we
+ 
+
+ align:start position:0%
+we uh we fry an egg for example if we
+want to get down to earth we denature we
+
+ align:start position:0%
+want to get down to earth we denature we
+ 
+
+ align:start position:0%
+want to get down to earth we denature we
+break up the three-dimensional the
+
+ align:start position:0%
+break up the three-dimensional the
+ 
+
+ align:start position:0%
+break up the three-dimensional the
+native three-dimensional structure of
+
+ align:start position:0%
+native three-dimensional structure of
+ 
+
+ align:start position:0%
+native three-dimensional structure of
+the albumin molecules that constitute
+
+ align:start position:0%
+the albumin molecules that constitute
+ 
+
+ align:start position:0%
+the albumin molecules that constitute
+the egg white and so when everything
+
+ align:start position:0%
+the egg white and so when everything
+ 
+
+ align:start position:0%
+the egg white and so when everything
+turns white what we've done is to take a
+
+ align:start position:0%
+turns white what we've done is to take a
+ 
+
+ align:start position:0%
+turns white what we've done is to take a
+native molecule like this
+
+ align:start position:0%
+native molecule like this
+ 
+
+ align:start position:0%
+native molecule like this
+heated it up to temperatures where the
+
+ align:start position:0%
+heated it up to temperatures where the
+ 
+
+ align:start position:0%
+heated it up to temperatures where the
+intramolecular bonds no longer stabilize
+
+ align:start position:0%
+intramolecular bonds no longer stabilize
+ 
+
+ align:start position:0%
+intramolecular bonds no longer stabilize
+notably hydrogen bonds no longer
+
+ align:start position:0%
+notably hydrogen bonds no longer
+ 
+
+ align:start position:0%
+notably hydrogen bonds no longer
+stabilize this three-dimensional
+
+ align:start position:0%
+stabilize this three-dimensional
+ 
+
+ align:start position:0%
+stabilize this three-dimensional
+configuration and we put it into a
+
+ align:start position:0%
+configuration and we put it into a
+ 
+
+ align:start position:0%
+configuration and we put it into a
+denatured state which might be all the
+
+ align:start position:0%
+denatured state which might be all the
+ 
+
+ align:start position:0%
+denatured state which might be all the
+way up here
+
+ align:start position:0%
+way up here
+ 
+
+ align:start position:0%
+way up here
+and therefore it this acquisition of a
+
+ align:start position:0%
+and therefore it this acquisition of a
+ 
+
+ align:start position:0%
+and therefore it this acquisition of a
+native configuration or a native state
+
+ align:start position:0%
+native configuration or a native state
+ 
+
+ align:start position:0%
+native configuration or a native state
+native representing the natural state
+
+ align:start position:0%
+native representing the natural state
+ 
+
+ align:start position:0%
+native representing the natural state
+is also reversible in many molecules
+
+ align:start position:0%
+is also reversible in many molecules
+ 
+
+ align:start position:0%
+is also reversible in many molecules
+simply by heating them up there are to
+
+ align:start position:0%
+simply by heating them up there are to
+ 
+
+ align:start position:0%
+simply by heating them up there are to
+be sure yet other molecules which are
+
+ align:start position:0%
+be sure yet other molecules which are
+ 
+
+ align:start position:0%
+be sure yet other molecules which are
+different from egg white from the
+
+ align:start position:0%
+different from egg white from the
+ 
+
+ align:start position:0%
+different from egg white from the
+albumin in egg white where if you cool
+
+ align:start position:0%
+albumin in egg white where if you cool
+ 
+
+ align:start position:0%
+albumin in egg white where if you cool
+them back down they'll spontaneously
+
+ align:start position:0%
+them back down they'll spontaneously
+ 
+
+ align:start position:0%
+them back down they'll spontaneously
+reassume their native structure many
+
+ align:start position:0%
+reassume their native structure many
+ 
+
+ align:start position:0%
+reassume their native structure many
+proteins most will not do so
+
+ align:start position:0%
+proteins most will not do so
+ 
+
+ align:start position:0%
+proteins most will not do so
+well how again let's go back to this
+
+ align:start position:0%
+well how again let's go back to this
+ 
+
+ align:start position:0%
+well how again let's go back to this
+issue of the acquisition of complex
+
+ align:start position:0%
+issue of the acquisition of complex
+ 
+
+ align:start position:0%
+issue of the acquisition of complex
+three-dimensional structure and here we
+
+ align:start position:0%
+three-dimensional structure and here we
+ 
+
+ align:start position:0%
+three-dimensional structure and here we
+begin to see how some of this
+
+ align:start position:0%
+begin to see how some of this
+ 
+
+ align:start position:0%
+begin to see how some of this
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+structure is acquired and stabilized
+
+ align:start position:0%
+structure is acquired and stabilized
+ 
+
+ align:start position:0%
+structure is acquired and stabilized
+through these intramolecular hydrogen
+
+ align:start position:0%
+through these intramolecular hydrogen
+ 
+
+ align:start position:0%
+through these intramolecular hydrogen
+bonds and there are many opportunities
+
+ align:start position:0%
+bonds and there are many opportunities
+ 
+
+ align:start position:0%
+bonds and there are many opportunities
+for these intramolecular hydrogen bonds
+
+ align:start position:0%
+for these intramolecular hydrogen bonds
+ 
+
+ align:start position:0%
+for these intramolecular hydrogen bonds
+because here we see one polypeptide
+
+ align:start position:0%
+because here we see one polypeptide
+ 
+
+ align:start position:0%
+because here we see one polypeptide
+chain here we see another
+
+ align:start position:0%
+chain here we see another
+ 
+
+ align:start position:0%
+chain here we see another
+and we see that the nh2 group right here
+
+ align:start position:0%
+and we see that the nh2 group right here
+ 
+
+ align:start position:0%
+and we see that the nh2 group right here
+I'm sorry the the nitrogen group here
+
+ align:start position:0%
+I'm sorry the the nitrogen group here
+ 
+
+ align:start position:0%
+I'm sorry the the nitrogen group here
+with with the proton side chain
+
+ align:start position:0%
+with with the proton side chain
+ 
+
+ align:start position:0%
+with with the proton side chain
+and the carbonyl group here with the
+
+ align:start position:0%
+and the carbonyl group here with the
+ 
+
+ align:start position:0%
+and the carbonyl group here with the
+oxygen are not encumbered they are in
+
+ align:start position:0%
+oxygen are not encumbered they are in
+ 
+
+ align:start position:0%
+oxygen are not encumbered they are in
+principle available to form hydrogen
+
+ align:start position:0%
+principle available to form hydrogen
+ 
+
+ align:start position:0%
+principle available to form hydrogen
+bonds with a polypeptide chain somewhere
+
+ align:start position:0%
+bonds with a polypeptide chain somewhere
+ 
+
+ align:start position:0%
+bonds with a polypeptide chain somewhere
+else now this other polypeptide chain
+
+ align:start position:0%
+else now this other polypeptide chain
+ 
+
+ align:start position:0%
+else now this other polypeptide chain
+could once again be from another protein
+
+ align:start position:0%
+could once again be from another protein
+ 
+
+ align:start position:0%
+could once again be from another protein
+from another polypeptide
+
+ align:start position:0%
+from another polypeptide
+ 
+
+ align:start position:0%
+from another polypeptide
+but more often than not we're once again
+
+ align:start position:0%
+but more often than not we're once again
+ 
+
+ align:start position:0%
+but more often than not we're once again
+dealing with intramolecular
+
+ align:start position:0%
+dealing with intramolecular
+ 
+
+ align:start position:0%
+dealing with intramolecular
+crosslinks but in this case the
+
+ align:start position:0%
+crosslinks but in this case the
+ 
+
+ align:start position:0%
+crosslinks but in this case the
+intramolecular crosslinks are not
+
+ align:start position:0%
+intramolecular crosslinks are not
+ 
+
+ align:start position:0%
+intramolecular crosslinks are not
+disulfide Bonds which are covalent and
+
+ align:start position:0%
+disulfide Bonds which are covalent and
+ 
+
+ align:start position:0%
+disulfide Bonds which are covalent and
+hard as stable as a rock in the absence
+
+ align:start position:0%
+hard as stable as a rock in the absence
+ 
+
+ align:start position:0%
+hard as stable as a rock in the absence
+of reducing agents here we're talking
+
+ align:start position:0%
+of reducing agents here we're talking
+ 
+
+ align:start position:0%
+of reducing agents here we're talking
+about much weaker bonds hydrogen bonds
+
+ align:start position:0%
+about much weaker bonds hydrogen bonds
+ 
+
+ align:start position:0%
+about much weaker bonds hydrogen bonds
+which also act between
+
+ align:start position:0%
+which also act between
+ 
+
+ align:start position:0%
+which also act between
+different Loops of the protein and serve
+
+ align:start position:0%
+different Loops of the protein and serve
+ 
+
+ align:start position:0%
+different Loops of the protein and serve
+once again to stabilize the
+
+ align:start position:0%
+once again to stabilize the
+ 
+
+ align:start position:0%
+once again to stabilize the
+three-dimensional structure of the
+
+ align:start position:0%
+three-dimensional structure of the
+ 
+
+ align:start position:0%
+three-dimensional structure of the
+native state of the protein
+
+ align:start position:0%
+native state of the protein
+ 
+
+ align:start position:0%
+native state of the protein
+and you can see how these these
+
+ align:start position:0%
+and you can see how these these
+ 
+
+ align:start position:0%
+and you can see how these these
+opportunities for forming multiple
+
+ align:start position:0%
+opportunities for forming multiple
+ 
+
+ align:start position:0%
+opportunities for forming multiple
+hydrogen bonds can create an enormous
+
+ align:start position:0%
+hydrogen bonds can create an enormous
+ 
+
+ align:start position:0%
+hydrogen bonds can create an enormous
+degree of stability
+
+ align:start position:0%
+degree of stability
+ 
+
+ align:start position:0%
+degree of stability
+and here are some examples of what we
+
+ align:start position:0%
+and here are some examples of what we
+ 
+
+ align:start position:0%
+and here are some examples of what we
+now call the secondary structure of the
+
+ align:start position:0%
+now call the secondary structure of the
+ 
+
+ align:start position:0%
+now call the secondary structure of the
+protein
+
+ align:start position:0%
+protein
+ 
+
+ align:start position:0%
+protein
+just a second ago or several minutes ago
+
+ align:start position:0%
+just a second ago or several minutes ago
+ 
+
+ align:start position:0%
+just a second ago or several minutes ago
+to be honest and I'm always honest with
+
+ align:start position:0%
+to be honest and I'm always honest with
+ 
+
+ align:start position:0%
+to be honest and I'm always honest with
+you class
+
+ align:start position:0%
+you class
+ 
+
+ align:start position:0%
+you class
+the primary structure is the amino acid
+
+ align:start position:0%
+the primary structure is the amino acid
+ 
+
+ align:start position:0%
+the primary structure is the amino acid
+sequence the secondary structure
+
+ align:start position:0%
+sequence the secondary structure
+ 
+
+ align:start position:0%
+sequence the secondary structure
+represents configurations like this here
+
+ align:start position:0%
+represents configurations like this here
+ 
+
+ align:start position:0%
+represents configurations like this here
+is an alpha helix
+
+ align:start position:0%
+is an alpha helix
+ 
+
+ align:start position:0%
+is an alpha helix
+here is a beta pleated sheet and what we
+
+ align:start position:0%
+here is a beta pleated sheet and what we
+ 
+
+ align:start position:0%
+here is a beta pleated sheet and what we
+see here in this Alpha Helix is we have
+
+ align:start position:0%
+see here in this Alpha Helix is we have
+ 
+
+ align:start position:0%
+see here in this Alpha Helix is we have
+a helical structure where the amine
+
+ align:start position:0%
+a helical structure where the amine
+ 
+
+ align:start position:0%
+a helical structure where the amine
+group down here the NH hydrogen bonds
+
+ align:start position:0%
+group down here the NH hydrogen bonds
+ 
+
+ align:start position:0%
+group down here the NH hydrogen bonds
+with a residue which is I think three
+
+ align:start position:0%
+with a residue which is I think three
+ 
+
+ align:start position:0%
+with a residue which is I think three
+and a half residues Upstream one two
+
+ align:start position:0%
+and a half residues Upstream one two
+ 
+
+ align:start position:0%
+and a half residues Upstream one two
+there's an amine down there so with a
+
+ align:start position:0%
+there's an amine down there so with a
+ 
+
+ align:start position:0%
+there's an amine down there so with a
+carbonyl group that's three and a half
+
+ align:start position:0%
+carbonyl group that's three and a half
+ 
+
+ align:start position:0%
+carbonyl group that's three and a half
+residues uh Upstream of it this one once
+
+ align:start position:0%
+residues uh Upstream of it this one once
+ 
+
+ align:start position:0%
+residues uh Upstream of it this one once
+again reaches three and a half uh
+
+ align:start position:0%
+again reaches three and a half uh
+ 
+
+ align:start position:0%
+again reaches three and a half uh
+residues Upstream not all the hydrogen
+
+ align:start position:0%
+residues Upstream not all the hydrogen
+ 
+
+ align:start position:0%
+residues Upstream not all the hydrogen
+bonds are shown in the background only
+
+ align:start position:0%
+bonds are shown in the background only
+ 
+
+ align:start position:0%
+bonds are shown in the background only
+the ones on on our side of the Helix are
+
+ align:start position:0%
+the ones on on our side of the Helix are
+ 
+
+ align:start position:0%
+the ones on on our side of the Helix are
+shown on the front side of the Helix but
+
+ align:start position:0%
+shown on the front side of the Helix but
+ 
+
+ align:start position:0%
+shown on the front side of the Helix but
+you can imagine that this can perpetuate
+
+ align:start position:0%
+you can imagine that this can perpetuate
+ 
+
+ align:start position:0%
+you can imagine that this can perpetuate
+itself and each of these carbonyls May
+
+ align:start position:0%
+itself and each of these carbonyls May
+ 
+
+ align:start position:0%
+itself and each of these carbonyls May
+associate with a proton
+
+ align:start position:0%
+associate with a proton
+ 
+
+ align:start position:0%
+associate with a proton
+from an NH group that's either above or
+
+ align:start position:0%
+from an NH group that's either above or
+ 
+
+ align:start position:0%
+from an NH group that's either above or
+below that particular residue and this
+
+ align:start position:0%
+below that particular residue and this
+ 
+
+ align:start position:0%
+below that particular residue and this
+in turn can create a helical structure
+
+ align:start position:0%
+in turn can create a helical structure
+ 
+
+ align:start position:0%
+in turn can create a helical structure
+by the way Proline doesn't fit well in
+
+ align:start position:0%
+by the way Proline doesn't fit well in
+ 
+
+ align:start position:0%
+by the way Proline doesn't fit well in
+in this if you add a ProLine in here
+
+ align:start position:0%
+in this if you add a ProLine in here
+ 
+
+ align:start position:0%
+in this if you add a ProLine in here
+Proline is known in the trade as a helix
+
+ align:start position:0%
+Proline is known in the trade as a helix
+ 
+
+ align:start position:0%
+Proline is known in the trade as a helix
+breaker
+
+ align:start position:0%
+breaker
+ 
+
+ align:start position:0%
+breaker
+why because it cannot twist itself
+
+ align:start position:0%
+why because it cannot twist itself
+ 
+
+ align:start position:0%
+why because it cannot twist itself
+around to form an alpha Helix and so if
+
+ align:start position:0%
+around to form an alpha Helix and so if
+ 
+
+ align:start position:0%
+around to form an alpha Helix and so if
+the primary amino acid were to dictate
+
+ align:start position:0%
+the primary amino acid were to dictate
+ 
+
+ align:start position:0%
+the primary amino acid were to dictate
+that a ProLine would be inserted right
+
+ align:start position:0%
+that a ProLine would be inserted right
+ 
+
+ align:start position:0%
+that a ProLine would be inserted right
+here for example then this Helix might
+
+ align:start position:0%
+here for example then this Helix might
+ 
+
+ align:start position:0%
+here for example then this Helix might
+exist down below and up above but it
+
+ align:start position:0%
+exist down below and up above but it
+ 
+
+ align:start position:0%
+exist down below and up above but it
+would not be continuous because the
+
+ align:start position:0%
+would not be continuous because the
+ 
+
+ align:start position:0%
+would not be continuous because the
+presence of a ProLine is highly
+
+ align:start position:0%
+presence of a ProLine is highly
+ 
+
+ align:start position:0%
+presence of a ProLine is highly
+disruptive of the formation of
+
+ align:start position:0%
+disruptive of the formation of
+ 
+
+ align:start position:0%
+disruptive of the formation of
+and Alpha helix this means that in
+
+ align:start position:0%
+and Alpha helix this means that in
+ 
+
+ align:start position:0%
+and Alpha helix this means that in
+principle you can make some predictions
+
+ align:start position:0%
+principle you can make some predictions
+ 
+
+ align:start position:0%
+principle you can make some predictions
+about the localized structure of a
+
+ align:start position:0%
+about the localized structure of a
+ 
+
+ align:start position:0%
+about the localized structure of a
+polypeptide by knowing whether or not
+
+ align:start position:0%
+polypeptide by knowing whether or not
+ 
+
+ align:start position:0%
+polypeptide by knowing whether or not
+Proline is present for example but that
+
+ align:start position:0%
+Proline is present for example but that
+ 
+
+ align:start position:0%
+Proline is present for example but that
+still doesn't give you the power to
+
+ align:start position:0%
+still doesn't give you the power to
+ 
+
+ align:start position:0%
+still doesn't give you the power to
+predict the entire three-dimensional
+
+ align:start position:0%
+predict the entire three-dimensional
+ 
+
+ align:start position:0%
+predict the entire three-dimensional
+structure of the finished protein itself
+
+ align:start position:0%
+structure of the finished protein itself
+ 
+
+ align:start position:0%
+structure of the finished protein itself
+now let's uh agree that this is the
+
+ align:start position:0%
+now let's uh agree that this is the
+ 
+
+ align:start position:0%
+now let's uh agree that this is the
+secondary structure of the protein I.E
+
+ align:start position:0%
+secondary structure of the protein I.E
+ 
+
+ align:start position:0%
+secondary structure of the protein I.E
+the various domains which often form
+
+ align:start position:0%
+the various domains which often form
+ 
+
+ align:start position:0%
+the various domains which often form
+Alpha helices within a certain segment
+
+ align:start position:0%
+Alpha helices within a certain segment
+ 
+
+ align:start position:0%
+Alpha helices within a certain segment
+of the protein or a certain segment of
+
+ align:start position:0%
+of the protein or a certain segment of
+ 
+
+ align:start position:0%
+of the protein or a certain segment of
+the protein will form beta pleated
+
+ align:start position:0%
+the protein will form beta pleated
+ 
+
+ align:start position:0%
+the protein will form beta pleated
+sheets and there's several are several
+
+ align:start position:0%
+sheets and there's several are several
+ 
+
+ align:start position:0%
+sheets and there's several are several
+other less common kinds of of a
+
+ align:start position:0%
+other less common kinds of of a
+ 
+
+ align:start position:0%
+other less common kinds of of a
+secondary structure and here we deal
+
+ align:start position:0%
+secondary structure and here we deal
+ 
+
+ align:start position:0%
+secondary structure and here we deal
+with tertiary structure now we're
+
+ align:start position:0%
+with tertiary structure now we're
+ 
+
+ align:start position:0%
+with tertiary structure now we're
+getting really interesting or maybe you
+
+ align:start position:0%
+getting really interesting or maybe you
+ 
+
+ align:start position:0%
+getting really interesting or maybe you
+don't like it but some people say it's
+
+ align:start position:0%
+don't like it but some people say it's
+ 
+
+ align:start position:0%
+don't like it but some people say it's
+really interesting because here are the
+
+ align:start position:0%
+really interesting because here are the
+ 
+
+ align:start position:0%
+really interesting because here are the
+tertiary structures of some arbitrarily
+
+ align:start position:0%
+tertiary structures of some arbitrarily
+ 
+
+ align:start position:0%
+tertiary structures of some arbitrarily
+chosen proteins
+
+ align:start position:0%
+chosen proteins
+ 
+
+ align:start position:0%
+chosen proteins
+here the tertiary structure of this
+
+ align:start position:0%
+here the tertiary structure of this
+ 
+
+ align:start position:0%
+here the tertiary structure of this
+particular protein and there and the
+
+ align:start position:0%
+particular protein and there and the
+ 
+
+ align:start position:0%
+particular protein and there and the
+identities have not are these are not
+
+ align:start position:0%
+identities have not are these are not
+ 
+
+ align:start position:0%
+identities have not are these are not
+given in our textbook and I'm sure if we
+
+ align:start position:0%
+given in our textbook and I'm sure if we
+ 
+
+ align:start position:0%
+given in our textbook and I'm sure if we
+spent two or three weeks we could find
+
+ align:start position:0%
+spent two or three weeks we could find
+ 
+
+ align:start position:0%
+spent two or three weeks we could find
+out what they were but anyhow here is a
+
+ align:start position:0%
+out what they were but anyhow here is a
+ 
+
+ align:start position:0%
+out what they were but anyhow here is a
+protein a three-dimensional structure of
+
+ align:start position:0%
+protein a three-dimensional structure of
+ 
+
+ align:start position:0%
+protein a three-dimensional structure of
+a protein
+
+ align:start position:0%
+a protein
+ 
+
+ align:start position:0%
+a protein
+where which is composed of four Alpha
+
+ align:start position:0%
+where which is composed of four Alpha
+ 
+
+ align:start position:0%
+where which is composed of four Alpha
+helices which go up another Alfie
+
+ align:start position:0%
+helices which go up another Alfie
+ 
+
+ align:start position:0%
+helices which go up another Alfie
+Alpha Helix Alpha Helix Alpha Helix
+
+ align:start position:0%
+Alpha Helix Alpha Helix Alpha Helix
+ 
+
+ align:start position:0%
+Alpha Helix Alpha Helix Alpha Helix
+Alpha Helix they're depicted here
+
+ align:start position:0%
+Alpha Helix they're depicted here
+ 
+
+ align:start position:0%
+Alpha Helix they're depicted here
+fortunately in four different colors
+
+ align:start position:0%
+fortunately in four different colors
+ 
+
+ align:start position:0%
+fortunately in four different colors
+and so we see that when we talk about
+
+ align:start position:0%
+and so we see that when we talk about
+ 
+
+ align:start position:0%
+and so we see that when we talk about
+tertiary structure we're talking about
+
+ align:start position:0%
+tertiary structure we're talking about
+ 
+
+ align:start position:0%
+tertiary structure we're talking about
+how the alpha helices are disposed with
+
+ align:start position:0%
+how the alpha helices are disposed with
+ 
+
+ align:start position:0%
+how the alpha helices are disposed with
+respect to one another
+
+ align:start position:0%
+respect to one another
+ 
+
+ align:start position:0%
+respect to one another
+the primary structures the amino acid
+
+ align:start position:0%
+the primary structures the amino acid
+ 
+
+ align:start position:0%
+the primary structures the amino acid
+sequence is not shown here the secondary
+
+ align:start position:0%
+sequence is not shown here the secondary
+ 
+
+ align:start position:0%
+sequence is not shown here the secondary
+structure represents these individual
+
+ align:start position:0%
+structure represents these individual
+ 
+
+ align:start position:0%
+structure represents these individual
+Alpha helices and the tertiary structure
+
+ align:start position:0%
+Alpha helices and the tertiary structure
+ 
+
+ align:start position:0%
+Alpha helices and the tertiary structure
+represents how these Alpha helices are
+
+ align:start position:0%
+represents how these Alpha helices are
+ 
+
+ align:start position:0%
+represents how these Alpha helices are
+arranged vis-a-vis one another here is a
+
+ align:start position:0%
+arranged vis-a-vis one another here is a
+ 
+
+ align:start position:0%
+arranged vis-a-vis one another here is a
+a protein which is structured much
+
+ align:start position:0%
+a protein which is structured much
+ 
+
+ align:start position:0%
+a protein which is structured much
+differently um
+
+ align:start position:0%
+differently um
+ 
+
+ align:start position:0%
+differently um
+here this is is uh
+
+ align:start position:0%
+here this is is uh
+ 
+
+ align:start position:0%
+here this is is uh
+is formed of many beta-plated sheets we
+
+ align:start position:0%
+is formed of many beta-plated sheets we
+ 
+
+ align:start position:0%
+is formed of many beta-plated sheets we
+saw them in the in the last figure in
+
+ align:start position:0%
+saw them in the in the last figure in
+ 
+
+ align:start position:0%
+saw them in the in the last figure in
+the last overhead you see it has a quite
+
+ align:start position:0%
+the last overhead you see it has a quite
+ 
+
+ align:start position:0%
+the last overhead you see it has a quite
+different uh overall three-dimensional
+
+ align:start position:0%
+different uh overall three-dimensional
+ 
+
+ align:start position:0%
+different uh overall three-dimensional
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+this could be the beginning of an alpha
+
+ align:start position:0%
+this could be the beginning of an alpha
+ 
+
+ align:start position:0%
+this could be the beginning of an alpha
+Helix down here although that's quite
+
+ align:start position:0%
+Helix down here although that's quite
+ 
+
+ align:start position:0%
+Helix down here although that's quite
+equivocal
+
+ align:start position:0%
+equivocal
+ 
+
+ align:start position:0%
+equivocal
+and here we see yet another point and
+
+ align:start position:0%
+and here we see yet another point and
+ 
+
+ align:start position:0%
+and here we see yet another point and
+that is that as we said before the
+
+ align:start position:0%
+that is that as we said before the
+ 
+
+ align:start position:0%
+that is that as we said before the
+tertiary structure independent of these
+
+ align:start position:0%
+tertiary structure independent of these
+ 
+
+ align:start position:0%
+tertiary structure independent of these
+Alpha and beta Alpha helices and beta
+
+ align:start position:0%
+Alpha and beta Alpha helices and beta
+ 
+
+ align:start position:0%
+Alpha and beta Alpha helices and beta
+pleated Chase may be stabilized by these
+
+ align:start position:0%
+pleated Chase may be stabilized by these
+ 
+
+ align:start position:0%
+pleated Chase may be stabilized by these
+covalent inter strand crosslinks formed
+
+ align:start position:0%
+covalent inter strand crosslinks formed
+ 
+
+ align:start position:0%
+covalent inter strand crosslinks formed
+by the uh cysteines
+
+ align:start position:0%
+by the uh cysteines
+ 
+
+ align:start position:0%
+by the uh cysteines
+and in the end if we put all that
+
+ align:start position:0%
+and in the end if we put all that
+ 
+
+ align:start position:0%
+and in the end if we put all that
+together then we come to the realization
+
+ align:start position:0%
+together then we come to the realization
+ 
+
+ align:start position:0%
+together then we come to the realization
+that the three-dimensional structure of
+
+ align:start position:0%
+that the three-dimensional structure of
+ 
+
+ align:start position:0%
+that the three-dimensional structure of
+a protein as determined by the art of
+
+ align:start position:0%
+a protein as determined by the art of
+ 
+
+ align:start position:0%
+a protein as determined by the art of
+x-ray
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there we go
+
+ align:start position:0%
+there we go
+ 
+
+ align:start position:0%
+there we go
+I'm not actually dyslexic
+
+ align:start position:0%
+I'm not actually dyslexic
+ 
+
+ align:start position:0%
+I'm not actually dyslexic
+I actually have a cousin who I won't
+
+ align:start position:0%
+I actually have a cousin who I won't
+ 
+
+ align:start position:0%
+I actually have a cousin who I won't
+mention whose son was so dyslexic that
+
+ align:start position:0%
+mention whose son was so dyslexic that
+ 
+
+ align:start position:0%
+mention whose son was so dyslexic that
+when he came to stairways he didn't know
+
+ align:start position:0%
+when he came to stairways he didn't know
+ 
+
+ align:start position:0%
+when he came to stairways he didn't know
+whether to put his foot up or down now
+
+ align:start position:0%
+whether to put his foot up or down now
+ 
+
+ align:start position:0%
+whether to put his foot up or down now
+that's difficulty this is
+
+ align:start position:0%
+that's difficulty this is
+ 
+
+ align:start position:0%
+that's difficulty this is
+this is not so bad okay anyhow
+
+ align:start position:0%
+this is not so bad okay anyhow
+ 
+
+ align:start position:0%
+this is not so bad okay anyhow
+because I solved it within less than two
+
+ align:start position:0%
+because I solved it within less than two
+ 
+
+ align:start position:0%
+because I solved it within less than two
+minutes time all right so here we see
+
+ align:start position:0%
+minutes time all right so here we see
+ 
+
+ align:start position:0%
+minutes time all right so here we see
+this is what the three-dimensional
+
+ align:start position:0%
+this is what the three-dimensional
+ 
+
+ align:start position:0%
+this is what the three-dimensional
+structure of a protein looks like this
+
+ align:start position:0%
+structure of a protein looks like this
+ 
+
+ align:start position:0%
+structure of a protein looks like this
+is called a space filling model because
+
+ align:start position:0%
+is called a space filling model because
+ 
+
+ align:start position:0%
+is called a space filling model because
+here one draws in as determined by x-ray
+
+ align:start position:0%
+here one draws in as determined by x-ray
+ 
+
+ align:start position:0%
+here one draws in as determined by x-ray
+crystallography what the ACT if we could
+
+ align:start position:0%
+crystallography what the ACT if we could
+ 
+
+ align:start position:0%
+crystallography what the ACT if we could
+see what a protein looks like what it
+
+ align:start position:0%
+see what a protein looks like what it
+ 
+
+ align:start position:0%
+see what a protein looks like what it
+actually must look like where each of
+
+ align:start position:0%
+actually must look like where each of
+ 
+
+ align:start position:0%
+actually must look like where each of
+the the atoms in including these side
+
+ align:start position:0%
+the the atoms in including these side
+ 
+
+ align:start position:0%
+the the atoms in including these side
+chains is actually depicted before when
+
+ align:start position:0%
+chains is actually depicted before when
+ 
+
+ align:start position:0%
+chains is actually depicted before when
+we use these far more schematic
+
+ align:start position:0%
+we use these far more schematic
+ 
+
+ align:start position:0%
+we use these far more schematic
+descriptions like here we were just
+
+ align:start position:0%
+descriptions like here we were just
+ 
+
+ align:start position:0%
+descriptions like here we were just
+talking about the overall structure of
+
+ align:start position:0%
+talking about the overall structure of
+ 
+
+ align:start position:0%
+talking about the overall structure of
+the backbone we weren't really
+
+ align:start position:0%
+the backbone we weren't really
+ 
+
+ align:start position:0%
+the backbone we weren't really
+indicating where the side chains were
+
+ align:start position:0%
+indicating where the side chains were
+ 
+
+ align:start position:0%
+indicating where the side chains were
+and what space they would fill up and if
+
+ align:start position:0%
+and what space they would fill up and if
+ 
+
+ align:start position:0%
+and what space they would fill up and if
+we give them the chance if we put in all
+
+ align:start position:0%
+we give them the chance if we put in all
+ 
+
+ align:start position:0%
+we give them the chance if we put in all
+of the um other atoms the side chains
+
+ align:start position:0%
+of the um other atoms the side chains
+ 
+
+ align:start position:0%
+of the um other atoms the side chains
+and we create a space filling molecule a
+
+ align:start position:0%
+and we create a space filling molecule a
+ 
+
+ align:start position:0%
+and we create a space filling molecule a
+model where the the actual atoms are
+
+ align:start position:0%
+model where the the actual atoms are
+ 
+
+ align:start position:0%
+model where the the actual atoms are
+shown this is what the protein would
+
+ align:start position:0%
+shown this is what the protein would
+ 
+
+ align:start position:0%
+shown this is what the protein would
+look like and the fact of the matter is
+
+ align:start position:0%
+look like and the fact of the matter is
+ 
+
+ align:start position:0%
+look like and the fact of the matter is
+that virtually all proteins have very
+
+ align:start position:0%
+that virtually all proteins have very
+ 
+
+ align:start position:0%
+that virtually all proteins have very
+specific structures it's not as if they
+
+ align:start position:0%
+specific structures it's not as if they
+ 
+
+ align:start position:0%
+specific structures it's not as if they
+can shift from one structure to another
+
+ align:start position:0%
+can shift from one structure to another
+ 
+
+ align:start position:0%
+can shift from one structure to another
+once they leave their normal native
+
+ align:start position:0%
+once they leave their normal native
+ 
+
+ align:start position:0%
+once they leave their normal native
+structure they will lose their ability
+
+ align:start position:0%
+structure they will lose their ability
+ 
+
+ align:start position:0%
+structure they will lose their ability
+to um to do what Their normal jobs are
+
+ align:start position:0%
+to um to do what Their normal jobs are
+ 
+
+ align:start position:0%
+to um to do what Their normal jobs are
+and this particular uh overhead happens
+
+ align:start position:0%
+and this particular uh overhead happens
+ 
+
+ align:start position:0%
+and this particular uh overhead happens
+to bring in yet another theme that we're
+
+ align:start position:0%
+to bring in yet another theme that we're
+ 
+
+ align:start position:0%
+to bring in yet another theme that we're
+going to focus on increasingly which is
+
+ align:start position:0%
+going to focus on increasingly which is
+ 
+
+ align:start position:0%
+going to focus on increasingly which is
+what do proteins do in cells I'm glad I
+
+ align:start position:0%
+what do proteins do in cells I'm glad I
+ 
+
+ align:start position:0%
+what do proteins do in cells I'm glad I
+asked that question one of the things
+
+ align:start position:0%
+asked that question one of the things
+ 
+
+ align:start position:0%
+asked that question one of the things
+they do is they act as catalysts IES
+
+ align:start position:0%
+they do is they act as catalysts IES
+ 
+
+ align:start position:0%
+they do is they act as catalysts IES
+enzymes
+
+ align:start position:0%
+enzymes
+ 
+
+ align:start position:0%
+enzymes
+the fact is as we'll discuss later
+
+ align:start position:0%
+the fact is as we'll discuss later
+ 
+
+ align:start position:0%
+the fact is as we'll discuss later
+virtually all biochemical reactions
+
+ align:start position:0%
+virtually all biochemical reactions
+ 
+
+ align:start position:0%
+virtually all biochemical reactions
+require an enzyme Catalyst in order to
+
+ align:start position:0%
+require an enzyme Catalyst in order to
+ 
+
+ align:start position:0%
+require an enzyme Catalyst in order to
+propel them forward that is to say if
+
+ align:start position:0%
+propel them forward that is to say if
+ 
+
+ align:start position:0%
+propel them forward that is to say if
+there's a biochemical reaction to occur
+
+ align:start position:0%
+there's a biochemical reaction to occur
+ 
+
+ align:start position:0%
+there's a biochemical reaction to occur
+almost always it will not occur
+
+ align:start position:0%
+almost always it will not occur
+ 
+
+ align:start position:0%
+almost always it will not occur
+spontaneously the same way that a
+
+ align:start position:0%
+spontaneously the same way that a
+ 
+
+ align:start position:0%
+spontaneously the same way that a
+hydroxyl ion and a hydrogen will join
+
+ align:start position:0%
+hydroxyl ion and a hydrogen will join
+ 
+
+ align:start position:0%
+hydroxyl ion and a hydrogen will join
+together spontaneously in water almost
+
+ align:start position:0%
+together spontaneously in water almost
+ 
+
+ align:start position:0%
+together spontaneously in water almost
+all biochemical reactions require the
+
+ align:start position:0%
+all biochemical reactions require the
+ 
+
+ align:start position:0%
+all biochemical reactions require the
+mediation of an enzyme
+
+ align:start position:0%
+mediation of an enzyme
+ 
+
+ align:start position:0%
+mediation of an enzyme
+which is a biological catalyst in order
+
+ align:start position:0%
+which is a biological catalyst in order
+ 
+
+ align:start position:0%
+which is a biological catalyst in order
+to encourage this to happen and this
+
+ align:start position:0%
+to encourage this to happen and this
+ 
+
+ align:start position:0%
+to encourage this to happen and this
+biological and almost all catalysts in
+
+ align:start position:0%
+biological and almost all catalysts in
+ 
+
+ align:start position:0%
+biological and almost all catalysts in
+in our cells are proteins
+
+ align:start position:0%
+in our cells are proteins
+ 
+
+ align:start position:0%
+in our cells are proteins
+so if you have uh 4 326 distinct
+
+ align:start position:0%
+so if you have uh 4 326 distinct
+ 
+
+ align:start position:0%
+so if you have uh 4 326 distinct
+biochemical uh reactions occurring in
+
+ align:start position:0%
+biochemical uh reactions occurring in
+ 
+
+ align:start position:0%
+biochemical uh reactions occurring in
+the cell that means that there's
+
+ align:start position:0%
+the cell that means that there's
+ 
+
+ align:start position:0%
+the cell that means that there's
+probably almost as many distinct enzymes
+
+ align:start position:0%
+probably almost as many distinct enzymes
+ 
+
+ align:start position:0%
+probably almost as many distinct enzymes
+each one of which is assigned to mediate
+
+ align:start position:0%
+each one of which is assigned to mediate
+ 
+
+ align:start position:0%
+each one of which is assigned to mediate
+one or another of those distinct uh
+
+ align:start position:0%
+one or another of those distinct uh
+ 
+
+ align:start position:0%
+one or another of those distinct uh
+biochemical reactions and here we see
+
+ align:start position:0%
+biochemical reactions and here we see
+ 
+
+ align:start position:0%
+biochemical reactions and here we see
+the fact this is an um an enzyme which
+
+ align:start position:0%
+the fact this is an um an enzyme which
+ 
+
+ align:start position:0%
+the fact this is an um an enzyme which
+happens to be called hexokinase recall
+
+ align:start position:0%
+happens to be called hexokinase recall
+ 
+
+ align:start position:0%
+happens to be called hexokinase recall
+that the ASE suffix at the end dictates
+
+ align:start position:0%
+that the ASE suffix at the end dictates
+ 
+
+ align:start position:0%
+that the ASE suffix at the end dictates
+uh that this is already an enzyme rather
+
+ align:start position:0%
+uh that this is already an enzyme rather
+ 
+
+ align:start position:0%
+uh that this is already an enzyme rather
+than a than a carbohydrate and this
+
+ align:start position:0%
+than a than a carbohydrate and this
+ 
+
+ align:start position:0%
+than a than a carbohydrate and this
+attaches uh in fact a phosphate group
+
+ align:start position:0%
+attaches uh in fact a phosphate group
+ 
+
+ align:start position:0%
+attaches uh in fact a phosphate group
+onto glucose and what happens is is that
+
+ align:start position:0%
+onto glucose and what happens is is that
+ 
+
+ align:start position:0%
+onto glucose and what happens is is that
+the glucose which is the substrate which
+
+ align:start position:0%
+the glucose which is the substrate which
+ 
+
+ align:start position:0%
+the glucose which is the substrate which
+is acted upon by the catalyst is pulled
+
+ align:start position:0%
+is acted upon by the catalyst is pulled
+ 
+
+ align:start position:0%
+is acted upon by the catalyst is pulled
+into this site
+
+ align:start position:0%
+into this site
+ 
+
+ align:start position:0%
+into this site
+in the protein which is highly
+
+ align:start position:0%
+in the protein which is highly
+ 
+
+ align:start position:0%
+in the protein which is highly
+specialized to mediate the enzymatic
+
+ align:start position:0%
+specialized to mediate the enzymatic
+ 
+
+ align:start position:0%
+specialized to mediate the enzymatic
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+almost all of the business of this
+
+ align:start position:0%
+almost all of the business of this
+ 
+
+ align:start position:0%
+almost all of the business of this
+complex enzyme is carried out right here
+
+ align:start position:0%
+complex enzyme is carried out right here
+ 
+
+ align:start position:0%
+complex enzyme is carried out right here
+and somehow a lot of the other amino
+
+ align:start position:0%
+and somehow a lot of the other amino
+ 
+
+ align:start position:0%
+and somehow a lot of the other amino
+acids that are located at a distance are
+
+ align:start position:0%
+acids that are located at a distance are
+ 
+
+ align:start position:0%
+acids that are located at a distance are
+doing other things like regulating the
+
+ align:start position:0%
+doing other things like regulating the
+ 
+
+ align:start position:0%
+doing other things like regulating the
+activity of the enzyme but the actual
+
+ align:start position:0%
+activity of the enzyme but the actual
+ 
+
+ align:start position:0%
+activity of the enzyme but the actual
+business end of the enzyme is present in
+
+ align:start position:0%
+business end of the enzyme is present in
+ 
+
+ align:start position:0%
+business end of the enzyme is present in
+what is called a catalytic cleft an
+
+ align:start position:0%
+what is called a catalytic cleft an
+ 
+
+ align:start position:0%
+what is called a catalytic cleft an
+active site of this enzyme in which the
+
+ align:start position:0%
+active site of this enzyme in which the
+ 
+
+ align:start position:0%
+active site of this enzyme in which the
+substrates are pulled in and are
+
+ align:start position:0%
+substrates are pulled in and are
+ 
+
+ align:start position:0%
+substrates are pulled in and are
+manipulated and changed chemically by
+
+ align:start position:0%
+manipulated and changed chemically by
+ 
+
+ align:start position:0%
+manipulated and changed chemically by
+the actions of of this particular enzyme
+
+ align:start position:0%
+the actions of of this particular enzyme
+ 
+
+ align:start position:0%
+the actions of of this particular enzyme
+now in saying that that virtually all
+
+ align:start position:0%
+now in saying that that virtually all
+ 
+
+ align:start position:0%
+now in saying that that virtually all
+catalysts but not all are proteins
+
+ align:start position:0%
+catalysts but not all are proteins
+ 
+
+ align:start position:0%
+catalysts but not all are proteins
+I also mean to say that proteins have a
+
+ align:start position:0%
+I also mean to say that proteins have a
+ 
+
+ align:start position:0%
+I also mean to say that proteins have a
+second major function in the body the
+
+ align:start position:0%
+second major function in the body the
+ 
+
+ align:start position:0%
+second major function in the body the
+first major function is to act as
+
+ align:start position:0%
+first major function is to act as
+ 
+
+ align:start position:0%
+first major function is to act as
+enzymes and catalysts the second major
+
+ align:start position:0%
+enzymes and catalysts the second major
+ 
+
+ align:start position:0%
+enzymes and catalysts the second major
+function is to create biochemical
+
+ align:start position:0%
+function is to create biochemical
+ 
+
+ align:start position:0%
+function is to create biochemical
+structures I.E structures of different
+
+ align:start position:0%
+structures I.E structures of different
+ 
+
+ align:start position:0%
+structures I.E structures of different
+cytoskeleton proteins such as I showed
+
+ align:start position:0%
+cytoskeleton proteins such as I showed
+ 
+
+ align:start position:0%
+cytoskeleton proteins such as I showed
+you uh uh two lectures ago and so we're
+
+ align:start position:0%
+you uh uh two lectures ago and so we're
+ 
+
+ align:start position:0%
+you uh uh two lectures ago and so we're
+going to come repeatedly to situations
+
+ align:start position:0%
+going to come repeatedly to situations
+ 
+
+ align:start position:0%
+going to come repeatedly to situations
+where uh complex structural entities in
+
+ align:start position:0%
+where uh complex structural entities in
+ 
+
+ align:start position:0%
+where uh complex structural entities in
+the cell are composed of different
+
+ align:start position:0%
+the cell are composed of different
+ 
+
+ align:start position:0%
+the cell are composed of different
+structural proteins again this is just a
+
+ align:start position:0%
+structural proteins again this is just a
+ 
+
+ align:start position:0%
+structural proteins again this is just a
+Prelude to be talking about these in
+
+ align:start position:0%
+Prelude to be talking about these in
+ 
+
+ align:start position:0%
+Prelude to be talking about these in
+Greater details these two major
+
+ align:start position:0%
+Greater details these two major
+ 
+
+ align:start position:0%
+Greater details these two major
+functions of enzymatic catalysis on the
+
+ align:start position:0%
+functions of enzymatic catalysis on the
+ 
+
+ align:start position:0%
+functions of enzymatic catalysis on the
+one hand and creating structure on the
+
+ align:start position:0%
+one hand and creating structure on the
+ 
+
+ align:start position:0%
+one hand and creating structure on the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+and so now we get to really four
+
+ align:start position:0%
+and so now we get to really four
+ 
+
+ align:start position:0%
+and so now we get to really four
+hierarchical levels of protein structure
+
+ align:start position:0%
+hierarchical levels of protein structure
+ 
+
+ align:start position:0%
+hierarchical levels of protein structure
+the primary uh
+
+ align:start position:0%
+the primary uh
+ 
+
+ align:start position:0%
+the primary uh
+the primary structure is the amino acid
+
+ align:start position:0%
+the primary structure is the amino acid
+ 
+
+ align:start position:0%
+the primary structure is the amino acid
+sequence
+
+ align:start position:0%
+sequence
+ 
+
+ align:start position:0%
+sequence
+and if we dwell for a second on this
+
+ align:start position:0%
+and if we dwell for a second on this
+ 
+
+ align:start position:0%
+and if we dwell for a second on this
+amino acid sequence let's realize that
+
+ align:start position:0%
+amino acid sequence let's realize that
+ 
+
+ align:start position:0%
+amino acid sequence let's realize that
+any single amino acid can follow any
+
+ align:start position:0%
+any single amino acid can follow any
+ 
+
+ align:start position:0%
+any single amino acid can follow any
+other amino acid so what that means is
+
+ align:start position:0%
+other amino acid so what that means is
+ 
+
+ align:start position:0%
+other amino acid so what that means is
+that if glycine is the first amino acid
+
+ align:start position:0%
+that if glycine is the first amino acid
+ 
+
+ align:start position:0%
+that if glycine is the first amino acid
+as it happens to be here serine is only
+
+ align:start position:0%
+as it happens to be here serine is only
+ 
+
+ align:start position:0%
+as it happens to be here serine is only
+one of 20 different possible second
+
+ align:start position:0%
+one of 20 different possible second
+ 
+
+ align:start position:0%
+one of 20 different possible second
+amino acids
+
+ align:start position:0%
+amino acids
+ 
+
+ align:start position:0%
+amino acids
+Spar aspartic acid is only um
+
+ align:start position:0%
+Spar aspartic acid is only um
+ 
+
+ align:start position:0%
+Spar aspartic acid is only um
+one of 20 different third amino acids as
+
+ align:start position:0%
+one of 20 different third amino acids as
+ 
+
+ align:start position:0%
+one of 20 different third amino acids as
+the third residue we often call these
+
+ align:start position:0%
+the third residue we often call these
+ 
+
+ align:start position:0%
+the third residue we often call these
+different residues the first residue
+
+ align:start position:0%
+different residues the first residue
+ 
+
+ align:start position:0%
+different residues the first residue
+second residue third residue fourth
+
+ align:start position:0%
+second residue third residue fourth
+ 
+
+ align:start position:0%
+second residue third residue fourth
+residue and fourth and so forth and keep
+
+ align:start position:0%
+residue and fourth and so forth and keep
+ 
+
+ align:start position:0%
+residue and fourth and so forth and keep
+in mind if we think about the
+
+ align:start position:0%
+in mind if we think about the
+ 
+
+ align:start position:0%
+in mind if we think about the
+combinatorial implications of that
+
+ align:start position:0%
+combinatorial implications of that
+ 
+
+ align:start position:0%
+combinatorial implications of that
+the first amino acid residue can have 20
+
+ align:start position:0%
+the first amino acid residue can have 20
+ 
+
+ align:start position:0%
+the first amino acid residue can have 20
+different ones the second can have 20
+
+ align:start position:0%
+different ones the second can have 20
+ 
+
+ align:start position:0%
+different ones the second can have 20
+different identities the third can have
+
+ align:start position:0%
+different identities the third can have
+ 
+
+ align:start position:0%
+different identities the third can have
+20 different identities that means if we
+
+ align:start position:0%
+20 different identities that means if we
+ 
+
+ align:start position:0%
+20 different identities that means if we
+make a
+
+ align:start position:0%
+make a
+ 
+
+ align:start position:0%
+make a
+a tripeptide a tripeptide has three
+
+ align:start position:0%
+a tripeptide a tripeptide has three
+ 
+
+ align:start position:0%
+a tripeptide a tripeptide has three
+amino acids in it that means we can make
+
+ align:start position:0%
+amino acids in it that means we can make
+ 
+
+ align:start position:0%
+amino acids in it that means we can make
+400 dipeptides
+
+ align:start position:0%
+400 dipeptides
+ 
+
+ align:start position:0%
+400 dipeptides
+400 distinct dipeptides with uh and we
+
+ align:start position:0%
+400 distinct dipeptides with uh and we
+ 
+
+ align:start position:0%
+400 distinct dipeptides with uh and we
+can make eight thousand distinct
+
+ align:start position:0%
+can make eight thousand distinct
+ 
+
+ align:start position:0%
+can make eight thousand distinct
+tripeptides
+
+ align:start position:0%
+tripeptides
+ 
+
+ align:start position:0%
+tripeptides
+now if you imagine that um there are
+
+ align:start position:0%
+now if you imagine that um there are
+ 
+
+ align:start position:0%
+now if you imagine that um there are
+that the average amino acid uh the the
+
+ align:start position:0%
+that the average amino acid uh the the
+ 
+
+ align:start position:0%
+that the average amino acid uh the the
+average protein in a cell is let's say
+
+ align:start position:0%
+average protein in a cell is let's say
+ 
+
+ align:start position:0%
+average protein in a cell is let's say
+150 amino acid residues long
+
+ align:start position:0%
+150 amino acid residues long
+ 
+
+ align:start position:0%
+150 amino acid residues long
+that means that in principle one could
+
+ align:start position:0%
+that means that in principle one could
+ 
+
+ align:start position:0%
+that means that in principle one could
+make
+
+ align:start position:0%
+make
+ 
+
+ align:start position:0%
+make
+uh 20 to the 150th power
+
+ align:start position:0%
+uh 20 to the 150th power
+ 
+
+ align:start position:0%
+uh 20 to the 150th power
+distinct
+
+ align:start position:0%
+distinct
+ 
+
+ align:start position:0%
+distinct
+amino acid sequences because of these
+
+ align:start position:0%
+amino acid sequences because of these
+ 
+
+ align:start position:0%
+amino acid sequences because of these
+absence of any constraints of what which
+
+ align:start position:0%
+absence of any constraints of what which
+ 
+
+ align:start position:0%
+absence of any constraints of what which
+amino acid will follow which other amino
+
+ align:start position:0%
+amino acid will follow which other amino
+ 
+
+ align:start position:0%
+amino acid will follow which other amino
+acids
+
+ align:start position:0%
+acids
+ 
+
+ align:start position:0%
+acids
+in other words if the average
+
+ align:start position:0%
+in other words if the average
+ 
+
+ align:start position:0%
+in other words if the average
+uh polypeptide has this many residues
+
+ align:start position:0%
+uh polypeptide has this many residues
+ 
+
+ align:start position:0%
+uh polypeptide has this many residues
+this is the number of distinct 150 amino
+
+ align:start position:0%
+this is the number of distinct 150 amino
+ 
+
+ align:start position:0%
+this is the number of distinct 150 amino
+acid residue long proteins that one
+
+ align:start position:0%
+acid residue long proteins that one
+ 
+
+ align:start position:0%
+acid residue long proteins that one
+could in principle synthesize
+
+ align:start position:0%
+could in principle synthesize
+ 
+
+ align:start position:0%
+could in principle synthesize
+I'm not saying all of them have ever
+
+ align:start position:0%
+I'm not saying all of them have ever
+ 
+
+ align:start position:0%
+I'm not saying all of them have ever
+been synthesized since the formation of
+
+ align:start position:0%
+been synthesized since the formation of
+ 
+
+ align:start position:0%
+been synthesized since the formation of
+Life on this planet indeed uh since some
+
+ align:start position:0%
+Life on this planet indeed uh since some
+ 
+
+ align:start position:0%
+Life on this planet indeed uh since some
+amino acid chains are 4 5 600 even 2 000
+
+ align:start position:0%
+amino acid chains are 4 5 600 even 2 000
+ 
+
+ align:start position:0%
+amino acid chains are 4 5 600 even 2 000
+amino acid uh residues long I think the
+
+ align:start position:0%
+amino acid uh residues long I think the
+ 
+
+ align:start position:0%
+amino acid uh residues long I think the
+one that is affected in muscular
+
+ align:start position:0%
+one that is affected in muscular
+ 
+
+ align:start position:0%
+one that is affected in muscular
+dystrophy is more than 2 000 amino acids
+
+ align:start position:0%
+dystrophy is more than 2 000 amino acids
+ 
+
+ align:start position:0%
+dystrophy is more than 2 000 amino acids
+dystrophin does anybody know here it's
+
+ align:start position:0%
+dystrophin does anybody know here it's
+ 
+
+ align:start position:0%
+dystrophin does anybody know here it's
+big anyhow imagine the number of
+
+ align:start position:0%
+big anyhow imagine the number of
+ 
+
+ align:start position:0%
+big anyhow imagine the number of
+possibilities so combinatorially life
+
+ align:start position:0%
+possibilities so combinatorially life
+ 
+
+ align:start position:0%
+possibilities so combinatorially life
+can make almost whatever types of amino
+
+ align:start position:0%
+can make almost whatever types of amino
+ 
+
+ align:start position:0%
+can make almost whatever types of amino
+acids it would like by dictating the
+
+ align:start position:0%
+acids it would like by dictating the
+ 
+
+ align:start position:0%
+acids it would like by dictating the
+sequence of amino acids now
+
+ align:start position:0%
+sequence of amino acids now
+ 
+
+ align:start position:0%
+sequence of amino acids now
+let's just go and look here again
+
+ align:start position:0%
+let's just go and look here again
+ 
+
+ align:start position:0%
+let's just go and look here again
+there's a secondary structure the
+
+ align:start position:0%
+there's a secondary structure the
+ 
+
+ align:start position:0%
+there's a secondary structure the
+tertiary structure is the way in which
+
+ align:start position:0%
+tertiary structure is the way in which
+ 
+
+ align:start position:0%
+tertiary structure is the way in which
+the different Alpha helices here or beta
+
+ align:start position:0%
+the different Alpha helices here or beta
+ 
+
+ align:start position:0%
+the different Alpha helices here or beta
+pleated sheets are disposed
+
+ align:start position:0%
+pleated sheets are disposed
+ 
+
+ align:start position:0%
+pleated sheets are disposed
+three-dimensionally with respect to one
+
+ align:start position:0%
+three-dimensionally with respect to one
+ 
+
+ align:start position:0%
+three-dimensionally with respect to one
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+and the quaternary structure
+
+ align:start position:0%
+and the quaternary structure
+ 
+
+ align:start position:0%
+and the quaternary structure
+represents how different single
+
+ align:start position:0%
+represents how different single
+ 
+
+ align:start position:0%
+represents how different single
+polypeptides are associated one with the
+
+ align:start position:0%
+polypeptides are associated one with the
+ 
+
+ align:start position:0%
+polypeptides are associated one with the
+other so for example hemoglobin is a
+
+ align:start position:0%
+other so for example hemoglobin is a
+ 
+
+ align:start position:0%
+other so for example hemoglobin is a
+tetramer
+
+ align:start position:0%
+tetramer
+ 
+
+ align:start position:0%
+tetramer
+hemoglobin doesn't exist as a monomeric
+
+ align:start position:0%
+hemoglobin doesn't exist as a monomeric
+ 
+
+ align:start position:0%
+hemoglobin doesn't exist as a monomeric
+protein in solution exists as a tetramer
+
+ align:start position:0%
+protein in solution exists as a tetramer
+ 
+
+ align:start position:0%
+protein in solution exists as a tetramer
+and there's two kinds of globin chains
+
+ align:start position:0%
+and there's two kinds of globin chains
+ 
+
+ align:start position:0%
+and there's two kinds of globin chains
+there's an alpha alpha kind and a beta
+
+ align:start position:0%
+there's an alpha alpha kind and a beta
+ 
+
+ align:start position:0%
+there's an alpha alpha kind and a beta
+kind and if we look in a very rough and
+
+ align:start position:0%
+kind and if we look in a very rough and
+ 
+
+ align:start position:0%
+kind and if we look in a very rough and
+schematic way at the way that a
+
+ align:start position:0%
+schematic way at the way that a
+ 
+
+ align:start position:0%
+schematic way at the way that a
+hemoglobin tetramer is arranged there
+
+ align:start position:0%
+hemoglobin tetramer is arranged there
+ 
+
+ align:start position:0%
+hemoglobin tetramer is arranged there
+are two alpha polypeptide chains and two
+
+ align:start position:0%
+are two alpha polypeptide chains and two
+ 
+
+ align:start position:0%
+are two alpha polypeptide chains and two
+beta polypeptide chains they're not
+
+ align:start position:0%
+beta polypeptide chains they're not
+ 
+
+ align:start position:0%
+beta polypeptide chains they're not
+covalently attached to one another
+
+ align:start position:0%
+covalently attached to one another
+ 
+
+ align:start position:0%
+covalently attached to one another
+they're associated with one another via
+
+ align:start position:0%
+they're associated with one another via
+ 
+
+ align:start position:0%
+they're associated with one another via
+hydrogen bonds and hydrophobic
+
+ align:start position:0%
+hydrogen bonds and hydrophobic
+ 
+
+ align:start position:0%
+hydrogen bonds and hydrophobic
+interactions and this is the actual
+
+ align:start position:0%
+interactions and this is the actual
+ 
+
+ align:start position:0%
+interactions and this is the actual
+native configuration of globin to Alpha
+
+ align:start position:0%
+native configuration of globin to Alpha
+ 
+
+ align:start position:0%
+native configuration of globin to Alpha
+and two beta chains it doesn't exist as
+
+ align:start position:0%
+and two beta chains it doesn't exist as
+ 
+
+ align:start position:0%
+and two beta chains it doesn't exist as
+a single amino acid in solution it
+
+ align:start position:0%
+a single amino acid in solution it
+ 
+
+ align:start position:0%
+a single amino acid in solution it
+exists as a tetramer and indeed most or
+
+ align:start position:0%
+exists as a tetramer and indeed most or
+ 
+
+ align:start position:0%
+exists as a tetramer and indeed most or
+I shouldn't say most but very many
+
+ align:start position:0%
+I shouldn't say most but very many
+ 
+
+ align:start position:0%
+I shouldn't say most but very many
+proteins exist in these um
+
+ align:start position:0%
+proteins exist in these um
+ 
+
+ align:start position:0%
+proteins exist in these um
+configurations where the where the
+
+ align:start position:0%
+configurations where the where the
+ 
+
+ align:start position:0%
+configurations where the where the
+tertiary structure represents uh four
+
+ align:start position:0%
+tertiary structure represents uh four
+ 
+
+ align:start position:0%
+tertiary structure represents uh four
+different amino acid chains
+
+ align:start position:0%
+different amino acid chains
+ 
+
+ align:start position:0%
+different amino acid chains
+so these are each of these has an n and
+
+ align:start position:0%
+so these are each of these has an n and
+ 
+
+ align:start position:0%
+so these are each of these has an n and
+C terminal each of these is chemically
+
+ align:start position:0%
+C terminal each of these is chemically
+ 
+
+ align:start position:0%
+C terminal each of these is chemically
+distinct these four could probably be
+
+ align:start position:0%
+distinct these four could probably be
+ 
+
+ align:start position:0%
+distinct these four could probably be
+taken apart from one another simply by
+
+ align:start position:0%
+taken apart from one another simply by
+ 
+
+ align:start position:0%
+taken apart from one another simply by
+raising the temperature and they
+
+ align:start position:0%
+raising the temperature and they
+ 
+
+ align:start position:0%
+raising the temperature and they
+associate like this and in in the
+
+ align:start position:0%
+associate like this and in in the
+ 
+
+ align:start position:0%
+associate like this and in in the
+absence of this Association if you just
+
+ align:start position:0%
+absence of this Association if you just
+ 
+
+ align:start position:0%
+absence of this Association if you just
+had one of these Alphas or one of these
+
+ align:start position:0%
+had one of these Alphas or one of these
+ 
+
+ align:start position:0%
+had one of these Alphas or one of these
+betas it wouldn't function well at all
+
+ align:start position:0%
+betas it wouldn't function well at all
+ 
+
+ align:start position:0%
+betas it wouldn't function well at all
+in fact it might be totally
+
+ align:start position:0%
+in fact it might be totally
+ 
+
+ align:start position:0%
+in fact it might be totally
+dysfunctional
+
+ align:start position:0%
+dysfunctional
+ 
+
+ align:start position:0%
+dysfunctional
+one other thing that may be implicit to
+
+ align:start position:0%
+one other thing that may be implicit to
+ 
+
+ align:start position:0%
+one other thing that may be implicit to
+you but I haven't said but that is very
+
+ align:start position:0%
+you but I haven't said but that is very
+ 
+
+ align:start position:0%
+you but I haven't said but that is very
+important to realize is the following
+
+ align:start position:0%
+important to realize is the following
+ 
+
+ align:start position:0%
+important to realize is the following
+let's imagine that this is the
+
+ align:start position:0%
+let's imagine that this is the
+ 
+
+ align:start position:0%
+let's imagine that this is the
+three-dimensional structure of a protein
+
+ align:start position:0%
+three-dimensional structure of a protein
+ 
+
+ align:start position:0%
+three-dimensional structure of a protein
+as it may well be
+
+ align:start position:0%
+as it may well be
+ 
+
+ align:start position:0%
+as it may well be
+let's now think about hydrophobic and
+
+ align:start position:0%
+let's now think about hydrophobic and
+ 
+
+ align:start position:0%
+let's now think about hydrophobic and
+hydrophilic amino acids
+
+ align:start position:0%
+hydrophilic amino acids
+ 
+
+ align:start position:0%
+hydrophilic amino acids
+the hydrophobic amino acids hate to be
+
+ align:start position:0%
+the hydrophobic amino acids hate to be
+ 
+
+ align:start position:0%
+the hydrophobic amino acids hate to be
+present in water and therefore they are
+
+ align:start position:0%
+present in water and therefore they are
+ 
+
+ align:start position:0%
+present in water and therefore they are
+we can imagine in this case correctly
+
+ align:start position:0%
+we can imagine in this case correctly
+ 
+
+ align:start position:0%
+we can imagine in this case correctly
+tucked away inside the interstices of
+
+ align:start position:0%
+tucked away inside the interstices of
+ 
+
+ align:start position:0%
+tucked away inside the interstices of
+the protein far away from the surface
+
+ align:start position:0%
+the protein far away from the surface
+ 
+
+ align:start position:0%
+the protein far away from the surface
+they don't have any contact with water
+
+ align:start position:0%
+they don't have any contact with water
+ 
+
+ align:start position:0%
+they don't have any contact with water
+conversely the highly charged
+
+ align:start position:0%
+conversely the highly charged
+ 
+
+ align:start position:0%
+conversely the highly charged
+hydrophilic amino acids are actually
+
+ align:start position:0%
+hydrophilic amino acids are actually
+ 
+
+ align:start position:0%
+hydrophilic amino acids are actually
+sticking out at the surface
+
+ align:start position:0%
+sticking out at the surface
+ 
+
+ align:start position:0%
+sticking out at the surface
+and this begins to yield yet another
+
+ align:start position:0%
+and this begins to yield yet another
+ 
+
+ align:start position:0%
+and this begins to yield yet another
+insight into how the three-dimensional
+
+ align:start position:0%
+insight into how the three-dimensional
+ 
+
+ align:start position:0%
+insight into how the three-dimensional
+stereochemistry of proteins is
+
+ align:start position:0%
+stereochemistry of proteins is
+ 
+
+ align:start position:0%
+stereochemistry of proteins is
+maintained and dictated
+
+ align:start position:0%
+maintained and dictated
+ 
+
+ align:start position:0%
+maintained and dictated
+because the hydrophobic amino acids
+
+ align:start position:0%
+because the hydrophobic amino acids
+ 
+
+ align:start position:0%
+because the hydrophobic amino acids
+through hydrophobic interactions
+
+ align:start position:0%
+through hydrophobic interactions
+ 
+
+ align:start position:0%
+through hydrophobic interactions
+stabilize the inner core of the protein
+
+ align:start position:0%
+stabilize the inner core of the protein
+ 
+
+ align:start position:0%
+stabilize the inner core of the protein
+that is that is well shielded from the
+
+ align:start position:0%
+that is that is well shielded from the
+ 
+
+ align:start position:0%
+that is that is well shielded from the
+aqueous solvent the hydrophilic amino
+
+ align:start position:0%
+aqueous solvent the hydrophilic amino
+ 
+
+ align:start position:0%
+aqueous solvent the hydrophilic amino
+acids are on the outside they like to be
+
+ align:start position:0%
+acids are on the outside they like to be
+ 
+
+ align:start position:0%
+acids are on the outside they like to be
+in Intimate contact with the water
+
+ align:start position:0%
+in Intimate contact with the water
+ 
+
+ align:start position:0%
+in Intimate contact with the water
+so we can we already now have talked
+
+ align:start position:0%
+so we can we already now have talked
+ 
+
+ align:start position:0%
+so we can we already now have talked
+about a number of distinct different uh
+
+ align:start position:0%
+about a number of distinct different uh
+ 
+
+ align:start position:0%
+about a number of distinct different uh
+interactions that are responsible for
+
+ align:start position:0%
+interactions that are responsible for
+ 
+
+ align:start position:0%
+interactions that are responsible for
+creating the three-dimensional
+
+ align:start position:0%
+creating the three-dimensional
+ 
+
+ align:start position:0%
+creating the three-dimensional
+stereochemistry of the protein
+
+ align:start position:0%
+stereochemistry of the protein
+ 
+
+ align:start position:0%
+stereochemistry of the protein
+first of all there are the um the
+
+ align:start position:0%
+first of all there are the um the
+ 
+
+ align:start position:0%
+first of all there are the um the
+disulfide bonds which create chain to
+
+ align:start position:0%
+disulfide bonds which create chain to
+ 
+
+ align:start position:0%
+disulfide bonds which create chain to
+chain uh covalent interactions there are
+
+ align:start position:0%
+chain uh covalent interactions there are
+ 
+
+ align:start position:0%
+chain uh covalent interactions there are
+the hydrogen bonds which in which
+
+ align:start position:0%
+the hydrogen bonds which in which
+ 
+
+ align:start position:0%
+the hydrogen bonds which in which
+different side chains can uh different
+
+ align:start position:0%
+different side chains can uh different
+ 
+
+ align:start position:0%
+different side chains can uh different
+uh chains can interact with one another
+
+ align:start position:0%
+uh chains can interact with one another
+ 
+
+ align:start position:0%
+uh chains can interact with one another
+and there are these hydrophobic and
+
+ align:start position:0%
+and there are these hydrophobic and
+ 
+
+ align:start position:0%
+and there are these hydrophobic and
+hydrophilic interactions
+
+ align:start position:0%
+hydrophilic interactions
+ 
+
+ align:start position:0%
+hydrophilic interactions
+and there are some relatively
+
+ align:start position:0%
+and there are some relatively
+ 
+
+ align:start position:0%
+and there are some relatively
+inconsequential Van Der waals
+
+ align:start position:0%
+inconsequential Van Der waals
+ 
+
+ align:start position:0%
+inconsequential Van Der waals
+interactions which are really not worth
+
+ align:start position:0%
+interactions which are really not worth
+ 
+
+ align:start position:0%
+interactions which are really not worth
+discussing although some people get
+
+ align:start position:0%
+discussing although some people get
+ 
+
+ align:start position:0%
+discussing although some people get
+really excited about them but we won't
+
+ align:start position:0%
+really excited about them but we won't
+ 
+
+ align:start position:0%
+really excited about them but we won't
+so here we now begin to see that we have
+
+ align:start position:0%
+so here we now begin to see that we have
+ 
+
+ align:start position:0%
+so here we now begin to see that we have
+really interesting polypeptides unlike
+
+ align:start position:0%
+really interesting polypeptides unlike
+ 
+
+ align:start position:0%
+really interesting polypeptides unlike
+the boring polypeptides that are
+
+ align:start position:0%
+the boring polypeptides that are
+ 
+
+ align:start position:0%
+the boring polypeptides that are
+ultimately
+
+ align:start position:0%
+ultimately
+ 
+
+ align:start position:0%
+ultimately
+um uh is the way one must judge
+
+ align:start position:0%
+um uh is the way one must judge
+ 
+
+ align:start position:0%
+um uh is the way one must judge
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+carbohydrates some people think
+
+ align:start position:0%
+carbohydrates some people think
+ 
+
+ align:start position:0%
+carbohydrates some people think
+carbohydrate chemistry is really
+
+ align:start position:0%
+carbohydrate chemistry is really
+ 
+
+ align:start position:0%
+carbohydrate chemistry is really
+interesting but entrepreneur it really
+
+ align:start position:0%
+interesting but entrepreneur it really
+ 
+
+ align:start position:0%
+interesting but entrepreneur it really
+isn't that interesting because you just
+
+ align:start position:0%
+isn't that interesting because you just
+ 
+
+ align:start position:0%
+isn't that interesting because you just
+have the same monomer
+
+ align:start position:0%
+have the same monomer
+ 
+
+ align:start position:0%
+have the same monomer
+in a 100 or 500 scratches here a protein
+
+ align:start position:0%
+in a 100 or 500 scratches here a protein
+ 
+
+ align:start position:0%
+in a 100 or 500 scratches here a protein
+is much more interesting because this of
+
+ align:start position:0%
+is much more interesting because this of
+ 
+
+ align:start position:0%
+is much more interesting because this of
+this enormous variability in amino acid
+
+ align:start position:0%
+this enormous variability in amino acid
+ 
+
+ align:start position:0%
+this enormous variability in amino acid
+sequence
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kinds of
+
+ align:start position:0%
+kinds of
+ 
+
+ align:start position:0%
+kinds of
+chemical reactivity
+
+ align:start position:0%
+chemical reactivity
+ 
+
+ align:start position:0%
+chemical reactivity
+features
+
+ align:start position:0%
+features
+ 
+
+ align:start position:0%
+features
+because of these these 20 different
+
+ align:start position:0%
+because of these these 20 different
+ 
+
+ align:start position:0%
+because of these these 20 different
+amino acids
+
+ align:start position:0%
+amino acids
+ 
+
+ align:start position:0%
+amino acids
+if you were to imagine life on another
+
+ align:start position:0%
+if you were to imagine life on another
+ 
+
+ align:start position:0%
+if you were to imagine life on another
+planet and we imagine that there were
+
+ align:start position:0%
+planet and we imagine that there were
+ 
+
+ align:start position:0%
+planet and we imagine that there were
+let's say amino acid likes uh molecules
+
+ align:start position:0%
+let's say amino acid likes uh molecules
+ 
+
+ align:start position:0%
+let's say amino acid likes uh molecules
+that were part of life
+
+ align:start position:0%
+that were part of life
+ 
+
+ align:start position:0%
+that were part of life
+maybe that other life wouldn't have
+
+ align:start position:0%
+maybe that other life wouldn't have
+ 
+
+ align:start position:0%
+maybe that other life wouldn't have
+exactly the same 20 amino acids as we do
+
+ align:start position:0%
+exactly the same 20 amino acids as we do
+ 
+
+ align:start position:0%
+exactly the same 20 amino acids as we do
+it almost certainly would be a
+
+ align:start position:0%
+it almost certainly would be a
+ 
+
+ align:start position:0%
+it almost certainly would be a
+water-based the way we are
+
+ align:start position:0%
+water-based the way we are
+ 
+
+ align:start position:0%
+water-based the way we are
+um but it would also rely on on hydrogen
+
+ align:start position:0%
+um but it would also rely on on hydrogen
+ 
+
+ align:start position:0%
+um but it would also rely on on hydrogen
+bonds and and and
+
+ align:start position:0%
+bonds and and and
+ 
+
+ align:start position:0%
+bonds and and and
+um hydrophilicity and hydrophobicity
+
+ align:start position:0%
+um hydrophilicity and hydrophobicity
+ 
+
+ align:start position:0%
+um hydrophilicity and hydrophobicity
+interactions uh in order to dictate the
+
+ align:start position:0%
+interactions uh in order to dictate the
+ 
+
+ align:start position:0%
+interactions uh in order to dictate the
+three-dimensional structure
+
+ align:start position:0%
+three-dimensional structure
+ 
+
+ align:start position:0%
+three-dimensional structure
+in the absence of this very specific
+
+ align:start position:0%
+in the absence of this very specific
+ 
+
+ align:start position:0%
+in the absence of this very specific
+three-dimensional structure I will tell
+
+ align:start position:0%
+three-dimensional structure I will tell
+ 
+
+ align:start position:0%
+three-dimensional structure I will tell
+you that this enzyme could not function
+
+ align:start position:0%
+you that this enzyme could not function
+ 
+
+ align:start position:0%
+you that this enzyme could not function
+and if you were to take this enzyme if
+
+ align:start position:0%
+and if you were to take this enzyme if
+ 
+
+ align:start position:0%
+and if you were to take this enzyme if
+it were a typical enzyme and you were to
+
+ align:start position:0%
+it were a typical enzyme and you were to
+ 
+
+ align:start position:0%
+it were a typical enzyme and you were to
+heat it up briefly uh even often
+
+ align:start position:0%
+heat it up briefly uh even often
+ 
+
+ align:start position:0%
+heat it up briefly uh even often
+slightly above normal body temperature
+
+ align:start position:0%
+slightly above normal body temperature
+ 
+
+ align:start position:0%
+slightly above normal body temperature
+it might denature I.E it might lose its
+
+ align:start position:0%
+it might denature I.E it might lose its
+ 
+
+ align:start position:0%
+it might denature I.E it might lose its
+its three-dimensional
+
+ align:start position:0%
+its three-dimensional
+ 
+
+ align:start position:0%
+its three-dimensional
+um structure irreversibly and once it
+
+ align:start position:0%
+um structure irreversibly and once it
+ 
+
+ align:start position:0%
+um structure irreversibly and once it
+were denatured once it was denatured
+
+ align:start position:0%
+were denatured once it was denatured
+ 
+
+ align:start position:0%
+were denatured once it was denatured
+this process of denaturation it might
+
+ align:start position:0%
+this process of denaturation it might
+ 
+
+ align:start position:0%
+this process of denaturation it might
+not be able to spontaneously reassume
+
+ align:start position:0%
+not be able to spontaneously reassume
+ 
+
+ align:start position:0%
+not be able to spontaneously reassume
+that pre-existing three-dimensional
+
+ align:start position:0%
+that pre-existing three-dimensional
+ 
+
+ align:start position:0%
+that pre-existing three-dimensional
+configuration and therefore would
+
+ align:start position:0%
+configuration and therefore would
+ 
+
+ align:start position:0%
+configuration and therefore would
+forever be inactive
+
+ align:start position:0%
+forever be inactive
+ 
+
+ align:start position:0%
+forever be inactive
+that means to say very explicitly that
+
+ align:start position:0%
+that means to say very explicitly that
+ 
+
+ align:start position:0%
+that means to say very explicitly that
+even though the amino acids that are
+
+ align:start position:0%
+even though the amino acids that are
+ 
+
+ align:start position:0%
+even though the amino acids that are
+creating that active catalytic site
+
+ align:start position:0%
+creating that active catalytic site
+ 
+
+ align:start position:0%
+creating that active catalytic site
+remain there
+
+ align:start position:0%
+remain there
+ 
+
+ align:start position:0%
+remain there
+they're highly specific
+
+ align:start position:0%
+they're highly specific
+ 
+
+ align:start position:0%
+they're highly specific
+three-dimensional uh disposition is
+
+ align:start position:0%
+three-dimensional uh disposition is
+ 
+
+ align:start position:0%
+three-dimensional uh disposition is
+critical for the continued actions of
+
+ align:start position:0%
+critical for the continued actions of
+ 
+
+ align:start position:0%
+critical for the continued actions of
+this enzyme and once they're
+
+ align:start position:0%
+this enzyme and once they're
+ 
+
+ align:start position:0%
+this enzyme and once they're
+three-dimensional
+
+ align:start position:0%
+three-dimensional
+ 
+
+ align:start position:0%
+three-dimensional
+dispositions are shifted around through
+
+ align:start position:0%
+dispositions are shifted around through
+ 
+
+ align:start position:0%
+dispositions are shifted around through
+the process of interactions then uh we
+
+ align:start position:0%
+the process of interactions then uh we
+ 
+
+ align:start position:0%
+the process of interactions then uh we
+have a trouble because the enzyme can no
+
+ align:start position:0%
+have a trouble because the enzyme can no
+ 
+
+ align:start position:0%
+have a trouble because the enzyme can no
+longer do its assigned task
+
+ align:start position:0%
+longer do its assigned task
+ 
+
+ align:start position:0%
+longer do its assigned task
+we're going to go now to uh an even
+
+ align:start position:0%
+we're going to go now to uh an even
+ 
+
+ align:start position:0%
+we're going to go now to uh an even
+higher order of complexity in one sense
+
+ align:start position:0%
+higher order of complexity in one sense
+ 
+
+ align:start position:0%
+higher order of complexity in one sense
+we're going to you go to the the royalty
+
+ align:start position:0%
+we're going to you go to the the royalty
+ 
+
+ align:start position:0%
+we're going to you go to the the royalty
+of the macromolecules which are the
+
+ align:start position:0%
+of the macromolecules which are the
+ 
+
+ align:start position:0%
+of the macromolecules which are the
+nucleic acids of course protein chemists
+
+ align:start position:0%
+nucleic acids of course protein chemists
+ 
+
+ align:start position:0%
+nucleic acids of course protein chemists
+would take great umbrage at the very
+
+ align:start position:0%
+would take great umbrage at the very
+ 
+
+ align:start position:0%
+would take great umbrage at the very
+notion that uh there are things better
+
+ align:start position:0%
+notion that uh there are things better
+ 
+
+ align:start position:0%
+notion that uh there are things better
+than proteins but the fact of the matter
+
+ align:start position:0%
+than proteins but the fact of the matter
+ 
+
+ align:start position:0%
+than proteins but the fact of the matter
+is entrepreneur uh there are I can't
+
+ align:start position:0%
+is entrepreneur uh there are I can't
+ 
+
+ align:start position:0%
+is entrepreneur uh there are I can't
+show you that overhead because it's from
+
+ align:start position:0%
+show you that overhead because it's from
+ 
+
+ align:start position:0%
+show you that overhead because it's from
+the other textbook
+
+ align:start position:0%
+the other textbook
+ 
+
+ align:start position:0%
+the other textbook
+which is copyright and we're being
+
+ align:start position:0%
+which is copyright and we're being
+ 
+
+ align:start position:0%
+which is copyright and we're being
+filmed
+
+ align:start position:0%
+filmed
+ 
+
+ align:start position:0%
+filmed
+how many people have had the backs of
+
+ align:start position:0%
+how many people have had the backs of
+ 
+
+ align:start position:0%
+how many people have had the backs of
+their heads immortalized on these videos
+
+ align:start position:0%
+their heads immortalized on these videos
+ 
+
+ align:start position:0%
+their heads immortalized on these videos
+did you call home and ask anybody to
+
+ align:start position:0%
+did you call home and ask anybody to
+ 
+
+ align:start position:0%
+did you call home and ask anybody to
+identify you
+
+ align:start position:0%
+identify you
+ 
+
+ align:start position:0%
+identify you
+I don't know but soon you'll be uh
+
+ align:start position:0%
+I don't know but soon you'll be uh
+ 
+
+ align:start position:0%
+I don't know but soon you'll be uh
+you'll have your 50 each of us is in has
+
+ align:start position:0%
+you'll have your 50 each of us is in has
+ 
+
+ align:start position:0%
+you'll have your 50 each of us is in has
+the Limelight for 15 minutes in a
+
+ align:start position:0%
+the Limelight for 15 minutes in a
+ 
+
+ align:start position:0%
+the Limelight for 15 minutes in a
+Lifetime right so you'll have your 15
+
+ align:start position:0%
+Lifetime right so you'll have your 15
+ 
+
+ align:start position:0%
+Lifetime right so you'll have your 15
+minutes okay here are here are some
+
+ align:start position:0%
+minutes okay here are here are some
+ 
+
+ align:start position:0%
+minutes okay here are here are some
+nucleic acids and let's look at these
+
+ align:start position:0%
+nucleic acids and let's look at these
+ 
+
+ align:start position:0%
+nucleic acids and let's look at these
+nucleic acids and the way they're put
+
+ align:start position:0%
+nucleic acids and the way they're put
+ 
+
+ align:start position:0%
+nucleic acids and the way they're put
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+keep in mind to anticipate what we're
+
+ align:start position:0%
+keep in mind to anticipate what we're
+ 
+
+ align:start position:0%
+keep in mind to anticipate what we're
+going to say next time once again we
+
+ align:start position:0%
+going to say next time once again we
+ 
+
+ align:start position:0%
+going to say next time once again we
+want to make end-to-end Aggregates we
+
+ align:start position:0%
+want to make end-to-end Aggregates we
+ 
+
+ align:start position:0%
+want to make end-to-end Aggregates we
+want to polymerize molecules
+
+ align:start position:0%
+want to polymerize molecules
+ 
+
+ align:start position:0%
+want to polymerize molecules
+um and in this case we want to do so
+
+ align:start position:0%
+um and in this case we want to do so
+ 
+
+ align:start position:0%
+um and in this case we want to do so
+once again through a dehydration
+
+ align:start position:0%
+once again through a dehydration
+ 
+
+ align:start position:0%
+once again through a dehydration
+reaction
+
+ align:start position:0%
+reaction
+ 
+
+ align:start position:0%
+reaction
+and moreover just to look at the
+
+ align:start position:0%
+and moreover just to look at the
+ 
+
+ align:start position:0%
+and moreover just to look at the
+building blocks of nucleic acids we
+
+ align:start position:0%
+building blocks of nucleic acids we
+ 
+
+ align:start position:0%
+building blocks of nucleic acids we
+start again in this case with two
+
+ align:start position:0%
+start again in this case with two
+ 
+
+ align:start position:0%
+start again in this case with two
+pentoses recall that they have four
+
+ align:start position:0%
+pentoses recall that they have four
+ 
+
+ align:start position:0%
+pentoses recall that they have four
+carbons one two three four no did I say
+
+ align:start position:0%
+carbons one two three four no did I say
+ 
+
+ align:start position:0%
+carbons one two three four no did I say
+four you know I meant five
+
+ align:start position:0%
+four you know I meant five
+ 
+
+ align:start position:0%
+four you know I meant five
+one two three four five so whenever I
+
+ align:start position:0%
+one two three four five so whenever I
+ 
+
+ align:start position:0%
+one two three four five so whenever I
+say four from now on I mean
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or whenever I say four I may also mean
+
+ align:start position:0%
+or whenever I say four I may also mean
+ 
+
+ align:start position:0%
+or whenever I say four I may also mean
+four okay one two three four five
+
+ align:start position:0%
+four okay one two three four five
+ 
+
+ align:start position:0%
+four okay one two three four five
+um and and let's look at the Two basic
+
+ align:start position:0%
+um and and let's look at the Two basic
+ 
+
+ align:start position:0%
+um and and let's look at the Two basic
+kinds of pentose molecules that are uh
+
+ align:start position:0%
+kinds of pentose molecules that are uh
+ 
+
+ align:start position:0%
+kinds of pentose molecules that are uh
+present in nucleic acid because they
+
+ align:start position:0%
+present in nucleic acid because they
+ 
+
+ align:start position:0%
+present in nucleic acid because they
+Define the essential difference between
+
+ align:start position:0%
+Define the essential difference between
+ 
+
+ align:start position:0%
+Define the essential difference between
+DNA and RNA
+
+ align:start position:0%
+DNA and RNA
+ 
+
+ align:start position:0%
+DNA and RNA
+here's a regular old rather familiar
+
+ align:start position:0%
+here's a regular old rather familiar
+ 
+
+ align:start position:0%
+here's a regular old rather familiar
+kind of pentose with five carbons
+
+ align:start position:0%
+kind of pentose with five carbons
+ 
+
+ align:start position:0%
+kind of pentose with five carbons
+and here's an unfamiliar kind of pentose
+
+ align:start position:0%
+and here's an unfamiliar kind of pentose
+ 
+
+ align:start position:0%
+and here's an unfamiliar kind of pentose
+which we call deoxyribose why because if
+
+ align:start position:0%
+which we call deoxyribose why because if
+ 
+
+ align:start position:0%
+which we call deoxyribose why because if
+you look really carefully you see that
+
+ align:start position:0%
+you look really carefully you see that
+ 
+
+ align:start position:0%
+you look really carefully you see that
+the hydroxyl group here which should be
+
+ align:start position:0%
+the hydroxyl group here which should be
+ 
+
+ align:start position:0%
+the hydroxyl group here which should be
+present in any self-respecting pentose
+
+ align:start position:0%
+present in any self-respecting pentose
+ 
+
+ align:start position:0%
+present in any self-respecting pentose
+is missing and is replaced simply by a
+
+ align:start position:0%
+is missing and is replaced simply by a
+ 
+
+ align:start position:0%
+is missing and is replaced simply by a
+hydrogen group I.E it's lost it's oxygen
+
+ align:start position:0%
+hydrogen group I.E it's lost it's oxygen
+ 
+
+ align:start position:0%
+hydrogen group I.E it's lost it's oxygen
+whence come with the word
+
+ align:start position:0%
+whence come with the word
+ 
+
+ align:start position:0%
+whence come with the word
+deoxyribose and ultimately clearly the
+
+ align:start position:0%
+deoxyribose and ultimately clearly the
+ 
+
+ align:start position:0%
+deoxyribose and ultimately clearly the
+word deoxyribose nucleic acid
+
+ align:start position:0%
+word deoxyribose nucleic acid
+ 
+
+ align:start position:0%
+word deoxyribose nucleic acid
+and one of the attributes one of the
+
+ align:start position:0%
+and one of the attributes one of the
+ 
+
+ align:start position:0%
+and one of the attributes one of the
+virtues of carbohydrates as we discussed
+
+ align:start position:0%
+virtues of carbohydrates as we discussed
+ 
+
+ align:start position:0%
+virtues of carbohydrates as we discussed
+last time were these numerous hydroxyl
+
+ align:start position:0%
+last time were these numerous hydroxyl
+ 
+
+ align:start position:0%
+last time were these numerous hydroxyl
+groups which represent opportunities for
+
+ align:start position:0%
+groups which represent opportunities for
+ 
+
+ align:start position:0%
+groups which represent opportunities for
+all kinds of dehydration reactions which
+
+ align:start position:0%
+all kinds of dehydration reactions which
+ 
+
+ align:start position:0%
+all kinds of dehydration reactions which
+can enable one to build much more
+
+ align:start position:0%
+can enable one to build much more
+ 
+
+ align:start position:0%
+can enable one to build much more
+complex molecules and here we see uh the
+
+ align:start position:0%
+complex molecules and here we see uh the
+ 
+
+ align:start position:0%
+complex molecules and here we see uh the
+structure of for example a
+
+ align:start position:0%
+structure of for example a
+ 
+
+ align:start position:0%
+structure of for example a
+deoxyribonucleotide whose detailed
+
+ align:start position:0%
+deoxyribonucleotide whose detailed
+ 
+
+ align:start position:0%
+deoxyribonucleotide whose detailed
+structure will will get into next time
+
+ align:start position:0%
+structure will will get into next time
+ 
+
+ align:start position:0%
+structure will will get into next time
+but just let's look at how these
+
+ align:start position:0%
+but just let's look at how these
+ 
+
+ align:start position:0%
+but just let's look at how these
+hydroxyl groups have been used the
+
+ align:start position:0%
+hydroxyl groups have been used the
+ 
+
+ align:start position:0%
+hydroxyl groups have been used the
+hydroxyl group in this case in DNA and
+
+ align:start position:0%
+hydroxyl group in this case in DNA and
+ 
+
+ align:start position:0%
+hydroxyl group in this case in DNA and
+by the way it notice notice that the
+
+ align:start position:0%
+by the way it notice notice that the
+ 
+
+ align:start position:0%
+by the way it notice notice that the
+structure I've shown here
+
+ align:start position:0%
+structure I've shown here
+ 
+
+ align:start position:0%
+structure I've shown here
+there's a side chain attached here and a
+
+ align:start position:0%
+there's a side chain attached here and a
+ 
+
+ align:start position:0%
+there's a side chain attached here and a
+side chain attached here and neither of
+
+ align:start position:0%
+side chain attached here and neither of
+ 
+
+ align:start position:0%
+side chain attached here and neither of
+those depends on whether or not there's
+
+ align:start position:0%
+those depends on whether or not there's
+ 
+
+ align:start position:0%
+those depends on whether or not there's
+a hydrogen or a hydroxyl right here
+
+ align:start position:0%
+a hydrogen or a hydroxyl right here
+ 
+
+ align:start position:0%
+a hydrogen or a hydroxyl right here
+and look what what's happened here here
+
+ align:start position:0%
+and look what what's happened here here
+ 
+
+ align:start position:0%
+and look what what's happened here here
+we have this hydroxyl
+
+ align:start position:0%
+we have this hydroxyl
+ 
+
+ align:start position:0%
+we have this hydroxyl
+over here to which a base has been
+
+ align:start position:0%
+over here to which a base has been
+ 
+
+ align:start position:0%
+over here to which a base has been
+attached covalently once again by a
+
+ align:start position:0%
+attached covalently once again by a
+ 
+
+ align:start position:0%
+attached covalently once again by a
+dehydration reaction and here we have a
+
+ align:start position:0%
+dehydration reaction and here we have a
+ 
+
+ align:start position:0%
+dehydration reaction and here we have a
+situation where actually three phosphate
+
+ align:start position:0%
+situation where actually three phosphate
+ 
+
+ align:start position:0%
+situation where actually three phosphate
+groups have been attached to the
+
+ align:start position:0%
+groups have been attached to the
+ 
+
+ align:start position:0%
+groups have been attached to the
+hydroxyl group in this direction
+
+ align:start position:0%
+hydroxyl group in this direction
+ 
+
+ align:start position:0%
+hydroxyl group in this direction
+and this represents the basic building
+
+ align:start position:0%
+and this represents the basic building
+ 
+
+ align:start position:0%
+and this represents the basic building
+blocks of nucleic acids now one of the
+
+ align:start position:0%
+blocks of nucleic acids now one of the
+ 
+
+ align:start position:0%
+blocks of nucleic acids now one of the
+things that's going to be really
+
+ align:start position:0%
+things that's going to be really
+ 
+
+ align:start position:0%
+things that's going to be really
+important and that you're going to have
+
+ align:start position:0%
+important and that you're going to have
+ 
+
+ align:start position:0%
+important and that you're going to have
+to memorize I told you you weren't going
+
+ align:start position:0%
+to memorize I told you you weren't going
+ 
+
+ align:start position:0%
+to memorize I told you you weren't going
+to have to memorize anything
+
+ align:start position:0%
+to have to memorize anything
+ 
+
+ align:start position:0%
+to have to memorize anything
+but you didn't believe me did you
+
+ align:start position:0%
+but you didn't believe me did you
+ 
+
+ align:start position:0%
+but you didn't believe me did you
+good okay one of the things you're gonna
+
+ align:start position:0%
+good okay one of the things you're gonna
+ 
+
+ align:start position:0%
+good okay one of the things you're gonna
+have to memorize is the numbering system
+
+ align:start position:0%
+have to memorize is the numbering system
+ 
+
+ align:start position:0%
+have to memorize is the numbering system
+here this is number one two three four
+
+ align:start position:0%
+here this is number one two three four
+ 
+
+ align:start position:0%
+here this is number one two three four
+five or to be totally Frank and you know
+
+ align:start position:0%
+five or to be totally Frank and you know
+ 
+
+ align:start position:0%
+five or to be totally Frank and you know
+I'm always that one prime two prime
+
+ align:start position:0%
+I'm always that one prime two prime
+ 
+
+ align:start position:0%
+I'm always that one prime two prime
+three prime four Prime five Prime
+
+ align:start position:0%
+three prime four Prime five Prime
+ 
+
+ align:start position:0%
+three prime four Prime five Prime
+and that numbering system it turns out
+
+ align:start position:0%
+and that numbering system it turns out
+ 
+
+ align:start position:0%
+and that numbering system it turns out
+is going to be very important for our
+
+ align:start position:0%
+is going to be very important for our
+ 
+
+ align:start position:0%
+is going to be very important for our
+subsequent discussions
+
+ align:start position:0%
+subsequent discussions
+ 
+
+ align:start position:0%
+subsequent discussions
+notice here that for example it's it's
+
+ align:start position:0%
+notice here that for example it's it's
+ 
+
+ align:start position:0%
+notice here that for example it's it's
+here at the two prime position that this
+
+ align:start position:0%
+here at the two prime position that this
+ 
+
+ align:start position:0%
+here at the two prime position that this
+deoxyribose is lacking the the oxygen
+
+ align:start position:0%
+deoxyribose is lacking the the oxygen
+ 
+
+ align:start position:0%
+deoxyribose is lacking the the oxygen
+that is present normally in um
+
+ align:start position:0%
+that is present normally in um
+ 
+
+ align:start position:0%
+that is present normally in um
+in in in RNA and with all this in mind
+
+ align:start position:0%
+in in in RNA and with all this in mind
+ 
+
+ align:start position:0%
+in in in RNA and with all this in mind
+we will wait in great suspense until
+
+ align:start position:0%
+we will wait in great suspense until
+ 
+
+ align:start position:0%
+we will wait in great suspense until
+Wednesday when we actually talk about
+
+ align:start position:0%
+Wednesday when we actually talk about
+ 
+
+ align:start position:0%
+Wednesday when we actually talk about
+how this is exploited to make highly uh
+
+ align:start position:0%
+how this is exploited to make highly uh
+ 
+
+ align:start position:0%
+how this is exploited to make highly uh
+complex polymers have a good two days
+
+ align:start position:0%
+complex polymers have a good two days
+ 
+
+ align:start position:0%
+complex polymers have a good two days
+see you Wednesday at 10.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
\ No newline at end of file
diff --git a/cQtCpJyl77o.txt b/cQtCpJyl77o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4973022fe65b80e0439ca37554de16c11f924972
--- /dev/null
+++ b/cQtCpJyl77o.txt
@@ -0,0 +1,523 @@
+align:start position:0%
+ 
+all right so let us revisit the example
+
+ align:start position:0%
+all right so let us revisit the example
+ 
+
+ align:start position:0%
+all right so let us revisit the example
+from last lecture so we have a Markov
+
+ align:start position:0%
+from last lecture so we have a Markov
+ 
+
+ align:start position:0%
+from last lecture so we have a Markov
+chain with two states 1 & 2 and this
+
+ align:start position:0%
+chain with two states 1 & 2 and this
+ 
+
+ align:start position:0%
+chain with two states 1 & 2 and this
+Markov chain as a single recurrent class
+
+ align:start position:0%
+Markov chain as a single recurrent class
+ 
+
+ align:start position:0%
+Markov chain as a single recurrent class
+right and then also it's not very thick
+
+ align:start position:0%
+right and then also it's not very thick
+ 
+
+ align:start position:0%
+right and then also it's not very thick
+right because we have Sal transition of
+
+ align:start position:0%
+right because we have Sal transition of
+ 
+
+ align:start position:0%
+right because we have Sal transition of
+this type so as a result this is well
+
+ align:start position:0%
+this type so as a result this is well
+ 
+
+ align:start position:0%
+this type so as a result this is well
+defined and this steady state
+
+ align:start position:0%
+defined and this steady state
+ 
+
+ align:start position:0%
+defined and this steady state
+probabilities from 1 to M in that case
+
+ align:start position:0%
+probabilities from 1 to M in that case
+ 
+
+ align:start position:0%
+probabilities from 1 to M in that case
+for us M equals 2 right so let us write
+
+ align:start position:0%
+for us M equals 2 right so let us write
+ 
+
+ align:start position:0%
+for us M equals 2 right so let us write
+this system and solve the system of
+
+ align:start position:0%
+this system and solve the system of
+ 
+
+ align:start position:0%
+this system and solve the system of
+linear equation for this example here so
+
+ align:start position:0%
+linear equation for this example here so
+ 
+
+ align:start position:0%
+linear equation for this example here so
+what we have is PI 1 equals PI 1 times
+
+ align:start position:0%
+what we have is PI 1 equals PI 1 times
+ 
+
+ align:start position:0%
+what we have is PI 1 equals PI 1 times
+0.5 plus PI 2 times 0.2 so that's the
+
+ align:start position:0%
+0.5 plus PI 2 times 0.2 so that's the
+ 
+
+ align:start position:0%
+0.5 plus PI 2 times 0.2 so that's the
+first equation the correspond to J
+
+ align:start position:0%
+first equation the correspond to J
+ 
+
+ align:start position:0%
+first equation the correspond to J
+equals 1 now for J equals 2 pi 2 equals
+
+ align:start position:0%
+equals 1 now for J equals 2 pi 2 equals
+ 
+
+ align:start position:0%
+equals 1 now for J equals 2 pi 2 equals
+PI 1 times 0.5 plus pi 2 times 0.8 so we
+
+ align:start position:0%
+PI 1 times 0.5 plus pi 2 times 0.8 so we
+ 
+
+ align:start position:0%
+PI 1 times 0.5 plus pi 2 times 0.8 so we
+have a system of two equations with two
+
+ align:start position:0%
+have a system of two equations with two
+ 
+
+ align:start position:0%
+have a system of two equations with two
+unknowns PI 1 and PI 2 let's rewrite
+
+ align:start position:0%
+unknowns PI 1 and PI 2 let's rewrite
+ 
+
+ align:start position:0%
+unknowns PI 1 and PI 2 let's rewrite
+them can I pass this one on this side
+
+ align:start position:0%
+them can I pass this one on this side
+ 
+
+ align:start position:0%
+them can I pass this one on this side
+and this one on this side so we get PI 1
+
+ align:start position:0%
+and this one on this side so we get PI 1
+ 
+
+ align:start position:0%
+and this one on this side so we get PI 1
+times 1 minus 0.5 0.5 equals pi 2 times
+
+ align:start position:0%
+times 1 minus 0.5 0.5 equals pi 2 times
+ 
+
+ align:start position:0%
+times 1 minus 0.5 0.5 equals pi 2 times
+0.2 and this 1 PI 2 times 1 minus 0.8 is
+
+ align:start position:0%
+0.2 and this 1 PI 2 times 1 minus 0.8 is
+ 
+
+ align:start position:0%
+0.2 and this 1 PI 2 times 1 minus 0.8 is
+zero point 2 equals PI 1 times 0.5 I we
+
+ align:start position:0%
+zero point 2 equals PI 1 times 0.5 I we
+ 
+
+ align:start position:0%
+zero point 2 equals PI 1 times 0.5 I we
+realize that these two happen to be the
+
+ align:start position:0%
+realize that these two happen to be the
+ 
+
+ align:start position:0%
+realize that these two happen to be the
+same
+
+ align:start position:0%
+same
+ 
+
+ align:start position:0%
+same
+so they are not enough to define a
+
+ align:start position:0%
+so they are not enough to define a
+ 
+
+ align:start position:0%
+so they are not enough to define a
+unique solution so we have to add
+
+ align:start position:0%
+unique solution so we have to add
+ 
+
+ align:start position:0%
+unique solution so we have to add
+another equations and we know that these
+
+ align:start position:0%
+another equations and we know that these
+ 
+
+ align:start position:0%
+another equations and we know that these
+are probabilities so PI 1 plus PI 2 have
+
+ align:start position:0%
+are probabilities so PI 1 plus PI 2 have
+ 
+
+ align:start position:0%
+are probabilities so PI 1 plus PI 2 have
+to be 1 and so now we're going to keep
+
+ align:start position:0%
+to be 1 and so now we're going to keep
+ 
+
+ align:start position:0%
+to be 1 and so now we're going to keep
+one of these two let's say this one I'm
+
+ align:start position:0%
+one of these two let's say this one I'm
+ 
+
+ align:start position:0%
+one of these two let's say this one I'm
+gonna write it here and we can rewrite
+
+ align:start position:0%
+gonna write it here and we can rewrite
+ 
+
+ align:start position:0%
+gonna write it here and we can rewrite
+it by saying that PI 1 times 1 over 2
+
+ align:start position:0%
+it by saying that PI 1 times 1 over 2
+ 
+
+ align:start position:0%
+it by saying that PI 1 times 1 over 2
+equals PI 2 times 1 over 5 so now we're
+
+ align:start position:0%
+equals PI 2 times 1 over 5 so now we're
+ 
+
+ align:start position:0%
+equals PI 2 times 1 over 5 so now we're
+gonna take that replace PI 1 equals 2/5
+
+ align:start position:0%
+gonna take that replace PI 1 equals 2/5
+ 
+
+ align:start position:0%
+gonna take that replace PI 1 equals 2/5
+of Pi to see the result of that and
+
+ align:start position:0%
+of Pi to see the result of that and
+ 
+
+ align:start position:0%
+of Pi to see the result of that and
+we're gonna use that PI 1 and replace it
+
+ align:start position:0%
+we're gonna use that PI 1 and replace it
+ 
+
+ align:start position:0%
+we're gonna use that PI 1 and replace it
+here so we end up by 2 times 2/5 plus 1
+
+ align:start position:0%
+here so we end up by 2 times 2/5 plus 1
+ 
+
+ align:start position:0%
+here so we end up by 2 times 2/5 plus 1
+equals 1 which means that from here we
+
+ align:start position:0%
+equals 1 which means that from here we
+ 
+
+ align:start position:0%
+equals 1 which means that from here we
+get that pi 2 equals 5 plus 2/7 so 5
+
+ align:start position:0%
+get that pi 2 equals 5 plus 2/7 so 5
+ 
+
+ align:start position:0%
+get that pi 2 equals 5 plus 2/7 so 5
+over 7 and then we use that replace it
+
+ align:start position:0%
+over 7 and then we use that replace it
+ 
+
+ align:start position:0%
+over 7 and then we use that replace it
+here and we end up adding PI 1 equals
+
+ align:start position:0%
+here and we end up adding PI 1 equals
+ 
+
+ align:start position:0%
+here and we end up adding PI 1 equals
+2/5 times 5 7 equals 2 7 and we check 5
+
+ align:start position:0%
+2/5 times 5 7 equals 2 7 and we check 5
+ 
+
+ align:start position:0%
+2/5 times 5 7 equals 2 7 and we check 5
+plus 2 equals 7 so these are real
+
+ align:start position:0%
+plus 2 equals 7 so these are real
+ 
+
+ align:start position:0%
+plus 2 equals 7 so these are real
+probabilities so the priority that you
+
+ align:start position:0%
+probabilities so the priority that you
+ 
+
+ align:start position:0%
+probabilities so the priority that you
+find yourself at state 1 at time 1
+
+ align:start position:0%
+find yourself at state 1 at time 1
+ 
+
+ align:start position:0%
+find yourself at state 1 at time 1
+trillion will be approximately 2 over 7
+
+ align:start position:0%
+trillion will be approximately 2 over 7
+ 
+
+ align:start position:0%
+trillion will be approximately 2 over 7
+the priority that you find yourself at
+
+ align:start position:0%
+the priority that you find yourself at
+ 
+
+ align:start position:0%
+the priority that you find yourself at
+state 1 at time to trillions is again
+
+ align:start position:0%
+state 1 at time to trillions is again
+ 
+
+ align:start position:0%
+state 1 at time to trillions is again
+approximately 2 over 7 so essentially
+
+ align:start position:0%
+approximately 2 over 7 so essentially
+ 
+
+ align:start position:0%
+approximately 2 over 7 so essentially
+what we have here is the probability of
+
+ align:start position:0%
+what we have here is the probability of
+ 
+
+ align:start position:0%
+what we have here is the probability of
+being in that state 1 settles in a
+
+ align:start position:0%
+being in that state 1 settles in a
+ 
+
+ align:start position:0%
+being in that state 1 settles in a
+steady value that's what the
+
+ align:start position:0%
+steady value that's what the
+ 
+
+ align:start position:0%
+steady value that's what the
+steady-state convergence means it's
+
+ align:start position:0%
+steady-state convergence means it's
+ 
+
+ align:start position:0%
+steady-state convergence means it's
+convergence of probabilities not
+
+ align:start position:0%
+convergence of probabilities not
+ 
+
+ align:start position:0%
+convergence of probabilities not
+convergence of the process itself again
+
+ align:start position:0%
+convergence of the process itself again
+ 
+
+ align:start position:0%
+convergence of the process itself again
+the process will keep jumping back and
+
+ align:start position:0%
+the process will keep jumping back and
+ 
+
+ align:start position:0%
+the process will keep jumping back and
+forth but the steady state priority will
+
+ align:start position:0%
+forth but the steady state priority will
+ 
+
+ align:start position:0%
+forth but the steady state priority will
+settle to a given value here in 1 that
+
+ align:start position:0%
+settle to a given value here in 1 that
+ 
+
+ align:start position:0%
+settle to a given value here in 1 that
+will be 2 over 7 and the steady state
+
+ align:start position:0%
+will be 2 over 7 and the steady state
+ 
+
+ align:start position:0%
+will be 2 over 7 and the steady state
+priority in being in 2 will settle to 5
+
+ align:start position:0%
+priority in being in 2 will settle to 5
+ 
+
+ align:start position:0%
+priority in being in 2 will settle to 5
+over 7 and finally in this example and
+
+ align:start position:0%
+over 7 and finally in this example and
+ 
+
+ align:start position:0%
+over 7 and finally in this example and
+marginally when we have a single class
+
+ align:start position:0%
+marginally when we have a single class
+ 
+
+ align:start position:0%
+marginally when we have a single class
+and no periodicity the initial state
+
+ align:start position:0%
+and no periodicity the initial state
+ 
+
+ align:start position:0%
+and no periodicity the initial state
+does not matter
\ No newline at end of file
diff --git a/czAWbZLxFNM.txt b/czAWbZLxFNM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..46d3485644fc8b6052e55851045600bbce29e6f3
--- /dev/null
+++ b/czAWbZLxFNM.txt
@@ -0,0 +1,3177 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high-quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: OK, OK, OK.
+
+Let's settle down.
+
+Weekend is over.
+
+Tomorrow, weekly quiz.
+
+Today I'll have office
+hours 3:00 to 4:00.
+
+I have to go down to Washington,
+so I've got to
+
+leave a little bit earlier
+than normal.
+
+So I will be available
+from 3:00 to 4:00
+
+The lecture has started and
+there's still way too much
+
+talking in here.
+
+Way too much.
+
+You know how much is too much?
+
+Any.
+
+Any.
+
+So last day, we started talking
+about oxide glasses,
+
+and we reasoned that we could
+have control of the properties
+
+by control of the composition.
+
+We started with a network
+former, which is some oxide
+
+that has the capacity for
+forming covalent bonds through
+
+a bridging oxygen.
+
+And then we wanted to drop the
+processing temperature, and we
+
+did so by adding modifiers.
+
+Intermediates, we haven't talked
+about and we're going
+
+to do that in just a moment.
+
+So if you look in the readings,
+this is from
+
+archival notes that were written
+by my predecessor,
+
+Professor Witt, these
+are compositions of
+
+some typical glasses.
+
+I don't expect you know these
+from memory, but I would
+
+expect you, if I gave you the
+composition, explain to me why
+
+the various constituents
+are there.
+
+So let's try few examples.
+
+The first one is soda-lime
+glass.
+
+And you see it contains
+silica, which
+
+is the network former.
+
+It contains sodium oxide,
+calcium oxide,
+
+and magnesium oxide.
+
+And these are alkaline earth
+oxides that are ionic, and so
+
+these are acting as network
+modifiers because they're
+
+donating oxide anions
+that go in and break
+
+the silicate chains.
+
+And then there's this Al203 and
+that's sort of halfway in
+
+between, isn't it?
+
+Silica is Group 4, or
+14, if you want to
+
+use the modern notation.
+
+Sodium is Group 1.
+
+Calcium, magnesium, Group 2.
+
+Alumina is Group 3, and it's
+sort of halfway in between.
+
+It's amphoteric.
+
+It can either be a former
+or a modifier.
+
+And in these instances,
+depending on how much modifier
+
+is present, alumina can act
+as an intermediate.
+
+And what's an intermediate do?
+
+An intermediate is
+a covalent oxide.
+
+It's a covalent oxide, or an
+oxide that can act as both
+
+covalent and ionic.
+
+But in this instance, it's
+acting covalent oxide with a
+
+different coordination number.
+
+And what does that mean?
+
+Different coordination number?
+
+It coordinates--
+
+remember last day I
+showed you B2O3?
+
+Borate glasses?
+
+So they have a coordination
+of three, whereas
+
+silicates have four.
+
+And what that means
+is that there's
+
+going to be a mismatch.
+
+There's still strong covalent
+bonds, but they don't fit
+
+quite right.
+
+And that's going to give
+even more free volume.
+
+And that excess free volume,
+through covalent bonds, gives
+
+you the ability to endure
+thermal shock.
+
+So if you want to impart thermal
+shock resistance in a
+
+glass, you give it lots of free
+volume so it can take the
+
+rapid change in temperature.
+
+So it's a covalent oxide with
+different coordination number.
+
+That is, nearest neighbors, in a
+covalent sense, from that of
+
+the network former.
+
+So you can add a borate or
+aluminate, what have you.
+
+And that'll give you thermal
+shock resistance.
+
+And so alumina here is acting
+as an intermediate.
+
+Let's go down here.
+
+There's borosilicate.
+
+borosilicate is the generic
+term for Pyrex.
+
+So Pyrex is a trade name.
+
+Pyrex was invented by Corning,
+and it contains silica as the
+
+network former.
+
+There's some sodium oxide,
+potassium oxide--
+
+in rather small amounts.
+
+You can see this isn't a heavily
+modified network, but
+
+look at this.
+
+13% B2O3 and 2% alumina.
+
+That's the modifier.
+
+And what was the hallmark
+of Pyrex?
+
+It had thermal shock
+resistance.
+
+So you could take it out of the
+oven and put it under cold
+
+water and it didn't shatter.
+
+And we have the same analogous
+behavior for glass ware in the
+
+laboratory.
+
+For all room temperature and
+low temperature work in the
+
+laboratory, we use Pyrex that
+has this resistance to
+
+chemicals and resistance
+to heat.
+
+This is the big one, here.
+
+And that gave birth to
+functional crockery in the
+
+kitchen, where you could work in
+glass instead of in metal.
+
+And down here we see glass--
+
+let's see, well, here's one.
+
+Light flint optical.
+
+See, that's 54%.
+
+It's down to 54% silica.
+
+And look at this-- boatloads
+of lead oxide.
+
+And the lead oxide is acting as
+a modifier and also changes
+
+the index of refraction.
+
+It modifies so much that we
+have almost down to the
+
+orthosilicate.
+
+So that the chains are modified
+to the point where
+
+they're almost all terminals.
+
+There's very little of this,
+and most of it is just
+
+terminal oxygens.
+
+And that means that it's more
+nearly crystalline, and
+
+therefore, you can cut it.
+
+And this is the lead crystal.
+
+Lead crystal has that
+high value.
+
+So you can see how
+that comes out.
+
+And this is also taken
+from the reading.
+
+It's a plot of viscosity
+versus temperature.
+
+Only it's a logarithmic plot.
+
+And what do you see?
+
+Here's pure silica.
+
+That's SiO2.
+
+And if I want to take it down
+to the point where, if the
+
+viscosity goes down, you
+have the ability to
+
+work with the glass.
+
+So if I want to melt silica,
+I've got to way, way up here.
+
+Over 2,000 Centigrade.
+
+So if I want to make bottles, if
+I want to make cookware, I
+
+don't want to run a lehr
+at this temperature.
+
+Lehr.
+
+L E H R.
+
+It's where you melt glass.
+
+Lehr.
+
+I don't want to run a lehr
+at this temperature.
+
+But you can see if I add
+modifier, the more modifier
+
+that I add, the more I
+break the network.
+
+So increasing modifier
+decreases network
+
+connectivity, and that means I
+can go to a lower temperature
+
+and get the same level
+of fluidity.
+
+So there's a whole bunch of
+definitions here that I'm not
+
+going to go over.
+
+You'll have this slide.
+
+But basically, it's just
+different points in
+
+processing.
+
+So if you go up here.
+
+Strain and annealing.
+
+I mean, these are very, very--
+
+you're especially working with
+solid, whereas softening
+
+point, you start getting
+the glass to flow.
+
+And the working point, that's
+the viscosity that
+
+you have to get below.
+
+Otherwise, the glass is going
+to be to resistant to flow.
+
+You want to get the glass tacky
+so that you can put it
+
+into an injection mold, shape
+it, as they do with bottles.
+
+They take a blob of glass and
+boom, they just throw it into
+
+a mold and it sprays out.
+
+And if you've got the right mass
+and the right spinning,
+
+it makes the wall thickness
+proper.
+
+But you can imagine, if the
+glass is really, really
+
+viscous, it's not going
+to flow well enough.
+
+If it's too fluid, it'll
+drip all over.
+
+So there's an optimum
+in there.
+
+And this is telling you
+how to figure out what
+
+that optimum is.
+
+And you can see that as you
+change the composition, here's
+
+the working value.
+
+This is the viscosity that you
+have to get below which in
+
+order to work.
+
+And you can see that as you add
+more and more modifier,
+
+you can take the temperature
+and get it way, way down.
+
+So to work with silica you have
+to be about around 2,000.
+
+With soda-lime you can
+be down around 800.
+
+So that's going to cut your
+energy costs, isn't it?
+
+And it's going to make
+it easier to recycle.
+
+What's the point of recycling if
+you consume as much energy
+
+to recycle as if you started
+with virgin material?
+
+At least with virgin material
+you can guarantee the quality
+
+of the feeds stock.
+
+So there's got to be
+some big saving.
+
+All right.
+
+So that gives you a some sense
+as to what we can do
+
+technologically with glasses.
+
+I want to show you one last
+thing with glasses, and then
+
+we're going to move on
+to another topic.
+
+You know, new week, new
+day, new topic.
+
+So I want to go back
+to this curve.
+
+So what am I showing you here?
+
+I'm showing you that as we
+change the cooling rate, we
+
+change the amount of quenched-in
+excess volume.
+
+So fast cooling quenches in more
+of the liquid free volume
+
+than slow cooling does.
+
+That's why this V excess is
+small here, whereas V excess
+
+is large here for
+the other one.
+
+I'm going to use that in
+glass strengthening.
+
+So I want to strengthen.
+
+Strengthening glasses.
+
+We're talking about silicates
+or borates.
+
+Strengthening oxide glasses.
+
+Glass is a fantastic material.
+
+It's really good in compression,
+but it's no good
+
+in tensions.
+
+You know this.
+
+If you try to bend glass,
+it'll break.
+
+Why?
+
+Not because it doesn't
+have dislocations.
+
+It's got strong covalent
+bonds.
+
+But you know, suppose you want
+to strengthen the windshield
+
+of your car so that
+when a stone hits
+
+it, it doesn't shatter.
+
+What can we do to give
+it added strength?
+
+So I'm going to show you two
+ways, and both of them operate
+
+under this principle that
+the yield stress--
+
+this is the stress that will
+break the glass, and I'm going
+
+to say the effective yield
+stress, what you
+
+experience in life--
+
+is equal to the sum of what I'm
+going to call the natural
+
+yield stress, which is the basic
+property of the glass.
+
+Plus, I'm going to increase
+the surface stress.
+
+What I'm going to do is I'm
+going to modify the surface,
+
+and I'm going to put an
+additive stress at the
+
+surface, and that's going to
+be a compressive stress.
+
+So that means now the effective
+stress that I need
+
+to break the glass is going
+to be greater than it
+
+otherwise would be.
+
+So the whole gambit here is
+surface strengthening.
+
+Service strengthening, which
+means surface modification.
+
+And I'm going to show you two
+ways to modify the surface to
+
+bring the strength
+of the glass up.
+
+The first way is thermal.
+
+Thermal treatment.
+
+And the thermal treatment is
+to strengthen the glass.
+
+Well, let's see.
+
+Let's keep it in the context
+of the windshield.
+
+The technical term
+for this, the
+
+technological term is tempering.
+
+So what I'm going to show you
+was how we can look at that
+
+volume versus temperature curve
+and understand how we
+
+make tempered glass for
+windshields and so.
+
+So I'm going to show you
+a slab of glass.
+
+Here's a slab of glass.
+
+And we just got below the
+softening point-- so T just
+
+less than T softening.
+
+So now this thing's going to
+start, it's continuing to
+
+become more and more viscous and
+getting closer and closer
+
+to glass transition
+temperature.
+
+And what we're going to do is
+we're going to introduce air
+
+jets at the surface
+of the glass.
+
+What that's going to do
+is it's going to cause
+
+accelerated cooling
+at the surface.
+
+And the same thing happens on
+both surfaces, so I'm going to
+
+cut this piece of glass in half,
+and we're just going to
+
+look at the upper surface.
+
+The same thing happens
+in a lower surface.
+
+So let's now blow this up.
+
+I'm just going to look at the
+upper-half surface and I'm
+
+going to divide it
+into two zones.
+
+This is the first level,
+most primitive
+
+finite element analysis.
+
+Finite element analysis.
+
+I'm going to divide it in two,
+and I'm going to say, this has
+
+got two zones.
+
+Two cooling zones.
+
+Here is the zone of
+the center, OK?
+
+This is the center.
+
+And I'm going to call this
+the inner portion.
+
+And then there's the
+outer portion.
+
+Well, take a look at
+this curve here.
+
+Which is going to have
+slower cooling?
+
+In the center or near
+the free surface?
+
+The slower cooling is in the
+center and according to this
+
+graph, the slow cooling has
+a smaller residual volume.
+
+I've written, V-interior.
+
+That's the green line.
+
+And then the upper one
+is a yellow line.
+
+So the upper one where it's high
+cooling, it's going to
+
+have a higher volume.
+
+So this is the second piece
+of finite element.
+
+So I'm going to model
+this one like so.
+
+So this is outer.
+
+And the same thing happens
+on the other side, OK?
+
+So it's happening on
+the bottom as well.
+
+But we're just looking
+at the top because
+
+there's symmetry here.
+
+So you see what I've done?
+
+This is longer because that
+graph says it wants to be
+
+occupying a larger volume.
+
+Problem is the glass
+can't do this.
+
+I can do this with a piece of
+chalk, but the glass isn't
+
+going to look like that.
+
+The glass is going to
+have a flat edge.
+
+And how can it have
+a flat edge?
+
+Because the bottom, here-- this
+is not to scale, let's
+
+make it more to scale--
+
+the top is a narrow zone and
+the bottom is a big, thick
+
+zone, isn't it?
+
+So this big, thick zone, which
+has a small volume, is going
+
+to pull on the thin upper
+zone, which has a large
+
+volume, and pull it in.
+
+Can you see that?
+
+And it's going to cause
+the introduction
+
+of compressive stresses.
+
+So we got to compressive
+stresses simply using that
+
+graph and a little bit of air.
+
+So you take that graph, put
+differential cooling, and now
+
+you've introduced compressive
+stress.
+
+And that's all tempered
+glass is.
+
+So the V-excess of the outer
+layer is greater than V-excess
+
+of the inner layer, or the
+interior, if you like.
+
+And why?
+
+Because the cooling rate, the
+change of temperature with
+
+time of the outer zone, is
+greater than the cooling rate
+
+of the inner or interior.
+
+And there it is.
+
+That's the beginning.
+
+And so now to fracture you have
+to apply a greater stress
+
+then you would have otherwise.
+
+So that's good, and that
+saves a lot of lives.
+
+There's another way.
+
+There's another way to surface
+strengthen, and that's a
+
+chemical treatment.
+
+And again, what am
+I trying to do?
+
+I'm trying to introduce a
+compressive stress, but I'm
+
+going to use a chemical means.
+
+And this one is called
+ion exchange.
+
+And this is used in
+technology, too.
+
+So now I'm going to take
+a piece of glass here.
+
+This is solid glass and let's
+put some components in here.
+
+So I'm going to put some silica
+as my network former.
+
+I'm going to put some
+sodium oxide.
+
+And I'm going to put some
+modifier, B2O3.
+
+So I got all three here.
+
+Former, modifier,
+intermediate.
+
+And just to put a little skin
+on the bones here, I want to
+
+show what the sodium oxide
+actually looks like.
+
+Sodium oxide goes in as sodium
+cations, and oxide anions.
+
+The oxide anions go in
+and they break some
+
+of the silica chains.
+
+But the sodiums don't get
+involved in that.
+
+They just sit around
+as spectators.
+
+Now what I'm going to do is
+I'm going to put this, I'm
+
+going to soak this
+in molten salt.
+
+Soak in molten salt.
+
+This is huge area of
+my own research.
+
+And the molten salt, one example
+might be I'm going to
+
+take potassium chloride.
+
+Remember, we talked about making
+aluminum or magnesium?
+
+This is one of the constituents
+of the melt in
+
+which we make electrolytic
+magnesium.
+
+Potassium chloride.
+
+And it exists as potassium
+cations and chloride anions.
+
+Chlorine is green,
+except we know--
+
+you know, this is the way
+chemistry books write it, but
+
+that's stupid because this is
+isoelectronic with argon.
+
+And it's not green.
+
+I know.
+
+I've looked at this stuff.
+
+It's clear, colorless,
+and transparent.
+
+The chloride ion has to be
+clear and colorless.
+
+It's got a complete shell,
+but the chemistry books
+
+will make it green.
+
+Anyway, here's the potassium
+ion here.
+
+And there's a lot of
+potassium ion here.
+
+There's no potassium ion
+inside the glass.
+
+There's sodium ion in the glass,
+there's no sodium ion
+
+in the molten salt.
+
+But these are both media
+in which ions live.
+
+So can you see this is sort of
+like the perfume bottle?
+
+Things move from high
+concentration to low
+
+concentration.
+
+Some sodium wants to leave
+and enter the melt.
+
+And some potassium wants
+to leave the melt
+
+and enter the glass.
+
+And where's the potassium
+going to go?
+
+It has to go where there
+used to be sodium.
+
+What's the relative size
+of potassium ion
+
+versus sodium ion?
+
+Potassium ion is bigger.
+
+So potassium ion goes and
+occupies a site formerly
+
+occupied by sodium and causes
+compressive stress, because
+
+you get all these big ions
+jamming in there and that's
+
+going to lead to compressive
+stress through ion exchange.
+
+So through ion exchange we
+can raised the temp.
+
+Since r, the radius of potassium
+is greater than the
+
+radius of the sodium, we get a
+force fit, and this is how we
+
+got solution hardening.
+
+Hardening is the metallurgical
+term for raising the strength.
+
+Hardening is equal to
+strength going up.
+
+So we get hardening
+by solution.
+
+So this is solution hardening.
+
+Solution hardening because the
+potassium ion is in there.
+
+So we have surface.
+
+And this gives a lot
+of strength.
+
+We do the same thing
+metallurgically if you
+
+carburize the surface
+of a piece of steel.
+
+Tool steels, for example,
+surface carburized.
+
+So we get hard surfaces
+that can cut.
+
+You say, well, why don't you
+just put the carbon in all the
+
+way through?
+
+Well, then the tool bit
+will be brittle.
+
+So you want something that's got
+toughness in the center so
+
+it can take the impact,
+but it's got surface
+
+hardness so it'll cut.
+
+And that's an engineered
+material.
+
+We've got one set of properties
+at the surface, and
+
+we've got another set of
+properties in the bulk.
+
+And it's all brought to you
+by control of chemistry.
+
+And then that's also control
+of chemistry.
+
+OK.
+
+So I mean, I could talk more
+and more and more.
+
+Glasses are just fascinating
+things.
+
+But we've got to get moving.
+
+So we're going to move
+to a new topic.
+
+We're going to move to
+a new topic today.
+
+We're going to start talking
+about kinetics.
+
+Kinetics.
+
+And what is kinetics?
+
+Kinetics is the topic that we
+put into 3.091, because it's
+
+important, of course, but it's
+all about the study of
+
+reaction rates.
+
+It's the study of reaction
+rates and mechanism.
+
+So why do we study?
+
+Well, we study it because
+I think it belongs here.
+
+But first of all, kinetics is
+related to productivity and
+
+resource utilization.
+
+You've got two factories.
+
+One produces 200 units per time,
+the other produces 100
+
+units per time.
+
+The one that's producing 100
+units per time probably isn't
+
+going to be in business
+that much longer.
+
+And it's all about understanding
+how to get more
+
+throughput per unit time, and
+that leads to competitiveness.
+
+So if you're interested in
+international competitiveness,
+
+you've got to know something
+about kinetics.
+
+The two go hand in glove.
+
+Second thing is energy
+and the environment.
+
+A number of you have come to
+talk to me after class, sent
+
+emails because you're interested
+in energy and the
+
+environment.
+
+Efficient use of energy involves
+understanding the
+
+kinetics so you can force
+chemical change with the least
+
+amount of energy utilization and
+do so in a way because its
+
+mechanism--
+
+if there's two mechanisms that
+allow you to get to the same
+
+end product, choose the one
+that has the least toxic
+
+impact on the environment.
+
+Otherwise, you're going to have
+to spend money to avoid
+
+the effluents, which then gets
+you back up to number one.
+
+Your cost of doing business is
+higher than the other guy.
+
+Guess what?
+
+You're creamed in
+the marketplace.
+
+And lastly, societal.
+
+And this is one that excites
+me, is kinetics leads to
+
+productivity, which keeps
+factories open, which keeps
+
+people working.
+
+So through understanding
+kinetics.
+
+You go and you look at places
+in the United States where
+
+factories have closed.
+
+In many, many instances it was
+because the technology lagged.
+
+If you could just keep
+things going faster.
+
+You've got to make things-- you
+know how fast you've got
+
+to make them go?
+
+You've got to make them go so
+fast that even if the foreign
+
+workers are paid zero, you can
+still beat them in the
+
+marketplace.
+
+That's your standard.
+
+So that's how you design
+your processes.
+
+You design your processes so
+that you can produce at very,
+
+very low cost.
+
+And there's a huge range
+in reaction rates.
+
+You know, you can start
+the range of
+
+rates, rates of reaction.
+
+At the one that you have
+very, very slow.
+
+And way over here you have very,
+very fast, all right?
+
+So on the slow end, you
+have stuff that's
+
+sort of cosmic scale.
+
+Geological.
+
+And then over here,
+what do we have?
+
+We have explosions.
+
+You might say, well, explosions
+are usually bad,
+
+aren't they?
+
+Well, no.
+
+I can give you an example of
+where explosion is used to
+
+your advantage.
+
+The airbag in the automobile.
+
+There is no pump, no mechanical
+pump fast enough to
+
+inflate an airbag on demand.
+
+So how do we make those
+airbags work?
+
+And I hope none of us ever
+has to be present at the
+
+deployment of those airbags.
+
+But you know, just academically
+let's talk about
+
+how they work.
+
+There's like an explosion that
+occurs when you're driving.
+
+There's an accelerometer and
+this is a key piece.
+
+The accelerometer has to make
+a decision whether you're
+
+applying the brakes just because
+you've lost focus and
+
+you're, you know, whoops!
+
+You've had that jerky brake.
+
+Or maybe this is one of those
+holy-mackerel moments, and
+
+your jamming on the
+brakes, and we'd
+
+better deploy the airbags.
+
+Once the accelerometer decides
+that this is one of those holy
+
+you-know-what moments, it sends
+an electric current
+
+through a wire, which then
+raises the temperature to 300
+
+degrees C and causes this
+reaction to take place.
+
+When this reaction takes
+place, this is a solid,
+
+nitrogen is a gas.
+
+So the gas has a much, much
+higher volume than the solid
+
+and within milliseconds
+you get inflation.
+
+Well, that's good and that
+inflates the bag and prevents
+
+you from hitting the hard
+parts of the car.
+
+But you see the other
+byproduct?
+
+That's sodium.
+
+And if you look on your Periodic
+Table, elemental
+
+sodium is liquid above
+98 degrees Celsius.
+
+So now you've got
+liquid sodium.
+
+There's no point preserving the
+safety of the occupants of
+
+the car just to cover them
+with liquid sodium.
+
+So we better do something
+about that.
+
+So being chemists, what we do
+is we add potassium nitrate
+
+inside the bag, as well.
+
+so.
+
+That that sodium is mopped up
+with potassium nitrate, which
+
+converts it to sodium oxide,
+potassium oxide, and a little
+
+more nitrogen.
+
+[BLOWING SOUND EFFECT]
+
+Keep the bag nice and firm.
+
+But now what happens when the
+Fires show up and they
+
+[SOUND EFFECT],
+
+you know, they start pouring
+water on it.
+
+This turns into caustic.
+
+So now you're going to get
+covered and wet lye.
+
+So that's probably not
+too good, either.
+
+Just remember, you've been
+physically saved from smashing
+
+your skull on the tempered
+windshield.
+
+So it's so far, so good.
+
+So now what?
+
+You want a mechanical, you
+want a Newtonian death?
+
+Or do you want a Coulombic
+death?
+
+I guess that's the
+question, here.
+
+And so we're going to keep doing
+some chemistry here and
+
+we're going to add silica.
+
+And what happens if we add
+silica to sodium oxide
+
+potassium oxide?
+
+Well that's a network former,
+these are network modifiers.
+
+We'll make an alkaline silicate
+glass and that's OK
+
+because we put food
+and beverages in
+
+alkaline silicate glasses.
+
+So everybody is happy.
+
+So that's all the chemistry that
+goes on inside an airbag.
+
+And we've got to understand
+the kinetics.
+
+So I hope I've whet
+your appetite.
+
+OK, that's enough of that.
+
+Now let's get to
+the real stuff.
+
+So let's write a general
+chemical reaction.
+
+The general reaction.
+
+What's the formalism if we want
+to set up the metrics?
+
+So I'm going to write just
+a plain, old equation.
+
+This is the classical
+P-Chem stuff.
+
+Little a moles of A, plus little
+b moles of B go to
+
+little c moles of C plus
+little d moles of D.
+
+So this could have
+been lecture two.
+
+Just a straight chemical
+reaction.
+
+Remember we were studying
+stoichiometry?
+
+So the constituents of the left
+side of the equation are
+
+called the reactants, whereas
+on the right side of the
+
+equation we have the products.
+
+And what kinetics gives us,
+kinetics tells us the rate of
+
+conversion.
+
+Or the rate of reaction.
+
+I'm using all these terms
+so you understand their
+
+equivalent.
+
+So we can write something like
+this where the conservation of
+
+mass kicks in.
+
+So I can't make products
+any faster
+
+than I consume reactants.
+
+There's no sources
+or sinks here.
+
+When I lose reactants,
+I make products.
+
+So I'm going to say, the rate of
+change of the total mass of
+
+the reactants-- this
+is summation sign--
+
+I'm just saying the rate of
+change of the sum of all of
+
+the reactions must equal
+the rate of change.
+
+So the loss rate of reactants
+must equal the gain rate of
+
+all of the products.
+
+That's just simple
+stoichiometry.
+
+Or some people call this
+conservation of mass or Law of
+
+Mass Action, what have you.
+
+And then we count by
+concentration, usually.
+
+Just reminder.
+
+This is lowercase c.
+
+So this is the concentration
+of species i
+
+goes as the mole number.
+
+n is mole number divided by
+the volume of the reactor.
+
+So this would be in moles
+per meter cubed if
+
+we were in SI units.
+
+So therefore the rate of change,
+the ci by dt, is
+
+really the rate of change of
+mole number, isn't it?
+
+It's moles of i disappearing,
+but the volume
+
+doesn't change, typically.
+
+And then the last thing is we
+can use this idea up here that
+
+concentration of products can
+only equal the loss rate of
+
+the reactant.
+
+So I can write, term by term,
+the normalized rate loss of
+
+the concentration of a divided
+by its stoichiometric
+
+coefficient, for example, would
+equal the normalized
+
+weight gain, or pardon me, the
+concentration gain of the
+
+concentration of d.
+
+So this is just saying a
+disappears no faster than d
+
+appears, mediated by the
+stoichiometric coefficients.
+
+So this is just Law of Mass
+Action, which is stoichiometry
+
+in motion, isn't it?
+
+That's all it is.
+
+Now here comes the cool
+thing kinetic theory.
+
+We look at any reaction, I can
+tell you right now what it
+
+looks like.
+
+If I applied concentration of
+i as a function of time, I
+
+start off with some value c
+naught, some initial value,
+
+and it just attenuates.
+
+We know that's going to happen
+as we consume the-- it falls
+
+and there's some
+curvature here.
+
+What we're trying to do next is
+to give some mathematical
+
+representation to this.
+
+Can we come up with a
+mathematical formulation of
+
+the shape of that curve?
+
+And we can, and here's
+the central
+
+tenet kinetic of theory.
+
+Kinetic theory says that the
+reaction rate can be expressed
+
+in terms of a driving force.
+
+And that driving force is the
+instant concentration.
+
+OK.
+
+These are lofty words.
+
+I'll show you what it means
+with illustration.
+
+So that's the overall idea.
+
+So now let's say that the rate
+of change, the instant rate of
+
+change of concentration ci, is
+proportional to the instant
+
+value of the concentration.
+
+And you know, the concentration
+
+is changing, right?
+
+As the concentration
+decreases, the
+
+rate of change decreases.
+
+So just this alone, this idea
+alone would rationalize a
+
+curve like that.
+
+As the concentration falls,
+the rate of change falls,
+
+which means the concentration
+falls, which means--
+
+and raised to some power--
+
+it's not linear, necessarily--
+
+raised to some power.
+
+There's a power law
+at work here.
+
+So now let's do this
+one more time.
+
+I'm going to write it
+mathematically.
+
+But I want you to first see
+the word, concepts.
+
+So let's write it
+mathematically.
+
+That means minus dci by dt--
+
+so this is time rate a change of
+concentration i, the minus
+
+means it's falling--
+
+is equal to the concentration
+of i raised to some power n.
+
+This is order reaction.
+
+It's not mole number
+over there.
+
+You've got to be pluralistic
+today.
+
+n is going to be used
+in different ways.
+
+So this is called order
+of reaction.
+
+And there's a constant.
+
+See up there?
+
+It's a proportionality.
+
+Here it's an equal sign,
+thanks to the constant.
+
+And this is called the
+rate constant.
+
+And this what all I need
+for plant design.
+
+Suppose I'm running a chemical
+plant and I'm taking a plus b
+
+and making c plus d and the
+management says, we want to
+
+double the rate of
+productivity.
+
+So you go, I know what to do.
+
+We'll increase the
+concentration.
+
+They say, by how much?
+
+Well, this allows you, if you
+know the value of k and n, you
+
+want to double this?
+
+Then you know what to do here.
+
+It's not necessarily double
+the concentration, Because
+
+this is a 1.5 power.
+
+By the way, this doesn't
+have to be an integer.
+
+Could be anything.
+
+Could be not necessarily integer
+and must be determined
+
+by experiment.
+
+You can't look at an equation
+and say, oh, that's going to
+
+be second order because
+there's a
+
+two in front of something.
+
+So here we are, plant
+designers.
+
+And the management wants
+to know, how do
+
+we make things happen?
+
+So I'm going to go back to that
+equation over there and
+
+I'll say that most generally,
+the rate of change of
+
+concentration of a will then go
+as rate constant times the
+
+concentration of a.
+
+See, the rate of change
+goes as something
+
+to the power alpha.
+
+But it could also be
+influenced by b.
+
+So I'm going to put-- this
+is the most general form.
+
+Then once you make your
+measurements, a lot
+
+of these fall out.
+
+I'm even going to put c
+I'm going to put d.
+
+Everything was in
+that equation.
+
+You might say, well,
+wait a minute.
+
+How can the rate of consumption
+of a be influenced
+
+by the concentration of d?
+
+d is a product.
+
+I'll give you two examples.
+
+One is that d, when I'm making
+d, d happens to have some
+
+catalytic value.
+
+So when I start making a convert
+to d, d catalyzes the
+
+reaction, which makes it go
+faster, which makes more d,
+
+which makes the reaction go
+faster, in which case this is
+
+going to have a profound
+effect.
+
+And unfortunately, there are
+some other situations where a
+
+converts to d and d retards
+the reaction.
+
+And so I start off with pretty
+decent conversion efficiency,
+
+but as I make more and more d,
+the d chokes the reaction, in
+
+which case the value here is
+going to have negative
+
+implications.
+
+So that's why you write it most
+generally, and then you
+
+go and you make some
+measurements in an experiment,
+
+and you figure out
+what these are.
+
+Some of them might be zeroes,
+and away you go.
+
+So I'll give you an
+example of one.
+
+Here's one.
+
+It's Monday after Halloween,
+so we'll get
+
+something kind of toxic.
+
+This was the manufacture of
+phosgene that was banned by
+
+international convention.
+
+It was used as one of the toxic
+gases for trench warfare
+
+in World War I.
+
+So it's made by the
+reaction of carbon
+
+monoxide and chlorine.
+
+COCL2.
+
+This is called phosgene.
+
+It's very bad stuff.
+
+I used it, actually,
+in my research.
+
+It has really good dehydration
+properties for salts.
+
+If you've got any moisture in
+potassium chloride, this'll go
+
+after it and turn the water into
+carbon dioxide and HCl.
+
+But you've got to be really,
+really careful with this.
+
+Gas leaks lead to a bad
+day at the lab.
+
+All right, this was banned.
+
+It's still use by tyrants
+throughout the world, and
+
+that's why we have international
+war tribunals.
+
+So here's the kinetics of it.
+
+Here's the kinetics of it.
+
+dc by dt.
+
+So this is the rate of
+consumption of carbon monoxide
+
+determined by experiment goes as
+the concentration of carbon
+
+monoxide and the concentration
+of chlorine raised
+
+to the power 3/2.
+
+So what I've done
+is mimic here.
+
+So in this case, gamma
+and delta are 0.
+
+Gamma equals delta equals 0, and
+it looks like beta equals
+
+1.5 and alpha equals 1.
+
+So I would say that this
+reaction is first order in
+
+carbon monoxide of order
+1.5 in chlorine, or
+
+overall, of order 2.5.
+
+Because, right?
+
+This is the order of reaction.
+
+This is c to the power
+1, isn't it?
+
+We don't write the 1.
+
+This is great.
+
+So we know, to increase the rate
+of reaction we increase
+
+the concentration.
+
+There's another way to increase
+the rate of reaction.
+
+What else can we do to increase
+the rate of reaction?
+
+Increase the temperature.
+
+Things go faster at higher
+temperatures.
+
+Again, how?
+
+How much?
+
+Suppose I said, I want to double
+the rate of reaction.
+
+Do I double the temperature?
+
+Do I raise the temperature
+by 10 degrees?
+
+How do I do that?
+
+So to increase rate of reaction,
+we can increase
+
+temperature.
+
+But how?
+
+And by the way, where
+is temperature here?
+
+I don't see temperature.
+
+I don't see temperature
+in this rate equation.
+
+You could say, well, if you
+increase the temperature
+
+you're going to increase
+the gas volume.
+
+But that's piddling
+effect, right?
+
+If I double the temperature,
+I double the gas volume.
+
+It doesn't change
+the mole number.
+
+The temperatures in here.
+
+That's where the temperature.
+
+Increase temperature,
+which then
+
+operates on the rate constant.
+
+That's the only place left
+in that formalism.
+
+But what's the quantitative
+value?
+
+Quantitative value was
+annunciated to us in 1889 by
+
+the Swedish chemist Arrhenius.
+
+And what Arrhenius found, he
+found that the rate constant
+
+varied with temperature in
+the following manner.
+
+Rate constant goes as the
+exponential of the ratio of
+
+minus some quantity call the
+activation energy e sub a--
+
+I'm going to tell you what
+that means in a minute--
+
+divided by the ratio of the
+product of the Boltzmann
+
+constant and temperature.
+
+And there's a constant of
+proportionality which we
+
+denote A in honor
+of Arrhenius.
+
+Or another way to write this
+is A times exponential--
+
+are you familiar with this?
+
+Instead of writing e to the
+something, if there's a messy
+
+argument up here you
+can write it exp.
+
+This is the same as this minus
+ea over the ratio of Boltzmann
+
+constant and temperature.
+
+So what's in here?
+
+What's in here?
+
+Boltzmann constant temperature,
+
+we've seen that already.
+
+What's the Boltzmann constant
+temperature product?
+
+That's the environment.
+
+That's the energy of
+the environment.
+
+So this is the final
+environment.
+
+And this thing up on top,
+ea, is a barrier.
+
+It's a barrier.
+
+Remember we saw the band gap?
+
+Same idea.
+
+Those ideas go all through
+physical chemistry.
+
+You got thermal energy that
+allows you to do this 10
+
+trillion times a second.
+
+Everybody in this room
+is doing this 10
+
+trillion times a second.
+
+That's what kT is.
+
+And then there's a
+barrier energy.
+
+Every once in a while
+something happens.
+
+Sometimes one in a million,
+sometimes one in a billion.
+
+Whatever.
+
+What Arrhenius found was this
+relationship, which means we
+
+could plot the variation
+of the rate constant.
+
+This is a mess, right?
+
+This is an exponential--
+
+look, the eye can only
+see straight lines.
+
+What if I show you this?
+
+What's that mean?
+
+I don't know.
+
+Is that first order?
+
+Second order?
+
+Is that Lagrangian?
+
+Is that exponential?
+
+I don't know.
+
+I know it's a curve.
+
+But what's this?
+
+I know what that is.
+
+And you know what that is.
+
+And you can tell goodness
+of fit.
+
+This is what science
+is all about.
+
+Forget all the other stuff.
+
+You know, all that UROP stuff.
+
+You're going to work in a
+lab and discover stuff.
+
+Forget that.
+
+This is what it's about.
+
+You got data.
+
+Data are all over the map.
+
+Here's the thing--
+
+I need to come up with some
+f function here versus a g
+
+function here that linearize
+my data.
+
+That's all science is about.
+
+And how do I get to f and g?
+
+Well, there's two ways.
+
+One is trial and error.
+
+The other way is physical
+understanding.
+
+And this is what Arrhenius
+taught us.
+
+Arrhenius taught us that the f
+function for how k varies with
+
+temperature, right?
+
+The problem, I'm trying
+to say, k versus t.
+
+That's what I'm trying to do.
+
+And if I plot k versus
+t I get a curve.
+
+No good.
+
+Instead, if I plot some f of
+k versus g of t, I get a
+
+straight line.
+
+And this is all science.
+
+So what's f of k?
+
+The natural logarithm
+of k, right?
+
+If I've got k equals a
+exponential, I take the
+
+natural log of this, and the
+natural log of an exponential
+
+is just the argument.
+
+And what's in the argument?
+
+What's the T function?
+
+1 over T.
+
+So if I plot the natural log of
+k versus the reciprocal of
+
+the absolute temperature, I get
+a straight line and its
+
+slope is minus ea, forgive me,
+minus ea over k-Boltzmann.
+
+Minus ea over k-Boltzmann.
+
+So now it's linearized and I can
+look at that and within an
+
+instant, anybody in this room
+can look at and say, the data
+
+conform or they don't.
+
+They don't.
+
+So now let's think about this.
+
+We say well, what's the
+value of this barrier?
+
+It's called activation energy.
+
+This barrier energy is called
+activation energy.
+
+ea is called the activation
+energy.
+
+And it typically, it varies,
+but it has values--
+
+just to give you a sense--
+about 1 electron volt.
+
+1 electron volt, which you
+know now is about 100
+
+kilojoules per mole, isn't it?
+
+I hear the chorus of yesses.
+
+1 electron volt.
+
+What is thermal energy?
+
+What's kT?
+
+kT at room temperature,
+k-Boltzmann at room
+
+temperature is about 1/40
+of an electron volt.
+
+Now, we are chemical machines.
+
+This conversation is occurring
+because all sorts of chemical
+
+processes are at work
+in me and you.
+
+And how's that happening?
+
+When all we've got to suck out
+of the environment is 1/40 of
+
+an electron volt and we need on
+the order one electron volt
+
+to drive certain processes.
+
+I guess we're all dead.
+
+Any ideas?
+
+Ay yay, yay.
+
+You guys need--
+
+what's that thing?
+
+You've got to call your
+lifeline or something?
+
+Come on.
+
+How does anything happen?
+
+How do we get--
+
+Why does anything happen
+in this world?
+
+Why should anything happen in a
+world with an environment of
+
+1/40 of an electron volt?
+
+AUDIENCE: Catalysts.
+
+PROFESSOR: Oh, catalysts.
+
+Catalysts.
+
+Yeah, yeah.
+
+I just went to the catalyst
+store and I got catalysts.
+
+Come on.
+
+AUDIENCE: Potential energy.
+
+PROFESSOR: Oh, potential
+energy.
+
+Jeez, this is good.
+
+Who can give me the
+wackiest answer?
+
+Can anybody give me
+the right answer?
+
+How come anything
+is happening?
+
+Over here.
+
+Again?
+
+AUDIENCE: Distribution
+of temperature.
+
+PROFESSOR: Thank you.
+
+Thank you.
+
+For a moment I thought
+we were all dead.
+
+At some level we were.
+
+So, yeah, it's
+Maxwell-Boltzmann.
+
+It's this, isn't it?
+
+And here's room temperature.
+
+And here is 1 electron volt.
+
+And this is it.
+
+And if you use this and you put
+it back to there, pretty
+
+soon you derive the Arrhenius
+equation.
+
+And if you increase
+the temperature
+
+you know what happens.
+
+After you increase the
+temperature, this.
+
+Time to use a hot
+color or chalk.
+
+So now this is T2
+greater than T1.
+
+That's what's going on.
+
+That's what's going on.
+
+So now what is this
+activation energy?
+
+What is the meaning of it?
+
+You know, I've told you there's
+a barrier energy.
+
+What does it mean?
+
+Well, you go to the textbook,
+you see goofy stuff like this.
+
+And this is not a slam
+against the textbook.
+
+This is a slam against all
+chemistry textbooks, because
+
+they all write this
+stupid stuff.
+
+You see? a plus b goes c plus
+d, the energy falls and you
+
+have to go over this
+activated complex.
+
+You memorize it, and I ask you
+to repeat, it and we leave the
+
+room and we think, wow, we
+know physical chemistry.
+
+There's nothing here.
+
+This is nothing.
+
+This is stupid.
+
+Now this is a little
+bit better.
+
+Can you see this?
+
+This is the Maxwell-Boltzmann.
+
+This is actually a beautiful
+graph up to a point.
+
+See the Maxwell-Boltzmann?
+
+Low temperature, high
+temperature.
+
+Only they've turned this
+thing on its side.
+
+See?
+
+And there's the energy
+you need to get over
+
+the activated complex.
+
+You see what's wrong
+with this graph?
+
+What's wrong with it?
+
+AUDIENCE: The product.
+
+PROFESSOR: Yeah, the product
+is at a higher
+
+level than the reactants.
+
+I looked at that and
+I thought, whoa!
+
+I guess you'll activate them,
+but they won't go anywhere.
+
+Anyway, so this is all stupid.
+
+What can we do?
+
+What can we do?
+
+So I decided to give you
+a mechanical analogy.
+
+So imagine this is
+the loudspeaker.
+
+Can you say the x?
+
+People in the back,
+can you see the x?
+
+Give me a thumbs up.
+
+Great eyes.
+
+All right.
+
+So what do we see here?
+
+The center of mass, I've
+indicated here.
+
+All right.
+
+So this is in a certain
+energy state.
+
+Let's get the right
+graph up there.
+
+This is awful.
+
+All right.
+
+So this is a plus b.
+
+Now this is c plus d.
+
+You see, the center
+of mass fell.
+
+It's lower.
+
+It's closer to the table
+than it is here.
+
+Can you see when I go like
+this, the photon goes?
+
+Watch this.
+
+Yeah, only I can see it.
+
+Your eyes don't go to that
+end of the spectrum.
+
+All right.
+
+But what's wrong with it?
+
+So why does the box
+not fall over?
+
+Why does it not fall over?
+
+We agreed that this is a lower
+energy state, and it is.
+
+You're correct.
+
+So why does the box manage to
+stay here and not fall over?
+
+AUDIENCE: [INAUDIBLE PHRASE]
+
+PROFESSOR: Exactly.
+
+This is the box at 0 Kelvin.
+
+Now we start raising the energy
+of the box, it starts
+
+doing this.
+
+Because above 0 Kelvin,
+it vibrates.
+
+The higher the temperature,
+the greater the vibration.
+
+But we're still in trouble here,
+you see, because you've
+
+only got 1/40 of an
+electron volt.
+
+So now we invoke distribution.
+
+I don't know what's happening
+with any box.
+
+Heisenberg tells me that.
+
+I don't know what's happening
+to any box.
+
+But if I take Avogadro's number
+of boxes I'll get this
+
+distribution.
+
+And some boxes will vibrate
+very little.
+
+And some boxes will
+vibrate a lot.
+
+And what's the critical
+level of vibration?
+
+It's to get to here.
+
+Because once it gets to here
+it's downhill all the way.
+
+And that would be the
+activation energy.
+
+And the fraction of boxes that
+get to the value of activation
+
+energy tip over and then I
+restore the distribution,
+
+because now this one's out of
+the game and now I distribute
+
+that energy over the
+remaining ones.
+
+And as I increase the
+temperature, the amplitude of
+
+the vibration increases, the
+average increases, the
+
+fraction in that red zone
+increases, and at some
+
+temperature it's so, so hot that
+they actually do this, in
+
+which case I have equilibrium.
+
+The two states are
+in equilibrium.
+
+So that's it.
+
+This is what's going on.
+
+So in three space, you can't go
+from here to here without
+
+going to here.
+
+You can try going this way so
+you-- no, you have to do this.
+
+It still has to be mechanically
+activated so we
+
+can show that this is what
+activation means.
+
+So we can plot--
+
+this deserves it's own board--
+
+so we will plot something
+like this.
+
+And now you'll see this.
+
+Sometimes they write
+this in the books.
+
+It's kind of goofy.
+
+But they write stuff
+like this.
+
+This is some kind of an
+energy coordinate.
+
+This is an energy coordinate.
+
+And this is called a reaction
+coordinate.
+
+OR sometimes they write
+extent of reaction.
+
+Again, some P-Chem term.
+
+They usually use Greek C just
+to make it lofty, but it's
+
+meaningless.
+
+And then so you write like
+this-- reactants here,
+
+products here, and this is
+exactly what we're seeing.
+
+What do we see?
+
+We see this.
+
+Here we have the box
+sitting like so.
+
+And then over here we have
+the box sitting like so.
+
+And right here we have
+the box up like so.
+
+And so now you have, here's
+the initial energy.
+
+This is the energy
+of the reactants.
+
+E of the reactants.
+
+This is E of the products.
+
+So then this distance
+here must be
+
+delta E of the reaction.
+
+And what's this?
+
+That's the activation energy.
+
+I have to come up with this;
+otherwise, I can't make the
+
+box fall over.
+
+So this is ea to go from here
+up onto the corner.
+
+And now you understand what
+all this stuff means.
+
+So that's here.
+
+And this is the activated
+complex.
+
+What's an activated complex?
+
+It's a box on its edge
+ready to fall over.
+
+That's what it is.
+
+All right.
+
+I think we're out of time, so
+let's cut to the end here.
+
+What've we got.
+
+Oh, just some plots.
+
+We'll get to that next day.
+
+All right.
+
+So I want to show
+you a little bit
+
+about first-order reactions.
+
+This is radiocarbon dating.
+
+n equals 1.
+
+And strictly speaking, this is
+not a chemical reaction, but
+
+it is first order.
+
+So I'll lump it in here.
+
+So this is a nuclear reaction.
+
+And what happens in the
+upper atmosphere?
+
+Radioactive carbon produced by
+cosmic rays, which generate
+
+neutrons in the upper atmosphere
+and then those
+
+neutrons attack nitrogen
+to make carbon 14.
+
+That's the radioactive
+form of carbon.
+
+Remember?
+
+It's present in one part per
+trillion, if you look on your
+
+Periodic Table for
+the isotopes.
+
+Now carbon 14 enters
+the carbon cycle.
+
+And so in all of us and in all
+living organisms the ratio of
+
+carbon 14 to carbon 12 is
+one part per trillion.
+
+And carbon 13 is also present.
+
+I don't know.
+
+What is it?
+
+1 point something percent?
+
+The thing is, the carbon
+14 is radioactive.
+
+And it decays.
+
+Like this.
+
+But what happens after
+somebody dies?
+
+Well, they stop exchanging
+nutrients with the
+
+surroundings.
+
+They stop breathing, so their
+carbon level is pegged as it
+
+was at the time of death.
+
+And now it's a one0way street.
+
+It's just carbon decay.
+
+And it turns out you can measure
+the ratio of carbon 14
+
+to carbon 12 to determine the
+age, which is given by 5,730
+
+years, which is the inverse
+of the rate constant.
+
+Now, you can't use this for
+crime scene investigations,
+
+but certainly you can start
+dating things hundreds of
+
+years old, not hundreds
+of minutes old.
+
+So there's a whole bunch of
+other things that can be used,
+
+not just carbon.
+
+So this is radiochemical
+dating.
+
+And these are used in trying to
+nail down art forgeries and
+
+all sorts of things.
+
+All right.
+
+So here, you can see these.
+
+These have all been
+radiocarbon dated.
+
+You know, the Dead Sea Scrolls
+were radiocarbon dated and
+
+they look like they're from
+about 2,000 years ago.
+
+Makes sense.
+
+You go out over here.
+
+They they found these Indian
+sandals from Oregon, and then
+
+they looked on an electron
+microscope, and they found
+
+something on the sandals that
+looks a little bit like that.
+
+That's a Nike swoosh.
+
+I don't know.
+
+You people are so--
+
+All right.
+
+So now I want to show you
+the Shroud of Turin.
+
+The Shroud of Turin, as you may
+know, for a long time was
+
+reputed to be the burial shroud
+of Jesus Christ. And
+
+this is taken from the National
+Geographic back in
+
+the late '80s.
+
+Back in the late '80s, they
+did a major study on it.
+
+So this is the artist rendition
+of how the shroud
+
+might have been wrapped
+around a body.
+
+The question is, what's
+the date of this?
+
+So we can use radiocarbon
+dating.
+
+And so here's the formation
+of carbon 14.
+
+Carbon 14 exchanges with
+carbon 12 in flax.
+
+So it's got one part
+per trillion.
+
+When the flax is harvested the
+carbon 14 starts to decay.
+
+And then we look at
+the weaving of the
+
+shroud and so on.
+
+And they had three different
+labs, they took samples from
+
+the shroud.
+
+And they concluded
+that the shroud
+
+dates from this period--
+
+1260 to 1390.
+
+And the first time it was
+mentioned in the literature
+
+was around 1354.
+
+So everything seems to make
+sense that this is not the
+
+burial shroud of Jesus Christ.
+It's something that has
+
+importance to certain members of
+the Roman Church, but it's
+
+scientifically not.
+
+You know, this stirs up
+a lot of passion.
+
+So people started saying,
+wait a minute.
+
+Wait a minute.
+
+There was a fire in 1532 and
+people repaired the shroud and
+
+they were using candlelight
+and maybe the paraffin and
+
+mold and so on covered
+the fibers.
+
+So now, are we looking at
+the surface effect?
+
+How do we know what
+really happened?
+
+The only way to know is to take
+the whole shroud, put in
+
+a big Cuisinart and break
+open the interior.
+
+Well, in point of fact, what
+they did was take fibers and
+
+look inside.
+
+And I think as of the late '90s,
+the Roman Church says,
+
+it's not the burial shroud
+of Jesus, but it is
+
+an object of reverence.
+
+And I think it's a good
+example of how science
+
+sometimes comes up against
+spirituality, and we have to
+
+be careful how we handle it.
+
+It's a delicate matter.
\ No newline at end of file
diff --git a/dTGVt1enLlc.txt b/dTGVt1enLlc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6707c27c87907572020d58cd1acea107bc2395a4
--- /dev/null
+++ b/dTGVt1enLlc.txt
@@ -0,0 +1,4875 @@
+align:start position:0%
+ 
+oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+anna jason
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+she's a nutritionist from mit magical
+
+ align:start position:0%
+she's a nutritionist from mit magical
+ 
+
+ align:start position:0%
+she's a nutritionist from mit magical
+wow and she also has the origins
+
+ align:start position:0%
+wow and she also has the origins
+ 
+
+ align:start position:0%
+wow and she also has the origins
+wow
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+can you say that again
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so i'm going to
+
+ align:start position:0%
+okay so i'm going to
+ 
+
+ align:start position:0%
+okay so i'm going to
+talk about mediterranean diet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you can get the sequel okay what is
+
+ align:start position:0%
+so you can get the sequel okay what is
+ 
+
+ align:start position:0%
+so you can get the sequel okay what is
+it
+
+ align:start position:0%
+it
+ 
+
+ align:start position:0%
+it
+what is this mediterranean diet that you
+
+ align:start position:0%
+what is this mediterranean diet that you
+ 
+
+ align:start position:0%
+what is this mediterranean diet that you
+hear so much about okay so there's no
+
+ align:start position:0%
+hear so much about okay so there's no
+ 
+
+ align:start position:0%
+hear so much about okay so there's no
+one particular official mediterranean
+
+ align:start position:0%
+one particular official mediterranean
+ 
+
+ align:start position:0%
+one particular official mediterranean
+diet people think it is but it's not
+
+ align:start position:0%
+diet people think it is but it's not
+ 
+
+ align:start position:0%
+diet people think it is but it's not
+it's really a food pattern that is
+
+ align:start position:0%
+it's really a food pattern that is
+ 
+
+ align:start position:0%
+it's really a food pattern that is
+shared by countries that room the
+
+ align:start position:0%
+shared by countries that room the
+ 
+
+ align:start position:0%
+shared by countries that room the
+mediterranean sea and you could put more
+
+ align:start position:0%
+mediterranean sea and you could put more
+ 
+
+ align:start position:0%
+mediterranean sea and you could put more
+countries here i didn't go crazy um you
+
+ align:start position:0%
+countries here i didn't go crazy um you
+ 
+
+ align:start position:0%
+countries here i didn't go crazy um you
+know you could add cyprus and you could
+
+ align:start position:0%
+know you could add cyprus and you could
+ 
+
+ align:start position:0%
+know you could add cyprus and you could
+add it i don't know if that's not a
+
+ align:start position:0%
+add it i don't know if that's not a
+ 
+
+ align:start position:0%
+add it i don't know if that's not a
+country but
+
+ align:start position:0%
+country but
+ 
+
+ align:start position:0%
+country but
+it's a region i'll say region so that's
+
+ align:start position:0%
+it's a region i'll say region so that's
+ 
+
+ align:start position:0%
+it's a region i'll say region so that's
+what we consider to be mediterranean
+
+ align:start position:0%
+what we consider to be mediterranean
+ 
+
+ align:start position:0%
+what we consider to be mediterranean
+that i'm going to get into the more
+
+ align:start position:0%
+that i'm going to get into the more
+ 
+
+ align:start position:0%
+that i'm going to get into the more
+specifics later
+
+ align:start position:0%
+specifics later
+ 
+
+ align:start position:0%
+specifics later
+long time ago 1958 ansel keys organized
+
+ align:start position:0%
+long time ago 1958 ansel keys organized
+ 
+
+ align:start position:0%
+long time ago 1958 ansel keys organized
+a seven-country study and those were the
+
+ align:start position:0%
+a seven-country study and those were the
+ 
+
+ align:start position:0%
+a seven-country study and those were the
+countries that were in his study and he
+
+ align:start position:0%
+countries that were in his study and he
+ 
+
+ align:start position:0%
+countries that were in his study and he
+had a hypothesis that
+
+ align:start position:0%
+had a hypothesis that
+ 
+
+ align:start position:0%
+had a hypothesis that
+a diet was very related to heart disease
+
+ align:start position:0%
+a diet was very related to heart disease
+ 
+
+ align:start position:0%
+a diet was very related to heart disease
+so he studied this for decades and then
+
+ align:start position:0%
+so he studied this for decades and then
+ 
+
+ align:start position:0%
+so he studied this for decades and then
+it did show that there was a lower
+
+ align:start position:0%
+it did show that there was a lower
+ 
+
+ align:start position:0%
+it did show that there was a lower
+prevalence of hypercholesterolemia
+
+ align:start position:0%
+prevalence of hypercholesterolemia
+ 
+
+ align:start position:0%
+prevalence of hypercholesterolemia
+that's high blood cholesterol and heart
+
+ align:start position:0%
+that's high blood cholesterol and heart
+ 
+
+ align:start position:0%
+that's high blood cholesterol and heart
+disease in populations of greece and
+
+ align:start position:0%
+disease in populations of greece and
+ 
+
+ align:start position:0%
+disease in populations of greece and
+italy especially greek island of crete
+
+ align:start position:0%
+italy especially greek island of crete
+ 
+
+ align:start position:0%
+italy especially greek island of crete
+and he attributed that to diet
+
+ align:start position:0%
+and he attributed that to diet
+ 
+
+ align:start position:0%
+and he attributed that to diet
+the cretins had like a 90
+
+ align:start position:0%
+the cretins had like a 90
+ 
+
+ align:start position:0%
+the cretins had like a 90
+less
+
+ align:start position:0%
+less
+ 
+
+ align:start position:0%
+less
+heart attack or heart
+
+ align:start position:0%
+heart attack or heart
+ 
+
+ align:start position:0%
+heart attack or heart
+problems which is huge huge yeah so he
+
+ align:start position:0%
+problems which is huge huge yeah so he
+ 
+
+ align:start position:0%
+problems which is huge huge yeah so he
+thought oh it's their diet and what
+
+ align:start position:0%
+thought oh it's their diet and what
+ 
+
+ align:start position:0%
+thought oh it's their diet and what
+about their diet um he thought it was
+
+ align:start position:0%
+about their diet um he thought it was
+ 
+
+ align:start position:0%
+about their diet um he thought it was
+the fact yeah since then right there
+
+ align:start position:0%
+the fact yeah since then right there
+ 
+
+ align:start position:0%
+the fact yeah since then right there
+have been many more studies that have
+
+ align:start position:0%
+have been many more studies that have
+ 
+
+ align:start position:0%
+have been many more studies that have
+looked at this hypothesis we had the
+
+ align:start position:0%
+looked at this hypothesis we had the
+ 
+
+ align:start position:0%
+looked at this hypothesis we had the
+framingham heart study which was done
+
+ align:start position:0%
+framingham heart study which was done
+ 
+
+ align:start position:0%
+framingham heart study which was done
+here in massachusetts nurses health
+
+ align:start position:0%
+here in massachusetts nurses health
+ 
+
+ align:start position:0%
+here in massachusetts nurses health
+study i think that was still going on
+
+ align:start position:0%
+study i think that was still going on
+ 
+
+ align:start position:0%
+study i think that was still going on
+women's health initiative the
+
+ align:start position:0%
+women's health initiative the
+ 
+
+ align:start position:0%
+women's health initiative the
+conclusions and the discussion from all
+
+ align:start position:0%
+conclusions and the discussion from all
+ 
+
+ align:start position:0%
+conclusions and the discussion from all
+the studies in the papers
+
+ align:start position:0%
+the studies in the papers
+ 
+
+ align:start position:0%
+the studies in the papers
+are that plants plant fats
+
+ align:start position:0%
+are that plants plant fats
+ 
+
+ align:start position:0%
+are that plants plant fats
+yield better cardiovascular health than
+
+ align:start position:0%
+yield better cardiovascular health than
+ 
+
+ align:start position:0%
+yield better cardiovascular health than
+animal fats so it's the same thing
+
+ align:start position:0%
+animal fats so it's the same thing
+ 
+
+ align:start position:0%
+animal fats so it's the same thing
+that ansel keys discover to say that
+
+ align:start position:0%
+that ansel keys discover to say that
+ 
+
+ align:start position:0%
+that ansel keys discover to say that
+animal fats in the abundance that
+
+ align:start position:0%
+animal fats in the abundance that
+ 
+
+ align:start position:0%
+animal fats in the abundance that
+americans ate them not a good thing
+
+ align:start position:0%
+americans ate them not a good thing
+ 
+
+ align:start position:0%
+americans ate them not a good thing
+as i was looking at all the studies you
+
+ align:start position:0%
+as i was looking at all the studies you
+ 
+
+ align:start position:0%
+as i was looking at all the studies you
+know preparing for this
+
+ align:start position:0%
+know preparing for this
+ 
+
+ align:start position:0%
+know preparing for this
+i was amazed
+
+ align:start position:0%
+i was amazed
+ 
+
+ align:start position:0%
+i was amazed
+that i was amazed that
+
+ align:start position:0%
+that i was amazed that
+ 
+
+ align:start position:0%
+that i was amazed that
+hundreds and hundreds and hundreds of
+
+ align:start position:0%
+hundreds and hundreds and hundreds of
+ 
+
+ align:start position:0%
+hundreds and hundreds and hundreds of
+studies not one of them said oh
+
+ align:start position:0%
+studies not one of them said oh
+ 
+
+ align:start position:0%
+studies not one of them said oh
+my mediterranean diet is not good
+
+ align:start position:0%
+my mediterranean diet is not good
+ 
+
+ align:start position:0%
+my mediterranean diet is not good
+since 204 i looked at 13 studies
+
+ align:start position:0%
+since 204 i looked at 13 studies
+ 
+
+ align:start position:0%
+since 204 i looked at 13 studies
+there is strong evidence and these are
+
+ align:start position:0%
+there is strong evidence and these are
+ 
+
+ align:start position:0%
+there is strong evidence and these are
+from the studies themselves the kaboom
+
+ align:start position:0%
+from the studies themselves the kaboom
+ 
+
+ align:start position:0%
+from the studies themselves the kaboom
+the researcher's conclusion strong
+
+ align:start position:0%
+the researcher's conclusion strong
+ 
+
+ align:start position:0%
+the researcher's conclusion strong
+evidence that replacing saturated fats
+
+ align:start position:0%
+evidence that replacing saturated fats
+ 
+
+ align:start position:0%
+evidence that replacing saturated fats
+with monounsaturated fats is associated
+
+ align:start position:0%
+with monounsaturated fats is associated
+ 
+
+ align:start position:0%
+with monounsaturated fats is associated
+with reducing cardiovascular mortalities
+
+ align:start position:0%
+with reducing cardiovascular mortalities
+ 
+
+ align:start position:0%
+with reducing cardiovascular mortalities
+or illnesses around heart disease and
+
+ align:start position:0%
+or illnesses around heart disease and
+ 
+
+ align:start position:0%
+or illnesses around heart disease and
+how does it do that how how does
+
+ align:start position:0%
+how does it do that how how does
+ 
+
+ align:start position:0%
+how does it do that how how does
+the switching of the fats
+
+ align:start position:0%
+the switching of the fats
+ 
+
+ align:start position:0%
+the switching of the fats
+reducing bad cholesterol that's ldl
+
+ align:start position:0%
+reducing bad cholesterol that's ldl
+ 
+
+ align:start position:0%
+reducing bad cholesterol that's ldl
+cholesterol decreasing blood
+
+ align:start position:0%
+cholesterol decreasing blood
+ 
+
+ align:start position:0%
+cholesterol decreasing blood
+triglycerides and reducing inflammation
+
+ align:start position:0%
+triglycerides and reducing inflammation
+ 
+
+ align:start position:0%
+triglycerides and reducing inflammation
+those are some of the mechanisms that
+
+ align:start position:0%
+those are some of the mechanisms that
+ 
+
+ align:start position:0%
+those are some of the mechanisms that
+help
+
+ align:start position:0%
+help
+ 
+
+ align:start position:0%
+help
+reduce cardiovascular risk
+
+ align:start position:0%
+reduce cardiovascular risk
+ 
+
+ align:start position:0%
+reduce cardiovascular risk
+and also more recently you know diabetes
+
+ align:start position:0%
+and also more recently you know diabetes
+ 
+
+ align:start position:0%
+and also more recently you know diabetes
+has really become the prevalence in
+
+ align:start position:0%
+has really become the prevalence in
+ 
+
+ align:start position:0%
+has really become the prevalence in
+america and the world
+
+ align:start position:0%
+america and the world
+ 
+
+ align:start position:0%
+america and the world
+strong evidence that monounsaturated
+
+ align:start position:0%
+strong evidence that monounsaturated
+ 
+
+ align:start position:0%
+strong evidence that monounsaturated
+fatty acids
+
+ align:start position:0%
+fatty acids
+ 
+
+ align:start position:0%
+fatty acids
+are associated with improving type 2
+
+ align:start position:0%
+are associated with improving type 2
+ 
+
+ align:start position:0%
+are associated with improving type 2
+diabetes it makes people less insulin
+
+ align:start position:0%
+diabetes it makes people less insulin
+ 
+
+ align:start position:0%
+diabetes it makes people less insulin
+systems so there's
+
+ align:start position:0%
+systems so there's
+ 
+
+ align:start position:0%
+systems so there's
+more health benefits
+
+ align:start position:0%
+more health benefits
+ 
+
+ align:start position:0%
+more health benefits
+it's not just cardiovascular health
+
+ align:start position:0%
+it's not just cardiovascular health
+ 
+
+ align:start position:0%
+it's not just cardiovascular health
+mediterranean diet
+
+ align:start position:0%
+mediterranean diet
+ 
+
+ align:start position:0%
+mediterranean diet
+has been
+
+ align:start position:0%
+has been
+ 
+
+ align:start position:0%
+has been
+reducing alzheimer's it's been shown to
+
+ align:start position:0%
+reducing alzheimer's it's been shown to
+ 
+
+ align:start position:0%
+reducing alzheimer's it's been shown to
+reduce parkinson's disease
+
+ align:start position:0%
+reduce parkinson's disease
+ 
+
+ align:start position:0%
+reduce parkinson's disease
+reduce the risk of depression reduce the
+
+ align:start position:0%
+reduce the risk of depression reduce the
+ 
+
+ align:start position:0%
+reduce the risk of depression reduce the
+risk of diabetes studies to show that
+
+ align:start position:0%
+risk of diabetes studies to show that
+ 
+
+ align:start position:0%
+risk of diabetes studies to show that
+mediterranean diet improves brain
+
+ align:start position:0%
+mediterranean diet improves brain
+ 
+
+ align:start position:0%
+mediterranean diet improves brain
+cognition so you think better which is
+
+ align:start position:0%
+cognition so you think better which is
+ 
+
+ align:start position:0%
+cognition so you think better which is
+good you remember things better so
+
+ align:start position:0%
+good you remember things better so
+ 
+
+ align:start position:0%
+good you remember things better so
+participating to the seminars yeah
+
+ align:start position:0%
+participating to the seminars yeah
+ 
+
+ align:start position:0%
+participating to the seminars yeah
+you're gonna be smarter tomorrow
+
+ align:start position:0%
+you're gonna be smarter tomorrow
+ 
+
+ align:start position:0%
+you're gonna be smarter tomorrow
+mediterranean diet has been shown to
+
+ align:start position:0%
+mediterranean diet has been shown to
+ 
+
+ align:start position:0%
+mediterranean diet has been shown to
+protect against some cancer's breasts
+
+ align:start position:0%
+protect against some cancer's breasts
+ 
+
+ align:start position:0%
+protect against some cancer's breasts
+and that should say prostate oh my god i
+
+ align:start position:0%
+and that should say prostate oh my god i
+ 
+
+ align:start position:0%
+and that should say prostate oh my god i
+said free state see what happens with
+
+ align:start position:0%
+said free state see what happens with
+ 
+
+ align:start position:0%
+said free state see what happens with
+spell check yeah okay
+
+ align:start position:0%
+spell check yeah okay
+ 
+
+ align:start position:0%
+spell check yeah okay
+so yeah um and living longer which is
+
+ align:start position:0%
+so yeah um and living longer which is
+ 
+
+ align:start position:0%
+so yeah um and living longer which is
+amazing there was one study that said
+
+ align:start position:0%
+amazing there was one study that said
+ 
+
+ align:start position:0%
+amazing there was one study that said
+people who follow meditate you know live
+
+ align:start position:0%
+people who follow meditate you know live
+ 
+
+ align:start position:0%
+people who follow meditate you know live
+like three years longer so
+
+ align:start position:0%
+like three years longer so
+ 
+
+ align:start position:0%
+like three years longer so
+oh and weight loss
+
+ align:start position:0%
+oh and weight loss
+ 
+
+ align:start position:0%
+oh and weight loss
+yeah weight management people who follow
+
+ align:start position:0%
+yeah weight management people who follow
+ 
+
+ align:start position:0%
+yeah weight management people who follow
+a more mediterranean style can be more
+
+ align:start position:0%
+a more mediterranean style can be more
+ 
+
+ align:start position:0%
+a more mediterranean style can be more
+successful at managing their weight than
+
+ align:start position:0%
+successful at managing their weight than
+ 
+
+ align:start position:0%
+successful at managing their weight than
+a low fat diet for instance
+
+ align:start position:0%
+a low fat diet for instance
+ 
+
+ align:start position:0%
+a low fat diet for instance
+okay so this is just a study just to
+
+ align:start position:0%
+okay so this is just a study just to
+ 
+
+ align:start position:0%
+okay so this is just a study just to
+show you that they there are hundreds of
+
+ align:start position:0%
+show you that they there are hundreds of
+ 
+
+ align:start position:0%
+show you that they there are hundreds of
+them that exist this is uh from
+
+ align:start position:0%
+them that exist this is uh from
+ 
+
+ align:start position:0%
+them that exist this is uh from
+nutrition journal it's recent
+
+ align:start position:0%
+nutrition journal it's recent
+ 
+
+ align:start position:0%
+nutrition journal it's recent
+people were following a mediterranean
+
+ align:start position:0%
+people were following a mediterranean
+ 
+
+ align:start position:0%
+people were following a mediterranean
+diet the people that found that followed
+
+ align:start position:0%
+diet the people that found that followed
+ 
+
+ align:start position:0%
+diet the people that found that followed
+the mediterranean diet more had less
+
+ align:start position:0%
+the mediterranean diet more had less
+ 
+
+ align:start position:0%
+the mediterranean diet more had less
+inflammation which is involved in
+
+ align:start position:0%
+inflammation which is involved in
+ 
+
+ align:start position:0%
+inflammation which is involved in
+disease
+
+ align:start position:0%
+disease
+ 
+
+ align:start position:0%
+disease
+reduce oxidative stress you know the
+
+ align:start position:0%
+reduce oxidative stress you know the
+ 
+
+ align:start position:0%
+reduce oxidative stress you know the
+free radicals higher circulating levels
+
+ align:start position:0%
+free radicals higher circulating levels
+ 
+
+ align:start position:0%
+free radicals higher circulating levels
+of antioxidants all which are associated
+
+ align:start position:0%
+of antioxidants all which are associated
+ 
+
+ align:start position:0%
+of antioxidants all which are associated
+with reduced risk of disease in general
+
+ align:start position:0%
+with reduced risk of disease in general
+ 
+
+ align:start position:0%
+with reduced risk of disease in general
+so that's one study with the mid diet
+
+ align:start position:0%
+so that's one study with the mid diet
+ 
+
+ align:start position:0%
+so that's one study with the mid diet
+here's the prostate cancer
+
+ align:start position:0%
+here's the prostate cancer
+ 
+
+ align:start position:0%
+here's the prostate cancer
+this was done in spain
+
+ align:start position:0%
+this was done in spain
+ 
+
+ align:start position:0%
+this was done in spain
+they looked at meta-analysis and they
+
+ align:start position:0%
+they looked at meta-analysis and they
+ 
+
+ align:start position:0%
+they looked at meta-analysis and they
+looked at a lot of studies and said here
+
+ align:start position:0%
+looked at a lot of studies and said here
+ 
+
+ align:start position:0%
+looked at a lot of studies and said here
+that they cited several characteristics
+
+ align:start position:0%
+that they cited several characteristics
+ 
+
+ align:start position:0%
+that they cited several characteristics
+of meta diet including highly data
+
+ align:start position:0%
+of meta diet including highly data
+ 
+
+ align:start position:0%
+of meta diet including highly data
+consumption of fruits vegetables grains
+
+ align:start position:0%
+consumption of fruits vegetables grains
+ 
+
+ align:start position:0%
+consumption of fruits vegetables grains
+tubers legumes olive oil is the main
+
+ align:start position:0%
+tubers legumes olive oil is the main
+ 
+
+ align:start position:0%
+tubers legumes olive oil is the main
+source of fats
+
+ align:start position:0%
+source of fats
+ 
+
+ align:start position:0%
+source of fats
+low intake of animal products
+
+ align:start position:0%
+low intake of animal products
+ 
+
+ align:start position:0%
+low intake of animal products
+and regular consumption of small fish so
+
+ align:start position:0%
+and regular consumption of small fish so
+ 
+
+ align:start position:0%
+and regular consumption of small fish so
+another study
+
+ align:start position:0%
+another study
+ 
+
+ align:start position:0%
+another study
+eating a diet with omega-3 fatty acids
+
+ align:start position:0%
+eating a diet with omega-3 fatty acids
+ 
+
+ align:start position:0%
+eating a diet with omega-3 fatty acids
+can improve insulin sensitivity and
+
+ align:start position:0%
+can improve insulin sensitivity and
+ 
+
+ align:start position:0%
+can improve insulin sensitivity and
+that's got to do with diabetes again
+
+ align:start position:0%
+that's got to do with diabetes again
+ 
+
+ align:start position:0%
+that's got to do with diabetes again
+here's another study adherence to
+
+ align:start position:0%
+here's another study adherence to
+ 
+
+ align:start position:0%
+here's another study adherence to
+mediterranean diet is associated with
+
+ align:start position:0%
+mediterranean diet is associated with
+ 
+
+ align:start position:0%
+mediterranean diet is associated with
+the risk of diabetes separate from the
+
+ align:start position:0%
+the risk of diabetes separate from the
+ 
+
+ align:start position:0%
+the risk of diabetes separate from the
+insulin eating a mediterranean-style
+
+ align:start position:0%
+insulin eating a mediterranean-style
+ 
+
+ align:start position:0%
+insulin eating a mediterranean-style
+diet rich in olive oil whole grains fish
+
+ align:start position:0%
+diet rich in olive oil whole grains fish
+ 
+
+ align:start position:0%
+diet rich in olive oil whole grains fish
+fruit may protect aging brains from
+
+ align:start position:0%
+fruit may protect aging brains from
+ 
+
+ align:start position:0%
+fruit may protect aging brains from
+damage associated with cognitive
+
+ align:start position:0%
+damage associated with cognitive
+ 
+
+ align:start position:0%
+damage associated with cognitive
+problems
+
+ align:start position:0%
+problems
+ 
+
+ align:start position:0%
+problems
+and so here's just a quick excerpt after
+
+ align:start position:0%
+and so here's just a quick excerpt after
+ 
+
+ align:start position:0%
+and so here's just a quick excerpt after
+reviewing the brain mris
+
+ align:start position:0%
+reviewing the brain mris
+ 
+
+ align:start position:0%
+reviewing the brain mris
+of the older people they found that
+
+ align:start position:0%
+of the older people they found that
+ 
+
+ align:start position:0%
+of the older people they found that
+people who followed the mediterranean
+
+ align:start position:0%
+people who followed the mediterranean
+ 
+
+ align:start position:0%
+people who followed the mediterranean
+diet more closely were up to 36 percent
+
+ align:start position:0%
+diet more closely were up to 36 percent
+ 
+
+ align:start position:0%
+diet more closely were up to 36 percent
+less likely to show brand damages
+
+ align:start position:0%
+less likely to show brand damages
+ 
+
+ align:start position:0%
+less likely to show brand damages
+here's another study
+
+ align:start position:0%
+here's another study
+ 
+
+ align:start position:0%
+here's another study
+from neurology and they're recent so
+
+ align:start position:0%
+from neurology and they're recent so
+ 
+
+ align:start position:0%
+from neurology and they're recent so
+again this was protecting against
+
+ align:start position:0%
+again this was protecting against
+ 
+
+ align:start position:0%
+again this was protecting against
+strokes
+
+ align:start position:0%
+strokes
+ 
+
+ align:start position:0%
+strokes
+so what is it about this mediterranean
+
+ align:start position:0%
+so what is it about this mediterranean
+ 
+
+ align:start position:0%
+so what is it about this mediterranean
+diet that can do it sounds like a
+
+ align:start position:0%
+diet that can do it sounds like a
+ 
+
+ align:start position:0%
+diet that can do it sounds like a
+miracle diet so the first thing the
+
+ align:start position:0%
+miracle diet so the first thing the
+ 
+
+ align:start position:0%
+miracle diet so the first thing the
+first big characteristic and i think
+
+ align:start position:0%
+first big characteristic and i think
+ 
+
+ align:start position:0%
+first big characteristic and i think
+everybody knows is the fact that the fat
+
+ align:start position:0%
+everybody knows is the fact that the fat
+ 
+
+ align:start position:0%
+everybody knows is the fact that the fat
+source is different in the mediterranean
+
+ align:start position:0%
+source is different in the mediterranean
+ 
+
+ align:start position:0%
+source is different in the mediterranean
+compared to us and western diets and it
+
+ align:start position:0%
+compared to us and western diets and it
+ 
+
+ align:start position:0%
+compared to us and western diets and it
+is olive oil and it's lots of olive oil
+
+ align:start position:0%
+is olive oil and it's lots of olive oil
+ 
+
+ align:start position:0%
+is olive oil and it's lots of olive oil
+mediterranean diets can be up to 40
+
+ align:start position:0%
+mediterranean diets can be up to 40
+ 
+
+ align:start position:0%
+mediterranean diets can be up to 40
+50 calories from fat
+
+ align:start position:0%
+50 calories from fat
+ 
+
+ align:start position:0%
+50 calories from fat
+so it's a lot of fat that's not a
+
+ align:start position:0%
+so it's a lot of fat that's not a
+ 
+
+ align:start position:0%
+so it's a lot of fat that's not a
+low-fat diet but they're not fat you see
+
+ align:start position:0%
+low-fat diet but they're not fat you see
+ 
+
+ align:start position:0%
+low-fat diet but they're not fat you see
+so fat doesn't make you fat the big
+
+ align:start position:0%
+so fat doesn't make you fat the big
+ 
+
+ align:start position:0%
+so fat doesn't make you fat the big
+characteristic here and what ansel keys
+
+ align:start position:0%
+characteristic here and what ansel keys
+ 
+
+ align:start position:0%
+characteristic here and what ansel keys
+discovered
+
+ align:start position:0%
+discovered
+ 
+
+ align:start position:0%
+discovered
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+that or what his hypothesis was that it
+
+ align:start position:0%
+that or what his hypothesis was that it
+ 
+
+ align:start position:0%
+that or what his hypothesis was that it
+was
+
+ align:start position:0%
+was
+ 
+
+ align:start position:0%
+was
+this kind of fat that had healthy
+
+ align:start position:0%
+this kind of fat that had healthy
+ 
+
+ align:start position:0%
+this kind of fat that had healthy
+benefits
+
+ align:start position:0%
+benefits
+ 
+
+ align:start position:0%
+benefits
+and just so you know that's an omega
+
+ align:start position:0%
+and just so you know that's an omega
+ 
+
+ align:start position:0%
+and just so you know that's an omega
+omega-9
+
+ align:start position:0%
+omega-9
+ 
+
+ align:start position:0%
+omega-9
+and i can also tell you that's pretty
+
+ align:start position:0%
+and i can also tell you that's pretty
+ 
+
+ align:start position:0%
+and i can also tell you that's pretty
+small but i just wanted to remind myself
+
+ align:start position:0%
+small but i just wanted to remind myself
+ 
+
+ align:start position:0%
+small but i just wanted to remind myself
+there's there's many other compounds in
+
+ align:start position:0%
+there's there's many other compounds in
+ 
+
+ align:start position:0%
+there's there's many other compounds in
+olive oil
+
+ align:start position:0%
+olive oil
+ 
+
+ align:start position:0%
+olive oil
+think of olive oil as like a fresh fruit
+
+ align:start position:0%
+think of olive oil as like a fresh fruit
+ 
+
+ align:start position:0%
+think of olive oil as like a fresh fruit
+nectar this is not an
+
+ align:start position:0%
+nectar this is not an
+ 
+
+ align:start position:0%
+nectar this is not an
+an oil that has been highly processed to
+
+ align:start position:0%
+an oil that has been highly processed to
+ 
+
+ align:start position:0%
+an oil that has been highly processed to
+get its fat like sesames and soy and
+
+ align:start position:0%
+get its fat like sesames and soy and
+ 
+
+ align:start position:0%
+get its fat like sesames and soy and
+those are made differently this is just
+
+ align:start position:0%
+those are made differently this is just
+ 
+
+ align:start position:0%
+those are made differently this is just
+the fruit and i have to mechanically get
+
+ align:start position:0%
+the fruit and i have to mechanically get
+ 
+
+ align:start position:0%
+the fruit and i have to mechanically get
+it out it's not with chemicals it
+
+ align:start position:0%
+it out it's not with chemicals it
+ 
+
+ align:start position:0%
+it out it's not with chemicals it
+shouldn't be anyone
+
+ align:start position:0%
+shouldn't be anyone
+ 
+
+ align:start position:0%
+shouldn't be anyone
+but so it's so it's got a lot of fresh
+
+ align:start position:0%
+but so it's so it's got a lot of fresh
+ 
+
+ align:start position:0%
+but so it's so it's got a lot of fresh
+compounds in there the fresher the
+
+ align:start position:0%
+compounds in there the fresher the
+ 
+
+ align:start position:0%
+compounds in there the fresher the
+better there were studies that say if
+
+ align:start position:0%
+better there were studies that say if
+ 
+
+ align:start position:0%
+better there were studies that say if
+you have fresh olive oil
+
+ align:start position:0%
+you have fresh olive oil
+ 
+
+ align:start position:0%
+you have fresh olive oil
+it's healthier for you than not so good
+
+ align:start position:0%
+it's healthier for you than not so good
+ 
+
+ align:start position:0%
+it's healthier for you than not so good
+quality olive oil okay so then
+
+ align:start position:0%
+quality olive oil okay so then
+ 
+
+ align:start position:0%
+quality olive oil okay so then
+mediterranean diets also have other fats
+
+ align:start position:0%
+mediterranean diets also have other fats
+ 
+
+ align:start position:0%
+mediterranean diets also have other fats
+in their diet they're not from olive oil
+
+ align:start position:0%
+in their diet they're not from olive oil
+ 
+
+ align:start position:0%
+in their diet they're not from olive oil
+they're not omega-9 they're omega-6 i
+
+ align:start position:0%
+they're not omega-9 they're omega-6 i
+ 
+
+ align:start position:0%
+they're not omega-9 they're omega-6 i
+know you've heard that and we never
+
+ align:start position:0%
+know you've heard that and we never
+ 
+
+ align:start position:0%
+know you've heard that and we never
+refer to this we always call this
+
+ align:start position:0%
+refer to this we always call this
+ 
+
+ align:start position:0%
+refer to this we always call this
+monounsaturated nuts and seeds sesames
+
+ align:start position:0%
+monounsaturated nuts and seeds sesames
+ 
+
+ align:start position:0%
+monounsaturated nuts and seeds sesames
+cashews walnuts
+
+ align:start position:0%
+cashews walnuts
+ 
+
+ align:start position:0%
+cashews walnuts
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+are considered polyunsaturated fats
+
+ align:start position:0%
+are considered polyunsaturated fats
+ 
+
+ align:start position:0%
+are considered polyunsaturated fats
+there's other fats in the diet fish
+
+ align:start position:0%
+there's other fats in the diet fish
+ 
+
+ align:start position:0%
+there's other fats in the diet fish
+those in the omega-3 polyunsaturated
+
+ align:start position:0%
+those in the omega-3 polyunsaturated
+ 
+
+ align:start position:0%
+those in the omega-3 polyunsaturated
+these are mono and these are
+
+ align:start position:0%
+these are mono and these are
+ 
+
+ align:start position:0%
+these are mono and these are
+polyunsaturated
+
+ align:start position:0%
+polyunsaturated
+ 
+
+ align:start position:0%
+polyunsaturated
+so fish is also very prominent in the
+
+ align:start position:0%
+so fish is also very prominent in the
+ 
+
+ align:start position:0%
+so fish is also very prominent in the
+mediterranean diet okay the other
+
+ align:start position:0%
+mediterranean diet okay the other
+ 
+
+ align:start position:0%
+mediterranean diet okay the other
+characteristic fresh fruits and
+
+ align:start position:0%
+characteristic fresh fruits and
+ 
+
+ align:start position:0%
+characteristic fresh fruits and
+vegetables are prominent they are not an
+
+ align:start position:0%
+vegetables are prominent they are not an
+ 
+
+ align:start position:0%
+vegetables are prominent they are not an
+afterthought the vegetables are the
+
+ align:start position:0%
+afterthought the vegetables are the
+ 
+
+ align:start position:0%
+afterthought the vegetables are the
+highlight
+
+ align:start position:0%
+highlight
+ 
+
+ align:start position:0%
+highlight
+of many meals
+
+ align:start position:0%
+of many meals
+ 
+
+ align:start position:0%
+of many meals
+there is meat in the mood training diet
+
+ align:start position:0%
+there is meat in the mood training diet
+ 
+
+ align:start position:0%
+there is meat in the mood training diet
+the portion is smaller
+
+ align:start position:0%
+the portion is smaller
+ 
+
+ align:start position:0%
+the portion is smaller
+it's just not always there living
+
+ align:start position:0%
+it's just not always there living
+ 
+
+ align:start position:0%
+it's just not always there living
+vegetarian meals
+
+ align:start position:0%
+vegetarian meals
+ 
+
+ align:start position:0%
+vegetarian meals
+so fresh fruits and vegetables are very
+
+ align:start position:0%
+so fresh fruits and vegetables are very
+ 
+
+ align:start position:0%
+so fresh fruits and vegetables are very
+very high and again this is part of the
+
+ align:start position:0%
+very high and again this is part of the
+ 
+
+ align:start position:0%
+very high and again this is part of the
+health benefits it's not just the fats
+
+ align:start position:0%
+health benefits it's not just the fats
+ 
+
+ align:start position:0%
+health benefits it's not just the fats
+so legumes uh and i by legumes i dried
+
+ align:start position:0%
+so legumes uh and i by legumes i dried
+ 
+
+ align:start position:0%
+so legumes uh and i by legumes i dried
+peas
+
+ align:start position:0%
+peas
+ 
+
+ align:start position:0%
+peas
+lentils beans
+
+ align:start position:0%
+lentils beans
+ 
+
+ align:start position:0%
+lentils beans
+the other thing that is left out of many
+
+ align:start position:0%
+the other thing that is left out of many
+ 
+
+ align:start position:0%
+the other thing that is left out of many
+much of the literature of fresh herbs
+
+ align:start position:0%
+much of the literature of fresh herbs
+ 
+
+ align:start position:0%
+much of the literature of fresh herbs
+and spices and i'll show you later that
+
+ align:start position:0%
+and spices and i'll show you later that
+ 
+
+ align:start position:0%
+and spices and i'll show you later that
+there are compounds in here there's
+
+ align:start position:0%
+there are compounds in here there's
+ 
+
+ align:start position:0%
+there are compounds in here there's
+vitamins there's minerals and i think
+
+ align:start position:0%
+vitamins there's minerals and i think
+ 
+
+ align:start position:0%
+vitamins there's minerals and i think
+that the key to the mediterranean diet
+
+ align:start position:0%
+that the key to the mediterranean diet
+ 
+
+ align:start position:0%
+that the key to the mediterranean diet
+is that
+
+ align:start position:0%
+is that
+ 
+
+ align:start position:0%
+is that
+all the foods there works
+
+ align:start position:0%
+all the foods there works
+ 
+
+ align:start position:0%
+all the foods there works
+synergistically oh and then there's the
+
+ align:start position:0%
+synergistically oh and then there's the
+ 
+
+ align:start position:0%
+synergistically oh and then there's the
+plain yogurt
+
+ align:start position:0%
+plain yogurt
+ 
+
+ align:start position:0%
+plain yogurt
+and cheese and those are fermented
+
+ align:start position:0%
+and cheese and those are fermented
+ 
+
+ align:start position:0%
+and cheese and those are fermented
+products i wouldn't say there's a lot of
+
+ align:start position:0%
+products i wouldn't say there's a lot of
+ 
+
+ align:start position:0%
+products i wouldn't say there's a lot of
+milk milk i do not see a lot of whole
+
+ align:start position:0%
+milk milk i do not see a lot of whole
+ 
+
+ align:start position:0%
+milk milk i do not see a lot of whole
+grains but it's there because of the
+
+ align:start position:0%
+grains but it's there because of the
+ 
+
+ align:start position:0%
+grains but it's there because of the
+literature and i think that other
+
+ align:start position:0%
+literature and i think that other
+ 
+
+ align:start position:0%
+literature and i think that other
+cultures use more like when you get more
+
+ align:start position:0%
+cultures use more like when you get more
+ 
+
+ align:start position:0%
+cultures use more like when you get more
+middle eastern turkey there's boulder
+
+ align:start position:0%
+middle eastern turkey there's boulder
+ 
+
+ align:start position:0%
+middle eastern turkey there's boulder
+etc but in greece italy we don't use
+
+ align:start position:0%
+etc but in greece italy we don't use
+ 
+
+ align:start position:0%
+etc but in greece italy we don't use
+whole grains they do now because they
+
+ align:start position:0%
+whole grains they do now because they
+ 
+
+ align:start position:0%
+whole grains they do now because they
+know it's supposed to be good but that's
+
+ align:start position:0%
+know it's supposed to be good but that's
+ 
+
+ align:start position:0%
+know it's supposed to be good but that's
+not i don't think that's i don't know if
+
+ align:start position:0%
+not i don't think that's i don't know if
+ 
+
+ align:start position:0%
+not i don't think that's i don't know if
+they were eating that in the 1950s maybe
+
+ align:start position:0%
+they were eating that in the 1950s maybe
+ 
+
+ align:start position:0%
+they were eating that in the 1950s maybe
+they were
+
+ align:start position:0%
+they were
+ 
+
+ align:start position:0%
+they were
+red wine is part of the mediterranean
+
+ align:start position:0%
+red wine is part of the mediterranean
+ 
+
+ align:start position:0%
+red wine is part of the mediterranean
+diet the big difference is
+
+ align:start position:0%
+diet the big difference is
+ 
+
+ align:start position:0%
+diet the big difference is
+they have much less saturated fat
+
+ align:start position:0%
+they have much less saturated fat
+ 
+
+ align:start position:0%
+they have much less saturated fat
+because they use foods and how do they
+
+ align:start position:0%
+because they use foods and how do they
+ 
+
+ align:start position:0%
+because they use foods and how do they
+get it it's because they don't eat a lot
+
+ align:start position:0%
+get it it's because they don't eat a lot
+ 
+
+ align:start position:0%
+get it it's because they don't eat a lot
+of meat their portion is small and they
+
+ align:start position:0%
+of meat their portion is small and they
+ 
+
+ align:start position:0%
+of meat their portion is small and they
+don't have it frequently like every day
+
+ align:start position:0%
+don't have it frequently like every day
+ 
+
+ align:start position:0%
+don't have it frequently like every day
+the other difference right is less salty
+
+ align:start position:0%
+the other difference right is less salty
+ 
+
+ align:start position:0%
+the other difference right is less salty
+and sweet processed foods america has
+
+ align:start position:0%
+and sweet processed foods america has
+ 
+
+ align:start position:0%
+and sweet processed foods america has
+lots of these cheeses potato chips
+
+ align:start position:0%
+lots of these cheeses potato chips
+ 
+
+ align:start position:0%
+lots of these cheeses potato chips
+pretzels just again i think that these
+
+ align:start position:0%
+pretzels just again i think that these
+ 
+
+ align:start position:0%
+pretzels just again i think that these
+and studies have shown
+
+ align:start position:0%
+and studies have shown
+ 
+
+ align:start position:0%
+and studies have shown
+these all of these fresh herbs and
+
+ align:start position:0%
+these all of these fresh herbs and
+ 
+
+ align:start position:0%
+these all of these fresh herbs and
+spices have health benefits they're not
+
+ align:start position:0%
+spices have health benefits they're not
+ 
+
+ align:start position:0%
+spices have health benefits they're not
+there just for flavor when you think
+
+ align:start position:0%
+there just for flavor when you think
+ 
+
+ align:start position:0%
+there just for flavor when you think
+about parsley lots of vitamin c vitamin
+
+ align:start position:0%
+about parsley lots of vitamin c vitamin
+ 
+
+ align:start position:0%
+about parsley lots of vitamin c vitamin
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+flavonoids
+
+ align:start position:0%
+flavonoids
+ 
+
+ align:start position:0%
+flavonoids
+these are compounds in foods that have
+
+ align:start position:0%
+these are compounds in foods that have
+ 
+
+ align:start position:0%
+these are compounds in foods that have
+health benefits and fresh garlic another
+
+ align:start position:0%
+health benefits and fresh garlic another
+ 
+
+ align:start position:0%
+health benefits and fresh garlic another
+very common thing it's not chopped
+
+ align:start position:0%
+very common thing it's not chopped
+ 
+
+ align:start position:0%
+very common thing it's not chopped
+already and it's not garlic powder like
+
+ align:start position:0%
+already and it's not garlic powder like
+ 
+
+ align:start position:0%
+already and it's not garlic powder like
+we would do here in the mediterranean
+
+ align:start position:0%
+we would do here in the mediterranean
+ 
+
+ align:start position:0%
+we would do here in the mediterranean
+diet these are all fish and there are
+
+ align:start position:0%
+diet these are all fish and there are
+ 
+
+ align:start position:0%
+diet these are all fish and there are
+dep sulphur compounds are helpful so in
+
+ align:start position:0%
+dep sulphur compounds are helpful so in
+ 
+
+ align:start position:0%
+dep sulphur compounds are helpful so in
+1992 the mediterranean diet you know we
+
+ align:start position:0%
+1992 the mediterranean diet you know we
+ 
+
+ align:start position:0%
+1992 the mediterranean diet you know we
+had our pyramid here then
+
+ align:start position:0%
+had our pyramid here then
+ 
+
+ align:start position:0%
+had our pyramid here then
+a group came out with a mediterranean
+
+ align:start position:0%
+a group came out with a mediterranean
+ 
+
+ align:start position:0%
+a group came out with a mediterranean
+diet pyramid so for those of you who
+
+ align:start position:0%
+diet pyramid so for those of you who
+ 
+
+ align:start position:0%
+diet pyramid so for those of you who
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+visuals this is the mediterranean diet
+
+ align:start position:0%
+visuals this is the mediterranean diet
+ 
+
+ align:start position:0%
+visuals this is the mediterranean diet
+on the bottom you know we're supposed to
+
+ align:start position:0%
+on the bottom you know we're supposed to
+ 
+
+ align:start position:0%
+on the bottom you know we're supposed to
+have the most of our foods come from
+
+ align:start position:0%
+have the most of our foods come from
+ 
+
+ align:start position:0%
+have the most of our foods come from
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+fresh vegetables grains
+
+ align:start position:0%
+fresh vegetables grains
+ 
+
+ align:start position:0%
+fresh vegetables grains
+olive oil they're grouped all together
+
+ align:start position:0%
+olive oil they're grouped all together
+ 
+
+ align:start position:0%
+olive oil they're grouped all together
+and then less protein
+
+ align:start position:0%
+and then less protein
+ 
+
+ align:start position:0%
+and then less protein
+less dairy and then
+
+ align:start position:0%
+less dairy and then
+ 
+
+ align:start position:0%
+less dairy and then
+meats and sweets are put in the same
+
+ align:start position:0%
+meats and sweets are put in the same
+ 
+
+ align:start position:0%
+meats and sweets are put in the same
+category which will feed very little
+
+ align:start position:0%
+category which will feed very little
+ 
+
+ align:start position:0%
+category which will feed very little
+yeah don't forget they have all this
+
+ align:start position:0%
+yeah don't forget they have all this
+ 
+
+ align:start position:0%
+yeah don't forget they have all this
+activity here too
+
+ align:start position:0%
+activity here too
+ 
+
+ align:start position:0%
+activity here too
+so this these are some mediterranean
+
+ align:start position:0%
+so this these are some mediterranean
+ 
+
+ align:start position:0%
+so this these are some mediterranean
+lifestyle and behaviors that i noticed
+
+ align:start position:0%
+lifestyle and behaviors that i noticed
+ 
+
+ align:start position:0%
+lifestyle and behaviors that i noticed
+myself when i go to greece all the time
+
+ align:start position:0%
+myself when i go to greece all the time
+ 
+
+ align:start position:0%
+myself when i go to greece all the time
+there's no such thing as eating in front
+
+ align:start position:0%
+there's no such thing as eating in front
+ 
+
+ align:start position:0%
+there's no such thing as eating in front
+of the tv or snacking that's not a
+
+ align:start position:0%
+of the tv or snacking that's not a
+ 
+
+ align:start position:0%
+of the tv or snacking that's not a
+concept i don't know if that's india in
+
+ align:start position:0%
+concept i don't know if that's india in
+ 
+
+ align:start position:0%
+concept i don't know if that's india in
+italy no you have your meals and you're
+
+ align:start position:0%
+italy no you have your meals and you're
+ 
+
+ align:start position:0%
+italy no you have your meals and you're
+done there's no
+
+ align:start position:0%
+done there's no
+ 
+
+ align:start position:0%
+done there's no
+no concept of that like oh well
+
+ align:start position:0%
+no concept of that like oh well
+ 
+
+ align:start position:0%
+no concept of that like oh well
+i in my practice here at medical that's
+
+ align:start position:0%
+i in my practice here at medical that's
+ 
+
+ align:start position:0%
+i in my practice here at medical that's
+a huge issue for us americans we're like
+
+ align:start position:0%
+a huge issue for us americans we're like
+ 
+
+ align:start position:0%
+a huge issue for us americans we're like
+oh what do i snack on at night people
+
+ align:start position:0%
+oh what do i snack on at night people
+ 
+
+ align:start position:0%
+oh what do i snack on at night people
+say
+
+ align:start position:0%
+say
+ 
+
+ align:start position:0%
+say
+i say well if you're not helping me
+
+ align:start position:0%
+i say well if you're not helping me
+ 
+
+ align:start position:0%
+i say well if you're not helping me
+don't stop uh they're sharing plates a
+
+ align:start position:0%
+don't stop uh they're sharing plates a
+ 
+
+ align:start position:0%
+don't stop uh they're sharing plates a
+lot of sharing it's not always common
+
+ align:start position:0%
+lot of sharing it's not always common
+ 
+
+ align:start position:0%
+lot of sharing it's not always common
+that everybody gets their own plate like
+
+ align:start position:0%
+that everybody gets their own plate like
+ 
+
+ align:start position:0%
+that everybody gets their own plate like
+we do a group goes out they've had their
+
+ align:start position:0%
+we do a group goes out they've had their
+ 
+
+ align:start position:0%
+we do a group goes out they've had their
+main meal in the daytime
+
+ align:start position:0%
+main meal in the daytime
+ 
+
+ align:start position:0%
+main meal in the daytime
+so the nighttime is kind of on less food
+
+ align:start position:0%
+so the nighttime is kind of on less food
+ 
+
+ align:start position:0%
+so the nighttime is kind of on less food
+and they share so the portions are
+
+ align:start position:0%
+and they share so the portions are
+ 
+
+ align:start position:0%
+and they share so the portions are
+smaller
+
+ align:start position:0%
+smaller
+ 
+
+ align:start position:0%
+smaller
+they have smaller plates
+
+ align:start position:0%
+they have smaller plates
+ 
+
+ align:start position:0%
+they have smaller plates
+they have their main uh meal in the
+
+ align:start position:0%
+they have their main uh meal in the
+ 
+
+ align:start position:0%
+they have their main uh meal in the
+middle of the day and there's always a
+
+ align:start position:0%
+middle of the day and there's always a
+ 
+
+ align:start position:0%
+middle of the day and there's always a
+nap
+
+ align:start position:0%
+nap
+ 
+
+ align:start position:0%
+nap
+which is my favorite part
+
+ align:start position:0%
+which is my favorite part
+ 
+
+ align:start position:0%
+which is my favorite part
+and there's also lots of walking this is
+
+ align:start position:0%
+and there's also lots of walking this is
+ 
+
+ align:start position:0%
+and there's also lots of walking this is
+another thing i notice people are
+
+ align:start position:0%
+another thing i notice people are
+ 
+
+ align:start position:0%
+another thing i notice people are
+walking like in most european cities or
+
+ align:start position:0%
+walking like in most european cities or
+ 
+
+ align:start position:0%
+walking like in most european cities or
+any big city lots of walking
+
+ align:start position:0%
+any big city lots of walking
+ 
+
+ align:start position:0%
+any big city lots of walking
+okay so i'm going to show you some
+
+ align:start position:0%
+okay so i'm going to show you some
+ 
+
+ align:start position:0%
+okay so i'm going to show you some
+common food patterns of greece
+
+ align:start position:0%
+common food patterns of greece
+ 
+
+ align:start position:0%
+common food patterns of greece
+real food there's no convenience process
+
+ align:start position:0%
+real food there's no convenience process
+ 
+
+ align:start position:0%
+real food there's no convenience process
+thing garlic in a jar and cheetos in a
+
+ align:start position:0%
+thing garlic in a jar and cheetos in a
+ 
+
+ align:start position:0%
+thing garlic in a jar and cheetos in a
+bag and frozen dinner not common at all
+
+ align:start position:0%
+bag and frozen dinner not common at all
+ 
+
+ align:start position:0%
+bag and frozen dinner not common at all
+no snack foods like bars we're obsessed
+
+ align:start position:0%
+no snack foods like bars we're obsessed
+ 
+
+ align:start position:0%
+no snack foods like bars we're obsessed
+with
+
+ align:start position:0%
+with
+ 
+
+ align:start position:0%
+with
+this doesn't exist it's fruit it's
+
+ align:start position:0%
+this doesn't exist it's fruit it's
+ 
+
+ align:start position:0%
+this doesn't exist it's fruit it's
+vegetable
+
+ align:start position:0%
+vegetable
+ 
+
+ align:start position:0%
+vegetable
+you know meat cheese done
+
+ align:start position:0%
+you know meat cheese done
+ 
+
+ align:start position:0%
+you know meat cheese done
+but no one knows not good may meals eat
+
+ align:start position:0%
+but no one knows not good may meals eat
+ 
+
+ align:start position:0%
+but no one knows not good may meals eat
+it too i think i said that
+
+ align:start position:0%
+it too i think i said that
+ 
+
+ align:start position:0%
+it too i think i said that
+meat is a much smaller part of the meal
+
+ align:start position:0%
+meat is a much smaller part of the meal
+ 
+
+ align:start position:0%
+meat is a much smaller part of the meal
+if it's present it's a small portion
+
+ align:start position:0%
+if it's present it's a small portion
+ 
+
+ align:start position:0%
+if it's present it's a small portion
+like three four ounces which is like a
+
+ align:start position:0%
+like three four ounces which is like a
+ 
+
+ align:start position:0%
+like three four ounces which is like a
+deck of cards which is what we say
+
+ align:start position:0%
+deck of cards which is what we say
+ 
+
+ align:start position:0%
+deck of cards which is what we say
+should be here in this country
+
+ align:start position:0%
+should be here in this country
+ 
+
+ align:start position:0%
+should be here in this country
+then a lot of one pot meals they have
+
+ align:start position:0%
+then a lot of one pot meals they have
+ 
+
+ align:start position:0%
+then a lot of one pot meals they have
+lots of vegetable dishes and i have
+
+ align:start position:0%
+lots of vegetable dishes and i have
+ 
+
+ align:start position:0%
+lots of vegetable dishes and i have
+pictures to show you that are in olive
+
+ align:start position:0%
+pictures to show you that are in olive
+ 
+
+ align:start position:0%
+pictures to show you that are in olive
+oil and it's the main entree it's not a
+
+ align:start position:0%
+oil and it's the main entree it's not a
+ 
+
+ align:start position:0%
+oil and it's the main entree it's not a
+side dish you will see
+
+ align:start position:0%
+side dish you will see
+ 
+
+ align:start position:0%
+side dish you will see
+i hope it looks good yeah fruit is a dis
+
+ align:start position:0%
+i hope it looks good yeah fruit is a dis
+ 
+
+ align:start position:0%
+i hope it looks good yeah fruit is a dis
+is fruit is the dessert
+
+ align:start position:0%
+is fruit is the dessert
+ 
+
+ align:start position:0%
+is fruit is the dessert
+greeks never have desserts after the
+
+ align:start position:0%
+greeks never have desserts after the
+ 
+
+ align:start position:0%
+greeks never have desserts after the
+meal and i don't know about italians
+
+ align:start position:0%
+meal and i don't know about italians
+ 
+
+ align:start position:0%
+meal and i don't know about italians
+but not every day not every day when
+
+ align:start position:0%
+but not every day not every day when
+ 
+
+ align:start position:0%
+but not every day not every day when
+sunday
+
+ align:start position:0%
+sunday
+ 
+
+ align:start position:0%
+sunday
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+desserts are a special time for greeks
+
+ align:start position:0%
+desserts are a special time for greeks
+ 
+
+ align:start position:0%
+desserts are a special time for greeks
+and they're eating alone like oh i'll
+
+ align:start position:0%
+and they're eating alone like oh i'll
+ 
+
+ align:start position:0%
+and they're eating alone like oh i'll
+have a coffee and a dessert for the
+
+ align:start position:0%
+have a coffee and a dessert for the
+ 
+
+ align:start position:0%
+have a coffee and a dessert for the
+other day
+
+ align:start position:0%
+other day
+ 
+
+ align:start position:0%
+other day
+it's it's an event there's no dessert oh
+
+ align:start position:0%
+it's it's an event there's no dessert oh
+ 
+
+ align:start position:0%
+it's it's an event there's no dessert oh
+like we do here it's all fruit is always
+
+ align:start position:0%
+like we do here it's all fruit is always
+ 
+
+ align:start position:0%
+like we do here it's all fruit is always
+served at the meal so it's not a snack
+
+ align:start position:0%
+served at the meal so it's not a snack
+ 
+
+ align:start position:0%
+served at the meal so it's not a snack
+and it's there
+
+ align:start position:0%
+and it's there
+ 
+
+ align:start position:0%
+and it's there
+and then that's my business about the
+
+ align:start position:0%
+and then that's my business about the
+ 
+
+ align:start position:0%
+and then that's my business about the
+sweets are eaten at a separate time so
+
+ align:start position:0%
+sweets are eaten at a separate time so
+ 
+
+ align:start position:0%
+sweets are eaten at a separate time so
+these are some common foods i don't know
+
+ align:start position:0%
+these are some common foods i don't know
+ 
+
+ align:start position:0%
+these are some common foods i don't know
+if you've ever heard of these who has
+
+ align:start position:0%
+if you've ever heard of these who has
+ 
+
+ align:start position:0%
+if you've ever heard of these who has
+been to whole foods you see giant beans
+
+ align:start position:0%
+been to whole foods you see giant beans
+ 
+
+ align:start position:0%
+been to whole foods you see giant beans
+in the salad bar have you seen those
+
+ align:start position:0%
+in the salad bar have you seen those
+ 
+
+ align:start position:0%
+in the salad bar have you seen those
+okay i have some of those that you're
+
+ align:start position:0%
+okay i have some of those that you're
+ 
+
+ align:start position:0%
+okay i have some of those that you're
+going to see
+
+ align:start position:0%
+going to see
+ 
+
+ align:start position:0%
+going to see
+those are usually cooked in a big oil
+
+ align:start position:0%
+those are usually cooked in a big oil
+ 
+
+ align:start position:0%
+those are usually cooked in a big oil
+dish
+
+ align:start position:0%
+dish
+ 
+
+ align:start position:0%
+dish
+stewed green beans is an is an entree
+
+ align:start position:0%
+stewed green beans is an is an entree
+ 
+
+ align:start position:0%
+stewed green beans is an is an entree
+you eat with a salad
+
+ align:start position:0%
+you eat with a salad
+ 
+
+ align:start position:0%
+you eat with a salad
+a piece of bread you're done
+
+ align:start position:0%
+a piece of bread you're done
+ 
+
+ align:start position:0%
+a piece of bread you're done
+uh bean soup you'll see i have stuff
+
+ align:start position:0%
+uh bean soup you'll see i have stuff
+ 
+
+ align:start position:0%
+uh bean soup you'll see i have stuff
+everybody knows what stuffed grapefruit
+
+ align:start position:0%
+everybody knows what stuffed grapefruit
+ 
+
+ align:start position:0%
+everybody knows what stuffed grapefruit
+is it's a great leaf a big leaf so it's
+
+ align:start position:0%
+is it's a great leaf a big leaf so it's
+ 
+
+ align:start position:0%
+is it's a great leaf a big leaf so it's
+a green leafy vegetable and then you
+
+ align:start position:0%
+a green leafy vegetable and then you
+ 
+
+ align:start position:0%
+a green leafy vegetable and then you
+stop it you take rice with lots of oil
+
+ align:start position:0%
+stop it you take rice with lots of oil
+ 
+
+ align:start position:0%
+stop it you take rice with lots of oil
+fresh spices maybe pine nuts maybe
+
+ align:start position:0%
+fresh spices maybe pine nuts maybe
+ 
+
+ align:start position:0%
+fresh spices maybe pine nuts maybe
+raisins
+
+ align:start position:0%
+raisins
+ 
+
+ align:start position:0%
+raisins
+put it on the leaf you roll the leaf and
+
+ align:start position:0%
+put it on the leaf you roll the leaf and
+ 
+
+ align:start position:0%
+put it on the leaf you roll the leaf and
+then you cook it these are also very
+
+ align:start position:0%
+then you cook it these are also very
+ 
+
+ align:start position:0%
+then you cook it these are also very
+common in grapefruit boiled greens you
+
+ align:start position:0%
+common in grapefruit boiled greens you
+ 
+
+ align:start position:0%
+common in grapefruit boiled greens you
+take beet greens you take not spinach
+
+ align:start position:0%
+take beet greens you take not spinach
+ 
+
+ align:start position:0%
+take beet greens you take not spinach
+you take
+
+ align:start position:0%
+you take
+ 
+
+ align:start position:0%
+you take
+swiss chard you just steam it or boil it
+
+ align:start position:0%
+swiss chard you just steam it or boil it
+ 
+
+ align:start position:0%
+swiss chard you just steam it or boil it
+put oil and lemon on it and that's the
+
+ align:start position:0%
+put oil and lemon on it and that's the
+ 
+
+ align:start position:0%
+put oil and lemon on it and that's the
+vegetables
+
+ align:start position:0%
+vegetables
+ 
+
+ align:start position:0%
+vegetables
+yeah lentil soup and the famous spinach
+
+ align:start position:0%
+yeah lentil soup and the famous spinach
+ 
+
+ align:start position:0%
+yeah lentil soup and the famous spinach
+pie yeah
+
+ align:start position:0%
+pie yeah
+ 
+
+ align:start position:0%
+pie yeah
+here we make it in america that is
+
+ align:start position:0%
+here we make it in america that is
+ 
+
+ align:start position:0%
+here we make it in america that is
+usually with butter in between the filo
+
+ align:start position:0%
+usually with butter in between the filo
+ 
+
+ align:start position:0%
+usually with butter in between the filo
+in grease it's often
+
+ align:start position:0%
+in grease it's often
+ 
+
+ align:start position:0%
+in grease it's often
+olive oil
+
+ align:start position:0%
+olive oil
+ 
+
+ align:start position:0%
+olive oil
+okay these are these are mine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i made those and i had them for dinner
+
+ align:start position:0%
+i made those and i had them for dinner
+ 
+
+ align:start position:0%
+i made those and i had them for dinner
+for lunch actually that's my little dog
+
+ align:start position:0%
+for lunch actually that's my little dog
+ 
+
+ align:start position:0%
+for lunch actually that's my little dog
+dish i didn't have time to make it look
+
+ align:start position:0%
+dish i didn't have time to make it look
+ 
+
+ align:start position:0%
+dish i didn't have time to make it look
+good but those are those giant beans
+
+ align:start position:0%
+good but those are those giant beans
+ 
+
+ align:start position:0%
+good but those are those giant beans
+and this is spinach carrots garlic
+
+ align:start position:0%
+and this is spinach carrots garlic
+ 
+
+ align:start position:0%
+and this is spinach carrots garlic
+they're huge yeah
+
+ align:start position:0%
+they're huge yeah
+ 
+
+ align:start position:0%
+they're huge yeah
+yeah they're like giant lima beans in a
+
+ align:start position:0%
+yeah they're like giant lima beans in a
+ 
+
+ align:start position:0%
+yeah they're like giant lima beans in a
+tomato and there's oil there if this was
+
+ align:start position:0%
+tomato and there's oil there if this was
+ 
+
+ align:start position:0%
+tomato and there's oil there if this was
+a if this was a more greek greek dish
+
+ align:start position:0%
+a if this was a more greek greek dish
+ 
+
+ align:start position:0%
+a if this was a more greek greek dish
+you would see the oil seeping out and i
+
+ align:start position:0%
+you would see the oil seeping out and i
+ 
+
+ align:start position:0%
+you would see the oil seeping out and i
+try and make it look calorie because
+
+ align:start position:0%
+try and make it look calorie because
+ 
+
+ align:start position:0%
+try and make it look calorie because
+you know i gotta worry about those
+
+ align:start position:0%
+you know i gotta worry about those
+ 
+
+ align:start position:0%
+you know i gotta worry about those
+things and then these i got this from
+
+ align:start position:0%
+things and then these i got this from
+ 
+
+ align:start position:0%
+things and then these i got this from
+the internet i thought that was a good
+
+ align:start position:0%
+the internet i thought that was a good
+ 
+
+ align:start position:0%
+the internet i thought that was a good
+picture these are those string beans
+
+ align:start position:0%
+picture these are those string beans
+ 
+
+ align:start position:0%
+picture these are those string beans
+this is a main dish it's not a side
+
+ align:start position:0%
+this is a main dish it's not a side
+ 
+
+ align:start position:0%
+this is a main dish it's not a side
+again it's oil tomato onion garlic
+
+ align:start position:0%
+again it's oil tomato onion garlic
+ 
+
+ align:start position:0%
+again it's oil tomato onion garlic
+this doesn't have a lot of oil but the
+
+ align:start position:0%
+this doesn't have a lot of oil but the
+ 
+
+ align:start position:0%
+this doesn't have a lot of oil but the
+next photo is my mother-in-law's who
+
+ align:start position:0%
+next photo is my mother-in-law's who
+ 
+
+ align:start position:0%
+next photo is my mother-in-law's who
+lives in greece and you can see big
+
+ align:start position:0%
+lives in greece and you can see big
+ 
+
+ align:start position:0%
+lives in greece and you can see big
+difference you see there's a lot of oil
+
+ align:start position:0%
+difference you see there's a lot of oil
+ 
+
+ align:start position:0%
+difference you see there's a lot of oil
+out there
+
+ align:start position:0%
+out there
+ 
+
+ align:start position:0%
+out there
+lots and she used to put more
+
+ align:start position:0%
+lots and she used to put more
+ 
+
+ align:start position:0%
+lots and she used to put more
+that was how don't forget oil and fat at
+
+ align:start position:0%
+that was how don't forget oil and fat at
+ 
+
+ align:start position:0%
+that was how don't forget oil and fat at
+a meal keeps us full
+
+ align:start position:0%
+a meal keeps us full
+ 
+
+ align:start position:0%
+a meal keeps us full
+fat when you when you have a no fat day
+
+ align:start position:0%
+fat when you when you have a no fat day
+ 
+
+ align:start position:0%
+fat when you when you have a no fat day
+no fat food you're going to be hungry
+
+ align:start position:0%
+no fat food you're going to be hungry
+ 
+
+ align:start position:0%
+no fat food you're going to be hungry
+and you're going to want to overeat
+
+ align:start position:0%
+and you're going to want to overeat
+ 
+
+ align:start position:0%
+and you're going to want to overeat
+usually carbohydrates
+
+ align:start position:0%
+usually carbohydrates
+ 
+
+ align:start position:0%
+usually carbohydrates
+yeah so these are stuffed grape leaves
+
+ align:start position:0%
+yeah so these are stuffed grape leaves
+ 
+
+ align:start position:0%
+yeah so these are stuffed grape leaves
+and squash blossoms
+
+ align:start position:0%
+and squash blossoms
+ 
+
+ align:start position:0%
+and squash blossoms
+so again i call this like real
+
+ align:start position:0%
+so again i call this like real
+ 
+
+ align:start position:0%
+so again i call this like real
+vegetarian food not isolated soy protein
+
+ align:start position:0%
+vegetarian food not isolated soy protein
+ 
+
+ align:start position:0%
+vegetarian food not isolated soy protein
+here's a greek salad a real greek salad
+
+ align:start position:0%
+here's a greek salad a real greek salad
+ 
+
+ align:start position:0%
+here's a greek salad a real greek salad
+what's different about this
+
+ align:start position:0%
+what's different about this
+ 
+
+ align:start position:0%
+what's different about this
+yes there's no lettuce
+
+ align:start position:0%
+yes there's no lettuce
+ 
+
+ align:start position:0%
+yes there's no lettuce
+anything else
+
+ align:start position:0%
+anything else
+ 
+
+ align:start position:0%
+anything else
+there's not half a pound of feta cheese
+
+ align:start position:0%
+there's not half a pound of feta cheese
+ 
+
+ align:start position:0%
+there's not half a pound of feta cheese
+on here
+
+ align:start position:0%
+on here
+ 
+
+ align:start position:0%
+on here
+and that creamy greek dressing which is
+
+ align:start position:0%
+and that creamy greek dressing which is
+ 
+
+ align:start position:0%
+and that creamy greek dressing which is
+not great
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just tomato
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is divine i love it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so now i have my famous tips of how
+
+ align:start position:0%
+okay so now i have my famous tips of how
+ 
+
+ align:start position:0%
+okay so now i have my famous tips of how
+you're gonna get a mediterranean diet
+
+ align:start position:0%
+you're gonna get a mediterranean diet
+ 
+
+ align:start position:0%
+you're gonna get a mediterranean diet
+here in america and by the way there was
+
+ align:start position:0%
+here in america and by the way there was
+ 
+
+ align:start position:0%
+here in america and by the way there was
+a study i didn't put in here but it was
+
+ align:start position:0%
+a study i didn't put in here but it was
+ 
+
+ align:start position:0%
+a study i didn't put in here but it was
+talking about how
+
+ align:start position:0%
+talking about how
+ 
+
+ align:start position:0%
+talking about how
+transporting can you transport the
+
+ align:start position:0%
+transporting can you transport the
+ 
+
+ align:start position:0%
+transporting can you transport the
+mediterranean diet to other countries
+
+ align:start position:0%
+mediterranean diet to other countries
+ 
+
+ align:start position:0%
+mediterranean diet to other countries
+like australia and america and the study
+
+ align:start position:0%
+like australia and america and the study
+ 
+
+ align:start position:0%
+like australia and america and the study
+said yes you can so there's hope for us
+
+ align:start position:0%
+said yes you can so there's hope for us
+ 
+
+ align:start position:0%
+said yes you can so there's hope for us
+okay so you're gonna do it cook and eat
+
+ align:start position:0%
+okay so you're gonna do it cook and eat
+ 
+
+ align:start position:0%
+okay so you're gonna do it cook and eat
+home more often because you know what
+
+ align:start position:0%
+home more often because you know what
+ 
+
+ align:start position:0%
+home more often because you know what
+you're doing you have a chance to eat
+
+ align:start position:0%
+you're doing you have a chance to eat
+ 
+
+ align:start position:0%
+you're doing you have a chance to eat
+healthier eating out all the time is not
+
+ align:start position:0%
+healthier eating out all the time is not
+ 
+
+ align:start position:0%
+healthier eating out all the time is not
+a healthy activity
+
+ align:start position:0%
+a healthy activity
+ 
+
+ align:start position:0%
+a healthy activity
+okay so in your cooking eat vegetarian
+
+ align:start position:0%
+okay so in your cooking eat vegetarian
+ 
+
+ align:start position:0%
+okay so in your cooking eat vegetarian
+one or two times a week as much as you
+
+ align:start position:0%
+one or two times a week as much as you
+ 
+
+ align:start position:0%
+one or two times a week as much as you
+want most people who are not vegetarians
+
+ align:start position:0%
+want most people who are not vegetarians
+ 
+
+ align:start position:0%
+want most people who are not vegetarians
+never have just a vegan meal that
+
+ align:start position:0%
+never have just a vegan meal that
+ 
+
+ align:start position:0%
+never have just a vegan meal that
+doesn't have this
+
+ align:start position:0%
+doesn't have this
+ 
+
+ align:start position:0%
+doesn't have this
+which is not the healthiest thing all
+
+ align:start position:0%
+which is not the healthiest thing all
+ 
+
+ align:start position:0%
+which is not the healthiest thing all
+those tofu
+
+ align:start position:0%
+those tofu
+ 
+
+ align:start position:0%
+those tofu
+i mean tofu by itself is much healthier
+
+ align:start position:0%
+i mean tofu by itself is much healthier
+ 
+
+ align:start position:0%
+i mean tofu by itself is much healthier
+than the isolated soy protein burgers
+
+ align:start position:0%
+than the isolated soy protein burgers
+ 
+
+ align:start position:0%
+than the isolated soy protein burgers
+and tofu dogs and
+
+ align:start position:0%
+and tofu dogs and
+ 
+
+ align:start position:0%
+and tofu dogs and
+all of that so so that's one way for you
+
+ align:start position:0%
+all of that so so that's one way for you
+ 
+
+ align:start position:0%
+all of that so so that's one way for you
+to get a mediterranean diet is try a
+
+ align:start position:0%
+to get a mediterranean diet is try a
+ 
+
+ align:start position:0%
+to get a mediterranean diet is try a
+more mediterranean vegetarian
+
+ align:start position:0%
+more mediterranean vegetarian
+ 
+
+ align:start position:0%
+more mediterranean vegetarian
+meal
+
+ align:start position:0%
+meal
+ 
+
+ align:start position:0%
+meal
+um okay so some of those are i didn't
+
+ align:start position:0%
+um okay so some of those are i didn't
+ 
+
+ align:start position:0%
+um okay so some of those are i didn't
+have pictures of falafel or hummus but
+
+ align:start position:0%
+have pictures of falafel or hummus but
+ 
+
+ align:start position:0%
+have pictures of falafel or hummus but
+those are also mediterranean very
+
+ align:start position:0%
+those are also mediterranean very
+ 
+
+ align:start position:0%
+those are also mediterranean very
+healthy dishes chickpeas tahini again
+
+ align:start position:0%
+healthy dishes chickpeas tahini again
+ 
+
+ align:start position:0%
+healthy dishes chickpeas tahini again
+the same
+
+ align:start position:0%
+the same
+ 
+
+ align:start position:0%
+the same
+yeah
+
+ align:start position:0%
+yeah
+ 
+
+ align:start position:0%
+yeah
+sesame seeds yeah good fats
+
+ align:start position:0%
+sesame seeds yeah good fats
+ 
+
+ align:start position:0%
+sesame seeds yeah good fats
+yeah uh use extra virgin olive oil for
+
+ align:start position:0%
+yeah uh use extra virgin olive oil for
+ 
+
+ align:start position:0%
+yeah uh use extra virgin olive oil for
+cooking salad for your cooking add that
+
+ align:start position:0%
+cooking salad for your cooking add that
+ 
+
+ align:start position:0%
+cooking salad for your cooking add that
+to salads don't use salad dressing which
+
+ align:start position:0%
+to salads don't use salad dressing which
+ 
+
+ align:start position:0%
+to salads don't use salad dressing which
+i think is my next tip because you don't
+
+ align:start position:0%
+i think is my next tip because you don't
+ 
+
+ align:start position:0%
+i think is my next tip because you don't
+get a good oil in a salad dressing and
+
+ align:start position:0%
+get a good oil in a salad dressing and
+ 
+
+ align:start position:0%
+get a good oil in a salad dressing and
+you get sugar and you get thickener and
+
+ align:start position:0%
+you get sugar and you get thickener and
+ 
+
+ align:start position:0%
+you get sugar and you get thickener and
+you get
+
+ align:start position:0%
+you get
+ 
+
+ align:start position:0%
+you get
+tons of salt and you get sugar and
+
+ align:start position:0%
+tons of salt and you get sugar and
+ 
+
+ align:start position:0%
+tons of salt and you get sugar and
+if you can get yourself a good olive oil
+
+ align:start position:0%
+if you can get yourself a good olive oil
+ 
+
+ align:start position:0%
+if you can get yourself a good olive oil
+put your own oil and vinegar or lemon
+
+ align:start position:0%
+put your own oil and vinegar or lemon
+ 
+
+ align:start position:0%
+put your own oil and vinegar or lemon
+you'll be healthier and you'll be
+
+ align:start position:0%
+you'll be healthier and you'll be
+ 
+
+ align:start position:0%
+you'll be healthier and you'll be
+getting
+
+ align:start position:0%
+getting
+ 
+
+ align:start position:0%
+getting
+the flavonoids and all those wonderful
+
+ align:start position:0%
+the flavonoids and all those wonderful
+ 
+
+ align:start position:0%
+the flavonoids and all those wonderful
+ingredients
+
+ align:start position:0%
+ingredients
+ 
+
+ align:start position:0%
+ingredients
+and it tastes better at first you you
+
+ align:start position:0%
+and it tastes better at first you you
+ 
+
+ align:start position:0%
+and it tastes better at first you you
+might not if you're used to salad
+
+ align:start position:0%
+might not if you're used to salad
+ 
+
+ align:start position:0%
+might not if you're used to salad
+dressing when i was growing up we had
+
+ align:start position:0%
+dressing when i was growing up we had
+ 
+
+ align:start position:0%
+dressing when i was growing up we had
+salad dressing that was what we had and
+
+ align:start position:0%
+salad dressing that was what we had and
+ 
+
+ align:start position:0%
+salad dressing that was what we had and
+we loved it my brother and i we shunned
+
+ align:start position:0%
+we loved it my brother and i we shunned
+ 
+
+ align:start position:0%
+we loved it my brother and i we shunned
+the olive oil and said well it's motor
+
+ align:start position:0%
+the olive oil and said well it's motor
+ 
+
+ align:start position:0%
+the olive oil and said well it's motor
+oil oh we didn't like it
+
+ align:start position:0%
+oil oh we didn't like it
+ 
+
+ align:start position:0%
+oil oh we didn't like it
+because this italian dressing was so
+
+ align:start position:0%
+because this italian dressing was so
+ 
+
+ align:start position:0%
+because this italian dressing was so
+sweet and
+
+ align:start position:0%
+sweet and
+ 
+
+ align:start position:0%
+sweet and
+sugar and spicy it's not 380 but it's
+
+ align:start position:0%
+sugar and spicy it's not 380 but it's
+ 
+
+ align:start position:0%
+sugar and spicy it's not 380 but it's
+not it's
+
+ align:start position:0%
+not it's
+ 
+
+ align:start position:0%
+not it's
+just like the greek dressing is not
+
+ align:start position:0%
+just like the greek dressing is not
+ 
+
+ align:start position:0%
+just like the greek dressing is not
+there's no dressing in greece it's just
+
+ align:start position:0%
+there's no dressing in greece it's just
+ 
+
+ align:start position:0%
+there's no dressing in greece it's just
+same yeah it's the same yeah and it's
+
+ align:start position:0%
+same yeah it's the same yeah and it's
+ 
+
+ align:start position:0%
+same yeah it's the same yeah and it's
+healthier
+
+ align:start position:0%
+healthier
+ 
+
+ align:start position:0%
+healthier
+so that's one way you can do it yes so i
+
+ align:start position:0%
+so that's one way you can do it yes so i
+ 
+
+ align:start position:0%
+so that's one way you can do it yes so i
+think i've really heard the support but
+
+ align:start position:0%
+think i've really heard the support but
+ 
+
+ align:start position:0%
+think i've really heard the support but
+what's the difference between the
+
+ align:start position:0%
+what's the difference between the
+ 
+
+ align:start position:0%
+what's the difference between the
+extroversion the version the mod version
+
+ align:start position:0%
+extroversion the version the mod version
+ 
+
+ align:start position:0%
+extroversion the version the mod version
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+oh good it's written there yeah extra
+
+ align:start position:0%
+oh good it's written there yeah extra
+ 
+
+ align:start position:0%
+oh good it's written there yeah extra
+virgin would be the first pressing
+
+ align:start position:0%
+virgin would be the first pressing
+ 
+
+ align:start position:0%
+virgin would be the first pressing
+and it would not be
+
+ align:start position:0%
+and it would not be
+ 
+
+ align:start position:0%
+and it would not be
+over acidic and over like have foul
+
+ align:start position:0%
+over acidic and over like have foul
+ 
+
+ align:start position:0%
+over acidic and over like have foul
+tasting
+
+ align:start position:0%
+tasting
+ 
+
+ align:start position:0%
+tasting
+foul flavors in it so it has to do with
+
+ align:start position:0%
+foul flavors in it so it has to do with
+ 
+
+ align:start position:0%
+foul flavors in it so it has to do with
+the quality and like the first pressing
+
+ align:start position:0%
+the quality and like the first pressing
+ 
+
+ align:start position:0%
+the quality and like the first pressing
+as opposed to because you can
+
+ align:start position:0%
+as opposed to because you can
+ 
+
+ align:start position:0%
+as opposed to because you can
+keep pressing this you know get the
+
+ align:start position:0%
+keep pressing this you know get the
+ 
+
+ align:start position:0%
+keep pressing this you know get the
+first extraction then keep pressing and
+
+ align:start position:0%
+first extraction then keep pressing and
+ 
+
+ align:start position:0%
+first extraction then keep pressing and
+then you get not so good olive oil and
+
+ align:start position:0%
+then you get not so good olive oil and
+ 
+
+ align:start position:0%
+then you get not so good olive oil and
+then you can have it mixed there was a
+
+ align:start position:0%
+then you can have it mixed there was a
+ 
+
+ align:start position:0%
+then you can have it mixed there was a
+big scandal i was telling you about that
+
+ align:start position:0%
+big scandal i was telling you about that
+ 
+
+ align:start position:0%
+big scandal i was telling you about that
+in a book i read big scandal with olive
+
+ align:start position:0%
+in a book i read big scandal with olive
+ 
+
+ align:start position:0%
+in a book i read big scandal with olive
+oil
+
+ align:start position:0%
+oil
+ 
+
+ align:start position:0%
+oil
+they mix soya oil in it because it's
+
+ align:start position:0%
+they mix soya oil in it because it's
+ 
+
+ align:start position:0%
+they mix soya oil in it because it's
+very profitable et cetera et cetera so
+
+ align:start position:0%
+very profitable et cetera et cetera so
+ 
+
+ align:start position:0%
+very profitable et cetera et cetera so
+that's the question yeah if it says pure
+
+ align:start position:0%
+that's the question yeah if it says pure
+ 
+
+ align:start position:0%
+that's the question yeah if it says pure
+or if it says blended i wouldn't buy it
+
+ align:start position:0%
+or if it says blended i wouldn't buy it
+ 
+
+ align:start position:0%
+or if it says blended i wouldn't buy it
+because they do sometimes they think
+
+ align:start position:0%
+because they do sometimes they think
+ 
+
+ align:start position:0%
+because they do sometimes they think
+that's cute it's not bad pure is not
+
+ align:start position:0%
+that's cute it's not bad pure is not
+ 
+
+ align:start position:0%
+that's cute it's not bad pure is not
+good pure is like the one of the last
+
+ align:start position:0%
+good pure is like the one of the last
+ 
+
+ align:start position:0%
+good pure is like the one of the last
+qualities
+
+ align:start position:0%
+qualities
+ 
+
+ align:start position:0%
+qualities
+correct
+
+ align:start position:0%
+correct
+ 
+
+ align:start position:0%
+correct
+pure is inferior to extra
+
+ align:start position:0%
+pure is inferior to extra
+ 
+
+ align:start position:0%
+pure is inferior to extra
+so it's the first pressing the extra
+
+ align:start position:0%
+so it's the first pressing the extra
+ 
+
+ align:start position:0%
+so it's the first pressing the extra
+version is the best
+
+ align:start position:0%
+version is the best
+ 
+
+ align:start position:0%
+version is the best
+and it's it's more expensive but um it's
+
+ align:start position:0%
+and it's it's more expensive but um it's
+ 
+
+ align:start position:0%
+and it's it's more expensive but um it's
+also the most it should be the most
+
+ align:start position:0%
+also the most it should be the most
+ 
+
+ align:start position:0%
+also the most it should be the most
+healthy one
+
+ align:start position:0%
+healthy one
+ 
+
+ align:start position:0%
+healthy one
+the other ones are not as healthy as
+
+ align:start position:0%
+the other ones are not as healthy as
+ 
+
+ align:start position:0%
+the other ones are not as healthy as
+this one so this is yeah
+
+ align:start position:0%
+this one so this is yeah
+ 
+
+ align:start position:0%
+this one so this is yeah
+so another way you can do is steam your
+
+ align:start position:0%
+so another way you can do is steam your
+ 
+
+ align:start position:0%
+so another way you can do is steam your
+leafy green vegetables branch out get
+
+ align:start position:0%
+leafy green vegetables branch out get
+ 
+
+ align:start position:0%
+leafy green vegetables branch out get
+some escarole
+
+ align:start position:0%
+some escarole
+ 
+
+ align:start position:0%
+some escarole
+you put it in your soups you can i boil
+
+ align:start position:0%
+you put it in your soups you can i boil
+ 
+
+ align:start position:0%
+you put it in your soups you can i boil
+mine boil i steam it and i put oil and
+
+ align:start position:0%
+mine boil i steam it and i put oil and
+ 
+
+ align:start position:0%
+mine boil i steam it and i put oil and
+lemon that's my side with a piece of
+
+ align:start position:0%
+lemon that's my side with a piece of
+ 
+
+ align:start position:0%
+lemon that's my side with a piece of
+chicken and i might have something else
+
+ align:start position:0%
+chicken and i might have something else
+ 
+
+ align:start position:0%
+chicken and i might have something else
+with it and that's my meal otherwise i
+
+ align:start position:0%
+with it and that's my meal otherwise i
+ 
+
+ align:start position:0%
+with it and that's my meal otherwise i
+don't get lippy green vegetables but
+
+ align:start position:0%
+don't get lippy green vegetables but
+ 
+
+ align:start position:0%
+don't get lippy green vegetables but
+this way is easy
+
+ align:start position:0%
+this way is easy
+ 
+
+ align:start position:0%
+this way is easy
+you also can then
+
+ align:start position:0%
+you also can then
+ 
+
+ align:start position:0%
+you also can then
+put lots of garlic and lots of oil in
+
+ align:start position:0%
+put lots of garlic and lots of oil in
+ 
+
+ align:start position:0%
+put lots of garlic and lots of oil in
+the frying pan and cook it that way
+
+ align:start position:0%
+the frying pan and cook it that way
+ 
+
+ align:start position:0%
+the frying pan and cook it that way
+you could do that too make your own
+
+ align:start position:0%
+you could do that too make your own
+ 
+
+ align:start position:0%
+you could do that too make your own
+salad dressing with real
+
+ align:start position:0%
+salad dressing with real
+ 
+
+ align:start position:0%
+salad dressing with real
+extra virgin olive oil so you don't use
+
+ align:start position:0%
+extra virgin olive oil so you don't use
+ 
+
+ align:start position:0%
+extra virgin olive oil so you don't use
+salad dressings because there's nothing
+
+ align:start position:0%
+salad dressings because there's nothing
+ 
+
+ align:start position:0%
+salad dressings because there's nothing
+healthy about the salad dressings we buy
+
+ align:start position:0%
+healthy about the salad dressings we buy
+ 
+
+ align:start position:0%
+healthy about the salad dressings we buy
+nothing they're wicked salty look at
+
+ align:start position:0%
+nothing they're wicked salty look at
+ 
+
+ align:start position:0%
+nothing they're wicked salty look at
+sugar
+
+ align:start position:0%
+sugar
+ 
+
+ align:start position:0%
+sugar
+reduce your intake of desserts put some
+
+ align:start position:0%
+reduce your intake of desserts put some
+ 
+
+ align:start position:0%
+reduce your intake of desserts put some
+parameters you know um around desserts
+
+ align:start position:0%
+parameters you know um around desserts
+ 
+
+ align:start position:0%
+parameters you know um around desserts
+so that you have it maybe on the weekend
+
+ align:start position:0%
+so that you have it maybe on the weekend
+ 
+
+ align:start position:0%
+so that you have it maybe on the weekend
+you have it twice a week you don't have
+
+ align:start position:0%
+you have it twice a week you don't have
+ 
+
+ align:start position:0%
+you have it twice a week you don't have
+cookies every single day or just because
+
+ align:start position:0%
+cookies every single day or just because
+ 
+
+ align:start position:0%
+cookies every single day or just because
+it's thursday night at nine o'clock i'm
+
+ align:start position:0%
+it's thursday night at nine o'clock i'm
+ 
+
+ align:start position:0%
+it's thursday night at nine o'clock i'm
+having cookies in front of the tv
+
+ align:start position:0%
+having cookies in front of the tv
+ 
+
+ align:start position:0%
+having cookies in front of the tv
+that's another thing we as americans
+
+ align:start position:0%
+that's another thing we as americans
+ 
+
+ align:start position:0%
+that's another thing we as americans
+struggle with that we want sweets all
+
+ align:start position:0%
+struggle with that we want sweets all
+ 
+
+ align:start position:0%
+struggle with that we want sweets all
+the time for no reason i think in these
+
+ align:start position:0%
+the time for no reason i think in these
+ 
+
+ align:start position:0%
+the time for no reason i think in these
+cultures it's used more for a
+
+ align:start position:0%
+cultures it's used more for a
+ 
+
+ align:start position:0%
+cultures it's used more for a
+celebration oh it's a holiday it's a
+
+ align:start position:0%
+celebration oh it's a holiday it's a
+ 
+
+ align:start position:0%
+celebration oh it's a holiday it's a
+special time it isn't just three o'clock
+
+ align:start position:0%
+special time it isn't just three o'clock
+ 
+
+ align:start position:0%
+special time it isn't just three o'clock
+on tuesday and i'll have a huge
+
+ align:start position:0%
+on tuesday and i'll have a huge
+ 
+
+ align:start position:0%
+on tuesday and i'll have a huge
+rebecca's cookie like this
+
+ align:start position:0%
+rebecca's cookie like this
+ 
+
+ align:start position:0%
+rebecca's cookie like this
+that's like a 600 calorie investment
+
+ align:start position:0%
+that's like a 600 calorie investment
+ 
+
+ align:start position:0%
+that's like a 600 calorie investment
+there with butter cookies are made with
+
+ align:start position:0%
+there with butter cookies are made with
+ 
+
+ align:start position:0%
+there with butter cookies are made with
+butter um here another way eat plain
+
+ align:start position:0%
+butter um here another way eat plain
+ 
+
+ align:start position:0%
+butter um here another way eat plain
+yogurt yolk and put your own fruit
+
+ align:start position:0%
+yogurt yolk and put your own fruit
+ 
+
+ align:start position:0%
+yogurt yolk and put your own fruit
+and maybe a drizzle the plain there's
+
+ align:start position:0%
+and maybe a drizzle the plain there's
+ 
+
+ align:start position:0%
+and maybe a drizzle the plain there's
+another classic greek food greek night
+
+ align:start position:0%
+another classic greek food greek night
+ 
+
+ align:start position:0%
+another classic greek food greek night
+honey
+
+ align:start position:0%
+honey
+ 
+
+ align:start position:0%
+honey
+nuts could go here too as opposed to
+
+ align:start position:0%
+nuts could go here too as opposed to
+ 
+
+ align:start position:0%
+nuts could go here too as opposed to
+those yogurts that have a lot of sugar
+
+ align:start position:0%
+those yogurts that have a lot of sugar
+ 
+
+ align:start position:0%
+those yogurts that have a lot of sugar
+added to them we like sweet foods here
+
+ align:start position:0%
+added to them we like sweet foods here
+ 
+
+ align:start position:0%
+added to them we like sweet foods here
+yes okay um have meat be a small part of
+
+ align:start position:0%
+yes okay um have meat be a small part of
+ 
+
+ align:start position:0%
+yes okay um have meat be a small part of
+the meal fine we said that
+
+ align:start position:0%
+the meal fine we said that
+ 
+
+ align:start position:0%
+the meal fine we said that
+eat fish with small bones enjoy smell
+
+ align:start position:0%
+eat fish with small bones enjoy smell
+ 
+
+ align:start position:0%
+eat fish with small bones enjoy smell
+sardines necklace on packaged foods
+
+ align:start position:0%
+sardines necklace on packaged foods
+ 
+
+ align:start position:0%
+sardines necklace on packaged foods
+boxed foods have this instead and then i
+
+ align:start position:0%
+boxed foods have this instead and then i
+ 
+
+ align:start position:0%
+boxed foods have this instead and then i
+think that's it i have one slide that
+
+ align:start position:0%
+think that's it i have one slide that
+ 
+
+ align:start position:0%
+think that's it i have one slide that
+says i'm gonna challenge you all what
+
+ align:start position:0%
+says i'm gonna challenge you all what
+ 
+
+ align:start position:0%
+says i'm gonna challenge you all what
+can you do now so after tonight after
+
+ align:start position:0%
+can you do now so after tonight after
+ 
+
+ align:start position:0%
+can you do now so after tonight after
+you listen to me and you know your diets
+
+ align:start position:0%
+you listen to me and you know your diets
+ 
+
+ align:start position:0%
+you listen to me and you know your diets
+what can you do now
+
+ align:start position:0%
+what can you do now
+ 
+
+ align:start position:0%
+what can you do now
+think of one item that you'd like to
+
+ align:start position:0%
+think of one item that you'd like to
+ 
+
+ align:start position:0%
+think of one item that you'd like to
+change about your diet
+
+ align:start position:0%
+change about your diet
+ 
+
+ align:start position:0%
+change about your diet
+that would lead you closer to a
+
+ align:start position:0%
+that would lead you closer to a
+ 
+
+ align:start position:0%
+that would lead you closer to a
+mediterranean diet you're not going to
+
+ align:start position:0%
+mediterranean diet you're not going to
+ 
+
+ align:start position:0%
+mediterranean diet you're not going to
+revamp your diet in a night but maybe
+
+ align:start position:0%
+revamp your diet in a night but maybe
+ 
+
+ align:start position:0%
+revamp your diet in a night but maybe
+you could do one thing
+
+ align:start position:0%
+you could do one thing
+ 
+
+ align:start position:0%
+you could do one thing
+you could try a little bit closer
+
+ align:start position:0%
+you could try a little bit closer
+ 
+
+ align:start position:0%
+you could try a little bit closer
+so that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/eXf2Zak-s0o.txt b/eXf2Zak-s0o.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d8d3f65eb23f8bb355d3e371efd8a23af41ac5b9
--- /dev/null
+++ b/eXf2Zak-s0o.txt
@@ -0,0 +1,195 @@
+align:start position:0%
+ 
+in this lecture we start our discussion
+
+ align:start position:0%
+in this lecture we start our discussion
+ 
+
+ align:start position:0%
+in this lecture we start our discussion
+of continuous random variables we will
+
+ align:start position:0%
+of continuous random variables we will
+ 
+
+ align:start position:0%
+of continuous random variables we will
+focus on the case of a single continuous
+
+ align:start position:0%
+focus on the case of a single continuous
+ 
+
+ align:start position:0%
+focus on the case of a single continuous
+random variable and will describe its
+
+ align:start position:0%
+random variable and will describe its
+ 
+
+ align:start position:0%
+random variable and will describe its
+distribution using a so called
+
+ align:start position:0%
+distribution using a so called
+ 
+
+ align:start position:0%
+distribution using a so called
+probability density function an object
+
+ align:start position:0%
+probability density function an object
+ 
+
+ align:start position:0%
+probability density function an object
+that will replace the PMF s from the
+
+ align:start position:0%
+that will replace the PMF s from the
+ 
+
+ align:start position:0%
+that will replace the PMF s from the
+discrete case we will then proceed to
+
+ align:start position:0%
+discrete case we will then proceed to
+ 
+
+ align:start position:0%
+discrete case we will then proceed to
+define the expectation and the variance
+
+ align:start position:0%
+define the expectation and the variance
+ 
+
+ align:start position:0%
+define the expectation and the variance
+of a continuous random variable and will
+
+ align:start position:0%
+of a continuous random variable and will
+ 
+
+ align:start position:0%
+of a continuous random variable and will
+see that their basic properties remain
+
+ align:start position:0%
+see that their basic properties remain
+ 
+
+ align:start position:0%
+see that their basic properties remain
+unchanged there will be one new concept
+
+ align:start position:0%
+unchanged there will be one new concept
+ 
+
+ align:start position:0%
+unchanged there will be one new concept
+the cumulative distribution function
+
+ align:start position:0%
+the cumulative distribution function
+ 
+
+ align:start position:0%
+the cumulative distribution function
+which will allow us to describe in a
+
+ align:start position:0%
+which will allow us to describe in a
+ 
+
+ align:start position:0%
+which will allow us to describe in a
+unified manner both discrete and
+
+ align:start position:0%
+unified manner both discrete and
+ 
+
+ align:start position:0%
+unified manner both discrete and
+continuous random variables even
+
+ align:start position:0%
+continuous random variables even
+ 
+
+ align:start position:0%
+continuous random variables even
+so-called mixed random variables that
+
+ align:start position:0%
+so-called mixed random variables that
+ 
+
+ align:start position:0%
+so-called mixed random variables that
+have both a discrete and the continuous
+
+ align:start position:0%
+have both a discrete and the continuous
+ 
+
+ align:start position:0%
+have both a discrete and the continuous
+component in the course of this lecture
+
+ align:start position:0%
+component in the course of this lecture
+ 
+
+ align:start position:0%
+component in the course of this lecture
+we will also introduce some of the most
+
+ align:start position:0%
+we will also introduce some of the most
+ 
+
+ align:start position:0%
+we will also introduce some of the most
+common continuous random variables
+
+ align:start position:0%
+common continuous random variables
+ 
+
+ align:start position:0%
+common continuous random variables
+uniform exponential and normal we will
+
+ align:start position:0%
+uniform exponential and normal we will
+ 
+
+ align:start position:0%
+uniform exponential and normal we will
+pay special attention to the normal
+
+ align:start position:0%
+pay special attention to the normal
+ 
+
+ align:start position:0%
+pay special attention to the normal
+distribution and the ways that we can
+
+ align:start position:0%
+distribution and the ways that we can
+ 
+
+ align:start position:0%
+distribution and the ways that we can
+calculate the Associated probabilities
\ No newline at end of file
diff --git a/fK9AGvLf3yw.txt b/fK9AGvLf3yw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c1473ac6908c7e3d6ce919913c804367aeaa782
--- /dev/null
+++ b/fK9AGvLf3yw.txt
@@ -0,0 +1,12688 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so we'll start with we'll
+
+ align:start position:0%
+ocw.mit.edu so we'll start with we'll
+ 
+
+ align:start position:0%
+ocw.mit.edu so we'll start with we'll
+start quickly going over the concept
+
+ align:start position:0%
+start quickly going over the concept
+ 
+
+ align:start position:0%
+start quickly going over the concept
+questions for the homework this
+
+ align:start position:0%
+questions for the homework this
+ 
+
+ align:start position:0%
+questions for the homework this
+week so you have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+two rotor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system it says if you give it a
+
+ align:start position:0%
+system it says if you give it a
+ 
+
+ align:start position:0%
+system it says if you give it a
+deflection exactly the mode shape of
+
+ align:start position:0%
+deflection exactly the mode shape of
+ 
+
+ align:start position:0%
+deflection exactly the mode shape of
+mode
+
+ align:start position:0%
+mode
+ 
+
+ align:start position:0%
+mode
+two what frequency components do you
+
+ align:start position:0%
+two what frequency components do you
+ 
+
+ align:start position:0%
+two what frequency components do you
+expect the transient response to
+
+ align:start position:0%
+expect the transient response to
+ 
+
+ align:start position:0%
+expect the transient response to
+have so some people most people said
+
+ align:start position:0%
+have so some people most people said
+ 
+
+ align:start position:0%
+have so some people most people said
+only Omega 2 but quite a few people said
+
+ align:start position:0%
+only Omega 2 but quite a few people said
+ 
+
+ align:start position:0%
+only Omega 2 but quite a few people said
+both so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this introduction to vibration that we
+
+ align:start position:0%
+this introduction to vibration that we
+ 
+
+ align:start position:0%
+this introduction to vibration that we
+have been doing for the last few
+
+ align:start position:0%
+have been doing for the last few
+ 
+
+ align:start position:0%
+have been doing for the last few
+lectures my goal in it is to have you
+
+ align:start position:0%
+lectures my goal in it is to have you
+ 
+
+ align:start position:0%
+lectures my goal in it is to have you
+folks go away with a pretty good
+
+ align:start position:0%
+folks go away with a pretty good
+ 
+
+ align:start position:0%
+folks go away with a pretty good
+conceptual understanding of the basics
+
+ align:start position:0%
+conceptual understanding of the basics
+ 
+
+ align:start position:0%
+conceptual understanding of the basics
+of vibration and on the the final exam
+
+ align:start position:0%
+of vibration and on the the final exam
+ 
+
+ align:start position:0%
+of vibration and on the the final exam
+I'm not going to have you derive
+
+ align:start position:0%
+I'm not going to have you derive
+ 
+
+ align:start position:0%
+I'm not going to have you derive
+anything you know
+
+ align:start position:0%
+anything you know
+ 
+
+ align:start position:0%
+anything you know
+like finding the natural frequencies of
+
+ align:start position:0%
+like finding the natural frequencies of
+ 
+
+ align:start position:0%
+like finding the natural frequencies of
+a 3X 3 degree Freedom system you know
+
+ align:start position:0%
+a 3X 3 degree Freedom system you know
+ 
+
+ align:start position:0%
+a 3X 3 degree Freedom system you know
+solving a sixth order system in Omega
+
+ align:start position:0%
+solving a sixth order system in Omega
+ 
+
+ align:start position:0%
+solving a sixth order system in Omega
+squar but I won't do that kind of thing
+
+ align:start position:0%
+squar but I won't do that kind of thing
+ 
+
+ align:start position:0%
+squar but I won't do that kind of thing
+to you but questions like this are
+
+ align:start position:0%
+to you but questions like this are
+ 
+
+ align:start position:0%
+to you but questions like this are
+really fair game so if uh we did this
+
+ align:start position:0%
+really fair game so if uh we did this
+ 
+
+ align:start position:0%
+really fair game so if uh we did this
+business by modal analysis and we did an
+
+ align:start position:0%
+business by modal analysis and we did an
+ 
+
+ align:start position:0%
+business by modal analysis and we did an
+example the other day where you where
+
+ align:start position:0%
+example the other day where you where
+ 
+
+ align:start position:0%
+example the other day where you where
+with the system we had here if you
+
+ align:start position:0%
+with the system we had here if you
+ 
+
+ align:start position:0%
+with the system we had here if you
+deflect it in exactly the shape of one
+
+ align:start position:0%
+deflect it in exactly the shape of one
+ 
+
+ align:start position:0%
+deflect it in exactly the shape of one
+mode what kind of response do you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get initial conditions that are shaped
+
+ align:start position:0%
+get initial conditions that are shaped
+ 
+
+ align:start position:0%
+get initial conditions that are shaped
+exactly like one of the mode
+
+ align:start position:0%
+exactly like one of the mode
+ 
+
+ align:start position:0%
+exactly like one of the mode
+shapes it has exactly that
+
+ align:start position:0%
+shapes it has exactly that
+ 
+
+ align:start position:0%
+shapes it has exactly that
+natural frequency well not only have
+
+ align:start position:0%
+natural frequency well not only have
+ 
+
+ align:start position:0%
+natural frequency well not only have
+only that natural frequency in it but
+
+ align:start position:0%
+only that natural frequency in it but
+ 
+
+ align:start position:0%
+only that natural frequency in it but
+the if you deflect it initially in the
+
+ align:start position:0%
+the if you deflect it initially in the
+ 
+
+ align:start position:0%
+the if you deflect it initially in the
+mode shape what will the responding
+
+ align:start position:0%
+mode shape what will the responding
+ 
+
+ align:start position:0%
+mode shape what will the responding
+motion look like just like the mode
+
+ align:start position:0%
+motion look like just like the mode
+ 
+
+ align:start position:0%
+motion look like just like the mode
+shape just like the mode shape and if
+
+ align:start position:0%
+shape just like the mode shape and if
+ 
+
+ align:start position:0%
+shape just like the mode shape and if
+the motion is in a particular mode shape
+
+ align:start position:0%
+the motion is in a particular mode shape
+ 
+
+ align:start position:0%
+the motion is in a particular mode shape
+it will be at this is Transit vibration
+
+ align:start position:0%
+it will be at this is Transit vibration
+ 
+
+ align:start position:0%
+it will be at this is Transit vibration
+no external Force you deflect it and let
+
+ align:start position:0%
+no external Force you deflect it and let
+ 
+
+ align:start position:0%
+no external Force you deflect it and let
+it go you will see only Motion in that
+
+ align:start position:0%
+it go you will see only Motion in that
+ 
+
+ align:start position:0%
+it go you will see only Motion in that
+mode if it's if you give it an initial
+
+ align:start position:0%
+mode if it's if you give it an initial
+ 
+
+ align:start position:0%
+mode if it's if you give it an initial
+deflections exactly in that mode shape
+
+ align:start position:0%
+deflections exactly in that mode shape
+ 
+
+ align:start position:0%
+deflections exactly in that mode shape
+if you did if you went to the other mode
+
+ align:start position:0%
+if you did if you went to the other mode
+ 
+
+ align:start position:0%
+if you did if you went to the other mode
+and deflected it that way and let go it
+
+ align:start position:0%
+and deflected it that way and let go it
+ 
+
+ align:start position:0%
+and deflected it that way and let go it
+would change frequency and would vibrate
+
+ align:start position:0%
+would change frequency and would vibrate
+ 
+
+ align:start position:0%
+would change frequency and would vibrate
+only in that shape and anything else in
+
+ align:start position:0%
+only in that shape and anything else in
+ 
+
+ align:start position:0%
+only in that shape and anything else in
+be any other combination of motions is
+
+ align:start position:0%
+be any other combination of motions is
+ 
+
+ align:start position:0%
+be any other combination of motions is
+some linear sum of those two mode shapes
+
+ align:start position:0%
+some linear sum of those two mode shapes
+ 
+
+ align:start position:0%
+some linear sum of those two mode shapes
+any other allowable motion of the system
+
+ align:start position:0%
+any other allowable motion of the system
+ 
+
+ align:start position:0%
+any other allowable motion of the system
+can be made up of some weighted sum of
+
+ align:start position:0%
+can be made up of some weighted sum of
+ 
+
+ align:start position:0%
+can be made up of some weighted sum of
+the two mode shapes right and that's the
+
+ align:start position:0%
+the two mode shapes right and that's the
+ 
+
+ align:start position:0%
+the two mode shapes right and that's the
+amount of each mode that you get is the
+
+ align:start position:0%
+amount of each mode that you get is the
+ 
+
+ align:start position:0%
+amount of each mode that you get is the
+weighted sum what are the the weightings
+
+ align:start position:0%
+weighted sum what are the the weightings
+ 
+
+ align:start position:0%
+weighted sum what are the the weightings
+but the weightings are there one zero
+
+ align:start position:0%
+but the weightings are there one zero
+ 
+
+ align:start position:0%
+but the weightings are there one zero
+then it's all one mode not of another if
+
+ align:start position:0%
+then it's all one mode not of another if
+ 
+
+ align:start position:0%
+then it's all one mode not of another if
+it takes some of each mode to give you
+
+ align:start position:0%
+it takes some of each mode to give you
+ 
+
+ align:start position:0%
+it takes some of each mode to give you
+the initial deflected shape that's how
+
+ align:start position:0%
+the initial deflected shape that's how
+ 
+
+ align:start position:0%
+the initial deflected shape that's how
+much of each mode you get so the answer
+
+ align:start position:0%
+much of each mode you get so the answer
+ 
+
+ align:start position:0%
+much of each mode you get so the answer
+to this question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is only mode two okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next I forget what you were given online
+
+ align:start position:0%
+next I forget what you were given online
+ 
+
+ align:start position:0%
+next I forget what you were given online
+apply the concept which modor is likely
+
+ align:start position:0%
+apply the concept which modor is likely
+ 
+
+ align:start position:0%
+apply the concept which modor is likely
+to dominate the steady state response
+
+ align:start position:0%
+to dominate the steady state response
+ 
+
+ align:start position:0%
+to dominate the steady state response
+for the exitation of
+
+ align:start position:0%
+for the exitation of
+ 
+
+ align:start position:0%
+for the exitation of
+Part D so it was probably being excited
+
+ align:start position:0%
+Part D so it was probably being excited
+ 
+
+ align:start position:0%
+Part D so it was probably being excited
+harmonically at the natural frequency of
+
+ align:start position:0%
+harmonically at the natural frequency of
+ 
+
+ align:start position:0%
+harmonically at the natural frequency of
+mode two so what do you which mode so
+
+ align:start position:0%
+mode two so what do you which mode so
+ 
+
+ align:start position:0%
+mode two so what do you which mode so
+harmonic excitation which mode do you
+
+ align:start position:0%
+harmonic excitation which mode do you
+ 
+
+ align:start position:0%
+harmonic excitation which mode do you
+expect to respond the most when you
+
+ align:start position:0%
+expect to respond the most when you
+ 
+
+ align:start position:0%
+expect to respond the most when you
+excited at one of the natural
+
+ align:start position:0%
+excited at one of the natural
+ 
+
+ align:start position:0%
+excited at one of the natural
+frequencies at that natural frequency
+
+ align:start position:0%
+frequencies at that natural frequency
+ 
+
+ align:start position:0%
+frequencies at that natural frequency
+why why
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well there's an igen value there but now
+
+ align:start position:0%
+well there's an igen value there but now
+ 
+
+ align:start position:0%
+well there's an igen value there but now
+we're talking about steady state
+
+ align:start position:0%
+we're talking about steady state
+ 
+
+ align:start position:0%
+we're talking about steady state
+response what's the transfer function of
+
+ align:start position:0%
+response what's the transfer function of
+ 
+
+ align:start position:0%
+response what's the transfer function of
+a single degree of Freedom system look
+
+ align:start position:0%
+a single degree of Freedom system look
+ 
+
+ align:start position:0%
+a single degree of Freedom system look
+like just trace it in the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+air right this is the response per unit
+
+ align:start position:0%
+air right this is the response per unit
+ 
+
+ align:start position:0%
+air right this is the response per unit
+input and where does it go way up high
+
+ align:start position:0%
+input and where does it go way up high
+ 
+
+ align:start position:0%
+input and where does it go way up high
+at the resonance and so if you have a
+
+ align:start position:0%
+at the resonance and so if you have a
+ 
+
+ align:start position:0%
+at the resonance and so if you have a
+two degree Freedom system how many
+
+ align:start position:0%
+two degree Freedom system how many
+ 
+
+ align:start position:0%
+two degree Freedom system how many
+resonances do you have what do you think
+
+ align:start position:0%
+resonances do you have what do you think
+ 
+
+ align:start position:0%
+resonances do you have what do you think
+the transfer function is going to look
+
+ align:start position:0%
+the transfer function is going to look
+ 
+
+ align:start position:0%
+the transfer function is going to look
+like for a two degree of Freedom system
+
+ align:start position:0%
+like for a two degree of Freedom system
+ 
+
+ align:start position:0%
+like for a two degree of Freedom system
+if you just plotted it just as plot as a
+
+ align:start position:0%
+if you just plotted it just as plot as a
+ 
+
+ align:start position:0%
+if you just plotted it just as plot as a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+frequency double Peak so the transfer
+
+ align:start position:0%
+frequency double Peak so the transfer
+ 
+
+ align:start position:0%
+frequency double Peak so the transfer
+function is likely to do that at one
+
+ align:start position:0%
+function is likely to do that at one
+ 
+
+ align:start position:0%
+function is likely to do that at one
+frequency and that at the next natural
+
+ align:start position:0%
+frequency and that at the next natural
+ 
+
+ align:start position:0%
+frequency and that at the next natural
+frequency okay and that's what we're
+
+ align:start position:0%
+frequency okay and that's what we're
+ 
+
+ align:start position:0%
+frequency okay and that's what we're
+going to talk about today in fact okay
+
+ align:start position:0%
+going to talk about today in fact okay
+ 
+
+ align:start position:0%
+going to talk about today in fact okay
+so if you excited the second natural
+
+ align:start position:0%
+so if you excited the second natural
+ 
+
+ align:start position:0%
+so if you excited the second natural
+frequency and it's lightly damped it's
+
+ align:start position:0%
+frequency and it's lightly damped it's
+ 
+
+ align:start position:0%
+frequency and it's lightly damped it's
+likely to be dominated by the second
+
+ align:start position:0%
+likely to be dominated by the second
+ 
+
+ align:start position:0%
+likely to be dominated by the second
+natur by the by that uh modal response
+
+ align:start position:0%
+natur by the by that uh modal response
+ 
+
+ align:start position:0%
+natur by the by that uh modal response
+is in that question if you is it
+
+ align:start position:0%
+is in that question if you is it
+ 
+
+ align:start position:0%
+is in that question if you is it
+guaranteed to be only that mode
+
+ align:start position:0%
+guaranteed to be only that mode
+ 
+
+ align:start position:0%
+guaranteed to be only that mode
+responding even if you drive it at the
+
+ align:start position:0%
+responding even if you drive it at the
+ 
+
+ align:start position:0%
+responding even if you drive it at the
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+frequency another way to saying this
+
+ align:start position:0%
+frequency another way to saying this
+ 
+
+ align:start position:0%
+frequency another way to saying this
+question can the first mode have some
+
+ align:start position:0%
+question can the first mode have some
+ 
+
+ align:start position:0%
+question can the first mode have some
+response at any frequency you excite the
+
+ align:start position:0%
+response at any frequency you excite the
+ 
+
+ align:start position:0%
+response at any frequency you excite the
+system at sure it has transfer function
+
+ align:start position:0%
+system at sure it has transfer function
+ 
+
+ align:start position:0%
+system at sure it has transfer function
+it's continuous and frequency it just
+
+ align:start position:0%
+it's continuous and frequency it just
+ 
+
+ align:start position:0%
+it's continuous and frequency it just
+won't be very big okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next ah what the value for what value is
+
+ align:start position:0%
+next ah what the value for what value is
+ 
+
+ align:start position:0%
+next ah what the value for what value is
+a makeover megaan is the force
+
+ align:start position:0%
+a makeover megaan is the force
+ 
+
+ align:start position:0%
+a makeover megaan is the force
+transmitted to the wall going to be the
+
+ align:start position:0%
+transmitted to the wall going to be the
+ 
+
+ align:start position:0%
+transmitted to the wall going to be the
+greatest
+
+ align:start position:0%
+greatest
+ 
+
+ align:start position:0%
+greatest
+so this is when we make this this this
+
+ align:start position:0%
+so this is when we make this this this
+ 
+
+ align:start position:0%
+so this is when we make this this this
+is now we're doing
+
+ align:start position:0%
+is now we're doing
+ 
+
+ align:start position:0%
+is now we're doing
+the it's rotating around okay so this
+
+ align:start position:0%
+the it's rotating around okay so this
+ 
+
+ align:start position:0%
+the it's rotating around okay so this
+thing has rotating
+
+ align:start position:0%
+thing has rotating
+ 
+
+ align:start position:0%
+thing has rotating
+mass now at a constant frequency so it's
+
+ align:start position:0%
+mass now at a constant frequency so it's
+ 
+
+ align:start position:0%
+mass now at a constant frequency so it's
+got you know a static
+
+ align:start position:0%
+got you know a static
+ 
+
+ align:start position:0%
+got you know a static
+unbalance and at what frequency would
+
+ align:start position:0%
+unbalance and at what frequency would
+ 
+
+ align:start position:0%
+unbalance and at what frequency would
+you expect the force transmitted to the
+
+ align:start position:0%
+you expect the force transmitted to the
+ 
+
+ align:start position:0%
+you expect the force transmitted to the
+wall would be the greatest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+at resonance because that's when you get
+
+ align:start position:0%
+at resonance because that's when you get
+ 
+
+ align:start position:0%
+at resonance because that's when you get
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+most response greatest response and the
+
+ align:start position:0%
+most response greatest response and the
+ 
+
+ align:start position:0%
+most response greatest response and the
+force transmitted to the wall is through
+
+ align:start position:0%
+force transmitted to the wall is through
+ 
+
+ align:start position:0%
+force transmitted to the wall is through
+the spring and through the dashbot and
+
+ align:start position:0%
+the spring and through the dashbot and
+ 
+
+ align:start position:0%
+the spring and through the dashbot and
+the bigger the Motions the bigger those
+
+ align:start position:0%
+the bigger the Motions the bigger those
+ 
+
+ align:start position:0%
+the bigger the Motions the bigger those
+forces are going to be okay
+
+ align:start position:0%
+forces are going to be okay
+ 
+
+ align:start position:0%
+forces are going to be okay
+next and so this is now if you account
+
+ align:start position:0%
+next and so this is now if you account
+ 
+
+ align:start position:0%
+next and so this is now if you account
+for the spring do you expect accounting
+
+ align:start position:0%
+for the spring do you expect accounting
+ 
+
+ align:start position:0%
+for the spring do you expect accounting
+for the mass of the spring to increase
+
+ align:start position:0%
+for the mass of the spring to increase
+ 
+
+ align:start position:0%
+for the mass of the spring to increase
+the predicted natural frequency or
+
+ align:start position:0%
+the predicted natural frequency or
+ 
+
+ align:start position:0%
+the predicted natural frequency or
+decrease it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+decrease I mean natural frequencies
+
+ align:start position:0%
+decrease I mean natural frequencies
+ 
+
+ align:start position:0%
+decrease I mean natural frequencies
+behave like square root of K Over M kind
+
+ align:start position:0%
+behave like square root of K Over M kind
+ 
+
+ align:start position:0%
+behave like square root of K Over M kind
+of thing right if you do anything that
+
+ align:start position:0%
+of thing right if you do anything that
+ 
+
+ align:start position:0%
+of thing right if you do anything that
+drives up the M natural frequency is
+
+ align:start position:0%
+drives up the M natural frequency is
+ 
+
+ align:start position:0%
+drives up the M natural frequency is
+going to go down another way of asking
+
+ align:start position:0%
+going to go down another way of asking
+ 
+
+ align:start position:0%
+going to go down another way of asking
+the same question is if you neglect Mass
+
+ align:start position:0%
+the same question is if you neglect Mass
+ 
+
+ align:start position:0%
+the same question is if you neglect Mass
+when you're estimating the natural
+
+ align:start position:0%
+when you're estimating the natural
+ 
+
+ align:start position:0%
+when you're estimating the natural
+frequency of a system how which way are
+
+ align:start position:0%
+frequency of a system how which way are
+ 
+
+ align:start position:0%
+frequency of a system how which way are
+you likely to be in
+
+ align:start position:0%
+you likely to be in
+ 
+
+ align:start position:0%
+you likely to be in
+error so when you this system normally
+
+ align:start position:0%
+error so when you this system normally
+ 
+
+ align:start position:0%
+error so when you this system normally
+we just ignore the mass of the springs
+
+ align:start position:0%
+we just ignore the mass of the springs
+ 
+
+ align:start position:0%
+we just ignore the mass of the springs
+and we calculate the natural frequency
+
+ align:start position:0%
+and we calculate the natural frequency
+ 
+
+ align:start position:0%
+and we calculate the natural frequency
+ofun of K Over m and we're almost
+
+ align:start position:0%
+ofun of K Over m and we're almost
+ 
+
+ align:start position:0%
+ofun of K Over m and we're almost
+certain to be predict what too high or
+
+ align:start position:0%
+certain to be predict what too high or
+ 
+
+ align:start position:0%
+certain to be predict what too high or
+too
+
+ align:start position:0%
+too
+ 
+
+ align:start position:0%
+too
+low too high because we've ignored some
+
+ align:start position:0%
+low too high because we've ignored some
+ 
+
+ align:start position:0%
+low too high because we've ignored some
+mass in the system okay next I think
+
+ align:start position:0%
+mass in the system okay next I think
+ 
+
+ align:start position:0%
+mass in the system okay next I think
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+it I want to get on with today's lecture
+
+ align:start position:0%
+it I want to get on with today's lecture
+ 
+
+ align:start position:0%
+it I want to get on with today's lecture
+we
+
+ align:start position:0%
+we
+ 
+
+ align:start position:0%
+we
+have done vibration from the point of
+
+ align:start position:0%
+have done vibration from the point of
+ 
+
+ align:start position:0%
+have done vibration from the point of
+view of single deegree Freedom systems
+
+ align:start position:0%
+view of single deegree Freedom systems
+ 
+
+ align:start position:0%
+view of single deegree Freedom systems
+transient response and steady state
+
+ align:start position:0%
+transient response and steady state
+ 
+
+ align:start position:0%
+transient response and steady state
+response and then we've started looking
+
+ align:start position:0%
+response and then we've started looking
+ 
+
+ align:start position:0%
+response and then we've started looking
+at multiple degree of Freedom systems
+
+ align:start position:0%
+at multiple degree of Freedom systems
+ 
+
+ align:start position:0%
+at multiple degree of Freedom systems
+but we actually started it from the
+
+ align:start position:0%
+but we actually started it from the
+ 
+
+ align:start position:0%
+but we actually started it from the
+point of view of modal analysis and we
+
+ align:start position:0%
+point of view of modal analysis and we
+ 
+
+ align:start position:0%
+point of view of modal analysis and we
+looked at two degree Freedom systems and
+
+ align:start position:0%
+looked at two degree Freedom systems and
+ 
+
+ align:start position:0%
+looked at two degree Freedom systems and
+found out found the modal contributions
+
+ align:start position:0%
+found out found the modal contributions
+ 
+
+ align:start position:0%
+found out found the modal contributions
+of each of the modes and sort of did
+
+ align:start position:0%
+of each of the modes and sort of did
+ 
+
+ align:start position:0%
+of each of the modes and sort of did
+them one at a time so is there another
+
+ align:start position:0%
+them one at a time so is there another
+ 
+
+ align:start position:0%
+them one at a time so is there another
+way one some one of you asked me after
+
+ align:start position:0%
+way one some one of you asked me after
+ 
+
+ align:start position:0%
+way one some one of you asked me after
+class last time well can't you just
+
+ align:start position:0%
+class last time well can't you just
+ 
+
+ align:start position:0%
+class last time well can't you just
+solve the equation the differential
+
+ align:start position:0%
+solve the equation the differential
+ 
+
+ align:start position:0%
+solve the equation the differential
+equations directly and not bother with
+
+ align:start position:0%
+equations directly and not bother with
+ 
+
+ align:start position:0%
+equations directly and not bother with
+separating the modes out and figuring
+
+ align:start position:0%
+separating the modes out and figuring
+ 
+
+ align:start position:0%
+separating the modes out and figuring
+out the modal contributions the answer
+
+ align:start position:0%
+out the modal contributions the answer
+ 
+
+ align:start position:0%
+out the modal contributions the answer
+is yes and you do it by a transfer
+
+ align:start position:0%
+is yes and you do it by a transfer
+ 
+
+ align:start position:0%
+is yes and you do it by a transfer
+functions except now you will need more
+
+ align:start position:0%
+functions except now you will need more
+ 
+
+ align:start position:0%
+functions except now you will need more
+than one if you have more than one
+
+ align:start position:0%
+than one if you have more than one
+ 
+
+ align:start position:0%
+than one if you have more than one
+degree of Freedom
+
+ align:start position:0%
+degree of Freedom
+ 
+
+ align:start position:0%
+degree of Freedom
+so that's we're going that's what we'll
+
+ align:start position:0%
+so that's we're going that's what we'll
+ 
+
+ align:start position:0%
+so that's we're going that's what we'll
+uh focus on
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+today and we're going to do it
+
+ align:start position:0%
+today and we're going to do it
+ 
+
+ align:start position:0%
+today and we're going to do it
+by thinking about the
+
+ align:start position:0%
+by thinking about the
+ 
+
+ align:start position:0%
+by thinking about the
+example actually from the homework so in
+
+ align:start position:0%
+example actually from the homework so in
+ 
+
+ align:start position:0%
+example actually from the homework so in
+the homework you have this problem of
+
+ align:start position:0%
+the homework you have this problem of
+ 
+
+ align:start position:0%
+the homework you have this problem of
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cart with the uh p with the
+
+ align:start position:0%
+cart with the uh p with the
+ 
+
+ align:start position:0%
+cart with the uh p with the
+this pendulum hanging off of
+
+ align:start position:0%
+this pendulum hanging off of
+ 
+
+ align:start position:0%
+this pendulum hanging off of
+it and we in problem three I think it is
+
+ align:start position:0%
+it and we in problem three I think it is
+ 
+
+ align:start position:0%
+it and we in problem three I think it is
+to say okay now the pendulum is going to
+
+ align:start position:0%
+to say okay now the pendulum is going to
+ 
+
+ align:start position:0%
+to say okay now the pendulum is going to
+around go around a constant rate and
+
+ align:start position:0%
+around go around a constant rate and
+ 
+
+ align:start position:0%
+around go around a constant rate and
+it's going to turn this into a rotating
+
+ align:start position:0%
+it's going to turn this into a rotating
+ 
+
+ align:start position:0%
+it's going to turn this into a rotating
+imbalance problem and I short and the I
+
+ align:start position:0%
+imbalance problem and I short and the I
+ 
+
+ align:start position:0%
+imbalance problem and I short and the I
+shorten it up so it's just a little Mass
+
+ align:start position:0%
+shorten it up so it's just a little Mass
+ 
+
+ align:start position:0%
+shorten it up so it's just a little Mass
+spinning
+
+ align:start position:0%
+spinning
+ 
+
+ align:start position:0%
+spinning
+around you have
+
+ align:start position:0%
+around you have
+ 
+
+ align:start position:0%
+around you have
+K1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C1 X1 here
+
+ align:start position:0%
+C1 X1 here
+ 
+
+ align:start position:0%
+C1 X1 here
+and I think it's drawn there as
+
+ align:start position:0%
+and I think it's drawn there as
+ 
+
+ align:start position:0%
+and I think it's drawn there as
+Theta this is point a about which it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+spins and you know the nonlinear
+
+ align:start position:0%
+spins and you know the nonlinear
+ 
+
+ align:start position:0%
+spins and you know the nonlinear
+equations of motion when for treating
+
+ align:start position:0%
+equations of motion when for treating
+ 
+
+ align:start position:0%
+equations of motion when for treating
+this as a simp as a two degree of
+
+ align:start position:0%
+this as a simp as a two degree of
+ 
+
+ align:start position:0%
+this as a simp as a two degree of
+Freedom system just a pendulum on a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+cart and that nonlinear
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion and I'm going to put subscripts
+
+ align:start position:0%
+motion and I'm going to put subscripts
+ 
+
+ align:start position:0%
+motion and I'm going to put subscripts
+here now I'm going to call this
+
+ align:start position:0%
+here now I'm going to call this
+ 
+
+ align:start position:0%
+here now I'm going to call this
+coordinate X1 because we're going to
+
+ align:start position:0%
+coordinate X1 because we're going to
+ 
+
+ align:start position:0%
+coordinate X1 because we're going to
+need a second second
+
+ align:start position:0%
+need a second second
+ 
+
+ align:start position:0%
+need a second second
+coordinate
+
+ align:start position:0%
+coordinate
+ 
+
+ align:start position:0%
+coordinate
+uh actually do we what am I saying we
+
+ align:start position:0%
+uh actually do we what am I saying we
+ 
+
+ align:start position:0%
+uh actually do we what am I saying we
+don't need to do
+
+ align:start position:0%
+don't need to do
+ 
+
+ align:start position:0%
+don't need to do
+that just X will do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we do need the M1 and M2 though and so
+
+ align:start position:0%
+we do need the M1 and M2 though and so
+ 
+
+ align:start position:0%
+we do need the M1 and M2 though and so
+that is all I'm going to move the
+
+ align:start position:0%
+that is all I'm going to move the
+ 
+
+ align:start position:0%
+that is all I'm going to move the
+remaining stuff to the right hand side
+
+ align:start position:0%
+remaining stuff to the right hand side
+ 
+
+ align:start position:0%
+remaining stuff to the right hand side
+so this is your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonlinear
+
+ align:start position:0%
+nonlinear
+ 
+
+ align:start position:0%
+nonlinear
+M2
+
+ align:start position:0%
+M2
+ 
+
+ align:start position:0%
+M2
+L Theta dble
+
+ align:start position:0%
+L Theta dble
+ 
+
+ align:start position:0%
+L Theta dble
+dot cos
+
+ align:start position:0%
+dot cos
+ 
+
+ align:start position:0%
+dot cos
+Theta minus Theta do^
+
+ align:start position:0%
+Theta minus Theta do^
+ 
+
+ align:start position:0%
+Theta minus Theta do^
+SAR s sin
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Theta on the right hand
+
+ align:start position:0%
+Theta on the right hand
+ 
+
+ align:start position:0%
+Theta on the right hand
+side and I think I need a minus if I do
+
+ align:start position:0%
+side and I think I need a minus if I do
+ 
+
+ align:start position:0%
+side and I think I need a minus if I do
+that now what I do in this problem I
+
+ align:start position:0%
+that now what I do in this problem I
+ 
+
+ align:start position:0%
+that now what I do in this problem I
+said let's let Theta dot equal Omega and
+
+ align:start position:0%
+said let's let Theta dot equal Omega and
+ 
+
+ align:start position:0%
+said let's let Theta dot equal Omega and
+that's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constant and so that says Theta double
+
+ align:start position:0%
+constant and so that says Theta double
+ 
+
+ align:start position:0%
+constant and so that says Theta double
+dot is zero when you do that then this
+
+ align:start position:0%
+dot is zero when you do that then this
+ 
+
+ align:start position:0%
+dot is zero when you do that then this
+term goes away and this becomes Omega s
+
+ align:start position:0%
+term goes away and this becomes Omega s
+ 
+
+ align:start position:0%
+term goes away and this becomes Omega s
+s minus * a minus this equals
+
+ align:start position:0%
+s minus * a minus this equals
+ 
+
+ align:start position:0%
+s minus * a minus this equals
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+M2
+
+ align:start position:0%
+M2
+ 
+
+ align:start position:0%
+M2
+L Omega
+
+ align:start position:0%
+L Omega
+ 
+
+ align:start position:0%
+L Omega
+squar
+
+ align:start position:0%
+squar
+ 
+
+ align:start position:0%
+squar
+s and Theta is just Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T So by
+
+ align:start position:0%
+T So by
+ 
+
+ align:start position:0%
+T So by
+forcing what was previously a unknown
+
+ align:start position:0%
+forcing what was previously a unknown
+ 
+
+ align:start position:0%
+forcing what was previously a unknown
+variable that you had to solve in this
+
+ align:start position:0%
+variable that you had to solve in this
+ 
+
+ align:start position:0%
+variable that you had to solve in this
+two for you had two equations and two
+
+ align:start position:0%
+two for you had two equations and two
+ 
+
+ align:start position:0%
+two for you had two equations and two
+unknown because you had two generalized
+
+ align:start position:0%
+unknown because you had two generalized
+ 
+
+ align:start position:0%
+unknown because you had two generalized
+coordinates that took to describe the
+
+ align:start position:0%
+coordinates that took to describe the
+ 
+
+ align:start position:0%
+coordinates that took to describe the
+motion of this thing X and Theta now
+
+ align:start position:0%
+motion of this thing X and Theta now
+ 
+
+ align:start position:0%
+motion of this thing X and Theta now
+once you prescribe Theta and it's given
+
+ align:start position:0%
+once you prescribe Theta and it's given
+ 
+
+ align:start position:0%
+once you prescribe Theta and it's given
+it's no longer a variable it's no longer
+
+ align:start position:0%
+it's no longer a variable it's no longer
+ 
+
+ align:start position:0%
+it's no longer a variable it's no longer
+a coordinate in your generalized in your
+
+ align:start position:0%
+a coordinate in your generalized in your
+ 
+
+ align:start position:0%
+a coordinate in your generalized in your
+equations of motion you have to solve
+
+ align:start position:0%
+equations of motion you have to solve
+ 
+
+ align:start position:0%
+equations of motion you have to solve
+for and it reduces this first dis
+
+ align:start position:0%
+for and it reduces this first dis
+ 
+
+ align:start position:0%
+for and it reduces this first dis
+equation to the equation of a single
+
+ align:start position:0%
+equation to the equation of a single
+ 
+
+ align:start position:0%
+equation to the equation of a single
+degree Freedom system on the left hand
+
+ align:start position:0%
+degree Freedom system on the left hand
+ 
+
+ align:start position:0%
+degree Freedom system on the left hand
+side is the response quantities just
+
+ align:start position:0%
+side is the response quantities just
+ 
+
+ align:start position:0%
+side is the response quantities just
+like usual MX do plus CX do plus KX and
+
+ align:start position:0%
+like usual MX do plus CX do plus KX and
+ 
+
+ align:start position:0%
+like usual MX do plus CX do plus KX and
+on the right hand side is a harmonic
+
+ align:start position:0%
+on the right hand side is a harmonic
+ 
+
+ align:start position:0%
+on the right hand side is a harmonic
+excitation and that's this unbalanced
+
+ align:start position:0%
+excitation and that's this unbalanced
+ 
+
+ align:start position:0%
+excitation and that's this unbalanced
+Mass going round and
+
+ align:start position:0%
+Mass going round and
+ 
+
+ align:start position:0%
+Mass going round and
+round so this has the form here this is
+
+ align:start position:0%
+round so this has the form here this is
+ 
+
+ align:start position:0%
+round so this has the form here this is
+some if you want to think of it this way
+
+ align:start position:0%
+some if you want to think of it this way
+ 
+
+ align:start position:0%
+some if you want to think of it this way
+this is some f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+KN and it looks like sin Omega T so this
+
+ align:start position:0%
+KN and it looks like sin Omega T so this
+ 
+
+ align:start position:0%
+KN and it looks like sin Omega T so this
+is just a single degree Freedom system
+
+ align:start position:0%
+is just a single degree Freedom system
+ 
+
+ align:start position:0%
+is just a single degree Freedom system
+excited by harmonic excitation and you
+
+ align:start position:0%
+excited by harmonic excitation and you
+ 
+
+ align:start position:0%
+excited by harmonic excitation and you
+know what it has a transfer function and
+
+ align:start position:0%
+know what it has a transfer function and
+ 
+
+ align:start position:0%
+know what it has a transfer function and
+you know know that there's going to be a
+
+ align:start position:0%
+you know know that there's going to be a
+ 
+
+ align:start position:0%
+you know know that there's going to be a
+resonance at the natural frequency of
+
+ align:start position:0%
+resonance at the natural frequency of
+ 
+
+ align:start position:0%
+resonance at the natural frequency of
+the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system and if you don't like working
+
+ align:start position:0%
+system and if you don't like working
+ 
+
+ align:start position:0%
+system and if you don't like working
+with s Omega T you know you could say
+
+ align:start position:0%
+with s Omega T you know you could say
+ 
+
+ align:start position:0%
+with s Omega T you know you could say
+well let's measure Omega Theta from here
+
+ align:start position:0%
+well let's measure Omega Theta from here
+ 
+
+ align:start position:0%
+well let's measure Omega Theta from here
+if you wanted to and now that's cosine
+
+ align:start position:0%
+if you wanted to and now that's cosine
+ 
+
+ align:start position:0%
+if you wanted to and now that's cosine
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+t Okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's sort of the setup
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me say one if I ask you to solve for
+
+ align:start position:0%
+let me say one if I ask you to solve for
+ 
+
+ align:start position:0%
+let me say one if I ask you to solve for
+the magnitude of the
+
+ align:start position:0%
+the magnitude of the
+ 
+
+ align:start position:0%
+the magnitude of the
+response X1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here how would you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so this is now single degree Freedom
+
+ align:start position:0%
+it so this is now single degree Freedom
+ 
+
+ align:start position:0%
+it so this is now single degree Freedom
+system excited by harmonic excitation
+
+ align:start position:0%
+system excited by harmonic excitation
+ 
+
+ align:start position:0%
+system excited by harmonic excitation
+steady state response how do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it this you do have to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know transfer function use a transfer
+
+ align:start position:0%
+know transfer function use a transfer
+ 
+
+ align:start position:0%
+know transfer function use a transfer
+function right so this is going to be
+
+ align:start position:0%
+function right so this is going to be
+ 
+
+ align:start position:0%
+function right so this is going to be
+the magnitude of the force times the
+
+ align:start position:0%
+the magnitude of the force times the
+ 
+
+ align:start position:0%
+the magnitude of the force times the
+magnitude of the
+
+ align:start position:0%
+magnitude of the
+ 
+
+ align:start position:0%
+magnitude of the
+HX F of Omega transfer
+
+ align:start position:0%
+HX F of Omega transfer
+ 
+
+ align:start position:0%
+HX F of Omega transfer
+function and that's how You' get the
+
+ align:start position:0%
+function and that's how You' get the
+ 
+
+ align:start position:0%
+function and that's how You' get the
+magnitude of the response and it
+
+ align:start position:0%
+magnitude of the response and it
+ 
+
+ align:start position:0%
+magnitude of the response and it
+happened to be at resonance then you
+
+ align:start position:0%
+happened to be at resonance then you
+ 
+
+ align:start position:0%
+happened to be at resonance then you
+know you'd be at the peak and if you're
+
+ align:start position:0%
+know you'd be at the peak and if you're
+ 
+
+ align:start position:0%
+know you'd be at the peak and if you're
+not at resonance wherever you happen to
+
+ align:start position:0%
+not at resonance wherever you happen to
+ 
+
+ align:start position:0%
+not at resonance wherever you happen to
+be in frequency is where you would
+
+ align:start position:0%
+be in frequency is where you would
+ 
+
+ align:start position:0%
+be in frequency is where you would
+evaluate this and there's your
+
+ align:start position:0%
+evaluate this and there's your
+ 
+
+ align:start position:0%
+evaluate this and there's your
+response
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a few years
+
+ align:start position:0%
+now a few years
+ 
+
+ align:start position:0%
+now a few years
+ago we every year twice a year in fact
+
+ align:start position:0%
+ago we every year twice a year in fact
+ 
+
+ align:start position:0%
+ago we every year twice a year in fact
+in they coming up in January we have
+
+ align:start position:0%
+in they coming up in January we have
+ 
+
+ align:start position:0%
+in they coming up in January we have
+doctoral exams for students who want to
+
+ align:start position:0%
+doctoral exams for students who want to
+ 
+
+ align:start position:0%
+doctoral exams for students who want to
+do phds in mechanical engineering and
+
+ align:start position:0%
+do phds in mechanical engineering and
+ 
+
+ align:start position:0%
+do phds in mechanical engineering and
+most departments at MIT have these also
+
+ align:start position:0%
+most departments at MIT have these also
+ 
+
+ align:start position:0%
+most departments at MIT have these also
+and in there's an in the Dynamics
+
+ align:start position:0%
+and in there's an in the Dynamics
+ 
+
+ align:start position:0%
+and in there's an in the Dynamics
+portion there's an oral exam part
+
+ align:start position:0%
+portion there's an oral exam part
+ 
+
+ align:start position:0%
+portion there's an oral exam part
+there's a written exam also but in the
+
+ align:start position:0%
+there's a written exam also but in the
+ 
+
+ align:start position:0%
+there's a written exam also but in the
+oral exam in
+
+ align:start position:0%
+oral exam in
+ 
+
+ align:start position:0%
+oral exam in
+this in this particular
+
+ align:start position:0%
+this in this particular
+ 
+
+ align:start position:0%
+this in this particular
+year gave a single degree Freedom system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and we posed and we all know that if we
+
+ align:start position:0%
+and we posed and we all know that if we
+ 
+
+ align:start position:0%
+and we posed and we all know that if we
+excite this thing with
+
+ align:start position:0%
+excite this thing with
+ 
+
+ align:start position:0%
+excite this thing with
+a harmonic excitation some
+
+ align:start position:0%
+a harmonic excitation some
+ 
+
+ align:start position:0%
+a harmonic excitation some
+F1
+
+ align:start position:0%
+F1
+ 
+
+ align:start position:0%
+F1
+cosine and I will I'll use complex
+
+ align:start position:0%
+cosine and I will I'll use complex
+ 
+
+ align:start position:0%
+cosine and I will I'll use complex
+notation because we're going to need it
+
+ align:start position:0%
+notation because we're going to need it
+ 
+
+ align:start position:0%
+notation because we're going to need it
+in a minute some fub1 e to the I Omega T
+
+ align:start position:0%
+in a minute some fub1 e to the I Omega T
+ 
+
+ align:start position:0%
+in a minute some fub1 e to the I Omega T
+that's the excitation we know what the
+
+ align:start position:0%
+that's the excitation we know what the
+ 
+
+ align:start position:0%
+that's the excitation we know what the
+steady state response to this looks like
+
+ align:start position:0%
+steady state response to this looks like
+ 
+
+ align:start position:0%
+steady state response to this looks like
+the magnitude looks like looks like that
+
+ align:start position:0%
+the magnitude looks like looks like that
+ 
+
+ align:start position:0%
+the magnitude looks like looks like that
+transfer function
+
+ align:start position:0%
+transfer function
+ 
+
+ align:start position:0%
+transfer function
+right but we Poe so most doctoral
+
+ align:start position:0%
+right but we Poe so most doctoral
+ 
+
+ align:start position:0%
+right but we Poe so most doctoral
+students would be doctoral students
+
+ align:start position:0%
+students would be doctoral students
+ 
+
+ align:start position:0%
+students would be doctoral students
+would know all about a single degree of
+
+ align:start position:0%
+would know all about a single degree of
+ 
+
+ align:start position:0%
+would know all about a single degree of
+Freedom system so we POS the following
+
+ align:start position:0%
+Freedom system so we POS the following
+ 
+
+ align:start position:0%
+Freedom system so we POS the following
+question well we know that the response
+
+ align:start position:0%
+question well we know that the response
+ 
+
+ align:start position:0%
+question well we know that the response
+of this is going to you know do
+
+ align:start position:0%
+of this is going to you know do
+ 
+
+ align:start position:0%
+of this is going to you know do
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+that and and you evaluate this at
+
+ align:start position:0%
+that and and you evaluate this at
+ 
+
+ align:start position:0%
+that and and you evaluate this at
+Whatever frequency you're interested in
+
+ align:start position:0%
+Whatever frequency you're interested in
+ 
+
+ align:start position:0%
+Whatever frequency you're interested in
+including right at
+
+ align:start position:0%
+including right at
+ 
+
+ align:start position:0%
+including right at
+resonance and the question we ask is it
+
+ align:start position:0%
+resonance and the question we ask is it
+ 
+
+ align:start position:0%
+resonance and the question we ask is it
+possible to add a second spring
+
+ align:start position:0%
+possible to add a second spring
+ 
+
+ align:start position:0%
+possible to add a second spring
+and a second Mass
+
+ align:start position:0%
+and a second Mass
+ 
+
+ align:start position:0%
+and a second Mass
+M2 and
+
+ align:start position:0%
+M2 and
+ 
+
+ align:start position:0%
+M2 and
+K2 such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that so is it possible to pick a K2 and
+
+ align:start position:0%
+that so is it possible to pick a K2 and
+ 
+
+ align:start position:0%
+that so is it possible to pick a K2 and
+an M2 such that with this excitation on
+
+ align:start position:0%
+an M2 such that with this excitation on
+ 
+
+ align:start position:0%
+an M2 such that with this excitation on
+here the motion of that thing will be
+
+ align:start position:0%
+here the motion of that thing will be
+ 
+
+ align:start position:0%
+here the motion of that thing will be
+zero okay and in order to solve this
+
+ align:start position:0%
+zero okay and in order to solve this
+ 
+
+ align:start position:0%
+zero okay and in order to solve this
+problem as soon as you put this on here
+
+ align:start position:0%
+problem as soon as you put this on here
+ 
+
+ align:start position:0%
+problem as soon as you put this on here
+and assume it's it's you know sliding
+
+ align:start position:0%
+and assume it's it's you know sliding
+ 
+
+ align:start position:0%
+and assume it's it's you know sliding
+along it's not can't fall it only has
+
+ align:start position:0%
+along it's not can't fall it only has
+ 
+
+ align:start position:0%
+along it's not can't fall it only has
+horizontal possible motion and we'd give
+
+ align:start position:0%
+horizontal possible motion and we'd give
+ 
+
+ align:start position:0%
+horizontal possible motion and we'd give
+it some coordinate describing it motion
+
+ align:start position:0%
+it some coordinate describing it motion
+ 
+
+ align:start position:0%
+it some coordinate describing it motion
+X2 so now how many degrees of freedom
+
+ align:start position:0%
+X2 so now how many degrees of freedom
+ 
+
+ align:start position:0%
+X2 so now how many degrees of freedom
+does this problem
+
+ align:start position:0%
+does this problem
+ 
+
+ align:start position:0%
+does this problem
+have two how many equations of motion do
+
+ align:start position:0%
+have two how many equations of motion do
+ 
+
+ align:start position:0%
+have two how many equations of motion do
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+expect okay how many peaks in this in a
+
+ align:start position:0%
+expect okay how many peaks in this in a
+ 
+
+ align:start position:0%
+expect okay how many peaks in this in a
+transfer function would you expect to
+
+ align:start position:0%
+transfer function would you expect to
+ 
+
+ align:start position:0%
+transfer function would you expect to
+see two resonances okay so now we need
+
+ align:start position:0%
+see two resonances okay so now we need
+ 
+
+ align:start position:0%
+see two resonances okay so now we need
+to know we need to know how to find
+
+ align:start position:0%
+to know we need to know how to find
+ 
+
+ align:start position:0%
+to know we need to know how to find
+transfer functions for a multiple degree
+
+ align:start position:0%
+transfer functions for a multiple degree
+ 
+
+ align:start position:0%
+transfer functions for a multiple degree
+Freedom system so in in everything I've
+
+ align:start position:0%
+Freedom system so in in everything I've
+ 
+
+ align:start position:0%
+Freedom system so in in everything I've
+said about two degree of Freedom systems
+
+ align:start position:0%
+said about two degree of Freedom systems
+ 
+
+ align:start position:0%
+said about two degree of Freedom systems
+I've
+
+ align:start position:0%
+I've
+ 
+
+ align:start position:0%
+I've
+been every is everything is
+
+ align:start position:0%
+been every is everything is
+ 
+
+ align:start position:0%
+been every is everything is
+generalizable to end degrees of freedom
+
+ align:start position:0%
+generalizable to end degrees of freedom
+ 
+
+ align:start position:0%
+generalizable to end degrees of freedom
+so what I'm going to show you now is how
+
+ align:start position:0%
+so what I'm going to show you now is how
+ 
+
+ align:start position:0%
+so what I'm going to show you now is how
+to do transfer function funs for multi-
+
+ align:start position:0%
+to do transfer function funs for multi-
+ 
+
+ align:start position:0%
+to do transfer function funs for multi-
+deegree Freedom systems and I'm going to
+
+ align:start position:0%
+deegree Freedom systems and I'm going to
+ 
+
+ align:start position:0%
+deegree Freedom systems and I'm going to
+do it by way of example of a two degree
+
+ align:start position:0%
+do it by way of example of a two degree
+ 
+
+ align:start position:0%
+do it by way of example of a two degree
+Freedom one but just keep in mind that
+
+ align:start position:0%
+Freedom one but just keep in mind that
+ 
+
+ align:start position:0%
+Freedom one but just keep in mind that
+you can General completely generalize
+
+ align:start position:0%
+you can General completely generalize
+ 
+
+ align:start position:0%
+you can General completely generalize
+this so
+
+ align:start position:0%
+this so
+ 
+
+ align:start position:0%
+this so
+here's there's my system two masses two
+
+ align:start position:0%
+here's there's my system two masses two
+ 
+
+ align:start position:0%
+here's there's my system two masses two
+Springs and I could even have dashbot in
+
+ align:start position:0%
+Springs and I could even have dashbot in
+ 
+
+ align:start position:0%
+Springs and I could even have dashbot in
+here a C1 and I might have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C2 okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I could even in general additionally
+
+ align:start position:0%
+and I could even in general additionally
+ 
+
+ align:start position:0%
+and I could even in general additionally
+have a force acting on the second Mass
+
+ align:start position:0%
+have a force acting on the second Mass
+ 
+
+ align:start position:0%
+have a force acting on the second Mass
+which I'll call F2 e to the I Omega T so
+
+ align:start position:0%
+which I'll call F2 e to the I Omega T so
+ 
+
+ align:start position:0%
+which I'll call F2 e to the I Omega T so
+that's kind of that's a completely
+
+ align:start position:0%
+that's kind of that's a completely
+ 
+
+ align:start position:0%
+that's kind of that's a completely
+General problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now now the equations of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion for this system you could write
+
+ align:start position:0%
+motion for this system you could write
+ 
+
+ align:start position:0%
+motion for this system you could write
+down I'm we've done it many times now
+
+ align:start position:0%
+down I'm we've done it many times now
+ 
+
+ align:start position:0%
+down I'm we've done it many times now
+this particular system even but we could
+
+ align:start position:0%
+this particular system even but we could
+ 
+
+ align:start position:0%
+this particular system even but we could
+write them in Matrix form as
+
+ align:start position:0%
+write them in Matrix form as
+ 
+
+ align:start position:0%
+write them in Matrix form as
+m xou dot plus c x dot plus a
+
+ align:start position:0%
+m xou dot plus c x dot plus a
+ 
+
+ align:start position:0%
+m xou dot plus c x dot plus a
+k stiffness Matrix x
+
+ align:start position:0%
+k stiffness Matrix x
+ 
+
+ align:start position:0%
+k stiffness Matrix x
+equals an excite the excitation in this
+
+ align:start position:0%
+equals an excite the excitation in this
+ 
+
+ align:start position:0%
+equals an excite the excitation in this
+two degree well I'll just keep this
+
+ align:start position:0%
+two degree well I'll just keep this
+ 
+
+ align:start position:0%
+two degree well I'll just keep this
+completely General this is any in in
+
+ align:start position:0%
+completely General this is any in in
+ 
+
+ align:start position:0%
+completely General this is any in in
+degree of Freedom system some f e to the
+
+ align:start position:0%
+degree of Freedom system some f e to the
+ 
+
+ align:start position:0%
+degree of Freedom system some f e to the
+I Omega
+
+ align:start position:0%
+I Omega
+ 
+
+ align:start position:0%
+I Omega
+T so here's kind of an important
+
+ align:start position:0%
+T so here's kind of an important
+ 
+
+ align:start position:0%
+T so here's kind of an important
+point we write out a set of we solve for
+
+ align:start position:0%
+point we write out a set of we solve for
+ 
+
+ align:start position:0%
+point we write out a set of we solve for
+the motion of a multiple degree Freedom
+
+ align:start position:0%
+the motion of a multiple degree Freedom
+ 
+
+ align:start position:0%
+the motion of a multiple degree Freedom
+system to a harmonic input we do it one
+
+ align:start position:0%
+system to a harmonic input we do it one
+ 
+
+ align:start position:0%
+system to a harmonic input we do it one
+frequency at a time so this doesn't mean
+
+ align:start position:0%
+frequency at a time so this doesn't mean
+ 
+
+ align:start position:0%
+frequency at a time so this doesn't mean
+that I could have force on the first
+
+ align:start position:0%
+that I could have force on the first
+ 
+
+ align:start position:0%
+that I could have force on the first
+mass at Omega one or make or at any at
+
+ align:start position:0%
+mass at Omega one or make or at any at
+ 
+
+ align:start position:0%
+mass at Omega one or make or at any at
+some omega and force of the second mass
+
+ align:start position:0%
+some omega and force of the second mass
+ 
+
+ align:start position:0%
+some omega and force of the second mass
+at some other Omega I'd never do that at
+
+ align:start position:0%
+at some other Omega I'd never do that at
+ 
+
+ align:start position:0%
+at some other Omega I'd never do that at
+the same time it's a linear system
+
+ align:start position:0%
+the same time it's a linear system
+ 
+
+ align:start position:0%
+the same time it's a linear system
+superposition holds you do things one
+
+ align:start position:0%
+superposition holds you do things one
+ 
+
+ align:start position:0%
+superposition holds you do things one
+frequency at a time get the answer and
+
+ align:start position:0%
+frequency at a time get the answer and
+ 
+
+ align:start position:0%
+frequency at a time get the answer and
+if you have another frequency part you
+
+ align:start position:0%
+if you have another frequency part you
+ 
+
+ align:start position:0%
+if you have another frequency part you
+do that separately then add the two
+
+ align:start position:0%
+do that separately then add the two
+ 
+
+ align:start position:0%
+do that separately then add the two
+answers so this is assumed all the
+
+ align:start position:0%
+answers so this is assumed all the
+ 
+
+ align:start position:0%
+answers so this is assumed all the
+forces acting on the masses are assumed
+
+ align:start position:0%
+forces acting on the masses are assumed
+ 
+
+ align:start position:0%
+forces acting on the masses are assumed
+to occur at one frequency but you can
+
+ align:start position:0%
+to occur at one frequency but you can
+ 
+
+ align:start position:0%
+to occur at one frequency but you can
+have different amplitudes on the
+
+ align:start position:0%
+have different amplitudes on the
+ 
+
+ align:start position:0%
+have different amplitudes on the
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+masses so that's what that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means so this then for the two degree of
+
+ align:start position:0%
+means so this then for the two degree of
+ 
+
+ align:start position:0%
+means so this then for the two degree of
+Freedom system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f for example F of
+
+ align:start position:0%
+f for example F of
+ 
+
+ align:start position:0%
+f for example F of
+T would be some constant F1 another
+
+ align:start position:0%
+T would be some constant F1 another
+ 
+
+ align:start position:0%
+T would be some constant F1 another
+constant magnitude FS2 e to the I Omega
+
+ align:start position:0%
+constant magnitude FS2 e to the I Omega
+ 
+
+ align:start position:0%
+constant magnitude FS2 e to the I Omega
+T that's what we mean by
+
+ align:start position:0%
+T that's what we mean by
+ 
+
+ align:start position:0%
+T that's what we mean by
+that so in this system and then what do
+
+ align:start position:0%
+that so in this system and then what do
+ 
+
+ align:start position:0%
+that so in this system and then what do
+we what's actually if you do that if
+
+ align:start position:0%
+we what's actually if you do that if
+ 
+
+ align:start position:0%
+we what's actually if you do that if
+these are just constants it's some
+
+ align:start position:0%
+these are just constants it's some
+ 
+
+ align:start position:0%
+these are just constants it's some
+constant force Vector appli it at a
+
+ align:start position:0%
+constant force Vector appli it at a
+ 
+
+ align:start position:0%
+constant force Vector appli it at a
+single
+
+ align:start position:0%
+single
+ 
+
+ align:start position:0%
+single
+frequency what frequency do you expect
+
+ align:start position:0%
+frequency what frequency do you expect
+ 
+
+ align:start position:0%
+frequency what frequency do you expect
+to see in the response of the system
+
+ align:start position:0%
+to see in the response of the system
+ 
+
+ align:start position:0%
+to see in the response of the system
+steady state
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+response right it's a linear system one
+
+ align:start position:0%
+response right it's a linear system one
+ 
+
+ align:start position:0%
+response right it's a linear system one
+of the lessons you really got want to go
+
+ align:start position:0%
+of the lessons you really got want to go
+ 
+
+ align:start position:0%
+of the lessons you really got want to go
+away with this is an intro to linear
+
+ align:start position:0%
+away with this is an intro to linear
+ 
+
+ align:start position:0%
+away with this is an intro to linear
+system steady state response of a linear
+
+ align:start position:0%
+system steady state response of a linear
+ 
+
+ align:start position:0%
+system steady state response of a linear
+system the frequency in is the frequency
+
+ align:start position:0%
+system the frequency in is the frequency
+ 
+
+ align:start position:0%
+system the frequency in is the frequency
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+okay all always true so we expect to see
+
+ align:start position:0%
+okay all always true so we expect to see
+ 
+
+ align:start position:0%
+okay all always true so we expect to see
+a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're going to get a solution of the
+
+ align:start position:0%
+we're going to get a solution of the
+ 
+
+ align:start position:0%
+we're going to get a solution of the
+form
+
+ align:start position:0%
+form
+ 
+
+ align:start position:0%
+form
+x equals some
+
+ align:start position:0%
+x equals some
+ 
+
+ align:start position:0%
+x equals some
+magnitude Vector times an e to the I
+
+ align:start position:0%
+magnitude Vector times an e to the I
+ 
+
+ align:start position:0%
+magnitude Vector times an e to the I
+Omega T also and the magnitude might be
+
+ align:start position:0%
+Omega T also and the magnitude might be
+ 
+
+ align:start position:0%
+Omega T also and the magnitude might be
+complex because there could be phase
+
+ align:start position:0%
+complex because there could be phase
+ 
+
+ align:start position:0%
+complex because there could be phase
+angle in there due to damping and so
+
+ align:start position:0%
+angle in there due to damping and so
+ 
+
+ align:start position:0%
+angle in there due to damping and so
+forth but they nonetheless they're
+
+ align:start position:0%
+forth but they nonetheless they're
+ 
+
+ align:start position:0%
+forth but they nonetheless they're
+constant what this part is a constant
+
+ align:start position:0%
+constant what this part is a constant
+ 
+
+ align:start position:0%
+constant what this part is a constant
+vector and that's its frequency
+
+ align:start position:0%
+vector and that's its frequency
+ 
+
+ align:start position:0%
+vector and that's its frequency
+dependence and if we know that is true
+
+ align:start position:0%
+dependence and if we know that is true
+ 
+
+ align:start position:0%
+dependence and if we know that is true
+then we can say well take the time
+
+ align:start position:0%
+then we can say well take the time
+ 
+
+ align:start position:0%
+then we can say well take the time
+derivative of that the only time
+
+ align:start position:0%
+derivative of that the only time
+ 
+
+ align:start position:0%
+derivative of that the only time
+dependent part is the e to the I Omega T
+
+ align:start position:0%
+dependent part is the e to the I Omega T
+ 
+
+ align:start position:0%
+dependent part is the e to the I Omega T
+So X do becomes I
+
+ align:start position:0%
+So X do becomes I
+ 
+
+ align:start position:0%
+So X do becomes I
+Omega
+
+ align:start position:0%
+Omega
+ 
+
+ align:start position:0%
+Omega
+x e to the I Omega T and X double dot
+
+ align:start position:0%
+x e to the I Omega T and X double dot
+ 
+
+ align:start position:0%
+x e to the I Omega T and X double dot
+becomes minus Omega
+
+ align:start position:0%
+becomes minus Omega
+ 
+
+ align:start position:0%
+becomes minus Omega
+SAR x e to the I Omega
+
+ align:start position:0%
+SAR x e to the I Omega
+ 
+
+ align:start position:0%
+SAR x e to the I Omega
+T so we can substitute this this and
+
+ align:start position:0%
+T so we can substitute this this and
+ 
+
+ align:start position:0%
+T so we can substitute this this and
+this into this
+
+ align:start position:0%
+this into this
+ 
+
+ align:start position:0%
+this into this
+equation this is these are Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation and when you do
+
+ align:start position:0%
+equation and when you do
+ 
+
+ align:start position:0%
+equation and when you do
+that minus Omega 2 * the mass
+
+ align:start position:0%
+that minus Omega 2 * the mass
+ 
+
+ align:start position:0%
+that minus Omega 2 * the mass
+Matrix I Omega * the C Matrix plus k
+
+ align:start position:0%
+Matrix I Omega * the C Matrix plus k
+ 
+
+ align:start position:0%
+Matrix I Omega * the C Matrix plus k
+k
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x e to the I Omega T
+
+ align:start position:0%
+x e to the I Omega T
+ 
+
+ align:start position:0%
+x e to the I Omega T
+equals Fe e to the I Omega
+
+ align:start position:0%
+equals Fe e to the I Omega
+ 
+
+ align:start position:0%
+equals Fe e to the I Omega
+T you can get rid of these and now you
+
+ align:start position:0%
+T you can get rid of these and now you
+ 
+
+ align:start position:0%
+T you can get rid of these and now you
+have a algebraic equation it's no longer
+
+ align:start position:0%
+have a algebraic equation it's no longer
+ 
+
+ align:start position:0%
+have a algebraic equation it's no longer
+a function of
+
+ align:start position:0%
+a function of
+ 
+
+ align:start position:0%
+a function of
+time function of your original Mass
+
+ align:start position:0%
+time function of your original Mass
+ 
+
+ align:start position:0%
+time function of your original Mass
+stamping and stiffness matrices and it's
+
+ align:start position:0%
+stamping and stiffness matrices and it's
+ 
+
+ align:start position:0%
+stamping and stiffness matrices and it's
+certainly a function of frequency and if
+
+ align:start position:0%
+certainly a function of frequency and if
+ 
+
+ align:start position:0%
+certainly a function of frequency and if
+you think back this is how how we derive
+
+ align:start position:0%
+you think back this is how how we derive
+ 
+
+ align:start position:0%
+you think back this is how how we derive
+the transfer function for a single
+
+ align:start position:0%
+the transfer function for a single
+ 
+
+ align:start position:0%
+the transfer function for a single
+degree Freedom system and this statement
+
+ align:start position:0%
+degree Freedom system and this statement
+ 
+
+ align:start position:0%
+degree Freedom system and this statement
+is true for single degree Freedom too if
+
+ align:start position:0%
+is true for single degree Freedom too if
+ 
+
+ align:start position:0%
+is true for single degree Freedom too if
+it was single degree Freedom that's just
+
+ align:start position:0%
+it was single degree Freedom that's just
+ 
+
+ align:start position:0%
+it was single degree Freedom that's just
+the mass that's just the damping that's
+
+ align:start position:0%
+the mass that's just the damping that's
+ 
+
+ align:start position:0%
+the mass that's just the damping that's
+just the
+
+ align:start position:0%
+just the
+ 
+
+ align:start position:0%
+just the
+stiffness and you could solve directly
+
+ align:start position:0%
+stiffness and you could solve directly
+ 
+
+ align:start position:0%
+stiffness and you could solve directly
+for the HX over F transfer function but
+
+ align:start position:0%
+for the HX over F transfer function but
+ 
+
+ align:start position:0%
+for the HX over F transfer function but
+with multiple degrees of freedom we
+
+ align:start position:0%
+with multiple degrees of freedom we
+ 
+
+ align:start position:0%
+with multiple degrees of freedom we
+can't just divide this quite divide this
+
+ align:start position:0%
+can't just divide this quite divide this
+ 
+
+ align:start position:0%
+can't just divide this quite divide this
+out this piece
+
+ align:start position:0%
+out this piece
+ 
+
+ align:start position:0%
+out this piece
+Here is known as the I'll write it as Z
+
+ align:start position:0%
+Here is known as the I'll write it as Z
+ 
+
+ align:start position:0%
+Here is known as the I'll write it as Z
+Omega Z of Omega this is known as the
+
+ align:start position:0%
+Omega Z of Omega this is known as the
+ 
+
+ align:start position:0%
+Omega Z of Omega this is known as the
+impedance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix and if I want to solve I'm
+
+ align:start position:0%
+Matrix and if I want to solve I'm
+ 
+
+ align:start position:0%
+Matrix and if I want to solve I'm
+looking for X I want to know my solution
+
+ align:start position:0%
+looking for X I want to know my solution
+ 
+
+ align:start position:0%
+looking for X I want to know my solution
+X so this is essentially of the form
+
+ align:start position:0%
+X so this is essentially of the form
+ 
+
+ align:start position:0%
+X so this is essentially of the form
+Z it's a matrix time x a vector equals f
+
+ align:start position:0%
+Z it's a matrix time x a vector equals f
+ 
+
+ align:start position:0%
+Z it's a matrix time x a vector equals f
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+vector and just using what you know
+
+ align:start position:0%
+vector and just using what you know
+ 
+
+ align:start position:0%
+vector and just using what you know
+about linear algebra to solve for x you
+
+ align:start position:0%
+about linear algebra to solve for x you
+ 
+
+ align:start position:0%
+about linear algebra to solve for x you
+just multiply through by Z
+
+ align:start position:0%
+just multiply through by Z
+ 
+
+ align:start position:0%
+just multiply through by Z
+inverse so
+
+ align:start position:0%
+inverse so
+ 
+
+ align:start position:0%
+inverse so
+x equals z inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F
+
+ align:start position:0%
+F
+ 
+
+ align:start position:0%
+F
+right and Z is a for a two degree
+
+ align:start position:0%
+right and Z is a for a two degree
+ 
+
+ align:start position:0%
+right and Z is a for a two degree
+Freedom system Z is a 2X two Matrix with
+
+ align:start position:0%
+Freedom system Z is a 2X two Matrix with
+ 
+
+ align:start position:0%
+Freedom system Z is a 2X two Matrix with
+frequency and everything in it but it's
+
+ align:start position:0%
+frequency and everything in it but it's
+ 
+
+ align:start position:0%
+frequency and everything in it but it's
+a 2X two so Z inverse will be a 2X two
+
+ align:start position:0%
+a 2X two so Z inverse will be a 2X two
+ 
+
+ align:start position:0%
+a 2X two so Z inverse will be a 2X two
+and for 2 x two we can just write down
+
+ align:start position:0%
+and for 2 x two we can just write down
+ 
+
+ align:start position:0%
+and for 2 x two we can just write down
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+answer but let's see I'll write out Z of
+
+ align:start position:0%
+answer but let's see I'll write out Z of
+ 
+
+ align:start position:0%
+answer but let's see I'll write out Z of
+Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so just to be clear about what all
+
+ align:start position:0%
+here so just to be clear about what all
+ 
+
+ align:start position:0%
+here so just to be clear about what all
+this is z of Omega is this and in this
+
+ align:start position:0%
+this is z of Omega is this and in this
+ 
+
+ align:start position:0%
+this is z of Omega is this and in this
+problem that's minus Omega s
+
+ align:start position:0%
+problem that's minus Omega s
+ 
+
+ align:start position:0%
+problem that's minus Omega s
+times a mass Matrix which looks like M1
+
+ align:start position:0%
+times a mass Matrix which looks like M1
+ 
+
+ align:start position:0%
+times a mass Matrix which looks like M1
+0 0
+
+ align:start position:0%
+0 0
+ 
+
+ align:start position:0%
+0 0
+M2 and you add to that a damping Matrix
+
+ align:start position:0%
+M2 and you add to that a damping Matrix
+ 
+
+ align:start position:0%
+M2 and you add to that a damping Matrix
+I Omega time C and the C from the
+
+ align:start position:0%
+I Omega time C and the C from the
+ 
+
+ align:start position:0%
+I Omega time C and the C from the
+equations of motion C1 +
+
+ align:start position:0%
+equations of motion C1 +
+ 
+
+ align:start position:0%
+equations of motion C1 +
+C2 minus C2 minus C2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C2 and plus r k Matrix
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K1 +
+
+ align:start position:0%
+K1 +
+ 
+
+ align:start position:0%
+K1 +
+K2 minus
+
+ align:start position:0%
+K2 minus
+ 
+
+ align:start position:0%
+K2 minus
+K2 minus
+
+ align:start position:0%
+K2 minus
+ 
+
+ align:start position:0%
+K2 minus
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+K2 so that's what the ZM of Omega
+
+ align:start position:0%
+K2 so that's what the ZM of Omega
+ 
+
+ align:start position:0%
+K2 so that's what the ZM of Omega
+actually looks
+
+ align:start position:0%
+actually looks
+ 
+
+ align:start position:0%
+actually looks
+like and so you would collect so the it
+
+ align:start position:0%
+like and so you would collect so the it
+ 
+
+ align:start position:0%
+like and so you would collect so the it
+it's a 2X two Matrix and its F upper
+
+ align:start position:0%
+it's a 2X two Matrix and its F upper
+ 
+
+ align:start position:0%
+it's a 2X two Matrix and its F upper
+left term is- Omega 2 M1 plus I Omega
+
+ align:start position:0%
+left term is- Omega 2 M1 plus I Omega
+ 
+
+ align:start position:0%
+left term is- Omega 2 M1 plus I Omega
+time this plus that collect them all
+
+ align:start position:0%
+time this plus that collect them all
+ 
+
+ align:start position:0%
+time this plus that collect them all
+together and this has a
+
+ align:start position:0%
+together and this has a
+ 
+
+ align:start position:0%
+together and this has a
+form this collects together in a form we
+
+ align:start position:0%
+form this collects together in a form we
+ 
+
+ align:start position:0%
+form this collects together in a form we
+have called
+
+ align:start position:0%
+have called
+ 
+
+ align:start position:0%
+have called
+z11
+
+ align:start position:0%
+z11
+ 
+
+ align:start position:0%
+z11
+z12
+
+ align:start position:0%
+z12
+ 
+
+ align:start position:0%
+z12
+z21
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z22 and very often z12 and z21 are
+
+ align:start position:0%
+z22 and very often z12 and z21 are
+ 
+
+ align:start position:0%
+z22 and very often z12 and z21 are
+symmetric not always the kind of
+
+ align:start position:0%
+symmetric not always the kind of
+ 
+
+ align:start position:0%
+symmetric not always the kind of
+problems we generally do here they will
+
+ align:start position:0%
+problems we generally do here they will
+ 
+
+ align:start position:0%
+problems we generally do here they will
+be and they will be generally symmetric
+
+ align:start position:0%
+be and they will be generally symmetric
+ 
+
+ align:start position:0%
+be and they will be generally symmetric
+if your coordinate system is measured
+
+ align:start position:0%
+if your coordinate system is measured
+ 
+
+ align:start position:0%
+if your coordinate system is measured
+from a stable measured from a static
+
+ align:start position:0%
+from a stable measured from a static
+ 
+
+ align:start position:0%
+from a stable measured from a static
+equilibrium position so if you've been
+
+ align:start position:0%
+equilibrium position so if you've been
+ 
+
+ align:start position:0%
+equilibrium position so if you've been
+doing two1 there's a thing called
+
+ align:start position:0%
+doing two1 there's a thing called
+ 
+
+ align:start position:0%
+doing two1 there's a thing called
+Maxwell's reciprocal theorem which for
+
+ align:start position:0%
+Maxwell's reciprocal theorem which for
+ 
+
+ align:start position:0%
+Maxwell's reciprocal theorem which for
+which proves this for the stiffness
+
+ align:start position:0%
+which proves this for the stiffness
+ 
+
+ align:start position:0%
+which proves this for the stiffness
+Matrix but they essentially need to be
+
+ align:start position:0%
+Matrix but they essentially need to be
+ 
+
+ align:start position:0%
+Matrix but they essentially need to be
+measured from static equilibrium
+
+ align:start position:0%
+measured from static equilibrium
+ 
+
+ align:start position:0%
+measured from static equilibrium
+positions but for today's example this
+
+ align:start position:0%
+positions but for today's example this
+ 
+
+ align:start position:0%
+positions but for today's example this
+is indeed symmetric minus C2 minus C2
+
+ align:start position:0%
+is indeed symmetric minus C2 minus C2
+ 
+
+ align:start position:0%
+is indeed symmetric minus C2 minus C2
+minus K2 minus K2 0 0 everything
+
+ align:start position:0%
+minus K2 minus K2 0 0 everything
+ 
+
+ align:start position:0%
+minus K2 minus K2 0 0 everything
+symmetric so we'll take advantage of
+
+ align:start position:0%
+symmetric so we'll take advantage of
+ 
+
+ align:start position:0%
+symmetric so we'll take advantage of
+that and I'll write out one of the
+
+ align:start position:0%
+that and I'll write out one of the
+ 
+
+ align:start position:0%
+that and I'll write out one of the
+components here z11 for example when you
+
+ align:start position:0%
+components here z11 for example when you
+ 
+
+ align:start position:0%
+components here z11 for example when you
+collect the terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together
+
+ align:start position:0%
+together
+ 
+
+ align:start position:0%
+together
+is in general it' be minus Omega
+
+ align:start position:0%
+is in general it' be minus Omega
+ 
+
+ align:start position:0%
+is in general it' be minus Omega
+SAR
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+M11 + I Omega C1 11 1 plus k11 the
+
+ align:start position:0%
+M11 + I Omega C1 11 1 plus k11 the
+ 
+
+ align:start position:0%
+M11 + I Omega C1 11 1 plus k11 the
+corner elements of these three
+
+ align:start position:0%
+corner elements of these three
+ 
+
+ align:start position:0%
+corner elements of these three
+pieces
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and in this problem that's
+
+ align:start position:0%
+and in this problem that's
+ 
+
+ align:start position:0%
+and in this problem that's
+minus Omega SAR
+
+ align:start position:0%
+minus Omega SAR
+ 
+
+ align:start position:0%
+minus Omega SAR
+M1
+
+ align:start position:0%
+M1
+ 
+
+ align:start position:0%
+M1
+plus I
+
+ align:start position:0%
+plus I
+ 
+
+ align:start position:0%
+plus I
+Omega C1 + C2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus K1
+
+ align:start position:0%
+plus K1
+ 
+
+ align:start position:0%
+plus K1
++ K2 you just substitute it
+
+ align:start position:0%
++ K2 you just substitute it
+ 
+
+ align:start position:0%
++ K2 you just substitute it
+in this this and this so that's z11 for
+
+ align:start position:0%
+in this this and this so that's z11 for
+ 
+
+ align:start position:0%
+in this this and this so that's z11 for
+example and the other ones you can
+
+ align:start position:0%
+example and the other ones you can
+ 
+
+ align:start position:0%
+example and the other ones you can
+figure out what each of the other terms
+
+ align:start position:0%
+figure out what each of the other terms
+ 
+
+ align:start position:0%
+figure out what each of the other terms
+would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so we've said that we're
+
+ align:start position:0%
+all right so we've said that we're
+ 
+
+ align:start position:0%
+all right so we've said that we're
+looking we want to know what the X's
+
+ align:start position:0%
+looking we want to know what the X's
+ 
+
+ align:start position:0%
+looking we want to know what the X's
+are and we know that we can get that by
+
+ align:start position:0%
+are and we know that we can get that by
+ 
+
+ align:start position:0%
+are and we know that we can get that by
+doing Z inverse time
+
+ align:start position:0%
+doing Z inverse time
+ 
+
+ align:start position:0%
+doing Z inverse time
+F and this is going this gives us our
+
+ align:start position:0%
+F and this is going this gives us our
+ 
+
+ align:start position:0%
+F and this is going this gives us our
+definition this Z inverse is our
+
+ align:start position:0%
+definition this Z inverse is our
+ 
+
+ align:start position:0%
+definition this Z inverse is our
+H our transfer function Matrix
+
+ align:start position:0%
+H our transfer function Matrix
+ 
+
+ align:start position:0%
+H our transfer function Matrix
+times F so just by getting Z inverse we
+
+ align:start position:0%
+times F so just by getting Z inverse we
+ 
+
+ align:start position:0%
+times F so just by getting Z inverse we
+get this little set of trans four
+
+ align:start position:0%
+get this little set of trans four
+ 
+
+ align:start position:0%
+get this little set of trans four
+transfer functions that we're interested
+
+ align:start position:0%
+transfer functions that we're interested
+ 
+
+ align:start position:0%
+transfer functions that we're interested
+in so
+
+ align:start position:0%
+in so
+ 
+
+ align:start position:0%
+in so
+H is an N
+
+ align:start position:0%
+H is an N
+ 
+
+ align:start position:0%
+H is an N
+byn
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Matrix of transfer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+functions
+
+ align:start position:0%
+functions
+ 
+
+ align:start position:0%
+functions
+okay so in the 2 by two
+
+ align:start position:0%
+okay so in the 2 by two
+ 
+
+ align:start position:0%
+okay so in the 2 by two
+for the or for the 2x two case or n
+
+ align:start position:0%
+for the or for the 2x two case or n
+ 
+
+ align:start position:0%
+for the or for the 2x two case or n
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+2 we know we can write out directly what
+
+ align:start position:0%
+2 we know we can write out directly what
+ 
+
+ align:start position:0%
+2 we know we can write out directly what
+Z inverse
+
+ align:start position:0%
+Z inverse
+ 
+
+ align:start position:0%
+Z inverse
+is and Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+inverse
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z22 minus
+
+ align:start position:0%
+z22 minus
+ 
+
+ align:start position:0%
+z22 minus
+z12 minus z12 when it's
+
+ align:start position:0%
+z12 minus z12 when it's
+ 
+
+ align:start position:0%
+z12 minus z12 when it's
+symmetric z11
+
+ align:start position:0%
+symmetric z11
+ 
+
+ align:start position:0%
+symmetric z11
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+over I write it all over the
+
+ align:start position:0%
+over I write it all over the
+ 
+
+ align:start position:0%
+over I write it all over the
+determinant of Z so this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+determinant so the determinant of Z I
+
+ align:start position:0%
+determinant so the determinant of Z I
+ 
+
+ align:start position:0%
+determinant so the determinant of Z I
+just do with these double bars so the
+
+ align:start position:0%
+just do with these double bars so the
+ 
+
+ align:start position:0%
+just do with these double bars so the
+whole this over the determinant of Z is
+
+ align:start position:0%
+whole this over the determinant of Z is
+ 
+
+ align:start position:0%
+whole this over the determinant of Z is
+the inverse of that
+
+ align:start position:0%
+the inverse of that
+ 
+
+ align:start position:0%
+the inverse of that
+Matrix and this gives you a new result
+
+ align:start position:0%
+Matrix and this gives you a new result
+ 
+
+ align:start position:0%
+Matrix and this gives you a new result
+which is
+
+ align:start position:0%
+which is
+ 
+
+ align:start position:0%
+which is
+h11
+
+ align:start position:0%
+h11
+ 
+
+ align:start position:0%
+h11
+h12
+
+ align:start position:0%
+h12
+ 
+
+ align:start position:0%
+h12
+h12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+H22 where
+
+ align:start position:0%
+H22 where
+ 
+
+ align:start position:0%
+H22 where
+H I
+
+ align:start position:0%
+H I
+ 
+
+ align:start position:0%
+H I
+J this is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+response at
+
+ align:start position:0%
+response at
+ 
+
+ align:start position:0%
+response at
+I
+
+ align:start position:0%
+I
+ 
+
+ align:start position:0%
+I
+per
+
+ align:start position:0%
+per
+ 
+
+ align:start position:0%
+per
+unit Force at
+
+ align:start position:0%
+unit Force at
+ 
+
+ align:start position:0%
+unit Force at
+J and I made this I I took advantage of
+
+ align:start position:0%
+J and I made this I I took advantage of
+ 
+
+ align:start position:0%
+J and I made this I I took advantage of
+the Symmetry here but this one would
+
+ align:start position:0%
+the Symmetry here but this one would
+ 
+
+ align:start position:0%
+the Symmetry here but this one would
+normally be called 2 one so this is
+
+ align:start position:0%
+normally be called 2 one so this is
+ 
+
+ align:start position:0%
+normally be called 2 one so this is
+response at one caused by the force at
+
+ align:start position:0%
+response at one caused by the force at
+ 
+
+ align:start position:0%
+response at one caused by the force at
+one so we
+
+ align:start position:0%
+one so we
+ 
+
+ align:start position:0%
+one so we
+have forces in our problem one is the
+
+ align:start position:0%
+have forces in our problem one is the
+ 
+
+ align:start position:0%
+have forces in our problem one is the
+force on the main Mass so how much
+
+ align:start position:0%
+force on the main Mass so how much
+ 
+
+ align:start position:0%
+force on the main Mass so how much
+response do you get at the main first
+
+ align:start position:0%
+response do you get at the main first
+ 
+
+ align:start position:0%
+response do you get at the main first
+mass due to the force on the first mass
+
+ align:start position:0%
+mass due to the force on the first mass
+ 
+
+ align:start position:0%
+mass due to the force on the first mass
+this is how much response you get on the
+
+ align:start position:0%
+this is how much response you get on the
+ 
+
+ align:start position:0%
+this is how much response you get on the
+first mass due to the excitation on the
+
+ align:start position:0%
+first mass due to the excitation on the
+ 
+
+ align:start position:0%
+first mass due to the excitation on the
+second Mass response on the second Mass
+
+ align:start position:0%
+second Mass response on the second Mass
+ 
+
+ align:start position:0%
+second Mass response on the second Mass
+due to the excitation on the first
+
+ align:start position:0%
+due to the excitation on the first
+ 
+
+ align:start position:0%
+due to the excitation on the first
+response on the second Mass due to the
+
+ align:start position:0%
+response on the second Mass due to the
+ 
+
+ align:start position:0%
+response on the second Mass due to the
+excitation on the second Mass so you get
+
+ align:start position:0%
+excitation on the second Mass so you get
+ 
+
+ align:start position:0%
+excitation on the second Mass so you get
+four possible contributions
+
+ align:start position:0%
+four possible contributions
+ 
+
+ align:start position:0%
+four possible contributions
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay and the determinant to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z for 2x two is also very
+
+ align:start position:0%
+Z for 2x two is also very
+ 
+
+ align:start position:0%
+Z for 2x two is also very
+straightforward
+
+ align:start position:0%
+straightforward
+ 
+
+ align:start position:0%
+straightforward
+z11
+
+ align:start position:0%
+z11
+ 
+
+ align:start position:0%
+z11
+z22 minus Z1 2
+
+ align:start position:0%
+z22 minus Z1 2
+ 
+
+ align:start position:0%
+z22 minus Z1 2
+squared so we can actually so we can and
+
+ align:start position:0%
+squared so we can actually so we can and
+ 
+
+ align:start position:0%
+squared so we can actually so we can and
+will work out uh exactly what the
+
+ align:start position:0%
+will work out uh exactly what the
+ 
+
+ align:start position:0%
+will work out uh exactly what the
+algebra tells us for this 2 by two
+
+ align:start position:0%
+algebra tells us for this 2 by two
+ 
+
+ align:start position:0%
+algebra tells us for this 2 by two
+case so we've already been discussing it
+
+ align:start position:0%
+case so we've already been discussing it
+ 
+
+ align:start position:0%
+case so we've already been discussing it
+but what do you expect let's say let's
+
+ align:start position:0%
+but what do you expect let's say let's
+ 
+
+ align:start position:0%
+but what do you expect let's say let's
+look at this one what do you suppose the
+
+ align:start position:0%
+look at this one what do you suppose the
+ 
+
+ align:start position:0%
+look at this one what do you suppose the
+response at one due to a harmonic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+excitation at one what
+
+ align:start position:0%
+excitation at one what
+ 
+
+ align:start position:0%
+excitation at one what
+how what do you think the sketch of the
+
+ align:start position:0%
+how what do you think the sketch of the
+ 
+
+ align:start position:0%
+how what do you think the sketch of the
+magnitude of
+
+ align:start position:0%
+magnitude of
+ 
+
+ align:start position:0%
+magnitude of
+h11 of Omega would look like as a
+
+ align:start position:0%
+h11 of Omega would look like as a
+ 
+
+ align:start position:0%
+h11 of Omega would look like as a
+function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency
+
+ align:start position:0%
+frequency
+ 
+
+ align:start position:0%
+frequency
+no but for the kind of problems we do
+
+ align:start position:0%
+no but for the kind of problems we do
+ 
+
+ align:start position:0%
+no but for the kind of problems we do
+probably and if it's simple beams or
+
+ align:start position:0%
+probably and if it's simple beams or
+ 
+
+ align:start position:0%
+probably and if it's simple beams or
+masses connected by strings by Springs
+
+ align:start position:0%
+masses connected by strings by Springs
+ 
+
+ align:start position:0%
+masses connected by strings by Springs
+if you choose your generalized
+
+ align:start position:0%
+if you choose your generalized
+ 
+
+ align:start position:0%
+if you choose your generalized
+coordinates in a way that is for example
+
+ align:start position:0%
+coordinates in a way that is for example
+ 
+
+ align:start position:0%
+coordinates in a way that is for example
+measuring the displacement of each Mass
+
+ align:start position:0%
+measuring the displacement of each Mass
+ 
+
+ align:start position:0%
+measuring the displacement of each Mass
+from an inertial static equilibrium
+
+ align:start position:0%
+from an inertial static equilibrium
+ 
+
+ align:start position:0%
+from an inertial static equilibrium
+starting point it'll be
+
+ align:start position:0%
+starting point it'll be
+ 
+
+ align:start position:0%
+starting point it'll be
+symmetric but if you if you measure the
+
+ align:start position:0%
+symmetric but if you if you measure the
+ 
+
+ align:start position:0%
+symmetric but if you if you measure the
+even in this two degree freedom I can
+
+ align:start position:0%
+even in this two degree freedom I can
+ 
+
+ align:start position:0%
+even in this two degree freedom I can
+make it non-symmetric just by choosing
+
+ align:start position:0%
+make it non-symmetric just by choosing
+ 
+
+ align:start position:0%
+make it non-symmetric just by choosing
+the coordinate for the second mass as to
+
+ align:start position:0%
+the coordinate for the second mass as to
+ 
+
+ align:start position:0%
+the coordinate for the second mass as to
+be relative to the first mass as soon as
+
+ align:start position:0%
+be relative to the first mass as soon as
+ 
+
+ align:start position:0%
+be relative to the first mass as soon as
+you do that it makes it non-symmetric
+
+ align:start position:0%
+you do that it makes it non-symmetric
+ 
+
+ align:start position:0%
+you do that it makes it non-symmetric
+you can still solve for transfer
+
+ align:start position:0%
+you can still solve for transfer
+ 
+
+ align:start position:0%
+you can still solve for transfer
+function to everything but it's mess it
+
+ align:start position:0%
+function to everything but it's mess it
+ 
+
+ align:start position:0%
+function to everything but it's mess it
+get gets Messier so notice I picked
+
+ align:start position:0%
+get gets Messier so notice I picked
+ 
+
+ align:start position:0%
+get gets Messier so notice I picked
+coordinates X1 relative to the inertial
+
+ align:start position:0%
+coordinates X1 relative to the inertial
+ 
+
+ align:start position:0%
+coordinates X1 relative to the inertial
+frame X2 relative to the same inertial
+
+ align:start position:0%
+frame X2 relative to the same inertial
+ 
+
+ align:start position:0%
+frame X2 relative to the same inertial
+frame and they're both measuring
+
+ align:start position:0%
+frame and they're both measuring
+ 
+
+ align:start position:0%
+frame and they're both measuring
+displacement from a static equilibrium
+
+ align:start position:0%
+displacement from a static equilibrium
+ 
+
+ align:start position:0%
+displacement from a static equilibrium
+position then then they are symmetric so
+
+ align:start position:0%
+position then then they are symmetric so
+ 
+
+ align:start position:0%
+position then then they are symmetric so
+and there's the determinant we need and
+
+ align:start position:0%
+and there's the determinant we need and
+ 
+
+ align:start position:0%
+and there's the determinant we need and
+this determinant see this is divided
+
+ align:start position:0%
+this determinant see this is divided
+ 
+
+ align:start position:0%
+this determinant see this is divided
+into all four of these
+
+ align:start position:0%
+into all four of these
+ 
+
+ align:start position:0%
+into all four of these
+terms so these four transfer functions
+
+ align:start position:0%
+terms so these four transfer functions
+ 
+
+ align:start position:0%
+terms so these four transfer functions
+all share the same denominator
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay they all have the same denominator
+
+ align:start position:0%
+okay they all have the same denominator
+ 
+
+ align:start position:0%
+okay they all have the same denominator
+so I just want you to tell me use your
+
+ align:start position:0%
+so I just want you to tell me use your
+ 
+
+ align:start position:0%
+so I just want you to tell me use your
+intuition tell me what this is going to
+
+ align:start position:0%
+intuition tell me what this is going to
+ 
+
+ align:start position:0%
+intuition tell me what this is going to
+look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like what's it look like for a single
+
+ align:start position:0%
+like what's it look like for a single
+ 
+
+ align:start position:0%
+like what's it look like for a single
+degree Freedom
+
+ align:start position:0%
+degree Freedom
+ 
+
+ align:start position:0%
+degree Freedom
+system it's hxf for a single degree fre
+
+ align:start position:0%
+system it's hxf for a single degree fre
+ 
+
+ align:start position:0%
+system it's hxf for a single degree fre
+it's h11 for a single degree Freedom
+
+ align:start position:0%
+it's h11 for a single degree Freedom
+ 
+
+ align:start position:0%
+it's h11 for a single degree Freedom
+system is a response of the system to a
+
+ align:start position:0%
+system is a response of the system to a
+ 
+
+ align:start position:0%
+system is a response of the system to a
+harmonic force on that single mass and
+
+ align:start position:0%
+harmonic force on that single mass and
+ 
+
+ align:start position:0%
+harmonic force on that single mass and
+that looks like what
+
+ align:start position:0%
+that looks like what
+ 
+
+ align:start position:0%
+that looks like what
+Peak right okay this one what do you
+
+ align:start position:0%
+Peak right okay this one what do you
+ 
+
+ align:start position:0%
+Peak right okay this one what do you
+think it's going to look
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like show me
+
+ align:start position:0%
+like show me
+ 
+
+ align:start position:0%
+like show me
+again okay but I see one Peak how many
+
+ align:start position:0%
+again okay but I see one Peak how many
+ 
+
+ align:start position:0%
+again okay but I see one Peak how many
+Peaks
+
+ align:start position:0%
+Peaks
+ 
+
+ align:start position:0%
+Peaks
+why two different natural frequencies
+
+ align:start position:0%
+why two different natural frequencies
+ 
+
+ align:start position:0%
+why two different natural frequencies
+right this thing is going to look
+
+ align:start position:0%
+right this thing is going to look
+ 
+
+ align:start position:0%
+right this thing is going to look
+something like
+
+ align:start position:0%
+something like
+ 
+
+ align:start position:0%
+something like
+this and I don't know quite how it
+
+ align:start position:0%
+this and I don't know quite how it
+ 
+
+ align:start position:0%
+this and I don't know quite how it
+behaves in here but it's going to do
+
+ align:start position:0%
+behaves in here but it's going to do
+ 
+
+ align:start position:0%
+behaves in here but it's going to do
+that for sure it's going to have two
+
+ align:start position:0%
+that for sure it's going to have two
+ 
+
+ align:start position:0%
+that for sure it's going to have two
+resonances this one and Omega 1 this
+
+ align:start position:0%
+resonances this one and Omega 1 this
+ 
+
+ align:start position:0%
+resonances this one and Omega 1 this
+wanted Omega 2 we already know that
+
+ align:start position:0%
+wanted Omega 2 we already know that
+ 
+
+ align:start position:0%
+wanted Omega 2 we already know that
+because we did it by modal analysis we
+
+ align:start position:0%
+because we did it by modal analysis we
+ 
+
+ align:start position:0%
+because we did it by modal analysis we
+know each mode is going to have a
+
+ align:start position:0%
+know each mode is going to have a
+ 
+
+ align:start position:0%
+know each mode is going to have a
+resonance in it okay so let's let's
+
+ align:start position:0%
+resonance in it okay so let's let's
+ 
+
+ align:start position:0%
+resonance in it okay so let's let's
+figure let's find out exactly what it
+
+ align:start position:0%
+figure let's find out exactly what it
+ 
+
+ align:start position:0%
+figure let's find out exactly what it
+looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so for this TW degree Freedom
+
+ align:start position:0%
+like so for this TW degree Freedom
+ 
+
+ align:start position:0%
+like so for this TW degree Freedom
+system there's an F1 and an
+
+ align:start position:0%
+system there's an F1 and an
+ 
+
+ align:start position:0%
+system there's an F1 and an
+F2 and we're looking for X1
+
+ align:start position:0%
+F2 and we're looking for X1
+ 
+
+ align:start position:0%
+F2 and we're looking for X1
+so X1 X2
+
+ align:start position:0%
+so X1 X2
+ 
+
+ align:start position:0%
+so X1 X2
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+h11
+
+ align:start position:0%
+h11
+ 
+
+ align:start position:0%
+h11
+h12
+
+ align:start position:0%
+h12
+ 
+
+ align:start position:0%
+h12
+h12
+
+ align:start position:0%
+h12
+ 
+
+ align:start position:0%
+h12
+H22
+
+ align:start position:0%
+H22
+ 
+
+ align:start position:0%
+H22
+times fub1
+
+ align:start position:0%
+times fub1
+ 
+
+ align:start position:0%
+times fub1
+FS2 so if I want to solve for
+
+ align:start position:0%
+FS2 so if I want to solve for
+ 
+
+ align:start position:0%
+FS2 so if I want to solve for
+X1 it's
+
+ align:start position:0%
+X1 it's
+ 
+
+ align:start position:0%
+X1 it's
+h11 F1 Plus h12
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+F2 and for the problem I'm going to
+
+ align:start position:0%
+F2 and for the problem I'm going to
+ 
+
+ align:start position:0%
+F2 and for the problem I'm going to
+solve today I'm going to
+
+ align:start position:0%
+solve today I'm going to
+ 
+
+ align:start position:0%
+solve today I'm going to
+let FS2 be zero just to just to keep it
+
+ align:start position:0%
+let FS2 be zero just to just to keep it
+ 
+
+ align:start position:0%
+let FS2 be zero just to just to keep it
+simple but also to address the original
+
+ align:start position:0%
+simple but also to address the original
+ 
+
+ align:start position:0%
+simple but also to address the original
+question that we asked the doctoral
+
+ align:start position:0%
+question that we asked the doctoral
+ 
+
+ align:start position:0%
+question that we asked the doctoral
+students you have a force on the first
+
+ align:start position:0%
+students you have a force on the first
+ 
+
+ align:start position:0%
+students you have a force on the first
+mass can I add a mass and a spring to it
+
+ align:start position:0%
+mass can I add a mass and a spring to it
+ 
+
+ align:start position:0%
+mass can I add a mass and a spring to it
+and in such a way that I can make the
+
+ align:start position:0%
+and in such a way that I can make the
+ 
+
+ align:start position:0%
+and in such a way that I can make the
+response of the first mass go to zero so
+
+ align:start position:0%
+response of the first mass go to zero so
+ 
+
+ align:start position:0%
+response of the first mass go to zero so
+there is no second Force there's only a
+
+ align:start position:0%
+there is no second Force there's only a
+ 
+
+ align:start position:0%
+there is no second Force there's only a
+first for and so this term goes
+
+ align:start position:0%
+first for and so this term goes
+ 
+
+ align:start position:0%
+first for and so this term goes
+away and so this problem X1 is
+
+ align:start position:0%
+away and so this problem X1 is
+ 
+
+ align:start position:0%
+away and so this problem X1 is
+h11
+
+ align:start position:0%
+h11
+ 
+
+ align:start position:0%
+h11
+F1 and we need therefore we need to know
+
+ align:start position:0%
+F1 and we need therefore we need to know
+ 
+
+ align:start position:0%
+F1 and we need therefore we need to know
+what
+
+ align:start position:0%
+what
+ 
+
+ align:start position:0%
+what
+uh h11 looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so
+
+ align:start position:0%
+like so
+ 
+
+ align:start position:0%
+like so
+h11 is going to be
+
+ align:start position:0%
+h11 is going to be
+ 
+
+ align:start position:0%
+h11 is going to be
+z22 divided by the determinant
+
+ align:start position:0%
+z22 divided by the determinant
+ 
+
+ align:start position:0%
+z22 divided by the determinant
+so X1 is going to be
+
+ align:start position:0%
+so X1 is going to be
+ 
+
+ align:start position:0%
+so X1 is going to be
+z22
+
+ align:start position:0%
+z22
+ 
+
+ align:start position:0%
+z22
+over z11
+
+ align:start position:0%
+over z11
+ 
+
+ align:start position:0%
+over z11
+z22 minus z12
+
+ align:start position:0%
+z22 minus z12
+ 
+
+ align:start position:0%
+z22 minus z12
+2ar times
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fub1 all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and actually I can do
+
+ align:start position:0%
+and actually I can do
+ 
+
+ align:start position:0%
+and actually I can do
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so and I'm going to let for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now damping be zero because it also just
+
+ align:start position:0%
+now damping be zero because it also just
+ 
+
+ align:start position:0%
+now damping be zero because it also just
+simplifies it for the purposes of
+
+ align:start position:0%
+simplifies it for the purposes of
+ 
+
+ align:start position:0%
+simplifies it for the purposes of
+illustration today and that's how it was
+
+ align:start position:0%
+illustration today and that's how it was
+ 
+
+ align:start position:0%
+illustration today and that's how it was
+posed to the doctoral student didn't
+
+ align:start position:0%
+posed to the doctoral student didn't
+ 
+
+ align:start position:0%
+posed to the doctoral student didn't
+even show any damping it was just a
+
+ align:start position:0%
+even show any damping it was just a
+ 
+
+ align:start position:0%
+even show any damping it was just a
+simple system a string and a
+
+ align:start position:0%
+simple system a string and a
+ 
+
+ align:start position:0%
+simple system a string and a
+mass how can you do this so we'll let
+
+ align:start position:0%
+mass how can you do this so we'll let
+ 
+
+ align:start position:0%
+mass how can you do this so we'll let
+the be zero and it considerably
+
+ align:start position:0%
+the be zero and it considerably
+ 
+
+ align:start position:0%
+the be zero and it considerably
+simplifies things then so
+
+ align:start position:0%
+simplifies things then so
+ 
+
+ align:start position:0%
+simplifies things then so
+um where's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+my so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z11 is minus Omega 2ar M1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus K1 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z22 minus Omega 2
+
+ align:start position:0%
+z22 minus Omega 2
+ 
+
+ align:start position:0%
+z22 minus Omega 2
+M2 plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2 and
+
+ align:start position:0%
+K2 and
+ 
+
+ align:start position:0%
+K2 and
+z12 run out of room
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+just minus
+
+ align:start position:0%
+just minus
+ 
+
+ align:start position:0%
+just minus
+K2 so now they're these are pretty
+
+ align:start position:0%
+K2 so now they're these are pretty
+ 
+
+ align:start position:0%
+K2 so now they're these are pretty
+simple expressions and all I have to do
+
+ align:start position:0%
+simple expressions and all I have to do
+ 
+
+ align:start position:0%
+simple expressions and all I have to do
+is plug them in here and notice what's
+
+ align:start position:0%
+is plug them in here and notice what's
+ 
+
+ align:start position:0%
+is plug them in here and notice what's
+going to happen z11 *
+
+ align:start position:0%
+going to happen z11 *
+ 
+
+ align:start position:0%
+going to happen z11 *
+z22 that's something involving aega SAR
+
+ align:start position:0%
+z22 that's something involving aega SAR
+ 
+
+ align:start position:0%
+z22 that's something involving aega SAR
+times another term involving Omega squar
+
+ align:start position:0%
+times another term involving Omega squar
+ 
+
+ align:start position:0%
+times another term involving Omega squar
+it's going to give you some a polinomial
+
+ align:start position:0%
+it's going to give you some a polinomial
+ 
+
+ align:start position:0%
+it's going to give you some a polinomial
+and Omega to the 4th this is a
+
+ align:start position:0%
+and Omega to the 4th this is a
+ 
+
+ align:start position:0%
+and Omega to the 4th this is a
+polinomial that has two roots and the
+
+ align:start position:0%
+polinomial that has two roots and the
+ 
+
+ align:start position:0%
+polinomial that has two roots and the
+two roots are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah natural frequencies it's the same
+
+ align:start position:0%
+yeah natural frequencies it's the same
+ 
+
+ align:start position:0%
+yeah natural frequencies it's the same
+the determinant of this of the Z Matrix
+
+ align:start position:0%
+the determinant of this of the Z Matrix
+ 
+
+ align:start position:0%
+the determinant of this of the Z Matrix
+is the same problem you solve when you
+
+ align:start position:0%
+is the same problem you solve when you
+ 
+
+ align:start position:0%
+is the same problem you solve when you
+found the roots of the uh characteristic
+
+ align:start position:0%
+found the roots of the uh characteristic
+ 
+
+ align:start position:0%
+found the roots of the uh characteristic
+equation it is the characteristic
+
+ align:start position:0%
+equation it is the characteristic
+ 
+
+ align:start position:0%
+equation it is the characteristic
+equation for the system the denominator
+
+ align:start position:0%
+equation for the system the denominator
+ 
+
+ align:start position:0%
+equation for the system the denominator
+the determinant of the Z Matrix
+
+ align:start position:0%
+the determinant of the Z Matrix
+ 
+
+ align:start position:0%
+the determinant of the Z Matrix
+therefore it's going to be a fourth
+
+ align:start position:0%
+therefore it's going to be a fourth
+ 
+
+ align:start position:0%
+therefore it's going to be a fourth
+order equation Omega it'll give you two
+
+ align:start position:0%
+order equation Omega it'll give you two
+ 
+
+ align:start position:0%
+order equation Omega it'll give you two
+roots for Omega squar they're your two
+
+ align:start position:0%
+roots for Omega squar they're your two
+ 
+
+ align:start position:0%
+roots for Omega squar they're your two
+un damp natural frequencies when we
+
+ align:start position:0%
+un damp natural frequencies when we
+ 
+
+ align:start position:0%
+un damp natural frequencies when we
+leave damping out of this expression and
+
+ align:start position:0%
+leave damping out of this expression and
+ 
+
+ align:start position:0%
+leave damping out of this expression and
+they'd be damped the damped Expressions
+
+ align:start position:0%
+they'd be damped the damped Expressions
+ 
+
+ align:start position:0%
+they'd be damped the damped Expressions
+they'd have complex stuff in them if you
+
+ align:start position:0%
+they'd have complex stuff in them if you
+ 
+
+ align:start position:0%
+they'd have complex stuff in them if you
+leave in the damping but they give us
+
+ align:start position:0%
+leave in the damping but they give us
+ 
+
+ align:start position:0%
+leave in the damping but they give us
+our two roots and they go in the
+
+ align:start position:0%
+our two roots and they go in the
+ 
+
+ align:start position:0%
+our two roots and they go in the
+denominator yeah the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+denominator yeah yeah yeah this is that
+
+ align:start position:0%
+denominator yeah yeah yeah this is that
+ 
+
+ align:start position:0%
+denominator yeah yeah yeah this is that
+that denominator is the characteristic
+
+ align:start position:0%
+that denominator is the characteristic
+ 
+
+ align:start position:0%
+that denominator is the characteristic
+equation that we did when we set it up
+
+ align:start position:0%
+equation that we did when we set it up
+ 
+
+ align:start position:0%
+equation that we did when we set it up
+to do the natural
+
+ align:start position:0%
+to do the natural
+ 
+
+ align:start position:0%
+to do the natural
+frequencies same equation
+
+ align:start position:0%
+frequencies same equation
+ 
+
+ align:start position:0%
+frequencies same equation
+so we know that this thing has two Roots
+
+ align:start position:0%
+so we know that this thing has two Roots
+ 
+
+ align:start position:0%
+so we know that this thing has two Roots
+one at each of the natural frequencies
+
+ align:start position:0%
+one at each of the natural frequencies
+ 
+
+ align:start position:0%
+one at each of the natural frequencies
+and when you are when Omega is at a
+
+ align:start position:0%
+and when you are when Omega is at a
+ 
+
+ align:start position:0%
+and when you are when Omega is at a
+natural frequency what is the value of
+
+ align:start position:0%
+natural frequency what is the value of
+ 
+
+ align:start position:0%
+natural frequency what is the value of
+this characteristic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation well no the characterist
+
+ align:start position:0%
+equation well no the characterist
+ 
+
+ align:start position:0%
+equation well no the characterist
+equation thing in the
+
+ align:start position:0%
+equation thing in the
+ 
+
+ align:start position:0%
+equation thing in the
+denominator at a root that expression
+
+ align:start position:0%
+denominator at a root that expression
+ 
+
+ align:start position:0%
+denominator at a root that expression
+goes to zero so you're dividing by zero
+
+ align:start position:0%
+goes to zero so you're dividing by zero
+ 
+
+ align:start position:0%
+goes to zero so you're dividing by zero
+that's what causes the Peaks that's
+
+ align:start position:0%
+that's what causes the Peaks that's
+ 
+
+ align:start position:0%
+that's what causes the Peaks that's
+where the Peaks come from is where these
+
+ align:start position:0%
+where the Peaks come from is where these
+ 
+
+ align:start position:0%
+where the Peaks come from is where these
+that denominator goes to zero and that's
+
+ align:start position:0%
+that denominator goes to zero and that's
+ 
+
+ align:start position:0%
+that denominator goes to zero and that's
+at the natural
+
+ align:start position:0%
+at the natural
+ 
+
+ align:start position:0%
+at the natural
+frequencies
+
+ align:start position:0%
+frequencies
+ 
+
+ align:start position:0%
+frequencies
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so X1 for this problem equals
+
+ align:start position:0%
+so X1 for this problem equals
+ 
+
+ align:start position:0%
+so X1 for this problem equals
+h11 F1 and now we can just write it out
+
+ align:start position:0%
+h11 F1 and now we can just write it out
+ 
+
+ align:start position:0%
+h11 F1 and now we can just write it out
+h11 is minus Omega
+
+ align:start position:0%
+h11 is minus Omega
+ 
+
+ align:start position:0%
+h11 is minus Omega
+SAR
+
+ align:start position:0%
+SAR
+ 
+
+ align:start position:0%
+SAR
+M2 plus K2
+
+ align:start position:0%
+M2 plus K2
+ 
+
+ align:start position:0%
+M2 plus K2
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+fub1 and the denominator the
+
+ align:start position:0%
+fub1 and the denominator the
+ 
+
+ align:start position:0%
+fub1 and the denominator the
+characteristic
+
+ align:start position:0%
+characteristic
+ 
+
+ align:start position:0%
+characteristic
+equation is minus Omega
+
+ align:start position:0%
+equation is minus Omega
+ 
+
+ align:start position:0%
+equation is minus Omega
+2ar M1
+
+ align:start position:0%
+2ar M1
+ 
+
+ align:start position:0%
+2ar M1
++ K1 +
+
+ align:start position:0%
++ K1 +
+ 
+
+ align:start position:0%
++ K1 +
+K2 * - Omega
+
+ align:start position:0%
+K2 * - Omega
+ 
+
+ align:start position:0%
+K2 * - Omega
+2ar
+
+ align:start position:0%
+2ar
+ 
+
+ align:start position:0%
+2ar
+M2 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2 minus K2
+
+ align:start position:0%
+K2 minus K2
+ 
+
+ align:start position:0%
+K2 minus K2
+2ar so so this whole thing down here
+
+ align:start position:0%
+2ar so so this whole thing down here
+ 
+
+ align:start position:0%
+2ar so so this whole thing down here
+there's your characteristic equation you
+
+ align:start position:0%
+there's your characteristic equation you
+ 
+
+ align:start position:0%
+there's your characteristic equation you
+multiply it out you get your fourth
+
+ align:start position:0%
+multiply it out you get your fourth
+ 
+
+ align:start position:0%
+multiply it out you get your fourth
+order polinomial solve it you get two
+
+ align:start position:0%
+order polinomial solve it you get two
+ 
+
+ align:start position:0%
+order polinomial solve it you get two
+Roots but this is now a total expression
+
+ align:start position:0%
+Roots but this is now a total expression
+ 
+
+ align:start position:0%
+Roots but this is now a total expression
+for the response we were looking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for so this right right away this gives
+
+ align:start position:0%
+for so this right right away this gives
+ 
+
+ align:start position:0%
+for so this right right away this gives
+me the answer to the question that was
+
+ align:start position:0%
+me the answer to the question that was
+ 
+
+ align:start position:0%
+me the answer to the question that was
+posed to the doctoral
+
+ align:start position:0%
+posed to the doctoral
+ 
+
+ align:start position:0%
+posed to the doctoral
+students so as there a
+
+ align:start position:0%
+students so as there a
+ 
+
+ align:start position:0%
+students so as there a
+value can you set K2 and M2 such that
+
+ align:start position:0%
+value can you set K2 and M2 such that
+ 
+
+ align:start position:0%
+value can you set K2 and M2 such that
+you can make the response of the system
+
+ align:start position:0%
+you can make the response of the system
+ 
+
+ align:start position:0%
+you can make the response of the system
+zero at a at a particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Omega all you have to do is make the
+
+ align:start position:0%
+Omega all you have to do is make the
+ 
+
+ align:start position:0%
+Omega all you have to do is make the
+numerator go to zero right
+
+ align:start position:0%
+numerator go to zero right
+ 
+
+ align:start position:0%
+numerator go to zero right
+so if if you make this go to zero X goes
+
+ align:start position:0%
+so if if you make this go to zero X goes
+ 
+
+ align:start position:0%
+so if if you make this go to zero X goes
+to zero so X1 equals 0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when minus Omega SAR
+
+ align:start position:0%
+when minus Omega SAR
+ 
+
+ align:start position:0%
+when minus Omega SAR
+M2 + K2 equal Z and that happens when K2
+
+ align:start position:0%
+M2 + K2 equal Z and that happens when K2
+ 
+
+ align:start position:0%
+M2 + K2 equal Z and that happens when K2
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+M2 equal Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2 but so how many once you set K2 and
+
+ align:start position:0%
+2 but so how many once you set K2 and
+ 
+
+ align:start position:0%
+2 but so how many once you set K2 and
+M2 how many
+
+ align:start position:0%
+M2 how many
+ 
+
+ align:start position:0%
+M2 how many
+frequencies will does this happen
+
+ align:start position:0%
+frequencies will does this happen
+ 
+
+ align:start position:0%
+frequencies will does this happen
+at at how many different operating
+
+ align:start position:0%
+at at how many different operating
+ 
+
+ align:start position:0%
+at at how many different operating
+points can you make the response of that
+
+ align:start position:0%
+points can you make the response of that
+ 
+
+ align:start position:0%
+points can you make the response of that
+main Mass go to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero well just one once you choose k q
+
+ align:start position:0%
+zero well just one once you choose k q
+ 
+
+ align:start position:0%
+zero well just one once you choose k q
+and M2 whatever you've chosen to be they
+
+ align:start position:0%
+and M2 whatever you've chosen to be they
+ 
+
+ align:start position:0%
+and M2 whatever you've chosen to be they
+give you some value of Omega and when I
+
+ align:start position:0%
+give you some value of Omega and when I
+ 
+
+ align:start position:0%
+give you some value of Omega and when I
+said I was kind of vague about what
+
+ align:start position:0%
+said I was kind of vague about what
+ 
+
+ align:start position:0%
+said I was kind of vague about what
+happens here this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h11 looks like that and right here
+
+ align:start position:0%
+h11 looks like that and right here
+ 
+
+ align:start position:0%
+h11 looks like that and right here
+right here is
+
+ align:start position:0%
+right here is
+ 
+
+ align:start position:0%
+right here is
+when Omega 2ar = K2
+
+ align:start position:0%
+when Omega 2ar = K2
+ 
+
+ align:start position:0%
+when Omega 2ar = K2
+over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+M2 theator Zer no no because look at the
+
+ align:start position:0%
+M2 theator Zer no no because look at the
+ 
+
+ align:start position:0%
+M2 theator Zer no no because look at the
+picture here where are the two natural
+
+ align:start position:0%
+picture here where are the two natural
+ 
+
+ align:start position:0%
+picture here where are the two natural
+frequencies of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system there's one here and there's one
+
+ align:start position:0%
+system there's one here and there's one
+ 
+
+ align:start position:0%
+system there's one here and there's one
+here and that's when the denominator
+
+ align:start position:0%
+here and that's when the denominator
+ 
+
+ align:start position:0%
+here and that's when the denominator
+goes to zero when the denominator goes
+
+ align:start position:0%
+goes to zero when the denominator goes
+ 
+
+ align:start position:0%
+goes to zero when the denominator goes
+to zero the response goes to Infinity
+
+ align:start position:0%
+to zero the response goes to Infinity
+ 
+
+ align:start position:0%
+to zero the response goes to Infinity
+with no damping so the system has two
+
+ align:start position:0%
+with no damping so the system has two
+ 
+
+ align:start position:0%
+with no damping so the system has two
+natural frequencies one to either side
+
+ align:start position:0%
+natural frequencies one to either side
+ 
+
+ align:start position:0%
+natural frequencies one to either side
+at this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point so I've used I made the
+
+ align:start position:0%
+point so I've used I made the
+ 
+
+ align:start position:0%
+point so I've used I made the
+um I've picked kind of a particular
+
+ align:start position:0%
+um I've picked kind of a particular
+ 
+
+ align:start position:0%
+um I've picked kind of a particular
+example to illustrate the use of a
+
+ align:start position:0%
+example to illustrate the use of a
+ 
+
+ align:start position:0%
+example to illustrate the use of a
+transfer function and the fact that you
+
+ align:start position:0%
+transfer function and the fact that you
+ 
+
+ align:start position:0%
+transfer function and the fact that you
+can have transfer functions for multiple
+
+ align:start position:0%
+can have transfer functions for multiple
+ 
+
+ align:start position:0%
+can have transfer functions for multiple
+degree Freedom systems and they
+
+ align:start position:0%
+degree Freedom systems and they
+ 
+
+ align:start position:0%
+degree Freedom systems and they
+essentially become transfer function
+
+ align:start position:0%
+essentially become transfer function
+ 
+
+ align:start position:0%
+essentially become transfer function
+matrices and you use which what what you
+
+ align:start position:0%
+matrices and you use which what what you
+ 
+
+ align:start position:0%
+matrices and you use which what what you
+need and for this problem we needed
+
+ align:start position:0%
+need and for this problem we needed
+ 
+
+ align:start position:0%
+need and for this problem we needed
+h11 worked it out there it is this this
+
+ align:start position:0%
+h11 worked it out there it is this this
+ 
+
+ align:start position:0%
+h11 worked it out there it is this this
+is a complete equation that describes
+
+ align:start position:0%
+is a complete equation that describes
+ 
+
+ align:start position:0%
+is a complete equation that describes
+for me the behavior of mass one per unit
+
+ align:start position:0%
+for me the behavior of mass one per unit
+ 
+
+ align:start position:0%
+for me the behavior of mass one per unit
+input force as a function frequency and
+
+ align:start position:0%
+input force as a function frequency and
+ 
+
+ align:start position:0%
+input force as a function frequency and
+it will always have a point right there
+
+ align:start position:0%
+it will always have a point right there
+ 
+
+ align:start position:0%
+it will always have a point right there
+that it goes to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero okay and if we we don't have any
+
+ align:start position:0%
+zero okay and if we we don't have any
+ 
+
+ align:start position:0%
+zero okay and if we we don't have any
+damping in here right so intuitively
+
+ align:start position:0%
+damping in here right so intuitively
+ 
+
+ align:start position:0%
+damping in here right so intuitively
+what do you think damping will do to
+
+ align:start position:0%
+what do you think damping will do to
+ 
+
+ align:start position:0%
+what do you think damping will do to
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plot what's first thing it does to the
+
+ align:start position:0%
+plot what's first thing it does to the
+ 
+
+ align:start position:0%
+plot what's first thing it does to the
+Peaks
+
+ align:start position:0%
+Peaks
+ 
+
+ align:start position:0%
+Peaks
+what they
+
+ align:start position:0%
+what they
+ 
+
+ align:start position:0%
+what they
+become finite right and so the small
+
+ align:start position:0%
+become finite right and so the small
+ 
+
+ align:start position:0%
+become finite right and so the small
+damping they going to have very high
+
+ align:start position:0%
+damping they going to have very high
+ 
+
+ align:start position:0%
+damping they going to have very high
+tops more damping they're going to be
+
+ align:start position:0%
+tops more damping they're going to be
+ 
+
+ align:start position:0%
+tops more damping they're going to be
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+so damping especially affects the Peaks
+
+ align:start position:0%
+so damping especially affects the Peaks
+ 
+
+ align:start position:0%
+so damping especially affects the Peaks
+damping will also pull this off the
+
+ align:start position:0%
+damping will also pull this off the
+ 
+
+ align:start position:0%
+damping will also pull this off the
+bottom a little bit it won't perfectly
+
+ align:start position:0%
+bottom a little bit it won't perfectly
+ 
+
+ align:start position:0%
+bottom a little bit it won't perfectly
+go to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right so I'm going to do I want to do a
+
+ align:start position:0%
+right so I'm going to do I want to do a
+ 
+
+ align:start position:0%
+right so I'm going to do I want to do a
+very particular case so an obvious one
+
+ align:start position:0%
+very particular case so an obvious one
+ 
+
+ align:start position:0%
+very particular case so an obvious one
+is your original system it might be you
+
+ align:start position:0%
+is your original system it might be you
+ 
+
+ align:start position:0%
+is your original system it might be you
+know just a mass spring with a rotor in
+
+ align:start position:0%
+know just a mass spring with a rotor in
+ 
+
+ align:start position:0%
+know just a mass spring with a rotor in
+it that's unbalanced and it's running
+
+ align:start position:0%
+it that's unbalanced and it's running
+ 
+
+ align:start position:0%
+it that's unbalanced and it's running
+near reson and it's vibrating like crazy
+
+ align:start position:0%
+near reson and it's vibrating like crazy
+ 
+
+ align:start position:0%
+near reson and it's vibrating like crazy
+a single degree Freedom system vibrating
+
+ align:start position:0%
+a single degree Freedom system vibrating
+ 
+
+ align:start position:0%
+a single degree Freedom system vibrating
+like crazy can I put on a second Mass
+
+ align:start position:0%
+like crazy can I put on a second Mass
+ 
+
+ align:start position:0%
+like crazy can I put on a second Mass
+spring and stop the motion well look we
+
+ align:start position:0%
+spring and stop the motion well look we
+ 
+
+ align:start position:0%
+spring and stop the motion well look we
+can theoretically and we'll do we'll
+
+ align:start position:0%
+can theoretically and we'll do we'll
+ 
+
+ align:start position:0%
+can theoretically and we'll do we'll
+just say let's let the problem we're
+
+ align:start position:0%
+just say let's let the problem we're
+ 
+
+ align:start position:0%
+just say let's let the problem we're
+trying to solve that first system had a
+
+ align:start position:0%
+trying to solve that first system had a
+ 
+
+ align:start position:0%
+trying to solve that first system had a
+natural frequency I'll call it cap Omega
+
+ align:start position:0%
+natural frequency I'll call it cap Omega
+ 
+
+ align:start position:0%
+natural frequency I'll call it cap Omega
+n that was the square root of K1 over
+
+ align:start position:0%
+n that was the square root of K1 over
+ 
+
+ align:start position:0%
+n that was the square root of K1 over
+M1 and I'm going to let that be equal
+
+ align:start position:0%
+M1 and I'm going to let that be equal
+ 
+
+ align:start position:0%
+M1 and I'm going to let that be equal
+toare < TK of K2 over M2 so I've now
+
+ align:start position:0%
+toare < TK of K2 over M2 so I've now
+ 
+
+ align:start position:0%
+toare < TK of K2 over M2 so I've now
+chosen K2 and M2 such they're exactly at
+
+ align:start position:0%
+chosen K2 and M2 such they're exactly at
+ 
+
+ align:start position:0%
+chosen K2 and M2 such they're exactly at
+the natural frequency of the original
+
+ align:start position:0%
+the natural frequency of the original
+ 
+
+ align:start position:0%
+the natural frequency of the original
+single degree Freedom
+
+ align:start position:0%
+single degree Freedom
+ 
+
+ align:start position:0%
+single degree Freedom
+system so this is the original system
+
+ align:start position:0%
+system so this is the original system
+ 
+
+ align:start position:0%
+system so this is the original system
+K1 M1 and it has that natural frequency
+
+ align:start position:0%
+K1 M1 and it has that natural frequency
+ 
+
+ align:start position:0%
+K1 M1 and it has that natural frequency
+and now I'm going to stick on a second
+
+ align:start position:0%
+and now I'm going to stick on a second
+ 
+
+ align:start position:0%
+and now I'm going to stick on a second
+Mass K2 M2 but the value of K2 over M2
+
+ align:start position:0%
+Mass K2 M2 but the value of K2 over M2
+ 
+
+ align:start position:0%
+Mass K2 M2 but the value of K2 over M2
+of the second little system by itself it
+
+ align:start position:0%
+of the second little system by itself it
+ 
+
+ align:start position:0%
+of the second little system by itself it
+has the same natural frequency as the
+
+ align:start position:0%
+has the same natural frequency as the
+ 
+
+ align:start position:0%
+has the same natural frequency as the
+first if you want to think of it that
+
+ align:start position:0%
+first if you want to think of it that
+ 
+
+ align:start position:0%
+first if you want to think of it that
+way if I make this fixed what's the
+
+ align:start position:0%
+way if I make this fixed what's the
+ 
+
+ align:start position:0%
+way if I make this fixed what's the
+natural frequency of that mass and
+
+ align:start position:0%
+natural frequency of that mass and
+ 
+
+ align:start position:0%
+natural frequency of that mass and
+spring same same natural frequency I'm
+
+ align:start position:0%
+spring same same natural frequency I'm
+ 
+
+ align:start position:0%
+spring same same natural frequency I'm
+just making it that way so this is now
+
+ align:start position:0%
+just making it that way so this is now
+ 
+
+ align:start position:0%
+just making it that way so this is now
+my system that's the that's the that's
+
+ align:start position:0%
+my system that's the that's the that's
+ 
+
+ align:start position:0%
+my system that's the that's the that's
+the parameters and now we can
+
+ align:start position:0%
+the parameters and now we can
+ 
+
+ align:start position:0%
+the parameters and now we can
+uh we can I'm going to plot give you a
+
+ align:start position:0%
+uh we can I'm going to plot give you a
+ 
+
+ align:start position:0%
+uh we can I'm going to plot give you a
+plot of the response of that particular
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I'm going you know how we
+
+ align:start position:0%
+okay I'm going you know how we
+ 
+
+ align:start position:0%
+okay I'm going you know how we
+non-dimensionalize the transfer the
+
+ align:start position:0%
+non-dimensionalize the transfer the
+ 
+
+ align:start position:0%
+non-dimensionalize the transfer the
+single degree of Freedom transfer
+
+ align:start position:0%
+single degree of Freedom transfer
+ 
+
+ align:start position:0%
+single degree of Freedom transfer
+function we said X divided by the static
+
+ align:start position:0%
+function we said X divided by the static
+ 
+
+ align:start position:0%
+function we said X divided by the static
+motion I want to do that again here so
+
+ align:start position:0%
+motion I want to do that again here so
+ 
+
+ align:start position:0%
+motion I want to do that again here so
+let's let's look at this
+
+ align:start position:0%
+let's let's look at this
+ 
+
+ align:start position:0%
+let's let's look at this
+system it's a two degree Freedom
+
+ align:start position:0%
+system it's a two degree Freedom
+ 
+
+ align:start position:0%
+system it's a two degree Freedom
+system has a force F1 on
+
+ align:start position:0%
+system has a force F1 on
+ 
+
+ align:start position:0%
+system has a force F1 on
+it and as the frequency goes to zero and
+
+ align:start position:0%
+it and as the frequency goes to zero and
+ 
+
+ align:start position:0%
+it and as the frequency goes to zero and
+has displacement X1 and X2 so at Omega =
+
+ align:start position:0%
+has displacement X1 and X2 so at Omega =
+ 
+
+ align:start position:0%
+has displacement X1 and X2 so at Omega =
+0 X1 = X1 s I'll call it X1 static and
+
+ align:start position:0%
+0 X1 = X1 s I'll call it X1 static and
+ 
+
+ align:start position:0%
+0 X1 = X1 s I'll call it X1 static and
+how much is
+
+ align:start position:0%
+how much is
+ 
+
+ align:start position:0%
+how much is
+it so what's the static displacement at
+
+ align:start position:0%
+it so what's the static displacement at
+ 
+
+ align:start position:0%
+it so what's the static displacement at
+zero frequency of this system to that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Force come on it's just a spring in a m
+
+ align:start position:0%
+Force come on it's just a spring in a m
+ 
+
+ align:start position:0%
+Force come on it's just a spring in a m
+just a spring in a
+
+ align:start position:0%
+just a spring in a
+ 
+
+ align:start position:0%
+just a spring in a
+force how much will that string spring
+
+ align:start position:0%
+force how much will that string spring
+ 
+
+ align:start position:0%
+force how much will that string spring
+stretch when you put a force F1 on
+
+ align:start position:0%
+stretch when you put a force F1 on
+ 
+
+ align:start position:0%
+stretch when you put a force F1 on
+it F1 over K so X1 static equals F1 over
+
+ align:start position:0%
+it F1 over K so X1 static equals F1 over
+ 
+
+ align:start position:0%
+it F1 over K so X1 static equals F1 over
+K1 and how and F2 is zero there's no F2
+
+ align:start position:0%
+K1 and how and F2 is zero there's no F2
+ 
+
+ align:start position:0%
+K1 and how and F2 is zero there's no F2
+Force so how much is X2
+
+ align:start position:0%
+Force so how much is X2
+ 
+
+ align:start position:0%
+Force so how much is X2
+static there's no forces on F on the
+
+ align:start position:0%
+static there's no forces on F on the
+ 
+
+ align:start position:0%
+static there's no forces on F on the
+second Mass how much will it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+move just moves the same amount as the
+
+ align:start position:0%
+move just moves the same amount as the
+ 
+
+ align:start position:0%
+move just moves the same amount as the
+first mass right so this is also this is
+
+ align:start position:0%
+first mass right so this is also this is
+ 
+
+ align:start position:0%
+first mass right so this is also this is
+X2
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+static because the forces on the system
+
+ align:start position:0%
+static because the forces on the system
+ 
+
+ align:start position:0%
+static because the forces on the system
+are F1 and zero there's no Force in this
+
+ align:start position:0%
+are F1 and zero there's no Force in this
+ 
+
+ align:start position:0%
+are F1 and zero there's no Force in this
+it's not going to do anything to that
+
+ align:start position:0%
+it's not going to do anything to that
+ 
+
+ align:start position:0%
+it's not going to do anything to that
+spring it'll just move with the whole
+
+ align:start position:0%
+spring it'll just move with the whole
+ 
+
+ align:start position:0%
+spring it'll just move with the whole
+system
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I want to plot X1 over X1
+
+ align:start position:0%
+okay so I want to plot X1 over X1
+ 
+
+ align:start position:0%
+okay so I want to plot X1 over X1
+static well X1 is in general X1 is a
+
+ align:start position:0%
+static well X1 is in general X1 is a
+ 
+
+ align:start position:0%
+static well X1 is in general X1 is a
+function of frequency is F1 times and
+
+ align:start position:0%
+function of frequency is F1 times and
+ 
+
+ align:start position:0%
+function of frequency is F1 times and
+I'm going to do the magnitudes here here
+
+ align:start position:0%
+I'm going to do the magnitudes here here
+ 
+
+ align:start position:0%
+I'm going to do the magnitudes here here
+times the magnitude of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h11 and I'm going to divide that
+
+ align:start position:0%
+h11 and I'm going to divide that
+ 
+
+ align:start position:0%
+h11 and I'm going to divide that
+by fub1
+
+ align:start position:0%
+by fub1
+ 
+
+ align:start position:0%
+by fub1
+over K1 so the f1s go away K1 comes in
+
+ align:start position:0%
+over K1 so the f1s go away K1 comes in
+ 
+
+ align:start position:0%
+over K1 so the f1s go away K1 comes in
+the numerator this looks like K1
+
+ align:start position:0%
+the numerator this looks like K1
+ 
+
+ align:start position:0%
+the numerator this looks like K1
+H1
+
+ align:start position:0%
+H1
+ 
+
+ align:start position:0%
+H1
+one so a
+
+ align:start position:0%
+one so a
+ 
+
+ align:start position:0%
+one so a
+plot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+of K1
+
+ align:start position:0%
+of K1
+ 
+
+ align:start position:0%
+of K1
+magnitude
+
+ align:start position:0%
+magnitude
+ 
+
+ align:start position:0%
+magnitude
+h11 we know what roughly what it's going
+
+ align:start position:0%
+h11 we know what roughly what it's going
+ 
+
+ align:start position:0%
+h11 we know what roughly what it's going
+to look
+
+ align:start position:0%
+to look
+ 
+
+ align:start position:0%
+to look
+like as a
+
+ align:start position:0%
+like as a
+ 
+
+ align:start position:0%
+like as a
+peak has a
+
+ align:start position:0%
+peak has a
+ 
+
+ align:start position:0%
+peak has a
+zero another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Peak over here this plot goes to one as
+
+ align:start position:0%
+Peak over here this plot goes to one as
+ 
+
+ align:start position:0%
+Peak over here this plot goes to one as
+X1 over this is also X1 over X1 static
+
+ align:start position:0%
+X1 over this is also X1 over X1 static
+ 
+
+ align:start position:0%
+X1 over this is also X1 over X1 static
+same thing it goes to one
+
+ align:start position:0%
+same thing it goes to one
+ 
+
+ align:start position:0%
+same thing it goes to one
+here it goes to
+
+ align:start position:0%
+here it goes to
+ 
+
+ align:start position:0%
+here it goes to
+zero here is Omega
+
+ align:start position:0%
+zero here is Omega
+ 
+
+ align:start position:0%
+zero here is Omega
+1 here's Omega
+
+ align:start position:0%
+1 here's Omega
+ 
+
+ align:start position:0%
+1 here's Omega
+2 and right here you're at the original
+
+ align:start position:0%
+2 and right here you're at the original
+ 
+
+ align:start position:0%
+2 and right here you're at the original
+cap Omega
+
+ align:start position:0%
+cap Omega
+ 
+
+ align:start position:0%
+cap Omega
+n because that's the way we've designed
+
+ align:start position:0%
+n because that's the way we've designed
+ 
+
+ align:start position:0%
+n because that's the way we've designed
+this thing and we know this is the way
+
+ align:start position:0%
+this thing and we know this is the way
+ 
+
+ align:start position:0%
+this thing and we know this is the way
+h11 behaves it goes to zero at the value
+
+ align:start position:0%
+h11 behaves it goes to zero at the value
+ 
+
+ align:start position:0%
+h11 behaves it goes to zero at the value
+we've chosen for square root of K2 over
+
+ align:start position:0%
+we've chosen for square root of K2 over
+ 
+
+ align:start position:0%
+we've chosen for square root of K2 over
+M2 so we started out with an original
+
+ align:start position:0%
+M2 so we started out with an original
+ 
+
+ align:start position:0%
+M2 so we started out with an original
+system that had a natural frequency here
+
+ align:start position:0%
+system that had a natural frequency here
+ 
+
+ align:start position:0%
+system that had a natural frequency here
+okay one over M1 was right here we stuck
+
+ align:start position:0%
+okay one over M1 was right here we stuck
+ 
+
+ align:start position:0%
+okay one over M1 was right here we stuck
+on this second little
+
+ align:start position:0%
+on this second little
+ 
+
+ align:start position:0%
+on this second little
+mass and it made it into a two degree
+
+ align:start position:0%
+mass and it made it into a two degree
+ 
+
+ align:start position:0%
+mass and it made it into a two degree
+Freedom system it no longer has a
+
+ align:start position:0%
+Freedom system it no longer has a
+ 
+
+ align:start position:0%
+Freedom system it no longer has a
+natural frequency there has a natural
+
+ align:start position:0%
+natural frequency there has a natural
+ 
+
+ align:start position:0%
+natural frequency there has a natural
+frequency below it and a natural
+
+ align:start position:0%
+frequency below it and a natural
+ 
+
+ align:start position:0%
+frequency below it and a natural
+frequency above it and it's zero right
+
+ align:start position:0%
+frequency above it and it's zero right
+ 
+
+ align:start position:0%
+frequency above it and it's zero right
+where the original natural frequency
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+was okay now the uh
+
+ align:start position:0%
+was okay now the uh
+ 
+
+ align:start position:0%
+was okay now the uh
+so you've got imagine what's going on in
+
+ align:start position:0%
+so you've got imagine what's going on in
+ 
+
+ align:start position:0%
+so you've got imagine what's going on in
+the system you've got this Force being
+
+ align:start position:0%
+the system you've got this Force being
+ 
+
+ align:start position:0%
+the system you've got this Force being
+applied to the first mass and the first
+
+ align:start position:0%
+applied to the first mass and the first
+ 
+
+ align:start position:0%
+applied to the first mass and the first
+mass isn't
+
+ align:start position:0%
+mass isn't
+ 
+
+ align:start position:0%
+mass isn't
+moving do you think the second mass is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+moving think about the free body diagram
+
+ align:start position:0%
+moving think about the free body diagram
+ 
+
+ align:start position:0%
+moving think about the free body diagram
+of the first mass f equals
+
+ align:start position:0%
+of the first mass f equals
+ 
+
+ align:start position:0%
+of the first mass f equals
+ma there's a force on that first mass F1
+
+ align:start position:0%
+ma there's a force on that first mass F1
+ 
+
+ align:start position:0%
+ma there's a force on that first mass F1
+cosine Omega T and it's not moving MX
+
+ align:start position:0%
+cosine Omega T and it's not moving MX
+ 
+
+ align:start position:0%
+cosine Omega T and it's not moving MX
+double mx1 double dot is
+
+ align:start position:0%
+double mx1 double dot is
+ 
+
+ align:start position:0%
+double mx1 double dot is
+zero so in order for the thing not to
+
+ align:start position:0%
+zero so in order for the thing not to
+ 
+
+ align:start position:0%
+zero so in order for the thing not to
+move there's a force on it there must be
+
+ align:start position:0%
+move there's a force on it there must be
+ 
+
+ align:start position:0%
+move there's a force on it there must be
+some other Force exactly canceling
+
+ align:start position:0%
+some other Force exactly canceling
+ 
+
+ align:start position:0%
+some other Force exactly canceling
+it right where's it come
+
+ align:start position:0%
+it right where's it come
+ 
+
+ align:start position:0%
+it right where's it come
+from Mass 2 through the spring right
+
+ align:start position:0%
+from Mass 2 through the spring right
+ 
+
+ align:start position:0%
+from Mass 2 through the spring right
+okay so I'd also like to know uh what's
+
+ align:start position:0%
+okay so I'd also like to know uh what's
+ 
+
+ align:start position:0%
+okay so I'd also like to know uh what's
+the mo what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2 well
+
+ align:start position:0%
+X2 well
+ 
+
+ align:start position:0%
+X2 well
+X2 is from our transfer function Matrix
+
+ align:start position:0%
+X2 is from our transfer function Matrix
+ 
+
+ align:start position:0%
+X2 is from our transfer function Matrix
+is the response of two
+
+ align:start position:0%
+is the response of two
+ 
+
+ align:start position:0%
+is the response of two
+due to a force at 1 * fub1 plus a
+
+ align:start position:0%
+due to a force at 1 * fub1 plus a
+ 
+
+ align:start position:0%
+due to a force at 1 * fub1 plus a
+response at two due to a force at 2 * F2
+
+ align:start position:0%
+response at two due to a force at 2 * F2
+ 
+
+ align:start position:0%
+response at two due to a force at 2 * F2
+but that second term is zero because F2
+
+ align:start position:0%
+but that second term is zero because F2
+ 
+
+ align:start position:0%
+but that second term is zero because F2
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero that's a one- term
+
+ align:start position:0%
+zero that's a one- term
+ 
+
+ align:start position:0%
+zero that's a one- term
+expression and H1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h21
+
+ align:start position:0%
+h21
+ 
+
+ align:start position:0%
+h21
+is z11 over the denominator and z11
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so X2 is going to look like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I did wrote that
+
+ align:start position:0%
+I did wrote that
+ 
+
+ align:start position:0%
+I did wrote that
+wrong this is not
+
+ align:start position:0%
+wrong this is not
+ 
+
+ align:start position:0%
+wrong this is not
+z11 it is z minus z12
+
+ align:start position:0%
+z11 it is z minus z12
+ 
+
+ align:start position:0%
+z11 it is z minus z12
+right like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that and if you work that out it's
+
+ align:start position:0%
+that and if you work that out it's
+ 
+
+ align:start position:0%
+that and if you work that out it's
+fub1 time
+
+ align:start position:0%
+fub1 time
+ 
+
+ align:start position:0%
+fub1 time
+K2
+
+ align:start position:0%
+K2
+ 
+
+ align:start position:0%
+K2
+over the same denominator
+
+ align:start position:0%
+over the same denominator
+ 
+
+ align:start position:0%
+over the same denominator
+but let's evaluate i' let let's evaluate
+
+ align:start position:0%
+but let's evaluate i' let let's evaluate
+ 
+
+ align:start position:0%
+but let's evaluate i' let let's evaluate
+here's our this is a frequency we've
+
+ align:start position:0%
+here's our this is a frequency we've
+ 
+
+ align:start position:0%
+here's our this is a frequency we've
+been interested in let's evaluate the
+
+ align:start position:0%
+been interested in let's evaluate the
+ 
+
+ align:start position:0%
+been interested in let's evaluate the
+response of
+
+ align:start position:0%
+response of
+ 
+
+ align:start position:0%
+response of
+X2 right at this operating
+
+ align:start position:0%
+X2 right at this operating
+ 
+
+ align:start position:0%
+X2 right at this operating
+point so this's evaluate this at Omega
+
+ align:start position:0%
+point so this's evaluate this at Omega
+ 
+
+ align:start position:0%
+point so this's evaluate this at Omega
+equals cap Omega
+
+ align:start position:0%
+equals cap Omega
+ 
+
+ align:start position:0%
+equals cap Omega
+n okay so that's
+
+ align:start position:0%
+n okay so that's
+ 
+
+ align:start position:0%
+n okay so that's
+K2 down
+
+ align:start position:0%
+K2 down
+ 
+
+ align:start position:0%
+K2 down
+here minus Omega SAR M1
+
+ align:start position:0%
+here minus Omega SAR M1
+ 
+
+ align:start position:0%
+here minus Omega SAR M1
+1 + K1 + K2 it's the same denominator as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+always
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2 I'm not going to write it all out
+
+ align:start position:0%
+K2 I'm not going to write it all out
+ 
+
+ align:start position:0%
+K2 I'm not going to write it all out
+it's exactly the same thing as before
+
+ align:start position:0%
+it's exactly the same thing as before
+ 
+
+ align:start position:0%
+it's exactly the same thing as before
+but I want to plug in to this
+
+ align:start position:0%
+but I want to plug in to this
+ 
+
+ align:start position:0%
+but I want to plug in to this
+denominator the operating
+
+ align:start position:0%
+denominator the operating
+ 
+
+ align:start position:0%
+denominator the operating
+frequency you know we're going to
+
+ align:start position:0%
+frequency you know we're going to
+ 
+
+ align:start position:0%
+frequency you know we're going to
+operate at cap Omega n which is k1 over
+
+ align:start position:0%
+operate at cap Omega n which is k1 over
+ 
+
+ align:start position:0%
+operate at cap Omega n which is k1 over
+M1 square square otk of K1 over M1 or
+
+ align:start position:0%
+M1 square square otk of K1 over M1 or
+ 
+
+ align:start position:0%
+M1 square square otk of K1 over M1 or
+Square otk of K2 over M2 I'm going to
+
+ align:start position:0%
+Square otk of K2 over M2 I'm going to
+ 
+
+ align:start position:0%
+Square otk of K2 over M2 I'm going to
+plug in in this and let's see what we
+
+ align:start position:0%
+plug in in this and let's see what we
+ 
+
+ align:start position:0%
+plug in in this and let's see what we
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'm going to eval
+
+ align:start position:0%
+and I'm going to eval
+ 
+
+ align:start position:0%
+and I'm going to eval
+let Omega
+
+ align:start position:0%
+let Omega
+ 
+
+ align:start position:0%
+let Omega
+equal
+
+ align:start position:0%
+equal
+ 
+
+ align:start position:0%
+equal
+K1 over M1 or K2 over M2 it's the same
+
+ align:start position:0%
+K1 over M1 or K2 over M2 it's the same
+ 
+
+ align:start position:0%
+K1 over M1 or K2 over M2 it's the same
+thing I going to plug them in whatever
+
+ align:start position:0%
+thing I going to plug them in whatever
+ 
+
+ align:start position:0%
+thing I going to plug them in whatever
+is convenient so here I'm going to put
+
+ align:start position:0%
+is convenient so here I'm going to put
+ 
+
+ align:start position:0%
+is convenient so here I'm going to put
+K1 over
+
+ align:start position:0%
+K1 over
+ 
+
+ align:start position:0%
+K1 over
+M1 and the m1's are going to cancel I'll
+
+ align:start position:0%
+M1 and the m1's are going to cancel I'll
+ 
+
+ align:start position:0%
+M1 and the m1's are going to cancel I'll
+be left with a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K1 F1 over K2 and down in denominator
+
+ align:start position:0%
+K1 F1 over K2 and down in denominator
+ 
+
+ align:start position:0%
+K1 F1 over K2 and down in denominator
+this is this term turns into K1 over M1
+
+ align:start position:0%
+this is this term turns into K1 over M1
+ 
+
+ align:start position:0%
+this is this term turns into K1 over M1
+so that's minus K1 + K1 plus
+
+ align:start position:0%
+so that's minus K1 + K1 plus
+ 
+
+ align:start position:0%
+so that's minus K1 + K1 plus
+K2 those two cancel I just get a K2 over
+
+ align:start position:0%
+K2 those two cancel I just get a K2 over
+ 
+
+ align:start position:0%
+K2 those two cancel I just get a K2 over
+here I'll use minus K2 over
+
+ align:start position:0%
+here I'll use minus K2 over
+ 
+
+ align:start position:0%
+here I'll use minus K2 over
+M2 * M2 +
+
+ align:start position:0%
+M2 * M2 +
+ 
+
+ align:start position:0%
+M2 * M2 +
+K2 and that gives me a minus K2 plus K2
+
+ align:start position:0%
+K2 and that gives me a minus K2 plus K2
+ 
+
+ align:start position:0%
+K2 and that gives me a minus K2 plus K2
+ooh this whole thing goes to
+
+ align:start position:0%
+ooh this whole thing goes to
+ 
+
+ align:start position:0%
+ooh this whole thing goes to
+zero and I'm left with
+
+ align:start position:0%
+zero and I'm left with
+ 
+
+ align:start position:0%
+zero and I'm left with
+minus K2 2ar and in the denominator a
+
+ align:start position:0%
+minus K2 2ar and in the denominator a
+ 
+
+ align:start position:0%
+minus K2 2ar and in the denominator a
+K2 this whole thing turns into fub1 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+K2 so the total response of that second
+
+ align:start position:0%
+K2 so the total response of that second
+ 
+
+ align:start position:0%
+K2 so the total response of that second
+mass at this operating frequency is just
+
+ align:start position:0%
+mass at this operating frequency is just
+ 
+
+ align:start position:0%
+mass at this operating frequency is just
+F1 over
+
+ align:start position:0%
+F1 over
+ 
+
+ align:start position:0%
+F1 over
+K2 and I would like to plot it as what
+
+ align:start position:0%
+K2 and I would like to plot it as what
+ 
+
+ align:start position:0%
+K2 and I would like to plot it as what
+does
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X2
+
+ align:start position:0%
+X2
+ 
+
+ align:start position:0%
+X2
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+X One static and X1 static and and X2
+
+ align:start position:0%
+X One static and X1 static and and X2
+ 
+
+ align:start position:0%
+X One static and X1 static and and X2
+static are the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same well that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is fub1 over
+
+ align:start position:0%
+is fub1 over
+ 
+
+ align:start position:0%
+is fub1 over
+K2 over fub1 over
+
+ align:start position:0%
+K2 over fub1 over
+ 
+
+ align:start position:0%
+K2 over fub1 over
+K1 the f1s go away and I get K1 over K2
+
+ align:start position:0%
+K1 the f1s go away and I get K1 over K2
+ 
+
+ align:start position:0%
+K1 the f1s go away and I get K1 over K2
+that also happens to be M1 over M2 and
+
+ align:start position:0%
+that also happens to be M1 over M2 and
+ 
+
+ align:start position:0%
+that also happens to be M1 over M2 and
+it's a quantity we call one over
+
+ align:start position:0%
+it's a quantity we call one over
+ 
+
+ align:start position:0%
+it's a quantity we call one over
+mu and this we have just
+
+ align:start position:0%
+mu and this we have just
+ 
+
+ align:start position:0%
+mu and this we have just
+designed what's called a dynamic
+
+ align:start position:0%
+designed what's called a dynamic
+ 
+
+ align:start position:0%
+designed what's called a dynamic
+absorber and a dynamic absorber is a
+
+ align:start position:0%
+absorber and a dynamic absorber is a
+ 
+
+ align:start position:0%
+absorber and a dynamic absorber is a
+little we little device you can use to
+
+ align:start position:0%
+little we little device you can use to
+ 
+
+ align:start position:0%
+little we little device you can use to
+stop
+
+ align:start position:0%
+stop
+ 
+
+ align:start position:0%
+stop
+vibration so when we were talking about
+
+ align:start position:0%
+vibration so when we were talking about
+ 
+
+ align:start position:0%
+vibration so when we were talking about
+vibration isolation and vibration
+
+ align:start position:0%
+vibration isolation and vibration
+ 
+
+ align:start position:0%
+vibration isolation and vibration
+mitigation a few days ago and I said
+
+ align:start position:0%
+mitigation a few days ago and I said
+ 
+
+ align:start position:0%
+mitigation a few days ago and I said
+you've got some rotating imbalance
+
+ align:start position:0%
+you've got some rotating imbalance
+ 
+
+ align:start position:0%
+you've got some rotating imbalance
+causing your something to shake will
+
+ align:start position:0%
+causing your something to shake will
+ 
+
+ align:start position:0%
+causing your something to shake will
+give me three ways of solving it he said
+
+ align:start position:0%
+give me three ways of solving it he said
+ 
+
+ align:start position:0%
+give me three ways of solving it he said
+balance the rotor what were the other
+
+ align:start position:0%
+balance the rotor what were the other
+ 
+
+ align:start position:0%
+balance the rotor what were the other
+two ways of perhaps reducing the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vibration
+
+ align:start position:0%
+vibration
+ 
+
+ align:start position:0%
+vibration
+pardon yeah but we also you know if you
+
+ align:start position:0%
+pardon yeah but we also you know if you
+ 
+
+ align:start position:0%
+pardon yeah but we also you know if you
+got something that's shaking like crazy
+
+ align:start position:0%
+got something that's shaking like crazy
+ 
+
+ align:start position:0%
+got something that's shaking like crazy
+and it's putting vibration into the
+
+ align:start position:0%
+and it's putting vibration into the
+ 
+
+ align:start position:0%
+and it's putting vibration into the
+floor or into the the table you can
+
+ align:start position:0%
+floor or into the the table you can
+ 
+
+ align:start position:0%
+floor or into the the table you can
+isolate it with a mass and a spring or
+
+ align:start position:0%
+isolate it with a mass and a spring or
+ 
+
+ align:start position:0%
+isolate it with a mass and a spring or
+the microscope over here that's
+
+ align:start position:0%
+the microscope over here that's
+ 
+
+ align:start position:0%
+the microscope over here that's
+vibrating like crazy you can isolate it
+
+ align:start position:0%
+vibrating like crazy you can isolate it
+ 
+
+ align:start position:0%
+vibrating like crazy you can isolate it
+with a mass or a spring so this is this
+
+ align:start position:0%
+with a mass or a spring so this is this
+ 
+
+ align:start position:0%
+with a mass or a spring so this is this
+topic of vibration isolation which is
+
+ align:start position:0%
+topic of vibration isolation which is
+ 
+
+ align:start position:0%
+topic of vibration isolation which is
+guaranteed to be on the
+
+ align:start position:0%
+guaranteed to be on the
+ 
+
+ align:start position:0%
+guaranteed to be on the
+final simple practical applications of
+
+ align:start position:0%
+final simple practical applications of
+ 
+
+ align:start position:0%
+final simple practical applications of
+single degre Freedom stuff so have three
+
+ align:start position:0%
+single degre Freedom stuff so have three
+ 
+
+ align:start position:0%
+single degre Freedom stuff so have three
+ways fix the rotor isolate it with a
+
+ align:start position:0%
+ways fix the rotor isolate it with a
+ 
+
+ align:start position:0%
+ways fix the rotor isolate it with a
+mass in a spring isolate the sensitive
+
+ align:start position:0%
+mass in a spring isolate the sensitive
+ 
+
+ align:start position:0%
+mass in a spring isolate the sensitive
+instrument mass of the spring now you
+
+ align:start position:0%
+instrument mass of the spring now you
+ 
+
+ align:start position:0%
+instrument mass of the spring now you
+have a fourth way if it's a particular
+
+ align:start position:0%
+have a fourth way if it's a particular
+ 
+
+ align:start position:0%
+have a fourth way if it's a particular
+operating frequency we can make it
+
+ align:start position:0%
+operating frequency we can make it
+ 
+
+ align:start position:0%
+operating frequency we can make it
+operate right here with this thing
+
+ align:start position:0%
+operate right here with this thing
+ 
+
+ align:start position:0%
+operate right here with this thing
+called the dynamic absorber this mu
+
+ align:start position:0%
+called the dynamic absorber this mu
+ 
+
+ align:start position:0%
+called the dynamic absorber this mu
+quantity is called the mass
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ratio and
+
+ align:start position:0%
+ratio and
+ 
+
+ align:start position:0%
+ratio and
+um that's M it's it's M2 over
+
+ align:start position:0%
+um that's M it's it's M2 over
+ 
+
+ align:start position:0%
+um that's M it's it's M2 over
+M1 basically these things are real
+
+ align:start position:0%
+M1 basically these things are real
+ 
+
+ align:start position:0%
+M1 basically these things are real
+they're actually used in real machines
+
+ align:start position:0%
+they're actually used in real machines
+ 
+
+ align:start position:0%
+they're actually used in real machines
+and usually you can't the this Dynamic
+
+ align:start position:0%
+and usually you can't the this Dynamic
+ 
+
+ align:start position:0%
+and usually you can't the this Dynamic
+resor thing you stick on there can't be
+
+ align:start position:0%
+resor thing you stick on there can't be
+ 
+
+ align:start position:0%
+resor thing you stick on there can't be
+as big as the original system it's going
+
+ align:start position:0%
+as big as the original system it's going
+ 
+
+ align:start position:0%
+as big as the original system it's going
+to be some small fraction the original
+
+ align:start position:0%
+to be some small fraction the original
+ 
+
+ align:start position:0%
+to be some small fraction the original
+system size five or 10% if you're lucky
+
+ align:start position:0%
+system size five or 10% if you're lucky
+ 
+
+ align:start position:0%
+system size five or 10% if you're lucky
+so the bigger this thing is you'll find
+
+ align:start position:0%
+so the bigger this thing is you'll find
+ 
+
+ align:start position:0%
+so the bigger this thing is you'll find
+out the better it works so what's how
+
+ align:start position:0%
+out the better it works so what's how
+ 
+
+ align:start position:0%
+out the better it works so what's how
+how how much is this little second Mass
+
+ align:start position:0%
+how how much is this little second Mass
+ 
+
+ align:start position:0%
+how how much is this little second Mass
+bouncing around well it's bouncing
+
+ align:start position:0%
+bouncing around well it's bouncing
+ 
+
+ align:start position:0%
+bouncing around well it's bouncing
+around compared to X1 static in the
+
+ align:start position:0%
+around compared to X1 static in the
+ 
+
+ align:start position:0%
+around compared to X1 static in the
+ratio of K1 to K2 which is this one over
+
+ align:start position:0%
+ratio of K1 to K2 which is this one over
+ 
+
+ align:start position:0%
+ratio of K1 to K2 which is this one over
+mu quantity so if mu is 10% if you've
+
+ align:start position:0%
+mu quantity so if mu is 10% if you've
+ 
+
+ align:start position:0%
+mu quantity so if mu is 10% if you've
+added the second mass is 10% the size of
+
+ align:start position:0%
+added the second mass is 10% the size of
+ 
+
+ align:start position:0%
+added the second mass is 10% the size of
+the first one one over mu is a factor of
+
+ align:start position:0%
+the first one one over mu is a factor of
+ 
+
+ align:start position:0%
+the first one one over mu is a factor of
+10 Okay so the this transfer function
+
+ align:start position:0%
+10 Okay so the this transfer function
+ 
+
+ align:start position:0%
+10 Okay so the this transfer function
+basically looks do I have something
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+colored so the X2 over X1 transfer
+
+ align:start position:0%
+colored so the X2 over X1 transfer
+ 
+
+ align:start position:0%
+colored so the X2 over X1 transfer
+function basically behaves the same way
+
+ align:start position:0%
+function basically behaves the same way
+ 
+
+ align:start position:0%
+function basically behaves the same way
+here and pretty much the same way out
+
+ align:start position:0%
+here and pretty much the same way out
+ 
+
+ align:start position:0%
+here and pretty much the same way out
+here and in here comes down like this
+
+ align:start position:0%
+here and in here comes down like this
+ 
+
+ align:start position:0%
+here and in here comes down like this
+and comes back up and this height right
+
+ align:start position:0%
+and comes back up and this height right
+ 
+
+ align:start position:0%
+and comes back up and this height right
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+here is 1 over
+
+ align:start position:0%
+here is 1 over
+ 
+
+ align:start position:0%
+here is 1 over
+mu so the smaller you make this thing
+
+ align:start position:0%
+mu so the smaller you make this thing
+ 
+
+ align:start position:0%
+mu so the smaller you make this thing
+the tinier you make it the more it has
+
+ align:start position:0%
+the tinier you make it the more it has
+ 
+
+ align:start position:0%
+the tinier you make it the more it has
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+shake to force the first mass to go to
+
+ align:start position:0%
+shake to force the first mass to go to
+ 
+
+ align:start position:0%
+shake to force the first mass to go to
+zero and so basically the way reason
+
+ align:start position:0%
+zero and so basically the way reason
+ 
+
+ align:start position:0%
+zero and so basically the way reason
+this thing works the free body diagram
+
+ align:start position:0%
+this thing works the free body diagram
+ 
+
+ align:start position:0%
+this thing works the free body diagram
+on the
+
+ align:start position:0%
+on the
+ 
+
+ align:start position:0%
+on the
+uh at this oper at this zero point the
+
+ align:start position:0%
+uh at this oper at this zero point the
+ 
+
+ align:start position:0%
+uh at this oper at this zero point the
+main Mass
+
+ align:start position:0%
+main Mass
+ 
+
+ align:start position:0%
+main Mass
+M1 X1 equals z here it's not moving it's
+
+ align:start position:0%
+M1 X1 equals z here it's not moving it's
+ 
+
+ align:start position:0%
+M1 X1 equals z here it's not moving it's
+got a force acting on it that is some
+
+ align:start position:0%
+got a force acting on it that is some
+ 
+
+ align:start position:0%
+got a force acting on it that is some
+fub1 cosine Omega T it's got a spring
+
+ align:start position:0%
+fub1 cosine Omega T it's got a spring
+ 
+
+ align:start position:0%
+fub1 cosine Omega T it's got a spring
+force acting on it from this second Mass
+
+ align:start position:0%
+force acting on it from this second Mass
+ 
+
+ align:start position:0%
+force acting on it from this second Mass
+going here's M2 over here and it's going
+
+ align:start position:0%
+going here's M2 over here and it's going
+ 
+
+ align:start position:0%
+going here's M2 over here and it's going
+back and forth like
+
+ align:start position:0%
+back and forth like
+ 
+
+ align:start position:0%
+back and forth like
+crazy putting Force through this spring
+
+ align:start position:0%
+crazy putting Force through this spring
+ 
+
+ align:start position:0%
+crazy putting Force through this spring
+and the spring Force had better be
+
+ align:start position:0%
+and the spring Force had better be
+ 
+
+ align:start position:0%
+and the spring Force had better be
+exactly equal to
+
+ align:start position:0%
+exactly equal to
+ 
+
+ align:start position:0%
+exactly equal to
+that so the F spring is going to be
+
+ align:start position:0%
+that so the F spring is going to be
+ 
+
+ align:start position:0%
+that so the F spring is going to be
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+fub1 and that will be equal to X2 *
+
+ align:start position:0%
+fub1 and that will be equal to X2 *
+ 
+
+ align:start position:0%
+fub1 and that will be equal to X2 *
+kx2 this the second Mass has to move
+
+ align:start position:0%
+kx2 this the second Mass has to move
+ 
+
+ align:start position:0%
+kx2 this the second Mass has to move
+enough that it'll compress the spring
+
+ align:start position:0%
+enough that it'll compress the spring
+ 
+
+ align:start position:0%
+enough that it'll compress the spring
+enough that it's provides a force equal
+
+ align:start position:0%
+enough that it's provides a force equal
+ 
+
+ align:start position:0%
+enough that it's provides a force equal
+and opposite to this one so that it's in
+
+ align:start position:0%
+and opposite to this one so that it's in
+ 
+
+ align:start position:0%
+and opposite to this one so that it's in
+stat it's in equilibrium and doesn't
+
+ align:start position:0%
+stat it's in equilibrium and doesn't
+ 
+
+ align:start position:0%
+stat it's in equilibrium and doesn't
+move all
+
+ align:start position:0%
+move all
+ 
+
+ align:start position:0%
+move all
+right yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that who asking a question yeah so the
+
+ align:start position:0%
+that who asking a question yeah so the
+ 
+
+ align:start position:0%
+that who asking a question yeah so the
+building um if you want the masses to be
+
+ align:start position:0%
+building um if you want the masses to be
+ 
+
+ align:start position:0%
+building um if you want the masses to be
+fairly equal to each other how's going
+
+ align:start position:0%
+fairly equal to each other how's going
+ 
+
+ align:start position:0%
+fairly equal to each other how's going
+to happen no so I mean not usually in
+
+ align:start position:0%
+to happen no so I mean not usually in
+ 
+
+ align:start position:0%
+to happen no so I mean not usually in
+real when people when Dynam Dynamic
+
+ align:start position:0%
+real when people when Dynam Dynamic
+ 
+
+ align:start position:0%
+real when people when Dynam Dynamic
+absorbers are are used in real things
+
+ align:start position:0%
+absorbers are are used in real things
+ 
+
+ align:start position:0%
+absorbers are are used in real things
+like the Handcock building and they're
+
+ align:start position:0%
+like the Handcock building and they're
+ 
+
+ align:start position:0%
+like the Handcock building and they're
+used in
+
+ align:start position:0%
+used in
+ 
+
+ align:start position:0%
+used in
+engines they're used in all sorts of
+
+ align:start position:0%
+engines they're used in all sorts of
+ 
+
+ align:start position:0%
+engines they're used in all sorts of
+little devices that you don't know where
+
+ align:start position:0%
+little devices that you don't know where
+ 
+
+ align:start position:0%
+little devices that you don't know where
+that they're there
+
+ align:start position:0%
+that they're there
+ 
+
+ align:start position:0%
+that they're there
+um and and you have to usually hide them
+
+ align:start position:0%
+um and and you have to usually hide them
+ 
+
+ align:start position:0%
+um and and you have to usually hide them
+inside the footprint of the original
+
+ align:start position:0%
+inside the footprint of the original
+ 
+
+ align:start position:0%
+inside the footprint of the original
+device so you don't want them you know
+
+ align:start position:0%
+device so you don't want them you know
+ 
+
+ align:start position:0%
+device so you don't want them you know
+for a real thing you don't want to have
+
+ align:start position:0%
+for a real thing you don't want to have
+ 
+
+ align:start position:0%
+for a real thing you don't want to have
+a pump you know with this huge appendage
+
+ align:start position:0%
+a pump you know with this huge appendage
+ 
+
+ align:start position:0%
+a pump you know with this huge appendage
+on it right it's just not practical so
+
+ align:start position:0%
+on it right it's just not practical so
+ 
+
+ align:start position:0%
+on it right it's just not practical so
+they tend to be small and so they as a
+
+ align:start position:0%
+they tend to be small and so they as a
+ 
+
+ align:start position:0%
+they tend to be small and so they as a
+consequence in order to make them work
+
+ align:start position:0%
+consequence in order to make them work
+ 
+
+ align:start position:0%
+consequence in order to make them work
+at this particular frequency they have
+
+ align:start position:0%
+at this particular frequency they have
+ 
+
+ align:start position:0%
+at this particular frequency they have
+to vibrate like crazy so the design cost
+
+ align:start position:0%
+to vibrate like crazy so the design cost
+ 
+
+ align:start position:0%
+to vibrate like crazy so the design cost
+of one of these things is you have to
+
+ align:start position:0%
+of one of these things is you have to
+ 
+
+ align:start position:0%
+of one of these things is you have to
+design it to be able to allow this
+
+ align:start position:0%
+design it to be able to allow this
+ 
+
+ align:start position:0%
+design it to be able to allow this
+second Mass to shake like I'll get out
+
+ align:start position:0%
+second Mass to shake like I'll get out
+ 
+
+ align:start position:0%
+second Mass to shake like I'll get out
+now how many frequenc quencies does this
+
+ align:start position:0%
+now how many frequenc quencies does this
+ 
+
+ align:start position:0%
+now how many frequenc quencies does this
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+at once you've designed it it only works
+
+ align:start position:0%
+at once you've designed it it only works
+ 
+
+ align:start position:0%
+at once you've designed it it only works
+at one frequency so this is only useful
+
+ align:start position:0%
+at one frequency so this is only useful
+ 
+
+ align:start position:0%
+at one frequency so this is only useful
+for something it has a a fixed operating
+
+ align:start position:0%
+for something it has a a fixed operating
+ 
+
+ align:start position:0%
+for something it has a a fixed operating
+frequency like a synchronous motor you
+
+ align:start position:0%
+frequency like a synchronous motor you
+ 
+
+ align:start position:0%
+frequency like a synchronous motor you
+won't this isn't a good good thing for
+
+ align:start position:0%
+won't this isn't a good good thing for
+ 
+
+ align:start position:0%
+won't this isn't a good good thing for
+something that has uh a range of
+
+ align:start position:0%
+something that has uh a range of
+ 
+
+ align:start position:0%
+something that has uh a range of
+frequencies over which it can work but
+
+ align:start position:0%
+frequencies over which it can work but
+ 
+
+ align:start position:0%
+frequencies over which it can work but
+there's a different more complicated
+
+ align:start position:0%
+there's a different more complicated
+ 
+
+ align:start position:0%
+there's a different more complicated
+Theory call of that there's a type of
+
+ align:start position:0%
+Theory call of that there's a type of
+ 
+
+ align:start position:0%
+Theory call of that there's a type of
+dynamic absorber that you can make work
+
+ align:start position:0%
+dynamic absorber that you can make work
+ 
+
+ align:start position:0%
+dynamic absorber that you can make work
+over a wide range of frequencies need to
+
+ align:start position:0%
+over a wide range of frequencies need to
+ 
+
+ align:start position:0%
+over a wide range of frequencies need to
+tell you one other thing when we put
+
+ align:start position:0%
+tell you one other thing when we put
+ 
+
+ align:start position:0%
+tell you one other thing when we put
+this thing on the original natural
+
+ align:start position:0%
+this thing on the original natural
+ 
+
+ align:start position:0%
+this thing on the original natural
+frequency of the first system was here
+
+ align:start position:0%
+frequency of the first system was here
+ 
+
+ align:start position:0%
+frequency of the first system was here
+and it created two new ones right you
+
+ align:start position:0%
+and it created two new ones right you
+ 
+
+ align:start position:0%
+and it created two new ones right you
+got a further
+
+ align:start position:0%
+got a further
+ 
+
+ align:start position:0%
+got a further
+question so how is making a VI vibrant
+
+ align:start position:0%
+question so how is making a VI vibrant
+ 
+
+ align:start position:0%
+question so how is making a VI vibrant
+like bad Health it's only going to work
+
+ align:start position:0%
+like bad Health it's only going to work
+ 
+
+ align:start position:0%
+like bad Health it's only going to work
+at that one frequency and you're always
+
+ align:start position:0%
+at that one frequency and you're always
+ 
+
+ align:start position:0%
+at that one frequency and you're always
+going to have that Gap so making you
+
+ align:start position:0%
+going to have that Gap so making you
+ 
+
+ align:start position:0%
+going to have that Gap so making you
+Library really fast how how would that
+
+ align:start position:0%
+Library really fast how how would that
+ 
+
+ align:start position:0%
+Library really fast how how would that
+help at all well it stops if the if for
+
+ align:start position:0%
+help at all well it stops if the if for
+ 
+
+ align:start position:0%
+help at all well it stops if the if for
+some reason you really don't want that
+
+ align:start position:0%
+some reason you really don't want that
+ 
+
+ align:start position:0%
+some reason you really don't want that
+first thing to shake this makes it stop
+
+ align:start position:0%
+first thing to shake this makes it stop
+ 
+
+ align:start position:0%
+first thing to shake this makes it stop
+shaking at that
+
+ align:start position:0%
+shaking at that
+ 
+
+ align:start position:0%
+shaking at that
+frequency so for example Le there's an
+
+ align:start position:0%
+frequency so for example Le there's an
+ 
+
+ align:start position:0%
+frequency so for example Le there's an
+one of the first one of the widest
+
+ align:start position:0%
+one of the first one of the widest
+ 
+
+ align:start position:0%
+one of the first one of the widest
+distributed textbooks in the world was
+
+ align:start position:0%
+distributed textbooks in the world was
+ 
+
+ align:start position:0%
+distributed textbooks in the world was
+written by an MIT Professor named den
+
+ align:start position:0%
+written by an MIT Professor named den
+ 
+
+ align:start position:0%
+written by an MIT Professor named den
+harthog and it's called mechanical
+
+ align:start position:0%
+harthog and it's called mechanical
+ 
+
+ align:start position:0%
+harthog and it's called mechanical
+vibration written in the 1930s it's got
+
+ align:start position:0%
+vibration written in the 1930s it's got
+ 
+
+ align:start position:0%
+vibration written in the 1930s it's got
+a wonderful chapter on Dynamic absorbers
+
+ align:start position:0%
+a wonderful chapter on Dynamic absorbers
+ 
+
+ align:start position:0%
+a wonderful chapter on Dynamic absorbers
+in it and the example that he gives of a
+
+ align:start position:0%
+in it and the example that he gives of a
+ 
+
+ align:start position:0%
+in it and the example that he gives of a
+real device that actually uses one was
+
+ align:start position:0%
+real device that actually uses one was
+ 
+
+ align:start position:0%
+real device that actually uses one was
+the kind was an electric uh hair clipper
+
+ align:start position:0%
+the kind was an electric uh hair clipper
+ 
+
+ align:start position:0%
+the kind was an electric uh hair clipper
+that you know barara uses now you know
+
+ align:start position:0%
+that you know barara uses now you know
+ 
+
+ align:start position:0%
+that you know barara uses now you know
+the head on a hair clipper it's got it
+
+ align:start position:0%
+the head on a hair clipper it's got it
+ 
+
+ align:start position:0%
+the head on a hair clipper it's got it
+it has to go back and forth like this
+
+ align:start position:0%
+it has to go back and forth like this
+ 
+
+ align:start position:0%
+it has to go back and forth like this
+you know to cut the hair right that is
+
+ align:start position:0%
+you know to cut the hair right that is
+ 
+
+ align:start position:0%
+you know to cut the hair right that is
+an oscillating mass and you're going to
+
+ align:start position:0%
+an oscillating mass and you're going to
+ 
+
+ align:start position:0%
+an oscillating mass and you're going to
+feel it that's an essentially you know
+
+ align:start position:0%
+feel it that's an essentially you know
+ 
+
+ align:start position:0%
+feel it that's an essentially you know
+you're going to feel the mass times the
+
+ align:start position:0%
+you're going to feel the mass times the
+ 
+
+ align:start position:0%
+you're going to feel the mass times the
+acceleration the m a Omega squar
+
+ align:start position:0%
+acceleration the m a Omega squar
+ 
+
+ align:start position:0%
+acceleration the m a Omega squar
+acceleration at the frequency it runs
+
+ align:start position:0%
+acceleration at the frequency it runs
+ 
+
+ align:start position:0%
+acceleration at the frequency it runs
+that so they did a clever thing they
+
+ align:start position:0%
+that so they did a clever thing they
+ 
+
+ align:start position:0%
+that so they did a clever thing they
+built inside the case of this thing a
+
+ align:start position:0%
+built inside the case of this thing a
+ 
+
+ align:start position:0%
+built inside the case of this thing a
+little second mass in a spring and so
+
+ align:start position:0%
+little second mass in a spring and so
+ 
+
+ align:start position:0%
+little second mass in a spring and so
+the when you're holding the razor the
+
+ align:start position:0%
+the when you're holding the razor the
+ 
+
+ align:start position:0%
+the when you're holding the razor the
+Clippers it didn't feel like
+
+ align:start position:0%
+Clippers it didn't feel like
+ 
+
+ align:start position:0%
+Clippers it didn't feel like
+it's okay so that's an ex was an example
+
+ align:start position:0%
+it's okay so that's an ex was an example
+ 
+
+ align:start position:0%
+it's okay so that's an ex was an example
+actually a great example in this 1938
+
+ align:start position:0%
+actually a great example in this 1938
+ 
+
+ align:start position:0%
+actually a great example in this 1938
+textbook okay and you just so you know I
+
+ align:start position:0%
+textbook okay and you just so you know I
+ 
+
+ align:start position:0%
+textbook okay and you just so you know I
+mean you really do have two natural
+
+ align:start position:0%
+mean you really do have two natural
+ 
+
+ align:start position:0%
+mean you really do have two natural
+frequencies when you do this and I'll
+
+ align:start position:0%
+frequencies when you do this and I'll
+ 
+
+ align:start position:0%
+frequencies when you do this and I'll
+write them like this Omega 1^ 2 and
+
+ align:start position:0%
+write them like this Omega 1^ 2 and
+ 
+
+ align:start position:0%
+write them like this Omega 1^ 2 and
+Omega 2^ 2 are the original frequency
+
+ align:start position:0%
+Omega 2^ 2 are the original frequency
+ 
+
+ align:start position:0%
+Omega 2^ 2 are the original frequency
+squared Time 1 + mu /
+
+ align:start position:0%
+squared Time 1 + mu /
+ 
+
+ align:start position:0%
+squared Time 1 + mu /
+2 plus or
+
+ align:start position:0%
+2 plus or
+ 
+
+ align:start position:0%
+2 plus or
+minus mu + mu^
+
+ align:start position:0%
+minus mu + mu^
+ 
+
+ align:start position:0%
+minus mu + mu^
+2 over 4
+
+ align:start position:0%
+2 over 4
+ 
+
+ align:start position:0%
+2 over 4
+square
+
+ align:start position:0%
+square
+ 
+
+ align:start position:0%
+square
+root so as your mass ratio gets
+
+ align:start position:0%
+root so as your mass ratio gets
+ 
+
+ align:start position:0%
+root so as your mass ratio gets
+bigger the two frequencies move further
+
+ align:start position:0%
+bigger the two frequencies move further
+ 
+
+ align:start position:0%
+bigger the two frequencies move further
+and further apart when the mass ratio is
+
+ align:start position:0%
+and further apart when the mass ratio is
+ 
+
+ align:start position:0%
+and further apart when the mass ratio is
+zero this quantity the two natural
+
+ align:start position:0%
+zero this quantity the two natural
+ 
+
+ align:start position:0%
+zero this quantity the two natural
+frequenc the only it goes to one natural
+
+ align:start position:0%
+frequenc the only it goes to one natural
+ 
+
+ align:start position:0%
+frequenc the only it goes to one natural
+frequency it's a single degree Freedom
+
+ align:start position:0%
+frequency it's a single degree Freedom
+ 
+
+ align:start position:0%
+frequency it's a single degree Freedom
+system and it's at the original value as
+
+ align:start position:0%
+system and it's at the original value as
+ 
+
+ align:start position:0%
+system and it's at the original value as
+the mass ratio gets bigger and bigger
+
+ align:start position:0%
+the mass ratio gets bigger and bigger
+ 
+
+ align:start position:0%
+the mass ratio gets bigger and bigger
+these two Roots this one and this
+
+ align:start position:0%
+these two Roots this one and this
+ 
+
+ align:start position:0%
+these two Roots this one and this
+one as you add Mass to that second
+
+ align:start position:0%
+one as you add Mass to that second
+ 
+
+ align:start position:0%
+one as you add Mass to that second
+system they spread apart and the bigger
+
+ align:start position:0%
+system they spread apart and the bigger
+ 
+
+ align:start position:0%
+system they spread apart and the bigger
+the the mass ratio the further apart the
+
+ align:start position:0%
+the the mass ratio the further apart the
+ 
+
+ align:start position:0%
+the the mass ratio the further apart the
+two natural frequencies
+
+ align:start position:0%
+two natural frequencies
+ 
+
+ align:start position:0%
+two natural frequencies
+become so we got 10 minutes left and I
+
+ align:start position:0%
+become so we got 10 minutes left and I
+ 
+
+ align:start position:0%
+become so we got 10 minutes left and I
+have a demo which is illustrates this
+
+ align:start position:0%
+have a demo which is illustrates this
+ 
+
+ align:start position:0%
+have a demo which is illustrates this
+thing it's a little delicate to make it
+
+ align:start position:0%
+thing it's a little delicate to make it
+ 
+
+ align:start position:0%
+thing it's a little delicate to make it
+work so uh because actually it was
+
+ align:start position:0%
+work so uh because actually it was
+ 
+
+ align:start position:0%
+work so uh because actually it was
+really frustrating I had it all set up
+
+ align:start position:0%
+really frustrating I had it all set up
+ 
+
+ align:start position:0%
+really frustrating I had it all set up
+it worked great in my
+
+ align:start position:0%
+it worked great in my
+ 
+
+ align:start position:0%
+it worked great in my
+office came in 10 minutes early today to
+
+ align:start position:0%
+office came in 10 minutes early today to
+ 
+
+ align:start position:0%
+office came in 10 minutes early today to
+set it up and the table in here is so
+
+ align:start position:0%
+set it up and the table in here is so
+ 
+
+ align:start position:0%
+set it up and the table in here is so
+flexible I can't make it behave like a
+
+ align:start position:0%
+flexible I can't make it behave like a
+ 
+
+ align:start position:0%
+flexible I can't make it behave like a
+fixed surface
+
+ align:start position:0%
+fixed surface
+ 
+
+ align:start position:0%
+fixed surface
+so I tweaked it and I think I've got it
+
+ align:start position:0%
+so I tweaked it and I think I've got it
+ 
+
+ align:start position:0%
+so I tweaked it and I think I've got it
+running now but now what what it is is a
+
+ align:start position:0%
+running now but now what what it is is a
+ 
+
+ align:start position:0%
+running now but now what what it is is a
+beam with my pen on it my little
+
+ align:start position:0%
+beam with my pen on it my little
+ 
+
+ align:start position:0%
+beam with my pen on it my little
+squiggle pen and you've seen this before
+
+ align:start position:0%
+squiggle pen and you've seen this before
+ 
+
+ align:start position:0%
+squiggle pen and you've seen this before
+it's it's a rotating Mass it's a static
+
+ align:start position:0%
+it's it's a rotating Mass it's a static
+ 
+
+ align:start position:0%
+it's it's a rotating Mass it's a static
+imbalance it shakes this beam okay and
+
+ align:start position:0%
+imbalance it shakes this beam okay and
+ 
+
+ align:start position:0%
+imbalance it shakes this beam okay and
+I've added to it a second little beam
+
+ align:start position:0%
+I've added to it a second little beam
+ 
+
+ align:start position:0%
+I've added to it a second little beam
+it's a little blade of Steel with a
+
+ align:start position:0%
+it's a little blade of Steel with a
+ 
+
+ align:start position:0%
+it's a little blade of Steel with a
+heavy magnet on it that's my M2 this is
+
+ align:start position:0%
+heavy magnet on it that's my M2 this is
+ 
+
+ align:start position:0%
+heavy magnet on it that's my M2 this is
+my K2 is this little beam this is the
+
+ align:start position:0%
+my K2 is this little beam this is the
+ 
+
+ align:start position:0%
+my K2 is this little beam this is the
+original system a mass it's at it close
+
+ align:start position:0%
+original system a mass it's at it close
+ 
+
+ align:start position:0%
+original system a mass it's at it close
+to a natural frequency and the rotation
+
+ align:start position:0%
+to a natural frequency and the rotation
+ 
+
+ align:start position:0%
+to a natural frequency and the rotation
+rate of the The Eccentric mass is right
+
+ align:start position:0%
+rate of the The Eccentric mass is right
+ 
+
+ align:start position:0%
+rate of the The Eccentric mass is right
+at the natural frequency of this beam so
+
+ align:start position:0%
+at the natural frequency of this beam so
+ 
+
+ align:start position:0%
+at the natural frequency of this beam so
+because it's delicate to set up I got to
+
+ align:start position:0%
+because it's delicate to set up I got to
+ 
+
+ align:start position:0%
+because it's delicate to set up I got to
+show you the system first with the
+
+ align:start position:0%
+show you the system first with the
+ 
+
+ align:start position:0%
+show you the system first with the
+second Mass attached to it and I think
+
+ align:start position:0%
+second Mass attached to it and I think
+ 
+
+ align:start position:0%
+second Mass attached to it and I think
+I've got it tweaked so that it'll sit
+
+ align:start position:0%
+I've got it tweaked so that it'll sit
+ 
+
+ align:start position:0%
+I've got it tweaked so that it'll sit
+there it's right at the operating point
+
+ align:start position:0%
+there it's right at the operating point
+ 
+
+ align:start position:0%
+there it's right at the operating point
+and you ought to see the second Mass
+
+ align:start position:0%
+and you ought to see the second Mass
+ 
+
+ align:start position:0%
+and you ought to see the second Mass
+moving like crazy and the the original
+
+ align:start position:0%
+moving like crazy and the the original
+ 
+
+ align:start position:0%
+moving like crazy and the the original
+Mass The Beam not moving much at all
+
+ align:start position:0%
+Mass The Beam not moving much at all
+ 
+
+ align:start position:0%
+Mass The Beam not moving much at all
+so let's see if we can make it
+
+ align:start position:0%
+so let's see if we can make it
+ 
+
+ align:start position:0%
+so let's see if we can make it
+work we're going to need to kill the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lights and you can see in
+
+ align:start position:0%
+lights and you can see in
+ 
+
+ align:start position:0%
+lights and you can see in
+here you can see the rotating Mass going
+
+ align:start position:0%
+here you can see the rotating Mass going
+ 
+
+ align:start position:0%
+here you can see the rotating Mass going
+around and around and so I have the
+
+ align:start position:0%
+around and around and so I have the
+ 
+
+ align:start position:0%
+around and around and so I have the
+strobe light detuned just a little bit
+
+ align:start position:0%
+strobe light detuned just a little bit
+ 
+
+ align:start position:0%
+strobe light detuned just a little bit
+so that you can see the system it's not
+
+ align:start position:0%
+so that you can see the system it's not
+ 
+
+ align:start position:0%
+so that you can see the system it's not
+quite synchronous you can watch this
+
+ align:start position:0%
+quite synchronous you can watch this
+ 
+
+ align:start position:0%
+quite synchronous you can watch this
+little white blob out here you see it
+
+ align:start position:0%
+little white blob out here you see it
+ 
+
+ align:start position:0%
+little white blob out here you see it
+going up and
+
+ align:start position:0%
+going up and
+ 
+
+ align:start position:0%
+going up and
+down that's your second mass and does
+
+ align:start position:0%
+down that's your second mass and does
+ 
+
+ align:start position:0%
+down that's your second mass and does
+the is the main beam it's moving a
+
+ align:start position:0%
+the is the main beam it's moving a
+ 
+
+ align:start position:0%
+the is the main beam it's moving a
+little bit but not
+
+ align:start position:0%
+little bit but not
+ 
+
+ align:start position:0%
+little bit but not
+much got a little damping and so it
+
+ align:start position:0%
+much got a little damping and so it
+ 
+
+ align:start position:0%
+much got a little damping and so it
+isn't perfectly down at that null point
+
+ align:start position:0%
+isn't perfectly down at that null point
+ 
+
+ align:start position:0%
+isn't perfectly down at that null point
+but very close so this is the system
+
+ align:start position:0%
+but very close so this is the system
+ 
+
+ align:start position:0%
+but very close so this is the system
+operating close to that n point so now
+
+ align:start position:0%
+operating close to that n point so now
+ 
+
+ align:start position:0%
+operating close to that n point so now
+if I
+
+ align:start position:0%
+if I
+ 
+
+ align:start position:0%
+if I
+remove the
+
+ align:start position:0%
+remove the
+ 
+
+ align:start position:0%
+remove the
+Dynamic absorber the second little Mass
+
+ align:start position:0%
+Dynamic absorber the second little Mass
+ 
+
+ align:start position:0%
+Dynamic absorber the second little Mass
+spring system then the main mass and the
+
+ align:start position:0%
+spring system then the main mass and the
+ 
+
+ align:start position:0%
+spring system then the main mass and the
+beam a of shake like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crazy
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay just changing the tuning a little
+
+ align:start position:0%
+okay just changing the tuning a little
+ 
+
+ align:start position:0%
+okay just changing the tuning a little
+here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I'm going to
+
+ align:start position:0%
+now I'm going to
+ 
+
+ align:start position:0%
+now I'm going to
+remove the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+absorber all
+
+ align:start position:0%
+absorber all
+ 
+
+ align:start position:0%
+absorber all
+right and now
+
+ align:start position:0%
+right and now
+ 
+
+ align:start position:0%
+right and now
+it's going like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+crazy so that's an
+
+ align:start position:0%
+crazy so that's an
+ 
+
+ align:start position:0%
+crazy so that's an
+illustration you come up the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lights now you hear it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+beating this little pen this little
+
+ align:start position:0%
+beating this little pen this little
+ 
+
+ align:start position:0%
+beating this little pen this little
+rotor in here is driven by a little DC
+
+ align:start position:0%
+rotor in here is driven by a little DC
+ 
+
+ align:start position:0%
+rotor in here is driven by a little DC
+motor and a single doua
+
+ align:start position:0%
+motor and a single doua
+ 
+
+ align:start position:0%
+motor and a single doua
+battery and it's not feedback controlled
+
+ align:start position:0%
+battery and it's not feedback controlled
+ 
+
+ align:start position:0%
+battery and it's not feedback controlled
+its frequency can vary and it isn't that
+
+ align:start position:0%
+its frequency can vary and it isn't that
+ 
+
+ align:start position:0%
+its frequency can vary and it isn't that
+powerful so this thing starts moving up
+
+ align:start position:0%
+powerful so this thing starts moving up
+ 
+
+ align:start position:0%
+powerful so this thing starts moving up
+and down it actually takes real torque
+
+ align:start position:0%
+and down it actually takes real torque
+ 
+
+ align:start position:0%
+and down it actually takes real torque
+to make that weight go around while this
+
+ align:start position:0%
+to make that weight go around while this
+ 
+
+ align:start position:0%
+to make that weight go around while this
+whole system is accelerating up and down
+
+ align:start position:0%
+whole system is accelerating up and down
+ 
+
+ align:start position:0%
+whole system is accelerating up and down
+and the motor just isn't up to it just
+
+ align:start position:0%
+and the motor just isn't up to it just
+ 
+
+ align:start position:0%
+and the motor just isn't up to it just
+isn't powerful enough so the speed
+
+ align:start position:0%
+isn't powerful enough so the speed
+ 
+
+ align:start position:0%
+isn't powerful enough so the speed
+changes so this isn't an this thing
+
+ align:start position:0%
+changes so this isn't an this thing
+ 
+
+ align:start position:0%
+changes so this isn't an this thing
+can't hold constant frequency anyway
+
+ align:start position:0%
+can't hold constant frequency anyway
+ 
+
+ align:start position:0%
+can't hold constant frequency anyway
+that's the uh so that's the demo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions so we've kind of embedded in
+
+ align:start position:0%
+questions so we've kind of embedded in
+ 
+
+ align:start position:0%
+questions so we've kind of embedded in
+this lecture this lecture was to
+
+ align:start position:0%
+this lecture this lecture was to
+ 
+
+ align:start position:0%
+this lecture this lecture was to
+introduce you to the idea that there are
+
+ align:start position:0%
+introduce you to the idea that there are
+ 
+
+ align:start position:0%
+introduce you to the idea that there are
+you can write a transfer function for a
+
+ align:start position:0%
+you can write a transfer function for a
+ 
+
+ align:start position:0%
+you can write a transfer function for a
+multiple degree of Freedom system has
+
+ align:start position:0%
+multiple degree of Freedom system has
+ 
+
+ align:start position:0%
+multiple degree of Freedom system has
+embedded in it all the natural
+
+ align:start position:0%
+embedded in it all the natural
+ 
+
+ align:start position:0%
+embedded in it all the natural
+frequencies of the system when you use a
+
+ align:start position:0%
+frequencies of the system when you use a
+ 
+
+ align:start position:0%
+frequencies of the system when you use a
+transfer function to calculate the
+
+ align:start position:0%
+transfer function to calculate the
+ 
+
+ align:start position:0%
+transfer function to calculate the
+response of the system you are getting
+
+ align:start position:0%
+response of the system you are getting
+ 
+
+ align:start position:0%
+response of the system you are getting
+the contributions of all the modes at
+
+ align:start position:0%
+the contributions of all the modes at
+ 
+
+ align:start position:0%
+the contributions of all the modes at
+once so you've essentially solve the
+
+ align:start position:0%
+once so you've essentially solve the
+ 
+
+ align:start position:0%
+once so you've essentially solve the
+equations of motion
+
+ align:start position:0%
+equations of motion
+ 
+
+ align:start position:0%
+equations of motion
+directly so you now have seen there's
+
+ align:start position:0%
+directly so you now have seen there's
+ 
+
+ align:start position:0%
+directly so you now have seen there's
+two ways to go about analyzing multiple
+
+ align:start position:0%
+two ways to go about analyzing multiple
+ 
+
+ align:start position:0%
+two ways to go about analyzing multiple
+degree of Freedom systems the technique
+
+ align:start position:0%
+degree of Freedom systems the technique
+ 
+
+ align:start position:0%
+degree of Freedom systems the technique
+known as modal analysis one mode at a
+
+ align:start position:0%
+known as modal analysis one mode at a
+ 
+
+ align:start position:0%
+known as modal analysis one mode at a
+time then add it together there or like
+
+ align:start position:0%
+time then add it together there or like
+ 
+
+ align:start position:0%
+time then add it together there or like
+with transfer functions where you're
+
+ align:start position:0%
+with transfer functions where you're
+ 
+
+ align:start position:0%
+with transfer functions where you're
+just solving the whole thing at once and
+
+ align:start position:0%
+just solving the whole thing at once and
+ 
+
+ align:start position:0%
+just solving the whole thing at once and
+each transfer function has in it all of
+
+ align:start position:0%
+each transfer function has in it all of
+ 
+
+ align:start position:0%
+each transfer function has in it all of
+the information about all of the modes
+
+ align:start position:0%
+the information about all of the modes
+ 
+
+ align:start position:0%
+the information about all of the modes
+of the system so if it's five degree
+
+ align:start position:0%
+of the system so if it's five degree
+ 
+
+ align:start position:0%
+of the system so if it's five degree
+Freedom system you're going to see five
+
+ align:start position:0%
+Freedom system you're going to see five
+ 
+
+ align:start position:0%
+Freedom system you're going to see five
+Peaks out
+
+ align:start position:0%
+Peaks out
+ 
+
+ align:start position:0%
+Peaks out
+here all right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions long run stuff but initially
+
+ align:start position:0%
+questions long run stuff but initially
+ 
+
+ align:start position:0%
+questions long run stuff but initially
+since you have a force on mass one does
+
+ align:start position:0%
+since you have a force on mass one does
+ 
+
+ align:start position:0%
+since you have a force on mass one does
+it have to out moving to get into moving
+
+ align:start position:0%
+it have to out moving to get into moving
+ 
+
+ align:start position:0%
+it have to out moving to get into moving
+and then it
+
+ align:start position:0%
+and then it
+ 
+
+ align:start position:0%
+and then it
+stops so there's going to be a transient
+
+ align:start position:0%
+stops so there's going to be a transient
+ 
+
+ align:start position:0%
+stops so there's going to be a transient
+phase sure when you any any system when
+
+ align:start position:0%
+phase sure when you any any system when
+ 
+
+ align:start position:0%
+phase sure when you any any system when
+you start it up is going to have
+
+ align:start position:0%
+you start it up is going to have
+ 
+
+ align:start position:0%
+you start it up is going to have
+transients and the
+
+ align:start position:0%
+transients and the
+ 
+
+ align:start position:0%
+transients and the
+transients are the equivalent of initial
+
+ align:start position:0%
+transients are the equivalent of initial
+ 
+
+ align:start position:0%
+transients are the equivalent of initial
+conditions so on displacement and
+
+ align:start position:0%
+conditions so on displacement and
+ 
+
+ align:start position:0%
+conditions so on displacement and
+velocity and the response of
+
+ align:start position:0%
+velocity and the response of
+ 
+
+ align:start position:0%
+velocity and the response of
+a linear system that vibrates that has
+
+ align:start position:0%
+a linear system that vibrates that has
+ 
+
+ align:start position:0%
+a linear system that vibrates that has
+natural frequencies to a set of initial
+
+ align:start position:0%
+natural frequencies to a set of initial
+ 
+
+ align:start position:0%
+natural frequencies to a set of initial
+conditions is vibration at what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequencies do you know how they
+
+ align:start position:0%
+frequencies do you know how they
+ 
+
+ align:start position:0%
+frequencies do you know how they
+overcome this in helicopters like the
+
+ align:start position:0%
+overcome this in helicopters like the
+ 
+
+ align:start position:0%
+overcome this in helicopters like the
+chin that we saw at the beginning of the
+
+ align:start position:0%
+chin that we saw at the beginning of the
+ 
+
+ align:start position:0%
+chin that we saw at the beginning of the
+year uh yeah the helicopter so I went to
+
+ align:start position:0%
+year uh yeah the helicopter so I went to
+ 
+
+ align:start position:0%
+year uh yeah the helicopter so I went to
+answer the question response to that
+
+ align:start position:0%
+answer the question response to that
+ 
+
+ align:start position:0%
+answer the question response to that
+transients is at the natural frequencies
+
+ align:start position:0%
+transients is at the natural frequencies
+ 
+
+ align:start position:0%
+transients is at the natural frequencies
+of the system maybe some combination the
+
+ align:start position:0%
+of the system maybe some combination the
+ 
+
+ align:start position:0%
+of the system maybe some combination the
+original displacement requires
+
+ align:start position:0%
+original displacement requires
+ 
+
+ align:start position:0%
+original displacement requires
+contributions of several modes you'll
+
+ align:start position:0%
+contributions of several modes you'll
+ 
+
+ align:start position:0%
+contributions of several modes you'll
+get Decay contributions at each of the
+
+ align:start position:0%
+get Decay contributions at each of the
+ 
+
+ align:start position:0%
+get Decay contributions at each of the
+natural frequencies and once they've
+
+ align:start position:0%
+natural frequencies and once they've
+ 
+
+ align:start position:0%
+natural frequencies and once they've
+died out this motor is started up the
+
+ align:start position:0%
+died out this motor is started up the
+ 
+
+ align:start position:0%
+died out this motor is started up the
+thing will settle into we call steady
+
+ align:start position:0%
+thing will settle into we call steady
+ 
+
+ align:start position:0%
+thing will settle into we call steady
+state response and it'll only be at the
+
+ align:start position:0%
+state response and it'll only be at the
+ 
+
+ align:start position:0%
+state response and it'll only be at the
+excitation frequency and I haven't shown
+
+ align:start position:0%
+excitation frequency and I haven't shown
+ 
+
+ align:start position:0%
+excitation frequency and I haven't shown
+you anything about you can can you solve
+
+ align:start position:0%
+you anything about you can can you solve
+ 
+
+ align:start position:0%
+you anything about you can can you solve
+the equations of motion from start up at
+
+ align:start position:0%
+the equations of motion from start up at
+ 
+
+ align:start position:0%
+the equations of motion from start up at
+time zero through the whole messy
+
+ align:start position:0%
+time zero through the whole messy
+ 
+
+ align:start position:0%
+time zero through the whole messy
+transient phase to steady state sure and
+
+ align:start position:0%
+transient phase to steady state sure and
+ 
+
+ align:start position:0%
+transient phase to steady state sure and
+we haven't talked at all about that and
+
+ align:start position:0%
+we haven't talked at all about that and
+ 
+
+ align:start position:0%
+we haven't talked at all about that and
+actually for for most vibration stuff it
+
+ align:start position:0%
+actually for for most vibration stuff it
+ 
+
+ align:start position:0%
+actually for for most vibration stuff it
+isn't very important steady St answer is
+
+ align:start position:0%
+isn't very important steady St answer is
+ 
+
+ align:start position:0%
+isn't very important steady St answer is
+important the transient answer is pretty
+
+ align:start position:0%
+important the transient answer is pretty
+ 
+
+ align:start position:0%
+important the transient answer is pretty
+important and for you to have a feeling
+
+ align:start position:0%
+important and for you to have a feeling
+ 
+
+ align:start position:0%
+important and for you to have a feeling
+for that you actually know quite a fair
+
+ align:start position:0%
+for that you actually know quite a fair
+ 
+
+ align:start position:0%
+for that you actually know quite a fair
+amount about the basic concept of how
+
+ align:start position:0%
+amount about the basic concept of how
+ 
+
+ align:start position:0%
+amount about the basic concept of how
+things vibrate now now your question
+
+ align:start position:0%
+things vibrate now now your question
+ 
+
+ align:start position:0%
+things vibrate now now your question
+about the helicopter so if you have a
+
+ align:start position:0%
+about the helicopter so if you have a
+ 
+
+ align:start position:0%
+about the helicopter so if you have a
+uniform helicopter blade I mean they
+
+ align:start position:0%
+uniform helicopter blade I mean they
+ 
+
+ align:start position:0%
+uniform helicopter blade I mean they
+they rigged that to do what it did they
+
+ align:start position:0%
+they rigged that to do what it did they
+ 
+
+ align:start position:0%
+they rigged that to do what it did they
+were I don't know what they're
+
+ align:start position:0%
+were I don't know what they're
+ 
+
+ align:start position:0%
+were I don't know what they're
+experimenting with but if you do there's
+
+ align:start position:0%
+experimenting with but if you do there's
+ 
+
+ align:start position:0%
+experimenting with but if you do there's
+a a problem that I've actually given in
+
+ align:start position:0%
+a a problem that I've actually given in
+ 
+
+ align:start position:0%
+a a problem that I've actually given in
+a vibration course if you design a
+
+ align:start position:0%
+a vibration course if you design a
+ 
+
+ align:start position:0%
+a vibration course if you design a
+really simple helicopter that has a
+
+ align:start position:0%
+really simple helicopter that has a
+ 
+
+ align:start position:0%
+really simple helicopter that has a
+uniform blade you know it's a uniform
+
+ align:start position:0%
+uniform blade you know it's a uniform
+ 
+
+ align:start position:0%
+uniform blade you know it's a uniform
+rod
+
+ align:start position:0%
+rod
+ 
+
+ align:start position:0%
+rod
+and it's pivoted at the center and you
+
+ align:start position:0%
+and it's pivoted at the center and you
+ 
+
+ align:start position:0%
+and it's pivoted at the center and you
+spin it up and if you spin it fast
+
+ align:start position:0%
+spin it up and if you spin it fast
+ 
+
+ align:start position:0%
+spin it up and if you spin it fast
+enough you know if you spin it slowly
+
+ align:start position:0%
+enough you know if you spin it slowly
+ 
+
+ align:start position:0%
+enough you know if you spin it slowly
+it'll droop because of gravity but if
+
+ align:start position:0%
+it'll droop because of gravity but if
+ 
+
+ align:start position:0%
+it'll droop because of gravity but if
+you spin it fast enough R Omega squar is
+
+ align:start position:0%
+you spin it fast enough R Omega squar is
+ 
+
+ align:start position:0%
+you spin it fast enough R Omega squar is
+a lot bigger than G and the thing
+
+ align:start position:0%
+a lot bigger than G and the thing
+ 
+
+ align:start position:0%
+a lot bigger than G and the thing
+flattens out and the blades are going
+
+ align:start position:0%
+flattens out and the blades are going
+ 
+
+ align:start position:0%
+flattens out and the blades are going
+round and round right the natural
+
+ align:start position:0%
+round and round right the natural
+ 
+
+ align:start position:0%
+round and round right the natural
+frequency of that system is exactly the
+
+ align:start position:0%
+frequency of that system is exactly the
+ 
+
+ align:start position:0%
+frequency of that system is exactly the
+rotation
+
+ align:start position:0%
+rotation
+ 
+
+ align:start position:0%
+rotation
+rate a uniform blade pivot at the center
+
+ align:start position:0%
+rate a uniform blade pivot at the center
+ 
+
+ align:start position:0%
+rate a uniform blade pivot at the center
+going around fast has a natural
+
+ align:start position:0%
+going around fast has a natural
+ 
+
+ align:start position:0%
+going around fast has a natural
+frequency like this it Happ s to be
+
+ align:start position:0%
+frequency like this it Happ s to be
+ 
+
+ align:start position:0%
+frequency like this it Happ s to be
+exactly at the rate of rotation so it is
+
+ align:start position:0%
+exactly at the rate of rotation so it is
+ 
+
+ align:start position:0%
+exactly at the rate of rotation so it is
+at any perturbation will start it doing
+
+ align:start position:0%
+at any perturbation will start it doing
+ 
+
+ align:start position:0%
+at any perturbation will start it doing
+bad things helicopters never ever
+
+ align:start position:0%
+bad things helicopters never ever
+ 
+
+ align:start position:0%
+bad things helicopters never ever
+designed like
+
+ align:start position:0%
+designed like
+ 
+
+ align:start position:0%
+designed like
+that the helicopter has a the rotor disc
+
+ align:start position:0%
+that the helicopter has a the rotor disc
+ 
+
+ align:start position:0%
+that the helicopter has a the rotor disc
+in here has a finite radius before the
+
+ align:start position:0%
+in here has a finite radius before the
+ 
+
+ align:start position:0%
+in here has a finite radius before the
+pin and then the blades are out
+
+ align:start position:0%
+pin and then the blades are out
+ 
+
+ align:start position:0%
+pin and then the blades are out
+here the pin around which and that
+
+ align:start position:0%
+here the pin around which and that
+ 
+
+ align:start position:0%
+here the pin around which and that
+changes the resonance frequency and of
+
+ align:start position:0%
+changes the resonance frequency and of
+ 
+
+ align:start position:0%
+changes the resonance frequency and of
+course you can change the mass
+
+ align:start position:0%
+course you can change the mass
+ 
+
+ align:start position:0%
+course you can change the mass
+distribution in the blade and so forth
+
+ align:start position:0%
+distribution in the blade and so forth
+ 
+
+ align:start position:0%
+distribution in the blade and so forth
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+uh you know what they had done in that
+
+ align:start position:0%
+uh you know what they had done in that
+ 
+
+ align:start position:0%
+uh you know what they had done in that
+that want that case to rig it so the
+
+ align:start position:0%
+that want that case to rig it so the
+ 
+
+ align:start position:0%
+that want that case to rig it so the
+thing beat itself to death I don't know
+
+ align:start position:0%
+thing beat itself to death I don't know
+ 
+
+ align:start position:0%
+thing beat itself to death I don't know
+but they there's good design practices
+
+ align:start position:0%
+but they there's good design practices
+ 
+
+ align:start position:0%
+but they there's good design practices
+with helicopters so that the the blade
+
+ align:start position:0%
+with helicopters so that the the blade
+ 
+
+ align:start position:0%
+with helicopters so that the the blade
+frequency is not at the rotation rate
+
+ align:start position:0%
+frequency is not at the rotation rate
+ 
+
+ align:start position:0%
+frequency is not at the rotation rate
+because at rotation rate you're going to
+
+ align:start position:0%
+because at rotation rate you're going to
+ 
+
+ align:start position:0%
+because at rotation rate you're going to
+a lot of excitation right hitting
+
+ align:start position:0%
+a lot of excitation right hitting
+ 
+
+ align:start position:0%
+a lot of excitation right hitting
+turbulence in the air and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+forth Yeah you mentioned that they use
+
+ align:start position:0%
+forth Yeah you mentioned that they use
+ 
+
+ align:start position:0%
+forth Yeah you mentioned that they use
+um something like this in a Handcock
+
+ align:start position:0%
+um something like this in a Handcock
+ 
+
+ align:start position:0%
+um something like this in a Handcock
+building I imagine that the wind force
+
+ align:start position:0%
+building I imagine that the wind force
+ 
+
+ align:start position:0%
+building I imagine that the wind force
+on the Handcock building does not have a
+
+ align:start position:0%
+on the Handcock building does not have a
+ 
+
+ align:start position:0%
+on the Handcock building does not have a
+uniform frequency all right is the idea
+
+ align:start position:0%
+uniform frequency all right is the idea
+ 
+
+ align:start position:0%
+uniform frequency all right is the idea
+that you know this will control
+
+ align:start position:0%
+that you know this will control
+ 
+
+ align:start position:0%
+that you know this will control
+basically the resonant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+frequency so the uh D the I've forgotten
+
+ align:start position:0%
+frequency so the uh D the I've forgotten
+ 
+
+ align:start position:0%
+frequency so the uh D the I've forgotten
+the correct name now even know I've used
+
+ align:start position:0%
+the correct name now even know I've used
+ 
+
+ align:start position:0%
+the correct name now even know I've used
+these many times now the uh optimally
+
+ align:start position:0%
+these many times now the uh optimally
+ 
+
+ align:start position:0%
+these many times now the uh optimally
+tuned and damped Dynamic absorber is
+
+ align:start position:0%
+tuned and damped Dynamic absorber is
+ 
+
+ align:start position:0%
+tuned and damped Dynamic absorber is
+sort of the second level of of uh this
+
+ align:start position:0%
+sort of the second level of of uh this
+ 
+
+ align:start position:0%
+sort of the second level of of uh this
+is of gradu of U Dynamic absorber
+
+ align:start position:0%
+is of gradu of U Dynamic absorber
+ 
+
+ align:start position:0%
+is of gradu of U Dynamic absorber
+design typically a two degree Freedom
+
+ align:start position:0%
+design typically a two degree Freedom
+ 
+
+ align:start position:0%
+design typically a two degree Freedom
+system looks like that if it's lightly
+
+ align:start position:0%
+system looks like that if it's lightly
+ 
+
+ align:start position:0%
+system looks like that if it's lightly
+damped but you can design that second
+
+ align:start position:0%
+damped but you can design that second
+ 
+
+ align:start position:0%
+damped but you can design that second
+Mass spring and a damper so that you can
+
+ align:start position:0%
+Mass spring and a damper so that you can
+ 
+
+ align:start position:0%
+Mass spring and a damper so that you can
+make the response the transfer function
+
+ align:start position:0%
+make the response the transfer function
+ 
+
+ align:start position:0%
+make the response the transfer function
+h11 here look like
+
+ align:start position:0%
+h11 here look like
+ 
+
+ align:start position:0%
+h11 here look like
+this where you get the two height the
+
+ align:start position:0%
+this where you get the two height the
+ 
+
+ align:start position:0%
+this where you get the two height the
+two peaks are of equal height and the
+
+ align:start position:0%
+two peaks are of equal height and the
+ 
+
+ align:start position:0%
+two peaks are of equal height and the
+worst you you can design them so that
+
+ align:start position:0%
+worst you you can design them so that
+ 
+
+ align:start position:0%
+worst you you can design them so that
+the worst case amplitude response over
+
+ align:start position:0%
+the worst case amplitude response over
+ 
+
+ align:start position:0%
+the worst case amplitude response over
+here is pretty low it's
+
+ align:start position:0%
+here is pretty low it's
+ 
+
+ align:start position:0%
+here is pretty low it's
+uh X1 static is
+
+ align:start position:0%
+uh X1 static is
+ 
+
+ align:start position:0%
+uh X1 static is
+like square otk of 1
+
+ align:start position:0%
+like square otk of 1
+ 
+
+ align:start position:0%
+like square otk of 1
+over 1 + mu or something like that so
+
+ align:start position:0%
+over 1 + mu or something like that so
+ 
+
+ align:start position:0%
+over 1 + mu or something like that so
+and the bigger you make this the better
+
+ align:start position:0%
+and the bigger you make this the better
+ 
+
+ align:start position:0%
+and the bigger you make this the better
+the performance so and but you have to
+
+ align:start position:0%
+the performance so and but you have to
+ 
+
+ align:start position:0%
+the performance so and but you have to
+have a you have to have Optimum damping
+
+ align:start position:0%
+have a you have to have Optimum damping
+ 
+
+ align:start position:0%
+have a you have to have Optimum damping
+and you have to have Optimum tuning and
+
+ align:start position:0%
+and you have to have Optimum tuning and
+ 
+
+ align:start position:0%
+and you have to have Optimum tuning and
+your tuning means if the the
+
+ align:start position:0%
+your tuning means if the the
+ 
+
+ align:start position:0%
+your tuning means if the the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+the we tune this thing so that K2 over
+
+ align:start position:0%
+the we tune this thing so that K2 over
+ 
+
+ align:start position:0%
+the we tune this thing so that K2 over
+M2 was exactly equal to a particular
+
+ align:start position:0%
+M2 was exactly equal to a particular
+ 
+
+ align:start position:0%
+M2 was exactly equal to a particular
+frequency in this case K1 over M1 but
+
+ align:start position:0%
+frequency in this case K1 over M1 but
+ 
+
+ align:start position:0%
+frequency in this case K1 over M1 but
+for the optimally tuned and damp Dynamic
+
+ align:start position:0%
+for the optimally tuned and damp Dynamic
+ 
+
+ align:start position:0%
+for the optimally tuned and damp Dynamic
+absorber you actually tune things it's
+
+ align:start position:0%
+absorber you actually tune things it's
+ 
+
+ align:start position:0%
+absorber you actually tune things it's
+tuned a little differently you put
+
+ align:start position:0%
+tuned a little differently you put
+ 
+
+ align:start position:0%
+tuned a little differently you put
+damping in it and you make it behave
+
+ align:start position:0%
+damping in it and you make it behave
+ 
+
+ align:start position:0%
+damping in it and you make it behave
+pretty well over the entire frequency
+
+ align:start position:0%
+pretty well over the entire frequency
+ 
+
+ align:start position:0%
+pretty well over the entire frequency
+range rather than
+
+ align:start position:0%
+range rather than
+ 
+
+ align:start position:0%
+range rather than
+almost perfect at one frequency and the
+
+ align:start position:0%
+almost perfect at one frequency and the
+ 
+
+ align:start position:0%
+almost perfect at one frequency and the
+Hancock Building had uh its transfer
+
+ align:start position:0%
+Hancock Building had uh its transfer
+ 
+
+ align:start position:0%
+Hancock Building had uh its transfer
+function so to speak without the dynamic
+
+ align:start position:0%
+function so to speak without the dynamic
+ 
+
+ align:start position:0%
+function so to speak without the dynamic
+absorber it had it has many many Peaks
+
+ align:start position:0%
+absorber it had it has many many Peaks
+ 
+
+ align:start position:0%
+absorber it had it has many many Peaks
+but it had two problematic ones that
+
+ align:start position:0%
+but it had two problematic ones that
+ 
+
+ align:start position:0%
+but it had two problematic ones that
+were very close together and they were
+
+ align:start position:0%
+were very close together and they were
+ 
+
+ align:start position:0%
+were very close together and they were
+at about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh8 radians per second or and like 081
+
+ align:start position:0%
+uh8 radians per second or and like 081
+ 
+
+ align:start position:0%
+uh8 radians per second or and like 081
+or something and this was
+
+ align:start position:0%
+or something and this was
+ 
+
+ align:start position:0%
+or something and this was
+bending and this was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+torsion it had these two resonances and
+
+ align:start position:0%
+torsion it had these two resonances and
+ 
+
+ align:start position:0%
+torsion it had these two resonances and
+the wind would come along and it excite
+
+ align:start position:0%
+the wind would come along and it excite
+ 
+
+ align:start position:0%
+the wind would come along and it excite
+both of them and the one resonance was
+
+ align:start position:0%
+both of them and the one resonance was
+ 
+
+ align:start position:0%
+both of them and the one resonance was
+just the same as this thing it just
+
+ align:start position:0%
+just the same as this thing it just
+ 
+
+ align:start position:0%
+just the same as this thing it just
+bends on the other resonance was the
+
+ align:start position:0%
+bends on the other resonance was the
+ 
+
+ align:start position:0%
+bends on the other resonance was the
+first mode in torsion so the if you were
+
+ align:start position:0%
+first mode in torsion so the if you were
+ 
+
+ align:start position:0%
+first mode in torsion so the if you were
+standing on one and building
+
+ align:start position:0%
+standing on one and building
+ 
+
+ align:start position:0%
+standing on one and building
+crosssection is a funny Hancock
+
+ align:start position:0%
+crosssection is a funny Hancock
+ 
+
+ align:start position:0%
+crosssection is a funny Hancock
+buildings looks kind of like that in
+
+ align:start position:0%
+buildings looks kind of like that in
+ 
+
+ align:start position:0%
+buildings looks kind of like that in
+cross-section and so it would it would
+
+ align:start position:0%
+cross-section and so it would it would
+ 
+
+ align:start position:0%
+cross-section and so it would it would
+rotate in torsion and deflect in bending
+
+ align:start position:0%
+rotate in torsion and deflect in bending
+ 
+
+ align:start position:0%
+rotate in torsion and deflect in bending
+so it would be rotating and
+
+ align:start position:0%
+so it would be rotating and
+ 
+
+ align:start position:0%
+so it would be rotating and
+deflecting and if they were in equal
+
+ align:start position:0%
+deflecting and if they were in equal
+ 
+
+ align:start position:0%
+deflecting and if they were in equal
+amounts and in close they're close in
+
+ align:start position:0%
+amounts and in close they're close in
+ 
+
+ align:start position:0%
+amounts and in close they're close in
+frequency if you were standing up there
+
+ align:start position:0%
+frequency if you were standing up there
+ 
+
+ align:start position:0%
+frequency if you were standing up there
+what would you
+
+ align:start position:0%
+what would you
+ 
+
+ align:start position:0%
+what would you
+feel they would beat the motion would
+
+ align:start position:0%
+feel they would beat the motion would
+ 
+
+ align:start position:0%
+feel they would beat the motion would
+beat you'd get a lot of motion because
+
+ align:start position:0%
+beat you'd get a lot of motion because
+ 
+
+ align:start position:0%
+beat you'd get a lot of motion because
+the if you were on one end of the
+
+ align:start position:0%
+the if you were on one end of the
+ 
+
+ align:start position:0%
+the if you were on one end of the
+building you'd get a lot of torsional
+
+ align:start position:0%
+building you'd get a lot of torsional
+ 
+
+ align:start position:0%
+building you'd get a lot of torsional
+motion out here combined with the
+
+ align:start position:0%
+motion out here combined with the
+ 
+
+ align:start position:0%
+motion out here combined with the
+bending motion
+
+ align:start position:0%
+bending motion
+ 
+
+ align:start position:0%
+bending motion
+and then they would cancel and then the
+
+ align:start position:0%
+and then they would cancel and then the
+ 
+
+ align:start position:0%
+and then they would cancel and then the
+beat would build up again and so that
+
+ align:start position:0%
+beat would build up again and so that
+ 
+
+ align:start position:0%
+beat would build up again and so that
+was what was happening in the building
+
+ align:start position:0%
+was what was happening in the building
+ 
+
+ align:start position:0%
+was what was happening in the building
+the uh and they put in
+
+ align:start position:0%
+the uh and they put in
+ 
+
+ align:start position:0%
+the uh and they put in
+two so on the 58th
+
+ align:start position:0%
+two so on the 58th
+ 
+
+ align:start position:0%
+two so on the 58th
+floor on each
+
+ align:start position:0%
+floor on each
+ 
+
+ align:start position:0%
+floor on each
+end they put in a mass spring
+
+ align:start position:0%
+end they put in a mass spring
+ 
+
+ align:start position:0%
+end they put in a mass spring
+system over here another
+
+ align:start position:0%
+system over here another
+ 
+
+ align:start position:0%
+system over here another
+one so that they would resist the
+
+ align:start position:0%
+one so that they would resist the
+ 
+
+ align:start position:0%
+one so that they would resist the
+torsion actually they really I Lin them
+
+ align:start position:0%
+torsion actually they really I Lin them
+ 
+
+ align:start position:0%
+torsion actually they really I Lin them
+up the wrong way they line up this way
+
+ align:start position:0%
+up the wrong way they line up this way
+ 
+
+ align:start position:0%
+up the wrong way they line up this way
+so it has two of them they can resist
+
+ align:start position:0%
+so it has two of them they can resist
+ 
+
+ align:start position:0%
+so it has two of them they can resist
+both the bending and the torsion that
+
+ align:start position:0%
+both the bending and the torsion that
+ 
+
+ align:start position:0%
+both the bending and the torsion that
+each weigh 300 tons and they were it was
+
+ align:start position:0%
+each weigh 300 tons and they were it was
+ 
+
+ align:start position:0%
+each weigh 300 tons and they were it was
+comb it's a box with 50 filled up with
+
+ align:start position:0%
+comb it's a box with 50 filled up with
+ 
+
+ align:start position:0%
+comb it's a box with 50 filled up with
+50 PB lead bricks and the box is about I
+
+ align:start position:0%
+50 PB lead bricks and the box is about I
+ 
+
+ align:start position:0%
+50 PB lead bricks and the box is about I
+it's been 20 years since I was up there
+
+ align:start position:0%
+it's been 20 years since I was up there
+ 
+
+ align:start position:0%
+it's been 20 years since I was up there
+but my recall is it's like 8 by 10 feet
+
+ align:start position:0%
+but my recall is it's like 8 by 10 feet
+ 
+
+ align:start position:0%
+but my recall is it's like 8 by 10 feet
+and yay tall and it slides on a
+
+ align:start position:0%
+and yay tall and it slides on a
+ 
+
+ align:start position:0%
+and yay tall and it slides on a
+pressurized oil film and the spring
+
+ align:start position:0%
+pressurized oil film and the spring
+ 
+
+ align:start position:0%
+pressurized oil film and the spring
+spring on it is a big pneumatic spring
+
+ align:start position:0%
+spring on it is a big pneumatic spring
+ 
+
+ align:start position:0%
+spring on it is a big pneumatic spring
+big air spring and a computer runs the
+
+ align:start position:0%
+big air spring and a computer runs the
+ 
+
+ align:start position:0%
+big air spring and a computer runs the
+whole system it's shut down till the
+
+ align:start position:0%
+whole system it's shut down till the
+ 
+
+ align:start position:0%
+whole system it's shut down till the
+wind gets above 40 m hour and then it
+
+ align:start position:0%
+wind gets above 40 m hour and then it
+ 
+
+ align:start position:0%
+wind gets above 40 m hour and then it
+turns it on and it's actually kind of
+
+ align:start position:0%
+turns it on and it's actually kind of
+ 
+
+ align:start position:0%
+turns it on and it's actually kind of
+self-tuning it can optimize itself and
+
+ align:start position:0%
+self-tuning it can optimize itself and
+ 
+
+ align:start position:0%
+self-tuning it can optimize itself and
+then it'll sit there and it's designed
+
+ align:start position:0%
+then it'll sit there and it's designed
+ 
+
+ align:start position:0%
+then it'll sit there and it's designed
+to do this because this building has
+
+ align:start position:0%
+to do this because this building has
+ 
+
+ align:start position:0%
+to do this because this building has
+these two problem
+
+ align:start position:0%
+these two problem
+ 
+
+ align:start position:0%
+these two problem
+frequencies and so it has been designed
+
+ align:start position:0%
+frequencies and so it has been designed
+ 
+
+ align:start position:0%
+frequencies and so it has been designed
+to uh address both of
+
+ align:start position:0%
+to uh address both of
+ 
+
+ align:start position:0%
+to uh address both of
+them yeah all right I think uh we I have
+
+ align:start position:0%
+them yeah all right I think uh we I have
+ 
+
+ align:start position:0%
+them yeah all right I think uh we I have
+to get out of here for the next class
+
+ align:start position:0%
+to get out of here for the next class
+ 
+
+ align:start position:0%
+to get out of here for the next class
+see you next Tuesday last lecture
\ No newline at end of file
diff --git a/h5KiY9lvHc4.txt b/h5KiY9lvHc4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b36fc8c2a468521d2307d6a4aa4d1ec8fdb1d2cf
--- /dev/null
+++ b/h5KiY9lvHc4.txt
@@ -0,0 +1,8392 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+to view additional materials from
+
+ align:start position:0%
+to view additional materials from
+ 
+
+ align:start position:0%
+to view additional materials from
+hundreds of MIT courses visit MIT open
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+ 
+
+ align:start position:0%
+hundreds of MIT courses visit MIT open
+courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu okay shall we start okay so
+
+ align:start position:0%
+ocw.mit.edu okay shall we start okay so
+ 
+
+ align:start position:0%
+ocw.mit.edu okay shall we start okay so
+um the the main job of today is igen
+
+ align:start position:0%
+um the the main job of today is igen
+ 
+
+ align:start position:0%
+um the the main job of today is igen
+values and igen vectors
+
+ align:start position:0%
+values and igen vectors
+ 
+
+ align:start position:0%
+values and igen vectors
+the next section in the book and a very
+
+ align:start position:0%
+the next section in the book and a very
+ 
+
+ align:start position:0%
+the next section in the book and a very
+big topic and things to say about it um
+
+ align:start position:0%
+big topic and things to say about it um
+ 
+
+ align:start position:0%
+big topic and things to say about it um
+I do want to begin with a recap of what
+
+ align:start position:0%
+I do want to begin with a recap of what
+ 
+
+ align:start position:0%
+I do want to begin with a recap of what
+I didn't quite finish last time uh so
+
+ align:start position:0%
+I didn't quite finish last time uh so
+ 
+
+ align:start position:0%
+I didn't quite finish last time uh so
+what we did was solve this very
+
+ align:start position:0%
+what we did was solve this very
+ 
+
+ align:start position:0%
+what we did was solve this very
+straightforward equation straightforward
+
+ align:start position:0%
+straightforward equation straightforward
+ 
+
+ align:start position:0%
+straightforward equation straightforward
+except that it has a point source a
+
+ align:start position:0%
+except that it has a point source a
+ 
+
+ align:start position:0%
+except that it has a point source a
+Delta function and we solved it both the
+
+ align:start position:0%
+Delta function and we solved it both the
+ 
+
+ align:start position:0%
+Delta function and we solved it both the
+fixed fixed case when uh straight line
+
+ align:start position:0%
+fixed fixed case when uh straight line
+ 
+
+ align:start position:0%
+fixed fixed case when uh straight line
+went up and back down and in the freef
+
+ align:start position:0%
+went up and back down and in the freef
+ 
+
+ align:start position:0%
+went up and back down and in the freef
+fixed case when it was a horizontal line
+
+ align:start position:0%
+fixed case when it was a horizontal line
+ 
+
+ align:start position:0%
+fixed case when it was a horizontal line
+and then down with slope minus one and
+
+ align:start position:0%
+and then down with slope minus one and
+ 
+
+ align:start position:0%
+and then down with slope minus one and
+and looking there are different ways to
+
+ align:start position:0%
+and looking there are different ways to
+ 
+
+ align:start position:0%
+and looking there are different ways to
+get to this answer but once you have it
+
+ align:start position:0%
+get to this answer but once you have it
+ 
+
+ align:start position:0%
+get to this answer but once you have it
+you can look at it and say well is it
+
+ align:start position:0%
+you can look at it and say well is it
+ 
+
+ align:start position:0%
+you can look at it and say well is it
+right certainly the boundary conditions
+
+ align:start position:0%
+right certainly the boundary conditions
+ 
+
+ align:start position:0%
+right certainly the boundary conditions
+are correct zero slope went through zero
+
+ align:start position:0%
+are correct zero slope went through zero
+ 
+
+ align:start position:0%
+are correct zero slope went through zero
+that's good and then the only thing you
+
+ align:start position:0%
+that's good and then the only thing you
+ 
+
+ align:start position:0%
+that's good and then the only thing you
+really have to check is does the slope
+
+ align:start position:0%
+really have to check is does the slope
+ 
+
+ align:start position:0%
+really have to check is does the slope
+drop by one at the point of the impulse
+
+ align:start position:0%
+drop by one at the point of the impulse
+ 
+
+ align:start position:0%
+drop by one at the point of the impulse
+because that's what this is forcing us
+
+ align:start position:0%
+because that's what this is forcing us
+ 
+
+ align:start position:0%
+because that's what this is forcing us
+to do it's saying the slope should drop
+
+ align:start position:0%
+to do it's saying the slope should drop
+ 
+
+ align:start position:0%
+to do it's saying the slope should drop
+by one and here the slope is 1 minus a
+
+ align:start position:0%
+by one and here the slope is 1 minus a
+ 
+
+ align:start position:0%
+by one and here the slope is 1 minus a
+going up and if I take the derivative
+
+ align:start position:0%
+going up and if I take the derivative
+ 
+
+ align:start position:0%
+going up and if I take the derivative
+it's minus a going
+
+ align:start position:0%
+it's minus a going
+ 
+
+ align:start position:0%
+it's minus a going
+down 1 minus a dropped to minus a good
+
+ align:start position:0%
+down 1 minus a dropped to minus a good
+ 
+
+ align:start position:0%
+down 1 minus a dropped to minus a good
+here the slope was zero here the slope
+
+ align:start position:0%
+here the slope was zero here the slope
+ 
+
+ align:start position:0%
+here the slope was zero here the slope
+was minus1 good okay so those are the
+
+ align:start position:0%
+was minus1 good okay so those are the
+ 
+
+ align:start position:0%
+was minus1 good okay so those are the
+right answers and that's
+
+ align:start position:0%
+right answers and that's
+ 
+
+ align:start position:0%
+right answers and that's
+a this is a simple but really uh great
+
+ align:start position:0%
+a this is a simple but really uh great
+ 
+
+ align:start position:0%
+a this is a simple but really uh great
+example and then what I wanted to do
+
+ align:start position:0%
+example and then what I wanted to do
+ 
+
+ align:start position:0%
+example and then what I wanted to do
+was catch the same thing for the
+
+ align:start position:0%
+was catch the same thing for the
+ 
+
+ align:start position:0%
+was catch the same thing for the
+matrices so those
+
+ align:start position:0%
+matrices so those
+ 
+
+ align:start position:0%
+matrices so those
+matrices uh we all know what K is and
+
+ align:start position:0%
+matrices uh we all know what K is and
+ 
+
+ align:start position:0%
+matrices uh we all know what K is and
+what T is so I'm solving I'm really
+
+ align:start position:0%
+what T is so I'm solving I'm really
+ 
+
+ align:start position:0%
+what T is so I'm solving I'm really
+solving
+
+ align:start position:0%
+solving
+ 
+
+ align:start position:0%
+solving
+k k inverse equal identity that's that's
+
+ align:start position:0%
+k k inverse equal identity that's that's
+ 
+
+ align:start position:0%
+k k inverse equal identity that's that's
+the equation I'm solving so I'm looking
+
+ align:start position:0%
+the equation I'm solving so I'm looking
+ 
+
+ align:start position:0%
+the equation I'm solving so I'm looking
+for K inverse and trying to get The
+
+ align:start position:0%
+for K inverse and trying to get The
+ 
+
+ align:start position:0%
+for K inverse and trying to get The
+Columns of the
+
+ align:start position:0%
+Columns of the
+ 
+
+ align:start position:0%
+Columns of the
+identity and you realize The Columns of
+
+ align:start position:0%
+identity and you realize The Columns of
+ 
+
+ align:start position:0%
+identity and you realize The Columns of
+the identity are just like Delta vectors
+
+ align:start position:0%
+the identity are just like Delta vectors
+ 
+
+ align:start position:0%
+the identity are just like Delta vectors
+they've got a one in one spot they're a
+
+ align:start position:0%
+they've got a one in one spot they're a
+ 
+
+ align:start position:0%
+they've got a one in one spot they're a
+point load just like this thing okay so
+
+ align:start position:0%
+point load just like this thing okay so
+ 
+
+ align:start position:0%
+point load just like this thing okay so
+can I just say how I get how I remember
+
+ align:start position:0%
+can I just say how I get how I remember
+ 
+
+ align:start position:0%
+can I just say how I get how I remember
+K inverse I finally you know again there
+
+ align:start position:0%
+K inverse I finally you know again there
+ 
+
+ align:start position:0%
+K inverse I finally you know again there
+are different ways to get to to
+
+ align:start position:0%
+are different ways to get to to
+ 
+
+ align:start position:0%
+are different ways to get to to
+it one way is matl just do it but
+
+ align:start position:0%
+it one way is matl just do it but
+ 
+
+ align:start position:0%
+it one way is matl just do it but
+uh I guess maybe the whole point is the
+
+ align:start position:0%
+uh I guess maybe the whole point is the
+ 
+
+ align:start position:0%
+uh I guess maybe the whole point is the
+whole point of
+
+ align:start position:0%
+whole point of
+ 
+
+ align:start position:0%
+whole point of
+these and and the igen values that are
+
+ align:start position:0%
+these and and the igen values that are
+ 
+
+ align:start position:0%
+these and and the igen values that are
+coming to is this
+
+ align:start position:0%
+coming to is this
+ 
+
+ align:start position:0%
+coming to is this
+that we have here the chance to see
+
+ align:start position:0%
+that we have here the chance to see
+ 
+
+ align:start position:0%
+that we have here the chance to see
+important special cases that work out
+
+ align:start position:0%
+important special cases that work out
+ 
+
+ align:start position:0%
+important special cases that work out
+normally we don't find the inverse print
+
+ align:start position:0%
+normally we don't find the inverse print
+ 
+
+ align:start position:0%
+normally we don't find the inverse print
+out the inverse of a matrix it's not
+
+ align:start position:0%
+out the inverse of a matrix it's not
+ 
+
+ align:start position:0%
+out the inverse of a matrix it's not
+nice normally we just let I find the
+
+ align:start position:0%
+nice normally we just let I find the
+ 
+
+ align:start position:0%
+nice normally we just let I find the
+igen values because that's a even worse
+
+ align:start position:0%
+igen values because that's a even worse
+ 
+
+ align:start position:0%
+igen values because that's a even worse
+calculation to find igen values in
+
+ align:start position:0%
+calculation to find igen values in
+ 
+
+ align:start position:0%
+calculation to find igen values in
+general for I'm talking here about our
+
+ align:start position:0%
+general for I'm talking here about our
+ 
+
+ align:start position:0%
+general for I'm talking here about our
+matrices of all sizes n byn nobody finds
+
+ align:start position:0%
+matrices of all sizes n byn nobody finds
+ 
+
+ align:start position:0%
+matrices of all sizes n byn nobody finds
+the igen values by hand of n byn
+
+ align:start position:0%
+the igen values by hand of n byn
+ 
+
+ align:start position:0%
+the igen values by hand of n byn
+matrices but these have terrific igen
+
+ align:start position:0%
+matrices but these have terrific igen
+ 
+
+ align:start position:0%
+matrices but these have terrific igen
+values and especially igen vectors so uh
+
+ align:start position:0%
+values and especially igen vectors so uh
+ 
+
+ align:start position:0%
+values and especially igen vectors so uh
+in a way this is a little bit like
+
+ align:start position:0%
+in a way this is a little bit like
+ 
+
+ align:start position:0%
+in a way this is a little bit like
+typical of math that you ask about
+
+ align:start position:0%
+typical of math that you ask about
+ 
+
+ align:start position:0%
+typical of math that you ask about
+General stuff where you write the
+
+ align:start position:0%
+General stuff where you write the
+ 
+
+ align:start position:0%
+General stuff where you write the
+equation with a with a matrix
+
+ align:start position:0%
+equation with a with a matrix
+ 
+
+ align:start position:0%
+equation with a with a matrix
+a and so that's the general information
+
+ align:start position:0%
+a and so that's the general information
+ 
+
+ align:start position:0%
+a and so that's the general information
+and then there's the specific special
+
+ align:start position:0%
+and then there's the specific special
+ 
+
+ align:start position:0%
+and then there's the specific special
+guys with special functions and here
+
+ align:start position:0%
+guys with special functions and here
+ 
+
+ align:start position:0%
+guys with special functions and here
+they'll be signs and cosiness and
+
+ align:start position:0%
+they'll be signs and cosiness and
+ 
+
+ align:start position:0%
+they'll be signs and cosiness and
+exponentials other places in applied
+
+ align:start position:0%
+exponentials other places in applied
+ 
+
+ align:start position:0%
+exponentials other places in applied
+math they're Bessel functions and the
+
+ align:start position:0%
+math they're Bessel functions and the
+ 
+
+ align:start position:0%
+math they're Bessel functions and the
+genre functions special guys so here
+
+ align:start position:0%
+genre functions special guys so here
+ 
+
+ align:start position:0%
+genre functions special guys so here
+these are special then and how how do I
+
+ align:start position:0%
+these are special then and how how do I
+ 
+
+ align:start position:0%
+these are special then and how how do I
+complete K inverse so this 432 1 well
+
+ align:start position:0%
+complete K inverse so this 432 1 well
+ 
+
+ align:start position:0%
+complete K inverse so this 432 1 well
+I'm let me let me complete T inverse you
+
+ align:start position:0%
+I'm let me let me complete T inverse you
+ 
+
+ align:start position:0%
+I'm let me let me complete T inverse you
+probably know T inverse already so T
+
+ align:start position:0%
+probably know T inverse already so T
+ 
+
+ align:start position:0%
+probably know T inverse already so T
+this is 4321 is when the when the load
+
+ align:start position:0%
+this is 4321 is when the when the load
+ 
+
+ align:start position:0%
+this is 4321 is when the when the load
+is way over at the far left and and it's
+
+ align:start position:0%
+is way over at the far left and and it's
+ 
+
+ align:start position:0%
+is way over at the far left and and it's
+just descending and now now I'm going to
+
+ align:start position:0%
+just descending and now now I'm going to
+ 
+
+ align:start position:0%
+just descending and now now I'm going to
+let me show you how I write it in so I I
+
+ align:start position:0%
+let me show you how I write it in so I I
+ 
+
+ align:start position:0%
+let me show you how I write it in so I I
+pay attention here to the diagonal so
+
+ align:start position:0%
+pay attention here to the diagonal so
+ 
+
+ align:start position:0%
+pay attention here to the diagonal so
+this will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+33 2
+
+ align:start position:0%
+33 2
+ 
+
+ align:start position:0%
+33 2
+1 do you see that the this is the this
+
+ align:start position:0%
+1 do you see that the this is the this
+ 
+
+ align:start position:0%
+1 do you see that the this is the this
+is that's the solution that's sort of
+
+ align:start position:0%
+is that's the solution that's sort of
+ 
+
+ align:start position:0%
+is that's the solution that's sort of
+like this
+
+ align:start position:0%
+like this
+ 
+
+ align:start position:0%
+like this
+one that's the second column of the
+
+ align:start position:0%
+one that's the second column of the
+ 
+
+ align:start position:0%
+one that's the second column of the
+inverse so it's solving I'm solving TT
+
+ align:start position:0%
+inverse so it's solving I'm solving TT
+ 
+
+ align:start position:0%
+inverse so it's solving I'm solving TT
+inverse equal I here it's the the second
+
+ align:start position:0%
+inverse equal I here it's the the second
+ 
+
+ align:start position:0%
+inverse equal I here it's the the second
+column is the guy with a one in the
+
+ align:start position:0%
+column is the guy with a one in the
+ 
+
+ align:start position:0%
+column is the guy with a one in the
+second place so it's so that's where the
+
+ align:start position:0%
+second place so it's so that's where the
+ 
+
+ align:start position:0%
+second place so it's so that's where the
+load is in position number two so I'm
+
+ align:start position:0%
+load is in position number two so I'm
+ 
+
+ align:start position:0%
+load is in position number two so I'm
+level 33 up to that load and then I'm
+
+ align:start position:0%
+level 33 up to that load and then I'm
+ 
+
+ align:start position:0%
+level 33 up to that load and then I'm
+dropping at I'm dropping after the load
+
+ align:start position:0%
+dropping at I'm dropping after the load
+ 
+
+ align:start position:0%
+dropping at I'm dropping after the load
+okay what's the what's the third column
+
+ align:start position:0%
+okay what's the what's the third column
+ 
+
+ align:start position:0%
+okay what's the what's the third column
+of T
+
+ align:start position:0%
+of T
+ 
+
+ align:start position:0%
+of T
+inverse so the third column I started
+
+ align:start position:0%
+inverse so the third column I started
+ 
+
+ align:start position:0%
+inverse so the third column I started
+with that First Column and I knew that
+
+ align:start position:0%
+with that First Column and I knew that
+ 
+
+ align:start position:0%
+with that First Column and I knew that
+the answer would be symmetric because T
+
+ align:start position:0%
+the answer would be symmetric because T
+ 
+
+ align:start position:0%
+the answer would be symmetric because T
+is symmetric so that allowed me to write
+
+ align:start position:0%
+is symmetric so that allowed me to write
+ 
+
+ align:start position:0%
+is symmetric so that allowed me to write
+the first row and now we can fill in the
+
+ align:start position:0%
+the first row and now we can fill in the
+ 
+
+ align:start position:0%
+the first row and now we can fill in the
+rest so what do you think if the point
+
+ align:start position:0%
+rest so what do you think if the point
+ 
+
+ align:start position:0%
+rest so what do you think if the point
+load is now I'm looking at the third
+
+ align:start position:0%
+load is now I'm looking at the third
+ 
+
+ align:start position:0%
+load is now I'm looking at the third
+column third column of the identity the
+
+ align:start position:0%
+column third column of the identity the
+ 
+
+ align:start position:0%
+column third column of the identity the
+load is moved down to position number
+
+ align:start position:0%
+load is moved down to position number
+ 
+
+ align:start position:0%
+load is moved down to position number
+three so what do I have there and there
+
+ align:start position:0%
+three so what do I have there and there
+ 
+
+ align:start position:0%
+three so what do I have there and there
+two and two and what do I have
+
+ align:start position:0%
+two and two and what do I have
+ 
+
+ align:start position:0%
+two and two and what do I have
+last one it's dropping to zero you could
+
+ align:start position:0%
+last one it's dropping to zero you could
+ 
+
+ align:start position:0%
+last one it's dropping to zero you could
+put zero and green here if you wanted
+
+ align:start position:0%
+put zero and green here if you wanted
+ 
+
+ align:start position:0%
+put zero and green here if you wanted
+zero is the is the
+
+ align:start position:0%
+zero is the is the
+ 
+
+ align:start position:0%
+zero is the is the
+Unseen last boundary you know a row at
+
+ align:start position:0%
+Unseen last boundary you know a row at
+ 
+
+ align:start position:0%
+Unseen last boundary you know a row at
+at at this end okay and finally What's
+
+ align:start position:0%
+at at this end okay and finally What's
+ 
+
+ align:start position:0%
+at at this end okay and finally What's
+Happening Here what what do I get from
+
+ align:start position:0%
+Happening Here what what do I get from
+ 
+
+ align:start position:0%
+Happening Here what what do I get from
+from
+
+ align:start position:0%
+from
+ 
+
+ align:start position:0%
+from
+that all one one one to the diagonal and
+
+ align:start position:0%
+that all one one one to the diagonal and
+ 
+
+ align:start position:0%
+that all one one one to the diagonal and
+then sure enough it drops to zero so
+
+ align:start position:0%
+then sure enough it drops to zero so
+ 
+
+ align:start position:0%
+then sure enough it drops to zero so
+this would be a case where the load is
+
+ align:start position:0%
+this would be a case where the load is
+ 
+
+ align:start position:0%
+this would be a case where the load is
+there it would be one one one one and
+
+ align:start position:0%
+there it would be one one one one and
+ 
+
+ align:start position:0%
+there it would be one one one one and
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+boom no it wouldn't be it'd be more like
+
+ align:start position:0%
+boom no it wouldn't be it'd be more like
+ 
+
+ align:start position:0%
+boom no it wouldn't be it'd be more like
+this one one one one and then down to Z
+
+ align:start position:0%
+this one one one one and then down to Z
+ 
+
+ align:start position:0%
+this one one one one and then down to Z
+to to
+
+ align:start position:0%
+to to
+ 
+
+ align:start position:0%
+to to
+okay that's a pretty clean in
+
+ align:start position:0%
+okay that's a pretty clean in
+ 
+
+ align:start position:0%
+okay that's a pretty clean in
+inverse that's a very beautiful
+
+ align:start position:0%
+inverse that's a very beautiful
+ 
+
+ align:start position:0%
+inverse that's a very beautiful
+Matrix don't you admire that Matrix I
+
+ align:start position:0%
+Matrix don't you admire that Matrix I
+ 
+
+ align:start position:0%
+Matrix don't you admire that Matrix I
+mean if they were all like that gee this
+
+ align:start position:0%
+mean if they were all like that gee this
+ 
+
+ align:start position:0%
+mean if they were all like that gee this
+would be a great world uh but uh uh of
+
+ align:start position:0%
+would be a great world uh but uh uh of
+ 
+
+ align:start position:0%
+would be a great world uh but uh uh of
+course um it's not
+
+ align:start position:0%
+course um it's not
+ 
+
+ align:start position:0%
+course um it's not
+sparse and and you have to face the
+
+ align:start position:0%
+sparse and and you have to face the
+ 
+
+ align:start position:0%
+sparse and and you have to face the
+that's why we don't often use the
+
+ align:start position:0%
+that's why we don't often use the
+ 
+
+ align:start position:0%
+that's why we don't often use the
+inverse because we had a sparse Matrix T
+
+ align:start position:0%
+inverse because we had a sparse Matrix T
+ 
+
+ align:start position:0%
+inverse because we had a sparse Matrix T
+that was really fast to compute with and
+
+ align:start position:0%
+that was really fast to compute with and
+ 
+
+ align:start position:0%
+that was really fast to compute with and
+here if I if you tell me the inverse
+
+ align:start position:0%
+here if I if you tell me the inverse
+ 
+
+ align:start position:0%
+here if I if you tell me the inverse
+you've actually slowed me down because
+
+ align:start position:0%
+you've actually slowed me down because
+ 
+
+ align:start position:0%
+you've actually slowed me down because
+I've I you've given me now a a dense
+
+ align:start position:0%
+I've I you've given me now a a dense
+ 
+
+ align:start position:0%
+I've I you've given me now a a dense
+Matrix no zeros even and uh uh U
+
+ align:start position:0%
+Matrix no zeros even and uh uh U
+ 
+
+ align:start position:0%
+Matrix no zeros even and uh uh U
+multiplying T inverse times the right
+
+ align:start position:0%
+multiplying T inverse times the right
+ 
+
+ align:start position:0%
+multiplying T inverse times the right
+side would be slower than just doing
+
+ align:start position:0%
+side would be slower than just doing
+ 
+
+ align:start position:0%
+side would be slower than just doing
+elimination okay now this is the kind of
+
+ align:start position:0%
+elimination okay now this is the kind of
+ 
+
+ align:start position:0%
+elimination okay now this is the kind of
+more interesting one because this is the
+
+ align:start position:0%
+more interesting one because this is the
+ 
+
+ align:start position:0%
+more interesting one because this is the
+one that has to go up to the diagonal
+
+ align:start position:0%
+one that has to go up to the diagonal
+ 
+
+ align:start position:0%
+one that has to go up to the diagonal
+and then down so so let me can I fill
+
+ align:start position:0%
+and then down so so let me can I fill
+ 
+
+ align:start position:0%
+and then down so so let me can I fill
+fill in what I think this the way this
+
+ align:start position:0%
+fill in what I think this the way this
+ 
+
+ align:start position:0%
+fill in what I think this the way this
+one goes I'm going upwards to the
+
+ align:start position:0%
+one goes I'm going upwards to the
+ 
+
+ align:start position:0%
+one goes I'm going upwards to the
+diagonal and then I'm coming down to
+
+ align:start position:0%
+diagonal and then I'm coming down to
+ 
+
+ align:start position:0%
+diagonal and then I'm coming down to
+zero remember that I'm coming down to
+
+ align:start position:0%
+zero remember that I'm coming down to
+ 
+
+ align:start position:0%
+zero remember that I'm coming down to
+zero on this K so 0 0 z0 is kind of the
+
+ align:start position:0%
+zero on this K so 0 0 z0 is kind of the
+ 
+
+ align:start position:0%
+zero on this K so 0 0 z0 is kind of the
+row number if that's row number zero
+
+ align:start position:0%
+row number if that's row number zero
+ 
+
+ align:start position:0%
+row number if that's row number zero
+here's one two three four the real
+
+ align:start position:0%
+here's one two three four the real
+ 
+
+ align:start position:0%
+here's one two three four the real
+things and then row five is is uh
+
+ align:start position:0%
+things and then row five is is uh
+ 
+
+ align:start position:0%
+things and then row five is is uh
+getting back to zero again okay so what
+
+ align:start position:0%
+getting back to zero again okay so what
+ 
+
+ align:start position:0%
+getting back to zero again okay so what
+do you think finish the rest of that
+
+ align:start position:0%
+do you think finish the rest of that
+ 
+
+ align:start position:0%
+do you think finish the rest of that
+column so you're telling me now the
+
+ align:start position:0%
+column so you're telling me now the
+ 
+
+ align:start position:0%
+column so you're telling me now the
+response to the load in position two so
+
+ align:start position:0%
+response to the load in position two so
+ 
+
+ align:start position:0%
+response to the load in position two so
+it's going to look like this
+
+ align:start position:0%
+it's going to look like this
+ 
+
+ align:start position:0%
+it's going to look like this
+in fact it's going to look very like
+
+ align:start position:0%
+in fact it's going to look very like
+ 
+
+ align:start position:0%
+in fact it's going to look very like
+this it'll be there's the three and then
+
+ align:start position:0%
+this it'll be there's the three and then
+ 
+
+ align:start position:0%
+this it'll be there's the three and then
+this is in position two and then I'm
+
+ align:start position:0%
+this is in position two and then I'm
+ 
+
+ align:start position:0%
+this is in position two and then I'm
+going to have something here and
+
+ align:start position:0%
+going to have something here and
+ 
+
+ align:start position:0%
+going to have something here and
+something here and it'll drop to
+
+ align:start position:0%
+something here and it'll drop to
+ 
+
+ align:start position:0%
+something here and it'll drop to
+zero what do I get
+
+ align:start position:0%
+zero what do I get
+ 
+
+ align:start position:0%
+zero what do I get
+42 6 4 2 zero it's dropping to zero okay
+
+ align:start position:0%
+42 6 4 2 zero it's dropping to zero okay
+ 
+
+ align:start position:0%
+42 6 4 2 zero it's dropping to zero okay
+I'm going to finish this in but then I'm
+
+ align:start position:0%
+I'm going to finish this in but then I'm
+ 
+
+ align:start position:0%
+I'm going to finish this in but then I'm
+going to look back and see have I have I
+
+ align:start position:0%
+going to look back and see have I have I
+ 
+
+ align:start position:0%
+going to look back and see have I have I
+really got it right okay how does this
+
+ align:start position:0%
+really got it right okay how does this
+ 
+
+ align:start position:0%
+really got it right okay how does this
+how does this go now two
+
+ align:start position:0%
+how does this go now two
+ 
+
+ align:start position:0%
+how does this go now two
+let's see it's now it's going up from 0
+
+ align:start position:0%
+let's see it's now it's going up from 0
+ 
+
+ align:start position:0%
+let's see it's now it's going up from 0
+to two to four to six that's on the
+
+ align:start position:0%
+to two to four to six that's on the
+ 
+
+ align:start position:0%
+to two to four to six that's on the
+diagonal now it starts down it's got to
+
+ align:start position:0%
+diagonal now it starts down it's got to
+ 
+
+ align:start position:0%
+diagonal now it starts down it's got to
+get to zero so that'll be a
+
+ align:start position:0%
+get to zero so that'll be a
+ 
+
+ align:start position:0%
+get to zero so that'll be a
+three here's a one going up two to three
+
+ align:start position:0%
+three here's a one going up two to three
+ 
+
+ align:start position:0%
+three here's a one going up two to three
+to four is that right and then drop fast
+
+ align:start position:0%
+to four is that right and then drop fast
+ 
+
+ align:start position:0%
+to four is that right and then drop fast
+to zero is that
+
+ align:start position:0%
+to zero is that
+ 
+
+ align:start position:0%
+to zero is that
+correct I think so yep
+
+ align:start position:0%
+correct I think so yep
+ 
+
+ align:start position:0%
+correct I think so yep
+except what wait a minute now okay we
+
+ align:start position:0%
+except what wait a minute now okay we
+ 
+
+ align:start position:0%
+except what wait a minute now okay we
+we've got the right overall picture
+
+ align:start position:0%
+we've got the right overall picture
+ 
+
+ align:start position:0%
+we've got the right overall picture
+climbing up dropping down climbing up
+
+ align:start position:0%
+climbing up dropping down climbing up
+ 
+
+ align:start position:0%
+climbing up dropping down climbing up
+dropping down climbing up dropping down
+
+ align:start position:0%
+dropping down climbing up dropping down
+ 
+
+ align:start position:0%
+dropping down climbing up dropping down
+all good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but we haven't yet got we haven't
+
+ align:start position:0%
+but we haven't yet got we haven't
+ 
+
+ align:start position:0%
+but we haven't yet got we haven't
+checked yet that the change in the
+
+ align:start position:0%
+checked yet that the change in the
+ 
+
+ align:start position:0%
+checked yet that the change in the
+slope was is supposed to be
+
+ align:start position:0%
+slope was is supposed to be
+ 
+
+ align:start position:0%
+slope was is supposed to be
+one and it's not here the slope is like
+
+ align:start position:0%
+one and it's not here the slope is like
+ 
+
+ align:start position:0%
+one and it's not here the slope is like
+three it's going up by threes and and
+
+ align:start position:0%
+three it's going up by threes and and
+ 
+
+ align:start position:0%
+three it's going up by threes and and
+then it's going down by
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+twos so we we we've gone from going up
+
+ align:start position:0%
+twos so we we we've gone from going up
+ 
+
+ align:start position:0%
+twos so we we we've gone from going up
+at a slope of three to down to a slope
+
+ align:start position:0%
+at a slope of three to down to a slope
+ 
+
+ align:start position:0%
+at a slope of three to down to a slope
+of two like up three down just like this
+
+ align:start position:0%
+of two like up three down just like this
+ 
+
+ align:start position:0%
+of two like up three down just like this
+but that would be a change in slope of
+
+ align:start position:0%
+but that would be a change in slope of
+ 
+
+ align:start position:0%
+but that would be a change in slope of
+five therefore there's a
+
+ align:start position:0%
+five therefore there's a
+ 
+
+ align:start position:0%
+five therefore there's a
+1 so this is going up with a slope of
+
+ align:start position:0%
+1 so this is going up with a slope of
+ 
+
+ align:start position:0%
+1 so this is going up with a slope of
+four and down with a slope of one four
+
+ align:start position:0%
+four and down with a slope of one four
+ 
+
+ align:start position:0%
+four and down with a slope of one four
+dropping to one when I divide by the
+
+ align:start position:0%
+dropping to one when I divide by the
+ 
+
+ align:start position:0%
+dropping to one when I divide by the
+five that's what I like here's up by
+
+ align:start position:0%
+five that's what I like here's up by
+ 
+
+ align:start position:0%
+five that's what I like here's up by
+twos down by threes again it's a change
+
+ align:start position:0%
+twos down by threes again it's a change
+ 
+
+ align:start position:0%
+twos down by threes again it's a change
+of five so I need the five up by ones
+
+ align:start position:0%
+of five so I need the five up by ones
+ 
+
+ align:start position:0%
+of five so I need the five up by ones
+down by four sudden that's a fast drop
+
+ align:start position:0%
+down by four sudden that's a fast drop
+ 
+
+ align:start position:0%
+down by four sudden that's a fast drop
+of four again the slope Changed by five
+
+ align:start position:0%
+of four again the slope Changed by five
+ 
+
+ align:start position:0%
+of four again the slope Changed by five
+dividing by five that's got it so that's
+
+ align:start position:0%
+dividing by five that's got it so that's
+ 
+
+ align:start position:0%
+dividing by five that's got it so that's
+my picture you could now create K
+
+ align:start position:0%
+my picture you could now create K
+ 
+
+ align:start position:0%
+my picture you could now create K
+inverse for any size and more than that
+
+ align:start position:0%
+inverse for any size and more than that
+ 
+
+ align:start position:0%
+inverse for any size and more than that
+sort of C into the into K inverse
+
+ align:start position:0%
+sort of C into the into K inverse
+ 
+
+ align:start position:0%
+sort of C into the into K inverse
+what's you know what what those numbers
+
+ align:start position:0%
+what's you know what what those numbers
+ 
+
+ align:start position:0%
+what's you know what what those numbers
+are because if I wrote the 5x5 or
+
+ align:start position:0%
+are because if I wrote the 5x5 or
+ 
+
+ align:start position:0%
+are because if I wrote the 5x5 or
+6x6 uh without uh doing at a column at a
+
+ align:start position:0%
+6x6 uh without uh doing at a column at a
+ 
+
+ align:start position:0%
+6x6 uh without uh doing at a column at a
+time it would look like a bunch of
+
+ align:start position:0%
+time it would look like a bunch of
+ 
+
+ align:start position:0%
+time it would look like a bunch of
+numbers but uh you you see it now do you
+
+ align:start position:0%
+numbers but uh you you see it now do you
+ 
+
+ align:start position:0%
+numbers but uh you you see it now do you
+see the you see the pattern right okay
+
+ align:start position:0%
+see the you see the pattern right okay
+ 
+
+ align:start position:0%
+see the you see the pattern right okay
+uh so that's what I I I that this is one
+
+ align:start position:0%
+uh so that's what I I I that this is one
+ 
+
+ align:start position:0%
+uh so that's what I I I that this is one
+way to get to those inverses and
+
+ align:start position:0%
+way to get to those inverses and
+ 
+
+ align:start position:0%
+way to get to those inverses and
+homework problems are offering other
+
+ align:start position:0%
+homework problems are offering other
+ 
+
+ align:start position:0%
+homework problems are offering other
+ways T in particular is
+
+ align:start position:0%
+ways T in particular is
+ 
+
+ align:start position:0%
+ways T in particular is
+quite easy to
+
+ align:start position:0%
+quite easy to
+ 
+
+ align:start position:0%
+quite easy to
+invert okay do I have any other comment
+
+ align:start position:0%
+invert okay do I have any other comment
+ 
+
+ align:start position:0%
+invert okay do I have any other comment
+on inverses before the lecture on igen
+
+ align:start position:0%
+on inverses before the lecture on igen
+ 
+
+ align:start position:0%
+on inverses before the lecture on igen
+values really starts maybe I do have one
+
+ align:start position:0%
+values really starts maybe I do have one
+ 
+
+ align:start position:0%
+values really starts maybe I do have one
+comment one important
+
+ align:start position:0%
+comment one important
+ 
+
+ align:start position:0%
+comment one important
+comment it's this and I won't develop it
+
+ align:start position:0%
+comment it's this and I won't develop it
+ 
+
+ align:start position:0%
+comment it's this and I won't develop it
+in full but let let's just say
+
+ align:start position:0%
+in full but let let's just say
+ 
+
+ align:start position:0%
+in full but let let's just say
+it what if the load is not a Delta
+
+ align:start position:0%
+it what if the load is not a Delta
+ 
+
+ align:start position:0%
+it what if the load is not a Delta
+function what if have other loads uh
+
+ align:start position:0%
+function what if have other loads uh
+ 
+
+ align:start position:0%
+function what if have other loads uh
+like the uniform load of all ones or any
+
+ align:start position:0%
+like the uniform load of all ones or any
+ 
+
+ align:start position:0%
+like the uniform load of all ones or any
+other load what if the discret load here
+
+ align:start position:0%
+other load what if the discret load here
+ 
+
+ align:start position:0%
+other load what if the discret load here
+is not a Delta Vector is not I now know
+
+ align:start position:0%
+is not a Delta Vector is not I now know
+ 
+
+ align:start position:0%
+is not a Delta Vector is not I now know
+the response yeah here here's it way I
+
+ align:start position:0%
+the response yeah here here's it way I
+ 
+
+ align:start position:0%
+the response yeah here here's it way I
+now know the responses to each column of
+
+ align:start position:0%
+now know the responses to each column of
+ 
+
+ align:start position:0%
+now know the responses to each column of
+the identity right if I put a load in
+
+ align:start position:0%
+the identity right if I put a load in
+ 
+
+ align:start position:0%
+the identity right if I put a load in
+position one there's the response if I
+
+ align:start position:0%
+position one there's the response if I
+ 
+
+ align:start position:0%
+position one there's the response if I
+put a load in position two there's the
+
+ align:start position:0%
+put a load in position two there's the
+ 
+
+ align:start position:0%
+put a load in position two there's the
+response now what if I have other
+
+ align:start position:0%
+response now what if I have other
+ 
+
+ align:start position:0%
+response now what if I have other
+loads what if let me take a typical load
+
+ align:start position:0%
+loads what if let me take a typical load
+ 
+
+ align:start position:0%
+loads what if let me take a typical load
+what if the load was well the one we
+
+ align:start position:0%
+what if the load was well the one we
+ 
+
+ align:start position:0%
+what if the load was well the one we
+looked at before if the load was 11 one1
+
+ align:start position:0%
+looked at before if the load was 11 one1
+ 
+
+ align:start position:0%
+looked at before if the load was 11 one1
+so that I had
+
+ align:start position:0%
+so that I had
+ 
+
+ align:start position:0%
+so that I had
+um the the bar was hanging by its own
+
+ align:start position:0%
+um the the bar was hanging by its own
+ 
+
+ align:start position:0%
+um the the bar was hanging by its own
+weight let's say uh
+
+ align:start position:0%
+weight let's say uh
+ 
+
+ align:start position:0%
+weight let's say uh
+so in in other words could I could I
+
+ align:start position:0%
+so in in other words could I could I
+ 
+
+ align:start position:0%
+so in in other words could I could I
+solve could I solve all problems by
+
+ align:start position:0%
+solve could I solve all problems by
+ 
+
+ align:start position:0%
+solve could I solve all problems by
+knowing these answers that that's the
+
+ align:start position:0%
+knowing these answers that that's the
+ 
+
+ align:start position:0%
+knowing these answers that that's the
+what I'm trying to get to if I know
+
+ align:start position:0%
+what I'm trying to get to if I know
+ 
+
+ align:start position:0%
+what I'm trying to get to if I know
+these special Delta loads then can I get
+
+ align:start position:0%
+these special Delta loads then can I get
+ 
+
+ align:start position:0%
+these special Delta loads then can I get
+the solution for every
+
+ align:start position:0%
+the solution for every
+ 
+
+ align:start position:0%
+the solution for every
+load yes no what do you think yes right
+
+ align:start position:0%
+load yes no what do you think yes right
+ 
+
+ align:start position:0%
+load yes no what do you think yes right
+okay now with this matrix it's kind of
+
+ align:start position:0%
+okay now with this matrix it's kind of
+ 
+
+ align:start position:0%
+okay now with this matrix it's kind of
+easy to see because if you know the
+
+ align:start position:0%
+easy to see because if you know the
+ 
+
+ align:start position:0%
+easy to see because if you know the
+inverse Matrix well you're obviously in
+
+ align:start position:0%
+inverse Matrix well you're obviously in
+ 
+
+ align:start position:0%
+inverse Matrix well you're obviously in
+business if I had another
+
+ align:start position:0%
+business if I had another
+ 
+
+ align:start position:0%
+business if I had another
+load say another load f for load
+
+ align:start position:0%
+load say another load f for load
+ 
+
+ align:start position:0%
+load say another load f for load
+I would just multiply by K inverse no
+
+ align:start position:0%
+I would just multiply by K inverse no
+ 
+
+ align:start position:0%
+I would just multiply by K inverse no
+problem but I want to look a little
+
+ align:start position:0%
+problem but I want to look a little
+ 
+
+ align:start position:0%
+problem but I want to look a little
+deeper because how I mean if I had other
+
+ align:start position:0%
+deeper because how I mean if I had other
+ 
+
+ align:start position:0%
+deeper because how I mean if I had other
+loads here than a Delta function if I
+
+ align:start position:0%
+loads here than a Delta function if I
+ 
+
+ align:start position:0%
+loads here than a Delta function if I
+had obviously if I had two Delta
+
+ align:start position:0%
+had obviously if I had two Delta
+ 
+
+ align:start position:0%
+had obviously if I had two Delta
+functions I could just combine the two
+
+ align:start position:0%
+functions I could just combine the two
+ 
+
+ align:start position:0%
+functions I could just combine the two
+solutions that's linearity that we're
+
+ align:start position:0%
+solutions that's linearity that we're
+ 
+
+ align:start position:0%
+solutions that's linearity that we're
+using all the time if I had 10 Delta
+
+ align:start position:0%
+using all the time if I had 10 Delta
+ 
+
+ align:start position:0%
+using all the time if I had 10 Delta
+functions I could combine them but then
+
+ align:start position:0%
+functions I could combine them but then
+ 
+
+ align:start position:0%
+functions I could combine them but then
+suppose I had a uh instead of a bunch of
+
+ align:start position:0%
+suppose I had a uh instead of a bunch of
+ 
+
+ align:start position:0%
+suppose I had a uh instead of a bunch of
+spikes it's a bunch of Point loads I had
+
+ align:start position:0%
+spikes it's a bunch of Point loads I had
+ 
+
+ align:start position:0%
+spikes it's a bunch of Point loads I had
+a distributed load like all ones how
+
+ align:start position:0%
+a distributed load like all ones how
+ 
+
+ align:start position:0%
+a distributed load like all ones how
+could I do it okay main point is I could
+
+ align:start position:0%
+could I do it okay main point is I could
+ 
+
+ align:start position:0%
+could I do it okay main point is I could
+right if I know these answers I know all
+
+ align:start position:0%
+right if I know these answers I know all
+ 
+
+ align:start position:0%
+right if I know these answers I know all
+answers if I know the response at to a
+
+ align:start position:0%
+answers if I know the response at to a
+ 
+
+ align:start position:0%
+answers if I know the response at to a
+load at each point then okay come back
+
+ align:start position:0%
+load at each point then okay come back
+ 
+
+ align:start position:0%
+load at each point then okay come back
+to the discrete one how would you what
+
+ align:start position:0%
+to the discrete one how would you what
+ 
+
+ align:start position:0%
+to the discrete one how would you what
+would be the answer if the load was one
+
+ align:start position:0%
+would be the answer if the load was one
+ 
+
+ align:start position:0%
+would be the answer if the load was one
+one one suppose suppose I now tried to
+
+ align:start position:0%
+one one suppose suppose I now tried to
+ 
+
+ align:start position:0%
+one one suppose suppose I now tried to
+solve the equation k u equal ones of
+
+ align:start position:0%
+solve the equation k u equal ones of
+ 
+
+ align:start position:0%
+solve the equation k u equal ones of
+four ones of four and one so so all
+
+ align:start position:0%
+four ones of four and one so so all
+ 
+
+ align:start position:0%
+four ones of four and one so so all
+ones what would be the answer how would
+
+ align:start position:0%
+ones what would be the answer how would
+ 
+
+ align:start position:0%
+ones what would be the answer how would
+I get
+
+ align:start position:0%
+I get
+ 
+
+ align:start position:0%
+I get
+it I would just add the
+
+ align:start position:0%
+it I would just add the
+ 
+
+ align:start position:0%
+it I would just add the
+columns now why would I do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that right because this the right hand
+
+ align:start position:0%
+that right because this the right hand
+ 
+
+ align:start position:0%
+that right because this the right hand
+side the input is the sum of the four
+
+ align:start position:0%
+side the input is the sum of the four
+ 
+
+ align:start position:0%
+side the input is the sum of the four
+columns the four special inputs so the
+
+ align:start position:0%
+columns the four special inputs so the
+ 
+
+ align:start position:0%
+columns the four special inputs so the
+output is the sum of the four outputs
+
+ align:start position:0%
+output is the sum of the four outputs
+ 
+
+ align:start position:0%
+output is the sum of the four outputs
+right in other words as you saw we must
+
+ align:start position:0%
+right in other words as you saw we must
+ 
+
+ align:start position:0%
+right in other words as you saw we must
+know everything and that's the way we
+
+ align:start position:0%
+know everything and that's the way we
+ 
+
+ align:start position:0%
+know everything and that's the way we
+really know it from by linearity if the
+
+ align:start position:0%
+really know it from by linearity if the
+ 
+
+ align:start position:0%
+really know it from by linearity if the
+input is a combination of these the
+
+ align:start position:0%
+input is a combination of these the
+ 
+
+ align:start position:0%
+input is a combination of these the
+output is the same combination of those
+
+ align:start position:0%
+output is the same combination of those
+ 
+
+ align:start position:0%
+output is the same combination of those
+right so for example in this T case if
+
+ align:start position:0%
+right so for example in this T case if
+ 
+
+ align:start position:0%
+right so for example in this T case if
+the input was if I did tuu equal that
+
+ align:start position:0%
+the input was if I did tuu equal that
+ 
+
+ align:start position:0%
+the input was if I did tuu equal that
+ones
+
+ align:start position:0%
+ones
+ 
+
+ align:start position:0%
+ones
+I would just add those and the output
+
+ align:start position:0%
+I would just add those and the output
+ 
+
+ align:start position:0%
+I would just add those and the output
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+74 that would be the output from
+
+ align:start position:0%
+74 that would be the output from
+ 
+
+ align:start position:0%
+74 that would be the output from
+1111 and now oh
+
+ align:start position:0%
+1111 and now oh
+ 
+
+ align:start position:0%
+1111 and now oh
+boy
+
+ align:start position:0%
+boy
+ 
+
+ align:start position:0%
+boy
+uh yeah I may I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+may actually let me just say let me just
+
+ align:start position:0%
+may actually let me just say let me just
+ 
+
+ align:start position:0%
+may actually let me just say let me just
+introduce a guy's name for this for
+
+ align:start position:0%
+introduce a guy's name for this for
+ 
+
+ align:start position:0%
+introduce a guy's name for this for
+these Solutions and not today
+
+ align:start position:0%
+these Solutions and not today
+ 
+
+ align:start position:0%
+these Solutions and not today
+show you you you have the idea of course
+
+ align:start position:0%
+show you you you have the idea of course
+ 
+
+ align:start position:0%
+show you you you have the idea of course
+here we added because everything was
+
+ align:start position:0%
+here we added because everything was
+ 
+
+ align:start position:0%
+here we added because everything was
+discreet so you know what we're going to
+
+ align:start position:0%
+discreet so you know what we're going to
+ 
+
+ align:start position:0%
+discreet so you know what we're going to
+do over here we'll take integrals right
+
+ align:start position:0%
+do over here we'll take integrals right
+ 
+
+ align:start position:0%
+do over here we'll take integrals right
+if if a general load will be an integral
+
+ align:start position:0%
+if if a general load will be an integral
+ 
+
+ align:start position:0%
+if if a general load will be an integral
+over Point
+
+ align:start position:0%
+over Point
+ 
+
+ align:start position:0%
+over Point
+loads that's the that's the idea a
+
+ align:start position:0%
+loads that's the that's the idea a
+ 
+
+ align:start position:0%
+loads that's the that's the idea a
+fundamental idea that some other
+
+ align:start position:0%
+fundamental idea that some other
+ 
+
+ align:start position:0%
+fundamental idea that some other
+load f ofx is an inte
+
+ align:start position:0%
+load f ofx is an inte
+ 
+
+ align:start position:0%
+load f ofx is an inte
+of these guys so that the solution will
+
+ align:start position:0%
+of these guys so that the solution will
+ 
+
+ align:start position:0%
+of these guys so that the solution will
+be the same integral of these guys let
+
+ align:start position:0%
+be the same integral of these guys let
+ 
+
+ align:start position:0%
+be the same integral of these guys let
+me not go there except to tell you the
+
+ align:start position:0%
+me not go there except to tell you the
+ 
+
+ align:start position:0%
+me not go there except to tell you the
+name because it's a very famous name
+
+ align:start position:0%
+name because it's a very famous name
+ 
+
+ align:start position:0%
+name because it's a very famous name
+this solution U with the Delta function
+
+ align:start position:0%
+this solution U with the Delta function
+ 
+
+ align:start position:0%
+this solution U with the Delta function
+is called the greens function so I've
+
+ align:start position:0%
+is called the greens function so I've
+ 
+
+ align:start position:0%
+is called the greens function so I've
+now introduced the idea this this is the
+
+ align:start position:0%
+now introduced the idea this this is the
+ 
+
+ align:start position:0%
+now introduced the idea this this is the
+greens function this guy is the greens
+
+ align:start position:0%
+greens function this guy is the greens
+ 
+
+ align:start position:0%
+greens function this guy is the greens
+function for the fix fixed problem
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this sky is the green function for
+
+ align:start position:0%
+and this sky is the green function for
+ 
+
+ align:start position:0%
+and this sky is the green function for
+the freefix
+
+ align:start position:0%
+the freefix
+ 
+
+ align:start position:0%
+the freefix
+problem and the whole point is maybe
+
+ align:start position:0%
+problem and the whole point is maybe
+ 
+
+ align:start position:0%
+problem and the whole point is maybe
+this is the one point I want you to sort
+
+ align:start position:0%
+this is the one point I want you to sort
+ 
+
+ align:start position:0%
+this is the one point I want you to sort
+of see Always by analogy the green
+
+ align:start position:0%
+of see Always by analogy the green
+ 
+
+ align:start position:0%
+of see Always by analogy the green
+function is just like the inverse
+
+ align:start position:0%
+function is just like the inverse
+ 
+
+ align:start position:0%
+function is just like the inverse
+knowing the green function is what is
+
+ align:start position:0%
+knowing the green function is what is
+ 
+
+ align:start position:0%
+knowing the green function is what is
+the green function the green function is
+
+ align:start position:0%
+the green function the green function is
+ 
+
+ align:start position:0%
+the green function the green function is
+the response at X to a the U at X when
+
+ align:start position:0%
+the response at X to a the U at X when
+ 
+
+ align:start position:0%
+the response at X to a the U at X when
+the input when the impulse is at a so it
+
+ align:start position:0%
+the input when the impulse is at a so it
+ 
+
+ align:start position:0%
+the input when the impulse is at a so it
+sort of depends on two things it depends
+
+ align:start position:0%
+sort of depends on two things it depends
+ 
+
+ align:start position:0%
+sort of depends on two things it depends
+on the position a of the input and it
+
+ align:start position:0%
+on the position a of the input and it
+ 
+
+ align:start position:0%
+on the position a of the input and it
+tells you the response at position X so
+
+ align:start position:0%
+tells you the response at position X so
+ 
+
+ align:start position:0%
+tells you the response at position X so
+the green function has and and often we
+
+ align:start position:0%
+the green function has and and often we
+ 
+
+ align:start position:0%
+the green function has and and often we
+would use the word the letter G for
+
+ align:start position:0%
+would use the word the letter G for
+ 
+
+ align:start position:0%
+would use the word the letter G for
+green okay so it it's a it it it depends
+
+ align:start position:0%
+green okay so it it's a it it it depends
+ 
+
+ align:start position:0%
+green okay so it it's a it it it depends
+on X and A and maybe I'm happy if you
+
+ align:start position:0%
+on X and A and maybe I'm happy if you
+ 
+
+ align:start position:0%
+on X and A and maybe I'm happy if you
+just sort of see yeah in some way
+
+ align:start position:0%
+just sort of see yeah in some way
+ 
+
+ align:start position:0%
+just sort of see yeah in some way
+what we did there is just like what we
+
+ align:start position:0%
+what we did there is just like what we
+ 
+
+ align:start position:0%
+what we did there is just like what we
+did here and therefore the greens
+
+ align:start position:0%
+did here and therefore the greens
+ 
+
+ align:start position:0%
+did here and therefore the greens
+function must be just the
+
+ align:start position:0%
+function must be just the
+ 
+
+ align:start position:0%
+function must be just the
+differential continuous version of a
+
+ align:start position:0%
+differential continuous version of a
+ 
+
+ align:start position:0%
+differential continuous version of a
+inverse
+
+ align:start position:0%
+inverse
+ 
+
+ align:start position:0%
+inverse
+Matrix I'm I'm let's let's uh move on to
+
+ align:start position:0%
+Matrix I'm I'm let's let's uh move on to
+ 
+
+ align:start position:0%
+Matrix I'm I'm let's let's uh move on to
+Icon values with this with that point
+
+ align:start position:0%
+Icon values with this with that point
+ 
+
+ align:start position:0%
+Icon values with this with that point
+sort of made but not driven home by many
+
+ align:start position:0%
+sort of made but not driven home by many
+ 
+
+ align:start position:0%
+sort of made but not driven home by many
+many examples okay
+
+ align:start position:0%
+many examples okay
+ 
+
+ align:start position:0%
+many examples okay
+question I'll take a question sure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah y why did why did I increase 036
+
+ align:start position:0%
+yeah y why did why did I increase 036
+ 
+
+ align:start position:0%
+yeah y why did why did I increase 036
+and then decrease
+
+ align:start position:0%
+and then decrease
+ 
+
+ align:start position:0%
+and then decrease
+six well it it's it's intuitively it's
+
+ align:start position:0%
+six well it it's it's intuitively it's
+ 
+
+ align:start position:0%
+six well it it's it's intuitively it's
+because this is copying this
+
+ align:start position:0%
+because this is copying this
+ 
+
+ align:start position:0%
+because this is copying this
+what's wonderful is that it's a perfect
+
+ align:start position:0%
+what's wonderful is that it's a perfect
+ 
+
+ align:start position:0%
+what's wonderful is that it's a perfect
+cup I mean intuitively the solution to
+
+ align:start position:0%
+cup I mean intuitively the solution to
+ 
+
+ align:start position:0%
+cup I mean intuitively the solution to
+our to our difference equation should be
+
+ align:start position:0%
+our to our difference equation should be
+ 
+
+ align:start position:0%
+our to our difference equation should be
+like the solution to our differential
+
+ align:start position:0%
+like the solution to our differential
+ 
+
+ align:start position:0%
+like the solution to our differential
+equation that's why
+
+ align:start position:0%
+equation that's why
+ 
+
+ align:start position:0%
+equation that's why
+we if we have some computation or some
+
+ align:start position:0%
+we if we have some computation or some
+ 
+
+ align:start position:0%
+we if we have some computation or some
+differential equation that we can't
+
+ align:start position:0%
+differential equation that we can't
+ 
+
+ align:start position:0%
+differential equation that we can't
+solve which would be much more typical
+
+ align:start position:0%
+solve which would be much more typical
+ 
+
+ align:start position:0%
+solve which would be much more typical
+than this one that we couldn't solve it
+
+ align:start position:0%
+than this one that we couldn't solve it
+ 
+
+ align:start position:0%
+than this one that we couldn't solve it
+exactly by pencil and paper we would go
+
+ align:start position:0%
+exactly by pencil and paper we would go
+ 
+
+ align:start position:0%
+exactly by pencil and paper we would go
+to we would replace derivatives by
+
+ align:start position:0%
+to we would replace derivatives by
+ 
+
+ align:start position:0%
+to we would replace derivatives by
+differences and go over here and we
+
+ align:start position:0%
+differences and go over here and we
+ 
+
+ align:start position:0%
+differences and go over here and we
+would hope that they were like you know
+
+ align:start position:0%
+would hope that they were like you know
+ 
+
+ align:start position:0%
+would hope that they were like you know
+pretty close here they're right they're
+
+ align:start position:0%
+pretty close here they're right they're
+ 
+
+ align:start position:0%
+pretty close here they're right they're
+the same
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah oh the other columns absolutely
+
+ align:start position:0%
+yeah oh the other columns absolutely
+ 
+
+ align:start position:0%
+yeah oh the other columns absolutely
+these guys yeah
+
+ align:start position:0%
+these guys yeah
+ 
+
+ align:start position:0%
+these guys yeah
+0246 going up 630 coming back yeah yeah
+
+ align:start position:0%
+0246 going up 630 coming back yeah yeah
+ 
+
+ align:start position:0%
+0246 going up 630 coming back yeah yeah
+so that's a that's a a discret thing of
+
+ align:start position:0%
+so that's a that's a a discret thing of
+ 
+
+ align:start position:0%
+so that's a that's a a discret thing of
+of one like that and then the next guy
+
+ align:start position:0%
+of one like that and then the next guy
+ 
+
+ align:start position:0%
+of one like that and then the next guy
+and the last guy would be a going up 1 2
+
+ align:start position:0%
+and the last guy would be a going up 1 2
+ 
+
+ align:start position:0%
+and the last guy would be a going up 1 2
+3 4 and then sudden
+
+ align:start position:0%
+3 4 and then sudden
+ 
+
+ align:start position:0%
+3 4 and then sudden
+drop yeah so that's that was thanks for
+
+ align:start position:0%
+drop yeah so that's that was thanks for
+ 
+
+ align:start position:0%
+drop yeah so that's that was thanks for
+all questions I mean this sort of by
+
+ align:start position:0%
+all questions I mean this sort of by
+ 
+
+ align:start position:0%
+all questions I mean this sort of by
+adding these guys in the first one
+
+ align:start position:0%
+adding these guys in the first one
+ 
+
+ align:start position:0%
+adding these guys in the first one
+actually went up that way you see the
+
+ align:start position:0%
+actually went up that way you see the
+ 
+
+ align:start position:0%
+actually went up that way you see the
+greens
+
+ align:start position:0%
+greens
+ 
+
+ align:start position:0%
+greens
+functions but of course this has a
+
+ align:start position:0%
+functions but of course this has a
+ 
+
+ align:start position:0%
+functions but of course this has a
+greens function for every a and you know
+
+ align:start position:0%
+greens function for every a and you know
+ 
+
+ align:start position:0%
+greens function for every a and you know
+X and A are running all the way from
+
+ align:start position:0%
+X and A are running all the way from
+ 
+
+ align:start position:0%
+X and A are running all the way from
+zero to one here they're just discrete
+
+ align:start position:0%
+zero to one here they're just discrete
+ 
+
+ align:start position:0%
+zero to one here they're just discrete
+positions
+
+ align:start position:0%
+positions
+ 
+
+ align:start position:0%
+positions
+thanks other points yeah yeah so so
+
+ align:start position:0%
+thanks other points yeah yeah so so
+ 
+
+ align:start position:0%
+thanks other points yeah yeah so so
+playing with these Delta functions and
+
+ align:start position:0%
+playing with these Delta functions and
+ 
+
+ align:start position:0%
+playing with these Delta functions and
+coming up with this
+
+ align:start position:0%
+coming up with this
+ 
+
+ align:start position:0%
+coming up with this
+solution well as I say different ways to
+
+ align:start position:0%
+solution well as I say different ways to
+ 
+
+ align:start position:0%
+solution well as I say different ways to
+do it uh I work through one way in class
+
+ align:start position:0%
+do it uh I work through one way in class
+ 
+
+ align:start position:0%
+do it uh I work through one way in class
+last time uh it takes practice so that's
+
+ align:start position:0%
+last time uh it takes practice so that's
+ 
+
+ align:start position:0%
+last time uh it takes practice so that's
+what the homework's really for is you
+
+ align:start position:0%
+what the homework's really for is you
+ 
+
+ align:start position:0%
+what the homework's really for is you
+know you can see me come up with this
+
+ align:start position:0%
+know you can see me come up with this
+ 
+
+ align:start position:0%
+know you can see me come up with this
+thing then you can in with Leisure you
+
+ align:start position:0%
+thing then you can in with Leisure you
+ 
+
+ align:start position:0%
+thing then you can in with Leisure you
+can follow those step St but you got to
+
+ align:start position:0%
+can follow those step St but you got to
+ 
+
+ align:start position:0%
+can follow those step St but you got to
+do it yourself to see
+
+ align:start position:0%
+do it yourself to see
+ 
+
+ align:start position:0%
+do it yourself to see
+okay I
+
+ align:start position:0%
+okay I
+ 
+
+ align:start position:0%
+okay I
+values and of course igen vectors we
+
+ align:start position:0%
+values and of course igen vectors we
+ 
+
+ align:start position:0%
+values and of course igen vectors we
+have to give them a fair shot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+okay all right Square
+
+ align:start position:0%
+okay all right Square
+ 
+
+ align:start position:0%
+okay all right Square
+Matrix now so I'm talking about general
+
+ align:start position:0%
+Matrix now so I'm talking about general
+ 
+
+ align:start position:0%
+Matrix now so I'm talking about general
+what IG vectors and igen values are and
+
+ align:start position:0%
+what IG vectors and igen values are and
+ 
+
+ align:start position:0%
+what IG vectors and igen values are and
+why do we want them I'm always trying to
+
+ align:start position:0%
+why do we want them I'm always trying to
+ 
+
+ align:start position:0%
+why do we want them I'm always trying to
+say what's the purpose you know I'm not
+
+ align:start position:0%
+say what's the purpose you know I'm not
+ 
+
+ align:start position:0%
+say what's the purpose you know I'm not
+doing this just for uh abstract L
+
+ align:start position:0%
+doing this just for uh abstract L
+ 
+
+ align:start position:0%
+doing this just for uh abstract L
+algebra that we do this we look for
+
+ align:start position:0%
+algebra that we do this we look for
+ 
+
+ align:start position:0%
+algebra that we do this we look for
+these things because they tremendously
+
+ align:start position:0%
+these things because they tremendously
+ 
+
+ align:start position:0%
+these things because they tremendously
+simplify a problem if we can find
+
+ align:start position:0%
+simplify a problem if we can find
+ 
+
+ align:start position:0%
+simplify a problem if we can find
+them so what's an igen Vector an the
+
+ align:start position:0%
+them so what's an igen Vector an the
+ 
+
+ align:start position:0%
+them so what's an igen Vector an the
+igen value is this number Lambda and the
+
+ align:start position:0%
+igen value is this number Lambda and the
+ 
+
+ align:start position:0%
+igen value is this number Lambda and the
+I Vector is this Vector Y and now how do
+
+ align:start position:0%
+I Vector is this Vector Y and now how do
+ 
+
+ align:start position:0%
+I Vector is this Vector Y and now how do
+you how do I do I think about
+
+ align:start position:0%
+you how do I do I think about
+ 
+
+ align:start position:0%
+you how do I do I think about
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+well suppose I take a vector and I
+
+ align:start position:0%
+well suppose I take a vector and I
+ 
+
+ align:start position:0%
+well suppose I take a vector and I
+multiply by a so the vectors headed off
+
+ align:start position:0%
+multiply by a so the vectors headed off
+ 
+
+ align:start position:0%
+multiply by a so the vectors headed off
+in some direction okay Vector there's a
+
+ align:start position:0%
+in some direction okay Vector there's a
+ 
+
+ align:start position:0%
+in some direction okay Vector there's a
+vector v If I multiply and I'm given
+
+ align:start position:0%
+vector v If I multiply and I'm given
+ 
+
+ align:start position:0%
+vector v If I multiply and I'm given
+this Matrix so I'm given the Matrix
+
+ align:start position:0%
+this Matrix so I'm given the Matrix
+ 
+
+ align:start position:0%
+this Matrix so I'm given the Matrix
+whatever my Matrix
+
+ align:start position:0%
+whatever my Matrix
+ 
+
+ align:start position:0%
+whatever my Matrix
+is could be one of those matrices any
+
+ align:start position:0%
+is could be one of those matrices any
+ 
+
+ align:start position:0%
+is could be one of those matrices any
+other Matrix If I multiply that by V I
+
+ align:start position:0%
+other Matrix If I multiply that by V I
+ 
+
+ align:start position:0%
+other Matrix If I multiply that by V I
+get some result AV
+
+ align:start position:0%
+get some result AV
+ 
+
+ align:start position:0%
+get some result AV
+okay what do I do I I look at that and I
+
+ align:start position:0%
+okay what do I do I I look at that and I
+ 
+
+ align:start position:0%
+okay what do I do I I look at that and I
+say that V was not an igen
+
+ align:start position:0%
+say that V was not an igen
+ 
+
+ align:start position:0%
+say that V was not an igen
+Vector I vectors are the special vectors
+
+ align:start position:0%
+Vector I vectors are the special vectors
+ 
+
+ align:start position:0%
+Vector I vectors are the special vectors
+which come out in the same direction AV
+
+ align:start position:0%
+which come out in the same direction AV
+ 
+
+ align:start position:0%
+which come out in the same direction AV
+comes out parallel to V so this was not
+
+ align:start position:0%
+comes out parallel to V so this was not
+ 
+
+ align:start position:0%
+comes out parallel to V so this was not
+an igen Vector that very few vectors are
+
+ align:start position:0%
+an igen Vector that very few vectors are
+ 
+
+ align:start position:0%
+an igen Vector that very few vectors are
+igen vectors they're they're very
+
+ align:start position:0%
+igen vectors they're they're very
+ 
+
+ align:start position:0%
+igen vectors they're they're very
+special most vectors that'll be a
+
+ align:start position:0%
+special most vectors that'll be a
+ 
+
+ align:start position:0%
+special most vectors that'll be a
+typical picture but there's a few of
+
+ align:start position:0%
+typical picture but there's a few of
+ 
+
+ align:start position:0%
+typical picture but there's a few of
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+where I have a vector Y and I multiply
+
+ align:start position:0%
+where I have a vector Y and I multiply
+ 
+
+ align:start position:0%
+where I have a vector Y and I multiply
+by a and then what's the point a y is in
+
+ align:start position:0%
+by a and then what's the point a y is in
+ 
+
+ align:start position:0%
+by a and then what's the point a y is in
+the same direction it's on that same
+
+ align:start position:0%
+the same direction it's on that same
+ 
+
+ align:start position:0%
+the same direction it's on that same
+line as y it could be might it might be
+
+ align:start position:0%
+line as y it could be might it might be
+ 
+
+ align:start position:0%
+line as y it could be might it might be
+twice as far out that would be a yal 2 y
+
+ align:start position:0%
+twice as far out that would be a yal 2 y
+ 
+
+ align:start position:0%
+twice as far out that would be a yal 2 y
+it might go backwards this would be a a
+
+ align:start position:0%
+it might go backwards this would be a a
+ 
+
+ align:start position:0%
+it might go backwards this would be a a
+possibility a y equal minus y
+
+ align:start position:0%
+possibility a y equal minus y
+ 
+
+ align:start position:0%
+possibility a y equal minus y
+it could be just uh halfway it could be
+
+ align:start position:0%
+it could be just uh halfway it could be
+ 
+
+ align:start position:0%
+it could be just uh halfway it could be
+not move at all yeah that's even a
+
+ align:start position:0%
+not move at all yeah that's even a
+ 
+
+ align:start position:0%
+not move at all yeah that's even a
+possibility a y equal z y count that
+
+ align:start position:0%
+possibility a y equal z y count that
+ 
+
+ align:start position:0%
+possibility a y equal z y count that
+those are those those y's and are igen
+
+ align:start position:0%
+those are those those y's and are igen
+ 
+
+ align:start position:0%
+those are those those y's and are igen
+vectors and the igen value is
+
+ align:start position:0%
+vectors and the igen value is
+ 
+
+ align:start position:0%
+vectors and the igen value is
+just from this point of view the I value
+
+ align:start position:0%
+just from this point of view the I value
+ 
+
+ align:start position:0%
+just from this point of view the I value
+is coming second because it's so y was a
+
+ align:start position:0%
+is coming second because it's so y was a
+ 
+
+ align:start position:0%
+is coming second because it's so y was a
+special Vector that kept its direction
+
+ align:start position:0%
+special Vector that kept its direction
+ 
+
+ align:start position:0%
+special Vector that kept its direction
+and then Lambda was just is just the
+
+ align:start position:0%
+and then Lambda was just is just the
+ 
+
+ align:start position:0%
+and then Lambda was just is just the
+number the two the zero the minus1 the2
+
+ align:start position:0%
+number the two the zero the minus1 the2
+ 
+
+ align:start position:0%
+number the two the zero the minus1 the2
+that tells
+
+ align:start position:0%
+that tells
+ 
+
+ align:start position:0%
+that tells
+you um stretching shrinking reversing
+
+ align:start position:0%
+you um stretching shrinking reversing
+ 
+
+ align:start position:0%
+you um stretching shrinking reversing
+whatever that's the number but Y is the
+
+ align:start position:0%
+whatever that's the number but Y is the
+ 
+
+ align:start position:0%
+whatever that's the number but Y is the
+vector and notice that we this you know
+
+ align:start position:0%
+vector and notice that we this you know
+ 
+
+ align:start position:0%
+vector and notice that we this you know
+if I knew
+
+ align:start position:0%
+if I knew
+ 
+
+ align:start position:0%
+if I knew
+why and and I knew it was an igen Vector
+
+ align:start position:0%
+why and and I knew it was an igen Vector
+ 
+
+ align:start position:0%
+why and and I knew it was an igen Vector
+then of course if I multiply by a I'll
+
+ align:start position:0%
+then of course if I multiply by a I'll
+ 
+
+ align:start position:0%
+then of course if I multiply by a I'll
+learn the igen value
+
+ align:start position:0%
+learn the igen value
+ 
+
+ align:start position:0%
+learn the igen value
+and if I knew an igen value you'll see
+
+ align:start position:0%
+and if I knew an igen value you'll see
+ 
+
+ align:start position:0%
+and if I knew an igen value you'll see
+how I could find the igen vector problem
+
+ align:start position:0%
+how I could find the igen vector problem
+ 
+
+ align:start position:0%
+how I could find the igen vector problem
+is you have to find them both and they
+
+ align:start position:0%
+is you have to find them both and they
+ 
+
+ align:start position:0%
+is you have to find them both and they
+multiply each other so we're not talking
+
+ align:start position:0%
+multiply each other so we're not talking
+ 
+
+ align:start position:0%
+multiply each other so we're not talking
+about linear equations anymore because
+
+ align:start position:0%
+about linear equations anymore because
+ 
+
+ align:start position:0%
+about linear equations anymore because
+one unknown is multiplying another but
+
+ align:start position:0%
+one unknown is multiplying another but
+ 
+
+ align:start position:0%
+one unknown is multiplying another but
+we'll find a way to look to discover I
+
+ align:start position:0%
+we'll find a way to look to discover I
+ 
+
+ align:start position:0%
+we'll find a way to look to discover I
+vectors and igen values you see the now
+
+ align:start position:0%
+vectors and igen values you see the now
+ 
+
+ align:start position:0%
+vectors and igen values you see the now
+here's I I said I would try to make
+
+ align:start position:0%
+here's I I said I would try to make
+ 
+
+ align:start position:0%
+here's I I said I would try to make
+clear what's the purpose the purpose
+
+ align:start position:0%
+clear what's the purpose the purpose
+ 
+
+ align:start position:0%
+clear what's the purpose the purpose
+is that in this
+
+ align:start position:0%
+is that in this
+ 
+
+ align:start position:0%
+is that in this
+direction on this y line line of
+
+ align:start position:0%
+direction on this y line line of
+ 
+
+ align:start position:0%
+direction on this y line line of
+multiples of y a is just acting like a
+
+ align:start position:0%
+multiples of y a is just acting like a
+ 
+
+ align:start position:0%
+multiples of y a is just acting like a
+number a is some big n byn thousand by
+
+ align:start position:0%
+number a is some big n byn thousand by
+ 
+
+ align:start position:0%
+number a is some big n byn thousand by
+thousand
+
+ align:start position:0%
+thousand
+ 
+
+ align:start position:0%
+thousand
+Matrix so a Million numbers but on this
+
+ align:start position:0%
+Matrix so a Million numbers but on this
+ 
+
+ align:start position:0%
+Matrix so a Million numbers but on this
+line once if we find it if we find a AN
+
+ align:start position:0%
+line once if we find it if we find a AN
+ 
+
+ align:start position:0%
+line once if we find it if we find a AN
+igen line you could say an igen
+
+ align:start position:0%
+igen line you could say an igen
+ 
+
+ align:start position:0%
+igen line you could say an igen
+Direction on that in that direction a
+
+ align:start position:0%
+Direction on that in that direction a
+ 
+
+ align:start position:0%
+Direction on that in that direction a
+all the complications of a are gone it's
+
+ align:start position:0%
+all the complications of a are gone it's
+ 
+
+ align:start position:0%
+all the complications of a are gone it's
+just acting like a number so in
+
+ align:start position:0%
+just acting like a number so in
+ 
+
+ align:start position:0%
+just acting like a number so in
+particular we could solve a thousand
+
+ align:start position:0%
+particular we could solve a thousand
+ 
+
+ align:start position:0%
+particular we could solve a thousand
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equations with a thousand unknown U's
+
+ align:start position:0%
+equations with a thousand unknown U's
+ 
+
+ align:start position:0%
+equations with a thousand unknown U's
+with this thousand by,
+
+ align:start position:0%
+with this thousand by,
+ 
+
+ align:start position:0%
+with this thousand by,
+Matrix we could find a solution one we
+
+ align:start position:0%
+Matrix we could find a solution one we
+ 
+
+ align:start position:0%
+Matrix we could find a solution one we
+can find a solution and that's this is
+
+ align:start position:0%
+can find a solution and that's this is
+ 
+
+ align:start position:0%
+can find a solution and that's this is
+where I the igen vector
+
+ align:start position:0%
+where I the igen vector
+ 
+
+ align:start position:0%
+where I the igen vector
+nigen value are going to pay off in for
+
+ align:start position:0%
+nigen value are going to pay off in for
+ 
+
+ align:start position:0%
+nigen value are going to pay off in for
+this this you recognize this Matrix a is
+
+ align:start position:0%
+this this you recognize this Matrix a is
+ 
+
+ align:start position:0%
+this this you recognize this Matrix a is
+a size a thousand so this is and U is a
+
+ align:start position:0%
+a size a thousand so this is and U is a
+ 
+
+ align:start position:0%
+a size a thousand so this is and U is a
+vector of a thousand unknowns so that's
+
+ align:start position:0%
+vector of a thousand unknowns so that's
+ 
+
+ align:start position:0%
+vector of a thousand unknowns so that's
+a system of a thousand equation but if
+
+ align:start position:0%
+a system of a thousand equation but if
+ 
+
+ align:start position:0%
+a system of a thousand equation but if
+we have found an igen vector and it's
+
+ align:start position:0%
+we have found an igen vector and it's
+ 
+
+ align:start position:0%
+we have found an igen vector and it's
+igen value
+
+ align:start position:0%
+igen value
+ 
+
+ align:start position:0%
+igen value
+then the equation will if it starts in
+
+ align:start position:0%
+then the equation will if it starts in
+ 
+
+ align:start position:0%
+then the equation will if it starts in
+that direction it'll stay in that
+
+ align:start position:0%
+that direction it'll stay in that
+ 
+
+ align:start position:0%
+that direction it'll stay in that
+direction and the Matrix will just be
+
+ align:start position:0%
+direction and the Matrix will just be
+ 
+
+ align:start position:0%
+direction and the Matrix will just be
+acting like a number and we know how to
+
+ align:start position:0%
+acting like a number and we know how to
+ 
+
+ align:start position:0%
+acting like a number and we know how to
+solve U Prime equal Lambda U right that
+
+ align:start position:0%
+solve U Prime equal Lambda U right that
+ 
+
+ align:start position:0%
+solve U Prime equal Lambda U right that
+one by one scalar problem we know how to
+
+ align:start position:0%
+one by one scalar problem we know how to
+ 
+
+ align:start position:0%
+one by one scalar problem we know how to
+solve the solution to that is e to the
+
+ align:start position:0%
+solve the solution to that is e to the
+ 
+
+ align:start position:0%
+solve the solution to that is e to the
+Lambda
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T and of course it could have a constant
+
+ align:start position:0%
+T and of course it could have a constant
+ 
+
+ align:start position:0%
+T and of course it could have a constant
+in it don't don't forget that that the
+
+ align:start position:0%
+in it don't don't forget that that the
+ 
+
+ align:start position:0%
+in it don't don't forget that that the
+these equations are linear uh If I
+
+ align:start position:0%
+these equations are linear uh If I
+ 
+
+ align:start position:0%
+these equations are linear uh If I
+multiply if I take two e to the Lambda T
+
+ align:start position:0%
+multiply if I take two e to the Lambda T
+ 
+
+ align:start position:0%
+multiply if I take two e to the Lambda T
+I have a two here and a two here and
+
+ align:start position:0%
+I have a two here and a two here and
+ 
+
+ align:start position:0%
+I have a two here and a two here and
+it's just as good so I better allow that
+
+ align:start position:0%
+it's just as good so I better allow that
+ 
+
+ align:start position:0%
+it's just as good so I better allow that
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well a constant times e Lambda T * y
+
+ align:start position:0%
+well a constant times e Lambda T * y
+ 
+
+ align:start position:0%
+well a constant times e Lambda T * y
+notice this is a vector it's a number
+
+ align:start position:0%
+notice this is a vector it's a number
+ 
+
+ align:start position:0%
+notice this is a vector it's a number
+times the number the growth so the
+
+ align:start position:0%
+times the number the growth so the
+ 
+
+ align:start position:0%
+times the number the growth so the
+Lambda is now for the differential
+
+ align:start position:0%
+Lambda is now for the differential
+ 
+
+ align:start position:0%
+Lambda is now for the differential
+equation the Lambda this this number
+
+ align:start position:0%
+equation the Lambda this this number
+ 
+
+ align:start position:0%
+equation the Lambda this this number
+Lambda is crucial it's telling us
+
+ align:start position:0%
+Lambda is crucial it's telling us
+ 
+
+ align:start position:0%
+Lambda is crucial it's telling us
+whether the solution grows whether it
+
+ align:start position:0%
+whether the solution grows whether it
+ 
+
+ align:start position:0%
+whether the solution grows whether it
+decays whether it oscillates and we're
+
+ align:start position:0%
+decays whether it oscillates and we're
+ 
+
+ align:start position:0%
+decays whether it oscillates and we're
+just looking at this one normal mode you
+
+ align:start position:0%
+just looking at this one normal mode you
+ 
+
+ align:start position:0%
+just looking at this one normal mode you
+could say normal mode for igen Vector
+
+ align:start position:0%
+could say normal mode for igen Vector
+ 
+
+ align:start position:0%
+could say normal mode for igen Vector
+why we certainly have not
+
+ align:start position:0%
+why we certainly have not
+ 
+
+ align:start position:0%
+why we certainly have not
+found all all possible solutions our uh
+
+ align:start position:0%
+found all all possible solutions our uh
+ 
+
+ align:start position:0%
+found all all possible solutions our uh
+this but this is we found if we if we
+
+ align:start position:0%
+this but this is we found if we if we
+ 
+
+ align:start position:0%
+this but this is we found if we if we
+have an igen Vector we found that one
+
+ align:start position:0%
+have an igen Vector we found that one
+ 
+
+ align:start position:0%
+have an igen Vector we found that one
+okay well so uh and just other uses but
+
+ align:start position:0%
+okay well so uh and just other uses but
+ 
+
+ align:start position:0%
+okay well so uh and just other uses but
+and then let me other uses what so let
+
+ align:start position:0%
+and then let me other uses what so let
+ 
+
+ align:start position:0%
+and then let me other uses what so let
+me write again the fundamental equation
+
+ align:start position:0%
+me write again the fundamental equation
+ 
+
+ align:start position:0%
+me write again the fundamental equation
+a yal Lambda y suppose so that was a
+
+ align:start position:0%
+a yal Lambda y suppose so that was a
+ 
+
+ align:start position:0%
+a yal Lambda y suppose so that was a
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equation going forward in time now uh if
+
+ align:start position:0%
+equation going forward in time now uh if
+ 
+
+ align:start position:0%
+equation going forward in time now uh if
+we go forward in steps we might multiply
+
+ align:start position:0%
+we go forward in steps we might multiply
+ 
+
+ align:start position:0%
+we go forward in steps we might multiply
+by a at every
+
+ align:start position:0%
+by a at every
+ 
+
+ align:start position:0%
+by a at every
+step so what tell me
+
+ align:start position:0%
+step so what tell me
+ 
+
+ align:start position:0%
+step so what tell me
+what tell me an igon Vector of a s
+
+ align:start position:0%
+what tell me an igon Vector of a s
+ 
+
+ align:start position:0%
+what tell me an igon Vector of a s
+I I'm looking for a vector that doesn't
+
+ align:start position:0%
+I I'm looking for a vector that doesn't
+ 
+
+ align:start position:0%
+I I'm looking for a vector that doesn't
+change direction when I multiply twice
+
+ align:start position:0%
+change direction when I multiply twice
+ 
+
+ align:start position:0%
+change direction when I multiply twice
+by
+
+ align:start position:0%
+by
+ 
+
+ align:start position:0%
+by
+a you're going to tell me it's why why
+
+ align:start position:0%
+a you're going to tell me it's why why
+ 
+
+ align:start position:0%
+a you're going to tell me it's why why
+will work if I multiply once by a I get
+
+ align:start position:0%
+will work if I multiply once by a I get
+ 
+
+ align:start position:0%
+will work if I multiply once by a I get
+Lambda time y when I multiply Again by a
+
+ align:start position:0%
+Lambda time y when I multiply Again by a
+ 
+
+ align:start position:0%
+Lambda time y when I multiply Again by a
+I get Lambda squ time y you see I
+
+ align:start position:0%
+I get Lambda squ time y you see I
+ 
+
+ align:start position:0%
+I get Lambda squ time y you see I
+values are
+
+ align:start position:0%
+values are
+ 
+
+ align:start position:0%
+values are
+great for powers of a matrix for
+
+ align:start position:0%
+great for powers of a matrix for
+ 
+
+ align:start position:0%
+great for powers of a matrix for
+differential
+
+ align:start position:0%
+differential
+ 
+
+ align:start position:0%
+differential
+equations the N power will just take the
+
+ align:start position:0%
+equations the N power will just take the
+ 
+
+ align:start position:0%
+equations the N power will just take the
+igon value to the N the nth power of a
+
+ align:start position:0%
+igon value to the N the nth power of a
+ 
+
+ align:start position:0%
+igon value to the N the nth power of a
+we'll just have Lambda to the nth
+
+ align:start position:0%
+we'll just have Lambda to the nth
+ 
+
+ align:start position:0%
+we'll just have Lambda to the nth
+there uh you know the
+
+ align:start position:0%
+there uh you know the
+ 
+
+ align:start position:0%
+there uh you know the
+pivots of a matrix are all messed up
+
+ align:start position:0%
+pivots of a matrix are all messed up
+ 
+
+ align:start position:0%
+pivots of a matrix are all messed up
+when when I Square it I I can't see
+
+ align:start position:0%
+when when I Square it I I can't see
+ 
+
+ align:start position:0%
+when when I Square it I I can't see
+what's happening with the pivots the
+
+ align:start position:0%
+what's happening with the pivots the
+ 
+
+ align:start position:0%
+what's happening with the pivots the
+igen values are a different way to look
+
+ align:start position:0%
+igen values are a different way to look
+ 
+
+ align:start position:0%
+igen values are a different way to look
+at a matrix the pivots are critical
+
+ align:start position:0%
+at a matrix the pivots are critical
+ 
+
+ align:start position:0%
+at a matrix the pivots are critical
+numbers for steady state problems the
+
+ align:start position:0%
+numbers for steady state problems the
+ 
+
+ align:start position:0%
+numbers for steady state problems the
+igen values are the critical numbers
+
+ align:start position:0%
+igen values are the critical numbers
+ 
+
+ align:start position:0%
+igen values are the critical numbers
+for moving problems dynamic problems
+
+ align:start position:0%
+for moving problems dynamic problems
+ 
+
+ align:start position:0%
+for moving problems dynamic problems
+things are oscillating or growing or
+
+ align:start position:0%
+things are oscillating or growing or
+ 
+
+ align:start position:0%
+things are oscillating or growing or
+decaying okay and by the way let's just
+
+ align:start position:0%
+decaying okay and by the way let's just
+ 
+
+ align:start position:0%
+decaying okay and by the way let's just
+recognize since this is the is the only
+
+ align:start position:0%
+recognize since this is the is the only
+ 
+
+ align:start position:0%
+recognize since this is the is the only
+is the thing that's changing in time
+
+ align:start position:0%
+is the thing that's changing in time
+ 
+
+ align:start position:0%
+is the thing that's changing in time
+what would be the
+
+ align:start position:0%
+what would be the
+ 
+
+ align:start position:0%
+what would be the
+uh I'll just go down here e to the
+
+ align:start position:0%
+uh I'll just go down here e to the
+ 
+
+ align:start position:0%
+uh I'll just go down here e to the
+Lambda T let's just look and see when
+
+ align:start position:0%
+Lambda T let's just look and see when
+ 
+
+ align:start position:0%
+Lambda T let's just look and see when
+would I have
+
+ align:start position:0%
+would I have
+ 
+
+ align:start position:0%
+would I have
+Decay which you might want to call
+
+ align:start position:0%
+Decay which you might want to call
+ 
+
+ align:start position:0%
+Decay which you might want to call
+stability a stable
+
+ align:start position:0%
+stability a stable
+ 
+
+ align:start position:0%
+stability a stable
+problem what would be the condition on
+
+ align:start position:0%
+problem what would be the condition on
+ 
+
+ align:start position:0%
+problem what would be the condition on
+Lambda to get for this to
+
+ align:start position:0%
+Lambda to get for this to
+ 
+
+ align:start position:0%
+Lambda to get for this to
+Decay Lambda less than zero now there's
+
+ align:start position:0%
+Decay Lambda less than zero now there's
+ 
+
+ align:start position:0%
+Decay Lambda less than zero now there's
+one little bit of bad news Lambda could
+
+ align:start position:0%
+one little bit of bad news Lambda could
+ 
+
+ align:start position:0%
+one little bit of bad news Lambda could
+be
+
+ align:start position:0%
+be
+ 
+
+ align:start position:0%
+be
+complex Lambda could
+
+ align:start position:0%
+complex Lambda could
+ 
+
+ align:start position:0%
+complex Lambda could
+be three + 4
+
+ align:start position:0%
+be three + 4
+ 
+
+ align:start position:0%
+be three + 4
+I it it can it can be a complex number
+
+ align:start position:0%
+I it it can it can be a complex number
+ 
+
+ align:start position:0%
+I it it can it can be a complex number
+these I values even
+
+ align:start position:0%
+these I values even
+ 
+
+ align:start position:0%
+these I values even
+if a is
+
+ align:start position:0%
+if a is
+ 
+
+ align:start position:0%
+if a is
+real oh you'll say how' that happen let
+
+ align:start position:0%
+real oh you'll say how' that happen let
+ 
+
+ align:start position:0%
+real oh you'll say how' that happen let
+me see better
+
+ align:start position:0%
+me see better
+ 
+
+ align:start position:0%
+me see better
+think well let me finish this thought
+
+ align:start position:0%
+think well let me finish this thought
+ 
+
+ align:start position:0%
+think well let me finish this thought
+suppose Lambda was 3 + 4 I what would be
+
+ align:start position:0%
+suppose Lambda was 3 + 4 I what would be
+ 
+
+ align:start position:0%
+suppose Lambda was 3 + 4 I what would be
+would it then so I'm thinking about what
+
+ align:start position:0%
+would it then so I'm thinking about what
+ 
+
+ align:start position:0%
+would it then so I'm thinking about what
+would e to the Lambda T do in that case
+
+ align:start position:0%
+would e to the Lambda T do in that case
+ 
+
+ align:start position:0%
+would e to the Lambda T do in that case
+so so this is small example e if if I
+
+ align:start position:0%
+so so this is small example e if if I
+ 
+
+ align:start position:0%
+so so this is small example e if if I
+had Lambda is 3 + 4 i t how what does
+
+ align:start position:0%
+had Lambda is 3 + 4 i t how what does
+ 
+
+ align:start position:0%
+had Lambda is 3 + 4 i t how what does
+that do as time
+
+ align:start position:0%
+that do as time
+ 
+
+ align:start position:0%
+that do as time
+grows it's going to grow and oscillate
+
+ align:start position:0%
+grows it's going to grow and oscillate
+ 
+
+ align:start position:0%
+grows it's going to grow and oscillate
+and what decides the
+
+ align:start position:0%
+and what decides the
+ 
+
+ align:start position:0%
+and what decides the
+growth the real part so it's really the
+
+ align:start position:0%
+growth the real part so it's really the
+ 
+
+ align:start position:0%
+growth the real part so it's really the
+Decay or growth is decided by the real
+
+ align:start position:0%
+Decay or growth is decided by the real
+ 
+
+ align:start position:0%
+Decay or growth is decided by the real
+part the three e to the 3 T that would
+
+ align:start position:0%
+part the three e to the 3 T that would
+ 
+
+ align:start position:0%
+part the three e to the 3 T that would
+be a growth so let me put growth
+
+ align:start position:0%
+be a growth so let me put growth
+ 
+
+ align:start position:0%
+be a growth so let me put growth
+and that would be of course
+
+ align:start position:0%
+and that would be of course
+ 
+
+ align:start position:0%
+and that would be of course
+unstable and that's a problem when I
+
+ align:start position:0%
+unstable and that's a problem when I
+ 
+
+ align:start position:0%
+unstable and that's a problem when I
+have a real part of Lambda bigger than
+
+ align:start position:0%
+have a real part of Lambda bigger than
+ 
+
+ align:start position:0%
+have a real part of Lambda bigger than
+zero and then if if Lambda is has a zero
+
+ align:start position:0%
+zero and then if if Lambda is has a zero
+ 
+
+ align:start position:0%
+zero and then if if Lambda is has a zero
+real part so it's pure oscillation let
+
+ align:start position:0%
+real part so it's pure oscillation let
+ 
+
+ align:start position:0%
+real part so it's pure oscillation let
+me just take a case like that so e to
+
+ align:start position:0%
+me just take a case like that so e to
+ 
+
+ align:start position:0%
+me just take a case like that so e to
+the 4 i
+
+ align:start position:0%
+the 4 i
+ 
+
+ align:start position:0%
+the 4 i
+t so that would be oscillating right
+
+ align:start position:0%
+t so that would be oscillating right
+ 
+
+ align:start position:0%
+t so that would be oscillating right
+yeah it's cos 4T plus I sin 4T it's just
+
+ align:start position:0%
+yeah it's cos 4T plus I sin 4T it's just
+ 
+
+ align:start position:0%
+yeah it's cos 4T plus I sin 4T it's just
+oscillate
+
+ align:start position:0%
+oscillate
+ 
+
+ align:start position:0%
+oscillate
+okay all right so in in this discussion
+
+ align:start position:0%
+okay all right so in in this discussion
+ 
+
+ align:start position:0%
+okay all right so in in this discussion
+we seen uh growth and Decay
+
+ align:start position:0%
+we seen uh growth and Decay
+ 
+
+ align:start position:0%
+we seen uh growth and Decay
+oh tell me the parallels because I'm
+
+ align:start position:0%
+oh tell me the parallels because I'm
+ 
+
+ align:start position:0%
+oh tell me the parallels because I'm
+always shooting for the parallels what
+
+ align:start position:0%
+always shooting for the parallels what
+ 
+
+ align:start position:0%
+always shooting for the parallels what
+about the growth of a what
+
+ align:start position:0%
+about the growth of a what
+ 
+
+ align:start position:0%
+about the growth of a what
+matrices
+
+ align:start position:0%
+matrices
+ 
+
+ align:start position:0%
+matrices
+yeah what how can I recognize a matrix
+
+ align:start position:0%
+yeah what how can I recognize a matrix
+ 
+
+ align:start position:0%
+yeah what how can I recognize a matrix
+whose powers
+
+ align:start position:0%
+whose powers
+ 
+
+ align:start position:0%
+whose powers
+grow how can I recognize a Matrix whose
+
+ align:start position:0%
+grow how can I recognize a Matrix whose
+ 
+
+ align:start position:0%
+grow how can I recognize a Matrix whose
+Powers go to zero so that would be the
+
+ align:start position:0%
+Powers go to zero so that would be the
+ 
+
+ align:start position:0%
+Powers go to zero so that would be the
+I'm asking you for Powers here over
+
+ align:start position:0%
+I'm asking you for Powers here over
+ 
+
+ align:start position:0%
+I'm asking you for Powers here over
+there for exponentials somehow so so
+
+ align:start position:0%
+there for exponentials somehow so so
+ 
+
+ align:start position:0%
+there for exponentials somehow so so
+here would be a a to higher and higher
+
+ align:start position:0%
+here would be a a to higher and higher
+ 
+
+ align:start position:0%
+here would be a a to higher and higher
+Powers goes to zero the zero Matrix in
+
+ align:start position:0%
+Powers goes to zero the zero Matrix in
+ 
+
+ align:start position:0%
+Powers goes to zero the zero Matrix in
+other words when I multiply multiply
+
+ align:start position:0%
+other words when I multiply multiply
+ 
+
+ align:start position:0%
+other words when I multiply multiply
+multiply by that Matrix I get smaller
+
+ align:start position:0%
+multiply by that Matrix I get smaller
+ 
+
+ align:start position:0%
+multiply by that Matrix I get smaller
+and smaller and smaller matrices zero in
+
+ align:start position:0%
+and smaller and smaller matrices zero in
+ 
+
+ align:start position:0%
+and smaller and smaller matrices zero in
+the limit what do you think's the test
+
+ align:start position:0%
+the limit what do you think's the test
+ 
+
+ align:start position:0%
+the limit what do you think's the test
+on the lambdas
+
+ align:start position:0%
+on the lambdas
+ 
+
+ align:start position:0%
+on the lambdas
+now so here's so what are the igen
+
+ align:start position:0%
+now so here's so what are the igen
+ 
+
+ align:start position:0%
+now so here's so what are the igen
+values of a to the
+
+ align:start position:0%
+values of a to the
+ 
+
+ align:start position:0%
+values of a to the
+K let's see if a had IG values Lambda a
+
+ align:start position:0%
+K let's see if a had IG values Lambda a
+ 
+
+ align:start position:0%
+K let's see if a had IG values Lambda a
+s will have IG values Lambda squar a cub
+
+ align:start position:0%
+s will have IG values Lambda squar a cub
+ 
+
+ align:start position:0%
+s will have IG values Lambda squar a cub
+will have IG values Lambda cubed a to
+
+ align:start position:0%
+will have IG values Lambda cubed a to
+ 
+
+ align:start position:0%
+will have IG values Lambda cubed a to
+the thousandth will have I values Lambda
+
+ align:start position:0%
+the thousandth will have I values Lambda
+ 
+
+ align:start position:0%
+the thousandth will have I values Lambda
+to the thousandth and what's the test
+
+ align:start position:0%
+to the thousandth and what's the test
+ 
+
+ align:start position:0%
+to the thousandth and what's the test
+for that to G be getting
+
+ align:start position:0%
+for that to G be getting
+ 
+
+ align:start position:0%
+for that to G be getting
+small Lambda below Lambda less than one
+
+ align:start position:0%
+small Lambda below Lambda less than one
+ 
+
+ align:start position:0%
+small Lambda below Lambda less than one
+so the test for stability will be in the
+
+ align:start position:0%
+so the test for stability will be in the
+ 
+
+ align:start position:0%
+so the test for stability will be in the
+discrete case it won't be the real it
+
+ align:start position:0%
+discrete case it won't be the real it
+ 
+
+ align:start position:0%
+discrete case it won't be the real it
+won't be the real part of Lambda it'll
+
+ align:start position:0%
+won't be the real part of Lambda it'll
+ 
+
+ align:start position:0%
+won't be the real part of Lambda it'll
+be the size of Lambda less than one and
+
+ align:start position:0%
+be the size of Lambda less than one and
+ 
+
+ align:start position:0%
+be the size of Lambda less than one and
+growth would be the size of Lambda
+
+ align:start position:0%
+growth would be the size of Lambda
+ 
+
+ align:start position:0%
+growth would be the size of Lambda
+greater than one yeah so and and and
+
+ align:start position:0%
+greater than one yeah so and and and
+ 
+
+ align:start position:0%
+greater than one yeah so and and and
+again there'll be this borderline case
+
+ align:start position:0%
+again there'll be this borderline case
+ 
+
+ align:start position:0%
+again there'll be this borderline case
+when the igen value has magnitude
+
+ align:start position:0%
+when the igen value has magnitude
+ 
+
+ align:start position:0%
+when the igen value has magnitude
+exactly what okay so you're
+
+ align:start position:0%
+exactly what okay so you're
+ 
+
+ align:start position:0%
+exactly what okay so you're
+seeing uh here and and also here the
+
+ align:start position:0%
+seeing uh here and and also here the
+ 
+
+ align:start position:0%
+seeing uh here and and also here the
+idea that we may have to deal with
+
+ align:start position:0%
+idea that we may have to deal with
+ 
+
+ align:start position:0%
+idea that we may have to deal with
+complex numbers
+
+ align:start position:0%
+complex numbers
+ 
+
+ align:start position:0%
+complex numbers
+here we don't have to deal with the
+
+ align:start position:0%
+here we don't have to deal with the
+ 
+
+ align:start position:0%
+here we don't have to deal with the
+whole world of complex functions and and
+
+ align:start position:0%
+whole world of complex functions and and
+ 
+
+ align:start position:0%
+whole world of complex functions and and
+everything but but it's possible for
+
+ align:start position:0%
+everything but but it's possible for
+ 
+
+ align:start position:0%
+everything but but it's possible for
+complex numbers to come
+
+ align:start position:0%
+complex numbers to come
+ 
+
+ align:start position:0%
+complex numbers to come
+in well while I'm saying that why don't
+
+ align:start position:0%
+in well while I'm saying that why don't
+ 
+
+ align:start position:0%
+in well while I'm saying that why don't
+I say give an example where it would
+
+ align:start position:0%
+I say give an example where it would
+ 
+
+ align:start position:0%
+I say give an example where it would
+come in suppose I so this is so this is
+
+ align:start position:0%
+come in suppose I so this is so this is
+ 
+
+ align:start position:0%
+come in suppose I so this is so this is
+a like a
+
+ align:start position:0%
+a like a
+ 
+
+ align:start position:0%
+a like a
+this is going to be a real
+
+ align:start position:0%
+this is going to be a real
+ 
+
+ align:start position:0%
+this is going to be a real
+Matrix with complex I
+
+ align:start position:0%
+Matrix with complex I
+ 
+
+ align:start position:0%
+Matrix with complex I
+values complex
+
+ align:start position:0%
+values complex
+ 
+
+ align:start position:0%
+values complex
+lambdas okay this is it'll be an
+
+ align:start position:0%
+lambdas okay this is it'll be an
+ 
+
+ align:start position:0%
+lambdas okay this is it'll be an
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so I guess I'm looking for a
+
+ align:start position:0%
+okay so I guess I'm looking for a
+ 
+
+ align:start position:0%
+okay so I guess I'm looking for a
+matrix
+
+ align:start position:0%
+matrix
+ 
+
+ align:start position:0%
+matrix
+where Y and ay never come out in the
+
+ align:start position:0%
+where Y and ay never come out in the
+ 
+
+ align:start position:0%
+where Y and ay never come out in the
+same direction for real
+
+ align:start position:0%
+same direction for real
+ 
+
+ align:start position:0%
+same direction for real
+wise I know okay here's a good Matrix
+
+ align:start position:0%
+wise I know okay here's a good Matrix
+ 
+
+ align:start position:0%
+wise I know okay here's a good Matrix
+take the Matrix that rotates every
+
+ align:start position:0%
+take the Matrix that rotates every
+ 
+
+ align:start position:0%
+take the Matrix that rotates every
+vector by 90
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+degrees or or by Theta by Theta but
+
+ align:start position:0%
+degrees or or by Theta by Theta but
+ 
+
+ align:start position:0%
+degrees or or by Theta by Theta but
+let's let's say here here's a matrix
+
+ align:start position:0%
+let's let's say here here's a matrix
+ 
+
+ align:start position:0%
+let's let's say here here's a matrix
+that rotates every vector by 90
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Dees I'm going to raise this board and
+
+ align:start position:0%
+Dees I'm going to raise this board and
+ 
+
+ align:start position:0%
+Dees I'm going to raise this board and
+hide it behind there in a minute I just
+
+ align:start position:0%
+hide it behind there in a minute I just
+ 
+
+ align:start position:0%
+hide it behind there in a minute I just
+wanted to just to open up this this
+
+ align:start position:0%
+wanted to just to open up this this
+ 
+
+ align:start position:0%
+wanted to just to open up this this
+thought that we do we will have to face
+
+ align:start position:0%
+thought that we do we will have to face
+ 
+
+ align:start position:0%
+thought that we do we will have to face
+complex numbers I'm I'm you probably
+
+ align:start position:0%
+complex numbers I'm I'm you probably
+ 
+
+ align:start position:0%
+complex numbers I'm I'm you probably
+have you know if you know how to
+
+ align:start position:0%
+have you know if you know how to
+ 
+
+ align:start position:0%
+have you know if you know how to
+multiply two complex numbers and add
+
+ align:start position:0%
+multiply two complex numbers and add
+ 
+
+ align:start position:0%
+multiply two complex numbers and add
+them
+
+ align:start position:0%
+them
+ 
+
+ align:start position:0%
+them
+uh you're okay this isn't going to turn
+
+ align:start position:0%
+uh you're okay this isn't going to turn
+ 
+
+ align:start position:0%
+uh you're okay this isn't going to turn
+into a big deal but let's just realize
+
+ align:start position:0%
+into a big deal but let's just realize
+ 
+
+ align:start position:0%
+into a big deal but let's just realize
+that suppose that Matrix if I put in a
+
+ align:start position:0%
+that suppose that Matrix if I put in a
+ 
+
+ align:start position:0%
+that suppose that Matrix if I put in a
+vector y
+
+ align:start position:0%
+vector y
+ 
+
+ align:start position:0%
+vector y
+and I multiply by that Matrix it'll turn
+
+ align:start position:0%
+and I multiply by that Matrix it'll turn
+ 
+
+ align:start position:0%
+and I multiply by that Matrix it'll turn
+it through 90
+
+ align:start position:0%
+it through 90
+ 
+
+ align:start position:0%
+it through 90
+de so it so y couldn't be an igen Vector
+
+ align:start position:0%
+de so it so y couldn't be an igen Vector
+ 
+
+ align:start position:0%
+de so it so y couldn't be an igen Vector
+that's the point I'm trying to make no
+
+ align:start position:0%
+that's the point I'm trying to make no
+ 
+
+ align:start position:0%
+that's the point I'm trying to make no
+real Vector of a ro could be the igen
+
+ align:start position:0%
+real Vector of a ro could be the igen
+ 
+
+ align:start position:0%
+real Vector of a ro could be the igen
+vector of a rotation Matrix because
+
+ align:start position:0%
+vector of a rotation Matrix because
+ 
+
+ align:start position:0%
+vector of a rotation Matrix because
+every Vector gets
+
+ align:start position:0%
+every Vector gets
+ 
+
+ align:start position:0%
+every Vector gets
+turned so that's an example where you'd
+
+ align:start position:0%
+turned so that's an example where you'd
+ 
+
+ align:start position:0%
+turned so that's an example where you'd
+have to go
+
+ align:start position:0%
+have to go
+ 
+
+ align:start position:0%
+have to go
+to complex vectors and I think if I
+
+ align:start position:0%
+to complex vectors and I think if I
+ 
+
+ align:start position:0%
+to complex vectors and I think if I
+tried if I tried the vector one 1 I so
+
+ align:start position:0%
+tried if I tried the vector one 1 I so
+ 
+
+ align:start position:0%
+tried if I tried the vector one 1 I so
+I'm letting the sare root of minus1 into
+
+ align:start position:0%
+I'm letting the sare root of minus1 into
+ 
+
+ align:start position:0%
+I'm letting the sare root of minus1 into
+here then I think it would come out uh
+
+ align:start position:0%
+here then I think it would come out uh
+ 
+
+ align:start position:0%
+here then I think it would come out uh
+let see if I do that multiplication I
+
+ align:start position:0%
+let see if I do that multiplication I
+ 
+
+ align:start position:0%
+let see if I do that multiplication I
+get minus I and I get one and I think
+
+ align:start position:0%
+get minus I and I get one and I think
+ 
+
+ align:start position:0%
+get minus I and I get one and I think
+that this
+
+ align:start position:0%
+that this
+ 
+
+ align:start position:0%
+that this
+is what is it this is probably minus I
+
+ align:start position:0%
+is what is it this is probably minus I
+ 
+
+ align:start position:0%
+is what is it this is probably minus I
+times that so this is minus I times the
+
+ align:start position:0%
+times that so this is minus I times the
+ 
+
+ align:start position:0%
+times that so this is minus I times the
+input
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no big deal that that was like you can
+
+ align:start position:0%
+no big deal that that was like you can
+ 
+
+ align:start position:0%
+no big deal that that was like you can
+forget that it's
+
+ align:start position:0%
+forget that it's
+ 
+
+ align:start position:0%
+forget that it's
+just complex numbers can come in right
+
+ align:start position:0%
+just complex numbers can come in right
+ 
+
+ align:start position:0%
+just complex numbers can come in right
+okay okay now let me come back to the
+
+ align:start position:0%
+okay okay now let me come back to the
+ 
+
+ align:start position:0%
+okay okay now let me come back to the
+main point about igen vectors okay okay
+
+ align:start position:0%
+main point about igen vectors okay okay
+ 
+
+ align:start position:0%
+main point about igen vectors okay okay
+all right so they they things can be
+
+ align:start position:0%
+all right so they they things can be
+ 
+
+ align:start position:0%
+all right so they they things can be
+complex all right
+
+ align:start position:0%
+complex all right
+ 
+
+ align:start position:0%
+complex all right
+so the main point is how do we use them
+
+ align:start position:0%
+so the main point is how do we use them
+ 
+
+ align:start position:0%
+so the main point is how do we use them
+and how many are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there
+
+ align:start position:0%
+there
+ 
+
+ align:start position:0%
+there
+well the here's the key that a typical
+
+ align:start position:0%
+well the here's the key that a typical
+ 
+
+ align:start position:0%
+well the here's the key that a typical
+good Matrix which includes every
+
+ align:start position:0%
+good Matrix which includes every
+ 
+
+ align:start position:0%
+good Matrix which includes every
+symmetric Matrix so it includes all of
+
+ align:start position:0%
+symmetric Matrix so it includes all of
+ 
+
+ align:start position:0%
+symmetric Matrix so it includes all of
+our examples and more if it's of size a
+
+ align:start position:0%
+our examples and more if it's of size a
+ 
+
+ align:start position:0%
+our examples and more if it's of size a
+thousand it will have a thousand
+
+ align:start position:0%
+thousand it will have a thousand
+ 
+
+ align:start position:0%
+thousand it will have a thousand
+different igen
+
+ align:start position:0%
+different igen
+ 
+
+ align:start position:0%
+different igen
+vectors and for our let me just say for
+
+ align:start position:0%
+vectors and for our let me just say for
+ 
+
+ align:start position:0%
+vectors and for our let me just say for
+our symmetric
+
+ align:start position:0%
+our symmetric
+ 
+
+ align:start position:0%
+our symmetric
+matrices those igen vectors will all be
+
+ align:start position:0%
+matrices those igen vectors will all be
+ 
+
+ align:start position:0%
+matrices those igen vectors will all be
+real they're they're great the igen
+
+ align:start position:0%
+real they're they're great the igen
+ 
+
+ align:start position:0%
+real they're they're great the igen
+vectors of symmetric matrices oh let me
+
+ align:start position:0%
+vectors of symmetric matrices oh let me
+ 
+
+ align:start position:0%
+vectors of symmetric matrices oh let me
+find them for one particular symmetric
+
+ align:start position:0%
+find them for one particular symmetric
+ 
+
+ align:start position:0%
+find them for one particular symmetric
+Matrix say this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+guy so that's a matrix 2 by two how many
+
+ align:start position:0%
+guy so that's a matrix 2 by two how many
+ 
+
+ align:start position:0%
+guy so that's a matrix 2 by two how many
+ion vectors am I now looking
+
+ align:start position:0%
+ion vectors am I now looking
+ 
+
+ align:start position:0%
+ion vectors am I now looking
+for
+
+ align:start position:0%
+for
+ 
+
+ align:start position:0%
+for
+two you could say how do I find
+
+ align:start position:0%
+two you could say how do I find
+ 
+
+ align:start position:0%
+two you could say how do I find
+them maybe with that 2 by two I can even
+
+ align:start position:0%
+them maybe with that 2 by two I can even
+ 
+
+ align:start position:0%
+them maybe with that 2 by two I can even
+just like uh wing it uh you you we can
+
+ align:start position:0%
+just like uh wing it uh you you we can
+ 
+
+ align:start position:0%
+just like uh wing it uh you you we can
+come up with a vector that that is an
+
+ align:start position:0%
+come up with a vector that that is an
+ 
+
+ align:start position:0%
+come up with a vector that that is an
+igen Vector that's that's not a that's
+
+ align:start position:0%
+igen Vector that's that's not a that's
+ 
+
+ align:start position:0%
+igen Vector that's that's not a that's
+actually that's what we're going to do
+
+ align:start position:0%
+actually that's what we're going to do
+ 
+
+ align:start position:0%
+actually that's what we're going to do
+here is we're going to guess the igen
+
+ align:start position:0%
+here is we're going to guess the igen
+ 
+
+ align:start position:0%
+here is we're going to guess the igen
+vectors and then we're going to show
+
+ align:start position:0%
+vectors and then we're going to show
+ 
+
+ align:start position:0%
+vectors and then we're going to show
+that they really are igen vectors and
+
+ align:start position:0%
+that they really are igen vectors and
+ 
+
+ align:start position:0%
+that they really are igen vectors and
+we'll know the igen values and it's
+
+ align:start position:0%
+we'll know the igen values and it's
+ 
+
+ align:start position:0%
+we'll know the igen values and it's
+fantastic so like let's start here with
+
+ align:start position:0%
+fantastic so like let's start here with
+ 
+
+ align:start position:0%
+fantastic so like let's start here with
+the 2 by two
+
+ align:start position:0%
+the 2 by two
+ 
+
+ align:start position:0%
+the 2 by two
+case anybody spot an igen Vector is one
+
+ align:start position:0%
+case anybody spot an igen Vector is one
+ 
+
+ align:start position:0%
+case anybody spot an igen Vector is one
+zero an igen Vector try one Zer what
+
+ align:start position:0%
+zero an igen Vector try one Zer what
+ 
+
+ align:start position:0%
+zero an igen Vector try one Zer what
+comes out of one
+
+ align:start position:0%
+comes out of one
+ 
+
+ align:start position:0%
+comes out of one
+zero well that picks the First Column
+
+ align:start position:0%
+zero well that picks the First Column
+ 
+
+ align:start position:0%
+zero well that picks the First Column
+right that's how I see multiplying by
+
+ align:start position:0%
+right that's how I see multiplying by
+ 
+
+ align:start position:0%
+right that's how I see multiplying by
+one zero that says take one of the First
+
+ align:start position:0%
+one zero that says take one of the First
+ 
+
+ align:start position:0%
+one zero that says take one of the First
+Column and is it an igen
+
+ align:start position:0%
+Column and is it an igen
+ 
+
+ align:start position:0%
+Column and is it an igen
+Vector yes no
+
+ align:start position:0%
+Vector yes no
+ 
+
+ align:start position:0%
+Vector yes no
+no this Vector is not in the same
+
+ align:start position:0%
+no this Vector is not in the same
+ 
+
+ align:start position:0%
+no this Vector is not in the same
+direction as that one no good okay now
+
+ align:start position:0%
+direction as that one no good okay now
+ 
+
+ align:start position:0%
+direction as that one no good okay now
+can you tell me one that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is you're going to guess it one one try
+
+ align:start position:0%
+is you're going to guess it one one try
+ 
+
+ align:start position:0%
+is you're going to guess it one one try
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+one do the multiplication and what do
+
+ align:start position:0%
+one do the multiplication and what do
+ 
+
+ align:start position:0%
+one do the multiplication and what do
+you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+get right what do I get from if I input
+
+ align:start position:0%
+get right what do I get from if I input
+ 
+
+ align:start position:0%
+get right what do I get from if I input
+this Vector Y what do I get get
+
+ align:start position:0%
+this Vector Y what do I get get
+ 
+
+ align:start position:0%
+this Vector Y what do I get get
+out actually I get y
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself right so so I get the point is it
+
+ align:start position:0%
+itself right so so I get the point is it
+ 
+
+ align:start position:0%
+itself right so so I get the point is it
+didn't change direction and it didn't
+
+ align:start position:0%
+didn't change direction and it didn't
+ 
+
+ align:start position:0%
+didn't change direction and it didn't
+even change length so what's the igen
+
+ align:start position:0%
+even change length so what's the igen
+ 
+
+ align:start position:0%
+even change length so what's the igen
+value for that so I've got one IG value
+
+ align:start position:0%
+value for that so I've got one IG value
+ 
+
+ align:start position:0%
+value for that so I've got one IG value
+now one igen vector one one and I've got
+
+ align:start position:0%
+now one igen vector one one and I've got
+ 
+
+ align:start position:0%
+now one igen vector one one and I've got
+the IG value uh so here are the vectors
+
+ align:start position:0%
+the IG value uh so here are the vectors
+ 
+
+ align:start position:0%
+the IG value uh so here are the vectors
+the Y's and here are the lambdas and
+
+ align:start position:0%
+the Y's and here are the lambdas and
+ 
+
+ align:start position:0%
+the Y's and here are the lambdas and
+I've got one of them and it's one
+
+ align:start position:0%
+I've got one of them and it's one
+ 
+
+ align:start position:0%
+I've got one of them and it's one
+right would you like to guess the other
+
+ align:start position:0%
+right would you like to guess the other
+ 
+
+ align:start position:0%
+right would you like to guess the other
+one I'm only looking for two because
+
+ align:start position:0%
+one I'm only looking for two because
+ 
+
+ align:start position:0%
+one I'm only looking for two because
+it's a 2X two Matrix so let me Erase
+
+ align:start position:0%
+it's a 2X two Matrix so let me Erase
+ 
+
+ align:start position:0%
+it's a 2X two Matrix so let me Erase
+here hope that you'll come up with
+
+ align:start position:0%
+here hope that you'll come up with
+ 
+
+ align:start position:0%
+here hope that you'll come up with
+another
+
+ align:start position:0%
+another
+ 
+
+ align:start position:0%
+another
+one one negative one is certainly worth
+
+ align:start position:0%
+one one negative one is certainly worth
+ 
+
+ align:start position:0%
+one one negative one is certainly worth
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+try let's test it is if it's an igen
+
+ align:start position:0%
+try let's test it is if it's an igen
+ 
+
+ align:start position:0%
+try let's test it is if it's an igen
+Vector then it should come out in the
+
+ align:start position:0%
+Vector then it should come out in the
+ 
+
+ align:start position:0%
+Vector then it should come out in the
+same direction what do I get when I do
+
+ align:start position:0%
+same direction what do I get when I do
+ 
+
+ align:start position:0%
+same direction what do I get when I do
+that if I do that multiplic
+
+ align:start position:0%
+that if I do that multiplic
+ 
+
+ align:start position:0%
+that if I do that multiplic
+three and I get three and minus three so
+
+ align:start position:0%
+three and I get three and minus three so
+ 
+
+ align:start position:0%
+three and I get three and minus three so
+have we got an igen Vector yep and and
+
+ align:start position:0%
+have we got an igen Vector yep and and
+ 
+
+ align:start position:0%
+have we got an igen Vector yep and and
+what's so if this was Y what is this
+
+ align:start position:0%
+what's so if this was Y what is this
+ 
+
+ align:start position:0%
+what's so if this was Y what is this
+Vector 3 y so there's the other igen
+
+ align:start position:0%
+Vector 3 y so there's the other igen
+ 
+
+ align:start position:0%
+Vector 3 y so there's the other igen
+Vector is one minus one and the other IG
+
+ align:start position:0%
+Vector is one minus one and the other IG
+ 
+
+ align:start position:0%
+Vector is one minus one and the other IG
+value is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three okay so we did it by spotting it
+
+ align:start position:0%
+three okay so we did it by spotting it
+ 
+
+ align:start position:0%
+three okay so we did it by spotting it
+here that's you know mad lab can't do it
+
+ align:start position:0%
+here that's you know mad lab can't do it
+ 
+
+ align:start position:0%
+here that's you know mad lab can't do it
+that way it's got to figure it out but
+
+ align:start position:0%
+that way it's got to figure it out but
+ 
+
+ align:start position:0%
+that way it's got to figure it out but
+we're ahead of mad lab this time okay
+
+ align:start position:0%
+we're ahead of mad lab this time okay
+ 
+
+ align:start position:0%
+we're ahead of mad lab this time okay
+all right so what do I notice what do I
+
+ align:start position:0%
+all right so what do I notice what do I
+ 
+
+ align:start position:0%
+all right so what do I notice what do I
+notice what do I notice about this
+
+ align:start position:0%
+notice what do I notice about this
+ 
+
+ align:start position:0%
+notice what do I notice about this
+Matrix it was
+
+ align:start position:0%
+Matrix it was
+ 
+
+ align:start position:0%
+Matrix it was
+symmetric and what do I notice about the
+
+ align:start position:0%
+symmetric and what do I notice about the
+ 
+
+ align:start position:0%
+symmetric and what do I notice about the
+igen
+
+ align:start position:0%
+igen
+ 
+
+ align:start position:0%
+igen
+vectors if I if I show you those two
+
+ align:start position:0%
+vectors if I if I show you those two
+ 
+
+ align:start position:0%
+vectors if I if I show you those two
+vectors 1 one and 1 minus
+
+ align:start position:0%
+vectors 1 one and 1 minus
+ 
+
+ align:start position:0%
+vectors 1 one and 1 minus
+one what do you see there they're
+
+ align:start position:0%
+one what do you see there they're
+ 
+
+ align:start position:0%
+one what do you see there they're
+orthogonal 1
+
+ align:start position:0%
+orthogonal 1
+ 
+
+ align:start position:0%
+orthogonal 1
+one is orthogonal to one minus
+
+ align:start position:0%
+one is orthogonal to one minus
+ 
+
+ align:start position:0%
+one is orthogonal to one minus
+perpendicular is the same as orthogonal
+
+ align:start position:0%
+perpendicular is the same as orthogonal
+ 
+
+ align:start position:0%
+perpendicular is the same as orthogonal
+the these are
+
+ align:start position:0%
+the these are
+ 
+
+ align:start position:0%
+the these are
+orthogonal perpendicular and and and
+
+ align:start position:0%
+orthogonal perpendicular and and and
+ 
+
+ align:start position:0%
+orthogonal perpendicular and and and
+what let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see I can draw them of course and see
+
+ align:start position:0%
+see I can draw them of course and see
+ 
+
+ align:start position:0%
+see I can draw them of course and see
+that one one will go here's if this is
+
+ align:start position:0%
+that one one will go here's if this is
+ 
+
+ align:start position:0%
+that one one will go here's if this is
+one it'll go here and one so that's 1
+
+ align:start position:0%
+one it'll go here and one so that's 1
+ 
+
+ align:start position:0%
+one it'll go here and one so that's 1
+one and 1 minus one will go there will
+
+ align:start position:0%
+one and 1 minus one will go there will
+ 
+
+ align:start position:0%
+one and 1 minus one will go there will
+go down this will be the other one one
+
+ align:start position:0%
+go down this will be the other one one
+ 
+
+ align:start position:0%
+go down this will be the other one one
+minus one so there's y1 there's Y 2 and
+
+ align:start position:0%
+minus one so there's y1 there's Y 2 and
+ 
+
+ align:start position:0%
+minus one so there's y1 there's Y 2 and
+they are
+
+ align:start position:0%
+they are
+ 
+
+ align:start position:0%
+they are
+perpendicular but of course I don't draw
+
+ align:start position:0%
+perpendicular but of course I don't draw
+ 
+
+ align:start position:0%
+perpendicular but of course I don't draw
+pictures all the time what how do I
+
+ align:start position:0%
+pictures all the time what how do I
+ 
+
+ align:start position:0%
+pictures all the time what how do I
+test what's the test for two vectors
+
+ align:start position:0%
+test what's the test for two vectors
+ 
+
+ align:start position:0%
+test what's the test for two vectors
+being
+
+ align:start position:0%
+being
+ 
+
+ align:start position:0%
+being
+orthogonal the dot product the dot
+
+ align:start position:0%
+orthogonal the dot product the dot
+ 
+
+ align:start position:0%
+orthogonal the dot product the dot
+product the inner product y transpose y1
+
+ align:start position:0%
+product the inner product y transpose y1
+ 
+
+ align:start position:0%
+product the inner product y transpose y1
+transpose
+
+ align:start position:0%
+transpose
+ 
+
+ align:start position:0%
+transpose
+Y2 or do you prefer to write it as y1
+
+ align:start position:0%
+Y2 or do you prefer to write it as y1
+ 
+
+ align:start position:0%
+Y2 or do you prefer to write it as y1
+with a DOT Y
+
+ align:start position:0%
+with a DOT Y
+ 
+
+ align:start position:0%
+with a DOT Y
+2 this one this is maybe better because
+
+ align:start position:0%
+2 this one this is maybe better because
+ 
+
+ align:start position:0%
+2 this one this is maybe better because
+it's Matrix notation and the point is
+
+ align:start position:0%
+it's Matrix notation and the point is
+ 
+
+ align:start position:0%
+it's Matrix notation and the point is
+orthogonal the dotproduct
+
+ align:start position:0%
+orthogonal the dotproduct
+ 
+
+ align:start position:0%
+orthogonal the dotproduct
+is zero right zero okay so that's good
+
+ align:start position:0%
+is zero right zero okay so that's good
+ 
+
+ align:start position:0%
+is zero right zero okay so that's good
+very good in
+
+ align:start position:0%
+very good in
+ 
+
+ align:start position:0%
+very good in
+fact symmet so here's a
+
+ align:start position:0%
+fact symmet so here's a
+ 
+
+ align:start position:0%
+fact symmet so here's a
+very important fact symmetric matrices
+
+ align:start position:0%
+very important fact symmetric matrices
+ 
+
+ align:start position:0%
+very important fact symmetric matrices
+have orthogonal IG
+
+ align:start position:0%
+have orthogonal IG
+ 
+
+ align:start position:0%
+have orthogonal IG
+vectors Sim so igen vectors what I'm
+
+ align:start position:0%
+vectors Sim so igen vectors what I'm
+ 
+
+ align:start position:0%
+vectors Sim so igen vectors what I'm
+trying to say is igen vectors and igen
+
+ align:start position:0%
+trying to say is igen vectors and igen
+ 
+
+ align:start position:0%
+trying to say is igen vectors and igen
+values are like a new way to look at a
+
+ align:start position:0%
+values are like a new way to look at a
+ 
+
+ align:start position:0%
+values are like a new way to look at a
+matrix a new way to see into
+
+ align:start position:0%
+matrix a new way to see into
+ 
+
+ align:start position:0%
+matrix a new way to see into
+it and when the Matrix is symmetric what
+
+ align:start position:0%
+it and when the Matrix is symmetric what
+ 
+
+ align:start position:0%
+it and when the Matrix is symmetric what
+we see is perpendicular igen vectors and
+
+ align:start position:0%
+we see is perpendicular igen vectors and
+ 
+
+ align:start position:0%
+we see is perpendicular igen vectors and
+what comment do you have about the
+
+ align:start position:0%
+what comment do you have about the
+ 
+
+ align:start position:0%
+what comment do you have about the
+values of this symmetric
+
+ align:start position:0%
+values of this symmetric
+ 
+
+ align:start position:0%
+values of this symmetric
+Matrix having remembering what
+
+ align:start position:0%
+Matrix having remembering what
+ 
+
+ align:start position:0%
+Matrix having remembering what
+was on the board for this anti-symmetric
+
+ align:start position:0%
+was on the board for this anti-symmetric
+ 
+
+ align:start position:0%
+was on the board for this anti-symmetric
+Matrix this anti what was the point
+
+ align:start position:0%
+Matrix this anti what was the point
+ 
+
+ align:start position:0%
+Matrix this anti what was the point
+about that anti-symmetric
+
+ align:start position:0%
+about that anti-symmetric
+ 
+
+ align:start position:0%
+about that anti-symmetric
+Matrix its igen values
+
+ align:start position:0%
+Matrix its igen values
+ 
+
+ align:start position:0%
+Matrix its igen values
+were imaginary actually an i there okay
+
+ align:start position:0%
+were imaginary actually an i there okay
+ 
+
+ align:start position:0%
+were imaginary actually an i there okay
+here's the opposite what's the what's
+
+ align:start position:0%
+here's the opposite what's the what's
+ 
+
+ align:start position:0%
+here's the opposite what's the what's
+the property of the igen values for for
+
+ align:start position:0%
+the property of the igen values for for
+ 
+
+ align:start position:0%
+the property of the igen values for for
+a symmetric Matrix that you would just
+
+ align:start position:0%
+a symmetric Matrix that you would just
+ 
+
+ align:start position:0%
+a symmetric Matrix that you would just
+guess they're real they're real
+
+ align:start position:0%
+guess they're real they're real
+ 
+
+ align:start position:0%
+guess they're real they're real
+symmetric matrices are great because
+
+ align:start position:0%
+symmetric matrices are great because
+ 
+
+ align:start position:0%
+symmetric matrices are great because
+they have real igen
+
+ align:start position:0%
+they have real igen
+ 
+
+ align:start position:0%
+they have real igen
+values and they have perpendicular igen
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and uh and actually probably if a matrix
+
+ align:start position:0%
+and uh and actually probably if a matrix
+ 
+
+ align:start position:0%
+and uh and actually probably if a matrix
+has real igen values and perpendicular
+
+ align:start position:0%
+has real igen values and perpendicular
+ 
+
+ align:start position:0%
+has real igen values and perpendicular
+igen vectors it's going to be symmetric
+
+ align:start position:0%
+igen vectors it's going to be symmetric
+ 
+
+ align:start position:0%
+igen vectors it's going to be symmetric
+so s symmetry is a great property and it
+
+ align:start position:0%
+so s symmetry is a great property and it
+ 
+
+ align:start position:0%
+so s symmetry is a great property and it
+shows up in a great way in this real I
+
+ align:start position:0%
+shows up in a great way in this real I
+ 
+
+ align:start position:0%
+shows up in a great way in this real I
+Val real lambdas and orthogonal y's
+
+ align:start position:0%
+Val real lambdas and orthogonal y's
+ 
+
+ align:start position:0%
+Val real lambdas and orthogonal y's
+shows up perfectly in the igen
+
+ align:start position:0%
+shows up perfectly in the igen
+ 
+
+ align:start position:0%
+shows up perfectly in the igen
+picture and let's see I was going to say
+
+ align:start position:0%
+picture and let's see I was going to say
+ 
+
+ align:start position:0%
+picture and let's see I was going to say
+oh yeah another here here's a handy
+
+ align:start position:0%
+oh yeah another here here's a handy
+ 
+
+ align:start position:0%
+oh yeah another here here's a handy
+little check on the igen values to see
+
+ align:start position:0%
+little check on the igen values to see
+ 
+
+ align:start position:0%
+little check on the igen values to see
+if we got it right of course we did I
+
+ align:start position:0%
+if we got it right of course we did I
+ 
+
+ align:start position:0%
+if we got it right of course we did I
+mean that's one and three we can get but
+
+ align:start position:0%
+mean that's one and three we can get but
+ 
+
+ align:start position:0%
+mean that's one and three we can get but
+let me let me just show you two two
+
+ align:start position:0%
+let me let me just show you two two
+ 
+
+ align:start position:0%
+let me let me just show you two two
+useful checks if you haven't seen igen
+
+ align:start position:0%
+useful checks if you haven't seen igen
+ 
+
+ align:start position:0%
+useful checks if you haven't seen igen
+values before if I add the igen
+
+ align:start position:0%
+values before if I add the igen
+ 
+
+ align:start position:0%
+values before if I add the igen
+values what do I get
+
+ align:start position:0%
+values what do I get
+ 
+
+ align:start position:0%
+values what do I get
+four and I compare that with adding down
+
+ align:start position:0%
+four and I compare that with adding down
+ 
+
+ align:start position:0%
+four and I compare that with adding down
+the diagonal of the Matrix two and two
+
+ align:start position:0%
+the diagonal of the Matrix two and two
+ 
+
+ align:start position:0%
+the diagonal of the Matrix two and two
+four and that check always works the sum
+
+ align:start position:0%
+four and that check always works the sum
+ 
+
+ align:start position:0%
+four and that check always works the sum
+of the igen values matches the sum down
+
+ align:start position:0%
+of the igen values matches the sum down
+ 
+
+ align:start position:0%
+of the igen values matches the sum down
+the diagonal so that that's it's like if
+
+ align:start position:0%
+the diagonal so that that's it's like if
+ 
+
+ align:start position:0%
+the diagonal so that that's it's like if
+you only had one if you got all the IG
+
+ align:start position:0%
+you only had one if you got all the IG
+ 
+
+ align:start position:0%
+you only had one if you got all the IG
+values but one that would tell you the
+
+ align:start position:0%
+values but one that would tell you the
+ 
+
+ align:start position:0%
+values but one that would tell you the
+last one because uh the some of the igen
+
+ align:start position:0%
+last one because uh the some of the igen
+ 
+
+ align:start position:0%
+last one because uh the some of the igen
+values matches the sum down the diagonal
+
+ align:start position:0%
+values matches the sum down the diagonal
+ 
+
+ align:start position:0%
+values matches the sum down the diagonal
+that's that's sort of you have no clue
+
+ align:start position:0%
+that's that's sort of you have no clue
+ 
+
+ align:start position:0%
+that's that's sort of you have no clue
+where that comes from but it it's true
+
+ align:start position:0%
+where that comes from but it it's true
+ 
+
+ align:start position:0%
+where that comes from but it it's true
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+another another useful fact if I
+
+ align:start position:0%
+another another useful fact if I
+ 
+
+ align:start position:0%
+another another useful fact if I
+multiply the I values what do I get
+
+ align:start position:0%
+multiply the I values what do I get
+ 
+
+ align:start position:0%
+multiply the I values what do I get
+three and now where do you see a three
+
+ align:start position:0%
+three and now where do you see a three
+ 
+
+ align:start position:0%
+three and now where do you see a three
+over here
+
+ align:start position:0%
+over here
+ 
+
+ align:start position:0%
+over here
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+determinant 4 minus one 3 so let me can
+
+ align:start position:0%
+determinant 4 minus one 3 so let me can
+ 
+
+ align:start position:0%
+determinant 4 minus one 3 so let me can
+I just write those two facts with no
+
+ align:start position:0%
+I just write those two facts with no
+ 
+
+ align:start position:0%
+I just write those two facts with no
+with no idea of proof the sum of the
+
+ align:start position:0%
+with no idea of proof the sum of the
+ 
+
+ align:start position:0%
+with no idea of proof the sum of the
+lambdas can I just I could write
+
+ align:start position:0%
+lambdas can I just I could write
+ 
+
+ align:start position:0%
+lambdas can I just I could write
+suum sum of this is for any Matrix the
+
+ align:start position:0%
+suum sum of this is for any Matrix the
+ 
+
+ align:start position:0%
+suum sum of this is for any Matrix the
+sum of the lambdas is equal to this the
+
+ align:start position:0%
+sum of the lambdas is equal to this the
+ 
+
+ align:start position:0%
+sum of the lambdas is equal to this the
+the it's called the trace of the
+
+ align:start position:0%
+the it's called the trace of the
+ 
+
+ align:start position:0%
+the it's called the trace of the
+Matrix the trace of the Matrix is the
+
+ align:start position:0%
+Matrix the trace of the Matrix is the
+ 
+
+ align:start position:0%
+Matrix the trace of the Matrix is the
+sum down the
+
+ align:start position:0%
+sum down the
+ 
+
+ align:start position:0%
+sum down the
+diagonal and the product of the
+
+ align:start position:0%
+diagonal and the product of the
+ 
+
+ align:start position:0%
+diagonal and the product of the
+lambdas L Lambda 1 * Lambda 2 is the
+
+ align:start position:0%
+lambdas L Lambda 1 * Lambda 2 is the
+ 
+
+ align:start position:0%
+lambdas L Lambda 1 * Lambda 2 is the
+determinant of the Matrix or if I had 10
+
+ align:start position:0%
+determinant of the Matrix or if I had 10
+ 
+
+ align:start position:0%
+determinant of the Matrix or if I had 10
+IG values I would multiply all 10 and
+
+ align:start position:0%
+IG values I would multiply all 10 and
+ 
+
+ align:start position:0%
+IG values I would multiply all 10 and
+I'd get the determinant
+
+ align:start position:0%
+I'd get the determinant
+ 
+
+ align:start position:0%
+I'd get the determinant
+okay okay so that's
+
+ align:start position:0%
+okay okay so that's
+ 
+
+ align:start position:0%
+okay okay so that's
+some facts about I values there's more
+
+ align:start position:0%
+some facts about I values there's more
+ 
+
+ align:start position:0%
+some facts about I values there's more
+of course in section
+
+ align:start position:0%
+of course in section
+ 
+
+ align:start position:0%
+of course in section
+1.5 uh about how you would find I values
+
+ align:start position:0%
+1.5 uh about how you would find I values
+ 
+
+ align:start position:0%
+1.5 uh about how you would find I values
+and how you would use
+
+ align:start position:0%
+and how you would use
+ 
+
+ align:start position:0%
+and how you would use
+them yeah yeah all right so we've got
+
+ align:start position:0%
+them yeah yeah all right so we've got
+ 
+
+ align:start position:0%
+them yeah yeah all right so we've got
+that's of course the key point is how
+
+ align:start position:0%
+that's of course the key point is how
+ 
+
+ align:start position:0%
+that's of course the key point is how
+would we use them oh let me let me uh
+
+ align:start position:0%
+would we use them oh let me let me uh
+ 
+
+ align:start position:0%
+would we use them oh let me let me uh
+say something more about that how to use
+
+ align:start position:0%
+say something more about that how to use
+ 
+
+ align:start position:0%
+say something more about that how to use
+I okay suppose I have this system of a
+
+ align:start position:0%
+I okay suppose I have this system of a
+ 
+
+ align:start position:0%
+I okay suppose I have this system of a
+thousand differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations okay linear constant
+
+ align:start position:0%
+equations okay linear constant
+ 
+
+ align:start position:0%
+equations okay linear constant
+coefficients starts from some
+
+ align:start position:0%
+coefficients starts from some
+ 
+
+ align:start position:0%
+coefficients starts from some
+U of
+
+ align:start position:0%
+U of
+ 
+
+ align:start position:0%
+U of
+zero okay all
+
+ align:start position:0%
+zero okay all
+ 
+
+ align:start position:0%
+zero okay all
+right how can how do igen values and IG
+
+ align:start position:0%
+right how can how do igen values and IG
+ 
+
+ align:start position:0%
+right how can how do igen values and IG
+vectors help well first I have to find
+
+ align:start position:0%
+vectors help well first I have to find
+ 
+
+ align:start position:0%
+vectors help well first I have to find
+them that's the job so suppose I find a
+
+ align:start position:0%
+them that's the job so suppose I find a
+ 
+
+ align:start position:0%
+them that's the job so suppose I find a
+th igen values and I vectors A
+
+ align:start position:0%
+th igen values and I vectors A
+ 
+
+ align:start position:0%
+th igen values and I vectors A
+times I Vector number I is I value
+
+ align:start position:0%
+times I Vector number I is I value
+ 
+
+ align:start position:0%
+times I Vector number I is I value
+number I times I Vector number I so
+
+ align:start position:0%
+number I times I Vector number I so
+ 
+
+ align:start position:0%
+number I times I Vector number I so
+these y1 to Y a000 so y1 to Y a000 are
+
+ align:start position:0%
+these y1 to Y a000 so y1 to Y a000 are
+ 
+
+ align:start position:0%
+these y1 to Y a000 so y1 to Y a000 are
+the igen
+
+ align:start position:0%
+the igen
+ 
+
+ align:start position:0%
+the igen
+vectors and each one has its own igen
+
+ align:start position:0%
+vectors and each one has its own igen
+ 
+
+ align:start position:0%
+vectors and each one has its own igen
+value Lambda 1 to Lambda
+
+ align:start position:0%
+value Lambda 1 to Lambda
+ 
+
+ align:start position:0%
+value Lambda 1 to Lambda
+th000 and
+
+ align:start position:0%
+th000 and
+ 
+
+ align:start position:0%
+th000 and
+now if I did that work sort of like in
+
+ align:start position:0%
+now if I did that work sort of like in
+ 
+
+ align:start position:0%
+now if I did that work sort of like in
+advance now I come to the differential
+
+ align:start position:0%
+advance now I come to the differential
+ 
+
+ align:start position:0%
+advance now I come to the differential
+equation how could I use
+
+ align:start position:0%
+equation how could I use
+ 
+
+ align:start position:0%
+equation how could I use
+this it's it's a the probably this is
+
+ align:start position:0%
+this it's it's a the probably this is
+ 
+
+ align:start position:0%
+this it's it's a the probably this is
+now going to be the most the the
+
+ align:start position:0%
+now going to be the most the the
+ 
+
+ align:start position:0%
+now going to be the most the the
+constant three step it's it's three
+
+ align:start position:0%
+constant three step it's it's three
+ 
+
+ align:start position:0%
+constant three step it's it's three
+steps to use it three steps to use these
+
+ align:start position:0%
+steps to use it three steps to use these
+ 
+
+ align:start position:0%
+steps to use it three steps to use these
+to get the
+
+ align:start position:0%
+to get the
+ 
+
+ align:start position:0%
+to get the
+answer okay ready for step one step one
+
+ align:start position:0%
+answer okay ready for step one step one
+ 
+
+ align:start position:0%
+answer okay ready for step one step one
+is Step One is break you not into igen
+
+ align:start position:0%
+is Step One is break you not into igen
+ 
+
+ align:start position:0%
+is Step One is break you not into igen
+vectors split separate write Express U
+
+ align:start position:0%
+vectors split separate write Express U
+ 
+
+ align:start position:0%
+vectors split separate write Express U
+of zero as a combination of igen vectors
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay now step
+
+ align:start position:0%
+okay now step
+ 
+
+ align:start position:0%
+okay now step
+two what happens to each igen Vector so
+
+ align:start position:0%
+two what happens to each igen Vector so
+ 
+
+ align:start position:0%
+two what happens to each igen Vector so
+this is where the differential equation
+
+ align:start position:0%
+this is where the differential equation
+ 
+
+ align:start position:0%
+this is where the differential equation
+starts from this is the the initial
+
+ align:start position:0%
+starts from this is the the initial
+ 
+
+ align:start position:0%
+starts from this is the the initial
+condition a th components of U at the
+
+ align:start position:0%
+condition a th components of U at the
+ 
+
+ align:start position:0%
+condition a th components of U at the
+start and it's separated into a
+
+ align:start position:0%
+start and it's separated into a
+ 
+
+ align:start position:0%
+start and it's separated into a
+thousand igen Vector pieces now step two
+
+ align:start position:0%
+thousand igen Vector pieces now step two
+ 
+
+ align:start position:0%
+thousand igen Vector pieces now step two
+is watch each h p separately so step two
+
+ align:start position:0%
+is watch each h p separately so step two
+ 
+
+ align:start position:0%
+is watch each h p separately so step two
+will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+multiply say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+C1 by e to the Lambda 1 T by its its
+
+ align:start position:0%
+C1 by e to the Lambda 1 T by its its
+ 
+
+ align:start position:0%
+C1 by e to the Lambda 1 T by its its
+growth this is following igen Vector
+
+ align:start position:0%
+growth this is following igen Vector
+ 
+
+ align:start position:0%
+growth this is following igen Vector
+number one and in general I would
+
+ align:start position:0%
+number one and in general I would
+ 
+
+ align:start position:0%
+number one and in general I would
+multiply every one of the C's by e to
+
+ align:start position:0%
+multiply every one of the C's by e to
+ 
+
+ align:start position:0%
+multiply every one of the C's by e to
+the those guys so what would I have now
+
+ align:start position:0%
+the those guys so what would I have now
+ 
+
+ align:start position:0%
+the those guys so what would I have now
+this is where this is this is one piece
+
+ align:start position:0%
+this is where this is this is one piece
+ 
+
+ align:start position:0%
+this is where this is this is one piece
+of the start and that gives me one piece
+
+ align:start position:0%
+of the start and that gives me one piece
+ 
+
+ align:start position:0%
+of the start and that gives me one piece
+of the of the finish so the FI the
+
+ align:start position:0%
+of the of the finish so the FI the
+ 
+
+ align:start position:0%
+of the of the finish so the FI the
+Finish is the
+
+ align:start position:0%
+Finish is the
+ 
+
+ align:start position:0%
+Finish is the
+answer is to add
+
+ align:start position:0%
+answer is to add
+ 
+
+ align:start position:0%
+answer is to add
+up the thousand
+
+ align:start position:0%
+up the thousand
+ 
+
+ align:start position:0%
+up the thousand
+pieces and if you're with me you see
+
+ align:start position:0%
+pieces and if you're with me you see
+ 
+
+ align:start position:0%
+pieces and if you're with me you see
+what those thousand pieces
+
+ align:start position:0%
+what those thousand pieces
+ 
+
+ align:start position:0%
+what those thousand pieces
+are here's a piece some multiple of the
+
+ align:start position:0%
+are here's a piece some multiple of the
+ 
+
+ align:start position:0%
+are here's a piece some multiple of the
+first igen Vector now if we only were
+
+ align:start position:0%
+first igen Vector now if we only were
+ 
+
+ align:start position:0%
+first igen Vector now if we only were
+working with that piece we follow it in
+
+ align:start position:0%
+working with that piece we follow it in
+ 
+
+ align:start position:0%
+working with that piece we follow it in
+time by multiplying it by e to the
+
+ align:start position:0%
+time by multiplying it by e to the
+ 
+
+ align:start position:0%
+time by multiplying it by e to the
+Lambda 1 T and what do we have at a
+
+ align:start position:0%
+Lambda 1 T and what do we have at a
+ 
+
+ align:start position:0%
+Lambda 1 T and what do we have at a
+later
+
+ align:start position:0%
+later
+ 
+
+ align:start position:0%
+later
+time C1 e to the Lambda 1 T y1 that's
+
+ align:start position:0%
+time C1 e to the Lambda 1 T y1 that's
+ 
+
+ align:start position:0%
+time C1 e to the Lambda 1 T y1 that's
+what this piece has this piece has grown
+
+ align:start position:0%
+what this piece has this piece has grown
+ 
+
+ align:start position:0%
+what this piece has this piece has grown
+into
+
+ align:start position:0%
+into
+ 
+
+ align:start position:0%
+into
+that and other pieces have grown into
+
+ align:start position:0%
+that and other pieces have grown into
+ 
+
+ align:start position:0%
+that and other pieces have grown into
+other things and what about the last
+
+ align:start position:0%
+other things and what about the last
+ 
+
+ align:start position:0%
+other things and what about the last
+piece so what does
+
+ align:start position:0%
+piece so what does
+ 
+
+ align:start position:0%
+piece so what does
+this what is it that I have to add up
+
+ align:start position:0%
+this what is it that I have to add up
+ 
+
+ align:start position:0%
+this what is it that I have to add up
+tell me what to write here c1000
+
+ align:start position:0%
+tell me what to write here c1000
+ 
+
+ align:start position:0%
+tell me what to write here c1000
+whatever that Co however much of igen
+
+ align:start position:0%
+whatever that Co however much of igen
+ 
+
+ align:start position:0%
+whatever that Co however much of igen
+vector 1,000 was in
+
+ align:start position:0%
+vector 1,000 was in
+ 
+
+ align:start position:0%
+vector 1,000 was in
+there and then
+
+ align:start position:0%
+there and then
+ 
+
+ align:start position:0%
+there and then
+finally never written left-handed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before e to the e to the
+
+ align:start position:0%
+before e to the e to the
+ 
+
+ align:start position:0%
+before e to the e to the
+who Lambda number 1,000 not 1,000 itself
+
+ align:start position:0%
+who Lambda number 1,000 not 1,000 itself
+ 
+
+ align:start position:0%
+who Lambda number 1,000 not 1,000 itself
+but the one its igen value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1,t this is just splitting this is
+
+ align:start position:0%
+1,t this is just splitting this is
+ 
+
+ align:start position:0%
+1,t this is just splitting this is
+constantly constantly uh the method the
+
+ align:start position:0%
+constantly constantly uh the method the
+ 
+
+ align:start position:0%
+constantly constantly uh the method the
+way to use igen values and igen vectors
+
+ align:start position:0%
+way to use igen values and igen vectors
+ 
+
+ align:start position:0%
+way to use igen values and igen vectors
+split the split the problem into the
+
+ align:start position:0%
+split the split the problem into the
+ 
+
+ align:start position:0%
+split the split the problem into the
+pieces that go that that are I vectors
+
+ align:start position:0%
+pieces that go that that are I vectors
+ 
+
+ align:start position:0%
+pieces that go that that are I vectors
+watch each piece add up the add up the
+
+ align:start position:0%
+watch each piece add up the add up the
+ 
+
+ align:start position:0%
+watch each piece add up the add up the
+pieces yeah that that's the that's why
+
+ align:start position:0%
+pieces yeah that that's the that's why
+ 
+
+ align:start position:0%
+pieces yeah that that's the that's why
+ion vectors are so important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah yes
+
+ align:start position:0%
+yeah yes
+ 
+
+ align:start position:0%
+yeah yes
+right well now very good
+
+ align:start position:0%
+right well now very good
+ 
+
+ align:start position:0%
+right well now very good
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+um let's see well the first thing we
+
+ align:start position:0%
+um let's see well the first thing we
+ 
+
+ align:start position:0%
+um let's see well the first thing we
+have to know is that we do find a
+
+ align:start position:0%
+have to know is that we do find a
+ 
+
+ align:start position:0%
+have to know is that we do find a
+thousand I
+
+ align:start position:0%
+thousand I
+ 
+
+ align:start position:0%
+thousand I
+vectors and So my answer is going to be
+
+ align:start position:0%
+vectors and So my answer is going to be
+ 
+
+ align:start position:0%
+vectors and So my answer is going to be
+for symmetric matrices everything always
+
+ align:start position:0%
+for symmetric matrices everything always
+ 
+
+ align:start position:0%
+for symmetric matrices everything always
+works for symmetric matrices if they
+
+ align:start position:0%
+works for symmetric matrices if they
+ 
+
+ align:start position:0%
+works for symmetric matrices if they
+size is a th000 they have a th000 i
+
+ align:start position:0%
+size is a th000 they have a th000 i
+ 
+
+ align:start position:0%
+size is a th000 they have a th000 i
+vector
+
+ align:start position:0%
+vector
+ 
+
+ align:start position:0%
+vector
+and next time we'll have a shot at some
+
+ align:start position:0%
+and next time we'll have a shot at some
+ 
+
+ align:start position:0%
+and next time we'll have a shot at some
+of these some what some of them are for
+
+ align:start position:0%
+of these some what some of them are for
+ 
+
+ align:start position:0%
+of these some what some of them are for
+these special
+
+ align:start position:0%
+these special
+ 
+
+ align:start position:0%
+these special
+matrices so this method always works if
+
+ align:start position:0%
+matrices so this method always works if
+ 
+
+ align:start position:0%
+matrices so this method always works if
+I've got a full family of independent
+
+ align:start position:0%
+I've got a full family of independent
+ 
+
+ align:start position:0%
+I've got a full family of independent
+igen vectors if it's of size a thousand
+
+ align:start position:0%
+igen vectors if it's of size a thousand
+ 
+
+ align:start position:0%
+igen vectors if it's of size a thousand
+I need you're right exactly right to see
+
+ align:start position:0%
+I need you're right exactly right to see
+ 
+
+ align:start position:0%
+I need you're right exactly right to see
+that this was the this was the the the
+
+ align:start position:0%
+that this was the this was the the the
+ 
+
+ align:start position:0%
+that this was the this was the the the
+questionable step if I haven't got a
+
+ align:start position:0%
+questionable step if I haven't got a
+ 
+
+ align:start position:0%
+questionable step if I haven't got a
+thousand I vectors I I'm not going to be
+
+ align:start position:0%
+thousand I vectors I I'm not going to be
+ 
+
+ align:start position:0%
+thousand I vectors I I'm not going to be
+able to take take that step and it
+
+ align:start position:0%
+able to take take that step and it
+ 
+
+ align:start position:0%
+able to take take that step and it
+happens I am sad to report that some
+
+ align:start position:0%
+happens I am sad to report that some
+ 
+
+ align:start position:0%
+happens I am sad to report that some
+matricies haven't got enough ion vectors
+
+ align:start position:0%
+matricies haven't got enough ion vectors
+ 
+
+ align:start position:0%
+matricies haven't got enough ion vectors
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+matrices they they get collapse you know
+
+ align:start position:0%
+matrices they they get collapse you know
+ 
+
+ align:start position:0%
+matrices they they get collapse you know
+this often always happens in in math
+
+ align:start position:0%
+this often always happens in in math
+ 
+
+ align:start position:0%
+this often always happens in in math
+somehow two igen vectors collapse into
+
+ align:start position:0%
+somehow two igen vectors collapse into
+ 
+
+ align:start position:0%
+somehow two igen vectors collapse into
+one and the Matrix is
+
+ align:start position:0%
+one and the Matrix is
+ 
+
+ align:start position:0%
+one and the Matrix is
+defective like it's a loser okay so now
+
+ align:start position:0%
+defective like it's a loser okay so now
+ 
+
+ align:start position:0%
+defective like it's a loser okay so now
+you have to of course this the equation
+
+ align:start position:0%
+you have to of course this the equation
+ 
+
+ align:start position:0%
+you have to of course this the equation
+still has a
+
+ align:start position:0%
+still has a
+ 
+
+ align:start position:0%
+still has a
+solution so there has to be something
+
+ align:start position:0%
+solution so there has to be something
+ 
+
+ align:start position:0%
+solution so there has to be something
+there but the IG ve the pure igen Vector
+
+ align:start position:0%
+there but the IG ve the pure igen Vector
+ 
+
+ align:start position:0%
+there but the IG ve the pure igen Vector
+method is not going to make it on those
+
+ align:start position:0%
+method is not going to make it on those
+ 
+
+ align:start position:0%
+method is not going to make it on those
+special matrices I could write down one
+
+ align:start position:0%
+special matrices I could write down one
+ 
+
+ align:start position:0%
+special matrices I could write down one
+but why should we give space to a loser
+
+ align:start position:0%
+but why should we give space to a loser
+ 
+
+ align:start position:0%
+but why should we give space to a loser
+okay so but what what what happens in
+
+ align:start position:0%
+okay so but what what what happens in
+ 
+
+ align:start position:0%
+okay so but what what what happens in
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+case you might remember from
+
+ align:start position:0%
+case you might remember from
+ 
+
+ align:start position:0%
+case you might remember from
+differential equations when two of these
+
+ align:start position:0%
+differential equations when two of these
+ 
+
+ align:start position:0%
+differential equations when two of these
+roots
+
+ align:start position:0%
+roots
+ 
+
+ align:start position:0%
+roots
+these are like Roots these lambdas are
+
+ align:start position:0%
+these are like Roots these lambdas are
+ 
+
+ align:start position:0%
+these are like Roots these lambdas are
+like roots that you found in solving a
+
+ align:start position:0%
+like roots that you found in solving a
+ 
+
+ align:start position:0%
+like roots that you found in solving a
+differential equation when two of them
+
+ align:start position:0%
+differential equation when two of them
+ 
+
+ align:start position:0%
+differential equation when two of them
+come together that's when the danger is
+
+ align:start position:0%
+come together that's when the danger is
+ 
+
+ align:start position:0%
+come together that's when the danger is
+when when I have a double ion value then
+
+ align:start position:0%
+when when I have a double ion value then
+ 
+
+ align:start position:0%
+when when I have a double ion value then
+there's a high risk that I've only got
+
+ align:start position:0%
+there's a high risk that I've only got
+ 
+
+ align:start position:0%
+there's a high risk that I've only got
+one IG vector and I I'll just put in
+
+ align:start position:0%
+one IG vector and I I'll just put in
+ 
+
+ align:start position:0%
+one IG vector and I I'll just put in
+this little thing what what the other so
+
+ align:start position:0%
+this little thing what what the other so
+ 
+
+ align:start position:0%
+this little thing what what the other so
+the e to the Lambda 1 T is fine but if
+
+ align:start position:0%
+the e to the Lambda 1 T is fine but if
+ 
+
+ align:start position:0%
+the e to the Lambda 1 T is fine but if
+that y1 is like
+
+ align:start position:0%
+that y1 is like
+ 
+
+ align:start position:0%
+that y1 is like
+if the Lambda one's in there twice I
+
+ align:start position:0%
+if the Lambda one's in there twice I
+ 
+
+ align:start position:0%
+if the Lambda one's in there twice I
+need something new and the new one you
+
+ align:start position:0%
+need something new and the new one you
+ 
+
+ align:start position:0%
+need something new and the new one you
+the new thing turns out to be t e the
+
+ align:start position:0%
+the new thing turns out to be t e the
+ 
+
+ align:start position:0%
+the new thing turns out to be t e the
+Lambda
+
+ align:start position:0%
+Lambda
+ 
+
+ align:start position:0%
+Lambda
+T does I don't know if anybody remembers
+
+ align:start position:0%
+T does I don't know if anybody remembers
+ 
+
+ align:start position:0%
+T does I don't know if anybody remembers
+this was probably hammered back in
+
+ align:start position:0%
+this was probably hammered back in
+ 
+
+ align:start position:0%
+this was probably hammered back in
+differential equations that if you had
+
+ align:start position:0%
+differential equations that if you had
+ 
+
+ align:start position:0%
+differential equations that if you had
+repeated something or other then this
+
+ align:start position:0%
+repeated something or other then this
+ 
+
+ align:start position:0%
+repeated something or other then this
+you you didn't get pure e to the Lambda
+
+ align:start position:0%
+you you didn't get pure e to the Lambda
+ 
+
+ align:start position:0%
+you you didn't get pure e to the Lambda
+T's you got also a t to the Lambda T
+
+ align:start position:0%
+T's you got also a t to the Lambda T
+ 
+
+ align:start position:0%
+T's you got also a t to the Lambda T
+anyway that's the answer that's that if
+
+ align:start position:0%
+anyway that's the answer that's that if
+ 
+
+ align:start position:0%
+anyway that's the answer that's that if
+we're short I vectors and it can happen
+
+ align:start position:0%
+we're short I vectors and it can happen
+ 
+
+ align:start position:0%
+we're short I vectors and it can happen
+but it won't for our good matrices okay
+
+ align:start position:0%
+but it won't for our good matrices okay
+ 
+
+ align:start position:0%
+but it won't for our good matrices okay
+so Monday I've got lots to
+
+ align:start position:0%
+so Monday I've got lots to
+ 
+
+ align:start position:0%
+so Monday I've got lots to
+do special Ian values and vectors and
+
+ align:start position:0%
+do special Ian values and vectors and
+ 
+
+ align:start position:0%
+do special Ian values and vectors and
+then positive definite
\ No newline at end of file
diff --git a/hBG7nMXTOcw.txt b/hBG7nMXTOcw.txt
new file mode 100644
index 0000000000000000000000000000000000000000..529039eec5febd11d2052ef3a38632be49efe51f
--- /dev/null
+++ b/hBG7nMXTOcw.txt
@@ -0,0 +1,11427 @@
+align:start position:0%
+ 
+just the last year the sharp projection
+
+ align:start position:0%
+just the last year the sharp projection
+ 
+
+ align:start position:0%
+just the last year the sharp projection
+theorem in R2 was was proven and um the
+
+ align:start position:0%
+theorem in R2 was was proven and um the
+ 
+
+ align:start position:0%
+theorem in R2 was was proven and um the
+proof is is fairly big. It's fairly
+
+ align:start position:0%
+proof is is fairly big. It's fairly
+ 
+
+ align:start position:0%
+proof is is fairly big. It's fairly
+complicated but for the last three
+
+ align:start position:0%
+complicated but for the last three
+ 
+
+ align:start position:0%
+complicated but for the last three
+classes um I'm going to want to circle
+
+ align:start position:0%
+classes um I'm going to want to circle
+ 
+
+ align:start position:0%
+classes um I'm going to want to circle
+back to that and talk about the new
+
+ align:start position:0%
+back to that and talk about the new
+ 
+
+ align:start position:0%
+back to that and talk about the new
+ideas in that proof.
+
+ align:start position:0%
+ideas in that proof.
+ 
+
+ align:start position:0%
+ideas in that proof.
+So it's been a while since we talked
+
+ align:start position:0%
+So it's been a while since we talked
+ 
+
+ align:start position:0%
+So it's been a while since we talked
+about it. So I thought we could start by
+
+ align:start position:0%
+about it. So I thought we could start by
+ 
+
+ align:start position:0%
+about it. So I thought we could start by
+by we'll start just by writing down what
+
+ align:start position:0%
+by we'll start just by writing down what
+ 
+
+ align:start position:0%
+by we'll start just by writing down what
+is the statement.
+
+ align:start position:0%
+is the statement.
+ 
+
+ align:start position:0%
+is the statement.
+Um okay so this projection theory I I
+
+ align:start position:0%
+Um okay so this projection theory I I
+ 
+
+ align:start position:0%
+Um okay so this projection theory I I
+like to think of it as a um geometric
+
+ align:start position:0%
+like to think of it as a um geometric
+ 
+
+ align:start position:0%
+like to think of it as a um geometric
+measure theory analog of the sum troder
+
+ align:start position:0%
+measure theory analog of the sum troder
+ 
+
+ align:start position:0%
+measure theory analog of the sum troder
+theorem. So I'm going to start by
+
+ align:start position:0%
+theorem. So I'm going to start by
+ 
+
+ align:start position:0%
+theorem. So I'm going to start by
+writing down the summary TH
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+start by writing down summary try
+
+ align:start position:0%
+start by writing down summary try
+ 
+
+ align:start position:0%
+start by writing down summary try
+and there are a bunch of different
+
+ align:start position:0%
+and there are a bunch of different
+ 
+
+ align:start position:0%
+and there are a bunch of different
+versions and we have I've picked out a
+
+ align:start position:0%
+versions and we have I've picked out a
+ 
+
+ align:start position:0%
+versions and we have I've picked out a
+particular version that sort of fits
+
+ align:start position:0%
+particular version that sort of fits
+ 
+
+ align:start position:0%
+particular version that sort of fits
+into the way the proof is going to go
+
+ align:start position:0%
+into the way the proof is going to go
+ 
+
+ align:start position:0%
+into the way the proof is going to go
+for this sharp projection theorem. Um
+
+ align:start position:0%
+for this sharp projection theorem. Um
+ 
+
+ align:start position:0%
+for this sharp projection theorem. Um
+okay so it says the following thing. So
+
+ align:start position:0%
+okay so it says the following thing. So
+ 
+
+ align:start position:0%
+okay so it says the following thing. So
+if E is a finite subset of R2
+
+ align:start position:0%
+if E is a finite subset of R2
+ 
+
+ align:start position:0%
+if E is a finite subset of R2
+um and then L is a set of lines
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or let's say it this way for every X in
+
+ align:start position:0%
+or let's say it this way for every X in
+ 
+
+ align:start position:0%
+or let's say it this way for every X in
+E we'll have L X E is a set of S lines
+
+ align:start position:0%
+E we'll have L X E is a set of S lines
+ 
+
+ align:start position:0%
+E we'll have L X E is a set of S lines
+that go through X and L uh is the union
+
+ align:start position:0%
+that go through X and L uh is the union
+ 
+
+ align:start position:0%
+that go through X and L uh is the union
+over x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we don't need this.
+
+ align:start position:0%
+we don't need this.
+ 
+
+ align:start position:0%
+we don't need this.
+So this set of lines L there's at least
+
+ align:start position:0%
+So this set of lines L there's at least
+ 
+
+ align:start position:0%
+So this set of lines L there's at least
+s of them through every point of e.
+
+ align:start position:0%
+s of them through every point of e.
+ 
+
+ align:start position:0%
+s of them through every point of e.
+Okay. Um so then conclusion is that the
+
+ align:start position:0%
+Okay. Um so then conclusion is that the
+ 
+
+ align:start position:0%
+Okay. Um so then conclusion is that the
+number of lines is at least the minimum
+
+ align:start position:0%
+number of lines is at least the minimum
+ 
+
+ align:start position:0%
+number of lines is at least the minimum
+of a couple of options. There's the size
+
+ align:start position:0%
+of a couple of options. There's the size
+ 
+
+ align:start position:0%
+of a couple of options. There's the size
+of E time S or there's the size of E to
+
+ align:start position:0%
+of E time S or there's the size of E to
+ 
+
+ align:start position:0%
+of E time S or there's the size of E to
+the 12 S to the three halfves. We'll
+
+ align:start position:0%
+the 12 S to the three halfves. We'll
+ 
+
+ align:start position:0%
+the 12 S to the three halfves. We'll
+call this um option A and option B.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, option A. It's very simple to
+
+ align:start position:0%
+Okay, option A. It's very simple to
+ 
+
+ align:start position:0%
+Okay, option A. It's very simple to
+imagine how this could arise. I have a
+
+ align:start position:0%
+imagine how this could arise. I have a
+ 
+
+ align:start position:0%
+imagine how this could arise. I have a
+bunch of points I set E and for each
+
+ align:start position:0%
+bunch of points I set E and for each
+ 
+
+ align:start position:0%
+bunch of points I set E and for each
+point I have S lines through it and
+
+ align:start position:0%
+point I have S lines through it and
+ 
+
+ align:start position:0%
+point I have S lines through it and
+they're just all different from each
+
+ align:start position:0%
+they're just all different from each
+ 
+
+ align:start position:0%
+they're just all different from each
+other. So I get E * S lex.
+
+ align:start position:0%
+other. So I get E * S lex.
+ 
+
+ align:start position:0%
+other. So I get E * S lex.
+Okay, option B
+
+ align:start position:0%
+Okay, option B
+ 
+
+ align:start position:0%
+Okay, option B
+is more more special, more remarkable,
+
+ align:start position:0%
+is more more special, more remarkable,
+ 
+
+ align:start position:0%
+is more more special, more remarkable,
+although not not that complicated. It's
+
+ align:start position:0%
+although not not that complicated. It's
+ 
+
+ align:start position:0%
+although not not that complicated. It's
+an integer grid and we talked about it a
+
+ align:start position:0%
+an integer grid and we talked about it a
+ 
+
+ align:start position:0%
+an integer grid and we talked about it a
+couple times in the beginning of the
+
+ align:start position:0%
+couple times in the beginning of the
+ 
+
+ align:start position:0%
+couple times in the beginning of the
+class.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So in the integer grid
+
+ align:start position:0%
+Okay. So in the integer grid
+ 
+
+ align:start position:0%
+Okay. So in the integer grid
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+some sense.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we might have a lot of lines through
+
+ align:start position:0%
+So we might have a lot of lines through
+ 
+
+ align:start position:0%
+So we might have a lot of lines through
+each point but still each line is going
+
+ align:start position:0%
+each point but still each line is going
+ 
+
+ align:start position:0%
+each point but still each line is going
+through many points. So the total number
+
+ align:start position:0%
+through many points. So the total number
+ 
+
+ align:start position:0%
+through many points. So the total number
+of lines is a lot less than E * S. And
+
+ align:start position:0%
+of lines is a lot less than E * S. And
+ 
+
+ align:start position:0%
+of lines is a lot less than E * S. And
+if you work it out you get this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that's the semir trotder
+
+ align:start position:0%
+Okay. So that's the semir trotder
+ 
+
+ align:start position:0%
+Okay. So that's the semir trotder
+theorem. Um, we saw early on that it
+
+ align:start position:0%
+theorem. Um, we saw early on that it
+ 
+
+ align:start position:0%
+theorem. Um, we saw early on that it
+implies a sharp projection theorem for
+
+ align:start position:0%
+implies a sharp projection theorem for
+ 
+
+ align:start position:0%
+implies a sharp projection theorem for
+finite sets in R2. And we're going to
+
+ align:start position:0%
+finite sets in R2. And we're going to
+ 
+
+ align:start position:0%
+finite sets in R2. And we're going to
+try to do some analog for like delta
+
+ align:start position:0%
+try to do some analog for like delta
+ 
+
+ align:start position:0%
+try to do some analog for like delta
+balls in R2.
+
+ align:start position:0%
+balls in R2.
+ 
+
+ align:start position:0%
+balls in R2.
+Okay, when we talk about delta balls, it
+
+ align:start position:0%
+Okay, when we talk about delta balls, it
+ 
+
+ align:start position:0%
+Okay, when we talk about delta balls, it
+matters how they're spaced. And the
+
+ align:start position:0%
+matters how they're spaced. And the
+ 
+
+ align:start position:0%
+matters how they're spaced. And the
+spacing condition we're going to talk
+
+ align:start position:0%
+spacing condition we're going to talk
+ 
+
+ align:start position:0%
+spacing condition we're going to talk
+about is the one that Pablo introduced,
+
+ align:start position:0%
+about is the one that Pablo introduced,
+ 
+
+ align:start position:0%
+about is the one that Pablo introduced,
+the delta SC condition. So I make a
+
+ align:start position:0%
+the delta SC condition. So I make a
+ 
+
+ align:start position:0%
+the delta SC condition. So I make a
+definition.
+
+ align:start position:0%
+definition.
+ 
+
+ align:start position:0%
+definition.
+So uh, if um, E is a subset of R to the
+
+ align:start position:0%
+So uh, if um, E is a subset of R to the
+ 
+
+ align:start position:0%
+So uh, if um, E is a subset of R to the
+D Let me say that E is delta S C F. Um,
+
+ align:start position:0%
+D Let me say that E is delta S C F. Um,
+ 
+
+ align:start position:0%
+D Let me say that E is delta S C F. Um,
+okay. So, first of all, I'm going to
+
+ align:start position:0%
+okay. So, first of all, I'm going to
+ 
+
+ align:start position:0%
+okay. So, first of all, I'm going to
+imagine here that E is contained in a
+
+ align:start position:0%
+imagine here that E is contained in a
+ 
+
+ align:start position:0%
+imagine here that E is contained in a
+unit ball
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or almost unit ball. Okay. And then um
+
+ align:start position:0%
+or almost unit ball. Okay. And then um
+ 
+
+ align:start position:0%
+or almost unit ball. Okay. And then um
+if you take E and you intersect it with
+
+ align:start position:0%
+if you take E and you intersect it with
+ 
+
+ align:start position:0%
+if you take E and you intersect it with
+a smaller ball,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's basically a new ball. If you take E
+
+ align:start position:0%
+it's basically a new ball. If you take E
+ 
+
+ align:start position:0%
+it's basically a new ball. If you take E
+and you intersect it with a smaller ball
+
+ align:start position:0%
+and you intersect it with a smaller ball
+ 
+
+ align:start position:0%
+and you intersect it with a smaller ball
+and take the delta covering number of
+
+ align:start position:0%
+and take the delta covering number of
+ 
+
+ align:start position:0%
+and take the delta covering number of
+that then that should be smaller than C
+
+ align:start position:0%
+that then that should be smaller than C
+ 
+
+ align:start position:0%
+that then that should be smaller than C
+* little R to the S times the delta
+
+ align:start position:0%
+* little R to the S times the delta
+ 
+
+ align:start position:0%
+* little R to the S times the delta
+covering number of the whole set.
+
+ align:start position:0%
+covering number of the whole set.
+ 
+
+ align:start position:0%
+covering number of the whole set.
+Um so for any X and for any R which
+
+ align:start position:0%
+Um so for any X and for any R which
+ 
+
+ align:start position:0%
+Um so for any X and for any R which
+should be at least delta
+
+ align:start position:0%
+should be at least delta
+ 
+
+ align:start position:0%
+should be at least delta
+so that's a delta SC it's a sort of a
+
+ align:start position:0%
+so that's a delta SC it's a sort of a
+ 
+
+ align:start position:0%
+so that's a delta SC it's a sort of a
+spacing condition on the set E that says
+
+ align:start position:0%
+spacing condition on the set E that says
+ 
+
+ align:start position:0%
+spacing condition on the set E that says
+that it's not too concentrated into any
+
+ align:start position:0%
+that it's not too concentrated into any
+ 
+
+ align:start position:0%
+that it's not too concentrated into any
+small
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here is the statement of the sharp
+
+ align:start position:0%
+so here is the statement of the sharp
+ 
+
+ align:start position:0%
+so here is the statement of the sharp
+projection theorem
+
+ align:start position:0%
+projection theorem
+ 
+
+ align:start position:0%
+projection theorem
+theorem of Orpinan Schmurkin Ren Wong
+
+ align:start position:0%
+theorem of Orpinan Schmurkin Ren Wong
+ 
+
+ align:start position:0%
+theorem of Orpinan Schmurkin Ren Wong
+from 2024.
+
+ align:start position:0%
+from 2024.
+ 
+
+ align:start position:0%
+from 2024.
+All right. So if E in R2 is a delta SC
+
+ align:start position:0%
+All right. So if E in R2 is a delta SC
+ 
+
+ align:start position:0%
+All right. So if E in R2 is a delta SC
+set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then um every X in E will have a set of
+
+ align:start position:0%
+then um every X in E will have a set of
+ 
+
+ align:start position:0%
+then um every X in E will have a set of
+tubes T subX.
+
+ align:start position:0%
+tubes T subX.
+ 
+
+ align:start position:0%
+tubes T subX.
+This is a set of delta twos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+through x.
+
+ align:start position:0%
+through x.
+ 
+
+ align:start position:0%
+through x.
+Um, and sorry, E is going to be this is
+
+ align:start position:0%
+Um, and sorry, E is going to be this is
+ 
+
+ align:start position:0%
+Um, and sorry, E is going to be this is
+it's just a notation choice, but if I
+
+ align:start position:0%
+it's just a notation choice, but if I
+ 
+
+ align:start position:0%
+it's just a notation choice, but if I
+don't match my notes, I'll go bananas.
+
+ align:start position:0%
+don't match my notes, I'll go bananas.
+ 
+
+ align:start position:0%
+don't match my notes, I'll go bananas.
+It's a delta TC set.
+
+ align:start position:0%
+It's a delta TC set.
+ 
+
+ align:start position:0%
+It's a delta TC set.
+Uh, okay. And so for each point, there's
+
+ align:start position:0%
+Uh, okay. And so for each point, there's
+ 
+
+ align:start position:0%
+Uh, okay. And so for each point, there's
+a set of tubes through it. And this set
+
+ align:start position:0%
+a set of tubes through it. And this set
+ 
+
+ align:start position:0%
+a set of tubes through it. And this set
+of tubes
+
+ align:start position:0%
+of tubes
+ 
+
+ align:start position:0%
+of tubes
+is a delta S C set
+
+ align:start position:0%
+is a delta S C set
+ 
+
+ align:start position:0%
+is a delta S C set
+um in in S1. So let's make a picture. So
+
+ align:start position:0%
+um in in S1. So let's make a picture. So
+ 
+
+ align:start position:0%
+um in in S1. So let's make a picture. So
+we have a set E which um you may as well
+
+ align:start position:0%
+we have a set E which um you may as well
+ 
+
+ align:start position:0%
+we have a set E which um you may as well
+think of as a as a set of delta balls.
+
+ align:start position:0%
+think of as a as a set of delta balls.
+ 
+
+ align:start position:0%
+think of as a as a set of delta balls.
+So there's E. And then for each of these
+
+ align:start position:0%
+So there's E. And then for each of these
+ 
+
+ align:start position:0%
+So there's E. And then for each of these
+delta balls, it lies in a bunch of
+
+ align:start position:0%
+delta balls, it lies in a bunch of
+ 
+
+ align:start position:0%
+delta balls, it lies in a bunch of
+tubes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And we'll repeat for all of these
+
+ align:start position:0%
+Okay. And we'll repeat for all of these
+ 
+
+ align:start position:0%
+Okay. And we'll repeat for all of these
+other guys. Maybe this tube keeps going
+
+ align:start position:0%
+other guys. Maybe this tube keeps going
+ 
+
+ align:start position:0%
+other guys. Maybe this tube keeps going
+and goes through there and tube there.
+
+ align:start position:0%
+and goes through there and tube there.
+ 
+
+ align:start position:0%
+and goes through there and tube there.
+Okay. But so if this is x, those tubes
+
+ align:start position:0%
+Okay. But so if this is x, those tubes
+ 
+
+ align:start position:0%
+Okay. But so if this is x, those tubes
+there, that's TX
+
+ align:start position:0%
+there, that's TX
+ 
+
+ align:start position:0%
+there, that's TX
+and they point in different directions.
+
+ align:start position:0%
+and they point in different directions.
+ 
+
+ align:start position:0%
+and they point in different directions.
+We can think of the directions as being
+
+ align:start position:0%
+We can think of the directions as being
+ 
+
+ align:start position:0%
+We can think of the directions as being
+parameterized by S1.
+
+ align:start position:0%
+parameterized by S1.
+ 
+
+ align:start position:0%
+parameterized by S1.
+And they are a delta SC set in S1. Yeah.
+
+ align:start position:0%
+And they are a delta SC set in S1. Yeah.
+ 
+
+ align:start position:0%
+And they are a delta SC set in S1. Yeah.
+What if you multiple tubes that are in
+
+ align:start position:0%
+What if you multiple tubes that are in
+ 
+
+ align:start position:0%
+What if you multiple tubes that are in
+the same direction of being offset from
+
+ align:start position:0%
+the same direction of being offset from
+ 
+
+ align:start position:0%
+the same direction of being offset from
+each other that I guess delta contain
+
+ align:start position:0%
+each other that I guess delta contain
+ 
+
+ align:start position:0%
+each other that I guess delta contain
+the same point? How does that
+
+ align:start position:0%
+the same point? How does that
+ 
+
+ align:start position:0%
+the same point? How does that
+>> Yeah. So if you Right. So if I had this
+
+ align:start position:0%
+>> Yeah. So if you Right. So if I had this
+ 
+
+ align:start position:0%
+>> Yeah. So if you Right. So if I had this
+point and then I had
+
+ align:start position:0%
+point and then I had
+ 
+
+ align:start position:0%
+point and then I had
+those Oh, I see. Um yeah, we'll think of
+
+ align:start position:0%
+those Oh, I see. Um yeah, we'll think of
+ 
+
+ align:start position:0%
+those Oh, I see. Um yeah, we'll think of
+those as the same tube.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um,
+
+ align:start position:0%
+Okay. Um,
+ 
+
+ align:start position:0%
+Okay. Um,
+so the the question was, you know, if I
+
+ align:start position:0%
+so the the question was, you know, if I
+ 
+
+ align:start position:0%
+so the the question was, you know, if I
+have my delta ball, could I have two
+
+ align:start position:0%
+have my delta ball, could I have two
+ 
+
+ align:start position:0%
+have my delta ball, could I have two
+delta tubes going through it that are
+
+ align:start position:0%
+delta tubes going through it that are
+ 
+
+ align:start position:0%
+delta tubes going through it that are
+going in the same direction or within an
+
+ align:start position:0%
+going in the same direction or within an
+ 
+
+ align:start position:0%
+going in the same direction or within an
+angle delta of each other? And I'm going
+
+ align:start position:0%
+angle delta of each other? And I'm going
+ 
+
+ align:start position:0%
+angle delta of each other? And I'm going
+to think of those as being basically the
+
+ align:start position:0%
+to think of those as being basically the
+ 
+
+ align:start position:0%
+to think of those as being basically the
+same tube.
+
+ align:start position:0%
+same tube.
+ 
+
+ align:start position:0%
+same tube.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Um, all right. Then t is the union overx
+
+ align:start position:0%
+Um, all right. Then t is the union overx
+ 
+
+ align:start position:0%
+Um, all right. Then t is the union overx
+tx
+
+ align:start position:0%
+tx
+ 
+
+ align:start position:0%
+tx
+which could be smaller than the sum of
+
+ align:start position:0%
+which could be smaller than the sum of
+ 
+
+ align:start position:0%
+which could be smaller than the sum of
+them because one tube might be in tx for
+
+ align:start position:0%
+them because one tube might be in tx for
+ 
+
+ align:start position:0%
+them because one tube might be in tx for
+two different x's.
+
+ align:start position:0%
+two different x's.
+ 
+
+ align:start position:0%
+two different x's.
+And the question is uh in terms of s and
+
+ align:start position:0%
+And the question is uh in terms of s and
+ 
+
+ align:start position:0%
+And the question is uh in terms of s and
+t how how big does this need to be?
+
+ align:start position:0%
+t how how big does this need to be?
+ 
+
+ align:start position:0%
+t how how big does this need to be?
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+cool. Okay. So then the conclusion is
+
+ align:start position:0%
+cool. Okay. So then the conclusion is
+ 
+
+ align:start position:0%
+cool. Okay. So then the conclusion is
+that the size of t is bigger than okay
+
+ align:start position:0%
+that the size of t is bigger than okay
+ 
+
+ align:start position:0%
+that the size of t is bigger than okay
+there's a little complicated stuff
+
+ align:start position:0%
+there's a little complicated stuff
+ 
+
+ align:start position:0%
+there's a little complicated stuff
+cepsilon delta to the epsilon big c to
+
+ align:start position:0%
+cepsilon delta to the epsilon big c to
+ 
+
+ align:start position:0%
+cepsilon delta to the epsilon big c to
+the minus order of 1
+
+ align:start position:0%
+the minus order of 1
+ 
+
+ align:start position:0%
+the minus order of 1
+um and then
+
+ align:start position:0%
+um and then
+ 
+
+ align:start position:0%
+um and then
+there's the minimum of okay so the e * s
+
+ align:start position:0%
+there's the minimum of okay so the e * s
+ 
+
+ align:start position:0%
+there's the minimum of okay so the e * s
+corresponds to delta to the minus t
+
+ align:start position:0%
+corresponds to delta to the minus t
+ 
+
+ align:start position:0%
+corresponds to delta to the minus t
+delta to the minus s the so this is this
+
+ align:start position:0%
+delta to the minus s the so this is this
+ 
+
+ align:start position:0%
+delta to the minus s the so this is this
+corresponds to There's somebody that
+
+ align:start position:0%
+corresponds to There's somebody that
+ 
+
+ align:start position:0%
+corresponds to There's somebody that
+corresponds to B. DeltaUS T / 2 Delta
+
+ align:start position:0%
+corresponds to B. DeltaUS T / 2 Delta
+ 
+
+ align:start position:0%
+corresponds to B. DeltaUS T / 2 Delta
+-3t / 2 that corresponds to B. And there
+
+ align:start position:0%
+-3t / 2 that corresponds to B. And there
+ 
+
+ align:start position:0%
+-3t / 2 that corresponds to B. And there
+is a new thing delta to the minus1 minus
+
+ align:start position:0%
+is a new thing delta to the minus1 minus
+ 
+
+ align:start position:0%
+is a new thing delta to the minus1 minus
+S that corresponds to C. Well, sorry
+
+ align:start position:0%
+S that corresponds to C. Well, sorry
+ 
+
+ align:start position:0%
+S that corresponds to C. Well, sorry
+that doesn't correspond to anything.
+
+ align:start position:0%
+that doesn't correspond to anything.
+ 
+
+ align:start position:0%
+that doesn't correspond to anything.
+There was no C up there. I will call it
+
+ align:start position:0%
+There was no C up there. I will call it
+ 
+
+ align:start position:0%
+There was no C up there. I will call it
+C.
+
+ align:start position:0%
+C.
+ 
+
+ align:start position:0%
+C.
+Okay. Who So who is C?
+
+ align:start position:0%
+Okay. Who So who is C?
+ 
+
+ align:start position:0%
+Okay. Who So who is C?
+Um,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so C is a new phenomenon that has to do
+
+ align:start position:0%
+so C is a new phenomenon that has to do
+ 
+
+ align:start position:0%
+so C is a new phenomenon that has to do
+with the fact that these tubes and balls
+
+ align:start position:0%
+with the fact that these tubes and balls
+ 
+
+ align:start position:0%
+with the fact that these tubes and balls
+have a thickness which we didn't have up
+
+ align:start position:0%
+have a thickness which we didn't have up
+ 
+
+ align:start position:0%
+have a thickness which we didn't have up
+there. So here E could just be a could
+
+ align:start position:0%
+there. So here E could just be a could
+ 
+
+ align:start position:0%
+there. So here E could just be a could
+be any set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then T is a random set
+
+ align:start position:0%
+and then T is a random set
+ 
+
+ align:start position:0%
+and then T is a random set
+of delta to the minus1 minus S or so
+
+ align:start position:0%
+of delta to the minus1 minus S or so
+ 
+
+ align:start position:0%
+of delta to the minus1 minus S or so
+tubes.
+
+ align:start position:0%
+tubes.
+ 
+
+ align:start position:0%
+tubes.
+And the probability that a delta tube
+
+ align:start position:0%
+And the probability that a delta tube
+ 
+
+ align:start position:0%
+And the probability that a delta tube
+goes through a given point is delta. So
+
+ align:start position:0%
+goes through a given point is delta. So
+ 
+
+ align:start position:0%
+goes through a given point is delta. So
+a typical point TX would would
+
+ align:start position:0%
+a typical point TX would would
+ 
+
+ align:start position:0%
+a typical point TX would would
+essentially be a random
+
+ align:start position:0%
+essentially be a random
+ 
+
+ align:start position:0%
+essentially be a random
+set of around delta to the minus s tubes
+
+ align:start position:0%
+set of around delta to the minus s tubes
+ 
+
+ align:start position:0%
+set of around delta to the minus s tubes
+and a random set there might be a couple
+
+ align:start position:0%
+and a random set there might be a couple
+ 
+
+ align:start position:0%
+and a random set there might be a couple
+that are close together but on the whole
+
+ align:start position:0%
+that are close together but on the whole
+ 
+
+ align:start position:0%
+that are close together but on the whole
+that would be that would be a delta s
+
+ align:start position:0%
+that would be that would be a delta s
+ 
+
+ align:start position:0%
+that would be that would be a delta s
+set of tubes.
+
+ align:start position:0%
+set of tubes.
+ 
+
+ align:start position:0%
+set of tubes.
+Okay so that's where this new option
+
+ align:start position:0%
+Okay so that's where this new option
+ 
+
+ align:start position:0%
+Okay so that's where this new option
+comes from. Cool. Okay. Yeah. and option
+
+ align:start position:0%
+comes from. Cool. Okay. Yeah. and option
+ 
+
+ align:start position:0%
+comes from. Cool. Okay. Yeah. and option
+B or is one of the exponents supposed to
+
+ align:start position:0%
+B or is one of the exponents supposed to
+ 
+
+ align:start position:0%
+B or is one of the exponents supposed to
+be an S fun?
+
+ align:start position:0%
+be an S fun?
+ 
+
+ align:start position:0%
+be an S fun?
+>> Yes, thank you.
+
+ align:start position:0%
+>> Yes, thank you.
+ 
+
+ align:start position:0%
+>> Yes, thank you.
+That's supposed to be an S,
+
+ align:start position:0%
+That's supposed to be an S,
+ 
+
+ align:start position:0%
+That's supposed to be an S,
+right? Okay, so let's put these on top
+
+ align:start position:0%
+right? Okay, so let's put these on top
+ 
+
+ align:start position:0%
+right? Okay, so let's put these on top
+of each other for a second.
+
+ align:start position:0%
+of each other for a second.
+ 
+
+ align:start position:0%
+of each other for a second.
+So the size of E corresponds to the
+
+ align:start position:0%
+So the size of E corresponds to the
+ 
+
+ align:start position:0%
+So the size of E corresponds to the
+delta to the minus T and big S
+
+ align:start position:0%
+delta to the minus T and big S
+ 
+
+ align:start position:0%
+delta to the minus T and big S
+corresponds to delta to the minus little
+
+ align:start position:0%
+corresponds to delta to the minus little
+ 
+
+ align:start position:0%
+corresponds to delta to the minus little
+S. And so so those match up
+
+ align:start position:0%
+S. And so so those match up
+ 
+
+ align:start position:0%
+S. And so so those match up
+and then C is something new.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good. Now, I realized I forgot one
+
+ align:start position:0%
+Okay, good. Now, I realized I forgot one
+ 
+
+ align:start position:0%
+Okay, good. Now, I realized I forgot one
+hypothesis that I'm going to add and
+
+ align:start position:0%
+hypothesis that I'm going to add and
+ 
+
+ align:start position:0%
+hypothesis that I'm going to add and
+then we'll pause and you can look at
+
+ align:start position:0%
+then we'll pause and you can look at
+ 
+
+ align:start position:0%
+then we'll pause and you can look at
+these statements.
+
+ align:start position:0%
+these statements.
+ 
+
+ align:start position:0%
+these statements.
+Okay, so
+
+ align:start position:0%
+Okay, so
+ 
+
+ align:start position:0%
+Okay, so
+we needed one more hypothesis in our
+
+ align:start position:0%
+we needed one more hypothesis in our
+ 
+
+ align:start position:0%
+we needed one more hypothesis in our
+list of hypotheses, which is that this S
+
+ align:start position:0%
+list of hypotheses, which is that this S
+ 
+
+ align:start position:0%
+list of hypotheses, which is that this S
+should be bigger than one.
+
+ align:start position:0%
+should be bigger than one.
+ 
+
+ align:start position:0%
+should be bigger than one.
+You see, if I just had one line going
+
+ align:start position:0%
+You see, if I just had one line going
+ 
+
+ align:start position:0%
+You see, if I just had one line going
+through each of these points, then I
+
+ align:start position:0%
+through each of these points, then I
+ 
+
+ align:start position:0%
+through each of these points, then I
+could just have one line and a bunch of
+
+ align:start position:0%
+could just have one line and a bunch of
+ 
+
+ align:start position:0%
+could just have one line and a bunch of
+points on it and one is not bigger than
+
+ align:start position:0%
+points on it and one is not bigger than
+ 
+
+ align:start position:0%
+points on it and one is not bigger than
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+Okay, so that's a special case. And
+
+ align:start position:0%
+Okay, so that's a special case. And
+ 
+
+ align:start position:0%
+Okay, so that's a special case. And
+there is an analogous condition here in
+
+ align:start position:0%
+there is an analogous condition here in
+ 
+
+ align:start position:0%
+there is an analogous condition here in
+our list of hypotheses. We need little s
+
+ align:start position:0%
+our list of hypotheses. We need little s
+ 
+
+ align:start position:0%
+our list of hypotheses. We need little s
+to be bigger than zero. This corresponds
+
+ align:start position:0%
+to be bigger than zero. This corresponds
+ 
+
+ align:start position:0%
+to be bigger than zero. This corresponds
+to having not just one tube through each
+
+ align:start position:0%
+to having not just one tube through each
+ 
+
+ align:start position:0%
+to having not just one tube through each
+of these points, but pretty many.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so that's the statement of summary
+
+ align:start position:0%
+Okay, so that's the statement of summary
+ 
+
+ align:start position:0%
+Okay, so that's the statement of summary
+trotder and the parallel statement of
+
+ align:start position:0%
+trotder and the parallel statement of
+ 
+
+ align:start position:0%
+trotder and the parallel statement of
+this is the firstenberg set conjecture
+
+ align:start position:0%
+this is the firstenberg set conjecture
+ 
+
+ align:start position:0%
+this is the firstenberg set conjecture
+um proven just recently.
+
+ align:start position:0%
+um proven just recently.
+ 
+
+ align:start position:0%
+um proven just recently.
+So let's pause there to digest and see
+
+ align:start position:0%
+So let's pause there to digest and see
+ 
+
+ align:start position:0%
+So let's pause there to digest and see
+if there are questions or comments about
+
+ align:start position:0%
+if there are questions or comments about
+ 
+
+ align:start position:0%
+if there are questions or comments about
+the statement of this theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah,
+
+ align:start position:0%
+Yeah,
+ 
+
+ align:start position:0%
+Yeah,
+>> I'm still having a hard time
+
+ align:start position:0%
+>> I'm still having a hard time
+ 
+
+ align:start position:0%
+>> I'm still having a hard time
+understanding what's going on in
+
+ align:start position:0%
+understanding what's going on in
+ 
+
+ align:start position:0%
+understanding what's going on in
+case C. Would it be possible to draw a
+
+ align:start position:0%
+case C. Would it be possible to draw a
+ 
+
+ align:start position:0%
+case C. Would it be possible to draw a
+typical example?
+
+ align:start position:0%
+typical example?
+ 
+
+ align:start position:0%
+typical example?
+>> Yeah, let's draw case C. Okay, so E
+
+ align:start position:0%
+>> Yeah, let's draw case C. Okay, so E
+ 
+
+ align:start position:0%
+>> Yeah, let's draw case C. Okay, so E
+could go anywhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then
+
+ align:start position:0%
+and then
+ 
+
+ align:start position:0%
+and then
+um I'm going to draw a random set of
+
+ align:start position:0%
+um I'm going to draw a random set of
+ 
+
+ align:start position:0%
+um I'm going to draw a random set of
+delt of of of tubes a bunch of them. So
+
+ align:start position:0%
+delt of of of tubes a bunch of them. So
+ 
+
+ align:start position:0%
+delt of of of tubes a bunch of them. So
+um okay, so here I go.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I I drew these tubes
+
+ align:start position:0%
+So I I drew these tubes
+ 
+
+ align:start position:0%
+So I I drew these tubes
+or I tried to do it without thinking at
+
+ align:start position:0%
+or I tried to do it without thinking at
+ 
+
+ align:start position:0%
+or I tried to do it without thinking at
+all about where the points are. There
+
+ align:start position:0%
+all about where the points are. There
+ 
+
+ align:start position:0%
+all about where the points are. There
+was nothing clever going on.
+
+ align:start position:0%
+was nothing clever going on.
+ 
+
+ align:start position:0%
+was nothing clever going on.
+Um but uh I drew a whole lot of them and
+
+ align:start position:0%
+Um but uh I drew a whole lot of them and
+ 
+
+ align:start position:0%
+Um but uh I drew a whole lot of them and
+uh one over a delta fraction if if I
+
+ align:start position:0%
+uh one over a delta fraction if if I
+ 
+
+ align:start position:0%
+uh one over a delta fraction if if I
+draw a random tube the probability that
+
+ align:start position:0%
+draw a random tube the probability that
+ 
+
+ align:start position:0%
+draw a random tube the probability that
+goes through here is delta. So if I draw
+
+ align:start position:0%
+goes through here is delta. So if I draw
+ 
+
+ align:start position:0%
+goes through here is delta. So if I draw
+uh m o times 1 over delta random tubes,
+
+ align:start position:0%
+uh m o times 1 over delta random tubes,
+ 
+
+ align:start position:0%
+uh m o times 1 over delta random tubes,
+I'll have about m of them going through
+
+ align:start position:0%
+I'll have about m of them going through
+ 
+
+ align:start position:0%
+I'll have about m of them going through
+this point. So let's say I do that. So I
+
+ align:start position:0%
+this point. So let's say I do that. So I
+ 
+
+ align:start position:0%
+this point. So let's say I do that. So I
+have about m tubes going through this
+
+ align:start position:0%
+have about m tubes going through this
+ 
+
+ align:start position:0%
+have about m tubes going through this
+point. Now what directions will they
+
+ align:start position:0%
+point. Now what directions will they
+ 
+
+ align:start position:0%
+point. Now what directions will they
+point in? Well, they'll point in random
+
+ align:start position:0%
+point in? Well, they'll point in random
+ 
+
+ align:start position:0%
+point in? Well, they'll point in random
+directions. And a random direction, a
+
+ align:start position:0%
+directions. And a random direction, a
+ 
+
+ align:start position:0%
+directions. And a random direction, a
+random set is a is a delta SC c set
+
+ align:start position:0%
+random set is a is a delta SC c set
+ 
+
+ align:start position:0%
+random set is a is a delta SC c set
+where s where delta to the minus s is
+
+ align:start position:0%
+where s where delta to the minus s is
+ 
+
+ align:start position:0%
+where s where delta to the minus s is
+the number of points.
+
+ align:start position:0%
+the number of points.
+ 
+
+ align:start position:0%
+the number of points.
+So so that's that's why we have this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so now let's start talk about the
+
+ align:start position:0%
+Okay, so now let's start talk about the
+ 
+
+ align:start position:0%
+Okay, so now let's start talk about the
+history of work on this problem.
+
+ align:start position:0%
+history of work on this problem.
+ 
+
+ align:start position:0%
+history of work on this problem.
+Um, and the going through the history of
+
+ align:start position:0%
+Um, and the going through the history of
+ 
+
+ align:start position:0%
+Um, and the going through the history of
+work on the problem will also be an
+
+ align:start position:0%
+work on the problem will also be an
+ 
+
+ align:start position:0%
+work on the problem will also be an
+excuse to kind of recap a big section
+
+ align:start position:0%
+excuse to kind of recap a big section
+ 
+
+ align:start position:0%
+excuse to kind of recap a big section
+big chunks of our class.
+
+ align:start position:0%
+big chunks of our class.
+ 
+
+ align:start position:0%
+big chunks of our class.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+history of work slash
+
+ align:start position:0%
+history of work slash
+ 
+
+ align:start position:0%
+history of work slash
+recap of the class.
+
+ align:start position:0%
+recap of the class.
+ 
+
+ align:start position:0%
+recap of the class.
+Okay. So first I'll do what I'll call
+
+ align:start position:0%
+Okay. So first I'll do what I'll call
+ 
+
+ align:start position:0%
+Okay. So first I'll do what I'll call
+classical bounds which are uh
+
+ align:start position:0%
+classical bounds which are uh
+ 
+
+ align:start position:0%
+classical bounds which are uh
+essentially due to calfman and falconer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and they were sort of written up in the
+
+ align:start position:0%
+and they were sort of written up in the
+ 
+
+ align:start position:0%
+and they were sort of written up in the
+context of this theorem. Calfman and
+
+ align:start position:0%
+context of this theorem. Calfman and
+ 
+
+ align:start position:0%
+context of this theorem. Calfman and
+falconer were talking about projection
+
+ align:start position:0%
+falconer were talking about projection
+ 
+
+ align:start position:0%
+falconer were talking about projection
+theory. This is a little bit more
+
+ align:start position:0%
+theory. This is a little bit more
+ 
+
+ align:start position:0%
+theory. This is a little bit more
+general um but they were written up. So
+
+ align:start position:0%
+general um but they were written up. So
+ 
+
+ align:start position:0%
+general um but they were written up. So
+this kofman kman and falconer were in
+
+ align:start position:0%
+this kofman kman and falconer were in
+ 
+
+ align:start position:0%
+this kofman kman and falconer were in
+the 60s and 70s. a pretty long time ago
+
+ align:start position:0%
+the 60s and 70s. a pretty long time ago
+ 
+
+ align:start position:0%
+the 60s and 70s. a pretty long time ago
+and then um adapted a bit by Wolf.
+
+ align:start position:0%
+and then um adapted a bit by Wolf.
+ 
+
+ align:start position:0%
+and then um adapted a bit by Wolf.
+Okay, the first classical argument is
+
+ align:start position:0%
+Okay, the first classical argument is
+ 
+
+ align:start position:0%
+Okay, the first classical argument is
+double counting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There actually two slightly different
+
+ align:start position:0%
+There actually two slightly different
+ 
+
+ align:start position:0%
+There actually two slightly different
+ways of dueling double counting and I'll
+
+ align:start position:0%
+ways of dueling double counting and I'll
+ 
+
+ align:start position:0%
+ways of dueling double counting and I'll
+tell you what they give. The first way
+
+ align:start position:0%
+tell you what they give. The first way
+ 
+
+ align:start position:0%
+tell you what they give. The first way
+gives that if s is at least t
+
+ align:start position:0%
+gives that if s is at least t
+ 
+
+ align:start position:0%
+gives that if s is at least t
+um then um the number of tubes is at
+
+ align:start position:0%
+um then um the number of tubes is at
+ 
+
+ align:start position:0%
+um then um the number of tubes is at
+least option a
+
+ align:start position:0%
+least option a
+ 
+
+ align:start position:0%
+least option a
+and this is sharp.
+
+ align:start position:0%
+and this is sharp.
+ 
+
+ align:start position:0%
+and this is sharp.
+Okay. So let's think about what it
+
+ align:start position:0%
+Okay. So let's think about what it
+ 
+
+ align:start position:0%
+Okay. So let's think about what it
+means.
+
+ align:start position:0%
+means.
+ 
+
+ align:start position:0%
+means.
+So s is at least t. That means that the
+
+ align:start position:0%
+So s is at least t. That means that the
+ 
+
+ align:start position:0%
+So s is at least t. That means that the
+number of directions through each point
+
+ align:start position:0%
+number of directions through each point
+ 
+
+ align:start position:0%
+number of directions through each point
+is bigger than the number of points.
+
+ align:start position:0%
+is bigger than the number of points.
+ 
+
+ align:start position:0%
+is bigger than the number of points.
+So um draw a little picture to the side
+
+ align:start position:0%
+So um draw a little picture to the side
+ 
+
+ align:start position:0%
+So um draw a little picture to the side
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+So I have a few points, not very many.
+
+ align:start position:0%
+So I have a few points, not very many.
+ 
+
+ align:start position:0%
+So I have a few points, not very many.
+And then through each tube I'm going to
+
+ align:start position:0%
+And then through each tube I'm going to
+ 
+
+ align:start position:0%
+And then through each tube I'm going to
+draw through each point I'm going to
+
+ align:start position:0%
+draw through each point I'm going to
+ 
+
+ align:start position:0%
+draw through each point I'm going to
+draw a bunch of tubes. And the number of
+
+ align:start position:0%
+draw a bunch of tubes. And the number of
+ 
+
+ align:start position:0%
+draw a bunch of tubes. And the number of
+directions is bigger than the number of
+
+ align:start position:0%
+directions is bigger than the number of
+ 
+
+ align:start position:0%
+directions is bigger than the number of
+points. So I have a picture like this.
+
+ align:start position:0%
+points. So I have a picture like this.
+ 
+
+ align:start position:0%
+points. So I have a picture like this.
+So what you see is that most of these
+
+ align:start position:0%
+So what you see is that most of these
+ 
+
+ align:start position:0%
+So what you see is that most of these
+tubes don't go through any other point
+
+ align:start position:0%
+tubes don't go through any other point
+ 
+
+ align:start position:0%
+tubes don't go through any other point
+besides the initial point.
+
+ align:start position:0%
+besides the initial point.
+ 
+
+ align:start position:0%
+besides the initial point.
+Uh and that gives an easy estimate for
+
+ align:start position:0%
+Uh and that gives an easy estimate for
+ 
+
+ align:start position:0%
+Uh and that gives an easy estimate for
+the number of tubes
+
+ align:start position:0%
+the number of tubes
+ 
+
+ align:start position:0%
+the number of tubes
+has to be at least the number of points
+
+ align:start position:0%
+has to be at least the number of points
+ 
+
+ align:start position:0%
+has to be at least the number of points
+times you know the number of tubes
+
+ align:start position:0%
+times you know the number of tubes
+ 
+
+ align:start position:0%
+times you know the number of tubes
+through.
+
+ align:start position:0%
+through.
+ 
+
+ align:start position:0%
+through.
+Okay. There is another way to do double
+
+ align:start position:0%
+Okay. There is another way to do double
+ 
+
+ align:start position:0%
+Okay. There is another way to do double
+counting and it says that in general so
+
+ align:start position:0%
+counting and it says that in general so
+ 
+
+ align:start position:0%
+counting and it says that in general so
+just if s is bigger than zero which
+
+ align:start position:0%
+just if s is bigger than zero which
+ 
+
+ align:start position:0%
+just if s is bigger than zero which
+we've been assuming then the number of
+
+ align:start position:0%
+we've been assuming then the number of
+ 
+
+ align:start position:0%
+we've been assuming then the number of
+tubes is at least delta to the minus 2s.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me just let me just leave this one
+
+ align:start position:0%
+let me just let me just leave this one
+ 
+
+ align:start position:0%
+let me just let me just leave this one
+as an exercise. We've done we've done
+
+ align:start position:0%
+as an exercise. We've done we've done
+ 
+
+ align:start position:0%
+as an exercise. We've done we've done
+some double counting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um then there was a forier method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um that we did in in class and the
+
+ align:start position:0%
+um that we did in in class and the
+ 
+
+ align:start position:0%
+um that we did in in class and the
+forier method showed that t was bigger
+
+ align:start position:0%
+forier method showed that t was bigger
+ 
+
+ align:start position:0%
+forier method showed that t was bigger
+than the minimum of two things. One of
+
+ align:start position:0%
+than the minimum of two things. One of
+ 
+
+ align:start position:0%
+than the minimum of two things. One of
+them is option C and the other one is
+
+ align:start position:0%
+them is option C and the other one is
+ 
+
+ align:start position:0%
+them is option C and the other one is
+delta to the 1 - S times option A.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And um so this number is smaller than
+
+ align:start position:0%
+And um so this number is smaller than
+ 
+
+ align:start position:0%
+And um so this number is smaller than
+one. So this is smaller than A. So this
+
+ align:start position:0%
+one. So this is smaller than A. So this
+ 
+
+ align:start position:0%
+one. So this is smaller than A. So this
+isn't sharp uh unless we're so lucky
+
+ align:start position:0%
+isn't sharp uh unless we're so lucky
+ 
+
+ align:start position:0%
+isn't sharp uh unless we're so lucky
+that S is equal to one in which case
+
+ align:start position:0%
+that S is equal to one in which case
+ 
+
+ align:start position:0%
+that S is equal to one in which case
+this is the minimum of A and C. And
+
+ align:start position:0%
+this is the minimum of A and C. And
+ 
+
+ align:start position:0%
+this is the minimum of A and C. And
+that's that's good. So this is sharp
+
+ align:start position:0%
+that's that's good. So this is sharp
+ 
+
+ align:start position:0%
+that's that's good. So this is sharp
+if s is equal to one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So I won't redo this one but this
+
+ align:start position:0%
+Okay. So I won't redo this one but this
+ 
+
+ align:start position:0%
+Okay. So I won't redo this one but this
+is uh just the forier method that we did
+
+ align:start position:0%
+is uh just the forier method that we did
+ 
+
+ align:start position:0%
+is uh just the forier method that we did
+in the in the third week of of our
+
+ align:start position:0%
+in the in the third week of of our
+ 
+
+ align:start position:0%
+in the in the third week of of our
+class.
+
+ align:start position:0%
+class.
+ 
+
+ align:start position:0%
+class.
+Okay. So the classical methods are
+
+ align:start position:0%
+Okay. So the classical methods are
+ 
+
+ align:start position:0%
+Okay. So the classical methods are
+occasionally sharp but usually not
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um and um okay so another comment about
+
+ align:start position:0%
+um and um okay so another comment about
+ 
+
+ align:start position:0%
+um and um okay so another comment about
+this story that about why why why this
+
+ align:start position:0%
+this story that about why why why this
+ 
+
+ align:start position:0%
+this story that about why why why this
+is difficult is that some of these
+
+ align:start position:0%
+is difficult is that some of these
+ 
+
+ align:start position:0%
+is difficult is that some of these
+statements are fields dependent. They're
+
+ align:start position:0%
+statements are fields dependent. They're
+ 
+
+ align:start position:0%
+statements are fields dependent. They're
+true over R, but they're false over C.
+
+ align:start position:0%
+true over R, but they're false over C.
+ 
+
+ align:start position:0%
+true over R, but they're false over C.
+But others others uh are true in all
+
+ align:start position:0%
+But others others uh are true in all
+ 
+
+ align:start position:0%
+But others others uh are true in all
+fields. Um so if we go back to the
+
+ align:start position:0%
+fields. Um so if we go back to the
+ 
+
+ align:start position:0%
+fields. Um so if we go back to the
+beginning,
+
+ align:start position:0%
+beginning,
+ 
+
+ align:start position:0%
+beginning,
+the summary detrader theorem is true in
+
+ align:start position:0%
+the summary detrader theorem is true in
+ 
+
+ align:start position:0%
+the summary detrader theorem is true in
+both R and C although it's not true in
+
+ align:start position:0%
+both R and C although it's not true in
+ 
+
+ align:start position:0%
+both R and C although it's not true in
+all fields
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is
+
+ align:start position:0%
+and is
+ 
+
+ align:start position:0%
+and is
+all C in some in some finite fields.
+
+ align:start position:0%
+all C in some in some finite fields.
+ 
+
+ align:start position:0%
+all C in some in some finite fields.
+Well, it's really it's false in all
+
+ align:start position:0%
+Well, it's really it's false in all
+ 
+
+ align:start position:0%
+Well, it's really it's false in all
+kinds of things.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+this theorem here is uh true r but it is
+
+ align:start position:0%
+this theorem here is uh true r but it is
+ 
+
+ align:start position:0%
+this theorem here is uh true r but it is
+false over
+
+ align:start position:0%
+false over
+ 
+
+ align:start position:0%
+false over
+and that counter examples kind of
+
+ align:start position:0%
+and that counter examples kind of
+ 
+
+ align:start position:0%
+and that counter examples kind of
+haunted all of us who have been working
+
+ align:start position:0%
+haunted all of us who have been working
+ 
+
+ align:start position:0%
+haunted all of us who have been working
+on this.
+
+ align:start position:0%
+on this.
+ 
+
+ align:start position:0%
+on this.
+And one feature of these classical
+
+ align:start position:0%
+And one feature of these classical
+ 
+
+ align:start position:0%
+And one feature of these classical
+methods is that they don't distinguish.
+
+ align:start position:0%
+methods is that they don't distinguish.
+ 
+
+ align:start position:0%
+methods is that they don't distinguish.
+um they work
+
+ align:start position:0%
+um they work
+ 
+
+ align:start position:0%
+um they work
+over R or C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um okay. So to prove this theorem
+
+ align:start position:0%
+Okay. Um okay. So to prove this theorem
+ 
+
+ align:start position:0%
+Okay. Um okay. So to prove this theorem
+we have to distinguish R and C. So we'll
+
+ align:start position:0%
+we have to distinguish R and C. So we'll
+ 
+
+ align:start position:0%
+we have to distinguish R and C. So we'll
+have to do something which in some way
+
+ align:start position:0%
+have to do something which in some way
+ 
+
+ align:start position:0%
+have to do something which in some way
+is different from these. Um and the next
+
+ align:start position:0%
+is different from these. Um and the next
+ 
+
+ align:start position:0%
+is different from these. Um and the next
+phase in the history is begins with Bans
+
+ align:start position:0%
+phase in the history is begins with Bans
+ 
+
+ align:start position:0%
+phase in the history is begins with Bans
+projection theorem. And I it's a phase
+
+ align:start position:0%
+projection theorem. And I it's a phase
+ 
+
+ align:start position:0%
+projection theorem. And I it's a phase
+that I'll label as epsilon improvements.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So for quite a while actually there
+
+ align:start position:0%
+So for quite a while actually there
+ 
+
+ align:start position:0%
+So for quite a while actually there
+really was no progress on these
+
+ align:start position:0%
+really was no progress on these
+ 
+
+ align:start position:0%
+really was no progress on these
+classical methods. These ma classical
+
+ align:start position:0%
+classical methods. These ma classical
+ 
+
+ align:start position:0%
+classical methods. These ma classical
+methods are from the 60s and 70s. Wolf
+
+ align:start position:0%
+methods are from the 60s and 70s. Wolf
+ 
+
+ align:start position:0%
+methods are from the 60s and 70s. Wolf
+adapted them to slightly more general
+
+ align:start position:0%
+adapted them to slightly more general
+ 
+
+ align:start position:0%
+adapted them to slightly more general
+setting but um but basically there was
+
+ align:start position:0%
+setting but um but basically there was
+ 
+
+ align:start position:0%
+setting but um but basically there was
+no progress for a long time. And phase
+
+ align:start position:0%
+no progress for a long time. And phase
+ 
+
+ align:start position:0%
+no progress for a long time. And phase
+two is the phase of epsilon
+
+ align:start position:0%
+two is the phase of epsilon
+ 
+
+ align:start position:0%
+two is the phase of epsilon
+improvements.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the dates of this phase are from
+
+ align:start position:0%
+And the dates of this phase are from
+ 
+
+ align:start position:0%
+And the dates of this phase are from
+around 2000 to very recently.
+
+ align:start position:0%
+around 2000 to very recently.
+ 
+
+ align:start position:0%
+around 2000 to very recently.
+Um, okay. Where is the Borgan projection
+
+ align:start position:0%
+Um, okay. Where is the Borgan projection
+ 
+
+ align:start position:0%
+Um, okay. Where is the Borgan projection
+theorem?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And it implies with a little work but
+
+ align:start position:0%
+And it implies with a little work but
+ 
+
+ align:start position:0%
+And it implies with a little work but
+not that much work an improvement over
+
+ align:start position:0%
+not that much work an improvement over
+ 
+
+ align:start position:0%
+not that much work an improvement over
+the classical methods in a very
+
+ align:start position:0%
+the classical methods in a very
+ 
+
+ align:start position:0%
+the classical methods in a very
+particular situation.
+
+ align:start position:0%
+particular situation.
+ 
+
+ align:start position:0%
+particular situation.
+So it says if t is one and s is 12
+
+ align:start position:0%
+So it says if t is one and s is 12
+ 
+
+ align:start position:0%
+So it says if t is one and s is 12
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this number of tubes is at least delta
+
+ align:start position:0%
+this number of tubes is at least delta
+ 
+
+ align:start position:0%
+this number of tubes is at least delta
+to the minus1
+
+ align:start position:0%
+to the minus1
+ 
+
+ align:start position:0%
+to the minus1
+minus some epsilon we're g
+
+ align:start position:0%
+minus some epsilon we're g
+ 
+
+ align:start position:0%
+minus some epsilon we're g
+um so if you just plug in the classical
+
+ align:start position:0%
+um so if you just plug in the classical
+ 
+
+ align:start position:0%
+um so if you just plug in the classical
+bounds up there it would give this and
+
+ align:start position:0%
+bounds up there it would give this and
+ 
+
+ align:start position:0%
+bounds up there it would give this and
+there's an improvement although only for
+
+ align:start position:0%
+there's an improvement although only for
+ 
+
+ align:start position:0%
+there's an improvement although only for
+a rather particular for one particular
+
+ align:start position:0%
+a rather particular for one particular
+ 
+
+ align:start position:0%
+a rather particular for one particular
+choice of the parameters.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um so that was uh in 2000
+
+ align:start position:0%
+Okay. Um so that was uh in 2000
+ 
+
+ align:start position:0%
+Okay. Um so that was uh in 2000
+and the next improvement
+
+ align:start position:0%
+and the next improvement
+ 
+
+ align:start position:0%
+and the next improvement
+is a theorem of Orphin and Schmurkin
+
+ align:start position:0%
+is a theorem of Orphin and Schmurkin
+ 
+
+ align:start position:0%
+is a theorem of Orphin and Schmurkin
+from 2021.
+
+ align:start position:0%
+from 2021.
+ 
+
+ align:start position:0%
+from 2021.
+And you could think of it as a
+
+ align:start position:0%
+And you could think of it as a
+ 
+
+ align:start position:0%
+And you could think of it as a
+generalization of this. It gives an
+
+ align:start position:0%
+generalization of this. It gives an
+ 
+
+ align:start position:0%
+generalization of this. It gives an
+epsilon improvement but in not just for
+
+ align:start position:0%
+epsilon improvement but in not just for
+ 
+
+ align:start position:0%
+epsilon improvement but in not just for
+this special value of the parameters but
+
+ align:start position:0%
+this special value of the parameters but
+ 
+
+ align:start position:0%
+this special value of the parameters but
+for lots of values of the parameters. So
+
+ align:start position:0%
+for lots of values of the parameters. So
+ 
+
+ align:start position:0%
+for lots of values of the parameters. So
+they proved that if t is bigger than s
+
+ align:start position:0%
+they proved that if t is bigger than s
+ 
+
+ align:start position:0%
+they proved that if t is bigger than s
+uh which is bigger than zero
+
+ align:start position:0%
+uh which is bigger than zero
+ 
+
+ align:start position:0%
+uh which is bigger than zero
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+the number of tubes is at least delta to
+
+ align:start position:0%
+the number of tubes is at least delta to
+ 
+
+ align:start position:0%
+the number of tubes is at least delta to
+the minus 2s minus epsilon.
+
+ align:start position:0%
+the minus 2s minus epsilon.
+ 
+
+ align:start position:0%
+the minus 2s minus epsilon.
+So delta to the minus 2s is what you
+
+ align:start position:0%
+So delta to the minus 2s is what you
+ 
+
+ align:start position:0%
+So delta to the minus 2s is what you
+would get classically by double
+
+ align:start position:0%
+would get classically by double
+ 
+
+ align:start position:0%
+would get classically by double
+counting. It takes half a page and then
+
+ align:start position:0%
+counting. It takes half a page and then
+ 
+
+ align:start position:0%
+counting. It takes half a page and then
+uh after 50 years and 50 pages you can
+
+ align:start position:0%
+uh after 50 years and 50 pages you can
+ 
+
+ align:start position:0%
+uh after 50 years and 50 pages you can
+get this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So in our class we
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+said a lot about the proof of the BADN
+
+ align:start position:0%
+said a lot about the proof of the BADN
+ 
+
+ align:start position:0%
+said a lot about the proof of the BADN
+projection theorem. I don't I wouldn't
+
+ align:start position:0%
+projection theorem. I don't I wouldn't
+ 
+
+ align:start position:0%
+projection theorem. I don't I wouldn't
+actually wouldn't say that we proved
+
+ align:start position:0%
+actually wouldn't say that we proved
+ 
+
+ align:start position:0%
+actually wouldn't say that we proved
+every did every step every detail and um
+
+ align:start position:0%
+every did every step every detail and um
+ 
+
+ align:start position:0%
+every did every step every detail and um
+uh this one. Okay, let me say so we
+
+ align:start position:0%
+uh this one. Okay, let me say so we
+ 
+
+ align:start position:0%
+uh this one. Okay, let me say so we
+haven't proven this in but let me just
+
+ align:start position:0%
+haven't proven this in but let me just
+ 
+
+ align:start position:0%
+haven't proven this in but let me just
+say something about the proof. So this
+
+ align:start position:0%
+say something about the proof. So this
+ 
+
+ align:start position:0%
+say something about the proof. So this
+is based on reg projection theorem
+
+ align:start position:0%
+is based on reg projection theorem
+ 
+
+ align:start position:0%
+is based on reg projection theorem
+um plus a bunch of ideas.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And so an emotional reaction that
+
+ align:start position:0%
+Okay. And so an emotional reaction that
+ 
+
+ align:start position:0%
+Okay. And so an emotional reaction that
+I had to to learning this and going
+
+ align:start position:0%
+I had to to learning this and going
+ 
+
+ align:start position:0%
+I had to to learning this and going
+through it with you is that it is it's
+
+ align:start position:0%
+through it with you is that it is it's
+ 
+
+ align:start position:0%
+through it with you is that it is it's
+hard work
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also epsilon is really tiny. seems
+
+ align:start position:0%
+and also epsilon is really tiny. seems
+ 
+
+ align:start position:0%
+and also epsilon is really tiny. seems
+like you know the harder the clever we
+
+ align:start position:0%
+like you know the harder the clever we
+ 
+
+ align:start position:0%
+like you know the harder the clever we
+are the harder we work we keep making
+
+ align:start position:0%
+are the harder we work we keep making
+ 
+
+ align:start position:0%
+are the harder we work we keep making
+epsilon smaller
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so this was the second phase of the
+
+ align:start position:0%
+okay so this was the second phase of the
+ 
+
+ align:start position:0%
+okay so this was the second phase of the
+history where people were able to make
+
+ align:start position:0%
+history where people were able to make
+ 
+
+ align:start position:0%
+history where people were able to make
+epsilon improvements I could also
+
+ align:start position:0%
+epsilon improvements I could also
+ 
+
+ align:start position:0%
+epsilon improvements I could also
+mention other theorems not about this
+
+ align:start position:0%
+mention other theorems not about this
+ 
+
+ align:start position:0%
+mention other theorems not about this
+exact problem but but in a similar
+
+ align:start position:0%
+exact problem but but in a similar
+ 
+
+ align:start position:0%
+exact problem but but in a similar
+spirit so for many different problems it
+
+ align:start position:0%
+spirit so for many different problems it
+ 
+
+ align:start position:0%
+spirit so for many different problems it
+was possible to make an epsilon
+
+ align:start position:0%
+was possible to make an epsilon
+ 
+
+ align:start position:0%
+was possible to make an epsilon
+improvement um by using burgans's
+
+ align:start position:0%
+improvement um by using burgans's
+ 
+
+ align:start position:0%
+improvement um by using burgans's
+projection theorem and by using and
+
+ align:start position:0%
+projection theorem and by using and
+ 
+
+ align:start position:0%
+projection theorem and by using and
+developing ideas related to the ones we
+
+ align:start position:0%
+developing ideas related to the ones we
+ 
+
+ align:start position:0%
+developing ideas related to the ones we
+put there. Uh okay, so it was hard work.
+
+ align:start position:0%
+put there. Uh okay, so it was hard work.
+ 
+
+ align:start position:0%
+put there. Uh okay, so it was hard work.
+Epsilon was really tiny. But one
+
+ align:start position:0%
+Epsilon was really tiny. But one
+ 
+
+ align:start position:0%
+Epsilon was really tiny. But one
+positive thing about it is that it did
+
+ align:start position:0%
+positive thing about it is that it did
+ 
+
+ align:start position:0%
+positive thing about it is that it did
+distinguish uh R from C. So both of
+
+ align:start position:0%
+distinguish uh R from C. So both of
+ 
+
+ align:start position:0%
+distinguish uh R from C. So both of
+these theorems are false over C. So we
+
+ align:start position:0%
+these theorems are false over C. So we
+ 
+
+ align:start position:0%
+these theorems are false over C. So we
+did start to do that.
+
+ align:start position:0%
+did start to do that.
+ 
+
+ align:start position:0%
+did start to do that.
+Okay. Um cool. So this theorem
+
+ align:start position:0%
+Okay. Um cool. So this theorem
+ 
+
+ align:start position:0%
+Okay. Um cool. So this theorem
+represents a third stage in the history
+
+ align:start position:0%
+represents a third stage in the history
+ 
+
+ align:start position:0%
+represents a third stage in the history
+where we didn't just improve by an
+
+ align:start position:0%
+where we didn't just improve by an
+ 
+
+ align:start position:0%
+where we didn't just improve by an
+epsilon over the classical results but
+
+ align:start position:0%
+epsilon over the classical results but
+ 
+
+ align:start position:0%
+epsilon over the classical results but
+we improved substantially and in fact
+
+ align:start position:0%
+we improved substantially and in fact
+ 
+
+ align:start position:0%
+we improved substantially and in fact
+proved people proved the sharp result.
+
+ align:start position:0%
+proved people proved the sharp result.
+ 
+
+ align:start position:0%
+proved people proved the sharp result.
+This is so so I should mention this.
+
+ align:start position:0%
+This is so so I should mention this.
+ 
+
+ align:start position:0%
+This is so so I should mention this.
+This is sharp.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is sharp
+
+ align:start position:0%
+This is sharp
+ 
+
+ align:start position:0%
+This is sharp
+for any essence.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Yeah.
+
+ align:start position:0%
+>> Yeah.
+ 
+
+ align:start position:0%
+>> Yeah.
+>> Is that delicac
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+or
+
+ align:start position:0%
+or
+ 
+
+ align:start position:0%
+or
+>> Yeah, it's sharp up to this. So
+
+ align:start position:0%
+>> Yeah, it's sharp up to this. So
+ 
+
+ align:start position:0%
+>> Yeah, it's sharp up to this. So
+sharp up to the delta to the epsilon.
+
+ align:start position:0%
+sharp up to the delta to the epsilon.
+ 
+
+ align:start position:0%
+sharp up to the delta to the epsilon.
+In future I'm going to abbreviate that
+
+ align:start position:0%
+In future I'm going to abbreviate that
+ 
+
+ align:start position:0%
+In future I'm going to abbreviate that
+mess by this. we won't be at the level
+
+ align:start position:0%
+mess by this. we won't be at the level
+ 
+
+ align:start position:0%
+mess by this. we won't be at the level
+of detail to have all of this in.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, um so this this the story I
+
+ align:start position:0%
+Okay. So, um so this this the story I
+ 
+
+ align:start position:0%
+Okay. So, um so this this the story I
+wanted to try to tell to explore over
+
+ align:start position:0%
+wanted to try to tell to explore over
+ 
+
+ align:start position:0%
+wanted to try to tell to explore over
+the last three classes is how is it
+
+ align:start position:0%
+the last three classes is how is it
+ 
+
+ align:start position:0%
+the last three classes is how is it
+possible to get from these epsilon
+
+ align:start position:0%
+possible to get from these epsilon
+ 
+
+ align:start position:0%
+possible to get from these epsilon
+improvements to sharp theorems. That's
+
+ align:start position:0%
+improvements to sharp theorems. That's
+ 
+
+ align:start position:0%
+improvements to sharp theorems. That's
+that's our our theme for the rest of the
+
+ align:start position:0%
+that's our our theme for the rest of the
+ 
+
+ align:start position:0%
+that's our our theme for the rest of the
+class. Um, and if I had to say it in a
+
+ align:start position:0%
+class. Um, and if I had to say it in a
+ 
+
+ align:start position:0%
+class. Um, and if I had to say it in a
+couple of sentences,
+
+ align:start position:0%
+couple of sentences,
+ 
+
+ align:start position:0%
+couple of sentences,
+what happened was people found a way
+
+ align:start position:0%
+what happened was people found a way
+ 
+
+ align:start position:0%
+what happened was people found a way
+where you can use an epsilon improvement
+
+ align:start position:0%
+where you can use an epsilon improvement
+ 
+
+ align:start position:0%
+where you can use an epsilon improvement
+theorem and you can use it over and over
+
+ align:start position:0%
+theorem and you can use it over and over
+ 
+
+ align:start position:0%
+theorem and you can use it over and over
+again and sort of each time you use it,
+
+ align:start position:0%
+again and sort of each time you use it,
+ 
+
+ align:start position:0%
+again and sort of each time you use it,
+you improve a little bit the exponent in
+
+ align:start position:0%
+you improve a little bit the exponent in
+ 
+
+ align:start position:0%
+you improve a little bit the exponent in
+your bound until you bring the exponent
+
+ align:start position:0%
+your bound until you bring the exponent
+ 
+
+ align:start position:0%
+your bound until you bring the exponent
+up to the sharp value.
+
+ align:start position:0%
+up to the sharp value.
+ 
+
+ align:start position:0%
+up to the sharp value.
+Okay? Now, it's not at all obvious how
+
+ align:start position:0%
+Okay? Now, it's not at all obvious how
+ 
+
+ align:start position:0%
+Okay? Now, it's not at all obvious how
+to do that, and that's what we're we're
+
+ align:start position:0%
+to do that, and that's what we're we're
+ 
+
+ align:start position:0%
+to do that, and that's what we're we're
+going to try to explain. uh um not with
+
+ align:start position:0%
+going to try to explain. uh um not with
+ 
+
+ align:start position:0%
+going to try to explain. uh um not with
+all details but to to make it seem like
+
+ align:start position:0%
+all details but to to make it seem like
+ 
+
+ align:start position:0%
+all details but to to make it seem like
+a plausible approach that you could that
+
+ align:start position:0%
+a plausible approach that you could that
+ 
+
+ align:start position:0%
+a plausible approach that you could that
+you could carry.
+
+ align:start position:0%
+you could carry.
+ 
+
+ align:start position:0%
+you could carry.
+Cool. Okay. So any questions or comments
+
+ align:start position:0%
+Cool. Okay. So any questions or comments
+ 
+
+ align:start position:0%
+Cool. Okay. So any questions or comments
+before we start? Yeah.
+
+ align:start position:0%
+before we start? Yeah.
+ 
+
+ align:start position:0%
+before we start? Yeah.
+>> Does doing that process make the like C
+
+ align:start position:0%
+>> Does doing that process make the like C
+ 
+
+ align:start position:0%
+>> Does doing that process make the like C
+to the O one constant kind of
+
+ align:start position:0%
+to the O one constant kind of
+ 
+
+ align:start position:0%
+to the O one constant kind of
+corresponding way I guess tiny compared
+
+ align:start position:0%
+corresponding way I guess tiny compared
+ 
+
+ align:start position:0%
+corresponding way I guess tiny compared
+to the epsilon constant?
+
+ align:start position:0%
+to the epsilon constant?
+ 
+
+ align:start position:0%
+to the epsilon constant?
+>> Um yeah. So I think the question is as
+
+ align:start position:0%
+>> Um yeah. So I think the question is as
+ 
+
+ align:start position:0%
+>> Um yeah. So I think the question is as
+as we as we use our epsilon improvement
+
+ align:start position:0%
+as we as we use our epsilon improvement
+ 
+
+ align:start position:0%
+as we as we use our epsilon improvement
+theorem many times does that cause this
+
+ align:start position:0%
+theorem many times does that cause this
+ 
+
+ align:start position:0%
+theorem many times does that cause this
+to become remarkably bad?
+
+ align:start position:0%
+to become remarkably bad?
+ 
+
+ align:start position:0%
+to become remarkably bad?
+I think it does. Okay. I think that this
+
+ align:start position:0%
+I think it does. Okay. I think that this
+ 
+
+ align:start position:0%
+I think it does. Okay. I think that this
+is remarkably bad.
+
+ align:start position:0%
+is remarkably bad.
+ 
+
+ align:start position:0%
+is remarkably bad.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. Great. So today I my first goal is
+
+ align:start position:0%
+Okay. Great. So today I my first goal is
+ 
+
+ align:start position:0%
+Okay. Great. So today I my first goal is
+I want to describe the simplest example
+
+ align:start position:0%
+I want to describe the simplest example
+ 
+
+ align:start position:0%
+I want to describe the simplest example
+where you can get where you can use an
+
+ align:start position:0%
+where you can get where you can use an
+ 
+
+ align:start position:0%
+where you can get where you can use an
+epsilon improvement theorem to prove a
+
+ align:start position:0%
+epsilon improvement theorem to prove a
+ 
+
+ align:start position:0%
+epsilon improvement theorem to prove a
+sharp theorem.
+
+ align:start position:0%
+sharp theorem.
+ 
+
+ align:start position:0%
+sharp theorem.
+And then after that if we have time I
+
+ align:start position:0%
+And then after that if we have time I
+ 
+
+ align:start position:0%
+And then after that if we have time I
+will outline the proof of the big thing.
+
+ align:start position:0%
+will outline the proof of the big thing.
+ 
+
+ align:start position:0%
+will outline the proof of the big thing.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, simplest
+
+ align:start position:0%
+Okay. So, simplest
+ 
+
+ align:start position:0%
+Okay. So, simplest
+example
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+where
+
+ align:start position:0%
+where
+ 
+
+ align:start position:0%
+where
+epsilon improvement
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+leads to sharp out.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this is a theorem of Beck from
+
+ align:start position:0%
+Okay, so this is a theorem of Beck from
+ 
+
+ align:start position:0%
+Okay, so this is a theorem of Beck from
+around 1980
+
+ align:start position:0%
+around 1980
+ 
+
+ align:start position:0%
+around 1980
+which is about the incidences of points
+
+ align:start position:0%
+which is about the incidences of points
+ 
+
+ align:start position:0%
+which is about the incidences of points
+and lines. So it's in the setting of the
+
+ align:start position:0%
+and lines. So it's in the setting of the
+ 
+
+ align:start position:0%
+and lines. So it's in the setting of the
+summary troder theorem.
+
+ align:start position:0%
+summary troder theorem.
+ 
+
+ align:start position:0%
+summary troder theorem.
+It says if E is a subset of R2 and it's
+
+ align:start position:0%
+It says if E is a subset of R2 and it's
+ 
+
+ align:start position:0%
+It says if E is a subset of R2 and it's
+not all on a line and in fact I'll say
+
+ align:start position:0%
+not all on a line and in fact I'll say
+ 
+
+ align:start position:0%
+not all on a line and in fact I'll say
+at most half of it is on a line. So for
+
+ align:start position:0%
+at most half of it is on a line. So for
+ 
+
+ align:start position:0%
+at most half of it is on a line. So for
+any line L
+
+ align:start position:0%
+any line L
+ 
+
+ align:start position:0%
+any line L
+L intersect E is at most half of it.
+
+ align:start position:0%
+L intersect E is at most half of it.
+ 
+
+ align:start position:0%
+L intersect E is at most half of it.
+Then the conclusion is there exists some
+
+ align:start position:0%
+Then the conclusion is there exists some
+ 
+
+ align:start position:0%
+Then the conclusion is there exists some
+point X in E. So that uh all right so
+
+ align:start position:0%
+point X in E. So that uh all right so
+ 
+
+ align:start position:0%
+point X in E. So that uh all right so
+let me make a definition. So I I'll draw
+
+ align:start position:0%
+let me make a definition. So I I'll draw
+ 
+
+ align:start position:0%
+let me make a definition. So I I'll draw
+a picture. So this is E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Here's our set E. Here's a point X.
+
+ align:start position:0%
+Here's our set E. Here's a point X.
+ 
+
+ align:start position:0%
+Here's our set E. Here's a point X.
+Starting at X, I will draw all the lines
+
+ align:start position:0%
+Starting at X, I will draw all the lines
+ 
+
+ align:start position:0%
+Starting at X, I will draw all the lines
+that start at X and go through some
+
+ align:start position:0%
+that start at X and go through some
+ 
+
+ align:start position:0%
+that start at X and go through some
+other points at E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So what's that set? So I'll call
+
+ align:start position:0%
+Okay. So what's that set? So I'll call
+ 
+
+ align:start position:0%
+Okay. So what's that set? So I'll call
+it L XE. This is the set of lines. So
+
+ align:start position:0%
+it L XE. This is the set of lines. So
+ 
+
+ align:start position:0%
+it L XE. This is the set of lines. So
+that lines L. So that X is in L and L
+
+ align:start position:0%
+that lines L. So that X is in L and L
+ 
+
+ align:start position:0%
+that lines L. So that X is in L and L
+intersect E is not just X. So it has
+
+ align:start position:0%
+intersect E is not just X. So it has
+ 
+
+ align:start position:0%
+intersect E is not just X. So it has
+size at least two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now the conclusion is there is a point
+
+ align:start position:0%
+Now the conclusion is there is a point
+ 
+
+ align:start position:0%
+Now the conclusion is there is a point
+in E so that the size of LXE is
+
+ align:start position:0%
+in E so that the size of LXE is
+ 
+
+ align:start position:0%
+in E so that the size of LXE is
+comparable to the size of E.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is clearly a sharp theorem because
+
+ align:start position:0%
+This is clearly a sharp theorem because
+ 
+
+ align:start position:0%
+This is clearly a sharp theorem because
+the largest possible size that this
+
+ align:start position:0%
+the largest possible size that this
+ 
+
+ align:start position:0%
+the largest possible size that this
+could be is the size of
+
+ align:start position:0%
+could be is the size of
+ 
+
+ align:start position:0%
+could be is the size of
+all right. Um let me do a proof sketch.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and we'll so we'll see that this
+
+ align:start position:0%
+Um and we'll so we'll see that this
+ 
+
+ align:start position:0%
+Um and we'll so we'll see that this
+follows from sem ready troder. Um but
+
+ align:start position:0%
+follows from sem ready troder. Um but
+ 
+
+ align:start position:0%
+follows from sem ready troder. Um but
+we'll also see that we don't really need
+
+ align:start position:0%
+we'll also see that we don't really need
+ 
+
+ align:start position:0%
+we'll also see that we don't really need
+the sharp exponents in semi troder. We
+
+ align:start position:0%
+the sharp exponents in semi troder. We
+ 
+
+ align:start position:0%
+the sharp exponents in semi troder. We
+just need to have something that's an
+
+ align:start position:0%
+just need to have something that's an
+ 
+
+ align:start position:0%
+just need to have something that's an
+epsilon better than um uh than a than a
+
+ align:start position:0%
+epsilon better than um uh than a than a
+ 
+
+ align:start position:0%
+epsilon better than um uh than a than a
+simple bound. That's why I've erased it
+
+ align:start position:0%
+simple bound. That's why I've erased it
+ 
+
+ align:start position:0%
+simple bound. That's why I've erased it
+but than the double counting kind of
+
+ align:start position:0%
+but than the double counting kind of
+ 
+
+ align:start position:0%
+but than the double counting kind of
+bound.
+
+ align:start position:0%
+bound.
+ 
+
+ align:start position:0%
+bound.
+Okay. So here we go. So the sketchy part
+
+ align:start position:0%
+Okay. So here we go. So the sketchy part
+ 
+
+ align:start position:0%
+Okay. So here we go. So the sketchy part
+of my proof sketch is that I will
+
+ align:start position:0%
+of my proof sketch is that I will
+ 
+
+ align:start position:0%
+of my proof sketch is that I will
+suppose that we are in the uniform case.
+
+ align:start position:0%
+suppose that we are in the uniform case.
+ 
+
+ align:start position:0%
+suppose that we are in the uniform case.
+Namely for every x in E, I will suppose
+
+ align:start position:0%
+Namely for every x in E, I will suppose
+ 
+
+ align:start position:0%
+Namely for every x in E, I will suppose
+that lx of E has size around S.
+
+ align:start position:0%
+that lx of E has size around S.
+ 
+
+ align:start position:0%
+that lx of E has size around S.
+So it's not really the case that they
+
+ align:start position:0%
+So it's not really the case that they
+ 
+
+ align:start position:0%
+So it's not really the case that they
+would all be comparable, but I'll just
+
+ align:start position:0%
+would all be comparable, but I'll just
+ 
+
+ align:start position:0%
+would all be comparable, but I'll just
+explain that special case.
+
+ align:start position:0%
+explain that special case.
+ 
+
+ align:start position:0%
+explain that special case.
+Okay. So now um how many lines are there
+
+ align:start position:0%
+Okay. So now um how many lines are there
+ 
+
+ align:start position:0%
+Okay. So now um how many lines are there
+in total? We can do a double count to
+
+ align:start position:0%
+in total? We can do a double count to
+ 
+
+ align:start position:0%
+in total? We can do a double count to
+find the total number of lines. So we're
+
+ align:start position:0%
+find the total number of lines. So we're
+ 
+
+ align:start position:0%
+find the total number of lines. So we're
+going to double count pairs um x l where
+
+ align:start position:0%
+going to double count pairs um x l where
+ 
+
+ align:start position:0%
+going to double count pairs um x l where
+x is in uh e
+
+ align:start position:0%
+x is in uh e
+ 
+
+ align:start position:0%
+x is in uh e
+and l is in our set of lines.
+
+ align:start position:0%
+and l is in our set of lines.
+ 
+
+ align:start position:0%
+and l is in our set of lines.
+So our total set of lines is going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So how big is le? Um well we could
+
+ align:start position:0%
+Okay. So how big is le? Um well we could
+ 
+
+ align:start position:0%
+Okay. So how big is le? Um well we could
+count the number of these pairs in two
+
+ align:start position:0%
+count the number of these pairs in two
+ 
+
+ align:start position:0%
+count the number of these pairs in two
+ways. We could count okay look at all
+
+ align:start position:0%
+ways. We could count okay look at all
+ 
+
+ align:start position:0%
+ways. We could count okay look at all
+the points of E and each of them is in S
+
+ align:start position:0%
+the points of E and each of them is in S
+ 
+
+ align:start position:0%
+the points of E and each of them is in S
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+or we could say look at each of these
+
+ align:start position:0%
+or we could say look at each of these
+ 
+
+ align:start position:0%
+or we could say look at each of these
+lines
+
+ align:start position:0%
+lines
+ 
+
+ align:start position:0%
+lines
+and um how many points are in each line?
+
+ align:start position:0%
+and um how many points are in each line?
+ 
+
+ align:start position:0%
+and um how many points are in each line?
+Well,
+
+ align:start position:0%
+Well,
+ 
+
+ align:start position:0%
+Well,
+the number of the size of
+
+ align:start position:0%
+the number of the size of
+ 
+
+ align:start position:0%
+the number of the size of
+uh S the size of E intersect L
+
+ align:start position:0%
+uh S the size of E intersect L
+ 
+
+ align:start position:0%
+uh S the size of E intersect L
+for a typical L and L XE would be the
+
+ align:start position:0%
+for a typical L and L XE would be the
+ 
+
+ align:start position:0%
+for a typical L and L XE would be the
+size of E divided by the size of L XE.
+
+ align:start position:0%
+size of E divided by the size of L XE.
+ 
+
+ align:start position:0%
+size of E divided by the size of L XE.
+Right? Because I have all the points in
+
+ align:start position:0%
+Right? Because I have all the points in
+ 
+
+ align:start position:0%
+Right? Because I have all the points in
+E. They are divided among the lines of
+
+ align:start position:0%
+E. They are divided among the lines of
+ 
+
+ align:start position:0%
+E. They are divided among the lines of
+LXE. Again, assuming it's uniform, they
+
+ align:start position:0%
+LXE. Again, assuming it's uniform, they
+ 
+
+ align:start position:0%
+LXE. Again, assuming it's uniform, they
+would all have around this size.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E over L XC
+
+ align:start position:0%
+E over L XC
+ 
+
+ align:start position:0%
+E over L XC
+which is S.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this is the number of points
+
+ align:start position:0%
+Okay. So this is the number of points
+ 
+
+ align:start position:0%
+Okay. So this is the number of points
+times they're each in S lines versus the
+
+ align:start position:0%
+times they're each in S lines versus the
+ 
+
+ align:start position:0%
+times they're each in S lines versus the
+number of lines times they each have
+
+ align:start position:0%
+number of lines times they each have
+ 
+
+ align:start position:0%
+number of lines times they each have
+this many points.
+
+ align:start position:0%
+this many points.
+ 
+
+ align:start position:0%
+this many points.
+Okay. So when we solve we see that the E
+
+ align:start position:0%
+Okay. So when we solve we see that the E
+ 
+
+ align:start position:0%
+Okay. So when we solve we see that the E
+actually drops out and we conclude that
+
+ align:start position:0%
+actually drops out and we conclude that
+ 
+
+ align:start position:0%
+actually drops out and we conclude that
+LE is around S squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So um our goal is to have a lower
+
+ align:start position:0%
+Okay. So um our goal is to have a lower
+ 
+
+ align:start position:0%
+Okay. So um our goal is to have a lower
+bound on on S. So we want to have a
+
+ align:start position:0%
+bound on on S. So we want to have a
+ 
+
+ align:start position:0%
+bound on on S. So we want to have a
+lower bound on LE and the semi trder
+
+ align:start position:0%
+lower bound on LE and the semi trder
+ 
+
+ align:start position:0%
+lower bound on LE and the semi trder
+theorem exactly gives us a lower bound
+
+ align:start position:0%
+theorem exactly gives us a lower bound
+ 
+
+ align:start position:0%
+theorem exactly gives us a lower bound
+on LE. So we can use it. So the semi
+
+ align:start position:0%
+on LE. So we can use it. So the semi
+ 
+
+ align:start position:0%
+on LE. So we can use it. So the semi
+trider theorem tells us that L
+
+ align:start position:0%
+trider theorem tells us that L
+ 
+
+ align:start position:0%
+trider theorem tells us that L
+is at least the minimum of S * E and S
+
+ align:start position:0%
+is at least the minimum of S * E and S
+ 
+
+ align:start position:0%
+is at least the minimum of S * E and S
+to the three * E to the 12. Okay, but
+
+ align:start position:0%
+to the three * E to the 12. Okay, but
+ 
+
+ align:start position:0%
+to the three * E to the 12. Okay, but
+this L E is is S squ. So if you compare
+
+ align:start position:0%
+this L E is is S squ. So if you compare
+ 
+
+ align:start position:0%
+this L E is is S squ. So if you compare
+these we can get a lower bound for S.
+
+ align:start position:0%
+these we can get a lower bound for S.
+ 
+
+ align:start position:0%
+these we can get a lower bound for S.
+In in this case we would have S^ squ is
+
+ align:start position:0%
+In in this case we would have S^ squ is
+ 
+
+ align:start position:0%
+In in this case we would have S^ squ is
+bigger than SE. So s is bigger than e
+
+ align:start position:0%
+bigger than SE. So s is bigger than e
+ 
+
+ align:start position:0%
+bigger than SE. So s is bigger than e
+and in this case we would have s^ squ is
+
+ align:start position:0%
+and in this case we would have s^ squ is
+ 
+
+ align:start position:0%
+and in this case we would have s^ squ is
+bigger than s^ 3 e to the 12 and with a
+
+ align:start position:0%
+bigger than s^ 3 e to the 12 and with a
+ 
+
+ align:start position:0%
+bigger than s^ 3 e to the 12 and with a
+little algebra that is again s bigger
+
+ align:start position:0%
+little algebra that is again s bigger
+ 
+
+ align:start position:0%
+little algebra that is again s bigger
+than e.
+
+ align:start position:0%
+than e.
+ 
+
+ align:start position:0%
+than e.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Um so
+
+ align:start position:0%
+Um so
+ 
+
+ align:start position:0%
+Um so
+right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Right.
+
+ align:start position:0%
+Right.
+ 
+
+ align:start position:0%
+Right.
+Now,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I claim that we didn't need to have
+
+ align:start position:0%
+now I claim that we didn't need to have
+ 
+
+ align:start position:0%
+now I claim that we didn't need to have
+this exact formula here. Let me write
+
+ align:start position:0%
+this exact formula here. Let me write
+ 
+
+ align:start position:0%
+this exact formula here. Let me write
+down all that we needed to to know.
+
+ align:start position:0%
+down all that we needed to to know.
+ 
+
+ align:start position:0%
+down all that we needed to to know.
+So what we needed to know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is just that if E is much bigger than S
+
+ align:start position:0%
+is just that if E is much bigger than S
+ 
+
+ align:start position:0%
+is just that if E is much bigger than S
+um then the size of L E is much bigger
+
+ align:start position:0%
+um then the size of L E is much bigger
+ 
+
+ align:start position:0%
+um then the size of L E is much bigger
+than S squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's a feature you can read off of
+
+ align:start position:0%
+So that's a feature you can read off of
+ 
+
+ align:start position:0%
+So that's a feature you can read off of
+this formula. If E is much bigger than
+
+ align:start position:0%
+this formula. If E is much bigger than
+ 
+
+ align:start position:0%
+this formula. If E is much bigger than
+S, then either one of these is much
+
+ align:start position:0%
+S, then either one of these is much
+ 
+
+ align:start position:0%
+S, then either one of these is much
+bigger than S^ squ. And that's all we
+
+ align:start position:0%
+bigger than S^ squ. And that's all we
+ 
+
+ align:start position:0%
+bigger than S^ squ. And that's all we
+needed to know because we know that L E
+
+ align:start position:0%
+needed to know because we know that L E
+ 
+
+ align:start position:0%
+needed to know because we know that L E
+is only S squ. So by the contraositive
+
+ align:start position:0%
+is only S squ. So by the contraositive
+ 
+
+ align:start position:0%
+is only S squ. So by the contraositive
+we could see that E
+
+ align:start position:0%
+we could see that E
+ 
+
+ align:start position:0%
+we could see that E
+S is not much smaller than E S should be
+
+ align:start position:0%
+S is not much smaller than E S should be
+ 
+
+ align:start position:0%
+S is not much smaller than E S should be
+at least around E.
+
+ align:start position:0%
+at least around E.
+ 
+
+ align:start position:0%
+at least around E.
+Okay. So this thing that we needed to
+
+ align:start position:0%
+Okay. So this thing that we needed to
+ 
+
+ align:start position:0%
+Okay. So this thing that we needed to
+know
+
+ align:start position:0%
+know
+ 
+
+ align:start position:0%
+know
+is very similar to the Orpin and
+
+ align:start position:0%
+is very similar to the Orpin and
+ 
+
+ align:start position:0%
+is very similar to the Orpin and
+Schmurkin theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+E is much bigger. So now let's look up
+
+ align:start position:0%
+E is much bigger. So now let's look up
+ 
+
+ align:start position:0%
+E is much bigger. So now let's look up
+at that Orpin and Schmurkin theorem says
+
+ align:start position:0%
+at that Orpin and Schmurkin theorem says
+ 
+
+ align:start position:0%
+at that Orpin and Schmurkin theorem says
+if T is bigger than S just bigger than
+
+ align:start position:0%
+if T is bigger than S just bigger than
+ 
+
+ align:start position:0%
+if T is bigger than S just bigger than
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+So T is measuring the size of our set E
+
+ align:start position:0%
+So T is measuring the size of our set E
+ 
+
+ align:start position:0%
+So T is measuring the size of our set E
+and little S corresponds to big S.
+
+ align:start position:0%
+and little S corresponds to big S.
+ 
+
+ align:start position:0%
+and little S corresponds to big S.
+So that first hypothesis is saying that
+
+ align:start position:0%
+So that first hypothesis is saying that
+ 
+
+ align:start position:0%
+So that first hypothesis is saying that
+the set is much bigger than the number
+
+ align:start position:0%
+the set is much bigger than the number
+ 
+
+ align:start position:0%
+the set is much bigger than the number
+of directions.
+
+ align:start position:0%
+of directions.
+ 
+
+ align:start position:0%
+of directions.
+And then the conclusion is that the
+
+ align:start position:0%
+And then the conclusion is that the
+ 
+
+ align:start position:0%
+And then the conclusion is that the
+number of lines is much bigger than S^
+
+ align:start position:0%
+number of lines is much bigger than S^
+ 
+
+ align:start position:0%
+number of lines is much bigger than S^
+squ. that thing is this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this matches
+
+ align:start position:0%
+Okay. So this matches
+ 
+
+ align:start position:0%
+Okay. So this matches
+the theorem of Orpin and Schmurkin the
+
+ align:start position:0%
+the theorem of Orpin and Schmurkin the
+ 
+
+ align:start position:0%
+the theorem of Orpin and Schmurkin the
+epsilon improvement theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So that suggests an idea that we
+
+ align:start position:0%
+Okay. So that suggests an idea that we
+ 
+
+ align:start position:0%
+Okay. So that suggests an idea that we
+could use that epsilon improvement
+
+ align:start position:0%
+could use that epsilon improvement
+ 
+
+ align:start position:0%
+could use that epsilon improvement
+theorem by Orpin and Schmurkin and put
+
+ align:start position:0%
+theorem by Orpin and Schmurkin and put
+ 
+
+ align:start position:0%
+theorem by Orpin and Schmurkin and put
+it into an argument like this one and
+
+ align:start position:0%
+it into an argument like this one and
+ 
+
+ align:start position:0%
+it into an argument like this one and
+prove some kind of generalization of
+
+ align:start position:0%
+prove some kind of generalization of
+ 
+
+ align:start position:0%
+prove some kind of generalization of
+Beck's theorem that might have a sharp
+
+ align:start position:0%
+Beck's theorem that might have a sharp
+ 
+
+ align:start position:0%
+Beck's theorem that might have a sharp
+conclusion even though we stuck into it
+
+ align:start position:0%
+conclusion even though we stuck into it
+ 
+
+ align:start position:0%
+conclusion even though we stuck into it
+just a epsilon improvement
+
+ align:start position:0%
+just a epsilon improvement
+ 
+
+ align:start position:0%
+just a epsilon improvement
+and that actually works. So I'm going to
+
+ align:start position:0%
+and that actually works. So I'm going to
+ 
+
+ align:start position:0%
+and that actually works. So I'm going to
+write it down now for us.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So this is called the continuum
+
+ align:start position:0%
+So this is called the continuum
+ 
+
+ align:start position:0%
+So this is called the continuum
+or we could call it in our class the
+
+ align:start position:0%
+or we could call it in our class the
+ 
+
+ align:start position:0%
+or we could call it in our class the
+delta ball version of back theory.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this is a theorem of merkin and
+
+ align:start position:0%
+Okay. So this is a theorem of merkin and
+ 
+
+ align:start position:0%
+Okay. So this is a theorem of merkin and
+wong in 23 I think.
+
+ align:start position:0%
+wong in 23 I think.
+ 
+
+ align:start position:0%
+wong in 23 I think.
+All right. So we're going to translate
+
+ align:start position:0%
+All right. So we're going to translate
+ 
+
+ align:start position:0%
+All right. So we're going to translate
+this theorem into the language of delta
+
+ align:start position:0%
+this theorem into the language of delta
+ 
+
+ align:start position:0%
+this theorem into the language of delta
+SC sets.
+
+ align:start position:0%
+SC sets.
+ 
+
+ align:start position:0%
+SC sets.
+So we're going to say if E is a deltaU
+
+ align:start position:0%
+So we're going to say if E is a deltaU
+ 
+
+ align:start position:0%
+So we're going to say if E is a deltaU
+set, I'm going to leave out the C. Uh
+
+ align:start position:0%
+set, I'm going to leave out the C. Uh
+ 
+
+ align:start position:0%
+set, I'm going to leave out the C. Uh
+things will depend on C, but E is a
+
+ align:start position:0%
+things will depend on C, but E is a
+ 
+
+ align:start position:0%
+things will depend on C, but E is a
+deltaU set. Okay, so that's our set. Now
+
+ align:start position:0%
+deltaU set. Okay, so that's our set. Now
+ 
+
+ align:start position:0%
+deltaU set. Okay, so that's our set. Now
+I need an analog of this hypothesis that
+
+ align:start position:0%
+I need an analog of this hypothesis that
+ 
+
+ align:start position:0%
+I need an analog of this hypothesis that
+E is not too much in the line. And the
+
+ align:start position:0%
+E is not too much in the line. And the
+ 
+
+ align:start position:0%
+E is not too much in the line. And the
+analog says that E will be not too much
+
+ align:start position:0%
+analog says that E will be not too much
+ 
+
+ align:start position:0%
+analog says that E will be not too much
+in any thin rectangle.
+
+ align:start position:0%
+in any thin rectangle.
+ 
+
+ align:start position:0%
+in any thin rectangle.
+So we'll say if R is a row by one
+
+ align:start position:0%
+So we'll say if R is a row by one
+ 
+
+ align:start position:0%
+So we'll say if R is a row by one
+rectangle
+
+ align:start position:0%
+rectangle
+ 
+
+ align:start position:0%
+rectangle
+um then
+
+ align:start position:0%
+um then
+ 
+
+ align:start position:0%
+um then
+if you take E and you intersect it with
+
+ align:start position:0%
+if you take E and you intersect it with
+ 
+
+ align:start position:0%
+if you take E and you intersect it with
+R take the delta covering number of that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+should be kind of smaller than the total
+
+ align:start position:0%
+should be kind of smaller than the total
+ 
+
+ align:start position:0%
+should be kind of smaller than the total
+delta covering number.
+
+ align:start position:0%
+delta covering number.
+ 
+
+ align:start position:0%
+delta covering number.
+Okay so it should be row to the ADA
+
+ align:start position:0%
+Okay so it should be row to the ADA
+ 
+
+ align:start position:0%
+Okay so it should be row to the ADA
+smaller than constant row to the ADA is
+
+ align:start position:0%
+smaller than constant row to the ADA is
+ 
+
+ align:start position:0%
+smaller than constant row to the ADA is
+smaller than the total delta covering
+
+ align:start position:0%
+smaller than the total delta covering
+ 
+
+ align:start position:0%
+smaller than the total delta covering
+number. Maybe we can we can put the C
+
+ align:start position:0%
+number. Maybe we can we can put the C
+ 
+
+ align:start position:0%
+number. Maybe we can we can put the C
+back here also. So who is ADA? At the
+
+ align:start position:0%
+back here also. So who is ADA? At the
+ 
+
+ align:start position:0%
+back here also. So who is ADA? At the
+very beginning of the story, we'll say
+
+ align:start position:0%
+very beginning of the story, we'll say
+ 
+
+ align:start position:0%
+very beginning of the story, we'll say
+for every
+
+ align:start position:0%
+for every
+ 
+
+ align:start position:0%
+for every
+ADA bigger than zero. So ADA should be a
+
+ align:start position:0%
+ADA bigger than zero. So ADA should be a
+ 
+
+ align:start position:0%
+ADA bigger than zero. So ADA should be a
+positive number. Okay. So this is a not
+
+ align:start position:0%
+positive number. Okay. So this is a not
+ 
+
+ align:start position:0%
+positive number. Okay. So this is a not
+super strong condition, but it's saying
+
+ align:start position:0%
+super strong condition, but it's saying
+ 
+
+ align:start position:0%
+super strong condition, but it's saying
+that E is not heavily concentrated into
+
+ align:start position:0%
+that E is not heavily concentrated into
+ 
+
+ align:start position:0%
+that E is not heavily concentrated into
+a thin rectangle.
+
+ align:start position:0%
+a thin rectangle.
+ 
+
+ align:start position:0%
+a thin rectangle.
+Okay. And then the conclusion is um
+
+ align:start position:0%
+Okay. And then the conclusion is um
+ 
+
+ align:start position:0%
+Okay. And then the conclusion is um
+there exists an x in e s so that
+
+ align:start position:0%
+there exists an x in e s so that
+ 
+
+ align:start position:0%
+there exists an x in e s so that
+um the size of lxe
+
+ align:start position:0%
+um the size of lxe
+ 
+
+ align:start position:0%
+um the size of lxe
+is greater than um
+
+ align:start position:0%
+is greater than um
+ 
+
+ align:start position:0%
+is greater than um
+uh the minimum
+
+ align:start position:0%
+uh the minimum
+ 
+
+ align:start position:0%
+uh the minimum
+of delta to the minus u and one. So this
+
+ align:start position:0%
+of delta to the minus u and one. So this
+ 
+
+ align:start position:0%
+of delta to the minus u and one. So this
+would be and sorry not one delta to the
+
+ align:start position:0%
+would be and sorry not one delta to the
+ 
+
+ align:start position:0%
+would be and sorry not one delta to the
+minus one.
+
+ align:start position:0%
+minus one.
+ 
+
+ align:start position:0%
+minus one.
+Okay. So what's going on here? The our
+
+ align:start position:0%
+Okay. So what's going on here? The our
+ 
+
+ align:start position:0%
+Okay. So what's going on here? The our
+original theorem would say that lxe e is
+
+ align:start position:0%
+original theorem would say that lxe e is
+ 
+
+ align:start position:0%
+original theorem would say that lxe e is
+at least the size of e and that's the
+
+ align:start position:0%
+at least the size of e and that's the
+ 
+
+ align:start position:0%
+at least the size of e and that's the
+size of so that's what it's doing here.
+
+ align:start position:0%
+size of so that's what it's doing here.
+ 
+
+ align:start position:0%
+size of so that's what it's doing here.
+On the other hand if I had every delta
+
+ align:start position:0%
+On the other hand if I had every delta
+ 
+
+ align:start position:0%
+On the other hand if I had every delta
+tube if lxe consisted of all the delta
+
+ align:start position:0%
+tube if lxe consisted of all the delta
+ 
+
+ align:start position:0%
+tube if lxe consisted of all the delta
+tubes through x there would only be
+
+ align:start position:0%
+tubes through x there would only be
+ 
+
+ align:start position:0%
+tubes through x there would only be
+delta inverse of them. So it couldn't
+
+ align:start position:0%
+delta inverse of them. So it couldn't
+ 
+
+ align:start position:0%
+delta inverse of them. So it couldn't
+possibly be bigger than this. So we have
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um cool. So that's the statement of the
+
+ align:start position:0%
+Um cool. So that's the statement of the
+ 
+
+ align:start position:0%
+Um cool. So that's the statement of the
+theorem and it is again uh sharp because
+
+ align:start position:0%
+theorem and it is again uh sharp because
+ 
+
+ align:start position:0%
+theorem and it is again uh sharp because
+as we just explained this couldn't
+
+ align:start position:0%
+as we just explained this couldn't
+ 
+
+ align:start position:0%
+as we just explained this couldn't
+possibly be bigger than this and it also
+
+ align:start position:0%
+possibly be bigger than this and it also
+ 
+
+ align:start position:0%
+possibly be bigger than this and it also
+couldn't possibly be bigger than this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+correct.
+
+ align:start position:0%
+correct.
+ 
+
+ align:start position:0%
+correct.
+So this theorem is sharp. It's also
+
+ align:start position:0%
+So this theorem is sharp. It's also
+ 
+
+ align:start position:0%
+So this theorem is sharp. It's also
+false over C.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? So the example over C would be
+
+ align:start position:0%
+Right? So the example over C would be
+ 
+
+ align:start position:0%
+Right? So the example over C would be
+that the set E
+
+ align:start position:0%
+that the set E
+ 
+
+ align:start position:0%
+that the set E
+could be uh R2 which is sitting in C2.
+
+ align:start position:0%
+could be uh R2 which is sitting in C2.
+ 
+
+ align:start position:0%
+could be uh R2 which is sitting in C2.
+And if you imagine R2, if you take any
+
+ align:start position:0%
+And if you imagine R2, if you take any
+ 
+
+ align:start position:0%
+And if you imagine R2, if you take any
+point in R2 and look at all of the
+
+ align:start position:0%
+point in R2 and look at all of the
+ 
+
+ align:start position:0%
+point in R2 and look at all of the
+lines, complex lines that um go through
+
+ align:start position:0%
+lines, complex lines that um go through
+ 
+
+ align:start position:0%
+lines, complex lines that um go through
+that point, um there aren't the the each
+
+ align:start position:0%
+that point, um there aren't the the each
+ 
+
+ align:start position:0%
+that point, um there aren't the the each
+one of them goes through many of the
+
+ align:start position:0%
+one of them goes through many of the
+ 
+
+ align:start position:0%
+one of them goes through many of the
+points of R2 and um and the number there
+
+ align:start position:0%
+points of R2 and um and the number there
+ 
+
+ align:start position:0%
+points of R2 and um and the number there
+aren't that many of them. It would
+
+ align:start position:0%
+aren't that many of them. It would
+ 
+
+ align:start position:0%
+aren't that many of them. It would
+violate this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this theorem is uh in the
+
+ align:start position:0%
+Okay, so this theorem is uh in the
+ 
+
+ align:start position:0%
+Okay, so this theorem is uh in the
+general spirit of projection theory. um
+
+ align:start position:0%
+general spirit of projection theory. um
+ 
+
+ align:start position:0%
+general spirit of projection theory. um
+it is a sharp theorem and it
+
+ align:start position:0%
+it is a sharp theorem and it
+ 
+
+ align:start position:0%
+it is a sharp theorem and it
+distinguishes R from C and I believe it
+
+ align:start position:0%
+distinguishes R from C and I believe it
+ 
+
+ align:start position:0%
+distinguishes R from C and I believe it
+is the first such theorem in the
+
+ align:start position:0%
+is the first such theorem in the
+ 
+
+ align:start position:0%
+is the first such theorem in the
+literature. So we were trying for 20
+
+ align:start position:0%
+literature. So we were trying for 20
+ 
+
+ align:start position:0%
+literature. So we were trying for 20
+plus years to distinguish R from C. For
+
+ align:start position:0%
+plus years to distinguish R from C. For
+ 
+
+ align:start position:0%
+plus years to distinguish R from C. For
+a long time we could only do it with
+
+ align:start position:0%
+a long time we could only do it with
+ 
+
+ align:start position:0%
+a long time we could only do it with
+epsilon improvements. But this is not
+
+ align:start position:0%
+epsilon improvements. But this is not
+ 
+
+ align:start position:0%
+epsilon improvements. But this is not
+just an epsilon improvement on what was
+
+ align:start position:0%
+just an epsilon improvement on what was
+ 
+
+ align:start position:0%
+just an epsilon improvement on what was
+known before. It's not just an epsilon
+
+ align:start position:0%
+known before. It's not just an epsilon
+ 
+
+ align:start position:0%
+known before. It's not just an epsilon
+improvement on what's true over over C.
+
+ align:start position:0%
+improvement on what's true over over C.
+ 
+
+ align:start position:0%
+improvement on what's true over over C.
+And it's a sharp theorem.
+
+ align:start position:0%
+And it's a sharp theorem.
+ 
+
+ align:start position:0%
+And it's a sharp theorem.
+Okay. Any questions or comments about
+
+ align:start position:0%
+Okay. Any questions or comments about
+ 
+
+ align:start position:0%
+Okay. Any questions or comments about
+the statement?
+
+ align:start position:0%
+the statement?
+ 
+
+ align:start position:0%
+the statement?
+So the problem depends on
+
+ align:start position:0%
+So the problem depends on
+ 
+
+ align:start position:0%
+So the problem depends on
+>> yeah so if you unpack this it must
+
+ align:start position:0%
+>> yeah so if you unpack this it must
+ 
+
+ align:start position:0%
+>> yeah so if you unpack this it must
+depend on ADA. Uh I think it is a
+
+ align:start position:0%
+depend on ADA. Uh I think it is a
+ 
+
+ align:start position:0%
+depend on ADA. Uh I think it is a
+constant depending on epsilon and ada
+
+ align:start position:0%
+constant depending on epsilon and ada
+ 
+
+ align:start position:0%
+constant depending on epsilon and ada
+delta to the epsilon and big c to the
+
+ align:start position:0%
+delta to the epsilon and big c to the
+ 
+
+ align:start position:0%
+delta to the epsilon and big c to the
+minus big.
+
+ align:start position:0%
+minus big.
+ 
+
+ align:start position:0%
+minus big.
+So it depends on it depends on aa
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's conceivable that this depends on
+
+ align:start position:0%
+it's conceivable that this depends on
+ 
+
+ align:start position:0%
+it's conceivable that this depends on
+ada. I'm not sure about that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Other questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Okay. So the the idea in the first
+
+ align:start position:0%
+Okay. Okay. So the the idea in the first
+ 
+
+ align:start position:0%
+Okay. Okay. So the the idea in the first
+place is to imitate this proof of Beex
+
+ align:start position:0%
+place is to imitate this proof of Beex
+ 
+
+ align:start position:0%
+place is to imitate this proof of Beex
+theorem proof that converts um a uh
+
+ align:start position:0%
+theorem proof that converts um a uh
+ 
+
+ align:start position:0%
+theorem proof that converts um a uh
+a an epsilon improvement on some simple
+
+ align:start position:0%
+a an epsilon improvement on some simple
+ 
+
+ align:start position:0%
+a an epsilon improvement on some simple
+estimate for sem ready troder into a
+
+ align:start position:0%
+estimate for sem ready troder into a
+ 
+
+ align:start position:0%
+estimate for sem ready troder into a
+sharp estimate for this beck kind of
+
+ align:start position:0%
+sharp estimate for this beck kind of
+ 
+
+ align:start position:0%
+sharp estimate for this beck kind of
+thing. Um but when we try to do that we
+
+ align:start position:0%
+thing. Um but when we try to do that we
+ 
+
+ align:start position:0%
+thing. Um but when we try to do that we
+will see that there is an issue with it.
+
+ align:start position:0%
+will see that there is an issue with it.
+ 
+
+ align:start position:0%
+will see that there is an issue with it.
+Um and and when we flesh out the proof a
+
+ align:start position:0%
+Um and and when we flesh out the proof a
+ 
+
+ align:start position:0%
+Um and and when we flesh out the proof a
+little more, it will involve using the
+
+ align:start position:0%
+little more, it will involve using the
+ 
+
+ align:start position:0%
+little more, it will involve using the
+Orpin and Schmurkin theorem not just
+
+ align:start position:0%
+Orpin and Schmurkin theorem not just
+ 
+
+ align:start position:0%
+Orpin and Schmurkin theorem not just
+once but many times at many different
+
+ align:start position:0%
+once but many times at many different
+ 
+
+ align:start position:0%
+once but many times at many different
+scales.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So let's sketch the proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So first plan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is to imitate
+
+ align:start position:0%
+is to imitate
+ 
+
+ align:start position:0%
+is to imitate
+the proof of uh of Beck.
+
+ align:start position:0%
+the proof of uh of Beck.
+ 
+
+ align:start position:0%
+the proof of uh of Beck.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Um okay. So let's carry that out over
+
+ align:start position:0%
+Um okay. So let's carry that out over
+ 
+
+ align:start position:0%
+Um okay. So let's carry that out over
+here. I'll put the beex proof up.
+
+ align:start position:0%
+here. I'll put the beex proof up.
+ 
+
+ align:start position:0%
+here. I'll put the beex proof up.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So attempt attempt one.
+
+ align:start position:0%
+So attempt attempt one.
+ 
+
+ align:start position:0%
+So attempt attempt one.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+All right. So let's say that lxe
+
+ align:start position:0%
+All right. So let's say that lxe
+ 
+
+ align:start position:0%
+All right. So let's say that lxe
+is a delta SC
+
+ align:start position:0%
+is a delta SC
+ 
+
+ align:start position:0%
+is a delta SC
+set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now that's related to the cardality of
+
+ align:start position:0%
+Now that's related to the cardality of
+ 
+
+ align:start position:0%
+Now that's related to the cardality of
+LXE. This is a theorem about the
+
+ align:start position:0%
+LXE. This is a theorem about the
+ 
+
+ align:start position:0%
+LXE. This is a theorem about the
+cardality of LXE. What is the
+
+ align:start position:0%
+cardality of LXE. What is the
+ 
+
+ align:start position:0%
+cardality of LXE. What is the
+relationship? Well, it implies that the
+
+ align:start position:0%
+relationship? Well, it implies that the
+ 
+
+ align:start position:0%
+relationship? Well, it implies that the
+cardality of lexe is at least uh around
+
+ align:start position:0%
+cardality of lexe is at least uh around
+ 
+
+ align:start position:0%
+cardality of lexe is at least uh around
+delta to the minus s, but it could be
+
+ align:start position:0%
+delta to the minus s, but it could be
+ 
+
+ align:start position:0%
+delta to the minus s, but it could be
+much bigger.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay, so an example where these would be
+
+ align:start position:0%
+Okay, so an example where these would be
+ 
+
+ align:start position:0%
+Okay, so an example where these would be
+about the same is if lxe was sort of
+
+ align:start position:0%
+about the same is if lxe was sort of
+ 
+
+ align:start position:0%
+about the same is if lxe was sort of
+like an s-dimensional caner set. An
+
+ align:start position:0%
+like an s-dimensional caner set. An
+ 
+
+ align:start position:0%
+like an s-dimensional caner set. An
+example where they would be very
+
+ align:start position:0%
+example where they would be very
+ 
+
+ align:start position:0%
+example where they would be very
+different is uh if is if LXE was very
+
+ align:start position:0%
+different is uh if is if LXE was very
+ 
+
+ align:start position:0%
+different is uh if is if LXE was very
+clumped. So here's a piece of S1 and
+
+ align:start position:0%
+clumped. So here's a piece of S1 and
+ 
+
+ align:start position:0%
+clumped. So here's a piece of S1 and
+maybe LXE
+
+ align:start position:0%
+maybe LXE
+ 
+
+ align:start position:0%
+maybe LXE
+is clumped like that. So these dots
+
+ align:start position:0%
+is clumped like that. So these dots
+ 
+
+ align:start position:0%
+is clumped like that. So these dots
+represent Lexi.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if it was if if Lex was really
+
+ align:start position:0%
+So if it was if if Lex was really
+ 
+
+ align:start position:0%
+So if it was if if Lex was really
+clumped into a much smaller interval
+
+ align:start position:0%
+clumped into a much smaller interval
+ 
+
+ align:start position:0%
+clumped into a much smaller interval
+then um S would actually have to be
+
+ align:start position:0%
+then um S would actually have to be
+ 
+
+ align:start position:0%
+then um S would actually have to be
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+This is not a delta SC set except for S
+
+ align:start position:0%
+This is not a delta SC set except for S
+ 
+
+ align:start position:0%
+This is not a delta SC set except for S
+equals Z.
+
+ align:start position:0%
+equals Z.
+ 
+
+ align:start position:0%
+equals Z.
+On the other hand, the cardality of LXC
+
+ align:start position:0%
+On the other hand, the cardality of LXC
+ 
+
+ align:start position:0%
+On the other hand, the cardality of LXC
+in this picture is is is large and in
+
+ align:start position:0%
+in this picture is is is large and in
+ 
+
+ align:start position:0%
+in this picture is is is large and in
+particular, it's much larger than delta
+
+ align:start position:0%
+particular, it's much larger than delta
+ 
+
+ align:start position:0%
+particular, it's much larger than delta
+to the minus0.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this S is some non-conentration
+
+ align:start position:0%
+Okay, so this S is some non-conentration
+ 
+
+ align:start position:0%
+Okay, so this S is some non-conentration
+condition and non-conentration forces
+
+ align:start position:0%
+condition and non-conentration forces
+ 
+
+ align:start position:0%
+condition and non-conentration forces
+our set to be pretty big. But it could
+
+ align:start position:0%
+our set to be pretty big. But it could
+ 
+
+ align:start position:0%
+our set to be pretty big. But it could
+also be much bigger than that if it was
+
+ align:start position:0%
+also be much bigger than that if it was
+ 
+
+ align:start position:0%
+also be much bigger than that if it was
+kind of clumped.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So let's uh let's try to imitate
+
+ align:start position:0%
+Okay. So let's uh let's try to imitate
+ 
+
+ align:start position:0%
+Okay. So let's uh let's try to imitate
+our proof. Uh I'm going to suppose that
+
+ align:start position:0%
+our proof. Uh I'm going to suppose that
+ 
+
+ align:start position:0%
+our proof. Uh I'm going to suppose that
+we're in the uniform case.
+
+ align:start position:0%
+we're in the uniform case.
+ 
+
+ align:start position:0%
+we're in the uniform case.
+So all of the lxe have the same s
+
+ align:start position:0%
+So all of the lxe have the same s
+ 
+
+ align:start position:0%
+So all of the lxe have the same s
+and the same size of lx.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we can do our same double
+
+ align:start position:0%
+Okay, we can do our same double
+ 
+
+ align:start position:0%
+Okay, we can do our same double
+counting.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That part doesn't change at all. And it
+
+ align:start position:0%
+That part doesn't change at all. And it
+ 
+
+ align:start position:0%
+That part doesn't change at all. And it
+has it gives us L E is at least
+
+ align:start position:0%
+has it gives us L E is at least
+ 
+
+ align:start position:0%
+has it gives us L E is at least
+L XE^2.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, sorry, is approximately LXE squ.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And so to get a lower bound on LXE, it
+
+ align:start position:0%
+And so to get a lower bound on LXE, it
+ 
+
+ align:start position:0%
+And so to get a lower bound on LXE, it
+suffices to get a lower bound on LE.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What happens here? Um so now we can
+
+ align:start position:0%
+What happens here? Um so now we can
+ 
+
+ align:start position:0%
+What happens here? Um so now we can
+apply the uh theorem of Orpin and
+
+ align:start position:0%
+apply the uh theorem of Orpin and
+ 
+
+ align:start position:0%
+apply the uh theorem of Orpin and
+Schmurkin epsilon improvement
+
+ align:start position:0%
+Schmurkin epsilon improvement
+ 
+
+ align:start position:0%
+Schmurkin epsilon improvement
+which I just erased in a suboptimal use
+
+ align:start position:0%
+which I just erased in a suboptimal use
+ 
+
+ align:start position:0%
+which I just erased in a suboptimal use
+of blackboards. Um but uh what it says
+
+ align:start position:0%
+of blackboards. Um but uh what it says
+ 
+
+ align:start position:0%
+of blackboards. Um but uh what it says
+in this case is uh that if u if s is
+
+ align:start position:0%
+in this case is uh that if u if s is
+ 
+
+ align:start position:0%
+in this case is uh that if u if s is
+smaller than the minimum of u and one
+
+ align:start position:0%
+smaller than the minimum of u and one
+ 
+
+ align:start position:0%
+smaller than the minimum of u and one
+but bigger than zero
+
+ align:start position:0%
+but bigger than zero
+ 
+
+ align:start position:0%
+but bigger than zero
+then we get
+
+ align:start position:0%
+then we get
+ 
+
+ align:start position:0%
+then we get
+le e is at least delta the minus 2s
+
+ align:start position:0%
+le e is at least delta the minus 2s
+ 
+
+ align:start position:0%
+le e is at least delta the minus 2s
+minus epsilon. So that this would be the
+
+ align:start position:0%
+minus epsilon. So that this would be the
+ 
+
+ align:start position:0%
+minus epsilon. So that this would be the
+classical bound
+
+ align:start position:0%
+classical bound
+ 
+
+ align:start position:0%
+classical bound
+and then we have this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And then we're interested in lxe.
+
+ align:start position:0%
+Okay. And then we're interested in lxe.
+ 
+
+ align:start position:0%
+Okay. And then we're interested in lxe.
+That tells us that lxe
+
+ align:start position:0%
+That tells us that lxe
+ 
+
+ align:start position:0%
+That tells us that lxe
+is at least delta to the minus s minus
+
+ align:start position:0%
+is at least delta to the minus s minus
+ 
+
+ align:start position:0%
+is at least delta to the minus s minus
+epsilon.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so let's take stock.
+
+ align:start position:0%
+Okay, so let's take stock.
+ 
+
+ align:start position:0%
+Okay, so let's take stock.
+If S were equal to the minimum of U and
+
+ align:start position:0%
+If S were equal to the minimum of U and
+ 
+
+ align:start position:0%
+If S were equal to the minimum of U and
+one, then LXE would be at least delta to
+
+ align:start position:0%
+one, then LXE would be at least delta to
+ 
+
+ align:start position:0%
+one, then LXE would be at least delta to
+the minus S. That would be the bound we
+
+ align:start position:0%
+the minus S. That would be the bound we
+ 
+
+ align:start position:0%
+the minus S. That would be the bound we
+want to prove. So in that case, we would
+
+ align:start position:0%
+want to prove. So in that case, we would
+ 
+
+ align:start position:0%
+want to prove. So in that case, we would
+be very happy.
+
+ align:start position:0%
+be very happy.
+ 
+
+ align:start position:0%
+be very happy.
+Okay. Now suppose S is in this range.
+
+ align:start position:0%
+Okay. Now suppose S is in this range.
+ 
+
+ align:start position:0%
+Okay. Now suppose S is in this range.
+Well, then we get this bound.
+
+ align:start position:0%
+Well, then we get this bound.
+ 
+
+ align:start position:0%
+Well, then we get this bound.
+This bound is a tiny bit better than
+
+ align:start position:0%
+This bound is a tiny bit better than
+ 
+
+ align:start position:0%
+This bound is a tiny bit better than
+this bound,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but that's all.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This argument didn't work so nicely as
+
+ align:start position:0%
+This argument didn't work so nicely as
+ 
+
+ align:start position:0%
+This argument didn't work so nicely as
+that argument because in that case there
+
+ align:start position:0%
+that argument because in that case there
+ 
+
+ align:start position:0%
+that argument because in that case there
+was no distinction between cardality and
+
+ align:start position:0%
+was no distinction between cardality and
+ 
+
+ align:start position:0%
+was no distinction between cardality and
+the value of s. In that case this was
+
+ align:start position:0%
+the value of s. In that case this was
+ 
+
+ align:start position:0%
+the value of s. In that case this was
+the same as this. So we would get a
+
+ align:start position:0%
+the same as this. So we would get a
+ 
+
+ align:start position:0%
+the same as this. So we would get a
+contradiction at this moment and we
+
+ align:start position:0%
+contradiction at this moment and we
+ 
+
+ align:start position:0%
+contradiction at this moment and we
+could we could conclude that actually s
+
+ align:start position:0%
+could we could conclude that actually s
+ 
+
+ align:start position:0%
+could we could conclude that actually s
+is the minimum of u and one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um so we did learn something. Um
+
+ align:start position:0%
+Um so we did learn something. Um
+ 
+
+ align:start position:0%
+Um so we did learn something. Um
+you know if if lxe were kind of spread
+
+ align:start position:0%
+you know if if lxe were kind of spread
+ 
+
+ align:start position:0%
+you know if if lxe were kind of spread
+out you then you might hope that the
+
+ align:start position:0%
+out you then you might hope that the
+ 
+
+ align:start position:0%
+out you then you might hope that the
+cardality would be about delta to the
+
+ align:start position:0%
+cardality would be about delta to the
+ 
+
+ align:start position:0%
+cardality would be about delta to the
+minus s and in that spread out case then
+
+ align:start position:0%
+minus s and in that spread out case then
+ 
+
+ align:start position:0%
+minus s and in that spread out case then
+we could get we would follow that that s
+
+ align:start position:0%
+we could get we would follow that that s
+ 
+
+ align:start position:0%
+we could get we would follow that that s
+was the minimum of u and one.
+
+ align:start position:0%
+was the minimum of u and one.
+ 
+
+ align:start position:0%
+was the minimum of u and one.
+So we see so we see this correlary
+
+ align:start position:0%
+So we see so we see this correlary
+ 
+
+ align:start position:0%
+So we see so we see this correlary
+if um
+
+ align:start position:0%
+if um
+ 
+
+ align:start position:0%
+if um
+lxe is a delta s set
+
+ align:start position:0%
+lxe is a delta s set
+ 
+
+ align:start position:0%
+lxe is a delta s set
+and the size of lxe
+
+ align:start position:0%
+and the size of lxe
+ 
+
+ align:start position:0%
+and the size of lxe
+is around delta to the minus s then we
+
+ align:start position:0%
+is around delta to the minus s then we
+ 
+
+ align:start position:0%
+is around delta to the minus s then we
+would get that the size of lxe is
+
+ align:start position:0%
+would get that the size of lxe is
+ 
+
+ align:start position:0%
+would get that the size of lxe is
+greater than around the minimum of delta
+
+ align:start position:0%
+greater than around the minimum of delta
+ 
+
+ align:start position:0%
+greater than around the minimum of delta
+to the minus u and delta to the minus1
+
+ align:start position:0%
+to the minus u and delta to the minus1
+ 
+
+ align:start position:0%
+to the minus u and delta to the minus1
+and we would be happy.
+
+ align:start position:0%
+and we would be happy.
+ 
+
+ align:start position:0%
+and we would be happy.
+But it's a big if and we don't
+
+ align:start position:0%
+But it's a big if and we don't
+ 
+
+ align:start position:0%
+But it's a big if and we don't
+understand yet very well what might
+
+ align:start position:0%
+understand yet very well what might
+ 
+
+ align:start position:0%
+understand yet very well what might
+happen if these sets were a little more
+
+ align:start position:0%
+happen if these sets were a little more
+ 
+
+ align:start position:0%
+happen if these sets were a little more
+clumped.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So um let me put up a summary
+
+ align:start position:0%
+All right. So um let me put up a summary
+ 
+
+ align:start position:0%
+All right. So um let me put up a summary
+of what we've learned so far. So lama
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if s is bigger than zero and a typical
+
+ align:start position:0%
+if s is bigger than zero and a typical
+ 
+
+ align:start position:0%
+if s is bigger than zero and a typical
+lxe
+
+ align:start position:0%
+lxe
+ 
+
+ align:start position:0%
+lxe
+is delta sc.
+
+ align:start position:0%
+is delta sc.
+ 
+
+ align:start position:0%
+is delta sc.
+Um then
+
+ align:start position:0%
+Um then
+ 
+
+ align:start position:0%
+Um then
+size of typical lxe is at least delta to
+
+ align:start position:0%
+size of typical lxe is at least delta to
+ 
+
+ align:start position:0%
+size of typical lxe is at least delta to
+the minus s minus epsilon or sorry yeah
+
+ align:start position:0%
+the minus s minus epsilon or sorry yeah
+ 
+
+ align:start position:0%
+the minus s minus epsilon or sorry yeah
+if
+
+ align:start position:0%
+if
+ 
+
+ align:start position:0%
+if
+0 is less than s is less than the
+
+ align:start position:0%
+0 is less than s is less than the
+ 
+
+ align:start position:0%
+0 is less than s is less than the
+minimum of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so the proof of this theorem we
+
+ align:start position:0%
+okay so the proof of this theorem we
+ 
+
+ align:start position:0%
+okay so the proof of this theorem we
+don't have it yet we have this lema um
+
+ align:start position:0%
+don't have it yet we have this lema um
+ 
+
+ align:start position:0%
+don't have it yet we have this lema um
+the proof of this theorem is by
+
+ align:start position:0%
+the proof of this theorem is by
+ 
+
+ align:start position:0%
+the proof of this theorem is by
+bootstrapping this lema using it many
+
+ align:start position:0%
+bootstrapping this lema using it many
+ 
+
+ align:start position:0%
+bootstrapping this lema using it many
+times at different scales and locations.
+
+ align:start position:0%
+times at different scales and locations.
+ 
+
+ align:start position:0%
+times at different scales and locations.
+So we are effectively using the epsilon
+
+ align:start position:0%
+So we are effectively using the epsilon
+ 
+
+ align:start position:0%
+So we are effectively using the epsilon
+improvement many times not just once and
+
+ align:start position:0%
+improvement many times not just once and
+ 
+
+ align:start position:0%
+improvement many times not just once and
+at many scales.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about it.
+
+ align:start position:0%
+about it.
+ 
+
+ align:start position:0%
+about it.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, let's do a sketch of this
+
+ align:start position:0%
+All right. So, let's do a sketch of this
+ 
+
+ align:start position:0%
+All right. So, let's do a sketch of this
+bootstrap iteration.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um so we're going to suppose
+
+ align:start position:0%
+Okay. Um so we're going to suppose
+ 
+
+ align:start position:0%
+Okay. Um so we're going to suppose
+that lxe first of all is uniform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and also that it is delta sc for some s
+
+ align:start position:0%
+and also that it is delta sc for some s
+ 
+
+ align:start position:0%
+and also that it is delta sc for some s
+which is bigger than zero. It's the
+
+ align:start position:0%
+which is bigger than zero. It's the
+ 
+
+ align:start position:0%
+which is bigger than zero. It's the
+start of our bootstrap.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So because it's uniform and it's a delta
+
+ align:start position:0%
+So because it's uniform and it's a delta
+ 
+
+ align:start position:0%
+So because it's uniform and it's a delta
+SC set then it follows that if you take
+
+ align:start position:0%
+SC set then it follows that if you take
+ 
+
+ align:start position:0%
+SC set then it follows that if you take
+its sort of its row neighborhood then
+
+ align:start position:0%
+its sort of its row neighborhood then
+ 
+
+ align:start position:0%
+its sort of its row neighborhood then
+this is a row SC set
+
+ align:start position:0%
+this is a row SC set
+ 
+
+ align:start position:0%
+this is a row SC set
+for every row.
+
+ align:start position:0%
+for every row.
+ 
+
+ align:start position:0%
+for every row.
+And now we can apply our lema.
+
+ align:start position:0%
+And now we can apply our lema.
+ 
+
+ align:start position:0%
+And now we can apply our lema.
+And the lema tells us that the cardality
+
+ align:start position:0%
+And the lema tells us that the cardality
+ 
+
+ align:start position:0%
+And the lema tells us that the cardality
+of lxe the row covering number of lxe
+
+ align:start position:0%
+of lxe the row covering number of lxe
+ 
+
+ align:start position:0%
+of lxe the row covering number of lxe
+is at least
+
+ align:start position:0%
+is at least
+ 
+
+ align:start position:0%
+is at least
+row to the minus s minus epsilon. So row
+
+ align:start position:0%
+row to the minus s minus epsilon. So row
+ 
+
+ align:start position:0%
+row to the minus s minus epsilon. So row
+to the minus s is what we get just from
+
+ align:start position:0%
+to the minus s is what we get just from
+ 
+
+ align:start position:0%
+to the minus s is what we get just from
+being a row sc set. But actually has to
+
+ align:start position:0%
+being a row sc set. But actually has to
+ 
+
+ align:start position:0%
+being a row sc set. But actually has to
+be a little bit bigger than that by our
+
+ align:start position:0%
+be a little bit bigger than that by our
+ 
+
+ align:start position:0%
+be a little bit bigger than that by our
+lema.
+
+ align:start position:0%
+lema.
+ 
+
+ align:start position:0%
+lema.
+And that's true for every row.
+
+ align:start position:0%
+And that's true for every row.
+ 
+
+ align:start position:0%
+And that's true for every row.
+And now since since we have a uniform
+
+ align:start position:0%
+And now since since we have a uniform
+ 
+
+ align:start position:0%
+And now since since we have a uniform
+set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and since these row covering numbers are
+
+ align:start position:0%
+and since these row covering numbers are
+ 
+
+ align:start position:0%
+and since these row covering numbers are
+a little bit bigger than expected tells
+
+ align:start position:0%
+a little bit bigger than expected tells
+ 
+
+ align:start position:0%
+a little bit bigger than expected tells
+us that lxe
+
+ align:start position:0%
+us that lxe
+ 
+
+ align:start position:0%
+us that lxe
+is a delta s plus epsilon c set.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, actually I should here I needed to
+
+ align:start position:0%
+Yeah, actually I should here I needed to
+ 
+
+ align:start position:0%
+Yeah, actually I should here I needed to
+put 0 is less than s is less than the
+
+ align:start position:0%
+put 0 is less than s is less than the
+ 
+
+ align:start position:0%
+put 0 is less than s is less than the
+minimum of e1.
+
+ align:start position:0%
+minimum of e1.
+ 
+
+ align:start position:0%
+minimum of e1.
+We used all of these are hypotheses of
+
+ align:start position:0%
+We used all of these are hypotheses of
+ 
+
+ align:start position:0%
+We used all of these are hypotheses of
+our lema. So we use them here.
+
+ align:start position:0%
+our lema. So we use them here.
+ 
+
+ align:start position:0%
+our lema. So we use them here.
+Okay. Now this is our starting
+
+ align:start position:0%
+Okay. Now this is our starting
+ 
+
+ align:start position:0%
+Okay. Now this is our starting
+hypothesis. So now we can iterate.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+So s keeps getting bigger and bigger as
+
+ align:start position:0%
+So s keeps getting bigger and bigger as
+ 
+
+ align:start position:0%
+So s keeps getting bigger and bigger as
+long as it's smaller than the minimum of
+
+ align:start position:0%
+long as it's smaller than the minimum of
+ 
+
+ align:start position:0%
+long as it's smaller than the minimum of
+u and one. And so it will approach the
+
+ align:start position:0%
+u and one. And so it will approach the
+ 
+
+ align:start position:0%
+u and one. And so it will approach the
+minimum of u and one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we're happy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So unlike in the proof of beex theorem
+
+ align:start position:0%
+So unlike in the proof of beex theorem
+ 
+
+ align:start position:0%
+So unlike in the proof of beex theorem
+we had to use this lama many times. We
+
+ align:start position:0%
+we had to use this lama many times. We
+ 
+
+ align:start position:0%
+we had to use this lama many times. We
+used it at many different scales and
+
+ align:start position:0%
+used it at many different scales and
+ 
+
+ align:start position:0%
+used it at many different scales and
+also we had to use it over and over
+
+ align:start position:0%
+also we had to use it over and over
+ 
+
+ align:start position:0%
+also we had to use it over and over
+again and each time we used it we
+
+ align:start position:0%
+again and each time we used it we
+ 
+
+ align:start position:0%
+again and each time we used it we
+improved this exponent a little bit
+
+ align:start position:0%
+improved this exponent a little bit
+ 
+
+ align:start position:0%
+improved this exponent a little bit
+until the exponent approached the
+
+ align:start position:0%
+until the exponent approached the
+ 
+
+ align:start position:0%
+until the exponent approached the
+exponent that we had in the classical
+
+ align:start position:0%
+exponent that we had in the classical
+ 
+
+ align:start position:0%
+exponent that we had in the classical
+vest.
+
+ align:start position:0%
+vest.
+ 
+
+ align:start position:0%
+vest.
+And so this is sort of typical of this
+
+ align:start position:0%
+And so this is sort of typical of this
+ 
+
+ align:start position:0%
+And so this is sort of typical of this
+new paradigm that you can take an
+
+ align:start position:0%
+new paradigm that you can take an
+ 
+
+ align:start position:0%
+new paradigm that you can take an
+epsilon improvement result and use it
+
+ align:start position:0%
+epsilon improvement result and use it
+ 
+
+ align:start position:0%
+epsilon improvement result and use it
+over and over again to keep epsilon
+
+ align:start position:0%
+over and over again to keep epsilon
+ 
+
+ align:start position:0%
+over and over again to keep epsilon
+improving something until the thing
+
+ align:start position:0%
+improving something until the thing
+ 
+
+ align:start position:0%
+improving something until the thing
+reaches the sharp value.
+
+ align:start position:0%
+reaches the sharp value.
+ 
+
+ align:start position:0%
+reaches the sharp value.
+Okay. Now you might be wondering how we
+
+ align:start position:0%
+Okay. Now you might be wondering how we
+ 
+
+ align:start position:0%
+Okay. Now you might be wondering how we
+started this argument. We needed to
+
+ align:start position:0%
+started this argument. We needed to
+ 
+
+ align:start position:0%
+started this argument. We needed to
+start with an S that was bigger than
+
+ align:start position:0%
+start with an S that was bigger than
+ 
+
+ align:start position:0%
+start with an S that was bigger than
+zero. And not every set is a delta SC c
+
+ align:start position:0%
+zero. And not every set is a delta SC c
+ 
+
+ align:start position:0%
+zero. And not every set is a delta SC c
+set for any s.
+
+ align:start position:0%
+set for any s.
+ 
+
+ align:start position:0%
+set for any s.
+Um so to start the argument
+
+ align:start position:0%
+Um so to start the argument
+ 
+
+ align:start position:0%
+Um so to start the argument
+we observe um that we had this
+
+ align:start position:0%
+we observe um that we had this
+ 
+
+ align:start position:0%
+we observe um that we had this
+non-conentration in rectangles
+
+ align:start position:0%
+non-conentration in rectangles
+ 
+
+ align:start position:0%
+non-conentration in rectangles
+condition.
+
+ align:start position:0%
+condition.
+ 
+
+ align:start position:0%
+condition.
+on concentration and rectangles
+
+ align:start position:0%
+on concentration and rectangles
+ 
+
+ align:start position:0%
+on concentration and rectangles
+condition here that our set is not too
+
+ align:start position:0%
+condition here that our set is not too
+ 
+
+ align:start position:0%
+condition here that our set is not too
+much in any rectangle.
+
+ align:start position:0%
+much in any rectangle.
+ 
+
+ align:start position:0%
+much in any rectangle.
+We haven't mentioned that hypothesis
+
+ align:start position:0%
+We haven't mentioned that hypothesis
+ 
+
+ align:start position:0%
+We haven't mentioned that hypothesis
+yet. We use it here to get started. So
+
+ align:start position:0%
+yet. We use it here to get started. So
+ 
+
+ align:start position:0%
+yet. We use it here to get started. So
+to start with
+
+ align:start position:0%
+to start with
+ 
+
+ align:start position:0%
+to start with
+non-conentration in rectangles uh easily
+
+ align:start position:0%
+non-conentration in rectangles uh easily
+ 
+
+ align:start position:0%
+non-conentration in rectangles uh easily
+implies that lxe is a delta ad set.
+
+ align:start position:0%
+implies that lxe is a delta ad set.
+ 
+
+ align:start position:0%
+implies that lxe is a delta ad set.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um because so if E looks like so there's
+
+ align:start position:0%
+Um because so if E looks like so there's
+ 
+
+ align:start position:0%
+Um because so if E looks like so there's
+not too much of E in any rectangle
+
+ align:start position:0%
+not too much of E in any rectangle
+ 
+
+ align:start position:0%
+not too much of E in any rectangle
+is our X. Therefore there aren't too
+
+ align:start position:0%
+is our X. Therefore there aren't too
+ 
+
+ align:start position:0%
+is our X. Therefore there aren't too
+many of these rectangles too much. You
+
+ align:start position:0%
+many of these rectangles too much. You
+ 
+
+ align:start position:0%
+many of these rectangles too much. You
+can't have if you had a lot of lxe in a
+
+ align:start position:0%
+can't have if you had a lot of lxe in a
+ 
+
+ align:start position:0%
+can't have if you had a lot of lxe in a
+small angular range it would mean you
+
+ align:start position:0%
+small angular range it would mean you
+ 
+
+ align:start position:0%
+small angular range it would mean you
+had a lot of E in a small rectangle. And
+
+ align:start position:0%
+had a lot of E in a small rectangle. And
+ 
+
+ align:start position:0%
+had a lot of E in a small rectangle. And
+that says this doesn't happen.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay cool. So now we have sketched the
+
+ align:start position:0%
+Okay cool. So now we have sketched the
+ 
+
+ align:start position:0%
+Okay cool. So now we have sketched the
+proof of the continuum beex theorem the
+
+ align:start position:0%
+proof of the continuum beex theorem the
+ 
+
+ align:start position:0%
+proof of the continuum beex theorem the
+first sharp theorem in projection theory
+
+ align:start position:0%
+first sharp theorem in projection theory
+ 
+
+ align:start position:0%
+first sharp theorem in projection theory
+distinguishing R from C. So let's take a
+
+ align:start position:0%
+distinguishing R from C. So let's take a
+ 
+
+ align:start position:0%
+distinguishing R from C. So let's take a
+take a couple minutes to digest see if
+
+ align:start position:0%
+take a couple minutes to digest see if
+ 
+
+ align:start position:0%
+take a couple minutes to digest see if
+you have questions or comments.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+>> On the uh I guess kind of the second
+
+ align:start position:0%
+>> On the uh I guess kind of the second
+ 
+
+ align:start position:0%
+>> On the uh I guess kind of the second
+step of proof would be Lexe row is that
+
+ align:start position:0%
+step of proof would be Lexe row is that
+ 
+
+ align:start position:0%
+step of proof would be Lexe row is that
+the intersection of LXE with a kind of
+
+ align:start position:0%
+the intersection of LXE with a kind of
+ 
+
+ align:start position:0%
+the intersection of LXE with a kind of
+row radius ball or
+
+ align:start position:0%
+row radius ball or
+ 
+
+ align:start position:0%
+row radius ball or
+>> sorry. Um so lxe e row is the row
+
+ align:start position:0%
+>> sorry. Um so lxe e row is the row
+ 
+
+ align:start position:0%
+>> sorry. Um so lxe e row is the row
+neighborhood
+
+ align:start position:0%
+neighborhood
+ 
+
+ align:start position:0%
+neighborhood
+of lx. Actually you can also you can
+
+ align:start position:0%
+of lx. Actually you can also you can
+ 
+
+ align:start position:0%
+of lx. Actually you can also you can
+also erase the row. Maybe that's the
+
+ align:start position:0%
+also erase the row. Maybe that's the
+ 
+
+ align:start position:0%
+also erase the row. Maybe that's the
+best thing to do.
+
+ align:start position:0%
+best thing to do.
+ 
+
+ align:start position:0%
+best thing to do.
+Okay. So lxe is a delta SC set and if
+
+ align:start position:0%
+Okay. So lxe is a delta SC set and if
+ 
+
+ align:start position:0%
+Okay. So lxe is a delta SC set and if
+it's uniform it's also a row SC set for
+
+ align:start position:0%
+it's uniform it's also a row SC set for
+ 
+
+ align:start position:0%
+it's uniform it's also a row SC set for
+all the bigger rows for row delta
+
+ align:start position:0%
+all the bigger rows for row delta
+ 
+
+ align:start position:0%
+all the bigger rows for row delta
+>> for yeah for all row. Yeah.
+
+ align:start position:0%
+>> for yeah for all row. Yeah.
+ 
+
+ align:start position:0%
+>> for yeah for all row. Yeah.
+Yeah. Thank you. Thank you.
+
+ align:start position:0%
+Yeah. Thank you. Thank you.
+ 
+
+ align:start position:0%
+Yeah. Thank you. Thank you.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. Yeah. So, so recap. So, we don't
+
+ align:start position:0%
+Okay. Yeah. So, so recap. So, we don't
+ 
+
+ align:start position:0%
+Okay. Yeah. So, so recap. So, we don't
+so we don't Yeah. We don't we don't need
+
+ align:start position:0%
+so we don't Yeah. We don't we don't need
+ 
+
+ align:start position:0%
+so we don't Yeah. We don't we don't need
+to mention the right. So, so say it
+
+ align:start position:0%
+to mention the right. So, so say it
+ 
+
+ align:start position:0%
+to mention the right. So, so say it
+again. So, LXE is is uniform set. If
+
+ align:start position:0%
+again. So, LXE is is uniform set. If
+ 
+
+ align:start position:0%
+again. So, LXE is is uniform set. If
+it's delta SC, then it's also row SC for
+
+ align:start position:0%
+it's delta SC, then it's also row SC for
+ 
+
+ align:start position:0%
+it's delta SC, then it's also row SC for
+all the bigger rows. And so, then we get
+
+ align:start position:0%
+all the bigger rows. And so, then we get
+ 
+
+ align:start position:0%
+all the bigger rows. And so, then we get
+these covering numbers and then get
+
+ align:start position:0%
+these covering numbers and then get
+ 
+
+ align:start position:0%
+these covering numbers and then get
+okay. Okay. So let me share a personal
+
+ align:start position:0%
+okay. Okay. So let me share a personal
+ 
+
+ align:start position:0%
+okay. Okay. So let me share a personal
+reaction. So when this paper came out
+
+ align:start position:0%
+reaction. So when this paper came out
+ 
+
+ align:start position:0%
+reaction. So when this paper came out
+first of all I was very impressed
+
+ align:start position:0%
+first of all I was very impressed
+ 
+
+ align:start position:0%
+first of all I was very impressed
+because it was you know I had been
+
+ align:start position:0%
+because it was you know I had been
+ 
+
+ align:start position:0%
+because it was you know I had been
+wondering about this for many years and
+
+ align:start position:0%
+wondering about this for many years and
+ 
+
+ align:start position:0%
+wondering about this for many years and
+it's the first sharp projection type
+
+ align:start position:0%
+it's the first sharp projection type
+ 
+
+ align:start position:0%
+it's the first sharp projection type
+theorem which distinguishes R from C.
+
+ align:start position:0%
+theorem which distinguishes R from C.
+ 
+
+ align:start position:0%
+theorem which distinguishes R from C.
+But I also
+
+ align:start position:0%
+But I also
+ 
+
+ align:start position:0%
+But I also
+felt kind of unsure whether this would
+
+ align:start position:0%
+felt kind of unsure whether this would
+ 
+
+ align:start position:0%
+felt kind of unsure whether this would
+open the door to prove sharp results for
+
+ align:start position:0%
+open the door to prove sharp results for
+ 
+
+ align:start position:0%
+open the door to prove sharp results for
+things like the first set problem. Uh
+
+ align:start position:0%
+things like the first set problem. Uh
+ 
+
+ align:start position:0%
+things like the first set problem. Uh
+maybe it's a sharp result but maybe it's
+
+ align:start position:0%
+maybe it's a sharp result but maybe it's
+ 
+
+ align:start position:0%
+maybe it's a sharp result but maybe it's
+about a kind of thing that somehow is
+
+ align:start position:0%
+about a kind of thing that somehow is
+ 
+
+ align:start position:0%
+about a kind of thing that somehow is
+more approachable. It was well known
+
+ align:start position:0%
+more approachable. It was well known
+ 
+
+ align:start position:0%
+more approachable. It was well known
+classically that a epsilon improvement
+
+ align:start position:0%
+classically that a epsilon improvement
+ 
+
+ align:start position:0%
+classically that a epsilon improvement
+of something implied a sharp version of
+
+ align:start position:0%
+of something implied a sharp version of
+ 
+
+ align:start position:0%
+of something implied a sharp version of
+the class of the incidence geometry
+
+ align:start position:0%
+the class of the incidence geometry
+ 
+
+ align:start position:0%
+the class of the incidence geometry
+something here and that's just not the
+
+ align:start position:0%
+something here and that's just not the
+ 
+
+ align:start position:0%
+something here and that's just not the
+case for semary trotder. Sem ready
+
+ align:start position:0%
+case for semary trotder. Sem ready
+ 
+
+ align:start position:0%
+case for semary trotder. Sem ready
+trotder is not known to follow from an
+
+ align:start position:0%
+trotder is not known to follow from an
+ 
+
+ align:start position:0%
+trotder is not known to follow from an
+epsilon improvement on on some classical
+
+ align:start position:0%
+epsilon improvement on on some classical
+ 
+
+ align:start position:0%
+epsilon improvement on on some classical
+thing. Um and so it wasn't clear to me
+
+ align:start position:0%
+thing. Um and so it wasn't clear to me
+ 
+
+ align:start position:0%
+thing. Um and so it wasn't clear to me
+if this would open the door to prove
+
+ align:start position:0%
+if this would open the door to prove
+ 
+
+ align:start position:0%
+if this would open the door to prove
+sharp theorems about all the things we
+
+ align:start position:0%
+sharp theorems about all the things we
+ 
+
+ align:start position:0%
+sharp theorems about all the things we
+most cared about.
+
+ align:start position:0%
+most cared about.
+ 
+
+ align:start position:0%
+most cared about.
+All right. Um so in the rest of this
+
+ align:start position:0%
+All right. Um so in the rest of this
+ 
+
+ align:start position:0%
+All right. Um so in the rest of this
+class what I want to do is to uh give a
+
+ align:start position:0%
+class what I want to do is to uh give a
+ 
+
+ align:start position:0%
+class what I want to do is to uh give a
+give a outline of the proof of the of
+
+ align:start position:0%
+give a outline of the proof of the of
+ 
+
+ align:start position:0%
+give a outline of the proof of the of
+the of the first set conjecture and the
+
+ align:start position:0%
+the of the first set conjecture and the
+ 
+
+ align:start position:0%
+the of the first set conjecture and the
+different ingredients that go into it of
+
+ align:start position:0%
+different ingredients that go into it of
+ 
+
+ align:start position:0%
+different ingredients that go into it of
+which this will turn out to be an
+
+ align:start position:0%
+which this will turn out to be an
+ 
+
+ align:start position:0%
+which this will turn out to be an
+important one.
+
+ align:start position:0%
+important one.
+ 
+
+ align:start position:0%
+important one.
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+cool. So the the first thing to say is
+
+ align:start position:0%
+cool. So the the first thing to say is
+ 
+
+ align:start position:0%
+cool. So the the first thing to say is
+that this proof breaks into cases
+
+ align:start position:0%
+that this proof breaks into cases
+ 
+
+ align:start position:0%
+that this proof breaks into cases
+according to the way the the set E is
+
+ align:start position:0%
+according to the way the the set E is
+ 
+
+ align:start position:0%
+according to the way the the set E is
+spaced that this del this delta TC set
+
+ align:start position:0%
+spaced that this del this delta TC set
+ 
+
+ align:start position:0%
+spaced that this del this delta TC set
+that definition on the one hand it's a
+
+ align:start position:0%
+that definition on the one hand it's a
+ 
+
+ align:start position:0%
+that definition on the one hand it's a
+good definition but under the umbrella
+
+ align:start position:0%
+good definition but under the umbrella
+ 
+
+ align:start position:0%
+good definition but under the umbrella
+of delta TC sets there are several diff
+
+ align:start position:0%
+of delta TC sets there are several diff
+ 
+
+ align:start position:0%
+of delta TC sets there are several diff
+quite different ways that the set E
+
+ align:start position:0%
+quite different ways that the set E
+ 
+
+ align:start position:0%
+quite different ways that the set E
+could be spaced and we have to pay
+
+ align:start position:0%
+could be spaced and we have to pay
+ 
+
+ align:start position:0%
+could be spaced and we have to pay
+attention to them and we have to treat
+
+ align:start position:0%
+attention to them and we have to treat
+ 
+
+ align:start position:0%
+attention to them and we have to treat
+them in different ways.
+
+ align:start position:0%
+them in different ways.
+ 
+
+ align:start position:0%
+them in different ways.
+All right. So, let's explain that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're going to split into cases
+
+ align:start position:0%
+So, we're going to split into cases
+ 
+
+ align:start position:0%
+So, we're going to split into cases
+according
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to how
+
+ align:start position:0%
+to how
+ 
+
+ align:start position:0%
+to how
+E is spaced.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So first of all, let's assume
+
+ align:start position:0%
+All right. So first of all, let's assume
+ 
+
+ align:start position:0%
+All right. So first of all, let's assume
+that E is uniform.
+
+ align:start position:0%
+that E is uniform.
+ 
+
+ align:start position:0%
+that E is uniform.
+And I'll now I mentioned the word
+
+ align:start position:0%
+And I'll now I mentioned the word
+ 
+
+ align:start position:0%
+And I'll now I mentioned the word
+uniform above, but now I'll remember
+
+ align:start position:0%
+uniform above, but now I'll remember
+ 
+
+ align:start position:0%
+uniform above, but now I'll remember
+recall exactly what is uniform.
+
+ align:start position:0%
+recall exactly what is uniform.
+ 
+
+ align:start position:0%
+recall exactly what is uniform.
+Okay. So first of all, our delta is
+
+ align:start position:0%
+Okay. So first of all, our delta is
+ 
+
+ align:start position:0%
+Okay. So first of all, our delta is
+going to be
+
+ align:start position:0%
+going to be
+ 
+
+ align:start position:0%
+going to be
+capital delta to the M where M is a
+
+ align:start position:0%
+capital delta to the M where M is a
+ 
+
+ align:start position:0%
+capital delta to the M where M is a
+large number.
+
+ align:start position:0%
+large number.
+ 
+
+ align:start position:0%
+large number.
+And uniform means that for every J going
+
+ align:start position:0%
+And uniform means that for every J going
+ 
+
+ align:start position:0%
+And uniform means that for every J going
+from one up to M and for every Q which
+
+ align:start position:0%
+from one up to M and for every Q which
+ 
+
+ align:start position:0%
+from one up to M and for every Q which
+is a delta to the J cub.
+
+ align:start position:0%
+is a delta to the J cub.
+ 
+
+ align:start position:0%
+is a delta to the J cub.
+Then when I take my set and I intersect
+
+ align:start position:0%
+Then when I take my set and I intersect
+ 
+
+ align:start position:0%
+Then when I take my set and I intersect
+it with Q and I cover it with cubes or
+
+ align:start position:0%
+it with Q and I cover it with cubes or
+ 
+
+ align:start position:0%
+it with Q and I cover it with cubes or
+balls at the next smaller scale delta to
+
+ align:start position:0%
+balls at the next smaller scale delta to
+ 
+
+ align:start position:0%
+balls at the next smaller scale delta to
+the J + one. Um that is is around RJ. So
+
+ align:start position:0%
+the J + one. Um that is is around RJ. So
+ 
+
+ align:start position:0%
+the J + one. Um that is is around RJ. So
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so I'll draw some pictures in a moment.
+
+ align:start position:0%
+so I'll draw some pictures in a moment.
+ 
+
+ align:start position:0%
+so I'll draw some pictures in a moment.
+The smallest this RJ could be is one and
+
+ align:start position:0%
+The smallest this RJ could be is one and
+ 
+
+ align:start position:0%
+The smallest this RJ could be is one and
+the biggest it could be is big delta to
+
+ align:start position:0%
+the biggest it could be is big delta to
+ 
+
+ align:start position:0%
+the biggest it could be is big delta to
+the minus2.
+
+ align:start position:0%
+the minus2.
+ 
+
+ align:start position:0%
+the minus2.
+Oh
+
+ align:start position:0%
+Oh
+ 
+
+ align:start position:0%
+Oh
+um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+actually yeah let me say a little bit
+
+ align:start position:0%
+actually yeah let me say a little bit
+ 
+
+ align:start position:0%
+actually yeah let me say a little bit
+more. So the delta covering number of v
+
+ align:start position:0%
+more. So the delta covering number of v
+ 
+
+ align:start position:0%
+more. So the delta covering number of v
+that's going to be the product j = 1 to
+
+ align:start position:0%
+that's going to be the product j = 1 to
+ 
+
+ align:start position:0%
+that's going to be the product j = 1 to
+m of rj.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um and another thing we we can say is if
+
+ align:start position:0%
+Um and another thing we we can say is if
+ 
+
+ align:start position:0%
+Um and another thing we we can say is if
+I if I were to take the product J equals
+
+ align:start position:0%
+I if I were to take the product J equals
+ 
+
+ align:start position:0%
+I if I were to take the product J equals
+1 to capital J of RJ that would be the
+
+ align:start position:0%
+1 to capital J of RJ that would be the
+ 
+
+ align:start position:0%
+1 to capital J of RJ that would be the
+covering number of E at scale delta to
+
+ align:start position:0%
+covering number of E at scale delta to
+ 
+
+ align:start position:0%
+covering number of E at scale delta to
+the capital J
+
+ align:start position:0%
+the capital J
+ 
+
+ align:start position:0%
+the capital J
+and that should be so
+
+ align:start position:0%
+and that should be so
+ 
+
+ align:start position:0%
+and that should be so
+um let's say so
+
+ align:start position:0%
+um let's say so
+ 
+
+ align:start position:0%
+um let's say so
+so if E is a deltat TC
+
+ align:start position:0%
+so if E is a deltat TC
+ 
+
+ align:start position:0%
+so if E is a deltat TC
+Then this should be at least 1 / C um
+
+ align:start position:0%
+Then this should be at least 1 / C um
+ 
+
+ align:start position:0%
+Then this should be at least 1 / C um
+delta J to the minus.
+
+ align:start position:0%
+delta J to the minus.
+ 
+
+ align:start position:0%
+delta J to the minus.
+So that gives some information about
+
+ align:start position:0%
+So that gives some information about
+ 
+
+ align:start position:0%
+So that gives some information about
+these products and
+
+ align:start position:0%
+these products and
+ 
+
+ align:start position:0%
+these products and
+being a delta TC set is equivalent to
+
+ align:start position:0%
+being a delta TC set is equivalent to
+ 
+
+ align:start position:0%
+being a delta TC set is equivalent to
+this information about these products.
+
+ align:start position:0%
+this information about these products.
+ 
+
+ align:start position:0%
+this information about these products.
+And so there are many ways that they
+
+ align:start position:0%
+And so there are many ways that they
+ 
+
+ align:start position:0%
+And so there are many ways that they
+could look.
+
+ align:start position:0%
+could look.
+ 
+
+ align:start position:0%
+could look.
+Okay, let me put up a couple of examples
+
+ align:start position:0%
+Okay, let me put up a couple of examples
+ 
+
+ align:start position:0%
+Okay, let me put up a couple of examples
+which also should hopefully clarify
+
+ align:start position:0%
+which also should hopefully clarify
+ 
+
+ align:start position:0%
+which also should hopefully clarify
+everything on this board and then we
+
+ align:start position:0%
+everything on this board and then we
+ 
+
+ align:start position:0%
+everything on this board and then we
+pause for questions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So the first example that I want
+
+ align:start position:0%
+Okay. So the first example that I want
+ 
+
+ align:start position:0%
+Okay. So the first example that I want
+to put up
+
+ align:start position:0%
+to put up
+ 
+
+ align:start position:0%
+to put up
+is that all the RJs are the same. So RJ
+
+ align:start position:0%
+is that all the RJs are the same. So RJ
+ 
+
+ align:start position:0%
+is that all the RJs are the same. So RJ
+is delta to the minus T for every J.
+
+ align:start position:0%
+is delta to the minus T for every J.
+ 
+
+ align:start position:0%
+is delta to the minus T for every J.
+Okay. And then you'll
+
+ align:start position:0%
+Okay. And then you'll
+ 
+
+ align:start position:0%
+Okay. And then you'll
+see that this this will be okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um all right. And I'd like to visualize
+
+ align:start position:0%
+Um all right. And I'd like to visualize
+ 
+
+ align:start position:0%
+Um all right. And I'd like to visualize
+this in two ways.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the first way I'd like to visualize
+
+ align:start position:0%
+So the first way I'd like to visualize
+ 
+
+ align:start position:0%
+So the first way I'd like to visualize
+is as a tree. Um so oh in my
+
+ align:start position:0%
+is as a tree. Um so oh in my
+ 
+
+ align:start position:0%
+is as a tree. Um so oh in my
+visualization I picked that delta is
+
+ align:start position:0%
+visualization I picked that delta is
+ 
+
+ align:start position:0%
+visualization I picked that delta is
+four. Delt no delta is uh 16. Um and no
+
+ align:start position:0%
+four. Delt no delta is uh 16. Um and no
+ 
+
+ align:start position:0%
+four. Delt no delta is uh 16. Um and no
+sorry del sorry delta is one pointer and
+
+ align:start position:0%
+sorry del sorry delta is one pointer and
+ 
+
+ align:start position:0%
+sorry del sorry delta is one pointer and
+we and t is going to be one.
+
+ align:start position:0%
+we and t is going to be one.
+ 
+
+ align:start position:0%
+we and t is going to be one.
+Okay. So in in my visualization delta to
+
+ align:start position:0%
+Okay. So in in my visualization delta to
+ 
+
+ align:start position:0%
+Okay. So in in my visualization delta to
+the minus one is going to be four. I'm
+
+ align:start position:0%
+the minus one is going to be four. I'm
+ 
+
+ align:start position:0%
+the minus one is going to be four. I'm
+going to have tree. So that be r1 guys
+
+ align:start position:0%
+going to have tree. So that be r1 guys
+ 
+
+ align:start position:0%
+going to have tree. So that be r1 guys
+coming out of it. And then each of these
+
+ align:start position:0%
+coming out of it. And then each of these
+ 
+
+ align:start position:0%
+coming out of it. And then each of these
+have r2 which is also four uh uh
+
+ align:start position:0%
+have r2 which is also four uh uh
+ 
+
+ align:start position:0%
+have r2 which is also four uh uh
+branches coming out. I won't draw that
+
+ align:start position:0%
+branches coming out. I won't draw that
+ 
+
+ align:start position:0%
+branches coming out. I won't draw that
+but they're all the same.
+
+ align:start position:0%
+but they're all the same.
+ 
+
+ align:start position:0%
+but they're all the same.
+Okay. Now let's do the next stage of our
+
+ align:start position:0%
+Okay. Now let's do the next stage of our
+ 
+
+ align:start position:0%
+Okay. Now let's do the next stage of our
+visualization. We started with a square.
+
+ align:start position:0%
+visualization. We started with a square.
+ 
+
+ align:start position:0%
+visualization. We started with a square.
+and we cut it into smaller squares of
+
+ align:start position:0%
+and we cut it into smaller squares of
+ 
+
+ align:start position:0%
+and we cut it into smaller squares of
+side length delta. So that looked like
+
+ align:start position:0%
+side length delta. So that looked like
+ 
+
+ align:start position:0%
+side length delta. So that looked like
+this.
+
+ align:start position:0%
+this.
+ 
+
+ align:start position:0%
+this.
+This is stage one
+
+ align:start position:0%
+This is stage one
+ 
+
+ align:start position:0%
+This is stage one
+and r sub one is four. So we took four.
+
+ align:start position:0%
+and r sub one is four. So we took four.
+ 
+
+ align:start position:0%
+and r sub one is four. So we took four.
+So maybe this one.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Stage two.
+
+ align:start position:0%
+Okay. Stage two.
+ 
+
+ align:start position:0%
+Okay. Stage two.
+inside of each of those four squares.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I took each of them and I cut them into
+
+ align:start position:0%
+I took each of them and I cut them into
+ 
+
+ align:start position:0%
+I took each of them and I cut them into
+a 4x4 grid of smaller squares. And I
+
+ align:start position:0%
+a 4x4 grid of smaller squares. And I
+ 
+
+ align:start position:0%
+a 4x4 grid of smaller squares. And I
+took four of them. So I'll do the
+
+ align:start position:0%
+took four of them. So I'll do the
+ 
+
+ align:start position:0%
+took four of them. So I'll do the
+cutting carefully here. Right. So maybe
+
+ align:start position:0%
+cutting carefully here. Right. So maybe
+ 
+
+ align:start position:0%
+cutting carefully here. Right. So maybe
+I took
+
+ align:start position:0%
+I took
+ 
+
+ align:start position:0%
+I took
+those four and then down here I took
+
+ align:start position:0%
+those four and then down here I took
+ 
+
+ align:start position:0%
+those four and then down here I took
+four
+
+ align:start position:0%
+four
+ 
+
+ align:start position:0%
+four
+and over here I took four and over here
+
+ align:start position:0%
+and over here I took four and over here
+ 
+
+ align:start position:0%
+and over here I took four and over here
+I took four.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So our set looks something like that at
+
+ align:start position:0%
+So our set looks something like that at
+ 
+
+ align:start position:0%
+So our set looks something like that at
+stage two in a new
+
+ align:start position:0%
+stage two in a new
+ 
+
+ align:start position:0%
+stage two in a new
+All right. So this is the first example.
+
+ align:start position:0%
+All right. So this is the first example.
+ 
+
+ align:start position:0%
+All right. So this is the first example.
+It's called the ad regular example.
+
+ align:start position:0%
+It's called the ad regular example.
+ 
+
+ align:start position:0%
+It's called the ad regular example.
+Alforce devided regular. Alforce and
+
+ align:start position:0%
+Alforce devided regular. Alforce and
+ 
+
+ align:start position:0%
+Alforce devided regular. Alforce and
+Devid are two people who worked on stuff
+
+ align:start position:0%
+Devid are two people who worked on stuff
+ 
+
+ align:start position:0%
+Devid are two people who worked on stuff
+that is related to this. And the word
+
+ align:start position:0%
+that is related to this. And the word
+ 
+
+ align:start position:0%
+that is related to this. And the word
+regular I think here refers to the fact
+
+ align:start position:0%
+regular I think here refers to the fact
+ 
+
+ align:start position:0%
+regular I think here refers to the fact
+that all the scales are the same as each
+
+ align:start position:0%
+that all the scales are the same as each
+ 
+
+ align:start position:0%
+that all the scales are the same as each
+other.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now let me show you an opposite extreme.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So this one is called the well
+
+ align:start position:0%
+Okay. So this one is called the well
+ 
+
+ align:start position:0%
+Okay. So this one is called the well
+spaced example.
+
+ align:start position:0%
+spaced example.
+ 
+
+ align:start position:0%
+spaced example.
+So in the well spaced example, RJ is as
+
+ align:start position:0%
+So in the well spaced example, RJ is as
+ 
+
+ align:start position:0%
+So in the well spaced example, RJ is as
+big as it could be its maximum value for
+
+ align:start position:0%
+big as it could be its maximum value for
+ 
+
+ align:start position:0%
+big as it could be its maximum value for
+some range of J
+
+ align:start position:0%
+some range of J
+ 
+
+ align:start position:0%
+some range of J
+and then RJ is one for larger of J.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So as a picture it would look like
+
+ align:start position:0%
+Okay. So as a picture it would look like
+ 
+
+ align:start position:0%
+Okay. So as a picture it would look like
+this. So we're going to visualize
+
+ align:start position:0%
+this. So we're going to visualize
+ 
+
+ align:start position:0%
+this. So we're going to visualize
+with uh big J is one, big F is two like
+
+ align:start position:0%
+with uh big J is one, big F is two like
+ 
+
+ align:start position:0%
+with uh big J is one, big F is two like
+over there. So we'll have two stages.
+
+ align:start position:0%
+over there. So we'll have two stages.
+ 
+
+ align:start position:0%
+over there. So we'll have two stages.
+And so our first stage is that R1 is 16.
+
+ align:start position:0%
+And so our first stage is that R1 is 16.
+ 
+
+ align:start position:0%
+And so our first stage is that R1 is 16.
+Draw it off. And then R2 is one. So from
+
+ align:start position:0%
+Draw it off. And then R2 is one. So from
+ 
+
+ align:start position:0%
+Draw it off. And then R2 is one. So from
+each uh point here, we have just one
+
+ align:start position:0%
+each uh point here, we have just one
+ 
+
+ align:start position:0%
+each uh point here, we have just one
+going down.
+
+ align:start position:0%
+going down.
+ 
+
+ align:start position:0%
+going down.
+So the tree looks like this instead of
+
+ align:start position:0%
+So the tree looks like this instead of
+ 
+
+ align:start position:0%
+So the tree looks like this instead of
+like that. A lot of branching at the
+
+ align:start position:0%
+like that. A lot of branching at the
+ 
+
+ align:start position:0%
+like that. A lot of branching at the
+beginning and then no branching after
+
+ align:start position:0%
+beginning and then no branching after
+ 
+
+ align:start position:0%
+beginning and then no branching after
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+Okay. What does it mean? Our set looks
+
+ align:start position:0%
+Okay. What does it mean? Our set looks
+ 
+
+ align:start position:0%
+Okay. What does it mean? Our set looks
+like in space. Well, first stage one, I
+
+ align:start position:0%
+like in space. Well, first stage one, I
+ 
+
+ align:start position:0%
+like in space. Well, first stage one, I
+take my square and I break it into 16
+
+ align:start position:0%
+take my square and I break it into 16
+ 
+
+ align:start position:0%
+take my square and I break it into 16
+squares of side length a quarter.
+
+ align:start position:0%
+squares of side length a quarter.
+ 
+
+ align:start position:0%
+squares of side length a quarter.
+And at stage one, I select all 16 of
+
+ align:start position:0%
+And at stage one, I select all 16 of
+ 
+
+ align:start position:0%
+And at stage one, I select all 16 of
+them. So the picture looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, now at stage two.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So I have cut my square into 16 squares
+
+ align:start position:0%
+So I have cut my square into 16 squares
+ 
+
+ align:start position:0%
+So I have cut my square into 16 squares
+of side length a quarter and I look
+
+ align:start position:0%
+of side length a quarter and I look
+ 
+
+ align:start position:0%
+of side length a quarter and I look
+inside each one of them. I cut that into
+
+ align:start position:0%
+inside each one of them. I cut that into
+ 
+
+ align:start position:0%
+inside each one of them. I cut that into
+16 squares a smaller size and I pick one
+
+ align:start position:0%
+16 squares a smaller size and I pick one
+ 
+
+ align:start position:0%
+16 squares a smaller size and I pick one
+of them
+
+ align:start position:0%
+of them
+ 
+
+ align:start position:0%
+of them
+and I do that in all in all the ones I
+
+ align:start position:0%
+and I do that in all in all the ones I
+ 
+
+ align:start position:0%
+and I do that in all in all the ones I
+selected at stage one which is all of
+
+ align:start position:0%
+selected at stage one which is all of
+ 
+
+ align:start position:0%
+selected at stage one which is all of
+them. So this set looks like this.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so this is called the well spaced set.
+
+ align:start position:0%
+so this is called the well spaced set.
+ 
+
+ align:start position:0%
+so this is called the well spaced set.
+So I could fix a t. I can make a delta t
+
+ align:start position:0%
+So I could fix a t. I can make a delta t
+ 
+
+ align:start position:0%
+So I could fix a t. I can make a delta t
+well spaced. I can fix t and delta. I
+
+ align:start position:0%
+well spaced. I can fix t and delta. I
+ 
+
+ align:start position:0%
+well spaced. I can fix t and delta. I
+can make a delta t wellspace set or I
+
+ align:start position:0%
+can make a delta t wellspace set or I
+ 
+
+ align:start position:0%
+can make a delta t wellspace set or I
+can make a delta t alph4's regular set.
+
+ align:start position:0%
+can make a delta t alph4's regular set.
+ 
+
+ align:start position:0%
+can make a delta t alph4's regular set.
+And they look rather different from each
+
+ align:start position:0%
+And they look rather different from each
+ 
+
+ align:start position:0%
+And they look rather different from each
+other. And there's also a gray area in
+
+ align:start position:0%
+other. And there's also a gray area in
+ 
+
+ align:start position:0%
+other. And there's also a gray area in
+between.
+
+ align:start position:0%
+between.
+ 
+
+ align:start position:0%
+between.
+Um so this one is distinguished by
+
+ align:start position:0%
+Um so this one is distinguished by
+ 
+
+ align:start position:0%
+Um so this one is distinguished by
+saying that the points
+
+ align:start position:0%
+saying that the points
+ 
+
+ align:start position:0%
+saying that the points
+are the most separated.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if these points were like electrons
+
+ align:start position:0%
+So if these points were like electrons
+ 
+
+ align:start position:0%
+So if these points were like electrons
+that were sitting in this ball and they
+
+ align:start position:0%
+that were sitting in this ball and they
+ 
+
+ align:start position:0%
+that were sitting in this ball and they
+repel each other, they would come to a
+
+ align:start position:0%
+repel each other, they would come to a
+ 
+
+ align:start position:0%
+repel each other, they would come to a
+position that's sort of like this. It
+
+ align:start position:0%
+position that's sort of like this. It
+ 
+
+ align:start position:0%
+position that's sort of like this. It
+would be well spaced.
+
+ align:start position:0%
+would be well spaced.
+ 
+
+ align:start position:0%
+would be well spaced.
+And this one is distinguished by being
+
+ align:start position:0%
+And this one is distinguished by being
+ 
+
+ align:start position:0%
+And this one is distinguished by being
+this is the most clumped
+
+ align:start position:0%
+this is the most clumped
+ 
+
+ align:start position:0%
+this is the most clumped
+which is allowed
+
+ align:start position:0%
+which is allowed
+ 
+
+ align:start position:0%
+which is allowed
+for a delta t set.
+
+ align:start position:0%
+for a delta t set.
+ 
+
+ align:start position:0%
+for a delta t set.
+So this isn't the most clumped possible
+
+ align:start position:0%
+So this isn't the most clumped possible
+ 
+
+ align:start position:0%
+So this isn't the most clumped possible
+set. I could take these delta balls. I
+
+ align:start position:0%
+set. I could take these delta balls. I
+ 
+
+ align:start position:0%
+set. I could take these delta balls. I
+could smoosh them all there. That would
+
+ align:start position:0%
+could smoosh them all there. That would
+ 
+
+ align:start position:0%
+could smoosh them all there. That would
+be more clumped. But if it's a delta t
+
+ align:start position:0%
+be more clumped. But if it's a delta t
+ 
+
+ align:start position:0%
+be more clumped. But if it's a delta t
+set, it's not allowed to do that. And
+
+ align:start position:0%
+set, it's not allowed to do that. And
+ 
+
+ align:start position:0%
+set, it's not allowed to do that. And
+this is the most clumped that it could
+
+ align:start position:0%
+this is the most clumped that it could
+ 
+
+ align:start position:0%
+this is the most clumped that it could
+be.
+
+ align:start position:0%
+be.
+ 
+
+ align:start position:0%
+be.
+subject to the definition of a delta t
+
+ align:start position:0%
+subject to the definition of a delta t
+ 
+
+ align:start position:0%
+subject to the definition of a delta t
+sub.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, cool. So,
+
+ align:start position:0%
+Okay, cool. So,
+ 
+
+ align:start position:0%
+Okay, cool. So,
+so there's a range of spacing conditions
+
+ align:start position:0%
+so there's a range of spacing conditions
+ 
+
+ align:start position:0%
+so there's a range of spacing conditions
+um and and this hopefully gives a sample
+
+ align:start position:0%
+um and and this hopefully gives a sample
+ 
+
+ align:start position:0%
+um and and this hopefully gives a sample
+of Yeah.
+
+ align:start position:0%
+of Yeah.
+ 
+
+ align:start position:0%
+of Yeah.
+>> Is there some sort of like energy
+
+ align:start position:0%
+>> Is there some sort of like energy
+ 
+
+ align:start position:0%
+>> Is there some sort of like energy
+condition or kind of quantitative
+
+ align:start position:0%
+condition or kind of quantitative
+ 
+
+ align:start position:0%
+condition or kind of quantitative
+measure of the clumping that would kind
+
+ align:start position:0%
+measure of the clumping that would kind
+ 
+
+ align:start position:0%
+measure of the clumping that would kind
+of allow you to separate the two cases
+
+ align:start position:0%
+of allow you to separate the two cases
+ 
+
+ align:start position:0%
+of allow you to separate the two cases
+because they're both delta SC,
+
+ align:start position:0%
+because they're both delta SC,
+ 
+
+ align:start position:0%
+because they're both delta SC,
+>> right? So the question is there is there
+
+ align:start position:0%
+>> right? So the question is there is there
+ 
+
+ align:start position:0%
+>> right? So the question is there is there
+a quantitative measure of clumping or
+
+ align:start position:0%
+a quantitative measure of clumping or
+ 
+
+ align:start position:0%
+a quantitative measure of clumping or
+concentrating or spacing that would
+
+ align:start position:0%
+concentrating or spacing that would
+ 
+
+ align:start position:0%
+concentrating or spacing that would
+allow us to distinguish them? Um I I
+
+ align:start position:0%
+allow us to distinguish them? Um I I
+ 
+
+ align:start position:0%
+allow us to distinguish them? Um I I
+think the nicest way to do that is this
+
+ align:start position:0%
+think the nicest way to do that is this
+ 
+
+ align:start position:0%
+think the nicest way to do that is this
+list of RJS or perhaps this list of uh
+
+ align:start position:0%
+list of RJS or perhaps this list of uh
+ 
+
+ align:start position:0%
+list of RJS or perhaps this list of uh
+this list of these numbers here. Yeah.
+
+ align:start position:0%
+this list of these numbers here. Yeah.
+ 
+
+ align:start position:0%
+this list of these numbers here. Yeah.
+So it's not just a single number, but it
+
+ align:start position:0%
+So it's not just a single number, but it
+ 
+
+ align:start position:0%
+So it's not just a single number, but it
+is quantitative. And if you're willing
+
+ align:start position:0%
+is quantitative. And if you're willing
+ 
+
+ align:start position:0%
+is quantitative. And if you're willing
+to have, you know, like a a list of
+
+ align:start position:0%
+to have, you know, like a a list of
+ 
+
+ align:start position:0%
+to have, you know, like a a list of
+numbers describing your set, then it
+
+ align:start position:0%
+numbers describing your set, then it
+ 
+
+ align:start position:0%
+numbers describing your set, then it
+does quite a good job.
+
+ align:start position:0%
+does quite a good job.
+ 
+
+ align:start position:0%
+does quite a good job.
+Um, it's really a modern innovation to
+
+ align:start position:0%
+Um, it's really a modern innovation to
+ 
+
+ align:start position:0%
+Um, it's really a modern innovation to
+focus on that. In in previous times,
+
+ align:start position:0%
+focus on that. In in previous times,
+ 
+
+ align:start position:0%
+focus on that. In in previous times,
+people wanted to describe the spacing of
+
+ align:start position:0%
+people wanted to describe the spacing of
+ 
+
+ align:start position:0%
+people wanted to describe the spacing of
+their set with one number, which would
+
+ align:start position:0%
+their set with one number, which would
+ 
+
+ align:start position:0%
+their set with one number, which would
+be like the dimension of the set or the
+
+ align:start position:0%
+be like the dimension of the set or the
+ 
+
+ align:start position:0%
+be like the dimension of the set or the
+energy or something. Um, and when they
+
+ align:start position:0%
+energy or something. Um, and when they
+ 
+
+ align:start position:0%
+energy or something. Um, and when they
+were describing with just one number,
+
+ align:start position:0%
+were describing with just one number,
+ 
+
+ align:start position:0%
+were describing with just one number,
+then it was lumping together these two
+
+ align:start position:0%
+then it was lumping together these two
+ 
+
+ align:start position:0%
+then it was lumping together these two
+rather different behaviors. And it turns
+
+ align:start position:0%
+rather different behaviors. And it turns
+ 
+
+ align:start position:0%
+rather different behaviors. And it turns
+out to be important to unlump them um
+
+ align:start position:0%
+out to be important to unlump them um
+ 
+
+ align:start position:0%
+out to be important to unlump them um
+for to prove this theorem at least with
+
+ align:start position:0%
+for to prove this theorem at least with
+ 
+
+ align:start position:0%
+for to prove this theorem at least with
+the proof that we have.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good. Uh, okay. So now I can write
+
+ align:start position:0%
+Okay, good. Uh, okay. So now I can write
+ 
+
+ align:start position:0%
+Okay, good. Uh, okay. So now I can write
+down the outline of the proof.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so here is the outline of the proof of
+
+ align:start position:0%
+so here is the outline of the proof of
+ 
+
+ align:start position:0%
+so here is the outline of the proof of
+the main theorem or let me say of the
+
+ align:start position:0%
+the main theorem or let me say of the
+ 
+
+ align:start position:0%
+the main theorem or let me say of the
+first conjecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+first.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay,
+
+ align:start position:0%
+Okay,
+ 
+
+ align:start position:0%
+Okay,
+so first main ingredient
+
+ align:start position:0%
+so first main ingredient
+ 
+
+ align:start position:0%
+so first main ingredient
+is a theorem of Borpin and a Schwarin
+
+ align:start position:0%
+is a theorem of Borpin and a Schwarin
+ 
+
+ align:start position:0%
+is a theorem of Borpin and a Schwarin
+from 24
+
+ align:start position:0%
+from 24
+ 
+
+ align:start position:0%
+from 24
+and they proved that the Fenberg
+
+ align:start position:0%
+and they proved that the Fenberg
+ 
+
+ align:start position:0%
+and they proved that the Fenberg
+conjecture holds in the ad regular case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this is based on it builds on
+
+ align:start position:0%
+Okay, so this is based on it builds on
+ 
+
+ align:start position:0%
+Okay, so this is based on it builds on
+the stuff builds on the stuff we talked
+
+ align:start position:0%
+the stuff builds on the stuff we talked
+ 
+
+ align:start position:0%
+the stuff builds on the stuff we talked
+about today. So it builds on the
+
+ align:start position:0%
+about today. So it builds on the
+ 
+
+ align:start position:0%
+about today. So it builds on the
+continuum bec theorem of OSW which in
+
+ align:start position:0%
+continuum bec theorem of OSW which in
+ 
+
+ align:start position:0%
+continuum bec theorem of OSW which in
+turn built on the epsilon improvement
+
+ align:start position:0%
+turn built on the epsilon improvement
+ 
+
+ align:start position:0%
+turn built on the epsilon improvement
+of uh or OS which in turn built on the
+
+ align:start position:0%
+of uh or OS which in turn built on the
+ 
+
+ align:start position:0%
+of uh or OS which in turn built on the
+BAN projection theorem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right, it's not at all obvious given
+
+ align:start position:0%
+All right, it's not at all obvious given
+ 
+
+ align:start position:0%
+All right, it's not at all obvious given
+the Beck theorem, just an ingredient.
+
+ align:start position:0%
+the Beck theorem, just an ingredient.
+ 
+
+ align:start position:0%
+the Beck theorem, just an ingredient.
+Um, and um, so there also some great
+
+ align:start position:0%
+Um, and um, so there also some great
+ 
+
+ align:start position:0%
+Um, and um, so there also some great
+ideas in that that we'll talk about next
+
+ align:start position:0%
+ideas in that that we'll talk about next
+ 
+
+ align:start position:0%
+ideas in that that we'll talk about next
+time. But also it involves some special
+
+ align:start position:0%
+time. But also it involves some special
+ 
+
+ align:start position:0%
+time. But also it involves some special
+structure
+
+ align:start position:0%
+structure
+ 
+
+ align:start position:0%
+structure
+of the AD regular case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, we'll talk about that a lot uh on
+
+ align:start position:0%
+Okay, we'll talk about that a lot uh on
+ 
+
+ align:start position:0%
+Okay, we'll talk about that a lot uh on
+Thursday.
+
+ align:start position:0%
+Thursday.
+ 
+
+ align:start position:0%
+Thursday.
+All right, the second ingredient is a
+
+ align:start position:0%
+All right, the second ingredient is a
+ 
+
+ align:start position:0%
+All right, the second ingredient is a
+theorem of Guth Solomon Wong. So I was
+
+ align:start position:0%
+theorem of Guth Solomon Wong. So I was
+ 
+
+ align:start position:0%
+theorem of Guth Solomon Wong. So I was
+involved a little bit. This a slightly
+
+ align:start position:0%
+involved a little bit. This a slightly
+ 
+
+ align:start position:0%
+involved a little bit. This a slightly
+older theorem. It's from 2019
+
+ align:start position:0%
+older theorem. It's from 2019
+ 
+
+ align:start position:0%
+older theorem. It's from 2019
+and we proved that the first invert
+
+ align:start position:0%
+and we proved that the first invert
+ 
+
+ align:start position:0%
+and we proved that the first invert
+conjecture holds in the well spaced
+
+ align:start position:0%
+conjecture holds in the well spaced
+ 
+
+ align:start position:0%
+conjecture holds in the well spaced
+case.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And it's based on the forier
+
+ align:start position:0%
+Okay. And it's based on the forier
+ 
+
+ align:start position:0%
+Okay. And it's based on the forier
+method.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, this is much less difficult than
+
+ align:start position:0%
+Okay, this is much less difficult than
+ 
+
+ align:start position:0%
+Okay, this is much less difficult than
+this. It's the 4A method that we
+
+ align:start position:0%
+this. It's the 4A method that we
+ 
+
+ align:start position:0%
+this. It's the 4A method that we
+explored for a while with a little bit
+
+ align:start position:0%
+explored for a while with a little bit
+ 
+
+ align:start position:0%
+explored for a while with a little bit
+of extra something something. How do you
+
+ align:start position:0%
+of extra something something. How do you
+ 
+
+ align:start position:0%
+of extra something something. How do you
+take advantage of being really well
+
+ align:start position:0%
+take advantage of being really well
+ 
+
+ align:start position:0%
+take advantage of being really well
+spaced instead of just ad regular
+
+ align:start position:0%
+spaced instead of just ad regular
+ 
+
+ align:start position:0%
+spaced instead of just ad regular
+okay
+
+ align:start position:0%
+okay
+ 
+
+ align:start position:0%
+okay
+good. All right. So now um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when I presented these two possibilities
+
+ align:start position:0%
+when I presented these two possibilities
+ 
+
+ align:start position:0%
+when I presented these two possibilities
+it the way I had thought about them is
+
+ align:start position:0%
+it the way I had thought about them is
+ 
+
+ align:start position:0%
+it the way I had thought about them is
+that these are just two opposite ends of
+
+ align:start position:0%
+that these are just two opposite ends of
+ 
+
+ align:start position:0%
+that these are just two opposite ends of
+a whole gray spectrum.
+
+ align:start position:0%
+a whole gray spectrum.
+ 
+
+ align:start position:0%
+a whole gray spectrum.
+And so if you have a method that works
+
+ align:start position:0%
+And so if you have a method that works
+ 
+
+ align:start position:0%
+And so if you have a method that works
+in one end and you have a method that
+
+ align:start position:0%
+in one end and you have a method that
+ 
+
+ align:start position:0%
+in one end and you have a method that
+works on the other end,
+
+ align:start position:0%
+works on the other end,
+ 
+
+ align:start position:0%
+works on the other end,
+I guess you might hope to have a general
+
+ align:start position:0%
+I guess you might hope to have a general
+ 
+
+ align:start position:0%
+I guess you might hope to have a general
+thing that sort of combines them both
+
+ align:start position:0%
+thing that sort of combines them both
+ 
+
+ align:start position:0%
+thing that sort of combines them both
+and and works for everything. But um but
+
+ align:start position:0%
+and and works for everything. But um but
+ 
+
+ align:start position:0%
+and and works for everything. But um but
+there's still all this stuff in the
+
+ align:start position:0%
+there's still all this stuff in the
+ 
+
+ align:start position:0%
+there's still all this stuff in the
+middle.
+
+ align:start position:0%
+middle.
+ 
+
+ align:start position:0%
+middle.
+Um and it turns out I think this is
+
+ align:start position:0%
+Um and it turns out I think this is
+ 
+
+ align:start position:0%
+Um and it turns out I think this is
+surprising and important in its own
+
+ align:start position:0%
+surprising and important in its own
+ 
+
+ align:start position:0%
+surprising and important in its own
+right that the proof of the theorem
+
+ align:start position:0%
+right that the proof of the theorem
+ 
+
+ align:start position:0%
+right that the proof of the theorem
+actually reduces to just those two cases
+
+ align:start position:0%
+actually reduces to just those two cases
+ 
+
+ align:start position:0%
+actually reduces to just those two cases
+or or um so the third ingredient
+
+ align:start position:0%
+or or um so the third ingredient
+ 
+
+ align:start position:0%
+or or um so the third ingredient
+is a multiscale argument
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which shows that the first conjecture
+
+ align:start position:0%
+which shows that the first conjecture
+ 
+
+ align:start position:0%
+which shows that the first conjecture
+actually reduces to
+
+ align:start position:0%
+actually reduces to
+ 
+
+ align:start position:0%
+actually reduces to
+the ad regular case and the what they
+
+ align:start position:0%
+the ad regular case and the what they
+ 
+
+ align:start position:0%
+the ad regular case and the what they
+call the semi wellspaced case.
+
+ align:start position:0%
+call the semi wellspaced case.
+ 
+
+ align:start position:0%
+call the semi wellspaced case.
+So this is a small generalization of
+
+ align:start position:0%
+So this is a small generalization of
+ 
+
+ align:start position:0%
+So this is a small generalization of
+this case that can be handled by more or
+
+ align:start position:0%
+this case that can be handled by more or
+ 
+
+ align:start position:0%
+this case that can be handled by more or
+less the same methods using for
+
+ align:start position:0%
+less the same methods using for
+ 
+
+ align:start position:0%
+less the same methods using for
+analysis.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. Um
+
+ align:start position:0%
+Okay. Um
+ 
+
+ align:start position:0%
+Okay. Um
+cool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So in in each of these I think
+
+ align:start position:0%
+Okay. So in in each of these I think
+ 
+
+ align:start position:0%
+Okay. So in in each of these I think
+there is something worth talking about
+
+ align:start position:0%
+there is something worth talking about
+ 
+
+ align:start position:0%
+there is something worth talking about
+and worth worth remembering an idea that
+
+ align:start position:0%
+and worth worth remembering an idea that
+ 
+
+ align:start position:0%
+and worth worth remembering an idea that
+could be useful in other in other pro
+
+ align:start position:0%
+could be useful in other in other pro
+ 
+
+ align:start position:0%
+could be useful in other in other pro
+certainly in other problems in this
+
+ align:start position:0%
+certainly in other problems in this
+ 
+
+ align:start position:0%
+certainly in other problems in this
+field and maybe in other parts of math.
+
+ align:start position:0%
+field and maybe in other parts of math.
+ 
+
+ align:start position:0%
+field and maybe in other parts of math.
+Uh we have two more classes so I'll
+
+ align:start position:0%
+Uh we have two more classes so I'll
+ 
+
+ align:start position:0%
+Uh we have two more classes so I'll
+vigil and wiggle and so my goal is in
+
+ align:start position:0%
+vigil and wiggle and so my goal is in
+ 
+
+ align:start position:0%
+vigil and wiggle and so my goal is in
+the two classes to say something
+
+ align:start position:0%
+the two classes to say something
+ 
+
+ align:start position:0%
+the two classes to say something
+substantial about each of these three
+
+ align:start position:0%
+substantial about each of these three
+ 
+
+ align:start position:0%
+substantial about each of these three
+ideas which fit together to prove the
+
+ align:start position:0%
+ideas which fit together to prove the
+ 
+
+ align:start position:0%
+ideas which fit together to prove the
+first and third conjecture.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, good. Any question la last
+
+ align:start position:0%
+Okay, good. Any question la last
+ 
+
+ align:start position:0%
+Okay, good. Any question la last
+questions or comments?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+>> Mhm.
+
+ align:start position:0%
+>> Mhm.
+ 
+
+ align:start position:0%
+>> Mhm.
+>> Within kind of each of these individual
+
+ align:start position:0%
+>> Within kind of each of these individual
+ 
+
+ align:start position:0%
+>> Within kind of each of these individual
+cases like how kind of much variation is
+
+ align:start position:0%
+cases like how kind of much variation is
+ 
+
+ align:start position:0%
+cases like how kind of much variation is
+there in the structure of the sets? Like
+
+ align:start position:0%
+there in the structure of the sets? Like
+ 
+
+ align:start position:0%
+there in the structure of the sets? Like
+I guess it's not going to be kind of
+
+ align:start position:0%
+I guess it's not going to be kind of
+ 
+
+ align:start position:0%
+I guess it's not going to be kind of
+rearranging kind of certain points
+
+ align:start position:0%
+rearranging kind of certain points
+ 
+
+ align:start position:0%
+rearranging kind of certain points
+within kind of one of the boxes does a
+
+ align:start position:0%
+within kind of one of the boxes does a
+ 
+
+ align:start position:0%
+within kind of one of the boxes does a
+lot or does a little
+
+ align:start position:0%
+lot or does a little
+ 
+
+ align:start position:0%
+lot or does a little
+Yeah. Okay. So the question is we've t
+
+ align:start position:0%
+Yeah. Okay. So the question is we've t
+ 
+
+ align:start position:0%
+Yeah. Okay. So the question is we've t
+so we've taken all the delta t sets we
+
+ align:start position:0%
+so we've taken all the delta t sets we
+ 
+
+ align:start position:0%
+so we've taken all the delta t sets we
+have then divided them according to
+
+ align:start position:0%
+have then divided them according to
+ 
+
+ align:start position:0%
+have then divided them according to
+their branching function and one extreme
+
+ align:start position:0%
+their branching function and one extreme
+ 
+
+ align:start position:0%
+their branching function and one extreme
+is the ad regular and one extreme is the
+
+ align:start position:0%
+is the ad regular and one extreme is the
+ 
+
+ align:start position:0%
+is the ad regular and one extreme is the
+wellspaced
+
+ align:start position:0%
+wellspaced
+ 
+
+ align:start position:0%
+wellspaced
+and then the question is if you look
+
+ align:start position:0%
+and then the question is if you look
+ 
+
+ align:start position:0%
+and then the question is if you look
+among different sets with the same
+
+ align:start position:0%
+among different sets with the same
+ 
+
+ align:start position:0%
+among different sets with the same
+branching function like among different
+
+ align:start position:0%
+branching function like among different
+ 
+
+ align:start position:0%
+branching function like among different
+ad regular sets how different are they
+
+ align:start position:0%
+ad regular sets how different are they
+ 
+
+ align:start position:0%
+ad regular sets how different are they
+from each other? Um
+
+ align:start position:0%
+from each other? Um
+ 
+
+ align:start position:0%
+from each other? Um
+well
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+uh I will try to sort of answer that by
+
+ align:start position:0%
+uh I will try to sort of answer that by
+ 
+
+ align:start position:0%
+uh I will try to sort of answer that by
+drawing a second ad regular set in blue
+
+ align:start position:0%
+drawing a second ad regular set in blue
+ 
+
+ align:start position:0%
+drawing a second ad regular set in blue
+that we can compare to the one in white.
+
+ align:start position:0%
+that we can compare to the one in white.
+ 
+
+ align:start position:0%
+that we can compare to the one in white.
+So I should pick four uh big squares and
+
+ align:start position:0%
+So I should pick four uh big squares and
+ 
+
+ align:start position:0%
+So I should pick four uh big squares and
+in each of them I'll draw four dots.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+I would say that the sort of
+
+ align:start position:0%
+I would say that the sort of
+ 
+
+ align:start position:0%
+I would say that the sort of
+spacing feel of these dots is is the
+
+ align:start position:0%
+spacing feel of these dots is is the
+ 
+
+ align:start position:0%
+spacing feel of these dots is is the
+same in all the examples that are ad
+
+ align:start position:0%
+same in all the examples that are ad
+ 
+
+ align:start position:0%
+same in all the examples that are ad
+regular. Um on the other hand actually
+
+ align:start position:0%
+regular. Um on the other hand actually
+ 
+
+ align:start position:0%
+regular. Um on the other hand actually
+let me draw another example. So this
+
+ align:start position:0%
+let me draw another example. So this
+ 
+
+ align:start position:0%
+let me draw another example. So this
+this would be here's another example.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+something else is a little different
+
+ align:start position:0%
+something else is a little different
+ 
+
+ align:start position:0%
+something else is a little different
+about this example. Um and so yeah, so
+
+ align:start position:0%
+about this example. Um and so yeah, so
+ 
+
+ align:start position:0%
+about this example. Um and so yeah, so
+there are some more delicate things that
+
+ align:start position:0%
+there are some more delicate things that
+ 
+
+ align:start position:0%
+there are some more delicate things that
+could be different about the different
+
+ align:start position:0%
+could be different about the different
+ 
+
+ align:start position:0%
+could be different about the different
+ad regular examples. Even though so so
+
+ align:start position:0%
+ad regular examples. Even though so so
+ 
+
+ align:start position:0%
+ad regular examples. Even though so so
+what's the same about them is you give
+
+ align:start position:0%
+what's the same about them is you give
+ 
+
+ align:start position:0%
+what's the same about them is you give
+me a radius your favorite radius you
+
+ align:start position:0%
+me a radius your favorite radius you
+ 
+
+ align:start position:0%
+me a radius your favorite radius you
+stick down a ball of that radius and
+
+ align:start position:0%
+stick down a ball of that radius and
+ 
+
+ align:start position:0%
+stick down a ball of that radius and
+count how many points are in there that
+
+ align:start position:0%
+count how many points are in there that
+ 
+
+ align:start position:0%
+count how many points are in there that
+will be the same for any a dregular set
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but there are delicate things actually
+
+ align:start position:0%
+but there are delicate things actually
+ 
+
+ align:start position:0%
+but there are delicate things actually
+another very important delicate thing
+
+ align:start position:0%
+another very important delicate thing
+ 
+
+ align:start position:0%
+another very important delicate thing
+that would be different is so for let's
+
+ align:start position:0%
+that would be different is so for let's
+ 
+
+ align:start position:0%
+that would be different is so for let's
+now think about the well spaced set an
+
+ align:start position:0%
+now think about the well spaced set an
+ 
+
+ align:start position:0%
+now think about the well spaced set an
+example of a well spaced set is an
+
+ align:start position:0%
+example of a well spaced set is an
+ 
+
+ align:start position:0%
+example of a well spaced set is an
+integer grid
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that has some special properties. It has
+
+ align:start position:0%
+that has some special properties. It has
+ 
+
+ align:start position:0%
+that has some special properties. It has
+like translation symmetry and stuff like
+
+ align:start position:0%
+like translation symmetry and stuff like
+ 
+
+ align:start position:0%
+like translation symmetry and stuff like
+that. A typical well spaced set will
+
+ align:start position:0%
+that. A typical well spaced set will
+ 
+
+ align:start position:0%
+that. A typical well spaced set will
+still have one point in each of these
+
+ align:start position:0%
+still have one point in each of these
+ 
+
+ align:start position:0%
+still have one point in each of these
+boxes, but it won't have additive
+
+ align:start position:0%
+boxes, but it won't have additive
+ 
+
+ align:start position:0%
+boxes, but it won't have additive
+structure. It won't have translation
+
+ align:start position:0%
+structure. It won't have translation
+ 
+
+ align:start position:0%
+structure. It won't have translation
+symmetry. It won't have and it won't
+
+ align:start position:0%
+symmetry. It won't have and it won't
+ 
+
+ align:start position:0%
+symmetry. It won't have and it won't
+have uh you know very many lines that go
+
+ align:start position:0%
+have uh you know very many lines that go
+ 
+
+ align:start position:0%
+have uh you know very many lines that go
+through many points. So those kinds of
+
+ align:start position:0%
+through many points. So those kinds of
+ 
+
+ align:start position:0%
+through many points. So those kinds of
+things are different among the different
+
+ align:start position:0%
+things are different among the different
+ 
+
+ align:start position:0%
+things are different among the different
+sets with the same spacing condition.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Uh okay. Well, let's stop there for
+
+ align:start position:0%
+Uh okay. Well, let's stop there for
+ 
+
+ align:start position:0%
+Uh okay. Well, let's stop there for
+today and we'll talk more about these
+
+ align:start position:0%
+today and we'll talk more about these
+ 
+
+ align:start position:0%
+today and we'll talk more about these
+things on our last two classes.
\ No newline at end of file
diff --git a/hRHzPaDpgu0.txt b/hRHzPaDpgu0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9cd46d3fc76b37da141bc60a63466e6752f9b3f7
--- /dev/null
+++ b/hRHzPaDpgu0.txt
@@ -0,0 +1,2900 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high-quality
+educational resources for free.
+
+To make a donation, or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: Particles
+in quantum mechanics.
+
+In particular, the ones that are
+identical and non-interacting.
+
+So basically, we were focusing
+on a type of Hamiltonian
+
+for a system of N
+particles, which
+
+could be written as the sum of
+contributions that correspond
+
+respectively to particle
+1, particle 2, particle N.
+
+So essentially, a sum of
+terms that are all the same.
+
+And one-particle
+terms is sufficient
+
+because we don't
+have interactions.
+
+So if we look at one of
+these H's-- so one of these
+
+one-particle Hamiltonians, we
+said that we could find some
+
+kind of basis for it.
+
+In particular, typically we
+were interested in particles
+
+in the box.
+
+We would label them
+with some wave number k.
+
+And there was an associated
+one-particle energy,
+
+which for the case of
+one-particle in box
+
+was h bar squared
+k squared over 2m.
+
+But in general, for the
+one-particle system,
+
+we can think of a ladder of
+possible values of energies.
+
+So there will be some
+k1, k2, k3, et cetera.
+
+They may be distributed in any
+particular way corresponding
+
+to different energies.
+
+Basically, you
+would have a number
+
+of possible states
+for one particle.
+
+So for the case of the particle
+in the box, the wave functions
+
+and coordinate space that we
+had x, k were of the form e
+
+to the i k dot x divided
+by square root of V.
+
+We allowed the energies where h
+bar squared k squared over 2m.
+
+And this discretization
+was because the values of k
+
+were multiples of 2 pi over
+l with integers in the three
+
+different directions.
+
+Assuming periodic
+boundary conditions
+
+or appropriate discretization
+for closed boundary conditions,
+
+or whatever you have.
+
+So that's the
+one-particle state.
+
+If the Hamiltonian
+is of this form,
+
+it is clear that we can
+multiply a bunch of these states
+
+and form another
+eigenstate for HN.
+
+Those we were calling
+product states.
+
+So you basically pick a
+bunch of these k's and you
+
+multiply them.
+
+So you have k1, k2, kN.
+
+And essentially, that
+would correspond,
+
+let's say, in coordinate
+representation
+
+to taking a bunch of x's and
+the corresponding k's and having
+
+a wave function of the form e to
+the i k alp-- sum over alpha k
+
+alpha x alpha, and then
+divided by V to the N over 2.
+
+So in this procedure,
+what did we do?
+
+We had a number of possibilities
+for the one-particle state.
+
+And in order to, let's say,
+make a two-particle state,
+
+we would pick two of
+these k's and multiply
+
+the corresponding
+wave functions.
+
+If you had three particles,
+we could pick another one.
+
+If you had four particles,
+we could potentially
+
+pick a second one
+twice, et cetera.
+
+So in general,
+basically we would
+
+put N of these crosses on
+these one-particle states
+
+that we've selected.
+
+Problem was that
+this was not allowed
+
+by quantum mechanics
+for identical particles.
+
+Because if we took one
+of these wave functions
+
+and exchanged two of
+the labels, x1 and x2,
+
+we could potentially get
+a different wave function.
+
+And in quantum mechanics, we
+said that the wave function
+
+has to be either symmetric or
+anti-symmetric with respect
+
+to exchange of a
+pair of particles.
+
+And also, whatever it implied
+for repeating this exchange
+
+many times to look at all
+possible permutations.
+
+So what we saw was that
+product states are good
+
+as long as you
+are thinking about
+
+distinguishable particles.
+
+But if you have
+identical particles,
+
+you had to appropriately
+symmetrize or anti-symmetrize
+
+these states.
+
+So what we ended up was
+a wabe of, for example,
+
+symmetrizing things for
+the case of fermions.
+
+So we could take a bunch
+of these k-values again.
+
+And a fermionic, or
+anti-symmetrized version,
+
+was then constructed by
+summing over all permutations.
+
+And for N particle, there would
+be N factorial permutations.
+
+Basically, doing a
+permutation of all of these
+
+indices k1, k2, et cetera,
+that we had selected for this.
+
+And for the case
+of fermions, we had
+
+to multiply each
+permutation with a sign that
+
+was plus for even permutations,
+minus for odd permutations.
+
+And this would give
+us N factorial terms.
+
+And the appropriate
+normalization
+
+was 1 over square
+root of N factorial.
+
+So this was for the
+case of fermions.
+
+And this was actually minus.
+
+I should have put
+in a minus here.
+
+And this would have
+been minus to the P.
+
+For the case of
+bosons, we basically
+
+dispensed with this factor
+of minus 1 to the P.
+
+So we had a Pk.
+
+Now, the corresponding
+normalization that we had here
+
+was slightly different.
+
+The point was that
+if we were doing
+
+this computation for
+the case of fermions,
+
+we could not allow
+a state where there
+
+is a double occupation of one
+of the one-particle state.
+
+Under exchange of
+the particles that
+
+would correspond
+to these k-values,
+
+I would get the same state back,
+but the exchange would give me
+
+a minus 1 and it
+would give me 0.
+
+So the fermionic wave function
+that I have constructed
+
+here, appropriately
+anti-symmetrized,
+
+exists only as long as
+there are no repeats.
+
+Whereas, for the case of bosons,
+I could put 2 over same place.
+
+I could put 3 somewhere else,
+any number that I liked,
+
+and there would be
+no problem with this.
+
+Except that the normalization
+would be more complicated.
+
+And we saw that
+appropriate normalization
+
+was a product over
+k nk factorial.
+
+So this was for fermions.
+
+This is for bosons.
+
+And the two I can
+submerge into one formula
+
+by writing a symmetrized
+or anti-symmetrized state,
+
+respectively indicated by eta,
+where we have eta is minus 1
+
+for fermions and eta
+is plus 1 for bosons,
+
+which is 1 over square
+root of N factorial product
+
+over k nk factorials.
+
+And then the sum over all
+N factorial permutations.
+
+This phase factor for fermions
+and nothing for bosons
+
+of the appropriately
+permuted set of k's.
+
+And in this way
+of noting things,
+
+I have to assign values nk which
+are either 0 or 1 for fermions.
+
+Because as we said, multiple
+occupations are not allowed.
+
+But there is no
+restriction for bosons.
+
+Except of course, that
+in this perspective,
+
+as I go along this k-axis,
+I have 0, 1, 0, 2, 1, 3, 0,
+
+0 for the occupations.
+
+Of course, what I
+need to construct
+
+whether I am dealing
+with bosons or fermions
+
+is that the sum over k nk is
+the total number of particles
+
+that I have.
+
+Now, the other thing to note
+is that once I have given you
+
+a picture such as this in terms
+of which one-particle states
+
+I want to look at, or which
+set of occupation numbers
+
+I have nk, then
+there is one and only
+
+one symmetrized or
+anti-symmetrized state.
+
+So over here, I
+could have permuted
+
+the k's in a number
+of possible ways.
+
+But as a result
+of symmetrization,
+
+anti-symmetrization,
+various ways
+
+of permuting the
+labels here ultimately
+
+come to the same set
+of occupation numbers.
+
+So it is possible to actually
+label the state rather than
+
+by the set of k's.
+
+By the set of nk's.
+
+It is kind of a more appropriate
+way of representing the system.
+
+So that's essentially
+the kinds of states
+
+that we are going to be using.
+
+Again, in talking about
+identical particles,
+
+which could be either
+bosons or fermions.
+
+Let's take a step back,
+remind you of something
+
+that we did before that
+had only one particle.
+
+Because I will soon
+go to many particles.
+
+But before that,
+let's remind you
+
+what the one particle
+in a box looked like.
+
+So indeed, in this case,
+the single-particle states
+
+were the ones that
+I told you before,
+
+2 pi over l some
+set of integers.
+
+Epsilon k, that was h bar
+squared k squared over 2m.
+
+If I want to calculate
+the partition function
+
+for one particle in the box,
+I have to do a trace of e
+
+to the minus beta
+h for one particle.
+
+The trace I can very
+easily calculate
+
+in the basis in which
+this is diagonal.
+
+That's the basis
+that is parameterized
+
+by these k-values.
+
+So I do a sum over k of
+e to the minus beta h
+
+bar squared k squared over 2m.
+
+And then in the limit
+of very large box,
+
+we saw that the sum
+over k I can replace
+
+with V integral
+over k 2 pi cubed.
+
+This was the density
+of states in k.
+
+e to the minus beta h bar
+squared k squared over 2m.
+
+And this was three
+Gaussian integrals
+
+that gave us the usual formula
+of V over lambda cubed, where
+
+lambda was this thermal
+[INAUDIBLE] wavelength
+
+h root 2 pi mk.
+
+But we said that the essence
+of statistical mechanics
+
+is to tell you
+about probabilities
+
+of various micro-states, various
+positions of the particle
+
+in the box, which in
+the quantum perspective
+
+is probability becomes
+a density matrix.
+
+And we evaluated
+this density matrix
+
+in the coordinate
+representation.
+
+And in the coordinate
+representation,
+
+essentially what
+we had to do was
+
+to go into the basis in
+which rho is diagonal.
+
+So we had x prime k.
+
+In the k basis, the density
+matrix is just this formula.
+
+It's the Boltzmann weight
+appropriately normalized by Z1.
+
+And then we go kx.
+
+And basically,
+again replacing this
+
+with V integral d cubed k 2 pi
+cubed e to the minus beta h bar
+
+squared k squared over 2m.
+
+These two factors of xk and x
+prime k gave us a factor of e
+
+to the kx, xk I have as
+ik dot x prime minus x.
+
+Completing the square.
+
+Actually, I had to divide by Z1.
+
+There is a factor of 1 over
+V from the normalization
+
+of these things.
+
+The two V's here cancel,
+but Z1 is proportional to V.
+
+The lambda cubes
+cancel and so what
+
+we have is 1 over
+V e to the minus x
+
+minus x prime squared
+pi over lambda squared.
+
+So basically, what
+you have here is
+
+that we have a box
+of volume V. There
+
+is a particle inside
+at some location x.
+
+And the probability
+to find it at location
+
+x is the diagonal
+element of this entity.
+
+It's just 1 over
+V. But this entity
+
+has off-diagonal elements
+reflecting the fact
+
+that the best that you can do
+to localize something in quantum
+
+mechanics is to make some
+kind of a wave packet.
+
+OK.
+
+So this we did last time.
+
+What we want to do now is
+to go from one particle
+
+to the case of N particles.
+
+So rather than
+having 1x prime, I
+
+will have a whole bunch of x
+primes labeled 1 through N.
+
+And I want to calculate the N
+particle density matrix that
+
+connects me from set of points
+x to another set of points
+
+x prime.
+
+So if you like in
+the previous picture,
+
+this would have been
+x1 and x1 prime,
+
+and then I now have x2 and x2
+prime, x3 and x3 prime, xN and
+
+xN prime.
+
+I have a bunch of
+different coordinates
+
+and I'd like to calculate that.
+
+OK.
+
+Once more, we know that rho
+is diagonal in the basis that
+
+is represented by
+these occupations
+
+of one-particle states.
+
+And so what I can
+do is I can sum over
+
+a whole bunch of plane waves.
+
+And I have to pick N factors
+of k out of this list
+
+in order to make one of these
+symmetrized or anti-symmetrized
+
+wave functions.
+
+But then I have to
+remember, as I said,
+
+that I should not over-count
+distinct set of k-values
+
+because permutations
+of these list of k's
+
+that I have over here,
+because of symmetrization
+
+or anti-symmetrization,
+will give me the same state.
+
+So I have to be
+careful about that.
+
+Then, I go from x prime to k.
+
+Now, the density matrix
+in the k-basis I know.
+
+It is simply e to the minus
+beta, the energy which
+
+is sum over alpha h bar squared
+k alpha squared over 2m.
+
+So I sum over the
+list of k alphas
+
+that appear in this series.
+
+There will be n of them.
+
+I have to
+appropriately normalize
+
+that by the N-particle partition
+function, which we have yet
+
+to calculate.
+
+And then I go back from k to x.
+
+Now, let's do this.
+
+The first thing that
+I mentioned last time
+
+is that I would,
+in principle, like
+
+to sum over k1 going
+over the entire list,
+
+k2 going the entire list, k3
+going over the entire list.
+
+That is, I would like to make
+the sum over k's unrestricted.
+
+But then I have to
+take into account
+
+the over-counting that I have.
+
+If I am looking at the case
+where all of the k's are
+
+distinct-- they don't show
+any double occupancy-- then
+
+I have over-counted by the
+number of permutations.
+
+Because any permutation would
+have given me the same number.
+
+So I have to divide by
+the number of permutations
+
+to avoid the over-counting
+due to symmetrization here.
+
+Now, when I have
+something like this,
+
+which is a multiple occupancy,
+I have overdone this division.
+
+I have to multiply
+by this factor,
+
+and that's the correct number
+of over-countings that I have.
+
+And as I said, this was a good
+thing because the quantity
+
+that I had the hardest
+time for, and comes
+
+in the normalizations
+that occurs here,
+
+is this factor of 1
+over nk factorial.
+
+Naturally, again,
+all of these things
+
+do depend on the symmetry.
+
+So I better make sure
+I indicate the index.
+
+Whether I'm calculating this
+density matrix for fermions
+
+or bosons, it is important.
+
+In either case-- well,
+what I need to do
+
+is to do a summation over P
+here for this one and P prime
+
+here or P prime here and P here.
+
+It doesn't matter, there's
+two sets of permutations
+
+that I have to do.
+
+In each case, I have to
+take care of this eta P,
+
+eta P prime.
+
+And then the normalization.
+
+So I divide by twice, or the
+square of the square root.
+
+I get the N factorial
+product over k nk factorial.
+
+And very nicely, the
+over-counting factor
+
+here cancels the
+normalization factor
+
+that I would have had here.
+
+So we got that.
+
+Now, what do we have?
+
+We have P prime permutation
+of these objects going to x,
+
+and then we have
+here P permutation
+
+of these k numbers going to x.
+
+I guess the first
+one I got wrong.
+
+I start with x prime.
+
+Go through P prime to k.
+
+And again, symmetries are
+already taken into account.
+
+I don't need to write that.
+
+And I have the factor
+of e to the minus beta h
+
+bar squared sum over
+alpha k alpha squared
+
+over 2m divided by ZN.
+
+OK, so let's bring all of the
+denominator factors out front.
+
+I have a ZN.
+
+I have an N factorial squared.
+
+Two factors of N factorial.
+
+I have a sum over two sets of
+permutations P and P prime.
+
+The product of the associated
+phase factor of their parities,
+
+and then I have this
+integration over k's.
+
+Now, unrestricted.
+
+Since it is unrestricted, I
+can integrate independently
+
+over each one of the k's, or
+sum over each one of them.
+
+When I sum, the sum
+becomes the integral
+
+over d cubed k alpha divided
+by 2 pi-- yeah, 2 pi cubed V.
+
+Basically, the density in
+replacing the sum over k
+
+alpha with the
+corresponding integration.
+
+So basically, this
+set of factors
+
+is what happened to that.
+
+OK, what do we have here?
+
+We have e to the i x--
+well, let's be careful here.
+
+I have e to the i x prime alpha
+acting on k of p prime alpha
+
+because I permuted
+the k-label that
+
+went with, say, the alpha
+component here with p prime.
+
+From here, I would
+have minus because it's
+
+the complex conjugate.
+
+I have x alpha k p alpha,
+because I permuted this by k.
+
+I have one of these factors for
+each V. With each one of them,
+
+there is a normalization
+of square root of V.
+
+So the two of them together will
+give me V. But that's only one
+
+of the N-particle So
+there are N of them.
+
+So if I want, I can
+extend this product
+
+to also encompass this term.
+
+And then having done so, I can
+also write here e to the minus
+
+beta h bar squared
+k alpha squared
+
+over 2m within the product.
+
+AUDIENCE: [INAUDIBLE] after
+this-- is it quantity xk minus
+
+[INAUDIBLE].
+
+PROFESSOR: I forgot an a here.
+
+What else did I miss out?
+
+AUDIENCE: [INAUDIBLE] quantity.
+
+PROFESSOR: So I forgot the i.
+
+OK, good?
+
+So the V's cancel out.
+
+All right, so that's fine.
+
+What do we have?
+
+We have 1 over ZN N
+factorial squared.
+
+Two sets of permutations
+summed over, p and p prime.
+
+Corresponding parities
+eta p eta of p prime.
+
+And then, I have a product
+of these integrations
+
+that I have to do that are
+three-dimensional Gaussians
+
+for each k alpha.
+
+What do I get?
+
+Well, first of all,
+if I didn't have this,
+
+if I just was doing
+the integration of e
+
+to the minus beta h bar
+squared k squared over 2m,
+
+I did that already.
+
+I get a 1 over lambda cubed.
+
+So basically, from each
+one of them I will get a 1
+
+over lambda cubed.
+
+But the integration is
+shifted by this amount.
+
+Actually, I already did the
+shifted integration here also
+
+for one particle.
+
+So I get the corresponding
+factor of e to the minus-- ah.
+
+I have to be a little
+bit careful over here
+
+because what I am integrating
+is over k alpha squared.
+
+Whereas, in the way that
+I have the list over here,
+
+I have x prime
+alpha and x alpha,
+
+but a different k
+playing around with each.
+
+What should I do?
+
+I really want this
+integration over k
+
+alpha to look like
+what I have over here.
+
+Well, as I sum over
+all possibilities
+
+in each one of these terms, I
+am bound to encounter k alpha.
+
+Essentially, I have permuted
+all of the k's that I originally
+
+had.
+
+So the k alpha has now been
+sent to some other location.
+
+But as I sum over all possible
+alpha, I will hit that.
+
+When I hit that, I will
+find that the thing that
+
+was multiplying k alpha is the
+inverse permutation of alpha.
+
+And the thing that was
+multiplying k alpha here
+
+is the inverse permutation of p.
+
+So then I can do the
+integration over k alpha easily.
+
+And so what do I have?
+
+I have x prime of
+p prime inverse
+
+alpha-- the inverse
+permutation-- minus x
+
+of p inverse alpha squared
+pi over lambda squared.
+
+Now, this is still
+inconvenient because I
+
+am summing over two N
+factorial sets of permutations.
+
+And I expect that since
+the sum only involves
+
+comparison of things that
+are occurring N times,
+
+as I go over the list of N
+factorial permutation squared,
+
+I will get the same
+thing appearing twice.
+
+So it is very much like when we
+are doing an integration over x
+
+and x prime, but
+the function only
+
+depends on x minus x prime.
+
+We get a factor of volume.
+
+Here, it is easy to
+see that one of these
+
+sums I can very easily do
+because it is just repetition
+
+of all of the results
+that I have previously.
+
+And there will be N
+factorial such terms.
+
+So doing that, I can get rid
+of one of the N factorials.
+
+And I will have only
+one permutation left,
+
+Q. And what will appear here
+would be the parity of this Q
+
+that is the combination,
+or if you like,
+
+the relative of these
+two permutations.
+
+And I have an
+exponential of minus sum
+
+over alpha x alpha minus
+x prime Q alpha squared
+
+pi over lambda squared.
+
+And I think I forgot a factor
+of lambda to the 3 [INAUDIBLE].
+
+This factor of lambda 3.
+
+So this is actually
+the final result.
+
+And let's see what
+that precisely
+
+means for two particles.
+
+So let's look at two particles.
+
+So for two particle,s I will
+have on one side coordinates
+
+of 1 prime and 2 prime.
+
+On the right-hand side, I
+have coordinates 1 and 2.
+
+And let's see what this
+density matrix tells us.
+
+It tells us that to go from x1
+prime x2 prime, a two particle
+
+density matrix connecting
+to x1 x2 on the other side,
+
+I have 1 over the two-particle
+partition function
+
+that i haven't yet calculated.
+
+Lambda to the sixth.
+
+N factorial in this case is 2.
+
+And then for two things,
+there are two permutations.
+
+So the identity
+maps 1 to 1, 2 to 2.
+
+And therefore, what
+I will get here
+
+would be exponential of minus
+x1' minus x1 prime squared
+
+pi over lambda squared minus
+x2 minus x2 prime squared pi
+
+over lambda squared.
+
+So that's Q being
+identity and identity
+
+has essentially 0 parity.
+
+It's an even permutation.
+
+The next thing is when
+I exchange 1 and 2.
+
+That would have odd parity.
+
+So I would get minus 1 for
+fermions, plus for bosons.
+
+And what I would get here
+is exponential of minus x1'
+
+minus x2 prime squared pi
+over lambda squared minus x2
+
+minus x1 prime squared
+pi over lambda squared.
+
+So essentially, one of
+the terms-- the first term
+
+is just the square of what I
+had before for one particle.
+
+I take the one-particle result,
+going from 1 to 1 prime,
+
+going from 2 to 2 prime
+and multiply them together.
+
+But then you say, I can't tell
+apart 2 prime and 1 prime.
+
+Maybe the thing that
+you are calling 1 prime
+
+is really 2 prime
+and vice versa.
+
+So I have to allow
+for the possibility
+
+that rather than
+x1 prime here, I
+
+should put x2 prime and
+the other way around.
+
+And this also corresponds
+to a permutation
+
+that is an exchange.
+
+It's an odd parity and will
+give you something like that.
+
+Say OK, I have no
+idea what that means.
+
+I'll tell you, OK, you were
+happy when I put x prime and x
+
+here because that
+was the probability
+
+to find the particle somewhere.
+
+So let me look at
+the diagonal term
+
+here, which is a probability.
+
+This should give
+me the probability
+
+to find one particle
+at position x1,
+
+one particle at position x2.
+
+Because the particles
+were non-interacting,
+
+one particle-- it
+could be anywhere.
+
+I had the 1 over V.
+Is it 1 over V squared
+
+or something like that?
+
+Well, we find that
+there is factor
+
+out front that we
+haven't yet evaluated.
+
+It turns out that this
+factor will give me a 1
+
+over V squared.
+
+And if I set x1
+prime to x1, x2 prime
+
+to x2, which is what I've done
+here, this factor becomes 1.
+
+But then the other factor will
+give me eta e to the minus 2
+
+pi over lambda squared
+x1 minus x2 squared.
+
+So the physical probability
+to find one particle-- or more
+
+correctly, a wave packet
+here and a wave package there
+
+is not 1 over V squared.
+
+It's some function of the
+separation between these two
+
+particles.
+
+So that separation
+is contained here.
+
+If I really call that
+separation to be r,
+
+this is an additional
+weight that depends on r.
+
+This is r squared.
+
+So you can think of this
+as an interaction, which
+
+is because solely of
+quantum statistics.
+
+And what is this interaction?
+
+This interaction V of r
+would be minus kT log of 1
+
+plus eta e to the minus 2 pi
+r squared over lambda squared.
+
+I will plot out for you
+what this V or r looks
+
+like as a function of how far
+apart the centers of these two
+
+wave packets are.
+
+You can see that the
+result depends on eta.
+
+If eta is minus 1, which is
+for the case of fermions,
+
+this is 1 minus something.
+
+It's something that
+is less than 1.
+
+[INAUDIBLE] would be negative.
+
+So the whole potential would
+be positive, or repulsive.
+
+At large distances, indeed it
+would be exponentially going
+
+to 0 because I can expand
+the log at large distances.
+
+So here I have a term
+that is minus 2 pi
+
+r squared over lambda squared.
+
+As I go towards r equals
+to 0, actually things
+
+become very bad because r
+goes to 0 I will get 1 minus 1
+
+and the log will diverge.
+
+So basically, there is, if you
+like, an effective potential
+
+that says you
+can't put these two
+
+fermions on top of each other.
+
+So there is a
+statistical potential.
+
+So this is for eta
+minus 1, or fermions.
+
+For the case of
+bosons, eta plus 1.
+
+It is log of 1 plus
+something, so it's
+
+a positive number
+inside the log.
+
+The potential will
+be attractive.
+
+And it will actually saturate
+to a value of kT log 2
+
+when r goes to 0.
+
+So this is again, eta of plus
+1 for the case of bosons.
+
+So the one thing that this
+formula does not have yet
+
+is the value for this
+partition function ZN.
+
+It gives you the qualitative
+behavior in either case.
+
+And let's calculate what ZN is.
+
+Well, basically, that
+would come from noting
+
+that the trace of
+rho has to be 1.
+
+So ZN is trace of e
+to the minus beta H.
+
+And essentially, I can take
+this ZN to the other side
+
+and evaluate this as x
+e to the minus beta H x.
+
+That is, I can calculate
+the diagonal elements
+
+of this matrix that
+I have calculated--
+
+that I have over there.
+
+So there is an
+overall factor of 1
+
+over lambda cubed to the power
+of N. I have N factorial.
+
+And then I have a sum over
+permutations Q eta of Q.
+
+The diagonal element
+is obtained by putting
+
+x prime to be the same as x.
+
+So I have exponential of minus
+x-- sum over alpha x alpha
+
+minus x of Q alpha.
+
+I set x prime to
+be the same as x.
+
+Squared.
+
+And then there's an overall
+pi over lambda squared.
+
+And if I am taking the trace,
+it means that I have to do
+
+integration over all x's.
+
+So I'm evaluating this trace
+in coordinate basis, which
+
+means that I should
+put x and x prime to be
+
+the same for the
+trace, and then I
+
+have to sum or integrate over
+all possible values of x.
+
+So let's do this.
+
+I have 1 over N factorial lambda
+cubed raised to the power of N.
+
+OK.
+
+Now I have to make
+a choice because I
+
+have a whole bunch of terms
+because of these permutations.
+
+Let's do them one by one.
+
+Let's first do the case
+where Q is identity.
+
+That is, I map
+everybody to themselves.
+
+Actually, let me write down
+the integrations first.
+
+I will do the integrations
+over all pairs
+
+of coordinates of
+these Gaussians.
+
+These Gaussians I will evaluate
+for different permutations.
+
+Let's look at the case
+where Q is identity.
+
+When Q is identity, essentially
+I will put all of the x prime
+
+to be the same as x.
+
+It is like what I did here
+for two particles and I got 1.
+
+I do the same thing for
+more than one particle.
+
+I will still get 1.
+
+Then, I will do the same
+thing that I did over here.
+
+Here, the next term that I
+did was to exchange 1 and 2.
+
+So this became x1 minus x2.
+
+I'll do the same thing here.
+
+I look at the case
+where Q corresponds
+
+to exchange of
+particles 1 and 2.
+
+And then that will
+give me a factor which
+
+is e to the minus pi over lambda
+squared x1 minus x2 squared.
+
+There are two of these making
+together 2 pi over lambda
+
+squared, which I hope
+I had there, too.
+
+But then there was a whole bunch
+of other terms that I can do.
+
+I can exchange,
+let's say, 7 and 9.
+
+And then I will get
+here 2 pi over lambda
+
+squared x7 minus x9 squared.
+
+And there's a whole
+bunch of such exchanges
+
+that I can make in
+which I just switch
+
+between two particles
+in this whole story.
+
+And clearly, the number of
+exchanges that I can make
+
+is the number of pairs,
+N N minus 1 over 2.
+
+Once I am done with
+all of the exchanges,
+
+then I have to go to
+the next thing that
+
+doesn't have an analog
+here for two particles.
+
+But if I take three
+particles, I can permute them
+
+like a triangle.
+
+So presumably there
+would be next set
+
+of terms, which is a permutation
+that is like 1, 2, 3, 2, 3, 1.
+
+There's a bunch of things that
+involve two permutations, four
+
+permutations, and so forth.
+
+So there is a whole
+list of things
+
+that would go to here where
+these two-particle exchanges
+
+are the simplest class.
+
+Now, as we shall see,
+there is a systematic way
+
+of looking at things where
+the two-particle exchanges are
+
+the first correction
+due to quantum effects.
+
+Three-particle exchanges would
+be higher-order corrections.
+
+And we can systematically
+do them in order.
+
+So let's see what happens if
+we compare the case where there
+
+is no exchange and the case
+where there is one exchange.
+
+When there is no
+exchange, I am essentially
+
+integrating over each
+position over the volume.
+
+So what I would get is V
+raised to the power of N.
+
+The next term?
+
+Well, I have to do
+the integrations.
+
+The integrations over x3, x4,
+x5, all the way to x to the N,
+
+there is no factors.
+
+So they will give me factors
+of V. And there are N minus 2
+
+of them.
+
+And then I have to do the
+integration over x1 and x2
+
+of this factor, but
+it's only a function
+
+of the relative coordinate.
+
+So there is one
+other integration
+
+that I can trivially do, which
+is the center of mass gives me
+
+a factor of V.
+And then I am left
+
+with the integral over the
+relative coordinate of e
+
+to the minus 2 pi r squared
+over lambda squared.
+
+And I forgot-- it's
+very important.
+
+This will carry a factor of eta
+because any exchange is odd.
+
+And so there will be
+a factor of eta here.
+
+And I said that I would
+get the same expression
+
+for any of my N N minus
+1 over 2 exchanges.
+
+So the result of all of
+these exchange calculations
+
+would be the same thing.
+
+And then there would
+be the contribution
+
+from three-body
+exchange and so forth.
+
+So let's re-organize this.
+
+I can pull out the factor
+of V to the N outside.
+
+So I would have V over lambda
+cubed to the power of N.
+
+So the first term is 1.
+
+The next term has
+the parity factor
+
+that distinguishes
+bosons and fermions, goes
+
+with a multiplicity of pairs
+which is N N minus 1 over 2.
+
+Since I already pulled
+out a factor of V to the N
+
+and I really had V to
+the N minus 1 here,
+
+I better put a factor
+of 1 over V here.
+
+And then I just am
+left with having
+
+to evaluate these
+Gaussian integrals.
+
+Each Gaussian
+integral will give me
+
+2 pi times the
+variance, which is
+
+lambda squared divided by 2 pi.
+
+And then there's
+actually a factor of 2.
+
+And there are three of
+them, so I will have 3/2.
+
+So what I get here is lambda
+cubed divided by 2 to the 3/2.
+
+Now, you can see that
+any time I go further
+
+in this series of
+exchanges, I will
+
+have more of these
+Gaussian factors.
+
+And whenever I have
+a Gaussian factor,
+
+I have an additional
+integration to do
+
+that has an x minus
+something squared in it.
+
+I will lose a factor of V. I
+don't have that factor of V.
+
+And so subsequent terms will
+be even smaller in powers of V.
+
+And presumably, compensated by
+corresponding factors of lambda
+
+squared-- lambda cubed.
+
+Now, first thing to note is
+that in the very, very high
+
+temperature limit,
+lambda goes to 0.
+
+So I can forget even
+this correction.
+
+What do I get?
+
+I get 1 over N factorial V over
+lambda cubed to the power of N.
+
+Remember that many, many
+lectures back we introduced
+
+by hand the factor of 1 over
+N factorial for measuring
+
+phase spaces of
+identical particles.
+
+And I promise to you
+that we would get it
+
+when we did identical
+particles in quantum mechanics,
+
+so here it is.
+
+So automatically, we
+did the calculation,
+
+keeping track of
+identity of particles
+
+at the level of quantum states.
+
+Went through the calculation and
+in the high temperature limit,
+
+we get this 1 over N
+factorial emerging.
+
+Secondly, we see that the
+corrections to ideal gas
+
+behavior emerge as a series in
+powers of lambda cubed over V.
+
+And for example, if I were to
+take the log of the partition
+
+function, I would
+get log of what
+
+I would have had classically,
+which is this V over lambda
+
+cubed to the power of N
+divided by N factorial.
+
+And then the log
+of this expression.
+
+And this I'm going to
+replace with N squared.
+
+There is not that
+much difference.
+
+And since I'm regarding this
+as a correction, log of 1
+
+plus something, I will
+replace with the something
+
+eta N squared 2V lambda cubed
+2 to the 3/2 plus higher order.
+
+What does this mean?
+
+Once we have the
+partition function,
+
+we can calculate pressure.
+
+Reminding you that beta
+p was the log Z by dV.
+
+The first part is
+the ideal gas that we
+
+had looked at classically.
+
+So once I go to the appropriate
+large-end limit of this,
+
+what this gives me is
+the density n over V.
+
+And then when I look
+at the derivative here,
+
+the derivative of 1/V will give
+me a minus 1 over V squared.
+
+So I will get minus eta.
+
+N over V, the whole
+thing squared.
+
+So I will have n squared
+lambda cubed 2 to the 5/2,
+
+and so forth.
+
+So I see that the
+pressure of this ideal gas
+
+with no interactions
+is already different
+
+from the classical result
+that we had calculated
+
+by a factor that actually
+reflects the statistics.
+
+For fermions eta of minus 1,
+you get an additional pressure
+
+because of the kind of repulsion
+that we have over here.
+
+Whereas, for bosons
+you get an attraction.
+
+You can see that also the
+thing that determines this--
+
+so basically, this
+corresponds to a second Virial
+
+coefficient, which is minus
+eta lambda cubed 2 to the 5/2,
+
+is the volume of
+these wave packets.
+
+So essentially,
+the corrections are
+
+of the order of n
+lambda cubed that
+
+is within one of these wave
+packets how many particles
+
+you will encounter.
+
+As you go to high temperature,
+the wave packets shrink.
+
+As you go to low temperature,
+the wave packets expand.
+
+If you like, the interactions
+become more important
+
+and you get corrections
+to ideal gas wave.
+
+AUDIENCE: You assume that
+we can use perturbation,
+
+but the higher terms actually
+had a factor [INAUDIBLE].
+
+And you can't really use
+perturbation in that.
+
+PROFESSOR: OK.
+
+So what you are worried
+about is the story here,
+
+that I took log of 1
+plus something here
+
+and I'm interested in the
+limit of n going to infinity,
+
+that finite density n over
+V. So already in that limit,
+
+you would say that
+this factor really
+
+is overwhelmingly
+larger than that.
+
+And as you say, the next
+factor will be even larger.
+
+So what is the justification
+in all of this?
+
+We have already encountered
+this same problem
+
+when we were doing
+these perturbations
+
+due to interactions.
+
+And the answer is that what
+you really want to ensure
+
+is that not log Z,
+but Z has a form
+
+that is e to the N something.
+
+And that something
+will have corrections,
+
+potentially that are powers
+of N, the density, which
+
+is N over V. And if you try to
+force it into a perturbation
+
+series such as this, naturally
+things like this happen.
+
+What does that really mean?
+
+That really means that the
+correct thing that you should
+
+be expanding is,
+indeed, log Z. If you
+
+were to do the kind of
+hand-waving that I did here
+
+and do the expansion for Z, if
+you also try to do it over here
+
+you will generate
+terms that look
+
+kind of at the wrong order.
+
+But higher order terms
+that you would get
+
+would naturally conspire so
+that when you evaluate log Z,
+
+they come out right.
+
+You have to do this correctly.
+
+And once you have
+done it correctly,
+
+then you can rely
+on the calculation
+
+that you did before
+as an example.
+
+And we did it correctly when
+we were doing these cluster
+
+expansions and the
+corresponding calculation we
+
+did for Q. We saw how the
+different diagrams were
+
+appearing in both
+Q and the log Q,
+
+and how they could be
+summed over in log Q.
+
+But indeed, this
+mathematically looks awkward
+
+and I kind of jumped a
+step in writing log of 1
+
+plus something that is huge
+as if it was a small number.
+
+All right.
+
+So we have a problem.
+
+We want to calculate
+the simplest
+
+system, which is the ideal gas.
+
+So classically, we did
+all of our calculations
+
+first for the ideal gas.
+
+We had exact results.
+
+Then, let's say we
+had interactions.
+
+We did perturbations around
+that and all of that.
+
+And we saw that having to do
+things for interacting systems
+
+is very difficult.
+
+Now, when we start to do
+calculations for the quantum
+
+problem, at least in the way
+that I set it up for you,
+
+it seems that quantum
+problems are inherently
+
+interacting problems.
+
+I showed you that even at
+the level of two particles,
+
+it is like having an interaction
+between bosons and fermions.
+
+For three particles,
+it becomes even worse
+
+because it's not only the
+two-particle interaction.
+
+Because of the
+three-particle exchanges,
+
+you would get an additional
+three-particle interaction,
+
+four-particle interaction,
+all of these things emerge.
+
+So really, if you
+want to look at this
+
+from the perspective of
+a partition function,
+
+we already see that
+the exchange term
+
+involved having to
+do a calculation that
+
+is equivalent to calculating
+the second Virial
+
+coefficient for an
+interacting system.
+
+The next one, for the
+third Virial coefficient,
+
+I would need to look at
+the three-body exchanges,
+
+kind of like the point
+clusters, four-point clusters,
+
+all kinds of other
+things are there.
+
+So is there any hope?
+
+And the answer is that it is
+all a matter of perspective.
+
+And somehow it is true
+that these particles
+
+in quantum mechanics
+because of the statistics
+
+are subject to all kinds of
+complicated interactions.
+
+But also, the
+underlying Hamiltonian
+
+is simple and non-interacting.
+
+We can enumerate all
+of the wave functions.
+
+Everything is simple.
+
+So by looking at things
+in the right basis,
+
+we should be able to calculate
+everything that we need.
+
+So here, I was kind of looking
+at calculating the partition
+
+function in the coordinate
+basis, which is the worst case
+
+scenario because the Hamiltonian
+is diagonal in the momentum
+
+basis.
+
+So let's calculate ZN trace
+of e to the minus beta H
+
+in the basis in
+which H is diagonal.
+
+So what are the eigenvalues
+and eigenfunctions?
+
+Well, the eigenfunctions are
+the symmetrized/anti-symmetrized
+
+quantities.
+
+The eigenvalues are simply
+e to the minus beta H
+
+bar squared k alpha
+squared over 2m.
+
+So this is basically
+the thing that I
+
+could write as the set
+of k's appropriately
+
+symmetrized or anti-symmetrized
+e to the minus beta
+
+sum over alpha H bar squared
+k alpha squared over 2m k eta.
+
+Actually, I'm going to-- rather
+than go through this procedure
+
+that we have up there
+in which I wrote
+
+these, what I need to do
+here is a sum over all k
+
+in order to evaluate the trace.
+
+So this is inherently a
+sum over all sets of k's.
+
+But this sum is
+restricted, just like what
+
+I had indicated for you before.
+
+Rather than trying
+to do it that way,
+
+I note that these
+k's I could also
+
+write in terms of these
+occupation numbers.
+
+So equivalently,
+my basis would be
+
+the set of occupation
+numbers times the energy.
+
+The energy is then e to the
+minus beta sum over k epsilon k
+
+nk, where epsilon
+k is this beta H
+
+bar squared k alpha
+squared over 2m.
+
+But I could do this in
+principle for any epsilon k
+
+that I have over here.
+
+So the result that I am writing
+for you is more general.
+
+Then I sandwich it
+again, since I'm
+
+calculating the trace,
+with the same state.
+
+Now, the states have
+this restriction
+
+that I have over there.
+
+That is, for the case of
+fermions, my nk can be 0 or 1.
+
+But there is no restriction
+for nk on the bosons.
+
+Except, of course, that there
+is this overall restriction
+
+that the sum over
+k nk has to be N
+
+because I am looking
+at N-particle states.
+
+Actually, I can remove
+this because in this basis,
+
+e to the minus
+beta H is diagonal.
+
+So I can, basically,
+remove these entities.
+
+And I'm just summing a
+bunch of exponentials.
+
+So that is good because I
+should be able to do for each nk
+
+a sum of e to something nk.
+
+Well, the problem is this
+that I can't sum over
+
+each nk independently.
+
+Essentially in the picture
+that I have over here,
+
+I have some n1 here.
+
+I have some n2 here.
+
+Some n3 here, which are
+the occupation numbers
+
+of these things.
+
+And for that
+partition function, I
+
+have to do the sum of
+these exponentials e
+
+to the minus epsilon 1 n1,
+e to the minus epsilon 2 n2.
+
+But the sum of all of these
+n's is kind of maxed out by N.
+
+I cannot independently sum
+over them going over the entire
+
+range.
+
+But we've seen previously
+how those constraints can
+
+be removed in
+statistical mechanics.
+
+So our usual trick.
+
+We go to the ensemble in
+which n can take any value.
+
+So we go to the grand
+canonical prescription.
+
+We remove this constraint on n
+by evaluating a grand partition
+
+function Q, which is a sum over
+all N of e to the beta mu N ZN.
+
+So we do, essentially,
+a Laplace transform.
+
+We exchange our n with
+the chemical potential mu.
+
+Then, this constraint no
+longer we need to worry about.
+
+So now I can sum over all
+of the nk's without worrying
+
+about any constraint, provided
+that I multiply with e
+
+to the beta mu n, which
+is a sum over k nk.
+
+And then, the factor
+that I have here,
+
+which is e to the minus beta
+sum over k epsilon of k nk.
+
+So essentially for each
+k, I can independently
+
+sum over its nk of e to the
+beta mu minus epsilon of k nk.
+
+Now, the symmetry issues remain.
+
+This answer still
+depends on whether or not
+
+I am calculating things
+for bosons or fermions
+
+because these sums are
+differently constrained
+
+whether I'm dealing
+with fermions.
+
+In which case, nk
+is only 0 or 1.
+
+Or bosons, in which case
+there is no constraint.
+
+So what do I get?
+
+For the case of fermions,
+I have a Q minus,
+
+which is product over all k.
+
+And for each k, the nk
+takes either 0 or 1.
+
+So if it takes 0, I will
+write e to the 0, which is 1.
+
+Or it takes 1.
+
+It is e to the beta
+mu minus epsilon of k.
+
+For the case of bosons,
+I have a Q plus.
+
+Q plus is, again, a product
+over Q. In this case,
+
+nk going from 0 to infinity, I
+am summing a geometric series
+
+that starts as 1, and
+then the subsequent terms
+
+are smaller by a factor of
+beta mu minus epsilon of k.
+
+Actually, for future
+reference note
+
+that I would be able to
+do this geometric sum
+
+provided that this combination
+beta mu minus epsilon of k
+
+is negative.
+
+So that the subsequent terms
+in this series are decaying.
+
+Typically, we would be
+interested in things
+
+like partition functions,
+grand partition functions.
+
+So we have something like log of
+Q, which would be a sum over k.
+
+And I would have either
+the log of this quantity
+
+or the log of this
+quantity with a minus sign.
+
+I can combine the
+two results together
+
+by putting a factor of minus
+eta because in taking the log,
+
+over here for the bosons I
+would pick a factor of minus 1
+
+because the thing is
+in the denominator.
+
+And then I would
+write the log of 1.
+
+And then I have in both
+cases, a factor which
+
+is e to the beta mu
+minus epsilon of k.
+
+But occurring with
+different signs
+
+for the bosons and
+fermions, which again I
+
+can combine into a single
+expression by putting a minus
+
+eta here.
+
+So this is a general
+result for any Hamiltonian
+
+that has the characteristic
+that we wrote over here.
+
+So this does not have to
+be particles in a box.
+
+It could be particles in
+a harmonic oscillator.
+
+These could be energy levels
+of a harmonic oscillator.
+
+All you need to do is to
+make the appropriate sum
+
+over the one-particle
+levels harmonic oscillator,
+
+or whatever else you have,
+of these factors that
+
+depend on the
+individual energy levels
+
+of the one-particle system.
+
+Now, one of the things
+that we will encounter
+
+having made this transition
+from canonical, where we knew
+
+how many particles we had, to
+grand canonical, where we only
+
+know the chemical potential,
+is that we would ultimately
+
+want to express things in terms
+of the number of particles.
+
+So it makes sense to
+calculate how many particles
+
+you have given that you have
+fixed the chemical potential.
+
+So for that we
+note the following.
+
+That essentially, we were able
+to do this calculation for Q
+
+because it was a
+product of contributions
+
+that we had for the individual
+one-particle states.
+
+So clearly, as far as this
+normalization is concerned,
+
+the individual one-particle
+states are independent.
+
+And indeed, what we can say
+is that in this ensemble,
+
+there is a classical probability
+for a set of occupation numbers
+
+of one particle
+states, which is simply
+
+a product over the different
+one-particle states of e
+
+to the beta mu minus epsilon
+k nk appropriately normalized.
+
+And again, the
+restriction on n's
+
+being 0 or 1 for
+fermions or anything
+
+for bosons would be
+implicit in either case.
+
+But in either case, essentially
+the occupation numbers
+
+are independently taken
+from distributions
+
+that I've discussed [INAUDIBLE].
+
+So you can, in
+fact, independently
+
+calculate the average
+occupation number
+
+that you have for each one of
+these single-particle states.
+
+And it's clear that you could
+get that by, for example,
+
+bringing down a
+factor of nk here.
+
+And you can bring
+down a factor of nk
+
+by taking a derivative of Q
+with respect to beta epsilon k
+
+with a minus sign
+and normalizing it,
+
+so you would have log.
+
+So you would have an
+expression such as this.
+
+So you basically would
+need to calculate,
+
+since you are taking
+derivative with respect
+
+to epsilon k the corresponding
+log for which epsilon
+
+k appears.
+
+Actually, for the
+case of fermions,
+
+really there are
+two possibilities.
+
+n is either 0 or 1.
+
+So you would say that the
+expectation value would
+
+be when it is 1, you have e to
+the beta epsilon of k minus mu.
+
+Oops.
+
+e to the beta mu
+minus epsilon of k.
+
+The two possibilities
+are 1 plus e
+
+to the beta mu
+minus epsilon of k.
+
+So when I look at
+some particular state,
+
+it is either empty.
+
+In which case, contributes 0.
+
+Or, it is occupied.
+
+In which case, it
+contributes this weight,
+
+which has to be
+appropriately normalized.
+
+If I do the same thing
+for the case of bosons,
+
+it is a bit more
+complicated because I
+
+have to look at this series
+rather than geometric 1
+
+plus x plus x squared
+plus x cubed is
+
+1 plus x plus 2x squared plus
+3x cubed, which can be obtained
+
+by taking the derivative
+of the appropriate log.
+
+Or you can fall back
+on your calculations
+
+of geometric series
+and convince yourself
+
+that it is essentially the same
+thing with a factor of minus
+
+here.
+
+So this is fermions
+and this is bosons.
+
+And indeed, I can put the
+two expressions together
+
+by dividing through this
+factor in both of them
+
+and write it as 1
+over Z inverse e
+
+to the beta epsilon
+of k minus eta,
+
+where for convenience
+I have introduced
+
+Z to be the contribution
+e to the beta.
+
+So for this system of
+non-interacting particles
+
+that are identical,
+we have expressions
+
+for log of the grand partition
+function, the grand potential.
+
+And for the average
+number of particles,
+
+which is an appropriate
+derivative of this,
+
+expressed in terms of the
+single-particle energy
+
+levels and the
+chemical potential.
+
+So next time, what
+we will do is we
+
+will start this
+with this expression
+
+for the case of the
+particles in a box
+
+to get the pressure of
+the ideal quantum gas
+
+as a function of mu.
+
+But we want to
+write the pressure
+
+as a function of density, so
+we will invert this expression
+
+to get density as a
+function of-- chemical
+
+potential as a function of
+density [INAUDIBLE] here.
+
+And therefore, get the
+expression for pressure
+
+as a function of density.
\ No newline at end of file
diff --git a/iJvEgQkLjow.txt b/iJvEgQkLjow.txt
new file mode 100644
index 0000000000000000000000000000000000000000..125bb5994519f64ece15aec7c2d0d6614db5bfb4
--- /dev/null
+++ b/iJvEgQkLjow.txt
@@ -0,0 +1,1243 @@
+align:start position:0%
+ 
+in this video we'll build a cart model
+
+ align:start position:0%
+in this video we'll build a cart model
+ 
+
+ align:start position:0%
+in this video we'll build a cart model
+to predict healthcare cost
+
+ align:start position:0%
+to predict healthcare cost
+ 
+
+ align:start position:0%
+to predict healthcare cost
+first let's make sure the packages are
+
+ align:start position:0%
+first let's make sure the packages are
+ 
+
+ align:start position:0%
+first let's make sure the packages are
+part and are part plot are loaded with
+
+ align:start position:0%
+part and are part plot are loaded with
+ 
+
+ align:start position:0%
+part and are part plot are loaded with
+the library function you should have
+
+ align:start position:0%
+the library function you should have
+ 
+
+ align:start position:0%
+the library function you should have
+already installed them in the previous
+
+ align:start position:0%
+already installed them in the previous
+ 
+
+ align:start position:0%
+already installed them in the previous
+lecture on predicting Supreme Court
+
+ align:start position:0%
+lecture on predicting Supreme Court
+ 
+
+ align:start position:0%
+lecture on predicting Supreme Court
+decisions now let's build our cart model
+
+ align:start position:0%
+decisions now let's build our cart model
+ 
+
+ align:start position:0%
+decisions now let's build our cart model
+will call it claims tree and we'll use
+
+ align:start position:0%
+will call it claims tree and we'll use
+ 
+
+ align:start position:0%
+will call it claims tree and we'll use
+the our part function to predict bucket
+
+ align:start position:0%
+the our part function to predict bucket
+ 
+
+ align:start position:0%
+the our part function to predict bucket
+2009 using as independent variables age
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+arthritis Alzheimer's cancer COPD
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+depression diabetes heart failure ihd
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+kidney osteoporosis and stroke we'll
+
+ align:start position:0%
+kidney osteoporosis and stroke we'll
+ 
+
+ align:start position:0%
+kidney osteoporosis and stroke we'll
+also use bucket 2008 and reimbursement
+
+ align:start position:0%
+also use bucket 2008 and reimbursement
+ 
+
+ align:start position:0%
+also use bucket 2008 and reimbursement
+2008 the dataset will use to build our
+
+ align:start position:0%
+2008 the dataset will use to build our
+ 
+
+ align:start position:0%
+2008 the dataset will use to build our
+model is claims trained
+
+ align:start position:0%
+model is claims trained
+ 
+
+ align:start position:0%
+model is claims trained
+and then we'll add the arguments method
+
+ align:start position:0%
+and then we'll add the arguments method
+ 
+
+ align:start position:0%
+and then we'll add the arguments method
+equals class since we have a
+
+ align:start position:0%
+equals class since we have a
+ 
+
+ align:start position:0%
+equals class since we have a
+classification problem here and CP
+
+ align:start position:0%
+classification problem here and CP
+ 
+
+ align:start position:0%
+classification problem here and CP
+equals zero point zero zero zero zero
+
+ align:start position:0%
+equals zero point zero zero zero zero
+ 
+
+ align:start position:0%
+equals zero point zero zero zero zero
+five note that even though we have a
+
+ align:start position:0%
+five note that even though we have a
+ 
+
+ align:start position:0%
+five note that even though we have a
+multi-class classification problem here
+
+ align:start position:0%
+multi-class classification problem here
+ 
+
+ align:start position:0%
+multi-class classification problem here
+we built our tree in the same way as a
+
+ align:start position:0%
+we built our tree in the same way as a
+ 
+
+ align:start position:0%
+we built our tree in the same way as a
+binary classification problem so go
+
+ align:start position:0%
+binary classification problem so go
+ 
+
+ align:start position:0%
+binary classification problem so go
+ahead and hit enter the CP value we're
+
+ align:start position:0%
+ahead and hit enter the CP value we're
+ 
+
+ align:start position:0%
+ahead and hit enter the CP value we're
+using here was selected through
+
+ align:start position:0%
+using here was selected through
+ 
+
+ align:start position:0%
+using here was selected through
+cross-validation on the training set we
+
+ align:start position:0%
+cross-validation on the training set we
+ 
+
+ align:start position:0%
+cross-validation on the training set we
+won't perform the cross-validation here
+
+ align:start position:0%
+won't perform the cross-validation here
+ 
+
+ align:start position:0%
+won't perform the cross-validation here
+because it takes a significant amount of
+
+ align:start position:0%
+because it takes a significant amount of
+ 
+
+ align:start position:0%
+because it takes a significant amount of
+time on a data set of this size remember
+
+ align:start position:0%
+time on a data set of this size remember
+ 
+
+ align:start position:0%
+time on a data set of this size remember
+that we have almost two hundred and
+
+ align:start position:0%
+that we have almost two hundred and
+ 
+
+ align:start position:0%
+that we have almost two hundred and
+seventy-five thousand observations in
+
+ align:start position:0%
+seventy-five thousand observations in
+ 
+
+ align:start position:0%
+seventy-five thousand observations in
+our training set but keep in mind that
+
+ align:start position:0%
+our training set but keep in mind that
+ 
+
+ align:start position:0%
+our training set but keep in mind that
+the R commands needed for
+
+ align:start position:0%
+the R commands needed for
+ 
+
+ align:start position:0%
+the R commands needed for
+cross-validation here are the same as
+
+ align:start position:0%
+cross-validation here are the same as
+ 
+
+ align:start position:0%
+cross-validation here are the same as
+those used in the previous lecture on
+
+ align:start position:0%
+those used in the previous lecture on
+ 
+
+ align:start position:0%
+those used in the previous lecture on
+predicting Supreme Court decisions so
+
+ align:start position:0%
+predicting Supreme Court decisions so
+ 
+
+ align:start position:0%
+predicting Supreme Court decisions so
+now that our models done let's take a
+
+ align:start position:0%
+now that our models done let's take a
+ 
+
+ align:start position:0%
+now that our models done let's take a
+look at our tree with the PRP function
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it might take a while to load because we
+
+ align:start position:0%
+it might take a while to load because we
+ 
+
+ align:start position:0%
+it might take a while to load because we
+have a huge tree here this makes sense
+
+ align:start position:0%
+have a huge tree here this makes sense
+ 
+
+ align:start position:0%
+have a huge tree here this makes sense
+for a few reasons
+
+ align:start position:0%
+for a few reasons
+ 
+
+ align:start position:0%
+for a few reasons
+one is the large number of observations
+
+ align:start position:0%
+one is the large number of observations
+ 
+
+ align:start position:0%
+one is the large number of observations
+in our training set another is that we
+
+ align:start position:0%
+in our training set another is that we
+ 
+
+ align:start position:0%
+in our training set another is that we
+have a 5 class classification problem so
+
+ align:start position:0%
+have a 5 class classification problem so
+ 
+
+ align:start position:0%
+have a 5 class classification problem so
+that classification is more complex than
+
+ align:start position:0%
+that classification is more complex than
+ 
+
+ align:start position:0%
+that classification is more complex than
+a binary classification case like the
+
+ align:start position:0%
+a binary classification case like the
+ 
+
+ align:start position:0%
+a binary classification case like the
+one we saw in the previous lecture the
+
+ align:start position:0%
+one we saw in the previous lecture the
+ 
+
+ align:start position:0%
+one we saw in the previous lecture the
+trees used by D to Hawkeye were also
+
+ align:start position:0%
+trees used by D to Hawkeye were also
+ 
+
+ align:start position:0%
+trees used by D to Hawkeye were also
+very large car trees while this hurts
+
+ align:start position:0%
+very large car trees while this hurts
+ 
+
+ align:start position:0%
+very large car trees while this hurts
+the interpret ability of the model it's
+
+ align:start position:0%
+the interpret ability of the model it's
+ 
+
+ align:start position:0%
+the interpret ability of the model it's
+still possible to describe each of the
+
+ align:start position:0%
+still possible to describe each of the
+ 
+
+ align:start position:0%
+still possible to describe each of the
+buckets of the tree according to the
+
+ align:start position:0%
+buckets of the tree according to the
+ 
+
+ align:start position:0%
+buckets of the tree according to the
+splits so now let's make predictions on
+
+ align:start position:0%
+splits so now let's make predictions on
+ 
+
+ align:start position:0%
+splits so now let's make predictions on
+the test set so go back to your R
+
+ align:start position:0%
+the test set so go back to your R
+ 
+
+ align:start position:0%
+the test set so go back to your R
+console and we'll call our predictions
+
+ align:start position:0%
+console and we'll call our predictions
+ 
+
+ align:start position:0%
+console and we'll call our predictions
+predict test
+
+ align:start position:0%
+predict test
+ 
+
+ align:start position:0%
+predict test
+where we'll use the predict function for
+
+ align:start position:0%
+where we'll use the predict function for
+ 
+
+ align:start position:0%
+where we'll use the predict function for
+our model claims tree and our new data
+
+ align:start position:0%
+our model claims tree and our new data
+ 
+
+ align:start position:0%
+our model claims tree and our new data
+is claims test and we want to add type
+
+ align:start position:0%
+is claims test and we want to add type
+ 
+
+ align:start position:0%
+is claims test and we want to add type
+equals class to get class predictions
+
+ align:start position:0%
+equals class to get class predictions
+ 
+
+ align:start position:0%
+equals class to get class predictions
+and we can make our classification
+
+ align:start position:0%
+and we can make our classification
+ 
+
+ align:start position:0%
+and we can make our classification
+matrix on the test set to compute the
+
+ align:start position:0%
+matrix on the test set to compute the
+ 
+
+ align:start position:0%
+matrix on the test set to compute the
+accuracy so we'll use the table function
+
+ align:start position:0%
+accuracy so we'll use the table function
+ 
+
+ align:start position:0%
+accuracy so we'll use the table function
+where the actual outcomes are claims
+
+ align:start position:0%
+where the actual outcomes are claims
+ 
+
+ align:start position:0%
+where the actual outcomes are claims
+test bucket 2009 and our predictions are
+
+ align:start position:0%
+test bucket 2009 and our predictions are
+ 
+
+ align:start position:0%
+test bucket 2009 and our predictions are
+predict tests so to compute the accuracy
+
+ align:start position:0%
+predict tests so to compute the accuracy
+ 
+
+ align:start position:0%
+predict tests so to compute the accuracy
+we need to add up the numbers on the
+
+ align:start position:0%
+we need to add up the numbers on the
+ 
+
+ align:start position:0%
+we need to add up the numbers on the
+diagonal and divide by the total number
+
+ align:start position:0%
+diagonal and divide by the total number
+ 
+
+ align:start position:0%
+diagonal and divide by the total number
+of observations in our test set so we
+
+ align:start position:0%
+of observations in our test set so we
+ 
+
+ align:start position:0%
+of observations in our test set so we
+have one hundred and fourteen thousand
+
+ align:start position:0%
+have one hundred and fourteen thousand
+ 
+
+ align:start position:0%
+have one hundred and fourteen thousand
+one hundred and forty-one plus sixteen
+
+ align:start position:0%
+one hundred and forty-one plus sixteen
+ 
+
+ align:start position:0%
+one hundred and forty-one plus sixteen
+thousand one hundred and two plus one
+
+ align:start position:0%
+thousand one hundred and two plus one
+ 
+
+ align:start position:0%
+thousand one hundred and two plus one
+hundred and eighteen plus two hundred
+
+ align:start position:0%
+hundred and eighteen plus two hundred
+ 
+
+ align:start position:0%
+hundred and eighteen plus two hundred
+and one plus zero and we'll divide by
+
+ align:start position:0%
+and one plus zero and we'll divide by
+ 
+
+ align:start position:0%
+and one plus zero and we'll divide by
+the number of rows in claims test so the
+
+ align:start position:0%
+the number of rows in claims test so the
+ 
+
+ align:start position:0%
+the number of rows in claims test so the
+accuracy of our model is point seven one
+
+ align:start position:0%
+accuracy of our model is point seven one
+ 
+
+ align:start position:0%
+accuracy of our model is point seven one
+three for the penalty error we can use
+
+ align:start position:0%
+three for the penalty error we can use
+ 
+
+ align:start position:0%
+three for the penalty error we can use
+our penalty matrix like we did in the
+
+ align:start position:0%
+our penalty matrix like we did in the
+ 
+
+ align:start position:0%
+our penalty matrix like we did in the
+previous video so scroll up to the
+
+ align:start position:0%
+previous video so scroll up to the
+ 
+
+ align:start position:0%
+previous video so scroll up to the
+classification matrix command and
+
+ align:start position:0%
+classification matrix command and
+ 
+
+ align:start position:0%
+classification matrix command and
+surround the table function by the as
+
+ align:start position:0%
+surround the table function by the as
+ 
+
+ align:start position:0%
+surround the table function by the as
+dot matrix function and then we'll
+
+ align:start position:0%
+dot matrix function and then we'll
+ 
+
+ align:start position:0%
+dot matrix function and then we'll
+multiply by penalty matrix so remember
+
+ align:start position:0%
+multiply by penalty matrix so remember
+ 
+
+ align:start position:0%
+multiply by penalty matrix so remember
+that this takes each entry in our
+
+ align:start position:0%
+that this takes each entry in our
+ 
+
+ align:start position:0%
+that this takes each entry in our
+classification matrix and multiplies it
+
+ align:start position:0%
+classification matrix and multiplies it
+ 
+
+ align:start position:0%
+classification matrix and multiplies it
+by the corresponding number in the
+
+ align:start position:0%
+by the corresponding number in the
+ 
+
+ align:start position:0%
+by the corresponding number in the
+penalty matrix so now we just need to
+
+ align:start position:0%
+penalty matrix so now we just need to
+ 
+
+ align:start position:0%
+penalty matrix so now we just need to
+add up all of the numbers in this matrix
+
+ align:start position:0%
+add up all of the numbers in this matrix
+ 
+
+ align:start position:0%
+add up all of the numbers in this matrix
+by surrounding it by the sum function
+
+ align:start position:0%
+by surrounding it by the sum function
+ 
+
+ align:start position:0%
+by surrounding it by the sum function
+and then dividing by the total number of
+
+ align:start position:0%
+and then dividing by the total number of
+ 
+
+ align:start position:0%
+and then dividing by the total number of
+observations in our test set or n row
+
+ align:start position:0%
+observations in our test set or n row
+ 
+
+ align:start position:0%
+observations in our test set or n row
+claims test so our penalty err is 0.75
+
+ align:start position:0%
+claims test so our penalty err is 0.75
+ 
+
+ align:start position:0%
+claims test so our penalty err is 0.75
+in the previous video we saw that our
+
+ align:start position:0%
+in the previous video we saw that our
+ 
+
+ align:start position:0%
+in the previous video we saw that our
+baseline method had an accuracy of 68%
+
+ align:start position:0%
+baseline method had an accuracy of 68%
+ 
+
+ align:start position:0%
+baseline method had an accuracy of 68%
+and a penalty err of 0.7 for so while we
+
+ align:start position:0%
+and a penalty err of 0.7 for so while we
+ 
+
+ align:start position:0%
+and a penalty err of 0.7 for so while we
+increase the accuracy the penalty air
+
+ align:start position:0%
+increase the accuracy the penalty air
+ 
+
+ align:start position:0%
+increase the accuracy the penalty air
+also went up why by default our part
+
+ align:start position:0%
+also went up why by default our part
+ 
+
+ align:start position:0%
+also went up why by default our part
+will try to maximize the overall
+
+ align:start position:0%
+will try to maximize the overall
+ 
+
+ align:start position:0%
+will try to maximize the overall
+accuracy and every type of error is seen
+
+ align:start position:0%
+accuracy and every type of error is seen
+ 
+
+ align:start position:0%
+accuracy and every type of error is seen
+as having a penalty of 1 our current
+
+ align:start position:0%
+as having a penalty of 1 our current
+ 
+
+ align:start position:0%
+as having a penalty of 1 our current
+model predicts 3 4 and 5 so rarely
+
+ align:start position:0%
+model predicts 3 4 and 5 so rarely
+ 
+
+ align:start position:0%
+model predicts 3 4 and 5 so rarely
+because there are very few observations
+
+ align:start position:0%
+because there are very few observations
+ 
+
+ align:start position:0%
+because there are very few observations
+in these classes so we don't really
+
+ align:start position:0%
+in these classes so we don't really
+ 
+
+ align:start position:0%
+in these classes so we don't really
+expect this model to do better on the
+
+ align:start position:0%
+expect this model to do better on the
+ 
+
+ align:start position:0%
+expect this model to do better on the
+penalty air than the baseline method so
+
+ align:start position:0%
+penalty air than the baseline method so
+ 
+
+ align:start position:0%
+penalty air than the baseline method so
+how can we fix this the armed part
+
+ align:start position:0%
+how can we fix this the armed part
+ 
+
+ align:start position:0%
+how can we fix this the armed part
+function allows us to specify a
+
+ align:start position:0%
+function allows us to specify a
+ 
+
+ align:start position:0%
+function allows us to specify a
+parameter called loss this is the
+
+ align:start position:0%
+parameter called loss this is the
+ 
+
+ align:start position:0%
+parameter called loss this is the
+penalty matrix we want to use when
+
+ align:start position:0%
+penalty matrix we want to use when
+ 
+
+ align:start position:0%
+penalty matrix we want to use when
+building our model so let's scroll back
+
+ align:start position:0%
+building our model so let's scroll back
+ 
+
+ align:start position:0%
+building our model so let's scroll back
+up to where we built our carp model at
+
+ align:start position:0%
+up to where we built our carp model at
+ 
+
+ align:start position:0%
+up to where we built our carp model at
+the end of the our part function will
+
+ align:start position:0%
+the end of the our part function will
+ 
+
+ align:start position:0%
+the end of the our part function will
+add the argument params equals list and
+
+ align:start position:0%
+add the argument params equals list and
+ 
+
+ align:start position:0%
+add the argument params equals list and
+then in parentheses loss equals penalty
+
+ align:start position:0%
+then in parentheses loss equals penalty
+ 
+
+ align:start position:0%
+then in parentheses loss equals penalty
+matrix this is the name of the penalty
+
+ align:start position:0%
+matrix this is the name of the penalty
+ 
+
+ align:start position:0%
+matrix this is the name of the penalty
+matrix we created close the parentheses
+
+ align:start position:0%
+matrix we created close the parentheses
+ 
+
+ align:start position:0%
+matrix we created close the parentheses
+and hit enter so why our while our model
+
+ align:start position:0%
+and hit enter so why our while our model
+ 
+
+ align:start position:0%
+and hit enter so why our while our model
+is being built let's think about what we
+
+ align:start position:0%
+is being built let's think about what we
+ 
+
+ align:start position:0%
+is being built let's think about what we
+expect to happen if the armed part
+
+ align:start position:0%
+expect to happen if the armed part
+ 
+
+ align:start position:0%
+expect to happen if the armed part
+function knows that will be giving a
+
+ align:start position:0%
+function knows that will be giving a
+ 
+
+ align:start position:0%
+function knows that will be giving a
+higher penalty to some types of errors
+
+ align:start position:0%
+higher penalty to some types of errors
+ 
+
+ align:start position:0%
+higher penalty to some types of errors
+over others it might choose different
+
+ align:start position:0%
+over others it might choose different
+ 
+
+ align:start position:0%
+over others it might choose different
+splits when building the model to
+
+ align:start position:0%
+splits when building the model to
+ 
+
+ align:start position:0%
+splits when building the model to
+minimize the worst types of errors we'll
+
+ align:start position:0%
+minimize the worst types of errors we'll
+ 
+
+ align:start position:0%
+minimize the worst types of errors we'll
+probably get a lower overall accuracy
+
+ align:start position:0%
+probably get a lower overall accuracy
+ 
+
+ align:start position:0%
+probably get a lower overall accuracy
+with this new model but hopefully the
+
+ align:start position:0%
+with this new model but hopefully the
+ 
+
+ align:start position:0%
+with this new model but hopefully the
+penalty error will be much lower too so
+
+ align:start position:0%
+penalty error will be much lower too so
+ 
+
+ align:start position:0%
+penalty error will be much lower too so
+now that our model is done let's
+
+ align:start position:0%
+now that our model is done let's
+ 
+
+ align:start position:0%
+now that our model is done let's
+regenerate our test set predictions by
+
+ align:start position:0%
+regenerate our test set predictions by
+ 
+
+ align:start position:0%
+regenerate our test set predictions by
+scrolling up to where we created predict
+
+ align:start position:0%
+scrolling up to where we created predict
+ 
+
+ align:start position:0%
+scrolling up to where we created predict
+test and hitting Enter and then
+
+ align:start position:0%
+test and hitting Enter and then
+ 
+
+ align:start position:0%
+test and hitting Enter and then
+recreating our classification matrix by
+
+ align:start position:0%
+recreating our classification matrix by
+ 
+
+ align:start position:0%
+recreating our classification matrix by
+scrolling up to the table function and
+
+ align:start position:0%
+scrolling up to the table function and
+ 
+
+ align:start position:0%
+scrolling up to the table function and
+hitting Enter again
+
+ align:start position:0%
+hitting Enter again
+ 
+
+ align:start position:0%
+hitting Enter again
+now let's add up the numbers on the
+
+ align:start position:0%
+now let's add up the numbers on the
+ 
+
+ align:start position:0%
+now let's add up the numbers on the
+diagonal 94 3 10 + 18 9 42 + 4690 2 + 6
+
+ align:start position:0%
+diagonal 94 3 10 + 18 9 42 + 4690 2 + 6
+ 
+
+ align:start position:0%
+diagonal 94 3 10 + 18 9 42 + 4690 2 + 6
+36 + 2 and divide by the number of rows
+
+ align:start position:0%
+36 + 2 and divide by the number of rows
+ 
+
+ align:start position:0%
+36 + 2 and divide by the number of rows
+in claims test and hit enter so the
+
+ align:start position:0%
+in claims test and hit enter so the
+ 
+
+ align:start position:0%
+in claims test and hit enter so the
+accuracy of this model is 0.6 4 7 and we
+
+ align:start position:0%
+accuracy of this model is 0.6 4 7 and we
+ 
+
+ align:start position:0%
+accuracy of this model is 0.6 4 7 and we
+can scroll up and can you compute the
+
+ align:start position:0%
+can scroll up and can you compute the
+ 
+
+ align:start position:0%
+can scroll up and can you compute the
+penalty air here by going back to the
+
+ align:start position:0%
+penalty air here by going back to the
+ 
+
+ align:start position:0%
+penalty air here by going back to the
+sum command and hitting Enter
+
+ align:start position:0%
+sum command and hitting Enter
+ 
+
+ align:start position:0%
+sum command and hitting Enter
+so the penalty of our new model is 0.64
+
+ align:start position:0%
+so the penalty of our new model is 0.64
+ 
+
+ align:start position:0%
+so the penalty of our new model is 0.64
+to our accuracy is now lower than the
+
+ align:start position:0%
+to our accuracy is now lower than the
+ 
+
+ align:start position:0%
+to our accuracy is now lower than the
+baseline method but our penalty air is
+
+ align:start position:0%
+baseline method but our penalty air is
+ 
+
+ align:start position:0%
+baseline method but our penalty air is
+also much lower note that we have
+
+ align:start position:0%
+also much lower note that we have
+ 
+
+ align:start position:0%
+also much lower note that we have
+significantly fewer independent
+
+ align:start position:0%
+significantly fewer independent
+ 
+
+ align:start position:0%
+significantly fewer independent
+variables than d2 hawk I had if we had
+
+ align:start position:0%
+variables than d2 hawk I had if we had
+ 
+
+ align:start position:0%
+variables than d2 hawk I had if we had
+the hundreds of codes and risk factors
+
+ align:start position:0%
+the hundreds of codes and risk factors
+ 
+
+ align:start position:0%
+the hundreds of codes and risk factors
+available to d2 Hawkeye we would
+
+ align:start position:0%
+available to d2 Hawkeye we would
+ 
+
+ align:start position:0%
+available to d2 Hawkeye we would
+hopefully do even better in the next
+
+ align:start position:0%
+hopefully do even better in the next
+ 
+
+ align:start position:0%
+hopefully do even better in the next
+video we'll discuss the accuracy of the
+
+ align:start position:0%
+video we'll discuss the accuracy of the
+ 
+
+ align:start position:0%
+video we'll discuss the accuracy of the
+models used by d2 Hawkeye and how
+
+ align:start position:0%
+models used by d2 Hawkeye and how
+ 
+
+ align:start position:0%
+models used by d2 Hawkeye and how
+analytics can provide an edge
\ No newline at end of file
diff --git a/ipSdsosGJBs.txt b/ipSdsosGJBs.txt
new file mode 100644
index 0000000000000000000000000000000000000000..07180d68cd274a2ea6544d2f7c09c5902fbfac1d
--- /dev/null
+++ b/ipSdsosGJBs.txt
@@ -0,0 +1,1131 @@
+align:start position:0%
+ 
+we have presented the complete solution
+
+ align:start position:0%
+we have presented the complete solution
+ 
+
+ align:start position:0%
+we have presented the complete solution
+to the linear list mean squares
+
+ align:start position:0%
+to the linear list mean squares
+ 
+
+ align:start position:0%
+to the linear list mean squares
+estimation problem when we want to
+
+ align:start position:0%
+estimation problem when we want to
+ 
+
+ align:start position:0%
+estimation problem when we want to
+estimate a certain unknown random
+
+ align:start position:0%
+estimate a certain unknown random
+ 
+
+ align:start position:0%
+estimate a certain unknown random
+variable on the basis of a different
+
+ align:start position:0%
+variable on the basis of a different
+ 
+
+ align:start position:0%
+variable on the basis of a different
+random variable X that we get to observe
+
+ align:start position:0%
+random variable X that we get to observe
+ 
+
+ align:start position:0%
+random variable X that we get to observe
+but what if we have multiple
+
+ align:start position:0%
+but what if we have multiple
+ 
+
+ align:start position:0%
+but what if we have multiple
+observations what would be the analogous
+
+ align:start position:0%
+observations what would be the analogous
+ 
+
+ align:start position:0%
+observations what would be the analogous
+formulation of the problem here is the
+
+ align:start position:0%
+formulation of the problem here is the
+ 
+
+ align:start position:0%
+formulation of the problem here is the
+idea once more we restrict ourselves to
+
+ align:start position:0%
+idea once more we restrict ourselves to
+ 
+
+ align:start position:0%
+idea once more we restrict ourselves to
+estimators that are linear functions of
+
+ align:start position:0%
+estimators that are linear functions of
+ 
+
+ align:start position:0%
+estimators that are linear functions of
+the data linear functions of the
+
+ align:start position:0%
+the data linear functions of the
+ 
+
+ align:start position:0%
+the data linear functions of the
+observations that we have and then we
+
+ align:start position:0%
+observations that we have and then we
+ 
+
+ align:start position:0%
+observations that we have and then we
+pose the problem on finding the best
+
+ align:start position:0%
+pose the problem on finding the best
+ 
+
+ align:start position:0%
+pose the problem on finding the best
+choices of these coefficients a 1 up to
+
+ align:start position:0%
+choices of these coefficients a 1 up to
+ 
+
+ align:start position:0%
+choices of these coefficients a 1 up to
+a n and B what does it mean to find the
+
+ align:start position:0%
+a n and B what does it mean to find the
+ 
+
+ align:start position:0%
+a n and B what does it mean to find the
+best choices it means that if we fix
+
+ align:start position:0%
+best choices it means that if we fix
+ 
+
+ align:start position:0%
+best choices it means that if we fix
+certain choices we obtain an estimator
+
+ align:start position:0%
+certain choices we obtain an estimator
+ 
+
+ align:start position:0%
+certain choices we obtain an estimator
+we look at the difference between the
+
+ align:start position:0%
+we look at the difference between the
+ 
+
+ align:start position:0%
+we look at the difference between the
+estimator and that quantity were trying
+
+ align:start position:0%
+estimator and that quantity were trying
+ 
+
+ align:start position:0%
+estimator and that quantity were trying
+to estimate take the square and then
+
+ align:start position:0%
+to estimate take the square and then
+ 
+
+ align:start position:0%
+to estimate take the square and then
+take the expectation so once more we're
+
+ align:start position:0%
+take the expectation so once more we're
+ 
+
+ align:start position:0%
+take the expectation so once more we're
+looking at the mean squared error of our
+
+ align:start position:0%
+looking at the mean squared error of our
+ 
+
+ align:start position:0%
+looking at the mean squared error of our
+estimator and we try to make it as small
+
+ align:start position:0%
+estimator and we try to make it as small
+ 
+
+ align:start position:0%
+estimator and we try to make it as small
+as possible so this is a well-defined
+
+ align:start position:0%
+as possible so this is a well-defined
+ 
+
+ align:start position:0%
+as possible so this is a well-defined
+optimization problem we have a quantity
+
+ align:start position:0%
+optimization problem we have a quantity
+ 
+
+ align:start position:0%
+optimization problem we have a quantity
+which is a function of certain
+
+ align:start position:0%
+which is a function of certain
+ 
+
+ align:start position:0%
+which is a function of certain
+parameters and we wish to find the
+
+ align:start position:0%
+parameters and we wish to find the
+ 
+
+ align:start position:0%
+parameters and we wish to find the
+choices for those parameters or those
+
+ align:start position:0%
+choices for those parameters or those
+ 
+
+ align:start position:0%
+choices for those parameters or those
+coefficients that will make this
+
+ align:start position:0%
+coefficients that will make this
+ 
+
+ align:start position:0%
+coefficients that will make this
+quantity as small as possible one first
+
+ align:start position:0%
+quantity as small as possible one first
+ 
+
+ align:start position:0%
+quantity as small as possible one first
+comment is similar to the case where we
+
+ align:start position:0%
+comment is similar to the case where we
+ 
+
+ align:start position:0%
+comment is similar to the case where we
+had a single measurement is the
+
+ align:start position:0%
+had a single measurement is the
+ 
+
+ align:start position:0%
+had a single measurement is the
+following
+
+ align:start position:0%
+following
+ 
+
+ align:start position:0%
+following
+if it turns out the conditional
+
+ align:start position:0%
+if it turns out the conditional
+ 
+
+ align:start position:0%
+if it turns out the conditional
+expectation of theta given all the data
+
+ align:start position:0%
+expectation of theta given all the data
+ 
+
+ align:start position:0%
+expectation of theta given all the data
+that we have is linear in X if it is of
+
+ align:start position:0%
+that we have is linear in X if it is of
+ 
+
+ align:start position:0%
+that we have is linear in X if it is of
+this form then what happens we know that
+
+ align:start position:0%
+this form then what happens we know that
+ 
+
+ align:start position:0%
+this form then what happens we know that
+this is the best possible estimator if
+
+ align:start position:0%
+this is the best possible estimator if
+ 
+
+ align:start position:0%
+this is the best possible estimator if
+it is also linear then it is the best
+
+ align:start position:0%
+it is also linear then it is the best
+ 
+
+ align:start position:0%
+it is also linear then it is the best
+estimator within the class of linear
+
+ align:start position:0%
+estimator within the class of linear
+ 
+
+ align:start position:0%
+estimator within the class of linear
+estimators as well and therefore the
+
+ align:start position:0%
+estimators as well and therefore the
+ 
+
+ align:start position:0%
+estimators as well and therefore the
+linear least mean squares estimator is
+
+ align:start position:0%
+linear least mean squares estimator is
+ 
+
+ align:start position:0%
+linear least mean squares estimator is
+the same as the general least mean
+
+ align:start position:0%
+the same as the general least mean
+ 
+
+ align:start position:0%
+the same as the general least mean
+squares estimator so if for some
+
+ align:start position:0%
+squares estimator so if for some
+ 
+
+ align:start position:0%
+squares estimator so if for some
+problems it turns out that this is
+
+ align:start position:0%
+problems it turns out that this is
+ 
+
+ align:start position:0%
+problems it turns out that this is
+linear then we automatically also have
+
+ align:start position:0%
+linear then we automatically also have
+ 
+
+ align:start position:0%
+linear then we automatically also have
+the optimal linear
+
+ align:start position:0%
+the optimal linear
+ 
+
+ align:start position:0%
+the optimal linear
+estimator and this is going to be the
+
+ align:start position:0%
+estimator and this is going to be the
+ 
+
+ align:start position:0%
+estimator and this is going to be the
+case once more for certain normal
+
+ align:start position:0%
+case once more for certain normal
+ 
+
+ align:start position:0%
+case once more for certain normal
+problems with a linear structure of the
+
+ align:start position:0%
+problems with a linear structure of the
+ 
+
+ align:start position:0%
+problems with a linear structure of the
+type that we have studied earlier now
+
+ align:start position:0%
+type that we have studied earlier now
+ 
+
+ align:start position:0%
+type that we have studied earlier now
+let us look into what it takes to carry
+
+ align:start position:0%
+let us look into what it takes to carry
+ 
+
+ align:start position:0%
+let us look into what it takes to carry
+out this optimization if we had a single
+
+ align:start position:0%
+out this optimization if we had a single
+ 
+
+ align:start position:0%
+out this optimization if we had a single
+observation then we have seen a closed
+
+ align:start position:0%
+observation then we have seen a closed
+ 
+
+ align:start position:0%
+observation then we have seen a closed
+form formula a fairly simple formula
+
+ align:start position:0%
+form formula a fairly simple formula
+ 
+
+ align:start position:0%
+form formula a fairly simple formula
+that tells us what the coefficients
+
+ align:start position:0%
+that tells us what the coefficients
+ 
+
+ align:start position:0%
+that tells us what the coefficients
+should be for the more general case
+
+ align:start position:0%
+should be for the more general case
+ 
+
+ align:start position:0%
+should be for the more general case
+formulas would not be as simple but we
+
+ align:start position:0%
+formulas would not be as simple but we
+ 
+
+ align:start position:0%
+formulas would not be as simple but we
+can make the following observations if
+
+ align:start position:0%
+can make the following observations if
+ 
+
+ align:start position:0%
+can make the following observations if
+you take this expression and expand it
+
+ align:start position:0%
+you take this expression and expand it
+ 
+
+ align:start position:0%
+you take this expression and expand it
+it's going to have a bunch of terms for
+
+ align:start position:0%
+it's going to have a bunch of terms for
+ 
+
+ align:start position:0%
+it's going to have a bunch of terms for
+example it's going to have a term of the
+
+ align:start position:0%
+example it's going to have a term of the
+ 
+
+ align:start position:0%
+example it's going to have a term of the
+form a1 squared times the expected value
+
+ align:start position:0%
+form a1 squared times the expected value
+ 
+
+ align:start position:0%
+form a1 squared times the expected value
+of x1 squared it's going to have a term
+
+ align:start position:0%
+of x1 squared it's going to have a term
+ 
+
+ align:start position:0%
+of x1 squared it's going to have a term
+such as twice a1 a2 times the expected
+
+ align:start position:0%
+such as twice a1 a2 times the expected
+ 
+
+ align:start position:0%
+such as twice a1 a2 times the expected
+value of x1 x2 and then there's going to
+
+ align:start position:0%
+value of x1 x2 and then there's going to
+ 
+
+ align:start position:0%
+value of x1 x2 and then there's going to
+be many more terms
+
+ align:start position:0%
+be many more terms
+ 
+
+ align:start position:0%
+be many more terms
+some of them will also involve products
+
+ align:start position:0%
+some of them will also involve products
+ 
+
+ align:start position:0%
+some of them will also involve products
+of theta with this so we might see that
+
+ align:start position:0%
+of theta with this so we might see that
+ 
+
+ align:start position:0%
+of theta with this so we might see that
+we have a term of the form a1 expected
+
+ align:start position:0%
+we have a term of the form a1 expected
+ 
+
+ align:start position:0%
+we have a term of the form a1 expected
+value of x1 theta and then there's going
+
+ align:start position:0%
+value of x1 theta and then there's going
+ 
+
+ align:start position:0%
+value of x1 theta and then there's going
+to be many many more terms what's the
+
+ align:start position:0%
+to be many many more terms what's the
+ 
+
+ align:start position:0%
+to be many many more terms what's the
+important thing to notice that this
+
+ align:start position:0%
+important thing to notice that this
+ 
+
+ align:start position:0%
+important thing to notice that this
+expression as a function of the
+
+ align:start position:0%
+expression as a function of the
+ 
+
+ align:start position:0%
+expression as a function of the
+coefficient involves terms either of
+
+ align:start position:0%
+coefficient involves terms either of
+ 
+
+ align:start position:0%
+coefficient involves terms either of
+this kind or of this kind or of that
+
+ align:start position:0%
+this kind or of this kind or of that
+ 
+
+ align:start position:0%
+this kind or of this kind or of that
+kind first-order or second-order terms
+
+ align:start position:0%
+kind first-order or second-order terms
+ 
+
+ align:start position:0%
+kind first-order or second-order terms
+to minimize this expression we're going
+
+ align:start position:0%
+to minimize this expression we're going
+ 
+
+ align:start position:0%
+to minimize this expression we're going
+to take the derivative of this and set
+
+ align:start position:0%
+to take the derivative of this and set
+ 
+
+ align:start position:0%
+to take the derivative of this and set
+it equal to 0
+
+ align:start position:0%
+it equal to 0
+ 
+
+ align:start position:0%
+it equal to 0
+when you take the derivative of a
+
+ align:start position:0%
+when you take the derivative of a
+ 
+
+ align:start position:0%
+when you take the derivative of a
+function that involves only quadratic
+
+ align:start position:0%
+function that involves only quadratic
+ 
+
+ align:start position:0%
+function that involves only quadratic
+and linear terms you get something
+
+ align:start position:0%
+and linear terms you get something
+ 
+
+ align:start position:0%
+and linear terms you get something
+that's linear in the coefficients the
+
+ align:start position:0%
+that's linear in the coefficients the
+ 
+
+ align:start position:0%
+that's linear in the coefficients the
+conclusion out of all this discussion is
+
+ align:start position:0%
+conclusion out of all this discussion is
+ 
+
+ align:start position:0%
+conclusion out of all this discussion is
+that when you actually go and carry out
+
+ align:start position:0%
+that when you actually go and carry out
+ 
+
+ align:start position:0%
+that when you actually go and carry out
+this minimization by setting the
+
+ align:start position:0%
+this minimization by setting the
+ 
+
+ align:start position:0%
+this minimization by setting the
+riveters to zero what you will end up
+
+ align:start position:0%
+riveters to zero what you will end up
+ 
+
+ align:start position:0%
+riveters to zero what you will end up
+doing is
+
+ align:start position:0%
+doing is
+ 
+
+ align:start position:0%
+doing is
+solving a system of linear equations in
+
+ align:start position:0%
+solving a system of linear equations in
+ 
+
+ align:start position:0%
+solving a system of linear equations in
+the coefficients that you are trying to
+
+ align:start position:0%
+the coefficients that you are trying to
+ 
+
+ align:start position:0%
+the coefficients that you are trying to
+determine and why is this interesting
+
+ align:start position:0%
+determine and why is this interesting
+ 
+
+ align:start position:0%
+determine and why is this interesting
+well it is because if you actually want
+
+ align:start position:0%
+well it is because if you actually want
+ 
+
+ align:start position:0%
+well it is because if you actually want
+to carry out this minimization all you
+
+ align:start position:0%
+to carry out this minimization all you
+ 
+
+ align:start position:0%
+to carry out this minimization all you
+need to do is to solve a linear system
+
+ align:start position:0%
+need to do is to solve a linear system
+ 
+
+ align:start position:0%
+need to do is to solve a linear system
+which is easily done on a computer the
+
+ align:start position:0%
+which is easily done on a computer the
+ 
+
+ align:start position:0%
+which is easily done on a computer the
+next observation is that this expression
+
+ align:start position:0%
+next observation is that this expression
+ 
+
+ align:start position:0%
+next observation is that this expression
+only involves expectations of various
+
+ align:start position:0%
+only involves expectations of various
+ 
+
+ align:start position:0%
+only involves expectations of various
+terms that are second-order in the
+
+ align:start position:0%
+terms that are second-order in the
+ 
+
+ align:start position:0%
+terms that are second-order in the
+random variables involved so it involves
+
+ align:start position:0%
+random variables involved so it involves
+ 
+
+ align:start position:0%
+random variables involved so it involves
+the expected value of x1 squared it
+
+ align:start position:0%
+the expected value of x1 squared it
+ 
+
+ align:start position:0%
+the expected value of x1 squared it
+involves this term which has something
+
+ align:start position:0%
+involves this term which has something
+ 
+
+ align:start position:0%
+involves this term which has something
+to do with the covariance of X 1 and X 2
+
+ align:start position:0%
+to do with the covariance of X 1 and X 2
+ 
+
+ align:start position:0%
+to do with the covariance of X 1 and X 2
+this term that has something to do with
+
+ align:start position:0%
+this term that has something to do with
+ 
+
+ align:start position:0%
+this term that has something to do with
+the covariance of X 1 with theta but
+
+ align:start position:0%
+the covariance of X 1 with theta but
+ 
+
+ align:start position:0%
+the covariance of X 1 with theta but
+these are all the only terms out of the
+
+ align:start position:0%
+these are all the only terms out of the
+ 
+
+ align:start position:0%
+these are all the only terms out of the
+distribution of the XS and the Thetas
+
+ align:start position:0%
+distribution of the XS and the Thetas
+ 
+
+ align:start position:0%
+distribution of the XS and the Thetas
+that will matter so similar to the case
+
+ align:start position:0%
+that will matter so similar to the case
+ 
+
+ align:start position:0%
+that will matter so similar to the case
+where we had a single observation in
+
+ align:start position:0%
+where we had a single observation in
+ 
+
+ align:start position:0%
+where we had a single observation in
+order to solve this problem we do not
+
+ align:start position:0%
+order to solve this problem we do not
+ 
+
+ align:start position:0%
+order to solve this problem we do not
+need to know the complete distribution
+
+ align:start position:0%
+need to know the complete distribution
+ 
+
+ align:start position:0%
+need to know the complete distribution
+of the x's and of theta it is enough to
+
+ align:start position:0%
+of the x's and of theta it is enough to
+ 
+
+ align:start position:0%
+of the x's and of theta it is enough to
+know all the means variances and
+
+ align:start position:0%
+know all the means variances and
+ 
+
+ align:start position:0%
+know all the means variances and
+covariances of the random variables that
+
+ align:start position:0%
+covariances of the random variables that
+ 
+
+ align:start position:0%
+covariances of the random variables that
+are involved and once more this makes
+
+ align:start position:0%
+are involved and once more this makes
+ 
+
+ align:start position:0%
+are involved and once more this makes
+this approach to estimation a practical
+
+ align:start position:0%
+this approach to estimation a practical
+ 
+
+ align:start position:0%
+this approach to estimation a practical
+one because we do not need to model in
+
+ align:start position:0%
+one because we do not need to model in
+ 
+
+ align:start position:0%
+one because we do not need to model in
+complete detail the distribution of the
+
+ align:start position:0%
+complete detail the distribution of the
+ 
+
+ align:start position:0%
+complete detail the distribution of the
+different random variables finally if we
+
+ align:start position:0%
+different random variables finally if we
+ 
+
+ align:start position:0%
+different random variables finally if we
+do not have just one unknown random
+
+ align:start position:0%
+do not have just one unknown random
+ 
+
+ align:start position:0%
+do not have just one unknown random
+variable but we have multiple random
+
+ align:start position:0%
+variable but we have multiple random
+ 
+
+ align:start position:0%
+variable but we have multiple random
+variables that we want to estimate what
+
+ align:start position:0%
+variables that we want to estimate what
+ 
+
+ align:start position:0%
+variables that we want to estimate what
+should we do
+
+ align:start position:0%
+should we do
+ 
+
+ align:start position:0%
+should we do
+well this is pretty simple you just
+
+ align:start position:0%
+well this is pretty simple you just
+ 
+
+ align:start position:0%
+well this is pretty simple you just
+apply this estimation methodology to
+
+ align:start position:0%
+apply this estimation methodology to
+ 
+
+ align:start position:0%
+apply this estimation methodology to
+each one of the unknown random variables
+
+ align:start position:0%
+each one of the unknown random variables
+ 
+
+ align:start position:0%
+each one of the unknown random variables
+separately to conclude this linear
+
+ align:start position:0%
+separately to conclude this linear
+ 
+
+ align:start position:0%
+separately to conclude this linear
+estimation methodology applies also to
+
+ align:start position:0%
+estimation methodology applies also to
+ 
+
+ align:start position:0%
+estimation methodology applies also to
+the case where you have multiple
+
+ align:start position:0%
+the case where you have multiple
+ 
+
+ align:start position:0%
+the case where you have multiple
+observations you need to solve a certain
+
+ align:start position:0%
+observations you need to solve a certain
+ 
+
+ align:start position:0%
+observations you need to solve a certain
+computational problem in order to find
+
+ align:start position:0%
+computational problem in order to find
+ 
+
+ align:start position:0%
+computational problem in order to find
+the structure of the best linear
+
+ align:start position:0%
+the structure of the best linear
+ 
+
+ align:start position:0%
+the structure of the best linear
+estimator but it is not a very difficult
+
+ align:start position:0%
+estimator but it is not a very difficult
+ 
+
+ align:start position:0%
+estimator but it is not a very difficult
+computational problem because all that
+
+ align:start position:0%
+computational problem because all that
+ 
+
+ align:start position:0%
+computational problem because all that
+it involves is to minimize a quadratic
+
+ align:start position:0%
+it involves is to minimize a quadratic
+ 
+
+ align:start position:0%
+it involves is to minimize a quadratic
+function of the coefficients that you're
+
+ align:start position:0%
+function of the coefficients that you're
+ 
+
+ align:start position:0%
+function of the coefficients that you're
+trying to determine and this leads us to
+
+ align:start position:0%
+trying to determine and this leads us to
+ 
+
+ align:start position:0%
+trying to determine and this leads us to
+having to solve a system of linear
+
+ align:start position:0%
+having to solve a system of linear
+ 
+
+ align:start position:0%
+having to solve a system of linear
+equations for all these reasons linear
+
+ align:start position:0%
+equations for all these reasons linear
+ 
+
+ align:start position:0%
+equations for all these reasons linear
+estimation or estimation using linear
+
+ align:start position:0%
+estimation or estimation using linear
+ 
+
+ align:start position:0%
+estimation or estimation using linear
+estimators is quite practical
\ No newline at end of file
diff --git a/jd4es6Bo600.txt b/jd4es6Bo600.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c3f3486422fdb54ebb91fefd669acaf251439884
--- /dev/null
+++ b/jd4es6Bo600.txt
@@ -0,0 +1,1171 @@
+align:start position:0%
+ 
+to find our spinal solution we just have
+
+ align:start position:0%
+to find our spinal solution we just have
+ 
+
+ align:start position:0%
+to find our spinal solution we just have
+to match the equation so sorry
+
+ align:start position:0%
+to match the equation so sorry
+ 
+
+ align:start position:0%
+to match the equation so sorry
+continuous at x equals a and what do we
+
+ align:start position:0%
+continuous at x equals a and what do we
+ 
+
+ align:start position:0%
+continuous at x equals a and what do we
+have well from 2 you have cosine of K a
+
+ align:start position:0%
+have well from 2 you have cosine of K a
+ 
+
+ align:start position:0%
+have well from 2 you have cosine of K a
+and from 4 you would have a equal e to
+
+ align:start position:0%
+and from 4 you would have a equal e to
+ 
+
+ align:start position:0%
+and from 4 you would have a equal e to
+the minus K a this is the value of this
+
+ align:start position:0%
+the minus K a this is the value of this
+ 
+
+ align:start position:0%
+the minus K a this is the value of this
+so the interior solution at X equal a
+
+ align:start position:0%
+so the interior solution at X equal a
+ 
+
+ align:start position:0%
+so the interior solution at X equal a
+must match the value of the exterior
+
+ align:start position:0%
+must match the value of the exterior
+ 
+
+ align:start position:0%
+must match the value of the exterior
+solution category sorry Prime must be
+
+ align:start position:0%
+solution category sorry Prime must be
+ 
+
+ align:start position:0%
+solution category sorry Prime must be
+continuous at x equals a as well well
+
+ align:start position:0%
+continuous at x equals a as well well
+ 
+
+ align:start position:0%
+continuous at x equals a as well well
+what is the derivative of this function
+
+ align:start position:0%
+what is the derivative of this function
+ 
+
+ align:start position:0%
+what is the derivative of this function
+is minus the sine of this is minus K
+
+ align:start position:0%
+is minus the sine of this is minus K
+ 
+
+ align:start position:0%
+is minus the sine of this is minus K
+sine of KX that becomes K a is equal to
+
+ align:start position:0%
+sine of KX that becomes K a is equal to
+ 
+
+ align:start position:0%
+sine of KX that becomes K a is equal to
+the derivative of that one which is
+
+ align:start position:0%
+the derivative of that one which is
+ 
+
+ align:start position:0%
+the derivative of that one which is
+minus Kappa a e to the minus Kappa will
+
+ align:start position:0%
+minus Kappa a e to the minus Kappa will
+ 
+
+ align:start position:0%
+minus Kappa a e to the minus Kappa will
+a two equations and how many unknowns
+
+ align:start position:0%
+a two equations and how many unknowns
+ 
+
+ align:start position:0%
+a two equations and how many unknowns
+well of there's a and some information
+
+ align:start position:0%
+well of there's a and some information
+ 
+
+ align:start position:0%
+well of there's a and some information
+about Kappa K and the easiest way to
+
+ align:start position:0%
+about Kappa K and the easiest way to
+ 
+
+ align:start position:0%
+about Kappa K and the easiest way to
+eliminate that is to divide them so you
+
+ align:start position:0%
+eliminate that is to divide them so you
+ 
+
+ align:start position:0%
+eliminate that is to divide them so you
+divide the bottom equation by this
+
+ align:start position:0%
+divide the bottom equation by this
+ 
+
+ align:start position:0%
+divide the bottom equation by this
+equation so what do we get
+
+ align:start position:0%
+equation so what do we get
+ 
+
+ align:start position:0%
+equation so what do we get
+divide the bottom by the top minus K and
+
+ align:start position:0%
+divide the bottom by the top minus K and
+ 
+
+ align:start position:0%
+divide the bottom by the top minus K and
+the - the minuses cancel we can cancel
+
+ align:start position:0%
+the - the minuses cancel we can cancel
+ 
+
+ align:start position:0%
+the - the minuses cancel we can cancel
+those minus sign and get K 10 K a is
+
+ align:start position:0%
+those minus sign and get K 10 K a is
+ 
+
+ align:start position:0%
+those minus sign and get K 10 K a is
+equal to minus Kappa but
+
+ align:start position:0%
+equal to minus Kappa but
+ 
+
+ align:start position:0%
+equal to minus Kappa but
+you're ready are convinced I hope on the
+
+ align:start position:0%
+you're ready are convinced I hope on the
+ 
+
+ align:start position:0%
+you're ready are convinced I hope on the
+idea that we should not use equations
+
+ align:start position:0%
+idea that we should not use equations
+ 
+
+ align:start position:0%
+idea that we should not use equations
+that have units so I will multiply by
+
+ align:start position:0%
+that have units so I will multiply by
+ 
+
+ align:start position:0%
+that have units so I will multiply by
+little a and little a to get a decent
+
+ align:start position:0%
+little a and little a to get a decent
+ 
+
+ align:start position:0%
+little a and little a to get a decent
+size and therefore that right-hand side
+
+ align:start position:0%
+size and therefore that right-hand side
+ 
+
+ align:start position:0%
+size and therefore that right-hand side
+becomes sy equals and the left-hand side
+
+ align:start position:0%
+becomes sy equals and the left-hand side
+ 
+
+ align:start position:0%
+becomes sy equals and the left-hand side
+becomes a de tan ADA
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay I want to make a little comment
+
+ align:start position:0%
+okay I want to make a little comment
+ 
+
+ align:start position:0%
+okay I want to make a little comment
+about this quantities already so all the
+
+ align:start position:0%
+about this quantities already so all the
+ 
+
+ align:start position:0%
+about this quantities already so all the
+problem has turned out into the
+
+ align:start position:0%
+problem has turned out into the
+ 
+
+ align:start position:0%
+problem has turned out into the
+following you were given a potential
+
+ align:start position:0%
+following you were given a potential
+ 
+
+ align:start position:0%
+following you were given a potential
+that determines a number Z naught if you
+
+ align:start position:0%
+that determines a number Z naught if you
+ 
+
+ align:start position:0%
+that determines a number Z naught if you
+know the width and everything you know Z
+
+ align:start position:0%
+know the width and everything you know Z
+ 
+
+ align:start position:0%
+know the width and everything you know Z
+naught now you have to calculate 8 and
+
+ align:start position:0%
+naught now you have to calculate 8 and
+ 
+
+ align:start position:0%
+naught now you have to calculate 8 and
+sy if you know either a top or side you
+
+ align:start position:0%
+sy if you know either a top or side you
+ 
+
+ align:start position:0%
+sy if you know either a top or side you
+know Kappa or K and if you know either K
+
+ align:start position:0%
+know Kappa or K and if you know either K
+ 
+
+ align:start position:0%
+know Kappa or K and if you know either K
+or Kappa since you know V naught you
+
+ align:start position:0%
+or Kappa since you know V naught you
+ 
+
+ align:start position:0%
+or Kappa since you know V naught you
+will know the energy so it it kind of
+
+ align:start position:0%
+will know the energy so it it kind of
+ 
+
+ align:start position:0%
+will know the energy so it it kind of
+neat to express this more clearly and I
+
+ align:start position:0%
+neat to express this more clearly and I
+ 
+
+ align:start position:0%
+neat to express this more clearly and I
+think it's maybe easier if one uses X I
+
+ align:start position:0%
+think it's maybe easier if one uses X I
+ 
+
+ align:start position:0%
+think it's maybe easier if one uses X I
+and look at size squared is Kappa
+
+ align:start position:0%
+and look at size squared is Kappa
+ 
+
+ align:start position:0%
+and look at size squared is Kappa
+squared times a squared and what is
+
+ align:start position:0%
+squared times a squared and what is
+ 
+
+ align:start position:0%
+squared times a squared and what is
+Kappa squared is over there to M
+
+ align:start position:0%
+Kappa squared is over there to M
+ 
+
+ align:start position:0%
+Kappa squared is over there to M
+absolute value of a squared over H bar
+
+ align:start position:0%
+absolute value of a squared over H bar
+ 
+
+ align:start position:0%
+absolute value of a squared over H bar
+squared now you want to find e you're
+
+ align:start position:0%
+squared now you want to find e you're
+ 
+
+ align:start position:0%
+squared now you want to find e you're
+gonna get it in some units even is nice
+
+ align:start position:0%
+gonna get it in some units even is nice
+ 
+
+ align:start position:0%
+gonna get it in some units even is nice
+to have it without units so I will
+
+ align:start position:0%
+to have it without units so I will
+ 
+
+ align:start position:0%
+to have it without units so I will
+multiply and divide by V naught 2 m
+
+ align:start position:0%
+multiply and divide by V naught 2 m
+ 
+
+ align:start position:0%
+multiply and divide by V naught 2 m
+v-not a squared over H squared absolute
+
+ align:start position:0%
+v-not a squared over H squared absolute
+ 
+
+ align:start position:0%
+v-not a squared over H squared absolute
+value of e over V not after all you
+
+ align:start position:0%
+value of e over V not after all you
+ 
+
+ align:start position:0%
+value of e over V not after all you
+probably prefer to know I over V naught
+
+ align:start position:0%
+probably prefer to know I over V naught
+ 
+
+ align:start position:0%
+probably prefer to know I over V naught
+which tells you how proportional the
+
+ align:start position:0%
+which tells you how proportional the
+ 
+
+ align:start position:0%
+which tells you how proportional the
+energy is to the depth of the potential
+
+ align:start position:0%
+energy is to the depth of the potential
+ 
+
+ align:start position:0%
+energy is to the depth of the potential
+and this is your famous constant Z
+
+ align:start position:0%
+and this is your famous constant Z
+ 
+
+ align:start position:0%
+and this is your famous constant Z
+naught so e over V naught is actually
+
+ align:start position:0%
+naught so e over V naught is actually
+ 
+
+ align:start position:0%
+naught so e over V naught is actually
+equal to X I over Z naught squared and
+
+ align:start position:0%
+equal to X I over Z naught squared and
+ 
+
+ align:start position:0%
+equal to X I over Z naught squared and
+this is something just to keep in mind
+
+ align:start position:0%
+this is something just to keep in mind
+ 
+
+ align:start position:0%
+this is something just to keep in mind
+if you know sy you certainly must know
+
+ align:start position:0%
+if you know sy you certainly must know
+ 
+
+ align:start position:0%
+if you know sy you certainly must know
+Zeno
+
+ align:start position:0%
+Zeno
+ 
+
+ align:start position:0%
+Zeno
+because that's not your potential and
+
+ align:start position:0%
+because that's not your potential and
+ 
+
+ align:start position:0%
+because that's not your potential and
+then you know how much is the energy all
+
+ align:start position:0%
+then you know how much is the energy all
+ 
+
+ align:start position:0%
+then you know how much is the energy all
+very convenient things so punchline for
+
+ align:start position:0%
+very convenient things so punchline for
+ 
+
+ align:start position:0%
+very convenient things so punchline for
+solutions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so what do we have we have two equations
+
+ align:start position:0%
+so what do we have we have two equations
+ 
+
+ align:start position:0%
+so what do we have we have two equations
+this equation maybe should be given a
+
+ align:start position:0%
+this equation maybe should be given a
+ 
+
+ align:start position:0%
+this equation maybe should be given a
+number sy equal eight at an ADA and ADA
+
+ align:start position:0%
+number sy equal eight at an ADA and ADA
+ 
+
+ align:start position:0%
+number sy equal eight at an ADA and ADA
+an X I squared will giving you Z squared
+
+ align:start position:0%
+an X I squared will giving you Z squared
+ 
+
+ align:start position:0%
+an X I squared will giving you Z squared
+so how do we solve it we solve it
+
+ align:start position:0%
+so how do we solve it we solve it
+ 
+
+ align:start position:0%
+so how do we solve it we solve it
+graphically we have side Anita and then
+
+ align:start position:0%
+graphically we have side Anita and then
+ 
+
+ align:start position:0%
+graphically we have side Anita and then
+we say oh let's try to plot the two
+
+ align:start position:0%
+we say oh let's try to plot the two
+ 
+
+ align:start position:0%
+we say oh let's try to plot the two
+equations well this is a circle in a
+
+ align:start position:0%
+equations well this is a circle in a
+ 
+
+ align:start position:0%
+equations well this is a circle in a
+square plus I squared now cyanate that
+
+ align:start position:0%
+square plus I squared now cyanate that
+ 
+
+ align:start position:0%
+square plus I squared now cyanate that
+must be positive so we look at solution
+
+ align:start position:0%
+must be positive so we look at solution
+ 
+
+ align:start position:0%
+must be positive so we look at solution
+just in this quadrant let's put here PI
+
+ align:start position:0%
+just in this quadrant let's put here PI
+ 
+
+ align:start position:0%
+just in this quadrant let's put here PI
+over 2 pi 3 PI over 2 2 pi
+
+ align:start position:0%
+over 2 pi 3 PI over 2 2 pi
+ 
+
+ align:start position:0%
+over 2 pi 3 PI over 2 2 pi
+and here is a 2 and there is sorry well
+
+ align:start position:0%
+and here is a 2 and there is sorry well
+ 
+
+ align:start position:0%
+and here is a 2 and there is sorry well
+this is a circle as we said but let's
+
+ align:start position:0%
+this is a circle as we said but let's
+ 
+
+ align:start position:0%
+this is a circle as we said but let's
+look at this sign equal in Turton ADA
+
+ align:start position:0%
+look at this sign equal in Turton ADA
+ 
+
+ align:start position:0%
+look at this sign equal in Turton ADA
+that vanishes as a that goes to 0 and
+
+ align:start position:0%
+that vanishes as a that goes to 0 and
+ 
+
+ align:start position:0%
+that vanishes as a that goes to 0 and
+will diverge at ETA equal PI over 2 so
+
+ align:start position:0%
+will diverge at ETA equal PI over 2 so
+ 
+
+ align:start position:0%
+will diverge at ETA equal PI over 2 so
+this part at least look like this and
+
+ align:start position:0%
+this part at least look like this and
+ 
+
+ align:start position:0%
+this part at least look like this and
+then it will go negative which we don't
+
+ align:start position:0%
+then it will go negative which we don't
+ 
+
+ align:start position:0%
+then it will go negative which we don't
+care from this region and then reach
+
+ align:start position:0%
+care from this region and then reach
+ 
+
+ align:start position:0%
+care from this region and then reach
+here at PI and after pi it will go
+
+ align:start position:0%
+here at PI and after pi it will go
+ 
+
+ align:start position:0%
+here at PI and after pi it will go
+positive again and it will reach another
+
+ align:start position:0%
+positive again and it will reach another
+ 
+
+ align:start position:0%
+positive again and it will reach another
+infinity here and then our at 3 pi a 2
+
+ align:start position:0%
+infinity here and then our at 3 pi a 2
+ 
+
+ align:start position:0%
+infinity here and then our at 3 pi a 2
+pi it will go again and reach another so
+
+ align:start position:0%
+pi it will go again and reach another so
+ 
+
+ align:start position:0%
+pi it will go again and reach another so
+these are this curves and the other
+
+ align:start position:0%
+these are this curves and the other
+ 
+
+ align:start position:0%
+these are this curves and the other
+curve the circle is just a circle here
+
+ align:start position:0%
+curve the circle is just a circle here
+ 
+
+ align:start position:0%
+curve the circle is just a circle here
+so for example I could have
+
+ align:start position:0%
+so for example I could have
+ 
+
+ align:start position:0%
+so for example I could have
+a circle like this so the radius of this
+
+ align:start position:0%
+a circle like this so the radius of this
+ 
+
+ align:start position:0%
+a circle like this so the radius of this
+circle is radius V naught and there you
+
+ align:start position:0%
+circle is radius V naught and there you
+ 
+
+ align:start position:0%
+circle is radius V naught and there you
+go you've solved the problem at least
+
+ align:start position:0%
+go you've solved the problem at least
+ 
+
+ align:start position:0%
+go you've solved the problem at least
+intuitively you'd know the answer and
+
+ align:start position:0%
+intuitively you'd know the answer and
+ 
+
+ align:start position:0%
+intuitively you'd know the answer and
+there's a lot of things that come out of
+
+ align:start position:0%
+there's a lot of things that come out of
+ 
+
+ align:start position:0%
+there's a lot of things that come out of
+this calculation if the radius Z naught
+
+ align:start position:0%
+this calculation if the radius Z naught
+ 
+
+ align:start position:0%
+this calculation if the radius Z naught
+is 3 PI over 2 for example and the
+
+ align:start position:0%
+is 3 PI over 2 for example and the
+ 
+
+ align:start position:0%
+is 3 PI over 2 for example and the
+radius Li not represents some potential
+
+ align:start position:0%
+radius Li not represents some potential
+ 
+
+ align:start position:0%
+radius Li not represents some potential
+of some depth and width there will be
+
+ align:start position:0%
+of some depth and width there will be
+ 
+
+ align:start position:0%
+of some depth and width there will be
+just two solutions these are these
+
+ align:start position:0%
+just two solutions these are these
+ 
+
+ align:start position:0%
+just two solutions these are these
+solutions this points represent values
+
+ align:start position:0%
+solutions this points represent values
+ 
+
+ align:start position:0%
+solutions this points represent values
+of sy and values of ADA from which you
+
+ align:start position:0%
+of sy and values of ADA from which you
+ 
+
+ align:start position:0%
+of sy and values of ADA from which you
+can read the energy in fact you can look
+
+ align:start position:0%
+can read the energy in fact you can look
+ 
+
+ align:start position:0%
+can read the energy in fact you can look
+at this state and say that's a state of
+
+ align:start position:0%
+at this state and say that's a state of
+ 
+
+ align:start position:0%
+at this state and say that's a state of
+largest song sy and therefore it's the
+
+ align:start position:0%
+largest song sy and therefore it's the
+ 
+
+ align:start position:0%
+largest song sy and therefore it's the
+state of largest absolute value of the
+
+ align:start position:0%
+state of largest absolute value of the
+ 
+
+ align:start position:0%
+state of largest absolute value of the
+energy it's the most deeply bound state
+
+ align:start position:0%
+energy it's the most deeply bound state
+ 
+
+ align:start position:0%
+energy it's the most deeply bound state
+then this is the next neatly bouncing
+
+ align:start position:0%
+then this is the next neatly bouncing
+ 
+
+ align:start position:0%
+then this is the next neatly bouncing
+there's two bound States in this case
+
+ align:start position:0%
+there's two bound States in this case
+ 
+
+ align:start position:0%
+there's two bound States in this case
+interestingly however shallow this
+
+ align:start position:0%
+interestingly however shallow this
+ 
+
+ align:start position:0%
+interestingly however shallow this
+potential might be however small Z
+
+ align:start position:0%
+potential might be however small Z
+ 
+
+ align:start position:0%
+potential might be however small Z
+naught the circle will always have one
+
+ align:start position:0%
+naught the circle will always have one
+ 
+
+ align:start position:0%
+naught the circle will always have one
+intersection so there will always be at
+
+ align:start position:0%
+intersection so there will always be at
+ 
+
+ align:start position:0%
+intersection so there will always be at
+least one solution that's the end of
+
+ align:start position:0%
+least one solution that's the end of
+ 
+
+ align:start position:0%
+least one solution that's the end of
+that story let me say that for the odd
+
+ align:start position:0%
+that story let me say that for the odd
+ 
+
+ align:start position:0%
+that story let me say that for the odd
+case of solutions
+
+ align:start position:0%
+case of solutions
+ 
+
+ align:start position:0%
+case of solutions
+I will not solve it it's a good thing to
+
+ align:start position:0%
+I will not solve it it's a good thing to
+ 
+
+ align:start position:0%
+I will not solve it it's a good thing to
+do in recitation or as part of the
+
+ align:start position:0%
+do in recitation or as part of the
+ 
+
+ align:start position:0%
+do in recitation or as part of the
+homework as well the answer for the odd
+
+ align:start position:0%
+homework as well the answer for the odd
+ 
+
+ align:start position:0%
+homework as well the answer for the odd
+case is that X I is equal to minus 8
+
+ align:start position:0%
+case is that X I is equal to minus 8
+ 
+
+ align:start position:0%
+case is that X I is equal to minus 8
+that cop ADA and in that case I'll give
+
+ align:start position:0%
+that cop ADA and in that case I'll give
+ 
+
+ align:start position:0%
+that cop ADA and in that case I'll give
+you a little preview of how this cut
+
+ align:start position:0%
+you a little preview of how this cut
+ 
+
+ align:start position:0%
+you a little preview of how this cut
+looks it looks like this and then there
+
+ align:start position:0%
+looks it looks like this and then there
+ 
+
+ align:start position:0%
+looks it looks like this and then there
+more branches
+
+ align:start position:0%
+more branches
+ 
+
+ align:start position:0%
+ 
+so for the odd solution you have this
+
+ align:start position:0%
+so for the odd solution you have this
+ 
+
+ align:start position:0%
+so for the odd solution you have this
+curves and if you have a circle
+
+ align:start position:0%
+curves and if you have a circle
+ 
+
+ align:start position:0%
+curves and if you have a circle
+sometimes you don't have a solution no
+
+ align:start position:0%
+sometimes you don't have a solution no
+ 
+
+ align:start position:0%
+sometimes you don't have a solution no
+it doesn't intersect this so this are
+
+ align:start position:0%
+it doesn't intersect this so this are
+ 
+
+ align:start position:0%
+it doesn't intersect this so this are
+solutions you will see and try to
+
+ align:start position:0%
+solutions you will see and try to
+ 
+
+ align:start position:0%
+solutions you will see and try to
+understand they don't always success you
+
+ align:start position:0%
+understand they don't always success you
+ 
+
+ align:start position:0%
+understand they don't always success you
+need a potentially sufficiently deep to
+
+ align:start position:0%
+need a potentially sufficiently deep to
+ 
+
+ align:start position:0%
+need a potentially sufficiently deep to
+get an art solution and then the odds
+
+ align:start position:0%
+get an art solution and then the odds
+ 
+
+ align:start position:0%
+get an art solution and then the odds
+and even solutions will interweave each
+
+ align:start position:0%
+and even solutions will interweave each
+ 
+
+ align:start position:0%
+and even solutions will interweave each
+other and there will be a nice story
+
+ align:start position:0%
+other and there will be a nice story
+ 
+
+ align:start position:0%
+other and there will be a nice story
+that you will explore in a lot of detail
+
+ align:start position:0%
+that you will explore in a lot of detail
+ 
+
+ align:start position:0%
+that you will explore in a lot of detail
+but the lesson is if we use the problem
+
+ align:start position:0%
+but the lesson is if we use the problem
+ 
+
+ align:start position:0%
+but the lesson is if we use the problem
+the unique free calculation in which you
+
+ align:start position:0%
+the unique free calculation in which you
+ 
+
+ align:start position:0%
+the unique free calculation in which you
+can get the nutrition of when solutions
+
+ align:start position:0%
+can get the nutrition of when solutions
+ 
+
+ align:start position:0%
+can get the nutrition of when solutions
+exist and when they don't but solving
+
+ align:start position:0%
+exist and when they don't but solving
+ 
+
+ align:start position:0%
+exist and when they don't but solving
+for the particular numbers are
+
+ align:start position:0%
+for the particular numbers are
+ 
+
+ align:start position:0%
+for the particular numbers are
+transcendental equations and you need a
+
+ align:start position:0%
+transcendental equations and you need a
+ 
+
+ align:start position:0%
+transcendental equations and you need a
+computer to solve
\ No newline at end of file
diff --git a/kAv5pahIevE.txt b/kAv5pahIevE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8744ffd63e94971047a22717fb1ceec07292aaaa
--- /dev/null
+++ b/kAv5pahIevE.txt
@@ -0,0 +1,1451 @@
+PROFESSOR: OK.
+
+I promised a video about
+limits and continuous
+
+functions and here it is.
+
+So I'll begin with the most
+basic idea and with a picture
+
+instead of definition in symbols
+first. So the most
+
+basic idea is that I have
+a bunch of numbers--
+
+let's make them positive
+numbers--
+
+and I want to know, what
+does it mean for them
+
+to approach a limit--
+
+capital A--
+
+as I go out this sequence of
+numbers, a1, a2, a3, a4.
+
+And let me say right away, the
+first four numbers, the first
+
+million numbers, make no
+difference about the limit.
+
+So here's what it means.
+
+For example, there's a
+equals 7, let's say.
+
+What does it mean for these
+numbers to approach 7?
+
+It means that if I take any thin
+little space around a,
+
+above and below, the numbers
+can start out whatever.
+
+They can go in there, they could
+go out, they could come
+
+back, whatever, they could
+grow way big, way small.
+
+But in the end, beyond some
+point, eventually, they have
+
+to get in that slit
+and stay in there.
+
+And the slit, then,
+could be smaller.
+
+And then they would have to get
+into that smaller slit and
+
+stay there.
+
+So that's what it means for
+the numbers to approach A,
+
+that eventually after any number
+of jogs around, they
+
+get inside and they stay
+there, however
+
+thin that slit is.
+
+A slight difference when
+a is 0, because
+
+the numbers are positive.
+
+They're coming down,
+they get in.
+
+And again, they must stay in.
+
+And then, again, I'm going to
+make the band tighter, and
+
+they have to get into
+that and stay there.
+
+And what does it mean for the
+numbers to approach infinity?
+
+That means that whatever--
+
+so this is often
+called epsilon.
+
+I'll use that Greek
+letter epsilon as
+
+a very small number.
+
+So this would be A minus
+epsilon, and this would be A
+
+plus epsilon.
+
+And then the epsilon could
+be made smaller.
+
+And now here is some
+big number,
+
+like even 1 over epsilon.
+
+So that's a giant number.
+
+And the limit is infinity if,
+again, they can dodge around
+
+for a while, they can go
+down, they can go up.
+
+But eventually, they
+must get above that
+
+line and stay there.
+
+And if I move the line up
+further, they have to get
+
+above that line for me to
+say that the limit is--
+
+so I have these possible
+limits.
+
+Infinite, some positive,
+ordinary number, and 0.
+
+Those are possible limits.
+
+But of course many sequences
+have no limit at all, like
+
+sine of n, it will just bounce
+around, cosine n--
+
+many, many things.
+
+OK.
+
+So I think that the way to get
+the idea, use the idea, is to
+
+ask some questions
+about limits.
+
+And we'll see that usually the
+answer is yes, OK, no problem.
+
+But once in a while, for certain
+limits are dangerous.
+
+So really always mathematicians
+are looking for
+
+what's special, what unusual
+thing could happen?
+
+Because the truth is, limits are
+ordinarily rather boring.
+
+If the an's approach 7 and the
+bn's approach 4, so the a's
+
+get close to 7 and the b's get
+close to 4, then their
+
+differences will get
+close to 7 minus 4.
+
+But is there any case in
+which that could fail?
+
+Is there any case among these
+in which we could not know
+
+what the limit was, and it might
+not exist, or it might
+
+be like any number?
+
+And I think that can happen
+in this, so I've got four
+
+different questions
+here, getting more
+
+interesting as we go down.
+
+In the first one, I can
+see only one problem.
+
+If the a's approach infinity, so
+they get very big, and the
+
+b's also approach infinity, get
+very big, so capital A and
+
+capital B become formally
+infinity minus infinity, and
+
+we don't know the
+answer there.
+
+That has no meaning.
+
+So this'll be my little
+list of danger.
+
+I mean, it's not like
+skydiving, but for a
+
+mathematician this
+is high risk.
+
+OK, so how could this happen?
+
+Well, the an might
+be n squared.
+
+And the bn might be only n.
+
+Right?
+
+So they're both going to
+infinity, n squared and n.
+
+But n squared is going faster.
+
+It's like a race.
+
+n squared will win, and the
+difference between them will
+
+actually grow faster
+and faster.
+
+Or they could go to
+infinity together.
+
+an and bn could both be n,
+both headed for infinity.
+
+The differences would be
+0 all along, n minus n.
+
+So the limit of the difference
+would be 0 minus 0.
+
+So this could be 0, but it could
+be infinity, it could be
+
+minus infinity, it could
+be anything.
+
+Any limit is possible there.
+
+Do you see that there
+is a case--
+
+it's sort of a special case,
+because it only happens when
+
+these limits are infinite--
+
+but now it's sort of OK
+to look at each--
+
+let me look at number two.
+
+How about multiplication?
+
+If I multiply a bunch of numbers
+that are headed for 7
+
+and a bunch of numbers that
+are headed for 4, their
+
+product is going
+to head for 28.
+
+This will be true.
+
+When could it fail?
+
+Well, again, it's going to be
+extreme cases, because if I
+
+have ordinary numbers for
+A and B like 7 and
+
+4, there's no doubt.
+
+But look at the extreme
+case of when A
+
+is 0 and B is infinite.
+
+So the an's are headed for 0.
+
+The bn's are getting bigger
+and bigger, the an's are
+
+getting small as we
+go far enough out.
+
+OK.
+
+In that case, well,
+again it's a race.
+
+The an's might be 1 over
+n squared, and the
+
+bn's might be n.
+
+So this would be n over
+n squared, and
+
+that would go to 0.
+
+But if I reverse those I could
+have n squared times 1 over n.
+
+The product could get bigger,
+or the product could--
+
+all possibilities.
+
+All possibilities there.
+
+So I cannot know what
+that one is.
+
+0 times infinity
+is meaningless.
+
+OK.
+
+What about number three?
+
+The danger increases as soon
+as we start dividing.
+
+I made the b's positive,
+but I don't know if
+
+capital B is positive.
+
+So the danger--
+
+and, in fact, the most important
+case for calculus--
+
+is 0 over 0.
+
+If the a's go to 0 and the b's
+go to 0, I can't tell what
+
+their ratio goes to, because it
+depends how fast they go.
+
+If the a's go quickly to 0 and
+the b's are rather slow
+
+getting there--
+
+in other words the b's would be
+a lot bigger than the a's
+
+even though both are
+going to 0--
+
+then that fraction
+would be small.
+
+But if I reverse them, the
+fraction would be large.
+
+So I think 0 over
+0 is a danger.
+
+I think there's another
+danger here.
+
+Yeah, maybe infinity
+over infinity.
+
+Again, that's a race that we
+can't tell, until we know
+
+details about the sequences,
+who's going to win.
+
+If they an's go off to infinity
+and the bn's go off
+
+to infinity, ah, a very
+important case.
+
+The ratio could be
+1 all along.
+
+The a's and b's could be the
+same, headed for infinity.
+
+Or the an's might be squaring
+the b's and going up faster,
+
+or the square root of the
+b's and going slower.
+
+So again, infinity over
+infinity, we can't--
+
+0 over infinity, if the a's are
+headed for 0 and the b's
+
+are headed big, then that ratio
+is going to be small and
+
+head for 0.
+
+0 over infinity, I'm OK with.
+
+Call it 0.
+
+Well, I don't know if
+that's legal, but
+
+anyway, let me do it.
+
+All right, last one of
+this kind, just for
+
+practice about limits.
+
+Again, you see what I'm
+constantly doing is thinking
+
+of examples that simply
+show that I can't
+
+be sure of the limit.
+
+So here normally I could be
+sure, if this is headed for 7
+
+to the fourth, that'll be the
+limit, whatever that is, 49
+
+squared, 2401, or something.
+
+But if--
+
+now when could it go wrong?
+
+Here's an interesting case.
+
+So this is my list of danger,
+and I think I'm in danger if
+
+they both go to 0.
+
+0 to the 0-th power, I don't
+know what that is.
+
+And actually, I don't know all
+the possibilities here.
+
+I can see one way would be let's
+suppose the b's were
+
+actually 0, or practically.
+
+Then things to the
+0 power are 1.
+
+So I could get the answer 1 here
+by fixing the b's at 0
+
+and letting these guys, they
+would all be to the 0 power,
+
+so they would all be 1.
+
+And in the limit,
+I would have 1.
+
+But I could also do
+it differently.
+
+I could fix these at 0 and let
+these guys get smaller.
+
+Then I would have 0 to powers.
+
+And zero to any power is 0.
+
+You see my little
+problem here?
+
+Let me write my little
+problem here.
+
+My problem is that a to the 0
+power would be 1, but 0 to the
+
+a-th power would be 0, or 0 to
+the b-th, maybe I should say.
+
+So if I'm in this situation and
+the a is shrinking to 0, I
+
+still have a limit of 1's.
+
+But if I'm in this situation and
+the b's are headed for 0,
+
+I have a limit of 0's.
+
+And maybe you could get
+1/2, I don't know how.
+
+And you have to allow me--
+because I have to finish this
+
+list, and I only have one
+more to tell you--
+
+that another case, a very
+interesting type of calculus
+
+case is the case where
+the a's go to 1 and
+
+the b's go to infinity.
+
+I don't know if you remember
+that this actually happened in
+
+the lecture on e, the number
+that comes in e to the x, the
+
+great number of calculus.
+
+Do you remember that?
+
+So I'm going to talk a little
+bit about the a's going to 1
+
+and the b's blowing up.
+
+So I'm getting things that are
+very near 1, but I'm taking
+
+many, many more of them.
+
+And I believe that I can
+get all kinds of
+
+different limits there.
+
+I believe I can get all kinds
+of different limits.
+
+Do you just--
+
+maybe on this next board.
+
+And then I promise to come
+back to the heart of the
+
+subject of limits and continuous
+functions.
+
+But I just think that one, the
+famous case of this one, was 1
+
+plus 1 over n.
+
+That's the a's, and that
+approaches what limit?
+
+One.
+
+The b's I'm going
+to take as n.
+
+So the b's are going
+to infinity.
+
+So I'm discussing
+this case here.
+
+So that's a case where
+this goes to 1,
+
+this goes to infinity.
+
+I had an email this week saying,
+wait a minute, I've
+
+got a little problem here,
+because I know 1 to the
+
+infinity is e.
+
+1 to the infinity is 3.
+
+Well, that's because it's true
+that that number approaches e.
+
+That's one of the many
+remarkable ways to produce the
+
+number e, the 2.7-something.
+
+But that's because the race
+between this and this was so
+
+evenly balanced.
+
+If I took these closer and
+closer to 1, like n squared,
+
+what would happen then?
+
+Then I'm taking numbers very,
+very near 1, I'm taking a
+
+power, but these are sort of
+near, those would approach--
+
+would you like to guess?
+
+One.
+
+These are so close to 1 that
+taking the nth power doesn't
+
+move them far.
+
+And you can guess that I could
+get infinity too, by taking n
+
+not still close to 1
+and taking some big
+
+power like n squared.
+
+Now I have things close to 1,
+but I'm taking so many of them
+
+that it would blow up.
+
+So again i think--So those are
+all cases where in the limit,
+
+I have 1, in the limit,
+I have infinity.
+
+But that combination 1 to the
+increasingly high powers can
+
+do different things.
+
+This was my little idea to
+show you the risky cases.
+
+OK.
+
+But actually, 0 over 0, that's
+what calculus is
+
+always doing, right?
+
+Because that's exactly what we
+have when we have a delta f
+
+over a delta x, a delta
+y over a delta x.
+
+They're both approaching 0 and
+we get a definite slope when
+
+the ratio goes to
+a good number.
+
+OK.
+
+So can I discuss 0 over 0?
+
+All right, phooey on this one.
+
+OK.
+
+So I now want to speak
+about the case when f
+
+of x goes to 0.
+
+Let's say f of x goes
+to 0 as x goes to 0.
+
+So there'll be an if here.
+
+I have to say what that means.
+
+And then I'm also going to have
+some g of x going to 0 as
+
+x goes to 0.
+
+OK, so both functions
+are decreasing.
+
+And my question, let me ask the
+question first, what about
+
+f of x over g of x?
+
+What does that do?
+
+And of course, just as I said
+up there, I can't tell yet.
+
+I have to know the
+f and the g.
+
+It's a race to 0, and I have to
+know who's the winner and
+
+by how much.
+
+But first, I'd better say what
+does it mean for a function to
+
+go to 0 as x goes to 0.
+
+Well, you know.
+
+Let me draw a graph
+of this function.
+
+OK, I'll just draw it.
+
+So f of x is going to 0.
+
+So here is x, and I'm going to
+graph f of x, and here is 0.
+
+So as x is coming down to 0, my
+f of x is also coming to 0.
+
+So it could come like so.
+
+That's a pretty sensible,
+smooth, nice approach to 0.
+
+That could be my f of x.
+
+And it may be a g of x is
+smaller, but also approaching
+
+0 in a nice, smooth way.
+
+This is a case where
+you can see those,
+
+as x goes that way--
+
+maybe the arrow should be going
+that way, because x is
+
+going to 0--
+
+my f of x is getting smaller, my
+g of x is getting smaller.
+
+And I'll say exactly what
+that means, but you
+
+know what it means.
+
+It means that if I put a little,
+like these lines, if I
+
+put a little band there,
+it gets into that band.
+
+Actually, g will get into
+the band sooner.
+
+But then f will safely
+get into the band.
+
+Now, the question is what about
+f of x over g of x?
+
+OK.
+
+Can we say?
+
+Now, I'm going to suppose
+that f of x has a
+
+definite slope, s.
+
+And this one has a definite
+slope, t.
+
+In other words, I am
+going to suppose--
+
+Here look, this is called,
+named after a French guy,
+
+L'Hopital, the hospital rule.
+
+OK, so it's just a little trick,
+because this comes up
+
+of what's happening
+in this race to 0.
+
+And the natural idea is that f
+of x is really, since f is 0
+
+there, and I'm really just
+going a little way.
+
+So maybe I call that delta x,
+just to emphasize that I'm
+
+looking really near 0.
+
+And that f of x is really
+going to be delta f.
+
+And that g of x is really going
+to be delta g, because
+
+let me draw the picture,
+delta f is that height.
+
+Here is delta x, and
+here is the height.
+
+It's because that
+point is 0, 0.
+
+So the differences I'm taking,
+the f of x in the delta, the f
+
+of x plus delta x is just f at
+delta x, just that height.
+
+And g is this smaller one.
+
+Do you have an idea of what
+this answer's going to be?
+
+If I look at that ratio of this
+
+function to this function--
+
+here the ratio, I don't know
+what, 3 or something.
+
+Here it's, I don't know,
+maybe 4, maybe more.
+
+As I'm getting closer and
+closer, this height is
+
+controlled by the slope.
+
+And this height, the g of x,
+is controlled by its slope.
+
+Look, here is the
+way to see it.
+
+Just divide top and
+bottom by delta x.
+
+Same thing.
+
+So I haven't changed
+anything yet.
+
+I divided the top and the
+bottom by delta x, just
+
+because now I'll let everything
+go to 0, delta x
+
+will go to 0, the delta f will
+go to 0, so the delta
+
+g will go to 0.
+
+But I know what this
+approaches.
+
+Delta f over delta x approaches
+the slope, s.
+
+And delta g over delta x
+approaches the other slope, t.
+
+So you see, this is L'Hopital's
+rule, that if f
+
+goes to 0, and if g goes to 0,
+and if they have nice slopes,
+
+then the ratio of f to g, which
+looks like 0 over 0, we
+
+can actually tell what it is by
+looking at the derivative,
+
+by looking at those slopes.
+
+It's the ratio of the slopes.
+
+OK, that takes a little
+thought and, of
+
+course, some practices.
+
+It also takes some examples to
+show what else could happen.
+
+Can I just draw another f,
+and you tell me what
+
+about f over g.
+
+I'm sorry to give you all these
+questions, but it's
+
+example, answer, that you
+get the hang of slopes.
+
+Suppose f goes much steeper.
+
+I mean, f could be the
+square root of x.
+
+There's f equal the
+square root of x.
+
+Square root of x has an
+infinite slope at 0.
+
+It's a good function to know,
+the square root of x, because
+
+this is x to the 1/2 power.
+
+And its derivative, its slope,
+we know will be 1/2 x to the
+
+minus 1/2 power.
+
+And then as x goes to
+0, that blows up the
+
+way the picture shows.
+
+Now, what would f over g, so
+this is a case where f hasn't
+
+got a slope.
+
+The slope is infinite now.
+s is now infinite.
+
+And that ratio is going
+to blow up.
+
+This one is getting
+to 0 but slowly.
+
+This f is staying much bigger
+than the g, and the ratio
+
+would be infinite.
+
+So there's a case where
+L'Hopital can't help because
+
+f, this slope s, which was fine
+for this nice function,
+
+is not fine for this function.
+
+The slope is infinite for that
+square root function.
+
+OK, a bunch of examples that
+begin to show what can happen
+
+and the need, really, for a
+little bit of care on what
+
+does it mean?
+
+What would I say about that
+square root function?
+
+So I'll even write
+that down here.
+
+f of x equals square root
+of x at x equals 0.
+
+What would I say about
+that function that
+
+we know it's picture?
+
+I would say it has
+infinite slope.
+
+Or if you prefer, its slope
+is not defined.
+
+We don't have a good number
+there for its slope.
+
+But I would still say the
+function is continuous because
+
+the darn thing does get
+below any band.
+
+If I draw a little band here,
+the function does get into
+
+that band and stay inside.
+
+It just took a long time.
+
+It stayed out of that band as
+long as it could and then
+
+finally fell in just
+at the last minute.
+
+OK, so I would say this function
+has the slope not
+
+defined, not OK at x equals 0.
+
+But f of x is continuous
+at x equals 0.
+
+So I'm trying to make the
+distinction between asking for
+
+the function to be continuous
+is not asking as much.
+
+If a function's got a nice
+slope, like g, that function's
+
+got to be continuous.
+
+And more, it has to have
+this good slope.
+
+This f of x, this square root
+function will be continuous.
+
+And now I have to tell you
+what continuous means.
+
+It's not asking for so much as
+a slope, because the slope
+
+could come down infinitely
+at the last minute.
+
+All right, so what's a
+continuous function?
+
+Continuous function means--
+
+a continuous function, f of x,
+at some point-- maybe here it
+
+was 0, I'd better allow
+any old point.
+
+So in words, it means f of
+x approaches f of a as x
+
+approaches a.
+
+That's what it means to be
+continuous at that point.
+
+It means that there is
+a number, a value
+
+for f at that point.
+
+And we approach that value as
+we get near that point.
+
+That seems such a
+natural idea.
+
+That's what it means for a
+function to be continuous.
+
+And with this piece of chalk
+or with your pen, it means
+
+that I can draw the function
+without lifting my pen.
+
+Of course, it could do
+some weird stuff.
+
+OK, let me just draw here.
+
+So here's a point, a, and here
+is my function, f, and
+
+there is f of a.
+
+So I'm saying that the function
+could come along, it
+
+could come down pretty steeply,
+but it will get to
+
+that point.
+
+It might go on, steeper below,
+or it might turn back.
+
+Or it might be level.
+
+But I can draw the whole
+thing continuously.
+
+But now that description
+with a piece of
+
+chalk isn't quite enough.
+
+And there's a formal definition
+
+that I have to explain.
+
+And it involves this same
+idea of epsilon, this
+
+same idea of a strip.
+
+It means that if I take a little
+strip around f of a--
+
+so here's f of a plus a little
+bit, and here's f of a minus a
+
+little bit--
+
+then that's continuous.
+
+That function is continuous,
+because--
+
+now, remember, epsilon could
+be smaller than I drew it,
+
+smaller than I can draw it,
+but still positive.
+
+Then the requirement is that it
+has to get near a, it has
+
+to get inside that band
+and stay there.
+
+It can bounce all
+over the place.
+
+But near the point, it's
+got to get close.
+
+And now, how do I express that
+in terms of epsilon?
+
+OK, well, there's a famous
+description.
+
+Yeah, what do I mean by get in
+there and stay in there?
+
+Ah!
+
+Can I just make a story?
+
+I'm going to use two Greek
+letters, epsilon and delta,
+
+hated by all calculus students
+and professors
+
+too, if they're truthful.
+
+OK, so the story goes,
+we choose a band.
+
+Ah, since their Greek letters,
+Socrates chooses epsilon.
+
+OK.
+
+So he's going to make it hard.
+
+He's going to make a
+narrow band there.
+
+And then the function has got to
+get into that band and stay
+
+there, close to a.
+
+OK, so what do I mean
+by close to a?
+
+Well, that's where
+delta comes in.
+
+That's, let's say, Socrates's
+student, Plato.
+
+Then Plato can pick his number,
+delta, which will be
+
+the width--
+
+see, he says, OK, if you get
+really close, I've got you.
+
+So he's trying to
+please Socrates.
+
+So he says, woo, sorry, a had
+better be in there somewhere.
+
+Now these bands are getting so
+close, my a is, of course--
+
+this is really a plus delta, and
+this guy is a minus delta.
+
+Are you kind of with me?
+
+The logic goes, for any epsilon
+chosen by Socrates,
+
+Plato can find a positive
+delta--
+
+epsilon, of course, was some
+positive number, delta might
+
+be an extremely small
+positive number--
+
+so that if the distance
+to a is smaller
+
+than Plato's distance--
+
+so if we're in that
+vertical band--
+
+then we're in Socrates's
+horizontal band.
+
+Then this f of x minus f
+of a is below epsilon.
+
+So Socrates sets up any tough
+requirement, any horizontal
+
+band, and then Plato meets
+that requirement, if the
+
+function is continuous, by
+choosing a vertical band that
+
+keeps everything inside
+Socrates's band.
+
+Do you see that?
+
+Well, it takes some thought.
+
+It takes some practice, and as
+always, it's not usually very
+
+hard to tell if a function
+is continuous.
+
+Let me show you one
+that isn't.
+
+A famous function that
+is not continuous.
+
+Here's the sine of 1 over
+x as x going to 0.
+
+What happens to the sine of
+1 over x when x goes to 0?
+
+Well, the sine, we know,
+oscillates minus 1, plus 1,
+
+minus 1, plus 1.
+
+But when it's a sine of 1 over
+x, that oscillation really
+
+takes off, because if x gets
+small, 1 over x is quickly
+
+getting larger.
+
+You're running along the sine
+curve in a faster and faster
+
+and faster way.
+
+I can't draw it.
+
+Here's 0.
+
+But it's not staying
+inside a band.
+
+Even with epsilon equalling 1/2,
+Socrates has got Plato.
+
+Plato can't keep it in a band of
+1/2 up and 1/2 down because
+
+the sine doesn't stay there.
+
+So there's a function that's
+not continuous.
+
+I could make it continuous by
+changing the function a
+
+little, maybe x times
+sine of 1 over x.
+
+That would bring the
+oscillations down and work.
+
+So there you go.
+
+That's epsilon and delta.
+
+And it takes a little
+practice.
+
+And I just have to remember--
+
+when you feel that the whole
+thing is a bad experience--
+
+some pity for a Socrates, who
+actually took poison.
+
+Not because Plato gave him one
+that he couldn't do, for some
+
+completely different reason.
+
+But this is the meaning of a
+continuous function, and by
+
+getting that meaning which took
+hundreds of years to see.
+
+And it takes some time to get
+these two different things, to
+
+get the logic straight.
+
+If x is close to a, then f
+of x is close to f of a.
+
+That's what this means, f
+of x approaching f of a.
+
+That's what Socrates and Plato
+together had to explain.
+
+OK, thank you.
+
+ANNOUNCER: This has been
+a production of MIT
+
+OpenCourseWare and
+Gilbert Strang.
+
+Funding for this video was
+provided by the Lord
+
+Foundation.
+
+To help OCW continue to provide
+free and open access
+
+to MIT courses, please
+make a donation at
+
+ocw.mit.edu/donate.
\ No newline at end of file
diff --git a/kUN6rJ21Hno.txt b/kUN6rJ21Hno.txt
new file mode 100644
index 0000000000000000000000000000000000000000..04f349bc60d11265337224f215dbb8879a4a527a
--- /dev/null
+++ b/kUN6rJ21Hno.txt
@@ -0,0 +1,4317 @@
+The following
+content is provided
+
+under a Creative
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue
+
+to offer high quality
+educational resources for free.
+
+To make a donation or
+view additional materials
+
+from hundreds of MIT courses,
+visit MIT OpenCourseWare
+
+at ocw.mit.edu.
+
+PROFESSOR: All right.
+
+We should probably get started.
+
+So RNA plays important
+regulatory and catalytic roles
+
+in biology, and so it's
+important to understand
+
+its function.
+
+And so that's going to be the
+main theme of today's lecture.
+
+But before we get
+to that, I wanted
+
+to briefly review what
+we went over last time.
+
+So we talked about hidden
+Markov models, some
+
+of the terminology, thinking
+of them as generative models,
+
+terminology of the different
+types of parameters,
+
+the initiation probabilities
+and transition probabilities
+
+and so forth.
+
+And Viterbi algorithm, just
+sort of the core algorithm
+
+used whenever you apply HMMs.
+
+Essentially, you always
+use the Viterbi algorithm.
+
+And then we gave as an
+example the CpG Island HMM,
+
+which is admittedly a
+bit of a toy example.
+
+It's not really
+used in practice,
+
+that illustrates the principles.
+
+And then today we're going
+to talk about a couple
+
+of real world HMMs.
+
+But before we get
+to that, I just
+
+wanted to-- sort
+of toward the end,
+
+we talked about the
+computational complexity
+
+of the algorithm, and concluded
+that if you have a case state
+
+HMM run on a sequence of length
+L, it's order k squared L.
+
+And this diagram is helpful
+to many people in sort
+
+of thinking about that.
+
+So you can have transitions
+from any state--
+
+for example, from this state--
+to any of the other five
+
+states, and there's
+five-state HMM.
+
+And when you're
+doing the Viterbi,
+
+you have to maximize over the
+five possible input transitions
+
+into each state.
+
+And so the full
+set of computations
+
+that you have to do from going
+from position i to i plus 1
+
+is k squared.
+
+Does that make sense?
+
+And then there's L different
+transitions you have to do,
+
+so it's k squared L.
+
+Any questions about that?
+
+OK.
+
+All right and, so the example
+that we gave is shown here.
+
+And what we did was to take an
+example sort of where you could
+
+sort of see the answer--
+not immediately see it,
+
+but if we're thinking about it
+a little, figure out the answer.
+
+And then we talked about how
+the Viterbi algorithm actually
+
+works, and why it makes the
+transitions at the right place.
+
+It seems to intuitively like it
+would make a transition later,
+
+but actually transitions
+at the right place.
+
+And one way to
+think about that is
+
+that these are not hard and
+fast decisions because you're
+
+optimizing two different paths.
+
+At every state, you're
+considering two possibilities.
+
+And so you explore the
+possibility of-- the first time
+
+you hit a c, you explore the
+possibility of transitioning
+
+from genome to
+island, but you're not
+
+confirming whether you're going
+to do that yet until you get
+
+to the end and see whether that
+path ends up having a higher
+
+probability at the end of the
+sequence than the alternative.
+
+So that's sort of one way
+of thinking about that.
+
+Any questions about
+this sort of thing,
+
+how to understand when a
+transition will be made?
+
+And I want to emphasize,
+for this simple HMM,
+
+we talked about
+you can kind of see
+
+what the answer's going to be.
+
+But if you have any HMM, any
+sort of interesting real world
+
+HMM with multiple
+states, there's
+
+no way you're going
+to be able to see it.
+
+Maybe you could guess
+what the answer might be,
+
+but you're not going to be able
+to be confident of what that
+
+is, which is why you have
+to actually implement it.
+
+All right, good.
+
+Let's talk about a couple
+of real world HMMs.
+
+So I mentioned gene finding.
+
+That's been a popular
+application of HMMs,
+
+both in prokaryotes
+and eukaryotes.
+
+There's some examples
+discussed in the text.
+
+Another very popular application
+are so-called profile HMMs.
+
+And so this is a
+hidden Markov model
+
+that's made based on a multiple
+alignment of proteins which
+
+have a related function
+or share a common domain.
+
+For example, there's
+a database called
+
+Pfam, which includes
+profile HMMs for hundreds
+
+of different types
+of protein domains.
+
+And so once you have many
+dozens or hundreds or thousands
+
+of examples of a
+protein domain, you
+
+can learn lots of
+things about it--
+
+not just what the
+frequencies of each residue
+
+are in each position,
+but how likely
+
+you are to have an
+insertion at each position.
+
+And if you do have
+an insertion, what
+
+types of amino acid residues
+are likely to be inserted
+
+in that position,
+and how often you
+
+are likely to have a
+deletion at each position
+
+in the multiple alignment.
+
+And so the challenge then
+is to take a query protein
+
+and to thread it through all
+of these profile HMMs and ask,
+
+does it have a significant
+match to any of them?
+
+And so that's basically
+how Pfam works.
+
+And the nice thing about
+HMMs is that they allow you
+
+to-- if you want to have
+the same probability
+
+of an insertion at each position
+in your multiple alignment,
+
+you can do that.
+
+But if you have enough data
+to observe that there's
+
+a five-fold higher likelihood of
+having an insertion at position
+
+three in a multiple alignment
+than there is at position two,
+
+you can put that in.
+
+You just change
+those probabilities.
+
+So in this HMM, each
+of the hidden states
+
+is either an M state, which is
+a match state, or an I state,
+
+or an insert state.
+
+And so those will emit
+actual amino acid residues.
+
+Or it could be a
+delete state, which
+
+is thought of as emitting
+a dash, a placeholder
+
+in the multiple alignment.
+
+So these are also widely used.
+
+And then one of my favorite
+examples-- it's fairly simple,
+
+but it turns out to
+be quite useful--
+
+is the so-called
+TMHMM for prediction
+
+of transmembrane
+helices in protein.
+
+So we know that many,
+especially eukaryotic proteins,
+
+are embedded in membranes.
+
+And there's one famous family
+of seven transmembrane helix
+
+proteins, and there
+are others that
+
+have one or a few
+transmembrane helices.
+
+And knowing that a protein
+has at least one transmembrane
+
+helix is very useful in terms
+of predicting its function.
+
+You predict it's localization.
+
+And knowing that it's a seven
+transmembrane helix protein
+
+is also useful.
+
+And so you want to predict
+whether the protein has
+
+transmembrane helices and
+what their orientation is.
+
+That is, proteins can
+have their end terminus
+
+either inside the cell
+or outside the cell.
+
+And then of course, where
+exactly those helices are.
+
+And this program has
+about a 97% accuracy,
+
+according to [? the author. ?]
+So it works very well.
+
+So what properties
+do you think--
+
+we said before that
+you have to have
+
+strongly different
+emission probabilities
+
+in the different hidden states
+to have a chance of being
+
+able to predict
+things accurately.
+
+So what properties do
+you think are captured
+
+in a model of
+transmembrane helices?
+
+What types of
+emission probabilities
+
+would you when you have for the
+different states in this model?
+
+Anyone?
+
+So for this protein,
+what kind of residues
+
+would you have in here?
+
+Oops, sorry.
+
+I'm having trouble
+with this thing.
+
+All right, here in the
+middle of the membrane,
+
+what kind of residues are
+you going to see there?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Those are
+going to be hydrophobic.
+
+Exactly.
+
+And what about right
+where the helix emerges
+
+from the membrane?
+
+[INAUDIBLE] charge residue's
+there to kind of anchor
+
+it and prevent it from
+sliding back into membrane.
+
+And then in general, both on
+the exterior and interior,
+
+you'll tend to have more
+hydrophilic residues.
+
+So that's sort of
+the basis of TMHMM.
+
+So this is the structure.
+
+And you'll notice that these are
+not exactly the hidden states
+
+that correspond to individual
+amino acid residues.
+
+These are like meta
+states, just to illustrate
+
+the overall structure.
+
+I'll show you the actual
+states on the next slide.
+
+But these were the
+types of states
+
+that the author, Anders
+[? Crow ?], decided to model.
+
+So he has sort of a-- focuses
+here on the helix core.
+
+There's also a cytoplasmic
+cap and a non-cytoplasmic cap.
+
+Oops, didn't mean that.
+
+And then there's sort of a
+globular domain on each side--
+
+both on the cytoplasmic
+side, or you
+
+could have one on the
+non-cytoplasmic side.
+
+OK, so there's going to be
+different compositions in each
+
+of these regions.
+
+Now one of the things we
+talked about with HMMs
+
+is that if you were-- now let's
+think about the helix core.
+
+The simplest model
+you might think of
+
+would be to have sort
+of a helix state,
+
+and then to allow that
+state to recur to itself.
+
+OK, so this type of thing where
+you then have some transition
+
+to some sort of cap state
+after, this would allow you
+
+to model helices of any length.
+
+But now how long are
+transmembrane helices?
+
+What does that
+distribution look like?
+
+Anyone have an idea?
+
+There's a certain
+physical dimension.
+
+[INAUDIBLE]
+
+It takes a certain number
+residues to get across here,
+
+and then that number
+is about 20-ish.
+
+So transmembrane helices
+tend to be sort of
+
+on the order of 20
+plus or minus a few.
+
+And so it's totally unrealistic
+to have a transmembrane helix
+
+that's, like, five
+residues long.
+
+So if you run this algorithm
+in generative mode,
+
+what distribution of helix
+lengths will you produce?
+
+We're running in
+generative mode where
+
+we're going to let,
+remember, to generate
+
+a series of hidden
+states and then
+
+associated amino acid sequences.
+
+It's coming from some,
+let's say-- I don't know.
+
+What kind of states are there
+here? [INAUDIBLE] plasmic.
+
+Let's say goes into
+helix, hangs out here.
+
+I'm sorry, is there an
+answer to this question?
+
+Anyone?
+
+I don't know how
+long-- if I let it run,
+
+it'll generate a random number.
+
+It depends on what this
+probability is here.
+
+Let's call this probability
+p, and then this
+
+would be 1 minus p.
+
+OK, so obviously if
+1 minus p is bigger,
+
+it'll tend to produce
+longer helices.
+
+But in general,
+what is the shape
+
+of the distribution there of
+consecutive helical states
+
+that this model will generate?
+
+AUDIENCE: Binomial.
+
+PROFESSOR: Binomial.
+
+OK, can you explain why?
+
+AUDIENCE: Because
+the helix would
+
+have to have probable--
+the helix of length n
+
+would occur 1 minus
+p to the n power.
+
+PROFESSOR: OK, so a helix of
+length 10 with a probability
+
+of then, say, let's call it L,
+for the length of the helix,
+
+equals n is 1 minus
+p to the n, right?
+
+Is that binomial?
+
+Someone else?
+
+AUDIENCE: Yeah.
+
+Is it a negative binomial?
+
+PROFESSOR: Negative binomial.
+
+OK.
+
+AUDIENCE: [INAUDIBLE] states and
+a helix state before moving out
+
+[INAUDIBLE].
+
+PROFESSOR: Yeah.
+
+So the distribution is
+going to be like that.
+
+You have to stay in here
+for n and then leave.
+
+So this is the
+simplest-- you can
+
+have special cases of binomial
+and negative binomial.
+
+But in general,
+this distribution
+
+is called the
+geometric distribution.
+
+Or a continuous version would
+be the exponential distribution.
+
+So what is the shape
+of this distribution?
+
+If I were to plot n down here on
+this axis, and the probability
+
+that L equals n on this
+axis, what kind of shape--
+
+could someone draw in the air?
+
+So you had up and then down?
+
+OK, so actually, it's
+going to be just down.
+
+Like that, right?
+
+Because as n increases,
+this goes down
+
+because 1 minus
+p is less than 1.
+
+So it just steadily goes down.
+
+And what is the mean
+of this distribution?
+
+Anyone remember this?
+
+Yeah, so there's sort
+of two versions of this
+
+that you'll see.
+
+One of them is the 1 minus p
+n minus 1 p, and one of them
+
+is this.
+
+And so this is the number of
+failures before a success,
+
+if you will.
+
+Successes lead to the helix.
+
+And this is the number of
+trials till the first success.
+
+So one of them has
+a mean that's 1/p,
+
+and the other has a mean
+that's 1 minus p over p.
+
+So usually, p is small, and
+so those are about the same.
+
+So 1/p.
+
+You could think that
+1/p is roughly right.
+
+And so if we were to model
+transmembrane helices,
+
+and if transmembrane
+heresies are about--
+
+I said about 20
+residues long-- you
+
+would set p to what value
+to get the right mean?
+
+AUDIENCE: 0.05.
+
+PROFESSOR: Yeah.
+
+0.05.
+
+1/20, so that 1 over that
+will be about 20, right?
+
+And then 1 minus p
+would, of course, be 0.9.
+
+So if I were to do that,
+I would get a distribution
+
+that looks about like
+this with a mean of 20.
+
+But if I were to then look
+at real transmembrane helices
+
+and look at their
+distribution, I
+
+would see something
+totally different.
+
+It would probably
+look like that.
+
+It would have a mean around 20.
+
+But the probability of anything
+less than 15 would be 0.
+
+That's too short.
+
+It can't go across the membrane.
+
+And then again, you don't
+have ones that are 40.
+
+They don't kind of wiggle around
+in there and then come out.
+
+They tend to just
+go straight across.
+
+So there's a problem here.
+
+You can see that if you want
+to make a more accurate model,
+
+you want to not only get the
+right emission probabilities
+
+with the right probabilities of
+hydrophobics and hydrophilics
+
+and the different
+states, but you also
+
+want to get the length right.
+
+And so the trick that--
+well, actually, yeah.
+
+Can anyone think of tricks
+to get the right length
+
+distribution here?
+
+How do we do better than this?
+
+Basically, hidden
+Markov models where
+
+you have a state that
+will recur to itself,
+
+it will always be a
+geometric distribution.
+
+The only choice you have is
+what is that probability.
+
+And so you can get
+any mean you want,
+
+but you always get this shape.
+
+So if you want a
+more general shape,
+
+what are some tricks
+that you could do?
+
+How could you change the model?
+
+any ideas?
+
+Yeah, go ahead.
+
+AUDIENCE: [INAUDIBLE] have
+multiple helix states.
+
+PROFESSOR: Multiple
+helix states.
+
+OK.
+
+How many?
+
+AUDIENCE: Proportional to the
+length we want, [INAUDIBLE].
+
+PROFESSOR: Like one for
+each possible length.
+
+AUDIENCE: It'd be
+less than one length.
+
+PROFESSOR: Or less than one.
+
+OK.
+
+So you could have
+something like-- I mean,
+
+let's say you have like this.
+
+Helix begin-- or,
+helix 1, helix 2.
+
+You allow each of these
+to recur to themselves.
+
+What does that get you?
+
+This actually gets you
+something a little bit better.
+
+It gives you a little bit
+about of-- it's more like that.
+
+So that's better.
+
+But if I want to get the exact
+distribution, then actually
+
+one-- so this is the solution
+that the authors actually used.
+
+They made essentially 25
+different helix states,
+
+and then they allowed various
+different transitions here.
+
+So it's a larger
+arbitrary here, but they
+
+have this special state three
+that can kind of take a jump.
+
+So it can just
+continue on to four,
+
+and that'll make your
+maximum length helix core.
+
+Or it can skip one, go
+to five, and that'll
+
+make a helix core that's one
+residue shorter than that,
+
+or it can skip
+two, and so forth.
+
+And you can set
+any probabilities
+
+you want on these transitions.
+
+As so you can fit basically
+an arbitrary distribution
+
+within a fixed range
+of lengths that's
+
+determined by how
+many states you have.
+
+OK, so they really wanted to get
+the length distribution right,
+
+and that's what they did.
+
+What's the cost of this?
+
+What's the downside?
+
+Simona?
+
+AUDIENCE: I was
+just going to ask,
+
+it looks like from
+this your minimum helix
+
+length could be four.
+
+PROFESSOR: Yeah.
+
+That's a good question.
+
+Well, we don't know what
+the probabilities-- they say
+
+said on that.
+
+Well, did they really mean that?
+
+And also, that's only the core,
+and maybe these cap things
+
+can be-- yeah, that seems
+a little short to me.
+
+So yeah, I agree.
+
+I'm not sure.
+
+It could just be for the
+sake of illustration,
+
+but they don't
+actually use those.
+
+But anyway, I'll probably
+have to read the paper.
+
+I haven't read this
+paper for many years
+
+so I don't remember
+exactly the answer to that.
+
+But I have a citation.
+
+You can look it up
+if you're curious.
+
+But the main point I
+wanted to make with this
+
+is just that by setting an
+arbitrary number of states
+
+and putting in possible
+transitions between them,
+
+you can actually construct
+any length of distribution
+
+you want.
+
+But there is a downside,
+and what is that downside?
+
+AUDIENCE: Computational cost.
+
+PROFESSOR: Yeah, the
+computational cost.
+
+Instead of having
+one helix state,
+
+now we've got 25 or something.
+
+So and the time goes up by the
+square of the number of states,
+
+so it's going to run slower.
+
+And you also have to estimate
+all these parameters.
+
+OK, so here's an example
+of the output of the TMHMM
+
+program for a mouse
+chloride channel gene, CLC6.
+
+So the program
+predicts that there
+
+are seven transmembrane
+helices, as shown
+
+by these little red blocks here.
+
+You can see they're all about
+the same-- about 20 or so--
+
+and that the program starts
+outside and ends inside.
+
+So let's say you were going
+to do some experiments
+
+on this protein to
+test this prediction.
+
+So one of the types of
+experiments people do
+
+is they put some
+sort of modifiable
+
+or modified residue
+into one of the spaces
+
+between the
+transmembrane helices.
+
+And then you can test,
+by modifying this cell
+
+with something that's a
+non-permeable chemical,
+
+can you modify that protein?
+
+So only if that stretches
+on the outside of the cell
+
+will you be able to predict it.
+
+So that's a way of
+testing the topology.
+
+So if you were doing those
+types of experiments,
+
+you might actually-- like
+maybe you're not sure
+
+if every transmembrane
+helix is correct.
+
+There could be some
+where the boundaries were
+
+a little off, or
+even a wrong helix.
+
+And so one of the
+things that you often
+
+want with a
+prediction is not only
+
+to know what is the optimal
+or most likely prediction,
+
+but also how confident
+is the algorithm in each
+
+of the parts of its prediction.
+
+How confident is it in the
+location of transmembrane helix
+
+three or the probability
+that actually there
+
+is a transmembrane helix three.
+
+And so the way that this program
+does that is using something
+
+called the
+forward-backward algorithm.
+
+So those of you who read
+the Rabener tutorial,
+
+it's described
+pretty well there.
+
+The basic idea is
+that I mentioned
+
+that this Po-- the probability
+of the observable sequence
+
+summing over all
+possible HMM structures
+
+or all possible sequences
+of hidden states--
+
+that is possible to calculate.
+
+And the way that
+you do it is you
+
+run an algorithm that's
+similar to the Viterbi,
+
+but instead of taking
+the maximum entering
+
+each hidden state at
+intermediate positions,
+
+you sum those inputs.
+
+So you just do the
+sum at every point.
+
+And it turns out that will
+calculate the sum of the two
+
+values at the end-- or
+the k values at the end
+
+will be equal to the sum of
+the probabilities of generating
+
+the observable sequence
+over all possible sequences
+
+of hidden states.
+
+OK, so that's useful.
+
+And then you can also
+run it backwards.
+
+There's no reason it has to be
+only going in one direction.
+
+And so what you do is you run
+these sort of summing versions
+
+of the Viterbi in both
+the forward direction
+
+and also run one in
+the backward direction.
+
+And then you take a
+particular position here--
+
+like let's say this is your
+helix state, for example.
+
+And we're interested
+in this position
+
+somewhere in the
+middle of the protein.
+
+Is that a helix or not?
+
+And so basically
+you take the value
+
+that you get here
+from the forward
+
+in your forward
+algorithm and the value
+
+that you get here in
+the backward algorithm,
+
+and multiply those two
+together, and divide by this Po.
+
+And that gives you
+the probability.
+
+So that ends up being
+a way of calculating
+
+the sum of all
+the parses that go
+
+through this particular
+position i in the sequence
+
+in that particular state.
+
+I mean, I realize that may
+not have been totally clear,
+
+and I don't want to take more
+time to totally go into it,
+
+but it is pretty well
+described and Rabener.
+
+And I'll just give
+you an example.
+
+So if you're motivated,
+please take a look at that.
+
+And if you have
+further questions,
+
+I'd be happy to discuss
+during office hours next week.
+
+And this is what it looks like
+for this particular protein.
+
+So you get something called the
+posterior probability, which
+
+is the sum of the probabilities
+of all the parses.
+
+And they've plotted it for
+the particular state that
+
+is in the Viterbi path, that
+is in the optimal parse--
+
+so for example, in blue here.
+
+Well, actually, they've done
+it for all the different states
+
+here.
+
+So blue is the probability
+that you're outside.
+
+OK, so it's very, very
+confident that the end terminus
+
+of the protein is
+outside the cell.
+
+It's very, very confident
+in the locations
+
+of transmembrane
+helices one and two.
+
+It actually more
+often than not thinks
+
+there's actually a
+third helix right here,
+
+but that didn't make it
+in the optional parse.
+
+That actually occurs in
+the majority of parses,
+
+but not in the optimal.
+
+And it's probably because it
+would then cause other things
+
+to be flipped later on if you
+had transmembrane helix there.
+
+It's not sure whether
+there's a helix there or not,
+
+but then it's
+confident in this one.
+
+OK, so this gives you an idea.
+
+Now if you wanted to do some
+sort of test of the prediction,
+
+you want to test probably
+first the higher confidence
+
+predictions, so you might
+do something right here.
+
+Or if maybe from
+experience you know
+
+that when it has a
+probability that's that high,
+
+it's always right, so
+there's no point testing it.
+
+So you should test one of these
+kind of less confident regions.
+
+So this actually makes the
+prediction much more useful
+
+to have some degree
+of confidence assigned
+
+to each part of the prediction.
+
+So for the remainder
+of today, I want
+
+to turn to the topic of
+RNA secondary structure.
+
+So at the beginning,
+I will sort of
+
+get through some nomenclature.
+
+And then to motivate the topic,
+give some biological examples
+
+of RNA structure.
+
+Gives me an excuse to show some
+pretty pictures of structure.
+
+And then we'll talk about
+two approaches which
+
+are two of the most widely used
+approaches toward predicting
+
+structure.
+
+So using evolution
+to predict structure
+
+by method of co-variations,
+which works well when you
+
+have many homologous sequences.
+
+And then using sort
+of first principles
+
+thermodynamics to predict
+secondary structure
+
+by energy minimization
+where obviously you
+
+don't need to have a
+homologous sequence present.
+
+And the nature
+biotechnology primer
+
+on RNA folding
+that I recommended
+
+is a good intro to the
+energy minimization approach.
+
+So what is RNA
+secondary structure?
+
+So you all know that
+RNAs, like proteins,
+
+have a three-dimensional
+tertiary fold structure that,
+
+in many cases, determines
+their function.
+
+But there's also sort of
+a simpler representation
+
+of this structure where you just
+describe which pairs of bases
+
+are hydrogen bonded
+to one other.
+
+OK, and so for RNA-- so
+it's a famous example
+
+of an RNA structure, this
+sort of clover leaf structure
+
+that all tRNAs have.
+
+The secondary structure of the
+tRNA is the set of base pairs.
+
+So it's this base pair
+here between the first base
+
+and this one toward
+the end, and then
+
+base right here, and so forth.
+
+And so if you specify
+all those base pairs,
+
+then you can then draw a picture
+like this, which gives you
+
+a good idea of what parts of
+the RNA molecule are accessible.
+
+So for example,
+it won't tell you
+
+where the anticodon
+loop is, which
+
+is sort of the business
+end of the tRNA.
+
+But it narrows it down
+to three possibilities.
+
+You might consider that,
+or that, or down here.
+
+It's unlikely to be
+something in here
+
+because these bases
+are already paired.
+
+They can't pair to message.
+
+So it gives you sort of a first
+approximation toward the 3D
+
+structure, and so
+it's quite useful.
+
+So how do we represent
+secondary structure?
+
+So there's a few different
+common representations
+
+that you'll see.
+
+So one is-- and this is sort
+of a computer-friendly but not
+
+terribly human-friendly
+representation,
+
+I would say-- is
+this sort of dot
+
+in parentheses notation here.
+
+So the dot is an unpaired
+base and the parenthesis
+
+is a paired base.
+
+And how do you know-- chalk
+is sort of non-uniformly
+
+distributed here-- so if you
+have a structure like this
+
+and you have these
+three parentheses, what
+
+are they paired to?
+
+Well, you don't know yet
+until you get further down.
+
+And then each left
+parenthesis has
+
+to have a right
+parenthesis somewhere.
+
+So now if we see
+this, then we know
+
+that there are two
+unpaired bases here,
+
+and then there's
+going to be three
+
+in a row that are
+paired-- these guys.
+
+We don't know what
+they're paired to yet.
+
+Then there's going to be a
+five base pair loop, maybe
+
+a little pentagon type thing.
+
+Two, three, four--
+oops-- four, five.
+
+And this one would be
+the right parentheses
+
+that pair with the left
+parentheses over here.
+
+I should probably
+draw this coming out
+
+to make it clearer
+that it's not paired.
+
+So this notation you
+can convert to this.
+
+So after a while, it's
+relatively easy to do this,
+
+except when they're super long.
+
+So that's what the left part
+of that would look like.
+
+So what about the right part?
+
+So the right part, we have
+something like one, two, three,
+
+four, bunch of dots, and then
+we have two, and then a dot,
+
+and then two.
+
+What does that thing look like?
+
+So that's going to look like
+four bases here in a stem.
+
+Big loop, and then there's
+going to be two bases that
+
+are paired, and then
+a bulge, and then
+
+two more that are paired.
+
+These things happen
+in real structures.
+
+OK and then the
+arced notation is
+
+a little more human-friendly.
+
+It actually draws an
+arc between each pair
+
+of bases that are
+hydrogen bonded.
+
+So I'm sure you can imagine
+what those structures would
+
+look like.
+
+And it turns out that the
+arcs are very important.
+
+Like whether those
+arcs cross each other
+
+or not is sort of a fundamental
+classification of RNA
+
+secondary structures, into
+the ones that are tractable
+
+and the ones that
+are really difficult.
+
+So pretty pictures of RNA.
+
+So this is a lower
+resolution cryo-EM structure
+
+of the bacterial ribosomes.
+
+Remember, ribosomes have two
+sub-units-- a large sub-unit,
+
+50S, and a small sub-unit, 30S.
+
+And if you crack it open--
+OK, so you basically split.
+
+You sort of break the ribosome
+like that, and you look inside,
+
+they're full of tRNAs.
+
+So there are three
+pockets that are normally
+
+distinguished within ribosomes.
+
+The A site-- this
+is the site where
+
+the tRNA enters
+that's going to add
+
+a new amino acid to the
+growing peptide chain.
+
+The P site, which is
+this tRNA will have it
+
+[INAUDIBLE] with the
+actual growing peptide.
+
+And then the exit tunnel where
+this tRNA will eventually--
+
+the exit, the E site,
+which is the one that
+
+was added a couple
+of residues ago.
+
+So people often think
+of RNA structure
+
+just in terms of these
+secondary structures
+
+because they're much
+easier to generate
+
+than tertiary structures, and
+they give you-- like for tRNA,
+
+it gives you some pretty good
+information about how it works.
+
+But for a large and complex
+structure like the ribosome,
+
+it turns out that
+RNA is actually not
+
+bad at building
+complex structures.
+
+I would say it's not
+as good as protein,
+
+but it is capable of
+constructing something
+
+like a long tube.
+
+And in fact, in
+the ribosome, you
+
+find such a long
+tube right here.
+
+That is where the peptide
+that's been synthesized
+
+exits the ribosome.
+
+And you'll notice it's not
+a large cavity in which
+
+the protein might start folding.
+
+It's a skinny tube that is thin
+enough that the polypeptide has
+
+to remain linear, cannot
+start folding back on itself.
+
+So you sort of
+extrude the protein
+
+in a linear, unfolded
+confirmation,
+
+and let it fold outside
+of the ribosome.
+
+If it could fold inside
+that, that might clog it up.
+
+That's probably one reason why
+it's not designed that way.
+
+I'm sure that was tried
+bye evolution and rejected.
+
+So if you look at the
+ribosome-- now remember,
+
+the ribosome is composed
+of both RNA and protein--
+
+you'll see that it's much
+more of one than the other.
+
+And so it's really much more
+of the fettuccine, which
+
+is the RNA part, than the
+linguini of the protein.
+
+And if you also look
+at the distribution
+
+of the proteins on
+the ribosome, you'll
+
+see that they're
+not in the core.
+
+They're kind of decorated
+around the edges.
+
+It really looks like something
+that was originally made out
+
+of RNA, and then you sort of
+added proteins as accessories
+
+later.
+
+And that's probably
+what happened.
+
+This is based on
+the structures that
+
+were solved a few years ago.
+
+If you then look at where
+the nearest proteins are
+
+to the active site-- actual
+catalytic site-- remember,
+
+the ribosome catalyzes peptide
+in addition to an amino acid
+
+to a growing peptide, so
+peptide bond formation--
+
+you'll find that the
+nearest proteins are around
+
+18 to 20 angstroms away.
+
+And this is too far
+to do any chemistry,
+
+so the active site
+residues or molecules
+
+need to be within
+a few angstroms
+
+to do any useful chemistry.
+
+And so this basically
+proves that the ribosome.
+
+Is a ribozyme.
+
+That is, it's an RNA enzyme.
+
+RNAs is [INAUDIBLE].
+
+So here is the
+structure of a ribosome.
+
+It's very kind of beautiful,
+and it's impressive
+
+that somebody can actually
+solve the structure of something
+
+this big.
+
+But what is actually
+the practical use
+
+of this structure?
+
+Turns out there's quite an
+important practical application
+
+of knowing the structure.
+
+Any ideas?
+
+AUDIENCE: Antibiotics.
+
+PROFESSOR: Antibiotics.
+
+Exactly.
+
+So many antibiotics work by
+taking advantage of differences
+
+between the prokaryotic
+ribosome structure
+
+and eukaryotic
+ribosome structure.
+
+So if you can make
+a small molecule--
+
+these are some examples--
+that will inhibit
+
+prokaryotic ribosomes
+but hopefully not
+
+inhibit eukaryotic
+ribosome, then
+
+you can kill bacteria that
+might be infecting you.
+
+So non-coding RNA.
+
+So there's many different
+families of non-coding RNAs,
+
+and I'm going to list
+some in a moment.
+
+And I'm going to
+actually challenge
+
+you, see if you can
+come up with any more
+
+families of non-coding RNAs.
+
+But they're receiving
+increasing interest,
+
+I would say, ever since
+micro RNA's were discovered.
+
+Sort of a boom in looking
+at different types
+
+of non-coding RNAs.
+
+Link RNA is also important and
+interesting, as well as many
+
+of the classical RNA's like
+tRNAs and rRNAs and snoRNAs.
+
+There may be new aspects of
+their regulation and function
+
+that will be interesting.
+
+And so when you're
+studying a non RNA,
+
+it's very, very helpful
+to know its structure.
+
+If it's going to base pair in
+trans with some other RNA--
+
+as tRNAs do, as micro RNA's
+do, for example, or snRNAs
+
+and snoRNAs-- then
+you want to know
+
+which parts of the
+molecule are free
+
+and which are
+internally based paired.
+
+And if you want to predict
+non RNAs genes in a genome,
+
+you may want to look
+for regions that
+
+are under selection for
+conservation of RNA structure,
+
+for conservation
+of the potential
+
+to base pair at some distance.
+
+If you see that,
+it's much more likely
+
+that that region of the genome
+encodes a non-coding RNA
+
+than it codes, for example--
+there's a coding axon
+
+or that it's a
+transcription factor binding
+
+site or something like that
+that functions at the DNA level.
+
+So having this
+notion of structure--
+
+even just secondary structure--
+is helpful for that application
+
+as well, and predicting
+functions as well,
+
+as I mentioned.
+
+So co-variation.
+
+So let's take a look
+at these sequences.
+
+So imagine you've discovered a
+new class of mini micro RNA's.
+
+They're only eight bases
+long, and you've sequence five
+
+homologues from your
+five favorite mammals.
+
+And these are the
+sequences that you get.
+
+And you know that
+they're homologous
+
+by [? a centimeter ?],
+they're in the same place
+
+in the genome, and they seem
+to have the same function.
+
+What could you say about
+their secondary structure
+
+based on this
+multiple alignment?
+
+You have to stare at it a
+little bit to see the pattern.
+
+There's a pattern here.
+
+Any ideas?
+
+Anyone have a guess about
+what the structure is?
+
+Yeah, go ahead.
+
+AUDIENCE: There's a two
+base pair stem, and then
+
+a four base loop.
+
+PROFESSOR: Two base pair
+stem, four base loop,
+
+and you have of the stem.
+
+So how do you know that?
+
+AUDIENCE: So if you
+look at the first two
+
+and last two bases
+of each sequence,
+
+the first and the
+eighths nucleotide
+
+can pair with each other, and so
+can the second and the seventh.
+
+PROFESSOR: Yeah.
+
+Everyone see that?
+
+So in the first
+column you have AUACG,
+
+and that's
+complementary to UAUGC.
+
+Each base is complementary.
+
+And the second position is
+CAGGU complementary to GUCUA.
+
+There's one slight
+exception there.
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Yeah.
+
+Well, it turns out that that
+RNA-- although the Watson Crick
+
+pairs GC and AU are the
+most stable-- GU pairs
+
+are only a little bit
+less stable than AU pairs,
+
+and they occur in
+natural RNA molecules.
+
+So GU is allowed in RNA
+even though you would never
+
+see that in DNA.
+
+OK, so everyone see that?
+
+So the structure is--
+I think I have it here.
+
+This would be co-variation
+You're changing the bases,
+
+but preserving the
+ability to pair.
+
+So when one base change-- when
+the first base changes from A
+
+to U, the last base
+changes from U to A
+
+in order to preserve
+that pairing.
+
+You wouldn't know that if
+you just had two sequences,
+
+but once you get
+several sequences,
+
+it can be pretty
+compelling and allow
+
+you to make a pretty
+strong inference that that
+
+is the structure
+of that molecule.
+
+So how would you do this?
+
+So imagine you had a more
+realistic example where
+
+you've got a non-coding RNA
+that's 100 or a few hundred
+
+bases long, and you might have
+a multiple alignment of 50
+
+homologous sequences.
+
+You want something,
+you're not going
+
+to be able to see it by eye.
+
+You need sort of a more
+objective criterion.
+
+So one method
+that's commonly used
+
+is this statistic IX
+mutual information.
+
+So if you look in your
+multiple alignment--
+
+I'll just draw this here.
+
+You have many sequences.
+
+You consider every
+pair of columns--
+
+this is a multiple alignment,
+so this column and this column--
+
+and you calculate
+what we're going
+
+to call-- what are we
+going to call it? f ix.
+
+That would be the frequency
+of a nucleotide x.
+
+You're in column i, so you just
+count how many A's, C's, G's,
+
+and T's there are.
+
+And similarly, f jy for
+all the possible values
+
+of x and all the
+possible values of y.
+
+So these are the base
+frequencies in each column.
+
+And then you calculate the
+dinucleotide frequencies xy
+
+at each pair of columns.
+
+So in this colony, you say if
+there's an A here and a C here,
+
+and then there's
+another AC down here,
+
+and there's a total of one,
+two, three, four, five, six,
+
+seven sequences,
+then f AC ij is 2/7.
+
+So you just calculate the
+frequency of each dinucleotide.
+
+These are no longer consecutive
+dinucleotides in a sequence
+
+necessarily there.
+
+They can be in
+arbitrary spacing.
+
+OK, so you calculate
+those and then
+
+you throw them
+into this formula,
+
+and out comes a number.
+
+So what does this
+formula remind of?
+
+Have you seen a
+similar formula before?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Someone said
+[INAUDIBLE] Yeah, go ahead.
+
+AUDIENCE: It reminds me of the
+Shannon entropy [INAUDIBLE].
+
+PROFESSOR: Yeah, it looks
+like Shannon entropy,
+
+but there's a log
+of a ratio in there,
+
+so it's not exactly
+Shannon entropy.
+
+So what other formula has
+a log of a ratio in it?
+
+AUDIENCE: [INAUDIBLE]
+
+PROFESSOR: Relative.
+
+So it actually looks
+like relative entropy.
+
+So relative entropy
+of what versus what?
+
+Who can sort of say more
+precisely if it's-- we'll say
+
+it's relative entropy of
+something versus a p versus q.
+
+And what is p and what is q?
+
+Yeah, in the back.
+
+AUDIENCE: Is it relative
+entropy of co-occurrence
+
+versus independent occurrence?
+
+PROFESSOR: Good.
+
+Yeah. co-occurence--
+everyone get that?
+
+Co-occurrence of a pair of
+nucleotide xy at positions ij.
+
+Versus q is an
+independent occurrence.
+
+So if x and y occurred
+independently,
+
+they would have this frequency.
+
+So if you think about it,
+you calculate the frequency
+
+of each base at each column
+in the multiple alignment.
+
+And this is like
+your null hypothesis.
+
+You're going to assume, what if
+they're evolving independently?
+
+So if it's not a folded
+RNA-- or if it's a folded RNA
+
+but those two columns
+don't happen to interact--
+
+there's no reason to suspect
+that those bases would
+
+have any relationship
+to each other.
+
+So this is like
+your expected value
+
+of the frequency of
+xy in position ij.
+
+And then this p is
+your observed value.
+
+So you're taking relative
+entropy of basically observed
+
+over expected.
+
+And so relative entropy
+has-- I haven't proved this,
+
+but it's non-negative.
+
+It can be 0, and then it
+goes up to some maximum,
+
+a positive value, but
+it's never negative.
+
+And what would it be if,
+in fact, p were equal to q?
+
+What would this formula give?
+
+This is where we're
+saying suppose.
+
+Suppose this.
+
+In general, this won't
+be sure, but suppose
+
+it was equal to that.
+
+We've got mi ij equals
+summation of what?
+
+That log of this,
+which is equal to this,
+
+so it's fx i fy j
+over the same thing--
+
+hope you can see that-- log
+of-- log of 1 is 0, right?
+
+So it's just 0.
+
+So if the nucleotides
+of the two columns
+
+occur completely independently,
+mutual information is 0.
+
+And that's one reason it's
+called mutual information.
+
+There's no information.
+
+Knowing what's in
+column i gives you
+
+no information about column j.
+
+So remember, relative entities
+are measures of information,
+
+not entropy.
+
+And what is the maximum value
+that the mutual information
+
+could have?
+
+Any ideas on that?
+
+Any guesses?
+
+Joe, yeah.
+
+AUDIENCE: You could have
+log base 2 log over f sub x,
+
+f sub y.
+
+PROFESSOR: Of 1?
+
+OK, so you're saying if one of
+the particular dinucleotides
+
+had a frequency of 1?
+
+AUDIENCE: Yeah.
+
+So if they're always the same
+whenever there's-- like an A,
+
+there's always going to be a T.
+
+PROFESSOR: Right.
+
+So whenever there's an A,
+there's always a G or a T.
+
+AUDIENCE: So then you'd
+get a 1 in the numerator,
+
+and they're relative
+probably in the bottom, which
+
+would be maximized if
+they were all even.
+
+PROFESSOR: If they were all?
+
+[INTERPOSING VOICES]
+
+PROFESSOR: If they were uniform.
+
+Yeah.
+
+So did everyone get that?
+
+So the maximum occurs if fx i
+and j-- they're both uniform,
+
+so they're a quarter for
+every base at both positions.
+
+That's the maximum entropy in
+the background distribution.
+
+But then if fx y ij equals
+1/4, for example, x equals y--
+
+or in our case, we're
+not interested in that.
+
+We're interested in x
+equals complement of y.
+
+C of y is going to be
+the complement of y.
+
+And 0 otherwise for x not
+equal complement of y.
+
+OK, so for example, if we have
+only the dinucleotides AT,
+
+CG, GC, and TA occur,
+and each of them
+
+occurs with a
+frequency of 1/4, then
+
+you'll have four terms in
+the sum because, remember,
+
+the 0 log 0 is 0.
+
+So you'll have four terms
+in the sum, and each of them
+
+will look like 1/4 log
+1/4 over a 1/4 times 1/4.
+
+And so this will be 4,
+so log 2 of 4 4 is 2.
+
+And so you have four terms
+that are each 1/4 times 2.
+
+And so you'll get 2.
+
+Well, this is not a sum.
+
+These are the four terms.
+
+These are the individual
+nonzero terms in that sum.
+
+Does that make sense?
+
+Everyone get this?
+
+So that's why this is a useful
+measure of co-variation.
+
+If what's in one
+column really strongly
+
+influences what's
+in the other column,
+
+and there's a lot of
+variation in the two columns,
+
+and so you can really see
+that co-variation well,
+
+then mutual information
+is maximized.
+
+And that's basically
+what we just said,
+
+is written down here.
+
+So it's maximal.
+
+They don't have to
+be complementary.
+
+It would achieve this maximum
+of 2 if they are complementary,
+
+but it would be also if they
+had some other very specific
+
+relationship between
+the nucleotides.
+
+So if you're going to use
+this, the way you would use it
+
+is take your multiple
+alignment, calculate
+
+the mutual information
+of each pair of columns--
+
+so you actually have to
+make a table, i versus j,
+
+all possible pairs
+of columns-- and then
+
+you're going to look for
+the really high values.
+
+And then when you find
+those high values, when
+
+you look at what actual bases
+are tending to occur together,
+
+you'll want to see
+that they're bases
+
+that are complementary
+to one another.
+
+And another thing
+that you'd want to see
+
+is you'd want to see that
+consecutive positions in one
+
+part of the alignment
+are co-varying
+
+with consecutive positions in
+another part of the alignment
+
+in the right way, in this sort
+of inverse complementary way
+
+that RNA likes to pair.
+
+Does that make sense?
+
+So in a sort of nested way
+in your multiple alignment,
+
+if you saw that this
+one co-varied with that,
+
+and then you also saw that
+the next base co-varied
+
+with the base right
+before this one,
+
+and this one co-varies
+with that one,
+
+that starts to look like a stem.
+
+It's much more likely that
+you have a three-base stem
+
+than that you just
+have some isolated base
+
+pair out in the
+middle of nowhere.
+
+It turns out it takes
+a few bases to make
+
+a good thermodynamically
+stable stem,
+
+and so you want to look
+for blocks of these things.
+
+And so this works pretty well.
+
+Yeah, actually, one point
+I want to make first
+
+is that mutual
+information is nice
+
+because it's kind
+of a useful concept
+
+and it also relates to some
+of the entropy and relative
+
+entropy that we've been talking
+about in the course before.
+
+But it's not the only statistic
+that would work in practice.
+
+You can use any measure of
+basically non-independence
+
+between distributions.
+
+A chi square statistic
+would probably
+
+work equally well in practice.
+
+And so here is a
+multiple alignment
+
+of a bunch of sequences.
+
+And what I've done is
+put boxes around columns
+
+that have significant
+
+mutual information with
+other sets of columns.
+
+So for example, this set of
+columns here at the left-- the
+
+far left-- has significant
+mutual information
+
+with the ones at the far right.
+
+And these ones,
+these four positions
+
+co-vary with these
+four, and so forth.
+
+So can you tell,
+based on looking
+
+at this pattern of
+co-variation, what
+
+the structure is going to be?
+
+OK, let's say we start up here.
+
+The first is going to
+pair with the last,
+
+with something at the end.
+
+Then we're going
+to have something
+
+here in the middle that pairs
+with something else nearby.
+
+Then we have something
+here that pairs
+
+with something else nearby,
+then we have another like that.
+
+Does that make sense?
+
+So that there's these
+three pairs of columns
+
+in the middle-- these two, these
+two, and these two-- and then
+
+they're surrounded
+by this thing,
+
+the first pairing with the last.
+
+And so it's a clover
+leaf, so that's tRNA.
+
+Yeah?
+
+AUDIENCE: So with that previous
+slide, this table here,
+
+you could create a
+co-variation matrix.
+
+How would that-- or,
+and it could be--
+
+PROFESSOR: How does that
+co-variations matrix--
+
+how do you convert it
+to this representations?
+
+AUDIENCE: I'm just wondering
+how this would go up.
+
+Like let's say you took
+the co-variation matrix--
+
+PROFESSOR: Oh, what
+would it look like?
+
+AUDIENCE: --and visualized
+it as a heat map--
+
+PROFESSOR: In the
+co-variation matrix.
+
+AUDIENCE: Yeah.
+
+What would it look like in
+this particular example?
+
+PROFESSOR: Yeah,
+that's a good question.
+
+OK, let's do that.
+
+I haven't thought
+about that before,
+
+so you'll have to
+help me on this.
+
+So here's the beginning.
+
+We're going to write
+the sequence from 1
+
+to n in both dimensions.
+
+And so here's the beginning,
+and it co-varies with the end.
+
+So this first would have a
+co-variation with the last,
+
+and then the second would
+co-vary with the second
+
+to last, and so forth.
+
+So you get a little
+diagonal down here.
+
+That's this top stem here.
+
+And then what about
+the second stem?
+
+So then you have
+something down here
+
+that's going to co-vary with
+something kind of near by it.
+
+So block two is going to
+co-vary with block three.
+
+And again, it's going to be
+this inverse complementary kind
+
+of thing like that.
+
+It's symmetrical, so
+you get this with that.
+
+But you only have
+to do one half,
+
+so you can just do
+this upper half here.
+
+So you get that.
+
+So it would look
+something like that.
+
+AUDIENCE: So with the
+diagonal line orthogonal
+
+to the diagonal of the matrix--
+
+PROFESSOR: Yeah, that's because
+they're inverse complementary.
+
+AUDIENCE: OK.
+
+PROFESSOR: That make sense?
+
+Good question.
+
+But we'll see an
+example like that later
+
+actually, as it turns out.
+
+All right, so here's
+my question for you.
+
+You're setting this
+non-coding RNA.
+
+It has some length.
+
+You have some
+number of sequences.
+
+They might have some structure.
+
+Is this method going to
+work for you, or is it not?
+
+What is required for it to work?
+
+For example, would
+I want to isolate
+
+this gene-- this
+non-coding RNA gene--
+
+just from primates, from
+like human, gorilla,
+
+chimp, orangutan, and
+do that alignment?
+
+Or would I want to go further?
+
+Would I want to go back to
+the rodents and dog, horse--
+
+how far do you want to go?
+
+Yeah, question.
+
+AUDIENCE: I think we a need a
+very strong sequence alignment
+
+for this, so we
+cannot go very far,
+
+because if you don't have
+a high percentage homology,
+
+then you will see all
+sorts of false positives.
+
+PROFESSOR: Absolutely.
+
+So if you go too far, your
+alignment will suffer,
+
+and you need an
+alignment in order
+
+to identify the
+corresponding columns.
+
+So that puts an upper limit
+on how far you can go.
+
+But excellent point.
+
+Is there a lower limit?
+
+Do you want to go as
+close as possible,
+
+like this example I gave
+with human, chimp, orangutan?
+
+Or is that too close?
+
+Why is too close bad?
+
+Tim?
+
+AUDIENCE: Maybe if
+you're too close,
+
+then the sequence is
+having to [INAUDIBLE]
+
+to give you enough
+information [INAUDIBLE].
+
+PROFESSOR: Yeah, exactly.
+
+They're all the same.
+
+Actually, you'll
+get 1 times 1 over 1
+
+in that mutual information
+statistic, which log of that
+
+is going to be 0.
+
+There's zero mutual information
+if they're all the same.
+
+So there has to
+be some variation,
+
+and the structure
+has to be conserved.
+
+That's key.
+
+You have to assume that the
+structure is well conserved
+
+and you have to have
+a good alignment
+
+and there has to
+be some variation,
+
+a certain amount of variation.
+
+Those are basically
+the three keys.
+
+Secondary structure has a more
+highly conserved sequence.
+
+Sufficient divergence so that
+you have these variations,
+
+and sufficient number of
+homologues you have to get good
+
+statistics, and not so far
+they your alignment is bad.
+
+Sorry about that.
+
+Sally?
+
+AUDIENCE: It seems
+like another thing
+
+that we assume here is that
+you can project it onto a plane
+
+and it will lie flat.
+
+So if you have some very
+important, weird folding
+
+that allows you to, say,
+crisscross the rainbow thing.
+
+PROFESSOR: Yeah,
+crisscross the rainbow.
+
+Yeah, very good question.
+
+So in the example
+of tRNA, if you
+
+were to do that arc
+diagram for tRNA,
+
+it would look like
+another big arc--
+
+that's the first and
+last-- and then you
+
+have these three nested arcs.
+
+Nothing crisscrossing.
+
+What if I saw-- [INAUDIBLE]--
+two blocks of sequence that
+
+have a relationship like that?
+
+Is that OK?
+
+With this method, the
+co-variation, that's OK.
+
+There's no problem there.
+
+What does this
+structure look like?
+
+So [INAUDIBLE] you have a
+stem, then you have a loop,
+
+and then a stem.
+
+So this is 1 pairs with 3.
+
+That's 1.
+
+That's 3.
+
+Then you've got 2 up
+here, but 2 pairs with 4.
+
+So here's 4 over
+here, so 4 is going
+
+to have to come back up
+here and pair with 2.
+
+This is 2 over here.
+
+So that is called a pseudoknot.
+
+It's not really a knot
+because this thing doesn't
+
+go through the
+loop, but it kind of
+
+behaves like a
+knot in some ways.
+
+And so do these actually
+occur in natural RNAs?
+
+Yes, Tim is nodding.
+
+And are they important?
+
+Can you give me an example
+where they are important
+
+biologically?
+
+AUDIENCE: [INAUDIBLE]
+
+[INTERPOSING VOICES]
+
+PROFESSOR: Riboswitches.
+
+We're going to come
+to what riboswitches
+
+are in a moment for
+those not familiar.
+
+And I think I have
+an example later
+
+of a pseudoknot
+that's important.
+
+So that's a good question.
+
+I think I should have added
+to this list the point
+
+that you made in
+the back that they
+
+have to be close enough that
+you can get a good alignment.
+
+I should add that to this last.
+
+Thanks.
+
+It's a good point.
+
+All right, so classes
+of non-coding RNAs.
+
+As promised, my
+favorites listed here.
+
+Everyone knows tRNAs, rRNAs.
+
+You can think of UTRs
+as being non RNAs.
+
+They often have
+structure that can
+
+be involved in
+regulating the message.
+
+snRNAs involved splicing.
+
+snoRNAs-- small
+nucleolar RNAs-- are
+
+involved in directing
+modification
+
+of other RNAs, such as ribosomal
+RNAs and snRNAs, for example.
+
+Terminators of
+transcription in prokaryotes
+
+are like little stem
+loop structures.
+
+RNaseP is an important enzyme.
+
+SRP is involved in targeting
+proteins with signal peptides
+
+to the export machinery.
+
+We won't go into tmRNA.
+
+micro RNAs and link
+RNAs, you probably
+
+know, and riboswitches.
+
+So Tim, can you tell us
+what a riboswitch is?
+
+AUDIENCE: A riboswitch
+is any RNA structure
+
+that changes
+confirmation according
+
+to some stimulus [INAUDIBLE]
+or something in the cell.
+
+It could be an ion, critical
+changes in the structure.
+
+[INAUDIBLE]
+
+PROFESSOR: Yeah, that was great.
+
+So just for those that
+may not have heard,
+
+I'll just say it again.
+
+So a riboswitch is
+any RNA that can
+
+have multiple confirmations,
+and changes confirmation
+
+in response to some stimulus--
+temperature, binding
+
+of some ligand, small molecules,
+something like that, et cetera.
+
+And often, one of
+those structures
+
+will block a particular
+regulatory element.
+
+I'll show an
+example in a moment.
+
+And so when it's in
+one confirmation,
+
+the gene will be repressed.
+
+And when it's in
+the other, it'll
+
+be on. so it's a way of using
+RNA's secondary structure
+
+to sense what's
+going on in the cell
+
+and to appropriately
+regulate gene expression.
+
+All right, so now we're going
+to talk about a second approach.
+
+So this would be the approach.
+
+You've got some RNA.
+
+It may not do something,
+and maybe you can't find any
+
+homologues.
+
+It might be some newly
+evolved species-specific RNA,
+
+or your studying
+some obscure species
+
+where you don't have a lot
+of genomic sequence around.
+
+So you want to use the
+first principles, approach,
+
+the energy
+minimization approach.
+
+Or maybe you have
+the homologues,
+
+but you don't trust
+your alignment.
+
+You want a second
+opinion on what
+
+the structure is going to be.
+
+So just in the way
+that protein folding--
+
+you could think of
+an equilibrium model
+
+where it's determined
+by folding free energy,
+
+and enthalpy will
+favor base pairing.
+
+You get gain some enthalpy
+when you form a hydrogen bond,
+
+and entropy will tend
+to favor unfolding.
+
+So an RNA molecule
+that's linear has
+
+all this confirmational
+flexibility,
+
+and lose some of that
+when you form a stem.
+
+It forms a helix.
+
+Those things don't have
+as much flexibility.
+
+And even the nucleotides in
+the loop are a little bit
+
+confirmationally--
+they're not as flexible
+
+as they were when it was linear.
+
+So that means that
+at high temperatures,
+
+it'll favor unfolding.
+
+So the earliest
+approaches were approaches
+
+that sought to maximize
+the number of base pairs.
+
+So they basically ignore entropy
+and focus on the enthalpy
+
+that you gain from
+forming base pairs.
+
+And so Ruth Nussinov
+described the first algorithm
+
+to figure out what is the
+maximum number of base pairs
+
+that you can form in an RNA.
+
+And so a way to
+think about this is
+
+imagine you've
+got this sequence.
+
+What is the largest
+number of base pairs
+
+I can form with this sequence?
+
+I could just draw all
+possible base pairs.
+
+That A can pair with that T.
+This A can pair with that T.
+
+They can't both pair
+simultaneously, right?
+
+And this C can pair with that G.
+So if we don't allow crossing,
+
+which-- coming back
+to Sally's point--
+
+this would cross this, right?
+
+So we're not going
+to allow that.
+
+So the best you could do be to
+have this A pair with this C
+
+and this C pair with this G
+and form this little structure.
+
+This is not realistic because
+RNA loops can't be one base.
+
+They minimum is about three.
+
+But just for the
+sake of argument,
+
+you can list all these
+out, but imagine now
+
+you've got 100 bases here.
+
+Every base will on
+average potentially
+
+be able to pair with
+24 or 25 other bases.
+
+So you're just going to have
+just an incredible mishmash
+
+of possible lines
+all crisscrossing.
+
+So how do you figure out how
+to maximize that pairing?
+
+Any ideas?
+
+Don, yeah?
+
+AUDIENCE: You look for
+sections of homology.
+
+PROFESSOR: We're
+not using homology.
+
+We're doing [INAUDIBLE]
+
+AUDIENCE: I'm sorry, not
+homology, but sections where--
+
+PROFESSOR: Complementary?
+
+AUDIENCE: Complementary.
+
+Yeah, that's the
+word I was thinking.
+
+PROFESSOR: The blocks
+are complementary.
+
+AUDIENCE: And then so--
+
+PROFESSOR: You could blast
+the sequence against inverse
+
+complements itself and
+look for little blocks.
+
+You could do that.
+
+That's not what
+people generally do,
+
+mostly because the blocks of
+complementarity in real RNA
+
+structures are really short.
+
+They can be two,
+three, four, bases.
+
+Sally, yeah?
+
+AUDIENCE: Could you use
+[INAUDIBLE] approach
+
+where you just start with a
+very small case and build up?
+
+PROFESSOR: So we've seen that
+work for protein sequence
+
+alignment.
+
+We've seen it work for
+the Viterbi algorithm.
+
+So that is sort of the go-to
+approach in bioinfomatics,
+
+is to use some sort of
+dynamic programming.
+
+Now this one for RNA
+secondary structure
+
+that Nussinov came up
+with is a little bit
+
+different than the others.
+
+So you'll see it has a
+kind of different flavor.
+
+It turns out to be
+actually it's a little hard
+
+to get your head around
+at the beginning,
+
+but it's actually
+easier to do by hand.
+
+So let's take a look at that.
+
+OK, so recursive
+maximization of base pairing.
+
+Now the thing about
+base pairing that's
+
+different from
+these other problems
+
+is that the first
+base in the sequence
+
+can base pair with the last.
+
+How do you chop up a sequence?
+
+Remember with Needleman-Wunsch
+and with Viterbi
+
+we go from the
+beginning to the end,
+
+and that's a logical order.
+
+But with base pairing, that's
+actually not a logical order.
+
+You can't really do it that way.
+
+So instead, you go
+from the inside out.
+
+You start in the
+middle of a sequence
+
+and work your way outwards
+in both directions.
+
+Or another way to think about
+it is you start with you write
+
+the sequence from 1
+to n on both axes,
+
+and then actually we'll see that
+we initiate the diagonal all
+
+to 0's.
+
+And then we think about
+these positions here next.
+
+So 1 versus 2.
+
+Could 1 pair with 2?
+
+And could 2 pair with 3?
+
+Those are like little
+bits of possible RNA
+
+secondary structure.
+
+Again, we're ignoring
+this fact that loops
+
+have to be certain minimum.
+
+This is sort of a
+simplified case.
+
+And then you build outwards.
+
+So you conclude that base 4
+here could pair with base 5,
+
+so we're going to put a 1 there.
+
+And then we're going
+to build outward
+
+from that toward the
+beginning of the sequence
+
+and toward the end, adding
+additional base pairs
+
+when we can.
+
+That's basically the way
+the [INAUDIBLE] works.
+
+And so that's one
+key idea, that we
+
+go from sort of
+close sequences, work
+
+outward, to faraway sequences.
+
+And the second key idea
+is that the relationship
+
+that, as you add more bases
+on the outside of what you've
+
+already got, that the optimal
+structure in that larger
+
+portion of sequence
+space is related
+
+to the optimal structures
+of smaller portions of it
+
+in one of four different ways.
+
+And these are the four ways.
+
+So let's look at these.
+
+So the first one is
+probably the simplest
+
+where if you're doing this,
+you're here somewhere,
+
+meaning you've compared
+sequences from position,
+
+let's say, i minus
+1 to j minus 1 here.
+
+And then we're going to
+consider adding-- actually,
+
+it depends how you
+number your sequence.
+
+Let me see how this is done.
+
+Sorry. i plus 1.
+
+i plus 1 to j minus 1.
+
+We figured out what the
+optimal structure is in here,
+
+let's suppose.
+
+And now we're going to
+consider adding one more
+
+base on either end.
+
+We're going to add j
+down here, and we're
+
+going to ask if it pairs with i.
+
+And if so, we're going to take
+whatever the optimal structure
+
+was in here and we're
+going to add one base pair,
+
+and we're going to
+add plus 1 because now
+
+it's got one additional.
+
+We're counting base pairs.
+
+So that's that first case there.
+
+And then the second case is
+you could also consider just
+
+adding one unpaired base onto
+whatever structure you had,
+
+and then you don't add one.
+
+And you could go in
+either direction.
+
+You can go sort of toward of
+the beginning of the sequence
+
+or toward the end
+of the sequence.
+
+And then the third
+one is the tricky one,
+
+is what's called a bifurcation.
+
+You could consider
+that actually i and j
+
+are both paired, but
+not with each other.
+
+That i pairs with something
+that was inside here
+
+and j pairs with something
+that was inside here.
+
+So your optimal parse
+from i to j, if you will,
+
+is not going to come from the
+optimal parse from i plus 1
+
+to j minus 1.
+
+It's going to come from
+rethinking this and doing
+
+the optimal parse from here
+to here and from here to here,
+
+and combining those two.
+
+So you're probably
+confused by now,
+
+so let me try to do an example.
+
+And then I have an analogy
+that will confuse you further.
+
+So ask me for that one.
+
+This was the simplest
+one I could come up
+
+with that has this property.
+
+OK, so we said before that
+if you were doing the optimal
+
+from 1 to 5, that it would be
+the AC pairing with the GT.
+
+We do that one.
+
+And now if you notice, this guy
+is kind of a similar sequence.
+
+I just added a T at the
+beginning and an A at the end.
+
+And so you can probably imagine
+that the best structure of this
+
+is here, those three.
+
+You've got three pairs of
+this sub-sequence here.
+
+That's as good as you
+can do with seven bases.
+
+You can only get three pairs.
+
+And this is as good as
+you can do with five,
+
+so these are clearly optimal.
+
+So the issue comes that if
+you're starting from somewhere
+
+in the middle here-- let's
+say you are-- let's see,
+
+so how would you be doing this?
+
+You start here.
+
+Let's suppose the first two
+you consider are these two.
+
+You consider pairing
+that T with that A.
+
+You can see this is
+not going to go well.
+
+You might end up with that
+as your optimal substructure
+
+of this region.
+
+Remember, you're working
+from the inside out,
+
+so you're going from here to
+here, and you end up with that.
+
+And what do you do here?
+
+You don't have a G
+to pair the C to,
+
+so you add another
+unpaired base.
+
+Now you've got this
+optimal substructure
+
+of a sequence that's
+almost the whole sequence.
+
+It's just missing the
+first and last bases,
+
+but it only has
+three base pairs.
+
+So when you go to add
+this, you can say,
+
+oh, I can't add any more base
+pairs, so I've only got three.
+
+But you should consider
+that we've already
+
+solved the optimal
+structure of that,
+
+and we had two nice pairs here.
+
+We had that pair and
+that pair, and we already
+
+solved the substructure
+of the optimal structure
+
+of this portion here, and
+you had those three pairs.
+
+And so you can combine those
+two and all of a sudden
+
+you can do much better.
+
+So that's what that
+bifurcation thing is about.
+
+So this is the
+recursion working out,
+
+and you can see that's
+the base pairing one.
+
+You can add one, or you can
+just add an unpaired base
+
+and you don't add anything.
+
+Or you consider all
+the possible locations
+
+of bifurcations in-between the
+two positions you're adding,
+
+i and j, and you consider
+all the possible pairs.
+
+And you just sum up each
+pair and go-- I'm sorry,
+
+you don't sum them up.
+
+You consider them all, and
+then you take the maximum.
+
+All right, so the algorithm
+is to take an n by n matrix,
+
+initialize the diagonal to 0,
+and initialize the sub-diagonal
+
+to 0 also.
+
+Just don't think
+too much about that.
+
+Just do it.
+
+And then fill in this
+matrix recursively
+
+from the diagonal
+up and to the right.
+
+And it actually doesn't matter
+what order you fill it in
+
+as long as you're kind
+of working your way up
+
+into the right.
+
+You have to have the thing
+to the left and the thing
+
+below already filled in if
+you're going to fill in a box.
+
+And then you keep track of
+the optimal score, which
+
+is going to be the
+sum of base pairs.
+
+And then you also keep
+track of how you got there.
+
+What base pair did you add
+so that you can trace back?
+
+And then when you get
+up to the upper right
+
+corner of this matrix,
+you then trace back.
+
+So here is a partially
+filled in this matrix.
+
+This is from that the
+Nature Biotechnology Review.
+
+And the 0's are filled in.
+
+So here's what I want
+you to do at home,
+
+is print out, photocopy or
+whatever-- make this matrix,
+
+or make a bigger
+version of it perhaps--
+
+and look at the sequence
+and fill in this matrix,
+
+and fill in the little arrows
+every time you add a base pair.
+
+It's actually not that hard.
+
+There are no bifurcations in
+this, so that's the tricky one.
+
+Ignore that one.
+
+You'll just be
+adding base pairs.
+
+It'll be pretty easy.
+
+And then you can
+reconstruct the sequence.
+
+So here it is filled in.
+
+And the answer is given,
+so you can check yourself.
+
+But do it without
+looking at the answer.
+
+And then you go to the
+upper right corner.
+
+That means that the
+optimal structure
+
+from the beginning of the
+sequence to the end-- which,
+
+of course, was our
+goal all along.
+
+And then you trace
+back and you can
+
+see whenever you're
+moving diagonally here,
+
+you're adding a base pair.
+
+Remember, you add
+one on each end,
+
+and so you're moving diagonally
+and adding the base pair,
+
+and you get this
+little structure here.
+
+So computational complexity
+of the algorithm.
+
+You could think about this
+but I'll just tell you.
+
+It's memory n squared
+because you've
+
+got to fill in this
+matrix, so square
+
+of the length of the sequence.
+
+Time n cubed.
+
+This is bad now.
+
+And why is it n cubed?
+
+It's n cubed because you have to
+fill in a matrix that's n by n.
+
+And then when you do
+that maximization step,
+
+that check for bifurcations,
+that's sort of of order n,
+
+as well.
+
+So n cubed-- so this means
+that RNA folding is slow.
+
+And in fact, some
+of the servers won't
+
+allow you to fold anything
+more than a thousand
+
+bases because they'll take
+forever or something like that.
+
+And it cannot
+handle pseudoknots.
+
+If you think through
+the recursion,
+
+pseudoknots will be a problem.
+
+I'm going to just
+show you-- yeah,
+
+I'll get to this-- that
+these are from the viruses.
+
+Real viruses, some of
+them have pseudoknots
+
+like these ones shown
+here, and some even
+
+have these kissing loops,
+which is another type where
+
+the two stem loops,
+the loops interact.
+
+And the pseudoknots
+in particular
+
+are important in the
+viral life cycle.
+
+They can actually cause
+programmed ribosomal frame
+
+shifting.
+
+When the ribosomes
+hits one of the things,
+
+normally it just denatures
+RNA secondary structure.
+
+When it hits a
+pseudoknot, it'll actually
+
+get knocked back by
+one and will start
+
+translating in a
+different frame.
+
+And that's actually
+useful to the virus
+
+to do that under
+certain circumstances.
+
+That's how HIV makes the
+replicated polymerase,
+
+is by doing a frame shift on
+the ribosome using a pseudoknot.
+
+So these things are important.
+
+And there's fancier
+methods that use
+
+more sophisticated
+thermodynamic models where
+
+GC counts more than AU.
+
+And I won't go into
+the details, but I just
+
+wanted to show you some
+pretty pictures here
+
+that the Zuker
+algorithm-- this is
+
+a real world RNA folding
+algorithm-- calculates not only
+
+the minimum energy fold,
+but also sub-optimal folds,
+
+and the probabilities of
+particular base pairs,
+
+summing over all the possible
+structures that RNA could form,
+
+weighted by their free energy.
+
+So it's the full
+partition function.
+
+It's not perfectly accurate.
+
+It gets about 70% of
+base pairs correct,
+
+which means it usually
+gets things right,
+
+but occasionally totally wrong.
+
+And there's a website for the
+Mfold server, which is actually
+
+one of the most beautiful
+websites in bioinfomatics,
+
+I would say.
+
+And also if you want
+to run it locally,
+
+you should download the
+Vienna RNAfold package,
+
+which has a very
+similar algorithm.
+
+And I just wanted to show
+you one or two examples.
+
+So this is the U5 snRNA.
+
+This is the output of Mfold.
+
+It predicts this structure.
+
+And then this what's called
+the energy dot plot, which
+
+shows the bases in the optimal
+structure down below here
+
+and then sort of these
+suboptimal structures here.
+
+And you can see
+there's no ambiguity.
+
+It's totally confident
+in this structure.
+
+Then I ran the lysine
+riboswitch through this program,
+
+and I got this.
+
+I got the minimum
+for energy structure
+
+down in the lower left.
+
+And then you see there's a
+lot of other colored dots.
+
+Those are from the
+suboptimal structures.
+
+So it looks like this thing
+has multiple structures, which
+
+of course it does.
+
+So the way that this one works
+is, in the absence of lysine,
+
+it forms this structure
+where the ribosome binding
+
+sequences-- this is
+prokaryotic-- is exposed.
+
+And so the ribosome
+can enter and translate
+
+these lysine
+biosynthetic enzymes.
+
+But then when lysine
+accumulates to a certain level,
+
+it can interact with the
+RNA and shift it's structure
+
+so that you now form
+this stem, which
+
+sequesters the ribosome
+binding sequence
+
+and blocks lysine biosynthesis.
+
+So a very clever system.
+
+And it turns out
+that there's dozens
+
+of these things in
+bacterial genomes,
+
+and they control a
+lot of metabolism.
+
+So they're very important.
+
+And there may be some
+in eukaryotes, too,
+
+and that would be good.
+
+If anyone's looking for
+a product, not happy
+
+with their current
+project, you might
+
+think about looking
+for more riboswitches.
+
+So I'm going to
+have to end there.
+
+And thank you guys
+for your attention,
+
+and good luck on the midterm.
\ No newline at end of file
diff --git a/lE217O9ZGws.txt b/lE217O9ZGws.txt
new file mode 100644
index 0000000000000000000000000000000000000000..249139deebd1b2e7d98f646171bc9c5863b9f56f
--- /dev/null
+++ b/lE217O9ZGws.txt
@@ -0,0 +1,1635 @@
+align:start position:0%
+ 
+during this course when we've had the
+
+ align:start position:0%
+during this course when we've had the
+ 
+
+ align:start position:0%
+during this course when we've had the
+need to plot a map we use the code that
+
+ align:start position:0%
+need to plot a map we use the code that
+ 
+
+ align:start position:0%
+need to plot a map we use the code that
+is provided by default by R uh but there
+
+ align:start position:0%
+is provided by default by R uh but there
+ 
+
+ align:start position:0%
+is provided by default by R uh but there
+are other ways to plot maps and make
+
+ align:start position:0%
+are other ways to plot maps and make
+ 
+
+ align:start position:0%
+are other ways to plot maps and make
+them easy to be tuned according on our
+
+ align:start position:0%
+them easy to be tuned according on our
+ 
+
+ align:start position:0%
+them easy to be tuned according on our
+taste so now I'm going to show you how
+
+ align:start position:0%
+taste so now I'm going to show you how
+ 
+
+ align:start position:0%
+taste so now I'm going to show you how
+to display nice map
+
+ align:start position:0%
+to display nice map
+ 
+
+ align:start position:0%
+to display nice map
+um that are easy to tune using ggplot
+
+ align:start position:0%
+um that are easy to tune using ggplot
+ 
+
+ align:start position:0%
+um that are easy to tune using ggplot
+and to do that I'm going to charge the
+
+ align:start position:0%
+and to do that I'm going to charge the
+ 
+
+ align:start position:0%
+and to do that I'm going to charge the
+map that we've been using our friend
+
+ align:start position:0%
+map that we've been using our friend
+ 
+
+ align:start position:0%
+map that we've been using our friend
+this temperature map um also to make the
+
+ align:start position:0%
+this temperature map um also to make the
+ 
+
+ align:start position:0%
+this temperature map um also to make the
+process easier or faster for R I'm going
+
+ align:start position:0%
+process easier or faster for R I'm going
+ 
+
+ align:start position:0%
+process easier or faster for R I'm going
+to aggregate this map to make it coarser
+
+ align:start position:0%
+to aggregate this map to make it coarser
+ 
+
+ align:start position:0%
+to aggregate this map to make it coarser
+uh in this case I'm going to use a
+
+ align:start position:0%
+uh in this case I'm going to use a
+ 
+
+ align:start position:0%
+uh in this case I'm going to use a
+factor of five so it means that from
+
+ align:start position:0%
+factor of five so it means that from
+ 
+
+ align:start position:0%
+factor of five so it means that from
+each five pixels I'm just creating one
+
+ align:start position:0%
+each five pixels I'm just creating one
+ 
+
+ align:start position:0%
+each five pixels I'm just creating one
+uh that's going to affect it's going to
+
+ align:start position:0%
+uh that's going to affect it's going to
+ 
+
+ align:start position:0%
+uh that's going to affect it's going to
+affect the result in this case it's
+
+ align:start position:0%
+affect the result in this case it's
+ 
+
+ align:start position:0%
+affect the result in this case it's
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+make the image to be um less defined but
+
+ align:start position:0%
+make the image to be um less defined but
+ 
+
+ align:start position:0%
+make the image to be um less defined but
+this is just because we aggregated the
+
+ align:start position:0%
+this is just because we aggregated the
+ 
+
+ align:start position:0%
+this is just because we aggregated the
+data and we also need to transform this
+
+ align:start position:0%
+data and we also need to transform this
+ 
+
+ align:start position:0%
+data and we also need to transform this
+map into a data frame this is a
+
+ align:start position:0%
+map into a data frame this is a
+ 
+
+ align:start position:0%
+map into a data frame this is a
+requirement to be able to plot it with
+
+ align:start position:0%
+requirement to be able to plot it with
+ 
+
+ align:start position:0%
+requirement to be able to plot it with
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+ggplot um so that's what I'm doing here
+
+ align:start position:0%
+ggplot um so that's what I'm doing here
+ 
+
+ align:start position:0%
+ggplot um so that's what I'm doing here
+as data frame by default this command is
+
+ align:start position:0%
+as data frame by default this command is
+ 
+
+ align:start position:0%
+as data frame by default this command is
+not included so this means that when
+
+ align:start position:0%
+not included so this means that when
+ 
+
+ align:start position:0%
+not included so this means that when
+transforming the map into a data frame
+
+ align:start position:0%
+transforming the map into a data frame
+ 
+
+ align:start position:0%
+transforming the map into a data frame
+we are maintaining latitude and
+
+ align:start position:0%
+we are maintaining latitude and
+ 
+
+ align:start position:0%
+we are maintaining latitude and
+longitude as a variable by default this
+
+ align:start position:0%
+longitude as a variable by default this
+ 
+
+ align:start position:0%
+longitude as a variable by default this
+is false so it wouldn't be well I'm just
+
+ align:start position:0%
+is false so it wouldn't be well I'm just
+ 
+
+ align:start position:0%
+is false so it wouldn't be well I'm just
+going to show you how it how it is by
+
+ align:start position:0%
+going to show you how it how it is by
+ 
+
+ align:start position:0%
+going to show you how it how it is by
+default see we only have one variable
+
+ align:start position:0%
+default see we only have one variable
+ 
+
+ align:start position:0%
+default see we only have one variable
+but in this case if we would give this
+
+ align:start position:0%
+but in this case if we would give this
+ 
+
+ align:start position:0%
+but in this case if we would give this
+to ggplot um that wouldn't be able to
+
+ align:start position:0%
+to ggplot um that wouldn't be able to
+ 
+
+ align:start position:0%
+to ggplot um that wouldn't be able to
+provide us a map because X and Y would
+
+ align:start position:0%
+provide us a map because X and Y would
+ 
+
+ align:start position:0%
+provide us a map because X and Y would
+be lacking so we need to include this
+
+ align:start position:0%
+be lacking so we need to include this
+ 
+
+ align:start position:0%
+be lacking so we need to include this
+chunk of code here that's going to give
+
+ align:start position:0%
+chunk of code here that's going to give
+ 
+
+ align:start position:0%
+chunk of code here that's going to give
+us the latitude to longitude ude so now
+
+ align:start position:0%
+us the latitude to longitude ude so now
+ 
+
+ align:start position:0%
+us the latitude to longitude ude so now
+we have three variables instead of one
+
+ align:start position:0%
+we have three variables instead of one
+ 
+
+ align:start position:0%
+we have three variables instead of one
+and if we click on here we have the X
+
+ align:start position:0%
+and if we click on here we have the X
+ 
+
+ align:start position:0%
+and if we click on here we have the X
+the Y and that's the name of the map
+
+ align:start position:0%
+the Y and that's the name of the map
+ 
+
+ align:start position:0%
+the Y and that's the name of the map
+that we've used just because it's very
+
+ align:start position:0%
+that we've used just because it's very
+ 
+
+ align:start position:0%
+that we've used just because it's very
+long and not easy to work with I decided
+
+ align:start position:0%
+long and not easy to work with I decided
+ 
+
+ align:start position:0%
+long and not easy to work with I decided
+to change that name into temp of
+
+ align:start position:0%
+to change that name into temp of
+ 
+
+ align:start position:0%
+to change that name into temp of
+temperature so that's what I'm doing
+
+ align:start position:0%
+temperature so that's what I'm doing
+ 
+
+ align:start position:0%
+temperature so that's what I'm doing
+here and I'm going to charge the
+
+ align:start position:0%
+here and I'm going to charge the
+ 
+
+ align:start position:0%
+here and I'm going to charge the
+packages we're going to need to do this
+
+ align:start position:0%
+packages we're going to need to do this
+ 
+
+ align:start position:0%
+packages we're going to need to do this
+process which is the map tools that is
+
+ align:start position:0%
+process which is the map tools that is
+ 
+
+ align:start position:0%
+process which is the map tools that is
+related to working with maps then we
+
+ align:start position:0%
+related to working with maps then we
+ 
+
+ align:start position:0%
+related to working with maps then we
+have the G plot 2 which um
+
+ align:start position:0%
+have the G plot 2 which um
+ 
+
+ align:start position:0%
+have the G plot 2 which um
+is the main package we're going to be
+
+ align:start position:0%
+is the main package we're going to be
+ 
+
+ align:start position:0%
+is the main package we're going to be
+using here and then we have this bis
+
+ align:start position:0%
+using here and then we have this bis
+ 
+
+ align:start position:0%
+using here and then we have this bis
+that is about the color palette we're
+
+ align:start position:0%
+that is about the color palette we're
+ 
+
+ align:start position:0%
+that is about the color palette we're
+going to use to create the
+
+ align:start position:0%
+going to use to create the
+ 
+
+ align:start position:0%
+going to use to create the
+map and I'm going to also charge this
+
+ align:start position:0%
+map and I'm going to also charge this
+ 
+
+ align:start position:0%
+map and I'm going to also charge this
+map that we've been using which is the
+
+ align:start position:0%
+map that we've been using which is the
+ 
+
+ align:start position:0%
+map that we've been using which is the
+one that separates um the water bodies
+
+ align:start position:0%
+one that separates um the water bodies
+ 
+
+ align:start position:0%
+one that separates um the water bodies
+so it's the shape of the
+
+ align:start position:0%
+so it's the shape of the
+ 
+
+ align:start position:0%
+so it's the shape of the
+ground and this would be the most
+
+ align:start position:0%
+ground and this would be the most
+ 
+
+ align:start position:0%
+ground and this would be the most
+simple code that would give us a map
+
+ align:start position:0%
+simple code that would give us a map
+ 
+
+ align:start position:0%
+simple code that would give us a map
+using ggplot so the this part here would
+
+ align:start position:0%
+using ggplot so the this part here would
+ 
+
+ align:start position:0%
+using ggplot so the this part here would
+not be necessary we could erase it but
+
+ align:start position:0%
+not be necessary we could erase it but
+ 
+
+ align:start position:0%
+not be necessary we could erase it but
+in this case I I am storing this code
+
+ align:start position:0%
+in this case I I am storing this code
+ 
+
+ align:start position:0%
+in this case I I am storing this code
+into this
+
+ align:start position:0%
+into this
+ 
+
+ align:start position:0%
+into this
+object um so I am saying R to r that I'm
+
+ align:start position:0%
+object um so I am saying R to r that I'm
+ 
+
+ align:start position:0%
+object um so I am saying R to r that I'm
+going to be using ggplot and our base
+
+ align:start position:0%
+going to be using ggplot and our base
+ 
+
+ align:start position:0%
+going to be using ggplot and our base
+it's going to be this data frame I'm
+
+ align:start position:0%
+it's going to be this data frame I'm
+ 
+
+ align:start position:0%
+it's going to be this data frame I'm
+going to add a plus I'm going to say to
+
+ align:start position:0%
+going to add a plus I'm going to say to
+ 
+
+ align:start position:0%
+going to add a plus I'm going to say to
+ggplot what do I want
+
+ align:start position:0%
+ggplot what do I want
+ 
+
+ align:start position:0%
+ggplot what do I want
+me why do I want GG plot to provide in
+
+ align:start position:0%
+me why do I want GG plot to provide in
+ 
+
+ align:start position:0%
+me why do I want GG plot to provide in
+this case I want to have a Gom raster so
+
+ align:start position:0%
+this case I want to have a Gom raster so
+ 
+
+ align:start position:0%
+this case I want to have a Gom raster so
+I want gplot to give me a raster based
+
+ align:start position:0%
+I want gplot to give me a raster based
+ 
+
+ align:start position:0%
+I want gplot to give me a raster based
+on this as an X this as a y so we could
+
+ align:start position:0%
+on this as an X this as a y so we could
+ 
+
+ align:start position:0%
+on this as an X this as a y so we could
+we could type it here and it would work
+
+ align:start position:0%
+we could type it here and it would work
+ 
+
+ align:start position:0%
+we could type it here and it would work
+equal way just if x or y would have
+
+ align:start position:0%
+equal way just if x or y would have
+ 
+
+ align:start position:0%
+equal way just if x or y would have
+different names it would have to specify
+
+ align:start position:0%
+different names it would have to specify
+ 
+
+ align:start position:0%
+different names it would have to specify
+these names right here and then in fill
+
+ align:start position:0%
+these names right here and then in fill
+ 
+
+ align:start position:0%
+these names right here and then in fill
+um I want ggplot to fill this X and Y
+
+ align:start position:0%
+um I want ggplot to fill this X and Y
+ 
+
+ align:start position:0%
+um I want ggplot to fill this X and Y
+with the temperature which is the third
+
+ align:start position:0%
+with the temperature which is the third
+ 
+
+ align:start position:0%
+with the temperature which is the third
+column that we have in that data frame
+
+ align:start position:0%
+column that we have in that data frame
+ 
+
+ align:start position:0%
+column that we have in that data frame
+so let's just run this piece of
+
+ align:start position:0%
+so let's just run this piece of
+ 
+
+ align:start position:0%
+so let's just run this piece of
+coat and see how it looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like okay this is clearly not the most
+
+ align:start position:0%
+like okay this is clearly not the most
+ 
+
+ align:start position:0%
+like okay this is clearly not the most
+beautiful plot you could have ever seen
+
+ align:start position:0%
+beautiful plot you could have ever seen
+ 
+
+ align:start position:0%
+beautiful plot you could have ever seen
+so but this is just the basic and we're
+
+ align:start position:0%
+so but this is just the basic and we're
+ 
+
+ align:start position:0%
+so but this is just the basic and we're
+going to keep improving this map line by
+
+ align:start position:0%
+going to keep improving this map line by
+ 
+
+ align:start position:0%
+going to keep improving this map line by
+line so you can see how each piece of
+
+ align:start position:0%
+line so you can see how each piece of
+ 
+
+ align:start position:0%
+line so you can see how each piece of
+code changes the result of the map we're
+
+ align:start position:0%
+code changes the result of the map we're
+ 
+
+ align:start position:0%
+code changes the result of the map we're
+going to
+
+ align:start position:0%
+going to
+ 
+
+ align:start position:0%
+going to
+have um first of all what I want to
+
+ align:start position:0%
+have um first of all what I want to
+ 
+
+ align:start position:0%
+have um first of all what I want to
+include here is the shape of the Earth
+
+ align:start position:0%
+include here is the shape of the Earth
+ 
+
+ align:start position:0%
+include here is the shape of the Earth
+so I want to include that map that we
+
+ align:start position:0%
+so I want to include that map that we
+ 
+
+ align:start position:0%
+so I want to include that map that we
+just uploaded on top of this one um to
+
+ align:start position:0%
+just uploaded on top of this one um to
+ 
+
+ align:start position:0%
+just uploaded on top of this one um to
+make a good differentiation between
+
+ align:start position:0%
+make a good differentiation between
+ 
+
+ align:start position:0%
+make a good differentiation between
+what's what's the C and what's not um so
+
+ align:start position:0%
+what's what's the C and what's not um so
+ 
+
+ align:start position:0%
+what's what's the C and what's not um so
+that's why I included this piece of code
+
+ align:start position:0%
+that's why I included this piece of code
+ 
+
+ align:start position:0%
+that's why I included this piece of code
+here I'm going to erase this plus to
+
+ align:start position:0%
+here I'm going to erase this plus to
+ 
+
+ align:start position:0%
+here I'm going to erase this plus to
+make the code to stop right here and see
+
+ align:start position:0%
+make the code to stop right here and see
+ 
+
+ align:start position:0%
+make the code to stop right here and see
+how that looks
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like okay now we has this we have this
+
+ align:start position:0%
+like okay now we has this we have this
+ 
+
+ align:start position:0%
+like okay now we has this we have this
+nice black line
+
+ align:start position:0%
+nice black line
+ 
+
+ align:start position:0%
+nice black line
+around um but now it turns out that I
+
+ align:start position:0%
+around um but now it turns out that I
+ 
+
+ align:start position:0%
+around um but now it turns out that I
+don't
+
+ align:start position:0%
+don't
+ 
+
+ align:start position:0%
+don't
+want this black shape here and I want to
+
+ align:start position:0%
+want this black shape here and I want to
+ 
+
+ align:start position:0%
+want this black shape here and I want to
+change the color palette so to do that
+
+ align:start position:0%
+change the color palette so to do that
+ 
+
+ align:start position:0%
+change the color palette so to do that
+I'm going to include this piece of coat
+
+ align:start position:0%
+I'm going to include this piece of coat
+ 
+
+ align:start position:0%
+I'm going to include this piece of coat
+as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+well right here and I'm saying that the
+
+ align:start position:0%
+well right here and I'm saying that the
+ 
+
+ align:start position:0%
+well right here and I'm saying that the
+na values are going to be na so I'm
+
+ align:start position:0%
+na values are going to be na so I'm
+ 
+
+ align:start position:0%
+na values are going to be na so I'm
+asking this code not to show me the Naas
+
+ align:start position:0%
+asking this code not to show me the Naas
+ 
+
+ align:start position:0%
+asking this code not to show me the Naas
+so that's going to erase this gray area
+
+ align:start position:0%
+so that's going to erase this gray area
+ 
+
+ align:start position:0%
+so that's going to erase this gray area
+here here also I'm going to change the
+
+ align:start position:0%
+here here also I'm going to change the
+ 
+
+ align:start position:0%
+here here also I'm going to change the
+direction of the color palette meaning
+
+ align:start position:0%
+direction of the color palette meaning
+ 
+
+ align:start position:0%
+direction of the color palette meaning
+that now the the
+
+ align:start position:0%
+that now the the
+ 
+
+ align:start position:0%
+that now the the
+black the black color is related to
+
+ align:start position:0%
+black the black color is related to
+ 
+
+ align:start position:0%
+black the black color is related to
+lower temperatures and I want it the
+
+ align:start position:0%
+lower temperatures and I want it the
+ 
+
+ align:start position:0%
+lower temperatures and I want it the
+other way around and also I am changing
+
+ align:start position:0%
+other way around and also I am changing
+ 
+
+ align:start position:0%
+other way around and also I am changing
+the color palette to have this shape if
+
+ align:start position:0%
+the color palette to have this shape if
+ 
+
+ align:start position:0%
+the color palette to have this shape if
+we go to the help with FN and F1 here we
+
+ align:start position:0%
+we go to the help with FN and F1 here we
+ 
+
+ align:start position:0%
+we go to the help with FN and F1 here we
+see that this the
+
+ align:start position:0%
+see that this the
+ 
+
+ align:start position:0%
+see that this the
+beginning of the help section
+
+ align:start position:0%
+beginning of the help section
+ 
+
+ align:start position:0%
+beginning of the help section
+if we scroll down we get to the
+
+ align:start position:0%
+if we scroll down we get to the
+ 
+
+ align:start position:0%
+if we scroll down we get to the
+different options we have for color
+
+ align:start position:0%
+different options we have for color
+ 
+
+ align:start position:0%
+different options we have for color
+palette these are the different options
+
+ align:start position:0%
+palette these are the different options
+ 
+
+ align:start position:0%
+palette these are the different options
+we have so if instead of this letter
+
+ align:start position:0%
+we have so if instead of this letter
+ 
+
+ align:start position:0%
+we have so if instead of this letter
+here I put an a b or c we would have
+
+ align:start position:0%
+here I put an a b or c we would have
+ 
+
+ align:start position:0%
+here I put an a b or c we would have
+different color palettes as an outcome I
+
+ align:start position:0%
+different color palettes as an outcome I
+ 
+
+ align:start position:0%
+different color palettes as an outcome I
+chose this one just
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because this is how our
+
+ align:start position:0%
+because this is how our
+ 
+
+ align:start position:0%
+because this is how our
+map has
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+changed
+
+ align:start position:0%
+changed
+ 
+
+ align:start position:0%
+changed
+oh I have to run it first of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+course and I have to put a plus because
+
+ align:start position:0%
+course and I have to put a plus because
+ 
+
+ align:start position:0%
+course and I have to put a plus because
+otherwise it wouldn't read this new line
+
+ align:start position:0%
+otherwise it wouldn't read this new line
+ 
+
+ align:start position:0%
+otherwise it wouldn't read this new line
+that I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+added okay I have changed the direction
+
+ align:start position:0%
+added okay I have changed the direction
+ 
+
+ align:start position:0%
+added okay I have changed the direction
+of the color palette as you can see now
+
+ align:start position:0%
+of the color palette as you can see now
+ 
+
+ align:start position:0%
+of the color palette as you can see now
+this gray area around has
+
+ align:start position:0%
+this gray area around has
+ 
+
+ align:start position:0%
+this gray area around has
+disappeared and the color palette also
+
+ align:start position:0%
+disappeared and the color palette also
+ 
+
+ align:start position:0%
+disappeared and the color palette also
+has changed I still want to keep
+
+ align:start position:0%
+has changed I still want to keep
+ 
+
+ align:start position:0%
+has changed I still want to keep
+improving this map because I don't like
+
+ align:start position:0%
+improving this map because I don't like
+ 
+
+ align:start position:0%
+improving this map because I don't like
+this background here that's something
+
+ align:start position:0%
+this background here that's something
+ 
+
+ align:start position:0%
+this background here that's something
+called the theme of the map uh you can
+
+ align:start position:0%
+called the theme of the map uh you can
+ 
+
+ align:start position:0%
+called the theme of the map uh you can
+change the theme um and in this case I
+
+ align:start position:0%
+change the theme um and in this case I
+ 
+
+ align:start position:0%
+change the theme um and in this case I
+want the theme
+
+ align:start position:0%
+want the theme
+ 
+
+ align:start position:0%
+want the theme
+minimal and I also don't like this chunk
+
+ align:start position:0%
+minimal and I also don't like this chunk
+ 
+
+ align:start position:0%
+minimal and I also don't like this chunk
+to be displayed so I decided to reduce
+
+ align:start position:0%
+to be displayed so I decided to reduce
+ 
+
+ align:start position:0%
+to be displayed so I decided to reduce
+the Y limits of the Y AIS and instead of
+
+ align:start position:0%
+the Y limits of the Y AIS and instead of
+ 
+
+ align:start position:0%
+the Y limits of the Y AIS and instead of
+being their total extent I'm just going
+
+ align:start position:0%
+being their total extent I'm just going
+ 
+
+ align:start position:0%
+being their total extent I'm just going
+to cut it at minus 60 so it's going to
+
+ align:start position:0%
+to cut it at minus 60 so it's going to
+ 
+
+ align:start position:0%
+to cut it at minus 60 so it's going to
+be cut somewhere like here um to do so
+
+ align:start position:0%
+be cut somewhere like here um to do so
+ 
+
+ align:start position:0%
+be cut somewhere like here um to do so
+just going to CP them
+
+ align:start position:0%
+just going to CP them
+ 
+
+ align:start position:0%
+just going to CP them
+plus this
+
+ align:start position:0%
+plus this
+ 
+
+ align:start position:0%
+plus this
+out make it nicer and
+
+ align:start position:0%
+out make it nicer and
+ 
+
+ align:start position:0%
+out make it nicer and
+close just run it and see how these
+
+ align:start position:0%
+close just run it and see how these
+ 
+
+ align:start position:0%
+close just run it and see how these
+affect our
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+map okay now we
+
+ align:start position:0%
+map okay now we
+ 
+
+ align:start position:0%
+map okay now we
+changed that great area we had in the
+
+ align:start position:0%
+changed that great area we had in the
+ 
+
+ align:start position:0%
+changed that great area we had in the
+background as well and we are no longer
+
+ align:start position:0%
+background as well and we are no longer
+ 
+
+ align:start position:0%
+background as well and we are no longer
+displaying the southern
+
+ align:start position:0%
+displaying the southern
+ 
+
+ align:start position:0%
+displaying the southern
+latitudes um now I want
+
+ align:start position:0%
+latitudes um now I want
+ 
+
+ align:start position:0%
+latitudes um now I want
+this to
+
+ align:start position:0%
+this to
+ 
+
+ align:start position:0%
+this to
+have a title and I want this to have
+
+ align:start position:0%
+have a title and I want this to have
+ 
+
+ align:start position:0%
+have a title and I want this to have
+also like not display this or
+
+ align:start position:0%
+also like not display this or
+ 
+
+ align:start position:0%
+also like not display this or
+that and I want to change the legend
+
+ align:start position:0%
+that and I want to change the legend
+ 
+
+ align:start position:0%
+that and I want to change the legend
+position instead of being on the right I
+
+ align:start position:0%
+position instead of being on the right I
+ 
+
+ align:start position:0%
+position instead of being on the right I
+want it to be on the left so all these
+
+ align:start position:0%
+want it to be on the left so all these
+ 
+
+ align:start position:0%
+want it to be on the left so all these
+changes are the ones that are
+
+ align:start position:0%
+changes are the ones that are
+ 
+
+ align:start position:0%
+changes are the ones that are
+implemented here this is not displaying
+
+ align:start position:0%
+implemented here this is not displaying
+ 
+
+ align:start position:0%
+implemented here this is not displaying
+X and Y um laps
+
+ align:start position:0%
+X and Y um laps
+ 
+
+ align:start position:0%
+X and Y um laps
+here this is going to be to change the
+
+ align:start position:0%
+here this is going to be to change the
+ 
+
+ align:start position:0%
+here this is going to be to change the
+position of the Legend um this is the
+
+ align:start position:0%
+position of the Legend um this is the
+ 
+
+ align:start position:0%
+position of the Legend um this is the
+title and this is going to
+
+ align:start position:0%
+title and this is going to
+ 
+
+ align:start position:0%
+title and this is going to
+change this here instead of temp I
+
+ align:start position:0%
+change this here instead of temp I
+ 
+
+ align:start position:0%
+change this here instead of temp I
+wanted to explain that it's the jary
+
+ align:start position:0%
+wanted to explain that it's the jary
+ 
+
+ align:start position:0%
+wanted to explain that it's the jary
+temperature so I'm going to include them
+
+ align:start position:0%
+temperature so I'm going to include them
+ 
+
+ align:start position:0%
+temperature so I'm going to include them
+all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is an example of how we
+
+ align:start position:0%
+and this is an example of how we
+ 
+
+ align:start position:0%
+and this is an example of how we
+can create and tune outcomes in a nice
+
+ align:start position:0%
+can create and tune outcomes in a nice
+ 
+
+ align:start position:0%
+can create and tune outcomes in a nice
+way uh so we can use this outcome as a a
+
+ align:start position:0%
+way uh so we can use this outcome as a a
+ 
+
+ align:start position:0%
+way uh so we can use this outcome as a a
+graphic representation in our uh
+
+ align:start position:0%
+graphic representation in our uh
+ 
+
+ align:start position:0%
+graphic representation in our uh
+scientific
+
+ align:start position:0%
+scientific
+ 
+
+ align:start position:0%
+scientific
+projects um okay this looks kind of nice
+
+ align:start position:0%
+projects um okay this looks kind of nice
+ 
+
+ align:start position:0%
+projects um okay this looks kind of nice
+and tidy here but what if we want to
+
+ align:start position:0%
+and tidy here but what if we want to
+ 
+
+ align:start position:0%
+and tidy here but what if we want to
+extract this image and store it in our
+
+ align:start position:0%
+extract this image and store it in our
+ 
+
+ align:start position:0%
+extract this image and store it in our
+computer a nice way to do it is using
+
+ align:start position:0%
+computer a nice way to do it is using
+ 
+
+ align:start position:0%
+computer a nice way to do it is using
+Tif extension uh what I have to do is
+
+ align:start position:0%
+Tif extension uh what I have to do is
+ 
+
+ align:start position:0%
+Tif extension uh what I have to do is
+just to write Tif write the file name
+
+ align:start position:0%
+just to write Tif write the file name
+ 
+
+ align:start position:0%
+just to write Tif write the file name
+where I want to um create or generate um
+
+ align:start position:0%
+where I want to um create or generate um
+ 
+
+ align:start position:0%
+where I want to um create or generate um
+this outcome the how big I want this
+
+ align:start position:0%
+this outcome the how big I want this
+ 
+
+ align:start position:0%
+this outcome the how big I want this
+image to be the resolution by default is
+
+ align:start position:0%
+image to be the resolution by default is
+ 
+
+ align:start position:0%
+image to be the resolution by default is
+100 I just put 200 here to make
+
+ align:start position:0%
+100 I just put 200 here to make
+ 
+
+ align:start position:0%
+100 I just put 200 here to make
+everything appear
+
+ align:start position:0%
+everything appear
+ 
+
+ align:start position:0%
+everything appear
+bigger and then you have to include here
+
+ align:start position:0%
+bigger and then you have to include here
+ 
+
+ align:start position:0%
+bigger and then you have to include here
+what's the object you want to store in
+
+ align:start position:0%
+what's the object you want to store in
+ 
+
+ align:start position:0%
+what's the object you want to store in
+that um object you just created and then
+
+ align:start position:0%
+that um object you just created and then
+ 
+
+ align:start position:0%
+that um object you just created and then
+click
+
+ align:start position:0%
+click
+ 
+
+ align:start position:0%
+click
+on this part which is giving the order
+
+ align:start position:0%
+on this part which is giving the order
+ 
+
+ align:start position:0%
+on this part which is giving the order
+to our to close that file and give it as
+
+ align:start position:0%
+to our to close that file and give it as
+ 
+
+ align:start position:0%
+to our to close that file and give it as
+a as an outcome so you can consult in
+
+ align:start position:0%
+a as an outcome so you can consult in
+ 
+
+ align:start position:0%
+a as an outcome so you can consult in
+your computer and use it um uh at your
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+convenience
\ No newline at end of file
diff --git a/lwhXMAu0SnI.txt b/lwhXMAu0SnI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ffeceda72605fedc36df5c66a45883bc5c12d283
--- /dev/null
+++ b/lwhXMAu0SnI.txt
@@ -0,0 +1,15723 @@
+align:start position:0%
+ 
+okay uh let me go ahead and get started
+
+ align:start position:0%
+okay uh let me go ahead and get started
+ 
+
+ align:start position:0%
+okay uh let me go ahead and get started
+so um uh you know today's topic um is
+
+ align:start position:0%
+so um uh you know today's topic um is
+ 
+
+ align:start position:0%
+so um uh you know today's topic um is
+going to be um entry and you know I
+
+ align:start position:0%
+going to be um entry and you know I
+ 
+
+ align:start position:0%
+going to be um entry and you know I
+think entry is an incredibly important
+
+ align:start position:0%
+think entry is an incredibly important
+ 
+
+ align:start position:0%
+think entry is an incredibly important
+topic in Iowa in fact you like one of
+
+ align:start position:0%
+topic in Iowa in fact you like one of
+ 
+
+ align:start position:0%
+topic in Iowa in fact you like one of
+the messages I'm going to talk about
+
+ align:start position:0%
+the messages I'm going to talk about
+ 
+
+ align:start position:0%
+the messages I'm going to talk about
+today is in some sense just about
+
+ align:start position:0%
+today is in some sense just about
+ 
+
+ align:start position:0%
+today is in some sense just about
+everything we've done in this semester
+
+ align:start position:0%
+everything we've done in this semester
+ 
+
+ align:start position:0%
+everything we've done in this semester
+so far is kind of like rounding error
+
+ align:start position:0%
+so far is kind of like rounding error
+ 
+
+ align:start position:0%
+so far is kind of like rounding error
+compared to what what we do now so um
+
+ align:start position:0%
+compared to what what we do now so um
+ 
+
+ align:start position:0%
+compared to what what we do now so um
+you know how do I think about entry um
+
+ align:start position:0%
+you know how do I think about entry um
+ 
+
+ align:start position:0%
+you know how do I think about entry um
+so you know so far we've talked about a
+
+ align:start position:0%
+so you know so far we've talked about a
+ 
+
+ align:start position:0%
+so you know so far we've talked about a
+lot of models that have uh the number of
+
+ align:start position:0%
+lot of models that have uh the number of
+ 
+
+ align:start position:0%
+lot of models that have uh the number of
+firms fixed and I've talked about lots
+
+ align:start position:0%
+firms fixed and I've talked about lots
+ 
+
+ align:start position:0%
+firms fixed and I've talked about lots
+of things about factors that affect
+
+ align:start position:0%
+of things about factors that affect
+ 
+
+ align:start position:0%
+of things about factors that affect
+pricing with the number of firms fixed
+
+ align:start position:0%
+pricing with the number of firms fixed
+ 
+
+ align:start position:0%
+pricing with the number of firms fixed
+you know Monopoly pricing if you have
+
+ align:start position:0%
+you know Monopoly pricing if you have
+ 
+
+ align:start position:0%
+you know Monopoly pricing if you have
+one firm how does that what what do they
+
+ align:start position:0%
+one firm how does that what what do they
+ 
+
+ align:start position:0%
+one firm how does that what what do they
+do and then you know static competition
+
+ align:start position:0%
+do and then you know static competition
+ 
+
+ align:start position:0%
+do and then you know static competition
+with vertical differentiation or
+
+ align:start position:0%
+with vertical differentiation or
+ 
+
+ align:start position:0%
+with vertical differentiation or
+horizontal differentiation or search
+
+ align:start position:0%
+horizontal differentiation or search
+ 
+
+ align:start position:0%
+horizontal differentiation or search
+costs or other things and it's always
+
+ align:start position:0%
+costs or other things and it's always
+ 
+
+ align:start position:0%
+costs or other things and it's always
+sort of the nature of the market is
+
+ align:start position:0%
+sort of the nature of the market is
+ 
+
+ align:start position:0%
+sort of the nature of the market is
+determining what's the level of markups
+
+ align:start position:0%
+determining what's the level of markups
+ 
+
+ align:start position:0%
+determining what's the level of markups
+and what inefficiencies there might
+
+ align:start position:0%
+and what inefficiencies there might
+ 
+
+ align:start position:0%
+and what inefficiencies there might
+be um but that's all taking Market
+
+ align:start position:0%
+be um but that's all taking Market
+ 
+
+ align:start position:0%
+be um but that's all taking Market
+structure is fixed and so you know
+
+ align:start position:0%
+structure is fixed and so you know
+ 
+
+ align:start position:0%
+structure is fixed and so you know
+starting today I'm going to think about
+
+ align:start position:0%
+starting today I'm going to think about
+ 
+
+ align:start position:0%
+starting today I'm going to think about
+like what happens if you allow the
+
+ align:start position:0%
+like what happens if you allow the
+ 
+
+ align:start position:0%
+like what happens if you allow the
+number of firms to change and so the
+
+ align:start position:0%
+number of firms to change and so the
+ 
+
+ align:start position:0%
+number of firms to change and so the
+simplest way to think about this is
+
+ align:start position:0%
+simplest way to think about this is
+ 
+
+ align:start position:0%
+simplest way to think about this is
+let's look at a two-stage models I'm
+
+ align:start position:0%
+let's look at a two-stage models I'm
+ 
+
+ align:start position:0%
+let's look at a two-stage models I'm
+going to start with the case of
+
+ align:start position:0%
+going to start with the case of
+ 
+
+ align:start position:0%
+going to start with the case of
+homogeneous Goods you can think of this
+
+ align:start position:0%
+homogeneous Goods you can think of this
+ 
+
+ align:start position:0%
+homogeneous Goods you can think of this
+as you know old-fashioned steel plants
+
+ align:start position:0%
+as you know old-fashioned steel plants
+ 
+
+ align:start position:0%
+as you know old-fashioned steel plants
+entering and each producing cold rolled
+
+ align:start position:0%
+entering and each producing cold rolled
+ 
+
+ align:start position:0%
+entering and each producing cold rolled
+steel or aluminum plants or S some
+
+ align:start position:0%
+steel or aluminum plants or S some
+ 
+
+ align:start position:0%
+steel or aluminum plants or S some
+industry that has a small number of
+
+ align:start position:0%
+industry that has a small number of
+ 
+
+ align:start position:0%
+industry that has a small number of
+firms because they're big sort of fixed
+
+ align:start position:0%
+firms because they're big sort of fixed
+ 
+
+ align:start position:0%
+firms because they're big sort of fixed
+cost of setting up plants and then they
+
+ align:start position:0%
+cost of setting up plants and then they
+ 
+
+ align:start position:0%
+cost of setting up plants and then they
+compete with each other so stage one we
+
+ align:start position:0%
+compete with each other so stage one we
+ 
+
+ align:start position:0%
+compete with each other so stage one we
+have a large number of potential
+
+ align:start position:0%
+have a large number of potential
+ 
+
+ align:start position:0%
+have a large number of potential
+entrance the potential entrance choose
+
+ align:start position:0%
+entrance the potential entrance choose
+ 
+
+ align:start position:0%
+entrance the potential entrance choose
+in or out if they decide to come in they
+
+ align:start position:0%
+in or out if they decide to come in they
+ 
+
+ align:start position:0%
+in or out if they decide to come in they
+pay some fixed entry cost K and I'm
+
+ align:start position:0%
+pay some fixed entry cost K and I'm
+ 
+
+ align:start position:0%
+pay some fixed entry cost K and I'm
+going to think about this as the most of
+
+ align:start position:0%
+going to think about this as the most of
+ 
+
+ align:start position:0%
+going to think about this as the most of
+the lecture is a sunk cost that is like
+
+ align:start position:0%
+the lecture is a sunk cost that is like
+ 
+
+ align:start position:0%
+the lecture is a sunk cost that is like
+once you build a steel plant it's a
+
+ align:start position:0%
+once you build a steel plant it's a
+ 
+
+ align:start position:0%
+once you build a steel plant it's a
+steel plant you can't use it for
+
+ align:start position:0%
+steel plant you can't use it for
+ 
+
+ align:start position:0%
+steel plant you can't use it for
+anything else you're not going to be
+
+ align:start position:0%
+anything else you're not going to be
+ 
+
+ align:start position:0%
+anything else you're not going to be
+able to sell it to somebody else to do
+
+ align:start position:0%
+able to sell it to somebody else to do
+ 
+
+ align:start position:0%
+able to sell it to somebody else to do
+something else with it um firms that
+
+ align:start position:0%
+something else with it um firms that
+ 
+
+ align:start position:0%
+something else with it um firms that
+choose to enter Then play some game like
+
+ align:start position:0%
+choose to enter Then play some game like
+ 
+
+ align:start position:0%
+choose to enter Then play some game like
+betran competition Cordo competition
+
+ align:start position:0%
+betran competition Cordo competition
+ 
+
+ align:start position:0%
+betran competition Cordo competition
+price competition with search Etc and
+
+ align:start position:0%
+price competition with search Etc and
+ 
+
+ align:start position:0%
+price competition with search Etc and
+assume firms have some variable costs um
+
+ align:start position:0%
+assume firms have some variable costs um
+ 
+
+ align:start position:0%
+assume firms have some variable costs um
+C of Q and then so how you going to
+
+ align:start position:0%
+C of Q and then so how you going to
+ 
+
+ align:start position:0%
+C of Q and then so how you going to
+solve this model I'm going to solve this
+
+ align:start position:0%
+solve this model I'm going to solve this
+ 
+
+ align:start position:0%
+solve this model I'm going to solve this
+model by backward induction you know I
+
+ align:start position:0%
+model by backward induction you know I
+ 
+
+ align:start position:0%
+model by backward induction you know I
+first start with the second stage in the
+
+ align:start position:0%
+first start with the second stage in the
+ 
+
+ align:start position:0%
+first start with the second stage in the
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+stage if they're n firms there going to
+
+ align:start position:0%
+stage if they're n firms there going to
+ 
+
+ align:start position:0%
+stage if they're n firms there going to
+be some equal ibrium price is p star of
+
+ align:start position:0%
+be some equal ibrium price is p star of
+ 
+
+ align:start position:0%
+be some equal ibrium price is p star of
+n um P star of n * qar of n minus C of
+
+ align:start position:0%
+n um P star of n * qar of n minus C of
+ 
+
+ align:start position:0%
+n um P star of n * qar of n minus C of
+qar of n is going to be the variable
+
+ align:start position:0%
+qar of n is going to be the variable
+ 
+
+ align:start position:0%
+qar of n is going to be the variable
+profits of the firms good if they enter
+
+ align:start position:0%
+profits of the firms good if they enter
+ 
+
+ align:start position:0%
+profits of the firms good if they enter
+and then you find the number of
+
+ align:start position:0%
+and then you find the number of
+ 
+
+ align:start position:0%
+and then you find the number of
+equilibrium entrance by looking at the
+
+ align:start position:0%
+equilibrium entrance by looking at the
+ 
+
+ align:start position:0%
+equilibrium entrance by looking at the
+first
+
+ align:start position:0%
+first
+ 
+
+ align:start position:0%
+first
+stage
+
+ align:start position:0%
+stage
+ 
+
+ align:start position:0%
+stage
+right and what's that going to be um
+
+ align:start position:0%
+right and what's that going to be um
+ 
+
+ align:start position:0%
+right and what's that going to be um
+okay first comment I guess these slides
+
+ align:start position:0%
+okay first comment I guess these slides
+ 
+
+ align:start position:0%
+okay first comment I guess these slides
+were made up in the co era where I would
+
+ align:start position:0%
+were made up in the co era where I would
+ 
+
+ align:start position:0%
+were made up in the co era where I would
+write on
+
+ align:start position:0%
+write on
+ 
+
+ align:start position:0%
+write on
+them uh write on my iPad but let me go
+
+ align:start position:0%
+them uh write on my iPad but let me go
+ 
+
+ align:start position:0%
+them uh write on my iPad but let me go
+ahead and do this on the board Bo
+
+ align:start position:0%
+ahead and do this on the board Bo
+ 
+
+ align:start position:0%
+ahead and do this on the board Bo
+so you know let me
+
+ align:start position:0%
+so you know let me
+ 
+
+ align:start position:0%
+so you know let me
+graph um what a profits look like as a
+
+ align:start position:0%
+graph um what a profits look like as a
+ 
+
+ align:start position:0%
+graph um what a profits look like as a
+function of the number of firms the
+
+ align:start position:0%
+function of the number of firms the
+ 
+
+ align:start position:0%
+function of the number of firms the
+easiest one to graph uh is
+
+ align:start position:0%
+easiest one to graph uh is
+ 
+
+ align:start position:0%
+easiest one to graph uh is
+Bertrand so one two three four five um
+
+ align:start position:0%
+Bertrand so one two three four five um
+ 
+
+ align:start position:0%
+Bertrand so one two three four five um
+you know betran
+
+ align:start position:0%
+you know betran
+ 
+
+ align:start position:0%
+you know betran
+competition you have this level of
+
+ align:start position:0%
+competition you have this level of
+ 
+
+ align:start position:0%
+competition you have this level of
+um profits PM if you have one firm uh
+
+ align:start position:0%
+um profits PM if you have one firm uh
+ 
+
+ align:start position:0%
+um profits PM if you have one firm uh
+and then as soon as you have two
+
+ align:start position:0%
+and then as soon as you have two
+ 
+
+ align:start position:0%
+and then as soon as you have two
+firms uh profits drop to zero another
+
+ align:start position:0%
+firms uh profits drop to zero another
+ 
+
+ align:start position:0%
+firms uh profits drop to zero another
+thing you could have is Coro
+
+ align:start position:0%
+thing you could have is Coro
+ 
+
+ align:start position:0%
+thing you could have is Coro
+competition uh if you have Coro
+
+ align:start position:0%
+competition uh if you have Coro
+ 
+
+ align:start position:0%
+competition uh if you have Coro
+competition you get exactly the same
+
+ align:start position:0%
+competition you get exactly the same
+ 
+
+ align:start position:0%
+competition you get exactly the same
+outcome when n equals
+
+ align:start position:0%
+outcome when n equals
+ 
+
+ align:start position:0%
+outcome when n equals
+1 uh but then profits sort of
+
+ align:start position:0%
+1 uh but then profits sort of
+ 
+
+ align:start position:0%
+1 uh but then profits sort of
+drop when you add two
+
+ align:start position:0%
+drop when you add two
+ 
+
+ align:start position:0%
+drop when you add two
+three four five whatever firms right if
+
+ align:start position:0%
+three four five whatever firms right if
+ 
+
+ align:start position:0%
+three four five whatever firms right if
+you think about like right if we did
+
+ align:start position:0%
+you think about like right if we did
+ 
+
+ align:start position:0%
+you think about like right if we did
+Coro with linear demand like Coro with
+
+ align:start position:0%
+Coro with linear demand like Coro with
+ 
+
+ align:start position:0%
+Coro with linear demand like Coro with
+linear demand you were getting like uh P
+
+ align:start position:0%
+linear demand you were getting like uh P
+ 
+
+ align:start position:0%
+linear demand you were getting like uh P
+star is approximately
+
+ align:start position:0%
+star is approximately
+ 
+
+ align:start position:0%
+star is approximately
+C+ one over or like simplest case um
+
+ align:start position:0%
+C+ one over or like simplest case um
+ 
+
+ align:start position:0%
+C+ one over or like simplest case um
+uh simplest case where Kuno was um uh n
+
+ align:start position:0%
+uh simplest case where Kuno was um uh n
+ 
+
+ align:start position:0%
+uh simplest case where Kuno was um uh n
+firms demand D ofp is one one over p and
+
+ align:start position:0%
+firms demand D ofp is one one over p and
+ 
+
+ align:start position:0%
+firms demand D ofp is one one over p and
+then I think in that model it was P star
+
+ align:start position:0%
+then I think in that model it was P star
+ 
+
+ align:start position:0%
+then I think in that model it was P star
+was equal to 1/ n + one and qar was
+
+ align:start position:0%
+was equal to 1/ n + one and qar was
+ 
+
+ align:start position:0%
+was equal to 1/ n + one and qar was
+equal to 1/ n + 1 so profits were like 1
+
+ align:start position:0%
+equal to 1/ n + 1 so profits were like 1
+ 
+
+ align:start position:0%
+equal to 1/ n + 1 so profits were like 1
+over n^
+
+ align:start position:0%
+over n^
+ 
+
+ align:start position:0%
+over n^
+SAR right so in Corno no profits
+
+ align:start position:0%
+SAR right so in Corno no profits
+ 
+
+ align:start position:0%
+SAR right so in Corno no profits
+approximately 1 over n s or 1 over n
+
+ align:start position:0%
+approximately 1 over n s or 1 over n
+ 
+
+ align:start position:0%
+approximately 1 over n s or 1 over n
+plus 1 squar whatever
+
+ align:start position:0%
+plus 1 squar whatever
+ 
+
+ align:start position:0%
+plus 1 squar whatever
+um you know another model I did was um
+
+ align:start position:0%
+um you know another model I did was um
+ 
+
+ align:start position:0%
+um you know another model I did was um
+uh model with search like in a model
+
+ align:start position:0%
+uh model with search like in a model
+ 
+
+ align:start position:0%
+uh model with search like in a model
+with search if you remember there was
+
+ align:start position:0%
+with search if you remember there was
+ 
+
+ align:start position:0%
+with search if you remember there was
+like the like the stall model you would
+
+ align:start position:0%
+like the like the stall model you would
+ 
+
+ align:start position:0%
+like the like the stall model you would
+always have the upper bound of the
+
+ align:start position:0%
+always have the upper bound of the
+ 
+
+ align:start position:0%
+always have the upper bound of the
+distribution always gave you the
+
+ align:start position:0%
+distribution always gave you the
+ 
+
+ align:start position:0%
+distribution always gave you the
+Monopoly profits uh as long as the
+
+ align:start position:0%
+Monopoly profits uh as long as the
+ 
+
+ align:start position:0%
+Monopoly profits uh as long as the
+search cost were an appropriate range uh
+
+ align:start position:0%
+search cost were an appropriate range uh
+ 
+
+ align:start position:0%
+search cost were an appropriate range uh
+and so that one you know declines
+
+ align:start position:0%
+and so that one you know declines
+ 
+
+ align:start position:0%
+and so that one you know declines
+something it's if you think about that
+
+ align:start position:0%
+something it's if you think about that
+ 
+
+ align:start position:0%
+something it's if you think about that
+that means it sort of declines
+
+ align:start position:0%
+that means it sort of declines
+ 
+
+ align:start position:0%
+that means it sort of declines
+slower because you know the firms are
+
+ align:start position:0%
+slower because you know the firms are
+ 
+
+ align:start position:0%
+slower because you know the firms are
+serving the nonshoppers
+
+ align:start position:0%
+serving the nonshoppers
+ 
+
+ align:start position:0%
+serving the nonshoppers
+uh so in the search model you're serving
+
+ align:start position:0%
+uh so in the search model you're serving
+ 
+
+ align:start position:0%
+uh so in the search model you're serving
+the non-shoppers you're always
+
+ align:start position:0%
+the non-shoppers you're always
+ 
+
+ align:start position:0%
+the non-shoppers you're always
+indifferent to charging the Monopoly
+
+ align:start position:0%
+indifferent to charging the Monopoly
+ 
+
+ align:start position:0%
+indifferent to charging the Monopoly
+price and so you get the Monopoly price
+
+ align:start position:0%
+price and so you get the Monopoly price
+ 
+
+ align:start position:0%
+price and so you get the Monopoly price
+divided by n plus divided by n you know
+
+ align:start position:0%
+divided by n plus divided by n you know
+ 
+
+ align:start position:0%
+divided by n plus divided by n you know
+times 1 minus mu is the profit so they
+
+ align:start position:0%
+times 1 minus mu is the profit so they
+ 
+
+ align:start position:0%
+times 1 minus mu is the profit so they
+go down like one over
+
+ align:start position:0%
+go down like one over
+ 
+
+ align:start position:0%
+go down like one over
+n um but whatever you have you know
+
+ align:start position:0%
+n um but whatever you have you know
+ 
+
+ align:start position:0%
+n um but whatever you have you know
+what's going to happen in this model in
+
+ align:start position:0%
+what's going to happen in this model in
+ 
+
+ align:start position:0%
+what's going to happen in this model in
+the first stage so if you have some
+
+ align:start position:0%
+the first stage so if you have some
+ 
+
+ align:start position:0%
+the first stage so if you have some
+level of fix let me sort of focus on
+
+ align:start position:0%
+level of fix let me sort of focus on
+ 
+
+ align:start position:0%
+level of fix let me sort of focus on
+Corno um let's suppose you do Corno and
+
+ align:start position:0%
+Corno um let's suppose you do Corno and
+ 
+
+ align:start position:0%
+Corno um let's suppose you do Corno and
+you have some fixed uh level of Entry
+
+ align:start position:0%
+you have some fixed uh level of Entry
+ 
+
+ align:start position:0%
+you have some fixed uh level of Entry
+cost k then in equilibrium you're going
+
+ align:start position:0%
+cost k then in equilibrium you're going
+ 
+
+ align:start position:0%
+cost k then in equilibrium you're going
+to have exactly two firms enter Because
+
+ align:start position:0%
+to have exactly two firms enter Because
+ 
+
+ align:start position:0%
+to have exactly two firms enter Because
+when two firms enter the firm's profits
+
+ align:start position:0%
+when two firms enter the firm's profits
+ 
+
+ align:start position:0%
+when two firms enter the firm's profits
+are above K if you had three firms in
+
+ align:start position:0%
+are above K if you had three firms in
+ 
+
+ align:start position:0%
+are above K if you had three firms in
+the market the profits would be below K
+
+ align:start position:0%
+the market the profits would be below K
+ 
+
+ align:start position:0%
+the market the profits would be below K
+so n equals 2 and so you know the number
+
+ align:start position:0%
+so n equals 2 and so you know the number
+ 
+
+ align:start position:0%
+so n equals 2 and so you know the number
+of firms it's it's locally invariant to
+
+ align:start position:0%
+of firms it's it's locally invariant to
+ 
+
+ align:start position:0%
+of firms it's it's locally invariant to
+K you know because you can sort of raise
+
+ align:start position:0%
+K you know because you can sort of raise
+ 
+
+ align:start position:0%
+K you know because you can sort of raise
+or lower costs and it doesn't effect
+
+ align:start position:0%
+or lower costs and it doesn't effect
+ 
+
+ align:start position:0%
+or lower costs and it doesn't effect
+things obviously if K drops then the
+
+ align:start position:0%
+things obviously if K drops then the
+ 
+
+ align:start position:0%
+things obviously if K drops then the
+third firm
+
+ align:start position:0%
+third firm
+ 
+
+ align:start position:0%
+third firm
+enters a ter piece of talk
+
+ align:start position:0%
+enters a ter piece of talk
+ 
+
+ align:start position:0%
+enters a ter piece of talk
+um okay um you could also think of a
+
+ align:start position:0%
+um okay um you could also think of a
+ 
+
+ align:start position:0%
+um okay um you could also think of a
+mixed strategy equilibrium solution like
+
+ align:start position:0%
+mixed strategy equilibrium solution like
+ 
+
+ align:start position:0%
+mixed strategy equilibrium solution like
+if if there's some large but finite
+
+ align:start position:0%
+if if there's some large but finite
+ 
+
+ align:start position:0%
+if if there's some large but finite
+number you know if there's some number
+
+ align:start position:0%
+number you know if there's some number
+ 
+
+ align:start position:0%
+number you know if there's some number
+of M of potential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+entrance uh where you know m is much
+
+ align:start position:0%
+entrance uh where you know m is much
+ 
+
+ align:start position:0%
+entrance uh where you know m is much
+bigger than n star you could also think
+
+ align:start position:0%
+bigger than n star you could also think
+ 
+
+ align:start position:0%
+bigger than n star you could also think
+of sort of M firms each mixing in or out
+
+ align:start position:0%
+of sort of M firms each mixing in or out
+ 
+
+ align:start position:0%
+of sort of M firms each mixing in or out
+uh and then you get a mixed strategy
+
+ align:start position:0%
+uh and then you get a mixed strategy
+ 
+
+ align:start position:0%
+uh and then you get a mixed strategy
+equilibrium in the mixed strategy
+
+ align:start position:0%
+equilibrium in the mixed strategy
+ 
+
+ align:start position:0%
+equilibrium in the mixed strategy
+equilibrium all the firms that are
+
+ align:start position:0%
+equilibrium all the firms that are
+ 
+
+ align:start position:0%
+equilibrium all the firms that are
+mixing are going to have to have
+
+ align:start position:0%
+mixing are going to have to have
+ 
+
+ align:start position:0%
+mixing are going to have to have
+expected profits exactly equal to K and
+
+ align:start position:0%
+expected profits exactly equal to K and
+ 
+
+ align:start position:0%
+expected profits exactly equal to K and
+so in that model all the firms that are
+
+ align:start position:0%
+so in that model all the firms that are
+ 
+
+ align:start position:0%
+so in that model all the firms that are
+mixing have expected profits exactly
+
+ align:start position:0%
+mixing have expected profits exactly
+ 
+
+ align:start position:0%
+mixing have expected profits exactly
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+k um therefore you know here you can
+
+ align:start position:0%
+k um therefore you know here you can
+ 
+
+ align:start position:0%
+k um therefore you know here you can
+think of it as you're know you're going
+
+ align:start position:0%
+think of it as you're know you're going
+ 
+
+ align:start position:0%
+think of it as you're know you're going
+to expect to get two plus firms between
+
+ align:start position:0%
+to expect to get two plus firms between
+ 
+
+ align:start position:0%
+to expect to get two plus firms between
+two and three firms in the market but if
+
+ align:start position:0%
+two and three firms in the market but if
+ 
+
+ align:start position:0%
+two and three firms in the market but if
+it's obviously if it's like you know
+
+ align:start position:0%
+it's obviously if it's like you know
+ 
+
+ align:start position:0%
+it's obviously if it's like you know
+plus on draws sometimes you'll get one
+
+ align:start position:0%
+plus on draws sometimes you'll get one
+ 
+
+ align:start position:0%
+plus on draws sometimes you'll get one
+two three four five or more um you know
+
+ align:start position:0%
+two three four five or more um you know
+ 
+
+ align:start position:0%
+two three four five or more um you know
+in models like a procurement auction
+
+ align:start position:0%
+in models like a procurement auction
+ 
+
+ align:start position:0%
+in models like a procurement auction
+where there's one date on which everyone
+
+ align:start position:0%
+where there's one date on which everyone
+ 
+
+ align:start position:0%
+where there's one date on which everyone
+has to submit sealed bids and no one
+
+ align:start position:0%
+has to submit sealed bids and no one
+ 
+
+ align:start position:0%
+has to submit sealed bids and no one
+knows how many other biders there are
+
+ align:start position:0%
+knows how many other biders there are
+ 
+
+ align:start position:0%
+knows how many other biders there are
+the sort of expected you know Pi of n
+
+ align:start position:0%
+the sort of expected you know Pi of n
+ 
+
+ align:start position:0%
+the sort of expected you know Pi of n
+equals K is probably the right approach
+
+ align:start position:0%
+equals K is probably the right approach
+ 
+
+ align:start position:0%
+equals K is probably the right approach
+if you have models like you know the
+
+ align:start position:0%
+if you have models like you know the
+ 
+
+ align:start position:0%
+if you have models like you know the
+steel plants where the firms are not
+
+ align:start position:0%
+steel plants where the firms are not
+ 
+
+ align:start position:0%
+steel plants where the firms are not
+entering simultaneously they're entering
+
+ align:start position:0%
+entering simultaneously they're entering
+ 
+
+ align:start position:0%
+entering simultaneously they're entering
+sequentially then it's probably like the
+
+ align:start position:0%
+sequentially then it's probably like the
+ 
+
+ align:start position:0%
+sequentially then it's probably like the
+pure strategy equilibrium is the one you
+
+ align:start position:0%
+pure strategy equilibrium is the one you
+ 
+
+ align:start position:0%
+pure strategy equilibrium is the one you
+want to focus on because you know no
+
+ align:start position:0%
+want to focus on because you know no
+ 
+
+ align:start position:0%
+want to focus on because you know no
+one's going to open a third Steel plant
+
+ align:start position:0%
+one's going to open a third Steel plant
+ 
+
+ align:start position:0%
+one's going to open a third Steel plant
+if the third steel plant's going to
+
+ align:start position:0%
+if the third steel plant's going to
+ 
+
+ align:start position:0%
+if the third steel plant's going to
+drive prices below where you need to
+
+ align:start position:0%
+drive prices below where you need to
+ 
+
+ align:start position:0%
+drive prices below where you need to
+cover the fixed costs
+
+ align:start position:0%
+cover the fixed costs
+ 
+
+ align:start position:0%
+cover the fixed costs
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um so observations um you know fixed
+
+ align:start position:0%
+um so observations um you know fixed
+ 
+
+ align:start position:0%
+um so observations um you know fixed
+costs and competition determine the
+
+ align:start position:0%
+costs and competition determine the
+ 
+
+ align:start position:0%
+costs and competition determine the
+number of entries deter number of
+
+ align:start position:0%
+number of entries deter number of
+ 
+
+ align:start position:0%
+number of entries deter number of
+entrance but with lower fixed costs we
+
+ align:start position:0%
+entrance but with lower fixed costs we
+ 
+
+ align:start position:0%
+entrance but with lower fixed costs we
+get more
+
+ align:start position:0%
+get more
+ 
+
+ align:start position:0%
+get more
+entry uh in many models the number of
+
+ align:start position:0%
+entry uh in many models the number of
+ 
+
+ align:start position:0%
+entry uh in many models the number of
+firms goes to Infinity as the fixed
+
+ align:start position:0%
+firms goes to Infinity as the fixed
+ 
+
+ align:start position:0%
+firms goes to Infinity as the fixed
+costs of Entry go to zero the only time
+
+ align:start position:0%
+costs of Entry go to zero the only time
+ 
+
+ align:start position:0%
+costs of Entry go to zero the only time
+that's not going to happen is if you had
+
+ align:start position:0%
+that's not going to happen is if you had
+ 
+
+ align:start position:0%
+that's not going to happen is if you had
+you know I you know like I talked about
+
+ align:start position:0%
+you know I you know like I talked about
+ 
+
+ align:start position:0%
+you know I you know like I talked about
+the low at demand models where price
+
+ align:start position:0%
+the low at demand models where price
+ 
+
+ align:start position:0%
+the low at demand models where price
+asmp tootes to a positive um no it's
+
+ align:start position:0%
+asmp tootes to a positive um no it's
+ 
+
+ align:start position:0%
+asmp tootes to a positive um no it's
+still going to work um so where are you
+
+ align:start position:0%
+still going to work um so where are you
+ 
+
+ align:start position:0%
+still going to work um so where are you
+not going to get in Star
+
+ align:start position:0%
+not going to get in Star
+ 
+
+ align:start position:0%
+not going to get in Star
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+uh you know you're not going to get
+
+ align:start position:0%
+uh you know you're not going to get
+ 
+
+ align:start position:0%
+uh you know you're not going to get
+NSTAR goes to Infinity like in in Coro
+
+ align:start position:0%
+NSTAR goes to Infinity like in in Coro
+ 
+
+ align:start position:0%
+NSTAR goes to Infinity like in in Coro
+you don't get NSTAR goes to Infinity
+
+ align:start position:0%
+you don't get NSTAR goes to Infinity
+ 
+
+ align:start position:0%
+you don't get NSTAR goes to Infinity
+because in Coro in fact you get NSTAR is
+
+ align:start position:0%
+because in Coro in fact you get NSTAR is
+ 
+
+ align:start position:0%
+because in Coro in fact you get NSTAR is
+one so if profits hit zero at some point
+
+ align:start position:0%
+one so if profits hit zero at some point
+ 
+
+ align:start position:0%
+one so if profits hit zero at some point
+before when n gets large and even with
+
+ align:start position:0%
+before when n gets large and even with
+ 
+
+ align:start position:0%
+before when n gets large and even with
+like no entry costs you can still get or
+
+ align:start position:0%
+like no entry costs you can still get or
+ 
+
+ align:start position:0%
+like no entry costs you can still get or
+small POS of Entry C you can still get
+
+ align:start position:0%
+small POS of Entry C you can still get
+ 
+
+ align:start position:0%
+small POS of Entry C you can still get
+finite entry um you know profits are in
+
+ align:start position:0%
+finite entry um you know profits are in
+ 
+
+ align:start position:0%
+finite entry um you know profits are in
+this model are rounding error and we
+
+ align:start position:0%
+this model are rounding error and we
+ 
+
+ align:start position:0%
+this model are rounding error and we
+spent all this time working on markups
+
+ align:start position:0%
+spent all this time working on markups
+ 
+
+ align:start position:0%
+spent all this time working on markups
+but you know here the profits are just
+
+ align:start position:0%
+but you know here the profits are just
+ 
+
+ align:start position:0%
+but you know here the profits are just
+if this happens to be the fixed cost you
+
+ align:start position:0%
+if this happens to be the fixed cost you
+ 
+
+ align:start position:0%
+if this happens to be the fixed cost you
+get pretty big profits if this was the
+
+ align:start position:0%
+get pretty big profits if this was the
+ 
+
+ align:start position:0%
+get pretty big profits if this was the
+fixed cost you get very little profits
+
+ align:start position:0%
+fixed cost you get very little profits
+ 
+
+ align:start position:0%
+fixed cost you get very little profits
+if the fixed costs um you know drop to
+
+ align:start position:0%
+if the fixed costs um you know drop to
+ 
+
+ align:start position:0%
+if the fixed costs um you know drop to
+here you get even higher profits when
+
+ align:start position:0%
+here you get even higher profits when
+ 
+
+ align:start position:0%
+here you get even higher profits when
+they drop more you get
+
+ align:start position:0%
+they drop more you get
+ 
+
+ align:start position:0%
+they drop more you get
+hardly any profits at all so you know
+
+ align:start position:0%
+hardly any profits at all so you know
+ 
+
+ align:start position:0%
+hardly any profits at all so you know
+equilibrium profits that we
+
+ align:start position:0%
+equilibrium profits that we
+ 
+
+ align:start position:0%
+equilibrium profits that we
+observed really don't have to be related
+
+ align:start position:0%
+observed really don't have to be related
+ 
+
+ align:start position:0%
+observed really don't have to be related
+to anything we've talked about so far
+
+ align:start position:0%
+to anything we've talked about so far
+ 
+
+ align:start position:0%
+to anything we've talked about so far
+because all that matters is like how
+
+ align:start position:0%
+because all that matters is like how
+ 
+
+ align:start position:0%
+because all that matters is like how
+many firms fit in the market and then
+
+ align:start position:0%
+many firms fit in the market and then
+ 
+
+ align:start position:0%
+many firms fit in the market and then
+everything else just determines where
+
+ align:start position:0%
+everything else just determines where
+ 
+
+ align:start position:0%
+everything else just determines where
+you are in between the profits with two
+
+ align:start position:0%
+you are in between the profits with two
+ 
+
+ align:start position:0%
+you are in between the profits with two
+firms or three firms or three firms and
+
+ align:start position:0%
+firms or three firms or three firms and
+ 
+
+ align:start position:0%
+firms or three firms or three firms and
+four firms and so profits just become
+
+ align:start position:0%
+four firms and so profits just become
+ 
+
+ align:start position:0%
+four firms and so profits just become
+this rounding eror that's just
+
+ align:start position:0%
+this rounding eror that's just
+ 
+
+ align:start position:0%
+this rounding eror that's just
+Coincidence of where entry costs big
+
+ align:start position:0%
+Coincidence of where entry costs big
+ 
+
+ align:start position:0%
+Coincidence of where entry costs big
+enough that like the last firm just
+
+ align:start position:0%
+enough that like the last firm just
+ 
+
+ align:start position:0%
+enough that like the last firm just
+barely gets in now that's um you know
+
+ align:start position:0%
+barely gets in now that's um you know
+ 
+
+ align:start position:0%
+barely gets in now that's um you know
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+is equilibrium profits taking the fixed
+
+ align:start position:0%
+is equilibrium profits taking the fixed
+ 
+
+ align:start position:0%
+is equilibrium profits taking the fixed
+cost of entry into account you know it's
+
+ align:start position:0%
+cost of entry into account you know it's
+ 
+
+ align:start position:0%
+cost of entry into account you know it's
+still the case that the markups are
+
+ align:start position:0%
+still the case that the markups are
+ 
+
+ align:start position:0%
+still the case that the markups are
+higher when you have smaller numbers of
+
+ align:start position:0%
+higher when you have smaller numbers of
+ 
+
+ align:start position:0%
+higher when you have smaller numbers of
+firms the markups are higher but it's
+
+ align:start position:0%
+firms the markups are higher but it's
+ 
+
+ align:start position:0%
+firms the markups are higher but it's
+just the markups just offset the fixed
+
+ align:start position:0%
+just the markups just offset the fixed
+ 
+
+ align:start position:0%
+just the markups just offset the fixed
+cost the firms are
+
+ align:start position:0%
+cost the firms are
+ 
+
+ align:start position:0%
+cost the firms are
+incurring
+
+ align:start position:0%
+incurring
+ 
+
+ align:start position:0%
+incurring
+um in many models the equilibrium firm
+
+ align:start position:0%
+um in many models the equilibrium firm
+ 
+
+ align:start position:0%
+um in many models the equilibrium firm
+size increases when the market size
+
+ align:start position:0%
+size increases when the market size
+ 
+
+ align:start position:0%
+size increases when the market size
+increases so I I give the you know Coro
+
+ align:start position:0%
+increases so I I give the you know Coro
+ 
+
+ align:start position:0%
+increases so I I give the you know Coro
+example here you in the Coro example
+
+ align:start position:0%
+example here you in the Coro example
+ 
+
+ align:start position:0%
+example here you in the Coro example
+suppose you have
+
+ align:start position:0%
+suppose you have
+ 
+
+ align:start position:0%
+suppose you have
+Little M consumers in the market and so
+
+ align:start position:0%
+Little M consumers in the market and so
+ 
+
+ align:start position:0%
+Little M consumers in the market and so
+demand becomes M time D of
+
+ align:start position:0%
+demand becomes M time D of
+ 
+
+ align:start position:0%
+demand becomes M time D of
+P let's suppose we double the market
+
+ align:start position:0%
+P let's suppose we double the market
+ 
+
+ align:start position:0%
+P let's suppose we double the market
+size if you double the market size and
+
+ align:start position:0%
+size if you double the market size and
+ 
+
+ align:start position:0%
+size if you double the market size and
+you double the number of firms then the
+
+ align:start position:0%
+you double the number of firms then the
+ 
+
+ align:start position:0%
+you double the number of firms then the
+number of customers per firm would be
+
+ align:start position:0%
+number of customers per firm would be
+ 
+
+ align:start position:0%
+number of customers per firm would be
+the same but there's a second effect of
+
+ align:start position:0%
+the same but there's a second effect of
+ 
+
+ align:start position:0%
+the same but there's a second effect of
+the prices decreasing and so if the
+
+ align:start position:0%
+the prices decreasing and so if the
+ 
+
+ align:start position:0%
+the prices decreasing and so if the
+prices
+
+ align:start position:0%
+prices
+ 
+
+ align:start position:0%
+prices
+decrease um you know the prices decrease
+
+ align:start position:0%
+decrease um you know the prices decrease
+ 
+
+ align:start position:0%
+decrease um you know the prices decrease
+then the firms are worse off um so like
+
+ align:start position:0%
+then the firms are worse off um so like
+ 
+
+ align:start position:0%
+then the firms are worse off um so like
+you know in Coro in some sense it's like
+
+ align:start position:0%
+you know in Coro in some sense it's like
+ 
+
+ align:start position:0%
+you know in Coro in some sense it's like
+the price profits are going down like
+
+ align:start position:0%
+the price profits are going down like
+ 
+
+ align:start position:0%
+the price profits are going down like
+one N squared uh with n firms profits
+
+ align:start position:0%
+one N squared uh with n firms profits
+ 
+
+ align:start position:0%
+one N squared uh with n firms profits
+are going up proportional to M if there
+
+ align:start position:0%
+are going up proportional to M if there
+ 
+
+ align:start position:0%
+are going up proportional to M if there
+if the number of customers goes up so
+
+ align:start position:0%
+if the number of customers goes up so
+ 
+
+ align:start position:0%
+if the number of customers goes up so
+it's you're going to get like you know
+
+ align:start position:0%
+it's you're going to get like you know
+ 
+
+ align:start position:0%
+it's you're going to get like you know
+firm growth is going to be like square
+
+ align:start position:0%
+firm growth is going to be like square
+ 
+
+ align:start position:0%
+firm growth is going to be like square
+root of the number of customers so as
+
+ align:start position:0%
+root of the number of customers so as
+ 
+
+ align:start position:0%
+root of the number of customers so as
+the firm as the like Market increases
+
+ align:start position:0%
+the firm as the like Market increases
+ 
+
+ align:start position:0%
+the firm as the like Market increases
+firms go up like square root of the
+
+ align:start position:0%
+firms go up like square root of the
+ 
+
+ align:start position:0%
+firms go up like square root of the
+number of customers goes up so like firm
+
+ align:start position:0%
+number of customers goes up so like firm
+ 
+
+ align:start position:0%
+number of customers goes up so like firm
+size goes up like square root of the
+
+ align:start position:0%
+size goes up like square root of the
+ 
+
+ align:start position:0%
+size goes up like square root of the
+number of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+customers any questions on these simple
+
+ align:start position:0%
+customers any questions on these simple
+ 
+
+ align:start position:0%
+customers any questions on these simple
+observations
+
+ align:start position:0%
+observations
+ 
+
+ align:start position:0%
+observations
+okay um you know first substantial topic
+
+ align:start position:0%
+okay um you know first substantial topic
+ 
+
+ align:start position:0%
+okay um you know first substantial topic
+I want to talk about today is um what's
+
+ align:start position:0%
+I want to talk about today is um what's
+ 
+
+ align:start position:0%
+I want to talk about today is um what's
+the efficiency of Entry do we get more
+
+ align:start position:0%
+the efficiency of Entry do we get more
+ 
+
+ align:start position:0%
+the efficiency of Entry do we get more
+firms in markets than we want do we get
+
+ align:start position:0%
+firms in markets than we want do we get
+ 
+
+ align:start position:0%
+firms in markets than we want do we get
+fewer firms in markets than we want and
+
+ align:start position:0%
+fewer firms in markets than we want and
+ 
+
+ align:start position:0%
+fewer firms in markets than we want and
+and you know this is an important
+
+ align:start position:0%
+and you know this is an important
+ 
+
+ align:start position:0%
+and you know this is an important
+practical question you know there are
+
+ align:start position:0%
+practical question you know there are
+ 
+
+ align:start position:0%
+practical question you know there are
+many many Industries in many many
+
+ align:start position:0%
+many many Industries in many many
+ 
+
+ align:start position:0%
+many many Industries in many many
+countries where the firms have gotten
+
+ align:start position:0%
+countries where the firms have gotten
+ 
+
+ align:start position:0%
+countries where the firms have gotten
+together and have some kind of
+
+ align:start position:0%
+together and have some kind of
+ 
+
+ align:start position:0%
+together and have some kind of
+government sanctioned uh entry uh
+
+ align:start position:0%
+government sanctioned uh entry uh
+ 
+
+ align:start position:0%
+government sanctioned uh entry uh
+limitations you know right there's a
+
+ align:start position:0%
+limitations you know right there's a
+ 
+
+ align:start position:0%
+limitations you know right there's a
+question of the Massachusetts ballot
+
+ align:start position:0%
+question of the Massachusetts ballot
+ 
+
+ align:start position:0%
+question of the Massachusetts ballot
+about should um should liquor stores or
+
+ align:start position:0%
+about should um should liquor stores or
+ 
+
+ align:start position:0%
+about should um should liquor stores or
+should firms be able to sell beer in
+
+ align:start position:0%
+should firms be able to sell beer in
+ 
+
+ align:start position:0%
+should firms be able to sell beer in
+more than nine stores in the state of
+
+ align:start position:0%
+more than nine stores in the state of
+ 
+
+ align:start position:0%
+more than nine stores in the state of
+Massachusetts you know for for many
+
+ align:start position:0%
+Massachusetts you know for for many
+ 
+
+ align:start position:0%
+Massachusetts you know for for many
+years you only allowed to sell beer I
+
+ align:start position:0%
+years you only allowed to sell beer I
+ 
+
+ align:start position:0%
+years you only allowed to sell beer I
+think in one store in the state of
+
+ align:start position:0%
+think in one store in the state of
+ 
+
+ align:start position:0%
+think in one store in the state of
+Massachusetts so like all the
+
+ align:start position:0%
+Massachusetts so like all the
+ 
+
+ align:start position:0%
+Massachusetts so like all the
+supermarkets you notice I don't know if
+
+ align:start position:0%
+supermarkets you notice I don't know if
+ 
+
+ align:start position:0%
+supermarkets you notice I don't know if
+those you here you know like you notice
+
+ align:start position:0%
+those you here you know like you notice
+ 
+
+ align:start position:0%
+those you here you know like you notice
+you go to supermarkets in other states
+
+ align:start position:0%
+you go to supermarkets in other states
+ 
+
+ align:start position:0%
+you go to supermarkets in other states
+have beer um supermarkets in
+
+ align:start position:0%
+have beer um supermarkets in
+ 
+
+ align:start position:0%
+have beer um supermarkets in
+Massachusetts typically didn't have beer
+
+ align:start position:0%
+Massachusetts typically didn't have beer
+ 
+
+ align:start position:0%
+Massachusetts typically didn't have beer
+because there was a law that said you
+
+ align:start position:0%
+because there was a law that said you
+ 
+
+ align:start position:0%
+because there was a law that said you
+could only sell beer in one one of your
+
+ align:start position:0%
+could only sell beer in one one of your
+ 
+
+ align:start position:0%
+could only sell beer in one one of your
+stores in the entire state of
+
+ align:start position:0%
+stores in the entire state of
+ 
+
+ align:start position:0%
+stores in the entire state of
+Massachusetts and so you know Star
+
+ align:start position:0%
+Massachusetts and so you know Star
+ 
+
+ align:start position:0%
+Massachusetts and so you know Star
+Market could had to pick one Star Market
+
+ align:start position:0%
+Market could had to pick one Star Market
+ 
+
+ align:start position:0%
+Market could had to pick one Star Market
+to have beer you know now there are now
+
+ align:start position:0%
+to have beer you know now there are now
+ 
+
+ align:start position:0%
+to have beer you know now there are now
+you can sell beer in nine star markets
+
+ align:start position:0%
+you can sell beer in nine star markets
+ 
+
+ align:start position:0%
+you can sell beer in nine star markets
+and they're sort of thinking of
+
+ align:start position:0%
+and they're sort of thinking of
+ 
+
+ align:start position:0%
+and they're sort of thinking of
+increasing that level but you
+
+ align:start position:0%
+increasing that level but you
+ 
+
+ align:start position:0%
+increasing that level but you
+know why do we get these entry laws well
+
+ align:start position:0%
+know why do we get these entry laws well
+ 
+
+ align:start position:0%
+know why do we get these entry laws well
+the firms that are in the market always
+
+ align:start position:0%
+the firms that are in the market always
+ 
+
+ align:start position:0%
+the firms that are in the market always
+argue that you know competi entry is
+
+ align:start position:0%
+argue that you know competi entry is
+ 
+
+ align:start position:0%
+argue that you know competi entry is
+wasteful and we need to save the mom and
+
+ align:start position:0%
+wasteful and we need to save the mom and
+ 
+
+ align:start position:0%
+wasteful and we need to save the mom and
+pop stores and the small businesses and
+
+ align:start position:0%
+pop stores and the small businesses and
+ 
+
+ align:start position:0%
+pop stores and the small businesses and
+protect them from quote excessive entry
+
+ align:start position:0%
+protect them from quote excessive entry
+ 
+
+ align:start position:0%
+protect them from quote excessive entry
+so anyway here's a discussion of do we
+
+ align:start position:0%
+so anyway here's a discussion of do we
+ 
+
+ align:start position:0%
+so anyway here's a discussion of do we
+think entry should or shouldn't would or
+
+ align:start position:0%
+think entry should or shouldn't would or
+ 
+
+ align:start position:0%
+think entry should or shouldn't would or
+would not be excessive in markets um
+
+ align:start position:0%
+would not be excessive in markets um
+ 
+
+ align:start position:0%
+would not be excessive in markets um
+what's the first best here I'm going to
+
+ align:start position:0%
+what's the first best here I'm going to
+ 
+
+ align:start position:0%
+what's the first best here I'm going to
+do the homogeneous case first you know
+
+ align:start position:0%
+do the homogeneous case first you know
+ 
+
+ align:start position:0%
+do the homogeneous case first you know
+homogeneous Goods there's no
+
+ align:start position:0%
+homogeneous Goods there's no
+ 
+
+ align:start position:0%
+homogeneous Goods there's no
+idiosyncratic preferences the first best
+
+ align:start position:0%
+idiosyncratic preferences the first best
+ 
+
+ align:start position:0%
+idiosyncratic preferences the first best
+is just one firm have that one firm
+
+ align:start position:0%
+is just one firm have that one firm
+ 
+
+ align:start position:0%
+is just one firm have that one firm
+price at marginal cost um that's
+
+ align:start position:0%
+price at marginal cost um that's
+ 
+
+ align:start position:0%
+price at marginal cost um that's
+typically not feasible because You' need
+
+ align:start position:0%
+typically not feasible because You' need
+ 
+
+ align:start position:0%
+typically not feasible because You' need
+price regulation to force the monopolis
+
+ align:start position:0%
+price regulation to force the monopolis
+ 
+
+ align:start position:0%
+price regulation to force the monopolis
+price at marginal cost so what we often
+
+ align:start position:0%
+price at marginal cost so what we often
+ 
+
+ align:start position:0%
+price at marginal cost so what we often
+compare it to is this second best where
+
+ align:start position:0%
+compare it to is this second best where
+ 
+
+ align:start position:0%
+compare it to is this second best where
+the second best you take P star of n as
+
+ align:start position:0%
+the second best you take P star of n as
+ 
+
+ align:start position:0%
+the second best you take P star of n as
+given you can't affect the nature of the
+
+ align:start position:0%
+given you can't affect the nature of the
+ 
+
+ align:start position:0%
+given you can't affect the nature of the
+competition and you just sort of say
+
+ align:start position:0%
+competition and you just sort of say
+ 
+
+ align:start position:0%
+competition and you just sort of say
+what would be the optimal number of
+
+ align:start position:0%
+what would be the optimal number of
+ 
+
+ align:start position:0%
+what would be the optimal number of
+firms and
+
+ align:start position:0%
+firms and
+ 
+
+ align:start position:0%
+firms and
+given that you know P star of ends can
+
+ align:start position:0%
+given that you know P star of ends can
+ 
+
+ align:start position:0%
+given that you know P star of ends can
+be determined in equilibrium and so this
+
+ align:start position:0%
+be determined in equilibrium and so this
+ 
+
+ align:start position:0%
+be determined in equilibrium and so this
+would be our welfare
+
+ align:start position:0%
+would be our welfare
+ 
+
+ align:start position:0%
+would be our welfare
+calculation uh the welfare with n
+
+ align:start position:0%
+calculation uh the welfare with n
+ 
+
+ align:start position:0%
+calculation uh the welfare with n
+firms it's equal to the
+
+ align:start position:0%
+firms it's equal to the
+ 
+
+ align:start position:0%
+firms it's equal to the
+integral 0 to n we do big or little Q
+
+ align:start position:0%
+integral 0 to n we do big or little Q
+ 
+
+ align:start position:0%
+integral 0 to n we do big or little Q
+little Q
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if you have n firms this is the
+
+ align:start position:0%
+okay so if you have n firms this is the
+ 
+
+ align:start position:0%
+okay so if you have n firms this is the
+gross Surplus produced by um firms
+
+ align:start position:0%
+gross Surplus produced by um firms
+ 
+
+ align:start position:0%
+gross Surplus produced by um firms
+producing total quantity n qar of
+
+ align:start position:0%
+producing total quantity n qar of
+ 
+
+ align:start position:0%
+producing total quantity n qar of
+n um this is the total production cost
+
+ align:start position:0%
+n um this is the total production cost
+ 
+
+ align:start position:0%
+n um this is the total production cost
+incurred when each of n firms produces
+
+ align:start position:0%
+incurred when each of n firms produces
+ 
+
+ align:start position:0%
+incurred when each of n firms produces
+quantity qar of N and these are the
+
+ align:start position:0%
+quantity qar of N and these are the
+ 
+
+ align:start position:0%
+quantity qar of N and these are the
+fixed costs okay so we want to maximize
+
+ align:start position:0%
+fixed costs okay so we want to maximize
+ 
+
+ align:start position:0%
+fixed costs okay so we want to maximize
+that um so the first theorem is that in
+
+ align:start position:0%
+that um so the first theorem is that in
+ 
+
+ align:start position:0%
+that um so the first theorem is that in
+this model with homogeneous Goods entry
+
+ align:start position:0%
+this model with homogeneous Goods entry
+ 
+
+ align:start position:0%
+this model with homogeneous Goods entry
+is always accessible so we do get too
+
+ align:start position:0%
+is always accessible so we do get too
+ 
+
+ align:start position:0%
+is always accessible so we do get too
+many firms in markets and we would like
+
+ align:start position:0%
+many firms in markets and we would like
+ 
+
+ align:start position:0%
+many firms in markets and we would like
+to restrict it why and here's a theorem
+
+ align:start position:0%
+to restrict it why and here's a theorem
+ 
+
+ align:start position:0%
+to restrict it why and here's a theorem
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+so you know suppos that this welfare
+
+ align:start position:0%
+so you know suppos that this welfare
+ 
+
+ align:start position:0%
+so you know suppos that this welfare
+function is concave I know I've talked
+
+ align:start position:0%
+function is concave I know I've talked
+ 
+
+ align:start position:0%
+function is concave I know I've talked
+about how things are often not concave
+
+ align:start position:0%
+about how things are often not concave
+ 
+
+ align:start position:0%
+about how things are often not concave
+welfare functions here would be concave
+
+ align:start position:0%
+welfare functions here would be concave
+ 
+
+ align:start position:0%
+welfare functions here would be concave
+because as you get you know as you get
+
+ align:start position:0%
+because as you get you know as you get
+ 
+
+ align:start position:0%
+because as you get you know as you get
+lots of firms you just ASM toote to line
+
+ align:start position:0%
+lots of firms you just ASM toote to line
+ 
+
+ align:start position:0%
+lots of firms you just ASM toote to line
+of slope K just it's in inefficient to
+
+ align:start position:0%
+of slope K just it's in inefficient to
+ 
+
+ align:start position:0%
+of slope K just it's in inefficient to
+keep paying these fixed entry costs over
+
+ align:start position:0%
+keep paying these fixed entry costs over
+ 
+
+ align:start position:0%
+keep paying these fixed entry costs over
+and over and over again um so suppose
+
+ align:start position:0%
+and over and over again um so suppose
+ 
+
+ align:start position:0%
+and over and over again um so suppose
+the welfare function is concave suppose
+
+ align:start position:0%
+the welfare function is concave suppose
+ 
+
+ align:start position:0%
+the welfare function is concave suppose
+the variable profits are decreasing in
+
+ align:start position:0%
+the variable profits are decreasing in
+ 
+
+ align:start position:0%
+the variable profits are decreasing in
+number of firms
+
+ align:start position:0%
+number of firms
+ 
+
+ align:start position:0%
+number of firms
+n and suppose that the equilibrium price
+
+ align:start position:0%
+n and suppose that the equilibrium price
+ 
+
+ align:start position:0%
+n and suppose that the equilibrium price
+and per firm quantities can be extended
+
+ align:start position:0%
+and per firm quantities can be extended
+ 
+
+ align:start position:0%
+and per firm quantities can be extended
+to differentiable functions that have
+
+ align:start position:0%
+to differentiable functions that have
+ 
+
+ align:start position:0%
+to differentiable functions that have
+these natural properties uh as the
+
+ align:start position:0%
+these natural properties uh as the
+ 
+
+ align:start position:0%
+these natural properties uh as the
+number of firms increases total output
+
+ align:start position:0%
+number of firms increases total output
+ 
+
+ align:start position:0%
+number of firms increases total output
+goes
+
+ align:start position:0%
+goes
+ 
+
+ align:start position:0%
+goes
+up uh as the number of firms goes up
+
+ align:start position:0%
+up uh as the number of firms goes up
+ 
+
+ align:start position:0%
+up uh as the number of firms goes up
+each individual firm's output goes
+
+ align:start position:0%
+each individual firm's output goes
+ 
+
+ align:start position:0%
+each individual firm's output goes
+down and at the equilibrium number of
+
+ align:start position:0%
+down and at the equilibrium number of
+ 
+
+ align:start position:0%
+down and at the equilibrium number of
+firms um uh price minus marginal cost is
+
+ align:start position:0%
+firms um uh price minus marginal cost is
+ 
+
+ align:start position:0%
+firms um uh price minus marginal cost is
+positive which it always should be or
+
+ align:start position:0%
+positive which it always should be or
+ 
+
+ align:start position:0%
+positive which it always should be or
+sorry this is given any number of firms
+
+ align:start position:0%
+sorry this is given any number of firms
+ 
+
+ align:start position:0%
+sorry this is given any number of firms
+given any number of firms n the
+
+ align:start position:0%
+given any number of firms n the
+ 
+
+ align:start position:0%
+given any number of firms n the
+resulting price would be above marginal
+
+ align:start position:0%
+resulting price would be above marginal
+ 
+
+ align:start position:0%
+resulting price would be above marginal
+cost uh the theorem is that then n is at
+
+ align:start position:0%
+cost uh the theorem is that then n is at
+ 
+
+ align:start position:0%
+cost uh the theorem is that then n is at
+least n second best minus one so it's
+
+ align:start position:0%
+least n second best minus one so it's
+ 
+
+ align:start position:0%
+least n second best minus one so it's
+it's entry is excessive although it can
+
+ align:start position:0%
+it's entry is excessive although it can
+ 
+
+ align:start position:0%
+it's entry is excessive although it can
+due to rounding errors be one too few um
+
+ align:start position:0%
+due to rounding errors be one too few um
+ 
+
+ align:start position:0%
+due to rounding errors be one too few um
+Bertrand is a case where it's one too
+
+ align:start position:0%
+Bertrand is a case where it's one too
+ 
+
+ align:start position:0%
+Bertrand is a case where it's one too
+few sometimes you'd like two firms you
+
+ align:start position:0%
+few sometimes you'd like two firms you
+ 
+
+ align:start position:0%
+few sometimes you'd like two firms you
+only get one uh but the general result
+
+ align:start position:0%
+only get one uh but the general result
+ 
+
+ align:start position:0%
+only get one uh but the general result
+is that you you get too many firms and
+
+ align:start position:0%
+is that you you get too many firms and
+ 
+
+ align:start position:0%
+is that you you get too many firms and
+and other than this possible rounding
+
+ align:start position:0%
+and other than this possible rounding
+ 
+
+ align:start position:0%
+and other than this possible rounding
+error
+
+ align:start position:0%
+error
+ 
+
+ align:start position:0%
+error
+issue
+
+ align:start position:0%
+issue
+ 
+
+ align:start position:0%
+issue
+um so proof um so first you know we've
+
+ align:start position:0%
+um so proof um so first you know we've
+ 
+
+ align:start position:0%
+um so proof um so first you know we've
+got this welfare function right the
+
+ align:start position:0%
+got this welfare function right the
+ 
+
+ align:start position:0%
+got this welfare function right the
+welfare function is naturally described
+
+ align:start position:0%
+welfare function is naturally described
+ 
+
+ align:start position:0%
+welfare function is naturally described
+only at a set of integer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points okay but you know in many of
+
+ align:start position:0%
+points okay but you know in many of
+ 
+
+ align:start position:0%
+points okay but you know in many of
+these models like Corno over there right
+
+ align:start position:0%
+these models like Corno over there right
+ 
+
+ align:start position:0%
+these models like Corno over there right
+you know you have like you know P star
+
+ align:start position:0%
+you know you have like you know P star
+ 
+
+ align:start position:0%
+you know you have like you know P star
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+P star of n = 1 n + 1 qar of
+
+ align:start position:0%
+P star of n = 1 n + 1 qar of
+ 
+
+ align:start position:0%
+P star of n = 1 n + 1 qar of
+n = 1 n + 1 so you can just naturally
+
+ align:start position:0%
+n = 1 n + 1 so you can just naturally
+ 
+
+ align:start position:0%
+n = 1 n + 1 so you can just naturally
+think treat this as a continuous
+
+ align:start position:0%
+think treat this as a continuous
+ 
+
+ align:start position:0%
+think treat this as a continuous
+function when n's a
+
+ align:start position:0%
+function when n's a
+ 
+
+ align:start position:0%
+function when n's a
+continuous variable like use a function
+
+ align:start position:0%
+continuous variable like use a function
+ 
+
+ align:start position:0%
+continuous variable like use a function
+qar of X = 1x + 1 and by doing that you
+
+ align:start position:0%
+qar of X = 1x + 1 and by doing that you
+ 
+
+ align:start position:0%
+qar of X = 1x + 1 and by doing that you
+sort of extend the welfare you just sort
+
+ align:start position:0%
+sort of extend the welfare you just sort
+ 
+
+ align:start position:0%
+sort of extend the welfare you just sort
+of draw a
+
+ align:start position:0%
+of draw a
+ 
+
+ align:start position:0%
+of draw a
+smooth curve through those welfare
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+points um I'm going to let n hat second
+
+ align:start position:0%
+points um I'm going to let n hat second
+ 
+
+ align:start position:0%
+points um I'm going to let n hat second
+best be the solution to where this
+
+ align:start position:0%
+best be the solution to where this
+ 
+
+ align:start position:0%
+best be the solution to where this
+thing's first order condition is zero um
+
+ align:start position:0%
+thing's first order condition is zero um
+ 
+
+ align:start position:0%
+thing's first order condition is zero um
+so that would be right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so n hat second best so I Define n hat
+
+ align:start position:0%
+so n hat second best so I Define n hat
+ 
+
+ align:start position:0%
+so n hat second best so I Define n hat
+second best to be the maximizer of the
+
+ align:start position:0%
+second best to be the maximizer of the
+ 
+
+ align:start position:0%
+second best to be the maximizer of the
+smooth
+
+ align:start position:0%
+smooth
+ 
+
+ align:start position:0%
+smooth
+curve um you know the second best is
+
+ align:start position:0%
+curve um you know the second best is
+ 
+
+ align:start position:0%
+curve um you know the second best is
+always going to be either if you know W
+
+ align:start position:0%
+always going to be either if you know W
+ 
+
+ align:start position:0%
+always going to be either if you know W
+is a concave function it's either going
+
+ align:start position:0%
+is a concave function it's either going
+ 
+
+ align:start position:0%
+is a concave function it's either going
+to be this point or this point so the
+
+ align:start position:0%
+to be this point or this point so the
+ 
+
+ align:start position:0%
+to be this point or this point so the
+optimal number of firms is always at
+
+ align:start position:0%
+optimal number of firms is always at
+ 
+
+ align:start position:0%
+optimal number of firms is always at
+most and what you get optim number of
+
+ align:start position:0%
+most and what you get optim number of
+ 
+
+ align:start position:0%
+most and what you get optim number of
+First is always at most what you get by
+
+ align:start position:0%
+First is always at most what you get by
+ 
+
+ align:start position:0%
+First is always at most what you get by
+just rounding up this point n hat second
+
+ align:start position:0%
+just rounding up this point n hat second
+ 
+
+ align:start position:0%
+just rounding up this point n hat second
+best um so what is the first order
+
+ align:start position:0%
+best um so what is the first order
+ 
+
+ align:start position:0%
+best um so what is the first order
+condition defining n hat second best
+
+ align:start position:0%
+condition defining n hat second best
+ 
+
+ align:start position:0%
+condition defining n hat second best
+well it's just you know the first order
+
+ align:start position:0%
+well it's just you know the first order
+ 
+
+ align:start position:0%
+well it's just you know the first order
+condition is DW of
+
+ align:start position:0%
+condition is DW of
+ 
+
+ align:start position:0%
+condition is DW of
+n
+
+ align:start position:0%
+n
+ 
+
+ align:start position:0%
+n
+DN equals evaluated at n hat second best
+
+ align:start position:0%
+DN equals evaluated at n hat second best
+ 
+
+ align:start position:0%
+DN equals evaluated at n hat second best
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+zero right that's what determines this
+
+ align:start position:0%
+zero right that's what determines this
+ 
+
+ align:start position:0%
+zero right that's what determines this
+point
+
+ align:start position:0%
+point
+ 
+
+ align:start position:0%
+point
+here um what does that derivative look
+
+ align:start position:0%
+here um what does that derivative look
+ 
+
+ align:start position:0%
+here um what does that derivative look
+like so I differentiate this expression
+
+ align:start position:0%
+like so I differentiate this expression
+ 
+
+ align:start position:0%
+like so I differentiate this expression
+with respect to n the first term only
+
+ align:start position:0%
+with respect to n the first term only
+ 
+
+ align:start position:0%
+with respect to n the first term only
+depends on N through the upper limit of
+
+ align:start position:0%
+depends on N through the upper limit of
+ 
+
+ align:start position:0%
+depends on N through the upper limit of
+integration um so the derivative of this
+
+ align:start position:0%
+integration um so the derivative of this
+ 
+
+ align:start position:0%
+integration um so the derivative of this
+with respect to n is just um the value
+
+ align:start position:0%
+with respect to n is just um the value
+ 
+
+ align:start position:0%
+with respect to n is just um the value
+of this evaluated at n qar of n p of NQ
+
+ align:start position:0%
+of this evaluated at n qar of n p of NQ
+ 
+
+ align:start position:0%
+of this evaluated at n qar of n p of NQ
+star of n times the amount by which the
+
+ align:start position:0%
+star of n times the amount by which the
+ 
+
+ align:start position:0%
+star of n times the amount by which the
+the upper limit moves when n changes so
+
+ align:start position:0%
+the upper limit moves when n changes so
+ 
+
+ align:start position:0%
+the upper limit moves when n changes so
+the derivative of this with respect to n
+
+ align:start position:0%
+the derivative of this with respect to n
+ 
+
+ align:start position:0%
+the derivative of this with respect to n
+is what I wrote down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here okay the second effect of n on
+
+ align:start position:0%
+here okay the second effect of n on
+ 
+
+ align:start position:0%
+here okay the second effect of n on
+welfare is this term changes n c of qar
+
+ align:start position:0%
+welfare is this term changes n c of qar
+ 
+
+ align:start position:0%
+welfare is this term changes n c of qar
+of n so the derivative of that with
+
+ align:start position:0%
+of n so the derivative of that with
+ 
+
+ align:start position:0%
+of n so the derivative of that with
+respect to n is C of qar of n plus n c
+
+ align:start position:0%
+respect to n is C of qar of n plus n c
+ 
+
+ align:start position:0%
+respect to n is C of qar of n plus n c
+Prime at qar of n qar Prime at n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so that's the derivative of the second
+
+ align:start position:0%
+so that's the derivative of the second
+ 
+
+ align:start position:0%
+so that's the derivative of the second
+term and then the derivative of the
+
+ align:start position:0%
+term and then the derivative of the
+ 
+
+ align:start position:0%
+term and then the derivative of the
+third term with respect to n is just
+
+ align:start position:0%
+third term with respect to n is just
+ 
+
+ align:start position:0%
+third term with respect to n is just
+K so I just differentiate this
+
+ align:start position:0%
+K so I just differentiate this
+ 
+
+ align:start position:0%
+K so I just differentiate this
+expression with respect to N I say that
+
+ align:start position:0%
+expression with respect to N I say that
+ 
+
+ align:start position:0%
+expression with respect to N I say that
+evaluated at n hat second best is going
+
+ align:start position:0%
+evaluated at n hat second best is going
+ 
+
+ align:start position:0%
+evaluated at n hat second best is going
+to be equal to
+
+ align:start position:0%
+to be equal to
+ 
+
+ align:start position:0%
+to be equal to
+zero and then I'm going to start
+
+ align:start position:0%
+zero and then I'm going to start
+ 
+
+ align:start position:0%
+zero and then I'm going to start
+grouping
+
+ align:start position:0%
+grouping
+ 
+
+ align:start position:0%
+grouping
+terms uh first term I pull together
+
+ align:start position:0%
+terms uh first term I pull together
+ 
+
+ align:start position:0%
+terms uh first term I pull together
+are um P * Q minus C of Q and so I'm
+
+ align:start position:0%
+are um P * Q minus C of Q and so I'm
+ 
+
+ align:start position:0%
+are um P * Q minus C of Q and so I'm
+going to take this term times this minus
+
+ align:start position:0%
+going to take this term times this minus
+ 
+
+ align:start position:0%
+going to take this term times this minus
+this and call that the variable profit
+
+ align:start position:0%
+this and call that the variable profit
+ 
+
+ align:start position:0%
+this and call that the variable profit
+so that's Pi V Star of
+
+ align:start position:0%
+so that's Pi V Star of
+ 
+
+ align:start position:0%
+so that's Pi V Star of
+n um what's left over everything that's
+
+ align:start position:0%
+n um what's left over everything that's
+ 
+
+ align:start position:0%
+n um what's left over everything that's
+left over has an N qar Prime of n well
+
+ align:start position:0%
+left over has an N qar Prime of n well
+ 
+
+ align:start position:0%
+left over has an N qar Prime of n well
+there are two terms left over this times
+
+ align:start position:0%
+there are two terms left over this times
+ 
+
+ align:start position:0%
+there are two terms left over this times
+this and this that have an N qar Prime
+
+ align:start position:0%
+this and this that have an N qar Prime
+ 
+
+ align:start position:0%
+this and this that have an N qar Prime
+at n and those become n qar Prime at n *
+
+ align:start position:0%
+at n and those become n qar Prime at n *
+ 
+
+ align:start position:0%
+at n and those become n qar Prime at n *
+price minus marginal
+
+ align:start position:0%
+price minus marginal
+ 
+
+ align:start position:0%
+price minus marginal
+cost and then the third thing that's
+
+ align:start position:0%
+cost and then the third thing that's
+ 
+
+ align:start position:0%
+cost and then the third thing that's
+left over is the K at the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+end and then under this assumption that
+
+ align:start position:0%
+end and then under this assumption that
+ 
+
+ align:start position:0%
+end and then under this assumption that
+I made that um uh price minus marginal
+
+ align:start position:0%
+I made that um uh price minus marginal
+ 
+
+ align:start position:0%
+I made that um uh price minus marginal
+cost is always positive at the
+
+ align:start position:0%
+cost is always positive at the
+ 
+
+ align:start position:0%
+cost is always positive at the
+equilibrium prices this is a positive
+
+ align:start position:0%
+equilibrium prices this is a positive
+ 
+
+ align:start position:0%
+equilibrium prices this is a positive
+number and so what that means is that
+
+ align:start position:0%
+number and so what that means is that
+ 
+
+ align:start position:0%
+number and so what that means is that
+um uh if you evaluate this at n hat
+
+ align:start position:0%
+um uh if you evaluate this at n hat
+ 
+
+ align:start position:0%
+um uh if you evaluate this at n hat
+second best I get um variable profit
+
+ align:start position:0%
+second best I get um variable profit
+ 
+
+ align:start position:0%
+second best I get um variable profit
+uh minus K plus this uh equals Zer is
+
+ align:start position:0%
+uh minus K plus this uh equals Zer is
+ 
+
+ align:start position:0%
+uh minus K plus this uh equals Zer is
+that tells me that the variable profit
+
+ align:start position:0%
+that tells me that the variable profit
+ 
+
+ align:start position:0%
+that tells me that the variable profit
+evaluated n second best minus K is
+
+ align:start position:0%
+evaluated n second best minus K is
+ 
+
+ align:start position:0%
+evaluated n second best minus K is
+strictly positive which means that One X
+
+ align:start position:0%
+strictly positive which means that One X
+ 
+
+ align:start position:0%
+strictly positive which means that One X
+you know at at n hat second
+
+ align:start position:0%
+you know at at n hat second
+ 
+
+ align:start position:0%
+you know at at n hat second
+best variable profit is is bigger than K
+
+ align:start position:0%
+best variable profit is is bigger than K
+ 
+
+ align:start position:0%
+best variable profit is is bigger than K
+so it means other firms would like to
+
+ align:start position:0%
+so it means other firms would like to
+ 
+
+ align:start position:0%
+so it means other firms would like to
+come in so you know if we had exactly
+
+ align:start position:0%
+come in so you know if we had exactly
+ 
+
+ align:start position:0%
+come in so you know if we had exactly
+this many firms not that this is an
+
+ align:start position:0%
+this many firms not that this is an
+ 
+
+ align:start position:0%
+this many firms not that this is an
+integer the next firm always wants to
+
+ align:start position:0%
+integer the next firm always wants to
+ 
+
+ align:start position:0%
+integer the next firm always wants to
+come in so that means the equilibrium
+
+ align:start position:0%
+come in so that means the equilibrium
+ 
+
+ align:start position:0%
+come in so that means the equilibrium
+entry
+
+ align:start position:0%
+entry
+ 
+
+ align:start position:0%
+entry
+uh equilibrium entry
+
+ align:start position:0%
+uh equilibrium entry
+ 
+
+ align:start position:0%
+uh equilibrium entry
+oops um so equilibrium entry is at least
+
+ align:start position:0%
+oops um so equilibrium entry is at least
+ 
+
+ align:start position:0%
+oops um so equilibrium entry is at least
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+here because at you know at this point
+
+ align:start position:0%
+here because at you know at this point
+ 
+
+ align:start position:0%
+here because at you know at this point
+we know a firm wants to come in at this
+
+ align:start position:0%
+we know a firm wants to come in at this
+ 
+
+ align:start position:0%
+we know a firm wants to come in at this
+point we don't know but if you're if
+
+ align:start position:0%
+point we don't know but if you're if
+ 
+
+ align:start position:0%
+point we don't know but if you're if
+you're less then you definitely want to
+
+ align:start position:0%
+you're less then you definitely want to
+ 
+
+ align:start position:0%
+you're less then you definitely want to
+come in because Pi V Star is a
+
+ align:start position:0%
+come in because Pi V Star is a
+ 
+
+ align:start position:0%
+come in because Pi V Star is a
+decreasing function so Pi V Star is
+
+ align:start position:0%
+decreasing function so Pi V Star is
+ 
+
+ align:start position:0%
+decreasing function so Pi V Star is
+bigger than k at this point so Pi V Star
+
+ align:start position:0%
+bigger than k at this point so Pi V Star
+ 
+
+ align:start position:0%
+bigger than k at this point so Pi V Star
+is also bigger than k at this point so n
+
+ align:start position:0%
+is also bigger than k at this point so n
+ 
+
+ align:start position:0%
+is also bigger than k at this point so n
+star you know is somewhere out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here so Nar is at least what you get is
+
+ align:start position:0%
+here so Nar is at least what you get is
+ 
+
+ align:start position:0%
+here so Nar is at least what you get is
+at least here uh and what did I say I
+
+ align:start position:0%
+at least here uh and what did I say I
+ 
+
+ align:start position:0%
+at least here uh and what did I say I
+said that you know the first
+
+ align:start position:0%
+said that you know the first
+ 
+
+ align:start position:0%
+said that you know the first
+best um and second
+
+ align:start position:0%
+best um and second
+ 
+
+ align:start position:0%
+best um and second
+best is one of these so if n second best
+
+ align:start position:0%
+best is one of these so if n second best
+ 
+
+ align:start position:0%
+best is one of these so if n second best
+is either this point or this point the
+
+ align:start position:0%
+is either this point or this point the
+ 
+
+ align:start position:0%
+is either this point or this point the
+equilibrium number is somewhere this
+
+ align:start position:0%
+equilibrium number is somewhere this
+ 
+
+ align:start position:0%
+equilibrium number is somewhere this
+point or higher we're always getting too
+
+ align:start position:0%
+point or higher we're always getting too
+ 
+
+ align:start position:0%
+point or higher we're always getting too
+many firms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in is that is that okay
+
+ align:start position:0%
+in is that is that okay
+ 
+
+ align:start position:0%
+in is that is that okay
+you know maybe I have the next page just
+
+ align:start position:0%
+you know maybe I have the next page just
+ 
+
+ align:start position:0%
+you know maybe I have the next page just
+sort of easier maybe simpler
+
+ align:start position:0%
+sort of easier maybe simpler
+ 
+
+ align:start position:0%
+sort of easier maybe simpler
+intuition you know in a homogeneous good
+
+ align:start position:0%
+intuition you know in a homogeneous good
+ 
+
+ align:start position:0%
+intuition you know in a homogeneous good
+model the only benefit that anyone gets
+
+ align:start position:0%
+model the only benefit that anyone gets
+ 
+
+ align:start position:0%
+model the only benefit that anyone gets
+from entry is that we reduce the dead
+
+ align:start position:0%
+from entry is that we reduce the dead
+ 
+
+ align:start position:0%
+from entry is that we reduce the dead
+weight loss we get quantity
+
+ align:start position:0%
+weight loss we get quantity
+ 
+
+ align:start position:0%
+weight loss we get quantity
+increases right so what are the total
+
+ align:start position:0%
+increases right so what are the total
+ 
+
+ align:start position:0%
+increases right so what are the total
+gross Surplus you know total consumer
+
+ align:start position:0%
+gross Surplus you know total consumer
+ 
+
+ align:start position:0%
+gross Surplus you know total consumer
+and and firm benefits from the extra
+
+ align:start position:0%
+and and firm benefits from the extra
+ 
+
+ align:start position:0%
+and and firm benefits from the extra
+entry it's just the extra quantity that
+
+ align:start position:0%
+entry it's just the extra quantity that
+ 
+
+ align:start position:0%
+entry it's just the extra quantity that
+gets produced times P star minus C where
+
+ align:start position:0%
+gets produced times P star minus C where
+ 
+
+ align:start position:0%
+gets produced times P star minus C where
+P star is like the equilibrium profit
+
+ align:start position:0%
+P star is like the equilibrium profit
+ 
+
+ align:start position:0%
+P star is like the equilibrium profit
+you get at the equilibrium number of
+
+ align:start position:0%
+you get at the equilibrium number of
+ 
+
+ align:start position:0%
+you get at the equilibrium number of
+firms so we LD in more firms the welfare
+
+ align:start position:0%
+firms so we LD in more firms the welfare
+ 
+
+ align:start position:0%
+firms so we LD in more firms the welfare
+benefit is just how much did quantity go
+
+ align:start position:0%
+benefit is just how much did quantity go
+ 
+
+ align:start position:0%
+benefit is just how much did quantity go
+up times P star minus C okay
+
+ align:start position:0%
+up times P star minus C okay
+ 
+
+ align:start position:0%
+up times P star minus C okay
+um what does the entering firm get the
+
+ align:start position:0%
+um what does the entering firm get the
+ 
+
+ align:start position:0%
+um what does the entering firm get the
+entering firm gets much more than this
+
+ align:start position:0%
+entering firm gets much more than this
+ 
+
+ align:start position:0%
+entering firm gets much more than this
+because it's not the entering firm is
+
+ align:start position:0%
+because it's not the entering firm is
+ 
+
+ align:start position:0%
+because it's not the entering firm is
+not just selling the amount by which
+
+ align:start position:0%
+not just selling the amount by which
+ 
+
+ align:start position:0%
+not just selling the amount by which
+quantity has gone up the entering firm
+
+ align:start position:0%
+quantity has gone up the entering firm
+ 
+
+ align:start position:0%
+quantity has gone up the entering firm
+is getting that Quant it's getting you
+
+ align:start position:0%
+is getting that Quant it's getting you
+ 
+
+ align:start position:0%
+is getting that Quant it's getting you
+know the extra quantity but it's also
+
+ align:start position:0%
+know the extra quantity but it's also
+ 
+
+ align:start position:0%
+know the extra quantity but it's also
+stealing some quantity away from all the
+
+ align:start position:0%
+stealing some quantity away from all the
+ 
+
+ align:start position:0%
+stealing some quantity away from all the
+other firms that were there before and
+
+ align:start position:0%
+other firms that were there before and
+ 
+
+ align:start position:0%
+other firms that were there before and
+so people call that the sort of business
+
+ align:start position:0%
+so people call that the sort of business
+ 
+
+ align:start position:0%
+so people call that the sort of business
+dealing effect that the amount by which
+
+ align:start position:0%
+dealing effect that the amount by which
+ 
+
+ align:start position:0%
+dealing effect that the amount by which
+quantity goes up which is the welfare
+
+ align:start position:0%
+quantity goes up which is the welfare
+ 
+
+ align:start position:0%
+quantity goes up which is the welfare
+gain is much smaller than the amount by
+
+ align:start position:0%
+gain is much smaller than the amount by
+ 
+
+ align:start position:0%
+gain is much smaller than the amount by
+which sales go up for the last firm that
+
+ align:start position:0%
+which sales go up for the last firm that
+ 
+
+ align:start position:0%
+which sales go up for the last firm that
+comes in so the last firm's profits you
+
+ align:start position:0%
+comes in so the last firm's profits you
+ 
+
+ align:start position:0%
+comes in so the last firm's profits you
+know the the social cost of it coming in
+
+ align:start position:0%
+know the the social cost of it coming in
+ 
+
+ align:start position:0%
+know the the social cost of it coming in
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+k um the social benefit of it coming in
+
+ align:start position:0%
+k um the social benefit of it coming in
+ 
+
+ align:start position:0%
+k um the social benefit of it coming in
+is like Delta Q * P minus C but its
+
+ align:start position:0%
+is like Delta Q * P minus C but its
+ 
+
+ align:start position:0%
+is like Delta Q * P minus C but its
+profits are much bigger than its
+
+ align:start position:0%
+profits are much bigger than its
+ 
+
+ align:start position:0%
+profits are much bigger than its
+variable profits are much bigger than
+
+ align:start position:0%
+variable profits are much bigger than
+ 
+
+ align:start position:0%
+variable profits are much bigger than
+Delta Q * P minus C because it's getting
+
+ align:start position:0%
+Delta Q * P minus C because it's getting
+ 
+
+ align:start position:0%
+Delta Q * P minus C because it's getting
+all the profits on all the other units
+
+ align:start position:0%
+all the profits on all the other units
+ 
+
+ align:start position:0%
+all the profits on all the other units
+it's taken away from other firms instead
+
+ align:start position:0%
+it's taken away from other firms instead
+ 
+
+ align:start position:0%
+it's taken away from other firms instead
+and so that's the business stealing
+
+ align:start position:0%
+and so that's the business stealing
+ 
+
+ align:start position:0%
+and so that's the business stealing
+effect and in this um homogeneous good
+
+ align:start position:0%
+effect and in this um homogeneous good
+ 
+
+ align:start position:0%
+effect and in this um homogeneous good
+model right that business dealing effect
+
+ align:start position:0%
+model right that business dealing effect
+ 
+
+ align:start position:0%
+model right that business dealing effect
+is positive therefore you get too much
+
+ align:start position:0%
+is positive therefore you get too much
+ 
+
+ align:start position:0%
+is positive therefore you get too much
+entry other than this possible rounding
+
+ align:start position:0%
+entry other than this possible rounding
+ 
+
+ align:start position:0%
+entry other than this possible rounding
+error question okay um you know as I
+
+ align:start position:0%
+error question okay um you know as I
+ 
+
+ align:start position:0%
+error question okay um you know as I
+said it's true up to a rounding error
+
+ align:start position:0%
+said it's true up to a rounding error
+ 
+
+ align:start position:0%
+said it's true up to a rounding error
+but if you do numerical examples you
+
+ align:start position:0%
+but if you do numerical examples you
+ 
+
+ align:start position:0%
+but if you do numerical examples you
+find that you often get many many more
+
+ align:start position:0%
+find that you often get many many more
+ 
+
+ align:start position:0%
+find that you often get many many more
+firms than the soci than than you want
+
+ align:start position:0%
+firms than the soci than than you want
+ 
+
+ align:start position:0%
+firms than the soci than than you want
+um socially uh and the reason is that
+
+ align:start position:0%
+um socially uh and the reason is that
+ 
+
+ align:start position:0%
+um socially uh and the reason is that
+you know it's not just some of the
+
+ align:start position:0%
+you know it's not just some of the
+ 
+
+ align:start position:0%
+you know it's not just some of the
+demand is is business dealing most of
+
+ align:start position:0%
+demand is is business dealing most of
+ 
+
+ align:start position:0%
+demand is is business dealing most of
+the demand is business dealing so like
+
+ align:start position:0%
+the demand is business dealing so like
+ 
+
+ align:start position:0%
+the demand is business dealing so like
+in this Kuno example D of p is 1 minus P
+
+ align:start position:0%
+in this Kuno example D of p is 1 minus P
+ 
+
+ align:start position:0%
+in this Kuno example D of p is 1 minus P
+qar of n is 1 over n +
+
+ align:start position:0%
+qar of n is 1 over n +
+ 
+
+ align:start position:0%
+qar of n is 1 over n +
+one so what do you get from adding an
+
+ align:start position:0%
+one so what do you get from adding an
+ 
+
+ align:start position:0%
+one so what do you get from adding an
+nth firm you know demand when you have n
+
+ align:start position:0%
+nth firm you know demand when you have n
+ 
+
+ align:start position:0%
+nth firm you know demand when you have n
+firms production goes up to n/ n plus 1
+
+ align:start position:0%
+firms production goes up to n/ n plus 1
+ 
+
+ align:start position:0%
+firms production goes up to n/ n plus 1
+where it used to be n minus one over n
+
+ align:start position:0%
+where it used to be n minus one over n
+ 
+
+ align:start position:0%
+where it used to be n minus one over n
+and so that difference is 1/ n * n +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+1 the nth firm is producing 1/ n + one
+
+ align:start position:0%
+1 the nth firm is producing 1/ n + one
+ 
+
+ align:start position:0%
+1 the nth firm is producing 1/ n + one
+so like 1/n fraction of its output is
+
+ align:start position:0%
+so like 1/n fraction of its output is
+ 
+
+ align:start position:0%
+so like 1/n fraction of its output is
+actual added output n minus one over n
+
+ align:start position:0%
+actual added output n minus one over n
+ 
+
+ align:start position:0%
+actual added output n minus one over n
+of its output is business dealing output
+
+ align:start position:0%
+of its output is business dealing output
+ 
+
+ align:start position:0%
+of its output is business dealing output
+and so in some sense the incentive that
+
+ align:start position:0%
+and so in some sense the incentive that
+ 
+
+ align:start position:0%
+and so in some sense the incentive that
+it has to enter is n times too large
+
+ align:start position:0%
+it has to enter is n times too large
+ 
+
+ align:start position:0%
+it has to enter is n times too large
+because it's it's sort of treating one
+
+ align:start position:0%
+because it's it's sort of treating one
+ 
+
+ align:start position:0%
+because it's it's sort of treating one
+over n plus one as it's as the benefit
+
+ align:start position:0%
+over n plus one as it's as the benefit
+ 
+
+ align:start position:0%
+over n plus one as it's as the benefit
+it's getting whereas one over n times
+
+ align:start position:0%
+it's getting whereas one over n times
+ 
+
+ align:start position:0%
+it's getting whereas one over n times
+that is actually the social benefit that
+
+ align:start position:0%
+that is actually the social benefit that
+ 
+
+ align:start position:0%
+that is actually the social benefit that
+it's producing okay and so you know
+
+ align:start position:0%
+it's producing okay and so you know
+ 
+
+ align:start position:0%
+it's producing okay and so you know
+because you know private benefit is n
+
+ align:start position:0%
+because you know private benefit is n
+ 
+
+ align:start position:0%
+because you know private benefit is n
+times the social benefit when private
+
+ align:start position:0%
+times the social benefit when private
+ 
+
+ align:start position:0%
+times the social benefit when private
+benefit is end times a social benefit
+
+ align:start position:0%
+benefit is end times a social benefit
+ 
+
+ align:start position:0%
+benefit is end times a social benefit
+you can get way way too many firms into
+
+ align:start position:0%
+you can get way way too many firms into
+ 
+
+ align:start position:0%
+you can get way way too many firms into
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+market
+
+ align:start position:0%
+market
+ 
+
+ align:start position:0%
+market
+okay okay so now let me think about you
+
+ align:start position:0%
+okay okay so now let me think about you
+ 
+
+ align:start position:0%
+okay okay so now let me think about you
+know that was entry when you have
+
+ align:start position:0%
+know that was entry when you have
+ 
+
+ align:start position:0%
+know that was entry when you have
+homogeneous Goods what happens when you
+
+ align:start position:0%
+homogeneous Goods what happens when you
+ 
+
+ align:start position:0%
+homogeneous Goods what happens when you
+get away from homog genous Goods when
+
+ align:start position:0%
+get away from homog genous Goods when
+ 
+
+ align:start position:0%
+get away from homog genous Goods when
+you get away from homogeneous Goods
+
+ align:start position:0%
+you get away from homogeneous Goods
+ 
+
+ align:start position:0%
+you get away from homogeneous Goods
+entry can be too high or too low okay
+
+ align:start position:0%
+entry can be too high or too low okay
+ 
+
+ align:start position:0%
+entry can be too high or too low okay
+and why is that well set General setup
+
+ align:start position:0%
+and why is that well set General setup
+ 
+
+ align:start position:0%
+and why is that well set General setup
+welfare when you have n firms it's going
+
+ align:start position:0%
+welfare when you have n firms it's going
+ 
+
+ align:start position:0%
+welfare when you have n firms it's going
+to be the sum of all the firms in the
+
+ align:start position:0%
+to be the sum of all the firms in the
+ 
+
+ align:start position:0%
+to be the sum of all the firms in the
+market of their variable
+
+ align:start position:0%
+market of their variable
+ 
+
+ align:start position:0%
+market of their variable
+profits plus the total consumer surplus
+
+ align:start position:0%
+profits plus the total consumer surplus
+ 
+
+ align:start position:0%
+profits plus the total consumer surplus
+in the market minus the fixed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+costs if I add an N plus first firm um I
+
+ align:start position:0%
+costs if I add an N plus first firm um I
+ 
+
+ align:start position:0%
+costs if I add an N plus first firm um I
+get the sum Over N plus one firms
+
+ align:start position:0%
+get the sum Over N plus one firms
+ 
+
+ align:start position:0%
+get the sum Over N plus one firms
+instead of n firms of the variable
+
+ align:start position:0%
+instead of n firms of the variable
+ 
+
+ align:start position:0%
+instead of n firms of the variable
+profits I now get consumer surplus when
+
+ align:start position:0%
+profits I now get consumer surplus when
+ 
+
+ align:start position:0%
+profits I now get consumer surplus when
+you have n plus1 firms but I pay higher
+
+ align:start position:0%
+you have n plus1 firms but I pay higher
+ 
+
+ align:start position:0%
+you have n plus1 firms but I pay higher
+fixed
+
+ align:start position:0%
+fixed
+ 
+
+ align:start position:0%
+fixed
+costs so what's the change in welfare
+
+ align:start position:0%
+costs so what's the change in welfare
+ 
+
+ align:start position:0%
+costs so what's the change in welfare
+from the last
+
+ align:start position:0%
+from the last
+ 
+
+ align:start position:0%
+from the last
+entrant um first let me group together
+
+ align:start position:0%
+entrant um first let me group together
+ 
+
+ align:start position:0%
+entrant um first let me group together
+the firm that's here that wasn't in this
+
+ align:start position:0%
+the firm that's here that wasn't in this
+ 
+
+ align:start position:0%
+the firm that's here that wasn't in this
+sum the N firm n plus one I get the
+
+ align:start position:0%
+sum the N firm n plus one I get the
+ 
+
+ align:start position:0%
+sum the N firm n plus one I get the
+variable profit of firm n plus one minus
+
+ align:start position:0%
+variable profit of firm n plus one minus
+ 
+
+ align:start position:0%
+variable profit of firm n plus one minus
+its fixed cost that's a difference
+
+ align:start position:0%
+its fixed cost that's a difference
+ 
+
+ align:start position:0%
+its fixed cost that's a difference
+here and then I get two other terms the
+
+ align:start position:0%
+here and then I get two other terms the
+ 
+
+ align:start position:0%
+here and then I get two other terms the
+first is subtracting the corresponding
+
+ align:start position:0%
+first is subtracting the corresponding
+ 
+
+ align:start position:0%
+first is subtracting the corresponding
+I's here I get sum IAL 1 to n variable
+
+ align:start position:0%
+I's here I get sum IAL 1 to n variable
+ 
+
+ align:start position:0%
+I's here I get sum IAL 1 to n variable
+profits of firm I with n plus one versus
+
+ align:start position:0%
+profits of firm I with n plus one versus
+ 
+
+ align:start position:0%
+profits of firm I with n plus one versus
+n firms and then I get the consumer
+
+ align:start position:0%
+n firms and then I get the consumer
+ 
+
+ align:start position:0%
+n firms and then I get the consumer
+surplus with n plus one minus n
+
+ align:start position:0%
+surplus with n plus one minus n
+ 
+
+ align:start position:0%
+surplus with n plus one minus n
+firms
+
+ align:start position:0%
+firms
+ 
+
+ align:start position:0%
+firms
+um so when I when I wrote here entry is
+
+ align:start position:0%
+um so when I when I wrote here entry is
+ 
+
+ align:start position:0%
+um so when I when I wrote here entry is
+socially optimal I probably should have
+
+ align:start position:0%
+socially optimal I probably should have
+ 
+
+ align:start position:0%
+socially optimal I probably should have
+said entry of firm n plus one is
+
+ align:start position:0%
+said entry of firm n plus one is
+ 
+
+ align:start position:0%
+said entry of firm n plus one is
+socially optimal if this Delta W is
+
+ align:start position:0%
+socially optimal if this Delta W is
+ 
+
+ align:start position:0%
+socially optimal if this Delta W is
+positive um
+
+ align:start position:0%
+positive um
+ 
+
+ align:start position:0%
+positive um
+why might free entry you know so what we
+
+ align:start position:0%
+why might free entry you know so what we
+ 
+
+ align:start position:0%
+why might free entry you know so what we
+want is if this is positive we want firm
+
+ align:start position:0%
+want is if this is positive we want firm
+ 
+
+ align:start position:0%
+want is if this is positive we want firm
+n plus one to come in and if firm if
+
+ align:start position:0%
+n plus one to come in and if firm if
+ 
+
+ align:start position:0%
+n plus one to come in and if firm if
+Delta W was negative we don't want firm
+
+ align:start position:0%
+Delta W was negative we don't want firm
+ 
+
+ align:start position:0%
+Delta W was negative we don't want firm
+n plus one to come
+
+ align:start position:0%
+n plus one to come
+ 
+
+ align:start position:0%
+n plus one to come
+in okay so first of all why might entry
+
+ align:start position:0%
+in okay so first of all why might entry
+ 
+
+ align:start position:0%
+in okay so first of all why might entry
+be excessive so entry would be excessive
+
+ align:start position:0%
+be excessive so entry would be excessive
+ 
+
+ align:start position:0%
+be excessive so entry would be excessive
+if this was positive but this was
+
+ align:start position:0%
+if this was positive but this was
+ 
+
+ align:start position:0%
+if this was positive but this was
+negative why could this be positive and
+
+ align:start position:0%
+negative why could this be positive and
+ 
+
+ align:start position:0%
+negative why could this be positive and
+this be negative well you know if this
+
+ align:start position:0%
+this be negative well you know if this
+ 
+
+ align:start position:0%
+this be negative well you know if this
+is positive to make a but small to make
+
+ align:start position:0%
+is positive to make a but small to make
+ 
+
+ align:start position:0%
+is positive to make a but small to make
+a firm want to come in
+
+ align:start position:0%
+a firm want to come in
+ 
+
+ align:start position:0%
+a firm want to come in
+but this is a big negative number and
+
+ align:start position:0%
+but this is a big negative number and
+ 
+
+ align:start position:0%
+but this is a big negative number and
+why could this be a big negative number
+
+ align:start position:0%
+why could this be a big negative number
+ 
+
+ align:start position:0%
+why could this be a big negative number
+you know this is how every other firm's
+
+ align:start position:0%
+you know this is how every other firm's
+ 
+
+ align:start position:0%
+you know this is how every other firm's
+profits are affected by me coming in if
+
+ align:start position:0%
+profits are affected by me coming in if
+ 
+
+ align:start position:0%
+profits are affected by me coming in if
+I drive down prices and I take quantity
+
+ align:start position:0%
+I drive down prices and I take quantity
+ 
+
+ align:start position:0%
+I drive down prices and I take quantity
+away from the other firms you know they
+
+ align:start position:0%
+away from the other firms you know they
+ 
+
+ align:start position:0%
+away from the other firms you know they
+suffer both because the profits they
+
+ align:start position:0%
+suffer both because the profits they
+ 
+
+ align:start position:0%
+suffer both because the profits they
+earn on the units they still sell go
+
+ align:start position:0%
+earn on the units they still sell go
+ 
+
+ align:start position:0%
+earn on the units they still sell go
+down and because that they don't sell
+
+ align:start position:0%
+down and because that they don't sell
+ 
+
+ align:start position:0%
+down and because that they don't sell
+some units and they don't own P star
+
+ align:start position:0%
+some units and they don't own P star
+ 
+
+ align:start position:0%
+some units and they don't own P star
+minus C so this is what we call again
+
+ align:start position:0%
+minus C so this is what we call again
+ 
+
+ align:start position:0%
+minus C so this is what we call again
+this is the business stealing effect if
+
+ align:start position:0%
+this is the business stealing effect if
+ 
+
+ align:start position:0%
+this is the business stealing effect if
+this business stealing number is NE is
+
+ align:start position:0%
+this business stealing number is NE is
+ 
+
+ align:start position:0%
+this business stealing number is NE is
+is always negative if it's a big
+
+ align:start position:0%
+is always negative if it's a big
+ 
+
+ align:start position:0%
+is always negative if it's a big
+negative number and this is a small
+
+ align:start position:0%
+negative number and this is a small
+ 
+
+ align:start position:0%
+negative number and this is a small
+positive number we can get the entrant
+
+ align:start position:0%
+positive number we can get the entrant
+ 
+
+ align:start position:0%
+positive number we can get the entrant
+coming in even though this business
+
+ align:start position:0%
+coming in even though this business
+ 
+
+ align:start position:0%
+coming in even though this business
+stealing term is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+negative um but then you know the second
+
+ align:start position:0%
+negative um but then you know the second
+ 
+
+ align:start position:0%
+negative um but then you know the second
+effect is that we could have firm n
+
+ align:start position:0%
+effect is that we could have firm n
+ 
+
+ align:start position:0%
+effect is that we could have firm n
+doesn't come in because this is
+
+ align:start position:0%
+doesn't come in because this is
+ 
+
+ align:start position:0%
+doesn't come in because this is
+negative uh and this is negative but
+
+ align:start position:0%
+negative uh and this is negative but
+ 
+
+ align:start position:0%
+negative uh and this is negative but
+Delta W is positive because there's a
+
+ align:start position:0%
+Delta W is positive because there's a
+ 
+
+ align:start position:0%
+Delta W is positive because there's a
+big increase in consumer surplus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you know I showed in the homogeneous
+
+ align:start position:0%
+and you know I showed in the homogeneous
+ 
+
+ align:start position:0%
+and you know I showed in the homogeneous
+good model this doesn't happen except
+
+ align:start position:0%
+good model this doesn't happen except
+ 
+
+ align:start position:0%
+good model this doesn't happen except
+with that ra into that rounding error
+
+ align:start position:0%
+with that ra into that rounding error
+ 
+
+ align:start position:0%
+with that ra into that rounding error
+effect but once you get to heterogeneous
+
+ align:start position:0%
+effect but once you get to heterogeneous
+ 
+
+ align:start position:0%
+effect but once you get to heterogeneous
+Goods like it could be that when you get
+
+ align:start position:0%
+Goods like it could be that when you get
+ 
+
+ align:start position:0%
+Goods like it could be that when you get
+more Goods in the market consumer
+
+ align:start position:0%
+more Goods in the market consumer
+ 
+
+ align:start position:0%
+more Goods in the market consumer
+surplus goes up by more than prices go
+
+ align:start position:0%
+surplus goes up by more than prices go
+ 
+
+ align:start position:0%
+surplus goes up by more than prices go
+down because consumers get a good that's
+
+ align:start position:0%
+down because consumers get a good that's
+ 
+
+ align:start position:0%
+down because consumers get a good that's
+better matched to their tastes and
+
+ align:start position:0%
+better matched to their tastes and
+ 
+
+ align:start position:0%
+better matched to their tastes and
+because the good new good is better
+
+ align:start position:0%
+because the good new good is better
+ 
+
+ align:start position:0%
+because the good new good is better
+matched to their tastes there's a big
+
+ align:start position:0%
+matched to their tastes there's a big
+ 
+
+ align:start position:0%
+matched to their tastes there's a big
+increase in consumer surplus that isn't
+
+ align:start position:0%
+increase in consumer surplus that isn't
+ 
+
+ align:start position:0%
+increase in consumer surplus that isn't
+just the loss and profits and so if the
+
+ align:start position:0%
+just the loss and profits and so if the
+ 
+
+ align:start position:0%
+just the loss and profits and so if the
+increase in consumer surplus is coming
+
+ align:start position:0%
+increase in consumer surplus is coming
+ 
+
+ align:start position:0%
+increase in consumer surplus is coming
+from other channels like match quality
+
+ align:start position:0%
+from other channels like match quality
+ 
+
+ align:start position:0%
+from other channels like match quality
+rather than just from prices going down
+
+ align:start position:0%
+rather than just from prices going down
+ 
+
+ align:start position:0%
+rather than just from prices going down
+then this term can outweigh the business
+
+ align:start position:0%
+then this term can outweigh the business
+ 
+
+ align:start position:0%
+then this term can outweigh the business
+dealing effect and you could have too
+
+ align:start position:0%
+dealing effect and you could have too
+ 
+
+ align:start position:0%
+dealing effect and you could have too
+few firms in a market okay because firms
+
+ align:start position:0%
+few firms in a market okay because firms
+ 
+
+ align:start position:0%
+few firms in a market okay because firms
+just firms don't inter you know like I
+
+ align:start position:0%
+just firms don't inter you know like I
+ 
+
+ align:start position:0%
+just firms don't inter you know like I
+mean firms not internalizing cons
+
+ align:start position:0%
+mean firms not internalizing cons
+ 
+
+ align:start position:0%
+mean firms not internalizing cons
+consumer surplus is why you get too few
+
+ align:start position:0%
+consumer surplus is why you get too few
+ 
+
+ align:start position:0%
+consumer surplus is why you get too few
+firms in the Bertrand model in the
+
+ align:start position:0%
+firms in the Bertrand model in the
+ 
+
+ align:start position:0%
+firms in the Bertrand model in the
+Bertrand model firms don't realize I
+
+ align:start position:0%
+Bertrand model firms don't realize I
+ 
+
+ align:start position:0%
+Bertrand model firms don't realize I
+come in yes I lose some money but all
+
+ align:start position:0%
+come in yes I lose some money but all
+ 
+
+ align:start position:0%
+come in yes I lose some money but all
+those consumers are way better off um
+
+ align:start position:0%
+those consumers are way better off um
+ 
+
+ align:start position:0%
+those consumers are way better off um
+because the consumer the price drops so
+
+ align:start position:0%
+because the consumer the price drops so
+ 
+
+ align:start position:0%
+because the consumer the price drops so
+much uh but in another model it's the
+
+ align:start position:0%
+much uh but in another model it's the
+ 
+
+ align:start position:0%
+much uh but in another model it's the
+consumers don't realize the firms don't
+
+ align:start position:0%
+consumers don't realize the firms don't
+ 
+
+ align:start position:0%
+consumers don't realize the firms don't
+realize that like I come in I don't make
+
+ align:start position:0%
+realize that like I come in I don't make
+ 
+
+ align:start position:0%
+realize that like I come in I don't make
+that much money but consumers are so
+
+ align:start position:0%
+that much money but consumers are so
+ 
+
+ align:start position:0%
+that much money but consumers are so
+happy to have my product that that
+
+ align:start position:0%
+happy to have my product that that
+ 
+
+ align:start position:0%
+happy to have my product that that
+social welfare is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+better
+
+ align:start position:0%
+better
+ 
+
+ align:start position:0%
+better
+um okay any questions but so you know in
+
+ align:start position:0%
+um okay any questions but so you know in
+ 
+
+ align:start position:0%
+um okay any questions but so you know in
+a general model the most General
+
+ align:start position:0%
+a general model the most General
+ 
+
+ align:start position:0%
+a general model the most General
+conclusion is that entry can be too high
+
+ align:start position:0%
+conclusion is that entry can be too high
+ 
+
+ align:start position:0%
+conclusion is that entry can be too high
+or too low socially and it depends on
+
+ align:start position:0%
+or too low socially and it depends on
+ 
+
+ align:start position:0%
+or too low socially and it depends on
+just which of these effects is more
+
+ align:start position:0%
+just which of these effects is more
+ 
+
+ align:start position:0%
+just which of these effects is more
+important the social welfare effect or
+
+ align:start position:0%
+important the social welfare effect or
+ 
+
+ align:start position:0%
+important the social welfare effect or
+the business stealing effect um prices
+
+ align:start position:0%
+the business stealing effect um prices
+ 
+
+ align:start position:0%
+the business stealing effect um prices
+going down alone is not enough is not
+
+ align:start position:0%
+going down alone is not enough is not
+ 
+
+ align:start position:0%
+going down alone is not enough is not
+enough to do it you have got to have
+
+ align:start position:0%
+enough to do it you have got to have
+ 
+
+ align:start position:0%
+enough to do it you have got to have
+other channels of the consumer surplus
+
+ align:start position:0%
+other channels of the consumer surplus
+ 
+
+ align:start position:0%
+other channels of the consumer surplus
+going
+
+ align:start position:0%
+going
+ 
+
+ align:start position:0%
+going
+up okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um I just sort of figured I'd put in one
+
+ align:start position:0%
+um I just sort of figured I'd put in one
+ 
+
+ align:start position:0%
+um I just sort of figured I'd put in one
+slide of what happens if I actually
+
+ align:start position:0%
+slide of what happens if I actually
+ 
+
+ align:start position:0%
+slide of what happens if I actually
+compute these things I I would say that
+
+ align:start position:0%
+compute these things I I would say that
+ 
+
+ align:start position:0%
+compute these things I I would say that
+if you write down the most obvious
+
+ align:start position:0%
+if you write down the most obvious
+ 
+
+ align:start position:0%
+if you write down the most obvious
+models you're going to write down to try
+
+ align:start position:0%
+models you're going to write down to try
+ 
+
+ align:start position:0%
+models you're going to write down to try
+to compute these things while this
+
+ align:start position:0%
+to compute these things while this
+ 
+
+ align:start position:0%
+to compute these things while this
+consumer Surplus effect means that
+
+ align:start position:0%
+consumer Surplus effect means that
+ 
+
+ align:start position:0%
+consumer Surplus effect means that
+welfare can we can get too few firms
+
+ align:start position:0%
+welfare can we can get too few firms
+ 
+
+ align:start position:0%
+welfare can we can get too few firms
+most models you write down if you're not
+
+ align:start position:0%
+most models you write down if you're not
+ 
+
+ align:start position:0%
+most models you write down if you're not
+thinking about writing down something to
+
+ align:start position:0%
+thinking about writing down something to
+ 
+
+ align:start position:0%
+thinking about writing down something to
+get it to happen you're going to also
+
+ align:start position:0%
+get it to happen you're going to also
+ 
+
+ align:start position:0%
+get it to happen you're going to also
+conclude that there's still way too many
+
+ align:start position:0%
+conclude that there's still way too many
+ 
+
+ align:start position:0%
+conclude that there's still way too many
+firms in markets so I I do an example
+
+ align:start position:0%
+firms in markets so I I do an example
+ 
+
+ align:start position:0%
+firms in markets so I I do an example
+here so you know consider a hoteling
+
+ align:start position:0%
+here so you know consider a hoteling
+ 
+
+ align:start position:0%
+here so you know consider a hoteling
+like model where you have a mass m of
+
+ align:start position:0%
+like model where you have a mass m of
+ 
+
+ align:start position:0%
+like model where you have a mass m of
+consumers and can I write over here so
+
+ align:start position:0%
+consumers and can I write over here so
+ 
+
+ align:start position:0%
+consumers and can I write over here so
+let's think
+
+ align:start position:0%
+let's think
+ 
+
+ align:start position:0%
+let's think
+about uh hotelling Circle so this is a
+
+ align:start position:0%
+about uh hotelling Circle so this is a
+ 
+
+ align:start position:0%
+about uh hotelling Circle so this is a
+um ice cream stand locating around like
+
+ align:start position:0%
+um ice cream stand locating around like
+ 
+
+ align:start position:0%
+um ice cream stand locating around like
+a Hawaiian island that has just beaches
+
+ align:start position:0%
+a Hawaiian island that has just beaches
+ 
+
+ align:start position:0%
+a Hawaiian island that has just beaches
+around the entire perimeter and so if
+
+ align:start position:0%
+around the entire perimeter and so if
+ 
+
+ align:start position:0%
+around the entire perimeter and so if
+you get n
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+firms you know they they suppose you get
+
+ align:start position:0%
+firms you know they they suppose you get
+ 
+
+ align:start position:0%
+firms you know they they suppose you get
+n firms they locate themselves evenly
+
+ align:start position:0%
+n firms they locate themselves evenly
+ 
+
+ align:start position:0%
+n firms they locate themselves evenly
+around the
+
+ align:start position:0%
+around the
+ 
+
+ align:start position:0%
+around the
+circle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um you know in this C+ T model like
+
+ align:start position:0%
+um you know in this C+ T model like
+ 
+
+ align:start position:0%
+um you know in this C+ T model like
+let's if you have n firms the dis the
+
+ align:start position:0%
+let's if you have n firms the dis the
+ 
+
+ align:start position:0%
+let's if you have n firms the dis the
+transportation cost distance between
+
+ align:start position:0%
+transportation cost distance between
+ 
+
+ align:start position:0%
+transportation cost distance between
+here and here is only going to be T Over
+
+ align:start position:0%
+here and here is only going to be T Over
+ 
+
+ align:start position:0%
+here and here is only going to be T Over
+N when you have n firms and so if the if
+
+ align:start position:0%
+N when you have n firms and so if the if
+ 
+
+ align:start position:0%
+N when you have n firms and so if the if
+it's t to walk the whole perimeter of
+
+ align:start position:0%
+it's t to walk the whole perimeter of
+ 
+
+ align:start position:0%
+it's t to walk the whole perimeter of
+the island it's t Over N when you put n
+
+ align:start position:0%
+the island it's t Over N when you put n
+ 
+
+ align:start position:0%
+the island it's t Over N when you put n
+firms around the
+
+ align:start position:0%
+firms around the
+ 
+
+ align:start position:0%
+firms around the
+perimeter okay so if you get n firms
+
+ align:start position:0%
+perimeter okay so if you get n firms
+ 
+
+ align:start position:0%
+perimeter okay so if you get n firms
+that are arranged evenly what you
+
+ align:start position:0%
+that are arranged evenly what you
+ 
+
+ align:start position:0%
+that are arranged evenly what you
+basically get is you know each firm here
+
+ align:start position:0%
+basically get is you know each firm here
+ 
+
+ align:start position:0%
+basically get is you know each firm here
+is just competing with the firm on its
+
+ align:start position:0%
+is just competing with the firm on its
+ 
+
+ align:start position:0%
+is just competing with the firm on its
+right and the firm on its left I didn't
+
+ align:start position:0%
+right and the firm on its left I didn't
+ 
+
+ align:start position:0%
+right and the firm on its left I didn't
+draw those so evenly but let's assume
+
+ align:start position:0%
+draw those so evenly but let's assume
+ 
+
+ align:start position:0%
+draw those so evenly but let's assume
+this distance is T Over N this distance
+
+ align:start position:0%
+this distance is T Over N this distance
+ 
+
+ align:start position:0%
+this distance is T Over N this distance
+is T Over N so it's just like I'm
+
+ align:start position:0%
+is T Over N so it's just like I'm
+ 
+
+ align:start position:0%
+is T Over N so it's just like I'm
+playing two simultaneous hoteling games
+
+ align:start position:0%
+playing two simultaneous hoteling games
+ 
+
+ align:start position:0%
+playing two simultaneous hoteling games
+one against this firm one against this
+
+ align:start position:0%
+one against this firm one against this
+ 
+
+ align:start position:0%
+one against this firm one against this
+firm term so the equilibrium becomes P
+
+ align:start position:0%
+firm term so the equilibrium becomes P
+ 
+
+ align:start position:0%
+firm term so the equilibrium becomes P
+staral C + t
+
+ align:start position:0%
+staral C + t
+ 
+
+ align:start position:0%
+staral C + t
+n uh what's the variable profit uh if
+
+ align:start position:0%
+n uh what's the variable profit uh if
+ 
+
+ align:start position:0%
+n uh what's the variable profit uh if
+there are M consumers on the beach um I
+
+ align:start position:0%
+there are M consumers on the beach um I
+ 
+
+ align:start position:0%
+there are M consumers on the beach um I
+get a fraction one over n of them in
+
+ align:start position:0%
+get a fraction one over n of them in
+ 
+
+ align:start position:0%
+get a fraction one over n of them in
+equilibrium and my markup is T Over N
+
+ align:start position:0%
+equilibrium and my markup is T Over N
+ 
+
+ align:start position:0%
+equilibrium and my markup is T Over N
+so my profits are
+
+ align:start position:0%
+so my profits are
+ 
+
+ align:start position:0%
+so my profits are
+M uh T over
+
+ align:start position:0%
+M uh T over
+ 
+
+ align:start position:0%
+M uh T over
+n^2 I set that equal to K a and then it
+
+ align:start position:0%
+n^2 I set that equal to K a and then it
+ 
+
+ align:start position:0%
+n^2 I set that equal to K a and then it
+just becomes Nal < TK of M * t k so
+
+ align:start position:0%
+just becomes Nal < TK of M * t k so
+ 
+
+ align:start position:0%
+just becomes Nal < TK of M * t k so
+that's you know again as I said you know
+
+ align:start position:0%
+that's you know again as I said you know
+ 
+
+ align:start position:0%
+that's you know again as I said you know
+this is a again larger firms theorem
+
+ align:start position:0%
+this is a again larger firms theorem
+ 
+
+ align:start position:0%
+this is a again larger firms theorem
+that says as the market size goes up the
+
+ align:start position:0%
+that says as the market size goes up the
+ 
+
+ align:start position:0%
+that says as the market size goes up the
+number of firms goes up in this model
+
+ align:start position:0%
+number of firms goes up in this model
+ 
+
+ align:start position:0%
+number of firms goes up in this model
+also like the square root of the number
+
+ align:start position:0%
+also like the square root of the number
+ 
+
+ align:start position:0%
+also like the square root of the number
+of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+customers okay um what's the social
+
+ align:start position:0%
+customers okay um what's the social
+ 
+
+ align:start position:0%
+customers okay um what's the social
+welfare um they M
+
+ align:start position:0%
+welfare um they M
+ 
+
+ align:start position:0%
+welfare um they M
+consumers um
+
+ align:start position:0%
+consumers um
+ 
+
+ align:start position:0%
+consumers um
+you know so suppose we're in this model
+
+ align:start position:0%
+you know so suppose we're in this model
+ 
+
+ align:start position:0%
+you know so suppose we're in this model
+and these things are both T Over
+
+ align:start position:0%
+and these things are both T Over
+ 
+
+ align:start position:0%
+and these things are both T Over
+N social welfare is just total gross
+
+ align:start position:0%
+N social welfare is just total gross
+ 
+
+ align:start position:0%
+N social welfare is just total gross
+Surplus received minus costs of
+
+ align:start position:0%
+Surplus received minus costs of
+ 
+
+ align:start position:0%
+Surplus received minus costs of
+production minus average mismatch
+
+ align:start position:0%
+production minus average mismatch
+ 
+
+ align:start position:0%
+production minus average mismatch
+disutility or or Transportation cost
+
+ align:start position:0%
+disutility or or Transportation cost
+ 
+
+ align:start position:0%
+disutility or or Transportation cost
+disutility you know this guy here sells
+
+ align:start position:0%
+disutility you know this guy here sells
+ 
+
+ align:start position:0%
+disutility you know this guy here sells
+to customers who are within distance T
+
+ align:start position:0%
+to customers who are within distance T
+ 
+
+ align:start position:0%
+to customers who are within distance T
+over 2N to the left
+
+ align:start position:0%
+over 2N to the left
+ 
+
+ align:start position:0%
+over 2N to the left
+and customers within T over 2N to the
+
+ align:start position:0%
+and customers within T over 2N to the
+ 
+
+ align:start position:0%
+and customers within T over 2N to the
+right so he's selling to customers who
+
+ align:start position:0%
+right so he's selling to customers who
+ 
+
+ align:start position:0%
+right so he's selling to customers who
+are you know T Over N is his distance so
+
+ align:start position:0%
+are you know T Over N is his distance so
+ 
+
+ align:start position:0%
+are you know T Over N is his distance so
+everybody equid distant between him and
+
+ align:start position:0%
+everybody equid distant between him and
+ 
+
+ align:start position:0%
+everybody equid distant between him and
+the next firm over buys from him if you
+
+ align:start position:0%
+the next firm over buys from him if you
+ 
+
+ align:start position:0%
+the next firm over buys from him if you
+sell to customers whose distance ranges
+
+ align:start position:0%
+sell to customers whose distance ranges
+ 
+
+ align:start position:0%
+sell to customers whose distance ranges
+from0 to T over 2N the average distance
+
+ align:start position:0%
+from0 to T over 2N the average distance
+ 
+
+ align:start position:0%
+from0 to T over 2N the average distance
+of that people have to travel is T over
+
+ align:start position:0%
+of that people have to travel is T over
+ 
+
+ align:start position:0%
+of that people have to travel is T over
+4N so this is the extra welfare increase
+
+ align:start position:0%
+4N so this is the extra welfare increase
+ 
+
+ align:start position:0%
+4N so this is the extra welfare increase
+that I mentioned that as n increases the
+
+ align:start position:0%
+that I mentioned that as n increases the
+ 
+
+ align:start position:0%
+that I mentioned that as n increases the
+distance traveled goes down down that
+
+ align:start position:0%
+distance traveled goes down down that
+ 
+
+ align:start position:0%
+distance traveled goes down down that
+causes a consumer surplus increase
+
+ align:start position:0%
+causes a consumer surplus increase
+ 
+
+ align:start position:0%
+causes a consumer surplus increase
+that's separate from the one that comes
+
+ align:start position:0%
+that's separate from the one that comes
+ 
+
+ align:start position:0%
+that's separate from the one that comes
+from the price is dropping okay anyway
+
+ align:start position:0%
+from the price is dropping okay anyway
+ 
+
+ align:start position:0%
+from the price is dropping okay anyway
+so in this model total social welfare is
+
+ align:start position:0%
+so in this model total social welfare is
+ 
+
+ align:start position:0%
+so in this model total social welfare is
+M * V minus M * cus M * T 4N minus
+
+ align:start position:0%
+M * V minus M * cus M * T 4N minus
+ 
+
+ align:start position:0%
+M * V minus M * cus M * T 4N minus
+NK uh notice that M * V minus C is
+
+ align:start position:0%
+NK uh notice that M * V minus C is
+ 
+
+ align:start position:0%
+NK uh notice that M * V minus C is
+completely independent of n in in you
+
+ align:start position:0%
+completely independent of n in in you
+ 
+
+ align:start position:0%
+completely independent of n in in you
+know the hoteling model you know
+
+ align:start position:0%
+know the hoteling model you know
+ 
+
+ align:start position:0%
+know the hoteling model you know
+assuming V is large everybody buys all
+
+ align:start position:0%
+assuming V is large everybody buys all
+ 
+
+ align:start position:0%
+assuming V is large everybody buys all
+the time so what we get is uh
+
+ align:start position:0%
+the time so what we get is uh
+ 
+
+ align:start position:0%
+the time so what we get is uh
+differentiating this with respect to n
+
+ align:start position:0%
+differentiating this with respect to n
+ 
+
+ align:start position:0%
+differentiating this with respect to n
+derivative of this with respect to n is
+
+ align:start position:0%
+derivative of this with respect to n is
+ 
+
+ align:start position:0%
+derivative of this with respect to n is
+Mt over 4 * 1 n^ 2 derivative of this
+
+ align:start position:0%
+Mt over 4 * 1 n^ 2 derivative of this
+ 
+
+ align:start position:0%
+Mt over 4 * 1 n^ 2 derivative of this
+with respect to n is just
+
+ align:start position:0%
+with respect to n is just
+ 
+
+ align:start position:0%
+with respect to n is just
+K and so what I get is that Mt over 4 *
+
+ align:start position:0%
+K and so what I get is that Mt over 4 *
+ 
+
+ align:start position:0%
+K and so what I get is that Mt over 4 *
+1 n^2 minus k evalate n second best
+
+ align:start position:0%
+1 n^2 minus k evalate n second best
+ 
+
+ align:start position:0%
+1 n^2 minus k evalate n second best
+equals
+
+ align:start position:0%
+equals
+ 
+
+ align:start position:0%
+equals
+zero n second best is square root of Mt
+
+ align:start position:0%
+zero n second best is square root of Mt
+ 
+
+ align:start position:0%
+zero n second best is square root of Mt
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+4K which is exactly half of uh
+
+ align:start position:0%
+4K which is exactly half of uh
+ 
+
+ align:start position:0%
+4K which is exactly half of uh
+Nar so this is saying in some sense in
+
+ align:start position:0%
+Nar so this is saying in some sense in
+ 
+
+ align:start position:0%
+Nar so this is saying in some sense in
+equilibrium you get exactly twice as
+
+ align:start position:0%
+equilibrium you get exactly twice as
+ 
+
+ align:start position:0%
+equilibrium you get exactly twice as
+many firms as you would
+
+ align:start position:0%
+many firms as you would
+ 
+
+ align:start position:0%
+many firms as you would
+like um and this is just you know it's
+
+ align:start position:0%
+like um and this is just you know it's
+ 
+
+ align:start position:0%
+like um and this is just you know it's
+another case that in this model um you
+
+ align:start position:0%
+another case that in this model um you
+ 
+
+ align:start position:0%
+another case that in this model um you
+know maybe this so this model has the
+
+ align:start position:0%
+know maybe this so this model has the
+ 
+
+ align:start position:0%
+know maybe this so this model has the
+welfare benefit of people getting better
+
+ align:start position:0%
+welfare benefit of people getting better
+ 
+
+ align:start position:0%
+welfare benefit of people getting better
+matches um this model has no Market
+
+ align:start position:0%
+matches um this model has no Market
+ 
+
+ align:start position:0%
+matches um this model has no Market
+expansion effect whatsoever right when
+
+ align:start position:0%
+expansion effect whatsoever right when
+ 
+
+ align:start position:0%
+expansion effect whatsoever right when
+you put in an nth firm it's 100%
+
+ align:start position:0%
+you put in an nth firm it's 100%
+ 
+
+ align:start position:0%
+you put in an nth firm it's 100%
+business dealing and so it turns out
+
+ align:start position:0%
+business dealing and so it turns out
+ 
+
+ align:start position:0%
+business dealing and so it turns out
+that because the extra Market expansion
+
+ align:start position:0%
+that because the extra Market expansion
+ 
+
+ align:start position:0%
+that because the extra Market expansion
+is 100% business dealing so business
+
+ align:start position:0%
+is 100% business dealing so business
+ 
+
+ align:start position:0%
+is 100% business dealing so business
+dealing is a big deal this extra benefit
+
+ align:start position:0%
+dealing is a big deal this extra benefit
+ 
+
+ align:start position:0%
+dealing is a big deal this extra benefit
+that you get from extra match quality
+
+ align:start position:0%
+that you get from extra match quality
+ 
+
+ align:start position:0%
+that you get from extra match quality
+isn't nearly large enough to overcome
+
+ align:start position:0%
+isn't nearly large enough to overcome
+ 
+
+ align:start position:0%
+isn't nearly large enough to overcome
+the business dealing uh negative and
+
+ align:start position:0%
+the business dealing uh negative and
+ 
+
+ align:start position:0%
+the business dealing uh negative and
+you're getting twice as many firms and
+
+ align:start position:0%
+you're getting twice as many firms and
+ 
+
+ align:start position:0%
+you're getting twice as many firms and
+you know and I think you know in some
+
+ align:start position:0%
+you know and I think you know in some
+ 
+
+ align:start position:0%
+you know and I think you know in some
+sense I Al view this as a important
+
+ align:start position:0%
+sense I Al view this as a important
+ 
+
+ align:start position:0%
+sense I Al view this as a important
+question you like you're going to write
+
+ align:start position:0%
+question you like you're going to write
+ 
+
+ align:start position:0%
+question you like you're going to write
+down models with low at demand and
+
+ align:start position:0%
+down models with low at demand and
+ 
+
+ align:start position:0%
+down models with low at demand and
+estimate how many firms you're going to
+
+ align:start position:0%
+estimate how many firms you're going to
+ 
+
+ align:start position:0%
+estimate how many firms you're going to
+get and how many firms you think are
+
+ align:start position:0%
+get and how many firms you think are
+ 
+
+ align:start position:0%
+get and how many firms you think are
+optimal or whatever you know a lot of
+
+ align:start position:0%
+optimal or whatever you know a lot of
+ 
+
+ align:start position:0%
+optimal or whatever you know a lot of
+models like this are are set up you know
+
+ align:start position:0%
+models like this are are set up you know
+ 
+
+ align:start position:0%
+models like this are are set up you know
+again I could have done this model and I
+
+ align:start position:0%
+again I could have done this model and I
+ 
+
+ align:start position:0%
+again I could have done this model and I
+could have sort of said I'm estimating
+
+ align:start position:0%
+could have sort of said I'm estimating
+ 
+
+ align:start position:0%
+could have sort of said I'm estimating
+Demand elasticities by estimating
+
+ align:start position:0%
+Demand elasticities by estimating
+ 
+
+ align:start position:0%
+Demand elasticities by estimating
+T but whatever whatever value of t i
+
+ align:start position:0%
+T but whatever whatever value of t i
+ 
+
+ align:start position:0%
+T but whatever whatever value of t i
+estimated when I estimated this model my
+
+ align:start position:0%
+estimated when I estimated this model my
+ 
+
+ align:start position:0%
+estimated when I estimated this model my
+my model I do my counterfactual and say
+
+ align:start position:0%
+my model I do my counterfactual and say
+ 
+
+ align:start position:0%
+my model I do my counterfactual and say
+how many firms would be socially optimal
+
+ align:start position:0%
+how many firms would be socially optimal
+ 
+
+ align:start position:0%
+how many firms would be socially optimal
+and socially optimal would be exactly
+
+ align:start position:0%
+and socially optimal would be exactly
+ 
+
+ align:start position:0%
+and socially optimal would be exactly
+half the number that are observed um so
+
+ align:start position:0%
+half the number that are observed um so
+ 
+
+ align:start position:0%
+half the number that are observed um so
+it it's just important to be aware of do
+
+ align:start position:0%
+it it's just important to be aware of do
+ 
+
+ align:start position:0%
+it it's just important to be aware of do
+models have built in answers as to
+
+ align:start position:0%
+models have built in answers as to
+ 
+
+ align:start position:0%
+models have built in answers as to
+whether the consumer surplus effect is
+
+ align:start position:0%
+whether the consumer surplus effect is
+ 
+
+ align:start position:0%
+whether the consumer surplus effect is
+going to outweigh the business dealing
+
+ align:start position:0%
+going to outweigh the business dealing
+ 
+
+ align:start position:0%
+going to outweigh the business dealing
+effect or not and this one it's totally
+
+ align:start position:0%
+effect or not and this one it's totally
+ 
+
+ align:start position:0%
+effect or not and this one it's totally
+built in and the answer is it's a factor
+
+ align:start position:0%
+built in and the answer is it's a factor
+ 
+
+ align:start position:0%
+built in and the answer is it's a factor
+of two um but I think you know it's
+
+ align:start position:0%
+of two um but I think you know it's
+ 
+
+ align:start position:0%
+of two um but I think you know it's
+generally true you know most models you
+
+ align:start position:0%
+generally true you know most models you
+ 
+
+ align:start position:0%
+generally true you know most models you
+write down you are going to get like a
+
+ align:start position:0%
+write down you are going to get like a
+ 
+
+ align:start position:0%
+write down you are going to get like a
+fact you know you are going to find that
+
+ align:start position:0%
+fact you know you are going to find that
+ 
+
+ align:start position:0%
+fact you know you are going to find that
+there are way too many firms and I don't
+
+ align:start position:0%
+there are way too many firms and I don't
+ 
+
+ align:start position:0%
+there are way too many firms and I don't
+know if
+
+ align:start position:0%
+know if
+ 
+
+ align:start position:0%
+know if
+I maybe I believe that you know how
+
+ align:start position:0%
+I maybe I believe that you know how
+ 
+
+ align:start position:0%
+I maybe I believe that you know how
+would you get
+
+ align:start position:0%
+would you get
+ 
+
+ align:start position:0%
+would you get
+um you know how would you get um bigger
+
+ align:start position:0%
+um you know how would you get um bigger
+ 
+
+ align:start position:0%
+um you know how would you get um bigger
+social welfare benefits you know there's
+
+ align:start position:0%
+social welfare benefits you know there's
+ 
+
+ align:start position:0%
+social welfare benefits you know there's
+sort of two ways you would get bigger
+
+ align:start position:0%
+sort of two ways you would get bigger
+ 
+
+ align:start position:0%
+sort of two ways you would get bigger
+social welfare benefits the first is you
+
+ align:start position:0%
+social welfare benefits the first is you
+ 
+
+ align:start position:0%
+social welfare benefits the first is you
+in this model people's utility for
+
+ align:start position:0%
+in this model people's utility for
+ 
+
+ align:start position:0%
+in this model people's utility for
+getting a product that's not IDE deal
+
+ align:start position:0%
+getting a product that's not IDE deal
+ 
+
+ align:start position:0%
+getting a product that's not IDE deal
+just goes down
+
+ align:start position:0%
+just goes down
+ 
+
+ align:start position:0%
+just goes down
+linearly if you imagine people's utility
+
+ align:start position:0%
+linearly if you imagine people's utility
+ 
+
+ align:start position:0%
+linearly if you imagine people's utility
+looked more like this so you know there
+
+ align:start position:0%
+looked more like this so you know there
+ 
+
+ align:start position:0%
+looked more like this so you know there
+are people who really really like having
+
+ align:start position:0%
+are people who really really like having
+ 
+
+ align:start position:0%
+are people who really really like having
+a product that's very close to
+
+ align:start position:0%
+a product that's very close to
+ 
+
+ align:start position:0%
+a product that's very close to
+their um very close to their ideal point
+
+ align:start position:0%
+their um very close to their ideal point
+ 
+
+ align:start position:0%
+their um very close to their ideal point
+so when you add an extra and have three
+
+ align:start position:0%
+so when you add an extra and have three
+ 
+
+ align:start position:0%
+so when you add an extra and have three
+ideal points instead of two you're
+
+ align:start position:0%
+ideal points instead of two you're
+ 
+
+ align:start position:0%
+ideal points instead of two you're
+giving some people lots and lots of
+
+ align:start position:0%
+giving some people lots and lots of
+ 
+
+ align:start position:0%
+giving some people lots and lots of
+extra utility so having something like
+
+ align:start position:0%
+extra utility so having something like
+ 
+
+ align:start position:0%
+extra utility so having something like
+this you know people who like things
+
+ align:start position:0%
+this you know people who like things
+ 
+
+ align:start position:0%
+this you know people who like things
+very close to their ideal point would be
+
+ align:start position:0%
+very close to their ideal point would be
+ 
+
+ align:start position:0%
+very close to their ideal point would be
+would be one way to get uh ex entry to
+
+ align:start position:0%
+would be one way to get uh ex entry to
+ 
+
+ align:start position:0%
+would be one way to get uh ex entry to
+be not too high um obviously you can
+
+ align:start position:0%
+be not too high um obviously you can
+ 
+
+ align:start position:0%
+be not too high um obviously you can
+only go so high here before the firm is
+
+ align:start position:0%
+only go so high here before the firm is
+ 
+
+ align:start position:0%
+only go so high here before the firm is
+going to give up on serving everyone and
+
+ align:start position:0%
+going to give up on serving everyone and
+ 
+
+ align:start position:0%
+going to give up on serving everyone and
+just serve the people who like its
+
+ align:start position:0%
+just serve the people who like its
+ 
+
+ align:start position:0%
+just serve the people who like its
+product a lot at a really high price um
+
+ align:start position:0%
+product a lot at a really high price um
+ 
+
+ align:start position:0%
+product a lot at a really high price um
+so that's going to be kind of like those
+
+ align:start position:0%
+so that's going to be kind of like those
+ 
+
+ align:start position:0%
+so that's going to be kind of like those
+information design things where you can
+
+ align:start position:0%
+information design things where you can
+ 
+
+ align:start position:0%
+information design things where you can
+only make the curve go up so much and
+
+ align:start position:0%
+only make the curve go up so much and
+ 
+
+ align:start position:0%
+only make the curve go up so much and
+have the firm still sell to everybody uh
+
+ align:start position:0%
+have the firm still sell to everybody uh
+ 
+
+ align:start position:0%
+have the firm still sell to everybody uh
+and then the other effect is you know
+
+ align:start position:0%
+and then the other effect is you know
+ 
+
+ align:start position:0%
+and then the other effect is you know
+here again 100% of your demand is
+
+ align:start position:0%
+here again 100% of your demand is
+ 
+
+ align:start position:0%
+here again 100% of your demand is
+business stealing if you think of like
+
+ align:start position:0%
+business stealing if you think of like
+ 
+
+ align:start position:0%
+business stealing if you think of like
+an infinite dimensional space where most
+
+ align:start position:0%
+an infinite dimensional space where most
+ 
+
+ align:start position:0%
+an infinite dimensional space where most
+people are not buying any product at all
+
+ align:start position:0%
+people are not buying any product at all
+ 
+
+ align:start position:0%
+people are not buying any product at all
+all so every new firm that comes in is
+
+ align:start position:0%
+all so every new firm that comes in is
+ 
+
+ align:start position:0%
+all so every new firm that comes in is
+mostly serving new customers you know so
+
+ align:start position:0%
+mostly serving new customers you know so
+ 
+
+ align:start position:0%
+mostly serving new customers you know so
+if you can make the business dealing
+
+ align:start position:0%
+if you can make the business dealing
+ 
+
+ align:start position:0%
+if you can make the business dealing
+effect small and make this consumer
+
+ align:start position:0%
+effect small and make this consumer
+ 
+
+ align:start position:0%
+effect small and make this consumer
+surplus large for people who get close
+
+ align:start position:0%
+surplus large for people who get close
+ 
+
+ align:start position:0%
+surplus large for people who get close
+matches those are the things that are
+
+ align:start position:0%
+matches those are the things that are
+ 
+
+ align:start position:0%
+matches those are the things that are
+going to make entry be insufficient in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+practice and I but I think if you want
+
+ align:start position:0%
+practice and I but I think if you want
+ 
+
+ align:start position:0%
+practice and I but I think if you want
+to do an empirical study you'd really
+
+ align:start position:0%
+to do an empirical study you'd really
+ 
+
+ align:start position:0%
+to do an empirical study you'd really
+want to think about do I have free
+
+ align:start position:0%
+want to think about do I have free
+ 
+
+ align:start position:0%
+want to think about do I have free
+parameters to capture what this Surplus
+
+ align:start position:0%
+parameters to capture what this Surplus
+ 
+
+ align:start position:0%
+parameters to capture what this Surplus
+looks like and do I have a free cap
+
+ align:start position:0%
+looks like and do I have a free cap
+ 
+
+ align:start position:0%
+looks like and do I have a free cap
+parameter to capture how much of the
+
+ align:start position:0%
+parameter to capture how much of the
+ 
+
+ align:start position:0%
+parameter to capture how much of the
+people are being added um to the model
+
+ align:start position:0%
+people are being added um to the model
+ 
+
+ align:start position:0%
+people are being added um to the model
+versus how many people are just business
+
+ align:start position:0%
+versus how many people are just business
+ 
+
+ align:start position:0%
+versus how many people are just business
+being business St for another
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+firm you know for instance like the
+
+ align:start position:0%
+firm you know for instance like the
+ 
+
+ align:start position:0%
+firm you know for instance like the
+nested loit has that extra parameter
+
+ align:start position:0%
+nested loit has that extra parameter
+ 
+
+ align:start position:0%
+nested loit has that extra parameter
+that substitution to the outside good is
+
+ align:start position:0%
+that substitution to the outside good is
+ 
+
+ align:start position:0%
+that substitution to the outside good is
+different from substitution to the
+
+ align:start position:0%
+different from substitution to the
+ 
+
+ align:start position:0%
+different from substitution to the
+inside Goods um and a pure loia with no
+
+ align:start position:0%
+inside Goods um and a pure loia with no
+ 
+
+ align:start position:0%
+inside Goods um and a pure loia with no
+outside good is a 100% business dealing
+
+ align:start position:0%
+outside good is a 100% business dealing
+ 
+
+ align:start position:0%
+outside good is a 100% business dealing
+model
+
+ align:start position:0%
+model
+ 
+
+ align:start position:0%
+model
+questions okay um entry with vertical
+
+ align:start position:0%
+questions okay um entry with vertical
+ 
+
+ align:start position:0%
+questions okay um entry with vertical
+differentiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so let's go back again review of
+
+ align:start position:0%
+okay so let's go back again review of
+ 
+
+ align:start position:0%
+okay so let's go back again review of
+our classic um vertical differentiation
+
+ align:start position:0%
+our classic um vertical differentiation
+ 
+
+ align:start position:0%
+our classic um vertical differentiation
+model you have consumers that have these
+
+ align:start position:0%
+model you have consumers that have these
+ 
+
+ align:start position:0%
+model you have consumers that have these
+vertical types Theta uh they have unit
+
+ align:start position:0%
+vertical types Theta uh they have unit
+ 
+
+ align:start position:0%
+vertical types Theta uh they have unit
+demands where you your utility is Theta
+
+ align:start position:0%
+demands where you your utility is Theta
+ 
+
+ align:start position:0%
+demands where you your utility is Theta
+times the quality of the good minus
+
+ align:start position:0%
+times the quality of the good minus
+ 
+
+ align:start position:0%
+times the quality of the good minus
+p uh let's assume that firms have fixed
+
+ align:start position:0%
+p uh let's assume that firms have fixed
+ 
+
+ align:start position:0%
+p uh let's assume that firms have fixed
+entry cost K and then they have constant
+
+ align:start position:0%
+entry cost K and then they have constant
+ 
+
+ align:start position:0%
+entry cost K and then they have constant
+marginal cost C ofs where the higher
+
+ align:start position:0%
+marginal cost C ofs where the higher
+ 
+
+ align:start position:0%
+marginal cost C ofs where the higher
+quality products are more expensive to
+
+ align:start position:0%
+quality products are more expensive to
+ 
+
+ align:start position:0%
+quality products are more expensive to
+produce so consider a two-stage game the
+
+ align:start position:0%
+produce so consider a two-stage game the
+ 
+
+ align:start position:0%
+produce so consider a two-stage game the
+first the firms are simultaneously
+
+ align:start position:0%
+first the firms are simultaneously
+ 
+
+ align:start position:0%
+first the firms are simultaneously
+choosing whether to enter and if they
+
+ align:start position:0%
+choosing whether to enter and if they
+ 
+
+ align:start position:0%
+choosing whether to enter and if they
+enter they're going to choose which
+
+ align:start position:0%
+enter they're going to choose which
+ 
+
+ align:start position:0%
+enter they're going to choose which
+quality level to
+
+ align:start position:0%
+quality level to
+ 
+
+ align:start position:0%
+quality level to
+produce uh and then once they've done
+
+ align:start position:0%
+produce uh and then once they've done
+ 
+
+ align:start position:0%
+produce uh and then once they've done
+that they compete in prices according to
+
+ align:start position:0%
+that they compete in prices according to
+ 
+
+ align:start position:0%
+that they compete in prices according to
+the vertical differentiation
+
+ align:start position:0%
+the vertical differentiation
+ 
+
+ align:start position:0%
+the vertical differentiation
+model and you know shacket and suton
+
+ align:start position:0%
+model and you know shacket and suton
+ 
+
+ align:start position:0%
+model and you know shacket and suton
+have this classic paper that shows that
+
+ align:start position:0%
+have this classic paper that shows that
+ 
+
+ align:start position:0%
+have this classic paper that shows that
+um you can get two different types of
+
+ align:start position:0%
+um you can get two different types of
+ 
+
+ align:start position:0%
+um you can get two different types of
+outcomes in this um first one is what
+
+ align:start position:0%
+outcomes in this um first one is what
+ 
+
+ align:start position:0%
+outcomes in this um first one is what
+they call the sort of natural lopoly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+case so imagine that
+
+ align:start position:0%
+case so imagine that
+ 
+
+ align:start position:0%
+case so imagine that
+um if I put s on this axis and I put
+
+ align:start position:0%
+um if I put s on this axis and I put
+ 
+
+ align:start position:0%
+um if I put s on this axis and I put
+uh what am I going to do
+
+ align:start position:0%
+uh what am I going to do
+ 
+
+ align:start position:0%
+uh what am I going to do
+um you know uh either the value that
+
+ align:start position:0%
+um you know uh either the value that
+ 
+
+ align:start position:0%
+um you know uh either the value that
+they get from s Theta s minus p on this
+
+ align:start position:0%
+they get from s Theta s minus p on this
+ 
+
+ align:start position:0%
+they get from s Theta s minus p on this
+Axis or I put C of s on this axis
+
+ align:start position:0%
+Axis or I put C of s on this axis
+ 
+
+ align:start position:0%
+Axis or I put C of s on this axis
+um so imagine that um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you imagine that you have relatively
+
+ align:start position:0%
+you imagine that you have relatively
+ 
+
+ align:start position:0%
+you imagine that you have relatively
+flat marginal cost curves so imagine
+
+ align:start position:0%
+flat marginal cost curves so imagine
+ 
+
+ align:start position:0%
+flat marginal cost curves so imagine
+that marginal cost um C of s looks like
+
+ align:start position:0%
+that marginal cost um C of s looks like
+ 
+
+ align:start position:0%
+that marginal cost um C of s looks like
+this that there's just not that much
+
+ align:start position:0%
+this that there's just not that much
+ 
+
+ align:start position:0%
+this that there's just not that much
+cost to producing high quality goods and
+
+ align:start position:0%
+cost to producing high quality goods and
+ 
+
+ align:start position:0%
+cost to producing high quality goods and
+suppose that you have like you know
+
+ align:start position:0%
+suppose that you have like you know
+ 
+
+ align:start position:0%
+suppose that you have like you know
+Theta lower bar um Time s looks like
+
+ align:start position:0%
+Theta lower bar um Time s looks like
+ 
+
+ align:start position:0%
+Theta lower bar um Time s looks like
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+and Theta upper bar
+
+ align:start position:0%
+and Theta upper bar
+ 
+
+ align:start position:0%
+and Theta upper bar
+s minus P looks like that okay so we
+
+ align:start position:0%
+s minus P looks like that okay so we
+ 
+
+ align:start position:0%
+s minus P looks like that okay so we
+have a model where everybody even the
+
+ align:start position:0%
+have a model where everybody even the
+ 
+
+ align:start position:0%
+have a model where everybody even the
+lowest possible types value quality more
+
+ align:start position:0%
+lowest possible types value quality more
+ 
+
+ align:start position:0%
+lowest possible types value quality more
+than it cost to produce the extra units
+
+ align:start position:0%
+than it cost to produce the extra units
+ 
+
+ align:start position:0%
+than it cost to produce the extra units
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+quality okay and there's some range here
+
+ align:start position:0%
+quality okay and there's some range here
+ 
+
+ align:start position:0%
+quality okay and there's some range here
+oops uh s lower bar s uper bar of the
+
+ align:start position:0%
+oops uh s lower bar s uper bar of the
+ 
+
+ align:start position:0%
+oops uh s lower bar s uper bar of the
+qualities that are available to be
+
+ align:start position:0%
+qualities that are available to be
+ 
+
+ align:start position:0%
+qualities that are available to be
+produced
+
+ align:start position:0%
+produced
+ 
+
+ align:start position:0%
+produced
+okay in a model like this what they call
+
+ align:start position:0%
+okay in a model like this what they call
+ 
+
+ align:start position:0%
+okay in a model like this what they call
+the natural oligopoly case
+
+ align:start position:0%
+the natural oligopoly case
+ 
+
+ align:start position:0%
+the natural oligopoly case
+everybody should efficient in an
+
+ align:start position:0%
+everybody should efficient in an
+ 
+
+ align:start position:0%
+everybody should efficient in an
+efficient market everyone should be
+
+ align:start position:0%
+efficient market everyone should be
+ 
+
+ align:start position:0%
+efficient market everyone should be
+buying the highest possible
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quality and so if you imagine what
+
+ align:start position:0%
+quality and so if you imagine what
+ 
+
+ align:start position:0%
+quality and so if you imagine what
+happened suppose you
+
+ align:start position:0%
+happened suppose you
+ 
+
+ align:start position:0%
+happened suppose you
+have firms lots of firms entering and
+
+ align:start position:0%
+have firms lots of firms entering and
+ 
+
+ align:start position:0%
+have firms lots of firms entering and
+producing different qualities and then
+
+ align:start position:0%
+producing different qualities and then
+ 
+
+ align:start position:0%
+producing different qualities and then
+what are they going to set their prices
+
+ align:start position:0%
+what are they going to set their prices
+ 
+
+ align:start position:0%
+what are they going to set their prices
+at okay well if you have lots of firms
+
+ align:start position:0%
+at okay well if you have lots of firms
+ 
+
+ align:start position:0%
+at okay well if you have lots of firms
+in the market the prices are going to
+
+ align:start position:0%
+in the market the prices are going to
+ 
+
+ align:start position:0%
+in the market the prices are going to
+fall you know these are prices I'm
+
+ align:start position:0%
+fall you know these are prices I'm
+ 
+
+ align:start position:0%
+fall you know these are prices I'm
+putting dots in here you know the prices
+
+ align:start position:0%
+putting dots in here you know the prices
+ 
+
+ align:start position:0%
+putting dots in here you know the prices
+are going to have to fall towards cost
+
+ align:start position:0%
+are going to have to fall towards cost
+ 
+
+ align:start position:0%
+are going to have to fall towards cost
+as n goes to as the number of firms into
+
+ align:start position:0%
+as n goes to as the number of firms into
+ 
+
+ align:start position:0%
+as n goes to as the number of firms into
+this finite product space goes to
+
+ align:start position:0%
+this finite product space goes to
+ 
+
+ align:start position:0%
+this finite product space goes to
+Infinity but then if the prices fall
+
+ align:start position:0%
+Infinity but then if the prices fall
+ 
+
+ align:start position:0%
+Infinity but then if the prices fall
+towards cost everyone is going to buy
+
+ align:start position:0%
+towards cost everyone is going to buy
+ 
+
+ align:start position:0%
+towards cost everyone is going to buy
+from the highest quality
+
+ align:start position:0%
+from the highest quality
+ 
+
+ align:start position:0%
+from the highest quality
+firm and so you just can't have prices
+
+ align:start position:0%
+firm and so you just can't have prices
+ 
+
+ align:start position:0%
+firm and so you just can't have prices
+falling to cost because if prices fall
+
+ align:start position:0%
+falling to cost because if prices fall
+ 
+
+ align:start position:0%
+falling to cost because if prices fall
+to cost all these firms make zero sales
+
+ align:start position:0%
+to cost all these firms make zero sales
+ 
+
+ align:start position:0%
+to cost all these firms make zero sales
+and then they are negative profits after
+
+ align:start position:0%
+and then they are negative profits after
+ 
+
+ align:start position:0%
+and then they are negative profits after
+paying their fixed cost
+
+ align:start position:0%
+paying their fixed cost
+ 
+
+ align:start position:0%
+paying their fixed cost
+K so if you have have this case where
+
+ align:start position:0%
+K so if you have have this case where
+ 
+
+ align:start position:0%
+K so if you have have this case where
+everybody should buy the same product
+
+ align:start position:0%
+everybody should buy the same product
+ 
+
+ align:start position:0%
+everybody should buy the same product
+there's only a finite number of firms in
+
+ align:start position:0%
+there's only a finite number of firms in
+ 
+
+ align:start position:0%
+there's only a finite number of firms in
+the market again this isn't an end goes
+
+ align:start position:0%
+the market again this isn't an end goes
+ 
+
+ align:start position:0%
+the market again this isn't an end goes
+to Infinity as K goes to zero for you
+
+ align:start position:0%
+to Infinity as K goes to zero for you
+ 
+
+ align:start position:0%
+to Infinity as K goes to zero for you
+know as K goes to zero you still get a
+
+ align:start position:0%
+know as K goes to zero you still get a
+ 
+
+ align:start position:0%
+know as K goes to zero you still get a
+finite number of firms it may be this
+
+ align:start position:0%
+finite number of firms it may be this
+ 
+
+ align:start position:0%
+finite number of firms it may be this
+Market can fit three firms or five or
+
+ align:start position:0%
+Market can fit three firms or five or
+ 
+
+ align:start position:0%
+Market can fit three firms or five or
+sixs or whatever but there's a finite
+
+ align:start position:0%
+sixs or whatever but there's a finite
+ 
+
+ align:start position:0%
+sixs or whatever but there's a finite
+amount of Entry that can ever
+
+ align:start position:0%
+amount of Entry that can ever
+ 
+
+ align:start position:0%
+amount of Entry that can ever
+occur uh if the same product is
+
+ align:start position:0%
+occur uh if the same product is
+ 
+
+ align:start position:0%
+occur uh if the same product is
+efficient for everyone to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+buy and then the second case they talk
+
+ align:start position:0%
+buy and then the second case they talk
+ 
+
+ align:start position:0%
+buy and then the second case they talk
+about is this specialization case um the
+
+ align:start position:0%
+about is this specialization case um the
+ 
+
+ align:start position:0%
+about is this specialization case um the
+specialization case would be if you have
+
+ align:start position:0%
+specialization case would be if you have
+ 
+
+ align:start position:0%
+specialization case would be if you have
+marginal
+
+ align:start position:0%
+marginal
+ 
+
+ align:start position:0%
+marginal
+costs that look like this you know
+
+ align:start position:0%
+costs that look like this you know
+ 
+
+ align:start position:0%
+costs that look like this you know
+marginal costs are initially
+
+ align:start position:0%
+marginal costs are initially
+ 
+
+ align:start position:0%
+marginal costs are initially
+low
+
+ align:start position:0%
+low
+ 
+
+ align:start position:0%
+low
+um uh but then they shoot up like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that okay if the marginal cost look like
+
+ align:start position:0%
+that okay if the marginal cost look like
+ 
+
+ align:start position:0%
+that okay if the marginal cost look like
+this right what's efficient for the
+
+ align:start position:0%
+this right what's efficient for the
+ 
+
+ align:start position:0%
+this right what's efficient for the
+Theta lower bar types the Theta lower
+
+ align:start position:0%
+Theta lower bar types the Theta lower
+ 
+
+ align:start position:0%
+Theta lower bar types the Theta lower
+bar types you know would
+
+ align:start position:0%
+bar types you know would
+ 
+
+ align:start position:0%
+bar types you know would
+pick the point you know right what's
+
+ align:start position:0%
+pick the point you know right what's
+ 
+
+ align:start position:0%
+pick the point you know right what's
+sufficient for them to do is where the
+
+ align:start position:0%
+sufficient for them to do is where the
+ 
+
+ align:start position:0%
+sufficient for them to do is where the
+marginal cost of producing extra quality
+
+ align:start position:0%
+marginal cost of producing extra quality
+ 
+
+ align:start position:0%
+marginal cost of producing extra quality
+is equal to the marginal benefit that
+
+ align:start position:0%
+is equal to the marginal benefit that
+ 
+
+ align:start position:0%
+is equal to the marginal benefit that
+they receive so the Theta lower bar
+
+ align:start position:0%
+they receive so the Theta lower bar
+ 
+
+ align:start position:0%
+they receive so the Theta lower bar
+types so this would be you know s star
+
+ align:start position:0%
+types so this would be you know s star
+ 
+
+ align:start position:0%
+types so this would be you know s star
+optimal uh for the Theta lower bar types
+
+ align:start position:0%
+optimal uh for the Theta lower bar types
+ 
+
+ align:start position:0%
+optimal uh for the Theta lower bar types
+they want to produce where the they
+
+ align:start position:0%
+they want to produce where the they
+ 
+
+ align:start position:0%
+they want to produce where the they
+should be buying the good where the
+
+ align:start position:0%
+should be buying the good where the
+ 
+
+ align:start position:0%
+should be buying the good where the
+marginal value of increase in quality is
+
+ align:start position:0%
+marginal value of increase in quality is
+ 
+
+ align:start position:0%
+marginal value of increase in quality is
+exactly equal to their willingness to
+
+ align:start position:0%
+exactly equal to their willingness to
+ 
+
+ align:start position:0%
+exactly equal to their willingness to
+pay and the Theta upper bar types maybe
+
+ align:start position:0%
+pay and the Theta upper bar types maybe
+ 
+
+ align:start position:0%
+pay and the Theta upper bar types maybe
+I should have made this steeper
+
+ align:start position:0%
+I should have made this steeper
+ 
+
+ align:start position:0%
+I should have made this steeper
+let me make Theta upper bar even steeper
+
+ align:start position:0%
+let me make Theta upper bar even steeper
+ 
+
+ align:start position:0%
+let me make Theta upper bar even steeper
+you know the Theta upper bar types are
+
+ align:start position:0%
+you know the Theta upper bar types are
+ 
+
+ align:start position:0%
+you know the Theta upper bar types are
+going to have a point where again
+
+ align:start position:0%
+going to have a point where again
+ 
+
+ align:start position:0%
+going to have a point where again
+they're going to buy up here where it
+
+ align:start position:0%
+they're going to buy up here where it
+ 
+
+ align:start position:0%
+they're going to buy up here where it
+has this greater slope so the SAR uh
+
+ align:start position:0%
+has this greater slope so the SAR uh
+ 
+
+ align:start position:0%
+has this greater slope so the SAR uh
+Theta upper bar they should be buying
+
+ align:start position:0%
+Theta upper bar they should be buying
+ 
+
+ align:start position:0%
+Theta upper bar they should be buying
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+product and everybody with a Theta in
+
+ align:start position:0%
+product and everybody with a Theta in
+ 
+
+ align:start position:0%
+product and everybody with a Theta in
+between should be buying something in
+
+ align:start position:0%
+between should be buying something in
+ 
+
+ align:start position:0%
+between should be buying something in
+between everybody should be picking the
+
+ align:start position:0%
+between everybody should be picking the
+ 
+
+ align:start position:0%
+between everybody should be picking the
+optimal product for everybody is the
+
+ align:start position:0%
+optimal product for everybody is the
+ 
+
+ align:start position:0%
+optimal product for everybody is the
+point on that curve that where
+
+ align:start position:0%
+point on that curve that where
+ 
+
+ align:start position:0%
+point on that curve that where
+you know it's efficient quality for them
+
+ align:start position:0%
+you know it's efficient quality for them
+ 
+
+ align:start position:0%
+you know it's efficient quality for them
+okay so if you have a model like this
+
+ align:start position:0%
+okay so if you have a model like this
+ 
+
+ align:start position:0%
+okay so if you have a model like this
+where efficient
+
+ align:start position:0%
+where efficient
+ 
+
+ align:start position:0%
+where efficient
+quality you know some people everybody
+
+ align:start position:0%
+quality you know some people everybody
+ 
+
+ align:start position:0%
+quality you know some people everybody
+has a different efficient quality then
+
+ align:start position:0%
+has a different efficient quality then
+ 
+
+ align:start position:0%
+has a different efficient quality then
+as then goes to Infinity you are going
+
+ align:start position:0%
+as then goes to Infinity you are going
+ 
+
+ align:start position:0%
+as then goes to Infinity you are going
+to get an infinitely divided model so
+
+ align:start position:0%
+to get an infinitely divided model so
+ 
+
+ align:start position:0%
+to get an infinitely divided model so
+every product is efficient for someone
+
+ align:start position:0%
+every product is efficient for someone
+ 
+
+ align:start position:0%
+every product is efficient for someone
+so the number of customers is large
+
+ align:start position:0%
+so the number of customers is large
+ 
+
+ align:start position:0%
+so the number of customers is large
+every all those products get produced
+
+ align:start position:0%
+every all those products get produced
+ 
+
+ align:start position:0%
+every all those products get produced
+they all sell to one over n of the
+
+ align:start position:0%
+they all sell to one over n of the
+ 
+
+ align:start position:0%
+they all sell to one over n of the
+people they sell to the people whose
+
+ align:start position:0%
+people they sell to the people whose
+ 
+
+ align:start position:0%
+people they sell to the people whose
+prices are whose values are marginal
+
+ align:start position:0%
+prices are whose values are marginal
+ 
+
+ align:start position:0%
+prices are whose values are marginal
+values are close to their marginal yes
+
+ align:start position:0%
+values are close to their marginal yes
+ 
+
+ align:start position:0%
+values are close to their marginal yes
+whose optimal qualities are close to
+
+ align:start position:0%
+whose optimal qualities are close to
+ 
+
+ align:start position:0%
+whose optimal qualities are close to
+their quality and and prices do fall
+
+ align:start position:0%
+their quality and and prices do fall
+ 
+
+ align:start position:0%
+their quality and and prices do fall
+towards marginal cost but even though
+
+ align:start position:0%
+towards marginal cost but even though
+ 
+
+ align:start position:0%
+towards marginal cost but even though
+prices fall to marginal cost everybody
+
+ align:start position:0%
+prices fall to marginal cost everybody
+ 
+
+ align:start position:0%
+prices fall to marginal cost everybody
+still buys a from a different
+
+ align:start position:0%
+still buys a from a different
+ 
+
+ align:start position:0%
+still buys a from a different
+firm so what happens with vertical
+
+ align:start position:0%
+firm so what happens with vertical
+ 
+
+ align:start position:0%
+firm so what happens with vertical
+differentiation is sometimes you only
+
+ align:start position:0%
+differentiation is sometimes you only
+ 
+
+ align:start position:0%
+differentiation is sometimes you only
+you can't get a lot of firms but
+
+ align:start position:0%
+you can't get a lot of firms but
+ 
+
+ align:start position:0%
+you can't get a lot of firms but
+sometimes you get the specialization and
+
+ align:start position:0%
+sometimes you get the specialization and
+ 
+
+ align:start position:0%
+sometimes you get the specialization and
+it all depends on whether different
+
+ align:start position:0%
+it all depends on whether different
+ 
+
+ align:start position:0%
+it all depends on whether different
+products are optimal for a different
+
+ align:start position:0%
+products are optimal for a different
+ 
+
+ align:start position:0%
+products are optimal for a different
+people
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions okay um so next thing next set
+
+ align:start position:0%
+questions okay um so next thing next set
+ 
+
+ align:start position:0%
+questions okay um so next thing next set
+of paper I want next paper I want to
+
+ align:start position:0%
+of paper I want next paper I want to
+ 
+
+ align:start position:0%
+of paper I want next paper I want to
+discuss is you know this paper is
+
+ align:start position:0%
+discuss is you know this paper is
+ 
+
+ align:start position:0%
+discuss is you know this paper is
+motivated by um there's a large
+
+ align:start position:0%
+motivated by um there's a large
+ 
+
+ align:start position:0%
+motivated by um there's a large
+literature on firm Dynamics and entry
+
+ align:start position:0%
+literature on firm Dynamics and entry
+ 
+
+ align:start position:0%
+literature on firm Dynamics and entry
+and exit uh that's generated by people
+
+ align:start position:0%
+and exit uh that's generated by people
+ 
+
+ align:start position:0%
+and exit uh that's generated by people
+looking at Census Data um so you know if
+
+ align:start position:0%
+looking at Census Data um so you know if
+ 
+
+ align:start position:0%
+looking at Census Data um so you know if
+um I don't know if I mentioned I think I
+
+ align:start position:0%
+um I don't know if I mentioned I think I
+ 
+
+ align:start position:0%
+um I don't know if I mentioned I think I
+mentioned this earlier in the semester
+
+ align:start position:0%
+mentioned this earlier in the semester
+ 
+
+ align:start position:0%
+mentioned this earlier in the semester
+so you know there's this great resource
+
+ align:start position:0%
+so you know there's this great resource
+ 
+
+ align:start position:0%
+so you know there's this great resource
+for Io Economist which is called the um
+
+ align:start position:0%
+for Io Economist which is called the um
+ 
+
+ align:start position:0%
+for Io Economist which is called the um
+uh you know sense to
+
+ align:start position:0%
+uh you know sense to
+ 
+
+ align:start position:0%
+uh you know sense to
+manufacturers so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the you the sense of Manufacturers is
+
+ align:start position:0%
+the you the sense of Manufacturers is
+ 
+
+ align:start position:0%
+the you the sense of Manufacturers is
+conducted by the US Census Bureau every
+
+ align:start position:0%
+conducted by the US Census Bureau every
+ 
+
+ align:start position:0%
+conducted by the US Census Bureau every
+five years um all the years that end in
+
+ align:start position:0%
+five years um all the years that end in
+ 
+
+ align:start position:0%
+five years um all the years that end in
+twos and sevens
+
+ align:start position:0%
+twos and sevens
+ 
+
+ align:start position:0%
+twos and sevens
+um sens of Manufacturers it's a complete
+
+ align:start position:0%
+um sens of Manufacturers it's a complete
+ 
+
+ align:start position:0%
+um sens of Manufacturers it's a complete
+census of every manufacturing firm in
+
+ align:start position:0%
+census of every manufacturing firm in
+ 
+
+ align:start position:0%
+census of every manufacturing firm in
+the United
+
+ align:start position:0%
+the United
+ 
+
+ align:start position:0%
+the United
+States uh in addition there census does
+
+ align:start position:0%
+States uh in addition there census does
+ 
+
+ align:start position:0%
+States uh in addition there census does
+something called the annual survey of
+
+ align:start position:0%
+something called the annual survey of
+ 
+
+ align:start position:0%
+something called the annual survey of
+Manufacturers it takes a subset of this
+
+ align:start position:0%
+Manufacturers it takes a subset of this
+ 
+
+ align:start position:0%
+Manufacturers it takes a subset of this
+and samples them to produce annual data
+
+ align:start position:0%
+and samples them to produce annual data
+ 
+
+ align:start position:0%
+and samples them to produce annual data
+instead of every fiveyear data um but
+
+ align:start position:0%
+instead of every fiveyear data um but
+ 
+
+ align:start position:0%
+instead of every fiveyear data um but
+anyway they sort
+
+ align:start position:0%
+anyway they sort
+ 
+
+ align:start position:0%
+anyway they sort
+of send out census forms to all
+
+ align:start position:0%
+of send out census forms to all
+ 
+
+ align:start position:0%
+of send out census forms to all
+manufacturing firms every five years
+
+ align:start position:0%
+manufacturing firms every five years
+ 
+
+ align:start position:0%
+manufacturing firms every five years
+asking them lots and lots of questions
+
+ align:start position:0%
+asking them lots and lots of questions
+ 
+
+ align:start position:0%
+asking them lots and lots of questions
+you know what do they produce how many
+
+ align:start position:0%
+you know what do they produce how many
+ 
+
+ align:start position:0%
+you know what do they produce how many
+you know how much do they sell of every
+
+ align:start position:0%
+you know how much do they sell of every
+ 
+
+ align:start position:0%
+you know how much do they sell of every
+different you know narrowly defined
+
+ align:start position:0%
+different you know narrowly defined
+ 
+
+ align:start position:0%
+different you know narrowly defined
+product how many employees do you have
+
+ align:start position:0%
+product how many employees do you have
+ 
+
+ align:start position:0%
+product how many employees do you have
+what's the value of your plant and
+
+ align:start position:0%
+what's the value of your plant and
+ 
+
+ align:start position:0%
+what's the value of your plant and
+Equipment how much electricity do you
+
+ align:start position:0%
+Equipment how much electricity do you
+ 
+
+ align:start position:0%
+Equipment how much electricity do you
+use so you get lots of data on these
+
+ align:start position:0%
+use so you get lots of data on these
+ 
+
+ align:start position:0%
+use so you get lots of data on these
+firms sometimes you know the accounting
+
+ align:start position:0%
+firms sometimes you know the accounting
+ 
+
+ align:start position:0%
+firms sometimes you know the accounting
+data of what are all their costs are
+
+ align:start position:0%
+data of what are all their costs are
+ 
+
+ align:start position:0%
+data of what are all their costs are
+hard to believe but one thing that's
+
+ align:start position:0%
+hard to believe but one thing that's
+ 
+
+ align:start position:0%
+hard to believe but one thing that's
+very good in that data is do you exist
+
+ align:start position:0%
+very good in that data is do you exist
+ 
+
+ align:start position:0%
+very good in that data is do you exist
+what's your address uh how many
+
+ align:start position:0%
+what's your address uh how many
+ 
+
+ align:start position:0%
+what's your address uh how many
+employees do you have um and so you know
+
+ align:start position:0%
+employees do you have um and so you know
+ 
+
+ align:start position:0%
+employees do you have um and so you know
+this lets you sort of if you want to
+
+ align:start position:0%
+this lets you sort of if you want to
+ 
+
+ align:start position:0%
+this lets you sort of if you want to
+study entry and exit that you can just
+
+ align:start position:0%
+study entry and exit that you can just
+ 
+
+ align:start position:0%
+study entry and exit that you can just
+you know there's a windowless room at
+
+ align:start position:0%
+you know there's a windowless room at
+ 
+
+ align:start position:0%
+you know there's a windowless room at
+the NBR where one can access census data
+
+ align:start position:0%
+the NBR where one can access census data
+ 
+
+ align:start position:0%
+the NBR where one can access census data
+now as a graduate student one of the
+
+ align:start position:0%
+now as a graduate student one of the
+ 
+
+ align:start position:0%
+now as a graduate student one of the
+difficulties is that um you try to
+
+ align:start position:0%
+difficulties is that um you try to
+ 
+
+ align:start position:0%
+difficulties is that um you try to
+access it through the NBR and there's
+
+ align:start position:0%
+access it through the NBR and there's
+ 
+
+ align:start position:0%
+access it through the NBR and there's
+like a two-year application process to
+
+ align:start position:0%
+like a two-year application process to
+ 
+
+ align:start position:0%
+like a two-year application process to
+be approved as a special sworn employee
+
+ align:start position:0%
+be approved as a special sworn employee
+ 
+
+ align:start position:0%
+be approved as a special sworn employee
+of the census and you know two years is
+
+ align:start position:0%
+of the census and you know two years is
+ 
+
+ align:start position:0%
+of the census and you know two years is
+a long time for a graduate student I
+
+ align:start position:0%
+a long time for a graduate student I
+ 
+
+ align:start position:0%
+a long time for a graduate student I
+don't know if I should say this on
+
+ align:start position:0%
+don't know if I should say this on
+ 
+
+ align:start position:0%
+don't know if I should say this on
+camera you know I think what people
+
+ align:start position:0%
+camera you know I think what people
+ 
+
+ align:start position:0%
+camera you know I think what people
+often do if they want to access census
+
+ align:start position:0%
+often do if they want to access census
+ 
+
+ align:start position:0%
+often do if they want to access census
+data is they get a ra job working with
+
+ align:start position:0%
+data is they get a ra job working with
+ 
+
+ align:start position:0%
+data is they get a ra job working with
+someone who has access to the Census
+
+ align:start position:0%
+someone who has access to the Census
+ 
+
+ align:start position:0%
+someone who has access to the Census
+Data learn the Census Data well enough
+
+ align:start position:0%
+Data learn the Census Data well enough
+ 
+
+ align:start position:0%
+Data learn the Census Data well enough
+that they can describe all of the
+
+ align:start position:0%
+that they can describe all of the
+ 
+
+ align:start position:0%
+that they can describe all of the
+regressions and code that they will run
+
+ align:start position:0%
+regressions and code that they will run
+ 
+
+ align:start position:0%
+regressions and code that they will run
+when they get access to the census data
+
+ align:start position:0%
+when they get access to the census data
+ 
+
+ align:start position:0%
+when they get access to the census data
+and then they have all the programs
+
+ align:start position:0%
+and then they have all the programs
+ 
+
+ align:start position:0%
+and then they have all the programs
+entirely written to just push the Run
+
+ align:start position:0%
+entirely written to just push the Run
+ 
+
+ align:start position:0%
+entirely written to just push the Run
+button when their access is eventually
+
+ align:start position:0%
+button when their access is eventually
+ 
+
+ align:start position:0%
+button when their access is eventually
+approved two years later and then they
+
+ align:start position:0%
+approved two years later and then they
+ 
+
+ align:start position:0%
+approved two years later and then they
+you know can write their paper using the
+
+ align:start position:0%
+you know can write their paper using the
+ 
+
+ align:start position:0%
+you know can write their paper using the
+Sens of manufacturer data um but anyway
+
+ align:start position:0%
+Sens of manufacturer data um but anyway
+ 
+
+ align:start position:0%
+Sens of manufacturer data um but anyway
+it's you know one thing that's very good
+
+ align:start position:0%
+it's you know one thing that's very good
+ 
+
+ align:start position:0%
+it's you know one thing that's very good
+to a Sensi data is you can get very good
+
+ align:start position:0%
+to a Sensi data is you can get very good
+ 
+
+ align:start position:0%
+to a Sensi data is you can get very good
+statistics on
+
+ align:start position:0%
+statistics on
+ 
+
+ align:start position:0%
+statistics on
+um you know how many firms enter every 5
+
+ align:start position:0%
+um you know how many firms enter every 5
+ 
+
+ align:start position:0%
+um you know how many firms enter every 5
+years how many firms grow like you know
+
+ align:start position:0%
+years how many firms grow like you know
+ 
+
+ align:start position:0%
+years how many firms grow like you know
+of firms that enter in in a 5year period
+
+ align:start position:0%
+of firms that enter in in a 5year period
+ 
+
+ align:start position:0%
+of firms that enter in in a 5year period
+how many of them uh are still there five
+
+ align:start position:0%
+how many of them uh are still there five
+ 
+
+ align:start position:0%
+how many of them uh are still there five
+years later of the ones that are still
+
+ align:start position:0%
+years later of the ones that are still
+ 
+
+ align:start position:0%
+years later of the ones that are still
+there five years later how many of them
+
+ align:start position:0%
+there five years later how many of them
+ 
+
+ align:start position:0%
+there five years later how many of them
+have grown how many of them have
+
+ align:start position:0%
+have grown how many of them have
+ 
+
+ align:start position:0%
+have grown how many of them have
+shrunk what's what's the relative
+
+ align:start position:0%
+shrunk what's what's the relative
+ 
+
+ align:start position:0%
+shrunk what's what's the relative
+profitability of the new firms versus
+
+ align:start position:0%
+profitability of the new firms versus
+ 
+
+ align:start position:0%
+profitability of the new firms versus
+the old firms um so there's a set of old
+
+ align:start position:0%
+the old firms um so there's a set of old
+ 
+
+ align:start position:0%
+the old firms um so there's a set of old
+papers I used to um teach here um you
+
+ align:start position:0%
+papers I used to um teach here um you
+ 
+
+ align:start position:0%
+papers I used to um teach here um you
+know obviously uh the you know classic
+
+ align:start position:0%
+know obviously uh the you know classic
+ 
+
+ align:start position:0%
+know obviously uh the you know classic
+one that's on my still on my syllabus is
+
+ align:start position:0%
+one that's on my still on my syllabus is
+ 
+
+ align:start position:0%
+one that's on my still on my syllabus is
+uh dun Roberts and
+
+ align:start position:0%
+uh dun Roberts and
+ 
+
+ align:start position:0%
+uh dun Roberts and
+Samuelson uh from the
+
+ align:start position:0%
+Samuelson uh from the
+ 
+
+ align:start position:0%
+Samuelson uh from the
+1970s that has first sort of just wrote
+
+ align:start position:0%
+1970s that has first sort of just wrote
+ 
+
+ align:start position:0%
+1970s that has first sort of just wrote
+lots and lots of statistics on what this
+
+ align:start position:0%
+lots and lots of statistics on what this
+ 
+
+ align:start position:0%
+lots and lots of statistics on what this
+sort of entry and exit looked like in
+
+ align:start position:0%
+sort of entry and exit looked like in
+ 
+
+ align:start position:0%
+sort of entry and exit looked like in
+the Census Data but you could sort of
+
+ align:start position:0%
+the Census Data but you could sort of
+ 
+
+ align:start position:0%
+the Census Data but you could sort of
+search for things that have cited to
+
+ align:start position:0%
+search for things that have cited to
+ 
+
+ align:start position:0%
+search for things that have cited to
+find many updates since then but let me
+
+ align:start position:0%
+find many updates since then but let me
+ 
+
+ align:start position:0%
+find many updates since then but let me
+say you know some of this sort of
+
+ align:start position:0%
+say you know some of this sort of
+ 
+
+ align:start position:0%
+say you know some of this sort of
+stylized facts here is that according to
+
+ align:start position:0%
+stylized facts here is that according to
+ 
+
+ align:start position:0%
+stylized facts here is that according to
+the census dat at least there's a lot of
+
+ align:start position:0%
+the census dat at least there's a lot of
+ 
+
+ align:start position:0%
+the census dat at least there's a lot of
+entry and exit uh and I think you know I
+
+ align:start position:0%
+entry and exit uh and I think you know I
+ 
+
+ align:start position:0%
+entry and exit uh and I think you know I
+think in some Industries we we know this
+
+ align:start position:0%
+think in some Industries we we know this
+ 
+
+ align:start position:0%
+think in some Industries we we know this
+like if you watch restaurants or
+
+ align:start position:0%
+like if you watch restaurants or
+ 
+
+ align:start position:0%
+like if you watch restaurants or
+something like that you're just aware
+
+ align:start position:0%
+something like that you're just aware
+ 
+
+ align:start position:0%
+something like that you're just aware
+that new restaurants are born all the
+
+ align:start position:0%
+that new restaurants are born all the
+ 
+
+ align:start position:0%
+that new restaurants are born all the
+time restaurants die all the time
+
+ align:start position:0%
+time restaurants die all the time
+ 
+
+ align:start position:0%
+time restaurants die all the time
+there's a tremendous amount of entry and
+
+ align:start position:0%
+there's a tremendous amount of entry and
+ 
+
+ align:start position:0%
+there's a tremendous amount of entry and
+exit into the restaurant business well
+
+ align:start position:0%
+exit into the restaurant business well
+ 
+
+ align:start position:0%
+exit into the restaurant business well
+the sort of surprising result from dun
+
+ align:start position:0%
+the sort of surprising result from dun
+ 
+
+ align:start position:0%
+the sort of surprising result from dun
+Roberts and Samson is that lots of other
+
+ align:start position:0%
+Roberts and Samson is that lots of other
+ 
+
+ align:start position:0%
+Roberts and Samson is that lots of other
+businesses seem to look like that too um
+
+ align:start position:0%
+businesses seem to look like that too um
+ 
+
+ align:start position:0%
+businesses seem to look like that too um
+now it you know it's not the case that
+
+ align:start position:0%
+now it you know it's not the case that
+ 
+
+ align:start position:0%
+now it you know it's not the case that
+there's a tremendous number of new
+
+ align:start position:0%
+there's a tremendous number of new
+ 
+
+ align:start position:0%
+there's a tremendous number of new
+apples and Samsungs every five years um
+
+ align:start position:0%
+apples and Samsungs every five years um
+ 
+
+ align:start position:0%
+apples and Samsungs every five years um
+but if you look at the firms that are
+
+ align:start position:0%
+but if you look at the firms that are
+ 
+
+ align:start position:0%
+but if you look at the firms that are
+classified into many narrowly defined
+
+ align:start position:0%
+classified into many narrowly defined
+ 
+
+ align:start position:0%
+classified into many narrowly defined
+businesses it seems like many more are
+
+ align:start position:0%
+businesses it seems like many more are
+ 
+
+ align:start position:0%
+businesses it seems like many more are
+like the um many more are like the
+
+ align:start position:0%
+like the um many more are like the
+ 
+
+ align:start position:0%
+like the um many more are like the
+restaurants than like the Apple and
+
+ align:start position:0%
+restaurants than like the Apple and
+ 
+
+ align:start position:0%
+restaurants than like the Apple and
+Samsung phone
+
+ align:start position:0%
+Samsung phone
+ 
+
+ align:start position:0%
+Samsung phone
+producers um anyway so what you know
+
+ align:start position:0%
+producers um anyway so what you know
+ 
+
+ align:start position:0%
+producers um anyway so what you know
+jovovich's paper is about trying to
+
+ align:start position:0%
+jovovich's paper is about trying to
+ 
+
+ align:start position:0%
+jovovich's paper is about trying to
+discuss you know just basic framework
+
+ align:start position:0%
+discuss you know just basic framework
+ 
+
+ align:start position:0%
+discuss you know just basic framework
+for how do we think about entry and exit
+
+ align:start position:0%
+for how do we think about entry and exit
+ 
+
+ align:start position:0%
+for how do we think about entry and exit
+in a way that would explain what all
+
+ align:start position:0%
+in a way that would explain what all
+ 
+
+ align:start position:0%
+in a way that would explain what all
+what's going on in the census data when
+
+ align:start position:0%
+what's going on in the census data when
+ 
+
+ align:start position:0%
+what's going on in the census data when
+all these new firms are coming in all
+
+ align:start position:0%
+all these new firms are coming in all
+ 
+
+ align:start position:0%
+all these new firms are coming in all
+these firms are EX visiting and and
+
+ align:start position:0%
+these firms are EX visiting and and
+ 
+
+ align:start position:0%
+these firms are EX visiting and and
+growth patterns and so on
+
+ align:start position:0%
+growth patterns and so on
+ 
+
+ align:start position:0%
+growth patterns and so on
+um so this is you know classic Model
+
+ align:start position:0%
+um so this is you know classic Model
+ 
+
+ align:start position:0%
+um so this is you know classic Model
+javanovich it's a macro is paper so
+
+ align:start position:0%
+javanovich it's a macro is paper so
+ 
+
+ align:start position:0%
+javanovich it's a macro is paper so
+there's a lot of this assuming Continuum
+
+ align:start position:0%
+there's a lot of this assuming Continuum
+ 
+
+ align:start position:0%
+there's a lot of this assuming Continuum
+of firms and whatever and assuming that
+
+ align:start position:0%
+of firms and whatever and assuming that
+ 
+
+ align:start position:0%
+of firms and whatever and assuming that
+everything works out evenly but all so
+
+ align:start position:0%
+everything works out evenly but all so
+ 
+
+ align:start position:0%
+everything works out evenly but all so
+looks a little different from IO but I I
+
+ align:start position:0%
+looks a little different from IO but I I
+ 
+
+ align:start position:0%
+looks a little different from IO but I I
+wanted to cover it so uh so we start in
+
+ align:start position:0%
+wanted to cover it so uh so we start in
+ 
+
+ align:start position:0%
+wanted to cover it so uh so we start in
+this model imagine we have a Continuum
+
+ align:start position:0%
+this model imagine we have a Continuum
+ 
+
+ align:start position:0%
+this model imagine we have a Continuum
+of small potential entrance that are out
+
+ align:start position:0%
+of small potential entrance that are out
+ 
+
+ align:start position:0%
+of small potential entrance that are out
+there and the these firms are going to
+
+ align:start position:0%
+there and the these firms are going to
+ 
+
+ align:start position:0%
+there and the these firms are going to
+have some fixed cost K of entering the
+
+ align:start position:0%
+have some fixed cost K of entering the
+ 
+
+ align:start position:0%
+have some fixed cost K of entering the
+industry and then if they enter the
+
+ align:start position:0%
+industry and then if they enter the
+ 
+
+ align:start position:0%
+industry and then if they enter the
+industry and then they decide to leave
+
+ align:start position:0%
+industry and then they decide to leave
+ 
+
+ align:start position:0%
+industry and then they decide to leave
+they're going to have some liquidation
+
+ align:start position:0%
+they're going to have some liquidation
+ 
+
+ align:start position:0%
+they're going to have some liquidation
+value W that's less than K so you're a
+
+ align:start position:0%
+value W that's less than K so you're a
+ 
+
+ align:start position:0%
+value W that's less than K so you're a
+restaurant you enter you pay K to set up
+
+ align:start position:0%
+restaurant you enter you pay K to set up
+ 
+
+ align:start position:0%
+restaurant you enter you pay K to set up
+your restaurant when you're done you
+
+ align:start position:0%
+your restaurant when you're done you
+ 
+
+ align:start position:0%
+your restaurant when you're done you
+know you can uh sell all your tables and
+
+ align:start position:0%
+know you can uh sell all your tables and
+ 
+
+ align:start position:0%
+know you can uh sell all your tables and
+your cooking equipment and the leases
+
+ align:start position:0%
+your cooking equipment and the leases
+ 
+
+ align:start position:0%
+your cooking equipment and the leases
+and whatever all the money you spent on
+
+ align:start position:0%
+and whatever all the money you spent on
+ 
+
+ align:start position:0%
+and whatever all the money you spent on
+advertising and other things that's sunk
+
+ align:start position:0%
+advertising and other things that's sunk
+ 
+
+ align:start position:0%
+advertising and other things that's sunk
+but there's some fraction of you know
+
+ align:start position:0%
+but there's some fraction of you know
+ 
+
+ align:start position:0%
+but there's some fraction of you know
+there's some amount W that you can get
+
+ align:start position:0%
+there's some amount W that you can get
+ 
+
+ align:start position:0%
+there's some amount W that you can get
+back when you close up
+
+ align:start position:0%
+back when you close up
+ 
+
+ align:start position:0%
+back when you close up
+okay uh janov assume that these firms
+
+ align:start position:0%
+okay uh janov assume that these firms
+ 
+
+ align:start position:0%
+okay uh janov assume that these firms
+have unknown types Theta I you can think
+
+ align:start position:0%
+have unknown types Theta I you can think
+ 
+
+ align:start position:0%
+have unknown types Theta I you can think
+of theta I as well it's it's like the
+
+ align:start position:0%
+of theta I as well it's it's like the
+ 
+
+ align:start position:0%
+of theta I as well it's it's like the
+inverse of their
+
+ align:start position:0%
+inverse of their
+ 
+
+ align:start position:0%
+inverse of their
+productivity um so Theta I is
+
+ align:start position:0%
+productivity um so Theta I is
+ 
+
+ align:start position:0%
+productivity um so Theta I is
+distributed normal zero um Sigma Theta
+
+ align:start position:0%
+distributed normal zero um Sigma Theta
+ 
+
+ align:start position:0%
+distributed normal zero um Sigma Theta
+squared this is like how good of a firm
+
+ align:start position:0%
+squared this is like how good of a firm
+ 
+
+ align:start position:0%
+squared this is like how good of a firm
+you are you could think of it as like in
+
+ align:start position:0%
+you are you could think of it as like in
+ 
+
+ align:start position:0%
+you are you could think of it as like in
+the restaurant
+
+ align:start position:0%
+the restaurant
+ 
+
+ align:start position:0%
+the restaurant
+case everybody thinks they have a have
+
+ align:start position:0%
+case everybody thinks they have a have
+ 
+
+ align:start position:0%
+case everybody thinks they have a have
+have food that people are going to like
+
+ align:start position:0%
+have food that people are going to like
+ 
+
+ align:start position:0%
+have food that people are going to like
+the taste of but you never know until
+
+ align:start position:0%
+the taste of but you never know until
+ 
+
+ align:start position:0%
+the taste of but you never know until
+you open your restaurant you see how
+
+ align:start position:0%
+you open your restaurant you see how
+ 
+
+ align:start position:0%
+you open your restaurant you see how
+popular it is so all these firms they
+
+ align:start position:0%
+popular it is so all these firms they
+ 
+
+ align:start position:0%
+popular it is so all these firms they
+all have some prior well in fact they
+
+ align:start position:0%
+all have some prior well in fact they
+ 
+
+ align:start position:0%
+all have some prior well in fact they
+all have in this model they all have
+
+ align:start position:0%
+all have in this model they all have
+ 
+
+ align:start position:0%
+all have in this model they all have
+exactly the same prior they all have the
+
+ align:start position:0%
+exactly the same prior they all have the
+ 
+
+ align:start position:0%
+exactly the same prior they all have the
+prior that my Theta I is drawn from this
+
+ align:start position:0%
+prior that my Theta I is drawn from this
+ 
+
+ align:start position:0%
+prior that my Theta I is drawn from this
+distribution but the only way to learn
+
+ align:start position:0%
+distribution but the only way to learn
+ 
+
+ align:start position:0%
+distribution but the only way to learn
+whether my Theta I is low in which I'm
+
+ align:start position:0%
+whether my Theta I is low in which I'm
+ 
+
+ align:start position:0%
+whether my Theta I is low in which I'm
+I'm going to be a very profitable firm
+
+ align:start position:0%
+I'm going to be a very profitable firm
+ 
+
+ align:start position:0%
+I'm going to be a very profitable firm
+or high in which I'm going to be a very
+
+ align:start position:0%
+or high in which I'm going to be a very
+ 
+
+ align:start position:0%
+or high in which I'm going to be a very
+unprofitable firm is to enter start
+
+ align:start position:0%
+unprofitable firm is to enter start
+ 
+
+ align:start position:0%
+unprofitable firm is to enter start
+selling some open my Restaurant start
+
+ align:start position:0%
+selling some open my Restaurant start
+ 
+
+ align:start position:0%
+selling some open my Restaurant start
+selling to customers see if people come
+
+ align:start position:0%
+selling to customers see if people come
+ 
+
+ align:start position:0%
+selling to customers see if people come
+and are willing to pay my prices and I I
+
+ align:start position:0%
+and are willing to pay my prices and I I
+ 
+
+ align:start position:0%
+and are willing to pay my prices and I I
+sell out or
+
+ align:start position:0%
+sell out or
+ 
+
+ align:start position:0%
+sell out or
+not so um he does this with the sort of
+
+ align:start position:0%
+not so um he does this with the sort of
+ 
+
+ align:start position:0%
+not so um he does this with the sort of
+thetas rather than like quality of the
+
+ align:start position:0%
+thetas rather than like quality of the
+ 
+
+ align:start position:0%
+thetas rather than like quality of the
+food he does this by your cost of
+
+ align:start position:0%
+food he does this by your cost of
+ 
+
+ align:start position:0%
+food he does this by your cost of
+producing as if it's your you know
+
+ align:start position:0%
+producing as if it's your you know
+ 
+
+ align:start position:0%
+producing as if it's your you know
+everyone's trying to come in they're all
+
+ align:start position:0%
+everyone's trying to come in they're all
+ 
+
+ align:start position:0%
+everyone's trying to come in they're all
+going to try to produce um you know some
+
+ align:start position:0%
+going to try to produce um you know some
+ 
+
+ align:start position:0%
+going to try to produce um you know some
+kind of Steel and then some of them end
+
+ align:start position:0%
+kind of Steel and then some of them end
+ 
+
+ align:start position:0%
+kind of Steel and then some of them end
+up being high cost producers some end up
+
+ align:start position:0%
+up being high cost producers some end up
+ 
+
+ align:start position:0%
+up being high cost producers some end up
+being lowc cost producers and and they
+
+ align:start position:0%
+being lowc cost producers and and they
+ 
+
+ align:start position:0%
+being lowc cost producers and and they
+that that's what determines their
+
+ align:start position:0%
+that that's what determines their
+ 
+
+ align:start position:0%
+that that's what determines their
+profitability so fiz period T costs
+
+ align:start position:0%
+profitability so fiz period T costs
+ 
+
+ align:start position:0%
+profitability so fiz period T costs
+there's this some common function C of
+
+ align:start position:0%
+there's this some common function C of
+ 
+
+ align:start position:0%
+there's this some common function C of
+Qi that applies to
+
+ align:start position:0%
+Qi that applies to
+ 
+
+ align:start position:0%
+Qi that applies to
+everyone but then it's multiplied by F
+
+ align:start position:0%
+everyone but then it's multiplied by F
+ 
+
+ align:start position:0%
+everyone but then it's multiplied by F
+of thet I plus Epsilon i t where Theta I
+
+ align:start position:0%
+of thet I plus Epsilon i t where Theta I
+ 
+
+ align:start position:0%
+of thet I plus Epsilon i t where Theta I
+is your permanent type and Epsilon i t
+
+ align:start position:0%
+is your permanent type and Epsilon i t
+ 
+
+ align:start position:0%
+is your permanent type and Epsilon i t
+is a
+
+ align:start position:0%
+is a
+ 
+
+ align:start position:0%
+is a
+shock um and what he's imagining is
+
+ align:start position:0%
+shock um and what he's imagining is
+ 
+
+ align:start position:0%
+shock um and what he's imagining is
+that F might be some function that looks
+
+ align:start position:0%
+that F might be some function that looks
+ 
+
+ align:start position:0%
+that F might be some function that looks
+like this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we make this
+
+ align:start position:0%
+so we make this
+ 
+
+ align:start position:0%
+so we make this
+one so if my type is exactly zero then
+
+ align:start position:0%
+one so if my type is exactly zero then
+ 
+
+ align:start position:0%
+one so if my type is exactly zero then
+uh or when I make this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh there are extra parameters in this
+
+ align:start position:0%
+uh there are extra parameters in this
+ 
+
+ align:start position:0%
+uh there are extra parameters in this
+model that probably shouldn't be there
+
+ align:start position:0%
+model that probably shouldn't be there
+ 
+
+ align:start position:0%
+model that probably shouldn't be there
+so um let's call this theta0 so if my
+
+ align:start position:0%
+so um let's call this theta0 so if my
+ 
+
+ align:start position:0%
+so um let's call this theta0 so if my
+type is exactly Theta 0
+
+ align:start position:0%
+type is exactly Theta 0
+ 
+
+ align:start position:0%
+type is exactly Theta 0
+um my cost is C of
+
+ align:start position:0%
+um my cost is C of
+ 
+
+ align:start position:0%
+um my cost is C of
+Q uh if my Theta is like negative
+
+ align:start position:0%
+Q uh if my Theta is like negative
+ 
+
+ align:start position:0%
+Q uh if my Theta is like negative
+Infinity then my cost is like 12 C of Q
+
+ align:start position:0%
+Infinity then my cost is like 12 C of Q
+ 
+
+ align:start position:0%
+Infinity then my cost is like 12 C of Q
+and if my Theta is like positive
+
+ align:start position:0%
+and if my Theta is like positive
+ 
+
+ align:start position:0%
+and if my Theta is like positive
+Infinity um so I'm graphing f ofx um
+
+ align:start position:0%
+Infinity um so I'm graphing f ofx um
+ 
+
+ align:start position:0%
+Infinity um so I'm graphing f ofx um
+maybe my cost is twice C of Q and so
+
+ align:start position:0%
+maybe my cost is twice C of Q and so
+ 
+
+ align:start position:0%
+maybe my cost is twice C of Q and so
+with these firms are entering if their
+
+ align:start position:0%
+with these firms are entering if their
+ 
+
+ align:start position:0%
+with these firms are entering if their
+costs are low they're going to earn
+
+ align:start position:0%
+costs are low they're going to earn
+ 
+
+ align:start position:0%
+costs are low they're going to earn
+positive profits High profits if their
+
+ align:start position:0%
+positive profits High profits if their
+ 
+
+ align:start position:0%
+positive profits High profits if their
+costs are high they're going to earn
+
+ align:start position:0%
+costs are high they're going to earn
+ 
+
+ align:start position:0%
+costs are high they're going to earn
+negative
+
+ align:start position:0%
+negative
+ 
+
+ align:start position:0%
+negative
+profits but he adds this random shock in
+
+ align:start position:0%
+profits but he adds this random shock in
+ 
+
+ align:start position:0%
+profits but he adds this random shock in
+you know so there's this random period
+
+ align:start position:0%
+you know so there's this random period
+ 
+
+ align:start position:0%
+you know so there's this random period
+by period shock so I enter I try to
+
+ align:start position:0%
+by period shock so I enter I try to
+ 
+
+ align:start position:0%
+by period shock so I enter I try to
+produce this period I turned out that I
+
+ align:start position:0%
+produce this period I turned out that I
+ 
+
+ align:start position:0%
+produce this period I turned out that I
+had high costs I don't know am I a high
+
+ align:start position:0%
+had high costs I don't know am I a high
+ 
+
+ align:start position:0%
+had high costs I don't know am I a high
+Theta type or was I just unlucky so
+
+ align:start position:0%
+Theta type or was I just unlucky so
+ 
+
+ align:start position:0%
+Theta type or was I just unlucky so
+again if you think about on the on the
+
+ align:start position:0%
+again if you think about on the on the
+ 
+
+ align:start position:0%
+again if you think about on the on the
+quality side you know I enter enter I
+
+ align:start position:0%
+quality side you know I enter enter I
+ 
+
+ align:start position:0%
+quality side you know I enter enter I
+start selling either this there's nobody
+
+ align:start position:0%
+start selling either this there's nobody
+ 
+
+ align:start position:0%
+start selling either this there's nobody
+at my restaurant is it that my quality
+
+ align:start position:0%
+at my restaurant is it that my quality
+ 
+
+ align:start position:0%
+at my restaurant is it that my quality
+is low or did I just have a bad shock
+
+ align:start position:0%
+is low or did I just have a bad shock
+ 
+
+ align:start position:0%
+is low or did I just have a bad shock
+that a bad random draw that week
+
+ align:start position:0%
+that a bad random draw that week
+ 
+
+ align:start position:0%
+that a bad random draw that week
+okay and so firms you know are symmet
+
+ align:start position:0%
+okay and so firms you know are symmet
+ 
+
+ align:start position:0%
+okay and so firms you know are symmet
+are you know it's symmetric information
+
+ align:start position:0%
+are you know it's symmetric information
+ 
+
+ align:start position:0%
+are you know it's symmetric information
+model firms don't know their types but
+
+ align:start position:0%
+model firms don't know their types but
+ 
+
+ align:start position:0%
+model firms don't know their types but
+every time they produce they get a
+
+ align:start position:0%
+every time they produce they get a
+ 
+
+ align:start position:0%
+every time they produce they get a
+signal about what their type is they
+
+ align:start position:0%
+signal about what their type is they
+ 
+
+ align:start position:0%
+signal about what their type is they
+update their beliefs and then by
+
+ align:start position:0%
+update their beliefs and then by
+ 
+
+ align:start position:0%
+update their beliefs and then by
+updating their beliefs you know they're
+
+ align:start position:0%
+updating their beliefs you know they're
+ 
+
+ align:start position:0%
+updating their beliefs you know they're
+going to sort of uh they're going to
+
+ align:start position:0%
+going to sort of uh they're going to
+ 
+
+ align:start position:0%
+going to sort of uh they're going to
+change two things um you know C is
+
+ align:start position:0%
+change two things um you know C is
+ 
+
+ align:start position:0%
+change two things um you know C is
+convex in this
+
+ align:start position:0%
+convex in this
+ 
+
+ align:start position:0%
+convex in this
+model so if I think my cost is low I'm
+
+ align:start position:0%
+model so if I think my cost is low I'm
+ 
+
+ align:start position:0%
+model so if I think my cost is low I'm
+going to produce a lot and continue
+
+ align:start position:0%
+going to produce a lot and continue
+ 
+
+ align:start position:0%
+going to produce a lot and continue
+going because I'm like I can produce a
+
+ align:start position:0%
+going because I'm like I can produce a
+ 
+
+ align:start position:0%
+going because I'm like I can produce a
+lot and earn positive profits at the
+
+ align:start position:0%
+lot and earn positive profits at the
+ 
+
+ align:start position:0%
+lot and earn positive profits at the
+equilibrium level P star if my cost is
+
+ align:start position:0%
+equilibrium level P star if my cost is
+ 
+
+ align:start position:0%
+equilibrium level P star if my cost is
+high I'm only going to produce a little
+
+ align:start position:0%
+high I'm only going to produce a little
+ 
+
+ align:start position:0%
+high I'm only going to produce a little
+because I want to get the signal and
+
+ align:start position:0%
+because I want to get the signal and
+ 
+
+ align:start position:0%
+because I want to get the signal and
+find out if I'm good or not but I'm only
+
+ align:start position:0%
+find out if I'm good or not but I'm only
+ 
+
+ align:start position:0%
+find out if I'm good or not but I'm only
+going to produce a little bit because
+
+ align:start position:0%
+going to produce a little bit because
+ 
+
+ align:start position:0%
+going to produce a little bit because
+I'm probably going to lose money on
+
+ align:start position:0%
+I'm probably going to lose money on
+ 
+
+ align:start position:0%
+I'm probably going to lose money on
+everything I produce
+
+ align:start position:0%
+everything I produce
+ 
+
+ align:start position:0%
+everything I produce
+okay so anyway he treats the entrance as
+
+ align:start position:0%
+okay so anyway he treats the entrance as
+ 
+
+ align:start position:0%
+okay so anyway he treats the entrance as
+a continuum per period And so with this
+
+ align:start position:0%
+a continuum per period And so with this
+ 
+
+ align:start position:0%
+a continuum per period And so with this
+Continuum of
+
+ align:start position:0%
+Continuum of
+ 
+
+ align:start position:0%
+Continuum of
+entrance you get a deterministic price
+
+ align:start position:0%
+entrance you get a deterministic price
+ 
+
+ align:start position:0%
+entrance you get a deterministic price
+sequence P1 P2 P3 and he also assumes
+
+ align:start position:0%
+sequence P1 P2 P3 and he also assumes
+ 
+
+ align:start position:0%
+sequence P1 P2 P3 and he also assumes
+that the firms are all price takers and
+
+ align:start position:0%
+that the firms are all price takers and
+ 
+
+ align:start position:0%
+that the firms are all price takers and
+they're just choosing Q to maximize the
+
+ align:start position:0%
+they're just choosing Q to maximize the
+ 
+
+ align:start position:0%
+they're just choosing Q to maximize the
+expectation over Theta I of the profits
+
+ align:start position:0%
+expectation over Theta I of the profits
+ 
+
+ align:start position:0%
+expectation over Theta I of the profits
+I'm going to get this period which is PT
+
+ align:start position:0%
+I'm going to get this period which is PT
+ 
+
+ align:start position:0%
+I'm going to get this period which is PT
+which I know times Q minus my cost of
+
+ align:start position:0%
+which I know times Q minus my cost of
+ 
+
+ align:start position:0%
+which I know times Q minus my cost of
+production C of Q F of theta I plus
+
+ align:start position:0%
+production C of Q F of theta I plus
+ 
+
+ align:start position:0%
+production C of Q F of theta I plus
+Epsilon i t and again there's
+
+ align:start position:0%
+Epsilon i t and again there's
+ 
+
+ align:start position:0%
+Epsilon i t and again there's
+expectation here because I don't know
+
+ align:start position:0%
+expectation here because I don't know
+ 
+
+ align:start position:0%
+expectation here because I don't know
+Theta I and actually also there's going
+
+ align:start position:0%
+Theta I and actually also there's going
+ 
+
+ align:start position:0%
+Theta I and actually also there's going
+to be an Epsilon I is also going to be
+
+ align:start position:0%
+to be an Epsilon I is also going to be
+ 
+
+ align:start position:0%
+to be an Epsilon I is also going to be
+random shock so I guess this really
+
+ align:start position:0%
+random shock so I guess this really
+ 
+
+ align:start position:0%
+random shock so I guess this really
+should be expectation over Theta I and
+
+ align:start position:0%
+should be expectation over Theta I and
+ 
+
+ align:start position:0%
+should be expectation over Theta I and
+Epsilon
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it okay so then
+
+ align:start position:0%
+it okay so then
+ 
+
+ align:start position:0%
+it okay so then
+um what's the optimal behavior for a
+
+ align:start position:0%
+um what's the optimal behavior for a
+ 
+
+ align:start position:0%
+um what's the optimal behavior for a
+firm um you know suppose that you think
+
+ align:start position:0%
+firm um you know suppose that you think
+ 
+
+ align:start position:0%
+firm um you know suppose that you think
+Theta is very low if you think Theta is
+
+ align:start position:0%
+Theta is very low if you think Theta is
+ 
+
+ align:start position:0%
+Theta is very low if you think Theta is
+very low then you think your costs are
+
+ align:start position:0%
+very low then you think your costs are
+ 
+
+ align:start position:0%
+very low then you think your costs are
+going to be very low you know that the
+
+ align:start position:0%
+going to be very low you know that the
+ 
+
+ align:start position:0%
+going to be very low you know that the
+prices are so you produce a very high
+
+ align:start position:0%
+prices are so you produce a very high
+ 
+
+ align:start position:0%
+prices are so you produce a very high
+quantity because you can produce a very
+
+ align:start position:0%
+quantity because you can produce a very
+ 
+
+ align:start position:0%
+quantity because you can produce a very
+high quantity with the increasing costs
+
+ align:start position:0%
+high quantity with the increasing costs
+ 
+
+ align:start position:0%
+high quantity with the increasing costs
+and still make a profit right so this is
+
+ align:start position:0%
+and still make a profit right so this is
+ 
+
+ align:start position:0%
+and still make a profit right so this is
+not a constant marginal cost model this
+
+ align:start position:0%
+not a constant marginal cost model this
+ 
+
+ align:start position:0%
+not a constant marginal cost model this
+is a marginal cost uh you know this is C
+
+ align:start position:0%
+is a marginal cost uh you know this is C
+ 
+
+ align:start position:0%
+is a marginal cost uh you know this is C
+of Q that's increasing in
+
+ align:start position:0%
+of Q that's increasing in
+ 
+
+ align:start position:0%
+of Q that's increasing in
+Q um if I have a
+
+ align:start position:0%
+Q um if I have a
+ 
+
+ align:start position:0%
+Q um if I have a
+medium uh expectation of theta then I'm
+
+ align:start position:0%
+medium uh expectation of theta then I'm
+ 
+
+ align:start position:0%
+medium uh expectation of theta then I'm
+going to produce some low quantity I'm
+
+ align:start position:0%
+going to produce some low quantity I'm
+ 
+
+ align:start position:0%
+going to produce some low quantity I'm
+going going to hope that I'm I'm better
+
+ align:start position:0%
+going going to hope that I'm I'm better
+ 
+
+ align:start position:0%
+going going to hope that I'm I'm better
+than I think I am but I'm just going to
+
+ align:start position:0%
+than I think I am but I'm just going to
+ 
+
+ align:start position:0%
+than I think I am but I'm just going to
+produce the units I can produce cheaply
+
+ align:start position:0%
+produce the units I can produce cheaply
+ 
+
+ align:start position:0%
+produce the units I can produce cheaply
+uh produce my initial cheap units and
+
+ align:start position:0%
+uh produce my initial cheap units and
+ 
+
+ align:start position:0%
+uh produce my initial cheap units and
+then leave it at that and then hope that
+
+ align:start position:0%
+then leave it at that and then hope that
+ 
+
+ align:start position:0%
+then leave it at that and then hope that
+I find out I'm better but at least make
+
+ align:start position:0%
+I find out I'm better but at least make
+ 
+
+ align:start position:0%
+I find out I'm better but at least make
+a profit on the ones I
+
+ align:start position:0%
+a profit on the ones I
+ 
+
+ align:start position:0%
+a profit on the ones I
+produce um if I have a high
+
+ align:start position:0%
+produce um if I have a high
+ 
+
+ align:start position:0%
+produce um if I have a high
+Theta uh if I have a high expectation of
+
+ align:start position:0%
+Theta uh if I have a high expectation of
+ 
+
+ align:start position:0%
+Theta uh if I have a high expectation of
+theta I think I'm a bad firm uh but I'm
+
+ align:start position:0%
+theta I think I'm a bad firm uh but I'm
+ 
+
+ align:start position:0%
+theta I think I'm a bad firm uh but I'm
+uncertain about how how bad I am then
+
+ align:start position:0%
+uncertain about how how bad I am then
+ 
+
+ align:start position:0%
+uncertain about how how bad I am then
+I'm going to produce a low qit and stay
+
+ align:start position:0%
+I'm going to produce a low qit and stay
+ 
+
+ align:start position:0%
+I'm going to produce a low qit and stay
+in the market and I'm just going to
+
+ align:start position:0%
+in the market and I'm just going to
+ 
+
+ align:start position:0%
+in the market and I'm just going to
+produce these very few units and sell
+
+ align:start position:0%
+produce these very few units and sell
+ 
+
+ align:start position:0%
+produce these very few units and sell
+try to sell those and hope that I'm
+
+ align:start position:0%
+try to sell those and hope that I'm
+ 
+
+ align:start position:0%
+try to sell those and hope that I'm
+better than I think I am uh but if I'm
+
+ align:start position:0%
+better than I think I am uh but if I'm
+ 
+
+ align:start position:0%
+better than I think I am uh but if I'm
+high uh Theta and I'm have low
+
+ align:start position:0%
+high uh Theta and I'm have low
+ 
+
+ align:start position:0%
+high uh Theta and I'm have low
+uncertainty then I'm just going to take
+
+ align:start position:0%
+uncertainty then I'm just going to take
+ 
+
+ align:start position:0%
+uncertainty then I'm just going to take
+the liquidation value W and get out of
+
+ align:start position:0%
+the liquidation value W and get out of
+ 
+
+ align:start position:0%
+the liquidation value W and get out of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+market okay so firms are making this uh
+
+ align:start position:0%
+market okay so firms are making this uh
+ 
+
+ align:start position:0%
+market okay so firms are making this uh
+you know endogenously choosing both what
+
+ align:start position:0%
+you know endogenously choosing both what
+ 
+
+ align:start position:0%
+you know endogenously choosing both what
+quantity do I produce and um what qu do
+
+ align:start position:0%
+quantity do I produce and um what qu do
+ 
+
+ align:start position:0%
+quantity do I produce and um what qu do
+I produce and do I exit or not um and
+
+ align:start position:0%
+I produce and do I exit or not um and
+ 
+
+ align:start position:0%
+I produce and do I exit or not um and
+and you know he separates these things
+
+ align:start position:0%
+and you know he separates these things
+ 
+
+ align:start position:0%
+and you know he separates these things
+so the amount I learn doesn't depend on
+
+ align:start position:0%
+so the amount I learn doesn't depend on
+ 
+
+ align:start position:0%
+so the amount I learn doesn't depend on
+the amount that I produced and so if I
+
+ align:start position:0%
+the amount that I produced and so if I
+ 
+
+ align:start position:0%
+the amount that I produced and so if I
+produce I'm going to produce the sort of
+
+ align:start position:0%
+produce I'm going to produce the sort of
+ 
+
+ align:start position:0%
+produce I'm going to produce the sort of
+static optimal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+quantity yes so someone's like believe
+
+ align:start position:0%
+quantity yes so someone's like believe
+ 
+
+ align:start position:0%
+quantity yes so someone's like believe
+their expectation data I just based on
+
+ align:start position:0%
+their expectation data I just based on
+ 
+
+ align:start position:0%
+their expectation data I just based on
+their previous observations of Thea it's
+
+ align:start position:0%
+their previous observations of Thea it's
+ 
+
+ align:start position:0%
+their previous observations of Thea it's
+based on their previous obser like every
+
+ align:start position:0%
+based on their previous obser like every
+ 
+
+ align:start position:0%
+based on their previous obser like every
+period you get an observation of theta I
+
+ align:start position:0%
+period you get an observation of theta I
+ 
+
+ align:start position:0%
+period you get an observation of theta I
+plus Epsilon it and so you have a you
+
+ align:start position:0%
+plus Epsilon it and so you have a you
+ 
+
+ align:start position:0%
+plus Epsilon it and so you have a you
+have a you it's a normal learning model
+
+ align:start position:0%
+have a you it's a normal learning model
+ 
+
+ align:start position:0%
+have a you it's a normal learning model
+I have a prior that it's normal zero
+
+ align:start position:0%
+I have a prior that it's normal zero
+ 
+
+ align:start position:0%
+I have a prior that it's normal zero
+Theta these epsilons are also normal so
+
+ align:start position:0%
+Theta these epsilons are also normal so
+ 
+
+ align:start position:0%
+Theta these epsilons are also normal so
+every time I enter I get a normal signal
+
+ align:start position:0%
+every time I enter I get a normal signal
+ 
+
+ align:start position:0%
+every time I enter I get a normal signal
+and then I just beige and update up and
+
+ align:start position:0%
+and then I just beige and update up and
+ 
+
+ align:start position:0%
+and then I just beige and update up and
+down and the number of signals that I
+
+ align:start position:0%
+down and the number of signals that I
+ 
+
+ align:start position:0%
+down and the number of signals that I
+get determines whether my posterior is
+
+ align:start position:0%
+get determines whether my posterior is
+ 
+
+ align:start position:0%
+get determines whether my posterior is
+diffuse or narrow or
+
+ align:start position:0%
+diffuse or narrow or
+ 
+
+ align:start position:0%
+diffuse or narrow or
+tight right so some sense the older I am
+
+ align:start position:0%
+tight right so some sense the older I am
+ 
+
+ align:start position:0%
+tight right so some sense the older I am
+the less uncertainty I have in like in
+
+ align:start position:0%
+the less uncertainty I have in like in
+ 
+
+ align:start position:0%
+the less uncertainty I have in like in
+nor with normal distributions it's just
+
+ align:start position:0%
+nor with normal distributions it's just
+ 
+
+ align:start position:0%
+nor with normal distributions it's just
+a purely one over
+
+ align:start position:0%
+a purely one over
+ 
+
+ align:start position:0%
+a purely one over
+n uncertainty diminishes like one over
+
+ align:start position:0%
+n uncertainty diminishes like one over
+ 
+
+ align:start position:0%
+n uncertainty diminishes like one over
+an like Get N observations
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay uh and so you know what he notes
+
+ align:start position:0%
+okay uh and so you know what he notes
+ 
+
+ align:start position:0%
+okay uh and so you know what he notes
+that a basic model like this uh makes a
+
+ align:start position:0%
+that a basic model like this uh makes a
+ 
+
+ align:start position:0%
+that a basic model like this uh makes a
+number of predictions about firm
+
+ align:start position:0%
+number of predictions about firm
+ 
+
+ align:start position:0%
+number of predictions about firm
+dynamics that seem to fit with what the
+
+ align:start position:0%
+dynamics that seem to fit with what the
+ 
+
+ align:start position:0%
+dynamics that seem to fit with what the
+basic census data on firm Dynamics look
+
+ align:start position:0%
+basic census data on firm Dynamics look
+ 
+
+ align:start position:0%
+basic census data on firm Dynamics look
+like so some
+
+ align:start position:0%
+like so some
+ 
+
+ align:start position:0%
+like so some
+observations um small firms grow faster
+
+ align:start position:0%
+observations um small firms grow faster
+ 
+
+ align:start position:0%
+observations um small firms grow faster
+and fail more often um why is that well
+
+ align:start position:0%
+and fail more often um why is that well
+ 
+
+ align:start position:0%
+and fail more often um why is that well
+a lot of the small firms are um you
+
+ align:start position:0%
+a lot of the small firms are um you
+ 
+
+ align:start position:0%
+a lot of the small firms are um you
+know a lot of the small firms are these
+
+ align:start position:0%
+know a lot of the small firms are these
+ 
+
+ align:start position:0%
+know a lot of the small firms are these
+people with high
+
+ align:start position:0%
+people with high
+ 
+
+ align:start position:0%
+people with high
+uncertainty right the small firms are
+
+ align:start position:0%
+uncertainty right the small firms are
+ 
+
+ align:start position:0%
+uncertainty right the small firms are
+new firms that come in or firms that
+
+ align:start position:0%
+new firms that come in or firms that
+ 
+
+ align:start position:0%
+new firms that come in or firms that
+have come in and gotten one bad
+
+ align:start position:0%
+have come in and gotten one bad
+ 
+
+ align:start position:0%
+have come in and gotten one bad
+draw they think their Theta is high but
+
+ align:start position:0%
+draw they think their Theta is high but
+ 
+
+ align:start position:0%
+draw they think their Theta is high but
+they're very uncertain about their Theta
+
+ align:start position:0%
+they're very uncertain about their Theta
+ 
+
+ align:start position:0%
+they're very uncertain about their Theta
+so they're producing small quantities if
+
+ align:start position:0%
+so they're producing small quantities if
+ 
+
+ align:start position:0%
+so they're producing small quantities if
+they find out that they're better firms
+
+ align:start position:0%
+they find out that they're better firms
+ 
+
+ align:start position:0%
+they find out that they're better firms
+they grow very
+
+ align:start position:0%
+they grow very
+ 
+
+ align:start position:0%
+they grow very
+quickly okay these guys the only way you
+
+ align:start position:0%
+quickly okay these guys the only way you
+ 
+
+ align:start position:0%
+quickly okay these guys the only way you
+can have a low expectation of theta is
+
+ align:start position:0%
+can have a low expectation of theta is
+ 
+
+ align:start position:0%
+can have a low expectation of theta is
+if you've gotten a lot of data and all
+
+ align:start position:0%
+if you've gotten a lot of data and all
+ 
+
+ align:start position:0%
+if you've gotten a lot of data and all
+the data says that your quantity is low
+
+ align:start position:0%
+the data says that your quantity is low
+ 
+
+ align:start position:0%
+the data says that your quantity is low
+your your costs are low therefore you're
+
+ align:start position:0%
+your your costs are low therefore you're
+ 
+
+ align:start position:0%
+your your costs are low therefore you're
+not going to grow very fast because
+
+ align:start position:0%
+not going to grow very fast because
+ 
+
+ align:start position:0%
+not going to grow very fast because
+you've already got a lot of data you're
+
+ align:start position:0%
+you've already got a lot of data you're
+ 
+
+ align:start position:0%
+you've already got a lot of data you're
+going to continue to think that your
+
+ align:start position:0%
+going to continue to think that your
+ 
+
+ align:start position:0%
+going to continue to think that your
+costs are low and you're going to sort
+
+ align:start position:0%
+costs are low and you're going to sort
+ 
+
+ align:start position:0%
+costs are low and you're going to sort
+of have roughly the same output but so
+
+ align:start position:0%
+of have roughly the same output but so
+ 
+
+ align:start position:0%
+of have roughly the same output but so
+this sort of small firms small firms are
+
+ align:start position:0%
+this sort of small firms small firms are
+ 
+
+ align:start position:0%
+this sort of small firms small firms are
+firms who have a lot of uncertainty but
+
+ align:start position:0%
+firms who have a lot of uncertainty but
+ 
+
+ align:start position:0%
+firms who have a lot of uncertainty but
+think their costs are relatively High
+
+ align:start position:0%
+think their costs are relatively High
+ 
+
+ align:start position:0%
+think their costs are relatively High
+therefore they grow fast if they stay in
+
+ align:start position:0%
+therefore they grow fast if they stay in
+ 
+
+ align:start position:0%
+therefore they grow fast if they stay in
+the market but they also just exit and
+
+ align:start position:0%
+the market but they also just exit and
+ 
+
+ align:start position:0%
+the market but they also just exit and
+fail fail much more
+
+ align:start position:0%
+fail fail much more
+ 
+
+ align:start position:0%
+fail fail much more
+often okay
+
+ align:start position:0%
+often okay
+ 
+
+ align:start position:0%
+often okay
+um bigger firms have higher profits so
+
+ align:start position:0%
+um bigger firms have higher profits so
+ 
+
+ align:start position:0%
+um bigger firms have higher profits so
+you know profits are quite different
+
+ align:start position:0%
+you know profits are quite different
+ 
+
+ align:start position:0%
+you know profits are quite different
+across firms the high-profit firms are
+
+ align:start position:0%
+across firms the high-profit firms are
+ 
+
+ align:start position:0%
+across firms the high-profit firms are
+the people who've been around for a
+
+ align:start position:0%
+the people who've been around for a
+ 
+
+ align:start position:0%
+the people who've been around for a
+while they've learned that their Theta
+
+ align:start position:0%
+while they've learned that their Theta
+ 
+
+ align:start position:0%
+while they've learned that their Theta
+is very low therefore they can produce
+
+ align:start position:0%
+is very low therefore they can produce
+ 
+
+ align:start position:0%
+is very low therefore they can produce
+way out here on their cost curve and
+
+ align:start position:0%
+way out here on their cost curve and
+ 
+
+ align:start position:0%
+way out here on their cost curve and
+still make a profit and they're making
+
+ align:start position:0%
+still make a profit and they're making
+ 
+
+ align:start position:0%
+still make a profit and they're making
+all these profits on the infam marginal
+
+ align:start position:0%
+all these profits on the infam marginal
+ 
+
+ align:start position:0%
+all these profits on the infam marginal
+units so the big firms are the big firms
+
+ align:start position:0%
+units so the big firms are the big firms
+ 
+
+ align:start position:0%
+units so the big firms are the big firms
+are the profitable firms um and they're
+
+ align:start position:0%
+are the profitable firms um and they're
+ 
+
+ align:start position:0%
+are the profitable firms um and they're
+profitable because they just are more
+
+ align:start position:0%
+profitable because they just are more
+ 
+
+ align:start position:0%
+profitable because they just are more
+efficient cost-wise than the other
+
+ align:start position:0%
+efficient cost-wise than the other
+ 
+
+ align:start position:0%
+efficient cost-wise than the other
+firms
+
+ align:start position:0%
+firms
+ 
+
+ align:start position:0%
+firms
+um if you think about you know is
+
+ align:start position:0%
+um if you think about you know is
+ 
+
+ align:start position:0%
+um if you think about you know is
+um how are industry concentration and
+
+ align:start position:0%
+um how are industry concentration and
+ 
+
+ align:start position:0%
+um how are industry concentration and
+profits related you know and right we
+
+ align:start position:0%
+profits related you know and right we
+ 
+
+ align:start position:0%
+profits related you know and right we
+have the sort of standard view that
+
+ align:start position:0%
+have the sort of standard view that
+ 
+
+ align:start position:0%
+have the sort of standard view that
+industry concentration profits are
+
+ align:start position:0%
+industry concentration profits are
+ 
+
+ align:start position:0%
+industry concentration profits are
+related because we put more firms into a
+
+ align:start position:0%
+related because we put more firms into a
+ 
+
+ align:start position:0%
+related because we put more firms into a
+Coro model or more firms into a a
+
+ align:start position:0%
+Coro model or more firms into a a
+ 
+
+ align:start position:0%
+Coro model or more firms into a a
+hoteling circle model markups
+
+ align:start position:0%
+hoteling circle model markups
+ 
+
+ align:start position:0%
+hoteling circle model markups
+drop um here um you know this is like
+
+ align:start position:0%
+drop um here um you know this is like
+ 
+
+ align:start position:0%
+drop um here um you know this is like
+this is a you know this is like a a
+
+ align:start position:0%
+this is a you know this is like a a
+ 
+
+ align:start position:0%
+this is a you know this is like a a
+perfect competition model it's but in
+
+ align:start position:0%
+perfect competition model it's but in
+ 
+
+ align:start position:0%
+perfect competition model it's but in
+equilibrium industry concentration is
+
+ align:start position:0%
+equilibrium industry concentration is
+ 
+
+ align:start position:0%
+equilibrium industry concentration is
+correlated in the cross section with
+
+ align:start position:0%
+correlated in the cross section with
+ 
+
+ align:start position:0%
+correlated in the cross section with
+high profits because an industry that
+
+ align:start position:0%
+high profits because an industry that
+ 
+
+ align:start position:0%
+high profits because an industry that
+happens to have a few very lowcost firms
+
+ align:start position:0%
+happens to have a few very lowcost firms
+ 
+
+ align:start position:0%
+happens to have a few very lowcost firms
+in it those firms will earn very high
+
+ align:start position:0%
+in it those firms will earn very high
+ 
+
+ align:start position:0%
+in it those firms will earn very high
+profits whereas if another industry all
+
+ align:start position:0%
+profits whereas if another industry all
+ 
+
+ align:start position:0%
+profits whereas if another industry all
+the firms have very similar costs then
+
+ align:start position:0%
+the firms have very similar costs then
+ 
+
+ align:start position:0%
+the firms have very similar costs then
+you're just going to have a large number
+
+ align:start position:0%
+you're just going to have a large number
+ 
+
+ align:start position:0%
+you're just going to have a large number
+of firms each earning individually low
+
+ align:start position:0%
+of firms each earning individually low
+ 
+
+ align:start position:0%
+of firms each earning individually low
+profits and so the firms that are going
+
+ align:start position:0%
+profits and so the firms that are going
+ 
+
+ align:start position:0%
+profits and so the firms that are going
+to look like the high profit Industries
+
+ align:start position:0%
+to look like the high profit Industries
+ 
+
+ align:start position:0%
+to look like the high profit Industries
+they're concentrated because they're the
+
+ align:start position:0%
+they're concentrated because they're the
+ 
+
+ align:start position:0%
+they're concentrated because they're the
+firms that just have a few firms that
+
+ align:start position:0%
+firms that just have a few firms that
+ 
+
+ align:start position:0%
+firms that just have a few firms that
+have Theta draws much lower than
+
+ align:start position:0%
+have Theta draws much lower than
+ 
+
+ align:start position:0%
+have Theta draws much lower than
+everybody else's Theta draw and so you
+
+ align:start position:0%
+everybody else's Theta draw and so you
+ 
+
+ align:start position:0%
+everybody else's Theta draw and so you
+get this correlation between profits and
+
+ align:start position:0%
+get this correlation between profits and
+ 
+
+ align:start position:0%
+get this correlation between profits and
+concentration that comes from the
+
+ align:start position:0%
+concentration that comes from the
+ 
+
+ align:start position:0%
+concentration that comes from the
+distribution of realized
+
+ align:start position:0%
+distribution of realized
+ 
+
+ align:start position:0%
+distribution of realized
+costs okay so we get a profit
+
+ align:start position:0%
+costs okay so we get a profit
+ 
+
+ align:start position:0%
+costs okay so we get a profit
+concentration cross-section but it's
+
+ align:start position:0%
+concentration cross-section but it's
+ 
+
+ align:start position:0%
+concentration cross-section but it's
+caused by a correlation with the omitted
+
+ align:start position:0%
+caused by a correlation with the omitted
+ 
+
+ align:start position:0%
+caused by a correlation with the omitted
+variable of distribution of firm costs
+
+ align:start position:0%
+variable of distribution of firm costs
+ 
+
+ align:start position:0%
+variable of distribution of firm costs
+rather than caused by competition of
+
+ align:start position:0%
+rather than caused by competition of
+ 
+
+ align:start position:0%
+rather than caused by competition of
+cost caal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+effect
+
+ align:start position:0%
+effect
+ 
+
+ align:start position:0%
+effect
+um industry concentration is also
+
+ align:start position:0%
+um industry concentration is also
+ 
+
+ align:start position:0%
+um industry concentration is also
+correlated with cross-sectional variance
+
+ align:start position:0%
+correlated with cross-sectional variance
+ 
+
+ align:start position:0%
+correlated with cross-sectional variance
+and profits so again if you have a
+
+ align:start position:0%
+and profits so again if you have a
+ 
+
+ align:start position:0%
+and profits so again if you have a
+industry that has if I do histograms of
+
+ align:start position:0%
+industry that has if I do histograms of
+ 
+
+ align:start position:0%
+industry that has if I do histograms of
+costs if I have a an industry that has
+
+ align:start position:0%
+costs if I have a an industry that has
+ 
+
+ align:start position:0%
+costs if I have a an industry that has
+like a mass of firms that have very low
+
+ align:start position:0%
+like a mass of firms that have very low
+ 
+
+ align:start position:0%
+like a mass of firms that have very low
+costs and then some firms that have
+
+ align:start position:0%
+costs and then some firms that have
+ 
+
+ align:start position:0%
+costs and then some firms that have
+higher
+
+ align:start position:0%
+higher
+ 
+
+ align:start position:0%
+higher
+costs this industry is going to end up
+
+ align:start position:0%
+costs this industry is going to end up
+ 
+
+ align:start position:0%
+costs this industry is going to end up
+very concentrated because the lowcost
+
+ align:start position:0%
+very concentrated because the lowcost
+ 
+
+ align:start position:0%
+very concentrated because the lowcost
+firms are going to produce a ton all
+
+ align:start position:0%
+firms are going to produce a ton all
+ 
+
+ align:start position:0%
+firms are going to produce a ton all
+these firms are going to produce small
+
+ align:start position:0%
+these firms are going to produce small
+ 
+
+ align:start position:0%
+these firms are going to produce small
+amounts and so we're going to see highly
+
+ align:start position:0%
+amounts and so we're going to see highly
+ 
+
+ align:start position:0%
+amounts and so we're going to see highly
+profitable firms and very non-profitable
+
+ align:start position:0%
+profitable firms and very non-profitable
+ 
+
+ align:start position:0%
+profitable firms and very non-profitable
+firms if you're going to have an
+
+ align:start position:0%
+firms if you're going to have an
+ 
+
+ align:start position:0%
+firms if you're going to have an
+industry that's not concentrated an
+
+ align:start position:0%
+industry that's not concentrated an
+ 
+
+ align:start position:0%
+industry that's not concentrated an
+industry that's not concentrated is one
+
+ align:start position:0%
+industry that's not concentrated is one
+ 
+
+ align:start position:0%
+industry that's not concentrated is one
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+has much less cost
+
+ align:start position:0%
+has much less cost
+ 
+
+ align:start position:0%
+has much less cost
+heterogenity and so if it's got much
+
+ align:start position:0%
+heterogenity and so if it's got much
+ 
+
+ align:start position:0%
+heterogenity and so if it's got much
+less cost heterogenity no one produces a
+
+ align:start position:0%
+less cost heterogenity no one produces a
+ 
+
+ align:start position:0%
+less cost heterogenity no one produces a
+large quantity and that also means that
+
+ align:start position:0%
+large quantity and that also means that
+ 
+
+ align:start position:0%
+large quantity and that also means that
+everyone's getting similar profits to
+
+ align:start position:0%
+everyone's getting similar profits to
+ 
+
+ align:start position:0%
+everyone's getting similar profits to
+everybody else because their costs are
+
+ align:start position:0%
+everybody else because their costs are
+ 
+
+ align:start position:0%
+everybody else because their costs are
+all similar to everybody else okay
+
+ align:start position:0%
+all similar to everybody else okay
+ 
+
+ align:start position:0%
+all similar to everybody else okay
+not note that like these guys are all
+
+ align:start position:0%
+not note that like these guys are all
+ 
+
+ align:start position:0%
+not note that like these guys are all
+making essentially zero profits and so
+
+ align:start position:0%
+making essentially zero profits and so
+ 
+
+ align:start position:0%
+making essentially zero profits and so
+it's sort of like small numbers and zero
+
+ align:start position:0%
+it's sort of like small numbers and zero
+ 
+
+ align:start position:0%
+it's sort of like small numbers and zero
+but small numbers and zero are not so
+
+ align:start position:0%
+but small numbers and zero are not so
+ 
+
+ align:start position:0%
+but small numbers and zero are not so
+different in this model um so anyway you
+
+ align:start position:0%
+different in this model um so anyway you
+ 
+
+ align:start position:0%
+different in this model um so anyway you
+get
+
+ align:start position:0%
+get
+ 
+
+ align:start position:0%
+get
+this concentration is both correlated
+
+ align:start position:0%
+this concentration is both correlated
+ 
+
+ align:start position:0%
+this concentration is both correlated
+with levels of profits and with
+
+ align:start position:0%
+with levels of profits and with
+ 
+
+ align:start position:0%
+with levels of profits and with
+cross-sectional variance and
+
+ align:start position:0%
+cross-sectional variance and
+ 
+
+ align:start position:0%
+cross-sectional variance and
+profits uh anyway so there's a you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+know large large literature on on the
+
+ align:start position:0%
+know large large literature on on the
+ 
+
+ align:start position:0%
+know large large literature on on the
+empirics of Entry that sort of bears out
+
+ align:start position:0%
+empirics of Entry that sort of bears out
+ 
+
+ align:start position:0%
+empirics of Entry that sort of bears out
+that many of these things seem to be
+
+ align:start position:0%
+that many of these things seem to be
+ 
+
+ align:start position:0%
+that many of these things seem to be
+true and I I guess this is sort of the
+
+ align:start position:0%
+true and I I guess this is sort of the
+ 
+
+ align:start position:0%
+true and I I guess this is sort of the
+way we often think about we make sense
+
+ align:start position:0%
+way we often think about we make sense
+ 
+
+ align:start position:0%
+way we often think about we make sense
+of that data is that it's not that all
+
+ align:start position:0%
+of that data is that it's not that all
+ 
+
+ align:start position:0%
+of that data is that it's not that all
+firms have the same technology some
+
+ align:start position:0%
+firms have the same technology some
+ 
+
+ align:start position:0%
+firms have the same technology some
+firms are just more efficient than
+
+ align:start position:0%
+firms are just more efficient than
+ 
+
+ align:start position:0%
+firms are just more efficient than
+others you know for no observable reason
+
+ align:start position:0%
+others you know for no observable reason
+ 
+
+ align:start position:0%
+others you know for no observable reason
+for no observable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reason okay any any questions on this
+
+ align:start position:0%
+reason okay any any questions on this
+ 
+
+ align:start position:0%
+reason okay any any questions on this
+framework I think that's all I had to
+
+ align:start position:0%
+framework I think that's all I had to
+ 
+
+ align:start position:0%
+framework I think that's all I had to
+say on it um yep so you know and what I
+
+ align:start position:0%
+say on it um yep so you know and what I
+ 
+
+ align:start position:0%
+say on it um yep so you know and what I
+want to do in this lecture and I covered
+
+ align:start position:0%
+want to do in this lecture and I covered
+ 
+
+ align:start position:0%
+want to do in this lecture and I covered
+this I I don't always teach jovanovich
+
+ align:start position:0%
+this I I don't always teach jovanovich
+ 
+
+ align:start position:0%
+this I I don't always teach jovanovich
+but um I want to you know I like to sort
+
+ align:start position:0%
+but um I want to you know I like to sort
+ 
+
+ align:start position:0%
+but um I want to you know I like to sort
+of have some recent uh recent
+
+ align:start position:0%
+of have some recent uh recent
+ 
+
+ align:start position:0%
+of have some recent uh recent
+theoretical papers in the class um so
+
+ align:start position:0%
+theoretical papers in the class um so
+ 
+
+ align:start position:0%
+theoretical papers in the class um so
+anyway this this is a paper by um nikil
+
+ align:start position:0%
+anyway this this is a paper by um nikil
+ 
+
+ align:start position:0%
+anyway this this is a paper by um nikil
+V who's an assistant professor in Paris
+
+ align:start position:0%
+V who's an assistant professor in Paris
+ 
+
+ align:start position:0%
+V who's an assistant professor in Paris
+um anyway so basically what VOD has done
+
+ align:start position:0%
+um anyway so basically what VOD has done
+ 
+
+ align:start position:0%
+um anyway so basically what VOD has done
+in this paper is gone back to jovanovich
+
+ align:start position:0%
+in this paper is gone back to jovanovich
+ 
+
+ align:start position:0%
+in this paper is gone back to jovanovich
+1982 and use jovanovich 1982 to think
+
+ align:start position:0%
+1982 and use jovanovich 1982 to think
+ 
+
+ align:start position:0%
+1982 and use jovanovich 1982 to think
+about um the effects of rating
+
+ align:start position:0%
+about um the effects of rating
+ 
+
+ align:start position:0%
+about um the effects of rating
+intermediaries and what types of
+
+ align:start position:0%
+intermediaries and what types of
+ 
+
+ align:start position:0%
+intermediaries and what types of
+policies rating we we want rating
+
+ align:start position:0%
+policies rating we we want rating
+ 
+
+ align:start position:0%
+policies rating we we want rating
+intermediaries to have or what effects
+
+ align:start position:0%
+intermediaries to have or what effects
+ 
+
+ align:start position:0%
+intermediaries to have or what effects
+rating intermediaries have so the by
+
+ align:start position:0%
+rating intermediaries have so the by
+ 
+
+ align:start position:0%
+rating intermediaries have so the by
+rating intermediaries he has like um
+
+ align:start position:0%
+rating intermediaries he has like um
+ 
+
+ align:start position:0%
+rating intermediaries he has like um
+thinking about like firms like Amazon
+
+ align:start position:0%
+thinking about like firms like Amazon
+ 
+
+ align:start position:0%
+thinking about like firms like Amazon
+and Yelp where sort of like on Amazon
+
+ align:start position:0%
+and Yelp where sort of like on Amazon
+ 
+
+ align:start position:0%
+and Yelp where sort of like on Amazon
+you can leave feedback like you know
+
+ align:start position:0%
+you can leave feedback like you know
+ 
+
+ align:start position:0%
+you can leave feedback like you know
+Amazon majority of the merchandise on
+
+ align:start position:0%
+Amazon majority of the merchandise on
+ 
+
+ align:start position:0%
+Amazon majority of the merchandise on
+Amazon is not actually sold by it's not
+
+ align:start position:0%
+Amazon is not actually sold by it's not
+ 
+
+ align:start position:0%
+Amazon is not actually sold by it's not
+by Amazon itself it's sold by Third
+
+ align:start position:0%
+by Amazon itself it's sold by Third
+ 
+
+ align:start position:0%
+by Amazon itself it's sold by Third
+parties selling on Amazon Amazon you
+
+ align:start position:0%
+parties selling on Amazon Amazon you
+ 
+
+ align:start position:0%
+parties selling on Amazon Amazon you
+know there are lots of you want to buy
+
+ align:start position:0%
+know there are lots of you want to buy
+ 
+
+ align:start position:0%
+know there are lots of you want to buy
+an umbrella on Amazon you go there and
+
+ align:start position:0%
+an umbrella on Amazon you go there and
+ 
+
+ align:start position:0%
+an umbrella on Amazon you go there and
+you sort of look at the reviews of that
+
+ align:start position:0%
+you sort of look at the reviews of that
+ 
+
+ align:start position:0%
+you sort of look at the reviews of that
+umbrella and and whether people say that
+
+ align:start position:0%
+umbrella and and whether people say that
+ 
+
+ align:start position:0%
+umbrella and and whether people say that
+umbrella is good or bad and then you buy
+
+ align:start position:0%
+umbrella is good or bad and then you buy
+ 
+
+ align:start position:0%
+umbrella is good or bad and then you buy
+it or not you know you get Yelp or trip
+
+ align:start position:0%
+it or not you know you get Yelp or trip
+ 
+
+ align:start position:0%
+it or not you know you get Yelp or trip
+advisor or whomever that has lots of
+
+ align:start position:0%
+advisor or whomever that has lots of
+ 
+
+ align:start position:0%
+advisor or whomever that has lots of
+reviews of restaurants and tells you is
+
+ align:start position:0%
+reviews of restaurants and tells you is
+ 
+
+ align:start position:0%
+reviews of restaurants and tells you is
+this a good restaurant is this a bad
+
+ align:start position:0%
+this a good restaurant is this a bad
+ 
+
+ align:start position:0%
+this a good restaurant is this a bad
+restaurant consumers use that to learn
+
+ align:start position:0%
+restaurant consumers use that to learn
+ 
+
+ align:start position:0%
+restaurant consumers use that to learn
+about product
+
+ align:start position:0%
+about product
+ 
+
+ align:start position:0%
+about product
+quality
+
+ align:start position:0%
+quality
+ 
+
+ align:start position:0%
+quality
+um and so you know what there's this
+
+ align:start position:0%
+um and so you know what there's this
+ 
+
+ align:start position:0%
+um and so you know what there's this
+sort of challenge in coming up with
+
+ align:start position:0%
+sort of challenge in coming up with
+ 
+
+ align:start position:0%
+sort of challenge in coming up with
+these in in this business model is that
+
+ align:start position:0%
+these in in this business model is that
+ 
+
+ align:start position:0%
+these in in this business model is that
+um you know
+
+ align:start position:0%
+um you know
+ 
+
+ align:start position:0%
+um you know
+there are big firms that everybody buys
+
+ align:start position:0%
+there are big firms that everybody buys
+ 
+
+ align:start position:0%
+there are big firms that everybody buys
+from on the big firms everybody buys
+
+ align:start position:0%
+from on the big firms everybody buys
+ 
+
+ align:start position:0%
+from on the big firms everybody buys
+from there going to be a zillion reviews
+
+ align:start position:0%
+from there going to be a zillion reviews
+ 
+
+ align:start position:0%
+from there going to be a zillion reviews
+and people are going to be able to find
+
+ align:start position:0%
+and people are going to be able to find
+ 
+
+ align:start position:0%
+and people are going to be able to find
+out the quality of those firms but you
+
+ align:start position:0%
+out the quality of those firms but you
+ 
+
+ align:start position:0%
+out the quality of those firms but you
+have many many small entrance and many
+
+ align:start position:0%
+have many many small entrance and many
+ 
+
+ align:start position:0%
+have many many small entrance and many
+many new entrance all the time into
+
+ align:start position:0%
+many new entrance all the time into
+ 
+
+ align:start position:0%
+many new entrance all the time into
+these models and it's the new entrance
+
+ align:start position:0%
+these models and it's the new entrance
+ 
+
+ align:start position:0%
+these models and it's the new entrance
+that people really want to know about
+
+ align:start position:0%
+that people really want to know about
+ 
+
+ align:start position:0%
+that people really want to know about
+and learn about whether their quality is
+
+ align:start position:0%
+and learn about whether their quality is
+ 
+
+ align:start position:0%
+and learn about whether their quality is
+good or bad but there's this effect of
+
+ align:start position:0%
+good or bad but there's this effect of
+ 
+
+ align:start position:0%
+good or bad but there's this effect of
+if you have new firms people are
+
+ align:start position:0%
+if you have new firms people are
+ 
+
+ align:start position:0%
+if you have new firms people are
+hesitant to buy from them because
+
+ align:start position:0%
+hesitant to buy from them because
+ 
+
+ align:start position:0%
+hesitant to buy from them because
+they're new and because people are
+
+ align:start position:0%
+they're new and because people are
+ 
+
+ align:start position:0%
+they're new and because people are
+hesitant to buy from them because
+
+ align:start position:0%
+hesitant to buy from them because
+ 
+
+ align:start position:0%
+hesitant to buy from them because
+they're new there are very few reviews
+
+ align:start position:0%
+they're new there are very few reviews
+ 
+
+ align:start position:0%
+they're new there are very few reviews
+and therefore they very few reviews
+
+ align:start position:0%
+and therefore they very few reviews
+ 
+
+ align:start position:0%
+and therefore they very few reviews
+therefore people can't learn about them
+
+ align:start position:0%
+therefore people can't learn about them
+ 
+
+ align:start position:0%
+therefore people can't learn about them
+and so he wants to think about is what
+
+ align:start position:0%
+and so he wants to think about is what
+ 
+
+ align:start position:0%
+and so he wants to think about is what
+would be the optimal um design for a
+
+ align:start position:0%
+would be the optimal um design for a
+ 
+
+ align:start position:0%
+would be the optimal um design for a
+rating
+
+ align:start position:0%
+rating
+ 
+
+ align:start position:0%
+rating
+intermediary that wanted to uh you know
+
+ align:start position:0%
+intermediary that wanted to uh you know
+ 
+
+ align:start position:0%
+intermediary that wanted to uh you know
+promote an efficient level of
+
+ align:start position:0%
+promote an efficient level of
+ 
+
+ align:start position:0%
+promote an efficient level of
+competition in some sense we we think
+
+ align:start position:0%
+competition in some sense we we think
+ 
+
+ align:start position:0%
+competition in some sense we we think
+there could be you know I I why could
+
+ align:start position:0%
+there could be you know I I why could
+ 
+
+ align:start position:0%
+there could be you know I I why could
+there be too little entry in models
+
+ align:start position:0%
+there be too little entry in models
+ 
+
+ align:start position:0%
+there be too little entry in models
+there could be too little entry here
+
+ align:start position:0%
+there could be too little entry here
+ 
+
+ align:start position:0%
+there could be too little entry here
+another reason I didn't put my theory in
+
+ align:start position:0%
+another reason I didn't put my theory in
+ 
+
+ align:start position:0%
+another reason I didn't put my theory in
+my first part was there' be too little
+
+ align:start position:0%
+my first part was there' be too little
+ 
+
+ align:start position:0%
+my first part was there' be too little
+entry because people don't know the
+
+ align:start position:0%
+entry because people don't know the
+ 
+
+ align:start position:0%
+entry because people don't know the
+quality of new firms and therefore they
+
+ align:start position:0%
+quality of new firms and therefore they
+ 
+
+ align:start position:0%
+quality of new firms and therefore they
+won't buy from new firms and therefore
+
+ align:start position:0%
+won't buy from new firms and therefore
+ 
+
+ align:start position:0%
+won't buy from new firms and therefore
+no one will enter and sort of have any
+
+ align:start position:0%
+no one will enter and sort of have any
+ 
+
+ align:start position:0%
+no one will enter and sort of have any
+people learn about their quality you
+
+ align:start position:0%
+people learn about their quality you
+ 
+
+ align:start position:0%
+people learn about their quality you
+know um jovanovich it was very
+
+ align:start position:0%
+know um jovanovich it was very
+ 
+
+ align:start position:0%
+know um jovanovich it was very
+convenient that the firms could enter
+
+ align:start position:0%
+convenient that the firms could enter
+ 
+
+ align:start position:0%
+convenient that the firms could enter
+and then produce these tiny quantities
+
+ align:start position:0%
+and then produce these tiny quantities
+ 
+
+ align:start position:0%
+and then produce these tiny quantities
+and get in highly informative signals
+
+ align:start position:0%
+and get in highly informative signals
+ 
+
+ align:start position:0%
+and get in highly informative signals
+about their quality and know whether to
+
+ align:start position:0%
+about their quality and know whether to
+ 
+
+ align:start position:0%
+about their quality and know whether to
+start producing more in practice you
+
+ align:start position:0%
+start producing more in practice you
+ 
+
+ align:start position:0%
+start producing more in practice you
+know that's not something restaurants
+
+ align:start position:0%
+know that's not something restaurants
+ 
+
+ align:start position:0%
+know that's not something restaurants
+can do is come in and produce a tiny
+
+ align:start position:0%
+can do is come in and produce a tiny
+ 
+
+ align:start position:0%
+can do is come in and produce a tiny
+quantity and get a lot of reviews on
+
+ align:start position:0%
+quantity and get a lot of reviews on
+ 
+
+ align:start position:0%
+quantity and get a lot of reviews on
+Yelp
+
+ align:start position:0%
+Yelp
+ 
+
+ align:start position:0%
+Yelp
+um okay so anyway models got a Continuum
+
+ align:start position:0%
+um okay so anyway models got a Continuum
+ 
+
+ align:start position:0%
+um okay so anyway models got a Continuum
+of small potential entrance so these
+
+ align:start position:0%
+of small potential entrance so these
+ 
+
+ align:start position:0%
+of small potential entrance so these
+think of these as new restaurants or new
+
+ align:start position:0%
+think of these as new restaurants or new
+ 
+
+ align:start position:0%
+think of these as new restaurants or new
+guys just trying to sell black f holding
+
+ align:start position:0%
+guys just trying to sell black f holding
+ 
+
+ align:start position:0%
+guys just trying to sell black f holding
+umbrellas on Amazon um they have a fixed
+
+ align:start position:0%
+umbrellas on Amazon um they have a fixed
+ 
+
+ align:start position:0%
+umbrellas on Amazon um they have a fixed
+cost K of
+
+ align:start position:0%
+cost K of
+ 
+
+ align:start position:0%
+cost K of
+entering um they're going to have some
+
+ align:start position:0%
+entering um they're going to have some
+ 
+
+ align:start position:0%
+entering um they're going to have some
+flow cost of operation I didn't put a
+
+ align:start position:0%
+flow cost of operation I didn't put a
+ 
+
+ align:start position:0%
+flow cost of operation I didn't put a
+letter down here maybe this is C but
+
+ align:start position:0%
+letter down here maybe this is C but
+ 
+
+ align:start position:0%
+letter down here maybe this is C but
+every period that I'm continuing to
+
+ align:start position:0%
+every period that I'm continuing to
+ 
+
+ align:start position:0%
+every period that I'm continuing to
+operate I have to pay some flow cost um
+
+ align:start position:0%
+operate I have to pay some flow cost um
+ 
+
+ align:start position:0%
+operate I have to pay some flow cost um
+just to make the model have a steady
+
+ align:start position:0%
+just to make the model have a steady
+ 
+
+ align:start position:0%
+just to make the model have a steady
+state equilibrium he has some exogenous
+
+ align:start position:0%
+state equilibrium he has some exogenous
+ 
+
+ align:start position:0%
+state equilibrium he has some exogenous
+death rate Delta so every firm with some
+
+ align:start position:0%
+death rate Delta so every firm with some
+ 
+
+ align:start position:0%
+death rate Delta so every firm with some
+probability just disappears in each
+
+ align:start position:0%
+probability just disappears in each
+ 
+
+ align:start position:0%
+probability just disappears in each
+period um and then uh firms have some
+
+ align:start position:0%
+period um and then uh firms have some
+ 
+
+ align:start position:0%
+period um and then uh firms have some
+discount rate
+
+ align:start position:0%
+discount rate
+ 
+
+ align:start position:0%
+discount rate
+row uh in his
+
+ align:start position:0%
+row uh in his
+ 
+
+ align:start position:0%
+row uh in his
+model simplest you know simplifying the
+
+ align:start position:0%
+model simplest you know simplifying the
+ 
+
+ align:start position:0%
+model simplest you know simplifying the
+theory by assuming that it's a discrete
+
+ align:start position:0%
+theory by assuming that it's a discrete
+ 
+
+ align:start position:0%
+theory by assuming that it's a discrete
+type model all restaurants have either
+
+ align:start position:0%
+type model all restaurants have either
+ 
+
+ align:start position:0%
+type model all restaurants have either
+quality zero or quality one so it's just
+
+ align:start position:0%
+quality zero or quality one so it's just
+ 
+
+ align:start position:0%
+quality zero or quality one so it's just
+a pure bimodal
+
+ align:start position:0%
+a pure bimodal
+ 
+
+ align:start position:0%
+a pure bimodal
+distribution uh again like in jovanovich
+
+ align:start position:0%
+distribution uh again like in jovanovich
+ 
+
+ align:start position:0%
+distribution uh again like in jovanovich
+it's a symmetric information model
+
+ align:start position:0%
+it's a symmetric information model
+ 
+
+ align:start position:0%
+it's a symmetric information model
+there's prior mean P0 that the firm has
+
+ align:start position:0%
+there's prior mean P0 that the firm has
+ 
+
+ align:start position:0%
+there's prior mean P0 that the firm has
+quality one and that information is
+
+ align:start position:0%
+quality one and that information is
+ 
+
+ align:start position:0%
+quality one and that information is
+symmetric among everyone in the market
+
+ align:start position:0%
+symmetric among everyone in the market
+ 
+
+ align:start position:0%
+symmetric among everyone in the market
+no one knows but everyone knows new
+
+ align:start position:0%
+no one knows but everyone knows new
+ 
+
+ align:start position:0%
+no one knows but everyone knows new
+restaurants there's probability P0 that
+
+ align:start position:0%
+restaurants there's probability P0 that
+ 
+
+ align:start position:0%
+restaurants there's probability P0 that
+their food is good probability one minus
+
+ align:start position:0%
+their food is good probability one minus
+ 
+
+ align:start position:0%
+their food is good probability one minus
+P0 that their food is bad okay uh every
+
+ align:start position:0%
+P0 that their food is bad okay uh every
+ 
+
+ align:start position:0%
+P0 that their food is bad okay uh every
+firm has exactly one
+
+ align:start position:0%
+firm has exactly one
+ 
+
+ align:start position:0%
+firm has exactly one
+table and the firms can do is set prices
+
+ align:start position:0%
+table and the firms can do is set prices
+ 
+
+ align:start position:0%
+table and the firms can do is set prices
+um qit for their table at time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T um what he assumes is that the you
+
+ align:start position:0%
+T um what he assumes is that the you
+ 
+
+ align:start position:0%
+T um what he assumes is that the you
+have this prior P knot and then you have
+
+ align:start position:0%
+have this prior P knot and then you have
+ 
+
+ align:start position:0%
+have this prior P knot and then you have
+a posterior every period um if somebody
+
+ align:start position:0%
+a posterior every period um if somebody
+ 
+
+ align:start position:0%
+a posterior every period um if somebody
+you know if you're
+
+ align:start position:0%
+you know if you're
+ 
+
+ align:start position:0%
+you know if you're
+operating then reviews arrive according
+
+ align:start position:0%
+operating then reviews arrive according
+ 
+
+ align:start position:0%
+operating then reviews arrive according
+to a passon process and those reviews
+
+ align:start position:0%
+to a passon process and those reviews
+ 
+
+ align:start position:0%
+to a passon process and those reviews
+are going to like make the quality the
+
+ align:start position:0%
+are going to like make the quality the
+ 
+
+ align:start position:0%
+are going to like make the quality the
+poster your quality go up or down
+
+ align:start position:0%
+poster your quality go up or down
+ 
+
+ align:start position:0%
+poster your quality go up or down
+whether it's a good review or a bad
+
+ align:start position:0%
+whether it's a good review or a bad
+ 
+
+ align:start position:0%
+whether it's a good review or a bad
+review he goes with this sort of
+
+ align:start position:0%
+review he goes with this sort of
+ 
+
+ align:start position:0%
+review he goes with this sort of
+continuous uh continuous time Brownie
+
+ align:start position:0%
+continuous uh continuous time Brownie
+ 
+
+ align:start position:0%
+continuous uh continuous time Brownie
+and motion learning process where my
+
+ align:start position:0%
+and motion learning process where my
+ 
+
+ align:start position:0%
+and motion learning process where my
+posterior pit of olves according to
+
+ align:start position:0%
+posterior pit of olves according to
+ 
+
+ align:start position:0%
+posterior pit of olves according to
+dpit
+
+ align:start position:0%
+dpit
+ 
+
+ align:start position:0%
+dpit
+equal < TK of Lambda it t pit 1us pit
+
+ align:start position:0%
+equal < TK of Lambda it t pit 1us pit
+ 
+
+ align:start position:0%
+equal < TK of Lambda it t pit 1us pit
+time DZ where zit is a brownie in motion
+
+ align:start position:0%
+time DZ where zit is a brownie in motion
+ 
+
+ align:start position:0%
+time DZ where zit is a brownie in motion
+um but you can roughly think of this as
+
+ align:start position:0%
+um but you can roughly think of this as
+ 
+
+ align:start position:0%
+um but you can roughly think of this as
+Lambda it is the review arrival rate and
+
+ align:start position:0%
+Lambda it is the review arrival rate and
+ 
+
+ align:start position:0%
+Lambda it is the review arrival rate and
+each of these is like a normal signal
+
+ align:start position:0%
+each of these is like a normal signal
+ 
+
+ align:start position:0%
+each of these is like a normal signal
+and so if it's a normal signal I'm going
+
+ align:start position:0%
+and so if it's a normal signal I'm going
+ 
+
+ align:start position:0%
+and so if it's a normal signal I'm going
+to get information that either pushes me
+
+ align:start position:0%
+to get information that either pushes me
+ 
+
+ align:start position:0%
+to get information that either pushes me
+to the right or left you know and sort
+
+ align:start position:0%
+to the right or left you know and sort
+ 
+
+ align:start position:0%
+to the right or left you know and sort
+of the uh variance of you know like
+
+ align:start position:0%
+of the uh variance of you know like
+ 
+
+ align:start position:0%
+of the uh variance of you know like
+since I have a brou quality the variance
+
+ align:start position:0%
+since I have a brou quality the variance
+ 
+
+ align:start position:0%
+since I have a brou quality the variance
+of my distribution is just pit1 minus
+
+ align:start position:0%
+of my distribution is just pit1 minus
+ 
+
+ align:start position:0%
+of my distribution is just pit1 minus
+pit if it's beri probability P so anyway
+
+ align:start position:0%
+pit if it's beri probability P so anyway
+ 
+
+ align:start position:0%
+pit if it's beri probability P so anyway
+the the new information is arriving with
+
+ align:start position:0%
+the the new information is arriving with
+ 
+
+ align:start position:0%
+the the new information is arriving with
+and and the and I'm getting square root
+
+ align:start position:0%
+and and the and I'm getting square root
+ 
+
+ align:start position:0%
+and and the and I'm getting square root
+of Lambda it is how much the standard
+
+ align:start position:0%
+of Lambda it is how much the standard
+ 
+
+ align:start position:0%
+of Lambda it is how much the standard
+deviation changes when you have Lambda
+
+ align:start position:0%
+deviation changes when you have Lambda
+ 
+
+ align:start position:0%
+deviation changes when you have Lambda
+it reviews and then DZ is a brownie in
+
+ align:start position:0%
+it reviews and then DZ is a brownie in
+ 
+
+ align:start position:0%
+it reviews and then DZ is a brownie in
+motion that's just positive or negative
+
+ align:start position:0%
+motion that's just positive or negative
+ 
+
+ align:start position:0%
+motion that's just positive or negative
+so you can think of it as the limit as
+
+ align:start position:0%
+so you can think of it as the limit as
+ 
+
+ align:start position:0%
+so you can think of it as the limit as
+you get just a number of a number of
+
+ align:start position:0%
+you get just a number of a number of
+ 
+
+ align:start position:0%
+you get just a number of a number of
+normally distributed signals saying this
+
+ align:start position:0%
+normally distributed signals saying this
+ 
+
+ align:start position:0%
+normally distributed signals saying this
+one was good this one was bad you know
+
+ align:start position:0%
+one was good this one was bad you know
+ 
+
+ align:start position:0%
+one was good this one was bad you know
+this good this bad this good this bad
+
+ align:start position:0%
+this good this bad this good this bad
+ 
+
+ align:start position:0%
+this good this bad this good this bad
+that pushes you back and forth in like a
+
+ align:start position:0%
+that pushes you back and forth in like a
+ 
+
+ align:start position:0%
+that pushes you back and forth in like a
+brownie and motion process you know
+
+ align:start position:0%
+brownie and motion process you know
+ 
+
+ align:start position:0%
+brownie and motion process you know
+um and you know why is he doing this in
+
+ align:start position:0%
+um and you know why is he doing this in
+ 
+
+ align:start position:0%
+um and you know why is he doing this in
+continuous time you know he's doing this
+
+ align:start position:0%
+continuous time you know he's doing this
+ 
+
+ align:start position:0%
+continuous time you know he's doing this
+in continuous time instead of in
+
+ align:start position:0%
+in continuous time instead of in
+ 
+
+ align:start position:0%
+in continuous time instead of in
+discreete time because you know it's
+
+ align:start position:0%
+discreete time because you know it's
+ 
+
+ align:start position:0%
+discreete time because you know it's
+sort of a state-of-the-art thing but
+
+ align:start position:0%
+sort of a state-of-the-art thing but
+ 
+
+ align:start position:0%
+sort of a state-of-the-art thing but
+it's just also the sometimes continuous
+
+ align:start position:0%
+it's just also the sometimes continuous
+ 
+
+ align:start position:0%
+it's just also the sometimes continuous
+models are easier to solve than discrete
+
+ align:start position:0%
+models are easier to solve than discrete
+ 
+
+ align:start position:0%
+models are easier to solve than discrete
+models you have to keep track of what
+
+ align:start position:0%
+models you have to keep track of what
+ 
+
+ align:start position:0%
+models you have to keep track of what
+your posterior could be if you've had
+
+ align:start position:0%
+your posterior could be if you've had
+ 
+
+ align:start position:0%
+your posterior could be if you've had
+three and four and five and seven
+
+ align:start position:0%
+three and four and five and seven
+ 
+
+ align:start position:0%
+three and four and five and seven
+signals The Continuous model easier to
+
+ align:start position:0%
+signals The Continuous model easier to
+ 
+
+ align:start position:0%
+signals The Continuous model easier to
+solve um so every consumer in each
+
+ align:start position:0%
+solve um so every consumer in each
+ 
+
+ align:start position:0%
+solve um so every consumer in each
+period um decides which so every
+
+ align:start position:0%
+period um decides which so every
+ 
+
+ align:start position:0%
+period um decides which so every
+consumer goes to exactly one restaurant
+
+ align:start position:0%
+consumer goes to exactly one restaurant
+ 
+
+ align:start position:0%
+consumer goes to exactly one restaurant
+they decide which um firm to visit if
+
+ align:start position:0%
+they decide which um firm to visit if
+ 
+
+ align:start position:0%
+they decide which um firm to visit if
+excess consumers visit any type of firm
+
+ align:start position:0%
+excess consumers visit any type of firm
+ 
+
+ align:start position:0%
+excess consumers visit any type of firm
+any firm then Services ration there's a
+
+ align:start position:0%
+any firm then Services ration there's a
+ 
+
+ align:start position:0%
+any firm then Services ration there's a
+line outside and only some of the people
+
+ align:start position:0%
+line outside and only some of the people
+ 
+
+ align:start position:0%
+line outside and only some of the people
+go in um consumers get utility Theta I
+
+ align:start position:0%
+go in um consumers get utility Theta I
+ 
+
+ align:start position:0%
+go in um consumers get utility Theta I
+plus Epsilon i j uh if they're served by
+
+ align:start position:0%
+plus Epsilon i j uh if they're served by
+ 
+
+ align:start position:0%
+plus Epsilon i j uh if they're served by
+restaurant I
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh okay so given that all the firms
+
+ align:start position:0%
+uh okay so given that all the firms
+ 
+
+ align:start position:0%
+uh okay so given that all the firms
+priors are common knowledge in
+
+ align:start position:0%
+priors are common knowledge in
+ 
+
+ align:start position:0%
+priors are common knowledge in
+equilibrium everyone's going to get
+
+ align:start position:0%
+equilibrium everyone's going to get
+ 
+
+ align:start position:0%
+equilibrium everyone's going to get
+served with probability one at firms
+
+ align:start position:0%
+served with probability one at firms
+ 
+
+ align:start position:0%
+served with probability one at firms
+that have a rating of at least p p Tilda
+
+ align:start position:0%
+that have a rating of at least p p Tilda
+ 
+
+ align:start position:0%
+that have a rating of at least p p Tilda
+and you know if if your prior is like
+
+ align:start position:0%
+and you know if if your prior is like
+ 
+
+ align:start position:0%
+and you know if if your prior is like
+you know you have one table so it's
+
+ align:start position:0%
+you know you have one table so it's
+ 
+
+ align:start position:0%
+you know you have one table so it's
+going to be like a you're going to clear
+
+ align:start position:0%
+going to be like a you're going to clear
+ 
+
+ align:start position:0%
+going to be like a you're going to clear
+the market if your quality is high
+
+ align:start position:0%
+the market if your quality is high
+ 
+
+ align:start position:0%
+the market if your quality is high
+enough you're going to price at some you
+
+ align:start position:0%
+enough you're going to price at some you
+ 
+
+ align:start position:0%
+enough you're going to price at some you
+if your quality is at least ptil you're
+
+ align:start position:0%
+if your quality is at least ptil you're
+ 
+
+ align:start position:0%
+if your quality is at least ptil you're
+going to price at some equal ibrium
+
+ align:start position:0%
+going to price at some equal ibrium
+ 
+
+ align:start position:0%
+going to price at some equal ibrium
+price that gets people to come to your
+
+ align:start position:0%
+price that gets people to come to your
+ 
+
+ align:start position:0%
+price that gets people to come to your
+restaurant and you're going to price
+
+ align:start position:0%
+restaurant and you're going to price
+ 
+
+ align:start position:0%
+restaurant and you're going to price
+that exactly one customer comes if your
+
+ align:start position:0%
+that exactly one customer comes if your
+ 
+
+ align:start position:0%
+that exactly one customer comes if your
+price is attracting multiple customers
+
+ align:start position:0%
+price is attracting multiple customers
+ 
+
+ align:start position:0%
+price is attracting multiple customers
+you should be raising your price and
+
+ align:start position:0%
+you should be raising your price and
+ 
+
+ align:start position:0%
+you should be raising your price and
+getting fewer customers till you fill
+
+ align:start position:0%
+getting fewer customers till you fill
+ 
+
+ align:start position:0%
+getting fewer customers till you fill
+your
+
+ align:start position:0%
+your
+ 
+
+ align:start position:0%
+your
+capacity um at all higher
+
+ align:start position:0%
+capacity um at all higher
+ 
+
+ align:start position:0%
+capacity um at all higher
+prices everyone is going to be um yeah
+
+ align:start position:0%
+prices everyone is going to be um yeah
+ 
+
+ align:start position:0%
+prices everyone is going to be um yeah
+so you you can tell nil is a theorist
+
+ align:start position:0%
+so you you can tell nil is a theorist
+ 
+
+ align:start position:0%
+so you you can tell nil is a theorist
+not an Iowa Economist he's using Q for
+
+ align:start position:0%
+not an Iowa Economist he's using Q for
+ 
+
+ align:start position:0%
+not an Iowa Economist he's using Q for
+prices and P for qualities rather than P
+
+ align:start position:0%
+prices and P for qualities rather than P
+ 
+
+ align:start position:0%
+prices and P for qualities rather than P
+for prices and S for qualities so anyway
+
+ align:start position:0%
+for prices and S for qualities so anyway
+ 
+
+ align:start position:0%
+for prices and S for qualities so anyway
+the are setting these prices Q in
+
+ align:start position:0%
+the are setting these prices Q in
+ 
+
+ align:start position:0%
+the are setting these prices Q in
+equilibrium the prices are just P minus
+
+ align:start position:0%
+equilibrium the prices are just P minus
+ 
+
+ align:start position:0%
+equilibrium the prices are just P minus
+a constant uh and that makes consumers
+
+ align:start position:0%
+a constant uh and that makes consumers
+ 
+
+ align:start position:0%
+a constant uh and that makes consumers
+indifferent to going to all high quality
+
+ align:start position:0%
+indifferent to going to all high quality
+ 
+
+ align:start position:0%
+indifferent to going to all high quality
+restaurants and has all high quality
+
+ align:start position:0%
+restaurants and has all high quality
+ 
+
+ align:start position:0%
+restaurants and has all high quality
+restaurants attracting exactly one
+
+ align:start position:0%
+restaurants attracting exactly one
+ 
+
+ align:start position:0%
+restaurants attracting exactly one
+customer you know why you price it P
+
+ align:start position:0%
+customer you know why you price it P
+ 
+
+ align:start position:0%
+customer you know why you price it P
+minus W it's because there are
+
+ align:start position:0%
+minus W it's because there are
+ 
+
+ align:start position:0%
+minus W it's because there are
+lowquality restaurants that people
+
+ align:start position:0%
+lowquality restaurants that people
+ 
+
+ align:start position:0%
+lowquality restaurants that people
+aren't going to want to go to that are
+
+ align:start position:0%
+aren't going to want to go to that are
+ 
+
+ align:start position:0%
+aren't going to want to go to that are
+willing to sell it a loss because they
+
+ align:start position:0%
+willing to sell it a loss because they
+ 
+
+ align:start position:0%
+willing to sell it a loss because they
+sell at a loss they get people to come
+
+ align:start position:0%
+sell at a loss they get people to come
+ 
+
+ align:start position:0%
+sell at a loss they get people to come
+and review
+
+ align:start position:0%
+and review
+ 
+
+ align:start position:0%
+and review
+them okay so in his model the basically
+
+ align:start position:0%
+them okay so in his model the basically
+ 
+
+ align:start position:0%
+them okay so in his model the basically
+the Lambda it the review arrival rate is
+
+ align:start position:0%
+the Lambda it the review arrival rate is
+ 
+
+ align:start position:0%
+the Lambda it the review arrival rate is
+going to be a sum of two terms it's
+
+ align:start position:0%
+going to be a sum of two terms it's
+ 
+
+ align:start position:0%
+going to be a sum of two terms it's
+going to be a sum Lambda is going to be
+
+ align:start position:0%
+going to be a sum Lambda is going to be
+ 
+
+ align:start position:0%
+going to be a sum Lambda is going to be
+the number of customers who visit your
+
+ align:start position:0%
+the number of customers who visit your
+ 
+
+ align:start position:0%
+the number of customers who visit your
+restaurant um because it's optimal to do
+
+ align:start position:0%
+restaurant um because it's optimal to do
+ 
+
+ align:start position:0%
+restaurant um because it's optimal to do
+so plus Epsilon so there's this Epsilon
+
+ align:start position:0%
+so plus Epsilon so there's this Epsilon
+ 
+
+ align:start position:0%
+so plus Epsilon so there's this Epsilon
+background rate of arrivals of we'll
+
+ align:start position:0%
+background rate of arrivals of we'll
+ 
+
+ align:start position:0%
+background rate of arrivals of we'll
+call them tourists from out of town who
+
+ align:start position:0%
+call them tourists from out of town who
+ 
+
+ align:start position:0%
+call them tourists from out of town who
+have no idea what the qualities are and
+
+ align:start position:0%
+have no idea what the qualities are and
+ 
+
+ align:start position:0%
+have no idea what the qualities are and
+just show up randomly at your restaurant
+
+ align:start position:0%
+just show up randomly at your restaurant
+ 
+
+ align:start position:0%
+just show up randomly at your restaurant
+so most reviews come from the one one
+
+ align:start position:0%
+so most reviews come from the one one
+ 
+
+ align:start position:0%
+so most reviews come from the one one
+person who buy who knows your quality
+
+ align:start position:0%
+person who buy who knows your quality
+ 
+
+ align:start position:0%
+person who buy who knows your quality
+and buys it but there is this Epsilon
+
+ align:start position:0%
+and buys it but there is this Epsilon
+ 
+
+ align:start position:0%
+and buys it but there is this Epsilon
+arrival rate
+
+ align:start position:0%
+arrival rate
+ 
+
+ align:start position:0%
+arrival rate
+okay um the firms that are hanging
+
+ align:start position:0%
+okay um the firms that are hanging
+ 
+
+ align:start position:0%
+okay um the firms that are hanging
+around that have low quality they would
+
+ align:start position:0%
+around that have low quality they would
+ 
+
+ align:start position:0%
+around that have low quality they would
+like people to come to their restaurant
+
+ align:start position:0%
+like people to come to their restaurant
+ 
+
+ align:start position:0%
+like people to come to their restaurant
+and review it so they can learn if their
+
+ align:start position:0%
+and review it so they can learn if their
+ 
+
+ align:start position:0%
+and review it so they can learn if their
+quality is high and they can start
+
+ align:start position:0%
+quality is high and they can start
+ 
+
+ align:start position:0%
+quality is high and they can start
+charging more money for their restaurant
+
+ align:start position:0%
+charging more money for their restaurant
+ 
+
+ align:start position:0%
+charging more money for their restaurant
+if it's high or exit if their quality is
+
+ align:start position:0%
+if it's high or exit if their quality is
+ 
+
+ align:start position:0%
+if it's high or exit if their quality is
+low uh but there's only so much they're
+
+ align:start position:0%
+low uh but there's only so much they're
+ 
+
+ align:start position:0%
+low uh but there's only so much they're
+willing to pay to you know like so
+
+ align:start position:0%
+willing to pay to you know like so
+ 
+
+ align:start position:0%
+willing to pay to you know like so
+they're willing to sort of price below
+
+ align:start position:0%
+they're willing to sort of price below
+ 
+
+ align:start position:0%
+they're willing to sort of price below
+cost to get people to come to their
+
+ align:start position:0%
+cost to get people to come to their
+ 
+
+ align:start position:0%
+cost to get people to come to their
+restaurant there's only so much you're
+
+ align:start position:0%
+restaurant there's only so much you're
+ 
+
+ align:start position:0%
+restaurant there's only so much you're
+willing to do that because at some point
+
+ align:start position:0%
+willing to do that because at some point
+ 
+
+ align:start position:0%
+willing to do that because at some point
+you're just better off exiting okay
+
+ align:start position:0%
+you're just better off exiting okay
+ 
+
+ align:start position:0%
+you're just better off exiting okay
+anyway so that that's why you have this
+
+ align:start position:0%
+anyway so that that's why you have this
+ 
+
+ align:start position:0%
+anyway so that that's why you have this
+sort of positive W that is everybody is
+
+ align:start position:0%
+sort of positive W that is everybody is
+ 
+
+ align:start position:0%
+sort of positive W that is everybody is
+everybody is giving consumers some
+
+ align:start position:0%
+everybody is giving consumers some
+ 
+
+ align:start position:0%
+everybody is giving consumers some
+Surplus because the guys who are on the
+
+ align:start position:0%
+Surplus because the guys who are on the
+ 
+
+ align:start position:0%
+Surplus because the guys who are on the
+outside looking in are going to give the
+
+ align:start position:0%
+outside looking in are going to give the
+ 
+
+ align:start position:0%
+outside looking in are going to give the
+consumer some Surplus to try to get the
+
+ align:start position:0%
+consumer some Surplus to try to get the
+ 
+
+ align:start position:0%
+consumer some Surplus to try to get the
+customers to
+
+ align:start position:0%
+customers to
+ 
+
+ align:start position:0%
+customers to
+come okay so I'm going to write V of P
+
+ align:start position:0%
+come okay so I'm going to write V of P
+ 
+
+ align:start position:0%
+come okay so I'm going to write V of P
+for the value function of a firm that
+
+ align:start position:0%
+for the value function of a firm that
+ 
+
+ align:start position:0%
+for the value function of a firm that
+has posterior p uh free entry implies
+
+ align:start position:0%
+has posterior p uh free entry implies
+ 
+
+ align:start position:0%
+has posterior p uh free entry implies
+that V of P not equals K when the firms
+
+ align:start position:0%
+that V of P not equals K when the firms
+ 
+
+ align:start position:0%
+that V of P not equals K when the firms
+are entering it must be that their
+
+ align:start position:0%
+are entering it must be that their
+ 
+
+ align:start position:0%
+are entering it must be that their
+lifetime expected discounted value of
+
+ align:start position:0%
+lifetime expected discounted value of
+ 
+
+ align:start position:0%
+lifetime expected discounted value of
+profits is exactly equal to the fixed
+
+ align:start position:0%
+profits is exactly equal to the fixed
+ 
+
+ align:start position:0%
+profits is exactly equal to the fixed
+costs um and then exit occurs when your
+
+ align:start position:0%
+costs um and then exit occurs when your
+ 
+
+ align:start position:0%
+costs um and then exit occurs when your
+posterior gets down to P lower bar where
+
+ align:start position:0%
+posterior gets down to P lower bar where
+ 
+
+ align:start position:0%
+posterior gets down to P lower bar where
+V of P lower bar is zero and V of P
+
+ align:start position:0%
+V of P lower bar is zero and V of P
+ 
+
+ align:start position:0%
+V of P lower bar is zero and V of P
+lower bar is zero in this model without
+
+ align:start position:0%
+lower bar is zero in this model without
+ 
+
+ align:start position:0%
+lower bar is zero in this model without
+the scrappage because there's this flow
+
+ align:start position:0%
+the scrappage because there's this flow
+ 
+
+ align:start position:0%
+the scrappage because there's this flow
+cost of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+operation you know a complicated model
+
+ align:start position:0%
+operation you know a complicated model
+ 
+
+ align:start position:0%
+operation you know a complicated model
+but I sort of thought what I would do is
+
+ align:start position:0%
+but I sort of thought what I would do is
+ 
+
+ align:start position:0%
+but I sort of thought what I would do is
+here just sort of show you a couple of
+
+ align:start position:0%
+here just sort of show you a couple of
+ 
+
+ align:start position:0%
+here just sort of show you a couple of
+the graphs and talk through uh when what
+
+ align:start position:0%
+the graphs and talk through uh when what
+ 
+
+ align:start position:0%
+the graphs and talk through uh when what
+ends up happening so first observation
+
+ align:start position:0%
+ends up happening so first observation
+ 
+
+ align:start position:0%
+ends up happening so first observation
+um so it's not yeah so if you're a new
+
+ align:start position:0%
+um so it's not yeah so if you're a new
+ 
+
+ align:start position:0%
+um so it's not yeah so if you're a new
+firm um and people you know you're not
+
+ align:start position:0%
+firm um and people you know you're not
+ 
+
+ align:start position:0%
+firm um and people you know you're not
+like there's some sense
+
+ align:start position:0%
+like there's some sense
+ 
+
+ align:start position:0%
+like there's some sense
+um in equilibrium like if if the number
+
+ align:start position:0%
+um in equilibrium like if if the number
+ 
+
+ align:start position:0%
+um in equilibrium like if if the number
+of customers is is X the X best
+
+ align:start position:0%
+of customers is is X the X best
+ 
+
+ align:start position:0%
+of customers is is X the X best
+restaurants are going to all get one
+
+ align:start position:0%
+restaurants are going to all get one
+ 
+
+ align:start position:0%
+restaurants are going to all get one
+customer each and every restaurant below
+
+ align:start position:0%
+customer each and every restaurant below
+ 
+
+ align:start position:0%
+customer each and every restaurant below
+X is going to get no
+
+ align:start position:0%
+X is going to get no
+ 
+
+ align:start position:0%
+X is going to get no
+customers other than the randomly
+
+ align:start position:0%
+customers other than the randomly
+ 
+
+ align:start position:0%
+customers other than the randomly
+arriving tourists um but firms if you're
+
+ align:start position:0%
+arriving tourists um but firms if you're
+ 
+
+ align:start position:0%
+arriving tourists um but firms if you're
+just on the outside looking in so if
+
+ align:start position:0%
+just on the outside looking in so if
+ 
+
+ align:start position:0%
+just on the outside looking in so if
+like you know if we have this sort of uh
+
+ align:start position:0%
+like you know if we have this sort of uh
+ 
+
+ align:start position:0%
+like you know if we have this sort of uh
+posterior on my quality I think it is
+
+ align:start position:0%
+posterior on my quality I think it is
+ 
+
+ align:start position:0%
+posterior on my quality I think it is
+Pete tild I called it so everybody up
+
+ align:start position:0%
+Pete tild I called it so everybody up
+ 
+
+ align:start position:0%
+Pete tild I called it so everybody up
+here fills their restaurant everybody
+
+ align:start position:0%
+here fills their restaurant everybody
+ 
+
+ align:start position:0%
+here fills their restaurant everybody
+else here only gets the Epsilon flow of
+
+ align:start position:0%
+else here only gets the Epsilon flow of
+ 
+
+ align:start position:0%
+else here only gets the Epsilon flow of
+tourists um if your quality is right
+
+ align:start position:0%
+tourists um if your quality is right
+ 
+
+ align:start position:0%
+tourists um if your quality is right
+here you're willing to lose some money
+
+ align:start position:0%
+here you're willing to lose some money
+ 
+
+ align:start position:0%
+here you're willing to lose some money
+in order to get the customers to visit
+
+ align:start position:0%
+in order to get the customers to visit
+ 
+
+ align:start position:0%
+in order to get the customers to visit
+your restaurant to find out whether your
+
+ align:start position:0%
+your restaurant to find out whether your
+ 
+
+ align:start position:0%
+your restaurant to find out whether your
+restaurant is Goods you can get in or
+
+ align:start position:0%
+restaurant is Goods you can get in or
+ 
+
+ align:start position:0%
+restaurant is Goods you can get in or
+out of the
+
+ align:start position:0%
+out of the
+ 
+
+ align:start position:0%
+out of the
+market so anyway firms pric somewhat
+
+ align:start position:0%
+market so anyway firms pric somewhat
+ 
+
+ align:start position:0%
+market so anyway firms pric somewhat
+below cost to attract customers you know
+
+ align:start position:0%
+below cost to attract customers you know
+ 
+
+ align:start position:0%
+below cost to attract customers you know
+because this guy is is selling at a this
+
+ align:start position:0%
+because this guy is is selling at a this
+ 
+
+ align:start position:0%
+because this guy is is selling at a this
+guy's willing to sell at a loss
+
+ align:start position:0%
+guy's willing to sell at a loss
+ 
+
+ align:start position:0%
+guy's willing to sell at a loss
+everybody else has they can everybody
+
+ align:start position:0%
+everybody else has they can everybody
+ 
+
+ align:start position:0%
+everybody else has they can everybody
+else can only charge their sort of
+
+ align:start position:0%
+else can only charge their sort of
+ 
+
+ align:start position:0%
+else can only charge their sort of
+marginal value above this guy um their
+
+ align:start position:0%
+marginal value above this guy um their
+ 
+
+ align:start position:0%
+marginal value above this guy um their
+marginal quality above that guy so
+
+ align:start position:0%
+marginal quality above that guy so
+ 
+
+ align:start position:0%
+marginal quality above that guy so
+consumers get you know consumers get
+
+ align:start position:0%
+consumers get you know consumers get
+ 
+
+ align:start position:0%
+consumers get you know consumers get
+some profit what what what is the
+
+ align:start position:0%
+some profit what what what is the
+ 
+
+ align:start position:0%
+some profit what what what is the
+consumer surplus the consumer surplus
+
+ align:start position:0%
+consumer surplus the consumer surplus
+ 
+
+ align:start position:0%
+consumer surplus the consumer surplus
+here is the amount of money this guy's
+
+ align:start position:0%
+here is the amount of money this guy's
+ 
+
+ align:start position:0%
+here is the amount of money this guy's
+willing to lose because the amount of
+
+ align:start position:0%
+willing to lose because the amount of
+ 
+
+ align:start position:0%
+willing to lose because the amount of
+money that this guy is willing to lose
+
+ align:start position:0%
+money that this guy is willing to lose
+ 
+
+ align:start position:0%
+money that this guy is willing to lose
+is uh the the W is then whatever what
+
+ align:start position:0%
+is uh the the W is then whatever what
+ 
+
+ align:start position:0%
+is uh the the W is then whatever what
+you get at all higher quality restaurant
+
+ align:start position:0%
+you get at all higher quality restaurant
+ 
+
+ align:start position:0%
+you get at all higher quality restaurant
+um with full information uh learning
+
+ align:start position:0%
+um with full information uh learning
+ 
+
+ align:start position:0%
+um with full information uh learning
+about new entrance is very slow uh and
+
+ align:start position:0%
+about new entrance is very slow uh and
+ 
+
+ align:start position:0%
+about new entrance is very slow uh and
+firms exit after they just get some bad
+
+ align:start position:0%
+firms exit after they just get some bad
+ 
+
+ align:start position:0%
+firms exit after they just get some bad
+news so here is his
+
+ align:start position:0%
+news so here is his
+ 
+
+ align:start position:0%
+news so here is his
+um you know this is an example where um
+
+ align:start position:0%
+um you know this is an example where um
+ 
+
+ align:start position:0%
+um you know this is an example where um
+peot the prior is in the range where
+
+ align:start position:0%
+peot the prior is in the range where
+ 
+
+ align:start position:0%
+peot the prior is in the range where
+you're not in in the money on on
+
+ align:start position:0%
+you're not in in the money on on
+ 
+
+ align:start position:0%
+you're not in in the money on on
+customers so at a peot restaurant
+
+ align:start position:0%
+customers so at a peot restaurant
+ 
+
+ align:start position:0%
+customers so at a peot restaurant
+uh you're not you're not getting very
+
+ align:start position:0%
+uh you're not you're not getting very
+ 
+
+ align:start position:0%
+uh you're not you're not getting very
+many you're not you're you're out of the
+
+ align:start position:0%
+many you're not you're you're out of the
+ 
+
+ align:start position:0%
+many you're not you're you're out of the
+money customers are not coming to you
+
+ align:start position:0%
+money customers are not coming to you
+ 
+
+ align:start position:0%
+money customers are not coming to you
+and so what we get is there's a lot of
+
+ align:start position:0%
+and so what we get is there's a lot of
+ 
+
+ align:start position:0%
+and so what we get is there's a lot of
+firms who just entered about who the
+
+ align:start position:0%
+firms who just entered about who the
+ 
+
+ align:start position:0%
+firms who just entered about who the
+prior quality is p not and only Epsilon
+
+ align:start position:0%
+prior quality is p not and only Epsilon
+ 
+
+ align:start position:0%
+prior quality is p not and only Epsilon
+people go to them and so we get a lot of
+
+ align:start position:0%
+people go to them and so we get a lot of
+ 
+
+ align:start position:0%
+people go to them and so we get a lot of
+mass there because when they're only
+
+ align:start position:0%
+mass there because when they're only
+ 
+
+ align:start position:0%
+mass there because when they're only
+Epsilon customers people don't learn
+
+ align:start position:0%
+Epsilon customers people don't learn
+ 
+
+ align:start position:0%
+Epsilon customers people don't learn
+much and your posterior about their
+
+ align:start position:0%
+much and your posterior about their
+ 
+
+ align:start position:0%
+much and your posterior about their
+quality doesn't move very fast if you
+
+ align:start position:0%
+quality doesn't move very fast if you
+ 
+
+ align:start position:0%
+quality doesn't move very fast if you
+get one or two bad
+
+ align:start position:0%
+get one or two bad
+ 
+
+ align:start position:0%
+get one or two bad
+reviews then you just you just exit so
+
+ align:start position:0%
+reviews then you just you just exit so
+ 
+
+ align:start position:0%
+reviews then you just you just exit so
+bad you know like you your start here
+
+ align:start position:0%
+bad you know like you your start here
+ 
+
+ align:start position:0%
+bad you know like you your start here
+you get a bad review or two you just
+
+ align:start position:0%
+you get a bad review or two you just
+ 
+
+ align:start position:0%
+you get a bad review or two you just
+exit the market and then Al so there
+
+ align:start position:0%
+exit the market and then Al so there
+ 
+
+ align:start position:0%
+exit the market and then Al so there
+aren't many firms down here with these
+
+ align:start position:0%
+aren't many firms down here with these
+ 
+
+ align:start position:0%
+aren't many firms down here with these
+qualities because two bad reviews you
+
+ align:start position:0%
+qualities because two bad reviews you
+ 
+
+ align:start position:0%
+qualities because two bad reviews you
+leave and then even if you would have
+
+ align:start position:0%
+leave and then even if you would have
+ 
+
+ align:start position:0%
+leave and then even if you would have
+gotten a third review coming back up
+
+ align:start position:0%
+gotten a third review coming back up
+ 
+
+ align:start position:0%
+gotten a third review coming back up
+you're not there
+
+ align:start position:0%
+you're not there
+ 
+
+ align:start position:0%
+you're not there
+anymore
+
+ align:start position:0%
+anymore
+ 
+
+ align:start position:0%
+anymore
+um then there are fewer firms with
+
+ align:start position:0%
+um then there are fewer firms with
+ 
+
+ align:start position:0%
+um then there are fewer firms with
+qualities here because once your quality
+
+ align:start position:0%
+qualities here because once your quality
+ 
+
+ align:start position:0%
+qualities here because once your quality
+your posterior gets above P upper bar
+
+ align:start position:0%
+your posterior gets above P upper bar
+ 
+
+ align:start position:0%
+your posterior gets above P upper bar
+people learn about you very quickly
+
+ align:start position:0%
+people learn about you very quickly
+ 
+
+ align:start position:0%
+people learn about you very quickly
+people learn about you very quickly your
+
+ align:start position:0%
+people learn about you very quickly your
+ 
+
+ align:start position:0%
+people learn about you very quickly your
+distribution moves and either moves back
+
+ align:start position:0%
+distribution moves and either moves back
+ 
+
+ align:start position:0%
+distribution moves and either moves back
+to this range where no one's coming to
+
+ align:start position:0%
+to this range where no one's coming to
+ 
+
+ align:start position:0%
+to this range where no one's coming to
+your restaurant or it moves up and and
+
+ align:start position:0%
+your restaurant or it moves up and and
+ 
+
+ align:start position:0%
+your restaurant or it moves up and and
+people learn it's good and you know in
+
+ align:start position:0%
+people learn it's good and you know in
+ 
+
+ align:start position:0%
+people learn it's good and you know in
+this model everyone's either zero or one
+
+ align:start position:0%
+this model everyone's either zero or one
+ 
+
+ align:start position:0%
+this model everyone's either zero or one
+so very quickly people learn that you're
+
+ align:start position:0%
+so very quickly people learn that you're
+ 
+
+ align:start position:0%
+so very quickly people learn that you're
+a quality One
+
+ align:start position:0%
+a quality One
+ 
+
+ align:start position:0%
+a quality One
+Restaurant okay so we get this sort of
+
+ align:start position:0%
+Restaurant okay so we get this sort of
+ 
+
+ align:start position:0%
+Restaurant okay so we get this sort of
+distribution of firm qualities where
+
+ align:start position:0%
+distribution of firm qualities where
+ 
+
+ align:start position:0%
+distribution of firm qualities where
+there are a lot of firms that are having
+
+ align:start position:0%
+there are a lot of firms that are having
+ 
+
+ align:start position:0%
+there are a lot of firms that are having
+trouble attracting anyone reviews they
+
+ align:start position:0%
+trouble attracting anyone reviews they
+ 
+
+ align:start position:0%
+trouble attracting anyone reviews they
+stay hang out here and their their
+
+ align:start position:0%
+stay hang out here and their their
+ 
+
+ align:start position:0%
+stay hang out here and their their
+poster don't move much and then once you
+
+ align:start position:0%
+poster don't move much and then once you
+ 
+
+ align:start position:0%
+poster don't move much and then once you
+get a some threshold you move very
+
+ align:start position:0%
+get a some threshold you move very
+ 
+
+ align:start position:0%
+get a some threshold you move very
+quickly either back into the range where
+
+ align:start position:0%
+quickly either back into the range where
+ 
+
+ align:start position:0%
+quickly either back into the range where
+you don't learn much or into the year
+
+ align:start position:0%
+you don't learn much or into the year
+ 
+
+ align:start position:0%
+you don't learn much or into the year
+quality is one and then people all start
+
+ align:start position:0%
+quality is one and then people all start
+ 
+
+ align:start position:0%
+quality is one and then people all start
+going
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
+
+ align:start position:0%
+you
+ 
+
+ align:start position:0%
+you
+um you know consumer welfare under any
+
+ align:start position:0%
+um you know consumer welfare under any
+ 
+
+ align:start position:0%
+um you know consumer welfare under any
+policy is the W that arises given the
+
+ align:start position:0%
+policy is the W that arises given the
+ 
+
+ align:start position:0%
+policy is the W that arises given the
+policy so consumer
+
+ align:start position:0%
+policy so consumer
+ 
+
+ align:start position:0%
+policy so consumer
+optimality like what's best for
+
+ align:start position:0%
+optimality like what's best for
+ 
+
+ align:start position:0%
+optimality like what's best for
+consumers if like you're trying to if
+
+ align:start position:0%
+consumers if like you're trying to if
+ 
+
+ align:start position:0%
+consumers if like you're trying to if
+you're Yelp and you're trying to design
+
+ align:start position:0%
+you're Yelp and you're trying to design
+ 
+
+ align:start position:0%
+you're Yelp and you're trying to design
+my platform to be consumer optimal so
+
+ align:start position:0%
+my platform to be consumer optimal so
+ 
+
+ align:start position:0%
+my platform to be consumer optimal so
+people will continue to use Yelp what's
+
+ align:start position:0%
+people will continue to use Yelp what's
+ 
+
+ align:start position:0%
+people will continue to use Yelp what's
+optimal for the firm to do is to give
+
+ align:start position:0%
+optimal for the firm to do is to give
+ 
+
+ align:start position:0%
+optimal for the firm to do is to give
+firms an incentive to be willing to
+
+ align:start position:0%
+firms an incentive to be willing to
+ 
+
+ align:start position:0%
+firms an incentive to be willing to
+price Billow cost to have firms learn
+
+ align:start position:0%
+price Billow cost to have firms learn
+ 
+
+ align:start position:0%
+price Billow cost to have firms learn
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+them and so then what do you get about
+
+ align:start position:0%
+them and so then what do you get about
+ 
+
+ align:start position:0%
+them and so then what do you get about
+what would be the optimal policy if
+
+ align:start position:0%
+what would be the optimal policy if
+ 
+
+ align:start position:0%
+what would be the optimal policy if
+you're trying to get these guys to be
+
+ align:start position:0%
+you're trying to get these guys to be
+ 
+
+ align:start position:0%
+you're trying to get these guys to be
+willing to pay a lot to get more
+
+ align:start position:0%
+willing to pay a lot to get more
+ 
+
+ align:start position:0%
+willing to pay a lot to get more
+reviews um and it turns out that one of
+
+ align:start position:0%
+reviews um and it turns out that one of
+ 
+
+ align:start position:0%
+reviews um and it turns out that one of
+the answer is that you want to have a
+
+ align:start position:0%
+the answer is that you want to have a
+ 
+
+ align:start position:0%
+the answer is that you want to have a
+partially revealing customer policy
+
+ align:start position:0%
+partially revealing customer policy
+ 
+
+ align:start position:0%
+partially revealing customer policy
+where you don't um publish all the
+
+ align:start position:0%
+where you don't um publish all the
+ 
+
+ align:start position:0%
+where you don't um publish all the
+reviews about high quality firms what
+
+ align:start position:0%
+reviews about high quality firms what
+ 
+
+ align:start position:0%
+reviews about high quality firms what
+you want to do is in some sense as soon
+
+ align:start position:0%
+you want to do is in some sense as soon
+ 
+
+ align:start position:0%
+you want to do is in some sense as soon
+soon as a firm's posterior passes P
+
+ align:start position:0%
+soon as a firm's posterior passes P
+ 
+
+ align:start position:0%
+soon as a firm's posterior passes P
+Tilda you want to stop publishing any
+
+ align:start position:0%
+Tilda you want to stop publishing any
+ 
+
+ align:start position:0%
+Tilda you want to stop publishing any
+reviews about them
+
+ align:start position:0%
+reviews about them
+ 
+
+ align:start position:0%
+reviews about them
+whatsoever and you do that because that
+
+ align:start position:0%
+whatsoever and you do that because that
+ 
+
+ align:start position:0%
+whatsoever and you do that because that
+way you know by having sort of a flat
+
+ align:start position:0%
+way you know by having sort of a flat
+ 
+
+ align:start position:0%
+way you know by having sort of a flat
+benefit from being quality P Tilda or
+
+ align:start position:0%
+benefit from being quality P Tilda or
+ 
+
+ align:start position:0%
+benefit from being quality P Tilda or
+all the way up to here when you have
+
+ align:start position:0%
+all the way up to here when you have
+ 
+
+ align:start position:0%
+all the way up to here when you have
+sort of a flatter benefit from high
+
+ align:start position:0%
+sort of a flatter benefit from high
+ 
+
+ align:start position:0%
+sort of a flatter benefit from high
+quality there's greater incentive to
+
+ align:start position:0%
+quality there's greater incentive to
+ 
+
+ align:start position:0%
+quality there's greater incentive to
+make the jump from here up to
+
+ align:start position:0%
+make the jump from here up to
+ 
+
+ align:start position:0%
+make the jump from here up to
+here um and therefore these firms are
+
+ align:start position:0%
+here um and therefore these firms are
+ 
+
+ align:start position:0%
+here um and therefore these firms are
+willing to price further below cost in
+
+ align:start position:0%
+willing to price further below cost in
+ 
+
+ align:start position:0%
+willing to price further below cost in
+order to make that jump and then you
+
+ align:start position:0%
+order to make that jump and then you
+ 
+
+ align:start position:0%
+order to make that jump and then you
+know you are disadvantaging some firms
+
+ align:start position:0%
+know you are disadvantaging some firms
+ 
+
+ align:start position:0%
+know you are disadvantaging some firms
+you're hurting firms up here helping
+
+ align:start position:0%
+you're hurting firms up here helping
+ 
+
+ align:start position:0%
+you're hurting firms up here helping
+firms down here by not promoting qu
+
+ align:start position:0%
+firms down here by not promoting qu
+ 
+
+ align:start position:0%
+firms down here by not promoting qu
+providing quality information on them
+
+ align:start position:0%
+providing quality information on them
+ 
+
+ align:start position:0%
+providing quality information on them
+that lets them show that they're really
+
+ align:start position:0%
+that lets them show that they're really
+ 
+
+ align:start position:0%
+that lets them show that they're really
+good um but since new firms are much
+
+ align:start position:0%
+good um but since new firms are much
+ 
+
+ align:start position:0%
+good um but since new firms are much
+more likely to be here than they are to
+
+ align:start position:0%
+more likely to be here than they are to
+ 
+
+ align:start position:0%
+more likely to be here than they are to
+be here when you're here you're willing
+
+ align:start position:0%
+be here when you're here you're willing
+ 
+
+ align:start position:0%
+be here when you're here you're willing
+to pay more to get up if you sort of
+
+ align:start position:0%
+to pay more to get up if you sort of
+ 
+
+ align:start position:0%
+to pay more to get up if you sort of
+take some of the Surplus away from the
+
+ align:start position:0%
+take some of the Surplus away from the
+ 
+
+ align:start position:0%
+take some of the Surplus away from the
+really successful firms and give it to
+
+ align:start position:0%
+really successful firms and give it to
+ 
+
+ align:start position:0%
+really successful firms and give it to
+the moderately successful firms that
+
+ align:start position:0%
+the moderately successful firms that
+ 
+
+ align:start position:0%
+the moderately successful firms that
+raises the incentive to price in that
+
+ align:start position:0%
+raises the incentive to price in that
+ 
+
+ align:start position:0%
+raises the incentive to price in that
+way so so what he argues is that you
+
+ align:start position:0%
+way so so what he argues is that you
+ 
+
+ align:start position:0%
+way so so what he argues is that you
+know what what a platform would like to
+
+ align:start position:0%
+know what what a platform would like to
+ 
+
+ align:start position:0%
+know what what a platform would like to
+do in in this model is to actually give
+
+ align:start position:0%
+do in in this model is to actually give
+ 
+
+ align:start position:0%
+do in in this model is to actually give
+incomplete information about restaurants
+
+ align:start position:0%
+incomplete information about restaurants
+ 
+
+ align:start position:0%
+incomplete information about restaurants
+and to sort of selectively give
+
+ align:start position:0%
+and to sort of selectively give
+ 
+
+ align:start position:0%
+and to sort of selectively give
+information where uh we restrict
+
+ align:start position:0%
+information where uh we restrict
+ 
+
+ align:start position:0%
+information where uh we restrict
+information about the good products so
+
+ align:start position:0%
+information about the good products so
+ 
+
+ align:start position:0%
+information about the good products so
+that we have
+
+ align:start position:0%
+that we have
+ 
+
+ align:start position:0%
+that we have
+more so that there's more of a benefit
+
+ align:start position:0%
+more so that there's more of a benefit
+ 
+
+ align:start position:0%
+more so that there's more of a benefit
+to having a pretty good reputation so
+
+ align:start position:0%
+to having a pretty good reputation so
+ 
+
+ align:start position:0%
+to having a pretty good reputation so
+that new firms will then invest more in
+
+ align:start position:0%
+that new firms will then invest more in
+ 
+
+ align:start position:0%
+that new firms will then invest more in
+trying to get the pretty good reputation
+
+ align:start position:0%
+trying to get the pretty good reputation
+ 
+
+ align:start position:0%
+trying to get the pretty good reputation
+and then obviously all the other firms
+
+ align:start position:0%
+and then obviously all the other firms
+ 
+
+ align:start position:0%
+and then obviously all the other firms
+are pricing you know off have to price
+
+ align:start position:0%
+are pricing you know off have to price
+ 
+
+ align:start position:0%
+are pricing you know off have to price
+to out compete those guys
+
+ align:start position:0%
+to out compete those guys
+ 
+
+ align:start position:0%
+to out compete those guys
+okay okay that is it I that's what I had
+
+ align:start position:0%
+okay okay that is it I that's what I had
+ 
+
+ align:start position:0%
+okay okay that is it I that's what I had
+for today so uh Wednesday I'm going to
+
+ align:start position:0%
+for today so uh Wednesday I'm going to
+ 
+
+ align:start position:0%
+for today so uh Wednesday I'm going to
+talk about uh empirical work on Entry uh
+
+ align:start position:0%
+talk about uh empirical work on Entry uh
+ 
+
+ align:start position:0%
+talk about uh empirical work on Entry uh
+I would say you know breast Nan Reese is
+
+ align:start position:0%
+I would say you know breast Nan Reese is
+ 
+
+ align:start position:0%
+I would say you know breast Nan Reese is
+really a be is really the classic paper
+
+ align:start position:0%
+really a be is really the classic paper
+ 
+
+ align:start position:0%
+really a be is really the classic paper
+on Entry again breast and hand Reese is
+
+ align:start position:0%
+on Entry again breast and hand Reese is
+ 
+
+ align:start position:0%
+on Entry again breast and hand Reese is
+a little old by now so I would say that
+
+ align:start position:0%
+a little old by now so I would say that
+ 
+
+ align:start position:0%
+a little old by now so I would say that
+if you want to read things you know I
+
+ align:start position:0%
+if you want to read things you know I
+ 
+
+ align:start position:0%
+if you want to read things you know I
+will tell you what's in breast and Han
+
+ align:start position:0%
+will tell you what's in breast and Han
+ 
+
+ align:start position:0%
+will tell you what's in breast and Han
+and Reese with slightly more modern
+
+ align:start position:0%
+and Reese with slightly more modern
+ 
+
+ align:start position:0%
+and Reese with slightly more modern
+econometrics or what would be in it and
+
+ align:start position:0%
+econometrics or what would be in it and
+ 
+
+ align:start position:0%
+econometrics or what would be in it and
+then maybe read uh Barry W Fogle or look
+
+ align:start position:0%
+then maybe read uh Barry W Fogle or look
+ 
+
+ align:start position:0%
+then maybe read uh Barry W Fogle or look
+at like one of the bronen maybe brenberg
+
+ align:start position:0%
+at like one of the bronen maybe brenberg
+ 
+
+ align:start position:0%
+at like one of the bronen maybe brenberg
+D dubet or whatever but sort of talk
+
+ align:start position:0%
+D dubet or whatever but sort of talk
+ 
+
+ align:start position:0%
+D dubet or whatever but sort of talk
+about those four papers
\ No newline at end of file
diff --git a/lyR4HQ01nos.txt b/lyR4HQ01nos.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ece608243e54fa1b30e93eccc13549719c09a8c8
--- /dev/null
+++ b/lyR4HQ01nos.txt
@@ -0,0 +1,643 @@
+align:start position:0%
+ 
+um the students spend about six hours in
+
+ align:start position:0%
+um the students spend about six hours in
+ 
+
+ align:start position:0%
+um the students spend about six hours in
+class uh each week and right at the
+
+ align:start position:0%
+class uh each week and right at the
+ 
+
+ align:start position:0%
+class uh each week and right at the
+beginning of the semester most of those
+
+ align:start position:0%
+beginning of the semester most of those
+ 
+
+ align:start position:0%
+beginning of the semester most of those
+six hours are either lectures or uh
+
+ align:start position:0%
+six hours are either lectures or uh
+ 
+
+ align:start position:0%
+six hours are either lectures or uh
+activities or workshops that we have
+
+ align:start position:0%
+activities or workshops that we have
+ 
+
+ align:start position:0%
+activities or workshops that we have
+planned to have inside the the class is
+
+ align:start position:0%
+planned to have inside the the class is
+ 
+
+ align:start position:0%
+planned to have inside the the class is
+very very tightly programmed um this may
+
+ align:start position:0%
+very very tightly programmed um this may
+ 
+
+ align:start position:0%
+very very tightly programmed um this may
+involve say brainstorming for the the
+
+ align:start position:0%
+involve say brainstorming for the the
+ 
+
+ align:start position:0%
+involve say brainstorming for the the
+team projects or forming up with teams
+
+ align:start position:0%
+team projects or forming up with teams
+ 
+
+ align:start position:0%
+team projects or forming up with teams
+uh going through the project uh
+
+ align:start position:0%
+uh going through the project uh
+ 
+
+ align:start position:0%
+uh going through the project uh
+constraints teaching them the techniques
+
+ align:start position:0%
+constraints teaching them the techniques
+ 
+
+ align:start position:0%
+constraints teaching them the techniques
+that we want them to learn near the end
+
+ align:start position:0%
+that we want them to learn near the end
+ 
+
+ align:start position:0%
+that we want them to learn near the end
+of the semester we heavily scale back
+
+ align:start position:0%
+of the semester we heavily scale back
+ 
+
+ align:start position:0%
+of the semester we heavily scale back
+the programmed content we uh give
+
+ align:start position:0%
+the programmed content we uh give
+ 
+
+ align:start position:0%
+the programmed content we uh give
+students a lot of class time just to
+
+ align:start position:0%
+students a lot of class time just to
+ 
+
+ align:start position:0%
+students a lot of class time just to
+meet up with the teams because for many
+
+ align:start position:0%
+meet up with the teams because for many
+ 
+
+ align:start position:0%
+meet up with the teams because for many
+many teams it's difficult enough to
+
+ align:start position:0%
+many teams it's difficult enough to
+ 
+
+ align:start position:0%
+many teams it's difficult enough to
+gather you know six people uh in the
+
+ align:start position:0%
+gather you know six people uh in the
+ 
+
+ align:start position:0%
+gather you know six people uh in the
+same room at the same place at the same
+
+ align:start position:0%
+same room at the same place at the same
+ 
+
+ align:start position:0%
+same room at the same place at the same
+time to get eight of them in the same
+
+ align:start position:0%
+time to get eight of them in the same
+ 
+
+ align:start position:0%
+time to get eight of them in the same
+room well if you're doing it during
+
+ align:start position:0%
+room well if you're doing it during
+ 
+
+ align:start position:0%
+room well if you're doing it during
+class time at least you know everybody's
+
+ align:start position:0%
+class time at least you know everybody's
+ 
+
+ align:start position:0%
+class time at least you know everybody's
+going to be there so uh so we try to
+
+ align:start position:0%
+going to be there so uh so we try to
+ 
+
+ align:start position:0%
+going to be there so uh so we try to
+give as much time as possible later in
+
+ align:start position:0%
+give as much time as possible later in
+ 
+
+ align:start position:0%
+give as much time as possible later in
+the semester for teams to actually work
+
+ align:start position:0%
+the semester for teams to actually work
+ 
+
+ align:start position:0%
+the semester for teams to actually work
+on their project but sometimes that is
+
+ align:start position:0%
+on their project but sometimes that is
+ 
+
+ align:start position:0%
+on their project but sometimes that is
+planned out like play test sessions for
+
+ align:start position:0%
+planned out like play test sessions for
+ 
+
+ align:start position:0%
+planned out like play test sessions for
+instance where um students play each
+
+ align:start position:0%
+instance where um students play each
+ 
+
+ align:start position:0%
+instance where um students play each
+other's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+games yeah the first um half of the
+
+ align:start position:0%
+games yeah the first um half of the
+ 
+
+ align:start position:0%
+games yeah the first um half of the
+semester is all the lecture and the
+
+ align:start position:0%
+semester is all the lecture and the
+ 
+
+ align:start position:0%
+semester is all the lecture and the
+workshops are are given by by the staff
+
+ align:start position:0%
+workshops are are given by by the staff
+ 
+
+ align:start position:0%
+workshops are are given by by the staff
+um but by the second half of the
+
+ align:start position:0%
+um but by the second half of the
+ 
+
+ align:start position:0%
+um but by the second half of the
+semester we're getting them to see other
+
+ align:start position:0%
+semester we're getting them to see other
+ 
+
+ align:start position:0%
+semester we're getting them to see other
+aspects of game development So within M
+
+ align:start position:0%
+aspects of game development So within M
+ 
+
+ align:start position:0%
+aspects of game development So within M
+students um and actually this year a few
+
+ align:start position:0%
+students um and actually this year a few
+ 
+
+ align:start position:0%
+students um and actually this year a few
+Wellsley students most of our students
+
+ align:start position:0%
+Wellsley students most of our students
+ 
+
+ align:start position:0%
+Wellsley students most of our students
+are going to be coming to to us with a
+
+ align:start position:0%
+are going to be coming to to us with a
+ 
+
+ align:start position:0%
+are going to be coming to to us with a
+programming background a few might have
+
+ align:start position:0%
+programming background a few might have
+ 
+
+ align:start position:0%
+programming background a few might have
+some design um classes under the belt
+
+ align:start position:0%
+some design um classes under the belt
+ 
+
+ align:start position:0%
+some design um classes under the belt
+maybe they've taken one of our game
+
+ align:start position:0%
+maybe they've taken one of our game
+ 
+
+ align:start position:0%
+maybe they've taken one of our game
+design classes or another design class
+
+ align:start position:0%
+design classes or another design class
+ 
+
+ align:start position:0%
+design classes or another design class
+offered at M some of the students are
+
+ align:start position:0%
+offered at M some of the students are
+ 
+
+ align:start position:0%
+offered at M some of the students are
+going to have some art aptitude like
+
+ align:start position:0%
+going to have some art aptitude like
+ 
+
+ align:start position:0%
+going to have some art aptitude like
+visual art aptitude some a little bit
+
+ align:start position:0%
+visual art aptitude some a little bit
+ 
+
+ align:start position:0%
+visual art aptitude some a little bit
+more um uh sound design or music
+
+ align:start position:0%
+more um uh sound design or music
+ 
+
+ align:start position:0%
+more um uh sound design or music
+composition aptitude but for the most
+
+ align:start position:0%
+composition aptitude but for the most
+ 
+
+ align:start position:0%
+composition aptitude but for the most
+part they don't know what it's like to
+
+ align:start position:0%
+part they don't know what it's like to
+ 
+
+ align:start position:0%
+part they don't know what it's like to
+be an artist they don't know what it's
+
+ align:start position:0%
+be an artist they don't know what it's
+ 
+
+ align:start position:0%
+be an artist they don't know what it's
+like to be a sound designer on a game
+
+ align:start position:0%
+like to be a sound designer on a game
+ 
+
+ align:start position:0%
+like to be a sound designer on a game
+development project um and they might
+
+ align:start position:0%
+development project um and they might
+ 
+
+ align:start position:0%
+development project um and they might
+actually not know anything about the
+
+ align:start position:0%
+actually not know anything about the
+ 
+
+ align:start position:0%
+actually not know anything about the
+business of games so the last half of
+
+ align:start position:0%
+business of games so the last half of
+ 
+
+ align:start position:0%
+business of games so the last half of
+the semester is bringing in guest
+
+ align:start position:0%
+the semester is bringing in guest
+ 
+
+ align:start position:0%
+the semester is bringing in guest
+lectures from the industry um we've got
+
+ align:start position:0%
+lectures from the industry um we've got
+ 
+
+ align:start position:0%
+lectures from the industry um we've got
+a great Network here in Boston um an
+
+ align:start position:0%
+a great Network here in Boston um an
+ 
+
+ align:start position:0%
+a great Network here in Boston um an
+independent game developer Network um
+
+ align:start position:0%
+independent game developer Network um
+ 
+
+ align:start position:0%
+independent game developer Network um
+also um quite a few of the AAA larger
+
+ align:start position:0%
+also um quite a few of the AAA larger
+ 
+
+ align:start position:0%
+also um quite a few of the AAA larger
+studios are here so we we mine our
+
+ align:start position:0%
+studios are here so we we mine our
+ 
+
+ align:start position:0%
+studios are here so we we mine our
+Network and each year we get new um
+
+ align:start position:0%
+Network and each year we get new um
+ 
+
+ align:start position:0%
+Network and each year we get new um
+speakers to come talk to them about how
+
+ align:start position:0%
+speakers to come talk to them about how
+ 
+
+ align:start position:0%
+speakers to come talk to them about how
+to work with an artist how to work with
+
+ align:start position:0%
+to work with an artist how to work with
+ 
+
+ align:start position:0%
+to work with an artist how to work with
+a sound designer what it actually means
+
+ align:start position:0%
+a sound designer what it actually means
+ 
+
+ align:start position:0%
+a sound designer what it actually means
+to be an art director in a in a game
+
+ align:start position:0%
+to be an art director in a in a game
+ 
+
+ align:start position:0%
+to be an art director in a in a game
+company or what it actually doesn't mean
+
+ align:start position:0%
+company or what it actually doesn't mean
+ 
+
+ align:start position:0%
+company or what it actually doesn't mean
+to even be a level designer um on a on a
+
+ align:start position:0%
+to even be a level designer um on a on a
+ 
+
+ align:start position:0%
+to even be a level designer um on a on a
+large project um but then Al we're
+
+ align:start position:0%
+large project um but then Al we're
+ 
+
+ align:start position:0%
+large project um but then Al we're
+bringing people in to talk about
+
+ align:start position:0%
+bringing people in to talk about
+ 
+
+ align:start position:0%
+bringing people in to talk about
+business models um Kickstarter is often
+
+ align:start position:0%
+business models um Kickstarter is often
+ 
+
+ align:start position:0%
+business models um Kickstarter is often
+an interesting topic for the students
+
+ align:start position:0%
+an interesting topic for the students
+ 
+
+ align:start position:0%
+an interesting topic for the students
+things we try to balance it between
+
+ align:start position:0%
+things we try to balance it between
+ 
+
+ align:start position:0%
+things we try to balance it between
+here's what the industry looks like and
+
+ align:start position:0%
+here's what the industry looks like and
+ 
+
+ align:start position:0%
+here's what the industry looks like and
+here's the things are going to help you
+
+ align:start position:0%
+here's the things are going to help you
+ 
+
+ align:start position:0%
+here's the things are going to help you
+right now with the the the game that
+
+ align:start position:0%
+right now with the the the game that
+ 
+
+ align:start position:0%
+right now with the the the game that
+you're working on now and if you wanted
+
+ align:start position:0%
+you're working on now and if you wanted
+ 
+
+ align:start position:0%
+you're working on now and if you wanted
+to take the game a little bit further
+
+ align:start position:0%
+to take the game a little bit further
+ 
+
+ align:start position:0%
+to take the game a little bit further
+after the course here's the things that
+
+ align:start position:0%
+after the course here's the things that
+ 
+
+ align:start position:0%
+after the course here's the things that
+you could do um things like fundraising
+
+ align:start position:0%
+you could do um things like fundraising
+ 
+
+ align:start position:0%
+you could do um things like fundraising
+um submitting it to festivals um
+
+ align:start position:0%
+um submitting it to festivals um
+ 
+
+ align:start position:0%
+um submitting it to festivals um
+marketing it and things and just getting
+
+ align:start position:0%
+marketing it and things and just getting
+ 
+
+ align:start position:0%
+marketing it and things and just getting
+other people to play it
\ No newline at end of file
diff --git a/mrvBnZIEsZY.txt b/mrvBnZIEsZY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2403fa6e1b2855474db091fded1975bfba08fc2c
--- /dev/null
+++ b/mrvBnZIEsZY.txt
@@ -0,0 +1,323 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT open courseware continue
+
+ align:start position:0%
+will help MIT open courseware continue
+ 
+
+ align:start position:0%
+will help MIT open courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free to make a donation or
+
+ align:start position:0%
+resources for free to make a donation or
+ 
+
+ align:start position:0%
+resources for free to make a donation or
+view additional materials from hundreds
+
+ align:start position:0%
+view additional materials from hundreds
+ 
+
+ align:start position:0%
+view additional materials from hundreds
+of MIT courses visit MIT opencourseware
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+ 
+
+ align:start position:0%
+of MIT courses visit MIT opencourseware
+at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mit.edu so now we have this this
+
+ align:start position:0%
+ocw.mit.edu so now we have this this
+ 
+
+ align:start position:0%
+ocw.mit.edu so now we have this this
+last
+
+ align:start position:0%
+last
+ 
+
+ align:start position:0%
+last
+exercise I'm creating a my sum I'm going
+
+ align:start position:0%
+exercise I'm creating a my sum I'm going
+ 
+
+ align:start position:0%
+exercise I'm creating a my sum I'm going
+to go through all of these values and
+
+ align:start position:0%
+to go through all of these values and
+ 
+
+ align:start position:0%
+to go through all of these values and
+you guys have already told me what
+
+ align:start position:0%
+you guys have already told me what
+ 
+
+ align:start position:0%
+you guys have already told me what
+values these are 5 7 9 not
+
+ align:start position:0%
+values these are 5 7 9 not
+ 
+
+ align:start position:0%
+values these are 5 7 9 not
+11 and I'm going to add to my sum so I'm
+
+ align:start position:0%
+11 and I'm going to add to my sum so I'm
+ 
+
+ align:start position:0%
+11 and I'm going to add to my sum so I'm
+going to keep a running sum adding all
+
+ align:start position:0%
+going to keep a running sum adding all
+ 
+
+ align:start position:0%
+going to keep a running sum adding all
+of these values together
+
+ align:start position:0%
+of these values together
+ 
+
+ align:start position:0%
+of these values together
+okay so the very first time through the
+
+ align:start position:0%
+okay so the very first time through the
+ 
+
+ align:start position:0%
+okay so the very first time through the
+loop my sum gets the value of
+
+ align:start position:0%
+loop my sum gets the value of
+ 
+
+ align:start position:0%
+loop my sum gets the value of
+five okay that's this line here the next
+
+ align:start position:0%
+five okay that's this line here the next
+ 
+
+ align:start position:0%
+five okay that's this line here the next
+thing I'm I see inside this Loop is an
+
+ align:start position:0%
+thing I'm I see inside this Loop is an
+ 
+
+ align:start position:0%
+thing I'm I see inside this Loop is an
+if statement if my sum is equal to five
+
+ align:start position:0%
+if statement if my sum is equal to five
+ 
+
+ align:start position:0%
+if statement if my sum is equal to five
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+true so I'm going to go inside this if
+
+ align:start position:0%
+true so I'm going to go inside this if
+ 
+
+ align:start position:0%
+true so I'm going to go inside this if
+statement the next thing I see is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+break if I see this break am I
+
+ align:start position:0%
+break if I see this break am I
+ 
+
+ align:start position:0%
+break if I see this break am I
+evaluating this am I evaluating this
+
+ align:start position:0%
+evaluating this am I evaluating this
+ 
+
+ align:start position:0%
+evaluating this am I evaluating this
+line or
+
+ align:start position:0%
+line or
+ 
+
+ align:start position:0%
+line or
+not no exactly because when whenever
+
+ align:start position:0%
+not no exactly because when whenever
+ 
+
+ align:start position:0%
+not no exactly because when whenever
+python sees break it's going to say I'm
+
+ align:start position:0%
+python sees break it's going to say I'm
+ 
+
+ align:start position:0%
+python sees break it's going to say I'm
+going to stop right here exit out of the
+
+ align:start position:0%
+going to stop right here exit out of the
+ 
+
+ align:start position:0%
+going to stop right here exit out of the
+loop that I'm currently in and go to the
+
+ align:start position:0%
+loop that I'm currently in and go to the
+ 
+
+ align:start position:0%
+loop that I'm currently in and go to the
+statement that's immediately right after
+
+ align:start position:0%
+statement that's immediately right after
+ 
+
+ align:start position:0%
+statement that's immediately right after
+it so what this is going to print is my
+
+ align:start position:0%
+it so what this is going to print is my
+ 
+
+ align:start position:0%
+it so what this is going to print is my
+sum and that's the exercise we were
+
+ align:start position:0%
+sum and that's the exercise we were
+ 
+
+ align:start position:0%
+sum and that's the exercise we were
+looking at let's see how the class
+
+ align:start position:0%
+looking at let's see how the class
+ 
+
+ align:start position:0%
+looking at let's see how the class
+did pretty
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good hopefully if you answered one of
+
+ align:start position:0%
+good hopefully if you answered one of
+ 
+
+ align:start position:0%
+good hopefully if you answered one of
+these um the explanation was was all
+
+ align:start position:0%
+these um the explanation was was all
+ 
+
+ align:start position:0%
+these um the explanation was was all
+right if not just go back and try to
+
+ align:start position:0%
+right if not just go back and try to
+ 
+
+ align:start position:0%
+right if not just go back and try to
+work through it step by step
\ No newline at end of file
diff --git a/nwZ9FbZtOv0.txt b/nwZ9FbZtOv0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..085a988b51bdc4383cf1aa1767dd19897d11c93c
--- /dev/null
+++ b/nwZ9FbZtOv0.txt
@@ -0,0 +1,3024 @@
+align:start position:0%
+ 
+n2o5 is a reagent that was used to
+
+ align:start position:0%
+n2o5 is a reagent that was used to
+ 
+
+ align:start position:0%
+n2o5 is a reagent that was used to
+synthesize explosives like tnt
+
+ align:start position:0%
+synthesize explosives like tnt
+ 
+
+ align:start position:0%
+synthesize explosives like tnt
+unfortunately it decomposes relatively
+
+ align:start position:0%
+unfortunately it decomposes relatively
+ 
+
+ align:start position:0%
+unfortunately it decomposes relatively
+quickly at or above room temperature
+
+ align:start position:0%
+quickly at or above room temperature
+ 
+
+ align:start position:0%
+quickly at or above room temperature
+so if you accidentally leave a bottle of
+
+ align:start position:0%
+so if you accidentally leave a bottle of
+ 
+
+ align:start position:0%
+so if you accidentally leave a bottle of
+it out on the counter you could be in
+
+ align:start position:0%
+it out on the counter you could be in
+ 
+
+ align:start position:0%
+it out on the counter you could be in
+trouble
+
+ align:start position:0%
+trouble
+ 
+
+ align:start position:0%
+trouble
+in this video we'll approximate the
+
+ align:start position:0%
+in this video we'll approximate the
+ 
+
+ align:start position:0%
+in this video we'll approximate the
+decomposition rate equation
+
+ align:start position:0%
+decomposition rate equation
+ 
+
+ align:start position:0%
+decomposition rate equation
+to figure out whether a batch of n2o5
+
+ align:start position:0%
+to figure out whether a batch of n2o5
+ 
+
+ align:start position:0%
+to figure out whether a batch of n2o5
+that you left at room temperature can
+
+ align:start position:0%
+that you left at room temperature can
+ 
+
+ align:start position:0%
+that you left at room temperature can
+still be used
+
+ align:start position:0%
+still be used
+ 
+
+ align:start position:0%
+still be used
+we'll also determine under what
+
+ align:start position:0%
+we'll also determine under what
+ 
+
+ align:start position:0%
+we'll also determine under what
+conditions our approximation
+
+ align:start position:0%
+conditions our approximation
+ 
+
+ align:start position:0%
+conditions our approximation
+is valid this video is part of the
+
+ align:start position:0%
+is valid this video is part of the
+ 
+
+ align:start position:0%
+is valid this video is part of the
+linearity video series
+
+ align:start position:0%
+linearity video series
+ 
+
+ align:start position:0%
+linearity video series
+many complex systems are modeled or
+
+ align:start position:0%
+many complex systems are modeled or
+ 
+
+ align:start position:0%
+many complex systems are modeled or
+approximated linearly because of the
+
+ align:start position:0%
+approximated linearly because of the
+ 
+
+ align:start position:0%
+approximated linearly because of the
+mathematical advantages
+
+ align:start position:0%
+mathematical advantages
+ 
+
+ align:start position:0%
+mathematical advantages
+hi my name is ben brubacher and i'm a
+
+ align:start position:0%
+hi my name is ben brubacher and i'm a
+ 
+
+ align:start position:0%
+hi my name is ben brubacher and i'm a
+professor in the department of
+
+ align:start position:0%
+professor in the department of
+ 
+
+ align:start position:0%
+professor in the department of
+mathematics at mit
+
+ align:start position:0%
+mathematics at mit
+ 
+
+ align:start position:0%
+mathematics at mit
+today we'll be talking about linear
+
+ align:start position:0%
+today we'll be talking about linear
+ 
+
+ align:start position:0%
+today we'll be talking about linear
+approximations
+
+ align:start position:0%
+approximations
+ 
+
+ align:start position:0%
+approximations
+in mathematical terms this is just
+
+ align:start position:0%
+in mathematical terms this is just
+ 
+
+ align:start position:0%
+in mathematical terms this is just
+another name for the tangent line to a
+
+ align:start position:0%
+another name for the tangent line to a
+ 
+
+ align:start position:0%
+another name for the tangent line to a
+function
+
+ align:start position:0%
+function
+ 
+
+ align:start position:0%
+function
+but the name suggests more linear
+
+ align:start position:0%
+but the name suggests more linear
+ 
+
+ align:start position:0%
+but the name suggests more linear
+approximations can be used to simplify
+
+ align:start position:0%
+approximations can be used to simplify
+ 
+
+ align:start position:0%
+approximations can be used to simplify
+mathematical models that are not
+
+ align:start position:0%
+mathematical models that are not
+ 
+
+ align:start position:0%
+mathematical models that are not
+analytically solvable
+
+ align:start position:0%
+analytically solvable
+ 
+
+ align:start position:0%
+analytically solvable
+the approximated model will have a
+
+ align:start position:0%
+the approximated model will have a
+ 
+
+ align:start position:0%
+the approximated model will have a
+solution that is only acceptable under
+
+ align:start position:0%
+solution that is only acceptable under
+ 
+
+ align:start position:0%
+solution that is only acceptable under
+suitable conditions
+
+ align:start position:0%
+suitable conditions
+ 
+
+ align:start position:0%
+suitable conditions
+however it can still illuminate the
+
+ align:start position:0%
+however it can still illuminate the
+ 
+
+ align:start position:0%
+however it can still illuminate the
+behavior of a system
+
+ align:start position:0%
+behavior of a system
+ 
+
+ align:start position:0%
+behavior of a system
+within a certain acceptable range
+
+ align:start position:0%
+within a certain acceptable range
+ 
+
+ align:start position:0%
+within a certain acceptable range
+before watching this video you should
+
+ align:start position:0%
+before watching this video you should
+ 
+
+ align:start position:0%
+before watching this video you should
+know the definition of the derivative
+
+ align:start position:0%
+know the definition of the derivative
+ 
+
+ align:start position:0%
+know the definition of the derivative
+and how to write the equation of a line
+
+ align:start position:0%
+and how to write the equation of a line
+ 
+
+ align:start position:0%
+and how to write the equation of a line
+with a given slope that passes through a
+
+ align:start position:0%
+with a given slope that passes through a
+ 
+
+ align:start position:0%
+with a given slope that passes through a
+given point
+
+ align:start position:0%
+given point
+ 
+
+ align:start position:0%
+given point
+after watching this video you should be
+
+ align:start position:0%
+after watching this video you should be
+ 
+
+ align:start position:0%
+after watching this video you should be
+able to recognize the linear
+
+ align:start position:0%
+able to recognize the linear
+ 
+
+ align:start position:0%
+able to recognize the linear
+approximation of a function
+
+ align:start position:0%
+approximation of a function
+ 
+
+ align:start position:0%
+approximation of a function
+as the tangent line to the function
+
+ align:start position:0%
+as the tangent line to the function
+ 
+
+ align:start position:0%
+as the tangent line to the function
+apply linear approximations to solve
+
+ align:start position:0%
+apply linear approximations to solve
+ 
+
+ align:start position:0%
+apply linear approximations to solve
+simple differential equations
+
+ align:start position:0%
+simple differential equations
+ 
+
+ align:start position:0%
+simple differential equations
+and explain the limitations of linear
+
+ align:start position:0%
+and explain the limitations of linear
+ 
+
+ align:start position:0%
+and explain the limitations of linear
+approximations both mathematically and
+
+ align:start position:0%
+approximations both mathematically and
+ 
+
+ align:start position:0%
+approximations both mathematically and
+graphically
+
+ align:start position:0%
+graphically
+ 
+
+ align:start position:0%
+graphically
+let's begin by defining the linear
+
+ align:start position:0%
+let's begin by defining the linear
+ 
+
+ align:start position:0%
+let's begin by defining the linear
+approximation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+recall that if a function is
+
+ align:start position:0%
+recall that if a function is
+ 
+
+ align:start position:0%
+recall that if a function is
+differentiable at a point c
+
+ align:start position:0%
+differentiable at a point c
+ 
+
+ align:start position:0%
+differentiable at a point c
+then when we zoom in on the point c the
+
+ align:start position:0%
+then when we zoom in on the point c the
+ 
+
+ align:start position:0%
+then when we zoom in on the point c the
+function begins to look more and more
+
+ align:start position:0%
+function begins to look more and more
+ 
+
+ align:start position:0%
+function begins to look more and more
+like a line
+
+ align:start position:0%
+like a line
+ 
+
+ align:start position:0%
+like a line
+this only works when the function is
+
+ align:start position:0%
+this only works when the function is
+ 
+
+ align:start position:0%
+this only works when the function is
+smooth it doesn't have any kinks
+
+ align:start position:0%
+smooth it doesn't have any kinks
+ 
+
+ align:start position:0%
+smooth it doesn't have any kinks
+corners or discontinuities
+
+ align:start position:0%
+corners or discontinuities
+ 
+
+ align:start position:0%
+corners or discontinuities
+given a function f of x which is
+
+ align:start position:0%
+given a function f of x which is
+ 
+
+ align:start position:0%
+given a function f of x which is
+differentiable at the point c
+
+ align:start position:0%
+differentiable at the point c
+ 
+
+ align:start position:0%
+differentiable at the point c
+we define the linear approximation to be
+
+ align:start position:0%
+we define the linear approximation to be
+ 
+
+ align:start position:0%
+we define the linear approximation to be
+the tangent line to the function at c
+
+ align:start position:0%
+the tangent line to the function at c
+ 
+
+ align:start position:0%
+the tangent line to the function at c
+this is the line whose slope
+
+ align:start position:0%
+this is the line whose slope
+ 
+
+ align:start position:0%
+this is the line whose slope
+equals f prime of c the derivative of f
+
+ align:start position:0%
+equals f prime of c the derivative of f
+ 
+
+ align:start position:0%
+equals f prime of c the derivative of f
+at c
+
+ align:start position:0%
+at c
+ 
+
+ align:start position:0%
+at c
+as an example let's look at the
+
+ align:start position:0%
+as an example let's look at the
+ 
+
+ align:start position:0%
+as an example let's look at the
+following cubic equation
+
+ align:start position:0%
+following cubic equation
+ 
+
+ align:start position:0%
+following cubic equation
+f of x is 1 30th x
+
+ align:start position:0%
+f of x is 1 30th x
+ 
+
+ align:start position:0%
+f of x is 1 30th x
+times x minus 2 times x plus 5.
+
+ align:start position:0%
+times x minus 2 times x plus 5.
+ 
+
+ align:start position:0%
+times x minus 2 times x plus 5.
+this function is differentiable
+
+ align:start position:0%
+this function is differentiable
+ 
+
+ align:start position:0%
+this function is differentiable
+everywhere and so in particular
+
+ align:start position:0%
+everywhere and so in particular
+ 
+
+ align:start position:0%
+everywhere and so in particular
+it's differentiable at the point x
+
+ align:start position:0%
+it's differentiable at the point x
+ 
+
+ align:start position:0%
+it's differentiable at the point x
+equals 3.
+
+ align:start position:0%
+equals 3.
+ 
+
+ align:start position:0%
+equals 3.
+find the equation of the tangent line to
+
+ align:start position:0%
+find the equation of the tangent line to
+ 
+
+ align:start position:0%
+find the equation of the tangent line to
+this cubic equation
+
+ align:start position:0%
+this cubic equation
+ 
+
+ align:start position:0%
+this cubic equation
+at x equals 3 for yourself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the meanwhile we've also found the
+
+ align:start position:0%
+in the meanwhile we've also found the
+ 
+
+ align:start position:0%
+in the meanwhile we've also found the
+equation for the tangent line
+
+ align:start position:0%
+equation for the tangent line
+ 
+
+ align:start position:0%
+equation for the tangent line
+to do this we found the value of the
+
+ align:start position:0%
+to do this we found the value of the
+ 
+
+ align:start position:0%
+to do this we found the value of the
+function at 3 which we found to be
+
+ align:start position:0%
+function at 3 which we found to be
+ 
+
+ align:start position:0%
+function at 3 which we found to be
+four-fifths
+
+ align:start position:0%
+four-fifths
+ 
+
+ align:start position:0%
+four-fifths
+and then we computed the derivative and
+
+ align:start position:0%
+and then we computed the derivative and
+ 
+
+ align:start position:0%
+and then we computed the derivative and
+evaluated it at x
+
+ align:start position:0%
+evaluated it at x
+ 
+
+ align:start position:0%
+evaluated it at x
+equals 3 which we found to be 7 6.
+
+ align:start position:0%
+equals 3 which we found to be 7 6.
+ 
+
+ align:start position:0%
+equals 3 which we found to be 7 6.
+we'll write the tangent line as t sub 3
+
+ align:start position:0%
+we'll write the tangent line as t sub 3
+ 
+
+ align:start position:0%
+we'll write the tangent line as t sub 3
+of x to remind
+
+ align:start position:0%
+of x to remind
+ 
+
+ align:start position:0%
+of x to remind
+us that we are finding the tangent to
+
+ align:start position:0%
+us that we are finding the tangent to
+ 
+
+ align:start position:0%
+us that we are finding the tangent to
+our function at the point three
+
+ align:start position:0%
+our function at the point three
+ 
+
+ align:start position:0%
+our function at the point three
+then the equation for the line can be
+
+ align:start position:0%
+then the equation for the line can be
+ 
+
+ align:start position:0%
+then the equation for the line can be
+written as t sub three of x
+
+ align:start position:0%
+written as t sub three of x
+ 
+
+ align:start position:0%
+written as t sub three of x
+equals four fifths plus seven sixths
+
+ align:start position:0%
+equals four fifths plus seven sixths
+ 
+
+ align:start position:0%
+equals four fifths plus seven sixths
+times x minus three
+
+ align:start position:0%
+times x minus three
+ 
+
+ align:start position:0%
+times x minus three
+let's take a look at the graphs of f of
+
+ align:start position:0%
+let's take a look at the graphs of f of
+ 
+
+ align:start position:0%
+let's take a look at the graphs of f of
+x and t sub 3 of x
+
+ align:start position:0%
+x and t sub 3 of x
+ 
+
+ align:start position:0%
+x and t sub 3 of x
+the function f x is graphed in red the
+
+ align:start position:0%
+the function f x is graphed in red the
+ 
+
+ align:start position:0%
+the function f x is graphed in red the
+further we zoom into the graph at x
+
+ align:start position:0%
+further we zoom into the graph at x
+ 
+
+ align:start position:0%
+further we zoom into the graph at x
+equals 3 the more it begins to resemble
+
+ align:start position:0%
+equals 3 the more it begins to resemble
+ 
+
+ align:start position:0%
+equals 3 the more it begins to resemble
+a straight line
+
+ align:start position:0%
+a straight line
+ 
+
+ align:start position:0%
+a straight line
+the slope of the line approaches the
+
+ align:start position:0%
+the slope of the line approaches the
+ 
+
+ align:start position:0%
+the slope of the line approaches the
+value of the slope at the tangent line
+
+ align:start position:0%
+value of the slope at the tangent line
+ 
+
+ align:start position:0%
+value of the slope at the tangent line
+at 3
+
+ align:start position:0%
+at 3
+ 
+
+ align:start position:0%
+at 3
+which is drawn in blue
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the tangent line certainly seems to be a
+
+ align:start position:0%
+the tangent line certainly seems to be a
+ 
+
+ align:start position:0%
+the tangent line certainly seems to be a
+good approximation to our function when
+
+ align:start position:0%
+good approximation to our function when
+ 
+
+ align:start position:0%
+good approximation to our function when
+we are close to x equals 3
+
+ align:start position:0%
+we are close to x equals 3
+ 
+
+ align:start position:0%
+we are close to x equals 3
+but what about when we zoom out is it
+
+ align:start position:0%
+but what about when we zoom out is it
+ 
+
+ align:start position:0%
+but what about when we zoom out is it
+still a good approximation
+
+ align:start position:0%
+still a good approximation
+ 
+
+ align:start position:0%
+still a good approximation
+let's give a mathematical justification
+
+ align:start position:0%
+let's give a mathematical justification
+ 
+
+ align:start position:0%
+let's give a mathematical justification
+that the tangent line
+
+ align:start position:0%
+that the tangent line
+ 
+
+ align:start position:0%
+that the tangent line
+is a good approximation our function is
+
+ align:start position:0%
+is a good approximation our function is
+ 
+
+ align:start position:0%
+is a good approximation our function is
+differentiable at a point say
+
+ align:start position:0%
+differentiable at a point say
+ 
+
+ align:start position:0%
+differentiable at a point say
+x equals 3. this is equivalent to the
+
+ align:start position:0%
+x equals 3. this is equivalent to the
+ 
+
+ align:start position:0%
+x equals 3. this is equivalent to the
+statement that when x is near 3
+
+ align:start position:0%
+statement that when x is near 3
+ 
+
+ align:start position:0%
+statement that when x is near 3
+the slope of the secant line is
+
+ align:start position:0%
+the slope of the secant line is
+ 
+
+ align:start position:0%
+the slope of the secant line is
+approximately equal
+
+ align:start position:0%
+approximately equal
+ 
+
+ align:start position:0%
+approximately equal
+to the slope of the tangent line that is
+
+ align:start position:0%
+to the slope of the tangent line that is
+ 
+
+ align:start position:0%
+to the slope of the tangent line that is
+for x near 3 f of x minus f of 3
+
+ align:start position:0%
+for x near 3 f of x minus f of 3
+ 
+
+ align:start position:0%
+for x near 3 f of x minus f of 3
+divided by x minus 3 is approximately
+
+ align:start position:0%
+divided by x minus 3 is approximately
+ 
+
+ align:start position:0%
+divided by x minus 3 is approximately
+equal to the value of the derivative at
+
+ align:start position:0%
+equal to the value of the derivative at
+ 
+
+ align:start position:0%
+equal to the value of the derivative at
+3.
+
+ align:start position:0%
+3.
+ 
+
+ align:start position:0%
+3.
+in order to see why these statements are
+
+ align:start position:0%
+in order to see why these statements are
+ 
+
+ align:start position:0%
+in order to see why these statements are
+equivalent we need to explain
+
+ align:start position:0%
+equivalent we need to explain
+ 
+
+ align:start position:0%
+equivalent we need to explain
+what we mean by approximately equal to
+
+ align:start position:0%
+what we mean by approximately equal to
+ 
+
+ align:start position:0%
+what we mean by approximately equal to
+this means that we can make the
+
+ align:start position:0%
+this means that we can make the
+ 
+
+ align:start position:0%
+this means that we can make the
+difference between these two sides as
+
+ align:start position:0%
+difference between these two sides as
+ 
+
+ align:start position:0%
+difference between these two sides as
+small as any error bound we choose
+
+ align:start position:0%
+small as any error bound we choose
+ 
+
+ align:start position:0%
+small as any error bound we choose
+provided that we choose x close enough
+
+ align:start position:0%
+provided that we choose x close enough
+ 
+
+ align:start position:0%
+provided that we choose x close enough
+to three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and this is exactly the definition of
+
+ align:start position:0%
+and this is exactly the definition of
+ 
+
+ align:start position:0%
+and this is exactly the definition of
+differentiability at the point three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to relate all of this to linear
+
+ align:start position:0%
+to relate all of this to linear
+ 
+
+ align:start position:0%
+to relate all of this to linear
+approximations we use a bit of algebra
+
+ align:start position:0%
+approximations we use a bit of algebra
+ 
+
+ align:start position:0%
+approximations we use a bit of algebra
+first we multiply both sides by x minus
+
+ align:start position:0%
+first we multiply both sides by x minus
+ 
+
+ align:start position:0%
+first we multiply both sides by x minus
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+and we get f of x minus f of 3
+
+ align:start position:0%
+and we get f of x minus f of 3
+ 
+
+ align:start position:0%
+and we get f of x minus f of 3
+approximately equal to f prime of 3
+
+ align:start position:0%
+approximately equal to f prime of 3
+ 
+
+ align:start position:0%
+approximately equal to f prime of 3
+times x minus 3.
+
+ align:start position:0%
+times x minus 3.
+ 
+
+ align:start position:0%
+times x minus 3.
+adding f of 3 to both sides we get that
+
+ align:start position:0%
+adding f of 3 to both sides we get that
+ 
+
+ align:start position:0%
+adding f of 3 to both sides we get that
+f of x is approximately equal to f
+
+ align:start position:0%
+f of x is approximately equal to f
+ 
+
+ align:start position:0%
+f of x is approximately equal to f
+of 3 plus f prime of 3 times
+
+ align:start position:0%
+of 3 plus f prime of 3 times
+ 
+
+ align:start position:0%
+of 3 plus f prime of 3 times
+x minus 3. and this right hand side
+
+ align:start position:0%
+x minus 3. and this right hand side
+ 
+
+ align:start position:0%
+x minus 3. and this right hand side
+is then the equation for the tangent
+
+ align:start position:0%
+is then the equation for the tangent
+ 
+
+ align:start position:0%
+is then the equation for the tangent
+line at three
+
+ align:start position:0%
+line at three
+ 
+
+ align:start position:0%
+line at three
+so indeed the tangent line closely
+
+ align:start position:0%
+so indeed the tangent line closely
+ 
+
+ align:start position:0%
+so indeed the tangent line closely
+approximates the function
+
+ align:start position:0%
+approximates the function
+ 
+
+ align:start position:0%
+approximates the function
+as long as x is close to three
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here we see the tangent line drawn in
+
+ align:start position:0%
+here we see the tangent line drawn in
+ 
+
+ align:start position:0%
+here we see the tangent line drawn in
+blue the function drawn in red the
+
+ align:start position:0%
+blue the function drawn in red the
+ 
+
+ align:start position:0%
+blue the function drawn in red the
+graphs demonstrate our mathematical
+
+ align:start position:0%
+graphs demonstrate our mathematical
+ 
+
+ align:start position:0%
+graphs demonstrate our mathematical
+proof
+
+ align:start position:0%
+proof
+ 
+
+ align:start position:0%
+proof
+that a tangent line is a good
+
+ align:start position:0%
+that a tangent line is a good
+ 
+
+ align:start position:0%
+that a tangent line is a good
+approximation near x equals three
+
+ align:start position:0%
+approximation near x equals three
+ 
+
+ align:start position:0%
+approximation near x equals three
+but the further we get from x equals
+
+ align:start position:0%
+but the further we get from x equals
+ 
+
+ align:start position:0%
+but the further we get from x equals
+three the worse the approximation
+
+ align:start position:0%
+three the worse the approximation
+ 
+
+ align:start position:0%
+three the worse the approximation
+seems you might have noticed that the
+
+ align:start position:0%
+seems you might have noticed that the
+ 
+
+ align:start position:0%
+seems you might have noticed that the
+function and the tangent line intersect
+
+ align:start position:0%
+function and the tangent line intersect
+ 
+
+ align:start position:0%
+function and the tangent line intersect
+at x equals minus nine
+
+ align:start position:0%
+at x equals minus nine
+ 
+
+ align:start position:0%
+at x equals minus nine
+is the tangent line a good approximation
+
+ align:start position:0%
+is the tangent line a good approximation
+ 
+
+ align:start position:0%
+is the tangent line a good approximation
+for the function near x
+
+ align:start position:0%
+for the function near x
+ 
+
+ align:start position:0%
+for the function near x
+equals minus nine
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no it isn't if we move a small distance
+
+ align:start position:0%
+no it isn't if we move a small distance
+ 
+
+ align:start position:0%
+no it isn't if we move a small distance
+along the tangent line away from x
+
+ align:start position:0%
+along the tangent line away from x
+ 
+
+ align:start position:0%
+along the tangent line away from x
+equals minus nine
+
+ align:start position:0%
+equals minus nine
+ 
+
+ align:start position:0%
+equals minus nine
+this does not model the behavior of the
+
+ align:start position:0%
+this does not model the behavior of the
+ 
+
+ align:start position:0%
+this does not model the behavior of the
+function near x equals minus nine
+
+ align:start position:0%
+function near x equals minus nine
+ 
+
+ align:start position:0%
+function near x equals minus nine
+this property is extremely important in
+
+ align:start position:0%
+this property is extremely important in
+ 
+
+ align:start position:0%
+this property is extremely important in
+applications
+
+ align:start position:0%
+applications
+ 
+
+ align:start position:0%
+applications
+no measurement or observed quantity is
+
+ align:start position:0%
+no measurement or observed quantity is
+ 
+
+ align:start position:0%
+no measurement or observed quantity is
+ever given exactly
+
+ align:start position:0%
+ever given exactly
+ 
+
+ align:start position:0%
+ever given exactly
+the linearization of a function that is
+
+ align:start position:0%
+the linearization of a function that is
+ 
+
+ align:start position:0%
+the linearization of a function that is
+differentiable at x
+
+ align:start position:0%
+differentiable at x
+ 
+
+ align:start position:0%
+differentiable at x
+equals c is just another name for the
+
+ align:start position:0%
+equals c is just another name for the
+ 
+
+ align:start position:0%
+equals c is just another name for the
+tangent line through c
+
+ align:start position:0%
+tangent line through c
+ 
+
+ align:start position:0%
+tangent line through c
+the key properties of this tangent line
+
+ align:start position:0%
+the key properties of this tangent line
+ 
+
+ align:start position:0%
+the key properties of this tangent line
+are that it shares the same value
+
+ align:start position:0%
+are that it shares the same value
+ 
+
+ align:start position:0%
+are that it shares the same value
+as the function and the same first
+
+ align:start position:0%
+as the function and the same first
+ 
+
+ align:start position:0%
+as the function and the same first
+derivative of the function at x equals c
+
+ align:start position:0%
+derivative of the function at x equals c
+ 
+
+ align:start position:0%
+derivative of the function at x equals c
+and we've seen through both graphical
+
+ align:start position:0%
+and we've seen through both graphical
+ 
+
+ align:start position:0%
+and we've seen through both graphical
+intuition and the definition of the
+
+ align:start position:0%
+intuition and the definition of the
+ 
+
+ align:start position:0%
+intuition and the definition of the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+that this linearization closely
+
+ align:start position:0%
+that this linearization closely
+ 
+
+ align:start position:0%
+that this linearization closely
+approximates the function for points x
+
+ align:start position:0%
+approximates the function for points x
+ 
+
+ align:start position:0%
+approximates the function for points x
+sufficiently close to c let's see how we
+
+ align:start position:0%
+sufficiently close to c let's see how we
+ 
+
+ align:start position:0%
+sufficiently close to c let's see how we
+can apply a linear approximation
+
+ align:start position:0%
+can apply a linear approximation
+ 
+
+ align:start position:0%
+can apply a linear approximation
+to simplify a problem
+
+ align:start position:0%
+to simplify a problem
+ 
+
+ align:start position:0%
+to simplify a problem
+let's suppose you are participating in
+
+ align:start position:0%
+let's suppose you are participating in
+ 
+
+ align:start position:0%
+let's suppose you are participating in
+undergraduate research
+
+ align:start position:0%
+undergraduate research
+ 
+
+ align:start position:0%
+undergraduate research
+in a chemistry lab you've been using a
+
+ align:start position:0%
+in a chemistry lab you've been using a
+ 
+
+ align:start position:0%
+in a chemistry lab you've been using a
+.01 molar solution of n2o5
+
+ align:start position:0%
+.01 molar solution of n2o5
+ 
+
+ align:start position:0%
+.01 molar solution of n2o5
+and you bring it out of the refrigerator
+
+ align:start position:0%
+and you bring it out of the refrigerator
+ 
+
+ align:start position:0%
+and you bring it out of the refrigerator
+at 9 00 am monday morning
+
+ align:start position:0%
+at 9 00 am monday morning
+ 
+
+ align:start position:0%
+at 9 00 am monday morning
+and promptly forget about it leaving it
+
+ align:start position:0%
+and promptly forget about it leaving it
+ 
+
+ align:start position:0%
+and promptly forget about it leaving it
+on the counter in the lab
+
+ align:start position:0%
+on the counter in the lab
+ 
+
+ align:start position:0%
+on the counter in the lab
+which is 25 degrees celsius when you
+
+ align:start position:0%
+which is 25 degrees celsius when you
+ 
+
+ align:start position:0%
+which is 25 degrees celsius when you
+realize you left the solution out
+
+ align:start position:0%
+realize you left the solution out
+ 
+
+ align:start position:0%
+realize you left the solution out
+one hour has passed you panic
+
+ align:start position:0%
+one hour has passed you panic
+ 
+
+ align:start position:0%
+one hour has passed you panic
+the problem is that n2o5 decomposes into
+
+ align:start position:0%
+the problem is that n2o5 decomposes into
+ 
+
+ align:start position:0%
+the problem is that n2o5 decomposes into
+no2
+
+ align:start position:0%
+no2
+ 
+
+ align:start position:0%
+no2
+and o2 at room temperature if the
+
+ align:start position:0%
+and o2 at room temperature if the
+ 
+
+ align:start position:0%
+and o2 at room temperature if the
+molarity of the solution has changed
+
+ align:start position:0%
+molarity of the solution has changed
+ 
+
+ align:start position:0%
+molarity of the solution has changed
+significantly
+
+ align:start position:0%
+significantly
+ 
+
+ align:start position:0%
+significantly
+it might ruin your experiments
+
+ align:start position:0%
+it might ruin your experiments
+ 
+
+ align:start position:0%
+it might ruin your experiments
+experiments have shown that the rate of
+
+ align:start position:0%
+experiments have shown that the rate of
+ 
+
+ align:start position:0%
+experiments have shown that the rate of
+decomposition follows first order
+
+ align:start position:0%
+decomposition follows first order
+ 
+
+ align:start position:0%
+decomposition follows first order
+kinetics
+
+ align:start position:0%
+kinetics
+ 
+
+ align:start position:0%
+kinetics
+this means that the instantaneous rate
+
+ align:start position:0%
+this means that the instantaneous rate
+ 
+
+ align:start position:0%
+this means that the instantaneous rate
+of change in concentration of n2o5
+
+ align:start position:0%
+of change in concentration of n2o5
+ 
+
+ align:start position:0%
+of change in concentration of n2o5
+is proportional to the concentration of
+
+ align:start position:0%
+is proportional to the concentration of
+ 
+
+ align:start position:0%
+is proportional to the concentration of
+n2o5
+
+ align:start position:0%
+n2o5
+ 
+
+ align:start position:0%
+n2o5
+the constant of proportionality k has
+
+ align:start position:0%
+the constant of proportionality k has
+ 
+
+ align:start position:0%
+the constant of proportionality k has
+been found experimentally
+
+ align:start position:0%
+been found experimentally
+ 
+
+ align:start position:0%
+been found experimentally
+to be 1.72 times 10 to the negative
+
+ align:start position:0%
+to be 1.72 times 10 to the negative
+ 
+
+ align:start position:0%
+to be 1.72 times 10 to the negative
+5 inverse seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because you're panicking you're having a
+
+ align:start position:0%
+because you're panicking you're having a
+ 
+
+ align:start position:0%
+because you're panicking you're having a
+hard time solving this differential
+
+ align:start position:0%
+hard time solving this differential
+ 
+
+ align:start position:0%
+hard time solving this differential
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+instead find the approximate
+
+ align:start position:0%
+instead find the approximate
+ 
+
+ align:start position:0%
+instead find the approximate
+decomposition in the n2o5
+
+ align:start position:0%
+decomposition in the n2o5
+ 
+
+ align:start position:0%
+decomposition in the n2o5
+solution after one hour using a linear
+
+ align:start position:0%
+solution after one hour using a linear
+ 
+
+ align:start position:0%
+solution after one hour using a linear
+approximation at time
+
+ align:start position:0%
+approximation at time
+ 
+
+ align:start position:0%
+approximation at time
+t equals zero note that because the
+
+ align:start position:0%
+t equals zero note that because the
+ 
+
+ align:start position:0%
+t equals zero note that because the
+reaction constant has units of inverse
+
+ align:start position:0%
+reaction constant has units of inverse
+ 
+
+ align:start position:0%
+reaction constant has units of inverse
+seconds
+
+ align:start position:0%
+seconds
+ 
+
+ align:start position:0%
+seconds
+the variable t must have units of
+
+ align:start position:0%
+the variable t must have units of
+ 
+
+ align:start position:0%
+the variable t must have units of
+seconds
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in order to produce a linear
+
+ align:start position:0%
+in order to produce a linear
+ 
+
+ align:start position:0%
+in order to produce a linear
+approximation at t equals zero
+
+ align:start position:0%
+approximation at t equals zero
+ 
+
+ align:start position:0%
+approximation at t equals zero
+we need two ingredients the
+
+ align:start position:0%
+we need two ingredients the
+ 
+
+ align:start position:0%
+we need two ingredients the
+concentration
+
+ align:start position:0%
+concentration
+ 
+
+ align:start position:0%
+concentration
+at time zero and the value of the
+
+ align:start position:0%
+at time zero and the value of the
+ 
+
+ align:start position:0%
+at time zero and the value of the
+derivative at time
+
+ align:start position:0%
+derivative at time
+ 
+
+ align:start position:0%
+derivative at time
+0. the initial concentration
+
+ align:start position:0%
+0. the initial concentration
+ 
+
+ align:start position:0%
+0. the initial concentration
+was .01 molar to find the value of the
+
+ align:start position:0%
+was .01 molar to find the value of the
+ 
+
+ align:start position:0%
+was .01 molar to find the value of the
+derivative
+
+ align:start position:0%
+derivative
+ 
+
+ align:start position:0%
+derivative
+we use our differential equation and we
+
+ align:start position:0%
+we use our differential equation and we
+ 
+
+ align:start position:0%
+we use our differential equation and we
+find that the value of the derivative
+
+ align:start position:0%
+find that the value of the derivative
+ 
+
+ align:start position:0%
+find that the value of the derivative
+at time t equals 0 is just minus k
+
+ align:start position:0%
+at time t equals 0 is just minus k
+ 
+
+ align:start position:0%
+at time t equals 0 is just minus k
+times the initial concentration at t
+
+ align:start position:0%
+times the initial concentration at t
+ 
+
+ align:start position:0%
+times the initial concentration at t
+equals 0
+
+ align:start position:0%
+equals 0
+ 
+
+ align:start position:0%
+equals 0
+or negative k times 0.01 molar
+
+ align:start position:0%
+or negative k times 0.01 molar
+ 
+
+ align:start position:0%
+or negative k times 0.01 molar
+remember that k has units of inverse
+
+ align:start position:0%
+remember that k has units of inverse
+ 
+
+ align:start position:0%
+remember that k has units of inverse
+seconds
+
+ align:start position:0%
+seconds
+ 
+
+ align:start position:0%
+seconds
+putting this all together into the
+
+ align:start position:0%
+putting this all together into the
+ 
+
+ align:start position:0%
+putting this all together into the
+formula for the tangent line at 0
+
+ align:start position:0%
+formula for the tangent line at 0
+ 
+
+ align:start position:0%
+formula for the tangent line at 0
+we see that the linear approximation is
+
+ align:start position:0%
+we see that the linear approximation is
+ 
+
+ align:start position:0%
+we see that the linear approximation is
+given by
+
+ align:start position:0%
+given by
+ 
+
+ align:start position:0%
+given by
+t 0 of t is .01 molar times
+
+ align:start position:0%
+t 0 of t is .01 molar times
+ 
+
+ align:start position:0%
+t 0 of t is .01 molar times
+1 minus kt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now we're interested in approximating
+
+ align:start position:0%
+now we're interested in approximating
+ 
+
+ align:start position:0%
+now we're interested in approximating
+the value at 1 hour or
+
+ align:start position:0%
+the value at 1 hour or
+ 
+
+ align:start position:0%
+the value at 1 hour or
+3 600 seconds plugging in the value for
+
+ align:start position:0%
+3 600 seconds plugging in the value for
+ 
+
+ align:start position:0%
+3 600 seconds plugging in the value for
+k
+
+ align:start position:0%
+k
+ 
+
+ align:start position:0%
+k
+we find that to two significant figures
+
+ align:start position:0%
+we find that to two significant figures
+ 
+
+ align:start position:0%
+we find that to two significant figures
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+zero at thirty six hundred seconds
+
+ align:start position:0%
+zero at thirty six hundred seconds
+ 
+
+ align:start position:0%
+zero at thirty six hundred seconds
+equals point zero zero
+
+ align:start position:0%
+equals point zero zero
+ 
+
+ align:start position:0%
+equals point zero zero
+nine four molar so the molarity is not
+
+ align:start position:0%
+nine four molar so the molarity is not
+ 
+
+ align:start position:0%
+nine four molar so the molarity is not
+so different
+
+ align:start position:0%
+so different
+ 
+
+ align:start position:0%
+so different
+now you are feeling relieved so when you
+
+ align:start position:0%
+now you are feeling relieved so when you
+ 
+
+ align:start position:0%
+now you are feeling relieved so when you
+look back at the reaction rate
+
+ align:start position:0%
+look back at the reaction rate
+ 
+
+ align:start position:0%
+look back at the reaction rate
+you realize that in fact a first order
+
+ align:start position:0%
+you realize that in fact a first order
+ 
+
+ align:start position:0%
+you realize that in fact a first order
+reaction rate is telling you
+
+ align:start position:0%
+reaction rate is telling you
+ 
+
+ align:start position:0%
+reaction rate is telling you
+that the concentration is some function
+
+ align:start position:0%
+that the concentration is some function
+ 
+
+ align:start position:0%
+that the concentration is some function
+of time whose derivative is proportional
+
+ align:start position:0%
+of time whose derivative is proportional
+ 
+
+ align:start position:0%
+of time whose derivative is proportional
+to itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the function with this property is the
+
+ align:start position:0%
+the function with this property is the
+ 
+
+ align:start position:0%
+the function with this property is the
+exponential function
+
+ align:start position:0%
+exponential function
+ 
+
+ align:start position:0%
+exponential function
+so the concentration function is equal
+
+ align:start position:0%
+so the concentration function is equal
+ 
+
+ align:start position:0%
+so the concentration function is equal
+to some constant
+
+ align:start position:0%
+to some constant
+ 
+
+ align:start position:0%
+to some constant
+times e to the negative kt
+
+ align:start position:0%
+times e to the negative kt
+ 
+
+ align:start position:0%
+times e to the negative kt
+the constant must be the initial
+
+ align:start position:0%
+the constant must be the initial
+ 
+
+ align:start position:0%
+the constant must be the initial
+concentration which is 0.01 molar
+
+ align:start position:0%
+concentration which is 0.01 molar
+ 
+
+ align:start position:0%
+concentration which is 0.01 molar
+so the concentration of n2o5 at time t
+
+ align:start position:0%
+so the concentration of n2o5 at time t
+ 
+
+ align:start position:0%
+so the concentration of n2o5 at time t
+is equal to 0.01 times e to the negative
+
+ align:start position:0%
+is equal to 0.01 times e to the negative
+ 
+
+ align:start position:0%
+is equal to 0.01 times e to the negative
+kt
+
+ align:start position:0%
+kt
+ 
+
+ align:start position:0%
+kt
+evaluating this expression at time t
+
+ align:start position:0%
+evaluating this expression at time t
+ 
+
+ align:start position:0%
+evaluating this expression at time t
+equals 3600
+
+ align:start position:0%
+equals 3600
+ 
+
+ align:start position:0%
+equals 3600
+we find that the exact concentration is
+
+ align:start position:0%
+we find that the exact concentration is
+ 
+
+ align:start position:0%
+we find that the exact concentration is
+also
+
+ align:start position:0%
+also
+ 
+
+ align:start position:0%
+also
+.0094 molar to two significant figures
+
+ align:start position:0%
+.0094 molar to two significant figures
+ 
+
+ align:start position:0%
+.0094 molar to two significant figures
+to be more precise we can look at the
+
+ align:start position:0%
+to be more precise we can look at the
+ 
+
+ align:start position:0%
+to be more precise we can look at the
+error which is the absolute value of the
+
+ align:start position:0%
+error which is the absolute value of the
+ 
+
+ align:start position:0%
+error which is the absolute value of the
+exact solution minus the approximate
+
+ align:start position:0%
+exact solution minus the approximate
+ 
+
+ align:start position:0%
+exact solution minus the approximate
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+all divided by the value of the exact
+
+ align:start position:0%
+all divided by the value of the exact
+ 
+
+ align:start position:0%
+all divided by the value of the exact
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+the error at time t equals 3 600 seconds
+
+ align:start position:0%
+the error at time t equals 3 600 seconds
+ 
+
+ align:start position:0%
+the error at time t equals 3 600 seconds
+is .002 or 0.2 percent
+
+ align:start position:0%
+is .002 or 0.2 percent
+ 
+
+ align:start position:0%
+is .002 or 0.2 percent
+this is really quite good generally
+
+ align:start position:0%
+this is really quite good generally
+ 
+
+ align:start position:0%
+this is really quite good generally
+speaking
+
+ align:start position:0%
+speaking
+ 
+
+ align:start position:0%
+speaking
+we might consider an error of less than
+
+ align:start position:0%
+we might consider an error of less than
+ 
+
+ align:start position:0%
+we might consider an error of less than
+five percent to be acceptable
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so our linear approximation was
+
+ align:start position:0%
+so our linear approximation was
+ 
+
+ align:start position:0%
+so our linear approximation was
+definitely within the acceptable range
+
+ align:start position:0%
+definitely within the acceptable range
+ 
+
+ align:start position:0%
+definitely within the acceptable range
+one hour later but now it's tuesday
+
+ align:start position:0%
+one hour later but now it's tuesday
+ 
+
+ align:start position:0%
+one hour later but now it's tuesday
+you leave the n205 on the counter for a
+
+ align:start position:0%
+you leave the n205 on the counter for a
+ 
+
+ align:start position:0%
+you leave the n205 on the counter for a
+full 10 hours
+
+ align:start position:0%
+full 10 hours
+ 
+
+ align:start position:0%
+full 10 hours
+curses we know that the exact solution
+
+ align:start position:0%
+curses we know that the exact solution
+ 
+
+ align:start position:0%
+curses we know that the exact solution
+is an exponential decay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so do you think that the linear
+
+ align:start position:0%
+so do you think that the linear
+ 
+
+ align:start position:0%
+so do you think that the linear
+approximation will be an overestimate
+
+ align:start position:0%
+approximation will be an overestimate
+ 
+
+ align:start position:0%
+approximation will be an overestimate
+an underestimate or equal to the exact
+
+ align:start position:0%
+an underestimate or equal to the exact
+ 
+
+ align:start position:0%
+an underestimate or equal to the exact
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+after 10 hours
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the linear approximation of the
+
+ align:start position:0%
+the linear approximation of the
+ 
+
+ align:start position:0%
+the linear approximation of the
+concentration after 10 hours
+
+ align:start position:0%
+concentration after 10 hours
+ 
+
+ align:start position:0%
+concentration after 10 hours
+at room temperature is t 0 of
+
+ align:start position:0%
+at room temperature is t 0 of
+ 
+
+ align:start position:0%
+at room temperature is t 0 of
+36 000 seconds equal to .0038 molar
+
+ align:start position:0%
+36 000 seconds equal to .0038 molar
+ 
+
+ align:start position:0%
+36 000 seconds equal to .0038 molar
+the exact solution of the concentration
+
+ align:start position:0%
+the exact solution of the concentration
+ 
+
+ align:start position:0%
+the exact solution of the concentration
+after 10 hours
+
+ align:start position:0%
+after 10 hours
+ 
+
+ align:start position:0%
+after 10 hours
+is .0054 molar
+
+ align:start position:0%
+is .0054 molar
+ 
+
+ align:start position:0%
+is .0054 molar
+comparing these two solutions we see
+
+ align:start position:0%
+comparing these two solutions we see
+ 
+
+ align:start position:0%
+comparing these two solutions we see
+that the linear approximation
+
+ align:start position:0%
+that the linear approximation
+ 
+
+ align:start position:0%
+that the linear approximation
+is an underestimate as we would expect
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the error is 0.29 or 29 percent
+
+ align:start position:0%
+the error is 0.29 or 29 percent
+ 
+
+ align:start position:0%
+the error is 0.29 or 29 percent
+so a linear approximation is definitely
+
+ align:start position:0%
+so a linear approximation is definitely
+ 
+
+ align:start position:0%
+so a linear approximation is definitely
+not acceptable
+
+ align:start position:0%
+not acceptable
+ 
+
+ align:start position:0%
+not acceptable
+for this time range
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but now you begin to wonder for what
+
+ align:start position:0%
+but now you begin to wonder for what
+ 
+
+ align:start position:0%
+but now you begin to wonder for what
+times is the linear approximation at t
+
+ align:start position:0%
+times is the linear approximation at t
+ 
+
+ align:start position:0%
+times is the linear approximation at t
+equals 0 within the 5 percent error of
+
+ align:start position:0%
+equals 0 within the 5 percent error of
+ 
+
+ align:start position:0%
+equals 0 within the 5 percent error of
+the exact solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because we are only interested in
+
+ align:start position:0%
+because we are only interested in
+ 
+
+ align:start position:0%
+because we are only interested in
+positive time values
+
+ align:start position:0%
+positive time values
+ 
+
+ align:start position:0%
+positive time values
+you should have found that the
+
+ align:start position:0%
+you should have found that the
+ 
+
+ align:start position:0%
+you should have found that the
+approximation is acceptable for positive
+
+ align:start position:0%
+approximation is acceptable for positive
+ 
+
+ align:start position:0%
+approximation is acceptable for positive
+times
+
+ align:start position:0%
+times
+ 
+
+ align:start position:0%
+times
+t less than 16 700 seconds which is
+
+ align:start position:0%
+t less than 16 700 seconds which is
+ 
+
+ align:start position:0%
+t less than 16 700 seconds which is
+about
+
+ align:start position:0%
+about
+ 
+
+ align:start position:0%
+about
+4.5 hours now that you've carefully
+
+ align:start position:0%
+4.5 hours now that you've carefully
+ 
+
+ align:start position:0%
+4.5 hours now that you've carefully
+examined this problem using linear
+
+ align:start position:0%
+examined this problem using linear
+ 
+
+ align:start position:0%
+examined this problem using linear
+approximation
+
+ align:start position:0%
+approximation
+ 
+
+ align:start position:0%
+approximation
+it's probably time to tell your graduate
+
+ align:start position:0%
+it's probably time to tell your graduate
+ 
+
+ align:start position:0%
+it's probably time to tell your graduate
+student advisor
+
+ align:start position:0%
+student advisor
+ 
+
+ align:start position:0%
+student advisor
+that you need to order a new batch of
+
+ align:start position:0%
+that you need to order a new batch of
+ 
+
+ align:start position:0%
+that you need to order a new batch of
+0.01 molar n2o5
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's review the linear approximation to
+
+ align:start position:0%
+let's review the linear approximation to
+ 
+
+ align:start position:0%
+let's review the linear approximation to
+a function at a point c
+
+ align:start position:0%
+a function at a point c
+ 
+
+ align:start position:0%
+a function at a point c
+is the tangent line of a function at c
+
+ align:start position:0%
+is the tangent line of a function at c
+ 
+
+ align:start position:0%
+is the tangent line of a function at c
+this linear approximation
+
+ align:start position:0%
+this linear approximation
+ 
+
+ align:start position:0%
+this linear approximation
+only accurately models the function for
+
+ align:start position:0%
+only accurately models the function for
+ 
+
+ align:start position:0%
+only accurately models the function for
+points sufficiently close to c
+
+ align:start position:0%
+points sufficiently close to c
+ 
+
+ align:start position:0%
+points sufficiently close to c
+it is easy to read off the derivative at
+
+ align:start position:0%
+it is easy to read off the derivative at
+ 
+
+ align:start position:0%
+it is easy to read off the derivative at
+a point
+
+ align:start position:0%
+a point
+ 
+
+ align:start position:0%
+a point
+from a differential equation and thus
+
+ align:start position:0%
+from a differential equation and thus
+ 
+
+ align:start position:0%
+from a differential equation and thus
+give a linear approximation to the
+
+ align:start position:0%
+give a linear approximation to the
+ 
+
+ align:start position:0%
+give a linear approximation to the
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+in our example with the concentration of
+
+ align:start position:0%
+in our example with the concentration of
+ 
+
+ align:start position:0%
+in our example with the concentration of
+n2o5
+
+ align:start position:0%
+n2o5
+ 
+
+ align:start position:0%
+n2o5
+we could also solve the differential
+
+ align:start position:0%
+we could also solve the differential
+ 
+
+ align:start position:0%
+we could also solve the differential
+equation exactly
+
+ align:start position:0%
+equation exactly
+ 
+
+ align:start position:0%
+equation exactly
+and demonstrate that the approximation
+
+ align:start position:0%
+and demonstrate that the approximation
+ 
+
+ align:start position:0%
+and demonstrate that the approximation
+was acceptable
+
+ align:start position:0%
+was acceptable
+ 
+
+ align:start position:0%
+was acceptable
+near the point of approximation t equals
+
+ align:start position:0%
+near the point of approximation t equals
+ 
+
+ align:start position:0%
+near the point of approximation t equals
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+but not so for larger time intervals
+
+ align:start position:0%
+but not so for larger time intervals
+ 
+
+ align:start position:0%
+but not so for larger time intervals
+notice that we used this simple example
+
+ align:start position:0%
+notice that we used this simple example
+ 
+
+ align:start position:0%
+notice that we used this simple example
+to illustrate linear approximation
+
+ align:start position:0%
+to illustrate linear approximation
+ 
+
+ align:start position:0%
+to illustrate linear approximation
+because we could also solve it exactly
+
+ align:start position:0%
+because we could also solve it exactly
+ 
+
+ align:start position:0%
+because we could also solve it exactly
+and use the exact solution to determine
+
+ align:start position:0%
+and use the exact solution to determine
+ 
+
+ align:start position:0%
+and use the exact solution to determine
+the error
+
+ align:start position:0%
+the error
+ 
+
+ align:start position:0%
+the error
+this is somewhat misleading since we
+
+ align:start position:0%
+this is somewhat misleading since we
+ 
+
+ align:start position:0%
+this is somewhat misleading since we
+often want to use linear approximation
+
+ align:start position:0%
+often want to use linear approximation
+ 
+
+ align:start position:0%
+often want to use linear approximation
+precisely when the differential equation
+
+ align:start position:0%
+precisely when the differential equation
+ 
+
+ align:start position:0%
+precisely when the differential equation
+that describes our physical situation
+
+ align:start position:0%
+that describes our physical situation
+ 
+
+ align:start position:0%
+that describes our physical situation
+does not have an analytic solution
+
+ align:start position:0%
+does not have an analytic solution
+ 
+
+ align:start position:0%
+does not have an analytic solution
+so you may wonder is there any way to
+
+ align:start position:0%
+so you may wonder is there any way to
+ 
+
+ align:start position:0%
+so you may wonder is there any way to
+estimate the error in a linear
+
+ align:start position:0%
+estimate the error in a linear
+ 
+
+ align:start position:0%
+estimate the error in a linear
+approximation without knowing the exact
+
+ align:start position:0%
+approximation without knowing the exact
+ 
+
+ align:start position:0%
+approximation without knowing the exact
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+the answer is yes however it involves
+
+ align:start position:0%
+the answer is yes however it involves
+ 
+
+ align:start position:0%
+the answer is yes however it involves
+taylor's remainder theorem
+
+ align:start position:0%
+taylor's remainder theorem
+ 
+
+ align:start position:0%
+taylor's remainder theorem
+which finds an acceptable range in terms
+
+ align:start position:0%
+which finds an acceptable range in terms
+ 
+
+ align:start position:0%
+which finds an acceptable range in terms
+of higher order derivatives
+
+ align:start position:0%
+of higher order derivatives
+ 
+
+ align:start position:0%
+of higher order derivatives
+and is beyond the scope of this video
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/p_10lgn2BiI.txt b/p_10lgn2BiI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..307ce3a2fbb115dd77699134cdbcd073106ce776
--- /dev/null
+++ b/p_10lgn2BiI.txt
@@ -0,0 +1,11699 @@
+align:start position:0%
+ 
+so in the lectures are going to record
+
+ align:start position:0%
+so in the lectures are going to record
+ 
+
+ align:start position:0%
+so in the lectures are going to record
+today we're going to conclude cosmology
+
+ align:start position:0%
+today we're going to conclude cosmology
+ 
+
+ align:start position:0%
+today we're going to conclude cosmology
+and then we're going to begin talking
+
+ align:start position:0%
+and then we're going to begin talking
+ 
+
+ align:start position:0%
+and then we're going to begin talking
+about another system in which we solve
+
+ align:start position:0%
+about another system in which we solve
+ 
+
+ align:start position:0%
+about another system in which we solve
+the Einstein field equations using a
+
+ align:start position:0%
+the Einstein field equations using a
+ 
+
+ align:start position:0%
+the Einstein field equations using a
+symmetry so this is one where we will
+
+ align:start position:0%
+symmetry so this is one where we will
+ 
+
+ align:start position:0%
+symmetry so this is one where we will
+again consider systems that are
+
+ align:start position:0%
+again consider systems that are
+ 
+
+ align:start position:0%
+again consider systems that are
+spherically symmetric but we're gonna
+
+ align:start position:0%
+spherically symmetric but we're gonna
+ 
+
+ align:start position:0%
+spherically symmetric but we're gonna
+consider them to be compact ok in other
+
+ align:start position:0%
+consider them to be compact ok in other
+ 
+
+ align:start position:0%
+consider them to be compact ok in other
+words things that are sort of rather
+
+ align:start position:0%
+words things that are sort of rather
+ 
+
+ align:start position:0%
+words things that are sort of rather
+than filling the whole universe the
+
+ align:start position:0%
+than filling the whole universe the
+ 
+
+ align:start position:0%
+than filling the whole universe the
+space-time that arises from a source
+
+ align:start position:0%
+space-time that arises from a source
+ 
+
+ align:start position:0%
+space-time that arises from a source
+that's localized in some particular
+
+ align:start position:0%
+that's localized in some particular
+ 
+
+ align:start position:0%
+that's localized in some particular
+region in space so let me just do a
+
+ align:start position:0%
+region in space so let me just do a
+ 
+
+ align:start position:0%
+region in space so let me just do a
+quick recap of what we did in the
+
+ align:start position:0%
+quick recap of what we did in the
+ 
+
+ align:start position:0%
+quick recap of what we did in the
+previous lectures previous lecture that
+
+ align:start position:0%
+previous lectures previous lecture that
+ 
+
+ align:start position:0%
+previous lectures previous lecture that
+I recorded so by arguing solely from the
+
+ align:start position:0%
+I recorded so by arguing solely from the
+ 
+
+ align:start position:0%
+I recorded so by arguing solely from the
+basis of how to make a space-time that
+
+ align:start position:0%
+basis of how to make a space-time that
+ 
+
+ align:start position:0%
+basis of how to make a space-time that
+is as symmetric as possible in space but
+
+ align:start position:0%
+is as symmetric as possible in space but
+ 
+
+ align:start position:0%
+is as symmetric as possible in space but
+has a time asymmetry so the past and the
+
+ align:start position:0%
+has a time asymmetry so the past and the
+ 
+
+ align:start position:0%
+has a time asymmetry so the past and the
+future looked different we came up with
+
+ align:start position:0%
+future looked different we came up with
+ 
+
+ align:start position:0%
+future looked different we came up with
+the robertson-walker metric okay which i
+
+ align:start position:0%
+the robertson-walker metric okay which i
+ 
+
+ align:start position:0%
+the robertson-walker metric okay which i
+will call the r:w metric which has the
+
+ align:start position:0%
+will call the r:w metric which has the
+ 
+
+ align:start position:0%
+will call the r:w metric which has the
+form i've written there on the top line
+
+ align:start position:0%
+form i've written there on the top line
+ 
+
+ align:start position:0%
+form i've written there on the top line
+there were actually several forms for
+
+ align:start position:0%
+there were actually several forms for
+ 
+
+ align:start position:0%
+there were actually several forms for
+this I've actually written down two
+
+ align:start position:0%
+this I've actually written down two
+ 
+
+ align:start position:0%
+this I've actually written down two
+variants of it on the board here key
+
+ align:start position:0%
+variants of it on the board here key
+ 
+
+ align:start position:0%
+variants of it on the board here key
+things which I want to highlight is that
+
+ align:start position:0%
+things which I want to highlight is that
+ 
+
+ align:start position:0%
+things which I want to highlight is that
+there is in the way I've written it on
+
+ align:start position:0%
+there is in the way I've written it on
+ 
+
+ align:start position:0%
+there is in the way I've written it on
+the first line there's a hidden scale
+
+ align:start position:0%
+the first line there's a hidden scale
+ 
+
+ align:start position:0%
+the first line there's a hidden scale
+and there are zero which you can think
+
+ align:start position:0%
+and there are zero which you can think
+ 
+
+ align:start position:0%
+and there are zero which you can think
+of as essentially setting an overall
+
+ align:start position:0%
+of as essentially setting an overall
+ 
+
+ align:start position:0%
+of as essentially setting an overall
+length scale to everything that could be
+
+ align:start position:0%
+length scale to everything that could be
+ 
+
+ align:start position:0%
+length scale to everything that could be
+measured there is a parameter either K
+
+ align:start position:0%
+measured there is a parameter either K
+ 
+
+ align:start position:0%
+measured there is a parameter either K
+or Kappa K is either minus one zero or
+
+ align:start position:0%
+or Kappa K is either minus one zero or
+ 
+
+ align:start position:0%
+or Kappa K is either minus one zero or
+one Kappa is just K with a factor of
+
+ align:start position:0%
+one Kappa is just K with a factor of
+ 
+
+ align:start position:0%
+one Kappa is just K with a factor of
+that length scale squared thrown in
+
+ align:start position:0%
+that length scale squared thrown in
+ 
+
+ align:start position:0%
+that length scale squared thrown in
+there we define the overall scale factor
+
+ align:start position:0%
+there we define the overall scale factor
+ 
+
+ align:start position:0%
+there we define the overall scale factor
+to be it's just a it's a number and we
+
+ align:start position:0%
+to be it's just a it's a number and we
+ 
+
+ align:start position:0%
+to be it's just a it's a number and we
+define it so that its value is one right
+
+ align:start position:0%
+define it so that its value is one right
+ 
+
+ align:start position:0%
+define it so that its value is one right
+now and then everything is scaled to the
+
+ align:start position:0%
+now and then everything is scaled to the
+ 
+
+ align:start position:0%
+now and then everything is scaled to the
+way distances look at the present time a
+
+ align:start position:0%
+way distances look at the present time a
+ 
+
+ align:start position:0%
+way distances look at the present time a
+second form of that to me which is
+
+ align:start position:0%
+second form of that to me which is
+ 
+
+ align:start position:0%
+second form of that to me which is
+essentially that's a change of variables
+
+ align:start position:0%
+essentially that's a change of variables
+ 
+
+ align:start position:0%
+essentially that's a change of variables
+as you change your you change your
+
+ align:start position:0%
+as you change your you change your
+ 
+
+ align:start position:0%
+as you change your you change your
+radial coordinates to this parameter KY
+
+ align:start position:0%
+radial coordinates to this parameter KY
+ 
+
+ align:start position:0%
+radial coordinates to this parameter KY
+and depending on the value of K what you
+
+ align:start position:0%
+and depending on the value of K what you
+ 
+
+ align:start position:0%
+and depending on the value of K what you
+find then is that the relationship
+
+ align:start position:0%
+find then is that the relationship
+ 
+
+ align:start position:0%
+find then is that the relationship
+between the radius R and the coordinate
+
+ align:start position:0%
+between the radius R and the coordinate
+ 
+
+ align:start position:0%
+between the radius R and the coordinate
+Chi if K
+
+ align:start position:0%
+Chi if K
+ 
+
+ align:start position:0%
+Chi if K
+equals one you have what we call a
+
+ align:start position:0%
+equals one you have what we call a
+ 
+
+ align:start position:0%
+equals one you have what we call a
+closed universe and the radius is equal
+
+ align:start position:0%
+closed universe and the radius is equal
+ 
+
+ align:start position:0%
+closed universe and the radius is equal
+to sign you sign the parameter Chi if
+
+ align:start position:0%
+to sign you sign the parameter Chi if
+ 
+
+ align:start position:0%
+to sign you sign the parameter Chi if
+you have an open universe K equals minus
+
+ align:start position:0%
+you have an open universe K equals minus
+ 
+
+ align:start position:0%
+you have an open universe K equals minus
+1 then the radius is the Cinch of that
+
+ align:start position:0%
+1 then the radius is the Cinch of that
+ 
+
+ align:start position:0%
+1 then the radius is the Cinch of that
+parameter chi and for a flat universe k
+
+ align:start position:0%
+parameter chi and for a flat universe k
+ 
+
+ align:start position:0%
+parameter chi and for a flat universe k
+equals 0
+
+ align:start position:0%
+equals 0
+ 
+
+ align:start position:0%
+equals 0
+they are simply 1 is just the other
+
+ align:start position:0%
+they are simply 1 is just the other
+ 
+
+ align:start position:0%
+they are simply 1 is just the other
+modulo a choice of units with the r 0
+
+ align:start position:0%
+modulo a choice of units with the r 0
+ 
+
+ align:start position:0%
+modulo a choice of units with the r 0
+there all this is just geometry ok so I
+
+ align:start position:0%
+there all this is just geometry ok so I
+ 
+
+ align:start position:0%
+there all this is just geometry ok so I
+when you write this down you're agnostic
+
+ align:start position:0%
+when you write this down you're agnostic
+ 
+
+ align:start position:0%
+when you write this down you're agnostic
+about the form of a and you have no
+
+ align:start position:0%
+about the form of a and you have no
+ 
+
+ align:start position:0%
+about the form of a and you have no
+information about the value of K so to
+
+ align:start position:0%
+information about the value of K so to
+ 
+
+ align:start position:0%
+information about the value of K so to
+get more insight into what's going on
+
+ align:start position:0%
+get more insight into what's going on
+ 
+
+ align:start position:0%
+get more insight into what's going on
+you need a couple this to your source
+
+ align:start position:0%
+you need a couple this to your source
+ 
+
+ align:start position:0%
+you need a couple this to your source
+and so we take these things and using
+
+ align:start position:0%
+and so we take these things and using
+ 
+
+ align:start position:0%
+and so we take these things and using
+the Einstein field equations you equate
+
+ align:start position:0%
+the Einstein field equations you equate
+ 
+
+ align:start position:0%
+the Einstein field equations you equate
+these two a perfect fluid stress energy
+
+ align:start position:0%
+these two a perfect fluid stress energy
+ 
+
+ align:start position:0%
+these two a perfect fluid stress energy
+tensor what you what pops out of that
+
+ align:start position:0%
+tensor what you what pops out of that
+ 
+
+ align:start position:0%
+tensor what you what pops out of that
+are a pair of equations that arise from
+
+ align:start position:0%
+are a pair of equations that arise from
+ 
+
+ align:start position:0%
+are a pair of equations that arise from
+the Einstein field equations I call
+
+ align:start position:0%
+the Einstein field equations I call
+ 
+
+ align:start position:0%
+the Einstein field equations I call
+these f1 and f2 these are the two
+
+ align:start position:0%
+these f1 and f2 these are the two
+ 
+
+ align:start position:0%
+these f1 and f2 these are the two
+Friedmann equations f1 tells me about
+
+ align:start position:0%
+Friedmann equations f1 tells me about
+ 
+
+ align:start position:0%
+Friedmann equations f1 tells me about
+the velocity associate at that expansion
+
+ align:start position:0%
+the velocity associate at that expansion
+ 
+
+ align:start position:0%
+the velocity associate at that expansion
+parameter this is an a dot divided by a
+
+ align:start position:0%
+parameter this is an a dot divided by a
+ 
+
+ align:start position:0%
+parameter this is an a dot divided by a
+squared we call that the Hubble
+
+ align:start position:0%
+squared we call that the Hubble
+ 
+
+ align:start position:0%
+squared we call that the Hubble
+parameter H of a squared and it's
+
+ align:start position:0%
+parameter H of a squared and it's
+ 
+
+ align:start position:0%
+parameter H of a squared and it's
+related to the density of the source of
+
+ align:start position:0%
+related to the density of the source of
+ 
+
+ align:start position:0%
+related to the density of the source of
+your universe as well as this Kappa term
+
+ align:start position:0%
+your universe as well as this Kappa term
+ 
+
+ align:start position:0%
+your universe as well as this Kappa term
+ok and as we saw last time we can get
+
+ align:start position:0%
+ok and as we saw last time we can get
+ 
+
+ align:start position:0%
+ok and as we saw last time we can get
+some information about Kappa from this
+
+ align:start position:0%
+some information about Kappa from this
+ 
+
+ align:start position:0%
+some information about Kappa from this
+equation the second Freedman equation
+
+ align:start position:0%
+equation the second Freedman equation
+ 
+
+ align:start position:0%
+equation the second Freedman equation
+relates the acceleration of this
+
+ align:start position:0%
+relates the acceleration of this
+ 
+
+ align:start position:0%
+relates the acceleration of this
+expansion term a double dot dot by the
+
+ align:start position:0%
+expansion term a double dot dot by the
+ 
+
+ align:start position:0%
+expansion term a double dot dot by the
+way is d by DT a double dot divided by a
+
+ align:start position:0%
+way is d by DT a double dot divided by a
+ 
+
+ align:start position:0%
+way is d by DT a double dot divided by a
+is simply related to a quantity that is
+
+ align:start position:0%
+is simply related to a quantity that is
+ 
+
+ align:start position:0%
+is simply related to a quantity that is
+the density plus 3 times the pressure of
+
+ align:start position:0%
+the density plus 3 times the pressure of
+ 
+
+ align:start position:0%
+the density plus 3 times the pressure of
+this perfect fluid that makes up our
+
+ align:start position:0%
+this perfect fluid that makes up our
+ 
+
+ align:start position:0%
+this perfect fluid that makes up our
+universe we also find by requiring that
+
+ align:start position:0%
+universe we also find by requiring that
+ 
+
+ align:start position:0%
+universe we also find by requiring that
+local energy conservation be held in
+
+ align:start position:0%
+local energy conservation be held in
+ 
+
+ align:start position:0%
+local energy conservation be held in
+other words that your stress energy
+
+ align:start position:0%
+other words that your stress energy
+ 
+
+ align:start position:0%
+other words that your stress energy
+tensor be divergence free we have a
+
+ align:start position:0%
+tensor be divergence free we have a
+ 
+
+ align:start position:0%
+tensor be divergence free we have a
+constraint that relates the amount of
+
+ align:start position:0%
+constraint that relates the amount of
+ 
+
+ align:start position:0%
+constraint that relates the amount of
+energy the rate of change of energy and
+
+ align:start position:0%
+energy the rate of change of energy and
+ 
+
+ align:start position:0%
+energy the rate of change of energy and
+a fiducial volume to the negative of
+
+ align:start position:0%
+a fiducial volume to the negative of
+ 
+
+ align:start position:0%
+a fiducial volume to the negative of
+pressure times the rate of change of
+
+ align:start position:0%
+pressure times the rate of change of
+ 
+
+ align:start position:0%
+pressure times the rate of change of
+that fiducial volume and this as I
+
+ align:start position:0%
+that fiducial volume and this as I
+ 
+
+ align:start position:0%
+that fiducial volume and this as I
+discussed in the last lecture is
+
+ align:start position:0%
+discussed in the last lecture is
+ 
+
+ align:start position:0%
+discussed in the last lecture is
+essentially nothing more than the first
+
+ align:start position:0%
+essentially nothing more than the first
+ 
+
+ align:start position:0%
+essentially nothing more than the first
+law of thermodynamics
+
+ align:start position:0%
+law of thermodynamics
+ 
+
+ align:start position:0%
+law of thermodynamics
+sort of written up in fancy language
+
+ align:start position:0%
+sort of written up in fancy language
+ 
+
+ align:start position:0%
+sort of written up in fancy language
+appropriate to a cosmological space-time
+
+ align:start position:0%
+appropriate to a cosmological space-time
+ 
+
+ align:start position:0%
+appropriate to a cosmological space-time
+as we move forward we find it useful to
+
+ align:start position:0%
+as we move forward we find it useful to
+ 
+
+ align:start position:0%
+as we move forward we find it useful to
+make a couple of definitions so if you
+
+ align:start position:0%
+make a couple of definitions so if you
+ 
+
+ align:start position:0%
+make a couple of definitions so if you
+divide the Hubble parameter squared by
+
+ align:start position:0%
+divide the Hubble parameter squared by
+ 
+
+ align:start position:0%
+divide the Hubble parameter squared by
+Newton's gravitational constant that's
+
+ align:start position:0%
+Newton's gravitational constant that's
+ 
+
+ align:start position:0%
+Newton's gravitational constant that's
+got the dimensions of density and so
+
+ align:start position:0%
+got the dimensions of density and so
+ 
+
+ align:start position:0%
+got the dimensions of density and so
+we're gonna define a critical density to
+
+ align:start position:0%
+we're gonna define a critical density to
+ 
+
+ align:start position:0%
+we're gonna define a critical density to
+be three H squared over 8 pi J and we're
+
+ align:start position:0%
+be three H squared over 8 pi J and we're
+ 
+
+ align:start position:0%
+be three H squared over 8 pi J and we're
+going to define sort of density
+
+ align:start position:0%
+going to define sort of density
+ 
+
+ align:start position:0%
+going to define sort of density
+parameters Omega as the actual physical
+
+ align:start position:0%
+parameters Omega as the actual physical
+ 
+
+ align:start position:0%
+parameters Omega as the actual physical
+densities normalized to that critical
+
+ align:start position:0%
+densities normalized to that critical
+ 
+
+ align:start position:0%
+densities normalized to that critical
+density and when you do this you find
+
+ align:start position:0%
+density and when you do this you find
+ 
+
+ align:start position:0%
+density and when you do this you find
+that the critical assuming you know the
+
+ align:start position:0%
+that the critical assuming you know the
+ 
+
+ align:start position:0%
+that the critical assuming you know the
+first Fremont equation can be written as
+
+ align:start position:0%
+first Fremont equation can be written as
+ 
+
+ align:start position:0%
+first Fremont equation can be written as
+Omega plus a typo Omega plus Omega
+
+ align:start position:0%
+Omega plus a typo Omega plus Omega
+ 
+
+ align:start position:0%
+Omega plus a typo Omega plus Omega
+curvature equals one where Omega
+
+ align:start position:0%
+curvature equals one where Omega
+ 
+
+ align:start position:0%
+curvature equals one where Omega
+curvature pardon the typo here Omega
+
+ align:start position:0%
+curvature pardon the typo here Omega
+ 
+
+ align:start position:0%
+curvature pardon the typo here Omega
+curvature is not actually related to a
+
+ align:start position:0%
+curvature is not actually related to a
+ 
+
+ align:start position:0%
+curvature is not actually related to a
+density but it sort of plays 1 in this
+
+ align:start position:0%
+density but it sort of plays 1 in this
+ 
+
+ align:start position:0%
+density but it sort of plays 1 in this
+equation it is just a that has the
+
+ align:start position:0%
+equation it is just a that has the
+ 
+
+ align:start position:0%
+equation it is just a that has the
+proper dimensions to do what it's
+
+ align:start position:0%
+proper dimensions to do what it's
+ 
+
+ align:start position:0%
+proper dimensions to do what it's
+necessary to fit this equation and it's
+
+ align:start position:0%
+necessary to fit this equation and it's
+ 
+
+ align:start position:0%
+necessary to fit this equation and it's
+it only depends on what the curvature
+
+ align:start position:0%
+it only depends on what the curvature
+ 
+
+ align:start position:0%
+it only depends on what the curvature
+parameter is so remember that this Kappa
+
+ align:start position:0%
+parameter is so remember that this Kappa
+ 
+
+ align:start position:0%
+parameter is so remember that this Kappa
+is essentially minus 1 0 or 1 modulo a
+
+ align:start position:0%
+is essentially minus 1 0 or 1 modulo a
+ 
+
+ align:start position:0%
+is essentially minus 1 0 or 1 modulo a
+factor of my overall scale so this is
+
+ align:start position:0%
+factor of my overall scale so this is
+ 
+
+ align:start position:0%
+factor of my overall scale so this is
+either a positive number 0 or a negative
+
+ align:start position:0%
+either a positive number 0 or a negative
+ 
+
+ align:start position:0%
+either a positive number 0 or a negative
+number all right so let's carry things
+
+ align:start position:0%
+number all right so let's carry things
+ 
+
+ align:start position:0%
+number all right so let's carry things
+forward from here mute my computer so
+
+ align:start position:0%
+forward from here mute my computer so
+ 
+
+ align:start position:0%
+forward from here mute my computer so
+I'm not distracted by things coming in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we now have everything we need using
+
+ align:start position:0%
+we now have everything we need using
+ 
+
+ align:start position:0%
+we now have everything we need using
+this framework to build a universe so
+
+ align:start position:0%
+this framework to build a universe so
+ 
+
+ align:start position:0%
+this framework to build a universe so
+let's write down the recipe to build a
+
+ align:start position:0%
+let's write down the recipe to build a
+ 
+
+ align:start position:0%
+let's write down the recipe to build a
+universe or I should say to build a
+
+ align:start position:0%
+universe or I should say to build a
+ 
+
+ align:start position:0%
+universe or I should say to build a
+model of the universe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so first thing you do is pick your
+
+ align:start position:0%
+so first thing you do is pick your
+ 
+
+ align:start position:0%
+so first thing you do is pick your
+spatial curvature so pick the parameter
+
+ align:start position:0%
+spatial curvature so pick the parameter
+ 
+
+ align:start position:0%
+spatial curvature so pick the parameter
+K to the -1 0 or 1 pick a mixture of
+
+ align:start position:0%
+K to the -1 0 or 1 pick a mixture of
+ 
+
+ align:start position:0%
+K to the -1 0 or 1 pick a mixture of
+species that contributes to the energy
+
+ align:start position:0%
+species that contributes to the energy
+ 
+
+ align:start position:0%
+species that contributes to the energy
+density budget of your model universe so
+
+ align:start position:0%
+density budget of your model universe so
+ 
+
+ align:start position:0%
+density budget of your model universe so
+what you would say is that the total
+
+ align:start position:0%
+what you would say is that the total
+ 
+
+ align:start position:0%
+what you would say is that the total
+density of things in your universe it's
+
+ align:start position:0%
+density of things in your universe it's
+ 
+
+ align:start position:0%
+density of things in your universe it's
+a sum over whatever mixture of stuff is
+
+ align:start position:0%
+a sum over whatever mixture of stuff is
+ 
+
+ align:start position:0%
+a sum over whatever mixture of stuff is
+in your universe you will find it
+
+ align:start position:0%
+in your universe you will find it
+ 
+
+ align:start position:0%
+in your universe you will find it
+helpful to specify an equation of state
+
+ align:start position:0%
+helpful to specify an equation of state
+ 
+
+ align:start position:0%
+helpful to specify an equation of state
+for each species cosmologists typically
+
+ align:start position:0%
+for each species cosmologists typically
+ 
+
+ align:start position:0%
+for each species cosmologists typically
+choose an equation of state that has the
+
+ align:start position:0%
+choose an equation of state that has the
+ 
+
+ align:start position:0%
+choose an equation of state that has the
+following form okay so you require your
+
+ align:start position:0%
+following form okay so you require your
+ 
+
+ align:start position:0%
+following form okay so you require your
+species if you follow this model that
+
+ align:start position:0%
+species if you follow this model that
+ 
+
+ align:start position:0%
+species if you follow this model that
+most cosmologists use each species will
+
+ align:start position:0%
+most cosmologists use each species will
+ 
+
+ align:start position:0%
+most cosmologists use each species will
+have a pressure that is linear in the
+
+ align:start position:0%
+have a pressure that is linear in the
+ 
+
+ align:start position:0%
+have a pressure that is linear in the
+density
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you do choose that form then when you
+
+ align:start position:0%
+if you do choose that form then when you
+ 
+
+ align:start position:0%
+if you do choose that form then when you
+enforce local conservation of energy
+
+ align:start position:0%
+enforce local conservation of energy
+ 
+
+ align:start position:0%
+enforce local conservation of energy
+what you will then find is that for
+
+ align:start position:0%
+what you will then find is that for
+ 
+
+ align:start position:0%
+what you will then find is that for
+every one of your species
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there is a simple relationship there's a
+
+ align:start position:0%
+there is a simple relationship there's a
+ 
+
+ align:start position:0%
+there is a simple relationship there's a
+simple differential equation that
+
+ align:start position:0%
+simple differential equation that
+ 
+
+ align:start position:0%
+simple differential equation that
+governs how that species evolves as the
+
+ align:start position:0%
+governs how that species evolves as the
+ 
+
+ align:start position:0%
+governs how that species evolves as the
+scale factor changes this can be
+
+ align:start position:0%
+scale factor changes this can be
+ 
+
+ align:start position:0%
+scale factor changes this can be
+immediately integrated up to find that
+
+ align:start position:0%
+immediately integrated up to find that
+ 
+
+ align:start position:0%
+immediately integrated up to find that
+the amount of at some particular moment
+
+ align:start position:0%
+the amount of at some particular moment
+ 
+
+ align:start position:0%
+the amount of at some particular moment
+the density of species I depends on how
+
+ align:start position:0%
+the density of species I depends on how
+ 
+
+ align:start position:0%
+the density of species I depends on how
+it looks and so with zero again denotes
+
+ align:start position:0%
+it looks and so with zero again denotes
+ 
+
+ align:start position:0%
+it looks and so with zero again denotes
+now it is simply proportional to some
+
+ align:start position:0%
+now it is simply proportional to some
+ 
+
+ align:start position:0%
+now it is simply proportional to some
+power of the scale factor where the
+
+ align:start position:0%
+power of the scale factor where the
+ 
+
+ align:start position:0%
+power of the scale factor where the
+power that enters here give me simply
+
+ align:start position:0%
+power that enters here give me simply
+ 
+
+ align:start position:0%
+power that enters here give me simply
+calculated given that equation of state
+
+ align:start position:0%
+calculated given that equation of state
+ 
+
+ align:start position:0%
+calculated given that equation of state
+parameter once you have these things
+
+ align:start position:0%
+parameter once you have these things
+ 
+
+ align:start position:0%
+parameter once you have these things
+together you're ready to roll okay you
+
+ align:start position:0%
+together you're ready to roll okay you
+ 
+
+ align:start position:0%
+together you're ready to roll okay you
+got your frémont equations you've got
+
+ align:start position:0%
+got your frémont equations you've got
+ 
+
+ align:start position:0%
+got your frémont equations you've got
+all the constraints and information you
+
+ align:start position:0%
+all the constraints and information you
+ 
+
+ align:start position:0%
+all the constraints and information you
+need to dig into these equations sit
+
+ align:start position:0%
+need to dig into these equations sit
+ 
+
+ align:start position:0%
+need to dig into these equations sit
+down make your models have a party now
+
+ align:start position:0%
+down make your models have a party now
+ 
+
+ align:start position:0%
+down make your models have a party now
+what we really want to do okay we are
+
+ align:start position:0%
+what we really want to do okay we are
+ 
+
+ align:start position:0%
+what we really want to do okay we are
+physicists and our goal in doing these
+
+ align:start position:0%
+physicists and our goal in doing these
+ 
+
+ align:start position:0%
+physicists and our goal in doing these
+models is to come up with some kind of a
+
+ align:start position:0%
+models is to come up with some kind of a
+ 
+
+ align:start position:0%
+models is to come up with some kind of a
+description of the universe and compare
+
+ align:start position:0%
+description of the universe and compare
+ 
+
+ align:start position:0%
+description of the universe and compare
+it with our data so that we can see what
+
+ align:start position:0%
+it with our data so that we can see what
+ 
+
+ align:start position:0%
+it with our data so that we can see what
+is the nature of the universe that we
+
+ align:start position:0%
+is the nature of the universe that we
+ 
+
+ align:start position:0%
+is the nature of the universe that we
+actually live in okay so what is of
+
+ align:start position:0%
+actually live in okay so what is of
+ 
+
+ align:start position:0%
+actually live in okay so what is of
+interest to us is how does varying all
+
+ align:start position:0%
+interest to us is how does varying all
+ 
+
+ align:start position:0%
+interest to us is how does varying all
+these different terms
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+change what we're going to talk about
+
+ align:start position:0%
+change what we're going to talk about
+ 
+
+ align:start position:0%
+change what we're going to talk about
+various observables but really if you
+
+ align:start position:0%
+various observables but really if you
+ 
+
+ align:start position:0%
+various observables but really if you
+think about this model how does it
+
+ align:start position:0%
+think about this model how does it
+ 
+
+ align:start position:0%
+think about this model how does it
+change the evolution of the scale factor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+everything is bound up in that that is
+
+ align:start position:0%
+everything is bound up in that that is
+ 
+
+ align:start position:0%
+everything is bound up in that that is
+the key thing okay so if I can make a
+
+ align:start position:0%
+the key thing okay so if I can make a
+ 
+
+ align:start position:0%
+the key thing okay so if I can make a
+mathematical model that describes a
+
+ align:start position:0%
+mathematical model that describes a
+ 
+
+ align:start position:0%
+mathematical model that describes a
+universe with all these various
+
+ align:start position:0%
+universe with all these various
+ 
+
+ align:start position:0%
+universe with all these various
+different kinds of ingredients I can sit
+
+ align:start position:0%
+different kinds of ingredients I can sit
+ 
+
+ align:start position:0%
+different kinds of ingredients I can sit
+down and make if I make a really
+
+ align:start position:0%
+down and make if I make a really
+ 
+
+ align:start position:0%
+down and make if I make a really
+complicated thing I probably can't do
+
+ align:start position:0%
+complicated thing I probably can't do
+ 
+
+ align:start position:0%
+complicated thing I probably can't do
+this analytically so that's fine I will
+
+ align:start position:0%
+this analytically so that's fine I will
+ 
+
+ align:start position:0%
+this analytically so that's fine I will
+make a differential equation integrator
+
+ align:start position:0%
+make a differential equation integrator
+ 
+
+ align:start position:0%
+make a differential equation integrator
+that solves all these couple
+
+ align:start position:0%
+that solves all these couple
+ 
+
+ align:start position:0%
+that solves all these couple
+differential equations and I will then
+
+ align:start position:0%
+differential equations and I will then
+ 
+
+ align:start position:0%
+differential equations and I will then
+make predictions for how a of T evolves
+
+ align:start position:0%
+make predictions for how a of T evolves
+ 
+
+ align:start position:0%
+make predictions for how a of T evolves
+depending upon what the different
+
+ align:start position:0%
+depending upon what the different
+ 
+
+ align:start position:0%
+depending upon what the different
+mixtures of species are what the Kircher
+
+ align:start position:0%
+mixtures of species are what the Kircher
+ 
+
+ align:start position:0%
+mixtures of species are what the Kircher
+term is equal to all those together and
+
+ align:start position:0%
+term is equal to all those together and
+ 
+
+ align:start position:0%
+term is equal to all those together and
+make my model but I goal as a physicist
+
+ align:start position:0%
+make my model but I goal as a physicist
+ 
+
+ align:start position:0%
+make my model but I goal as a physicist
+is then to compare this two data and so
+
+ align:start position:0%
+is then to compare this two data and so
+ 
+
+ align:start position:0%
+is then to compare this two data and so
+what I need to do is to come up with
+
+ align:start position:0%
+what I need to do is to come up with
+ 
+
+ align:start position:0%
+what I need to do is to come up with
+some kind of a way this will then be
+
+ align:start position:0%
+some kind of a way this will then be
+ 
+
+ align:start position:0%
+some kind of a way this will then be
+useful we then need some kind of an
+
+ align:start position:0%
+useful we then need some kind of an
+ 
+
+ align:start position:0%
+useful we then need some kind of an
+observational surrogate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for a of t okay what I would like to do
+
+ align:start position:0%
+for a of t okay what I would like to do
+ 
+
+ align:start position:0%
+for a of t okay what I would like to do
+is say great model a predicts the
+
+ align:start position:0%
+is say great model a predicts the
+ 
+
+ align:start position:0%
+is say great model a predicts the
+following evolution of the scale factor
+
+ align:start position:0%
+following evolution of the scale factor
+ 
+
+ align:start position:0%
+following evolution of the scale factor
+model B predicts this machine for the
+
+ align:start position:0%
+model B predicts this machine for the
+ 
+
+ align:start position:0%
+model B predicts this machine for the
+scale factor can I look at the universe
+
+ align:start position:0%
+scale factor can I look at the universe
+ 
+
+ align:start position:0%
+scale factor can I look at the universe
+and deduce whether we are closer to
+
+ align:start position:0%
+and deduce whether we are closer to
+ 
+
+ align:start position:0%
+and deduce whether we are closer to
+model a or closer to model B and in
+
+ align:start position:0%
+model a or closer to model B and in
+ 
+
+ align:start position:0%
+model a or closer to model B and in
+order to do that I need to know how do I
+
+ align:start position:0%
+order to do that I need to know how do I
+ 
+
+ align:start position:0%
+order to do that I need to know how do I
+measure a of T and as we're going to see
+
+ align:start position:0%
+measure a of T and as we're going to see
+ 
+
+ align:start position:0%
+measure a of T and as we're going to see
+this really boils down to two things I
+
+ align:start position:0%
+this really boils down to two things I
+ 
+
+ align:start position:0%
+this really boils down to two things I
+need to be able to deduce if I look at
+
+ align:start position:0%
+need to be able to deduce if I look at
+ 
+
+ align:start position:0%
+need to be able to deduce if I look at
+some event in the universe if I look at
+
+ align:start position:0%
+some event in the universe if I look at
+ 
+
+ align:start position:0%
+some event in the universe if I look at
+something I want to know what scale
+
+ align:start position:0%
+something I want to know what scale
+ 
+
+ align:start position:0%
+something I want to know what scale
+factor to associate with that I need to
+
+ align:start position:0%
+factor to associate with that I need to
+ 
+
+ align:start position:0%
+factor to associate with that I need to
+measure a and I need to know what T to
+
+ align:start position:0%
+measure a and I need to know what T to
+ 
+
+ align:start position:0%
+measure a and I need to know what T to
+label that a with so you know this is
+
+ align:start position:0%
+label that a with so you know this is
+ 
+
+ align:start position:0%
+label that a with so you know this is
+kind of sounds like I'm you know reading
+
+ align:start position:0%
+kind of sounds like I'm you know reading
+ 
+
+ align:start position:0%
+kind of sounds like I'm you know reading
+from the the Journal of duh but if I
+
+ align:start position:0%
+from the the Journal of duh but if I
+ 
+
+ align:start position:0%
+from the the Journal of duh but if I
+want to do this what it basically boils
+
+ align:start position:0%
+want to do this what it basically boils
+ 
+
+ align:start position:0%
+want to do this what it basically boils
+down to is I need to know how to
+
+ align:start position:0%
+down to is I need to know how to
+ 
+
+ align:start position:0%
+down to is I need to know how to
+associate an A with things that I
+
+ align:start position:0%
+associate an A with things that I
+ 
+
+ align:start position:0%
+associate an A with things that I
+measure and how to associate the T with
+
+ align:start position:0%
+measure and how to associate the T with
+ 
+
+ align:start position:0%
+measure and how to associate the T with
+the things that I measure that's what
+
+ align:start position:0%
+the things that I measure that's what
+ 
+
+ align:start position:0%
+the things that I measure that's what
+we're going to talk about today what are
+
+ align:start position:0%
+we're going to talk about today what are
+ 
+
+ align:start position:0%
+we're going to talk about today what are
+the actual observational surrogates the
+
+ align:start position:0%
+the actual observational surrogates the
+ 
+
+ align:start position:0%
+the actual observational surrogates the
+ways in which we can go out point
+
+ align:start position:0%
+ways in which we can go out point
+ 
+
+ align:start position:0%
+ways in which we can go out point
+telescopes and other instruments at
+
+ align:start position:0%
+telescopes and other instruments at
+ 
+
+ align:start position:0%
+telescopes and other instruments at
+things in the sky and deduce what a of T
+
+ align:start position:0%
+things in the sky and deduce what a of T
+ 
+
+ align:start position:0%
+things in the sky and deduce what a of T
+is for the kind of events the kind of
+
+ align:start position:0%
+is for the kind of events the kind of
+ 
+
+ align:start position:0%
+is for the kind of events the kind of
+things that we are going to measure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's talk about how I can measure the
+
+ align:start position:0%
+let's talk about how I can measure the
+ 
+
+ align:start position:0%
+let's talk about how I can measure the
+scale factor first
+
+ align:start position:0%
+scale factor first
+ 
+
+ align:start position:0%
+scale factor first
+okay so let's ignore the fact that the T
+
+ align:start position:0%
+okay so let's ignore the fact that the T
+ 
+
+ align:start position:0%
+okay so let's ignore the fact that the T
+in here how can I measure a we saw a
+
+ align:start position:0%
+in here how can I measure a we saw a
+ 
+
+ align:start position:0%
+in here how can I measure a we saw a
+hint of this in the previous lecture
+
+ align:start position:0%
+hint of this in the previous lecture
+ 
+
+ align:start position:0%
+hint of this in the previous lecture
+that I recorded so recall
+
+ align:start position:0%
+that I recorded so recall
+ 
+
+ align:start position:0%
+that I recorded so recall
+pardon me I've got a bit of extra junk
+
+ align:start position:0%
+pardon me I've got a bit of extra junk
+ 
+
+ align:start position:0%
+pardon me I've got a bit of extra junk
+here in my notes
+
+ align:start position:0%
+here in my notes
+ 
+
+ align:start position:0%
+here in my notes
+recall that in my previous lecture we
+
+ align:start position:0%
+recall that in my previous lecture we
+ 
+
+ align:start position:0%
+recall that in my previous lecture we
+looked at the way different kinds of
+
+ align:start position:0%
+looked at the way different kinds of
+ 
+
+ align:start position:0%
+looked at the way different kinds of
+densities behave but that got the result
+
+ align:start position:0%
+densities behave but that got the result
+ 
+
+ align:start position:0%
+densities behave but that got the result
+right here for matter which had a an
+
+ align:start position:0%
+right here for matter which had a an
+ 
+
+ align:start position:0%
+right here for matter which had a an
+equation state parameter of 0 what we
+
+ align:start position:0%
+equation state parameter of 0 what we
+ 
+
+ align:start position:0%
+equation state parameter of 0 what we
+found was that the density that the
+
+ align:start position:0%
+found was that the density that the
+ 
+
+ align:start position:0%
+found was that the density that the
+density associated with that matter it
+
+ align:start position:0%
+density associated with that matter it
+ 
+
+ align:start position:0%
+density associated with that matter it
+just fell as the scale factor to the
+
+ align:start position:0%
+just fell as the scale factor to the
+ 
+
+ align:start position:0%
+just fell as the scale factor to the
+inverse third power that's essentially
+
+ align:start position:0%
+inverse third power that's essentially
+ 
+
+ align:start position:0%
+inverse third power that's essentially
+saying that the number of particles of
+
+ align:start position:0%
+saying that the number of particles of
+ 
+
+ align:start position:0%
+saying that the number of particles of
+stuff is
+
+ align:start position:0%
+stuff is
+ 
+
+ align:start position:0%
+stuff is
+constant and so as the universe expands
+
+ align:start position:0%
+constant and so as the universe expands
+ 
+
+ align:start position:0%
+constant and so as the universe expands
+it just goes with the volume of the
+
+ align:start position:0%
+it just goes with the volume of the
+ 
+
+ align:start position:0%
+it just goes with the volume of the
+universe if it was radiation we found it
+
+ align:start position:0%
+universe if it was radiation we found it
+ 
+
+ align:start position:0%
+universe if it was radiation we found it
+went as a scale factor to the inverse
+
+ align:start position:0%
+went as a scale factor to the inverse
+ 
+
+ align:start position:0%
+went as a scale factor to the inverse
+force power and that's consistent with
+
+ align:start position:0%
+force power and that's consistent with
+ 
+
+ align:start position:0%
+force power and that's consistent with
+sort of diluting the density as the
+
+ align:start position:0%
+sort of diluting the density as the
+ 
+
+ align:start position:0%
+sort of diluting the density as the
+volume gets larger provided we also
+
+ align:start position:0%
+volume gets larger provided we also
+ 
+
+ align:start position:0%
+volume gets larger provided we also
+decreased the energy per particle of
+
+ align:start position:0%
+decreased the energy per particle of
+ 
+
+ align:start position:0%
+decreased the energy per particle of
+radiation per photon per graviton per
+
+ align:start position:0%
+radiation per photon per graviton per
+ 
+
+ align:start position:0%
+radiation per photon per graviton per
+whatever on if I require that that the
+
+ align:start position:0%
+whatever on if I require that that the
+ 
+
+ align:start position:0%
+whatever on if I require that that the
+energy per sort of quantum of radiation
+
+ align:start position:0%
+energy per sort of quantum of radiation
+ 
+
+ align:start position:0%
+energy per sort of quantum of radiation
+is redshifted with this thing that that
+
+ align:start position:0%
+is redshifted with this thing that that
+ 
+
+ align:start position:0%
+is redshifted with this thing that that
+explains the density fall-off law that
+
+ align:start position:0%
+explains the density fall-off law that
+ 
+
+ align:start position:0%
+explains the density fall-off law that
+we found for radiation and so that sort
+
+ align:start position:0%
+we found for radiation and so that sort
+ 
+
+ align:start position:0%
+we found for radiation and so that sort
+of suggests that what we're gonna find
+
+ align:start position:0%
+of suggests that what we're gonna find
+ 
+
+ align:start position:0%
+of suggests that what we're gonna find
+is that the scale factor is directly
+
+ align:start position:0%
+is that the scale factor is directly
+ 
+
+ align:start position:0%
+is that the scale factor is directly
+tied to a redshift measure okay um I
+
+ align:start position:0%
+tied to a redshift measure okay um I
+ 
+
+ align:start position:0%
+tied to a redshift measure okay um I
+just realized what this page of notes
+
+ align:start position:0%
+just realized what this page of notes
+ 
+
+ align:start position:0%
+just realized what this page of notes
+was my apologies I'm getting myself
+
+ align:start position:0%
+was my apologies I'm getting myself
+ 
+
+ align:start position:0%
+was my apologies I'm getting myself
+organized here let's make that a little
+
+ align:start position:0%
+organized here let's make that a little
+ 
+
+ align:start position:0%
+organized here let's make that a little
+bit more rigorous now okay so that's
+
+ align:start position:0%
+bit more rigorous now okay so that's
+ 
+
+ align:start position:0%
+bit more rigorous now okay so that's
+argument on the basis of how the density
+
+ align:start position:0%
+argument on the basis of how the density
+ 
+
+ align:start position:0%
+argument on the basis of how the density
+of radiation behaves it's not a bad one
+
+ align:start position:0%
+of radiation behaves it's not a bad one
+ 
+
+ align:start position:0%
+of radiation behaves it's not a bad one
+as a first passed it is quite indicative
+
+ align:start position:0%
+as a first passed it is quite indicative
+ 
+
+ align:start position:0%
+as a first passed it is quite indicative
+but let's come at it from another point
+
+ align:start position:0%
+but let's come at it from another point
+ 
+
+ align:start position:0%
+but let's come at it from another point
+of view and this allows me to introduce
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in a brief aside a topic that it's quite
+
+ align:start position:0%
+in a brief aside a topic that it's quite
+ 
+
+ align:start position:0%
+in a brief aside a topic that it's quite
+useful here so we talked about killing
+
+ align:start position:0%
+useful here so we talked about killing
+ 
+
+ align:start position:0%
+useful here so we talked about killing
+vectors a couple of weeks ago let's now
+
+ align:start position:0%
+vectors a couple of weeks ago let's now
+ 
+
+ align:start position:0%
+vectors a couple of weeks ago let's now
+talk about a generalization of this
+
+ align:start position:0%
+talk about a generalization of this
+ 
+
+ align:start position:0%
+talk about a generalization of this
+known as killing tensors so we call that
+
+ align:start position:0%
+known as killing tensors so we call that
+ 
+
+ align:start position:0%
+known as killing tensors so we call that
+a killing vector was defined as a
+
+ align:start position:0%
+a killing vector was defined as a
+ 
+
+ align:start position:0%
+a killing vector was defined as a
+particular vector in my space-time
+
+ align:start position:0%
+particular vector in my space-time
+ 
+
+ align:start position:0%
+particular vector in my space-time
+manifold such that if I Lee transports
+
+ align:start position:0%
+manifold such that if I Lee transports
+ 
+
+ align:start position:0%
+manifold such that if I Lee transports
+the metric along that killing vector I
+
+ align:start position:0%
+the metric along that killing vector I
+ 
+
+ align:start position:0%
+the metric along that killing vector I
+get zero this then leads to the
+
+ align:start position:0%
+get zero this then leads to the
+ 
+
+ align:start position:0%
+get zero this then leads to the
+statements that if I put together the
+
+ align:start position:0%
+statements that if I put together the
+ 
+
+ align:start position:0%
+statements that if I put together the
+symmetrized covariant gradient of the
+
+ align:start position:0%
+symmetrized covariant gradient of the
+ 
+
+ align:start position:0%
+symmetrized covariant gradient of the
+killing factor I get zero another way to
+
+ align:start position:0%
+killing factor I get zero another way to
+ 
+
+ align:start position:0%
+killing factor I get zero another way to
+write this is to use this notation
+
+ align:start position:0%
+write this is to use this notation
+ 
+
+ align:start position:0%
+write this is to use this notation
+whoops
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so these are equations that tell us
+
+ align:start position:0%
+okay so these are equations that tell us
+ 
+
+ align:start position:0%
+okay so these are equations that tell us
+about the way that killing vectors
+
+ align:start position:0%
+about the way that killing vectors
+ 
+
+ align:start position:0%
+about the way that killing vectors
+behave a killing tensor is just a
+
+ align:start position:0%
+behave a killing tensor is just a
+ 
+
+ align:start position:0%
+behave a killing tensor is just a
+generalization of this idea to an object
+
+ align:start position:0%
+generalization of this idea to an object
+ 
+
+ align:start position:0%
+generalization of this idea to an object
+that has more than one index on it okay
+
+ align:start position:0%
+that has more than one index on it okay
+ 
+
+ align:start position:0%
+that has more than one index on it okay
+to a more to a higher rank tensor II
+
+ align:start position:0%
+to a more to a higher rank tensor II
+ 
+
+ align:start position:0%
+to a more to a higher rank tensor II
+object so we consider this to be a rank
+
+ align:start position:0%
+object so we consider this to be a rank
+ 
+
+ align:start position:0%
+object so we consider this to be a rank
+one killing tensor a rank n killing
+
+ align:start position:0%
+one killing tensor a rank n killing
+ 
+
+ align:start position:0%
+one killing tensor a rank n killing
+tensor satisfies so let's say K is my
+
+ align:start position:0%
+tensor satisfies so let's say K is my
+ 
+
+ align:start position:0%
+tensor satisfies so let's say K is my
+killing tensor so imagine I have n
+
+ align:start position:0%
+killing tensor so imagine I have n
+ 
+
+ align:start position:0%
+killing tensor so imagine I have n
+indices here if I take the covariant
+
+ align:start position:0%
+indices here if I take the covariant
+ 
+
+ align:start position:0%
+indices here if I take the covariant
+gradient of that killing tensor and I
+
+ align:start position:0%
+gradient of that killing tensor and I
+ 
+
+ align:start position:0%
+gradient of that killing tensor and I
+symmetrize over all n indices that gives
+
+ align:start position:0%
+symmetrize over all n indices that gives
+ 
+
+ align:start position:0%
+symmetrize over all n indices that gives
+me zero this defines a killing tensor
+
+ align:start position:0%
+me zero this defines a killing tensor
+ 
+
+ align:start position:0%
+me zero this defines a killing tensor
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+starting with this definition it's not
+
+ align:start position:0%
+starting with this definition it's not
+ 
+
+ align:start position:0%
+starting with this definition it's not
+at all hard to show that if I define a
+
+ align:start position:0%
+at all hard to show that if I define a
+ 
+
+ align:start position:0%
+at all hard to show that if I define a
+parameter K
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+which is what I get when I contract the
+
+ align:start position:0%
+which is what I get when I contract the
+ 
+
+ align:start position:0%
+which is what I get when I contract the
+killing tensor every one of its indices
+
+ align:start position:0%
+killing tensor every one of its indices
+ 
+
+ align:start position:0%
+killing tensor every one of its indices
+with the four velocity of a Judy's ik
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so if my you satisfy is the G DS
+
+ align:start position:0%
+okay so if my you satisfy is the G DS
+ 
+
+ align:start position:0%
+okay so if my you satisfy is the G DS
+equation or this could be you know what
+
+ align:start position:0%
+equation or this could be you know what
+ 
+
+ align:start position:0%
+equation or this could be you know what
+this right this has a momentum well what
+
+ align:start position:0%
+this right this has a momentum well what
+ 
+
+ align:start position:0%
+this right this has a momentum well what
+you say is the tangents to a world line
+
+ align:start position:0%
+you say is the tangents to a world line
+ 
+
+ align:start position:0%
+you say is the tangents to a world line
+could be either a velocity or a momentum
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if I define the scalar K by
+
+ align:start position:0%
+so if I define the scalar K by
+ 
+
+ align:start position:0%
+so if I define the scalar K by
+contracting my killing tensor with and
+
+ align:start position:0%
+contracting my killing tensor with and
+ 
+
+ align:start position:0%
+contracting my killing tensor with and
+copies of the tangent of the world Y and
+
+ align:start position:0%
+copies of the tangent of the world Y and
+ 
+
+ align:start position:0%
+copies of the tangent of the world Y and
+that thing satisfies a Judy's equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then the following is true okay you guys
+
+ align:start position:0%
+then the following is true okay you guys
+ 
+
+ align:start position:0%
+then the following is true okay you guys
+did this on a homework exercise for when
+
+ align:start position:0%
+did this on a homework exercise for when
+ 
+
+ align:start position:0%
+did this on a homework exercise for when
+we thought about a space time you did
+
+ align:start position:0%
+we thought about a space time you did
+ 
+
+ align:start position:0%
+we thought about a space time you did
+something that's similar to this I
+
+ align:start position:0%
+something that's similar to this I
+ 
+
+ align:start position:0%
+something that's similar to this I
+should say for a spacetime containing an
+
+ align:start position:0%
+should say for a spacetime containing an
+ 
+
+ align:start position:0%
+should say for a spacetime containing an
+electromagnetic field we talked about
+
+ align:start position:0%
+electromagnetic field we talked about
+ 
+
+ align:start position:0%
+electromagnetic field we talked about
+how this works for the case of a killing
+
+ align:start position:0%
+how this works for the case of a killing
+ 
+
+ align:start position:0%
+how this works for the case of a killing
+vector hopefully you can kind of see the
+
+ align:start position:0%
+vector hopefully you can kind of see the
+ 
+
+ align:start position:0%
+vector hopefully you can kind of see the
+way you would do this calculation at
+
+ align:start position:0%
+way you would do this calculation at
+ 
+
+ align:start position:0%
+way you would do this calculation at
+this point now the reason I'm doing this
+
+ align:start position:0%
+this point now the reason I'm doing this
+ 
+
+ align:start position:0%
+this point now the reason I'm doing this
+aside is that if you have a free bin'
+
+ align:start position:0%
+aside is that if you have a free bin'
+ 
+
+ align:start position:0%
+aside is that if you have a free bin'
+robertson-walker space-time such space
+
+ align:start position:0%
+robertson-walker space-time such space
+ 
+
+ align:start position:0%
+robertson-walker space-time such space
+times actually have a very useful
+
+ align:start position:0%
+times actually have a very useful
+ 
+
+ align:start position:0%
+times actually have a very useful
+killing tensor
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's define okay two indices mu nu
+
+ align:start position:0%
+so let's define okay two indices mu nu
+ 
+
+ align:start position:0%
+so let's define okay two indices mu nu
+and this is just given by the scale
+
+ align:start position:0%
+and this is just given by the scale
+ 
+
+ align:start position:0%
+and this is just given by the scale
+factor multiplying the metric you move
+
+ align:start position:0%
+factor multiplying the metric you move
+ 
+
+ align:start position:0%
+factor multiplying the metric you move
+you mu you new okay where this you comes
+
+ align:start position:0%
+you mu you new okay where this you comes
+ 
+
+ align:start position:0%
+you mu you new okay where this you comes
+from the for velocity of a co moving
+
+ align:start position:0%
+from the for velocity of a co moving
+ 
+
+ align:start position:0%
+from the for velocity of a co moving
+fluid element so this is the for
+
+ align:start position:0%
+fluid element so this is the for
+ 
+
+ align:start position:0%
+fluid element so this is the for
+velocity that we use to construct the
+
+ align:start position:0%
+velocity that we use to construct the
+ 
+
+ align:start position:0%
+velocity that we use to construct the
+stress energy tensor that is the source
+
+ align:start position:0%
+stress energy tensor that is the source
+ 
+
+ align:start position:0%
+stress energy tensor that is the source
+of our Friedmann equations so here's how
+
+ align:start position:0%
+of our Friedmann equations so here's how
+ 
+
+ align:start position:0%
+of our Friedmann equations so here's how
+we're gonna use this let's look at what
+
+ align:start position:0%
+we're gonna use this let's look at what
+ 
+
+ align:start position:0%
+we're gonna use this let's look at what
+we get for this killing vector CB this
+
+ align:start position:0%
+we get for this killing vector CB this
+ 
+
+ align:start position:0%
+we get for this killing vector CB this
+killing tensor when I consider it along
+
+ align:start position:0%
+killing tensor when I consider it along
+ 
+
+ align:start position:0%
+killing tensor when I consider it along
+a null Judy's ik we're gonna want to
+
+ align:start position:0%
+a null Judy's ik we're gonna want to
+ 
+
+ align:start position:0%
+a null Judy's ik we're gonna want to
+think about null Judy's it's a lot
+
+ align:start position:0%
+think about null Judy's it's a lot
+ 
+
+ align:start position:0%
+think about null Judy's it's a lot
+because the way that we are going to
+
+ align:start position:0%
+because the way that we are going to
+ 
+
+ align:start position:0%
+because the way that we are going to
+probe our universe is with radiation
+
+ align:start position:0%
+probe our universe is with radiation
+ 
+
+ align:start position:0%
+probe our universe is with radiation
+we're going to look at it with these
+
+ align:start position:0%
+we're going to look at it with these
+ 
+
+ align:start position:0%
+we're going to look at it with these
+like telescopes these days people are
+
+ align:start position:0%
+like telescopes these days people are
+ 
+
+ align:start position:0%
+like telescopes these days people are
+starting to probe it with things like
+
+ align:start position:0%
+starting to probe it with things like
+ 
+
+ align:start position:0%
+starting to probe it with things like
+gravitational wave detectors all things
+
+ align:start position:0%
+gravitational wave detectors all things
+ 
+
+ align:start position:0%
+gravitational wave detectors all things
+that involve radiation that moves on
+
+ align:start position:0%
+that involve radiation that moves on
+ 
+
+ align:start position:0%
+that involve radiation that moves on
+null geodesics so let's examine the
+
+ align:start position:0%
+null geodesics so let's examine the
+ 
+
+ align:start position:0%
+null geodesics so let's examine the
+Associated conserved quantity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and is associated with a null Judaism so
+
+ align:start position:0%
+and is associated with a null Judaism so
+ 
+
+ align:start position:0%
+and is associated with a null Judaism so
+let's say V what's making a P actually
+
+ align:start position:0%
+let's say V what's making a P actually
+ 
+
+ align:start position:0%
+let's say V what's making a P actually
+so it's me a null geodesic so we're
+
+ align:start position:0%
+so it's me a null geodesic so we're
+ 
+
+ align:start position:0%
+so it's me a null geodesic so we're
+gonna imagine it's radiation that is
+
+ align:start position:0%
+gonna imagine it's radiation that is
+ 
+
+ align:start position:0%
+gonna imagine it's radiation that is
+following it has a four momentum P mu
+
+ align:start position:0%
+following it has a four momentum P mu
+ 
+
+ align:start position:0%
+following it has a four momentum P mu
+and let's define K k sub ng for my null
+
+ align:start position:0%
+and let's define K k sub ng for my null
+ 
+
+ align:start position:0%
+and let's define K k sub ng for my null
+dude is ik that is going to be came u nu
+
+ align:start position:0%
+dude is ik that is going to be came u nu
+ 
+
+ align:start position:0%
+dude is ik that is going to be came u nu
+P mu P nu let's plug in the definition
+
+ align:start position:0%
+P mu P nu let's plug in the definition
+ 
+
+ align:start position:0%
+P mu P nu let's plug in the definition
+of my killing tensor so this is a
+
+ align:start position:0%
+of my killing tensor so this is a
+ 
+
+ align:start position:0%
+of my killing tensor so this is a
+squared of T G mu nu P mu P nu this is
+
+ align:start position:0%
+squared of T G mu nu P mu P nu this is
+ 
+
+ align:start position:0%
+squared of T G mu nu P mu P nu this is
+zero its analgesic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then I get u mu P nu u nu p nu now
+
+ align:start position:0%
+then I get u mu P nu u nu p nu now
+ 
+
+ align:start position:0%
+then I get u mu P nu u nu p nu now
+remind you of something this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+go back to a nice little Easter egg an
+
+ align:start position:0%
+go back to a nice little Easter egg an
+ 
+
+ align:start position:0%
+go back to a nice little Easter egg an
+exercise you guys did a long time ago if
+
+ align:start position:0%
+exercise you guys did a long time ago if
+ 
+
+ align:start position:0%
+exercise you guys did a long time ago if
+I look at the dot product of a for
+
+ align:start position:0%
+I look at the dot product of a for
+ 
+
+ align:start position:0%
+I look at the dot product of a for
+momentum and a for velocity what I get
+
+ align:start position:0%
+momentum and a for velocity what I get
+ 
+
+ align:start position:0%
+momentum and a for velocity what I get
+is the energy associated with that for
+
+ align:start position:0%
+is the energy associated with that for
+ 
+
+ align:start position:0%
+is the energy associated with that for
+momentum as measured by the observer
+
+ align:start position:0%
+momentum as measured by the observer
+ 
+
+ align:start position:0%
+momentum as measured by the observer
+who's for velocity is U so what we get
+
+ align:start position:0%
+who's for velocity is U so what we get
+ 
+
+ align:start position:0%
+who's for velocity is U so what we get
+here is two copies of the energy of that
+
+ align:start position:0%
+here is two copies of the energy of that
+ 
+
+ align:start position:0%
+here is two copies of the energy of that
+null geodesic as measured by the
+
+ align:start position:0%
+null geodesic as measured by the
+ 
+
+ align:start position:0%
+null geodesic as measured by the
+observer who is Co moving so what this
+
+ align:start position:0%
+observer who is Co moving so what this
+ 
+
+ align:start position:0%
+observer who is Co moving so what this
+null geodesic with this quantity
+
+ align:start position:0%
+null geodesic with this quantity
+ 
+
+ align:start position:0%
+null geodesic with this quantity
+associate this null to DS ik is is two
+
+ align:start position:0%
+associate this null to DS ik is is two
+ 
+
+ align:start position:0%
+associate this null to DS ik is is two
+factors two powers of the scale factor
+
+ align:start position:0%
+factors two powers of the scale factor
+ 
+
+ align:start position:0%
+factors two powers of the scale factor
+times the energy that would be measured
+
+ align:start position:0%
+times the energy that would be measured
+ 
+
+ align:start position:0%
+times the energy that would be measured
+by someone who is Co moving with the
+
+ align:start position:0%
+by someone who is Co moving with the
+ 
+
+ align:start position:0%
+by someone who is Co moving with the
+fluid that fills my universe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay energy of pmu as measured by ummul
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and remember this is a constant so as
+
+ align:start position:0%
+and remember this is a constant so as
+ 
+
+ align:start position:0%
+and remember this is a constant so as
+this radiation travels across the
+
+ align:start position:0%
+this radiation travels across the
+ 
+
+ align:start position:0%
+this radiation travels across the
+universe you know as its radiation
+
+ align:start position:0%
+universe you know as its radiation
+ 
+
+ align:start position:0%
+universe you know as its radiation
+travels across the universe the product
+
+ align:start position:0%
+travels across the universe the product
+ 
+
+ align:start position:0%
+travels across the universe the product
+of the scale factor and the energy
+
+ align:start position:0%
+of the scale factor and the energy
+ 
+
+ align:start position:0%
+of the scale factor and the energy
+associate that radiation as measured by
+
+ align:start position:0%
+associate that radiation as measured by
+ 
+
+ align:start position:0%
+associate that radiation as measured by
+comoving observers is a constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this is telling us that the energy as
+
+ align:start position:0%
+so this is telling us that the energy as
+ 
+
+ align:start position:0%
+so this is telling us that the energy as
+measured by a comoving observer let's
+
+ align:start position:0%
+measured by a comoving observer let's
+ 
+
+ align:start position:0%
+measured by a comoving observer let's
+say it is emitted at some time with a
+
+ align:start position:0%
+say it is emitted at some time with a
+ 
+
+ align:start position:0%
+say it is emitted at some time with a
+scale factor is a when it propagates to
+
+ align:start position:0%
+scale factor is a when it propagates to
+ 
+
+ align:start position:0%
+scale factor is a when it propagates to
+us we define our scale factor as one the
+
+ align:start position:0%
+us we define our scale factor as one the
+ 
+
+ align:start position:0%
+us we define our scale factor as one the
+energy will have fallen down by a factor
+
+ align:start position:0%
+energy will have fallen down by a factor
+ 
+
+ align:start position:0%
+energy will have fallen down by a factor
+of one over a okay so this makes a
+
+ align:start position:0%
+of one over a okay so this makes a
+ 
+
+ align:start position:0%
+of one over a okay so this makes a
+little bit more rigorous that's
+
+ align:start position:0%
+little bit more rigorous that's
+ 
+
+ align:start position:0%
+little bit more rigorous that's
+intuitive argument that we saw from
+
+ align:start position:0%
+intuitive argument that we saw from
+ 
+
+ align:start position:0%
+intuitive argument that we saw from
+considering how the density of radiation
+
+ align:start position:0%
+considering how the density of radiation
+ 
+
+ align:start position:0%
+considering how the density of radiation
+fell off what we see is the energy is
+
+ align:start position:0%
+fell off what we see is the energy is
+ 
+
+ align:start position:0%
+fell off what we see is the energy is
+indeed redshifting with the scale factor
+
+ align:start position:0%
+indeed redshifting with the scale factor
+ 
+
+ align:start position:0%
+indeed redshifting with the scale factor
+so if I use the fact that the energy
+
+ align:start position:0%
+so if I use the fact that the energy
+ 
+
+ align:start position:0%
+so if I use the fact that the energy
+that I observe by me if I'm measuring
+
+ align:start position:0%
+that I observe by me if I'm measuring
+ 
+
+ align:start position:0%
+that I observe by me if I'm measuring
+light light has a frequency of Omega
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what I see is the Omega that I observe
+
+ align:start position:0%
+what I see is the Omega that I observe
+ 
+
+ align:start position:0%
+what I see is the Omega that I observe
+at my scale factor which I define to be
+
+ align:start position:0%
+at my scale factor which I define to be
+ 
+
+ align:start position:0%
+at my scale factor which I define to be
+one normalized to that when it was
+
+ align:start position:0%
+one normalized to that when it was
+ 
+
+ align:start position:0%
+one normalized to that when it was
+emitted it looks like the scale factor
+
+ align:start position:0%
+emitted it looks like the scale factor
+ 
+
+ align:start position:0%
+emitted it looks like the scale factor
+when it was emitted divided by a now a
+
+ align:start position:0%
+when it was emitted divided by a now a
+ 
+
+ align:start position:0%
+when it was emitted divided by a now a
+observed I call this one I can flip this
+
+ align:start position:0%
+observed I call this one I can flip this
+ 
+
+ align:start position:0%
+observed I call this one I can flip this
+over another way of saying this is that
+
+ align:start position:0%
+over another way of saying this is that
+ 
+
+ align:start position:0%
+over another way of saying this is that
+if I write it in terms of wavelengths of
+
+ align:start position:0%
+if I write it in terms of wavelengths of
+ 
+
+ align:start position:0%
+if I write it in terms of wavelengths of
+the radiation the wavelength of the
+
+ align:start position:0%
+the radiation the wavelength of the
+ 
+
+ align:start position:0%
+the radiation the wavelength of the
+radiation and when it was emitted versus
+
+ align:start position:0%
+radiation and when it was emitted versus
+ 
+
+ align:start position:0%
+radiation and when it was emitted versus
+the wavelength that we observe it tells
+
+ align:start position:0%
+the wavelength that we observe it tells
+ 
+
+ align:start position:0%
+the wavelength that we observe it tells
+me about the scale factor when the
+
+ align:start position:0%
+me about the scale factor when the
+ 
+
+ align:start position:0%
+me about the scale factor when the
+radiation was emitted
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+astronomers like to work with redshift
+
+ align:start position:0%
+astronomers like to work with redshift
+ 
+
+ align:start position:0%
+astronomers like to work with redshift
+when they study things like zoom but
+
+ align:start position:0%
+when they study things like zoom but
+ 
+
+ align:start position:0%
+when they study things like zoom but
+they'd like to work with lave length
+
+ align:start position:0%
+they'd like to work with lave length
+ 
+
+ align:start position:0%
+they'd like to work with lave length
+when they study things like the spectra
+
+ align:start position:0%
+when they study things like the spectra
+ 
+
+ align:start position:0%
+when they study things like the spectra
+of distant astronomical objects and they
+
+ align:start position:0%
+of distant astronomical objects and they
+ 
+
+ align:start position:0%
+of distant astronomical objects and they
+use it to define a notion of redshift so
+
+ align:start position:0%
+use it to define a notion of redshift so
+ 
+
+ align:start position:0%
+use it to define a notion of redshift so
+we define the redshift Z to be the
+
+ align:start position:0%
+we define the redshift Z to be the
+ 
+
+ align:start position:0%
+we define the redshift Z to be the
+wavelength that we observe minus the
+
+ align:start position:0%
+wavelength that we observe minus the
+ 
+
+ align:start position:0%
+wavelength that we observe minus the
+wavelength at the radiation net when it
+
+ align:start position:0%
+wavelength at the radiation net when it
+ 
+
+ align:start position:0%
+wavelength at the radiation net when it
+is emitted divided by the wavelength
+
+ align:start position:0%
+is emitted divided by the wavelength
+ 
+
+ align:start position:0%
+is emitted divided by the wavelength
+when it was emitted put all of these
+
+ align:start position:0%
+when it was emitted put all of these
+ 
+
+ align:start position:0%
+when it was emitted put all of these
+definitions together and what this tells
+
+ align:start position:0%
+definitions together and what this tells
+ 
+
+ align:start position:0%
+definitions together and what this tells
+me is that the scale factor at which the
+
+ align:start position:0%
+me is that the scale factor at which the
+ 
+
+ align:start position:0%
+me is that the scale factor at which the
+radiation was emitted
+
+ align:start position:0%
+radiation was emitted
+ 
+
+ align:start position:0%
+radiation was emitted
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+it's simply related to the redshift that
+
+ align:start position:0%
+it's simply related to the redshift that
+ 
+
+ align:start position:0%
+it's simply related to the redshift that
+we observe so this at last gives us a
+
+ align:start position:0%
+we observe so this at last gives us a
+ 
+
+ align:start position:0%
+we observe so this at last gives us a
+direct and not terribly difficult to use
+
+ align:start position:0%
+direct and not terribly difficult to use
+ 
+
+ align:start position:0%
+direct and not terribly difficult to use
+observational proxy that directly
+
+ align:start position:0%
+observational proxy that directly
+ 
+
+ align:start position:0%
+observational proxy that directly
+encodes the scale factor of our universe
+
+ align:start position:0%
+encodes the scale factor of our universe
+ 
+
+ align:start position:0%
+encodes the scale factor of our universe
+suppose we measure the spectrum of
+
+ align:start position:0%
+suppose we measure the spectrum of
+ 
+
+ align:start position:0%
+suppose we measure the spectrum of
+radiation from some source and we see
+
+ align:start position:0%
+radiation from some source and we see
+ 
+
+ align:start position:0%
+radiation from some source and we see
+the the distinct sort of fingerprint
+
+ align:start position:0%
+the the distinct sort of fingerprint
+ 
+
+ align:start position:0%
+the the distinct sort of fingerprint
+associated with emission from a
+
+ align:start position:0%
+associated with emission from a
+ 
+
+ align:start position:0%
+associated with emission from a
+particular set of atomic transitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we generally find is from
+
+ align:start position:0%
+what we generally find is from
+ 
+
+ align:start position:0%
+what we generally find is from
+well-known fingerprints of well
+
+ align:start position:0%
+well-known fingerprints of well
+ 
+
+ align:start position:0%
+well-known fingerprints of well
+characterized transitions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but in general they are stretched by
+
+ align:start position:0%
+but in general they are stretched by
+ 
+
+ align:start position:0%
+but in general they are stretched by
+some factor that we call the redshift Z
+
+ align:start position:0%
+some factor that we call the redshift Z
+ 
+
+ align:start position:0%
+some factor that we call the redshift Z
+actually usually stretch by when you go
+
+ align:start position:0%
+actually usually stretch by when you go
+ 
+
+ align:start position:0%
+actually usually stretch by when you go
+through this you'll find that what you
+
+ align:start position:0%
+through this you'll find that what you
+ 
+
+ align:start position:0%
+through this you'll find that what you
+measure is actually stretched by one
+
+ align:start position:0%
+measure is actually stretched by one
+ 
+
+ align:start position:0%
+measure is actually stretched by one
+plus C you measure that you have
+
+ align:start position:0%
+plus C you measure that you have
+ 
+
+ align:start position:0%
+plus C you measure that you have
+measured the scale factor at which this
+
+ align:start position:0%
+measured the scale factor at which this
+ 
+
+ align:start position:0%
+measured the scale factor at which this
+radiation was measured was emitted so
+
+ align:start position:0%
+radiation was measured was emitted so
+ 
+
+ align:start position:0%
+radiation was measured was emitted so
+this is beautiful this is a way in which
+
+ align:start position:0%
+this is beautiful this is a way in which
+ 
+
+ align:start position:0%
+this is beautiful this is a way in which
+the universe hands us the tool by which
+
+ align:start position:0%
+the universe hands us the tool by which
+ 
+
+ align:start position:0%
+the universe hands us the tool by which
+we can directly characterize the sum of
+
+ align:start position:0%
+we can directly characterize the sum of
+ 
+
+ align:start position:0%
+we can directly characterize the sum of
+the geometry of the universe at which
+
+ align:start position:0%
+the geometry of the universe at which
+ 
+
+ align:start position:0%
+the geometry of the universe at which
+light has been emitted okay this is
+
+ align:start position:0%
+light has been emitted okay this is
+ 
+
+ align:start position:0%
+light has been emitted okay this is
+actually one of the reasons why a lot of
+
+ align:start position:0%
+actually one of the reasons why a lot of
+ 
+
+ align:start position:0%
+actually one of the reasons why a lot of
+people who do cosmology observational
+
+ align:start position:0%
+people who do cosmology observational
+ 
+
+ align:start position:0%
+people who do cosmology observational
+cosmology also happen to be expert
+
+ align:start position:0%
+cosmology also happen to be expert
+ 
+
+ align:start position:0%
+cosmology also happen to be expert
+atomic spectroscopy okay because you
+
+ align:start position:0%
+atomic spectroscopy okay because you
+ 
+
+ align:start position:0%
+atomic spectroscopy okay because you
+want to know to very high precision what
+
+ align:start position:0%
+want to know to very high precision what
+ 
+
+ align:start position:0%
+want to know to very high precision what
+is the characteristics of the hydrogen
+
+ align:start position:0%
+is the characteristics of the hydrogen
+ 
+
+ align:start position:0%
+is the characteristics of the hydrogen
+embalmer lines some of the most
+
+ align:start position:0%
+embalmer lines some of the most
+ 
+
+ align:start position:0%
+embalmer lines some of the most
+important sources for doing these tend
+
+ align:start position:0%
+important sources for doing these tend
+ 
+
+ align:start position:0%
+important sources for doing these tend
+to be galaxies in which there's a lot of
+
+ align:start position:0%
+to be galaxies in which there's a lot of
+ 
+
+ align:start position:0%
+to be galaxies in which there's a lot of
+matter falling on to black holes some of
+
+ align:start position:0%
+matter falling on to black holes some of
+ 
+
+ align:start position:0%
+matter falling on to black holes some of
+the topics we'll be talking about in an
+
+ align:start position:0%
+the topics we'll be talking about in an
+ 
+
+ align:start position:0%
+the topics we'll be talking about in an
+upcoming video as that material falls in
+
+ align:start position:0%
+upcoming video as that material falls in
+ 
+
+ align:start position:0%
+upcoming video as that material falls in
+it gets hot it generates a lot of
+
+ align:start position:0%
+it gets hot it generates a lot of
+ 
+
+ align:start position:0%
+it gets hot it generates a lot of
+radiation and you'll see things like
+
+ align:start position:0%
+radiation and you'll see things like
+ 
+
+ align:start position:0%
+radiation and you'll see things like
+transition lines associated with carbon
+
+ align:start position:0%
+transition lines associated with carbon
+ 
+
+ align:start position:0%
+transition lines associated with carbon
+and iron but often all reddened by a
+
+ align:start position:0%
+and iron but often all reddened by a
+ 
+
+ align:start position:0%
+and iron but often all reddened by a
+factor of several when you sort of go oh
+
+ align:start position:0%
+factor of several when you sort of go oh
+ 
+
+ align:start position:0%
+factor of several when you sort of go oh
+look at that carbon falling on to a
+
+ align:start position:0%
+look at that carbon falling on to a
+ 
+
+ align:start position:0%
+look at that carbon falling on to a
+black hole at redshift 4.8 that is
+
+ align:start position:0%
+black hole at redshift 4.8 that is
+ 
+
+ align:start position:0%
+black hole at redshift 4.8 that is
+happening at a time when the scale
+
+ align:start position:0%
+happening at a time when the scale
+ 
+
+ align:start position:0%
+happening at a time when the scale
+factor the universe was 1 over 4.8 or
+
+ align:start position:0%
+factor the universe was 1 over 4.8 or
+ 
+
+ align:start position:0%
+factor the universe was 1 over 4.8 or
+one number 5.8 forgot to my factor of 1
+
+ align:start position:0%
+one number 5.8 forgot to my factor of 1
+ 
+
+ align:start position:0%
+one number 5.8 forgot to my factor of 1
+plus there
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you measure the redshift and you have
+
+ align:start position:0%
+so you measure the redshift and you have
+ 
+
+ align:start position:0%
+so you measure the redshift and you have
+measured the scale factor but you don't
+
+ align:start position:0%
+measured the scale factor but you don't
+ 
+
+ align:start position:0%
+measured the scale factor but you don't
+know when that light was emitted we need
+
+ align:start position:0%
+know when that light was emitted we need
+ 
+
+ align:start position:0%
+know when that light was emitted we need
+to connect the scale factor that we can
+
+ align:start position:0%
+to connect the scale factor that we can
+ 
+
+ align:start position:0%
+to connect the scale factor that we can
+measure so directly in so beautifully to
+
+ align:start position:0%
+measure so directly in so beautifully to
+ 
+
+ align:start position:0%
+measure so directly in so beautifully to
+the time at which it was emitted okay we
+
+ align:start position:0%
+the time at which it was emitted okay we
+ 
+
+ align:start position:0%
+the time at which it was emitted okay we
+now have a way of determining a but we
+
+ align:start position:0%
+now have a way of determining a but we
+ 
+
+ align:start position:0%
+now have a way of determining a but we
+need a as a function of T okay and in
+
+ align:start position:0%
+need a as a function of T okay and in
+ 
+
+ align:start position:0%
+need a as a function of T okay and in
+truth we do this kind of via a surrogate
+
+ align:start position:0%
+truth we do this kind of via a surrogate
+ 
+
+ align:start position:0%
+truth we do this kind of via a surrogate
+because we are using radiation as our
+
+ align:start position:0%
+because we are using radiation as our
+ 
+
+ align:start position:0%
+because we are using radiation as our
+tool for probing the scale factor we
+
+ align:start position:0%
+tool for probing the scale factor we
+ 
+
+ align:start position:0%
+tool for probing the scale factor we
+really don't measure T directly okay
+
+ align:start position:0%
+really don't measure T directly okay
+ 
+
+ align:start position:0%
+really don't measure T directly okay
+when we look at light and it's coming to
+
+ align:start position:0%
+when we look at light and it's coming to
+ 
+
+ align:start position:0%
+when we look at light and it's coming to
+us it doesn't say I was emitted on March
+
+ align:start position:0%
+us it doesn't say I was emitted on March
+ 
+
+ align:start position:0%
+us it doesn't say I was emitted on March
+27th of the year negative six point
+
+ align:start position:0%
+27th of the year negative six point
+ 
+
+ align:start position:0%
+27th of the year negative six point
+eight billion BC or something like that
+
+ align:start position:0%
+eight billion BC or something like that
+ 
+
+ align:start position:0%
+eight billion BC or something like that
+we do know though that it traveled
+
+ align:start position:0%
+we do know though that it traveled
+ 
+
+ align:start position:0%
+we do know though that it traveled
+towards us at the speed of light on a
+
+ align:start position:0%
+towards us at the speed of light on a
+ 
+
+ align:start position:0%
+towards us at the speed of light on a
+null geodesic and because it's a null
+
+ align:start position:0%
+null geodesic and because it's a null
+ 
+
+ align:start position:0%
+null geodesic and because it's a null
+geodesic there's a very simple simple a
+
+ align:start position:0%
+geodesic there's a very simple simple a
+ 
+
+ align:start position:0%
+geodesic there's a very simple simple a
+little bit of an overstatement but there
+
+ align:start position:0%
+little bit of an overstatement but there
+ 
+
+ align:start position:0%
+little bit of an overstatement but there
+is at least a calculable connection
+
+ align:start position:0%
+is at least a calculable connection
+ 
+
+ align:start position:0%
+is at least a calculable connection
+because it's moving at the speed of
+
+ align:start position:0%
+because it's moving at the speed of
+ 
+
+ align:start position:0%
+because it's moving at the speed of
+light we can simply should stop using
+
+ align:start position:0%
+light we can simply should stop using
+ 
+
+ align:start position:0%
+light we can simply should stop using
+that word
+
+ align:start position:0%
+that word
+ 
+
+ align:start position:0%
+that word
+we can connect time to space and so
+
+ align:start position:0%
+we can connect time to space and so
+ 
+
+ align:start position:0%
+we can connect time to space and so
+rather than directly determining the
+
+ align:start position:0%
+rather than directly determining the
+ 
+
+ align:start position:0%
+rather than directly determining the
+time at which the radiation was emitted
+
+ align:start position:0%
+time at which the radiation was emitted
+ 
+
+ align:start position:0%
+time at which the radiation was emitted
+we want to calculate the distance of the
+
+ align:start position:0%
+we want to calculate the distance of the
+ 
+
+ align:start position:0%
+we want to calculate the distance of the
+source from us that emitted it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so rather than directly building up a of
+
+ align:start position:0%
+so rather than directly building up a of
+ 
+
+ align:start position:0%
+so rather than directly building up a of
+tea we're going to build up an a of D
+
+ align:start position:0%
+tea we're going to build up an a of D
+ 
+
+ align:start position:0%
+tea we're going to build up an a of D
+okay where D is the distance of the
+
+ align:start position:0%
+okay where D is the distance of the
+ 
+
+ align:start position:0%
+okay where D is the distance of the
+source and if you're used to working in
+
+ align:start position:0%
+source and if you're used to working in
+ 
+
+ align:start position:0%
+source and if you're used to working in
+sort of Euclidean geometry so we go ah
+
+ align:start position:0%
+sort of Euclidean geometry so we go ah
+ 
+
+ align:start position:0%
+sort of Euclidean geometry so we go ah
+okay great I know that light travels at
+
+ align:start position:0%
+okay great I know that light travels at
+ 
+
+ align:start position:0%
+okay great I know that light travels at
+the speed of light so all I need to do
+
+ align:start position:0%
+the speed of light so all I need to do
+ 
+
+ align:start position:0%
+the speed of light so all I need to do
+is divide the distance by C and I've got
+
+ align:start position:0%
+is divide the distance by C and I've got
+ 
+
+ align:start position:0%
+is divide the distance by C and I've got
+the time and I build a of T conceptually
+
+ align:start position:0%
+the time and I build a of T conceptually
+ 
+
+ align:start position:0%
+the time and I build a of T conceptually
+that is roughly right and that gives at
+
+ align:start position:0%
+that is roughly right and that gives at
+ 
+
+ align:start position:0%
+that is roughly right and that gives at
+least a cartoon or the idea that's going
+
+ align:start position:0%
+least a cartoon or the idea that's going
+ 
+
+ align:start position:0%
+least a cartoon or the idea that's going
+on here but we have to be a little bit
+
+ align:start position:0%
+on here but we have to be a little bit
+ 
+
+ align:start position:0%
+on here but we have to be a little bit
+careful okay because it turns out when
+
+ align:start position:0%
+careful okay because it turns out when
+ 
+
+ align:start position:0%
+careful okay because it turns out when
+you are making measurements in a curved
+
+ align:start position:0%
+you are making measurements in a curved
+ 
+
+ align:start position:0%
+you are making measurements in a curved
+space-time the notion of distance that
+
+ align:start position:0%
+space-time the notion of distance that
+ 
+
+ align:start position:0%
+space-time the notion of distance that
+you use depends on how you make the
+
+ align:start position:0%
+you use depends on how you make the
+ 
+
+ align:start position:0%
+you use depends on how you make the
+distance measurement so this leads us
+
+ align:start position:0%
+distance measurement so this leads us
+ 
+
+ align:start position:0%
+distance measurement so this leads us
+now to our discussion of distance
+
+ align:start position:0%
+now to our discussion of distance
+ 
+
+ align:start position:0%
+now to our discussion of distance
+measures in cosmological spacetimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so just to get a little bit of intuition
+
+ align:start position:0%
+so just to get a little bit of intuition
+ 
+
+ align:start position:0%
+so just to get a little bit of intuition
+as to what's needed or look at the kind
+
+ align:start position:0%
+as to what's needed or look at the kind
+ 
+
+ align:start position:0%
+as to what's needed or look at the kind
+of calculation we're going to need to do
+
+ align:start position:0%
+of calculation we're going to need to do
+ 
+
+ align:start position:0%
+of calculation we're going to need to do
+let me describe one distance measure
+
+ align:start position:0%
+let me describe one distance measure
+ 
+
+ align:start position:0%
+let me describe one distance measure
+that is observation it's just about
+
+ align:start position:0%
+that is observation it's just about
+ 
+
+ align:start position:0%
+that is observation it's just about
+useless but it's not a bad thing to at
+
+ align:start position:0%
+useless but it's not a bad thing to at
+ 
+
+ align:start position:0%
+useless but it's not a bad thing to at
+least you know begin to get a get a
+
+ align:start position:0%
+least you know begin to get a get a
+ 
+
+ align:start position:0%
+least you know begin to get a get a
+handle on the way different the way
+
+ align:start position:0%
+handle on the way different the way
+ 
+
+ align:start position:0%
+handle on the way different the way
+different parameters of the space-time
+
+ align:start position:0%
+different parameters of the space-time
+ 
+
+ align:start position:0%
+different parameters of the space-time
+come in and influence what the distance
+
+ align:start position:0%
+come in and influence what the distance
+ 
+
+ align:start position:0%
+come in and influence what the distance
+measure means so let's just think about
+
+ align:start position:0%
+measure means so let's just think about
+ 
+
+ align:start position:0%
+measure means so let's just think about
+the proper distance from us to a source
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see let's imagine that let's
+
+ align:start position:0%
+so let's see let's imagine that let's
+ 
+
+ align:start position:0%
+so let's see let's imagine that let's
+just begin by first let's write down my
+
+ align:start position:0%
+just begin by first let's write down my
+ 
+
+ align:start position:0%
+just begin by first let's write down my
+line element and here's the form that
+
+ align:start position:0%
+line element and here's the form that
+ 
+
+ align:start position:0%
+line element and here's the form that
+I'm going to use okay so here's my line
+
+ align:start position:0%
+I'm going to use okay so here's my line
+ 
+
+ align:start position:0%
+I'm going to use okay so here's my line
+element this is my differential
+
+ align:start position:0%
+element this is my differential
+ 
+
+ align:start position:0%
+element this is my differential
+connection between two events spaced
+
+ align:start position:0%
+connection between two events spaced
+ 
+
+ align:start position:0%
+connection between two events spaced
+between one another by DT D KY D theta D
+
+ align:start position:0%
+between one another by DT D KY D theta D
+ 
+
+ align:start position:0%
+between one another by DT D KY D theta D
+Phi all hidden in that angular angular
+
+ align:start position:0%
+Phi all hidden in that angular angular
+ 
+
+ align:start position:0%
+Phi all hidden in that angular angular
+element D Omega so let's imagine that we
+
+ align:start position:0%
+element D Omega so let's imagine that we
+ 
+
+ align:start position:0%
+element D Omega so let's imagine that we
+want to consider two sources that are
+
+ align:start position:0%
+want to consider two sources that are
+ 
+
+ align:start position:0%
+want to consider two sources that are
+separated purely in the radial direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so my angular displacement machine the
+
+ align:start position:0%
+so my angular displacement machine the
+ 
+
+ align:start position:0%
+so my angular displacement machine the
+two events it's going to be zero so the
+
+ align:start position:0%
+two events it's going to be zero so the
+ 
+
+ align:start position:0%
+two events it's going to be zero so the
+only thing I need to care about is D Chi
+
+ align:start position:0%
+only thing I need to care about is D Chi
+ 
+
+ align:start position:0%
+only thing I need to care about is D Chi
+and let's imagine that I determine the
+
+ align:start position:0%
+and let's imagine that I determine the
+ 
+
+ align:start position:0%
+and let's imagine that I determine the
+distance between these two at some
+
+ align:start position:0%
+distance between these two at some
+ 
+
+ align:start position:0%
+distance between these two at some
+instant okay so then you just get DS
+
+ align:start position:0%
+instant okay so then you just get DS
+ 
+
+ align:start position:0%
+instant okay so then you just get DS
+squared equals a squared r0 squared D KY
+
+ align:start position:0%
+squared equals a squared r0 squared D KY
+ 
+
+ align:start position:0%
+squared equals a squared r0 squared D KY
+squared and you can integrate this up
+
+ align:start position:0%
+squared and you can integrate this up
+ 
+
+ align:start position:0%
+squared and you can integrate this up
+and you get our first distance measure D
+
+ align:start position:0%
+and you get our first distance measure D
+ 
+
+ align:start position:0%
+and you get our first distance measure D
+sub P equals scale factor your overall
+
+ align:start position:0%
+sub P equals scale factor your overall
+ 
+
+ align:start position:0%
+sub P equals scale factor your overall
+distance scale are 0 and Chi so Carol's
+
+ align:start position:0%
+distance scale are 0 and Chi so Carol's
+ 
+
+ align:start position:0%
+distance scale are 0 and Chi so Carol's
+textbook calls this the instantaneous
+
+ align:start position:0%
+textbook calls this the instantaneous
+ 
+
+ align:start position:0%
+textbook calls this the instantaneous
+physical distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's think about what this means if you
+
+ align:start position:0%
+let's think about what this means if you
+ 
+
+ align:start position:0%
+let's think about what this means if you
+do this this is basically the distance
+
+ align:start position:0%
+do this this is basically the distance
+ 
+
+ align:start position:0%
+do this this is basically the distance
+you would get if you took a yardstick
+
+ align:start position:0%
+you would get if you took a yardstick
+ 
+
+ align:start position:0%
+you would get if you took a yardstick
+you put one end at yourself you're gonna
+
+ align:start position:0%
+you put one end at yourself you're gonna
+ 
+
+ align:start position:0%
+you put one end at yourself you're gonna
+call yourself Chi equals zero you put
+
+ align:start position:0%
+call yourself Chi equals zero you put
+ 
+
+ align:start position:0%
+call yourself Chi equals zero you put
+the other end of the yardstick at the
+
+ align:start position:0%
+the other end of the yardstick at the
+ 
+
+ align:start position:0%
+the other end of the yardstick at the
+object in your universe at some of some
+
+ align:start position:0%
+object in your universe at some of some
+ 
+
+ align:start position:0%
+object in your universe at some of some
+distance Chi in these coordinates and
+
+ align:start position:0%
+distance Chi in these coordinates and
+ 
+
+ align:start position:0%
+distance Chi in these coordinates and
+that's the distance D sub P is the
+
+ align:start position:0%
+that's the distance D sub P is the
+ 
+
+ align:start position:0%
+that's the distance D sub P is the
+distance that you measure it is done
+
+ align:start position:0%
+distance that you measure it is done
+ 
+
+ align:start position:0%
+distance that you measure it is done
+you're sort of imagining that both of
+
+ align:start position:0%
+you're sort of imagining that both of
+ 
+
+ align:start position:0%
+you're sort of imagining that both of
+the events at the end of this yardstick
+
+ align:start position:0%
+the events at the end of this yardstick
+ 
+
+ align:start position:0%
+the events at the end of this yardstick
+you're sort of ascertaining their
+
+ align:start position:0%
+you're sort of ascertaining their
+ 
+
+ align:start position:0%
+you're sort of ascertaining their
+position at exactly the same instant
+
+ align:start position:0%
+position at exactly the same instant
+ 
+
+ align:start position:0%
+position at exactly the same instant
+hence the term instantaneous and you get
+
+ align:start position:0%
+hence the term instantaneous and you get
+ 
+
+ align:start position:0%
+hence the term instantaneous and you get
+something out of it that encodes some
+
+ align:start position:0%
+something out of it that encodes some
+ 
+
+ align:start position:0%
+something out of it that encodes some
+important aspects of how we think about
+
+ align:start position:0%
+important aspects of how we think about
+ 
+
+ align:start position:0%
+important aspects of how we think about
+distances in cosmology so notice
+
+ align:start position:0%
+distances in cosmology so notice
+ 
+
+ align:start position:0%
+distances in cosmology so notice
+everything scales with the overall
+
+ align:start position:0%
+everything scales with the overall
+ 
+
+ align:start position:0%
+everything scales with the overall
+length scale that we associate it with
+
+ align:start position:0%
+length scale that we associate it with
+ 
+
+ align:start position:0%
+length scale that we associate it with
+our spatial slices with our spatial
+
+ align:start position:0%
+our spatial slices with our spatial
+ 
+
+ align:start position:0%
+our spatial slices with our spatial
+sector of this metric the are zero
+
+ align:start position:0%
+sector of this metric the are zero
+ 
+
+ align:start position:0%
+sector of this metric the are zero
+notice that whatever is going on with
+
+ align:start position:0%
+notice that whatever is going on with
+ 
+
+ align:start position:0%
+notice that whatever is going on with
+your scale factor your a your distance
+
+ align:start position:0%
+your scale factor your a your distance
+ 
+
+ align:start position:0%
+your scale factor your a your distance
+is going to track that as a consequence
+
+ align:start position:0%
+is going to track that as a consequence
+ 
+
+ align:start position:0%
+is going to track that as a consequence
+of this two objects that are sitting in
+
+ align:start position:0%
+of this two objects that are sitting in
+ 
+
+ align:start position:0%
+of this two objects that are sitting in
+what we call the Hubble flow in other
+
+ align:start position:0%
+what we call the Hubble flow in other
+ 
+
+ align:start position:0%
+what we call the Hubble flow in other
+words two objects that are Co moving
+
+ align:start position:0%
+words two objects that are Co moving
+ 
+
+ align:start position:0%
+words two objects that are Co moving
+with the the fluid that makes up the
+
+ align:start position:0%
+with the the fluid that makes up the
+ 
+
+ align:start position:0%
+with the the fluid that makes up the
+source of our universe they have an
+
+ align:start position:0%
+source of our universe they have an
+ 
+
+ align:start position:0%
+source of our universe they have an
+apparent motion with respect to each
+
+ align:start position:0%
+apparent motion with respect to each
+ 
+
+ align:start position:0%
+apparent motion with respect to each
+other
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I take the time derivative of this via
+
+ align:start position:0%
+I take the time derivative of this via
+ 
+
+ align:start position:0%
+I take the time derivative of this via
+parent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes the apparent is just a dot R zero
+
+ align:start position:0%
+yes the apparent is just a dot R zero
+ 
+
+ align:start position:0%
+yes the apparent is just a dot R zero
+Chi which is equal to the Hubble
+
+ align:start position:0%
+Chi which is equal to the Hubble
+ 
+
+ align:start position:0%
+Chi which is equal to the Hubble
+parameter times DP okay recall that the
+
+ align:start position:0%
+parameter times DP okay recall that the
+ 
+
+ align:start position:0%
+parameter times DP okay recall that the
+Hubble parameter it is a dot over a and
+
+ align:start position:0%
+Hubble parameter it is a dot over a and
+ 
+
+ align:start position:0%
+Hubble parameter it is a dot over a and
+if I'm doing this right now that's the
+
+ align:start position:0%
+if I'm doing this right now that's the
+ 
+
+ align:start position:0%
+if I'm doing this right now that's the
+Hubble value of the Hubble parameter now
+
+ align:start position:0%
+Hubble value of the Hubble parameter now
+ 
+
+ align:start position:0%
+Hubble value of the Hubble parameter now
+so this is the Hubble expansion laws a
+
+ align:start position:0%
+so this is the Hubble expansion laws a
+ 
+
+ align:start position:0%
+so this is the Hubble expansion laws a
+very famous Hubble expansion law okay so
+
+ align:start position:0%
+very famous Hubble expansion law okay so
+ 
+
+ align:start position:0%
+very famous Hubble expansion law okay so
+we can see it hidden in this not even
+
+ align:start position:0%
+we can see it hidden in this not even
+ 
+
+ align:start position:0%
+we can see it hidden in this not even
+really hidden that's quite apparent in
+
+ align:start position:0%
+really hidden that's quite apparent in
+ 
+
+ align:start position:0%
+really hidden that's quite apparent in
+this notion of an instantaneous physical
+
+ align:start position:0%
+this notion of an instantaneous physical
+ 
+
+ align:start position:0%
+this notion of an instantaneous physical
+distance let me just finally emphasize
+
+ align:start position:0%
+distance let me just finally emphasize
+ 
+
+ align:start position:0%
+distance let me just finally emphasize
+though that the instance in a'ti that is
+
+ align:start position:0%
+though that the instance in a'ti that is
+ 
+
+ align:start position:0%
+though that the instance in a'ti that is
+part of this objects name instantaneous
+
+ align:start position:0%
+part of this objects name instantaneous
+ 
+
+ align:start position:0%
+part of this objects name instantaneous
+measurements are not done okay so i as i
+
+ align:start position:0%
+measurements are not done okay so i as i
+ 
+
+ align:start position:0%
+measurements are not done okay so i as i
+said i mean this is it sounds like i'm
+
+ align:start position:0%
+said i mean this is it sounds like i'm
+ 
+
+ align:start position:0%
+said i mean this is it sounds like i'm
+being slightly facetious but it's not
+
+ align:start position:0%
+being slightly facetious but it's not
+ 
+
+ align:start position:0%
+being slightly facetious but it's not
+the meaning of this distance measure is
+
+ align:start position:0%
+the meaning of this distance measure is
+ 
+
+ align:start position:0%
+the meaning of this distance measure is
+like I said it's a yardstick where I
+
+ align:start position:0%
+like I said it's a yardstick where I
+ 
+
+ align:start position:0%
+like I said it's a yardstick where I
+have an event at me the other end of my
+
+ align:start position:0%
+have an event at me the other end of my
+ 
+
+ align:start position:0%
+have an event at me the other end of my
+yardstick is at my cosmological event
+
+ align:start position:0%
+yardstick is at my cosmological event
+ 
+
+ align:start position:0%
+yardstick is at my cosmological event
+those are typically separated by
+
+ align:start position:0%
+those are typically separated by
+ 
+
+ align:start position:0%
+those are typically separated by
+millions billions of light years okay
+
+ align:start position:0%
+millions billions of light years okay
+ 
+
+ align:start position:0%
+millions billions of light years okay
+even if you could okay
+
+ align:start position:0%
+even if you could okay
+ 
+
+ align:start position:0%
+even if you could okay
+the facetious bit was imagining this a
+
+ align:start position:0%
+the facetious bit was imagining this a
+ 
+
+ align:start position:0%
+the facetious bit was imagining this a
+yardstick but the non facetious point I
+
+ align:start position:0%
+yardstick but the non facetious point I
+ 
+
+ align:start position:0%
+yardstick but the non facetious point I
+want to make is we do not make
+
+ align:start position:0%
+want to make is we do not make
+ 
+
+ align:start position:0%
+want to make is we do not make
+instantaneous measurements with that
+
+ align:start position:0%
+instantaneous measurements with that
+ 
+
+ align:start position:0%
+instantaneous measurements with that
+okay when I measure an event that is
+
+ align:start position:0%
+okay when I measure an event that is
+ 
+
+ align:start position:0%
+okay when I measure an event that is
+billions of light years away I am of
+
+ align:start position:0%
+billions of light years away I am of
+ 
+
+ align:start position:0%
+billions of light years away I am of
+course measuring it using lights and I'm
+
+ align:start position:0%
+course measuring it using lights and I'm
+ 
+
+ align:start position:0%
+course measuring it using lights and I'm
+seeing light that was emitted billions
+
+ align:start position:0%
+seeing light that was emitted billions
+ 
+
+ align:start position:0%
+seeing light that was emitted billions
+of years ago so we need to think a
+
+ align:start position:0%
+of years ago so we need to think a
+ 
+
+ align:start position:0%
+of years ago so we need to think a
+little bit more carefully about how to
+
+ align:start position:0%
+little bit more carefully about how to
+ 
+
+ align:start position:0%
+little bit more carefully about how to
+define distance in terms of quantities
+
+ align:start position:0%
+define distance in terms of quantities
+ 
+
+ align:start position:0%
+define distance in terms of quantities
+that really correspond to measurements
+
+ align:start position:0%
+that really correspond to measurements
+ 
+
+ align:start position:0%
+that really correspond to measurements
+we can make
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and to get a little intuition here are
+
+ align:start position:0%
+and to get a little intuition here are
+ 
+
+ align:start position:0%
+and to get a little intuition here are
+three ways where if you were living in
+
+ align:start position:0%
+three ways where if you were living in
+ 
+
+ align:start position:0%
+three ways where if you were living in
+Euclidean space and you were looking at
+
+ align:start position:0%
+Euclidean space and you were looking at
+ 
+
+ align:start position:0%
+Euclidean space and you were looking at
+light from distant objects here are
+
+ align:start position:0%
+light from distant objects here are
+ 
+
+ align:start position:0%
+light from distant objects here are
+three ways that you could define
+
+ align:start position:0%
+three ways that you could define
+ 
+
+ align:start position:0%
+three ways that you could define
+distance so if space-time were that of
+
+ align:start position:0%
+distance so if space-time were that of
+ 
+
+ align:start position:0%
+distance so if space-time were that of
+special relativity well let's just say
+
+ align:start position:0%
+special relativity well let's just say
+ 
+
+ align:start position:0%
+special relativity well let's just say
+if space were purely Euclidean let's
+
+ align:start position:0%
+if space were purely Euclidean let's
+ 
+
+ align:start position:0%
+if space were purely Euclidean let's
+just leave it like that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here are three notions that we could use
+
+ align:start position:0%
+here are three notions that we could use
+ 
+
+ align:start position:0%
+here are three notions that we could use
+what imagine there was some source of
+
+ align:start position:0%
+what imagine there was some source of
+ 
+
+ align:start position:0%
+what imagine there was some source of
+radiation in the universe that you
+
+ align:start position:0%
+radiation in the universe that you
+ 
+
+ align:start position:0%
+radiation in the universe that you
+understood so well that you knew its
+
+ align:start position:0%
+understood so well that you knew its
+ 
+
+ align:start position:0%
+understood so well that you knew its
+intrinsic luminosity what you could do
+
+ align:start position:0%
+intrinsic luminosity what you could do
+ 
+
+ align:start position:0%
+intrinsic luminosity what you could do
+is compare the intrinsic luminosity of a
+
+ align:start position:0%
+is compare the intrinsic luminosity of a
+ 
+
+ align:start position:0%
+is compare the intrinsic luminosity of a
+source to its apparent brightness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's let f be the flux we measure
+
+ align:start position:0%
+so let's let f be the flux we measure
+ 
+
+ align:start position:0%
+so let's let f be the flux we measure
+from this source this will be related to
+
+ align:start position:0%
+from this source this will be related to
+ 
+
+ align:start position:0%
+from this source this will be related to
+L the luminosity which suspend disbelief
+
+ align:start position:0%
+L the luminosity which suspend disbelief
+ 
+
+ align:start position:0%
+L the luminosity which suspend disbelief
+for a moment want to sort of imagine
+
+ align:start position:0%
+for a moment want to sort of imagine
+ 
+
+ align:start position:0%
+for a moment want to sort of imagine
+that we know it for some reason and if
+
+ align:start position:0%
+that we know it for some reason and if
+ 
+
+ align:start position:0%
+that we know it for some reason and if
+we imagine this is an isotropic emitter
+
+ align:start position:0%
+we imagine this is an isotropic emitter
+ 
+
+ align:start position:0%
+we imagine this is an isotropic emitter
+this will be related by a factor of four
+
+ align:start position:0%
+this will be related by a factor of four
+ 
+
+ align:start position:0%
+this will be related by a factor of four
+pi and the distance between us and that
+
+ align:start position:0%
+pi and the distance between us and that
+ 
+
+ align:start position:0%
+pi and the distance between us and that
+source let's call this D sub L this is a
+
+ align:start position:0%
+source let's call this D sub L this is a
+ 
+
+ align:start position:0%
+source let's call this D sub L this is a
+luminosity distance it is a distance it
+
+ align:start position:0%
+luminosity distance it is a distance it
+ 
+
+ align:start position:0%
+luminosity distance it is a distance it
+is a distance that we measure by
+
+ align:start position:0%
+is a distance that we measure by
+ 
+
+ align:start position:0%
+is a distance that we measure by
+inferring the behavior of luminosity of
+
+ align:start position:0%
+inferring the behavior of luminosity of
+ 
+
+ align:start position:0%
+inferring the behavior of luminosity of
+a distant object now it turns out and
+
+ align:start position:0%
+a distant object now it turns out and
+ 
+
+ align:start position:0%
+a distant object now it turns out and
+this is a subject for a different class
+
+ align:start position:0%
+this is a subject for a different class
+ 
+
+ align:start position:0%
+this is a subject for a different class
+but nature actually gives us some
+
+ align:start position:0%
+but nature actually gives us some
+ 
+
+ align:start position:0%
+but nature actually gives us some
+objects whose luminosity is known or at
+
+ align:start position:0%
+objects whose luminosity is known or at
+ 
+
+ align:start position:0%
+objects whose luminosity is known or at
+least can be calibrated in the case of
+
+ align:start position:0%
+least can be calibrated in the case of
+ 
+
+ align:start position:0%
+least can be calibrated in the case of
+much of what is done in cosmology today
+
+ align:start position:0%
+much of what is done in cosmology today
+ 
+
+ align:start position:0%
+much of what is done in cosmology today
+we can take advantage of the behavior of
+
+ align:start position:0%
+we can take advantage of the behavior of
+ 
+
+ align:start position:0%
+we can take advantage of the behavior of
+certain stars whose luminosity is
+
+ align:start position:0%
+certain stars whose luminosity is
+ 
+
+ align:start position:0%
+certain stars whose luminosity is
+strongly correlated to the way that they
+
+ align:start position:0%
+strongly correlated to the way that they
+ 
+
+ align:start position:0%
+strongly correlated to the way that they
+that their these are stars whose
+
+ align:start position:0%
+that their these are stars whose
+ 
+
+ align:start position:0%
+that their these are stars whose
+luminosity is variable and we can use
+
+ align:start position:0%
+luminosity is variable and we can use
+ 
+
+ align:start position:0%
+luminosity is variable and we can use
+the fact that their variability is
+
+ align:start position:0%
+the fact that their variability is
+ 
+
+ align:start position:0%
+the fact that their variability is
+correlated to the luminosity to infer
+
+ align:start position:0%
+correlated to the luminosity to infer
+ 
+
+ align:start position:0%
+correlated to the luminosity to infer
+what their absolute luminosity actually
+
+ align:start position:0%
+what their absolute luminosity actually
+ 
+
+ align:start position:0%
+what their absolute luminosity actually
+is there are other supernova events
+
+ align:start position:0%
+is there are other supernova events
+ 
+
+ align:start position:0%
+is there are other supernova events
+whose luminosity likewise
+
+ align:start position:0%
+whose luminosity likewise
+ 
+
+ align:start position:0%
+whose luminosity likewise
+appears to follow a universal law it's
+
+ align:start position:0%
+appears to follow a universal law it's
+ 
+
+ align:start position:0%
+appears to follow a universal law it's
+related to the fact that the explosions
+
+ align:start position:0%
+related to the fact that the explosions
+ 
+
+ align:start position:0%
+related to the fact that the explosions
+of these objects are the properties of
+
+ align:start position:0%
+of these objects are the properties of
+ 
+
+ align:start position:0%
+of these objects are the properties of
+those explosions are actually set by the
+
+ align:start position:0%
+those explosions are actually set by the
+ 
+
+ align:start position:0%
+those explosions are actually set by the
+micro physics of the stars that set them
+
+ align:start position:0%
+micro physics of the stars that set them
+ 
+
+ align:start position:0%
+micro physics of the stars that set them
+more recently we've been able to exploit
+
+ align:start position:0%
+more recently we've been able to exploit
+ 
+
+ align:start position:0%
+more recently we've been able to exploit
+the fact that gravitational wave sources
+
+ align:start position:0%
+the fact that gravitational wave sources
+ 
+
+ align:start position:0%
+the fact that gravitational wave sources
+have an intrinsic luminosity in
+
+ align:start position:0%
+have an intrinsic luminosity in
+ 
+
+ align:start position:0%
+have an intrinsic luminosity in
+gravitational waves that the EDT
+
+ align:start position:0%
+gravitational waves that the EDT
+ 
+
+ align:start position:0%
+gravitational waves that the EDT
+associate the gravitation waves that
+
+ align:start position:0%
+associate the gravitation waves that
+ 
+
+ align:start position:0%
+associate the gravitation waves that
+they emit which depends on the source
+
+ align:start position:0%
+they emit which depends on the source
+ 
+
+ align:start position:0%
+they emit which depends on the source
+gravitational physics in a very simple
+
+ align:start position:0%
+gravitational physics in a very simple
+ 
+
+ align:start position:0%
+gravitational physics in a very simple
+predictable way that doesn't depend on
+
+ align:start position:0%
+predictable way that doesn't depend on
+ 
+
+ align:start position:0%
+predictable way that doesn't depend on
+very many parameters my she did a little
+
+ align:start position:0%
+very many parameters my she did a little
+ 
+
+ align:start position:0%
+very many parameters my she did a little
+bit of
+
+ align:start position:0%
+bit of
+ 
+
+ align:start position:0%
+bit of
+work on that over the course of my
+
+ align:start position:0%
+work on that over the course of my
+ 
+
+ align:start position:0%
+work on that over the course of my
+career and it's a very exciting
+
+ align:start position:0%
+career and it's a very exciting
+ 
+
+ align:start position:0%
+career and it's a very exciting
+development that we can now use these
+
+ align:start position:0%
+development that we can now use these
+ 
+
+ align:start position:0%
+development that we can now use these
+the way of setting sort of the intrinsic
+
+ align:start position:0%
+the way of setting sort of the intrinsic
+ 
+
+ align:start position:0%
+the way of setting sort of the intrinsic
+luminosity of certain sources at a rate
+
+ align:start position:0%
+luminosity of certain sources at a rate
+ 
+
+ align:start position:0%
+luminosity of certain sources at a rate
+if you can take advantage of these
+
+ align:start position:0%
+if you can take advantage of these
+ 
+
+ align:start position:0%
+if you can take advantage of these
+objects that have a known luminosity and
+
+ align:start position:0%
+objects that have a known luminosity and
+ 
+
+ align:start position:0%
+objects that have a known luminosity and
+you can then measure the flux of
+
+ align:start position:0%
+you can then measure the flux of
+ 
+
+ align:start position:0%
+you can then measure the flux of
+radiation in your detector from these
+
+ align:start position:0%
+radiation in your detector from these
+ 
+
+ align:start position:0%
+radiation in your detector from these
+things you have learned the distance at
+
+ align:start position:0%
+things you have learned the distance at
+ 
+
+ align:start position:0%
+things you have learned the distance at
+least you have learned this particular
+
+ align:start position:0%
+least you have learned this particular
+ 
+
+ align:start position:0%
+least you have learned this particular
+measure of the distance let's measure
+
+ align:start position:0%
+measure of the distance let's measure
+ 
+
+ align:start position:0%
+measure of the distance let's measure
+one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+measure to is compare imagining of some
+
+ align:start position:0%
+measure to is compare imagining of some
+ 
+
+ align:start position:0%
+measure to is compare imagining of some
+object in the sky that has a particular
+
+ align:start position:0%
+object in the sky that has a particular
+ 
+
+ align:start position:0%
+object in the sky that has a particular
+intrinsic size associated with it okay
+
+ align:start position:0%
+intrinsic size associated with it okay
+ 
+
+ align:start position:0%
+intrinsic size associated with it okay
+you can sort of think of the objects
+
+ align:start position:0%
+you can sort of think of the objects
+ 
+
+ align:start position:0%
+you can sort of think of the objects
+whose luminosity you know about as
+
+ align:start position:0%
+whose luminosity you know about as
+ 
+
+ align:start position:0%
+whose luminosity you know about as
+standard candles imagine if nature
+
+ align:start position:0%
+standard candles imagine if nature
+ 
+
+ align:start position:0%
+standard candles imagine if nature
+builds standard yard sticks there's some
+
+ align:start position:0%
+builds standard yard sticks there's some
+ 
+
+ align:start position:0%
+builds standard yard sticks there's some
+object whose size you always know well
+
+ align:start position:0%
+object whose size you always know well
+ 
+
+ align:start position:0%
+object whose size you always know well
+let's compare that physical size to the
+
+ align:start position:0%
+let's compare that physical size to the
+ 
+
+ align:start position:0%
+let's compare that physical size to the
+angular size that you measure the angle
+
+ align:start position:0%
+angular size that you measure the angle
+ 
+
+ align:start position:0%
+angular size that you measure the angle
+that the object sub tends in the sky is
+
+ align:start position:0%
+that the object sub tends in the sky is
+ 
+
+ align:start position:0%
+that the object sub tends in the sky is
+going to be that intrinsic size Delta L
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+divided by the distance we'll call this
+
+ align:start position:0%
+divided by the distance we'll call this
+ 
+
+ align:start position:0%
+divided by the distance we'll call this
+distance D sub a for the angular
+
+ align:start position:0%
+distance D sub a for the angular
+ 
+
+ align:start position:0%
+distance D sub a for the angular
+diameter distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and believe it or not nature in fact
+
+ align:start position:0%
+and believe it or not nature in fact
+ 
+
+ align:start position:0%
+and believe it or not nature in fact
+provides standard yardstick for the type
+
+ align:start position:0%
+provides standard yardstick for the type
+ 
+
+ align:start position:0%
+provides standard yardstick for the type
+so that we can we can actually do this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+finally at least as a matter of
+
+ align:start position:0%
+finally at least as a matter of
+ 
+
+ align:start position:0%
+finally at least as a matter of
+principle
+
+ align:start position:0%
+principle
+ 
+
+ align:start position:0%
+principle
+imagine you add some objects that's
+
+ align:start position:0%
+imagine you add some objects that's
+ 
+
+ align:start position:0%
+imagine you add some objects that's
+moving across the sky with a speed that
+
+ align:start position:0%
+moving across the sky with a speed that
+ 
+
+ align:start position:0%
+moving across the sky with a speed that
+you know you could compare that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+transverse speed to an apparent angular
+
+ align:start position:0%
+transverse speed to an apparent angular
+ 
+
+ align:start position:0%
+transverse speed to an apparent angular
+speed so the theta dot the angular speed
+
+ align:start position:0%
+speed so the theta dot the angular speed
+ 
+
+ align:start position:0%
+speed so the theta dot the angular speed
+that you measure that would be the
+
+ align:start position:0%
+that you measure that would be the
+ 
+
+ align:start position:0%
+that you measure that would be the
+velocity perpendicular to your
+
+ align:start position:0%
+velocity perpendicular to your
+ 
+
+ align:start position:0%
+velocity perpendicular to your
+line-of-sight divided by the distance
+
+ align:start position:0%
+line-of-sight divided by the distance
+ 
+
+ align:start position:0%
+line-of-sight divided by the distance
+we'll call this D sub M the proper
+
+ align:start position:0%
+we'll call this D sub M the proper
+ 
+
+ align:start position:0%
+we'll call this D sub M the proper
+motion distance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if our universe were Euclidean not
+
+ align:start position:0%
+so if our universe were Euclidean not
+ 
+
+ align:start position:0%
+so if our universe were Euclidean not
+only would it be easy for us to use
+
+ align:start position:0%
+only would it be easy for us to use
+ 
+
+ align:start position:0%
+only would it be easy for us to use
+these three bit measures of distance all
+
+ align:start position:0%
+these three bit measures of distance all
+ 
+
+ align:start position:0%
+these three bit measures of distance all
+three of them would give the same result
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is all jazz geometry turns out when
+
+ align:start position:0%
+this is all jazz geometry turns out when
+ 
+
+ align:start position:0%
+this is all jazz geometry turns out when
+you study these notions of distance in
+
+ align:start position:0%
+you study these notions of distance in
+ 
+
+ align:start position:0%
+you study these notions of distance in
+an f RW spacetime there's some variation
+
+ align:start position:0%
+an f RW spacetime there's some variation
+ 
+
+ align:start position:0%
+an f RW spacetime there's some variation
+that enters let me just emphasize here
+
+ align:start position:0%
+that enters let me just emphasize here
+ 
+
+ align:start position:0%
+that enters let me just emphasize here
+that there is an excellent summary on
+
+ align:start position:0%
+that there is an excellent summary on
+ 
+
+ align:start position:0%
+that there is an excellent summary on
+this stuff I can't remember Phi the link
+
+ align:start position:0%
+this stuff I can't remember Phi the link
+ 
+
+ align:start position:0%
+this stuff I can't remember Phi the link
+this to the course website or not I
+
+ align:start position:0%
+this to the course website or not I
+ 
+
+ align:start position:0%
+this to the course website or not I
+shouldn't I shall an excellent summary
+
+ align:start position:0%
+shouldn't I shall an excellent summary
+ 
+
+ align:start position:0%
+shouldn't I shall an excellent summary
+of all this are really emphasizing
+
+ align:start position:0%
+of all this are really emphasizing
+ 
+
+ align:start position:0%
+of all this are really emphasizing
+observational e significant aspects of
+
+ align:start position:0%
+observational e significant aspects of
+ 
+
+ align:start position:0%
+observational e significant aspects of
+these things comes from the article that
+
+ align:start position:0%
+these things comes from the article that
+ 
+
+ align:start position:0%
+these things comes from the article that
+is on the archive called
+
+ align:start position:0%
+is on the archive called
+ 
+
+ align:start position:0%
+is on the archive called
+whoops distance measures in cosmology by
+
+ align:start position:0%
+whoops distance measures in cosmology by
+ 
+
+ align:start position:0%
+whoops distance measures in cosmology by
+David Hogg colleague at New York
+
+ align:start position:0%
+David Hogg colleague at New York
+ 
+
+ align:start position:0%
+David Hogg colleague at New York
+University you can find this on the
+
+ align:start position:0%
+University you can find this on the
+ 
+
+ align:start position:0%
+University you can find this on the
+astra ph archive 9905
+
+ align:start position:0%
+astra ph archive 9905
+ 
+
+ align:start position:0%
+astra ph archive 9905
+one one six hard for me to believe this
+
+ align:start position:0%
+one one six hard for me to believe this
+ 
+
+ align:start position:0%
+one one six hard for me to believe this
+is almost twenty one twenty one years
+
+ align:start position:0%
+is almost twenty one twenty one years
+ 
+
+ align:start position:0%
+is almost twenty one twenty one years
+old now this is a gem of a paper hog
+
+ align:start position:0%
+old now this is a gem of a paper hog
+ 
+
+ align:start position:0%
+old now this is a gem of a paper hog
+never submitted to any journal just
+
+ align:start position:0%
+never submitted to any journal just
+ 
+
+ align:start position:0%
+never submitted to any journal just
+posted on the archive so that the
+
+ align:start position:0%
+posted on the archive so that the
+ 
+
+ align:start position:0%
+posted on the archive so that the
+community could take advantage of it um
+
+ align:start position:0%
+community could take advantage of it um
+ 
+
+ align:start position:0%
+community could take advantage of it um
+what we're going to do so the text book
+
+ align:start position:0%
+what we're going to do so the text book
+ 
+
+ align:start position:0%
+what we're going to do so the text book
+by carol goes through the calculation of
+
+ align:start position:0%
+by carol goes through the calculation of
+ 
+
+ align:start position:0%
+by carol goes through the calculation of
+d sub l on a problem set you will do d
+
+ align:start position:0%
+d sub l on a problem set you will do d
+ 
+
+ align:start position:0%
+d sub l on a problem set you will do d
+sub m we're going to go through d sub
+
+ align:start position:0%
+sub m we're going to go through d sub
+ 
+
+ align:start position:0%
+sub m we're going to go through d sub
+act just so you can see some of the the
+
+ align:start position:0%
+act just so you can see some of the the
+ 
+
+ align:start position:0%
+act just so you can see some of the the
+way that this works let me emphasize one
+
+ align:start position:0%
+way that this works let me emphasize one
+ 
+
+ align:start position:0%
+way that this works let me emphasize one
+thing all of these measures
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+use the first Friedman equation okay so
+
+ align:start position:0%
+use the first Friedman equation okay so
+ 
+
+ align:start position:0%
+use the first Friedman equation okay so
+writing your Friedman equation like so I
+
+ align:start position:0%
+writing your Friedman equation like so I
+ 
+
+ align:start position:0%
+writing your Friedman equation like so I
+is a sum of all the different species of
+
+ align:start position:0%
+is a sum of all the different species of
+ 
+
+ align:start position:0%
+is a sum of all the different species of
+things that can contribute including
+
+ align:start position:0%
+things that can contribute including
+ 
+
+ align:start position:0%
+things that can contribute including
+curvature so recall that even though
+
+ align:start position:0%
+curvature so recall that even though
+ 
+
+ align:start position:0%
+curvature so recall that even though
+curvature isn't really a density you can
+
+ align:start position:0%
+curvature isn't really a density you can
+ 
+
+ align:start position:0%
+curvature isn't really a density you can
+combine enough factors to make it act as
+
+ align:start position:0%
+combine enough factors to make it act as
+ 
+
+ align:start position:0%
+combine enough factors to make it act as
+though it were a density you assume a
+
+ align:start position:0%
+though it were a density you assume a
+ 
+
+ align:start position:0%
+though it were a density you assume a
+parallel so this n sub I is related to
+
+ align:start position:0%
+parallel so this n sub I is related to
+ 
+
+ align:start position:0%
+parallel so this n sub I is related to
+the equation state parameter for each
+
+ align:start position:0%
+the equation state parameter for each
+ 
+
+ align:start position:0%
+the equation state parameter for each
+one of these species and let's now take
+
+ align:start position:0%
+one of these species and let's now take
+ 
+
+ align:start position:0%
+one of these species and let's now take
+advantage of the fact that we know the
+
+ align:start position:0%
+advantage of the fact that we know the
+ 
+
+ align:start position:0%
+advantage of the fact that we know the
+scale factor directly ties to redshift I
+
+ align:start position:0%
+scale factor directly ties to redshift I
+ 
+
+ align:start position:0%
+scale factor directly ties to redshift I
+can rewrite this as how the density of
+
+ align:start position:0%
+can rewrite this as how the density of
+ 
+
+ align:start position:0%
+can rewrite this as how the density of
+all's of the function of redshift so
+
+ align:start position:0%
+all's of the function of redshift so
+ 
+
+ align:start position:0%
+all's of the function of redshift so
+when you put all of this together
+
+ align:start position:0%
+when you put all of this together
+ 
+
+ align:start position:0%
+when you put all of this together
+this allows us to write H of a as H of Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is given by the Hubble parameter
+
+ align:start position:0%
+this is given by the Hubble parameter
+ 
+
+ align:start position:0%
+this is given by the Hubble parameter
+now times some function e of Z
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that is simply you sort of divide
+
+ align:start position:0%
+and that is simply you sort of divide
+ 
+
+ align:start position:0%
+and that is simply you sort of divide
+everything out to normalize to the
+
+ align:start position:0%
+everything out to normalize to the
+ 
+
+ align:start position:0%
+everything out to normalize to the
+critical density and that is a sum over
+
+ align:start position:0%
+critical density and that is a sum over
+ 
+
+ align:start position:0%
+critical density and that is a sum over
+all these densities with the with the
+
+ align:start position:0%
+all these densities with the with the
+ 
+
+ align:start position:0%
+all these densities with the with the
+redshift weighting like some so let me
+
+ align:start position:0%
+redshift weighting like some so let me
+ 
+
+ align:start position:0%
+redshift weighting like some so let me
+do an example like I said so if you read
+
+ align:start position:0%
+do an example like I said so if you read
+ 
+
+ align:start position:0%
+do an example like I said so if you read
+Carroll you will see the calculation of
+
+ align:start position:0%
+Carroll you will see the calculation of
+ 
+
+ align:start position:0%
+Carroll you will see the calculation of
+the luminosity distance if you do the
+
+ align:start position:0%
+the luminosity distance if you do the
+ 
+
+ align:start position:0%
+the luminosity distance if you do the
+cosmology problem sets that will be
+
+ align:start position:0%
+cosmology problem sets that will be
+ 
+
+ align:start position:0%
+cosmology problem sets that will be
+believe it's pset 8 you will explore the
+
+ align:start position:0%
+believe it's pset 8 you will explore the
+ 
+
+ align:start position:0%
+believe it's pset 8 you will explore the
+proper motion distance so let's do the
+
+ align:start position:0%
+proper motion distance so let's do the
+ 
+
+ align:start position:0%
+proper motion distance so let's do the
+angular diameter distance seeing someone
+
+ align:start position:0%
+angular diameter distance seeing someone
+ 
+
+ align:start position:0%
+angular diameter distance seeing someone
+work through this I think it's probably
+
+ align:start position:0%
+work through this I think it's probably
+ 
+
+ align:start position:0%
+work through this I think it's probably
+useful for helping to solidify the way
+
+ align:start position:0%
+useful for helping to solidify the way
+ 
+
+ align:start position:0%
+useful for helping to solidify the way
+in which these distance measures work
+
+ align:start position:0%
+in which these distance measures work
+ 
+
+ align:start position:0%
+in which these distance measures work
+and how how it is that one can tie
+
+ align:start position:0%
+and how how it is that one can tie
+ 
+
+ align:start position:0%
+and how how it is that one can tie
+together important observables so let's
+
+ align:start position:0%
+together important observables so let's
+ 
+
+ align:start position:0%
+together important observables so let's
+consider some source that we observe
+
+ align:start position:0%
+consider some source that we observe
+ 
+
+ align:start position:0%
+consider some source that we observe
+that according to us subtends an angle
+
+ align:start position:0%
+that according to us subtends an angle
+ 
+
+ align:start position:0%
+that according to us subtends an angle
+Delta Phi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+every spatial sector is spherically
+
+ align:start position:0%
+every spatial sector is spherically
+ 
+
+ align:start position:0%
+every spatial sector is spherically
+symmetric on and so we can orient our
+
+ align:start position:0%
+symmetric on and so we can orient our
+ 
+
+ align:start position:0%
+symmetric on and so we can orient our
+coordinate system so that this thing you
+
+ align:start position:0%
+coordinate system so that this thing you
+ 
+
+ align:start position:0%
+coordinate system so that this thing you
+know we're sort of a standard ruler what
+
+ align:start position:0%
+know we're sort of a standard ruler what
+ 
+
+ align:start position:0%
+know we're sort of a standard ruler what
+we're going to do is orient our
+
+ align:start position:0%
+we're going to do is orient our
+ 
+
+ align:start position:0%
+we're going to do is orient our
+coordinate systems so that that object
+
+ align:start position:0%
+coordinate systems so that that object
+ 
+
+ align:start position:0%
+coordinate systems so that that object
+lies in the theta equals PI over 2 plane
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ok the proper size of that source okay
+
+ align:start position:0%
+ok the proper size of that source okay
+ 
+
+ align:start position:0%
+ok the proper size of that source okay
+so this thing is just it's sitting in
+
+ align:start position:0%
+so this thing is just it's sitting in
+ 
+
+ align:start position:0%
+so this thing is just it's sitting in
+the sky there the proper size of the
+
+ align:start position:0%
+the sky there the proper size of the
+ 
+
+ align:start position:0%
+the sky there the proper size of the
+source you can get this in the line
+
+ align:start position:0%
+source you can get this in the line
+ 
+
+ align:start position:0%
+source you can get this in the line
+element the Delta L of the source will
+
+ align:start position:0%
+element the Delta L of the source will
+ 
+
+ align:start position:0%
+element the Delta L of the source will
+be the scale factor at the time at which
+
+ align:start position:0%
+be the scale factor at the time at which
+ 
+
+ align:start position:0%
+be the scale factor at the time at which
+it is emitted are zero okay so this is
+
+ align:start position:0%
+it is emitted are zero okay so this is
+ 
+
+ align:start position:0%
+it is emitted are zero okay so this is
+using one of the forms of the frw line
+
+ align:start position:0%
+using one of the forms of the frw line
+ 
+
+ align:start position:0%
+using one of the forms of the frw line
+elements I Pro it down the beginning of
+
+ align:start position:0%
+elements I Pro it down the beginning of
+ 
+
+ align:start position:0%
+elements I Pro it down the beginning of
+this lecture and so the angular diameter
+
+ align:start position:0%
+this lecture and so the angular diameter
+ 
+
+ align:start position:0%
+this lecture and so the angular diameter
+distance it's a quantity that I've
+
+ align:start position:0%
+distance it's a quantity that I've
+ 
+
+ align:start position:0%
+distance it's a quantity that I've
+defined over here it's just the ratio of
+
+ align:start position:0%
+defined over here it's just the ratio of
+ 
+
+ align:start position:0%
+defined over here it's just the ratio of
+this length to that angle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay let's rewrite this using the
+
+ align:start position:0%
+okay let's rewrite this using the
+ 
+
+ align:start position:0%
+okay let's rewrite this using the
+redshift redshift is something that I
+
+ align:start position:0%
+redshift redshift is something that I
+ 
+
+ align:start position:0%
+redshift redshift is something that I
+actually directly observe so there we go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is not wrong but it's flawed so
+
+ align:start position:0%
+this is not wrong but it's flawed so
+ 
+
+ align:start position:0%
+this is not wrong but it's flawed so
+this is true this is absolutely true
+
+ align:start position:0%
+this is true this is absolutely true
+ 
+
+ align:start position:0%
+this is true this is absolutely true
+here's the problem I don't know the
+
+ align:start position:0%
+here's the problem I don't know the
+ 
+
+ align:start position:0%
+here's the problem I don't know the
+overall scale of my universe and this
+
+ align:start position:0%
+overall scale of my universe and this
+ 
+
+ align:start position:0%
+overall scale of my universe and this
+coordinate chi doesn't really have an
+
+ align:start position:0%
+coordinate chi doesn't really have an
+ 
+
+ align:start position:0%
+coordinate chi doesn't really have an
+observable meaning to it okay it's how I
+
+ align:start position:0%
+observable meaning to it okay it's how I
+ 
+
+ align:start position:0%
+observable meaning to it okay it's how I
+label events but I look at some quasar
+
+ align:start position:0%
+label events but I look at some quasar
+ 
+
+ align:start position:0%
+label events but I look at some quasar
+in the sky and I'm like what's your chi
+
+ align:start position:0%
+in the sky and I'm like what's your chi
+ 
+
+ align:start position:0%
+in the sky and I'm like what's your chi
+so what we need to do is reformulate the
+
+ align:start position:0%
+so what we need to do is reformulate the
+ 
+
+ align:start position:0%
+so what we need to do is reformulate the
+numerator of this expression in such a
+
+ align:start position:0%
+numerator of this expression in such a
+ 
+
+ align:start position:0%
+numerator of this expression in such a
+way as to get rid of that chi and then
+
+ align:start position:0%
+way as to get rid of that chi and then
+ 
+
+ align:start position:0%
+way as to get rid of that chi and then
+see what happens see if we have a way to
+
+ align:start position:0%
+see what happens see if we have a way to
+ 
+
+ align:start position:0%
+see what happens see if we have a way to
+get rid of that r0 let's worry about Chi
+
+ align:start position:0%
+get rid of that r0 let's worry about Chi
+ 
+
+ align:start position:0%
+get rid of that r0 let's worry about Chi
+first we're going to eliminate it by
+
+ align:start position:0%
+first we're going to eliminate it by
+ 
+
+ align:start position:0%
+first we're going to eliminate it by
+taking advantage of the fact that the
+
+ align:start position:0%
+taking advantage of the fact that the
+ 
+
+ align:start position:0%
+taking advantage of the fact that the
+radiation I am measuring comes to me on
+
+ align:start position:0%
+radiation I am measuring comes to me on
+ 
+
+ align:start position:0%
+radiation I am measuring comes to me on
+a null path
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not to say anything all paths I'm gonna
+
+ align:start position:0%
+not to say anything all paths I'm gonna
+ 
+
+ align:start position:0%
+not to say anything all paths I'm gonna
+imagine it's a radial one okay we are
+
+ align:start position:0%
+imagine it's a radial one okay we are
+ 
+
+ align:start position:0%
+imagine it's a radial one okay we are
+allowed to be somewhat self-centered and
+
+ align:start position:0%
+allowed to be somewhat self-centered and
+ 
+
+ align:start position:0%
+allowed to be somewhat self-centered and
+defying the frw cosmology we put
+
+ align:start position:0%
+defying the frw cosmology we put
+ 
+
+ align:start position:0%
+defying the frw cosmology we put
+ourselves at the origin so any light
+
+ align:start position:0%
+ourselves at the origin so any light
+ 
+
+ align:start position:0%
+ourselves at the origin so any light
+that reaches us moves on a purely radial
+
+ align:start position:0%
+that reaches us moves on a purely radial
+ 
+
+ align:start position:0%
+that reaches us moves on a purely radial
+trajectory from its source to us so
+
+ align:start position:0%
+trajectory from its source to us so
+ 
+
+ align:start position:0%
+trajectory from its source to us so
+looking at how the time and the radial
+
+ align:start position:0%
+looking at how the time and the radial
+ 
+
+ align:start position:0%
+looking at how the time and the radial
+coordinate chi are related for a radial
+
+ align:start position:0%
+coordinate chi are related for a radial
+ 
+
+ align:start position:0%
+coordinate chi are related for a radial
+null path we go into my frw metric I get
+
+ align:start position:0%
+null path we go into my frw metric I get
+ 
+
+ align:start position:0%
+null path we go into my frw metric I get
+this so I can integrate this up to
+
+ align:start position:0%
+this so I can integrate this up to
+ 
+
+ align:start position:0%
+this so I can integrate this up to
+figure out what K is so this is right
+
+ align:start position:0%
+figure out what K is so this is right
+ 
+
+ align:start position:0%
+figure out what K is so this is right
+let's massage it a little bit to put it
+
+ align:start position:0%
+let's massage it a little bit to put it
+ 
+
+ align:start position:0%
+let's massage it a little bit to put it
+in a form it's a little bit more useful
+
+ align:start position:0%
+in a form it's a little bit more useful
+ 
+
+ align:start position:0%
+in a form it's a little bit more useful
+to us let's change our variable change
+
+ align:start position:0%
+to us let's change our variable change
+ 
+
+ align:start position:0%
+to us let's change our variable change
+our variable of integration from time to
+
+ align:start position:0%
+our variable of integration from time to
+ 
+
+ align:start position:0%
+our variable of integration from time to
+a so this will be an integral from the
+
+ align:start position:0%
+a so this will be an integral from the
+ 
+
+ align:start position:0%
+a so this will be an integral from the
+scale factor at which the radiation is
+
+ align:start position:0%
+scale factor at which the radiation is
+ 
+
+ align:start position:0%
+scale factor at which the radiation is
+emitted to the scale factor which we
+
+ align:start position:0%
+emitted to the scale factor which we
+ 
+
+ align:start position:0%
+emitted to the scale factor which we
+observe it ie now and we do that change
+
+ align:start position:0%
+observe it ie now and we do that change
+ 
+
+ align:start position:0%
+observe it ie now and we do that change
+of variables your integrals changes like
+
+ align:start position:0%
+of variables your integrals changes like
+ 
+
+ align:start position:0%
+of variables your integrals changes like
+so let's rewrite this once more to
+
+ align:start position:0%
+so let's rewrite this once more to
+ 
+
+ align:start position:0%
+so let's rewrite this once more to
+insert my Hubble parameter
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and let's change variables once more
+
+ align:start position:0%
+and let's change variables once more
+ 
+
+ align:start position:0%
+and let's change variables once more
+we're gonna use the fact that our direct
+
+ align:start position:0%
+we're gonna use the fact that our direct
+ 
+
+ align:start position:0%
+we're gonna use the fact that our direct
+measurable is redshift and so if we use
+
+ align:start position:0%
+measurable is redshift and so if we use
+ 
+
+ align:start position:0%
+measurable is redshift and so if we use
+a equals 1 over 1 plus C I can further
+
+ align:start position:0%
+a equals 1 over 1 plus C I can further
+ 
+
+ align:start position:0%
+a equals 1 over 1 plus C I can further
+write this as an integral over redshift
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like so and that h0 can come out of my
+
+ align:start position:0%
+like so and that h0 can come out of my
+ 
+
+ align:start position:0%
+like so and that h0 can come out of my
+integral so this is a form that is now
+
+ align:start position:0%
+integral so this is a form that is now
+ 
+
+ align:start position:0%
+integral so this is a form that is now
+finally formulated in terms of an
+
+ align:start position:0%
+finally formulated in terms of an
+ 
+
+ align:start position:0%
+finally formulated in terms of an
+observable redshift and my model
+
+ align:start position:0%
+observable redshift and my model
+ 
+
+ align:start position:0%
+observable redshift and my model
+dependent parameters
+
+ align:start position:0%
+dependent parameters
+ 
+
+ align:start position:0%
+dependent parameters
+okay the various omegas that when I
+
+ align:start position:0%
+okay the various omegas that when I
+ 
+
+ align:start position:0%
+okay the various omegas that when I
+construct my universe model I am free to
+
+ align:start position:0%
+construct my universe model I am free to
+ 
+
+ align:start position:0%
+construct my universe model I am free to
+set or if I am a phenomenologist that
+
+ align:start position:0%
+set or if I am a phenomenologist that
+ 
+
+ align:start position:0%
+set or if I am a phenomenologist that
+are going to be knobs that I turn to try
+
+ align:start position:0%
+are going to be knobs that I turn to try
+ 
+
+ align:start position:0%
+are going to be knobs that I turn to try
+to design a model universe that matches
+
+ align:start position:0%
+to design a model universe that matches
+ 
+
+ align:start position:0%
+to design a model universe that matches
+the data that I am measuring are zero
+
+ align:start position:0%
+the data that I am measuring are zero
+ 
+
+ align:start position:0%
+the data that I am measuring are zero
+though is still kind of annoying we
+
+ align:start position:0%
+though is still kind of annoying we
+ 
+
+ align:start position:0%
+though is still kind of annoying we
+don't know what this guy is so what we
+
+ align:start position:0%
+don't know what this guy is so what we
+ 
+
+ align:start position:0%
+don't know what this guy is so what we
+do is eliminate our 0 in favor of a
+
+ align:start position:0%
+do is eliminate our 0 in favor of a
+ 
+
+ align:start position:0%
+do is eliminate our 0 in favor of a
+curve curvature density parameter so
+
+ align:start position:0%
+curve curvature density parameter so
+ 
+
+ align:start position:0%
+curve curvature density parameter so
+using the fact that Omega curvature go
+
+ align:start position:0%
+using the fact that Omega curvature go
+ 
+
+ align:start position:0%
+using the fact that Omega curvature go
+back to how this was originally defined
+
+ align:start position:0%
+back to how this was originally defined
+ 
+
+ align:start position:0%
+back to how this was originally defined
+it was negative Kappa over H zero
+
+ align:start position:0%
+it was negative Kappa over H zero
+ 
+
+ align:start position:0%
+it was negative Kappa over H zero
+squared and that's negative K over r0
+
+ align:start position:0%
+squared and that's negative K over r0
+ 
+
+ align:start position:0%
+squared and that's negative K over r0
+squared H zero squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that tells me that r0 is the Hubble
+
+ align:start position:0%
+that tells me that r0 is the Hubble
+ 
+
+ align:start position:0%
+that tells me that r0 is the Hubble
+constant now divided by the square root
+
+ align:start position:0%
+constant now divided by the square root
+ 
+
+ align:start position:0%
+constant now divided by the square root
+of the absolute value of the curvature
+
+ align:start position:0%
+of the absolute value of the curvature
+ 
+
+ align:start position:0%
+of the absolute value of the curvature
+at least if K equals plus or minus one
+
+ align:start position:0%
+at least if K equals plus or minus one
+ 
+
+ align:start position:0%
+at least if K equals plus or minus one
+what happens when it's not plus or minus
+
+ align:start position:0%
+what happens when it's not plus or minus
+ 
+
+ align:start position:0%
+what happens when it's not plus or minus
+one okay if it's equal to zero well hold
+
+ align:start position:0%
+one okay if it's equal to zero well hold
+ 
+
+ align:start position:0%
+one okay if it's equal to zero well hold
+that thought okay so let's put all these
+
+ align:start position:0%
+that thought okay so let's put all these
+ 
+
+ align:start position:0%
+that thought okay so let's put all these
+pieces together so assembling all the
+
+ align:start position:0%
+pieces together so assembling all the
+ 
+
+ align:start position:0%
+pieces together so assembling all the
+ingredients I have here what we find is
+
+ align:start position:0%
+ingredients I have here what we find is
+ 
+
+ align:start position:0%
+ingredients I have here what we find is
+the angular diameter distance there's a
+
+ align:start position:0%
+the angular diameter distance there's a
+ 
+
+ align:start position:0%
+the angular diameter distance there's a
+factor of 1 over 1 plus c1 over the
+
+ align:start position:0%
+factor of 1 over 1 plus c1 over the
+ 
+
+ align:start position:0%
+factor of 1 over 1 plus c1 over the
+Hubble constant remember Hubble has
+
+ align:start position:0%
+Hubble constant remember Hubble has
+ 
+
+ align:start position:0%
+Hubble constant remember Hubble has
+units of 1 over length excuse me 1 over
+
+ align:start position:0%
+units of 1 over length excuse me 1 over
+ 
+
+ align:start position:0%
+units of 1 over length excuse me 1 over
+time and with the factor of the speed of
+
+ align:start position:0%
+time and with the factor of the speed of
+ 
+
+ align:start position:0%
+time and with the factor of the speed of
+light that is a 1 over length so 1 over
+
+ align:start position:0%
+light that is a 1 over length so 1 over
+ 
+
+ align:start position:0%
+light that is a 1 over length so 1 over
+the Hubble parameter now is essentially
+
+ align:start position:0%
+the Hubble parameter now is essentially
+ 
+
+ align:start position:0%
+the Hubble parameter now is essentially
+a kind of fiducial overall distance
+
+ align:start position:0%
+a kind of fiducial overall distance
+ 
+
+ align:start position:0%
+a kind of fiducial overall distance
+scale and then our solution breaks up
+
+ align:start position:0%
+scale and then our solution breaks up
+ 
+
+ align:start position:0%
+scale and then our solution breaks up
+into three branches depending upon what
+
+ align:start position:0%
+into three branches depending upon what
+ 
+
+ align:start position:0%
+into three branches depending upon what
+the weather K equals minus 1 0 or 1 so
+
+ align:start position:0%
+the weather K equals minus 1 0 or 1 so
+ 
+
+ align:start position:0%
+the weather K equals minus 1 0 or 1 so
+you get one term where it involves minus
+
+ align:start position:0%
+you get one term where it involves minus
+ 
+
+ align:start position:0%
+you get one term where it involves minus
+square root the absolute value of the
+
+ align:start position:0%
+square root the absolute value of the
+ 
+
+ align:start position:0%
+square root the absolute value of the
+curvature parameter times sine of that
+
+ align:start position:0%
+curvature parameter times sine of that
+ 
+
+ align:start position:0%
+curvature parameter times sine of that
+same absolute value of the curvature
+
+ align:start position:0%
+same absolute value of the curvature
+ 
+
+ align:start position:0%
+same absolute value of the curvature
+parameters square root
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's your K equals +1 branch for
+
+ align:start position:0%
+so here's your K equals +1 branch for
+ 
+
+ align:start position:0%
+so here's your K equals +1 branch for
+your k equals zero branch basically what
+
+ align:start position:0%
+your k equals zero branch basically what
+ 
+
+ align:start position:0%
+your k equals zero branch basically what
+you'll find when you plug in your s of K
+
+ align:start position:0%
+you'll find when you plug in your s of K
+ 
+
+ align:start position:0%
+you'll find when you plug in your s of K
+is that r0 cancels out okay so that ends
+
+ align:start position:0%
+is that r0 cancels out okay so that ends
+ 
+
+ align:start position:0%
+is that r0 cancels out okay so that ends
+up being a parameter you do not need to
+
+ align:start position:0%
+up being a parameter you do not need to
+ 
+
+ align:start position:0%
+up being a parameter you do not need to
+worry about and I suggest you just work
+
+ align:start position:0%
+worry about and I suggest you just work
+ 
+
+ align:start position:0%
+worry about and I suggest you just work
+through the algebra and you'll find it
+
+ align:start position:0%
+through the algebra and you'll find it
+ 
+
+ align:start position:0%
+through the algebra and you'll find it
+in for K equals zero it simply looks
+
+ align:start position:0%
+in for K equals zero it simply looks
+ 
+
+ align:start position:0%
+in for K equals zero it simply looks
+like this and then finally if you are in
+
+ align:start position:0%
+like this and then finally if you are in
+ 
+
+ align:start position:0%
+like this and then finally if you are in
+an open universe supposed to be
+
+ align:start position:0%
+an open universe supposed to be
+ 
+
+ align:start position:0%
+an open universe supposed to be
+curvature
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what we get is this so this is a
+
+ align:start position:0%
+what we get is this so this is a
+ 
+
+ align:start position:0%
+what we get is this so this is a
+distance measure that tells me how
+
+ align:start position:0%
+distance measure that tells me how
+ 
+
+ align:start position:0%
+distance measure that tells me how
+angular diameter distance it depends on
+
+ align:start position:0%
+angular diameter distance it depends on
+ 
+
+ align:start position:0%
+angular diameter distance it depends on
+observable parameters Hubble is
+
+ align:start position:0%
+observable parameters Hubble is
+ 
+
+ align:start position:0%
+observable parameters Hubble is
+something that we can measure redshift
+
+ align:start position:0%
+something that we can measure redshift
+ 
+
+ align:start position:0%
+something that we can measure redshift
+is something we can measure and it
+
+ align:start position:0%
+is something we can measure and it
+ 
+
+ align:start position:0%
+is something we can measure and it
+depends on model parameters the
+
+ align:start position:0%
+depends on model parameters the
+ 
+
+ align:start position:0%
+depends on model parameters the
+different densities that go into e of Z
+
+ align:start position:0%
+different densities that go into e of Z
+ 
+
+ align:start position:0%
+different densities that go into e of Z
+and which I have on the board right here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the different densities to go into e of
+
+ align:start position:0%
+the different densities to go into e of
+ 
+
+ align:start position:0%
+the different densities to go into e of
+Z my apologies I left out that H o there
+
+ align:start position:0%
+Z my apologies I left out that H o there
+ 
+
+ align:start position:0%
+Z my apologies I left out that H o there
+and your choice of the curvature when
+
+ align:start position:0%
+and your choice of the curvature when
+ 
+
+ align:start position:0%
+and your choice of the curvature when
+you analyze these three distances here's
+
+ align:start position:0%
+you analyze these three distances here's
+ 
+
+ align:start position:0%
+you analyze these three distances here's
+what you find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and find that the luminosity distance is
+
+ align:start position:0%
+and find that the luminosity distance is
+ 
+
+ align:start position:0%
+and find that the luminosity distance is
+related to the proper motion distance by
+
+ align:start position:0%
+related to the proper motion distance by
+ 
+
+ align:start position:0%
+related to the proper motion distance by
+a factor of 1 plus Z and that's related
+
+ align:start position:0%
+a factor of 1 plus Z and that's related
+ 
+
+ align:start position:0%
+a factor of 1 plus Z and that's related
+to the angular diameter distance by a
+
+ align:start position:0%
+to the angular diameter distance by a
+ 
+
+ align:start position:0%
+to the angular diameter distance by a
+factor of 1 plus Z squared
+
+ align:start position:0%
+factor of 1 plus Z squared
+ 
+
+ align:start position:0%
+factor of 1 plus Z squared
+so when you read Carroll you will find
+
+ align:start position:0%
+so when you read Carroll you will find
+ 
+
+ align:start position:0%
+so when you read Carroll you will find
+that that 1 plus Z factor there that
+
+ align:start position:0%
+that that 1 plus Z factor there that
+ 
+
+ align:start position:0%
+that that 1 plus Z factor there that
+sumi 1 plus Z to the minus 1 power turns
+
+ align:start position:0%
+sumi 1 plus Z to the minus 1 power turns
+ 
+
+ align:start position:0%
+sumi 1 plus Z to the minus 1 power turns
+into a 1 plus Z so that camp that 1 plus
+
+ align:start position:0%
+into a 1 plus Z so that camp that 1 plus
+ 
+
+ align:start position:0%
+into a 1 plus Z so that camp that 1 plus
+Z 1 over 1 plus e turns into a 1 plus Z
+
+ align:start position:0%
+Z 1 over 1 plus e turns into a 1 plus Z
+ 
+
+ align:start position:0%
+Z 1 over 1 plus e turns into a 1 plus Z
+and when you do it on the pset you do
+
+ align:start position:0%
+and when you do it on the pset you do
+ 
+
+ align:start position:0%
+and when you do it on the pset you do
+the proper motion distance there will
+
+ align:start position:0%
+the proper motion distance there will
+ 
+
+ align:start position:0%
+the proper motion distance there will
+just be no 1 plus Z factor in front of
+
+ align:start position:0%
+just be no 1 plus Z factor in front of
+ 
+
+ align:start position:0%
+just be no 1 plus Z factor in front of
+everything so the name of the game when
+
+ align:start position:0%
+everything so the name of the game when
+ 
+
+ align:start position:0%
+everything so the name of the game when
+one is doing cosmology as a physicist is
+
+ align:start position:0%
+one is doing cosmology as a physicist is
+ 
+
+ align:start position:0%
+one is doing cosmology as a physicist is
+to find quantities that you can measure
+
+ align:start position:0%
+to find quantities that you can measure
+ 
+
+ align:start position:0%
+to find quantities that you can measure
+that allow you to determine luminosity
+
+ align:start position:0%
+that allow you to determine luminosity
+ 
+
+ align:start position:0%
+that allow you to determine luminosity
+distances angular diameter distances
+
+ align:start position:0%
+distances angular diameter distances
+ 
+
+ align:start position:0%
+distances angular diameter distances
+proper motion distances now it turns out
+
+ align:start position:0%
+proper motion distances now it turns out
+ 
+
+ align:start position:0%
+proper motion distances now it turns out
+that the proper motion distance is not a
+
+ align:start position:0%
+that the proper motion distance is not a
+ 
+
+ align:start position:0%
+that the proper motion distance is not a
+very practical one for most for
+
+ align:start position:0%
+very practical one for most for
+ 
+
+ align:start position:0%
+very practical one for most for
+basically any cosmological interesting
+
+ align:start position:0%
+basically any cosmological interesting
+ 
+
+ align:start position:0%
+basically any cosmological interesting
+source they are simply so far away that
+
+ align:start position:0%
+source they are simply so far away that
+ 
+
+ align:start position:0%
+source they are simply so far away that
+even for a source moving essentially at
+
+ align:start position:0%
+even for a source moving essentially at
+ 
+
+ align:start position:0%
+even for a source moving essentially at
+the speed of light the amount of angular
+
+ align:start position:0%
+the speed of light the amount of angular
+ 
+
+ align:start position:0%
+the speed of light the amount of angular
+motion that can be seen over essentially
+
+ align:start position:0%
+motion that can be seen over essentially
+ 
+
+ align:start position:0%
+motion that can be seen over essentially
+a human lifetime is negligible so this
+
+ align:start position:0%
+a human lifetime is negligible so this
+ 
+
+ align:start position:0%
+a human lifetime is negligible so this
+turns into something that high that's
+
+ align:start position:0%
+turns into something that high that's
+ 
+
+ align:start position:0%
+turns into something that high that's
+okay yeah I'm doing some pre recording
+
+ align:start position:0%
+okay yeah I'm doing some pre recording
+ 
+
+ align:start position:0%
+okay yeah I'm doing some pre recording
+of lectures no I was warned you guys
+
+ align:start position:0%
+of lectures no I was warned you guys
+ 
+
+ align:start position:0%
+of lectures no I was warned you guys
+might come by I have my ID with me and
+
+ align:start position:0%
+might come by I have my ID with me and
+ 
+
+ align:start position:0%
+might come by I have my ID with me and
+things like that so appreciate it so
+
+ align:start position:0%
+things like that so appreciate it so
+ 
+
+ align:start position:0%
+things like that so appreciate it so
+those of you watching the video at home
+
+ align:start position:0%
+those of you watching the video at home
+ 
+
+ align:start position:0%
+those of you watching the video at home
+as you can see the MIT police is keeping
+
+ align:start position:0%
+as you can see the MIT police is keeping
+ 
+
+ align:start position:0%
+as you can see the MIT police is keeping
+us safe ah scared the crap out of me for
+
+ align:start position:0%
+us safe ah scared the crap out of me for
+ 
+
+ align:start position:0%
+us safe ah scared the crap out of me for
+a second there but it's all good all
+
+ align:start position:0%
+a second there but it's all good all
+ 
+
+ align:start position:0%
+a second there but it's all good all
+right so let's go back to this for a
+
+ align:start position:0%
+right so let's go back to this for a
+ 
+
+ align:start position:0%
+right so let's go back to this for a
+second so the proper motion distance is
+
+ align:start position:0%
+second so the proper motion distance is
+ 
+
+ align:start position:0%
+second so the proper motion distance is
+something that is not particularly
+
+ align:start position:0%
+something that is not particularly
+ 
+
+ align:start position:0%
+something that is not particularly
+practical because as I said even if you
+
+ align:start position:0%
+practical because as I said even if you
+ 
+
+ align:start position:0%
+practical because as I said even if you
+have an object that is moving close to
+
+ align:start position:0%
+have an object that is moving close to
+ 
+
+ align:start position:0%
+have an object that is moving close to
+the speed of light
+
+ align:start position:0%
+the speed of light
+ 
+
+ align:start position:0%
+the speed of light
+this is not something that even over the
+
+ align:start position:0%
+this is not something that even over the
+ 
+
+ align:start position:0%
+this is not something that even over the
+course of a human lifetime you are
+
+ align:start position:0%
+course of a human lifetime you are
+ 
+
+ align:start position:0%
+course of a human lifetime you are
+likely to see a significant angular
+
+ align:start position:0%
+likely to see a significant angular
+ 
+
+ align:start position:0%
+likely to see a significant angular
+motion so this is gently not used but
+
+ align:start position:0%
+motion so this is gently not used but
+ 
+
+ align:start position:0%
+motion so this is gently not used but
+luminosity distances and angular
+
+ align:start position:0%
+luminosity distances and angular
+ 
+
+ align:start position:0%
+luminosity distances and angular
+diameter distances that is in fact
+
+ align:start position:0%
+diameter distances that is in fact
+ 
+
+ align:start position:0%
+diameter distances that is in fact
+extremely important and a lot of
+
+ align:start position:0%
+extremely important and a lot of
+ 
+
+ align:start position:0%
+extremely important and a lot of
+cosmology is based on looking for well
+
+ align:start position:0%
+cosmology is based on looking for well
+ 
+
+ align:start position:0%
+cosmology is based on looking for well
+understood well understood objects where
+
+ align:start position:0%
+understood well understood objects where
+ 
+
+ align:start position:0%
+understood well understood objects where
+we can calibrate the physical size and
+
+ align:start position:0%
+we can calibrate the physical size and
+ 
+
+ align:start position:0%
+we can calibrate the physical size and
+infer the angular diameter distance or
+
+ align:start position:0%
+infer the angular diameter distance or
+ 
+
+ align:start position:0%
+infer the angular diameter distance or
+we know the intrinsic brightness and we
+
+ align:start position:0%
+we know the intrinsic brightness and we
+ 
+
+ align:start position:0%
+we know the intrinsic brightness and we
+can determine the luminosity distance so
+
+ align:start position:0%
+can determine the luminosity distance so
+ 
+
+ align:start position:0%
+can determine the luminosity distance so
+let me just give a a quick snapshot of
+
+ align:start position:0%
+let me just give a a quick snapshot of
+ 
+
+ align:start position:0%
+let me just give a a quick snapshot of
+where the measurements come from in
+
+ align:start position:0%
+where the measurements come from in
+ 
+
+ align:start position:0%
+where the measurements come from in
+modern cosmology that are driving our
+
+ align:start position:0%
+modern cosmology that are driving our
+ 
+
+ align:start position:0%
+modern cosmology that are driving our
+cosmological model so one of the most
+
+ align:start position:0%
+cosmological model so one of the most
+ 
+
+ align:start position:0%
+cosmological model so one of the most
+important is the Cosmic Microwave
+
+ align:start position:0%
+important is the Cosmic Microwave
+ 
+
+ align:start position:0%
+important is the Cosmic Microwave
+Background so vastly oversimplifying
+
+ align:start position:0%
+Background so vastly oversimplifying
+ 
+
+ align:start position:0%
+Background so vastly oversimplifying
+when we look at the Cosmic Microwave
+
+ align:start position:0%
+when we look at the Cosmic Microwave
+ 
+
+ align:start position:0%
+when we look at the Cosmic Microwave
+Background after sort of removing
+
+ align:start position:0%
+Background after sort of removing
+ 
+
+ align:start position:0%
+Background after sort of removing
+removing things like the the flow of our
+
+ align:start position:0%
+removing things like the the flow of our
+ 
+
+ align:start position:0%
+removing things like the the flow of our
+solar system with respect to the the
+
+ align:start position:0%
+solar system with respect to the the
+ 
+
+ align:start position:0%
+solar system with respect to the the
+rest frame of to meet the the comoving
+
+ align:start position:0%
+rest frame of to meet the the comoving
+ 
+
+ align:start position:0%
+rest frame of to meet the the comoving
+reference frame of the cause of the the
+
+ align:start position:0%
+reference frame of the cause of the the
+ 
+
+ align:start position:0%
+reference frame of the cause of the the
+fluid that makes up our universe the
+
+ align:start position:0%
+fluid that makes up our universe the
+ 
+
+ align:start position:0%
+fluid that makes up our universe the
+size of hot and cold spots is a standard
+
+ align:start position:0%
+size of hot and cold spots is a standard
+ 
+
+ align:start position:0%
+size of hot and cold spots is a standard
+ruler
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by looking at the distribution of sizes
+
+ align:start position:0%
+by looking at the distribution of sizes
+ 
+
+ align:start position:0%
+by looking at the distribution of sizes
+that we see from these things we can
+
+ align:start position:0%
+that we see from these things we can
+ 
+
+ align:start position:0%
+that we see from these things we can
+determine the angular diameter distance
+
+ align:start position:0%
+determine the angular diameter distance
+ 
+
+ align:start position:0%
+determine the angular diameter distance
+to the Cosmic Microwave Background with
+
+ align:start position:0%
+to the Cosmic Microwave Background with
+ 
+
+ align:start position:0%
+to the Cosmic Microwave Background with
+very high precision this ends up being
+
+ align:start position:0%
+very high precision this ends up being
+ 
+
+ align:start position:0%
+very high precision this ends up being
+one of the most important constraints on
+
+ align:start position:0%
+one of the most important constraints on
+ 
+
+ align:start position:0%
+one of the most important constraints on
+determining what the curvature parameter
+
+ align:start position:0%
+determining what the curvature parameter
+ 
+
+ align:start position:0%
+determining what the curvature parameter
+actually is and it is largely thanks to
+
+ align:start position:0%
+actually is and it is largely thanks to
+ 
+
+ align:start position:0%
+actually is and it is largely thanks to
+the Cosmic Microwave Background that
+
+ align:start position:0%
+the Cosmic Microwave Background that
+ 
+
+ align:start position:0%
+the Cosmic Microwave Background that
+current prejudice I would say the
+
+ align:start position:0%
+current prejudice I would say the
+ 
+
+ align:start position:0%
+current prejudice I would say the
+current best wisdom choose your your
+
+ align:start position:0%
+current best wisdom choose your your
+ 
+
+ align:start position:0%
+current best wisdom choose your your
+descriptor as you wish is that K equals
+
+ align:start position:0%
+descriptor as you wish is that K equals
+ 
+
+ align:start position:0%
+descriptor as you wish is that K equals
+zero in our universe is in fact
+
+ align:start position:0%
+zero in our universe is in fact
+ 
+
+ align:start position:0%
+zero in our universe is in fact
+spatially flat second one is what are
+
+ align:start position:0%
+spatially flat second one is what are
+ 
+
+ align:start position:0%
+spatially flat second one is what are
+called type 1a supernovae these are
+
+ align:start position:0%
+called type 1a supernovae these are
+ 
+
+ align:start position:0%
+called type 1a supernovae these are
+essentially the the thermo nuclear
+
+ align:start position:0%
+essentially the the thermo nuclear
+ 
+
+ align:start position:0%
+essentially the the thermo nuclear
+detonations of white dwarfs it's not
+
+ align:start position:0%
+detonations of white dwarfs it's not
+ 
+
+ align:start position:0%
+detonations of white dwarfs it's not
+even released thermonuclear it's just my
+
+ align:start position:0%
+even released thermonuclear it's just my
+ 
+
+ align:start position:0%
+even released thermonuclear it's just my
+apologies I'm confusing a different
+
+ align:start position:0%
+apologies I'm confusing a different
+ 
+
+ align:start position:0%
+apologies I'm confusing a different
+event that involves white dwarfs the
+
+ align:start position:0%
+event that involves white dwarfs the
+ 
+
+ align:start position:0%
+event that involves white dwarfs the
+type 1 days are not the thermonuclear
+
+ align:start position:0%
+type 1 days are not the thermonuclear
+ 
+
+ align:start position:0%
+type 1 days are not the thermonuclear
+explosions of these things this is
+
+ align:start position:0%
+explosions of these things this is
+ 
+
+ align:start position:0%
+explosions of these things this is
+actually the core collapse of a white
+
+ align:start position:0%
+actually the core collapse of a white
+ 
+
+ align:start position:0%
+actually the core collapse of a white
+dwarf star so this is what happens when
+
+ align:start position:0%
+dwarf star so this is what happens when
+ 
+
+ align:start position:0%
+dwarf star so this is what happens when
+a white dwarf it creats or in some way
+
+ align:start position:0%
+a white dwarf it creats or in some way
+ 
+
+ align:start position:0%
+a white dwarf it creats or in some way
+accumulates enough mass such that it can
+
+ align:start position:0%
+accumulates enough mass such that it can
+ 
+
+ align:start position:0%
+accumulates enough mass such that it can
+no longer electron degeneracy pressure
+
+ align:start position:0%
+no longer electron degeneracy pressure
+ 
+
+ align:start position:0%
+no longer electron degeneracy pressure
+is no longer sufficient to hold it
+
+ align:start position:0%
+is no longer sufficient to hold it
+ 
+
+ align:start position:0%
+is no longer sufficient to hold it
+against gravitational collapse and the
+
+ align:start position:0%
+against gravitational collapse and the
+ 
+
+ align:start position:0%
+against gravitational collapse and the
+whole thing basically collapses into a
+
+ align:start position:0%
+whole thing basically collapses into a
+ 
+
+ align:start position:0%
+whole thing basically collapses into a
+neutron star that happens at a defined
+
+ align:start position:0%
+neutron star that happens at a defined
+ 
+
+ align:start position:0%
+neutron star that happens at a defined
+mass the Chandrasekar mass named after
+
+ align:start position:0%
+mass the Chandrasekar mass named after
+ 
+
+ align:start position:0%
+mass the Chandrasekar mass named after
+one of my scientific heroes Subramanya
+
+ align:start position:0%
+one of my scientific heroes Subramanya
+ 
+
+ align:start position:0%
+one of my scientific heroes Subramanya
+and Chandra Sekhar and because it sort
+
+ align:start position:0%
+and Chandra Sekhar and because it sort
+ 
+
+ align:start position:0%
+and Chandra Sekhar and because it sort
+of has a defined mass associated with it
+
+ align:start position:0%
+of has a defined mass associated with it
+ 
+
+ align:start position:0%
+of has a defined mass associated with it
+every event basically has the same
+
+ align:start position:0%
+every event basically has the same
+ 
+
+ align:start position:0%
+every event basically has the same
+amount of matter participating this is a
+
+ align:start position:0%
+amount of matter participating this is a
+ 
+
+ align:start position:0%
+amount of matter participating this is a
+standard candle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see so there's a couple others and
+
+ align:start position:0%
+let's see so there's a couple others and
+ 
+
+ align:start position:0%
+let's see so there's a couple others and
+I'm not gonna talk about in too much
+
+ align:start position:0%
+I'm not gonna talk about in too much
+ 
+
+ align:start position:0%
+I'm not gonna talk about in too much
+detail here while I'm erasing the board
+
+ align:start position:0%
+detail here while I'm erasing the board
+ 
+
+ align:start position:0%
+detail here while I'm erasing the board
+I would just mention them so by looking
+
+ align:start position:0%
+I would just mention them so by looking
+ 
+
+ align:start position:0%
+I would just mention them so by looking
+at things like the clustering of
+
+ align:start position:0%
+at things like the clustering of
+ 
+
+ align:start position:0%
+at things like the clustering of
+galaxies we can measure the distribution
+
+ align:start position:0%
+galaxies we can measure the distribution
+ 
+
+ align:start position:0%
+galaxies we can measure the distribution
+of mass in the universe that allows us
+
+ align:start position:0%
+of mass in the universe that allows us
+ 
+
+ align:start position:0%
+of mass in the universe that allows us
+to determine the Omega M parameter
+
+ align:start position:0%
+to determine the Omega M parameter
+ 
+
+ align:start position:0%
+to determine the Omega M parameter
+that's one of the bits of information
+
+ align:start position:0%
+that's one of the bits of information
+ 
+
+ align:start position:0%
+that's one of the bits of information
+that tells us that much of the universe
+
+ align:start position:0%
+that tells us that much of the universe
+ 
+
+ align:start position:0%
+that tells us that much of the universe
+is made of matter that apparently does
+
+ align:start position:0%
+is made of matter that apparently does
+ 
+
+ align:start position:0%
+is made of matter that apparently does
+not participate in standard model
+
+ align:start position:0%
+not participate in standard model
+ 
+
+ align:start position:0%
+not participate in standard model
+processes as we know them today the
+
+ align:start position:0%
+processes as we know them today the
+ 
+
+ align:start position:0%
+processes as we know them today the
+so-called Dark Matter problem we can
+
+ align:start position:0%
+so-called Dark Matter problem we can
+ 
+
+ align:start position:0%
+so-called Dark Matter problem we can
+look at chemical abundances which tells
+
+ align:start position:0%
+look at chemical abundances which tells
+ 
+
+ align:start position:0%
+look at chemical abundances which tells
+us about the behavior of nuclear
+
+ align:start position:0%
+us about the behavior of nuclear
+ 
+
+ align:start position:0%
+us about the behavior of nuclear
+processes in the very early universe and
+
+ align:start position:0%
+processes in the very early universe and
+ 
+
+ align:start position:0%
+processes in the very early universe and
+the last ones I will mention here is we
+
+ align:start position:0%
+the last ones I will mention here is we
+ 
+
+ align:start position:0%
+the last ones I will mention here is we
+can look at nearby
+
+ align:start position:0%
+can look at nearby
+ 
+
+ align:start position:0%
+can look at nearby
+standard candles and nearby standard
+
+ align:start position:0%
+standard candles and nearby standard
+ 
+
+ align:start position:0%
+standard candles and nearby standard
+candles allow us to probe the local
+
+ align:start position:0%
+candles allow us to probe the local
+ 
+
+ align:start position:0%
+candles allow us to probe the local
+Hubble law and determine h0 combined
+
+ align:start position:0%
+Hubble law and determine h0 combined
+ 
+
+ align:start position:0%
+Hubble law and determine h0 combined
+probe and hubble probe okay and when I
+
+ align:start position:0%
+probe and hubble probe okay and when I
+ 
+
+ align:start position:0%
+probe and hubble probe okay and when I
+say nearby that usually means events
+
+ align:start position:0%
+say nearby that usually means events
+ 
+
+ align:start position:0%
+say nearby that usually means events
+that are merely a few tens of millions
+
+ align:start position:0%
+that are merely a few tens of millions
+ 
+
+ align:start position:0%
+that are merely a few tens of millions
+of light years away it's worth noting
+
+ align:start position:0%
+of light years away it's worth noting
+ 
+
+ align:start position:0%
+of light years away it's worth noting
+that all of these various techniques all
+
+ align:start position:0%
+that all of these various techniques all
+ 
+
+ align:start position:0%
+that all of these various techniques all
+of these different things you can kind
+
+ align:start position:0%
+of these different things you can kind
+ 
+
+ align:start position:0%
+of these different things you can kind
+of even see it when you think about the
+
+ align:start position:0%
+of even see it when you think about the
+ 
+
+ align:start position:0%
+of even see it when you think about the
+mathematical form of everything that
+
+ align:start position:0%
+mathematical form of everything that
+ 
+
+ align:start position:0%
+mathematical form of everything that
+went into our distance measures they're
+
+ align:start position:0%
+went into our distance measures they're
+ 
+
+ align:start position:0%
+went into our distance measures they're
+all highly entangled with each other and
+
+ align:start position:0%
+all highly entangled with each other and
+ 
+
+ align:start position:0%
+all highly entangled with each other and
+so to do this kind of thing properly you
+
+ align:start position:0%
+so to do this kind of thing properly you
+ 
+
+ align:start position:0%
+so to do this kind of thing properly you
+need to take just a crapload of data
+
+ align:start position:0%
+need to take just a crapload of data
+ 
+
+ align:start position:0%
+need to take just a crapload of data
+combine all of your data sets and do a
+
+ align:start position:0%
+combine all of your data sets and do a
+ 
+
+ align:start position:0%
+combine all of your data sets and do a
+joint analysis of everything looking at
+
+ align:start position:0%
+joint analysis of everything looking at
+ 
+
+ align:start position:0%
+joint analysis of everything looking at
+the way varying the parameters and all
+
+ align:start position:0%
+the way varying the parameters and all
+ 
+
+ align:start position:0%
+the way varying the parameters and all
+the different models affects the outcome
+
+ align:start position:0%
+the different models affects the outcome
+ 
+
+ align:start position:0%
+the different models affects the outcome
+of your observables
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you also have to carefully take into
+
+ align:start position:0%
+you also have to carefully take into
+ 
+
+ align:start position:0%
+you also have to carefully take into
+account the fact that when you measure
+
+ align:start position:0%
+account the fact that when you measure
+ 
+
+ align:start position:0%
+account the fact that when you measure
+something you measure it with errors and
+
+ align:start position:0%
+something you measure it with errors and
+ 
+
+ align:start position:0%
+something you measure it with errors and
+so you know many of these things are not
+
+ align:start position:0%
+so you know many of these things are not
+ 
+
+ align:start position:0%
+so you know many of these things are not
+known turns out you can usually measure
+
+ align:start position:0%
+known turns out you can usually measure
+ 
+
+ align:start position:0%
+known turns out you can usually measure
+redshift quite precisely but these
+
+ align:start position:0%
+redshift quite precisely but these
+ 
+
+ align:start position:0%
+redshift quite precisely but these
+distances always come with some error
+
+ align:start position:0%
+distances always come with some error
+ 
+
+ align:start position:0%
+distances always come with some error
+bar associated with them and so that
+
+ align:start position:0%
+bar associated with them and so that
+ 
+
+ align:start position:0%
+bar associated with them and so that
+means that the distance you associate
+
+ align:start position:0%
+means that the distance you associate
+ 
+
+ align:start position:0%
+means that the distance you associate
+with a particular redshift which is
+
+ align:start position:0%
+with a particular redshift which is
+ 
+
+ align:start position:0%
+with a particular redshift which is
+equivalent to associating a time with a
+
+ align:start position:0%
+equivalent to associating a time with a
+ 
+
+ align:start position:0%
+equivalent to associating a time with a
+redshift you know there's some error bar
+
+ align:start position:0%
+redshift you know there's some error bar
+ 
+
+ align:start position:0%
+redshift you know there's some error bar
+on that and that can lead to significant
+
+ align:start position:0%
+on that and that can lead to significant
+ 
+
+ align:start position:0%
+on that and that can lead to significant
+skew and what you determined from things
+
+ align:start position:0%
+skew and what you determined from things
+ 
+
+ align:start position:0%
+skew and what you determined from things
+so there's a lot more we could say but
+
+ align:start position:0%
+so there's a lot more we could say but
+ 
+
+ align:start position:0%
+so there's a lot more we could say but
+time is finite and we need to change
+
+ align:start position:0%
+time is finite and we need to change
+ 
+
+ align:start position:0%
+time is finite and we need to change
+topic so I'm going to conclude this
+
+ align:start position:0%
+topic so I'm going to conclude this
+ 
+
+ align:start position:0%
+topic so I'm going to conclude this
+lecture by talking about two mysteries
+
+ align:start position:0%
+lecture by talking about two mysteries
+ 
+
+ align:start position:0%
+lecture by talking about two mysteries
+in the cosmological model that have been
+
+ align:start position:0%
+in the cosmological model that have been
+ 
+
+ align:start position:0%
+in the cosmological model that have been
+the focus of a lot of research attention
+
+ align:start position:0%
+the focus of a lot of research attention
+ 
+
+ align:start position:0%
+the focus of a lot of research attention
+over the past several decades so two
+
+ align:start position:0%
+over the past several decades so two
+ 
+
+ align:start position:0%
+over the past several decades so two
+mysteries one why is it that our
+
+ align:start position:0%
+mysteries one why is it that our
+ 
+
+ align:start position:0%
+mysteries one why is it that our
+universe appears to be flat spatially
+
+ align:start position:0%
+universe appears to be flat spatially
+ 
+
+ align:start position:0%
+universe appears to be flat spatially
+flat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the frame why this is a bit of a
+
+ align:start position:0%
+so the frame why this is a bit of a
+ 
+
+ align:start position:0%
+so the frame why this is a bit of a
+mystery if you didn't sort of go come on
+
+ align:start position:0%
+mystery if you didn't sort of go come on
+ 
+
+ align:start position:0%
+mystery if you didn't sort of go come on
+you know you just you've got three
+
+ align:start position:0%
+you know you just you've got three
+ 
+
+ align:start position:0%
+you know you just you've got three
+choices for the parameter you got zero
+
+ align:start position:0%
+choices for the parameter you got zero
+ 
+
+ align:start position:0%
+choices for the parameter you got zero
+well let's begin by thinking about the
+
+ align:start position:0%
+well let's begin by thinking about the
+ 
+
+ align:start position:0%
+well let's begin by thinking about the
+first Freedman equation I can write this
+
+ align:start position:0%
+first Freedman equation I can write this
+ 
+
+ align:start position:0%
+first Freedman equation I can write this
+like so or I can use this form where I
+
+ align:start position:0%
+like so or I can use this form where I
+ 
+
+ align:start position:0%
+like so or I can use this form where I
+say Omega plus Omega curvature I'm just
+
+ align:start position:0%
+say Omega plus Omega curvature I'm just
+ 
+
+ align:start position:0%
+say Omega plus Omega curvature I'm just
+gonna call that Omega C for now that
+
+ align:start position:0%
+gonna call that Omega C for now that
+ 
+
+ align:start position:0%
+gonna call that Omega C for now that
+equals one the expectation had long been
+
+ align:start position:0%
+equals one the expectation had long been
+ 
+
+ align:start position:0%
+equals one the expectation had long been
+that our universe would basically be
+
+ align:start position:0%
+that our universe would basically be
+ 
+
+ align:start position:0%
+that our universe would basically be
+dominated by various species of matter
+
+ align:start position:0%
+dominated by various species of matter
+ 
+
+ align:start position:0%
+dominated by various species of matter
+and radiation for much of its history
+
+ align:start position:0%
+and radiation for much of its history
+ 
+
+ align:start position:0%
+and radiation for much of its history
+especially in the early universe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's awful was radiation-dominated you
+
+ align:start position:0%
+it's awful was radiation-dominated you
+ 
+
+ align:start position:0%
+it's awful was radiation-dominated you
+would expect it's the density to go as a
+
+ align:start position:0%
+would expect it's the density to go as a
+ 
+
+ align:start position:0%
+would expect it's the density to go as a
+to the minus four and if it's
+
+ align:start position:0%
+to the minus four and if it's
+ 
+
+ align:start position:0%
+to the minus four and if it's
+matter-dominated you expected to go is a
+
+ align:start position:0%
+matter-dominated you expected to go is a
+ 
+
+ align:start position:0%
+matter-dominated you expected to go is a
+to the minus three now your curvature
+
+ align:start position:0%
+to the minus three now your curvature
+ 
+
+ align:start position:0%
+to the minus three now your curvature
+density goes as a to the minus two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and so what this means that is that if
+
+ align:start position:0%
+and so what this means that is that if
+ 
+
+ align:start position:0%
+and so what this means that is that if
+you look at the ratio of Omega curvature
+
+ align:start position:0%
+you look at the ratio of Omega curvature
+ 
+
+ align:start position:0%
+you look at the ratio of Omega curvature
+to Omega this will be proportional to a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formatter a squared for radiation if
+
+ align:start position:0%
+formatter a squared for radiation if
+ 
+
+ align:start position:0%
+formatter a squared for radiation if
+your universe it just you know in some
+
+ align:start position:0%
+your universe it just you know in some
+ 
+
+ align:start position:0%
+your universe it just you know in some
+sense looking at these parameter K of
+
+ align:start position:0%
+sense looking at these parameter K of
+ 
+
+ align:start position:0%
+sense looking at these parameter K of
+the minus 1 0 1 that's a little bit
+
+ align:start position:0%
+the minus 1 0 1 that's a little bit
+ 
+
+ align:start position:0%
+the minus 1 0 1 that's a little bit
+misleading it's probably a little bit
+
+ align:start position:0%
+misleading it's probably a little bit
+ 
+
+ align:start position:0%
+misleading it's probably a little bit
+more useful to think about things in
+
+ align:start position:0%
+more useful to think about things in
+ 
+
+ align:start position:0%
+more useful to think about things in
+terms of the Kappa parameter and when
+
+ align:start position:0%
+terms of the Kappa parameter and when
+ 
+
+ align:start position:0%
+terms of the Kappa parameter and when
+you look at that your flat universe is a
+
+ align:start position:0%
+you look at that your flat universe is a
+ 
+
+ align:start position:0%
+you look at that your flat universe is a
+set of measure 0 in the set of all
+
+ align:start position:0%
+set of measure 0 in the set of all
+ 
+
+ align:start position:0%
+set of measure 0 in the set of all
+possible curvature parameters that you
+
+ align:start position:0%
+possible curvature parameters that you
+ 
+
+ align:start position:0%
+possible curvature parameters that you
+could have and physicists tend to get
+
+ align:start position:0%
+could have and physicists tend to get
+ 
+
+ align:start position:0%
+could have and physicists tend to get
+suspicious when something that you know
+
+ align:start position:0%
+suspicious when something that you know
+ 
+
+ align:start position:0%
+suspicious when something that you know
+could take on any range of possible
+
+ align:start position:0%
+could take on any range of possible
+ 
+
+ align:start position:0%
+could take on any range of possible
+random values between minus infinity and
+
+ align:start position:0%
+random values between minus infinity and
+ 
+
+ align:start position:0%
+random values between minus infinity and
+infinity picks out 0 that tends to tell
+
+ align:start position:0%
+infinity picks out 0 that tends to tell
+ 
+
+ align:start position:0%
+infinity picks out 0 that tends to tell
+us that there may be some principle at
+
+ align:start position:0%
+us that there may be some principle at
+ 
+
+ align:start position:0%
+us that there may be some principle at
+play that actually drives things to
+
+ align:start position:0%
+play that actually drives things to
+ 
+
+ align:start position:0%
+play that actually drives things to
+being 0 looking at it this way imagine
+
+ align:start position:0%
+being 0 looking at it this way imagine
+ 
+
+ align:start position:0%
+being 0 looking at it this way imagine
+you have a universe that at early 10th
+
+ align:start position:0%
+you have a universe that at early 10th
+ 
+
+ align:start position:0%
+you have a universe that at early 10th
+at early times is very close to being
+
+ align:start position:0%
+at early times is very close to being
+ 
+
+ align:start position:0%
+at early times is very close to being
+flat but not quite any slight deviation
+
+ align:start position:0%
+flat but not quite any slight deviation
+ 
+
+ align:start position:0%
+flat but not quite any slight deviation
+from flatness
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+grows as the universe expands that's
+
+ align:start position:0%
+grows as the universe expands that's
+ 
+
+ align:start position:0%
+grows as the universe expands that's
+mystery one mystery - why is the Cosmic
+
+ align:start position:0%
+mystery one mystery - why is the Cosmic
+ 
+
+ align:start position:0%
+mystery one mystery - why is the Cosmic
+Microwave Background so homogeneous so
+
+ align:start position:0%
+Microwave Background so homogeneous so
+ 
+
+ align:start position:0%
+Microwave Background so homogeneous so
+when we look at the Cosmic Microwave
+
+ align:start position:0%
+when we look at the Cosmic Microwave
+ 
+
+ align:start position:0%
+when we look at the Cosmic Microwave
+Background we see that it has the same
+
+ align:start position:0%
+Background we see that it has the same
+ 
+
+ align:start position:0%
+Background we see that it has the same
+properties the light has the same
+
+ align:start position:0%
+properties the light has the same
+ 
+
+ align:start position:0%
+properties the light has the same
+brightness it has the same temperature
+
+ align:start position:0%
+brightness it has the same temperature
+ 
+
+ align:start position:0%
+brightness it has the same temperature
+associated with it - it's in a part in a
+
+ align:start position:0%
+associated with it - it's in a part in a
+ 
+
+ align:start position:0%
+associated with it - it's in a part in a
+hundred thousand now the standard model
+
+ align:start position:0%
+hundred thousand now the standard model
+ 
+
+ align:start position:0%
+hundred thousand now the standard model
+of our universe tells us that at very
+
+ align:start position:0%
+of our universe tells us that at very
+ 
+
+ align:start position:0%
+of our universe tells us that at very
+early times the universe was essentially
+
+ align:start position:0%
+early times the universe was essentially
+ 
+
+ align:start position:0%
+early times the universe was essentially
+a dense hot plasma this thing cooled as
+
+ align:start position:0%
+a dense hot plasma this thing cooled as
+ 
+
+ align:start position:0%
+a dense hot plasma this thing cooled as
+the universe expanded much the same way
+
+ align:start position:0%
+the universe expanded much the same way
+ 
+
+ align:start position:0%
+the universe expanded much the same way
+that if you have a bag of gas you
+
+ align:start position:0%
+that if you have a bag of gas you
+ 
+
+ align:start position:0%
+that if you have a bag of gas you
+squeeze it very rapidly it will get hot
+
+ align:start position:0%
+squeeze it very rapidly it will get hot
+ 
+
+ align:start position:0%
+squeeze it very rapidly it will get hot
+you stretch it very rapidly it will cool
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so when we as a few more details of this
+
+ align:start position:0%
+so when we as a few more details of this
+ 
+
+ align:start position:0%
+so when we as a few more details of this
+in my notes but when we look at this one
+
+ align:start position:0%
+in my notes but when we look at this one
+ 
+
+ align:start position:0%
+in my notes but when we look at this one
+of the things that we see is that in a
+
+ align:start position:0%
+of the things that we see is that in a
+ 
+
+ align:start position:0%
+of the things that we see is that in a
+universe that is only only driven by
+
+ align:start position:0%
+universe that is only only driven by
+ 
+
+ align:start position:0%
+universe that is only only driven by
+matter or by radiation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so sort of the matter-dominated and
+
+ align:start position:0%
+so sort of the matter-dominated and
+ 
+
+ align:start position:0%
+so sort of the matter-dominated and
+radiation dominated picture it shows us
+
+ align:start position:0%
+radiation dominated picture it shows us
+ 
+
+ align:start position:0%
+radiation dominated picture it shows us
+that points on opposite sides of the sky
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we're actually out of causal contact
+
+ align:start position:0%
+we're actually out of causal contact
+ 
+
+ align:start position:0%
+we're actually out of causal contact
+with each other in the earliest moments
+
+ align:start position:0%
+with each other in the earliest moments
+ 
+
+ align:start position:0%
+with each other in the earliest moments
+of the universe in other words I look at
+
+ align:start position:0%
+of the universe in other words I look at
+ 
+
+ align:start position:0%
+of the universe in other words I look at
+the sky and the patch of sky over here
+
+ align:start position:0%
+the sky and the patch of sky over here
+ 
+
+ align:start position:0%
+the sky and the patch of sky over here
+was out of causal contact with a patch
+
+ align:start position:0%
+was out of causal contact with a patch
+ 
+
+ align:start position:0%
+was out of causal contact with a patch
+of sky over here in the earliest days of
+
+ align:start position:0%
+of sky over here in the earliest days of
+ 
+
+ align:start position:0%
+of sky over here in the earliest days of
+the universe
+
+ align:start position:0%
+the universe
+ 
+
+ align:start position:0%
+the universe
+and yet they had the same temperature
+
+ align:start position:0%
+and yet they had the same temperature
+ 
+
+ align:start position:0%
+and yet they had the same temperature
+which suggests that they were in thermal
+
+ align:start position:0%
+which suggests that they were in thermal
+ 
+
+ align:start position:0%
+which suggests that they were in thermal
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+how can two disparate unconnected patch
+
+ align:start position:0%
+how can two disparate unconnected patch
+ 
+
+ align:start position:0%
+how can two disparate unconnected patch
+of the sky have the same temperature if
+
+ align:start position:0%
+of the sky have the same temperature if
+ 
+
+ align:start position:0%
+of the sky have the same temperature if
+they cannot exchange information okay
+
+ align:start position:0%
+they cannot exchange information okay
+ 
+
+ align:start position:0%
+they cannot exchange information okay
+you can imagine it being a coincidence
+
+ align:start position:0%
+you can imagine it being a coincidence
+ 
+
+ align:start position:0%
+you can imagine it being a coincidence
+if one little bit of the sky has the
+
+ align:start position:0%
+if one little bit of the sky has the
+ 
+
+ align:start position:0%
+if one little bit of the sky has the
+same temperature as a bit on the other
+
+ align:start position:0%
+same temperature as a bit on the other
+ 
+
+ align:start position:0%
+same temperature as a bit on the other
+bit of another piece but in fact when
+
+ align:start position:0%
+bit of another piece but in fact when
+ 
+
+ align:start position:0%
+bit of another piece but in fact when
+you do this calculation you find huge
+
+ align:start position:0%
+you do this calculation you find huge
+ 
+
+ align:start position:0%
+you do this calculation you find huge
+patch of the sky could not communicate
+
+ align:start position:0%
+patch of the sky could not communicate
+ 
+
+ align:start position:0%
+patch of the sky could not communicate
+with any other um and so how then is it
+
+ align:start position:0%
+with any other um and so how then is it
+ 
+
+ align:start position:0%
+with any other um and so how then is it
+that the entire sky that we can observe
+
+ align:start position:0%
+that the entire sky that we can observe
+ 
+
+ align:start position:0%
+that the entire sky that we can observe
+has the same temperature at the earliest
+
+ align:start position:0%
+has the same temperature at the earliest
+ 
+
+ align:start position:0%
+has the same temperature at the earliest
+times to within a part in a hundred
+
+ align:start position:0%
+times to within a part in a hundred
+ 
+
+ align:start position:0%
+times to within a part in a hundred
+thousand you guys will explore this on I
+
+ align:start position:0%
+thousand you guys will explore this on I
+ 
+
+ align:start position:0%
+thousand you guys will explore this on I
+believe it's problem set eight the
+
+ align:start position:0%
+believe it's problem set eight the
+ 
+
+ align:start position:0%
+believe it's problem set eight the
+solution to both of these problems that
+
+ align:start position:0%
+solution to both of these problems that
+ 
+
+ align:start position:0%
+solution to both of these problems that
+has been proposed
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's cosmic inflation so what you do is
+
+ align:start position:0%
+it's cosmic inflation so what you do is
+ 
+
+ align:start position:0%
+it's cosmic inflation so what you do is
+imagine that at some earlier moment in
+
+ align:start position:0%
+imagine that at some earlier moment in
+ 
+
+ align:start position:0%
+imagine that at some earlier moment in
+the universe our universe was filled
+
+ align:start position:0%
+the universe our universe was filled
+ 
+
+ align:start position:0%
+the universe our universe was filled
+with some strange field and I'll
+
+ align:start position:0%
+with some strange field and I'll
+ 
+
+ align:start position:0%
+with some strange field and I'll
+describe the properties of that field in
+
+ align:start position:0%
+describe the properties of that field in
+ 
+
+ align:start position:0%
+describe the properties of that field in
+just a moment such that it acted like it
+
+ align:start position:0%
+just a moment such that it acted like it
+ 
+
+ align:start position:0%
+just a moment such that it acted like it
+had a cosmological constant in such an
+
+ align:start position:0%
+had a cosmological constant in such an
+ 
+
+ align:start position:0%
+had a cosmological constant in such an
+epic the scale factor of the universe
+
+ align:start position:0%
+epic the scale factor of the universe
+ 
+
+ align:start position:0%
+epic the scale factor of the universe
+goes as exponentially with the square
+
+ align:start position:0%
+goes as exponentially with the square
+ 
+
+ align:start position:0%
+goes as exponentially with the square
+root of the sides of the cosmological
+
+ align:start position:0%
+root of the sides of the cosmological
+ 
+
+ align:start position:0%
+root of the sides of the cosmological
+constant what you find when you look at
+
+ align:start position:0%
+constant what you find when you look at
+ 
+
+ align:start position:0%
+constant what you find when you look at
+this is that this it's still of course
+
+ align:start position:0%
+this is that this it's still of course
+ 
+
+ align:start position:0%
+this is that this it's still of course
+goes there's a to the minus two but a to
+
+ align:start position:0%
+goes there's a to the minus two but a to
+ 
+
+ align:start position:0%
+goes there's a to the minus two but a to
+the minus will so sorry way back up for
+
+ align:start position:0%
+the minus will so sorry way back up for
+ 
+
+ align:start position:0%
+the minus will so sorry way back up for
+a second so my scale factor in this case
+
+ align:start position:0%
+a second so my scale factor in this case
+ 
+
+ align:start position:0%
+a second so my scale factor in this case
+you'll find goes as a to the minus two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that's because the density
+
+ align:start position:0%
+and that's because the density
+ 
+
+ align:start position:0%
+and that's because the density
+associated cosmological constant remains
+
+ align:start position:0%
+associated cosmological constant remains
+ 
+
+ align:start position:0%
+associated cosmological constant remains
+constant
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so even if you start in the early
+
+ align:start position:0%
+so even if you start in the early
+ 
+
+ align:start position:0%
+so even if you start in the early
+universe with some random value for the
+
+ align:start position:0%
+universe with some random value for the
+ 
+
+ align:start position:0%
+universe with some random value for the
+curvature if you are in this epoch of
+
+ align:start position:0%
+curvature if you are in this epoch of
+ 
+
+ align:start position:0%
+curvature if you are in this epoch of
+exponential inflation just for you know
+
+ align:start position:0%
+exponential inflation just for you know
+ 
+
+ align:start position:0%
+exponential inflation just for you know
+you have to worry about timescales a
+
+ align:start position:0%
+you have to worry about timescales a
+ 
+
+ align:start position:0%
+you have to worry about timescales a
+little bit but if you do it long enough
+
+ align:start position:0%
+little bit but if you do it long enough
+ 
+
+ align:start position:0%
+little bit but if you do it long enough
+you can drive this very very close to
+
+ align:start position:0%
+you can drive this very very close to
+ 
+
+ align:start position:0%
+you can drive this very very close to
+zero so much so that when you then move
+
+ align:start position:0%
+zero so much so that when you then move
+ 
+
+ align:start position:0%
+zero so much so that when you then move
+forward let's say you come out of this
+
+ align:start position:0%
+forward let's say you come out of this
+ 
+
+ align:start position:0%
+forward let's say you come out of this
+period of cosmic inflation and you enter
+
+ align:start position:0%
+period of cosmic inflation and you enter
+ 
+
+ align:start position:0%
+period of cosmic inflation and you enter
+a universe that is radiation dominated
+
+ align:start position:0%
+a universe that is radiation dominated
+ 
+
+ align:start position:0%
+a universe that is radiation dominated
+or matter-dominated it will then begin
+
+ align:start position:0%
+or matter-dominated it will then begin
+ 
+
+ align:start position:0%
+or matter-dominated it will then begin
+to grow but if you drive it sufficiently
+
+ align:start position:0%
+to grow but if you drive it sufficiently
+ 
+
+ align:start position:0%
+to grow but if you drive it sufficiently
+close to zero doesn't matter you're
+
+ align:start position:0%
+close to zero doesn't matter you're
+ 
+
+ align:start position:0%
+close to zero doesn't matter you're
+never going to catch up with what
+
+ align:start position:0%
+never going to catch up with what
+ 
+
+ align:start position:0%
+never going to catch up with what
+inflation did to you on the piece that
+
+ align:start position:0%
+inflation did to you on the piece that
+ 
+
+ align:start position:0%
+inflation did to you on the piece that
+you will also show that if you have a
+
+ align:start position:0%
+you will also show that if you have a
+ 
+
+ align:start position:0%
+you will also show that if you have a
+period of inflation like this then what
+
+ align:start position:0%
+period of inflation like this then what
+ 
+
+ align:start position:0%
+period of inflation like this then what
+that also cures the problem of peace of
+
+ align:start position:0%
+that also cures the problem of peace of
+ 
+
+ align:start position:0%
+that also cures the problem of peace of
+the sky being out of causal contact so
+
+ align:start position:0%
+the sky being out of causal contact so
+ 
+
+ align:start position:0%
+the sky being out of causal contact so
+when you do that what you find is that
+
+ align:start position:0%
+when you do that what you find is that
+ 
+
+ align:start position:0%
+when you do that what you find is that
+essentially everything is in causal
+
+ align:start position:0%
+essentially everything is in causal
+ 
+
+ align:start position:0%
+essentially everything is in causal
+contact early on it may sort of come out
+
+ align:start position:0%
+contact early on it may sort of come out
+ 
+
+ align:start position:0%
+contact early on it may sort of come out
+of causal contact after inflation has
+
+ align:start position:0%
+of causal contact after inflation has
+ 
+
+ align:start position:0%
+of causal contact after inflation has
+ended more on that in just a moment and
+
+ align:start position:0%
+ended more on that in just a moment and
+ 
+
+ align:start position:0%
+ended more on that in just a moment and
+then you know things sort of changed as
+
+ align:start position:0%
+then you know things sort of changed as
+ 
+
+ align:start position:0%
+then you know things sort of changed as
+the universe can use to evolve okay so
+
+ align:start position:0%
+the universe can use to evolve okay so
+ 
+
+ align:start position:0%
+the universe can use to evolve okay so
+it looks like recording is back on my
+
+ align:start position:0%
+it looks like recording is back on my
+ 
+
+ align:start position:0%
+it looks like recording is back on my
+apologies everyone so as I was in the
+
+ align:start position:0%
+apologies everyone so as I was in the
+ 
+
+ align:start position:0%
+apologies everyone so as I was in the
+middle of talk I talked a little bit too
+
+ align:start position:0%
+middle of talk I talked a little bit too
+ 
+
+ align:start position:0%
+middle of talk I talked a little bit too
+long in this this particular lecture so
+
+ align:start position:0%
+long in this this particular lecture so
+ 
+
+ align:start position:0%
+long in this this particular lecture so
+we're gonna spill over into a little bit
+
+ align:start position:0%
+we're gonna spill over into a little bit
+ 
+
+ align:start position:0%
+we're gonna spill over into a little bit
+of an addendum just a five ish minute
+
+ align:start position:0%
+of an addendum just a five ish minute
+ 
+
+ align:start position:0%
+of an addendum just a five ish minute
+piece that goes a bit beyond this doing
+
+ align:start position:0%
+piece that goes a bit beyond this doing
+ 
+
+ align:start position:0%
+piece that goes a bit beyond this doing
+this by myself is a little bit weird I'm
+
+ align:start position:0%
+this by myself is a little bit weird I'm
+ 
+
+ align:start position:0%
+this by myself is a little bit weird I'm
+tired and I will confess I got a little
+
+ align:start position:0%
+tired and I will confess I got a little
+ 
+
+ align:start position:0%
+tired and I will confess I got a little
+bit rattled when the police came in to
+
+ align:start position:0%
+bit rattled when the police came in to
+ 
+
+ align:start position:0%
+bit rattled when the police came in to
+check in on me let's back up for a
+
+ align:start position:0%
+check in on me let's back up for a
+ 
+
+ align:start position:0%
+check in on me let's back up for a
+second so I was talking about two
+
+ align:start position:0%
+second so I was talking about two
+ 
+
+ align:start position:0%
+second so I was talking about two
+mysteries of the modern cosmological
+
+ align:start position:0%
+mysteries of the modern cosmological
+ 
+
+ align:start position:0%
+mysteries of the modern cosmological
+model one of them is this question of
+
+ align:start position:0%
+model one of them is this question of
+ 
+
+ align:start position:0%
+model one of them is this question of
+why the universe is so apparently flat
+
+ align:start position:0%
+why the universe is so apparently flat
+ 
+
+ align:start position:0%
+why the universe is so apparently flat
+the spatial sector the universe appears
+
+ align:start position:0%
+the spatial sector the universe appears
+ 
+
+ align:start position:0%
+the spatial sector the universe appears
+to be flat and we have this expectation
+
+ align:start position:0%
+to be flat and we have this expectation
+ 
+
+ align:start position:0%
+to be flat and we have this expectation
+that the universe is either radiation
+
+ align:start position:0%
+that the universe is either radiation
+ 
+
+ align:start position:0%
+that the universe is either radiation
+dominated or matter dominated
+
+ align:start position:0%
+dominated or matter dominated
+ 
+
+ align:start position:0%
+dominated or matter dominated
+which would give us that the density
+
+ align:start position:0%
+which would give us that the density
+ 
+
+ align:start position:0%
+which would give us that the density
+associated with radiation if it's
+
+ align:start position:0%
+associated with radiation if it's
+ 
+
+ align:start position:0%
+associated with radiation if it's
+radiation dominated then the density of
+
+ align:start position:0%
+radiation dominated then the density of
+ 
+
+ align:start position:0%
+radiation dominated then the density of
+stuff in our universe would fall off
+
+ align:start position:0%
+stuff in our universe would fall off
+ 
+
+ align:start position:0%
+stuff in our universe would fall off
+there's the scale factor to the fourth
+
+ align:start position:0%
+there's the scale factor to the fourth
+ 
+
+ align:start position:0%
+there's the scale factor to the fourth
+power if it's matter dominant it's scale
+
+ align:start position:0%
+power if it's matter dominant it's scale
+ 
+
+ align:start position:0%
+power if it's matter dominant it's scale
+factor to the third power when you
+
+ align:start position:0%
+factor to the third power when you
+ 
+
+ align:start position:0%
+factor to the third power when you
+define a density associate with the
+
+ align:start position:0%
+define a density associate with the
+ 
+
+ align:start position:0%
+define a density associate with the
+curvature it falls off as a scale factor
+
+ align:start position:0%
+curvature it falls off as a scale factor
+ 
+
+ align:start position:0%
+curvature it falls off as a scale factor
+to the second power and so if we look at
+
+ align:start position:0%
+to the second power and so if we look at
+ 
+
+ align:start position:0%
+to the second power and so if we look at
+the ratio of the curvature density to
+
+ align:start position:0%
+the ratio of the curvature density to
+ 
+
+ align:start position:0%
+the ratio of the curvature density to
+any other kind of density it grows as
+
+ align:start position:0%
+any other kind of density it grows as
+ 
+
+ align:start position:0%
+any other kind of density it grows as
+the universe expands so any slight
+
+ align:start position:0%
+the universe expands so any slight
+ 
+
+ align:start position:0%
+the universe expands so any slight
+deviation from flatness we would expect
+
+ align:start position:0%
+deviation from flatness we would expect
+ 
+
+ align:start position:0%
+deviation from flatness we would expect
+to grow okay and that's just confusing
+
+ align:start position:0%
+to grow okay and that's just confusing
+ 
+
+ align:start position:0%
+to grow okay and that's just confusing
+why is it when we make the various
+
+ align:start position:0%
+why is it when we make the various
+ 
+
+ align:start position:0%
+why is it when we make the various
+measurements that we have been making
+
+ align:start position:0%
+measurements that we have been making
+ 
+
+ align:start position:0%
+measurements that we have been making
+for the past several decades all the
+
+ align:start position:0%
+for the past several decades all the
+ 
+
+ align:start position:0%
+for the past several decades all the
+evidence is pointing to a universe that
+
+ align:start position:0%
+evidence is pointing to a universe that
+ 
+
+ align:start position:0%
+evidence is pointing to a universe that
+has a flatness of zero okay but any
+
+ align:start position:0%
+has a flatness of zero okay but any
+ 
+
+ align:start position:0%
+has a flatness of zero okay but any
+slave if you sort of imagined that the
+
+ align:start position:0%
+slave if you sort of imagined that the
+ 
+
+ align:start position:0%
+slave if you sort of imagined that the
+parameter Kappa can be any number
+
+ align:start position:0%
+parameter Kappa can be any number
+ 
+
+ align:start position:0%
+parameter Kappa can be any number
+between minus infinity to infinity
+
+ align:start position:0%
+between minus infinity to infinity
+ 
+
+ align:start position:0%
+between minus infinity to infinity
+why is nature picking out zero another
+
+ align:start position:0%
+why is nature picking out zero another
+ 
+
+ align:start position:0%
+why is nature picking out zero another
+mystery is why is the Cosmic Microwave
+
+ align:start position:0%
+mystery is why is the Cosmic Microwave
+ 
+
+ align:start position:0%
+mystery is why is the Cosmic Microwave
+Background so Huma homogeneous we
+
+ align:start position:0%
+Background so Huma homogeneous we
+ 
+
+ align:start position:0%
+Background so Huma homogeneous we
+believed that the universe was a very
+
+ align:start position:0%
+believed that the universe was a very
+ 
+
+ align:start position:0%
+believed that the universe was a very
+hot dense plasma at very early times it
+
+ align:start position:0%
+hot dense plasma at very early times it
+ 
+
+ align:start position:0%
+hot dense plasma at very early times it
+cooled as the universe expanded and when
+
+ align:start position:0%
+cooled as the universe expanded and when
+ 
+
+ align:start position:0%
+cooled as the universe expanded and when
+we we measure the radiation from that
+
+ align:start position:0%
+we we measure the radiation from that
+ 
+
+ align:start position:0%
+we we measure the radiation from that
+that cooling expanding ball of clouds no
+
+ align:start position:0%
+that cooling expanding ball of clouds no
+ 
+
+ align:start position:0%
+that cooling expanding ball of clouds no
+what we find is that it has the same
+
+ align:start position:0%
+what we find is that it has the same
+ 
+
+ align:start position:0%
+what we find is that it has the same
+temperature at every point on the sky to
+
+ align:start position:0%
+temperature at every point on the sky to
+ 
+
+ align:start position:0%
+temperature at every point on the sky to
+within a part in a hundred thousand but
+
+ align:start position:0%
+within a part in a hundred thousand but
+ 
+
+ align:start position:0%
+within a part in a hundred thousand but
+when one looks at the behavior of of how
+
+ align:start position:0%
+when one looks at the behavior of of how
+ 
+
+ align:start position:0%
+when one looks at the behavior of of how
+how light moves around in the early
+
+ align:start position:0%
+how light moves around in the early
+ 
+
+ align:start position:0%
+how light moves around in the early
+universe if the universe is mad or
+
+ align:start position:0%
+universe if the universe is mad or
+ 
+
+ align:start position:0%
+universe if the universe is mad or
+dominated or radiation dominated what
+
+ align:start position:0%
+dominated or radiation dominated what
+ 
+
+ align:start position:0%
+dominated or radiation dominated what
+you find is that a piece of the sky over
+
+ align:start position:0%
+you find is that a piece of the sky over
+ 
+
+ align:start position:0%
+you find is that a piece of the sky over
+here cannot communicate with a piece of
+
+ align:start position:0%
+here cannot communicate with a piece of
+ 
+
+ align:start position:0%
+here cannot communicate with a piece of
+sky over here we're over here over here
+
+ align:start position:0%
+sky over here we're over here over here
+ 
+
+ align:start position:0%
+sky over here we're over here over here
+you actually find that the size of the
+
+ align:start position:0%
+you actually find that the size of the
+ 
+
+ align:start position:0%
+you actually find that the size of the
+sky that came that if I look at a piece
+
+ align:start position:0%
+sky that came that if I look at a piece
+ 
+
+ align:start position:0%
+sky that came that if I look at a piece
+of sky over here how much the universe
+
+ align:start position:0%
+of sky over here how much the universe
+ 
+
+ align:start position:0%
+of sky over here how much the universe
+could have talked to it's surprisingly
+
+ align:start position:0%
+could have talked to it's surprisingly
+ 
+
+ align:start position:0%
+could have talked to it's surprisingly
+small so how is it that the entire
+
+ align:start position:0%
+small so how is it that the entire
+ 
+
+ align:start position:0%
+small so how is it that the entire
+universe has the same temperature how is
+
+ align:start position:0%
+universe has the same temperature how is
+ 
+
+ align:start position:0%
+universe has the same temperature how is
+that they are apparently in thermal
+
+ align:start position:0%
+that they are apparently in thermal
+ 
+
+ align:start position:0%
+that they are apparently in thermal
+equilibrium even if they cannot exchange
+
+ align:start position:0%
+equilibrium even if they cannot exchange
+ 
+
+ align:start position:0%
+equilibrium even if they cannot exchange
+information so I spend some while
+
+ align:start position:0%
+information so I spend some while
+ 
+
+ align:start position:0%
+information so I spend some while
+talking to myself after the cameras went
+
+ align:start position:0%
+talking to myself after the cameras went
+ 
+
+ align:start position:0%
+talking to myself after the cameras went
+out
+
+ align:start position:0%
+out
+ 
+
+ align:start position:0%
+out
+so I just sketch what I wrote down a
+
+ align:start position:0%
+so I just sketch what I wrote down a
+ 
+
+ align:start position:0%
+so I just sketch what I wrote down a
+proposed solution to this to both of
+
+ align:start position:0%
+proposed solution to this to both of
+ 
+
+ align:start position:0%
+proposed solution to this to both of
+these mysteries is when it's known as
+
+ align:start position:0%
+these mysteries is when it's known as
+ 
+
+ align:start position:0%
+these mysteries is when it's known as
+cosmic inflation something that our own
+
+ align:start position:0%
+cosmic inflation something that our own
+ 
+
+ align:start position:0%
+cosmic inflation something that our own
+Alan Guth shares a lot of the credit for
+
+ align:start position:0%
+Alan Guth shares a lot of the credit for
+ 
+
+ align:start position:0%
+Alan Guth shares a lot of the credit for
+helping to develop so recall if we have
+
+ align:start position:0%
+helping to develop so recall if we have
+ 
+
+ align:start position:0%
+helping to develop so recall if we have
+a cosmological constant then the scale
+
+ align:start position:0%
+a cosmological constant then the scale
+ 
+
+ align:start position:0%
+a cosmological constant then the scale
+factor grows exponentially and the
+
+ align:start position:0%
+factor grows exponentially and the
+ 
+
+ align:start position:0%
+factor grows exponentially and the
+density of stuff associate that
+
+ align:start position:0%
+density of stuff associate that
+ 
+
+ align:start position:0%
+density of stuff associate that
+cosmological constant is constant okay
+
+ align:start position:0%
+cosmological constant is constant okay
+ 
+
+ align:start position:0%
+cosmological constant is constant okay
+as the universe expands the density the
+
+ align:start position:0%
+as the universe expands the density the
+ 
+
+ align:start position:0%
+as the universe expands the density the
+energy density associated that
+
+ align:start position:0%
+energy density associated that
+ 
+
+ align:start position:0%
+energy density associated that
+cosmological constant does not change if
+
+ align:start position:0%
+cosmological constant does not change if
+ 
+
+ align:start position:0%
+cosmological constant does not change if
+our universe is dominated by such a
+
+ align:start position:0%
+our universe is dominated by such a
+ 
+
+ align:start position:0%
+our universe is dominated by such a
+constant then the ratio of density is
+
+ align:start position:0%
+constant then the ratio of density is
+ 
+
+ align:start position:0%
+constant then the ratio of density is
+associate with curvature the densities
+
+ align:start position:0%
+associate with curvature the densities
+ 
+
+ align:start position:0%
+associate with curvature the densities
+associated cosmological constant
+
+ align:start position:0%
+associated cosmological constant
+ 
+
+ align:start position:0%
+associated cosmological constant
+actually falls off inversely with the
+
+ align:start position:0%
+actually falls off inversely with the
+ 
+
+ align:start position:0%
+actually falls off inversely with the
+curvature scale squared and the
+
+ align:start position:0%
+curvature scale squared and the
+ 
+
+ align:start position:0%
+curvature scale squared and the
+curvature scale is growing exponentially
+
+ align:start position:0%
+curvature scale is growing exponentially
+ 
+
+ align:start position:0%
+curvature scale is growing exponentially
+it means that Omega C is being driven to
+
+ align:start position:0%
+it means that Omega C is being driven to
+ 
+
+ align:start position:0%
+it means that Omega C is being driven to
+zero relative to the density in
+
+ align:start position:0%
+zero relative to the density in
+ 
+
+ align:start position:0%
+zero relative to the density in
+cosmological constant as e to the e to a
+
+ align:start position:0%
+cosmological constant as e to the e to a
+ 
+
+ align:start position:0%
+cosmological constant as e to the e to a
+factor like this it's being
+
+ align:start position:0%
+factor like this it's being
+ 
+
+ align:start position:0%
+factor like this it's being
+exponentially driven close to zero to do
+
+ align:start position:0%
+exponentially driven close to zero to do
+ 
+
+ align:start position:0%
+exponentially driven close to zero to do
+a little bit of work to figure out what
+
+ align:start position:0%
+a little bit of work to figure out what
+ 
+
+ align:start position:0%
+a little bit of work to figure out what
+the timescales associate this are but
+
+ align:start position:0%
+the timescales associate this are but
+ 
+
+ align:start position:0%
+the timescales associate this are but
+this sort of suggests that if you can
+
+ align:start position:0%
+this sort of suggests that if you can
+ 
+
+ align:start position:0%
+this sort of suggests that if you can
+put the universe in a state where it
+
+ align:start position:0%
+put the universe in a state where it
+ 
+
+ align:start position:0%
+put the universe in a state where it
+looks like a cause much more constant
+
+ align:start position:0%
+looks like a cause much more constant
+ 
+
+ align:start position:0%
+looks like a cause much more constant
+you can drive the density associate with
+
+ align:start position:0%
+you can drive the density associate with
+ 
+
+ align:start position:0%
+you can drive the density associate with
+curvature as close to zero as you want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+recall that a cosmological constant is
+
+ align:start position:0%
+recall that a cosmological constant is
+ 
+
+ align:start position:0%
+recall that a cosmological constant is
+actually equivalent to there being a
+
+ align:start position:0%
+actually equivalent to there being a
+ 
+
+ align:start position:0%
+actually equivalent to there being a
+vacuum energy if we think about the
+
+ align:start position:0%
+vacuum energy if we think about the
+ 
+
+ align:start position:0%
+vacuum energy if we think about the
+universe being filled with some kind of
+
+ align:start position:0%
+universe being filled with some kind of
+ 
+
+ align:start position:0%
+universe being filled with some kind of
+a scalar field at early times it can
+
+ align:start position:0%
+a scalar field at early times it can
+ 
+
+ align:start position:0%
+a scalar field at early times it can
+play the role of such a vacuum energy
+
+ align:start position:0%
+play the role of such a vacuum energy
+ 
+
+ align:start position:0%
+play the role of such a vacuum energy
+without going into the details one finds
+
+ align:start position:0%
+without going into the details one finds
+ 
+
+ align:start position:0%
+without going into the details one finds
+that in an expanding universe there is
+
+ align:start position:0%
+that in an expanding universe there is
+ 
+
+ align:start position:0%
+that in an expanding universe there is
+an equation of motion for that scalar
+
+ align:start position:0%
+an equation of motion for that scalar
+ 
+
+ align:start position:0%
+an equation of motion for that scalar
+field how the field itself behaves as
+
+ align:start position:0%
+field how the field itself behaves as
+ 
+
+ align:start position:0%
+field how the field itself behaves as
+driven by a differential equation looks
+
+ align:start position:0%
+driven by a differential equation looks
+ 
+
+ align:start position:0%
+driven by a differential equation looks
+like this here's your Hubble parameter
+
+ align:start position:0%
+like this here's your Hubble parameter
+ 
+
+ align:start position:0%
+like this here's your Hubble parameter
+so this has to do with the scale factor
+
+ align:start position:0%
+so this has to do with the scale factor
+ 
+
+ align:start position:0%
+so this has to do with the scale factor
+in here V is a potential for this scalar
+
+ align:start position:0%
+in here V is a potential for this scalar
+ 
+
+ align:start position:0%
+in here V is a potential for this scalar
+field which I'm not going to say too
+
+ align:start position:0%
+field which I'm not going to say too
+ 
+
+ align:start position:0%
+field which I'm not going to say too
+much about take this guy couple it to
+
+ align:start position:0%
+much about take this guy couple it to
+ 
+
+ align:start position:0%
+much about take this guy couple it to
+your Fremont equations and the one
+
+ align:start position:0%
+your Fremont equations and the one
+ 
+
+ align:start position:0%
+your Fremont equations and the one
+that's most important is the first
+
+ align:start position:0%
+that's most important is the first
+ 
+
+ align:start position:0%
+that's most important is the first
+Freeman equation what you see is that V
+
+ align:start position:0%
+Freeman equation what you see is that V
+ 
+
+ align:start position:0%
+Freeman equation what you see is that V
+of Phi is playing the role of a of a
+
+ align:start position:0%
+of Phi is playing the role of a of a
+ 
+
+ align:start position:0%
+of Phi is playing the role of a of a
+cosmological constants playing the role
+
+ align:start position:0%
+cosmological constants playing the role
+ 
+
+ align:start position:0%
+cosmological constants playing the role
+of a density so if we can put the
+
+ align:start position:0%
+of a density so if we can put the
+ 
+
+ align:start position:0%
+of a density so if we can put the
+universe
+
+ align:start position:0%
+universe
+ 
+
+ align:start position:0%
+universe
+into a state where it is in fact being
+
+ align:start position:0%
+into a state where it is in fact being
+ 
+
+ align:start position:0%
+into a state where it is in fact being
+dominated by this scalar field by the
+
+ align:start position:0%
+dominated by this scalar field by the
+ 
+
+ align:start position:0%
+dominated by this scalar field by the
+potential associate with the scalar
+
+ align:start position:0%
+potential associate with the scalar
+ 
+
+ align:start position:0%
+potential associate with the scalar
+field it will inflate okay a lot of the
+
+ align:start position:0%
+field it will inflate okay a lot of the
+ 
+
+ align:start position:0%
+field it will inflate okay a lot of the
+research in early universe physics that
+
+ align:start position:0%
+research in early universe physics that
+ 
+
+ align:start position:0%
+research in early universe physics that
+was going on over the past couple
+
+ align:start position:0%
+was going on over the past couple
+ 
+
+ align:start position:0%
+was going on over the past couple
+decades has gone into understanding what
+
+ align:start position:0%
+decades has gone into understanding what
+ 
+
+ align:start position:0%
+decades has gone into understanding what
+are the consequences of such a such a
+
+ align:start position:0%
+are the consequences of such a such a
+ 
+
+ align:start position:0%
+are the consequences of such a such a
+potential can we make such a potential
+
+ align:start position:0%
+potential can we make such a potential
+ 
+
+ align:start position:0%
+potential can we make such a potential
+do the laws of physics ferment something
+
+ align:start position:0%
+do the laws of physics ferment something
+ 
+
+ align:start position:0%
+do the laws of physics ferment something
+like this to exist if the universe is in
+
+ align:start position:0%
+like this to exist if the universe is in
+ 
+
+ align:start position:0%
+like this to exist if the universe is in
+this state early on what changed how is
+
+ align:start position:0%
+this state early on what changed how is
+ 
+
+ align:start position:0%
+this state early on what changed how is
+it that this thing evolves there's an
+
+ align:start position:0%
+it that this thing evolves there's an
+ 
+
+ align:start position:0%
+it that this thing evolves there's an
+equation of motion here so this scalar
+
+ align:start position:0%
+equation of motion here so this scalar
+ 
+
+ align:start position:0%
+equation of motion here so this scalar
+field is presumably evolving in some
+
+ align:start position:0%
+field is presumably evolving in some
+ 
+
+ align:start position:0%
+field is presumably evolving in some
+kind of a way is there a potential is
+
+ align:start position:0%
+kind of a way is there a potential is
+ 
+
+ align:start position:0%
+kind of a way is there a potential is
+this nature permit us to have a field of
+
+ align:start position:0%
+this nature permit us to have a field of
+ 
+
+ align:start position:0%
+this nature permit us to have a field of
+the sort with a potential that sort of
+
+ align:start position:0%
+the sort with a potential that sort of
+ 
+
+ align:start position:0%
+the sort with a potential that sort of
+goes away after some time once it goes
+
+ align:start position:0%
+goes away after some time once it goes
+ 
+
+ align:start position:0%
+goes away after some time once it goes
+away what happens to that field is there
+
+ align:start position:0%
+away what happens to that field is there
+ 
+
+ align:start position:0%
+away what happens to that field is there
+any smoking gun associate as this you
+
+ align:start position:0%
+any smoking gun associate as this you
+ 
+
+ align:start position:0%
+any smoking gun associate as this you
+know we look at the universe and this is
+
+ align:start position:0%
+know we look at the universe and this is
+ 
+
+ align:start position:0%
+know we look at the universe and this is
+a plausible explanation for why the
+
+ align:start position:0%
+a plausible explanation for why the
+ 
+
+ align:start position:0%
+a plausible explanation for why the
+universe appears to be spatially flat
+
+ align:start position:0%
+universe appears to be spatially flat
+ 
+
+ align:start position:0%
+universe appears to be spatially flat
+and why the Cosmic Microwave Background
+
+ align:start position:0%
+and why the Cosmic Microwave Background
+ 
+
+ align:start position:0%
+and why the Cosmic Microwave Background
+is so humid genius is there anything
+
+ align:start position:0%
+is so humid genius is there anything
+ 
+
+ align:start position:0%
+is so humid genius is there anything
+else that we can look at that would
+
+ align:start position:0%
+else that we can look at that would
+ 
+
+ align:start position:0%
+else that we can look at that would
+basically say yes the universe did in
+
+ align:start position:0%
+basically say yes the universe did in
+ 
+
+ align:start position:0%
+basically say yes the universe did in
+fact have this kind of an expansion
+
+ align:start position:0%
+fact have this kind of an expansion
+ 
+
+ align:start position:0%
+fact have this kind of an expansion
+without getting into the weeds too much
+
+ align:start position:0%
+without getting into the weeds too much
+ 
+
+ align:start position:0%
+without getting into the weeds too much
+it turns out that if the universe
+
+ align:start position:0%
+it turns out that if the universe
+ 
+
+ align:start position:0%
+it turns out that if the universe
+expanded like this we would expect there
+
+ align:start position:0%
+expanded like this we would expect there
+ 
+
+ align:start position:0%
+expanded like this we would expect there
+to be a primordial background of
+
+ align:start position:0%
+to be a primordial background of
+ 
+
+ align:start position:0%
+to be a primordial background of
+gravitational waves very low-frequency
+
+ align:start position:0%
+gravitational waves very low-frequency
+ 
+
+ align:start position:0%
+gravitational waves very low-frequency
+gravitational waves sort of a moaning
+
+ align:start position:0%
+gravitational waves sort of a moaning
+ 
+
+ align:start position:0%
+gravitational waves sort of a moaning
+background filling the universe and so
+
+ align:start position:0%
+background filling the universe and so
+ 
+
+ align:start position:0%
+background filling the universe and so
+there's a lot of experiments looking for
+
+ align:start position:0%
+there's a lot of experiments looking for
+ 
+
+ align:start position:0%
+there's a lot of experiments looking for
+the imprints of such gravitational waves
+
+ align:start position:0%
+the imprints of such gravitational waves
+ 
+
+ align:start position:0%
+the imprints of such gravitational waves
+on our universe if it is measured it
+
+ align:start position:0%
+on our universe if it is measured it
+ 
+
+ align:start position:0%
+on our universe if it is measured it
+would allow us to directly probe what
+
+ align:start position:0%
+would allow us to directly probe what
+ 
+
+ align:start position:0%
+would allow us to directly probe what
+this inflationary potential actually is
+
+ align:start position:0%
+this inflationary potential actually is
+ 
+
+ align:start position:0%
+this inflationary potential actually is
+I'm going to conclude our discussion of
+
+ align:start position:0%
+I'm going to conclude our discussion of
+ 
+
+ align:start position:0%
+I'm going to conclude our discussion of
+cosmology here so some of these some of
+
+ align:start position:0%
+cosmology here so some of these some of
+ 
+
+ align:start position:0%
+cosmology here so some of these some of
+the quantitative details the way in
+
+ align:start position:0%
+the quantitative details the way in
+ 
+
+ align:start position:0%
+the quantitative details the way in
+which inflation can cure the flatness
+
+ align:start position:0%
+which inflation can cure the flatness
+ 
+
+ align:start position:0%
+which inflation can cure the flatness
+problem and cure the homogeneity problem
+
+ align:start position:0%
+problem and cure the homogeneity problem
+ 
+
+ align:start position:0%
+problem and cure the homogeneity problem
+you'll explore on problem set seven
+
+ align:start position:0%
+you'll explore on problem set seven
+ 
+
+ align:start position:0%
+you'll explore on problem set seven
+going into the weeds of how one makes
+
+ align:start position:0%
+going into the weeds of how one makes
+ 
+
+ align:start position:0%
+going into the weeds of how one makes
+with the scalar field designs of
+
+ align:start position:0%
+with the scalar field designs of
+ 
+
+ align:start position:0%
+with the scalar field designs of
+potential and does things like this
+
+ align:start position:0%
+potential and does things like this
+ 
+
+ align:start position:0%
+potential and does things like this
+beyond the scope of eight 962 there are
+
+ align:start position:0%
+beyond the scope of eight 962 there are
+ 
+
+ align:start position:0%
+beyond the scope of eight 962 there are
+courses like this and I would not be
+
+ align:start position:0%
+courses like this and I would not be
+ 
+
+ align:start position:0%
+courses like this and I would not be
+surprised if some of the people in this
+
+ align:start position:0%
+surprised if some of the people in this
+ 
+
+ align:start position:0%
+surprised if some of the people in this
+class spend a lot more time studying
+
+ align:start position:0%
+class spend a lot more time studying
+ 
+
+ align:start position:0%
+class spend a lot more time studying
+this in their futures than I have in my
+
+ align:start position:0%
+this in their futures than I have in my
+ 
+
+ align:start position:0%
+this in their futures than I have in my
+life all right so that is where we will
+
+ align:start position:0%
+life all right so that is where we will
+ 
+
+ align:start position:0%
+life all right so that is where we will
+conclude our discussion of cosmology
\ No newline at end of file
diff --git a/plrrHK_cNtM.txt b/plrrHK_cNtM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f38644cde94c9852a464d0a647b2182e2605d63e
--- /dev/null
+++ b/plrrHK_cNtM.txt
@@ -0,0 +1,595 @@
+align:start position:0%
+ 
+the fields of a circular cylindrical
+
+ align:start position:0%
+the fields of a circular cylindrical
+ 
+
+ align:start position:0%
+the fields of a circular cylindrical
+solenoid can be found using the
+
+ align:start position:0%
+solenoid can be found using the
+ 
+
+ align:start position:0%
+solenoid can be found using the
+biot-savart law if these plain parallel
+
+ align:start position:0%
+biot-savart law if these plain parallel
+ 
+
+ align:start position:0%
+biot-savart law if these plain parallel
+plates were of infinite extent an
+
+ align:start position:0%
+plates were of infinite extent an
+ 
+
+ align:start position:0%
+plates were of infinite extent an
+applied voltage would give an electric
+
+ align:start position:0%
+applied voltage would give an electric
+ 
+
+ align:start position:0%
+applied voltage would give an electric
+field that is uniform what this plane
+
+ align:start position:0%
+field that is uniform what this plane
+ 
+
+ align:start position:0%
+field that is uniform what this plane
+parallel capacitor is two electric
+
+ align:start position:0%
+parallel capacitor is two electric
+ 
+
+ align:start position:0%
+parallel capacitor is two electric
+fields and infinitely long solenoid is
+
+ align:start position:0%
+fields and infinitely long solenoid is
+ 
+
+ align:start position:0%
+fields and infinitely long solenoid is
+to magnetic fields that is if this
+
+ align:start position:0%
+to magnetic fields that is if this
+ 
+
+ align:start position:0%
+to magnetic fields that is if this
+solenoid were infinitely long a current
+
+ align:start position:0%
+solenoid were infinitely long a current
+ 
+
+ align:start position:0%
+solenoid were infinitely long a current
+in the winding would produce a magnetic
+
+ align:start position:0%
+in the winding would produce a magnetic
+ 
+
+ align:start position:0%
+in the winding would produce a magnetic
+field intensity that is essentially
+
+ align:start position:0%
+field intensity that is essentially
+ 
+
+ align:start position:0%
+field intensity that is essentially
+uniform inside and equal to the surface
+
+ align:start position:0%
+uniform inside and equal to the surface
+ 
+
+ align:start position:0%
+uniform inside and equal to the surface
+current density outside the field would
+
+ align:start position:0%
+current density outside the field would
+ 
+
+ align:start position:0%
+current density outside the field would
+be essentially zero this solenoid is
+
+ align:start position:0%
+be essentially zero this solenoid is
+ 
+
+ align:start position:0%
+be essentially zero this solenoid is
+large enough that we can poke around in
+
+ align:start position:0%
+large enough that we can poke around in
+ 
+
+ align:start position:0%
+large enough that we can poke around in
+it with a magnetometer probe and see how
+
+ align:start position:0%
+it with a magnetometer probe and see how
+ 
+
+ align:start position:0%
+it with a magnetometer probe and see how
+the magnetic field is actually
+
+ align:start position:0%
+the magnetic field is actually
+ 
+
+ align:start position:0%
+the magnetic field is actually
+distributed when the length is finite
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this axial whole probe shows us the
+
+ align:start position:0%
+this axial whole probe shows us the
+ 
+
+ align:start position:0%
+this axial whole probe shows us the
+magnitude and direction of the field the
+
+ align:start position:0%
+magnitude and direction of the field the
+ 
+
+ align:start position:0%
+magnitude and direction of the field the
+probe measures the field along its axis
+
+ align:start position:0%
+probe measures the field along its axis
+ 
+
+ align:start position:0%
+probe measures the field along its axis
+the lower scope trace records the pro
+
+ align:start position:0%
+the lower scope trace records the pro
+ 
+
+ align:start position:0%
+the lower scope trace records the pro
+back put the upper scope trace shows the
+
+ align:start position:0%
+back put the upper scope trace shows the
+ 
+
+ align:start position:0%
+back put the upper scope trace shows the
+coil current when the probe is oriented
+
+ align:start position:0%
+coil current when the probe is oriented
+ 
+
+ align:start position:0%
+coil current when the probe is oriented
+this way the axial component of magnetic
+
+ align:start position:0%
+this way the axial component of magnetic
+ 
+
+ align:start position:0%
+this way the axial component of magnetic
+field is measured when the probe is
+
+ align:start position:0%
+field is measured when the probe is
+ 
+
+ align:start position:0%
+field is measured when the probe is
+oriented this way the radial component
+
+ align:start position:0%
+oriented this way the radial component
+ 
+
+ align:start position:0%
+oriented this way the radial component
+of magnetic field is measured let's
+
+ align:start position:0%
+of magnetic field is measured let's
+ 
+
+ align:start position:0%
+of magnetic field is measured let's
+measure the axial magnetic field
+
+ align:start position:0%
+measure the axial magnetic field
+ 
+
+ align:start position:0%
+measure the axial magnetic field
+component along the axis of the cylinder
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on the axis the radial component is of
+
+ align:start position:0%
+on the axis the radial component is of
+ 
+
+ align:start position:0%
+on the axis the radial component is of
+course zero because of symmetry well
+
+ align:start position:0%
+course zero because of symmetry well
+ 
+
+ align:start position:0%
+course zero because of symmetry well
+inside the solenoid the field intensity
+
+ align:start position:0%
+inside the solenoid the field intensity
+ 
+
+ align:start position:0%
+inside the solenoid the field intensity
+in the Z Direction tends to be uniform
+
+ align:start position:0%
+in the Z Direction tends to be uniform
+ 
+
+ align:start position:0%
+in the Z Direction tends to be uniform
+everywhere
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the infinitely long solenoid can be
+
+ align:start position:0%
+the infinitely long solenoid can be
+ 
+
+ align:start position:0%
+the infinitely long solenoid can be
+regarded as the analog for mqs systems
+
+ align:start position:0%
+regarded as the analog for mqs systems
+ 
+
+ align:start position:0%
+regarded as the analog for mqs systems
+of the eqs plane parallel plate
+
+ align:start position:0%
+of the eqs plane parallel plate
+ 
+
+ align:start position:0%
+of the eqs plane parallel plate
+capacitor let's measure the magnetic
+
+ align:start position:0%
+capacitor let's measure the magnetic
+ 
+
+ align:start position:0%
+capacitor let's measure the magnetic
+field well inside the solenoid we
+
+ align:start position:0%
+field well inside the solenoid we
+ 
+
+ align:start position:0%
+field well inside the solenoid we
+measure about 2.3 gals just inside the
+
+ align:start position:0%
+measure about 2.3 gals just inside the
+ 
+
+ align:start position:0%
+measure about 2.3 gals just inside the
+winding as compared to the prediction of
+
+ align:start position:0%
+winding as compared to the prediction of
+ 
+
+ align:start position:0%
+winding as compared to the prediction of
+two and a half Gauss let's see what the
+
+ align:start position:0%
+two and a half Gauss let's see what the
+ 
+
+ align:start position:0%
+two and a half Gauss let's see what the
+tangential flux density is just outside
+
+ align:start position:0%
+tangential flux density is just outside
+ 
+
+ align:start position:0%
+tangential flux density is just outside
+at the same axial location just outside
+
+ align:start position:0%
+at the same axial location just outside
+ 
+
+ align:start position:0%
+at the same axial location just outside
+the flux density forwards by more than a
+
+ align:start position:0%
+the flux density forwards by more than a
+ 
+
+ align:start position:0%
+the flux density forwards by more than a
+factor of 10 to 0.15 Gauss just as the
+
+ align:start position:0%
+factor of 10 to 0.15 Gauss just as the
+ 
+
+ align:start position:0%
+factor of 10 to 0.15 Gauss just as the
+capacitor can be constructed to create a
+
+ align:start position:0%
+capacitor can be constructed to create a
+ 
+
+ align:start position:0%
+capacitor can be constructed to create a
+uniform electric field between the
+
+ align:start position:0%
+uniform electric field between the
+ 
+
+ align:start position:0%
+uniform electric field between the
+plates with zero field outside the
+
+ align:start position:0%
+plates with zero field outside the
+ 
+
+ align:start position:0%
+plates with zero field outside the
+region bounded by the plates so to you
+
+ align:start position:0%
+region bounded by the plates so to you
+ 
+
+ align:start position:0%
+region bounded by the plates so to you
+the long solenoid gives rise to a
+
+ align:start position:0%
+the long solenoid gives rise to a
+ 
+
+ align:start position:0%
+the long solenoid gives rise to a
+uniform magnetic field throughout the
+
+ align:start position:0%
+uniform magnetic field throughout the
+ 
+
+ align:start position:0%
+uniform magnetic field throughout the
+interior region all solenoid length is
+
+ align:start position:0%
+interior region all solenoid length is
+ 
+
+ align:start position:0%
+interior region all solenoid length is
+finite so the field inside is only
+
+ align:start position:0%
+finite so the field inside is only
+ 
+
+ align:start position:0%
+finite so the field inside is only
+approximately uniform
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and the exterior field is only
+
+ align:start position:0%
+and the exterior field is only
+ 
+
+ align:start position:0%
+and the exterior field is only
+approximately zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+another way to demonstrate the
+
+ align:start position:0%
+another way to demonstrate the
+ 
+
+ align:start position:0%
+another way to demonstrate the
+discontinuity in magnetic field between
+
+ align:start position:0%
+discontinuity in magnetic field between
+ 
+
+ align:start position:0%
+discontinuity in magnetic field between
+inside and outside the solenoid is to
+
+ align:start position:0%
+inside and outside the solenoid is to
+ 
+
+ align:start position:0%
+inside and outside the solenoid is to
+use this transverse probe this probe
+
+ align:start position:0%
+use this transverse probe this probe
+ 
+
+ align:start position:0%
+use this transverse probe this probe
+measures magnetic fields transverse to
+
+ align:start position:0%
+measures magnetic fields transverse to
+ 
+
+ align:start position:0%
+measures magnetic fields transverse to
+its flat surface here for example is the
+
+ align:start position:0%
+its flat surface here for example is the
+ 
+
+ align:start position:0%
+its flat surface here for example is the
+on-axis field turning the probe by 90
+
+ align:start position:0%
+on-axis field turning the probe by 90
+ 
+
+ align:start position:0%
+on-axis field turning the probe by 90
+degrees gives a zero signal which shows
+
+ align:start position:0%
+degrees gives a zero signal which shows
+ 
+
+ align:start position:0%
+degrees gives a zero signal which shows
+the field is purely axial we now place
+
+ align:start position:0%
+the field is purely axial we now place
+ 
+
+ align:start position:0%
+the field is purely axial we now place
+this probe just outside the solenoid in
+
+ align:start position:0%
+this probe just outside the solenoid in
+ 
+
+ align:start position:0%
+this probe just outside the solenoid in
+the orientation to measure the small
+
+ align:start position:0%
+the orientation to measure the small
+ 
+
+ align:start position:0%
+the orientation to measure the small
+tangential field component as the probe
+
+ align:start position:0%
+tangential field component as the probe
+ 
+
+ align:start position:0%
+tangential field component as the probe
+passes through the current carrying
+
+ align:start position:0%
+passes through the current carrying
+ 
+
+ align:start position:0%
+passes through the current carrying
+winding the magnetic field abruptly
+
+ align:start position:0%
+winding the magnetic field abruptly
+ 
+
+ align:start position:0%
+winding the magnetic field abruptly
+rises to the interior field value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/pmI0Bl3ozWU.txt b/pmI0Bl3ozWU.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7e764a3a52b02611e767d62def4d0027ca9d2359
--- /dev/null
+++ b/pmI0Bl3ozWU.txt
@@ -0,0 +1,27 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um
+
+ align:start position:0%
+um
+ 
+
+ align:start position:0%
+um
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+you
\ No newline at end of file
diff --git a/pqFskmxJZCo.txt b/pqFskmxJZCo.txt
new file mode 100644
index 0000000000000000000000000000000000000000..6c390e41b52af6b14f1656c90789d0b1dbdc4679
--- /dev/null
+++ b/pqFskmxJZCo.txt
@@ -0,0 +1,1995 @@
+align:start position:0%
+ 
+just informal
+
+ align:start position:0%
+just informal
+ 
+
+ align:start position:0%
+just informal
+if you want to be a little bit more
+
+ align:start position:0%
+if you want to be a little bit more
+ 
+
+ align:start position:0%
+if you want to be a little bit more
+formal you can say
+
+ align:start position:0%
+formal you can say
+ 
+
+ align:start position:0%
+formal you can say
+what well we're not going to bed yet
+
+ align:start position:0%
+what well we're not going to bed yet
+ 
+
+ align:start position:0%
+what well we're not going to bed yet
+you're saying you're going to die
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+today is an important day in italy
+
+ align:start position:0%
+today is an important day in italy
+ 
+
+ align:start position:0%
+today is an important day in italy
+because it's the beginning
+
+ align:start position:0%
+because it's the beginning
+ 
+
+ align:start position:0%
+because it's the beginning
+of carne vale
+
+ align:start position:0%
+of carne vale
+ 
+
+ align:start position:0%
+of carne vale
+carnevales is carnival i think you are
+
+ align:start position:0%
+carnevales is carnival i think you are
+ 
+
+ align:start position:0%
+carnevales is carnival i think you are
+familiar
+
+ align:start position:0%
+familiar
+ 
+
+ align:start position:0%
+familiar
+originally italy the celebration of
+
+ align:start position:0%
+originally italy the celebration of
+ 
+
+ align:start position:0%
+originally italy the celebration of
+carnival was the celebration
+
+ align:start position:0%
+carnival was the celebration
+ 
+
+ align:start position:0%
+carnival was the celebration
+of the end of the winter and the
+
+ align:start position:0%
+of the end of the winter and the
+ 
+
+ align:start position:0%
+of the end of the winter and the
+beginning of the spring
+
+ align:start position:0%
+beginning of the spring
+ 
+
+ align:start position:0%
+beginning of the spring
+it should be much later here in boston
+
+ align:start position:0%
+it should be much later here in boston
+ 
+
+ align:start position:0%
+it should be much later here in boston
+it's not usually february
+
+ align:start position:0%
+it's not usually february
+ 
+
+ align:start position:0%
+it's not usually february
+in italy usually middle of february is a
+
+ align:start position:0%
+in italy usually middle of february is a
+ 
+
+ align:start position:0%
+in italy usually middle of february is a
+good time when it starts to get warmer
+
+ align:start position:0%
+good time when it starts to get warmer
+ 
+
+ align:start position:0%
+good time when it starts to get warmer
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+it's not spring but it's the beginning
+
+ align:start position:0%
+it's not spring but it's the beginning
+ 
+
+ align:start position:0%
+it's not spring but it's the beginning
+so carne vale is carnival
+
+ align:start position:0%
+so carne vale is carnival
+ 
+
+ align:start position:0%
+so carne vale is carnival
+it starts today and it will end on
+
+ align:start position:0%
+it starts today and it will end on
+ 
+
+ align:start position:0%
+it starts today and it will end on
+tuesday
+
+ align:start position:0%
+tuesday
+ 
+
+ align:start position:0%
+tuesday
+next tuesday tuesday is
+
+ align:start position:0%
+next tuesday tuesday is
+ 
+
+ align:start position:0%
+next tuesday tuesday is
+martini today and we call
+
+ align:start position:0%
+martini today and we call
+ 
+
+ align:start position:0%
+martini today and we call
+this specific tuesday
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+means fats
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah it's fat tuesday so why is fat
+
+ align:start position:0%
+yeah it's fat tuesday so why is fat
+ 
+
+ align:start position:0%
+yeah it's fat tuesday so why is fat
+tuesday
+
+ align:start position:0%
+tuesday
+ 
+
+ align:start position:0%
+tuesday
+well because typically we would eat very
+
+ align:start position:0%
+well because typically we would eat very
+ 
+
+ align:start position:0%
+well because typically we would eat very
+very fat
+
+ align:start position:0%
+very fat
+ 
+
+ align:start position:0%
+very fat
+food and you have some examples
+
+ align:start position:0%
+food and you have some examples
+ 
+
+ align:start position:0%
+food and you have some examples
+here these are some typical sweets that
+
+ align:start position:0%
+here these are some typical sweets that
+ 
+
+ align:start position:0%
+here these are some typical sweets that
+we eat for carnevale
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+they're both deep fried so we're not
+
+ align:start position:0%
+they're both deep fried so we're not
+ 
+
+ align:start position:0%
+they're both deep fried so we're not
+going to do them they're not
+
+ align:start position:0%
+going to do them they're not
+ 
+
+ align:start position:0%
+going to do them they're not
+particularly healthy
+
+ align:start position:0%
+particularly healthy
+ 
+
+ align:start position:0%
+particularly healthy
+but if you want the recipe i need you
+
+ align:start position:0%
+but if you want the recipe i need you
+ 
+
+ align:start position:0%
+but if you want the recipe i need you
+the recipe anyway
+
+ align:start position:0%
+the recipe anyway
+ 
+
+ align:start position:0%
+the recipe anyway
+they're very very tasty the idea is that
+
+ align:start position:0%
+they're very very tasty the idea is that
+ 
+
+ align:start position:0%
+they're very very tasty the idea is that
+this celebration was initially a pagan
+
+ align:start position:0%
+this celebration was initially a pagan
+ 
+
+ align:start position:0%
+this celebration was initially a pagan
+celebration
+
+ align:start position:0%
+celebration
+ 
+
+ align:start position:0%
+celebration
+and then it became a christian
+
+ align:start position:0%
+and then it became a christian
+ 
+
+ align:start position:0%
+and then it became a christian
+celebration
+
+ align:start position:0%
+celebration
+ 
+
+ align:start position:0%
+celebration
+like a huge party where everything
+
+ align:start position:0%
+like a huge party where everything
+ 
+
+ align:start position:0%
+like a huge party where everything
+or almost everything is allowed
+
+ align:start position:0%
+or almost everything is allowed
+ 
+
+ align:start position:0%
+or almost everything is allowed
+before the beginning of juarez
+
+ align:start position:0%
+before the beginning of juarez
+ 
+
+ align:start position:0%
+before the beginning of juarez
+had lent that is a period where
+
+ align:start position:0%
+had lent that is a period where
+ 
+
+ align:start position:0%
+had lent that is a period where
+period more of any turns a period where
+
+ align:start position:0%
+period more of any turns a period where
+ 
+
+ align:start position:0%
+period more of any turns a period where
+many
+
+ align:start position:0%
+many
+ 
+
+ align:start position:0%
+many
+many people decide for example to let go
+
+ align:start position:0%
+many people decide for example to let go
+ 
+
+ align:start position:0%
+many people decide for example to let go
+of some luxuries of some things they
+
+ align:start position:0%
+of some luxuries of some things they
+ 
+
+ align:start position:0%
+of some luxuries of some things they
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+so it's like the last huge party you can
+
+ align:start position:0%
+so it's like the last huge party you can
+ 
+
+ align:start position:0%
+so it's like the last huge party you can
+eat everything in fact and afterwards
+
+ align:start position:0%
+eat everything in fact and afterwards
+ 
+
+ align:start position:0%
+eat everything in fact and afterwards
+maybe you decide oh
+
+ align:start position:0%
+maybe you decide oh
+ 
+
+ align:start position:0%
+maybe you decide oh
+i'm gonna diet i'm not going to eat
+
+ align:start position:0%
+i'm gonna diet i'm not going to eat
+ 
+
+ align:start position:0%
+i'm gonna diet i'm not going to eat
+anything so for carnivale
+
+ align:start position:0%
+anything so for carnivale
+ 
+
+ align:start position:0%
+anything so for carnivale
+carnival people usually wear costumes
+
+ align:start position:0%
+carnival people usually wear costumes
+ 
+
+ align:start position:0%
+carnival people usually wear costumes
+kind of like halloween here and mostly
+
+ align:start position:0%
+kind of like halloween here and mostly
+ 
+
+ align:start position:0%
+kind of like halloween here and mostly
+kids
+
+ align:start position:0%
+kids
+ 
+
+ align:start position:0%
+kids
+like it's very unusual that you walk
+
+ align:start position:0%
+like it's very unusual that you walk
+ 
+
+ align:start position:0%
+like it's very unusual that you walk
+anywhere in italy and you find everybody
+
+ align:start position:0%
+anywhere in italy and you find everybody
+ 
+
+ align:start position:0%
+anywhere in italy and you find everybody
+in costume
+
+ align:start position:0%
+in costume
+ 
+
+ align:start position:0%
+in costume
+but well there are like kids especially
+
+ align:start position:0%
+but well there are like kids especially
+ 
+
+ align:start position:0%
+but well there are like kids especially
+and there are some parties and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are some i'm sorry for the quality
+
+ align:start position:0%
+there are some i'm sorry for the quality
+ 
+
+ align:start position:0%
+there are some i'm sorry for the quality
+but you have a printout actually of the
+
+ align:start position:0%
+but you have a printout actually of the
+ 
+
+ align:start position:0%
+but you have a printout actually of the
+macbook
+
+ align:start position:0%
+macbook
+ 
+
+ align:start position:0%
+macbook
+and there are some huge huge
+
+ align:start position:0%
+and there are some huge huge
+ 
+
+ align:start position:0%
+and there are some huge huge
+celebrations
+
+ align:start position:0%
+celebrations
+ 
+
+ align:start position:0%
+celebrations
+the most famous are the carnivale of
+
+ align:start position:0%
+the most famous are the carnivale of
+ 
+
+ align:start position:0%
+the most famous are the carnivale of
+diarrhea girl is in tuscany
+
+ align:start position:0%
+diarrhea girl is in tuscany
+ 
+
+ align:start position:0%
+diarrhea girl is in tuscany
+there is carnevale ibrea
+
+ align:start position:0%
+there is carnevale ibrea
+ 
+
+ align:start position:0%
+there is carnevale ibrea
+ibrea is in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and for the carnivale of the apart from
+
+ align:start position:0%
+and for the carnivale of the apart from
+ 
+
+ align:start position:0%
+and for the carnivale of the apart from
+wearing costumes there is also a very
+
+ align:start position:0%
+wearing costumes there is also a very
+ 
+
+ align:start position:0%
+wearing costumes there is also a very
+famous
+
+ align:start position:0%
+famous
+ 
+
+ align:start position:0%
+famous
+bottle with oranges people throw
+
+ align:start position:0%
+bottle with oranges people throw
+ 
+
+ align:start position:0%
+bottle with oranges people throw
+oranges if you google it you see the
+
+ align:start position:0%
+oranges if you google it you see the
+ 
+
+ align:start position:0%
+oranges if you google it you see the
+images is really really
+
+ align:start position:0%
+images is really really
+ 
+
+ align:start position:0%
+images is really really
+something and then probably the most
+
+ align:start position:0%
+something and then probably the most
+ 
+
+ align:start position:0%
+something and then probably the most
+famous carnival
+
+ align:start position:0%
+famous carnival
+ 
+
+ align:start position:0%
+famous carnival
+in italy is incarnate venezia
+
+ align:start position:0%
+in italy is incarnate venezia
+ 
+
+ align:start position:0%
+in italy is incarnate venezia
+venice there it is
+
+ align:start position:0%
+venice there it is
+ 
+
+ align:start position:0%
+venice there it is
+so in venezuela
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there are a lot of parades and there are
+
+ align:start position:0%
+there are a lot of parades and there are
+ 
+
+ align:start position:0%
+there are a lot of parades and there are
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+characteristic costumes traditional
+
+ align:start position:0%
+characteristic costumes traditional
+ 
+
+ align:start position:0%
+characteristic costumes traditional
+costumes so you should enjoy carnevale
+
+ align:start position:0%
+costumes so you should enjoy carnevale
+ 
+
+ align:start position:0%
+costumes so you should enjoy carnevale
+during the weekend you have a long
+
+ align:start position:0%
+during the weekend you have a long
+ 
+
+ align:start position:0%
+during the weekend you have a long
+weekend for a different reason
+
+ align:start position:0%
+weekend for a different reason
+ 
+
+ align:start position:0%
+weekend for a different reason
+but okay enjoy nevada until
+
+ align:start position:0%
+but okay enjoy nevada until
+ 
+
+ align:start position:0%
+but okay enjoy nevada until
+tuesday until because afterwards
+
+ align:start position:0%
+tuesday until because afterwards
+ 
+
+ align:start position:0%
+tuesday until because afterwards
+we can't celebrate anymore so let's try
+
+ align:start position:0%
+we can't celebrate anymore so let's try
+ 
+
+ align:start position:0%
+we can't celebrate anymore so let's try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+review what you did the idea is this
+
+ align:start position:0%
+review what you did the idea is this
+ 
+
+ align:start position:0%
+review what you did the idea is this
+each of you can stand up
+
+ align:start position:0%
+each of you can stand up
+ 
+
+ align:start position:0%
+each of you can stand up
+look at the others and say ciao
+
+ align:start position:0%
+look at the others and say ciao
+ 
+
+ align:start position:0%
+look at the others and say ciao
+you say your name and then just
+
+ align:start position:0%
+you say your name and then just
+ 
+
+ align:start position:0%
+you say your name and then just
+tell us something that you remember from
+
+ align:start position:0%
+tell us something that you remember from
+ 
+
+ align:start position:0%
+tell us something that you remember from
+last week
+
+ align:start position:0%
+last week
+ 
+
+ align:start position:0%
+last week
+it can be anything that could it can be
+
+ align:start position:0%
+it can be anything that could it can be
+ 
+
+ align:start position:0%
+it can be anything that could it can be
+another sentence
+
+ align:start position:0%
+another sentence
+ 
+
+ align:start position:0%
+another sentence
+it could be even just the way that you
+
+ align:start position:0%
+it could be even just the way that you
+ 
+
+ align:start position:0%
+it could be even just the way that you
+pronounce the letter a
+
+ align:start position:0%
+pronounce the letter a
+ 
+
+ align:start position:0%
+pronounce the letter a
+that's uh okay you can come here and say
+
+ align:start position:0%
+that's uh okay you can come here and say
+ 
+
+ align:start position:0%
+that's uh okay you can come here and say
+hey ciao
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we say oh
+
+ align:start position:0%
+we say oh
+ 
+
+ align:start position:0%
+we say oh
+the vowels
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ciao michael mcclara
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+our second lesson and
+
+ align:start position:0%
+our second lesson and
+ 
+
+ align:start position:0%
+our second lesson and
+i can ask each of you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do it one word at a time you
+
+ align:start position:0%
+let's do it one word at a time you
+ 
+
+ align:start position:0%
+let's do it one word at a time you
+remember
+
+ align:start position:0%
+remember
+ 
+
+ align:start position:0%
+remember
+omit the subject too because it's not
+
+ align:start position:0%
+omit the subject too because it's not
+ 
+
+ align:start position:0%
+omit the subject too because it's not
+that important
+
+ align:start position:0%
+that important
+ 
+
+ align:start position:0%
+that important
+unless i really want to emphasize then i
+
+ align:start position:0%
+unless i really want to emphasize then i
+ 
+
+ align:start position:0%
+unless i really want to emphasize then i
+would i would say so i start from here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's do another round we can ask
+
+ align:start position:0%
+let's do another round we can ask
+ 
+
+ align:start position:0%
+let's do another round we can ask
+each other where do we come from and you
+
+ align:start position:0%
+each other where do we come from and you
+ 
+
+ align:start position:0%
+each other where do we come from and you
+can say i come from
+
+ align:start position:0%
+can say i come from
+ 
+
+ align:start position:0%
+can say i come from
+wherever you come from i said milano i'm
+
+ align:start position:0%
+wherever you come from i said milano i'm
+ 
+
+ align:start position:0%
+wherever you come from i said milano i'm
+not exactly from
+
+ align:start position:0%
+not exactly from
+ 
+
+ align:start position:0%
+not exactly from
+milan i'm from a small town close to
+
+ align:start position:0%
+milan i'm from a small town close to
+ 
+
+ align:start position:0%
+milan i'm from a small town close to
+milan
+
+ align:start position:0%
+milan
+ 
+
+ align:start position:0%
+milan
+on big lake that's the largest lake in
+
+ align:start position:0%
+on big lake that's the largest lake in
+ 
+
+ align:start position:0%
+on big lake that's the largest lake in
+italy
+
+ align:start position:0%
+italy
+ 
+
+ align:start position:0%
+italy
+named lake
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lagos
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but i think that most of you come from
+
+ align:start position:0%
+but i think that most of you come from
+ 
+
+ align:start position:0%
+but i think that most of you come from
+this unity
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's say
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you have a feminine it could be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so texas is not a city
+
+ align:start position:0%
+so texas is not a city
+ 
+
+ align:start position:0%
+so texas is not a city
+it's a state so you put the article and
+
+ align:start position:0%
+it's a state so you put the article and
+ 
+
+ align:start position:0%
+it's a state so you put the article and
+you say
+
+ align:start position:0%
+you say
+ 
+
+ align:start position:0%
+you say
+vengo dal texas
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+texas
+
+ align:start position:0%
+texas
+ 
+
+ align:start position:0%
+texas
+yeah so now you know how to introduce
+
+ align:start position:0%
+yeah so now you know how to introduce
+ 
+
+ align:start position:0%
+yeah so now you know how to introduce
+yourself
+
+ align:start position:0%
+yourself
+ 
+
+ align:start position:0%
+yourself
+how to say where you come from
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me look around
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so we are trying to learn
+
+ align:start position:0%
+yeah so we are trying to learn
+ 
+
+ align:start position:0%
+yeah so we are trying to learn
+demonstrative objectives so in english
+
+ align:start position:0%
+demonstrative objectives so in english
+ 
+
+ align:start position:0%
+demonstrative objectives so in english
+you have this that these
+
+ align:start position:0%
+you have this that these
+ 
+
+ align:start position:0%
+you have this that these
+those let's start with the singular
+
+ align:start position:0%
+those let's start with the singular
+ 
+
+ align:start position:0%
+those let's start with the singular
+in italian we have questo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+code
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay you see they all end with an o so
+
+ align:start position:0%
+okay you see they all end with an o so
+ 
+
+ align:start position:0%
+okay you see they all end with an o so
+that's
+
+ align:start position:0%
+that's
+ 
+
+ align:start position:0%
+that's
+masculine how come that we have three
+
+ align:start position:0%
+masculine how come that we have three
+ 
+
+ align:start position:0%
+masculine how come that we have three
+choices
+
+ align:start position:0%
+choices
+ 
+
+ align:start position:0%
+choices
+instead of just two this and that well
+
+ align:start position:0%
+instead of just two this and that well
+ 
+
+ align:start position:0%
+instead of just two this and that well
+questo means this and it's something
+
+ align:start position:0%
+questo means this and it's something
+ 
+
+ align:start position:0%
+questo means this and it's something
+that is close to me
+
+ align:start position:0%
+that is close to me
+ 
+
+ align:start position:0%
+that is close to me
+when i'm talking about something that's
+
+ align:start position:0%
+when i'm talking about something that's
+ 
+
+ align:start position:0%
+when i'm talking about something that's
+close to me
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is something that is far from me but is
+
+ align:start position:0%
+is something that is far from me but is
+ 
+
+ align:start position:0%
+is something that is far from me but is
+close to you it's not really very common
+
+ align:start position:0%
+close to you it's not really very common
+ 
+
+ align:start position:0%
+close to you it's not really very common
+you won't hear it when you talk to the
+
+ align:start position:0%
+you won't hear it when you talk to the
+ 
+
+ align:start position:0%
+you won't hear it when you talk to the
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+italian unless he or he comes from
+
+ align:start position:0%
+italian unless he or he comes from
+ 
+
+ align:start position:0%
+italian unless he or he comes from
+tuscany
+
+ align:start position:0%
+tuscany
+ 
+
+ align:start position:0%
+tuscany
+then there is a chance that they will
+
+ align:start position:0%
+then there is a chance that they will
+ 
+
+ align:start position:0%
+then there is a chance that they will
+use podesta
+
+ align:start position:0%
+use podesta
+ 
+
+ align:start position:0%
+use podesta
+but from now on we will just stick to
+
+ align:start position:0%
+but from now on we will just stick to
+ 
+
+ align:start position:0%
+but from now on we will just stick to
+cuesto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for that so in principle is when it's
+
+ align:start position:0%
+for that so in principle is when it's
+ 
+
+ align:start position:0%
+for that so in principle is when it's
+far from
+
+ align:start position:0%
+far from
+ 
+
+ align:start position:0%
+far from
+both of us so as i told you already last
+
+ align:start position:0%
+both of us so as i told you already last
+ 
+
+ align:start position:0%
+both of us so as i told you already last
+time
+
+ align:start position:0%
+time
+ 
+
+ align:start position:0%
+time
+in italian we conjugate everything so
+
+ align:start position:0%
+in italian we conjugate everything so
+ 
+
+ align:start position:0%
+in italian we conjugate everything so
+if an adjective refers to a noun that's
+
+ align:start position:0%
+if an adjective refers to a noun that's
+ 
+
+ align:start position:0%
+if an adjective refers to a noun that's
+feminine
+
+ align:start position:0%
+feminine
+ 
+
+ align:start position:0%
+feminine
+or masculine the ending changes
+
+ align:start position:0%
+or masculine the ending changes
+ 
+
+ align:start position:0%
+or masculine the ending changes
+so in english you would say
+
+ align:start position:0%
+so in english you would say
+ 
+
+ align:start position:0%
+so in english you would say
+this onion and
+
+ align:start position:0%
+this onion and
+ 
+
+ align:start position:0%
+this onion and
+this book
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in italian i would say questo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+foreign
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if it's masculine it becomes questi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and if it's feminine it becomes quest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and now you can try to read without me
+
+ align:start position:0%
+and now you can try to read without me
+ 
+
+ align:start position:0%
+and now you can try to read without me
+what's going on
+
+ align:start position:0%
+what's going on
+ 
+
+ align:start position:0%
+what's going on
+with that and those
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's see what i told you earlier
+
+ align:start position:0%
+so let's see what i told you earlier
+ 
+
+ align:start position:0%
+so let's see what i told you earlier
+questa questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+i forgot
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+adjective similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is bigger
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+d that would be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+itself
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+since we want to go ahead and learn
+
+ align:start position:0%
+since we want to go ahead and learn
+ 
+
+ align:start position:0%
+since we want to go ahead and learn
+how to say la let's see
+
+ align:start position:0%
+how to say la let's see
+ 
+
+ align:start position:0%
+how to say la let's see
+exactly where this word come from sulla
+
+ align:start position:0%
+exactly where this word come from sulla
+ 
+
+ align:start position:0%
+exactly where this word come from sulla
+is a composition of
+
+ align:start position:0%
+is a composition of
+ 
+
+ align:start position:0%
+is a composition of
+soup that means on
+
+ align:start position:0%
+soup that means on
+ 
+
+ align:start position:0%
+soup that means on
+and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that would be the article
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and then we just put them together and
+
+ align:start position:0%
+and then we just put them together and
+ 
+
+ align:start position:0%
+and then we just put them together and
+it becomes
+
+ align:start position:0%
+it becomes
+ 
+
+ align:start position:0%
+it becomes
+okay so take it some time and try you
+
+ align:start position:0%
+okay so take it some time and try you
+ 
+
+ align:start position:0%
+okay so take it some time and try you
+can discuss you can do this together
+
+ align:start position:0%
+can discuss you can do this together
+ 
+
+ align:start position:0%
+can discuss you can do this together
+try to come out with some new ten
+
+ align:start position:0%
+try to come out with some new ten
+ 
+
+ align:start position:0%
+try to come out with some new ten
+sentences involving
+
+ align:start position:0%
+sentences involving
+ 
+
+ align:start position:0%
+sentences involving
+the adjectivity and some of the words
+
+ align:start position:0%
+the adjectivity and some of the words
+ 
+
+ align:start position:0%
+the adjectivity and some of the words
+that you already know
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let me write it down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+people look at you like where do you
+
+ align:start position:0%
+people look at you like where do you
+ 
+
+ align:start position:0%
+people look at you like where do you
+come from
+
+ align:start position:0%
+come from
+ 
+
+ align:start position:0%
+come from
+united states
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we put an apostrophe that little sign is
+
+ align:start position:0%
+we put an apostrophe that little sign is
+ 
+
+ align:start position:0%
+we put an apostrophe that little sign is
+an apostrophe
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you can say questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so yeah one way to refer to apples and
+
+ align:start position:0%
+so yeah one way to refer to apples and
+ 
+
+ align:start position:0%
+so yeah one way to refer to apples and
+pears
+
+ align:start position:0%
+pears
+ 
+
+ align:start position:0%
+pears
+is to call them homie
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+typically if you are talking about this
+
+ align:start position:0%
+typically if you are talking about this
+ 
+
+ align:start position:0%
+typically if you are talking about this
+fruit
+
+ align:start position:0%
+fruit
+ 
+
+ align:start position:0%
+fruit
+then you say you call it milan
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so this fruit is mela
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and i can say mela
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+with me
+
+ align:start position:0%
+with me
+ 
+
+ align:start position:0%
+with me
+well i actually have two oh
+
+ align:start position:0%
+well i actually have two oh
+ 
+
+ align:start position:0%
+well i actually have two oh
+yeah so it was questa now i have two
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when we have only one cuesta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+who wants to write the nest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+very good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you see we don't add an s like in
+
+ align:start position:0%
+so you see we don't add an s like in
+ 
+
+ align:start position:0%
+so you see we don't add an s like in
+english to make the plural
+
+ align:start position:0%
+english to make the plural
+ 
+
+ align:start position:0%
+english to make the plural
+we change the ending of the word
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+next time we will actually conjugate the
+
+ align:start position:0%
+next time we will actually conjugate the
+ 
+
+ align:start position:0%
+next time we will actually conjugate the
+whole verb to be
+
+ align:start position:0%
+whole verb to be
+ 
+
+ align:start position:0%
+whole verb to be
+in the present okay
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+good
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so tonight we're going to cook a dish
+
+ align:start position:0%
+so tonight we're going to cook a dish
+ 
+
+ align:start position:0%
+so tonight we're going to cook a dish
+that's typical from northern italy
+
+ align:start position:0%
+that's typical from northern italy
+ 
+
+ align:start position:0%
+that's typical from northern italy
+it's called risotto
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/qdbkvD4N-us.txt b/qdbkvD4N-us.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2cdbaa274de926365b44c88f25c426726503b322
--- /dev/null
+++ b/qdbkvD4N-us.txt
@@ -0,0 +1,7992 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ocw.mmit.edu. So far, we had a function
+
+ align:start position:0%
+ocw.mmit.edu. So far, we had a function
+ 
+
+ align:start position:0%
+ocw.mmit.edu. So far, we had a function
+and then we differentiated to get an
+
+ align:start position:0%
+and then we differentiated to get an
+ 
+
+ align:start position:0%
+and then we differentiated to get an
+equation of this type. But now we're
+
+ align:start position:0%
+equation of this type. But now we're
+ 
+
+ align:start position:0%
+equation of this type. But now we're
+given this equation and we want to go
+
+ align:start position:0%
+given this equation and we want to go
+ 
+
+ align:start position:0%
+given this equation and we want to go
+backwards. Want to find the stochastic
+
+ align:start position:0%
+backwards. Want to find the stochastic
+ 
+
+ align:start position:0%
+backwards. Want to find the stochastic
+process that satisfies this equation. So
+
+ align:start position:0%
+process that satisfies this equation. So
+ 
+
+ align:start position:0%
+process that satisfies this equation. So
+goal is to find a stochastic
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process XT satisfying this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation. Okay. In other words, we want
+
+ align:start position:0%
+equation. Okay. In other words, we want
+ 
+
+ align:start position:0%
+equation. Okay. In other words, we want
+x of t to be the integral of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mu ds plus
+
+ align:start position:0%
+mu ds plus
+ 
+
+ align:start position:0%
+mu ds plus
+sigma d
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+s. The goal is clear. We want
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+And so these type of equations are
+
+ align:start position:0%
+And so these type of equations are
+ 
+
+ align:start position:0%
+And so these type of equations are
+called differential equations. I hope
+
+ align:start position:0%
+called differential equations. I hope
+ 
+
+ align:start position:0%
+called differential equations. I hope
+you already know
+
+ align:start position:0%
+you already know
+ 
+
+ align:start position:0%
+you already know
+that also for PTE partial differential
+
+ align:start position:0%
+that also for PTE partial differential
+ 
+
+ align:start position:0%
+that also for PTE partial differential
+equations. So even when it's not
+
+ align:start position:0%
+equations. So even when it's not
+ 
+
+ align:start position:0%
+equations. So even when it's not
+stochastic these are not easy
+
+ align:start position:0%
+stochastic these are not easy
+ 
+
+ align:start position:0%
+stochastic these are not easy
+problems at least not easy in the sense
+
+ align:start position:0%
+problems at least not easy in the sense
+ 
+
+ align:start position:0%
+problems at least not easy in the sense
+that if you're given an equation
+
+ align:start position:0%
+that if you're given an equation
+ 
+
+ align:start position:0%
+that if you're given an equation
+typically you don't expect to have a
+
+ align:start position:0%
+typically you don't expect to have a
+ 
+
+ align:start position:0%
+typically you don't expect to have a
+closed form solution. So even if you
+
+ align:start position:0%
+closed form solution. So even if you
+ 
+
+ align:start position:0%
+closed form solution. So even if you
+find this x most of the times it's not
+
+ align:start position:0%
+find this x most of the times it's not
+ 
+
+ align:start position:0%
+find this x most of the times it's not
+in a very good form.
+
+ align:start position:0%
+in a very good form.
+ 
+
+ align:start position:0%
+in a very good form.
+Still a very important result that you
+
+ align:start position:0%
+Still a very important result that you
+ 
+
+ align:start position:0%
+Still a very important result that you
+should first know before trying to solve
+
+ align:start position:0%
+should first know before trying to solve
+ 
+
+ align:start position:0%
+should first know before trying to solve
+any of the differential equation is
+
+ align:start position:0%
+any of the differential equation is
+ 
+
+ align:start position:0%
+any of the differential equation is
+that as long as mu and sigma are
+
+ align:start position:0%
+that as long as mu and sigma are
+ 
+
+ align:start position:0%
+that as long as mu and sigma are
+reasonable functions there does exist a
+
+ align:start position:0%
+reasonable functions there does exist a
+ 
+
+ align:start position:0%
+reasonable functions there does exist a
+solution and it's
+
+ align:start position:0%
+solution and it's
+ 
+
+ align:start position:0%
+solution and it's
+unique. So we have the same
+
+ align:start position:0%
+unique. So we have the same
+ 
+
+ align:start position:0%
+unique. So we have the same
+correspondence with this PD. they're
+
+ align:start position:0%
+correspondence with this PD. they're
+ 
+
+ align:start position:0%
+correspondence with this PD. they're
+given a PD given a differential equation
+
+ align:start position:0%
+given a PD given a differential equation
+ 
+
+ align:start position:0%
+given a PD given a differential equation
+not a stoastic differential equation you
+
+ align:start position:0%
+not a stoastic differential equation you
+ 
+
+ align:start position:0%
+not a stoastic differential equation you
+know that if you're given a reasonable
+
+ align:start position:0%
+know that if you're given a reasonable
+ 
+
+ align:start position:0%
+know that if you're given a reasonable
+differential equation then you have a
+
+ align:start position:0%
+differential equation then you have a
+ 
+
+ align:start position:0%
+differential equation then you have a
+unique a solution exists and it's unique
+
+ align:start position:0%
+unique a solution exists and it's unique
+ 
+
+ align:start position:0%
+unique a solution exists and it's unique
+so the same principle holds in stoastic
+
+ align:start position:0%
+so the same principle holds in stoastic
+ 
+
+ align:start position:0%
+so the same principle holds in stoastic
+world let me state it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formally this stoastic equation
+
+ align:start position:0%
+formally this stoastic equation
+ 
+
+ align:start position:0%
+formally this stoastic equation
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+has a solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh that is
+
+ align:start position:0%
+uh that is
+ 
+
+ align:start position:0%
+uh that is
+unique. Okay. Uh, of course with
+
+ align:start position:0%
+unique. Okay. Uh, of course with
+ 
+
+ align:start position:0%
+unique. Okay. Uh, of course with
+boundary
+
+ align:start position:0%
+boundary
+ 
+
+ align:start position:0%
+boundary
+condition has a
+
+ align:start position:0%
+condition has a
+ 
+
+ align:start position:0%
+condition has a
+solution
+
+ align:start position:0%
+solution
+ 
+
+ align:start position:0%
+solution
+and given the initial points
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X. Oh yeah. So if you're given the
+
+ align:start position:0%
+X. Oh yeah. So if you're given the
+ 
+
+ align:start position:0%
+X. Oh yeah. So if you're given the
+initial point of the stoastic process,
+
+ align:start position:0%
+initial point of the stoastic process,
+ 
+
+ align:start position:0%
+initial point of the stoastic process,
+then the solution is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+unique. Just
+
+ align:start position:0%
+unique. Just
+ 
+
+ align:start position:0%
+unique. Just
+check. Yes.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+As long
+
+ align:start position:0%
+As long
+ 
+
+ align:start position:0%
+As long
+as mu and sigma are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+reasonable. One way can be reasonable if
+
+ align:start position:0%
+reasonable. One way can be reasonable if
+ 
+
+ align:start position:0%
+reasonable. One way can be reasonable if
+it satisfies this conditions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So these are very technical conditions
+
+ align:start position:0%
+So these are very technical conditions
+ 
+
+ align:start position:0%
+So these are very technical conditions
+but at least let me parse to you what
+
+ align:start position:0%
+but at least let me parse to you what
+ 
+
+ align:start position:0%
+but at least let me parse to you what
+they are. They say if you fix a time
+
+ align:start position:0%
+they are. They say if you fix a time
+ 
+
+ align:start position:0%
+they are. They say if you fix a time
+coordinate and you change x, you look at
+
+ align:start position:0%
+coordinate and you change x, you look at
+ 
+
+ align:start position:0%
+coordinate and you change x, you look at
+the difference between the values of mu
+
+ align:start position:0%
+the difference between the values of mu
+ 
+
+ align:start position:0%
+the difference between the values of mu
+when you change the second variable and
+
+ align:start position:0%
+when you change the second variable and
+ 
+
+ align:start position:0%
+when you change the second variable and
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+sigma. Then the change in your function
+
+ align:start position:0%
+sigma. Then the change in your function
+ 
+
+ align:start position:0%
+sigma. Then the change in your function
+is bounded by the distance between the
+
+ align:start position:0%
+is bounded by the distance between the
+ 
+
+ align:start position:0%
+is bounded by the distance between the
+two points by some constant k. Okay. So
+
+ align:start position:0%
+two points by some constant k. Okay. So
+ 
+
+ align:start position:0%
+two points by some constant k. Okay. So
+mu and sigma cannot change too much when
+
+ align:start position:0%
+mu and sigma cannot change too much when
+ 
+
+ align:start position:0%
+mu and sigma cannot change too much when
+you change your space variable a little
+
+ align:start position:0%
+you change your space variable a little
+ 
+
+ align:start position:0%
+you change your space variable a little
+bit. It can only change up to the
+
+ align:start position:0%
+bit. It can only change up to the
+ 
+
+ align:start position:0%
+bit. It can only change up to the
+distance of how much you change the
+
+ align:start position:0%
+distance of how much you change the
+ 
+
+ align:start position:0%
+distance of how much you change the
+coordinate. So that's the first
+
+ align:start position:0%
+coordinate. So that's the first
+ 
+
+ align:start position:0%
+coordinate. So that's the first
+condition. Second condition
+
+ align:start position:0%
+condition. Second condition
+ 
+
+ align:start position:0%
+condition. Second condition
+says yeah when you grow your
+
+ align:start position:0%
+says yeah when you grow your
+ 
+
+ align:start position:0%
+says yeah when you grow your
+x it's very similar condition
+
+ align:start position:0%
+x it's very similar condition
+ 
+
+ align:start position:0%
+x it's very similar condition
+essentially says it cannot blow up too
+
+ align:start position:0%
+essentially says it cannot blow up too
+ 
+
+ align:start position:0%
+essentially says it cannot blow up too
+fast the whole thing. This one is
+
+ align:start position:0%
+fast the whole thing. This one is
+ 
+
+ align:start position:0%
+fast the whole thing. This one is
+something about the difference between
+
+ align:start position:0%
+something about the difference between
+ 
+
+ align:start position:0%
+something about the difference between
+two values. This one is about how it
+
+ align:start position:0%
+two values. This one is about how it
+ 
+
+ align:start position:0%
+two values. This one is about how it
+expands as your space variable
+
+ align:start position:0%
+expands as your space variable
+ 
+
+ align:start position:0%
+expands as your space variable
+grows. These are technical conditions
+
+ align:start position:0%
+grows. These are technical conditions
+ 
+
+ align:start position:0%
+grows. These are technical conditions
+and many
+
+ align:start position:0%
+and many
+ 
+
+ align:start position:0%
+and many
+cases
+
+ align:start position:0%
+cases
+ 
+
+ align:start position:0%
+cases
+just they will hold. Don't worry too
+
+ align:start position:0%
+just they will hold. Don't worry too
+ 
+
+ align:start position:0%
+just they will hold. Don't worry too
+much about the technical
+
+ align:start position:0%
+much about the technical
+ 
+
+ align:start position:0%
+much about the technical
+conditions. Important thing here is that
+
+ align:start position:0%
+conditions. Important thing here is that
+ 
+
+ align:start position:0%
+conditions. Important thing here is that
+given a given a differential equation
+
+ align:start position:0%
+given a given a differential equation
+ 
+
+ align:start position:0%
+given a given a differential equation
+you don't expect to have a good form
+
+ align:start position:0%
+you don't expect to have a good form
+ 
+
+ align:start position:0%
+you don't expect to have a good form
+closed form but you do expect to have a
+
+ align:start position:0%
+closed form but you do expect to have a
+ 
+
+ align:start position:0%
+closed form but you do expect to have a
+solution of some form.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's work out some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+examples. Here is one of the few
+
+ align:start position:0%
+examples. Here is one of the few
+ 
+
+ align:start position:0%
+examples. Here is one of the few
+different stoastic differential
+
+ align:start position:0%
+different stoastic differential
+ 
+
+ align:start position:0%
+different stoastic differential
+equations that can be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solved. This one can be solved. and you
+
+ align:start position:0%
+solved. This one can be solved. and you
+ 
+
+ align:start position:0%
+solved. This one can be solved. and you
+already know what like what x
+
+ align:start position:0%
+already know what like what x
+ 
+
+ align:start position:0%
+already know what like what x
+is but let's pretend you don't know how
+
+ align:start position:0%
+is but let's pretend you don't know how
+ 
+
+ align:start position:0%
+is but let's pretend you don't know how
+to you don't know what x is and let's
+
+ align:start position:0%
+to you don't know what x is and let's
+ 
+
+ align:start position:0%
+to you don't know what x is and let's
+try to solve it this doesn't this
+
+ align:start position:0%
+try to solve it this doesn't this
+ 
+
+ align:start position:0%
+try to solve it this doesn't this
+approach I will show you an approach
+
+ align:start position:0%
+approach I will show you an approach
+ 
+
+ align:start position:0%
+approach I will show you an approach
+where which can solve some differential
+
+ align:start position:0%
+where which can solve some differential
+ 
+
+ align:start position:0%
+where which can solve some differential
+equations some some sdes but this really
+
+ align:start position:0%
+equations some some sdes but this really
+ 
+
+ align:start position:0%
+equations some some sdes but this really
+it won't happen that much still it's
+
+ align:start position:0%
+it won't happen that much still it's
+ 
+
+ align:start position:0%
+it won't happen that much still it's
+like a starting
+
+ align:start position:0%
+like a starting
+ 
+
+ align:start position:0%
+like a starting
+point okay there's that set that and
+
+ align:start position:0%
+point okay there's that set that and
+ 
+
+ align:start position:0%
+point okay there's that set that and
+assume x0
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Z and mu sigma are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+constants. Just like when solving
+
+ align:start position:0%
+constants. Just like when solving
+ 
+
+ align:start position:0%
+constants. Just like when solving
+differential equations, first thing
+
+ align:start position:0%
+differential equations, first thing
+ 
+
+ align:start position:0%
+differential equations, first thing
+you'll do is just guess. Suppose guess
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+If you want this to happen,
+
+ align:start position:0%
+If you want this to happen,
+ 
+
+ align:start position:0%
+If you want this to happen,
+then d of x of
+
+ align:start position:0%
+then d of x of
+ 
+
+ align:start position:0%
+then d of x of
+t
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is just the second
+
+ align:start position:0%
+X is just the second
+ 
+
+ align:start position:0%
+X is just the second
+variable and then these two have to
+
+ align:start position:0%
+variable and then these two have to
+ 
+
+ align:start position:0%
+variable and then these two have to
+match. That has to be equal to that.
+
+ align:start position:0%
+match. That has to be equal to that.
+ 
+
+ align:start position:0%
+match. That has to be equal to that.
+That has to be equal to that. So we know
+
+ align:start position:0%
+That has to be equal to that. So we know
+ 
+
+ align:start position:0%
+That has to be equal to that. So we know
+that del F over D
+
+ align:start position:0%
+that del F over D
+ 
+
+ align:start position:0%
+that del F over D
+X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T mu of X of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T= mu of X.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so we assume that this is a
+
+ align:start position:0%
+Okay, so we assume that this is a
+ 
+
+ align:start position:0%
+Okay, so we assume that this is a
+solution then differentiated that and
+
+ align:start position:0%
+solution then differentiated that and
+ 
+
+ align:start position:0%
+solution then differentiated that and
+then if that's a solution these all have
+
+ align:start position:0%
+then if that's a solution these all have
+ 
+
+ align:start position:0%
+then if that's a solution these all have
+to match. You get this equation. Now if
+
+ align:start position:0%
+to match. You get this equation. Now if
+ 
+
+ align:start position:0%
+to match. You get this equation. Now if
+you look at that that tells you that f
+
+ align:start position:0%
+you look at that that tells you that f
+ 
+
+ align:start position:0%
+you look at that that tells you that f
+is an exponential function in the x
+
+ align:start position:0%
+is an exponential function in the x
+ 
+
+ align:start position:0%
+is an exponential function in the x
+variable. So it's e to the sigma x *
+
+ align:start position:0%
+variable. So it's e to the sigma x *
+ 
+
+ align:start position:0%
+variable. So it's e to the sigma x *
+x and then we have a constant term plus
+
+ align:start position:0%
+x and then we have a constant term plus
+ 
+
+ align:start position:0%
+x and then we have a constant term plus
+some a times a function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t. The only way we can happen is if it's
+
+ align:start position:0%
+t. The only way we can happen is if it's
+ 
+
+ align:start position:0%
+t. The only way we can happen is if it's
+in this form. So it's exponential
+
+ align:start position:0%
+in this form. So it's exponential
+ 
+
+ align:start position:0%
+in this form. So it's exponential
+function in x and in the second uh in
+
+ align:start position:0%
+function in x and in the second uh in
+ 
+
+ align:start position:0%
+function in x and in the second uh in
+the time
+
+ align:start position:0%
+the time
+ 
+
+ align:start position:0%
+the time
+variable it's just some constant. when
+
+ align:start position:0%
+variable it's just some constant. when
+ 
+
+ align:start position:0%
+variable it's just some constant. when
+you fix a t it's a constant and when
+
+ align:start position:0%
+you fix a t it's a constant and when
+ 
+
+ align:start position:0%
+you fix a t it's a constant and when
+when you fix a t and change x it has to
+
+ align:start position:0%
+when you fix a t and change x it has to
+ 
+
+ align:start position:0%
+when you fix a t and change x it has to
+look like exponential function but it
+
+ align:start position:0%
+look like exponential function but it
+ 
+
+ align:start position:0%
+look like exponential function but it
+has to be in this form just by the
+
+ align:start position:0%
+has to be in this form just by the
+ 
+
+ align:start position:0%
+has to be in this form just by the
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+equation. Now go back to the this
+
+ align:start position:0%
+equation. Now go back to the this
+ 
+
+ align:start position:0%
+equation. Now go back to the this
+equation you get is partial f over
+
+ align:start position:0%
+equation you get is partial f over
+ 
+
+ align:start position:0%
+equation you get is partial f over
+partial t is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now a * g prime of
+
+ align:start position:0%
+now a * g prime of
+ 
+
+ align:start position:0%
+now a * g prime of
+t. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Excuse me. Mhm. U that one in second
+
+ align:start position:0%
+Excuse me. Mhm. U that one in second
+ 
+
+ align:start position:0%
+Excuse me. Mhm. U that one in second
+last line. Uh yeah. So why is it minus
+
+ align:start position:0%
+last line. Uh yeah. So why is it minus
+ 
+
+ align:start position:0%
+last line. Uh yeah. So why is it minus
+muf at the end? Are you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay? Okay. And then let's plug it in.
+
+ align:start position:0%
+okay? Okay. And then let's plug it in.
+ 
+
+ align:start position:0%
+okay? Okay. And then let's plug it in.
+So we have a of g prime t
+
+ align:start position:0%
+So we have a of g prime t
+ 
+
+ align:start position:0%
+So we have a of g prime t
+ff plus 12 of sigma square
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+f. In other words, a of g prime of t is
+
+ align:start position:0%
+f. In other words, a of g prime of t is
+ 
+
+ align:start position:0%
+f. In other words, a of g prime of t is
+u
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+-²
+
+ align:start position:0%
+-²
+ 
+
+ align:start position:0%
+-²
+gt is u
+
+ align:start position:0%
+gt is u
+ 
+
+ align:start position:0%
+gt is u
+* some constant c1 +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+c2. Okay. And then what we got is
+
+ align:start position:0%
+c2. Okay. And then what we got is
+ 
+
+ align:start position:0%
+c2. Okay. And then what we got is
+original function f of t of x is e to
+
+ align:start position:0%
+original function f of t of x is e to
+ 
+
+ align:start position:0%
+original function f of t of x is e to
+the sigma x + mu - 1 /2 sigma^ 2 t plus
+
+ align:start position:0%
+the sigma x + mu - 1 /2 sigma^ 2 t plus
+ 
+
+ align:start position:0%
+the sigma x + mu - 1 /2 sigma^ 2 t plus
+some
+
+ align:start position:0%
+some
+ 
+
+ align:start position:0%
+some
+constant and that
+
+ align:start position:0%
+constant and that
+ 
+
+ align:start position:0%
+constant and that
+constant can be chosen because we have
+
+ align:start position:0%
+constant can be chosen because we have
+ 
+
+ align:start position:0%
+constant can be chosen because we have
+the initial condition x of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+0 equals
+
+ align:start position:0%
+0 equals
+ 
+
+ align:start position:0%
+0 equals
+z. That means if t is equal to z, f0 of
+
+ align:start position:0%
+z. That means if t is equal to z, f0 of
+ 
+
+ align:start position:0%
+z. That means if t is equal to z, f0 of
+0 is equal to e to the c. That has to be
+
+ align:start position:0%
+0 is equal to e to the c. That has to be
+ 
+
+ align:start position:0%
+0 is equal to e to the c. That has to be
+x0. In different words, this is just x0
+
+ align:start position:0%
+x0. In different words, this is just x0
+ 
+
+ align:start position:0%
+x0. In different words, this is just x0
+* e sigma x + mu - 4 sigma square t.
+
+ align:start position:0%
+* e sigma x + mu - 4 sigma square t.
+ 
+
+ align:start position:0%
+* e sigma x + mu - 4 sigma square t.
+Just as we expected, we got
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. Okay. So, some stoastic difference
+
+ align:start position:0%
+this. Okay. So, some stoastic difference
+ 
+
+ align:start position:0%
+this. Okay. So, some stoastic difference
+different differential equations can be
+
+ align:start position:0%
+different differential equations can be
+ 
+
+ align:start position:0%
+different differential equations can be
+solved
+
+ align:start position:0%
+solved
+ 
+
+ align:start position:0%
+solved
+by analyzing it. But I'm not necessarily
+
+ align:start position:0%
+by analyzing it. But I'm not necessarily
+ 
+
+ align:start position:0%
+by analyzing it. But I'm not necessarily
+saying that this is a better way to do
+
+ align:start position:0%
+saying that this is a better way to do
+ 
+
+ align:start position:0%
+saying that this is a better way to do
+it than just guessing. Just looking at
+
+ align:start position:0%
+it than just guessing. Just looking at
+ 
+
+ align:start position:0%
+it than just guessing. Just looking at
+it and you know okay it has to be a
+
+ align:start position:0%
+it and you know okay it has to be a
+ 
+
+ align:start position:0%
+it and you know okay it has to be a
+different uh exponential function. You
+
+ align:start position:0%
+different uh exponential function. You
+ 
+
+ align:start position:0%
+different uh exponential function. You
+know what I'll just change figure out
+
+ align:start position:0%
+know what I'll just change figure out
+ 
+
+ align:start position:0%
+know what I'll just change figure out
+what these are and I will come up with
+
+ align:start position:0%
+what these are and I will come up with
+ 
+
+ align:start position:0%
+what these are and I will come up with
+this formula without going through all
+
+ align:start position:0%
+this formula without going through all
+ 
+
+ align:start position:0%
+this formula without going through all
+those
+
+ align:start position:0%
+those
+ 
+
+ align:start position:0%
+those
+analysis. I'm not saying that's the
+
+ align:start position:0%
+analysis. I'm not saying that's the
+ 
+
+ align:start position:0%
+analysis. I'm not saying that's the
+worst way than actually going through
+
+ align:start position:0%
+worst way than actually going through
+ 
+
+ align:start position:0%
+worst way than actually going through
+the analysis because in fact what we did
+
+ align:start position:0%
+the analysis because in fact what we did
+ 
+
+ align:start position:0%
+the analysis because in fact what we did
+is we kind of already knew the answer
+
+ align:start position:0%
+is we kind of already knew the answer
+ 
+
+ align:start position:0%
+is we kind of already knew the answer
+was fit and was and are fitting into
+
+ align:start position:0%
+was fit and was and are fitting into
+ 
+
+ align:start position:0%
+was fit and was and are fitting into
+that answer right now.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Still, it can be one approach where you
+
+ align:start position:0%
+Still, it can be one approach where you
+ 
+
+ align:start position:0%
+Still, it can be one approach where you
+don't have a reasonable guess of what
+
+ align:start position:0%
+don't have a reasonable guess of what
+ 
+
+ align:start position:0%
+don't have a reasonable guess of what
+the xt has to be. Maybe try to break it
+
+ align:start position:0%
+the xt has to be. Maybe try to break it
+ 
+
+ align:start position:0%
+the xt has to be. Maybe try to break it
+down into pieces like this and backtrack
+
+ align:start position:0%
+down into pieces like this and backtrack
+ 
+
+ align:start position:0%
+down into pieces like this and backtrack
+to figure out the function. Let me give
+
+ align:start position:0%
+to figure out the function. Let me give
+ 
+
+ align:start position:0%
+to figure out the function. Let me give
+you one more example where we do have an
+
+ align:start position:0%
+you one more example where we do have an
+ 
+
+ align:start position:0%
+you one more example where we do have an
+explicit solution and then I'll move on
+
+ align:start position:0%
+explicit solution and then I'll move on
+ 
+
+ align:start position:0%
+explicit solution and then I'll move on
+and to and show you how to do when there
+
+ align:start position:0%
+and to and show you how to do when there
+ 
+
+ align:start position:0%
+and to and show you how to do when there
+is no explicit solution or when you
+
+ align:start position:0%
+is no explicit solution or when you
+ 
+
+ align:start position:0%
+is no explicit solution or when you
+don't know how to find an explicit
+
+ align:start position:0%
+don't know how to find an explicit
+ 
+
+ align:start position:0%
+don't know how to find an explicit
+solution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Maybe let's keep that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, second equation. Let's call
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this. What's the difference? The only
+
+ align:start position:0%
+this. What's the difference? The only
+ 
+
+ align:start position:0%
+this. What's the difference? The only
+difference is that you don't have an x
+
+ align:start position:0%
+difference is that you don't have an x
+ 
+
+ align:start position:0%
+difference is that you don't have an x
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+previously our main drift term also was
+
+ align:start position:0%
+previously our main drift term also was
+ 
+
+ align:start position:0%
+previously our main drift term also was
+proportional to the current value and
+
+ align:start position:0%
+proportional to the current value and
+ 
+
+ align:start position:0%
+proportional to the current value and
+the error was also uh dependent on the
+
+ align:start position:0%
+the error was also uh dependent on the
+ 
+
+ align:start position:0%
+the error was also uh dependent on the
+current value uh what is it proportional
+
+ align:start position:0%
+current value uh what is it proportional
+ 
+
+ align:start position:0%
+current value uh what is it proportional
+to the current value. But here now the
+
+ align:start position:0%
+to the current value. But here now the
+ 
+
+ align:start position:0%
+to the current value. But here now the
+drift term is something like an
+
+ align:start position:0%
+drift term is something like an
+ 
+
+ align:start position:0%
+drift term is something like an
+exponential minus
+
+ align:start position:0%
+exponential minus
+ 
+
+ align:start position:0%
+exponential minus
+exponential but still it's proportional
+
+ align:start position:0%
+exponential but still it's proportional
+ 
+
+ align:start position:0%
+exponential but still it's proportional
+to the current value but the error term
+
+ align:start position:0%
+to the current value but the error term
+ 
+
+ align:start position:0%
+to the current value but the error term
+is just some noise just irrelevant of
+
+ align:start position:0%
+is just some noise just irrelevant of
+ 
+
+ align:start position:0%
+is just some noise just irrelevant of
+what the value is. This has the same
+
+ align:start position:0%
+what the value is. This has the same
+ 
+
+ align:start position:0%
+what the value is. This has the same
+variance the error. So it's a slightly
+
+ align:start position:0%
+variance the error. So it's a slightly
+ 
+
+ align:start position:0%
+variance the error. So it's a slightly
+different
+
+ align:start position:0%
+different
+ 
+
+ align:start position:0%
+different
+uh what is it? It's a slightly different
+
+ align:start position:0%
+uh what is it? It's a slightly different
+ 
+
+ align:start position:0%
+uh what is it? It's a slightly different
+process and it's known as
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+orange
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process
+
+ align:start position:0%
+process
+ 
+
+ align:start position:0%
+process
+lens
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+process. Okay. And this is used to model
+
+ align:start position:0%
+process. Okay. And this is used to model
+ 
+
+ align:start position:0%
+process. Okay. And this is used to model
+a mean reverting stoastic process for
+
+ align:start position:0%
+a mean reverting stoastic process for
+ 
+
+ align:start position:0%
+a mean reverting stoastic process for
+alpha greater than zero. Notice that if
+
+ align:start position:0%
+alpha greater than zero. Notice that if
+ 
+
+ align:start position:0%
+alpha greater than zero. Notice that if
+x deviates from zero, this gives a force
+
+ align:start position:0%
+x deviates from zero, this gives a force
+ 
+
+ align:start position:0%
+x deviates from zero, this gives a force
+that drives the stoastic process back to
+
+ align:start position:0%
+that drives the stoastic process back to
+ 
+
+ align:start position:0%
+that drives the stoastic process back to
+zero. Okay, this negatively proportional
+
+ align:start position:0%
+zero. Okay, this negatively proportional
+ 
+
+ align:start position:0%
+zero. Okay, this negatively proportional
+to your current
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value. So yeah, this is used to model
+
+ align:start position:0%
+value. So yeah, this is used to model
+ 
+
+ align:start position:0%
+value. So yeah, this is used to model
+some mean reverting stoastic processes.
+
+ align:start position:0%
+some mean reverting stoastic processes.
+ 
+
+ align:start position:0%
+some mean reverting stoastic processes.
+and they first used it to what's it to
+
+ align:start position:0%
+and they first used it to what's it to
+ 
+
+ align:start position:0%
+and they first used it to what's it to
+study the behavior of
+
+ align:start position:0%
+study the behavior of
+ 
+
+ align:start position:0%
+study the behavior of
+gases.
+
+ align:start position:0%
+gases.
+ 
+
+ align:start position:0%
+gases.
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+Okay, I don't exactly see why, but
+
+ align:start position:0%
+Okay, I don't exactly see why, but
+ 
+
+ align:start position:0%
+Okay, I don't exactly see why, but
+that's what they say.
+
+ align:start position:0%
+that's what they say.
+ 
+
+ align:start position:0%
+that's what they say.
+So anyway, so this is another thing that
+
+ align:start position:0%
+So anyway, so this is another thing that
+ 
+
+ align:start position:0%
+So anyway, so this is another thing that
+can be solved by doing similar
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+analysis, but if you try the same
+
+ align:start position:0%
+analysis, but if you try the same
+ 
+
+ align:start position:0%
+analysis, but if you try the same
+method, it will
+
+ align:start position:0%
+method, it will
+ 
+
+ align:start position:0%
+method, it will
+fail. So it's a test function your guess
+
+ align:start position:0%
+fail. So it's a test function your guess
+ 
+
+ align:start position:0%
+fail. So it's a test function your guess
+initial guess will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be a 0 is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to so honestly I don't know how to come
+
+ align:start position:0%
+to so honestly I don't know how to come
+ 
+
+ align:start position:0%
+to so honestly I don't know how to come
+up with this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes, probably if you're really
+
+ align:start position:0%
+Yes, probably if you're really
+ 
+
+ align:start position:0%
+Yes, probably if you're really
+experienced with the stoastic
+
+ align:start position:0%
+experienced with the stoastic
+ 
+
+ align:start position:0%
+experienced with the stoastic
+differential equations, you'll
+
+ align:start position:0%
+differential equations, you'll
+ 
+
+ align:start position:0%
+differential equations, you'll
+see like some form like you'll have some
+
+ align:start position:0%
+see like some form like you'll have some
+ 
+
+ align:start position:0%
+see like some form like you'll have some
+feeling on like how the process will
+
+ align:start position:0%
+feeling on like how the process will
+ 
+
+ align:start position:0%
+feeling on like how the process will
+look like and then try this, try that
+
+ align:start position:0%
+look like and then try this, try that
+ 
+
+ align:start position:0%
+look like and then try this, try that
+and eventually something might succeed.
+
+ align:start position:0%
+and eventually something might succeed.
+ 
+
+ align:start position:0%
+and eventually something might succeed.
+So that's the best explanation I can
+
+ align:start position:0%
+So that's the best explanation I can
+ 
+
+ align:start position:0%
+So that's the best explanation I can
+give. I can't really give you an
+
+ align:start position:0%
+give. I can't really give you an
+ 
+
+ align:start position:0%
+give. I can't really give you an
+intuition why that's the right guess
+
+ align:start position:0%
+intuition why that's the right guess
+ 
+
+ align:start position:0%
+intuition why that's the right guess
+given some stoastic differential
+
+ align:start position:0%
+given some stoastic differential
+ 
+
+ align:start position:0%
+given some stoastic differential
+equation. I don't know how to say that
+
+ align:start position:0%
+equation. I don't know how to say that
+ 
+
+ align:start position:0%
+equation. I don't know how to say that
+you should start with this kind of
+
+ align:start position:0%
+you should start with this kind of
+ 
+
+ align:start position:0%
+you should start with this kind of
+function this kind of function. Okay.
+
+ align:start position:0%
+function this kind of function. Okay.
+ 
+
+ align:start position:0%
+function this kind of function. Okay.
+And it was the same when if you remember
+
+ align:start position:0%
+And it was the same when if you remember
+ 
+
+ align:start position:0%
+And it was the same when if you remember
+how you solve like ordinary differential
+
+ align:start position:0%
+how you solve like ordinary differential
+ 
+
+ align:start position:0%
+how you solve like ordinary differential
+equations or partial differential
+
+ align:start position:0%
+equations or partial differential
+ 
+
+ align:start position:0%
+equations or partial differential
+equations. Most of the times there is no
+
+ align:start position:0%
+equations. Most of the times there is no
+ 
+
+ align:start position:0%
+equations. Most of the times there is no
+good guess. It's only when your given
+
+ align:start position:0%
+good guess. It's only when your given
+ 
+
+ align:start position:0%
+good guess. It's only when your given
+formula has some specific form such a
+
+ align:start position:0%
+formula has some specific form such a
+ 
+
+ align:start position:0%
+formula has some specific form such a
+thing
+
+ align:start position:0%
+thing
+ 
+
+ align:start position:0%
+thing
+happens. So let's see what happens here.
+
+ align:start position:0%
+happens. So let's see what happens here.
+ 
+
+ align:start position:0%
+happens. So let's see what happens here.
+that was
+
+ align:start position:0%
+that was
+ 
+
+ align:start position:0%
+that was
+given. Now let's do exactly the same as
+
+ align:start position:0%
+given. Now let's do exactly the same as
+ 
+
+ align:start position:0%
+given. Now let's do exactly the same as
+before. Differentiate
+
+ align:start position:0%
+before. Differentiate
+ 
+
+ align:start position:0%
+before. Differentiate
+it and let me go slow. So we have a
+
+ align:start position:0%
+it and let me go slow. So we have a
+ 
+
+ align:start position:0%
+it and let me go slow. So we have a
+prime of t by chain rule a prime of t
+
+ align:start position:0%
+prime of t by chain rule a prime of t
+ 
+
+ align:start position:0%
+prime of t by chain rule a prime of t
+and that
+
+ align:start position:0%
+and that
+ 
+
+ align:start position:0%
+and that
+value that part will be equal to xt over
+
+ align:start position:0%
+value that part will be equal to xt over
+ 
+
+ align:start position:0%
+value that part will be equal to xt over
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+t. This is chain rule. So I
+
+ align:start position:0%
+t. This is chain rule. So I
+ 
+
+ align:start position:0%
+t. This is chain rule. So I
+differentiate that to get a prime t.
+
+ align:start position:0%
+differentiate that to get a prime t.
+ 
+
+ align:start position:0%
+differentiate that to get a prime t.
+That stays just as it was. But that can
+
+ align:start position:0%
+That stays just as it was. But that can
+ 
+
+ align:start position:0%
+That stays just as it was. But that can
+be rewritten as xt / a t and then plus a
+
+ align:start position:0%
+be rewritten as xt / a t and then plus a
+ 
+
+ align:start position:0%
+be rewritten as xt / a t and then plus a
+t * the differential of that
+
+ align:start position:0%
+t * the differential of that
+ 
+
+ align:start position:0%
+t * the differential of that
+one. And that is just b t dbt.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You don't have to differentiate that
+
+ align:start position:0%
+You don't have to differentiate that
+ 
+
+ align:start position:0%
+You don't have to differentiate that
+once more even though it's stochastic
+
+ align:start position:0%
+once more even though it's stochastic
+ 
+
+ align:start position:0%
+once more even though it's stochastic
+calculus because now that's a very
+
+ align:start position:0%
+calculus because now that's a very
+ 
+
+ align:start position:0%
+calculus because now that's a very
+subtle point and there's also one
+
+ align:start position:0%
+subtle point and there's also one
+ 
+
+ align:start position:0%
+subtle point and there's also one
+exercise about it in your homework. But
+
+ align:start position:0%
+exercise about it in your homework. But
+ 
+
+ align:start position:0%
+exercise about it in your homework. But
+when you're inte when you have a given
+
+ align:start position:0%
+when you're inte when you have a given
+ 
+
+ align:start position:0%
+when you're inte when you have a given
+stoastic process written already in this
+
+ align:start position:0%
+stoastic process written already in this
+ 
+
+ align:start position:0%
+stoastic process written already in this
+integral
+
+ align:start position:0%
+integral
+ 
+
+ align:start position:0%
+integral
+form if you remember the definition of
+
+ align:start position:0%
+form if you remember the definition of
+ 
+
+ align:start position:0%
+form if you remember the definition of
+an integral at least how I defined it is
+
+ align:start position:0%
+an integral at least how I defined it is
+ 
+
+ align:start position:0%
+an integral at least how I defined it is
+that it was an inverse operation of a
+
+ align:start position:0%
+that it was an inverse operation of a
+ 
+
+ align:start position:0%
+that it was an inverse operation of a
+differential. So when you differentiate
+
+ align:start position:0%
+differential. So when you differentiate
+ 
+
+ align:start position:0%
+differential. So when you differentiate
+this you just get that term. What I'm
+
+ align:start position:0%
+this you just get that term. What I'm
+ 
+
+ align:start position:0%
+this you just get that term. What I'm
+trying to say is there is no term no
+
+ align:start position:0%
+trying to say is there is no term no
+ 
+
+ align:start position:0%
+trying to say is there is no term no
+term where you have to differentiate
+
+ align:start position:0%
+term where you have to differentiate
+ 
+
+ align:start position:0%
+term where you have to differentiate
+this one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+more prime
+
+ align:start position:0%
+more prime
+ 
+
+ align:start position:0%
+more prime
+dt something like that you don't have
+
+ align:start position:0%
+dt something like that you don't have
+ 
+
+ align:start position:0%
+dt something like that you don't have
+this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+term. This can be confusing but think
+
+ align:start position:0%
+term. This can be confusing but think
+ 
+
+ align:start position:0%
+term. This can be confusing but think
+about it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah. Okay. Now we laid it
+
+ align:start position:0%
+Yeah. Okay. Now we laid it
+ 
+
+ align:start position:0%
+Yeah. Okay. Now we laid it
+out and just compare. So minus alpha of
+
+ align:start position:0%
+out and just compare. So minus alpha of
+ 
+
+ align:start position:0%
+out and just compare. So minus alpha of
+x of t is equal to a prime t / a
+
+ align:start position:0%
+x of t is equal to a prime t / a
+ 
+
+ align:start position:0%
+x of t is equal to a prime t / a
+t
+
+ align:start position:0%
+t
+ 
+
+ align:start position:0%
+t
+xt. And your second term a uh sigma dbt
+
+ align:start position:0%
+xt. And your second term a uh sigma dbt
+ 
+
+ align:start position:0%
+xt. And your second term a uh sigma dbt
+is equal to a t *
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+bt. Okay. But these two
+
+ align:start position:0%
+bt. Okay. But these two
+ 
+
+ align:start position:0%
+bt. Okay. But these two
+cancel and we see that uh a t has to
+
+ align:start position:0%
+cancel and we see that uh a t has to
+ 
+
+ align:start position:0%
+cancel and we see that uh a t has to
+be e to the minus alpha
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+tus. This says that it's an
+
+ align:start position:0%
+tus. This says that it's an
+ 
+
+ align:start position:0%
+tus. This says that it's an
+exponential. Now plug it in here. you
+
+ align:start position:0%
+exponential. Now plug it in here. you
+ 
+
+ align:start position:0%
+exponential. Now plug it in here. you
+get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+BT. That's it. So plug it back in. X of
+
+ align:start position:0%
+BT. That's it. So plug it back in. X of
+ 
+
+ align:start position:0%
+BT. That's it. So plug it back in. X of
+t is e to the minus alpha t of x
+
+ align:start position:0%
+t is e to the minus alpha t of x
+ 
+
+ align:start position:0%
+t is e to the minus alpha t of x
+of0 plus 0 to
+
+ align:start position:0%
+of0 plus 0 to
+ 
+
+ align:start position:0%
+of0 plus 0 to
+t sigma to the alpha s
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so this is a variance expectation
+
+ align:start position:0%
+Okay, so this is a variance expectation
+ 
+
+ align:start position:0%
+Okay, so this is a variance expectation
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+zero because that's a brownian motion.
+
+ align:start position:0%
+zero because that's a brownian motion.
+ 
+
+ align:start position:0%
+zero because that's a brownian motion.
+This term as we expected as time passes
+
+ align:start position:0%
+This term as we expected as time passes
+ 
+
+ align:start position:0%
+This term as we expected as time passes
+goes to
+
+ align:start position:0%
+goes to
+ 
+
+ align:start position:0%
+goes to
+zero. Okay, exponential
+
+ align:start position:0%
+zero. Okay, exponential
+ 
+
+ align:start position:0%
+zero. Okay, exponential
+decay and that is kind of hinted by this
+
+ align:start position:0%
+decay and that is kind of hinted by this
+ 
+
+ align:start position:0%
+decay and that is kind of hinted by this
+fact the mean reversion. So if you start
+
+ align:start position:0%
+fact the mean reversion. So if you start
+ 
+
+ align:start position:0%
+fact the mean reversion. So if you start
+from some value at least the drift term
+
+ align:start position:0%
+from some value at least the drift term
+ 
+
+ align:start position:0%
+from some value at least the drift term
+will go to zero quite
+
+ align:start position:0%
+will go to zero quite
+ 
+
+ align:start position:0%
+will go to zero quite
+quickly and then the important term will
+
+ align:start position:0%
+quickly and then the important term will
+ 
+
+ align:start position:0%
+quickly and then the important term will
+be the noise term or the variance
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+term. Any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+questions?
+
+ align:start position:0%
+questions?
+ 
+
+ align:start position:0%
+questions?
+Okay. And I'm really emphasizing a a lot
+
+ align:start position:0%
+Okay. And I'm really emphasizing a a lot
+ 
+
+ align:start position:0%
+Okay. And I'm really emphasizing a a lot
+of times this a lot of times today or
+
+ align:start position:0%
+of times this a lot of times today or
+ 
+
+ align:start position:0%
+of times this a lot of times today or
+really you can forget about what I did
+
+ align:start position:0%
+really you can forget about what I did
+ 
+
+ align:start position:0%
+really you can forget about what I did
+in the past two boards this board and
+
+ align:start position:0%
+in the past two boards this board and
+ 
+
+ align:start position:0%
+in the past two boards this board and
+the previous board because most of the
+
+ align:start position:0%
+the previous board because most of the
+ 
+
+ align:start position:0%
+the previous board because most of the
+times it will be
+
+ align:start position:0%
+times it will be
+ 
+
+ align:start position:0%
+times it will be
+useless. And so now I will describe what
+
+ align:start position:0%
+useless. And so now I will describe what
+ 
+
+ align:start position:0%
+useless. And so now I will describe what
+you will do if you're given a stoastic
+
+ align:start position:0%
+you will do if you're given a stoastic
+ 
+
+ align:start position:0%
+you will do if you're given a stoastic
+differential equation and you have a
+
+ align:start position:0%
+differential equation and you have a
+ 
+
+ align:start position:0%
+differential equation and you have a
+computer in front of you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What if such method
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fails? And it will fail most of the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+times.
+
+ align:start position:0%
+times.
+ 
+
+ align:start position:0%
+times.
+Okay, that's when we use these
+
+ align:start position:0%
+Okay, that's when we use these
+ 
+
+ align:start position:0%
+Okay, that's when we use these
+techniques called finite difference
+
+ align:start position:0%
+techniques called finite difference
+ 
+
+ align:start position:0%
+techniques called finite difference
+method.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Monte Carlo
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+simulation our tree
+
+ align:start position:0%
+simulation our tree
+ 
+
+ align:start position:0%
+simulation our tree
+method.
+
+ align:start position:0%
+method.
+ 
+
+ align:start position:0%
+method.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yes, the finite difference method. You
+
+ align:start position:0%
+Yes, the finite difference method. You
+ 
+
+ align:start position:0%
+Yes, the finite difference method. You
+probably already saw it if you saw uh
+
+ align:start position:0%
+probably already saw it if you saw uh
+ 
+
+ align:start position:0%
+probably already saw it if you saw uh
+took a differential equation course, but
+
+ align:start position:0%
+took a differential equation course, but
+ 
+
+ align:start position:0%
+took a differential equation course, but
+let me review
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. This is for
+
+ align:start position:0%
+it. This is for
+ 
+
+ align:start position:0%
+it. This is for
+PDEs or ODS for OD PD not stoastic
+
+ align:start position:0%
+PDEs or ODS for OD PD not stoastic
+ 
+
+ align:start position:0%
+PDEs or ODS for OD PD not stoastic
+differential equations but it can be
+
+ align:start position:0%
+differential equations but it can be
+ 
+
+ align:start position:0%
+differential equations but it can be
+adapted to work for stoastic
+
+ align:start position:0%
+adapted to work for stoastic
+ 
+
+ align:start position:0%
+adapted to work for stoastic
+differential equations. So I I'll work
+
+ align:start position:0%
+differential equations. So I I'll work
+ 
+
+ align:start position:0%
+differential equations. So I I'll work
+with an
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example. Let U of T be U prime of
+
+ align:start position:0%
+example. Let U of T be U prime of
+ 
+
+ align:start position:0%
+example. Let U of T be U prime of
+T +
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+2. Huh? U prime of T be U
+
+ align:start position:0%
+2. Huh? U prime of T be U
+ 
+
+ align:start position:0%
+2. Huh? U prime of T be U
+T + 2. U Z is equal to
+
+ align:start position:0%
+T + 2. U Z is equal to
+ 
+
+ align:start position:0%
+T + 2. U Z is equal to
+Z. Now this has an exact solution, but
+
+ align:start position:0%
+Z. Now this has an exact solution, but
+ 
+
+ align:start position:0%
+Z. Now this has an exact solution, but
+let's pretend that there is no exact
+
+ align:start position:0%
+let's pretend that there is no exact
+ 
+
+ align:start position:0%
+let's pretend that there is no exact
+solution. And if you want to do it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerically, you want to find the value
+
+ align:start position:0%
+numerically, you want to find the value
+ 
+
+ align:start position:0%
+numerically, you want to find the value
+of u = u1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+numerically. Here's what you're going to
+
+ align:start position:0%
+numerically. Here's what you're going to
+ 
+
+ align:start position:0%
+numerically. Here's what you're going to
+do. You're going to chop up the interval
+
+ align:start position:0%
+do. You're going to chop up the interval
+ 
+
+ align:start position:0%
+do. You're going to chop up the interval
+from 0 to one into very fine pieces. So
+
+ align:start position:0%
+from 0 to one into very fine pieces. So
+ 
+
+ align:start position:0%
+from 0 to one into very fine pieces. So
+from 0 to
+
+ align:start position:0%
+from 0 to
+ 
+
+ align:start position:0%
+from 0 to
+one, chop it down into tiny
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pieces. And since I'm in front of a
+
+ align:start position:0%
+pieces. And since I'm in front of a
+ 
+
+ align:start position:0%
+pieces. And since I'm in front of a
+blackboard, my tiny piece will be one
+
+ align:start position:0%
+blackboard, my tiny piece will be one
+ 
+
+ align:start position:0%
+blackboard, my tiny piece will be one
+over two and one. I'll just take two
+
+ align:start position:0%
+over two and one. I'll just take two
+ 
+
+ align:start position:0%
+over two and one. I'll just take two
+steps.
+
+ align:start position:0%
+steps.
+ 
+
+ align:start position:0%
+steps.
+But you should think of it as really
+
+ align:start position:0%
+But you should think of it as really
+ 
+
+ align:start position:0%
+But you should think of it as really
+repeating this a lot of
+
+ align:start position:0%
+repeating this a lot of
+ 
+
+ align:start position:0%
+repeating this a lot of
+times. I'll call my step to be h. So in
+
+ align:start position:0%
+times. I'll call my step to be h. So in
+ 
+
+ align:start position:0%
+times. I'll call my step to be h. So in
+my case, I'm increasing my steps by one
+
+ align:start position:0%
+my case, I'm increasing my steps by one
+ 
+
+ align:start position:0%
+my case, I'm increasing my steps by one
+over two at each
+
+ align:start position:0%
+over two at each
+ 
+
+ align:start position:0%
+over two at each
+time. So what is u of 1
+
+ align:start position:0%
+time. So what is u of 1
+ 
+
+ align:start position:0%
+time. So what is u of 1
+/2? Approximately by Taylor's formula,
+
+ align:start position:0%
+/2? Approximately by Taylor's formula,
+ 
+
+ align:start position:0%
+/2? Approximately by Taylor's formula,
+it's
+
+ align:start position:0%
+it's
+ 
+
+ align:start position:0%
+it's
+u0
+
+ align:start position:0%
+u0
+ 
+
+ align:start position:0%
+u0
+plus 12 * u prime of 0. That's
+
+ align:start position:0%
+plus 12 * u prime of 0. That's
+ 
+
+ align:start position:0%
+plus 12 * u prime of 0. That's
+approximation.
+
+ align:start position:0%
+approximation.
+ 
+
+ align:start position:0%
+approximation.
+Okay, U0 we already know is given to be
+
+ align:start position:0%
+Okay, U0 we already know is given to be
+ 
+
+ align:start position:0%
+Okay, U0 we already know is given to be
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero. U prime of 0 on the other hand is
+
+ align:start position:0%
+zero. U prime of 0 on the other hand is
+ 
+
+ align:start position:0%
+zero. U prime of 0 on the other hand is
+given by this differential
+
+ align:start position:0%
+given by this differential
+ 
+
+ align:start position:0%
+given by this differential
+equation. So it's 1 / 2 * 5 * u 0 + 2 u0
+
+ align:start position:0%
+equation. So it's 1 / 2 * 5 * u 0 + 2 u0
+ 
+
+ align:start position:0%
+equation. So it's 1 / 2 * 5 * u 0 + 2 u0
+is 0. So we get equal to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one like we have this value equal to one
+
+ align:start position:0%
+one like we have this value equal to one
+ 
+
+ align:start position:0%
+one like we have this value equal to one
+approximately I don't know what happens
+
+ align:start position:0%
+approximately I don't know what happens
+ 
+
+ align:start position:0%
+approximately I don't know what happens
+but it will be close to one and then for
+
+ align:start position:0%
+but it will be close to one and then for
+ 
+
+ align:start position:0%
+but it will be close to one and then for
+the next thing
+
+ align:start position:0%
+the next thing
+ 
+
+ align:start position:0%
+the next thing
+u1 this one is again by tailaylor
+
+ align:start position:0%
+u1 this one is again by tailaylor
+ 
+
+ align:start position:0%
+u1 this one is again by tailaylor
+approximation it's u of 1
+
+ align:start position:0%
+approximation it's u of 1
+ 
+
+ align:start position:0%
+approximation it's u of 1
+/2 plus 1 /2 u prime of 1
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2 and now you know the value of u of 1
+
+ align:start position:0%
+/2 and now you know the value of u of 1
+ 
+
+ align:start position:0%
+/2 and now you know the value of u of 1
+/2 approximate value by this so plug it
+
+ align:start position:0%
+/2 approximate value by this so plug it
+ 
+
+ align:start position:0%
+/2 approximate value by this so plug it
+in you have 1 + 1 /2 and again 5 * u1 /2
+
+ align:start position:0%
+in you have 1 + 1 /2 and again 5 * u1 /2
+ 
+
+ align:start position:0%
+in you have 1 + 1 /2 and again 5 * u1 /2
++ 2 which when you do the computation it
+
+ align:start position:0%
++ 2 which when you do the computation it
+ 
+
+ align:start position:0%
++ 2 which when you do the computation it
+should give 9
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+/2. It's really
+
+ align:start position:0%
+/2. It's really
+ 
+
+ align:start position:0%
+/2. It's really
+simple. The key idea here is just u
+
+ align:start position:0%
+simple. The key idea here is just u
+ 
+
+ align:start position:0%
+simple. The key idea here is just u
+prime is given by an
+
+ align:start position:0%
+prime is given by an
+ 
+
+ align:start position:0%
+prime is given by an
+equation this equation. So you can
+
+ align:start position:0%
+equation this equation. So you can
+ 
+
+ align:start position:0%
+equation this equation. So you can
+compute it once you know the value of u
+
+ align:start position:0%
+compute it once you know the value of u
+ 
+
+ align:start position:0%
+compute it once you know the value of u
+at that point. Okay. And basically the
+
+ align:start position:0%
+at that point. Okay. And basically the
+ 
+
+ align:start position:0%
+at that point. Okay. And basically the
+method is saying take H to be very small
+
+ align:start position:0%
+method is saying take H to be very small
+ 
+
+ align:start position:0%
+method is saying take H to be very small
+like one over 100. Then you just repeat
+
+ align:start position:0%
+like one over 100. Then you just repeat
+ 
+
+ align:start position:0%
+like one over 100. Then you just repeat
+it one over 100 times. So the equation
+
+ align:start position:0%
+it one over 100 times. So the equation
+ 
+
+ align:start position:0%
+it one over 100 times. So the equation
+is the I + one step value can be
+
+ align:start position:0%
+is the I + one step value can be
+ 
+
+ align:start position:0%
+is the I + one step value can be
+approximated from the ice
+
+ align:start position:0%
+approximated from the ice
+ 
+
+ align:start position:0%
+approximated from the ice
+value plus uh H * U prime by
+
+ align:start position:0%
+value plus uh H * U prime by
+ 
+
+ align:start position:0%
+value plus uh H * U prime by
+H and repeat it and repeat it and you
+
+ align:start position:0%
+H and repeat it and repeat it and you
+ 
+
+ align:start position:0%
+H and repeat it and repeat it and you
+reach U of one. And there's a theorem
+
+ align:start position:0%
+reach U of one. And there's a theorem
+ 
+
+ align:start position:0%
+reach U of one. And there's a theorem
+saying again if u is a reasonable fun if
+
+ align:start position:0%
+saying again if u is a reasonable fun if
+ 
+
+ align:start position:0%
+saying again if u is a reasonable fun if
+the differential equation is reasonable
+
+ align:start position:0%
+the differential equation is reasonable
+ 
+
+ align:start position:0%
+the differential equation is reasonable
+then that will approach the true value
+
+ align:start position:0%
+then that will approach the true value
+ 
+
+ align:start position:0%
+then that will approach the true value
+as you take h to be smaller and smaller.
+
+ align:start position:0%
+as you take h to be smaller and smaller.
+ 
+
+ align:start position:0%
+as you take h to be smaller and smaller.
+Okay that's called the finite difference
+
+ align:start position:0%
+Okay that's called the finite difference
+ 
+
+ align:start position:0%
+Okay that's called the finite difference
+method for differential
+
+ align:start position:0%
+method for differential
+ 
+
+ align:start position:0%
+method for differential
+equations. And you can do the exact same
+
+ align:start position:0%
+equations. And you can do the exact same
+ 
+
+ align:start position:0%
+equations. And you can do the exact same
+thing for two variables. Let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+see. And what we showed was for one
+
+ align:start position:0%
+see. And what we showed was for one
+ 
+
+ align:start position:0%
+see. And what we showed was for one
+variable finite difference
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+method. We want to find the value of u
+
+ align:start position:0%
+method. We want to find the value of u
+ 
+
+ align:start position:0%
+method. We want to find the value of u
+function u of
+
+ align:start position:0%
+function u of
+ 
+
+ align:start position:0%
+function u of
+t. We took values of 0 h 2 h 3 h. using
+
+ align:start position:0%
+t. We took values of 0 h 2 h 3 h. using
+ 
+
+ align:start position:0%
+t. We took values of 0 h 2 h 3 h. using
+that we did some approximation like that
+
+ align:start position:0%
+that we did some approximation like that
+ 
+
+ align:start position:0%
+that we did some approximation like that
+and found the
+
+ align:start position:0%
+and found the
+ 
+
+ align:start position:0%
+and found the
+value. Now suppose we want to find
+
+ align:start position:0%
+value. Now suppose we want to find
+ 
+
+ align:start position:0%
+value. Now suppose we want to find
+similarly a two variable function let's
+
+ align:start position:0%
+similarly a two variable function let's
+ 
+
+ align:start position:0%
+similarly a two variable function let's
+say v of t and
+
+ align:start position:0%
+say v of t and
+ 
+
+ align:start position:0%
+say v of t and
+x and we want to find the value of v of
+
+ align:start position:0%
+x and we want to find the value of v of
+ 
+
+ align:start position:0%
+x and we want to find the value of v of
+
+ align:start position:0%
+ 
+
+ align:start position:0%
+one now the boundary conditions are
+
+ align:start position:0%
+one now the boundary conditions are
+ 
+
+ align:start position:0%
+one now the boundary conditions are
+these we already know these
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+values I won't really show you by
+
+ align:start position:0%
+values I won't really show you by
+ 
+
+ align:start position:0%
+values I won't really show you by
+example but what we're going to do now
+
+ align:start position:0%
+example but what we're going to do now
+ 
+
+ align:start position:0%
+example but what we're going to do now
+is compute this value based on these two
+
+ align:start position:0%
+is compute this value based on these two
+ 
+
+ align:start position:0%
+is compute this value based on these two
+variable okay so it's Just the same
+
+ align:start position:0%
+variable okay so it's Just the same
+ 
+
+ align:start position:0%
+variable okay so it's Just the same
+tailor expansion for two variables will
+
+ align:start position:0%
+tailor expansion for two variables will
+ 
+
+ align:start position:0%
+tailor expansion for two variables will
+allow you to compute this value from
+
+ align:start position:0%
+allow you to compute this value from
+ 
+
+ align:start position:0%
+allow you to compute this value from
+these two variable values. Then compute
+
+ align:start position:0%
+these two variable values. Then compute
+ 
+
+ align:start position:0%
+these two variable values. Then compute
+this from these two. That's from these
+
+ align:start position:0%
+this from these two. That's from these
+ 
+
+ align:start position:0%
+this from these two. That's from these
+two. Just fill out the whole grid like
+
+ align:start position:0%
+two. Just fill out the whole grid like
+ 
+
+ align:start position:0%
+two. Just fill out the whole grid like
+that. Just fill out layer by
+
+ align:start position:0%
+that. Just fill out layer by
+ 
+
+ align:start position:0%
+that. Just fill out layer by
+layer. At some point you're going to
+
+ align:start position:0%
+layer. At some point you're going to
+ 
+
+ align:start position:0%
+layer. At some point you're going to
+reach this and then you'll have an
+
+ align:start position:0%
+reach this and then you'll have an
+ 
+
+ align:start position:0%
+reach this and then you'll have an
+approximate value of that. Okay? So you
+
+ align:start position:0%
+approximate value of that. Okay? So you
+ 
+
+ align:start position:0%
+approximate value of that. Okay? So you
+chop up your domain into fine
+
+ align:start position:0%
+chop up your domain into fine
+ 
+
+ align:start position:0%
+chop up your domain into fine
+pieces and then take the limit and most
+
+ align:start position:0%
+pieces and then take the limit and most
+ 
+
+ align:start position:0%
+pieces and then take the limit and most
+cases it will work.
+
+ align:start position:0%
+cases it will work.
+ 
+
+ align:start position:0%
+cases it will work.
+Okay, why does it not work for stokastic
+
+ align:start position:0%
+Okay, why does it not work for stokastic
+ 
+
+ align:start position:0%
+Okay, why does it not work for stokastic
+differential
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equations kind of works but the only
+
+ align:start position:0%
+equations kind of works but the only
+ 
+
+ align:start position:0%
+equations kind of works but the only
+problem is we don't know which value
+
+ align:start position:0%
+problem is we don't know which value
+ 
+
+ align:start position:0%
+problem is we don't know which value
+we're looking at. we want we're
+
+ align:start position:0%
+we're looking at. we want we're
+ 
+
+ align:start position:0%
+we're looking at. we want we're
+interested
+
+ align:start position:0%
+interested
+ 
+
+ align:start position:0%
+interested
+in. So let me phrase it a little
+
+ align:start position:0%
+in. So let me phrase it a little
+ 
+
+ align:start position:0%
+in. So let me phrase it a little
+bit
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+differently. You're given a differential
+
+ align:start position:0%
+differently. You're given a differential
+ 
+
+ align:start position:0%
+differently. You're given a differential
+equation of the form dx= mud dt plus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t dv of
+
+ align:start position:0%
+t dv of
+ 
+
+ align:start position:0%
+t dv of
+t. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and time
+
+ align:start position:0%
+and time
+ 
+
+ align:start position:0%
+and time
+variable and space variable.
+
+ align:start position:0%
+variable and space variable.
+ 
+
+ align:start position:0%
+variable and space variable.
+So if you want to compute your value at
+
+ align:start position:0%
+So if you want to compute your value at
+ 
+
+ align:start position:0%
+So if you want to compute your value at
+time uh h 2 h based on value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+h in this picture I told you that this
+
+ align:start position:0%
+h in this picture I told you that this
+ 
+
+ align:start position:0%
+h in this picture I told you that this
+point came from these two
+
+ align:start position:0%
+point came from these two
+ 
+
+ align:start position:0%
+point came from these two
+points but when it's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stochastic it could depend on everything
+
+ align:start position:0%
+stochastic it could depend on everything
+ 
+
+ align:start position:0%
+stochastic it could depend on everything
+you don't know where it came from. This
+
+ align:start position:0%
+you don't know where it came from. This
+ 
+
+ align:start position:0%
+you don't know where it came from. This
+point could have come from here. It
+
+ align:start position:0%
+point could have come from here. It
+ 
+
+ align:start position:0%
+point could have come from here. It
+could have came from here. It could have
+
+ align:start position:0%
+could have came from here. It could have
+ 
+
+ align:start position:0%
+could have came from here. It could have
+came from here. Came from here. You
+
+ align:start position:0%
+came from here. Came from here. You
+ 
+
+ align:start position:0%
+came from here. Came from here. You
+don't really know. But what you know is
+
+ align:start position:0%
+don't really know. But what you know is
+ 
+
+ align:start position:0%
+don't really know. But what you know is
+you have a probability
+
+ align:start position:0%
+you have a probability
+ 
+
+ align:start position:0%
+you have a probability
+distribution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So yeah, what what I'm trying to say is
+
+ align:start position:0%
+So yeah, what what I'm trying to say is
+ 
+
+ align:start position:0%
+So yeah, what what I'm trying to say is
+now if you want to adapt this method,
+
+ align:start position:0%
+now if you want to adapt this method,
+ 
+
+ align:start position:0%
+now if you want to adapt this method,
+what you're going to do is
+
+ align:start position:0%
+what you're going to do is
+ 
+
+ align:start position:0%
+what you're going to do is
+take a sample brownian motion
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+path. That means just according to the
+
+ align:start position:0%
+path. That means just according to the
+ 
+
+ align:start position:0%
+path. That means just according to the
+rand uh distribution of the brownian
+
+ align:start position:0%
+rand uh distribution of the brownian
+ 
+
+ align:start position:0%
+rand uh distribution of the brownian
+motion take one
+
+ align:start position:0%
+motion take one
+ 
+
+ align:start position:0%
+motion take one
+pass and use that pass. Once we fix a
+
+ align:start position:0%
+pass and use that pass. Once we fix a
+ 
+
+ align:start position:0%
+pass and use that pass. Once we fix a
+pass once a pass is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed we can exactly know where each
+
+ align:start position:0%
+fixed we can exactly know where each
+ 
+
+ align:start position:0%
+fixed we can exactly know where each
+value comes from. We
+
+ align:start position:0%
+value comes from. We
+ 
+
+ align:start position:0%
+value comes from. We
+know how to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+backtrack. That means instead of all
+
+ align:start position:0%
+backtrack. That means instead of all
+ 
+
+ align:start position:0%
+backtrack. That means instead of all
+these possibilities, we have one fixed
+
+ align:start position:0%
+these possibilities, we have one fixed
+ 
+
+ align:start position:0%
+these possibilities, we have one fixed
+possibility like
+
+ align:start position:0%
+possibility like
+ 
+
+ align:start position:0%
+possibility like
+that.
+
+ align:start position:0%
+that.
+ 
+
+ align:start position:0%
+that.
+Okay. So just use that finite difference
+
+ align:start position:0%
+Okay. So just use that finite difference
+ 
+
+ align:start position:0%
+Okay. So just use that finite difference
+method. What's that fixed
+
+ align:start position:0%
+method. What's that fixed
+ 
+
+ align:start position:0%
+method. What's that fixed
+pass? That will be the idea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let me do it a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+formally. So here is how it
+
+ align:start position:0%
+formally. So here is how it
+ 
+
+ align:start position:0%
+formally. So here is how it
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+works.
+
+ align:start position:0%
+works.
+ 
+
+ align:start position:0%
+works.
+If we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+fixed sample pass for bound
+
+ align:start position:0%
+fixed sample pass for bound
+ 
+
+ align:start position:0%
+fixed sample pass for bound
+motion of
+
+ align:start position:0%
+motion of
+ 
+
+ align:start position:0%
+motion of
+BT,
+
+ align:start position:0%
+BT,
+ 
+
+ align:start position:0%
+BT,
+then X at time I + 1 of
+
+ align:start position:0%
+then X at time I + 1 of
+ 
+
+ align:start position:0%
+then X at time I + 1 of
+H is equal to approximately equal to X
+
+ align:start position:0%
+H is equal to approximately equal to X
+ 
+
+ align:start position:0%
+H is equal to approximately equal to X
+at time A of H.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus h *
+
+ align:start position:0%
+plus h *
+ 
+
+ align:start position:0%
+plus h *
+dx at that time a
+
+ align:start position:0%
+dx at that time a
+ 
+
+ align:start position:0%
+dx at that time a
+ih just by the exact same uh scalar
+
+ align:start position:0%
+ih just by the exact same uh scalar
+ 
+
+ align:start position:0%
+ih just by the exact same uh scalar
+expression and then d of x we know to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+be that is equal to
+
+ align:start position:0%
+be that is equal to
+ 
+
+ align:start position:0%
+be that is equal to
+mu of
+
+ align:start position:0%
+mu of
+ 
+
+ align:start position:0%
+mu of
+dt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+plus oh mu of dt is h. So let me write
+
+ align:start position:0%
+plus oh mu of dt is h. So let me write
+ 
+
+ align:start position:0%
+plus oh mu of dt is h. So let me write
+it like that. Sigma time d of x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+db and these mu depend on their passes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right x at i of
+
+ align:start position:0%
+right x at i of
+ 
+
+ align:start position:0%
+right x at i of
+h
+
+ align:start position:0%
+h
+ 
+
+ align:start position:0%
+h
+dt sigma
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that here to here is tailor
+
+ align:start position:0%
+So that here to here is tailor
+ 
+
+ align:start position:0%
+So that here to here is tailor
+expansion. Here to here I'm going to use
+
+ align:start position:0%
+expansion. Here to here I'm going to use
+ 
+
+ align:start position:0%
+expansion. Here to here I'm going to use
+the differential equation. D of x is
+
+ align:start position:0%
+the differential equation. D of x is
+ 
+
+ align:start position:0%
+the differential equation. D of x is
+equal to mud dt plus sigma dbt. Yes. Do
+
+ align:start position:0%
+equal to mud dt plus sigma dbt. Yes. Do
+ 
+
+ align:start position:0%
+equal to mud dt plus sigma dbt. Yes. Do
+we need that before? No we don't
+
+ align:start position:0%
+we need that before? No we don't
+ 
+
+ align:start position:0%
+we need that before? No we don't
+actually. Oh yeah I was. Thank you very
+
+ align:start position:0%
+actually. Oh yeah I was. Thank you very
+ 
+
+ align:start position:0%
+actually. Oh yeah I was. Thank you very
+much. That was what confused
+
+ align:start position:0%
+much. That was what confused
+ 
+
+ align:start position:0%
+much. That was what confused
+me. Yes, thank you very much. And now we
+
+ align:start position:0%
+me. Yes, thank you very much. And now we
+ 
+
+ align:start position:0%
+me. Yes, thank you very much. And now we
+can compute everything. This one we're
+
+ align:start position:0%
+can compute everything. This one we're
+ 
+
+ align:start position:0%
+can compute everything. This one we're
+assuming that we know the
+
+ align:start position:0%
+assuming that we know the
+ 
+
+ align:start position:0%
+assuming that we know the
+value. That one can be computed from
+
+ align:start position:0%
+value. That one can be computed from
+ 
+
+ align:start position:0%
+value. That one can be computed from
+these two coordinates because we we now
+
+ align:start position:0%
+these two coordinates because we we now
+ 
+
+ align:start position:0%
+these two coordinates because we we now
+have a fixed fixed path x. We know what
+
+ align:start position:0%
+have a fixed fixed path x. We know what
+ 
+
+ align:start position:0%
+have a fixed fixed path x. We know what
+x of ih is dt. We take it to be h
+
+ align:start position:0%
+x of ih is dt. We take it to be h
+ 
+
+ align:start position:0%
+x of ih is dt. We take it to be h
+approximated as h or time difference.
+
+ align:start position:0%
+approximated as h or time difference.
+ 
+
+ align:start position:0%
+approximated as h or time difference.
+Again sigma can be computed DB now can
+
+ align:start position:0%
+Again sigma can be computed DB now can
+ 
+
+ align:start position:0%
+Again sigma can be computed DB now can
+be computed from BT because we have a
+
+ align:start position:0%
+be computed from BT because we have a
+ 
+
+ align:start position:0%
+be computed from BT because we have a
+fixed path again we know that is equal
+
+ align:start position:0%
+fixed path again we know that is equal
+ 
+
+ align:start position:0%
+fixed path again we know that is equal
+to B of I + 1 of H minus B of I of
+
+ align:start position:0%
+to B of I + 1 of H minus B of I of
+ 
+
+ align:start position:0%
+to B of I + 1 of H minus B of I of
+H where's this fixed path they're
+
+ align:start position:0%
+H where's this fixed path they're
+ 
+
+ align:start position:0%
+H where's this fixed path they're
+basically exactly the same if you have a
+
+ align:start position:0%
+basically exactly the same if you have a
+ 
+
+ align:start position:0%
+basically exactly the same if you have a
+fixed path
+
+ align:start position:0%
+fixed path
+ 
+
+ align:start position:0%
+fixed path
+B the problem is we don't have a fixed
+
+ align:start position:0%
+B the problem is we don't have a fixed
+ 
+
+ align:start position:0%
+B the problem is we don't have a fixed
+path B that's where Monte Carlo
+
+ align:start position:0%
+path B that's where Monte Carlo
+ 
+
+ align:start position:0%
+path B that's where Monte Carlo
+simulation comes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, so Monte Carlo simulation is just
+
+ align:start position:0%
+Okay, so Monte Carlo simulation is just
+ 
+
+ align:start position:0%
+Okay, so Monte Carlo simulation is just
+a way to draw from some uh probability
+
+ align:start position:0%
+a way to draw from some uh probability
+ 
+
+ align:start position:0%
+a way to draw from some uh probability
+distribution a lot of samples. So if you
+
+ align:start position:0%
+distribution a lot of samples. So if you
+ 
+
+ align:start position:0%
+distribution a lot of samples. So if you
+know now if you know can know how to
+
+ align:start position:0%
+know now if you know can know how to
+ 
+
+ align:start position:0%
+know now if you know can know how to
+draw samples from the brownian motions
+
+ align:start position:0%
+draw samples from the brownian motions
+ 
+
+ align:start position:0%
+draw samples from the brownian motions
+and what you're going to do is draw a
+
+ align:start position:0%
+and what you're going to do is draw a
+ 
+
+ align:start position:0%
+and what you're going to do is draw a
+lot of samples for each sample do this
+
+ align:start position:0%
+lot of samples for each sample do this
+ 
+
+ align:start position:0%
+lot of samples for each sample do this
+to compute the value of x0 can
+
+ align:start position:0%
+to compute the value of x0 can
+ 
+
+ align:start position:0%
+to compute the value of x0 can
+compute x of
+
+ align:start position:0%
+compute x of
+ 
+
+ align:start position:0%
+compute x of
+one. So according to a different B
+
+ align:start position:0%
+one. So according to a different B
+ 
+
+ align:start position:0%
+one. So according to a different B
+you'll get a different value and in the
+
+ align:start position:0%
+you'll get a different value and in the
+ 
+
+ align:start position:0%
+you'll get a different value and in the
+end you'll have obtain a probability
+
+ align:start position:0%
+end you'll have obtain a probability
+ 
+
+ align:start position:0%
+end you'll have obtain a probability
+distribution. So by repeating the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+experiment
+
+ align:start position:0%
+experiment
+ 
+
+ align:start position:0%
+experiment
+experiment that means just redraw the
+
+ align:start position:0%
+experiment that means just redraw the
+ 
+
+ align:start position:0%
+experiment that means just redraw the
+path again and again you'll get
+
+ align:start position:0%
+path again and again you'll get
+ 
+
+ align:start position:0%
+path again and again you'll get
+different values of x sub1 that means
+
+ align:start position:0%
+different values of x sub1 that means
+ 
+
+ align:start position:0%
+different values of x sub1 that means
+you get a distribution of x of one
+
+ align:start position:0%
+you get a distribution of x of one
+ 
+
+ align:start position:0%
+you get a distribution of x of one
+obtain
+
+ align:start position:0%
+obtain
+ 
+
+ align:start position:0%
+obtain
+distribution of x
+
+ align:start position:0%
+distribution of x
+ 
+
+ align:start position:0%
+distribution of x
+sub1 and that's
+
+ align:start position:0%
+sub1 and that's
+ 
+
+ align:start position:0%
+sub1 and that's
+it and that will approach the real
+
+ align:start position:0%
+it and that will approach the real
+ 
+
+ align:start position:0%
+it and that will approach the real
+distribution of x sub1.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's how you numerically solve a
+
+ align:start position:0%
+So that's how you numerically solve a
+ 
+
+ align:start position:0%
+So that's how you numerically solve a
+stoastic differential
+
+ align:start position:0%
+stoastic differential
+ 
+
+ align:start position:0%
+stoastic differential
+equation. Again there's this finite
+
+ align:start position:0%
+equation. Again there's this finite
+ 
+
+ align:start position:0%
+equation. Again there's this finite
+difference method that can be used to
+
+ align:start position:0%
+difference method that can be used to
+ 
+
+ align:start position:0%
+difference method that can be used to
+solve differential
+
+ align:start position:0%
+solve differential
+ 
+
+ align:start position:0%
+solve differential
+equations. But the reason it doesn't
+
+ align:start position:0%
+equations. But the reason it doesn't
+ 
+
+ align:start position:0%
+equations. But the reason it doesn't
+apply to stoastic differential equations
+
+ align:start position:0%
+apply to stoastic differential equations
+ 
+
+ align:start position:0%
+apply to stoastic differential equations
+is because there's underlying
+
+ align:start position:0%
+is because there's underlying
+ 
+
+ align:start position:0%
+is because there's underlying
+uncertainty that coming from Brownian
+
+ align:start position:0%
+uncertainty that coming from Brownian
+ 
+
+ align:start position:0%
+uncertainty that coming from Brownian
+motion. However, once you fix a brownian
+
+ align:start position:0%
+motion. However, once you fix a brownian
+ 
+
+ align:start position:0%
+motion. However, once you fix a brownian
+motion, then you can use that finite
+
+ align:start position:0%
+motion, then you can use that finite
+ 
+
+ align:start position:0%
+motion, then you can use that finite
+difference method to compute X of one.
+
+ align:start position:0%
+difference method to compute X of one.
+ 
+
+ align:start position:0%
+difference method to compute X of one.
+So based on that idea, you just draw a
+
+ align:start position:0%
+So based on that idea, you just draw a
+ 
+
+ align:start position:0%
+So based on that idea, you just draw a
+lot of samples of the Brownian
+
+ align:start position:0%
+lot of samples of the Brownian
+ 
+
+ align:start position:0%
+lot of samples of the Brownian
+pass draw uh compute a lot of values X
+
+ align:start position:0%
+pass draw uh compute a lot of values X
+ 
+
+ align:start position:0%
+pass draw uh compute a lot of values X
+of one and obtain a probability
+
+ align:start position:0%
+of one and obtain a probability
+ 
+
+ align:start position:0%
+of one and obtain a probability
+distribution of X of one.
+
+ align:start position:0%
+distribution of X of one.
+ 
+
+ align:start position:0%
+distribution of X of one.
+Okay, that's the underlying
+
+ align:start position:0%
+Okay, that's the underlying
+ 
+
+ align:start position:0%
+Okay, that's the underlying
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+principle. And of course, you can't do
+
+ align:start position:0%
+principle. And of course, you can't do
+ 
+
+ align:start position:0%
+principle. And of course, you can't do
+it by hand, so you need a computer.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then what is tree
+
+ align:start position:0%
+Then what is tree
+ 
+
+ align:start position:0%
+Then what is tree
+method? That's
+
+ align:start position:0%
+method? That's
+ 
+
+ align:start position:0%
+method? That's
+cool. Tree method is based on this idea.
+
+ align:start position:0%
+cool. Tree method is based on this idea.
+ 
+
+ align:start position:0%
+cool. Tree method is based on this idea.
+If you remember boundarian
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+motion is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+limit
+
+ align:start position:0%
+limit
+ 
+
+ align:start position:0%
+limit
+of simple random
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+walk.
+
+ align:start position:0%
+walk.
+ 
+
+ align:start position:0%
+walk.
+Okay, th this gives you a kind of
+
+ align:start position:0%
+Okay, th this gives you a kind of
+ 
+
+ align:start position:0%
+Okay, th this gives you a kind of
+approximate way to draw brown motions.
+
+ align:start position:0%
+approximate way to draw brown motions.
+ 
+
+ align:start position:0%
+approximate way to draw brown motions.
+Draw a sample from Brownium motions. How
+
+ align:start position:0%
+Draw a sample from Brownium motions. How
+ 
+
+ align:start position:0%
+Draw a sample from Brownium motions. How
+do you do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that? At time zero, you have zero. At
+
+ align:start position:0%
+that? At time zero, you have zero. At
+ 
+
+ align:start position:0%
+that? At time zero, you have zero. At
+time really time uh tiny
+
+ align:start position:0%
+time really time uh tiny
+ 
+
+ align:start position:0%
+time really time uh tiny
+h you'll have + one or minus one with
+
+ align:start position:0%
+h you'll have + one or minus one with
+ 
+
+ align:start position:0%
+h you'll have + one or minus one with
+same probability.
+
+ align:start position:0%
+same probability.
+ 
+
+ align:start position:0%
+same probability.
+Then it goes up or down again, up or
+
+ align:start position:0%
+Then it goes up or down again, up or
+ 
+
+ align:start position:0%
+Then it goes up or down again, up or
+down
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+again and so
+
+ align:start position:0%
+again and so
+ 
+
+ align:start position:0%
+again and so
+on. And you know exactly the probability
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+distribution. So the probability that it
+
+ align:start position:0%
+distribution. So the probability that it
+ 
+
+ align:start position:0%
+distribution. So the probability that it
+ends up here is half ends up here is
+
+ align:start position:0%
+ends up here is half ends up here is
+ 
+
+ align:start position:0%
+ends up here is half ends up here is
+half
+
+ align:start position:0%
+half
+ 
+
+ align:start position:0%
+half
+1/4 and so on. So instead of drawing
+
+ align:start position:0%
+1/4 and so on. So instead of drawing
+ 
+
+ align:start position:0%
+1/4 and so on. So instead of drawing
+from this sample path, what you're going
+
+ align:start position:0%
+from this sample path, what you're going
+ 
+
+ align:start position:0%
+from this sample path, what you're going
+to do is just compute every val compute
+
+ align:start position:0%
+to do is just compute every val compute
+ 
+
+ align:start position:0%
+to do is just compute every val compute
+the value of our function at these
+
+ align:start position:0%
+the value of our function at these
+ 
+
+ align:start position:0%
+the value of our function at these
+points.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+But then the probability distribution
+
+ align:start position:0%
+But then the probability distribution
+ 
+
+ align:start position:0%
+But then the probability distribution
+because we know the probability
+
+ align:start position:0%
+because we know the probability
+ 
+
+ align:start position:0%
+because we know the probability
+distribution that the path will end up
+
+ align:start position:0%
+distribution that the path will end up
+ 
+
+ align:start position:0%
+distribution that the path will end up
+at these points. Suppose
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that you computed all these values
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here then I draw too many 1 2 3 4 5 this
+
+ align:start position:0%
+here then I draw too many 1 2 3 4 5 this
+ 
+
+ align:start position:0%
+here then I draw too many 1 2 3 4 5 this
+1 over 32 probability here 5 choose 1 5
+
+ align:start position:0%
+1 over 32 probability here 5 choose 1 5
+ 
+
+ align:start position:0%
+1 over 32 probability here 5 choose 1 5
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+32 5 choose 2 is 5 4 10 over
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+32 suppose that some stoastic process
+
+ align:start position:0%
+32 suppose that some stoastic process
+ 
+
+ align:start position:0%
+32 suppose that some stoastic process
+after following this has value one here,
+
+ align:start position:0%
+after following this has value one here,
+ 
+
+ align:start position:0%
+after following this has value one here,
+two here, three here, four, five and six
+
+ align:start position:0%
+two here, three here, four, five and six
+ 
+
+ align:start position:0%
+two here, three here, four, five and six
+here. And
+
+ align:start position:0%
+here. And
+ 
+
+ align:start position:0%
+here. And
+approximately if you take a brown
+
+ align:start position:0%
+approximately if you take a brown
+ 
+
+ align:start position:0%
+approximately if you take a brown
+motion, it will have one with
+
+ align:start position:0%
+motion, it will have one with
+ 
+
+ align:start position:0%
+motion, it will have one with
+probability 1 over 32, two with
+
+ align:start position:0%
+probability 1 over 32, two with
+ 
+
+ align:start position:0%
+probability 1 over 32, two with
+probability 5 over 32 and so on.
+
+ align:start position:0%
+probability 5 over 32 and so on.
+ 
+
+ align:start position:0%
+probability 5 over 32 and so on.
+Okay, maybe I didn't explain that well,
+
+ align:start position:0%
+Okay, maybe I didn't explain that well,
+ 
+
+ align:start position:0%
+Okay, maybe I didn't explain that well,
+but basically tree method just says you
+
+ align:start position:0%
+but basically tree method just says you
+ 
+
+ align:start position:0%
+but basically tree method just says you
+can discretise the outcome of the
+
+ align:start position:0%
+can discretise the outcome of the
+ 
+
+ align:start position:0%
+can discretise the outcome of the
+brownian
+
+ align:start position:0%
+brownian
+ 
+
+ align:start position:0%
+brownian
+motion based on the fact that it's a
+
+ align:start position:0%
+motion based on the fact that it's a
+ 
+
+ align:start position:0%
+motion based on the fact that it's a
+limit of simple random
+
+ align:start position:0%
+limit of simple random
+ 
+
+ align:start position:0%
+limit of simple random
+walk. So just do the exact same method
+
+ align:start position:0%
+walk. So just do the exact same method
+ 
+
+ align:start position:0%
+walk. So just do the exact same method
+for a simple random walk instead of
+
+ align:start position:0%
+for a simple random walk instead of
+ 
+
+ align:start position:0%
+for a simple random walk instead of
+browning motion and then take it to the
+
+ align:start position:0%
+browning motion and then take it to the
+ 
+
+ align:start position:0%
+browning motion and then take it to the
+limit. That's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+principle.
+
+ align:start position:0%
+principle.
+ 
+
+ align:start position:0%
+principle.
+Yeah. But yeah, I don't know what's
+
+ align:start position:0%
+Yeah. But yeah, I don't know what's
+ 
+
+ align:start position:0%
+Yeah. But yeah, I don't know what's
+being used in practice, but it seems
+
+ align:start position:0%
+being used in practice, but it seems
+ 
+
+ align:start position:0%
+being used in practice, but it seems
+like these two are the more important
+
+ align:start position:0%
+like these two are the more important
+ 
+
+ align:start position:0%
+like these two are the more important
+ones. This is more like if you want to
+
+ align:start position:0%
+ones. This is more like if you want to
+ 
+
+ align:start position:0%
+ones. This is more like if you want to
+do it by hand because you can't really
+
+ align:start position:0%
+do it by hand because you can't really
+ 
+
+ align:start position:0%
+do it by hand because you can't really
+do every single possibility that makes
+
+ align:start position:0%
+do every single possibility that makes
+ 
+
+ align:start position:0%
+do every single possibility that makes
+you only a finite
+
+ align:start position:0%
+you only a finite
+ 
+
+ align:start position:0%
+you only a finite
+possibility. So
+
+ align:start position:0%
+possibility. So
+ 
+
+ align:start position:0%
+possibility. So
+any questions?
+
+ align:start position:0%
+any questions?
+ 
+
+ align:start position:0%
+any questions?
+Yeah. So uh here you said we get u by
+
+ align:start position:0%
+Yeah. So uh here you said we get u by
+ 
+
+ align:start position:0%
+Yeah. So uh here you said we get u by
+repeating the experiment we get uh kind
+
+ align:start position:0%
+repeating the experiment we get uh kind
+ 
+
+ align:start position:0%
+repeating the experiment we get uh kind
+of a distribution for x1. Mhm. Uh I was
+
+ align:start position:0%
+of a distribution for x1. Mhm. Uh I was
+ 
+
+ align:start position:0%
+of a distribution for x1. Mhm. Uh I was
+wondering we could also get the
+
+ align:start position:0%
+wondering we could also get the
+ 
+
+ align:start position:0%
+wondering we could also get the
+distribution for not just x1 but also
+
+ align:start position:0%
+distribution for not just x1 but also
+ 
+
+ align:start position:0%
+distribution for not just x1 but also
+for x ih all the intermediate values.
+
+ align:start position:0%
+for x ih all the intermediate values.
+ 
+
+ align:start position:0%
+for x ih all the intermediate values.
+Yeah. Yeah. But the problem is we're
+
+ align:start position:0%
+Yeah. Yeah. But the problem is we're
+ 
+
+ align:start position:0%
+Yeah. Yeah. But the problem is we're
+taking different values of h. H will be
+
+ align:start position:0%
+taking different values of h. H will be
+ 
+
+ align:start position:0%
+taking different values of h. H will be
+smaller and smaller but for those values
+
+ align:start position:0%
+smaller and smaller but for those values
+ 
+
+ align:start position:0%
+smaller and smaller but for those values
+we took Yeah. We will get some
+
+ align:start position:0%
+we took Yeah. We will get some
+ 
+
+ align:start position:0%
+we took Yeah. We will get some
+distribution right. So we might have
+
+ align:start position:0%
+distribution right. So we might have
+ 
+
+ align:start position:0%
+distribution right. So we might have
+distributions for x of t for many
+
+ align:start position:0%
+distributions for x of t for many
+ 
+
+ align:start position:0%
+distributions for x of t for many
+different points. Right. Yeah. Yeah. So
+
+ align:start position:0%
+different points. Right. Yeah. Yeah. So
+ 
+
+ align:start position:0%
+different points. Right. Yeah. Yeah. So
+maybe we could uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right but one thing you have to be
+
+ align:start position:0%
+right but one thing you have to be
+ 
+
+ align:start position:0%
+right but one thing you have to be
+careful is let's suppose you take h= one
+
+ align:start position:0%
+careful is let's suppose you take h= one
+ 
+
+ align:start position:0%
+careful is let's suppose you take h= one
+over
+
+ align:start position:0%
+over
+ 
+
+ align:start position:0%
+over
+100 then this will give you a pretty
+
+ align:start position:0%
+100 then this will give you a pretty
+ 
+
+ align:start position:0%
+100 then this will give you a pretty
+fairly good approximation for x of one
+
+ align:start position:0%
+fairly good approximation for x of one
+ 
+
+ align:start position:0%
+fairly good approximation for x of one
+but it won't give you a good
+
+ align:start position:0%
+but it won't give you a good
+ 
+
+ align:start position:0%
+but it won't give you a good
+approximation for x of 1 over 50. Yeah.
+
+ align:start position:0%
+approximation for x of 1 over 50. Yeah.
+ 
+
+ align:start position:0%
+approximation for x of 1 over 50. Yeah.
+So probably you can also get
+
+ align:start position:0%
+So probably you can also get
+ 
+
+ align:start position:0%
+So probably you can also get
+distribution where it's so 1 over 3 1
+
+ align:start position:0%
+distribution where it's so 1 over 3 1
+ 
+
+ align:start position:0%
+distribution where it's so 1 over 3 1
+over 4 but at some point the uh
+
+ align:start position:0%
+over 4 but at some point the uh
+ 
+
+ align:start position:0%
+over 4 but at some point the uh
+approximation will be very very
+
+ align:start position:0%
+approximation will be very very
+ 
+
+ align:start position:0%
+approximation will be very very
+bad. So the key is to choose the right h
+
+ align:start position:0%
+bad. So the key is to choose the right h
+ 
+
+ align:start position:0%
+bad. So the key is to choose the right h
+because if you pick h to be too small
+
+ align:start position:0%
+because if you pick h to be too small
+ 
+
+ align:start position:0%
+because if you pick h to be too small
+you'll have have a very good
+
+ align:start position:0%
+you'll have have a very good
+ 
+
+ align:start position:0%
+you'll have have a very good
+approximation to your distribution but
+
+ align:start position:0%
+approximation to your distribution but
+ 
+
+ align:start position:0%
+approximation to your distribution but
+at the same time it'll take too much
+
+ align:start position:0%
+at the same time it'll take too much
+ 
+
+ align:start position:0%
+at the same time it'll take too much
+time to compute it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So any remarks from the more practical
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+side? Okay. So that's actually all all I
+
+ align:start position:0%
+side? Okay. So that's actually all all I
+ 
+
+ align:start position:0%
+side? Okay. So that's actually all all I
+wanted to say about stoastic
+
+ align:start position:0%
+wanted to say about stoastic
+ 
+
+ align:start position:0%
+wanted to say about stoastic
+differential equations. Really uh the
+
+ align:start position:0%
+differential equations. Really uh the
+ 
+
+ align:start position:0%
+differential equations. Really uh the
+basic principle is there is such thing
+
+ align:start position:0%
+basic principle is there is such thing
+ 
+
+ align:start position:0%
+basic principle is there is such thing
+called stoastic differential equation.
+
+ align:start position:0%
+called stoastic differential equation.
+ 
+
+ align:start position:0%
+called stoastic differential equation.
+It can be solved but most of the times
+
+ align:start position:0%
+It can be solved but most of the times
+ 
+
+ align:start position:0%
+It can be solved but most of the times
+it won't have a closed form formula. And
+
+ align:start position:0%
+it won't have a closed form formula. And
+ 
+
+ align:start position:0%
+it won't have a closed form formula. And
+if you want to do it numerically here
+
+ align:start position:0%
+if you want to do it numerically here
+ 
+
+ align:start position:0%
+if you want to do it numerically here
+are some possibilities. Okay, but I
+
+ align:start position:0%
+are some possibilities. Okay, but I
+ 
+
+ align:start position:0%
+are some possibilities. Okay, but I
+won't go any further any deeper
+
+ align:start position:0%
+won't go any further any deeper
+ 
+
+ align:start position:0%
+won't go any further any deeper
+inside. So the last meth math lecture I
+
+ align:start position:0%
+inside. So the last meth math lecture I
+ 
+
+ align:start position:0%
+inside. So the last meth math lecture I
+will conclude with heat equation.
+
+ align:start position:0%
+will conclude with heat equation.
+ 
+
+ align:start position:0%
+will conclude with heat equation.
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah, computations of various prices.
+
+ align:start position:0%
+Yeah, computations of various prices.
+ 
+
+ align:start position:0%
+Yeah, computations of various prices.
+Some some of the derivatives are sort of
+
+ align:start position:0%
+Some some of the derivatives are sort of
+ 
+
+ align:start position:0%
+Some some of the derivatives are sort of
+path independent or have path
+
+ align:start position:0%
+path independent or have path
+ 
+
+ align:start position:0%
+path independent or have path
+independent solutions. So that you know
+
+ align:start position:0%
+independent solutions. So that you know
+ 
+
+ align:start position:0%
+independent solutions. So that you know
+you you basically are looking at say the
+
+ align:start position:0%
+you you basically are looking at say the
+ 
+
+ align:start position:0%
+you you basically are looking at say the
+distribution at the terminal value and
+
+ align:start position:0%
+distribution at the terminal value and
+ 
+
+ align:start position:0%
+distribution at the terminal value and
+that determines the price of the
+
+ align:start position:0%
+that determines the price of the
+ 
+
+ align:start position:0%
+that determines the price of the
+derivative. There are you know there are
+
+ align:start position:0%
+derivative. There are you know there are
+ 
+
+ align:start position:0%
+derivative. There are you know there are
+other derivatives where things really
+
+ align:start position:0%
+other derivatives where things really
+ 
+
+ align:start position:0%
+other derivatives where things really
+are path dependent
+
+ align:start position:0%
+are path dependent
+ 
+
+ align:start position:0%
+are path dependent
+um like uh with options with where you
+
+ align:start position:0%
+um like uh with options with where you
+ 
+
+ align:start position:0%
+um like uh with options with where you
+have early exercise possibilities. Um
+
+ align:start position:0%
+have early exercise possibilities. Um
+ 
+
+ align:start position:0%
+have early exercise possibilities. Um
+when do you exercise early or not? then
+
+ align:start position:0%
+when do you exercise early or not? then
+ 
+
+ align:start position:0%
+when do you exercise early or not? then
+the tree methods are really good because
+
+ align:start position:0%
+the tree methods are really good because
+ 
+
+ align:start position:0%
+the tree methods are really good because
+at each element of the tree you can
+
+ align:start position:0%
+at each element of the tree you can
+ 
+
+ align:start position:0%
+at each element of the tree you can
+condition on whatever the path was. So
+
+ align:start position:0%
+condition on whatever the path was. So
+ 
+
+ align:start position:0%
+condition on whatever the path was. So
+um so keep that in mind that when
+
+ align:start position:0%
+um so keep that in mind that when
+ 
+
+ align:start position:0%
+um so keep that in mind that when
+there's path dependence in the problem
+
+ align:start position:0%
+there's path dependence in the problem
+ 
+
+ align:start position:0%
+there's path dependence in the problem
+you'll probably want to use one of these
+
+ align:start position:0%
+you'll probably want to use one of these
+ 
+
+ align:start position:0%
+you'll probably want to use one of these
+methods. Thanks. I know that if you're
+
+ align:start position:0%
+methods. Thanks. I know that if you're
+ 
+
+ align:start position:0%
+methods. Thanks. I know that if you're
+trying to break it down into simple
+
+ align:start position:0%
+trying to break it down into simple
+ 
+
+ align:start position:0%
+trying to break it down into simple
+random walks um you can only
+
+ align:start position:0%
+random walks um you can only
+ 
+
+ align:start position:0%
+random walks um you can only
+use no uh plus minus but if you were to
+
+ align:start position:0%
+use no uh plus minus but if you were to
+ 
+
+ align:start position:0%
+use no uh plus minus but if you were to
+I've heard of people trying to use a
+
+ align:start position:0%
+I've heard of people trying to use a
+ 
+
+ align:start position:0%
+I've heard of people trying to use a
+instead of a binomial tromial tree. Yes.
+
+ align:start position:0%
+instead of a binomial tromial tree. Yes.
+ 
+
+ align:start position:0%
+instead of a binomial tromial tree. Yes.
+Uh so this statement actually is quite a
+
+ align:start position:0%
+Uh so this statement actually is quite a
+ 
+
+ align:start position:0%
+Uh so this statement actually is quite a
+universal statement. Brownian motion is
+
+ align:start position:0%
+universal statement. Brownian motion is
+ 
+
+ align:start position:0%
+universal statement. Brownian motion is
+a limit of many things not just simple
+
+ align:start position:0%
+a limit of many things not just simple
+ 
+
+ align:start position:0%
+a limit of many things not just simple
+random law. For example, if you take +
+
+ align:start position:0%
+random law. For example, if you take +
+ 
+
+ align:start position:0%
+random law. For example, if you take +
+one 0 or minus one and take it to the
+
+ align:start position:0%
+one 0 or minus one and take it to the
+ 
+
+ align:start position:0%
+one 0 or minus one and take it to the
+limit that will also converge to the
+
+ align:start position:0%
+limit that will also converge to the
+ 
+
+ align:start position:0%
+limit that will also converge to the
+simple brownian motion that will be the
+
+ align:start position:0%
+simple brownian motion that will be the
+ 
+
+ align:start position:0%
+simple brownian motion that will be the
+tromial and so on. Yeah. And as Peter
+
+ align:start position:0%
+tromial and so on. Yeah. And as Peter
+ 
+
+ align:start position:0%
+tromial and so on. Yeah. And as Peter
+said, if you're going to use tree method
+
+ align:start position:0%
+said, if you're going to use tree method
+ 
+
+ align:start position:0%
+said, if you're going to use tree method
+to compute something, that will increase
+
+ align:start position:0%
+to compute something, that will increase
+ 
+
+ align:start position:0%
+to compute something, that will increase
+accuracy if you like take more
+
+ align:start position:0%
+accuracy if you like take more
+ 
+
+ align:start position:0%
+accuracy if you like take more
+possibilities at each
+
+ align:start position:0%
+possibilities at each
+ 
+
+ align:start position:0%
+possibilities at each
+step. There's two ways to increase the
+
+ align:start position:0%
+step. There's two ways to increase the
+ 
+
+ align:start position:0%
+step. There's two ways to increase the
+increase the accuracy is take more
+
+ align:start position:0%
+increase the accuracy is take more
+ 
+
+ align:start position:0%
+increase the accuracy is take more
+possibilities at each step or take
+
+ align:start position:0%
+possibilities at each step or take
+ 
+
+ align:start position:0%
+possibilities at each step or take
+smaller time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+scales. Okay, so let's move on to the
+
+ align:start position:0%
+scales. Okay, so let's move on to the
+ 
+
+ align:start position:0%
+scales. Okay, so let's move on to the
+final topic, heat equation.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+heat equation is not a stoastic
+
+ align:start position:0%
+heat equation is not a stoastic
+ 
+
+ align:start position:0%
+heat equation is not a stoastic
+differential equation. First of
+
+ align:start position:0%
+differential equation. First of
+ 
+
+ align:start position:0%
+differential equation. First of
+all, it's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+PTE. That equation is known as a heat
+
+ align:start position:0%
+PTE. That equation is known as a heat
+ 
+
+ align:start position:0%
+PTE. That equation is known as a heat
+equation. where T is like the time
+
+ align:start position:0%
+equation. where T is like the time
+ 
+
+ align:start position:0%
+equation. where T is like the time
+variable. X is like the space variable.
+
+ align:start position:0%
+variable. X is like the space variable.
+ 
+
+ align:start position:0%
+variable. X is like the space variable.
+And the reason we're interested in in
+
+ align:start position:0%
+And the reason we're interested in in
+ 
+
+ align:start position:0%
+And the reason we're interested in in
+this heat equation in this course is if
+
+ align:start position:0%
+this heat equation in this course is if
+ 
+
+ align:start position:0%
+this heat equation in this course is if
+you came to the previous
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+lecture the maybe from vessel last
+
+ align:start position:0%
+lecture the maybe from vessel last
+ 
+
+ align:start position:0%
+lecture the maybe from vessel last
+week the brown uh what is it black shows
+
+ align:start position:0%
+week the brown uh what is it black shows
+ 
+
+ align:start position:0%
+week the brown uh what is it black shows
+equation after changing change of
+
+ align:start position:0%
+equation after changing change of
+ 
+
+ align:start position:0%
+equation after changing change of
+variables can be uh reduced to heat
+
+ align:start position:0%
+variables can be uh reduced to heat
+ 
+
+ align:start position:0%
+variables can be uh reduced to heat
+equation. Okay, that's one reason we're
+
+ align:start position:0%
+equation. Okay, that's one reason we're
+ 
+
+ align:start position:0%
+equation. Okay, that's one reason we're
+interested in it. And this is a really
+
+ align:start position:0%
+interested in it. And this is a really
+ 
+
+ align:start position:0%
+interested in it. And this is a really
+really famous equation also in physics.
+
+ align:start position:0%
+really famous equation also in physics.
+ 
+
+ align:start position:0%
+really famous equation also in physics.
+So it was known before lectur's
+
+ align:start position:0%
+So it was known before lectur's
+ 
+
+ align:start position:0%
+So it was known before lectur's
+equation particularly this will can be a
+
+ align:start position:0%
+equation particularly this will can be a
+ 
+
+ align:start position:0%
+equation particularly this will can be a
+model or equations that model this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+situation. So you have an infinite
+
+ align:start position:0%
+situation. So you have an infinite
+ 
+
+ align:start position:0%
+situation. So you have an infinite
+bar very uh long and thin. It's
+
+ align:start position:0%
+bar very uh long and thin. It's
+ 
+
+ align:start position:0%
+bar very uh long and thin. It's
+perfectly
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+insulated. So, heat can only travel uh
+
+ align:start position:0%
+insulated. So, heat can only travel uh
+ 
+
+ align:start position:0%
+insulated. So, heat can only travel uh
+along the
+
+ align:start position:0%
+along the
+ 
+
+ align:start position:0%
+along the
+x-axis. And then at time
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+z. Okay. At time
+
+ align:start position:0%
+z. Okay. At time
+ 
+
+ align:start position:0%
+z. Okay. At time
+z, you know the heat distribution.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Then this equation tells you the
+
+ align:start position:0%
+Then this equation tells you the
+ 
+
+ align:start position:0%
+Then this equation tells you the
+behavior of how the heat will be
+
+ align:start position:0%
+behavior of how the heat will be
+ 
+
+ align:start position:0%
+behavior of how the heat will be
+distributed at time t. So u of t of
+
+ align:start position:0%
+distributed at time t. So u of t of
+ 
+
+ align:start position:0%
+distributed at time t. So u of t of
+x will be for fixed t will be the
+
+ align:start position:0%
+x will be for fixed t will be the
+ 
+
+ align:start position:0%
+x will be for fixed t will be the
+distribution of the heat over the
+
+ align:start position:0%
+distribution of the heat over the
+ 
+
+ align:start position:0%
+distribution of the heat over the
+x-axis. That's why it's called the heat
+
+ align:start position:0%
+x-axis. That's why it's called the heat
+ 
+
+ align:start position:0%
+x-axis. That's why it's called the heat
+equation. That's where the name comes
+
+ align:start position:0%
+equation. That's where the name comes
+ 
+
+ align:start position:0%
+equation. That's where the name comes
+[Applause]
+
+ align:start position:0%
+[Applause]
+ 
+
+ align:start position:0%
+[Applause]
+from. And this equation is very well
+
+ align:start position:0%
+from. And this equation is very well
+ 
+
+ align:start position:0%
+from. And this equation is very well
+understood. it does have a closed forms
+
+ align:start position:0%
+understood. it does have a closed forms
+ 
+
+ align:start position:0%
+understood. it does have a closed forms
+uh closed form solution and that's what
+
+ align:start position:0%
+uh closed form solution and that's what
+ 
+
+ align:start position:0%
+uh closed form solution and that's what
+I want to talk
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+about. Okay. So a few observations
+
+ align:start position:0%
+about. Okay. So a few observations
+ 
+
+ align:start position:0%
+about. Okay. So a few observations
+before actually solving
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. Remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one. If u1 and u2 satisfies heat
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+equation then u1 plus u2 also
+
+ align:start position:0%
+equation then u1 plus u2 also
+ 
+
+ align:start position:0%
+equation then u1 plus u2 also
+satisfies also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this that's called
+
+ align:start position:0%
+this that's called
+ 
+
+ align:start position:0%
+this that's called
+linearity. Just plug it in and you can
+
+ align:start position:0%
+linearity. Just plug it in and you can
+ 
+
+ align:start position:0%
+linearity. Just plug it in and you can
+figure it out.
+
+ align:start position:0%
+figure it out.
+ 
+
+ align:start position:0%
+figure it out.
+More generally that
+
+ align:start position:0%
+More generally that
+ 
+
+ align:start position:0%
+More generally that
+means if you integrate a family of
+
+ align:start position:0%
+means if you integrate a family of
+ 
+
+ align:start position:0%
+means if you integrate a family of
+functions
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ds
+
+ align:start position:0%
+ds
+ 
+
+ align:start position:0%
+ds
+where us all
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfy
+
+ align:start position:0%
+satisfy
+ 
+
+ align:start position:0%
+satisfy
+star
+
+ align:start position:0%
+star
+ 
+
+ align:start position:0%
+star
+then
+
+ align:start position:0%
+then
+ 
+
+ align:start position:0%
+then
+this also
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+satisfies
+
+ align:start position:0%
+satisfies
+ 
+
+ align:start position:0%
+satisfies
+star okay as long as you use reasonable
+
+ align:start position:0%
+star okay as long as you use reasonable
+ 
+
+ align:start position:0%
+star okay as long as you use reasonable
+function I'll just assume that we can
+
+ align:start position:0%
+function I'll just assume that we can
+ 
+
+ align:start position:0%
+function I'll just assume that we can
+switch the order of integration and
+
+ align:start position:0%
+switch the order of integration and
+ 
+
+ align:start position:0%
+switch the order of integration and
+differentiation so it's the same thing
+
+ align:start position:0%
+differentiation so it's the same thing
+ 
+
+ align:start position:0%
+differentiation so it's the same thing
+instead of summation I'm taking
+
+ align:start position:0%
+instead of summation I'm taking
+ 
+
+ align:start position:0%
+instead of summation I'm taking
+integration of a lot of
+
+ align:start position:0%
+integration of a lot of
+ 
+
+ align:start position:0%
+integration of a lot of
+solutions
+
+ align:start position:0%
+solutions
+ 
+
+ align:start position:0%
+solutions
+okay and why is that
+
+ align:start position:0%
+okay and why is that
+ 
+
+ align:start position:0%
+okay and why is that
+helpful this is
+
+ align:start position:0%
+helpful this is
+ 
+
+ align:start position:0%
+helpful this is
+helpful because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now it suffices
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+solve
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for what is it? Initial condition
+
+ align:start position:0%
+for what is it? Initial condition
+ 
+
+ align:start position:0%
+for what is it? Initial condition
+u of t of x equals delta delta
+
+ align:start position:0%
+u of t of x equals delta delta
+ 
+
+ align:start position:0%
+u of t of x equals delta delta
+function of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero.
+
+ align:start position:0%
+zero.
+ 
+
+ align:start position:0%
+zero.
+Okay, that one is a little bit subtle.
+
+ align:start position:0%
+Okay, that one is a little bit subtle.
+ 
+
+ align:start position:0%
+Okay, that one is a little bit subtle.
+The direct delta function is just it's
+
+ align:start position:0%
+The direct delta function is just it's
+ 
+
+ align:start position:0%
+The direct delta function is just it's
+like an infinite mass at x equals z.
+
+ align:start position:0%
+like an infinite mass at x equals z.
+ 
+
+ align:start position:0%
+like an infinite mass at x equals z.
+It's zero everywhere
+
+ align:start position:0%
+It's zero everywhere
+ 
+
+ align:start position:0%
+It's zero everywhere
+else. And basically in this example,
+
+ align:start position:0%
+else. And basically in this example,
+ 
+
+ align:start position:0%
+else. And basically in this example,
+what you're saying is at time zero,
+
+ align:start position:0%
+what you're saying is at time zero,
+ 
+
+ align:start position:0%
+what you're saying is at time zero,
+you're putting like a massive amount of
+
+ align:start position:0%
+you're putting like a massive amount of
+ 
+
+ align:start position:0%
+you're putting like a massive amount of
+heat at a single point and you're
+
+ align:start position:0%
+heat at a single point and you're
+ 
+
+ align:start position:0%
+heat at a single point and you're
+observing what's going to happen
+
+ align:start position:0%
+observing what's going to happen
+ 
+
+ align:start position:0%
+observing what's going to happen
+afterwards. How this heat will spread
+
+ align:start position:0%
+afterwards. How this heat will spread
+ 
+
+ align:start position:0%
+afterwards. How this heat will spread
+out. If you understand that, you can
+
+ align:start position:0%
+out. If you understand that, you can
+ 
+
+ align:start position:0%
+out. If you understand that, you can
+understand all initial conditions. Why
+
+ align:start position:0%
+understand all initial conditions. Why
+ 
+
+ align:start position:0%
+understand all initial conditions. Why
+is that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because if u subs tx uh ux tx
+
+ align:start position:0%
+Because if u subs tx uh ux tx
+ 
+
+ align:start position:0%
+Because if u subs tx uh ux tx
+u0 is such
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then integration of let me get it right
+
+ align:start position:0%
+then integration of let me get it right
+ 
+
+ align:start position:0%
+then integration of let me get it right
+u of
+
+ align:start position:0%
+u of
+ 
+
+ align:start position:0%
+u of
+t of s -
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+T is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution with initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X. What is it?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Sorry about that. This is really the
+
+ align:start position:0%
+Sorry about that. This is really the
+ 
+
+ align:start position:0%
+Sorry about that. This is really the
+key.
+
+ align:start position:0%
+key.
+ 
+
+ align:start position:0%
+key.
+If you have a solution to the direct
+
+ align:start position:0%
+If you have a solution to the direct
+ 
+
+ align:start position:0%
+If you have a solution to the direct
+delta solution uh direct delta initial
+
+ align:start position:0%
+delta solution uh direct delta initial
+ 
+
+ align:start position:0%
+delta solution uh direct delta initial
+condition then you can superimpose a lot
+
+ align:start position:0%
+condition then you can superimpose a lot
+ 
+
+ align:start position:0%
+condition then you can superimpose a lot
+of those solutions to obtain a solution
+
+ align:start position:0%
+of those solutions to obtain a solution
+ 
+
+ align:start position:0%
+of those solutions to obtain a solution
+for an arbitrary initial
+
+ align:start position:0%
+for an arbitrary initial
+ 
+
+ align:start position:0%
+for an arbitrary initial
+condition because so this is based on
+
+ align:start position:0%
+condition because so this is based on
+ 
+
+ align:start position:0%
+condition because so this is based on
+that principle because each of them is
+
+ align:start position:0%
+that principle because each of them is
+ 
+
+ align:start position:0%
+that principle because each of them is
+now a solution. If you superose
+
+ align:start position:0%
+now a solution. If you superose
+ 
+
+ align:start position:0%
+now a solution. If you superose
+this then that is a solution and then if
+
+ align:start position:0%
+this then that is a solution and then if
+ 
+
+ align:start position:0%
+this then that is a solution and then if
+you plug it in you figure out that
+
+ align:start position:0%
+you plug it in you figure out that
+ 
+
+ align:start position:0%
+you plug it in you figure out that
+actually it has satisfies this initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+condition. That was my f as a first
+
+ align:start position:0%
+condition. That was my f as a first
+ 
+
+ align:start position:0%
+condition. That was my f as a first
+observation.
+
+ align:start position:0%
+observation.
+ 
+
+ align:start position:0%
+observation.
+Second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+observation, second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remark
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is for the initial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+value. U0x equals the direct delta
+
+ align:start position:0%
+value. U0x equals the direct delta
+ 
+
+ align:start position:0%
+value. U0x equals the direct delta
+function.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you is the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+solution is our
+
+ align:start position:0%
+solution is our
+ 
+
+ align:start position:0%
+solution is our
+solution. So we know the solution for
+
+ align:start position:0%
+solution. So we know the solution for
+ 
+
+ align:start position:0%
+solution. So we know the solution for
+the direct delta function. First part we
+
+ align:start position:0%
+the direct delta function. First part we
+ 
+
+ align:start position:0%
+the direct delta function. First part we
+figured out that if we know the solution
+
+ align:start position:0%
+figured out that if we know the solution
+ 
+
+ align:start position:0%
+figured out that if we know the solution
+for the direct delta function and we can
+
+ align:start position:0%
+for the direct delta function and we can
+ 
+
+ align:start position:0%
+for the direct delta function and we can
+solve it for every single initial value
+
+ align:start position:0%
+solve it for every single initial value
+ 
+
+ align:start position:0%
+solve it for every single initial value
+and for the initial value direct delta
+
+ align:start position:0%
+and for the initial value direct delta
+ 
+
+ align:start position:0%
+and for the initial value direct delta
+that is a distribution that's uh that is
+
+ align:start position:0%
+that is a distribution that's uh that is
+ 
+
+ align:start position:0%
+that is a distribution that's uh that is
+the solution that solves the
+
+ align:start position:0%
+the solution that solves the
+ 
+
+ align:start position:0%
+the solution that solves the
+differential equation. So let me say a
+
+ align:start position:0%
+differential equation. So let me say a
+ 
+
+ align:start position:0%
+differential equation. So let me say a
+few words about this equation. Actually
+
+ align:start position:0%
+few words about this equation. Actually
+ 
+
+ align:start position:0%
+few words about this equation. Actually
+one
+
+ align:start position:0%
+one
+ 
+
+ align:start position:0%
+one
+word. Have you seen this equation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+before? Right? It's a PDF of normal
+
+ align:start position:0%
+before? Right? It's a PDF of normal
+ 
+
+ align:start position:0%
+before? Right? It's a PDF of normal
+distribution. So what does it mean? It
+
+ align:start position:0%
+distribution. So what does it mean? It
+ 
+
+ align:start position:0%
+distribution. So what does it mean? It
+means in this example if you have a heat
+
+ align:start position:0%
+means in this example if you have a heat
+ 
+
+ align:start position:0%
+means in this example if you have a heat
+traveling along the x-axis perfectly
+
+ align:start position:0%
+traveling along the x-axis perfectly
+ 
+
+ align:start position:0%
+traveling along the x-axis perfectly
+insulated if you put a massive heat at
+
+ align:start position:0%
+insulated if you put a massive heat at
+ 
+
+ align:start position:0%
+insulated if you put a massive heat at
+this zero at one point at time zero then
+
+ align:start position:0%
+this zero at one point at time zero then
+ 
+
+ align:start position:0%
+this zero at one point at time zero then
+at time t your heat will be distributed
+
+ align:start position:0%
+at time t your heat will be distributed
+ 
+
+ align:start position:0%
+at time t your heat will be distributed
+according to the normal distribution. In
+
+ align:start position:0%
+according to the normal distribution. In
+ 
+
+ align:start position:0%
+according to the normal distribution. In
+other words, assume that you have a
+
+ align:start position:0%
+other words, assume that you have a
+ 
+
+ align:start position:0%
+other words, assume that you have a
+bunch of particle. Heat is just a bunch
+
+ align:start position:0%
+bunch of particle. Heat is just a bunch
+ 
+
+ align:start position:0%
+bunch of particle. Heat is just a bunch
+of particles. say millions of particles
+
+ align:start position:0%
+of particles. say millions of particles
+ 
+
+ align:start position:0%
+of particles. say millions of particles
+at a single
+
+ align:start position:0%
+at a single
+ 
+
+ align:start position:0%
+at a single
+point and then at time uh you grab it
+
+ align:start position:0%
+point and then at time uh you grab it
+ 
+
+ align:start position:0%
+point and then at time uh you grab it
+and then time t equals z you release
+
+ align:start position:0%
+and then time t equals z you release
+ 
+
+ align:start position:0%
+and then time t equals z you release
+them then from it's like they're
+
+ align:start position:0%
+them then from it's like they're
+ 
+
+ align:start position:0%
+them then from it's like they're
+distributed now the particle at time t
+
+ align:start position:0%
+distributed now the particle at time t
+ 
+
+ align:start position:0%
+distributed now the particle at time t
+will be distributed according to a
+
+ align:start position:0%
+will be distributed according to a
+ 
+
+ align:start position:0%
+will be distributed according to a
+normal distribution in other words each
+
+ align:start position:0%
+normal distribution in other words each
+ 
+
+ align:start position:0%
+normal distribution in other words each
+particle is like a brownian
+
+ align:start position:0%
+particle is like a brownian
+ 
+
+ align:start position:0%
+particle is like a brownian
+motion so for particle by
+
+ align:start position:0%
+motion so for particle by
+ 
+
+ align:start position:0%
+motion so for particle by
+particle the location of its particle at
+
+ align:start position:0%
+particle the location of its particle at
+ 
+
+ align:start position:0%
+particle the location of its particle at
+and t will be kind of like distributed
+
+ align:start position:0%
+and t will be kind of like distributed
+ 
+
+ align:start position:0%
+and t will be kind of like distributed
+like a brownian motion. So the overall
+
+ align:start position:0%
+like a brownian motion. So the overall
+ 
+
+ align:start position:0%
+like a brownian motion. So the overall
+if you have a massive amount of
+
+ align:start position:0%
+if you have a massive amount of
+ 
+
+ align:start position:0%
+if you have a massive amount of
+particles altogether their distribution
+
+ align:start position:0%
+particles altogether their distribution
+ 
+
+ align:start position:0%
+particles altogether their distribution
+will look like a normal distribution.
+
+ align:start position:0%
+will look like a normal distribution.
+ 
+
+ align:start position:0%
+will look like a normal distribution.
+That's like its
+
+ align:start position:0%
+That's like its
+ 
+
+ align:start position:0%
+That's like its
+content. So that's also one way you see
+
+ align:start position:0%
+content. So that's also one way you see
+ 
+
+ align:start position:0%
+content. So that's also one way you see
+the appearance of a brownian motion
+
+ align:start position:0%
+the appearance of a brownian motion
+ 
+
+ align:start position:0%
+the appearance of a brownian motion
+inside this
+
+ align:start position:0%
+inside this
+ 
+
+ align:start position:0%
+inside this
+equation. Okay, it's like a br bunch of
+
+ align:start position:0%
+equation. Okay, it's like a br bunch of
+ 
+
+ align:start position:0%
+equation. Okay, it's like a br bunch of
+brown motions and happen happening
+
+ align:start position:0%
+brown motions and happen happening
+ 
+
+ align:start position:0%
+brown motions and happen happening
+together at the exact same time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+now we can just write down the
+
+ align:start position:0%
+now we can just write down the
+ 
+
+ align:start position:0%
+now we can just write down the
+solution. Let me be a little bit more
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+precise. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for the heat equation delta u by delta
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+t with initial value
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u of 0 x equals some initial value let's
+
+ align:start position:0%
+u of 0 x equals some initial value let's
+ 
+
+ align:start position:0%
+u of 0 x equals some initial value let's
+say v of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x and t greater than equal to zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The solution
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is given
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+by integration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+u at t.x
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+X is equal
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+to
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Neess. Let me get it right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x -
+
+ align:start position:0%
+x -
+ 
+
+ align:start position:0%
+x -
+6 that's the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+same basically I'm just combining this
+
+ align:start position:0%
+same basically I'm just combining this
+ 
+
+ align:start position:0%
+same basically I'm just combining this
+solution to there plug it in that here
+
+ align:start position:0%
+solution to there plug it in that here
+ 
+
+ align:start position:0%
+solution to there plug it in that here
+you get
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have an explicit solution no
+
+ align:start position:0%
+So you have an explicit solution no
+ 
+
+ align:start position:0%
+So you have an explicit solution no
+matter what the initial conditions
+
+ align:start position:0%
+matter what the initial conditions
+ 
+
+ align:start position:0%
+matter what the initial conditions
+are. Initial conditions are given as you
+
+ align:start position:0%
+are. Initial conditions are given as you
+ 
+
+ align:start position:0%
+are. Initial conditions are given as you
+can find an explicit solution at time
+
+ align:start position:0%
+can find an explicit solution at time
+ 
+
+ align:start position:0%
+can find an explicit solution at time
+t for all
+
+ align:start position:0%
+t for all
+ 
+
+ align:start position:0%
+t for all
+x. Okay, that means once you uh change
+
+ align:start position:0%
+x. Okay, that means once you uh change
+ 
+
+ align:start position:0%
+x. Okay, that means once you uh change
+the black shells equation into the heat
+
+ align:start position:0%
+the black shells equation into the heat
+ 
+
+ align:start position:0%
+the black shells equation into the heat
+equation, you know you have you now have
+
+ align:start position:0%
+equation, you know you have you now have
+ 
+
+ align:start position:0%
+equation, you know you have you now have
+a closed form solution for
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. In that case, what will happen is
+
+ align:start position:0%
+it. In that case, what will happen is
+ 
+
+ align:start position:0%
+it. In that case, what will happen is
+like the initial it's like a backward
+
+ align:start position:0%
+like the initial it's like a backward
+ 
+
+ align:start position:0%
+like the initial it's like a backward
+heat equation and what will happen is
+
+ align:start position:0%
+heat equation and what will happen is
+ 
+
+ align:start position:0%
+heat equation and what will happen is
+the initial condition you should think
+
+ align:start position:0%
+the initial condition you should think
+ 
+
+ align:start position:0%
+the initial condition you should think
+of as is the final payout function. the
+
+ align:start position:0%
+of as is the final payout function. the
+ 
+
+ align:start position:0%
+of as is the final payout function. the
+final payout function you integrate
+
+ align:start position:0%
+final payout function you integrate
+ 
+
+ align:start position:0%
+final payout function you integrate
+according to this distribution and then
+
+ align:start position:0%
+according to this distribution and then
+ 
+
+ align:start position:0%
+according to this distribution and then
+you get the value at time t equals
+
+ align:start position:0%
+you get the value at time t equals
+ 
+
+ align:start position:0%
+you get the value at time t equals
+z
+
+ align:start position:0%
+z
+ 
+
+ align:start position:0%
+z
+okay the detail like yeah one of the
+
+ align:start position:0%
+okay the detail like yeah one of the
+ 
+
+ align:start position:0%
+okay the detail like yeah one of the
+final project is to actually carry out
+
+ align:start position:0%
+final project is to actually carry out
+ 
+
+ align:start position:0%
+final project is to actually carry out
+all the details so I will stop here
+
+ align:start position:0%
+all the details so I will stop here
+ 
+
+ align:start position:0%
+all the details so I will stop here
+anyway we didn't see how the black
+
+ align:start position:0%
+anyway we didn't see how the black
+ 
+
+ align:start position:0%
+anyway we didn't see how the black
+should equation actually changed into a
+
+ align:start position:0%
+should equation actually changed into a
+ 
+
+ align:start position:0%
+should equation actually changed into a
+heat equation so
+
+ align:start position:0%
+heat equation so
+ 
+
+ align:start position:0%
+heat equation so
+yep if you want to do that project it
+
+ align:start position:0%
+yep if you want to do that project it
+ 
+
+ align:start position:0%
+yep if you want to do that project it
+will be good to have this in and it will
+
+ align:start position:0%
+will be good to have this in and it will
+ 
+
+ align:start position:0%
+will be good to have this in and it will
+help. Any
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question? Okay. So, I think that's all I
+
+ align:start position:0%
+question? Okay. So, I think that's all I
+ 
+
+ align:start position:0%
+question? Okay. So, I think that's all I
+have. I think I'll end a little bit
+
+ align:start position:0%
+have. I think I'll end a little bit
+ 
+
+ align:start position:0%
+have. I think I'll end a little bit
+early today. So, that will be the last
+
+ align:start position:0%
+early today. So, that will be the last
+ 
+
+ align:start position:0%
+early today. So, that will be the last
+me math lecture for the semester. From
+
+ align:start position:0%
+me math lecture for the semester. From
+ 
+
+ align:start position:0%
+me math lecture for the semester. From
+now on, you'll only have application
+
+ align:start position:0%
+now on, you'll only have application
+ 
+
+ align:start position:0%
+now on, you'll only have application
+lectures. There are great lectures
+
+ align:start position:0%
+lectures. There are great lectures
+ 
+
+ align:start position:0%
+lectures. There are great lectures
+coming
+
+ align:start position:0%
+coming
+ 
+
+ align:start position:0%
+coming
+up. I hope and I
+
+ align:start position:0%
+up. I hope and I
+ 
+
+ align:start position:0%
+up. I hope and I
+know so yeah, you should come and really
+
+ align:start position:0%
+know so yeah, you should come and really
+ 
+
+ align:start position:0%
+know so yeah, you should come and really
+enjoy. Now you've went through all this
+
+ align:start position:0%
+enjoy. Now you've went through all this
+ 
+
+ align:start position:0%
+enjoy. Now you've went through all this
+hard work. Now, now it's time to enjoy.
\ No newline at end of file
diff --git a/qg_HT3CjFI4.txt b/qg_HT3CjFI4.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1818a2cc3932d1c64db40dcaaf4e61d3dceeff04
--- /dev/null
+++ b/qg_HT3CjFI4.txt
@@ -0,0 +1,9131 @@
+align:start position:0%
+ 
+but before I I I I do that before I get
+
+ align:start position:0%
+but before I I I I do that before I get
+ 
+
+ align:start position:0%
+but before I I I I do that before I get
+into the islm model um let me spend a
+
+ align:start position:0%
+into the islm model um let me spend a
+ 
+
+ align:start position:0%
+into the islm model um let me spend a
+little time telling you what is going on
+
+ align:start position:0%
+little time telling you what is going on
+ 
+
+ align:start position:0%
+little time telling you what is going on
+uh in the US economy and
+
+ align:start position:0%
+uh in the US economy and
+ 
+
+ align:start position:0%
+uh in the US economy and
+as as this will relate to the kind of
+
+ align:start position:0%
+as as this will relate to the kind of
+ 
+
+ align:start position:0%
+as as this will relate to the kind of
+things I will discuss later in the in
+
+ align:start position:0%
+things I will discuss later in the in
+ 
+
+ align:start position:0%
+things I will discuss later in the in
+this lecture so what you see there is is
+
+ align:start position:0%
+this lecture so what you see there is is
+ 
+
+ align:start position:0%
+this lecture so what you see there is is
+the path of net worth so wealth
+
+ align:start position:0%
+the path of net worth so wealth
+ 
+
+ align:start position:0%
+the path of net worth so wealth
+essentially of households and nonprofit
+
+ align:start position:0%
+essentially of households and nonprofit
+ 
+
+ align:start position:0%
+essentially of households and nonprofit
+organizations households primarily in
+
+ align:start position:0%
+organizations households primarily in
+ 
+
+ align:start position:0%
+organizations households primarily in
+the US and what you can see is that you
+
+ align:start position:0%
+the US and what you can see is that you
+ 
+
+ align:start position:0%
+the US and what you can see is that you
+know there's a more or less steady Trend
+
+ align:start position:0%
+know there's a more or less steady Trend
+ 
+
+ align:start position:0%
+know there's a more or less steady Trend
+obviously in recessions net wealth tends
+
+ align:start position:0%
+obviously in recessions net wealth tends
+ 
+
+ align:start position:0%
+obviously in recessions net wealth tends
+to declin ER and it certainly early on
+
+ align:start position:0%
+to declin ER and it certainly early on
+ 
+
+ align:start position:0%
+to declin ER and it certainly early on
+in the covid recession it declined very
+
+ align:start position:0%
+in the covid recession it declined very
+ 
+
+ align:start position:0%
+in the covid recession it declined very
+dramatically because the price price of
+
+ align:start position:0%
+dramatically because the price price of
+ 
+
+ align:start position:0%
+dramatically because the price price of
+equity the price of houses everything
+
+ align:start position:0%
+equity the price of houses everything
+ 
+
+ align:start position:0%
+equity the price of houses everything
+decline with the initial shock but what
+
+ align:start position:0%
+decline with the initial shock but what
+ 
+
+ align:start position:0%
+decline with the initial shock but what
+you see after that is a dramatic rise in
+
+ align:start position:0%
+you see after that is a dramatic rise in
+ 
+
+ align:start position:0%
+you see after that is a dramatic rise in
+wealth in the US and all around the
+
+ align:start position:0%
+wealth in the US and all around the
+ 
+
+ align:start position:0%
+wealth in the US and all around the
+world but particularly in the US and and
+
+ align:start position:0%
+world but particularly in the US and and
+ 
+
+ align:start position:0%
+world but particularly in the US and and
+what is behind that well there are two
+
+ align:start position:0%
+what is behind that well there are two
+ 
+
+ align:start position:0%
+what is behind that well there are two
+things are behind that but the main one
+
+ align:start position:0%
+things are behind that but the main one
+ 
+
+ align:start position:0%
+things are behind that but the main one
+is asset prices you know you have
+
+ align:start position:0%
+is asset prices you know you have
+ 
+
+ align:start position:0%
+is asset prices you know you have
+massive rallies in the equity Market the
+
+ align:start position:0%
+massive rallies in the equity Market the
+ 
+
+ align:start position:0%
+massive rallies in the equity Market the
+price of houses sort of skyrocketed
+
+ align:start position:0%
+price of houses sort of skyrocketed
+ 
+
+ align:start position:0%
+price of houses sort of skyrocketed
+everywhere and so on last year 2022 was
+
+ align:start position:0%
+everywhere and so on last year 2022 was
+ 
+
+ align:start position:0%
+everywhere and so on last year 2022 was
+a bad year for for asset values the
+
+ align:start position:0%
+a bad year for for asset values the
+ 
+
+ align:start position:0%
+a bad year for for asset values the
+equity Market declined pretty sharply in
+
+ align:start position:0%
+equity Market declined pretty sharply in
+ 
+
+ align:start position:0%
+equity Market declined pretty sharply in
+the US but it's still I mean it's a
+
+ align:start position:0%
+the US but it's still I mean it's a
+ 
+
+ align:start position:0%
+the US but it's still I mean it's a
+small decline relative to the big build
+
+ align:start position:0%
+small decline relative to the big build
+ 
+
+ align:start position:0%
+small decline relative to the big build
+up on wealth
+
+ align:start position:0%
+up on wealth
+ 
+
+ align:start position:0%
+up on wealth
+now why do I do you think that in this
+
+ align:start position:0%
+now why do I do you think that in this
+ 
+
+ align:start position:0%
+now why do I do you think that in this
+course I would be talking about this at
+
+ align:start position:0%
+course I would be talking about this at
+ 
+
+ align:start position:0%
+course I would be talking about this at
+this
+
+ align:start position:0%
+this
+ 
+
+ align:start position:0%
+this
+point what happens what do remember
+
+ align:start position:0%
+point what happens what do remember
+ 
+
+ align:start position:0%
+point what happens what do remember
+we're we're in this part of the course
+
+ align:start position:0%
+we're we're in this part of the course
+ 
+
+ align:start position:0%
+we're we're in this part of the course
+we're trying to come up with a model of
+
+ align:start position:0%
+we're trying to come up with a model of
+ 
+
+ align:start position:0%
+we're trying to come up with a model of
+aggregate demand and then how aggre
+
+ align:start position:0%
+aggregate demand and then how aggre
+ 
+
+ align:start position:0%
+aggregate demand and then how aggre
+demand reacts to policy that's the name
+
+ align:start position:0%
+demand reacts to policy that's the name
+ 
+
+ align:start position:0%
+demand reacts to policy that's the name
+of the game in this part of the course
+
+ align:start position:0%
+of the game in this part of the course
+ 
+
+ align:start position:0%
+of the game in this part of the course
+so if I tell you that wealth increase a
+
+ align:start position:0%
+so if I tell you that wealth increase a
+ 
+
+ align:start position:0%
+so if I tell you that wealth increase a
+lot why do you think I'm telling you
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that aggregate demand consumers feel
+
+ align:start position:0%
+that aggregate demand consumers feel
+ 
+
+ align:start position:0%
+that aggregate demand consumers feel
+rich they will tend to consume more that
+
+ align:start position:0%
+rich they will tend to consume more that
+ 
+
+ align:start position:0%
+rich they will tend to consume more that
+will increase aggregate demand so the
+
+ align:start position:0%
+will increase aggregate demand so the
+ 
+
+ align:start position:0%
+will increase aggregate demand so the
+point I'm highlighting to here is that
+
+ align:start position:0%
+point I'm highlighting to here is that
+ 
+
+ align:start position:0%
+point I'm highlighting to here is that
+there's a big force behind increasing
+
+ align:start position:0%
+there's a big force behind increasing
+ 
+
+ align:start position:0%
+there's a big force behind increasing
+aggregate demand which is consumers feel
+
+ align:start position:0%
+aggregate demand which is consumers feel
+ 
+
+ align:start position:0%
+aggregate demand which is consumers feel
+richer by the way something similar is
+
+ align:start position:0%
+richer by the way something similar is
+ 
+
+ align:start position:0%
+richer by the way something similar is
+happening in corporations and investment
+
+ align:start position:0%
+happening in corporations and investment
+ 
+
+ align:start position:0%
+happening in corporations and investment
+is also pretty high because of that real
+
+ align:start position:0%
+is also pretty high because of that real
+ 
+
+ align:start position:0%
+is also pretty high because of that real
+investment the other source of of of of
+
+ align:start position:0%
+investment the other source of of of of
+ 
+
+ align:start position:0%
+investment the other source of of of of
+increasing wealth which is not as
+
+ align:start position:0%
+increasing wealth which is not as
+ 
+
+ align:start position:0%
+increasing wealth which is not as
+dramatic as the previous one but is very
+
+ align:start position:0%
+dramatic as the previous one but is very
+ 
+
+ align:start position:0%
+dramatic as the previous one but is very
+important especially in lower income
+
+ align:start position:0%
+important especially in lower income
+ 
+
+ align:start position:0%
+important especially in lower income
+segments of the population which tend to
+
+ align:start position:0%
+segments of the population which tend to
+ 
+
+ align:start position:0%
+segments of the population which tend to
+have a higher propensity to consume is
+
+ align:start position:0%
+have a higher propensity to consume is
+ 
+
+ align:start position:0%
+have a higher propensity to consume is
+that ER incomes did not decline a lot
+
+ align:start position:0%
+that ER incomes did not decline a lot
+ 
+
+ align:start position:0%
+that ER incomes did not decline a lot
+during during
+
+ align:start position:0%
+during during
+ 
+
+ align:start position:0%
+during during
+covid and in some cases they even
+
+ align:start position:0%
+covid and in some cases they even
+ 
+
+ align:start position:0%
+covid and in some cases they even
+increased because of the large transfers
+
+ align:start position:0%
+increased because of the large transfers
+ 
+
+ align:start position:0%
+increased because of the large transfers
+that we saw from the government to
+
+ align:start position:0%
+that we saw from the government to
+ 
+
+ align:start position:0%
+that we saw from the government to
+individual households especially lower
+
+ align:start position:0%
+individual households especially lower
+ 
+
+ align:start position:0%
+individual households especially lower
+income households and at the same time
+
+ align:start position:0%
+income households and at the same time
+ 
+
+ align:start position:0%
+income households and at the same time
+there wasn't much to spend
+
+ align:start position:0%
+there wasn't much to spend
+ 
+
+ align:start position:0%
+there wasn't much to spend
+on so that meant that the saving rate
+
+ align:start position:0%
+on so that meant that the saving rate
+ 
+
+ align:start position:0%
+on so that meant that the saving rate
+also went up a lot in the US during the
+
+ align:start position:0%
+also went up a lot in the US during the
+ 
+
+ align:start position:0%
+also went up a lot in the US during the
+covid recession okay so people save a
+
+ align:start position:0%
+covid recession okay so people save a
+ 
+
+ align:start position:0%
+covid recession okay so people save a
+lot more that's sort of the average
+
+ align:start position:0%
+lot more that's sort of the average
+ 
+
+ align:start position:0%
+lot more that's sort of the average
+saving of household saies you know this
+
+ align:start position:0%
+saving of household saies you know this
+ 
+
+ align:start position:0%
+saving of household saies you know this
+is by quarter I think no by monthly but
+
+ align:start position:0%
+is by quarter I think no by monthly but
+ 
+
+ align:start position:0%
+is by quarter I think no by monthly but
+that's what we saw in the past look at
+
+ align:start position:0%
+that's what we saw in the past look at
+ 
+
+ align:start position:0%
+that's what we saw in the past look at
+during the covid recession people save a
+
+ align:start position:0%
+during the covid recession people save a
+ 
+
+ align:start position:0%
+during the covid recession people save a
+lot
+
+ align:start position:0%
+lot
+ 
+
+ align:start position:0%
+lot
+more and what you're seeing today is
+
+ align:start position:0%
+more and what you're seeing today is
+ 
+
+ align:start position:0%
+more and what you're seeing today is
+obviously they save a lot more that's
+
+ align:start position:0%
+obviously they save a lot more that's
+ 
+
+ align:start position:0%
+obviously they save a lot more that's
+part of the increasing net we worth is
+
+ align:start position:0%
+part of the increasing net we worth is
+ 
+
+ align:start position:0%
+part of the increasing net we worth is
+is due to this it's small relative to
+
+ align:start position:0%
+is due to this it's small relative to
+ 
+
+ align:start position:0%
+is due to this it's small relative to
+the amount of wealth we saw increased
+
+ align:start position:0%
+the amount of wealth we saw increased
+ 
+
+ align:start position:0%
+the amount of wealth we saw increased
+but but this was about this excess
+
+ align:start position:0%
+but but this was about this excess
+ 
+
+ align:start position:0%
+but but this was about this excess
+saving amounted to about 2.7 2.8
+
+ align:start position:0%
+saving amounted to about 2.7 2.8
+ 
+
+ align:start position:0%
+saving amounted to about 2.7 2.8
+trillion dollar so you get a sense of
+
+ align:start position:0%
+trillion dollar so you get a sense of
+ 
+
+ align:start position:0%
+trillion dollar so you get a sense of
+the order of magnitude and what we is
+
+ align:start position:0%
+the order of magnitude and what we is
+ 
+
+ align:start position:0%
+the order of magnitude and what we is
+happening now is that people are
+
+ align:start position:0%
+happening now is that people are
+ 
+
+ align:start position:0%
+happening now is that people are
+dissaving so now people are saving less
+
+ align:start position:0%
+dissaving so now people are saving less
+ 
+
+ align:start position:0%
+dissaving so now people are saving less
+than they used to because now they have
+
+ align:start position:0%
+than they used to because now they have
+ 
+
+ align:start position:0%
+than they used to because now they have
+opportunity to spend their stuff on okay
+
+ align:start position:0%
+opportunity to spend their stuff on okay
+ 
+
+ align:start position:0%
+opportunity to spend their stuff on okay
+and so that's you see massive demand for
+
+ align:start position:0%
+and so that's you see massive demand for
+ 
+
+ align:start position:0%
+and so that's you see massive demand for
+travel massive demand for restant hotels
+
+ align:start position:0%
+travel massive demand for restant hotels
+ 
+
+ align:start position:0%
+travel massive demand for restant hotels
+and stuff like that well that's has a
+
+ align:start position:0%
+and stuff like that well that's has a
+ 
+
+ align:start position:0%
+and stuff like that well that's has a
+lot to do with people had the money to
+
+ align:start position:0%
+lot to do with people had the money to
+ 
+
+ align:start position:0%
+lot to do with people had the money to
+do it they hadn't been able to do it for
+
+ align:start position:0%
+do it they hadn't been able to do it for
+ 
+
+ align:start position:0%
+do it they hadn't been able to do it for
+a while so now they're doing a lot of
+
+ align:start position:0%
+a while so now they're doing a lot of
+ 
+
+ align:start position:0%
+a while so now they're doing a lot of
+that why would I be telling you this now
+
+ align:start position:0%
+that why would I be telling you this now
+ 
+
+ align:start position:0%
+that why would I be telling you this now
+in the course in it is part of the
+
+ align:start position:0%
+in the course in it is part of the
+ 
+
+ align:start position:0%
+in the course in it is part of the
+course for the same reason I told you
+
+ align:start position:0%
+course for the same reason I told you
+ 
+
+ align:start position:0%
+course for the same reason I told you
+that net worth went a lot I mean people
+
+ align:start position:0%
+that net worth went a lot I mean people
+ 
+
+ align:start position:0%
+that net worth went a lot I mean people
+have the savings and they're really
+
+ align:start position:0%
+have the savings and they're really
+ 
+
+ align:start position:0%
+have the savings and they're really
+willing to spend it that puts lots of
+
+ align:start position:0%
+willing to spend it that puts lots of
+ 
+
+ align:start position:0%
+willing to spend it that puts lots of
+upward pressure on our great demand
+
+ align:start position:0%
+upward pressure on our great demand
+ 
+
+ align:start position:0%
+upward pressure on our great demand
+okay these pictures capture more or less
+
+ align:start position:0%
+okay these pictures capture more or less
+ 
+
+ align:start position:0%
+okay these pictures capture more or less
+the same this is captures very much much
+
+ align:start position:0%
+the same this is captures very much much
+ 
+
+ align:start position:0%
+the same this is captures very much much
+what I said in the previous slide you
+
+ align:start position:0%
+what I said in the previous slide you
+ 
+
+ align:start position:0%
+what I said in the previous slide you
+see the personal saving rate that's the
+
+ align:start position:0%
+see the personal saving rate that's the
+ 
+
+ align:start position:0%
+see the personal saving rate that's the
+average I don't remember over oh seveny
+
+ align:start position:0%
+average I don't remember over oh seveny
+ 
+
+ align:start position:0%
+average I don't remember over oh seveny
+year average and you see what happened
+
+ align:start position:0%
+year average and you see what happened
+ 
+
+ align:start position:0%
+year average and you see what happened
+during covid big spike in the saving
+
+ align:start position:0%
+during covid big spike in the saving
+ 
+
+ align:start position:0%
+during covid big spike in the saving
+rate and now big big decline in the
+
+ align:start position:0%
+rate and now big big decline in the
+ 
+
+ align:start position:0%
+rate and now big big decline in the
+saving rate where the saving rate is
+
+ align:start position:0%
+saving rate where the saving rate is
+ 
+
+ align:start position:0%
+saving rate where the saving rate is
+much lower than what normally is and
+
+ align:start position:0%
+much lower than what normally is and
+ 
+
+ align:start position:0%
+much lower than what normally is and
+remember the saving rate is is your
+
+ align:start position:0%
+remember the saving rate is is your
+ 
+
+ align:start position:0%
+remember the saving rate is is your
+income minus your consumption so if
+
+ align:start position:0%
+income minus your consumption so if
+ 
+
+ align:start position:0%
+income minus your consumption so if
+you're saving less you're consuming more
+
+ align:start position:0%
+you're saving less you're consuming more
+ 
+
+ align:start position:0%
+you're saving less you're consuming more
+relative to your income no that's that's
+
+ align:start position:0%
+relative to your income no that's that's
+ 
+
+ align:start position:0%
+relative to your income no that's that's
+the way it
+
+ align:start position:0%
+the way it
+ 
+
+ align:start position:0%
+the way it
+works obviously there's lots of
+
+ align:start position:0%
+works obviously there's lots of
+ 
+
+ align:start position:0%
+works obviously there's lots of
+heterogeneity some people made a lot of
+
+ align:start position:0%
+heterogeneity some people made a lot of
+ 
+
+ align:start position:0%
+heterogeneity some people made a lot of
+money some people didn't make a lot of
+
+ align:start position:0%
+money some people didn't make a lot of
+ 
+
+ align:start position:0%
+money some people didn't make a lot of
+money during covid H some people Save A
+
+ align:start position:0%
+money during covid H some people Save A
+ 
+
+ align:start position:0%
+money during covid H some people Save A
+Lot some people didn't save a lot and
+
+ align:start position:0%
+Lot some people didn't save a lot and
+ 
+
+ align:start position:0%
+Lot some people didn't save a lot and
+and and and in fact we do know that that
+
+ align:start position:0%
+and and and in fact we do know that that
+ 
+
+ align:start position:0%
+and and and in fact we do know that that
+sort of on the lower income segments a
+
+ align:start position:0%
+sort of on the lower income segments a
+ 
+
+ align:start position:0%
+sort of on the lower income segments a
+lot of the excess saving is already gone
+
+ align:start position:0%
+lot of the excess saving is already gone
+ 
+
+ align:start position:0%
+lot of the excess saving is already gone
+I mean accumulated early on but they
+
+ align:start position:0%
+I mean accumulated early on but they
+ 
+
+ align:start position:0%
+I mean accumulated early on but they
+spent it also much
+
+ align:start position:0%
+spent it also much
+ 
+
+ align:start position:0%
+spent it also much
+earlier um so but what you're beginning
+
+ align:start position:0%
+earlier um so but what you're beginning
+ 
+
+ align:start position:0%
+earlier um so but what you're beginning
+to see in some of those segments is even
+
+ align:start position:0%
+to see in some of those segments is even
+ 
+
+ align:start position:0%
+to see in some of those segments is even
+though the don't have excess savings
+
+ align:start position:0%
+though the don't have excess savings
+ 
+
+ align:start position:0%
+though the don't have excess savings
+they're borrowing a lot so now you see
+
+ align:start position:0%
+they're borrowing a lot so now you see
+ 
+
+ align:start position:0%
+they're borrowing a lot so now you see
+credit card borrowing which had declined
+
+ align:start position:0%
+credit card borrowing which had declined
+ 
+
+ align:start position:0%
+credit card borrowing which had declined
+a lot and now has increased quite a bit
+
+ align:start position:0%
+a lot and now has increased quite a bit
+ 
+
+ align:start position:0%
+a lot and now has increased quite a bit
+and again what do you borrow for well
+
+ align:start position:0%
+and again what do you borrow for well
+ 
+
+ align:start position:0%
+and again what do you borrow for well
+for consumption so that also
+
+ align:start position:0%
+for consumption so that also
+ 
+
+ align:start position:0%
+for consumption so that also
+funds additional consumption so for all
+
+ align:start position:0%
+funds additional consumption so for all
+ 
+
+ align:start position:0%
+funds additional consumption so for all
+these reasons in this Mo at this moment
+
+ align:start position:0%
+these reasons in this Mo at this moment
+ 
+
+ align:start position:0%
+these reasons in this Mo at this moment
+the US economy and many economies around
+
+ align:start position:0%
+the US economy and many economies around
+ 
+
+ align:start position:0%
+the US economy and many economies around
+the world are so what we call
+
+ align:start position:0%
+the world are so what we call
+ 
+
+ align:start position:0%
+the world are so what we call
+overheating there a lot of demand for
+
+ align:start position:0%
+overheating there a lot of demand for
+ 
+
+ align:start position:0%
+overheating there a lot of demand for
+the for the production that capacity of
+
+ align:start position:0%
+the for the production that capacity of
+ 
+
+ align:start position:0%
+the for the production that capacity of
+the economy and that translates the the
+
+ align:start position:0%
+the economy and that translates the the
+ 
+
+ align:start position:0%
+the economy and that translates the the
+problem say well what's wrong with that
+
+ align:start position:0%
+problem say well what's wrong with that
+ 
+
+ align:start position:0%
+problem say well what's wrong with that
+well the problem is something you don't
+
+ align:start position:0%
+well the problem is something you don't
+ 
+
+ align:start position:0%
+well the problem is something you don't
+understand at this part of the course
+
+ align:start position:0%
+understand at this part of the course
+ 
+
+ align:start position:0%
+understand at this part of the course
+you understand but you don't have a
+
+ align:start position:0%
+you understand but you don't have a
+ 
+
+ align:start position:0%
+you understand but you don't have a
+model for but you will have six Le six
+
+ align:start position:0%
+model for but you will have six Le six
+ 
+
+ align:start position:0%
+model for but you will have six Le six
+lectur more or less from now is that
+
+ align:start position:0%
+lectur more or less from now is that
+ 
+
+ align:start position:0%
+lectur more or less from now is that
+that leads to high inflation you don't
+
+ align:start position:0%
+that leads to high inflation you don't
+ 
+
+ align:start position:0%
+that leads to high inflation you don't
+know that but intuition tells you that
+
+ align:start position:0%
+know that but intuition tells you that
+ 
+
+ align:start position:0%
+know that but intuition tells you that
+is a lot of demand relative to supply
+
+ align:start position:0%
+is a lot of demand relative to supply
+ 
+
+ align:start position:0%
+is a lot of demand relative to supply
+well prices tend to go up this that
+
+ align:start position:0%
+well prices tend to go up this that
+ 
+
+ align:start position:0%
+well prices tend to go up this that
+happens in micro and it also happens in
+
+ align:start position:0%
+happens in micro and it also happens in
+ 
+
+ align:start position:0%
+happens in micro and it also happens in
+macro we'll learn that later but in any
+
+ align:start position:0%
+macro we'll learn that later but in any
+ 
+
+ align:start position:0%
+macro we'll learn that later but in any
+event as a result of this the US economy
+
+ align:start position:0%
+event as a result of this the US economy
+ 
+
+ align:start position:0%
+event as a result of this the US economy
+is overheating and therefore monetary
+
+ align:start position:0%
+is overheating and therefore monetary
+ 
+
+ align:start position:0%
+is overheating and therefore monetary
+policy has been very contractionary the
+
+ align:start position:0%
+policy has been very contractionary the
+ 
+
+ align:start position:0%
+policy has been very contractionary the
+FED has been tightening interest rate to
+
+ align:start position:0%
+FED has been tightening interest rate to
+ 
+
+ align:start position:0%
+FED has been tightening interest rate to
+cool down the economy so how does that
+
+ align:start position:0%
+cool down the economy so how does that
+ 
+
+ align:start position:0%
+cool down the economy so how does that
+happen well that's what the kind of
+
+ align:start position:0%
+happen well that's what the kind of
+ 
+
+ align:start position:0%
+happen well that's what the kind of
+things that we can answer with the islm
+
+ align:start position:0%
+things that we can answer with the islm
+ 
+
+ align:start position:0%
+things that we can answer with the islm
+model okay so the FED is very islm like
+
+ align:start position:0%
+model okay so the FED is very islm like
+ 
+
+ align:start position:0%
+model okay so the FED is very islm like
+I mean that's the way they think the
+
+ align:start position:0%
+I mean that's the way they think the
+ 
+
+ align:start position:0%
+I mean that's the way they think the
+model is richer they have more equations
+
+ align:start position:0%
+model is richer they have more equations
+ 
+
+ align:start position:0%
+model is richer they have more equations
+and so on but they are thinking in terms
+
+ align:start position:0%
+and so on but they are thinking in terms
+ 
+
+ align:start position:0%
+and so on but they are thinking in terms
+of the mechanism that we're about to
+
+ align:start position:0%
+of the mechanism that we're about to
+ 
+
+ align:start position:0%
+of the mechanism that we're about to
+sort of summarize in the eslm mod okay
+
+ align:start position:0%
+sort of summarize in the eslm mod okay
+ 
+
+ align:start position:0%
+sort of summarize in the eslm mod okay
+so if you have an economy that has this
+
+ align:start position:0%
+so if you have an economy that has this
+ 
+
+ align:start position:0%
+so if you have an economy that has this
+problem and you are in the Central Bank
+
+ align:start position:0%
+problem and you are in the Central Bank
+ 
+
+ align:start position:0%
+problem and you are in the Central Bank
+you need to use monetary policy well to
+
+ align:start position:0%
+you need to use monetary policy well to
+ 
+
+ align:start position:0%
+you need to use monetary policy well to
+understand how the thing works you need
+
+ align:start position:0%
+understand how the thing works you need
+ 
+
+ align:start position:0%
+understand how the thing works you need
+the eslm model that's a starting point
+
+ align:start position:0%
+the eslm model that's a starting point
+ 
+
+ align:start position:0%
+the eslm model that's a starting point
+then you can add bells and whistles but
+
+ align:start position:0%
+then you can add bells and whistles but
+ 
+
+ align:start position:0%
+then you can add bells and whistles but
+your starting point is the model we're
+
+ align:start position:0%
+your starting point is the model we're
+ 
+
+ align:start position:0%
+your starting point is the model we're
+about to see anyway so so what you see
+
+ align:start position:0%
+about to see anyway so so what you see
+ 
+
+ align:start position:0%
+about to see anyway so so what you see
+is what I was saying is that all that
+
+ align:start position:0%
+is what I was saying is that all that
+ 
+
+ align:start position:0%
+is what I was saying is that all that
+wealth all that excess saving all that
+
+ align:start position:0%
+wealth all that excess saving all that
+ 
+
+ align:start position:0%
+wealth all that excess saving all that
+pent up demand if you will led to lots
+
+ align:start position:0%
+pent up demand if you will led to lots
+ 
+
+ align:start position:0%
+pent up demand if you will led to lots
+of H led to a very an economy it's
+
+ align:start position:0%
+of H led to a very an economy it's
+ 
+
+ align:start position:0%
+of H led to a very an economy it's
+overheating and you can see here what
+
+ align:start position:0%
+overheating and you can see here what
+ 
+
+ align:start position:0%
+overheating and you can see here what
+happened I disentangle between a
+
+ align:start position:0%
+happened I disentangle between a
+ 
+
+ align:start position:0%
+happened I disentangle between a
+consumption of goods and consumption of
+
+ align:start position:0%
+consumption of goods and consumption of
+ 
+
+ align:start position:0%
+consumption of goods and consumption of
+services you consumption of servic is
+
+ align:start position:0%
+services you consumption of servic is
+ 
+
+ align:start position:0%
+services you consumption of servic is
+about two third of consumption remember
+
+ align:start position:0%
+about two third of consumption remember
+ 
+
+ align:start position:0%
+about two third of consumption remember
+we talk about that and goods is about
+
+ align:start position:0%
+we talk about that and goods is about
+ 
+
+ align:start position:0%
+we talk about that and goods is about
+one3 what happens is is in the scales
+
+ align:start position:0%
+one3 what happens is is in the scales
+ 
+
+ align:start position:0%
+one3 what happens is is in the scales
+are different noce this is for goods
+
+ align:start position:0%
+are different noce this is for goods
+ 
+
+ align:start position:0%
+are different noce this is for goods
+this that's for for services but what
+
+ align:start position:0%
+this that's for for services but what
+ 
+
+ align:start position:0%
+this that's for for services but what
+you what you see here is that you know
+
+ align:start position:0%
+you what you see here is that you know
+ 
+
+ align:start position:0%
+you what you see here is that you know
+that was the trend so consumption in
+
+ align:start position:0%
+that was the trend so consumption in
+ 
+
+ align:start position:0%
+that was the trend so consumption in
+Services was growing at a steady Pace
+
+ align:start position:0%
+Services was growing at a steady Pace
+ 
+
+ align:start position:0%
+Services was growing at a steady Pace
+then covid came and collapsed I mean you
+
+ align:start position:0%
+then covid came and collapsed I mean you
+ 
+
+ align:start position:0%
+then covid came and collapsed I mean you
+couldn't go to restaurant you couldn't
+
+ align:start position:0%
+couldn't go to restaurant you couldn't
+ 
+
+ align:start position:0%
+couldn't go to restaurant you couldn't
+travel you couldn't do anything so
+
+ align:start position:0%
+travel you couldn't do anything so
+ 
+
+ align:start position:0%
+travel you couldn't do anything so
+consumption in Services collapsed and
+
+ align:start position:0%
+consumption in Services collapsed and
+ 
+
+ align:start position:0%
+consumption in Services collapsed and
+now has been recovering and and and and
+
+ align:start position:0%
+now has been recovering and and and and
+ 
+
+ align:start position:0%
+now has been recovering and and and and
+that recovery pick up pace last year
+
+ align:start position:0%
+that recovery pick up pace last year
+ 
+
+ align:start position:0%
+that recovery pick up pace last year
+actually 2021 already pick up pace and
+
+ align:start position:0%
+actually 2021 already pick up pace and
+ 
+
+ align:start position:0%
+actually 2021 already pick up pace and
+by now we're above the trend okay so
+
+ align:start position:0%
+by now we're above the trend okay so
+ 
+
+ align:start position:0%
+by now we're above the trend okay so
+service consumption that collapsed
+
+ align:start position:0%
+service consumption that collapsed
+ 
+
+ align:start position:0%
+service consumption that collapsed
+during covid now has fully
+
+ align:start position:0%
+during covid now has fully
+ 
+
+ align:start position:0%
+during covid now has fully
+recovered while at the same time the
+
+ align:start position:0%
+recovered while at the same time the
+ 
+
+ align:start position:0%
+recovered while at the same time the
+capacity to produce in the service
+
+ align:start position:0%
+capacity to produce in the service
+ 
+
+ align:start position:0%
+capacity to produce in the service
+sector hasn't recovered equally but that
+
+ align:start position:0%
+sector hasn't recovered equally but that
+ 
+
+ align:start position:0%
+sector hasn't recovered equally but that
+and we'll get that to that after quiz
+
+ align:start position:0%
+and we'll get that to that after quiz
+ 
+
+ align:start position:0%
+and we'll get that to that after quiz
+one what happens to Goods consumption
+
+ align:start position:0%
+one what happens to Goods consumption
+ 
+
+ align:start position:0%
+one what happens to Goods consumption
+well also initially collaps but then
+
+ align:start position:0%
+well also initially collaps but then
+ 
+
+ align:start position:0%
+well also initially collaps but then
+well you know people were Bor at home
+
+ align:start position:0%
+well you know people were Bor at home
+ 
+
+ align:start position:0%
+well you know people were Bor at home
+they couldn't do anything they bought
+
+ align:start position:0%
+they couldn't do anything they bought
+ 
+
+ align:start position:0%
+they couldn't do anything they bought
+lots of gadgets and and stuff like that
+
+ align:start position:0%
+lots of gadgets and and stuff like that
+ 
+
+ align:start position:0%
+lots of gadgets and and stuff like that
+so Goods consumption went up very
+
+ align:start position:0%
+so Goods consumption went up very
+ 
+
+ align:start position:0%
+so Goods consumption went up very
+sharply during covid way above the trend
+
+ align:start position:0%
+sharply during covid way above the trend
+ 
+
+ align:start position:0%
+sharply during covid way above the trend
+you see there's covid collapse and then
+
+ align:start position:0%
+you see there's covid collapse and then
+ 
+
+ align:start position:0%
+you see there's covid collapse and then
+people began to buy all sort of gadgets
+
+ align:start position:0%
+people began to buy all sort of gadgets
+ 
+
+ align:start position:0%
+people began to buy all sort of gadgets
+okay and so now it's slowing down but
+
+ align:start position:0%
+okay and so now it's slowing down but
+ 
+
+ align:start position:0%
+okay and so now it's slowing down but
+still if you look rela to Trend
+
+ align:start position:0%
+still if you look rela to Trend
+ 
+
+ align:start position:0%
+still if you look rela to Trend
+consumption of goods is way above what
+
+ align:start position:0%
+consumption of goods is way above what
+ 
+
+ align:start position:0%
+consumption of goods is way above what
+would have been in the absence of this
+
+ align:start position:0%
+would have been in the absence of this
+ 
+
+ align:start position:0%
+would have been in the absence of this
+episode so the sum of the two things
+
+ align:start position:0%
+episode so the sum of the two things
+ 
+
+ align:start position:0%
+episode so the sum of the two things
+tells you that you have an economy with
+
+ align:start position:0%
+tells you that you have an economy with
+ 
+
+ align:start position:0%
+tells you that you have an economy with
+a lot of consumption and that and that
+
+ align:start position:0%
+a lot of consumption and that and that
+ 
+
+ align:start position:0%
+a lot of consumption and that and that
+at this moment the FED wants to cool
+
+ align:start position:0%
+at this moment the FED wants to cool
+ 
+
+ align:start position:0%
+at this moment the FED wants to cool
+down okay it's too much for the economy
+
+ align:start position:0%
+down okay it's too much for the economy
+ 
+
+ align:start position:0%
+down okay it's too much for the economy
+to take so the FED wants to cool it down
+
+ align:start position:0%
+to take so the FED wants to cool it down
+ 
+
+ align:start position:0%
+to take so the FED wants to cool it down
+and and we're going to see how how you
+
+ align:start position:0%
+and and we're going to see how how you
+ 
+
+ align:start position:0%
+and and we're going to see how how you
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+that okay so now let's get into into
+
+ align:start position:0%
+that okay so now let's get into into
+ 
+
+ align:start position:0%
+that okay so now let's get into into
+this set of lectures and please please
+
+ align:start position:0%
+this set of lectures and please please
+ 
+
+ align:start position:0%
+this set of lectures and please please
+stop if there's anything that is unclear
+
+ align:start position:0%
+stop if there's anything that is unclear
+ 
+
+ align:start position:0%
+stop if there's anything that is unclear
+because as I said this is probably if IA
+
+ align:start position:0%
+because as I said this is probably if IA
+ 
+
+ align:start position:0%
+because as I said this is probably if IA
+of the summer you have forgotten
+
+ align:start position:0%
+of the summer you have forgotten
+ 
+
+ align:start position:0%
+of the summer you have forgotten
+everything you have learned this course
+
+ align:start position:0%
+everything you have learned this course
+ 
+
+ align:start position:0%
+everything you have learned this course
+but you remember these two lectures well
+
+ align:start position:0%
+but you remember these two lectures well
+ 
+
+ align:start position:0%
+but you remember these two lectures well
+I'll be happy okay so so stop it if you
+
+ align:start position:0%
+I'll be happy okay so so stop it if you
+ 
+
+ align:start position:0%
+I'll be happy okay so so stop it if you
+do in fact I I normally I I I have
+
+ align:start position:0%
+do in fact I I normally I I I have
+ 
+
+ align:start position:0%
+do in fact I I normally I I I have
+taught this lecture in one I I decided
+
+ align:start position:0%
+taught this lecture in one I I decided
+ 
+
+ align:start position:0%
+taught this lecture in one I I decided
+to try to slow it down as much as I can
+
+ align:start position:0%
+to try to slow it down as much as I can
+ 
+
+ align:start position:0%
+to try to slow it down as much as I can
+because again I think it's particularly
+
+ align:start position:0%
+because again I think it's particularly
+ 
+
+ align:start position:0%
+because again I think it's particularly
+important for this course and for your
+
+ align:start position:0%
+important for this course and for your
+ 
+
+ align:start position:0%
+important for this course and for your
+stock of knowledge
+
+ align:start position:0%
+stock of knowledge
+ 
+
+ align:start position:0%
+stock of knowledge
+so so one of the thing the main things
+
+ align:start position:0%
+so so one of the thing the main things
+ 
+
+ align:start position:0%
+so so one of the thing the main things
+we're going to be able to do with this
+
+ align:start position:0%
+we're going to be able to do with this
+ 
+
+ align:start position:0%
+we're going to be able to do with this
+small been saying is we're going to be
+
+ align:start position:0%
+small been saying is we're going to be
+ 
+
+ align:start position:0%
+small been saying is we're going to be
+able to discuss the main macroeconomic
+
+ align:start position:0%
+able to discuss the main macroeconomic
+ 
+
+ align:start position:0%
+able to discuss the main macroeconomic
+policy tools which are monetary policy
+
+ align:start position:0%
+policy tools which are monetary policy
+ 
+
+ align:start position:0%
+policy tools which are monetary policy
+monetary policies is the main antic
+
+ align:start position:0%
+monetary policies is the main antic
+ 
+
+ align:start position:0%
+monetary policies is the main antic
+cyclical pool tool but we're also going
+
+ align:start position:0%
+cyclical pool tool but we're also going
+ 
+
+ align:start position:0%
+cyclical pool tool but we're also going
+to be able to understand fiscal policy
+
+ align:start position:0%
+to be able to understand fiscal policy
+ 
+
+ align:start position:0%
+to be able to understand fiscal policy
+and fiscal policy is not exactly
+
+ align:start position:0%
+and fiscal policy is not exactly
+ 
+
+ align:start position:0%
+and fiscal policy is not exactly
+equivalent to monetary policy it works
+
+ align:start position:0%
+equivalent to monetary policy it works
+ 
+
+ align:start position:0%
+equivalent to monetary policy it works
+through different mechanisms allows you
+
+ align:start position:0%
+through different mechanisms allows you
+ 
+
+ align:start position:0%
+through different mechanisms allows you
+to do things that are more targeted
+
+ align:start position:0%
+to do things that are more targeted
+ 
+
+ align:start position:0%
+to do things that are more targeted
+transfer resources to a specific group
+
+ align:start position:0%
+transfer resources to a specific group
+ 
+
+ align:start position:0%
+transfer resources to a specific group
+of people and so on ER and sometimes
+
+ align:start position:0%
+of people and so on ER and sometimes
+ 
+
+ align:start position:0%
+of people and so on ER and sometimes
+monetary policy is just not enough and
+
+ align:start position:0%
+monetary policy is just not enough and
+ 
+
+ align:start position:0%
+monetary policy is just not enough and
+the covid-19 initial recession was
+
+ align:start position:0%
+the covid-19 initial recession was
+ 
+
+ align:start position:0%
+the covid-19 initial recession was
+clearly a case of that and you had to go
+
+ align:start position:0%
+clearly a case of that and you had to go
+ 
+
+ align:start position:0%
+clearly a case of that and you had to go
+all in and and and we'll see what what
+
+ align:start position:0%
+all in and and and we'll see what what
+ 
+
+ align:start position:0%
+all in and and and we'll see what what
+what we did there it was pretty dramatic
+
+ align:start position:0%
+what we did there it was pretty dramatic
+ 
+
+ align:start position:0%
+what we did there it was pretty dramatic
+as an intervention I think that's the
+
+ align:start position:0%
+as an intervention I think that's the
+ 
+
+ align:start position:0%
+as an intervention I think that's the
+covid-19 recession LED probably to what
+
+ align:start position:0%
+covid-19 recession LED probably to what
+ 
+
+ align:start position:0%
+covid-19 recession LED probably to what
+no not probably surely to the largest
+
+ align:start position:0%
+no not probably surely to the largest
+ 
+
+ align:start position:0%
+no not probably surely to the largest
+combined packaging history of policy
+
+ align:start position:0%
+combined packaging history of policy
+ 
+
+ align:start position:0%
+combined packaging history of policy
+support okay in terms of monetary policy
+
+ align:start position:0%
+support okay in terms of monetary policy
+ 
+
+ align:start position:0%
+support okay in terms of monetary policy
+and uh and fiscal
+
+ align:start position:0%
+and uh and fiscal
+ 
+
+ align:start position:0%
+and uh and fiscal
+policy
+
+ align:start position:0%
+policy
+ 
+
+ align:start position:0%
+policy
+so so that's what so what we're want to
+
+ align:start position:0%
+so so that's what so what we're want to
+ 
+
+ align:start position:0%
+so so that's what so what we're want to
+so we're going to after these two
+
+ align:start position:0%
+so we're going to after these two
+ 
+
+ align:start position:0%
+so we're going to after these two
+lectures you're going to get to
+
+ align:start position:0%
+lectures you're going to get to
+ 
+
+ align:start position:0%
+lectures you're going to get to
+understand essentially uh The Joint
+
+ align:start position:0%
+understand essentially uh The Joint
+ 
+
+ align:start position:0%
+understand essentially uh The Joint
+determination of output and interest
+
+ align:start position:0%
+determination of output and interest
+ 
+
+ align:start position:0%
+determination of output and interest
+rate H and we're going to be able to
+
+ align:start position:0%
+rate H and we're going to be able to
+ 
+
+ align:start position:0%
+rate H and we're going to be able to
+study as I said before the impact of
+
+ align:start position:0%
+study as I said before the impact of
+ 
+
+ align:start position:0%
+study as I said before the impact of
+monetary and fiscal policy and this
+
+ align:start position:0%
+monetary and fiscal policy and this
+ 
+
+ align:start position:0%
+monetary and fiscal policy and this
+framework that we're going to use to
+
+ align:start position:0%
+framework that we're going to use to
+ 
+
+ align:start position:0%
+framework that we're going to use to
+develop to to study this is what hick
+
+ align:start position:0%
+develop to to study this is what hick
+ 
+
+ align:start position:0%
+develop to to study this is what hick
+and Hansen initially called the
+
+ align:start position:0%
+and Hansen initially called the
+ 
+
+ align:start position:0%
+and Hansen initially called the
+islm
+
+ align:start position:0%
+islm
+ 
+
+ align:start position:0%
+islm
+model I already sort of hinted that that
+
+ align:start position:0%
+model I already sort of hinted that that
+ 
+
+ align:start position:0%
+model I already sort of hinted that that
+this was coming but why do you think the
+
+ align:start position:0%
+this was coming but why do you think the
+ 
+
+ align:start position:0%
+this was coming but why do you think the
+name
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I not the that I separate that is se you
+
+ align:start position:0%
+I not the that I separate that is se you
+ 
+
+ align:start position:0%
+I not the that I separate that is se you
+will separate is from LM remember what
+
+ align:start position:0%
+will separate is from LM remember what
+ 
+
+ align:start position:0%
+will separate is from LM remember what
+we're trying to do here we're trying to
+
+ align:start position:0%
+we're trying to do here we're trying to
+ 
+
+ align:start position:0%
+we're trying to do here we're trying to
+look at the Joint determination of
+
+ align:start position:0%
+look at the Joint determination of
+ 
+
+ align:start position:0%
+look at the Joint determination of
+output and interest rate that is we're
+
+ align:start position:0%
+output and interest rate that is we're
+ 
+
+ align:start position:0%
+output and interest rate that is we're
+trying to determine at at the Joint
+
+ align:start position:0%
+trying to determine at at the Joint
+ 
+
+ align:start position:0%
+trying to determine at at the Joint
+equilibrium of goods markets and
+
+ align:start position:0%
+equilibrium of goods markets and
+ 
+
+ align:start position:0%
+equilibrium of goods markets and
+financial
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+markets when we describe the equilibrium
+
+ align:start position:0%
+markets when we describe the equilibrium
+ 
+
+ align:start position:0%
+markets when we describe the equilibrium
+in the goods Market we said there is an
+
+ align:start position:0%
+in the goods Market we said there is an
+ 
+
+ align:start position:0%
+in the goods Market we said there is an
+alternative way of describing remember I
+
+ align:start position:0%
+alternative way of describing remember I
+ 
+
+ align:start position:0%
+alternative way of describing remember I
+said it as investment equal to savings I
+
+ align:start position:0%
+said it as investment equal to savings I
+ 
+
+ align:start position:0%
+said it as investment equal to savings I
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+S okay so the is part of the name comes
+
+ align:start position:0%
+S okay so the is part of the name comes
+ 
+
+ align:start position:0%
+S okay so the is part of the name comes
+from the part that has to do with
+
+ align:start position:0%
+from the part that has to do with
+ 
+
+ align:start position:0%
+from the part that has to do with
+equilibrium in the Goods Market is
+
+ align:start position:0%
+equilibrium in the Goods Market is
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market is
+investment equal to savings and the LM
+
+ align:start position:0%
+investment equal to savings and the LM
+ 
+
+ align:start position:0%
+investment equal to savings and the LM
+part has to do remember L was that
+
+ align:start position:0%
+part has to do remember L was that
+ 
+
+ align:start position:0%
+part has to do remember L was that
+component of aggregate demand we we had
+
+ align:start position:0%
+component of aggregate demand we we had
+ 
+
+ align:start position:0%
+component of aggregate demand we we had
+in the financial markets we look at
+
+ align:start position:0%
+in the financial markets we look at
+ 
+
+ align:start position:0%
+in the financial markets we look at
+equilibrium as aggregate demand demand
+
+ align:start position:0%
+equilibrium as aggregate demand demand
+ 
+
+ align:start position:0%
+equilibrium as aggregate demand demand
+for money equal to supply of money
+
+ align:start position:0%
+for money equal to supply of money
+ 
+
+ align:start position:0%
+for money equal to supply of money
+supply of money was M demand for money
+
+ align:start position:0%
+supply of money was M demand for money
+ 
+
+ align:start position:0%
+supply of money was M demand for money
+was y * L of I and there therefore the
+
+ align:start position:0%
+was y * L of I and there therefore the
+ 
+
+ align:start position:0%
+was y * L of I and there therefore the
+LM part okay that's the reason that's a
+
+ align:start position:0%
+LM part okay that's the reason that's a
+ 
+
+ align:start position:0%
+LM part okay that's the reason that's a
+nemonic for why this model is called the
+
+ align:start position:0%
+nemonic for why this model is called the
+ 
+
+ align:start position:0%
+nemonic for why this model is called the
+is LM the is stands for the part that
+
+ align:start position:0%
+is LM the is stands for the part that
+ 
+
+ align:start position:0%
+is LM the is stands for the part that
+has to do with equilibrium in the Goods
+
+ align:start position:0%
+has to do with equilibrium in the Goods
+ 
+
+ align:start position:0%
+has to do with equilibrium in the Goods
+Market the L has to do with the part has
+
+ align:start position:0%
+Market the L has to do with the part has
+ 
+
+ align:start position:0%
+Market the L has to do with the part has
+to do with equilibrium Financial Market
+
+ align:start position:0%
+to do with equilibrium Financial Market
+ 
+
+ align:start position:0%
+to do with equilibrium Financial Market
+this model is a model that combines
+
+ align:start position:0%
+this model is a model that combines
+ 
+
+ align:start position:0%
+this model is a model that combines
+those two equilibrium okay so we're
+
+ align:start position:0%
+those two equilibrium okay so we're
+ 
+
+ align:start position:0%
+those two equilibrium okay so we're
+going to be interest interesting points
+
+ align:start position:0%
+going to be interest interesting points
+ 
+
+ align:start position:0%
+going to be interest interesting points
+in which both markets are in equilibrium
+
+ align:start position:0%
+in which both markets are in equilibrium
+ 
+
+ align:start position:0%
+in which both markets are in equilibrium
+that's the name of the game
+
+ align:start position:0%
+that's the name of the game
+ 
+
+ align:start position:0%
+that's the name of the game
+here so let's first develop the is
+
+ align:start position:0%
+here so let's first develop the is
+ 
+
+ align:start position:0%
+here so let's first develop the is
+relation and the yes relation is really
+
+ align:start position:0%
+relation and the yes relation is really
+ 
+
+ align:start position:0%
+relation and the yes relation is really
+going back to lecture three we're going
+
+ align:start position:0%
+going back to lecture three we're going
+ 
+
+ align:start position:0%
+going back to lecture three we're going
+to go back to lecture three use the same
+
+ align:start position:0%
+to go back to lecture three use the same
+ 
+
+ align:start position:0%
+to go back to lecture three use the same
+model we use in lecture three with one
+
+ align:start position:0%
+model we use in lecture three with one
+ 
+
+ align:start position:0%
+model we use in lecture three with one
+change and that change is a remember in
+
+ align:start position:0%
+change and that change is a remember in
+ 
+
+ align:start position:0%
+change and that change is a remember in
+in in lecture three we work a lot on a
+
+ align:start position:0%
+in in lecture three we work a lot on a
+ 
+
+ align:start position:0%
+in in lecture three we work a lot on a
+consumption the only endogenous the only
+
+ align:start position:0%
+consumption the only endogenous the only
+ 
+
+ align:start position:0%
+consumption the only endogenous the only
+function we had was a consumption
+
+ align:start position:0%
+function we had was a consumption
+ 
+
+ align:start position:0%
+function we had was a consumption
+function remember remember and then all
+
+ align:start position:0%
+function remember remember and then all
+ 
+
+ align:start position:0%
+function remember remember and then all
+the rest we took as sort of given
+
+ align:start position:0%
+the rest we took as sort of given
+ 
+
+ align:start position:0%
+the rest we took as sort of given
+government expenditure was given
+
+ align:start position:0%
+government expenditure was given
+ 
+
+ align:start position:0%
+government expenditure was given
+investment was given all that was given
+
+ align:start position:0%
+investment was given all that was given
+ 
+
+ align:start position:0%
+investment was given all that was given
+well we're going to relax one of those
+
+ align:start position:0%
+well we're going to relax one of those
+ 
+
+ align:start position:0%
+well we're going to relax one of those
+here and we're going to we're going to
+
+ align:start position:0%
+here and we're going to we're going to
+ 
+
+ align:start position:0%
+here and we're going to we're going to
+flesh out a little more of this
+
+ align:start position:0%
+flesh out a little more of this
+ 
+
+ align:start position:0%
+flesh out a little more of this
+investment here make get make it closer
+
+ align:start position:0%
+investment here make get make it closer
+ 
+
+ align:start position:0%
+investment here make get make it closer
+to what what a a realistic function it's
+
+ align:start position:0%
+to what what a a realistic function it's
+ 
+
+ align:start position:0%
+to what what a a realistic function it's
+not a constant obviously it's not to
+
+ align:start position:0%
+not a constant obviously it's not to
+ 
+
+ align:start position:0%
+not a constant obviously it's not to
+exogenous to equilibrium output and so
+
+ align:start position:0%
+exogenous to equilibrium output and so
+ 
+
+ align:start position:0%
+exogenous to equilibrium output and so
+on in fact we do know that real
+
+ align:start position:0%
+on in fact we do know that real
+ 
+
+ align:start position:0%
+on in fact we do know that real
+investment this is physical investment
+
+ align:start position:0%
+investment this is physical investment
+ 
+
+ align:start position:0%
+investment this is physical investment
+remember this is what is this ey is
+
+ align:start position:0%
+remember this is what is this ey is
+ 
+
+ align:start position:0%
+remember this is what is this ey is
+investment this is purchase of goods and
+
+ align:start position:0%
+investment this is purchase of goods and
+ 
+
+ align:start position:0%
+investment this is purchase of goods and
+services by firms for the purpose of
+
+ align:start position:0%
+services by firms for the purpose of
+ 
+
+ align:start position:0%
+services by firms for the purpose of
+building Capital Equipment structures
+
+ align:start position:0%
+building Capital Equipment structures
+ 
+
+ align:start position:0%
+building Capital Equipment structures
+and stuff like that I saw in PIAA very
+
+ align:start position:0%
+and stuff like that I saw in PIAA very
+ 
+
+ align:start position:0%
+and stuff like that I saw in PIAA very
+quickly I'm not into that but I see more
+
+ align:start position:0%
+quickly I'm not into that but I see more
+ 
+
+ align:start position:0%
+quickly I'm not into that but I see more
+or less the
+
+ align:start position:0%
+or less the
+ 
+
+ align:start position:0%
+or less the
+flow that somebody asked should bonds be
+
+ align:start position:0%
+flow that somebody asked should bonds be
+ 
+
+ align:start position:0%
+flow that somebody asked should bonds be
+included in
+
+ align:start position:0%
+included in
+ 
+
+ align:start position:0%
+included in
+investment what is the
+
+ align:start position:0%
+investment what is the
+ 
+
+ align:start position:0%
+investment what is the
+answer in that investment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I should purchase of bonds be included
+
+ align:start position:0%
+I should purchase of bonds be included
+ 
+
+ align:start position:0%
+I should purchase of bonds be included
+in that investment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no this is purchase of goods and
+
+ align:start position:0%
+no this is purchase of goods and
+ 
+
+ align:start position:0%
+no this is purchase of goods and
+services by firms no Capital machines
+
+ align:start position:0%
+services by firms no Capital machines
+ 
+
+ align:start position:0%
+services by firms no Capital machines
+stuff like that the other thing is a
+
+ align:start position:0%
+stuff like that the other thing is a
+ 
+
+ align:start position:0%
+stuff like that the other thing is a
+financial investment it's nothing to do
+
+ align:start position:0%
+financial investment it's nothing to do
+ 
+
+ align:start position:0%
+financial investment it's nothing to do
+with the Goods Market something that has
+
+ align:start position:0%
+with the Goods Market something that has
+ 
+
+ align:start position:0%
+with the Goods Market something that has
+to do with the financial Market not with
+
+ align:start position:0%
+to do with the financial Market not with
+ 
+
+ align:start position:0%
+to do with the financial Market not with
+a Goods Market a so that investment is
+
+ align:start position:0%
+a Goods Market a so that investment is
+ 
+
+ align:start position:0%
+a Goods Market a so that investment is
+real investment again purchase of
+
+ align:start position:0%
+real investment again purchase of
+ 
+
+ align:start position:0%
+real investment again purchase of
+capital buildings for the purpose of
+
+ align:start position:0%
+capital buildings for the purpose of
+ 
+
+ align:start position:0%
+capital buildings for the purpose of
+production and stuff like
+
+ align:start position:0%
+production and stuff like
+ 
+
+ align:start position:0%
+production and stuff like
+that okay and and this this in
+
+ align:start position:0%
+that okay and and this this in
+ 
+
+ align:start position:0%
+that okay and and this this in
+investment is is is a function of two
+
+ align:start position:0%
+investment is is is a function of two
+ 
+
+ align:start position:0%
+investment is is is a function of two
+things at least the first one is
+
+ align:start position:0%
+things at least the first one is
+ 
+
+ align:start position:0%
+things at least the first one is
+activity when output is high sales are
+
+ align:start position:0%
+activity when output is high sales are
+ 
+
+ align:start position:0%
+activity when output is high sales are
+high companies tend to invest more they
+
+ align:start position:0%
+high companies tend to invest more they
+ 
+
+ align:start position:0%
+high companies tend to invest more they
+buy more equipment they buy more
+
+ align:start position:0%
+buy more equipment they buy more
+ 
+
+ align:start position:0%
+buy more equipment they buy more
+buildings they expand okay so investment
+
+ align:start position:0%
+buildings they expand okay so investment
+ 
+
+ align:start position:0%
+buildings they expand okay so investment
+is an increasing function of output very
+
+ align:start position:0%
+is an increasing function of output very
+ 
+
+ align:start position:0%
+is an increasing function of output very
+much like consumption remember was an
+
+ align:start position:0%
+much like consumption remember was an
+ 
+
+ align:start position:0%
+much like consumption remember was an
+increasing function of output because
+
+ align:start position:0%
+increasing function of output because
+ 
+
+ align:start position:0%
+increasing function of output because
+income is increasing in output so was an
+
+ align:start position:0%
+income is increasing in output so was an
+ 
+
+ align:start position:0%
+income is increasing in output so was an
+increasing function out so this we
+
+ align:start position:0%
+increasing function out so this we
+ 
+
+ align:start position:0%
+increasing function out so this we
+already had SE functions that look like
+
+ align:start position:0%
+already had SE functions that look like
+ 
+
+ align:start position:0%
+already had SE functions that look like
+that and we already know what it does to
+
+ align:start position:0%
+that and we already know what it does to
+ 
+
+ align:start position:0%
+that and we already know what it does to
+aggregate demand no it makes that curve
+
+ align:start position:0%
+aggregate demand no it makes that curve
+ 
+
+ align:start position:0%
+aggregate demand no it makes that curve
+steeper remember and if the multiplier
+
+ align:start position:0%
+steeper remember and if the multiplier
+ 
+
+ align:start position:0%
+steeper remember and if the multiplier
+is behind that well investment gives you
+
+ align:start position:0%
+is behind that well investment gives you
+ 
+
+ align:start position:0%
+is behind that well investment gives you
+something similar there but there is a
+
+ align:start position:0%
+something similar there but there is a
+ 
+
+ align:start position:0%
+something similar there but there is a
+second component which is also present
+
+ align:start position:0%
+second component which is also present
+ 
+
+ align:start position:0%
+second component which is also present
+in consumption but it's not as important
+
+ align:start position:0%
+in consumption but it's not as important
+ 
+
+ align:start position:0%
+in consumption but it's not as important
+as if for investment which is the
+
+ align:start position:0%
+as if for investment which is the
+ 
+
+ align:start position:0%
+as if for investment which is the
+interest
+
+ align:start position:0%
+interest
+ 
+
+ align:start position:0%
+interest
+rate in particular when the interest
+
+ align:start position:0%
+rate in particular when the interest
+ 
+
+ align:start position:0%
+rate in particular when the interest
+rate goes up for any given level of
+
+ align:start position:0%
+rate goes up for any given level of
+ 
+
+ align:start position:0%
+rate goes up for any given level of
+income or output then investment goes
+
+ align:start position:0%
+income or output then investment goes
+ 
+
+ align:start position:0%
+income or output then investment goes
+down why do you think that's the case
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yes most of investment is funded with
+
+ align:start position:0%
+yes most of investment is funded with
+ 
+
+ align:start position:0%
+yes most of investment is funded with
+borrowing and borrowing becomes more
+
+ align:start position:0%
+borrowing and borrowing becomes more
+ 
+
+ align:start position:0%
+borrowing and borrowing becomes more
+expensive so so so you don't do it even
+
+ align:start position:0%
+expensive so so so you don't do it even
+ 
+
+ align:start position:0%
+expensive so so so you don't do it even
+if you don't need to borrow There's an
+
+ align:start position:0%
+if you don't need to borrow There's an
+ 
+
+ align:start position:0%
+if you don't need to borrow There's an
+opportunity cost of those funds you can
+
+ align:start position:0%
+opportunity cost of those funds you can
+ 
+
+ align:start position:0%
+opportunity cost of those funds you can
+use it to build machines to produce or
+
+ align:start position:0%
+use it to build machines to produce or
+ 
+
+ align:start position:0%
+use it to build machines to produce or
+you can do something else like like have
+
+ align:start position:0%
+you can do something else like like have
+ 
+
+ align:start position:0%
+you can do something else like like have
+an investment Financial investment so it
+
+ align:start position:0%
+an investment Financial investment so it
+ 
+
+ align:start position:0%
+an investment Financial investment so it
+whether you borrow or not still if the
+
+ align:start position:0%
+whether you borrow or not still if the
+ 
+
+ align:start position:0%
+whether you borrow or not still if the
+interest rate is
+
+ align:start position:0%
+interest rate is
+ 
+
+ align:start position:0%
+interest rate is
+higher the opportunity cost of building
+
+ align:start position:0%
+higher the opportunity cost of building
+ 
+
+ align:start position:0%
+higher the opportunity cost of building
+factories is higher High okay and and so
+
+ align:start position:0%
+factories is higher High okay and and so
+ 
+
+ align:start position:0%
+factories is higher High okay and and so
+that's a reason investment is decreasing
+
+ align:start position:0%
+that's a reason investment is decreasing
+ 
+
+ align:start position:0%
+that's a reason investment is decreasing
+with respect to the interest
+
+ align:start position:0%
+with respect to the interest
+ 
+
+ align:start position:0%
+with respect to the interest
+rate so now we go back to H our
+
+ align:start position:0%
+rate so now we go back to H our
+ 
+
+ align:start position:0%
+rate so now we go back to H our
+equilibrium in the Goods Market which we
+
+ align:start position:0%
+equilibrium in the Goods Market which we
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market which we
+said production is whatever aggregate
+
+ align:start position:0%
+said production is whatever aggregate
+ 
+
+ align:start position:0%
+said production is whatever aggregate
+demand wants so output is going to be
+
+ align:start position:0%
+demand wants so output is going to be
+ 
+
+ align:start position:0%
+demand wants so output is going to be
+equal to aggregate demand aggregate
+
+ align:start position:0%
+equal to aggregate demand aggregate
+ 
+
+ align:start position:0%
+equal to aggregate demand aggregate
+demand is the same old aggregate demand
+
+ align:start position:0%
+demand is the same old aggregate demand
+ 
+
+ align:start position:0%
+demand is the same old aggregate demand
+we had except that now we flesh out what
+
+ align:start position:0%
+we had except that now we flesh out what
+ 
+
+ align:start position:0%
+we had except that now we flesh out what
+is inside that investment function there
+
+ align:start position:0%
+is inside that investment function there
+ 
+
+ align:start position:0%
+is inside that investment function there
+which we have another function is
+
+ align:start position:0%
+which we have another function is
+ 
+
+ align:start position:0%
+which we have another function is
+increasing in output like consumption
+
+ align:start position:0%
+increasing in output like consumption
+ 
+
+ align:start position:0%
+increasing in output like consumption
+was and
+
+ align:start position:0%
+was and
+ 
+
+ align:start position:0%
+was and
+but we also have something that is
+
+ align:start position:0%
+but we also have something that is
+ 
+
+ align:start position:0%
+but we also have something that is
+decreasing in the interest rate and so
+
+ align:start position:0%
+decreasing in the interest rate and so
+ 
+
+ align:start position:0%
+decreasing in the interest rate and so
+this is what we call the is relation and
+
+ align:start position:0%
+this is what we call the is relation and
+ 
+
+ align:start position:0%
+this is what we call the is relation and
+the the is relation
+
+ align:start position:0%
+the the is relation
+ 
+
+ align:start position:0%
+the the is relation
+therefore has all the combinations of
+
+ align:start position:0%
+therefore has all the combinations of
+ 
+
+ align:start position:0%
+therefore has all the combinations of
+output and interest rate that are
+
+ align:start position:0%
+output and interest rate that are
+ 
+
+ align:start position:0%
+output and interest rate that are
+consistent with equilibrium in the Goods
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+ 
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+Market listen at what I said I said the
+
+ align:start position:0%
+Market listen at what I said I said the
+ 
+
+ align:start position:0%
+Market listen at what I said I said the
+I relation or I curve has all the
+
+ align:start position:0%
+I relation or I curve has all the
+ 
+
+ align:start position:0%
+I relation or I curve has all the
+combinations of output and interest rate
+
+ align:start position:0%
+combinations of output and interest rate
+ 
+
+ align:start position:0%
+combinations of output and interest rate
+combinations of output and interest rate
+
+ align:start position:0%
+combinations of output and interest rate
+ 
+
+ align:start position:0%
+combinations of output and interest rate
+that are consistent with equilibrium in
+
+ align:start position:0%
+that are consistent with equilibrium in
+ 
+
+ align:start position:0%
+that are consistent with equilibrium in
+the Goods
+
+ align:start position:0%
+the Goods
+ 
+
+ align:start position:0%
+the Goods
+Market what about lecture
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+three we already had that but interest
+
+ align:start position:0%
+three we already had that but interest
+ 
+
+ align:start position:0%
+three we already had that but interest
+Play No role so we found one point there
+
+ align:start position:0%
+Play No role so we found one point there
+ 
+
+ align:start position:0%
+Play No role so we found one point there
+there's one level of output which is
+
+ align:start position:0%
+there's one level of output which is
+ 
+
+ align:start position:0%
+there's one level of output which is
+consistent with equilibrium in the Goods
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+ 
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+Market that's what we found now since we
+
+ align:start position:0%
+Market that's what we found now since we
+ 
+
+ align:start position:0%
+Market that's what we found now since we
+have an interest rate there we have two
+
+ align:start position:0%
+have an interest rate there we have two
+ 
+
+ align:start position:0%
+have an interest rate there we have two
+variables for one curve so we can trace
+
+ align:start position:0%
+variables for one curve so we can trace
+ 
+
+ align:start position:0%
+variables for one curve so we can trace
+a curve which not only one
+
+ align:start position:0%
+a curve which not only one
+ 
+
+ align:start position:0%
+a curve which not only one
+point okay
+
+ align:start position:0%
+point okay
+ 
+
+ align:start position:0%
+point okay
+you can trace a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+and good and that's what we call the as
+
+ align:start position:0%
+and good and that's what we call the as
+ 
+
+ align:start position:0%
+and good and that's what we call the as
+relation
+
+ align:start position:0%
+relation
+ 
+
+ align:start position:0%
+relation
+so I remember I told you when we look at
+
+ align:start position:0%
+so I remember I told you when we look at
+ 
+
+ align:start position:0%
+so I remember I told you when we look at
+the Goods Market equ remember this
+
+ align:start position:0%
+the Goods Market equ remember this
+ 
+
+ align:start position:0%
+the Goods Market equ remember this
+diagram because you're going to come
+
+ align:start position:0%
+diagram because you're going to come
+ 
+
+ align:start position:0%
+diagram because you're going to come
+back to it many
+
+ align:start position:0%
+back to it many
+ 
+
+ align:start position:0%
+back to it many
+times there you are so remember when we
+
+ align:start position:0%
+times there you are so remember when we
+ 
+
+ align:start position:0%
+times there you are so remember when we
+look at equilibrium in the Goods Market
+
+ align:start position:0%
+look at equilibrium in the Goods Market
+ 
+
+ align:start position:0%
+look at equilibrium in the Goods Market
+we had something like that I'm I'm just
+
+ align:start position:0%
+we had something like that I'm I'm just
+ 
+
+ align:start position:0%
+we had something like that I'm I'm just
+making it curve rather than linear
+
+ align:start position:0%
+making it curve rather than linear
+ 
+
+ align:start position:0%
+making it curve rather than linear
+simply because I haven't specified the
+
+ align:start position:0%
+simply because I haven't specified the
+ 
+
+ align:start position:0%
+simply because I haven't specified the
+functional form of investment but
+
+ align:start position:0%
+functional form of investment but
+ 
+
+ align:start position:0%
+functional form of investment but
+doesn't matter really make it linear
+
+ align:start position:0%
+doesn't matter really make it linear
+ 
+
+ align:start position:0%
+doesn't matter really make it linear
+okay but remember we had that's the way
+
+ align:start position:0%
+okay but remember we had that's the way
+ 
+
+ align:start position:0%
+okay but remember we had that's the way
+we found equilibrium in the Goods Market
+
+ align:start position:0%
+we found equilibrium in the Goods Market
+ 
+
+ align:start position:0%
+we found equilibrium in the Goods Market
+we have an aggregate demand and it was
+
+ align:start position:0%
+we have an aggregate demand and it was
+ 
+
+ align:start position:0%
+we have an aggregate demand and it was
+increased the slope was positive because
+
+ align:start position:0%
+increased the slope was positive because
+ 
+
+ align:start position:0%
+increased the slope was positive because
+we had a margin of PR to consume that's
+
+ align:start position:0%
+we had a margin of PR to consume that's
+ 
+
+ align:start position:0%
+we had a margin of PR to consume that's
+the reason we had this was not flat but
+
+ align:start position:0%
+the reason we had this was not flat but
+ 
+
+ align:start position:0%
+the reason we had this was not flat but
+upward sloping no and we found
+
+ align:start position:0%
+upward sloping no and we found
+ 
+
+ align:start position:0%
+upward sloping no and we found
+equilibrium output that way okay so
+
+ align:start position:0%
+equilibrium output that way okay so
+ 
+
+ align:start position:0%
+equilibrium output that way okay so
+that's this is lecture three we're back
+
+ align:start position:0%
+that's this is lecture three we're back
+ 
+
+ align:start position:0%
+that's this is lecture three we're back
+in lecture three
+
+ align:start position:0%
+in lecture three
+ 
+
+ align:start position:0%
+in lecture three
+here with two things two differences the
+
+ align:start position:0%
+here with two things two differences the
+ 
+
+ align:start position:0%
+here with two things two differences the
+first one is that this ZZ curve relative
+
+ align:start position:0%
+first one is that this ZZ curve relative
+ 
+
+ align:start position:0%
+first one is that this ZZ curve relative
+to the one had in lecture three is a
+
+ align:start position:0%
+to the one had in lecture three is a
+ 
+
+ align:start position:0%
+to the one had in lecture three is a
+little steeper why is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that why is it a little steeper than by
+
+ align:start position:0%
+that why is it a little steeper than by
+ 
+
+ align:start position:0%
+that why is it a little steeper than by
+steeper I mean if income goes up then
+
+ align:start position:0%
+steeper I mean if income goes up then
+ 
+
+ align:start position:0%
+steeper I mean if income goes up then
+aggregate demand goes up by more than
+
+ align:start position:0%
+aggregate demand goes up by more than
+ 
+
+ align:start position:0%
+aggregate demand goes up by more than
+than it used to go
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+up exactly because what made it is
+
+ align:start position:0%
+up exactly because what made it is
+ 
+
+ align:start position:0%
+up exactly because what made it is
+upward sloping before was the margin of
+
+ align:start position:0%
+upward sloping before was the margin of
+ 
+
+ align:start position:0%
+upward sloping before was the margin of
+to consume but now there is also a
+
+ align:start position:0%
+to consume but now there is also a
+ 
+
+ align:start position:0%
+to consume but now there is also a
+margin of to invest which is also
+
+ align:start position:0%
+margin of to invest which is also
+ 
+
+ align:start position:0%
+margin of to invest which is also
+positive and that's the reason it's a
+
+ align:start position:0%
+positive and that's the reason it's a
+ 
+
+ align:start position:0%
+positive and that's the reason it's a
+little steeper more interesting for this
+
+ align:start position:0%
+little steeper more interesting for this
+ 
+
+ align:start position:0%
+little steeper more interesting for this
+part of the lecture though for the
+
+ align:start position:0%
+part of the lecture though for the
+ 
+
+ align:start position:0%
+part of the lecture though for the
+construction of the curve is that is a
+
+ align:start position:0%
+construction of the curve is that is a
+ 
+
+ align:start position:0%
+construction of the curve is that is a
+parameter that we have there in ZZ what
+
+ align:start position:0%
+parameter that we have there in ZZ what
+ 
+
+ align:start position:0%
+parameter that we have there in ZZ what
+are the parameters we had before in that
+
+ align:start position:0%
+are the parameters we had before in that
+ 
+
+ align:start position:0%
+are the parameters we had before in that
+curve we had things like going
+
+ align:start position:0%
+curve we had things like going
+ 
+
+ align:start position:0%
+curve we had things like going
+expenditure taxes the the autonomous
+
+ align:start position:0%
+expenditure taxes the the autonomous
+ 
+
+ align:start position:0%
+expenditure taxes the the autonomous
+consumption that's the kind of stuff
+
+ align:start position:0%
+consumption that's the kind of stuff
+ 
+
+ align:start position:0%
+consumption that's the kind of stuff
+that we had as parameters of that ZZ
+
+ align:start position:0%
+that we had as parameters of that ZZ
+ 
+
+ align:start position:0%
+that we had as parameters of that ZZ
+curve by parameters I mean if we change
+
+ align:start position:0%
+curve by parameters I mean if we change
+ 
+
+ align:start position:0%
+curve by parameters I mean if we change
+those parameter we shift that
+
+ align:start position:0%
+those parameter we shift that
+ 
+
+ align:start position:0%
+those parameter we shift that
+curve now for this particular ZZ we have
+
+ align:start position:0%
+curve now for this particular ZZ we have
+ 
+
+ align:start position:0%
+curve now for this particular ZZ we have
+an extra parameter which is very
+
+ align:start position:0%
+an extra parameter which is very
+ 
+
+ align:start position:0%
+an extra parameter which is very
+interesting what is that it's there I
+
+ align:start position:0%
+interesting what is that it's there I
+ 
+
+ align:start position:0%
+interesting what is that it's there I
+think it's the interest
+
+ align:start position:0%
+think it's the interest
+ 
+
+ align:start position:0%
+think it's the interest
+rate no that curve holds for some given
+
+ align:start position:0%
+rate no that curve holds for some given
+ 
+
+ align:start position:0%
+rate no that curve holds for some given
+interest
+
+ align:start position:0%
+interest
+ 
+
+ align:start position:0%
+interest
+rate if I move the interest I'm going to
+
+ align:start position:0%
+rate if I move the interest I'm going to
+ 
+
+ align:start position:0%
+rate if I move the interest I'm going to
+move this curve
+
+ align:start position:0%
+move this curve
+ 
+
+ align:start position:0%
+move this curve
+around that's very important
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+one of the parameters there the star
+
+ align:start position:0%
+one of the parameters there the star
+ 
+
+ align:start position:0%
+one of the parameters there the star
+parameter I would say for this for this
+
+ align:start position:0%
+parameter I would say for this for this
+ 
+
+ align:start position:0%
+parameter I would say for this for this
+minute of the lecture at least for this
+
+ align:start position:0%
+minute of the lecture at least for this
+ 
+
+ align:start position:0%
+minute of the lecture at least for this
+moment in the lecture is the interest
+
+ align:start position:0%
+moment in the lecture is the interest
+ 
+
+ align:start position:0%
+moment in the lecture is the interest
+rate I can find an equilibrium because I
+
+ align:start position:0%
+rate I can find an equilibrium because I
+ 
+
+ align:start position:0%
+rate I can find an equilibrium because I
+couldn't find an equilibrium in the
+
+ align:start position:0%
+couldn't find an equilibrium in the
+ 
+
+ align:start position:0%
+couldn't find an equilibrium in the
+Goods Market if you don't tell me what
+
+ align:start position:0%
+Goods Market if you don't tell me what
+ 
+
+ align:start position:0%
+Goods Market if you don't tell me what
+the interest rate is because you know
+
+ align:start position:0%
+the interest rate is because you know
+ 
+
+ align:start position:0%
+the interest rate is because you know
+it's a curve remember I told you it's a
+
+ align:start position:0%
+it's a curve remember I told you it's a
+ 
+
+ align:start position:0%
+it's a curve remember I told you it's a
+relationship a curve so if I tell you I
+
+ align:start position:0%
+relationship a curve so if I tell you I
+ 
+
+ align:start position:0%
+relationship a curve so if I tell you I
+tell you what the interest rate is then
+
+ align:start position:0%
+tell you what the interest rate is then
+ 
+
+ align:start position:0%
+tell you what the interest rate is then
+you can find the equilibrium in the
+
+ align:start position:0%
+you can find the equilibrium in the
+ 
+
+ align:start position:0%
+you can find the equilibrium in the
+Goods Market because you can fix this
+
+ align:start position:0%
+Goods Market because you can fix this
+ 
+
+ align:start position:0%
+Goods Market because you can fix this
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+okay that's for one given interest
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rate
+
+ align:start position:0%
+rate
+ 
+
+ align:start position:0%
+rate
+okay do do you understand that that's
+
+ align:start position:0%
+okay do do you understand that that's
+ 
+
+ align:start position:0%
+okay do do you understand that that's
+important
+
+ align:start position:0%
+important
+ 
+
+ align:start position:0%
+important
+yes those of you that are awake do you
+
+ align:start position:0%
+yes those of you that are awake do you
+ 
+
+ align:start position:0%
+yes those of you that are awake do you
+understand it or not not everyone is in
+
+ align:start position:0%
+understand it or not not everyone is in
+ 
+
+ align:start position:0%
+understand it or not not everyone is in
+the same page here okay
+
+ align:start position:0%
+the same page here okay
+ 
+
+ align:start position:0%
+the same page here okay
+good ER so let's now with that what
+
+ align:start position:0%
+good ER so let's now with that what
+ 
+
+ align:start position:0%
+good ER so let's now with that what
+we're going to do next is construct the
+
+ align:start position:0%
+we're going to do next is construct the
+ 
+
+ align:start position:0%
+we're going to do next is construct the
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+curve and and and how going remember
+
+ align:start position:0%
+curve and and and how going remember
+ 
+
+ align:start position:0%
+curve and and and how going remember
+what what I want to try to do is Con
+
+ align:start position:0%
+what what I want to try to do is Con
+ 
+
+ align:start position:0%
+what what I want to try to do is Con
+constructing the space of interest rate
+
+ align:start position:0%
+constructing the space of interest rate
+ 
+
+ align:start position:0%
+constructing the space of interest rate
+and output a curve which we're going to
+
+ align:start position:0%
+and output a curve which we're going to
+ 
+
+ align:start position:0%
+and output a curve which we're going to
+call the as
+
+ align:start position:0%
+call the as
+ 
+
+ align:start position:0%
+call the as
+curve at this point here we have a point
+
+ align:start position:0%
+curve at this point here we have a point
+ 
+
+ align:start position:0%
+curve at this point here we have a point
+in that curve because for one level of
+
+ align:start position:0%
+in that curve because for one level of
+ 
+
+ align:start position:0%
+in that curve because for one level of
+interest rate I found the equilibrium
+
+ align:start position:0%
+interest rate I found the equilibrium
+ 
+
+ align:start position:0%
+interest rate I found the equilibrium
+output so to construct the curve what I
+
+ align:start position:0%
+output so to construct the curve what I
+ 
+
+ align:start position:0%
+output so to construct the curve what I
+need to do is start moving the interest
+
+ align:start position:0%
+need to do is start moving the interest
+ 
+
+ align:start position:0%
+need to do is start moving the interest
+rate and see how the equilibrium output
+
+ align:start position:0%
+rate and see how the equilibrium output
+ 
+
+ align:start position:0%
+rate and see how the equilibrium output
+changes and that will trace a curve okay
+
+ align:start position:0%
+changes and that will trace a curve okay
+ 
+
+ align:start position:0%
+changes and that will trace a curve okay
+and that's going to be my
+
+ align:start position:0%
+and that's going to be my
+ 
+
+ align:start position:0%
+and that's going to be my
+is curve or relationship so let's do
+
+ align:start position:0%
+is curve or relationship so let's do
+ 
+
+ align:start position:0%
+is curve or relationship so let's do
+that
+
+ align:start position:0%
+that
+ 
+
+ align:start position:0%
+that
+that's a construction of the
+
+ align:start position:0%
+that's a construction of the
+ 
+
+ align:start position:0%
+that's a construction of the
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+so in the previous chart we found point
+
+ align:start position:0%
+so in the previous chart we found point
+ 
+
+ align:start position:0%
+so in the previous chart we found point
+a so point a there is that point okay
+
+ align:start position:0%
+a so point a there is that point okay
+ 
+
+ align:start position:0%
+a so point a there is that point okay
+there we are we had some interest
+
+ align:start position:0%
+there we are we had some interest
+ 
+
+ align:start position:0%
+there we are we had some interest
+rate this interest rate I mean believe
+
+ align:start position:0%
+rate this interest rate I mean believe
+ 
+
+ align:start position:0%
+rate this interest rate I mean believe
+me that was a parameter of the ZZ curve
+
+ align:start position:0%
+me that was a parameter of the ZZ curve
+ 
+
+ align:start position:0%
+me that was a parameter of the ZZ curve
+I showed you before gave us equilibrium
+
+ align:start position:0%
+I showed you before gave us equilibrium
+ 
+
+ align:start position:0%
+I showed you before gave us equilibrium
+output
+
+ align:start position:0%
+output
+ 
+
+ align:start position:0%
+output
+a so that's a point in the yes because
+
+ align:start position:0%
+a so that's a point in the yes because
+ 
+
+ align:start position:0%
+a so that's a point in the yes because
+that's a combination of interest rate
+
+ align:start position:0%
+that's a combination of interest rate
+ 
+
+ align:start position:0%
+that's a combination of interest rate
+and output which is consistent with
+
+ align:start position:0%
+and output which is consistent with
+ 
+
+ align:start position:0%
+and output which is consistent with
+equilibrium in the Goods Market that's a
+
+ align:start position:0%
+equilibrium in the Goods Market that's a
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market that's a
+point in the is that's a definition of
+
+ align:start position:0%
+point in the is that's a definition of
+ 
+
+ align:start position:0%
+point in the is that's a definition of
+is so now what I'm going to do to
+
+ align:start position:0%
+is so now what I'm going to do to
+ 
+
+ align:start position:0%
+is so now what I'm going to do to
+construct my is is okay let me move the
+
+ align:start position:0%
+construct my is is okay let me move the
+ 
+
+ align:start position:0%
+construct my is is okay let me move the
+interest rate let me raise interest rate
+
+ align:start position:0%
+interest rate let me raise interest rate
+ 
+
+ align:start position:0%
+interest rate let me raise interest rate
+from I to I prime okay that's an
+
+ align:start position:0%
+from I to I prime okay that's an
+ 
+
+ align:start position:0%
+from I to I prime okay that's an
+increase in the interest rate and now
+
+ align:start position:0%
+increase in the interest rate and now
+ 
+
+ align:start position:0%
+increase in the interest rate and now
+let me find what is a new equilibrium in
+
+ align:start position:0%
+let me find what is a new equilibrium in
+ 
+
+ align:start position:0%
+let me find what is a new equilibrium in
+the goods market for a given interest
+
+ align:start position:0%
+the goods market for a given interest
+ 
+
+ align:start position:0%
+the goods market for a given interest
+rate Which is higher than the one I used
+
+ align:start position:0%
+rate Which is higher than the one I used
+ 
+
+ align:start position:0%
+rate Which is higher than the one I used
+to have well that amounts to Shifting
+
+ align:start position:0%
+to have well that amounts to Shifting
+ 
+
+ align:start position:0%
+to have well that amounts to Shifting
+the ZZ curve down
+
+ align:start position:0%
+the ZZ curve down
+ 
+
+ align:start position:0%
+the ZZ curve down
+why does it increasing the interest rate
+
+ align:start position:0%
+why does it increasing the interest rate
+ 
+
+ align:start position:0%
+why does it increasing the interest rate
+shift the ZZ curve down the aggregate
+
+ align:start position:0%
+shift the ZZ curve down the aggregate
+ 
+
+ align:start position:0%
+shift the ZZ curve down the aggregate
+demand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+down it makes investment decline exactly
+
+ align:start position:0%
+down it makes investment decline exactly
+ 
+
+ align:start position:0%
+down it makes investment decline exactly
+B is for investment declines okay so
+
+ align:start position:0%
+B is for investment declines okay so
+ 
+
+ align:start position:0%
+B is for investment declines okay so
+that means for any given level of output
+
+ align:start position:0%
+that means for any given level of output
+ 
+
+ align:start position:0%
+that means for any given level of output
+now aggregate demand is lower because
+
+ align:start position:0%
+now aggregate demand is lower because
+ 
+
+ align:start position:0%
+now aggregate demand is lower because
+investment is lower and then you get the
+
+ align:start position:0%
+investment is lower and then you get the
+ 
+
+ align:start position:0%
+investment is lower and then you get the
+multiplier to do it stck no and
+
+ align:start position:0%
+multiplier to do it stck no and
+ 
+
+ align:start position:0%
+multiplier to do it stck no and
+therefore you tend end up with a
+
+ align:start position:0%
+therefore you tend end up with a
+ 
+
+ align:start position:0%
+therefore you tend end up with a
+declining output which is even larger
+
+ align:start position:0%
+declining output which is even larger
+ 
+
+ align:start position:0%
+declining output which is even larger
+than the declining invest the initial
+
+ align:start position:0%
+than the declining invest the initial
+ 
+
+ align:start position:0%
+than the declining invest the initial
+declining invest M as a result of
+
+ align:start position:0%
+declining invest M as a result of
+ 
+
+ align:start position:0%
+declining invest M as a result of
+increase in the interest rate that's
+
+ align:start position:0%
+increase in the interest rate that's
+ 
+
+ align:start position:0%
+increase in the interest rate that's
+what a multiplier does no so say
+
+ align:start position:0%
+what a multiplier does no so say
+ 
+
+ align:start position:0%
+what a multiplier does no so say
+interest rate increased by 100 100 basis
+
+ align:start position:0%
+interest rate increased by 100 100 basis
+ 
+
+ align:start position:0%
+interest rate increased by 100 100 basis
+points that reduce investment by a say10
+
+ align:start position:0%
+points that reduce investment by a say10
+ 
+
+ align:start position:0%
+points that reduce investment by a say10
+billion and equilibrium output ends up
+
+ align:start position:0%
+billion and equilibrium output ends up
+ 
+
+ align:start position:0%
+billion and equilibrium output ends up
+falling by $15 billion because of the
+
+ align:start position:0%
+falling by $15 billion because of the
+ 
+
+ align:start position:0%
+falling by $15 billion because of the
+multiplier and so on okay but the point
+
+ align:start position:0%
+multiplier and so on okay but the point
+ 
+
+ align:start position:0%
+multiplier and so on okay but the point
+is after I do all my convergence to this
+
+ align:start position:0%
+is after I do all my convergence to this
+ 
+
+ align:start position:0%
+is after I do all my convergence to this
+new lower equilibrium level of output I
+
+ align:start position:0%
+new lower equilibrium level of output I
+ 
+
+ align:start position:0%
+new lower equilibrium level of output I
+have a second point in my as curve
+
+ align:start position:0%
+have a second point in my as curve
+ 
+
+ align:start position:0%
+have a second point in my as curve
+because that's a combination of a new
+
+ align:start position:0%
+because that's a combination of a new
+ 
+
+ align:start position:0%
+because that's a combination of a new
+interest rate I prime an output that is
+
+ align:start position:0%
+interest rate I prime an output that is
+ 
+
+ align:start position:0%
+interest rate I prime an output that is
+consistent with equilibrium in the Goods
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+ 
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+Market how do I know that it's
+
+ align:start position:0%
+Market how do I know that it's
+ 
+
+ align:start position:0%
+Market how do I know that it's
+consistent with equili in the Goods
+
+ align:start position:0%
+consistent with equili in the Goods
+ 
+
+ align:start position:0%
+consistent with equili in the Goods
+Market because I'm there I'm crossing 45
+
+ align:start position:0%
+Market because I'm there I'm crossing 45
+ 
+
+ align:start position:0%
+Market because I'm there I'm crossing 45
+degree line that means output equal to
+
+ align:start position:0%
+degree line that means output equal to
+ 
+
+ align:start position:0%
+degree line that means output equal to
+aggregate demand that's equilibrium in
+
+ align:start position:0%
+aggregate demand that's equilibrium in
+ 
+
+ align:start position:0%
+aggregate demand that's equilibrium in
+the Goods
+
+ align:start position:0%
+the Goods
+ 
+
+ align:start position:0%
+the Goods
+Market okay
+
+ align:start position:0%
+Market okay
+ 
+
+ align:start position:0%
+Market okay
+so and of course you can keep going no
+
+ align:start position:0%
+so and of course you can keep going no
+ 
+
+ align:start position:0%
+so and of course you can keep going no
+and trace an entire curve and all that
+
+ align:start position:0%
+and trace an entire curve and all that
+ 
+
+ align:start position:0%
+and trace an entire curve and all that
+you'll do is you'll change the interest
+
+ align:start position:0%
+you'll do is you'll change the interest
+ 
+
+ align:start position:0%
+you'll do is you'll change the interest
+rate that will shift this curve then you
+
+ align:start position:0%
+rate that will shift this curve then you
+ 
+
+ align:start position:0%
+rate that will shift this curve then you
+do the multiplier and endend up with a
+
+ align:start position:0%
+do the multiplier and endend up with a
+ 
+
+ align:start position:0%
+do the multiplier and endend up with a
+new
+
+ align:start position:0%
+new
+ 
+
+ align:start position:0%
+new
+equilibrium and that's another point for
+
+ align:start position:0%
+equilibrium and that's another point for
+ 
+
+ align:start position:0%
+equilibrium and that's another point for
+your curve
+
+ align:start position:0%
+your curve
+ 
+
+ align:start position:0%
+your curve
+okay so is it clear how we constructed
+
+ align:start position:0%
+okay so is it clear how we constructed
+ 
+
+ align:start position:0%
+okay so is it clear how we constructed
+that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve very important okay
+
+ align:start position:0%
+curve very important okay
+ 
+
+ align:start position:0%
+curve very important okay
+good it's also very important to
+
+ align:start position:0%
+good it's also very important to
+ 
+
+ align:start position:0%
+good it's also very important to
+understand well so why is it downward
+
+ align:start position:0%
+understand well so why is it downward
+ 
+
+ align:start position:0%
+understand well so why is it downward
+sloping yeah that's a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+question why is it downward sloping
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what does it mean that it's downward
+
+ align:start position:0%
+what does it mean that it's downward
+ 
+
+ align:start position:0%
+what does it mean that it's downward
+slope that means that combination of
+
+ align:start position:0%
+slope that means that combination of
+ 
+
+ align:start position:0%
+slope that means that combination of
+output and interest rate that are
+
+ align:start position:0%
+output and interest rate that are
+ 
+
+ align:start position:0%
+output and interest rate that are
+consistent with equilibrium output are
+
+ align:start position:0%
+consistent with equilibrium output are
+ 
+
+ align:start position:0%
+consistent with equilibrium output are
+negatively correlated meaning you know I
+
+ align:start position:0%
+negatively correlated meaning you know I
+ 
+
+ align:start position:0%
+negatively correlated meaning you know I
+have a combination of high output and
+
+ align:start position:0%
+have a combination of high output and
+ 
+
+ align:start position:0%
+have a combination of high output and
+low interest rate is consistent
+
+ align:start position:0%
+low interest rate is consistent
+ 
+
+ align:start position:0%
+low interest rate is consistent
+or low high interest rate and low output
+
+ align:start position:0%
+or low high interest rate and low output
+ 
+
+ align:start position:0%
+or low high interest rate and low output
+that's what I find
+
+ align:start position:0%
+that's what I find
+ 
+
+ align:start position:0%
+that's what I find
+here but why is that why what is the
+
+ align:start position:0%
+here but why is that why what is the
+ 
+
+ align:start position:0%
+here but why is that why what is the
+logic of that behind that or the
+
+ align:start position:0%
+logic of that behind that or the
+ 
+
+ align:start position:0%
+logic of that behind that or the
+mechanism well the way to think about
+
+ align:start position:0%
+mechanism well the way to think about
+ 
+
+ align:start position:0%
+mechanism well the way to think about
+that is exactly the way I I did this
+
+ align:start position:0%
+that is exactly the way I I did this
+ 
+
+ align:start position:0%
+that is exactly the way I I did this
+experiment is okay let me think what
+
+ align:start position:0%
+experiment is okay let me think what
+ 
+
+ align:start position:0%
+experiment is okay let me think what
+happens if I increase the interest rate
+
+ align:start position:0%
+happens if I increase the interest rate
+ 
+
+ align:start position:0%
+happens if I increase the interest rate
+and I keep the level of output where it
+
+ align:start position:0%
+and I keep the level of output where it
+ 
+
+ align:start position:0%
+and I keep the level of output where it
+was so what happens if I increase the
+
+ align:start position:0%
+was so what happens if I increase the
+ 
+
+ align:start position:0%
+was so what happens if I increase the
+interest rate and I I keep the level of
+
+ align:start position:0%
+interest rate and I I keep the level of
+ 
+
+ align:start position:0%
+interest rate and I I keep the level of
+output at the level it
+
+ align:start position:0%
+output at the level it
+ 
+
+ align:start position:0%
+output at the level it
+was my claim is that that's not an
+
+ align:start position:0%
+was my claim is that that's not an
+ 
+
+ align:start position:0%
+was my claim is that that's not an
+equilibrium in the Goods Market what
+
+ align:start position:0%
+equilibrium in the Goods Market what
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market what
+what is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it so I'm saying suppose I increase the
+
+ align:start position:0%
+it so I'm saying suppose I increase the
+ 
+
+ align:start position:0%
+it so I'm saying suppose I increase the
+interest rate but I keep the output
+
+ align:start position:0%
+interest rate but I keep the output
+ 
+
+ align:start position:0%
+interest rate but I keep the output
+constant so output is here higher
+
+ align:start position:0%
+constant so output is here higher
+ 
+
+ align:start position:0%
+constant so output is here higher
+interest rate aggregate demand is
+
+ align:start position:0%
+interest rate aggregate demand is
+ 
+
+ align:start position:0%
+interest rate aggregate demand is
+there so what what is the problem I'm
+
+ align:start position:0%
+there so what what is the problem I'm
+ 
+
+ align:start position:0%
+there so what what is the problem I'm
+saying my claim is that's not an
+
+ align:start position:0%
+saying my claim is that's not an
+ 
+
+ align:start position:0%
+saying my claim is that's not an
+equilibrium in the Goods Market we're
+
+ align:start position:0%
+equilibrium in the Goods Market we're
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market we're
+going to need a lower level of output to
+
+ align:start position:0%
+going to need a lower level of output to
+ 
+
+ align:start position:0%
+going to need a lower level of output to
+have an equilibrium in the Goods Market
+
+ align:start position:0%
+have an equilibrium in the Goods Market
+ 
+
+ align:start position:0%
+have an equilibrium in the Goods Market
+that's the reason it's downward sloping
+
+ align:start position:0%
+that's the reason it's downward sloping
+ 
+
+ align:start position:0%
+that's the reason it's downward sloping
+but why is that not an equilibrium in
+
+ align:start position:0%
+but why is that not an equilibrium in
+ 
+
+ align:start position:0%
+but why is that not an equilibrium in
+the Goods
+
+ align:start position:0%
+the Goods
+ 
+
+ align:start position:0%
+the Goods
+Market or what is the nature of the dise
+
+ align:start position:0%
+Market or what is the nature of the dise
+ 
+
+ align:start position:0%
+Market or what is the nature of the dise
+equilibrium in the Market there what do
+
+ align:start position:0%
+equilibrium in the Market there what do
+ 
+
+ align:start position:0%
+equilibrium in the Market there what do
+we have an excess demand excess
+
+ align:start position:0%
+we have an excess demand excess
+ 
+
+ align:start position:0%
+we have an excess demand excess
+Supply excess Supply meaning there isn't
+
+ align:start position:0%
+Supply excess Supply meaning there isn't
+ 
+
+ align:start position:0%
+Supply excess Supply meaning there isn't
+enough demand to support that
+
+ align:start position:0%
+enough demand to support that
+ 
+
+ align:start position:0%
+enough demand to support that
+Supply so supply has to fall in order to
+
+ align:start position:0%
+Supply so supply has to fall in order to
+ 
+
+ align:start position:0%
+Supply so supply has to fall in order to
+restore equilibrium in that market in
+
+ align:start position:0%
+restore equilibrium in that market in
+ 
+
+ align:start position:0%
+restore equilibrium in that market in
+the Goods Market okay and since one
+
+ align:start position:0%
+the Goods Market okay and since one
+ 
+
+ align:start position:0%
+the Goods Market okay and since one
+drags the other one it has to Fall by a
+
+ align:start position:0%
+drags the other one it has to Fall by a
+ 
+
+ align:start position:0%
+drags the other one it has to Fall by a
+lot that that has to do with the slope
+
+ align:start position:0%
+lot that that has to do with the slope
+ 
+
+ align:start position:0%
+lot that that has to do with the slope
+of this
+
+ align:start position:0%
+of this
+ 
+
+ align:start position:0%
+of this
+curve that's the reason it's negatively
+
+ align:start position:0%
+curve that's the reason it's negatively
+ 
+
+ align:start position:0%
+curve that's the reason it's negatively
+so that's first thing you have to
+
+ align:start position:0%
+so that's first thing you have to
+ 
+
+ align:start position:0%
+so that's first thing you have to
+understand understand when you construct
+
+ align:start position:0%
+understand understand when you construct
+ 
+
+ align:start position:0%
+understand understand when you construct
+this curve I know I'm going slowly but
+
+ align:start position:0%
+this curve I know I'm going slowly but
+ 
+
+ align:start position:0%
+this curve I know I'm going slowly but
+it's important when you con please try
+
+ align:start position:0%
+it's important when you con please try
+ 
+
+ align:start position:0%
+it's important when you con please try
+to
+
+ align:start position:0%
+to
+ 
+
+ align:start position:0%
+to
+understand why is that another way of
+
+ align:start position:0%
+understand why is that another way of
+ 
+
+ align:start position:0%
+understand why is that another way of
+saying
+
+ align:start position:0%
+saying
+ 
+
+ align:start position:0%
+saying
+it when I when I find the when I change
+
+ align:start position:0%
+it when I when I find the when I change
+ 
+
+ align:start position:0%
+it when I when I find the when I change
+the equilibrium output along this S
+
+ align:start position:0%
+the equilibrium output along this S
+ 
+
+ align:start position:0%
+the equilibrium output along this S
+curve by moving the inid around what I'm
+
+ align:start position:0%
+curve by moving the inid around what I'm
+ 
+
+ align:start position:0%
+curve by moving the inid around what I'm
+doing is I'm moving along an is curve
+
+ align:start position:0%
+doing is I'm moving along an is curve
+ 
+
+ align:start position:0%
+doing is I'm moving along an is curve
+okay so if I if the only reason why
+
+ align:start position:0%
+okay so if I if the only reason why
+ 
+
+ align:start position:0%
+okay so if I if the only reason why
+equilibrium out with is changing is
+
+ align:start position:0%
+equilibrium out with is changing is
+ 
+
+ align:start position:0%
+equilibrium out with is changing is
+because I'm moving the interest rate
+
+ align:start position:0%
+because I'm moving the interest rate
+ 
+
+ align:start position:0%
+because I'm moving the interest rate
+that's a movement along the S
+
+ align:start position:0%
+that's a movement along the S
+ 
+
+ align:start position:0%
+that's a movement along the S
+curve okay so I'm I'm tracing points of
+
+ align:start position:0%
+curve okay so I'm I'm tracing points of
+ 
+
+ align:start position:0%
+curve okay so I'm I'm tracing points of
+the as curve good and I want to draw a
+
+ align:start position:0%
+the as curve good and I want to draw a
+ 
+
+ align:start position:0%
+the as curve good and I want to draw a
+contrast between these movements along
+
+ align:start position:0%
+contrast between these movements along
+ 
+
+ align:start position:0%
+contrast between these movements along
+the is curve versus things that shift
+
+ align:start position:0%
+the is curve versus things that shift
+ 
+
+ align:start position:0%
+the is curve versus things that shift
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+curve okay for
+
+ align:start position:0%
+curve okay for
+ 
+
+ align:start position:0%
+curve okay for
+example
+
+ align:start position:0%
+example
+ 
+
+ align:start position:0%
+example
+that so suppose I increase taxes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+increase taxes the government increases
+
+ align:start position:0%
+increase taxes the government increases
+ 
+
+ align:start position:0%
+increase taxes the government increases
+taxes my claim is that the is shift to
+
+ align:start position:0%
+taxes my claim is that the is shift to
+ 
+
+ align:start position:0%
+taxes my claim is that the is shift to
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+left that is for any given level of
+
+ align:start position:0%
+left that is for any given level of
+ 
+
+ align:start position:0%
+left that is for any given level of
+interest rate pick any interest you
+
+ align:start position:0%
+interest rate pick any interest you
+ 
+
+ align:start position:0%
+interest rate pick any interest you
+want say this one you're going to have a
+
+ align:start position:0%
+want say this one you're going to have a
+ 
+
+ align:start position:0%
+want say this one you're going to have a
+lower equilibrium output consistent with
+
+ align:start position:0%
+lower equilibrium output consistent with
+ 
+
+ align:start position:0%
+lower equilibrium output consistent with
+that interest rate if you have a lower
+
+ align:start position:0%
+that interest rate if you have a lower
+ 
+
+ align:start position:0%
+that interest rate if you have a lower
+equilibrium consistent with the same
+
+ align:start position:0%
+equilibrium consistent with the same
+ 
+
+ align:start position:0%
+equilibrium consistent with the same
+interest rate that has shifted the
+
+ align:start position:0%
+interest rate that has shifted the
+ 
+
+ align:start position:0%
+interest rate that has shifted the
+is has to be a different is
+
+ align:start position:0%
+is has to be a different is
+ 
+
+ align:start position:0%
+is has to be a different is
+okay and and think that I can do that
+
+ align:start position:0%
+okay and and think that I can do that
+ 
+
+ align:start position:0%
+okay and and think that I can do that
+for any given level of in I pick this
+
+ align:start position:0%
+for any given level of in I pick this
+ 
+
+ align:start position:0%
+for any given level of in I pick this
+one but I could have pick that one would
+
+ align:start position:0%
+one but I could have pick that one would
+ 
+
+ align:start position:0%
+one but I could have pick that one would
+have been the same I'm saying you
+
+ align:start position:0%
+have been the same I'm saying you
+ 
+
+ align:start position:0%
+have been the same I'm saying you
+increase
+
+ align:start position:0%
+increase
+ 
+
+ align:start position:0%
+increase
+taxes that's going to lead to lower
+
+ align:start position:0%
+taxes that's going to lead to lower
+ 
+
+ align:start position:0%
+taxes that's going to lead to lower
+equilibrium
+
+ align:start position:0%
+equilibrium
+ 
+
+ align:start position:0%
+equilibrium
+output so that means that for this
+
+ align:start position:0%
+output so that means that for this
+ 
+
+ align:start position:0%
+output so that means that for this
+higher level of taxes I will have to
+
+ align:start position:0%
+higher level of taxes I will have to
+ 
+
+ align:start position:0%
+higher level of taxes I will have to
+trace a different test
+
+ align:start position:0%
+trace a different test
+ 
+
+ align:start position:0%
+trace a different test
+curve I can start moving the interest
+
+ align:start position:0%
+curve I can start moving the interest
+ 
+
+ align:start position:0%
+curve I can start moving the interest
+rate around but I'm going to have a
+
+ align:start position:0%
+rate around but I'm going to have a
+ 
+
+ align:start position:0%
+rate around but I'm going to have a
+lower level of output for any given
+
+ align:start position:0%
+lower level of output for any given
+ 
+
+ align:start position:0%
+lower level of output for any given
+level of interest rate because I have
+
+ align:start position:0%
+level of interest rate because I have
+ 
+
+ align:start position:0%
+level of interest rate because I have
+higher taxes
+
+ align:start position:0%
+higher taxes
+ 
+
+ align:start position:0%
+higher taxes
+so how do I know that an increas in
+
+ align:start position:0%
+so how do I know that an increas in
+ 
+
+ align:start position:0%
+so how do I know that an increas in
+taxes will do this Which diagram would
+
+ align:start position:0%
+taxes will do this Which diagram would
+ 
+
+ align:start position:0%
+taxes will do this Which diagram would
+you go to to try to understand
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this so or let me ask it
+
+ align:start position:0%
+this so or let me ask it
+ 
+
+ align:start position:0%
+this so or let me ask it
+differently how do I know that this
+
+ align:start position:0%
+differently how do I know that this
+ 
+
+ align:start position:0%
+differently how do I know that this
+stuff shift to the left so I give you
+
+ align:start position:0%
+stuff shift to the left so I give you
+ 
+
+ align:start position:0%
+stuff shift to the left so I give you
+more open space how do I know that this
+
+ align:start position:0%
+more open space how do I know that this
+ 
+
+ align:start position:0%
+more open space how do I know that this
+increasing taxes will shift this is
+
+ align:start position:0%
+increasing taxes will shift this is
+ 
+
+ align:start position:0%
+increasing taxes will shift this is
+curve to the left how would you go about
+
+ align:start position:0%
+curve to the left how would you go about
+ 
+
+ align:start position:0%
+curve to the left how would you go about
+thinking
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+not going to spend as much money less
+
+ align:start position:0%
+not going to spend as much money less
+ 
+
+ align:start position:0%
+not going to spend as much money less
+outcome there will be less aggregate
+
+ align:start position:0%
+outcome there will be less aggregate
+ 
+
+ align:start position:0%
+outcome there will be less aggregate
+demand and less aggregate demand leads
+
+ align:start position:0%
+demand and less aggregate demand leads
+ 
+
+ align:start position:0%
+demand and less aggregate demand leads
+to less output because output is
+
+ align:start position:0%
+to less output because output is
+ 
+
+ align:start position:0%
+to less output because output is
+aggregate demand deter exactly that's
+
+ align:start position:0%
+aggregate demand deter exactly that's
+ 
+
+ align:start position:0%
+aggregate demand deter exactly that's
+what equilibrium in the Goods Market so
+
+ align:start position:0%
+what equilibrium in the Goods Market so
+ 
+
+ align:start position:0%
+what equilibrium in the Goods Market so
+you can go back to this diagram this
+
+ align:start position:0%
+you can go back to this diagram this
+ 
+
+ align:start position:0%
+you can go back to this diagram this
+goes in the I could say ignore these
+
+ align:start position:0%
+goes in the I could say ignore these
+ 
+
+ align:start position:0%
+goes in the I could say ignore these
+labels here and say look for any given
+
+ align:start position:0%
+labels here and say look for any given
+ 
+
+ align:start position:0%
+labels here and say look for any given
+level of interest rate pick any if I
+
+ align:start position:0%
+level of interest rate pick any if I
+ 
+
+ align:start position:0%
+level of interest rate pick any if I
+increase tax I'm going to shift the Z ZZ
+
+ align:start position:0%
+increase tax I'm going to shift the Z ZZ
+ 
+
+ align:start position:0%
+increase tax I'm going to shift the Z ZZ
+curve
+
+ align:start position:0%
+curve
+ 
+
+ align:start position:0%
+curve
+down okay so ignore the this charar
+
+ align:start position:0%
+down okay so ignore the this charar
+ 
+
+ align:start position:0%
+down okay so ignore the this charar
+suppose that I fix the interest rate but
+
+ align:start position:0%
+suppose that I fix the interest rate but
+ 
+
+ align:start position:0%
+suppose that I fix the interest rate but
+I now change taxes increase taxes well
+
+ align:start position:0%
+I now change taxes increase taxes well
+ 
+
+ align:start position:0%
+I now change taxes increase taxes well
+I'm going to do exactly the same here
+
+ align:start position:0%
+I'm going to do exactly the same here
+ 
+
+ align:start position:0%
+I'm going to do exactly the same here
+I'm going to move this down and it's
+
+ align:start position:0%
+I'm going to move this down and it's
+ 
+
+ align:start position:0%
+I'm going to move this down and it's
+going to be a different is curve though
+
+ align:start position:0%
+going to be a different is curve though
+ 
+
+ align:start position:0%
+going to be a different is curve though
+because I shouldn't have used this
+
+ align:start position:0%
+because I shouldn't have used this
+ 
+
+ align:start position:0%
+because I shouldn't have used this
+diagram let me keep your answer I should
+
+ align:start position:0%
+diagram let me keep your answer I should
+ 
+
+ align:start position:0%
+diagram let me keep your answer I should
+have put a new diagram but it's it's
+
+ align:start position:0%
+have put a new diagram but it's it's
+ 
+
+ align:start position:0%
+have put a new diagram but it's it's
+lecture three in lecture three we did
+
+ align:start position:0%
+lecture three in lecture three we did
+ 
+
+ align:start position:0%
+lecture three in lecture three we did
+see that that an increase in tax would
+
+ align:start position:0%
+see that that an increase in tax would
+ 
+
+ align:start position:0%
+see that that an increase in tax would
+lead to lower equilibrium output
+
+ align:start position:0%
+lead to lower equilibrium output
+ 
+
+ align:start position:0%
+lead to lower equilibrium output
+in fact we know exactly by how much if
+
+ align:start position:0%
+in fact we know exactly by how much if
+ 
+
+ align:start position:0%
+in fact we know exactly by how much if
+if taxes increase by 100 then you know
+
+ align:start position:0%
+if taxes increase by 100 then you know
+ 
+
+ align:start position:0%
+if taxes increase by 100 then you know
+that equilibrium output would decline by
+
+ align:start position:0%
+that equilibrium output would decline by
+ 
+
+ align:start position:0%
+that equilibrium output would decline by
+C1 times 1 / minus
+
+ align:start position:0%
+C1 times 1 / minus
+ 
+
+ align:start position:0%
+C1 times 1 / minus
+C1 changing taxes here would be a little
+
+ align:start position:0%
+C1 changing taxes here would be a little
+ 
+
+ align:start position:0%
+C1 changing taxes here would be a little
+different because there is also remember
+
+ align:start position:0%
+different because there is also remember
+ 
+
+ align:start position:0%
+different because there is also remember
+investment also has a propensity to to
+
+ align:start position:0%
+investment also has a propensity to to
+ 
+
+ align:start position:0%
+investment also has a propensity to to
+to to spend as a function of output so
+
+ align:start position:0%
+to to spend as a function of output so
+ 
+
+ align:start position:0%
+to to spend as a function of output so
+so it would be a little different but
+
+ align:start position:0%
+so it would be a little different but
+ 
+
+ align:start position:0%
+so it would be a little different but
+that's the kind of
+
+ align:start position:0%
+that's the kind of
+ 
+
+ align:start position:0%
+that's the kind of
+calculation okay what else would shift
+
+ align:start position:0%
+calculation okay what else would shift
+ 
+
+ align:start position:0%
+calculation okay what else would shift
+the the is this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+way decrease in governance friend would
+
+ align:start position:0%
+way decrease in governance friend would
+ 
+
+ align:start position:0%
+way decrease in governance friend would
+do that what
+
+ align:start position:0%
+do that what
+ 
+
+ align:start position:0%
+do that what
+else this this another thing I want you
+
+ align:start position:0%
+else this this another thing I want you
+ 
+
+ align:start position:0%
+else this this another thing I want you
+to think of any everything because for
+
+ align:start position:0%
+to think of any everything because for
+ 
+
+ align:start position:0%
+to think of any everything because for
+sure you're going to face that in the
+
+ align:start position:0%
+sure you're going to face that in the
+ 
+
+ align:start position:0%
+sure you're going to face that in the
+quiz that anything that would shift the
+
+ align:start position:0%
+quiz that anything that would shift the
+ 
+
+ align:start position:0%
+quiz that anything that would shift the
+curve what else would shift the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+curve yeah that's true but but but
+
+ align:start position:0%
+curve yeah that's true but but but
+ 
+
+ align:start position:0%
+curve yeah that's true but but but
+that's not for this part of the course
+
+ align:start position:0%
+that's not for this part of the course
+ 
+
+ align:start position:0%
+that's not for this part of the course
+remember we're in a close economy so
+
+ align:start position:0%
+remember we're in a close economy so
+ 
+
+ align:start position:0%
+remember we're in a close economy so
+here we assume xal to m equal to zero I
+
+ align:start position:0%
+here we assume xal to m equal to zero I
+ 
+
+ align:start position:0%
+here we assume xal to m equal to zero I
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+zero that comes from after quiz one what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+else things that were captur remember
+
+ align:start position:0%
+else things that were captur remember
+ 
+
+ align:start position:0%
+else things that were captur remember
+when I began this lecture I show you
+
+ align:start position:0%
+when I began this lecture I show you
+ 
+
+ align:start position:0%
+when I began this lecture I show you
+wealth what had happened and so on well
+
+ align:start position:0%
+wealth what had happened and so on well
+ 
+
+ align:start position:0%
+wealth what had happened and so on well
+there's nowhere wealth in this model
+
+ align:start position:0%
+there's nowhere wealth in this model
+ 
+
+ align:start position:0%
+there's nowhere wealth in this model
+here it's just output but wealth affects
+
+ align:start position:0%
+here it's just output but wealth affects
+ 
+
+ align:start position:0%
+here it's just output but wealth affects
+how much consumers consume so autonomous
+
+ align:start position:0%
+how much consumers consume so autonomous
+ 
+
+ align:start position:0%
+how much consumers consume so autonomous
+consumption there were lots of stuff
+
+ align:start position:0%
+consumption there were lots of stuff
+ 
+
+ align:start position:0%
+consumption there were lots of stuff
+hidden in that c0 that constant c0
+
+ align:start position:0%
+hidden in that c0 that constant c0
+ 
+
+ align:start position:0%
+hidden in that c0 that constant c0
+remember c0 plus C1 one well c0 captures
+
+ align:start position:0%
+remember c0 plus C1 one well c0 captures
+ 
+
+ align:start position:0%
+remember c0 plus C1 one well c0 captures
+things like how confident were consumers
+
+ align:start position:0%
+things like how confident were consumers
+ 
+
+ align:start position:0%
+things like how confident were consumers
+how wealthy they felt and stuff like
+
+ align:start position:0%
+how wealthy they felt and stuff like
+ 
+
+ align:start position:0%
+how wealthy they felt and stuff like
+that so anything that shift C down
+
+ align:start position:0%
+that so anything that shift C down
+ 
+
+ align:start position:0%
+that so anything that shift C down
+consumer sentiment declines wealth
+
+ align:start position:0%
+consumer sentiment declines wealth
+ 
+
+ align:start position:0%
+consumer sentiment declines wealth
+declines something like that will also
+
+ align:start position:0%
+declines something like that will also
+ 
+
+ align:start position:0%
+declines something like that will also
+shift yes to the left okay so that's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+important good so now so we're done with
+
+ align:start position:0%
+important good so now so we're done with
+ 
+
+ align:start position:0%
+important good so now so we're done with
+is for
+
+ align:start position:0%
+is for
+ 
+
+ align:start position:0%
+is for
+now now with the is alone I cannot find
+
+ align:start position:0%
+now now with the is alone I cannot find
+ 
+
+ align:start position:0%
+now now with the is alone I cannot find
+what I want I want to find equili
+
+ align:start position:0%
+what I want I want to find equili
+ 
+
+ align:start position:0%
+what I want I want to find equili
+combinations of interest rate and output
+
+ align:start position:0%
+combinations of interest rate and output
+ 
+
+ align:start position:0%
+combinations of interest rate and output
+that are consistent with equilibrium in
+
+ align:start position:0%
+that are consistent with equilibrium in
+ 
+
+ align:start position:0%
+that are consistent with equilibrium in
+the goods and financial markets this
+
+ align:start position:0%
+the goods and financial markets this
+ 
+
+ align:start position:0%
+the goods and financial markets this
+doesn't do it because it gives you only
+
+ align:start position:0%
+doesn't do it because it gives you only
+ 
+
+ align:start position:0%
+doesn't do it because it gives you only
+combinations that are consistent with
+
+ align:start position:0%
+combinations that are consistent with
+ 
+
+ align:start position:0%
+combinations that are consistent with
+equilibrium in the Goods Market
+
+ align:start position:0%
+equilibrium in the Goods Market
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market
+okay and in fact okay so I now need to
+
+ align:start position:0%
+okay and in fact okay so I now need to
+ 
+
+ align:start position:0%
+okay and in fact okay so I now need to
+look at Financial Market which is the
+
+ align:start position:0%
+look at Financial Market which is the
+ 
+
+ align:start position:0%
+look at Financial Market which is the
+other side the LM relation ship and
+
+ align:start position:0%
+other side the LM relation ship and
+ 
+
+ align:start position:0%
+other side the LM relation ship and
+remember what we had is we had
+
+ align:start position:0%
+remember what we had is we had
+ 
+
+ align:start position:0%
+remember what we had is we had
+equilibrium in the in the financial
+
+ align:start position:0%
+equilibrium in the in the financial
+ 
+
+ align:start position:0%
+equilibrium in the in the financial
+Market we had two instruments that we
+
+ align:start position:0%
+Market we had two instruments that we
+ 
+
+ align:start position:0%
+Market we had two instruments that we
+could use remember we had only two
+
+ align:start position:0%
+could use remember we had only two
+ 
+
+ align:start position:0%
+could use remember we had only two
+assets money and bonds so we could look
+
+ align:start position:0%
+assets money and bonds so we could look
+ 
+
+ align:start position:0%
+assets money and bonds so we could look
+at the equilibrium in in in the in money
+
+ align:start position:0%
+at the equilibrium in in in the in money
+ 
+
+ align:start position:0%
+at the equilibrium in in in the in money
+or equilibrium in bonds is the
+
+ align:start position:0%
+or equilibrium in bonds is the
+ 
+
+ align:start position:0%
+or equilibrium in bonds is the
+same but we we did it all in in terms of
+
+ align:start position:0%
+same but we we did it all in in terms of
+ 
+
+ align:start position:0%
+same but we we did it all in in terms of
+money it's the same because given wealth
+
+ align:start position:0%
+money it's the same because given wealth
+ 
+
+ align:start position:0%
+money it's the same because given wealth
+if one is in equilibrium the other one
+
+ align:start position:0%
+if one is in equilibrium the other one
+ 
+
+ align:start position:0%
+if one is in equilibrium the other one
+has to be in equilibrium as well so I I
+
+ align:start position:0%
+has to be in equilibrium as well so I I
+ 
+
+ align:start position:0%
+has to be in equilibrium as well so I I
+only need to look at one and we're
+
+ align:start position:0%
+only need to look at one and we're
+ 
+
+ align:start position:0%
+only need to look at one and we're
+looking at money okay so money is equal
+
+ align:start position:0%
+looking at money okay so money is equal
+ 
+
+ align:start position:0%
+looking at money okay so money is equal
+to money
+
+ align:start position:0%
+to money
+ 
+
+ align:start position:0%
+to money
+demand I'm going to divide both sides by
+
+ align:start position:0%
+demand I'm going to divide both sides by
+ 
+
+ align:start position:0%
+demand I'm going to divide both sides by
+P this is not going to be very important
+
+ align:start position:0%
+P this is not going to be very important
+ 
+
+ align:start position:0%
+P this is not going to be very important
+now but later we will be and so we're
+
+ align:start position:0%
+now but later we will be and so we're
+ 
+
+ align:start position:0%
+now but later we will be and so we're
+going to have that this is is
+
+ align:start position:0%
+going to have that this is is
+ 
+
+ align:start position:0%
+going to have that this is is
+equilibrium in in in financial Market
+
+ align:start position:0%
+equilibrium in in in financial Market
+ 
+
+ align:start position:0%
+equilibrium in in in financial Market
+means that real real H money supply
+
+ align:start position:0%
+means that real real H money supply
+ 
+
+ align:start position:0%
+means that real real H money supply
+equals real money demand okay that's
+
+ align:start position:0%
+equals real money demand okay that's
+ 
+
+ align:start position:0%
+equals real money demand okay that's
+what we have
+
+ align:start position:0%
+what we have
+ 
+
+ align:start position:0%
+what we have
+here so this you already see it traces
+
+ align:start position:0%
+here so this you already see it traces
+ 
+
+ align:start position:0%
+here so this you already see it traces
+combinations of out put an interest rate
+
+ align:start position:0%
+combinations of out put an interest rate
+ 
+
+ align:start position:0%
+combinations of out put an interest rate
+which are consistent with equilibrium in
+
+ align:start position:0%
+which are consistent with equilibrium in
+ 
+
+ align:start position:0%
+which are consistent with equilibrium in
+financial
+
+ align:start position:0%
+financial
+ 
+
+ align:start position:0%
+financial
+markets
+
+ align:start position:0%
+markets
+ 
+
+ align:start position:0%
+markets
+okay in the past that's the way the LM
+
+ align:start position:0%
+okay in the past that's the way the LM
+ 
+
+ align:start position:0%
+okay in the past that's the way the LM
+would be
+
+ align:start position:0%
+would be
+ 
+
+ align:start position:0%
+would be
+described we would fix M and say well
+
+ align:start position:0%
+described we would fix M and say well
+ 
+
+ align:start position:0%
+described we would fix M and say well
+this will give you an upward sloping
+
+ align:start position:0%
+this will give you an upward sloping
+ 
+
+ align:start position:0%
+this will give you an upward sloping
+curve no because this is downward
+
+ align:start position:0%
+curve no because this is downward
+ 
+
+ align:start position:0%
+curve no because this is downward
+sloping so if this guy goes up I need to
+
+ align:start position:0%
+sloping so if this guy goes up I need to
+ 
+
+ align:start position:0%
+sloping so if this guy goes up I need to
+if this is constant this guy goes up
+
+ align:start position:0%
+if this is constant this guy goes up
+ 
+
+ align:start position:0%
+if this is constant this guy goes up
+well this guy needs to come down what
+
+ align:start position:0%
+well this guy needs to come down what
+ 
+
+ align:start position:0%
+well this guy needs to come down what
+does that what does bring L down well I
+
+ align:start position:0%
+does that what does bring L down well I
+ 
+
+ align:start position:0%
+does that what does bring L down well I
+go up because L Prime is negative so
+
+ align:start position:0%
+go up because L Prime is negative so
+ 
+
+ align:start position:0%
+go up because L Prime is negative so
+that's the way LM used to be described
+
+ align:start position:0%
+that's the way LM used to be described
+ 
+
+ align:start position:0%
+that's the way LM used to be described
+your life is a lot simpler today it's a
+
+ align:start position:0%
+your life is a lot simpler today it's a
+ 
+
+ align:start position:0%
+your life is a lot simpler today it's a
+lot simpler because central banks don't
+
+ align:start position:0%
+lot simpler because central banks don't
+ 
+
+ align:start position:0%
+lot simpler because central banks don't
+Target monetary aggates they don't
+
+ align:start position:0%
+Target monetary aggates they don't
+ 
+
+ align:start position:0%
+Target monetary aggates they don't
+Target M they target the interest rate
+
+ align:start position:0%
+Target M they target the interest rate
+ 
+
+ align:start position:0%
+Target M they target the interest rate
+directly so they tell you the answer
+
+ align:start position:0%
+directly so they tell you the answer
+ 
+
+ align:start position:0%
+directly so they tell you the answer
+already they
+
+ align:start position:0%
+already they
+ 
+
+ align:start position:0%
+already they
+said what Central Bank when it does
+
+ align:start position:0%
+said what Central Bank when it does
+ 
+
+ align:start position:0%
+said what Central Bank when it does
+policy says look I tell you what I will
+
+ align:start position:0%
+policy says look I tell you what I will
+ 
+
+ align:start position:0%
+policy says look I tell you what I will
+be then if output moves around whatever
+
+ align:start position:0%
+be then if output moves around whatever
+ 
+
+ align:start position:0%
+be then if output moves around whatever
+that's that's problem it's a problem for
+
+ align:start position:0%
+that's that's problem it's a problem for
+ 
+
+ align:start position:0%
+that's that's problem it's a problem for
+M we'll provide the M that the market
+
+ align:start position:0%
+M we'll provide the M that the market
+ 
+
+ align:start position:0%
+M we'll provide the M that the market
+needs in order to have interest rate
+
+ align:start position:0%
+needs in order to have interest rate
+ 
+
+ align:start position:0%
+needs in order to have interest rate
+equal to the one we want okay so so it's
+
+ align:start position:0%
+equal to the one we want okay so so it's
+ 
+
+ align:start position:0%
+equal to the one we want okay so so it's
+it's it it is true that it captures all
+
+ align:start position:0%
+it's it it is true that it captures all
+ 
+
+ align:start position:0%
+it's it it is true that it captures all
+the combinations of output and interest
+
+ align:start position:0%
+the combinations of output and interest
+ 
+
+ align:start position:0%
+the combinations of output and interest
+that are consistent with equilibrium in
+
+ align:start position:0%
+that are consistent with equilibrium in
+ 
+
+ align:start position:0%
+that are consistent with equilibrium in
+the financial markets but it's very
+
+ align:start position:0%
+the financial markets but it's very
+ 
+
+ align:start position:0%
+the financial markets but it's very
+simple because the the the what the FED
+
+ align:start position:0%
+simple because the the the what the FED
+ 
+
+ align:start position:0%
+simple because the the the what the FED
+does in the US other central banks do is
+
+ align:start position:0%
+does in the US other central banks do is
+ 
+
+ align:start position:0%
+does in the US other central banks do is
+they say okay this is the interest rate
+
+ align:start position:0%
+they say okay this is the interest rate
+ 
+
+ align:start position:0%
+they say okay this is the interest rate
+we want and now you can put any amount
+
+ align:start position:0%
+we want and now you can put any amount
+ 
+
+ align:start position:0%
+we want and now you can put any amount
+of output you want as long as we remain
+
+ align:start position:0%
+of output you want as long as we remain
+ 
+
+ align:start position:0%
+of output you want as long as we remain
+committed to this interest rate it will
+
+ align:start position:0%
+committed to this interest rate it will
+ 
+
+ align:start position:0%
+committed to this interest rate it will
+be consistent with equilibrium in the in
+
+ align:start position:0%
+be consistent with equilibrium in the in
+ 
+
+ align:start position:0%
+be consistent with equilibrium in the in
+the financial markets because we will do
+
+ align:start position:0%
+the financial markets because we will do
+ 
+
+ align:start position:0%
+the financial markets because we will do
+it so and the way we will do it so is
+
+ align:start position:0%
+it so and the way we will do it so is
+ 
+
+ align:start position:0%
+it so and the way we will do it so is
+we'll provide as much M as the market
+
+ align:start position:0%
+we'll provide as much M as the market
+ 
+
+ align:start position:0%
+we'll provide as much M as the market
+needs so that that combination of output
+
+ align:start position:0%
+needs so that that combination of output
+ 
+
+ align:start position:0%
+needs so that that combination of output
+and interest rate is an equilibrium in
+
+ align:start position:0%
+and interest rate is an equilibrium in
+ 
+
+ align:start position:0%
+and interest rate is an equilibrium in
+the financial Market that is that's a
+
+ align:start position:0%
+the financial Market that is that's a
+ 
+
+ align:start position:0%
+the financial Market that is that's a
+very long way of saying that the FED
+
+ align:start position:0%
+very long way of saying that the FED
+ 
+
+ align:start position:0%
+very long way of saying that the FED
+sets I and then m is whatever this is
+
+ align:start position:0%
+sets I and then m is whatever this is
+ 
+
+ align:start position:0%
+sets I and then m is whatever this is
+needed for this equation to be in
+
+ align:start position:0%
+needed for this equation to be in
+ 
+
+ align:start position:0%
+needed for this equation to be in
+equilibrium so if output Rises and The
+
+ align:start position:0%
+equilibrium so if output Rises and The
+ 
+
+ align:start position:0%
+equilibrium so if output Rises and The
+Fed doesn't want to change the interest
+
+ align:start position:0%
+Fed doesn't want to change the interest
+ 
+
+ align:start position:0%
+Fed doesn't want to change the interest
+rate that means you need to change m
+
+ align:start position:0%
+rate that means you need to change m
+ 
+
+ align:start position:0%
+rate that means you need to change m
+okay so suppose that the FED says I want
+
+ align:start position:0%
+okay so suppose that the FED says I want
+ 
+
+ align:start position:0%
+okay so suppose that the FED says I want
+this interest rate to be fixed at this
+
+ align:start position:0%
+this interest rate to be fixed at this
+ 
+
+ align:start position:0%
+this interest rate to be fixed at this
+level call it I zero and now output
+
+ align:start position:0%
+level call it I zero and now output
+ 
+
+ align:start position:0%
+level call it I zero and now output
+turns out to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+higher what will the FED do in order to
+
+ align:start position:0%
+higher what will the FED do in order to
+ 
+
+ align:start position:0%
+higher what will the FED do in order to
+ensure that I remains at i z what if the
+
+ align:start position:0%
+ensure that I remains at i z what if the
+ 
+
+ align:start position:0%
+ensure that I remains at i z what if the
+FED doesn't do
+
+ align:start position:0%
+FED doesn't do
+ 
+
+ align:start position:0%
+FED doesn't do
+anything so the FED says I want I equals
+
+ align:start position:0%
+anything so the FED says I want I equals
+ 
+
+ align:start position:0%
+anything so the FED says I want I equals
+z and and the FED is calculated that
+
+ align:start position:0%
+z and and the FED is calculated that
+ 
+
+ align:start position:0%
+z and and the FED is calculated that
+output will be about certain level and
+
+ align:start position:0%
+output will be about certain level and
+ 
+
+ align:start position:0%
+output will be about certain level and
+it turns out that output is higher
+
+ align:start position:0%
+it turns out that output is higher
+ 
+
+ align:start position:0%
+it turns out that output is higher
+what happens if the FED doesn't
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+react and keeps the interest rate at I
+
+ align:start position:0%
+react and keeps the interest rate at I
+ 
+
+ align:start position:0%
+react and keeps the interest rate at I
+zero and output T to be higher than what
+
+ align:start position:0%
+zero and output T to be higher than what
+ 
+
+ align:start position:0%
+zero and output T to be higher than what
+they thought when they provided the M
+
+ align:start position:0%
+they thought when they provided the M
+ 
+
+ align:start position:0%
+they thought when they provided the M
+that they thought the market needed to
+
+ align:start position:0%
+that they thought the market needed to
+ 
+
+ align:start position:0%
+that they thought the market needed to
+be in equilibrium of that interest rate
+
+ align:start position:0%
+be in equilibrium of that interest rate
+ 
+
+ align:start position:0%
+be in equilibrium of that interest rate
+what will
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+happen well the interest rate will go up
+
+ align:start position:0%
+happen well the interest rate will go up
+ 
+
+ align:start position:0%
+happen well the interest rate will go up
+because money demand will exceed money
+
+ align:start position:0%
+because money demand will exceed money
+ 
+
+ align:start position:0%
+because money demand will exceed money
+supply well the only way to restory
+
+ align:start position:0%
+supply well the only way to restory
+ 
+
+ align:start position:0%
+supply well the only way to restory
+equilibrium is for interest rate to go
+
+ align:start position:0%
+equilibrium is for interest rate to go
+ 
+
+ align:start position:0%
+equilibrium is for interest rate to go
+up but the FED doesn't want that so what
+
+ align:start position:0%
+up but the FED doesn't want that so what
+ 
+
+ align:start position:0%
+up but the FED doesn't want that so what
+the FED will do is when it feels that it
+
+ align:start position:0%
+the FED will do is when it feels that it
+ 
+
+ align:start position:0%
+the FED will do is when it feels that it
+feels the interest rat are going up they
+
+ align:start position:0%
+feels the interest rat are going up they
+ 
+
+ align:start position:0%
+feels the interest rat are going up they
+will provide more money so so they can
+
+ align:start position:0%
+will provide more money so so they can
+ 
+
+ align:start position:0%
+will provide more money so so they can
+restore equilibrium in the financial
+
+ align:start position:0%
+restore equilibrium in the financial
+ 
+
+ align:start position:0%
+restore equilibrium in the financial
+Market at that level of interest rate
+
+ align:start position:0%
+Market at that level of interest rate
+ 
+
+ align:start position:0%
+Market at that level of interest rate
+despite the fact that output end up
+
+ align:start position:0%
+despite the fact that output end up
+ 
+
+ align:start position:0%
+despite the fact that output end up
+being higher than they thought so all
+
+ align:start position:0%
+being higher than they thought so all
+ 
+
+ align:start position:0%
+being higher than they thought so all
+this is a long winded way to say that
+
+ align:start position:0%
+this is a long winded way to say that
+ 
+
+ align:start position:0%
+this is a long winded way to say that
+the LM is the modern LM is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+horizontal a few years ago that curve
+
+ align:start position:0%
+horizontal a few years ago that curve
+ 
+
+ align:start position:0%
+horizontal a few years ago that curve
+would have been upward sloping but given
+
+ align:start position:0%
+would have been upward sloping but given
+ 
+
+ align:start position:0%
+would have been upward sloping but given
+the way monetary policy is conducted
+
+ align:start position:0%
+the way monetary policy is conducted
+ 
+
+ align:start position:0%
+the way monetary policy is conducted
+nowadays your life is a lot simpler the
+
+ align:start position:0%
+nowadays your life is a lot simpler the
+ 
+
+ align:start position:0%
+nowadays your life is a lot simpler the
+L is a horizontal curve okay the FED
+
+ align:start position:0%
+L is a horizontal curve okay the FED
+ 
+
+ align:start position:0%
+L is a horizontal curve okay the FED
+tells you the Central Bank tells you H
+
+ align:start position:0%
+tells you the Central Bank tells you H
+ 
+
+ align:start position:0%
+tells you the Central Bank tells you H
+what the interest rate has to be and
+
+ align:start position:0%
+what the interest rate has to be and
+ 
+
+ align:start position:0%
+what the interest rate has to be and
+then it will give whatever M will
+
+ align:start position:0%
+then it will give whatever M will
+ 
+
+ align:start position:0%
+then it will give whatever M will
+provide whatever m is needed so that's
+
+ align:start position:0%
+provide whatever m is needed so that's
+ 
+
+ align:start position:0%
+provide whatever m is needed so that's
+the equilibrium
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+industry so what shift the modern LM
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and by modern I only mean the book
+
+ align:start position:0%
+and by modern I only mean the book
+ 
+
+ align:start position:0%
+and by modern I only mean the book
+doesn't use the terminology but by
+
+ align:start position:0%
+doesn't use the terminology but by
+ 
+
+ align:start position:0%
+doesn't use the terminology but by
+modern I mean that the FED decides what
+
+ align:start position:0%
+modern I mean that the FED decides what
+ 
+
+ align:start position:0%
+modern I mean that the FED decides what
+the interest it
+
+ align:start position:0%
+the interest it
+ 
+
+ align:start position:0%
+the interest it
+is exactly the only thing that will
+
+ align:start position:0%
+is exactly the only thing that will
+ 
+
+ align:start position:0%
+is exactly the only thing that will
+shift into to your life is very simple
+
+ align:start position:0%
+shift into to your life is very simple
+ 
+
+ align:start position:0%
+shift into to your life is very simple
+the only thing that will shift the mod
+
+ align:start position:0%
+the only thing that will shift the mod
+ 
+
+ align:start position:0%
+the only thing that will shift the mod
+LM is that the FED changes its
+
+ align:start position:0%
+LM is that the FED changes its
+ 
+
+ align:start position:0%
+LM is that the FED changes its
+mind a few years back it would have been
+
+ align:start position:0%
+mind a few years back it would have been
+ 
+
+ align:start position:0%
+mind a few years back it would have been
+more
+
+ align:start position:0%
+more
+ 
+
+ align:start position:0%
+more
+complicated a change in money demand
+
+ align:start position:0%
+complicated a change in money demand
+ 
+
+ align:start position:0%
+complicated a change in money demand
+a a change in money supply all those
+
+ align:start position:0%
+a a change in money supply all those
+ 
+
+ align:start position:0%
+a a change in money supply all those
+things will be Shifting the LM around
+
+ align:start position:0%
+things will be Shifting the LM around
+ 
+
+ align:start position:0%
+things will be Shifting the LM around
+now in this setup is very simple no it
+
+ align:start position:0%
+now in this setup is very simple no it
+ 
+
+ align:start position:0%
+now in this setup is very simple no it
+will change only if the feds changes his
+
+ align:start position:0%
+will change only if the feds changes his
+ 
+
+ align:start position:0%
+will change only if the feds changes his
+mind now obviously the FED is not just a
+
+ align:start position:0%
+mind now obviously the FED is not just a
+ 
+
+ align:start position:0%
+mind now obviously the FED is not just a
+moody institution it will change the
+
+ align:start position:0%
+moody institution it will change the
+ 
+
+ align:start position:0%
+moody institution it will change the
+mind and sometimes is forced to change
+
+ align:start position:0%
+mind and sometimes is forced to change
+ 
+
+ align:start position:0%
+mind and sometimes is forced to change
+its
+
+ align:start position:0%
+its
+ 
+
+ align:start position:0%
+its
+mind I mean they're not happy with the
+
+ align:start position:0%
+mind I mean they're not happy with the
+ 
+
+ align:start position:0%
+mind I mean they're not happy with the
+interest rate they're setting
+
+ align:start position:0%
+interest rate they're setting
+ 
+
+ align:start position:0%
+interest rate they're setting
+nowadays they' been forced into that
+
+ align:start position:0%
+nowadays they' been forced into that
+ 
+
+ align:start position:0%
+nowadays they' been forced into that
+were very reluctant to go into very high
+
+ align:start position:0%
+were very reluctant to go into very high
+ 
+
+ align:start position:0%
+were very reluctant to go into very high
+interest rate but you know what is
+
+ align:start position:0%
+interest rate but you know what is
+ 
+
+ align:start position:0%
+interest rate but you know what is
+happening around with very high
+
+ align:start position:0%
+happening around with very high
+ 
+
+ align:start position:0%
+happening around with very high
+consumption and the impact that it's
+
+ align:start position:0%
+consumption and the impact that it's
+ 
+
+ align:start position:0%
+consumption and the impact that it's
+having on inflation they have been
+
+ align:start position:0%
+having on inflation they have been
+ 
+
+ align:start position:0%
+having on inflation they have been
+forced into moving interest rate not
+
+ align:start position:0%
+forced into moving interest rate not
+ 
+
+ align:start position:0%
+forced into moving interest rate not
+only very high but also very fast and
+
+ align:start position:0%
+only very high but also very fast and
+ 
+
+ align:start position:0%
+only very high but also very fast and
+and and and uh that was very risky we
+
+ align:start position:0%
+and and and uh that was very risky we
+ 
+
+ align:start position:0%
+and and and uh that was very risky we
+have been lucky that that nothing has
+
+ align:start position:0%
+have been lucky that that nothing has
+ 
+
+ align:start position:0%
+have been lucky that that nothing has
+really broken when normally when central
+
+ align:start position:0%
+really broken when normally when central
+ 
+
+ align:start position:0%
+really broken when normally when central
+banks raise interest so fast they break
+
+ align:start position:0%
+banks raise interest so fast they break
+ 
+
+ align:start position:0%
+banks raise interest so fast they break
+something along the way somebody's very
+
+ align:start position:0%
+something along the way somebody's very
+ 
+
+ align:start position:0%
+something along the way somebody's very
+lever out there some bank or something
+
+ align:start position:0%
+lever out there some bank or something
+ 
+
+ align:start position:0%
+lever out there some bank or something
+like that and you can you can blow up
+
+ align:start position:0%
+like that and you can you can blow up
+ 
+
+ align:start position:0%
+like that and you can you can blow up
+the UK we had a little scare with some
+
+ align:start position:0%
+the UK we had a little scare with some
+ 
+
+ align:start position:0%
+the UK we had a little scare with some
+insurance companies but
+
+ align:start position:0%
+insurance companies but
+ 
+
+ align:start position:0%
+insurance companies but
+but but was for a different reason
+
+ align:start position:0%
+but but was for a different reason
+ 
+
+ align:start position:0%
+but but was for a different reason
+but but it's it's scary to move policy
+
+ align:start position:0%
+but but it's it's scary to move policy
+ 
+
+ align:start position:0%
+but but it's it's scary to move policy
+very fast because this is a very
+
+ align:start position:0%
+very fast because this is a very
+ 
+
+ align:start position:0%
+very fast because this is a very
+important price for financial markets
+
+ align:start position:0%
+important price for financial markets
+ 
+
+ align:start position:0%
+important price for financial markets
+everything in financial Market gets
+
+ align:start position:0%
+everything in financial Market gets
+ 
+
+ align:start position:0%
+everything in financial Market gets
+priced off that's a starting any pricing
+
+ align:start position:0%
+priced off that's a starting any pricing
+ 
+
+ align:start position:0%
+priced off that's a starting any pricing
+model for stocks for anything will start
+
+ align:start position:0%
+model for stocks for anything will start
+ 
+
+ align:start position:0%
+model for stocks for anything will start
+from that policy rate then everything
+
+ align:start position:0%
+from that policy rate then everything
+ 
+
+ align:start position:0%
+from that policy rate then everything
+builds from there so if this has to move
+
+ align:start position:0%
+builds from there so if this has to move
+ 
+
+ align:start position:0%
+builds from there so if this has to move
+fast you can have lots of
+
+ align:start position:0%
+fast you can have lots of
+ 
+
+ align:start position:0%
+fast you can have lots of
+dislocation so my goal for today is to
+
+ align:start position:0%
+dislocation so my goal for today is to
+ 
+
+ align:start position:0%
+dislocation so my goal for today is to
+just to give you the instr and then
+
+ align:start position:0%
+just to give you the instr and then
+ 
+
+ align:start position:0%
+just to give you the instr and then
+we're going to all talk about
+
+ align:start position:0%
+we're going to all talk about
+ 
+
+ align:start position:0%
+we're going to all talk about
+combinations things that we did in
+
+ align:start position:0%
+combinations things that we did in
+ 
+
+ align:start position:0%
+combinations things that we did in
+certain episodes and and things of that
+
+ align:start position:0%
+certain episodes and and things of that
+ 
+
+ align:start position:0%
+certain episodes and and things of that
+kind okay good so again this part of the
+
+ align:start position:0%
+kind okay good so again this part of the
+ 
+
+ align:start position:0%
+kind okay good so again this part of the
+course is this part of the of the ISL
+
+ align:start position:0%
+course is this part of the of the ISL
+ 
+
+ align:start position:0%
+course is this part of the of the ISL
+mod is very easy and it's a lot easier
+
+ align:start position:0%
+mod is very easy and it's a lot easier
+ 
+
+ align:start position:0%
+mod is very easy and it's a lot easier
+now than it was a few years back okay so
+
+ align:start position:0%
+now than it was a few years back okay so
+ 
+
+ align:start position:0%
+now than it was a few years back okay so
+what does the eslm mo the slm M me
+
+ align:start position:0%
+what does the eslm mo the slm M me
+ 
+
+ align:start position:0%
+what does the eslm mo the slm M me
+simply mean puts the two curves together
+
+ align:start position:0%
+simply mean puts the two curves together
+ 
+
+ align:start position:0%
+simply mean puts the two curves together
+now we have two Curves in the space of
+
+ align:start position:0%
+now we have two Curves in the space of
+ 
+
+ align:start position:0%
+now we have two Curves in the space of
+output and interest rate and two
+
+ align:start position:0%
+output and interest rate and two
+ 
+
+ align:start position:0%
+output and interest rate and two
+unknowns which is output and interest
+
+ align:start position:0%
+unknowns which is output and interest
+ 
+
+ align:start position:0%
+unknowns which is output and interest
+rate
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so we have one combination only a that
+
+ align:start position:0%
+so we have one combination only a that
+ 
+
+ align:start position:0%
+so we have one combination only a that
+is consistent with both equilibrium in
+
+ align:start position:0%
+is consistent with both equilibrium in
+ 
+
+ align:start position:0%
+is consistent with both equilibrium in
+the Goods Market and equilibrium in
+
+ align:start position:0%
+the Goods Market and equilibrium in
+ 
+
+ align:start position:0%
+the Goods Market and equilibrium in
+financial Market that's the point
+
+ align:start position:0%
+financial Market that's the point
+ 
+
+ align:start position:0%
+financial Market that's the point
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+okay what happens to points to the right
+
+ align:start position:0%
+okay what happens to points to the right
+ 
+
+ align:start position:0%
+okay what happens to points to the right
+suppose I I I what happen What Happens
+
+ align:start position:0%
+suppose I I I what happen What Happens
+ 
+
+ align:start position:0%
+suppose I I I what happen What Happens
+here if I show you this point in this
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+space what what's wrong with that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+point so point to the a point along the
+
+ align:start position:0%
+point so point to the a point along the
+ 
+
+ align:start position:0%
+point so point to the a point along the
+lamp but to the right what's wrong
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+there well if it is along the LM I know
+
+ align:start position:0%
+there well if it is along the LM I know
+ 
+
+ align:start position:0%
+there well if it is along the LM I know
+that I'm okay with financial Market that
+
+ align:start position:0%
+that I'm okay with financial Market that
+ 
+
+ align:start position:0%
+that I'm okay with financial Market that
+those points are consistent with
+
+ align:start position:0%
+those points are consistent with
+ 
+
+ align:start position:0%
+those points are consistent with
+equilibrium in financial
+
+ align:start position:0%
+equilibrium in financial
+ 
+
+ align:start position:0%
+equilibrium in financial
+Market but it's not my equilibrium and
+
+ align:start position:0%
+Market but it's not my equilibrium and
+ 
+
+ align:start position:0%
+Market but it's not my equilibrium and
+it has to be in consistent with the
+
+ align:start position:0%
+it has to be in consistent with the
+ 
+
+ align:start position:0%
+it has to be in consistent with the
+other one it's not consistent with
+
+ align:start position:0%
+other one it's not consistent with
+ 
+
+ align:start position:0%
+other one it's not consistent with
+equilibrium in the Goods Market in fact
+
+ align:start position:0%
+equilibrium in the Goods Market in fact
+ 
+
+ align:start position:0%
+equilibrium in the Goods Market in fact
+you know more than that what's wrong
+
+ align:start position:0%
+you know more than that what's wrong
+ 
+
+ align:start position:0%
+you know more than that what's wrong
+with Goods Market there's an imbalance
+
+ align:start position:0%
+with Goods Market there's an imbalance
+ 
+
+ align:start position:0%
+with Goods Market there's an imbalance
+there but in which
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+direction that point
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here what do you mean by excess of
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+goods no demand is exactly insufficient
+
+ align:start position:0%
+goods no demand is exactly insufficient
+ 
+
+ align:start position:0%
+goods no demand is exactly insufficient
+demand there's too much output for that
+
+ align:start position:0%
+demand there's too much output for that
+ 
+
+ align:start position:0%
+demand there's too much output for that
+demand so that's the reason it's not
+
+ align:start position:0%
+demand so that's the reason it's not
+ 
+
+ align:start position:0%
+demand so that's the reason it's not
+consistent with equilibrium in the Goods
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+ 
+
+ align:start position:0%
+consistent with equilibrium in the Goods
+Market okay to the left is the opposite
+
+ align:start position:0%
+Market okay to the left is the opposite
+ 
+
+ align:start position:0%
+Market okay to the left is the opposite
+no to the left we have insufficient
+
+ align:start position:0%
+no to the left we have insufficient
+ 
+
+ align:start position:0%
+no to the left we have insufficient
+output for the demand we have so it's
+
+ align:start position:0%
+output for the demand we have so it's
+ 
+
+ align:start position:0%
+output for the demand we have so it's
+not consistent with equilibrium in the
+
+ align:start position:0%
+not consistent with equilibrium in the
+ 
+
+ align:start position:0%
+not consistent with equilibrium in the
+the Goods Market so the only point that
+
+ align:start position:0%
+the Goods Market so the only point that
+ 
+
+ align:start position:0%
+the Goods Market so the only point that
+is consistent oh well you can think what
+
+ align:start position:0%
+is consistent oh well you can think what
+ 
+
+ align:start position:0%
+is consistent oh well you can think what
+happens with a point here for
+
+ align:start position:0%
+happens with a point here for
+ 
+
+ align:start position:0%
+happens with a point here for
+example that point because it's in the
+
+ align:start position:0%
+example that point because it's in the
+ 
+
+ align:start position:0%
+example that point because it's in the
+curve is consistent with equilibrium in
+
+ align:start position:0%
+curve is consistent with equilibrium in
+ 
+
+ align:start position:0%
+curve is consistent with equilibrium in
+the Goods Market but it's not consistent
+
+ align:start position:0%
+the Goods Market but it's not consistent
+ 
+
+ align:start position:0%
+the Goods Market but it's not consistent
+with equilibrium in Financial Market
+
+ align:start position:0%
+with equilibrium in Financial Market
+ 
+
+ align:start position:0%
+with equilibrium in Financial Market
+okay what do we have there supposed
+
+ align:start position:0%
+okay what do we have there supposed
+ 
+
+ align:start position:0%
+okay what do we have there supposed
+having in that point the interest rate
+
+ align:start position:0%
+having in that point the interest rate
+ 
+
+ align:start position:0%
+having in that point the interest rate
+is too high so that means the money
+
+ align:start position:0%
+is too high so that means the money
+ 
+
+ align:start position:0%
+is too high so that means the money
+demand is low so too much money demand
+
+ align:start position:0%
+demand is low so too much money demand
+ 
+
+ align:start position:0%
+demand is low so too much money demand
+for money supply okay that's that's what
+
+ align:start position:0%
+for money supply okay that's that's what
+ 
+
+ align:start position:0%
+for money supply okay that's that's what
+you have so those are not so so that's
+
+ align:start position:0%
+you have so those are not so so that's
+ 
+
+ align:start position:0%
+you have so those are not so so that's
+at the end of the day you know this is
+
+ align:start position:0%
+at the end of the day you know this is
+ 
+
+ align:start position:0%
+at the end of the day you know this is
+the only equilibrium point we have and
+
+ align:start position:0%
+the only equilibrium point we have and
+ 
+
+ align:start position:0%
+the only equilibrium point we have and
+and all the experiments I want to do
+
+ align:start position:0%
+and all the experiments I want to do
+ 
+
+ align:start position:0%
+and all the experiments I want to do
+next have to do with moving one curve or
+
+ align:start position:0%
+next have to do with moving one curve or
+ 
+
+ align:start position:0%
+next have to do with moving one curve or
+the other and see what happens to trace
+
+ align:start position:0%
+the other and see what happens to trace
+ 
+
+ align:start position:0%
+the other and see what happens to trace
+new equilibrium points okay but try to
+
+ align:start position:0%
+new equilibrium points okay but try to
+ 
+
+ align:start position:0%
+new equilibrium points okay but try to
+understand
+
+ align:start position:0%
+understand
+ 
+
+ align:start position:0%
+understand
+very well these diagrams of what
+
+ align:start position:0%
+very well these diagrams of what
+ 
+
+ align:start position:0%
+very well these diagrams of what
+happens when I move up horizontally and
+
+ align:start position:0%
+happens when I move up horizontally and
+ 
+
+ align:start position:0%
+happens when I move up horizontally and
+so on and convince yourself that this is
+
+ align:start position:0%
+so on and convince yourself that this is
+ 
+
+ align:start position:0%
+so on and convince yourself that this is
+the only combination it's pretty easy to
+
+ align:start position:0%
+the only combination it's pretty easy to
+ 
+
+ align:start position:0%
+the only combination it's pretty easy to
+convince yourself it's the only
+
+ align:start position:0%
+convince yourself it's the only
+ 
+
+ align:start position:0%
+convince yourself it's the only
+combination but think a little try to
+
+ align:start position:0%
+combination but think a little try to
+ 
+
+ align:start position:0%
+combination but think a little try to
+get away from point A and see what
+
+ align:start position:0%
+get away from point A and see what
+ 
+
+ align:start position:0%
+get away from point A and see what
+happens I guess the best way to do that
+
+ align:start position:0%
+happens I guess the best way to do that
+ 
+
+ align:start position:0%
+happens I guess the best way to do that
+is just to do experiment meaning move
+
+ align:start position:0%
+is just to do experiment meaning move
+ 
+
+ align:start position:0%
+is just to do experiment meaning move
+parameters of these curves and see how
+
+ align:start position:0%
+parameters of these curves and see how
+ 
+
+ align:start position:0%
+parameters of these curves and see how
+equilibrium output changes and so
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+on so let's do the first
+
+ align:start position:0%
+on so let's do the first
+ 
+
+ align:start position:0%
+on so let's do the first
+experiment and yeah
+
+ align:start position:0%
+experiment and yeah
+ 
+
+ align:start position:0%
+experiment and yeah
+maybe so let's let's let's play with
+
+ align:start position:0%
+maybe so let's let's let's play with
+ 
+
+ align:start position:0%
+maybe so let's let's let's play with
+this so now you have you have your model
+
+ align:start position:0%
+this so now you have you have your model
+ 
+
+ align:start position:0%
+this so now you have you have your model
+and now we can start asking interesting
+
+ align:start position:0%
+and now we can start asking interesting
+ 
+
+ align:start position:0%
+and now we can start asking interesting
+questions the first thing you can ask is
+
+ align:start position:0%
+questions the first thing you can ask is
+ 
+
+ align:start position:0%
+questions the first thing you can ask is
+well fiscal policy how does it
+
+ align:start position:0%
+well fiscal policy how does it
+ 
+
+ align:start position:0%
+well fiscal policy how does it
+work
+
+ align:start position:0%
+work
+ 
+
+ align:start position:0%
+work
+well
+
+ align:start position:0%
+well
+ 
+
+ align:start position:0%
+well
+sorry so here this this is a contraction
+
+ align:start position:0%
+sorry so here this this is a contraction
+ 
+
+ align:start position:0%
+sorry so here this this is a contraction
+in fiscal policy so the same as we did
+
+ align:start position:0%
+in fiscal policy so the same as we did
+ 
+
+ align:start position:0%
+in fiscal policy so the same as we did
+before remember we increase taxes or we
+
+ align:start position:0%
+before remember we increase taxes or we
+ 
+
+ align:start position:0%
+before remember we increase taxes or we
+could have reduced go expenditure
+
+ align:start position:0%
+could have reduced go expenditure
+ 
+
+ align:start position:0%
+could have reduced go expenditure
+whatever that would have shifted the we
+
+ align:start position:0%
+whatever that would have shifted the we
+ 
+
+ align:start position:0%
+whatever that would have shifted the we
+we did that when when we look at the we
+
+ align:start position:0%
+we did that when when we look at the we
+ 
+
+ align:start position:0%
+we did that when when we look at the we
+did exactly that we shift the to to to
+
+ align:start position:0%
+did exactly that we shift the to to to
+ 
+
+ align:start position:0%
+did exactly that we shift the to to to
+the left and what happens here is well
+
+ align:start position:0%
+the left and what happens here is well
+ 
+
+ align:start position:0%
+the left and what happens here is well
+if you shift the to the left there's a
+
+ align:start position:0%
+if you shift the to the left there's a
+ 
+
+ align:start position:0%
+if you shift the to the left there's a
+new combination of output and interest
+
+ align:start position:0%
+new combination of output and interest
+ 
+
+ align:start position:0%
+new combination of output and interest
+rate that is that is consistent with
+
+ align:start position:0%
+rate that is that is consistent with
+ 
+
+ align:start position:0%
+rate that is that is consistent with
+equilibrium both markets that's a lower
+
+ align:start position:0%
+equilibrium both markets that's a lower
+ 
+
+ align:start position:0%
+equilibrium both markets that's a lower
+output okay so if the FED doesn't do
+
+ align:start position:0%
+output okay so if the FED doesn't do
+ 
+
+ align:start position:0%
+output okay so if the FED doesn't do
+anything that means it keeps the LM
+
+ align:start position:0%
+anything that means it keeps the LM
+ 
+
+ align:start position:0%
+anything that means it keeps the LM
+there and there's a contractionary
+
+ align:start position:0%
+there and there's a contractionary
+ 
+
+ align:start position:0%
+there and there's a contractionary
+fiscal policy well that will lead to
+
+ align:start position:0%
+fiscal policy well that will lead to
+ 
+
+ align:start position:0%
+fiscal policy well that will lead to
+contraction in output as well that's the
+
+ align:start position:0%
+contraction in output as well that's the
+ 
+
+ align:start position:0%
+contraction in output as well that's the
+reason we call it contraction not only
+
+ align:start position:0%
+reason we call it contraction not only
+ 
+
+ align:start position:0%
+reason we call it contraction not only
+because fiscal not not only because
+
+ align:start position:0%
+because fiscal not not only because
+ 
+
+ align:start position:0%
+because fiscal not not only because
+govern expenditure decline but it's if
+
+ align:start position:0%
+govern expenditure decline but it's if
+ 
+
+ align:start position:0%
+govern expenditure decline but it's if
+taxes increase that's contractionary
+
+ align:start position:0%
+taxes increase that's contractionary
+ 
+
+ align:start position:0%
+taxes increase that's contractionary
+because it reduces aggregate demand and
+
+ align:start position:0%
+because it reduces aggregate demand and
+ 
+
+ align:start position:0%
+because it reduces aggregate demand and
+the equilibrium that will reduce output
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's canonical contractionary
+
+ align:start position:0%
+okay so that's canonical contractionary
+ 
+
+ align:start position:0%
+okay so that's canonical contractionary
+fiscal policy you move output to the
+
+ align:start position:0%
+fiscal policy you move output to the
+ 
+
+ align:start position:0%
+fiscal policy you move output to the
+left interest rate doesn't move because
+
+ align:start position:0%
+left interest rate doesn't move because
+ 
+
+ align:start position:0%
+left interest rate doesn't move because
+that's controlled by the FED but but
+
+ align:start position:0%
+that's controlled by the FED but but
+ 
+
+ align:start position:0%
+that's controlled by the FED but but
+output declines okay so if somebody ask
+
+ align:start position:0%
+output declines okay so if somebody ask
+ 
+
+ align:start position:0%
+output declines okay so if somebody ask
+you what happens if if if there's a
+
+ align:start position:0%
+you what happens if if if there's a
+ 
+
+ align:start position:0%
+you what happens if if if there's a
+fiscal contraction you were asking a bit
+
+ align:start position:0%
+fiscal contraction you were asking a bit
+ 
+
+ align:start position:0%
+fiscal contraction you were asking a bit
+the the opposite side you know that
+
+ align:start position:0%
+the the opposite side you know that
+ 
+
+ align:start position:0%
+the the opposite side you know that
+people may have spent we have perhaps a
+
+ align:start position:0%
+people may have spent we have perhaps a
+ 
+
+ align:start position:0%
+people may have spent we have perhaps a
+fiscal expansion that was very large but
+
+ align:start position:0%
+fiscal expansion that was very large but
+ 
+
+ align:start position:0%
+fiscal expansion that was very large but
+what happens with a fiscal contraction
+
+ align:start position:0%
+what happens with a fiscal contraction
+ 
+
+ align:start position:0%
+what happens with a fiscal contraction
+well that will lead to lower equilibrium
+
+ align:start position:0%
+well that will lead to lower equilibrium
+ 
+
+ align:start position:0%
+well that will lead to lower equilibrium
+output I keep pring the lower equ what
+
+ align:start position:0%
+output I keep pring the lower equ what
+ 
+
+ align:start position:0%
+output I keep pring the lower equ what
+happens if you have a very large fiscal
+
+ align:start position:0%
+happens if you have a very large fiscal
+ 
+
+ align:start position:0%
+happens if you have a very large fiscal
+expansion what what happens if you have
+
+ align:start position:0%
+expansion what what happens if you have
+ 
+
+ align:start position:0%
+expansion what what happens if you have
+a very large fysical
+
+ align:start position:0%
+a very large fysical
+ 
+
+ align:start position:0%
+a very large fysical
+expansion what moves Ah that's something
+
+ align:start position:0%
+expansion what moves Ah that's something
+ 
+
+ align:start position:0%
+expansion what moves Ah that's something
+that's you should that's a question you
+
+ align:start position:0%
+that's you should that's a question you
+ 
+
+ align:start position:0%
+that's you should that's a question you
+should always ask yourself when when
+
+ align:start position:0%
+should always ask yourself when when
+ 
+
+ align:start position:0%
+should always ask yourself when when
+there is any question
+
+ align:start position:0%
+there is any question
+ 
+
+ align:start position:0%
+there is any question
+islm of islm you should ask which curve
+
+ align:start position:0%
+islm of islm you should ask which curve
+ 
+
+ align:start position:0%
+islm of islm you should ask which curve
+moves start from that always okay so if
+
+ align:start position:0%
+moves start from that always okay so if
+ 
+
+ align:start position:0%
+moves start from that always okay so if
+if we ask you any question about that is
+
+ align:start position:0%
+if we ask you any question about that is
+ 
+
+ align:start position:0%
+if we ask you any question about that is
+obvious about aslm the first thing you
+
+ align:start position:0%
+obvious about aslm the first thing you
+ 
+
+ align:start position:0%
+obvious about aslm the first thing you
+should ask is which Curve will
+
+ align:start position:0%
+should ask is which Curve will
+ 
+
+ align:start position:0%
+should ask is which Curve will
+move
+
+ align:start position:0%
+move
+ 
+
+ align:start position:0%
+move
+so suppose I tell you
+
+ align:start position:0%
+so suppose I tell you
+ 
+
+ align:start position:0%
+so suppose I tell you
+um due to covid the covid shock there
+
+ align:start position:0%
+um due to covid the covid shock there
+ 
+
+ align:start position:0%
+um due to covid the covid shock there
+was a massive ER transfer
+
+ align:start position:0%
+was a massive ER transfer
+ 
+
+ align:start position:0%
+was a massive ER transfer
+income transfer to lowincome individuals
+
+ align:start position:0%
+income transfer to lowincome individuals
+ 
+
+ align:start position:0%
+income transfer to lowincome individuals
+that is we had a very expansionary
+
+ align:start position:0%
+that is we had a very expansionary
+ 
+
+ align:start position:0%
+that is we had a very expansionary
+fiscal
+
+ align:start position:0%
+fiscal
+ 
+
+ align:start position:0%
+fiscal
+policy first thing you should ask is
+
+ align:start position:0%
+policy first thing you should ask is
+ 
+
+ align:start position:0%
+policy first thing you should ask is
+okay which curve moves the LM or the is
+
+ align:start position:0%
+okay which curve moves the LM or the is
+ 
+
+ align:start position:0%
+okay which curve moves the LM or the is
+if I do
+
+ align:start position:0%
+if I do
+ 
+
+ align:start position:0%
+if I do
+that is the is shift to the right does
+
+ align:start position:0%
+that is the is shift to the right does
+ 
+
+ align:start position:0%
+that is the is shift to the right does
+the LM move no has nothing to do with
+
+ align:start position:0%
+the LM move no has nothing to do with
+ 
+
+ align:start position:0%
+the LM move no has nothing to do with
+monetary policy
+
+ align:start position:0%
+monetary policy
+ 
+
+ align:start position:0%
+monetary policy
+okay so that's the first thing you need
+
+ align:start position:0%
+okay so that's the first thing you need
+ 
+
+ align:start position:0%
+okay so that's the first thing you need
+to do which curve is
+
+ align:start position:0%
+to do which curve is
+ 
+
+ align:start position:0%
+to do which curve is
+moving okay if it is fiscal that's a
+
+ align:start position:0%
+moving okay if it is fiscal that's a
+ 
+
+ align:start position:0%
+moving okay if it is fiscal that's a
+Goods Market thing that means it's going
+
+ align:start position:0%
+Goods Market thing that means it's going
+ 
+
+ align:start position:0%
+Goods Market thing that means it's going
+to move the yes not the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+LM what is the mechanism here what
+
+ align:start position:0%
+LM what is the mechanism here what
+ 
+
+ align:start position:0%
+LM what is the mechanism here what
+happened
+
+ align:start position:0%
+happened
+ 
+
+ align:start position:0%
+happened
+well remember what we have is I told you
+
+ align:start position:0%
+well remember what we have is I told you
+ 
+
+ align:start position:0%
+well remember what we have is I told you
+go always back to this diagram if you
+
+ align:start position:0%
+go always back to this diagram if you
+ 
+
+ align:start position:0%
+go always back to this diagram if you
+increase taxes and you keep keep the
+
+ align:start position:0%
+increase taxes and you keep keep the
+ 
+
+ align:start position:0%
+increase taxes and you keep keep the
+interest rate constant and you start
+
+ align:start position:0%
+interest rate constant and you start
+ 
+
+ align:start position:0%
+interest rate constant and you start
+from there so so the interest rate
+
+ align:start position:0%
+from there so so the interest rate
+ 
+
+ align:start position:0%
+from there so so the interest rate
+doesn't move then that will do what what
+
+ align:start position:0%
+doesn't move then that will do what what
+ 
+
+ align:start position:0%
+doesn't move then that will do what what
+increasing taxes did in lecture three
+
+ align:start position:0%
+increasing taxes did in lecture three
+ 
+
+ align:start position:0%
+increasing taxes did in lecture three
+will reduce aggregate demand and then
+
+ align:start position:0%
+will reduce aggregate demand and then
+ 
+
+ align:start position:0%
+will reduce aggregate demand and then
+the multiplier will take us to a larger
+
+ align:start position:0%
+the multiplier will take us to a larger
+ 
+
+ align:start position:0%
+the multiplier will take us to a larger
+decline that the initial fiscal
+
+ align:start position:0%
+decline that the initial fiscal
+ 
+
+ align:start position:0%
+decline that the initial fiscal
+contraction okay and that's a decline in
+
+ align:start position:0%
+contraction okay and that's a decline in
+ 
+
+ align:start position:0%
+contraction okay and that's a decline in
+equilibrium output so that y1 there is
+
+ align:start position:0%
+equilibrium output so that y1 there is
+ 
+
+ align:start position:0%
+equilibrium output so that y1 there is
+exactly a this one
+
+ align:start position:0%
+exactly a this one
+ 
+
+ align:start position:0%
+exactly a this one
+here that y Prime okay I haven't moved
+
+ align:start position:0%
+here that y Prime okay I haven't moved
+ 
+
+ align:start position:0%
+here that y Prime okay I haven't moved
+the interest rate I kept it at the same
+
+ align:start position:0%
+the interest rate I kept it at the same
+ 
+
+ align:start position:0%
+the interest rate I kept it at the same
+level I had a fysical
+
+ align:start position:0%
+level I had a fysical
+ 
+
+ align:start position:0%
+level I had a fysical
+contraction that's what we describe with
+
+ align:start position:0%
+contraction that's what we describe with
+ 
+
+ align:start position:0%
+contraction that's what we describe with
+that diagram well that's my new is I
+
+ align:start position:0%
+that diagram well that's my new is I
+ 
+
+ align:start position:0%
+that diagram well that's my new is I
+have a new
+
+ align:start position:0%
+have a new
+ 
+
+ align:start position:0%
+have a new
+is because for any for the same interest
+
+ align:start position:0%
+is because for any for the same interest
+ 
+
+ align:start position:0%
+is because for any for the same interest
+rate I have a lower equilibrium output
+
+ align:start position:0%
+rate I have a lower equilibrium output
+ 
+
+ align:start position:0%
+rate I have a lower equilibrium output
+and it happens that the FED DM change
+
+ align:start position:0%
+and it happens that the FED DM change
+ 
+
+ align:start position:0%
+and it happens that the FED DM change
+the interest rate so that's going to be
+
+ align:start position:0%
+the interest rate so that's going to be
+ 
+
+ align:start position:0%
+the interest rate so that's going to be
+my equilibrium output the whole curve
+
+ align:start position:0%
+my equilibrium output the whole curve
+ 
+
+ align:start position:0%
+my equilibrium output the whole curve
+moved to the left that would could tell
+
+ align:start position:0%
+moved to the left that would could tell
+ 
+
+ align:start position:0%
+moved to the left that would could tell
+three slides ago but now I know more I
+
+ align:start position:0%
+three slides ago but now I know more I
+ 
+
+ align:start position:0%
+three slides ago but now I know more I
+also know that since the FED hasn't
+
+ align:start position:0%
+also know that since the FED hasn't
+ 
+
+ align:start position:0%
+also know that since the FED hasn't
+reacted I I know exactly what is the new
+
+ align:start position:0%
+reacted I I know exactly what is the new
+ 
+
+ align:start position:0%
+reacted I I know exactly what is the new
+equilibrium output which is this I don't
+
+ align:start position:0%
+equilibrium output which is this I don't
+ 
+
+ align:start position:0%
+equilibrium output which is this I don't
+before we could only tell that the curve
+
+ align:start position:0%
+before we could only tell that the curve
+ 
+
+ align:start position:0%
+before we could only tell that the curve
+has shift to the left now since the fan
+
+ align:start position:0%
+has shift to the left now since the fan
+ 
+
+ align:start position:0%
+has shift to the left now since the fan
+react to that fiscal contraction I also
+
+ align:start position:0%
+react to that fiscal contraction I also
+ 
+
+ align:start position:0%
+react to that fiscal contraction I also
+know the equilibrium output will end up
+
+ align:start position:0%
+know the equilibrium output will end up
+ 
+
+ align:start position:0%
+know the equilibrium output will end up
+at White Prim okay good so I'm want to
+
+ align:start position:0%
+at White Prim okay good so I'm want to
+ 
+
+ align:start position:0%
+at White Prim okay good so I'm want to
+stop here and and and in the next
+
+ align:start position:0%
+stop here and and and in the next
+ 
+
+ align:start position:0%
+stop here and and and in the next
+lecture we'll
+
+ align:start position:0%
+lecture we'll
+ 
+
+ align:start position:0%
+lecture we'll
+continue with this
\ No newline at end of file
diff --git a/r9Jwtxf4SA0.txt b/r9Jwtxf4SA0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..390c7d2fba4766dcd1246fb5aefbdbef08eef7c2
--- /dev/null
+++ b/r9Jwtxf4SA0.txt
@@ -0,0 +1,1158 @@
+ANNOUNCER: The following content
+is provided under a
+
+Creative Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation, or to view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: Hi.
+
+Our lesson today is called
+the 'Inverse Logarithm'.
+
+And what it will do, among other
+things, is give us a
+
+very nice chance to revisit
+inverse functions in general,
+
+only now applied specifically
+to the natural logarithm
+
+function that we talked
+about last time.
+
+So I call today's lesson, as I
+say, 'Inverse Logarithms'.
+
+And to see what's coming up
+here, simply recall that last
+
+time, we invented, so to speak,
+a new function called
+
+the 'natural log of x'.
+
+This had nothing to
+do with exponents.
+
+It was what?
+
+This was the function whose
+derivative with respect to 'x'
+
+was '1/x' and passed through
+the point (1 , 0).
+
+That uniquely defined this
+particular function.
+
+The point being what?
+
+That this particular function,
+since the domain is for
+
+positive 'x', '1/x'
+is positive.
+
+The curve is always rising,
+which means that the function
+
+itself must be one to one.
+
+And because the function is one
+to one, it means that the
+
+inverse function exists.
+
+This is no different from any
+other example of forming f
+
+inverse, given a one to one
+function called 'f'.
+
+So what we do is now,
+and remember how
+
+you invert this function.
+
+If you want to do this thing
+in slow motion, you first
+
+rotate this through 90 degrees,
+then flip it over.
+
+If you want to do it faster, the
+inverse graph of this is
+
+the reflection of this curve
+with respect to the line 'y'
+
+equals 'x'.
+
+In any event, if we do this, we
+find that the graph of the
+
+function 'y' equals
+'inverse log x' is
+
+this particular curve.
+
+And notice the correspondence.
+
+If this is the point (1 , 0) on
+the log curve, the inverse
+
+point is (0 , 1).
+
+In other words, the inverse
+log of 0 is 1.
+
+OK.
+
+Now, the idea is something
+like this.
+
+Just to have a review,
+again, of how--
+
+see, the punchline I want to
+make for today's lesson, right
+
+at the beginning, is that the
+nice thing about studying
+
+inverse functions is that once
+you know the function of which
+
+you're taking the inverse, you
+automatically get all the
+
+mileage you want out of
+the inverse function.
+
+Well, by way of illustration,
+if the function natural log
+
+had the usual logarithmic
+property, we would suspect
+
+that its inverse
+should have the
+
+usual exponential property.
+
+Now what is the usual
+exponential property?
+
+The exponential function is
+characterized by what?
+
+That if you take 'f of 'x1 plus
+x2'', that's 'f of x1'
+
+times 'f of x2'.
+
+So you think of it
+in terms of the
+
+usual exponential notation.
+
+If you have, say, 10 raised to
+the 'x1 plus x2' power, that's
+
+the same as 10 to the
+'x1' power times
+
+10 to the 'x2' power.
+
+In other words, if our ln
+function is genuinely a
+
+logarithmic function, we would
+expect the inverse of that
+
+function to be a genuine
+exponential function.
+
+And just to work with inverses
+again, let's see if this is
+
+indeed true.
+
+Let's see if it's really true
+that the 'inverse log of 'x1
+
+plus x2'' is the 'inverse
+log of x1' times the
+
+'inverse log of x2'.
+
+You see, the whole
+idea is what?
+
+Let's give these things names.
+
+Let 'y1' be the 'inverse log
+of x1' and 'y2' be the
+
+'inverse log of x2'.
+
+Now, since we've already
+studied the natural log
+
+function, the most natural thing
+to do here is to invert
+
+these, namely 'y1' equals the
+inverse 'natural log of x1' is
+
+the same as saying 'x1' is
+the 'natural log of y1'.
+
+And similarly, this is the same
+as saying that 'x2' is
+
+the 'natural log of y2'.
+
+And now we add equals to equals,
+and we get that 'x1
+
+plus x2' is 'natural log y1'
+plus 'natural log y2'.
+
+But allegedly, we understand the
+properties of the natural
+
+log, because if we didn't
+understand those, it would be
+
+kind of futile to be studying
+the inverse function.
+
+What do we know about
+the natural log?
+
+We know that the 'natural
+log of 'y1 times y2', by
+
+definition of a logarithmic
+function, is 'log
+
+y1' plus 'log y2'.
+
+In other words, 'natural log y1'
+plus 'natural log y2', by
+
+the property of being
+logarithmic, is just the
+
+'natural log of 'y1
+times y2''.
+
+And now, taking this
+relationship and inverting it
+
+to say this is the same
+as saying what?
+
+The 'inverse natural log of 'x1
+plus x2'' is equal to 'y1'
+
+times 'y2'.
+
+And if we now observe that 'y1'
+was the 'inverse natural
+
+log of x1', and 'y2' is the
+'inverse natural log of x2',
+
+we have the result that we
+claimed we would have at the
+
+beginning here.
+
+Now again, here's one example
+where it's not the result that
+
+I'm not interested in.
+
+But I'm interested in showing,
+again, what we meant when we
+
+said that once we learn a new
+concept, we can bring to it
+
+all of our old knowledge.
+
+You see, all of these things
+come from our basic
+
+definition.
+
+Well, let's carry on
+one step further.
+
+You see, this was an arithmetic
+property.
+
+Let's see if we can get some
+calculus properties about the
+
+inverse natural log based on our
+knowledge of the natural
+
+log itself.
+
+Well, for example, in a course
+of this type, the most natural
+
+thing to do, I guess, is given
+any function, we would always
+
+like to be able to talk about
+its derivative, provided, of
+
+course, the function
+is differentiable.
+
+So for example, a typical
+question that one might ask is
+
+find 'dy dx', if 'y' is 'inverse
+natural log x'.
+
+Again, this works the same way
+as it did for the inverse trig
+
+functions, for the inverse of
+everything that we've done so
+
+far in this course.
+
+We start with this particular
+relationship and right away
+
+translate it into that which
+we're more familiar with,
+
+namely we translate 'y' equals
+the 'inverse natural log of x'
+
+into 'x' equals 'natural
+log y'.
+
+Now you see again, since I know
+how to differentiate 'log
+
+y' with respect to 'y', the
+derivative of 'natural log y'
+
+with respect to 'y' was
+by definition '1/y'.
+
+From this relationship
+here, I can find
+
+that 'dx dy' is '1/y'.
+
+And knowing that 'dx dy' is
+'1/y', using my inverse
+
+function general theory that
+tells me that to find the
+
+derivative of 'y' with respect
+to 'x', all I have to do is
+
+invert the derivative of 'x'
+with respect to 'y', I wind up
+
+with the fact that 'dy dx'
+is equal to 'y' itself.
+
+In other words, the 'inverse
+log x' function is
+
+characterized by the fact that
+it's its own derivative.
+
+In other words, it's a
+non-destructible type of
+
+function with respect
+to differentiation.
+
+This is a rather powerful
+property.
+
+You see what this thing says?
+
+It says that the derivative
+of 'y' with respect
+
+to 'x' is 'y' itself.
+
+By the way, just as an aside, we
+can do the converse of this
+
+particular problem.
+
+You see, we started with 'y'
+equals 'inverse log x' and
+
+showed that this particular
+equation was satisfied.
+
+Notice that if we start with
+this particular equation,
+
+starting with 'dy dx' equals
+'y', separate the variables,
+
+and lo and behold, we wind up
+with 'dy over y' equals 'dx'.
+
+And without carrying out the
+details, I leave this to you,
+
+because it is straightforward.
+
+Notice that as we look at the
+left hand side here, we
+
+hopefully will think
+immediately
+
+of the natural logarithm.
+
+Namely, what do we want here?
+
+The function whose derivative
+with respect to 'y' is '1/y'.
+
+Again, you see what I'm saying
+is notice that if we had
+
+started with this particular
+differential equation, we
+
+could have shown that a
+logarithm, and hence solving
+
+for 'y' explicitly, would
+have led to the
+
+inverse logarithm also.
+
+But at any rate, notice then
+that we can find the
+
+derivative of the inverse log
+just by knowing how to find
+
+the derivative of the natural
+log itself, which is as we
+
+expect things should be.
+
+Again, and this is a notational
+thing, we do not
+
+use the language in general
+"inverse log x."
+
+In other words, it's quite
+conventional to talk about
+
+'inverse sine x'.
+
+You may notice that sometimes
+in the text, sometimes in my
+
+lectures I may have used
+the word 'arcsin x'.
+
+But the general notation
+is sine to the minus 1.
+
+However, when it comes to the
+natural logarithm function,
+
+the inverse is usually
+not written as
+
+'inverse natural log x'.
+
+It's usually abbreviated, and
+let me say this, by the symbol
+
+'e to the x'.
+
+Now the reason I say by
+the symbol is this.
+
+If I wanted to, I can say, look,
+If I've never heard of
+
+exponents before, let this
+symbol be an abbreviation for
+
+'inverse log x'.
+
+Does 'inverse log x' exists?
+
+Yes, I even drew the graph of
+it at the beginning of this
+
+particular lecture.
+
+However, again, if you are
+tempted to use exponents, the
+
+notation 'e to the x' is in
+keeping in line with the idea
+
+of our previous lecture.
+
+I say what?
+
+This matches the identification
+of 'natural log
+
+x' with the 'log of x'
+to the base 'e'.
+
+Remember, in our previous
+lecture, we mentioned that
+
+this particular function exists
+without having to talk
+
+about a base.
+
+But if you wanted to identify
+it with a traditional
+
+logarithm, the base you would
+have to pick is the base 'e',
+
+where we showed that 'e' was
+some number between 2 and 4.
+
+In other words, again, it's just
+like our 'dy dx' versus
+
+'dy' divided by 'dx' and
+other symbols that we
+
+invented this way.
+
+Namely, if I look at 'e to the
+x' as being the inverse of the
+
+natural log, or whether I look
+at it as being 'e' raised to
+
+the 'x' power, where 'e' is that
+number that's someplace
+
+between 2 and 4, I don't get
+into any trouble either way
+
+because of the natural
+identification of choosing e
+
+to be the base of my system.
+
+But I just mention
+that in passing.
+
+Now you see, the rest
+of today's lecture
+
+will go fairly quickly.
+
+And the reason that it will go
+fairly quickly is that once
+
+we've established what the
+function is that we're talking
+
+about, every other property of
+that function is going to
+
+follow from the principles that
+we've already learned.
+
+For example, in terms of our
+new notation, since the
+
+derivative of 'e to the x' with
+respect to 'x' is 'e to
+
+the x' itself, remember,
+'e to the x' now can
+
+be viewed as what?
+
+'e to the x' power, or, to be on
+safer grounds, if you want
+
+to be consistent, it's just an
+abbreviation for 'inverse
+
+natural log x'.
+
+But at any rate, if 'u' is now
+any differentiable function of
+
+'x', notice that to find the
+derivative of 'e to the u'
+
+with respect to 'x', by the
+chain rule, I can say what?
+
+It's the derivative of 'e to
+the u' with respect to 'u'
+
+times 'du dx'.
+
+We've just shown that the
+derivative of 'e to the u'
+
+with respect to 'u' is
+'e' to the 'u' again.
+
+And therefore, the derivative
+of 'e to the u' with respect
+
+to 'x' is 'e to the
+u' times 'du dx'.
+
+By the way, this again leads to
+another interesting thing
+
+that makes integrals tough
+to handle, in a way.
+
+We've mentioned this before,
+but here's another nice,
+
+natural environment to bring
+this problem up in again.
+
+When we discussed the second
+fundamental theorem of
+
+integral calculus to show how
+one actually would have to
+
+understand areas to be able
+to find a function whose
+
+derivative was 'e to the
+'minus x squared', we
+
+mentioned, we didn't prove it,
+we mentioned that there was no
+
+familiar function whose
+derivative with respect to 'x'
+
+was 'e to the 'minus
+x squared'.
+
+So this would be a very
+difficult problem to handle.
+
+Now, let's look at
+this one instead.
+
+Let's look at integral '2x 'e
+to the minus x squared' dx'.
+
+To the untrained eye, it would
+appear that this is even
+
+messier than this.
+
+In other words, this is just 'e
+to the 'minus x squared''.
+
+This one has 'e to the 'minus
+x squared'' with a '2x'
+
+dangling in front of it, and
+that looks even tougher.
+
+But notice that if we look
+at our exponent, 'minus x
+
+squared', the derivative, or the
+differential of 'minus x
+
+squared' is what?
+
+It's 'minus '2x dx''.
+
+In other words, the '2x dx' is
+precisely what you need to
+
+reduce this to the form integral
+''e to the u' du'.
+
+In other words, working this
+thing out in more specific
+
+detail, if I let 'u' equal
+'minus x squared', 'du'
+
+becomes 'minus '2x dx'', and
+therefore integral '2x 'e to
+
+the 'minus x squared'' dx'
+just becomes what?
+
+Well, the 'e to the 'minus x
+squared'' just becomes 'e to
+
+the minus u'.
+
+And '2x dx' is just
+'minus du'.
+
+OK?
+
+I'm sorry, 'u' is 'minus
+x squared'.
+
+'u' is 'minus x squared'.
+
+So 'minus x squared' is 'u'.
+
+So this becomes 'minus
+e to the 'u du''.
+
+And that, of course,
+is just minus.
+
+See, the minus will
+come outside.
+
+The integral of 'e to the u'
+with respect to 'u' is
+
+just 'e to the u'.
+
+And since 'u' is equal to 'minus
+x squared', all we're
+
+saying is that if you
+differentiate minus 'e' to the
+
+'minus x squared', you
+wind up with what?
+
+'2x 'e to the 'minus x
+squared'', the reason being
+
+that you must multiply this by
+the derivative of the exponent
+
+with respect to 'x'.
+
+The root of the exponent
+is 'minus 2x'.
+
+'Minus 2x' times minus
+1 is '2x'.
+
+If you want to see this in
+more concise differential
+
+notation, you see, what we're
+saying is that the integral of
+
+'e' to some power with respect
+to that same power is 'e' to
+
+that power plus a constant.
+
+In other words, the function
+that one would have to
+
+integrate 'e to the 'minus x
+squared'' with respect to to
+
+wind up with 'e to the 'minus x
+squared'' would be 'minus x
+
+squared' itself.
+
+And you see, now, in the next
+step, since this is a true
+
+statement, the differential
+of 'minus x squared'
+
+is minus '2x dx'.
+
+And now you see, factoring out
+the minus sign and multiplying
+
+through by minus 1, we arrive
+at the same result that we
+
+wound up with before.
+
+But again, this is the kind of
+material that we can drill on
+
+extensively in the exercises
+in this particular unit.
+
+The technique is what?
+
+That the basic building block
+of the so-called exponential
+
+function, the inverse natural
+log, is that when you
+
+differentiate it, you
+essentially do not destroy it.
+
+In other words, the derivative
+of 'e to the u' with respect
+
+to 'x' is 'e to the
+u' times 'du dx'.
+
+And I thought that in closing
+today's lesson, I might as
+
+well show you a very powerful
+application of this particular
+
+result in a non-obvious
+situation.
+
+And it's something that
+we call second-order
+
+differential equations.
+
+I've picked out here a
+differential equation.
+
+Let me just show you what I
+have in mind over here.
+
+Suppose I tell you that 'y'
+is a twice-differentiable
+
+function of 'x' that satisfies
+the following identity, that
+
+the second derivative of 'y'
+with respect to 'x' minus 5
+
+times the first derivative of
+'y' with respect to 'x' plus 6
+
+times 'y' is identically 0.
+
+And the question is, if this
+equation is to be obeyed, what
+
+must 'y' be?
+
+And a very interesting technique
+for solving this
+
+kind of a problem, you see, this
+is called a second-order
+
+differential equation because
+the highest derivative that
+
+appears is the second
+derivative.
+
+OK, a rather powerful
+technique using the
+
+exponential is available to us
+for problems of this sort.
+
+And the idea hinges on this.
+
+As a trial solution, which I'll
+call 'y sub t', let's try
+
+'e to the rx', where 'r' happens
+to be a constant.
+
+You see, the whole idea is if I
+differentiate 'e to the rx'
+
+with respect to 'x', I get 'e
+to the rx' back again, only
+
+with a factor of 'r', namely the
+derivative of my exponent
+
+in this case.
+
+See, 'r' is a constant.
+
+The derivative of 'rx' with
+respect to 'x' is just 'r'.
+
+So notice that the first
+derivative of 'y sub t' with
+
+respect to 'x' is 'r
+'e to the rx''.
+
+The second derivative
+of 'y sub t' with
+
+respect to 'x' is what?
+
+'r' is a constant.
+
+I differentiate 'e to the rx'.
+
+That brings down another factor
+of 'r' and leaves me
+
+with 'e to the rx'.
+
+You see, the whole idea being,
+notice that 'e to the rx' is a
+
+common factor of 'y sub t', 'y
+sub 't prime'', 'y sub 't
+
+double prime''.
+
+If I now substitute these
+results back into my original
+
+equation, look what I wind up
+with. 'y double prime' becomes
+
+'r squared 'e to the rx''.
+
+Minus '5y prime', that's minus
+'5r 'e to the rx'', plus '6y',
+
+'6e to the rx'.
+
+And that must equal zero.
+
+And here's the key point.
+
+'e to the rx' is now
+a common factor.
+
+I factor that out.
+
+If the product of two numbers
+is 0, one of the
+
+factors must be 0.
+
+But notice from our graph of the
+exponential, the inverse
+
+logarithm, 'e to the x', 'e to
+the rx' can never be negative
+
+and can never be 0,
+in fact. 'e to the
+
+rx' is always positive.
+
+Therefore, if 'e to the rx' is
+always positive, it must be
+
+the other factor which is 0.
+
+But 'r squared' minus '5r' plus
+6 is not a second-order
+
+differential equation.
+
+It's a second-degree polynomial
+equation.
+
+It's a familiar quadratic
+equation, which I can solve
+
+quite easily.
+
+In other words, I find what?
+
+That 'r' must be either 2,
+or 'r' must equal 3.
+
+In other words, my claim is that
+either 'e to the 2x' or
+
+'e to the 3x' must
+be a solution of
+
+this particular equation.
+
+Of course, we can do more with
+that, which we will in a later
+
+part of calculus, not in
+this package's work.
+
+But we're not going to study
+differential equations in
+
+great detail here.
+
+But for our present purposes,
+I think this illustrates how
+
+one can use the fact that it's
+a rather powerful structural
+
+property when the derivative of
+a function with respect to
+
+'x' is the function itself.
+
+By the way, as a quick check,
+notice that if 'y' equals 'e
+
+to the 2x', 'y prime' is
+twice 'e to the 2x'.
+
+'y double prime' is
+'4 e to the 2x'.
+
+And therefore 'y double prime'
+minus '5y prime'
+
+plus '6y' is what?
+
+It's '4e to the 2x' minus '10 e
+to the 2x', '6 e to the 2x'.
+
+And that, in fact, is genuinely,
+identically zero.
+
+In a similar way, checking out
+'y' equals 'e to the 3x', we
+
+get 'y prime' is '3e to the 3x',
+'y double prime' is '9e
+
+to the 3x'.
+
+Therefore, '9e to the 3x' minus
+'15 e to the 3x' plus
+
+'6e to the 3x' is again,
+identically 0.
+
+And again, you see what this
+powerful technique is.
+
+In general, if 'a' and 'b' are
+constants, the substitution 'y
+
+sub t' equals 'e to the rx'.
+
+And there'll be a problem in the
+exercises on this to give
+
+you additional drill.
+
+But that substitution transforms
+the second or the
+
+differential equation, 'y double
+prime' plus 'ay prime'
+
+plus 'by' equals 0, into an
+equivalent quadratic equation,
+
+'r squared' plus 'ar'
+plus 'b' equals 0.
+
+And you see from this equation,
+using the quadratic
+
+formula, we can find the values
+of 'r' that satisfy
+
+this, and that gives
+us a couple of
+
+solutions to the equation.
+
+Well, at any rate, I
+deliberately want this lecture
+
+to stay short to make the
+most important impact.
+
+And that is again what?
+
+That once we knew what the
+natural log function was, and
+
+we defined the inverse natural
+log function, everything that
+
+we wanted to know about the
+inverse natural log followed
+
+from the properties
+of the log itself.
+
+And this is basically the
+lesson for today.
+
+We will continue the discussion
+of exponential
+
+functions from a different
+point of
+
+view in our next lecture.
+
+But until that next
+lecture, goodbye.
+
+ANNOUNCER: Funding for the
+publication of this video was
+
+provided by the Gabriella and
+Paul Rosenbaum Foundation.
+
+Help OCW continue to provide
+free and open access to MIT
+
+courses by making a donation
+at ocw.mit.edu/donate.
\ No newline at end of file
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new file mode 100644
index 0000000000000000000000000000000000000000..7dc19067a20c7923ceb8eb40245763c739e72dd9
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+++ b/rV5eSoBqrsY.txt
@@ -0,0 +1,3777 @@
+We're quite lucky today to have Bob Sieck
+talk to us about launch operations.
+
+Bob joined NASA early in his career after
+a spell with the Air Force.
+
+This was in the early '60s.
+
+And he worked on prelaunch checkout and servicing
+of Gemini and Apollo.
+
+Then went into the Shuttle Program.
+
+He worked on ground operations for the Approach
+and Landing Tests.
+
+We will hear more about that testing when
+Gordon Fullerton comes here at the beginning
+
+of December.
+
+And then he worked as Launch Director for
+a lot of the early Shuttle missions, including
+
+my first flight.
+
+And then went to be the Shuttle Operations
+Director at Kennedy Space Center.
+
+But then after the Challenger accident he
+came back and worked on another, I don't know,
+
+40 or so launches.
+
+I think my last launch was in '96.
+
+You had already graduated, right?
+
+Yeah.
+
+But Bob was the Launch Director of the first
+four of my flights.
+
+He is the head of the whole team of really
+thousands of people who are responsible for
+
+getting the Shuttle ready to fly and for certifying
+that, in fact, it is ready to fly.
+
+It is a very complicated, critical and from
+the safety point of view absolutely one of
+
+the most important things we do, is to figure
+out when this incredibly complex vehicle is
+
+really ready to go.
+
+Bob is going to talk to us both about some
+of the technical aspects of the launch operations.
+
+But also I hope, from a systems engineering
+point of view, we will have a chance towards
+
+the end to talk about some of the planning
+that was going on while the Shuttle was being
+
+designed and some of the compromises which
+had to be made, some of which we've already
+
+addressed, between the efficiency of turning
+around and maintaining a vehicle like the
+
+Shuttle vis-à-vis the actually initial upfront
+cost of it.
+
+With that as an introduction, Bob, I will
+turn it over to you.
+
+Thanks, Jeff.
+
+And good morning.
+
+As Jeff indicated, I got into the business
+of launching people and payloads into space
+
+a long time ago.
+
+I was privileged to be part of all of the
+human space flight programs, so I did a lot
+
+of that.
+
+What I didn't do, I saw most of.
+
+And I have an opinion on all of it, so please
+ask questions.
+
+If I don't have the answer, I am sure to have
+an opinion.
+
+I am going to spend a little bit of time,
+we talk about launch operations, but that's
+
+the final three to four days of a campaign
+that begins three to four months before you
+
+actually start the countdown clocks and put
+the astronauts in the vehicle and go fly.
+
+So I am going to spend some time on the background
+of preparing the Shuttle, the ground systems,
+
+the flight systems prior to the launch count
+process particularly to talk about the engineering
+
+involvement and the responsibilities in those
+processes.
+
+But, in order to talk about launching, I have
+to talk some about the operations of putting
+
+the final pieces together and doing the tests
+and inspections prior to launch.
+
+And then I want to get into the real meat
+of it which is the human factors, the role
+
+of the engineer, the role of the managers
+in the process of testing, inspecting, checking
+
+the flight systems, the ground systems and
+certifying that it is OK to put the crew in
+
+and go fly.
+
+And that's where we're going to spend most
+of our time, but I've got to go through some
+
+background first.
+
+I don't know how many of you have been to
+the Kennedy Space Center.
+
+Anybody been down there?
+
+OK, so you've seen it.
+
+It is a city where we've launched everything
+since the beginning programs, Mercury, Gemini,
+
+Apollo.
+
+The most prominent fixture is this Vehicle
+Assembly Building which was used for the Apollo
+
+Program to put together the 300 foot tall
+Saturn-Apollo rocket.
+
+Shuttle is about half that size but we use
+this building to do the assembly.
+
+And I will talk a little bit about that later.
+
+But it is a city.
+
+We have our own power systems.
+
+We have facilities to check out the orbiter
+to process the solid rocket motors.
+
+We have administrative homes for the people.
+
+And, of course, we have the highly visible
+launch pads that are out on the ocean.
+
+And we also have a runway.
+
+When the weather cooperates and we can bring
+the shuttles back to Florida, we can take
+
+care of the landing and recovery there.
+
+The process.
+
+We'll talk a little bit about the process.
+
+When an orbiter returns from its previous
+mission, it goes through essentially a disassembly,
+
+inspection and then build it back up and test
+it to make sure that it is still within the
+
+certification base that the engineers set
+up for it that you've already heard from previous
+
+to this lecture.
+
+You would like to think that if the Orbiter
+flies and the rest of the element is a successful
+
+mission you can just do it like an airplane,
+take down the down cargo, whatever, get it
+
+configured for the next payload that is going
+to go up, clean the windshield, so to speak,
+
+and the crew cabin and go fly it again.
+
+But the rules don't allow you to do that.
+
+The rules that the other engineers who have
+talked to you have set up are such that you
+
+have to assume that in some way, even though
+during the mission everything seemed to work
+
+OK, that that hardware was compromised through
+the process of reentering, landing, refurbishing
+
+those systems that have to be refurbished.
+
+Something may have been invalidated.
+
+So you have to test all that stuff that worked
+just fine in the previous mission, plus all
+
+of the systems that were not used in the previous
+mission, particularly the backup system, the
+
+things that you would have to rely on in the
+event that the primary system doesn't cooperate
+
+during the next mission.
+
+And, because of the way the Orbiter was built
+with its miles of wiring and thousands of
+
+components that are active components, you
+have to disassemble a lot of that stuff in
+
+order to meet the requirements that the program
+is levied on.
+
+After the Orbiter lands and you get it safe
+and the crew is out and you take out the payload,
+
+we spend a minimum of two to three months,
+roughly a quarter of a million labor hours
+
+of touch labor on the Orbiter to do this disassembly,
+test, inspection, refurbishment process before
+
+we move it from the hanger, take it to that
+Vehicle Assembly Building, integrate it with
+
+the tank and the solid rocket boosters and
+take it on out to the launch pad to go fly
+
+again.
+
+And that's where the lion's share of the work
+is.
+
+The work on the tank and the payloads and
+the solid rocket boosters is all peripheral
+
+to the processing of the Orbiter.
+
+Yes, sir.
+
+[AUDIENCE QUESTION] Do you find a lot of failures
+when you go through?
+
+We find very few.
+
+And you could do the tradeoff of, well, is
+this effort worth it?
+
+But, on the other hand, the few that you find,
+you're glad that you found them because if
+
+not you may not have discovered them until
+you got out to the launch pad and serviced
+
+your hazardous systems.
+
+Or, worse yet, you find out when you get in
+the mission.
+
+And then the impact of that could be not only
+a safety impact but could be a higher consequence
+
+than spending the month to two months in an
+orbiter processing facility doing that work.
+
+Yes?
+
+But is there a learning curve?
+
+I mean after each mission do you know which
+system you have to look at specifically?
+
+We look at it and say this system is performing
+just fine so we don't have to do this intense
+
+invasive inspection and test every flight.
+
+Maybe we can just do it once a calendar year
+or every two to three missions, whatever the
+
+designer thinks is the criteria for checking
+on the health of this system.
+
+And we've done that over the years.
+
+And after we've had a couple of years of missions
+where everything is working just fine, we
+
+start relaxing these requirements.
+
+And then something like Challenger happens
+or something like Columbia happens and the
+
+pendulum of conservatism swings the other
+direction.
+
+And we do more tests and more inspections
+to verify the hardware because people want
+
+to be able to say, and we want to be able
+to say, well, we've done everything possible
+
+to make sure that that's a 100% functional,
+operating, safe orbiter.
+
+And so getting this process down to where
+it meets the original advertising brochure
+
+which was we're going to fly these things
+every two to three weeks, you start in that
+
+direction.
+
+And then events occur either during the mission
+or you have the really bad incidents like
+
+Challenger and Columbia.
+
+And the conservatism swings the other way
+and you end up doing more work.
+
+And, in addition to that, engineers, because
+we are what we are, I was one, we have all
+
+this hardware available, we like to modify
+it.
+
+We change it.
+
+We upgrade it because there is new technology
+available in computers or in composite materials.
+
+So, when the orbiter gets to this processing
+facility, regardless of how well the mission
+
+flew, the designers, with their good intensions,
+say we want this orbiter to last another five
+
+years or ten years so we want you to do this
+upgrade to the avionics system or we want
+
+to change out all of the actuators that hold
+the payload in the payload bay and this and
+
+that.
+
+So you modify.
+
+And that adds more time.
+
+It makes more complexity to the process which
+invites more tests and inspections.
+
+You're constantly in a mode where unfortunately,
+if the mission flies perfectly, by the time
+
+you plan your campaign through the processing
+facility -- 
+
+You plan your campaign with schedules to last
+two months maybe, roughly a third of the work
+
+you do is work that you hadn't planned when
+you initially brought that orbiter into the
+
+orbiter processing facility.
+
+It's nonstandard work.
+
+It is stuff that you uncover in the process
+of doing your test or inspection or its new
+
+requirements or new changes that come from
+the designers that have to be implemented.
+
+And, from an efficiency standpoint, if you're
+in the manufacturing or production business,
+
+that is not efficient.
+
+If a third of your work that you laid out
+for the next two months, at the end of that
+
+two month period, a third of it was stuff
+that you had not planned on doing which means
+
+you don't have the parts ready, you don't
+have the engineering, you don't have the instructions.
+
+Yes?
+
+Do you build in time to cover that now?
+
+Contingency time, yes.
+
+Let me go back to that.
+
+We set up our team and operations to run five
+days a week, two shifts a day leaving the
+
+weekends free to catch up for this nonstandard
+stuff.
+
+We essentially end up running a six day work
+week if we're in a standard template of flying
+
+three missions a year, which we're not now
+because we're still recovering from the Columbia
+
+accident.
+
+We end up working six days a week and roughly
+every three or four days we will work a continuous
+
+around the clock 24 hour operation.
+
+We try to maintain that original schedule
+but we only make it roughly 50% of the time
+
+due to this, again, nonstandard work, the
+extra stuff that works its way in.
+
+And that's why we have a big team.
+
+Our team is made up of the United Space Alliance
+as a contractor.
+
+They do the hands-on work.
+
+They have the technicians.
+
+They have the engineers that staff the consoles.
+
+And they are roughly a 6,000 population at
+Kennedy Space Center.
+
+They take care of the orbiter, the tank, the
+boosters.
+
+They are responsible for maintaining all of
+our equipment that hooks into the shuttle
+
+that is required, the process of servicing
+it.
+
+And they have ties to the contractors, the
+original equipment manufacturers that built
+
+the hardware.
+
+Technically, they can gain access to all the
+original manufacturing records for the parts
+
+that are in the shuttle.
+
+NASA's responsibility -- 
+NASA owns the requirements for the Shuttle.
+
+We delegated all the operational work to the
+contractors, but it's a national resource.
+
+Taxpayers paid for it.
+
+The government has a responsibility.
+
+They cannot divest themselves from that.
+
+NASA owns the requirements for saying what
+you test, what you inspect and what the specifications
+
+are for acceptable performance of that.
+
+That is controlled by NASA.
+
+The management of the contractor at Kennedy
+is done by NASA engineers in an organization
+
+that has roughly 500 people out of the 2000
+population at Kennedy Space Center of civil
+
+service people.
+
+500 are directly associated with the Shuttle.
+
+The rest do payload work.
+
+The Space Station, of course, is a big work
+item now at the Kennedy Space Center.
+
+And they are responsible for the requirements.
+
+If somebody wants to change the requirement,
+a NASA person has to approve that change.
+
+And we do insight and everything the contractor
+does.
+
+We have at each one of the milestones, when
+we leave the processing facility, when we
+
+leave the Vehicle Assembly Building and when
+we get ready to launch, there is a review
+
+conducted by NASA to review the work that
+was done by the contractor during the preceding
+
+weeks or months.
+
+And NASA approves moving the vehicle onto
+the next stage of its assembly prior to launch.
+
+And the launch director specifically is responsible
+not only for those last few days of the campaign,
+
+so to speak, leading up to launch, but also
+insuring the government contractor team has
+
+all the tools available to them to be successful.
+
+Is the work being scheduled in an orderly
+fashion?
+
+Is the ever-tightening budget constraining
+their ability to get their work done?
+
+Is there too much scheduled pressure to meet
+a milestone?
+
+That is the launch director's job.
+
+The launch director doesn't just come in the
+last three days of the campaign with a tie
+
+and a suit and orchestrate the countdown.
+
+They have a responsibility from the beginning
+to the end of the campaign.
+
+Engineering.
+
+I have already addressed this, but the NASA
+engineers manage the requirements, the changes
+
+to the requirements.
+
+They are the ones in addition to the contractor,
+this is a check and balance, that look at
+
+all the data, the engineering results of the
+tests and the inspections.
+
+And they approve that they met the requirements.
+
+Also, they participate in critical operations.
+
+A critical operation is a test on a specific
+system.
+
+Servicing of the vehicle for launch count
+or any of the non-standard work that comes
+
+up during the process.
+
+They audit what the contractor does.
+
+And, of course, because we're the customer
+and they are the contractor, we have a lot
+
+of criteria to grade them on for their award
+fee performance.
+
+The operations people manage the scheduling.
+
+As I indicated, we like to work five days
+a week, two shifts a day.
+
+We really end up working six days a week and
+sometimes around the clock.
+
+The scheduling activity is dynamic.
+
+And NASA approves all the scheduling.
+
+We have to approve all the overtime.
+
+We have the authority to say stop or go not
+only in launch count but anywhere in the campaign
+
+of processing the hardware, as well as the
+big picture schedule, you know, how many times
+
+a year you're going to fly and which orbiter
+is assigned to which payload in those missions.
+
+That is still a NASA responsibility.
+
+Orbiter processing facility, like I mentioned
+before, it is like a hanger for an airplane.
+
+A big part of the work effort used to be the
+tile.
+
+I think you already had a presentation on
+tile.
+
+There are 25,000 to 30,000 of these little
+bricks glued to the vehicle.
+
+We classically damage about a hundred of them
+on each mission due to ice and things coming
+
+off the tank that have to be replaced, but
+we also pull another hundred or so off just
+
+to inspect the integrity of the glue that
+is holding the tile to the structure of the
+
+vehicle.
+
+Because a lot of those little bricks have
+been glued on there for 25 years and have
+
+flown 25 to 30 missions.
+
+Although we have offline test programs that
+try to duplicate the environment that the
+
+tile sees either from a calendar standpoint
+or the thermal cycles of the mission, you
+
+would like to go to the real hardware and
+see what is happening.
+
+We do that invasive type of work of actually
+destroying tile, pulling it off the vehicle
+
+just to make sure that the aging process is
+not causing any degradation of the system.
+
+We pull the engines out and do the maintenance
+on the engines offline because the aft fuselage
+
+of the orbiter is a terrible place to work.
+
+Any of the hardware we can get out of there
+and do it on the bench, it is much better
+
+to do that than to try to do it in the vehicle
+with people crawling all over wire bundles
+
+and structure and that sort of thing.
+
+They are concerned about the collateral damage
+to do the other work in that compartment of
+
+the vehicle where the engines are.
+
+Of course, you've got to take the accommodations
+from the previous mission out of the payload
+
+bay and put in the new stuff for the next
+mission.
+
+I already mentioned modifications.
+
+Unfortunately, we change more stuff than we
+probably should but in order to keep up with
+
+the aging of the vehicle and the new technology
+that goes with the territory of flying a system
+
+that was designed over 30 years ago.
+
+And we prepared for the next milestone which
+was the vehicle assembly building operations.
+
+This is where we put the big pieces together.
+
+The solid rocket boosters are stacked.
+
+There are four segments in each booster.
+
+That is a very critical process but only takes
+less than a month to do.
+
+The external tank comes in essentially ready
+to fly from Mississippi.
+
+Except, as you know now, because of the Columbia
+accident, we are still looking at the ramifications
+
+of these lines and other fittings on the tank.
+
+The acreage foam on the tank, just to digress
+a little bit, is sprayed on.
+
+And that stuff is tough.
+
+Early in the program we had problems with
+some of that coming off, but we solved that
+
+years ago.
+
+What we haven't solved is where you have to
+do a manual application of foam over a fitting
+
+that is there because that is where the crane
+is attached to it or because there is a line
+
+there that has to be installed at the Kennedy
+Space Center.
+
+You cannot do it back at the factory.
+
+Putting that thermal protection system foam
+on there is a labor-intensive process.
+
+It is a critical technique process.
+
+And, obviously, there are still flaws in the
+process that the engineers haven't sorted
+
+out yet.
+
+And that is why that stuff keeps coming off
+the tank in those places.
+
+But the solid rocket motors are attached to
+this mobile launch platform with four bolts
+
+the diameter of my wrist.
+
+The structure engineers really figured this
+out good.
+
+There are four on each one of those that are
+attached to the launch platform.
+
+The tank is attached to the boosters with
+four attach points, and those are bolts, again,
+
+that are the diameter of my wrist.
+
+And then the orbiter is hung on the tank in
+three places with the same sized bolts.
+
+You've got six million pounds of weight that
+is attached to the mobile launch platform
+
+that is held up by these four bolts, well,
+eight total on the solid rocket motors.
+
+And they work out the dynamics of when the
+engines start because the vehicles sways like
+
+this because the center of gravity is not
+right over where those eight bolts are attached.
+
+And that system works fine.
+
+It always amazed me that you could hang that
+much weight on those few bolts that are only
+
+the diameter of this, but it works.
+
+The orbiter is brought over after its campaign,
+it's hung on the tank and we test all those
+
+connections between the solid rocket booster,
+the platform, the tank and the orbiter.
+
+And that only takes about a week to do that.
+
+And, if that looks good, we have a review
+of all of that work.
+
+And if the review says we didn't leave anything
+undone, that we shouldn't take out the launch
+
+pad then we go out to the launch pad.
+
+[AUDIENCE QUESTION] Sure.
+
+Say a little bit about this difference from
+just bringing your car into have a 50,000
+
+mile checkup, that is the clean room aspects,
+the following of procedures, of having a checker.
+
+Sure.
+
+Well, a 50,000 mile checkup on a car is usually
+an external inspection.
+
+You change the oil and the filter and you
+check all the belts and the radiator hoses
+
+and you change all the fluids.
+
+Well, you do that with the orbiter also.
+
+But, in the case of the orbiter, you want
+to know whether you are this far away from
+
+having to do a valve job or the rings in the
+engine have now got so many thousand miles
+
+on them.
+
+We have the equivalent.
+
+You take the heads off the engine and you
+give it a valve job.
+
+And you take the pistons out of the block
+and you check for scoring in the block.
+
+You take the transmission out and you pull
+the gears out and make sure that the synchronizers
+
+are still OK.
+
+And you go through the rear-end.
+
+And you take all the avionics out.
+
+Or, you take your carry-on test equipment
+in and you hook it up to these connectors
+
+on the airflow meter and the computer in your
+vehicle and you run all those diagnostics
+
+to make sure all that stuff, even though it
+worked fine after you turned that ignition
+
+key off the last time, that all the redundancies
+and all the capability is still within that
+
+hardware and all the margins are still there.
+
+And then you button it back up and you make
+sure you button it back up properly, all of
+
+which is pre-established quite rigid flowcharts,
+checklists.
+
+A checker checking the checker.
+
+Oh, yes, and you have inspectors where there
+are critical things.
+
+If you're torquing the connecting rods onto
+the crankshaft, it says that you've got to
+
+do those bolts at 50 something foot pounds.
+
+And the technician will do that.
+
+And there will be an inspector there verifying
+that he set the torque wrench at 50 foot pounds
+
+and it really clicked there, and they stamp
+the procedure that it was done that way.
+
+I wanted to just add to that, I mean, even
+more emphasis.
+
+You don't do anything to the vehicle or to
+the payload unless you have a written procedure.
+
+What is absolutely not allowed is oh, there
+is a little problem, something didn't work
+
+the way it was supposed to in the test.
+
+Let's just fiddle around.
+
+Let's throw a few switches and see what happens.
+
+Well, I mean, that is normally the way you
+work at things if you're in a laboratory or
+
+working on your car.
+
+But the thing is you need absolute traceability.
+
+Because if something later on turns up out
+of spec or there is an anomaly during flight,
+
+you need to be able to recreate everything
+that was done to the orbiter.
+
+That is why we keep such good records on parts.
+
+Well, you can tell you that story about the
+tires that you just mentioned.
+
+People keep track of where all the parts of
+the orbiter came from, the lot numbers.
+
+And so, if any problem turns up, you can actually
+then trace on the orbiter and see if it affects
+
+there.
+
+All the work is done for approved work authorization
+documents, every step, every touch labor item
+
+that is done on the vehicle.
+
+And if you deviate from that procedure, which
+is approved by engineering, you have to get
+
+engineering approval to deviate from it.
+
+The assembly process, the standard work process
+of putting the vehicle together after a mission,
+
+there is over two million verifiable work
+items for the standard flow.
+
+And that doesn't include modifications or
+the nonstandard work that comes up, the proverbial
+
+glitch that occurs when you're checking out
+your computer system or when you pressurize
+
+this fluid system and the leak rate is higher
+than the specification allows.
+
+Well, engineering comes in and says OK, here
+is the trouble procedure.
+
+Here is what you're going to pursue, but you
+don't do any of that until the engineers write
+
+the procedure and give it to the technicians
+or the console operators that say OK, here
+
+is what you're going to do to try to find
+out the source of this leak.
+
+As Jeff indicated, you don't just start throwing
+switches and turning valves and say well,
+
+let's see if we can find out what's going
+on here.
+
+It is all pre-approved.
+
+And the reason for that is when you have these
+reviews that culminate into final review before
+
+you get ready to fly, you want to be able
+to say that this vehicle is assembled per
+
+print, that the designer's requirements, the
+people that you've already heard from that
+
+certified that this system will work just
+fine in flight if it looks like this when
+
+we launch it, you're trying to prove that
+this is what it looks like when you launch
+
+it and it is within the certification base
+and it is per the engineering drawings that
+
+we were given and it met all these requirements.
+
+Otherwise, you are guessing that it is OK
+to go fly the machine.
+
+And you cannot do that in this business.
+
+[AUDIENCE QUESTION] Yes.
+
+Does that seem to create any sort of tension
+on the engineers feeling like their hands
+
+are tied to go out and do stuff?
+
+Well, no, because they are the ones that ultimately
+say what goes in those two million steps.
+
+And if they want to add more tests or checks
+or inspections it is within their purview
+
+to propose that.
+
+The program, there is a group of senior engineers
+that are on these what we call control boards
+
+that approve the requirements that are implemented
+at the Kennedy Space Center.
+
+And they can say yeah, that's a good idea
+or, no, we don't want to change this, go back
+
+and give us some more rationale for what you
+think is a good idea to do to this system.
+
+In that respect, it is probably somewhat frustrating
+for the engineers because they cannot do anything
+
+different from last time unless they can justify
+the rationale for it.
+
+But that's the way it ought to be.
+
+The launch pad.
+
+The facilities at the launch pad are pretty
+simple.
+
+These are the same launch pads we flew from
+in Apollo.
+
+We've got storage facilities for the liquid
+hydrogen, liquid oxygen.
+
+We try to spend a minimum amount of time at
+the launch pad because Florida is a nice place
+
+to be on spring break but it's a bad place
+to have exotic hardware sitting outdoors with
+
+all that salt, humidity and all the other
+elements that mother nature throws at you
+
+like lightening.
+
+And, I think you can see down here, we have
+a good lightening protection system.
+
+There is a single mast with two wires that
+go out about a half a mile from the launch
+
+pad.
+
+It makes a good Faraday shield.
+
+And over the years we've been whacked a lot
+of times with lightening.
+
+In fact, it's a good attraction for lightening.
+
+And we have never gotten energy inside of
+that Faraday shield to damage any hardware.
+
+However, when we get lightening down there,
+we tell the workers to stand down and, of
+
+course, seek safe haven.
+
+But we have instrumented it.
+
+And it has taken some big hits, but we haven't
+gotten anything major inside that would cause
+
+us a problem from electric.
+
+Yes?
+
+After you take the Shuttle out onto the launch
+pad, is it very expensive to roll it back
+
+when you find a problem and then bring it
+back out again?
+
+Yes, it is.
+
+And that's why we have these reviews before
+we commit it to go to the launch pad to make
+
+sure that we're not taking any unknowns or
+any work out to the launch pad that should
+
+rightfully be done either in the Vehicle Assembly
+Building or further back in the Orbiter Processing
+
+Facility.
+
+It is a lengthy process because it takes about
+a week to hook everything up at the pad and
+
+check it before you go into the process of
+servicing the propellants and doing the hazardous
+
+work which has to all be undone if you roll
+back to the Vehicle Assembly Building.
+
+You've got to make sure you're really ready
+to go before you head on out there.
+
+Yes?
+
+Approximately how many times has that happened?
+
+Going back?
+
+Well, we probably have done it for technical
+reasons maybe 20% of the time.
+
+For weather reasons like we're worried about
+a hurricane or something like that the same,
+
+about 20% of the time.
+
+One out of every five times we've gone to
+the launch pad, we've had to come back for
+
+either a weather problem or a technical problem
+that either occurred at the launch pad or
+
+it's something that happened with a different
+vehicle in the fleet that may still be in
+
+the Orbiter Processing Facility or a components
+that is similar to one that is on the Shuttle
+
+that is at the pad that they were doing testing
+in the laboratory or doing what we call fleet
+
+leader testing at one of the NASA facilities.
+
+And they said, you know, there is an inherent
+flaw in this auxiliary power unit and we have
+
+to change the ones that are in the orbiter
+because they were manufactured at the same
+
+time or they have the same component on them
+and you cannot do that work out at the launch
+
+pad so you've got to roll it back.
+
+So the hardware at the pad may be just fine
+from the standpoint that you followed your
+
+processes and they checked out great in the
+previous part of the campaign.
+
+But an offline issue can cause you to say
+no, we've got to roll back and go change out
+
+this hardware or fix it or further test it
+before we can commit it to go fly.
+
+We have a big water tower out there also which
+I will talk about later.
+
+That is our sound suppression system.
+
+But basically a month is the maximum time
+you like to spend out there.
+
+We used to put a lot of payloads in the Orbiter
+Processing Facility when we were flying laboratories
+
+and that sort of thing.
+
+Space Station hardware, we install all that
+out at the launch pad now.
+
+And we test all the connections at the new
+facility.
+
+And we have a simulated launch count with
+the astronauts.
+
+And this is a tradition that goes back to
+the Mercury program.
+
+They bring the astronauts down to the Cape.
+
+They go through a day, two days of training,
+emergency egress, familiarization with the
+
+hardware, And then we have a simulated launch
+count without the propellants and all the
+
+hazardous stuff just to, if nothing else,
+remind the launch team that this is more than
+
+just a machine.
+
+We are going to fly people in this thing.
+
+And this occurs roughly two weeks before launch.
+
+And it is a good readiness test for the whole
+team.
+
+It's serious.
+
+We're a couple weeks before flight.
+
+The crew is in town.
+
+This vehicle is going to look the best it
+ever has.
+
+And we do a simulated launch countdown to
+within a couple seconds of liftoff.
+
+And then we do a simulated abort with the
+safeing of the vehicle and the crew gets out.
+
+And I will just add something.
+
+That is always something the crew looked forward
+to, first of all, because you actually get
+
+to get in the vehicle which, despite the fact
+that we have pretty good simulators in Houston,
+
+there is nothing like actually crawling inside
+the shuttle that you're going to fly in.
+
+And there is a lot of safety training that
+you do down at the Cape which is really kind
+
+of fun.
+
+You don't have any pictures of the launch
+escape, the pad slide wire basket?
+
+No, I don't think so.
+
+There is a requirement that you need to be
+able to get off the pad quickly if there is
+
+a launch emergency.
+
+And, of course, on the real launch day, unlike
+the simulated countdown where the pad is crawling
+
+with people, on launch day there are very
+few people, even when you're getting into
+
+the vehicle because it is fueled.
+
+And then everybody else leaves.
+
+So they have this big slide wire where if
+you have to get out of the orbiter in a hurray
+
+you go out and you jump in the bag, hit a
+little guillotine and it cuts you loose and
+
+you slide all the way down.
+
+Actually, in the early days, the astronauts
+kept saying we need to try this out.
+
+And they said no, you cannot do it because
+it hasn't been man rated.
+
+We said wait a minute.
+
+Well, it's rated for emergency use only so
+you cannot try it out.
+
+And then after Challenger they insisted that
+somebody actually ride down in it.
+
+Not every crew.
+
+Just one person tried it out.
+
+But the other thing that you do, once you
+get down to the bottom there is an underground
+
+bunker that you run into.
+
+And either you stay there and wait for help
+or they have these armored personnel carriers
+
+sitting around there with little tanks which
+you get in.
+
+And you've got to be able to drive your tank.
+
+They have a breakout section of the fence
+so you drive the tank through the fence out
+
+to a helicopter pickup point.
+
+So we all have to go out and learn how to
+drive the tank.
+
+And we drive over the sand dunes and everything.
+
+And then also they have a big pool which they
+light on fire.
+
+And they give you a big fireman's hose and
+they show you how to make your way through
+
+a fire by squirting a water path in front
+of you.
+
+All the little things you dream of as a kid,
+to be a fireman, drive a tank.
+
+So it's good fun.
+
+But it is part of the extensive safety procedures
+that they have.
+
+And all these things periodically they have
+to exercise.
+
+They do go through, every once in a while,
+a disaster drill down at the Cape where they
+
+simulate an emergency where they have to pick
+up the crew either outside the launch pad
+
+or either out in the ocean.
+
+And you've got to keep people at full operational
+readiness.
+
+That's one of the aspects of training.
+
+We train for the anomalies, the nonstandard
+things.
+
+The standard work, they do so much of that
+anyway you don't have to train for that.
+
+You don't have to train to put a payload in
+the payload bay.
+
+You don't have to train to power up your system
+and run your system checkout because that
+
+is a repetitive thing.
+
+But the nonstandard stuff, when things go
+wrong, that's where the emphasis of the training
+
+is.
+
+And, like Jeff said, it's a lot of fun.
+
+It's fun for the launch team, too.
+
+We have a control center at the Cape, and
+it is called the Launch Control Center.
+
+You would think this is where you launch it
+from.
+
+Well, you do that.
+
+But all of the other work that is done in
+the preceding three months is controlled from
+
+the Launch Control Center by test conductors
+and engineers who wrote the procedures and
+
+the software that implement all the requirements.
+
+And they control the activity on the orbiter
+or the tank or the boosters when it is still
+
+back in the offline facilities or the Vehicle
+Assembly Building or out to the launch pad.
+
+They do it from the Launch Control Center.
+
+We automate what we can from there.
+
+But for the manual activity -- And a lot of
+it is manual because regrettably you cannot
+
+do all this refurbishment on the shuttle with
+automated systems.
+
+It wasn't built that way.
+
+It is all managed from out Launch Control
+Center with old computers but with a great
+
+team 
+
+of people.
+
+The software we use in the computers, I am
+not going to go into a lot of detail because
+
+it is really old stuff, but it works.
+
+It is like the software program that the FAA
+uses to track airplanes.
+
+It is hacker-proof.
+
+There are no external interfaces outside of
+the Launch Control Center firewall.
+
+It works just fine.
+
+And that is where we do the management of
+our day-to-day operations from our Launch
+
+Control Room.
+
+And we call it the LPS Launch Processing System
+software.
+
+We've tried to change it a couple of times
+over the years.
+
+Buy new hardware.
+
+We have supplemented it with laptops so that
+we can do more human engineering displays,
+
+but the computers are the same ones that we
+bought back in the late '70s.
+
+But then so are the computers that are on
+the orbiter that fly the machine.
+
+So it works.
+
+This is a bit repetitive, but I want to go
+through it again to make sure to emphasize
+
+what the role of the engineering is.
+
+The designers that you've heard from, they
+certified their design.
+
+And they did extensive testing, just like
+Detroit does on a car on the door latch.
+
+And they've tested that door latch and said,
+well, this thing out to be good for 250,000
+
+miles or 20 years or so many gazillion opening
+and closings of the door before it wears out
+
+and you've got to replace it.
+
+Well, they did all that.
+
+And to make sure that that hardware is still
+within the certification base, they developed
+
+requirements, sent them down to the Cape.
+
+We put them in the procedures, either manual
+procedures or software to implement those
+
+requirements.
+
+And the team, United Space Alliance the contractor
+and the NASA engineers will certify at each
+
+of the milestone reviews and the process of
+moving the hardware out to the pad they've
+
+met those requirements.
+
+And they did that either by participating
+in the activity or by reviewing the test data.
+
+And that allows us to sign a certificate of
+flight readiness a few days before launch
+
+that all the requirements have been met.
+
+When we get into launch count, we take in
+a subset of those requirements that when everything
+
+is powered up and ready to go fly all of these
+systems that are active ought to look like
+
+this.
+
+The voltages should be between this upper
+limit and this lower limit.
+
+The pressure should be between here and here.
+
+These indicators should show that they are
+open and these indicators should say that
+
+this latch is closed or the valve is closed
+or whatever.
+
+And we put that in what is called launch commit
+criteria.
+
+And that is the acceptable limit for the performance
+of that hardware when you're at that point
+
+which is nine minutes before launch when everybody
+commits that they are ready to go fly.
+
+And all those requirements, again, are implemented
+by procedures in software.
+
+And the three days of launch count have roughly,
+these are numbers, but about 500 requirements.
+
+There are thousands of measurements associated
+with those requirements.
+
+And most of the looking at those measurements
+is done by computers, obviously.
+
+But you have the engineer involved because
+if it is not within limits you turn to the
+
+engineer for what is wrong.
+
+Is there any chance to go fix this or do we
+have to change hardware?
+
+Do we have to do trouble shooting?
+
+So it's not a hands-off operation, obviously.
+
+The 
+structure of the launch team, the launch director
+
+is shown in the middle, but that doesn't mean
+he or she is the only one with a go or a no-go
+
+button.
+
+The people the implement the requirements,
+there are roughly 150 of them in our Control
+
+Center, and they are the ones that provide
+the go, no-go for all the subsystems both
+
+flight and ground that everything is operating
+within the limits.
+
+They report that to a team of test conductors,
+NASA and contractor, and that's reported to
+
+the launch director.
+
+We are not along, obviously.
+
+We have an engineering support area, which
+are all the hidden senior engineers that you
+
+don't see on television.
+
+And there is a room full of about 150 to 200
+of those.
+
+And they are looking at the performance of
+these systems as they are activated in launch
+
+count.
+
+And they've got all the trend data, the previous
+history of it.
+
+And they're looking at things like, well,
+all right, everything is in limits, but is
+
+it within family?
+
+The last time the system performed the voltage
+with this or the pressure was this.
+
+Well, it's still in limits.
+
+But it's not the same as it was before so
+we go look at it.
+
+Well, that's for this group of engineers over
+here.
+
+These guys and gals are running through their
+procedures.
+
+And, if everything was within limits, we just
+turn to the next page and go onto the next
+
+one.
+
+And they also have the emergency procedures.
+
+If something bad happens these are the people
+that will implement the emergency procedures.
+
+This offline support, they're out there.
+
+They're the senior people, they've been there
+before, they've been out there who knows how
+
+many years and they're asking questions like
+that didn't look right or we missed that step,
+
+go back and check it again.
+
+That's what they are for.
+
+The mission management team over here, these
+are the people that do the certificate of
+
+flight readiness.
+
+These are the folks that stand up in the readiness
+reviews and say I gave the Cape folks a good
+
+set of requirements.
+
+There is nothing that happened with the hardware
+that they're responsible for.
+
+And all those offline facilities are on previous
+missions.
+
+That shouldn't have any cloud over this mission.
+
+They are responsible for certifying that.
+
+And they do that through a structure of the
+mission management team.
+
+You've got, of course, the flight director
+with flight rules and the flight team that
+
+they look at during the launch count process.
+
+And you will hear more about that from Wayne
+Hale.
+
+And they, obviously, have a go, no-go input
+to the launch director in the decision process
+
+also.
+
+We have an integration activity.
+
+They system engineers are each responsible
+for, you know, they have boundary conditions
+
+on what they are responsible for.
+
+It is these pieces of hardware.
+
+It is this wiring.
+
+It is these actuators or latches or whatever.
+
+But a lot of that stuff fits together.
+
+Integration is a technical term for making
+sure that this person talks to this person
+
+and that they are hooked in with this one.
+
+That activity is done by a console in the
+Control Room, again, with senior engineers
+
+who actually manage all the automated software
+that runs the last couple hours of launch
+
+count that really launches the vehicle.
+
+And they are tied in with that.
+
+You also have the more subjective stuff.
+
+We launch on a public range.
+
+Public safety is obviously an issue, so the
+range has to make sure that it is safe to
+
+fly from a public standpoint, there are no
+boats in the launch danger area, no airplanes
+
+and that the weather meets the criteria of
+being able to track the vehicle should it
+
+go off course.
+
+And, of course, the payload has to certify,
+particularly if there is an active payload,
+
+that all of their launch commit criteria is
+met.
+
+And last, but certainly not least, you have
+safety oversight of all of that activity.
+
+And what I don't show on there, of course,
+is the flight crew, but they are obviously
+
+in communication with all of these people.
+
+So that is the network.
+
+But everybody out here has no-go authority.
+
+Anybody can come on the Net or press their
+switch and say I've got a problem, we're not
+
+going anywhere.
+
+And it is the launch director and the launch
+team's responsibility to make sure that problem
+
+is addressed, hold at the convenient, graceful
+to stop all the activity hold point until
+
+the issue is resolved.
+
+The real job, and I'll get into this later,
+of the launch director is to say no when everybody
+
+else wants to go because, as you get further
+into the launch count, the "launch fever"
+
+process sets in.
+
+It is a natural thing, it seems to be.
+
+People want to go.
+
+I want to ask you about that a little bit,
+I know we'll get into it later on, but flight
+
+rules and the launch decision, there are flight
+rules that say you must scrub if these conditions
+
+are not met.
+
+Right.
+
+And, yet, there is a tendency to allow judgment
+to come in.
+
+Let's take an example of a limit on crosswind
+at you landing to the return to launch site.
+
+You see it go above limits, but the rules
+strictly says no, you cannot go.
+
+Talk about that a little bit.
+
+That is what we use the mission management
+team for.
+
+And you bring up the weather example.
+
+Most of this stuff is pretty straightforward.
+
+It is either the voltage pressure temperature
+is in limits or out of limits.
+
+A person can question that and say I don't
+like the trend, and you've got to stop and
+
+clear the air if they say I want more discussion
+on this, I want more data review and that
+
+sort of thing.
+
+If it is a discussion like that involves activity
+outside of the Control Room beyond the purview
+
+of the console operators that are running
+through the procedure, we rely on the mission
+
+management team to manage that activity so
+the console operators can concentrate on their
+
+launch commit criteria and their procedures
+and their software.
+
+Something like crosswind limits, if there
+is a debate with the flight director and the
+
+weather people, we hold the clock and say
+mission management team, that is yours.
+
+You manage it, and whatever you have to do
+to resolve the decision, we'll scrub if need-be,
+
+we'll hold if need-be, or if the community
+can get comfortable that these crosswinds
+
+that are peaking occasionally out of spec,
+that it's OK to go fly anyway, then we will
+
+wait to hear from the flight director that
+that's OK.
+
+We don't insulate the Control Room from that,
+but we don't want to burden the control center
+
+with work and what is an offline issue.
+
+And it is up to the mission management team
+to disposition that.
+
+And you bring up weather because weather is
+one of the few things that there is really
+
+a lot of judgment still involved.
+
+Is the weather good enough to go fly?
+
+And it is probably the only thing that is
+in that category because everybody has an
+
+opinion on the weather.
+
+And Florida weather is dynamic.
+
+And usually, unless it is wintertime, there
+are clouds.
+
+And there is always a tendency, if you've
+held for weather or the weather is marginal,
+
+to hold longer to see if the weather gets
+better.
+
+And the real issue for the launch director
+is to try to convince people, if the weather
+
+is good enough, that this is good enough.
+
+And, yeah, you could wait longer for it to
+get better but it's good enough.
+
+We're running out of window time.
+
+All the time we sit here on the ground with
+all these systems humming along, the probability
+
+of some glitch or something coming up to scrub
+you is increased.
+
+And just as a personal note, when I was I
+the Air Force, I was a weather forecaster
+
+for Missile Operations.
+
+And I felt that that was a waste of an engineer's
+time because I was a graduate engineer with
+
+my diploma sticking out of my pocket.
+
+I wanted to go launch missiles and rockets,
+and the Air Force said Lieutenant Sieck is
+
+going to be a weather forecaster supporting
+Missile Operations.
+
+I endured that for a couple of years and put
+all of that experience in my hip pocket.
+
+And I didn't need it until I got into this
+launch director job.
+
+And I spent many hours talking to the weather
+people who provide the forecast for the launch
+
+going over all of the data and the technical
+aspects of the weather situation to see if
+
+there it was prudent to sit here any longer
+and wait for the weather to improve or whether
+
+it was better to scrub, get these guys out
+of their uncomfortable suits and send them
+
+back to crew quarters and recycle for the
+next day.
+
+And they won't necessarily scrub, but you
+have to disposition their concern.
+
+And you will hold until their concern is taken
+care of.
+
+Yes?
+
+This is unrelated, but you know how the Russians,
+in going out to the launch pad, use a rail
+
+track and they have the rocket flat?
+
+Can you do that with the shuttle?
+
+Instead of stacking it like this and then
+rolling it out, would it be better, easier?
+
+Well, the problem with that are the solid
+rocket boosters.
+
+They weight approximately, when assembled,
+a little less than three million pounds a
+
+piece.
+
+And the joints that caused the Challenger
+accident are critical.
+
+And I don't know if they went through the
+technical aspects of the design, but these
+
+things are 14 feet in diameter.
+
+Each segment weighs 300,000 pounds and they
+have these two cleavaces that come together
+
+with O rings in there.
+
+And what caused the Challenger accident was
+there was rotation in these joints to the
+
+point where the O rings, because of cold weather,
+weren't making a good seal and caused a gas
+
+path.
+
+And 1200 degree temperature.
+
+Exhaust plume just cut through the metal once
+it found a path.
+
+So you want to maintain the integrity of these
+joints.
+
+If you stacked them horizontally, and that
+could be done, and then you lift this thing
+
+vertically, the joints aren't certified to
+maintain their integrity doing that.
+
+Plus, you'd need some kind of huge crane to
+pull this 3 million pounds from horizontal
+
+to vertical.
+
+I think it's something that could have been
+done, had it been built into the design at
+
+the beginning.
+
+And the Russians have a tradition of doing
+this.
+
+And so that is the way they design their rockets.
+
+For whatever reason, we never started that
+way.
+
+From the very beginning, our rockets got stacked
+vertically.
+
+And that's the way all of the American rockets
+have been designed.
+
+Yes?
+
+[AUDIENCE QUESTION] The launch director, whether
+it is flight worthy, actually, that mission
+
+management team is responsible for the flight
+worthiness because they encompass not only
+
+watching what you did in launch count, but
+the certification of all this hardware before
+
+it even got to the launch pad.
+
+And, ultimately, the launch director is responsible
+for conducting an orderly launch and making
+
+sure that this mission management team doesn't
+have any issues, that that engineering team
+
+doesn't have any issues, that the console
+operators have really completed their procedures.
+
+That is their responsibility.
+
+And, if there is any fuzz on that, so to speak,
+even though console operators say they're
+
+go, and the mission management team says they're
+go and flight says they're go, if there is
+
+any concern about that, it's the launch director's
+job to say no, we're not going to go fly today.
+
+We are going to give you another day or two
+days to do more homework, look at more data,
+
+have more discussions.
+
+We're going to scrub today, even though everybody
+may say we're go.
+
+And that has happened before.
+
+And I always wondered, after not too many
+times, when I've said no, when everybody wants
+
+to go, whether I'll get the phone call saying
+well, I'm glad you made it safe today, Sieck,
+
+but you don't have this job tomorrow.
+
+Well, I never got that call.
+
+Never did.
+
+The process, not to bore you with it, but
+since it is an operation, normally we try
+
+to launch in the middle of a week, Wednesday
+or Thursday.
+
+We usually take the weekend off before that
+to clean up everything and give the launch
+
+team a rest, so we power up everything.
+
+And that's the way we start the process.
+
+And that's a couple of shifts worth of work
+to bring up the ground systems, the flight
+
+systems, make sure that all the avionics hardware
+really comes to life.
+
+And we put in a no work hold at the end of
+that to take care of any problems.
+
+If that all goes well then we get into the
+more critical activity that has time constraints
+
+associated with it.
+
+We load the fuel cell.
+
+That is the power plants and the orbiter reactants,
+liquid hydrogen and liquid oxygen, because
+
+they have limited life.
+
+Even if you don't have the fuel cells activated
+that stuff boils off and you lose it and that
+
+could count against your mission capability.
+
+And that is a hazardous operation also.
+
+And then we put in another no work hold at
+the end of that.
+
+And then we have a period of time where we
+bring up the final systems, put in the time
+
+critical storage, particularly when we're
+flying laboratories and you put in plants
+
+or critters or whatever it may be either in
+the crew module or the payload bay.
+
+And the last 12 hours down here is when you
+really have got to make sure this is a real
+
+decision point right here.
+
+Are we going to load the external tank, put
+a cycle on the tank?
+
+And we know that putting liquid hydrogen and
+liquid oxygen, and there is roughly half a
+
+million gallons in a tank, puts stresses into
+the hardware.
+
+You really don't want to do that unless you're
+pretty sure you're going to launch that day
+
+or that night.
+
+We have a meeting before that to make sure
+the weather looks pretty good and that the
+
+mission management team is not working any
+offline issues.
+
+And that has happened before.
+
+A war story for you.
+
+In the early '80s, in one of our missions,
+we assembled the mission management team to
+
+decide whether or not we ought to go load
+the external tank and go fly.
+
+Everything looked pretty good.
+
+And the orbiter project manager said well,
+I need to make you aware of this.
+
+I just got a telegram from the manufacturers
+of the tires.
+
+And the manufacturer said they were inspecting
+a lot, a lot of the tires of which we have
+
+two of them from the same lot on the Orbiter,
+and they found some blems on these tires.
+
+And they don't know whether it's a manufacturing
+flaw or an aging defect.
+
+And we don't know whether it affects the integrity
+of the tires.
+
+But since we knew you were launching tomorrow,
+we thought we would share this with you.
+
+Warm regards, BF Goodrich, I think it was
+at the time.
+
+Well, the mission management team threw on
+that on the table and said hey, we've got
+
+to go work this.
+
+These people, we don't know, they haven't
+said they're not certifying the tires.
+
+They just said they've got a problem.
+
+Well, that's fine.
+
+The mission management team, go work that
+and let's talk about whether or not it's prudent,
+
+under these circumstances, to go load the
+tank with some probability that we get all
+
+the way down to T minus nine minutes and you
+folks are going to say hey, we need to look
+
+at more test data on these tires or have more
+discussions with BF Goodrich on whether or
+
+not we go fly today.
+
+Well, you don't want to load the tank and
+go through all that if that's what you think
+
+the situation is going to be eight hours away
+from that.
+
+And you've put a cycle on the tank, you've
+used up a lot of cryos that you cannot save
+
+because of the heat leak.
+
+Plus, your launch team has put a cycle on,
+depending on the time of day, they've been
+
+up all day, all night or whatever.
+
+Those are the kinds of issues that you need
+to make sure get worked.
+
+And the mission management team has to handle
+that, but the launch director has to decide
+
+just go work that for another day or two.
+
+We're not going to load the tank.
+
+Or, what's the promise of this coming to fruition,
+the possibility so that it makes sense to
+
+go try to fly?
+
+What did you do with the tires?
+
+In that case, we went ahead and tanked.
+
+The subsystem manager for that, which you
+may have already heard from, went back to
+
+a lot of the test data that they had run on
+the tires, that they had been fairly recent.
+
+Langley, I think, was involved in it.
+
+And they said we don't have to worry about
+those blems being a problem for the tires
+
+that are on the Orbiter which, by the way,
+you don't have any access to at the launch
+
+pad.
+
+If we were going to change the tires, you
+would have to roll back to the Orbiter Processing
+
+Facility.
+
+And that would be a couple of month's worth
+of impact to that flight.
+
+We ended up not doing anything with the tires,
+but it had the mission management team really
+
+busy for about eight hours.
+
+And this process takes about three days.
+
+And we have refined those procedures, as you
+might expect over the years, to make this
+
+as an efficient and repetitive a process as
+we can.
+
+In addition to minimizing the hazards to the
+people and the equipment.
+
+Before we got to terminal count, usually we
+take like a two minute break.
+
+This is a good time to do that.
+
+Terminal count phase.
+
+After the tank is loaded, half a million gallons
+of liquid hydrogen, liquid oxygen, and there
+
+are no leaks, and we have leak detectors all
+over the vehicle, and we've scrubbed a lot
+
+of launches because of leaks, we give the
+crew a go to come on out.
+
+And a crew of seven or eight people, it takes
+an hour and a half to get them all in and
+
+get them connected, check their communications
+and that sort of thing.
+
+Roughly three hours before launch we bring
+them out, we get them all connected, we close
+
+the hatch and we verify the integrity of the
+crew module.
+
+And clockwise we're down to T minus 20 minutes,
+but if it's a rendezvous window, and most
+
+of them are now.
+
+The launch window is only five to ten minutes
+long so we have to be in phase with the same
+
+plane that the Space Station is in and we've
+got to get in phase with being able to catch
+
+the Space Station or have it catch us.
+
+The launch window, we don't have enough energy
+in the Shuttle to steer to any orbit we'd
+
+like to.
+
+The launch window is only about ten minutes
+long, so we put in a long hold at T minus
+
+nine minutes for those kinds of missions.
+
+It is the equivalent of the two minute timeout
+in a professional football game.
+
+Everybody has a chance to review their information,
+discuss their strategies, if it's a long launch
+
+window, if it was just a lab mission then
+we only wait for ten minutes at this T minus
+
+nine mark.
+
+But, if it's a short window, we set up the
+clock such that we hold there for almost an
+
+hour.
+
+And then, as you saw on that previous chart,
+we do a poll of all those people and make
+
+sure that they are all still go and they're
+not working any problems or issues.
+
+And then we start this automated software
+program that looks at, in addition to the
+
+systems engineers and their consoles looking
+at all their information, we have an automated
+
+program called the Ground Launch Sequencer
+that looks at all the measurements, all the
+
+parameters to make sure that they are within
+limits.
+
+And it issues all the commands to the vehicle
+and the ground support equipment.
+
+And we did that so we could manage the repeatability
+of that process.
+
+And you had to take the human factor button
+pressing out of the process as much as possible.
+
+And there is not a lot of work that goes on
+in there.
+
+And there is very little manual work.
+
+You get five minutes.
+
+The orbiter access arm, their ability o get
+out of the vehicle in a big hurry is retracted.
+
+It takes two to three minutes to pull that
+back, but we can get it back up to the vehicle
+
+in less than 30 seconds which is about the
+amount of time it takes them to unstrap and
+
+get out of there anyway if there's a fire
+or something bad like that, that they have
+
+to do an emergency egress.
+
+They start the propulsion units on the Orbiter
+that pressurize the hydraulic system.
+
+Just like on an airplane, there is an automated
+test of all the aero surfaces like they do
+
+on the end of a runway.
+
+But this is done by the computer and it wiggles
+the elevons and the rudder and the main engines
+
+to make sure all of that works.
+
+And we also start the conditioning of the
+propellant at the engine interface.
+
+And they already had the discussion about
+the main engines.
+
+You have to make sure that the quality of
+the fluid in the external tank and the quality
+
+of it that's right there at the injector of
+the engine is within the temperature and density
+
+parameters that the engine was certified at.
+
+Because we have to drain the propellant out
+of the fill lines.
+
+And, once we've started doing that, that propellant
+starts heating up right there on those valves
+
+that are going to go into the injector and
+start the main engines on the Orbiter.
+
+That limits our ability to stop and hold after
+that.
+
+We are good for four to five minutes after
+that starts.
+
+And that process starts at T minus five minutes.
+
+After that point in time, we are either going
+to launch or scrub in the next ten minutes.
+
+And then we pressurize the oxygen tank and
+we pressurize the hydrogen tank, but anywhere
+
+in this period of time we can stop.
+
+If an engineer or the automated sequencer
+says something is out of limits, we will stop
+
+at those milestones and disposition that problem
+if we can.
+
+But, per our rules, we won't waive any requirements
+at that point.
+
+Even though an engineer may have a perfectly
+good explanation as to why this temperature,
+
+pressure or whatever, our limit is not being
+met, if the launch commit criteria, the launch
+
+rules says no, it has to be like this, then
+we're not going to go launch that day.
+
+We won't.
+
+After 31 seconds, the solid rocket boosters
+come to life.
+
+The propellant doesn't ignite, but their hydraulic
+system is powered up.
+
+Their avionics systems are powered up.
+
+Their engine nozzles are checked again in
+an automatic sequence.
+
+And at 10 seconds, if everything looks good
+and all these measurements that our Ground
+
+Launch Sequencer has been looking at, we send
+up the computer data bus a go to the onboard
+
+computers that said all of our stuff has been
+satisfied.
+
+Now, we're still looking at a few things.
+
+We're looking at those bolts that are holding
+the solid rocket motors to the launch pad.
+
+And the ability to blow the nuts that are
+holding them, should that system fail, we
+
+would send the cutoff to the onboard computers.
+
+Regardless of where the engines were in their
+startup sequence, the three main engines,
+
+everything will stop.
+
+And hopefully it will gracefully come to a
+stop and we will safe all the systems and
+
+go from there.
+
+But that is the final handshake that is preplanned
+between flight and ground is that ten seconds
+
+when we send a command up to the computer
+saying we are all go.
+
+We can still shut you off, and we can shut
+you off manually, too.
+
+If a console operator sees something happening
+that they think could compromise the safety
+
+of the launch, they can call for a cutoff.
+
+And we have a switch that says cutoff.
+
+It sends a command to the onboard computers,
+and it will stop everything within 10 to 20
+
+milliseconds.
+
+But you don't like to put humans in a position
+to have to make that call.
+
+And that's why all of the critical stuff is
+done by the computers.
+
+And I mentioned the Ground Launch Sequencer.
+
+That's a console and operators in the back
+of the Control Room.
+
+And they are the ones, by the way, that determine
+nobody presses a button for launch.
+
+A woman in the back of the Control Room types
+the liftoff time into the computer when the
+
+launch director tells her, hey, look, it looks
+like we're going to come out of our T minus
+
+nine minute hold at this point in time.
+
+So here is the liftoff time.
+
+Put that in the computer.
+
+And after that it's a hands-off operation.
+
+Can I ask, are these commands being physically
+sent, I mean they're hard line cable?
+
+It's what we call a launch data vest.
+
+It's a cable that is connected from the computers
+in the Control Room through the liftoff umbilical
+
+into the Orbiter computers.
+
+It's a data train.
+
+And when is that connection broken?
+
+At liftoff.
+
+The onboard computers will check the health
+of the main engines, and if the three main
+
+engines are within all of their operating
+parameters, the turbines and the pumps and
+
+the temperatures then it sends a command to
+those eight bolts that hold the solid rocket
+
+boosters to the mobile launch platform and
+the bolts that hold the external tank vent
+
+arm to the tank.
+
+And the two Orbiter umbilicals that says fire
+the nuts, we're going to go.
+
+And that is orchestrated by the onboard computers.
+
+And when that happens you're flying, you're
+going.
+
+The command to ignite the igniters on the
+solid rocket motors is sent at that time also
+
+by the onboard computers within a couple of
+milliseconds.
+
+So all that happens at once.
+
+And it's an onboard automated thing.
+
+I talked about the human factor that repeatability
+is important.
+
+And I mentioned I gave the engineers, you
+know, I always threw rocks at them because
+
+they always want to change things.
+
+It is the launch director's responsibility
+to manage.
+
+They're the owner, so to speak, of the launch
+count procedures, the 5,000 pages of documentation
+
+and the 500 or so software programs that are
+executed in the launch count process.
+
+And we discouraged changes to that for obvious
+reasons.
+
+Unless there is a modification to the flight
+hardware or the ground hardware or we found
+
+something in our previous launch attempt that
+said we need to fix this or there's an opportunity
+
+to increase the margins, we don't change it.
+
+We try to maintain the procedure and the hardware
+the way it always has been.
+
+And it essentially is.
+
+We do training, obviously, but we train for
+the nonstandard work.
+
+Just like in the flight team, we have a simulation
+supervisor that throws diabolical failures
+
+out there and we have computer programs and
+into the control center we bring the launch
+
+team, power up the consoles.
+
+And their displays look like the shuttle is
+at the pad and it is getting ready to launch
+
+and we throw failures at them to test their
+reaction and to find bugs in our safing procedures.
+
+And we've done that over the years.
+
+I think the next generation of vehicles will
+probably have more automation.
+
+And that will probably be a better thing but
+you will never take the console operator out
+
+of the Control Center either, the Launch Control
+Center or the Flight Control Center.
+
+You need the person there to disposition the
+problems, but predictability is what we're
+
+always after.
+
+And stable procedures, be they flight or ground,
+give predictable results.
+
+And that is why we automate.
+
+And we control change, too.
+
+Responsibility.
+
+I talked about the engineers.
+
+I didn't mention, I don't think, technicians
+and inspectors.
+
+But when a technician stamps a procedure that
+I torque that bolt and the inspector stamps
+
+that same procedure and said I saw him torque
+that bolt, that is their warranty that that
+
+event really happened.
+
+And that paper trail and that warranty is
+very important.
+
+When an engineer signs a procedure that tested
+the Flight Control System that said I reviewed
+
+all the data, didn't see any glitches, everything
+met specifications, that signature is his
+
+or her warranty that the procedure ran correctly
+and that they understood the requirements
+
+that were implemented by that procedure.
+
+And the requirements were met.
+
+And that is important.
+
+Our whole concept of launch readiness is based
+on people being responsible for their system,
+
+be it the designer that signs it that says
+there is nothing going on offline, there are
+
+no faxes out there that say there is a cloud
+over the tires.
+
+Or, my last test of the main engines at Stennis,
+there was nothing there that says these three
+
+engines that are on this orbiter shouldn't
+work just fine.
+
+And they do that in a flight readiness process.
+
+That is their warranty and responsibility.
+
+And we hammer this home.
+
+And it probably comes from, I had this quote
+in my office for years and I am going to bore
+
+you with it, and maybe some of you can guess
+where this came from.
+
+Responsibility is a unique concept.
+
+It can only reside in here in a single individual.
+
+You may share it with others, but your portion
+is not diminished.
+
+You may delegate it but it is still with you.
+
+You may disclaim it but you cannot divest
+yourself of it.
+
+Even if you do not recognize it or admit its
+presence, you cannot escape it.
+
+If responsibility is rightfully yours, no
+evasion or ignorance or passing the blame
+
+can shift the burden to someone else.
+
+And this is what we push home.
+
+And, by the way, this quote was Admiral Rickover
+who was testifying before Congress after the
+
+first nuclear submarine accident.
+
+And he was saying I am responsible.
+
+It is my program, it is my submarine, I am
+responsible.
+
+Even though somebody else was commanding it,
+it doesn't matter, I am responsible.
+
+And we impress that on the managers, the engineers,
+the technicians, the inspectors, you know,
+
+you're important.
+
+And the work you do is important.
+
+And when you sign or stamp that procedure
+or give a go on the Net that is your warranty
+
+that everything is working and you understand
+the requirements.
+
+Very important in the business that we're
+in.
+
+Decision making.
+
+On the chart.
+
+This structure has been in place since the
+Mercury program.
+
+There is nothing new here.
+
+And the only issue comes in when there is
+a gray area.
+
+Who makes the call and how much judgment is
+involved in the call?
+
+And I gave you the example of weather.
+
+Everybody has an opinion on it.
+
+It can be judgmental.
+
+Well, the weather decision is if it is launch
+weather related it is the launch director's
+
+responsibility to determine if it's good enough.
+
+If the flight director has an issue with the
+return to launch site winds, that ultimately
+
+is his or her decision.
+
+The people may get involved in it and they
+may have offline discussions with the flight
+
+director, but it is still ultimately his decision.
+
+And that is the way it has to be because they
+are responsible.
+
+This mission management team is not responsible
+for the go, no-go decision on weather on launch
+
+day.
+
+It's the flight director for the flight stuff.
+
+It is the launch director for the launch-related
+stuff.
+
+And it is set up that way so there is no fuzz
+on it.
+
+Other people can have an opinion, other people
+can have input, but unless this person up
+
+here says launch director we're no go, it
+is the launch director's decision in that
+
+case.
+
+Communication.
+
+Real important.
+
+And I will give you an example of that.
+
+Apollo 13.
+
+Most of you probably don't remember Apollo
+13, but Apollo 13 was like Challenger and
+
+the Columbia except we didn't lose the flight
+crew.
+
+But it was just as disastrous an event.
+
+And by all rights the crew shouldn't have
+made it safety back to earth, but thanks to
+
+the heroics of the flight crew and the flight
+team and the timing of when that event occurred
+
+they were able to get back home.
+
+But that was all caused by activity that was
+done on the ground well before the launch.
+
+And, specifically since I was involved in
+that, I remember this like it was yesterday.
+
+Of course, part of that is an old age thing.
+
+Stuff that happened 40 years ago comes in
+loud and clear.
+
+Stuff that happened four days ago, I have
+a hard time remembering.
+
+But we had a tank in the spacecraft that we
+ran our simulated launch count.
+
+And back then we put propellants in the vehicle,
+all the hazardous stuff and detanks.
+
+And we couldn't detank the liquid oxygen out
+of this tank.
+
+They had the fuel cells on the spacecraft.
+
+And just a little more history.
+
+The tank had been dropped when it was installed
+back in California, but engineers and managers
+
+did some tests and some rationale on saying
+well, it's still OK to install it.
+
+We got it down the Cape.
+
+We put the liquid oxygen in it and all the
+rest of the system.
+
+We couldn't get it out of this tank.
+
+And after reviewing it they found, well, the
+stand pipe in there that is used to drain
+
+it on the ground was probably bent or damaged
+and that's why we cannot get it out.
+
+So the managers and engineers got together
+for a few days and said turn the heaters on
+
+in the tank and vent the liquid oxygen off.
+
+Heat it up and it will boil off as oxygen
+gas through another loop that takes it through
+
+the fuel cells and out vent on the vehicle.
+
+Use the heaters to go do that.
+
+So they developed the procedure and we went
+on station at night a week after we had the
+
+anomaly and turned everything on and turned
+on the heaters.
+
+And it is fine.
+
+You can see the liquid is turning to gas and
+it is coming out.
+
+And the console operator in our Control Room
+said hey, Sieck, I cannot monitor the temperature
+
+in this tank anymore.
+
+Well, why is that?
+
+Well, the range on the temperature is from
+ambient down to minus 300 degrees because
+
+it's measured in liquid oxygen.
+
+And it is upper limits.
+
+It started heating up, and now I cannot tell
+you whether it is 50 degrees or 350 degrees.
+
+I said OK, stop.
+
+So we stopped the test and got all these managers
+involved, including the people that built
+
+the tank and say hey, we've lost visibility.
+
+We're putting energy into this tank that has
+liquid oxygen in it.
+
+We cannot monitor the temperature anymore.
+
+The pressure seems to be fine.
+
+They said don't worry about it.
+
+There is a thermostat in there that is heat
+sensitive, and it will open up the power to
+
+the heaters if it gets to some limit in there.
+
+Just keep your eye on the pressure.
+
+Make sure the pressure doesn't get too high.
+
+Well, of course the pressure isn't going to
+get too high because the vent is open.
+
+So we said fine.
+
+We turned the ground power supplies on and
+let the thing cook for 10 to 12 hours.
+
+And what we didn't know was that the thermostat
+wasn't certified to the voltage we were using
+
+from our ground power supplies because we
+didn't tell them, although our requirements
+
+allowed it, that we cranked the power supplies
+up to 50 volts.
+
+And why did we do that?
+
+Well, the more energy you put into the tank
+the higher the heaters get and the quicker
+
+the liquid oxygen boils off.
+
+You know, high school physics.
+
+But we didn't tell them that.
+
+And the people that built the tank and built
+that thermostat had only certified it to the
+
+voltage of fuel cell supply which is half
+that value.
+
+So the thermostat welded together, the points
+did, and we had continuous power going on
+
+in there for eight to ten hours.
+
+It got to 800, 900 degrees in the tank.
+
+We burned all the insulation off the wires
+to the fans and the heaters.
+
+And, from that point on, we were just waiting
+for something to happen to make those wires
+
+come together.
+
+And if you didn't turn the power on you're
+going to get a spark in an oxygen tank.
+
+Not a good thing.
+
+Well, that is what happened a day into the
+mission when they were heading to the moon.
+
+And they turned the heaters and the fans on
+to stir the cryogenics because they were worried
+
+about stratification and zero gravity.
+
+And they got the spark and it blew up the
+service module.
+
+The point is that communication, we wrote
+down in our procedures what we did, but we
+
+didn't communicate that on a real-time basis.
+
+And, although we reviewed the procedures afterward,
+as the rest of the team did, the designer
+
+who was 1500 miles away who had approved what
+we did over an intercom system didn't review
+
+our paperwork.
+
+You hit that thing with 50 volts, it's only
+certified for 25 volts, even though our requirements
+
+allowed us to use 50 volts.
+
+It is a case where requirements didn't preclude
+us from launching hardware then in hindsight
+
+was flawed.
+
+But, on the other hand, communication, we
+didn't tell them in real-time.
+
+And, as a result, Apollo 13 happened.
+
+So I learned that lesson early on.
+
+I mean even if you're boring them with what
+appears to be minutia, you're going to tell
+
+them everything and document everything.
+
+And, thankfully, they went through our procedures
+and said well, there it is.
+
+And I thought we'd get fired.
+
+And actually we got patted on the back for
+documenting what we had done so it made it
+
+easier to zero in on the root cause of the
+problem.
+
+And, as a result, we fixed that and we were
+able to fly again in a few months as opposed
+
+to having to go through a Challenger or Columbia
+type of activity.
+
+Very important.
+
+Launch fever.
+
+The human factor.
+
+It is hard to describe what the environment
+is in the spacecraft a few minutes before
+
+launch or in the Control Room.
+
+But there is a lot of tension and there is
+a lot of energy.
+
+And everybody in there, for the most part,
+has been awake for the last 10 to 12 hours.
+
+And they came to work that day or that night
+with all hopes of safely launching the Space
+
+Shuttle.
+
+And they really don't want anything to go
+wrong with their system or somebody else's
+
+system.
+
+I mean that's the mood.
+
+Because, if something goes wrong, you're going
+to come back tomorrow or the next day or the
+
+next week.
+
+So they really want to hear this everybody,
+you know, when they do the polls they go,
+
+go, go, go.
+
+And the hardest thing is saying no when everything
+sounds like it's go.
+
+And there are a lot of times when we've had
+problems with ground support equipment.
+
+It is old.
+
+I wish we had all new stuff for Shuttle.
+
+A lot of this stuff is the same we used on
+Apollo.
+
+And, in spite of our efforts to maintain it,
+it is all out in the corrosive atmosphere
+
+at the launch pad.
+
+And that stuff constantly gave us problems.
+
+And we would lose some of our redundant systems
+and some of our primary systems.
+
+And more than once in launch count, when we'd
+have a problem out there, the team would come
+
+to the launch director through that organization
+chart you saw and say we've got an idea.
+
+We think if we patch around this and then
+hook this up to this and we throw these switches
+
+and we get this result that it will be OK
+and we can go fly without this power supply
+
+being active or this purge system operating
+normally and all these other things that we've
+
+got out there.
+
+And what you have to do as launch director
+is say well, just sit back and analyze whether
+
+or not -- I mean you rely on your engineers
+to use their Yankee ingenuity to fix a problem,
+
+but you have to assess whether or not they're
+literally shot-gunning it and coming up with
+
+the proverbial quick fix because they want
+to go home in an hour or so and celebrate
+
+a good launch.
+
+Just like these guys want to get out of those
+uncomfortable suits they have been sitting
+
+in for the last couple hours and either get
+out of the spacecraft or get up there in zero
+
+G.
+
+As a launch director, you have to assess well,
+OK, but is this really the right thing to
+
+do or are they working this too hard?
+
+If you gave them another 24 hours to look
+at the data and think about their approach
+
+to a fix would the answer be any different?
+
+And there have been a few times when they
+said well, that sounds pretty good right now
+
+but I am going to give you another 24 hours
+to think about it so we're going to scrub
+
+for the day.
+
+And you can hear the big groan in the Control
+Room.
+
+And you can just see it going through their
+heads, well, this guy has lost confidence
+
+in us.
+
+I mean we all came to work, we get paid to
+solve problems and get things done, and he
+
+is telling us that ain't a good answer, that
+ain't a good fix.
+
+So you have to balance that when you're in
+charge, but the real job of the launch director
+
+is to say no when everybody else wants to
+go.
+
+That is really what you are there for.
+
+Because these guys get tunnel vision.
+
+They want to go fly.
+
+The console operators, things are on automatic
+in that last nine minutes, and they just hope
+
+they don't get that little red or yellow light
+on their screen that says hey, you better
+
+go look at this, it isn't working right.
+
+The last people you want to ask is it OK to
+launch is the crew.
+
+They'll say yes, no matter what is happening.
+
+And we do ask them, by the way, but it is
+a formality because we know what the answer
+
+is.
+
+Unless he's got a fire extinguisher up there
+putting out something in the spacecraft, he
+
+is going to say we're go.
+
+And that is also why we put in a rule that
+says after five minutes, for these critical
+
+launch commit criteria items, the 500 that
+you absolutely have to look at and certify,
+
+you don't proposition us with a change to
+that after five minutes because we're not
+
+going to entertain it.
+
+If they're out of limits we're not going today
+or tonight.
+
+It is going to be at least 24 hours.
+
+A long time.
+
+But the team that does it, I mean they are
+good, they are professionals.
+
+And we talk a lot about the Apollo program
+and how great things were back then, but I
+
+just gave you the example of Apollo 13.
+
+The Shuttle team versus the Apollo team has
+a much higher degree of difficulty situation
+
+to deal with.
+
+There are fewer people on Shuttle, yet it's
+a more complex vehicle than the whole Apollo
+
+system.
+
+The Saturn 5 rocket and the spacecraft were
+simple compared to the Shuttle system.
+
+And we had 25,000 people at the Cape in the
+Apollo program flying two to three times a
+
+year.
+
+And in the Shuttle program back in the early
+'90s we flew seven times a year with 6,000
+
+people with a vehicle that is more complex,
+older.
+
+In the Apollo program our ground equipment
+was new and all the flight hardware was new.
+
+It wasn't reused.
+
+It was fresh out of the box factory pristine
+stuff.
+
+And requirements were easy, you know, it had
+to act and look brand-new or you replaced
+
+it.
+
+The Shuttle, because it is 20, 30 years old,
+depending on which orbiter and the ground
+
+equipment which is 30 to 40 years old, there
+are requirements that allow fair wear and
+
+tear.
+
+The engineers are constantly pushed with is
+this good enough?
+
+These wire bundles are frayed and there are
+dings in this line and that weld is looking
+
+like it has corrosion on it, is it good enough?
+
+Well, they are constantly propositioning where
+back in the Apollo program you didn't have
+
+to mess with that gray area stuff.
+
+It either looked or acted brand-new or you
+replaced it.
+
+And replacing it was easy because money was
+unlimited.
+
+As a journeyman engineer on Apollo I was told
+whatever you need you can have.
+
+System engineers seek more test equipment,
+you need more technicians to be trained on
+
+this over here, whatever you need just ask
+for it.
+
+Money is not an object.
+
+As a manager on the Shuttle program when I
+finally got promoted out of the job I liked
+
+to launch director, I had to tell the journeymen
+engineers this is all the money you get for
+
+next year.
+
+And be real efficient with this and frugal
+because next year you're probably going to
+
+get less.
+
+And your strategy and approach to issues is
+much different if you have those two different
+
+environments to deal with.
+
+And finally the other thing that Shuttle deals
+with today versus Apollo is the acceptance
+
+of risk.
+
+I mean I already mentioned Apollo 13.
+
+Back then if you made a mistake you were patted
+on the back and told hey, nice try.
+
+Now, is there anything that can be done to
+better enhance your probability of success?
+
+Whereas, in the Shuttle program, risk aversion
+in this country, I don't want to get started
+
+on that tangent, is becoming more and more
+a lifestyle.
+
+We don't want to do things we might lose or
+we might not win or we may not be successful.
+
+And risk, you know, there is less tolerance
+to it.
+
+And, when you have a problem like Columbia
+or Challenger, you get half a dozen boarding
+
+parties coming into NASA saying here is what
+you need to do differently or this is wrong
+
+with your agency and this and this and you
+need to go fix that.
+
+And, again, back in Apollo, it was what do
+you need to be successful?
+
+Much different.
+
+And it makes it difficult to operate.
+
+Bob, could you comment upon risk aversion
+and the launch director and whether there
+
+were more aggressive and more conservative
+people who have had your job?
+
+Well, I would say, before I was launch director,
+there was one.
+
+And he was more aggressive than I was.
+
+He was the console MANOPS person.
+
+And he would push, and he would push until
+you would say uncle, I surrender or whatever,
+
+and then he would make a judgment call.
+
+I was more conservative than that.
+
+I trained the one immediately after me.
+
+And he was pretty much the same but he got
+the highly visible job, management say that
+
+this guy was good, we'll take him away from
+here and go put him over here managing this
+
+large organization and worrying about budgets
+and contracts.
+
+That is the same thing that happened to me.
+
+And that's unfortunate, but NASA's strongest
+suit is not succession planning, unfortunately.
+
+It just isn't.
+
+Yes?
+
+Are you saying the Shuttle program is too
+risk averse?
+
+Because you also said that, for example, it
+is your job as launch director to be conservative
+
+and to say no when everyone else is saying
+yes.
+
+No, I wouldn't say that the Shuttle program
+is risk adverse.
+
+I would say our society is risk adverse.
+
+And you see some of that permeating into the
+Shuttle program, but not to the point where
+
+I would say it is detrimental.
+
+I mean asking questions, digging in to understand
+what your risks are is an important thing
+
+to do.
+
+And early in the Shuttle program we didn't
+do that.
+
+We had a lot of confidence in hardware after
+the first few missions.
+
+It's just like a new car.
+
+You put 5000 miles on it, you get the bugs
+out of it and you fully expect it to last
+
+another so many hundred thousand miles.
+
+Well, that was the same expectation in the
+Shuttle program.
+
+You fly a few flights and you learn that the
+tiles really stayed glued to the Orbiter and
+
+the thermal control system really responds
+as it should on orbit and managing the temperature
+
+and the coolant leaks and that sort of thing.
+
+And you build up confidence and you say it
+should work now.
+
+We got the bugs out of it and we can go fly
+this thing as often as those guys at the Cape
+
+can turn it around.
+
+But what they didn't consider and what all
+these engineers, with all due respect that
+
+you heard from that certify their systems,
+they didn't totally capture the environment
+
+that the Shuttle sees over the long period
+of time in their initial certification.
+
+They didn't capture it.
+
+And that environment includes not only what
+happens in space or the calendar exposure
+
+to just time on some of these systems that
+have soft goods in them, for instance, O rings
+
+and that sort of thing, but it is the environment
+of the Cape with people constantly removing
+
+hardware, disconnecting things, moving wire
+bundles out of the way to get access to this
+
+or that other component to implement the requirements
+that were levied on the Cape to do the tests
+
+and inspections.
+
+And they are very invasive, and collateral
+damage is a way of life when you're crawling
+
+around in the Orbiter.
+
+To put in policy that tries to compensate
+for the fact that the certification didn't
+
+capture that environment that this hardware
+has seen for the last 20 to 30 years, to reduce
+
+the unknowns involved in that, that is the
+right thing to do.
+
+You're trying to reduce the risk of reflying
+a very complex vehicle.
+
+So that is fine, but you take that to a limit.
+
+I mean you can talk yourself into never flying
+which would be pretty easy to go do.
+
+And then this recovery after the Columbia
+accident, that was starting to happen.
+
+The managers, because they had this investigation
+board report that says NASA, you've become
+
+complacent and overconfident.
+
+And, by the way, in my opinion that is somewhat
+of a bum rap to say that NASA in general,
+
+and particularly the Shuttle program, had
+fallen into that mode.
+
+But, to have the pendulum swing the other
+way to understand what your risks are and
+
+then you can have knowledge on whether you
+decide to accept it or not, that is a good
+
+thing.
+
+What didn't happen after Columbia, but we
+did do after Challenger, is after we understood
+
+the root cause of the accident and some of
+the other factors like communication that
+
+we're part of that, reviewed all the systems
+and all the requirements, the managers said
+
+look, we're willing to accept some risk.
+
+You people who are responsible for these systems
+and these processes at the Cape, you need
+
+to quantify that for us and bring it to us.
+
+And we will either say OK, we won't accept
+that, you go back and change your system or
+
+change your limits or do more tests or whatever,
+or we will accept it.
+
+We will say we'll accept that risk, management
+will accept some risk.
+
+That happened after Challenger, and we were
+able to fly again roughly two years later
+
+after we recertified the design to the solid
+rocket motors.
+
+That didn't happen after Columbia.
+
+And you can speculate whether or not we could
+have flown six months ago or a year ago or
+
+we should have waited longer to fly because
+we still had a piece of foam come off the
+
+tank.
+
+You could debate that.
+
+But management never acknowledged that they
+were willing to accept some risk after Columbia.
+
+They did say tell us what the risk is but
+we really want you to crank it down to zero.
+
+We don't want to take any risk, unlike Challenger.
+
+Now, is that bad?
+
+See, what really happened with Columbia was
+the mission management team's discipline had
+
+eroded.
+
+There were communication issues.
+
+And, if you're a student of that investigation,
+they didn't grade out very well.
+
+But the investigation said there is complacency
+and overconfidence in the system.
+
+Well, having been part of the system prior
+to my retirement five years ago, you never
+
+found any complacency or overconfidence with
+the engineers, technicians, inspectors or
+
+the managers that I knew.
+
+Now, they weren't as smart as they thought
+they were or, in some cases, as smart as they
+
+needed to be.
+
+But that is not the same as complacency or
+overconfidence.
+
+Because the latter to me implies an attitude
+problem that I've got it, I know it all, I
+
+am smart as I need to be.
+
+And, for the most part, you know, there were
+some people I didn't like because I thought
+
+he or she was arrogant or something like that,
+but I never sensed an attitude problem with
+
+the Shuttle team.
+
+From the technicians, many of which I knew
+and grew up with, to the top managers in the
+
+Shuttle program, I never sensed that.
+
+But were we not as smart as we thought we
+were or as smart as we needed to be?
+
+Were there signs that there was something
+going on here that you ought to go fix?
+
+Yes.
+
+But, again, they didn't just blow off, so
+to speak, these problems we were having with
+
+foam on the tank and these other systems which,
+to me, would have been complacency or overconfidence.
+
+Anything else?
+
+We're just about out of time.
+
+I've got two announcements.
+
+I've been working with the Stellar people.
+
+As you know, some of the pdf files that I've
+tried to load didn't load.
+
+They cannot really figure out why, but I have
+sent them the files, they've loaded most of
+
+them on so hopefully almost everything is
+there.
+
+We're continuing to work at it, but hopefully
+all the things that you need access to you
+
+can find.
+
+I said there were two things, but that's the
+only one I remember.
+
+Well, let me close with one note then.
+
+I am glad you're here.
+
+Thanks for your choice to pursue an engineering
+career.
+
+Doing things that are hard, I have found that
+in my travels that unfortunately there are
+
+fewer people deciding to pursue the tough
+curriculums and the occupations that require
+
+a lot of work and have some risk associated
+with them.
+
+But it is encouraging to see people in graduate
+school that want to do what I did.
+
+I am not sure how much engineering I did in
+my 40 year career.
+
+I did a lot of managing and a lot of other
+assignments, but I am sure you can accomplish
+
+a lot.
+
+I had a grandmother who was born at the end
+of the 19th century.
+
+And, when she was your age, there weren't
+any computers, airplanes, cars, TV and that
+
+sort of thing.
+
+Yet, in her lifetime, she got to see her favorite
+grandson, Bobby, help put a man on the moon.
+
+And I don't know what can be done in your
+lifetime, but you can make great things happen
+
+with the career you have chosen.
+
+So thanks for choosing, really.
+
+Bob, thanks very much.
+
+A pleasure.
+
+[APPLAUSE]
\ No newline at end of file
diff --git a/uyNj56g5rHY.txt b/uyNj56g5rHY.txt
new file mode 100644
index 0000000000000000000000000000000000000000..11f350d718511c06c8216cfbb979e06622cddba9
--- /dev/null
+++ b/uyNj56g5rHY.txt
@@ -0,0 +1,731 @@
+align:start position:0%
+ 
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+[Applause]
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What are you working on? I've got a
+
+ align:start position:0%
+What are you working on? I've got a
+ 
+
+ align:start position:0%
+What are you working on? I've got a
+great new idea. I'm going to make cocoa
+
+ align:start position:0%
+great new idea. I'm going to make cocoa
+ 
+
+ align:start position:0%
+great new idea. I'm going to make cocoa
+beans that reproduce as fast as viruses.
+
+ align:start position:0%
+beans that reproduce as fast as viruses.
+ 
+
+ align:start position:0%
+beans that reproduce as fast as viruses.
+That way, we'll have enough cocoa beans
+
+ align:start position:0%
+That way, we'll have enough cocoa beans
+ 
+
+ align:start position:0%
+That way, we'll have enough cocoa beans
+to make as much chocolate as we want.
+
+ align:start position:0%
+to make as much chocolate as we want.
+ 
+
+ align:start position:0%
+to make as much chocolate as we want.
+You know how much I like chocolate.
+
+ align:start position:0%
+You know how much I like chocolate.
+ 
+
+ align:start position:0%
+You know how much I like chocolate.
+Explain your project a little more. How
+
+ align:start position:0%
+Explain your project a little more. How
+ 
+
+ align:start position:0%
+Explain your project a little more. How
+are you going to engineer this yummy
+
+ align:start position:0%
+are you going to engineer this yummy
+ 
+
+ align:start position:0%
+are you going to engineer this yummy
+idea? Well, viruses reproduce really
+
+ align:start position:0%
+idea? Well, viruses reproduce really
+ 
+
+ align:start position:0%
+idea? Well, viruses reproduce really
+fast, so I thought that I could take
+
+ align:start position:0%
+fast, so I thought that I could take
+ 
+
+ align:start position:0%
+fast, so I thought that I could take
+that part from a virus and put it into a
+
+ align:start position:0%
+that part from a virus and put it into a
+ 
+
+ align:start position:0%
+that part from a virus and put it into a
+cocoa plant. Plants are pretty safe to
+
+ align:start position:0%
+cocoa plant. Plants are pretty safe to
+ 
+
+ align:start position:0%
+cocoa plant. Plants are pretty safe to
+work with, but viruses can be dangerous.
+
+ align:start position:0%
+work with, but viruses can be dangerous.
+ 
+
+ align:start position:0%
+work with, but viruses can be dangerous.
+Which virus were you thinking about
+
+ align:start position:0%
+Which virus were you thinking about
+ 
+
+ align:start position:0%
+Which virus were you thinking about
+using? Well, I read that Ebola virus has
+
+ align:start position:0%
+using? Well, I read that Ebola virus has
+ 
+
+ align:start position:0%
+using? Well, I read that Ebola virus has
+a short sequence that Ebola Ebola is a
+
+ align:start position:0%
+a short sequence that Ebola Ebola is a
+ 
+
+ align:start position:0%
+a short sequence that Ebola Ebola is a
+biosafety level four agent. Well, the
+
+ align:start position:0%
+biosafety level four agent. Well, the
+ 
+
+ align:start position:0%
+biosafety level four agent. Well, the
+worst are level five, so I thought it
+
+ align:start position:0%
+worst are level five, so I thought it
+ 
+
+ align:start position:0%
+worst are level five, so I thought it
+was safe enough. Level five? There is no
+
+ align:start position:0%
+was safe enough. Level five? There is no
+ 
+
+ align:start position:0%
+was safe enough. Level five? There is no
+biosafety level five. You'd need lots
+
+ align:start position:0%
+biosafety level five. You'd need lots
+ 
+
+ align:start position:0%
+biosafety level five. You'd need lots
+and lots of training to work in any
+
+ align:start position:0%
+and lots of training to work in any
+ 
+
+ align:start position:0%
+and lots of training to work in any
+level three or four facility and you'd
+
+ align:start position:0%
+level three or four facility and you'd
+ 
+
+ align:start position:0%
+level three or four facility and you'd
+have to wait a few years since they
+
+ align:start position:0%
+have to wait a few years since they
+ 
+
+ align:start position:0%
+have to wait a few years since they
+don't let miners in those labs. But
+
+ align:start position:0%
+don't let miners in those labs. But
+ 
+
+ align:start position:0%
+don't let miners in those labs. But
+there was this show on TV where they
+
+ align:start position:0%
+there was this show on TV where they
+ 
+
+ align:start position:0%
+there was this show on TV where they
+what you see on TV and in movies can be
+
+ align:start position:0%
+what you see on TV and in movies can be
+ 
+
+ align:start position:0%
+what you see on TV and in movies can be
+very deceiving. But let's talk about all
+
+ align:start position:0%
+very deceiving. But let's talk about all
+ 
+
+ align:start position:0%
+very deceiving. But let's talk about all
+the biosafety levels. If we're going to
+
+ align:start position:0%
+the biosafety levels. If we're going to
+ 
+
+ align:start position:0%
+the biosafety levels. If we're going to
+make your viral cocoa beans, we need to
+
+ align:start position:0%
+make your viral cocoa beans, we need to
+ 
+
+ align:start position:0%
+make your viral cocoa beans, we need to
+come up with a way that keeps everyone
+
+ align:start position:0%
+come up with a way that keeps everyone
+ 
+
+ align:start position:0%
+come up with a way that keeps everyone
+safe inside the lab and outside too.
+
+ align:start position:0%
+safe inside the lab and outside too.
+ 
+
+ align:start position:0%
+safe inside the lab and outside too.
+Okay, I do know that biosafety is a
+
+ align:start position:0%
+Okay, I do know that biosafety is a
+ 
+
+ align:start position:0%
+Okay, I do know that biosafety is a
+combination of safe lab practices and
+
+ align:start position:0%
+combination of safe lab practices and
+ 
+
+ align:start position:0%
+combination of safe lab practices and
+techniques. wearing the right safety
+
+ align:start position:0%
+techniques. wearing the right safety
+ 
+
+ align:start position:0%
+techniques. wearing the right safety
+equipment and working in a lab designed
+
+ align:start position:0%
+equipment and working in a lab designed
+ 
+
+ align:start position:0%
+equipment and working in a lab designed
+to contain the experiment. But with
+
+ align:start position:0%
+to contain the experiment. But with
+ 
+
+ align:start position:0%
+to contain the experiment. But with
+biosafety level one, that just means a
+
+ align:start position:0%
+biosafety level one, that just means a
+ 
+
+ align:start position:0%
+biosafety level one, that just means a
+room with screened windows and a door
+
+ align:start position:0%
+room with screened windows and a door
+ 
+
+ align:start position:0%
+room with screened windows and a door
+that closes. That doesn't sound like
+
+ align:start position:0%
+that closes. That doesn't sound like
+ 
+
+ align:start position:0%
+that closes. That doesn't sound like
+much. That's because BL1 experiments use
+
+ align:start position:0%
+much. That's because BL1 experiments use
+ 
+
+ align:start position:0%
+much. That's because BL1 experiments use
+only well-characterized microbes that
+
+ align:start position:0%
+only well-characterized microbes that
+ 
+
+ align:start position:0%
+only well-characterized microbes that
+don't make a healthy person sick. But
+
+ align:start position:0%
+don't make a healthy person sick. But
+ 
+
+ align:start position:0%
+don't make a healthy person sick. But
+remember, there's no eating or drinking
+
+ align:start position:0%
+remember, there's no eating or drinking
+ 
+
+ align:start position:0%
+remember, there's no eating or drinking
+in the lab since you wouldn't want to
+
+ align:start position:0%
+in the lab since you wouldn't want to
+ 
+
+ align:start position:0%
+in the lab since you wouldn't want to
+eat your experiments. When do I get to
+
+ align:start position:0%
+eat your experiments. When do I get to
+ 
+
+ align:start position:0%
+eat your experiments. When do I get to
+wear a lab coat like yours? If you're
+
+ align:start position:0%
+wear a lab coat like yours? If you're
+ 
+
+ align:start position:0%
+wear a lab coat like yours? If you're
+working at biosafety level two, you'll
+
+ align:start position:0%
+working at biosafety level two, you'll
+ 
+
+ align:start position:0%
+working at biosafety level two, you'll
+have to wear it. and gloves, too. Since
+
+ align:start position:0%
+have to wear it. and gloves, too. Since
+ 
+
+ align:start position:0%
+have to wear it. and gloves, too. Since
+some BL2 agents can be infectious, BL2
+
+ align:start position:0%
+some BL2 agents can be infectious, BL2
+ 
+
+ align:start position:0%
+some BL2 agents can be infectious, BL2
+labs have impervious benches, and most
+
+ align:start position:0%
+labs have impervious benches, and most
+ 
+
+ align:start position:0%
+labs have impervious benches, and most
+of the work is done in biological safety
+
+ align:start position:0%
+of the work is done in biological safety
+ 
+
+ align:start position:0%
+of the work is done in biological safety
+cabinets. Lots of BL2 workers also get
+
+ align:start position:0%
+cabinets. Lots of BL2 workers also get
+ 
+
+ align:start position:0%
+cabinets. Lots of BL2 workers also get
+immunizations if they'll be working with
+
+ align:start position:0%
+immunizations if they'll be working with
+ 
+
+ align:start position:0%
+immunizations if they'll be working with
+certain agents. I hate getting shots.
+
+ align:start position:0%
+certain agents. I hate getting shots.
+ 
+
+ align:start position:0%
+certain agents. I hate getting shots.
+Well, not all level two agents require
+
+ align:start position:0%
+Well, not all level two agents require
+ 
+
+ align:start position:0%
+Well, not all level two agents require
+immunizations. Really, the rules for BL1
+
+ align:start position:0%
+immunizations. Really, the rules for BL1
+ 
+
+ align:start position:0%
+immunizations. Really, the rules for BL1
+and BL2 are pretty basic because the
+
+ align:start position:0%
+and BL2 are pretty basic because the
+ 
+
+ align:start position:0%
+and BL2 are pretty basic because the
+agents have minimal risk associated with
+
+ align:start position:0%
+agents have minimal risk associated with
+ 
+
+ align:start position:0%
+agents have minimal risk associated with
+them. But let's think for a minute about
+
+ align:start position:0%
+them. But let's think for a minute about
+ 
+
+ align:start position:0%
+them. But let's think for a minute about
+what biosafety you'd need for your
+
+ align:start position:0%
+what biosafety you'd need for your
+ 
+
+ align:start position:0%
+what biosafety you'd need for your
+mashup of a virus with a cocoa plant.
+
+ align:start position:0%
+mashup of a virus with a cocoa plant.
+ 
+
+ align:start position:0%
+mashup of a virus with a cocoa plant.
+Well, maybe more protective clothes like
+
+ align:start position:0%
+Well, maybe more protective clothes like
+ 
+
+ align:start position:0%
+Well, maybe more protective clothes like
+the workers in biosafety level 3 labs.
+
+ align:start position:0%
+the workers in biosafety level 3 labs.
+ 
+
+ align:start position:0%
+the workers in biosafety level 3 labs.
+They wear full suits and maybe masks or
+
+ align:start position:0%
+They wear full suits and maybe masks or
+ 
+
+ align:start position:0%
+They wear full suits and maybe masks or
+something. It's nothing I can't handle.
+
+ align:start position:0%
+something. It's nothing I can't handle.
+ 
+
+ align:start position:0%
+something. It's nothing I can't handle.
+Imagine me in a space suit. Very cool.
+
+ align:start position:0%
+Imagine me in a space suit. Very cool.
+ 
+
+ align:start position:0%
+Imagine me in a space suit. Very cool.
+And think about how much chocolate we'll
+
+ align:start position:0%
+And think about how much chocolate we'll
+ 
+
+ align:start position:0%
+And think about how much chocolate we'll
+have. Earth to dude. Level three agents
+
+ align:start position:0%
+have. Earth to dude. Level three agents
+ 
+
+ align:start position:0%
+have. Earth to dude. Level three agents
+are very serious, potentially lethal.
+
+ align:start position:0%
+are very serious, potentially lethal.
+ 
+
+ align:start position:0%
+are very serious, potentially lethal.
+And level four agents like Ebola virus
+
+ align:start position:0%
+And level four agents like Ebola virus
+ 
+
+ align:start position:0%
+And level four agents like Ebola virus
+have such a high lethal risk that there
+
+ align:start position:0%
+have such a high lethal risk that there
+ 
+
+ align:start position:0%
+have such a high lethal risk that there
+are only a few places in the world where
+
+ align:start position:0%
+are only a few places in the world where
+ 
+
+ align:start position:0%
+are only a few places in the world where
+they're studied. Restrictions for
+
+ align:start position:0%
+they're studied. Restrictions for
+ 
+
+ align:start position:0%
+they're studied. Restrictions for
+working with these agents are very
+
+ align:start position:0%
+working with these agents are very
+ 
+
+ align:start position:0%
+working with these agents are very
+tight. Everything entering or leaving
+
+ align:start position:0%
+tight. Everything entering or leaving
+ 
+
+ align:start position:0%
+tight. Everything entering or leaving
+BL3 and BL4 labs has to be
+
+ align:start position:0%
+BL3 and BL4 labs has to be
+ 
+
+ align:start position:0%
+BL3 and BL4 labs has to be
+decontaminated. Sometimes the lab has to
+
+ align:start position:0%
+decontaminated. Sometimes the lab has to
+ 
+
+ align:start position:0%
+decontaminated. Sometimes the lab has to
+be in its own building to control foot
+
+ align:start position:0%
+be in its own building to control foot
+ 
+
+ align:start position:0%
+be in its own building to control foot
+traffic. I know I don't want to work
+
+ align:start position:0%
+traffic. I know I don't want to work
+ 
+
+ align:start position:0%
+traffic. I know I don't want to work
+where there are double door entries and
+
+ align:start position:0%
+where there are double door entries and
+ 
+
+ align:start position:0%
+where there are double door entries and
+airlock rooms. I think that sounds like
+
+ align:start position:0%
+airlock rooms. I think that sounds like
+ 
+
+ align:start position:0%
+airlock rooms. I think that sounds like
+fun. If you're so excited about the
+
+ align:start position:0%
+fun. If you're so excited about the
+ 
+
+ align:start position:0%
+fun. If you're so excited about the
+protective clothing, we can always be
+
+ align:start position:0%
+protective clothing, we can always be
+ 
+
+ align:start position:0%
+protective clothing, we can always be
+overly cautious in a level one or two
+
+ align:start position:0%
+overly cautious in a level one or two
+ 
+
+ align:start position:0%
+overly cautious in a level one or two
+facility. But can't we find another way
+
+ align:start position:0%
+facility. But can't we find another way
+ 
+
+ align:start position:0%
+facility. But can't we find another way
+to make more cocoa beans? Okay, maybe we
+
+ align:start position:0%
+to make more cocoa beans? Okay, maybe we
+ 
+
+ align:start position:0%
+to make more cocoa beans? Okay, maybe we
+can find another virus that's not so
+
+ align:start position:0%
+can find another virus that's not so
+ 
+
+ align:start position:0%
+can find another virus that's not so
+dangerous and we can keep working on
+
+ align:start position:0%
+dangerous and we can keep working on
+ 
+
+ align:start position:0%
+dangerous and we can keep working on
+your chocolate idea. Let's start looking
+
+ align:start position:0%
+your chocolate idea. Let's start looking
+ 
+
+ align:start position:0%
+your chocolate idea. Let's start looking
+in here.
\ No newline at end of file
diff --git a/uyz1UQEu-kk.txt b/uyz1UQEu-kk.txt
new file mode 100644
index 0000000000000000000000000000000000000000..077ce6c6d1fc3ca229cf01680f842223c3a2ecd8
--- /dev/null
+++ b/uyz1UQEu-kk.txt
@@ -0,0 +1,8283 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common License. Your support
+
+ align:start position:0%
+a Creative Common License. Your support
+ 
+
+ align:start position:0%
+a Creative Common License. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer high-quality educational
+
+ align:start position:0%
+to offer high-quality educational
+ 
+
+ align:start position:0%
+to offer high-quality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or view additional materials from
+
+ align:start position:0%
+or view additional materials from
+ 
+
+ align:start position:0%
+or view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I uh gave you an extension for your
+
+ align:start position:0%
+I uh gave you an extension for your
+ 
+
+ align:start position:0%
+I uh gave you an extension for your
+paper Wednesday, so you don't have to
+
+ align:start position:0%
+paper Wednesday, so you don't have to
+ 
+
+ align:start position:0%
+paper Wednesday, so you don't have to
+ask. It's just automatic. If you want to
+
+ align:start position:0%
+ask. It's just automatic. If you want to
+ 
+
+ align:start position:0%
+ask. It's just automatic. If you want to
+give it to me today, that's fine, too.
+
+ align:start position:0%
+give it to me today, that's fine, too.
+ 
+
+ align:start position:0%
+give it to me today, that's fine, too.
+Uh everybody's busy this time of year,
+
+ align:start position:0%
+Uh everybody's busy this time of year,
+ 
+
+ align:start position:0%
+Uh everybody's busy this time of year,
+so I try to leave a little flexibility
+
+ align:start position:0%
+so I try to leave a little flexibility
+ 
+
+ align:start position:0%
+so I try to leave a little flexibility
+in there. If Wednesday doesn't work for
+
+ align:start position:0%
+in there. If Wednesday doesn't work for
+ 
+
+ align:start position:0%
+in there. If Wednesday doesn't work for
+you, talk to me after class. Uh, I don't
+
+ align:start position:0%
+you, talk to me after class. Uh, I don't
+ 
+
+ align:start position:0%
+you, talk to me after class. Uh, I don't
+like to have you lag too far behind
+
+ align:start position:0%
+like to have you lag too far behind
+ 
+
+ align:start position:0%
+like to have you lag too far behind
+because then it kind of messes up other
+
+ align:start position:0%
+because then it kind of messes up other
+ 
+
+ align:start position:0%
+because then it kind of messes up other
+stuff that you have to do. I'd rather
+
+ align:start position:0%
+stuff that you have to do. I'd rather
+ 
+
+ align:start position:0%
+stuff that you have to do. I'd rather
+have you do something maybe less
+
+ align:start position:0%
+have you do something maybe less
+ 
+
+ align:start position:0%
+have you do something maybe less
+perfect, but get it in on time so you
+
+ align:start position:0%
+perfect, but get it in on time so you
+ 
+
+ align:start position:0%
+perfect, but get it in on time so you
+can, you know, MIT has always uh got 15
+
+ align:start position:0%
+can, you know, MIT has always uh got 15
+ 
+
+ align:start position:0%
+can, you know, MIT has always uh got 15
+things for you to do every time you turn
+
+ align:start position:0%
+things for you to do every time you turn
+ 
+
+ align:start position:0%
+things for you to do every time you turn
+around. So,
+
+ align:start position:0%
+around. So,
+ 
+
+ align:start position:0%
+around. So,
+uh, okay. So we are now uh looking at
+
+ align:start position:0%
+uh, okay. So we are now uh looking at
+ 
+
+ align:start position:0%
+uh, okay. So we are now uh looking at
+some a number of works uh post Darwinian
+
+ align:start position:0%
+some a number of works uh post Darwinian
+ 
+
+ align:start position:0%
+some a number of works uh post Darwinian
+works works that came out after the
+
+ align:start position:0%
+works works that came out after the
+ 
+
+ align:start position:0%
+works works that came out after the
+origin. Not that they wouldn't have come
+
+ align:start position:0%
+origin. Not that they wouldn't have come
+ 
+
+ align:start position:0%
+origin. Not that they wouldn't have come
+out without the origin, but certainly
+
+ align:start position:0%
+out without the origin, but certainly
+ 
+
+ align:start position:0%
+out without the origin, but certainly
+this book wouldn't have. This book uh
+
+ align:start position:0%
+this book wouldn't have. This book uh
+ 
+
+ align:start position:0%
+this book wouldn't have. This book uh
+Butler's Arowan uh which is nowhere
+
+ align:start position:0%
+Butler's Arowan uh which is nowhere
+ 
+
+ align:start position:0%
+Butler's Arowan uh which is nowhere
+spelled backwards more or less
+
+ align:start position:0%
+spelled backwards more or less
+ 
+
+ align:start position:0%
+spelled backwards more or less
+uh is a uh it's a type of utopia, what
+
+ align:start position:0%
+uh is a uh it's a type of utopia, what
+ 
+
+ align:start position:0%
+uh is a uh it's a type of utopia, what
+we call a
+
+ align:start position:0%
+we call a
+ 
+
+ align:start position:0%
+we call a
+dystopia, and it's kind of riffing and
+
+ align:start position:0%
+dystopia, and it's kind of riffing and
+ 
+
+ align:start position:0%
+dystopia, and it's kind of riffing and
+playing with some of the ideas of
+
+ align:start position:0%
+playing with some of the ideas of
+ 
+
+ align:start position:0%
+playing with some of the ideas of
+evolution. Uh, and it is a satire. So,
+
+ align:start position:0%
+evolution. Uh, and it is a satire. So,
+ 
+
+ align:start position:0%
+evolution. Uh, and it is a satire. So,
+satires are hard for people to read. Uh,
+
+ align:start position:0%
+satires are hard for people to read. Uh,
+ 
+
+ align:start position:0%
+satires are hard for people to read. Uh,
+a lot of people just don't quite get the
+
+ align:start position:0%
+a lot of people just don't quite get the
+ 
+
+ align:start position:0%
+a lot of people just don't quite get the
+satire because, you know, it seems to be
+
+ align:start position:0%
+satire because, you know, it seems to be
+ 
+
+ align:start position:0%
+satire because, you know, it seems to be
+saying things that are totally
+
+ align:start position:0%
+saying things that are totally
+ 
+
+ align:start position:0%
+saying things that are totally
+outrageous and yet it's saying them that
+
+ align:start position:0%
+outrageous and yet it's saying them that
+ 
+
+ align:start position:0%
+outrageous and yet it's saying them that
+are in a way that's tongue and cheek.
+
+ align:start position:0%
+are in a way that's tongue and cheek.
+ 
+
+ align:start position:0%
+are in a way that's tongue and cheek.
+And so with Butler, you have to sort of
+
+ align:start position:0%
+And so with Butler, you have to sort of
+ 
+
+ align:start position:0%
+And so with Butler, you have to sort of
+think a little bit before you interpret
+
+ align:start position:0%
+think a little bit before you interpret
+ 
+
+ align:start position:0%
+think a little bit before you interpret
+what he's saying literally because there
+
+ align:start position:0%
+what he's saying literally because there
+ 
+
+ align:start position:0%
+what he's saying literally because there
+all kinds of uh weird little uh
+
+ align:start position:0%
+all kinds of uh weird little uh
+ 
+
+ align:start position:0%
+all kinds of uh weird little uh
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+uh behaviors in the book uh uh among the
+
+ align:start position:0%
+uh behaviors in the book uh uh among the
+ 
+
+ align:start position:0%
+uh behaviors in the book uh uh among the
+people that uh uh this this uh uh
+
+ align:start position:0%
+people that uh uh this this uh uh
+ 
+
+ align:start position:0%
+people that uh uh this this uh uh
+voyager, this traveler discovers. So,
+
+ align:start position:0%
+voyager, this traveler discovers. So,
+ 
+
+ align:start position:0%
+voyager, this traveler discovers. So,
+uh, I thought maybe it'd be helpful for
+
+ align:start position:0%
+uh, I thought maybe it'd be helpful for
+ 
+
+ align:start position:0%
+uh, I thought maybe it'd be helpful for
+us to say a little bit, uh, about
+
+ align:start position:0%
+us to say a little bit, uh, about
+ 
+
+ align:start position:0%
+us to say a little bit, uh, about
+utopias before we read the, uh, before
+
+ align:start position:0%
+utopias before we read the, uh, before
+ 
+
+ align:start position:0%
+utopias before we read the, uh, before
+we get into the book.
+
+ align:start position:0%
+we get into the book.
+ 
+
+ align:start position:0%
+we get into the book.
+Um, so what do you know about
+
+ align:start position:0%
+Um, so what do you know about
+ 
+
+ align:start position:0%
+Um, so what do you know about
+utopias? Have you read a few of them or
+
+ align:start position:0%
+utopias? Have you read a few of them or
+ 
+
+ align:start position:0%
+utopias? Have you read a few of them or
+you've come across them
+
+ align:start position:0%
+you've come across them
+ 
+
+ align:start position:0%
+you've come across them
+before? I mean, I I would love to teach
+
+ align:start position:0%
+before? I mean, I I would love to teach
+ 
+
+ align:start position:0%
+before? I mean, I I would love to teach
+a course just on utopias because it's a
+
+ align:start position:0%
+a course just on utopias because it's a
+ 
+
+ align:start position:0%
+a course just on utopias because it's a
+fascinating type of uh, literature. But
+
+ align:start position:0%
+fascinating type of uh, literature. But
+ 
+
+ align:start position:0%
+fascinating type of uh, literature. But
+uh what are some of the uh what are the
+
+ align:start position:0%
+uh what are some of the uh what are the
+ 
+
+ align:start position:0%
+uh what are some of the uh what are the
+things? Has anybody read any utopias or
+
+ align:start position:0%
+things? Has anybody read any utopias or
+ 
+
+ align:start position:0%
+things? Has anybody read any utopias or
+dystopias?
+
+ align:start position:0%
+dystopias?
+ 
+
+ align:start position:0%
+dystopias?
+What's that? Okay. Elorado and Volter
+
+ align:start position:0%
+What's that? Okay. Elorado and Volter
+ 
+
+ align:start position:0%
+What's that? Okay. Elorado and Volter
+was a a little a little chapter of a
+
+ align:start position:0%
+was a a little a little chapter of a
+ 
+
+ align:start position:0%
+was a a little a little chapter of a
+utopia.
+
+ align:start position:0%
+utopia.
+ 
+
+ align:start position:0%
+utopia.
+Is that a single working example? Yeah.
+
+ align:start position:0%
+Is that a single working example? Yeah.
+ 
+
+ align:start position:0%
+Is that a single working example? Yeah.
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Okay. Uh what uh
+
+ align:start position:0%
+Okay. Uh what uh
+ 
+
+ align:start position:0%
+Okay. Uh what uh
+I mean most of you have read 1984 I I
+
+ align:start position:0%
+I mean most of you have read 1984 I I
+ 
+
+ align:start position:0%
+I mean most of you have read 1984 I I
+assume or uh Animal Farm. Yeah, these
+
+ align:start position:0%
+assume or uh Animal Farm. Yeah, these
+ 
+
+ align:start position:0%
+assume or uh Animal Farm. Yeah, these
+are inverted utopias. These are what we
+
+ align:start position:0%
+are inverted utopias. These are what we
+ 
+
+ align:start position:0%
+are inverted utopias. These are what we
+call
+
+ align:start position:0%
+call
+ 
+
+ align:start position:0%
+call
+dystopias. Uh they use some of the rules
+
+ align:start position:0%
+dystopias. Uh they use some of the rules
+ 
+
+ align:start position:0%
+dystopias. Uh they use some of the rules
+of utopia, but they present a world that
+
+ align:start position:0%
+of utopia, but they present a world that
+ 
+
+ align:start position:0%
+of utopia, but they present a world that
+is highly
+
+ align:start position:0%
+is highly
+ 
+
+ align:start position:0%
+is highly
+undesirable. But people have been
+
+ align:start position:0%
+undesirable. But people have been
+ 
+
+ align:start position:0%
+undesirable. But people have been
+writing utopias for hundreds of years.
+
+ align:start position:0%
+writing utopias for hundreds of years.
+ 
+
+ align:start position:0%
+writing utopias for hundreds of years.
+And uh what is uh
+
+ align:start position:0%
+And uh what is uh
+ 
+
+ align:start position:0%
+And uh what is uh
+so just to
+
+ align:start position:0%
+so just to
+ 
+
+ align:start position:0%
+so just to
+um some of the I just sent these to you
+
+ align:start position:0%
+um some of the I just sent these to you
+ 
+
+ align:start position:0%
+um some of the I just sent these to you
+just to give you some things to think
+
+ align:start position:0%
+just to give you some things to think
+ 
+
+ align:start position:0%
+just to give you some things to think
+about. These were in a packet I sent
+
+ align:start position:0%
+about. These were in a packet I sent
+ 
+
+ align:start position:0%
+about. These were in a packet I sent
+out.
+
+ align:start position:0%
+out.
+ 
+
+ align:start position:0%
+out.
+Um but a lot of them play with ideas.
+
+ align:start position:0%
+Um but a lot of them play with ideas.
+ 
+
+ align:start position:0%
+Um but a lot of them play with ideas.
+They're idea. They're works of ideas.
+
+ align:start position:0%
+They're idea. They're works of ideas.
+ 
+
+ align:start position:0%
+They're idea. They're works of ideas.
+works in which people
+
+ align:start position:0%
+works in which people
+ 
+
+ align:start position:0%
+works in which people
+uh think about idealized societies of
+
+ align:start position:0%
+uh think about idealized societies of
+ 
+
+ align:start position:0%
+uh think about idealized societies of
+various sorts. Uh and there are some
+
+ align:start position:0%
+various sorts. Uh and there are some
+ 
+
+ align:start position:0%
+various sorts. Uh and there are some
+different types that I mean there the
+
+ align:start position:0%
+different types that I mean there the
+ 
+
+ align:start position:0%
+different types that I mean there the
+classifications are not hard
+
+ align:start position:0%
+classifications are not hard
+ 
+
+ align:start position:0%
+classifications are not hard
+classifications. Some of them blend from
+
+ align:start position:0%
+classifications. Some of them blend from
+ 
+
+ align:start position:0%
+classifications. Some of them blend from
+one to the other but they tend to come
+
+ align:start position:0%
+one to the other but they tend to come
+ 
+
+ align:start position:0%
+one to the other but they tend to come
+out in a variety of forms.
+
+ align:start position:0%
+out in a variety of forms.
+ 
+
+ align:start position:0%
+out in a variety of forms.
+Um, of course there are the earthly
+
+ align:start position:0%
+Um, of course there are the earthly
+ 
+
+ align:start position:0%
+Um, of course there are the earthly
+paradise, earthly paradise utopias.
+
+ align:start position:0%
+paradise, earthly paradise utopias.
+ 
+
+ align:start position:0%
+paradise, earthly paradise utopias.
+People have written about worlds in
+
+ align:start position:0%
+People have written about worlds in
+ 
+
+ align:start position:0%
+People have written about worlds in
+which uh they
+
+ align:start position:0%
+which uh they
+ 
+
+ align:start position:0%
+which uh they
+imagine uh sort of perfect condition for
+
+ align:start position:0%
+imagine uh sort of perfect condition for
+ 
+
+ align:start position:0%
+imagine uh sort of perfect condition for
+humans. Uh and examples of this would be
+
+ align:start position:0%
+humans. Uh and examples of this would be
+ 
+
+ align:start position:0%
+humans. Uh and examples of this would be
+uh old myths uh and and also in some
+
+ align:start position:0%
+uh old myths uh and and also in some
+ 
+
+ align:start position:0%
+uh old myths uh and and also in some
+sense Genesis the uh the paradise uh of
+
+ align:start position:0%
+sense Genesis the uh the paradise uh of
+ 
+
+ align:start position:0%
+sense Genesis the uh the paradise uh of
+the Bible and other other religious
+
+ align:start position:0%
+the Bible and other other religious
+ 
+
+ align:start position:0%
+the Bible and other other religious
+traditions have sort of paradisel like
+
+ align:start position:0%
+traditions have sort of paradisel like
+ 
+
+ align:start position:0%
+traditions have sort of paradisel like
+conditions where uh people may have
+
+ align:start position:0%
+conditions where uh people may have
+ 
+
+ align:start position:0%
+conditions where uh people may have
+lived before
+
+ align:start position:0%
+lived before
+ 
+
+ align:start position:0%
+lived before
+they they committed
+
+ align:start position:0%
+they they committed
+ 
+
+ align:start position:0%
+they they committed
+some terrible sin and were thrust out of
+
+ align:start position:0%
+some terrible sin and were thrust out of
+ 
+
+ align:start position:0%
+some terrible sin and were thrust out of
+the out of the paradise. So this uh this
+
+ align:start position:0%
+the out of the paradise. So this uh this
+ 
+
+ align:start position:0%
+the out of the paradise. So this uh this
+idea of paradise is is uh very much u
+
+ align:start position:0%
+idea of paradise is is uh very much u
+ 
+
+ align:start position:0%
+idea of paradise is is uh very much u
+here's uh earthly paradise of uh a
+
+ align:start position:0%
+here's uh earthly paradise of uh a
+ 
+
+ align:start position:0%
+here's uh earthly paradise of uh a
+bos famous artist
+
+ align:start position:0%
+bos famous artist
+ 
+
+ align:start position:0%
+bos famous artist
+uh and he's uh this was done in 1510 and
+
+ align:start position:0%
+uh and he's uh this was done in 1510 and
+ 
+
+ align:start position:0%
+uh and he's uh this was done in 1510 and
+you you sort of if you study this you
+
+ align:start position:0%
+you you sort of if you study this you
+ 
+
+ align:start position:0%
+you you sort of if you study this you
+see all forms of pleasure. This is a
+
+ align:start position:0%
+see all forms of pleasure. This is a
+ 
+
+ align:start position:0%
+see all forms of pleasure. This is a
+kind of earthly paradise where
+
+ align:start position:0%
+kind of earthly paradise where
+ 
+
+ align:start position:0%
+kind of earthly paradise where
+everybody's enjoying you know some some
+
+ align:start position:0%
+everybody's enjoying you know some some
+ 
+
+ align:start position:0%
+everybody's enjoying you know some some
+some expression of the
+
+ align:start position:0%
+some expression of the
+ 
+
+ align:start position:0%
+some expression of the
+senses. So oftentimes earthly paradises
+
+ align:start position:0%
+senses. So oftentimes earthly paradises
+ 
+
+ align:start position:0%
+senses. So oftentimes earthly paradises
+have uh uh some of the traits are you
+
+ align:start position:0%
+have uh uh some of the traits are you
+ 
+
+ align:start position:0%
+have uh uh some of the traits are you
+know complete
+
+ align:start position:0%
+know complete
+ 
+
+ align:start position:0%
+know complete
+comfort and and escape from the ills of
+
+ align:start position:0%
+comfort and and escape from the ills of
+ 
+
+ align:start position:0%
+comfort and and escape from the ills of
+the world. It's a very non-malthusian
+
+ align:start position:0%
+the world. It's a very non-malthusian
+ 
+
+ align:start position:0%
+the world. It's a very non-malthusian
+world the the sort of uh type of world
+
+ align:start position:0%
+world the the sort of uh type of world
+ 
+
+ align:start position:0%
+world the the sort of uh type of world
+that might exist. Uh, and of course
+
+ align:start position:0%
+that might exist. Uh, and of course
+ 
+
+ align:start position:0%
+that might exist. Uh, and of course
+we're always interested in I mean there
+
+ align:start position:0%
+we're always interested in I mean there
+ 
+
+ align:start position:0%
+we're always interested in I mean there
+there's something about these uh a world
+
+ align:start position:0%
+there's something about these uh a world
+ 
+
+ align:start position:0%
+there's something about these uh a world
+a paradise a world a paradise that's
+
+ align:start position:0%
+a paradise a world a paradise that's
+ 
+
+ align:start position:0%
+a paradise a world a paradise that's
+attractive and we do our best with our
+
+ align:start position:0%
+attractive and we do our best with our
+ 
+
+ align:start position:0%
+attractive and we do our best with our
+technologies and so forth to create
+
+ align:start position:0%
+technologies and so forth to create
+ 
+
+ align:start position:0%
+technologies and so forth to create
+better surroundings for ourselves. So
+
+ align:start position:0%
+better surroundings for ourselves. So
+ 
+
+ align:start position:0%
+better surroundings for ourselves. So
+this is a kind of a a human impulse to
+
+ align:start position:0%
+this is a kind of a a human impulse to
+ 
+
+ align:start position:0%
+this is a kind of a a human impulse to
+improve the conditions of existence as
+
+ align:start position:0%
+improve the conditions of existence as
+ 
+
+ align:start position:0%
+improve the conditions of existence as
+as Darwin might say conditions of
+
+ align:start position:0%
+as Darwin might say conditions of
+ 
+
+ align:start position:0%
+as Darwin might say conditions of
+existence that's what we all survive in
+
+ align:start position:0%
+existence that's what we all survive in
+ 
+
+ align:start position:0%
+existence that's what we all survive in
+and they're harsh and they're uh for
+
+ align:start position:0%
+and they're harsh and they're uh for
+ 
+
+ align:start position:0%
+and they're harsh and they're uh for
+most organisms
+
+ align:start position:0%
+most organisms
+ 
+
+ align:start position:0%
+most organisms
+unmanageable. Um and so humans have this
+
+ align:start position:0%
+unmanageable. Um and so humans have this
+ 
+
+ align:start position:0%
+unmanageable. Um and so humans have this
+capacity to change their conditions of
+
+ align:start position:0%
+capacity to change their conditions of
+ 
+
+ align:start position:0%
+capacity to change their conditions of
+existence.
+
+ align:start position:0%
+existence.
+ 
+
+ align:start position:0%
+existence.
+That's very much what we're doing here
+
+ align:start position:0%
+That's very much what we're doing here
+ 
+
+ align:start position:0%
+That's very much what we're doing here
+today. It's around freezing outside this
+
+ align:start position:0%
+today. It's around freezing outside this
+ 
+
+ align:start position:0%
+today. It's around freezing outside this
+morning and we're sitting on in here in
+
+ align:start position:0%
+morning and we're sitting on in here in
+ 
+
+ align:start position:0%
+morning and we're sitting on in here in
+this nice warm room and sort of so we
+
+ align:start position:0%
+this nice warm room and sort of so we
+ 
+
+ align:start position:0%
+this nice warm room and sort of so we
+have changed our conditions of existence
+
+ align:start position:0%
+have changed our conditions of existence
+ 
+
+ align:start position:0%
+have changed our conditions of existence
+if you will and we do this on a massive
+
+ align:start position:0%
+if you will and we do this on a massive
+ 
+
+ align:start position:0%
+if you will and we do this on a massive
+scale in in contemporary society.
+
+ align:start position:0%
+scale in in contemporary society.
+ 
+
+ align:start position:0%
+scale in in contemporary society.
+Uh other types of utopic literature
+
+ align:start position:0%
+Uh other types of utopic literature
+ 
+
+ align:start position:0%
+Uh other types of utopic literature
+include sort of
+
+ align:start position:0%
+include sort of
+ 
+
+ align:start position:0%
+include sort of
+political and social
+
+ align:start position:0%
+political and social
+ 
+
+ align:start position:0%
+political and social
+uh worlds that uh have been uh posited
+
+ align:start position:0%
+uh worlds that uh have been uh posited
+ 
+
+ align:start position:0%
+uh worlds that uh have been uh posited
+by thinkers through the
+
+ align:start position:0%
+by thinkers through the
+ 
+
+ align:start position:0%
+by thinkers through the
+ages. Uh Plato's Republic was a kind of
+
+ align:start position:0%
+ages. Uh Plato's Republic was a kind of
+ 
+
+ align:start position:0%
+ages. Uh Plato's Republic was a kind of
+a a world in which he imagined what the
+
+ align:start position:0%
+a a world in which he imagined what the
+ 
+
+ align:start position:0%
+a a world in which he imagined what the
+right and perfect or best
+
+ align:start position:0%
+right and perfect or best
+ 
+
+ align:start position:0%
+right and perfect or best
+kind of political world might be um and
+
+ align:start position:0%
+kind of political world might be um and
+ 
+
+ align:start position:0%
+kind of political world might be um and
+a world of u u that would
+
+ align:start position:0%
+a world of u u that would
+ 
+
+ align:start position:0%
+a world of u u that would
+work in some sense for the greatest
+
+ align:start position:0%
+work in some sense for the greatest
+ 
+
+ align:start position:0%
+work in some sense for the greatest
+benefit of
+
+ align:start position:0%
+benefit of
+ 
+
+ align:start position:0%
+benefit of
+society. Um other people have imagined
+
+ align:start position:0%
+society. Um other people have imagined
+ 
+
+ align:start position:0%
+society. Um other people have imagined
+uh Thomas Moore was a uh uh another
+
+ align:start position:0%
+uh Thomas Moore was a uh uh another
+ 
+
+ align:start position:0%
+uh Thomas Moore was a uh uh another
+thinker who actually wrote one of the
+
+ align:start position:0%
+thinker who actually wrote one of the
+ 
+
+ align:start position:0%
+thinker who actually wrote one of the
+first utopias. He he he titled it
+
+ align:start position:0%
+first utopias. He he he titled it
+ 
+
+ align:start position:0%
+first utopias. He he he titled it
+utopia. What does utopia mean?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Utopia in like the roots or no? No.
+
+ align:start position:0%
+Utopia in like the roots or no? No.
+ 
+
+ align:start position:0%
+Utopia in like the roots or no? No.
+Perfect society.
+
+ align:start position:0%
+Perfect society.
+ 
+
+ align:start position:0%
+Perfect society.
+Well, that's that's what we associate
+
+ align:start position:0%
+Well, that's that's what we associate
+ 
+
+ align:start position:0%
+Well, that's that's what we associate
+with it. But the word itself means
+
+ align:start position:0%
+with it. But the word itself means
+ 
+
+ align:start position:0%
+with it. But the word itself means
+nowhere.
+
+ align:start position:0%
+nowhere.
+ 
+
+ align:start position:0%
+nowhere.
+So it it it's it's an admission that it
+
+ align:start position:0%
+So it it it's it's an admission that it
+ 
+
+ align:start position:0%
+So it it it's it's an admission that it
+doesn't in some sense utopic literature
+
+ align:start position:0%
+doesn't in some sense utopic literature
+ 
+
+ align:start position:0%
+doesn't in some sense utopic literature
+starts with the
+
+ align:start position:0%
+starts with the
+ 
+
+ align:start position:0%
+starts with the
+uh admission
+
+ align:start position:0%
+uh admission
+ 
+
+ align:start position:0%
+uh admission
+that this does not exist. So it's a it's
+
+ align:start position:0%
+that this does not exist. So it's a it's
+ 
+
+ align:start position:0%
+that this does not exist. So it's a it's
+a kind of a complex thought experiment
+
+ align:start position:0%
+a kind of a complex thought experiment
+ 
+
+ align:start position:0%
+a kind of a complex thought experiment
+you might say. How would we organize
+
+ align:start position:0%
+you might say. How would we organize
+ 
+
+ align:start position:0%
+you might say. How would we organize
+ourselves if we did it in the best way
+
+ align:start position:0%
+ourselves if we did it in the best way
+ 
+
+ align:start position:0%
+ourselves if we did it in the best way
+we possibly could? that idealism
+
+ align:start position:0%
+we possibly could? that idealism
+ 
+
+ align:start position:0%
+we possibly could? that idealism
+um can be supported in a variety of ways
+
+ align:start position:0%
+um can be supported in a variety of ways
+ 
+
+ align:start position:0%
+um can be supported in a variety of ways
+and we have other types of utopias or
+
+ align:start position:0%
+and we have other types of utopias or
+ 
+
+ align:start position:0%
+and we have other types of utopias or
+utopic uh works uh that are based on
+
+ align:start position:0%
+utopic uh works uh that are based on
+ 
+
+ align:start position:0%
+utopic uh works uh that are based on
+technology. How how is technology
+
+ align:start position:0%
+technology. How how is technology
+ 
+
+ align:start position:0%
+technology. How how is technology
+utopic? What is it about technology that
+
+ align:start position:0%
+utopic? What is it about technology that
+ 
+
+ align:start position:0%
+utopic? What is it about technology that
+pursues utopian ideals?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, I mean we never technology can
+
+ align:start position:0%
+Well, I mean we never technology can
+ 
+
+ align:start position:0%
+Well, I mean we never technology can
+never quite make things perfect, but in
+
+ align:start position:0%
+never quite make things perfect, but in
+ 
+
+ align:start position:0%
+never quite make things perfect, but in
+coming up with like technological
+
+ align:start position:0%
+coming up with like technological
+ 
+
+ align:start position:0%
+coming up with like technological
+advances, our goal is to like increase
+
+ align:start position:0%
+advances, our goal is to like increase
+ 
+
+ align:start position:0%
+advances, our goal is to like increase
+probably standard of living in some way
+
+ align:start position:0%
+probably standard of living in some way
+ 
+
+ align:start position:0%
+probably standard of living in some way
+for somebody.
+
+ align:start position:0%
+for somebody.
+ 
+
+ align:start position:0%
+for somebody.
+So I guess advances in technology some
+
+ align:start position:0%
+So I guess advances in technology some
+ 
+
+ align:start position:0%
+So I guess advances in technology some
+may see as leading us toward a utopic
+
+ align:start position:0%
+may see as leading us toward a utopic
+ 
+
+ align:start position:0%
+may see as leading us toward a utopic
+place but then
+
+ align:start position:0%
+place but then
+ 
+
+ align:start position:0%
+place but then
+also like technological advances are
+
+ align:start position:0%
+also like technological advances are
+ 
+
+ align:start position:0%
+also like technological advances are
+also kind of what are getting us into a
+
+ align:start position:0%
+also kind of what are getting us into a
+ 
+
+ align:start position:0%
+also kind of what are getting us into a
+lot of trouble with like population size
+
+ align:start position:0%
+lot of trouble with like population size
+ 
+
+ align:start position:0%
+lot of trouble with like population size
+and everything. So I feel like it can be
+
+ align:start position:0%
+and everything. So I feel like it can be
+ 
+
+ align:start position:0%
+and everything. So I feel like it can be
+a little bit deceiving.
+
+ align:start position:0%
+a little bit deceiving.
+ 
+
+ align:start position:0%
+a little bit deceiving.
+Well, yeah, there there's a cost to
+
+ align:start position:0%
+Well, yeah, there there's a cost to
+ 
+
+ align:start position:0%
+Well, yeah, there there's a cost to
+things that uh that are developed and
+
+ align:start position:0%
+things that uh that are developed and
+ 
+
+ align:start position:0%
+things that uh that are developed and
+sometimes those costs turned out to have
+
+ align:start position:0%
+sometimes those costs turned out to have
+ 
+
+ align:start position:0%
+sometimes those costs turned out to have
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+secondary elements that are, you know,
+
+ align:start position:0%
+secondary elements that are, you know,
+ 
+
+ align:start position:0%
+secondary elements that are, you know,
+rather overwhelming, but yes, there's
+
+ align:start position:0%
+rather overwhelming, but yes, there's
+ 
+
+ align:start position:0%
+rather overwhelming, but yes, there's
+that. Jake, did you have something to
+
+ align:start position:0%
+that. Jake, did you have something to
+ 
+
+ align:start position:0%
+that. Jake, did you have something to
+add to that? say that technology uh well
+
+ align:start position:0%
+add to that? say that technology uh well
+ 
+
+ align:start position:0%
+add to that? say that technology uh well
+like you said with uh the conditions of
+
+ align:start position:0%
+like you said with uh the conditions of
+ 
+
+ align:start position:0%
+like you said with uh the conditions of
+existence the I mean it can't bring us
+
+ align:start position:0%
+existence the I mean it can't bring us
+ 
+
+ align:start position:0%
+existence the I mean it can't bring us
+at least as far as we are can't bring us
+
+ align:start position:0%
+at least as far as we are can't bring us
+ 
+
+ align:start position:0%
+at least as far as we are can't bring us
+all the way to utopia but it I mean it
+
+ align:start position:0%
+all the way to utopia but it I mean it
+ 
+
+ align:start position:0%
+all the way to utopia but it I mean it
+moves us in the right direction it takes
+
+ align:start position:0%
+moves us in the right direction it takes
+ 
+
+ align:start position:0%
+moves us in the right direction it takes
+thing takes bad things and makes them
+
+ align:start position:0%
+thing takes bad things and makes them
+ 
+
+ align:start position:0%
+thing takes bad things and makes them
+either a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+nonfactor good
+
+ align:start position:0%
+nonfactor good
+ 
+
+ align:start position:0%
+nonfactor good
+things and as you say we're we're trying
+
+ align:start position:0%
+things and as you say we're we're trying
+ 
+
+ align:start position:0%
+things and as you say we're we're trying
+to improve the human
+
+ align:start position:0%
+to improve the human
+ 
+
+ align:start position:0%
+to improve the human
+tradition. Utopias have also been part
+
+ align:start position:0%
+tradition. Utopias have also been part
+ 
+
+ align:start position:0%
+tradition. Utopias have also been part
+of the satirical tradition. Uh Butler's
+
+ align:start position:0%
+of the satirical tradition. Uh Butler's
+ 
+
+ align:start position:0%
+of the satirical tradition. Uh Butler's
+uh one of his uh one of the one of the
+
+ align:start position:0%
+uh one of his uh one of the one of the
+ 
+
+ align:start position:0%
+uh one of his uh one of the one of the
+writers who he modeled his work on or
+
+ align:start position:0%
+writers who he modeled his work on or
+ 
+
+ align:start position:0%
+writers who he modeled his work on or
+who he not modeled so much but he was
+
+ align:start position:0%
+who he not modeled so much but he was
+ 
+
+ align:start position:0%
+who he not modeled so much but he was
+thinking of was uh Jonathan Swift who
+
+ align:start position:0%
+thinking of was uh Jonathan Swift who
+ 
+
+ align:start position:0%
+thinking of was uh Jonathan Swift who
+wrote Goliver's
+
+ align:start position:0%
+wrote Goliver's
+ 
+
+ align:start position:0%
+wrote Goliver's
+Travels and uh anybody here read
+
+ align:start position:0%
+Travels and uh anybody here read
+ 
+
+ align:start position:0%
+Travels and uh anybody here read
+Goliver's Travels see the work? I don't
+
+ align:start position:0%
+Goliver's Travels see the work? I don't
+ 
+
+ align:start position:0%
+Goliver's Travels see the work? I don't
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah. Yeah. Well, after that, well,
+
+ align:start position:0%
+Yeah. Yeah. Well, after that, well,
+ 
+
+ align:start position:0%
+Yeah. Yeah. Well, after that, well,
+Goliver's Travels is uh, you know, it's
+
+ align:start position:0%
+Goliver's Travels is uh, you know, it's
+ 
+
+ align:start position:0%
+Goliver's Travels is uh, you know, it's
+a it's a it's sort of just a a fantasy,
+
+ align:start position:0%
+a it's a it's sort of just a a fantasy,
+ 
+
+ align:start position:0%
+a it's a it's sort of just a a fantasy,
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+fiction that is u written by Jonathan
+
+ align:start position:0%
+fiction that is u written by Jonathan
+ 
+
+ align:start position:0%
+fiction that is u written by Jonathan
+Swift in the early 18th century of this
+
+ align:start position:0%
+Swift in the early 18th century of this
+ 
+
+ align:start position:0%
+Swift in the early 18th century of this
+voyager who goes out and he voyages to
+
+ align:start position:0%
+voyager who goes out and he voyages to
+ 
+
+ align:start position:0%
+voyager who goes out and he voyages to
+all these different lands and in each
+
+ align:start position:0%
+all these different lands and in each
+ 
+
+ align:start position:0%
+all these different lands and in each
+land he discovers, you know, different
+
+ align:start position:0%
+land he discovers, you know, different
+ 
+
+ align:start position:0%
+land he discovers, you know, different
+types of people who he interacts with
+
+ align:start position:0%
+types of people who he interacts with
+ 
+
+ align:start position:0%
+types of people who he interacts with
+and through these interactions
+
+ align:start position:0%
+and through these interactions
+ 
+
+ align:start position:0%
+and through these interactions
+uh Swift is able
+
+ align:start position:0%
+uh Swift is able
+ 
+
+ align:start position:0%
+uh Swift is able
+to write uh satirical
+
+ align:start position:0%
+to write uh satirical
+ 
+
+ align:start position:0%
+to write uh satirical
+portraits of
+
+ align:start position:0%
+portraits of
+ 
+
+ align:start position:0%
+portraits of
+contemporary British
+
+ align:start position:0%
+contemporary British
+ 
+
+ align:start position:0%
+contemporary British
+society. He uses this travel to kind of
+
+ align:start position:0%
+society. He uses this travel to kind of
+ 
+
+ align:start position:0%
+society. He uses this travel to kind of
+fantasize in ways that are critical of
+
+ align:start position:0%
+fantasize in ways that are critical of
+ 
+
+ align:start position:0%
+fantasize in ways that are critical of
+society. So that's so that's that's a
+
+ align:start position:0%
+society. So that's so that's that's a
+ 
+
+ align:start position:0%
+society. So that's so that's that's a
+direct model for Butler's work. Okay. So
+
+ align:start position:0%
+direct model for Butler's work. Okay. So
+ 
+
+ align:start position:0%
+direct model for Butler's work. Okay. So
+back to Butler.
+
+ align:start position:0%
+back to Butler.
+ 
+
+ align:start position:0%
+back to Butler.
+Um, so yes, utopia is a is a is a
+
+ align:start position:0%
+Um, so yes, utopia is a is a is a
+ 
+
+ align:start position:0%
+Um, so yes, utopia is a is a is a
+nowhere. It's a generally highly
+
+ align:start position:0%
+nowhere. It's a generally highly
+ 
+
+ align:start position:0%
+nowhere. It's a generally highly
+idealized uh human- centered tradition.
+
+ align:start position:0%
+idealized uh human- centered tradition.
+ 
+
+ align:start position:0%
+idealized uh human- centered tradition.
+um and
+
+ align:start position:0%
+um and
+ 
+
+ align:start position:0%
+um and
+oftentimes is either
+
+ align:start position:0%
+oftentimes is either
+ 
+
+ align:start position:0%
+oftentimes is either
+uh offering or seeking a sort of uh
+
+ align:start position:0%
+uh offering or seeking a sort of uh
+ 
+
+ align:start position:0%
+uh offering or seeking a sort of uh
+perfect
+
+ align:start position:0%
+perfect
+ 
+
+ align:start position:0%
+perfect
+adaptation between the human and his or
+
+ align:start position:0%
+adaptation between the human and his or
+ 
+
+ align:start position:0%
+adaptation between the human and his or
+her environment. So that's that's sort
+
+ align:start position:0%
+her environment. So that's that's sort
+ 
+
+ align:start position:0%
+her environment. So that's that's sort
+of the the goal and this is secured in a
+
+ align:start position:0%
+of the the goal and this is secured in a
+ 
+
+ align:start position:0%
+of the the goal and this is secured in a
+variety of ways. can be secured uh you
+
+ align:start position:0%
+variety of ways. can be secured uh you
+ 
+
+ align:start position:0%
+variety of ways. can be secured uh you
+know sometimes politically through
+
+ align:start position:0%
+know sometimes politically through
+ 
+
+ align:start position:0%
+know sometimes politically through
+organization technologically through
+
+ align:start position:0%
+organization technologically through
+ 
+
+ align:start position:0%
+organization technologically through
+technological development uh and
+
+ align:start position:0%
+technological development uh and
+ 
+
+ align:start position:0%
+technological development uh and
+sometimes uh through uh religious
+
+ align:start position:0%
+sometimes uh through uh religious
+ 
+
+ align:start position:0%
+sometimes uh through uh religious
+religions I mean religions are
+
+ align:start position:0%
+religions I mean religions are
+ 
+
+ align:start position:0%
+religions I mean religions are
+definitely
+
+ align:start position:0%
+definitely
+ 
+
+ align:start position:0%
+definitely
+uh ways in which people try to adapt to
+
+ align:start position:0%
+uh ways in which people try to adapt to
+ 
+
+ align:start position:0%
+uh ways in which people try to adapt to
+their circumstances
+
+ align:start position:0%
+their circumstances
+ 
+
+ align:start position:0%
+their circumstances
+u and you know they're they're they're
+
+ align:start position:0%
+u and you know they're they're they're
+ 
+
+ align:start position:0%
+u and you know they're they're they're
+driven by ideas every every much as uh
+
+ align:start position:0%
+driven by ideas every every much as uh
+ 
+
+ align:start position:0%
+driven by ideas every every much as uh
+some of these others other utopic
+
+ align:start position:0%
+some of these others other utopic
+ 
+
+ align:start position:0%
+some of these others other utopic
+traditions are. Uh Butler went to New
+
+ align:start position:0%
+traditions are. Uh Butler went to New
+ 
+
+ align:start position:0%
+traditions are. Uh Butler went to New
+Zealand in the
+
+ align:start position:0%
+Zealand in the
+ 
+
+ align:start position:0%
+Zealand in the
+1860s as a young man. He uh he was um a
+
+ align:start position:0%
+1860s as a young man. He uh he was um a
+ 
+
+ align:start position:0%
+1860s as a young man. He uh he was um a
+graduate of Cambridge University.
+
+ align:start position:0%
+graduate of Cambridge University.
+ 
+
+ align:start position:0%
+graduate of Cambridge University.
+uh he uh was originally following a
+
+ align:start position:0%
+uh he uh was originally following a
+ 
+
+ align:start position:0%
+uh he uh was originally following a
+course of
+
+ align:start position:0%
+course of
+ 
+
+ align:start position:0%
+course of
+math study of
+
+ align:start position:0%
+math study of
+ 
+
+ align:start position:0%
+math study of
+mathematics, but at the end it just he
+
+ align:start position:0%
+mathematics, but at the end it just he
+ 
+
+ align:start position:0%
+mathematics, but at the end it just he
+couldn't quite keep it together. And so
+
+ align:start position:0%
+couldn't quite keep it together. And so
+ 
+
+ align:start position:0%
+couldn't quite keep it together. And so
+he ended up
+
+ align:start position:0%
+he ended up
+ 
+
+ align:start position:0%
+he ended up
+graduating in sort of religious uh more
+
+ align:start position:0%
+graduating in sort of religious uh more
+ 
+
+ align:start position:0%
+graduating in sort of religious uh more
+of a religious studies studies in in the
+
+ align:start position:0%
+of a religious studies studies in in the
+ 
+
+ align:start position:0%
+of a religious studies studies in in the
+Bible and things of that sort. um sort
+
+ align:start position:0%
+Bible and things of that sort. um sort
+ 
+
+ align:start position:0%
+Bible and things of that sort. um sort
+of a
+
+ align:start position:0%
+of a
+ 
+
+ align:start position:0%
+of a
+pre-clerical educational prep. And at
+
+ align:start position:0%
+pre-clerical educational prep. And at
+ 
+
+ align:start position:0%
+pre-clerical educational prep. And at
+one time he was considering uh becoming
+
+ align:start position:0%
+one time he was considering uh becoming
+ 
+
+ align:start position:0%
+one time he was considering uh becoming
+a cleric
+
+ align:start position:0%
+a cleric
+ 
+
+ align:start position:0%
+a cleric
+uh uh some sort of u uh religious uh
+
+ align:start position:0%
+uh uh some sort of u uh religious uh
+ 
+
+ align:start position:0%
+uh uh some sort of u uh religious uh
+uh leader.
+
+ align:start position:0%
+uh leader.
+ 
+
+ align:start position:0%
+uh leader.
+So at the end of his studies, he decided
+
+ align:start position:0%
+So at the end of his studies, he decided
+ 
+
+ align:start position:0%
+So at the end of his studies, he decided
+this was not something he could really
+
+ align:start position:0%
+this was not something he could really
+ 
+
+ align:start position:0%
+this was not something he could really
+do. who he just didn't want to be didn't
+
+ align:start position:0%
+do. who he just didn't want to be didn't
+ 
+
+ align:start position:0%
+do. who he just didn't want to be didn't
+want to become part of uh he he didn't
+
+ align:start position:0%
+want to become part of uh he he didn't
+ 
+
+ align:start position:0%
+want to become part of uh he he didn't
+want to become a cleric and go out and
+
+ align:start position:0%
+want to become a cleric and go out and
+ 
+
+ align:start position:0%
+want to become a cleric and go out and
+have a you know a group of people who he
+
+ align:start position:0%
+have a you know a group of people who he
+ 
+
+ align:start position:0%
+have a you know a group of people who he
+led and so forth. He he just felt that
+
+ align:start position:0%
+led and so forth. He he just felt that
+ 
+
+ align:start position:0%
+led and so forth. He he just felt that
+this was not an appropriate
+
+ align:start position:0%
+this was not an appropriate
+ 
+
+ align:start position:0%
+this was not an appropriate
+uh form of uh employment and life work
+
+ align:start position:0%
+uh form of uh employment and life work
+ 
+
+ align:start position:0%
+uh form of uh employment and life work
+for him. But his father disagreed with
+
+ align:start position:0%
+for him. But his father disagreed with
+ 
+
+ align:start position:0%
+for him. But his father disagreed with
+him very strongly because his father was
+
+ align:start position:0%
+him very strongly because his father was
+ 
+
+ align:start position:0%
+him very strongly because his father was
+was a cleric and uh they had monumental
+
+ align:start position:0%
+was a cleric and uh they had monumental
+ 
+
+ align:start position:0%
+was a cleric and uh they had monumental
+fights and so they finally settled it
+
+ align:start position:0%
+fights and so they finally settled it
+ 
+
+ align:start position:0%
+fights and so they finally settled it
+that Butler would immigrate to New
+
+ align:start position:0%
+that Butler would immigrate to New
+ 
+
+ align:start position:0%
+that Butler would immigrate to New
+Zealand and so off he went. So he he uh
+
+ align:start position:0%
+Zealand and so off he went. So he he uh
+ 
+
+ align:start position:0%
+Zealand and so off he went. So he he uh
+he went to New Zealand and he was there
+
+ align:start position:0%
+he went to New Zealand and he was there
+ 
+
+ align:start position:0%
+he went to New Zealand and he was there
+in uh uh
+
+ align:start position:0%
+in uh uh
+ 
+
+ align:start position:0%
+in uh uh
+1859 when Darwin's origin came out and
+
+ align:start position:0%
+1859 when Darwin's origin came out and
+ 
+
+ align:start position:0%
+1859 when Darwin's origin came out and
+he was fascinated by the
+
+ align:start position:0%
+he was fascinated by the
+ 
+
+ align:start position:0%
+he was fascinated by the
+book because uh he was a sheep he owned
+
+ align:start position:0%
+book because uh he was a sheep he owned
+ 
+
+ align:start position:0%
+book because uh he was a sheep he owned
+a sheep station there and he did a lot
+
+ align:start position:0%
+a sheep station there and he did a lot
+ 
+
+ align:start position:0%
+a sheep station there and he did a lot
+of
+
+ align:start position:0%
+of
+ 
+
+ align:start position:0%
+of
+breeding. So when he got Darwin's origin
+
+ align:start position:0%
+breeding. So when he got Darwin's origin
+ 
+
+ align:start position:0%
+breeding. So when he got Darwin's origin
+uh variation under domestication and all
+
+ align:start position:0%
+uh variation under domestication and all
+ 
+
+ align:start position:0%
+uh variation under domestication and all
+this uh language uh it made a whole lot
+
+ align:start position:0%
+this uh language uh it made a whole lot
+ 
+
+ align:start position:0%
+this uh language uh it made a whole lot
+of sense to him and of course he was uh
+
+ align:start position:0%
+of sense to him and of course he was uh
+ 
+
+ align:start position:0%
+of sense to him and of course he was uh
+a graduate of Darwin's university too.
+
+ align:start position:0%
+a graduate of Darwin's university too.
+ 
+
+ align:start position:0%
+a graduate of Darwin's university too.
+So he had read uh many of the works that
+
+ align:start position:0%
+So he had read uh many of the works that
+ 
+
+ align:start position:0%
+So he had read uh many of the works that
+Darwin had read including
+
+ align:start position:0%
+Darwin had read including
+ 
+
+ align:start position:0%
+Darwin had read including
+Paley and Paley turns up back in in this
+
+ align:start position:0%
+Paley and Paley turns up back in in this
+ 
+
+ align:start position:0%
+Paley and Paley turns up back in in this
+book and in fact Paley is one of the key
+
+ align:start position:0%
+book and in fact Paley is one of the key
+ 
+
+ align:start position:0%
+book and in fact Paley is one of the key
+uh one of the key objects of the
+
+ align:start position:0%
+uh one of the key objects of the
+ 
+
+ align:start position:0%
+uh one of the key objects of the
+satire and you know in a in an
+
+ align:start position:0%
+satire and you know in a in an
+ 
+
+ align:start position:0%
+satire and you know in a in an
+interesting not not in a a nasty way but
+
+ align:start position:0%
+interesting not not in a a nasty way but
+ 
+
+ align:start position:0%
+interesting not not in a a nasty way but
+in a fascinating intellectual way.
+
+ align:start position:0%
+in a fascinating intellectual way.
+ 
+
+ align:start position:0%
+in a fascinating intellectual way.
+Okay. So,
+
+ align:start position:0%
+Okay. So,
+ 
+
+ align:start position:0%
+Okay. So,
+uh this is uh uh this is this is the
+
+ align:start position:0%
+uh this is uh uh this is this is the
+ 
+
+ align:start position:0%
+uh this is uh uh this is this is the
+setting for this
+
+ align:start position:0%
+setting for this
+ 
+
+ align:start position:0%
+setting for this
+work. Okay.
+
+ align:start position:0%
+work. Okay.
+ 
+
+ align:start position:0%
+work. Okay.
+So, excuse me. Um
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+uh what's what's going on in this book?
+
+ align:start position:0%
+uh what's what's going on in this book?
+ 
+
+ align:start position:0%
+uh what's what's going on in this book?
+What are some of the things that uh you
+
+ align:start position:0%
+What are some of the things that uh you
+ 
+
+ align:start position:0%
+What are some of the things that uh you
+noted here? And uh what are some of the
+
+ align:start position:0%
+noted here? And uh what are some of the
+ 
+
+ align:start position:0%
+noted here? And uh what are some of the
+big ideas here that Butler? It's it's a
+
+ align:start position:0%
+big ideas here that Butler? It's it's a
+ 
+
+ align:start position:0%
+big ideas here that Butler? It's it's a
+tale. Yes, it's a tale of a guy who goes
+
+ align:start position:0%
+tale. Yes, it's a tale of a guy who goes
+ 
+
+ align:start position:0%
+tale. Yes, it's a tale of a guy who goes
+over the hill. Actually, this
+
+ align:start position:0%
+over the hill. Actually, this
+ 
+
+ align:start position:0%
+over the hill. Actually, this
+hill was uh if you go way back up way
+
+ align:start position:0%
+hill was uh if you go way back up way
+ 
+
+ align:start position:0%
+hill was uh if you go way back up way
+back up in this area up here, someplace
+
+ align:start position:0%
+back up in this area up here, someplace
+ 
+
+ align:start position:0%
+back up in this area up here, someplace
+up here is actually where he he actually
+
+ align:start position:0%
+up here is actually where he he actually
+ 
+
+ align:start position:0%
+up here is actually where he he actually
+went up there. So the uh the start of
+
+ align:start position:0%
+went up there. So the uh the start of
+ 
+
+ align:start position:0%
+went up there. So the uh the start of
+the book actually is quite accurate with
+
+ align:start position:0%
+the book actually is quite accurate with
+ 
+
+ align:start position:0%
+the book actually is quite accurate with
+uh he was a pretty good uh
+
+ align:start position:0%
+uh he was a pretty good uh
+ 
+
+ align:start position:0%
+uh he was a pretty good uh
+hiking he was a budding mountaineer not
+
+ align:start position:0%
+hiking he was a budding mountaineer not
+ 
+
+ align:start position:0%
+hiking he was a budding mountaineer not
+quite there but he was pretty pretty
+
+ align:start position:0%
+quite there but he was pretty pretty
+ 
+
+ align:start position:0%
+quite there but he was pretty pretty
+good on his feet and he
+
+ align:start position:0%
+good on his feet and he
+ 
+
+ align:start position:0%
+good on his feet and he
+uh so this is the the mountain range
+
+ align:start position:0%
+uh so this is the the mountain range
+ 
+
+ align:start position:0%
+uh so this is the the mountain range
+that uh the
+
+ align:start position:0%
+that uh the
+ 
+
+ align:start position:0%
+that uh the
+narrator in Arowan goes over and he goes
+
+ align:start position:0%
+narrator in Arowan goes over and he goes
+ 
+
+ align:start position:0%
+narrator in Arowan goes over and he goes
+over this mountain range And as uh as as
+
+ align:start position:0%
+over this mountain range And as uh as as
+ 
+
+ align:start position:0%
+over this mountain range And as uh as as
+Candid as uh Candid did in in Vololier's
+
+ align:start position:0%
+Candid as uh Candid did in in Vololier's
+ 
+
+ align:start position:0%
+Candid as uh Candid did in in Vololier's
+Candid uh over the mountain range into
+
+ align:start position:0%
+Candid uh over the mountain range into
+ 
+
+ align:start position:0%
+Candid uh over the mountain range into
+this world, this kind of new
+
+ align:start position:0%
+this world, this kind of new
+ 
+
+ align:start position:0%
+this world, this kind of new
+world and it's a kind of a utopia. So
+
+ align:start position:0%
+world and it's a kind of a utopia. So
+ 
+
+ align:start position:0%
+world and it's a kind of a utopia. So
+it's it's one of So it's going to be a
+
+ align:start position:0%
+it's it's one of So it's going to be a
+ 
+
+ align:start position:0%
+it's it's one of So it's going to be a
+thought experiment. That's what it is.
+
+ align:start position:0%
+thought experiment. That's what it is.
+ 
+
+ align:start position:0%
+thought experiment. That's what it is.
+It's a whole bunch of encounters and he
+
+ align:start position:0%
+It's a whole bunch of encounters and he
+ 
+
+ align:start position:0%
+It's a whole bunch of encounters and he
+develops a society. So what are some of
+
+ align:start position:0%
+develops a society. So what are some of
+ 
+
+ align:start position:0%
+develops a society. So what are some of
+the characteristics of this society that
+
+ align:start position:0%
+the characteristics of this society that
+ 
+
+ align:start position:0%
+the characteristics of this society that
+he discovers?
+
+ align:start position:0%
+he discovers?
+ 
+
+ align:start position:0%
+he discovers?
+Claire, well, anything to do with
+
+ align:start position:0%
+Claire, well, anything to do with
+ 
+
+ align:start position:0%
+Claire, well, anything to do with
+illness is almost like a crime. Um,
+
+ align:start position:0%
+illness is almost like a crime. Um,
+ 
+
+ align:start position:0%
+illness is almost like a crime. Um,
+people are imprisoned if they're seen as
+
+ align:start position:0%
+people are imprisoned if they're seen as
+ 
+
+ align:start position:0%
+people are imprisoned if they're seen as
+being sickly at all, whereas like things
+
+ align:start position:0%
+being sickly at all, whereas like things
+ 
+
+ align:start position:0%
+being sickly at all, whereas like things
+that people would be imprisoned for in
+
+ align:start position:0%
+that people would be imprisoned for in
+ 
+
+ align:start position:0%
+that people would be imprisoned for in
+our world aren't punished really at all.
+
+ align:start position:0%
+our world aren't punished really at all.
+ 
+
+ align:start position:0%
+our world aren't punished really at all.
+And it seems like beauty and aesthetic
+
+ align:start position:0%
+And it seems like beauty and aesthetic
+ 
+
+ align:start position:0%
+And it seems like beauty and aesthetic
+things are very selective for. Okay.
+
+ align:start position:0%
+things are very selective for. Okay.
+ 
+
+ align:start position:0%
+things are very selective for. Okay.
+Yes. So he says here, here's a a short
+
+ align:start position:0%
+Yes. So he says here, here's a a short
+ 
+
+ align:start position:0%
+Yes. So he says here, here's a a short
+or here's a quote. Lastly, I should say
+
+ align:start position:0%
+or here's a quote. Lastly, I should say
+ 
+
+ align:start position:0%
+or here's a quote. Lastly, I should say
+that the people were of a physical
+
+ align:start position:0%
+that the people were of a physical
+ 
+
+ align:start position:0%
+that the people were of a physical
+beauty which was simply
+
+ align:start position:0%
+beauty which was simply
+ 
+
+ align:start position:0%
+beauty which was simply
+amazing. The women were vigorous and had
+
+ align:start position:0%
+amazing. The women were vigorous and had
+ 
+
+ align:start position:0%
+amazing. The women were vigorous and had
+a most majestic gate, their heads being
+
+ align:start position:0%
+a most majestic gate, their heads being
+ 
+
+ align:start position:0%
+a most majestic gate, their heads being
+set on upon their shoulders with a grace
+
+ align:start position:0%
+set on upon their shoulders with a grace
+ 
+
+ align:start position:0%
+set on upon their shoulders with a grace
+beyond all power of expression.
+
+ align:start position:0%
+beyond all power of expression.
+ 
+
+ align:start position:0%
+beyond all power of expression.
+The men were as handsome as the women
+
+ align:start position:0%
+The men were as handsome as the women
+ 
+
+ align:start position:0%
+The men were as handsome as the women
+were beautiful. I felt simply abashed in
+
+ align:start position:0%
+were beautiful. I felt simply abashed in
+ 
+
+ align:start position:0%
+were beautiful. I felt simply abashed in
+the presence of such a splendid type. A
+
+ align:start position:0%
+the presence of such a splendid type. A
+ 
+
+ align:start position:0%
+the presence of such a splendid type. A
+compound that is all that is best in
+
+ align:start position:0%
+compound that is all that is best in
+ 
+
+ align:start position:0%
+compound that is all that is best in
+Egyptian, Greek, and Italian, so on and
+
+ align:start position:0%
+Egyptian, Greek, and Italian, so on and
+ 
+
+ align:start position:0%
+Egyptian, Greek, and Italian, so on and
+so forth. What What's he encountering
+
+ align:start position:0%
+so forth. What What's he encountering
+ 
+
+ align:start position:0%
+so forth. What What's he encountering
+here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Beautiful people, Jake.
+
+ align:start position:0%
+Beautiful people, Jake.
+ 
+
+ align:start position:0%
+Beautiful people, Jake.
+Well, beautiful people, basically. And
+
+ align:start position:0%
+Well, beautiful people, basically. And
+ 
+
+ align:start position:0%
+Well, beautiful people, basically. And
+And why are they beautiful? Uh how did
+
+ align:start position:0%
+And why are they beautiful? Uh how did
+ 
+
+ align:start position:0%
+And why are they beautiful? Uh how did
+they be how did they come to be so
+
+ align:start position:0%
+they be how did they come to be so
+ 
+
+ align:start position:0%
+they be how did they come to be so
+beautiful? They selected themselves for
+
+ align:start position:0%
+beautiful? They selected themselves for
+ 
+
+ align:start position:0%
+beautiful? They selected themselves for
+basically they took people who are like
+
+ align:start position:0%
+basically they took people who are like
+ 
+
+ align:start position:0%
+basically they took people who are like
+really sickly and stuff and sent them to
+
+ align:start position:0%
+really sickly and stuff and sent them to
+ 
+
+ align:start position:0%
+really sickly and stuff and sent them to
+prison basically. Okay. They got in
+
+ align:start position:0%
+prison basically. Okay. They got in
+ 
+
+ align:start position:0%
+prison basically. Okay. They got in
+trouble. All right. So you you get into
+
+ align:start position:0%
+trouble. All right. So you you get into
+ 
+
+ align:start position:0%
+trouble. All right. So you you get into
+you get into trouble in this society. If
+
+ align:start position:0%
+you get into trouble in this society. If
+ 
+
+ align:start position:0%
+you get into trouble in this society. If
+what are some of the reasons for getting
+
+ align:start position:0%
+what are some of the reasons for getting
+ 
+
+ align:start position:0%
+what are some of the reasons for getting
+how can you get into trouble
+
+ align:start position:0%
+how can you get into trouble
+ 
+
+ align:start position:0%
+how can you get into trouble
+Chris? I think it was
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+for example.
+
+ align:start position:0%
+for example.
+ 
+
+ align:start position:0%
+for example.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Probably anything mechanical, right? Or
+
+ align:start position:0%
+Probably anything mechanical, right? Or
+ 
+
+ align:start position:0%
+Probably anything mechanical, right? Or
+any sort of Oh, yeah. If if you have if
+
+ align:start position:0%
+any sort of Oh, yeah. If if you have if
+ 
+
+ align:start position:0%
+any sort of Oh, yeah. If if you have if
+you have a a watch or anything
+
+ align:start position:0%
+you have a a watch or anything
+ 
+
+ align:start position:0%
+you have a a watch or anything
+mechanical, watch out. You're going to
+
+ align:start position:0%
+mechanical, watch out. You're going to
+ 
+
+ align:start position:0%
+mechanical, watch out. You're going to
+get We'll We'll come back to that.
+
+ align:start position:0%
+get We'll We'll come back to that.
+ 
+
+ align:start position:0%
+get We'll We'll come back to that.
+That's that's a big that's a big
+
+ align:start position:0%
+That's that's a big that's a big
+ 
+
+ align:start position:0%
+That's that's a big that's a big
+uh air or uh
+
+ align:start position:0%
+uh air or uh
+ 
+
+ align:start position:0%
+uh air or uh
+crime. It's it's a type of crime.
+
+ align:start position:0%
+crime. It's it's a type of crime.
+ 
+
+ align:start position:0%
+crime. It's it's a type of crime.
+Yeah. One that I didn't really
+
+ align:start position:0%
+Yeah. One that I didn't really
+ 
+
+ align:start position:0%
+Yeah. One that I didn't really
+understand was that you weren't
+
+ align:start position:0%
+understand was that you weren't
+ 
+
+ align:start position:0%
+understand was that you weren't
+imprisoned if you committed like theft.
+
+ align:start position:0%
+imprisoned if you committed like theft.
+ 
+
+ align:start position:0%
+imprisoned if you committed like theft.
+I didn't really understand that. Yeah.
+
+ align:start position:0%
+I didn't really understand that. Yeah.
+ 
+
+ align:start position:0%
+I didn't really understand that. Yeah.
+These people have the really bizarre
+
+ align:start position:0%
+These people have the really bizarre
+ 
+
+ align:start position:0%
+These people have the really bizarre
+opinion that if you embezzle or you
+
+ align:start position:0%
+opinion that if you embezzle or you
+ 
+
+ align:start position:0%
+opinion that if you embezzle or you
+steal, you are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what? They don't treat it as a crime, do
+
+ align:start position:0%
+what? They don't treat it as a crime, do
+ 
+
+ align:start position:0%
+what? They don't treat it as a crime, do
+they? They treat it as a illness. You
+
+ align:start position:0%
+they? They treat it as a illness. You
+ 
+
+ align:start position:0%
+they? They treat it as a illness. You
+are ill. you should be you should be you
+
+ align:start position:0%
+are ill. you should be you should be you
+ 
+
+ align:start position:0%
+are ill. you should be you should be you
+know you need to get help from your
+
+ align:start position:0%
+know you need to get help from your
+ 
+
+ align:start position:0%
+know you need to get help from your
+local straightener and you
+
+ align:start position:0%
+local straightener and you
+ 
+
+ align:start position:0%
+local straightener and you
+know and yet if you are if you have
+
+ align:start position:0%
+know and yet if you are if you have
+ 
+
+ align:start position:0%
+know and yet if you are if you have
+pulmonary
+
+ align:start position:0%
+pulmonary
+ 
+
+ align:start position:0%
+pulmonary
+consumption i.e. TB,
+
+ align:start position:0%
+consumption i.e. TB,
+ 
+
+ align:start position:0%
+consumption i.e. TB,
+tuberculosis. How do they treat that?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+ you up.
+
+ align:start position:0%
+ you up.
+ 
+
+ align:start position:0%
+ you up.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is allowed to persist in their
+
+ align:start position:0%
+Is allowed to persist in their
+ 
+
+ align:start position:0%
+Is allowed to persist in their
+Charles, what do you think of this this
+
+ align:start position:0%
+Charles, what do you think of this this
+ 
+
+ align:start position:0%
+Charles, what do you think of this this
+arrangement? I think it's like it's kind
+
+ align:start position:0%
+arrangement? I think it's like it's kind
+ 
+
+ align:start position:0%
+arrangement? I think it's like it's kind
+of a reverse. It's like a he's trying to
+
+ align:start position:0%
+of a reverse. It's like a he's trying to
+ 
+
+ align:start position:0%
+of a reverse. It's like a he's trying to
+reverse just the kind of the values and
+
+ align:start position:0%
+reverse just the kind of the values and
+ 
+
+ align:start position:0%
+reverse just the kind of the values and
+the underlying fabric of society between
+
+ align:start position:0%
+the underlying fabric of society between
+ 
+
+ align:start position:0%
+the underlying fabric of society between
+society he portrays and our society and
+
+ align:start position:0%
+society he portrays and our society and
+ 
+
+ align:start position:0%
+society he portrays and our society and
+it's like it's just like there's like a
+
+ align:start position:0%
+it's like it's just like there's like a
+ 
+
+ align:start position:0%
+it's like it's just like there's like a
+humorous aspect to it that kind of it's
+
+ align:start position:0%
+humorous aspect to it that kind of it's
+ 
+
+ align:start position:0%
+humorous aspect to it that kind of it's
+like in it's a little bit satirical just
+
+ align:start position:0%
+like in it's a little bit satirical just
+ 
+
+ align:start position:0%
+like in it's a little bit satirical just
+there's like a little bit a lot
+
+ align:start position:0%
+there's like a little bit a lot
+ 
+
+ align:start position:0%
+there's like a little bit a lot
+obviously that's like that's subjective
+
+ align:start position:0%
+obviously that's like that's subjective
+ 
+
+ align:start position:0%
+obviously that's like that's subjective
+but I think there's like an element
+
+ align:start position:0%
+but I think there's like an element
+ 
+
+ align:start position:0%
+but I think there's like an element
+that really just makes you think about
+
+ align:start position:0%
+that really just makes you think about
+ 
+
+ align:start position:0%
+that really just makes you think about
+why. Okay, that's Yeah, it uh it
+
+ align:start position:0%
+why. Okay, that's Yeah, it uh it
+ 
+
+ align:start position:0%
+why. Okay, that's Yeah, it uh it
+occurred to me that while this isn't a
+
+ align:start position:0%
+occurred to me that while this isn't a
+ 
+
+ align:start position:0%
+occurred to me that while this isn't a
+perfect uh analysis that at least to
+
+ align:start position:0%
+perfect uh analysis that at least to
+ 
+
+ align:start position:0%
+perfect uh analysis that at least to
+some extent it seems like the selection
+
+ align:start position:0%
+some extent it seems like the selection
+ 
+
+ align:start position:0%
+some extent it seems like the selection
+forces in Arowan
+
+ align:start position:0%
+forces in Arowan
+ 
+
+ align:start position:0%
+forces in Arowan
+are switched in uh from the ones we have
+
+ align:start position:0%
+are switched in uh from the ones we have
+ 
+
+ align:start position:0%
+are switched in uh from the ones we have
+where the natural selection forces in
+
+ align:start position:0%
+where the natural selection forces in
+ 
+
+ align:start position:0%
+where the natural selection forces in
+our world are the ones that the people
+
+ align:start position:0%
+our world are the ones that the people
+ 
+
+ align:start position:0%
+our world are the ones that the people
+put pressure on there like the sickness
+
+ align:start position:0%
+put pressure on there like the sickness
+ 
+
+ align:start position:0%
+put pressure on there like the sickness
+this and that sensing and the one that
+
+ align:start position:0%
+this and that sensing and the one that
+ 
+
+ align:start position:0%
+this and that sensing and the one that
+people put on here are more of the
+
+ align:start position:0%
+people put on here are more of the
+ 
+
+ align:start position:0%
+people put on here are more of the
+natural. Okay, now you're getting at
+
+ align:start position:0%
+natural. Okay, now you're getting at
+ 
+
+ align:start position:0%
+natural. Okay, now you're getting at
+something. Yes, there is there's
+
+ align:start position:0%
+something. Yes, there is there's
+ 
+
+ align:start position:0%
+something. Yes, there is there's
+something going on here with this
+
+ align:start position:0%
+something going on here with this
+ 
+
+ align:start position:0%
+something going on here with this
+selection and this whole phenomenon and
+
+ align:start position:0%
+selection and this whole phenomenon and
+ 
+
+ align:start position:0%
+selection and this whole phenomenon and
+think
+
+ align:start position:0%
+think
+ 
+
+ align:start position:0%
+think
+Darwin, you know, Darwin's world in the
+
+ align:start position:0%
+Darwin, you know, Darwin's world in the
+ 
+
+ align:start position:0%
+Darwin, you know, Darwin's world in the
+origin, humans are outside. How how does
+
+ align:start position:0%
+origin, humans are outside. How how does
+ 
+
+ align:start position:0%
+origin, humans are outside. How how does
+Darwin's world work? Does it work like
+
+ align:start position:0%
+Darwin's world work? Does it work like
+ 
+
+ align:start position:0%
+Darwin's world work? Does it work like
+our social world or does it work like
+
+ align:start position:0%
+our social world or does it work like
+ 
+
+ align:start position:0%
+our social world or does it work like
+this world that Butler's painting for
+
+ align:start position:0%
+this world that Butler's painting for
+ 
+
+ align:start position:0%
+this world that Butler's painting for
+us? In some sense, a thought experiment
+
+ align:start position:0%
+us? In some sense, a thought experiment
+ 
+
+ align:start position:0%
+us? In some sense, a thought experiment
+is this. What what would a society look
+
+ align:start position:0%
+is this. What what would a society look
+ 
+
+ align:start position:0%
+is this. What what would a society look
+like if it behaved according to
+
+ align:start position:0%
+like if it behaved according to
+ 
+
+ align:start position:0%
+like if it behaved according to
+Darwinian principles and strengthen
+
+ align:start position:0%
+Darwinian principles and strengthen
+ 
+
+ align:start position:0%
+Darwinian principles and strengthen
+those principles?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Is this making any sense, David?
+
+ align:start position:0%
+Is this making any sense, David?
+ 
+
+ align:start position:0%
+Is this making any sense, David?
+Well, it's it's sort of a difficult
+
+ align:start position:0%
+Well, it's it's sort of a difficult
+ 
+
+ align:start position:0%
+Well, it's it's sort of a difficult
+question to answer just because
+
+ align:start position:0%
+question to answer just because
+ 
+
+ align:start position:0%
+question to answer just because
+Darwinian principles say um
+
+ align:start position:0%
+Darwinian principles say um
+ 
+
+ align:start position:0%
+Darwinian principles say um
+people act based for their survival and
+
+ align:start position:0%
+people act based for their survival and
+ 
+
+ align:start position:0%
+people act based for their survival and
+for reproduction based on their traits.
+
+ align:start position:0%
+for reproduction based on their traits.
+ 
+
+ align:start position:0%
+for reproduction based on their traits.
+Um but part of Darwinian Darwin's theory
+
+ align:start position:0%
+Um but part of Darwinian Darwin's theory
+ 
+
+ align:start position:0%
+Um but part of Darwinian Darwin's theory
+is sort of similar to Smith's where
+
+ align:start position:0%
+is sort of similar to Smith's where
+ 
+
+ align:start position:0%
+is sort of similar to Smith's where
+Smith says people act on their own
+
+ align:start position:0%
+Smith says people act on their own
+ 
+
+ align:start position:0%
+Smith says people act on their own
+behavior but that's best for society. Um
+
+ align:start position:0%
+behavior but that's best for society. Um
+ 
+
+ align:start position:0%
+behavior but that's best for society. Um
+if everyone acted
+
+ align:start position:0%
+if everyone acted
+ 
+
+ align:start position:0%
+if everyone acted
+solely like Darwin like Darwin's um
+
+ align:start position:0%
+solely like Darwin like Darwin's um
+ 
+
+ align:start position:0%
+solely like Darwin like Darwin's um
+evolutionary pressures I don't think
+
+ align:start position:0%
+evolutionary pressures I don't think
+ 
+
+ align:start position:0%
+evolutionary pressures I don't think
+we'd be able to have the society we had
+
+ align:start position:0%
+we'd be able to have the society we had
+ 
+
+ align:start position:0%
+we'd be able to have the society we had
+right now. Um
+
+ align:start position:0%
+right now. Um
+ 
+
+ align:start position:0%
+right now. Um
+that's a very big that's a very Yes. And
+
+ align:start position:0%
+that's a very big that's a very Yes. And
+ 
+
+ align:start position:0%
+that's a very big that's a very Yes. And
+and this is this
+
+ align:start position:0%
+and this is this
+ 
+
+ align:start position:0%
+and this is this
+is when you read this and you get into
+
+ align:start position:0%
+is when you read this and you get into
+ 
+
+ align:start position:0%
+is when you read this and you get into
+it, you realize they're punishing
+
+ align:start position:0%
+it, you realize they're punishing
+ 
+
+ align:start position:0%
+it, you realize they're punishing
+illness. What happens to those analopee
+
+ align:start position:0%
+illness. What happens to those analopee
+ 
+
+ align:start position:0%
+illness. What happens to those analopee
+out in the plains who are ill?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+They tend to be the ones that get a a
+
+ align:start position:0%
+They tend to be the ones that get a a
+ 
+
+ align:start position:0%
+They tend to be the ones that get a a
+little slower and get picked off.
+
+ align:start position:0%
+little slower and get picked off.
+ 
+
+ align:start position:0%
+little slower and get picked off.
+Uh what about the little fish or
+
+ align:start position:0%
+Uh what about the little fish or
+ 
+
+ align:start position:0%
+Uh what about the little fish or
+whatever that is good at stealing you
+
+ align:start position:0%
+whatever that is good at stealing you
+ 
+
+ align:start position:0%
+whatever that is good at stealing you
+know the rocks from or whatever uh from
+
+ align:start position:0%
+know the rocks from or whatever uh from
+ 
+
+ align:start position:0%
+know the rocks from or whatever uh from
+its neighbor
+
+ align:start position:0%
+its neighbor
+ 
+
+ align:start position:0%
+its neighbor
+it like it will tend to live over its
+
+ align:start position:0%
+it like it will tend to live over its
+ 
+
+ align:start position:0%
+it like it will tend to live over its
+neighbor. Yeah. Theft does not get
+
+ align:start position:0%
+neighbor. Yeah. Theft does not get
+ 
+
+ align:start position:0%
+neighbor. Yeah. Theft does not get
+punished in nature.
+
+ align:start position:0%
+punished in nature.
+ 
+
+ align:start position:0%
+punished in nature.
+I mean, theft can be, you know, if if if
+
+ align:start position:0%
+I mean, theft can be, you know, if if if
+ 
+
+ align:start position:0%
+I mean, theft can be, you know, if if if
+you know how to if you're if you're a
+
+ align:start position:0%
+you know how to if you're if you're a
+ 
+
+ align:start position:0%
+you know how to if you're if you're a
+cuckoo and you can lay your eggs in the
+
+ align:start position:0%
+cuckoo and you can lay your eggs in the
+ 
+
+ align:start position:0%
+cuckoo and you can lay your eggs in the
+bird's nest and have somebody else uh
+
+ align:start position:0%
+bird's nest and have somebody else uh
+ 
+
+ align:start position:0%
+bird's nest and have somebody else uh
+hey, you don't have to go to all the
+
+ align:start position:0%
+hey, you don't have to go to all the
+ 
+
+ align:start position:0%
+hey, you don't have to go to all the
+trouble to feed the young. So, in the
+
+ align:start position:0%
+trouble to feed the young. So, in the
+ 
+
+ align:start position:0%
+trouble to feed the young. So, in the
+natural
+
+ align:start position:0%
+natural
+ 
+
+ align:start position:0%
+natural
+world, our moral uh the way we think of
+
+ align:start position:0%
+world, our moral uh the way we think of
+ 
+
+ align:start position:0%
+world, our moral uh the way we think of
+our society and a moral framework is is
+
+ align:start position:0%
+our society and a moral framework is is
+ 
+
+ align:start position:0%
+our society and a moral framework is is
+pretty much absent in the natural world.
+
+ align:start position:0%
+pretty much absent in the natural world.
+ 
+
+ align:start position:0%
+pretty much absent in the natural world.
+I mean things just basically are have a
+
+ align:start position:0%
+I mean things just basically are have a
+ 
+
+ align:start position:0%
+I mean things just basically are have a
+fundamental utilitarian. Is that right?
+
+ align:start position:0%
+fundamental utilitarian. Is that right?
+ 
+
+ align:start position:0%
+fundamental utilitarian. Is that right?
+Is that what you're going to I was just
+
+ align:start position:0%
+Is that what you're going to I was just
+ 
+
+ align:start position:0%
+Is that what you're going to I was just
+going to add to the question that you
+
+ align:start position:0%
+going to add to the question that you
+ 
+
+ align:start position:0%
+going to add to the question that you
+asked. Well, I think that if you so like
+
+ align:start position:0%
+asked. Well, I think that if you so like
+ 
+
+ align:start position:0%
+asked. Well, I think that if you so like
+basically Darwin's principle is based on
+
+ align:start position:0%
+basically Darwin's principle is based on
+ 
+
+ align:start position:0%
+basically Darwin's principle is based on
+like how nature has there's like a like
+
+ align:start position:0%
+like how nature has there's like a like
+ 
+
+ align:start position:0%
+like how nature has there's like a like
+nature the selection process in nature
+
+ align:start position:0%
+nature the selection process in nature
+ 
+
+ align:start position:0%
+nature the selection process in nature
+is like an invisible hand. And if you
+
+ align:start position:0%
+is like an invisible hand. And if you
+ 
+
+ align:start position:0%
+is like an invisible hand. And if you
+try to strengthen those principles, you
+
+ align:start position:0%
+try to strengthen those principles, you
+ 
+
+ align:start position:0%
+try to strengthen those principles, you
+decrease the chance of something that's
+
+ align:start position:0%
+decrease the chance of something that's
+ 
+
+ align:start position:0%
+decrease the chance of something that's
+not like that's not fit to survive like
+
+ align:start position:0%
+not like that's not fit to survive like
+ 
+
+ align:start position:0%
+not like that's not fit to survive like
+the chance of that something to survive
+
+ align:start position:0%
+the chance of that something to survive
+ 
+
+ align:start position:0%
+the chance of that something to survive
+like you make sure that if something is
+
+ align:start position:0%
+like you make sure that if something is
+ 
+
+ align:start position:0%
+like you make sure that if something is
+even the least bit um incompatible with
+
+ align:start position:0%
+even the least bit um incompatible with
+ 
+
+ align:start position:0%
+even the least bit um incompatible with
+its surroundings that it gets eliminated
+
+ align:start position:0%
+its surroundings that it gets eliminated
+ 
+
+ align:start position:0%
+its surroundings that it gets eliminated
+immediately. Yeah, I think like the
+
+ align:start position:0%
+immediately. Yeah, I think like the
+ 
+
+ align:start position:0%
+immediately. Yeah, I think like the
+result of this um would be like like
+
+ align:start position:0%
+result of this um would be like like
+ 
+
+ align:start position:0%
+result of this um would be like like
+suppose you had like obviously every
+
+ align:start position:0%
+suppose you had like obviously every
+ 
+
+ align:start position:0%
+suppose you had like obviously every
+person is multiaceted and you might not
+
+ align:start position:0%
+person is multiaceted and you might not
+ 
+
+ align:start position:0%
+person is multiaceted and you might not
+be so great at one thing but you might
+
+ align:start position:0%
+be so great at one thing but you might
+ 
+
+ align:start position:0%
+be so great at one thing but you might
+have a hidden talent and if you select
+
+ align:start position:0%
+have a hidden talent and if you select
+ 
+
+ align:start position:0%
+have a hidden talent and if you select
+against this person before they discover
+
+ align:start position:0%
+against this person before they discover
+ 
+
+ align:start position:0%
+against this person before they discover
+what they're good at before they find
+
+ align:start position:0%
+what they're good at before they find
+ 
+
+ align:start position:0%
+what they're good at before they find
+like their little corner in the world
+
+ align:start position:0%
+like their little corner in the world
+ 
+
+ align:start position:0%
+like their little corner in the world
+where they're good at doing something
+
+ align:start position:0%
+where they're good at doing something
+ 
+
+ align:start position:0%
+where they're good at doing something
+that can help the rest. like you're
+
+ align:start position:0%
+that can help the rest. like you're
+ 
+
+ align:start position:0%
+that can help the rest. like you're
+eliminating a lot of possibilities and
+
+ align:start position:0%
+eliminating a lot of possibilities and
+ 
+
+ align:start position:0%
+eliminating a lot of possibilities and
+so like in some ways you're selecting
+
+ align:start position:0%
+so like in some ways you're selecting
+ 
+
+ align:start position:0%
+so like in some ways you're selecting
+for the best but like you're also
+
+ align:start position:0%
+for the best but like you're also
+ 
+
+ align:start position:0%
+for the best but like you're also
+narrowing down and like there's only so
+
+ align:start position:0%
+narrowing down and like there's only so
+ 
+
+ align:start position:0%
+narrowing down and like there's only so
+much that a very narrow and not very
+
+ align:start position:0%
+much that a very narrow and not very
+ 
+
+ align:start position:0%
+much that a very narrow and not very
+like
+
+ align:start position:0%
+like
+ 
+
+ align:start position:0%
+like
+multi-purpose serving like community can
+
+ align:start position:0%
+multi-purpose serving like community can
+ 
+
+ align:start position:0%
+multi-purpose serving like community can
+do like not lot of variety. Yeah. Uh
+
+ align:start position:0%
+do like not lot of variety. Yeah. Uh
+ 
+
+ align:start position:0%
+do like not lot of variety. Yeah. Uh
+humans uh in in in this little work
+
+ align:start position:0%
+humans uh in in in this little work
+ 
+
+ align:start position:0%
+humans uh in in in this little work
+uh in Arowan are kind of uh
+
+ align:start position:0%
+uh in Arowan are kind of uh
+ 
+
+ align:start position:0%
+uh in Arowan are kind of uh
+uh they have
+
+ align:start position:0%
+uh they have
+ 
+
+ align:start position:0%
+uh they have
+adopted a
+
+ align:start position:0%
+adopted a
+ 
+
+ align:start position:0%
+adopted a
+philosophy that is based
+
+ align:start position:0%
+philosophy that is based
+ 
+
+ align:start position:0%
+philosophy that is based
+on natural world type of dynamics that
+
+ align:start position:0%
+on natural world type of dynamics that
+ 
+
+ align:start position:0%
+on natural world type of dynamics that
+we find which Butler found in in in in
+
+ align:start position:0%
+we find which Butler found in in in in
+ 
+
+ align:start position:0%
+we find which Butler found in in in in
+Darwin's uh uh
+
+ align:start position:0%
+Darwin's uh uh
+ 
+
+ align:start position:0%
+Darwin's uh uh
+origin and that dynamic is
+
+ align:start position:0%
+origin and that dynamic is
+ 
+
+ align:start position:0%
+origin and that dynamic is
+manifestly and very obviously hugely
+
+ align:start position:0%
+manifestly and very obviously hugely
+ 
+
+ align:start position:0%
+manifestly and very obviously hugely
+different from the world that we live
+
+ align:start position:0%
+different from the world that we live
+ 
+
+ align:start position:0%
+different from the world that we live
+in. We do not select people in our
+
+ align:start position:0%
+in. We do not select people in our
+ 
+
+ align:start position:0%
+in. We do not select people in our
+society uh and punish them for being ill
+
+ align:start position:0%
+society uh and punish them for being ill
+ 
+
+ align:start position:0%
+society uh and punish them for being ill
+do
+
+ align:start position:0%
+do
+ 
+
+ align:start position:0%
+do
+we David? Uh we don't but we do
+
+ align:start position:0%
+we David? Uh we don't but we do
+ 
+
+ align:start position:0%
+we David? Uh we don't but we do
+um sort of reward those who are who like
+
+ align:start position:0%
+um sort of reward those who are who like
+ 
+
+ align:start position:0%
+um sort of reward those who are who like
+are better and like I say this like
+
+ align:start position:0%
+are better and like I say this like
+ 
+
+ align:start position:0%
+are better and like I say this like
+physical appearance like people who are
+
+ align:start position:0%
+physical appearance like people who are
+ 
+
+ align:start position:0%
+physical appearance like people who are
+who look better usually make more money
+
+ align:start position:0%
+who look better usually make more money
+ 
+
+ align:start position:0%
+who look better usually make more money
+um whether or not you if you're taller
+
+ align:start position:0%
+um whether or not you if you're taller
+ 
+
+ align:start position:0%
+um whether or not you if you're taller
+you uh by each inch adds so much to your
+
+ align:start position:0%
+you uh by each inch adds so much to your
+ 
+
+ align:start position:0%
+you uh by each inch adds so much to your
+average there's actually I read an
+
+ align:start position:0%
+average there's actually I read an
+ 
+
+ align:start position:0%
+average there's actually I read an
+article about how
+
+ align:start position:0%
+article about how
+ 
+
+ align:start position:0%
+article about how
+I don't I read an article about how
+
+ align:start position:0%
+I don't I read an article about how
+ 
+
+ align:start position:0%
+I don't I read an article about how
+there was an appearance bias and how
+
+ align:start position:0%
+there was an appearance bias and how
+ 
+
+ align:start position:0%
+there was an appearance bias and how
+people are now trying to like get
+
+ align:start position:0%
+people are now trying to like get
+ 
+
+ align:start position:0%
+people are now trying to like get
+legislation to stop that cuz um it was
+
+ align:start position:0%
+legislation to stop that cuz um it was
+ 
+
+ align:start position:0%
+legislation to stop that cuz um it was
+unequal. But so part of what you're
+
+ align:start position:0%
+unequal. But so part of what you're
+ 
+
+ align:start position:0%
+unequal. But so part of what you're
+saying is we fight we fight socially
+
+ align:start position:0%
+saying is we fight we fight socially
+ 
+
+ align:start position:0%
+saying is we fight we fight socially
+against evolutionary pressures
+
+ align:start position:0%
+against evolutionary pressures
+ 
+
+ align:start position:0%
+against evolutionary pressures
+evolutionary pressures. That's what our
+
+ align:start position:0%
+evolutionary pressures. That's what our
+ 
+
+ align:start position:0%
+evolutionary pressures. That's what our
+laws are. Our laws for equity and
+
+ align:start position:0%
+laws are. Our laws for equity and
+ 
+
+ align:start position:0%
+laws are. Our laws for equity and
+equality and so forth are trying to
+
+ align:start position:0%
+equality and so forth are trying to
+ 
+
+ align:start position:0%
+equality and so forth are trying to
+fight
+
+ align:start position:0%
+fight
+ 
+
+ align:start position:0%
+fight
+against any kind of uh natural selection
+
+ align:start position:0%
+against any kind of uh natural selection
+ 
+
+ align:start position:0%
+against any kind of uh natural selection
+principles because the world the natural
+
+ align:start position:0%
+principles because the world the natural
+ 
+
+ align:start position:0%
+principles because the world the natural
+world of Darwin is not the model for the
+
+ align:start position:0%
+world of Darwin is not the model for the
+ 
+
+ align:start position:0%
+world of Darwin is not the model for the
+social world of
+
+ align:start position:0%
+social world of
+ 
+
+ align:start position:0%
+social world of
+humans. And to the degree that you see
+
+ align:start position:0%
+humans. And to the degree that you see
+ 
+
+ align:start position:0%
+humans. And to the degree that you see
+the absurdity of these uh arrangements
+
+ align:start position:0%
+the absurdity of these uh arrangements
+ 
+
+ align:start position:0%
+the absurdity of these uh arrangements
+where they're punishing people for being
+
+ align:start position:0%
+where they're punishing people for being
+ 
+
+ align:start position:0%
+where they're punishing people for being
+ill and you think that's really not
+
+ align:start position:0%
+ill and you think that's really not
+ 
+
+ align:start position:0%
+ill and you think that's really not
+right, you are basically
+
+ align:start position:0%
+right, you are basically
+ 
+
+ align:start position:0%
+right, you are basically
+reflecting a uh idea of the world that
+
+ align:start position:0%
+reflecting a uh idea of the world that
+ 
+
+ align:start position:0%
+reflecting a uh idea of the world that
+we try to cultivate in our societies. So
+
+ align:start position:0%
+we try to cultivate in our societies. So
+ 
+
+ align:start position:0%
+we try to cultivate in our societies. So
+our societies are not based on
+
+ align:start position:0%
+our societies are not based on
+ 
+
+ align:start position:0%
+our societies are not based on
+evolutionary principles in the sense
+
+ align:start position:0%
+evolutionary principles in the sense
+ 
+
+ align:start position:0%
+evolutionary principles in the sense
+that we're using those evolutionary
+
+ align:start position:0%
+that we're using those evolutionary
+ 
+
+ align:start position:0%
+that we're using those evolutionary
+principles to
+
+ align:start position:0%
+principles to
+ 
+
+ align:start position:0%
+principles to
+uh create the rules of the societ the
+
+ align:start position:0%
+uh create the rules of the societ the
+ 
+
+ align:start position:0%
+uh create the rules of the societ the
+behavior of the
+
+ align:start position:0%
+behavior of the
+ 
+
+ align:start position:0%
+behavior of the
+society. I don't know if this is all
+
+ align:start position:0%
+society. I don't know if this is all
+ 
+
+ align:start position:0%
+society. I don't know if this is all
+coming through. Maybe this this work is
+
+ align:start position:0%
+coming through. Maybe this this work is
+ 
+
+ align:start position:0%
+coming through. Maybe this this work is
+uh yeah Chris I think if we did apply
+
+ align:start position:0%
+uh yeah Chris I think if we did apply
+ 
+
+ align:start position:0%
+uh yeah Chris I think if we did apply
+Dar Darwin's principles to society we
+
+ align:start position:0%
+Dar Darwin's principles to society we
+ 
+
+ align:start position:0%
+Dar Darwin's principles to society we
+converge to a bunch of like type A
+
+ align:start position:0%
+converge to a bunch of like type A
+ 
+
+ align:start position:0%
+converge to a bunch of like type A
+individuals you know always on their
+
+ align:start position:0%
+individuals you know always on their
+ 
+
+ align:start position:0%
+individuals you know always on their
+blackberries always trying to produce as
+
+ align:start position:0%
+blackberries always trying to produce as
+ 
+
+ align:start position:0%
+blackberries always trying to produce as
+much trying to micromanage trying to
+
+ align:start position:0%
+much trying to micromanage trying to
+ 
+
+ align:start position:0%
+much trying to micromanage trying to
+produce as much as they can to gain as
+
+ align:start position:0%
+produce as much as they can to gain as
+ 
+
+ align:start position:0%
+produce as much as they can to gain as
+much revenue as they can and outlast
+
+ align:start position:0%
+much revenue as they can and outlast
+ 
+
+ align:start position:0%
+much revenue as they can and outlast
+everyone else.
+
+ align:start position:0%
+everyone else.
+ 
+
+ align:start position:0%
+everyone else.
+Okay. Uh well yeah maybe so uh but a lot
+
+ align:start position:0%
+Okay. Uh well yeah maybe so uh but a lot
+ 
+
+ align:start position:0%
+Okay. Uh well yeah maybe so uh but a lot
+of these people work within the rules
+
+ align:start position:0%
+of these people work within the rules
+ 
+
+ align:start position:0%
+of these people work within the rules
+you know within the laws. So we have a
+
+ align:start position:0%
+you know within the laws. So we have a
+ 
+
+ align:start position:0%
+you know within the laws. So we have a
+whole law we we have laws and a whole
+
+ align:start position:0%
+whole law we we have laws and a whole
+ 
+
+ align:start position:0%
+whole law we we have laws and a whole
+system of
+
+ align:start position:0%
+system of
+ 
+
+ align:start position:0%
+system of
+regulation of social behavior that we
+
+ align:start position:0%
+regulation of social behavior that we
+ 
+
+ align:start position:0%
+regulation of social behavior that we
+uh that we promulgate in order to
+
+ align:start position:0%
+uh that we promulgate in order to
+ 
+
+ align:start position:0%
+uh that we promulgate in order to
+avoid simply uh might makes right. I
+
+ align:start position:0%
+avoid simply uh might makes right. I
+ 
+
+ align:start position:0%
+avoid simply uh might makes right. I
+mean, might makes right in nature, does
+
+ align:start position:0%
+mean, might makes right in nature, does
+ 
+
+ align:start position:0%
+mean, might makes right in nature, does
+it not?
+
+ align:start position:0%
+it not?
+ 
+
+ align:start position:0%
+it not?
+Might is not supposed to make right in
+
+ align:start position:0%
+Might is not supposed to make right in
+ 
+
+ align:start position:0%
+Might is not supposed to make right in
+our society, is it?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's not supposed Yeah. Sometimes we
+
+ align:start position:0%
+It's not supposed Yeah. Sometimes we
+ 
+
+ align:start position:0%
+It's not supposed Yeah. Sometimes we
+wonder, but yeah, I'm going to disagree
+
+ align:start position:0%
+wonder, but yeah, I'm going to disagree
+ 
+
+ align:start position:0%
+wonder, but yeah, I'm going to disagree
+with pretty much everything that's been
+
+ align:start position:0%
+with pretty much everything that's been
+ 
+
+ align:start position:0%
+with pretty much everything that's been
+said in the last five minutes because I
+
+ align:start position:0%
+said in the last five minutes because I
+ 
+
+ align:start position:0%
+said in the last five minutes because I
+think our society is much closer than to
+
+ align:start position:0%
+think our society is much closer than to
+ 
+
+ align:start position:0%
+think our society is much closer than to
+this than we're willing to admit. We
+
+ align:start position:0%
+this than we're willing to admit. We
+ 
+
+ align:start position:0%
+this than we're willing to admit. We
+absolutely punish people for illness.
+
+ align:start position:0%
+absolutely punish people for illness.
+ 
+
+ align:start position:0%
+absolutely punish people for illness.
+Anytime someone is schizophrenic or
+
+ align:start position:0%
+Anytime someone is schizophrenic or
+ 
+
+ align:start position:0%
+Anytime someone is schizophrenic or
+bipolar or you know has this stuff we
+
+ align:start position:0%
+bipolar or you know has this stuff we
+ 
+
+ align:start position:0%
+bipolar or you know has this stuff we
+put them on drugs we lock them in
+
+ align:start position:0%
+put them on drugs we lock them in
+ 
+
+ align:start position:0%
+put them on drugs we lock them in
+hospitals if someone's underachieving
+
+ align:start position:0%
+hospitals if someone's underachieving
+ 
+
+ align:start position:0%
+hospitals if someone's underachieving
+they suddenly get punished not in a
+
+ align:start position:0%
+they suddenly get punished not in a
+ 
+
+ align:start position:0%
+they suddenly get punished not in a
+direct way but they absolutely get
+
+ align:start position:0%
+direct way but they absolutely get
+ 
+
+ align:start position:0%
+direct way but they absolutely get
+pushed down to a level of society that
+
+ align:start position:0%
+pushed down to a level of society that
+ 
+
+ align:start position:0%
+pushed down to a level of society that
+can absolutely be considered punishment
+
+ align:start position:0%
+can absolutely be considered punishment
+ 
+
+ align:start position:0%
+can absolutely be considered punishment
+we're not willing to look we don't want
+
+ align:start position:0%
+we're not willing to look we don't want
+ 
+
+ align:start position:0%
+we're not willing to look we don't want
+to look at our world and say that's it
+
+ align:start position:0%
+to look at our world and say that's it
+ 
+
+ align:start position:0%
+to look at our world and say that's it
+and so we can step aside but I will
+
+ align:start position:0%
+and so we can step aside but I will
+ 
+
+ align:start position:0%
+and so we can step aside but I will
+stand firm absolutely that we do this
+
+ align:start position:0%
+stand firm absolutely that we do this
+ 
+
+ align:start position:0%
+stand firm absolutely that we do this
+all the time well but there's punishment
+
+ align:start position:0%
+all the time well but there's punishment
+ 
+
+ align:start position:0%
+all the time well but there's punishment
+in the sense that they get like looked
+
+ align:start position:0%
+in the sense that they get like looked
+ 
+
+ align:start position:0%
+in the sense that they get like looked
+down on by society but it's not
+
+ align:start position:0%
+down on by society but it's not
+ 
+
+ align:start position:0%
+down on by society but it's not
+punishment and they don't actually
+
+ align:start position:0%
+punishment and they don't actually
+ 
+
+ align:start position:0%
+punishment and they don't actually
+reproduce. Well, how do you how do you
+
+ align:start position:0%
+reproduce. Well, how do you how do you
+ 
+
+ align:start position:0%
+reproduce. Well, how do you how do you
+want to make them because the thing is
+
+ align:start position:0%
+want to make them because the thing is
+ 
+
+ align:start position:0%
+want to make them because the thing is
+is you can change the metrics slightly,
+
+ align:start position:0%
+is you can change the metrics slightly,
+ 
+
+ align:start position:0%
+is you can change the metrics slightly,
+but once you can pick whatever you want,
+
+ align:start position:0%
+but once you can pick whatever you want,
+ 
+
+ align:start position:0%
+but once you can pick whatever you want,
+but we'll always have that kind that
+
+ align:start position:0%
+but we'll always have that kind that
+ 
+
+ align:start position:0%
+but we'll always have that kind that
+form of punishment. And one of the
+
+ align:start position:0%
+form of punishment. And one of the
+ 
+
+ align:start position:0%
+form of punishment. And one of the
+things is, you know, if you steal a
+
+ align:start position:0%
+things is, you know, if you steal a
+ 
+
+ align:start position:0%
+things is, you know, if you steal a
+watch that morals can be at least
+
+ align:start position:0%
+watch that morals can be at least
+ 
+
+ align:start position:0%
+watch that morals can be at least
+according to this this culture, morals
+
+ align:start position:0%
+according to this this culture, morals
+ 
+
+ align:start position:0%
+according to this this culture, morals
+are sculpted. Morals can be moved, but
+
+ align:start position:0%
+are sculpted. Morals can be moved, but
+ 
+
+ align:start position:0%
+are sculpted. Morals can be moved, but
+when you have genetic material, you
+
+ align:start position:0%
+when you have genetic material, you
+ 
+
+ align:start position:0%
+when you have genetic material, you
+can't change that. So, if someone's
+
+ align:start position:0%
+can't change that. So, if someone's
+ 
+
+ align:start position:0%
+can't change that. So, if someone's
+sick, lock them away because there's
+
+ align:start position:0%
+sick, lock them away because there's
+ 
+
+ align:start position:0%
+sick, lock them away because there's
+without technology, there's nothing we
+
+ align:start position:0%
+without technology, there's nothing we
+ 
+
+ align:start position:0%
+without technology, there's nothing we
+can do to fix that. But if we have a
+
+ align:start position:0%
+can do to fix that. But if we have a
+ 
+
+ align:start position:0%
+can do to fix that. But if we have a
+good, you know, upstanding moral code,
+
+ align:start position:0%
+good, you know, upstanding moral code,
+ 
+
+ align:start position:0%
+good, you know, upstanding moral code,
+we can send someone to a straightener
+
+ align:start position:0%
+we can send someone to a straightener
+ 
+
+ align:start position:0%
+we can send someone to a straightener
+and just correct their kind of cognitive
+
+ align:start position:0%
+and just correct their kind of cognitive
+ 
+
+ align:start position:0%
+and just correct their kind of cognitive
+structures to make everything better.
+
+ align:start position:0%
+structures to make everything better.
+ 
+
+ align:start position:0%
+structures to make everything better.
+With like with
+
+ align:start position:0%
+With like with
+ 
+
+ align:start position:0%
+With like with
+evolutionary punishment is like just in
+
+ align:start position:0%
+evolutionary punishment is like just in
+ 
+
+ align:start position:0%
+evolutionary punishment is like just in
+a singular sense not allowing somebody
+
+ align:start position:0%
+a singular sense not allowing somebody
+ 
+
+ align:start position:0%
+a singular sense not allowing somebody
+to reproduce. And there are plenty of
+
+ align:start position:0%
+to reproduce. And there are plenty of
+ 
+
+ align:start position:0%
+to reproduce. And there are plenty of
+like sickly individuals who if they were
+
+ align:start position:0%
+like sickly individuals who if they were
+ 
+
+ align:start position:0%
+like sickly individuals who if they were
+parts of herds out in nature, they
+
+ align:start position:0%
+parts of herds out in nature, they
+ 
+
+ align:start position:0%
+parts of herds out in nature, they
+wouldn't be allowed to reproduce and
+
+ align:start position:0%
+wouldn't be allowed to reproduce and
+ 
+
+ align:start position:0%
+wouldn't be allowed to reproduce and
+they wouldn't persist. But for us, we
+
+ align:start position:0%
+they wouldn't persist. But for us, we
+ 
+
+ align:start position:0%
+they wouldn't persist. But for us, we
+are allowed to. So I agree that yes,
+
+ align:start position:0%
+are allowed to. So I agree that yes,
+ 
+
+ align:start position:0%
+are allowed to. So I agree that yes,
+like sick certain sicknesses are
+
+ align:start position:0%
+like sick certain sicknesses are
+ 
+
+ align:start position:0%
+like sick certain sicknesses are
+punished in a certain sense, but if
+
+ align:start position:0%
+punished in a certain sense, but if
+ 
+
+ align:start position:0%
+punished in a certain sense, but if
+you're talking about like evolutionary
+
+ align:start position:0%
+you're talking about like evolutionary
+ 
+
+ align:start position:0%
+you're talking about like evolutionary
+mechanisms, I don't really think that we
+
+ align:start position:0%
+mechanisms, I don't really think that we
+ 
+
+ align:start position:0%
+mechanisms, I don't really think that we
+punish for that.
+
+ align:start position:0%
+punish for that.
+ 
+
+ align:start position:0%
+punish for that.
+Okay. Yeah. Well, you know, I I I I have
+
+ align:start position:0%
+Okay. Yeah. Well, you know, I I I I have
+ 
+
+ align:start position:0%
+Okay. Yeah. Well, you know, I I I I have
+to say uh I think you're both right
+
+ align:start position:0%
+to say uh I think you're both right
+ 
+
+ align:start position:0%
+to say uh I think you're both right
+because this is what this is what
+
+ align:start position:0%
+because this is what this is what
+ 
+
+ align:start position:0%
+because this is what this is what
+Butler's trying to do. He's trying to
+
+ align:start position:0%
+Butler's trying to do. He's trying to
+ 
+
+ align:start position:0%
+Butler's trying to do. He's trying to
+make us think a little more deeply about
+
+ align:start position:0%
+make us think a little more deeply about
+ 
+
+ align:start position:0%
+make us think a little more deeply about
+how people really do behave. the
+
+ align:start position:0%
+how people really do behave. the
+ 
+
+ align:start position:0%
+how people really do behave. the
+development of eugenics in the 19th
+
+ align:start position:0%
+development of eugenics in the 19th
+ 
+
+ align:start position:0%
+development of eugenics in the 19th
+century. Uh so we're we're we're
+
+ align:start position:0%
+century. Uh so we're we're we're
+ 
+
+ align:start position:0%
+century. Uh so we're we're we're
+starting we're we're getting in this
+
+ align:start position:0%
+starting we're we're getting in this
+ 
+
+ align:start position:0%
+starting we're we're getting in this
+book is taking us into that
+
+ align:start position:0%
+book is taking us into that
+ 
+
+ align:start position:0%
+book is taking us into that
+territory. It's a it's a satire. So it's
+
+ align:start position:0%
+territory. It's a it's a satire. So it's
+ 
+
+ align:start position:0%
+territory. It's a it's a satire. So it's
+you know he's not recommending anything
+
+ align:start position:0%
+you know he's not recommending anything
+ 
+
+ align:start position:0%
+you know he's not recommending anything
+in this book. It's just it's a book to
+
+ align:start position:0%
+in this book. It's just it's a book to
+ 
+
+ align:start position:0%
+in this book. It's just it's a book to
+try to make you think to make you think
+
+ align:start position:0%
+try to make you think to make you think
+ 
+
+ align:start position:0%
+try to make you think to make you think
+about you know what is the base of your
+
+ align:start position:0%
+about you know what is the base of your
+ 
+
+ align:start position:0%
+about you know what is the base of your
+society. Is your society
+
+ align:start position:0%
+society. Is your society
+ 
+
+ align:start position:0%
+society. Is your society
+uh entirely a natural thing, an
+
+ align:start position:0%
+uh entirely a natural thing, an
+ 
+
+ align:start position:0%
+uh entirely a natural thing, an
+expression of natural principles, or is
+
+ align:start position:0%
+expression of natural principles, or is
+ 
+
+ align:start position:0%
+expression of natural principles, or is
+it something quite
+
+ align:start position:0%
+it something quite
+ 
+
+ align:start position:0%
+it something quite
+different? It's an effort to
+
+ align:start position:0%
+different? It's an effort to
+ 
+
+ align:start position:0%
+different? It's an effort to
+fight the the the world or to resist
+
+ align:start position:0%
+fight the the the world or to resist
+ 
+
+ align:start position:0%
+fight the the the world or to resist
+becoming part of this natural
+
+ align:start position:0%
+becoming part of this natural
+ 
+
+ align:start position:0%
+becoming part of this natural
+world that Darwin had painted with such
+
+ align:start position:0%
+world that Darwin had painted with such
+ 
+
+ align:start position:0%
+world that Darwin had painted with such
+force and compelling.
+
+ align:start position:0%
+force and compelling.
+ 
+
+ align:start position:0%
+force and compelling.
+uh uh
+
+ align:start position:0%
+uh uh
+ 
+
+ align:start position:0%
+uh uh
+detail. And so Butler is saying, "Okay,
+
+ align:start position:0%
+detail. And so Butler is saying, "Okay,
+ 
+
+ align:start position:0%
+detail. And so Butler is saying, "Okay,
+that world exists out there." But is
+
+ align:start position:0%
+that world exists out there." But is
+ 
+
+ align:start position:0%
+that world exists out there." But is
+that the world in which we exist? Are we
+
+ align:start position:0%
+that the world in which we exist? Are we
+ 
+
+ align:start position:0%
+that the world in which we exist? Are we
+trying to create that, recreate that
+
+ align:start position:0%
+trying to create that, recreate that
+ 
+
+ align:start position:0%
+trying to create that, recreate that
+world? And I agree with Devon. I I I I
+
+ align:start position:0%
+world? And I agree with Devon. I I I I
+ 
+
+ align:start position:0%
+world? And I agree with Devon. I I I I
+think I think his answer is highly
+
+ align:start position:0%
+think I think his answer is highly
+ 
+
+ align:start position:0%
+think I think his answer is highly
+ambiguous because yes, ostensibly we
+
+ align:start position:0%
+ambiguous because yes, ostensibly we
+ 
+
+ align:start position:0%
+ambiguous because yes, ostensibly we
+fight against what we call
+
+ align:start position:0%
+fight against what we call
+ 
+
+ align:start position:0%
+fight against what we call
+injustice. You know, the punishment of
+
+ align:start position:0%
+injustice. You know, the punishment of
+ 
+
+ align:start position:0%
+injustice. You know, the punishment of
+the weak and you know, holding people
+
+ align:start position:0%
+the weak and you know, holding people
+ 
+
+ align:start position:0%
+the weak and you know, holding people
+who are unfortunate to uh uh in in some
+
+ align:start position:0%
+who are unfortunate to uh uh in in some
+ 
+
+ align:start position:0%
+who are unfortunate to uh uh in in some
+way as as responsible for their
+
+ align:start position:0%
+way as as responsible for their
+ 
+
+ align:start position:0%
+way as as responsible for their
+misfortunes.
+
+ align:start position:0%
+misfortunes.
+ 
+
+ align:start position:0%
+misfortunes.
+But there there are it's it's not just
+
+ align:start position:0%
+But there there are it's it's not just
+ 
+
+ align:start position:0%
+But there there are it's it's not just
+that simple. There there are other
+
+ align:start position:0%
+that simple. There there are other
+ 
+
+ align:start position:0%
+that simple. There there are other
+elements that we still express in spite
+
+ align:start position:0%
+elements that we still express in spite
+ 
+
+ align:start position:0%
+elements that we still express in spite
+of ourselves or in spite of, you know,
+
+ align:start position:0%
+of ourselves or in spite of, you know,
+ 
+
+ align:start position:0%
+of ourselves or in spite of, you know,
+the the ideals that we espouse with our
+
+ align:start position:0%
+the the ideals that we espouse with our
+ 
+
+ align:start position:0%
+the the ideals that we espouse with our
+our laws and our social and our
+
+ align:start position:0%
+our laws and our social and our
+ 
+
+ align:start position:0%
+our laws and our social and our
+religious principles.
+
+ align:start position:0%
+religious principles.
+ 
+
+ align:start position:0%
+religious principles.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+so he's not arguing for he's just trying
+
+ align:start position:0%
+so he's not arguing for he's just trying
+ 
+
+ align:start position:0%
+so he's not arguing for he's just trying
+to make you think about this and and
+
+ align:start position:0%
+to make you think about this and and
+ 
+
+ align:start position:0%
+to make you think about this and and
+sift through the world you live in and
+
+ align:start position:0%
+sift through the world you live in and
+ 
+
+ align:start position:0%
+sift through the world you live in and
+try to understand it in a little more
+
+ align:start position:0%
+try to understand it in a little more
+ 
+
+ align:start position:0%
+try to understand it in a little more
+complex
+
+ align:start position:0%
+complex
+ 
+
+ align:start position:0%
+complex
+way. So why why are these people so down
+
+ align:start position:0%
+way. So why why are these people so down
+ 
+
+ align:start position:0%
+way. So why why are these people so down
+on machines? What is it about machines
+
+ align:start position:0%
+on machines? What is it about machines
+ 
+
+ align:start position:0%
+on machines? What is it about machines
+that they think compromises their
+
+ align:start position:0%
+that they think compromises their
+ 
+
+ align:start position:0%
+that they think compromises their
+society? Because they you know they find
+
+ align:start position:0%
+society? Because they you know they find
+ 
+
+ align:start position:0%
+society? Because they you know they find
+his watch and he gets thrown in jail.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And he he he can't resist uh mentioning
+
+ align:start position:0%
+And he he he can't resist uh mentioning
+ 
+
+ align:start position:0%
+And he he he can't resist uh mentioning
+Paley says uh Paley said that uh even
+
+ align:start position:0%
+Paley says uh Paley said that uh even
+ 
+
+ align:start position:0%
+Paley says uh Paley said that uh even
+quote a savage who saw this watch would
+
+ align:start position:0%
+quote a savage who saw this watch would
+ 
+
+ align:start position:0%
+quote a savage who saw this watch would
+know it was made by you know some some
+
+ align:start position:0%
+know it was made by you know some some
+ 
+
+ align:start position:0%
+know it was made by you know some some
+deliberate force and so on and so forth.
+
+ align:start position:0%
+deliberate force and so on and so forth.
+ 
+
+ align:start position:0%
+deliberate force and so on and so forth.
+Why why are these people why is this
+
+ align:start position:0%
+Why why are these people why is this
+ 
+
+ align:start position:0%
+Why why are these people why is this
+culture so afraid of watches? Kevin uh
+
+ align:start position:0%
+culture so afraid of watches? Kevin uh
+ 
+
+ align:start position:0%
+culture so afraid of watches? Kevin uh
+to pull out a quote. I learned about
+
+ align:start position:0%
+to pull out a quote. I learned about
+ 
+
+ align:start position:0%
+to pull out a quote. I learned about
+four that 400 years previously the state
+
+ align:start position:0%
+four that 400 years previously the state
+ 
+
+ align:start position:0%
+four that 400 years previously the state
+of mechanical knowledge was so far
+
+ align:start position:0%
+of mechanical knowledge was so far
+ 
+
+ align:start position:0%
+of mechanical knowledge was so far
+beyond our own and was so adv advancing
+
+ align:start position:0%
+beyond our own and was so adv advancing
+ 
+
+ align:start position:0%
+beyond our own and was so adv advancing
+uh until one of the most learned
+
+ align:start position:0%
+uh until one of the most learned
+ 
+
+ align:start position:0%
+uh until one of the most learned
+professors of hypothetics wrote an
+
+ align:start position:0%
+professors of hypothetics wrote an
+ 
+
+ align:start position:0%
+professors of hypothetics wrote an
+extraordinary book from which I proposed
+
+ align:start position:0%
+extraordinary book from which I proposed
+ 
+
+ align:start position:0%
+extraordinary book from which I proposed
+to give extracts later on proving that
+
+ align:start position:0%
+to give extracts later on proving that
+ 
+
+ align:start position:0%
+to give extracts later on proving that
+machines were ultimately destined to
+
+ align:start position:0%
+machines were ultimately destined to
+ 
+
+ align:start position:0%
+machines were ultimately destined to
+supplant the race of man and to become
+
+ align:start position:0%
+supplant the race of man and to become
+ 
+
+ align:start position:0%
+supplant the race of man and to become
+uh to become uh instinct in the vitality
+
+ align:start position:0%
+uh to become uh instinct in the vitality
+ 
+
+ align:start position:0%
+uh to become uh instinct in the vitality
+of it different form and superior to
+
+ align:start position:0%
+of it different form and superior to
+ 
+
+ align:start position:0%
+of it different form and superior to
+that of animals as animals and vegetable
+
+ align:start position:0%
+that of animals as animals and vegetable
+ 
+
+ align:start position:0%
+that of animals as animals and vegetable
+life. So, okay, prophet wrote a book
+
+ align:start position:0%
+life. So, okay, prophet wrote a book
+ 
+
+ align:start position:0%
+life. So, okay, prophet wrote a book
+that is that is the the mad professor
+
+ align:start position:0%
+that is that is the the mad professor
+ 
+
+ align:start position:0%
+that is that is the the mad professor
+who we're going to read his his his his
+
+ align:start position:0%
+who we're going to read his his his his
+ 
+
+ align:start position:0%
+who we're going to read his his his his
+uh his theories for the next class
+
+ align:start position:0%
+uh his theories for the next class
+ 
+
+ align:start position:0%
+uh his theories for the next class
+because he has this whole theory about
+
+ align:start position:0%
+because he has this whole theory about
+ 
+
+ align:start position:0%
+because he has this whole theory about
+these machines having the
+
+ align:start position:0%
+these machines having the
+ 
+
+ align:start position:0%
+these machines having the
+capacity to
+
+ align:start position:0%
+capacity to
+ 
+
+ align:start position:0%
+capacity to
+evolve. They don't necessarily do it all
+
+ align:start position:0%
+evolve. They don't necessarily do it all
+ 
+
+ align:start position:0%
+evolve. They don't necessarily do it all
+by themselves but they have help from
+
+ align:start position:0%
+by themselves but they have help from
+ 
+
+ align:start position:0%
+by themselves but they have help from
+humans. But you know there are many
+
+ align:start position:0%
+humans. But you know there are many
+ 
+
+ align:start position:0%
+humans. But you know there are many
+examples in nature where other organisms
+
+ align:start position:0%
+examples in nature where other organisms
+ 
+
+ align:start position:0%
+examples in nature where other organisms
+help uh other organisms uh
+
+ align:start position:0%
+help uh other organisms uh
+ 
+
+ align:start position:0%
+help uh other organisms uh
+u
+
+ align:start position:0%
+u
+ 
+
+ align:start position:0%
+u
+reproduce. So we're going to get into
+
+ align:start position:0%
+reproduce. So we're going to get into
+ 
+
+ align:start position:0%
+reproduce. So we're going to get into
+that in in a big way for next class. But
+
+ align:start position:0%
+that in in a big way for next class. But
+ 
+
+ align:start position:0%
+that in in a big way for next class. But
+that's that's part of it. So they're
+
+ align:start position:0%
+that's that's part of it. So they're
+ 
+
+ align:start position:0%
+that's that's part of it. So they're
+potential
+
+ align:start position:0%
+potential
+ 
+
+ align:start position:0%
+potential
+competition. What are these machines
+
+ align:start position:0%
+competition. What are these machines
+ 
+
+ align:start position:0%
+competition. What are these machines
+also doing as far as the fitness of the
+
+ align:start position:0%
+also doing as far as the fitness of the
+ 
+
+ align:start position:0%
+also doing as far as the fitness of the
+individual?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do machines do machines have any
+
+ align:start position:0%
+What do machines do machines have any
+ 
+
+ align:start position:0%
+What do machines do machines have any
+impact on the uh the fitness of the
+
+ align:start position:0%
+impact on the uh the fitness of the
+ 
+
+ align:start position:0%
+impact on the uh the fitness of the
+individual? Jennifer,
+
+ align:start position:0%
+individual? Jennifer,
+ 
+
+ align:start position:0%
+individual? Jennifer,
+um feel like they're kind of like a way
+
+ align:start position:0%
+um feel like they're kind of like a way
+ 
+
+ align:start position:0%
+um feel like they're kind of like a way
+of like cheating yet. I mean, as I've
+
+ align:start position:0%
+of like cheating yet. I mean, as I've
+ 
+
+ align:start position:0%
+of like cheating yet. I mean, as I've
+said to you, if I don't have my
+
+ align:start position:0%
+said to you, if I don't have my
+ 
+
+ align:start position:0%
+said to you, if I don't have my
+glasses and I live in a a world that uh
+
+ align:start position:0%
+glasses and I live in a a world that uh
+ 
+
+ align:start position:0%
+glasses and I live in a a world that uh
+you know, so these allow
+
+ align:start position:0%
+you know, so these allow
+ 
+
+ align:start position:0%
+you know, so these allow
+me to survive on a
+
+ align:start position:0%
+me to survive on a
+ 
+
+ align:start position:0%
+me to survive on a
+par with other people,
+
+ align:start position:0%
+par with other people,
+ 
+
+ align:start position:0%
+par with other people,
+but what happens to my offspring
+
+ align:start position:0%
+but what happens to my offspring
+ 
+
+ align:start position:0%
+but what happens to my offspring
+potentially?
+
+ align:start position:0%
+potentially?
+ 
+
+ align:start position:0%
+potentially?
+Yes. Then they also like wouldn't be
+
+ align:start position:0%
+Yes. Then they also like wouldn't be
+ 
+
+ align:start position:0%
+Yes. Then they also like wouldn't be
+able to see it. So I feel like the more
+
+ align:start position:0%
+able to see it. So I feel like the more
+ 
+
+ align:start position:0%
+able to see it. So I feel like the more
+you have to rely on machines, the less
+
+ align:start position:0%
+you have to rely on machines, the less
+ 
+
+ align:start position:0%
+you have to rely on machines, the less
+fit you have to be. So it's kind of
+
+ align:start position:0%
+fit you have to be. So it's kind of
+ 
+
+ align:start position:0%
+fit you have to be. So it's kind of
+Absolutely. Absolutely. So more
+
+ align:start position:0%
+Absolutely. Absolutely. So more
+ 
+
+ align:start position:0%
+Absolutely. Absolutely. So more
+machines, less fit. That's why the
+
+ align:start position:0%
+machines, less fit. That's why the
+ 
+
+ align:start position:0%
+machines, less fit. That's why the
+Armonians are so upset about machines
+
+ align:start position:0%
+Armonians are so upset about machines
+ 
+
+ align:start position:0%
+Armonians are so upset about machines
+because they're trying to emulate
+
+ align:start position:0%
+because they're trying to emulate
+ 
+
+ align:start position:0%
+because they're trying to emulate
+nature. Uh and machines allow less fit
+
+ align:start position:0%
+nature. Uh and machines allow less fit
+ 
+
+ align:start position:0%
+nature. Uh and machines allow less fit
+people to operate on a
+
+ align:start position:0%
+people to operate on a
+ 
+
+ align:start position:0%
+people to operate on a
+par. So they get rid of machines.
+
+ align:start position:0%
+par. So they get rid of machines.
+ 
+
+ align:start position:0%
+par. So they get rid of machines.
+Uh
+
+ align:start position:0%
+Uh
+ 
+
+ align:start position:0%
+Uh
+okay. So this is a society with a
+
+ align:start position:0%
+okay. So this is a society with a
+ 
+
+ align:start position:0%
+okay. So this is a society with a
+vengeance trying to uh just uh adopt the
+
+ align:start position:0%
+vengeance trying to uh just uh adopt the
+ 
+
+ align:start position:0%
+vengeance trying to uh just uh adopt the
+principles of uh uh natural selection in
+
+ align:start position:0%
+principles of uh uh natural selection in
+ 
+
+ align:start position:0%
+principles of uh uh natural selection in
+the natural world as the
+
+ align:start position:0%
+the natural world as the
+ 
+
+ align:start position:0%
+the natural world as the
+code for their social and cultural
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+behavior. And you can see what the
+
+ align:start position:0%
+behavior. And you can see what the
+ 
+
+ align:start position:0%
+behavior. And you can see what the
+results
+
+ align:start position:0%
+results
+ 
+
+ align:start position:0%
+results
+are. They're very very beautiful.
+
+ align:start position:0%
+are. They're very very beautiful.
+ 
+
+ align:start position:0%
+are. They're very very beautiful.
+Remember what he says. They all look
+
+ align:start position:0%
+Remember what he says. They all look
+ 
+
+ align:start position:0%
+Remember what he says. They all look
+like they're and you know if somebody's
+
+ align:start position:0%
+like they're and you know if somebody's
+ 
+
+ align:start position:0%
+like they're and you know if somebody's
+ill, they don't tell
+
+ align:start position:0%
+ill, they don't tell
+ 
+
+ align:start position:0%
+ill, they don't tell
+anybody. You want somebody to know that
+
+ align:start position:0%
+anybody. You want somebody to know that
+ 
+
+ align:start position:0%
+anybody. You want somebody to know that
+you're ill because uh that exposes you
+
+ align:start position:0%
+you're ill because uh that exposes you
+ 
+
+ align:start position:0%
+you're ill because uh that exposes you
+to their, you know, judgment and you may
+
+ align:start position:0%
+to their, you know, judgment and you may
+ 
+
+ align:start position:0%
+to their, you know, judgment and you may
+ultimately find yourself uh in the
+
+ align:start position:0%
+ultimately find yourself uh in the
+ 
+
+ align:start position:0%
+ultimately find yourself uh in the
+docket in
+
+ align:start position:0%
+docket in
+ 
+
+ align:start position:0%
+docket in
+court, personal bere bereavement court.
+
+ align:start position:0%
+court, personal bere bereavement court.
+ 
+
+ align:start position:0%
+court, personal bere bereavement court.
+that young man whose wife
+
+ align:start position:0%
+that young man whose wife
+ 
+
+ align:start position:0%
+that young man whose wife
+died. He what did he have to argue in
+
+ align:start position:0%
+died. He what did he have to argue in
+ 
+
+ align:start position:0%
+died. He what did he have to argue in
+order to get some kind of uh uh uh
+
+ align:start position:0%
+order to get some kind of uh uh uh
+ 
+
+ align:start position:0%
+order to get some kind of uh uh uh
+better sentence from the court?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+remember he said a uh the court said an
+
+ align:start position:0%
+remember he said a uh the court said an
+ 
+
+ align:start position:0%
+remember he said a uh the court said an
+extenduating circumstance was that he
+
+ align:start position:0%
+extenduating circumstance was that he
+ 
+
+ align:start position:0%
+extenduating circumstance was that he
+took out an insurance policy on his wife
+
+ align:start position:0%
+took out an insurance policy on his wife
+ 
+
+ align:start position:0%
+took out an insurance policy on his wife
+before so therefore he had a little bit
+
+ align:start position:0%
+before so therefore he had a little bit
+ 
+
+ align:start position:0%
+before so therefore he had a little bit
+of luck and so he didn't get punished
+
+ align:start position:0%
+of luck and so he didn't get punished
+ 
+
+ align:start position:0%
+of luck and so he didn't get punished
+quite as severely. So, you know, it's
+
+ align:start position:0%
+quite as severely. So, you know, it's
+ 
+
+ align:start position:0%
+quite as severely. So, you know, it's
+it's it's weird fascinating stuff, but
+
+ align:start position:0%
+it's it's weird fascinating stuff, but
+ 
+
+ align:start position:0%
+it's it's weird fascinating stuff, but
+you see what's happening here is
+
+ align:start position:0%
+you see what's happening here is
+ 
+
+ align:start position:0%
+you see what's happening here is
+Butler's playing with
+
+ align:start position:0%
+Butler's playing with
+ 
+
+ align:start position:0%
+Butler's playing with
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+social kind of
+
+ align:start position:0%
+social kind of
+ 
+
+ align:start position:0%
+social kind of
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+platitudes of his time and he's saying,
+
+ align:start position:0%
+platitudes of his time and he's saying,
+ 
+
+ align:start position:0%
+platitudes of his time and he's saying,
+you know, if you look underneath these,
+
+ align:start position:0%
+you know, if you look underneath these,
+ 
+
+ align:start position:0%
+you know, if you look underneath these,
+it's it's it's a lot more complex than
+
+ align:start position:0%
+it's it's it's a lot more complex than
+ 
+
+ align:start position:0%
+it's it's it's a lot more complex than
+people like to think.
+
+ align:start position:0%
+people like to think.
+ 
+
+ align:start position:0%
+people like to think.
+Um so this uh personal bereavement court
+
+ align:start position:0%
+Um so this uh personal bereavement court
+ 
+
+ align:start position:0%
+Um so this uh personal bereavement court
+uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+um well men Victorian England has
+
+ align:start position:0%
+um well men Victorian England has
+ 
+
+ align:start position:0%
+um well men Victorian England has
+developed partially out of this this
+
+ align:start position:0%
+developed partially out of this this
+ 
+
+ align:start position:0%
+developed partially out of this this
+tradition of
+
+ align:start position:0%
+tradition of
+ 
+
+ align:start position:0%
+tradition of
+uh natural naturalism if you will
+
+ align:start position:0%
+uh natural naturalism if you will
+ 
+
+ align:start position:0%
+uh natural naturalism if you will
+uh a a set of a series of developments
+
+ align:start position:0%
+uh a a set of a series of developments
+ 
+
+ align:start position:0%
+uh a a set of a series of developments
+that uh ultimately ely collected into
+
+ align:start position:0%
+that uh ultimately ely collected into
+ 
+
+ align:start position:0%
+that uh ultimately ely collected into
+what you could say loosely was a
+
+ align:start position:0%
+what you could say loosely was a
+ 
+
+ align:start position:0%
+what you could say loosely was a
+eugenical movement. Um and in some ways
+
+ align:start position:0%
+eugenical movement. Um and in some ways
+ 
+
+ align:start position:0%
+eugenical movement. Um and in some ways
+Butler's Butler identifies
+
+ align:start position:0%
+Butler's Butler identifies
+ 
+
+ align:start position:0%
+Butler's Butler identifies
+uh the the the one of the core concepts
+
+ align:start position:0%
+uh the the the one of the core concepts
+ 
+
+ align:start position:0%
+uh the the the one of the core concepts
+of eugenic thinking which is
+
+ align:start position:0%
+of eugenic thinking which is
+ 
+
+ align:start position:0%
+of eugenic thinking which is
+what what concepts that he
+
+ align:start position:0%
+what what concepts that he
+ 
+
+ align:start position:0%
+what what concepts that he
+develops is at the core of eugenics.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I guess that you can make a perfect by
+
+ align:start position:0%
+I guess that you can make a perfect by
+ 
+
+ align:start position:0%
+I guess that you can make a perfect by
+only allowing people who exhibit traits
+
+ align:start position:0%
+only allowing people who exhibit traits
+ 
+
+ align:start position:0%
+only allowing people who exhibit traits
+of expertise. Yeah.
+
+ align:start position:0%
+of expertise. Yeah.
+ 
+
+ align:start position:0%
+of expertise. Yeah.
+That through social policies and various
+
+ align:start position:0%
+That through social policies and various
+ 
+
+ align:start position:0%
+That through social policies and various
+kinds of uh
+
+ align:start position:0%
+kinds of uh
+ 
+
+ align:start position:0%
+kinds of uh
+top-down
+
+ align:start position:0%
+top-down
+ 
+
+ align:start position:0%
+top-down
+principles you can steer the
+
+ align:start position:0%
+principles you can steer the
+ 
+
+ align:start position:0%
+principles you can steer the
+society toward a greater average health
+
+ align:start position:0%
+society toward a greater average health
+ 
+
+ align:start position:0%
+society toward a greater average health
+and capacity.
+
+ align:start position:0%
+and capacity.
+ 
+
+ align:start position:0%
+and capacity.
+So the selection of of uh of uh of the
+
+ align:start position:0%
+So the selection of of uh of uh of the
+ 
+
+ align:start position:0%
+So the selection of of uh of uh of the
+the the best and the brightest if you
+
+ align:start position:0%
+the the best and the brightest if you
+ 
+
+ align:start position:0%
+the the best and the brightest if you
+will put it in short
+
+ align:start position:0%
+will put it in short
+ 
+
+ align:start position:0%
+will put it in short
+end. Eugenicists were
+
+ align:start position:0%
+end. Eugenicists were
+ 
+
+ align:start position:0%
+end. Eugenicists were
+concerned
+
+ align:start position:0%
+concerned
+ 
+
+ align:start position:0%
+concerned
+that contemporary
+
+ align:start position:0%
+that contemporary
+ 
+
+ align:start position:0%
+that contemporary
+societies in to the extent that
+
+ align:start position:0%
+societies in to the extent that
+ 
+
+ align:start position:0%
+societies in to the extent that
+they promulgated the principles of
+
+ align:start position:0%
+they promulgated the principles of
+ 
+
+ align:start position:0%
+they promulgated the principles of
+treatment, equal treatment of people and
+
+ align:start position:0%
+treatment, equal treatment of people and
+ 
+
+ align:start position:0%
+treatment, equal treatment of people and
+and the laws which protected people who
+
+ align:start position:0%
+and the laws which protected people who
+ 
+
+ align:start position:0%
+and the laws which protected people who
+were
+
+ align:start position:0%
+were
+ 
+
+ align:start position:0%
+were
+vulnerable were the eugenicists were
+
+ align:start position:0%
+vulnerable were the eugenicists were
+ 
+
+ align:start position:0%
+vulnerable were the eugenicists were
+concerned that this
+
+ align:start position:0%
+concerned that this
+ 
+
+ align:start position:0%
+concerned that this
+was leading toward weak weaker
+
+ align:start position:0%
+was leading toward weak weaker
+ 
+
+ align:start position:0%
+was leading toward weak weaker
+populations in the sense of
+
+ align:start position:0%
+populations in the sense of
+ 
+
+ align:start position:0%
+populations in the sense of
+Butler because you know on the sheep on
+
+ align:start position:0%
+Butler because you know on the sheep on
+ 
+
+ align:start position:0%
+Butler because you know on the sheep on
+the sheep farm you really do you you
+
+ align:start position:0%
+the sheep farm you really do you you
+ 
+
+ align:start position:0%
+the sheep farm you really do you you
+select the strongest to breed and you
+
+ align:start position:0%
+select the strongest to breed and you
+ 
+
+ align:start position:0%
+select the strongest to breed and you
+know you get a better herd and you just
+
+ align:start position:0%
+know you get a better herd and you just
+ 
+
+ align:start position:0%
+know you get a better herd and you just
+keep doing that and eventually your her
+
+ align:start position:0%
+keep doing that and eventually your her
+ 
+
+ align:start position:0%
+keep doing that and eventually your her
+gets better and better. And so
+
+ align:start position:0%
+gets better and better. And so
+ 
+
+ align:start position:0%
+gets better and better. And so
+eugenicis were
+
+ align:start position:0%
+eugenicis were
+ 
+
+ align:start position:0%
+eugenicis were
+aware that one way of thinking about
+
+ align:start position:0%
+aware that one way of thinking about
+ 
+
+ align:start position:0%
+aware that one way of thinking about
+society would be to try to find ways
+
+ align:start position:0%
+society would be to try to find ways
+ 
+
+ align:start position:0%
+society would be to try to find ways
+to use those
+
+ align:start position:0%
+to use those
+ 
+
+ align:start position:0%
+to use those
+principles.
+
+ align:start position:0%
+principles.
+ 
+
+ align:start position:0%
+principles.
+Um now this as I as I keep saying this
+
+ align:start position:0%
+Um now this as I as I keep saying this
+ 
+
+ align:start position:0%
+Um now this as I as I keep saying this
+is not what Butler is advocating. It's
+
+ align:start position:0%
+is not what Butler is advocating. It's
+ 
+
+ align:start position:0%
+is not what Butler is advocating. It's
+just he's trying to get you to think
+
+ align:start position:0%
+just he's trying to get you to think
+ 
+
+ align:start position:0%
+just he's trying to get you to think
+along these lines so that you understand
+
+ align:start position:0%
+along these lines so that you understand
+ 
+
+ align:start position:0%
+along these lines so that you understand
+some of the implications of it.
+
+ align:start position:0%
+some of the implications of it.
+ 
+
+ align:start position:0%
+some of the implications of it.
+I mean, when you see this poor man with
+
+ align:start position:0%
+I mean, when you see this poor man with
+ 
+
+ align:start position:0%
+I mean, when you see this poor man with
+pulmonary consumption being sentenced to
+
+ align:start position:0%
+pulmonary consumption being sentenced to
+ 
+
+ align:start position:0%
+pulmonary consumption being sentenced to
+hard labor, you realize how absurd it
+
+ align:start position:0%
+hard labor, you realize how absurd it
+ 
+
+ align:start position:0%
+hard labor, you realize how absurd it
+is.
+
+ align:start position:0%
+is.
+ 
+
+ align:start position:0%
+is.
+However, he's tricked you into thinking
+
+ align:start position:0%
+However, he's tricked you into thinking
+ 
+
+ align:start position:0%
+However, he's tricked you into thinking
+about the cost of
+
+ align:start position:0%
+about the cost of
+ 
+
+ align:start position:0%
+about the cost of
+that. And the cost of that is, you know,
+
+ align:start position:0%
+that. And the cost of that is, you know,
+ 
+
+ align:start position:0%
+that. And the cost of that is, you know,
+uh that, you know, there's this this
+
+ align:start position:0%
+uh that, you know, there's this this
+ 
+
+ align:start position:0%
+uh that, you know, there's this this
+other
+
+ align:start position:0%
+other
+ 
+
+ align:start position:0%
+other
+side. So there was a lot of uh there was
+
+ align:start position:0%
+side. So there was a lot of uh there was
+ 
+
+ align:start position:0%
+side. So there was a lot of uh there was
+a lot of um sort of eugenical thinking
+
+ align:start position:0%
+a lot of um sort of eugenical thinking
+ 
+
+ align:start position:0%
+a lot of um sort of eugenical thinking
+that developed in mid Victorian England.
+
+ align:start position:0%
+that developed in mid Victorian England.
+ 
+
+ align:start position:0%
+that developed in mid Victorian England.
+And Darwin was not a gen eugenicist, but
+
+ align:start position:0%
+And Darwin was not a gen eugenicist, but
+ 
+
+ align:start position:0%
+And Darwin was not a gen eugenicist, but
+his cousin Francis Golton who was pretty
+
+ align:start position:0%
+his cousin Francis Golton who was pretty
+ 
+
+ align:start position:0%
+his cousin Francis Golton who was pretty
+influential and was a a brilliant
+
+ align:start position:0%
+influential and was a a brilliant
+ 
+
+ align:start position:0%
+influential and was a a brilliant
+u uh
+
+ align:start position:0%
+u uh
+ 
+
+ align:start position:0%
+u uh
+thinker was one of the pioneers of
+
+ align:start position:0%
+thinker was one of the pioneers of
+ 
+
+ align:start position:0%
+thinker was one of the pioneers of
+eugenics and u he was one of the first
+
+ align:start position:0%
+eugenics and u he was one of the first
+ 
+
+ align:start position:0%
+eugenics and u he was one of the first
+uh Gton was a
+
+ align:start position:0%
+uh Gton was a
+ 
+
+ align:start position:0%
+uh Gton was a
+statistician. He was fascinated with uh
+
+ align:start position:0%
+statistician. He was fascinated with uh
+ 
+
+ align:start position:0%
+statistician. He was fascinated with uh
+the metrics of uh humans, understanding
+
+ align:start position:0%
+the metrics of uh humans, understanding
+ 
+
+ align:start position:0%
+the metrics of uh humans, understanding
+humans in a statistical metrical way.
+
+ align:start position:0%
+humans in a statistical metrical way.
+ 
+
+ align:start position:0%
+humans in a statistical metrical way.
+Uh the person
+
+ align:start position:0%
+Uh the person
+ 
+
+ align:start position:0%
+Uh the person
+who developed the the the system for
+
+ align:start position:0%
+who developed the the the system for
+ 
+
+ align:start position:0%
+who developed the the the system for
+fingerprinting, identifying unique
+
+ align:start position:0%
+fingerprinting, identifying unique
+ 
+
+ align:start position:0%
+fingerprinting, identifying unique
+individuals through fingerprints, he was
+
+ align:start position:0%
+individuals through fingerprints, he was
+ 
+
+ align:start position:0%
+individuals through fingerprints, he was
+really into this stuff. uh uh and he was
+
+ align:start position:0%
+really into this stuff. uh uh and he was
+ 
+
+ align:start position:0%
+really into this stuff. uh uh and he was
+quite interested in the whole idea that
+
+ align:start position:0%
+quite interested in the whole idea that
+ 
+
+ align:start position:0%
+quite interested in the whole idea that
+levels of
+
+ align:start position:0%
+levels of
+ 
+
+ align:start position:0%
+levels of
+intelligence high intelligence
+
+ align:start position:0%
+intelligence high intelligence
+ 
+
+ align:start position:0%
+intelligence high intelligence
+were transported down through the
+
+ align:start position:0%
+were transported down through the
+ 
+
+ align:start position:0%
+were transported down through the
+generations and families.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+He wrote a book called inherit
+
+ align:start position:0%
+He wrote a book called inherit
+ 
+
+ align:start position:0%
+He wrote a book called inherit
+hereditary
+
+ align:start position:0%
+hereditary
+ 
+
+ align:start position:0%
+hereditary
+genius in which uh he studied uh members
+
+ align:start position:0%
+genius in which uh he studied uh members
+ 
+
+ align:start position:0%
+genius in which uh he studied uh members
+of great science families and you know
+
+ align:start position:0%
+of great science families and you know
+ 
+
+ align:start position:0%
+of great science families and you know
+what they did what what the next
+
+ align:start position:0%
+what they did what what the next
+ 
+
+ align:start position:0%
+what they did what what the next
+generation did and he tried to develop
+
+ align:start position:0%
+generation did and he tried to develop
+ 
+
+ align:start position:0%
+generation did and he tried to develop
+this kind of
+
+ align:start position:0%
+this kind of
+ 
+
+ align:start position:0%
+this kind of
+uh this this conceptual framework for
+
+ align:start position:0%
+uh this this conceptual framework for
+ 
+
+ align:start position:0%
+uh this this conceptual framework for
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+about how we could
+
+ align:start position:0%
+about how we could
+ 
+
+ align:start position:0%
+about how we could
+improve how Human societies might
+
+ align:start position:0%
+improve how Human societies might
+ 
+
+ align:start position:0%
+improve how Human societies might
+improve
+
+ align:start position:0%
+improve
+ 
+
+ align:start position:0%
+improve
+their average level of intellect
+
+ align:start position:0%
+their average level of intellect
+ 
+
+ align:start position:0%
+their average level of intellect
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+performance and the other side of it
+
+ align:start position:0%
+performance and the other side of it
+ 
+
+ align:start position:0%
+performance and the other side of it
+resist the uh the process of sort of I
+
+ align:start position:0%
+resist the uh the process of sort of I
+ 
+
+ align:start position:0%
+resist the uh the process of sort of I
+mean we call it a gene pool now but he
+
+ align:start position:0%
+mean we call it a gene pool now but he
+ 
+
+ align:start position:0%
+mean we call it a gene pool now but he
+didn't have those words before he was
+
+ align:start position:0%
+didn't have those words before he was
+ 
+
+ align:start position:0%
+didn't have those words before he was
+but he knew basically that uh there were
+
+ align:start position:0%
+but he knew basically that uh there were
+ 
+
+ align:start position:0%
+but he knew basically that uh there were
+principles of
+
+ align:start position:0%
+principles of
+ 
+
+ align:start position:0%
+principles of
+inheritance. So, uh this is what he was
+
+ align:start position:0%
+inheritance. So, uh this is what he was
+ 
+
+ align:start position:0%
+inheritance. So, uh this is what he was
+he was uh he was interested in doing.
+
+ align:start position:0%
+he was uh he was interested in doing.
+ 
+
+ align:start position:0%
+he was uh he was interested in doing.
+Um
+
+ align:start position:0%
+Um
+ 
+
+ align:start position:0%
+Um
+Darwin I don't myself consider Darwin a
+
+ align:start position:0%
+Darwin I don't myself consider Darwin a
+ 
+
+ align:start position:0%
+Darwin I don't myself consider Darwin a
+eugenicist of any type but he does say
+
+ align:start position:0%
+eugenicist of any type but he does say
+ 
+
+ align:start position:0%
+eugenicist of any type but he does say
+in his book that you know people who are
+
+ align:start position:0%
+in his book that you know people who are
+ 
+
+ align:start position:0%
+in his book that you know people who are
+poor should refrain from marrying and
+
+ align:start position:0%
+poor should refrain from marrying and
+ 
+
+ align:start position:0%
+poor should refrain from marrying and
+having children stuff like that. uh you
+
+ align:start position:0%
+having children stuff like that. uh you
+ 
+
+ align:start position:0%
+having children stuff like that. uh you
+know at some level it's just good advice
+
+ align:start position:0%
+know at some level it's just good advice
+ 
+
+ align:start position:0%
+know at some level it's just good advice
+you know can't
+
+ align:start position:0%
+you know can't
+ 
+
+ align:start position:0%
+you know can't
+afford try to try to work within your
+
+ align:start position:0%
+afford try to try to work within your
+ 
+
+ align:start position:0%
+afford try to try to work within your
+means so uh but uh his his cousin Gton
+
+ align:start position:0%
+means so uh but uh his his cousin Gton
+ 
+
+ align:start position:0%
+means so uh but uh his his cousin Gton
+was much more into you know
+
+ align:start position:0%
+was much more into you know
+ 
+
+ align:start position:0%
+was much more into you know
+understanding some of these principles
+
+ align:start position:0%
+understanding some of these principles
+ 
+
+ align:start position:0%
+understanding some of these principles
+and the a society developed in England
+
+ align:start position:0%
+and the a society developed in England
+ 
+
+ align:start position:0%
+and the a society developed in England
+eugenical society of of of
+
+ align:start position:0%
+eugenical society of of of
+ 
+
+ align:start position:0%
+eugenical society of of of
+London we're going to read a work later
+
+ align:start position:0%
+London we're going to read a work later
+ 
+
+ align:start position:0%
+London we're going to read a work later
+in the term
+
+ align:start position:0%
+in the term
+ 
+
+ align:start position:0%
+in the term
+uh by Thomas Henry Huxley which attacks
+
+ align:start position:0%
+uh by Thomas Henry Huxley which attacks
+ 
+
+ align:start position:0%
+uh by Thomas Henry Huxley which attacks
+this whole movement of eugenical
+
+ align:start position:0%
+this whole movement of eugenical
+ 
+
+ align:start position:0%
+this whole movement of eugenical
+thinking but it was quite strong in
+
+ align:start position:0%
+thinking but it was quite strong in
+ 
+
+ align:start position:0%
+thinking but it was quite strong in
+England and you know people like to say
+
+ align:start position:0%
+England and you know people like to say
+ 
+
+ align:start position:0%
+England and you know people like to say
+oh the Germans came up with eugenics and
+
+ align:start position:0%
+oh the Germans came up with eugenics and
+ 
+
+ align:start position:0%
+oh the Germans came up with eugenics and
+they did terrible things in the second
+
+ align:start position:0%
+they did terrible things in the second
+ 
+
+ align:start position:0%
+they did terrible things in the second
+world war but you know eugenics as a set
+
+ align:start position:0%
+world war but you know eugenics as a set
+ 
+
+ align:start position:0%
+world war but you know eugenics as a set
+of ideas was around long before the
+
+ align:start position:0%
+of ideas was around long before the
+ 
+
+ align:start position:0%
+of ideas was around long before the
+third reich I can tell you that uh and
+
+ align:start position:0%
+third reich I can tell you that uh and
+ 
+
+ align:start position:0%
+third reich I can tell you that uh and
+it was uh there was a movement in
+
+ align:start position:0%
+it was uh there was a movement in
+ 
+
+ align:start position:0%
+it was uh there was a movement in
+America I mean you know there's there's
+
+ align:start position:0%
+America I mean you know there's there's
+ 
+
+ align:start position:0%
+America I mean you know there's there's
+a whole history of this this type of
+
+ align:start position:0%
+a whole history of this this type of
+ 
+
+ align:start position:0%
+a whole history of this this type of
+thinking and it it emerged
+
+ align:start position:0%
+thinking and it it emerged
+ 
+
+ align:start position:0%
+thinking and it it emerged
+out of the kind of
+
+ align:start position:0%
+out of the kind of
+ 
+
+ align:start position:0%
+out of the kind of
+naturalism that Charles Darwin was part
+
+ align:start position:0%
+naturalism that Charles Darwin was part
+ 
+
+ align:start position:0%
+naturalism that Charles Darwin was part
+of. But it just indicates that you know
+
+ align:start position:0%
+of. But it just indicates that you know
+ 
+
+ align:start position:0%
+of. But it just indicates that you know
+ideas can be used in a variety of ways.
+
+ align:start position:0%
+ideas can be used in a variety of ways.
+ 
+
+ align:start position:0%
+ideas can be used in a variety of ways.
+Darwin as I said did not use them this
+
+ align:start position:0%
+Darwin as I said did not use them this
+ 
+
+ align:start position:0%
+Darwin as I said did not use them this
+way. He was not a
+
+ align:start position:0%
+way. He was not a
+ 
+
+ align:start position:0%
+way. He was not a
+eugenicist. Uh I mean there may be
+
+ align:start position:0%
+eugenicist. Uh I mean there may be
+ 
+
+ align:start position:0%
+eugenicist. Uh I mean there may be
+anybody who wants to argue that but I
+
+ align:start position:0%
+anybody who wants to argue that but I
+ 
+
+ align:start position:0%
+anybody who wants to argue that but I
+certainly don't but Gton definitely was
+
+ align:start position:0%
+certainly don't but Gton definitely was
+ 
+
+ align:start position:0%
+certainly don't but Gton definitely was
+yeah how does social Darwinism relate to
+
+ align:start position:0%
+yeah how does social Darwinism relate to
+ 
+
+ align:start position:0%
+yeah how does social Darwinism relate to
+eugenics uh it's an expression eugenics
+
+ align:start position:0%
+eugenics uh it's an expression eugenics
+ 
+
+ align:start position:0%
+eugenics uh it's an expression eugenics
+social darism is and eugenics are the
+
+ align:start position:0%
+social darism is and eugenics are the
+ 
+
+ align:start position:0%
+social darism is and eugenics are the
+same yeah okay so so we'll we'll see
+
+ align:start position:0%
+same yeah okay so so we'll we'll see
+ 
+
+ align:start position:0%
+same yeah okay so so we'll we'll see
+more of this it's it's just a it's a
+
+ align:start position:0%
+more of this it's it's just a it's a
+ 
+
+ align:start position:0%
+more of this it's it's just a it's a
+it's a side of this kind of thinking
+
+ align:start position:0%
+it's a side of this kind of thinking
+ 
+
+ align:start position:0%
+it's a side of this kind of thinking
+that uh needs to be
+
+ align:start position:0%
+that uh needs to be
+ 
+
+ align:start position:0%
+that uh needs to be
+understood and addressed and Butler here
+
+ align:start position:0%
+understood and addressed and Butler here
+ 
+
+ align:start position:0%
+understood and addressed and Butler here
+is one of the first harbinger of you
+
+ align:start position:0%
+is one of the first harbinger of you
+ 
+
+ align:start position:0%
+is one of the first harbinger of you
+know this whole wave of
+
+ align:start position:0%
+know this whole wave of
+ 
+
+ align:start position:0%
+know this whole wave of
+thinking
+
+ align:start position:0%
+thinking
+ 
+
+ align:start position:0%
+thinking
+butler there's nothing in his work that
+
+ align:start position:0%
+butler there's nothing in his work that
+ 
+
+ align:start position:0%
+butler there's nothing in his work that
+suggests that he was a eugenicist but in
+
+ align:start position:0%
+suggests that he was a eugenicist but in
+ 
+
+ align:start position:0%
+suggests that he was a eugenicist but in
+u in his um arowan he's sort of
+
+ align:start position:0%
+u in his um arowan he's sort of
+ 
+
+ align:start position:0%
+u in his um arowan he's sort of
+exploring this territory and opening
+
+ align:start position:0%
+exploring this territory and opening
+ 
+
+ align:start position:0%
+exploring this territory and opening
+them up and saying you know here are
+
+ align:start position:0%
+them up and saying you know here are
+ 
+
+ align:start position:0%
+them up and saying you know here are
+ways in which you can think here's here
+
+ align:start position:0%
+ways in which you can think here's here
+ 
+
+ align:start position:0%
+ways in which you can think here's here
+are ways in which you can use Darwinism
+
+ align:start position:0%
+are ways in which you can use Darwinism
+ 
+
+ align:start position:0%
+are ways in which you can use Darwinism
+to think about society
+
+ align:start position:0%
+to think about society
+ 
+
+ align:start position:0%
+to think about society
+be aware. Just a couple of things before
+
+ align:start position:0%
+be aware. Just a couple of things before
+ 
+
+ align:start position:0%
+be aware. Just a couple of things before
+we leave. Uh what about the religious
+
+ align:start position:0%
+we leave. Uh what about the religious
+ 
+
+ align:start position:0%
+we leave. Uh what about the religious
+establishment? What did anybody get
+
+ align:start position:0%
+establishment? What did anybody get
+ 
+
+ align:start position:0%
+establishment? What did anybody get
+through the musical bank
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+section? Religion in among the Aeronians
+
+ align:start position:0%
+section? Religion in among the Aeronians
+ 
+
+ align:start position:0%
+section? Religion in among the Aeronians
+is pretty much just a empty
+
+ align:start position:0%
+is pretty much just a empty
+ 
+
+ align:start position:0%
+is pretty much just a empty
+uh uh it's it's it's sort of an empty
+
+ align:start position:0%
+uh uh it's it's it's sort of an empty
+ 
+
+ align:start position:0%
+uh uh it's it's it's sort of an empty
+ceremony. People go to these places and
+
+ align:start position:0%
+ceremony. People go to these places and
+ 
+
+ align:start position:0%
+ceremony. People go to these places and
+they
+
+ align:start position:0%
+they
+ 
+
+ align:start position:0%
+they
+uh show a certain kind of uh face if you
+
+ align:start position:0%
+uh show a certain kind of uh face if you
+ 
+
+ align:start position:0%
+uh show a certain kind of uh face if you
+will but fundamentally they don't really
+
+ align:start position:0%
+will but fundamentally they don't really
+ 
+
+ align:start position:0%
+will but fundamentally they don't really
+have much uh conviction that anything
+
+ align:start position:0%
+have much uh conviction that anything
+ 
+
+ align:start position:0%
+have much uh conviction that anything
+important is going to happen in the
+
+ align:start position:0%
+important is going to happen in the
+ 
+
+ align:start position:0%
+important is going to happen in the
+so-called now the musical banks are
+
+ align:start position:0%
+so-called now the musical banks are
+ 
+
+ align:start position:0%
+so-called now the musical banks are
+his the Awanians uh what what what the
+
+ align:start position:0%
+his the Awanians uh what what what the
+ 
+
+ align:start position:0%
+his the Awanians uh what what what the
+uh narrator here calls the Awanian
+
+ align:start position:0%
+uh narrator here calls the Awanian
+ 
+
+ align:start position:0%
+uh narrator here calls the Awanian
+places of uh
+
+ align:start position:0%
+places of uh
+ 
+
+ align:start position:0%
+places of uh
+worship and u these are banks that uh
+
+ align:start position:0%
+worship and u these are banks that uh
+ 
+
+ align:start position:0%
+worship and u these are banks that uh
+these are basically places where people
+
+ align:start position:0%
+these are basically places where people
+ 
+
+ align:start position:0%
+these are basically places where people
+go to be seen and they want to be
+
+ align:start position:0%
+go to be seen and they want to be
+ 
+
+ align:start position:0%
+go to be seen and they want to be
+associated with but fundamentally they
+
+ align:start position:0%
+associated with but fundamentally they
+ 
+
+ align:start position:0%
+associated with but fundamentally they
+don't pay any attention to them. This is
+
+ align:start position:0%
+don't pay any attention to them. This is
+ 
+
+ align:start position:0%
+don't pay any attention to them. This is
+pretty much Butler's view of of
+
+ align:start position:0%
+pretty much Butler's view of of
+ 
+
+ align:start position:0%
+pretty much Butler's view of of
+organized religion of his time. Butler's
+
+ align:start position:0%
+organized religion of his time. Butler's
+ 
+
+ align:start position:0%
+organized religion of his time. Butler's
+father was a cleric. This this is
+
+ align:start position:0%
+father was a cleric. This this is
+ 
+
+ align:start position:0%
+father was a cleric. This this is
+Butler's father's church here in uh in
+
+ align:start position:0%
+Butler's father's church here in uh in
+ 
+
+ align:start position:0%
+Butler's father's church here in uh in
+Langar uh England. And uh it's actually
+
+ align:start position:0%
+Langar uh England. And uh it's actually
+ 
+
+ align:start position:0%
+Langar uh England. And uh it's actually
+quite an interesting church. I went
+
+ align:start position:0%
+quite an interesting church. I went
+ 
+
+ align:start position:0%
+quite an interesting church. I went
+there to visit it once. Uh it sits up on
+
+ align:start position:0%
+there to visit it once. Uh it sits up on
+ 
+
+ align:start position:0%
+there to visit it once. Uh it sits up on
+this sort of null. His father renovated
+
+ align:start position:0%
+this sort of null. His father renovated
+ 
+
+ align:start position:0%
+this sort of null. His father renovated
+it. And apparently most people think he
+
+ align:start position:0%
+it. And apparently most people think he
+ 
+
+ align:start position:0%
+it. And apparently most people think he
+remodeled it. He he took his father took
+
+ align:start position:0%
+remodeled it. He he took his father took
+ 
+
+ align:start position:0%
+remodeled it. He he took his father took
+the the distinctive features of of of
+
+ align:start position:0%
+the the distinctive features of of of
+ 
+
+ align:start position:0%
+the the distinctive features of of of
+the church and kind
+
+ align:start position:0%
+the church and kind
+ 
+
+ align:start position:0%
+the church and kind
+of okay
+
+ align:start position:0%
+of okay
+ 
+
+ align:start position:0%
+of okay
+so what we're uh so this world is a
+
+ align:start position:0%
+so what we're uh so this world is a
+ 
+
+ align:start position:0%
+so what we're uh so this world is a
+world of biological juosition with
+
+ align:start position:0%
+world of biological juosition with
+ 
+
+ align:start position:0%
+world of biological juosition with
+social and uh there's a kind of a humor
+
+ align:start position:0%
+social and uh there's a kind of a humor
+ 
+
+ align:start position:0%
+social and uh there's a kind of a humor
+to it a satire to it butler's making use
+
+ align:start position:0%
+to it a satire to it butler's making use
+ 
+
+ align:start position:0%
+to it a satire to it butler's making use
+of this and
+
+ align:start position:0%
+of this and
+ 
+
+ align:start position:0%
+of this and
+uh I've given you a little dancing
+
+ align:start position:0%
+uh I've given you a little dancing
+ 
+
+ align:start position:0%
+uh I've given you a little dancing
+hippos uh clip here from Fantasia
+
+ align:start position:0%
+hippos uh clip here from Fantasia
+ 
+
+ align:start position:0%
+hippos uh clip here from Fantasia
+And part of the humor of that is seeing
+
+ align:start position:0%
+And part of the humor of that is seeing
+ 
+
+ align:start position:0%
+And part of the humor of that is seeing
+something natural do something
+
+ align:start position:0%
+something natural do something
+ 
+
+ align:start position:0%
+something natural do something
+unnatural. There there there's a kind of
+
+ align:start position:0%
+unnatural. There there there's a kind of
+ 
+
+ align:start position:0%
+unnatural. There there there's a kind of
+humor to it. And that's part of the
+
+ align:start position:0%
+humor to it. And that's part of the
+ 
+
+ align:start position:0%
+humor to it. And that's part of the
+source of the humor in in Arrowan.
\ No newline at end of file
diff --git a/vN5Yn-niTXE.txt b/vN5Yn-niTXE.txt
new file mode 100644
index 0000000000000000000000000000000000000000..67f2579030b7b59d9b361fa0e973875b9b6d8b59
--- /dev/null
+++ b/vN5Yn-niTXE.txt
@@ -0,0 +1,11635 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all right so let's get started so today
+
+ align:start position:0%
+all right so let's get started so today
+ 
+
+ align:start position:0%
+all right so let's get started so today
+or last lecture we talked about
+
+ align:start position:0%
+or last lecture we talked about
+ 
+
+ align:start position:0%
+or last lecture we talked about
+different device parameters mainly our
+
+ align:start position:0%
+different device parameters mainly our
+ 
+
+ align:start position:0%
+different device parameters mainly our
+series resistance and shunt resistance
+
+ align:start position:0%
+series resistance and shunt resistance
+ 
+
+ align:start position:0%
+series resistance and shunt resistance
+and how that affects our efficiencies
+
+ align:start position:0%
+and how that affects our efficiencies
+ 
+
+ align:start position:0%
+and how that affects our efficiencies
+today we're going to talk a lot about
+
+ align:start position:0%
+today we're going to talk a lot about
+ 
+
+ align:start position:0%
+today we're going to talk a lot about
+different material properties and how
+
+ align:start position:0%
+different material properties and how
+ 
+
+ align:start position:0%
+different material properties and how
+they affect certain device
+
+ align:start position:0%
+they affect certain device
+ 
+
+ align:start position:0%
+they affect certain device
+characteristics and mainly just affect
+
+ align:start position:0%
+characteristics and mainly just affect
+ 
+
+ align:start position:0%
+characteristics and mainly just affect
+our output efficiency so we've been
+
+ align:start position:0%
+our output efficiency so we've been
+ 
+
+ align:start position:0%
+our output efficiency so we've been
+talking a lot about the fundamentals I'm
+
+ align:start position:0%
+talking a lot about the fundamentals I'm
+ 
+
+ align:start position:0%
+talking a lot about the fundamentals I'm
+sure you guys are loving this right now
+
+ align:start position:0%
+sure you guys are loving this right now
+ 
+
+ align:start position:0%
+sure you guys are loving this right now
+so we're gonna complete this in probably
+
+ align:start position:0%
+so we're gonna complete this in probably
+ 
+
+ align:start position:0%
+so we're gonna complete this in probably
+the next three lectures and then move on
+
+ align:start position:0%
+the next three lectures and then move on
+ 
+
+ align:start position:0%
+the next three lectures and then move on
+to a lot of the kind of cross-cutting
+
+ align:start position:0%
+to a lot of the kind of cross-cutting
+ 
+
+ align:start position:0%
+to a lot of the kind of cross-cutting
+themes in PV some advanced concepts you
+
+ align:start position:0%
+themes in PV some advanced concepts you
+ 
+
+ align:start position:0%
+themes in PV some advanced concepts you
+know different device architectures and
+
+ align:start position:0%
+know different device architectures and
+ 
+
+ align:start position:0%
+know different device architectures and
+that kind of thing and so that is coming
+
+ align:start position:0%
+that kind of thing and so that is coming
+ 
+
+ align:start position:0%
+that kind of thing and so that is coming
+in the future but we're still doing
+
+ align:start position:0%
+in the future but we're still doing
+ 
+
+ align:start position:0%
+in the future but we're still doing
+fundamentals today and so I know you're
+
+ align:start position:0%
+fundamentals today and so I know you're
+ 
+
+ align:start position:0%
+fundamentals today and so I know you're
+probably all aware of this equation and
+
+ align:start position:0%
+probably all aware of this equation and
+ 
+
+ align:start position:0%
+probably all aware of this equation and
+again this is kind of the progress we've
+
+ align:start position:0%
+again this is kind of the progress we've
+ 
+
+ align:start position:0%
+again this is kind of the progress we've
+made so we're almost all the way through
+
+ align:start position:0%
+made so we're almost all the way through
+ 
+
+ align:start position:0%
+made so we're almost all the way through
+explaining basic device physics and
+
+ align:start position:0%
+explaining basic device physics and
+ 
+
+ align:start position:0%
+explaining basic device physics and
+basic semiconductor physics too so you
+
+ align:start position:0%
+basic semiconductor physics too so you
+ 
+
+ align:start position:0%
+basic semiconductor physics too so you
+can understand simple devices and it's
+
+ align:start position:0%
+can understand simple devices and it's
+ 
+
+ align:start position:0%
+can understand simple devices and it's
+always important to remember that your
+
+ align:start position:0%
+always important to remember that your
+ 
+
+ align:start position:0%
+always important to remember that your
+device is like a leaky bucket and you're
+
+ align:start position:0%
+device is like a leaky bucket and you're
+ 
+
+ align:start position:0%
+device is like a leaky bucket and you're
+limited by the largest hole in that
+
+ align:start position:0%
+limited by the largest hole in that
+ 
+
+ align:start position:0%
+limited by the largest hole in that
+bucket so the weakest aspect of your
+
+ align:start position:0%
+bucket so the weakest aspect of your
+ 
+
+ align:start position:0%
+bucket so the weakest aspect of your
+solar cell is really what's going to
+
+ align:start position:0%
+solar cell is really what's going to
+ 
+
+ align:start position:0%
+solar cell is really what's going to
+limit your device performance and
+
+ align:start position:0%
+limit your device performance and
+ 
+
+ align:start position:0%
+limit your device performance and
+especially if any of you here are trying
+
+ align:start position:0%
+especially if any of you here are trying
+ 
+
+ align:start position:0%
+especially if any of you here are trying
+to make devices it's really important to
+
+ align:start position:0%
+to make devices it's really important to
+ 
+
+ align:start position:0%
+to make devices it's really important to
+think about all of these things when
+
+ align:start position:0%
+think about all of these things when
+ 
+
+ align:start position:0%
+think about all of these things when
+building it and this is very difficult
+
+ align:start position:0%
+building it and this is very difficult
+ 
+
+ align:start position:0%
+building it and this is very difficult
+to do I can certainly tell you that okay
+
+ align:start position:0%
+to do I can certainly tell you that okay
+ 
+
+ align:start position:0%
+to do I can certainly tell you that okay
+so I kind of like this slide what this
+
+ align:start position:0%
+so I kind of like this slide what this
+ 
+
+ align:start position:0%
+so I kind of like this slide what this
+is is saying what's the thing we care
+
+ align:start position:0%
+is is saying what's the thing we care
+ 
+
+ align:start position:0%
+is is saying what's the thing we care
+about most in our solar cells well as
+
+ align:start position:0%
+about most in our solar cells well as
+ 
+
+ align:start position:0%
+about most in our solar cells well as
+scientists other than dollars per watt
+
+ align:start position:0%
+scientists other than dollars per watt
+ 
+
+ align:start position:0%
+scientists other than dollars per watt
+we want to maximize our efficiency for a
+
+ align:start position:0%
+we want to maximize our efficiency for a
+ 
+
+ align:start position:0%
+we want to maximize our efficiency for a
+certain price and our efficiency there
+
+ align:start position:0%
+certain price and our efficiency there
+ 
+
+ align:start position:0%
+certain price and our efficiency there
+are several parameters that go into it
+
+ align:start position:0%
+are several parameters that go into it
+ 
+
+ align:start position:0%
+are several parameters that go into it
+again we talked about our JSC our
+
+ align:start position:0%
+again we talked about our JSC our
+ 
+
+ align:start position:0%
+again we talked about our JSC our
+short-circuit current our open circuit
+
+ align:start position:0%
+short-circuit current our open circuit
+ 
+
+ align:start position:0%
+short-circuit current our open circuit
+voltage and our fill factor and that
+
+ align:start position:0%
+voltage and our fill factor and that
+ 
+
+ align:start position:0%
+voltage and our fill factor and that
+gives us our output energy or output
+
+ align:start position:0%
+gives us our output energy or output
+ 
+
+ align:start position:0%
+gives us our output energy or output
+power and we divide that by the input
+
+ align:start position:0%
+power and we divide that by the input
+ 
+
+ align:start position:0%
+power and we divide that by the input
+power which is the solar insolation now
+
+ align:start position:0%
+power which is the solar insolation now
+ 
+
+ align:start position:0%
+power which is the solar insolation now
+we can split up that again in the open
+
+ align:start position:0%
+we can split up that again in the open
+ 
+
+ align:start position:0%
+we can split up that again in the open
+circuit voltage short circuit current
+
+ align:start position:0%
+circuit voltage short circuit current
+ 
+
+ align:start position:0%
+circuit voltage short circuit current
+and fill factor we talked a little bit
+
+ align:start position:0%
+and fill factor we talked a little bit
+ 
+
+ align:start position:0%
+and fill factor we talked a little bit
+last lecture about fill factor and how
+
+ align:start position:0%
+last lecture about fill factor and how
+ 
+
+ align:start position:0%
+last lecture about fill factor and how
+that's influenced by
+
+ align:start position:0%
+that's influenced by
+ 
+
+ align:start position:0%
+that's influenced by
+different resistive losses in our solar
+
+ align:start position:0%
+different resistive losses in our solar
+ 
+
+ align:start position:0%
+different resistive losses in our solar
+cell today we're gonna mainly be focused
+
+ align:start position:0%
+cell today we're gonna mainly be focused
+ 
+
+ align:start position:0%
+cell today we're gonna mainly be focused
+on short circuit current and things like
+
+ align:start position:0%
+on short circuit current and things like
+ 
+
+ align:start position:0%
+on short circuit current and things like
+internal quantum efficiency which are
+
+ align:start position:0%
+internal quantum efficiency which are
+ 
+
+ align:start position:0%
+internal quantum efficiency which are
+highly affected by our diffusion length
+
+ align:start position:0%
+highly affected by our diffusion length
+ 
+
+ align:start position:0%
+highly affected by our diffusion length
+and the diffusion length is often
+
+ align:start position:0%
+and the diffusion length is often
+ 
+
+ align:start position:0%
+and the diffusion length is often
+limited by certain defects in our
+
+ align:start position:0%
+limited by certain defects in our
+ 
+
+ align:start position:0%
+limited by certain defects in our
+materials and we're gonna get into why
+
+ align:start position:0%
+materials and we're gonna get into why
+ 
+
+ align:start position:0%
+materials and we're gonna get into why
+that is and to a certain extent we'll
+
+ align:start position:0%
+that is and to a certain extent we'll
+ 
+
+ align:start position:0%
+that is and to a certain extent we'll
+talk about open circuit voltage because
+
+ align:start position:0%
+talk about open circuit voltage because
+ 
+
+ align:start position:0%
+talk about open circuit voltage because
+your JSC can really has a large effect
+
+ align:start position:0%
+your JSC can really has a large effect
+ 
+
+ align:start position:0%
+your JSC can really has a large effect
+on your open circuit voltage so what
+
+ align:start position:0%
+on your open circuit voltage so what
+ 
+
+ align:start position:0%
+on your open circuit voltage so what
+we're gonna learn today is what is
+
+ align:start position:0%
+we're gonna learn today is what is
+ 
+
+ align:start position:0%
+we're gonna learn today is what is
+minority carrier diffusion length it was
+
+ align:start position:0%
+minority carrier diffusion length it was
+ 
+
+ align:start position:0%
+minority carrier diffusion length it was
+in the homework hopefully you guys have
+
+ align:start position:0%
+in the homework hopefully you guys have
+ 
+
+ align:start position:0%
+in the homework hopefully you guys have
+some idea coming to lecture but today
+
+ align:start position:0%
+some idea coming to lecture but today
+ 
+
+ align:start position:0%
+some idea coming to lecture but today
+we're gonna talk about a little more in
+
+ align:start position:0%
+we're gonna talk about a little more in
+ 
+
+ align:start position:0%
+we're gonna talk about a little more in
+depth and why it's important and how
+
+ align:start position:0%
+depth and why it's important and how
+ 
+
+ align:start position:0%
+depth and why it's important and how
+it's affected what are the parameters
+
+ align:start position:0%
+it's affected what are the parameters
+ 
+
+ align:start position:0%
+it's affected what are the parameters
+that determine it so mainly diffusivity
+
+ align:start position:0%
+that determine it so mainly diffusivity
+ 
+
+ align:start position:0%
+that determine it so mainly diffusivity
+and lifetime we're gonna describe how
+
+ align:start position:0%
+and lifetime we're gonna describe how
+ 
+
+ align:start position:0%
+and lifetime we're gonna describe how
+it's actually measured in a solar cell
+
+ align:start position:0%
+it's actually measured in a solar cell
+ 
+
+ align:start position:0%
+it's actually measured in a solar cell
+there's actually really cool measurement
+
+ align:start position:0%
+there's actually really cool measurement
+ 
+
+ align:start position:0%
+there's actually really cool measurement
+and we actually have the capabilities in
+
+ align:start position:0%
+and we actually have the capabilities in
+ 
+
+ align:start position:0%
+and we actually have the capabilities in
+our lab and possibly some of you when
+
+ align:start position:0%
+our lab and possibly some of you when
+ 
+
+ align:start position:0%
+our lab and possibly some of you when
+you're making cells will be able to do
+
+ align:start position:0%
+you're making cells will be able to do
+ 
+
+ align:start position:0%
+you're making cells will be able to do
+that measurement we're also going to
+
+ align:start position:0%
+that measurement we're also going to
+ 
+
+ align:start position:0%
+that measurement we're also going to
+look at some of the things that live at
+
+ align:start position:0%
+look at some of the things that live at
+ 
+
+ align:start position:0%
+look at some of the things that live at
+lifetime to some of the basic
+
+ align:start position:0%
+lifetime to some of the basic
+ 
+
+ align:start position:0%
+lifetime to some of the basic
+recombination mechanisms also look at
+
+ align:start position:0%
+recombination mechanisms also look at
+ 
+
+ align:start position:0%
+recombination mechanisms also look at
+how your excess carrier concentration
+
+ align:start position:0%
+how your excess carrier concentration
+ 
+
+ align:start position:0%
+how your excess carrier concentration
+changes as a function of lifetime and
+
+ align:start position:0%
+changes as a function of lifetime and
+ 
+
+ align:start position:0%
+changes as a function of lifetime and
+generation light and then also talk
+
+ align:start position:0%
+generation light and then also talk
+ 
+
+ align:start position:0%
+generation light and then also talk
+about the last material parameter which
+
+ align:start position:0%
+about the last material parameter which
+ 
+
+ align:start position:0%
+about the last material parameter which
+is mobility which discusses kind of how
+
+ align:start position:0%
+is mobility which discusses kind of how
+ 
+
+ align:start position:0%
+is mobility which discusses kind of how
+well these excited charges can move
+
+ align:start position:0%
+well these excited charges can move
+ 
+
+ align:start position:0%
+well these excited charges can move
+around within your material so without
+
+ align:start position:0%
+around within your material so without
+ 
+
+ align:start position:0%
+around within your material so without
+further ado your minority carrier
+
+ align:start position:0%
+further ado your minority carrier
+ 
+
+ align:start position:0%
+further ado your minority carrier
+diffusion length definition is really
+
+ align:start position:0%
+diffusion length definition is really
+ 
+
+ align:start position:0%
+diffusion length definition is really
+simple if you generate let's say a
+
+ align:start position:0%
+simple if you generate let's say a
+ 
+
+ align:start position:0%
+simple if you generate let's say a
+photon comes and hits a silicon atom and
+
+ align:start position:0%
+photon comes and hits a silicon atom and
+ 
+
+ align:start position:0%
+photon comes and hits a silicon atom and
+generates
+
+ align:start position:0%
+generates
+ 
+
+ align:start position:0%
+generates
+an electron pair over here how far or
+
+ align:start position:0%
+an electron pair over here how far or
+ 
+
+ align:start position:0%
+an electron pair over here how far or
+how much volume can it explore that
+
+ align:start position:0%
+how much volume can it explore that
+ 
+
+ align:start position:0%
+how much volume can it explore that
+volume it can explore is described by
+
+ align:start position:0%
+volume it can explore is described by
+ 
+
+ align:start position:0%
+volume it can explore is described by
+some characteristic radius and that
+
+ align:start position:0%
+some characteristic radius and that
+ 
+
+ align:start position:0%
+some characteristic radius and that
+radius is known as the diffusion length
+
+ align:start position:0%
+radius is known as the diffusion length
+ 
+
+ align:start position:0%
+radius is known as the diffusion length
+and it's really important to solar cells
+
+ align:start position:0%
+and it's really important to solar cells
+ 
+
+ align:start position:0%
+and it's really important to solar cells
+because when you think about these
+
+ align:start position:0%
+because when you think about these
+ 
+
+ align:start position:0%
+because when you think about these
+carriers that you're generating when
+
+ align:start position:0%
+carriers that you're generating when
+ 
+
+ align:start position:0%
+carriers that you're generating when
+they if they can only explore a very
+
+ align:start position:0%
+they if they can only explore a very
+ 
+
+ align:start position:0%
+they if they can only explore a very
+short area they're not going to make it
+
+ align:start position:0%
+short area they're not going to make it
+ 
+
+ align:start position:0%
+short area they're not going to make it
+this is a very good solar cell so the
+
+ align:start position:0%
+this is a very good solar cell so the
+ 
+
+ align:start position:0%
+this is a very good solar cell so the
+diffusion length is really long and all
+
+ align:start position:0%
+diffusion length is really long and all
+ 
+
+ align:start position:0%
+diffusion length is really long and all
+these carriers generated there we'll be
+
+ align:start position:0%
+these carriers generated there we'll be
+ 
+
+ align:start position:0%
+these carriers generated there we'll be
+able to make our Junction so again just
+
+ align:start position:0%
+able to make our Junction so again just
+ 
+
+ align:start position:0%
+able to make our Junction so again just
+so we're familiar this is our base and a
+
+ align:start position:0%
+so we're familiar this is our base and a
+ 
+
+ align:start position:0%
+so we're familiar this is our base and a
+top we have our our emitter so our the
+
+ align:start position:0%
+top we have our our emitter so our the
+ 
+
+ align:start position:0%
+top we have our our emitter so our the
+junction would be at this line right
+
+ align:start position:0%
+junction would be at this line right
+ 
+
+ align:start position:0%
+junction would be at this line right
+here on that plane
+
+ align:start position:0%
+here on that plane
+ 
+
+ align:start position:0%
+here on that plane
+if we have a really bad solar cell so
+
+ align:start position:0%
+if we have a really bad solar cell so
+ 
+
+ align:start position:0%
+if we have a really bad solar cell so
+let's say a lot of defects present a lot
+
+ align:start position:0%
+let's say a lot of defects present a lot
+ 
+
+ align:start position:0%
+let's say a lot of defects present a lot
+of areas for these excited carriers to
+
+ align:start position:0%
+of areas for these excited carriers to
+ 
+
+ align:start position:0%
+of areas for these excited carriers to
+recombine they won't make it to the
+
+ align:start position:0%
+recombine they won't make it to the
+ 
+
+ align:start position:0%
+recombine they won't make it to the
+junction they'll have a very short
+
+ align:start position:0%
+junction they'll have a very short
+ 
+
+ align:start position:0%
+junction they'll have a very short
+diffusion length and as a result your
+
+ align:start position:0%
+diffusion length and as a result your
+ 
+
+ align:start position:0%
+diffusion length and as a result your
+short-circuit current and your vo si
+
+ align:start position:0%
+short-circuit current and your vo si
+ 
+
+ align:start position:0%
+short-circuit current and your vo si
+will suffer dramatically so it's really
+
+ align:start position:0%
+will suffer dramatically so it's really
+ 
+
+ align:start position:0%
+will suffer dramatically so it's really
+important to get good crystal quality
+
+ align:start position:0%
+important to get good crystal quality
+ 
+
+ align:start position:0%
+important to get good crystal quality
+and good material quality but up to a
+
+ align:start position:0%
+and good material quality but up to a
+ 
+
+ align:start position:0%
+and good material quality but up to a
+certain point right there's kind of
+
+ align:start position:0%
+certain point right there's kind of
+ 
+
+ align:start position:0%
+certain point right there's kind of
+diminishing returns as you go to higher
+
+ align:start position:0%
+diminishing returns as you go to higher
+ 
+
+ align:start position:0%
+diminishing returns as you go to higher
+and higher qualities and we'll talk
+
+ align:start position:0%
+and higher qualities and we'll talk
+ 
+
+ align:start position:0%
+and higher qualities and we'll talk
+about that in a second so if we assume
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what this is showing is how our short
+
+ align:start position:0%
+what this is showing is how our short
+ 
+
+ align:start position:0%
+what this is showing is how our short
+circuit current scales with our
+
+ align:start position:0%
+circuit current scales with our
+ 
+
+ align:start position:0%
+circuit current scales with our
+diffusion length so we have some
+
+ align:start position:0%
+diffusion length so we have some
+ 
+
+ align:start position:0%
+diffusion length so we have some
+something called the generation rate and
+
+ align:start position:0%
+something called the generation rate and
+ 
+
+ align:start position:0%
+something called the generation rate and
+this is often proportional to the photon
+
+ align:start position:0%
+this is often proportional to the photon
+ 
+
+ align:start position:0%
+this is often proportional to the photon
+flux on your material so the number of
+
+ align:start position:0%
+flux on your material so the number of
+ 
+
+ align:start position:0%
+flux on your material so the number of
+photons hitting your solar cell and this
+
+ align:start position:0%
+photons hitting your solar cell and this
+ 
+
+ align:start position:0%
+photons hitting your solar cell and this
+generation rate is something the number
+
+ align:start position:0%
+generation rate is something the number
+ 
+
+ align:start position:0%
+generation rate is something the number
+of carriers produced a second in some
+
+ align:start position:0%
+of carriers produced a second in some
+ 
+
+ align:start position:0%
+of carriers produced a second in some
+given volume so it's a volumetric term
+
+ align:start position:0%
+given volume so it's a volumetric term
+ 
+
+ align:start position:0%
+given volume so it's a volumetric term
+and if we assume that everything within
+
+ align:start position:0%
+and if we assume that everything within
+ 
+
+ align:start position:0%
+and if we assume that everything within
+one diffusion length of our Junction
+
+ align:start position:0%
+one diffusion length of our Junction
+ 
+
+ align:start position:0%
+one diffusion length of our Junction
+gets collected that'll all be counted as
+
+ align:start position:0%
+gets collected that'll all be counted as
+ 
+
+ align:start position:0%
+gets collected that'll all be counted as
+short-circuit current so you basically
+
+ align:start position:0%
+short-circuit current so you basically
+ 
+
+ align:start position:0%
+short-circuit current so you basically
+your JSC has this kind of linear
+
+ align:start position:0%
+your JSC has this kind of linear
+ 
+
+ align:start position:0%
+your JSC has this kind of linear
+dependence on your diffusion length but
+
+ align:start position:0%
+dependence on your diffusion length but
+ 
+
+ align:start position:0%
+dependence on your diffusion length but
+that's only true up to a certain point
+
+ align:start position:0%
+that's only true up to a certain point
+ 
+
+ align:start position:0%
+that's only true up to a certain point
+right so if for example if we have a
+
+ align:start position:0%
+right so if for example if we have a
+ 
+
+ align:start position:0%
+right so if for example if we have a
+diffusion length that's much longer than
+
+ align:start position:0%
+diffusion length that's much longer than
+ 
+
+ align:start position:0%
+diffusion length that's much longer than
+the device thickness it's really not
+
+ align:start position:0%
+the device thickness it's really not
+ 
+
+ align:start position:0%
+the device thickness it's really not
+going to get again diminishing returns
+
+ align:start position:0%
+going to get again diminishing returns
+ 
+
+ align:start position:0%
+going to get again diminishing returns
+as you go to longer and longer diffusion
+
+ align:start position:0%
+as you go to longer and longer diffusion
+ 
+
+ align:start position:0%
+as you go to longer and longer diffusion
+lengths so this is a calculation I did
+
+ align:start position:0%
+lengths so this is a calculation I did
+ 
+
+ align:start position:0%
+lengths so this is a calculation I did
+using a 1d simulation program called PC
+
+ align:start position:0%
+using a 1d simulation program called PC
+ 
+
+ align:start position:0%
+using a 1d simulation program called PC
+1d which if you want to play around with
+
+ align:start position:0%
+1d which if you want to play around with
+ 
+
+ align:start position:0%
+1d which if you want to play around with
+it's free
+
+ align:start position:0%
+it's free
+ 
+
+ align:start position:0%
+it's free
+it's a lot of fun to use actually and
+
+ align:start position:0%
+it's a lot of fun to use actually and
+ 
+
+ align:start position:0%
+it's a lot of fun to use actually and
+you can put in things like lifetimes and
+
+ align:start position:0%
+you can put in things like lifetimes and
+ 
+
+ align:start position:0%
+you can put in things like lifetimes and
+I very basically the lifetime which
+
+ align:start position:0%
+I very basically the lifetime which
+ 
+
+ align:start position:0%
+I very basically the lifetime which
+we'll get to in a second how that
+
+ align:start position:0%
+we'll get to in a second how that
+ 
+
+ align:start position:0%
+we'll get to in a second how that
+changes the diffusion length and you can
+
+ align:start position:0%
+changes the diffusion length and you can
+ 
+
+ align:start position:0%
+changes the diffusion length and you can
+see that there actually is a linear
+
+ align:start position:0%
+see that there actually is a linear
+ 
+
+ align:start position:0%
+see that there actually is a linear
+relation until the diffusion length is
+
+ align:start position:0%
+relation until the diffusion length is
+ 
+
+ align:start position:0%
+relation until the diffusion length is
+about on the order of 300 microns which
+
+ align:start position:0%
+about on the order of 300 microns which
+ 
+
+ align:start position:0%
+about on the order of 300 microns which
+is the device thickness so you can see
+
+ align:start position:0%
+is the device thickness so you can see
+ 
+
+ align:start position:0%
+is the device thickness so you can see
+this kind of trailing off and become sub
+
+ align:start position:0%
+this kind of trailing off and become sub
+ 
+
+ align:start position:0%
+this kind of trailing off and become sub
+linear in its response yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so let's let's let's think about it one
+
+ align:start position:0%
+so let's let's let's think about it one
+ 
+
+ align:start position:0%
+so let's let's let's think about it one
+step back why do we care about minority
+
+ align:start position:0%
+step back why do we care about minority
+ 
+
+ align:start position:0%
+step back why do we care about minority
+carriers right so if let's say you
+
+ align:start position:0%
+carriers right so if let's say you
+ 
+
+ align:start position:0%
+carriers right so if let's say you
+generate an electron hole pair and
+
+ align:start position:0%
+generate an electron hole pair and
+ 
+
+ align:start position:0%
+generate an electron hole pair and
+n-type material the hole wants to move
+
+ align:start position:0%
+n-type material the hole wants to move
+ 
+
+ align:start position:0%
+n-type material the hole wants to move
+to the p-type side right and it's the
+
+ align:start position:0%
+to the p-type side right and it's the
+ 
+
+ align:start position:0%
+to the p-type side right and it's the
+electric field will actually repel and
+
+ align:start position:0%
+electric field will actually repel and
+ 
+
+ align:start position:0%
+electric field will actually repel and
+keep it on the electron on the on the on
+
+ align:start position:0%
+keep it on the electron on the on the on
+ 
+
+ align:start position:0%
+keep it on the electron on the on the on
+the n-type side so it's your minority
+
+ align:start position:0%
+the n-type side so it's your minority
+ 
+
+ align:start position:0%
+the n-type side so it's your minority
+carriers that matter in terms of the
+
+ align:start position:0%
+carriers that matter in terms of the
+ 
+
+ align:start position:0%
+carriers that matter in terms of the
+separation and we'll talk about that
+
+ align:start position:0%
+separation and we'll talk about that
+ 
+
+ align:start position:0%
+separation and we'll talk about that
+again if that's still fuzzy in people's
+
+ align:start position:0%
+again if that's still fuzzy in people's
+ 
+
+ align:start position:0%
+again if that's still fuzzy in people's
+heads and so what carrier what matters
+
+ align:start position:0%
+heads and so what carrier what matters
+ 
+
+ align:start position:0%
+heads and so what carrier what matters
+in terms of you talking about deriving
+
+ align:start position:0%
+in terms of you talking about deriving
+ 
+
+ align:start position:0%
+in terms of you talking about deriving
+the ideal diode equation well yeah but
+
+ align:start position:0%
+the ideal diode equation well yeah but
+ 
+
+ align:start position:0%
+the ideal diode equation well yeah but
+in order to be separated which is the
+
+ align:start position:0%
+in order to be separated which is the
+ 
+
+ align:start position:0%
+in order to be separated which is the
+first part that we care about we it
+
+ align:start position:0%
+first part that we care about we it
+ 
+
+ align:start position:0%
+first part that we care about we it
+matters that it's reached the junction
+
+ align:start position:0%
+matters that it's reached the junction
+ 
+
+ align:start position:0%
+matters that it's reached the junction
+and so it's that concentration at the
+
+ align:start position:0%
+and so it's that concentration at the
+ 
+
+ align:start position:0%
+and so it's that concentration at the
+junction that determines the flux across
+
+ align:start position:0%
+junction that determines the flux across
+ 
+
+ align:start position:0%
+junction that determines the flux across
+the junction so make sense okay okay and
+
+ align:start position:0%
+the junction so make sense okay okay and
+ 
+
+ align:start position:0%
+the junction so make sense okay okay and
+so there's also this other loose
+
+ align:start position:0%
+so there's also this other loose
+ 
+
+ align:start position:0%
+so there's also this other loose
+dependence on vo C on your diffusion
+
+ align:start position:0%
+dependence on vo C on your diffusion
+ 
+
+ align:start position:0%
+dependence on vo C on your diffusion
+length and so if you recall from a few
+
+ align:start position:0%
+length and so if you recall from a few
+ 
+
+ align:start position:0%
+length and so if you recall from a few
+lectures ago this is your the equation
+
+ align:start position:0%
+lectures ago this is your the equation
+ 
+
+ align:start position:0%
+lectures ago this is your the equation
+for vo C is dependent on your
+
+ align:start position:0%
+for vo C is dependent on your
+ 
+
+ align:start position:0%
+for vo C is dependent on your
+short-circuit current temperature and
+
+ align:start position:0%
+short-circuit current temperature and
+ 
+
+ align:start position:0%
+short-circuit current temperature and
+your saturation current which you can
+
+ align:start position:0%
+your saturation current which you can
+ 
+
+ align:start position:0%
+your saturation current which you can
+also often think of as your reverse bias
+
+ align:start position:0%
+also often think of as your reverse bias
+ 
+
+ align:start position:0%
+also often think of as your reverse bias
+current and your saturation current is
+
+ align:start position:0%
+current and your saturation current is
+ 
+
+ align:start position:0%
+current and your saturation current is
+dependent on your diffusion length JSC
+
+ align:start position:0%
+dependent on your diffusion length JSC
+ 
+
+ align:start position:0%
+dependent on your diffusion length JSC
+if you've recall was linearly
+
+ align:start position:0%
+if you've recall was linearly
+ 
+
+ align:start position:0%
+if you've recall was linearly
+proportional to the diffusion length so
+
+ align:start position:0%
+proportional to the diffusion length so
+ 
+
+ align:start position:0%
+proportional to the diffusion length so
+the vo C actually scales with the
+
+ align:start position:0%
+the vo C actually scales with the
+ 
+
+ align:start position:0%
+the vo C actually scales with the
+natural log of the square of the
+
+ align:start position:0%
+natural log of the square of the
+ 
+
+ align:start position:0%
+natural log of the square of the
+diffusion length and if you pull out
+
+ align:start position:0%
+diffusion length and if you pull out
+ 
+
+ align:start position:0%
+diffusion length and if you pull out
+that exponent it just squares with the
+
+ align:start position:0%
+that exponent it just squares with the
+ 
+
+ align:start position:0%
+that exponent it just squares with the
+natural log of your diffusion length and
+
+ align:start position:0%
+natural log of your diffusion length and
+ 
+
+ align:start position:0%
+natural log of your diffusion length and
+again very very simple analogy we're
+
+ align:start position:0%
+again very very simple analogy we're
+ 
+
+ align:start position:0%
+again very very simple analogy we're
+assuming again that fill factor is not
+
+ align:start position:0%
+assuming again that fill factor is not
+ 
+
+ align:start position:0%
+assuming again that fill factor is not
+really affected by your diffusion length
+
+ align:start position:0%
+really affected by your diffusion length
+ 
+
+ align:start position:0%
+really affected by your diffusion length
+and that your efficiency is proportional
+
+ align:start position:0%
+and that your efficiency is proportional
+ 
+
+ align:start position:0%
+and that your efficiency is proportional
+to the product of your JSC and your vo C
+
+ align:start position:0%
+to the product of your JSC and your vo C
+ 
+
+ align:start position:0%
+to the product of your JSC and your vo C
+so your short circuit current your open
+
+ align:start position:0%
+so your short circuit current your open
+ 
+
+ align:start position:0%
+so your short circuit current your open
+circuit voltage and you can see as you
+
+ align:start position:0%
+circuit voltage and you can see as you
+ 
+
+ align:start position:0%
+circuit voltage and you can see as you
+go to longer diffusion lengths there's
+
+ align:start position:0%
+go to longer diffusion lengths there's
+ 
+
+ align:start position:0%
+go to longer diffusion lengths there's
+this area of diminishing return and
+
+ align:start position:0%
+this area of diminishing return and
+ 
+
+ align:start position:0%
+this area of diminishing return and
+again there's two different regimes here
+
+ align:start position:0%
+again there's two different regimes here
+ 
+
+ align:start position:0%
+again there's two different regimes here
+one is when your diffusion length is
+
+ align:start position:0%
+one is when your diffusion length is
+ 
+
+ align:start position:0%
+one is when your diffusion length is
+again much less than your device
+
+ align:start position:0%
+again much less than your device
+ 
+
+ align:start position:0%
+again much less than your device
+thickness you can see that uses a huge
+
+ align:start position:0%
+thickness you can see that uses a huge
+ 
+
+ align:start position:0%
+thickness you can see that uses a huge
+increase in efficiency but as your
+
+ align:start position:0%
+increase in efficiency but as your
+ 
+
+ align:start position:0%
+increase in efficiency but as your
+diffusion leaks gets well well above
+
+ align:start position:0%
+diffusion leaks gets well well above
+ 
+
+ align:start position:0%
+diffusion leaks gets well well above
+your device thickness that becomes less
+
+ align:start position:0%
+your device thickness that becomes less
+ 
+
+ align:start position:0%
+your device thickness that becomes less
+and less important okay so how do you
+
+ align:start position:0%
+and less important okay so how do you
+ 
+
+ align:start position:0%
+and less important okay so how do you
+deal with this so if you have let's say
+
+ align:start position:0%
+deal with this so if you have let's say
+ 
+
+ align:start position:0%
+deal with this so if you have let's say
+suppose you want to make a really cheap
+
+ align:start position:0%
+suppose you want to make a really cheap
+ 
+
+ align:start position:0%
+suppose you want to make a really cheap
+solar cell and you have a very dirty
+
+ align:start position:0%
+solar cell and you have a very dirty
+ 
+
+ align:start position:0%
+solar cell and you have a very dirty
+material with very short lifetime shown
+
+ align:start position:0%
+material with very short lifetime shown
+ 
+
+ align:start position:0%
+material with very short lifetime shown
+here there's kind of several ideas of
+
+ align:start position:0%
+here there's kind of several ideas of
+ 
+
+ align:start position:0%
+here there's kind of several ideas of
+what you can do you can have a very very
+
+ align:start position:0%
+what you can do you can have a very very
+ 
+
+ align:start position:0%
+what you can do you can have a very very
+thin device now that's a problem if you
+
+ align:start position:0%
+thin device now that's a problem if you
+ 
+
+ align:start position:0%
+thin device now that's a problem if you
+can't absorb it very well so you can
+
+ align:start position:0%
+can't absorb it very well so you can
+ 
+
+ align:start position:0%
+can't absorb it very well so you can
+have some kind of optical tricks you can
+
+ align:start position:0%
+have some kind of optical tricks you can
+ 
+
+ align:start position:0%
+have some kind of optical tricks you can
+do surface texturing there's all sorts
+
+ align:start position:0%
+do surface texturing there's all sorts
+ 
+
+ align:start position:0%
+do surface texturing there's all sorts
+of other ideas for basically having the
+
+ align:start position:0%
+of other ideas for basically having the
+ 
+
+ align:start position:0%
+of other ideas for basically having the
+carriers come in at angles or having a
+
+ align:start position:0%
+carriers come in at angles or having a
+ 
+
+ align:start position:0%
+carriers come in at angles or having a
+good reflector on the back so that's
+
+ align:start position:0%
+good reflector on the back so that's
+ 
+
+ align:start position:0%
+good reflector on the back so that's
+ways you can with you can work with very
+
+ align:start position:0%
+ways you can with you can work with very
+ 
+
+ align:start position:0%
+ways you can with you can work with very
+low diffusion length materials and still
+
+ align:start position:0%
+low diffusion length materials and still
+ 
+
+ align:start position:0%
+low diffusion length materials and still
+get a device efficiency that's not not
+
+ align:start position:0%
+get a device efficiency that's not not
+ 
+
+ align:start position:0%
+get a device efficiency that's not not
+too bad okay now we're going to talk
+
+ align:start position:0%
+too bad okay now we're going to talk
+ 
+
+ align:start position:0%
+too bad okay now we're going to talk
+quickly about how our minority carrier
+
+ align:start position:0%
+quickly about how our minority carrier
+ 
+
+ align:start position:0%
+quickly about how our minority carrier
+diffusion length is measured and again
+
+ align:start position:0%
+diffusion length is measured and again
+ 
+
+ align:start position:0%
+diffusion length is measured and again
+this is something we're able to do in
+
+ align:start position:0%
+this is something we're able to do in
+ 
+
+ align:start position:0%
+this is something we're able to do in
+our lab and one of the important things
+
+ align:start position:0%
+our lab and one of the important things
+ 
+
+ align:start position:0%
+our lab and one of the important things
+to say is define is collection
+
+ align:start position:0%
+to say is define is collection
+ 
+
+ align:start position:0%
+to say is define is collection
+probability so for example if this is
+
+ align:start position:0%
+probability so for example if this is
+ 
+
+ align:start position:0%
+probability so for example if this is
+our junction right here or our space
+
+ align:start position:0%
+our junction right here or our space
+ 
+
+ align:start position:0%
+our junction right here or our space
+charge region if you generate a carrier
+
+ align:start position:0%
+charge region if you generate a carrier
+ 
+
+ align:start position:0%
+charge region if you generate a carrier
+let's say very very close to the
+
+ align:start position:0%
+let's say very very close to the
+ 
+
+ align:start position:0%
+let's say very very close to the
+junction it's going to have a high or
+
+ align:start position:0%
+junction it's going to have a high or
+ 
+
+ align:start position:0%
+junction it's going to have a high or
+near Unity probability of making it to
+
+ align:start position:0%
+near Unity probability of making it to
+ 
+
+ align:start position:0%
+near Unity probability of making it to
+the direction and being collected if
+
+ align:start position:0%
+the direction and being collected if
+ 
+
+ align:start position:0%
+the direction and being collected if
+it's generated very very very far away
+
+ align:start position:0%
+it's generated very very very far away
+ 
+
+ align:start position:0%
+it's generated very very very far away
+it's going to have a lower probability
+
+ align:start position:0%
+it's going to have a lower probability
+ 
+
+ align:start position:0%
+it's going to have a lower probability
+and that's what this graph is trying to
+
+ align:start position:0%
+and that's what this graph is trying to
+ 
+
+ align:start position:0%
+and that's what this graph is trying to
+show is that right near the junction you
+
+ align:start position:0%
+show is that right near the junction you
+ 
+
+ align:start position:0%
+show is that right near the junction you
+have near Unity collection probability
+
+ align:start position:0%
+have near Unity collection probability
+ 
+
+ align:start position:0%
+have near Unity collection probability
+and as you go away it comes down and the
+
+ align:start position:0%
+and as you go away it comes down and the
+ 
+
+ align:start position:0%
+and as you go away it comes down and the
+different colored lines are showing kind
+
+ align:start position:0%
+different colored lines are showing kind
+ 
+
+ align:start position:0%
+different colored lines are showing kind
+of different ways of increasing that
+
+ align:start position:0%
+of different ways of increasing that
+ 
+
+ align:start position:0%
+of different ways of increasing that
+diffusion length surface passivation is
+
+ align:start position:0%
+diffusion length surface passivation is
+ 
+
+ align:start position:0%
+diffusion length surface passivation is
+important we'll talk about what that is
+
+ align:start position:0%
+important we'll talk about what that is
+ 
+
+ align:start position:0%
+important we'll talk about what that is
+soon and also diffusion lengths you if
+
+ align:start position:0%
+soon and also diffusion lengths you if
+ 
+
+ align:start position:0%
+soon and also diffusion lengths you if
+you're limited by
+
+ align:start position:0%
+you're limited by
+ 
+
+ align:start position:0%
+you're limited by
+fusion length you can see this very very
+
+ align:start position:0%
+fusion length you can see this very very
+ 
+
+ align:start position:0%
+fusion length you can see this very very
+sharp drop-off right here it's
+
+ align:start position:0%
+sharp drop-off right here it's
+ 
+
+ align:start position:0%
+sharp drop-off right here it's
+technically defined as reaching the
+
+ align:start position:0%
+technically defined as reaching the
+ 
+
+ align:start position:0%
+technically defined as reaching the
+junction and being separated which in
+
+ align:start position:0%
+junction and being separated which in
+ 
+
+ align:start position:0%
+junction and being separated which in
+essence will hopefully be the same thing
+
+ align:start position:0%
+essence will hopefully be the same thing
+ 
+
+ align:start position:0%
+essence will hopefully be the same thing
+yeah it can it can affect the diffusion
+
+ align:start position:0%
+yeah it can it can affect the diffusion
+ 
+
+ align:start position:0%
+yeah it can it can affect the diffusion
+length and will or the effective
+
+ align:start position:0%
+length and will or the effective
+ 
+
+ align:start position:0%
+length and will or the effective
+diffusion might we'll get to that in a
+
+ align:start position:0%
+diffusion might we'll get to that in a
+ 
+
+ align:start position:0%
+diffusion might we'll get to that in a
+second it'll be a bit later this is kind
+
+ align:start position:0%
+second it'll be a bit later this is kind
+ 
+
+ align:start position:0%
+second it'll be a bit later this is kind
+of just showing that there's a lot of
+
+ align:start position:0%
+of just showing that there's a lot of
+ 
+
+ align:start position:0%
+of just showing that there's a lot of
+different material parameters not just
+
+ align:start position:0%
+different material parameters not just
+ 
+
+ align:start position:0%
+different material parameters not just
+your diffusion length that can really
+
+ align:start position:0%
+your diffusion length that can really
+ 
+
+ align:start position:0%
+your diffusion length that can really
+affect your device performance in your
+
+ align:start position:0%
+affect your device performance in your
+ 
+
+ align:start position:0%
+affect your device performance in your
+collection probability Oh so if you
+
+ align:start position:0%
+collection probability Oh so if you
+ 
+
+ align:start position:0%
+collection probability Oh so if you
+recall a few slides back we said that
+
+ align:start position:0%
+recall a few slides back we said that
+ 
+
+ align:start position:0%
+recall a few slides back we said that
+our short-circuit current was directly
+
+ align:start position:0%
+our short-circuit current was directly
+ 
+
+ align:start position:0%
+our short-circuit current was directly
+proportional to our diffusion length and
+
+ align:start position:0%
+proportional to our diffusion length and
+ 
+
+ align:start position:0%
+proportional to our diffusion length and
+the reason is that if you're generating
+
+ align:start position:0%
+the reason is that if you're generating
+ 
+
+ align:start position:0%
+the reason is that if you're generating
+carriers within the diffusion length you
+
+ align:start position:0%
+carriers within the diffusion length you
+ 
+
+ align:start position:0%
+carriers within the diffusion length you
+generally think of that as the region of
+
+ align:start position:0%
+generally think of that as the region of
+ 
+
+ align:start position:0%
+generally think of that as the region of
+which you're actually collecting those
+
+ align:start position:0%
+which you're actually collecting those
+ 
+
+ align:start position:0%
+which you're actually collecting those
+carriers right and if you go back to the
+
+ align:start position:0%
+carriers right and if you go back to the
+ 
+
+ align:start position:0%
+carriers right and if you go back to the
+next slide that kind of makes sense and
+
+ align:start position:0%
+next slide that kind of makes sense and
+ 
+
+ align:start position:0%
+next slide that kind of makes sense and
+so this is highlighted so this is our
+
+ align:start position:0%
+so this is highlighted so this is our
+ 
+
+ align:start position:0%
+so this is highlighted so this is our
+junction here we have our n-type
+
+ align:start position:0%
+junction here we have our n-type
+ 
+
+ align:start position:0%
+junction here we have our n-type
+material on top our p-type below and
+
+ align:start position:0%
+material on top our p-type below and
+ 
+
+ align:start position:0%
+material on top our p-type below and
+within a diffusion length of your
+
+ align:start position:0%
+within a diffusion length of your
+ 
+
+ align:start position:0%
+within a diffusion length of your
+minority carrier so on your p-type side
+
+ align:start position:0%
+minority carrier so on your p-type side
+ 
+
+ align:start position:0%
+minority carrier so on your p-type side
+you hear about the diffusion length of
+
+ align:start position:0%
+you hear about the diffusion length of
+ 
+
+ align:start position:0%
+you hear about the diffusion length of
+your electrons and the n-type side you
+
+ align:start position:0%
+your electrons and the n-type side you
+ 
+
+ align:start position:0%
+your electrons and the n-type side you
+care about the diffusion length of your
+
+ align:start position:0%
+care about the diffusion length of your
+ 
+
+ align:start position:0%
+care about the diffusion length of your
+holes and that's the region where you're
+
+ align:start position:0%
+holes and that's the region where you're
+ 
+
+ align:start position:0%
+holes and that's the region where you're
+really collecting carriers of course
+
+ align:start position:0%
+really collecting carriers of course
+ 
+
+ align:start position:0%
+really collecting carriers of course
+there's like a tail off but the first
+
+ align:start position:0%
+there's like a tail off but the first
+ 
+
+ align:start position:0%
+there's like a tail off but the first
+order approximation this is actually a
+
+ align:start position:0%
+order approximation this is actually a
+ 
+
+ align:start position:0%
+order approximation this is actually a
+very good one and so now putting those
+
+ align:start position:0%
+very good one and so now putting those
+ 
+
+ align:start position:0%
+very good one and so now putting those
+all together if we know how our carriers
+
+ align:start position:0%
+all together if we know how our carriers
+ 
+
+ align:start position:0%
+all together if we know how our carriers
+are generated as a function of X and we
+
+ align:start position:0%
+are generated as a function of X and we
+ 
+
+ align:start position:0%
+are generated as a function of X and we
+know what the collection probability is
+
+ align:start position:0%
+know what the collection probability is
+ 
+
+ align:start position:0%
+know what the collection probability is
+as a function of X based on diffusion
+
+ align:start position:0%
+as a function of X based on diffusion
+ 
+
+ align:start position:0%
+as a function of X based on diffusion
+length surface passivation and other
+
+ align:start position:0%
+length surface passivation and other
+ 
+
+ align:start position:0%
+length surface passivation and other
+parameters we can multiply them and then
+
+ align:start position:0%
+parameters we can multiply them and then
+ 
+
+ align:start position:0%
+parameters we can multiply them and then
+integrate to actually get what our
+
+ align:start position:0%
+integrate to actually get what our
+ 
+
+ align:start position:0%
+integrate to actually get what our
+illuminated current will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the emitter hmm for most models you
+
+ align:start position:0%
+the emitter hmm for most models you
+ 
+
+ align:start position:0%
+the emitter hmm for most models you
+pretty much assume that anything
+
+ align:start position:0%
+pretty much assume that anything
+ 
+
+ align:start position:0%
+pretty much assume that anything
+absorbed I mean first of all the space
+
+ align:start position:0%
+absorbed I mean first of all the space
+ 
+
+ align:start position:0%
+absorbed I mean first of all the space
+charge region is very very narrow
+
+ align:start position:0%
+charge region is very very narrow
+ 
+
+ align:start position:0%
+charge region is very very narrow
+it's almost assumed just to be
+
+ align:start position:0%
+it's almost assumed just to be
+ 
+
+ align:start position:0%
+it's almost assumed just to be
+negligibly thin and the emitter is
+
+ align:start position:0%
+negligibly thin and the emitter is
+ 
+
+ align:start position:0%
+negligibly thin and the emitter is
+generally very very short and the
+
+ align:start position:0%
+generally very very short and the
+ 
+
+ align:start position:0%
+generally very very short and the
+diffusion lengths are so poor in the
+
+ align:start position:0%
+diffusion lengths are so poor in the
+ 
+
+ align:start position:0%
+diffusion lengths are so poor in the
+emitter for reasons we'll get to soon
+
+ align:start position:0%
+emitter for reasons we'll get to soon
+ 
+
+ align:start position:0%
+emitter for reasons we'll get to soon
+that it's almost a dead layer your
+
+ align:start position:0%
+that it's almost a dead layer your
+ 
+
+ align:start position:0%
+that it's almost a dead layer your
+response at the very short wavelengths
+
+ align:start position:0%
+response at the very short wavelengths
+ 
+
+ align:start position:0%
+response at the very short wavelengths
+where you're absorbing most your light
+
+ align:start position:0%
+where you're absorbing most your light
+ 
+
+ align:start position:0%
+where you're absorbing most your light
+in the emitter generally don't add to
+
+ align:start position:0%
+in the emitter generally don't add to
+ 
+
+ align:start position:0%
+in the emitter generally don't add to
+your short-circuit current and we'll
+
+ align:start position:0%
+your short-circuit current and we'll
+ 
+
+ align:start position:0%
+your short-circuit current and we'll
+talk about that soon so excellent
+
+ align:start position:0%
+talk about that soon so excellent
+ 
+
+ align:start position:0%
+talk about that soon so excellent
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+yeah wait sorry say that again so for
+
+ align:start position:0%
+yeah wait sorry say that again so for
+ 
+
+ align:start position:0%
+yeah wait sorry say that again so for
+certain wavelengths of light let's say
+
+ align:start position:0%
+certain wavelengths of light let's say
+ 
+
+ align:start position:0%
+certain wavelengths of light let's say
+that are this out this curve this is for
+
+ align:start position:0%
+that are this out this curve this is for
+ 
+
+ align:start position:0%
+that are this out this curve this is for
+kind of representing beer Lambert's law
+
+ align:start position:0%
+kind of representing beer Lambert's law
+ 
+
+ align:start position:0%
+kind of representing beer Lambert's law
+if it attenuates less drastically that
+
+ align:start position:0%
+if it attenuates less drastically that
+ 
+
+ align:start position:0%
+if it attenuates less drastically that
+characteristic absorption length if it's
+
+ align:start position:0%
+characteristic absorption length if it's
+ 
+
+ align:start position:0%
+characteristic absorption length if it's
+a lot longer than this length here then
+
+ align:start position:0%
+a lot longer than this length here then
+ 
+
+ align:start position:0%
+a lot longer than this length here then
+yes you can assume that this emitter
+
+ align:start position:0%
+yes you can assume that this emitter
+ 
+
+ align:start position:0%
+yes you can assume that this emitter
+region is negligibly thin and that's a
+
+ align:start position:0%
+region is negligibly thin and that's a
+ 
+
+ align:start position:0%
+region is negligibly thin and that's a
+little bit what the homework goes over
+
+ align:start position:0%
+little bit what the homework goes over
+ 
+
+ align:start position:0%
+little bit what the homework goes over
+as well in problem 3 excellent question
+
+ align:start position:0%
+as well in problem 3 excellent question
+ 
+
+ align:start position:0%
+as well in problem 3 excellent question
+and so what we care about is kind of the
+
+ align:start position:0%
+and so what we care about is kind of the
+ 
+
+ align:start position:0%
+and so what we care about is kind of the
+spectral response of our short-circuit
+
+ align:start position:0%
+spectral response of our short-circuit
+ 
+
+ align:start position:0%
+spectral response of our short-circuit
+current so what what this is is this is
+
+ align:start position:0%
+current so what what this is is this is
+ 
+
+ align:start position:0%
+current so what what this is is this is
+a quantum efficiency tool this is
+
+ align:start position:0%
+a quantum efficiency tool this is
+ 
+
+ align:start position:0%
+a quantum efficiency tool this is
+something we have in our lab it's a
+
+ align:start position:0%
+something we have in our lab it's a
+ 
+
+ align:start position:0%
+something we have in our lab it's a
+really fun tool to play around with how
+
+ align:start position:0%
+really fun tool to play around with how
+ 
+
+ align:start position:0%
+really fun tool to play around with how
+it works is you basically have let's say
+
+ align:start position:0%
+it works is you basically have let's say
+ 
+
+ align:start position:0%
+it works is you basically have let's say
+we have a light source that's white
+
+ align:start position:0%
+we have a light source that's white
+ 
+
+ align:start position:0%
+we have a light source that's white
+light and it goes through a series of
+
+ align:start position:0%
+light and it goes through a series of
+ 
+
+ align:start position:0%
+light and it goes through a series of
+filters there's a monochromator which
+
+ align:start position:0%
+filters there's a monochromator which
+ 
+
+ align:start position:0%
+filters there's a monochromator which
+basically it diffracts the light so it
+
+ align:start position:0%
+basically it diffracts the light so it
+ 
+
+ align:start position:0%
+basically it diffracts the light so it
+spatially separates the light kind of
+
+ align:start position:0%
+spatially separates the light kind of
+ 
+
+ align:start position:0%
+spatially separates the light kind of
+like a rainbow and then you can focus
+
+ align:start position:0%
+like a rainbow and then you can focus
+ 
+
+ align:start position:0%
+like a rainbow and then you can focus
+that on to your solar cell and measure
+
+ align:start position:0%
+that on to your solar cell and measure
+ 
+
+ align:start position:0%
+that on to your solar cell and measure
+the current output and under short
+
+ align:start position:0%
+the current output and under short
+ 
+
+ align:start position:0%
+the current output and under short
+circuit conditions and that will tell
+
+ align:start position:0%
+circuit conditions and that will tell
+ 
+
+ align:start position:0%
+circuit conditions and that will tell
+you because you know the carrier
+
+ align:start position:0%
+you because you know the carrier
+ 
+
+ align:start position:0%
+you because you know the carrier
+generation profile for different
+
+ align:start position:0%
+generation profile for different
+ 
+
+ align:start position:0%
+generation profile for different
+wavelengths of light because you know
+
+ align:start position:0%
+wavelengths of light because you know
+ 
+
+ align:start position:0%
+wavelengths of light because you know
+what alpha is for silicon you can
+
+ align:start position:0%
+what alpha is for silicon you can
+ 
+
+ align:start position:0%
+what alpha is for silicon you can
+actually pretty well calculate what what
+
+ align:start position:0%
+actually pretty well calculate what what
+ 
+
+ align:start position:0%
+actually pretty well calculate what what
+your diffusion length is and we'll talk
+
+ align:start position:0%
+your diffusion length is and we'll talk
+ 
+
+ align:start position:0%
+your diffusion length is and we'll talk
+about that on the next slide so this is
+
+ align:start position:0%
+about that on the next slide so this is
+ 
+
+ align:start position:0%
+about that on the next slide so this is
+kind of what your quantum efficiency
+
+ align:start position:0%
+kind of what your quantum efficiency
+ 
+
+ align:start position:0%
+kind of what your quantum efficiency
+walk like this is I think
+
+ align:start position:0%
+walk like this is I think
+ 
+
+ align:start position:0%
+walk like this is I think
+actually don't know this is
+
+ align:start position:0%
+actually don't know this is
+ 
+
+ align:start position:0%
+actually don't know this is
+internal-external but they're just
+
+ align:start position:0%
+internal-external but they're just
+ 
+
+ align:start position:0%
+internal-external but they're just
+related by a factor of one over R so
+
+ align:start position:0%
+related by a factor of one over R so
+ 
+
+ align:start position:0%
+related by a factor of one over R so
+here your blue response so everything
+
+ align:start position:0%
+here your blue response so everything
+ 
+
+ align:start position:0%
+here your blue response so everything
+that's absorbed right in the near
+
+ align:start position:0%
+that's absorbed right in the near
+ 
+
+ align:start position:0%
+that's absorbed right in the near
+surface region in your emitter generally
+
+ align:start position:0%
+surface region in your emitter generally
+ 
+
+ align:start position:0%
+surface region in your emitter generally
+doesn't get collected and this is due to
+
+ align:start position:0%
+doesn't get collected and this is due to
+ 
+
+ align:start position:0%
+doesn't get collected and this is due to
+really bad diffusion links in the
+
+ align:start position:0%
+really bad diffusion links in the
+ 
+
+ align:start position:0%
+really bad diffusion links in the
+emitter region as you go to longer
+
+ align:start position:0%
+emitter region as you go to longer
+ 
+
+ align:start position:0%
+emitter region as you go to longer
+wavelengths which are due the absorption
+
+ align:start position:0%
+wavelengths which are due the absorption
+ 
+
+ align:start position:0%
+wavelengths which are due the absorption
+length is much much deeper you're
+
+ align:start position:0%
+length is much much deeper you're
+ 
+
+ align:start position:0%
+length is much much deeper you're
+collecting a lot of it and then what do
+
+ align:start position:0%
+collecting a lot of it and then what do
+ 
+
+ align:start position:0%
+collecting a lot of it and then what do
+you think is happening here you're
+
+ align:start position:0%
+you think is happening here you're
+ 
+
+ align:start position:0%
+you think is happening here you're
+generally these longer wavelengths your
+
+ align:start position:0%
+generally these longer wavelengths your
+ 
+
+ align:start position:0%
+generally these longer wavelengths your
+alpha is is so low that you're not
+
+ align:start position:0%
+alpha is is so low that you're not
+ 
+
+ align:start position:0%
+alpha is is so low that you're not
+actually absorbing much of this light
+
+ align:start position:0%
+actually absorbing much of this light
+ 
+
+ align:start position:0%
+actually absorbing much of this light
+which is part of the reason that you're
+
+ align:start position:0%
+which is part of the reason that you're
+ 
+
+ align:start position:0%
+which is part of the reason that you're
+not collecting it or that you're
+
+ align:start position:0%
+not collecting it or that you're
+ 
+
+ align:start position:0%
+not collecting it or that you're
+absorbing it so far away from the
+
+ align:start position:0%
+absorbing it so far away from the
+ 
+
+ align:start position:0%
+absorbing it so far away from the
+junction that it's not being able to
+
+ align:start position:0%
+junction that it's not being able to
+ 
+
+ align:start position:0%
+junction that it's not being able to
+diffuse there and so that's kind of how
+
+ align:start position:0%
+diffuse there and so that's kind of how
+ 
+
+ align:start position:0%
+diffuse there and so that's kind of how
+you can look at these quantum efficiency
+
+ align:start position:0%
+you can look at these quantum efficiency
+ 
+
+ align:start position:0%
+you can look at these quantum efficiency
+curves and it's this region here that's
+
+ align:start position:0%
+curves and it's this region here that's
+ 
+
+ align:start position:0%
+curves and it's this region here that's
+really limited by diffusion lengths and
+
+ align:start position:0%
+really limited by diffusion lengths and
+ 
+
+ align:start position:0%
+really limited by diffusion lengths and
+again you have a homework problem
+
+ align:start position:0%
+again you have a homework problem
+ 
+
+ align:start position:0%
+again you have a homework problem
+discussing how that's done some of the
+
+ align:start position:0%
+discussing how that's done some of the
+ 
+
+ align:start position:0%
+discussing how that's done some of the
+cool other tools I lab can kind of do
+
+ align:start position:0%
+cool other tools I lab can kind of do
+ 
+
+ align:start position:0%
+cool other tools I lab can kind of do
+this but it requires a little more
+
+ align:start position:0%
+this but it requires a little more
+ 
+
+ align:start position:0%
+this but it requires a little more
+I don't know handwork on the operator
+
+ align:start position:0%
+I don't know handwork on the operator
+ 
+
+ align:start position:0%
+I don't know handwork on the operator
+but if you can take different eqe curves
+
+ align:start position:0%
+but if you can take different eqe curves
+ 
+
+ align:start position:0%
+but if you can take different eqe curves
+or iqe curves at different points on
+
+ align:start position:0%
+or iqe curves at different points on
+ 
+
+ align:start position:0%
+or iqe curves at different points on
+your solar cell and you get those
+
+ align:start position:0%
+your solar cell and you get those
+ 
+
+ align:start position:0%
+your solar cell and you get those
+spectrums you'll get a whole bunch of
+
+ align:start position:0%
+spectrums you'll get a whole bunch of
+ 
+
+ align:start position:0%
+spectrums you'll get a whole bunch of
+different spectrum you'll scan with your
+
+ align:start position:0%
+different spectrum you'll scan with your
+ 
+
+ align:start position:0%
+different spectrum you'll scan with your
+your light beam you can actually get the
+
+ align:start position:0%
+your light beam you can actually get the
+ 
+
+ align:start position:0%
+your light beam you can actually get the
+fusion lines as a function of position
+
+ align:start position:0%
+fusion lines as a function of position
+ 
+
+ align:start position:0%
+fusion lines as a function of position
+and get a spatial map of your different
+
+ align:start position:0%
+and get a spatial map of your different
+ 
+
+ align:start position:0%
+and get a spatial map of your different
+diffusion lengths and it's really
+
+ align:start position:0%
+diffusion lengths and it's really
+ 
+
+ align:start position:0%
+diffusion lengths and it's really
+helpful if you're trying to find spatial
+
+ align:start position:0%
+helpful if you're trying to find spatial
+ 
+
+ align:start position:0%
+helpful if you're trying to find spatial
+inhomogeneities in your cell so I
+
+ align:start position:0%
+inhomogeneities in your cell so I
+ 
+
+ align:start position:0%
+inhomogeneities in your cell so I
+believe that this is some multi
+
+ align:start position:0%
+believe that this is some multi
+ 
+
+ align:start position:0%
+believe that this is some multi
+crystalline cell and you see all sorts
+
+ align:start position:0%
+crystalline cell and you see all sorts
+ 
+
+ align:start position:0%
+crystalline cell and you see all sorts
+of grain boundaries and those are areas
+
+ align:start position:0%
+of grain boundaries and those are areas
+ 
+
+ align:start position:0%
+of grain boundaries and those are areas
+of very short diffusion length and we'll
+
+ align:start position:0%
+of very short diffusion length and we'll
+ 
+
+ align:start position:0%
+of very short diffusion length and we'll
+talk about why that's the case
+
+ align:start position:0%
+talk about why that's the case
+ 
+
+ align:start position:0%
+talk about why that's the case
+actually on the next couple slides
+
+ align:start position:0%
+actually on the next couple slides
+ 
+
+ align:start position:0%
+actually on the next couple slides
+question yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so you're okay so alpha is what tells
+
+ align:start position:0%
+so you're okay so alpha is what tells
+ 
+
+ align:start position:0%
+so you're okay so alpha is what tells
+you is your absorption coefficient right
+
+ align:start position:0%
+you is your absorption coefficient right
+ 
+
+ align:start position:0%
+you is your absorption coefficient right
+and it's often in units of one over
+
+ align:start position:0%
+and it's often in units of one over
+ 
+
+ align:start position:0%
+and it's often in units of one over
+centimeters so inverse centimeters and
+
+ align:start position:0%
+centimeters so inverse centimeters and
+ 
+
+ align:start position:0%
+centimeters so inverse centimeters and
+so if you plot what that looks like it's
+
+ align:start position:0%
+so if you plot what that looks like it's
+ 
+
+ align:start position:0%
+so if you plot what that looks like it's
+some exponential function with X right
+
+ align:start position:0%
+some exponential function with X right
+ 
+
+ align:start position:0%
+some exponential function with X right
+and the point two which is attenuated by
+
+ align:start position:0%
+and the point two which is attenuated by
+ 
+
+ align:start position:0%
+and the point two which is attenuated by
+a factor of one over EE
+
+ align:start position:0%
+a factor of one over EE
+ 
+
+ align:start position:0%
+a factor of one over EE
+that point is one over alpha and that's
+
+ align:start position:0%
+that point is one over alpha and that's
+ 
+
+ align:start position:0%
+that point is one over alpha and that's
+often called the absorption depth or am
+
+ align:start position:0%
+often called the absorption depth or am
+ 
+
+ align:start position:0%
+often called the absorption depth or am
+I thinking of absorption length of that
+
+ align:start position:0%
+I thinking of absorption length of that
+ 
+
+ align:start position:0%
+I thinking of absorption length of that
+wavelength and alpha will vary as a
+
+ align:start position:0%
+wavelength and alpha will vary as a
+ 
+
+ align:start position:0%
+wavelength and alpha will vary as a
+function of wavelength if you recall
+
+ align:start position:0%
+function of wavelength if you recall
+ 
+
+ align:start position:0%
+function of wavelength if you recall
+that if you look at lambda for silicon
+
+ align:start position:0%
+that if you look at lambda for silicon
+ 
+
+ align:start position:0%
+that if you look at lambda for silicon
+it's something that continues to go down
+
+ align:start position:0%
+it's something that continues to go down
+ 
+
+ align:start position:0%
+it's something that continues to go down
+at longer wavelengths so the short
+
+ align:start position:0%
+at longer wavelengths so the short
+ 
+
+ align:start position:0%
+at longer wavelengths so the short
+wavelengths are absorbed very strongly
+
+ align:start position:0%
+wavelengths are absorbed very strongly
+ 
+
+ align:start position:0%
+wavelengths are absorbed very strongly
+and so most of the light is absorbed
+
+ align:start position:0%
+and so most of the light is absorbed
+ 
+
+ align:start position:0%
+and so most of the light is absorbed
+very very close to the surface where the
+
+ align:start position:0%
+very very close to the surface where the
+ 
+
+ align:start position:0%
+very very close to the surface where the
+longer wavelengths most of the light is
+
+ align:start position:0%
+longer wavelengths most of the light is
+ 
+
+ align:start position:0%
+longer wavelengths most of the light is
+actually absorbed better they're far
+
+ align:start position:0%
+actually absorbed better they're far
+ 
+
+ align:start position:0%
+actually absorbed better they're far
+from the surface that make sense and so
+
+ align:start position:0%
+from the surface that make sense and so
+ 
+
+ align:start position:0%
+from the surface that make sense and so
+there's a difference between your
+
+ align:start position:0%
+there's a difference between your
+ 
+
+ align:start position:0%
+there's a difference between your
+absorption length and your diffusion
+
+ align:start position:0%
+absorption length and your diffusion
+ 
+
+ align:start position:0%
+absorption length and your diffusion
+length and that ratio is what's really
+
+ align:start position:0%
+length and that ratio is what's really
+ 
+
+ align:start position:0%
+length and that ratio is what's really
+important right if you're absorbing
+
+ align:start position:0%
+important right if you're absorbing
+ 
+
+ align:start position:0%
+important right if you're absorbing
+really far away from the junction but
+
+ align:start position:0%
+really far away from the junction but
+ 
+
+ align:start position:0%
+really far away from the junction but
+you have a long diffusion length there's
+
+ align:start position:0%
+you have a long diffusion length there's
+ 
+
+ align:start position:0%
+you have a long diffusion length there's
+a greater chance of it making there and
+
+ align:start position:0%
+a greater chance of it making there and
+ 
+
+ align:start position:0%
+a greater chance of it making there and
+it's that ratio that's really really
+
+ align:start position:0%
+it's that ratio that's really really
+ 
+
+ align:start position:0%
+it's that ratio that's really really
+important does that answer your question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so what limits is minority carrier
+
+ align:start position:0%
+okay so what limits is minority carrier
+ 
+
+ align:start position:0%
+okay so what limits is minority carrier
+diffusion length we're gonna get to the
+
+ align:start position:0%
+diffusion length we're gonna get to the
+ 
+
+ align:start position:0%
+diffusion length we're gonna get to the
+equation a second for the minority
+
+ align:start position:0%
+equation a second for the minority
+ 
+
+ align:start position:0%
+equation a second for the minority
+carrier diffusion length but basically
+
+ align:start position:0%
+carrier diffusion length but basically
+ 
+
+ align:start position:0%
+carrier diffusion length but basically
+when you excite an electron hole pair
+
+ align:start position:0%
+when you excite an electron hole pair
+ 
+
+ align:start position:0%
+when you excite an electron hole pair
+you have this mobile electron and it's
+
+ align:start position:0%
+you have this mobile electron and it's
+ 
+
+ align:start position:0%
+you have this mobile electron and it's
+in this excited state you've given it
+
+ align:start position:0%
+in this excited state you've given it
+ 
+
+ align:start position:0%
+in this excited state you've given it
+this energy from a photon and now can
+
+ align:start position:0%
+this energy from a photon and now can
+ 
+
+ align:start position:0%
+this energy from a photon and now can
+move around and it can only exist for a
+
+ align:start position:0%
+move around and it can only exist for a
+ 
+
+ align:start position:0%
+move around and it can only exist for a
+certain amount of time before it finds
+
+ align:start position:0%
+certain amount of time before it finds
+ 
+
+ align:start position:0%
+certain amount of time before it finds
+another hole and recombine and that
+
+ align:start position:0%
+another hole and recombine and that
+ 
+
+ align:start position:0%
+another hole and recombine and that
+event again is called recombination and
+
+ align:start position:0%
+event again is called recombination and
+ 
+
+ align:start position:0%
+event again is called recombination and
+a lot of this is actually determined by
+
+ align:start position:0%
+a lot of this is actually determined by
+ 
+
+ align:start position:0%
+a lot of this is actually determined by
+the size of grain
+
+ align:start position:0%
+the size of grain
+ 
+
+ align:start position:0%
+the size of grain
+in your material if you've seen think on
+
+ align:start position:0%
+in your material if you've seen think on
+ 
+
+ align:start position:0%
+in your material if you've seen think on
+the the cell that Tonio brought in
+
+ align:start position:0%
+the the cell that Tonio brought in
+ 
+
+ align:start position:0%
+the the cell that Tonio brought in
+earlier
+
+ align:start position:0%
+earlier
+ 
+
+ align:start position:0%
+earlier
+sorry I don't have a good example it
+
+ align:start position:0%
+sorry I don't have a good example it
+ 
+
+ align:start position:0%
+sorry I don't have a good example it
+didn't just look like one kind of flat
+
+ align:start position:0%
+didn't just look like one kind of flat
+ 
+
+ align:start position:0%
+didn't just look like one kind of flat
+plane you could see like different grain
+
+ align:start position:0%
+plane you could see like different grain
+ 
+
+ align:start position:0%
+plane you could see like different grain
+orientations and the edges of those
+
+ align:start position:0%
+orientations and the edges of those
+ 
+
+ align:start position:0%
+orientations and the edges of those
+grains are called grain boundaries and
+
+ align:start position:0%
+grains are called grain boundaries and
+ 
+
+ align:start position:0%
+grains are called grain boundaries and
+those can act as kind of recombination
+
+ align:start position:0%
+those can act as kind of recombination
+ 
+
+ align:start position:0%
+those can act as kind of recombination
+centers and actually reduce your that's
+
+ align:start position:0%
+centers and actually reduce your that's
+ 
+
+ align:start position:0%
+centers and actually reduce your that's
+called your lifetime which we're gonna
+
+ align:start position:0%
+called your lifetime which we're gonna
+ 
+
+ align:start position:0%
+called your lifetime which we're gonna
+get to on this slide okay so this slide
+
+ align:start position:0%
+get to on this slide okay so this slide
+ 
+
+ align:start position:0%
+get to on this slide okay so this slide
+has a lot of stuff going on what it's
+
+ align:start position:0%
+has a lot of stuff going on what it's
+ 
+
+ align:start position:0%
+has a lot of stuff going on what it's
+saying is that your diffusion length is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+characteristic of the diffusivity the
+
+ align:start position:0%
+characteristic of the diffusivity the
+ 
+
+ align:start position:0%
+characteristic of the diffusivity the
+product the square root of the product
+
+ align:start position:0%
+product the square root of the product
+ 
+
+ align:start position:0%
+product the square root of the product
+of your diffusivity in your lifetime the
+
+ align:start position:0%
+of your diffusivity in your lifetime the
+ 
+
+ align:start position:0%
+of your diffusivity in your lifetime the
+way I like to think of diffusivity is
+
+ align:start position:0%
+way I like to think of diffusivity is
+ 
+
+ align:start position:0%
+way I like to think of diffusivity is
+that you have it goes up with
+
+ align:start position:0%
+that you have it goes up with
+ 
+
+ align:start position:0%
+that you have it goes up with
+temperature and it's also affected by
+
+ align:start position:0%
+temperature and it's also affected by
+ 
+
+ align:start position:0%
+temperature and it's also affected by
+your mobility the mobility is saying
+
+ align:start position:0%
+your mobility the mobility is saying
+ 
+
+ align:start position:0%
+your mobility the mobility is saying
+that if you apply let's say an external
+
+ align:start position:0%
+that if you apply let's say an external
+ 
+
+ align:start position:0%
+that if you apply let's say an external
+field an electric field how well can
+
+ align:start position:0%
+field an electric field how well can
+ 
+
+ align:start position:0%
+field an electric field how well can
+those electrons move around so we're
+
+ align:start position:0%
+those electrons move around so we're
+ 
+
+ align:start position:0%
+those electrons move around so we're
+really high mobility means that those
+
+ align:start position:0%
+really high mobility means that those
+ 
+
+ align:start position:0%
+really high mobility means that those
+electrons can move really easily and
+
+ align:start position:0%
+electrons can move really easily and
+ 
+
+ align:start position:0%
+electrons can move really easily and
+you'll accelerate them really quickly
+
+ align:start position:0%
+you'll accelerate them really quickly
+ 
+
+ align:start position:0%
+you'll accelerate them really quickly
+we're very low mobility means that
+
+ align:start position:0%
+we're very low mobility means that
+ 
+
+ align:start position:0%
+we're very low mobility means that
+they're gonna continue to hit into
+
+ align:start position:0%
+they're gonna continue to hit into
+ 
+
+ align:start position:0%
+they're gonna continue to hit into
+things and bump around and not move
+
+ align:start position:0%
+things and bump around and not move
+ 
+
+ align:start position:0%
+things and bump around and not move
+around too well and your diffusion is
+
+ align:start position:0%
+around too well and your diffusion is
+ 
+
+ align:start position:0%
+around too well and your diffusion is
+this kind of thermal process if you
+
+ align:start position:0%
+this kind of thermal process if you
+ 
+
+ align:start position:0%
+this kind of thermal process if you
+think of let's say gases in a room and
+
+ align:start position:0%
+think of let's say gases in a room and
+ 
+
+ align:start position:0%
+think of let's say gases in a room and
+you have a hot gas that's going to
+
+ align:start position:0%
+you have a hot gas that's going to
+ 
+
+ align:start position:0%
+you have a hot gas that's going to
+diffuse a lot faster so it's the product
+
+ align:start position:0%
+diffuse a lot faster so it's the product
+ 
+
+ align:start position:0%
+diffuse a lot faster so it's the product
+of these two things it's it's kind of
+
+ align:start position:0%
+of these two things it's it's kind of
+ 
+
+ align:start position:0%
+of these two things it's it's kind of
+how well it can move around times it's
+
+ align:start position:0%
+how well it can move around times it's
+ 
+
+ align:start position:0%
+how well it can move around times it's
+kind of thermal energy that it has to
+
+ align:start position:0%
+kind of thermal energy that it has to
+ 
+
+ align:start position:0%
+kind of thermal energy that it has to
+move around the energy it has for moving
+
+ align:start position:0%
+move around the energy it has for moving
+ 
+
+ align:start position:0%
+move around the energy it has for moving
+and so that's kind of what the
+
+ align:start position:0%
+and so that's kind of what the
+ 
+
+ align:start position:0%
+and so that's kind of what the
+diffusivity means to me the life time
+
+ align:start position:0%
+diffusivity means to me the life time
+ 
+
+ align:start position:0%
+diffusivity means to me the life time
+again is what I mentioned earlier is
+
+ align:start position:0%
+again is what I mentioned earlier is
+ 
+
+ align:start position:0%
+again is what I mentioned earlier is
+that when you create this excited
+
+ align:start position:0%
+that when you create this excited
+ 
+
+ align:start position:0%
+that when you create this excited
+electron that's now free to move this
+
+ align:start position:0%
+electron that's now free to move this
+ 
+
+ align:start position:0%
+electron that's now free to move this
+mobile electron it can move around in
+
+ align:start position:0%
+mobile electron it can move around in
+ 
+
+ align:start position:0%
+mobile electron it can move around in
+explore a certain area that area or
+
+ align:start position:0%
+explore a certain area that area or
+ 
+
+ align:start position:0%
+explore a certain area that area or
+sorry volume is defined by the diffusion
+
+ align:start position:0%
+sorry volume is defined by the diffusion
+ 
+
+ align:start position:0%
+sorry volume is defined by the diffusion
+length and it exists in that excited
+
+ align:start position:0%
+length and it exists in that excited
+ 
+
+ align:start position:0%
+length and it exists in that excited
+state for some amount of time tau and
+
+ align:start position:0%
+state for some amount of time tau and
+ 
+
+ align:start position:0%
+state for some amount of time tau and
+that tau is not you know the not every
+
+ align:start position:0%
+that tau is not you know the not every
+ 
+
+ align:start position:0%
+that tau is not you know the not every
+carrier that's generated necessarily has
+
+ align:start position:0%
+carrier that's generated necessarily has
+ 
+
+ align:start position:0%
+carrier that's generated necessarily has
+that lifetime but it's a characteristic
+
+ align:start position:0%
+that lifetime but it's a characteristic
+ 
+
+ align:start position:0%
+that lifetime but it's a characteristic
+lifetime that it could have oh yeah and
+
+ align:start position:0%
+lifetime that it could have oh yeah and
+ 
+
+ align:start position:0%
+lifetime that it could have oh yeah and
+then they're pointed out here what they
+
+ align:start position:0%
+then they're pointed out here what they
+ 
+
+ align:start position:0%
+then they're pointed out here what they
+are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so that's what affects our
+
+ align:start position:0%
+okay so that's what affects our
+ 
+
+ align:start position:0%
+okay so that's what affects our
+diffusion like so in the next bunch of
+
+ align:start position:0%
+diffusion like so in the next bunch of
+ 
+
+ align:start position:0%
+diffusion like so in the next bunch of
+slides we're going to talk about mainly
+
+ align:start position:0%
+slides we're going to talk about mainly
+ 
+
+ align:start position:0%
+slides we're going to talk about mainly
+how we can affect tau so tau is mainly
+
+ align:start position:0%
+how we can affect tau so tau is mainly
+ 
+
+ align:start position:0%
+how we can affect tau so tau is mainly
+affected by recombination centers so
+
+ align:start position:0%
+affected by recombination centers so
+ 
+
+ align:start position:0%
+affected by recombination centers so
+defects and semiconductors and a few
+
+ align:start position:0%
+defects and semiconductors and a few
+ 
+
+ align:start position:0%
+defects and semiconductors and a few
+other things that we're going to talk
+
+ align:start position:0%
+other things that we're going to talk
+ 
+
+ align:start position:0%
+other things that we're going to talk
+about and then this is almost kind of
+
+ align:start position:0%
+about and then this is almost kind of
+ 
+
+ align:start position:0%
+about and then this is almost kind of
+limited depending on what kind of
+
+ align:start position:0%
+limited depending on what kind of
+ 
+
+ align:start position:0%
+limited depending on what kind of
+materials you're using the mobility and
+
+ align:start position:0%
+materials you're using the mobility and
+ 
+
+ align:start position:0%
+materials you're using the mobility and
+so we'll talk about that as well so all
+
+ align:start position:0%
+so we'll talk about that as well so all
+ 
+
+ align:start position:0%
+so we'll talk about that as well so all
+right what effects lifetime we're gonna
+
+ align:start position:0%
+right what effects lifetime we're gonna
+ 
+
+ align:start position:0%
+right what effects lifetime we're gonna
+go over again basic recombination
+
+ align:start position:0%
+go over again basic recombination
+ 
+
+ align:start position:0%
+go over again basic recombination
+mechanisms and semiconductors there's a
+
+ align:start position:0%
+mechanisms and semiconductors there's a
+ 
+
+ align:start position:0%
+mechanisms and semiconductors there's a
+lot of them a lot of them have some
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+rather complex kind of equations behind
+
+ align:start position:0%
+rather complex kind of equations behind
+ 
+
+ align:start position:0%
+rather complex kind of equations behind
+them we're not gonna delve too deeply
+
+ align:start position:0%
+them we're not gonna delve too deeply
+ 
+
+ align:start position:0%
+them we're not gonna delve too deeply
+into how to derive them you're welcome
+
+ align:start position:0%
+into how to derive them you're welcome
+ 
+
+ align:start position:0%
+into how to derive them you're welcome
+to do that it was actually kind of fun
+
+ align:start position:0%
+to do that it was actually kind of fun
+ 
+
+ align:start position:0%
+to do that it was actually kind of fun
+to do on my own and refresh myself so
+
+ align:start position:0%
+to do on my own and refresh myself so
+ 
+
+ align:start position:0%
+to do on my own and refresh myself so
+it's really useful and also be able to
+
+ align:start position:0%
+it's really useful and also be able to
+ 
+
+ align:start position:0%
+it's really useful and also be able to
+calculate our excess carrier
+
+ align:start position:0%
+calculate our excess carrier
+ 
+
+ align:start position:0%
+calculate our excess carrier
+concentration which we're gonna do in
+
+ align:start position:0%
+concentration which we're gonna do in
+ 
+
+ align:start position:0%
+concentration which we're gonna do in
+the next couple slides so okay and let's
+
+ align:start position:0%
+the next couple slides so okay and let's
+ 
+
+ align:start position:0%
+the next couple slides so okay and let's
+say for p-type material or sorry n-type
+
+ align:start position:0%
+say for p-type material or sorry n-type
+ 
+
+ align:start position:0%
+say for p-type material or sorry n-type
+material the number of mobile electrons
+
+ align:start position:0%
+material the number of mobile electrons
+ 
+
+ align:start position:0%
+material the number of mobile electrons
+you have is defined as N and not is very
+
+ align:start position:0%
+you have is defined as N and not is very
+ 
+
+ align:start position:0%
+you have is defined as N and not is very
+frequently your dopant density so these
+
+ align:start position:0%
+frequently your dopant density so these
+ 
+
+ align:start position:0%
+frequently your dopant density so these
+come up with 1/2 the time sorry wrong
+
+ align:start position:0%
+come up with 1/2 the time sorry wrong
+ 
+
+ align:start position:0%
+come up with 1/2 the time sorry wrong
+direction are generally the doping
+
+ align:start position:0%
+direction are generally the doping
+ 
+
+ align:start position:0%
+direction are generally the doping
+concentration right so if you're putting
+
+ align:start position:0%
+concentration right so if you're putting
+ 
+
+ align:start position:0%
+concentration right so if you're putting
+in phosphorous atoms into your silicon
+
+ align:start position:0%
+in phosphorous atoms into your silicon
+ 
+
+ align:start position:0%
+in phosphorous atoms into your silicon
+it would be the concentration of
+
+ align:start position:0%
+it would be the concentration of
+ 
+
+ align:start position:0%
+it would be the concentration of
+phosphorous atoms your Delta n is how
+
+ align:start position:0%
+phosphorous atoms your Delta n is how
+ 
+
+ align:start position:0%
+phosphorous atoms your Delta n is how
+many extra electrons are you adding
+
+ align:start position:0%
+many extra electrons are you adding
+ 
+
+ align:start position:0%
+many extra electrons are you adding
+mobile electrons due to the photo
+
+ align:start position:0%
+mobile electrons due to the photo
+ 
+
+ align:start position:0%
+mobile electrons due to the photo
+excitation of light right and so that's
+
+ align:start position:0%
+excitation of light right and so that's
+ 
+
+ align:start position:0%
+excitation of light right and so that's
+what this is saying is that you have
+
+ align:start position:0%
+what this is saying is that you have
+ 
+
+ align:start position:0%
+what this is saying is that you have
+some your Delta n is equal to your
+
+ align:start position:0%
+some your Delta n is equal to your
+ 
+
+ align:start position:0%
+some your Delta n is equal to your
+generation rate so your generation rate
+
+ align:start position:0%
+generation rate so your generation rate
+ 
+
+ align:start position:0%
+generation rate so your generation rate
+is generally in units of carriers per
+
+ align:start position:0%
+is generally in units of carriers per
+ 
+
+ align:start position:0%
+is generally in units of carriers per
+volume per second so how many carriers
+
+ align:start position:0%
+volume per second so how many carriers
+ 
+
+ align:start position:0%
+volume per second so how many carriers
+you're generating in a certain volume
+
+ align:start position:0%
+you're generating in a certain volume
+ 
+
+ align:start position:0%
+you're generating in a certain volume
+and because Delta n is actually a
+
+ align:start position:0%
+and because Delta n is actually a
+ 
+
+ align:start position:0%
+and because Delta n is actually a
+density you need to say okay how long do
+
+ align:start position:0%
+density you need to say okay how long do
+ 
+
+ align:start position:0%
+density you need to say okay how long do
+those carriers last once they're excited
+
+ align:start position:0%
+those carriers last once they're excited
+ 
+
+ align:start position:0%
+those carriers last once they're excited
+and so is this GTL product is what gives
+
+ align:start position:0%
+and so is this GTL product is what gives
+ 
+
+ align:start position:0%
+and so is this GTL product is what gives
+you your Delta n now when working with
+
+ align:start position:0%
+you your Delta n now when working with
+ 
+
+ align:start position:0%
+you your Delta n now when working with
+silicon it's really important to
+
+ align:start position:0%
+silicon it's really important to
+ 
+
+ align:start position:0%
+silicon it's really important to
+understand what the different ratios are
+
+ align:start position:0%
+understand what the different ratios are
+ 
+
+ align:start position:0%
+understand what the different ratios are
+of N and not Delta n your doping
+
+ align:start position:0%
+of N and not Delta n your doping
+ 
+
+ align:start position:0%
+of N and not Delta n your doping
+concentrations so getting these relative
+
+ align:start position:0%
+concentrations so getting these relative
+ 
+
+ align:start position:0%
+concentrations so getting these relative
+numbers in your head is an important
+
+ align:start position:0%
+numbers in your head is an important
+ 
+
+ align:start position:0%
+numbers in your head is an important
+step in moving forward so
+
+ align:start position:0%
+step in moving forward so
+ 
+
+ align:start position:0%
+step in moving forward so
+let's say we subject a piece of silicon
+
+ align:start position:0%
+let's say we subject a piece of silicon
+ 
+
+ align:start position:0%
+let's say we subject a piece of silicon
+to am 1.5 spectra yeah so you're G oh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry this is a little off there we go
+
+ align:start position:0%
+sorry this is a little off there we go
+ 
+
+ align:start position:0%
+sorry this is a little off there we go
+sorry about that when I added some
+
+ align:start position:0%
+sorry about that when I added some
+ 
+
+ align:start position:0%
+sorry about that when I added some
+equations so your your generation rate
+
+ align:start position:0%
+equations so your your generation rate
+ 
+
+ align:start position:0%
+equations so your your generation rate
+is on the order of 10 to the 16 a
+
+ align:start position:0%
+is on the order of 10 to the 16 a
+ 
+
+ align:start position:0%
+is on the order of 10 to the 16 a
+carrier lifetime for silicon this is not
+
+ align:start position:0%
+carrier lifetime for silicon this is not
+ 
+
+ align:start position:0%
+carrier lifetime for silicon this is not
+a great lifetime but in okay one is
+
+ align:start position:0%
+a great lifetime but in okay one is
+ 
+
+ align:start position:0%
+a great lifetime but in okay one is
+about 10 microseconds and so as a result
+
+ align:start position:0%
+about 10 microseconds and so as a result
+ 
+
+ align:start position:0%
+about 10 microseconds and so as a result
+of that you'll get about 10 to the 11
+
+ align:start position:0%
+of that you'll get about 10 to the 11
+ 
+
+ align:start position:0%
+of that you'll get about 10 to the 11
+carrier excess carriers per centimeter
+
+ align:start position:0%
+carrier excess carriers per centimeter
+ 
+
+ align:start position:0%
+carrier excess carriers per centimeter
+cubed and if we can't compare that so
+
+ align:start position:0%
+cubed and if we can't compare that so
+ 
+
+ align:start position:0%
+cubed and if we can't compare that so
+for every excess electron we make
+
+ align:start position:0%
+for every excess electron we make
+ 
+
+ align:start position:0%
+for every excess electron we make
+remember we also leave behind a hole so
+
+ align:start position:0%
+remember we also leave behind a hole so
+ 
+
+ align:start position:0%
+remember we also leave behind a hole so
+we have a delta n is generally equal to
+
+ align:start position:0%
+we have a delta n is generally equal to
+ 
+
+ align:start position:0%
+we have a delta n is generally equal to
+Delta P and that's about ten to the
+
+ align:start position:0%
+Delta P and that's about ten to the
+ 
+
+ align:start position:0%
+Delta P and that's about ten to the
+eleventh if we look at our intrinsic
+
+ align:start position:0%
+eleventh if we look at our intrinsic
+ 
+
+ align:start position:0%
+eleventh if we look at our intrinsic
+carrier concentration so if we had no
+
+ align:start position:0%
+carrier concentration so if we had no
+ 
+
+ align:start position:0%
+carrier concentration so if we had no
+dopants how many carriers would we have
+
+ align:start position:0%
+dopants how many carriers would we have
+ 
+
+ align:start position:0%
+dopants how many carriers would we have
+just for the thermal excitation and
+
+ align:start position:0%
+just for the thermal excitation and
+ 
+
+ align:start position:0%
+just for the thermal excitation and
+that's about ten to the ten and so you
+
+ align:start position:0%
+that's about ten to the ten and so you
+ 
+
+ align:start position:0%
+that's about ten to the ten and so you
+can see that your Delta n is actually
+
+ align:start position:0%
+can see that your Delta n is actually
+ 
+
+ align:start position:0%
+can see that your Delta n is actually
+larger than your intrinsic carrier
+
+ align:start position:0%
+larger than your intrinsic carrier
+ 
+
+ align:start position:0%
+larger than your intrinsic carrier
+concentration for silicon under normal
+
+ align:start position:0%
+concentration for silicon under normal
+ 
+
+ align:start position:0%
+concentration for silicon under normal
+illumination conditions now let's take
+
+ align:start position:0%
+illumination conditions now let's take
+ 
+
+ align:start position:0%
+illumination conditions now let's take
+an example suppose we add phosphorus at
+
+ align:start position:0%
+an example suppose we add phosphorus at
+ 
+
+ align:start position:0%
+an example suppose we add phosphorus at
+the order of about 10 to the 16 so
+
+ align:start position:0%
+the order of about 10 to the 16 so
+ 
+
+ align:start position:0%
+the order of about 10 to the 16 so
+that's generally about what a base
+
+ align:start position:0%
+that's generally about what a base
+ 
+
+ align:start position:0%
+that's generally about what a base
+doping concentration should be in that
+
+ align:start position:0%
+doping concentration should be in that
+ 
+
+ align:start position:0%
+doping concentration should be in that
+realm might be a little high but you can
+
+ align:start position:0%
+realm might be a little high but you can
+ 
+
+ align:start position:0%
+realm might be a little high but you can
+see that your while your Delta P is much
+
+ align:start position:0%
+see that your while your Delta P is much
+ 
+
+ align:start position:0%
+see that your while your Delta P is much
+greater than P naught so P naught would
+
+ align:start position:0%
+greater than P naught so P naught would
+ 
+
+ align:start position:0%
+greater than P naught so P naught would
+be how many holes do you have which is a
+
+ align:start position:0%
+be how many holes do you have which is a
+ 
+
+ align:start position:0%
+be how many holes do you have which is a
+ratio of your intrinsic carrier squared
+
+ align:start position:0%
+ratio of your intrinsic carrier squared
+ 
+
+ align:start position:0%
+ratio of your intrinsic carrier squared
+over your dopant density and that's
+
+ align:start position:0%
+over your dopant density and that's
+ 
+
+ align:start position:0%
+over your dopant density and that's
+about 10 to the fourth so it's way way
+
+ align:start position:0%
+about 10 to the fourth so it's way way
+ 
+
+ align:start position:0%
+about 10 to the fourth so it's way way
+less then your then what was there
+
+ align:start position:0%
+less then your then what was there
+ 
+
+ align:start position:0%
+less then your then what was there
+without excitation right so the number
+
+ align:start position:0%
+without excitation right so the number
+ 
+
+ align:start position:0%
+without excitation right so the number
+of holes without any light shining on as
+
+ align:start position:0%
+of holes without any light shining on as
+ 
+
+ align:start position:0%
+of holes without any light shining on as
+P naught you generate a bunch of holes
+
+ align:start position:0%
+P naught you generate a bunch of holes
+ 
+
+ align:start position:0%
+P naught you generate a bunch of holes
+Delta P by shining light on it and you
+
+ align:start position:0%
+Delta P by shining light on it and you
+ 
+
+ align:start position:0%
+Delta P by shining light on it and you
+can see that these numbers are
+
+ align:start position:0%
+can see that these numbers are
+ 
+
+ align:start position:0%
+can see that these numbers are
+drastically different and of course your
+
+ align:start position:0%
+drastically different and of course your
+ 
+
+ align:start position:0%
+drastically different and of course your
+dopant density is actually much much
+
+ align:start position:0%
+dopant density is actually much much
+ 
+
+ align:start position:0%
+dopant density is actually much much
+larger than your Delta n so that on your
+
+ align:start position:0%
+larger than your Delta n so that on your
+ 
+
+ align:start position:0%
+larger than your Delta n so that on your
+majority carriers don't change very much
+
+ align:start position:0%
+majority carriers don't change very much
+ 
+
+ align:start position:0%
+majority carriers don't change very much
+but your minority carriers change very
+
+ align:start position:0%
+but your minority carriers change very
+ 
+
+ align:start position:0%
+but your minority carriers change very
+very drastically that's really what this
+
+ align:start position:0%
+very drastically that's really what this
+ 
+
+ align:start position:0%
+very drastically that's really what this
+is trying to say here under excitation
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay what is lifetime all right so I
+
+ align:start position:0%
+okay what is lifetime all right so I
+ 
+
+ align:start position:0%
+okay what is lifetime all right so I
+hope that bubble shouldn't be up yet
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we measure tau by creating some
+
+ align:start position:0%
+okay so we measure tau by creating some
+ 
+
+ align:start position:0%
+okay so we measure tau by creating some
+excess carrier population and then watch
+
+ align:start position:0%
+excess carrier population and then watch
+ 
+
+ align:start position:0%
+excess carrier population and then watch
+them decay and they decay at some rate
+
+ align:start position:0%
+them decay and they decay at some rate
+ 
+
+ align:start position:0%
+them decay and they decay at some rate
+recombination rate and under steady
+
+ align:start position:0%
+recombination rate and under steady
+ 
+
+ align:start position:0%
+recombination rate and under steady
+state conditions so under a constant
+
+ align:start position:0%
+state conditions so under a constant
+ 
+
+ align:start position:0%
+state conditions so under a constant
+elimination if we're not looking at
+
+ align:start position:0%
+elimination if we're not looking at
+ 
+
+ align:start position:0%
+elimination if we're not looking at
+transients your recombination rate is
+
+ align:start position:0%
+transients your recombination rate is
+ 
+
+ align:start position:0%
+transients your recombination rate is
+actually equal to your generation rate
+
+ align:start position:0%
+actually equal to your generation rate
+ 
+
+ align:start position:0%
+actually equal to your generation rate
+so if you compare the two equations on
+
+ align:start position:0%
+so if you compare the two equations on
+ 
+
+ align:start position:0%
+so if you compare the two equations on
+the previous slide they're true under
+
+ align:start position:0%
+the previous slide they're true under
+ 
+
+ align:start position:0%
+the previous slide they're true under
+steady state conditions so that's my
+
+ align:start position:0%
+steady state conditions so that's my
+ 
+
+ align:start position:0%
+steady state conditions so that's my
+public and so your lifetimes will add up
+
+ align:start position:0%
+public and so your lifetimes will add up
+ 
+
+ align:start position:0%
+public and so your lifetimes will add up
+like parallel resistors so we have tau
+
+ align:start position:0%
+like parallel resistors so we have tau
+ 
+
+ align:start position:0%
+like parallel resistors so we have tau
+bulk which is kind of the effective
+
+ align:start position:0%
+bulk which is kind of the effective
+ 
+
+ align:start position:0%
+bulk which is kind of the effective
+lifetime of these photo excited carriers
+
+ align:start position:0%
+lifetime of these photo excited carriers
+ 
+
+ align:start position:0%
+lifetime of these photo excited carriers
+and it's equal to this the 1 over tau
+
+ align:start position:0%
+and it's equal to this the 1 over tau
+ 
+
+ align:start position:0%
+and it's equal to this the 1 over tau
+bulk is equal to 1 over tau radiative so
+
+ align:start position:0%
+bulk is equal to 1 over tau radiative so
+ 
+
+ align:start position:0%
+bulk is equal to 1 over tau radiative so
+this is radiative recombination and this
+
+ align:start position:0%
+this is radiative recombination and this
+ 
+
+ align:start position:0%
+this is radiative recombination and this
+has to do with basically if you read the
+
+ align:start position:0%
+has to do with basically if you read the
+ 
+
+ align:start position:0%
+has to do with basically if you read the
+shockley-queisser efficiency limit paper
+
+ align:start position:0%
+shockley-queisser efficiency limit paper
+ 
+
+ align:start position:0%
+shockley-queisser efficiency limit paper
+this is the lifetime that they assumed
+
+ align:start position:0%
+this is the lifetime that they assumed
+ 
+
+ align:start position:0%
+this is the lifetime that they assumed
+was limiting and for silicon this is
+
+ align:start position:0%
+was limiting and for silicon this is
+ 
+
+ align:start position:0%
+was limiting and for silicon this is
+observed like that this is never ever
+
+ align:start position:0%
+observed like that this is never ever
+ 
+
+ align:start position:0%
+observed like that this is never ever
+the limiting factor and a lot of direct
+
+ align:start position:0%
+the limiting factor and a lot of direct
+ 
+
+ align:start position:0%
+the limiting factor and a lot of direct
+band act materials for those of you
+
+ align:start position:0%
+band act materials for those of you
+ 
+
+ align:start position:0%
+band act materials for those of you
+don't know what that is don't worry
+
+ align:start position:0%
+don't know what that is don't worry
+ 
+
+ align:start position:0%
+don't know what that is don't worry
+about it that's often the limiting
+
+ align:start position:0%
+about it that's often the limiting
+ 
+
+ align:start position:0%
+about it that's often the limiting
+factor and it has to do with the
+
+ align:start position:0%
+factor and it has to do with the
+ 
+
+ align:start position:0%
+factor and it has to do with the
+absorption is always equal to the
+
+ align:start position:0%
+absorption is always equal to the
+ 
+
+ align:start position:0%
+absorption is always equal to the
+emissivity in a material for a direct
+
+ align:start position:0%
+emissivity in a material for a direct
+ 
+
+ align:start position:0%
+emissivity in a material for a direct
+bandgap material radiative recombination
+
+ align:start position:0%
+bandgap material radiative recombination
+ 
+
+ align:start position:0%
+bandgap material radiative recombination
+can be an issue right and I'll talk
+
+ align:start position:0%
+can be an issue right and I'll talk
+ 
+
+ align:start position:0%
+can be an issue right and I'll talk
+about that in a second
+
+ align:start position:0%
+about that in a second
+ 
+
+ align:start position:0%
+about that in a second
+and there's also another recombination
+
+ align:start position:0%
+and there's also another recombination
+ 
+
+ align:start position:0%
+and there's also another recombination
+called O'Shay recombination it's not
+
+ align:start position:0%
+called O'Shay recombination it's not
+ 
+
+ align:start position:0%
+called O'Shay recombination it's not
+audre like I thought when I first came
+
+ align:start position:0%
+audre like I thought when I first came
+ 
+
+ align:start position:0%
+audre like I thought when I first came
+here is O'Shea kind of like I don't know
+
+ align:start position:0%
+here is O'Shea kind of like I don't know
+ 
+
+ align:start position:0%
+here is O'Shea kind of like I don't know
+Oh Jay Simpson I guess and its dominant
+
+ align:start position:0%
+Oh Jay Simpson I guess and its dominant
+ 
+
+ align:start position:0%
+Oh Jay Simpson I guess and its dominant
+only under very high injection
+
+ align:start position:0%
+only under very high injection
+ 
+
+ align:start position:0%
+only under very high injection
+conditions or very high doping density
+
+ align:start position:0%
+conditions or very high doping density
+ 
+
+ align:start position:0%
+conditions or very high doping density
+so in your emitter layer where there's
+
+ align:start position:0%
+so in your emitter layer where there's
+ 
+
+ align:start position:0%
+so in your emitter layer where there's
+really really high doping densities
+
+ align:start position:0%
+really really high doping densities
+ 
+
+ align:start position:0%
+really really high doping densities
+you're going to have a lot of Roche
+
+ align:start position:0%
+you're going to have a lot of Roche
+ 
+
+ align:start position:0%
+you're going to have a lot of Roche
+recombination and the last one is
+
+ align:start position:0%
+recombination and the last one is
+ 
+
+ align:start position:0%
+recombination and the last one is
+shockley-read-hall so these are three
+
+ align:start position:0%
+shockley-read-hall so these are three
+ 
+
+ align:start position:0%
+shockley-read-hall so these are three
+guys they came up with this kind of
+
+ align:start position:0%
+guys they came up with this kind of
+ 
+
+ align:start position:0%
+guys they came up with this kind of
+model for how recombination happens in
+
+ align:start position:0%
+model for how recombination happens in
+ 
+
+ align:start position:0%
+model for how recombination happens in
+defective material so materials with
+
+ align:start position:0%
+defective material so materials with
+ 
+
+ align:start position:0%
+defective material so materials with
+levels
+
+ align:start position:0%
+levels
+ 
+
+ align:start position:0%
+levels
+electronic levels in the mid gap and
+
+ align:start position:0%
+electronic levels in the mid gap and
+ 
+
+ align:start position:0%
+electronic levels in the mid gap and
+again these add like parallel resistors
+
+ align:start position:0%
+again these add like parallel resistors
+ 
+
+ align:start position:0%
+again these add like parallel resistors
+so you're always so if you remember back
+
+ align:start position:0%
+so you're always so if you remember back
+ 
+
+ align:start position:0%
+so you're always so if you remember back
+to the the leaky bucket these are your
+
+ align:start position:0%
+to the the leaky bucket these are your
+ 
+
+ align:start position:0%
+to the the leaky bucket these are your
+leaky buckets for diffusion length right
+
+ align:start position:0%
+leaky buckets for diffusion length right
+ 
+
+ align:start position:0%
+leaky buckets for diffusion length right
+you're always limited by your shortest
+
+ align:start position:0%
+you're always limited by your shortest
+ 
+
+ align:start position:0%
+you're always limited by your shortest
+diffusion length or sorry your shortest
+
+ align:start position:0%
+diffusion length or sorry your shortest
+ 
+
+ align:start position:0%
+diffusion length or sorry your shortest
+lifetime and this is often your limiting
+
+ align:start position:0%
+lifetime and this is often your limiting
+ 
+
+ align:start position:0%
+lifetime and this is often your limiting
+lifetime is your shock would be a hog
+
+ align:start position:0%
+lifetime is your shock would be a hog
+ 
+
+ align:start position:0%
+lifetime is your shock would be a hog
+recombination okay silicon okay so
+
+ align:start position:0%
+recombination okay silicon okay so
+ 
+
+ align:start position:0%
+recombination okay silicon okay so
+radiative recombination so you can
+
+ align:start position:0%
+radiative recombination so you can
+ 
+
+ align:start position:0%
+radiative recombination so you can
+probably guess from the name that
+
+ align:start position:0%
+probably guess from the name that
+ 
+
+ align:start position:0%
+probably guess from the name that
+radiative recombination involves the
+
+ align:start position:0%
+radiative recombination involves the
+ 
+
+ align:start position:0%
+radiative recombination involves the
+photon the ability to absorb photons
+
+ align:start position:0%
+photon the ability to absorb photons
+ 
+
+ align:start position:0%
+photon the ability to absorb photons
+also means you have the ability to emit
+
+ align:start position:0%
+also means you have the ability to emit
+ 
+
+ align:start position:0%
+also means you have the ability to emit
+them and so silicon or many
+
+ align:start position:0%
+them and so silicon or many
+ 
+
+ align:start position:0%
+them and so silicon or many
+semiconductors will emit photons when
+
+ align:start position:0%
+semiconductors will emit photons when
+ 
+
+ align:start position:0%
+semiconductors will emit photons when
+you get a recombination event across the
+
+ align:start position:0%
+you get a recombination event across the
+ 
+
+ align:start position:0%
+you get a recombination event across the
+band and when that happens you emit a
+
+ align:start position:0%
+band and when that happens you emit a
+ 
+
+ align:start position:0%
+band and when that happens you emit a
+photon under equilibrium conditions so
+
+ align:start position:0%
+photon under equilibrium conditions so
+ 
+
+ align:start position:0%
+photon under equilibrium conditions so
+equilibrium means no outside excitation
+
+ align:start position:0%
+equilibrium means no outside excitation
+ 
+
+ align:start position:0%
+equilibrium means no outside excitation
+doesn't mean steady-state so this is
+
+ align:start position:0%
+doesn't mean steady-state so this is
+ 
+
+ align:start position:0%
+doesn't mean steady-state so this is
+let's say in the dark you get your
+
+ align:start position:0%
+let's say in the dark you get your
+ 
+
+ align:start position:0%
+let's say in the dark you get your
+recombination rate is equal to your
+
+ align:start position:0%
+recombination rate is equal to your
+ 
+
+ align:start position:0%
+recombination rate is equal to your
+generation right right because it's in
+
+ align:start position:0%
+generation right right because it's in
+ 
+
+ align:start position:0%
+generation right right because it's in
+thermal equilibrium with the area around
+
+ align:start position:0%
+thermal equilibrium with the area around
+ 
+
+ align:start position:0%
+thermal equilibrium with the area around
+it so it's absorbing photons and
+
+ align:start position:0%
+it so it's absorbing photons and
+ 
+
+ align:start position:0%
+it so it's absorbing photons and
+emitting them at the same rate and this
+
+ align:start position:0%
+emitting them at the same rate and this
+ 
+
+ align:start position:0%
+emitting them at the same rate and this
+is equal to B so some material parameter
+
+ align:start position:0%
+is equal to B so some material parameter
+ 
+
+ align:start position:0%
+is equal to B so some material parameter
+times your hole and electron
+
+ align:start position:0%
+times your hole and electron
+ 
+
+ align:start position:0%
+times your hole and electron
+concentration and again under
+
+ align:start position:0%
+concentration and again under
+ 
+
+ align:start position:0%
+concentration and again under
+equilibrium conditions that's equal to
+
+ align:start position:0%
+equilibrium conditions that's equal to
+ 
+
+ align:start position:0%
+equilibrium conditions that's equal to
+your intrinsic carrier concentration
+
+ align:start position:0%
+your intrinsic carrier concentration
+ 
+
+ align:start position:0%
+your intrinsic carrier concentration
+right your NP product is equal to NI
+
+ align:start position:0%
+right your NP product is equal to NI
+ 
+
+ align:start position:0%
+right your NP product is equal to NI
+square now when you shine light on it
+
+ align:start position:0%
+square now when you shine light on it
+ 
+
+ align:start position:0%
+square now when you shine light on it
+your n which is equal to there we go
+
+ align:start position:0%
+your n which is equal to there we go
+ 
+
+ align:start position:0%
+your n which is equal to there we go
+and naught plus Delta n so this is your
+
+ align:start position:0%
+and naught plus Delta n so this is your
+ 
+
+ align:start position:0%
+and naught plus Delta n so this is your
+excited carrier so your excess carriers
+
+ align:start position:0%
+excited carrier so your excess carriers
+ 
+
+ align:start position:0%
+excited carrier so your excess carriers
+so your n now increases and is greater
+
+ align:start position:0%
+so your n now increases and is greater
+ 
+
+ align:start position:0%
+so your n now increases and is greater
+than n sub I and your net recombination
+
+ align:start position:0%
+than n sub I and your net recombination
+ 
+
+ align:start position:0%
+than n sub I and your net recombination
+rate is determined by this equation
+
+ align:start position:0%
+rate is determined by this equation
+ 
+
+ align:start position:0%
+rate is determined by this equation
+right here so BN P minus B ni square so
+
+ align:start position:0%
+right here so BN P minus B ni square so
+ 
+
+ align:start position:0%
+right here so BN P minus B ni square so
+the difference between your equilibrium
+
+ align:start position:0%
+the difference between your equilibrium
+ 
+
+ align:start position:0%
+the difference between your equilibrium
+and your now excited carrier
+
+ align:start position:0%
+and your now excited carrier
+ 
+
+ align:start position:0%
+and your now excited carrier
+concentrations it's a material parameter
+
+ align:start position:0%
+concentrations it's a material parameter
+ 
+
+ align:start position:0%
+concentrations it's a material parameter
+yeah it depends on for silicon I forget
+
+ align:start position:0%
+yeah it depends on for silicon I forget
+ 
+
+ align:start position:0%
+yeah it depends on for silicon I forget
+what's on the next slide it's 10 to the
+
+ align:start position:0%
+what's on the next slide it's 10 to the
+ 
+
+ align:start position:0%
+what's on the next slide it's 10 to the
+minus 15 I don't know for other
+
+ align:start position:0%
+minus 15 I don't know for other
+ 
+
+ align:start position:0%
+minus 15 I don't know for other
+materials but I presume that that would
+
+ align:start position:0%
+materials but I presume that that would
+ 
+
+ align:start position:0%
+materials but I presume that that would
+change
+
+ align:start position:0%
+change
+ 
+
+ align:start position:0%
+change
+probably be a lot higher for other
+
+ align:start position:0%
+probably be a lot higher for other
+ 
+
+ align:start position:0%
+probably be a lot higher for other
+materials and it turns out your
+
+ align:start position:0%
+materials and it turns out your
+ 
+
+ align:start position:0%
+materials and it turns out your
+radiative recombination lifetimes when
+
+ align:start position:0%
+radiative recombination lifetimes when
+ 
+
+ align:start position:0%
+radiative recombination lifetimes when
+you plug these numbers in and you make
+
+ align:start position:0%
+you plug these numbers in and you make
+ 
+
+ align:start position:0%
+you plug these numbers in and you make
+some assumptions about what's really
+
+ align:start position:0%
+some assumptions about what's really
+ 
+
+ align:start position:0%
+some assumptions about what's really
+small compared to each other you get
+
+ align:start position:0%
+small compared to each other you get
+ 
+
+ align:start position:0%
+small compared to each other you get
+these equations here and again this is
+
+ align:start position:0%
+these equations here and again this is
+ 
+
+ align:start position:0%
+these equations here and again this is
+tau is equal to Delta n over R and so
+
+ align:start position:0%
+tau is equal to Delta n over R and so
+ 
+
+ align:start position:0%
+tau is equal to Delta n over R and so
+you get that and now if you look at it
+
+ align:start position:0%
+you get that and now if you look at it
+ 
+
+ align:start position:0%
+you get that and now if you look at it
+for silicon you get B is about two times
+
+ align:start position:0%
+for silicon you get B is about two times
+ 
+
+ align:start position:0%
+for silicon you get B is about two times
+ten to the minus fifteen your Delta n I
+
+ align:start position:0%
+ten to the minus fifteen your Delta n I
+ 
+
+ align:start position:0%
+ten to the minus fifteen your Delta n I
+put or sorry yeah and I determined just
+
+ align:start position:0%
+put or sorry yeah and I determined just
+ 
+
+ align:start position:0%
+put or sorry yeah and I determined just
+was 10 to the 16 some doping
+
+ align:start position:0%
+was 10 to the 16 some doping
+ 
+
+ align:start position:0%
+was 10 to the 16 some doping
+concentration and your radiative
+
+ align:start position:0%
+concentration and your radiative
+ 
+
+ align:start position:0%
+concentration and your radiative
+lifetime is incredibly incredibly long
+
+ align:start position:0%
+lifetime is incredibly incredibly long
+ 
+
+ align:start position:0%
+lifetime is incredibly incredibly long
+about 50 milliseconds and if you
+
+ align:start position:0%
+about 50 milliseconds and if you
+ 
+
+ align:start position:0%
+about 50 milliseconds and if you
+remember from before when I was
+
+ align:start position:0%
+remember from before when I was
+ 
+
+ align:start position:0%
+remember from before when I was
+calculating a generation rate for
+
+ align:start position:0%
+calculating a generation rate for
+ 
+
+ align:start position:0%
+calculating a generation rate for
+silicon we used about 10 microseconds so
+
+ align:start position:0%
+silicon we used about 10 microseconds so
+ 
+
+ align:start position:0%
+silicon we used about 10 microseconds so
+this is really really long and so radio
+
+ align:start position:0%
+this is really really long and so radio
+ 
+
+ align:start position:0%
+this is really really long and so radio
+recombination is very very slow and it's
+
+ align:start position:0%
+recombination is very very slow and it's
+ 
+
+ align:start position:0%
+recombination is very very slow and it's
+rarely ever the limiting lifetime in
+
+ align:start position:0%
+rarely ever the limiting lifetime in
+ 
+
+ align:start position:0%
+rarely ever the limiting lifetime in
+silicon based solar cells however as as
+
+ align:start position:0%
+silicon based solar cells however as as
+ 
+
+ align:start position:0%
+silicon based solar cells however as as
+you mentioned earlier it's actually a
+
+ align:start position:0%
+you mentioned earlier it's actually a
+ 
+
+ align:start position:0%
+you mentioned earlier it's actually a
+big problem in direct bandgap materials
+
+ align:start position:0%
+big problem in direct bandgap materials
+ 
+
+ align:start position:0%
+big problem in direct bandgap materials
+and if you think of there are some
+
+ align:start position:0%
+and if you think of there are some
+ 
+
+ align:start position:0%
+and if you think of there are some
+materials who actually want a very short
+
+ align:start position:0%
+materials who actually want a very short
+ 
+
+ align:start position:0%
+materials who actually want a very short
+radiative recombination time so for
+
+ align:start position:0%
+radiative recombination time so for
+ 
+
+ align:start position:0%
+radiative recombination time so for
+example if you're trying to make an LED
+
+ align:start position:0%
+example if you're trying to make an LED
+ 
+
+ align:start position:0%
+example if you're trying to make an LED
+you inject carriers using a voltage that
+
+ align:start position:0%
+you inject carriers using a voltage that
+ 
+
+ align:start position:0%
+you inject carriers using a voltage that
+recombination emits photons and then you
+
+ align:start position:0%
+recombination emits photons and then you
+ 
+
+ align:start position:0%
+recombination emits photons and then you
+get light and that's basically how an
+
+ align:start position:0%
+get light and that's basically how an
+ 
+
+ align:start position:0%
+get light and that's basically how an
+LED works so okay so now we'll talk
+
+ align:start position:0%
+LED works so okay so now we'll talk
+ 
+
+ align:start position:0%
+LED works so okay so now we'll talk
+about a little bit shockley-read-hall
+
+ align:start position:0%
+about a little bit shockley-read-hall
+ 
+
+ align:start position:0%
+about a little bit shockley-read-hall
+recombination so this is something that
+
+ align:start position:0%
+recombination so this is something that
+ 
+
+ align:start position:0%
+recombination so this is something that
+our lab works I think very very well in
+
+ align:start position:0%
+our lab works I think very very well in
+ 
+
+ align:start position:0%
+our lab works I think very very well in
+we do a lot of like defects and
+
+ align:start position:0%
+we do a lot of like defects and
+ 
+
+ align:start position:0%
+we do a lot of like defects and
+semiconductors specifically iron and so
+
+ align:start position:0%
+semiconductors specifically iron and so
+ 
+
+ align:start position:0%
+semiconductors specifically iron and so
+iron is one of these really really awful
+
+ align:start position:0%
+iron is one of these really really awful
+ 
+
+ align:start position:0%
+iron is one of these really really awful
+contaminants and solar cells just a
+
+ align:start position:0%
+contaminants and solar cells just a
+ 
+
+ align:start position:0%
+contaminants and solar cells just a
+little bit of iron I think Tony Craig
+
+ align:start position:0%
+little bit of iron I think Tony Craig
+ 
+
+ align:start position:0%
+little bit of iron I think Tony Craig
+Miller I think I don't remember what
+
+ align:start position:0%
+Miller I think I don't remember what
+ 
+
+ align:start position:0%
+Miller I think I don't remember what
+year production this was maybe it was
+
+ align:start position:0%
+year production this was maybe it was
+ 
+
+ align:start position:0%
+year production this was maybe it was
+2009 but 2 grams of iron could
+
+ align:start position:0%
+2009 but 2 grams of iron could
+ 
+
+ align:start position:0%
+2009 but 2 grams of iron could
+contaminate the entire year supply of
+
+ align:start position:0%
+contaminate the entire year supply of
+ 
+
+ align:start position:0%
+contaminate the entire year supply of
+silicon detrimental e so that's a lot
+
+ align:start position:0%
+silicon detrimental e so that's a lot
+ 
+
+ align:start position:0%
+silicon detrimental e so that's a lot
+yes you do for a single panel and you'll
+
+ align:start position:0%
+yes you do for a single panel and you'll
+ 
+
+ align:start position:0%
+yes you do for a single panel and you'll
+it shocked me anyhow so basically we're
+
+ align:start position:0%
+it shocked me anyhow so basically we're
+ 
+
+ align:start position:0%
+it shocked me anyhow so basically we're
+trying to say here is that you have iron
+
+ align:start position:0%
+trying to say here is that you have iron
+ 
+
+ align:start position:0%
+trying to say here is that you have iron
+atoms and it can sit in different areas
+
+ align:start position:0%
+atoms and it can sit in different areas
+ 
+
+ align:start position:0%
+atoms and it can sit in different areas
+of your lattice but you have these
+
+ align:start position:0%
+of your lattice but you have these
+ 
+
+ align:start position:0%
+of your lattice but you have these
+defects that
+
+ align:start position:0%
+defects that
+ 
+
+ align:start position:0%
+defects that
+exist and they introduce different
+
+ align:start position:0%
+exist and they introduce different
+ 
+
+ align:start position:0%
+exist and they introduce different
+energy levels within the bandgap right
+
+ align:start position:0%
+energy levels within the bandgap right
+ 
+
+ align:start position:0%
+energy levels within the bandgap right
+so the outer electrons of iron can
+
+ align:start position:0%
+so the outer electrons of iron can
+ 
+
+ align:start position:0%
+so the outer electrons of iron can
+either sit at these sites so these blue
+
+ align:start position:0%
+either sit at these sites so these blue
+ 
+
+ align:start position:0%
+either sit at these sites so these blue
+sites were their donors or they can
+
+ align:start position:0%
+sites were their donors or they can
+ 
+
+ align:start position:0%
+sites were their donors or they can
+create acceptor States kind of like
+
+ align:start position:0%
+create acceptor States kind of like
+ 
+
+ align:start position:0%
+create acceptor States kind of like
+boron does but they're much higher up
+
+ align:start position:0%
+boron does but they're much higher up
+ 
+
+ align:start position:0%
+boron does but they're much higher up
+into the gap and these act as
+
+ align:start position:0%
+into the gap and these act as
+ 
+
+ align:start position:0%
+into the gap and these act as
+recombination centers and we'll talk
+
+ align:start position:0%
+recombination centers and we'll talk
+ 
+
+ align:start position:0%
+recombination centers and we'll talk
+about why that is in a second
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so these trap levels can interact with
+
+ align:start position:0%
+so these trap levels can interact with
+ 
+
+ align:start position:0%
+so these trap levels can interact with
+mobile carriers in a whole bunch of
+
+ align:start position:0%
+mobile carriers in a whole bunch of
+ 
+
+ align:start position:0%
+mobile carriers in a whole bunch of
+different ways okay it can capture an
+
+ align:start position:0%
+different ways okay it can capture an
+ 
+
+ align:start position:0%
+different ways okay it can capture an
+electron that electron can then sit
+
+ align:start position:0%
+electron that electron can then sit
+ 
+
+ align:start position:0%
+electron that electron can then sit
+there if there's enough heat energy it
+
+ align:start position:0%
+there if there's enough heat energy it
+ 
+
+ align:start position:0%
+there if there's enough heat energy it
+might actually get promoted and jump out
+
+ align:start position:0%
+might actually get promoted and jump out
+ 
+
+ align:start position:0%
+might actually get promoted and jump out
+of that and then which case it wouldn't
+
+ align:start position:0%
+of that and then which case it wouldn't
+ 
+
+ align:start position:0%
+of that and then which case it wouldn't
+have actually decreased your excess
+
+ align:start position:0%
+have actually decreased your excess
+ 
+
+ align:start position:0%
+have actually decreased your excess
+carrier population it can also capture
+
+ align:start position:0%
+carrier population it can also capture
+ 
+
+ align:start position:0%
+carrier population it can also capture
+holes and they can also emit holes and
+
+ align:start position:0%
+holes and they can also emit holes and
+ 
+
+ align:start position:0%
+holes and they can also emit holes and
+there's a bunch of things that go into
+
+ align:start position:0%
+there's a bunch of things that go into
+ 
+
+ align:start position:0%
+there's a bunch of things that go into
+these equations here it depends on a lot
+
+ align:start position:0%
+these equations here it depends on a lot
+ 
+
+ align:start position:0%
+these equations here it depends on a lot
+of the energy of this trap state it
+
+ align:start position:0%
+of the energy of this trap state it
+ 
+
+ align:start position:0%
+of the energy of this trap state it
+depends on the carrier excitation we'll
+
+ align:start position:0%
+depends on the carrier excitation we'll
+ 
+
+ align:start position:0%
+depends on the carrier excitation we'll
+talk about that another few slides and
+
+ align:start position:0%
+talk about that another few slides and
+ 
+
+ align:start position:0%
+talk about that another few slides and
+it also depends on these kind of what
+
+ align:start position:0%
+it also depends on these kind of what
+ 
+
+ align:start position:0%
+it also depends on these kind of what
+are like effective I forget the exact
+
+ align:start position:0%
+are like effective I forget the exact
+ 
+
+ align:start position:0%
+are like effective I forget the exact
+word of the effective hole and electron
+
+ align:start position:0%
+word of the effective hole and electron
+ 
+
+ align:start position:0%
+word of the effective hole and electron
+lifetimes and those are limited by your
+
+ align:start position:0%
+lifetimes and those are limited by your
+ 
+
+ align:start position:0%
+lifetimes and those are limited by your
+trap density so these are can be thought
+
+ align:start position:0%
+trap density so these are can be thought
+ 
+
+ align:start position:0%
+trap density so these are can be thought
+of suppose that each let's say each iron
+
+ align:start position:0%
+of suppose that each let's say each iron
+ 
+
+ align:start position:0%
+of suppose that each let's say each iron
+atom is introducing one trap level it
+
+ align:start position:0%
+atom is introducing one trap level it
+ 
+
+ align:start position:0%
+atom is introducing one trap level it
+would be the number of trap levels the
+
+ align:start position:0%
+would be the number of trap levels the
+ 
+
+ align:start position:0%
+would be the number of trap levels the
+density of trap levels within your
+
+ align:start position:0%
+density of trap levels within your
+ 
+
+ align:start position:0%
+density of trap levels within your
+system times some thermal energy so and
+
+ align:start position:0%
+system times some thermal energy so and
+ 
+
+ align:start position:0%
+system times some thermal energy so and
+then a capture cross section which is
+
+ align:start position:0%
+then a capture cross section which is
+ 
+
+ align:start position:0%
+then a capture cross section which is
+saying okay that trap state exists in
+
+ align:start position:0%
+saying okay that trap state exists in
+ 
+
+ align:start position:0%
+saying okay that trap state exists in
+one location kind of how much area can
+
+ align:start position:0%
+one location kind of how much area can
+ 
+
+ align:start position:0%
+one location kind of how much area can
+it see in terms of what effective area
+
+ align:start position:0%
+it see in terms of what effective area
+ 
+
+ align:start position:0%
+it see in terms of what effective area
+is at capturing electrons and and
+
+ align:start position:0%
+is at capturing electrons and and
+ 
+
+ align:start position:0%
+is at capturing electrons and and
+oftentimes at an under the right
+
+ align:start position:0%
+oftentimes at an under the right
+ 
+
+ align:start position:0%
+oftentimes at an under the right
+conditions so with very very deep traps
+
+ align:start position:0%
+conditions so with very very deep traps
+ 
+
+ align:start position:0%
+conditions so with very very deep traps
+so traps mid gap under low injections
+
+ align:start position:0%
+so traps mid gap under low injections
+ 
+
+ align:start position:0%
+so traps mid gap under low injections
+your shocker recall recombination is
+
+ align:start position:0%
+your shocker recall recombination is
+ 
+
+ align:start position:0%
+your shocker recall recombination is
+actually one of those two lifetimes and
+
+ align:start position:0%
+actually one of those two lifetimes and
+ 
+
+ align:start position:0%
+actually one of those two lifetimes and
+it's a very simple equation in under
+
+ align:start position:0%
+it's a very simple equation in under
+ 
+
+ align:start position:0%
+it's a very simple equation in under
+very very high injection conditions it's
+
+ align:start position:0%
+very very high injection conditions it's
+ 
+
+ align:start position:0%
+very very high injection conditions it's
+actually summing them up and if you look
+
+ align:start position:0%
+actually summing them up and if you look
+ 
+
+ align:start position:0%
+actually summing them up and if you look
+in the previous slide if you go to Delta
+
+ align:start position:0%
+in the previous slide if you go to Delta
+ 
+
+ align:start position:0%
+in the previous slide if you go to Delta
+n goes to infinity you can see that this
+
+ align:start position:0%
+n goes to infinity you can see that this
+ 
+
+ align:start position:0%
+n goes to infinity you can see that this
+becomes true
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's a good question that would be my
+
+ align:start position:0%
+that's a good question that would be my
+ 
+
+ align:start position:0%
+that's a good question that would be my
+guess
+
+ align:start position:0%
+guess
+ 
+
+ align:start position:0%
+guess
+yeah sorry there's another question back
+
+ align:start position:0%
+yeah sorry there's another question back
+ 
+
+ align:start position:0%
+yeah sorry there's another question back
+there or like I can Hank so then it is
+
+ align:start position:0%
+there or like I can Hank so then it is
+ 
+
+ align:start position:0%
+there or like I can Hank so then it is
+iron it were stupid or worse still Oh in
+
+ align:start position:0%
+iron it were stupid or worse still Oh in
+ 
+
+ align:start position:0%
+iron it were stupid or worse still Oh in
+terms of capture cross-section yeah I
+
+ align:start position:0%
+terms of capture cross-section yeah I
+ 
+
+ align:start position:0%
+terms of capture cross-section yeah I
+know they're both bad really bad i Tonio
+
+ align:start position:0%
+know they're both bad really bad i Tonio
+ 
+
+ align:start position:0%
+know they're both bad really bad i Tonio
+do you know that off the top your head
+
+ align:start position:0%
+do you know that off the top your head
+ 
+
+ align:start position:0%
+do you know that off the top your head
+I'm sure so gold is gold has a larger
+
+ align:start position:0%
+I'm sure so gold is gold has a larger
+ 
+
+ align:start position:0%
+I'm sure so gold is gold has a larger
+life ending at that lower concentration
+
+ align:start position:0%
+life ending at that lower concentration
+ 
+
+ align:start position:0%
+life ending at that lower concentration
+since iron it's perhaps one of the worst
+
+ align:start position:0%
+since iron it's perhaps one of the worst
+ 
+
+ align:start position:0%
+since iron it's perhaps one of the worst
+and that's why you're not allowed to
+
+ align:start position:0%
+and that's why you're not allowed to
+ 
+
+ align:start position:0%
+and that's why you're not allowed to
+wear old jewelry leaders they ask you to
+
+ align:start position:0%
+wear old jewelry leaders they ask you to
+ 
+
+ align:start position:0%
+wear old jewelry leaders they ask you to
+take off your high end ears okay so no
+
+ align:start position:0%
+take off your high end ears okay so no
+ 
+
+ align:start position:0%
+take off your high end ears okay so no
+bling in the cleaner there you go
+
+ align:start position:0%
+bling in the cleaner there you go
+ 
+
+ align:start position:0%
+bling in the cleaner there you go
+and so for the material scientists and
+
+ align:start position:0%
+and so for the material scientists and
+ 
+
+ align:start position:0%
+and so for the material scientists and
+physicists in the room if that does not
+
+ align:start position:0%
+physicists in the room if that does not
+ 
+
+ align:start position:0%
+physicists in the room if that does not
+apply to you don't worry this is just to
+
+ align:start position:0%
+apply to you don't worry this is just to
+ 
+
+ align:start position:0%
+apply to you don't worry this is just to
+explain what's going on
+
+ align:start position:0%
+explain what's going on
+ 
+
+ align:start position:0%
+explain what's going on
+often when you want recombination to it
+
+ align:start position:0%
+often when you want recombination to it
+ 
+
+ align:start position:0%
+often when you want recombination to it
+happen so this is a momentum or K versus
+
+ align:start position:0%
+happen so this is a momentum or K versus
+ 
+
+ align:start position:0%
+happen so this is a momentum or K versus
+energy it requires not only the emission
+
+ align:start position:0%
+energy it requires not only the emission
+ 
+
+ align:start position:0%
+energy it requires not only the emission
+of a photon but also a phonon to change
+
+ align:start position:0%
+of a photon but also a phonon to change
+ 
+
+ align:start position:0%
+of a photon but also a phonon to change
+its momentum when you introduce a trap
+
+ align:start position:0%
+its momentum when you introduce a trap
+ 
+
+ align:start position:0%
+its momentum when you introduce a trap
+level are these localized impurities
+
+ align:start position:0%
+level are these localized impurities
+ 
+
+ align:start position:0%
+level are these localized impurities
+because it's localized in real space its
+
+ align:start position:0%
+because it's localized in real space its
+ 
+
+ align:start position:0%
+because it's localized in real space its
+delocalized in k space so you have this
+
+ align:start position:0%
+delocalized in k space so you have this
+ 
+
+ align:start position:0%
+delocalized in k space so you have this
+kind of flat level and k and you have
+
+ align:start position:0%
+kind of flat level and k and you have
+ 
+
+ align:start position:0%
+kind of flat level and k and you have
+these very very efficient pathways for
+
+ align:start position:0%
+these very very efficient pathways for
+ 
+
+ align:start position:0%
+these very very efficient pathways for
+recombination if that doesn't resonate
+
+ align:start position:0%
+recombination if that doesn't resonate
+ 
+
+ align:start position:0%
+recombination if that doesn't resonate
+with you don't worry about it right now
+
+ align:start position:0%
+with you don't worry about it right now
+ 
+
+ align:start position:0%
+with you don't worry about it right now
+so okay so here we see that really the
+
+ align:start position:0%
+so okay so here we see that really the
+ 
+
+ align:start position:0%
+so okay so here we see that really the
+impurities can have a very very large
+
+ align:start position:0%
+impurities can have a very very large
+ 
+
+ align:start position:0%
+impurities can have a very very large
+effect if you think of the doping
+
+ align:start position:0%
+effect if you think of the doping
+ 
+
+ align:start position:0%
+effect if you think of the doping
+densities that we put in we've been
+
+ align:start position:0%
+densities that we put in we've been
+ 
+
+ align:start position:0%
+densities that we put in we've been
+using about 10 to the 15 10 to the 16
+
+ align:start position:0%
+using about 10 to the 15 10 to the 16
+ 
+
+ align:start position:0%
+using about 10 to the 15 10 to the 16
+for our dopant densities this is on the
+
+ align:start position:0%
+for our dopant densities this is on the
+ 
+
+ align:start position:0%
+for our dopant densities this is on the
+order of like a million less and it can
+
+ align:start position:0%
+order of like a million less and it can
+ 
+
+ align:start position:0%
+order of like a million less and it can
+have a huge impact on lifetime so one of
+
+ align:start position:0%
+have a huge impact on lifetime so one of
+ 
+
+ align:start position:0%
+have a huge impact on lifetime so one of
+the worst again as we said was ion and
+
+ align:start position:0%
+the worst again as we said was ion and
+ 
+
+ align:start position:0%
+the worst again as we said was ion and
+these interstitial irons are especially
+
+ align:start position:0%
+these interstitial irons are especially
+ 
+
+ align:start position:0%
+these interstitial irons are especially
+bad and that tend to the I don't know it
+
+ align:start position:0%
+bad and that tend to the I don't know it
+ 
+
+ align:start position:0%
+bad and that tend to the I don't know it
+looks like 10 to the 11
+
+ align:start position:0%
+looks like 10 to the 11
+ 
+
+ align:start position:0%
+looks like 10 to the 11
+very very low concentrations that's one
+
+ align:start position:0%
+very very low concentrations that's one
+ 
+
+ align:start position:0%
+very very low concentrations that's one
+in 10 to the 12 so that's one in a
+
+ align:start position:0%
+in 10 to the 12 so that's one in a
+ 
+
+ align:start position:0%
+in 10 to the 12 so that's one in a
+trillion atoms or iron can detrimental
+
+ align:start position:0%
+trillion atoms or iron can detrimental
+ 
+
+ align:start position:0%
+trillion atoms or iron can detrimental
+impact your solar cell so that's really
+
+ align:start position:0%
+impact your solar cell so that's really
+ 
+
+ align:start position:0%
+impact your solar cell so that's really
+really bad so keeping fabs clean so
+
+ align:start position:0%
+really bad so keeping fabs clean so
+ 
+
+ align:start position:0%
+really bad so keeping fabs clean so
+again no jewelry and other things can
+
+ align:start position:0%
+again no jewelry and other things can
+ 
+
+ align:start position:0%
+again no jewelry and other things can
+really that can actually have a very
+
+ align:start position:0%
+really that can actually have a very
+ 
+
+ align:start position:0%
+really that can actually have a very
+large effect on your device performance
+
+ align:start position:0%
+large effect on your device performance
+ 
+
+ align:start position:0%
+large effect on your device performance
+and if you plot that versus your
+
+ align:start position:0%
+and if you plot that versus your
+ 
+
+ align:start position:0%
+and if you plot that versus your
+dislocation density you can see that if
+
+ align:start position:0%
+dislocation density you can see that if
+ 
+
+ align:start position:0%
+dislocation density you can see that if
+you have it's especially bad for very
+
+ align:start position:0%
+you have it's especially bad for very
+ 
+
+ align:start position:0%
+you have it's especially bad for very
+very high lifetime silicon just a few
+
+ align:start position:0%
+very high lifetime silicon just a few
+ 
+
+ align:start position:0%
+very high lifetime silicon just a few
+dislocations can actually really really
+
+ align:start position:0%
+dislocations can actually really really
+ 
+
+ align:start position:0%
+dislocations can actually really really
+hurt it but the effect is mitigated if
+
+ align:start position:0%
+hurt it but the effect is mitigated if
+ 
+
+ align:start position:0%
+hurt it but the effect is mitigated if
+you're already starting with very low
+
+ align:start position:0%
+you're already starting with very low
+ 
+
+ align:start position:0%
+you're already starting with very low
+lifetime so again and again this is
+
+ align:start position:0%
+lifetime so again and again this is
+ 
+
+ align:start position:0%
+lifetime so again and again this is
+something our lab works on quite
+
+ align:start position:0%
+something our lab works on quite
+ 
+
+ align:start position:0%
+something our lab works on quite
+extensively is it's not just the number
+
+ align:start position:0%
+extensively is it's not just the number
+ 
+
+ align:start position:0%
+extensively is it's not just the number
+of iron atoms so if you take a piece of
+
+ align:start position:0%
+of iron atoms so if you take a piece of
+ 
+
+ align:start position:0%
+of iron atoms so if you take a piece of
+silicon and you want to know its
+
+ align:start position:0%
+silicon and you want to know its
+ 
+
+ align:start position:0%
+silicon and you want to know its
+lifetime or how iron impacts is lifetime
+
+ align:start position:0%
+lifetime or how iron impacts is lifetime
+ 
+
+ align:start position:0%
+lifetime or how iron impacts is lifetime
+it's not just a total number of iron
+
+ align:start position:0%
+it's not just a total number of iron
+ 
+
+ align:start position:0%
+it's not just a total number of iron
+atoms in it it's also how they're
+
+ align:start position:0%
+atoms in it it's also how they're
+ 
+
+ align:start position:0%
+atoms in it it's also how they're
+distributed so if you have let's say
+
+ align:start position:0%
+distributed so if you have let's say
+ 
+
+ align:start position:0%
+distributed so if you have let's say
+clusters of iron atoms that would count
+
+ align:start position:0%
+clusters of iron atoms that would count
+ 
+
+ align:start position:0%
+clusters of iron atoms that would count
+as one defect or effectively less than
+
+ align:start position:0%
+as one defect or effectively less than
+ 
+
+ align:start position:0%
+as one defect or effectively less than
+the number of atoms in it and so
+
+ align:start position:0%
+the number of atoms in it and so
+ 
+
+ align:start position:0%
+the number of atoms in it and so
+clustering these things can actually be
+
+ align:start position:0%
+clustering these things can actually be
+ 
+
+ align:start position:0%
+clustering these things can actually be
+really really a good way of cleaning up
+
+ align:start position:0%
+really really a good way of cleaning up
+ 
+
+ align:start position:0%
+really really a good way of cleaning up
+your your solar cell material and this
+
+ align:start position:0%
+your your solar cell material and this
+ 
+
+ align:start position:0%
+your your solar cell material and this
+is an effect called gettering and if you
+
+ align:start position:0%
+is an effect called gettering and if you
+ 
+
+ align:start position:0%
+is an effect called gettering and if you
+can kind of get are these impurity atoms
+
+ align:start position:0%
+can kind of get are these impurity atoms
+ 
+
+ align:start position:0%
+can kind of get are these impurity atoms
+into one location they'll have less of a
+
+ align:start position:0%
+into one location they'll have less of a
+ 
+
+ align:start position:0%
+into one location they'll have less of a
+detrimental impact on your material so
+
+ align:start position:0%
+detrimental impact on your material so
+ 
+
+ align:start position:0%
+detrimental impact on your material so
+this is kind of a tricky one to explain
+
+ align:start position:0%
+this is kind of a tricky one to explain
+ 
+
+ align:start position:0%
+this is kind of a tricky one to explain
+but this is a so shockley-read-hall
+
+ align:start position:0%
+but this is a so shockley-read-hall
+ 
+
+ align:start position:0%
+but this is a so shockley-read-hall
+recombination can also show up in
+
+ align:start position:0%
+recombination can also show up in
+ 
+
+ align:start position:0%
+recombination can also show up in
+something called surface recombination
+
+ align:start position:0%
+something called surface recombination
+ 
+
+ align:start position:0%
+something called surface recombination
+so if you look at your silicon lattice
+
+ align:start position:0%
+so if you look at your silicon lattice
+ 
+
+ align:start position:0%
+so if you look at your silicon lattice
+each silicon atom has four valence
+
+ align:start position:0%
+each silicon atom has four valence
+ 
+
+ align:start position:0%
+each silicon atom has four valence
+electrons and it bonds to four silicon
+
+ align:start position:0%
+electrons and it bonds to four silicon
+ 
+
+ align:start position:0%
+electrons and it bonds to four silicon
+atoms around it and it has satisfied
+
+ align:start position:0%
+atoms around it and it has satisfied
+ 
+
+ align:start position:0%
+atoms around it and it has satisfied
+covalent bonds so this silicon atom has
+
+ align:start position:0%
+covalent bonds so this silicon atom has
+ 
+
+ align:start position:0%
+covalent bonds so this silicon atom has
+all its bond satisfied all its bonds
+
+ align:start position:0%
+all its bond satisfied all its bonds
+ 
+
+ align:start position:0%
+all its bond satisfied all its bonds
+satisfied until you get to the surface
+
+ align:start position:0%
+satisfied until you get to the surface
+ 
+
+ align:start position:0%
+satisfied until you get to the surface
+and at the surface you have what are
+
+ align:start position:0%
+and at the surface you have what are
+ 
+
+ align:start position:0%
+and at the surface you have what are
+called dangling bonds and these dangling
+
+ align:start position:0%
+called dangling bonds and these dangling
+ 
+
+ align:start position:0%
+called dangling bonds and these dangling
+bonds can actually introduce trap States
+
+ align:start position:0%
+bonds can actually introduce trap States
+ 
+
+ align:start position:0%
+bonds can actually introduce trap States
+and you can see that it actually
+
+ align:start position:0%
+and you can see that it actually
+ 
+
+ align:start position:0%
+and you can see that it actually
+introduces a whole ton of levels within
+
+ align:start position:0%
+introduces a whole ton of levels within
+ 
+
+ align:start position:0%
+introduces a whole ton of levels within
+the bandgap that can provide
+
+ align:start position:0%
+the bandgap that can provide
+ 
+
+ align:start position:0%
+the bandgap that can provide
+shockley-read-hall recombination
+
+ align:start position:0%
+shockley-read-hall recombination
+ 
+
+ align:start position:0%
+shockley-read-hall recombination
+pathways for your carriers means the
+
+ align:start position:0%
+pathways for your carriers means the
+ 
+
+ align:start position:0%
+pathways for your carriers means the
+surfaces are incredibly important
+
+ align:start position:0%
+surfaces are incredibly important
+ 
+
+ align:start position:0%
+surfaces are incredibly important
+and the way we tend to think of it and
+
+ align:start position:0%
+and the way we tend to think of it and
+ 
+
+ align:start position:0%
+and the way we tend to think of it and
+this is kind of a concept that might be
+
+ align:start position:0%
+this is kind of a concept that might be
+ 
+
+ align:start position:0%
+this is kind of a concept that might be
+difficult to grasp at first but it
+
+ align:start position:0%
+difficult to grasp at first but it
+ 
+
+ align:start position:0%
+difficult to grasp at first but it
+scales with two things there's two
+
+ align:start position:0%
+scales with two things there's two
+ 
+
+ align:start position:0%
+scales with two things there's two
+things going on you can think of that
+
+ align:start position:0%
+things going on you can think of that
+ 
+
+ align:start position:0%
+things going on you can think of that
+this is the width of your cell and you
+
+ align:start position:0%
+this is the width of your cell and you
+ 
+
+ align:start position:0%
+this is the width of your cell and you
+have some surface recombination velocity
+
+ align:start position:0%
+have some surface recombination velocity
+ 
+
+ align:start position:0%
+have some surface recombination velocity
+which is some kind of characteristic of
+
+ align:start position:0%
+which is some kind of characteristic of
+ 
+
+ align:start position:0%
+which is some kind of characteristic of
+how well they can recombine at the
+
+ align:start position:0%
+how well they can recombine at the
+ 
+
+ align:start position:0%
+how well they can recombine at the
+surface
+
+ align:start position:0%
+surface
+ 
+
+ align:start position:0%
+surface
+and let's say infinite surface
+
+ align:start position:0%
+and let's say infinite surface
+ 
+
+ align:start position:0%
+and let's say infinite surface
+recombination velocities it means that
+
+ align:start position:0%
+recombination velocities it means that
+ 
+
+ align:start position:0%
+recombination velocities it means that
+any carrier that comes and hits that
+
+ align:start position:0%
+any carrier that comes and hits that
+ 
+
+ align:start position:0%
+any carrier that comes and hits that
+surface will most surely recombine so
+
+ align:start position:0%
+surface will most surely recombine so
+ 
+
+ align:start position:0%
+surface will most surely recombine so
+this drops to zero so then you're
+
+ align:start position:0%
+this drops to zero so then you're
+ 
+
+ align:start position:0%
+this drops to zero so then you're
+limited by okay how well can they
+
+ align:start position:0%
+limited by okay how well can they
+ 
+
+ align:start position:0%
+limited by okay how well can they
+actually diffuse to your surface so it's
+
+ align:start position:0%
+actually diffuse to your surface so it's
+ 
+
+ align:start position:0%
+actually diffuse to your surface so it's
+it's again some kind of ratio of your
+
+ align:start position:0%
+it's again some kind of ratio of your
+ 
+
+ align:start position:0%
+it's again some kind of ratio of your
+cell thickness squared over the
+
+ align:start position:0%
+cell thickness squared over the
+ 
+
+ align:start position:0%
+cell thickness squared over the
+diffusivity or carrier diffusivity and
+
+ align:start position:0%
+diffusivity or carrier diffusivity and
+ 
+
+ align:start position:0%
+diffusivity or carrier diffusivity and
+that that gives you an idea of what your
+
+ align:start position:0%
+that that gives you an idea of what your
+ 
+
+ align:start position:0%
+that that gives you an idea of what your
+limiting factors are so under very low
+
+ align:start position:0%
+limiting factors are so under very low
+ 
+
+ align:start position:0%
+limiting factors are so under very low
+surface recombination velocities you're
+
+ align:start position:0%
+surface recombination velocities you're
+ 
+
+ align:start position:0%
+surface recombination velocities you're
+limited by this term here the first one
+
+ align:start position:0%
+limited by this term here the first one
+ 
+
+ align:start position:0%
+limited by this term here the first one
+and under very high ones you're limited
+
+ align:start position:0%
+and under very high ones you're limited
+ 
+
+ align:start position:0%
+and under very high ones you're limited
+by this term and so there's two kind of
+
+ align:start position:0%
+by this term and so there's two kind of
+ 
+
+ align:start position:0%
+by this term and so there's two kind of
+effects going on there and it's
+
+ align:start position:0%
+effects going on there and it's
+ 
+
+ align:start position:0%
+effects going on there and it's
+summarized as well here it at at very
+
+ align:start position:0%
+summarized as well here it at at very
+ 
+
+ align:start position:0%
+summarized as well here it at at very
+very low service recombination
+
+ align:start position:0%
+very low service recombination
+ 
+
+ align:start position:0%
+very low service recombination
+velocities your house surfaces almost
+
+ align:start position:0%
+velocities your house surfaces almost
+ 
+
+ align:start position:0%
+velocities your house surfaces almost
+goes to infinity very high and you can
+
+ align:start position:0%
+goes to infinity very high and you can
+ 
+
+ align:start position:0%
+goes to infinity very high and you can
+passivate these bonds using hydrogen so
+
+ align:start position:0%
+passivate these bonds using hydrogen so
+ 
+
+ align:start position:0%
+passivate these bonds using hydrogen so
+for example if you use hydrofluoric acid
+
+ align:start position:0%
+for example if you use hydrofluoric acid
+ 
+
+ align:start position:0%
+for example if you use hydrofluoric acid
+what it does is it edges away the
+
+ align:start position:0%
+what it does is it edges away the
+ 
+
+ align:start position:0%
+what it does is it edges away the
+silicon oxide layer that sits there and
+
+ align:start position:0%
+silicon oxide layer that sits there and
+ 
+
+ align:start position:0%
+silicon oxide layer that sits there and
+you have these hydrogen atoms then now
+
+ align:start position:0%
+you have these hydrogen atoms then now
+ 
+
+ align:start position:0%
+you have these hydrogen atoms then now
+sit and satisfy these bombs and if
+
+ align:start position:0%
+sit and satisfy these bombs and if
+ 
+
+ align:start position:0%
+sit and satisfy these bombs and if
+they're perfectly satisfied you'll have
+
+ align:start position:0%
+they're perfectly satisfied you'll have
+ 
+
+ align:start position:0%
+they're perfectly satisfied you'll have
+a mobile carrier it'll actually
+
+ align:start position:0%
+a mobile carrier it'll actually
+ 
+
+ align:start position:0%
+a mobile carrier it'll actually
+elastically scattered off not lose any
+
+ align:start position:0%
+elastically scattered off not lose any
+ 
+
+ align:start position:0%
+elastically scattered off not lose any
+energy and not recombine through these
+
+ align:start position:0%
+energy and not recombine through these
+ 
+
+ align:start position:0%
+energy and not recombine through these
+trap States yeah
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what is if you if you actually I've seen
+
+ align:start position:0%
+what is if you if you actually I've seen
+ 
+
+ align:start position:0%
+what is if you if you actually I've seen
+some diagrams of what silicon oxide
+
+ align:start position:0%
+some diagrams of what silicon oxide
+ 
+
+ align:start position:0%
+some diagrams of what silicon oxide
+looks like on silicon it passivates many
+
+ align:start position:0%
+looks like on silicon it passivates many
+ 
+
+ align:start position:0%
+looks like on silicon it passivates many
+of the bonds you're absolutely right HF
+
+ align:start position:0%
+of the bonds you're absolutely right HF
+ 
+
+ align:start position:0%
+of the bonds you're absolutely right HF
+is actually probably the best the
+
+ align:start position:0%
+is actually probably the best the
+ 
+
+ align:start position:0%
+is actually probably the best the
+problem is that it etches glass and
+
+ align:start position:0%
+problem is that it etches glass and
+ 
+
+ align:start position:0%
+problem is that it etches glass and
+other things that are in your solar cell
+
+ align:start position:0%
+other things that are in your solar cell
+ 
+
+ align:start position:0%
+other things that are in your solar cell
+material and it's incredibly dangerous
+
+ align:start position:0%
+material and it's incredibly dangerous
+ 
+
+ align:start position:0%
+material and it's incredibly dangerous
+it can kill you rather dramatically so
+
+ align:start position:0%
+it can kill you rather dramatically so
+ 
+
+ align:start position:0%
+it can kill you rather dramatically so
+it's only used in laboratory settings if
+
+ align:start position:0%
+it's only used in laboratory settings if
+ 
+
+ align:start position:0%
+it's only used in laboratory settings if
+you're trying to actually take lifetime
+
+ align:start position:0%
+you're trying to actually take lifetime
+ 
+
+ align:start position:0%
+you're trying to actually take lifetime
+measurements and negate the effect of
+
+ align:start position:0%
+measurements and negate the effect of
+ 
+
+ align:start position:0%
+measurements and negate the effect of
+surface recombination silicon oxide can
+
+ align:start position:0%
+surface recombination silicon oxide can
+ 
+
+ align:start position:0%
+surface recombination silicon oxide can
+be a good one if you actually look at
+
+ align:start position:0%
+be a good one if you actually look at
+ 
+
+ align:start position:0%
+be a good one if you actually look at
+the structure there's a few dangling
+
+ align:start position:0%
+the structure there's a few dangling
+ 
+
+ align:start position:0%
+the structure there's a few dangling
+bonds within there but it can passivate
+
+ align:start position:0%
+bonds within there but it can passivate
+ 
+
+ align:start position:0%
+bonds within there but it can passivate
+most of them just not all of them
+
+ align:start position:0%
+most of them just not all of them
+ 
+
+ align:start position:0%
+most of them just not all of them
+another good passivation technique is
+
+ align:start position:0%
+another good passivation technique is
+ 
+
+ align:start position:0%
+another good passivation technique is
+actually the silicon nitride AARC coding
+
+ align:start position:0%
+actually the silicon nitride AARC coding
+ 
+
+ align:start position:0%
+actually the silicon nitride AARC coding
+it passivates the surface very well so
+
+ align:start position:0%
+it passivates the surface very well so
+ 
+
+ align:start position:0%
+it passivates the surface very well so
+yeah good question and there's other
+
+ align:start position:0%
+yeah good question and there's other
+ 
+
+ align:start position:0%
+yeah good question and there's other
+ways to mitigate surface recombination
+
+ align:start position:0%
+ways to mitigate surface recombination
+ 
+
+ align:start position:0%
+ways to mitigate surface recombination
+so we'll talk about that I think in
+
+ align:start position:0%
+so we'll talk about that I think in
+ 
+
+ align:start position:0%
+so we'll talk about that I think in
+either next lecture or the one after
+
+ align:start position:0%
+either next lecture or the one after
+ 
+
+ align:start position:0%
+either next lecture or the one after
+that so so yeah this slide is just
+
+ align:start position:0%
+that so so yeah this slide is just
+ 
+
+ align:start position:0%
+that so so yeah this slide is just
+telling us that if we bury our thickness
+
+ align:start position:0%
+telling us that if we bury our thickness
+ 
+
+ align:start position:0%
+telling us that if we bury our thickness
+of our silicon we can actually measure
+
+ align:start position:0%
+of our silicon we can actually measure
+ 
+
+ align:start position:0%
+of our silicon we can actually measure
+our service recombination velocity and
+
+ align:start position:0%
+our service recombination velocity and
+ 
+
+ align:start position:0%
+our service recombination velocity and
+we can fit it so we can figure out our
+
+ align:start position:0%
+we can fit it so we can figure out our
+ 
+
+ align:start position:0%
+we can fit it so we can figure out our
+tau surface which is really important
+
+ align:start position:0%
+tau surface which is really important
+ 
+
+ align:start position:0%
+tau surface which is really important
+material parameter generally I think
+
+ align:start position:0%
+material parameter generally I think
+ 
+
+ align:start position:0%
+material parameter generally I think
+good surface recombination velocities or
+
+ align:start position:0%
+good surface recombination velocities or
+ 
+
+ align:start position:0%
+good surface recombination velocities or
+anywhere from like 10 to maybe in the
+
+ align:start position:0%
+anywhere from like 10 to maybe in the
+ 
+
+ align:start position:0%
+anywhere from like 10 to maybe in the
+hundreds for centimeters per second and
+
+ align:start position:0%
+hundreds for centimeters per second and
+ 
+
+ align:start position:0%
+hundreds for centimeters per second and
+really bad ones are much much higher
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay and the last type of recombination
+
+ align:start position:0%
+okay and the last type of recombination
+ 
+
+ align:start position:0%
+okay and the last type of recombination
+mechanism we're gonna talk about today
+
+ align:start position:0%
+mechanism we're gonna talk about today
+ 
+
+ align:start position:0%
+mechanism we're gonna talk about today
+is o.j recombination and this looks like
+
+ align:start position:0%
+is o.j recombination and this looks like
+ 
+
+ align:start position:0%
+is o.j recombination and this looks like
+when I first saw this I'm like why on
+
+ align:start position:0%
+when I first saw this I'm like why on
+ 
+
+ align:start position:0%
+when I first saw this I'm like why on
+earth would this ever happen and the
+
+ align:start position:0%
+earth would this ever happen and the
+ 
+
+ align:start position:0%
+earth would this ever happen and the
+fact is it doesn't until you get to very
+
+ align:start position:0%
+fact is it doesn't until you get to very
+ 
+
+ align:start position:0%
+fact is it doesn't until you get to very
+very high carrier concentrations so you
+
+ align:start position:0%
+very high carrier concentrations so you
+ 
+
+ align:start position:0%
+very high carrier concentrations so you
+can see that it involves three particles
+
+ align:start position:0%
+can see that it involves three particles
+ 
+
+ align:start position:0%
+can see that it involves three particles
+let's say an n-type silicon it needs two
+
+ align:start position:0%
+let's say an n-type silicon it needs two
+ 
+
+ align:start position:0%
+let's say an n-type silicon it needs two
+electrons and a hole what happens is is
+
+ align:start position:0%
+electrons and a hole what happens is is
+ 
+
+ align:start position:0%
+electrons and a hole what happens is is
+that you get the simultaneous relaxation
+
+ align:start position:0%
+that you get the simultaneous relaxation
+ 
+
+ align:start position:0%
+that you get the simultaneous relaxation
+and excitation so you get this
+
+ align:start position:0%
+and excitation so you get this
+ 
+
+ align:start position:0%
+and excitation so you get this
+relaxation of this excited electron into
+
+ align:start position:0%
+relaxation of this excited electron into
+ 
+
+ align:start position:0%
+relaxation of this excited electron into
+a hole and then you get this
+
+ align:start position:0%
+a hole and then you get this
+ 
+
+ align:start position:0%
+a hole and then you get this
+excitation of this other electron into a
+
+ align:start position:0%
+excitation of this other electron into a
+ 
+
+ align:start position:0%
+excitation of this other electron into a
+higher energy state and then it thermal
+
+ align:start position:0%
+higher energy state and then it thermal
+ 
+
+ align:start position:0%
+higher energy state and then it thermal
+ices down in releases of phonon releases
+
+ align:start position:0%
+ices down in releases of phonon releases
+ 
+
+ align:start position:0%
+ices down in releases of phonon releases
+heat yeah Jessica so this is going to be
+
+ align:start position:0%
+heat yeah Jessica so this is going to be
+ 
+
+ align:start position:0%
+heat yeah Jessica so this is going to be
+our n-type material and again because
+
+ align:start position:0%
+our n-type material and again because
+ 
+
+ align:start position:0%
+our n-type material and again because
+this type of recombination event
+
+ align:start position:0%
+this type of recombination event
+ 
+
+ align:start position:0%
+this type of recombination event
+requires two particles it requires two
+
+ align:start position:0%
+requires two particles it requires two
+ 
+
+ align:start position:0%
+requires two particles it requires two
+electrons so it's N squared in one hole
+
+ align:start position:0%
+electrons so it's N squared in one hole
+ 
+
+ align:start position:0%
+electrons so it's N squared in one hole
+so the recombination rate goes up with P
+
+ align:start position:0%
+so the recombination rate goes up with P
+ 
+
+ align:start position:0%
+so the recombination rate goes up with P
+N squared at high enough concentrations
+
+ align:start position:0%
+N squared at high enough concentrations
+ 
+
+ align:start position:0%
+N squared at high enough concentrations
+and so your towel goes up with the one
+
+ align:start position:0%
+and so your towel goes up with the one
+ 
+
+ align:start position:0%
+and so your towel goes up with the one
+over N squared and this is particularly
+
+ align:start position:0%
+over N squared and this is particularly
+ 
+
+ align:start position:0%
+over N squared and this is particularly
+bad again only at very because it goes
+
+ align:start position:0%
+bad again only at very because it goes
+ 
+
+ align:start position:0%
+bad again only at very because it goes
+up with a square of the carrier
+
+ align:start position:0%
+up with a square of the carrier
+ 
+
+ align:start position:0%
+up with a square of the carrier
+concentration it's really bad at a very
+
+ align:start position:0%
+concentration it's really bad at a very
+ 
+
+ align:start position:0%
+concentration it's really bad at a very
+high carrier concentration so if we look
+
+ align:start position:0%
+high carrier concentration so if we look
+ 
+
+ align:start position:0%
+high carrier concentration so if we look
+at this plot we can see that our
+
+ align:start position:0%
+at this plot we can see that our
+ 
+
+ align:start position:0%
+at this plot we can see that our
+minority carrier lifetime drops well
+
+ align:start position:0%
+minority carrier lifetime drops well
+ 
+
+ align:start position:0%
+minority carrier lifetime drops well
+below a microsecond around 10 to the 18
+
+ align:start position:0%
+below a microsecond around 10 to the 18
+ 
+
+ align:start position:0%
+below a microsecond around 10 to the 18
+so you generally want to stay out of
+
+ align:start position:0%
+so you generally want to stay out of
+ 
+
+ align:start position:0%
+so you generally want to stay out of
+that range of doping concentrations in
+
+ align:start position:0%
+that range of doping concentrations in
+ 
+
+ align:start position:0%
+that range of doping concentrations in
+your base because you'll have very very
+
+ align:start position:0%
+your base because you'll have very very
+ 
+
+ align:start position:0%
+your base because you'll have very very
+bad lifetimes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sorry this is our didn't label this
+
+ align:start position:0%
+sorry this is our didn't label this
+ 
+
+ align:start position:0%
+sorry this is our didn't label this
+you're right this is the valence band
+
+ align:start position:0%
+you're right this is the valence band
+ 
+
+ align:start position:0%
+you're right this is the valence band
+that's the conduction band okay all
+
+ align:start position:0%
+that's the conduction band okay all
+ 
+
+ align:start position:0%
+that's the conduction band okay all
+right and so this is kind of driving
+
+ align:start position:0%
+right and so this is kind of driving
+ 
+
+ align:start position:0%
+right and so this is kind of driving
+home again that leaky bucket idea is
+
+ align:start position:0%
+home again that leaky bucket idea is
+ 
+
+ align:start position:0%
+home again that leaky bucket idea is
+that you're really limited by your worst
+
+ align:start position:0%
+that you're really limited by your worst
+ 
+
+ align:start position:0%
+that you're really limited by your worst
+lifetime and so if you remember what
+
+ align:start position:0%
+lifetime and so if you remember what
+ 
+
+ align:start position:0%
+lifetime and so if you remember what
+we're thinking about parallel circuits
+
+ align:start position:0%
+we're thinking about parallel circuits
+ 
+
+ align:start position:0%
+we're thinking about parallel circuits
+here your bulk or your effective
+
+ align:start position:0%
+here your bulk or your effective
+ 
+
+ align:start position:0%
+here your bulk or your effective
+lifetime of each carrier is determined
+
+ align:start position:0%
+lifetime of each carrier is determined
+ 
+
+ align:start position:0%
+lifetime of each carrier is determined
+by these three here your radiative sorry
+
+ align:start position:0%
+by these three here your radiative sorry
+ 
+
+ align:start position:0%
+by these three here your radiative sorry
+that should be a band which is the same
+
+ align:start position:0%
+that should be a band which is the same
+ 
+
+ align:start position:0%
+that should be a band which is the same
+as your radiative recombination O'Shay
+
+ align:start position:0%
+as your radiative recombination O'Shay
+ 
+
+ align:start position:0%
+as your radiative recombination O'Shay
+in chocolate Reed Hall and so in
+
+ align:start position:0%
+in chocolate Reed Hall and so in
+ 
+
+ align:start position:0%
+in chocolate Reed Hall and so in
+different excess carrier densities so
+
+ align:start position:0%
+different excess carrier densities so
+ 
+
+ align:start position:0%
+different excess carrier densities so
+we're varying Delta n by shining various
+
+ align:start position:0%
+we're varying Delta n by shining various
+ 
+
+ align:start position:0%
+we're varying Delta n by shining various
+intensities of light and we can kind of
+
+ align:start position:0%
+intensities of light and we can kind of
+ 
+
+ align:start position:0%
+intensities of light and we can kind of
+activate different limiting lifetimes so
+
+ align:start position:0%
+activate different limiting lifetimes so
+ 
+
+ align:start position:0%
+activate different limiting lifetimes so
+it very low you're a limited by
+
+ align:start position:0%
+it very low you're a limited by
+ 
+
+ align:start position:0%
+it very low you're a limited by
+shockley-read-hall and Chakra Greenhalgh
+
+ align:start position:0%
+shockley-read-hall and Chakra Greenhalgh
+ 
+
+ align:start position:0%
+shockley-read-hall and Chakra Greenhalgh
+can actually go down with higher
+
+ align:start position:0%
+can actually go down with higher
+ 
+
+ align:start position:0%
+can actually go down with higher
+illumination conditions and your O'Shay
+
+ align:start position:0%
+illumination conditions and your O'Shay
+ 
+
+ align:start position:0%
+illumination conditions and your O'Shay
+remember against really really bad
+
+ align:start position:0%
+remember against really really bad
+ 
+
+ align:start position:0%
+remember against really really bad
+around 10 to the 18 becomes your
+
+ align:start position:0%
+around 10 to the 18 becomes your
+ 
+
+ align:start position:0%
+around 10 to the 18 becomes your
+limiting so your tell bulk is always
+
+ align:start position:0%
+limiting so your tell bulk is always
+ 
+
+ align:start position:0%
+limiting so your tell bulk is always
+doing is never doing better than your
+
+ align:start position:0%
+doing is never doing better than your
+ 
+
+ align:start position:0%
+doing is never doing better than your
+worst lifetime hello Jay this came out
+
+ align:start position:0%
+worst lifetime hello Jay this came out
+ 
+
+ align:start position:0%
+worst lifetime hello Jay this came out
+of Dana MacDonald's thesis talam it er
+
+ align:start position:0%
+of Dana MacDonald's thesis talam it er
+ 
+
+ align:start position:0%
+of Dana MacDonald's thesis talam it er
+is it's complicated because it has other
+
+ align:start position:0%
+is it's complicated because it has other
+ 
+
+ align:start position:0%
+is it's complicated because it has other
+influences in it Oh Jay I always think
+
+ align:start position:0%
+influences in it Oh Jay I always think
+ 
+
+ align:start position:0%
+influences in it Oh Jay I always think
+of recombination in the emitter is Oh
+
+ align:start position:0%
+of recombination in the emitter is Oh
+ 
+
+ align:start position:0%
+of recombination in the emitter is Oh
+Jay but you also have other carriers
+
+ align:start position:0%
+Jay but you also have other carriers
+ 
+
+ align:start position:0%
+Jay but you also have other carriers
+coming in due to injection currents
+
+ align:start position:0%
+coming in due to injection currents
+ 
+
+ align:start position:0%
+coming in due to injection currents
+right or and so your excess carrier
+
+ align:start position:0%
+right or and so your excess carrier
+ 
+
+ align:start position:0%
+right or and so your excess carrier
+population is also a function of that
+
+ align:start position:0%
+population is also a function of that
+ 
+
+ align:start position:0%
+population is also a function of that
+and so the equation for it gets a little
+
+ align:start position:0%
+and so the equation for it gets a little
+ 
+
+ align:start position:0%
+and so the equation for it gets a little
+more complicated but it would make sense
+
+ align:start position:0%
+more complicated but it would make sense
+ 
+
+ align:start position:0%
+more complicated but it would make sense
+that as you increase illumination you're
+
+ align:start position:0%
+that as you increase illumination you're
+ 
+
+ align:start position:0%
+that as you increase illumination you're
+increasing your your current into the
+
+ align:start position:0%
+increasing your your current into the
+ 
+
+ align:start position:0%
+increasing your your current into the
+emitter and you would get more carriers
+
+ align:start position:0%
+emitter and you would get more carriers
+ 
+
+ align:start position:0%
+emitter and you would get more carriers
+and it would decrease and it looks
+
+ align:start position:0%
+and it would decrease and it looks
+ 
+
+ align:start position:0%
+and it would decrease and it looks
+almost exactly like Oh Jay in this in
+
+ align:start position:0%
+almost exactly like Oh Jay in this in
+ 
+
+ align:start position:0%
+almost exactly like Oh Jay in this in
+this regime over here I'm not sure the
+
+ align:start position:0%
+this regime over here I'm not sure the
+ 
+
+ align:start position:0%
+this regime over here I'm not sure the
+other things that go into it but if you
+
+ align:start position:0%
+other things that go into it but if you
+ 
+
+ align:start position:0%
+other things that go into it but if you
+look up as theses I think it gives a
+
+ align:start position:0%
+look up as theses I think it gives a
+ 
+
+ align:start position:0%
+look up as theses I think it gives a
+pretty good description okay so you're
+
+ align:start position:0%
+pretty good description okay so you're
+ 
+
+ align:start position:0%
+pretty good description okay so you're
+probably bored of hearing me say this
+
+ align:start position:0%
+probably bored of hearing me say this
+ 
+
+ align:start position:0%
+probably bored of hearing me say this
+but again it's we're always limited by
+
+ align:start position:0%
+but again it's we're always limited by
+ 
+
+ align:start position:0%
+but again it's we're always limited by
+our weakest so in defect mitigated
+
+ align:start position:0%
+our weakest so in defect mitigated
+ 
+
+ align:start position:0%
+our weakest so in defect mitigated
+recombination material so we're
+
+ align:start position:0%
+recombination material so we're
+ 
+
+ align:start position:0%
+recombination material so we're
+the your shortest lifetime is due to
+
+ align:start position:0%
+the your shortest lifetime is due to
+ 
+
+ align:start position:0%
+the your shortest lifetime is due to
+some kind of shockley-read-hall
+
+ align:start position:0%
+some kind of shockley-read-hall
+ 
+
+ align:start position:0%
+some kind of shockley-read-hall
+recombination it's always your lifetime
+
+ align:start position:0%
+recombination it's always your lifetime
+ 
+
+ align:start position:0%
+recombination it's always your lifetime
+for shockley-read-hall is always going
+
+ align:start position:0%
+for shockley-read-hall is always going
+ 
+
+ align:start position:0%
+for shockley-read-hall is always going
+to be much much shorter than your
+
+ align:start position:0%
+to be much much shorter than your
+ 
+
+ align:start position:0%
+to be much much shorter than your
+radiative lifetimes which is a
+
+ align:start position:0%
+radiative lifetimes which is a
+ 
+
+ align:start position:0%
+radiative lifetimes which is a
+characteristic we can exploit for
+
+ align:start position:0%
+characteristic we can exploit for
+ 
+
+ align:start position:0%
+characteristic we can exploit for
+measuring the lifetimes of our materials
+
+ align:start position:0%
+measuring the lifetimes of our materials
+ 
+
+ align:start position:0%
+measuring the lifetimes of our materials
+so because very very few carriers will
+
+ align:start position:0%
+so because very very few carriers will
+ 
+
+ align:start position:0%
+so because very very few carriers will
+actually radiatively recombine and emit
+
+ align:start position:0%
+actually radiatively recombine and emit
+ 
+
+ align:start position:0%
+actually radiatively recombine and emit
+a photon that if more of them are ready
+
+ align:start position:0%
+a photon that if more of them are ready
+ 
+
+ align:start position:0%
+a photon that if more of them are ready
+to leak recombining then we know that
+
+ align:start position:0%
+to leak recombining then we know that
+ 
+
+ align:start position:0%
+to leak recombining then we know that
+it's a very high lifetime material if
+
+ align:start position:0%
+it's a very high lifetime material if
+ 
+
+ align:start position:0%
+it's a very high lifetime material if
+there's a lot of defects and we have
+
+ align:start position:0%
+there's a lot of defects and we have
+ 
+
+ align:start position:0%
+there's a lot of defects and we have
+very very short lifetimes very few of
+
+ align:start position:0%
+very very short lifetimes very few of
+ 
+
+ align:start position:0%
+very very short lifetimes very few of
+them will radiatively recombine and so
+
+ align:start position:0%
+them will radiatively recombine and so
+ 
+
+ align:start position:0%
+them will radiatively recombine and so
+this emission of photons with energy at
+
+ align:start position:0%
+this emission of photons with energy at
+ 
+
+ align:start position:0%
+this emission of photons with energy at
+the bandgap it can kind of give us an
+
+ align:start position:0%
+the bandgap it can kind of give us an
+ 
+
+ align:start position:0%
+the bandgap it can kind of give us an
+idea of the lifetime within our material
+
+ align:start position:0%
+idea of the lifetime within our material
+ 
+
+ align:start position:0%
+idea of the lifetime within our material
+and that's how we measure it's a
+
+ align:start position:0%
+and that's how we measure it's a
+ 
+
+ align:start position:0%
+and that's how we measure it's a
+technique called photo luminescence and
+
+ align:start position:0%
+technique called photo luminescence and
+ 
+
+ align:start position:0%
+technique called photo luminescence and
+what you do is you shine light on it
+
+ align:start position:0%
+what you do is you shine light on it
+ 
+
+ align:start position:0%
+what you do is you shine light on it
+generally with a laser we put a diffuser
+
+ align:start position:0%
+generally with a laser we put a diffuser
+ 
+
+ align:start position:0%
+generally with a laser we put a diffuser
+in front of the laser so the laser beam
+
+ align:start position:0%
+in front of the laser so the laser beam
+ 
+
+ align:start position:0%
+in front of the laser so the laser beam
+spreads its photons over a large area we
+
+ align:start position:0%
+spreads its photons over a large area we
+ 
+
+ align:start position:0%
+spreads its photons over a large area we
+excite all these carriers so this laser
+
+ align:start position:0%
+excite all these carriers so this laser
+ 
+
+ align:start position:0%
+excite all these carriers so this laser
+has very very short wavelengths and I
+
+ align:start position:0%
+has very very short wavelengths and I
+ 
+
+ align:start position:0%
+has very very short wavelengths and I
+think in our very short it's 900
+
+ align:start position:0%
+think in our very short it's 900
+ 
+
+ align:start position:0%
+think in our very short it's 900
+nanometers
+
+ align:start position:0%
+nanometers
+ 
+
+ align:start position:0%
+nanometers
+silicon's bandgap corresponds to about
+
+ align:start position:0%
+silicon's bandgap corresponds to about
+ 
+
+ align:start position:0%
+silicon's bandgap corresponds to about
+1108 nanometers and so 900 is easily
+
+ align:start position:0%
+1108 nanometers and so 900 is easily
+ 
+
+ align:start position:0%
+1108 nanometers and so 900 is easily
+absorbed not just right near the emitter
+
+ align:start position:0%
+absorbed not just right near the emitter
+ 
+
+ align:start position:0%
+absorbed not just right near the emitter
+but also somewhat well deep into the
+
+ align:start position:0%
+but also somewhat well deep into the
+ 
+
+ align:start position:0%
+but also somewhat well deep into the
+below the junction as well and then as
+
+ align:start position:0%
+below the junction as well and then as
+ 
+
+ align:start position:0%
+below the junction as well and then as
+we begin to see recombination when
+
+ align:start position:0%
+we begin to see recombination when
+ 
+
+ align:start position:0%
+we begin to see recombination when
+radiative recombination happens we emit
+
+ align:start position:0%
+radiative recombination happens we emit
+ 
+
+ align:start position:0%
+radiative recombination happens we emit
+a photon and that can happen in certain
+
+ align:start position:0%
+a photon and that can happen in certain
+ 
+
+ align:start position:0%
+a photon and that can happen in certain
+areas better than others and it a lot of
+
+ align:start position:0%
+areas better than others and it a lot of
+ 
+
+ align:start position:0%
+areas better than others and it a lot of
+it depends on like I said defect density
+
+ align:start position:0%
+it depends on like I said defect density
+ 
+
+ align:start position:0%
+it depends on like I said defect density
+and other lifetime limiting defects and
+
+ align:start position:0%
+and other lifetime limiting defects and
+ 
+
+ align:start position:0%
+and other lifetime limiting defects and
+it's a good way to kind of like
+
+ align:start position:0%
+it's a good way to kind of like
+ 
+
+ align:start position:0%
+it's a good way to kind of like
+spatially locate where problems are in
+
+ align:start position:0%
+spatially locate where problems are in
+ 
+
+ align:start position:0%
+spatially locate where problems are in
+your solar cell any other questions that
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it depends on your camera right so we
+
+ align:start position:0%
+it depends on your camera right so we
+ 
+
+ align:start position:0%
+it depends on your camera right so we
+use I think a germanium camera to detect
+
+ align:start position:0%
+use I think a germanium camera to detect
+ 
+
+ align:start position:0%
+use I think a germanium camera to detect
+those photons because silicon won't have
+
+ align:start position:0%
+those photons because silicon won't have
+ 
+
+ align:start position:0%
+those photons because silicon won't have
+a very good response and yeah it depends
+
+ align:start position:0%
+a very good response and yeah it depends
+ 
+
+ align:start position:0%
+a very good response and yeah it depends
+on the CCD array within your camera it
+
+ align:start position:0%
+on the CCD array within your camera it
+ 
+
+ align:start position:0%
+on the CCD array within your camera it
+can be really good I do a similar
+
+ align:start position:0%
+can be really good I do a similar
+ 
+
+ align:start position:0%
+can be really good I do a similar
+technique to measure shunts and we have
+
+ align:start position:0%
+technique to measure shunts and we have
+ 
+
+ align:start position:0%
+technique to measure shunts and we have
+a microscope objective we just have to
+
+ align:start position:0%
+a microscope objective we just have to
+ 
+
+ align:start position:0%
+a microscope objective we just have to
+zoom in really really far and then we
+
+ align:start position:0%
+zoom in really really far and then we
+ 
+
+ align:start position:0%
+zoom in really really far and then we
+just scan over an area okay and last
+
+ align:start position:0%
+just scan over an area okay and last
+ 
+
+ align:start position:0%
+just scan over an area okay and last
+little thing is that if you recall let
+
+ align:start position:0%
+little thing is that if you recall let
+ 
+
+ align:start position:0%
+little thing is that if you recall let
+me this slide traps can not only trap an
+
+ align:start position:0%
+me this slide traps can not only trap an
+ 
+
+ align:start position:0%
+me this slide traps can not only trap an
+electron but you can also emit an
+
+ align:start position:0%
+electron but you can also emit an
+ 
+
+ align:start position:0%
+electron but you can also emit an
+electron assuming it has enough thermal
+
+ align:start position:0%
+electron assuming it has enough thermal
+ 
+
+ align:start position:0%
+electron assuming it has enough thermal
+energy and you can see that on this plot
+
+ align:start position:0%
+energy and you can see that on this plot
+ 
+
+ align:start position:0%
+energy and you can see that on this plot
+and so this is an Arrhenius plot so
+
+ align:start position:0%
+and so this is an Arrhenius plot so
+ 
+
+ align:start position:0%
+and so this is an Arrhenius plot so
+again
+
+ align:start position:0%
+again
+ 
+
+ align:start position:0%
+again
+high temperatures aren't this direction
+
+ align:start position:0%
+high temperatures aren't this direction
+ 
+
+ align:start position:0%
+high temperatures aren't this direction
+low temperature over here and you can
+
+ align:start position:0%
+low temperature over here and you can
+ 
+
+ align:start position:0%
+low temperature over here and you can
+see that your lifetime actually
+
+ align:start position:0%
+see that your lifetime actually
+ 
+
+ align:start position:0%
+see that your lifetime actually
+increases at higher temperatures because
+
+ align:start position:0%
+increases at higher temperatures because
+ 
+
+ align:start position:0%
+increases at higher temperatures because
+electrons that see that trap fall into
+
+ align:start position:0%
+electrons that see that trap fall into
+ 
+
+ align:start position:0%
+electrons that see that trap fall into
+it then can easily come back out of it
+
+ align:start position:0%
+it then can easily come back out of it
+ 
+
+ align:start position:0%
+it then can easily come back out of it
+because they have enough thermal energy
+
+ align:start position:0%
+because they have enough thermal energy
+ 
+
+ align:start position:0%
+because they have enough thermal energy
+to escape and that's really what this is
+
+ align:start position:0%
+to escape and that's really what this is
+ 
+
+ align:start position:0%
+to escape and that's really what this is
+depicting so what one of the things I
+
+ align:start position:0%
+depicting so what one of the things I
+ 
+
+ align:start position:0%
+depicting so what one of the things I
+think for researchers in the room who
+
+ align:start position:0%
+think for researchers in the room who
+ 
+
+ align:start position:0%
+think for researchers in the room who
+are studying these types of materials
+
+ align:start position:0%
+are studying these types of materials
+ 
+
+ align:start position:0%
+are studying these types of materials
+varying temperature is often a really
+
+ align:start position:0%
+varying temperature is often a really
+ 
+
+ align:start position:0%
+varying temperature is often a really
+really good way of looking at electronic
+
+ align:start position:0%
+really good way of looking at electronic
+ 
+
+ align:start position:0%
+really good way of looking at electronic
+structure of materials and it can be
+
+ align:start position:0%
+structure of materials and it can be
+ 
+
+ align:start position:0%
+structure of materials and it can be
+very very powerful and this is one
+
+ align:start position:0%
+very very powerful and this is one
+ 
+
+ align:start position:0%
+very very powerful and this is one
+example of a tool to look at this kind
+
+ align:start position:0%
+example of a tool to look at this kind
+ 
+
+ align:start position:0%
+example of a tool to look at this kind
+of these types of traps okay oh good we
+
+ align:start position:0%
+of these types of traps okay oh good we
+ 
+
+ align:start position:0%
+of these types of traps okay oh good we
+have plenty of time we actually might
+
+ align:start position:0%
+have plenty of time we actually might
+ 
+
+ align:start position:0%
+have plenty of time we actually might
+end early
+
+ align:start position:0%
+end early
+ 
+
+ align:start position:0%
+end early
+okay so now we're going to talk about
+
+ align:start position:0%
+okay so now we're going to talk about
+ 
+
+ align:start position:0%
+okay so now we're going to talk about
+mobility we've given a lot of sorry
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's that's a good question so
+
+ align:start position:0%
+that's that's a good question so
+ 
+
+ align:start position:0%
+that's that's a good question so
+phosphorus actually has if you draw it
+
+ align:start position:0%
+phosphorus actually has if you draw it
+ 
+
+ align:start position:0%
+phosphorus actually has if you draw it
+on an E versus X diagram so if we have
+
+ align:start position:0%
+on an E versus X diagram so if we have
+ 
+
+ align:start position:0%
+on an E versus X diagram so if we have
+our conduction band here our valence
+
+ align:start position:0%
+our conduction band here our valence
+ 
+
+ align:start position:0%
+our conduction band here our valence
+band here we said iron put states in the
+
+ align:start position:0%
+band here we said iron put states in the
+ 
+
+ align:start position:0%
+band here we said iron put states in the
+middle of the gap phosphorus and boron
+
+ align:start position:0%
+middle of the gap phosphorus and boron
+ 
+
+ align:start position:0%
+middle of the gap phosphorus and boron
+actually put States very very very close
+
+ align:start position:0%
+actually put States very very very close
+ 
+
+ align:start position:0%
+actually put States very very very close
+to the valence band conduction band if
+
+ align:start position:0%
+to the valence band conduction band if
+ 
+
+ align:start position:0%
+to the valence band conduction band if
+you go to low enough temperature so
+
+ align:start position:0%
+you go to low enough temperature so
+ 
+
+ align:start position:0%
+you go to low enough temperature so
+let's say you know below 100 Kelvin you
+
+ align:start position:0%
+let's say you know below 100 Kelvin you
+ 
+
+ align:start position:0%
+let's say you know below 100 Kelvin you
+can actually freeze out those donor
+
+ align:start position:0%
+can actually freeze out those donor
+ 
+
+ align:start position:0%
+can actually freeze out those donor
+electrons onto the phosphorous atoms and
+
+ align:start position:0%
+electrons onto the phosphorous atoms and
+ 
+
+ align:start position:0%
+electrons onto the phosphorous atoms and
+below certain concentrations of
+
+ align:start position:0%
+below certain concentrations of
+ 
+
+ align:start position:0%
+below certain concentrations of
+phosphorus atoms for example so below
+
+ align:start position:0%
+phosphorus atoms for example so below
+ 
+
+ align:start position:0%
+phosphorus atoms for example so below
+like 10 to the 18 at 0 Kelvin you cannot
+
+ align:start position:0%
+like 10 to the 18 at 0 Kelvin you cannot
+ 
+
+ align:start position:0%
+like 10 to the 18 at 0 Kelvin you cannot
+conduct electricity it actually becomes
+
+ align:start position:0%
+conduct electricity it actually becomes
+ 
+
+ align:start position:0%
+conduct electricity it actually becomes
+a total insulator this is an excellent
+
+ align:start position:0%
+a total insulator this is an excellent
+ 
+
+ align:start position:0%
+a total insulator this is an excellent
+question but at room temperature when
+
+ align:start position:0%
+question but at room temperature when
+ 
+
+ align:start position:0%
+question but at room temperature when
+Katy is on the order so Katy is your
+
+ align:start position:0%
+Katy is on the order so Katy is your
+ 
+
+ align:start position:0%
+Katy is on the order so Katy is your
+thermal energy and at room temperature
+
+ align:start position:0%
+thermal energy and at room temperature
+ 
+
+ align:start position:0%
+thermal energy and at room temperature
+if you put that 4 electrons
+
+ align:start position:0%
+if you put that 4 electrons
+ 
+
+ align:start position:0%
+if you put that 4 electrons
+it's 0.026 electron volts or 26 milli
+
+ align:start position:0%
+it's 0.026 electron volts or 26 milli
+ 
+
+ align:start position:0%
+it's 0.026 electron volts or 26 milli
+electron volts this is a good number to
+
+ align:start position:0%
+electron volts this is a good number to
+ 
+
+ align:start position:0%
+electron volts this is a good number to
+have in mind by the way when that number
+
+ align:start position:0%
+have in mind by the way when that number
+ 
+
+ align:start position:0%
+have in mind by the way when that number
+is on the order of this binding energy
+
+ align:start position:0%
+is on the order of this binding energy
+ 
+
+ align:start position:0%
+is on the order of this binding energy
+for phosphorous they're almost always
+
+ align:start position:0%
+for phosphorous they're almost always
+ 
+
+ align:start position:0%
+for phosphorous they're almost always
+fully ionized and free but that's a very
+
+ align:start position:0%
+fully ionized and free but that's a very
+ 
+
+ align:start position:0%
+fully ionized and free but that's a very
+good question
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+alright alright so if we remember our
+
+ align:start position:0%
+alright alright so if we remember our
+ 
+
+ align:start position:0%
+alright alright so if we remember our
+definition of mobility it's related to
+
+ align:start position:0%
+definition of mobility it's related to
+ 
+
+ align:start position:0%
+definition of mobility it's related to
+our diffusivity and again our mobility
+
+ align:start position:0%
+our diffusivity and again our mobility
+ 
+
+ align:start position:0%
+our diffusivity and again our mobility
+is saying how well these excited charges
+
+ align:start position:0%
+is saying how well these excited charges
+ 
+
+ align:start position:0%
+is saying how well these excited charges
+can move around and it's also related
+
+ align:start position:0%
+can move around and it's also related
+ 
+
+ align:start position:0%
+can move around and it's also related
+how much thermal energy these charges
+
+ align:start position:0%
+how much thermal energy these charges
+ 
+
+ align:start position:0%
+how much thermal energy these charges
+have so that's why we have this KB T
+
+ align:start position:0%
+have so that's why we have this KB T
+ 
+
+ align:start position:0%
+have so that's why we have this KB T
+factor and what's plotted on the right
+
+ align:start position:0%
+factor and what's plotted on the right
+ 
+
+ align:start position:0%
+factor and what's plotted on the right
+is the Shocker quasar efficiency limit
+
+ align:start position:0%
+is the Shocker quasar efficiency limit
+ 
+
+ align:start position:0%
+is the Shocker quasar efficiency limit
+which are those stars and then how if
+
+ align:start position:0%
+which are those stars and then how if
+ 
+
+ align:start position:0%
+which are those stars and then how if
+you let's say you reduce your mobility
+
+ align:start position:0%
+you let's say you reduce your mobility
+ 
+
+ align:start position:0%
+you let's say you reduce your mobility
+by let's say a factor of 10 or 100
+
+ align:start position:0%
+by let's say a factor of 10 or 100
+ 
+
+ align:start position:0%
+by let's say a factor of 10 or 100
+what's the impact on the overall
+
+ align:start position:0%
+what's the impact on the overall
+ 
+
+ align:start position:0%
+what's the impact on the overall
+efficiency and you can see that if you
+
+ align:start position:0%
+efficiency and you can see that if you
+ 
+
+ align:start position:0%
+efficiency and you can see that if you
+detrimental impacts your mobility you
+
+ align:start position:0%
+detrimental impacts your mobility you
+ 
+
+ align:start position:0%
+detrimental impacts your mobility you
+can really have a large effect on your
+
+ align:start position:0%
+can really have a large effect on your
+ 
+
+ align:start position:0%
+can really have a large effect on your
+diffusion length and it can really hurt
+
+ align:start position:0%
+diffusion length and it can really hurt
+ 
+
+ align:start position:0%
+diffusion length and it can really hurt
+your device performance so it's really
+
+ align:start position:0%
+your device performance so it's really
+ 
+
+ align:start position:0%
+your device performance so it's really
+important material parameter to think
+
+ align:start position:0%
+important material parameter to think
+ 
+
+ align:start position:0%
+important material parameter to think
+about okay so there's lots of ways that
+
+ align:start position:0%
+about okay so there's lots of ways that
+ 
+
+ align:start position:0%
+about okay so there's lots of ways that
+these mobile electrons can do what's
+
+ align:start position:0%
+these mobile electrons can do what's
+ 
+
+ align:start position:0%
+these mobile electrons can do what's
+called scattering so if I'm mobile
+
+ align:start position:0%
+called scattering so if I'm mobile
+ 
+
+ align:start position:0%
+called scattering so if I'm mobile
+electron I'm moving down through the
+
+ align:start position:0%
+electron I'm moving down through the
+ 
+
+ align:start position:0%
+electron I'm moving down through the
+silicon lattice and let's say I see a
+
+ align:start position:0%
+silicon lattice and let's say I see a
+ 
+
+ align:start position:0%
+silicon lattice and let's say I see a
+defect and this defect because it has
+
+ align:start position:0%
+defect and this defect because it has
+ 
+
+ align:start position:0%
+defect and this defect because it has
+these extra electrons it creates this
+
+ align:start position:0%
+these extra electrons it creates this
+ 
+
+ align:start position:0%
+these extra electrons it creates this
+kind of area of charge it can see that
+
+ align:start position:0%
+kind of area of charge it can see that
+ 
+
+ align:start position:0%
+kind of area of charge it can see that
+it can scatter off of it and lose its
+
+ align:start position:0%
+it can scatter off of it and lose its
+ 
+
+ align:start position:0%
+it can scatter off of it and lose its
+energy and so that's called a scattering
+
+ align:start position:0%
+energy and so that's called a scattering
+ 
+
+ align:start position:0%
+energy and so that's called a scattering
+event and that can well not really lose
+
+ align:start position:0%
+event and that can well not really lose
+ 
+
+ align:start position:0%
+event and that can well not really lose
+its energy sorry it'll change direction
+
+ align:start position:0%
+its energy sorry it'll change direction
+ 
+
+ align:start position:0%
+its energy sorry it'll change direction
+it kind of impacts the the movement of
+
+ align:start position:0%
+it kind of impacts the the movement of
+ 
+
+ align:start position:0%
+it kind of impacts the the movement of
+that carrier and there's all sorts of
+
+ align:start position:0%
+that carrier and there's all sorts of
+ 
+
+ align:start position:0%
+that carrier and there's all sorts of
+other defects scattering mechanisms you
+
+ align:start position:0%
+other defects scattering mechanisms you
+ 
+
+ align:start position:0%
+other defects scattering mechanisms you
+can also scatter with an oscillating
+
+ align:start position:0%
+can also scatter with an oscillating
+ 
+
+ align:start position:0%
+can also scatter with an oscillating
+atom or a phonon that's another type of
+
+ align:start position:0%
+atom or a phonon that's another type of
+ 
+
+ align:start position:0%
+atom or a phonon that's another type of
+scattering mechanism and it's heavily
+
+ align:start position:0%
+scattering mechanism and it's heavily
+ 
+
+ align:start position:0%
+scattering mechanism and it's heavily
+dependent on what you put into your
+
+ align:start position:0%
+dependent on what you put into your
+ 
+
+ align:start position:0%
+dependent on what you put into your
+material and we'll talk about that in a
+
+ align:start position:0%
+material and we'll talk about that in a
+ 
+
+ align:start position:0%
+material and we'll talk about that in a
+second
+
+ align:start position:0%
+second
+ 
+
+ align:start position:0%
+second
+and for a lot of materials that are
+
+ align:start position:0%
+and for a lot of materials that are
+ 
+
+ align:start position:0%
+and for a lot of materials that are
+let's say porous or amorphous in some
+
+ align:start position:0%
+let's say porous or amorphous in some
+ 
+
+ align:start position:0%
+let's say porous or amorphous in some
+way or even a lot of like let's say
+
+ align:start position:0%
+way or even a lot of like let's say
+ 
+
+ align:start position:0%
+way or even a lot of like let's say
+organic semiconductors having a good
+
+ align:start position:0%
+organic semiconductors having a good
+ 
+
+ align:start position:0%
+organic semiconductors having a good
+percolation Network is really important
+
+ align:start position:0%
+percolation Network is really important
+ 
+
+ align:start position:0%
+percolation Network is really important
+to transport these charges and often
+
+ align:start position:0%
+to transport these charges and often
+ 
+
+ align:start position:0%
+to transport these charges and often
+it's a very limiting factor and let's
+
+ align:start position:0%
+it's a very limiting factor and let's
+ 
+
+ align:start position:0%
+it's a very limiting factor and let's
+say like organic photovoltaics so this
+
+ align:start position:0%
+say like organic photovoltaics so this
+ 
+
+ align:start position:0%
+say like organic photovoltaics so this
+is a relatively simple scattering
+
+ align:start position:0%
+is a relatively simple scattering
+ 
+
+ align:start position:0%
+is a relatively simple scattering
+mechanism we appointed himself
+
+ align:start position:0%
+mechanism we appointed himself
+ 
+
+ align:start position:0%
+mechanism we appointed himself
+what's going on here is that we can see
+
+ align:start position:0%
+what's going on here is that we can see
+ 
+
+ align:start position:0%
+what's going on here is that we can see
+that as we add carriers so this is and
+
+ align:start position:0%
+that as we add carriers so this is and
+ 
+
+ align:start position:0%
+that as we add carriers so this is and
+it's ten to the 14th very very low
+
+ align:start position:0%
+it's ten to the 14th very very low
+ 
+
+ align:start position:0%
+it's ten to the 14th very very low
+concentration of dopants as we increase
+
+ align:start position:0%
+concentration of dopants as we increase
+ 
+
+ align:start position:0%
+concentration of dopants as we increase
+the number of carriers are scattering
+
+ align:start position:0%
+the number of carriers are scattering
+ 
+
+ align:start position:0%
+the number of carriers are scattering
+off of those ionized impurities so every
+
+ align:start position:0%
+off of those ionized impurities so every
+ 
+
+ align:start position:0%
+off of those ionized impurities so every
+time you add a phosphorus atom let's say
+
+ align:start position:0%
+time you add a phosphorus atom let's say
+ 
+
+ align:start position:0%
+time you add a phosphorus atom let's say
+you introduce a static positive charge
+
+ align:start position:0%
+you introduce a static positive charge
+ 
+
+ align:start position:0%
+you introduce a static positive charge
+and a mobile negative charge when that
+
+ align:start position:0%
+and a mobile negative charge when that
+ 
+
+ align:start position:0%
+and a mobile negative charge when that
+electron leaves and so you now have all
+
+ align:start position:0%
+electron leaves and so you now have all
+ 
+
+ align:start position:0%
+electron leaves and so you now have all
+of these scattering centers of positive
+
+ align:start position:0%
+of these scattering centers of positive
+ 
+
+ align:start position:0%
+of these scattering centers of positive
+charge and so as you increase the number
+
+ align:start position:0%
+charge and so as you increase the number
+ 
+
+ align:start position:0%
+charge and so as you increase the number
+of dopants this is for silicon you
+
+ align:start position:0%
+of dopants this is for silicon you
+ 
+
+ align:start position:0%
+of dopants this is for silicon you
+decrease the mobility of your of your
+
+ align:start position:0%
+decrease the mobility of your of your
+ 
+
+ align:start position:0%
+decrease the mobility of your of your
+material and it's also greatly a
+
+ align:start position:0%
+material and it's also greatly a
+ 
+
+ align:start position:0%
+material and it's also greatly a
+function of temperature I think that's
+
+ align:start position:0%
+function of temperature I think that's
+ 
+
+ align:start position:0%
+function of temperature I think that's
+mostly due to either phonon scattering
+
+ align:start position:0%
+mostly due to either phonon scattering
+ 
+
+ align:start position:0%
+mostly due to either phonon scattering
+that right there's there any other
+
+ align:start position:0%
+that right there's there any other
+ 
+
+ align:start position:0%
+that right there's there any other
+mechanism I'm missing Tonio
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+but importantly is that higher
+
+ align:start position:0%
+but importantly is that higher
+ 
+
+ align:start position:0%
+but importantly is that higher
+temperatures you may generally get a
+
+ align:start position:0%
+temperatures you may generally get a
+ 
+
+ align:start position:0%
+temperatures you may generally get a
+much lower lower mobility and again
+
+ align:start position:0%
+much lower lower mobility and again
+ 
+
+ align:start position:0%
+much lower lower mobility and again
+hitting home for this is not sure
+
+ align:start position:0%
+hitting home for this is not sure
+ 
+
+ align:start position:0%
+hitting home for this is not sure
+necessarily for silicon but for a lot of
+
+ align:start position:0%
+necessarily for silicon but for a lot of
+ 
+
+ align:start position:0%
+necessarily for silicon but for a lot of
+like these hetero Junction devices so
+
+ align:start position:0%
+like these hetero Junction devices so
+ 
+
+ align:start position:0%
+like these hetero Junction devices so
+for example organics have very very low
+
+ align:start position:0%
+for example organics have very very low
+ 
+
+ align:start position:0%
+for example organics have very very low
+diffusion lengths and a lot of it's
+
+ align:start position:0%
+diffusion lengths and a lot of it's
+ 
+
+ align:start position:0%
+diffusion lengths and a lot of it's
+limited by mobility and so what you do
+
+ align:start position:0%
+limited by mobility and so what you do
+ 
+
+ align:start position:0%
+limited by mobility and so what you do
+is you make these inter digitated P or P
+
+ align:start position:0%
+is you make these inter digitated P or P
+ 
+
+ align:start position:0%
+is you make these inter digitated P or P
+I what I would call PN and I forget the
+
+ align:start position:0%
+I what I would call PN and I forget the
+ 
+
+ align:start position:0%
+I what I would call PN and I forget the
+exact analogy but P and n layers that
+
+ align:start position:0%
+exact analogy but P and n layers that
+ 
+
+ align:start position:0%
+exact analogy but P and n layers that
+inter digitated so that they only have
+
+ align:start position:0%
+inter digitated so that they only have
+ 
+
+ align:start position:0%
+inter digitated so that they only have
+to diffuse not the width of the device
+
+ align:start position:0%
+to diffuse not the width of the device
+ 
+
+ align:start position:0%
+to diffuse not the width of the device
+but the length of those fingers so you
+
+ align:start position:0%
+but the length of those fingers so you
+ 
+
+ align:start position:0%
+but the length of those fingers so you
+effectively need a much shorter
+
+ align:start position:0%
+effectively need a much shorter
+ 
+
+ align:start position:0%
+effectively need a much shorter
+diffusion length and so this is talking
+
+ align:start position:0%
+diffusion length and so this is talking
+ 
+
+ align:start position:0%
+diffusion length and so this is talking
+about some of those other different
+
+ align:start position:0%
+about some of those other different
+ 
+
+ align:start position:0%
+about some of those other different
+ideas and a hetero Junction is two
+
+ align:start position:0%
+ideas and a hetero Junction is two
+ 
+
+ align:start position:0%
+ideas and a hetero Junction is two
+different materials
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that's an inter digitated p.m. structure
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah so what we're gonna be talking
+
+ align:start position:0%
+yeah so what we're gonna be talking
+ 
+
+ align:start position:0%
+yeah so what we're gonna be talking
+about is kind of the products of N and
+
+ align:start position:0%
+about is kind of the products of N and
+ 
+
+ align:start position:0%
+about is kind of the products of N and
+mu and if you recall that your
+
+ align:start position:0%
+mu and if you recall that your
+ 
+
+ align:start position:0%
+mu and if you recall that your
+conductivity so hold on let's go back
+
+ align:start position:0%
+conductivity so hold on let's go back
+ 
+
+ align:start position:0%
+conductivity so hold on let's go back
+what we have here is that we have a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+highly doped semiconductor so this is
+
+ align:start position:0%
+highly doped semiconductor so this is
+ 
+
+ align:start position:0%
+highly doped semiconductor so this is
+about 10 to the 16 and then we have our
+
+ align:start position:0%
+about 10 to the 16 and then we have our
+ 
+
+ align:start position:0%
+about 10 to the 16 and then we have our
+intrinsic silicon so this has no dopants
+
+ align:start position:0%
+intrinsic silicon so this has no dopants
+ 
+
+ align:start position:0%
+intrinsic silicon so this has no dopants
+in it whatsoever and now you remember
+
+ align:start position:0%
+in it whatsoever and now you remember
+ 
+
+ align:start position:0%
+in it whatsoever and now you remember
+from last lecture when we applied a
+
+ align:start position:0%
+from last lecture when we applied a
+ 
+
+ align:start position:0%
+from last lecture when we applied a
+voltage across the terminals a current
+
+ align:start position:0%
+voltage across the terminals a current
+ 
+
+ align:start position:0%
+voltage across the terminals a current
+started to flow and when we heat it up
+
+ align:start position:0%
+started to flow and when we heat it up
+ 
+
+ align:start position:0%
+started to flow and when we heat it up
+what had happened your members current
+
+ align:start position:0%
+what had happened your members current
+ 
+
+ align:start position:0%
+what had happened your members current
+increased and that's due to more
+
+ align:start position:0%
+increased and that's due to more
+ 
+
+ align:start position:0%
+increased and that's due to more
+thermally excited carriers and so you're
+
+ align:start position:0%
+thermally excited carriers and so you're
+ 
+
+ align:start position:0%
+thermally excited carriers and so you're
+injured intrinsic carrier concentration
+
+ align:start position:0%
+injured intrinsic carrier concentration
+ 
+
+ align:start position:0%
+injured intrinsic carrier concentration
+goes up right and so your inch what was
+
+ align:start position:0%
+goes up right and so your inch what was
+ 
+
+ align:start position:0%
+goes up right and so your inch what was
+for room temperature what's the
+
+ align:start position:0%
+for room temperature what's the
+ 
+
+ align:start position:0%
+for room temperature what's the
+intrinsic carrier concentration it's
+
+ align:start position:0%
+intrinsic carrier concentration it's
+ 
+
+ align:start position:0%
+intrinsic carrier concentration it's
+about 10 to the 10 and that range and so
+
+ align:start position:0%
+about 10 to the 10 and that range and so
+ 
+
+ align:start position:0%
+about 10 to the 10 and that range and so
+an increase a small increase in
+
+ align:start position:0%
+an increase a small increase in
+ 
+
+ align:start position:0%
+an increase a small increase in
+temperature can greatly increase the
+
+ align:start position:0%
+temperature can greatly increase the
+ 
+
+ align:start position:0%
+temperature can greatly increase the
+intrinsic carrier concentration may be
+
+ align:start position:0%
+intrinsic carrier concentration may be
+ 
+
+ align:start position:0%
+intrinsic carrier concentration may be
+something like 10 to the 12 now in a
+
+ align:start position:0%
+something like 10 to the 12 now in a
+ 
+
+ align:start position:0%
+something like 10 to the 12 now in a
+dope semiconductor is that going to
+
+ align:start position:0%
+dope semiconductor is that going to
+ 
+
+ align:start position:0%
+dope semiconductor is that going to
+affect it as much how about you guys
+
+ align:start position:0%
+affect it as much how about you guys
+ 
+
+ align:start position:0%
+affect it as much how about you guys
+think about that for a little bit
+
+ align:start position:0%
+think about that for a little bit
+ 
+
+ align:start position:0%
+think about that for a little bit
+meet and talk to your neighbor and so
+
+ align:start position:0%
+meet and talk to your neighbor and so
+ 
+
+ align:start position:0%
+meet and talk to your neighbor and so
+I'm going to keep both of these up along
+
+ align:start position:0%
+I'm going to keep both of these up along
+ 
+
+ align:start position:0%
+I'm going to keep both of these up along
+with a high doping concentration and one
+
+ align:start position:0%
+with a high doping concentration and one
+ 
+
+ align:start position:0%
+with a high doping concentration and one
+with a low and which one do you think
+
+ align:start position:0%
+with a low and which one do you think
+ 
+
+ align:start position:0%
+with a low and which one do you think
+will have the highest relative change in
+
+ align:start position:0%
+will have the highest relative change in
+ 
+
+ align:start position:0%
+will have the highest relative change in
+conductivity and in which direction so
+
+ align:start position:0%
+conductivity and in which direction so
+ 
+
+ align:start position:0%
+conductivity and in which direction so
+I'll give you three minutes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+okay so we're now going to subject
+
+ align:start position:0%
+okay so we're now going to subject
+ 
+
+ align:start position:0%
+okay so we're now going to subject
+you've seen this demo before we're now
+
+ align:start position:0%
+you've seen this demo before we're now
+ 
+
+ align:start position:0%
+you've seen this demo before we're now
+going to subject our intrinsic carrier
+
+ align:start position:0%
+going to subject our intrinsic carrier
+ 
+
+ align:start position:0%
+going to subject our intrinsic carrier
+to my hairdryer and right now we're
+
+ align:start position:0%
+to my hairdryer and right now we're
+ 
+
+ align:start position:0%
+to my hairdryer and right now we're
+getting let's see it's about 10 micro
+
+ align:start position:0%
+getting let's see it's about 10 micro
+ 
+
+ align:start position:0%
+getting let's see it's about 10 micro
+amps and if we heat this guy out
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then mix these two look ah there we go
+
+ align:start position:0%
+then mix these two look ah there we go
+ 
+
+ align:start position:0%
+then mix these two look ah there we go
+okay so you can see we get a rather
+
+ align:start position:0%
+okay so you can see we get a rather
+ 
+
+ align:start position:0%
+okay so you can see we get a rather
+large increase in kind that was up to a
+
+ align:start position:0%
+large increase in kind that was up to a
+ 
+
+ align:start position:0%
+large increase in kind that was up to a
+hundred micro so a factor of ten so
+
+ align:start position:0%
+hundred micro so a factor of ten so
+ 
+
+ align:start position:0%
+hundred micro so a factor of ten so
+quite a large increase okay so let's see
+
+ align:start position:0%
+quite a large increase okay so let's see
+ 
+
+ align:start position:0%
+quite a large increase okay so let's see
+a show of hands so right now we're
+
+ align:start position:0%
+a show of hands so right now we're
+ 
+
+ align:start position:0%
+a show of hands so right now we're
+getting maybe we need to put this on
+
+ align:start position:0%
+getting maybe we need to put this on
+ 
+
+ align:start position:0%
+getting maybe we need to put this on
+milliamps yeah so we're getting about
+
+ align:start position:0%
+milliamps yeah so we're getting about
+ 
+
+ align:start position:0%
+milliamps yeah so we're getting about
+fifty eight milliamps of current through
+
+ align:start position:0%
+fifty eight milliamps of current through
+ 
+
+ align:start position:0%
+fifty eight milliamps of current through
+the semiconductor who thinks that the
+
+ align:start position:0%
+the semiconductor who thinks that the
+ 
+
+ align:start position:0%
+the semiconductor who thinks that the
+currents gonna increase when we add more
+
+ align:start position:0%
+currents gonna increase when we add more
+ 
+
+ align:start position:0%
+currents gonna increase when we add more
+thermal carriers this is for the doped
+
+ align:start position:0%
+thermal carriers this is for the doped
+ 
+
+ align:start position:0%
+thermal carriers this is for the doped
+one we just saw the intrinsic yeah yeah
+
+ align:start position:0%
+one we just saw the intrinsic yeah yeah
+ 
+
+ align:start position:0%
+one we just saw the intrinsic yeah yeah
+what do you think it'll go up the
+
+ align:start position:0%
+what do you think it'll go up the
+ 
+
+ align:start position:0%
+what do you think it'll go up the
+conductivity so this is for the dope
+
+ align:start position:0%
+conductivity so this is for the dope
+ 
+
+ align:start position:0%
+conductivity so this is for the dope
+semiconductor now who thinks it's gonna
+
+ align:start position:0%
+semiconductor now who thinks it's gonna
+ 
+
+ align:start position:0%
+semiconductor now who thinks it's gonna
+stay the same
+
+ align:start position:0%
+stay the same
+ 
+
+ align:start position:0%
+stay the same
+who thinks is gonna go down all right so
+
+ align:start position:0%
+who thinks is gonna go down all right so
+ 
+
+ align:start position:0%
+who thinks is gonna go down all right so
+this is split Wow alright so right now
+
+ align:start position:0%
+this is split Wow alright so right now
+ 
+
+ align:start position:0%
+this is split Wow alright so right now
+we're getting about 57 milliamps and
+
+ align:start position:0%
+we're getting about 57 milliamps and
+ 
+
+ align:start position:0%
+we're getting about 57 milliamps and
+let's heat this guy up and see what
+
+ align:start position:0%
+let's heat this guy up and see what
+ 
+
+ align:start position:0%
+let's heat this guy up and see what
+happens as you can see it's actually
+
+ align:start position:0%
+happens as you can see it's actually
+ 
+
+ align:start position:0%
+happens as you can see it's actually
+going down it's now 52 50 49 so what's
+
+ align:start position:0%
+going down it's now 52 50 49 so what's
+ 
+
+ align:start position:0%
+going down it's now 52 50 49 so what's
+important is that we're measuring
+
+ align:start position:0%
+important is that we're measuring
+ 
+
+ align:start position:0%
+important is that we're measuring
+conductivity it's not only how many
+
+ align:start position:0%
+conductivity it's not only how many
+ 
+
+ align:start position:0%
+conductivity it's not only how many
+carriers we have but also how well they
+
+ align:start position:0%
+carriers we have but also how well they
+ 
+
+ align:start position:0%
+carriers we have but also how well they
+can move around and it's again that
+
+ align:start position:0%
+can move around and it's again that
+ 
+
+ align:start position:0%
+can move around and it's again that
+product of number of carriers comes with
+
+ align:start position:0%
+product of number of carriers comes with
+ 
+
+ align:start position:0%
+product of number of carriers comes with
+mobility and again each of those
+
+ align:start position:0%
+mobility and again each of those
+ 
+
+ align:start position:0%
+mobility and again each of those
+carriers carries an electric charge so
+
+ align:start position:0%
+carriers carries an electric charge so
+ 
+
+ align:start position:0%
+carriers carries an electric charge so
+we put the electric charge of an
+
+ align:start position:0%
+we put the electric charge of an
+ 
+
+ align:start position:0%
+we put the electric charge of an
+electron in front of it oh this is what
+
+ align:start position:0%
+electron in front of it oh this is what
+ 
+
+ align:start position:0%
+electron in front of it oh this is what
+I'm supposed to have up in the
+
+ align:start position:0%
+I'm supposed to have up in the
+ 
+
+ align:start position:0%
+I'm supposed to have up in the
+background while that was happening yeah
+
+ align:start position:0%
+background while that was happening yeah
+ 
+
+ align:start position:0%
+background while that was happening yeah
+so again remember there was huge changes
+
+ align:start position:0%
+so again remember there was huge changes
+ 
+
+ align:start position:0%
+so again remember there was huge changes
+one was measuring milliamps one was
+
+ align:start position:0%
+one was measuring milliamps one was
+ 
+
+ align:start position:0%
+one was measuring milliamps one was
+measuring micro amps so if we look at
+
+ align:start position:0%
+measuring micro amps so if we look at
+ 
+
+ align:start position:0%
+measuring micro amps so if we look at
+room temperature we have about ten to
+
+ align:start position:0%
+room temperature we have about ten to
+ 
+
+ align:start position:0%
+room temperature we have about ten to
+the ten intrinsic carriers right so this
+
+ align:start position:0%
+the ten intrinsic carriers right so this
+ 
+
+ align:start position:0%
+the ten intrinsic carriers right so this
+is for intrinsic silicon with no dopants
+
+ align:start position:0%
+is for intrinsic silicon with no dopants
+ 
+
+ align:start position:0%
+is for intrinsic silicon with no dopants
+whatsoever as we increase the heat even
+
+ align:start position:0%
+whatsoever as we increase the heat even
+ 
+
+ align:start position:0%
+whatsoever as we increase the heat even
+when I don't think we're getting to 500
+
+ align:start position:0%
+when I don't think we're getting to 500
+ 
+
+ align:start position:0%
+when I don't think we're getting to 500
+degrees but let's say we get to 400
+
+ align:start position:0%
+degrees but let's say we get to 400
+ 
+
+ align:start position:0%
+degrees but let's say we get to 400
+we're only going up by a factor of a
+
+ align:start position:0%
+we're only going up by a factor of a
+ 
+
+ align:start position:0%
+we're only going up by a factor of a
+hundred which is substantial right but
+
+ align:start position:0%
+hundred which is substantial right but
+ 
+
+ align:start position:0%
+hundred which is substantial right but
+if we had 10 to the 16 carriers
+
+ align:start position:0%
+if we had 10 to the 16 carriers
+ 
+
+ align:start position:0%
+if we had 10 to the 16 carriers
+originally from our dopants these added
+
+ align:start position:0%
+originally from our dopants these added
+ 
+
+ align:start position:0%
+originally from our dopants these added
+number of intrinsic carrier's aren't
+
+ align:start position:0%
+number of intrinsic carrier's aren't
+ 
+
+ align:start position:0%
+number of intrinsic carrier's aren't
+going to have really much of an effect
+
+ align:start position:0%
+going to have really much of an effect
+ 
+
+ align:start position:0%
+going to have really much of an effect
+at all in terms of the conductivity so
+
+ align:start position:0%
+at all in terms of the conductivity so
+ 
+
+ align:start position:0%
+at all in terms of the conductivity so
+what's really affecting the doped case
+
+ align:start position:0%
+what's really affecting the doped case
+ 
+
+ align:start position:0%
+what's really affecting the doped case
+is that our mobility actually goes to
+
+ align:start position:0%
+is that our mobility actually goes to
+ 
+
+ align:start position:0%
+is that our mobility actually goes to
+with temperature due to these scattering
+
+ align:start position:0%
+with temperature due to these scattering
+ 
+
+ align:start position:0%
+with temperature due to these scattering
+events with temperature and for
+
+ align:start position:0%
+events with temperature and for
+ 
+
+ align:start position:0%
+events with temperature and for
+intrinsic silicon you get a little bit
+
+ align:start position:0%
+intrinsic silicon you get a little bit
+ 
+
+ align:start position:0%
+intrinsic silicon you get a little bit
+better mobility so it's a little bit
+
+ align:start position:0%
+better mobility so it's a little bit
+ 
+
+ align:start position:0%
+better mobility so it's a little bit
+higher but they both have the same
+
+ align:start position:0%
+higher but they both have the same
+ 
+
+ align:start position:0%
+higher but they both have the same
+general trend of lower mobility but only
+
+ align:start position:0%
+general trend of lower mobility but only
+ 
+
+ align:start position:0%
+general trend of lower mobility but only
+by let's say this is about a factor of
+
+ align:start position:0%
+by let's say this is about a factor of
+ 
+
+ align:start position:0%
+by let's say this is about a factor of
+10 where it was about a factor of
+
+ align:start position:0%
+10 where it was about a factor of
+ 
+
+ align:start position:0%
+10 where it was about a factor of
+hundred for the for the intrinsic
+
+ align:start position:0%
+hundred for the for the intrinsic
+ 
+
+ align:start position:0%
+hundred for the for the intrinsic
+carrier so again our carriers and the
+
+ align:start position:0%
+carrier so again our carriers and the
+ 
+
+ align:start position:0%
+carrier so again our carriers and the
+intrinsic case go up by a factor of 100
+
+ align:start position:0%
+intrinsic case go up by a factor of 100
+ 
+
+ align:start position:0%
+intrinsic case go up by a factor of 100
+our mobility goes up by a factor of 10
+
+ align:start position:0%
+our mobility goes up by a factor of 10
+ 
+
+ align:start position:0%
+our mobility goes up by a factor of 10
+so the conductivity then has to increase
+
+ align:start position:0%
+so the conductivity then has to increase
+ 
+
+ align:start position:0%
+so the conductivity then has to increase
+by a factor of 10 and for our dope
+
+ align:start position:0%
+by a factor of 10 and for our dope
+ 
+
+ align:start position:0%
+by a factor of 10 and for our dope
+semiconductor really the heat is just
+
+ align:start position:0%
+semiconductor really the heat is just
+ 
+
+ align:start position:0%
+semiconductor really the heat is just
+hurting our conductivity because of the
+
+ align:start position:0%
+hurting our conductivity because of the
+ 
+
+ align:start position:0%
+hurting our conductivity because of the
+decrease in mobility and the thermal
+
+ align:start position:0%
+decrease in mobility and the thermal
+ 
+
+ align:start position:0%
+decrease in mobility and the thermal
+carriers don't really add they're washed
+
+ align:start position:0%
+carriers don't really add they're washed
+ 
+
+ align:start position:0%
+carriers don't really add they're washed
+out by the the sea of doping atoms that
+
+ align:start position:0%
+out by the the sea of doping atoms that
+ 
+
+ align:start position:0%
+out by the the sea of doping atoms that
+are really adding all the carriers
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+would you ever want your solar cell that
+
+ align:start position:0%
+would you ever want your solar cell that
+ 
+
+ align:start position:0%
+would you ever want your solar cell that
+hot that's a big question so let's go
+
+ align:start position:0%
+hot that's a big question so let's go
+ 
+
+ align:start position:0%
+hot that's a big question so let's go
+there's an equation for that and we'll
+
+ align:start position:0%
+there's an equation for that and we'll
+ 
+
+ align:start position:0%
+there's an equation for that and we'll
+talk about that later too okay so if you
+
+ align:start position:0%
+talk about that later too okay so if you
+ 
+
+ align:start position:0%
+talk about that later too okay so if you
+look at our vo see if we have a large
+
+ align:start position:0%
+look at our vo see if we have a large
+ 
+
+ align:start position:0%
+look at our vo see if we have a large
+saturation current that means that we're
+
+ align:start position:0%
+saturation current that means that we're
+ 
+
+ align:start position:0%
+saturation current that means that we're
+gonna have a very low vo C right we have
+
+ align:start position:0%
+gonna have a very low vo C right we have
+ 
+
+ align:start position:0%
+gonna have a very low vo C right we have
+this reverse current that's going in the
+
+ align:start position:0%
+this reverse current that's going in the
+ 
+
+ align:start position:0%
+this reverse current that's going in the
+opposite direction of our illumination
+
+ align:start position:0%
+opposite direction of our illumination
+ 
+
+ align:start position:0%
+opposite direction of our illumination
+current that's opposing that
+
+ align:start position:0%
+current that's opposing that
+ 
+
+ align:start position:0%
+current that's opposing that
+illumination current and so if it's
+
+ align:start position:0%
+illumination current and so if it's
+ 
+
+ align:start position:0%
+illumination current and so if it's
+large then it'll hurt our vo C and you
+
+ align:start position:0%
+large then it'll hurt our vo C and you
+ 
+
+ align:start position:0%
+large then it'll hurt our vo C and you
+can see that it scales with D which
+
+ align:start position:0%
+can see that it scales with D which
+ 
+
+ align:start position:0%
+can see that it scales with D which
+scales with KT and so we get this
+
+ align:start position:0%
+scales with KT and so we get this
+ 
+
+ align:start position:0%
+scales with KT and so we get this
+increase in temperature is increasing
+
+ align:start position:0%
+increase in temperature is increasing
+ 
+
+ align:start position:0%
+increase in temperature is increasing
+this J naught and so for most types of
+
+ align:start position:0%
+this J naught and so for most types of
+ 
+
+ align:start position:0%
+this J naught and so for most types of
+cells heat is very very bad especially
+
+ align:start position:0%
+cells heat is very very bad especially
+ 
+
+ align:start position:0%
+cells heat is very very bad especially
+for crystalline silicon for amorphous
+
+ align:start position:0%
+for crystalline silicon for amorphous
+ 
+
+ align:start position:0%
+for crystalline silicon for amorphous
+silicon that's different well I'm not
+
+ align:start position:0%
+silicon that's different well I'm not
+ 
+
+ align:start position:0%
+silicon that's different well I'm not
+gonna get into that today but for a
+
+ align:start position:0%
+gonna get into that today but for a
+ 
+
+ align:start position:0%
+gonna get into that today but for a
+crystalline silicon it's it's heat is
+
+ align:start position:0%
+crystalline silicon it's it's heat is
+ 
+
+ align:start position:0%
+crystalline silicon it's it's heat is
+generally very bad for the performance
+
+ align:start position:0%
+generally very bad for the performance
+ 
+
+ align:start position:0%
+generally very bad for the performance
+and when you do testing so for example
+
+ align:start position:0%
+and when you do testing so for example
+ 
+
+ align:start position:0%
+and when you do testing so for example
+when NREL does tensing they'll rate all
+
+ align:start position:0%
+when NREL does tensing they'll rate all
+ 
+
+ align:start position:0%
+when NREL does tensing they'll rate all
+your cells at you know am 1.5 g some
+
+ align:start position:0%
+your cells at you know am 1.5 g some
+ 
+
+ align:start position:0%
+your cells at you know am 1.5 g some
+calibrated solar simulator that's you
+
+ align:start position:0%
+calibrated solar simulator that's you
+ 
+
+ align:start position:0%
+calibrated solar simulator that's you
+know illuminating your sample and
+
+ align:start position:0%
+know illuminating your sample and
+ 
+
+ align:start position:0%
+know illuminating your sample and
+they're kept at constant temperature so
+
+ align:start position:0%
+they're kept at constant temperature so
+ 
+
+ align:start position:0%
+they're kept at constant temperature so
+the temperatures always reported and
+
+ align:start position:0%
+the temperatures always reported and
+ 
+
+ align:start position:0%
+the temperatures always reported and
+it's generally kept at 25 C so the
+
+ align:start position:0%
+it's generally kept at 25 C so the
+ 
+
+ align:start position:0%
+it's generally kept at 25 C so the
+temperatures are very important
+
+ align:start position:0%
+temperatures are very important
+ 
+
+ align:start position:0%
+temperatures are very important
+characteristic but to answer your
+
+ align:start position:0%
+characteristic but to answer your
+ 
+
+ align:start position:0%
+characteristic but to answer your
+question if again we looked at an
+
+ align:start position:0%
+question if again we looked at an
+ 
+
+ align:start position:0%
+question if again we looked at an
+Arrhenius plot so this is 1 over KT so
+
+ align:start position:0%
+Arrhenius plot so this is 1 over KT so
+ 
+
+ align:start position:0%
+Arrhenius plot so this is 1 over KT so
+this is high temperatures over here low
+
+ align:start position:0%
+this is high temperatures over here low
+ 
+
+ align:start position:0%
+this is high temperatures over here low
+temperatures over here and this is
+
+ align:start position:0%
+temperatures over here and this is
+ 
+
+ align:start position:0%
+temperatures over here and this is
+carrier concentration at very very high
+
+ align:start position:0%
+carrier concentration at very very high
+ 
+
+ align:start position:0%
+carrier concentration at very very high
+temperatures the when when your thermal
+
+ align:start position:0%
+temperatures the when when your thermal
+ 
+
+ align:start position:0%
+temperatures the when when your thermal
+carrier so if you extend this out to
+
+ align:start position:0%
+carrier so if you extend this out to
+ 
+
+ align:start position:0%
+carrier so if you extend this out to
+higher temperature you can see that this
+
+ align:start position:0%
+higher temperature you can see that this
+ 
+
+ align:start position:0%
+higher temperature you can see that this
+will actually surpass the number of
+
+ align:start position:0%
+will actually surpass the number of
+ 
+
+ align:start position:0%
+will actually surpass the number of
+dopant atoms and you'll actually
+
+ align:start position:0%
+dopant atoms and you'll actually
+ 
+
+ align:start position:0%
+dopant atoms and you'll actually
+increase so this is high temperature
+
+ align:start position:0%
+increase so this is high temperature
+ 
+
+ align:start position:0%
+increase so this is high temperature
+over here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+your carrier concentration will actually
+
+ align:start position:0%
+your carrier concentration will actually
+ 
+
+ align:start position:0%
+your carrier concentration will actually
+increase at much much lower sorry much
+
+ align:start position:0%
+increase at much much lower sorry much
+ 
+
+ align:start position:0%
+increase at much much lower sorry much
+much higher temperatures and this is
+
+ align:start position:0%
+much higher temperatures and this is
+ 
+
+ align:start position:0%
+much higher temperatures and this is
+what's the extrinsic region so your
+
+ align:start position:0%
+what's the extrinsic region so your
+ 
+
+ align:start position:0%
+what's the extrinsic region so your
+donor concentration is pretty much only
+
+ align:start position:0%
+donor concentration is pretty much only
+ 
+
+ align:start position:0%
+donor concentration is pretty much only
+determined by your dopant density so
+
+ align:start position:0%
+determined by your dopant density so
+ 
+
+ align:start position:0%
+determined by your dopant density so
+this is MD and then at low enough
+
+ align:start position:0%
+this is MD and then at low enough
+ 
+
+ align:start position:0%
+this is MD and then at low enough
+temperature so this is very low
+
+ align:start position:0%
+temperature so this is very low
+ 
+
+ align:start position:0%
+temperature so this is very low
+temperatures you actually start freezing
+
+ align:start position:0%
+temperatures you actually start freezing
+ 
+
+ align:start position:0%
+temperatures you actually start freezing
+out your donor electrons into these
+
+ align:start position:0%
+out your donor electrons into these
+ 
+
+ align:start position:0%
+out your donor electrons into these
+donor states so that actually sums it up
+
+ align:start position:0%
+donor states so that actually sums it up
+ 
+
+ align:start position:0%
+donor states so that actually sums it up
+if you guys have other questions feel
+
+ align:start position:0%
+if you guys have other questions feel
+ 
+
+ align:start position:0%
+if you guys have other questions feel
+free to ask them but we actually can end
+
+ align:start position:0%
+free to ask them but we actually can end
+ 
+
+ align:start position:0%
+free to ask them but we actually can end
+a little bit early I do have your
+
+ align:start position:0%
+a little bit early I do have your
+ 
+
+ align:start position:0%
+a little bit early I do have your
+homework so if you want those come up
+
+ align:start position:0%
+homework so if you want those come up
+ 
+
+ align:start position:0%
+homework so if you want those come up
+here and I think Tonio posted the
+
+ align:start position:0%
+here and I think Tonio posted the
+ 
+
+ align:start position:0%
+here and I think Tonio posted the
+projects online so you can finish
+
+ align:start position:0%
+projects online so you can finish
+ 
+
+ align:start position:0%
+projects online so you can finish
+homework number three that's it
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you
\ No newline at end of file
diff --git a/wyT7EFJlBak.txt b/wyT7EFJlBak.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b59cbd5e1159dedc8a4e6f66a8837f77c9792f12
--- /dev/null
+++ b/wyT7EFJlBak.txt
@@ -0,0 +1,2499 @@
+align:start position:0%
+ 
+the following content is provided under
+
+ align:start position:0%
+the following content is provided under
+ 
+
+ align:start position:0%
+the following content is provided under
+a Creative Commons license your support
+
+ align:start position:0%
+a Creative Commons license your support
+ 
+
+ align:start position:0%
+a Creative Commons license your support
+will help MIT OpenCourseWare continue to
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+ 
+
+ align:start position:0%
+will help MIT OpenCourseWare continue to
+offer high quality educational resources
+
+ align:start position:0%
+offer high quality educational resources
+ 
+
+ align:start position:0%
+offer high quality educational resources
+for free
+
+ align:start position:0%
+for free
+ 
+
+ align:start position:0%
+for free
+to make a donation or view additional
+
+ align:start position:0%
+to make a donation or view additional
+ 
+
+ align:start position:0%
+to make a donation or view additional
+materials from hundreds of MIT courses
+
+ align:start position:0%
+materials from hundreds of MIT courses
+ 
+
+ align:start position:0%
+materials from hundreds of MIT courses
+visit MIT opencourseware at ocw.mit.edu
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+ 
+
+ align:start position:0%
+visit MIT opencourseware at ocw.mit.edu
+welcome to the metabolism portion of
+
+ align:start position:0%
+welcome to the metabolism portion of
+ 
+
+ align:start position:0%
+welcome to the metabolism portion of
+biological chemistry 507 my name is
+
+ align:start position:0%
+biological chemistry 507 my name is
+ 
+
+ align:start position:0%
+biological chemistry 507 my name is
+Johnny Sigmund and I teach this course
+
+ align:start position:0%
+Johnny Sigmund and I teach this course
+ 
+
+ align:start position:0%
+Johnny Sigmund and I teach this course
+with Joann stubby I'm primarily a
+
+ align:start position:0%
+with Joann stubby I'm primarily a
+ 
+
+ align:start position:0%
+with Joann stubby I'm primarily a
+chalkboard teacher as you'll notice from
+
+ align:start position:0%
+chalkboard teacher as you'll notice from
+ 
+
+ align:start position:0%
+chalkboard teacher as you'll notice from
+my notes in order to make things as
+
+ align:start position:0%
+my notes in order to make things as
+ 
+
+ align:start position:0%
+my notes in order to make things as
+simple as possible I use a lot of
+
+ align:start position:0%
+simple as possible I use a lot of
+ 
+
+ align:start position:0%
+simple as possible I use a lot of
+abbreviations in my abbreviations list
+
+ align:start position:0%
+abbreviations in my abbreviations list
+ 
+
+ align:start position:0%
+abbreviations in my abbreviations list
+will be appended elsewhere let's start
+
+ align:start position:0%
+will be appended elsewhere let's start
+ 
+
+ align:start position:0%
+will be appended elsewhere let's start
+by looking at a metabolic chart figure
+
+ align:start position:0%
+by looking at a metabolic chart figure
+ 
+
+ align:start position:0%
+by looking at a metabolic chart figure
+16 - 1 from the textbook obviously it
+
+ align:start position:0%
+16 - 1 from the textbook obviously it
+ 
+
+ align:start position:0%
+16 - 1 from the textbook obviously it
+looks very complex part of the challenge
+
+ align:start position:0%
+looks very complex part of the challenge
+ 
+
+ align:start position:0%
+looks very complex part of the challenge
+of both teaching and learning
+
+ align:start position:0%
+of both teaching and learning
+ 
+
+ align:start position:0%
+of both teaching and learning
+biochemistry is finding a way to look at
+
+ align:start position:0%
+biochemistry is finding a way to look at
+ 
+
+ align:start position:0%
+biochemistry is finding a way to look at
+this pigs breakfast of biochemical
+
+ align:start position:0%
+this pigs breakfast of biochemical
+ 
+
+ align:start position:0%
+this pigs breakfast of biochemical
+reactions and find its underlying
+
+ align:start position:0%
+reactions and find its underlying
+ 
+
+ align:start position:0%
+reactions and find its underlying
+structure for the purpose of this course
+
+ align:start position:0%
+structure for the purpose of this course
+ 
+
+ align:start position:0%
+structure for the purpose of this course
+the underlying structure we're going to
+
+ align:start position:0%
+the underlying structure we're going to
+ 
+
+ align:start position:0%
+the underlying structure we're going to
+look for is the biochemical pathways
+
+ align:start position:0%
+look for is the biochemical pathways
+ 
+
+ align:start position:0%
+look for is the biochemical pathways
+that let us function for example a
+
+ align:start position:0%
+that let us function for example a
+ 
+
+ align:start position:0%
+that let us function for example a
+pathway could involve making ATP or it
+
+ align:start position:0%
+pathway could involve making ATP or it
+ 
+
+ align:start position:0%
+pathway could involve making ATP or it
+could be putting an amino group onto an
+
+ align:start position:0%
+could be putting an amino group onto an
+ 
+
+ align:start position:0%
+could be putting an amino group onto an
+alpha keto acid in order to make an
+
+ align:start position:0%
+alpha keto acid in order to make an
+ 
+
+ align:start position:0%
+alpha keto acid in order to make an
+amino acid although a few people think
+
+ align:start position:0%
+amino acid although a few people think
+ 
+
+ align:start position:0%
+amino acid although a few people think
+of biochemistry is simple formatting the
+
+ align:start position:0%
+of biochemistry is simple formatting the
+ 
+
+ align:start position:0%
+of biochemistry is simple formatting the
+pigs breakfast into pathways that have
+
+ align:start position:0%
+pigs breakfast into pathways that have
+ 
+
+ align:start position:0%
+pigs breakfast into pathways that have
+functional meaning helps us simplify
+
+ align:start position:0%
+functional meaning helps us simplify
+ 
+
+ align:start position:0%
+functional meaning helps us simplify
+them and make them easier to remember
+
+ align:start position:0%
+them and make them easier to remember
+ 
+
+ align:start position:0%
+them and make them easier to remember
+the second simplifying point is that all
+
+ align:start position:0%
+the second simplifying point is that all
+ 
+
+ align:start position:0%
+the second simplifying point is that all
+biochemical pathways are reversible the
+
+ align:start position:0%
+biochemical pathways are reversible the
+ 
+
+ align:start position:0%
+biochemical pathways are reversible the
+gray vertical bar in the middle of this
+
+ align:start position:0%
+gray vertical bar in the middle of this
+ 
+
+ align:start position:0%
+gray vertical bar in the middle of this
+figure is the biochemical pathway of
+
+ align:start position:0%
+figure is the biochemical pathway of
+ 
+
+ align:start position:0%
+figure is the biochemical pathway of
+glycolysis going from glucose to
+
+ align:start position:0%
+glycolysis going from glucose to
+ 
+
+ align:start position:0%
+glycolysis going from glucose to
+pyruvate there are 10 steps some of
+
+ align:start position:0%
+pyruvate there are 10 steps some of
+ 
+
+ align:start position:0%
+pyruvate there are 10 steps some of
+these steps have a negative Delta G that
+
+ align:start position:0%
+these steps have a negative Delta G that
+ 
+
+ align:start position:0%
+these steps have a negative Delta G that
+is they are favorable in the direction
+
+ align:start position:0%
+is they are favorable in the direction
+ 
+
+ align:start position:0%
+is they are favorable in the direction
+drawn and some of them have a positive
+
+ align:start position:0%
+drawn and some of them have a positive
+ 
+
+ align:start position:0%
+drawn and some of them have a positive
+Delta G that is those steps are
+
+ align:start position:0%
+Delta G that is those steps are
+ 
+
+ align:start position:0%
+Delta G that is those steps are
+favorable in the opposite direction but
+
+ align:start position:0%
+favorable in the opposite direction but
+ 
+
+ align:start position:0%
+favorable in the opposite direction but
+overall when you sum them up all of the
+
+ align:start position:0%
+overall when you sum them up all of the
+ 
+
+ align:start position:0%
+overall when you sum them up all of the
+free energies of the glycolytic pathway
+
+ align:start position:0%
+free energies of the glycolytic pathway
+ 
+
+ align:start position:0%
+free energies of the glycolytic pathway
+you get a negative number which means
+
+ align:start position:0%
+you get a negative number which means
+ 
+
+ align:start position:0%
+you get a negative number which means
+that the pathway of glycolysis is
+
+ align:start position:0%
+that the pathway of glycolysis is
+ 
+
+ align:start position:0%
+that the pathway of glycolysis is
+overall thermodynamically irreversible
+
+ align:start position:0%
+overall thermodynamically irreversible
+ 
+
+ align:start position:0%
+overall thermodynamically irreversible
+and progresses from glucose to pyruvate
+
+ align:start position:0%
+and progresses from glucose to pyruvate
+ 
+
+ align:start position:0%
+and progresses from glucose to pyruvate
+it turns out that there's another
+
+ align:start position:0%
+it turns out that there's another
+ 
+
+ align:start position:0%
+it turns out that there's another
+pathway called gluconeogenesis that
+
+ align:start position:0%
+pathway called gluconeogenesis that
+ 
+
+ align:start position:0%
+pathway called gluconeogenesis that
+pathway it involves taking non
+
+ align:start position:0%
+pathway it involves taking non
+ 
+
+ align:start position:0%
+pathway it involves taking non
+carbohydrate precursors such as pyruvate
+
+ align:start position:0%
+carbohydrate precursors such as pyruvate
+ 
+
+ align:start position:0%
+carbohydrate precursors such as pyruvate
+that's just one example
+
+ align:start position:0%
+that's just one example
+ 
+
+ align:start position:0%
+that's just one example
+kill and converting that precursor to
+
+ align:start position:0%
+kill and converting that precursor to
+ 
+
+ align:start position:0%
+kill and converting that precursor to
+glucose in other words gluconeogenesis
+
+ align:start position:0%
+glucose in other words gluconeogenesis
+ 
+
+ align:start position:0%
+glucose in other words gluconeogenesis
+in effect is the reverse of glycolysis
+
+ align:start position:0%
+in effect is the reverse of glycolysis
+ 
+
+ align:start position:0%
+in effect is the reverse of glycolysis
+as I said the pathway going from glucose
+
+ align:start position:0%
+as I said the pathway going from glucose
+ 
+
+ align:start position:0%
+as I said the pathway going from glucose
+down to pyruvate is exergonic so what
+
+ align:start position:0%
+down to pyruvate is exergonic so what
+ 
+
+ align:start position:0%
+down to pyruvate is exergonic so what
+about the pathway from pyruvate up to
+
+ align:start position:0%
+about the pathway from pyruvate up to
+ 
+
+ align:start position:0%
+about the pathway from pyruvate up to
+glucose in order to make the pathway go
+
+ align:start position:0%
+glucose in order to make the pathway go
+ 
+
+ align:start position:0%
+glucose in order to make the pathway go
+from pyruvate to glucose what nature did
+
+ align:start position:0%
+from pyruvate to glucose what nature did
+ 
+
+ align:start position:0%
+from pyruvate to glucose what nature did
+was invent several biochemical steps
+
+ align:start position:0%
+was invent several biochemical steps
+ 
+
+ align:start position:0%
+was invent several biochemical steps
+that are highly exergonic that is what
+
+ align:start position:0%
+that are highly exergonic that is what
+ 
+
+ align:start position:0%
+that are highly exergonic that is what
+we'll see is they're going to require
+
+ align:start position:0%
+we'll see is they're going to require
+ 
+
+ align:start position:0%
+we'll see is they're going to require
+ATP or some other form of energy input
+
+ align:start position:0%
+ATP or some other form of energy input
+ 
+
+ align:start position:0%
+ATP or some other form of energy input
+in order to make the entire pathway of
+
+ align:start position:0%
+in order to make the entire pathway of
+ 
+
+ align:start position:0%
+in order to make the entire pathway of
+gluconeogenesis exergonic exergonic as
+
+ align:start position:0%
+gluconeogenesis exergonic exergonic as
+ 
+
+ align:start position:0%
+gluconeogenesis exergonic exergonic as
+is required of all pathways so we can
+
+ align:start position:0%
+is required of all pathways so we can
+ 
+
+ align:start position:0%
+is required of all pathways so we can
+indeed convert pyruvate to glucose but
+
+ align:start position:0%
+indeed convert pyruvate to glucose but
+ 
+
+ align:start position:0%
+indeed convert pyruvate to glucose but
+it will require energy input to make the
+
+ align:start position:0%
+it will require energy input to make the
+ 
+
+ align:start position:0%
+it will require energy input to make the
+pathway of gluconeogenesis have a net
+
+ align:start position:0%
+pathway of gluconeogenesis have a net
+ 
+
+ align:start position:0%
+pathway of gluconeogenesis have a net
+negative Delta G that is be favorable
+
+ align:start position:0%
+negative Delta G that is be favorable
+ 
+
+ align:start position:0%
+negative Delta G that is be favorable
+the third thing that actually makes
+
+ align:start position:0%
+the third thing that actually makes
+ 
+
+ align:start position:0%
+the third thing that actually makes
+biochemistry tractable is the fact that
+
+ align:start position:0%
+biochemistry tractable is the fact that
+ 
+
+ align:start position:0%
+biochemistry tractable is the fact that
+nature uses only a very limited
+
+ align:start position:0%
+nature uses only a very limited
+ 
+
+ align:start position:0%
+nature uses only a very limited
+repertoire of chemical reactions
+
+ align:start position:0%
+repertoire of chemical reactions
+ 
+
+ align:start position:0%
+repertoire of chemical reactions
+Joanne showed us that despite the
+
+ align:start position:0%
+Joanne showed us that despite the
+ 
+
+ align:start position:0%
+Joanne showed us that despite the
+complexity of this overall metabolic
+
+ align:start position:0%
+complexity of this overall metabolic
+ 
+
+ align:start position:0%
+complexity of this overall metabolic
+chart there are only about nine or ten
+
+ align:start position:0%
+chart there are only about nine or ten
+ 
+
+ align:start position:0%
+chart there are only about nine or ten
+discrete chemical reactions that nature
+
+ align:start position:0%
+discrete chemical reactions that nature
+ 
+
+ align:start position:0%
+discrete chemical reactions that nature
+uses so at any given step for example in
+
+ align:start position:0%
+uses so at any given step for example in
+ 
+
+ align:start position:0%
+uses so at any given step for example in
+glycolysis you really only have about
+
+ align:start position:0%
+glycolysis you really only have about
+ 
+
+ align:start position:0%
+glycolysis you really only have about
+nine or ten options and of that nine or
+
+ align:start position:0%
+nine or ten options and of that nine or
+ 
+
+ align:start position:0%
+nine or ten options and of that nine or
+ten only about one or two perhaps three
+
+ align:start position:0%
+ten only about one or two perhaps three
+ 
+
+ align:start position:0%
+ten only about one or two perhaps three
+would be chemically reasonable if you
+
+ align:start position:0%
+would be chemically reasonable if you
+ 
+
+ align:start position:0%
+would be chemically reasonable if you
+know your organic chemistry and these
+
+ align:start position:0%
+know your organic chemistry and these
+ 
+
+ align:start position:0%
+know your organic chemistry and these
+nine or ten reaction types you should be
+
+ align:start position:0%
+nine or ten reaction types you should be
+ 
+
+ align:start position:0%
+nine or ten reaction types you should be
+able to navigate the biochemical chart
+
+ align:start position:0%
+able to navigate the biochemical chart
+ 
+
+ align:start position:0%
+able to navigate the biochemical chart
+with comparative ease the fourth point I
+
+ align:start position:0%
+with comparative ease the fourth point I
+ 
+
+ align:start position:0%
+with comparative ease the fourth point I
+wanted to make is perhaps one of the
+
+ align:start position:0%
+wanted to make is perhaps one of the
+ 
+
+ align:start position:0%
+wanted to make is perhaps one of the
+most important is that all biochemical
+
+ align:start position:0%
+most important is that all biochemical
+ 
+
+ align:start position:0%
+most important is that all biochemical
+pathways are regulated chaos would
+
+ align:start position:0%
+pathways are regulated chaos would
+ 
+
+ align:start position:0%
+pathways are regulated chaos would
+result for example if you made glucose
+
+ align:start position:0%
+result for example if you made glucose
+ 
+
+ align:start position:0%
+result for example if you made glucose
+and at the same time took that molecule
+
+ align:start position:0%
+and at the same time took that molecule
+ 
+
+ align:start position:0%
+and at the same time took that molecule
+of glucose and degraded it that's an
+
+ align:start position:0%
+of glucose and degraded it that's an
+ 
+
+ align:start position:0%
+of glucose and degraded it that's an
+example of what we call a futile cycle
+
+ align:start position:0%
+example of what we call a futile cycle
+ 
+
+ align:start position:0%
+example of what we call a futile cycle
+sometimes util cycles can be beneficial
+
+ align:start position:0%
+sometimes util cycles can be beneficial
+ 
+
+ align:start position:0%
+sometimes util cycles can be beneficial
+to a cell for example that could be a
+
+ align:start position:0%
+to a cell for example that could be a
+ 
+
+ align:start position:0%
+to a cell for example that could be a
+way of generating heat but most of the
+
+ align:start position:0%
+way of generating heat but most of the
+ 
+
+ align:start position:0%
+way of generating heat but most of the
+time we want to avoid them because we
+
+ align:start position:0%
+time we want to avoid them because we
+ 
+
+ align:start position:0%
+time we want to avoid them because we
+usually want to avoid futile cycles
+
+ align:start position:0%
+usually want to avoid futile cycles
+ 
+
+ align:start position:0%
+usually want to avoid futile cycles
+nature uses pathway regulation to avoid
+
+ align:start position:0%
+nature uses pathway regulation to avoid
+ 
+
+ align:start position:0%
+nature uses pathway regulation to avoid
+them to provide directionality to
+
+ align:start position:0%
+them to provide directionality to
+ 
+
+ align:start position:0%
+them to provide directionality to
+pathways what nature does is work
+
+ align:start position:0%
+pathways what nature does is work
+ 
+
+ align:start position:0%
+pathways what nature does is work
+thermodynamically irreversible steps
+
+ align:start position:0%
+thermodynamically irreversible steps
+ 
+
+ align:start position:0%
+thermodynamically irreversible steps
+into the front end and back end of the
+
+ align:start position:0%
+into the front end and back end of the
+ 
+
+ align:start position:0%
+into the front end and back end of the
+pathway sometimes nature puts in an
+
+ align:start position:0%
+pathway sometimes nature puts in an
+ 
+
+ align:start position:0%
+pathway sometimes nature puts in an
+irreversible step in the middle of the
+
+ align:start position:0%
+irreversible step in the middle of the
+ 
+
+ align:start position:0%
+irreversible step in the middle of the
+pathway
+
+ align:start position:0%
+pathway
+ 
+
+ align:start position:0%
+pathway
+if that pathway has a branch point that
+
+ align:start position:0%
+if that pathway has a branch point that
+ 
+
+ align:start position:0%
+if that pathway has a branch point that
+happens with glycolysis cells will see
+
+ align:start position:0%
+happens with glycolysis cells will see
+ 
+
+ align:start position:0%
+happens with glycolysis cells will see
+sometimes regulation is affected by
+
+ align:start position:0%
+sometimes regulation is affected by
+ 
+
+ align:start position:0%
+sometimes regulation is affected by
+putting covalent functionalities such as
+
+ align:start position:0%
+putting covalent functionalities such as
+ 
+
+ align:start position:0%
+putting covalent functionalities such as
+a phosphate onto an amino acid on a
+
+ align:start position:0%
+a phosphate onto an amino acid on a
+ 
+
+ align:start position:0%
+a phosphate onto an amino acid on a
+protein that modification could increase
+
+ align:start position:0%
+protein that modification could increase
+ 
+
+ align:start position:0%
+protein that modification could increase
+or decrease the biochemical activity of
+
+ align:start position:0%
+or decrease the biochemical activity of
+ 
+
+ align:start position:0%
+or decrease the biochemical activity of
+that protein often a phosphorylated
+
+ align:start position:0%
+that protein often a phosphorylated
+ 
+
+ align:start position:0%
+that protein often a phosphorylated
+protein is highly active turning on a
+
+ align:start position:0%
+protein is highly active turning on a
+ 
+
+ align:start position:0%
+protein is highly active turning on a
+pathway and it is DS phosphorylated when
+
+ align:start position:0%
+pathway and it is DS phosphorylated when
+ 
+
+ align:start position:0%
+pathway and it is DS phosphorylated when
+the pathway needs to be turned off a
+
+ align:start position:0%
+the pathway needs to be turned off a
+ 
+
+ align:start position:0%
+the pathway needs to be turned off a
+second way to regulate a step in the
+
+ align:start position:0%
+second way to regulate a step in the
+ 
+
+ align:start position:0%
+second way to regulate a step in the
+pathway is by allosteric regulation of
+
+ align:start position:0%
+pathway is by allosteric regulation of
+ 
+
+ align:start position:0%
+pathway is by allosteric regulation of
+the enzymes of the pathway in that case
+
+ align:start position:0%
+the enzymes of the pathway in that case
+ 
+
+ align:start position:0%
+the enzymes of the pathway in that case
+a small molecule will interact with the
+
+ align:start position:0%
+a small molecule will interact with the
+ 
+
+ align:start position:0%
+a small molecule will interact with the
+enzyme in order to increase or decrease
+
+ align:start position:0%
+enzyme in order to increase or decrease
+ 
+
+ align:start position:0%
+enzyme in order to increase or decrease
+its activity Joanne taught us about
+
+ align:start position:0%
+its activity Joanne taught us about
+ 
+
+ align:start position:0%
+its activity Joanne taught us about
+Alice Terry when she taught us how
+
+ align:start position:0%
+Alice Terry when she taught us how
+ 
+
+ align:start position:0%
+Alice Terry when she taught us how
+hemoglobin is regulated to reiterate
+
+ align:start position:0%
+hemoglobin is regulated to reiterate
+ 
+
+ align:start position:0%
+hemoglobin is regulated to reiterate
+nature uses these regulatable enzymes at
+
+ align:start position:0%
+nature uses these regulatable enzymes at
+ 
+
+ align:start position:0%
+nature uses these regulatable enzymes at
+key places in overall metabolic pathways
+
+ align:start position:0%
+key places in overall metabolic pathways
+ 
+
+ align:start position:0%
+key places in overall metabolic pathways
+to enable us to be able to achieve the
+
+ align:start position:0%
+to enable us to be able to achieve the
+ 
+
+ align:start position:0%
+to enable us to be able to achieve the
+function of the pathway without wasting
+
+ align:start position:0%
+function of the pathway without wasting
+ 
+
+ align:start position:0%
+function of the pathway without wasting
+energy or resources the last
+
+ align:start position:0%
+energy or resources the last
+ 
+
+ align:start position:0%
+energy or resources the last
+introductory point I want to make is
+
+ align:start position:0%
+introductory point I want to make is
+ 
+
+ align:start position:0%
+introductory point I want to make is
+that all biochemical pathways tend to be
+
+ align:start position:0%
+that all biochemical pathways tend to be
+ 
+
+ align:start position:0%
+that all biochemical pathways tend to be
+compartmentalized at least in mammalian
+
+ align:start position:0%
+compartmentalized at least in mammalian
+ 
+
+ align:start position:0%
+compartmentalized at least in mammalian
+cells although it's increasingly
+
+ align:start position:0%
+cells although it's increasingly
+ 
+
+ align:start position:0%
+cells although it's increasingly
+becoming obvious that even in bacteria
+
+ align:start position:0%
+becoming obvious that even in bacteria
+ 
+
+ align:start position:0%
+becoming obvious that even in bacteria
+there is some form of
+
+ align:start position:0%
+there is some form of
+ 
+
+ align:start position:0%
+there is some form of
+compartmentalization that is clustering
+
+ align:start position:0%
+compartmentalization that is clustering
+ 
+
+ align:start position:0%
+compartmentalization that is clustering
+of enzymes for a particular pathway in a
+
+ align:start position:0%
+of enzymes for a particular pathway in a
+ 
+
+ align:start position:0%
+of enzymes for a particular pathway in a
+particular area of the cell for example
+
+ align:start position:0%
+particular area of the cell for example
+ 
+
+ align:start position:0%
+particular area of the cell for example
+in a mammalian cell the mitochondrion is
+
+ align:start position:0%
+in a mammalian cell the mitochondrion is
+ 
+
+ align:start position:0%
+in a mammalian cell the mitochondrion is
+the site of fatty acid beta oxidation or
+
+ align:start position:0%
+the site of fatty acid beta oxidation or
+ 
+
+ align:start position:0%
+the site of fatty acid beta oxidation or
+breakdown the tricarboxylic acid cycle
+
+ align:start position:0%
+breakdown the tricarboxylic acid cycle
+ 
+
+ align:start position:0%
+breakdown the tricarboxylic acid cycle
+and enzymes of the pyruvate
+
+ align:start position:0%
+and enzymes of the pyruvate
+ 
+
+ align:start position:0%
+and enzymes of the pyruvate
+dehydrogenase complex are also
+
+ align:start position:0%
+dehydrogenase complex are also
+ 
+
+ align:start position:0%
+dehydrogenase complex are also
+mitochondrial the cytoplasm is the site
+
+ align:start position:0%
+mitochondrial the cytoplasm is the site
+ 
+
+ align:start position:0%
+mitochondrial the cytoplasm is the site
+where we do fatty acid biosynthesis most
+
+ align:start position:0%
+where we do fatty acid biosynthesis most
+ 
+
+ align:start position:0%
+where we do fatty acid biosynthesis most
+of gluconeogenesis glycolysis and the
+
+ align:start position:0%
+of gluconeogenesis glycolysis and the
+ 
+
+ align:start position:0%
+of gluconeogenesis glycolysis and the
+pentose phosphate pathway
+
+ align:start position:0%
+pentose phosphate pathway
+ 
+
+ align:start position:0%
+pentose phosphate pathway
+compartmentalization helps keep the
+
+ align:start position:0%
+compartmentalization helps keep the
+ 
+
+ align:start position:0%
+compartmentalization helps keep the
+metabolic chart tidy and organized with
+
+ align:start position:0%
+metabolic chart tidy and organized with
+ 
+
+ align:start position:0%
+metabolic chart tidy and organized with
+that in the way of an introduction let's
+
+ align:start position:0%
+that in the way of an introduction let's
+ 
+
+ align:start position:0%
+that in the way of an introduction let's
+turn to my lecture notes which i present
+
+ align:start position:0%
+turn to my lecture notes which i present
+ 
+
+ align:start position:0%
+turn to my lecture notes which i present
+in the format of storyboards in the
+
+ align:start position:0%
+in the format of storyboards in the
+ 
+
+ align:start position:0%
+in the format of storyboards in the
+first storyboard panel a I give the
+
+ align:start position:0%
+first storyboard panel a I give the
+ 
+
+ align:start position:0%
+first storyboard panel a I give the
+definition of metabolism as the linked
+
+ align:start position:0%
+definition of metabolism as the linked
+ 
+
+ align:start position:0%
+definition of metabolism as the linked
+set of biochemical reactions by which we
+
+ align:start position:0%
+set of biochemical reactions by which we
+ 
+
+ align:start position:0%
+set of biochemical reactions by which we
+obtain and use free energy that is Delta
+
+ align:start position:0%
+obtain and use free energy that is Delta
+ 
+
+ align:start position:0%
+obtain and use free energy that is Delta
+G for life we use that free energy for a
+
+ align:start position:0%
+G for life we use that free energy for a
+ 
+
+ align:start position:0%
+G for life we use that free energy for a
+lot of things but the use is really
+
+ align:start position:0%
+lot of things but the use is really
+ 
+
+ align:start position:0%
+lot of things but the use is really
+divided into three areas the first is to
+
+ align:start position:0%
+divided into three areas the first is to
+ 
+
+ align:start position:0%
+divided into three areas the first is to
+do mechanical work the second is to
+
+ align:start position:0%
+do mechanical work the second is to
+ 
+
+ align:start position:0%
+do mechanical work the second is to
+generate concentration gradients and the
+
+ align:start position:0%
+generate concentration gradients and the
+ 
+
+ align:start position:0%
+generate concentration gradients and the
+third
+
+ align:start position:0%
+third
+ 
+
+ align:start position:0%
+third
+is for biosynthesis in a few minutes I'm
+
+ align:start position:0%
+is for biosynthesis in a few minutes I'm
+ 
+
+ align:start position:0%
+is for biosynthesis in a few minutes I'm
+going to be giving you an example of all
+
+ align:start position:0%
+going to be giving you an example of all
+ 
+
+ align:start position:0%
+going to be giving you an example of all
+three panel B biochemists divide
+
+ align:start position:0%
+three panel B biochemists divide
+ 
+
+ align:start position:0%
+three panel B biochemists divide
+metabolism to two subcategories
+
+ align:start position:0%
+metabolism to two subcategories
+ 
+
+ align:start position:0%
+metabolism to two subcategories
+catabolism and anabolism briefly
+
+ align:start position:0%
+catabolism and anabolism briefly
+ 
+
+ align:start position:0%
+catabolism and anabolism briefly
+catabolism consists of the energy
+
+ align:start position:0%
+catabolism consists of the energy
+ 
+
+ align:start position:0%
+catabolism consists of the energy
+yielding pathways an analysis basically
+
+ align:start position:0%
+yielding pathways an analysis basically
+ 
+
+ align:start position:0%
+yielding pathways an analysis basically
+biosynthesis we use the free energy that
+
+ align:start position:0%
+biosynthesis we use the free energy that
+ 
+
+ align:start position:0%
+biosynthesis we use the free energy that
+we generate through catabolism in order
+
+ align:start position:0%
+we generate through catabolism in order
+ 
+
+ align:start position:0%
+we generate through catabolism in order
+to assemble complex molecules by way of
+
+ align:start position:0%
+to assemble complex molecules by way of
+ 
+
+ align:start position:0%
+to assemble complex molecules by way of
+an Abba lism let's look at panel C we're
+
+ align:start position:0%
+an Abba lism let's look at panel C we're
+ 
+
+ align:start position:0%
+an Abba lism let's look at panel C we're
+going to start 5:07 with the discussion
+
+ align:start position:0%
+going to start 5:07 with the discussion
+ 
+
+ align:start position:0%
+going to start 5:07 with the discussion
+of catabolism that is the energy
+
+ align:start position:0%
+of catabolism that is the energy
+ 
+
+ align:start position:0%
+of catabolism that is the energy
+yielding pathways by way of definitions
+
+ align:start position:0%
+yielding pathways by way of definitions
+ 
+
+ align:start position:0%
+yielding pathways by way of definitions
+a reduced molecule is one that is
+
+ align:start position:0%
+a reduced molecule is one that is
+ 
+
+ align:start position:0%
+a reduced molecule is one that is
+abundantly supplied with electrons
+
+ align:start position:0%
+abundantly supplied with electrons
+ 
+
+ align:start position:0%
+abundantly supplied with electrons
+examples are carbohydrates fats and
+
+ align:start position:0%
+examples are carbohydrates fats and
+ 
+
+ align:start position:0%
+examples are carbohydrates fats and
+proteins these are typically our foods
+
+ align:start position:0%
+proteins these are typically our foods
+ 
+
+ align:start position:0%
+proteins these are typically our foods
+the process of catabolism involves
+
+ align:start position:0%
+the process of catabolism involves
+ 
+
+ align:start position:0%
+the process of catabolism involves
+finding a way to liberate the electrons
+
+ align:start position:0%
+finding a way to liberate the electrons
+ 
+
+ align:start position:0%
+finding a way to liberate the electrons
+from those reduced substances and
+
+ align:start position:0%
+from those reduced substances and
+ 
+
+ align:start position:0%
+from those reduced substances and
+transfer those electrons to mobile
+
+ align:start position:0%
+transfer those electrons to mobile
+ 
+
+ align:start position:0%
+transfer those electrons to mobile
+electron carriers such as nad plus to
+
+ align:start position:0%
+electron carriers such as nad plus to
+ 
+
+ align:start position:0%
+electron carriers such as nad plus to
+form NADH or nadp+ to form NADPH the
+
+ align:start position:0%
+form NADH or nadp+ to form NADPH the
+ 
+
+ align:start position:0%
+form NADH or nadp+ to form NADPH the
+process by which electrons are removed
+
+ align:start position:0%
+process by which electrons are removed
+ 
+
+ align:start position:0%
+process by which electrons are removed
+from a molecule is called oxidation and
+
+ align:start position:0%
+from a molecule is called oxidation and
+ 
+
+ align:start position:0%
+from a molecule is called oxidation and
+the oxidation products are for example
+
+ align:start position:0%
+the oxidation products are for example
+ 
+
+ align:start position:0%
+the oxidation products are for example
+carbon dioxide that we breathe out or in
+
+ align:start position:0%
+carbon dioxide that we breathe out or in
+ 
+
+ align:start position:0%
+carbon dioxide that we breathe out or in
+some organisms lactate or other simple
+
+ align:start position:0%
+some organisms lactate or other simple
+ 
+
+ align:start position:0%
+some organisms lactate or other simple
+molecules that are excreted simple that
+
+ align:start position:0%
+molecules that are excreted simple that
+ 
+
+ align:start position:0%
+molecules that are excreted simple that
+is compared to the complex reduced
+
+ align:start position:0%
+is compared to the complex reduced
+ 
+
+ align:start position:0%
+is compared to the complex reduced
+molecules that we consume as food nadh
+
+ align:start position:0%
+molecules that we consume as food nadh
+ 
+
+ align:start position:0%
+molecules that we consume as food nadh
+and fadh2 molecules that Joanne taught
+
+ align:start position:0%
+and fadh2 molecules that Joanne taught
+ 
+
+ align:start position:0%
+and fadh2 molecules that Joanne taught
+us are what I'll refer to as mobile
+
+ align:start position:0%
+us are what I'll refer to as mobile
+ 
+
+ align:start position:0%
+us are what I'll refer to as mobile
+electron carriers they can usually move
+
+ align:start position:0%
+electron carriers they can usually move
+ 
+
+ align:start position:0%
+electron carriers they can usually move
+around inside the cell although
+
+ align:start position:0%
+around inside the cell although
+ 
+
+ align:start position:0%
+around inside the cell although
+sometimes they're embedded within
+
+ align:start position:0%
+sometimes they're embedded within
+ 
+
+ align:start position:0%
+sometimes they're embedded within
+enzymes that is usually the case with
+
+ align:start position:0%
+enzymes that is usually the case with
+ 
+
+ align:start position:0%
+enzymes that is usually the case with
+fadh2 we consume an enormous lee large
+
+ align:start position:0%
+fadh2 we consume an enormous lee large
+ 
+
+ align:start position:0%
+fadh2 we consume an enormous lee large
+number of reduced substances due to the
+
+ align:start position:0%
+number of reduced substances due to the
+ 
+
+ align:start position:0%
+number of reduced substances due to the
+complexities of our diets and catabolism
+
+ align:start position:0%
+complexities of our diets and catabolism
+ 
+
+ align:start position:0%
+complexities of our diets and catabolism
+revolves taking the electrons out of
+
+ align:start position:0%
+revolves taking the electrons out of
+ 
+
+ align:start position:0%
+revolves taking the electrons out of
+this enormous leave ass array of
+
+ align:start position:0%
+this enormous leave ass array of
+ 
+
+ align:start position:0%
+this enormous leave ass array of
+substrates and transferring those
+
+ align:start position:0%
+substrates and transferring those
+ 
+
+ align:start position:0%
+substrates and transferring those
+electrons to a small number of reduced
+
+ align:start position:0%
+electrons to a small number of reduced
+ 
+
+ align:start position:0%
+electrons to a small number of reduced
+electron carriers for example an ad or
+
+ align:start position:0%
+electron carriers for example an ad or
+ 
+
+ align:start position:0%
+electron carriers for example an ad or
+Flavin's in the process of respiration
+
+ align:start position:0%
+Flavin's in the process of respiration
+ 
+
+ align:start position:0%
+Flavin's in the process of respiration
+which we'll come to later the electrons
+
+ align:start position:0%
+which we'll come to later the electrons
+ 
+
+ align:start position:0%
+which we'll come to later the electrons
+are further transferred from the reduced
+
+ align:start position:0%
+are further transferred from the reduced
+ 
+
+ align:start position:0%
+are further transferred from the reduced
+electron carriers all the way to
+
+ align:start position:0%
+electron carriers all the way to
+ 
+
+ align:start position:0%
+electron carriers all the way to
+molecular oxygen the reduction of
+
+ align:start position:0%
+molecular oxygen the reduction of
+ 
+
+ align:start position:0%
+molecular oxygen the reduction of
+molecular oxygen is a highly exothermic
+
+ align:start position:0%
+molecular oxygen is a highly exothermic
+ 
+
+ align:start position:0%
+molecular oxygen is a highly exothermic
+reaction we're going to be able to use
+
+ align:start position:0%
+reaction we're going to be able to use
+ 
+
+ align:start position:0%
+reaction we're going to be able to use
+the energy that's generated by
+
+ align:start position:0%
+the energy that's generated by
+ 
+
+ align:start position:0%
+the energy that's generated by
+oxygen reduction in order to make ATP
+
+ align:start position:0%
+oxygen reduction in order to make ATP
+ 
+
+ align:start position:0%
+oxygen reduction in order to make ATP
+and to do some other important
+
+ align:start position:0%
+and to do some other important
+ 
+
+ align:start position:0%
+and to do some other important
+biochemical activities now I'm going to
+
+ align:start position:0%
+biochemical activities now I'm going to
+ 
+
+ align:start position:0%
+biochemical activities now I'm going to
+introduce a physiological scenario and
+
+ align:start position:0%
+introduce a physiological scenario and
+ 
+
+ align:start position:0%
+introduce a physiological scenario and
+use it in order to introduce the pathway
+
+ align:start position:0%
+use it in order to introduce the pathway
+ 
+
+ align:start position:0%
+use it in order to introduce the pathway
+of glycolysis in class at this point I
+
+ align:start position:0%
+of glycolysis in class at this point I
+ 
+
+ align:start position:0%
+of glycolysis in class at this point I
+usually ask a student to stand up and
+
+ align:start position:0%
+usually ask a student to stand up and
+ 
+
+ align:start position:0%
+usually ask a student to stand up and
+sit down as you can imagine being called
+
+ align:start position:0%
+sit down as you can imagine being called
+ 
+
+ align:start position:0%
+sit down as you can imagine being called
+out in class creates more than a little
+
+ align:start position:0%
+out in class creates more than a little
+ 
+
+ align:start position:0%
+out in class creates more than a little
+bit of anxiety in the student let's look
+
+ align:start position:0%
+bit of anxiety in the student let's look
+ 
+
+ align:start position:0%
+bit of anxiety in the student let's look
+at panel D the signal to stand up and
+
+ align:start position:0%
+at panel D the signal to stand up and
+ 
+
+ align:start position:0%
+at panel D the signal to stand up and
+sit down is processed by the brain and
+
+ align:start position:0%
+sit down is processed by the brain and
+ 
+
+ align:start position:0%
+sit down is processed by the brain and
+an electrical signal then goes by the
+
+ align:start position:0%
+an electrical signal then goes by the
+ 
+
+ align:start position:0%
+an electrical signal then goes by the
+nerves to the muscles enabling the
+
+ align:start position:0%
+nerves to the muscles enabling the
+ 
+
+ align:start position:0%
+nerves to the muscles enabling the
+student to stand up the anxiety of being
+
+ align:start position:0%
+student to stand up the anxiety of being
+ 
+
+ align:start position:0%
+student to stand up the anxiety of being
+called on by the teacher in class
+
+ align:start position:0%
+called on by the teacher in class
+ 
+
+ align:start position:0%
+called on by the teacher in class
+results in a nervous excitation of the
+
+ align:start position:0%
+results in a nervous excitation of the
+ 
+
+ align:start position:0%
+results in a nervous excitation of the
+adrenal gland specifically in the
+
+ align:start position:0%
+adrenal gland specifically in the
+ 
+
+ align:start position:0%
+adrenal gland specifically in the
+andrina medulla which releases
+
+ align:start position:0%
+andrina medulla which releases
+ 
+
+ align:start position:0%
+andrina medulla which releases
+epinephrine epinephrine is also known as
+
+ align:start position:0%
+epinephrine epinephrine is also known as
+ 
+
+ align:start position:0%
+epinephrine epinephrine is also known as
+adrenaline it goes to the muscles as
+
+ align:start position:0%
+adrenaline it goes to the muscles as
+ 
+
+ align:start position:0%
+adrenaline it goes to the muscles as
+well as other organs of the body as
+
+ align:start position:0%
+well as other organs of the body as
+ 
+
+ align:start position:0%
+well as other organs of the body as
+we'll see later in 507 and the
+
+ align:start position:0%
+we'll see later in 507 and the
+ 
+
+ align:start position:0%
+we'll see later in 507 and the
+epinephrine will interact at cell
+
+ align:start position:0%
+epinephrine will interact at cell
+ 
+
+ align:start position:0%
+epinephrine will interact at cell
+membranes by way of transmembrane
+
+ align:start position:0%
+membranes by way of transmembrane
+ 
+
+ align:start position:0%
+membranes by way of transmembrane
+receptors in order to turn on pathways
+
+ align:start position:0%
+receptors in order to turn on pathways
+ 
+
+ align:start position:0%
+receptors in order to turn on pathways
+of catabolism in order to generate the
+
+ align:start position:0%
+of catabolism in order to generate the
+ 
+
+ align:start position:0%
+of catabolism in order to generate the
+ATP that's needed to help the student
+
+ align:start position:0%
+ATP that's needed to help the student
+ 
+
+ align:start position:0%
+ATP that's needed to help the student
+deal with this stressful situation this
+
+ align:start position:0%
+deal with this stressful situation this
+ 
+
+ align:start position:0%
+deal with this stressful situation this
+is sometimes called the fight-or-flight
+
+ align:start position:0%
+is sometimes called the fight-or-flight
+ 
+
+ align:start position:0%
+is sometimes called the fight-or-flight
+response at this point in the class if I
+
+ align:start position:0%
+response at this point in the class if I
+ 
+
+ align:start position:0%
+response at this point in the class if I
+really wanted to make my point and have
+
+ align:start position:0%
+really wanted to make my point and have
+ 
+
+ align:start position:0%
+really wanted to make my point and have
+it transferred to every student
+
+ align:start position:0%
+it transferred to every student
+ 
+
+ align:start position:0%
+it transferred to every student
+I'd announce a pop quiz the announcement
+
+ align:start position:0%
+I'd announce a pop quiz the announcement
+ 
+
+ align:start position:0%
+I'd announce a pop quiz the announcement
+of a pop quiz would cause kind of this
+
+ align:start position:0%
+of a pop quiz would cause kind of this
+ 
+
+ align:start position:0%
+of a pop quiz would cause kind of this
+cold feeling throughout your gut that's
+
+ align:start position:0%
+cold feeling throughout your gut that's
+ 
+
+ align:start position:0%
+cold feeling throughout your gut that's
+actually the feeling of adrenaline
+
+ align:start position:0%
+actually the feeling of adrenaline
+ 
+
+ align:start position:0%
+actually the feeling of adrenaline
+preparing your body to deal with the
+
+ align:start position:0%
+preparing your body to deal with the
+ 
+
+ align:start position:0%
+preparing your body to deal with the
+stress situation in that case of the
+
+ align:start position:0%
+stress situation in that case of the
+ 
+
+ align:start position:0%
+stress situation in that case of the
+quiz let's look at panel II as a
+
+ align:start position:0%
+quiz let's look at panel II as a
+ 
+
+ align:start position:0%
+quiz let's look at panel II as a
+scenario progresses let me introduce a
+
+ align:start position:0%
+scenario progresses let me introduce a
+ 
+
+ align:start position:0%
+scenario progresses let me introduce a
+few biochemical players glycogen
+
+ align:start position:0%
+few biochemical players glycogen
+ 
+
+ align:start position:0%
+few biochemical players glycogen
+phosphorylase glucose glucose
+
+ align:start position:0%
+phosphorylase glucose glucose
+ 
+
+ align:start position:0%
+phosphorylase glucose glucose
+6-phosphate and glucose 1-phosphate
+
+ align:start position:0%
+6-phosphate and glucose 1-phosphate
+ 
+
+ align:start position:0%
+6-phosphate and glucose 1-phosphate
+in panel F we see a muscle cell the
+
+ align:start position:0%
+in panel F we see a muscle cell the
+ 
+
+ align:start position:0%
+in panel F we see a muscle cell the
+epinephrine in the blood is only going
+
+ align:start position:0%
+epinephrine in the blood is only going
+ 
+
+ align:start position:0%
+epinephrine in the blood is only going
+to reach a concentration of about 10 to
+
+ align:start position:0%
+to reach a concentration of about 10 to
+ 
+
+ align:start position:0%
+to reach a concentration of about 10 to
+the minus 10 molar that's a very very
+
+ align:start position:0%
+the minus 10 molar that's a very very
+ 
+
+ align:start position:0%
+the minus 10 molar that's a very very
+low concentration the epinephrine is
+
+ align:start position:0%
+low concentration the epinephrine is
+ 
+
+ align:start position:0%
+low concentration the epinephrine is
+going to interact at the beta and alpha
+
+ align:start position:0%
+going to interact at the beta and alpha
+ 
+
+ align:start position:0%
+going to interact at the beta and alpha
+adrenergic receptors in the muscle cell
+
+ align:start position:0%
+adrenergic receptors in the muscle cell
+ 
+
+ align:start position:0%
+adrenergic receptors in the muscle cell
+membrane this interaction results in the
+
+ align:start position:0%
+membrane this interaction results in the
+ 
+
+ align:start position:0%
+membrane this interaction results in the
+activation of a kinase that is a
+
+ align:start position:0%
+activation of a kinase that is a
+ 
+
+ align:start position:0%
+activation of a kinase that is a
+molecule that transfers a phosphate
+
+ align:start position:0%
+molecule that transfers a phosphate
+ 
+
+ align:start position:0%
+molecule that transfers a phosphate
+group and that kinase which is called SP
+
+ align:start position:0%
+group and that kinase which is called SP
+ 
+
+ align:start position:0%
+group and that kinase which is called SP
+k4
+
+ align:start position:0%
+k4
+ 
+
+ align:start position:0%
+k4
+days phosphorylase kinase phosphorylates
+
+ align:start position:0%
+days phosphorylase kinase phosphorylates
+ 
+
+ align:start position:0%
+days phosphorylase kinase phosphorylates
+serine 14 on glycogen phosphorylase
+
+ align:start position:0%
+serine 14 on glycogen phosphorylase
+ 
+
+ align:start position:0%
+serine 14 on glycogen phosphorylase
+phosphorylation activates glycogen
+
+ align:start position:0%
+phosphorylation activates glycogen
+ 
+
+ align:start position:0%
+phosphorylation activates glycogen
+phosphorylase which will then begin to
+
+ align:start position:0%
+phosphorylase which will then begin to
+ 
+
+ align:start position:0%
+phosphorylase which will then begin to
+degrade glycogen the polymeric storage
+
+ align:start position:0%
+degrade glycogen the polymeric storage
+ 
+
+ align:start position:0%
+degrade glycogen the polymeric storage
+form of glucose in us that is mammals to
+
+ align:start position:0%
+form of glucose in us that is mammals to
+ 
+
+ align:start position:0%
+form of glucose in us that is mammals to
+produce initially glucose 1-phosphate
+
+ align:start position:0%
+produce initially glucose 1-phosphate
+ 
+
+ align:start position:0%
+produce initially glucose 1-phosphate
+glucose 1-phosphate will then go through
+
+ align:start position:0%
+glucose 1-phosphate will then go through
+ 
+
+ align:start position:0%
+glucose 1-phosphate will then go through
+a number of transformations and
+
+ align:start position:0%
+a number of transformations and
+ 
+
+ align:start position:0%
+a number of transformations and
+eventually be converted into other forms
+
+ align:start position:0%
+eventually be converted into other forms
+ 
+
+ align:start position:0%
+eventually be converted into other forms
+of glucose and then other molecules that
+
+ align:start position:0%
+of glucose and then other molecules that
+ 
+
+ align:start position:0%
+of glucose and then other molecules that
+will generate energy in nutshell this
+
+ align:start position:0%
+will generate energy in nutshell this
+ 
+
+ align:start position:0%
+will generate energy in nutshell this
+stand up sit down scenario results in
+
+ align:start position:0%
+stand up sit down scenario results in
+ 
+
+ align:start position:0%
+stand up sit down scenario results in
+the generation of energy in a matter of
+
+ align:start position:0%
+the generation of energy in a matter of
+ 
+
+ align:start position:0%
+the generation of energy in a matter of
+seconds which is one of the things that
+
+ align:start position:0%
+seconds which is one of the things that
+ 
+
+ align:start position:0%
+seconds which is one of the things that
+we use metabolism for another thing i
+
+ align:start position:0%
+we use metabolism for another thing i
+ 
+
+ align:start position:0%
+we use metabolism for another thing i
+said earlier was that you use metabolic
+
+ align:start position:0%
+said earlier was that you use metabolic
+ 
+
+ align:start position:0%
+said earlier was that you use metabolic
+energy to generate concentration
+
+ align:start position:0%
+energy to generate concentration
+ 
+
+ align:start position:0%
+energy to generate concentration
+gradients and it turns out that
+
+ align:start position:0%
+gradients and it turns out that
+ 
+
+ align:start position:0%
+gradients and it turns out that
+generation of concentration gradients is
+
+ align:start position:0%
+generation of concentration gradients is
+ 
+
+ align:start position:0%
+generation of concentration gradients is
+absolutely critical for muscle activity
+
+ align:start position:0%
+absolutely critical for muscle activity
+ 
+
+ align:start position:0%
+absolutely critical for muscle activity
+the sarcoplasmic reticulum in our muscle
+
+ align:start position:0%
+the sarcoplasmic reticulum in our muscle
+ 
+
+ align:start position:0%
+the sarcoplasmic reticulum in our muscle
+cells must accumulate calcium and
+
+ align:start position:0%
+cells must accumulate calcium and
+ 
+
+ align:start position:0%
+cells must accumulate calcium and
+release it at precisely defined moments
+
+ align:start position:0%
+release it at precisely defined moments
+ 
+
+ align:start position:0%
+release it at precisely defined moments
+in order to enable the muscle to be able
+
+ align:start position:0%
+in order to enable the muscle to be able
+ 
+
+ align:start position:0%
+in order to enable the muscle to be able
+to work that concentration gradient of
+
+ align:start position:0%
+to work that concentration gradient of
+ 
+
+ align:start position:0%
+to work that concentration gradient of
+calcium has to be created and it's
+
+ align:start position:0%
+calcium has to be created and it's
+ 
+
+ align:start position:0%
+calcium has to be created and it's
+created with the energy that we get from
+
+ align:start position:0%
+created with the energy that we get from
+ 
+
+ align:start position:0%
+created with the energy that we get from
+metabolism again we'll see how calcium
+
+ align:start position:0%
+metabolism again we'll see how calcium
+ 
+
+ align:start position:0%
+metabolism again we'll see how calcium
+gradients help boot up energy generation
+
+ align:start position:0%
+gradients help boot up energy generation
+ 
+
+ align:start position:0%
+gradients help boot up energy generation
+in the last lecture which deals with
+
+ align:start position:0%
+in the last lecture which deals with
+ 
+
+ align:start position:0%
+in the last lecture which deals with
+pathway regulation
\ No newline at end of file
diff --git a/xCCeV-glFdM.txt b/xCCeV-glFdM.txt
new file mode 100644
index 0000000000000000000000000000000000000000..27a00a5997e13aa828bde2d37551c3af60547d2b
--- /dev/null
+++ b/xCCeV-glFdM.txt
@@ -0,0 +1,2667 @@
+align:start position:0%
+ 
+Okay. Um, it's time to move on to second
+
+ align:start position:0%
+Okay. Um, it's time to move on to second
+ 
+
+ align:start position:0%
+Okay. Um, it's time to move on to second
+order equations. First order equations
+
+ align:start position:0%
+order equations. First order equations
+ 
+
+ align:start position:0%
+order equations. First order equations
+we've done pretty carefully. Second
+
+ align:start position:0%
+we've done pretty carefully. Second
+ 
+
+ align:start position:0%
+we've done pretty carefully. Second
+order equations are a step harder and
+
+ align:start position:0%
+order equations are a step harder and
+ 
+
+ align:start position:0%
+order equations are a step harder and
+but they come up in nature. They come in
+
+ align:start position:0%
+but they come up in nature. They come in
+ 
+
+ align:start position:0%
+but they come up in nature. They come in
+every application because they include a
+
+ align:start position:0%
+every application because they include a
+ 
+
+ align:start position:0%
+every application because they include a
+an acceleration a second derivative.
+
+ align:start position:0%
+an acceleration a second derivative.
+ 
+
+ align:start position:0%
+an acceleration a second derivative.
+Okay. So this would be a second order
+
+ align:start position:0%
+Okay. So this would be a second order
+ 
+
+ align:start position:0%
+Okay. So this would be a second order
+equation because of that second
+
+ align:start position:0%
+equation because of that second
+ 
+
+ align:start position:0%
+equation because of that second
+derivative. I'm often going to have
+
+ align:start position:0%
+derivative. I'm often going to have
+ 
+
+ align:start position:0%
+derivative. I'm often going to have
+constant A, B, and C. We have enough
+
+ align:start position:0%
+constant A, B, and C. We have enough
+ 
+
+ align:start position:0%
+constant A, B, and C. We have enough
+difficulties to without allowing those
+
+ align:start position:0%
+difficulties to without allowing those
+ 
+
+ align:start position:0%
+difficulties to without allowing those
+to change. So A, B, C constants.
+
+ align:start position:0%
+to change. So A, B, C constants.
+ 
+
+ align:start position:0%
+to change. So A, B, C constants.
+Uh, and I doing the null solution to
+
+ align:start position:0%
+Uh, and I doing the null solution to
+ 
+
+ align:start position:0%
+Uh, and I doing the null solution to
+start with.
+
+ align:start position:0%
+start with.
+ 
+
+ align:start position:0%
+start with.
+Later there'll be a forcing term on the
+
+ align:start position:0%
+Later there'll be a forcing term on the
+ 
+
+ align:start position:0%
+Later there'll be a forcing term on the
+right hand side but today for this video
+
+ align:start position:0%
+right hand side but today for this video
+ 
+
+ align:start position:0%
+right hand side but today for this video
+null solutions and the point is now
+
+ align:start position:0%
+null solutions and the point is now
+ 
+
+ align:start position:0%
+null solutions and the point is now
+what's new is that there are two null
+
+ align:start position:0%
+what's new is that there are two null
+ 
+
+ align:start position:0%
+what's new is that there are two null
+solutions. So y null will be a
+
+ align:start position:0%
+solutions. So y null will be a
+ 
+
+ align:start position:0%
+solutions. So y null will be a
+combination of e and they're both
+
+ align:start position:0%
+combination of e and they're both
+ 
+
+ align:start position:0%
+combination of e and they're both
+exponentials. The having constant
+
+ align:start position:0%
+exponentials. The having constant
+ 
+
+ align:start position:0%
+exponentials. The having constant
+coefficients there means exponentials in
+
+ align:start position:0%
+coefficients there means exponentials in
+ 
+
+ align:start position:0%
+coefficients there means exponentials in
+the solution. So e to the some exponent
+
+ align:start position:0%
+the solution. So e to the some exponent
+ 
+
+ align:start position:0%
+the solution. So e to the some exponent
+and another one to a
+
+ align:start position:0%
+and another one to a
+ 
+
+ align:start position:0%
+and another one to a
+hopefully different exponent.
+
+ align:start position:0%
+hopefully different exponent.
+ 
+
+ align:start position:0%
+hopefully different exponent.
+Sometimes if s1 equals s2 that'll be a
+
+ align:start position:0%
+Sometimes if s1 equals s2 that'll be a
+ 
+
+ align:start position:0%
+Sometimes if s1 equals s2 that'll be a
+special case and we'll have a slight
+
+ align:start position:0%
+special case and we'll have a slight
+ 
+
+ align:start position:0%
+special case and we'll have a slight
+change but this is typical. So we have
+
+ align:start position:0%
+change but this is typical. So we have
+ 
+
+ align:start position:0%
+change but this is typical. So we have
+two constants c1 and c2 in the null
+
+ align:start position:0%
+two constants c1 and c2 in the null
+ 
+
+ align:start position:0%
+two constants c1 and c2 in the null
+solutions and we need two initial
+
+ align:start position:0%
+solutions and we need two initial
+ 
+
+ align:start position:0%
+solutions and we need two initial
+conditions to determine those constants.
+
+ align:start position:0%
+conditions to determine those constants.
+ 
+
+ align:start position:0%
+conditions to determine those constants.
+So previously for a first order equation
+
+ align:start position:0%
+So previously for a first order equation
+ 
+
+ align:start position:0%
+So previously for a first order equation
+we were given y of zero.
+
+ align:start position:0%
+we were given y of zero.
+ 
+
+ align:start position:0%
+we were given y of zero.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+when we have acceleration
+
+ align:start position:0%
+when we have acceleration
+ 
+
+ align:start position:0%
+when we have acceleration
+we give the initial velocity y prime of
+
+ align:start position:0%
+we give the initial velocity y prime of
+ 
+
+ align:start position:0%
+we give the initial velocity y prime of
+zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Y prime I use may I use prime
+
+ align:start position:0%
+Y prime I use may I use prime
+ 
+
+ align:start position:0%
+Y prime I use may I use prime
+as a shorthand for derivative?
+
+ align:start position:0%
+as a shorthand for derivative?
+ 
+
+ align:start position:0%
+as a shorthand for derivative?
+y prime of zero is dydt
+
+ align:start position:0%
+y prime of zero is dydt
+ 
+
+ align:start position:0%
+y prime of zero is dydt
+at zero. So two conditions will at the
+
+ align:start position:0%
+at zero. So two conditions will at the
+ 
+
+ align:start position:0%
+at zero. So two conditions will at the
+right time determine those two
+
+ align:start position:0%
+right time determine those two
+ 
+
+ align:start position:0%
+right time determine those two
+constants. And just to say again so
+
+ align:start position:0%
+constants. And just to say again so
+ 
+
+ align:start position:0%
+constants. And just to say again so
+second derivative will be y doublep
+
+ align:start position:0%
+second derivative will be y doublep
+ 
+
+ align:start position:0%
+second derivative will be y doublep
+prime
+
+ align:start position:0%
+prime
+ 
+
+ align:start position:0%
+prime
+and that represents in physics it
+
+ align:start position:0%
+and that represents in physics it
+ 
+
+ align:start position:0%
+and that represents in physics it
+represents acceleration
+
+ align:start position:0%
+represents acceleration
+ 
+
+ align:start position:0%
+represents acceleration
+change in velocity. Change in y prime is
+
+ align:start position:0%
+change in velocity. Change in y prime is
+ 
+
+ align:start position:0%
+change in velocity. Change in y prime is
+yblep prime. And in a graph of a
+
+ align:start position:0%
+yblep prime. And in a graph of a
+ 
+
+ align:start position:0%
+yblep prime. And in a graph of a
+function, yblep prime shows up in
+
+ align:start position:0%
+function, yblep prime shows up in
+ 
+
+ align:start position:0%
+function, yblep prime shows up in
+bending of the graph. Bending of the
+
+ align:start position:0%
+bending of the graph. Bending of the
+ 
+
+ align:start position:0%
+bending of the graph. Bending of the
+graph because bending is a change in
+
+ align:start position:0%
+graph because bending is a change in
+ 
+
+ align:start position:0%
+graph because bending is a change in
+slope. Bending is a change
+
+ align:start position:0%
+slope. Bending is a change
+ 
+
+ align:start position:0%
+slope. Bending is a change
+in the slope.
+
+ align:start position:0%
+in the slope.
+ 
+
+ align:start position:0%
+in the slope.
+And the slope is y prime the first
+
+ align:start position:0%
+And the slope is y prime the first
+ 
+
+ align:start position:0%
+And the slope is y prime the first
+derivative. So to measure changes in y
+
+ align:start position:0%
+derivative. So to measure changes in y
+ 
+
+ align:start position:0%
+derivative. So to measure changes in y
+prime which will bend the graph the the
+
+ align:start position:0%
+prime which will bend the graph the the
+ 
+
+ align:start position:0%
+prime which will bend the graph the the
+my chalk would be a tangent line. As
+
+ align:start position:0%
+my chalk would be a tangent line. As
+ 
+
+ align:start position:0%
+my chalk would be a tangent line. As
+that changes that gives us a yblep prime
+
+ align:start position:0%
+that changes that gives us a yblep prime
+ 
+
+ align:start position:0%
+that changes that gives us a yblep prime
+a second derivative. Okay. So I'm ready
+
+ align:start position:0%
+a second derivative. Okay. So I'm ready
+ 
+
+ align:start position:0%
+a second derivative. Okay. So I'm ready
+for some examples.
+
+ align:start position:0%
+for some examples.
+ 
+
+ align:start position:0%
+for some examples.
+And the first example, the most basic
+
+ align:start position:0%
+And the first example, the most basic
+ 
+
+ align:start position:0%
+And the first example, the most basic
+equation of motion in
+
+ align:start position:0%
+equation of motion in
+ 
+
+ align:start position:0%
+equation of motion in
+uh physics and engineering, I would say
+
+ align:start position:0%
+uh physics and engineering, I would say
+ 
+
+ align:start position:0%
+uh physics and engineering, I would say
+it's called harmonic motion and B is
+
+ align:start position:0%
+it's called harmonic motion and B is
+ 
+
+ align:start position:0%
+it's called harmonic motion and B is
+zero. That's the key point. B is zero.
+
+ align:start position:0%
+zero. That's the key point. B is zero.
+ 
+
+ align:start position:0%
+zero. That's the key point. B is zero.
+So we have a it's Newton's law. And so a
+
+ align:start position:0%
+So we have a it's Newton's law. And so a
+ 
+
+ align:start position:0%
+So we have a it's Newton's law. And so a
+will be the mass m
+
+ align:start position:0%
+will be the mass m
+ 
+
+ align:start position:0%
+will be the mass m
+yblep prime second derivative
+
+ align:start position:0%
+yblep prime second derivative
+ 
+
+ align:start position:0%
+yblep prime second derivative
+b is zero
+
+ align:start position:0%
+b is zero
+ 
+
+ align:start position:0%
+b is zero
+later b will be a damping term a a
+
+ align:start position:0%
+later b will be a damping term a a
+ 
+
+ align:start position:0%
+later b will be a damping term a a
+friction term a resistance term but
+
+ align:start position:0%
+friction term a resistance term but
+ 
+
+ align:start position:0%
+friction term a resistance term but
+let's have that zero so we're going to
+
+ align:start position:0%
+let's have that zero so we're going to
+ 
+
+ align:start position:0%
+let's have that zero so we're going to
+have perpetual motion here plus the
+
+ align:start position:0%
+have perpetual motion here plus the
+ 
+
+ align:start position:0%
+have perpetual motion here plus the
+force so this is Newton's law m a is f=
+
+ align:start position:0%
+force so this is Newton's law m a is f=
+ 
+
+ align:start position:0%
+force so this is Newton's law m a is f=
+ma the force is proportional with a
+
+ align:start position:0%
+ma the force is proportional with a
+ 
+
+ align:start position:0%
+ma the force is proportional with a
+minus sign. So it's going to come on
+
+ align:start position:0%
+minus sign. So it's going to come on
+ 
+
+ align:start position:0%
+minus sign. So it's going to come on
+this side as a plus proportional
+
+ align:start position:0%
+this side as a plus proportional
+ 
+
+ align:start position:0%
+this side as a plus proportional
+to y. There's the equation.
+
+ align:start position:0%
+to y. There's the equation.
+ 
+
+ align:start position:0%
+to y. There's the equation.
+No, no y prime term.
+
+ align:start position:0%
+No, no y prime term.
+ 
+
+ align:start position:0%
+No, no y prime term.
+m yp prime + k y = z.
+
+ align:start position:0%
+m yp prime + k y = z.
+ 
+
+ align:start position:0%
+m yp prime + k y = z.
+Starting from an initial position and an
+
+ align:start position:0%
+Starting from an initial position and an
+ 
+
+ align:start position:0%
+Starting from an initial position and an
+initial velocity, it's like a spring
+
+ align:start position:0%
+initial velocity, it's like a spring
+ 
+
+ align:start position:0%
+initial velocity, it's like a spring
+going up and down.
+
+ align:start position:0%
+going up and down.
+ 
+
+ align:start position:0%
+going up and down.
+or a clock pendulum going going back and
+
+ align:start position:0%
+or a clock pendulum going going back and
+ 
+
+ align:start position:0%
+or a clock pendulum going going back and
+forth and it we'll see it it so it's
+
+ align:start position:0%
+forth and it we'll see it it so it's
+ 
+
+ align:start position:0%
+forth and it we'll see it it so it's
+going to be well we want to solve that
+
+ align:start position:0%
+going to be well we want to solve that
+ 
+
+ align:start position:0%
+going to be well we want to solve that
+equation
+
+ align:start position:0%
+equation
+ 
+
+ align:start position:0%
+equation
+so do we see solutions to that
+
+ align:start position:0%
+so do we see solutions to that
+ 
+
+ align:start position:0%
+so do we see solutions to that
+so if I had if m and k were one suppose
+
+ align:start position:0%
+so if I had if m and k were one suppose
+ 
+
+ align:start position:0%
+so if I had if m and k were one suppose
+m and k were one I'm looking for second
+
+ align:start position:0%
+m and k were one I'm looking for second
+ 
+
+ align:start position:0%
+m and k were one I'm looking for second
+derivative plus the function is zero
+
+ align:start position:0%
+derivative plus the function is zero
+ 
+
+ align:start position:0%
+derivative plus the function is zero
+second derivative is minus the function
+
+ align:start position:0%
+second derivative is minus the function
+ 
+
+ align:start position:0%
+second derivative is minus the function
+I Immediately think of sin t and cosine
+
+ align:start position:0%
+I Immediately think of sin t and cosine
+ 
+
+ align:start position:0%
+I Immediately think of sin t and cosine
+t ss and cosiness because the second
+
+ align:start position:0%
+t ss and cosiness because the second
+ 
+
+ align:start position:0%
+t ss and cosiness because the second
+derivative the first derivative of s is
+
+ align:start position:0%
+derivative the first derivative of s is
+ 
+
+ align:start position:0%
+derivative the first derivative of s is
+cosine the second derivative is minus
+
+ align:start position:0%
+cosine the second derivative is minus
+ 
+
+ align:start position:0%
+cosine the second derivative is minus
+the sign it gives us the minus sign here
+
+ align:start position:0%
+the sign it gives us the minus sign here
+ 
+
+ align:start position:0%
+the sign it gives us the minus sign here
+the plus sign there zero. So the the
+
+ align:start position:0%
+the plus sign there zero. So the the
+ 
+
+ align:start position:0%
+the plus sign there zero. So the the
+these special solutions here are y
+
+ align:start position:0%
+these special solutions here are y
+ 
+
+ align:start position:0%
+these special solutions here are y
+is this is the null I'm finding the null
+
+ align:start position:0%
+is this is the null I'm finding the null
+ 
+
+ align:start position:0%
+is this is the null I'm finding the null
+solution is let me call them c1 times
+
+ align:start position:0%
+solution is let me call them c1 times
+ 
+
+ align:start position:0%
+solution is let me call them c1 times
+the cosine and now I have to figure out
+
+ align:start position:0%
+the cosine and now I have to figure out
+ 
+
+ align:start position:0%
+the cosine and now I have to figure out
+the cosine of what
+
+ align:start position:0%
+the cosine of what
+ 
+
+ align:start position:0%
+the cosine of what
+I want the cosine
+
+ align:start position:0%
+I want the cosine
+ 
+
+ align:start position:0%
+I want the cosine
+to satisfy to be a null solution satisfy
+
+ align:start position:0%
+to satisfy to be a null solution satisfy
+ 
+
+ align:start position:0%
+to satisfy to be a null solution satisfy
+my equation let me put it in it there's
+
+ align:start position:0%
+my equation let me put it in it there's
+ 
+
+ align:start position:0%
+my equation let me put it in it there's
+a square root of k over mt
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and you have to see that if I take two
+
+ align:start position:0%
+and you have to see that if I take two
+ 
+
+ align:start position:0%
+and you have to see that if I take two
+derivatives of the cosine that will
+
+ align:start position:0%
+derivatives of the cosine that will
+ 
+
+ align:start position:0%
+derivatives of the cosine that will
+produce minus the cosine which I want
+
+ align:start position:0%
+produce minus the cosine which I want
+ 
+
+ align:start position:0%
+produce minus the cosine which I want
+and because of that the chain rule will
+
+ align:start position:0%
+and because of that the chain rule will
+ 
+
+ align:start position:0%
+and because of that the chain rule will
+bring out this square root twice so it
+
+ align:start position:0%
+bring out this square root twice so it
+ 
+
+ align:start position:0%
+bring out this square root twice so it
+will bring bring out the factor km m
+
+ align:start position:0%
+will bring bring out the factor km m
+ 
+
+ align:start position:0%
+will bring bring out the factor km m
+for yblep prime and that factor k / m.
+
+ align:start position:0%
+for yblep prime and that factor k / m.
+ 
+
+ align:start position:0%
+for yblep prime and that factor k / m.
+The m's will cancel and I'll have the k
+
+ align:start position:0%
+The m's will cancel and I'll have the k
+ 
+
+ align:start position:0%
+The m's will cancel and I'll have the k
+that matches that k. It's a solution.
+
+ align:start position:0%
+that matches that k. It's a solution.
+ 
+
+ align:start position:0%
+that matches that k. It's a solution.
+And the other solution is just like it.
+
+ align:start position:0%
+And the other solution is just like it.
+ 
+
+ align:start position:0%
+And the other solution is just like it.
+It's the sign
+
+ align:start position:0%
+It's the sign
+ 
+
+ align:start position:0%
+It's the sign
+of this square root of k / m t.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's worth putting a box around.
+
+ align:start position:0%
+That's worth putting a box around.
+ 
+
+ align:start position:0%
+That's worth putting a box around.
+That's what I mean by free harmonic
+
+ align:start position:0%
+That's what I mean by free harmonic
+ 
+
+ align:start position:0%
+That's what I mean by free harmonic
+motion.
+
+ align:start position:0%
+motion.
+ 
+
+ align:start position:0%
+motion.
+Something is just oscillating
+
+ align:start position:0%
+Something is just oscillating
+ 
+
+ align:start position:0%
+Something is just oscillating
+in rotation problem. Something is just
+
+ align:start position:0%
+in rotation problem. Something is just
+ 
+
+ align:start position:0%
+in rotation problem. Something is just
+going around a circle at a constant
+
+ align:start position:0%
+going around a circle at a constant
+ 
+
+ align:start position:0%
+going around a circle at a constant
+speed. So, and notice well notice I
+
+ align:start position:0%
+speed. So, and notice well notice I
+ 
+
+ align:start position:0%
+speed. So, and notice well notice I
+haven't
+
+ align:start position:0%
+haven't
+ 
+
+ align:start position:0%
+haven't
+these are not the same as those
+
+ align:start position:0%
+these are not the same as those
+ 
+
+ align:start position:0%
+these are not the same as those
+cosiness are related to exponentials but
+
+ align:start position:0%
+cosiness are related to exponentials but
+ 
+
+ align:start position:0%
+cosiness are related to exponentials but
+not identical. So I could write the
+
+ align:start position:0%
+not identical. So I could write the
+ 
+
+ align:start position:0%
+not identical. So I could write the
+answer this way with using cosine and s
+
+ align:start position:0%
+answer this way with using cosine and s
+ 
+
+ align:start position:0%
+answer this way with using cosine and s
+or as you'll see I can write the same
+
+ align:start position:0%
+or as you'll see I can write the same
+ 
+
+ align:start position:0%
+or as you'll see I can write the same
+the same formula using exponentials
+
+ align:start position:0%
+the same formula using exponentials
+ 
+
+ align:start position:0%
+the same formula using exponentials
+complex exponentials. Everybody
+
+ align:start position:0%
+complex exponentials. Everybody
+ 
+
+ align:start position:0%
+complex exponentials. Everybody
+remembers the big formula that allows
+
+ align:start position:0%
+remembers the big formula that allows
+ 
+
+ align:start position:0%
+remembers the big formula that allows
+complex numbers in here is Oiler's
+
+ align:start position:0%
+complex numbers in here is Oiler's
+ 
+
+ align:start position:0%
+complex numbers in here is Oiler's
+formula that the exponential of I omega
+
+ align:start position:0%
+formula that the exponential of I omega
+ 
+
+ align:start position:0%
+formula that the exponential of I omega
+t is the cosine plus i * the s of omega
+
+ align:start position:0%
+t is the cosine plus i * the s of omega
+ 
+
+ align:start position:0%
+t is the cosine plus i * the s of omega
+t. I'll write it again. That that that's
+
+ align:start position:0%
+t. I'll write it again. That that that's
+ 
+
+ align:start position:0%
+t. I'll write it again. That that that's
+a solution. It's got the two it's got
+
+ align:start position:0%
+a solution. It's got the two it's got
+ 
+
+ align:start position:0%
+a solution. It's got the two it's got
+two null solutions. They're independent.
+
+ align:start position:0%
+two null solutions. They're independent.
+ 
+
+ align:start position:0%
+two null solutions. They're independent.
+They're different. If we've got two
+
+ align:start position:0%
+They're different. If we've got two
+ 
+
+ align:start position:0%
+They're different. If we've got two
+constants, because our equation is
+
+ align:start position:0%
+constants, because our equation is
+ 
+
+ align:start position:0%
+constants, because our equation is
+linear, we can safely multiply by any
+
+ align:start position:0%
+linear, we can safely multiply by any
+ 
+
+ align:start position:0%
+linear, we can safely multiply by any
+constant and add solutions and they stay
+
+ align:start position:0%
+constant and add solutions and they stay
+ 
+
+ align:start position:0%
+constant and add solutions and they stay
+solutions because we have a linear
+
+ align:start position:0%
+solutions because we have a linear
+ 
+
+ align:start position:0%
+solutions because we have a linear
+equation and zero on the right hand
+
+ align:start position:0%
+equation and zero on the right hand
+ 
+
+ align:start position:0%
+equation and zero on the right hand
+side. Good.
+
+ align:start position:0%
+side. Good.
+ 
+
+ align:start position:0%
+side. Good.
+Uh, of course, we can't write this
+
+ align:start position:0%
+Uh, of course, we can't write this
+ 
+
+ align:start position:0%
+Uh, of course, we can't write this
+square root of a over m k over m
+
+ align:start position:0%
+square root of a over m k over m
+ 
+
+ align:start position:0%
+square root of a over m k over m
+forever. Let let me do what everybody
+
+ align:start position:0%
+forever. Let let me do what everybody
+ 
+
+ align:start position:0%
+forever. Let let me do what everybody
+does. Introduce omega. It's omega
+
+ align:start position:0%
+does. Introduce omega. It's omega
+ 
+
+ align:start position:0%
+does. Introduce omega. It's omega
+natural. The N here stands for the
+
+ align:start position:0%
+natural. The N here stands for the
+ 
+
+ align:start position:0%
+natural. The N here stands for the
+natural frequency. The frequency that
+
+ align:start position:0%
+natural frequency. The frequency that
+ 
+
+ align:start position:0%
+natural frequency. The frequency that
+that clock is going at. And that is the
+
+ align:start position:0%
+that clock is going at. And that is the
+ 
+
+ align:start position:0%
+that clock is going at. And that is the
+square root of K over M.
+
+ align:start position:0%
+square root of K over M.
+ 
+
+ align:start position:0%
+square root of K over M.
+So our equation, we could rewrite that
+
+ align:start position:0%
+So our equation, we could rewrite that
+ 
+
+ align:start position:0%
+So our equation, we could rewrite that
+equation. Let me rewrite that equation
+
+ align:start position:0%
+equation. Let me rewrite that equation
+ 
+
+ align:start position:0%
+equation. Let me rewrite that equation
+to make it simple. I'll divide by M. No
+
+ align:start position:0%
+to make it simple. I'll divide by M. No
+ 
+
+ align:start position:0%
+to make it simple. I'll divide by M. No
+problem to divide by M. So then I have
+
+ align:start position:0%
+problem to divide by M. So then I have
+ 
+
+ align:start position:0%
+problem to divide by M. So then I have
+yp prime plus k / m which is omega n^2
+
+ align:start position:0%
+yp prime plus k / m which is omega n^2
+ 
+
+ align:start position:0%
+yp prime plus k / m which is omega n^2
+the natural frequency squared y equals
+
+ align:start position:0%
+the natural frequency squared y equals
+ 
+
+ align:start position:0%
+the natural frequency squared y equals
+zero. That's let's put a box around that
+
+ align:start position:0%
+zero. That's let's put a box around that
+ 
+
+ align:start position:0%
+zero. That's let's put a box around that
+one because that's you couldn't couldn't
+
+ align:start position:0%
+one because that's you couldn't couldn't
+ 
+
+ align:start position:0%
+one because that's you couldn't couldn't
+be better than that. The constant a is
+
+ align:start position:0%
+be better than that. The constant a is
+ 
+
+ align:start position:0%
+be better than that. The constant a is
+one. The constant b is zero. the
+
+ align:start position:0%
+one. The constant b is zero. the
+ 
+
+ align:start position:0%
+one. The constant b is zero. the
+constant C is a known omega n^ squ
+
+ align:start position:0%
+constant C is a known omega n^ squ
+ 
+
+ align:start position:0%
+constant C is a known omega n^ squ
+depending on the the the pendulum
+
+ align:start position:0%
+depending on the the the pendulum
+ 
+
+ align:start position:0%
+depending on the the the pendulum
+itself. Okay. And the solutions then
+
+ align:start position:0%
+itself. Okay. And the solutions then
+ 
+
+ align:start position:0%
+itself. Okay. And the solutions then
+I'll just copy this solution. Y null is
+
+ align:start position:0%
+I'll just copy this solution. Y null is
+ 
+
+ align:start position:0%
+I'll just copy this solution. Y null is
+c1 cosine of omega n t because omega n
+
+ align:start position:0%
+c1 cosine of omega n t because omega n
+ 
+
+ align:start position:0%
+c1 cosine of omega n t because omega n
+is that square root and c2 sine of omega
+
+ align:start position:0%
+is that square root and c2 sine of omega
+ 
+
+ align:start position:0%
+is that square root and c2 sine of omega
+n t. Oh well, wait a minute. I can
+
+ align:start position:0%
+n t. Oh well, wait a minute. I can
+ 
+
+ align:start position:0%
+n t. Oh well, wait a minute. I can
+figure out what C1 and C2 are.
+
+ align:start position:0%
+figure out what C1 and C2 are.
+ 
+
+ align:start position:0%
+figure out what C1 and C2 are.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+coming from the initial conditions,
+
+ align:start position:0%
+coming from the initial conditions,
+ 
+
+ align:start position:0%
+coming from the initial conditions,
+right? The initial conditions. If I plug
+
+ align:start position:0%
+right? The initial conditions. If I plug
+ 
+
+ align:start position:0%
+right? The initial conditions. If I plug
+in t equals 0,
+
+ align:start position:0%
+in t equals 0,
+ 
+
+ align:start position:0%
+in t equals 0,
+then I want to get the answer y of 0.
+
+ align:start position:0%
+then I want to get the answer y of 0.
+ 
+
+ align:start position:0%
+then I want to get the answer y of 0.
+The the known initial condition, the
+
+ align:start position:0%
+The the known initial condition, the
+ 
+
+ align:start position:0%
+The the known initial condition, the
+place the pendulum started swinging
+
+ align:start position:0%
+place the pendulum started swinging
+ 
+
+ align:start position:0%
+place the pendulum started swinging
+from, the place the spring you you
+
+ align:start position:0%
+from, the place the spring you you
+ 
+
+ align:start position:0%
+from, the place the spring you you
+pulled the spring a distance y of 0, you
+
+ align:start position:0%
+pulled the spring a distance y of 0, you
+ 
+
+ align:start position:0%
+pulled the spring a distance y of 0, you
+let go
+
+ align:start position:0%
+let go
+ 
+
+ align:start position:0%
+let go
+at t equals 0.
+
+ align:start position:0%
+at t equals 0.
+ 
+
+ align:start position:0%
+at t equals 0.
+So I'm plugging in tals 0. At tals 0,
+
+ align:start position:0%
+So I'm plugging in tals 0. At tals 0,
+ 
+
+ align:start position:0%
+So I'm plugging in tals 0. At tals 0,
+that's zero. Forget the sign. This is
+
+ align:start position:0%
+that's zero. Forget the sign. This is
+ 
+
+ align:start position:0%
+that's zero. Forget the sign. This is
+one. So I I discover that C1 should be Y
+
+ align:start position:0%
+one. So I I discover that C1 should be Y
+ 
+
+ align:start position:0%
+one. So I I discover that C1 should be Y
+of zero. Simple. C1 is Y of zero
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+because that gives me the right answer
+
+ align:start position:0%
+because that gives me the right answer
+ 
+
+ align:start position:0%
+because that gives me the right answer
+at T equals Z. And what about C2? Can I
+
+ align:start position:0%
+at T equals Z. And what about C2? Can I
+ 
+
+ align:start position:0%
+at T equals Z. And what about C2? Can I
+figure out C2? Well, that's going to
+
+ align:start position:0%
+figure out C2? Well, that's going to
+ 
+
+ align:start position:0%
+figure out C2? Well, that's going to
+involve the initial velocity, the
+
+ align:start position:0%
+involve the initial velocity, the
+ 
+
+ align:start position:0%
+involve the initial velocity, the
+derivative at t=0.
+
+ align:start position:0%
+derivative at t=0.
+ 
+
+ align:start position:0%
+derivative at t=0.
+So the der because the derivative of the
+
+ align:start position:0%
+So the der because the derivative of the
+ 
+
+ align:start position:0%
+So the der because the derivative of the
+sign is the cosine which equals 1 at t=
+
+ align:start position:0%
+sign is the cosine which equals 1 at t=
+ 
+
+ align:start position:0%
+sign is the cosine which equals 1 at t=
+0.
+
+ align:start position:0%
+0.
+ 
+
+ align:start position:0%
+0.
+The derivative of this is the sign which
+
+ align:start position:0%
+The derivative of this is the sign which
+ 
+
+ align:start position:0%
+The derivative of this is the sign which
+is zero. So the when I'm looking at y
+
+ align:start position:0%
+is zero. So the when I'm looking at y
+ 
+
+ align:start position:0%
+is zero. So the when I'm looking at y
+prime, the derivative,
+
+ align:start position:0%
+prime, the derivative,
+ 
+
+ align:start position:0%
+prime, the derivative,
+I'm looking here at t equals z. And I
+
+ align:start position:0%
+I'm looking here at t equals z. And I
+ 
+
+ align:start position:0%
+I'm looking here at t equals z. And I
+want y prime of zero.
+
+ align:start position:0%
+want y prime of zero.
+ 
+
+ align:start position:0%
+want y prime of zero.
+But I don't just want y prime of zero.
+
+ align:start position:0%
+But I don't just want y prime of zero.
+ 
+
+ align:start position:0%
+But I don't just want y prime of zero.
+Do you see that? That doesn't have the
+
+ align:start position:0%
+Do you see that? That doesn't have the
+ 
+
+ align:start position:0%
+Do you see that? That doesn't have the
+right derivative at t equals z. Because
+
+ align:start position:0%
+right derivative at t equals z. Because
+ 
+
+ align:start position:0%
+right derivative at t equals z. Because
+when I take the derivative and omega n,
+
+ align:start position:0%
+when I take the derivative and omega n,
+ 
+
+ align:start position:0%
+when I take the derivative and omega n,
+that constant, you remember that
+
+ align:start position:0%
+that constant, you remember that
+ 
+
+ align:start position:0%
+that constant, you remember that
+constant, the derivative of of this will
+
+ align:start position:0%
+constant, the derivative of of this will
+ 
+
+ align:start position:0%
+constant, the derivative of of this will
+bring out an omega n. So I better have
+
+ align:start position:0%
+bring out an omega n. So I better have
+ 
+
+ align:start position:0%
+bring out an omega n. So I better have
+an omega n down here to cancel it. And
+
+ align:start position:0%
+an omega n down here to cancel it. And
+ 
+
+ align:start position:0%
+an omega n down here to cancel it. And
+now I've got it.
+
+ align:start position:0%
+now I've got it.
+ 
+
+ align:start position:0%
+now I've got it.
+That tells me the motion
+
+ align:start position:0%
+That tells me the motion
+ 
+
+ align:start position:0%
+That tells me the motion
+forever and ever.
+
+ align:start position:0%
+forever and ever.
+ 
+
+ align:start position:0%
+forever and ever.
+Energy is constant. Potential energy
+
+ align:start position:0%
+Energy is constant. Potential energy
+ 
+
+ align:start position:0%
+Energy is constant. Potential energy
+plus kinetic energy. I could speak about
+
+ align:start position:0%
+plus kinetic energy. I could speak about
+ 
+
+ align:start position:0%
+plus kinetic energy. I could speak about
+energy but I won't.
+
+ align:start position:0%
+energy but I won't.
+ 
+
+ align:start position:0%
+energy but I won't.
+That's that motion continues forever.
+
+ align:start position:0%
+That's that motion continues forever.
+ 
+
+ align:start position:0%
+That's that motion continues forever.
+Free harmonic motion. Free harmonic
+
+ align:start position:0%
+Free harmonic motion. Free harmonic
+ 
+
+ align:start position:0%
+Free harmonic motion. Free harmonic
+motion. Okay. It it goes on and on.
+
+ align:start position:0%
+motion. Okay. It it goes on and on.
+ 
+
+ align:start position:0%
+motion. Okay. It it goes on and on.
+Okay. And again, uh, I could write this
+
+ align:start position:0%
+Okay. And again, uh, I could write this
+ 
+
+ align:start position:0%
+Okay. And again, uh, I could write this
+in terms of complex exponentials, but
+
+ align:start position:0%
+in terms of complex exponentials, but
+ 
+
+ align:start position:0%
+in terms of complex exponentials, but
+I'm pretty happy with that form. It's
+
+ align:start position:0%
+I'm pretty happy with that form. It's
+ 
+
+ align:start position:0%
+I'm pretty happy with that form. It's
+hard to beat that form. Okay. So, uh,
+
+ align:start position:0%
+hard to beat that form. Okay. So, uh,
+ 
+
+ align:start position:0%
+hard to beat that form. Okay. So, uh,
+what else to what else to do here? First
+
+ align:start position:0%
+what else to what else to do here? First
+ 
+
+ align:start position:0%
+what else to what else to do here? First
+of all, we're going to have
+
+ align:start position:0%
+of all, we're going to have
+ 
+
+ align:start position:0%
+of all, we're going to have
+cosine omega t's for quite a while.
+
+ align:start position:0%
+cosine omega t's for quite a while.
+ 
+
+ align:start position:0%
+cosine omega t's for quite a while.
+I better d draw the graph of that simple
+
+ align:start position:0%
+I better d draw the graph of that simple
+ 
+
+ align:start position:0%
+I better d draw the graph of that simple
+familiar function. And
+
+ align:start position:0%
+familiar function. And
+ 
+
+ align:start position:0%
+familiar function. And
+so here's a graph of cosine omega t. So
+
+ align:start position:0%
+so here's a graph of cosine omega t. So
+ 
+
+ align:start position:0%
+so here's a graph of cosine omega t. So
+here's t,
+
+ align:start position:0%
+here's t,
+ 
+
+ align:start position:0%
+here's t,
+here's cosine of omega, here's zero,
+
+ align:start position:0%
+here's cosine of omega, here's zero,
+ 
+
+ align:start position:0%
+here's cosine of omega, here's zero,
+here's two. Well, let me see what I get.
+
+ align:start position:0%
+here's two. Well, let me see what I get.
+ 
+
+ align:start position:0%
+here's two. Well, let me see what I get.
+So I go cosine of omega. Cosine of omega
+
+ align:start position:0%
+So I go cosine of omega. Cosine of omega
+ 
+
+ align:start position:0%
+So I go cosine of omega. Cosine of omega
+t is what I'm drawing. Not cosine t.
+
+ align:start position:0%
+t is what I'm drawing. Not cosine t.
+ 
+
+ align:start position:0%
+t is what I'm drawing. Not cosine t.
+Cosine t would go 0 to 2 pi. But I have
+
+ align:start position:0%
+Cosine t would go 0 to 2 pi. But I have
+ 
+
+ align:start position:0%
+Cosine t would go 0 to 2 pi. But I have
+cosine of omega t. So cosine of omega t
+
+ align:start position:0%
+cosine of omega t. So cosine of omega t
+ 
+
+ align:start position:0%
+cosine of omega t. So cosine of omega t
+is what I want to graph. So it starts at
+
+ align:start position:0%
+is what I want to graph. So it starts at
+ 
+
+ align:start position:0%
+is what I want to graph. So it starts at
+at one and it comes back it drops comes
+
+ align:start position:0%
+at one and it comes back it drops comes
+ 
+
+ align:start position:0%
+at one and it comes back it drops comes
+back up comes back to one. But what is
+
+ align:start position:0%
+back up comes back to one. But what is
+ 
+
+ align:start position:0%
+back up comes back to one. But what is
+this t final?
+
+ align:start position:0%
+this t final?
+ 
+
+ align:start position:0%
+this t final?
+The the period this t is the period
+
+ align:start position:0%
+The the period this t is the period
+ 
+
+ align:start position:0%
+The the period this t is the period
+of the oscillation.
+
+ align:start position:0%
+of the oscillation.
+ 
+
+ align:start position:0%
+of the oscillation.
+It's the time it takes for the swing to
+
+ align:start position:0%
+It's the time it takes for the swing to
+ 
+
+ align:start position:0%
+It's the time it takes for the swing to
+go up and back. It's And what is that?
+
+ align:start position:0%
+go up and back. It's And what is that?
+ 
+
+ align:start position:0%
+go up and back. It's And what is that?
+That would be So I'm looking So I'm
+
+ align:start position:0%
+That would be So I'm looking So I'm
+ 
+
+ align:start position:0%
+That would be So I'm looking So I'm
+graphing coine of omega t is what I'm
+
+ align:start position:0%
+graphing coine of omega t is what I'm
+ 
+
+ align:start position:0%
+graphing coine of omega t is what I'm
+graphing.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So omega t starts out at zero where t is
+
+ align:start position:0%
+So omega t starts out at zero where t is
+ 
+
+ align:start position:0%
+So omega t starts out at zero where t is
+zero and it goes up to So I want omega
+
+ align:start position:0%
+zero and it goes up to So I want omega
+ 
+
+ align:start position:0%
+zero and it goes up to So I want omega
+t. when I get here this omega t should
+
+ align:start position:0%
+t. when I get here this omega t should
+ 
+
+ align:start position:0%
+t. when I get here this omega t should
+be 2 pi
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+right
+
+ align:start position:0%
+right
+ 
+
+ align:start position:0%
+right
+then I've completed the cosine
+
+ align:start position:0%
+then I've completed the cosine
+ 
+
+ align:start position:0%
+then I've completed the cosine
+uh one
+
+ align:start position:0%
+uh one
+ 
+
+ align:start position:0%
+uh one
+one uh rotation around the circle one
+
+ align:start position:0%
+one uh rotation around the circle one
+ 
+
+ align:start position:0%
+one uh rotation around the circle one
+movement of the pendulum back and forth
+
+ align:start position:0%
+movement of the pendulum back and forth
+ 
+
+ align:start position:0%
+movement of the pendulum back and forth
+is in that picture now okay so omega t
+
+ align:start position:0%
+is in that picture now okay so omega t
+ 
+
+ align:start position:0%
+is in that picture now okay so omega t
+is 2 pi right
+
+ align:start position:0%
+is 2 pi right
+ 
+
+ align:start position:0%
+is 2 pi right
+the period is t. I think of omega as the
+
+ align:start position:0%
+the period is t. I think of omega as the
+ 
+
+ align:start position:0%
+the period is t. I think of omega as the
+circular frequency. Omega is in Omega is
+
+ align:start position:0%
+circular frequency. Omega is in Omega is
+ 
+
+ align:start position:0%
+circular frequency. Omega is in Omega is
+in radians
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+per
+
+ align:start position:0%
+per
+ 
+
+ align:start position:0%
+per
+second.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's that's my that's the units. And
+
+ align:start position:0%
+That's that's my that's the units. And
+ 
+
+ align:start position:0%
+That's that's my that's the units. And
+units truly are important to keep track.
+
+ align:start position:0%
+units truly are important to keep track.
+ 
+
+ align:start position:0%
+units truly are important to keep track.
+O omega that's omega radians per second
+
+ align:start position:0%
+O omega that's omega radians per second
+ 
+
+ align:start position:0%
+O omega that's omega radians per second
+when I multiply by the period the t in
+
+ align:start position:0%
+when I multiply by the period the t in
+ 
+
+ align:start position:0%
+when I multiply by the period the t in
+seconds I get 2 pi radians okay now in
+
+ align:start position:0%
+seconds I get 2 pi radians okay now in
+ 
+
+ align:start position:0%
+seconds I get 2 pi radians okay now in
+engineers and in everyday use there's
+
+ align:start position:0%
+engineers and in everyday use there's
+ 
+
+ align:start position:0%
+engineers and in everyday use there's
+another frequency
+
+ align:start position:0%
+another frequency
+ 
+
+ align:start position:0%
+another frequency
+called f for frequency probably okay so
+
+ align:start position:0%
+called f for frequency probably okay so
+ 
+
+ align:start position:0%
+called f for frequency probably okay so
+f you should know about f
+
+ align:start position:0%
+f you should know about f
+ 
+
+ align:start position:0%
+f you should know about f
+and its frequency is in hertz. So f is
+
+ align:start position:0%
+and its frequency is in hertz. So f is
+ 
+
+ align:start position:0%
+and its frequency is in hertz. So f is
+measured in hertz.
+
+ align:start position:0%
+measured in hertz.
+ 
+
+ align:start position:0%
+measured in hertz.
+H e r tz.
+
+ align:start position:0%
+H e r tz.
+ 
+
+ align:start position:0%
+H e r tz.
+H er tz
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+named after the guy, not the tomato
+
+ align:start position:0%
+named after the guy, not the tomato
+ 
+
+ align:start position:0%
+named after the guy, not the tomato
+uh ketchup guy, but the Oh, that's
+
+ align:start position:0%
+uh ketchup guy, but the Oh, that's
+ 
+
+ align:start position:0%
+uh ketchup guy, but the Oh, that's
+hints. Anyway, sorry about that. Uh
+
+ align:start position:0%
+hints. Anyway, sorry about that. Uh
+ 
+
+ align:start position:0%
+hints. Anyway, sorry about that. Uh
+Herz,
+
+ align:start position:0%
+Herz,
+ 
+
+ align:start position:0%
+Herz,
+not the car. That's what I was trying to
+
+ align:start position:0%
+not the car. That's what I was trying to
+ 
+
+ align:start position:0%
+not the car. That's what I was trying to
+say. but the the German guy who
+
+ align:start position:0%
+say. but the the German guy who
+ 
+
+ align:start position:0%
+say. but the the German guy who
+was involved early with this stuff. So
+
+ align:start position:0%
+was involved early with this stuff. So
+ 
+
+ align:start position:0%
+was involved early with this stuff. So
+what is f?
+
+ align:start position:0%
+what is f?
+ 
+
+ align:start position:0%
+what is f?
+F is
+
+ align:start position:0%
+F is
+ 
+
+ align:start position:0%
+F is
+one. F * t is one. Instead of dealing
+
+ align:start position:0%
+one. F * t is one. Instead of dealing
+ 
+
+ align:start position:0%
+one. F * t is one. Instead of dealing
+with 2 pi, which counts radians, the one
+
+ align:start position:0%
+with 2 pi, which counts radians, the one
+ 
+
+ align:start position:0%
+with 2 pi, which counts radians, the one
+just counts complete loops, complete
+
+ align:start position:0%
+just counts complete loops, complete
+ 
+
+ align:start position:0%
+just counts complete loops, complete
+oscillations. So, so, so f f compared to
+
+ align:start position:0%
+oscillations. So, so, so f f compared to
+ 
+
+ align:start position:0%
+oscillations. So, so, so f f compared to
+omega uh f is smaller by a factor 2 pi.
+
+ align:start position:0%
+omega uh f is smaller by a factor 2 pi.
+ 
+
+ align:start position:0%
+omega uh f is smaller by a factor 2 pi.
+So, f * t is 1. f is 1 / t. Omega is 2
+
+ align:start position:0%
+So, f * t is 1. f is 1 / t. Omega is 2
+ 
+
+ align:start position:0%
+So, f * t is 1. f is 1 / t. Omega is 2
+pi / t. So, putting these together, all
+
+ align:start position:0%
+pi / t. So, putting these together, all
+ 
+
+ align:start position:0%
+pi / t. So, putting these together, all
+I'm saying is omega is 2<unk>i * f.
+
+ align:start position:0%
+I'm saying is omega is 2<unk>i * f.
+ 
+
+ align:start position:0%
+I'm saying is omega is 2<unk>i * f.
+So when we say we're getting 60 cycles,
+
+ align:start position:0%
+So when we say we're getting 60 cycles,
+ 
+
+ align:start position:0%
+So when we say we're getting 60 cycles,
+so that's what I would measure TF in. FF
+
+ align:start position:0%
+so that's what I would measure TF in. FF
+ 
+
+ align:start position:0%
+so that's what I would measure TF in. FF
+would be in cycles
+
+ align:start position:0%
+would be in cycles
+ 
+
+ align:start position:0%
+would be in cycles
+is cycles
+
+ align:start position:0%
+is cycles
+ 
+
+ align:start position:0%
+is cycles
+per second.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+One cycle, 2 pi radians.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This isn't big heavy math, but it's more
+
+ align:start position:0%
+This isn't big heavy math, but it's more
+ 
+
+ align:start position:0%
+This isn't big heavy math, but it's more
+important than a lot of math just to get
+
+ align:start position:0%
+important than a lot of math just to get
+ 
+
+ align:start position:0%
+important than a lot of math just to get
+these
+
+ align:start position:0%
+these
+ 
+
+ align:start position:0%
+these
+letters straight. So there's capital T,
+
+ align:start position:0%
+letters straight. So there's capital T,
+ 
+
+ align:start position:0%
+letters straight. So there's capital T,
+the period, and two measures of
+
+ align:start position:0%
+the period, and two measures of
+ 
+
+ align:start position:0%
+the period, and two measures of
+frequency. One is omega in radians per
+
+ align:start position:0%
+frequency. One is omega in radians per
+ 
+
+ align:start position:0%
+frequency. One is omega in radians per
+second, and the other is F in cycle,
+
+ align:start position:0%
+second, and the other is F in cycle,
+ 
+
+ align:start position:0%
+second, and the other is F in cycle,
+full cycles per second. So one is 2 pi
+
+ align:start position:0%
+full cycles per second. So one is 2 pi
+ 
+
+ align:start position:0%
+full cycles per second. So one is 2 pi
+times the other. Good. Okay. And we have
+
+ align:start position:0%
+times the other. Good. Okay. And we have
+ 
+
+ align:start position:0%
+times the other. Good. Okay. And we have
+this. Okay. I think we're uh
+
+ align:start position:0%
+this. Okay. I think we're uh
+ 
+
+ align:start position:0%
+this. Okay. I think we're uh
+we've got the key ideas here then for
+
+ align:start position:0%
+we've got the key ideas here then for
+ 
+
+ align:start position:0%
+we've got the key ideas here then for
+unforced motion pure oscillation going
+
+ align:start position:0%
+unforced motion pure oscillation going
+ 
+
+ align:start position:0%
+unforced motion pure oscillation going
+on forever.
+
+ align:start position:0%
+on forever.
+ 
+
+ align:start position:0%
+on forever.
+And uh let me just
+
+ align:start position:0%
+And uh let me just
+ 
+
+ align:start position:0%
+And uh let me just
+write what I already mentioned. A
+
+ align:start position:0%
+write what I already mentioned. A
+ 
+
+ align:start position:0%
+write what I already mentioned. A
+different way to express y would be with
+
+ align:start position:0%
+different way to express y would be with
+ 
+
+ align:start position:0%
+different way to express y would be with
+small c's
+
+ align:start position:0%
+small c's
+ 
+
+ align:start position:0%
+small c's
+e to the i omega n t and c2 e to the
+
+ align:start position:0%
+e to the i omega n t and c2 e to the
+ 
+
+ align:start position:0%
+e to the i omega n t and c2 e to the
+minus i omega n t. All I'm saying is
+
+ align:start position:0%
+minus i omega n t. All I'm saying is
+ 
+
+ align:start position:0%
+minus i omega n t. All I'm saying is
+that this form with exponentials
+
+ align:start position:0%
+that this form with exponentials
+ 
+
+ align:start position:0%
+that this form with exponentials
+is is entirely equivalent to this form
+
+ align:start position:0%
+is is entirely equivalent to this form
+ 
+
+ align:start position:0%
+is is entirely equivalent to this form
+with cosine and sign.
+
+ align:start position:0%
+with cosine and sign.
+ 
+
+ align:start position:0%
+with cosine and sign.
+That form allows me two constants
+
+ align:start position:0%
+That form allows me two constants
+ 
+
+ align:start position:0%
+That form allows me two constants
+capital C1 and C2. This form allows me
+
+ align:start position:0%
+capital C1 and C2. This form allows me
+ 
+
+ align:start position:0%
+capital C1 and C2. This form allows me
+two constants little one and C C2. And
+
+ align:start position:0%
+two constants little one and C C2. And
+ 
+
+ align:start position:0%
+two constants little one and C C2. And
+from that I have that. From this I have
+
+ align:start position:0%
+from that I have that. From this I have
+ 
+
+ align:start position:0%
+from that I have that. From this I have
+this. So So we really do have
+
+ align:start position:0%
+this. So So we really do have
+ 
+
+ align:start position:0%
+this. So So we really do have
+exponentials here. And the key message
+
+ align:start position:0%
+exponentials here. And the key message
+ 
+
+ align:start position:0%
+exponentials here. And the key message
+is that for pure oscillation those
+
+ align:start position:0%
+is that for pure oscillation those
+ 
+
+ align:start position:0%
+is that for pure oscillation those
+exponentials are pure imaginary exponent
+
+ align:start position:0%
+exponentials are pure imaginary exponent
+ 
+
+ align:start position:0%
+exponentials are pure imaginary exponent
+i omega nt. Okay that's the best example
+
+ align:start position:0%
+i omega nt. Okay that's the best example
+ 
+
+ align:start position:0%
+i omega nt. Okay that's the best example
+the simplest example the first example.
+
+ align:start position:0%
+the simplest example the first example.
+ 
+
+ align:start position:0%
+the simplest example the first example.
+Thanks.
\ No newline at end of file
diff --git a/xgUCzL3TD1g.txt b/xgUCzL3TD1g.txt
new file mode 100644
index 0000000000000000000000000000000000000000..244575924159079a09c7adc8aa48656f113a5e50
--- /dev/null
+++ b/xgUCzL3TD1g.txt
@@ -0,0 +1,2031 @@
+The following content is
+provided under a Creative
+
+Commons license.
+
+Your support will help MIT
+OpenCourseWare continue to
+
+offer high quality educational
+resources for free.
+
+To make a donation or view
+additional materials from
+
+hundreds of MIT courses, visit
+MIT OpenCourseWare at
+
+ocw.mit.edu.
+
+PROFESSOR: So, last time we
+started in on a discussion of
+
+a new topic, with was
+statistical mechanics.
+
+So what we're trying to do now
+is revisit the thermodynamics
+
+that we've spent most of the
+term deriving and trying to
+
+use in a microscopic approach.
+
+So our hope is to be able to
+start with a microscopic model
+
+of matter, starting with atoms
+and molecules that we
+
+know are out there.
+
+And formulate thermodynamics
+starting from that microscopic
+
+point of view.
+
+In contrast to the way it was
+first formulated historically,
+
+and the way we've presented it
+also, which is as an entirely
+
+empirical subject based on
+macroscopic observation and
+
+deduction from that.
+
+So, we looked at the
+probabilities that states with
+
+different energies would be
+occupied and we inferred that
+
+there would be a simple way to
+describe the distribution of
+
+atoms or molecules in states
+of different levels.
+
+First of all, although I didn't
+state it explicitly,
+
+essentially assumed there is
+that if I've got a bunch of
+
+molecules, and I've got states
+that they could be in of equal
+
+energy, then the probability
+that they would be in one or
+
+another of those states
+is the same.
+
+If the energies of the states
+are equal, the probabilities
+
+that those states will
+be occupied.
+
+That they'll be populated by
+molecules, will be equal.
+
+And then we deduced what's
+called the Boltzmann
+
+probability distribution.
+
+Which says that the probability
+that a molecular
+
+state, i, will be occupied is
+proportional to e to the minus
+
+Ei over kT, where little
+Ei is the energy of
+
+that molecular state.
+
+And then realizing that the
+probability that some state
+
+out there has to be occupied,
+we saw that of course if we
+
+sum over all these probabilities
+that sum has to
+
+equal one, right?
+
+In other words, the sum
+over all of i of P of
+
+i is equal to one.
+
+So that means that we could
+write not just that this is
+
+proportional to this, but we
+could write that Pi is equal
+
+to e to the minus Ei over
+kT divided by the
+
+sum of all such terms.
+
+So now we know how to figure
+out how likely it is that a
+
+certain state is occupied.
+
+And what it means is, let's say
+we have a whole bunch of
+
+states whose energy is pretty
+low compared to kT. kT, the
+
+Boltzmann constant times
+temperature is energy units.
+
+So if it's pretty warm, maybe
+it's room temperature, maybe
+
+it's warmer.
+
+And there are a whole lot of
+states that are accessible
+
+because the energies
+are less than kT.
+
+What does that mean?
+
+That means that you could put a
+bunch of different i's here
+
+whose energies are all quite
+low compared to kT.
+
+And they'll all have significant
+probabilities.
+
+Now let's decrease the energy.
+
+Go to cold temperature.
+
+So kT becomes really small.
+
+So that e to the minus energy
+over kT starts to, if this
+
+gets to be bigger than kT by a
+lot, then this whole thing is
+
+a very small number.
+
+Suddenly, you get very few
+states accessible.
+
+So if we just plot this
+distribution, of course it's
+
+easy to do, it's just a
+decaying exponential.
+
+So Pi, which is a
+function of Ei.
+
+It just looks like this.
+
+And here are a bunch
+of states.
+
+And if we have a classical
+mechanics picture of matter,
+
+then there would just be
+continuous states.
+
+And if we have a quantum
+mechanical picture of matter,
+
+there might be individual states
+with gaps in between
+
+the energies.
+
+Either way, what happens, what
+this is saying is, if we go
+
+out to higher and higher
+energies, then you have a
+
+smaller and smaller probability
+to be in
+
+a state like that.
+
+And if you go to low energies,
+the probability gets bigger.
+
+And it depends on temperature.
+
+Because it's the ratio between
+the energy and kT that
+
+dictates the size
+of that term.
+
+So let's say this is moderate
+temperature.
+
+If we go to low temperature, it
+might look more like this.
+
+Hardly any states can be
+occupied because even states
+
+of rather moderate energies,
+suddenly now those energies
+
+are much bigger than kT.
+
+In other words, kT is measuring
+thermal energy.
+
+It's saying there's not enough
+thermal energy to populate, to
+
+knock things into states
+whose energy is
+
+much higher than that.
+
+So you have a very precipitous
+decay.
+
+If you go to the other
+extreme, of very high
+
+temperature, then this will
+tend to flatten out.
+
+Eventually it'll decay, but
+it may take a long time.
+
+Because now kT is enormous.
+
+So the energy has to
+get to be very big.
+
+Before it's bigger than kT.
+
+And as long as it
+isn't, then this
+
+exponential term is not small.
+
+So there be a whole bunch of
+states that may be occupied.
+
+In other words, a whole bunch
+of states that are thermally
+
+accessible at equilibrium.
+
+Systems at thermal equilibrium,
+molecules are
+
+getting knocked around
+with whatever
+
+thermal energy is available.
+
+Crashing into each other or into
+the walls of a vessel.
+
+And there'll be a distribution
+of molecular energies.
+
+And that distribution is skewed
+either low or high
+
+depending on the temperature.
+
+So that's what that
+distribution, the Boltzmann
+
+distribution, is telling us.
+
+This is often called a Boltzmann
+factor, because it's
+
+telling what the population of
+some particular state is.
+
+OK.
+
+Now, this is just dealing with
+individual molecule states.
+
+Then we said, OK, what about
+the whole system?
+
+Well, the same kind of relation
+holds there, too.
+
+In other words, if these are
+individual molecule energies,
+
+now if I look at the entire
+system, right well, still,
+
+there's no reason that same
+distribution doesn't hold.
+
+And it does.
+
+So in other words, Pi of Ei,
+that's the whole system
+
+energy, is e to the minus Ei
+over kT, over the sum over i,
+
+Ei over kT.
+
+Now, this i doesn't refer to
+a single molecule state.
+
+We're talking about
+a whole system.
+
+It might be a mole of atoms or
+molecules in the gas phase, or
+
+what have you.
+
+It refers to a system state
+where the energy, the state of
+
+every one of those atoms or
+molecules is specified.
+
+So this is a system
+microstate.
+
+Every molecular state
+is specified.
+
+So for a mole of stuff, that
+means there might be 10 to the
+
+24 or so molecular states that
+this single subscript is
+
+indicating.
+
+But the point is, those
+states exist.
+
+They have a total energy.
+
+What's the probability that the
+whole system will be in
+
+such a state?
+
+Still going to be proportional
+to the total system energy.
+
+It turns out that these
+summations end up taking on an
+
+enormous importance in
+statistical mechanics.
+
+And the reason is, as we'll see
+shortly, it turns out that
+
+every single macroscopic
+thermodynamic function can be
+
+derived by knowing just that.
+
+Just these sums, what are called
+partition functions.
+
+So of course they take on
+enormous importance.
+
+So, we call them partition
+functions because what they're
+
+doing is, they're indicating
+how the molecules are
+
+partitioned among the different
+available levels.
+
+The molecules or
+a whole system.
+
+So the molecular partition
+function is labeled little q.
+
+And the system partition
+function is labeled big Q.
+
+It's called the canonical
+partition function.
+
+And because they are going
+to take on such special
+
+importance, let's just look at
+some of their properties for
+
+different kinds of systems
+and in general.
+
+OK, first of all, let's talk
+about units and values.
+
+They are unitless.
+
+This is an exponential
+function.
+
+Here are units of energy
+and energy.
+
+But this is a unitless
+was number.
+
+It's just some number, right?
+
+Could be 1.
+
+Could be 10.
+
+Could be 50.
+
+Whatever, right?
+
+Could be 10 to the 24.
+
+Its magnitude tells you about
+more or less how many states
+
+are thermally accessible.
+
+Because, look at it.
+
+And then go back to the example
+that I showed you if
+
+lots of these terms are big, are
+significant because this
+
+is really a big number, right?
+
+It's really hot.
+
+So lots of states have energies
+lower than kT, which
+
+means this is not too small, for
+lots and lots of values of
+
+i, then this just
+keeps adding up.
+
+And of course, same here.
+
+So the number might
+be very large.
+
+But if we're in the low
+temperature limit, maybe we're
+
+in such low temperature that
+only the lowest possible state
+
+is occupied.
+
+And everything else,
+it's just too cold.
+
+There's not enough thermal
+energy to occupy anything but
+
+the very lowest state
+available.
+
+Well, in that case the lowest
+state, this would be one.
+
+Essentially we could
+label this zero.
+
+We could put the energy, the
+zero of energy there.
+
+Everything else is really big
+compared to kT, which means
+
+this exponential gets to be a
+really small number for every
+
+state except one.
+
+And this is just equal to one.
+
+In other words, the magnitude
+of these numbers tells us
+
+about how many states are
+accessible, thermally
+
+accessible, to molecules
+or to a whole system.
+
+So let's just go through a
+couple of specific examples to
+
+try to make that a little
+more concrete.
+
+One is, let's start in
+the simplest case.
+
+Which it'll turn out
+I just alluded to.
+
+Let's consider a perfect atomic
+crystal at essentially
+
+zero degrees Kelvin.
+
+Zero Kelvin.
+
+So every atom.
+
+Or even if it's a molecular
+crystal, every molecule,
+
+they're all in the
+ground state.
+
+There's no excess
+thermal energy.
+
+Every molecule is in
+its proper place.
+
+Every atom, if it's
+an atomic lattice.
+
+In other words, it's in
+the ground state.
+
+That's it.
+
+So again, we can place the
+zero where we like.
+
+We'll place it there.
+
+That one, for that one state,
+this will be equal to one.
+
+And for everything else
+it'll be zero.
+
+So Q is just the sum of e
+to the minus Ei over kT.
+
+It's equal to e to the minus
+zero over kT plus e to the
+
+minus E1 over kT plus e to
+the minus E2 over kT.
+
+But remember, T is
+really tiny.
+
+It's almost zero
+degrees Kelvin.
+
+So all these things are
+much bigger than that.
+
+So this is vanishingly small.
+
+This is vanishingly small.
+
+The whole thing is approximately
+equal to one.
+
+That's it.
+
+Also, if we say OK, now what's
+the probability of the system
+
+being in a particular state.
+
+Well, we have an expression
+for that.
+
+So let's look at P0.
+
+It's e to the minus E0
+over kT over the sum.
+
+Which we've just seen.
+
+So it's e to the minus E0 over
+to kT divided by e to the
+
+minus E0 over kT plus e to the
+minus E1 over kT, and so on.
+
+This is the only term
+that's significant.
+
+So it's approximately
+equal to one.
+
+Now, while I've got this written
+here, let's just make
+
+sure we've got something
+clear.
+
+What if we hadn't arbitrarily
+set the zero of
+
+energy equal to zero?
+
+I mean, it's arbitrary, right?
+
+We can put the zero of
+energy anywhere.
+
+And you might think, well, gee
+that's going to have a big
+
+effect on everything.
+
+Well, it would have an effect
+on the actual number that we
+
+get for Q. But what you'll see
+is that any measurable
+
+quantity that we calculate
+won't be affected.
+
+It's only the zero of the energy
+scale that's going to
+
+be affected.
+
+So for example, let's look
+at this probability.
+
+It doesn't matter where we
+put the zero of energy.
+
+This term is still going
+to be enormously bigger
+
+then the next one.
+
+And the next one.
+
+And the next one.
+
+So in this sum only this term
+is going to matter.
+
+It's going to cancel
+with this term.
+
+So whether or not these
+individual terms are equal to
+
+one, which happens if we set
+this to zero, or whether
+
+they're equal to some
+other number.
+
+Still, the probability that the
+system is in the lowest
+
+state is one, right?
+
+That doesn't depend on where we
+arbitrarily put the zero of
+
+the energy scale.
+
+The state is still going to
+be in the ground state, at
+
+essentially zero
+degrees Kelvin.
+
+And it'll turn out to be that
+way with any property that we
+
+can measure.
+
+Only the zero of this scale
+moves if we arbitrarily move
+
+it somewhere.
+
+But the observable, measurable
+quantities that we calculate,
+
+they won't change.
+
+Other than that scale.
+
+So that's one simple example.
+
+Now let's look at
+another example.
+
+Let's consider a mole of atoms,
+roaming around in the
+
+gas phase at room temperature.
+
+OK, so now what I want to do
+is just have a simple model
+
+for their translational
+motion.
+
+And of course, we could
+do that either quantum
+
+mechanically or classically
+solve for that.
+
+We're going to use an
+even simpler model.
+
+And this model is going to be
+very, very useful for a lot of
+
+the things that we'll treat.
+
+It's called a lattice model.
+
+All it means is, we're
+going to divide up
+
+the available volume.
+
+This room, for example,
+into zillions
+
+of tiny little elements.
+
+Little volume elements.
+
+Each one about the
+size of an atom.
+
+The idea being, we're going to
+specify the state of the atom
+
+by saying where is it.
+
+Is it in this lattice sight,
+in this one, in this
+
+one, in this one.
+
+So it's a lattice model.
+
+Might be an atom there.
+
+Might be one there.
+
+So we're going to divide
+the volume up.
+
+So let's call our atomic volume
+little v. Our total
+
+volume big V. And an atomic
+volume, it's going to be on
+
+the order of 1 angstroms
+cubed.
+
+Or 10 to the minus
+30 meters cubed.
+
+And our room, our volume
+macroscopic one, might be on
+
+the order of one meter cubed.
+
+Ordinary sort of size.
+
+So now let's figure out our
+molecular partition function.
+
+Now, implicit in this, we're
+basically saying that the
+
+energy, the translational
+energy, is basically zero.
+
+In other words, all these states
+have the same energy.
+
+They're just located in
+different positions.
+
+At any given instant of time.
+
+And what that means is all
+these terms, all these
+
+Boltzmann factors, we just
+set them equal to one.
+
+We'll set the zero of energy
+there, be done with it.
+
+It's a simple model.
+
+But it's going to give us the
+right order of magnitude that
+
+we're after.
+
+So, how many states are there
+that are accessible?
+
+Well, on the order of 10
+to the 30th, right?
+
+So q, little q, we'll call it
+little q translational, it's
+
+just discussing where
+things are.
+
+Is on the order of
+10 to the 30th.
+
+And if we do a more careful
+treatment, if we treat the
+
+translational energy of atoms,
+either classically or quantum
+
+mechanically and solve it.
+
+We'll still get, we still
+do get, about the
+
+same order of magnitude.
+
+Now let's treat the
+whole system.
+
+So, what happens?
+
+What are our total
+possible states?
+
+Because we have to add this up
+for every possible state.
+
+Well, let's start with
+the first atom.
+
+It has to be somewhere.
+
+It has 10 to the 30th
+possibilities for
+
+where it can be.
+
+Let's start with the
+second atom.
+
+And put it somewhere.
+
+Well, it has 10 to the 30th
+minus one, which is still
+
+pretty close to 10
+to the 30th.
+
+Let's let's go to
+the third atom.
+
+And the fourth.
+
+If we have about a mole of
+atoms, let's say 10 to the
+
+24th atoms, that's still going
+to occupy a very small
+
+fraction of the site.
+
+Only one in a million.
+
+So we don't have to keep
+careful track.
+
+Every one of them, we can just
+say, look, there are 10 to the
+
+30th available sites.
+
+Because we're not going to worry
+about a change in one in
+
+a millionth.
+
+So what that means is, capital
+Q, trans for the system, is 10
+
+to the 30th times
+10 to the 30th.
+
+In other words, let's now
+take the whole state.
+
+Well, I could put
+atom one here.
+
+I have 10 to the 30th
+possibilities.
+
+Atom two, I can put
+anywhere else.
+
+So the joint probability of
+that particular state, for
+
+just the two atoms, is 10th to
+the 30th times 10 to the 30th.
+
+It's 10 to the 30th squared.
+
+So this is going
+to keep going.
+
+It's going to be 10 to the
+30th to the Nth power.
+
+Where N is the number
+of atoms, which
+
+is 10 of the 24th.
+
+Huge number, right?
+
+It is a huge number.
+
+And that, too, if we treat the
+whole thing classically or
+
+quantum mechanically and
+work it all out.
+
+We'll get that number.
+
+Or something on that order.
+
+Because you know there really
+is a simply astronomical
+
+number of states accessible to
+the whole bunch of atoms or
+
+molecules in this room.
+
+It really is that big.
+
+So in other words, capital
+Q is just an
+
+astronomical number.
+
+And it is the case.
+
+OK.
+
+There's an important
+sort of nuance
+
+that we need to introduce.
+
+And it's the following.
+
+Turns out, it is an astronomical
+number.
+
+But a tiny bit less astronomical
+than what I've
+
+treated so far would indicate.
+
+So let's look a little
+more carefully.
+
+What I've said is that Q
+translational is little q
+
+translational, that is, that
+10 to the 30th number.
+
+To the Nth power.
+
+But there's one failing here.
+
+Which is, when I got that, when
+I decided that if I have
+
+just the first two atoms I've
+got 10th to the 30th times 10
+
+to the 30th possible states, the
+trouble with that is then
+
+if I keep counting all the
+possible atoms starting with
+
+each one, I'll double-count
+it, right?
+
+In other words, what if I
+interchange those two atoms?
+
+Well, those states are
+identical, right?
+
+Indistinguishable.
+
+And it's only distinguishable
+states that count.
+
+When you specify these
+things, these are
+
+indicating distinct states.
+
+In some way, at least in
+
+principle, measurably different.
+
+If the atom's are identical, in
+other words, if it's a mole
+
+of the same stuff, I don't have
+a way of distinguishing
+
+between those two.
+
+I have to correct for that.
+
+And when I come to the third
+atom, I have to correct for
+
+all the possible interchanges.
+
+Of course, it's three
+factorial.
+
+And in general, it's
+N factorial.
+
+So this result needs
+to be modified.
+
+This is true for distinguishable
+particles.
+
+In other words, if I had all
+different atoms, so I could
+
+label them all, then I don't
+have that correction.
+
+Because then there's really a
+difference between that state
+
+and the state with the two
+atoms interchanged.
+
+But if it's a mole of identical
+atoms, that's no
+
+longer the case.
+
+So then, Q translational is
+little q translational to the
+
+N power divided by
+N factorial.
+
+It's still going to be an
+absolutely enormous number.
+
+But it's going to be a little
+less absolutely enormous than
+
+it was a minute ago.
+
+Now finally, I just want
+to introduce a handy
+
+approximation to N factorial
+that's going to turn out to be
+
+very useful again and again.
+
+And that's called Stirling's
+approximation.
+
+For the log of a big number,
+ln N factorial is N log N
+
+minus N. If we take e to those,
+both sides, then we
+
+find that N factorial is equal
+to e to the minus N
+
+N to the nth power.
+
+So this, then, is approximately
+equal to q
+
+translational to
+the Nth power.
+
+Over N to the N times e to the
+minus N. Now let's put the
+
+numbers back in.
+
+There's our 10 to the 30th to
+the 10 to the 24th power.
+
+And now we're going to diminish
+that just a bit.
+
+It's N to the Nth power.
+
+So it's 10 to the 24th to the
+10 to the 24th power.
+
+Times e to the minus 10
+to the 24th power.
+
+So, we can cancel
+something here.
+
+So we have 10 to the 6th to the
+10 to the 24th power times
+
+e to the 10 to the 24th
+power. e is about 10
+
+to the 0.4th power.
+
+So this whole thing is about 10
+to the 6.4th power to the
+
+10 to the 24th power
+It's still a
+
+pretty respectable number.
+
+You could still say
+astronomical.
+
+But maybe astronomical,
+but not quite to
+
+the edge of the universe.
+
+Whereas the one before maybe hit
+the edge of the universe
+
+and then beyond.
+
+So that's our second example.
+
+And again, part of what I'm
+trying to do here is just
+
+introduce some ideas.
+
+Things like this
+way of modeling
+
+positions and so forth.
+
+But also, again, orders
+of magnitude.
+
+How big are these numbers.
+
+For different sorts
+of systems.
+
+So let's do one more example.
+
+Now, let's consider a
+polymer in a liquid.
+
+And it has different
+configurations.
+
+And they might be a little
+bit different in energy.
+
+For example, some configurations
+might bring
+
+neighboring regions of the
+polymer into proximity where
+
+they could hydrogen bond.
+
+And the point is that then the
+molecular energies involved
+
+will change a little bit.
+
+Because of some sorts of
+interactions that are possible
+
+in some configurations.
+
+And not in other
+configurations.
+
+So what I'm trying to do is
+introduce a very simple
+
+framework through which we
+might be able to look at
+
+things like protein folding,
+or DNA hydrogen bonding.
+
+Things like this.
+
+And just in a simple way model
+how those work and what the
+
+forces are that drive them.
+
+So we'll think about polymer
+configurations.
+
+So let's look at a few
+configurations.
+
+Here is going to be one.
+
+I'm going to label
+this one here.
+
+And then here are
+a few others.
+
+So I've labeled them this way
+so that you can see how they
+
+are distinct from each other.
+
+This one would have a possible
+interaction.
+
+So we'll label its energy.
+
+So this is molecular state
+i, here's going to
+
+be our energy, Ei.
+
+And let's call this one
+negative e int, for an
+
+interaction energy
+that's favorable.
+
+And these will be zero.
+
+Let's just put that there.
+
+Zero, zero, zero.
+
+And let's also indicate
+the degeneracy.
+
+How many states, different
+states are there
+
+with the same energy.
+
+And that's called gi.
+
+And here it's one.
+
+And here are these three.
+
+So that's the framework
+of our model.
+
+Well, so what's our molecular
+partition function for this
+
+configurational degree
+of freedom?
+
+Well, we can label it little
+q configurational.
+
+So we're going to sum over these
+states. e to the minus
+
+Ei for the different
+configurations over kT.
+
+So it's e to the
+e int over kT.
+
+Plus three times e to the zero
+over kT, we'll get all those
+
+other three terms.
+
+So that's it.
+
+It's e to the e int over
+kT plus three.
+
+Remember, the interaction energy
+is negative e int.
+
+It's a favorable interaction.
+e int is a positive number.
+
+So that's our result.
+
+Now we've described the
+probabilities in terms of the
+
+states that can be occupied.
+
+That is, we've added it up.
+
+But of course, even the way
+I wrote it just out of
+
+convenience, I didn't
+actually write out
+
+each term in the sum.
+
+In the notes I actually
+did that.
+
+But of course it's not necessary
+to write e to the
+
+zero over kT plus e to the zero
+over kT and write that
+
+three times for each
+of these three.
+
+Rather, it's convenient to
+group them together.
+
+And the point I'm illustrating
+here is that in our
+
+expression, for the partition
+function, we've written that
+
+in terms of the individual
+states.
+
+But we doing a sum over the
+individual molecular states.
+
+But we could also sum
+over energy levels.
+
+Including the degeneracy.
+
+So we could say, let's not do
+the sum over every state.
+
+After all, what if there are a
+hundred states that had the
+
+same energy.
+
+Rather than just three.
+
+Gets to be kind of
+painful, right?
+
+Instead let's just sum
+over energy levels.
+
+They're all going to be the
+same factor anyway.
+
+And then we'll have, we'll
+just explicitly write the
+
+degeneracy in there.
+
+So, we can write the partition
+function as a
+
+sum over energy level.
+
+So, in other words q is the
+sum over i, e to the
+
+minus Ei over kT.
+
+That's individual molecular
+states i.
+
+But we also could write it as
+the sum over i, where this now
+
+is molecular energy levels i.
+
+And then we need to incorporate
+the degeneracy gi
+
+e to the minus Ei over kT.
+
+Same thing, of course.
+
+But again, sometimes much
+more convenient to
+
+write things this way.
+
+And of course, we can write
+the probabilities of the
+
+occupancies in the
+same way, too.
+
+That is, we could talk about the
+Pi in terms of individual
+
+states. e to the minus Ei over
+kT over q, the whole sum.
+
+Or Pi summing over energy
+levels, gi e to the minus Ei
+
+over kT, divided by q.
+
+Here, of course, this
+is bigger if
+
+it's degenerate, right?
+
+It's saying that the probability
+of being in this
+
+energy level is three times the
+probability of it being in
+
+any individual one
+of the states.
+
+But sometimes it's useful
+to keep track of
+
+things in this way.
+
+What it shows you too is that,
+remember when we looked at,
+
+did I erase it?
+
+I guess it's gone.
+
+When we looked at this
+probability distribution for
+
+the occupancies of the levels,
+of course, what it says is at
+
+any temperature, the lowest
+level is the most probable.
+
+For intermediate temperatures.
+
+For low temperatures, for
+high temperatures.
+
+At high temperature, it might be
+only a little more probable
+
+than the next one over, and the
+next one, and so forth.
+
+But the very lowest state
+always has the highest
+
+probability.
+
+But the lowest energy doesn't
+always have the highest
+
+probability because
+of degeneracies.
+
+There might be many states
+with an energy up here.
+
+And the probability of any one
+of them is only a little lower
+
+than the probability of
+the lowest energy.
+
+That could be the case here.
+
+Let's say, the interaction
+energy
+
+isn't enormously strong.
+
+So there is some energetic
+favoring of this state.
+
+Maybe there are 10% at
+room temperature.
+
+Maybe it turns out there are 10%
+more molecules like this
+
+than in any one of
+these states.
+
+But of course, these three
+altogether mean that there are
+
+many more molecules at
+this energy than
+
+at the lowest energy.
+
+Now of course we could do the
+same thing for the canonical
+
+partition function.
+
+Not just the molecular one.
+
+So in other words, capital Q sum
+over i system microstates.
+
+e to the minus capital
+Ei over kT.
+
+But we could also write it
+as a sum over energies.
+
+Sum over system energies.
+
+Ei.
+
+And then we have to include
+the degeneracy.
+
+Capital Omega i e to the
+minus Ei over kT.
+
+Degeneracy of the system
+energy Ei.
+
+Little g here is the
+degeneracy of
+
+molecular energy Ei.
+
+Now, same form.
+
+Just an important difference,
+though.
+
+This number, this little gi, is
+typically a small number.
+
+It could be one, it
+could be a few.
+
+This number is usually
+astronomical.
+
+That's basically, that is,
+what we calculated here.
+
+In other words, how many total
+system states are there with a
+
+particular energy.
+
+Well, in many, many, many
+cases the answer is some
+
+astronomical number.
+
+So this number might often
+be between one and ten.
+
+This number might be
+10 to the 24th.
+
+It might be 10 to the 24th
+to a large power.
+
+And, of course, that has a big
+effect on the way things end
+
+up working.
+
+In statistical mechanics
+and in thermodynamics.
+
+A lot of thermodynamics results
+are the way they are
+
+because you have so many
+possible states with a
+
+particular energy.
+
+That that energy can be strongly
+favored just by
+
+virtue of the number of
+states that there are.
+
+Just the way, in a very small
+way, this energy might be
+
+favored just because there are
+more states with it then there
+
+are states here.
+
+But again, with the
+system, it's not a
+
+factor of three to one.
+
+It might be a factor of
+10 to the 24th to
+
+the power of something.
+
+It might be just enormously
+larger than other
+
+possibilities that'll tend
+to put the energy
+
+at a certain place.
+
+And just to continue, of course,
+the same thing goes
+
+for the system probabilities.
+
+Pi, right, which is e to the
+minus Ei over kT divided by
+
+capital Q. If this is a sum over
+states, or omega i e to
+
+the minus Ei over kT over Q,
+let's write this over, if now
+
+we're calculating
+the probability
+
+of an energy level.
+
+And it's important to make
+the distinction.
+
+Because in many cases, that's
+what we care about.
+
+What's the energy
+of the system?
+
+And we often don't care about
+exactly where's that molecule
+
+and that one, and that one,
+and that one, right?
+
+The individual states that might
+be involved that would
+
+comprise that energy.
+
+Now, what I want to do is start
+deriving thermodynamics.
+
+Like I promised, we're going
+to be able to derive every
+
+thermodynamic quantity
+if we just know
+
+the partition function.
+
+So now I just want
+to show that that
+
+might really be true.
+
+So, the point is that from Q
+we're going to get all of our
+
+thermodynamics.
+
+And let's start with
+the energy.
+
+Remember u, right?
+
+That's our system energy.
+
+It's an average energy.
+
+It's an average of the energy
+that we would get by looking
+
+at the states that the system
+might be occupying.
+
+So we can write it
+as a sum over i.
+
+Of Pi times Ei.
+
+In other words, it's going to be
+determined by the energy of
+
+any system state times the
+probability that the system is
+
+in that state.
+
+Add them all up.
+
+Well, we know what that is.
+
+It's the sum i of Ei, e to the
+minus Ei over kT divided by Q.
+
+Now, I'm going to just make
+a simple substitution.
+
+I'm going to use the term beta
+to mean one over kT.
+
+I'm really just using that so I
+don't need to use the chain
+
+rule a billion times and
+doing derivatives.
+
+So I'm going to write this is
+sum over i Ei e to the minus
+
+beta Ei over Q.
+
+So Q, then, in this term is
+just a sum over i e to the
+
+minus beta Ei.
+
+So.
+
+Now I do want to take
+some derivatives.
+
+If I take dQ / d beta, keeping
+V and N constant, then I get
+
+derivative with respect
+to beta.
+
+Sum over i e to the
+minus beta Ei.
+
+So that's going to bring
+out Ei, right?
+
+So it's going to bring out minus
+Ei minus the sum over i,
+
+Ei e to the minus beta Ei.
+
+That obviously looks
+like a handy thing.
+
+Because that looks
+like that term.
+
+Then, our average energy,
+remember, it's one over Q. Sum
+
+of i, Ei e to the
+minus beta Ei.
+
+So now, it's just minus one
+over q, dQ / d beta.
+
+So that's just the same as
+minus d log Q / d beta.
+
+And now I'm going to
+use the chain rule.
+
+So it's minus d log Q /
+dT times dT / d beta.
+
+All at constant V and N. Now I
+can easily get dT / d beta.
+
+Because d beta / dT is just
+minus one over kT squared.
+
+It's just the derivative of one
+over kT with respect to T.
+
+So finally, my average E, which
+is u, is just kT squared
+
+times d log Q / dT constant
+V, N. That's terrific.
+
+In other words, if I have an
+expression for Q, I know the
+
+partition function, and I
+can calculate it at any
+
+temperature.
+
+I just need to take log of it,
+take its derivative with
+
+respect to temperature.
+
+Multiply it by k T squared
+and I've got my energy.
+
+Not very complicated, right?
+
+So in other words, macroscopic
+thermodynamic properties come
+
+straight out of our microscopic
+model of
+
+statistical mechanics.
+
+Statistical thermodynamics.
+
+Now I'm just going to state the
+next result, just because
+
+I want to get there and it'll be
+followed up more next time.
+
+But it's the following.
+
+You can see, of course, our Q
+is a function of V and N and
+
+T. It's a function of V because
+in principle the
+
+energies that are going
+into all this can be
+
+a function of volume.
+
+What thermodynamic function
+is naturally a
+
+function of N, V, T?
+
+Who remembers?
+
+Gibbs free energy?
+
+Helmholtz free energy?
+
+Enthalpy?
+
+Which one?
+
+Nobody knows.
+
+What's a function of N, V, and
+T. Or, V and T, is what we
+
+really formulate it as.
+
+N was introduced later.
+
+The Helmholtz free energy.
+
+Thank you.
+
+What that suggests is that
+actually the simplest and most
+
+natural connection between Q and
+macroscopic thermodynamics
+
+is to the Helmholtz
+free energy.
+
+And the result that you'll see
+derived next time is A is just
+
+minus kT log of Q. What
+a simple result.
+
+And you'll see the derivations
+in your notes.
+
+You can see it's a couple
+of lines, right?
+
+But of course, if you know A,
+and you know E, you know
+
+everything, right?
+
+Because S is in there.
+
+And then other combinations
+can give S and G and mu.
+
+And p.
+
+And anything else you want.
+
+So that's the point, is that
+all of macroscopic
+
+thermodynamics follows.
+
+And you'll see that elaborated
+more next time.
+
+And in addition, a very simple
+natural expression for the
+
+entropy in terms of the states
+available follows, that we've
+
+alluded to before.
+
+And now you'll see
+it played out.
+
+Right.
\ No newline at end of file
diff --git a/ycO0Vn_w9Q0.txt b/ycO0Vn_w9Q0.txt
new file mode 100644
index 0000000000000000000000000000000000000000..672cff55debef74b6a5b43c4dcd4e680f76a49ab
--- /dev/null
+++ b/ycO0Vn_w9Q0.txt
@@ -0,0 +1,1819 @@
+align:start position:0%
+ 
+hi welcome back to recitation
+
+ align:start position:0%
+hi welcome back to recitation
+ 
+
+ align:start position:0%
+hi welcome back to recitation
+in lecture you learned about some new
+
+ align:start position:0%
+in lecture you learned about some new
+ 
+
+ align:start position:0%
+in lecture you learned about some new
+tools for computing certain limits in
+
+ align:start position:0%
+tools for computing certain limits in
+ 
+
+ align:start position:0%
+tools for computing certain limits in
+particular you learned about l'hopital's
+
+ align:start position:0%
+particular you learned about l'hopital's
+ 
+
+ align:start position:0%
+particular you learned about l'hopital's
+rule so now you have the ability to
+
+ align:start position:0%
+rule so now you have the ability to
+ 
+
+ align:start position:0%
+rule so now you have the ability to
+compute easily some limits that before
+
+ align:start position:0%
+compute easily some limits that before
+ 
+
+ align:start position:0%
+compute easily some limits that before
+might have been difficult to do so I
+
+ align:start position:0%
+might have been difficult to do so I
+ 
+
+ align:start position:0%
+might have been difficult to do so I
+have here four examples of limits some
+
+ align:start position:0%
+have here four examples of limits some
+ 
+
+ align:start position:0%
+have here four examples of limits some
+of which or maybe all of which or maybe
+
+ align:start position:0%
+of which or maybe all of which or maybe
+ 
+
+ align:start position:0%
+of which or maybe all of which or maybe
+none of which sure well definitely some
+
+ align:start position:0%
+none of which sure well definitely some
+ 
+
+ align:start position:0%
+none of which sure well definitely some
+of which will be you could use
+
+ align:start position:0%
+of which will be you could use
+ 
+
+ align:start position:0%
+of which will be you could use
+l'hopital's rule on so here they are why
+
+ align:start position:0%
+l'hopital's rule on so here they are why
+ 
+
+ align:start position:0%
+l'hopital's rule on so here they are why
+don't you pause the video take a few
+
+ align:start position:0%
+don't you pause the video take a few
+ 
+
+ align:start position:0%
+don't you pause the video take a few
+minutes to to work them out come back
+
+ align:start position:0%
+minutes to to work them out come back
+ 
+
+ align:start position:0%
+minutes to to work them out come back
+and we can work them out together
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+welcome back so we have these four
+
+ align:start position:0%
+welcome back so we have these four
+ 
+
+ align:start position:0%
+welcome back so we have these four
+limits here and let's start solving them
+
+ align:start position:0%
+limits here and let's start solving them
+ 
+
+ align:start position:0%
+limits here and let's start solving them
+shall we so I'll just go from the first
+
+ align:start position:0%
+shall we so I'll just go from the first
+ 
+
+ align:start position:0%
+shall we so I'll just go from the first
+one and then I'll I'll you know go
+
+ align:start position:0%
+one and then I'll I'll you know go
+ 
+
+ align:start position:0%
+one and then I'll I'll you know go
+through them in order so limit a is the
+
+ align:start position:0%
+through them in order so limit a is the
+ 
+
+ align:start position:0%
+through them in order so limit a is the
+limit as X goes to 1 of X to the a minus
+
+ align:start position:0%
+limit as X goes to 1 of X to the a minus
+ 
+
+ align:start position:0%
+limit as X goes to 1 of X to the a minus
+1 over X to the B minus 1 if we want to
+
+ align:start position:0%
+1 over X to the B minus 1 if we want to
+ 
+
+ align:start position:0%
+1 over X to the B minus 1 if we want to
+use l'hopital's rule we have to first
+
+ align:start position:0%
+use l'hopital's rule we have to first
+ 
+
+ align:start position:0%
+use l'hopital's rule we have to first
+check that this is a limit of an
+
+ align:start position:0%
+check that this is a limit of an
+ 
+
+ align:start position:0%
+check that this is a limit of an
+appropriate kind of expression so that's
+
+ align:start position:0%
+appropriate kind of expression so that's
+ 
+
+ align:start position:0%
+appropriate kind of expression so that's
+in particular a limit that is a 0 over 0
+
+ align:start position:0%
+in particular a limit that is a 0 over 0
+ 
+
+ align:start position:0%
+in particular a limit that is a 0 over 0
+or infinity over infinity form so an
+
+ align:start position:0%
+or infinity over infinity form so an
+ 
+
+ align:start position:0%
+or infinity over infinity form so an
+indeterminate quotient and as X goes to
+
+ align:start position:0%
+indeterminate quotient and as X goes to
+ 
+
+ align:start position:0%
+indeterminate quotient and as X goes to
+1 we see that X to the a goes to 1 so X
+
+ align:start position:0%
+1 we see that X to the a goes to 1 so X
+ 
+
+ align:start position:0%
+1 we see that X to the a goes to 1 so X
+to the a minus 1 goes to 0 and similarly
+
+ align:start position:0%
+to the a minus 1 goes to 0 and similarly
+ 
+
+ align:start position:0%
+to the a minus 1 goes to 0 and similarly
+X to the B goes to 1 so X to the B minus
+
+ align:start position:0%
+X to the B goes to 1 so X to the B minus
+ 
+
+ align:start position:0%
+X to the B goes to 1 so X to the B minus
+1 goes to 0 so indeed this is a 0 over 0
+
+ align:start position:0%
+1 goes to 0 so indeed this is a 0 over 0
+ 
+
+ align:start position:0%
+1 goes to 0 so indeed this is a 0 over 0
+indeterminate form so we can apply
+
+ align:start position:0%
+indeterminate form so we can apply
+ 
+
+ align:start position:0%
+indeterminate form so we can apply
+l'hopital's rule so we apply l'hopital's
+
+ align:start position:0%
+l'hopital's rule so we apply l'hopital's
+ 
+
+ align:start position:0%
+l'hopital's rule so we apply l'hopital's
+rule and it says that the limit as X
+
+ align:start position:0%
+rule and it says that the limit as X
+ 
+
+ align:start position:0%
+rule and it says that the limit as X
+goes to 1 of X to the a minus 1 over X
+
+ align:start position:0%
+goes to 1 of X to the a minus 1 over X
+ 
+
+ align:start position:0%
+goes to 1 of X to the a minus 1 over X
+to the B minus 1 ok so what do we do
+
+ align:start position:0%
+to the B minus 1 ok so what do we do
+ 
+
+ align:start position:0%
+to the B minus 1 ok so what do we do
+what l'hopital's rule says is we can
+
+ align:start position:0%
+what l'hopital's rule says is we can
+ 
+
+ align:start position:0%
+what l'hopital's rule says is we can
+take the the derivative of the top and
+
+ align:start position:0%
+take the the derivative of the top and
+ 
+
+ align:start position:0%
+take the the derivative of the top and
+the derivative of the bottom and then
+
+ align:start position:0%
+the derivative of the bottom and then
+ 
+
+ align:start position:0%
+the derivative of the bottom and then
+the limit of the the left side side will
+
+ align:start position:0%
+the limit of the the left side side will
+ 
+
+ align:start position:0%
+the limit of the the left side side will
+be equal to the limit of the result
+
+ align:start position:0%
+be equal to the limit of the result
+ 
+
+ align:start position:0%
+be equal to the limit of the result
+provided the the result actually has an
+
+ align:start position:0%
+provided the the result actually has an
+ 
+
+ align:start position:0%
+provided the the result actually has an
+existent limit either a real number or
+
+ align:start position:0%
+existent limit either a real number or
+ 
+
+ align:start position:0%
+existent limit either a real number or
+infinity or minus infinity so in this
+
+ align:start position:0%
+infinity or minus infinity so in this
+ 
+
+ align:start position:0%
+infinity or minus infinity so in this
+case this says that this expression is
+
+ align:start position:0%
+case this says that this expression is
+ 
+
+ align:start position:0%
+case this says that this expression is
+equal to
+
+ align:start position:0%
+equal to
+ 
+
+ align:start position:0%
+equal to
+the limits at the same limit as X goes
+
+ align:start position:0%
+the limits at the same limit as X goes
+ 
+
+ align:start position:0%
+the limits at the same limit as X goes
+to one of okay so the derivative of the
+
+ align:start position:0%
+to one of okay so the derivative of the
+ 
+
+ align:start position:0%
+to one of okay so the derivative of the
+top is a X to the a minus 1 and the
+
+ align:start position:0%
+top is a X to the a minus 1 and the
+ 
+
+ align:start position:0%
+top is a X to the a minus 1 and the
+derivative of the bottom is B X to the B
+
+ align:start position:0%
+derivative of the bottom is B X to the B
+ 
+
+ align:start position:0%
+derivative of the bottom is B X to the B
+minus 1 so l'hopital's rule says that
+
+ align:start position:0%
+minus 1 so l'hopital's rule says that
+ 
+
+ align:start position:0%
+minus 1 so l'hopital's rule says that
+these two limits are equal provided that
+
+ align:start position:0%
+these two limits are equal provided that
+ 
+
+ align:start position:0%
+these two limits are equal provided that
+the second limit exists so what is the
+
+ align:start position:0%
+the second limit exists so what is the
+ 
+
+ align:start position:0%
+the second limit exists so what is the
+second limit well we can okay we can do
+
+ align:start position:0%
+second limit well we can okay we can do
+ 
+
+ align:start position:0%
+second limit well we can okay we can do
+some simplifications here here there
+
+ align:start position:0%
+some simplifications here here there
+ 
+
+ align:start position:0%
+some simplifications here here there
+what there wasn't you know a lot of
+
+ align:start position:0%
+what there wasn't you know a lot of
+ 
+
+ align:start position:0%
+what there wasn't you know a lot of
+obvious simplifying to be done but here
+
+ align:start position:0%
+obvious simplifying to be done but here
+ 
+
+ align:start position:0%
+obvious simplifying to be done but here
+there's an obvious simplification step
+
+ align:start position:0%
+there's an obvious simplification step
+ 
+
+ align:start position:0%
+there's an obvious simplification step
+so this is equal to the limit as X goes
+
+ align:start position:0%
+so this is equal to the limit as X goes
+ 
+
+ align:start position:0%
+so this is equal to the limit as X goes
+to one of so so a over B is just a
+
+ align:start position:0%
+to one of so so a over B is just a
+ 
+
+ align:start position:0%
+to one of so so a over B is just a
+constant and now the powers of X this is
+
+ align:start position:0%
+constant and now the powers of X this is
+ 
+
+ align:start position:0%
+constant and now the powers of X this is
+X to the a minus B but as X goes to one
+
+ align:start position:0%
+X to the a minus B but as X goes to one
+ 
+
+ align:start position:0%
+X to the a minus B but as X goes to one
+X to the a minus B goes to one no matter
+
+ align:start position:0%
+X to the a minus B goes to one no matter
+ 
+
+ align:start position:0%
+X to the a minus B goes to one no matter
+what a and B are so at this point this
+
+ align:start position:0%
+what a and B are so at this point this
+ 
+
+ align:start position:0%
+what a and B are so at this point this
+isn't an indeterminate form anymore this
+
+ align:start position:0%
+isn't an indeterminate form anymore this
+ 
+
+ align:start position:0%
+isn't an indeterminate form anymore this
+is a nice simple limit we can just plug
+
+ align:start position:0%
+is a nice simple limit we can just plug
+ 
+
+ align:start position:0%
+is a nice simple limit we can just plug
+in so this is just equal to a ok so
+
+ align:start position:0%
+in so this is just equal to a ok so
+ 
+
+ align:start position:0%
+in so this is just equal to a ok so
+that's that's part a straightforward
+
+ align:start position:0%
+that's that's part a straightforward
+ 
+
+ align:start position:0%
+that's that's part a straightforward
+application of l'hopital's rule let's go
+
+ align:start position:0%
+application of l'hopital's rule let's go
+ 
+
+ align:start position:0%
+application of l'hopital's rule let's go
+look at Part B so Part B asked us for
+
+ align:start position:0%
+look at Part B so Part B asked us for
+ 
+
+ align:start position:0%
+look at Part B so Part B asked us for
+the limit as X goes to zero of sine 5x
+
+ align:start position:0%
+the limit as X goes to zero of sine 5x
+ 
+
+ align:start position:0%
+the limit as X goes to zero of sine 5x
+over X so I'll put that right here maybe
+
+ align:start position:0%
+over X so I'll put that right here maybe
+ 
+
+ align:start position:0%
+over X so I'll put that right here maybe
+I'll draw a little border so the limit
+
+ align:start position:0%
+I'll draw a little border so the limit
+ 
+
+ align:start position:0%
+I'll draw a little border so the limit
+as X goes to zero of sine of 5x divided
+
+ align:start position:0%
+as X goes to zero of sine of 5x divided
+ 
+
+ align:start position:0%
+as X goes to zero of sine of 5x divided
+by X so again that there's a there's a
+
+ align:start position:0%
+by X so again that there's a there's a
+ 
+
+ align:start position:0%
+by X so again that there's a there's a
+question of you know is this limit do we
+
+ align:start position:0%
+question of you know is this limit do we
+ 
+
+ align:start position:0%
+question of you know is this limit do we
+know what it is already
+
+ align:start position:0%
+know what it is already
+ 
+
+ align:start position:0%
+know what it is already
+and the answer is maybe we do and maybe
+
+ align:start position:0%
+and the answer is maybe we do and maybe
+ 
+
+ align:start position:0%
+and the answer is maybe we do and maybe
+we don't but suppose we don't so in that
+
+ align:start position:0%
+we don't but suppose we don't so in that
+ 
+
+ align:start position:0%
+we don't but suppose we don't so in that
+case can we apply l'hopital's rule
+
+ align:start position:0%
+case can we apply l'hopital's rule
+ 
+
+ align:start position:0%
+case can we apply l'hopital's rule
+well we check and as X goes to zero sine
+
+ align:start position:0%
+well we check and as X goes to zero sine
+ 
+
+ align:start position:0%
+well we check and as X goes to zero sine
+of 5x so as X goes to zero five X goes
+
+ align:start position:0%
+of 5x so as X goes to zero five X goes
+ 
+
+ align:start position:0%
+of 5x so as X goes to zero five X goes
+to zero so sine of 5 X goes to zero and
+
+ align:start position:0%
+to zero so sine of 5 X goes to zero and
+ 
+
+ align:start position:0%
+to zero so sine of 5 X goes to zero and
+X goes to zero so this is another zero
+
+ align:start position:0%
+X goes to zero so this is another zero
+ 
+
+ align:start position:0%
+X goes to zero so this is another zero
+over zero form so we can apply
+
+ align:start position:0%
+over zero form so we can apply
+ 
+
+ align:start position:0%
+over zero form so we can apply
+l'hopital's rule
+
+ align:start position:0%
+l'hopital's rule
+ 
+
+ align:start position:0%
+l'hopital's rule
+so l'hopital's rule says that this is
+
+ align:start position:0%
+so l'hopital's rule says that this is
+ 
+
+ align:start position:0%
+so l'hopital's rule says that this is
+equal to the limit as X goes to zero of
+
+ align:start position:0%
+equal to the limit as X goes to zero of
+ 
+
+ align:start position:0%
+equal to the limit as X goes to zero of
+well we take the derivative of the top
+
+ align:start position:0%
+well we take the derivative of the top
+ 
+
+ align:start position:0%
+well we take the derivative of the top
+and divide by the derivative of the
+
+ align:start position:0%
+and divide by the derivative of the
+ 
+
+ align:start position:0%
+and divide by the derivative of the
+bottom so the derivative of the top is
+
+ align:start position:0%
+bottom so the derivative of the top is
+ 
+
+ align:start position:0%
+bottom so the derivative of the top is
+just five cosine
+
+ align:start position:0%
+just five cosine
+ 
+
+ align:start position:0%
+just five cosine
+five X and the derivative of the bottom
+
+ align:start position:0%
+five X and the derivative of the bottom
+ 
+
+ align:start position:0%
+five X and the derivative of the bottom
+is one so l'hopital's rule says the
+
+ align:start position:0%
+is one so l'hopital's rule says the
+ 
+
+ align:start position:0%
+is one so l'hopital's rule says the
+limit here is equal to the limit here
+
+ align:start position:0%
+limit here is equal to the limit here
+ 
+
+ align:start position:0%
+limit here is equal to the limit here
+provided this limit exists and now as X
+
+ align:start position:0%
+provided this limit exists and now as X
+ 
+
+ align:start position:0%
+provided this limit exists and now as X
+goes to zero well okay five one is
+
+ align:start position:0%
+goes to zero well okay five one is
+ 
+
+ align:start position:0%
+goes to zero well okay five one is
+constant so we're just looking at the
+
+ align:start position:0%
+constant so we're just looking at the
+ 
+
+ align:start position:0%
+constant so we're just looking at the
+limit of cosine 5x here as X goes to 0
+
+ align:start position:0%
+limit of cosine 5x here as X goes to 0
+ 
+
+ align:start position:0%
+limit of cosine 5x here as X goes to 0
+that just approaches five times cosine
+
+ align:start position:0%
+that just approaches five times cosine
+ 
+
+ align:start position:0%
+that just approaches five times cosine
+of 0 which is 1 so this is equal to
+
+ align:start position:0%
+of 0 which is 1 so this is equal to
+ 
+
+ align:start position:0%
+of 0 which is 1 so this is equal to
+sorry the cosine of zero part is 1 so
+
+ align:start position:0%
+sorry the cosine of zero part is 1 so
+ 
+
+ align:start position:0%
+sorry the cosine of zero part is 1 so
+it's 5 times 1 which is 5 now I should
+
+ align:start position:0%
+it's 5 times 1 which is 5 now I should
+ 
+
+ align:start position:0%
+it's 5 times 1 which is 5 now I should
+note that that we didn't actually really
+
+ align:start position:0%
+note that that we didn't actually really
+ 
+
+ align:start position:0%
+note that that we didn't actually really
+need l'hopital's rule for this one one
+
+ align:start position:0%
+need l'hopital's rule for this one one
+ 
+
+ align:start position:0%
+need l'hopital's rule for this one one
+thing you can remember is that this
+
+ align:start position:0%
+thing you can remember is that this
+ 
+
+ align:start position:0%
+thing you can remember is that this
+limit is is is actually the definition
+
+ align:start position:0%
+limit is is is actually the definition
+ 
+
+ align:start position:0%
+limit is is is actually the definition
+of the derivative of sine of five x at x
+
+ align:start position:0%
+of the derivative of sine of five x at x
+ 
+
+ align:start position:0%
+of the derivative of sine of five x at x
+equals zero so what we just did with
+
+ align:start position:0%
+equals zero so what we just did with
+ 
+
+ align:start position:0%
+equals zero so what we just did with
+l'hopital's rule was use the derivative
+
+ align:start position:0%
+l'hopital's rule was use the derivative
+ 
+
+ align:start position:0%
+l'hopital's rule was use the derivative
+to compute the derivative if you like so
+
+ align:start position:0%
+to compute the derivative if you like so
+ 
+
+ align:start position:0%
+to compute the derivative if you like so
+so we use the fact that we already knew
+
+ align:start position:0%
+so we use the fact that we already knew
+ 
+
+ align:start position:0%
+so we use the fact that we already knew
+the derivative in order to compute it we
+
+ align:start position:0%
+the derivative in order to compute it we
+ 
+
+ align:start position:0%
+the derivative in order to compute it we
+could also just say by definition this
+
+ align:start position:0%
+could also just say by definition this
+ 
+
+ align:start position:0%
+could also just say by definition this
+is the derivative of sine 5x at zero
+
+ align:start position:0%
+is the derivative of sine 5x at zero
+ 
+
+ align:start position:0%
+is the derivative of sine 5x at zero
+which is five cosine of 0 which is 1
+
+ align:start position:0%
+which is five cosine of 0 which is 1
+ 
+
+ align:start position:0%
+which is five cosine of 0 which is 1
+which is 5
+
+ align:start position:0%
+which is 5
+ 
+
+ align:start position:0%
+which is 5
+rather okay so that's Part B now Part C
+
+ align:start position:0%
+rather okay so that's Part B now Part C
+ 
+
+ align:start position:0%
+rather okay so that's Part B now Part C
+asks for the limit as X goes to zero of
+
+ align:start position:0%
+asks for the limit as X goes to zero of
+ 
+
+ align:start position:0%
+asks for the limit as X goes to zero of
+x squared minus 6x plus two yes over X
+
+ align:start position:0%
+x squared minus 6x plus two yes over X
+ 
+
+ align:start position:0%
+x squared minus 6x plus two yes over X
+plus one so this limit you can't apply
+
+ align:start position:0%
+plus one so this limit you can't apply
+ 
+
+ align:start position:0%
+plus one so this limit you can't apply
+l'hopital's rule
+
+ align:start position:0%
+l'hopital's rule
+ 
+
+ align:start position:0%
+l'hopital's rule
+why can't you apply l'hopital's rule
+
+ align:start position:0%
+why can't you apply l'hopital's rule
+ 
+
+ align:start position:0%
+why can't you apply l'hopital's rule
+well because it's not an indeterminate
+
+ align:start position:0%
+well because it's not an indeterminate
+ 
+
+ align:start position:0%
+well because it's not an indeterminate
+form this limit is really easy to
+
+ align:start position:0%
+form this limit is really easy to
+ 
+
+ align:start position:0%
+form this limit is really easy to
+compute you can just plug in x equals
+
+ align:start position:0%
+compute you can just plug in x equals
+ 
+
+ align:start position:0%
+compute you can just plug in x equals
+zero here the top is going to 2 and the
+
+ align:start position:0%
+zero here the top is going to 2 and the
+ 
+
+ align:start position:0%
+zero here the top is going to 2 and the
+bottom is going to 1 so the whole limit
+
+ align:start position:0%
+bottom is going to 1 so the whole limit
+ 
+
+ align:start position:0%
+bottom is going to 1 so the whole limit
+is going to 2 divided by 1 which is 2 so
+
+ align:start position:0%
+is going to 2 divided by 1 which is 2 so
+ 
+
+ align:start position:0%
+is going to 2 divided by 1 which is 2 so
+there's there's no you don't not only
+
+ align:start position:0%
+there's there's no you don't not only
+ 
+
+ align:start position:0%
+there's there's no you don't not only
+you don't need l'hopital's rule and also
+
+ align:start position:0%
+you don't need l'hopital's rule and also
+ 
+
+ align:start position:0%
+you don't need l'hopital's rule and also
+you can't apply l'hopital's rule this is
+
+ align:start position:0%
+you can't apply l'hopital's rule this is
+ 
+
+ align:start position:0%
+you can't apply l'hopital's rule this is
+not a forum in which l'hopital's rule
+
+ align:start position:0%
+not a forum in which l'hopital's rule
+ 
+
+ align:start position:0%
+not a forum in which l'hopital's rule
+applies it's not an indeterminate form
+
+ align:start position:0%
+applies it's not an indeterminate form
+ 
+
+ align:start position:0%
+applies it's not an indeterminate form
+okay so but okay but the result is is
+
+ align:start position:0%
+okay so but okay but the result is is
+ 
+
+ align:start position:0%
+okay so but okay but the result is is
+very easy to compute good so that's 2
+
+ align:start position:0%
+very easy to compute good so that's 2
+ 
+
+ align:start position:0%
+very easy to compute good so that's 2
+and we've got our last one now which is
+
+ align:start position:0%
+and we've got our last one now which is
+ 
+
+ align:start position:0%
+and we've got our last one now which is
+d limit
+
+ align:start position:0%
+d limit
+ 
+
+ align:start position:0%
+d limit
+as X goes to infinity of Ln of 1 plus e
+
+ align:start position:0%
+as X goes to infinity of Ln of 1 plus e
+ 
+
+ align:start position:0%
+as X goes to infinity of Ln of 1 plus e
+to the 3x quantity divided by 2x plus 5
+
+ align:start position:0%
+to the 3x quantity divided by 2x plus 5
+ 
+
+ align:start position:0%
+to the 3x quantity divided by 2x plus 5
+okay well is it obvious what this limit
+
+ align:start position:0%
+okay well is it obvious what this limit
+ 
+
+ align:start position:0%
+okay well is it obvious what this limit
+is not not to me so okay so so then we
+
+ align:start position:0%
+is not not to me so okay so so then we
+ 
+
+ align:start position:0%
+is not not to me so okay so so then we
+can check can we apply it so it's it's a
+
+ align:start position:0%
+can check can we apply it so it's it's a
+ 
+
+ align:start position:0%
+can check can we apply it so it's it's a
+quotient so can we apply l'hopital's
+
+ align:start position:0%
+quotient so can we apply l'hopital's
+ 
+
+ align:start position:0%
+quotient so can we apply l'hopital's
+rule well we can apply l'hopital's rule
+
+ align:start position:0%
+rule well we can apply l'hopital's rule
+ 
+
+ align:start position:0%
+rule well we can apply l'hopital's rule
+if it's an indeterminate quotient so
+
+ align:start position:0%
+if it's an indeterminate quotient so
+ 
+
+ align:start position:0%
+if it's an indeterminate quotient so
+what's happening is X so as to infinity
+
+ align:start position:0%
+what's happening is X so as to infinity
+ 
+
+ align:start position:0%
+what's happening is X so as to infinity
+well let's do the bottom first because
+
+ align:start position:0%
+well let's do the bottom first because
+ 
+
+ align:start position:0%
+well let's do the bottom first because
+that's easy as X goes to infinity 2 X
+
+ align:start position:0%
+that's easy as X goes to infinity 2 X
+ 
+
+ align:start position:0%
+that's easy as X goes to infinity 2 X
+plus 5 goes to infinity and ok as X goes
+
+ align:start position:0%
+plus 5 goes to infinity and ok as X goes
+ 
+
+ align:start position:0%
+plus 5 goes to infinity and ok as X goes
+to infinity
+
+ align:start position:0%
+to infinity
+ 
+
+ align:start position:0%
+to infinity
+either the 3 X goes to infinity so 1
+
+ align:start position:0%
+either the 3 X goes to infinity so 1
+ 
+
+ align:start position:0%
+either the 3 X goes to infinity so 1
+plus e to the 3 X goes to infinity so
+
+ align:start position:0%
+plus e to the 3 X goes to infinity so
+ 
+
+ align:start position:0%
+plus e to the 3 X goes to infinity so
+log of 1 plus e to the 3 X goes to
+
+ align:start position:0%
+log of 1 plus e to the 3 X goes to
+ 
+
+ align:start position:0%
+log of 1 plus e to the 3 X goes to
+infinity so this is an infinity over
+
+ align:start position:0%
+infinity so this is an infinity over
+ 
+
+ align:start position:0%
+infinity so this is an infinity over
+infinity form that's an indeterminate
+
+ align:start position:0%
+infinity form that's an indeterminate
+ 
+
+ align:start position:0%
+infinity form that's an indeterminate
+form and indeterminate quotient so we
+
+ align:start position:0%
+form and indeterminate quotient so we
+ 
+
+ align:start position:0%
+form and indeterminate quotient so we
+can apply l'hopital's rule
+
+ align:start position:0%
+can apply l'hopital's rule
+ 
+
+ align:start position:0%
+can apply l'hopital's rule
+so l'hopital's rule says that this is
+
+ align:start position:0%
+so l'hopital's rule says that this is
+ 
+
+ align:start position:0%
+so l'hopital's rule says that this is
+equal to the limit of the quotient of
+
+ align:start position:0%
+equal to the limit of the quotient of
+ 
+
+ align:start position:0%
+equal to the limit of the quotient of
+the ratio of the derivatives provided
+
+ align:start position:0%
+the ratio of the derivatives provided
+ 
+
+ align:start position:0%
+the ratio of the derivatives provided
+that that that limit exists so this is
+
+ align:start position:0%
+that that that limit exists so this is
+ 
+
+ align:start position:0%
+that that that limit exists so this is
+equal to the limit as X goes to infinity
+
+ align:start position:0%
+equal to the limit as X goes to infinity
+ 
+
+ align:start position:0%
+equal to the limit as X goes to infinity
+of ok so we need to look at the ratio of
+
+ align:start position:0%
+of ok so we need to look at the ratio of
+ 
+
+ align:start position:0%
+of ok so we need to look at the ratio of
+the derivatives so the bottom one is
+
+ align:start position:0%
+the derivatives so the bottom one is
+ 
+
+ align:start position:0%
+the derivatives so the bottom one is
+easy that's two for the top one to
+
+ align:start position:0%
+easy that's two for the top one to
+ 
+
+ align:start position:0%
+easy that's two for the top one to
+compute this derivative we need to use
+
+ align:start position:0%
+compute this derivative we need to use
+ 
+
+ align:start position:0%
+compute this derivative we need to use
+the chain rule here so you take the
+
+ align:start position:0%
+the chain rule here so you take the
+ 
+
+ align:start position:0%
+the chain rule here so you take the
+derivative of this and you get well it's
+
+ align:start position:0%
+derivative of this and you get well it's
+ 
+
+ align:start position:0%
+derivative of this and you get well it's
+a log so on the bottom we get 1 plus e
+
+ align:start position:0%
+a log so on the bottom we get 1 plus e
+ 
+
+ align:start position:0%
+a log so on the bottom we get 1 plus e
+to the 3x and then then by the chain
+
+ align:start position:0%
+to the 3x and then then by the chain
+ 
+
+ align:start position:0%
+to the 3x and then then by the chain
+rule up top you get 3 e to the 3x or
+
+ align:start position:0%
+rule up top you get 3 e to the 3x or
+ 
+
+ align:start position:0%
+rule up top you get 3 e to the 3x or
+just rewriting this a little bit in a
+
+ align:start position:0%
+just rewriting this a little bit in a
+ 
+
+ align:start position:0%
+just rewriting this a little bit in a
+nicer form this is the limit as X goes
+
+ align:start position:0%
+nicer form this is the limit as X goes
+ 
+
+ align:start position:0%
+nicer form this is the limit as X goes
+to infinity of 3 over 2 times e to the
+
+ align:start position:0%
+to infinity of 3 over 2 times e to the
+ 
+
+ align:start position:0%
+to infinity of 3 over 2 times e to the
+3x over 1 plus e to the 3x all right so
+
+ align:start position:0%
+3x over 1 plus e to the 3x all right so
+ 
+
+ align:start position:0%
+3x over 1 plus e to the 3x all right so
+now the question is what do we do from
+
+ align:start position:0%
+now the question is what do we do from
+ 
+
+ align:start position:0%
+now the question is what do we do from
+here well is this limit obvious well ok
+
+ align:start position:0%
+here well is this limit obvious well ok
+ 
+
+ align:start position:0%
+here well is this limit obvious well ok
+so there are
+
+ align:start position:0%
+so there are
+ 
+
+ align:start position:0%
+so there are
+you know to two situations here one is
+
+ align:start position:0%
+you know to two situations here one is
+ 
+
+ align:start position:0%
+you know to two situations here one is
+you you might look at this and you might
+
+ align:start position:0%
+you you might look at this and you might
+ 
+
+ align:start position:0%
+you you might look at this and you might
+already know what this limit is and the
+
+ align:start position:0%
+already know what this limit is and the
+ 
+
+ align:start position:0%
+already know what this limit is and the
+reason you might know that is that X
+
+ align:start position:0%
+reason you might know that is that X
+ 
+
+ align:start position:0%
+reason you might know that is that X
+goes to infinity e to the 3x is going to
+
+ align:start position:0%
+goes to infinity e to the 3x is going to
+ 
+
+ align:start position:0%
+goes to infinity e to the 3x is going to
+infinity and e to the 3x and 1 plus e to
+
+ align:start position:0%
+infinity and e to the 3x and 1 plus e to
+ 
+
+ align:start position:0%
+infinity and e to the 3x and 1 plus e to
+the 3x is going to infinity so this is
+
+ align:start position:0%
+the 3x is going to infinity so this is
+ 
+
+ align:start position:0%
+the 3x is going to infinity so this is
+an infinity over infinity indeterminate
+
+ align:start position:0%
+an infinity over infinity indeterminate
+ 
+
+ align:start position:0%
+an infinity over infinity indeterminate
+form and so you could apply l'hopital's
+
+ align:start position:0%
+form and so you could apply l'hopital's
+ 
+
+ align:start position:0%
+form and so you could apply l'hopital's
+rule to it again okay that that that's
+
+ align:start position:0%
+rule to it again okay that that that's
+ 
+
+ align:start position:0%
+rule to it again okay that that that's
+one thing you could do but you might
+
+ align:start position:0%
+one thing you could do but you might
+ 
+
+ align:start position:0%
+one thing you could do but you might
+also look at it and say well these two
+
+ align:start position:0%
+also look at it and say well these two
+ 
+
+ align:start position:0%
+also look at it and say well these two
+things are going to infinity at exactly
+
+ align:start position:0%
+things are going to infinity at exactly
+ 
+
+ align:start position:0%
+things are going to infinity at exactly
+the same rate right this plus one is is
+
+ align:start position:0%
+the same rate right this plus one is is
+ 
+
+ align:start position:0%
+the same rate right this plus one is is
+almost totally irrelevant I mean
+
+ align:start position:0%
+almost totally irrelevant I mean
+ 
+
+ align:start position:0%
+almost totally irrelevant I mean
+actually for purposes of estimating the
+
+ align:start position:0%
+actually for purposes of estimating the
+ 
+
+ align:start position:0%
+actually for purposes of estimating the
+magnitude of this fraction it is totally
+
+ align:start position:0%
+magnitude of this fraction it is totally
+ 
+
+ align:start position:0%
+magnitude of this fraction it is totally
+irrelevant when you take you know when
+
+ align:start position:0%
+irrelevant when you take you know when
+ 
+
+ align:start position:0%
+irrelevant when you take you know when
+3x is big then say e to the 3x is like a
+
+ align:start position:0%
+3x is big then say e to the 3x is like a
+ 
+
+ align:start position:0%
+3x is big then say e to the 3x is like a
+billion or something so e to the 3x is a
+
+ align:start position:0%
+billion or something so e to the 3x is a
+ 
+
+ align:start position:0%
+billion or something so e to the 3x is a
+billion so you have a billion over a
+
+ align:start position:0%
+billion so you have a billion over a
+ 
+
+ align:start position:0%
+billion so you have a billion over a
+billion and one right so it's very very
+
+ align:start position:0%
+billion and one right so it's very very
+ 
+
+ align:start position:0%
+billion and one right so it's very very
+very close to one and it's gonna closer
+
+ align:start position:0%
+very close to one and it's gonna closer
+ 
+
+ align:start position:0%
+very close to one and it's gonna closer
+and closer to one to one so okay so if
+
+ align:start position:0%
+and closer to one to one so okay so if
+ 
+
+ align:start position:0%
+and closer to one to one so okay so if
+you if you didn't trust that analysis
+
+ align:start position:0%
+you if you didn't trust that analysis
+ 
+
+ align:start position:0%
+you if you didn't trust that analysis
+based on magnitudes I mean the idea here
+
+ align:start position:0%
+based on magnitudes I mean the idea here
+ 
+
+ align:start position:0%
+based on magnitudes I mean the idea here
+is just that the most significant term
+
+ align:start position:0%
+is just that the most significant term
+ 
+
+ align:start position:0%
+is just that the most significant term
+and the top is the e to the 3x the most
+
+ align:start position:0%
+and the top is the e to the 3x the most
+ 
+
+ align:start position:0%
+and the top is the e to the 3x the most
+significant term in the bottom is e to
+
+ align:start position:0%
+significant term in the bottom is e to
+ 
+
+ align:start position:0%
+significant term in the bottom is e to
+the 3x they dominate everything else
+
+ align:start position:0%
+the 3x they dominate everything else
+ 
+
+ align:start position:0%
+the 3x they dominate everything else
+that appears which is just this little
+
+ align:start position:0%
+that appears which is just this little
+ 
+
+ align:start position:0%
+that appears which is just this little
+one so that's gonna give you a ratio of
+
+ align:start position:0%
+one so that's gonna give you a ratio of
+ 
+
+ align:start position:0%
+one so that's gonna give you a ratio of
+1 if you don't trust that analysis you
+
+ align:start position:0%
+1 if you don't trust that analysis you
+ 
+
+ align:start position:0%
+1 if you don't trust that analysis you
+can apply l'hopital's rule again and
+
+ align:start position:0%
+can apply l'hopital's rule again and
+ 
+
+ align:start position:0%
+can apply l'hopital's rule again and
+l'hopital's rule will tell you exactly
+
+ align:start position:0%
+l'hopital's rule will tell you exactly
+ 
+
+ align:start position:0%
+l'hopital's rule will tell you exactly
+the equivalent thing when you take a
+
+ align:start position:0%
+the equivalent thing when you take a
+ 
+
+ align:start position:0%
+the equivalent thing when you take a
+derivative you'll be left with 3 e to
+
+ align:start position:0%
+derivative you'll be left with 3 e to
+ 
+
+ align:start position:0%
+derivative you'll be left with 3 e to
+the 3x over 3 e to the 3x which is just
+
+ align:start position:0%
+the 3x over 3 e to the 3x which is just
+ 
+
+ align:start position:0%
+the 3x over 3 e to the 3x which is just
+1 so in either case this part goes to 1
+
+ align:start position:0%
+1 so in either case this part goes to 1
+ 
+
+ align:start position:0%
+1 so in either case this part goes to 1
+so 3 halves times it goes right to 3
+
+ align:start position:0%
+so 3 halves times it goes right to 3
+ 
+
+ align:start position:0%
+so 3 halves times it goes right to 3
+halves alright so there you have it four
+
+ align:start position:0%
+halves alright so there you have it four
+ 
+
+ align:start position:0%
+halves alright so there you have it four
+limits computed with l'hopital's rule
+
+ align:start position:0%
+limits computed with l'hopital's rule
+ 
+
+ align:start position:0%
+limits computed with l'hopital's rule
+well one of them computed without
+
+ align:start position:0%
+well one of them computed without
+ 
+
+ align:start position:0%
+well one of them computed without
+l'hopital's rule remember you always
+
+ align:start position:0%
+l'hopital's rule remember you always
+ 
+
+ align:start position:0%
+l'hopital's rule remember you always
+have to check that you actually have an
+
+ align:start position:0%
+have to check that you actually have an
+ 
+
+ align:start position:0%
+have to check that you actually have an
+indeterminate form before you apply
+
+ align:start position:0%
+indeterminate form before you apply
+ 
+
+ align:start position:0%
+indeterminate form before you apply
+l'hopital's rule and that's all i have
+
+ align:start position:0%
+l'hopital's rule and that's all i have
+ 
+
+ align:start position:0%
+l'hopital's rule and that's all i have
+to say about that so I'll end there
\ No newline at end of file
diff --git a/zNCBDrnT05E.txt b/zNCBDrnT05E.txt
new file mode 100644
index 0000000000000000000000000000000000000000..64b573b734eed491fa170dbcbce80161ea577e83
--- /dev/null
+++ b/zNCBDrnT05E.txt
@@ -0,0 +1,11187 @@
+align:start position:0%
+ 
+The following content is provided under
+
+ align:start position:0%
+The following content is provided under
+ 
+
+ align:start position:0%
+The following content is provided under
+a Creative Common license. Your support
+
+ align:start position:0%
+a Creative Common license. Your support
+ 
+
+ align:start position:0%
+a Creative Common license. Your support
+will help MIT Open Courseware continue
+
+ align:start position:0%
+will help MIT Open Courseware continue
+ 
+
+ align:start position:0%
+will help MIT Open Courseware continue
+to offer highquality educational
+
+ align:start position:0%
+to offer highquality educational
+ 
+
+ align:start position:0%
+to offer highquality educational
+resources for free. To make a donation
+
+ align:start position:0%
+resources for free. To make a donation
+ 
+
+ align:start position:0%
+resources for free. To make a donation
+or to view additional materials from
+
+ align:start position:0%
+or to view additional materials from
+ 
+
+ align:start position:0%
+or to view additional materials from
+hundreds of MIT courses, visit MIT Open
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+ 
+
+ align:start position:0%
+hundreds of MIT courses, visit MIT Open
+Courseware at ocw.mmit.edu.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+The there's a reading the the new
+
+ align:start position:0%
+The there's a reading the the new
+ 
+
+ align:start position:0%
+The there's a reading the the new
+reading is on stellar. It's an excerpt
+
+ align:start position:0%
+reading is on stellar. It's an excerpt
+ 
+
+ align:start position:0%
+reading is on stellar. It's an excerpt
+from a textbook on dynamics by professor
+
+ align:start position:0%
+from a textbook on dynamics by professor
+ 
+
+ align:start position:0%
+from a textbook on dynamics by professor
+Jim Williams who recently who was in uh
+
+ align:start position:0%
+Jim Williams who recently who was in uh
+ 
+
+ align:start position:0%
+Jim Williams who recently who was in uh
+in the mechanical engineering department
+
+ align:start position:0%
+in the mechanical engineering department
+ 
+
+ align:start position:0%
+in the mechanical engineering department
+here at MIT and just recently retired.
+
+ align:start position:0%
+here at MIT and just recently retired.
+ 
+
+ align:start position:0%
+here at MIT and just recently retired.
+This reading is essentially a review of
+
+ align:start position:0%
+This reading is essentially a review of
+ 
+
+ align:start position:0%
+This reading is essentially a review of
+everything we've done in kinematics. So
+
+ align:start position:0%
+everything we've done in kinematics. So
+ 
+
+ align:start position:0%
+everything we've done in kinematics. So
+it gives you a different point of view.
+
+ align:start position:0%
+it gives you a different point of view.
+ 
+
+ align:start position:0%
+it gives you a different point of view.
+It's extremely well written. it. So it
+
+ align:start position:0%
+It's extremely well written. it. So it
+ 
+
+ align:start position:0%
+It's extremely well written. it. So it
+goes through things like derivatives of
+
+ align:start position:0%
+goes through things like derivatives of
+ 
+
+ align:start position:0%
+goes through things like derivatives of
+rotating vectors. It has three or four
+
+ align:start position:0%
+rotating vectors. It has three or four
+ 
+
+ align:start position:0%
+rotating vectors. It has three or four
+really terrific examples of problems
+
+ align:start position:0%
+really terrific examples of problems
+ 
+
+ align:start position:0%
+really terrific examples of problems
+that uh are solved using the techniques
+
+ align:start position:0%
+that uh are solved using the techniques
+ 
+
+ align:start position:0%
+that uh are solved using the techniques
+that we've used up to this point. So
+
+ align:start position:0%
+that we've used up to this point. So
+ 
+
+ align:start position:0%
+that we've used up to this point. So
+it's a good way to re review for the
+
+ align:start position:0%
+it's a good way to re review for the
+ 
+
+ align:start position:0%
+it's a good way to re review for the
+quiz which is coming up a week from
+
+ align:start position:0%
+quiz which is coming up a week from
+ 
+
+ align:start position:0%
+quiz which is coming up a week from
+Thursday on October 14th. That quiz will
+
+ align:start position:0%
+Thursday on October 14th. That quiz will
+ 
+
+ align:start position:0%
+Thursday on October 14th. That quiz will
+be here.
+
+ align:start position:0%
+be here.
+ 
+
+ align:start position:0%
+be here.
+closed book, one sheet of notes, piece
+
+ align:start position:0%
+closed book, one sheet of notes, piece
+ 
+
+ align:start position:0%
+closed book, one sheet of notes, piece
+of paper, both sides as your for
+
+ align:start position:0%
+of paper, both sides as your for
+ 
+
+ align:start position:0%
+of paper, both sides as your for
+reference material.
+
+ align:start position:0%
+reference material.
+ 
+
+ align:start position:0%
+reference material.
+Okay, survey results. So, you have pet
+
+ align:start position:0%
+Okay, survey results. So, you have pet
+ 
+
+ align:start position:0%
+Okay, survey results. So, you have pet
+set 4. It has uh I think five questions
+
+ align:start position:0%
+set 4. It has uh I think five questions
+ 
+
+ align:start position:0%
+set 4. It has uh I think five questions
+on it. We'll quickly take a look at the
+
+ align:start position:0%
+on it. We'll quickly take a look at the
+ 
+
+ align:start position:0%
+on it. We'll quickly take a look at the
+at the problems that you're working on
+
+ align:start position:0%
+at the problems that you're working on
+ 
+
+ align:start position:0%
+at the problems that you're working on
+right now. So, here's this uh yo-yo like
+
+ align:start position:0%
+right now. So, here's this uh yo-yo like
+ 
+
+ align:start position:0%
+right now. So, here's this uh yo-yo like
+thing, a spool. It's all There were some
+
+ align:start position:0%
+thing, a spool. It's all There were some
+ 
+
+ align:start position:0%
+thing, a spool. It's all There were some
+questions on NB. The inner piece doesn't
+
+ align:start position:0%
+questions on NB. The inner piece doesn't
+ 
+
+ align:start position:0%
+questions on NB. The inner piece doesn't
+rotate relative to the outer piece. It's
+
+ align:start position:0%
+rotate relative to the outer piece. It's
+ 
+
+ align:start position:0%
+rotate relative to the outer piece. It's
+all one solid spool, but it has two
+
+ align:start position:0%
+all one solid spool, but it has two
+ 
+
+ align:start position:0%
+all one solid spool, but it has two
+different radi that uh uh are in
+
+ align:start position:0%
+different radi that uh uh are in
+ 
+
+ align:start position:0%
+different radi that uh uh are in
+functioning in the problem. And the
+
+ align:start position:0%
+functioning in the problem. And the
+ 
+
+ align:start position:0%
+functioning in the problem. And the
+question is, will the spool roll to the
+
+ align:start position:0%
+question is, will the spool roll to the
+ 
+
+ align:start position:0%
+question is, will the spool roll to the
+left or to the right when the string is
+
+ align:start position:0%
+left or to the right when the string is
+ 
+
+ align:start position:0%
+left or to the right when the string is
+pulled to the right? So, we're going to
+
+ align:start position:0%
+pulled to the right? So, we're going to
+ 
+
+ align:start position:0%
+pulled to the right? So, we're going to
+come back to it. I'm just going to run
+
+ align:start position:0%
+come back to it. I'm just going to run
+ 
+
+ align:start position:0%
+come back to it. I'm just going to run
+through all the questions quickly. The
+
+ align:start position:0%
+through all the questions quickly. The
+ 
+
+ align:start position:0%
+through all the questions quickly. The
+second one was this somewhat familiar
+
+ align:start position:0%
+second one was this somewhat familiar
+ 
+
+ align:start position:0%
+second one was this somewhat familiar
+problem you've done uh done. Now the uh
+
+ align:start position:0%
+problem you've done uh done. Now the uh
+ 
+
+ align:start position:0%
+problem you've done uh done. Now the uh
+the question asks you about
+
+ align:start position:0%
+the question asks you about
+ 
+
+ align:start position:0%
+the question asks you about
+how fast it will be it has to go before
+
+ align:start position:0%
+how fast it will be it has to go before
+ 
+
+ align:start position:0%
+how fast it will be it has to go before
+the thing starts sliding up and this the
+
+ align:start position:0%
+the thing starts sliding up and this the
+ 
+
+ align:start position:0%
+the thing starts sliding up and this the
+survey question if the starting position
+
+ align:start position:0%
+survey question if the starting position
+ 
+
+ align:start position:0%
+survey question if the starting position
+of the spool is moved down the rod
+
+ align:start position:0%
+of the spool is moved down the rod
+ 
+
+ align:start position:0%
+of the spool is moved down the rod
+will the angular rate be higher when the
+
+ align:start position:0%
+will the angular rate be higher when the
+ 
+
+ align:start position:0%
+will the angular rate be higher when the
+spool begins to slide up the rod you
+
+ align:start position:0%
+spool begins to slide up the rod you
+ 
+
+ align:start position:0%
+spool begins to slide up the rod you
+have to go faster to get it to go okay
+
+ align:start position:0%
+have to go faster to get it to go okay
+ 
+
+ align:start position:0%
+have to go faster to get it to go okay
+next
+
+ align:start position:0%
+next
+ 
+
+ align:start position:0%
+next
+okay this is finding the equation of
+
+ align:start position:0%
+okay this is finding the equation of
+ 
+
+ align:start position:0%
+okay this is finding the equation of
+motion for a pendulum and everybody
+
+ align:start position:0%
+motion for a pendulum and everybody
+ 
+
+ align:start position:0%
+motion for a pendulum and everybody
+knows the natural frequency of a
+
+ align:start position:0%
+knows the natural frequency of a
+ 
+
+ align:start position:0%
+knows the natural frequency of a
+pendulum square root of G over L but
+
+ align:start position:0%
+pendulum square root of G over L but
+ 
+
+ align:start position:0%
+pendulum square root of G over L but
+this pendulum has a torsional spring
+
+ align:start position:0%
+this pendulum has a torsional spring
+ 
+
+ align:start position:0%
+this pendulum has a torsional spring
+added to it and the question is square
+
+ align:start position:0%
+added to it and the question is square
+ 
+
+ align:start position:0%
+added to it and the question is square
+root G over L doesn't involve the mass
+
+ align:start position:0%
+root G over L doesn't involve the mass
+ 
+
+ align:start position:0%
+root G over L doesn't involve the mass
+but will the natural frequency now that
+
+ align:start position:0%
+but will the natural frequency now that
+ 
+
+ align:start position:0%
+but will the natural frequency now that
+you put the torsional spring on it will
+
+ align:start position:0%
+you put the torsional spring on it will
+ 
+
+ align:start position:0%
+you put the torsional spring on it will
+it will it now involve the mass no
+
+ align:start position:0%
+it will it now involve the mass no
+ 
+
+ align:start position:0%
+it will it now involve the mass no
+reason you should know this you've
+
+ align:start position:0%
+reason you should know this you've
+ 
+
+ align:start position:0%
+reason you should know this you've
+probably never done this problem before
+
+ align:start position:0%
+probably never done this problem before
+ 
+
+ align:start position:0%
+probably never done this problem before
+and uh we'll come back to that next
+
+ align:start position:0%
+and uh we'll come back to that next
+ 
+
+ align:start position:0%
+and uh we'll come back to that next
+the fourth problem two degree freedom
+
+ align:start position:0%
+the fourth problem two degree freedom
+ 
+
+ align:start position:0%
+the fourth problem two degree freedom
+system and want you to uh come up with
+
+ align:start position:0%
+system and want you to uh come up with
+ 
+
+ align:start position:0%
+system and want you to uh come up with
+the equations of motion. But the survey
+
+ align:start position:0%
+the equations of motion. But the survey
+ 
+
+ align:start position:0%
+the equations of motion. But the survey
+question, if K1 didn't exist, this is
+
+ align:start position:0%
+question, if K1 didn't exist, this is
+ 
+
+ align:start position:0%
+question, if K1 didn't exist, this is
+just two masses coupled by a spring.
+
+ align:start position:0%
+just two masses coupled by a spring.
+ 
+
+ align:start position:0%
+just two masses coupled by a spring.
+It's no, this thing is no longer
+
+ align:start position:0%
+It's no, this thing is no longer
+ 
+
+ align:start position:0%
+It's no, this thing is no longer
+constrained in the X direction. There's
+
+ align:start position:0%
+constrained in the X direction. There's
+ 
+
+ align:start position:0%
+constrained in the X direction. There's
+no X constraints on the system.
+
+ align:start position:0%
+no X constraints on the system.
+ 
+
+ align:start position:0%
+no X constraints on the system.
+So if that if that's the case, this
+
+ align:start position:0%
+So if that if that's the case, this
+ 
+
+ align:start position:0%
+So if that if that's the case, this
+system still has two natural
+
+ align:start position:0%
+system still has two natural
+ 
+
+ align:start position:0%
+system still has two natural
+frequencies.
+
+ align:start position:0%
+frequencies.
+ 
+
+ align:start position:0%
+frequencies.
+An object that can a system that can
+
+ align:start position:0%
+An object that can a system that can
+ 
+
+ align:start position:0%
+An object that can a system that can
+vibrate essentially has as many natural
+
+ align:start position:0%
+vibrate essentially has as many natural
+ 
+
+ align:start position:0%
+vibrate essentially has as many natural
+frequencies as it does equations of
+
+ align:start position:0%
+frequencies as it does equations of
+ 
+
+ align:start position:0%
+frequencies as it does equations of
+motion. This one requires two equations
+
+ align:start position:0%
+motion. This one requires two equations
+ 
+
+ align:start position:0%
+motion. This one requires two equations
+of motion, but it will have one zero
+
+ align:start position:0%
+of motion, but it will have one zero
+ 
+
+ align:start position:0%
+of motion, but it will have one zero
+natural frequency and the other one
+
+ align:start position:0%
+natural frequency and the other one
+ 
+
+ align:start position:0%
+natural frequency and the other one
+greater than zero. In the second case,
+
+ align:start position:0%
+greater than zero. In the second case,
+ 
+
+ align:start position:0%
+greater than zero. In the second case,
+when it's greater than zero,
+
+ align:start position:0%
+when it's greater than zero,
+ 
+
+ align:start position:0%
+when it's greater than zero,
+this thing is oscillating somehow. It
+
+ align:start position:0%
+this thing is oscillating somehow. It
+ 
+
+ align:start position:0%
+this thing is oscillating somehow. It
+has no extra strength. What can you say
+
+ align:start position:0%
+has no extra strength. What can you say
+ 
+
+ align:start position:0%
+has no extra strength. What can you say
+about the position of the center of
+
+ align:start position:0%
+about the position of the center of
+ 
+
+ align:start position:0%
+about the position of the center of
+mass?
+
+ align:start position:0%
+mass?
+ 
+
+ align:start position:0%
+mass?
+So, let's look at the results. So this
+
+ align:start position:0%
+So, let's look at the results. So this
+ 
+
+ align:start position:0%
+So, let's look at the results. So this
+is the first one is the spool problem.
+
+ align:start position:0%
+is the first one is the spool problem.
+ 
+
+ align:start position:0%
+is the first one is the spool problem.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+let's
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+here's the spool.
+
+ align:start position:0%
+here's the spool.
+ 
+
+ align:start position:0%
+here's the spool.
+Here's the table. Here's the inner
+
+ align:start position:0%
+Here's the table. Here's the inner
+ 
+
+ align:start position:0%
+Here's the table. Here's the inner
+radius. It's got a string wrapped on it.
+
+ align:start position:0%
+radius. It's got a string wrapped on it.
+ 
+
+ align:start position:0%
+radius. It's got a string wrapped on it.
+You're pulling the string this way at V
+
+ align:start position:0%
+You're pulling the string this way at V
+ 
+
+ align:start position:0%
+You're pulling the string this way at V
+in the I direction. This will be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+O
+
+ align:start position:0%
+O
+ 
+
+ align:start position:0%
+O
+XY.
+
+ align:start position:0%
+XY.
+ 
+
+ align:start position:0%
+XY.
+And now the question is when you pull on
+
+ align:start position:0%
+And now the question is when you pull on
+ 
+
+ align:start position:0%
+And now the question is when you pull on
+this, which way will the spool go? And
+
+ align:start position:0%
+this, which way will the spool go? And
+ 
+
+ align:start position:0%
+this, which way will the spool go? And
+most of you said it'll go to the left.
+
+ align:start position:0%
+most of you said it'll go to the left.
+ 
+
+ align:start position:0%
+most of you said it'll go to the left.
+So I made this I made this up. We're
+
+ align:start position:0%
+So I made this I made this up. We're
+ 
+
+ align:start position:0%
+So I made this I made this up. We're
+going to do the experiment.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, I've wrapped Teflon tape on this
+
+ align:start position:0%
+So, I've wrapped Teflon tape on this
+ 
+
+ align:start position:0%
+So, I've wrapped Teflon tape on this
+spool.
+
+ align:start position:0%
+spool.
+ 
+
+ align:start position:0%
+spool.
+It's got a C battery in the center to
+
+ align:start position:0%
+It's got a C battery in the center to
+ 
+
+ align:start position:0%
+It's got a C battery in the center to
+give it a little bit of weight.
+
+ align:start position:0%
+give it a little bit of weight.
+ 
+
+ align:start position:0%
+give it a little bit of weight.
+And here's the experiment.
+
+ align:start position:0%
+And here's the experiment.
+ 
+
+ align:start position:0%
+And here's the experiment.
+And the guys in the booth, I hope, have
+
+ align:start position:0%
+And the guys in the booth, I hope, have
+ 
+
+ align:start position:0%
+And the guys in the booth, I hope, have
+a minute to be to zoom in on it. I'm
+
+ align:start position:0%
+a minute to be to zoom in on it. I'm
+ 
+
+ align:start position:0%
+a minute to be to zoom in on it. I'm
+going to let go. And now I'm going to
+
+ align:start position:0%
+going to let go. And now I'm going to
+ 
+
+ align:start position:0%
+going to let go. And now I'm going to
+start pulling. Whoops. I need to put a
+
+ align:start position:0%
+start pulling. Whoops. I need to put a
+ 
+
+ align:start position:0%
+start pulling. Whoops. I need to put a
+little more out here.
+
+ align:start position:0%
+little more out here.
+ 
+
+ align:start position:0%
+little more out here.
+Pull on the tape.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You believe it?
+
+ align:start position:0%
+You believe it?
+ 
+
+ align:start position:0%
+You believe it?
+So, I've done the reverse of what's say
+
+ align:start position:0%
+So, I've done the reverse of what's say
+ 
+
+ align:start position:0%
+So, I've done the reverse of what's say
+there. I'm pulling that way, but it goes
+
+ align:start position:0%
+there. I'm pulling that way, but it goes
+ 
+
+ align:start position:0%
+there. I'm pulling that way, but it goes
+in the same direction as you pull it.
+
+ align:start position:0%
+in the same direction as you pull it.
+ 
+
+ align:start position:0%
+in the same direction as you pull it.
+So, the answer to this question is it
+
+ align:start position:0%
+So, the answer to this question is it
+ 
+
+ align:start position:0%
+So, the answer to this question is it
+would go to the right.
+
+ align:start position:0%
+would go to the right.
+ 
+
+ align:start position:0%
+would go to the right.
+Kind of unbelievable almost, right? Huh?
+
+ align:start position:0%
+Kind of unbelievable almost, right? Huh?
+ 
+
+ align:start position:0%
+Kind of unbelievable almost, right? Huh?
+How does it do that?
+
+ align:start position:0%
+How does it do that?
+ 
+
+ align:start position:0%
+How does it do that?
+Let's do it again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. Now, show you something else.
+
+ align:start position:0%
+All right. Now, show you something else.
+ 
+
+ align:start position:0%
+All right. Now, show you something else.
+If you that hasn't sort of boggled your
+
+ align:start position:0%
+If you that hasn't sort of boggled your
+ 
+
+ align:start position:0%
+If you that hasn't sort of boggled your
+mind,
+
+ align:start position:0%
+mind,
+ 
+
+ align:start position:0%
+mind,
+then what's it going to do if I pull
+
+ align:start position:0%
+then what's it going to do if I pull
+ 
+
+ align:start position:0%
+then what's it going to do if I pull
+straight up?
+
+ align:start position:0%
+straight up?
+ 
+
+ align:start position:0%
+straight up?
+How many think it's going to go that
+
+ align:start position:0%
+How many think it's going to go that
+ 
+
+ align:start position:0%
+How many think it's going to go that
+way? Raise your hand.
+
+ align:start position:0%
+way? Raise your hand.
+ 
+
+ align:start position:0%
+way? Raise your hand.
+How many think it's going to go that
+
+ align:start position:0%
+How many think it's going to go that
+ 
+
+ align:start position:0%
+How many think it's going to go that
+way? Raise your hand. All right,
+
+ align:start position:0%
+way? Raise your hand. All right,
+ 
+
+ align:start position:0%
+way? Raise your hand. All right,
+sure enough. Now, that means it must be
+
+ align:start position:0%
+sure enough. Now, that means it must be
+ 
+
+ align:start position:0%
+sure enough. Now, that means it must be
+some angle in between in which it will
+
+ align:start position:0%
+some angle in between in which it will
+ 
+
+ align:start position:0%
+some angle in between in which it will
+do neither. It'll start to slip.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right about there.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Neat little problem.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And now this you know doing this problem
+
+ align:start position:0%
+And now this you know doing this problem
+ 
+
+ align:start position:0%
+And now this you know doing this problem
+is all about
+
+ align:start position:0%
+is all about
+ 
+
+ align:start position:0%
+is all about
+computing velocities
+
+ align:start position:0%
+computing velocities
+ 
+
+ align:start position:0%
+computing velocities
+using concepts like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so if we call this a
+
+ align:start position:0%
+so if we call this a
+ 
+
+ align:start position:0%
+so if we call this a
+b c I think it's the other way around in
+
+ align:start position:0%
+b c I think it's the other way around in
+ 
+
+ align:start position:0%
+b c I think it's the other way around in
+the in the problem excuse me a b
+
+ align:start position:0%
+the in the problem excuse me a b
+ 
+
+ align:start position:0%
+the in the problem excuse me a b
+c and E
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the key to this problem is being able to
+
+ align:start position:0%
+the key to this problem is being able to
+ 
+
+ align:start position:0%
+the key to this problem is being able to
+figure out what the velocity of this
+
+ align:start position:0%
+figure out what the velocity of this
+ 
+
+ align:start position:0%
+figure out what the velocity of this
+point C is.
+
+ align:start position:0%
+point C is.
+ 
+
+ align:start position:0%
+point C is.
+And the first thing to understand this
+
+ align:start position:0%
+And the first thing to understand this
+ 
+
+ align:start position:0%
+And the first thing to understand this
+is the velocity of the end of the tape
+
+ align:start position:0%
+is the velocity of the end of the tape
+ 
+
+ align:start position:0%
+is the velocity of the end of the tape
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+a
+
+ align:start position:0%
+a
+ 
+
+ align:start position:0%
+a
+an in a fixed reference frame.
+
+ align:start position:0%
+an in a fixed reference frame.
+ 
+
+ align:start position:0%
+an in a fixed reference frame.
+So every point on the tape moves at the
+
+ align:start position:0%
+So every point on the tape moves at the
+ 
+
+ align:start position:0%
+So every point on the tape moves at the
+same speed. That means where it touches
+
+ align:start position:0%
+same speed. That means where it touches
+ 
+
+ align:start position:0%
+same speed. That means where it touches
+right here is also moving at that speed.
+
+ align:start position:0%
+right here is also moving at that speed.
+ 
+
+ align:start position:0%
+right here is also moving at that speed.
+So the velocity
+
+ align:start position:0%
+So the velocity
+ 
+
+ align:start position:0%
+So the velocity
+of C with respect to O is V I. And
+
+ align:start position:0%
+of C with respect to O is V I. And
+ 
+
+ align:start position:0%
+of C with respect to O is V I. And
+that's kind of the key to the problem.
+
+ align:start position:0%
+that's kind of the key to the problem.
+ 
+
+ align:start position:0%
+that's kind of the key to the problem.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+if that's also equal to the velocity of
+
+ align:start position:0%
+if that's also equal to the velocity of
+ 
+
+ align:start position:0%
+if that's also equal to the velocity of
+D with respect to O plus the velocity of
+
+ align:start position:0%
+D with respect to O plus the velocity of
+ 
+
+ align:start position:0%
+D with respect to O plus the velocity of
+C with respect to D
+
+ align:start position:0%
+C with respect to D
+ 
+
+ align:start position:0%
+C with respect to D
+and
+
+ align:start position:0%
+and
+ 
+
+ align:start position:0%
+and
+the velocity of D is this point of
+
+ align:start position:0%
+the velocity of D is this point of
+ 
+
+ align:start position:0%
+the velocity of D is this point of
+contact with the ground. What's that
+
+ align:start position:0%
+contact with the ground. What's that
+ 
+
+ align:start position:0%
+contact with the ground. What's that
+velocity?
+
+ align:start position:0%
+velocity?
+ 
+
+ align:start position:0%
+velocity?
+Zero. This is back to those
+
+ align:start position:0%
+Zero. This is back to those
+ 
+
+ align:start position:0%
+Zero. This is back to those
+instantaneous center of rotation things.
+
+ align:start position:0%
+instantaneous center of rotation things.
+ 
+
+ align:start position:0%
+instantaneous center of rotation things.
+zero there is what makes this equation
+
+ align:start position:0%
+zero there is what makes this equation
+ 
+
+ align:start position:0%
+zero there is what makes this equation
+easy.
+
+ align:start position:0%
+easy.
+ 
+
+ align:start position:0%
+easy.
+And then you have an you know how to
+
+ align:start position:0%
+And then you have an you know how to
+ 
+
+ align:start position:0%
+And then you have an you know how to
+compute the velocity of a rotating
+
+ align:start position:0%
+compute the velocity of a rotating
+ 
+
+ align:start position:0%
+compute the velocity of a rotating
+vector. This one's not changing length,
+
+ align:start position:0%
+vector. This one's not changing length,
+ 
+
+ align:start position:0%
+vector. This one's not changing length,
+but it is surely rotating about this
+
+ align:start position:0%
+but it is surely rotating about this
+ 
+
+ align:start position:0%
+but it is surely rotating about this
+point. And so there's going to be an
+
+ align:start position:0%
+point. And so there's going to be an
+ 
+
+ align:start position:0%
+point. And so there's going to be an
+omega cross r in here. And that'll allow
+
+ align:start position:0%
+omega cross r in here. And that'll allow
+ 
+
+ align:start position:0%
+omega cross r in here. And that'll allow
+you to solve for omega. And then once
+
+ align:start position:0%
+you to solve for omega. And then once
+ 
+
+ align:start position:0%
+you to solve for omega. And then once
+you know for omega, then you can solve
+
+ align:start position:0%
+you know for omega, then you can solve
+ 
+
+ align:start position:0%
+you know for omega, then you can solve
+for a, which is the real question that
+
+ align:start position:0%
+for a, which is the real question that
+ 
+
+ align:start position:0%
+for a, which is the real question that
+was asked. Okay,
+
+ align:start position:0%
+was asked. Okay,
+ 
+
+ align:start position:0%
+was asked. Okay,
+next one.
+
+ align:start position:0%
+next one.
+ 
+
+ align:start position:0%
+next one.
+This is
+
+ align:start position:0%
+This is
+ 
+
+ align:start position:0%
+This is
+the uh Oh yeah. So the starting position
+
+ align:start position:0%
+the uh Oh yeah. So the starting position
+ 
+
+ align:start position:0%
+the uh Oh yeah. So the starting position
+this is a spool.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Here's the arm
+
+ align:start position:0%
+Here's the arm
+ 
+
+ align:start position:0%
+Here's the arm
+and here is that it's the question is at
+
+ align:start position:0%
+and here is that it's the question is at
+ 
+
+ align:start position:0%
+and here is that it's the question is at
+0.25 m up here. And if you move it down
+
+ align:start position:0%
+0.25 m up here. And if you move it down
+ 
+
+ align:start position:0%
+0.25 m up here. And if you move it down
+to 0.15,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+will the system be able to go faster
+
+ align:start position:0%
+will the system be able to go faster
+ 
+
+ align:start position:0%
+will the system be able to go faster
+before it breaks loose or not? And your
+
+ align:start position:0%
+before it breaks loose or not? And your
+ 
+
+ align:start position:0%
+before it breaks loose or not? And your
+answer was most people said yes. And
+
+ align:start position:0%
+answer was most people said yes. And
+ 
+
+ align:start position:0%
+answer was most people said yes. And
+that basically that's true.
+
+ align:start position:0%
+that basically that's true.
+ 
+
+ align:start position:0%
+that basically that's true.
+What is it that's driving that thing
+
+ align:start position:0%
+What is it that's driving that thing
+ 
+
+ align:start position:0%
+What is it that's driving that thing
+providing the uh force that is trying to
+
+ align:start position:0%
+providing the uh force that is trying to
+ 
+
+ align:start position:0%
+providing the uh force that is trying to
+push it up the sleeve?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the the rod is as it going around is
+
+ align:start position:0%
+So the the rod is as it going around is
+ 
+
+ align:start position:0%
+So the the rod is as it going around is
+trying to drive that thing in a circle
+
+ align:start position:0%
+trying to drive that thing in a circle
+ 
+
+ align:start position:0%
+trying to drive that thing in a circle
+and therefore it is being accelerated
+
+ align:start position:0%
+and therefore it is being accelerated
+ 
+
+ align:start position:0%
+and therefore it is being accelerated
+in in this to the central point. So it
+
+ align:start position:0%
+in in this to the central point. So it
+ 
+
+ align:start position:0%
+in in this to the central point. So it
+has centripal acceleration and that
+
+ align:start position:0%
+has centripal acceleration and that
+ 
+
+ align:start position:0%
+has centripal acceleration and that
+requires forces and they come through
+
+ align:start position:0%
+requires forces and they come through
+ 
+
+ align:start position:0%
+requires forces and they come through
+the rod and that will develop normal
+
+ align:start position:0%
+the rod and that will develop normal
+ 
+
+ align:start position:0%
+the rod and that will develop normal
+forces and friction. So when you
+
+ align:start position:0%
+forces and friction. So when you
+ 
+
+ align:start position:0%
+forces and friction. So when you
+when you slide down the rod some to that
+
+ align:start position:0%
+when you slide down the rod some to that
+ 
+
+ align:start position:0%
+when you slide down the rod some to that
+new position is has that centrial
+
+ align:start position:0%
+new position is has that centrial
+ 
+
+ align:start position:0%
+new position is has that centrial
+acceleration gone up or down?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+R has gotten smaller. Centripal
+
+ align:start position:0%
+R has gotten smaller. Centripal
+ 
+
+ align:start position:0%
+R has gotten smaller. Centripal
+acceleration is
+
+ align:start position:0%
+acceleration is
+ 
+
+ align:start position:0%
+acceleration is
+r omega squared. Right? So you you might
+
+ align:start position:0%
+r omega squared. Right? So you you might
+ 
+
+ align:start position:0%
+r omega squared. Right? So you you might
+be speaking algebraically that so the
+
+ align:start position:0%
+be speaking algebraically that so the
+ 
+
+ align:start position:0%
+be speaking algebraically that so the
+magnitude of that centripal acceleration
+
+ align:start position:0%
+magnitude of that centripal acceleration
+ 
+
+ align:start position:0%
+magnitude of that centripal acceleration
+has gone up or down if you bring it
+
+ align:start position:0%
+has gone up or down if you bring it
+ 
+
+ align:start position:0%
+has gone up or down if you bring it
+closer to the axis
+
+ align:start position:0%
+closer to the axis
+ 
+
+ align:start position:0%
+closer to the axis
+down. Okay. So you can go faster to get
+
+ align:start position:0%
+down. Okay. So you can go faster to get
+ 
+
+ align:start position:0%
+down. Okay. So you can go faster to get
+up to the same uh level of acceleration
+
+ align:start position:0%
+up to the same uh level of acceleration
+ 
+
+ align:start position:0%
+up to the same uh level of acceleration
+where it'll break free. Next
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is oh the natural frequency of the
+
+ align:start position:0%
+this is oh the natural frequency of the
+ 
+
+ align:start position:0%
+this is oh the natural frequency of the
+pendulum. Some of you said yes, some of
+
+ align:start position:0%
+pendulum. Some of you said yes, some of
+ 
+
+ align:start position:0%
+pendulum. Some of you said yes, some of
+you said no, some not sure. You're going
+
+ align:start position:0%
+you said no, some not sure. You're going
+ 
+
+ align:start position:0%
+you said no, some not sure. You're going
+to find out. you're going to figure out
+
+ align:start position:0%
+to find out. you're going to figure out
+ 
+
+ align:start position:0%
+to find out. you're going to figure out
+the equation of motion of the system and
+
+ align:start position:0%
+the equation of motion of the system and
+ 
+
+ align:start position:0%
+the equation of motion of the system and
+it includes that torsional spring and
+
+ align:start position:0%
+it includes that torsional spring and
+ 
+
+ align:start position:0%
+it includes that torsional spring and
+mass is definitely going to be in it. So
+
+ align:start position:0%
+mass is definitely going to be in it. So
+ 
+
+ align:start position:0%
+mass is definitely going to be in it. So
+look for an answer that includes ma uh
+
+ align:start position:0%
+look for an answer that includes ma uh
+ 
+
+ align:start position:0%
+look for an answer that includes ma uh
+that you'll see that
+
+ align:start position:0%
+that you'll see that
+ 
+
+ align:start position:0%
+that you'll see that
+mass is going to show up in a way that
+
+ align:start position:0%
+mass is going to show up in a way that
+ 
+
+ align:start position:0%
+mass is going to show up in a way that
+if you solve for the natural frequency
+
+ align:start position:0%
+if you solve for the natural frequency
+ 
+
+ align:start position:0%
+if you solve for the natural frequency
+it won't it won't be uh it won't leave
+
+ align:start position:0%
+it won't it won't be uh it won't leave
+ 
+
+ align:start position:0%
+it won't it won't be uh it won't leave
+the final equation. Okay.
+
+ align:start position:0%
+the final equation. Okay.
+ 
+
+ align:start position:0%
+the final equation. Okay.
+And
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is the one about the two masses.
+
+ align:start position:0%
+So this is the one about the two masses.
+ 
+
+ align:start position:0%
+So this is the one about the two masses.
+And if the spring were zero, the second
+
+ align:start position:0%
+And if the spring were zero, the second
+ 
+
+ align:start position:0%
+And if the spring were zero, the second
+natural frequency of the system, the
+
+ align:start position:0%
+natural frequency of the system, the
+ 
+
+ align:start position:0%
+natural frequency of the system, the
+first natural frequency, when you have a
+
+ align:start position:0%
+first natural frequency, when you have a
+ 
+
+ align:start position:0%
+first natural frequency, when you have a
+system that has what's called a rigid
+
+ align:start position:0%
+system that has what's called a rigid
+ 
+
+ align:start position:0%
+system that has what's called a rigid
+body degree of freedom, when this thing
+
+ align:start position:0%
+body degree of freedom, when this thing
+ 
+
+ align:start position:0%
+body degree of freedom, when this thing
+when there's no K1 spring, this system
+
+ align:start position:0%
+when there's no K1 spring, this system
+ 
+
+ align:start position:0%
+when there's no K1 spring, this system
+looks like two masses on wheels
+
+ align:start position:0%
+looks like two masses on wheels
+ 
+
+ align:start position:0%
+looks like two masses on wheels
+connected by a spring and a dash pot.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And in the x direction there are no
+
+ align:start position:0%
+And in the x direction there are no
+ 
+
+ align:start position:0%
+And in the x direction there are no
+constraints.
+
+ align:start position:0%
+constraints.
+ 
+
+ align:start position:0%
+constraints.
+So if I set this system to vibrating,
+
+ align:start position:0%
+So if I set this system to vibrating,
+ 
+
+ align:start position:0%
+So if I set this system to vibrating,
+what can you say about the motion of its
+
+ align:start position:0%
+what can you say about the motion of its
+ 
+
+ align:start position:0%
+what can you say about the motion of its
+center of mass?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So could you find the center of mass of
+
+ align:start position:0%
+So could you find the center of mass of
+ 
+
+ align:start position:0%
+So could you find the center of mass of
+that system? Got to give you the masses
+
+ align:start position:0%
+that system? Got to give you the masses
+ 
+
+ align:start position:0%
+that system? Got to give you the masses
+of it. But you have some m1
+
+ align:start position:0%
+of it. But you have some m1
+ 
+
+ align:start position:0%
+of it. But you have some m1
+and an m2 and we'll give we'll call this
+
+ align:start position:0%
+and an m2 and we'll give we'll call this
+ 
+
+ align:start position:0%
+and an m2 and we'll give we'll call this
+the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+x in that direction. Could you determine
+
+ align:start position:0%
+x in that direction. Could you determine
+ 
+
+ align:start position:0%
+x in that direction. Could you determine
+the center of mass of the system? You
+
+ align:start position:0%
+the center of mass of the system? You
+ 
+
+ align:start position:0%
+the center of mass of the system? You
+know how to do that, right? It's going
+
+ align:start position:0%
+know how to do that, right? It's going
+ 
+
+ align:start position:0%
+know how to do that, right? It's going
+to be depend if they were equal in mass,
+
+ align:start position:0%
+to be depend if they were equal in mass,
+ 
+
+ align:start position:0%
+to be depend if they were equal in mass,
+it'd be right in the center. If this was
+
+ align:start position:0%
+it'd be right in the center. If this was
+ 
+
+ align:start position:0%
+it'd be right in the center. If this was
+bigger, it would be over here. Something
+
+ align:start position:0%
+bigger, it would be over here. Something
+ 
+
+ align:start position:0%
+bigger, it would be over here. Something
+like that. But so the we know that for a
+
+ align:start position:0%
+like that. But so the we know that for a
+ 
+
+ align:start position:0%
+like that. But so the we know that for a
+system of particles
+
+ align:start position:0%
+system of particles
+ 
+
+ align:start position:0%
+system of particles
+the sum of the external forces on the
+
+ align:start position:0%
+the sum of the external forces on the
+ 
+
+ align:start position:0%
+the sum of the external forces on the
+system is equal to the mass of the
+
+ align:start position:0%
+system is equal to the mass of the
+ 
+
+ align:start position:0%
+system is equal to the mass of the
+system times the acceleration of the
+
+ align:start position:0%
+system times the acceleration of the
+ 
+
+ align:start position:0%
+system times the acceleration of the
+what?
+
+ align:start position:0%
+what?
+ 
+
+ align:start position:0%
+what?
+Center of mass.
+
+ align:start position:0%
+Center of mass.
+ 
+
+ align:start position:0%
+Center of mass.
+What are the external forces in the
+
+ align:start position:0%
+What are the external forces in the
+ 
+
+ align:start position:0%
+What are the external forces in the
+horizontal direction?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How big are they?
+
+ align:start position:0%
+How big are they?
+ 
+
+ align:start position:0%
+How big are they?
+Zero. Therefore, what can be the
+
+ align:start position:0%
+Zero. Therefore, what can be the
+ 
+
+ align:start position:0%
+Zero. Therefore, what can be the
+acceleration of the center of mass?
+
+ align:start position:0%
+acceleration of the center of mass?
+ 
+
+ align:start position:0%
+acceleration of the center of mass?
+Zero. This thing will actually in this
+
+ align:start position:0%
+Zero. This thing will actually in this
+ 
+
+ align:start position:0%
+Zero. This thing will actually in this
+second natural frequency it'll sit there
+
+ align:start position:0%
+second natural frequency it'll sit there
+ 
+
+ align:start position:0%
+second natural frequency it'll sit there
+and just oscillate back and forth. One
+
+ align:start position:0%
+and just oscillate back and forth. One
+ 
+
+ align:start position:0%
+and just oscillate back and forth. One
+mass going in one direction, one the
+
+ align:start position:0%
+mass going in one direction, one the
+ 
+
+ align:start position:0%
+mass going in one direction, one the
+other and but it center of mass won't
+
+ align:start position:0%
+other and but it center of mass won't
+ 
+
+ align:start position:0%
+other and but it center of mass won't
+move. The other degree of freedom and
+
+ align:start position:0%
+move. The other degree of freedom and
+ 
+
+ align:start position:0%
+move. The other degree of freedom and
+the other natural frequency, the one
+
+ align:start position:0%
+the other natural frequency, the one
+ 
+
+ align:start position:0%
+the other natural frequency, the one
+that has zero natural frequency is rigid
+
+ align:start position:0%
+that has zero natural frequency is rigid
+ 
+
+ align:start position:0%
+that has zero natural frequency is rigid
+body motion. No relative motion. Give
+
+ align:start position:0%
+body motion. No relative motion. Give
+ 
+
+ align:start position:0%
+body motion. No relative motion. Give
+this thing a little push, some initial
+
+ align:start position:0%
+this thing a little push, some initial
+ 
+
+ align:start position:0%
+this thing a little push, some initial
+momentum. It'll just sit there and roll
+
+ align:start position:0%
+momentum. It'll just sit there and roll
+ 
+
+ align:start position:0%
+momentum. It'll just sit there and roll
+forever. The mass is not moving relative
+
+ align:start position:0%
+forever. The mass is not moving relative
+ 
+
+ align:start position:0%
+forever. The mass is not moving relative
+to one another. It just rolls and rolls
+
+ align:start position:0%
+to one another. It just rolls and rolls
+ 
+
+ align:start position:0%
+to one another. It just rolls and rolls
+and rolls and rolls and never comes
+
+ align:start position:0%
+and rolls and rolls and never comes
+ 
+
+ align:start position:0%
+and rolls and rolls and never comes
+back. infinite period zero natural
+
+ align:start position:0%
+back. infinite period zero natural
+ 
+
+ align:start position:0%
+back. infinite period zero natural
+frequency. Okay, we're talking about
+
+ align:start position:0%
+frequency. Okay, we're talking about
+ 
+
+ align:start position:0%
+frequency. Okay, we're talking about
+fictitious forces the other day and um
+
+ align:start position:0%
+fictitious forces the other day and um
+ 
+
+ align:start position:0%
+fictitious forces the other day and um
+there are times when they are they're
+
+ align:start position:0%
+there are times when they are they're
+ 
+
+ align:start position:0%
+there are times when they are they're
+useful but they're sort of like giving a
+
+ align:start position:0%
+useful but they're sort of like giving a
+ 
+
+ align:start position:0%
+useful but they're sort of like giving a
+little kid a loaded gun. You know, you
+
+ align:start position:0%
+little kid a loaded gun. You know, you
+ 
+
+ align:start position:0%
+little kid a loaded gun. You know, you
+can really get yourself in trouble
+
+ align:start position:0%
+can really get yourself in trouble
+ 
+
+ align:start position:0%
+can really get yourself in trouble
+quickly. So, I'm not not advocating a
+
+ align:start position:0%
+quickly. So, I'm not not advocating a
+ 
+
+ align:start position:0%
+quickly. So, I'm not not advocating a
+lot of use of it, but it's good to have
+
+ align:start position:0%
+lot of use of it, but it's good to have
+ 
+
+ align:start position:0%
+lot of use of it, but it's good to have
+a little insight. One of one of the
+
+ align:start position:0%
+a little insight. One of one of the
+ 
+
+ align:start position:0%
+a little insight. One of one of the
+students when I after the lecture last
+
+ align:start position:0%
+students when I after the lecture last
+ 
+
+ align:start position:0%
+students when I after the lecture last
+time a student um mentioned to me he
+
+ align:start position:0%
+time a student um mentioned to me he
+ 
+
+ align:start position:0%
+time a student um mentioned to me he
+said the you know the way I was taught
+
+ align:start position:0%
+said the you know the way I was taught
+ 
+
+ align:start position:0%
+said the you know the way I was taught
+about fictitious forces is that we use
+
+ align:start position:0%
+about fictitious forces is that we use
+ 
+
+ align:start position:0%
+about fictitious forces is that we use
+them to patch up a problem when we're
+
+ align:start position:0%
+them to patch up a problem when we're
+ 
+
+ align:start position:0%
+them to patch up a problem when we're
+trying to work in a non-inertial frame.
+
+ align:start position:0%
+trying to work in a non-inertial frame.
+ 
+
+ align:start position:0%
+trying to work in a non-inertial frame.
+How can you make Newton's laws apply
+
+ align:start position:0%
+How can you make Newton's laws apply
+ 
+
+ align:start position:0%
+How can you make Newton's laws apply
+if you are in an in a non-inertial
+
+ align:start position:0%
+if you are in an in a non-inertial
+ 
+
+ align:start position:0%
+if you are in an in a non-inertial
+frame? Otherwise an accelerating
+
+ align:start position:0%
+frame? Otherwise an accelerating
+ 
+
+ align:start position:0%
+frame? Otherwise an accelerating
+reference frame. So, I just thought I
+
+ align:start position:0%
+reference frame. So, I just thought I
+ 
+
+ align:start position:0%
+reference frame. So, I just thought I
+would revisit a little bit of what we
+
+ align:start position:0%
+would revisit a little bit of what we
+ 
+
+ align:start position:0%
+would revisit a little bit of what we
+said the other day you with uh
+
+ align:start position:0%
+said the other day you with uh
+ 
+
+ align:start position:0%
+said the other day you with uh
+explaining things that way a little bit.
+
+ align:start position:0%
+explaining things that way a little bit.
+ 
+
+ align:start position:0%
+explaining things that way a little bit.
+So, it might just turn out to be
+
+ align:start position:0%
+So, it might just turn out to be
+ 
+
+ align:start position:0%
+So, it might just turn out to be
+familiar with you for you. And let's
+
+ align:start position:0%
+familiar with you for you. And let's
+ 
+
+ align:start position:0%
+familiar with you for you. And let's
+just look.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+This is go back quickly and revisit that
+
+ align:start position:0%
+This is go back quickly and revisit that
+ 
+
+ align:start position:0%
+This is go back quickly and revisit that
+elevator problem. So, you remember
+
+ align:start position:0%
+elevator problem. So, you remember
+ 
+
+ align:start position:0%
+elevator problem. So, you remember
+you're you're here. You got some mass m.
+
+ align:start position:0%
+you're you're here. You got some mass m.
+ 
+
+ align:start position:0%
+you're you're here. You got some mass m.
+You're standing on some scales.
+
+ align:start position:0%
+You're standing on some scales.
+ 
+
+ align:start position:0%
+You're standing on some scales.
+And I'm we want I want to know what the
+
+ align:start position:0%
+And I'm we want I want to know what the
+ 
+
+ align:start position:0%
+And I'm we want I want to know what the
+scales are going to read. Now, we did
+
+ align:start position:0%
+scales are going to read. Now, we did
+ 
+
+ align:start position:0%
+scales are going to read. Now, we did
+this one quickly the other day. I'm just
+
+ align:start position:0%
+this one quickly the other day. I'm just
+ 
+
+ align:start position:0%
+this one quickly the other day. I'm just
+going to revisit it. The uh
+
+ align:start position:0%
+going to revisit it. The uh
+ 
+
+ align:start position:0%
+going to revisit it. The uh
+and it's accelerating. This is point A.
+
+ align:start position:0%
+and it's accelerating. This is point A.
+ 
+
+ align:start position:0%
+and it's accelerating. This is point A.
+And here down here is O, my inertial
+
+ align:start position:0%
+And here down here is O, my inertial
+ 
+
+ align:start position:0%
+And here down here is O, my inertial
+frame.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And the acceleration of A with respect
+
+ align:start position:0%
+And the acceleration of A with respect
+ 
+
+ align:start position:0%
+And the acceleration of A with respect
+to O is plus a quarter of G in the
+
+ align:start position:0%
+to O is plus a quarter of G in the
+ 
+
+ align:start position:0%
+to O is plus a quarter of G in the
+J hat direction. Okay.
+
+ align:start position:0%
+J hat direction. Okay.
+ 
+
+ align:start position:0%
+J hat direction. Okay.
+Now this thing when you think about this
+
+ align:start position:0%
+Now this thing when you think about this
+ 
+
+ align:start position:0%
+Now this thing when you think about this
+if you were want you're trying to do
+
+ align:start position:0%
+if you were want you're trying to do
+ 
+
+ align:start position:0%
+if you were want you're trying to do
+physics in the elevator but it's an
+
+ align:start position:0%
+physics in the elevator but it's an
+ 
+
+ align:start position:0%
+physics in the elevator but it's an
+accelerating frame. So Newton's laws
+
+ align:start position:0%
+accelerating frame. So Newton's laws
+ 
+
+ align:start position:0%
+accelerating frame. So Newton's laws
+don't apply.
+
+ align:start position:0%
+don't apply.
+ 
+
+ align:start position:0%
+don't apply.
+And in fact, so you're in the elevator,
+
+ align:start position:0%
+And in fact, so you're in the elevator,
+ 
+
+ align:start position:0%
+And in fact, so you're in the elevator,
+you can't see that you're accelerating,
+
+ align:start position:0%
+you can't see that you're accelerating,
+ 
+
+ align:start position:0%
+you can't see that you're accelerating,
+but you could measure your weight, for
+
+ align:start position:0%
+but you could measure your weight, for
+ 
+
+ align:start position:0%
+but you could measure your weight, for
+example.
+
+ align:start position:0%
+example.
+ 
+
+ align:start position:0%
+example.
+So,
+
+ align:start position:0%
+So,
+ 
+
+ align:start position:0%
+So,
+how do you fix up
+
+ align:start position:0%
+how do you fix up
+ 
+
+ align:start position:0%
+how do you fix up
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+equations so that you can predict the
+
+ align:start position:0%
+equations so that you can predict the
+ 
+
+ align:start position:0%
+equations so that you can predict the
+right answer?
+
+ align:start position:0%
+right answer?
+ 
+
+ align:start position:0%
+right answer?
+And to do that basically you have to add
+
+ align:start position:0%
+And to do that basically you have to add
+ 
+
+ align:start position:0%
+And to do that basically you have to add
+in
+
+ align:start position:0%
+in
+ 
+
+ align:start position:0%
+in
+a force a fictitious force that accounts
+
+ align:start position:0%
+a force a fictitious force that accounts
+ 
+
+ align:start position:0%
+a force a fictitious force that accounts
+for the
+
+ align:start position:0%
+for the
+ 
+
+ align:start position:0%
+for the
+additional forces you will feel in this
+
+ align:start position:0%
+additional forces you will feel in this
+ 
+
+ align:start position:0%
+additional forces you will feel in this
+system
+
+ align:start position:0%
+system
+ 
+
+ align:start position:0%
+system
+due to the acceleration.
+
+ align:start position:0%
+due to the acceleration.
+ 
+
+ align:start position:0%
+due to the acceleration.
+Okay. So
+
+ align:start position:0%
+Okay. So
+ 
+
+ align:start position:0%
+Okay. So
+remember the way we did this problem. If
+
+ align:start position:0%
+remember the way we did this problem. If
+ 
+
+ align:start position:0%
+remember the way we did this problem. If
+you do this problem just in the
+
+ align:start position:0%
+you do this problem just in the
+ 
+
+ align:start position:0%
+you do this problem just in the
+straightforward way, the summation of
+
+ align:start position:0%
+straightforward way, the summation of
+ 
+
+ align:start position:0%
+straightforward way, the summation of
+the external forces
+
+ align:start position:0%
+the external forces
+ 
+
+ align:start position:0%
+the external forces
+in the y direction
+
+ align:start position:0%
+in the y direction
+ 
+
+ align:start position:0%
+in the y direction
+is the mass times the acceleration a
+
+ align:start position:0%
+is the mass times the acceleration a
+ 
+
+ align:start position:0%
+is the mass times the acceleration a
+with respect to o.
+
+ align:start position:0%
+with respect to o.
+ 
+
+ align:start position:0%
+with respect to o.
+And we need a free body diagram. In the
+
+ align:start position:0%
+And we need a free body diagram. In the
+ 
+
+ align:start position:0%
+And we need a free body diagram. In the
+free body diagram of this just this mass
+
+ align:start position:0%
+free body diagram of this just this mass
+ 
+
+ align:start position:0%
+free body diagram of this just this mass
+here,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+you have an mg
+
+ align:start position:0%
+you have an mg
+ 
+
+ align:start position:0%
+you have an mg
+downwards and an n upwards. And so you'd
+
+ align:start position:0%
+downwards and an n upwards. And so you'd
+ 
+
+ align:start position:0%
+downwards and an n upwards. And so you'd
+say this is equal to n minus
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mg.
+
+ align:start position:0%
+mg.
+ 
+
+ align:start position:0%
+mg.
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+if you are trying to do this experime
+
+ align:start position:0%
+if you are trying to do this experime
+ 
+
+ align:start position:0%
+if you are trying to do this experime
+you're doing this experiment inside you
+
+ align:start position:0%
+you're doing this experiment inside you
+ 
+
+ align:start position:0%
+you're doing this experiment inside you
+can measure this n that's going to be
+
+ align:start position:0%
+can measure this n that's going to be
+ 
+
+ align:start position:0%
+can measure this n that's going to be
+your weight and you would like to do
+
+ align:start position:0%
+your weight and you would like to do
+ 
+
+ align:start position:0%
+your weight and you would like to do
+this by fictitious forces you say that
+
+ align:start position:0%
+this by fictitious forces you say that
+ 
+
+ align:start position:0%
+this by fictitious forces you say that
+ah the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+summation of the external real forces
+
+ align:start position:0%
+summation of the external real forces
+ 
+
+ align:start position:0%
+summation of the external real forces
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+this mass times the acceleration of A
+
+ align:start position:0%
+this mass times the acceleration of A
+ 
+
+ align:start position:0%
+this mass times the acceleration of A
+with respect to
+
+ align:start position:0%
+with respect to
+ 
+
+ align:start position:0%
+with respect to
+O has got to be equal to zero. And
+
+ align:start position:0%
+O has got to be equal to zero. And
+ 
+
+ align:start position:0%
+O has got to be equal to zero. And
+that's then
+
+ align:start position:0%
+that's then
+ 
+
+ align:start position:0%
+that's then
+N minus
+
+ align:start position:0%
+N minus
+ 
+
+ align:start position:0%
+N minus
+MG
+
+ align:start position:0%
+MG
+ 
+
+ align:start position:0%
+MG
+minus MG
+
+ align:start position:0%
+minus MG
+ 
+
+ align:start position:0%
+minus MG
+over 4. Here's your fictitious force.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that's as if then you've come over
+
+ align:start position:0%
+And that's as if then you've come over
+ 
+
+ align:start position:0%
+And that's as if then you've come over
+here and you've added
+
+ align:start position:0%
+here and you've added
+ 
+
+ align:start position:0%
+here and you've added
+a force an additional force on this free
+
+ align:start position:0%
+a force an additional force on this free
+ 
+
+ align:start position:0%
+a force an additional force on this free
+body diagram that looks like mg g over4.
+
+ align:start position:0%
+body diagram that looks like mg g over4.
+ 
+
+ align:start position:0%
+body diagram that looks like mg g over4.
+And now you say the sum of these forces
+
+ align:start position:0%
+And now you say the sum of these forces
+ 
+
+ align:start position:0%
+And now you say the sum of these forces
+this is the correction
+
+ align:start position:0%
+this is the correction
+ 
+
+ align:start position:0%
+this is the correction
+that's allowing you now to work in this
+
+ align:start position:0%
+that's allowing you now to work in this
+ 
+
+ align:start position:0%
+that's allowing you now to work in this
+accelerating frame.
+
+ align:start position:0%
+accelerating frame.
+ 
+
+ align:start position:0%
+accelerating frame.
+If you treat do this free body diagram
+
+ align:start position:0%
+If you treat do this free body diagram
+ 
+
+ align:start position:0%
+If you treat do this free body diagram
+and sum these up then you will find the
+
+ align:start position:0%
+and sum these up then you will find the
+ 
+
+ align:start position:0%
+and sum these up then you will find the
+uh
+
+ align:start position:0%
+uh
+ 
+
+ align:start position:0%
+uh
+this expression which you can solve for
+
+ align:start position:0%
+this expression which you can solve for
+ 
+
+ align:start position:0%
+this expression which you can solve for
+n and you'll get m 5 over 4 g. Okay, in
+
+ align:start position:0%
+n and you'll get m 5 over 4 g. Okay, in
+ 
+
+ align:start position:0%
+n and you'll get m 5 over 4 g. Okay, in
+fact if you stood in the scales that's
+
+ align:start position:0%
+fact if you stood in the scales that's
+ 
+
+ align:start position:0%
+fact if you stood in the scales that's
+what you get.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. So, I want to I want to do
+
+ align:start position:0%
+All right. So, I want to I want to do
+ 
+
+ align:start position:0%
+All right. So, I want to I want to do
+this is example one. I want to do sort
+
+ align:start position:0%
+this is example one. I want to do sort
+ 
+
+ align:start position:0%
+this is example one. I want to do sort
+of example 1.5. The cable breaks
+
+ align:start position:0%
+of example 1.5. The cable breaks
+ 
+
+ align:start position:0%
+of example 1.5. The cable breaks
+on this elevator.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Your free body diagram still has an mg
+
+ align:start position:0%
+Your free body diagram still has an mg
+ 
+
+ align:start position:0%
+Your free body diagram still has an mg
+on it.
+
+ align:start position:0%
+on it.
+ 
+
+ align:start position:0%
+on it.
+You're still inside. You're still
+
+ align:start position:0%
+You're still inside. You're still
+ 
+
+ align:start position:0%
+You're still inside. You're still
+measuring forces.
+
+ align:start position:0%
+measuring forces.
+ 
+
+ align:start position:0%
+measuring forces.
+And you want to use this idea of a
+
+ align:start position:0%
+And you want to use this idea of a
+ 
+
+ align:start position:0%
+And you want to use this idea of a
+fictitious force to help you sort out
+
+ align:start position:0%
+fictitious force to help you sort out
+ 
+
+ align:start position:0%
+fictitious force to help you sort out
+what forces will you feel inside that
+
+ align:start position:0%
+what forces will you feel inside that
+ 
+
+ align:start position:0%
+what forces will you feel inside that
+elevator.
+
+ align:start position:0%
+elevator.
+ 
+
+ align:start position:0%
+elevator.
+Okay?
+
+ align:start position:0%
+Okay?
+ 
+
+ align:start position:0%
+Okay?
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+so just just you know you know how to do
+
+ align:start position:0%
+so just just you know you know how to do
+ 
+
+ align:start position:0%
+so just just you know you know how to do
+the answer in the straightforward way.
+
+ align:start position:0%
+the answer in the straightforward way.
+ 
+
+ align:start position:0%
+the answer in the straightforward way.
+the ex sum of the external forces
+
+ align:start position:0%
+the ex sum of the external forces
+ 
+
+ align:start position:0%
+the ex sum of the external forces
+is minus mg
+
+ align:start position:0%
+is minus mg
+ 
+
+ align:start position:0%
+is minus mg
+and that's equal to the mass times the
+
+ align:start position:0%
+and that's equal to the mass times the
+ 
+
+ align:start position:0%
+and that's equal to the mass times the
+acceleration of a with respect to o and
+
+ align:start position:0%
+acceleration of a with respect to o and
+ 
+
+ align:start position:0%
+acceleration of a with respect to o and
+therefore
+
+ align:start position:0%
+therefore
+ 
+
+ align:start position:0%
+therefore
+acceleration of a with respect to o is
+
+ align:start position:0%
+acceleration of a with respect to o is
+ 
+
+ align:start position:0%
+acceleration of a with respect to o is
+just minus g right
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so
+
+ align:start position:0%
+so
+ 
+
+ align:start position:0%
+so
+mean and you could have told me that you
+
+ align:start position:0%
+mean and you could have told me that you
+ 
+
+ align:start position:0%
+mean and you could have told me that you
+know that's trivial that you drop the
+
+ align:start position:0%
+know that's trivial that you drop the
+ 
+
+ align:start position:0%
+know that's trivial that you drop the
+thing accelerates at the at acceleration
+
+ align:start position:0%
+thing accelerates at the at acceleration
+ 
+
+ align:start position:0%
+thing accelerates at the at acceleration
+of gravity. So, I want to think I want
+
+ align:start position:0%
+of gravity. So, I want to think I want
+ 
+
+ align:start position:0%
+of gravity. So, I want to think I want
+to know what's what's the how you're
+
+ align:start position:0%
+to know what's what's the how you're
+ 
+
+ align:start position:0%
+to know what's what's the how you're
+doing the experiment inside. You don't
+
+ align:start position:0%
+doing the experiment inside. You don't
+ 
+
+ align:start position:0%
+doing the experiment inside. You don't
+know that you're accelerating. All
+
+ align:start position:0%
+know that you're accelerating. All
+ 
+
+ align:start position:0%
+know that you're accelerating. All
+you're doing is measurements, but you've
+
+ align:start position:0%
+you're doing is measurements, but you've
+ 
+
+ align:start position:0%
+you're doing is measurements, but you've
+been you've been told how to correct it.
+
+ align:start position:0%
+been you've been told how to correct it.
+ 
+
+ align:start position:0%
+been you've been told how to correct it.
+So, let's put in the fictitious force,
+
+ align:start position:0%
+So, let's put in the fictitious force,
+ 
+
+ align:start position:0%
+So, let's put in the fictitious force,
+which is minus m a0. And that means mass
+
+ align:start position:0%
+which is minus m a0. And that means mass
+ 
+
+ align:start position:0%
+which is minus m a0. And that means mass
+times acceleration.
+
+ align:start position:0%
+times acceleration.
+ 
+
+ align:start position:0%
+times acceleration.
+This one
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the mass times the acceleration is
+
+ align:start position:0%
+the mass times the acceleration is
+ 
+
+ align:start position:0%
+the mass times the acceleration is
+downwards. So minus that the fictitious
+
+ align:start position:0%
+downwards. So minus that the fictitious
+ 
+
+ align:start position:0%
+downwards. So minus that the fictitious
+force is an mg g force upwards. And what
+
+ align:start position:0%
+force is an mg g force upwards. And what
+ 
+
+ align:start position:0%
+force is an mg g force upwards. And what
+do you feel?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+What do the scales read?
+
+ align:start position:0%
+What do the scales read?
+ 
+
+ align:start position:0%
+What do the scales read?
+Nothing. You feel absolutely nothing.
+
+ align:start position:0%
+Nothing. You feel absolutely nothing.
+ 
+
+ align:start position:0%
+Nothing. You feel absolutely nothing.
+Right?
+
+ align:start position:0%
+Right?
+ 
+
+ align:start position:0%
+Right?
+Okay. So just an aside kind of question.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Because I know this is confused
+
+ align:start position:0%
+Because I know this is confused
+ 
+
+ align:start position:0%
+Because I know this is confused
+occasionally we all get confused around
+
+ align:start position:0%
+occasionally we all get confused around
+ 
+
+ align:start position:0%
+occasionally we all get confused around
+this is is gravity
+
+ align:start position:0%
+this is is gravity
+ 
+
+ align:start position:0%
+this is is gravity
+now in these pro problems that we do is
+
+ align:start position:0%
+now in these pro problems that we do is
+ 
+
+ align:start position:0%
+now in these pro problems that we do is
+gravity
+
+ align:start position:0%
+gravity
+ 
+
+ align:start position:0%
+gravity
+and acceleration.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+We all we say all the time I use the
+
+ align:start position:0%
+We all we say all the time I use the
+ 
+
+ align:start position:0%
+We all we say all the time I use the
+phrase the acceleration of gravity. How
+
+ align:start position:0%
+phrase the acceleration of gravity. How
+ 
+
+ align:start position:0%
+phrase the acceleration of gravity. How
+many times have you ever said that? Have
+
+ align:start position:0%
+many times have you ever said that? Have
+ 
+
+ align:start position:0%
+many times have you ever said that? Have
+you ever said that? The acceleration of
+
+ align:start position:0%
+you ever said that? The acceleration of
+ 
+
+ align:start position:0%
+you ever said that? The acceleration of
+gravity. What do we mean? What we mean
+
+ align:start position:0%
+gravity. What do we mean? What we mean
+ 
+
+ align:start position:0%
+gravity. What do we mean? What we mean
+is this is when you let something drop
+
+ align:start position:0%
+is this is when you let something drop
+ 
+
+ align:start position:0%
+is this is when you let something drop
+in freef fall, it'll accelerate at g.
+
+ align:start position:0%
+in freef fall, it'll accelerate at g.
+ 
+
+ align:start position:0%
+in freef fall, it'll accelerate at g.
+But the way we apply for when we're
+
+ align:start position:0%
+But the way we apply for when we're
+ 
+
+ align:start position:0%
+But the way we apply for when we're
+writing out equations of motion, we say
+
+ align:start position:0%
+writing out equations of motion, we say
+ 
+
+ align:start position:0%
+writing out equations of motion, we say
+the sum of the external forces is equal
+
+ align:start position:0%
+the sum of the external forces is equal
+ 
+
+ align:start position:0%
+the sum of the external forces is equal
+to mass times the acceleration. Where
+
+ align:start position:0%
+to mass times the acceleration. Where
+ 
+
+ align:start position:0%
+to mass times the acceleration. Where
+does gravity go? It's a force.
+
+ align:start position:0%
+does gravity go? It's a force.
+ 
+
+ align:start position:0%
+does gravity go? It's a force.
+So this is another thing not to let not
+
+ align:start position:0%
+So this is another thing not to let not
+ 
+
+ align:start position:0%
+So this is another thing not to let not
+to get confused by by is to think about
+
+ align:start position:0%
+to get confused by by is to think about
+ 
+
+ align:start position:0%
+to get confused by by is to think about
+gravity as being an acceleration. We
+
+ align:start position:0%
+gravity as being an acceleration. We
+ 
+
+ align:start position:0%
+gravity as being an acceleration. We
+spent a lot of time figuring out ways to
+
+ align:start position:0%
+spent a lot of time figuring out ways to
+ 
+
+ align:start position:0%
+spent a lot of time figuring out ways to
+write accelerations, right, in rotating,
+
+ align:start position:0%
+write accelerations, right, in rotating,
+ 
+
+ align:start position:0%
+write accelerations, right, in rotating,
+translating reference frames. Gravity
+
+ align:start position:0%
+translating reference frames. Gravity
+ 
+
+ align:start position:0%
+translating reference frames. Gravity
+never pops up in there. It always comes
+
+ align:start position:0%
+never pops up in there. It always comes
+ 
+
+ align:start position:0%
+never pops up in there. It always comes
+up on the force side of the equation.
+
+ align:start position:0%
+up on the force side of the equation.
+ 
+
+ align:start position:0%
+up on the force side of the equation.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Ah. All right. So, one one last
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+example from last time, but it's
+
+ align:start position:0%
+example from last time, but it's
+ 
+
+ align:start position:0%
+example from last time, but it's
+relevant to
+
+ align:start position:0%
+relevant to
+ 
+
+ align:start position:0%
+relevant to
+problem on the homework. So we have this
+
+ align:start position:0%
+problem on the homework. So we have this
+ 
+
+ align:start position:0%
+problem on the homework. So we have this
+shaft spinning.
+
+ align:start position:0%
+shaft spinning.
+ 
+
+ align:start position:0%
+shaft spinning.
+This is the Z-axis
+
+ align:start position:0%
+This is the Z-axis
+ 
+
+ align:start position:0%
+This is the Z-axis
+spinning at constant rate omega.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we'll use this is R
+
+ align:start position:0%
+And we'll use this is R
+ 
+
+ align:start position:0%
+And we'll use this is R
+hat and this is Z K hat. These are these
+
+ align:start position:0%
+hat and this is Z K hat. These are these
+ 
+
+ align:start position:0%
+hat and this is Z K hat. These are these
+two position. These are the length R hat
+
+ align:start position:0%
+two position. These are the length R hat
+ 
+
+ align:start position:0%
+two position. These are the length R hat
+direction and the height Z using
+
+ align:start position:0%
+direction and the height Z using
+ 
+
+ align:start position:0%
+direction and the height Z using
+cylindrical coordinates. And now I just
+
+ align:start position:0%
+cylindrical coordinates. And now I just
+ 
+
+ align:start position:0%
+cylindrical coordinates. And now I just
+want you to let's just use this notion
+
+ align:start position:0%
+want you to let's just use this notion
+ 
+
+ align:start position:0%
+want you to let's just use this notion
+of fictitious forces to figure out what
+
+ align:start position:0%
+of fictitious forces to figure out what
+ 
+
+ align:start position:0%
+of fictitious forces to figure out what
+the first what's the what's the
+
+ align:start position:0%
+the first what's the what's the
+ 
+
+ align:start position:0%
+the first what's the what's the
+fictitious force on this system.
+
+ align:start position:0%
+fictitious force on this system.
+ 
+
+ align:start position:0%
+fictitious force on this system.
+So we're trying to account you're out
+
+ align:start position:0%
+So we're trying to account you're out
+ 
+
+ align:start position:0%
+So we're trying to account you're out
+there remember this is now this notion
+
+ align:start position:0%
+there remember this is now this notion
+ 
+
+ align:start position:0%
+there remember this is now this notion
+of you're out there where this mass is
+
+ align:start position:0%
+of you're out there where this mass is
+ 
+
+ align:start position:0%
+of you're out there where this mass is
+you're riding with this mass and you're
+
+ align:start position:0%
+you're riding with this mass and you're
+ 
+
+ align:start position:0%
+you're riding with this mass and you're
+trying to say what are the forces what
+
+ align:start position:0%
+trying to say what are the forces what
+ 
+
+ align:start position:0%
+trying to say what are the forces what
+forces am I going to feel? You want to
+
+ align:start position:0%
+forces am I going to feel? You want to
+ 
+
+ align:start position:0%
+forces am I going to feel? You want to
+be able to predict it correctly. So you
+
+ align:start position:0%
+be able to predict it correctly. So you
+ 
+
+ align:start position:0%
+be able to predict it correctly. So you
+have to find a fictitious force that you
+
+ align:start position:0%
+have to find a fictitious force that you
+ 
+
+ align:start position:0%
+have to find a fictitious force that you
+can bring in that accounts for an
+
+ align:start position:0%
+can bring in that accounts for an
+ 
+
+ align:start position:0%
+can bring in that accounts for an
+acceleration. And what acceleration is
+
+ align:start position:0%
+acceleration. And what acceleration is
+ 
+
+ align:start position:0%
+acceleration. And what acceleration is
+are we feeling out there?
+
+ align:start position:0%
+are we feeling out there?
+ 
+
+ align:start position:0%
+are we feeling out there?
+Centripal, right? And the centripal
+
+ align:start position:0%
+Centripal, right? And the centripal
+ 
+
+ align:start position:0%
+Centripal, right? And the centripal
+acceleration
+
+ align:start position:0%
+acceleration
+ 
+
+ align:start position:0%
+acceleration
+the uh we want the sum of the external
+
+ align:start position:0%
+the uh we want the sum of the external
+ 
+
+ align:start position:0%
+the uh we want the sum of the external
+forces
+
+ align:start position:0%
+forces
+ 
+
+ align:start position:0%
+forces
+and this is going to be in the r hat
+
+ align:start position:0%
+and this is going to be in the r hat
+ 
+
+ align:start position:0%
+and this is going to be in the r hat
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+m times the and now this is we need
+
+ align:start position:0%
+m times the and now this is we need
+ 
+
+ align:start position:0%
+m times the and now this is we need
+reference frames here. So you have a
+
+ align:start position:0%
+reference frames here. So you have a
+ 
+
+ align:start position:0%
+reference frames here. So you have a
+fixed frame O
+
+ align:start position:0%
+fixed frame O
+ 
+
+ align:start position:0%
+fixed frame O
+XY you have a rotating frame here A X
+
+ align:start position:0%
+XY you have a rotating frame here A X
+ 
+
+ align:start position:0%
+XY you have a rotating frame here A X
+prime Yprime Zprime and this is your
+
+ align:start position:0%
+prime Yprime Zprime and this is your
+ 
+
+ align:start position:0%
+prime Yprime Zprime and this is your
+point B up here.
+
+ align:start position:0%
+point B up here.
+ 
+
+ align:start position:0%
+point B up here.
+So
+
+ align:start position:0%
+So
+ 
+
+ align:start position:0%
+So
+the sum of the external forces minus the
+
+ align:start position:0%
+the sum of the external forces minus the
+ 
+
+ align:start position:0%
+the sum of the external forces minus the
+mass times the acceleration of B with
+
+ align:start position:0%
+mass times the acceleration of B with
+ 
+
+ align:start position:0%
+mass times the acceleration of B with
+respect to zero is got to be equal to
+
+ align:start position:0%
+respect to zero is got to be equal to
+ 
+
+ align:start position:0%
+respect to zero is got to be equal to
+zero. That's how that's what this how
+
+ align:start position:0%
+zero. That's how that's what this how
+ 
+
+ align:start position:0%
+zero. That's how that's what this how
+this fictitious force thing works. So
+
+ align:start position:0%
+this fictitious force thing works. So
+ 
+
+ align:start position:0%
+this fictitious force thing works. So
+what on the free body diagram of this
+
+ align:start position:0%
+what on the free body diagram of this
+ 
+
+ align:start position:0%
+what on the free body diagram of this
+thing, what are the actual forces on it?
+
+ align:start position:0%
+thing, what are the actual forces on it?
+ 
+
+ align:start position:0%
+thing, what are the actual forces on it?
+Well, this rod has to there's certainly
+
+ align:start position:0%
+Well, this rod has to there's certainly
+ 
+
+ align:start position:0%
+Well, this rod has to there's certainly
+a weight
+
+ align:start position:0%
+a weight
+ 
+
+ align:start position:0%
+a weight
+downwards.
+
+ align:start position:0%
+downwards.
+ 
+
+ align:start position:0%
+downwards.
+There must be some supporting force
+
+ align:start position:0%
+There must be some supporting force
+ 
+
+ align:start position:0%
+There must be some supporting force
+upwards because we'll put that in in the
+
+ align:start position:0%
+upwards because we'll put that in in the
+ 
+
+ align:start position:0%
+upwards because we'll put that in in the
+Z direction here because this thing
+
+ align:start position:0%
+Z direction here because this thing
+ 
+
+ align:start position:0%
+Z direction here because this thing
+certainly doesn't accelerate up and
+
+ align:start position:0%
+certainly doesn't accelerate up and
+ 
+
+ align:start position:0%
+certainly doesn't accelerate up and
+down. So, the rod's lifting it up
+
+ align:start position:0%
+down. So, the rod's lifting it up
+ 
+
+ align:start position:0%
+down. So, the rod's lifting it up
+somehow. The rod is also putting on some
+
+ align:start position:0%
+somehow. The rod is also putting on some
+ 
+
+ align:start position:0%
+somehow. The rod is also putting on some
+has potentially some radial component
+
+ align:start position:0%
+has potentially some radial component
+ 
+
+ align:start position:0%
+has potentially some radial component
+and I'm just drawing it in the positive
+
+ align:start position:0%
+and I'm just drawing it in the positive
+ 
+
+ align:start position:0%
+and I'm just drawing it in the positive
+direction. And those those are my
+
+ align:start position:0%
+direction. And those those are my
+ 
+
+ align:start position:0%
+direction. And those those are my
+forces.
+
+ align:start position:0%
+forces.
+ 
+
+ align:start position:0%
+forces.
+And we've in this problem omega dot
+
+ align:start position:0%
+And we've in this problem omega dot
+ 
+
+ align:start position:0%
+And we've in this problem omega dot
+theta dot equals zero and r dot and r
+
+ align:start position:0%
+theta dot equals zero and r dot and r
+ 
+
+ align:start position:0%
+theta dot equals zero and r dot and r
+dot were zero. So it's constant rotation
+
+ align:start position:0%
+dot were zero. So it's constant rotation
+ 
+
+ align:start position:0%
+dot were zero. So it's constant rotation
+rate. No geometry changes here.
+
+ align:start position:0%
+rate. No geometry changes here.
+ 
+
+ align:start position:0%
+rate. No geometry changes here.
+Okay. So we did we cranked cranked
+
+ align:start position:0%
+Okay. So we did we cranked cranked
+ 
+
+ align:start position:0%
+Okay. So we did we cranked cranked
+through this problem before. And now I
+
+ align:start position:0%
+through this problem before. And now I
+ 
+
+ align:start position:0%
+through this problem before. And now I
+want to make this correction. And I want
+
+ align:start position:0%
+want to make this correction. And I want
+ 
+
+ align:start position:0%
+want to make this correction. And I want
+to add this fictitious force in the
+
+ align:start position:0%
+to add this fictitious force in the
+ 
+
+ align:start position:0%
+to add this fictitious force in the
+acceleration is minus r omega^ 2 in the
+
+ align:start position:0%
+acceleration is minus r omega^ 2 in the
+ 
+
+ align:start position:0%
+acceleration is minus r omega^ 2 in the
+r hat direction. So minus m * that is a
+
+ align:start position:0%
+r hat direction. So minus m * that is a
+ 
+
+ align:start position:0%
+r hat direction. So minus m * that is a
+plus I get an m
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+r
+
+ align:start position:0%
+r
+ 
+
+ align:start position:0%
+r
+omega squared
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and pointing outwards.
+
+ align:start position:0%
+and pointing outwards.
+ 
+
+ align:start position:0%
+and pointing outwards.
+Okay. And so the sum of the forces
+
+ align:start position:0%
+Okay. And so the sum of the forces
+ 
+
+ align:start position:0%
+Okay. And so the sum of the forces
+in the radial direction
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus or
+
+ align:start position:0%
+minus or
+ 
+
+ align:start position:0%
+minus or
+sum of the forces in the radial
+
+ align:start position:0%
+sum of the forces in the radial
+ 
+
+ align:start position:0%
+sum of the forces in the radial
+direction now
+
+ align:start position:0%
+direction now
+ 
+
+ align:start position:0%
+direction now
+minus this m a b with respect to o.
+
+ align:start position:0%
+minus this m a b with respect to o.
+ 
+
+ align:start position:0%
+minus this m a b with respect to o.
+Well, what are the sum of the real
+
+ align:start position:0%
+Well, what are the sum of the real
+ 
+
+ align:start position:0%
+Well, what are the sum of the real
+forces? Just nr
+
+ align:start position:0%
+forces? Just nr
+ 
+
+ align:start position:0%
+forces? Just nr
+and this minus mass times the
+
+ align:start position:0%
+and this minus mass times the
+ 
+
+ align:start position:0%
+and this minus mass times the
+acceleration. That's your m r 2
+
+ align:start position:0%
+acceleration. That's your m r 2
+ 
+
+ align:start position:0%
+acceleration. That's your m r 2
+m r omega squ and that's got to be zero.
+
+ align:start position:0%
+m r omega squ and that's got to be zero.
+ 
+
+ align:start position:0%
+m r omega squ and that's got to be zero.
+So you find out that this there is a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+all is zero. Therefore,
+
+ align:start position:0%
+all is zero. Therefore,
+ 
+
+ align:start position:0%
+all is zero. Therefore,
+solve for nr is minus
+
+ align:start position:0%
+solve for nr is minus
+ 
+
+ align:start position:0%
+solve for nr is minus
+m r omega^ 2. So that rod out here is
+
+ align:start position:0%
+m r omega^ 2. So that rod out here is
+ 
+
+ align:start position:0%
+m r omega^ 2. So that rod out here is
+pulling that constantly pulling it in to
+
+ align:start position:0%
+pulling that constantly pulling it in to
+ 
+
+ align:start position:0%
+pulling that constantly pulling it in to
+make it go around the circle. And but
+
+ align:start position:0%
+make it go around the circle. And but
+ 
+
+ align:start position:0%
+make it go around the circle. And but
+we've just done this now by this notion
+
+ align:start position:0%
+we've just done this now by this notion
+ 
+
+ align:start position:0%
+we've just done this now by this notion
+of a fictitious force. So
+
+ align:start position:0%
+of a fictitious force. So
+ 
+
+ align:start position:0%
+of a fictitious force. So
+let's go back to this problem now. Well,
+
+ align:start position:0%
+let's go back to this problem now. Well,
+ 
+
+ align:start position:0%
+let's go back to this problem now. Well,
+actually, I'll just take one final step.
+
+ align:start position:0%
+actually, I'll just take one final step.
+ 
+
+ align:start position:0%
+actually, I'll just take one final step.
+If that's the here's your now your um
+
+ align:start position:0%
+If that's the here's your now your um
+ 
+
+ align:start position:0%
+If that's the here's your now your um
+free body diagram touched up with this
+
+ align:start position:0%
+free body diagram touched up with this
+ 
+
+ align:start position:0%
+free body diagram touched up with this
+fictitious force so that we can work as
+
+ align:start position:0%
+fictitious force so that we can work as
+ 
+
+ align:start position:0%
+fictitious force so that we can work as
+if we're here. And by the way, if you
+
+ align:start position:0%
+if we're here. And by the way, if you
+ 
+
+ align:start position:0%
+if we're here. And by the way, if you
+could, you know, if you uh could
+
+ align:start position:0%
+could, you know, if you uh could
+ 
+
+ align:start position:0%
+could, you know, if you uh could
+measure, if you had a strain gauge or
+
+ align:start position:0%
+measure, if you had a strain gauge or
+ 
+
+ align:start position:0%
+measure, if you had a strain gauge or
+something, so you could measure the
+
+ align:start position:0%
+something, so you could measure the
+ 
+
+ align:start position:0%
+something, so you could measure the
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+that this rod
+
+ align:start position:0%
+that this rod
+ 
+
+ align:start position:0%
+that this rod
+is putting on that mass. If you can
+
+ align:start position:0%
+is putting on that mass. If you can
+ 
+
+ align:start position:0%
+is putting on that mass. If you can
+measure it out there, this would be what
+
+ align:start position:0%
+measure it out there, this would be what
+ 
+
+ align:start position:0%
+measure it out there, this would be what
+you would measure.
+
+ align:start position:0%
+you would measure.
+ 
+
+ align:start position:0%
+you would measure.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Now, what about the torque that that
+
+ align:start position:0%
+Now, what about the torque that that
+ 
+
+ align:start position:0%
+Now, what about the torque that that
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+creates around here?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So you have an outward force m r omega
+
+ align:start position:0%
+So you have an outward force m r omega
+ 
+
+ align:start position:0%
+So you have an outward force m r omega
+squar that's cent c c c c c c c c c c c
+
+ align:start position:0%
+squar that's cent c c c c c c c c c c c
+ 
+
+ align:start position:0%
+squar that's cent c c c c c c c c c c c
+c c c c c c c c c centrifugal force this
+
+ align:start position:0%
+c c c c c c c c c centrifugal force this
+ 
+
+ align:start position:0%
+c c c c c c c c c centrifugal force this
+fictitious force
+
+ align:start position:0%
+fictitious force
+ 
+
+ align:start position:0%
+fictitious force
+going pulling out up here what moment
+
+ align:start position:0%
+going pulling out up here what moment
+ 
+
+ align:start position:0%
+going pulling out up here what moment
+does that create down here
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+what's the magnitude first
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and that'll be a torque
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+around
+
+ align:start position:0%
+around
+ 
+
+ align:start position:0%
+around
+say in the theta direction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So what's the moment arm?
+
+ align:start position:0%
+So what's the moment arm?
+ 
+
+ align:start position:0%
+So what's the moment arm?
+The moment arm
+
+ align:start position:0%
+The moment arm
+ 
+
+ align:start position:0%
+The moment arm
+the moment arm Z. Okay. So then the
+
+ align:start position:0%
+the moment arm Z. Okay. So then the
+ 
+
+ align:start position:0%
+the moment arm Z. Okay. So then the
+torque is going to be for R cross F and
+
+ align:start position:0%
+torque is going to be for R cross F and
+ 
+
+ align:start position:0%
+torque is going to be for R cross F and
+it's going to be the uh M R Z omega^ 2
+
+ align:start position:0%
+it's going to be the uh M R Z omega^ 2
+ 
+
+ align:start position:0%
+it's going to be the uh M R Z omega^ 2
+Okay. And it's trying to that centripal
+
+ align:start position:0%
+Okay. And it's trying to that centripal
+ 
+
+ align:start position:0%
+Okay. And it's trying to that centripal
+force is trying to bend it out.
+
+ align:start position:0%
+force is trying to bend it out.
+ 
+
+ align:start position:0%
+force is trying to bend it out.
+Therefore, the torque down here required
+
+ align:start position:0%
+Therefore, the torque down here required
+ 
+
+ align:start position:0%
+Therefore, the torque down here required
+to keep it from doing so is actually in
+
+ align:start position:0%
+to keep it from doing so is actually in
+ 
+
+ align:start position:0%
+to keep it from doing so is actually in
+the other direction.
+
+ align:start position:0%
+the other direction.
+ 
+
+ align:start position:0%
+the other direction.
+So the torque that this system must put
+
+ align:start position:0%
+So the torque that this system must put
+ 
+
+ align:start position:0%
+So the torque that this system must put
+on this bar is minus.
+
+ align:start position:0%
+on this bar is minus.
+ 
+
+ align:start position:0%
+on this bar is minus.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So let's go to this problem. If this is
+
+ align:start position:0%
+So let's go to this problem. If this is
+ 
+
+ align:start position:0%
+So let's go to this problem. If this is
+the point about which we're computing
+
+ align:start position:0%
+the point about which we're computing
+ 
+
+ align:start position:0%
+the point about which we're computing
+the moments, then there's centrip
+
+ align:start position:0%
+the moments, then there's centrip
+ 
+
+ align:start position:0%
+the moments, then there's centrip
+centripal accelerations in this problem.
+
+ align:start position:0%
+centripal accelerations in this problem.
+ 
+
+ align:start position:0%
+centripal accelerations in this problem.
+But in what direction are they?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Either one of those masses.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pardon?
+
+ align:start position:0%
+Pardon?
+ 
+
+ align:start position:0%
+Pardon?
+So each little mass like one of those
+
+ align:start position:0%
+So each little mass like one of those
+ 
+
+ align:start position:0%
+So each little mass like one of those
+the upper mass m over two it's spinning
+
+ align:start position:0%
+the upper mass m over two it's spinning
+ 
+
+ align:start position:0%
+the upper mass m over two it's spinning
+and it's shown in its as it's coming
+
+ align:start position:0%
+and it's shown in its as it's coming
+ 
+
+ align:start position:0%
+and it's shown in its as it's coming
+around the wheel. It's up at the top.
+
+ align:start position:0%
+around the wheel. It's up at the top.
+ 
+
+ align:start position:0%
+around the wheel. It's up at the top.
+What direction is the fictitious force
+
+ align:start position:0%
+What direction is the fictitious force
+ 
+
+ align:start position:0%
+What direction is the fictitious force
+that it's putting on that system?
+
+ align:start position:0%
+that it's putting on that system?
+ 
+
+ align:start position:0%
+that it's putting on that system?
+Radial outwards, right? And does it have
+
+ align:start position:0%
+Radial outwards, right? And does it have
+ 
+
+ align:start position:0%
+Radial outwards, right? And does it have
+any moment arm? That force going up with
+
+ align:start position:0%
+any moment arm? That force going up with
+ 
+
+ align:start position:0%
+any moment arm? That force going up with
+respect to that point in the center? No.
+
+ align:start position:0%
+respect to that point in the center? No.
+ 
+
+ align:start position:0%
+respect to that point in the center? No.
+So, it creates no moment. The bottom one
+
+ align:start position:0%
+So, it creates no moment. The bottom one
+ 
+
+ align:start position:0%
+So, it creates no moment. The bottom one
+by just symmetry doesn't either. This
+
+ align:start position:0%
+by just symmetry doesn't either. This
+ 
+
+ align:start position:0%
+by just symmetry doesn't either. This
+one over here,
+
+ align:start position:0%
+one over here,
+ 
+
+ align:start position:0%
+one over here,
+it also has a a fictitious force you can
+
+ align:start position:0%
+it also has a a fictitious force you can
+ 
+
+ align:start position:0%
+it also has a a fictitious force you can
+think of. which is outward m omega squar
+
+ align:start position:0%
+think of. which is outward m omega squar
+ 
+
+ align:start position:0%
+think of. which is outward m omega squar
+what's its moment arm with respect to
+
+ align:start position:0%
+what's its moment arm with respect to
+ 
+
+ align:start position:0%
+what's its moment arm with respect to
+that to our origin here zero again it
+
+ align:start position:0%
+that to our origin here zero again it
+ 
+
+ align:start position:0%
+that to our origin here zero again it
+produces no moment it produces an
+
+ align:start position:0%
+produces no moment it produces an
+ 
+
+ align:start position:0%
+produces no moment it produces an
+unbalanced force though right it's going
+
+ align:start position:0%
+unbalanced force though right it's going
+ 
+
+ align:start position:0%
+unbalanced force though right it's going
+around producing an unbalanced force uh
+
+ align:start position:0%
+around producing an unbalanced force uh
+ 
+
+ align:start position:0%
+around producing an unbalanced force uh
+this problem the upper one's the
+
+ align:start position:0%
+this problem the upper one's the
+ 
+
+ align:start position:0%
+this problem the upper one's the
+fictitious forces up the lower one which
+
+ align:start position:0%
+fictitious forces up the lower one which
+ 
+
+ align:start position:0%
+fictitious forces up the lower one which
+direction is it
+
+ align:start position:0%
+direction is it
+ 
+
+ align:start position:0%
+direction is it
+down it's perfectly balanced they're
+
+ align:start position:0%
+down it's perfectly balanced they're
+ 
+
+ align:start position:0%
+down it's perfectly balanced they're
+just equal and opposite just going
+
+ align:start position:0%
+just equal and opposite just going
+ 
+
+ align:start position:0%
+just equal and opposite just going
+around you'd feel no you'd feel nothing
+
+ align:start position:0%
+around you'd feel no you'd feel nothing
+ 
+
+ align:start position:0%
+around you'd feel no you'd feel nothing
+uncomfortable this one you'd feel this
+
+ align:start position:0%
+uncomfortable this one you'd feel this
+ 
+
+ align:start position:0%
+uncomfortable this one you'd feel this
+motorcycle trying to hop down the road.
+
+ align:start position:0%
+motorcycle trying to hop down the road.
+ 
+
+ align:start position:0%
+motorcycle trying to hop down the road.
+Okay, it really happens, right? But this
+
+ align:start position:0%
+Okay, it really happens, right? But this
+ 
+
+ align:start position:0%
+Okay, it really happens, right? But this
+one, what happens?
+
+ align:start position:0%
+one, what happens?
+ 
+
+ align:start position:0%
+one, what happens?
+Does this mass m over2, what direction
+
+ align:start position:0%
+Does this mass m over2, what direction
+ 
+
+ align:start position:0%
+Does this mass m over2, what direction
+is the centripal acceleration? I'll
+
+ align:start position:0%
+is the centripal acceleration? I'll
+ 
+
+ align:start position:0%
+is the centripal acceleration? I'll
+change the wording a little bit. The
+
+ align:start position:0%
+change the wording a little bit. The
+ 
+
+ align:start position:0%
+change the wording a little bit. The
+upper mass in case B, which direction is
+
+ align:start position:0%
+upper mass in case B, which direction is
+ 
+
+ align:start position:0%
+upper mass in case B, which direction is
+the centripal acceleration?
+
+ align:start position:0%
+the centripal acceleration?
+ 
+
+ align:start position:0%
+the centripal acceleration?
+Straight down, right? And the bottom
+
+ align:start position:0%
+Straight down, right? And the bottom
+ 
+
+ align:start position:0%
+Straight down, right? And the bottom
+mass, what direction?
+
+ align:start position:0%
+mass, what direction?
+ 
+
+ align:start position:0%
+mass, what direction?
+Straight up.
+
+ align:start position:0%
+Straight up.
+ 
+
+ align:start position:0%
+Straight up.
+Straight up. And the fictitious forces
+
+ align:start position:0%
+Straight up. And the fictitious forces
+ 
+
+ align:start position:0%
+Straight up. And the fictitious forces
+that are that reflect those two
+
+ align:start position:0%
+that are that reflect those two
+ 
+
+ align:start position:0%
+that are that reflect those two
+accelerations are the top one is up and
+
+ align:start position:0%
+accelerations are the top one is up and
+ 
+
+ align:start position:0%
+accelerations are the top one is up and
+the bottom one is down. But they produce
+
+ align:start position:0%
+the bottom one is down. But they produce
+ 
+
+ align:start position:0%
+the bottom one is down. But they produce
+a a net that do they have a moment arm
+
+ align:start position:0%
+a a net that do they have a moment arm
+ 
+
+ align:start position:0%
+a a net that do they have a moment arm
+that they act on with respect to that
+
+ align:start position:0%
+that they act on with respect to that
+ 
+
+ align:start position:0%
+that they act on with respect to that
+center. Yeah. This little distance here
+
+ align:start position:0%
+center. Yeah. This little distance here
+ 
+
+ align:start position:0%
+center. Yeah. This little distance here
+I think it's called B in the problem. So
+
+ align:start position:0%
+I think it's called B in the problem. So
+ 
+
+ align:start position:0%
+I think it's called B in the problem. So
+this thing m over two r omega^ 2* b is a
+
+ align:start position:0%
+this thing m over two r omega^ 2* b is a
+ 
+
+ align:start position:0%
+this thing m over two r omega^ 2* b is a
+torque about the x- axis. And this one
+
+ align:start position:0%
+torque about the x- axis. And this one
+ 
+
+ align:start position:0%
+torque about the x- axis. And this one
+down here is another m over 2 r omega^
+
+ align:start position:0%
+down here is another m over 2 r omega^
+ 
+
+ align:start position:0%
+down here is another m over 2 r omega^
+2. And it's another torque in the same
+
+ align:start position:0%
+2. And it's another torque in the same
+ 
+
+ align:start position:0%
+2. And it's another torque in the same
+direction. So this thing produces quite
+
+ align:start position:0%
+direction. So this thing produces quite
+ 
+
+ align:start position:0%
+direction. So this thing produces quite
+a strong moment. But the but the wheel
+
+ align:start position:0%
+a strong moment. But the but the wheel
+ 
+
+ align:start position:0%
+a strong moment. But the but the wheel
+as the wheel turns
+
+ align:start position:0%
+as the wheel turns
+ 
+
+ align:start position:0%
+as the wheel turns
+that moment goes
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+starts off it's about the x axis here.
+
+ align:start position:0%
+starts off it's about the x axis here.
+ 
+
+ align:start position:0%
+starts off it's about the x axis here.
+But when that weight gets to 90 degrees,
+
+ align:start position:0%
+But when that weight gets to 90 degrees,
+ 
+
+ align:start position:0%
+But when that weight gets to 90 degrees,
+what direction is the moment
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+switches to the all the way around to
+
+ align:start position:0%
+switches to the all the way around to
+ 
+
+ align:start position:0%
+switches to the all the way around to
+the the y axis?
+
+ align:start position:0%
+the the y axis?
+ 
+
+ align:start position:0%
+the the y axis?
+Okay, so it's going to be a moment. The
+
+ align:start position:0%
+Okay, so it's going to be a moment. The
+ 
+
+ align:start position:0%
+Okay, so it's going to be a moment. The
+answer to this problem is going to look
+
+ align:start position:0%
+answer to this problem is going to look
+ 
+
+ align:start position:0%
+answer to this problem is going to look
+in time is going to look something like
+
+ align:start position:0%
+in time is going to look something like
+ 
+
+ align:start position:0%
+in time is going to look something like
+m r omega^ 2 z sin or cosine omega t. So
+
+ align:start position:0%
+m r omega^ 2 z sin or cosine omega t. So
+ 
+
+ align:start position:0%
+m r omega^ 2 z sin or cosine omega t. So
+the moment in this around the x- axis is
+
+ align:start position:0%
+the moment in this around the x- axis is
+ 
+
+ align:start position:0%
+the moment in this around the x- axis is
+kind it's going to be trying to the
+
+ align:start position:0%
+kind it's going to be trying to the
+ 
+
+ align:start position:0%
+kind it's going to be trying to the
+bike's going to be trying to go back and
+
+ align:start position:0%
+bike's going to be trying to go back and
+ 
+
+ align:start position:0%
+bike's going to be trying to go back and
+forth like this. Okay. At ome with
+
+ align:start position:0%
+forth like this. Okay. At ome with
+ 
+
+ align:start position:0%
+forth like this. Okay. At ome with
+frequency omega. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's um I was going to say that's it
+
+ align:start position:0%
+So let's um I was going to say that's it
+ 
+
+ align:start position:0%
+So let's um I was going to say that's it
+for fictitious forces but it's not. I
+
+ align:start position:0%
+for fictitious forces but it's not. I
+ 
+
+ align:start position:0%
+for fictitious forces but it's not. I
+got a great demo for you.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+we have a slope.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I've got a cart
+
+ align:start position:0%
+I've got a cart
+ 
+
+ align:start position:0%
+I've got a cart
+on wheels here. And I actually do
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And I'm going to put a
+
+ align:start position:0%
+And I'm going to put a
+ 
+
+ align:start position:0%
+And I'm going to put a
+box here.
+
+ align:start position:0%
+box here.
+ 
+
+ align:start position:0%
+box here.
+And in the box, I got the wrong color
+
+ align:start position:0%
+And in the box, I got the wrong color
+ 
+
+ align:start position:0%
+And in the box, I got the wrong color
+here, but I'll try colored chalk for the
+
+ align:start position:0%
+here, but I'll try colored chalk for the
+ 
+
+ align:start position:0%
+here, but I'll try colored chalk for the
+first time. In the box, I've got a
+
+ align:start position:0%
+first time. In the box, I've got a
+ 
+
+ align:start position:0%
+first time. In the box, I've got a
+fluid.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the box has a lid on it so I
+
+ align:start position:0%
+Okay. And the box has a lid on it so I
+ 
+
+ align:start position:0%
+Okay. And the box has a lid on it so I
+don't make a mess.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now, I'm going to
+
+ align:start position:0%
+Now, I'm going to
+ 
+
+ align:start position:0%
+Now, I'm going to
+I'm actually going to do this
+
+ align:start position:0%
+I'm actually going to do this
+ 
+
+ align:start position:0%
+I'm actually going to do this
+experiment. I brought my ramp. We're
+
+ align:start position:0%
+experiment. I brought my ramp. We're
+ 
+
+ align:start position:0%
+experiment. I brought my ramp. We're
+going to set up this ramp. This box is
+
+ align:start position:0%
+going to set up this ramp. This box is
+ 
+
+ align:start position:0%
+going to set up this ramp. This box is
+going to be rolling down this hill and
+
+ align:start position:0%
+going to be rolling down this hill and
+ 
+
+ align:start position:0%
+going to be rolling down this hill and
+basically not no losses, no friction
+
+ align:start position:0%
+basically not no losses, no friction
+ 
+
+ align:start position:0%
+basically not no losses, no friction
+holding it back. It's just going to be
+
+ align:start position:0%
+holding it back. It's just going to be
+ 
+
+ align:start position:0%
+holding it back. It's just going to be
+able to take off and accelerate down
+
+ align:start position:0%
+able to take off and accelerate down
+ 
+
+ align:start position:0%
+able to take off and accelerate down
+that hill.
+
+ align:start position:0%
+that hill.
+ 
+
+ align:start position:0%
+that hill.
+Um,
+
+ align:start position:0%
+Um,
+ 
+
+ align:start position:0%
+Um,
+and I want to know
+
+ align:start position:0%
+and I want to know
+ 
+
+ align:start position:0%
+and I want to know
+A,
+
+ align:start position:0%
+A,
+ 
+
+ align:start position:0%
+A,
+B, C.
+
+ align:start position:0%
+B, C.
+ 
+
+ align:start position:0%
+B, C.
+When it's rolling down that hill, will
+
+ align:start position:0%
+When it's rolling down that hill, will
+ 
+
+ align:start position:0%
+When it's rolling down that hill, will
+the level will the bo fluid in the box
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+look like that?
+
+ align:start position:0%
+look like that?
+ 
+
+ align:start position:0%
+look like that?
+Look like
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+that or
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, we're going to take our poll here.
+
+ align:start position:0%
+So, we're going to take our poll here.
+ 
+
+ align:start position:0%
+So, we're going to take our poll here.
+So, how many believe that
+
+ align:start position:0%
+So, how many believe that
+ 
+
+ align:start position:0%
+So, how many believe that
+when it's rolling down the hill, the
+
+ align:start position:0%
+when it's rolling down the hill, the
+ 
+
+ align:start position:0%
+when it's rolling down the hill, the
+fluid will stay level, parallel to the
+
+ align:start position:0%
+fluid will stay level, parallel to the
+ 
+
+ align:start position:0%
+fluid will stay level, parallel to the
+ground? Let's raise your hands if you
+
+ align:start position:0%
+ground? Let's raise your hands if you
+ 
+
+ align:start position:0%
+ground? Let's raise your hands if you
+think this I want everybody to make a
+
+ align:start position:0%
+think this I want everybody to make a
+ 
+
+ align:start position:0%
+think this I want everybody to make a
+guess here. Everybody get in. Raise them
+
+ align:start position:0%
+guess here. Everybody get in. Raise them
+ 
+
+ align:start position:0%
+guess here. Everybody get in. Raise them
+high if you think it's going to stay
+
+ align:start position:0%
+high if you think it's going to stay
+ 
+
+ align:start position:0%
+high if you think it's going to stay
+level.
+
+ align:start position:0%
+level.
+ 
+
+ align:start position:0%
+level.
+Okay, maybe a quarter of you. How many
+
+ align:start position:0%
+Okay, maybe a quarter of you. How many
+ 
+
+ align:start position:0%
+Okay, maybe a quarter of you. How many
+think it's going to do this?
+
+ align:start position:0%
+think it's going to do this?
+ 
+
+ align:start position:0%
+think it's going to do this?
+Okay, a few more. And how many think
+
+ align:start position:0%
+Okay, a few more. And how many think
+ 
+
+ align:start position:0%
+Okay, a few more. And how many think
+it's going to do this?
+
+ align:start position:0%
+it's going to do this?
+ 
+
+ align:start position:0%
+it's going to do this?
+All right, so I want you to, you know,
+
+ align:start position:0%
+All right, so I want you to, you know,
+ 
+
+ align:start position:0%
+All right, so I want you to, you know,
+get in natural little groups there of
+
+ align:start position:0%
+get in natural little groups there of
+ 
+
+ align:start position:0%
+get in natural little groups there of
+two or three people and talk about this
+
+ align:start position:0%
+two or three people and talk about this
+ 
+
+ align:start position:0%
+two or three people and talk about this
+for a couple of minutes and see if you
+
+ align:start position:0%
+for a couple of minutes and see if you
+ 
+
+ align:start position:0%
+for a couple of minutes and see if you
+can convince your neighbor that you're
+
+ align:start position:0%
+can convince your neighbor that you're
+ 
+
+ align:start position:0%
+can convince your neighbor that you're
+right. Figure this out. Stop and talk
+
+ align:start position:0%
+right. Figure this out. Stop and talk
+ 
+
+ align:start position:0%
+right. Figure this out. Stop and talk
+about it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And and let's set up to do the
+
+ align:start position:0%
+And and let's set up to do the
+ 
+
+ align:start position:0%
+And and let's set up to do the
+experiment.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Actually, I think if we do it up here.
+
+ align:start position:0%
+Actually, I think if we do it up here.
+ 
+
+ align:start position:0%
+Actually, I think if we do it up here.
+Yeah. So, like that.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, you hold the ramp. Yeah. You come
+
+ align:start position:0%
+So, you hold the ramp. Yeah. You come
+ 
+
+ align:start position:0%
+So, you hold the ramp. Yeah. You come
+here.
+
+ align:start position:0%
+here.
+ 
+
+ align:start position:0%
+here.
+[Music]
+
+ align:start position:0%
+[Music]
+ 
+
+ align:start position:0%
+[Music]
+We'll just practice our setup here for a
+
+ align:start position:0%
+We'll just practice our setup here for a
+ 
+
+ align:start position:0%
+We'll just practice our setup here for a
+second. So, you're going to have to hold
+
+ align:start position:0%
+second. So, you're going to have to hold
+ 
+
+ align:start position:0%
+second. So, you're going to have to hold
+it quite a bit higher.
+
+ align:start position:0%
+it quite a bit higher.
+ 
+
+ align:start position:0%
+it quite a bit higher.
+Okay. And actually now when we get it
+
+ align:start position:0%
+Okay. And actually now when we get it
+ 
+
+ align:start position:0%
+Okay. And actually now when we get it
+ready to go.
+
+ align:start position:0%
+ready to go.
+ 
+
+ align:start position:0%
+ready to go.
+How sealed is that?
+
+ align:start position:0%
+How sealed is that?
+ 
+
+ align:start position:0%
+How sealed is that?
+Pardon? Very well sealed. So I'm going
+
+ align:start position:0%
+Pardon? Very well sealed. So I'm going
+ 
+
+ align:start position:0%
+Pardon? Very well sealed. So I'm going
+to have you also you hold it and you
+
+ align:start position:0%
+to have you also you hold it and you
+ 
+
+ align:start position:0%
+to have you also you hold it and you
+release it. Right. And that's about the
+
+ align:start position:0%
+release it. Right. And that's about the
+ 
+
+ align:start position:0%
+release it. Right. And that's about the
+right because I got to catch it so it
+
+ align:start position:0%
+right because I got to catch it so it
+ 
+
+ align:start position:0%
+right because I got to catch it so it
+doesn't uh
+
+ align:start position:0%
+doesn't uh
+ 
+
+ align:start position:0%
+doesn't uh
+All right. Now we're going to stop.
+
+ align:start position:0%
+All right. Now we're going to stop.
+ 
+
+ align:start position:0%
+All right. Now we're going to stop.
+We're not going to do it right away. I'm
+
+ align:start position:0%
+We're not going to do it right away. I'm
+ 
+
+ align:start position:0%
+We're not going to do it right away. I'm
+going to I'm going to get him to answer
+
+ align:start position:0%
+going to I'm going to get him to answer
+ 
+
+ align:start position:0%
+going to I'm going to get him to answer
+the question a second time.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Good idea.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. And I think that'll work just
+
+ align:start position:0%
+All right. And I think that'll work just
+ 
+
+ align:start position:0%
+All right. And I think that'll work just
+great.
+
+ align:start position:0%
+great.
+ 
+
+ align:start position:0%
+great.
+And we're not going to give it away.
+
+ align:start position:0%
+And we're not going to give it away.
+ 
+
+ align:start position:0%
+And we're not going to give it away.
+Okay. So, set it down and we'll do the
+
+ align:start position:0%
+Okay. So, set it down and we'll do the
+ 
+
+ align:start position:0%
+Okay. So, set it down and we'll do the
+thing. Just Just drop it.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. So, let's do the uh let's do the
+
+ align:start position:0%
+Okay. So, let's do the uh let's do the
+ 
+
+ align:start position:0%
+Okay. So, let's do the uh let's do the
+quiz again.
+
+ align:start position:0%
+quiz again.
+ 
+
+ align:start position:0%
+quiz again.
+I want to see if any of you convinced
+
+ align:start position:0%
+I want to see if any of you convinced
+ 
+
+ align:start position:0%
+I want to see if any of you convinced
+your neighbor to change their vote. So,
+
+ align:start position:0%
+your neighbor to change their vote. So,
+ 
+
+ align:start position:0%
+your neighbor to change their vote. So,
+how many believe that it's going to be
+
+ align:start position:0%
+how many believe that it's going to be
+ 
+
+ align:start position:0%
+how many believe that it's going to be
+A?
+
+ align:start position:0%
+A?
+ 
+
+ align:start position:0%
+A?
+H one or two. Interesting. That count
+
+ align:start position:0%
+H one or two. Interesting. That count
+ 
+
+ align:start position:0%
+H one or two. Interesting. That count
+went down. How many believe it's going
+
+ align:start position:0%
+went down. How many believe it's going
+ 
+
+ align:start position:0%
+went down. How many believe it's going
+to be B? A lot of people went up. How
+
+ align:start position:0%
+to be B? A lot of people went up. How
+ 
+
+ align:start position:0%
+to be B? A lot of people went up. How
+many think it's going to be C? Okay.
+
+ align:start position:0%
+many think it's going to be C? Okay.
+ 
+
+ align:start position:0%
+many think it's going to be C? Okay.
+Okay, still a couple hold outs. Let's do
+
+ align:start position:0%
+Okay, still a couple hold outs. Let's do
+ 
+
+ align:start position:0%
+Okay, still a couple hold outs. Let's do
+the experiment.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So guys in the booth, can you get a good
+
+ align:start position:0%
+So guys in the booth, can you get a good
+ 
+
+ align:start position:0%
+So guys in the booth, can you get a good
+shot of this? I hope I want this. So it
+
+ align:start position:0%
+shot of this? I hope I want this. So it
+ 
+
+ align:start position:0%
+shot of this? I hope I want this. So it
+p
+
+ align:start position:0%
+p
+ 
+
+ align:start position:0%
+p
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+Move the chalk. Yep.
+
+ align:start position:0%
+Move the chalk. Yep.
+ 
+
+ align:start position:0%
+Move the chalk. Yep.
+And
+
+ align:start position:0%
+And
+ 
+
+ align:start position:0%
+And
+I'm going to have to catch it. All
+
+ align:start position:0%
+I'm going to have to catch it. All
+ 
+
+ align:start position:0%
+I'm going to have to catch it. All
+right. Let her rip.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Which way?
+
+ align:start position:0%
+Which way?
+ 
+
+ align:start position:0%
+Which way?
+Yeah, let's do it again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Just make sure the guys in the booth got
+
+ align:start position:0%
+Just make sure the guys in the booth got
+ 
+
+ align:start position:0%
+Just make sure the guys in the booth got
+a good shot of this. Okay, once more.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Pretty neat, huh?
+
+ align:start position:0%
+Pretty neat, huh?
+ 
+
+ align:start position:0%
+Pretty neat, huh?
+So,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+if you're if you're skiing
+
+ align:start position:0%
+if you're if you're skiing
+ 
+
+ align:start position:0%
+if you're if you're skiing
+downhill, you're going down the hill
+
+ align:start position:0%
+downhill, you're going down the hill
+ 
+
+ align:start position:0%
+downhill, you're going down the hill
+accelerating.
+
+ align:start position:0%
+accelerating.
+ 
+
+ align:start position:0%
+accelerating.
+Which way do you feel the forces on your
+
+ align:start position:0%
+Which way do you feel the forces on your
+ 
+
+ align:start position:0%
+Which way do you feel the forces on your
+body?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+You you feel forces pulling you down
+
+ align:start position:0%
+You you feel forces pulling you down
+ 
+
+ align:start position:0%
+You you feel forces pulling you down
+straight. You feel forces pulling you
+
+ align:start position:0%
+straight. You feel forces pulling you
+ 
+
+ align:start position:0%
+straight. You feel forces pulling you
+down the hill. field forces pulling you
+
+ align:start position:0%
+down the hill. field forces pulling you
+ 
+
+ align:start position:0%
+down the hill. field forces pulling you
+into the hill.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So this is straightforward application
+
+ align:start position:0%
+So this is straightforward application
+ 
+
+ align:start position:0%
+So this is straightforward application
+of this.
+
+ align:start position:0%
+of this.
+ 
+
+ align:start position:0%
+of this.
+In order for this thing to have this,
+
+ align:start position:0%
+In order for this thing to have this,
+ 
+
+ align:start position:0%
+In order for this thing to have this,
+this slope of that liquid was parallel
+
+ align:start position:0%
+this slope of that liquid was parallel
+ 
+
+ align:start position:0%
+this slope of that liquid was parallel
+to the slope.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+let's see if we I think I get my notes
+
+ align:start position:0%
+let's see if we I think I get my notes
+ 
+
+ align:start position:0%
+let's see if we I think I get my notes
+back out here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So let's do this just quickly do this
+
+ align:start position:0%
+So let's do this just quickly do this
+ 
+
+ align:start position:0%
+So let's do this just quickly do this
+problem rig sort of rigorously the way
+
+ align:start position:0%
+problem rig sort of rigorously the way
+ 
+
+ align:start position:0%
+problem rig sort of rigorously the way
+we would do it uh straight
+
+ align:start position:0%
+we would do it uh straight
+ 
+
+ align:start position:0%
+we would do it uh straight
+straightforward with accelerations and
+
+ align:start position:0%
+straightforward with accelerations and
+ 
+
+ align:start position:0%
+straightforward with accelerations and
+free body diagrams and so forth. We're
+
+ align:start position:0%
+free body diagrams and so forth. We're
+ 
+
+ align:start position:0%
+free body diagrams and so forth. We're
+going to have some normal force
+
+ align:start position:0%
+going to have some normal force
+ 
+
+ align:start position:0%
+going to have some normal force
+pushing up. There's no I said no
+
+ align:start position:0%
+pushing up. There's no I said no
+ 
+
+ align:start position:0%
+pushing up. There's no I said no
+friction. This thing's slippery surface.
+
+ align:start position:0%
+friction. This thing's slippery surface.
+ 
+
+ align:start position:0%
+friction. This thing's slippery surface.
+Just as if it was sliding down. Got to
+
+ align:start position:0%
+Just as if it was sliding down. Got to
+ 
+
+ align:start position:0%
+Just as if it was sliding down. Got to
+do do rollers in the classroom. Uh it's
+
+ align:start position:0%
+do do rollers in the classroom. Uh it's
+ 
+
+ align:start position:0%
+do do rollers in the classroom. Uh it's
+got an mg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and there are no other external forces.
+
+ align:start position:0%
+and there are no other external forces.
+ 
+
+ align:start position:0%
+and there are no other external forces.
+Okay. And we know then that the
+
+ align:start position:0%
+Okay. And we know then that the
+ 
+
+ align:start position:0%
+Okay. And we know then that the
+summation of the external forces
+
+ align:start position:0%
+summation of the external forces
+ 
+
+ align:start position:0%
+summation of the external forces
+has got to be the
+
+ align:start position:0%
+has got to be the
+ 
+
+ align:start position:0%
+has got to be the
+mass times the acceleration. And I'm
+
+ align:start position:0%
+mass times the acceleration. And I'm
+ 
+
+ align:start position:0%
+mass times the acceleration. And I'm
+going to make this
+
+ align:start position:0%
+going to make this
+ 
+
+ align:start position:0%
+going to make this
+here. I'll call this point A in the
+
+ align:start position:0%
+here. I'll call this point A in the
+ 
+
+ align:start position:0%
+here. I'll call this point A in the
+center. And I'm going to make my
+
+ align:start position:0%
+center. And I'm going to make my
+ 
+
+ align:start position:0%
+center. And I'm going to make my
+inertial reference frame X down the
+
+ align:start position:0%
+inertial reference frame X down the
+ 
+
+ align:start position:0%
+inertial reference frame X down the
+hill, Y perpendicular to the hill. Okay.
+
+ align:start position:0%
+hill, Y perpendicular to the hill. Okay.
+ 
+
+ align:start position:0%
+hill, Y perpendicular to the hill. Okay.
+So the mass times the acceleration of A
+
+ align:start position:0%
+So the mass times the acceleration of A
+ 
+
+ align:start position:0%
+So the mass times the acceleration of A
+with respect to O is then equal and I
+
+ align:start position:0%
+with respect to O is then equal and I
+ 
+
+ align:start position:0%
+with respect to O is then equal and I
+can this is my then external forces. So
+
+ align:start position:0%
+can this is my then external forces. So
+ 
+
+ align:start position:0%
+can this is my then external forces. So
+this this is my X direction.
+
+ align:start position:0%
+this this is my X direction.
+ 
+
+ align:start position:0%
+this this is my X direction.
+So I'm going to break this G mg force
+
+ align:start position:0%
+So I'm going to break this G mg force
+ 
+
+ align:start position:0%
+So I'm going to break this G mg force
+force into two components. One down the
+
+ align:start position:0%
+force into two components. One down the
+ 
+
+ align:start position:0%
+force into two components. One down the
+hill. Guess I need an angle.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Let's see.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So if
+
+ align:start position:0%
+So if
+ 
+
+ align:start position:0%
+So if
+this is theta,
+
+ align:start position:0%
+this is theta,
+ 
+
+ align:start position:0%
+this is theta,
+then this is
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+theta here.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. And the force down the hill is
+
+ align:start position:0%
+Okay. And the force down the hill is
+ 
+
+ align:start position:0%
+Okay. And the force down the hill is
+that component is mg
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+sin theta.
+
+ align:start position:0%
+sin theta.
+ 
+
+ align:start position:0%
+sin theta.
+And the force this direction
+
+ align:start position:0%
+And the force this direction
+ 
+
+ align:start position:0%
+And the force this direction
+is then going to be
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and I'll just I'll give us some unit
+
+ align:start position:0%
+and I'll just I'll give us some unit
+ 
+
+ align:start position:0%
+and I'll just I'll give us some unit
+vectors here to keep things straight.
+
+ align:start position:0%
+vectors here to keep things straight.
+ 
+
+ align:start position:0%
+vectors here to keep things straight.
+This this force
+
+ align:start position:0%
+This this force
+ 
+
+ align:start position:0%
+This this force
+is minus mg
+
+ align:start position:0%
+is minus mg
+ 
+
+ align:start position:0%
+is minus mg
+cossine theta in the J hat direction.
+
+ align:start position:0%
+cossine theta in the J hat direction.
+ 
+
+ align:start position:0%
+cossine theta in the J hat direction.
+So the sum of the forces here
+
+ align:start position:0%
+So the sum of the forces here
+ 
+
+ align:start position:0%
+So the sum of the forces here
+all of them are
+
+ align:start position:0%
+all of them are
+ 
+
+ align:start position:0%
+all of them are
+mg
+
+ align:start position:0%
+mg
+ 
+
+ align:start position:0%
+mg
+sin theta ihat
+
+ align:start position:0%
+sin theta ihat
+ 
+
+ align:start position:0%
+sin theta ihat
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+mg cosine theta
+
+ align:start position:0%
+mg cosine theta
+ 
+
+ align:start position:0%
+mg cosine theta
+j hat plus n in the jhat direction. So
+
+ align:start position:0%
+j hat plus n in the jhat direction. So
+ 
+
+ align:start position:0%
+j hat plus n in the jhat direction. So
+that's the total vector sum and that
+
+ align:start position:0%
+that's the total vector sum and that
+ 
+
+ align:start position:0%
+that's the total vector sum and that
+would be that's got to be equal to my
+
+ align:start position:0%
+would be that's got to be equal to my
+ 
+
+ align:start position:0%
+would be that's got to be equal to my
+mass times the acceleration of A with
+
+ align:start position:0%
+mass times the acceleration of A with
+ 
+
+ align:start position:0%
+mass times the acceleration of A with
+respect to O.
+
+ align:start position:0%
+respect to O.
+ 
+
+ align:start position:0%
+respect to O.
+And we know that's straight down the
+
+ align:start position:0%
+And we know that's straight down the
+ 
+
+ align:start position:0%
+And we know that's straight down the
+hill. So this is only going to be in the
+
+ align:start position:0%
+hill. So this is only going to be in the
+ 
+
+ align:start position:0%
+hill. So this is only going to be in the
+I. This one's only going to be in the
+
+ align:start position:0%
+I. This one's only going to be in the
+ 
+
+ align:start position:0%
+I. This one's only going to be in the
+ihat direction. We know the acceleration
+
+ align:start position:0%
+ihat direction. We know the acceleration
+ 
+
+ align:start position:0%
+ihat direction. We know the acceleration
+perpendicular to the hill has got to be
+
+ align:start position:0%
+perpendicular to the hill has got to be
+ 
+
+ align:start position:0%
+perpendicular to the hill has got to be
+zero. Okay. So if we just add up the
+
+ align:start position:0%
+zero. Okay. So if we just add up the
+ 
+
+ align:start position:0%
+zero. Okay. So if we just add up the
+components of this thing
+
+ align:start position:0%
+components of this thing
+ 
+
+ align:start position:0%
+components of this thing
+in the ihat direction just the x
+
+ align:start position:0%
+in the ihat direction just the x
+ 
+
+ align:start position:0%
+in the ihat direction just the x
+direction
+
+ align:start position:0%
+direction
+ 
+
+ align:start position:0%
+direction
+then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I have only this term and that term and
+
+ align:start position:0%
+I have only this term and that term and
+ 
+
+ align:start position:0%
+I have only this term and that term and
+I find that the
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+mg
+
+ align:start position:0%
+mg
+ 
+
+ align:start position:0%
+mg
+sin theta equals
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Right? And so
+
+ align:start position:0%
+Right? And so
+ 
+
+ align:start position:0%
+Right? And so
+the acceleration of A with respect to O
+
+ align:start position:0%
+the acceleration of A with respect to O
+ 
+
+ align:start position:0%
+the acceleration of A with respect to O
+is just g sin theta.
+
+ align:start position:0%
+is just g sin theta.
+ 
+
+ align:start position:0%
+is just g sin theta.
+Okay. Well, that's pretty trivial and it
+
+ align:start position:0%
+Okay. Well, that's pretty trivial and it
+ 
+
+ align:start position:0%
+Okay. Well, that's pretty trivial and it
+doesn't give us much insight
+
+ align:start position:0%
+doesn't give us much insight
+ 
+
+ align:start position:0%
+doesn't give us much insight
+about
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it. Actually, that doesn't give me much
+
+ align:start position:0%
+it. Actually, that doesn't give me much
+ 
+
+ align:start position:0%
+it. Actually, that doesn't give me much
+insight about why that's the answer.
+
+ align:start position:0%
+insight about why that's the answer.
+ 
+
+ align:start position:0%
+insight about why that's the answer.
+Okay. So actually this is a time when
+
+ align:start position:0%
+Okay. So actually this is a time when
+ 
+
+ align:start position:0%
+Okay. So actually this is a time when
+maybe thinking about a you're in that
+
+ align:start position:0%
+maybe thinking about a you're in that
+ 
+
+ align:start position:0%
+maybe thinking about a you're in that
+frame you're you're going down the hill
+
+ align:start position:0%
+frame you're you're going down the hill
+ 
+
+ align:start position:0%
+frame you're you're going down the hill
+you're skiing and you're now in an
+
+ align:start position:0%
+you're skiing and you're now in an
+ 
+
+ align:start position:0%
+you're skiing and you're now in an
+accelerating reference frame and you
+
+ align:start position:0%
+accelerating reference frame and you
+ 
+
+ align:start position:0%
+accelerating reference frame and you
+want to say I want to work from this
+
+ align:start position:0%
+want to say I want to work from this
+ 
+
+ align:start position:0%
+want to say I want to work from this
+frame what do I have to what fictitious
+
+ align:start position:0%
+frame what do I have to what fictitious
+ 
+
+ align:start position:0%
+frame what do I have to what fictitious
+force do I have to add to that free body
+
+ align:start position:0%
+force do I have to add to that free body
+ 
+
+ align:start position:0%
+force do I have to add to that free body
+diagram so I can account for my for my
+
+ align:start position:0%
+diagram so I can account for my for my
+ 
+
+ align:start position:0%
+diagram so I can account for my for my
+acceleration
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So remember this the fictitious force we
+
+ align:start position:0%
+So remember this the fictitious force we
+ 
+
+ align:start position:0%
+So remember this the fictitious force we
+want to deal deal with has to do with
+
+ align:start position:0%
+want to deal deal with has to do with
+ 
+
+ align:start position:0%
+want to deal deal with has to do with
+this guy. We're we're in the moving
+
+ align:start position:0%
+this guy. We're we're in the moving
+ 
+
+ align:start position:0%
+this guy. We're we're in the moving
+frame. We can't we can't judge this.
+
+ align:start position:0%
+frame. We can't we can't judge this.
+ 
+
+ align:start position:0%
+frame. We can't we can't judge this.
+We're just told that it exists and we
+
+ align:start position:0%
+We're just told that it exists and we
+ 
+
+ align:start position:0%
+We're just told that it exists and we
+need to correct for it. So we need a
+
+ align:start position:0%
+need to correct for it. So we need a
+ 
+
+ align:start position:0%
+need to correct for it. So we need a
+fictitious force that's minus m a with
+
+ align:start position:0%
+fictitious force that's minus m a with
+ 
+
+ align:start position:0%
+fictitious force that's minus m a with
+respect to o. So that would be minus mg
+
+ align:start position:0%
+respect to o. So that would be minus mg
+ 
+
+ align:start position:0%
+respect to o. So that would be minus mg
+sin theta and that would be in this
+
+ align:start position:0%
+sin theta and that would be in this
+ 
+
+ align:start position:0%
+sin theta and that would be in this
+direction. So dash lines here is my
+
+ align:start position:0%
+direction. So dash lines here is my
+ 
+
+ align:start position:0%
+direction. So dash lines here is my
+mg sin theta fictitious force
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+in the other direction was the real
+
+ align:start position:0%
+in the other direction was the real
+ 
+
+ align:start position:0%
+in the other direction was the real
+force the component of gravity mg sin
+
+ align:start position:0%
+force the component of gravity mg sin
+ 
+
+ align:start position:0%
+force the component of gravity mg sin
+theta
+
+ align:start position:0%
+theta
+ 
+
+ align:start position:0%
+theta
+in this direction was my normal force
+
+ align:start position:0%
+in this direction was my normal force
+ 
+
+ align:start position:0%
+in this direction was my normal force
+and in this direction is my component of
+
+ align:start position:0%
+and in this direction is my component of
+ 
+
+ align:start position:0%
+and in this direction is my component of
+gravity that is my mg G cosine theta.
+
+ align:start position:0%
+gravity that is my mg G cosine theta.
+ 
+
+ align:start position:0%
+gravity that is my mg G cosine theta.
+Okay,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+it's a real force. So yeah, these these
+
+ align:start position:0%
+it's a real force. So yeah, these these
+ 
+
+ align:start position:0%
+it's a real force. So yeah, these these
+real forces and this fictitious force.
+
+ align:start position:0%
+real forces and this fictitious force.
+ 
+
+ align:start position:0%
+real forces and this fictitious force.
+But now we say the sum of these all
+
+ align:start position:0%
+But now we say the sum of these all
+ 
+
+ align:start position:0%
+But now we say the sum of these all
+these forces have to sum to zero.
+
+ align:start position:0%
+these forces have to sum to zero.
+ 
+
+ align:start position:0%
+these forces have to sum to zero.
+So we but look look what happens here.
+
+ align:start position:0%
+So we but look look what happens here.
+ 
+
+ align:start position:0%
+So we but look look what happens here.
+So what's the what ex what force do you
+
+ align:start position:0%
+So what's the what ex what force do you
+ 
+
+ align:start position:0%
+So what's the what ex what force do you
+feel
+
+ align:start position:0%
+feel
+ 
+
+ align:start position:0%
+feel
+in the reference frame? You're the skier
+
+ align:start position:0%
+in the reference frame? You're the skier
+ 
+
+ align:start position:0%
+in the reference frame? You're the skier
+going down the hill. What forces the net
+
+ align:start position:0%
+going down the hill. What forces the net
+ 
+
+ align:start position:0%
+going down the hill. What forces the net
+forces do you feel on you that are in
+
+ align:start position:0%
+forces do you feel on you that are in
+ 
+
+ align:start position:0%
+forces do you feel on you that are in
+the x direction down the hill
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+zero
+
+ align:start position:0%
+zero
+ 
+
+ align:start position:0%
+zero
+it's exactly the reason I did that silly
+
+ align:start position:0%
+it's exactly the reason I did that silly
+ 
+
+ align:start position:0%
+it's exactly the reason I did that silly
+freef fall problem a minute ago when you
+
+ align:start position:0%
+freef fall problem a minute ago when you
+ 
+
+ align:start position:0%
+freef fall problem a minute ago when you
+drop something
+
+ align:start position:0%
+drop something
+ 
+
+ align:start position:0%
+drop something
+when you're weightless the scales are
+
+ align:start position:0%
+when you're weightless the scales are
+ 
+
+ align:start position:0%
+when you're weightless the scales are
+reading the cable broke in the elevator
+
+ align:start position:0%
+reading the cable broke in the elevator
+ 
+
+ align:start position:0%
+reading the cable broke in the elevator
+scales read zero the fictitious force
+
+ align:start position:0%
+scales read zero the fictitious force
+ 
+
+ align:start position:0%
+scales read zero the fictitious force
+was equal and opposite to the
+
+ align:start position:0%
+was equal and opposite to the
+ 
+
+ align:start position:0%
+was equal and opposite to the
+gravitational force you feel and the
+
+ align:start position:0%
+gravitational force you feel and the
+ 
+
+ align:start position:0%
+gravitational force you feel and the
+scales would show no force in the in the
+
+ align:start position:0%
+scales would show no force in the in the
+ 
+
+ align:start position:0%
+scales would show no force in the in the
+freef fall direction. In this case,
+
+ align:start position:0%
+freef fall direction. In this case,
+ 
+
+ align:start position:0%
+freef fall direction. In this case,
+you're not freef fall, but you're freef
+
+ align:start position:0%
+you're not freef fall, but you're freef
+ 
+
+ align:start position:0%
+you're not freef fall, but you're freef
+fall down a slope and the component down
+
+ align:start position:0%
+fall down a slope and the component down
+ 
+
+ align:start position:0%
+fall down a slope and the component down
+the slope, you have no net force in that
+
+ align:start position:0%
+the slope, you have no net force in that
+ 
+
+ align:start position:0%
+the slope, you have no net force in that
+direction. So, if you're
+
+ align:start position:0%
+direction. So, if you're
+ 
+
+ align:start position:0%
+direction. So, if you're
+in the reference frame of that moving
+
+ align:start position:0%
+in the reference frame of that moving
+ 
+
+ align:start position:0%
+in the reference frame of that moving
+cart, the only actual force you feel is
+
+ align:start position:0%
+cart, the only actual force you feel is
+ 
+
+ align:start position:0%
+cart, the only actual force you feel is
+N.
+
+ align:start position:0%
+N.
+ 
+
+ align:start position:0%
+N.
+You will feel a force on your feet
+
+ align:start position:0%
+You will feel a force on your feet
+ 
+
+ align:start position:0%
+You will feel a force on your feet
+equal to mg cosine theta.
+
+ align:start position:0%
+equal to mg cosine theta.
+ 
+
+ align:start position:0%
+equal to mg cosine theta.
+So if theta goes to 90° you're in freef
+
+ align:start position:0%
+So if theta goes to 90° you're in freef
+ 
+
+ align:start position:0%
+So if theta goes to 90° you're in freef
+fall and you feel it goes to zero. Theta
+
+ align:start position:0%
+fall and you feel it goes to zero. Theta
+ 
+
+ align:start position:0%
+fall and you feel it goes to zero. Theta
+is 0 degrees it's max and you would feel
+
+ align:start position:0%
+is 0 degrees it's max and you would feel
+ 
+
+ align:start position:0%
+is 0 degrees it's max and you would feel
+mg. Okay. So here just this this one
+
+ align:start position:0%
+mg. Okay. So here just this this one
+ 
+
+ align:start position:0%
+mg. Okay. So here just this this one
+this is an example for me where this
+
+ align:start position:0%
+this is an example for me where this
+ 
+
+ align:start position:0%
+this is an example for me where this
+notion of a fictitious force kind of
+
+ align:start position:0%
+notion of a fictitious force kind of
+ 
+
+ align:start position:0%
+notion of a fictitious force kind of
+helps me figure out what's going on.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+pretty amazing.
+
+ align:start position:0%
+pretty amazing.
+ 
+
+ align:start position:0%
+pretty amazing.
+Okay, so we're going to uh move on from
+
+ align:start position:0%
+Okay, so we're going to uh move on from
+ 
+
+ align:start position:0%
+Okay, so we're going to uh move on from
+this kind of discussion of fict
+
+ align:start position:0%
+this kind of discussion of fict
+ 
+
+ align:start position:0%
+this kind of discussion of fict
+fictitious forces and things. So let's
+
+ align:start position:0%
+fictitious forces and things. So let's
+ 
+
+ align:start position:0%
+fictitious forces and things. So let's
+it's been an hour. U we'll take a little
+
+ align:start position:0%
+it's been an hour. U we'll take a little
+ 
+
+ align:start position:0%
+it's been an hour. U we'll take a little
+break for a second. Also, if you got any
+
+ align:start position:0%
+break for a second. Also, if you got any
+ 
+
+ align:start position:0%
+break for a second. Also, if you got any
+questions about what we've covered up to
+
+ align:start position:0%
+questions about what we've covered up to
+ 
+
+ align:start position:0%
+questions about what we've covered up to
+this point, think about them and ask
+
+ align:start position:0%
+this point, think about them and ask
+ 
+
+ align:start position:0%
+this point, think about them and ask
+them in a minute. So just take a short
+
+ align:start position:0%
+them in a minute. So just take a short
+ 
+
+ align:start position:0%
+them in a minute. So just take a short
+break. So while I've been uh while
+
+ align:start position:0%
+break. So while I've been uh while
+ 
+
+ align:start position:0%
+break. So while I've been uh while
+you've been taking a break, a couple of
+
+ align:start position:0%
+you've been taking a break, a couple of
+ 
+
+ align:start position:0%
+you've been taking a break, a couple of
+people came up and asked questions. One
+
+ align:start position:0%
+people came up and asked questions. One
+ 
+
+ align:start position:0%
+people came up and asked questions. One
+of them was are fictitious forces real
+
+ align:start position:0%
+of them was are fictitious forces real
+ 
+
+ align:start position:0%
+of them was are fictitious forces real
+and the and the other is you know why
+
+ align:start position:0%
+and the and the other is you know why
+ 
+
+ align:start position:0%
+and the and the other is you know why
+does the water move?
+
+ align:start position:0%
+does the water move?
+ 
+
+ align:start position:0%
+does the water move?
+All right.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So the answer to the answer to the first
+
+ align:start position:0%
+So the answer to the answer to the first
+ 
+
+ align:start position:0%
+So the answer to the answer to the first
+question
+
+ align:start position:0%
+question
+ 
+
+ align:start position:0%
+question
+if you want to be careful
+
+ align:start position:0%
+if you want to be careful
+ 
+
+ align:start position:0%
+if you want to be careful
+and do the problem rigorously
+
+ align:start position:0%
+and do the problem rigorously
+ 
+
+ align:start position:0%
+and do the problem rigorously
+don't mess with fictitious forces.
+
+ align:start position:0%
+don't mess with fictitious forces.
+ 
+
+ align:start position:0%
+don't mess with fictitious forces.
+The only
+
+ align:start position:0%
+The only
+ 
+
+ align:start position:0%
+The only
+real forces in the problem are the ones
+
+ align:start position:0%
+real forces in the problem are the ones
+ 
+
+ align:start position:0%
+real forces in the problem are the ones
+that you would put on a free body
+
+ align:start position:0%
+that you would put on a free body
+ 
+
+ align:start position:0%
+that you would put on a free body
+diagram such that that the sum of the
+
+ align:start position:0%
+diagram such that that the sum of the
+ 
+
+ align:start position:0%
+diagram such that that the sum of the
+external forces equals the mass times
+
+ align:start position:0%
+external forces equals the mass times
+ 
+
+ align:start position:0%
+external forces equals the mass times
+acceleration. And these forces are
+
+ align:start position:0%
+acceleration. And these forces are
+ 
+
+ align:start position:0%
+acceleration. And these forces are
+always real ones. They are gravity. They
+
+ align:start position:0%
+always real ones. They are gravity. They
+ 
+
+ align:start position:0%
+always real ones. They are gravity. They
+are normal forces. They're friction
+
+ align:start position:0%
+are normal forces. They're friction
+ 
+
+ align:start position:0%
+are normal forces. They're friction
+forces. They're spring forces. They're
+
+ align:start position:0%
+forces. They're spring forces. They're
+ 
+
+ align:start position:0%
+forces. They're spring forces. They're
+dash pot forces. They're all these
+
+ align:start position:0%
+dash pot forces. They're all these
+ 
+
+ align:start position:0%
+dash pot forces. They're all these
+mechanical things, but they're real
+
+ align:start position:0%
+mechanical things, but they're real
+ 
+
+ align:start position:0%
+mechanical things, but they're real
+forces. In the rod, that thing's
+
+ align:start position:0%
+forces. In the rod, that thing's
+ 
+
+ align:start position:0%
+forces. In the rod, that thing's
+spinning around. That rod since it's a
+
+ align:start position:0%
+spinning around. That rod since it's a
+ 
+
+ align:start position:0%
+spinning around. That rod since it's a
+rigid thing it can support bending. So
+
+ align:start position:0%
+rigid thing it can support bending. So
+ 
+
+ align:start position:0%
+rigid thing it can support bending. So
+it can put a she it has shear force. It
+
+ align:start position:0%
+it can put a she it has shear force. It
+ 
+
+ align:start position:0%
+it can put a she it has shear force. It
+can have axial forces. Those are real
+
+ align:start position:0%
+can have axial forces. Those are real
+ 
+
+ align:start position:0%
+can have axial forces. Those are real
+forces that it can put on the mass.
+
+ align:start position:0%
+forces that it can put on the mass.
+ 
+
+ align:start position:0%
+forces that it can put on the mass.
+Fictitious forces are not forces. They
+
+ align:start position:0%
+Fictitious forces are not forces. They
+ 
+
+ align:start position:0%
+Fictitious forces are not forces. They
+are minus a mass times a real what?
+
+ align:start position:0%
+are minus a mass times a real what?
+ 
+
+ align:start position:0%
+are minus a mass times a real what?
+Acceleration.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So real forces real accelerations. We
+
+ align:start position:0%
+So real forces real accelerations. We
+ 
+
+ align:start position:0%
+So real forces real accelerations. We
+use this notion of a fictitious force as
+
+ align:start position:0%
+use this notion of a fictitious force as
+ 
+
+ align:start position:0%
+use this notion of a fictitious force as
+a convenience but it is a highly
+
+ align:start position:0%
+a convenience but it is a highly
+ 
+
+ align:start position:0%
+a convenience but it is a highly
+dangerous tool.
+
+ align:start position:0%
+dangerous tool.
+ 
+
+ align:start position:0%
+dangerous tool.
+Okay. But actually if once you get used
+
+ align:start position:0%
+Okay. But actually if once you get used
+ 
+
+ align:start position:0%
+Okay. But actually if once you get used
+to it a little bit it can give you some
+
+ align:start position:0%
+to it a little bit it can give you some
+ 
+
+ align:start position:0%
+to it a little bit it can give you some
+really quick insight. But I would always
+
+ align:start position:0%
+really quick insight. But I would always
+ 
+
+ align:start position:0%
+really quick insight. But I would always
+if I have doubts I'd always go back and
+
+ align:start position:0%
+if I have doubts I'd always go back and
+ 
+
+ align:start position:0%
+if I have doubts I'd always go back and
+just do the problem in a rigorous way
+
+ align:start position:0%
+just do the problem in a rigorous way
+ 
+
+ align:start position:0%
+just do the problem in a rigorous way
+and just check that your insight was
+
+ align:start position:0%
+and just check that your insight was
+ 
+
+ align:start position:0%
+and just check that your insight was
+right. But it could give you great
+
+ align:start position:0%
+right. But it could give you great
+ 
+
+ align:start position:0%
+right. But it could give you great
+insight to starting a problem. You know
+
+ align:start position:0%
+insight to starting a problem. You know
+ 
+
+ align:start position:0%
+insight to starting a problem. You know
+to expect a centrifugal term in your
+
+ align:start position:0%
+to expect a centrifugal term in your
+ 
+
+ align:start position:0%
+to expect a centrifugal term in your
+results. you know to expect a coriololis
+
+ align:start position:0%
+results. you know to expect a coriololis
+ 
+
+ align:start position:0%
+results. you know to expect a coriololis
+term. You just you know that they're
+
+ align:start position:0%
+term. You just you know that they're
+ 
+
+ align:start position:0%
+term. You just you know that they're
+going to be there because you you you
+
+ align:start position:0%
+going to be there because you you you
+ 
+
+ align:start position:0%
+going to be there because you you you
+sometimes you u
+
+ align:start position:0%
+sometimes you u
+ 
+
+ align:start position:0%
+sometimes you u
+you you know you feel them. The reason
+
+ align:start position:0%
+you you know you feel them. The reason
+ 
+
+ align:start position:0%
+you you know you feel them. The reason
+we like to use them is because you
+
+ align:start position:0%
+we like to use them is because you
+ 
+
+ align:start position:0%
+we like to use them is because you
+actually can feel them.
+
+ align:start position:0%
+actually can feel them.
+ 
+
+ align:start position:0%
+actually can feel them.
+They actually affect what you feel.
+
+ align:start position:0%
+They actually affect what you feel.
+ 
+
+ align:start position:0%
+They actually affect what you feel.
+So when you're in the uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+when you're in that first in that first
+
+ align:start position:0%
+when you're in that first in that first
+ 
+
+ align:start position:0%
+when you're in that first in that first
+problem of the elevator problem the
+
+ align:start position:0%
+problem of the elevator problem the
+ 
+
+ align:start position:0%
+problem of the elevator problem the
+answer
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I didn't actually write it
+
+ align:start position:0%
+I didn't actually write it
+ 
+
+ align:start position:0%
+I didn't actually write it
+here it is the normal force that you
+
+ align:start position:0%
+here it is the normal force that you
+ 
+
+ align:start position:0%
+here it is the normal force that you
+feel that the scales weighs is 54g
+
+ align:start position:0%
+feel that the scales weighs is 54g
+ 
+
+ align:start position:0%
+feel that the scales weighs is 54g
+and it's the sum of gravity and that
+
+ align:start position:0%
+and it's the sum of gravity and that
+ 
+
+ align:start position:0%
+and it's the sum of gravity and that
+fictitious force
+
+ align:start position:0%
+fictitious force
+ 
+
+ align:start position:0%
+fictitious force
+It's mg plus m * a quart of a g.
+
+ align:start position:0%
+It's mg plus m * a quart of a g.
+ 
+
+ align:start position:0%
+It's mg plus m * a quart of a g.
+And so because you actually and and it's
+
+ align:start position:0%
+And so because you actually and and it's
+ 
+
+ align:start position:0%
+And so because you actually and and it's
+in this moving reference this
+
+ align:start position:0%
+in this moving reference this
+ 
+
+ align:start position:0%
+in this moving reference this
+accelerating reference frame inside an
+
+ align:start position:0%
+accelerating reference frame inside an
+ 
+
+ align:start position:0%
+accelerating reference frame inside an
+elevator where you can't directly
+
+ align:start position:0%
+elevator where you can't directly
+ 
+
+ align:start position:0%
+elevator where you can't directly
+measure the acceleration. All you can
+
+ align:start position:0%
+measure the acceleration. All you can
+ 
+
+ align:start position:0%
+measure the acceleration. All you can
+measure is the force
+
+ align:start position:0%
+measure is the force
+ 
+
+ align:start position:0%
+measure is the force
+but you you know what the acceleration
+
+ align:start position:0%
+but you you know what the acceleration
+ 
+
+ align:start position:0%
+but you you know what the acceleration
+is. It's given. So you stick it in as a
+
+ align:start position:0%
+is. It's given. So you stick it in as a
+ 
+
+ align:start position:0%
+is. It's given. So you stick it in as a
+fix and you find out that the real
+
+ align:start position:0%
+fix and you find out that the real
+ 
+
+ align:start position:0%
+fix and you find out that the real
+normal force that you measure actually
+
+ align:start position:0%
+normal force that you measure actually
+ 
+
+ align:start position:0%
+normal force that you measure actually
+has in it that piece that comes from the
+
+ align:start position:0%
+has in it that piece that comes from the
+ 
+
+ align:start position:0%
+has in it that piece that comes from the
+fictitious force. Okay. Why does the
+
+ align:start position:0%
+fictitious force. Okay. Why does the
+ 
+
+ align:start position:0%
+fictitious force. Okay. Why does the
+water move? Right? This this has to do
+
+ align:start position:0%
+water move? Right? This this has to do
+ 
+
+ align:start position:0%
+water move? Right? This this has to do
+this really the same discussion. The the
+
+ align:start position:0%
+this really the same discussion. The the
+ 
+
+ align:start position:0%
+this really the same discussion. The the
+fictitious force
+
+ align:start position:0%
+fictitious force
+ 
+
+ align:start position:0%
+fictitious force
+up the hill and the real force down the
+
+ align:start position:0%
+up the hill and the real force down the
+ 
+
+ align:start position:0%
+up the hill and the real force down the
+hill exactly cancel.
+
+ align:start position:0%
+hill exactly cancel.
+ 
+
+ align:start position:0%
+hill exactly cancel.
+If you could, if you're standing on
+
+ align:start position:0%
+If you could, if you're standing on
+ 
+
+ align:start position:0%
+If you could, if you're standing on
+scales that actually can measure side
+
+ align:start position:0%
+scales that actually can measure side
+ 
+
+ align:start position:0%
+scales that actually can measure side
+force as well as normal force, you
+
+ align:start position:0%
+force as well as normal force, you
+ 
+
+ align:start position:0%
+force as well as normal force, you
+standing on the scales, you would feel
+
+ align:start position:0%
+standing on the scales, you would feel
+ 
+
+ align:start position:0%
+standing on the scales, you would feel
+no side forces up and down the hill.
+
+ align:start position:0%
+no side forces up and down the hill.
+ 
+
+ align:start position:0%
+no side forces up and down the hill.
+None.
+
+ align:start position:0%
+None.
+ 
+
+ align:start position:0%
+None.
+You measure a normal force and the
+
+ align:start position:0%
+You measure a normal force and the
+ 
+
+ align:start position:0%
+You measure a normal force and the
+normal force you measure will be mg
+
+ align:start position:0%
+normal force you measure will be mg
+ 
+
+ align:start position:0%
+normal force you measure will be mg
+cosine theta.
+
+ align:start position:0%
+cosine theta.
+ 
+
+ align:start position:0%
+cosine theta.
+So the force on any
+
+ align:start position:0%
+So the force on any
+ 
+
+ align:start position:0%
+So the force on any
+you know any object in that accelerating
+
+ align:start position:0%
+you know any object in that accelerating
+ 
+
+ align:start position:0%
+you know any object in that accelerating
+reference frame it essentially thinks
+
+ align:start position:0%
+reference frame it essentially thinks
+ 
+
+ align:start position:0%
+reference frame it essentially thinks
+that all forces are perpendic that it
+
+ align:start position:0%
+that all forces are perpendic that it
+ 
+
+ align:start position:0%
+that all forces are perpendic that it
+that you feel in that reference frame
+
+ align:start position:0%
+that you feel in that reference frame
+ 
+
+ align:start position:0%
+that you feel in that reference frame
+are perpendicular to the hill.
+
+ align:start position:0%
+are perpendicular to the hill.
+ 
+
+ align:start position:0%
+are perpendicular to the hill.
+So if why does water seek level
+
+ align:start position:0%
+So if why does water seek level
+ 
+
+ align:start position:0%
+So if why does water seek level
+because the force gravity is down and
+
+ align:start position:0%
+because the force gravity is down and
+ 
+
+ align:start position:0%
+because the force gravity is down and
+the surface of the water goes
+
+ align:start position:0%
+the surface of the water goes
+ 
+
+ align:start position:0%
+the surface of the water goes
+perpendicular to the gravitational
+
+ align:start position:0%
+perpendicular to the gravitational
+ 
+
+ align:start position:0%
+perpendicular to the gravitational
+force. That's just the nature of fluids.
+
+ align:start position:0%
+force. That's just the nature of fluids.
+ 
+
+ align:start position:0%
+force. That's just the nature of fluids.
+So if the force on all those fluid
+
+ align:start position:0%
+So if the force on all those fluid
+ 
+
+ align:start position:0%
+So if the force on all those fluid
+particles is is this angle, what's the
+
+ align:start position:0%
+particles is is this angle, what's the
+ 
+
+ align:start position:0%
+particles is is this angle, what's the
+fluid level going to do? So that the
+
+ align:start position:0%
+fluid level going to do? So that the
+ 
+
+ align:start position:0%
+fluid level going to do? So that the
+pressure on the surface is equal
+
+ align:start position:0%
+pressure on the surface is equal
+ 
+
+ align:start position:0%
+pressure on the surface is equal
+everywhere. And if you go a foot down,
+
+ align:start position:0%
+everywhere. And if you go a foot down,
+ 
+
+ align:start position:0%
+everywhere. And if you go a foot down,
+you'd have equal pressure everywhere in
+
+ align:start position:0%
+you'd have equal pressure everywhere in
+ 
+
+ align:start position:0%
+you'd have equal pressure everywhere in
+the fluid.
+
+ align:start position:0%
+the fluid.
+ 
+
+ align:start position:0%
+the fluid.
+So it it just see what
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so the water moves so that its surface
+
+ align:start position:0%
+so the water moves so that its surface
+ 
+
+ align:start position:0%
+so the water moves so that its surface
+will be perpendicular to what it thinks
+
+ align:start position:0%
+will be perpendicular to what it thinks
+ 
+
+ align:start position:0%
+will be perpendicular to what it thinks
+is it thinks that this is kind of being
+
+ align:start position:0%
+is it thinks that this is kind of being
+ 
+
+ align:start position:0%
+is it thinks that this is kind of being
+the local gravity. The local gravity is
+
+ align:start position:0%
+the local gravity. The local gravity is
+ 
+
+ align:start position:0%
+the local gravity. The local gravity is
+pointed in that direction. So the
+
+ align:start position:0%
+pointed in that direction. So the
+ 
+
+ align:start position:0%
+pointed in that direction. So the
+surface level seeks that level.
+
+ align:start position:0%
+surface level seeks that level.
+ 
+
+ align:start position:0%
+surface level seeks that level.
+If somebody else can say it better than
+
+ align:start position:0%
+If somebody else can say it better than
+ 
+
+ align:start position:0%
+If somebody else can say it better than
+that Tom Dave Matt anybody
+
+ align:start position:0%
+that Tom Dave Matt anybody
+ 
+
+ align:start position:0%
+that Tom Dave Matt anybody
+these are
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Yeah.
+
+ align:start position:0%
+Yeah.
+ 
+
+ align:start position:0%
+Yeah.
+Yeah.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well,
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+yeah. You're as if you you're on the
+
+ align:start position:0%
+yeah. You're as if you you're on the
+ 
+
+ align:start position:0%
+yeah. You're as if you you're on the
+body and you're trying to sum up all the
+
+ align:start position:0%
+body and you're trying to sum up all the
+ 
+
+ align:start position:0%
+body and you're trying to sum up all the
+forces you feel and accounting also for
+
+ align:start position:0%
+forces you feel and accounting also for
+ 
+
+ align:start position:0%
+forces you feel and accounting also for
+the fact that this is accelerating. And
+
+ align:start position:0%
+the fact that this is accelerating. And
+ 
+
+ align:start position:0%
+the fact that this is accelerating. And
+the fix it force is this fictitious
+
+ align:start position:0%
+the fix it force is this fictitious
+ 
+
+ align:start position:0%
+the fix it force is this fictitious
+force that's due to the body's
+
+ align:start position:0%
+force that's due to the body's
+ 
+
+ align:start position:0%
+force that's due to the body's
+acceleration. You have to know that
+
+ align:start position:0%
+acceleration. You have to know that
+ 
+
+ align:start position:0%
+acceleration. You have to know that
+you're accelerating to be able to put
+
+ align:start position:0%
+you're accelerating to be able to put
+ 
+
+ align:start position:0%
+you're accelerating to be able to put
+this term in.
+
+ align:start position:0%
+this term in.
+ 
+
+ align:start position:0%
+this term in.
+And all it comes from this equation
+
+ align:start position:0%
+And all it comes from this equation
+ 
+
+ align:start position:0%
+And all it comes from this equation
+gener thinking of this as a generic
+
+ align:start position:0%
+gener thinking of this as a generic
+ 
+
+ align:start position:0%
+gener thinking of this as a generic
+equation by taking this term and just
+
+ align:start position:0%
+equation by taking this term and just
+ 
+
+ align:start position:0%
+equation by taking this term and just
+moving it to this side and setting
+
+ align:start position:0%
+moving it to this side and setting
+ 
+
+ align:start position:0%
+moving it to this side and setting
+everything equal to zero.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Lots of puzzlemen around this. This
+
+ align:start position:0%
+Lots of puzzlemen around this. This
+ 
+
+ align:start position:0%
+Lots of puzzlemen around this. This
+what happens if you make the angle of
+
+ align:start position:0%
+what happens if you make the angle of
+ 
+
+ align:start position:0%
+what happens if you make the angle of
+the ram like very steep
+
+ align:start position:0%
+the ram like very steep
+ 
+
+ align:start position:0%
+the ram like very steep
+very steep. So if it goes to 90°
+
+ align:start position:0%
+very steep. So if it goes to 90°
+ 
+
+ align:start position:0%
+very steep. So if it goes to 90°
+you're in freef fall you will measure
+
+ align:start position:0%
+you're in freef fall you will measure
+ 
+
+ align:start position:0%
+you're in freef fall you will measure
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+this cosine theta goes to zero and goes
+
+ align:start position:0%
+this cosine theta goes to zero and goes
+ 
+
+ align:start position:0%
+this cosine theta goes to zero and goes
+to zero.
+
+ align:start position:0%
+to zero.
+ 
+
+ align:start position:0%
+to zero.
+This term stays the same. This goes to
+
+ align:start position:0%
+This term stays the same. This goes to
+ 
+
+ align:start position:0%
+This term stays the same. This goes to
+mg that way. This goes mg that way. and
+
+ align:start position:0%
+mg that way. This goes mg that way. and
+ 
+
+ align:start position:0%
+mg that way. This goes mg that way. and
+it's in equilibrium and both
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+then you're going to have very very
+
+ align:start position:0%
+then you're going to have very very
+ 
+
+ align:start position:0%
+then you're going to have very very
+small normal force.
+
+ align:start position:0%
+small normal force.
+ 
+
+ align:start position:0%
+small normal force.
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+I couldn't hear the last comment. The
+
+ align:start position:0%
+I couldn't hear the last comment. The
+ 
+
+ align:start position:0%
+I couldn't hear the last comment. The
+water wouldn't go all the way to the
+
+ align:start position:0%
+water wouldn't go all the way to the
+ 
+
+ align:start position:0%
+water wouldn't go all the way to the
+side.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Well, you know, the water unfortunately,
+
+ align:start position:0%
+Well, you know, the water unfortunately,
+ 
+
+ align:start position:0%
+Well, you know, the water unfortunately,
+I mean, it with the tiniest little bit
+
+ align:start position:0%
+I mean, it with the tiniest little bit
+ 
+
+ align:start position:0%
+I mean, it with the tiniest little bit
+of normal uh acceler normal force here,
+
+ align:start position:0%
+of normal uh acceler normal force here,
+ 
+
+ align:start position:0%
+of normal uh acceler normal force here,
+the water will seek that level, but when
+
+ align:start position:0%
+the water will seek that level, but when
+ 
+
+ align:start position:0%
+the water will seek that level, but when
+it gets to zero, it's kind of all
+
+ align:start position:0%
+it gets to zero, it's kind of all
+ 
+
+ align:start position:0%
+it gets to zero, it's kind of all
+the water is just going to be in freef
+
+ align:start position:0%
+the water is just going to be in freef
+ 
+
+ align:start position:0%
+the water is just going to be in freef
+fall. It's going to form surface tension
+
+ align:start position:0%
+fall. It's going to form surface tension
+ 
+
+ align:start position:0%
+fall. It's going to form surface tension
+takes over, right? Yeah. This argument
+
+ align:start position:0%
+takes over, right? Yeah. This argument
+ 
+
+ align:start position:0%
+takes over, right? Yeah. This argument
+that equal pressure is the same as it
+
+ align:start position:0%
+that equal pressure is the same as it
+ 
+
+ align:start position:0%
+that equal pressure is the same as it
+was just on a flat surface accelerating.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. If you were ah good question. If
+
+ align:start position:0%
+Okay. If you were ah good question. If
+ 
+
+ align:start position:0%
+Okay. If you were ah good question. If
+you're on a flat surface accelerating,
+
+ align:start position:0%
+you're on a flat surface accelerating,
+ 
+
+ align:start position:0%
+you're on a flat surface accelerating,
+if you were accelerating and this cart
+
+ align:start position:0%
+if you were accelerating and this cart
+ 
+
+ align:start position:0%
+if you were accelerating and this cart
+accelerates with a fluid on it and it's
+
+ align:start position:0%
+accelerates with a fluid on it and it's
+ 
+
+ align:start position:0%
+accelerates with a fluid on it and it's
+accelerating in that direction,
+
+ align:start position:0%
+accelerating in that direction,
+ 
+
+ align:start position:0%
+accelerating in that direction,
+what would the surface of the liquid do?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+stay level or change?
+
+ align:start position:0%
+stay level or change?
+ 
+
+ align:start position:0%
+stay level or change?
+Okay. Does it slope back or does it
+
+ align:start position:0%
+Okay. Does it slope back or does it
+ 
+
+ align:start position:0%
+Okay. Does it slope back or does it
+slope forward? I'm accelerating in that
+
+ align:start position:0%
+slope forward? I'm accelerating in that
+ 
+
+ align:start position:0%
+slope forward? I'm accelerating in that
+direction.
+
+ align:start position:0%
+direction.
+ 
+
+ align:start position:0%
+direction.
+There's a centrifugal
+
+ align:start position:0%
+There's a centrifugal
+ 
+
+ align:start position:0%
+There's a centrifugal
+not a fictitious force pushing back on
+
+ align:start position:0%
+not a fictitious force pushing back on
+ 
+
+ align:start position:0%
+not a fictitious force pushing back on
+it pushes it makes it pile up at the
+
+ align:start position:0%
+it pushes it makes it pile up at the
+ 
+
+ align:start position:0%
+it pushes it makes it pile up at the
+back.
+
+ align:start position:0%
+back.
+ 
+
+ align:start position:0%
+back.
+Okay, one more.
+
+ align:start position:0%
+Okay, one more.
+ 
+
+ align:start position:0%
+Okay, one more.
+You're in the elevator. You're
+
+ align:start position:0%
+You're in the elevator. You're
+ 
+
+ align:start position:0%
+You're in the elevator. You're
+accelerating a quarter of a g.
+
+ align:start position:0%
+accelerating a quarter of a g.
+ 
+
+ align:start position:0%
+accelerating a quarter of a g.
+You feel the scales tells you weigh, you
+
+ align:start position:0%
+You feel the scales tells you weigh, you
+ 
+
+ align:start position:0%
+You feel the scales tells you weigh, you
+know, 25% more than you used to. And you
+
+ align:start position:0%
+know, 25% more than you used to. And you
+ 
+
+ align:start position:0%
+know, 25% more than you used to. And you
+have a pendulum. And on before the
+
+ align:start position:0%
+have a pendulum. And on before the
+ 
+
+ align:start position:0%
+have a pendulum. And on before the
+elevator starts, it's got a 1se second
+
+ align:start position:0%
+elevator starts, it's got a 1se second
+ 
+
+ align:start position:0%
+elevator starts, it's got a 1se second
+natural period.
+
+ align:start position:0%
+natural period.
+ 
+
+ align:start position:0%
+natural period.
+And now the elevator gets going, does
+
+ align:start position:0%
+And now the elevator gets going, does
+ 
+
+ align:start position:0%
+And now the elevator gets going, does
+the period change?
+
+ align:start position:0%
+the period change?
+ 
+
+ align:start position:0%
+the period change?
+Higher or lower?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. The So the natural frequency of
+
+ align:start position:0%
+Okay. The So the natural frequency of
+ 
+
+ align:start position:0%
+Okay. The So the natural frequency of
+the pendulum, simple pendulum, square
+
+ align:start position:0%
+the pendulum, simple pendulum, square
+ 
+
+ align:start position:0%
+the pendulum, simple pendulum, square
+root of G over L. What do you what do
+
+ align:start position:0%
+root of G over L. What do you what do
+ 
+
+ align:start position:0%
+root of G over L. What do you what do
+you guess that the natural frequency is
+
+ align:start position:0%
+you guess that the natural frequency is
+ 
+
+ align:start position:0%
+you guess that the natural frequency is
+if you're going up at a quarter of a G?
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Say again.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+as if you have a higher or lower
+
+ align:start position:0%
+as if you have a higher or lower
+ 
+
+ align:start position:0%
+as if you have a higher or lower
+acceleration of gravity around.
+
+ align:start position:0%
+acceleration of gravity around.
+ 
+
+ align:start position:0%
+acceleration of gravity around.
+It's like you have a higher
+
+ align:start position:0%
+It's like you have a higher
+ 
+
+ align:start position:0%
+It's like you have a higher
+gravitational force is what you think
+
+ align:start position:0%
+gravitational force is what you think
+ 
+
+ align:start position:0%
+gravitational force is what you think
+you're feeling. Is that going to make
+
+ align:start position:0%
+you're feeling. Is that going to make
+ 
+
+ align:start position:0%
+you're feeling. Is that going to make
+put make the tension in this string
+
+ align:start position:0%
+put make the tension in this string
+ 
+
+ align:start position:0%
+put make the tension in this string
+higher? Is that going to make the weight
+
+ align:start position:0%
+higher? Is that going to make the weight
+ 
+
+ align:start position:0%
+higher? Is that going to make the weight
+of the pendulum feel greater? Yeah. By
+
+ align:start position:0%
+of the pendulum feel greater? Yeah. By
+ 
+
+ align:start position:0%
+of the pendulum feel greater? Yeah. By
+five for fours. And you'll find out you
+
+ align:start position:0%
+five for fours. And you'll find out you
+ 
+
+ align:start position:0%
+five for fours. And you'll find out you
+work out. It gets kind of messy to prove
+
+ align:start position:0%
+work out. It gets kind of messy to prove
+ 
+
+ align:start position:0%
+work out. It gets kind of messy to prove
+this uh rigorously, but it's going to
+
+ align:start position:0%
+this uh rigorously, but it's going to
+ 
+
+ align:start position:0%
+this uh rigorously, but it's going to
+look something like the square root of
+
+ align:start position:0%
+look something like the square root of
+ 
+
+ align:start position:0%
+look something like the square root of
+54 G over L. Okay. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. We got a little time left. I
+
+ align:start position:0%
+All right. We got a little time left. I
+ 
+
+ align:start position:0%
+All right. We got a little time left. I
+might not be able to completely finish
+
+ align:start position:0%
+might not be able to completely finish
+ 
+
+ align:start position:0%
+might not be able to completely finish
+this, but I do want to show you
+
+ align:start position:0%
+this, but I do want to show you
+ 
+
+ align:start position:0%
+this, but I do want to show you
+something.
+
+ align:start position:0%
+something.
+ 
+
+ align:start position:0%
+something.
+You had a
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Hold it up so they can see. It
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+gets pretty violent, doesn't it? Pass it
+
+ align:start position:0%
+gets pretty violent, doesn't it? Pass it
+ 
+
+ align:start position:0%
+gets pretty violent, doesn't it? Pass it
+around.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay. This this thing is shaking like
+
+ align:start position:0%
+Okay. This this thing is shaking like
+ 
+
+ align:start position:0%
+Okay. This this thing is shaking like
+crazy.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+All right. I'll let you and I'll uh
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right. In the absence of external
+
+ align:start position:0%
+All right. In the absence of external
+ 
+
+ align:start position:0%
+All right. In the absence of external
+forces, what can you say about the
+
+ align:start position:0%
+forces, what can you say about the
+ 
+
+ align:start position:0%
+forces, what can you say about the
+motion of its center of gravity? Do you
+
+ align:start position:0%
+motion of its center of gravity? Do you
+ 
+
+ align:start position:0%
+motion of its center of gravity? Do you
+think in the at least this direction?
+
+ align:start position:0%
+think in the at least this direction?
+ 
+
+ align:start position:0%
+think in the at least this direction?
+can't move right in the up up and down
+
+ align:start position:0%
+can't move right in the up up and down
+ 
+
+ align:start position:0%
+can't move right in the up up and down
+direction. It uh uh the center of
+
+ align:start position:0%
+direction. It uh uh the center of
+ 
+
+ align:start position:0%
+direction. It uh uh the center of
+gravity does move because I'm putting a
+
+ align:start position:0%
+gravity does move because I'm putting a
+ 
+
+ align:start position:0%
+gravity does move because I'm putting a
+force on it through the cord. Okay, this
+
+ align:start position:0%
+force on it through the cord. Okay, this
+ 
+
+ align:start position:0%
+force on it through the cord. Okay, this
+is there's this has a relation to a
+
+ align:start position:0%
+is there's this has a relation to a
+ 
+
+ align:start position:0%
+is there's this has a relation to a
+problem that you were had on problem set
+
+ align:start position:0%
+problem that you were had on problem set
+ 
+
+ align:start position:0%
+problem that you were had on problem set
+two.
+
+ align:start position:0%
+two.
+ 
+
+ align:start position:0%
+two.
+I wanted to go back and talk about it a
+
+ align:start position:0%
+I wanted to go back and talk about it a
+ 
+
+ align:start position:0%
+I wanted to go back and talk about it a
+little bit because
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+this is that thing with a track in it
+
+ align:start position:0%
+this is that thing with a track in it
+ 
+
+ align:start position:0%
+this is that thing with a track in it
+and has a roller going around and it's
+
+ align:start position:0%
+and has a roller going around and it's
+ 
+
+ align:start position:0%
+and has a roller going around and it's
+going around at constant speed. And this
+
+ align:start position:0%
+going around at constant speed. And this
+ 
+
+ align:start position:0%
+going around at constant speed. And this
+has mass m this has mass the outside
+
+ align:start position:0%
+has mass m this has mass the outside
+ 
+
+ align:start position:0%
+has mass m this has mass the outside
+thing is just the mass of this block.
+
+ align:start position:0%
+thing is just the mass of this block.
+ 
+
+ align:start position:0%
+thing is just the mass of this block.
+Okay? And this there's an internal donut
+
+ align:start position:0%
+Okay? And this there's an internal donut
+ 
+
+ align:start position:0%
+Okay? And this there's an internal donut
+in here, a toid. And this mass is made
+
+ align:start position:0%
+in here, a toid. And this mass is made
+ 
+
+ align:start position:0%
+in here, a toid. And this mass is made
+to go running around around inside. And
+
+ align:start position:0%
+to go running around around inside. And
+ 
+
+ align:start position:0%
+to go running around around inside. And
+you were asked to figure out the
+
+ align:start position:0%
+you were asked to figure out the
+ 
+
+ align:start position:0%
+you were asked to figure out the
+acceleration of that guy. But this
+
+ align:start position:0%
+acceleration of that guy. But this
+ 
+
+ align:start position:0%
+acceleration of that guy. But this
+thing's on wheels.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Now
+
+ align:start position:0%
+Now
+ 
+
+ align:start position:0%
+Now
+this problem and I I apologize for for
+
+ align:start position:0%
+this problem and I I apologize for for
+ 
+
+ align:start position:0%
+this problem and I I apologize for for
+posing this problem the way I did. I
+
+ align:start position:0%
+posing this problem the way I did. I
+ 
+
+ align:start position:0%
+posing this problem the way I did. I
+should have posed it in the following
+
+ align:start position:0%
+should have posed it in the following
+ 
+
+ align:start position:0%
+should have posed it in the following
+sense following way. These two problems
+
+ align:start position:0%
+sense following way. These two problems
+ 
+
+ align:start position:0%
+sense following way. These two problems
+are really equal to one another.
+
+ align:start position:0%
+are really equal to one another.
+ 
+
+ align:start position:0%
+are really equal to one another.
+I have a rod. I have a mass on the end.
+
+ align:start position:0%
+I have a rod. I have a mass on the end.
+ 
+
+ align:start position:0%
+I have a rod. I have a mass on the end.
+This radius here we said was E. This
+
+ align:start position:0%
+This radius here we said was E. This
+ 
+
+ align:start position:0%
+This radius here we said was E. This
+radius is E. The mass is the same. It's
+
+ align:start position:0%
+radius is E. The mass is the same. It's
+ 
+
+ align:start position:0%
+radius is E. The mass is the same. It's
+m. This was going around at
+
+ align:start position:0%
+m. This was going around at
+ 
+
+ align:start position:0%
+m. This was going around at
+omega. This is going around at omega.
+
+ align:start position:0%
+omega. This is going around at omega.
+ 
+
+ align:start position:0%
+omega. This is going around at omega.
+This is on wheels. Exactly. These two
+
+ align:start position:0%
+This is on wheels. Exactly. These two
+ 
+
+ align:start position:0%
+This is on wheels. Exactly. These two
+problems are
+
+ align:start position:0%
+problems are
+ 
+
+ align:start position:0%
+problems are
+identical because if the geometry is the
+
+ align:start position:0%
+identical because if the geometry is the
+ 
+
+ align:start position:0%
+identical because if the geometry is the
+same, the rotation rates the same, the
+
+ align:start position:0%
+same, the rotation rates the same, the
+ 
+
+ align:start position:0%
+same, the rotation rates the same, the
+masses are the same, the acceleration of
+
+ align:start position:0%
+masses are the same, the acceleration of
+ 
+
+ align:start position:0%
+masses are the same, the acceleration of
+this bead here, this roller is the same
+
+ align:start position:0%
+this bead here, this roller is the same
+ 
+
+ align:start position:0%
+this bead here, this roller is the same
+in this problem as it is in that
+
+ align:start position:0%
+in this problem as it is in that
+ 
+
+ align:start position:0%
+in this problem as it is in that
+problem. just that this problem is much
+
+ align:start position:0%
+problem. just that this problem is much
+ 
+
+ align:start position:0%
+problem. just that this problem is much
+easier to figure out the forces. This
+
+ align:start position:0%
+easier to figure out the forces. This
+ 
+
+ align:start position:0%
+easier to figure out the forces. This
+turned out to be kind of nasty. And I
+
+ align:start position:0%
+turned out to be kind of nasty. And I
+ 
+
+ align:start position:0%
+turned out to be kind of nasty. And I
+said last time that the solution to the
+
+ align:start position:0%
+said last time that the solution to the
+ 
+
+ align:start position:0%
+said last time that the solution to the
+B part, which is the normal force that
+
+ align:start position:0%
+B part, which is the normal force that
+ 
+
+ align:start position:0%
+B part, which is the normal force that
+this is put on this roller, I said that
+
+ align:start position:0%
+this is put on this roller, I said that
+ 
+
+ align:start position:0%
+this is put on this roller, I said that
+answer was wrong. I actually am wrong
+
+ align:start position:0%
+answer was wrong. I actually am wrong
+ 
+
+ align:start position:0%
+answer was wrong. I actually am wrong
+about that. I I was thinking of a
+
+ align:start position:0%
+about that. I I was thinking of a
+ 
+
+ align:start position:0%
+about that. I I was thinking of a
+different answer. I was thinking of this
+
+ align:start position:0%
+different answer. I was thinking of this
+ 
+
+ align:start position:0%
+different answer. I was thinking of this
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+uh the pro the answer that was given the
+
+ align:start position:0%
+uh the pro the answer that was given the
+ 
+
+ align:start position:0%
+uh the pro the answer that was given the
+normal force that is by the track places
+
+ align:start position:0%
+normal force that is by the track places
+ 
+
+ align:start position:0%
+normal force that is by the track places
+on the roller or the vice versa is
+
+ align:start position:0%
+on the roller or the vice versa is
+ 
+
+ align:start position:0%
+on the roller or the vice versa is
+actually what was given is correct. It
+
+ align:start position:0%
+actually what was given is correct. It
+ 
+
+ align:start position:0%
+actually what was given is correct. It
+wasn't what I actually was seeking when
+
+ align:start position:0%
+wasn't what I actually was seeking when
+ 
+
+ align:start position:0%
+wasn't what I actually was seeking when
+I wrote the problem. Sometimes you know
+
+ align:start position:0%
+I wrote the problem. Sometimes you know
+ 
+
+ align:start position:0%
+I wrote the problem. Sometimes you know
+you when you're making up problems you
+
+ align:start position:0%
+you when you're making up problems you
+ 
+
+ align:start position:0%
+you when you're making up problems you
+have an end result in mind and then you
+
+ align:start position:0%
+have an end result in mind and then you
+ 
+
+ align:start position:0%
+have an end result in mind and then you
+wrote it wrong. I wrote it wrong. So
+
+ align:start position:0%
+wrote it wrong. I wrote it wrong. So
+ 
+
+ align:start position:0%
+wrote it wrong. I wrote it wrong. So
+let's do this problem
+
+ align:start position:0%
+let's do this problem
+ 
+
+ align:start position:0%
+let's do this problem
+and I want to do I want this is partly
+
+ align:start position:0%
+and I want to do I want this is partly
+ 
+
+ align:start position:0%
+and I want to do I want this is partly
+re uh to review a couple of things for
+
+ align:start position:0%
+re uh to review a couple of things for
+ 
+
+ align:start position:0%
+re uh to review a couple of things for
+you. So I want to find the what I really
+
+ align:start position:0%
+you. So I want to find the what I really
+ 
+
+ align:start position:0%
+you. So I want to find the what I really
+want is I want to find
+
+ align:start position:0%
+want is I want to find
+ 
+
+ align:start position:0%
+want is I want to find
+the equation of motion
+
+ align:start position:0%
+the equation of motion
+ 
+
+ align:start position:0%
+the equation of motion
+in
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+how do I draw my
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+so here's my x yz inertial reference
+
+ align:start position:0%
+so here's my x yz inertial reference
+ 
+
+ align:start position:0%
+so here's my x yz inertial reference
+frame. I just lined it up here with the
+
+ align:start position:0%
+frame. I just lined it up here with the
+ 
+
+ align:start position:0%
+frame. I just lined it up here with the
+know the center of this thing to start
+
+ align:start position:0%
+know the center of this thing to start
+ 
+
+ align:start position:0%
+know the center of this thing to start
+with. Doesn't really matter. So I want
+
+ align:start position:0%
+with. Doesn't really matter. So I want
+ 
+
+ align:start position:0%
+with. Doesn't really matter. So I want
+to find an equation of motion in the x
+
+ align:start position:0%
+to find an equation of motion in the x
+ 
+
+ align:start position:0%
+to find an equation of motion in the x
+direction.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And we don't have time to do this whole
+
+ align:start position:0%
+And we don't have time to do this whole
+ 
+
+ align:start position:0%
+And we don't have time to do this whole
+problem here. So I'm going to do the
+
+ align:start position:0%
+problem here. So I'm going to do the
+ 
+
+ align:start position:0%
+problem here. So I'm going to do the
+first piece of it is
+
+ align:start position:0%
+first piece of it is
+ 
+
+ align:start position:0%
+first piece of it is
+just to give you some review and
+
+ align:start position:0%
+just to give you some review and
+ 
+
+ align:start position:0%
+just to give you some review and
+exercise in figuring out degrees of
+
+ align:start position:0%
+exercise in figuring out degrees of
+ 
+
+ align:start position:0%
+exercise in figuring out degrees of
+freedom. How many I I I'm implying that
+
+ align:start position:0%
+freedom. How many I I I'm implying that
+ 
+
+ align:start position:0%
+freedom. How many I I I'm implying that
+I I can write one equation. It may take
+
+ align:start position:0%
+I I can write one equation. It may take
+ 
+
+ align:start position:0%
+I I can write one equation. It may take
+more than that. So the number of degrees
+
+ align:start position:0%
+more than that. So the number of degrees
+ 
+
+ align:start position:0%
+more than that. So the number of degrees
+of freedom we said is equal to the
+
+ align:start position:0%
+of freedom we said is equal to the
+ 
+
+ align:start position:0%
+of freedom we said is equal to the
+number of
+
+ align:start position:0%
+number of
+ 
+
+ align:start position:0%
+number of
+required
+
+ align:start position:0%
+required
+ 
+
+ align:start position:0%
+required
+can't write today
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+independent
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+coordinates.
+
+ align:start position:0%
+coordinates.
+ 
+
+ align:start position:0%
+coordinates.
+So the number of coordinates required to
+
+ align:start position:0%
+So the number of coordinates required to
+ 
+
+ align:start position:0%
+So the number of coordinates required to
+completely describe the motion and we
+
+ align:start position:0%
+completely describe the motion and we
+ 
+
+ align:start position:0%
+completely describe the motion and we
+came up with a little expression for
+
+ align:start position:0%
+came up with a little expression for
+ 
+
+ align:start position:0%
+came up with a little expression for
+that. It's six times the number of rigid
+
+ align:start position:0%
+that. It's six times the number of rigid
+ 
+
+ align:start position:0%
+that. It's six times the number of rigid
+bodies plus 3 * the number of particles.
+
+ align:start position:0%
+bodies plus 3 * the number of particles.
+ 
+
+ align:start position:0%
+bodies plus 3 * the number of particles.
+So this is rigid bodies.
+
+ align:start position:0%
+So this is rigid bodies.
+ 
+
+ align:start position:0%
+So this is rigid bodies.
+This is particles
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+minus
+
+ align:start position:0%
+minus
+ 
+
+ align:start position:0%
+minus
+C and these are the constraints.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So, let's figure that out for this
+
+ align:start position:0%
+So, let's figure that out for this
+ 
+
+ align:start position:0%
+So, let's figure that out for this
+problem.
+
+ align:start position:0%
+problem.
+ 
+
+ align:start position:0%
+problem.
+Oops.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+How many constraints? It's just a quick
+
+ align:start position:0%
+How many constraints? It's just a quick
+ 
+
+ align:start position:0%
+How many constraints? It's just a quick
+practice.
+
+ align:start position:0%
+practice.
+ 
+
+ align:start position:0%
+practice.
+So constraints and I'm going to start
+
+ align:start position:0%
+So constraints and I'm going to start
+ 
+
+ align:start position:0%
+So constraints and I'm going to start
+off with on
+
+ align:start position:0%
+off with on
+ 
+
+ align:start position:0%
+off with on
+the main block. Okay. So
+
+ align:start position:0%
+the main block. Okay. So
+ 
+
+ align:start position:0%
+the main block. Okay. So
+there's on the main block there's no Y
+
+ align:start position:0%
+there's on the main block there's no Y
+ 
+
+ align:start position:0%
+there's on the main block there's no Y
+motion. There's no Z motion. These
+
+ align:start position:0%
+motion. There's no Z motion. These
+ 
+
+ align:start position:0%
+motion. There's no Z motion. These
+rollers don't let it come in or out. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+no Y or Z motion.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So that's two constraints.
+
+ align:start position:0%
+So that's two constraints.
+ 
+
+ align:start position:0%
+So that's two constraints.
+Okay. What about rotations on the main
+
+ align:start position:0%
+Okay. What about rotations on the main
+ 
+
+ align:start position:0%
+Okay. What about rotations on the main
+block? How many constraints are we
+
+ align:start position:0%
+block? How many constraints are we
+ 
+
+ align:start position:0%
+block? How many constraints are we
+assuming here?
+
+ align:start position:0%
+assuming here?
+ 
+
+ align:start position:0%
+assuming here?
+Three. We're not allowing it to roll in
+
+ align:start position:0%
+Three. We're not allowing it to roll in
+ 
+
+ align:start position:0%
+Three. We're not allowing it to roll in
+the X, the Y, or the Z.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So there's three more constraints.
+
+ align:start position:0%
+So there's three more constraints.
+ 
+
+ align:start position:0%
+So there's three more constraints.
+And now on the little mass.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+Okay, on the little mass there's no Z
+
+ align:start position:0%
+Okay, on the little mass there's no Z
+ 
+
+ align:start position:0%
+Okay, on the little mass there's no Z
+motion. That's out of the board.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+That's one more constraint.
+
+ align:start position:0%
+That's one more constraint.
+ 
+
+ align:start position:0%
+That's one more constraint.
+And then
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+omega t
+
+ align:start position:0%
+omega t
+ 
+
+ align:start position:0%
+omega t
+is the angle that this thing that's
+
+ align:start position:0%
+is the angle that this thing that's
+ 
+
+ align:start position:0%
+is the angle that this thing that's
+theta.
+
+ align:start position:0%
+theta.
+ 
+
+ align:start position:0%
+theta.
+This is specified.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+It's a given in the problem. It's not
+
+ align:start position:0%
+It's a given in the problem. It's not
+ 
+
+ align:start position:0%
+It's a given in the problem. It's not
+unknown. It's just that's what's going
+
+ align:start position:0%
+unknown. It's just that's what's going
+ 
+
+ align:start position:0%
+unknown. It's just that's what's going
+that's what makes this thing do its
+
+ align:start position:0%
+that's what makes this thing do its
+ 
+
+ align:start position:0%
+that's what makes this thing do its
+thing. It's going round and round. And
+
+ align:start position:0%
+thing. It's going round and round. And
+ 
+
+ align:start position:0%
+thing. It's going round and round. And
+so this is not an unknown. And therefore
+
+ align:start position:0%
+so this is not an unknown. And therefore
+ 
+
+ align:start position:0%
+so this is not an unknown. And therefore
+you can say that the y
+
+ align:start position:0%
+you can say that the y
+ 
+
+ align:start position:0%
+you can say that the y
+motion of this particle
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+e
+
+ align:start position:0%
+e
+ 
+
+ align:start position:0%
+e
+sin omega t.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+And that's a constraint.
+
+ align:start position:0%
+And that's a constraint.
+ 
+
+ align:start position:0%
+And that's a constraint.
+And the X motion
+
+ align:start position:0%
+And the X motion
+ 
+
+ align:start position:0%
+And the X motion
+is
+
+ align:start position:0%
+is
+ 
+
+ align:start position:0%
+is
+the motion of
+
+ align:start position:0%
+the motion of
+ 
+
+ align:start position:0%
+the motion of
+the
+
+ align:start position:0%
+the
+ 
+
+ align:start position:0%
+the
+main block to which it's attached
+
+ align:start position:0%
+main block to which it's attached
+ 
+
+ align:start position:0%
+main block to which it's attached
+plus an E cosine
+
+ align:start position:0%
+plus an E cosine
+ 
+
+ align:start position:0%
+plus an E cosine
+omega t.
+
+ align:start position:0%
+omega t.
+ 
+
+ align:start position:0%
+omega t.
+And that's another these are known. This
+
+ align:start position:0%
+And that's another these are known. This
+ 
+
+ align:start position:0%
+And that's another these are known. This
+is you've already accounted for this.
+
+ align:start position:0%
+is you've already accounted for this.
+ 
+
+ align:start position:0%
+is you've already accounted for this.
+That's that's the main masses motion. So
+
+ align:start position:0%
+That's that's the main masses motion. So
+ 
+
+ align:start position:0%
+That's that's the main masses motion. So
+this is something known. So these mount
+
+ align:start position:0%
+this is something known. So these mount
+ 
+
+ align:start position:0%
+this is something known. So these mount
+up each one of these. This gives you a
+
+ align:start position:0%
+up each one of these. This gives you a
+ 
+
+ align:start position:0%
+up each one of these. This gives you a
+constraint and this gives you a
+
+ align:start position:0%
+constraint and this gives you a
+ 
+
+ align:start position:0%
+constraint and this gives you a
+constraint. And so let's add them up. So
+
+ align:start position:0%
+constraint. And so let's add them up. So
+ 
+
+ align:start position:0%
+constraint. And so let's add them up. So
+two and three or five six 7 8.
+
+ align:start position:0%
+two and three or five six 7 8.
+ 
+
+ align:start position:0%
+two and three or five six 7 8.
+So you can actually completely describe
+
+ align:start position:0%
+So you can actually completely describe
+ 
+
+ align:start position:0%
+So you can actually completely describe
+the motion of this thing with one
+
+ align:start position:0%
+the motion of this thing with one
+ 
+
+ align:start position:0%
+the motion of this thing with one
+equation of motion. Okay.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+All right.
+
+ align:start position:0%
+All right.
+ 
+
+ align:start position:0%
+All right.
+So I'm seeking so I want to find
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+the sum of the external forces
+
+ align:start position:0%
+the sum of the external forces
+ 
+
+ align:start position:0%
+the sum of the external forces
+on
+
+ align:start position:0%
+on
+ 
+
+ align:start position:0%
+on
+the main block
+
+ align:start position:0%
+the main block
+ 
+
+ align:start position:0%
+the main block
+in the x direction. Okay.
+
+ align:start position:0%
+in the x direction. Okay.
+ 
+
+ align:start position:0%
+in the x direction. Okay.
+And that's going to be we know that
+
+ align:start position:0%
+And that's going to be we know that
+ 
+
+ align:start position:0%
+And that's going to be we know that
+that's the mass of that block times x
+
+ align:start position:0%
+that's the mass of that block times x
+ 
+
+ align:start position:0%
+that's the mass of that block times x
+dot. So x is going to be the coordinate
+
+ align:start position:0%
+dot. So x is going to be the coordinate
+ 
+
+ align:start position:0%
+dot. So x is going to be the coordinate
+that describes the motion of that mass
+
+ align:start position:0%
+that describes the motion of that mass
+ 
+
+ align:start position:0%
+that describes the motion of that mass
+mb.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So we need a free body diagram of MB.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So here's the block.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+There'll be a normal force up. There's
+
+ align:start position:0%
+There'll be a normal force up. There's
+ 
+
+ align:start position:0%
+There'll be a normal force up. There's
+going to be m BG downwards.
+
+ align:start position:0%
+going to be m BG downwards.
+ 
+
+ align:start position:0%
+going to be m BG downwards.
+And the only other forces acting on this
+
+ align:start position:0%
+And the only other forces acting on this
+ 
+
+ align:start position:0%
+And the only other forces acting on this
+block are
+
+ align:start position:0%
+block are
+ 
+
+ align:start position:0%
+block are
+a force that's comes through this rod
+
+ align:start position:0%
+a force that's comes through this rod
+ 
+
+ align:start position:0%
+a force that's comes through this rod
+that's holding the
+
+ align:start position:0%
+that's holding the
+ 
+
+ align:start position:0%
+that's holding the
+that mass, the little mass. Okay. and
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+and it's I'm just going to draw it at
+
+ align:start position:0%
+and it's I'm just going to draw it at
+ 
+
+ align:start position:0%
+and it's I'm just going to draw it at
+some arbitrary angle, not necessarily
+
+ align:start position:0%
+some arbitrary angle, not necessarily
+ 
+
+ align:start position:0%
+some arbitrary angle, not necessarily
+theta. It's going to be a force.
+
+ align:start position:0%
+theta. It's going to be a force.
+ 
+
+ align:start position:0%
+theta. It's going to be a force.
+I'm going to call that
+
+ align:start position:0%
+I'm going to call that
+ 
+
+ align:start position:0%
+I'm going to call that
+force
+
+ align:start position:0%
+force
+ 
+
+ align:start position:0%
+force
+on this main mass. And it's and it's a
+
+ align:start position:0%
+on this main mass. And it's and it's a
+ 
+
+ align:start position:0%
+on this main mass. And it's and it's a
+vector for the moment. It'll have two
+
+ align:start position:0%
+vector for the moment. It'll have two
+ 
+
+ align:start position:0%
+vector for the moment. It'll have two
+components in the x and y directions.
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+So in order to write an equation so in
+
+ align:start position:0%
+So in order to write an equation so in
+ 
+
+ align:start position:0%
+So in order to write an equation so in
+the y direction it's trivial n is equal
+
+ align:start position:0%
+the y direction it's trivial n is equal
+ 
+
+ align:start position:0%
+the y direction it's trivial n is equal
+to you know uh mg mg in this direction
+
+ align:start position:0%
+to you know uh mg mg in this direction
+ 
+
+ align:start position:0%
+to you know uh mg mg in this direction
+we have to have to break this into two
+
+ align:start position:0%
+we have to have to break this into two
+ 
+
+ align:start position:0%
+we have to have to break this into two
+components. We need to know the
+
+ align:start position:0%
+components. We need to know the
+ 
+
+ align:start position:0%
+components. We need to know the
+component of this in the x direction and
+
+ align:start position:0%
+component of this in the x direction and
+ 
+
+ align:start position:0%
+component of this in the x direction and
+put it in here and we'll be and we'll be
+
+ align:start position:0%
+put it in here and we'll be and we'll be
+ 
+
+ align:start position:0%
+put it in here and we'll be and we'll be
+done. Okay. So
+
+ align:start position:0%
+ 
+ 
+
+ align:start position:0%
+ 
+now I'm going to use um third law.
+
+ align:start position:0%
+now I'm going to use um third law.
+ 
+
+ align:start position:0%
+now I'm going to use um third law.
+The force that that
+
+ align:start position:0%
+The force that that
+ 
+
+ align:start position:0%
+The force that that
+rod places on this body
+
+ align:start position:0%
+rod places on this body
+ 
+
+ align:start position:0%
+rod places on this body
+is equal and opposite to the force that
+
+ align:start position:0%
+is equal and opposite to the force that
+ 
+
+ align:start position:0%
+is equal and opposite to the force that
+the rod places on the mass going round
+
+ align:start position:0%
+the rod places on the mass going round
+ 
+
+ align:start position:0%
+the rod places on the mass going round
+and round. You agree with me?
+
+ align:start position:0%
+and round. You agree with me?
+ 
+
+ align:start position:0%
+and round. You agree with me?
+Okay.
+
+ align:start position:0%
+Okay.
+ 
+
+ align:start position:0%
+Okay.
+So, what we really what we need to do
+
+ align:start position:0%
+So, what we really what we need to do
+ 
+
+ align:start position:0%
+So, what we really what we need to do
+next is here's the mass up here going
+
+ align:start position:0%
+next is here's the mass up here going
+ 
+
+ align:start position:0%
+next is here's the mass up here going
+round and round and the forces on it is
+
+ align:start position:0%
+round and round and the forces on it is
+ 
+
+ align:start position:0%
+round and round and the forces on it is
+it has an mg
+
+ align:start position:0%
+it has an mg
+ 
+
+ align:start position:0%
+it has an mg
+downward and it has some force on it.
+
+ align:start position:0%
+downward and it has some force on it.
+ 
+
+ align:start position:0%
+downward and it has some force on it.
+That is the force on the little mass.
+
+ align:start position:0%
+That is the force on the little mass.
+ 
+
+ align:start position:0%
+That is the force on the little mass.
+And you're going to find that F on the
+
+ align:start position:0%
+And you're going to find that F on the
+ 
+
+ align:start position:0%
+And you're going to find that F on the
+little mass equals minus F on the
+
+ align:start position:0%
+little mass equals minus F on the
+ 
+
+ align:start position:0%
+little mass equals minus F on the
+big mass due to third law
+
+ align:start position:0%
+big mass due to third law
+ 
+
+ align:start position:0%
+big mass due to third law
+considerations.
+
+ align:start position:0%
+considerations.
+ 
+
+ align:start position:0%
+considerations.
+So all I have to do is then figure out
+
+ align:start position:0%
+So all I have to do is then figure out
+ 
+
+ align:start position:0%
+So all I have to do is then figure out
+the X component of this force, put a
+
+ align:start position:0%
+the X component of this force, put a
+ 
+
+ align:start position:0%
+the X component of this force, put a
+minus sign in front of it, and I'm
+
+ align:start position:0%
+minus sign in front of it, and I'm
+ 
+
+ align:start position:0%
+minus sign in front of it, and I'm
+basically done.
+
+ align:start position:0%
+basically done.
+ 
+
+ align:start position:0%
+basically done.
+And and to do that, I say F equals MA. I
+
+ align:start position:0%
+And and to do that, I say F equals MA. I
+ 
+
+ align:start position:0%
+And and to do that, I say F equals MA. I
+don't have time to finish that today.
+
+ align:start position:0%
+don't have time to finish that today.
+ 
+
+ align:start position:0%
+don't have time to finish that today.
+I'll show you it next time. and we'll
+
+ align:start position:0%
+I'll show you it next time. and we'll
+ 
+
+ align:start position:0%
+I'll show you it next time. and we'll
+figure out the uh equation of motion for
+
+ align:start position:0%
+figure out the uh equation of motion for
+ 
+
+ align:start position:0%
+figure out the uh equation of motion for
+this thing. Now, in in dragging all this
+
+ align:start position:0%
+this thing. Now, in in dragging all this
+ 
+
+ align:start position:0%
+this thing. Now, in in dragging all this
+stuff here today, I forgot to bring my
+
+ align:start position:0%
+stuff here today, I forgot to bring my
+ 
+
+ align:start position:0%
+stuff here today, I forgot to bring my
+muddy cards. So, you got a minute and if
+
+ align:start position:0%
+muddy cards. So, you got a minute and if
+ 
+
+ align:start position:0%
+muddy cards. So, you got a minute and if
+any of you have just a burning question
+
+ align:start position:0%
+any of you have just a burning question
+ 
+
+ align:start position:0%
+any of you have just a burning question
+you want to answer or something you
+
+ align:start position:0%
+you want to answer or something you
+ 
+
+ align:start position:0%
+you want to answer or something you
+really liked or if if you don't mind,
+
+ align:start position:0%
+really liked or if if you don't mind,
+ 
+
+ align:start position:0%
+really liked or if if you don't mind,
+just take a piece of paper, make a note
+
+ align:start position:0%
+just take a piece of paper, make a note
+ 
+
+ align:start position:0%
+just take a piece of paper, make a note
+on it, and drop it off on the way out.
+
+ align:start position:0%
+on it, and drop it off on the way out.
+ 
+
+ align:start position:0%
+on it, and drop it off on the way out.
+Thanks a lot. See you on Thursday.
\ No newline at end of file
diff --git a/zYcRXHYKYTI.txt b/zYcRXHYKYTI.txt
new file mode 100644
index 0000000000000000000000000000000000000000..01b5e83895ed7819076b5cd426d6bd0e8685fc66
--- /dev/null
+++ b/zYcRXHYKYTI.txt
@@ -0,0 +1,1403 @@
+align:start position:0%
+ 
+we're going to take a look at how point
+
+ align:start position:0%
+we're going to take a look at how point
+ 
+
+ align:start position:0%
+we're going to take a look at how point
+of view and Composition
+
+ align:start position:0%
+of view and Composition
+ 
+
+ align:start position:0%
+of view and Composition
+are very clearly connected but before we
+
+ align:start position:0%
+are very clearly connected but before we
+ 
+
+ align:start position:0%
+are very clearly connected but before we
+show the connections we have to sort of
+
+ align:start position:0%
+show the connections we have to sort of
+ 
+
+ align:start position:0%
+show the connections we have to sort of
+define visually define what i mean by
+
+ align:start position:0%
+define visually define what i mean by
+ 
+
+ align:start position:0%
+define visually define what i mean by
+point of view for example so take a look
+
+ align:start position:0%
+point of view for example so take a look
+ 
+
+ align:start position:0%
+point of view for example so take a look
+at these four images now it doesn't look
+
+ align:start position:0%
+at these four images now it doesn't look
+ 
+
+ align:start position:0%
+at these four images now it doesn't look
+at it but these images are of the
+
+ align:start position:0%
+at it but these images are of the
+ 
+
+ align:start position:0%
+at it but these images are of the
+identical sample just simply taken with
+
+ align:start position:0%
+identical sample just simply taken with
+ 
+
+ align:start position:0%
+identical sample just simply taken with
+four different points of view there it's
+
+ align:start position:0%
+four different points of view there it's
+ 
+
+ align:start position:0%
+four different points of view there it's
+true that I also change the background
+
+ align:start position:0%
+true that I also change the background
+ 
+
+ align:start position:0%
+true that I also change the background
+on them but generally what I did was I
+
+ align:start position:0%
+on them but generally what I did was I
+ 
+
+ align:start position:0%
+on them but generally what I did was I
+moved the sample around or the camera
+
+ align:start position:0%
+moved the sample around or the camera
+ 
+
+ align:start position:0%
+moved the sample around or the camera
+and we get four really completely
+
+ align:start position:0%
+and we get four really completely
+ 
+
+ align:start position:0%
+and we get four really completely
+different-looking visual ideas of what
+
+ align:start position:0%
+different-looking visual ideas of what
+ 
+
+ align:start position:0%
+different-looking visual ideas of what
+this stuff was about which one is right
+
+ align:start position:0%
+this stuff was about which one is right
+ 
+
+ align:start position:0%
+this stuff was about which one is right
+I'm not sure there is a right in any of
+
+ align:start position:0%
+I'm not sure there is a right in any of
+ 
+
+ align:start position:0%
+I'm not sure there is a right in any of
+this that's one of the fun things about
+
+ align:start position:0%
+this that's one of the fun things about
+ 
+
+ align:start position:0%
+this that's one of the fun things about
+this kind of work there are no hard fast
+
+ align:start position:0%
+this kind of work there are no hard fast
+ 
+
+ align:start position:0%
+this kind of work there are no hard fast
+rules that we have to follow but I
+
+ align:start position:0%
+rules that we have to follow but I
+ 
+
+ align:start position:0%
+rules that we have to follow but I
+wanted to give this example to show you
+
+ align:start position:0%
+wanted to give this example to show you
+ 
+
+ align:start position:0%
+wanted to give this example to show you
+that just by simply changing the angle
+
+ align:start position:0%
+that just by simply changing the angle
+ 
+
+ align:start position:0%
+that just by simply changing the angle
+of your camera or moving your material
+
+ align:start position:0%
+of your camera or moving your material
+ 
+
+ align:start position:0%
+of your camera or moving your material
+around you see different things again
+
+ align:start position:0%
+around you see different things again
+ 
+
+ align:start position:0%
+around you see different things again
+we're learning to see in this course so
+
+ align:start position:0%
+we're learning to see in this course so
+ 
+
+ align:start position:0%
+we're learning to see in this course so
+in this situation I wanted to show the
+
+ align:start position:0%
+in this situation I wanted to show the
+ 
+
+ align:start position:0%
+in this situation I wanted to show the
+fabrication of this particular pyramid
+
+ align:start position:0%
+fabrication of this particular pyramid
+ 
+
+ align:start position:0%
+fabrication of this particular pyramid
+sort of telling a story in a particular
+
+ align:start position:0%
+sort of telling a story in a particular
+ 
+
+ align:start position:0%
+sort of telling a story in a particular
+image for now just take a real good look
+
+ align:start position:0%
+image for now just take a real good look
+ 
+
+ align:start position:0%
+image for now just take a real good look
+at this pyramid that was made with this
+
+ align:start position:0%
+at this pyramid that was made with this
+ 
+
+ align:start position:0%
+at this pyramid that was made with this
+wafer that was imprinted with a pattern
+
+ align:start position:0%
+wafer that was imprinted with a pattern
+ 
+
+ align:start position:0%
+wafer that was imprinted with a pattern
+and I felt that this was not quite right
+
+ align:start position:0%
+and I felt that this was not quite right
+ 
+
+ align:start position:0%
+and I felt that this was not quite right
+because there was a little ambiguity and
+
+ align:start position:0%
+because there was a little ambiguity and
+ 
+
+ align:start position:0%
+because there was a little ambiguity and
+where the pyramids point is it's a
+
+ align:start position:0%
+where the pyramids point is it's a
+ 
+
+ align:start position:0%
+where the pyramids point is it's a
+little too close to the curve of the
+
+ align:start position:0%
+little too close to the curve of the
+ 
+
+ align:start position:0%
+little too close to the curve of the
+wafer so by simply raising the camera
+
+ align:start position:0%
+wafer so by simply raising the camera
+ 
+
+ align:start position:0%
+wafer so by simply raising the camera
+ever so slightly we get it nice and
+
+ align:start position:0%
+ever so slightly we get it nice and
+ 
+
+ align:start position:0%
+ever so slightly we get it nice and
+clean line without well let's continue
+
+ align:start position:0%
+clean line without well let's continue
+ 
+
+ align:start position:0%
+clean line without well let's continue
+calling it ambiguity for the time being
+
+ align:start position:0%
+calling it ambiguity for the time being
+ 
+
+ align:start position:0%
+calling it ambiguity for the time being
+here
+
+ align:start position:0%
+here
+ 
+
+ align:start position:0%
+here
+is an example where for this particular
+
+ align:start position:0%
+is an example where for this particular
+ 
+
+ align:start position:0%
+is an example where for this particular
+device of micro rotor I shot it from
+
+ align:start position:0%
+device of micro rotor I shot it from
+ 
+
+ align:start position:0%
+device of micro rotor I shot it from
+above because I was using a
+
+ align:start position:0%
+above because I was using a
+ 
+
+ align:start position:0%
+above because I was using a
+stereomicroscope I had this brand new
+
+ align:start position:0%
+stereomicroscope I had this brand new
+ 
+
+ align:start position:0%
+stereomicroscope I had this brand new
+piece of equipment that I had to use of
+
+ align:start position:0%
+piece of equipment that I had to use of
+ 
+
+ align:start position:0%
+piece of equipment that I had to use of
+course because it's brand new and from
+
+ align:start position:0%
+course because it's brand new and from
+ 
+
+ align:start position:0%
+course because it's brand new and from
+that point of view very unfortunately
+
+ align:start position:0%
+that point of view very unfortunately
+ 
+
+ align:start position:0%
+that point of view very unfortunately
+you see all kinds of dust and yuck which
+
+ align:start position:0%
+you see all kinds of dust and yuck which
+ 
+
+ align:start position:0%
+you see all kinds of dust and yuck which
+I could not get rid of because I don't
+
+ align:start position:0%
+I could not get rid of because I don't
+ 
+
+ align:start position:0%
+I could not get rid of because I don't
+have control over the light so I simply
+
+ align:start position:0%
+have control over the light so I simply
+ 
+
+ align:start position:0%
+have control over the light so I simply
+changed back to my camera and my one of
+
+ align:start position:0%
+changed back to my camera and my one of
+ 
+
+ align:start position:0%
+changed back to my camera and my one of
+five lens with a different point of view
+
+ align:start position:0%
+five lens with a different point of view
+ 
+
+ align:start position:0%
+five lens with a different point of view
+which gave me a much cleaner image many
+
+ align:start position:0%
+which gave me a much cleaner image many
+ 
+
+ align:start position:0%
+which gave me a much cleaner image many
+times we get stuck on a particular
+
+ align:start position:0%
+times we get stuck on a particular
+ 
+
+ align:start position:0%
+times we get stuck on a particular
+approach to looking at things let's say
+
+ align:start position:0%
+approach to looking at things let's say
+ 
+
+ align:start position:0%
+approach to looking at things let's say
+directly from above and it doesn't
+
+ align:start position:0%
+directly from above and it doesn't
+ 
+
+ align:start position:0%
+directly from above and it doesn't
+necessarily give the best image here's
+
+ align:start position:0%
+necessarily give the best image here's
+ 
+
+ align:start position:0%
+necessarily give the best image here's
+an example where this is a pdms that's
+
+ align:start position:0%
+an example where this is a pdms that's
+ 
+
+ align:start position:0%
+an example where this is a pdms that's
+been etched with a grading on it and I
+
+ align:start position:0%
+been etched with a grading on it and I
+ 
+
+ align:start position:0%
+been etched with a grading on it and I
+took it with this particular view and
+
+ align:start position:0%
+took it with this particular view and
+ 
+
+ align:start position:0%
+took it with this particular view and
+just by simply changing the pdms to a
+
+ align:start position:0%
+just by simply changing the pdms to a
+ 
+
+ align:start position:0%
+just by simply changing the pdms to a
+slightly different position we get a
+
+ align:start position:0%
+slightly different position we get a
+ 
+
+ align:start position:0%
+slightly different position we get a
+different point of view let's go back
+
+ align:start position:0%
+different point of view let's go back
+ 
+
+ align:start position:0%
+different point of view let's go back
+and forth on this and see it's kind of
+
+ align:start position:0%
+and forth on this and see it's kind of
+ 
+
+ align:start position:0%
+and forth on this and see it's kind of
+fun to do this anyway but you'll notice
+
+ align:start position:0%
+fun to do this anyway but you'll notice
+ 
+
+ align:start position:0%
+fun to do this anyway but you'll notice
+that you really this one has a better
+
+ align:start position:0%
+that you really this one has a better
+ 
+
+ align:start position:0%
+that you really this one has a better
+approach to looking at the refraction
+
+ align:start position:0%
+approach to looking at the refraction
+ 
+
+ align:start position:0%
+approach to looking at the refraction
+but at the same time you notice when we
+
+ align:start position:0%
+but at the same time you notice when we
+ 
+
+ align:start position:0%
+but at the same time you notice when we
+I did that the shadow is changing in its
+
+ align:start position:0%
+I did that the shadow is changing in its
+ 
+
+ align:start position:0%
+I did that the shadow is changing in its
+position again this is encouraging you
+
+ align:start position:0%
+position again this is encouraging you
+ 
+
+ align:start position:0%
+position again this is encouraging you
+to understand that when you change your
+
+ align:start position:0%
+to understand that when you change your
+ 
+
+ align:start position:0%
+to understand that when you change your
+point of view of course you're also
+
+ align:start position:0%
+point of view of course you're also
+ 
+
+ align:start position:0%
+point of view of course you're also
+changing your composition in this
+
+ align:start position:0%
+changing your composition in this
+ 
+
+ align:start position:0%
+changing your composition in this
+situation I had a petri dish with
+
+ align:start position:0%
+situation I had a petri dish with
+ 
+
+ align:start position:0%
+situation I had a petri dish with
+various gels that had different colors
+
+ align:start position:0%
+various gels that had different colors
+ 
+
+ align:start position:0%
+various gels that had different colors
+let's just leave it at that for the time
+
+ align:start position:0%
+let's just leave it at that for the time
+ 
+
+ align:start position:0%
+let's just leave it at that for the time
+being this was my primary initial point
+
+ align:start position:0%
+being this was my primary initial point
+ 
+
+ align:start position:0%
+being this was my primary initial point
+of view and I thought it was kind of
+
+ align:start position:0%
+of view and I thought it was kind of
+ 
+
+ align:start position:0%
+of view and I thought it was kind of
+boring and so the point of view was a
+
+ align:start position:0%
+boring and so the point of view was a
+ 
+
+ align:start position:0%
+boring and so the point of view was a
+little tighter in that I chose to get
+
+ align:start position:0%
+little tighter in that I chose to get
+ 
+
+ align:start position:0%
+little tighter in that I chose to get
+the camera closer and I
+
+ align:start position:0%
+the camera closer and I
+ 
+
+ align:start position:0%
+the camera closer and I
+also included different kinds of gels in
+
+ align:start position:0%
+also included different kinds of gels in
+ 
+
+ align:start position:0%
+also included different kinds of gels in
+this situation larger ones it is a
+
+ align:start position:0%
+this situation larger ones it is a
+ 
+
+ align:start position:0%
+this situation larger ones it is a
+different point of view in terms of your
+
+ align:start position:0%
+different point of view in terms of your
+ 
+
+ align:start position:0%
+different point of view in terms of your
+selection of what it is that you are
+
+ align:start position:0%
+selection of what it is that you are
+ 
+
+ align:start position:0%
+selection of what it is that you are
+going to be showing so these are not
+
+ align:start position:0%
+going to be showing so these are not
+ 
+
+ align:start position:0%
+going to be showing so these are not
+very deep changes but enough to make
+
+ align:start position:0%
+very deep changes but enough to make
+ 
+
+ align:start position:0%
+very deep changes but enough to make
+very very different images as for
+
+ align:start position:0%
+very very different images as for
+ 
+
+ align:start position:0%
+very very different images as for
+example this one which is a glass wafer
+
+ align:start position:0%
+example this one which is a glass wafer
+ 
+
+ align:start position:0%
+example this one which is a glass wafer
+that's been etched so that they're
+
+ align:start position:0%
+that's been etched so that they're
+ 
+
+ align:start position:0%
+that's been etched so that they're
+creating channels on the wafer from this
+
+ align:start position:0%
+creating channels on the wafer from this
+ 
+
+ align:start position:0%
+creating channels on the wafer from this
+point of view and here is another point
+
+ align:start position:0%
+point of view and here is another point
+ 
+
+ align:start position:0%
+point of view and here is another point
+of view where I'm not showing the whole
+
+ align:start position:0%
+of view where I'm not showing the whole
+ 
+
+ align:start position:0%
+of view where I'm not showing the whole
+thing and maybe we don't have to show
+
+ align:start position:0%
+thing and maybe we don't have to show
+ 
+
+ align:start position:0%
+thing and maybe we don't have to show
+the whole thing all the time maybe we
+
+ align:start position:0%
+the whole thing all the time maybe we
+ 
+
+ align:start position:0%
+the whole thing all the time maybe we
+can show the work by something that is
+
+ align:start position:0%
+can show the work by something that is
+ 
+
+ align:start position:0%
+can show the work by something that is
+in my opinion a more interesting
+
+ align:start position:0%
+in my opinion a more interesting
+ 
+
+ align:start position:0%
+in my opinion a more interesting
+composition and a different point of
+
+ align:start position:0%
+composition and a different point of
+ 
+
+ align:start position:0%
+composition and a different point of
+view here a small change take a look at
+
+ align:start position:0%
+view here a small change take a look at
+ 
+
+ align:start position:0%
+view here a small change take a look at
+both of these and I hope you see that in
+
+ align:start position:0%
+both of these and I hope you see that in
+ 
+
+ align:start position:0%
+both of these and I hope you see that in
+the first one it was a bit of a sloppy
+
+ align:start position:0%
+the first one it was a bit of a sloppy
+ 
+
+ align:start position:0%
+the first one it was a bit of a sloppy
+point of view in the sense that i'm
+
+ align:start position:0%
+point of view in the sense that i'm
+ 
+
+ align:start position:0%
+point of view in the sense that i'm
+showing labels that really is not
+
+ align:start position:0%
+showing labels that really is not
+ 
+
+ align:start position:0%
+showing labels that really is not
+something of value and so by simply
+
+ align:start position:0%
+something of value and so by simply
+ 
+
+ align:start position:0%
+something of value and so by simply
+moving the camera slightly then focusing
+
+ align:start position:0%
+moving the camera slightly then focusing
+ 
+
+ align:start position:0%
+moving the camera slightly then focusing
+a little closer it's a cleaner point of
+
+ align:start position:0%
+a little closer it's a cleaner point of
+ 
+
+ align:start position:0%
+a little closer it's a cleaner point of
+view again this is also about God
+
+ align:start position:0%
+view again this is also about God
+ 
+
+ align:start position:0%
+view again this is also about God
+position but they are very much
+
+ align:start position:0%
+position but they are very much
+ 
+
+ align:start position:0%
+position but they are very much
+connected here is this researchers point
+
+ align:start position:0%
+connected here is this researchers point
+ 
+
+ align:start position:0%
+connected here is this researchers point
+of view where he decided to show the
+
+ align:start position:0%
+of view where he decided to show the
+ 
+
+ align:start position:0%
+of view where he decided to show the
+flexibility of this material and include
+
+ align:start position:0%
+flexibility of this material and include
+ 
+
+ align:start position:0%
+flexibility of this material and include
+hands which is a good idea when you want
+
+ align:start position:0%
+hands which is a good idea when you want
+ 
+
+ align:start position:0%
+hands which is a good idea when you want
+to show scale for me I decided to be a
+
+ align:start position:0%
+to show scale for me I decided to be a
+ 
+
+ align:start position:0%
+to show scale for me I decided to be a
+little more playful and just playing
+
+ align:start position:0%
+little more playful and just playing
+ 
+
+ align:start position:0%
+little more playful and just playing
+more around the flexibility in showing
+
+ align:start position:0%
+more around the flexibility in showing
+ 
+
+ align:start position:0%
+more around the flexibility in showing
+the shadows of it and we did get a cover
+
+ align:start position:0%
+the shadows of it and we did get a cover
+ 
+
+ align:start position:0%
+the shadows of it and we did get a cover
+of a journal which was nice whole
+
+ align:start position:0%
+of a journal which was nice whole
+ 
+
+ align:start position:0%
+of a journal which was nice whole
+different point of view same material
+
+ align:start position:0%
+different point of view same material
+ 
+
+ align:start position:0%
+different point of view same material
+both are good you know there's not again
+
+ align:start position:0%
+both are good you know there's not again
+ 
+
+ align:start position:0%
+both are good you know there's not again
+it not one is better than the other
+
+ align:start position:0%
+it not one is better than the other
+ 
+
+ align:start position:0%
+it not one is better than the other
+necessarily i decided
+
+ align:start position:0%
+necessarily i decided
+ 
+
+ align:start position:0%
+necessarily i decided
+to dig out from the depths of my slide
+
+ align:start position:0%
+to dig out from the depths of my slide
+ 
+
+ align:start position:0%
+to dig out from the depths of my slide
+collection when i was an architectural
+
+ align:start position:0%
+collection when i was an architectural
+ 
+
+ align:start position:0%
+collection when i was an architectural
+photographer to show you a difference
+
+ align:start position:0%
+photographer to show you a difference
+ 
+
+ align:start position:0%
+photographer to show you a difference
+that does somewhat inform us in this
+
+ align:start position:0%
+that does somewhat inform us in this
+ 
+
+ align:start position:0%
+that does somewhat inform us in this
+course here's a beautiful space in
+
+ align:start position:0%
+course here's a beautiful space in
+ 
+
+ align:start position:0%
+course here's a beautiful space in
+california designed by the simone Iguchi
+
+ align:start position:0%
+california designed by the simone Iguchi
+ 
+
+ align:start position:0%
+california designed by the simone Iguchi
+this is the first image that I made and
+
+ align:start position:0%
+this is the first image that I made and
+ 
+
+ align:start position:0%
+this is the first image that I made and
+here is the second image that I made
+
+ align:start position:0%
+here is the second image that I made
+ 
+
+ align:start position:0%
+here is the second image that I made
+let's go back and forth a little on this
+
+ align:start position:0%
+let's go back and forth a little on this
+ 
+
+ align:start position:0%
+let's go back and forth a little on this
+as well and you see in this second image
+
+ align:start position:0%
+as well and you see in this second image
+ 
+
+ align:start position:0%
+as well and you see in this second image
+I decided to have the camera points
+
+ align:start position:0%
+I decided to have the camera points
+ 
+
+ align:start position:0%
+I decided to have the camera points
+slightly upward of changing the point of
+
+ align:start position:0%
+slightly upward of changing the point of
+ 
+
+ align:start position:0%
+slightly upward of changing the point of
+view so that we see a slant of sky I
+
+ align:start position:0%
+view so that we see a slant of sky I
+ 
+
+ align:start position:0%
+view so that we see a slant of sky I
+think this is a better image I think
+
+ align:start position:0%
+think this is a better image I think
+ 
+
+ align:start position:0%
+think this is a better image I think
+it's more interesting but I also think
+
+ align:start position:0%
+it's more interesting but I also think
+ 
+
+ align:start position:0%
+it's more interesting but I also think
+that it allows the viewer to sort of
+
+ align:start position:0%
+that it allows the viewer to sort of
+ 
+
+ align:start position:0%
+that it allows the viewer to sort of
+parties paid more in the image that is
+
+ align:start position:0%
+parties paid more in the image that is
+ 
+
+ align:start position:0%
+parties paid more in the image that is
+to kind of go along upward and be part
+
+ align:start position:0%
+to kind of go along upward and be part
+ 
+
+ align:start position:0%
+to kind of go along upward and be part
+of paying attention to what is going on
+
+ align:start position:0%
+of paying attention to what is going on
+ 
+
+ align:start position:0%
+of paying attention to what is going on
+with the sky I think showing the edges
+
+ align:start position:0%
+with the sky I think showing the edges
+ 
+
+ align:start position:0%
+with the sky I think showing the edges
+and the connection between the edge and
+
+ align:start position:0%
+and the connection between the edge and
+ 
+
+ align:start position:0%
+and the connection between the edge and
+something beyond is an interesting view
+
+ align:start position:0%
+something beyond is an interesting view
+ 
+
+ align:start position:0%
+something beyond is an interesting view
+of how to show things as I did hear back
+
+ align:start position:0%
+of how to show things as I did hear back
+ 
+
+ align:start position:0%
+of how to show things as I did hear back
+to our world when I needed to show
+
+ align:start position:0%
+to our world when I needed to show
+ 
+
+ align:start position:0%
+to our world when I needed to show
+bubbles for a book that we did I decided
+
+ align:start position:0%
+bubbles for a book that we did I decided
+ 
+
+ align:start position:0%
+bubbles for a book that we did I decided
+to keep the edge of the plate showing
+
+ align:start position:0%
+to keep the edge of the plate showing
+ 
+
+ align:start position:0%
+to keep the edge of the plate showing
+and show the background it is a point of
+
+ align:start position:0%
+and show the background it is a point of
+ 
+
+ align:start position:0%
+and show the background it is a point of
+view that I felt sort of worked in here
+
+ align:start position:0%
+view that I felt sort of worked in here
+ 
+
+ align:start position:0%
+view that I felt sort of worked in here
+is another point of view with the same
+
+ align:start position:0%
+is another point of view with the same
+ 
+
+ align:start position:0%
+is another point of view with the same
+material which is better I the
+
+ align:start position:0%
+material which is better I the
+ 
+
+ align:start position:0%
+material which is better I the
+interested to hear your opinions here
+
+ align:start position:0%
+interested to hear your opinions here
+ 
+
+ align:start position:0%
+interested to hear your opinions here
+is a device with the researchers point
+
+ align:start position:0%
+is a device with the researchers point
+ 
+
+ align:start position:0%
+is a device with the researchers point
+of view of it and this is my point of
+
+ align:start position:0%
+of view of it and this is my point of
+ 
+
+ align:start position:0%
+of view of it and this is my point of
+view where I first of all like to get it
+
+ align:start position:0%
+view where I first of all like to get it
+ 
+
+ align:start position:0%
+view where I first of all like to get it
+in focus but since we're talking about
+
+ align:start position:0%
+in focus but since we're talking about
+ 
+
+ align:start position:0%
+in focus but since we're talking about
+point of view I'll stay with that and
+
+ align:start position:0%
+point of view I'll stay with that and
+ 
+
+ align:start position:0%
+point of view I'll stay with that and
+all I did was I put it on a white
+
+ align:start position:0%
+all I did was I put it on a white
+ 
+
+ align:start position:0%
+all I did was I put it on a white
+background and I just slanted the device
+
+ align:start position:0%
+background and I just slanted the device
+ 
+
+ align:start position:0%
+background and I just slanted the device
+and the camera of this point of view and
+
+ align:start position:0%
+and the camera of this point of view and
+ 
+
+ align:start position:0%
+and the camera of this point of view and
+I think it's a much more successful
+
+ align:start position:0%
+I think it's a much more successful
+ 
+
+ align:start position:0%
+I think it's a much more successful
+picture and finally
+
+ align:start position:0%
+picture and finally
+ 
+
+ align:start position:0%
+picture and finally
+in this situation when you do have a
+
+ align:start position:0%
+in this situation when you do have a
+ 
+
+ align:start position:0%
+in this situation when you do have a
+device that is almost pretty much
+
+ align:start position:0%
+device that is almost pretty much
+ 
+
+ align:start position:0%
+device that is almost pretty much
+symmetrical if you're going to take a
+
+ align:start position:0%
+symmetrical if you're going to take a
+ 
+
+ align:start position:0%
+symmetrical if you're going to take a
+photograph from above you just better
+
+ align:start position:0%
+photograph from above you just better
+ 
+
+ align:start position:0%
+photograph from above you just better
+make sure that you make the image
+
+ align:start position:0%
+make sure that you make the image
+ 
+
+ align:start position:0%
+make sure that you make the image
+symmetrical as well take a look at this
+
+ align:start position:0%
+symmetrical as well take a look at this
+ 
+
+ align:start position:0%
+symmetrical as well take a look at this
+first one again and you know there's
+
+ align:start position:0%
+first one again and you know there's
+ 
+
+ align:start position:0%
+first one again and you know there's
+nothing worse than an almost okay image
+
+ align:start position:0%
+nothing worse than an almost okay image
+ 
+
+ align:start position:0%
+nothing worse than an almost okay image
+if it were really really off symmetry
+
+ align:start position:0%
+if it were really really off symmetry
+ 
+
+ align:start position:0%
+if it were really really off symmetry
+that would work better than just a tad
+
+ align:start position:0%
+that would work better than just a tad
+ 
+
+ align:start position:0%
+that would work better than just a tad
+off symmetry so my suggestion is to if
+
+ align:start position:0%
+off symmetry so my suggestion is to if
+ 
+
+ align:start position:0%
+off symmetry so my suggestion is to if
+you do decide to make a symmetrical like
+
+ align:start position:0%
+you do decide to make a symmetrical like
+ 
+
+ align:start position:0%
+you do decide to make a symmetrical like
+image just make sure it is a symmetrical
+
+ align:start position:0%
+image just make sure it is a symmetrical
+ 
+
+ align:start position:0%
+image just make sure it is a symmetrical
+point of view
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